LMFDB - Embedded newform 1.42.a.a.1.2

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			1.2
Root			$698.922$ 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)

$f(q)$	$=$	$q-81363.7 q^{2} +3.82217e9 q^{3} -2.19240e12 q^{4} +9.10518e13 q^{5} -3.10986e14 q^{6} -1.69829e16 q^{7} +3.57303e17 q^{8} -2.18640e19 q^{9} +O(q^{10})$	\(q-81363.7 q^{2} +3.82217e9 q^{3} -2.19240e12 q^{4} +9.10518e13 q^{5} -3.10986e14 q^{6} -1.69829e16 q^{7} +3.57303e17 q^{8} -2.18640e19 q^{9} -7.40831e18 q^{10} -3.48555e21 q^{11} -8.37973e21 q^{12} -1.03131e23 q^{13} +1.38179e21 q^{14} +3.48015e23 q^{15} +4.79207e24 q^{16} +1.01608e25 q^{17} +1.77894e24 q^{18} -1.72697e26 q^{19} -1.99622e26 q^{20} -6.49115e25 q^{21} +2.83598e26 q^{22} +1.09881e28 q^{23} +1.36567e27 q^{24} -3.71843e28 q^{25} +8.39114e27 q^{26} -2.22974e29 q^{27} +3.72334e28 q^{28} +1.22079e30 q^{29} -2.83158e28 q^{30} +5.57694e29 q^{31} -1.17562e30 q^{32} -1.33224e31 q^{33} -8.26720e29 q^{34} -1.54633e30 q^{35} +4.79348e31 q^{36} +1.14515e32 q^{37} +1.40513e31 q^{38} -3.94185e32 q^{39} +3.25331e31 q^{40} -6.17804e32 q^{41} +5.28145e30 q^{42} -1.51443e32 q^{43} +7.64174e33 q^{44} -1.99076e33 q^{45} -8.94030e32 q^{46} -1.94739e34 q^{47} +1.83161e34 q^{48} -4.42792e34 q^{49} +3.02545e33 q^{50} +3.88362e34 q^{51} +2.26105e35 q^{52} -1.38685e35 q^{53} +1.81420e34 q^{54} -3.17366e35 q^{55} -6.06805e33 q^{56} -6.60078e35 q^{57} -9.93283e34 q^{58} +2.19974e36 q^{59} -7.62989e35 q^{60} +2.83478e36 q^{61} -4.53761e34 q^{62} +3.71315e35 q^{63} -1.04422e37 q^{64} -9.39028e36 q^{65} +1.08396e36 q^{66} +2.71602e37 q^{67} -2.22766e37 q^{68} +4.19982e37 q^{69} +1.25815e35 q^{70} +4.91576e37 q^{71} -7.81208e36 q^{72} -2.29426e38 q^{73} -9.31739e36 q^{74} -1.42125e38 q^{75} +3.78622e38 q^{76} +5.91949e37 q^{77} +3.20723e37 q^{78} +1.69414e38 q^{79} +4.36327e38 q^{80} -5.47960e37 q^{81} +5.02668e37 q^{82} -3.52307e39 q^{83} +1.42312e38 q^{84} +9.25158e38 q^{85} +1.23220e37 q^{86} +4.66608e39 q^{87} -1.24540e39 q^{88} +6.37675e39 q^{89} +1.61976e38 q^{90} +1.75147e39 q^{91} -2.40903e40 q^{92} +2.13160e39 q^{93} +1.58447e39 q^{94} -1.57244e40 q^{95} -4.49341e39 q^{96} +3.79303e40 q^{97} +3.60272e39 q^{98} +7.62083e40 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−81363.7	−0.0548676	−0.0274338	−	0.999624i	$-0.508734\pi$
$2$	−81363.7	−0.0548676	−0.0274338	+	0.999624i	$0.508734\pi$
$3$	3.82217e9	0.632884	0.316442	−	0.948612i	$-0.397512\pi$
$3$	3.82217e9	0.632884	0.316442	+	0.948612i	$0.397512\pi$
$4$	−2.19240e12	−0.996990
$5$	9.10518e13	0.426976	0.213488	−	0.976946i	$-0.431518\pi$
$5$	9.10518e13	0.426976	0.213488	+	0.976946i	$0.431518\pi$
$6$	−3.10986e14	−0.0347248
$7$	−1.69829e16	−0.0804457	−0.0402228	−	0.999191i	$-0.512807\pi$
$7$	−1.69829e16	−0.0804457	−0.0402228	+	0.999191i	$0.512807\pi$
$8$	3.57303e17	0.109570
$9$	−2.18640e19	−0.599458
$10$	−7.40831e18	−0.0234271
$11$	−3.48555e21	−1.56215	−0.781073	−	0.624440i	$-0.785327\pi$
$11$	−3.48555e21	−1.56215	−0.781073	+	0.624440i	$0.785327\pi$
$12$	−8.37973e21	−0.630978
$13$	−1.03131e23	−1.50505	−0.752526	−	0.658563i	$-0.771165\pi$
$13$	−1.03131e23	−1.50505	−0.752526	+	0.658563i	$0.771165\pi$
$14$	1.38179e21	0.00441386
$15$	3.48015e23	0.270226
$16$	4.79207e24	0.990978
$17$	1.01608e25	0.606352	0.303176	−	0.952935i	$-0.401953\pi$
$17$	1.01608e25	0.606352	0.303176	+	0.952935i	$0.401953\pi$
$18$	1.77894e24	0.0328908
$19$	−1.72697e26	−1.05399	−0.526995	−	0.849868i	$-0.676681\pi$
$19$	−1.72697e26	−1.05399	−0.526995	+	0.849868i	$0.676681\pi$
$20$	−1.99622e26	−0.425691
$21$	−6.49115e25	−0.0509127
$22$	2.83598e26	0.0857112
$23$	1.09881e28	1.33506	0.667530	−	0.744583i	$-0.267352\pi$
$23$	1.09881e28	1.33506	0.667530	+	0.744583i	$0.267352\pi$
$24$	1.36567e27	0.0693451
$25$	−3.71843e28	−0.817692
$26$	8.39114e27	0.0825786
$27$	−2.22974e29	−1.01227
$28$	3.72334e28	0.0802035
$29$	1.22079e30	1.28081	0.640403	−	0.768039i	$-0.278767\pi$
$29$	1.22079e30	1.28081	0.640403	+	0.768039i	$0.278767\pi$
$30$	−2.83158e28	−0.0148267
