LMFDB - Embedded newform 1.46.a.a.1.3

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			1.3
Root			$10585.6$ 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)

$f(q)$	$=$	$q+7.36851e6 q^{2} -5.75337e10 q^{3} +1.91106e13 q^{4} +5.97253e15 q^{5} -4.23938e17 q^{6} -1.35754e19 q^{7} -1.18440e20 q^{8} +3.55813e20 q^{9} +O(q^{10})$	\(q+7.36851e6 q^{2} -5.75337e10 q^{3} +1.91106e13 q^{4} +5.97253e15 q^{5} -4.23938e17 q^{6} -1.35754e19 q^{7} -1.18440e20 q^{8} +3.55813e20 q^{9} +4.40087e22 q^{10} -4.62684e23 q^{11} -1.09950e24 q^{12} +1.84657e24 q^{13} -1.00031e26 q^{14} -3.43622e26 q^{15} -1.54512e27 q^{16} +5.39007e27 q^{17} +2.62181e27 q^{18} +2.04232e28 q^{19} +1.14139e29 q^{20} +7.81043e29 q^{21} -3.40930e30 q^{22} -4.06607e30 q^{23} +6.81427e30 q^{24} +7.24945e30 q^{25} +1.36065e31 q^{26} +1.49501e32 q^{27} -2.59434e32 q^{28} +6.91615e32 q^{29} -2.53198e33 q^{30} -4.29419e32 q^{31} -7.21801e33 q^{32} +2.66199e34 q^{33} +3.97168e34 q^{34} -8.10796e34 q^{35} +6.79980e33 q^{36} -1.38069e35 q^{37} +1.50489e35 q^{38} -1.06240e35 q^{39} -7.07385e35 q^{40} +9.02413e35 q^{41} +5.75513e36 q^{42} -2.22460e36 q^{43} -8.84218e36 q^{44} +2.12510e36 q^{45} -2.99609e37 q^{46} -1.00563e37 q^{47} +8.88964e37 q^{48} +7.72848e37 q^{49} +5.34177e37 q^{50} -3.10111e38 q^{51} +3.52891e37 q^{52} -2.47477e38 q^{53} +1.10160e39 q^{54} -2.76340e39 q^{55} +1.60787e39 q^{56} -1.17502e39 q^{57} +5.09618e39 q^{58} +1.01841e40 q^{59} -6.56683e39 q^{60} -2.35593e40 q^{61} -3.16418e39 q^{62} -4.83030e39 q^{63} +1.17807e39 q^{64} +1.10287e40 q^{65} +1.96149e41 q^{66} -2.39925e41 q^{67} +1.03008e41 q^{68} +2.33936e41 q^{69} -5.97436e41 q^{70} +4.61674e40 q^{71} -4.21424e40 q^{72} +6.89694e41 q^{73} -1.01736e42 q^{74} -4.17088e41 q^{75} +3.90301e41 q^{76} +6.28113e42 q^{77} -7.82832e41 q^{78} -1.80775e42 q^{79} -9.22828e42 q^{80} -9.65254e42 q^{81} +6.64944e42 q^{82} +1.09933e42 q^{83} +1.49262e43 q^{84} +3.21924e43 q^{85} -1.63920e43 q^{86} -3.97912e43 q^{87} +5.48002e43 q^{88} -5.72005e43 q^{89} +1.56589e43 q^{90} -2.50680e43 q^{91} -7.77051e43 q^{92} +2.47061e43 q^{93} -7.41002e43 q^{94} +1.21978e44 q^{95} +4.15279e44 q^{96} -2.85037e44 q^{97} +5.69474e44 q^{98} -1.64629e44 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	7.36851e6	1.24224	0.621119	−	0.783716i	$-0.286678\pi$
$2$	7.36851e6	1.24224	0.621119	+	0.783716i	$0.286678\pi$
$3$	−5.75337e10	−1.05851	−0.529254	−	0.848464i	$-0.677528\pi$
$3$	−5.75337e10	−1.05851	−0.529254	+	0.848464i	$0.677528\pi$
$4$	1.91106e13	0.543156
$5$	5.97253e15	1.12030	0.560149	−	0.828392i	$-0.310744\pi$
$5$	5.97253e15	1.12030	0.560149	+	0.828392i	$0.310744\pi$
$6$	−4.23938e17	−1.31492
$7$	−1.35754e19	−1.31234	−0.656171	−	0.754612i	$-0.727825\pi$
$7$	−1.35754e19	−1.31234	−0.656171	+	0.754612i	$0.727825\pi$
$8$	−1.18440e20	−0.567509
$9$	3.55813e20	0.120438
$10$	4.40087e22	1.39168
$11$	−4.62684e23	−1.71376	−0.856879	−	0.515518i	$-0.827600\pi$
$11$	−4.62684e23	−1.71376	−0.856879	+	0.515518i	$0.827600\pi$
$12$	−1.09950e24	−0.574935
$13$	1.84657e24	0.159456	0.0797280	−	0.996817i	$-0.474595\pi$
$13$	1.84657e24	0.159456	0.0797280	+	0.996817i	$0.474595\pi$
$14$	−1.00031e26	−1.63024
$15$	−3.43622e26	−1.18584
$16$	−1.54512e27	−1.24814
$17$	5.39007e27	1.11300	0.556498	−	0.830849i	$-0.312145\pi$
$17$	5.39007e27	1.11300	0.556498	+	0.830849i	$0.312145\pi$
$18$	2.62181e27	0.149613
$19$	2.04232e28	0.345278	0.172639	−	0.984985i	$-0.444771\pi$
$19$	2.04232e28	0.345278	0.172639	+	0.984985i	$0.444771\pi$
$20$	1.14139e29	0.608497
$21$	7.81043e29	1.38912
$22$	−3.40930e30	−2.12890
$23$	−4.06607e30	−0.933896	−0.466948	−	0.884285i	$-0.654647\pi$
$23$	−4.06607e30	−0.933896	−0.466948	+	0.884285i	$0.654647\pi$
$24$	6.81427e30	0.600712
$25$	7.24945e30	0.255067
$26$	1.36065e31	0.198082
$27$	1.49501e32	0.931023
$28$	−2.59434e32	−0.712807
$29$	6.91615e32	0.862799	0.431400	−	0.902161i	$-0.358020\pi$
$29$	6.91615e32	0.862799	0.431400	+	0.902161i	$0.358020\pi$
$30$	−2.53198e33	−1.47310
$31$	−4.29419e32	−0.119466	−0.0597329	−	0.998214i	$-0.519025\pi$
$31$	−4.29419e32	−0.119466	−0.0597329	+	0.998214i	$0.519025\pi$
$32$	−7.21801e33	−0.982976
$33$	2.66199e34	1.81403
$34$	3.97168e34	1.38261
$35$	−8.10796e34	−1.47021
$36$	6.79980e33	0.0654169
$37$	−1.38069e35	−0.717062	−0.358531	−	0.933518i	$-0.616722\pi$
$37$	−1.38069e35	−0.717062	−0.358531	+	0.933518i	$0.616722\pi$
$38$	1.50489e35	0.428917
$39$	−1.06240e35	−0.168785
$40$	−7.07385e35	−0.635779
$41$	9.02413e35	0.465338	0.232669	−	0.972556i	$-0.425254\pi$
$41$	9.02413e35	0.465338	0.232669	+	0.972556i	$0.425254\pi$
$42$	5.75513e36	1.72562
$43$	−2.22460e36	−0.392837	−0.196418	−	0.980520i	$-0.562931\pi$
$43$	−2.22460e36	−0.392837	−0.196418	+	0.980520i	$0.562931\pi$
$44$	−8.84218e36	−0.930839
$45$	2.12510e36	0.134927
$46$	−2.99609e37	−1.16012
$47$	−1.00563e37	−0.240014	−0.120007	−	0.992773i	$-0.538292\pi$
$47$	−1.00563e37	−0.240014	−0.120007	+	0.992773i	$0.538292\pi$
$48$	8.88964e37	1.32116
$49$	7.72848e37	0.722241
$50$	5.34177e37	0.316855
$51$	−3.10111e38	−1.17811
$52$	3.52891e37	0.0866095
$53$	−2.47477e38	−0.395666	−0.197833	−	0.980236i	$-0.563390\pi$
$53$	−2.47477e38	−0.395666	−0.197833	+	0.980236i	$0.563390\pi$
$54$	1.10160e39	1.15655
$55$	−2.76340e39	−1.91992
$56$	1.60787e39	0.744765
$57$	−1.17502e39	−0.365479
$58$	5.09618e39	1.07180
$59$	1.01841e40	1.45798	0.728991	−	0.684524i	$-0.239990\pi$
$59$	1.01841e40	1.45798	0.728991	+	0.684524i	$0.239990\pi$
$60$	−6.56683e39	−0.644099
$61$	−2.35593e40	−1.59309	−0.796545	−	0.604580i	$-0.793341\pi$
$61$	−2.35593e40	−1.59309	−0.796545	+	0.604580i	$0.793341\pi$
$62$	−3.16418e39	−0.148405
$63$	−4.83030e39	−0.158056
$64$	1.17807e39	0.0270473
$65$	1.10287e40	0.178638
$66$	1.96149e41	2.25345
$67$	−2.39925e41	−1.96513	−0.982567	−	0.185910i	$-0.940477\pi$
$67$	−2.39925e41	−1.96513	−0.982567	+	0.185910i	$0.940477\pi$
$68$	1.03008e41	0.604531
$69$	2.33936e41	0.988536
$70$	−5.97436e41	−1.82636
$71$	4.61674e40	0.102570	0.0512852	−	0.998684i	$-0.483668\pi$
$71$	4.61674e40	0.102570	0.0512852	+	0.998684i	$0.483668\pi$
$72$	−4.21424e40	−0.0683499
