LMFDB - Embedded newform 1.42.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,42,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, 42, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 42);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 42 $
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:	$10.6471670456$
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} - 2784108376x + 1945534874860 $ x^3 - x^2 - 2784108376*x + 1945534874860
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{11}\cdot 3^{3}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$52412.2$ 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)

$f(q)$	$=$	$q+2.40087e6 q^{2} -6.65953e9 q^{3} +3.56518e12 q^{4} -3.38080e14 q^{5} -1.59887e16 q^{6} -9.19453e16 q^{7} +3.27996e18 q^{8} +7.87633e18 q^{9} +O(q^{10})$	\(q+2.40087e6 q^{2} -6.65953e9 q^{3} +3.56518e12 q^{4} -3.38080e14 q^{5} -1.59887e16 q^{6} -9.19453e16 q^{7} +3.27996e18 q^{8} +7.87633e18 q^{9} -8.11687e20 q^{10} +2.15850e21 q^{11} -2.37424e22 q^{12} -8.71848e22 q^{13} -2.20749e23 q^{14} +2.25145e24 q^{15} +3.48699e22 q^{16} +5.13467e24 q^{17} +1.89101e25 q^{18} +4.11372e25 q^{19} -1.20531e27 q^{20} +6.12312e26 q^{21} +5.18229e27 q^{22} +2.60656e27 q^{23} -2.18430e28 q^{24} +6.88231e28 q^{25} -2.09320e29 q^{26} +1.90440e29 q^{27} -3.27801e29 q^{28} -4.19842e29 q^{29} +5.40545e30 q^{30} -2.68405e30 q^{31} -7.12899e30 q^{32} -1.43746e31 q^{33} +1.23277e31 q^{34} +3.10848e31 q^{35} +2.80805e31 q^{36} -1.06323e32 q^{37} +9.87652e31 q^{38} +5.80610e32 q^{39} -1.10889e33 q^{40} -1.44220e33 q^{41} +1.47009e33 q^{42} -7.60160e31 q^{43} +7.69544e33 q^{44} -2.66283e33 q^{45} +6.25802e33 q^{46} -3.36927e34 q^{47} -2.32217e32 q^{48} -3.61137e34 q^{49} +1.65236e35 q^{50} -3.41945e34 q^{51} -3.10829e35 q^{52} +3.75996e35 q^{53} +4.57223e35 q^{54} -7.29746e35 q^{55} -3.01577e35 q^{56} -2.73954e35 q^{57} -1.00799e36 q^{58} -6.72854e34 q^{59} +8.02682e36 q^{60} -2.74886e35 q^{61} -6.44406e36 q^{62} -7.24191e35 q^{63} -1.71925e37 q^{64} +2.94754e37 q^{65} -3.45116e37 q^{66} +2.47724e37 q^{67} +1.83060e37 q^{68} -1.73585e37 q^{69} +7.46308e37 q^{70} -1.25628e38 q^{71} +2.58340e37 q^{72} +2.44972e38 q^{73} -2.55268e38 q^{74} -4.58329e38 q^{75} +1.46661e38 q^{76} -1.98464e38 q^{77} +1.39397e39 q^{78} +6.92089e38 q^{79} -1.17888e37 q^{80} -1.55552e39 q^{81} -3.46253e39 q^{82} +1.80861e39 q^{83} +2.18300e39 q^{84} -1.73593e39 q^{85} -1.82505e38 q^{86} +2.79595e39 q^{87} +7.07980e39 q^{88} -7.15901e39 q^{89} -6.39311e39 q^{90} +8.01623e39 q^{91} +9.29284e39 q^{92} +1.78745e40 q^{93} -8.08920e40 q^{94} -1.39076e40 q^{95} +4.74757e40 q^{96} +7.50364e40 q^{97} -8.67045e40 q^{98} +1.70011e40 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 344688 q^{2} - 10820953044 q^{3} + 6271704903936 q^{4} - 212302350281550 q^{5} + 49\!\cdots\!76 q^{6}+ \cdots + 13\!\cdots\!19 q^{9}+O(q^{10}) $ 3 * q - 344688 * q^2 - 10820953044 * q^3 + 6271704903936 * q^4 - 212302350281550 * q^5 + 4970194114982976 * q^6 + 57878416258239192 * q^7 - 3555831711183237120 * q^8 + 13277004110931878919 * q^9	$ 3 q - 344688 q^{2} - 10820953044 q^{3} + 6271704903936 q^{4} - 212302350281550 q^{5} + 49\!\cdots\!76 q^{6}+ \cdots + 45\!\cdots\!28 q^{99}+O(q^{100}) $ 3 * q - 344688 * q^2 - 10820953044 * q^3 + 6271704903936 * q^4 - 212302350281550 * q^5 + 4970194114982976 * q^6 + 57878416258239192 * q^7 - 3555831711183237120 * q^8 + 13277004110931878919 * q^9 - 911610678410074173600 * q^10 - 3064080929502798535164 * q^11 - 71233189317945674062848 * q^12 - 98515763053518962936694 * q^13 - 663773359066872932212608 * q^14 + 2322231962154213782968200 * q^15 + 13217913642093764057038848 * q^16 + 35582277130790298867301302 * q^17 - 51949630971262524069430704 * q^18 - 233456308095243376865478180 * q^19 - 1234817679506740618000857600 * q^20 - 784315067894306487816760224 * q^21 + 10093688647003206881596695744 * q^22 + 2812708670812770779627026056 * q^23 + 36949405163940557660187279360 * q^24 - 12630087813294771903109831875 * q^25 - 445502868787427067716672131104 * q^26 + 40981593702376529051426180280 * q^27 + 526606706694181610802628184064 * q^28 - 12736322664295346653179017670 * q^29 + 6115742110948196616210957398400 * q^30 - 55977552834365071134409017504 * q^31 - 14842037794660482009412112744448 * q^32 - 13829226714693448959900097020528 * q^33 - 42547131667082319398961759011808 * q^34 + 35330944415319146254058128592400 * q^35 + 209583308279267044115700704156928 * q^36 + 4945769903781582545269841455122 * q^37 + 384288369224763756133358504473920 * q^38 - 546470556552953849463965686898712 * q^39 - 1326138456985596139721995183104000 * q^40 - 3123151500646359746292805811918274 * q^41 + 5023322329604694017661024056308224 * q^42 + 1491980858362212236675453498061156 * q^43 + 6827579920847638909574240093432832 * q^44 - 3706804708974790460103758635956150 * q^45 + 34089155258950859800971794327519616 * q^46 - 63038106682044077762675687404413168 * q^47 - 48906179099557375982971001333612544 * q^48 - 97136113131667199274890334287198229 * q^49 + 286202165340727366859498513545830000 * q^50 - 157319866621422817701623275797858024 * q^51 + 364999309722184195149034320029732352 * q^52 + 79896749344137562310547533743021506 * q^53 + 279506543662409583024224141017979520 * q^54 - 1107430856215374719020572615529578600 * q^55 - 1507500925934438536531619079138017280 * q^56 - 120534128028213908789981458568129040 * q^57 + 1060511497310363735425511566792954080 * q^58 + 192512048683375799719343226678403860 * q^59 + 5905677886285900358494072637173094400 * q^60 + 8740556115036354715092732710435455386 * q^61 - 12005332293025961804297174175449366016 * q^62 + 4195060549596204507618981258341049336 * q^63 - 28669651485797320669854651690478731264 * q^64 + 23272939413910136331858458170260680700 * q^65 - 70374114793184440562716940658640274688 * q^66 + 11266872945514675454702655007279407852 * q^67 + 95413181576279049358373233907724317184 * q^68 + 110718129232411678126981084073658946848 * q^69 + 59324379124057015483688060122385068800 * q^70 - 140970915469820223119231433051520161384 * q^71 - 178095780793081630529589944776993320960 * q^72 + 45825493210252135256288871746499029406 * q^73 - 255935787825178849200244145003411599008 * q^74 - 247029389196459510298088488221820147500 * q^75 + 26100578647791289060370838422069130240 * q^76 - 429017620126390531124795910645506217696 * q^77 + 3378623821652934155171000156043557135232 * q^78 - 520184835554750143118446358634240850320 * q^79 + 715918562852781559130521454428746547200 * q^80 - 3191652631710460747876906046824191542997 * q^81 - 579816777788457983576303882284492608096 * q^82 - 619777491338381742927488037142663372644 * q^83 - 4198672691855986319203859063793898610688 * q^84 - 106299433069331216483654652405294143100 * q^85 - 4751113477095326918262488958359640807744 * q^86 + 13958176049210326842816445061163645008040 * q^87 + 18329036816788093472347699011602935234560 * q^88 - 142389067128374093799211866144944441010 * q^89 - 8753545150081132110036071066039970208800 * q^90 + 25080596935320871627133801126628392473296 * q^91 - 67617289414955565381239604024555789723648 * q^92 + 3477058704647981071307340824432458334592 * q^93 - 53008068396962431152763933809330449227008 * q^94 - 33170437179755379504247502944935502503000 * q^95 + 95174464657114272630879818889875681181696 * q^96 + 116011691364103339137369463947331771078182 * q^97 - 38494567059701712876195969460820421029616 * q^98 + 45849669342635847189814810549498192693428 * 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 $

