LMFDB - Embedded newform 1.46.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,46,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, 46, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 46);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 46 $
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:	$12.8255726074$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 148878150x + 389915850150 $ x^3 - x^2 - 148878150*x + 389915850150
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{14}\cdot 3^{6}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-13344.8$ 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)

$f(q)$	$=$	$q-6.41537e6 q^{2} -1.72036e10 q^{3} +5.97255e12 q^{4} +2.46761e15 q^{5} +1.10367e17 q^{6} +1.29065e19 q^{7} +1.87405e20 q^{8} -2.65835e21 q^{9} +O(q^{10})$	\(q-6.41537e6 q^{2} -1.72036e10 q^{3} +5.97255e12 q^{4} +2.46761e15 q^{5} +1.10367e17 q^{6} +1.29065e19 q^{7} +1.87405e20 q^{8} -2.65835e21 q^{9} -1.58306e22 q^{10} +7.78755e22 q^{11} -1.02749e23 q^{12} -1.84585e25 q^{13} -8.27997e25 q^{14} -4.24517e25 q^{15} -1.41241e27 q^{16} -2.82858e27 q^{17} +1.70543e28 q^{18} +8.52388e28 q^{19} +1.47379e28 q^{20} -2.22037e29 q^{21} -4.99600e29 q^{22} -2.09625e30 q^{23} -3.22403e30 q^{24} -2.23326e31 q^{25} +1.18418e32 q^{26} +9.65579e31 q^{27} +7.70845e31 q^{28} -1.33372e33 q^{29} +2.72343e32 q^{30} -9.42299e32 q^{31} +2.46741e33 q^{32} -1.33974e33 q^{33} +1.81464e34 q^{34} +3.18481e34 q^{35} -1.58771e34 q^{36} -8.78606e34 q^{37} -5.46838e35 q^{38} +3.17552e35 q^{39} +4.62441e35 q^{40} +2.03901e36 q^{41} +1.42445e36 q^{42} -6.02099e36 q^{43} +4.65116e35 q^{44} -6.55977e36 q^{45} +1.34482e37 q^{46} -4.75078e37 q^{47} +2.42985e37 q^{48} +5.95698e37 q^{49} +1.43272e38 q^{50} +4.86617e37 q^{51} -1.10244e38 q^{52} -7.36820e38 q^{53} -6.19454e38 q^{54} +1.92166e38 q^{55} +2.41873e39 q^{56} -1.46641e39 q^{57} +8.55629e39 q^{58} -9.51309e39 q^{59} -2.53545e38 q^{60} -1.95631e39 q^{61} +6.04519e39 q^{62} -3.43099e40 q^{63} +3.38654e40 q^{64} -4.55483e40 q^{65} +8.59491e39 q^{66} +2.10749e41 q^{67} -1.68938e40 q^{68} +3.60631e40 q^{69} -2.04317e41 q^{70} -5.43331e41 q^{71} -4.98187e41 q^{72} +8.99506e41 q^{73} +5.63658e41 q^{74} +3.84201e41 q^{75} +5.09093e41 q^{76} +1.00510e42 q^{77} -2.03721e42 q^{78} -7.61415e41 q^{79} -3.48528e42 q^{80} +6.19245e42 q^{81} -1.30810e43 q^{82} +6.62221e42 q^{83} -1.32613e42 q^{84} -6.97983e42 q^{85} +3.86268e43 q^{86} +2.29447e43 q^{87} +1.45942e43 q^{88} -6.63932e43 q^{89} +4.20833e43 q^{90} -2.38234e44 q^{91} -1.25200e43 q^{92} +1.62109e43 q^{93} +3.04780e44 q^{94} +2.10336e44 q^{95} -4.24483e43 q^{96} +1.95163e44 q^{97} -3.82162e44 q^{98} -2.07020e44 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3814272 q^{2} + 5359866876 q^{3} - 1915164893184 q^{4} - 912448458460350 q^{5} - 84\!\cdots\!24 q^{6}+ \cdots + 11\!\cdots\!19 q^{9}+O(q^{10}) $ 3 * q + 3814272 * q^2 + 5359866876 * q^3 - 1915164893184 * q^4 - 912448458460350 * q^5 - 84402581069044224 * q^6 - 7619710926638056008 * q^7 - 108947667758662287360 * q^8 + 1158701600689591796919 * q^9	$ 3 q + 3814272 q^{2} + 5359866876 q^{3} - 1915164893184 q^{4} - 912448458460350 q^{5} - 84\!\cdots\!24 q^{6}+ \cdots - 52\!\cdots\!12 q^{99}+O(q^{100}) $ 3 * q + 3814272 * q^2 + 5359866876 * q^3 - 1915164893184 * q^4 - 912448458460350 * q^5 - 84402581069044224 * q^6 - 7619710926638056008 * q^7 - 108947667758662287360 * q^8 + 1158701600689591796919 * q^9 + 1419132609182896876800 * q^10 - 292602117773160656797644 * q^11 - 3364742928052149867675648 * q^12 - 24359353574857845965202054 * q^13 - 202717255077168503234024448 * q^14 - 1135189552611303064861248600 * q^15 - 2516639057595474468963090432 * q^16 + 1167342337360426664689201782 * q^17 + 29579133880859462479907669376 * q^18 + 139928385765722236845372310380 * q^19 + 381381185200730248341345484800 * q^20 + 2269674947269963115109120096 * q^21 - 3645081261141863565639576301056 * q^22 - 10673923189590823281275419815384 * q^23 - 10660038263992615442172723855360 * q^24 + 43966129876780298643382415638125 * q^25 + 109857986164645419011108420802816 * q^26 + 286662461859179128178856521495640 * q^27 + 5309187993026577435829326249984 * q^28 - 670860386246579691273176792023830 * q^29 - 4402953564890863333453835153587200 * q^30 - 4362750588615761992088215111558944 * q^31 + 2770584927822325193163626168451072 * q^32 + 32665703367813314965816678845383952 * q^33 + 53874322809182721932452359249215232 * q^34 + 15776204147695493575553971787662800 * q^35 - 102525010025813312391010920028741632 * q^36 - 389811033762613666259144433874550238 * q^37 - 298309080939187021552909089031242240 * q^38 - 409236468450733544586776272530045432 * q^39 + 1418999553421731071561941465300992000 * q^40 + 2715552056267791317916826925062933406 * q^41 + 5586686494853964635832792594060570624 * q^42 + 1244478438653295151469201253707220756 * q^43 - 10866498414076105454653552938468999168 * q^44 - 36806221258052298400850661208655540550 * q^45 - 29420915174298432781096019434857298944 * q^46 - 5368746178058366301880916464880208048 * q^47 + 148508904948621262654306355588068540416 * q^48 + 78160841959900415140960388420190127371 * q^49 + 365636939507033508238037233476615120000 * q^50 - 373116254852470180408674865132312910664 * q^51 + 134213023925843531561035140325636718592 * q^52 - 1852254617049027724838330153197946097774 * q^53 + 598319193424014381333123622203435924480 * q^54 - 3433604438201040460840734686798586808200 * q^55 + 5263223929490768485344096600823148052480 * q^56 + 103199557648847905550120265832946125680 * q^57 + 13570181249555445898814714558437144899840 * q^58 - 3587009869064273690797416085301514120060 * q^59 + 13404510441959335634932360628989029580800 * q^60 - 51762384161673790814764907347052617635894 * q^61 - 5676710491956141755174145478721599328256 * q^62 - 63198441434102160493715367231351517178664 * q^63 + 41050065173647728685920731234203689025536 * q^64 + 37939089079008549181090608539522846859900 * q^65 + 225875143847752677055610226576839213770752 * q^66 + 14148137855196379836825399018252188940732 * q^67 + 123753416143995711246382651604664796299264 * q^68 - 91367025965579022204230939913277492454112 * q^69 - 615758273709518152674920733006194538854400 * q^70 - 125388248998914140052658001286881482385544 * q^71 - 1156126662482217982994085922934573149716480 * q^72 + 545662435246745842274304841909717562787966 * q^73 - 922589101552630918194661534146849410212608 * q^74 + 4696791604551172366648127047375667988322500 * q^75 - 25740309904677479085695622290576752803840 * q^76 + 6645319565466313145724427222526529624900384 * q^77 - 4595509600825448911666359841694663296601088 * q^78 + 906179897072215837642402032445458679683120 * q^79 - 16837014550545085717858942703269209282969600 * q^80 - 10433460971272354761639583481407161767228277 * q^81 - 7077813252702994823298504428501096216345856 * q^82 + 1486742880234689875145309838364765216168236 * q^83 + 28631042844956213576694159923345730259648512 * q^84 + 38251451691354483777201487197950382555147300 * q^85 + 49387084957597704283946327082198769274651136 * q^86 - 19149930875978892871878601194088020234221880 * q^87 + 52989682432050008057661862219403039374049280 * q^88 - 157452314112877728949303270670086721758716690 * q^89 - 34876870282343920020702397831481807365113600 * q^90 - 209450940191589584493053736413801309667114864 * q^91 + 31580552157061127996902171853509709970604032 * q^92 - 198656173601061645852049647068499329296299648 * q^93 + 380017168558424107350771392050931198759503872 * q^94 + 11835463674693195649110972576862856536029000 * q^95 + 975255232802529934245987844944349186989490176 * q^96 + 371229894708856356492851438771649466869172902 * q^97 + 19381455993535436564386424979420682870187904 * q^98 - 52499767038004223859624250804879775541363612 * 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 $

