LMFDB - Embedded newform 1.58.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,58,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, 58, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 58);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 58 $
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:	$20.5766433651$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 20682206675887x^{2} + 1182366456513663853x + 45927816189452762789055234 $ x^4 - x^3 - 20682206675887x^2 + 1182366456513663853x + 45927816189452762789055234
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{25}\cdot 3^{10}\cdot 5^{2}\cdot 7\cdot 19 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$4.22205e6$ 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)

$f(q)$	$=$	$q+5.53538e8 q^{2} -2.70314e13 q^{3} +1.62289e17 q^{4} -5.73891e19 q^{5} -1.49629e22 q^{6} +1.73157e24 q^{7} +1.00602e25 q^{8} -8.39347e26 q^{9} +O(q^{10})$	\(q+5.53538e8 q^{2} -2.70314e13 q^{3} +1.62289e17 q^{4} -5.73891e19 q^{5} -1.49629e22 q^{6} +1.73157e24 q^{7} +1.00602e25 q^{8} -8.39347e26 q^{9} -3.17671e28 q^{10} -7.30202e29 q^{11} -4.38691e30 q^{12} -7.35382e31 q^{13} +9.58490e32 q^{14} +1.55131e33 q^{15} -1.78197e34 q^{16} -5.76619e34 q^{17} -4.64611e35 q^{18} +2.98197e36 q^{19} -9.31365e36 q^{20} -4.68067e37 q^{21} -4.04195e38 q^{22} -2.19312e38 q^{23} -2.71941e38 q^{24} -3.64538e39 q^{25} -4.07062e40 q^{26} +6.51292e40 q^{27} +2.81015e41 q^{28} +2.03714e41 q^{29} +8.58708e41 q^{30} -2.38910e41 q^{31} -1.13137e43 q^{32} +1.97384e43 q^{33} -3.19181e43 q^{34} -9.93732e43 q^{35} -1.36217e44 q^{36} +2.29845e44 q^{37} +1.65064e45 q^{38} +1.98784e45 q^{39} -5.77345e44 q^{40} -8.95674e45 q^{41} -2.59093e46 q^{42} +7.06441e46 q^{43} -1.18504e47 q^{44} +4.81694e46 q^{45} -1.21398e47 q^{46} +3.69252e47 q^{47} +4.81691e47 q^{48} +1.51722e48 q^{49} -2.01786e48 q^{50} +1.55868e48 q^{51} -1.19345e49 q^{52} -2.42540e49 q^{53} +3.60515e49 q^{54} +4.19057e49 q^{55} +1.74199e49 q^{56} -8.06069e49 q^{57} +1.12764e50 q^{58} -8.00310e49 q^{59} +2.51761e50 q^{60} -4.03965e50 q^{61} -1.32246e50 q^{62} -1.45339e51 q^{63} -3.69448e51 q^{64} +4.22029e51 q^{65} +1.09259e52 q^{66} +9.38429e51 q^{67} -9.35792e51 q^{68} +5.92831e51 q^{69} -5.50069e52 q^{70} -5.52770e51 q^{71} -8.44398e51 q^{72} -6.25437e52 q^{73} +1.27228e53 q^{74} +9.85397e52 q^{75} +4.83943e53 q^{76} -1.26440e54 q^{77} +1.10035e54 q^{78} +2.30242e53 q^{79} +1.02266e54 q^{80} -4.42721e53 q^{81} -4.95790e54 q^{82} -1.95040e54 q^{83} -7.59624e54 q^{84} +3.30917e54 q^{85} +3.91042e55 q^{86} -5.50668e54 q^{87} -7.34596e54 q^{88} +2.14905e54 q^{89} +2.66636e55 q^{90} -1.27336e56 q^{91} -3.55921e55 q^{92} +6.45807e54 q^{93} +2.04395e56 q^{94} -1.71133e56 q^{95} +3.05825e56 q^{96} -7.81319e56 q^{97} +8.39837e56 q^{98} +6.12893e56 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 217744560 q^{2} + 37475862172560 q^{3} + 29\!\cdots\!28 q^{4}+ \cdots + 80\!\cdots\!32 q^{9}+O(q^{10}) $ 4 * q - 217744560 * q^2 + 37475862172560 * q^3 + 293124896311376128 * q^4 - 106961276207842698600 * q^5 - 33990084162012424888512 * q^6 + 952854504056592488640800 * q^7 - 88551069216810449485639680 * q^8 + 807299095982681497210590132 * q^9	$ 4 q - 217744560 q^{2} + 37475862172560 q^{3} + 29\!\cdots\!28 q^{4}+ \cdots + 12\!\cdots\!04 q^{99}+O(q^{100}) $ 4 * q - 217744560 * q^2 + 37475862172560 * q^3 + 293124896311376128 * q^4 - 106961276207842698600 * q^5 - 33990084162012424888512 * q^6 + 952854504056592488640800 * q^7 - 88551069216810449485639680 * q^8 + 807299095982681497210590132 * q^9 + 44476431289760320477662520800 * q^10 - 462030036788542994175991820112 * q^11 + 10003750272364901761239114286080 * q^12 - 35670303061909387812013418679880 * q^13 + 70403094050531232484583448299136 * q^14 - 3873003953749638547444662603837600 * q^15 + 13566910890781728442321186411577344 * q^16 + 13820011728830480443629140931368520 * q^17 - 1287737321088043352155941276317529840 * q^18 + 336853252899071533902360882896311760 * q^19 - 50382729988973225454329459567578483200 * q^20 - 114908173756075652427942608537020743552 * q^21 - 661915503282569637498974918979285510720 * q^22 - 2975542065258688382050024994957196661920 * q^23 - 10578976944220511671340845604322576875520 * q^24 - 9469406228848045007865812554313674602500 * q^25 - 17469964426099436483582477475571041235872 * q^26 + 76349739563972016366032809192591896661920 * q^27 + 649254606795882967703588744692964385720320 * q^28 + 692903173502123074211699189163367889819640 * q^29 + 5634330080537746852583656641742556105212800 * q^30 - 899836592298317074905406089703577976621952 * q^31 - 14233950964359390830124363997913062975733760 * q^32 - 29363967329346027307019371741967172628226880 * q^33 - 169043128317257524614754408952689830505725024 * q^34 - 229326244292419606493088342114240299318011200 * q^35 + 284785472553153735165042638775100342213281024 * q^36 + 1088031360501840746049603861287321623324833560 * q^37 + 1556247388283245464794907962939214603341474880 * q^38 + 4179255936739867118004084422081931511953729504 * q^39 + 11751904708902009656918381872378671214758912000 * q^40 - 11103291557355181141038304173539140276092022872 * q^41 - 59279988331696939901744072326763120527717946880 * q^42 - 61754953860901881142563948460092952248410491600 * q^43 - 133524603192894473629581294520903680469781443584 * q^44 - 107702873160032711230811245899648546573795049800 * q^45 + 784819010796366200631618785819800311186796983168 * q^46 + 363083109323271524824455302894174707948361522880 * q^47 + 2742506186706372359330741580910160874632313569280 * q^48 + 1216129915477179767594559246649850886387208070628 * q^49 - 5243147625423300757899019878966089303259662130000 * q^50 - 764600229637750496670397948984385624631693707232 * q^51 - 22843788670121162835092909423272591563858567692800 * q^52 - 35290483593822076697173728695179253314838955459240 * q^53 + 12366575839681539833915263850508773584456529324160 * q^54 + 49196225093152182399971681538771907122934246240800 * q^55 + 63731767886683182211705479053660664279663635496960 * q^56 + 207676196582248616809244588606912583584671767915840 * q^57 + 617562539749243989517600779192095966343296224852320 * q^58 + 67768373912933539906296460571320281490527711258480 * q^59 - 1815042162748644358648991332911151647292658713651200 * q^60 - 1547288835446782082478245361946256543823484047403912 * q^61 - 749692944011811307313821057793297922348443552785920 * q^62 - 1569461042763431092010126958426126899190556123563360 * q^63 - 1990114977445631941316528741938069721703684937613312 * q^64 + 8063572248542729948506878297975365372089154570456400 * q^65 + 16489629555376763758820085001622755676656730822766336 * q^66 + 15272577061969964687199674310464241542844062558207120 * q^67 + 41305128999321265264790818598430329317542515380584960 * q^68 - 65786095162933072363901793014646952768970242331074176 * q^69 - 24325103535157938973881571830399397699429009026566400 * q^70 - 73888360588713834794031605853188887812717485611902432 * q^71 - 210328265328797773276338939967226276847978373484605440 * q^72 - 130297268842197178419561798573986372195905283718671320 * q^73 + 7685145516671187561069432006215096921673721366642656 * q^74 + 403928833669880609006163131916358629442839611491110000 * q^75 + 1456086045339107958455546112995861351598648681192657920 * q^76 - 106427745818663343042165176190596036157925407112924800 * q^77 + 2074950811168633790188899303505400649698048509219286400 * q^78 - 828943058463042070981602117491995742498435075805703360 * q^79 - 2284181918093911007938097065798931209886961598847385600 * q^80 - 7963307412965608591332950484302680892196600516966334236 * q^81 - 1883428276461442027198836795157559789817480540746193120 * q^82 - 9840480688986571601216593400698100805429733592804704560 * q^83 + 13541340719968270381664710206581288963145836751957467136 * q^84 - 14840134943015755845177119052592106190913842871494565200 * q^85 + 67988974963281087138264344329950027971018743502811738048 * q^86 - 27365055454269193487844075068414523895320708309490878240 * q^87 + 61847074514255305493001192533786291945351930637515735040 * q^88 - 10663966381455218428814337779016832517355842990125366680 * q^89 + 144098850070698626396745850922715348604587043628376674400 * q^90 - 254422712153651549623482540524255137118230327668042523712 * q^91 - 274534438781355859366149237613545893970204939554260346880 * q^92 - 414128946656565192633171191785208529876343680904079162880 * q^93 + 632898423704876935427548603685166753697821378730383050496 * q^94 - 532156934024946939894578863048125180396162968766201396000 * q^95 + 663745987198780197281626102963422448954448917470231134208 * q^96 - 152729877520747450623636953478949994021736793474425664120 * q^97 + 2296925218269808931776551039888426925574868525366690486480 * q^98 + 123613071571796047703935039848745969833181068960384152304 * 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 $

$2$	5.53538e8	1.45812	0.729059	−	0.684451i	$-0.239958\pi$
$2$	5.53538e8	1.45812	0.729059	+	0.684451i	$0.239958\pi$
$3$	−2.70314e13	−0.682201	−0.341101	−	0.940027i	$-0.610800\pi$
$3$	−2.70314e13	−0.682201	−0.341101	+	0.940027i	$0.610800\pi$
$4$	1.62289e17	1.12611
$5$	−5.73891e19	−0.688945	−0.344472	−	0.938796i	$-0.611942\pi$
$5$	−5.73891e19	−0.688945	−0.344472	+	0.938796i	$0.611942\pi$
$6$	−1.49629e22	−0.994730
$7$	1.73157e24	1.42281	0.711403	−	0.702785i	$-0.248060\pi$
$7$	1.73157e24	1.42281	0.711403	+	0.702785i	$0.248060\pi$
$8$	1.00602e25	0.183883
$9$	−8.39347e26	−0.534601
$10$	−3.17671e28	−1.00456
$11$	−7.30202e29	−1.52669	−0.763346	−	0.645989i	$-0.776445\pi$
$11$	−7.30202e29	−1.52669	−0.763346	+	0.645989i	$0.776445\pi$
$12$	−4.38691e30	−0.768234
$13$	−7.35382e31	−1.31561	−0.657805	−	0.753188i	$-0.728515\pi$
$13$	−7.35382e31	−1.31561	−0.657805	+	0.753188i	$0.728515\pi$
$14$	9.58490e32	2.07462
$15$	1.55131e33	0.469999
$16$	−1.78197e34	−0.857987
$17$	−5.76619e34	−0.493281	−0.246641	−	0.969107i	$-0.579327\pi$
$17$	−5.76619e34	−0.493281	−0.246641	+	0.969107i	$0.579327\pi$
$18$	−4.64611e35	−0.779512
$19$	2.98197e36	1.07158	0.535792	−	0.844350i	$-0.320013\pi$
$19$	2.98197e36	1.07158	0.535792	+	0.844350i	$0.320013\pi$
$20$	−9.31365e36	−0.775828
$21$	−4.68067e37	−0.970640
$22$	−4.04195e38	−2.22610
$23$	−2.19312e38	−0.340267	−0.170133	−	0.985421i	$-0.554420\pi$
$23$	−2.19312e38	−0.340267	−0.170133	+	0.985421i	$0.554420\pi$
$24$	−2.71941e38	−0.125445
$25$	−3.64538e39	−0.525355
$26$	−4.07062e40	−1.91832
$27$	6.51292e40	1.04691
$28$	2.81015e41	1.60224
$29$	2.03714e41	0.427247	0.213623	−	0.976916i	$-0.431474\pi$
$29$	2.03714e41	0.427247	0.213623	+	0.976916i	$0.431474\pi$
$30$	8.58708e41	0.685315
$31$	−2.38910e41	−0.0748904	−0.0374452	−	0.999299i	$-0.511922\pi$
$31$	−2.38910e41	−0.0748904	−0.0374452	+	0.999299i	$0.511922\pi$
$32$	−1.13137e43	−1.43493
$33$	1.97384e43	1.04151
$34$	−3.19181e43	−0.719263
$35$	−9.93732e43	−0.980235
$36$	−1.36217e44	−0.602020
$37$	2.29845e44	0.465249	0.232625	−	0.972567i	$-0.425269\pi$
$37$	2.29845e44	0.465249	0.232625	+	0.972567i	$0.425269\pi$
$38$	1.65064e45	1.56250
$39$	1.98784e45	0.897511
$40$	−5.77345e44	−0.126685
$41$	−8.95674e45	−0.972322	−0.486161	−	0.873869i	$-0.661603\pi$
$41$	−8.95674e45	−0.972322	−0.486161	+	0.873869i	$0.661603\pi$
$42$	−2.59093e46	−1.41531
$43$	7.06441e46	1.97344	0.986722	−	0.162417i	$-0.0519289\pi$
$43$	7.06441e46	1.97344	0.986722	+	0.162417i	$0.0519289\pi$
$44$	−1.18504e47	−1.71922
$45$	4.81694e46	0.368311
$46$	−1.21398e47	−0.496149
$47$	3.69252e47	0.817586	0.408793	−	0.912627i	$-0.365950\pi$
$47$	3.69252e47	0.817586	0.408793	+	0.912627i	$0.365950\pi$
$48$	4.81691e47	0.585320
$49$	1.51722e48	1.02438
$50$	−2.01786e48	−0.766030
$51$	1.55868e48	0.336517
$52$	−1.19345e49	−1.48152
$53$	−2.42540e49	−1.74953	−0.874766	−	0.484546i	$-0.838985\pi$
$53$	−2.42540e49	−1.74953	−0.874766	+	0.484546i	$0.838985\pi$
$54$	3.60515e49	1.52651
$55$	4.19057e49	1.05181
$56$	1.74199e49	0.261629
$57$	−8.06069e49	−0.731036
$58$	1.12764e50	0.622976
$59$	−8.00310e49	−0.271629	−0.135814	−	0.990734i	$-0.543365\pi$
$59$	−8.00310e49	−0.271629	−0.135814	+	0.990734i	$0.543365\pi$
$60$	2.51761e50	0.529271
$61$	−4.03965e50	−0.530205	−0.265102	−	0.964220i	$-0.585406\pi$
$61$	−4.03965e50	−0.530205	−0.265102	+	0.964220i	$0.585406\pi$
$62$	−1.32246e50	−0.109199
$63$	−1.45339e51	−0.760634
$64$	−3.69448e51	−1.23431
$65$	4.22029e51	0.906383
$66$	1.09259e52	1.51865
$67$	9.38429e51	0.849707	0.424854	−	0.905262i	$-0.360326\pi$
$67$	9.38429e51	0.849707	0.424854	+	0.905262i	$0.360326\pi$
$68$	−9.35792e51	−0.555489
$69$	5.92831e51	0.232130
$70$	−5.50069e52	−1.42930
$71$	−5.52770e51	−0.0958697	−0.0479349	−	0.998850i	$-0.515264\pi$
$71$	−5.52770e51	−0.0958697	−0.0479349	+	0.998850i	$0.515264\pi$
$72$	−8.44398e51	−0.0983040
$73$	−6.25437e52	−0.491453	−0.245726	−	0.969339i	$-0.579027\pi$
$73$	−6.25437e52	−0.491453	−0.245726	+	0.969339i	$0.579027\pi$
$74$	1.27228e53	0.678389
$75$	9.85397e52	0.358398
$76$	4.83943e53	1.20672
$77$	−1.26440e54	−2.17219
$78$	1.10035e54	1.30868
$79$	2.30242e53	0.190464	0.0952318	−	0.995455i	$-0.469641\pi$
$79$	2.30242e53	0.190464	0.0952318	+	0.995455i	$0.469641\pi$
$80$	1.02266e54	0.591106
$81$	−4.42721e53	−0.179600
$82$	−4.95790e54	−1.41776
$83$	−1.95040e54	−0.394820	−0.197410	−	0.980321i	$-0.563253\pi$
$83$	−1.95040e54	−0.394820	−0.197410	+	0.980321i	$0.563253\pi$
$84$	−7.59624e54	−1.09305
$85$	3.30917e54	0.339844
$86$	3.91042e55	2.87752
$87$	−5.50668e54	−0.291468
$88$	−7.34596e54	−0.280732
$89$	2.14905e54	0.0595158	0.0297579	−	0.999557i	$-0.490526\pi$
$89$	2.14905e54	0.0595158	0.0297579	+	0.999557i	$0.490526\pi$
$90$	2.66636e55	0.537041
$91$	−1.27336e56	−1.87186
$92$	−3.55921e55	−0.383178
$93$	6.45807e54	0.0510903
$94$	2.04395e56	1.19214
$95$	−1.71133e56	−0.738262
$96$	3.05825e56	0.978911
$97$	−7.81319e56	−1.86138	−0.930688	−	0.365814i	$-0.880791\pi$
$97$	−7.81319e56	−1.86138	−0.930688	+	0.365814i	$0.880791\pi$
$98$	8.39837e56	1.49366
$99$	6.12893e56	0.816172
$100$	−5.91607e56	−0.591607
$101$	4.11110e56	0.309599	0.154799	−	0.987946i	$-0.450527\pi$
$101$	4.11110e56	0.309599	0.154799	+	0.987946i	$0.450527\pi$
$102$	8.62790e56	0.490682
$103$	−3.17626e57	−1.36790	−0.683952	−	0.729527i	$-0.739740\pi$
$103$	−3.17626e57	−1.36790	−0.683952	+	0.729527i	$0.739740\pi$
$104$	−7.39807e56	−0.241918
$105$	2.68620e57	0.668718
$106$	−1.34255e58	−2.55102
$107$	6.11648e57	0.889331	0.444666	−	0.895697i	$-0.353323\pi$
$107$	6.11648e57	0.889331	0.444666	+	0.895697i	$0.353323\pi$
$108$	1.05698e58	1.17893
$109$	8.40119e57	0.720586	0.360293	−	0.932839i	$-0.382677\pi$
$109$	8.40119e57	0.720586	0.360293	+	0.932839i	$0.382677\pi$
$110$	2.31964e58	1.53366
$111$	−6.21303e57	−0.317394
$112$	−3.08560e58	−1.22075
$113$	−1.54195e58	−0.473516	−0.236758	−	0.971569i	$-0.576085\pi$
$113$	−1.54195e58	−0.473516	−0.236758	+	0.971569i	$0.576085\pi$
$114$	−4.46190e58	−1.06594
$115$	1.25861e58	0.234425
$116$	3.30607e58	0.481126
$117$	6.17241e58	0.703327
$118$	−4.43002e58	−0.396067
$119$	−9.98456e58	−0.701844
$120$	1.56064e58	0.0864247
$121$	3.04434e59	1.33079
$122$	−2.23610e59	−0.773102
$123$	2.42113e59	0.663319
$124$	−3.87726e58	−0.0843348
$125$	6.07422e59	1.05089
$126$	−8.04505e59	−1.10909
$127$	−3.16282e59	−0.348072	−0.174036	−	0.984739i	$-0.555681\pi$
$127$	−3.16282e59	−0.348072	−0.174036	+	0.984739i	$0.555681\pi$