$73$	6.89694e41	0.820148	0.410074	−	0.912052i	$-0.365503\pi$
$73$	6.89694e41	0.820148	0.410074	+	0.912052i	$0.365503\pi$
$74$	−1.01736e42	−0.890762
$75$	−4.17088e41	−0.269991
$76$	3.90301e41	0.187540
$77$	6.28113e42	2.24904
$78$	−7.82832e41	−0.209672
$79$	−1.80775e42	−0.363520	−0.181760	−	0.983343i	$-0.558179\pi$
$79$	−1.80775e42	−0.363520	−0.181760	+	0.983343i	$0.558179\pi$
$80$	−9.22828e42	−1.39829
$81$	−9.65254e42	−1.10593
$82$	6.64944e42	0.578061
$83$	1.09933e42	0.0727566	0.0363783	−	0.999338i	$-0.488418\pi$
$83$	1.09933e42	0.0727566	0.0363783	+	0.999338i	$0.488418\pi$
$84$	1.49262e43	0.754512
$85$	3.21924e43	1.24689
$86$	−1.63920e43	−0.487997
$87$	−3.97912e43	−0.913279
$88$	5.48002e43	0.972573
$89$	−5.72005e43	−0.787272	−0.393636	−	0.919266i	$-0.628783\pi$
$89$	−5.72005e43	−0.787272	−0.393636	+	0.919266i	$0.628783\pi$
$90$	1.56589e43	0.167611
$91$	−2.50680e43	−0.209261
$92$	−7.77051e43	−0.507252
$93$	2.47061e43	0.126455
$94$	−7.41002e43	−0.298155
$95$	1.21978e44	0.386814
$96$	4.15279e44	1.04049
$97$	−2.85037e44	−0.565635	−0.282818	−	0.959174i	$-0.591269\pi$
$97$	−2.85037e44	−0.565635	−0.282818	+	0.959174i	$0.591269\pi$
$98$	5.69474e44	0.897196
$99$	−1.64629e44	−0.206402
$100$	1.38542e44	0.138542
$101$	−1.12852e45	−0.902146	−0.451073	−	0.892487i	$-0.648959\pi$
$101$	−1.12852e45	−0.902146	−0.451073	+	0.892487i	$0.648959\pi$
$102$	−2.28505e45	−1.46350
$103$	4.56079e44	0.234532	0.117266	−	0.993101i	$-0.462587\pi$
$103$	4.56079e44	0.234532	0.117266	+	0.993101i	$0.462587\pi$
$104$	−2.18707e44	−0.0904927
$105$	4.66481e45	1.55623
$106$	−1.82354e45	−0.491511
$107$	7.56988e45	1.65179	0.825894	−	0.563826i	$-0.190671\pi$
$107$	7.56988e45	1.65179	0.825894	+	0.563826i	$0.190671\pi$
$108$	2.85706e45	0.505691
$109$	−8.09431e45	−1.16435	−0.582175	−	0.813063i	$-0.697798\pi$
$109$	−8.09431e45	−1.16435	−0.582175	+	0.813063i	$0.697798\pi$
$110$	−2.03621e46	−2.38500
$111$	7.94361e45	0.759015
$112$	2.09756e46	1.63798
$113$	−6.69178e45	−0.427836	−0.213918	−	0.976852i	$-0.568622\pi$
$113$	−6.69178e45	−0.427836	−0.213918	+	0.976852i	$0.568622\pi$
$114$	−8.65818e45	−0.454012
$115$	−2.42847e46	−1.04624
$116$	1.32172e46	0.468635
$117$	6.57034e44	0.0192046
$118$	7.50416e46	1.81116
$119$	−7.31724e46	−1.46063
$120$	4.06985e46	0.672977
$121$	1.41186e47	1.93697
$122$	−1.73597e47	−1.97900
$123$	−5.19192e46	−0.492564
$124$	−8.20647e45	−0.0648886
$125$	−1.26452e47	−0.834546
$126$	−3.55922e46	−0.196344
$127$	4.47769e46	0.206762	0.103381	−	0.994642i	$-0.467034\pi$
$127$	4.47769e46	0.206762	0.103381	+	0.994642i	$0.467034\pi$
$128$	2.62642e47	1.01657
$129$	1.27990e47	0.415821
$130$	8.12652e46	0.221911
$131$	4.74426e46	0.109035	0.0545173	−	0.998513i	$-0.482638\pi$
$131$	4.74426e46	0.109035	0.0545173	+	0.998513i	$0.482638\pi$
$132$	5.08724e47	0.985300
$133$	−2.77254e47	−0.453122
$134$	−1.76789e48	−2.44116
$135$	8.92902e47	1.04302
$136$	−6.38398e47	−0.631635
$137$	−5.92244e47	−0.496922	−0.248461	−	0.968642i	$-0.579925\pi$
$137$	−5.92244e47	−0.496922	−0.248461	+	0.968642i	$0.579925\pi$
$138$	1.72376e48	1.22800
$139$	1.01012e48	0.611701	0.305851	−	0.952080i	$-0.401059\pi$
$139$	1.01012e48	0.611701	0.305851	+	0.952080i	$0.401059\pi$
$140$	−1.54948e48	−0.798556
$141$	5.78577e47	0.254057
$142$	3.40185e47	0.127417
$143$	−8.54380e47	−0.273269
$144$	−5.49773e47	−0.150324
$145$	4.13070e48	0.966592
$146$	5.08202e48	1.01882
$147$	−4.44648e48	−0.764498
$148$	−2.63858e48	−0.389477
$149$	−1.22411e49	−1.55285	−0.776426	−	0.630208i	$-0.782969\pi$
$149$	−1.22411e49	−1.55285	−0.776426	+	0.630208i	$0.782969\pi$
$150$	−3.07332e48	−0.335393
$151$	1.39518e48	0.131114	0.0655572	−	0.997849i	$-0.479118\pi$
$151$	1.39518e48	0.131114	0.0655572	+	0.997849i	$0.479118\pi$
$152$	−2.41892e48	−0.195948
$153$	1.91786e48	0.134047
$154$	4.62826e49	2.79384
$155$	−2.56472e48	−0.133837
$156$	−2.03031e48	−0.0916769
$157$	−1.81397e49	−0.709393	−0.354697	−	0.934981i	$-0.615416\pi$
$157$	−1.81397e49	−0.709393	−0.354697	+	0.934981i	$0.615416\pi$
$158$	−1.33204e49	−0.451578
$159$	1.42383e49	0.418815
$160$	−4.31098e49	−1.10123
$161$	5.51986e49	1.22559
$162$	−7.11249e49	−1.37383
$163$	−6.75472e49	−1.13602	−0.568010	−	0.823022i	$-0.692287\pi$
$163$	−6.75472e49	−1.13602	−0.568010	+	0.823022i	$0.692287\pi$
$164$	1.72457e49	0.252751
$165$	1.58989e50	2.03225
$166$	8.10045e48	0.0903810
$167$	4.33548e49	0.422587	0.211294	−	0.977423i	$-0.432232\pi$
$167$	4.33548e49	0.422587	0.211294	+	0.977423i	$0.432232\pi$
$168$	−9.25065e49	−0.788340
$169$	−1.30697e50	−0.974574
$170$	2.37210e50	1.54893
$171$	7.26685e48	0.0415847
$172$	−4.25135e49	−0.213372
$173$	1.27763e49	0.0562816	0.0281408	−	0.999604i	$-0.491041\pi$
$173$	1.27763e49	0.0562816	0.0281408	+	0.999604i	$0.491041\pi$
$174$	−2.93202e50	−1.13451
$175$	−9.84143e49	−0.334736
$176$	7.14903e50	2.13901
$177$	−5.85928e50	−1.54328
$178$	−4.21483e50	−0.977980
$179$	−1.84054e50	−0.376489	−0.188244	−	0.982122i	$-0.560280\pi$
$179$	−1.84054e50	−0.376489	−0.188244	+	0.982122i	$0.560280\pi$
$180$	4.06120e49	0.0732864
$181$	1.05925e51	1.68745	0.843725	−	0.536775i	$-0.180358\pi$
$181$	1.05925e51	1.68745	0.843725	+	0.536775i	$0.180358\pi$
$182$	−1.84714e50	−0.259952
$183$	1.35545e51	1.68630
$184$	4.81584e50	0.529994
$185$	−8.24620e50	−0.803323
$186$	1.82047e50	0.157088
$187$	−2.49390e51	−1.90741
$188$	−1.92183e50	−0.130365
$189$	−2.02954e51	−1.22182
$190$	8.98800e50	0.480515
$191$	1.00828e51	0.478992	0.239496	−	0.970897i	$-0.423018\pi$
$191$	1.00828e51	0.478992	0.239496	+	0.970897i	$0.423018\pi$
$192$	−6.77790e49	−0.0286297
$193$	4.75247e51	1.78600	0.892998	−	0.450061i	$-0.148598\pi$
$193$	4.75247e51	1.78600	0.892998	+	0.450061i	$0.148598\pi$
$194$	−2.10030e51	−0.702654
$195$	−6.34523e50	−0.189090
$196$	1.47696e51	0.392290
$197$	1.24255e51	0.294324	0.147162	−	0.989112i	$-0.452986\pi$
$197$	1.24255e51	0.294324	0.147162	+	0.989112i	$0.452986\pi$
$198$	−1.21307e51	−0.256401
$199$	−3.30064e51	−0.622880	−0.311440	−	0.950266i	$-0.600811\pi$
$199$	−3.30064e51	−0.622880	−0.311440	+	0.950266i	$0.600811\pi$
$200$	−8.58623e50	−0.144753
$201$	1.38038e52	2.08011