$2$	2.40087e6	1.61903	0.809514	−	0.587100i	$-0.199730\pi$
$2$	2.40087e6	1.61903	0.809514	+	0.587100i	$0.199730\pi$
$3$	−6.65953e9	−1.10270	−0.551351	−	0.834274i	$-0.685887\pi$
$3$	−6.65953e9	−1.10270	−0.551351	+	0.834274i	$0.685887\pi$
$4$	3.56518e12	1.62125
$5$	−3.38080e14	−1.58538	−0.792691	−	0.609624i	$-0.791321\pi$
$5$	−3.38080e14	−1.58538	−0.792691	+	0.609624i	$0.791321\pi$
$6$	−1.59887e16	−1.78530
$7$	−9.19453e16	−0.435532	−0.217766	−	0.976001i	$-0.569877\pi$
$7$	−9.19453e16	−0.435532	−0.217766	+	0.976001i	$0.569877\pi$
$8$	3.27996e18	1.00583
$9$	7.87633e18	0.215949
$10$	−8.11687e20	−2.56678
$11$	2.15850e21	0.967392	0.483696	−	0.875236i	$-0.339294\pi$
$11$	2.15850e21	0.967392	0.483696	+	0.875236i	$0.339294\pi$
$12$	−2.37424e22	−1.78776
$13$	−8.71848e22	−1.27234	−0.636169	−	0.771550i	$-0.719482\pi$
$13$	−8.71848e22	−1.27234	−0.636169	+	0.771550i	$0.719482\pi$
$14$	−2.20749e23	−0.705138
$15$	2.25145e24	1.74820
$16$	3.48699e22	0.00721093
$17$	5.13467e24	0.306415	0.153207	−	0.988194i	$-0.451040\pi$
$17$	5.13467e24	0.306415	0.153207	+	0.988194i	$0.451040\pi$
$18$	1.89101e25	0.349628
$19$	4.11372e25	0.251065	0.125532	−	0.992090i	$-0.459936\pi$
$19$	4.11372e25	0.251065	0.125532	+	0.992090i	$0.459936\pi$
$20$	−1.20531e27	−2.57031
$21$	6.12312e26	0.480261
$22$	5.18229e27	1.56624
$23$	2.60656e27	0.316699	0.158350	−	0.987383i	$-0.449383\pi$
$23$	2.60656e27	0.316699	0.158350	+	0.987383i	$0.449383\pi$
$24$	−2.18430e28	−1.10913
$25$	6.88231e28	1.51344
$26$	−2.09320e29	−2.05995
$27$	1.90440e29	0.864573
$28$	−3.27801e29	−0.706107
$29$	−4.19842e29	−0.440480	−0.220240	−	0.975446i	$-0.570684\pi$
$29$	−4.19842e29	−0.440480	−0.220240	+	0.975446i	$0.570684\pi$
$30$	5.40545e30	2.83039
$31$	−2.68405e30	−0.717589	−0.358794	−	0.933417i	$-0.616812\pi$
$31$	−2.68405e30	−0.717589	−0.358794	+	0.933417i	$0.616812\pi$
$32$	−7.12899e30	−0.994154
$33$	−1.43746e31	−1.06674
$34$	1.23277e31	0.496094
$35$	3.10848e31	0.690484
$36$	2.80805e31	0.350109
$37$	−1.06323e32	−0.755947	−0.377974	−	0.925816i	$-0.623379\pi$
$37$	−1.06323e32	−0.755947	−0.377974	+	0.925816i	$0.623379\pi$
$38$	9.87652e31	0.406481
$39$	5.80610e32	1.40301
$40$	−1.10889e33	−1.59462
$41$	−1.44220e33	−1.25013	−0.625065	−	0.780573i	$-0.714928\pi$
$41$	−1.44220e33	−1.25013	−0.625065	+	0.780573i	$0.714928\pi$
$42$	1.47009e33	0.777557
$43$	−7.60160e31	−0.0248200	−0.0124100	−	0.999923i	$-0.503950\pi$
$43$	−7.60160e31	−0.0248200	−0.0124100	+	0.999923i	$0.503950\pi$
$44$	7.69544e33	1.56839
$45$	−2.66283e33	−0.342362
$46$	6.25802e33	0.512745
$47$	−3.36927e34	−1.77636	−0.888179	−	0.459499i	$-0.848029\pi$
$47$	−3.36927e34	−1.77636	−0.888179	+	0.459499i	$0.848029\pi$
$48$	−2.32217e32	−0.00795151
$49$	−3.61137e34	−0.810312
$50$	1.65236e35	2.45030
$51$	−3.41945e34	−0.337884
$52$	−3.10829e35	−2.06278
$53$	3.75996e35	1.68861	0.844303	−	0.535866i	$-0.180015\pi$
$53$	3.75996e35	1.68861	0.844303	+	0.535866i	$0.180015\pi$
$54$	4.57223e35	1.39977
$55$	−7.29746e35	−1.53369
$56$	−3.01577e35	−0.438070
$57$	−2.73954e35	−0.276849
$58$	−1.00799e36	−0.713150
$59$	−6.72854e34	−0.0335316	−0.0167658	−	0.999859i	$-0.505337\pi$
$59$	−6.72854e34	−0.0335316	−0.0167658	+	0.999859i	$0.505337\pi$
$60$	8.02682e36	2.83428
$61$	−2.74886e35	−0.0691657	−0.0345828	−	0.999402i	$-0.511010\pi$
$61$	−2.74886e35	−0.0691657	−0.0345828	+	0.999402i	$0.511010\pi$
$62$	−6.44406e36	−1.16180
$63$	−7.24191e35	−0.0940528
$64$	−1.71925e37	−1.61677
$65$	2.94754e37	2.01714
$66$	−3.45116e37	−1.72709
$67$	2.47724e37	0.910824	0.455412	−	0.890281i	$-0.349492\pi$
$67$	2.47724e37	0.910824	0.455412	+	0.890281i	$0.349492\pi$
$68$	1.83060e37	0.496776
$69$	−1.73585e37	−0.349225
$70$	7.46308e37	1.11791
$71$	−1.25628e38	−1.40698	−0.703491	−	0.710704i	$-0.748377\pi$
$71$	−1.25628e38	−1.40698	−0.703491	+	0.710704i	$0.748377\pi$
$72$	2.58340e37	0.217208
$73$	2.44972e38	1.55238	0.776189	−	0.630500i	$-0.217150\pi$
$73$	2.44972e38	1.55238	0.776189	+	0.630500i	$0.217150\pi$
$74$	−2.55268e38	−1.22390
$75$	−4.58329e38	−1.66887
$76$	1.46661e38	0.407040
$77$	−1.98464e38	−0.421330
$78$	1.39397e39	2.27151
$79$	6.92089e38	0.868574	0.434287	−	0.900775i	$-0.357000\pi$
$79$	6.92089e38	0.868574	0.434287	+	0.900775i	$0.357000\pi$
$80$	−1.17888e37	−0.0114321
$81$	−1.55552e39	−1.16932
$82$	−3.46253e39	−2.02400
$83$	1.80861e39	0.824600	0.412300	−	0.911048i	$-0.364726\pi$
$83$	1.80861e39	0.824600	0.412300	+	0.911048i	$0.364726\pi$
$84$	2.18300e39	0.778625
$85$	−1.73593e39	−0.485784
$86$	−1.82505e38	−0.0401843
$87$	2.79595e39	0.485718
$88$	7.07980e39	0.973031
$89$	−7.15901e39	−0.780473	−0.390237	−	0.920715i	$-0.627607\pi$
$89$	−7.15901e39	−0.780473	−0.390237	+	0.920715i	$0.627607\pi$
$90$	−6.39311e39	−0.554295
$91$	8.01623e39	0.554143
$92$	9.29284e39	0.513450
$93$	1.78745e40	0.791286
$94$	−8.08920e40	−2.87597
$95$	−1.39076e40	−0.398034
$96$	4.74757e40	1.09625
$97$	7.50364e40	1.40104	0.700521	−	0.713632i	$-0.252951\pi$
$97$	7.50364e40	1.40104	0.700521	+	0.713632i	$0.252951\pi$
$98$	−8.67045e40	−1.31192
$99$	1.70011e40	0.208908
$100$	2.45366e41	2.45366
$101$	−9.43857e40	−0.769694	−0.384847	−	0.922980i	$-0.625746\pi$
$101$	−9.43857e40	−0.769694	−0.384847	+	0.922980i	$0.625746\pi$
$102$	−8.20967e40	−0.547044
$103$	−2.03470e41	−1.11003	−0.555017	−	0.831839i	$-0.687288\pi$
$103$	−2.03470e41	−1.11003	−0.555017	+	0.831839i	$0.687288\pi$
$104$	−2.85963e41	−1.27975
$105$	−2.07010e41	−0.761397
$106$	9.02720e41	2.73390
$107$	−1.95974e41	−0.489589	−0.244794	−	0.969575i	$-0.578720\pi$
$107$	−1.95974e41	−0.489589	−0.244794	+	0.969575i	$0.578720\pi$
$108$	6.78953e41	1.40169
$109$	1.27681e41	0.218214	0.109107	−	0.994030i	$-0.465201\pi$
$109$	1.27681e41	0.218214	0.109107	+	0.994030i	$0.465201\pi$
$110$	−1.75203e42	−2.48308
$111$	7.08060e41	0.833584
$112$	−3.20613e39	−0.00314059
$113$	1.47167e42	1.20144	0.600720	−	0.799460i	$-0.294881\pi$
$113$	1.47167e42	1.20144	0.600720	+	0.799460i	$0.294881\pi$
$114$	−6.57730e41	−0.448227
$115$	−8.81225e41	−0.502089
$116$	−1.49681e42	−0.714131
$117$	−6.86696e41	−0.274761
$118$	−1.61544e41	−0.0542886
$119$	−4.72109e41	−0.133453
$120$	7.38467e42	1.75839
$121$	−3.19384e41	−0.0641524
$122$	−6.59966e41	−0.111981
$123$	9.60435e42	1.37852
$124$	−9.56910e42	−1.16339
$125$	−7.89360e42	−0.813992
$126$	−1.73869e42	−0.152274
$127$	−3.99623e42	−0.297628	−0.148814	−	0.988865i	$-0.547546\pi$
$127$	−3.99623e42	−0.297628	−0.148814	+	0.988865i	$0.547546\pi$
$128$	−2.56002e43	−1.62345
$129$	5.06230e41	0.0273690
$130$	7.07668e43	3.26581
$131$	1.69219e43	0.667404	0.333702	−	0.942679i	$-0.391702\pi$
$131$	1.69219e43	0.667404	0.333702	+	0.942679i	$0.391702\pi$
$132$	−5.12480e43	−1.72946
$133$	−3.78237e42	−0.109347
$134$	5.94754e43	1.47465
$135$	−6.43840e43	−1.37068
$136$	1.68415e43	0.308201
$137$	−3.96792e43	−0.624873	−0.312436	−	0.949939i	$-0.601145\pi$
$137$	−3.96792e43	−0.624873	−0.312436	+	0.949939i	$0.601145\pi$
$138$	−4.16755e43	−0.565405
$139$	−2.45873e43	−0.287679	−0.143839	−	0.989601i	$-0.545945\pi$
$139$	−2.45873e43	−0.287679	−0.143839	+	0.989601i	$0.545945\pi$
$140$	1.10823e44	1.11945
$141$	2.24378e44	1.95879