$128$	−4.14560e59	−0.364841
$129$	−1.90961e60	−1.34629
$130$	2.33609e60	1.32161
$131$	−3.68185e60	−1.67430	−0.837151	−	0.546972i	$-0.815780\pi$
$131$	−3.68185e60	−1.67430	−0.837151	+	0.546972i	$0.815780\pi$
$132$	3.20333e60	1.17286
$133$	5.16349e60	1.52466
$134$	5.19456e60	1.23897
$135$	−3.73771e60	−0.721261
$136$	−5.80089e59	−0.0907059
$137$	−1.04894e61	−1.33111	−0.665556	−	0.746348i	$-0.731805\pi$
$137$	−1.04894e61	−1.33111	−0.665556	+	0.746348i	$0.731805\pi$
$138$	3.28155e60	0.338474
$139$	1.22228e60	0.102624	0.0513120	−	0.998683i	$-0.483660\pi$
$139$	1.22228e60	0.102624	0.0513120	+	0.998683i	$0.483660\pi$
$140$	−1.61272e61	−1.10385
$141$	−9.98139e60	−0.557759
$142$	−3.05979e60	−0.139789
$143$	5.36978e61	2.00853
$144$	1.49569e61	0.458681
$145$	−1.16910e61	−0.294349
$146$	−3.46203e61	−0.716597
$147$	−4.10125e61	−0.698830
$148$	3.73014e61	0.523922
$149$	8.31521e61	0.963973	0.481986	−	0.876179i	$-0.339915\pi$
$149$	8.31521e61	0.963973	0.481986	+	0.876179i	$0.339915\pi$
$150$	5.45455e61	0.522586
$151$	−5.57147e61	−0.441699	−0.220850	−	0.975308i	$-0.570883\pi$
$151$	−5.57147e61	−0.441699	−0.220850	+	0.975308i	$0.570883\pi$
$152$	2.99992e61	0.197046
$153$	4.83984e61	0.263709
$154$	−6.99891e62	−3.16731
$155$	1.37108e61	0.0515954
$156$	3.22605e62	1.01070
$157$	−4.30047e61	−0.112299	−0.0561495	−	0.998422i	$-0.517882\pi$
$157$	−4.30047e61	−0.112299	−0.0561495	+	0.998422i	$0.517882\pi$
$158$	1.27448e62	0.277718
$159$	6.55620e62	1.19353
$160$	6.49284e62	0.988587
$161$	−3.79754e62	−0.484133
$162$	−2.45063e62	−0.261878
$163$	9.67107e62	0.867217	0.433608	−	0.901101i	$-0.357240\pi$
$163$	9.67107e62	0.867217	0.433608	+	0.901101i	$0.357240\pi$
$164$	−1.45358e63	−1.09494
$165$	−1.13277e63	−0.717544
$166$	−1.07962e63	−0.575694
$167$	−7.18239e62	−0.322738	−0.161369	−	0.986894i	$-0.551591\pi$
$167$	−7.18239e62	−0.322738	−0.161369	+	0.986894i	$0.551591\pi$
$168$	−4.70884e62	−0.178484
$169$	2.28343e63	0.730832
$170$	1.83175e63	0.495533
$171$	−2.50291e63	−0.572870
$172$	1.14648e64	2.22231
$173$	−6.75233e63	−1.10953	−0.554766	−	0.832006i	$-0.687192\pi$
$173$	−6.75233e63	−1.10953	−0.554766	+	0.832006i	$0.687192\pi$
$174$	−3.04816e63	−0.424995
$175$	−6.31223e63	−0.747478
$176$	1.30120e64	1.30988
$177$	2.16335e63	0.185305
$178$	1.18958e63	0.0867810
$179$	−1.83369e64	−1.14029	−0.570145	−	0.821544i	$-0.693113\pi$
$179$	−1.83369e64	−1.14029	−0.570145	+	0.821544i	$0.693113\pi$
$180$	7.81739e63	0.414758
$181$	2.93424e64	1.32940	0.664701	−	0.747109i	$-0.268559\pi$
$181$	2.93424e64	1.32940	0.664701	+	0.747109i	$0.268559\pi$
$182$	−7.04856e64	−2.72939
$183$	1.09197e64	0.361707
$184$	−2.20632e63	−0.0625692
$185$	−1.31906e64	−0.320531
$186$	3.57479e63	0.0744958
$187$	4.21049e64	0.753089
$188$	5.99257e64	0.920692
$189$	1.12776e65	1.48955
$190$	−9.47286e64	−1.07647
$191$	7.51650e64	0.735469	0.367735	−	0.929931i	$-0.380133\pi$
$191$	7.51650e64	0.735469	0.367735	+	0.929931i	$0.380133\pi$
$192$	9.98670e64	0.842048
$193$	−2.27174e65	−1.65187	−0.825934	−	0.563767i	$-0.809352\pi$
$193$	−2.27174e65	−1.65187	−0.825934	+	0.563767i	$0.809352\pi$
$194$	−4.32490e65	−2.71411
$195$	−1.14080e65	−0.618336
$196$	2.46228e65	1.15356
$197$	1.70014e65	0.688966	0.344483	−	0.938793i	$-0.388054\pi$
$197$	1.70014e65	0.688966	0.344483	+	0.938793i	$0.388054\pi$
$198$	3.39260e65	1.19008
$199$	−1.15949e65	−0.352335	−0.176167	−	0.984360i	$-0.556370\pi$
$199$	−1.15949e65	−0.352335	−0.176167	+	0.984360i	$0.556370\pi$
$200$	−3.66732e64	−0.0966037
$201$	−2.53670e65	−0.579672
$202$	2.27565e65	0.451432
$203$	3.52745e65	0.607889
$204$	2.52958e65	0.378955
$205$	5.14019e65	0.669876
$206$	−1.75818e66	−1.99456
$207$	1.84079e65	0.181907
$208$	1.31043e66	1.12878
$209$	−2.17744e66	−1.63598
$210$	1.48691e66	0.975069
$211$	1.06248e66	0.608513	0.304256	−	0.952590i	$-0.401592\pi$
$211$	1.06248e66	0.608513	0.304256	+	0.952590i	$0.401592\pi$
$212$	−3.93618e66	−1.97016
$213$	1.49421e65	0.0654025
$214$	3.38570e66	1.29675
$215$	−4.05420e66	−1.35959
$216$	6.55211e65	0.192508
$217$	−4.13689e65	−0.106554
$218$	4.65038e66	1.05070
$219$	1.69064e66	0.335270
$220$	6.80085e66	1.18445
$221$	4.24035e66	0.648966
$222$	−3.43915e66	−0.462798
$223$	−2.87994e66	−0.340953	−0.170477	−	0.985362i	$-0.554531\pi$
$223$	−2.87994e66	−0.340953	−0.170477	+	0.985362i	$0.554531\pi$
$224$	−1.95905e67	−2.04163
$225$	3.05974e66	0.280855
$226$	−8.53528e66	−0.690442
$227$	−3.22619e66	−0.230119	−0.115060	−	0.993359i	$-0.536706\pi$
$227$	−3.22619e66	−0.230119	−0.115060	+	0.993359i	$0.536706\pi$
$228$	−1.30817e67	−0.823227
$229$	1.68626e67	0.936729	0.468364	−	0.883535i	$-0.344843\pi$
$229$	1.68626e67	0.936729	0.468364	+	0.883535i	$0.344843\pi$
$230$	6.96691e66	0.341820
$231$	3.41784e67	1.48187
$232$	2.04940e66	0.0785633
$233$	−7.12806e66	−0.241728	−0.120864	−	0.992669i	$-0.538567\pi$
$233$	−7.12806e66	−0.241728	−0.120864	+	0.992669i	$0.538567\pi$
$234$	3.41666e67	1.02553
$235$	−2.11910e67	−0.563272
$236$	−1.29882e67	−0.305884
$237$	−6.22375e66	−0.129934
$238$	−5.52683e67	−1.02337
$239$	2.00791e67	0.329916	0.164958	−	0.986301i	$-0.447251\pi$
$239$	2.00791e67	0.329916	0.164958	+	0.986301i	$0.447251\pi$
$240$	−2.76438e67	−0.403253
$241$	−6.70399e66	−0.0868655	−0.0434328	−	0.999056i	$-0.513829\pi$
$241$	−6.70399e66	−0.0868655	−0.0434328	+	0.999056i	$0.513829\pi$
$242$	1.68516e68	1.94045
$243$	−9.02882e67	−0.924384
$244$	−6.55593e67	−0.597069
$245$	−8.70717e67	−0.705738
$246$	1.34019e68	0.967198
$247$	−2.19289e68	−1.40979
$248$	−2.40348e66	−0.0137711
$249$	5.27221e67	0.269347
$250$	3.36232e68	1.53232
$251$	3.34366e68	1.35994	0.679972	−	0.733238i	$-0.261992\pi$
$251$	3.34366e68	1.35994	0.679972	+	0.733238i	$0.261992\pi$
$252$	−2.35869e68	−0.856557
$253$	1.60142e68	0.519483
$254$	−1.75074e68	−0.507530
$255$	−8.94514e67	−0.231842
$256$	3.02956e68	0.702328
$257$	−4.95475e68	−1.02785	−0.513923	−	0.857836i	$-0.671808\pi$
$257$	−4.95475e68	−1.02785	−0.513923	+	0.857836i	$0.671808\pi$
$258$	−1.05704e69	−1.96305
$259$	3.97992e68	0.661959
$260$	6.84909e68	1.02069
$261$	−1.70987e68	−0.228407
$262$	−2.03804e69	−2.44133
$263$	8.05983e68	0.866138	0.433069	−	0.901361i	$-0.357431\pi$
$263$	8.05983e68	0.866138	0.433069	+	0.901361i	$0.357431\pi$
$264$	1.98572e68	0.191516
$265$	1.39192e69	1.20533
$266$	2.85819e69	2.22313
$267$	−5.80919e67	−0.0406017
$268$	1.52297e69	0.956864
$269$	−2.33736e69	−1.32064	−0.660321	−	0.750983i	$-0.729580\pi$
$269$	−2.33736e69	−1.32064	−0.660321	+	0.750983i	$0.729580\pi$
$270$	−2.06896e69	−1.05168
$271$	−3.12621e69	−1.43019	−0.715094	−	0.699028i	$-0.753616\pi$
$271$	−3.12621e69	−1.43019	−0.715094	+	0.699028i	$0.753616\pi$
$272$	1.02752e69	0.423229
$273$	3.44208e69	1.27698
$274$	−5.80628e69	−1.94092
$275$	2.66187e69	0.802055
$276$	9.62103e68	0.261404
$277$	−1.22764e69	−0.300883	−0.150442	−	0.988619i	$-0.548070\pi$
$277$	−1.22764e69	−0.300883	−0.150442	+	0.988619i	$0.548070\pi$
$278$	6.76579e68	0.149638
$279$	2.00528e68	0.0400365
$280$	−9.99712e68	−0.180248
$281$	9.23459e69	1.50414	0.752068	−	0.659085i	$-0.229056\pi$
$281$	9.23459e69	1.50414	0.752068	+	0.659085i	$0.229056\pi$
$282$	−5.52508e69	−0.813278
$283$	−1.08004e70	−1.43723	−0.718616	−	0.695407i	$-0.755224\pi$
$283$	−1.08004e70	−1.43723	−0.718616	+	0.695407i	$0.755224\pi$
$284$	−8.97088e68	−0.107960
$285$	4.62596e69	0.503644
$286$	2.97238e70	2.92868
$287$	−1.55092e70	−1.38342
$288$	9.49612e69	0.767115
$289$	−1.03394e70	−0.756673
$290$	−6.47141e69	−0.429196
$291$	2.11201e70	1.26983
$292$	−1.01502e70	−0.553430
$293$	−2.83940e70	−1.40443	−0.702215	−	0.711965i	$-0.747805\pi$
$293$	−2.83940e70	−1.40443	−0.702215	+	0.711965i	$0.747805\pi$
$294$	−2.27020e70	−1.01898