$202$	−8.31549e51	−1.12068
$203$	−9.38896e51	−1.13229
$204$	−5.92640e51	−0.639901
$205$	5.38969e51	0.521317
$206$	3.36062e51	0.291345
$207$	−1.44676e51	−0.112477
$208$	−2.85317e51	−0.199023
$209$	−9.44951e51	−0.591722
$210$	3.43727e52	1.93321
$211$	−1.03587e52	−0.523540	−0.261770	−	0.965130i	$-0.584306\pi$
$211$	−1.03587e52	−0.523540	−0.261770	+	0.965130i	$0.584306\pi$
$212$	−4.72945e51	−0.214908
$213$	−2.65618e51	−0.108572
$214$	5.57788e52	2.05191
$215$	−1.32865e52	−0.440094
$216$	−1.77069e52	−0.528363
$217$	5.82954e51	0.156780
$218$	−5.96430e52	−1.44640
$219$	−3.96806e52	−0.868132
$220$	−5.28102e52	−1.04282
$221$	9.95315e51	0.177474
$222$	5.85326e52	0.942878
$223$	5.37304e52	0.782277	0.391139	−	0.920332i	$-0.372081\pi$
$223$	5.37304e52	0.782277	0.391139	+	0.920332i	$0.372081\pi$
$224$	9.79874e52	1.29000
$225$	2.57945e51	0.0307199
$226$	−4.93085e52	−0.531474
$227$	2.78314e52	0.271615	0.135807	−	0.990735i	$-0.456637\pi$
$227$	2.78314e52	0.271615	0.135807	+	0.990735i	$0.456637\pi$
$228$	−2.24554e52	−0.198512
$229$	2.18798e53	1.75285	0.876425	−	0.481539i	$-0.159922\pi$
$229$	2.18798e53	1.75285	0.876425	+	0.481539i	$0.159922\pi$
$230$	−1.78942e53	−1.29968
$231$	−3.61377e53	−2.38062
$232$	−8.19147e52	−0.489646
$233$	3.51723e53	1.90850	0.954252	−	0.299004i	$-0.0966545\pi$
$233$	3.51723e53	1.90850	0.954252	+	0.299004i	$0.0966545\pi$
$234$	4.84136e51	0.0238567
$235$	−6.00617e52	−0.268888
$236$	1.94624e53	0.791912
$237$	1.04006e53	0.384789
$238$	−5.39172e53	−1.81445
$239$	−4.11764e53	−1.26094	−0.630472	−	0.776212i	$-0.717139\pi$
$239$	−4.11764e53	−1.26094	−0.630472	+	0.776212i	$0.717139\pi$
$240$	5.30937e53	1.48010
$241$	−2.61521e53	−0.663931	−0.331966	−	0.943291i	$-0.607712\pi$
$241$	−2.61521e53	−0.663931	−0.331966	+	0.943291i	$0.607712\pi$
$242$	1.04033e54	2.40617
$243$	1.13673e53	0.239616
$244$	−4.50232e53	−0.865297
$245$	4.61586e53	0.809125
$246$	−3.82567e53	−0.611882
$247$	3.77130e52	0.0550566
$248$	5.08603e52	0.0677979
$249$	−6.32487e52	−0.0770134
$250$	−9.31763e53	−1.03671
$251$	−1.56252e54	−1.58916	−0.794581	−	0.607158i	$-0.792309\pi$
$251$	−1.56252e54	−1.58916	−0.794581	+	0.607158i	$0.792309\pi$
$252$	−9.23101e52	−0.0858493
$253$	1.88131e54	1.60047
$254$	3.29939e53	0.256847
$255$	−1.85215e54	−1.31984
$256$	1.89383e54	1.23578
$257$	1.24463e53	0.0743951	0.0371975	−	0.999308i	$-0.488157\pi$
$257$	1.24463e53	0.0743951	0.0371975	+	0.999308i	$0.488157\pi$
$258$	9.43093e53	0.516549
$259$	1.87434e54	0.941030
$260$	2.10766e53	0.0970285
$261$	2.46086e53	0.103914
$262$	3.49582e53	0.135447
$263$	−2.80486e54	−0.997487	−0.498743	−	0.866750i	$-0.666205\pi$
$263$	−2.80486e54	−0.997487	−0.498743	+	0.866750i	$0.666205\pi$
$264$	−3.15286e54	−1.02948
$265$	−1.47807e54	−0.443264
$266$	−2.04295e54	−0.562886
$267$	3.29096e54	0.833334
$268$	−4.58511e54	−1.06737
$269$	1.28461e54	0.275009	0.137504	−	0.990501i	$-0.456092\pi$
$269$	1.28461e54	0.275009	0.137504	+	0.990501i	$0.456092\pi$
$270$	6.57936e54	1.29568
$271$	9.12323e54	1.65325	0.826627	−	0.562750i	$-0.190257\pi$
$271$	9.12323e54	1.65325	0.826627	+	0.562750i	$0.190257\pi$
$272$	−8.32830e54	−1.38917
$273$	1.44225e54	0.221504
$274$	−4.36396e54	−0.617295
$275$	−3.35421e54	−0.437124
$276$	4.47066e54	0.536930
$277$	−8.28825e53	−0.0917630	−0.0458815	−	0.998947i	$-0.514610\pi$
$277$	−8.28825e53	−0.0917630	−0.0458815	+	0.998947i	$0.514610\pi$
$278$	7.44307e54	0.759879
$279$	−1.52793e53	−0.0143883
$280$	9.60304e54	0.834359
$281$	−5.88447e54	−0.471862	−0.235931	−	0.971770i	$-0.575814\pi$
$281$	−5.88447e54	−0.471862	−0.235931	+	0.971770i	$0.575814\pi$
$282$	4.26326e54	0.315600
$283$	−2.28277e55	−1.56051	−0.780257	−	0.625458i	$-0.784912\pi$
$283$	−2.28277e55	−1.56051	−0.780257	+	0.625458i	$0.784912\pi$
$284$	8.82287e53	0.0557118
$285$	−7.01787e54	−0.409445
$286$	−6.29551e54	−0.339465
$287$	−1.22506e55	−0.610683
$288$	−2.56826e54	−0.118388
$289$	5.59968e54	0.238760
$290$	3.04371e55	1.20074
$291$	1.63992e55	0.598729
$292$	1.31805e55	0.445468
$293$	2.32198e55	0.726671	0.363335	−	0.931658i	$-0.381638\pi$
$293$	2.32198e55	0.726671	0.363335	+	0.931658i	$0.381638\pi$
$294$	−3.27639e55	−0.949689
$295$	6.08248e55	1.63337
$296$	1.63528e55	0.406939
$297$	−6.91719e55	−1.59555
$298$	−9.01988e55	−1.92901
$299$	−7.50829e54	−0.148915
$300$	−7.97080e54	−0.146647
$301$	3.01999e55	0.515536
$302$	1.02804e55	0.162875
$303$	6.49277e55	0.954929
$304$	−3.15563e55	−0.430954
$305$	−1.40708e56	−1.78473
$306$	1.41317e55	0.166519
$307$	1.19437e56	1.30775	0.653875	−	0.756603i	$-0.273142\pi$
$307$	1.19437e56	1.30775	0.653875	+	0.756603i	$0.273142\pi$
$308$	1.20036e56	1.22158
$309$	−2.62399e55	−0.248254
$310$	−1.88982e55	−0.166258
$311$	1.65762e56	1.35636	0.678181	−	0.734895i	$-0.262768\pi$
$311$	1.65762e56	1.35636	0.678181	+	0.734895i	$0.262768\pi$
$312$	1.25830e55	0.0957872
$313$	−2.27179e56	−1.60924	−0.804619	−	0.593792i	$-0.797630\pi$
$313$	−2.27179e56	−1.60924	−0.804619	+	0.593792i	$0.797630\pi$
$314$	−1.33662e56	−0.881236
$315$	−2.88492e55	−0.177070
$316$	−3.45472e55	−0.197448
$317$	3.49229e56	1.85899	0.929494	−	0.368836i	$-0.120244\pi$
$317$	3.49229e56	1.85899	0.929494	+	0.368836i	$0.120244\pi$
$318$	1.04915e56	0.520269
$319$	−3.20000e56	−1.47863
$320$	7.03609e54	0.0303010
$321$	−4.35523e56	−1.74843
$322$	4.06731e56	1.52248
$323$	1.10083e56	0.384293
$324$	−1.84466e56	−0.600695
$325$	1.33866e55	0.0406720
$326$	−4.97722e56	−1.41121
$327$	4.65695e56	1.23247
$328$	−1.06882e56	−0.264083
$329$	1.36519e56	0.314981
$330$	1.17151e57	2.52454
$331$	1.49551e55	0.0301065	0.0150533	−	0.999887i	$-0.495208\pi$
$331$	1.49551e55	0.0301065	0.0150533	+	0.999887i	$0.495208\pi$
$332$	2.10089e55	0.0395182
$333$	−4.91266e55	−0.0863618
$334$	3.19460e56	0.524954
$335$	−1.43296e57	−2.20154
$336$	−1.20681e57	−1.73382
$337$	3.73633e56	0.502080	0.251040	−	0.967977i	$-0.419227\pi$
$337$	3.73633e56	0.502080	0.251040	+	0.967977i	$0.419227\pi$
$338$	−9.63043e56	−1.21065
$339$	3.85003e56	0.452867
$340$	6.15216e56	0.677255
$341$	1.98686e56	0.204735
$342$	5.35459e55	0.0516581
$343$	4.03490e56	0.364515
$344$	2.63481e56	0.222938