$142$	−3.01616e44	−2.27795
$143$	−1.88189e44	−1.23085
$144$	2.74647e41	0.00155720
$145$	1.41940e44	0.698330
$146$	5.88147e44	2.51334
$147$	2.40500e44	0.893532
$148$	−3.79060e44	−1.22558
$149$	−2.54122e42	−0.00715687	−0.00357844	−	0.999994i	$-0.501139\pi$
$149$	−2.54122e42	−0.00715687	−0.00357844	+	0.999994i	$0.501139\pi$
$150$	−1.10039e45	−2.70194
$151$	7.23871e43	0.155108	0.0775539	−	0.996988i	$-0.475289\pi$
$151$	7.23871e43	0.155108	0.0775539	+	0.996988i	$0.475289\pi$
$152$	1.34928e44	0.252528
$153$	4.04423e43	0.0661701
$154$	−4.76488e44	−0.682145
$155$	9.07422e44	1.13765
$156$	2.06998e45	2.27463
$157$	−1.76934e45	−1.70557	−0.852783	−	0.522266i	$-0.825087\pi$
$157$	−1.76934e45	−1.70557	−0.852783	+	0.522266i	$0.825087\pi$
$158$	1.66162e45	1.40625
$159$	−2.50396e45	−1.86203
$160$	2.41017e45	1.57611
$161$	−2.39661e44	−0.137933
$162$	−3.73460e45	−1.89316
$163$	1.55154e45	0.693295	0.346648	−	0.937995i	$-0.387320\pi$
$163$	1.55154e45	0.693295	0.346648	+	0.937995i	$0.387320\pi$
$164$	−5.14168e45	−2.02678
$165$	4.85976e45	1.69120
$166$	4.34224e45	1.33505
$167$	−5.53546e45	−1.50476	−0.752378	−	0.658732i	$-0.771093\pi$
$167$	−5.53546e45	−1.50476	−0.752378	+	0.658732i	$0.771093\pi$
$168$	2.00836e45	0.483060
$169$	2.90574e45	0.618842
$170$	−4.16774e45	−0.786499
$171$	3.24010e44	0.0542173
$172$	−2.71010e44	−0.0402395
$173$	6.50011e45	0.856990	0.428495	−	0.903544i	$-0.359044\pi$
$173$	6.50011e45	0.856990	0.428495	+	0.903544i	$0.359044\pi$
$174$	6.71272e45	0.786392
$175$	−6.32796e45	−0.659149
$176$	7.52669e43	0.00697580
$177$	4.48089e44	0.0369753
$178$	−1.71879e46	−1.26361
$179$	−1.33774e46	−0.876765	−0.438383	−	0.898788i	$-0.644449\pi$
$179$	−1.33774e46	−0.876765	−0.438383	+	0.898788i	$0.644449\pi$
$180$	−9.49344e45	−0.555057
$181$	1.31888e46	0.688328	0.344164	−	0.938910i	$-0.388162\pi$
$181$	1.31888e46	0.688328	0.344164	+	0.938910i	$0.388162\pi$
$182$	1.92460e46	0.897173
$183$	1.83061e45	0.0762691
$184$	8.54941e45	0.318545
$185$	3.59456e46	1.19847
$186$	4.29144e46	1.28111
$187$	1.10832e46	0.296423
$188$	−1.20121e47	−2.87993
$189$	−1.75101e46	−0.376549
$190$	−3.33905e46	−0.644428
$191$	−1.01788e47	−1.76406	−0.882031	−	0.471192i	$-0.843824\pi$
$191$	−1.01788e47	−1.76406	−0.882031	+	0.471192i	$0.843824\pi$
$192$	1.14494e47	1.78282
$193$	8.24135e46	1.15365	0.576824	−	0.816868i	$-0.304292\pi$
$193$	8.24135e46	1.15365	0.576824	+	0.816868i	$0.304292\pi$
$194$	1.80153e47	2.26833
$195$	−1.96292e47	−2.22430
$196$	−1.28752e47	−1.31372
$197$	2.27618e46	0.209242	0.104621	−	0.994512i	$-0.466637\pi$
$197$	2.27618e46	0.209242	0.104621	+	0.994512i	$0.466637\pi$
$198$	4.08174e46	0.338228
$199$	1.53840e47	1.14969	0.574846	−	0.818262i	$-0.305062\pi$
$199$	1.53840e47	1.14969	0.574846	+	0.818262i	$0.305062\pi$
$200$	2.25737e47	1.52226
$201$	−1.64972e47	−1.00437
$202$	−2.26608e47	−1.24616
$203$	3.86025e46	0.191843
$204$	−1.21909e47	−0.547796
$205$	4.87577e47	1.98193
$206$	−4.88505e47	−1.79718
$207$	2.05301e46	0.0683910
$208$	−3.04013e45	−0.00917474
$209$	8.87947e46	0.242878
$210$	−4.97006e47	−1.23272
$211$	−7.00983e47	−1.57731	−0.788655	−	0.614836i	$-0.789222\pi$
$211$	−7.00983e47	−1.57731	−0.788655	+	0.614836i	$0.789222\pi$
$212$	1.34049e48	2.73766
$213$	8.36620e47	1.55148
$214$	−4.70509e47	−0.792658
$215$	2.56994e46	0.0393491
$216$	6.24637e47	0.869612
$217$	2.46786e47	0.312533
$218$	3.06546e47	0.353295
$219$	−1.63140e48	−1.71181
$220$	−2.60167e48	−2.48649
$221$	−4.47665e47	−0.389863
$222$	1.69996e48	1.34960
$223$	−2.18317e47	−0.158066	−0.0790330	−	0.996872i	$-0.525183\pi$
$223$	−2.18317e47	−0.158066	−0.0790330	+	0.996872i	$0.525183\pi$
$224$	6.55477e47	0.432985
$225$	5.42073e47	0.326826
$226$	3.53329e48	1.94516
$227$	−1.64330e48	−0.826391	−0.413196	−	0.910642i	$-0.635587\pi$
$227$	−1.64330e48	−0.826391	−0.413196	+	0.910642i	$0.635587\pi$
$228$	−9.76695e47	−0.448843
$229$	2.31385e48	0.972093	0.486047	−	0.873933i	$-0.338438\pi$
$229$	2.31385e48	0.972093	0.486047	+	0.873933i	$0.338438\pi$
$230$	−2.11571e48	−0.812897
$231$	1.32168e48	0.464601
$232$	−1.37706e48	−0.443048
$233$	−5.25096e48	−1.54683	−0.773414	−	0.633901i	$-0.781453\pi$
$233$	−5.25096e48	−1.54683	−0.773414	+	0.633901i	$0.781453\pi$
$234$	−1.64867e48	−0.444845
$235$	1.13908e49	2.81620
$236$	−2.39884e47	−0.0543633
$237$	−4.60899e48	−0.957777
$238$	−1.13347e48	−0.216065
$239$	−4.02474e48	−0.704013	−0.352007	−	0.935998i	$-0.614501\pi$
$239$	−4.02474e48	−0.704013	−0.352007	+	0.935998i	$0.614501\pi$
$240$	7.85080e46	0.0126062
$241$	−2.82992e48	−0.417277	−0.208638	−	0.977993i	$-0.566903\pi$
$241$	−2.82992e48	−0.417277	−0.208638	+	0.977993i	$0.566903\pi$
$242$	−7.66800e47	−0.103865
$243$	3.41307e48	0.424832
$244$	−9.80016e47	−0.112135
$245$	1.22093e49	1.28465
$246$	2.30588e49	2.23186
$247$	−3.58654e48	−0.319439
$248$	−8.80357e48	−0.721771
$249$	−1.20445e49	−0.909287
$250$	−1.89516e49	−1.31788
$251$	2.68976e48	0.172346	0.0861732	−	0.996280i	$-0.472536\pi$
$251$	2.68976e48	0.172346	0.0861732	+	0.996280i	$0.472536\pi$
$252$	−2.58187e48	−0.152484
$253$	5.62627e48	0.306372
$254$	−9.59444e48	−0.481868
$255$	1.15605e49	0.535675
$256$	−2.36562e49	−1.01164
$257$	−6.05982e48	−0.239238	−0.119619	−	0.992820i	$-0.538167\pi$
$257$	−6.05982e48	−0.239238	−0.119619	+	0.992820i	$0.538167\pi$
$258$	1.21540e48	0.0443112
$259$	9.77589e48	0.329239
$260$	1.05085e50	3.27030
$261$	−3.30681e48	−0.0951215
$262$	4.06275e49	1.08055
$263$	−4.72993e49	−1.16349	−0.581743	−	0.813372i	$-0.697629\pi$
$263$	−4.72993e49	−1.16349	−0.581743	+	0.813372i	$0.697629\pi$
$264$	−4.71482e49	−1.07296
$265$	−1.27117e50	−2.67709
$266$	−9.08100e48	−0.177035
$267$	4.76757e49	0.860629
$268$	8.83179e49	1.47668
$269$	3.21338e49	0.497784	0.248892	−	0.968531i	$-0.419934\pi$
$269$	3.21338e49	0.497784	0.248892	+	0.968531i	$0.419934\pi$
$270$	−1.54578e50	−2.21917
$271$	1.33856e50	1.78142	0.890709	−	0.454574i	$-0.150208\pi$
$271$	1.33856e50	1.78142	0.890709	+	0.454574i	$0.150208\pi$
$272$	1.79046e47	0.00220954
$273$	−5.33843e49	−0.611054
$274$	−9.52648e49	−1.01169
$275$	1.48555e50	1.46409
$276$	−6.18859e49	−0.566182
$277$	5.53962e49	0.470592	0.235296	−	0.971924i	$-0.424394\pi$
$277$	5.53962e49	0.470592	0.235296	+	0.971924i	$0.424394\pi$
$278$	−5.90310e49	−0.465760
$279$	−2.11404e49	−0.154963
$280$	1.01957e50	0.694508
$281$	−2.22399e49	−0.140816	−0.0704082	−	0.997518i	$-0.522430\pi$
$281$	−2.22399e49	−0.140816	−0.0704082	+	0.997518i	$0.522430\pi$
$282$	5.38703e50	3.17134
$283$	−1.61973e50	−0.886790	−0.443395	−	0.896326i	$-0.646226\pi$
$283$	−1.61973e50	−0.886790	−0.443395	+	0.896326i	$0.646226\pi$
$284$	−4.47884e50	−2.28108
$285$	9.26184e49	0.438912
$286$	−4.51817e50	−1.99278
$287$	1.32603e50	0.544471
$288$	−5.61503e49	−0.214687
$289$	−2.54441e50	−0.906110
$290$	3.40780e50	1.13062
$291$	−4.99707e50	−1.54493
$292$	8.73367e50	2.51680
$293$	4.58527e49	0.123191	0.0615955	−	0.998101i	$-0.480381\pi$
$293$	4.58527e49	0.123191	0.0615955	+	0.998101i	$0.480381\pi$
$294$	5.77411e50	1.44665
$295$	2.27478e49	0.0531604
$296$	−3.48735e50	−0.760353
$297$	4.11066e50	0.836381
$298$	−6.10115e48	−0.0115872
$299$	−2.27252e50	−0.402948
$300$	−1.63402e51	−2.70566
$301$	6.98931e48	0.0108099
$302$	1.73792e50	0.251124
$303$	6.28564e50	0.848742
$304$	1.43445e48	0.00181041
$305$	9.29333e49	0.109654
$306$	9.70970e49	0.107131
$307$	−1.04806e51	−1.08156	−0.540779	−	0.841165i	$-0.681871\pi$