$295$	4.59291e69	0.187137
$296$	2.31228e69	0.0855513
$297$	−4.75575e70	−1.59831
$298$	4.60279e70	1.40559
$299$	1.61278e70	0.447659
$300$	1.59920e70	0.403595
$301$	1.22325e71	2.80783
$302$	−3.08402e70	−0.644049
$303$	−1.11129e70	−0.211209
$304$	−5.31378e70	−0.919405
$305$	2.31832e70	0.365282
$306$	2.67903e70	0.384519
$307$	−1.10985e70	−0.145152	−0.0725758	−	0.997363i	$-0.523122\pi$
$307$	−1.10985e70	−0.145152	−0.0725758	+	0.997363i	$0.523122\pi$
$308$	−2.05198e71	−2.44612
$309$	8.58588e70	0.933185
$310$	7.58948e69	0.0752322
$311$	−6.69279e70	−0.605252	−0.302626	−	0.953109i	$-0.597863\pi$
$311$	−6.69279e70	−0.605252	−0.302626	+	0.953109i	$0.597863\pi$
$312$	1.99980e70	0.165037
$313$	−2.50208e70	−0.188489	−0.0942447	−	0.995549i	$-0.530044\pi$
$313$	−2.50208e70	−0.188489	−0.0942447	+	0.995549i	$0.530044\pi$
$314$	−2.38047e70	−0.163745
$315$	8.34086e70	0.524035
$316$	3.73658e70	0.214483
$317$	−5.25497e70	−0.275665	−0.137832	−	0.990456i	$-0.544014\pi$
$317$	−5.25497e70	−0.275665	−0.137832	+	0.990456i	$0.544014\pi$
$318$	3.62911e71	1.74031
$319$	−1.48753e71	−0.652274
$320$	2.12023e71	0.850372
$321$	−1.65337e71	−0.606703
$322$	−2.10208e71	−0.705924
$323$	−1.71946e71	−0.528592
$324$	−7.18489e70	−0.202249
$325$	2.68075e71	0.691162
$326$	5.35331e71	1.26450
$327$	−2.27096e71	−0.491585
$328$	−9.01064e70	−0.178793
$329$	6.39385e71	1.16327
$330$	−6.27031e71	−1.04626
$331$	−9.56169e71	−1.46365	−0.731824	−	0.681493i	$-0.761331\pi$
$331$	−9.56169e71	−1.46365	−0.731824	+	0.681493i	$0.761331\pi$
$332$	−3.16530e71	−0.444610
$333$	−1.92920e71	−0.248723
$334$	−3.97573e71	−0.470590
$335$	−5.38556e71	−0.585402
$336$	8.34081e71	0.832796
$337$	1.76322e72	1.61753	0.808767	−	0.588129i	$-0.200135\pi$
$337$	1.76322e72	1.61753	0.808767	+	0.588129i	$0.200135\pi$
$338$	1.26397e72	1.06564
$339$	4.16810e71	0.323033
$340$	5.37043e71	0.382701
$341$	1.74453e71	0.114335
$342$	−1.38546e72	−0.835312
$343$	6.25150e70	0.0346818
$344$	7.10692e71	0.362882
$345$	−3.40221e71	−0.159925
$346$	−3.73767e72	−1.61783
$347$	−6.61886e71	−0.263872	−0.131936	−	0.991258i	$-0.542119\pi$
$347$	−6.61886e71	−0.263872	−0.131936	+	0.991258i	$0.542119\pi$
$348$	−8.93676e71	−0.328225
$349$	9.07996e71	0.307298	0.153649	−	0.988126i	$-0.450898\pi$
$349$	9.07996e71	0.307298	0.153649	+	0.988126i	$0.450898\pi$
$350$	−3.49406e72	−1.08991
$351$	−4.78948e72	−1.37732
$352$	8.26129e72	2.19070
$353$	5.41374e72	1.32409	0.662047	−	0.749463i	$-0.269688\pi$
$353$	5.41374e72	1.32409	0.662047	+	0.749463i	$0.269688\pi$
$354$	1.19750e72	0.270197
$355$	3.17230e71	0.0660490
$356$	3.48769e71	0.0670213
$357$	2.69896e72	0.478799
$358$	−1.01502e73	−1.66268
$359$	2.45434e72	0.371316	0.185658	−	0.982614i	$-0.440558\pi$
$359$	2.45434e72	0.371316	0.185658	+	0.982614i	$0.440558\pi$
$360$	4.84593e71	0.0677260
$361$	1.14835e72	0.148292
$362$	1.62422e73	1.93843
$363$	−8.22927e72	−0.907867
$364$	−2.06654e73	−2.10792
$365$	3.58933e72	0.338584
$366$	6.04450e72	0.527411
$367$	2.34838e72	0.189577	0.0947884	−	0.995497i	$-0.469783\pi$
$367$	2.34838e72	0.189577	0.0947884	+	0.995497i	$0.469783\pi$
$368$	3.90807e72	0.291944
$369$	7.51781e72	0.519804
$370$	−7.30150e72	−0.467372
$371$	−4.19975e73	−2.48924
$372$	1.04808e72	0.0575333
$373$	1.74828e73	0.889017	0.444508	−	0.895775i	$-0.353378\pi$
$373$	1.74828e73	0.889017	0.444508	+	0.895775i	$0.353378\pi$
$374$	2.33067e73	1.09809
$375$	−1.64195e73	−0.716916
$376$	3.71474e72	0.150340
$377$	−1.49808e73	−0.562090
$378$	6.24256e73	2.17193
$379$	−3.75968e72	−0.121320	−0.0606601	−	0.998158i	$-0.519321\pi$
$379$	−3.75968e72	−0.121320	−0.0606601	+	0.998158i	$0.519321\pi$
$380$	−2.77731e73	−0.831364
$381$	8.54955e72	0.237455
$382$	4.16067e73	1.07240
$383$	−6.45017e71	−0.0154314	−0.00771571	−	0.999970i	$-0.502456\pi$
$383$	−6.45017e71	−0.0154314	−0.00771571	+	0.999970i	$0.502456\pi$
$384$	1.12061e73	0.248895
$385$	7.25625e73	1.49652
$386$	−1.25750e74	−2.40862
$387$	−5.92949e73	−1.05501
$388$	−1.26800e74	−2.09611
$389$	5.53257e73	0.849890	0.424945	−	0.905219i	$-0.360293\pi$
$389$	5.53257e73	0.849890	0.424945	+	0.905219i	$0.360293\pi$
$390$	−6.31479e73	−0.901607
$391$	1.26460e73	0.167847
$392$	1.52635e73	0.188365
$393$	9.95254e73	1.14221
$394$	9.41094e73	1.00459
$395$	−1.32134e73	−0.131219
$396$	9.94661e73	0.919099
$397$	1.86449e74	1.60336	0.801679	−	0.597755i	$-0.203940\pi$
$397$	1.86449e74	1.60336	0.801679	+	0.597755i	$0.203940\pi$
$398$	−6.41824e73	−0.513746
$399$	−1.39576e74	−1.04012
$400$	6.49596e73	0.450747
$401$	−1.73462e74	−1.12096	−0.560481	−	0.828167i	$-0.689384\pi$
$401$	−1.73462e74	−1.12096	−0.560481	+	0.828167i	$0.689384\pi$
$402$	−1.40416e74	−0.845230
$403$	1.75690e73	0.0985266
$404$	6.67189e73	0.348642
$405$	2.54074e73	0.123735
$406$	1.95258e74	0.886374
$407$	−1.67833e74	−0.710293
$408$	1.56806e73	0.0618797
$409$	−3.96597e74	−1.45960	−0.729801	−	0.683659i	$-0.760388\pi$
$409$	−3.96597e74	−1.45960	−0.729801	+	0.683659i	$0.760388\pi$
$410$	2.84529e74	0.976759
$411$	2.83543e74	0.908086
$412$	−5.15474e74	−1.54041
$413$	−1.38579e74	−0.386475
$414$	1.01895e74	0.265242
$415$	1.11932e74	0.272009
$416$	8.31989e74	1.88781
$417$	−3.30399e73	−0.0700102
$418$	−1.20530e75	−2.38545
$419$	−4.17745e73	−0.0772345	−0.0386172	−	0.999254i	$-0.512295\pi$
$419$	−4.17745e73	−0.0772345	−0.0386172	+	0.999254i	$0.512295\pi$
$420$	4.35941e74	0.753049
$421$	9.67632e74	1.56196	0.780981	−	0.624555i	$-0.214720\pi$
$421$	9.67632e74	1.56196	0.780981	+	0.624555i	$0.214720\pi$
$422$	5.88122e74	0.887284
$423$	−3.09930e74	−0.437083
$424$	−2.44000e74	−0.321709
$425$	2.10200e74	0.259148
$426$	8.27105e73	0.0953646
$427$	−6.99494e74	−0.754379
$428$	9.92640e74	1.00148
$429$	−1.45152e75	−1.37022
$430$	−2.24416e75	−1.98245
$431$	−1.16942e74	−0.0966873	−0.0483437	−	0.998831i	$-0.515394\pi$
$431$	−1.16942e74	−0.0966873	−0.0483437	+	0.998831i	$0.515394\pi$
$432$	−1.16058e75	−0.898232
$433$	2.10856e75	1.52785	0.763927	−	0.645303i	$-0.223269\pi$
$433$	2.10856e75	1.52785	0.763927	+	0.645303i	$0.223269\pi$
$434$	−2.28993e74	−0.155369
$435$	3.16024e74	0.200806
$436$	1.36343e75	0.811459
$437$	−6.53983e74	−0.364624
$438$	9.35835e74	0.488863
$439$	2.17642e75	1.06538	0.532688	−	0.846312i	$-0.321182\pi$
$439$	2.17642e75	1.06538	0.532688	+	0.846312i	$0.321182\pi$
$440$	4.21578e74	0.193409
$441$	−1.27347e75	−0.547633
$442$	2.34720e75	0.946270
$443$	1.83482e75	0.693565	0.346783	−	0.937946i	$-0.387274\pi$
$443$	1.83482e75	0.693565	0.346783	+	0.937946i	$0.387274\pi$
$444$	−1.00831e75	−0.357420
$445$	−1.23332e74	−0.0410031
$446$	−1.59416e75	−0.497150
$447$	−2.24772e75	−0.657623
$448$	−6.39725e75	−1.75618
$449$	−4.48278e75	−1.15485	−0.577427	−	0.816442i	$-0.695943\pi$
$449$	−4.48278e75	−1.15485	−0.577427	+	0.816442i	$0.695943\pi$
$450$	1.69368e75	0.409520
$451$	6.54023e75	1.48444
$452$	−2.50242e75	−0.533231
$453$	1.50604e75	0.301328
$454$	−1.78582e75	−0.335541
$455$	7.30773e75	1.28961
$456$	−8.10919e74	−0.134425
$457$	−3.95280e75	−0.615592	−0.307796	−	0.951452i	$-0.599591\pi$
$457$	−3.95280e75	−0.615592	−0.307796	+	0.951452i	$0.599591\pi$
$458$	9.33411e75	1.36586
$459$	−3.75547e75	−0.516420
$460$	2.04260e75	0.263988
$461$	−1.53587e76	−1.86586	−0.932931	−	0.360056i	$-0.882757\pi$
$461$	−1.53587e76	−1.86586	−0.932931	+	0.360056i	$0.882757\pi$
$462$	1.89190e76	2.16074
$463$	−9.97013e75	−1.07064	−0.535319	−	0.844650i	$-0.679809\pi$
$463$	−9.97013e75	−1.07064	−0.535319	+	0.844650i	$0.679809\pi$
$464$	−3.63012e75	−0.366572
$465$	−3.70623e74	−0.0351984
$466$	−3.94565e75	−0.352469
$467$	1.73821e76	1.46074	0.730369	−	0.683053i	$-0.239348\pi$
$467$	1.73821e76	1.46074	0.730369	+	0.683053i	$0.239348\pi$
$468$	1.00172e76	0.792024
$469$	1.62495e76	1.20897