$31$	5.57694e29	0.149101	0.0745506	−	0.997217i	$-0.476248\pi$
$31$	5.57694e29	0.149101	0.0745506	+	0.997217i	$0.476248\pi$
$32$	−1.17562e30	−0.163943
$33$	−1.33224e31	−0.988657
$34$	−8.26720e29	−0.0332691
$35$	−1.54633e30	−0.0343484
$36$	4.79348e31	0.597654
$37$	1.14515e32	0.814194	0.407097	−	0.913385i	$-0.366541\pi$
$37$	1.14515e32	0.814194	0.407097	+	0.913385i	$0.366541\pi$
$38$	1.40513e31	0.0578299
$39$	−3.94185e32	−0.952522
$40$	3.25331e31	0.0467838
$41$	−6.17804e32	−0.535527	−0.267764	−	0.963485i	$-0.586285\pi$
$41$	−6.17804e32	−0.535527	−0.267764	+	0.963485i	$0.586285\pi$
$42$	5.28145e30	0.00279346
$43$	−1.51443e32	−0.0494478	−0.0247239	−	0.999694i	$-0.507871\pi$
$43$	−1.51443e32	−0.0494478	−0.0247239	+	0.999694i	$0.507871\pi$
$44$	7.64174e33	1.55744
$45$	−1.99076e33	−0.255954
$46$	−8.94030e32	−0.0732515
$47$	−1.94739e34	−1.02671	−0.513354	−	0.858177i	$-0.671597\pi$
$47$	−1.94739e34	−1.02671	−0.513354	+	0.858177i	$0.671597\pi$
$48$	1.83161e34	0.627174
$49$	−4.42792e34	−0.993528
$50$	3.02545e33	0.0448648
$51$	3.88362e34	0.383750
$52$	2.26105e35	1.50052
$53$	−1.38685e35	−0.622837	−0.311418	−	0.950273i	$-0.600804\pi$
$53$	−1.38685e35	−0.622837	−0.311418	+	0.950273i	$0.600804\pi$
$54$	1.81420e34	0.0555409
$55$	−3.17366e35	−0.666999
$56$	−6.06805e33	−0.00881443
$57$	−6.60078e35	−0.667053
$58$	−9.93283e34	−0.0702747
$59$	2.19974e36	1.09624	0.548119	−	0.836400i	$-0.315344\pi$
$59$	2.19974e36	1.09624	0.548119	+	0.836400i	$0.315344\pi$
$60$	−7.62989e35	−0.269413
$61$	2.83478e36	0.713277	0.356639	−	0.934242i	$-0.383923\pi$
$61$	2.83478e36	0.713277	0.356639	+	0.934242i	$0.383923\pi$
$62$	−4.53761e34	−0.00818083
$63$	3.71315e35	0.0482238
$64$	−1.04422e37	−0.981983
$65$	−9.39028e36	−0.642621
$66$	1.08396e36	0.0542452
$67$	2.71602e37	0.998617	0.499308	−	0.866424i	$-0.333587\pi$
$67$	2.71602e37	0.998617	0.499308	+	0.866424i	$0.333587\pi$
$68$	−2.22766e37	−0.604526
$69$	4.19982e37	0.844937
$70$	1.25815e35	0.00188461
$71$	4.91576e37	0.550548	0.275274	−	0.961366i	$-0.411231\pi$
$71$	4.91576e37	0.550548	0.275274	+	0.961366i	$0.411231\pi$
$72$	−7.81208e36	−0.0656827
$73$	−2.29426e38	−1.45386	−0.726932	−	0.686709i	$-0.759055\pi$
$73$	−2.29426e38	−1.45386	−0.726932	+	0.686709i	$0.759055\pi$
$74$	−9.31739e36	−0.0446729
$75$	−1.42125e38	−0.517504
$76$	3.78622e38	1.05082
$77$	5.91949e37	0.125668
$78$	3.20723e37	0.0522626
$79$	1.69414e38	0.212615	0.106307	−	0.994333i	$-0.466097\pi$
$79$	1.69414e38	0.212615	0.106307	+	0.994333i	$0.466097\pi$
$80$	4.36327e38	0.423124
$81$	−5.47960e37	−0.0411913
$82$	5.02668e37	0.0293831
$83$	−3.52307e39	−1.60628	−0.803138	−	0.595793i	$-0.796838\pi$
$83$	−3.52307e39	−1.60628	−0.803138	+	0.595793i	$0.796838\pi$
$84$	1.42312e38	0.0507595
$85$	9.25158e38	0.258898
$86$	1.23220e37	0.00271308
$87$	4.66608e39	0.810601
$88$	−1.24540e39	−0.171164
$89$	6.37675e39	0.695192	0.347596	−	0.937644i	$-0.386998\pi$
$89$	6.37675e39	0.695192	0.347596	+	0.937644i	$0.386998\pi$
$90$	1.61976e38	0.0140436
$91$	1.75147e39	0.121075
$92$	−2.40903e40	−1.33104
$93$	2.13160e39	0.0943638
$94$	1.58447e39	0.0563330
$95$	−1.57244e40	−0.450029
$96$	−4.49341e39	−0.103757
$97$	3.79303e40	0.708216	0.354108	−	0.935205i	$-0.384785\pi$
$97$	3.79303e40	0.708216	0.354108	+	0.935205i	$0.384785\pi$
$98$	3.60272e39	0.0545125
$99$	7.62083e40	0.936441
$100$	8.15230e40	0.815230
$101$	−2.06559e41	−1.68444	−0.842222	−	0.539131i	$-0.818753\pi$
$101$	−2.06559e41	−1.68444	−0.842222	+	0.539131i	$0.818753\pi$
$102$	−3.15986e39	−0.0210554
$103$	−2.70863e40	−0.147770	−0.0738851	−	0.997267i	$-0.523540\pi$
$103$	−2.70863e40	−0.147770	−0.0738851	+	0.997267i	$0.523540\pi$
$104$	−3.68491e40	−0.164909
$105$	−5.91031e39	−0.0217385
$106$	1.12839e40	0.0341736
$107$	−3.86524e41	−0.965626	−0.482813	−	0.875723i	$-0.660385\pi$
$107$	−3.86524e41	−0.965626	−0.482813	+	0.875723i	$0.660385\pi$
$108$	4.88849e41	1.00922
$109$	5.41460e41	0.925387	0.462693	−	0.886518i	$-0.346883\pi$
$109$	5.41460e41	0.925387	0.462693	+	0.886518i	$0.346883\pi$
$110$	2.58221e40	0.0365966