$345$	1.39719e57	1.10746
$346$	9.41420e55	0.0699151
$347$	9.19083e56	0.639649	0.319824	−	0.947477i	$-0.396376\pi$
$347$	9.19083e56	0.639649	0.319824	+	0.947477i	$0.396376\pi$
$348$	−7.60434e56	−0.496054
$349$	−1.53571e57	−0.939158	−0.469579	−	0.882891i	$-0.655594\pi$
$349$	−1.53571e57	−0.939158	−0.469579	+	0.882891i	$0.655594\pi$
$350$	−7.25167e56	−0.415822
$351$	2.76065e56	0.148457
$352$	3.33966e57	1.68458
$353$	−1.08285e57	−0.512435	−0.256217	−	0.966619i	$-0.582476\pi$
$353$	−1.08285e57	−0.512435	−0.256217	+	0.966619i	$0.582476\pi$
$354$	−4.31742e57	−1.91713
$355$	2.75736e56	0.114909
$356$	−1.09314e57	−0.427612
$357$	4.20988e57	1.54609
$358$	−1.35620e57	−0.467689
$359$	−9.45652e56	−0.306271	−0.153136	−	0.988205i	$-0.548937\pi$
$359$	−9.45652e56	−0.306271	−0.153136	+	0.988205i	$0.548937\pi$
$360$	−2.51697e56	−0.0765722
$361$	−3.08163e57	−0.880783
$362$	7.80511e57	2.09622
$363$	−8.12297e57	−2.05029
$364$	−4.79064e56	−0.113661
$365$	4.11922e57	0.918810
$366$	9.98766e57	2.09478
$367$	−8.46364e57	−1.66944	−0.834719	−	0.550675i	$-0.814370\pi$
$367$	−8.46364e57	−1.66944	−0.834719	+	0.550675i	$0.814370\pi$
$368$	6.28257e57	1.16563
$369$	3.21090e56	0.0560446
$370$	−6.07623e57	−0.997919
$371$	3.35961e57	0.519249
$372$	4.72148e56	0.0686851
$373$	7.28034e57	0.997017	0.498509	−	0.866885i	$-0.333881\pi$
$373$	7.28034e57	0.997017	0.498509	+	0.866885i	$0.333881\pi$
$374$	−1.83763e58	−2.36945
$375$	7.27525e57	0.883374
$376$	1.19107e57	0.136210
$377$	1.27712e57	0.137578
$378$	−1.49547e58	−1.51779
$379$	−1.15746e58	−1.10694	−0.553471	−	0.832868i	$-0.686697\pi$
$379$	−1.15746e58	−1.10694	−0.553471	+	0.832868i	$0.686697\pi$
$380$	2.33108e57	0.210100
$381$	−2.57618e57	−0.218859
$382$	7.42949e57	0.595022
$383$	1.13149e58	0.854436	0.427218	−	0.904149i	$-0.359494\pi$
$383$	1.13149e58	0.854436	0.427218	+	0.904149i	$0.359494\pi$
$384$	−1.51107e58	−1.07605
$385$	3.75143e58	2.51959
$386$	3.50187e58	2.21863
$387$	−7.91542e56	−0.0473127
$388$	−5.44723e57	−0.307229
$389$	−3.09651e58	−1.64819	−0.824094	−	0.566453i	$-0.808315\pi$
$389$	−3.09651e58	−1.64819	−0.824094	+	0.566453i	$0.808315\pi$
$390$	−4.67549e57	−0.234895
$391$	−2.19164e58	−1.03942
$392$	−9.15359e57	−0.409878
$393$	−2.72955e57	−0.115414
$394$	9.15577e57	0.365620
$395$	−1.07968e58	−0.407251
$396$	−3.14616e57	−0.112109
$397$	2.54438e58	0.856633	0.428317	−	0.903629i	$-0.359107\pi$
$397$	2.54438e58	0.856633	0.428317	+	0.903629i	$0.359107\pi$
$398$	−2.43208e58	−0.773766
$399$	1.59514e58	0.479633
$400$	−1.12013e58	−0.318359
$401$	−2.41926e58	−0.650031	−0.325016	−	0.945709i	$-0.605370\pi$
$401$	−2.41926e58	−0.650031	−0.325016	+	0.945709i	$0.605370\pi$
$402$	1.01713e59	2.58399
$403$	−7.92954e56	−0.0190495
$404$	−2.15666e58	−0.490007
$405$	−5.76501e58	−1.23897
$406$	−6.91827e58	−1.40657
$407$	6.38823e58	1.22887
$408$	3.67294e58	0.668590
$409$	4.68095e58	0.806418	0.403209	−	0.915108i	$-0.367895\pi$
$409$	4.68095e58	0.806418	0.403209	+	0.915108i	$0.367895\pi$
$410$	3.97140e58	0.647600
$411$	3.40740e58	0.525996
$412$	8.71595e57	0.127388
$413$	−1.38253e59	−1.91337
$414$	−1.06605e58	−0.139723
$415$	6.56581e57	0.0815091
$416$	−1.33286e58	−0.156741
$417$	−5.81158e58	−0.647490
$418$	−6.96288e58	−0.735060
$419$	4.10143e58	0.410317	0.205158	−	0.978729i	$-0.434229\pi$
$419$	4.10143e58	0.410317	0.205158	+	0.978729i	$0.434229\pi$
$420$	8.91474e58	0.845278
$421$	−5.12871e58	−0.460958	−0.230479	−	0.973077i	$-0.574029\pi$
$421$	−5.12871e58	−0.460958	−0.230479	+	0.973077i	$0.574029\pi$
$422$	−7.63282e58	−0.650362
$423$	−3.57817e57	−0.0289070
$424$	2.93112e58	0.224544
$425$	3.90751e58	0.283889
$426$	−1.95721e58	−0.134872
$427$	3.19826e59	2.09068
$428$	1.44665e59	0.897179
$429$	4.91556e58	0.289257
$430$	−9.79019e58	−0.546702
$431$	−1.63043e59	−0.864100	−0.432050	−	0.901850i	$-0.642210\pi$
$431$	−1.63043e59	−0.864100	−0.432050	+	0.901850i	$0.642210\pi$
$432$	−2.30997e59	−1.16204
$433$	2.91636e59	1.39272	0.696360	−	0.717692i	$-0.254802\pi$
$433$	2.91636e59	1.39272	0.696360	+	0.717692i	$0.254802\pi$
$434$	4.29551e58	0.194758
$435$	−2.37654e59	−1.02315
$436$	−1.54687e59	−0.632424
$437$	−8.30423e58	−0.322453
$438$	−2.92387e59	−1.07843
$439$	−2.21702e59	−0.776816	−0.388408	−	0.921488i	$-0.626975\pi$
$439$	−2.21702e59	−0.776816	−0.388408	+	0.921488i	$0.626975\pi$
$440$	3.27296e59	1.08957
$441$	2.74989e58	0.0869856
$442$	7.33399e58	0.220465
$443$	3.23420e59	0.924024	0.462012	−	0.886874i	$-0.347128\pi$
$443$	3.23420e59	0.924024	0.462012	+	0.886874i	$0.347128\pi$
$444$	1.51807e59	0.412264
$445$	−3.41632e59	−0.881980
$446$	3.95913e59	0.971775
$447$	7.04277e59	1.64371
$448$	−1.59928e58	−0.0354952
$449$	−5.32736e59	−1.12453	−0.562263	−	0.826959i	$-0.690069\pi$
$449$	−5.32736e59	−1.12453	−0.562263	+	0.826959i	$0.690069\pi$
$450$	1.90067e58	0.0381615
$451$	−4.17532e59	−0.797477
$452$	−1.27884e59	−0.232382
$453$	−8.02701e58	−0.138786
$454$	2.05076e59	0.337410
$455$	−1.49719e59	−0.234434
$456$	1.39169e59	0.207412
$457$	−1.11648e60	−1.58393	−0.791967	−	0.610564i	$-0.790943\pi$
$457$	−1.11648e60	−1.58393	−0.791967	+	0.610564i	$0.790943\pi$
$458$	1.61221e60	2.17746
$459$	8.05822e59	1.03622
$460$	−4.64096e59	−0.568273
$461$	8.63646e59	1.00708	0.503541	−	0.863971i	$-0.332030\pi$
$461$	8.63646e59	1.00708	0.503541	+	0.863971i	$0.332030\pi$
$462$	−2.66281e60	−2.95730
$463$	−7.81313e59	−0.826519	−0.413260	−	0.910613i	$-0.635610\pi$
$463$	−7.81313e59	−0.826519	−0.413260	+	0.910613i	$0.635610\pi$
$464$	−1.06863e60	−1.07689
$465$	1.47558e59	0.141668
$466$	2.59168e60	2.37082
$467$	−1.35783e60	−1.18363	−0.591816	−	0.806073i	$-0.701589\pi$
$467$	−1.35783e60	−1.18363	−0.591816	+	0.806073i	$0.701589\pi$
$468$	1.25563e58	0.0104311
$469$	3.25708e60	2.57893
$470$	−4.42566e59	−0.334023
$471$	1.04364e60	0.750898
$472$	−1.20620e60	−0.827417
$473$	1.02929e60	0.673227
$474$	7.66372e59	0.477999
$475$	1.48057e59	0.0880691
$476$	−1.39837e60	−0.793351
$477$	−8.80557e58	−0.0476534
$478$	−3.03409e60	−1.56639
$479$	−1.42047e60	−0.699653	−0.349827	−	0.936814i	$-0.613760\pi$
$479$	−1.42047e60	−0.699653	−0.349827	+	0.936814i	$0.613760\pi$