$2$	−6.41537e6	−1.08155	−0.540775	−	0.841167i	$-0.681869\pi$
$2$	−6.41537e6	−1.08155	−0.540775	+	0.841167i	$0.681869\pi$
$3$	−1.72036e10	−0.316512	−0.158256	−	0.987398i	$-0.550587\pi$
$3$	−1.72036e10	−0.316512	−0.158256	+	0.987398i	$0.550587\pi$
$4$	5.97255e12	0.169750
$5$	2.46761e15	0.462862	0.231431	−	0.972851i	$-0.425659\pi$
$5$	2.46761e15	0.462862	0.231431	+	0.972851i	$0.425659\pi$
$6$	1.10367e17	0.342324
$7$	1.29065e19	1.24767	0.623837	−	0.781554i	$-0.285573\pi$
$7$	1.29065e19	1.24767	0.623837	+	0.781554i	$0.285573\pi$
$8$	1.87405e20	0.897957
$9$	−2.65835e21	−0.899820
$10$	−1.58306e22	−0.500608
$11$	7.78755e22	0.288447	0.144223	−	0.989545i	$-0.453932\pi$
$11$	7.78755e22	0.288447	0.144223	+	0.989545i	$0.453932\pi$
$12$	−1.02749e23	−0.0537280
$13$	−1.84585e25	−1.59393	−0.796967	−	0.604022i	$-0.793564\pi$
$13$	−1.84585e25	−1.59393	−0.796967	+	0.604022i	$0.793564\pi$
$14$	−8.27997e25	−1.34942
$15$	−4.24517e25	−0.146502
$16$	−1.41241e27	−1.14094
$17$	−2.82858e27	−0.584073	−0.292037	−	0.956407i	$-0.594333\pi$
$17$	−2.82858e27	−0.584073	−0.292037	+	0.956407i	$0.594333\pi$
$18$	1.70543e28	0.973200
$19$	8.52388e28	1.44106	0.720529	−	0.693425i	$-0.243899\pi$
$19$	8.52388e28	1.44106	0.720529	+	0.693425i	$0.243899\pi$
$20$	1.47379e28	0.0785709
$21$	−2.22037e29	−0.394904
$22$	−4.99600e29	−0.311970
$23$	−2.09625e30	−0.481468	−0.240734	−	0.970591i	$-0.577388\pi$
$23$	−2.09625e30	−0.481468	−0.240734	+	0.970591i	$0.577388\pi$
$24$	−3.22403e30	−0.284214
$25$	−2.23326e31	−0.785759
$26$	1.18418e32	1.72392
$27$	9.65579e31	0.601316
$28$	7.70845e31	0.211793
$29$	−1.33372e33	−1.66383	−0.831915	−	0.554903i	$-0.812755\pi$
$29$	−1.33372e33	−1.66383	−0.831915	+	0.554903i	$0.812755\pi$
$30$	2.72343e32	0.158449
$31$	−9.42299e32	−0.262150	−0.131075	−	0.991372i	$-0.541843\pi$
$31$	−9.42299e32	−0.262150	−0.131075	+	0.991372i	$0.541843\pi$
$32$	2.46741e33	0.336022
$33$	−1.33974e33	−0.0912969
$34$	1.81464e34	0.631704
$35$	3.18481e34	0.577501
$36$	−1.58771e34	−0.152745
$37$	−8.78606e34	−0.456305	−0.228153	−	0.973625i	$-0.573269\pi$
$37$	−8.78606e34	−0.456305	−0.228153	+	0.973625i	$0.573269\pi$
$38$	−5.46838e35	−1.55858
$39$	3.17552e35	0.504500
$40$	4.62441e35	0.415630
$41$	2.03901e36	1.05144	0.525718	−	0.850659i	$-0.323797\pi$
$41$	2.03901e36	1.05144	0.525718	+	0.850659i	$0.323797\pi$
$42$	1.42445e36	0.427109
$43$	−6.02099e36	−1.06323	−0.531615	−	0.846986i	$-0.678415\pi$
$43$	−6.02099e36	−1.06323	−0.531615	+	0.846986i	$0.678415\pi$
$44$	4.65116e35	0.0489639
$45$	−6.55977e36	−0.416492
$46$	1.34482e37	0.520732
$47$	−4.75078e37	−1.13387	−0.566935	−	0.823763i	$-0.691871\pi$
$47$	−4.75078e37	−1.13387	−0.566935	+	0.823763i	$0.691871\pi$
$48$	2.42985e37	0.361120
$49$	5.95698e37	0.556691
$50$	1.43272e38	0.849837
$51$	4.86617e37	0.184866
$52$	−1.10244e38	−0.270571
$53$	−7.36820e38	−1.17802	−0.589012	−	0.808124i	$-0.700483\pi$
$53$	−7.36820e38	−1.17802	−0.589012	+	0.808124i	$0.700483\pi$
$54$	−6.19454e38	−0.650354
$55$	1.92166e38	0.133511
$56$	2.41873e39	1.12036
$57$	−1.46641e39	−0.456112
$58$	8.55629e39	1.79951
$59$	−9.51309e39	−1.36192	−0.680960	−	0.732321i	$-0.738437\pi$
$59$	−9.51309e39	−1.36192	−0.680960	+	0.732321i	$0.738437\pi$
$60$	−2.53545e38	−0.0248687
$61$	−1.95631e39	−0.132287	−0.0661433	−	0.997810i	$-0.521069\pi$
$61$	−1.95631e39	−0.132287	−0.0661433	+	0.997810i	$0.521069\pi$
$62$	6.04519e39	0.283529
$63$	−3.43099e40	−1.12268
$64$	3.38654e40	0.777511
$65$	−4.55483e40	−0.737772
$66$	8.59491e39	0.0987422
$67$	2.10749e41	1.72617	0.863083	−	0.505062i	$-0.168530\pi$
$67$	2.10749e41	1.72617	0.863083	+	0.505062i	$0.168530\pi$
$68$	−1.68938e40	−0.0991466
$69$	3.60631e40	0.152391
$70$	−2.04317e41	−0.624596
$71$	−5.43331e41	−1.20712	−0.603561	−	0.797317i	$-0.706252\pi$
$71$	−5.43331e41	−1.20712	−0.603561	+	0.797317i	$0.706252\pi$
$72$	−4.98187e41	−0.807999
$73$	8.99506e41	1.06965	0.534823	−	0.844964i	$-0.320378\pi$
$73$	8.99506e41	1.06965	0.534823	+	0.844964i	$0.320378\pi$
$74$	5.63658e41	0.493517
$75$	3.84201e41	0.248702
$76$	5.09093e41	0.244620
$77$	1.00510e42	0.359888
$78$	−2.03721e42	−0.545642
$79$	−7.61415e41	−0.153113	−0.0765565	−	0.997065i	$-0.524393\pi$
$79$	−7.61415e41	−0.153113	−0.0765565	+	0.997065i	$0.524393\pi$
$80$	−3.48528e42	−0.528095
$81$	6.19245e42	0.709496
$82$	−1.30810e43	−1.13718
$83$	6.62221e42	0.438274	0.219137	−	0.975694i	$-0.429676\pi$
$83$	6.62221e42	0.438274	0.219137	+	0.975694i	$0.429676\pi$
$84$	−1.32613e42	−0.0670351
$85$	−6.97983e42	−0.270345
$86$	3.86268e43	1.14994
$87$	2.29447e43	0.526623
$88$	1.45942e43	0.259013
$89$	−6.63932e43	−0.913794	−0.456897	−	0.889520i	$-0.651039\pi$
$89$	−6.63932e43	−0.913794	−0.456897	+	0.889520i	$0.651039\pi$
$90$	4.20833e43	0.450457
$91$	−2.38234e44	−1.98871
$92$	−1.25200e43	−0.0817293
$93$	1.62109e43	0.0829738
$94$	3.04780e44	1.22634
$95$	2.10336e44	0.667011
$96$	−4.24483e43	−0.106355
$97$	1.95163e44	0.387288	0.193644	−	0.981072i	$-0.437969\pi$
$97$	1.95163e44	0.387288	0.193644	+	0.981072i	$0.437969\pi$
$98$	−3.82162e44	−0.602090
$99$	−2.07020e44	−0.259550
$100$	−1.33383e44	−0.133383
$101$	−3.07178e44	−0.245561	−0.122780	−	0.992434i	$-0.539181\pi$
$101$	−3.07178e44	−0.245561	−0.122780	+	0.992434i	$0.539181\pi$
$102$	−3.12182e44	−0.199942
$103$	1.90315e45	0.978666	0.489333	−	0.872097i	$-0.337240\pi$
$103$	1.90315e45	0.978666	0.489333	+	0.872097i	$0.337240\pi$
$104$	−3.45920e45	−1.43128
$105$	−5.47902e44	−0.182786
$106$	4.72697e45	1.27409
$107$	1.11782e45	0.243915	0.121958	−	0.992535i	$-0.461083\pi$
$107$	1.11782e45	0.243915	0.121958	+	0.992535i	$0.461083\pi$
$108$	5.76697e44	0.102074
$109$	3.21871e45	0.463005	0.231502	−	0.972834i	$-0.425636\pi$
$109$	3.21871e45	0.463005	0.231502	+	0.972834i	$0.425636\pi$
$110$	−1.23282e45	−0.144399
$111$	1.51152e45	0.144426
$112$	−1.82292e46	−1.42352
$113$	−1.15806e46	−0.740397	−0.370198	−	0.928953i	$-0.620710\pi$
$113$	−1.15806e46	−0.740397	−0.370198	+	0.928953i	$0.620710\pi$
$114$	9.40757e45	0.493308
$115$	−5.17274e45	−0.222853
$116$	−7.96570e45	−0.282435
$117$	4.90691e46	1.43425
$118$	6.10300e46	1.47298
$119$	−3.65069e46	−0.728733
$120$	−7.95565e45	−0.131552
$121$	−6.68259e46	−0.916798
$122$	1.25504e46	0.143075
$123$	−3.50783e46	−0.332792
$124$	−5.62793e45	−0.0445001
$125$	−1.25242e47	−0.826560
$126$	2.20110e47	1.21424
$127$	6.85398e46	0.316489	0.158245	−	0.987400i	$-0.449417\pi$
$127$	6.85398e46	0.316489	0.158245	+	0.987400i	$0.449417\pi$
$128$	−3.04073e47	−1.17694
$129$	1.03583e47	0.336525
$130$	2.92209e47	0.797937
$131$	−3.50099e46	−0.0804613	−0.0402306	−	0.999190i	$-0.512809\pi$
$131$	−3.50099e46	−0.0804613	−0.0402306	+	0.999190i	$0.512809\pi$
$132$	−8.00166e45	−0.0154977
$133$	1.10013e48	1.79797
$134$	−1.35203e48	−1.86693
$135$	2.38267e47	0.278326
$136$	−5.30088e47	−0.524472
$137$	−1.53504e48	−1.28798	−0.643989	−	0.765035i	$-0.722722\pi$
$137$	−1.53504e48	−1.28798	−0.643989	+	0.765035i	$0.722722\pi$
$138$	−2.31358e47	−0.164818
$139$	1.45287e48	0.879818	0.439909	−	0.898042i	$-0.355011\pi$