$111$	4.37696e41	0.515290
$112$	−8.13834e40	−0.0797198
$113$	−1.99438e42	−1.62817	−0.814086	−	0.580744i	$-0.802762\pi$
$113$	−1.99438e42	−1.62817	−0.814086	+	0.580744i	$0.802762\pi$
$114$	5.37064e40	0.0365996
$115$	1.00048e42	0.570038
$116$	−2.67647e42	−1.27695
$117$	2.25487e42	0.902216
$118$	−1.78979e41	−0.0601479
$119$	−1.72560e41	−0.0487784
$120$	1.24347e41	0.0296087
$121$	7.17056e42	1.44030
$122$	−2.30649e41	−0.0391358
$123$	−2.36135e42	−0.338926
$124$	−1.22269e42	−0.148652
$125$	−7.52625e42	−0.776111
$126$	−3.02116e40	−0.00264592
$127$	−7.87891e42	−0.586800	−0.293400	−	0.955990i	$-0.594787\pi$
$127$	−7.87891e42	−0.586800	−0.293400	+	0.955990i	$0.594787\pi$
$128$	3.43483e42	0.217822
$129$	−5.78842e41	−0.0312947
$130$	7.64028e41	0.0352591
$131$	8.75549e42	0.345318	0.172659	−	0.984982i	$-0.444764\pi$
$131$	8.75549e42	0.345318	0.172659	+	0.984982i	$0.444764\pi$
$132$	2.92080e43	0.985680
$133$	2.93290e42	0.0847889
$134$	−2.20985e42	−0.0547917
$135$	−2.03022e43	−0.432215
$136$	3.63048e42	0.0664380
$137$	−1.30585e43	−0.205647	−0.102824	−	0.994700i	$-0.532788\pi$
$137$	−1.30585e43	−0.205647	−0.102824	+	0.994700i	$0.532788\pi$
$138$	−3.41713e42	−0.0463597
$139$	−7.47721e43	−0.874855	−0.437428	−	0.899254i	$-0.644110\pi$
$139$	−7.47721e43	−0.874855	−0.437428	+	0.899254i	$0.644110\pi$
$140$	3.39017e42	0.0342450
$141$	−7.44325e43	−0.649787
$142$	−3.99965e42	−0.0302072
$143$	3.59469e44	2.35111
$144$	−1.04774e44	−0.594050
$145$	1.11155e44	0.546873
$146$	1.86670e43	0.0797701
$147$	−1.69243e44	−0.628788
$148$	−2.51064e44	−0.811743
$149$	3.41118e44	0.960696	0.480348	−	0.877078i	$-0.340510\pi$
$149$	3.41118e44	0.960696	0.480348	+	0.877078i	$0.340510\pi$
$150$	1.15638e43	0.0283942
$151$	−4.86675e44	−1.04282	−0.521412	−	0.853305i	$-0.674595\pi$
$151$	−4.86675e44	−1.04282	−0.521412	+	0.853305i	$0.674595\pi$
$152$	−6.17052e43	−0.115486
$153$	−2.22156e44	−0.363483
$154$	−4.81631e42	−0.00689509
$155$	5.07791e43	0.0636627
$156$	8.64212e44	0.949655
$157$	1.02260e45	0.985744	0.492872	−	0.870102i	$-0.335947\pi$
$157$	1.02260e45	0.985744	0.492872	+	0.870102i	$0.335947\pi$
$158$	−1.37841e43	−0.0116657
$159$	−5.30077e44	−0.394183
$160$	−1.07042e44	−0.0699995
$161$	−1.86609e44	−0.107400
$162$	4.45840e42	0.00226007
$163$	−2.57464e45	−1.15046	−0.575228	−	0.817993i	$-0.695087\pi$
$163$	−2.57464e45	−1.15046	−0.575228	+	0.817993i	$0.695087\pi$
$164$	1.35447e45	0.533915
$165$	−1.21302e45	−0.422133
$166$	2.86650e44	0.0881325
$167$	−1.90182e45	−0.516991	−0.258495	−	0.966013i	$-0.583227\pi$
$167$	−1.90182e45	−0.516991	−0.258495	+	0.966013i	$0.583227\pi$
$168$	−2.31931e43	−0.00557851
$169$	5.94059e45	1.26518
$170$	−7.52743e43	−0.0142051
$171$	3.77586e45	0.631823
$172$	3.32025e44	0.0492989
$173$	−1.22944e45	−0.162092	−0.0810462	−	0.996710i	$-0.525826\pi$
$173$	−1.22944e45	−0.162092	−0.0810462	+	0.996710i	$0.525826\pi$
$174$	−3.79649e44	−0.0444757
$175$	6.31498e44	0.0657797
$176$	−1.67030e46	−1.54805
$177$	8.40776e45	0.693791
$178$	−5.18837e44	−0.0381435
$179$	−2.04820e46	−1.34241	−0.671206	−	0.741271i	$-0.734223\pi$
$179$	−2.04820e46	−1.34241	−0.671206	+	0.741271i	$0.734223\pi$
$180$	4.36455e45	0.255184
$181$	1.96476e46	1.02541	0.512706	−	0.858564i	$-0.328643\pi$
$181$	1.96476e46	1.02541	0.512706	+	0.858564i	$0.328643\pi$
$182$	−1.42506e44	−0.00664309
$183$	1.08350e46	0.451421
$184$	3.92607e45	0.146282
$185$	1.04268e46	0.347641
$186$	−1.73435e44	−0.00517751
$187$	−3.54160e46	−0.947210
$188$	4.26947e46	1.02362
$189$	3.78675e45	0.0814328
$190$	1.27940e45	0.0246920
$191$	−8.46016e46	−1.46620	−0.733102	−	0.680118i	$-0.761928\pi$
$191$	−8.46016e46	−1.46620	−0.733102	+	0.680118i	$0.761928\pi$
$192$	−3.99119e46	−0.621481
$193$	1.25564e46	0.175768	0.0878840	−	0.996131i	$-0.471990\pi$
$193$	1.25564e46	0.175768	0.0878840	+	0.996131i	$0.471990\pi$
$194$	−3.08615e45	−0.0388581
$195$	−3.58912e46	−0.406704
$196$	9.70779e46	0.990538
$197$	1.78208e47	1.63821	0.819103	−	0.573647i	$-0.194472\pi$
$197$	1.78208e47	1.63821	0.819103	+	0.573647i	$0.194472\pi$