$480$	2.48027e60	1.16566
$481$	−2.54954e59	−0.114340
$482$	−1.92702e60	−0.824761
$483$	−3.17578e60	−1.29730
$484$	2.69816e60	1.05208
$485$	−1.70239e60	−0.633680
$486$	8.37600e59	0.297660
$487$	5.47125e59	0.185646	0.0928229	−	0.995683i	$-0.470411\pi$
$487$	5.47125e59	0.185646	0.0928229	+	0.995683i	$0.470411\pi$
$488$	2.79035e60	0.904092
$489$	3.88624e60	1.20249
$490$	3.40120e60	1.00513
$491$	−5.08915e60	−1.43652	−0.718260	−	0.695775i	$-0.755061\pi$
$491$	−5.08915e60	−1.43652	−0.718260	+	0.695775i	$0.755061\pi$
$492$	−9.92207e59	−0.267539
$493$	3.72785e60	0.960292
$494$	2.77888e59	0.0683934
$495$	−9.83253e59	−0.231232
$496$	6.63504e59	0.149110
$497$	−6.26741e59	−0.134607
$498$	−4.66049e59	−0.0956690
$499$	2.10435e59	0.0412910	0.0206455	−	0.999787i	$-0.493428\pi$
$499$	2.10435e59	0.0412910	0.0206455	+	0.999787i	$0.493428\pi$
$500$	−2.41658e60	−0.453289
$501$	−2.49436e60	−0.447312
$502$	−1.15135e61	−1.97412
$503$	4.53975e60	0.744307	0.372153	−	0.928171i	$-0.378620\pi$
$503$	4.53975e60	0.744307	0.372153	+	0.928171i	$0.378620\pi$
$504$	5.72100e59	0.0896984
$505$	−6.74010e60	−1.01067
$506$	1.38624e61	1.98817
$507$	7.51948e60	1.03159
$508$	8.55714e59	0.112304
$509$	2.61966e60	0.328923	0.164462	−	0.986383i	$-0.447411\pi$
$509$	2.61966e60	0.328923	0.164462	+	0.986383i	$0.447411\pi$
$510$	−1.36476e61	−1.63956
$511$	−9.36288e60	−1.07631
$512$	4.71382e60	0.518560
$513$	3.05330e60	0.321461
$514$	9.17106e59	0.0924165
$515$	2.72395e60	0.262746
$516$	2.44596e60	0.225856
$517$	4.65290e60	0.411327
$518$	1.38111e61	1.16898
$519$	−7.35065e59	−0.0595745
$520$	−1.30624e60	−0.101379
$521$	−2.08020e61	−1.54617	−0.773083	−	0.634305i	$-0.781287\pi$
$521$	−2.08020e61	−1.54617	−0.773083	+	0.634305i	$0.781287\pi$
$522$	1.81328e60	0.129086
$523$	2.10397e61	1.43467	0.717336	−	0.696728i	$-0.245361\pi$
$523$	2.10397e61	1.43467	0.717336	+	0.696728i	$0.245361\pi$
$524$	9.06658e59	0.0592229
$525$	5.66214e60	0.354320
$526$	−2.06677e61	−1.23912
$527$	−2.31460e60	−0.132965
$528$	−4.11310e61	−2.26415
$529$	−2.42332e60	−0.127838
$530$	−1.08912e61	−0.550639
$531$	3.62363e60	0.175597
$532$	−5.29849e60	−0.246116
$533$	1.66637e60	0.0742009
$534$	2.42495e61	1.03520
$535$	4.52114e61	1.85049
$536$	2.84166e61	1.11523
$537$	1.05893e61	0.398516
$538$	9.46570e60	0.341627
$539$	−3.57585e61	−1.23775
$540$	1.70639e61	0.566524
$541$	−2.45649e61	−0.782306	−0.391153	−	0.920326i	$-0.627924\pi$
$541$	−2.45649e61	−0.782306	−0.391153	+	0.920326i	$0.627924\pi$
$542$	6.72246e61	2.05374
$543$	−6.09426e61	−1.78618
$544$	−3.89056e61	−1.09405
$545$	−4.83435e61	−1.30442
$546$	1.06273e61	0.275161
$547$	4.92625e61	1.22406	0.612028	−	0.790836i	$-0.290354\pi$
$547$	4.92625e61	1.22406	0.612028	+	0.790836i	$0.290354\pi$
$548$	−1.13182e61	−0.269906
$549$	−8.38268e60	−0.191869
$550$	−2.47155e61	−0.543012
$551$	1.41250e61	0.297905
$552$	−2.77073e61	−0.561003
$553$	2.45409e61	0.477062
$554$	−6.10721e60	−0.113992
$555$	4.74435e61	0.850323
$556$	1.93040e61	0.332249
$557$	−1.15656e62	−1.91173	−0.955863	−	0.293813i	$-0.905076\pi$
$557$	−1.15656e62	−1.91173	−0.955863	+	0.293813i	$0.905076\pi$
$558$	−1.12586e60	−0.0178737
$559$	−4.10789e60	−0.0626402
$560$	1.25278e62	1.83503
$561$	1.43483e62	2.01900
$562$	−4.33598e61	−0.586165
$563$	−5.89709e61	−0.765947	−0.382974	−	0.923759i	$-0.625100\pi$
$563$	−5.89709e61	−0.765947	−0.382974	+	0.923759i	$0.625100\pi$
$564$	1.10570e61	0.137993
$565$	−3.99669e61	−0.479303
$566$	−1.68206e62	−1.93853
$567$	1.31037e62	1.45136
$568$	−5.46805e60	−0.0582096
$569$	7.93806e61	0.812248	0.406124	−	0.913818i	$-0.366880\pi$
$569$	7.93806e61	0.812248	0.406124	+	0.913818i	$0.366880\pi$
$570$	−5.17113e61	−0.508629
$571$	7.67118e61	0.725354	0.362677	−	0.931915i	$-0.381863\pi$
$571$	7.67118e61	0.725354	0.362677	+	0.931915i	$0.381863\pi$
$572$	−1.63277e61	−0.148428
$573$	−5.80098e61	−0.507017
$574$	−9.02689e61	−0.758614
$575$	−2.94768e61	−0.238207
$576$	4.19174e59	0.00325753
$577$	6.82798e60	0.0510313	0.0255156	−	0.999674i	$-0.491877\pi$
$577$	6.82798e60	0.0510313	0.0255156	+	0.999674i	$0.491877\pi$
$578$	4.12613e61	0.296597
$579$	−2.73427e62	−1.89049
$580$	7.89401e61	0.525011
$581$	−1.49239e61	−0.0954815
$582$	1.20838e62	0.743765
$583$	1.14504e62	0.678076
$584$	−8.16871e61	−0.465441
$585$	3.92416e60	0.0215149
$586$	1.71096e62	0.902698
$587$	1.68156e62	0.853800	0.426900	−	0.904299i	$-0.359606\pi$
$587$	1.68156e62	0.853800	0.426900	+	0.904299i	$0.359606\pi$
$588$	−8.49750e61	−0.415242
$589$	−8.77013e60	−0.0412489
$590$	4.48189e62	2.02904
$591$	−7.14887e61	−0.311544
$592$	2.13333e62	0.894992
$593$	−7.10812e61	−0.287094	−0.143547	−	0.989644i	$-0.545851\pi$
$593$	−7.10812e61	−0.287094	−0.143547	+	0.989644i	$0.545851\pi$
$594$	−5.09694e62	−1.98205
$595$	−4.37025e62	−1.63634
$596$	−2.33935e62	−0.843441
$597$	1.89898e62	0.659323
$598$	−5.53250e61	−0.184988
$599$	−3.72514e62	−1.19961	−0.599804	−	0.800147i	$-0.704755\pi$
$599$	−3.72514e62	−1.19961	−0.599804	+	0.800147i	$0.704755\pi$
$600$	4.93997e61	0.153222
$601$	1.98326e61	0.0592520	0.0296260	−	0.999561i	$-0.490568\pi$
$601$	1.98326e61	0.0592520	0.0296260	+	0.999561i	$0.490568\pi$
$602$	2.22528e62	0.640419
$603$	−8.53683e61	−0.236678
$604$	2.66628e61	0.0712156
$605$	8.43241e62	2.16998
$606$	4.78421e62	1.18625
$607$	−3.31764e62	−0.792653	−0.396327	−	0.918110i	$-0.629715\pi$
$607$	−3.31764e62	−0.792653	−0.396327	+	0.918110i	$0.629715\pi$
$608$	−1.47415e62	−0.339400
$609$	5.40182e62	1.19853
$610$	−1.03681e63	−2.21707
$611$	−1.85697e61	−0.0382717
$612$	3.66514e61	0.0728088
$613$	4.55123e62	0.871501	0.435750	−	0.900068i	$-0.356483\pi$
$613$	4.55123e62	0.871501	0.435750	+	0.900068i	$0.356483\pi$
$614$	8.80072e62	1.62454
$615$	−3.10089e62	−0.551818
$616$	−7.43935e62	−1.27635
$617$	−4.88458e62	−0.808000	−0.404000	−	0.914759i	$-0.632380\pi$
$617$	−4.88458e62	−0.808000	−0.404000	+	0.914759i	$0.632380\pi$
$618$	−1.93349e62	−0.308391
$619$	3.98061e62	0.612223	0.306111	−	0.951996i	$-0.400972\pi$
$619$	3.98061e62	0.612223	0.306111	+	0.951996i	$0.400972\pi$
$620$	−4.90134e61	−0.0726946
$621$	−6.07883e62	−0.869479