$139$	1.45287e48	0.879818	0.439909	+	0.898042i	$0.355011\pi$
$140$	1.90215e47	0.0980309
$141$	8.17304e47	0.358884
$142$	3.48566e48	1.30556
$143$	−1.43746e48	−0.459765
$144$	3.75468e48	1.02664
$145$	−3.29110e48	−0.770123
$146$	−5.77066e48	−1.15688
$147$	−1.02481e48	−0.176200
$148$	−5.24752e47	−0.0774579
$149$	6.21806e47	0.0788794	0.0394397	−	0.999222i	$-0.487443\pi$
$149$	6.21806e47	0.0788794	0.0394397	+	0.999222i	$0.487443\pi$
$150$	−2.46479e48	−0.268984
$151$	−5.84550e48	−0.549339	−0.274670	−	0.961539i	$-0.588568\pi$
$151$	−5.84550e48	−0.549339	−0.274670	+	0.961539i	$0.588568\pi$
$152$	1.59741e49	1.29401
$153$	7.51935e48	0.525561
$154$	−6.44807e48	−0.389236
$155$	−2.32523e48	−0.121339
$156$	1.89660e48	0.0856389
$157$	2.07022e48	0.0809607	0.0404804	−	0.999180i	$-0.487111\pi$
$157$	2.07022e48	0.0809607	0.0404804	+	0.999180i	$0.487111\pi$
$158$	4.88476e48	0.165599
$159$	1.26759e49	0.372859
$160$	6.08861e48	0.155532
$161$	−2.70552e49	−0.600715
$162$	−3.97269e49	−0.767355
$163$	−4.16253e49	−0.700062	−0.350031	−	0.936738i	$-0.613829\pi$
$163$	−4.16253e49	−0.700062	−0.350031	+	0.936738i	$0.613829\pi$
$164$	1.21781e49	0.178481
$165$	−3.30595e48	−0.0422579
$166$	−4.24839e49	−0.474015
$167$	1.93069e50	1.88188	0.940941	−	0.338570i	$-0.109943\pi$
$167$	1.93069e50	1.88188	0.940941	+	0.338570i	$0.109943\pi$
$168$	−4.16108e49	−0.354607
$169$	2.06609e50	1.54063
$170$	4.47782e49	0.292392
$171$	−2.26595e50	−1.29669
$172$	−3.59607e49	−0.180484
$173$	−8.78028e48	−0.0386786	−0.0193393	−	0.999813i	$-0.506156\pi$
$173$	−8.78028e48	−0.0386786	−0.0193393	+	0.999813i	$0.506156\pi$
$174$	−1.47199e50	−0.569569
$175$	−2.88235e50	−0.980371
$176$	−1.09992e50	−0.329099
$177$	1.63659e50	0.431064
$178$	4.25937e50	0.988314
$179$	3.03604e50	0.621032	0.310516	−	0.950568i	$-0.399498\pi$
$179$	3.03604e50	0.621032	0.310516	+	0.950568i	$0.399498\pi$
$180$	−3.91786e49	−0.0706997
$181$	−1.05625e51	−1.68268	−0.841338	−	0.540509i	$-0.818232\pi$
$181$	−1.05625e51	−1.68268	−0.841338	+	0.540509i	$0.818232\pi$
$182$	1.52836e51	2.15089
$183$	3.36555e49	0.0418703
$184$	−3.92847e50	−0.432337
$185$	−2.16806e50	−0.211206
$186$	−1.03999e50	−0.0897403
$187$	−2.20277e50	−0.168474
$188$	−2.83743e50	−0.192475
$189$	1.24622e51	0.750247
$190$	−1.34938e51	−0.721405
$191$	−1.95146e51	−0.927060	−0.463530	−	0.886081i	$-0.653417\pi$
$191$	−1.95146e51	−0.927060	−0.463530	+	0.886081i	$0.653417\pi$
$192$	−5.82606e50	−0.246092
$193$	2.53211e51	0.951574	0.475787	−	0.879561i	$-0.342163\pi$
$193$	2.53211e51	0.951574	0.475787	+	0.879561i	$0.342163\pi$
$194$	−1.25205e51	−0.418872
$195$	7.83594e50	0.233514
$196$	3.55784e50	0.0944985
$197$	5.70705e51	1.35183	0.675914	−	0.736981i	$-0.263749\pi$
$197$	5.70705e51	1.35183	0.675914	+	0.736981i	$0.263749\pi$
$198$	1.32811e51	0.280716
$199$	2.85140e51	0.538102	0.269051	−	0.963126i	$-0.413290\pi$
$199$	2.85140e51	0.538102	0.269051	+	0.963126i	$0.413290\pi$
$200$	−4.18523e51	−0.705577
$201$	−3.62564e51	−0.546353
$202$	1.97066e51	0.265586
$203$	−1.72136e52	−2.07592
$204$	2.90634e50	0.0313811
$205$	5.03149e51	0.486670
$206$	−1.22094e52	−1.05848
$207$	5.57257e51	0.433235
$208$	2.60709e52	1.81858
$209$	6.63802e51	0.415668
$210$	3.51499e51	0.197692
$211$	−1.00404e52	−0.507455	−0.253728	−	0.967276i	$-0.581657\pi$
$211$	−1.00404e52	−0.507455	−0.253728	+	0.967276i	$0.581657\pi$
$212$	−4.40070e51	−0.199970
$213$	9.34723e51	0.382069
$214$	−7.17125e51	−0.263806
$215$	−1.48574e52	−0.492129
$216$	1.80954e52	0.539956
$217$	−1.21617e52	−0.327078
$218$	−2.06492e52	−0.500763
$219$	−1.54747e52	−0.338556
$220$	1.14772e51	0.0226635
$221$	5.22112e52	0.930975
$222$	−9.69694e51	−0.156204
$223$	−1.08955e53	−1.58630	−0.793151	−	0.609025i	$-0.791561\pi$
$223$	−1.08955e53	−1.58630	−0.793151	+	0.609025i	$0.791561\pi$
$224$	3.18456e52	0.419246
$225$	5.93679e52	0.707041
$226$	7.42935e52	0.800776
$227$	8.59683e51	0.0838990	0.0419495	−	0.999120i	$-0.486643\pi$
$227$	8.59683e51	0.0838990	0.0419495	+	0.999120i	$0.486643\pi$
$228$	−8.75823e51	−0.0774252
$229$	8.54768e52	0.684779	0.342389	−	0.939558i	$-0.388764\pi$
$229$	8.54768e52	0.684779	0.342389	+	0.939558i	$0.388764\pi$
$230$	3.31850e52	0.241027
$231$	−1.72913e52	−0.113909
$232$	−2.49945e53	−1.49405
$233$	1.94501e53	1.05539	0.527695	−	0.849434i	$-0.323057\pi$
$233$	1.94501e53	1.05539	0.527695	+	0.849434i	$0.323057\pi$
$234$	−3.14796e53	−1.55122
$235$	−1.17231e53	−0.524825
$236$	−5.68175e52	−0.231186
$237$	1.30991e52	0.0484621
$238$	2.34205e53	0.788161
$239$	−4.67858e52	−0.143272	−0.0716360	−	0.997431i	$-0.522822\pi$
$239$	−4.67858e52	−0.143272	−0.0716360	+	0.997431i	$0.522822\pi$
$240$	5.99592e52	0.167149
$241$	5.41561e53	1.37488	0.687438	−	0.726243i	$-0.258735\pi$
$241$	5.41561e53	1.37488	0.687438	+	0.726243i	$0.258735\pi$
$242$	4.28713e53	0.991563
$243$	−3.91795e53	−0.825881
$244$	−1.16842e52	−0.0224557
$245$	1.46995e53	0.257671
$246$	2.25040e53	0.359932
$247$	−1.57338e54	−2.29695
$248$	−1.76591e53	−0.235400
$249$	−1.13926e53	−0.138719
$250$	8.03473e53	0.893966
$251$	2.39905e53	0.243995	0.121997	−	0.992530i	$-0.461070\pi$
$251$	2.39905e53	0.243995	0.121997	+	0.992530i	$0.461070\pi$
$252$	−2.04918e53	−0.190576
$253$	−1.63247e53	−0.138878
$254$	−4.39708e53	−0.342299
$255$	1.20078e53	0.0855676
$256$	7.59209e53	0.495407
$257$	1.10513e54	0.660569	0.330285	−	0.943881i	$-0.392855\pi$
$257$	1.10513e54	0.660569	0.330285	+	0.943881i	$0.392855\pi$
$258$	−6.64520e53	−0.363969
$259$	−1.13397e54	−0.569321
$260$	−2.72040e53	−0.125237
$261$	3.54549e54	1.49715
$262$	2.24601e53	0.0870229
$263$	9.95471e53	0.354017	0.177009	−	0.984209i	$-0.443358\pi$
$263$	9.95471e53	0.354017	0.177009	+	0.984209i	$0.443358\pi$
$264$	−2.51073e53	−0.0819807
$265$	−1.81818e54	−0.545263
$266$	−7.05775e54	−1.94460
$267$	1.14220e54	0.289227
$268$	1.25871e54	0.293017
$269$	−1.90365e54	−0.407532	−0.203766	−	0.979020i	$-0.565318\pi$
$269$	−1.90365e54	−0.407532	−0.203766	+	0.979020i	$0.565318\pi$
$270$	−1.52857e54	−0.301024
$271$	−2.11803e54	−0.383815	−0.191908	−	0.981413i	$-0.561467\pi$
$271$	−2.11803e54	−0.383815	−0.191908	+	0.981413i	$0.561467\pi$
$272$	3.99511e54	0.666390
$273$	4.09847e54	0.629452
$274$	9.84787e54	1.39301
$275$	−1.73916e54	−0.226650
$276$	2.15389e53	0.0258683
$277$	7.86883e54	0.871195	0.435598	−	0.900141i	$-0.356537\pi$
$277$	7.86883e54	0.871195	0.435598	+	0.900141i	$0.356537\pi$
$278$	−9.32067e54	−0.951567
$279$	2.50496e54	0.235888
$280$	5.96848e54	0.518571
$281$	−2.25442e55	−1.80777	−0.903883	−	0.427781i	$-0.859296\pi$
$281$	−2.25442e55	−1.80777	−0.903883	+	0.427781i	$0.859296\pi$
$282$	−5.24330e54	−0.388150
$283$	−5.22384e54	−0.357104	−0.178552	−	0.983930i	$-0.557141\pi$
$283$	−5.22384e54	−0.357104	−0.178552	+	0.983930i	$0.557141\pi$
$284$	−3.24507e54	−0.204909
$285$	−3.61854e54	−0.211117
$286$	9.22186e54	0.497259
$287$	2.63164e55	1.31185
$288$	−6.55924e54	−0.302359
$289$	−1.54523e55	−0.658858
$290$	2.11136e55	0.832927
$291$	−3.35751e54	−0.122582
$292$	5.37235e54	0.181573
$293$	1.63631e55	0.512088	0.256044	−	0.966665i	$-0.417581\pi$
$293$	1.63631e55	0.512088	0.256044	+	0.966665i	$0.417581\pi$
$294$	6.57456e54	0.190569
$295$	−2.34746e55	−0.630381
$296$	−1.64655e55	−0.409742
$297$	7.51950e54	0.173448
$298$	−3.98911e54	−0.0853121
$299$	3.86936e55	0.767428
$300$	2.29466e54	0.0422173
$301$	−7.77096e55	−1.32657
$302$	3.75010e55	0.594138
$303$	5.28456e54	0.0777230
$304$	−1.20392e56	−1.64415
$305$	−4.82741e54	−0.0612305
$306$	−4.82394e55	−0.568420