$470$	−1.17301e76	−0.821318
$471$	1.16248e75	0.0766105
$472$	−8.05126e74	−0.0499478
$473$	−5.15845e76	−3.01284
$474$	−3.44509e75	−0.189460
$475$	−1.08704e76	−0.562962
$476$	−1.62039e76	−0.790353
$477$	2.03576e76	0.935302
$478$	1.11146e76	0.481057
$479$	4.23660e76	1.72765	0.863825	−	0.503792i	$-0.168062\pi$
$479$	4.23660e76	1.72765	0.863825	+	0.503792i	$0.168062\pi$
$480$	−1.75510e76	−0.674416
$481$	−1.69024e76	−0.612087
$482$	−3.71091e75	−0.126660
$483$	1.02653e76	0.330276
$484$	4.94064e76	1.49862
$485$	4.48392e76	1.28239
$486$	−4.99780e76	−1.34786
$487$	5.84344e76	1.48625	0.743127	−	0.669150i	$-0.233342\pi$
$487$	5.84344e76	1.48625	0.743127	+	0.669150i	$0.233342\pi$
$488$	−4.06396e75	−0.0974956
$489$	−2.61422e76	−0.591616
$490$	−4.81975e76	−1.02905
$491$	−6.78737e75	−0.136735	−0.0683674	−	0.997660i	$-0.521779\pi$
$491$	−6.78737e75	−0.136735	−0.0683674	+	0.997660i	$0.521779\pi$
$492$	3.92924e76	0.746970
$493$	−1.17466e76	−0.210753
$494$	−1.21385e77	−2.05564
$495$	−3.51734e76	−0.562298
$496$	4.25730e75	0.0642550
$497$	−9.57159e75	−0.136404
$498$	2.91837e76	0.392739
$499$	−5.64507e76	−0.717470	−0.358735	−	0.933440i	$-0.616792\pi$
$499$	−5.64507e76	−0.717470	−0.358735	+	0.933440i	$0.616792\pi$
$500$	9.85783e76	1.18341
$501$	1.94150e76	0.220172
$502$	1.85084e77	1.98296
$503$	−5.04907e76	−0.511121	−0.255560	−	0.966793i	$-0.582260\pi$
$503$	−5.04907e76	−0.511121	−0.255560	+	0.966793i	$0.582260\pi$
$504$	−1.46213e76	−0.139867
$505$	−2.35933e76	−0.213297
$506$	8.86449e76	0.757467
$507$	−6.17244e76	−0.498574
$508$	−5.13293e76	−0.391967
$509$	4.11773e75	0.0297304	0.0148652	−	0.999890i	$-0.495268\pi$
$509$	4.11773e75	0.0297304	0.0148652	+	0.999890i	$0.495268\pi$
$510$	−4.95148e76	−0.338053
$511$	−1.08299e77	−0.699242
$512$	2.27442e77	1.38892
$513$	1.94213e77	1.12185
$514$	−2.74265e77	−1.49872
$515$	1.82283e77	0.942410
$516$	−3.09909e77	−1.51607
$517$	−2.69629e77	−1.24820
$518$	2.20304e77	0.965215
$519$	1.82525e77	0.756924
$520$	4.24569e76	0.166668
$521$	1.02108e77	0.379476	0.189738	−	0.981835i	$-0.439236\pi$
$521$	1.02108e77	0.379476	0.189738	+	0.981835i	$0.439236\pi$
$522$	−9.46478e76	−0.333044
$523$	−2.23818e77	−0.745756	−0.372878	−	0.927880i	$-0.621629\pi$
$523$	−2.23818e77	−0.745756	−0.372878	+	0.927880i	$0.621629\pi$
$524$	−5.97525e77	−1.88545
$525$	1.70628e77	0.509930
$526$	4.46143e77	1.26293
$527$	1.37760e76	0.0369420
$528$	−3.51732e77	−0.893603
$529$	−3.67321e77	−0.884219
$530$	7.70480e77	1.75752
$531$	6.71737e76	0.145213
$532$	8.37980e77	1.71693
$533$	6.58662e77	1.27920
$534$	−3.21561e76	−0.0592021
$535$	−3.51019e77	−0.612700
$536$	9.44076e76	0.156247
$537$	4.95673e77	0.777907
$538$	−1.29382e78	−1.92565
$539$	−1.10787e78	−1.56391
$540$	−6.06590e77	−0.812219
$541$	1.21627e78	1.54493	0.772465	−	0.635058i	$-0.219024\pi$
$541$	1.21627e78	1.54493	0.772465	+	0.635058i	$0.219024\pi$
$542$	−1.73048e78	−2.08539
$543$	−7.93166e77	−0.906920
$544$	6.52370e77	0.707824
$545$	−4.82137e77	−0.496444
$546$	1.90532e78	1.86199
$547$	1.21557e78	1.12757	0.563784	−	0.825922i	$-0.309345\pi$
$547$	1.21557e78	1.12757	0.563784	+	0.825922i	$0.309345\pi$
$548$	−1.70232e78	−1.49898
$549$	3.39067e77	0.283448
$550$	1.47344e78	1.16949
$551$	6.07471e77	0.457830
$552$	5.96399e76	0.0426848
$553$	3.98679e77	0.270993
$554$	−6.79547e77	−0.438724
$555$	3.56560e77	0.218667
$556$	1.98363e77	0.115566
$557$	7.59355e77	0.420312	0.210156	−	0.977668i	$-0.432603\pi$
$557$	7.59355e77	0.420312	0.210156	+	0.977668i	$0.432603\pi$
$558$	1.11000e77	0.0583780
$559$	−5.19504e78	−2.59628
$560$	1.77080e78	0.841028
$561$	−1.13815e78	−0.513758
$562$	5.11170e78	2.19321
$563$	−1.41654e78	−0.577750	−0.288875	−	0.957367i	$-0.593281\pi$
$563$	−1.41654e78	−0.577750	−0.288875	+	0.957367i	$0.593281\pi$
$564$	−1.61987e78	−0.628097
$565$	8.84912e77	0.326226
$566$	−5.97845e78	−2.09566
$567$	−7.66601e77	−0.255536
$568$	−5.56096e76	−0.0176288
$569$	3.73439e78	1.12595	0.562976	−	0.826473i	$-0.309656\pi$
$569$	3.73439e78	1.12595	0.562976	+	0.826473i	$0.309656\pi$
$570$	2.56065e78	0.734372
$571$	−2.85981e78	−0.780205	−0.390103	−	0.920771i	$-0.627560\pi$
$571$	−2.85981e78	−0.780205	−0.390103	+	0.920771i	$0.627560\pi$
$572$	8.71458e78	2.26183
$573$	−2.03181e78	−0.501738
$574$	−8.58494e78	−2.01720
$575$	7.99477e77	0.178761
$576$	3.10095e78	0.659864
$577$	−6.21461e77	−0.125865	−0.0629323	−	0.998018i	$-0.520045\pi$
$577$	−6.21461e77	−0.125865	−0.0629323	+	0.998018i	$0.520045\pi$
$578$	−5.72328e78	−1.10332
$579$	6.14083e78	1.12691
$580$	−1.89732e78	−0.331470
$581$	−3.37726e78	−0.561752
$582$	1.16908e79	1.85157
$583$	1.77104e79	2.67100
$584$	−6.29201e77	−0.0903697
$585$	−3.54229e78	−0.484554
$586$	−1.57172e79	−2.04782
$587$	−8.78907e77	−0.109083	−0.0545415	−	0.998512i	$-0.517370\pi$
$587$	−8.78907e77	−0.109083	−0.0545415	+	0.998512i	$0.517370\pi$
$588$	−6.65589e78	−0.786960
$589$	−7.12424e77	−0.0802514
$590$	2.54235e78	0.272868
$591$	−4.59572e78	−0.470014
$592$	−4.09576e78	−0.399178
$593$	5.98581e77	0.0555986	0.0277993	−	0.999614i	$-0.491150\pi$
$593$	5.98581e77	0.0555986	0.0277993	+	0.999614i	$0.491150\pi$
$594$	−2.63249e79	−2.33052
$595$	5.73005e78	0.483532
$596$	1.34947e79	1.08554
$597$	3.13427e78	0.240363
$598$	8.92737e78	0.652739
$599$	−7.80722e78	−0.544292	−0.272146	−	0.962256i	$-0.587733\pi$
$599$	−7.80722e78	−0.544292	−0.272146	+	0.962256i	$0.587733\pi$
$600$	9.91327e77	0.0659032
$601$	2.32310e78	0.147280	0.0736402	−	0.997285i	$-0.476538\pi$
$601$	2.32310e78	0.147280	0.0736402	+	0.997285i	$0.476538\pi$
$602$	6.77116e79	4.09415
$603$	−7.87667e78	−0.454255
$604$	−9.04190e78	−0.497401
$605$	−1.74712e79	−0.916842
$606$	−6.15141e78	−0.307967
$607$	3.13355e79	1.49679	0.748393	−	0.663256i	$-0.230826\pi$
$607$	3.13355e79	1.49679	0.748393	+	0.663256i	$0.230826\pi$
$608$	−3.37372e79	−1.53765
$609$	−9.53519e78	−0.414703
$610$	1.28328e79	0.532625
$611$	−2.71541e79	−1.07563
$612$	7.85454e78	0.296965
$613$	−5.21011e79	−1.88028	−0.940141	−	0.340785i	$-0.889307\pi$
$613$	−5.21011e79	−1.88028	−0.940141	+	0.340785i	$0.889307\pi$
$614$	−6.14346e78	−0.211648
$615$	−1.38947e79	−0.456990
$616$	−1.27200e79	−0.399428
$617$	5.17934e79	1.55291	0.776457	−	0.630171i	$-0.217015\pi$
$617$	5.17934e79	1.55291	0.776457	+	0.630171i	$0.217015\pi$
$618$	4.75261e79	1.36069
$619$	3.30194e79	0.902787	0.451393	−	0.892325i	$-0.350927\pi$
$619$	3.30194e79	0.902787	0.451393	+	0.892325i	$0.350927\pi$
$620$	2.22513e78	0.0581020
$621$	−1.42836e79	−0.356228
$622$	−3.70472e79	−0.882529
$623$	3.72123e78	0.0846794
$624$	−3.54227e79	−0.770053
$625$	−9.56453e78	−0.198648
$626$	−1.38499e79	−0.274840
$627$	5.88593e79	1.11607
$628$	−6.97921e78	−0.126461
$629$	−1.32533e79	−0.229499
$630$	4.61699e79	0.764105
$631$	6.69899e79	1.05967	0.529837	−	0.848099i	$-0.322253\pi$
$631$	6.69899e79	1.05967	0.529837	+	0.848099i	$0.322253\pi$
$632$	2.31627e78	0.0350230
$633$	−2.87202e79	−0.415128
$634$	−2.90883e79	−0.401952
$635$	1.81512e79	0.239802
$636$	1.06400e80	1.34405
$637$	−1.11573e80	−1.34768
$638$	−8.23403e79	−0.951093
$639$	4.63966e78	0.0512521
$640$	2.37913e79	0.251355
$641$	−2.93073e78	−0.0296157	−0.0148079	−	0.999890i	$-0.504714\pi$
$641$	−2.93073e78	−0.0296157	−0.0148079	+	0.999890i	$0.504714\pi$
$642$	−9.15203e79	−0.884645
$643$	1.95210e79	0.180505	0.0902523	−	0.995919i	$-0.471233\pi$
$643$	1.95210e79	0.180505	0.0902523	+	0.995919i	$0.471233\pi$
$644$	−6.16301e79	−0.545187
$645$	1.09591e80	0.927517
$646$	−9.51789e79	−0.770750
$647$	−1.48582e80	−1.15132	−0.575659	−	0.817690i	$-0.695255\pi$
$647$	−1.48582e80	−1.15132	−0.575659	+	0.817690i	$0.695255\pi$
$648$	−4.45385e78	−0.0330254
$649$	5.84388e79	0.414694
$650$	1.48390e80	1.00780
$651$	1.11826e79	0.0726916