$622$	1.22142e63	1.68493
$623$	7.76521e62	1.03317
$624$	1.64154e62	0.210667
$625$	−9.61281e62	−1.19001
$626$	−1.67397e63	−1.99906
$627$	5.43665e62	0.626342
$628$	−3.46660e62	−0.385312
$629$	−7.44200e62	−0.798087
$630$	−2.12575e62	−0.219963
$631$	2.17238e62	0.216908	0.108454	−	0.994101i	$-0.465410\pi$
$631$	2.17238e62	0.216908	0.108454	+	0.994101i	$0.465410\pi$
$632$	2.14109e62	0.206301
$633$	5.95974e62	0.554171
$634$	2.57330e63	2.30931
$635$	2.67432e62	0.231635
$636$	2.72103e62	0.227482
$637$	1.42712e62	0.115166
$638$	−2.35792e63	−1.83681
$639$	1.64269e61	0.0123534
$640$	1.56864e63	1.13887
$641$	1.15093e63	0.806757	0.403379	−	0.915033i	$-0.367836\pi$
$641$	1.15093e63	0.806757	0.403379	+	0.915033i	$0.367836\pi$
$642$	−3.20916e63	−2.17197
$643$	1.21311e63	0.792781	0.396391	−	0.918082i	$-0.370263\pi$
$643$	1.21311e63	0.792781	0.396391	+	0.918082i	$0.370263\pi$
$644$	1.05488e63	0.665688
$645$	7.64422e62	0.465843
$646$	8.11145e62	0.477383
$647$	−2.91798e63	−1.65858	−0.829290	−	0.558818i	$-0.811255\pi$
$647$	−2.91798e63	−1.65858	−0.829290	+	0.558818i	$0.811255\pi$
$648$	1.14324e63	0.627627
$649$	−4.71202e63	−2.49863
$650$	9.86396e61	0.0505244
$651$	−3.35395e62	−0.165953
$652$	−1.29087e63	−0.617037
$653$	−9.80474e62	−0.452782	−0.226391	−	0.974036i	$-0.572693\pi$
$653$	−9.80474e62	−0.452782	−0.226391	+	0.974036i	$0.572693\pi$
$654$	3.43148e63	1.53103
$655$	2.83353e62	0.122151
$656$	−1.39434e63	−0.580806
$657$	2.45402e62	0.0987773
$658$	1.00594e63	0.391282
$659$	1.71493e63	0.644651	0.322325	−	0.946629i	$-0.395535\pi$
$659$	1.71493e63	0.644651	0.322325	+	0.946629i	$0.395535\pi$
$660$	3.03837e63	1.10383
$661$	4.68459e63	1.64490	0.822448	−	0.568840i	$-0.192608\pi$
$661$	4.68459e63	1.64490	0.822448	+	0.568840i	$0.192608\pi$
$662$	1.10197e62	0.0373995
$663$	−5.72642e62	−0.187857
$664$	−1.30205e62	−0.0412900
$665$	−1.65591e63	−0.507632
$666$	−3.61990e62	−0.107282
$667$	−2.81216e63	−0.805765
$668$	8.28537e62	0.229531
$669$	−3.09131e63	−0.828046
$670$	−1.05588e64	−2.73483
$671$	1.09005e64	2.73017
$672$	−5.63758e63	−1.36548
$673$	1.53030e63	0.358458	0.179229	−	0.983807i	$-0.442640\pi$
$673$	1.53030e63	0.358458	0.179229	+	0.983807i	$0.442640\pi$
$674$	2.75312e63	0.623703
$675$	1.08380e63	0.237474
$676$	−2.49770e63	−0.529346
$677$	−2.15211e63	−0.441184	−0.220592	−	0.975366i	$-0.570799\pi$
$677$	−2.15211e63	−0.441184	−0.220592	+	0.975366i	$0.570799\pi$
$678$	2.83690e63	0.562569
$679$	3.86949e63	0.742307
$680$	−3.81285e63	−0.707619
$681$	−1.60124e63	−0.287506
$682$	1.46402e63	0.254330
$683$	5.70299e63	0.958599	0.479299	−	0.877651i	$-0.340891\pi$
$683$	5.70299e63	0.958599	0.479299	+	0.877651i	$0.340891\pi$
$684$	1.38874e62	0.0225870
$685$	−3.53720e63	−0.556700
$686$	2.97312e63	0.452814
$687$	−1.25882e64	−1.85540
$688$	3.43728e63	0.490315
$689$	−4.56985e62	−0.0630913
$690$	1.02952e64	1.37572
$691$	−8.52122e62	−0.110216	−0.0551081	−	0.998480i	$-0.517550\pi$
$691$	−8.52122e62	−0.110216	−0.0551081	+	0.998480i	$0.517550\pi$
$692$	2.44162e62	0.0305697
$693$	2.23491e63	0.270870
$694$	6.77227e63	0.794596
$695$	6.03297e63	0.685288
$696$	4.71285e63	0.518294
$697$	4.86407e63	0.517919
$698$	−1.13159e64	−1.16666
$699$	−2.02359e64	−2.02017
$700$	−1.88076e63	−0.181814
$701$	−1.29219e64	−1.20968	−0.604842	−	0.796346i	$-0.706764\pi$
$701$	−1.29219e64	−1.20968	−0.604842	+	0.796346i	$0.706764\pi$
$702$	2.03419e63	0.184419
$703$	−2.81981e63	−0.247585
$704$	−5.45077e62	−0.0463524
$705$	3.45557e63	0.284620
$706$	−7.97902e63	−0.636566
$707$	1.53201e64	1.18392
$708$	−1.11975e64	−0.838245
$709$	8.82566e63	0.640040	0.320020	−	0.947411i	$-0.396310\pi$
$709$	8.82566e63	0.640040	0.320020	+	0.947411i	$0.396310\pi$
$710$	2.03176e63	0.142745
$711$	−6.43220e62	−0.0437818
$712$	6.77481e63	0.446784
$713$	1.74605e63	0.111569
$714$	3.10205e64	1.92061
$715$	−5.10281e63	−0.306143
$716$	−3.51739e63	−0.204492
$717$	2.36903e64	1.33472
$718$	−6.96805e63	−0.380462
$719$	−1.32233e64	−0.699747	−0.349873	−	0.936797i	$-0.613775\pi$
$719$	−1.32233e64	−0.699747	−0.349873	+	0.936797i	$0.613775\pi$
$720$	−3.28354e63	−0.168407
$721$	−6.19146e63	−0.307786
$722$	−2.27071e64	−1.09414
$723$	1.50463e64	0.702776
$724$	2.02429e64	0.916550
$725$	5.01383e63	0.220072
$726$	−5.98542e64	−2.54695
$727$	−3.36741e64	−1.38922	−0.694611	−	0.719386i	$-0.744423\pi$
$727$	−3.36741e64	−1.38922	−0.694611	+	0.719386i	$0.744423\pi$
$728$	2.96904e63	0.118757
$729$	2.19766e64	0.852298
$730$	3.03525e64	1.14138
$731$	−1.19908e64	−0.437226
$732$	2.59035e64	0.915923
$733$	−1.74069e64	−0.596873	−0.298437	−	0.954429i	$-0.596465\pi$
$733$	−1.74069e64	−0.596873	−0.298437	+	0.954429i	$0.596465\pi$
$734$	−6.23644e64	−2.07384
$735$	−2.65567e64	−0.856465
$736$	2.93489e64	0.917997
$737$	1.11009e65	3.36776
$738$	2.36596e63	0.0696207
$739$	1.59709e64	0.455858	0.227929	−	0.973678i	$-0.426805\pi$
$739$	1.59709e64	0.455858	0.227929	+	0.973678i	$0.426805\pi$
$740$	−1.57590e64	−0.436330
$741$	−2.16977e63	−0.0582778
$742$	2.47553e64	0.645031
$743$	−1.55533e64	−0.393164	−0.196582	−	0.980487i	$-0.562984\pi$
$743$	−1.55533e64	−0.393164	−0.196582	+	0.980487i	$0.562984\pi$
$744$	−2.92618e63	−0.0717646
$745$	−7.31105e64	−1.73966
$746$	5.36453e64	1.23853
$747$	3.91157e62	0.00876269
$748$	−4.76600e64	−1.03602
$749$	−1.02764e65	−2.16771
$750$	5.36078e64	1.09736
$751$	5.84568e64	1.16128	0.580639	−	0.814161i	$-0.302803\pi$
$751$	5.84568e64	1.16128	0.580639	+	0.814161i	$0.302803\pi$
$752$	1.55382e64	0.299571
$753$	8.98978e64	1.68214
$754$	9.41046e63	0.170905
$755$	8.33279e63	0.146887
$756$	−3.87858e64	−0.663639
$757$	−1.20065e64	−0.199416	−0.0997080	−	0.995017i	$-0.531791\pi$
$757$	−1.20065e64	−0.199416	−0.0997080	+	0.995017i	$0.531791\pi$
$758$	−8.52879e64	−1.37509
$759$	−1.08239e65	−1.69411
$760$	−1.44471e64	−0.219520
$761$	−3.56581e64	−0.526022	−0.263011	−	0.964793i	$-0.584716\pi$
$761$	−3.56581e64	−0.526022	−0.263011	+	0.964793i	$0.584716\pi$
$762$	−1.89826e64	−0.271875
$763$	1.09884e65	1.52803
$764$	1.92688e64	0.260168
$765$	1.14545e64	0.150173
$766$	8.33743e64	1.06141
$767$	1.88057e64	0.232484
$768$	−1.08959e65	−1.30808