$307$	1.67269e56	1.83148	0.915741	−	0.401768i	$-0.131604\pi$
$307$	1.67269e56	1.83148	0.915741	+	0.401768i	$0.131604\pi$
$308$	6.00300e54	0.0610910
$309$	−3.27409e55	−0.309760
$310$	1.49172e55	0.131235
$311$	2.38430e56	1.95097	0.975487	−	0.220058i	$-0.0706246\pi$
$311$	2.38430e56	1.95097	0.975487	+	0.220058i	$0.0706246\pi$
$312$	5.95107e55	0.453019
$313$	−7.01155e55	−0.496668	−0.248334	−	0.968674i	$-0.579883\pi$
$313$	−7.01155e55	−0.496668	−0.248334	+	0.968674i	$0.579883\pi$
$314$	−1.32812e55	−0.0875631
$315$	−8.46634e55	−0.519647
$316$	−4.54759e54	−0.0259910
$317$	−2.68335e56	−1.42838	−0.714191	−	0.699951i	$-0.753205\pi$
$317$	−2.68335e56	−1.42838	−0.714191	+	0.699951i	$0.753205\pi$
$318$	−8.13208e55	−0.403266
$319$	−1.03864e56	−0.479926
$320$	8.35666e55	0.359880
$321$	−1.92306e55	−0.0772021
$322$	1.73569e56	0.649704
$323$	−2.41105e56	−0.841683
$324$	3.69848e55	0.120437
$325$	4.12226e56	1.25245
$326$	2.67042e56	0.757152
$327$	−5.53733e55	−0.146547
$328$	3.82120e56	0.944144
$329$	−6.13157e56	−1.41470
$330$	2.12089e55	0.0457040
$331$	1.90982e56	0.384470	0.192235	−	0.981349i	$-0.438426\pi$
$331$	1.90982e56	0.384470	0.192235	+	0.981349i	$0.438426\pi$
$332$	3.95515e55	0.0743971
$333$	2.33564e56	0.410593
$334$	−1.23861e57	−2.03535
$335$	5.20047e56	0.798977
$336$	3.13608e56	0.450560
$337$	2.57253e56	0.345691	0.172845	−	0.984949i	$-0.444704\pi$
$337$	2.57253e56	0.345691	0.172845	+	0.984949i	$0.444704\pi$
$338$	−1.32547e57	−1.66627
$339$	1.99227e56	0.234345
$340$	−4.16874e55	−0.0458912
$341$	−7.33820e55	−0.0756164
$342$	1.45369e57	1.40244
$343$	−6.12245e56	−0.553105
$344$	−1.12836e57	−0.954735
$345$	8.89896e55	0.0705358
$346$	5.63287e55	0.0418329
$347$	1.10908e57	0.771878	0.385939	−	0.922524i	$-0.373877\pi$
$347$	1.10908e57	0.771878	0.385939	+	0.922524i	$0.373877\pi$
$348$	1.37039e56	0.0893943
$349$	1.91424e57	1.17064	0.585321	−	0.810802i	$-0.300968\pi$
$349$	1.91424e57	1.17064	0.585321	+	0.810802i	$0.300968\pi$
$350$	1.84913e57	1.06032
$351$	−1.78231e57	−0.958459
$352$	1.92151e56	0.0969243
$353$	−1.00890e57	−0.477437	−0.238719	−	0.971089i	$-0.576727\pi$
$353$	−1.00890e57	−0.477437	−0.238719	+	0.971089i	$0.576727\pi$
$354$	−1.04993e57	−0.466217
$355$	−1.34073e57	−0.558731
$356$	−3.96537e56	−0.155117
$357$	6.28050e56	0.230653
$358$	−1.94773e57	−0.671677
$359$	−5.19166e57	−1.68144	−0.840720	−	0.541470i	$-0.817868\pi$
$359$	−5.19166e57	−1.68144	−0.840720	+	0.541470i	$0.817868\pi$
$360$	−1.22933e57	−0.373992
$361$	3.76691e57	1.07665
$362$	6.77626e57	1.81990
$363$	1.14964e57	0.290178
$364$	−1.42286e57	−0.337584
$365$	2.21963e57	0.495098
$366$	−2.15912e56	−0.0452849
$367$	5.07031e57	1.00011	0.500056	−	0.865993i	$-0.333313\pi$
$367$	5.07031e57	1.00011	0.500056	+	0.865993i	$0.333313\pi$
$368$	2.96077e57	0.549324
$369$	−5.42041e57	−0.946103
$370$	1.39089e57	0.228430
$371$	−9.50974e57	−1.46979
$372$	9.68205e55	0.0140848
$373$	−5.35043e57	−0.732723	−0.366362	−	0.930473i	$-0.619397\pi$
$373$	−5.35043e57	−0.732723	−0.366362	+	0.930473i	$0.619397\pi$
$374$	1.41316e57	0.182213
$375$	2.15461e57	0.261616
$376$	−8.90317e57	−1.01817
$377$	2.46184e58	2.65204
$378$	−7.99496e57	−0.811430
$379$	−1.65597e58	−1.58369	−0.791846	−	0.610720i	$-0.790880\pi$
$379$	−1.65597e58	−1.58369	−0.791846	+	0.610720i	$0.790880\pi$
$380$	1.25624e57	0.113225
$381$	−1.17913e57	−0.100173
$382$	1.25193e58	1.00266
$383$	4.08813e56	0.0308711	0.0154356	−	0.999881i	$-0.495087\pi$
$383$	4.08813e56	0.0308711	0.0154356	+	0.999881i	$0.495087\pi$
$384$	5.23115e57	0.372515
$385$	2.48019e57	0.166578
$386$	−1.62444e58	−1.02917
$387$	1.60059e58	0.956716
$388$	1.16562e57	0.0657423
$389$	8.62061e57	0.458851	0.229426	−	0.973326i	$-0.426315\pi$
$389$	8.62061e57	0.458851	0.229426	+	0.973326i	$0.426315\pi$
$390$	−5.02705e57	−0.252557
$391$	5.92941e57	0.281213
$392$	1.11637e58	0.499885
$393$	6.02296e56	0.0254670
$394$	−3.66128e58	−1.46207
$395$	−1.87888e57	−0.0708702
$396$	−1.23644e57	−0.0440587
$397$	−9.58101e57	−0.322571	−0.161285	−	0.986908i	$-0.551564\pi$
$397$	−9.58101e57	−0.322571	−0.161285	+	0.986908i	$0.551564\pi$
$398$	−1.82928e58	−0.581984
$399$	−1.89262e58	−0.569080
$400$	3.15428e58	0.896500
$401$	−3.87566e58	−1.04135	−0.520676	−	0.853755i	$-0.674320\pi$
$401$	−3.87566e58	−1.04135	−0.520676	+	0.853755i	$0.674320\pi$
$402$	2.32598e58	0.590908
$403$	1.73934e58	0.417850
$404$	−1.83464e57	−0.0416840
$405$	1.52806e58	0.328399
$406$	1.10431e59	2.24521
$407$	−6.84219e57	−0.131620
$408$	9.11941e57	0.166002
$409$	−2.12182e58	−0.365539	−0.182769	−	0.983156i	$-0.558506\pi$
$409$	−2.12182e58	−0.365539	−0.182769	+	0.983156i	$0.558506\pi$
$410$	−3.22788e58	−0.526358
$411$	2.64083e58	0.407661
$412$	1.13666e58	0.166129
$413$	−1.22780e59	−1.69923
$414$	−3.57501e58	−0.468565
$415$	1.63410e58	0.202860
$416$	−4.55447e58	−0.535596
$417$	−2.49945e58	−0.278473
$418$	−4.25853e58	−0.449566
$419$	7.28603e58	0.728913	0.364456	−	0.931220i	$-0.381255\pi$
$419$	7.28603e58	0.728913	0.364456	+	0.931220i	$0.381255\pi$
$420$	−3.27237e57	−0.0310280
$421$	6.69387e58	0.601631	0.300815	−	0.953682i	$-0.402741\pi$
$421$	6.69387e58	0.601631	0.300815	+	0.953682i	$0.402741\pi$
$422$	6.44132e58	0.548838
$423$	1.26292e59	1.02028
$424$	−1.38083e59	−1.05781
$425$	6.31695e58	0.458941
$426$	−5.99659e58	−0.413227
$427$	−2.52490e58	−0.165051
$428$	6.67627e57	0.0414046
$429$	2.47295e58	0.145521
$430$	9.53160e58	0.532262
$431$	1.33907e59	0.709684	0.354842	−	0.934926i	$-0.384535\pi$
$431$	1.33907e59	0.709684	0.354842	+	0.934926i	$0.384535\pi$
$432$	−1.36379e59	−0.686063
$433$	−1.66678e59	−0.795976	−0.397988	−	0.917391i	$-0.630292\pi$
$433$	−1.66678e59	−0.795976	−0.397988	+	0.917391i	$0.630292\pi$
$434$	7.80220e58	0.353751
$435$	5.66186e58	0.243754
$436$	1.92239e58	0.0785952
$437$	−1.78682e59	−0.693823
$438$	9.92761e58	0.366165
$439$	−1.80307e59	−0.631774	−0.315887	−	0.948797i	$-0.602302\pi$
$439$	−1.80307e59	−0.631774	−0.315887	+	0.948797i	$0.602302\pi$
$440$	3.60129e58	0.119887
$441$	−1.58357e59	−0.500922
$442$	−3.34954e59	−1.00690
$443$	1.21940e59	0.348388	0.174194	−	0.984711i	$-0.444268\pi$
$443$	1.21940e59	0.348388	0.174194	+	0.984711i	$0.444268\pi$
$444$	9.02762e57	0.0245164
$445$	−1.63833e59	−0.422961
$446$	6.98983e59	1.71566
$447$	−1.06973e58	−0.0249663
$448$	4.37082e59	0.970081
$449$	4.77895e59	1.00877	0.504383	−	0.863480i	$-0.331720\pi$
$449$	4.77895e59	1.00877	0.504383	+	0.863480i	$0.331720\pi$
$450$	−3.80867e59	−0.764701
$451$	1.58789e59	0.303283
$452$	−6.91655e58	−0.125682
$453$	1.00564e59	0.173873
$454$	−5.51518e58	−0.0907410
$455$	−5.87868e59	−0.920499
$456$	−2.74812e59	−0.409569
$457$	2.48102e59	0.351978	0.175989	−	0.984392i	$-0.443688\pi$
$457$	2.48102e59	0.351978	0.175989	+	0.984392i	$0.443688\pi$
$458$	−5.48365e59	−0.740622
$459$	−2.73121e59	−0.351213
$460$	−3.08944e58	−0.0378294
$461$	−1.59001e60	−1.85408	−0.927040	−	0.374962i	$-0.877656\pi$
$461$	−1.59001e60	−1.85408	−0.927040	+	0.374962i	$0.877656\pi$
$462$	1.10930e59	0.123198
$463$	9.67043e59	1.02300	0.511498	−	0.859285i	$-0.329091\pi$
$463$	9.67043e59	1.02300	0.511498	+	0.859285i	$0.329091\pi$
$464$	1.88375e60	1.89832
$465$	4.00022e58	0.0384054
$466$	−1.24779e60	−1.14146
$467$	−1.81440e59	−0.158162	−0.0790812	−	0.996868i	$-0.525199\pi$
$467$	−1.81440e59	−0.158162	−0.0790812	+	0.996868i	$0.525199\pi$
$468$	2.93068e59	0.243465
$469$	2.72002e60	2.15369
$470$	7.52078e59	0.567624
$471$	−3.56152e58	−0.0256251
$472$	−1.78280e60	−1.22294