$198$	−6.20059e45	−0.0513803
$199$	−1.36946e47	−1.02343	−0.511717	−	0.859154i	$-0.670990\pi$
$199$	−1.36946e47	−1.02343	−0.511717	+	0.859154i	$0.670990\pi$
$200$	−1.32861e46	−0.0895945
$201$	1.03811e47	0.632008
$202$	1.68064e46	0.0924214
$203$	−2.07326e46	−0.103035
$204$	−8.51447e46	−0.382595
$205$	−5.62521e46	−0.228657
$206$	2.20384e45	0.00810780
$207$	−2.40243e47	−0.800312
$208$	−4.94212e47	−1.49147
$209$	6.01945e47	1.64649
$210$	4.80885e44	0.00119274
$211$	1.52351e47	0.342812	0.171406	−	0.985200i	$-0.445169\pi$
$211$	1.52351e47	0.342812	0.171406	+	0.985200i	$0.445169\pi$
$212$	3.04053e47	0.620962
$213$	1.87889e47	0.348433
$214$	3.14490e46	0.0529816
$215$	−1.37892e46	−0.0211130
$216$	−7.96692e46	−0.110915
$217$	−9.47128e45	−0.0119946
$218$	−4.40552e46	−0.0507737
$219$	−8.76904e47	−0.920127
$220$	6.95794e47	0.664991
$221$	−1.04789e48	−0.912591
$222$	−3.56126e46	−0.0282727
$223$	−5.14471e47	−0.372487	−0.186243	−	0.982504i	$-0.559631\pi$
$223$	−5.14471e47	−0.372487	−0.186243	+	0.982504i	$0.559631\pi$
$224$	1.99654e46	0.0131885
$225$	8.12999e47	0.490172
$226$	1.62270e47	0.0893339
$227$	1.86061e47	0.0935677	0.0467838	−	0.998905i	$-0.485103\pi$
$227$	1.86061e47	0.0935677	0.0467838	+	0.998905i	$0.485103\pi$
$228$	1.44716e48	0.665045
$229$	1.08478e48	0.455738	0.227869	−	0.973692i	$-0.426824\pi$
$229$	1.08478e48	0.455738	0.227869	+	0.973692i	$0.426824\pi$
$230$	−8.14030e46	−0.0312766
$231$	2.26253e47	0.0795331
$232$	4.36193e47	0.140338
$233$	−1.31896e48	−0.388541	−0.194270	−	0.980948i	$-0.562234\pi$
$233$	−1.31896e48	−0.388541	−0.194270	+	0.980948i	$0.562234\pi$
$234$	−1.83464e47	−0.0495024
$235$	−1.77313e48	−0.438380
$236$	−4.82271e48	−1.09294
$237$	6.47528e47	0.134560
$238$	1.40401e46	0.00267635
$239$	−2.46866e48	−0.431821	−0.215911	−	0.976413i	$-0.569272\pi$
$239$	−2.46866e48	−0.431821	−0.215911	+	0.976413i	$0.569272\pi$
$240$	1.66771e48	0.267788
$241$	7.05413e48	1.04015	0.520073	−	0.854122i	$-0.325905\pi$
$241$	7.05413e48	1.04015	0.520073	+	0.854122i	$0.325905\pi$
$242$	−5.83423e47	−0.0790258
$243$	7.92309e48	0.986202
$244$	−6.21499e48	−0.711130
$245$	−4.03170e48	−0.424213
$246$	1.92128e47	0.0185961
$247$	1.78105e49	1.58631
$248$	1.99266e47	0.0163370
$249$	−1.34657e49	−1.01659
$250$	6.12364e47	0.0425833
$251$	−1.10391e48	−0.0707330	−0.0353665	−	0.999374i	$-0.511260\pi$
$251$	−1.10391e48	−0.0707330	−0.0353665	+	0.999374i	$0.511260\pi$
$252$	−8.14073e47	−0.0480786
$253$	−3.82995e49	−2.08556
$254$	6.41058e47	0.0321963
$255$	3.53611e48	0.163852
$256$	2.26832e49	0.970031
$257$	1.99173e49	0.786324	0.393162	−	0.919469i	$-0.371381\pi$
$257$	1.99173e49	0.786324	0.393162	+	0.919469i	$0.371381\pi$
$258$	4.70967e46	0.00171707
$259$	−1.94480e48	−0.0654984
$260$	2.05873e49	0.640686
$261$	−2.66915e49	−0.767790
$262$	−7.12379e47	−0.0189468
$263$	3.95658e49	0.973255	0.486627	−	0.873610i	$-0.338227\pi$
$263$	3.95658e49	0.973255	0.486627	+	0.873610i	$0.338227\pi$
$264$	−4.76012e48	−0.108327
$265$	−1.26275e49	−0.265936
$266$	−2.38632e47	−0.00465217
$267$	2.43730e49	0.439975
$268$	−5.95460e49	−0.995611
$269$	−7.39690e49	−1.14585	−0.572926	−	0.819607i	$-0.694192\pi$
$269$	−7.39690e49	−1.14585	−0.572926	+	0.819607i	$0.694192\pi$
$270$	1.65186e48	0.0237146
$271$	−2.66721e49	−0.354966	−0.177483	−	0.984124i	$-0.556795\pi$
$271$	−2.66721e49	−0.354966	−0.177483	+	0.984124i	$0.556795\pi$
$272$	4.86913e49	0.600881
$273$	6.69441e48	0.0766263
$274$	1.06249e48	0.0112834
$275$	1.29608e50	1.27735
$276$	−9.20770e49	−0.842393
$277$	1.32709e50	1.12737	0.563684	−	0.825991i	$-0.309384\pi$
$277$	1.32709e50	1.12737	0.563684	+	0.825991i	$0.309384\pi$
$278$	6.08374e48	0.0480012
$279$	−1.21935e49	−0.0893800
$280$	−5.52506e47	−0.00376355
$281$	1.25230e49	0.0792918	0.0396459	−	0.999214i	$-0.487377\pi$
$281$	1.25230e49	0.0792918	0.0396459	+	0.999214i	$0.487377\pi$
$282$	6.05611e48	0.0356522
$283$	−9.97157e49	−0.545936	−0.272968	−	0.962023i	$-0.588005\pi$
$283$	−9.97157e49	−0.545936	−0.272968	+	0.962023i	$0.588005\pi$