$769$	−1.39554e65	−1.62704	−0.813521	−	0.581536i	$-0.802452\pi$
$769$	−1.39554e65	−1.62704	−0.813521	+	0.581536i	$0.802452\pi$
$770$	2.76424e65	3.12993
$771$	−7.16080e63	−0.0787478
$772$	9.08227e64	0.970075
$773$	1.32949e65	1.37926	0.689629	−	0.724163i	$-0.257773\pi$
$773$	1.32949e65	1.37926	0.689629	+	0.724163i	$0.257773\pi$
$774$	−5.83249e63	−0.0587736
$775$	−3.11305e63	−0.0304718
$776$	3.37596e64	0.321003
$777$	−1.07838e65	−0.996088
$778$	−2.28167e65	−2.04744
$779$	1.84302e64	0.160671
$780$	−1.21261e64	−0.102705
$781$	−2.13609e64	−0.175781
$782$	−1.61491e65	−1.29121
$783$	1.03397e65	0.803285
$784$	−1.19414e65	−0.901456
$785$	−1.08340e65	−0.794732
$786$	−2.01127e64	−0.143372
$787$	1.01514e65	0.703227	0.351613	−	0.936145i	$-0.385633\pi$
$787$	1.01514e65	0.703227	0.351613	+	0.936145i	$0.385633\pi$
$788$	2.37460e64	0.159864
$789$	1.61374e65	1.05585
$790$	−7.95566e64	−0.505902
$791$	9.08437e64	0.561466
$792$	1.94986e64	0.117135
$793$	−4.35039e64	−0.254028
$794$	1.87483e65	1.06414
$795$	8.50387e64	0.469198
$796$	−6.30773e64	−0.338321
$797$	6.73597e64	0.351227	0.175613	−	0.984459i	$-0.443809\pi$
$797$	6.73597e64	0.351227	0.175613	+	0.984459i	$0.443809\pi$
$798$	1.17538e65	0.595819
$799$	−5.42043e64	−0.267135
$800$	−5.23266e64	−0.250725
$801$	−2.03527e64	−0.0948178
$802$	−1.78264e65	−0.807494
$803$	−3.19111e65	−1.40553
$804$	2.63798e65	1.12982
$805$	3.29675e65	1.37303
$806$	−5.84289e63	−0.0236641
$807$	−7.39086e64	−0.291099
$808$	1.33661e65	0.511976
$809$	−2.59532e65	−0.966829	−0.483414	−	0.875392i	$-0.660604\pi$
$809$	−2.59532e65	−0.966829	−0.483414	+	0.875392i	$0.660604\pi$
$810$	−4.24796e65	−1.53910
$811$	3.24133e65	1.14223	0.571115	−	0.820870i	$-0.306511\pi$
$811$	3.24133e65	1.14223	0.571115	+	0.820870i	$0.306511\pi$
$812$	−1.79429e65	−0.615009
$813$	−5.24893e65	−1.74998
$814$	4.70717e65	1.52655
$815$	−4.03428e65	−1.27268
$816$	4.79158e65	1.47045
$817$	−4.54336e64	−0.135638
$818$	3.44917e65	1.00176
$819$	−8.91950e63	−0.0252030
$820$	1.03000e65	0.283157
$821$	−6.22943e65	−1.66620	−0.833100	−	0.553123i	$-0.813436\pi$
$821$	−6.22943e65	−1.66620	−0.833100	+	0.553123i	$0.813436\pi$
$822$	2.51075e65	0.653412
$823$	1.49111e65	0.377585	0.188792	−	0.982017i	$-0.439543\pi$
$823$	1.49111e65	0.377585	0.188792	+	0.982017i	$0.439543\pi$
$824$	−5.40179e64	−0.133099
$825$	1.92980e65	0.462699
$826$	−1.01872e66	−2.37686
$827$	7.39891e65	1.67994	0.839970	−	0.542633i	$-0.182573\pi$
$827$	7.39891e65	1.67994	0.839970	+	0.542633i	$0.182573\pi$
$828$	−2.76485e64	−0.0610926
$829$	6.47384e65	1.39215	0.696073	−	0.717971i	$-0.254929\pi$
$829$	6.47384e65	1.39215	0.696073	+	0.717971i	$0.254929\pi$
$830$	4.83802e64	0.101254
$831$	4.76853e64	0.0971319
$832$	2.17540e63	0.00431285
$833$	4.16570e65	0.803852
$834$	−4.28227e65	−0.804337
$835$	2.58938e65	0.473424
$836$	−1.80586e65	−0.321398
$837$	−6.41987e64	−0.111225
$838$	3.02214e65	0.509711
$839$	−4.81442e65	−0.790497	−0.395248	−	0.918574i	$-0.629341\pi$
$839$	−4.81442e65	−0.790497	−0.395248	+	0.918574i	$0.629341\pi$
$840$	−5.52498e65	−0.883176
$841$	−1.64223e65	−0.255578
$842$	−3.77910e65	−0.572619
$843$	3.38555e65	0.499469
$844$	−1.97961e65	−0.284364
$845$	−7.80592e65	−1.09181
$846$	−2.63658e64	−0.0359093
$847$	−1.91666e66	−2.54196
$848$	3.82382e65	0.493845
$849$	1.31336e66	1.65182
$850$	2.87925e65	0.352658
$851$	5.61397e65	0.669661
$852$	−5.07612e64	−0.0589713
$853$	1.52156e66	1.72162	0.860808	−	0.508929i	$-0.169959\pi$
$853$	1.52156e66	1.72162	0.860808	+	0.508929i	$0.169959\pi$
$854$	2.35665e66	2.59712
$855$	4.34015e64	0.0465872
$856$	−8.96575e65	−0.937404
$857$	−5.36235e63	−0.00546118	−0.00273059	−	0.999996i	$-0.500869\pi$
$857$	−5.36235e63	−0.00546118	−0.00273059	+	0.999996i	$0.500869\pi$
$858$	3.62204e65	0.359327
$859$	−1.03735e66	−1.00249	−0.501243	−	0.865306i	$-0.667124\pi$
$859$	−1.03735e66	−1.00249	−0.501243	+	0.865306i	$0.667124\pi$
$860$	−2.53914e65	−0.239040
$861$	7.04824e65	0.646412
$862$	−1.20139e66	−1.07342
$863$	−1.99751e66	−1.73878	−0.869391	−	0.494124i	$-0.835489\pi$
$863$	−1.99751e66	−1.73878	−0.869391	+	0.494124i	$0.835489\pi$
$864$	−1.07910e66	−0.915173
$865$	7.63066e64	0.0630521
$866$	2.14893e66	1.73009
$867$	−3.22170e65	−0.252729
$868$	1.11406e65	0.0851560
$869$	8.36417e65	0.622985
$870$	−1.75116e66	−1.27099
$871$	−4.43038e65	−0.313352
$872$	9.58687e65	0.660779
$873$	−1.01420e65	−0.0681243
$874$	−6.11898e65	−0.400564
$875$	1.71664e66	1.09521
$876$	−7.58321e65	−0.471532
$877$	−4.71670e65	−0.285856	−0.142928	−	0.989733i	$-0.545652\pi$
$877$	−4.71670e65	−0.285856	−0.142928	+	0.989733i	$0.545652\pi$
$878$	−1.63361e66	−0.964991
$879$	−1.33592e66	−0.769187
$880$	4.26978e66	2.39632
$881$	−4.33691e65	−0.237259	−0.118629	−	0.992939i	$-0.537850\pi$
$881$	−4.33691e65	−0.237259	−0.118629	+	0.992939i	$0.537850\pi$
$882$	2.02626e65	0.108057
$883$	2.23934e66	1.16413	0.582067	−	0.813141i	$-0.302244\pi$
$883$	2.23934e66	1.16413	0.582067	+	0.813141i	$0.302244\pi$
$884$	1.90211e65	0.0963961
$885$	−3.49948e66	−1.72894
$886$	2.38312e66	1.14786
$887$	−4.37952e65	−0.205658	−0.102829	−	0.994699i	$-0.532789\pi$
$887$	−4.37952e65	−0.205658	−0.102829	+	0.994699i	$0.532789\pi$
$888$	−9.40838e65	−0.430748
$889$	−6.07865e65	−0.271342
$890$	−2.51732e66	−1.09563
$891$	4.46608e66	1.89530
$892$	1.02682e66	0.424899
$893$	−2.05383e65	−0.0828716
$894$	5.18947e66	2.04187
$895$	−1.09927e66	−0.421780
$896$	−3.56547e66	−1.33409
$897$	4.31980e65	0.157628
$898$	−3.92547e66	−1.39693
$899$	−2.96993e65	−0.103075
$900$	4.92948e64	0.0166857
$901$	−1.33392e66	−0.440375
$902$	−3.07659e66	−0.990656
$903$	−1.73751e66	−0.545699
$904$	7.92573e65	0.242800
$905$	6.32641e66	1.89045
$906$	−5.91471e65	−0.172405
$907$	−4.19442e66	−1.19264	−0.596319	−	0.802748i	$-0.703370\pi$
$907$	−4.19442e66	−1.19264	−0.596319	+	0.802748i	$0.703370\pi$
$908$	5.31875e65	0.147529
$909$	−4.01541e65	−0.108653
$910$	−1.10321e66	−0.291223
$911$	3.79357e66	0.976979	0.488489	−	0.872570i	$-0.337548\pi$
$911$	3.79357e66	0.976979	0.488489	+	0.872570i	$0.337548\pi$
$912$	1.81555e66	0.456168
$913$	−5.08645e65	−0.124687