$473$	−4.68887e59	−0.306685
$474$	−8.40353e58	−0.0524142
$475$	−1.90360e60	−1.13232
$476$	−2.18040e59	−0.123703
$477$	1.95872e60	1.06001
$478$	3.00148e59	0.154956
$479$	−1.15748e60	−0.570117	−0.285059	−	0.958510i	$-0.592013\pi$
$479$	−1.15748e60	−0.570117	−0.285059	+	0.958510i	$0.592013\pi$
$480$	−1.04746e59	−0.0492277
$481$	1.62177e60	0.727321
$482$	−3.47431e60	−1.48700
$483$	4.65446e59	0.190134
$484$	−3.99121e59	−0.155627
$485$	4.81587e59	0.179261
$486$	2.51351e60	0.893231
$487$	−1.82685e60	−0.619871	−0.309935	−	0.950758i	$-0.600307\pi$
$487$	−1.82685e60	−0.619871	−0.309935	+	0.950758i	$0.600307\pi$
$488$	−3.66621e59	−0.118788
$489$	7.16104e59	0.221578
$490$	−9.43028e59	−0.278684
$491$	−2.65564e60	−0.749609	−0.374805	−	0.927104i	$-0.622290\pi$
$491$	−2.65564e60	−0.749609	−0.374805	+	0.927104i	$0.622290\pi$
$492$	−2.09507e59	−0.0564916
$493$	3.77252e60	0.971799
$494$	1.00938e61	2.48427
$495$	−5.10846e59	−0.120136
$496$	1.33091e60	0.299096
$497$	−7.01248e60	−1.50610
$498$	7.30875e59	0.150032
$499$	2.18380e60	0.428500	0.214250	−	0.976779i	$-0.431269\pi$
$499$	2.18380e60	0.428500	0.214250	+	0.976779i	$0.431269\pi$
$500$	−7.48014e59	−0.140309
$501$	−3.32148e60	−0.595639
$502$	−1.53908e60	−0.263893
$503$	−4.41130e60	−0.723247	−0.361624	−	0.932324i	$-0.617777\pi$
$503$	−4.41130e60	−0.723247	−0.361624	+	0.932324i	$0.617777\pi$
$504$	−6.42983e60	−1.00812
$505$	−7.57995e59	−0.113661
$506$	1.04729e60	0.150203
$507$	−3.55441e60	−0.487628
$508$	4.09357e59	0.0537241
$509$	3.40004e60	0.426908	0.213454	−	0.976953i	$-0.431529\pi$
$509$	3.40004e60	0.426908	0.213454	+	0.976953i	$0.431529\pi$
$510$	−7.70344e59	−0.0925457
$511$	1.16094e61	1.33457
$512$	5.82802e60	0.641131
$513$	8.23048e60	0.866532
$514$	−7.08982e60	−0.714439
$515$	4.69622e60	0.452987
$516$	6.18652e59	0.0571253
$517$	−3.69969e60	−0.327061
$518$	7.27483e60	0.615749
$519$	1.51052e59	0.0122423
$520$	−8.53596e60	−0.662487
$521$	7.11610e60	0.528924	0.264462	−	0.964396i	$-0.414806\pi$
$521$	7.11610e60	0.528924	0.264462	+	0.964396i	$0.414806\pi$
$522$	−2.27456e61	−1.61924
$523$	−6.62508e60	−0.451755	−0.225878	−	0.974156i	$-0.572525\pi$
$523$	−6.62508e60	−0.451755	−0.225878	+	0.974156i	$0.572525\pi$
$524$	−2.09099e59	−0.0136583
$525$	4.95867e60	0.310300
$526$	−6.38631e60	−0.382887
$527$	2.66536e60	0.153115
$528$	1.89226e60	0.104164
$529$	−1.45620e61	−0.768189
$530$	1.16643e61	0.589729
$531$	2.52891e61	1.22548
$532$	6.57059e60	0.305206
$533$	−3.76371e61	−1.67592
$534$	−7.32763e60	−0.312814
$535$	2.75836e60	0.112899
$536$	3.94953e61	1.55002
$537$	−5.22307e60	−0.196564
$538$	1.22126e61	0.440766
$539$	4.63903e60	0.160576
$540$	1.42306e60	0.0472460
$541$	−3.34138e61	−1.06411	−0.532056	−	0.846709i	$-0.678581\pi$
$541$	−3.34138e61	−1.06411	−0.532056	+	0.846709i	$0.678581\pi$
$542$	1.35879e61	0.415116
$543$	1.81713e61	0.532588
$544$	−6.97927e60	−0.196261
$545$	7.94252e60	0.214307
$546$	−2.62932e61	−0.680783
$547$	3.86064e61	0.959277	0.479638	−	0.877466i	$-0.340768\pi$
$547$	3.86064e61	0.959277	0.479638	+	0.877466i	$0.340768\pi$
$548$	−9.16813e60	−0.218634
$549$	5.20055e60	0.119034
$550$	1.11574e61	0.245133
$551$	−1.13684e62	−2.39767
$552$	6.75838e60	0.136840
$553$	−9.82717e60	−0.191035
$554$	−5.04815e61	−0.942241
$555$	3.72984e60	0.0668494
$556$	8.67733e60	0.149349
$557$	5.55735e61	0.918598	0.459299	−	0.888282i	$-0.348101\pi$
$557$	5.55735e61	0.918598	0.459299	+	0.888282i	$0.348101\pi$
$558$	−1.60702e61	−0.255125
$559$	1.11138e62	1.69472
$560$	−4.49826e61	−0.658891
$561$	3.78955e60	0.0533241
$562$	1.44629e62	1.95519
$563$	−1.22198e61	−0.158718	−0.0793589	−	0.996846i	$-0.525287\pi$
$563$	−1.22198e61	−0.158718	−0.0793589	+	0.996846i	$0.525287\pi$
$564$	4.88139e60	0.0609206
$565$	−2.85763e61	−0.342701
$566$	3.35128e61	0.386226
$567$	7.99227e61	0.885220
$568$	−1.01823e62	−1.08394
$569$	−1.79144e62	−1.83306	−0.916529	−	0.399967i	$-0.869022\pi$
$569$	−1.79144e62	−1.83306	−0.916529	+	0.399967i	$0.869022\pi$
$570$	2.32142e61	0.228334
$571$	−4.92064e61	−0.465274	−0.232637	−	0.972564i	$-0.574735\pi$
$571$	−4.92064e61	−0.465274	−0.232637	+	0.972564i	$0.574735\pi$
$572$	−8.58533e60	−0.0780452
$573$	3.35720e61	0.293426
$574$	−1.68829e62	−1.41883
$575$	4.68148e61	0.378318
$576$	−9.00260e61	−0.699620
$577$	1.61247e62	1.20513	0.602566	−	0.798069i	$-0.294145\pi$
$577$	1.61247e62	1.20513	0.602566	+	0.798069i	$0.294145\pi$
$578$	9.91323e61	0.712588
$579$	−4.35613e61	−0.301185
$580$	−1.96562e61	−0.130729
$581$	8.54693e61	0.546823
$582$	2.15397e61	0.132578
$583$	−5.73802e61	−0.339797
$584$	1.68572e62	0.960495
$585$	1.21083e62	0.663862
$586$	−1.04975e62	−0.553849
$587$	−1.02006e62	−0.517925	−0.258962	−	0.965887i	$-0.583381\pi$
$587$	−1.02006e62	−0.517925	−0.258962	+	0.965887i	$0.583381\pi$
$588$	−6.12076e60	−0.0299099
$589$	−8.03204e61	−0.377774
$590$	1.50598e62	0.681788
$591$	−9.81816e61	−0.427870
$592$	1.24095e62	0.520615
$593$	9.42772e61	0.380782	0.190391	−	0.981708i	$-0.439024\pi$
$593$	9.42772e61	0.380782	0.190391	+	0.981708i	$0.439024\pi$
$594$	−4.82403e61	−0.187592
$595$	−9.00849e61	−0.337303
$596$	3.71377e60	0.0133898
$597$	−4.90543e61	−0.170316
$598$	−2.48234e62	−0.830012
$599$	−2.30170e62	−0.741217	−0.370609	−	0.928789i	$-0.620851\pi$
$599$	−2.30170e62	−0.741217	−0.370609	+	0.928789i	$0.620851\pi$
$600$	7.20010e61	0.223324
$601$	1.32397e62	0.395552	0.197776	−	0.980247i	$-0.436628\pi$
$601$	1.32397e62	0.395552	0.197776	+	0.980247i	$0.436628\pi$
$602$	4.98536e62	1.43475
$603$	−5.60245e62	−1.55324
$604$	−3.49126e61	−0.0932504
$605$	−1.64900e62	−0.424351
$606$	−3.39024e61	−0.0840613
$607$	−1.86733e62	−0.446145	−0.223073	−	0.974802i	$-0.571609\pi$
$607$	−1.86733e62	−0.446145	−0.223073	+	0.974802i	$0.571609\pi$
$608$	2.10319e62	0.484227
$609$	2.96135e62	0.657053
$610$	3.09696e61	0.0662238
$611$	8.76921e62	1.80731
$612$	4.49097e61	0.0892141
$613$	7.96288e62	1.52479	0.762394	−	0.647113i	$-0.224024\pi$
$613$	7.96288e62	1.52479	0.762394	+	0.647113i	$0.224024\pi$
$614$	−1.07309e63	−1.98084
$615$	−8.65596e61	−0.154037
$616$	1.88360e62	0.323163
$617$	−1.66014e62	−0.274617	−0.137309	−	0.990528i	$-0.543845\pi$
$617$	−1.66014e62	−0.274617	−0.137309	+	0.990528i	$0.543845\pi$
$618$	2.10045e62	0.335021
$619$	4.17933e62	0.642786	0.321393	−	0.946946i	$-0.395849\pi$
$619$	4.17933e62	0.642786	0.321393	+	0.946946i	$0.395849\pi$
$620$	−1.38875e61	−0.0205974
$621$	−2.02410e62	−0.289515
$622$	−1.52961e63	−2.11008
$623$	−8.56901e62	−1.14012
$624$	−4.48513e62	−0.575602
$625$	3.25683e62	0.403176
$626$	4.49817e62	0.537171
$627$	−1.14198e62	−0.131564
$628$	1.23645e61	0.0137431
$629$	2.48521e62	0.266516
$630$	5.43147e62	0.562024
$631$	4.78834e62	0.478106	0.239053	−	0.971007i	$-0.423163\pi$
$631$	4.78834e62	0.478106	0.239053	+	0.971007i	$0.423163\pi$
$632$	−1.42693e62	−0.137489
$633$	1.72732e62	0.160616
$634$	1.72147e63	1.54487
$635$	1.69129e62	0.146491
$636$	7.57077e61	0.0632929
$637$	−1.09957e63	−0.887330
$638$	6.66325e62	0.519064
$639$	1.44436e63	1.08619
$640$	−7.50334e62	−0.544760
$641$	−2.18288e63	−1.53011	−0.765056	−	0.643964i	$-0.777289\pi$
$641$	−2.18288e63	−1.53011	−0.765056	+	0.643964i	$0.777289\pi$
$642$	1.23371e62	0.0834979
$643$	−1.90128e63	−1.24251	−0.621255	−	0.783609i	$-0.713377\pi$
$643$	−1.90128e63	−1.24251	−0.621255	+	0.783609i	$0.713377\pi$
$644$	−1.61589e62	−0.101972
$645$	2.55601e62	0.155765
$646$	1.54677e63	0.910323
$647$	5.73318e62	0.325874	0.162937	−	0.986637i	$-0.447903\pi$