$284$	−1.07773e50	−0.548890
$285$	−6.01013e49	−0.284816
$286$	−2.92478e49	−0.129000
$287$	1.04921e49	0.0430808
$288$	2.57038e49	0.0982767
$289$	−1.77564e50	−0.632337
$290$	−9.04402e48	−0.0300056
$291$	1.44976e50	0.448218
$292$	5.02994e50	1.44949
$293$	−3.65149e50	−0.981035	−0.490517	−	0.871431i	$-0.663192\pi$
$293$	−3.65149e50	−0.981035	−0.490517	+	0.871431i	$0.663192\pi$
$294$	1.37702e49	0.0345001
$295$	2.00290e50	0.468067
$296$	4.09166e49	0.0892113
$297$	7.77187e50	1.58131
$298$	−2.77546e49	−0.0527111
$299$	−1.13321e51	−2.00933
$300$	3.11594e50	0.515946
$301$	2.57195e48	0.00397786
$302$	3.95977e49	0.0572173
$303$	−7.89504e50	−1.06606
$304$	−8.27578e50	−1.04448
$305$	2.58112e50	0.304552
$306$	1.80754e49	0.0199434
$307$	1.30418e51	1.34586	0.672932	−	0.739705i	$-0.265035\pi$
$307$	1.30418e51	1.34586	0.672932	+	0.739705i	$0.265035\pi$
$308$	−1.29779e50	−0.125290
$309$	−1.03528e50	−0.0935214
$310$	−4.13157e48	−0.00349302
$311$	3.10188e50	0.245492	0.122746	−	0.992438i	$-0.460830\pi$
$311$	3.10188e50	0.245492	0.122746	+	0.992438i	$0.460830\pi$
$312$	−1.40843e50	−0.104368
$313$	9.82549e50	0.681860	0.340930	−	0.940089i	$-0.389258\pi$
$313$	9.82549e50	0.681860	0.340930	+	0.940089i	$0.389258\pi$
$314$	−8.32028e49	−0.0540854
$315$	3.38089e49	0.0205904
$316$	−3.71423e50	−0.211975
$317$	2.98911e51	1.59892	0.799462	−	0.600717i	$-0.205118\pi$
$317$	2.98911e51	1.59892	0.799462	+	0.600717i	$0.205118\pi$
$318$	4.31291e49	0.0216279
$319$	−4.25514e51	−2.00081
$320$	−9.50784e50	−0.419283
$321$	−1.47736e51	−0.611129
$322$	1.51832e49	0.00589276
$323$	−1.75474e51	−0.639089
$324$	1.20135e50	0.0410673
$325$	3.83486e51	1.23067
$326$	2.09482e50	0.0631227
$327$	2.06955e51	0.585662
$328$	−2.20743e50	−0.0586777
$329$	3.30724e50	0.0825942
$330$	9.86962e49	0.0231614
$331$	−3.54686e51	−0.782294	−0.391147	−	0.920328i	$-0.627922\pi$
$331$	−3.54686e51	−0.782294	−0.391147	+	0.920328i	$0.627922\pi$
$332$	7.72398e51	1.60144
$333$	−2.50377e51	−0.488076
$334$	1.54739e50	0.0283660
$335$	2.47298e51	0.426385
$336$	−3.11061e50	−0.0504534
$337$	−3.30444e51	−0.504295	−0.252147	−	0.967689i	$-0.581137\pi$
$337$	−3.30444e51	−0.504295	−0.252147	+	0.967689i	$0.581137\pi$
$338$	−4.83349e50	−0.0694174
$339$	−7.62286e51	−1.03044
$340$	−2.02832e51	−0.258118
$341$	−1.94387e51	−0.232918
$342$	−3.07218e50	−0.0346666
$343$	1.50888e51	0.160371
$344$	−5.41112e49	−0.00541800
$345$	3.82401e51	0.360768
$346$	1.00032e50	0.00889362
$347$	1.33458e52	1.11838	0.559189	−	0.829040i	$-0.311113\pi$
$347$	1.33458e52	1.11838	0.559189	+	0.829040i	$0.311113\pi$
$348$	−1.02299e52	−0.808161
$349$	5.90464e51	0.439817	0.219908	−	0.975521i	$-0.429424\pi$
$349$	5.90464e51	0.439817	0.219908	+	0.975521i	$0.429424\pi$
$350$	−5.13810e49	−0.00360918
$351$	2.29956e52	1.52352
$352$	4.09768e51	0.256102
$353$	−2.48492e52	−1.46531	−0.732657	−	0.680598i	$-0.761720\pi$
$353$	−2.48492e52	−1.46531	−0.732657	+	0.680598i	$0.761720\pi$
$354$	−6.84087e50	−0.0380666
$355$	4.47589e51	0.235071
$356$	−1.39804e52	−0.693099
$357$	−6.59553e50	−0.0308710
$358$	1.66649e51	0.0736549
$359$	−2.54547e52	−1.06251	−0.531254	−	0.847213i	$-0.678279\pi$
$359$	−2.54547e52	−1.06251	−0.531254	+	0.847213i	$0.678279\pi$
$360$	−7.11304e50	−0.0280449
$361$	2.97723e51	0.110896
$362$	−1.59860e51	−0.0562619
$363$	2.74071e52	0.911542
$364$	−3.83993e51	−0.120710
$365$	−2.08897e52	−0.620765
$366$	−8.81577e50	−0.0247684
$367$	8.12057e51	0.215741	0.107870	−	0.994165i	$-0.465597\pi$
$367$	8.12057e51	0.215741	0.107870	+	0.994165i	$0.465597\pi$
$368$	5.26556e52	1.32301
$369$	1.35077e52	0.321026
$370$	−8.48365e50	−0.0190742
$371$	2.35528e51	0.0501045
$372$	−4.67333e51	−0.0940797
$373$	9.33073e51	0.177781	0.0888903	−	0.996041i	$-0.471668\pi$
$373$	9.33073e51	0.177781	0.0888903	+	0.996041i	$0.471668\pi$
$374$	2.88158e51	0.0519711
$375$	−2.87666e52	−0.491188
$376$	−6.95808e51	−0.112496
$377$	−1.25902e53	−1.92768
$378$	−3.08104e50	−0.00446802
$379$	2.43584e52	0.334614	0.167307	−	0.985905i	$-0.446493\pi$