$307$	−1.04806e51	−1.08156	−0.540779	+	0.841165i	$0.681871\pi$
$308$	−7.07560e50	−0.683083
$309$	1.35501e51	1.22404
$310$	2.17861e51	1.84189
$311$	−1.45879e51	−1.15453	−0.577265	−	0.816557i	$-0.695880\pi$
$311$	−1.45879e51	−1.15453	−0.577265	+	0.816557i	$0.695880\pi$
$312$	1.90438e51	1.41118
$313$	5.50229e50	0.381843	0.190922	−	0.981605i	$-0.438852\pi$
$313$	5.50229e50	0.381843	0.190922	+	0.981605i	$0.438852\pi$
$314$	−4.24796e51	−2.76136
$315$	2.44834e50	0.149110
$316$	2.46742e51	1.40818
$317$	2.01228e51	1.07640	0.538199	−	0.842818i	$-0.319105\pi$
$317$	2.01228e51	1.07640	0.538199	+	0.842818i	$0.319105\pi$
$318$	−6.01169e51	−3.01468
$319$	−9.06229e50	−0.426117
$320$	5.81243e51	2.56320
$321$	1.30510e51	0.539870
$322$	−5.75396e50	−0.223317
$323$	2.11226e50	0.0769299
$324$	−5.54569e51	−1.89576
$325$	−6.00033e51	−1.92560
$326$	3.72506e51	1.12246
$327$	−8.50295e50	−0.240625
$328$	−4.73035e51	−1.25742
$329$	3.09789e51	0.773660
$330$	1.16677e52	2.73810
$331$	7.84661e51	1.73065	0.865323	−	0.501215i	$-0.167113\pi$
$331$	7.84661e51	1.73065	0.865323	+	0.501215i	$0.167113\pi$
$332$	6.44800e51	1.33689
$333$	−8.37434e50	−0.163246
$334$	−1.32899e52	−2.43624
$335$	−8.37504e51	−1.44400
$336$	2.13513e49	0.00346313
$337$	1.59637e51	0.243624	0.121812	−	0.992553i	$-0.461129\pi$
$337$	1.59637e51	0.243624	0.121812	+	0.992553i	$0.461129\pi$
$338$	6.97632e51	1.00192
$339$	−9.80062e51	−1.32483
$340$	−6.18889e51	−0.787580
$341$	−5.79352e51	−0.694190
$342$	7.77907e50	0.0877794
$343$	7.41827e51	0.788448
$344$	−2.49329e50	−0.0249646
$345$	5.86854e51	0.553654
$346$	1.56060e52	1.38749
$347$	−3.39579e51	−0.284568	−0.142284	−	0.989826i	$-0.545445\pi$
$347$	−3.39579e51	−0.284568	−0.142284	+	0.989826i	$0.545445\pi$
$348$	9.96804e51	0.787473
$349$	9.21738e51	0.686572	0.343286	−	0.939231i	$-0.388460\pi$
$349$	9.21738e51	0.686572	0.343286	+	0.939231i	$0.388460\pi$
$350$	−1.51926e52	−1.06718
$351$	−1.66035e52	−1.10003
$352$	−1.53879e52	−0.961737
$353$	1.05771e52	0.623715	0.311857	−	0.950129i	$-0.399049\pi$
$353$	1.05771e52	0.623715	0.311857	+	0.950129i	$0.399049\pi$
$354$	1.07581e51	0.0598641
$355$	4.24721e52	2.23060
$356$	−2.55231e52	−1.26535
$357$	3.14402e51	0.147159
$358$	−3.21174e52	−1.41951
$359$	1.47439e52	0.615428	0.307714	−	0.951479i	$-0.400436\pi$
$359$	1.47439e52	0.615428	0.307714	+	0.951479i	$0.400436\pi$
$360$	−8.73396e51	−0.344358
$361$	−2.51548e52	−0.936966
$362$	3.16647e52	1.11442
$363$	2.12694e51	0.0707409
$364$	2.85793e52	0.898407
$365$	−8.28200e52	−2.46111
$366$	4.39506e51	0.123482
$367$	5.60693e52	1.48960	0.744802	−	0.667285i	$-0.232544\pi$
$367$	5.60693e52	1.48960	0.744802	+	0.667285i	$0.232544\pi$
$368$	9.08906e49	0.00228370
$369$	−1.13592e52	−0.269965
$370$	8.63009e52	1.94035
$371$	−3.45711e52	−0.735442
$372$	6.37257e52	1.28288
$373$	−8.78610e52	−1.67404	−0.837018	−	0.547175i	$-0.815703\pi$
$373$	−8.78610e52	−1.67404	−0.837018	+	0.547175i	$0.815703\pi$
$374$	2.66094e52	0.479918
$375$	5.25677e52	0.897590
$376$	−1.10511e53	−1.78671
$377$	3.66038e52	0.560440
$378$	−4.20395e52	−0.609644
$379$	−2.73345e52	−0.375498	−0.187749	−	0.982217i	$-0.560119\pi$
$379$	−2.73345e52	−0.375498	−0.187749	+	0.982217i	$0.560119\pi$
$380$	−4.95832e52	−0.645314
$381$	2.66130e52	0.328195
$382$	−2.44381e53	−2.85607
$383$	2.55810e52	0.283362	0.141681	−	0.989912i	$-0.454749\pi$
$383$	2.55810e52	0.283362	0.141681	+	0.989912i	$0.454749\pi$
$384$	1.70485e53	1.79018
$385$	6.70967e52	0.667969
$386$	1.97864e53	1.86779
$387$	−5.98726e50	−0.00535986
$388$	2.67518e53	2.27145
$389$	1.34317e53	1.08185	0.540923	−	0.841072i	$-0.318075\pi$
$389$	1.34317e53	1.08185	0.540923	+	0.841072i	$0.318075\pi$
$390$	−4.71273e53	−3.60121
$391$	1.33838e52	0.0970413
$392$	−1.18452e53	−0.815035
$393$	−1.12692e53	−0.735947
$394$	5.46483e52	0.338770
$395$	−2.33981e53	−1.37702
$396$	6.06118e52	0.338693
$397$	6.36376e52	0.337683	0.168841	−	0.985643i	$-0.445997\pi$
$397$	6.36376e52	0.337683	0.168841	+	0.985643i	$0.445997\pi$
$398$	3.69351e53	1.86138
$399$	2.51888e52	0.120577
$400$	2.39986e51	0.0109133
$401$	−1.74531e53	−0.754071	−0.377036	−	0.926199i	$-0.623057\pi$
$401$	−1.74531e53	−0.754071	−0.377036	+	0.926199i	$0.623057\pi$
$402$	−3.96078e53	−1.62610
$403$	2.34008e53	0.913015
$404$	−3.36501e53	−1.24787
$405$	5.25888e53	1.85381
$406$	9.26797e52	0.310600
$407$	−2.29498e53	−0.731298
$408$	−1.12157e53	−0.339853
$409$	−2.90188e53	−0.836279	−0.418140	−	0.908383i	$-0.637318\pi$
$409$	−2.90188e53	−0.836279	−0.418140	+	0.908383i	$0.637318\pi$
$410$	1.17061e54	3.20881
$411$	2.64245e53	0.689048
$412$	−7.25405e53	−1.79965
$413$	6.18657e51	0.0146041
$414$	4.92902e52	0.110727
$415$	−6.11453e53	−1.30731
$416$	6.21540e53	1.26490
$417$	1.63740e53	0.317223
$418$	2.13185e53	0.393227
$419$	−1.59662e53	−0.280424	−0.140212	−	0.990121i	$-0.544778\pi$
$419$	−1.59662e53	−0.280424	−0.140212	+	0.990121i	$0.544778\pi$
$420$	−7.38028e53	−1.23442
$421$	−4.06387e53	−0.647377	−0.323688	−	0.946164i	$-0.604923\pi$
$421$	−4.06387e53	−0.647377	−0.323688	+	0.946164i	$0.604923\pi$
$422$	−1.68297e54	−2.55371
$423$	−2.65375e53	−0.383603
$424$	1.23325e54	1.69845
$425$	3.53384e53	0.463739
$426$	2.00862e54	2.51189
$427$	2.52744e52	0.0301238
$428$	−6.98682e53	−0.793748
$429$	1.25325e54	1.35726
$430$	6.17011e52	0.0637074
$431$	−9.52197e53	−0.937438	−0.468719	−	0.883347i	$-0.655284\pi$
$431$	−9.52197e53	−0.937438	−0.468719	+	0.883347i	$0.655284\pi$
$432$	6.64064e51	0.00623438
$433$	4.92132e53	0.440636	0.220318	−	0.975428i	$-0.429291\pi$
$433$	4.92132e53	0.440636	0.220318	+	0.975428i	$0.429291\pi$
$434$	5.92501e53	0.505999
$435$	−9.45253e53	−0.770049
$436$	4.55205e53	0.353780
$437$	1.07227e53	0.0795120
$438$	−3.91678e54	−2.77147
$439$	1.37566e54	0.928940	0.464470	−	0.885589i	$-0.346245\pi$
$439$	1.37566e54	0.928940	0.464470	+	0.885589i	$0.346245\pi$
$440$	−2.39354e54	−1.54263
$441$	−2.84443e53	−0.174987
$442$	−1.07479e54	−0.631199
$443$	2.53462e54	1.42114	0.710570	−	0.703626i	$-0.248437\pi$
$443$	2.53462e54	1.42114	0.710570	+	0.703626i	$0.248437\pi$
$444$	2.52436e54	1.35145
$445$	2.42032e54	1.23735
$446$	−5.24152e53	−0.255913
$447$	1.69233e52	0.00789189
$448$	1.58077e54	0.704156
$449$	−3.83879e54	−1.63359	−0.816797	−	0.576926i	$-0.804252\pi$
$449$	−3.83879e54	−1.63359	−0.816797	+	0.576926i	$0.804252\pi$
$450$	1.30145e54	0.529140
$451$	−3.11298e54	−1.20937
$452$	5.24676e54	1.94784
$453$	−4.82064e53	−0.171038
$454$	−3.94535e54	−1.33795
$455$	−2.71013e54	−0.878528
$456$	−8.98559e53	−0.278463
$457$	5.46700e54	1.61982	0.809910	−	0.586554i	$-0.199516\pi$
$457$	5.46700e54	1.61982	0.809910	+	0.586554i	$0.199516\pi$
$458$	5.55527e54	1.57385
$459$	9.77848e53	0.264918
$460$	−3.14172e54	−0.814014
$461$	−6.86605e54	−1.70152	−0.850762	−	0.525551i	$-0.823859\pi$
$461$	−6.86605e54	−1.70152	−0.850762	+	0.525551i	$0.823859\pi$
$462$	3.17318e54	0.752202
$463$	2.69469e54	0.611082	0.305541	−	0.952179i	$-0.401163\pi$
$463$	2.69469e54	0.611082	0.305541	+	0.952179i	$0.401163\pi$
$464$	−1.46399e52	−0.00317628
$465$	−6.04300e54	−1.25449
$466$	−1.26069e55	−2.50436
$467$	−1.01233e54	−0.192453	−0.0962267	−	0.995359i	$-0.530677\pi$
$467$	−1.01233e54	−0.192453	−0.0962267	+	0.995359i	$0.530677\pi$
$468$	−2.44819e54	−0.445457
$469$	−2.27770e54	−0.396693
$470$	2.73480e55	4.55952
$471$	1.17830e55	1.88073
$472$	−2.20693e53	−0.0337271