$914$	−8.22681e66	−1.96762
$915$	8.09548e66	1.88916
$916$	4.18136e66	0.952071
$917$	−6.44053e65	−0.143091
$918$	5.93771e66	1.28724
$919$	2.48234e66	0.525125	0.262563	−	0.964915i	$-0.415432\pi$
$919$	2.48234e66	0.525125	0.262563	+	0.964915i	$0.415432\pi$
$920$	2.87628e66	0.593751
$921$	−6.87164e66	−1.38426
$922$	6.36379e66	1.25104
$923$	8.52513e64	0.0163555
$924$	−6.90613e66	−1.29305
$925$	−1.00092e66	−0.182899
$926$	−5.75712e66	−1.02673
$927$	1.62279e65	0.0282467
$928$	−4.99208e66	−0.848111
$929$	−3.46738e66	−0.574974	−0.287487	−	0.957784i	$-0.592820\pi$
$929$	−3.46738e66	−0.574974	−0.287487	+	0.957784i	$0.592820\pi$
$930$	1.08728e66	0.175985
$931$	1.57841e66	0.249374
$932$	6.72165e66	1.03662
$933$	−9.53689e66	−1.43572
$934$	−1.00052e67	−1.47035
$935$	−1.48949e67	−2.13686
$936$	−7.78189e64	−0.0108988
$937$	1.05128e67	1.43740	0.718701	−	0.695319i	$-0.244737\pi$
$937$	1.05128e67	1.43740	0.718701	+	0.695319i	$0.244737\pi$
$938$	2.39998e67	3.20364
$939$	1.30704e67	1.70339
$940$	−1.14782e66	−0.146048
$941$	2.44367e66	0.303582	0.151791	−	0.988413i	$-0.451496\pi$
$941$	2.44367e66	0.303582	0.151791	+	0.988413i	$0.451496\pi$
$942$	7.69009e66	0.932795
$943$	−3.66928e66	−0.434578
$944$	−1.57356e67	−1.81976
$945$	−1.21215e67	−1.36880
$946$	7.58433e66	0.836309
$947$	7.28326e66	0.784244	0.392122	−	0.919913i	$-0.371741\pi$
$947$	7.28326e66	0.784244	0.392122	+	0.919913i	$0.371741\pi$
$948$	1.98763e66	0.209000
$949$	1.27357e66	0.130777
$950$	1.09096e66	0.109403
$951$	−2.00924e67	−1.96775
$952$	8.66651e66	0.828921
$953$	−1.42251e66	−0.132882	−0.0664410	−	0.997790i	$-0.521164\pi$
$953$	−1.42251e66	−0.132882	−0.0664410	+	0.997790i	$0.521164\pi$
$954$	−6.48839e65	−0.0591969
$955$	6.02196e66	0.536614
$956$	−7.86907e66	−0.684890
$957$	1.84108e67	1.56514
$958$	−1.04667e67	−0.869136
$959$	8.03996e66	0.652131
$960$	−4.04812e65	−0.0320738
$961$	−1.27360e67	−0.985728
$962$	−1.87863e66	−0.142037
$963$	2.69346e66	0.198939
$964$	−4.99783e66	−0.360619
$965$	2.83843e67	2.00085
$966$	−2.34008e67	−1.61155
$967$	−8.11376e66	−0.545917	−0.272959	−	0.962026i	$-0.588002\pi$
$967$	−8.11376e66	−0.545917	−0.272959	+	0.962026i	$0.588002\pi$
$968$	−1.67221e67	−1.09925
$969$	−6.33346e66	−0.406777
$970$	−1.25441e67	−0.787182
$971$	2.08461e67	1.27818	0.639090	−	0.769132i	$-0.279311\pi$
$971$	2.08461e67	1.27818	0.639090	+	0.769132i	$0.279311\pi$
$972$	2.17236e66	0.130149
$973$	−1.37128e67	−0.802761
$974$	4.03150e66	0.230616
$975$	−7.70183e65	−0.0430517
$976$	3.64019e67	1.98839
$977$	1.98080e66	0.105734	0.0528668	−	0.998602i	$-0.483164\pi$
$977$	1.98080e66	0.105734	0.0528668	+	0.998602i	$0.483164\pi$
$978$	2.86358e67	1.49377
$979$	2.64658e67	1.34919
$980$	8.82119e66	0.439482
$981$	−2.88006e66	−0.140232
$982$	−3.74995e67	−1.78450
$983$	−3.93540e67	−1.83035	−0.915176	−	0.403055i	$-0.867948\pi$
$983$	−3.93540e67	−1.83035	−0.915176	+	0.403055i	$0.867948\pi$
$984$	6.14929e66	0.279534
$985$	7.42119e66	0.329730
$986$	2.74687e67	1.19291
$987$	−7.85442e66	−0.333410
$988$	7.20718e65	0.0299043
$989$	9.04539e66	0.366869
$990$	−7.24511e66	−0.287245
$991$	−3.91335e67	−1.51667	−0.758336	−	0.651864i	$-0.773987\pi$
$991$	−3.91335e67	−1.51667	−0.758336	+	0.651864i	$0.773987\pi$
$992$	3.09955e66	0.117432
$993$	−8.60424e65	−0.0318680
$994$	−4.61815e66	−0.167215
$995$	−1.97132e67	−0.697811
$996$	−1.20872e66	−0.0418303
$997$	−2.80874e67	−0.950323	−0.475161	−	0.879899i	$-0.657610\pi$
$997$	−2.80874e67	−0.950323	−0.475161	+	0.879899i	$0.657610\pi$
$998$	1.55059e66	0.0512933
$999$	−2.06415e67	−0.667601

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.46.a.a.1.3	✓	3	1.1	even	1	trivial
9.46.a.b.1.1		3	3.2	odd	2
16.46.a.c.1.3		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)

\(f(q)\)	\(=\)	\(q+7.36851e6 q^{2} -5.75337e10 q^{3} +1.91106e13 q^{4} +5.97253e15 q^{5} -4.23938e17 q^{6} -1.35754e19 q^{7} -1.18440e20 q^{8} +3.55813e20 q^{9} +O(q^{10})\)	\(q+7.36851e6 q^{2} -5.75337e10 q^{3} +1.91106e13 q^{4} +5.97253e15 q^{5} -4.23938e17 q^{6} -1.35754e19 q^{7} -1.18440e20 q^{8} +3.55813e20 q^{9} +4.40087e22 q^{10} -4.62684e23 q^{11} -1.09950e24 q^{12} +1.84657e24 q^{13} -1.00031e26 q^{14} -3.43622e26 q^{15} -1.54512e27 q^{16} +5.39007e27 q^{17} +2.62181e27 q^{18} +2.04232e28 q^{19} +1.14139e29 q^{20} +7.81043e29 q^{21} -3.40930e30 q^{22} -4.06607e30 q^{23} +6.81427e30 q^{24} +7.24945e30 q^{25} +1.36065e31 q^{26} +1.49501e32 q^{27} -2.59434e32 q^{28} +6.91615e32 q^{29} -2.53198e33 q^{30} -4.29419e32 q^{31} -7.21801e33 q^{32} +2.66199e34 q^{33} +3.97168e34 q^{34} -8.10796e34 q^{35} +6.79980e33 q^{36} -1.38069e35 q^{37} +1.50489e35 q^{38} -1.06240e35 q^{39} -7.07385e35 q^{40} +9.02413e35 q^{41} +5.75513e36 q^{42} -2.22460e36 q^{43} -8.84218e36 q^{44} +2.12510e36 q^{45} -2.99609e37 q^{46} -1.00563e37 q^{47} +8.88964e37 q^{48} +7.72848e37 q^{49} +5.34177e37 q^{50} -3.10111e38 q^{51} +3.52891e37 q^{52} -2.47477e38 q^{53} +1.10160e39 q^{54} -2.76340e39 q^{55} +1.60787e39 q^{56} -1.17502e39 q^{57} +5.09618e39 q^{58} +1.01841e40 q^{59} -6.56683e39 q^{60} -2.35593e40 q^{61} -3.16418e39 q^{62} -4.83030e39 q^{63} +1.17807e39 q^{64} +1.10287e40 q^{65} +1.96149e41 q^{66} -2.39925e41 q^{67} +1.03008e41 q^{68} +2.33936e41 q^{69} -5.97436e41 q^{70} +4.61674e40 q^{71} -4.21424e40 q^{72} +6.89694e41 q^{73} -1.01736e42 q^{74} -4.17088e41 q^{75} +3.90301e41 q^{76} +6.28113e42 q^{77} -7.82832e41 q^{78} -1.80775e42 q^{79} -9.22828e42 q^{80} -9.65254e42 q^{81} +6.64944e42 q^{82} +1.09933e42 q^{83} +1.49262e43 q^{84} +3.21924e43 q^{85} -1.63920e43 q^{86} -3.97912e43 q^{87} +5.48002e43 q^{88} -5.72005e43 q^{89} +1.56589e43 q^{90} -2.50680e43 q^{91} -7.77051e43 q^{92} +2.47061e43 q^{93} -7.41002e43 q^{94} +1.21978e44 q^{95} +4.15279e44 q^{96} -2.85037e44 q^{97} +5.69474e44 q^{98} -1.64629e44 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3814272 q^{2} + 5359866876 q^{3} - 1915164893184 q^{4} - 912448458460350 q^{5} - 84\!\cdots\!24 q^{6}+ \cdots + 11\!\cdots\!19 q^{9}+O(q^{10}) \) 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

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