$652$	1.56951e80	0.976581
$653$	−2.18670e79	−0.130246	−0.0651230	−	0.997877i	$-0.520744\pi$
$653$	−2.18670e79	−0.130246	−0.0651230	+	0.997877i	$0.520744\pi$
$654$	−1.25706e80	−0.716789
$655$	2.11298e80	1.15350
$656$	1.59606e80	0.834239
$657$	5.24959e79	0.262731
$658$	3.53924e80	1.69618
$659$	−1.87847e80	−0.862123	−0.431061	−	0.902323i	$-0.641861\pi$
$659$	−1.87847e80	−0.862123	−0.431061	+	0.902323i	$0.641861\pi$
$660$	−1.83836e80	−0.808034
$661$	1.81530e80	0.764202	0.382101	−	0.924121i	$-0.375201\pi$
$661$	1.81530e80	0.764202	0.382101	+	0.924121i	$0.375201\pi$
$662$	−5.29276e80	−2.13417
$663$	−1.14623e80	−0.442726
$664$	−1.96214e79	−0.0726005
$665$	−2.96328e80	−1.05040
$666$	−1.06788e80	−0.362667
$667$	−4.46770e79	−0.145378
$668$	−1.16563e80	−0.363438
$669$	7.78487e79	0.232599
$670$	−2.98111e80	−0.853585
$671$	2.94976e80	0.809460
$672$	5.29557e80	1.39280
$673$	−2.98186e80	−0.751722	−0.375861	−	0.926676i	$-0.622653\pi$
$673$	−2.98186e80	−0.751722	−0.375861	+	0.926676i	$0.622653\pi$
$674$	9.76008e80	2.35856
$675$	−2.37421e80	−0.549998
$676$	3.70577e80	0.822997
$677$	1.20802e80	0.257215	0.128607	−	0.991696i	$-0.458949\pi$
$677$	1.20802e80	0.257215	0.128607	+	0.991696i	$0.458949\pi$
$678$	2.30721e80	0.471021
$679$	−1.35291e81	−2.64838
$680$	3.32908e79	0.0624914
$681$	8.72083e79	0.156988
$682$	9.65662e79	0.166713
$683$	5.48713e80	0.908563	0.454282	−	0.890858i	$-0.349896\pi$
$683$	5.48713e80	0.908563	0.454282	+	0.890858i	$0.349896\pi$
$684$	−4.06196e80	−0.645115
$685$	6.01977e80	0.917062
$686$	3.46045e79	0.0505702
$687$	−4.55820e80	−0.639038
$688$	−1.25886e81	−1.69319
$689$	1.78360e81	2.30170
$690$	−1.88325e80	−0.233190
$691$	−4.95044e80	−0.588192	−0.294096	−	0.955776i	$-0.595019\pi$
$691$	−4.95044e80	−0.588192	−0.294096	+	0.955776i	$0.595019\pi$
$692$	−1.09583e81	−1.24945
$693$	1.06127e81	1.16125
$694$	−3.66379e80	−0.384756
$695$	−7.01456e79	−0.0707023
$696$	−5.53982e79	−0.0535960
$697$	5.16463e80	0.479628
$698$	5.02610e80	0.448076
$699$	1.92681e80	0.164907
$700$	−1.02441e81	−0.841742
$701$	−2.36063e81	−1.86236	−0.931181	−	0.364557i	$-0.881220\pi$
$701$	−2.36063e81	−1.86236	−0.931181	+	0.364557i	$0.881220\pi$
$702$	−2.65116e81	−2.00830
$703$	6.85391e80	0.498554
$704$	2.69772e81	1.88441
$705$	5.72823e80	0.384265
$706$	2.99671e81	1.93068
$707$	7.11866e80	0.440499
$708$	3.51089e80	0.208674
$709$	8.01304e80	0.457488	0.228744	−	0.973487i	$-0.426538\pi$
$709$	8.01304e80	0.457488	0.228744	+	0.973487i	$0.426538\pi$
$710$	1.75599e80	0.0963072
$711$	−1.93253e80	−0.101822
$712$	2.16199e79	0.0109439
$713$	5.23959e79	0.0254827
$714$	1.49398e81	0.698145
$715$	−3.08167e81	−1.38377
$716$	−2.97589e81	−1.28409
$717$	−5.42766e80	−0.225069
$718$	1.35857e81	0.541423
$719$	−9.88052e80	−0.378448	−0.189224	−	0.981934i	$-0.560597\pi$
$719$	−9.88052e80	−0.378448	−0.189224	+	0.981934i	$0.560597\pi$
$720$	−8.58364e80	−0.316006
$721$	−5.49991e81	−1.94626
$722$	6.35653e80	0.216227
$723$	1.81218e80	0.0592598
$724$	4.76197e81	1.49705
$725$	−7.42616e80	−0.224456
$726$	−4.55521e81	−1.32378
$727$	5.64962e81	1.57866	0.789330	−	0.613969i	$-0.210428\pi$
$727$	5.64962e81	1.57866	0.789330	+	0.613969i	$0.210428\pi$
$728$	−1.28103e81	−0.344202
$729$	3.13571e81	0.810216
$730$	1.98683e81	0.493696
$731$	−4.07347e81	−0.973464
$732$	1.77216e81	0.407321
$733$	5.01219e81	1.10806	0.554031	−	0.832496i	$-0.313089\pi$
$733$	5.01219e81	1.10806	0.554031	+	0.832496i	$0.313089\pi$
$734$	1.29992e81	0.276425
$735$	2.35367e81	0.481456
$736$	2.48123e81	0.488259
$737$	−6.85243e81	−1.29724
$738$	4.16140e81	0.757936
$739$	3.26269e81	0.571754	0.285877	−	0.958266i	$-0.407715\pi$
$739$	3.26269e81	0.571754	0.285877	+	0.958266i	$0.407715\pi$
$740$	−2.14070e81	−0.360953
$741$	5.92768e81	0.961759
$742$	−2.32472e82	−3.62961
$743$	−7.07350e81	−1.06280	−0.531402	−	0.847120i	$-0.678335\pi$
$743$	−7.07350e81	−1.06280	−0.531402	+	0.847120i	$0.678335\pi$
$744$	6.49693e79	0.00939463
$745$	−4.77203e81	−0.664124
$746$	9.67742e81	1.29629
$747$	1.63707e81	0.211071
$748$	6.83318e81	0.848061
$749$	1.05911e82	1.26535
$750$	−9.08881e81	−1.04535
$751$	1.07046e82	1.18531	0.592655	−	0.805456i	$-0.298080\pi$
$751$	1.07046e82	1.18531	0.592655	+	0.805456i	$0.298080\pi$
$752$	−6.57995e81	−0.701478
$753$	−9.03838e81	−0.927756
$754$	−8.29244e81	−0.819594
$755$	3.19742e81	0.304306
$756$	1.83023e82	1.67739
$757$	−1.14314e82	−1.00894	−0.504470	−	0.863429i	$-0.668312\pi$
$757$	−1.14314e82	−1.00894	−0.504470	+	0.863429i	$0.668312\pi$
$758$	−2.08113e81	−0.176899
$759$	−4.32887e81	−0.354392
$760$	−1.72163e81	−0.135754
$761$	−4.87710e81	−0.370424	−0.185212	−	0.982699i	$-0.559297\pi$
$761$	−4.87710e81	−0.370424	−0.185212	+	0.982699i	$0.559297\pi$
$762$	4.73251e81	0.346238
$763$	1.45472e82	1.02525
$764$	1.21985e82	0.828219
$765$	−2.77754e81	−0.181681
$766$	−3.57042e80	−0.0225009
$767$	5.88533e81	0.357358
$768$	−8.18932e81	−0.479129
$769$	1.13000e82	0.637059	0.318529	−	0.947913i	$-0.396811\pi$
$769$	1.13000e82	0.637059	0.318529	+	0.947913i	$0.396811\pi$
$770$	4.01662e82	2.18210
$771$	1.33934e82	0.701198
$772$	−3.68680e82	−1.86018
$773$	−3.32515e82	−1.61695	−0.808474	−	0.588532i	$-0.799706\pi$
$773$	−3.32515e82	−1.61695	−0.808474	+	0.588532i	$0.799706\pi$
$774$	−3.28220e82	−1.53832
$775$	8.70918e80	0.0393440
$776$	−7.86021e81	−0.342275
$777$	−1.07583e82	−0.451590
$778$	3.06249e82	1.23924
$779$	−2.67088e82	−1.04192
$780$	−1.85140e82	−0.696314
$781$	4.03634e81	0.146364
$782$	7.00002e81	0.244741
$783$	1.32677e82	0.447287
$784$	−2.70363e82	−0.878901
$785$	2.46800e81	0.0773678
$786$	5.50911e82	1.66548
$787$	5.65315e82	1.64820	0.824101	−	0.566443i	$-0.191681\pi$
$787$	5.65315e82	1.64820	0.824101	+	0.566443i	$0.191681\pi$
$788$	2.75915e82	0.775851
$789$	−2.17868e82	−0.590881
$790$	−7.31411e81	−0.191333
$791$	−2.66999e82	−0.673721
$792$	6.16581e81	0.150080
$793$	2.97069e82	0.697543
$794$	1.03207e83	2.33789
$795$	−3.76255e82	−0.822279
$796$	−1.88174e82	−0.396768
$797$	−7.23586e82	−1.47207	−0.736034	−	0.676944i	$-0.763304\pi$
$797$	−7.23586e82	−1.47207	−0.736034	+	0.676944i	$0.763304\pi$
$798$	−7.72609e82	−1.51662
$799$	−2.12918e82	−0.403300
$800$	4.12428e82	0.753847
$801$	−1.80380e81	−0.0318172
$802$	−9.60181e82	−1.63450
$803$	4.56695e82	0.750298
$804$	−4.11680e82	−0.652774
$805$	2.17938e82	0.333541
$806$	9.72512e81	0.143664
$807$	6.31820e82	0.900944
$808$	4.13584e81	0.0569299
$809$	5.48112e82	0.728344	0.364172	−	0.931332i	$-0.381352\pi$
$809$	5.48112e82	0.728344	0.364172	+	0.931332i	$0.381352\pi$
$810$	1.40639e82	0.180420
$811$	−1.19710e83	−1.48264	−0.741321	−	0.671151i	$-0.765800\pi$
$811$	−1.19710e83	−1.48264	−0.741321	+	0.671151i	$0.765800\pi$
$812$	5.72468e82	0.684549
$813$	8.45058e82	0.975677
$814$	−9.29021e82	−1.03569
$815$	−5.55014e82	−0.597465
$816$	−2.77752e82	−0.288727
$817$	2.10659e83	2.11471
$818$	−2.19531e83	−2.12827
$819$	1.06879e83	1.00070
$820$	8.34199e82	0.754354
$821$	6.61357e82	0.577638	0.288819	−	0.957384i	$-0.406737\pi$
$821$	6.61357e82	0.577638	0.288819	+	0.957384i	$0.406737\pi$
$822$	1.56952e83	1.32410
$823$	−1.16708e83	−0.951058	−0.475529	−	0.879700i	$-0.657743\pi$
$823$	−1.16708e83	−0.951058	−0.475529	+	0.879700i	$0.657743\pi$
$824$	−3.19538e82	−0.251534
$825$	−7.19539e82	−0.547163
$826$	−7.67088e82	−0.563526
$827$	−1.27355e83	−0.903874	−0.451937	−	0.892050i	$-0.649267\pi$
$827$	−1.27355e83	−0.903874	−0.451937	+	0.892050i	$0.649267\pi$
$828$	2.98741e82	0.204847
$829$	3.64013e81	0.0241164	0.0120582	−	0.999927i	$-0.496162\pi$
$829$	3.64013e81	0.0241164	0.0120582	+	0.999927i	$0.496162\pi$
$830$	6.19586e82	0.396622
$831$	3.31849e82	0.205263
$832$	2.71685e83	1.62387
$833$	−8.74856e82	−0.505306
$834$	−1.82889e82	−0.102083