$473$	−1.64081e53	−0.0240107
$474$	−1.10656e55	−1.55067
$475$	2.83119e54	0.379970
$476$	−1.68315e54	−0.216362
$477$	2.96147e54	0.364654
$478$	−9.66289e54	−1.13982
$479$	8.03512e54	0.908060	0.454030	−	0.890986i	$-0.349986\pi$
$479$	8.03512e54	0.908060	0.454030	+	0.890986i	$0.349986\pi$
$480$	−1.60506e55	−1.73798
$481$	9.26974e54	0.961820
$482$	−6.79428e54	−0.675583
$483$	1.59603e54	0.152098
$484$	−1.13866e54	−0.104007
$485$	−2.53683e55	−2.22119
$486$	8.19436e54	0.687815
$487$	3.58922e54	0.288839	0.144420	−	0.989517i	$-0.453868\pi$
$487$	3.58922e54	0.288839	0.144420	+	0.989517i	$0.453868\pi$
$488$	−9.01614e53	−0.0695688
$489$	−1.03326e55	−0.764497
$490$	2.93130e55	2.07989
$491$	8.12128e53	0.0552655	0.0276327	−	0.999618i	$-0.491203\pi$
$491$	8.12128e53	0.0552655	0.0276327	+	0.999618i	$0.491203\pi$
$492$	3.42412e55	2.23493
$493$	−2.15575e54	−0.134970
$494$	−8.61083e54	−0.517181
$495$	−5.74772e54	−0.331199
$496$	−9.35926e52	−0.00517448
$497$	1.15509e55	0.612785
$498$	−2.89173e55	−1.47216
$499$	−6.57141e54	−0.321068	−0.160534	−	0.987030i	$-0.551322\pi$
$499$	−6.57141e54	−0.321068	−0.160534	+	0.987030i	$0.551322\pi$
$500$	−2.81421e55	−1.31969
$501$	3.68636e55	1.65930
$502$	6.45777e54	0.279034
$503$	−3.12409e55	−1.29592	−0.647962	−	0.761672i	$-0.724379\pi$
$503$	−3.12409e55	−1.29592	−0.647962	+	0.761672i	$0.724379\pi$
$504$	−2.37532e54	−0.0946010
$505$	3.19099e55	1.22026
$506$	1.35080e55	0.496026
$507$	−1.93509e55	−0.682397
$508$	−1.42472e55	−0.482530
$509$	−2.10477e55	−0.684684	−0.342342	−	0.939575i	$-0.611220\pi$
$509$	−2.10477e55	−0.684684	−0.342342	+	0.939575i	$0.611220\pi$
$510$	2.77552e55	0.867273
$511$	−2.25240e55	−0.676110
$512$	−5.00094e53	−0.0144217
$513$	7.83418e54	0.217064
$514$	−1.45489e55	−0.387334
$515$	6.87889e55	1.75983
$516$	1.80480e54	0.0443721
$517$	−7.27259e55	−1.71843
$518$	2.34707e55	0.533047
$519$	−4.32877e55	−0.945004
$520$	9.66782e55	2.02890
$521$	1.04403e55	0.210639	0.105320	−	0.994438i	$-0.466413\pi$
$521$	1.04403e55	0.210639	0.105320	+	0.994438i	$0.466413\pi$
$522$	−7.93924e54	−0.154004
$523$	3.89473e55	0.726429	0.363215	−	0.931706i	$-0.381679\pi$
$523$	3.89473e55	0.726429	0.363215	+	0.931706i	$0.381679\pi$
$524$	6.03297e55	1.08203
$525$	4.21412e55	0.726844
$526$	−1.13560e56	−1.88372
$527$	−1.37817e55	−0.219880
$528$	−5.01242e53	−0.00769222
$529$	−6.09452e55	−0.899702
$530$	−3.05191e56	−4.33428
$531$	−5.29962e53	−0.00724114
$532$	−1.34848e55	−0.177279
$533$	1.25738e56	1.59059
$534$	1.14463e56	1.39338
$535$	6.62549e55	0.776185
$536$	8.12524e55	0.916132
$537$	8.90869e55	0.966810
$538$	7.71493e55	0.805926
$539$	−7.79515e55	−0.783890
$540$	−2.29540e56	−2.22222
$541$	7.83261e55	0.730067	0.365033	−	0.930994i	$-0.381058\pi$
$541$	7.83261e55	0.730067	0.365033	+	0.930994i	$0.381058\pi$
$542$	3.21370e56	2.88417
$543$	−8.78314e55	−0.759020
$544$	−3.66050e55	−0.304623
$545$	−4.31663e55	−0.345953
$546$	−1.28169e56	−0.989314
$547$	−1.75108e56	−1.30187	−0.650933	−	0.759135i	$-0.725622\pi$
$547$	−1.75108e56	−1.30187	−0.650933	+	0.759135i	$0.725622\pi$
$548$	−1.41463e56	−1.01308
$549$	−2.16509e54	−0.0149363
$550$	3.56662e56	2.37040
$551$	−1.72711e55	−0.110589
$552$	−5.69351e55	−0.351260
$553$	−6.36343e55	−0.378291
$554$	1.32999e56	0.761902
$555$	−2.39381e56	−1.32155
$556$	−8.76581e55	−0.466400
$557$	2.17848e56	1.11718	0.558588	−	0.829445i	$-0.311343\pi$
$557$	2.17848e56	1.11718	0.558588	+	0.829445i	$0.311343\pi$
$558$	−5.07555e55	−0.250889
$559$	6.62744e54	0.0315794
$560$	1.08393e54	0.00497903
$561$	−7.38089e55	−0.326866
$562$	−5.33952e55	−0.227986
$563$	3.30210e56	1.35947	0.679733	−	0.733459i	$-0.262095\pi$
$563$	3.30210e56	1.35947	0.679733	+	0.733459i	$0.262095\pi$
$564$	7.99946e56	3.17570
$565$	−4.97541e56	−1.90474
$566$	−3.88877e56	−1.43574
$567$	1.43022e56	0.509274
$568$	−4.12053e56	−1.41518
$569$	−8.68468e55	−0.287708	−0.143854	−	0.989599i	$-0.545950\pi$
$569$	−8.68468e55	−0.287708	−0.143854	+	0.989599i	$0.545950\pi$
$570$	2.22365e56	0.710611
$571$	4.87083e56	1.50163	0.750815	−	0.660512i	$-0.229661\pi$
$571$	4.87083e56	1.50163	0.750815	+	0.660512i	$0.229661\pi$
$572$	−6.70926e56	−1.99552
$573$	6.77862e56	1.94523
$574$	3.18363e56	0.881514
$575$	1.79391e56	0.479304
$576$	−1.35414e56	−0.349142
$577$	−7.14972e56	−1.77904	−0.889518	−	0.456900i	$-0.848960\pi$
$577$	−7.14972e56	−1.77904	−0.889518	+	0.456900i	$0.848960\pi$
$578$	−6.10880e56	−1.46702
$579$	−5.48835e56	−1.27213
$580$	5.06041e56	1.13217
$581$	−1.66293e56	−0.359139
$582$	−1.19973e57	−2.50129
$583$	8.11589e56	1.63354
$584$	8.03498e56	1.56143
$585$	2.32158e56	0.435600
$586$	1.10087e56	0.199450
$587$	4.35978e56	0.762752	0.381376	−	0.924420i	$-0.375450\pi$
$587$	4.35978e56	0.762752	0.381376	+	0.924420i	$0.375450\pi$
$588$	8.57426e56	1.44864
$589$	−1.10414e56	−0.180161
$590$	5.46147e55	0.0860682
$591$	−1.51583e56	−0.230732
$592$	−3.70747e54	−0.00545109
$593$	−8.14584e56	−1.15695	−0.578475	−	0.815700i	$-0.696352\pi$
$593$	−8.14584e56	−1.15695	−0.578475	+	0.815700i	$0.696352\pi$
$594$	9.86918e56	1.35413
$595$	1.59610e56	0.211574
$596$	−9.05989e54	−0.0116031
$597$	−1.02450e57	−1.26777
$598$	−5.45605e56	−0.652385
$599$	−1.46611e57	−1.69401	−0.847004	−	0.531587i	$-0.821596\pi$
$599$	−1.46611e57	−1.69401	−0.847004	+	0.531587i	$0.821596\pi$
$600$	−1.50330e57	−1.67859
$601$	1.27455e57	1.37540	0.687700	−	0.725995i	$-0.258620\pi$
$601$	1.27455e57	1.37540	0.687700	+	0.725995i	$0.258620\pi$
$602$	1.67805e55	0.0175015
$603$	1.95115e56	0.196692
$604$	2.58073e56	0.251469
$605$	1.07977e56	0.101706
$606$	1.50910e57	1.37414
$607$	7.08566e56	0.623752	0.311876	−	0.950123i	$-0.399043\pi$
$607$	7.08566e56	0.623752	0.311876	+	0.950123i	$0.399043\pi$
$608$	−2.93267e56	−0.249597
$609$	−2.57074e56	−0.211546
$610$	2.23121e56	0.177533
$611$	2.93750e57	2.26012
$612$	1.44184e56	0.107279
$613$	−1.17754e57	−0.847298	−0.423649	−	0.905827i	$-0.639251\pi$
$613$	−1.17754e57	−0.847298	−0.423649	+	0.905827i	$0.639251\pi$
$614$	−2.51626e57	−1.75107
$615$	−3.24703e57	−2.18548
$616$	−6.50955e56	−0.423786
$617$	1.61404e57	1.01641	0.508205	−	0.861236i	$-0.330309\pi$
$617$	1.61404e57	1.01641	0.508205	+	0.861236i	$0.330309\pi$
$618$	3.25321e57	1.98175
$619$	−6.36804e56	−0.375273	−0.187637	−	0.982239i	$-0.560083\pi$
$619$	−6.36804e56	−0.375273	−0.187637	+	0.982239i	$0.560083\pi$
$620$	3.23512e57	1.84442
$621$	4.96394e56	0.273810
$622$	−3.50238e57	−1.86922
$623$	6.58238e56	0.339921
$624$	2.02458e55	0.0101170
$625$	−4.61045e56	−0.222948
$626$	1.32103e57	0.618215
$627$	−5.91331e56	−0.267822
$628$	−6.30801e57	−2.76516
$629$	−5.45933e56	−0.231633
$630$	5.87816e56	0.241413
$631$	−2.73724e57	−1.08820	−0.544102	−	0.839019i	$-0.683130\pi$
$631$	−2.73724e57	−1.08820	−0.544102	+	0.839019i	$0.683130\pi$
$632$	2.27003e57	0.873636
$633$	4.66821e57	1.73930
$634$	4.83123e57	1.74272
$635$	1.35104e57	0.471854
$636$	−8.92706e57	−3.01882
$637$	3.14857e57	1.03099
$638$	−2.17574e57	−0.689896
$639$	−9.89483e56	−0.303837
$640$	8.65491e57	2.57379
$641$	−2.81100e57	−0.809602	−0.404801	−	0.914405i	$-0.632659\pi$
$641$	−2.81100e57	−0.809602	−0.404801	+	0.914405i	$0.632659\pi$
$642$	3.13337e57	0.874065
$643$	1.13133e57	0.305679	0.152840	−	0.988251i	$-0.451158\pi$
$643$	1.13133e57	0.305679	0.152840	+	0.988251i	$0.451158\pi$
$644$	−8.54433e56	−0.223624
$645$	−1.71146e56	−0.0433903
$646$	5.07127e56	0.124552