$379$	2.43584e52	0.334614	0.167307	+	0.985905i	$0.446493\pi$
$380$	3.44742e52	0.448674
$381$	−3.01145e52	−0.371376
$382$	6.88350e51	0.0804471
$383$	5.83695e52	0.646564	0.323282	−	0.946303i	$-0.395214\pi$
$383$	5.83695e52	0.646564	0.323282	+	0.946303i	$0.395214\pi$
$384$	1.31285e52	0.137856
$385$	5.38980e51	0.0536571
$386$	−1.02163e51	−0.00964397
$387$	3.31116e51	0.0296419
$388$	−8.31585e52	−0.706084
$389$	1.42025e53	1.14393	0.571964	−	0.820279i	$-0.306182\pi$
$389$	1.42025e53	1.14393	0.571964	+	0.820279i	$0.306182\pi$
$390$	2.92024e51	0.0223149
$391$	1.11647e53	0.809516
$392$	−1.58211e52	−0.108861
$393$	3.34649e52	0.218546
$394$	−1.44996e52	−0.0898844
$395$	1.54254e52	0.0907814
$396$	−1.67079e53	−0.933622
$397$	−2.90471e53	−1.54133	−0.770667	−	0.637238i	$-0.780077\pi$
$397$	−2.90471e53	−1.54133	−0.770667	+	0.637238i	$0.780077\pi$
$398$	1.11424e52	0.0561534
$399$	1.12100e52	0.0536615
$400$	−1.78190e53	−0.810314
$401$	2.01288e53	0.869677	0.434839	−	0.900508i	$-0.356805\pi$
$401$	2.01288e53	0.869677	0.434839	+	0.900508i	$0.356805\pi$
$402$	−8.44642e51	−0.0346768
$403$	−5.75157e52	−0.224405
$404$	4.52861e53	1.67937
$405$	−4.98927e51	−0.0175877
$406$	1.68688e51	0.00565330
$407$	−3.99149e53	−1.27189
$408$	1.38763e52	0.0420475
$409$	6.23107e53	1.79570	0.897852	−	0.440298i	$-0.145127\pi$
$409$	6.23107e53	1.79570	0.897852	+	0.440298i	$0.145127\pi$
$410$	4.57688e51	0.0125459
$411$	−4.99119e52	−0.130151
$412$	5.93841e52	0.147325
$413$	−3.73580e52	−0.0881876
$414$	1.95471e52	0.0439112
$415$	−3.20782e53	−0.685841
$416$	1.21243e53	0.246742
$417$	−2.85791e53	−0.553682
$418$	−4.89765e52	−0.0903388
$419$	−7.69430e53	−1.35139	−0.675696	−	0.737180i	$-0.736157\pi$
$419$	−7.69430e53	−1.35139	−0.675696	+	0.737180i	$0.736157\pi$
$420$	1.29578e52	0.0216731
$421$	3.14569e53	0.501110	0.250555	−	0.968102i	$-0.419387\pi$
$421$	3.14569e53	0.501110	0.250555	+	0.968102i	$0.419387\pi$
$422$	−1.23959e52	−0.0188093
$423$	4.25779e53	0.615469
$424$	−4.95525e52	−0.0682442
$425$	−3.77822e53	−0.495809
$426$	−1.52873e52	−0.0191177
$427$	−4.81429e52	−0.0573800
$428$	8.47417e53	0.962719
$429$	1.37395e54	1.48798
$430$	1.12194e51	0.00115842
$431$	−5.35565e53	−0.527264	−0.263632	−	0.964623i	$-0.584921\pi$
$431$	−5.35565e53	−0.527264	−0.263632	+	0.964623i	$0.584921\pi$
$432$	−1.06851e54	−1.00314
$433$	1.35139e54	1.20999	0.604993	−	0.796231i	$-0.293176\pi$
$433$	1.35139e54	1.20999	0.604993	+	0.796231i	$0.293176\pi$
$434$	7.70618e50	0.000658112 0
$435$	4.24855e53	0.346107
$436$	−1.18710e54	−0.922601
$437$	−1.89761e54	−1.40714
$438$	7.13482e52	0.0504852
$439$	2.63178e52	0.0177716	0.00888582	−	0.999961i	$-0.497172\pi$
$439$	2.63178e52	0.0177716	0.00888582	+	0.999961i	$0.497172\pi$
$440$	−1.13396e53	−0.0730831
$441$	9.68123e53	0.595579
$442$	8.52606e52	0.0500717
$443$	−9.66050e53	−0.541656	−0.270828	−	0.962628i	$-0.587297\pi$
$443$	−9.66050e53	−0.541656	−0.270828	+	0.962628i	$0.587297\pi$
$444$	−9.59607e53	−0.513739
$445$	5.80615e53	0.296830
$446$	4.18593e52	0.0204375
$447$	1.30381e54	0.608009
$448$	1.77340e53	0.0789962
$449$	−5.56332e53	−0.236747	−0.118373	−	0.992969i	$-0.537768\pi$
$449$	−5.56332e53	−0.236747	−0.118373	+	0.992969i	$0.537768\pi$
$450$	−6.61486e52	−0.0268946
$451$	2.15339e54	0.836571
$452$	4.37249e54	1.62327
$453$	−1.86015e54	−0.659987
$454$	−1.51386e52	−0.00513383
$455$	1.59474e53	0.0516961
$456$	−2.35848e53	−0.0730890
$457$	−2.92141e54	−0.865587	−0.432794	−	0.901493i	$-0.642472\pi$
$457$	−2.92141e54	−0.865587	−0.432794	+	0.901493i	$0.642472\pi$
$458$	−8.82619e52	−0.0250052
$459$	−2.26559e54	−0.613792
$460$	−2.19346e54	−0.568322
$461$	−1.66774e54	−0.413295	−0.206648	−	0.978415i	$-0.566255\pi$
$461$	−1.66774e54	−0.413295	−0.206648	+	0.978415i	$0.566255\pi$
$462$	−1.84088e52	−0.00436379
$463$	−2.72429e54	−0.617793	−0.308896	−	0.951096i	$-0.599960\pi$
$463$	−2.72429e54	−0.617793	−0.308896	+	0.951096i	$0.599960\pi$
$464$	5.85013e54	1.26925
$465$	1.94086e53	0.0402911
$466$	1.07316e53	0.0213183
$467$	4.71337e54	0.896057	0.448028	−	0.894019i	$-0.352126\pi$