$835$	4.12191e82	0.222349
$836$	−3.53376e83	−1.84229
$837$	−1.55600e82	−0.0784033
$838$	−2.31238e82	−0.112617
$839$	−3.53602e83	−1.66456	−0.832278	−	0.554358i	$-0.812964\pi$
$839$	−3.53602e83	−1.66456	−0.832278	+	0.554358i	$0.812964\pi$
$840$	2.70236e82	0.122966
$841$	−1.85846e83	−0.817460
$842$	5.35621e83	2.27753
$843$	−2.49624e83	−1.02612
$844$	1.72429e83	0.685252
$845$	−1.31044e83	−0.503503
$846$	−1.71558e83	−0.637319
$847$	5.27148e83	1.89346
$848$	4.32199e83	1.50108
$849$	2.91950e83	0.980482
$850$	1.16354e83	0.377868
$851$	−5.04078e82	−0.158309
$852$	2.42495e82	0.0736503
$853$	1.91943e83	0.563799	0.281900	−	0.959444i	$-0.409035\pi$
$853$	1.91943e83	0.563799	0.281900	+	0.959444i	$0.409035\pi$
$854$	−3.87197e83	−1.09997
$855$	1.43640e83	0.394676
$856$	6.15328e82	0.163533
$857$	5.27324e82	0.135558	0.0677788	−	0.997700i	$-0.478409\pi$
$857$	5.27324e82	0.135558	0.0677788	+	0.997700i	$0.478409\pi$
$858$	−8.03475e83	−1.99795
$859$	−6.67517e83	−1.60567	−0.802836	−	0.596199i	$-0.796677\pi$
$859$	−6.67517e83	−1.60567	−0.802836	+	0.596199i	$0.796677\pi$
$860$	−6.57955e83	−1.53105
$861$	4.19235e83	0.943774
$862$	−6.47321e82	−0.140982
$863$	−3.49069e82	−0.0735536	−0.0367768	−	0.999324i	$-0.511709\pi$
$863$	−3.49069e82	−0.0735536	−0.0367768	+	0.999324i	$0.511709\pi$
$864$	−7.36852e83	−1.50224
$865$	3.87511e83	0.764407
$866$	1.16717e84	2.22779
$867$	2.79489e83	0.516204
$868$	−6.71374e82	−0.119992
$869$	−1.68123e83	−0.290779
$870$	1.74931e83	0.292798
$871$	−6.90104e83	−1.11788
$872$	8.45175e82	0.132503
$873$	6.55798e83	0.995094
$874$	−3.62005e83	−0.531665
$875$	1.05179e84	1.49521
$876$	2.74374e83	0.377551
$877$	−9.49890e83	−1.26527	−0.632637	−	0.774448i	$-0.718028\pi$
$877$	−9.49890e83	−1.26527	−0.632637	+	0.774448i	$0.718028\pi$
$878$	1.20473e84	1.55344
$879$	7.67530e83	0.958104
$880$	−7.46746e83	−0.902437
$881$	−1.31438e84	−1.53783	−0.768914	−	0.639352i	$-0.779203\pi$
$881$	−1.31438e84	−1.53783	−0.768914	+	0.639352i	$0.779203\pi$
$882$	−7.04915e83	−0.798513
$883$	−1.00483e83	−0.110208	−0.0551039	−	0.998481i	$-0.517549\pi$
$883$	−1.00483e83	−0.110208	−0.0551039	+	0.998481i	$0.517549\pi$
$884$	6.88165e83	0.730807
$885$	−1.24153e83	−0.127665
$886$	1.01564e84	1.01130
$887$	−3.70423e83	−0.357170	−0.178585	−	0.983924i	$-0.557152\pi$
$887$	−3.70423e83	−0.357170	−0.178585	+	0.983924i	$0.557152\pi$
$888$	−6.25041e82	−0.0583632
$889$	−5.47665e83	−0.495239
$890$	−6.82692e82	−0.0597874
$891$	3.23276e83	0.274194
$892$	−4.67384e83	−0.383951
$893$	1.10110e84	0.876112
$894$	−1.24420e84	−0.958893
$895$	1.05234e84	0.785597
$896$	−7.17840e83	−0.519098
$897$	−4.35957e83	−0.305393
$898$	−2.48139e84	−1.68391
$899$	−4.86694e82	−0.0319967
$900$	4.96564e83	0.316274
$901$	1.39853e84	0.863012
$902$	3.62027e84	2.16448
$903$	−3.30662e84	−1.91550
$904$	−1.55123e83	−0.0870714
$905$	−1.68394e84	−0.915885
$906$	8.33653e83	0.439371
$907$	8.11922e83	0.414674	0.207337	−	0.978270i	$-0.433520\pi$
$907$	8.11922e83	0.414674	0.207337	+	0.978270i	$0.433520\pi$
$908$	−5.23576e83	−0.259139
$909$	−3.45064e83	−0.165512
$910$	4.04511e84	1.88040
$911$	2.56011e84	1.15341	0.576706	−	0.816952i	$-0.304338\pi$
$911$	2.56011e84	1.15341	0.576706	+	0.816952i	$0.304338\pi$
$912$	1.43639e84	0.627219
$913$	1.42419e84	0.602768
$914$	−2.18803e84	−0.897607
$915$	−6.26675e83	−0.249196
$916$	2.73663e84	1.05486
$917$	−6.37537e84	−2.38221
$918$	−2.07880e84	−0.753001
$919$	2.52653e84	0.887224	0.443612	−	0.896219i	$-0.353697\pi$
$919$	2.52653e84	0.887224	0.443612	+	0.896219i	$0.353697\pi$
$920$	1.26619e83	0.0431067
$921$	3.00009e83	0.0990226
$922$	−8.50165e84	−2.72065
$923$	4.06497e83	0.126127
$924$	5.54679e84	1.66875
$925$	−8.37872e83	−0.244421
$926$	−5.51885e84	−1.56112
$927$	2.66599e84	0.731283
$928$	−2.30476e84	−0.613068
$929$	−4.04290e84	−1.04291	−0.521453	−	0.853280i	$-0.674610\pi$
$929$	−4.04290e84	−1.04291	−0.521453	+	0.853280i	$0.674610\pi$
$930$	−2.05154e83	−0.0513235
$931$	4.52430e84	1.09770
$932$	−1.15681e84	−0.272213
$933$	1.80915e84	0.412904
$934$	9.62168e84	2.12993
$935$	−2.41636e84	−0.518837
$936$	6.20955e83	0.129330
$937$	1.04242e84	0.210603	0.105301	−	0.994440i	$-0.466419\pi$
$937$	1.04242e84	0.210603	0.105301	+	0.994440i	$0.466419\pi$
$938$	8.99474e84	1.76282
$939$	6.76346e83	0.128588
$940$	−3.43908e84	−0.634306
$941$	5.24956e84	0.939332	0.469666	−	0.882844i	$-0.344374\pi$
$941$	5.24956e84	0.939332	0.469666	+	0.882844i	$0.344374\pi$
$942$	6.43475e83	0.111707
$943$	1.96432e84	0.330849
$944$	1.42613e84	0.233054
$945$	−6.47209e84	−1.02621
$946$	−2.85540e85	−4.39308
$947$	5.56663e84	0.831033	0.415516	−	0.909586i	$-0.363601\pi$
$947$	5.56663e84	0.831033	0.415516	+	0.909586i	$0.363601\pi$
$948$	−1.01005e84	−0.146320
$949$	4.59935e84	0.646561
$950$	−6.01720e84	−0.820865
$951$	1.42049e84	0.188059
$952$	−1.00446e84	−0.129057
$953$	2.49500e84	0.311116	0.155558	−	0.987827i	$-0.450282\pi$
$953$	2.49500e84	0.311116	0.155558	+	0.987827i	$0.450282\pi$
$954$	1.12687e85	1.36378
$955$	−4.31365e84	−0.506698
$956$	3.25863e84	0.371522
$957$	4.02099e84	0.444982
$958$	2.34512e85	2.51912
$959$	−1.81631e85	−1.89391
$960$	−5.73128e84	−0.580125
$961$	−1.01198e85	−0.994391
$962$	−9.35611e84	−0.892495
$963$	−5.13384e84	−0.475438
$964$	−1.08799e84	−0.0978201
$965$	1.30373e85	1.13805
$966$	5.68223e84	0.481582
$967$	−5.75337e84	−0.473443	−0.236722	−	0.971578i	$-0.576073\pi$
$967$	−5.75337e84	−0.473443	−0.236722	+	0.971578i	$0.576073\pi$
$968$	3.06266e84	0.244709
$969$	4.64795e84	0.360606
$970$	2.48202e85	1.86987
$971$	−1.76323e85	−1.28991	−0.644956	−	0.764220i	$-0.723124\pi$
$971$	−1.76323e85	−1.28991	−0.644956	+	0.764220i	$0.723124\pi$
$972$	−1.46528e85	−1.04096
$973$	2.11646e84	0.146014
$974$	3.23457e85	2.16713
$975$	−7.24643e84	−0.471512
$976$	7.19854e84	0.454909
$977$	1.50599e85	0.924333	0.462166	−	0.886793i	$-0.347072\pi$
$977$	1.50599e85	0.924333	0.462166	+	0.886793i	$0.347072\pi$
$978$	−1.44707e85	−0.862647
$979$	−1.56924e84	−0.0908623
$980$	−1.41308e85	−0.794739
$981$	−7.05151e84	−0.385226
$982$	−3.75707e84	−0.199375
$983$	1.88227e85	0.970301	0.485150	−	0.874431i	$-0.338765\pi$
$983$	1.88227e85	0.970301	0.485150	+	0.874431i	$0.338765\pi$
$984$	2.43570e84	0.121973
$985$	−9.75697e84	−0.474660
$986$	−6.50217e84	−0.307303
$987$	−1.72835e85	−0.793582
$988$	−3.55883e85	−1.58757
$989$	−1.54931e85	−0.671497
$990$	−1.94698e85	−0.819896
$991$	3.71364e85	1.51950	0.759750	−	0.650215i	$-0.225321\pi$
$991$	3.71364e85	1.51950	0.759750	+	0.650215i	$0.225321\pi$
$992$	2.70296e84	0.107462
$993$	2.58466e85	0.998503
$994$	−5.29824e84	−0.198893
$995$	6.65423e84	0.242739
$996$	8.55625e84	0.303314
$997$	−1.73809e85	−0.598772	−0.299386	−	0.954132i	$-0.596782\pi$
$997$	−1.73809e85	−0.598772	−0.299386	+	0.954132i	$0.596782\pi$
$998$	−3.12476e85	−1.04616
$999$	1.49696e85	0.487073

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.58.a.a.1.4	✓	4
3.2	odd	2		9.58.a.b.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.58.a.a.1.4	✓	4	1.1	even	1	trivial