$647$	2.99702e57	0.713102	0.356551	−	0.934276i	$-0.383953\pi$
$647$	2.99702e57	0.713102	0.356551	+	0.934276i	$0.383953\pi$
$648$	−5.10203e57	−1.17613
$649$	−1.45236e56	−0.0324382
$650$	−1.44060e58	−3.11760
$651$	−1.64348e57	−0.344630
$652$	5.53153e57	1.12401
$653$	1.36513e57	0.268815	0.134407	−	0.990926i	$-0.457087\pi$
$653$	1.36513e57	0.268815	0.134407	+	0.990926i	$0.457087\pi$
$654$	−2.04145e57	−0.389579
$655$	−5.72096e57	−1.05809
$656$	−5.02893e55	−0.00901461
$657$	1.92948e57	0.335235
$658$	7.43764e57	1.25258
$659$	−8.45274e57	−1.37990	−0.689949	−	0.723858i	$-0.742367\pi$
$659$	−8.45274e57	−1.37990	−0.689949	+	0.723858i	$0.742367\pi$
$660$	1.73259e58	2.74186
$661$	−1.12370e58	−1.72393	−0.861964	−	0.506970i	$-0.830766\pi$
$661$	−1.12370e58	−1.72393	−0.861964	+	0.506970i	$0.830766\pi$
$662$	1.88387e58	2.80197
$663$	2.98124e57	0.429902
$664$	5.93216e57	0.829406
$665$	1.27874e57	0.173356
$666$	−2.01057e57	−0.264301
$667$	−1.09434e57	−0.139500
$668$	−1.97349e58	−2.43959
$669$	1.45389e57	0.174300
$670$	−2.01074e58	−2.33788
$671$	−5.93342e56	−0.0669103
$672$	−4.36517e57	−0.477453
$673$	1.32183e58	1.40239	0.701193	−	0.712971i	$-0.252651\pi$
$673$	1.32183e58	1.40239	0.701193	+	0.712971i	$0.252651\pi$
$674$	3.83269e57	0.394435
$675$	1.31067e58	1.30848
$676$	1.03595e58	1.00330
$677$	4.87678e57	0.458211	0.229105	−	0.973402i	$-0.426420\pi$
$677$	4.87678e57	0.458211	0.229105	+	0.973402i	$0.426420\pi$
$678$	−2.35301e58	−2.14494
$679$	−6.89924e57	−0.610198
$680$	−5.69377e57	−0.488616
$681$	1.09436e58	0.911262
$682$	−1.39095e58	−1.12391
$683$	2.89510e57	0.227007	0.113504	−	0.993538i	$-0.463793\pi$
$683$	2.89510e57	0.227007	0.113504	+	0.993538i	$0.463793\pi$
$684$	1.15515e57	0.0879001
$685$	1.34147e58	0.990662
$686$	1.78103e58	1.27652
$687$	−1.54092e58	−1.07193
$688$	−2.65067e54	−0.000178975 0
$689$	−3.27812e58	−2.14848
$690$	1.40896e58	0.896382
$691$	6.99589e57	0.432059	0.216029	−	0.976387i	$-0.430689\pi$
$691$	6.99589e57	0.432059	0.216029	+	0.976387i	$0.430689\pi$
$692$	2.31740e58	1.38940
$693$	−1.56317e57	−0.0909860
$694$	−8.15286e57	−0.460724
$695$	8.31247e57	0.456080
$696$	9.17060e57	0.488549
$697$	−7.40520e57	−0.383058
$698$	2.21298e58	1.11158
$699$	3.49689e58	1.70569
$700$	−2.25603e58	−1.06865
$701$	−6.70824e56	−0.0308595	−0.0154298	−	0.999881i	$-0.504912\pi$
$701$	−6.70824e56	−0.0308595	−0.0154298	+	0.999881i	$0.504912\pi$
$702$	−3.98629e58	−1.78098
$703$	−4.37383e57	−0.189792
$704$	−3.71100e58	−1.56405
$705$	−7.58576e58	−3.10543
$706$	2.53943e58	1.00981
$707$	8.67832e57	0.335226
$708$	1.59752e57	0.0599464
$709$	−1.26212e58	−0.460102	−0.230051	−	0.973179i	$-0.573889\pi$
$709$	−1.26212e58	−0.460102	−0.230051	+	0.973179i	$0.573889\pi$
$710$	1.01970e59	3.61141
$711$	5.45112e57	0.187568
$712$	−2.34813e58	−0.785022
$713$	−6.99613e57	−0.227260
$714$	7.54840e57	0.238255
$715$	6.36228e58	1.95137
$716$	−4.76926e58	−1.42146
$717$	2.68029e58	0.776316
$718$	3.53983e58	0.996396
$719$	−3.64927e58	−0.998307	−0.499153	−	0.866514i	$-0.666356\pi$
$719$	−3.64927e58	−0.998307	−0.499153	+	0.866514i	$0.666356\pi$
$720$	−9.28526e55	−0.00246875
$721$	1.87081e58	0.483455
$722$	−6.03936e58	−1.51698
$723$	1.88459e58	0.460132
$724$	4.70205e58	1.11595
$725$	−2.88948e58	−0.666639
$726$	5.10653e57	0.114532
$727$	−5.20217e58	−1.13430	−0.567152	−	0.823613i	$-0.691955\pi$
$727$	−5.20217e58	−1.13430	−0.567152	+	0.823613i	$0.691955\pi$
$728$	2.62929e58	0.557373
$729$	3.40049e58	0.700853
$730$	−1.98840e59	−3.98461
$731$	−3.90317e56	−0.00760521
$732$	6.52644e57	0.123652
$733$	2.57497e58	0.474396	0.237198	−	0.971461i	$-0.423771\pi$
$733$	2.57497e58	0.474396	0.237198	+	0.971461i	$0.423771\pi$
$734$	1.34615e59	2.41171
$735$	−8.13082e58	−1.41659
$736$	−1.85821e58	−0.314848
$737$	5.34713e58	0.881124
$738$	−2.72720e58	−0.437081
$739$	1.07870e59	1.68148	0.840738	−	0.541442i	$-0.182121\pi$
$739$	1.07870e59	1.68148	0.840738	+	0.541442i	$0.182121\pi$
$740$	1.28152e59	1.94302
$741$	2.38847e58	0.352246
$742$	−8.30009e58	−1.19070
$743$	−1.21669e59	−1.69788	−0.848942	−	0.528487i	$-0.822760\pi$
$743$	−1.21669e59	−1.69788	−0.848942	+	0.528487i	$0.822760\pi$
$744$	5.86276e58	0.795898
$745$	8.59134e56	0.0113464
$746$	−2.10943e59	−2.71031
$747$	1.42452e58	0.178072
$748$	3.95136e58	0.480577
$749$	1.80189e58	0.213231
$750$	1.26208e59	1.45322
$751$	6.80995e58	0.763001	0.381500	−	0.924369i	$-0.375408\pi$
$751$	6.80995e58	0.763001	0.381500	+	0.924369i	$0.375408\pi$
$752$	−1.17486e57	−0.0128092
$753$	−1.79125e58	−0.190046
$754$	8.78812e58	0.907368
$755$	−2.44726e58	−0.245905
$756$	−6.24266e58	−0.610482
$757$	−2.77019e58	−0.263660	−0.131830	−	0.991272i	$-0.542085\pi$
$757$	−2.77019e58	−0.263660	−0.131830	+	0.991272i	$0.542085\pi$
$758$	−6.56267e58	−0.607942
$759$	−3.74683e58	−0.337837
$760$	−4.56165e58	−0.400353
$761$	−7.33770e57	−0.0626866	−0.0313433	−	0.999509i	$-0.509979\pi$
$761$	−7.33770e57	−0.0626866	−0.0313433	+	0.999509i	$0.509979\pi$
$762$	6.38944e58	0.531356
$763$	−1.17397e58	−0.0950391
$764$	−3.62893e59	−2.85999
$765$	−1.36727e58	−0.104905
$766$	6.14167e58	0.458772
$767$	5.86626e57	0.0426635
$768$	1.57539e59	1.11554
$769$	7.07782e58	0.487988	0.243994	−	0.969777i	$-0.421542\pi$
$769$	7.07782e58	0.487988	0.243994	+	0.969777i	$0.421542\pi$
$770$	1.61091e59	1.08146
$771$	4.03555e58	0.263808
$772$	2.93819e59	1.87036
$773$	−6.55116e57	−0.0406105	−0.0203053	−	0.999794i	$-0.506464\pi$
$773$	−6.55116e57	−0.0406105	−0.0203053	+	0.999794i	$0.506464\pi$
$774$	−1.43747e57	−0.00867777
$775$	−1.84724e59	−1.08602
$776$	2.46116e59	1.40921
$777$	−6.51028e58	−0.363052
$778$	3.22479e59	1.75154
$779$	−5.93279e58	−0.313864
$780$	−6.99817e59	−3.60616
$781$	−2.71167e59	−1.36110
$782$	3.21329e58	0.157113
$783$	−7.99548e58	−0.380828
$784$	−1.25928e57	−0.00584311
$785$	5.98178e59	2.70397
$786$	−2.70560e59	−1.19152
$787$	−3.33588e59	−1.43129	−0.715647	−	0.698462i	$-0.753868\pi$
$787$	−3.33588e59	−1.43129	−0.715647	+	0.698462i	$0.753868\pi$
$788$	8.11500e58	0.339235
$789$	3.14991e59	1.28298
$790$	−5.61760e59	−2.22944
$791$	−1.35313e59	−0.523265
$792$	5.57628e58	0.210125
$793$	2.39659e58	0.0880020
$794$	1.52786e59	0.546718
$795$	8.46538e59	2.95203
$796$	5.48467e59	1.86394
$797$	−1.53090e59	−0.507050	−0.253525	−	0.967329i	$-0.581590\pi$
$797$	−1.53090e59	−0.507050	−0.253525	+	0.967329i	$0.581590\pi$
$798$	6.04752e58	0.195217
$799$	−1.73001e59	−0.544302
$800$	−4.90639e59	−1.50459
$801$	−5.63867e58	−0.168543
$802$	−4.19027e59	−1.22086
$803$	5.28772e59	1.50176
$804$	−5.88156e59	−1.62833
$805$	8.10245e58	0.218676
$806$	5.61824e59	1.47820
$807$	−2.13996e59	−0.548907
$808$	−3.09581e59	−0.774180
$809$	−1.38621e59	−0.337974	−0.168987	−	0.985618i	$-0.554050\pi$
$809$	−1.38621e59	−0.337974	−0.168987	+	0.985618i	$0.554050\pi$
$810$	1.26259e60	3.00137
$811$	8.92972e58	0.206971	0.103486	−	0.994631i	$-0.467000\pi$
$811$	8.92972e58	0.206971	0.103486	+	0.994631i	$0.467000\pi$
$812$	1.37625e59	0.311026
$813$	−8.91415e59	−1.96437
$814$	−5.50997e59	−1.18399
$815$	−5.24545e59	−1.09914
$816$	−1.19236e57	−0.00243646
$817$	−3.12708e57	−0.00623142
$818$	−6.96705e59	−1.35396
$819$	6.31385e58	0.119667
$820$	1.73830e60	3.21322
$821$	5.66077e59	1.02057	0.510283	−	0.860007i	$-0.329541\pi$
$821$	5.66077e59	1.02057	0.510283	+	0.860007i	$0.329541\pi$
$822$	6.34419e59	1.11559
$823$	−9.70422e59	−1.66442	−0.832212	−	0.554458i	$-0.812926\pi$