$467$	4.71337e54	0.896057	0.448028	+	0.894019i	$0.352126\pi$
$468$	−4.94357e54	−0.899500
$469$	−4.61259e53	−0.0803344
$470$	1.44269e53	0.0240528
$471$	3.90856e54	0.623861
$472$	7.85973e53	0.120115
$473$	5.27864e53	0.0772447
$474$	−5.26853e52	−0.00738301
$475$	6.42163e54	0.861839
$476$	3.78321e53	0.0486315
$477$	3.03222e54	0.373365
$478$	2.00859e53	0.0236930
$479$	−6.42979e54	−0.726639	−0.363320	−	0.931665i	$-0.618357\pi$
$479$	−6.42979e54	−0.726639	−0.363320	+	0.931665i	$0.618357\pi$
$480$	−4.09133e53	−0.0443016
$481$	−1.18101e55	−1.22540
$482$	−5.73950e53	−0.0570703
$483$	−7.13252e53	−0.0679715
$484$	−1.57208e55	−1.43596
$485$	3.45362e54	0.302391
$486$	−6.44652e53	−0.0541105
$487$	2.20621e55	1.77543	0.887714	−	0.460396i	$-0.152292\pi$
$487$	2.20621e55	1.77543	0.887714	+	0.460396i	$0.152292\pi$
$488$	1.01288e54	0.0781538
$489$	−9.84068e54	−0.728104
$490$	3.28034e53	0.0232755
$491$	−2.26714e54	−0.154279	−0.0771395	−	0.997020i	$-0.524579\pi$
$491$	−2.26714e54	−0.154279	−0.0771395	+	0.997020i	$0.524579\pi$
$492$	5.17703e54	0.337906
$493$	1.24042e55	0.776619
$494$	−1.44913e54	−0.0870370
$495$	6.93890e54	0.399838
$496$	2.67251e54	0.147756
$497$	−8.34840e53	−0.0442892
$498$	1.09562e54	0.0557776
$499$	−2.08851e54	−0.102041	−0.0510205	−	0.998698i	$-0.516247\pi$
$499$	−2.08851e54	−0.102041	−0.0510205	+	0.998698i	$0.516247\pi$
$500$	1.65006e55	0.773774
$501$	−7.26909e54	−0.327195
$502$	8.98182e52	0.00388095
$503$	−4.18071e55	−1.73423	−0.867115	−	0.498107i	$-0.834029\pi$
$503$	−4.18071e55	−1.73423	−0.867115	+	0.498107i	$0.834029\pi$
$504$	1.32672e53	0.00528388
$505$	−1.88076e55	−0.719217
$506$	3.11619e54	0.114429
$507$	2.27059e55	0.800712
$508$	1.72738e55	0.585033
$509$	−4.54501e55	−1.47850	−0.739248	−	0.673433i	$-0.764819\pi$
$509$	−4.54501e55	−1.47850	−0.739248	+	0.673433i	$0.764819\pi$
$510$	−2.87711e53	−0.00899017
$511$	3.89632e54	0.116957
$512$	−9.39886e54	−0.271045
$513$	3.85070e55	1.06692
$514$	−1.62055e54	−0.0431437
$515$	−2.46626e54	−0.0630943
$516$	1.26905e54	0.0312005
$517$	6.78774e55	1.60387
$518$	1.58236e53	0.00359374
$519$	−4.69913e54	−0.102586
$520$	−3.35517e54	−0.0704120
$521$	4.52665e55	0.913278	0.456639	−	0.889652i	$-0.349053\pi$
$521$	4.52665e55	0.913278	0.456639	+	0.889652i	$0.349053\pi$
$522$	2.17172e54	0.0421268
$523$	−1.00124e56	−1.86748	−0.933738	−	0.357957i	$-0.883473\pi$
$523$	−1.00124e56	−1.86748	−0.933738	+	0.357957i	$0.883473\pi$
$524$	−1.91956e55	−0.344278
$525$	2.41369e54	0.0416309
$526$	−3.21922e54	−0.0534002
$527$	5.66662e54	0.0904078
$528$	−6.38417e55	−0.979737
$529$	5.29981e55	0.782383
$530$	1.02742e54	0.0145913
$531$	−4.80952e55	−0.657149
$532$	−6.43011e54	−0.0845337
$533$	6.37148e55	0.805996
$534$	−1.98308e54	−0.0241404
$535$	−3.51937e55	−0.412299
$536$	9.70440e54	0.109418
$537$	−7.82857e55	−0.849590
$538$	6.01840e54	0.0628701
$539$	1.54338e56	1.55204
$540$	4.45105e55	0.430914
$541$	1.94080e55	0.180899	0.0904495	−	0.995901i	$-0.471170\pi$
$541$	1.94080e55	0.180899	0.0904495	+	0.995901i	$0.471170\pi$
$542$	2.17014e54	0.0194761
$543$	7.50963e55	0.648966
$544$	−1.19452e55	−0.0994069
$545$	4.93009e55	0.395118
$546$	−5.44682e53	−0.00420430
$547$	−1.89248e56	−1.40699	−0.703495	−	0.710700i	$-0.748378\pi$
$547$	−1.89248e56	−1.40699	−0.703495	+	0.710700i	$0.748378\pi$
$548$	2.86296e55	0.205028
$549$	−6.19798e55	−0.427580
$550$	−1.05454e55	−0.0700853
$551$	−2.10828e56	−1.34996
$552$	1.50061e55	0.0925798
$553$	−2.87714e54	−0.0171039
$554$	−1.07977e55	−0.0618560
$555$	3.98530e55	0.220017
$556$	1.63931e56	0.872222
$557$	−4.31584e55	−0.221327	−0.110663	−	0.993858i	$-0.535298\pi$
$557$	−4.31584e55	−0.221327	−0.110663	+	0.993858i	$0.535298\pi$
$558$	9.92105e53	0.00490407
$559$	1.56185e55	0.0744215
$560$	−7.41011e54	−0.0340385
$561$	−1.35366e56	−0.599474
$562$	−1.01892e54	−0.00435055
$563$	3.50637e56	1.44356	0.721781	−	0.692121i	$-0.243324\pi$
$563$	3.50637e56	1.44356	0.721781	+	0.692121i	$0.243324\pi$
$564$	1.63186e56	0.647831
$565$	−1.81592e56	−0.695191
$566$	8.11324e54	0.0299542