9.58.a.b.1.1		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 58 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+5.53538e8 q^{2} -2.70314e13 q^{3} +1.62289e17 q^{4} -5.73891e19 q^{5} -1.49629e22 q^{6} +1.73157e24 q^{7} +1.00602e25 q^{8} -8.39347e26 q^{9} +O(q^{10})\)	\(q+5.53538e8 q^{2} -2.70314e13 q^{3} +1.62289e17 q^{4} -5.73891e19 q^{5} -1.49629e22 q^{6} +1.73157e24 q^{7} +1.00602e25 q^{8} -8.39347e26 q^{9} -3.17671e28 q^{10} -7.30202e29 q^{11} -4.38691e30 q^{12} -7.35382e31 q^{13} +9.58490e32 q^{14} +1.55131e33 q^{15} -1.78197e34 q^{16} -5.76619e34 q^{17} -4.64611e35 q^{18} +2.98197e36 q^{19} -9.31365e36 q^{20} -4.68067e37 q^{21} -4.04195e38 q^{22} -2.19312e38 q^{23} -2.71941e38 q^{24} -3.64538e39 q^{25} -4.07062e40 q^{26} +6.51292e40 q^{27} +2.81015e41 q^{28} +2.03714e41 q^{29} +8.58708e41 q^{30} -2.38910e41 q^{31} -1.13137e43 q^{32} +1.97384e43 q^{33} -3.19181e43 q^{34} -9.93732e43 q^{35} -1.36217e44 q^{36} +2.29845e44 q^{37} +1.65064e45 q^{38} +1.98784e45 q^{39} -5.77345e44 q^{40} -8.95674e45 q^{41} -2.59093e46 q^{42} +7.06441e46 q^{43} -1.18504e47 q^{44} +4.81694e46 q^{45} -1.21398e47 q^{46} +3.69252e47 q^{47} +4.81691e47 q^{48} +1.51722e48 q^{49} -2.01786e48 q^{50} +1.55868e48 q^{51} -1.19345e49 q^{52} -2.42540e49 q^{53} +3.60515e49 q^{54} +4.19057e49 q^{55} +1.74199e49 q^{56} -8.06069e49 q^{57} +1.12764e50 q^{58} -8.00310e49 q^{59} +2.51761e50 q^{60} -4.03965e50 q^{61} -1.32246e50 q^{62} -1.45339e51 q^{63} -3.69448e51 q^{64} +4.22029e51 q^{65} +1.09259e52 q^{66} +9.38429e51 q^{67} -9.35792e51 q^{68} +5.92831e51 q^{69} -5.50069e52 q^{70} -5.52770e51 q^{71} -8.44398e51 q^{72} -6.25437e52 q^{73} +1.27228e53 q^{74} +9.85397e52 q^{75} +4.83943e53 q^{76} -1.26440e54 q^{77} +1.10035e54 q^{78} +2.30242e53 q^{79} +1.02266e54 q^{80} -4.42721e53 q^{81} -4.95790e54 q^{82} -1.95040e54 q^{83} -7.59624e54 q^{84} +3.30917e54 q^{85} +3.91042e55 q^{86} -5.50668e54 q^{87} -7.34596e54 q^{88} +2.14905e54 q^{89} +2.66636e55 q^{90} -1.27336e56 q^{91} -3.55921e55 q^{92} +6.45807e54 q^{93} +2.04395e56 q^{94} -1.71133e56 q^{95} +3.05825e56 q^{96} -7.81319e56 q^{97} +8.39837e56 q^{98} +6.12893e56 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 217744560 q^{2} + 37475862172560 q^{3} + 29\!\cdots\!28 q^{4}+ \cdots + 80\!\cdots\!32 q^{9}+O(q^{10}) \) 4 * q - 217744560 * q^2 + 37475862172560 * q^3 + 293124896311376128 * q^4 - 106961276207842698600 * q^5 - 33990084162012424888512 * q^6 + 952854504056592488640800 * q^7 - 88551069216810449485639680 * q^8 + 807299095982681497210590132 * q^9	\( 4 q - 217744560 q^{2} + 37475862172560 q^{3} + 29\!\cdots\!28 q^{4}+ \cdots + 12\!\cdots\!04 q^{99}+O(q^{100}) \) 4 * q - 217744560 * q^2 + 37475862172560 * q^3 + 293124896311376128 * q^4 - 106961276207842698600 * q^5 - 33990084162012424888512 * q^6 + 952854504056592488640800 * q^7 - 88551069216810449485639680 * q^8 + 807299095982681497210590132 * q^9 + 44476431289760320477662520800 * q^10 - 462030036788542994175991820112 * q^11 + 10003750272364901761239114286080 * q^12 - 35670303061909387812013418679880 * q^13 + 70403094050531232484583448299136 * q^14 - 3873003953749638547444662603837600 * q^15 + 13566910890781728442321186411577344 * q^16 + 13820011728830480443629140931368520 * q^17 - 1287737321088043352155941276317529840 * q^18 + 336853252899071533902360882896311760 * q^19 - 50382729988973225454329459567578483200 * q^20 - 114908173756075652427942608537020743552 * q^21 - 661915503282569637498974918979285510720 * q^22 - 2975542065258688382050024994957196661920 * q^23 - 10578976944220511671340845604322576875520 * q^24 - 9469406228848045007865812554313674602500 * q^25 - 17469964426099436483582477475571041235872 * q^26 + 76349739563972016366032809192591896661920 * q^27 + 649254606795882967703588744692964385720320 * q^28 + 692903173502123074211699189163367889819640 * q^29 + 5634330080537746852583656641742556105212800 * q^30 - 899836592298317074905406089703577976621952 * q^31 - 14233950964359390830124363997913062975733760 * q^32 - 29363967329346027307019371741967172628226880 * q^33 - 169043128317257524614754408952689830505725024 * q^34 - 229326244292419606493088342114240299318011200 * q^35 + 284785472553153735165042638775100342213281024 * q^36 + 1088031360501840746049603861287321623324833560 * q^37 + 1556247388283245464794907962939214603341474880 * q^38 + 4179255936739867118004084422081931511953729504 * q^39 + 11751904708902009656918381872378671214758912000 * q^40 - 11103291557355181141038304173539140276092022872 * q^41 - 59279988331696939901744072326763120527717946880 * q^42 - 61754953860901881142563948460092952248410491600 * q^43 - 133524603192894473629581294520903680469781443584 * q^44 - 107702873160032711230811245899648546573795049800 * q^45 + 784819010796366200631618785819800311186796983168 * q^46 + 363083109323271524824455302894174707948361522880 * q^47 + 2742506186706372359330741580910160874632313569280 * q^48 + 1216129915477179767594559246649850886387208070628 * q^49 - 5243147625423300757899019878966089303259662130000 * q^50 - 764600229637750496670397948984385624631693707232 * q^51 - 22843788670121162835092909423272591563858567692800 * q^52 - 35290483593822076697173728695179253314838955459240 * q^53 + 12366575839681539833915263850508773584456529324160 * q^54 + 49196225093152182399971681538771907122934246240800 * q^55 + 63731767886683182211705479053660664279663635496960 * q^56 + 207676196582248616809244588606912583584671767915840 * q^57 + 617562539749243989517600779192095966343296224852320 * q^58 + 67768373912933539906296460571320281490527711258480 * q^59 - 1815042162748644358648991332911151647292658713651200 * q^60 - 1547288835446782082478245361946256543823484047403912 * q^61 - 749692944011811307313821057793297922348443552785920 * q^62 - 1569461042763431092010126958426126899190556123563360 * q^63 - 1990114977445631941316528741938069721703684937613312 * q^64 + 8063572248542729948506878297975365372089154570456400 * q^65 + 16489629555376763758820085001622755676656730822766336 * q^66 + 15272577061969964687199674310464241542844062558207120 * q^67 + 41305128999321265264790818598430329317542515380584960 * q^68 - 65786095162933072363901793014646952768970242331074176 * q^69 - 24325103535157938973881571830399397699429009026566400 * q^70 - 73888360588713834794031605853188887812717485611902432 * q^71 - 210328265328797773276338939967226276847978373484605440 * q^72 - 130297268842197178419561798573986372195905283718671320 * q^73 + 7685145516671187561069432006215096921673721366642656 * q^74 + 403928833669880609006163131916358629442839611491110000 * q^75 + 1456086045339107958455546112995861351598648681192657920 * q^76 - 106427745818663343042165176190596036157925407112924800 * q^77 + 2074950811168633790188899303505400649698048509219286400 * q^78 - 828943058463042070981602117491995742498435075805703360 * q^79 - 2284181918093911007938097065798931209886961598847385600 * q^80 - 7963307412965608591332950484302680892196600516966334236 * q^81 - 1883428276461442027198836795157559789817480540746193120 * q^82 - 9840480688986571601216593400698100805429733592804704560 * q^83 + 13541340719968270381664710206581288963145836751957467136 * q^84 - 14840134943015755845177119052592106190913842871494565200 * q^85 + 67988974963281087138264344329950027971018743502811738048 * q^86 - 27365055454269193487844075068414523895320708309490878240 * q^87 + 61847074514255305493001192533786291945351930637515735040 * q^88 - 10663966381455218428814337779016832517355842990125366680 * q^89 + 144098850070698626396745850922715348604587043628376674400 * q^90 - 254422712153651549623482540524255137118230327668042523712 * q^91 - 274534438781355859366149237613545893970204939554260346880 * q^92 - 414128946656565192633171191785208529876343680904079162880 * q^93 + 632898423704876935427548603685166753697821378730383050496 * q^94 - 532156934024946939894578863048125180396162968766201396000 * q^95 + 663745987198780197281626102963422448954448917470231134208 * q^96 - 152729877520747450623636953478949994021736793474425664120 * q^97 + 2296925218269808931776551039888426925574868525366690486480 * q^98 + 123613071571796047703935039848745969833181068960384152304 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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