$647$	5.73318e62	0.325874	0.162937	+	0.986637i	$0.447903\pi$
$648$	1.16049e63	0.637097
$649$	−7.40837e62	−0.392841
$650$	−2.64458e63	−1.35459
$651$	2.09225e62	0.103524
$652$	−2.48609e62	−0.118836
$653$	1.09427e63	0.505335	0.252667	−	0.967553i	$-0.418692\pi$
$653$	1.09427e63	0.505335	0.252667	+	0.967553i	$0.418692\pi$
$654$	3.55240e62	0.158498
$655$	−8.63908e61	−0.0372425
$656$	−2.87992e63	−1.19962
$657$	−2.39120e63	−0.962488
$658$	3.93363e63	1.53007
$659$	3.42421e63	1.28718	0.643589	−	0.765372i	$-0.277445\pi$
$659$	3.42421e63	1.28718	0.643589	+	0.765372i	$0.277445\pi$
$660$	−1.97450e61	−0.00717328
$661$	2.99634e61	0.0105210	0.00526051	−	0.999986i	$-0.498326\pi$
$661$	2.99634e61	0.0105210	0.00526051	+	0.999986i	$0.498326\pi$
$662$	−1.22522e63	−0.415823
$663$	−8.98220e62	−0.294665
$664$	1.24103e63	0.393551
$665$	2.71470e63	0.832212
$666$	−1.49840e63	−0.444077
$667$	2.79581e63	0.801081
$668$	1.15312e63	0.319450
$669$	1.87441e63	0.502084
$670$	−3.33629e63	−0.864133
$671$	−1.52349e62	−0.0381576
$672$	−5.47858e62	−0.132696
$673$	−5.41615e63	−1.26868	−0.634340	−	0.773054i	$-0.718728\pi$
$673$	−5.41615e63	−1.26868	−0.634340	+	0.773054i	$0.718728\pi$
$674$	−1.65037e63	−0.373882
$675$	−2.15639e63	−0.472490
$676$	1.23398e63	0.261522
$677$	−4.55896e63	−0.934588	−0.467294	−	0.884102i	$-0.654771\pi$
$677$	−4.55896e63	−0.934588	−0.467294	+	0.884102i	$0.654771\pi$
$678$	−1.27811e63	−0.253455
$679$	2.51887e63	0.483210
$680$	−1.30805e63	−0.242758
$681$	−1.47896e62	−0.0265551
$682$	4.70772e62	0.0817829
$683$	1.04266e64	1.75257	0.876287	−	0.481790i	$-0.160013\pi$
$683$	1.04266e64	1.75257	0.876287	+	0.481790i	$0.160013\pi$
$684$	−1.35335e63	−0.220114
$685$	−3.78789e63	−0.596156
$686$	3.92777e63	0.598210
$687$	−1.47051e63	−0.216741
$688$	8.50410e63	1.21308
$689$	1.36006e64	1.87769
$690$	−5.70901e62	−0.0762880
$691$	−9.60653e63	−1.24254	−0.621270	−	0.783597i	$-0.713383\pi$
$691$	−9.60653e63	−1.24254	−0.621270	+	0.783597i	$0.713383\pi$
$692$	−5.24407e61	−0.00656570
$693$	−2.67190e63	−0.323834
$694$	−7.11514e63	−0.834825
$695$	3.58511e63	0.407234
$696$	4.29994e63	0.472884
$697$	−5.76750e63	−0.614116
$698$	−1.22805e64	−1.26611
$699$	−3.34611e63	−0.334044
$700$	−1.72150e63	−0.166418
$701$	−4.79975e63	−0.449327	−0.224664	−	0.974436i	$-0.572128\pi$
$701$	−4.79975e63	−0.449327	−0.224664	+	0.974436i	$0.572128\pi$
$702$	1.14342e64	1.03662
$703$	−7.48914e63	−0.657562
$704$	2.63728e63	0.224270
$705$	2.01679e63	0.166114
$706$	6.47245e63	0.516372
$707$	−3.96458e63	−0.306380
$708$	9.77464e62	0.0731732
$709$	9.62702e63	0.698155	0.349077	−	0.937094i	$-0.386495\pi$
$709$	9.62702e63	0.698155	0.349077	+	0.937094i	$0.386495\pi$
$710$	8.60126e63	0.604296
$711$	2.02411e63	0.137774
$712$	−1.24424e64	−0.820547
$713$	1.97530e63	0.126217
$714$	−4.02917e63	−0.249463
$715$	−3.54710e63	−0.212808
$716$	1.81329e63	0.105420
$717$	8.04883e62	0.0453474
$718$	3.33064e64	1.81856
$719$	−2.96105e64	−1.56692	−0.783459	−	0.621443i	$-0.786547\pi$
$719$	−2.96105e64	−1.56692	−0.783459	+	0.621443i	$0.786547\pi$
$720$	9.26508e63	0.475191
$721$	2.45629e64	1.22106
$722$	−2.41661e64	−1.16445
$723$	−9.31678e63	−0.435165
$724$	−6.30853e63	−0.285635
$725$	2.97854e64	1.30737
$726$	−7.37539e63	−0.313842
$727$	2.01758e64	0.832350	0.416175	−	0.909284i	$-0.363370\pi$
$727$	2.01758e64	0.832350	0.416175	+	0.909284i	$0.363370\pi$
$728$	−4.46461e64	−1.78578
$729$	−1.15542e64	−0.448095
$730$	−1.42397e64	−0.535473
$731$	1.70308e64	0.621005
$732$	2.01009e62	0.00710750
$733$	−2.30546e64	−0.790530	−0.395265	−	0.918567i	$-0.629347\pi$
$733$	−2.30546e64	−0.790530	−0.395265	+	0.918567i	$0.629347\pi$
$734$	−3.25279e64	−1.08167
$735$	−2.52884e63	−0.0815561
$736$	−5.17232e63	−0.161784
$737$	1.64122e64	0.497907
$738$	3.47739e64	1.02326
$739$	4.27723e64	1.22085	0.610425	−	0.792074i	$-0.290999\pi$
$739$	4.27723e64	1.22085	0.610425	+	0.792074i	$0.290999\pi$
$740$	−1.29488e63	−0.0358523
$741$	2.70677e64	0.727013
$742$	6.10084e64	1.58965
$743$	−6.07984e64	−1.53689	−0.768447	−	0.639913i	$-0.778970\pi$
$743$	−6.07984e64	−1.53689	−0.768447	+	0.639913i	$0.778970\pi$
$744$	3.03800e63	0.0745069
$745$	1.53437e63	0.0365103
$746$	3.43250e64	0.792477
$747$	−1.76041e64	−0.394368
$748$	−1.31562e63	−0.0285985
$749$	1.44272e64	0.304327
$750$	−1.38226e64	−0.282951
$751$	−8.42750e64	−1.67417	−0.837086	−	0.547071i	$-0.815743\pi$
$751$	−8.42750e64	−1.67417	−0.837086	+	0.547071i	$0.815743\pi$
$752$	6.71004e64	1.29367
$753$	−4.12723e63	−0.0772274
$754$	−1.57936e65	−2.86831
$755$	−1.44244e64	−0.254268
$756$	7.44312e63	0.127355
$757$	−1.62790e64	−0.270377	−0.135189	−	0.990820i	$-0.543164\pi$
$757$	−1.62790e64	−0.270377	−0.135189	+	0.990820i	$0.543164\pi$
$758$	1.06237e65	1.71284
$759$	2.80843e63	0.0439565
$760$	3.94180e64	0.598947
$761$	−1.06343e65	−1.56875	−0.784373	−	0.620289i	$-0.787015\pi$
$761$	−1.06343e65	−1.56875	−0.784373	+	0.620289i	$0.787015\pi$
$762$	7.56455e63	0.108342
$763$	4.15421e64	0.577679
$764$	−1.16552e64	−0.157369
$765$	1.85548e64	0.243262
$766$	−2.62269e63	−0.0333886
$767$	1.75597e65	2.17081
$768$	−1.30611e64	−0.156802
$769$	3.91583e64	0.456542	0.228271	−	0.973598i	$-0.426693\pi$
$769$	3.91583e64	0.456542	0.228271	+	0.973598i	$0.426693\pi$
$770$	−1.59113e64	−0.180163
$771$	−1.90122e64	−0.209078
$772$	1.51231e64	0.161530
$773$	−1.00996e65	−1.04777	−0.523885	−	0.851789i	$-0.675518\pi$
$773$	−1.00996e65	−1.04777	−0.523885	+	0.851789i	$0.675518\pi$
$774$	−1.02684e65	−1.03474
$775$	2.10440e64	0.205987
$776$	3.65745e64	0.347768
$777$	1.95083e64	0.180197
$778$	−5.53044e64	−0.496270
$779$	1.73803e65	1.51518
$780$	4.68006e63	0.0396390
$781$	−4.23122e64	−0.348190
$782$	−3.80394e64	−0.304145
$783$	−1.28781e65	−1.00049
$784$	−8.41370e64	−0.635149
$785$	5.10850e63	0.0374736
$786$	−3.86395e63	−0.0275438
$787$	1.02621e65	0.710896	0.355448	−	0.934696i	$-0.384328\pi$
$787$	1.02621e65	0.710896	0.355448	+	0.934696i	$0.384328\pi$
$788$	3.40856e64	0.229473
$789$	−1.71257e64	−0.112051
$790$	1.20537e64	0.0766496
$791$	−1.49464e65	−0.923774
$792$	−3.87966e64	−0.233065
$793$	3.61105e64	0.210856
$794$	6.14657e64	0.348876
$795$	3.12793e64	0.172582
$796$	1.70302e64	0.0913428
$797$	−7.78531e64	−0.405942	−0.202971	−	0.979185i	$-0.565060\pi$
$797$	−7.78531e64	−0.405942	−0.202971	+	0.979185i	$0.565060\pi$
$798$	1.21418e65	0.615488
$799$	1.34379e65	0.662263
$800$	−5.51038e64	−0.264032
$801$	1.76496e65	0.822250
$802$	2.48638e65	1.12627
$803$	7.00495e64	0.308536
$804$	−2.16543e64	−0.0927435
$805$	−6.67617e64	−0.278048
$806$	−1.11585e65	−0.451926
$807$	3.27496e64	0.128989
$808$	−5.75665e64	−0.220503
$809$	−3.71145e65	−1.38262	−0.691308	−	0.722560i	$-0.742965\pi$
$809$	−3.71145e65	−1.38262	−0.691308	+	0.722560i	$0.742965\pi$
$810$	−9.80304e64	−0.355180
$811$	−1.97077e65	−0.694490	−0.347245	−	0.937774i	$-0.612883\pi$
$811$	−1.97077e65	−0.694490	−0.347245	+	0.937774i	$0.612883\pi$
$812$	−1.02809e65	−0.352387
$813$	3.64376e64	0.121482
$814$	4.38952e64	0.142353
$815$	−1.02715e65	−0.324032
$816$	−6.87302e64	−0.210921
$817$	−5.13222e65	−1.53218
$818$	1.36122e65	0.395349
$819$	6.33308e65	1.78948
$820$	3.00508e64	0.0826123
$821$	4.18847e65	1.12030	0.560150	−	0.828391i	$-0.310743\pi$
$821$	4.18847e65	1.12030	0.560150	+	0.828391i	$0.310743\pi$
$822$	−1.69419e65	−0.440905
$823$	−5.89925e64	−0.149383	−0.0746914	−	0.997207i	$-0.523797\pi$
$823$	−5.89925e64	−0.149383	−0.0746914	+	0.997207i	$0.523797\pi$
$824$	3.56658e65	0.878799
$825$	2.99198e64	0.0717374