$823$	−9.70422e59	−1.66442	−0.832212	+	0.554458i	$0.812926\pi$
$824$	−6.67372e59	−1.11650
$825$	−9.89305e59	−1.61445
$826$	1.48532e58	0.0236444
$827$	1.07249e60	1.66545	0.832725	−	0.553687i	$-0.186780\pi$
$827$	1.07249e60	1.66545	0.832725	+	0.553687i	$0.186780\pi$
$828$	7.31934e58	0.110879
$829$	6.30712e59	0.932101	0.466051	−	0.884758i	$-0.345676\pi$
$829$	6.30712e59	0.932101	0.466051	+	0.884758i	$0.345676\pi$
$830$	−1.46802e60	−2.11657
$831$	−3.68913e59	−0.518923
$832$	1.49892e60	2.05708
$833$	−1.85432e59	−0.248292
$834$	3.93119e59	0.513594
$835$	1.87143e60	2.38561
$836$	3.16569e59	0.393767
$837$	−5.11151e59	−0.620408
$838$	−3.83330e59	−0.454015
$839$	6.10677e59	0.705815	0.352908	−	0.935658i	$-0.385193\pi$
$839$	6.10677e59	0.705815	0.352908	+	0.935658i	$0.385193\pi$
$840$	−6.78986e59	−0.765835
$841$	−7.32218e59	−0.805977
$842$	−9.75685e59	−1.04812
$843$	1.48107e59	0.155278
$844$	−2.49913e60	−2.55722
$845$	−9.82372e59	−0.981100
$846$	−6.37132e59	−0.621065
$847$	2.93658e58	0.0279404
$848$	1.31110e58	0.0121764
$849$	1.07866e60	0.977864
$850$	8.48430e59	0.750807
$851$	−2.77137e59	−0.239408
$852$	2.98270e60	2.51535
$853$	1.07715e60	0.886788	0.443394	−	0.896327i	$-0.353774\pi$
$853$	1.07715e60	0.886788	0.443394	+	0.896327i	$0.353774\pi$
$854$	6.06808e58	0.0487714
$855$	−1.09541e59	−0.0859552
$856$	−6.42788e59	−0.492442
$857$	−2.94243e59	−0.220090	−0.110045	−	0.993927i	$-0.535099\pi$
$857$	−2.94243e59	−0.220090	−0.110045	+	0.993927i	$0.535099\pi$
$858$	3.00889e60	2.19744
$859$	1.39886e59	0.0997504	0.0498752	−	0.998755i	$-0.484118\pi$
$859$	1.39886e59	0.0997504	0.0498752	+	0.998755i	$0.484118\pi$
$860$	9.16230e58	0.0637950
$861$	−8.83074e59	−0.600389
$862$	−2.28610e60	−1.51774
$863$	−3.64782e59	−0.236490	−0.118245	−	0.992984i	$-0.537727\pi$
$863$	−3.64782e59	−0.236490	−0.118245	+	0.992984i	$0.537727\pi$
$864$	−1.35765e60	−0.859519
$865$	−2.19756e60	−1.35866
$866$	1.18155e60	0.713402
$867$	1.69446e60	0.999168
$868$	8.79834e59	0.506695
$869$	1.49388e60	0.840251
$870$	−2.26943e60	−1.24673
$871$	−2.15978e60	−1.15887
$872$	4.18788e59	0.219486
$873$	5.91011e59	0.302554
$874$	2.57437e59	0.128732
$875$	7.25780e59	0.354519
$876$	−5.81622e60	−2.77528
$877$	3.99235e60	1.86096	0.930480	−	0.366341i	$-0.119390\pi$
$877$	3.99235e60	1.86096	0.930480	+	0.366341i	$0.119390\pi$
$878$	3.30278e60	1.50398
$879$	−3.05358e59	−0.135843
$880$	−2.54462e58	−0.0110593
$881$	1.50864e60	0.640589	0.320295	−	0.947318i	$-0.396218\pi$
$881$	1.50864e60	0.640589	0.320295	+	0.947318i	$0.396218\pi$
$882$	−6.82913e59	−0.283308
$883$	−4.31876e60	−1.75051	−0.875254	−	0.483663i	$-0.839306\pi$
$883$	−4.31876e60	−1.75051	−0.875254	+	0.483663i	$0.839306\pi$
$884$	−1.59601e60	−0.632067
$885$	−1.51490e59	−0.0586200
$886$	6.08531e60	2.30087
$887$	−4.39179e60	−1.62259	−0.811293	−	0.584640i	$-0.801236\pi$
$887$	−4.39179e60	−1.62259	−0.811293	+	0.584640i	$0.801236\pi$
$888$	2.32241e60	0.838442
$889$	3.67434e59	0.129626
$890$	5.81088e60	2.00330
$891$	−3.35759e60	−1.13119
$892$	−7.78340e59	−0.256265
$893$	−1.38602e60	−0.445981
$894$	4.06308e58	0.0127772
$895$	4.52261e60	1.39001
$896$	2.35382e60	0.707064
$897$	1.51339e60	0.444331
$898$	−9.21644e60	−2.64483
$899$	1.12688e60	0.316084
$900$	1.93259e60	0.529868
$901$	1.93062e60	0.517414
$902$	−7.47388e60	−1.95800
$903$	−4.65455e58	−0.0119201
$904$	4.82701e60	1.20844
$905$	−4.45887e60	−1.09126
$906$	−1.15738e60	−0.276915
$907$	1.38889e60	0.324875	0.162438	−	0.986719i	$-0.448064\pi$
$907$	1.38889e60	0.324875	0.162438	+	0.986719i	$0.448064\pi$
$908$	−5.85864e60	−1.33979
$909$	−7.43412e59	−0.166215
$910$	−6.50667e60	−1.42236
$911$	1.25104e60	0.267389	0.133694	−	0.991023i	$-0.457316\pi$
$911$	1.25104e60	0.267389	0.133694	+	0.991023i	$0.457316\pi$
$912$	−9.55277e57	−0.00199634
$913$	3.90388e60	0.797711
$914$	1.31256e61	2.62254
$915$	−6.18892e59	−0.120916
$916$	8.24929e60	1.57601
$917$	−1.55589e60	−0.290675
$918$	2.34769e60	0.428910
$919$	−1.70510e60	−0.304637	−0.152319	−	0.988331i	$-0.548674\pi$
$919$	−1.70510e60	−0.304637	−0.152319	+	0.988331i	$0.548674\pi$
$920$	−2.89038e60	−0.505016
$921$	6.97959e60	1.19264
$922$	−1.64845e61	−2.75482
$923$	1.09528e61	1.79016
$924$	4.71201e60	0.753236
$925$	−7.31747e60	−1.14408
$926$	6.46962e60	0.989359
$927$	−1.60259e60	−0.239711
$928$	2.99305e60	0.437905
$929$	−1.11160e60	−0.159084	−0.0795422	−	0.996832i	$-0.525346\pi$
$929$	−1.11160e60	−0.159084	−0.0795422	+	0.996832i	$0.525346\pi$
$930$	−1.45085e61	−2.03106
$931$	−1.48562e60	−0.203441
$932$	−1.87206e61	−2.50780
$933$	9.71487e60	1.27310
$934$	−2.43048e60	−0.311588
$935$	−3.74700e60	−0.469944
$936$	−2.25234e60	−0.276362
$937$	−6.31851e60	−0.758495	−0.379248	−	0.925295i	$-0.623817\pi$
$937$	−6.31851e60	−0.758495	−0.379248	+	0.925295i	$0.623817\pi$
$938$	−5.46848e60	−0.642257
$939$	−3.66427e60	−0.421059
$940$	4.06103e61	4.56578
$941$	−6.22380e59	−0.0684650	−0.0342325	−	0.999414i	$-0.510899\pi$
$941$	−6.22380e59	−0.0684650	−0.0342325	+	0.999414i	$0.510899\pi$
$942$	2.82894e61	3.04495
$943$	−3.75917e60	−0.395915
$944$	−2.34624e57	−0.000241794 0
$945$	5.91981e60	0.596974
$946$	−3.93937e59	−0.0388739
$947$	−1.79375e61	−1.73216	−0.866079	−	0.499907i	$-0.833368\pi$
$947$	−1.79375e61	−1.73216	−0.866079	+	0.499907i	$0.833368\pi$
$948$	−1.64319e61	−1.55280
$949$	−2.13578e61	−1.97515
$950$	6.79733e60	0.615183
$951$	−1.34008e61	−1.18695
$952$	−1.54850e60	−0.134231
$953$	1.46295e61	1.24116	0.620578	−	0.784145i	$-0.286898\pi$
$953$	1.46295e61	1.24116	0.620578	+	0.784145i	$0.286898\pi$
$954$	7.11012e60	0.590385
$955$	3.44125e61	2.79671
$956$	−1.43489e61	−1.14138
$957$	6.03506e60	0.469880
$958$	1.92913e61	1.47018
$959$	3.64832e60	0.272152
$960$	−3.87081e61	−2.82645
$961$	−6.78626e60	−0.485067
$962$	2.22555e61	1.55721
$963$	−1.54356e60	−0.105726
$964$	−1.00892e61	−0.676512
$965$	−2.78623e61	−1.82897
$966$	3.83186e60	0.246252
$967$	2.19658e61	1.38199	0.690993	−	0.722861i	$-0.257173\pi$
$967$	2.19658e61	1.38199	0.690993	+	0.722861i	$0.257173\pi$
$968$	−1.04757e60	−0.0645263
$969$	−1.40666e60	−0.0848307
$970$	−6.09060e61	−3.59617
$971$	8.01229e60	0.463193	0.231597	−	0.972812i	$-0.425605\pi$
$971$	8.01229e60	0.463193	0.231597	+	0.972812i	$0.425605\pi$
$972$	1.21682e61	0.688760
$973$	2.26069e60	0.125293
$974$	8.61726e60	0.467639
$975$	3.99594e61	2.12336
$976$	−9.58525e57	−0.000498749 0
$977$	−1.53487e60	−0.0782047	−0.0391024	−	0.999235i	$-0.512450\pi$
$977$	−1.53487e60	−0.0782047	−0.0391024	+	0.999235i	$0.512450\pi$
$978$	−2.48072e61	−1.23774
$979$	−1.54528e61	−0.755024
$980$	4.35283e61	2.08275
$981$	1.00566e60	0.0471232
$982$	1.94982e60	0.0894764
$983$	2.13980e61	0.961670	0.480835	−	0.876811i	$-0.340334\pi$
$983$	2.13980e61	0.961670	0.480835	+	0.876811i	$0.340334\pi$
$984$	3.15019e61	1.38655
$985$	−7.69531e60	−0.331729
$986$	−5.17568e60	−0.218520
$987$	−2.06305e61	−0.853115
$988$	−1.27866e61	−0.517892
$989$	−1.98140e59	−0.00786047
$990$	−1.37995e61	−0.536220
$991$	2.19295e61	0.834678	0.417339	−	0.908751i	$-0.362963\pi$
$991$	2.19295e61	0.834678	0.417339	+	0.908751i	$0.362963\pi$
$992$	1.91346e61	0.713393
$993$	−5.22547e61	−1.90838
$994$	2.77322e61	0.992117
$995$	−5.20102e61	−1.82270
$996$	−4.29406e61	−1.47419
$997$	1.15402e61	0.388116	0.194058	−	0.980990i	$-0.437835\pi$
$997$	1.15402e61	0.388116	0.194058	+	0.980990i	$0.437835\pi$
$998$	−1.57771e61	−0.519819
$999$	−2.02482e61	−0.653572

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.42.a.a.1.3	✓	3
3.2	odd	2		9.42.a.b.1.1		3
4.3	odd	2		16.42.a.c.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.42.a.a.1.3	✓	3	1.1	even	1	trivial
9.42.a.b.1.1		3	3.2	odd	2
16.42.a.c.1.2		3	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+2.40087e6 q^{2} -6.65953e9 q^{3} +3.56518e12 q^{4} -3.38080e14 q^{5} -1.59887e16 q^{6} -9.19453e16 q^{7} +3.27996e18 q^{8} +7.87633e18 q^{9} +O(q^{10})\)	\(q+2.40087e6 q^{2} -6.65953e9 q^{3} +3.56518e12 q^{4} -3.38080e14 q^{5} -1.59887e16 q^{6} -9.19453e16 q^{7} +3.27996e18 q^{8} +7.87633e18 q^{9} -8.11687e20 q^{10} +2.15850e21 q^{11} -2.37424e22 q^{12} -8.71848e22 q^{13} -2.20749e23 q^{14} +2.25145e24 q^{15} +3.48699e22 q^{16} +5.13467e24 q^{17} +1.89101e25 q^{18} +4.11372e25 q^{19} -1.20531e27 q^{20} +6.12312e26 q^{21} +5.18229e27 q^{22} +2.60656e27 q^{23} -2.18430e28 q^{24} +6.88231e28 q^{25} -2.09320e29 q^{26} +1.90440e29 q^{27} -3.27801e29 q^{28} -4.19842e29 q^{29} +5.40545e30 q^{30} -2.68405e30 q^{31} -7.12899e30 q^{32} -1.43746e31 q^{33} +1.23277e31 q^{34} +3.10848e31 q^{35} +2.80805e31 q^{36} -1.06323e32 q^{37} +9.87652e31 q^{38} +5.80610e32 q^{39} -1.10889e33 q^{40} -1.44220e33 q^{41} +1.47009e33 q^{42} -7.60160e31 q^{43} +7.69544e33 q^{44} -2.66283e33 q^{45} +6.25802e33 q^{46} -3.36927e34 q^{47} -2.32217e32 q^{48} -3.61137e34 q^{49} +1.65236e35 q^{50} -3.41945e34 q^{51} -3.10829e35 q^{52} +3.75996e35 q^{53} +4.57223e35 q^{54} -7.29746e35 q^{55} -3.01577e35 q^{56} -2.73954e35 q^{57} -1.00799e36 q^{58} -6.72854e34 q^{59} +8.02682e36 q^{60} -2.74886e35 q^{61} -6.44406e36 q^{62} -7.24191e35 q^{63} -1.71925e37 q^{64} +2.94754e37 q^{65} -3.45116e37 q^{66} +2.47724e37 q^{67} +1.83060e37 q^{68} -1.73585e37 q^{69} +7.46308e37 q^{70} -1.25628e38 q^{71} +2.58340e37 q^{72} +2.44972e38 q^{73} -2.55268e38 q^{74} -4.58329e38 q^{75} +1.46661e38 q^{76} -1.98464e38 q^{77} +1.39397e39 q^{78} +6.92089e38 q^{79} -1.17888e37 q^{80} -1.55552e39 q^{81} -3.46253e39 q^{82} +1.80861e39 q^{83} +2.18300e39 q^{84} -1.73593e39 q^{85} -1.82505e38 q^{86} +2.79595e39 q^{87} +7.07980e39 q^{88} -7.15901e39 q^{89} -6.39311e39 q^{90} +8.01623e39 q^{91} +9.29284e39 q^{92} +1.78745e40 q^{93} -8.08920e40 q^{94} -1.39076e40 q^{95} +4.74757e40 q^{96} +7.50364e40 q^{97} -8.67045e40 q^{98} +1.70011e40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 344688 q^{2} - 10820953044 q^{3} + 6271704903936 q^{4} - 212302350281550 q^{5} + 49\!\cdots\!76 q^{6}+ \cdots + 13\!\cdots\!19 q^{9}+O(q^{10}) \) 3 * q - 344688 * q^2 - 10820953044 * q^3 + 6271704903936 * q^4 - 212302350281550 * q^5 + 4970194114982976 * q^6 + 57878416258239192 * q^7 - 3555831711183237120 * q^8 + 13277004110931878919 * q^9	\( 3 q - 344688 q^{2} - 10820953044 q^{3} + 6271704903936 q^{4} - 212302350281550 q^{5} + 49\!\cdots\!76 q^{6}+ \cdots + 45\!\cdots\!28 q^{99}+O(q^{100}) \) 3 * q - 344688 * q^2 - 10820953044 * q^3 + 6271704903936 * q^4 - 212302350281550 * q^5 + 4970194114982976 * q^6 + 57878416258239192 * q^7 - 3555831711183237120 * q^8 + 13277004110931878919 * q^9 - 911610678410074173600 * q^10 - 3064080929502798535164 * q^11 - 71233189317945674062848 * q^12 - 98515763053518962936694 * q^13 - 663773359066872932212608 * q^14 + 2322231962154213782968200 * q^15 + 13217913642093764057038848 * q^16 + 35582277130790298867301302 * q^17 - 51949630971262524069430704 * q^18 - 233456308095243376865478180 * q^19 - 1234817679506740618000857600 * q^20 - 784315067894306487816760224 * q^21 + 10093688647003206881596695744 * q^22 + 2812708670812770779627026056 * q^23 + 36949405163940557660187279360 * q^24 - 12630087813294771903109831875 * q^25 - 445502868787427067716672131104 * q^26 + 40981593702376529051426180280 * q^27 + 526606706694181610802628184064 * q^28 - 12736322664295346653179017670 * q^29 + 6115742110948196616210957398400 * q^30 - 55977552834365071134409017504 * q^31 - 14842037794660482009412112744448 * q^32 - 13829226714693448959900097020528 * q^33 - 42547131667082319398961759011808 * q^34 + 35330944415319146254058128592400 * q^35 + 209583308279267044115700704156928 * q^36 + 4945769903781582545269841455122 * q^37 + 384288369224763756133358504473920 * q^38 - 546470556552953849463965686898712 * q^39 - 1326138456985596139721995183104000 * q^40 - 3123151500646359746292805811918274 * q^41 + 5023322329604694017661024056308224 * q^42 + 1491980858362212236675453498061156 * q^43 + 6827579920847638909574240093432832 * q^44 - 3706804708974790460103758635956150 * q^45 + 34089155258950859800971794327519616 * q^46 - 63038106682044077762675687404413168 * q^47 - 48906179099557375982971001333612544 * q^48 - 97136113131667199274890334287198229 * q^49 + 286202165340727366859498513545830000 * q^50 - 157319866621422817701623275797858024 * q^51 + 364999309722184195149034320029732352 * q^52 + 79896749344137562310547533743021506 * q^53 + 279506543662409583024224141017979520 * q^54 - 1107430856215374719020572615529578600 * q^55 - 1507500925934438536531619079138017280 * q^56 - 120534128028213908789981458568129040 * q^57 + 1060511497310363735425511566792954080 * q^58 + 192512048683375799719343226678403860 * q^59 + 5905677886285900358494072637173094400 * q^60 + 8740556115036354715092732710435455386 * q^61 - 12005332293025961804297174175449366016 * q^62 + 4195060549596204507618981258341049336 * q^63 - 28669651485797320669854651690478731264 * q^64 + 23272939413910136331858458170260680700 * q^65 - 70374114793184440562716940658640274688 * q^66 + 11266872945514675454702655007279407852 * q^67 + 95413181576279049358373233907724317184 * q^68 + 110718129232411678126981084073658946848 * q^69 + 59324379124057015483688060122385068800 * q^70 - 140970915469820223119231433051520161384 * q^71 - 178095780793081630529589944776993320960 * q^72 + 45825493210252135256288871746499029406 * q^73 - 255935787825178849200244145003411599008 * q^74 - 247029389196459510298088488221820147500 * q^75 + 26100578647791289060370838422069130240 * q^76 - 429017620126390531124795910645506217696 * q^77 + 3378623821652934155171000156043557135232 * q^78 - 520184835554750143118446358634240850320 * q^79 + 715918562852781559130521454428746547200 * q^80 - 3191652631710460747876906046824191542997 * q^81 - 579816777788457983576303882284492608096 * q^82 - 619777491338381742927488037142663372644 * q^83 - 4198672691855986319203859063793898610688 * q^84 - 106299433069331216483654652405294143100 * q^85 - 4751113477095326918262488958359640807744 * q^86 + 13958176049210326842816445061163645008040 * q^87 + 18329036816788093472347699011602935234560 * q^88 - 142389067128374093799211866144944441010 * q^89 - 8753545150081132110036071066039970208800 * q^90 + 25080596935320871627133801126628392473296 * q^91 - 67617289414955565381239604024555789723648 * q^92 + 3477058704647981071307340824432458334592 * q^93 - 53008068396962431152763933809330449227008 * q^94 - 33170437179755379504247502944935502503000 * q^95 + 95174464657114272630879818889875681181696 * q^96 + 116011691364103339137369463947331771078182 * q^97 - 38494567059701712876195969460820421029616 * q^98 + 45849669342635847189814810549498192693428 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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