$826$	7.87681e65	1.83780
$827$	−4.27471e65	−0.970583	−0.485292	−	0.874352i	$-0.661287\pi$
$827$	−4.27471e65	−0.970583	−0.485292	+	0.874352i	$0.661287\pi$
$828$	3.32825e64	0.0735416
$829$	6.40554e64	0.137746	0.0688730	−	0.997625i	$-0.478060\pi$
$829$	6.40554e64	0.137746	0.0688730	+	0.997625i	$0.478060\pi$
$830$	−1.04834e65	−0.219404
$831$	−1.35372e65	−0.275744
$832$	−6.25103e65	−1.23930
$833$	−1.68498e65	−0.325149
$834$	1.60349e65	0.301183
$835$	4.76420e65	0.871052
$836$	3.96459e64	0.0705598
$837$	−9.09863e64	−0.157635
$838$	−4.67426e65	−0.788356
$839$	−9.87581e65	−1.62154	−0.810772	−	0.585363i	$-0.800952\pi$
$839$	−9.87581e65	−1.62154	−0.810772	+	0.585363i	$0.800952\pi$
$840$	−1.02679e65	−0.164134
$841$	1.13625e66	1.76833
$842$	−4.29436e65	−0.650694
$843$	3.87840e65	0.572180
$844$	−5.99671e64	−0.0861406
$845$	5.09830e65	0.713098
$846$	−8.10211e65	−1.10348
$847$	−8.62486e65	−1.14387
$848$	1.04069e66	1.34405
$849$	8.98687e64	0.113028
$850$	−4.05256e65	−0.496367
$851$	1.84178e65	0.219696
$852$	5.58268e64	0.0648563
$853$	5.47101e65	0.619034	0.309517	−	0.950894i	$-0.399833\pi$
$853$	5.47101e65	0.619034	0.309517	+	0.950894i	$0.399833\pi$
$854$	1.61982e65	0.178511
$855$	−5.59147e65	−0.600190
$856$	2.09485e65	0.219025
$857$	3.91129e65	0.398338	0.199169	−	0.979965i	$-0.436176\pi$
$857$	3.91129e65	0.398338	0.199169	+	0.979965i	$0.436176\pi$
$858$	−1.58649e65	−0.157389
$859$	1.59577e66	1.54214	0.771072	−	0.636748i	$-0.219721\pi$
$859$	1.59577e66	1.54214	0.771072	+	0.636748i	$0.219721\pi$
$860$	−8.87369e64	−0.0835390
$861$	−4.52737e65	−0.415217
$862$	−8.59063e65	−0.767559
$863$	−1.43745e65	−0.125127	−0.0625633	−	0.998041i	$-0.519928\pi$
$863$	−1.43745e65	−0.125127	−0.0625633	+	0.998041i	$0.519928\pi$
$864$	2.38248e65	0.202055
$865$	−2.16663e64	−0.0179029
$866$	1.06930e66	0.860888
$867$	2.65835e65	0.208537
$868$	−7.26366e64	−0.0555216
$869$	−5.92956e64	−0.0441649
$870$	−3.63229e65	−0.263632
$871$	−3.89011e66	−2.75140
$872$	6.03201e65	0.415758
$873$	−5.18813e65	−0.348490
$874$	1.14631e66	0.750404
$875$	−1.61643e66	−1.03128
$876$	−9.24237e64	−0.0574699
$877$	−9.07110e65	−0.549755	−0.274878	−	0.961479i	$-0.588637\pi$
$877$	−9.07110e65	−0.549755	−0.274878	+	0.961479i	$0.588637\pi$
$878$	1.15674e66	0.683295
$879$	−2.81504e65	−0.162082
$880$	−2.71418e65	−0.152327
$881$	2.58911e66	1.41642	0.708212	−	0.706000i	$-0.249502\pi$
$881$	2.58911e66	1.41642	0.708212	+	0.706000i	$0.249502\pi$
$882$	1.01592e66	0.541772
$883$	1.38977e66	0.722480	0.361240	−	0.932473i	$-0.382353\pi$
$883$	1.38977e66	0.722480	0.361240	+	0.932473i	$0.382353\pi$
$884$	3.11834e65	0.158033
$885$	4.03847e65	0.199523
$886$	−7.82292e65	−0.376799
$887$	1.62550e66	0.763319	0.381660	−	0.924303i	$-0.375353\pi$
$887$	1.62550e66	0.763319	0.381660	+	0.924303i	$0.375353\pi$
$888$	2.83265e65	0.129689
$889$	8.84606e65	0.394875
$890$	1.05105e66	0.457453
$891$	4.82241e65	0.204652
$892$	−6.50737e65	−0.269275
$893$	−4.04951e66	−1.63397
$894$	6.86270e64	0.0270023
$895$	7.49176e65	0.287452
$896$	−3.92451e66	−1.46844
$897$	−6.65669e65	−0.242901
$898$	−3.06587e66	−1.09103
$899$	1.25676e66	0.436173
$900$	3.54578e65	0.120020
$901$	2.08415e66	0.688052
$902$	−1.01869e66	−0.328016
$903$	1.33688e66	0.419874
$904$	−2.17025e66	−0.664844
$905$	−2.60642e66	−0.778847
$906$	−6.45152e65	−0.188052
$907$	6.17539e66	1.75590	0.877951	−	0.478751i	$-0.158910\pi$
$907$	6.17539e66	1.75590	0.877951	+	0.478751i	$0.158910\pi$
$908$	5.13451e64	0.0142419
$909$	8.16586e65	0.220960
$910$	3.77139e66	0.995566
$911$	−2.64162e66	−0.680311	−0.340155	−	0.940369i	$-0.610480\pi$
$911$	−2.64162e66	−0.680311	−0.340155	+	0.940369i	$0.610480\pi$
$912$	2.07117e66	0.520395
$913$	5.15708e65	0.126419
$914$	−1.59166e66	−0.380682
$915$	8.30487e64	0.0193802
$916$	5.10515e65	0.116241
$917$	−4.51854e65	−0.100389
$918$	1.75217e66	0.379854
$919$	−8.03936e66	−1.70068	−0.850340	−	0.526234i	$-0.823604\pi$
$919$	−8.03936e66	−1.70068	−0.850340	+	0.526234i	$0.823604\pi$
$920$	−9.69394e65	−0.200113
$921$	−2.87763e66	−0.579687
$922$	1.02005e67	2.00528
$923$	1.00291e67	1.92407
$924$	−1.03273e65	−0.0193360
$925$	1.96216e66	0.358546
$926$	−6.20394e66	−1.10642
$927$	−5.05923e66	−0.880623
$928$	−3.29083e66	−0.559083
$929$	−6.85607e66	−1.13690	−0.568449	−	0.822718i	$-0.692457\pi$
$929$	−6.85607e66	−1.13690	−0.568449	+	0.822718i	$0.692457\pi$
$930$	−2.56629e65	−0.0415374
$931$	5.07766e66	0.802225
$932$	1.16167e66	0.179153
$933$	−4.10184e66	−0.617507
$934$	1.16400e66	0.171060
$935$	−5.43558e65	−0.0779802
$936$	9.19577e66	1.28790
$937$	−5.58369e66	−0.763450	−0.381725	−	0.924276i	$-0.624670\pi$
$937$	−5.58369e66	−0.763450	−0.381725	+	0.924276i	$0.624670\pi$
$938$	−1.74500e67	−2.32933
$939$	1.20624e66	0.157202
$940$	−7.00167e65	−0.0890891
$941$	8.59076e66	1.06725	0.533624	−	0.845722i	$-0.320830\pi$
$941$	8.59076e66	1.06725	0.533624	+	0.845722i	$0.320830\pi$
$942$	2.28485e65	0.0277148
$943$	−4.27428e66	−0.506233
$944$	1.34364e67	1.55386
$945$	3.07519e66	0.347261
$946$	3.00808e66	0.331695
$947$	1.38497e67	1.49131	0.745654	−	0.666334i	$-0.232137\pi$
$947$	1.38497e67	1.49131	0.745654	+	0.666334i	$0.232137\pi$
$948$	7.82349e64	0.00822646
$949$	−1.66035e67	−1.70495
$950$	1.22123e67	1.22466
$951$	4.61633e66	0.452101
$952$	−6.84156e66	−0.654371
$953$	1.29710e67	1.21166	0.605831	−	0.795593i	$-0.292841\pi$
$953$	1.29710e67	1.21166	0.605831	+	0.795593i	$0.292841\pi$
$954$	−1.25659e67	−1.14645
$955$	−4.81543e66	−0.429101
$956$	−2.79431e65	−0.0243205
$957$	1.78683e66	0.151903
$958$	7.42566e66	0.616610
$959$	−1.98120e67	−1.60698
$960$	−1.43764e66	−0.113907
$961$	−1.20325e67	−0.931277
$962$	−1.04043e67	−0.786634
$963$	−2.97157e66	−0.219480
$964$	3.23450e66	0.233385
$965$	6.24825e66	0.440447
$966$	−2.98601e66	−0.205639
$967$	2.84025e66	0.191100	0.0955502	−	0.995425i	$-0.469539\pi$
$967$	2.84025e66	0.191100	0.0955502	+	0.995425i	$0.469539\pi$
$968$	−1.25235e67	−0.823245
$969$	4.14786e66	0.266403
$970$	−3.08956e66	−0.193880
$971$	2.77039e67	1.69866	0.849332	−	0.527858i	$-0.177005\pi$
$971$	2.77039e67	1.69866	0.849332	+	0.527858i	$0.177005\pi$
$972$	−2.34001e66	−0.140193
$973$	1.87514e67	1.09773
$974$	1.17199e67	0.670421
$975$	−7.09176e66	−0.396415
$976$	2.76311e66	0.150930
$977$	1.30344e67	0.695766	0.347883	−	0.937538i	$-0.386901\pi$
$977$	1.30344e67	0.695766	0.347883	+	0.937538i	$0.386901\pi$
$978$	−4.59407e66	−0.239648
$979$	−5.17040e66	−0.263581
$980$	8.77936e65	0.0437398
$981$	−8.55645e66	−0.416621
$982$	1.70369e67	0.810740
$983$	−2.69857e67	−1.25510	−0.627551	−	0.778576i	$-0.715943\pi$
$983$	−2.69857e67	−1.25510	−0.627551	+	0.778576i	$0.715943\pi$
$984$	−6.57383e66	−0.298833
$985$	1.40828e67	0.625710
$986$	−2.42021e67	−1.05105
$987$	1.05485e67	0.447770
$988$	−9.39709e66	−0.389908
$989$	1.26215e67	0.511911
$990$	3.27726e66	0.129933
$991$	−3.22029e67	−1.24807	−0.624034	−	0.781397i	$-0.714507\pi$
$991$	−3.22029e67	−1.24807	−0.624034	+	0.781397i	$0.714507\pi$
$992$	−2.32504e66	−0.0880882
$993$	−3.28557e66	−0.121689
$994$	4.49876e67	1.62892
$995$	7.03615e66	0.249067
$996$	−6.80427e65	−0.0235476
$997$	−1.99799e67	−0.676009	−0.338005	−	0.941144i	$-0.609752\pi$
$997$	−1.99799e67	−0.676009	−0.338005	+	0.941144i	$0.609752\pi$
$998$	−1.40099e67	−0.463444
$999$	−8.48364e66	−0.274384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.46.a.a.1.1	✓	3
3.2	odd	2		9.46.a.b.1.3		3
4.3	odd	2		16.46.a.c.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.46.a.a.1.1	✓	3	1.1	even	1	trivial
9.46.a.b.1.3		3	3.2	odd	2
16.46.a.c.1.2		3	4.3	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:	\( k \)	\(=\)	\( 46 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-6.41537e6 q^{2} -1.72036e10 q^{3} +5.97255e12 q^{4} +2.46761e15 q^{5} +1.10367e17 q^{6} +1.29065e19 q^{7} +1.87405e20 q^{8} -2.65835e21 q^{9} +O(q^{10})\)	\(q-6.41537e6 q^{2} -1.72036e10 q^{3} +5.97255e12 q^{4} +2.46761e15 q^{5} +1.10367e17 q^{6} +1.29065e19 q^{7} +1.87405e20 q^{8} -2.65835e21 q^{9} -1.58306e22 q^{10} +7.78755e22 q^{11} -1.02749e23 q^{12} -1.84585e25 q^{13} -8.27997e25 q^{14} -4.24517e25 q^{15} -1.41241e27 q^{16} -2.82858e27 q^{17} +1.70543e28 q^{18} +8.52388e28 q^{19} +1.47379e28 q^{20} -2.22037e29 q^{21} -4.99600e29 q^{22} -2.09625e30 q^{23} -3.22403e30 q^{24} -2.23326e31 q^{25} +1.18418e32 q^{26} +9.65579e31 q^{27} +7.70845e31 q^{28} -1.33372e33 q^{29} +2.72343e32 q^{30} -9.42299e32 q^{31} +2.46741e33 q^{32} -1.33974e33 q^{33} +1.81464e34 q^{34} +3.18481e34 q^{35} -1.58771e34 q^{36} -8.78606e34 q^{37} -5.46838e35 q^{38} +3.17552e35 q^{39} +4.62441e35 q^{40} +2.03901e36 q^{41} +1.42445e36 q^{42} -6.02099e36 q^{43} +4.65116e35 q^{44} -6.55977e36 q^{45} +1.34482e37 q^{46} -4.75078e37 q^{47} +2.42985e37 q^{48} +5.95698e37 q^{49} +1.43272e38 q^{50} +4.86617e37 q^{51} -1.10244e38 q^{52} -7.36820e38 q^{53} -6.19454e38 q^{54} +1.92166e38 q^{55} +2.41873e39 q^{56} -1.46641e39 q^{57} +8.55629e39 q^{58} -9.51309e39 q^{59} -2.53545e38 q^{60} -1.95631e39 q^{61} +6.04519e39 q^{62} -3.43099e40 q^{63} +3.38654e40 q^{64} -4.55483e40 q^{65} +8.59491e39 q^{66} +2.10749e41 q^{67} -1.68938e40 q^{68} +3.60631e40 q^{69} -2.04317e41 q^{70} -5.43331e41 q^{71} -4.98187e41 q^{72} +8.99506e41 q^{73} +5.63658e41 q^{74} +3.84201e41 q^{75} +5.09093e41 q^{76} +1.00510e42 q^{77} -2.03721e42 q^{78} -7.61415e41 q^{79} -3.48528e42 q^{80} +6.19245e42 q^{81} -1.30810e43 q^{82} +6.62221e42 q^{83} -1.32613e42 q^{84} -6.97983e42 q^{85} +3.86268e43 q^{86} +2.29447e43 q^{87} +1.45942e43 q^{88} -6.63932e43 q^{89} +4.20833e43 q^{90} -2.38234e44 q^{91} -1.25200e43 q^{92} +1.62109e43 q^{93} +3.04780e44 q^{94} +2.10336e44 q^{95} -4.24483e43 q^{96} +1.95163e44 q^{97} -3.82162e44 q^{98} -2.07020e44 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3814272 q^{2} + 5359866876 q^{3} - 1915164893184 q^{4} - 912448458460350 q^{5} - 84\!\cdots\!24 q^{6}+ \cdots + 11\!\cdots\!19 q^{9}+O(q^{10}) \) 3 * q + 3814272 * q^2 + 5359866876 * q^3 - 1915164893184 * q^4 - 912448458460350 * q^5 - 84402581069044224 * q^6 - 7619710926638056008 * q^7 - 108947667758662287360 * q^8 + 1158701600689591796919 * q^9	\( 3 q + 3814272 q^{2} + 5359866876 q^{3} - 1915164893184 q^{4} - 912448458460350 q^{5} - 84\!\cdots\!24 q^{6}+ \cdots - 52\!\cdots\!12 q^{99}+O(q^{100}) \) 3 * q + 3814272 * q^2 + 5359866876 * q^3 - 1915164893184 * q^4 - 912448458460350 * q^5 - 84402581069044224 * q^6 - 7619710926638056008 * q^7 - 108947667758662287360 * q^8 + 1158701600689591796919 * q^9 + 1419132609182896876800 * q^10 - 292602117773160656797644 * q^11 - 3364742928052149867675648 * q^12 - 24359353574857845965202054 * q^13 - 202717255077168503234024448 * q^14 - 1135189552611303064861248600 * q^15 - 2516639057595474468963090432 * q^16 + 1167342337360426664689201782 * q^17 + 29579133880859462479907669376 * q^18 + 139928385765722236845372310380 * q^19 + 381381185200730248341345484800 * q^20 + 2269674947269963115109120096 * q^21 - 3645081261141863565639576301056 * q^22 - 10673923189590823281275419815384 * q^23 - 10660038263992615442172723855360 * q^24 + 43966129876780298643382415638125 * q^25 + 109857986164645419011108420802816 * q^26 + 286662461859179128178856521495640 * q^27 + 5309187993026577435829326249984 * q^28 - 670860386246579691273176792023830 * q^29 - 4402953564890863333453835153587200 * q^30 - 4362750588615761992088215111558944 * q^31 + 2770584927822325193163626168451072 * q^32 + 32665703367813314965816678845383952 * q^33 + 53874322809182721932452359249215232 * q^34 + 15776204147695493575553971787662800 * q^35 - 102525010025813312391010920028741632 * q^36 - 389811033762613666259144433874550238 * q^37 - 298309080939187021552909089031242240 * q^38 - 409236468450733544586776272530045432 * q^39 + 1418999553421731071561941465300992000 * q^40 + 2715552056267791317916826925062933406 * q^41 + 5586686494853964635832792594060570624 * q^42 + 1244478438653295151469201253707220756 * q^43 - 10866498414076105454653552938468999168 * q^44 - 36806221258052298400850661208655540550 * q^45 - 29420915174298432781096019434857298944 * q^46 - 5368746178058366301880916464880208048 * q^47 + 148508904948621262654306355588068540416 * q^48 + 78160841959900415140960388420190127371 * q^49 + 365636939507033508238037233476615120000 * q^50 - 373116254852470180408674865132312910664 * q^51 + 134213023925843531561035140325636718592 * q^52 - 1852254617049027724838330153197946097774 * q^53 + 598319193424014381333123622203435924480 * q^54 - 3433604438201040460840734686798586808200 * q^55 + 5263223929490768485344096600823148052480 * q^56 + 103199557648847905550120265832946125680 * q^57 + 13570181249555445898814714558437144899840 * q^58 - 3587009869064273690797416085301514120060 * q^59 + 13404510441959335634932360628989029580800 * q^60 - 51762384161673790814764907347052617635894 * q^61 - 5676710491956141755174145478721599328256 * q^62 - 63198441434102160493715367231351517178664 * q^63 + 41050065173647728685920731234203689025536 * q^64 + 37939089079008549181090608539522846859900 * q^65 + 225875143847752677055610226576839213770752 * q^66 + 14148137855196379836825399018252188940732 * q^67 + 123753416143995711246382651604664796299264 * q^68 - 91367025965579022204230939913277492454112 * q^69 - 615758273709518152674920733006194538854400 * q^70 - 125388248998914140052658001286881482385544 * q^71 - 1156126662482217982994085922934573149716480 * q^72 + 545662435246745842274304841909717562787966 * q^73 - 922589101552630918194661534146849410212608 * q^74 + 4696791604551172366648127047375667988322500 * q^75 - 25740309904677479085695622290576752803840 * q^76 + 6645319565466313145724427222526529624900384 * q^77 - 4595509600825448911666359841694663296601088 * q^78 + 906179897072215837642402032445458679683120 * q^79 - 16837014550545085717858942703269209282969600 * q^80 - 10433460971272354761639583481407161767228277 * q^81 - 7077813252702994823298504428501096216345856 * q^82 + 1486742880234689875145309838364765216168236 * q^83 + 28631042844956213576694159923345730259648512 * q^84 + 38251451691354483777201487197950382555147300 * q^85 + 49387084957597704283946327082198769274651136 * q^86 - 19149930875978892871878601194088020234221880 * q^87 + 52989682432050008057661862219403039374049280 * q^88 - 157452314112877728949303270670086721758716690 * q^89 - 34876870282343920020702397831481807365113600 * q^90 - 209450940191589584493053736413801309667114864 * q^91 + 31580552157061127996902171853509709970604032 * q^92 - 198656173601061645852049647068499329296299648 * q^93 + 380017168558424107350771392050931198759503872 * q^94 + 11835463674693195649110972576862856536029000 * q^95 + 975255232802529934245987844944349186989490176 * q^96 + 371229894708856356492851438771649466869172902 * q^97 + 19381455993535436564386424979420682870187904 * q^98 - 52499767038004223859624250804879775541363612 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more