$567$	9.30596e53	0.00331366
$568$	1.75642e55	0.0603235
$569$	3.92278e56	1.29955	0.649775	−	0.760127i	$-0.274863\pi$
$569$	3.92278e56	1.29955	0.649775	+	0.760127i	$0.274863\pi$
$570$	4.89006e54	0.0156271
$571$	3.12164e56	0.962370	0.481185	−	0.876619i	$-0.340206\pi$
$571$	3.12164e56	0.962370	0.481185	+	0.876619i	$0.340206\pi$
$572$	−7.88102e56	−2.34403
$573$	−3.23361e56	−0.927937
$574$	−8.53677e53	−0.00236374
$575$	−4.08584e56	−1.09167
$576$	2.28309e56	0.588658
$577$	5.15710e55	0.128322	0.0641611	−	0.997940i	$-0.479563\pi$
$577$	5.15710e55	0.128322	0.0641611	+	0.997940i	$0.479563\pi$
$578$	1.44473e55	0.0346948
$579$	4.79926e55	0.111241
$580$	−2.43698e56	−0.545227
$581$	5.98320e55	0.129218
$582$	−1.17958e55	−0.0245926
$583$	4.83394e56	0.972962
$584$	−8.19746e55	−0.159300
$585$	2.05310e56	0.385224
$586$	2.97099e55	0.0538270
$587$	−1.62999e56	−0.285170	−0.142585	−	0.989783i	$-0.545541\pi$
$587$	−1.62999e56	−0.285170	−0.142585	+	0.989783i	$0.545541\pi$
$588$	3.71048e56	0.626895
$589$	−9.63123e55	−0.157151
$590$	−1.62963e55	−0.0256817
$591$	6.81139e56	1.03679
$592$	5.48766e56	0.806848
$593$	−6.76525e56	−0.960866	−0.480433	−	0.877031i	$-0.659520\pi$
$593$	−6.76525e56	−0.960866	−0.480433	+	0.877031i	$0.659520\pi$
$594$	−6.32348e55	−0.0867629
$595$	−1.57119e55	−0.0208272
$596$	−7.47868e56	−0.957804
$597$	−5.23429e56	−0.647715
$598$	9.22024e55	0.110247
$599$	8.22842e56	0.950751	0.475376	−	0.879783i	$-0.342312\pi$
$599$	8.22842e56	0.950751	0.475376	+	0.879783i	$0.342312\pi$
$600$	−5.07815e55	−0.0567029
$601$	−1.40310e57	−1.51412	−0.757062	−	0.653343i	$-0.773366\pi$
$601$	−1.40310e57	−1.51412	−0.757062	+	0.653343i	$0.773366\pi$
$602$	−2.09264e53	−0.000218256 0
$603$	−5.93831e56	−0.598629
$604$	1.06699e57	1.03969
$605$	6.52892e56	0.614973
$606$	6.42370e55	0.0584920
$607$	−1.85452e57	−1.63254	−0.816271	−	0.577669i	$-0.803962\pi$
$607$	−1.85452e57	−1.63254	−0.816271	+	0.577669i	$0.803962\pi$
$608$	2.03026e56	0.172794
$609$	−7.92436e55	−0.0652093
$610$	−2.10010e55	−0.0167100
$611$	2.00837e57	1.54525
$612$	4.87056e56	0.362388
$613$	1.52593e57	1.09798	0.548992	−	0.835828i	$-0.315012\pi$
$613$	1.52593e57	1.09798	0.548992	+	0.835828i	$0.315012\pi$
$614$	−1.06113e56	−0.0738443
$615$	−2.15005e56	−0.144713
$616$	2.11505e55	0.0137694
$617$	2.09012e56	0.131621	0.0658105	−	0.997832i	$-0.479037\pi$
$617$	2.09012e56	0.131621	0.0658105	+	0.997832i	$0.479037\pi$
$618$	8.42346e54	0.00513129
$619$	−5.03746e56	−0.296861	−0.148431	−	0.988923i	$-0.547422\pi$
$619$	−5.03746e56	−0.296861	−0.148431	+	0.988923i	$0.547422\pi$
$620$	−1.11328e56	−0.0634710
$621$	−2.45005e57	−1.35144
$622$	−2.52381e55	−0.0134696
$623$	−1.08296e56	−0.0559251
$624$	−1.88896e57	−0.943929
$625$	1.00567e57	0.486311
$626$	−7.99438e55	−0.0374120
$627$	2.30074e57	1.04203
$628$	−2.24196e57	−0.982776
$629$	1.16357e57	0.493688
$630$	−2.75082e54	−0.00112975
$631$	−2.05980e57	−0.818887	−0.409444	−	0.912335i	$-0.634277\pi$
$631$	−2.05980e57	−0.818887	−0.409444	+	0.912335i	$0.634277\pi$
$632$	6.05320e55	0.0232962
$633$	5.82312e56	0.216960
$634$	−2.43205e56	−0.0877291
$635$	−7.17389e56	−0.250549
$636$	1.16214e57	0.392996
$637$	4.56657e57	1.49531
$638$	3.46214e56	0.109779
$639$	−1.07478e57	−0.330030
$640$	3.12747e56	0.0930046
$641$	4.32782e57	1.24646	0.623232	−	0.782037i	$-0.285819\pi$
$641$	4.32782e57	1.24646	0.623232	+	0.782037i	$0.285819\pi$
$642$	1.20203e56	0.0335312
$643$	−2.48467e57	−0.671341	−0.335670	−	0.941980i	$-0.608963\pi$
$643$	−2.48467e57	−0.671341	−0.335670	+	0.941980i	$0.608963\pi$
$644$	4.09123e56	0.107076
$645$	−5.27046e55	−0.0133621
$646$	1.42772e56	0.0350653
$647$	−4.23499e57	−1.00766	−0.503831	−	0.863802i	$-0.668077\pi$
$647$	−4.23499e57	−1.00766	−0.503831	+	0.863802i	$0.668077\pi$
$648$	−1.95788e55	−0.00451333
$649$	−7.66730e57	−1.71248
$650$	−3.12019e56	−0.0675238
$651$	−3.62008e55	−0.00759115
$652$	5.64464e57	1.14699
$653$	−1.80067e57	−0.354580	−0.177290	−	0.984159i	$-0.556733\pi$
$653$	−1.80067e57	−0.354580	−0.177290	+	0.984159i	$0.556733\pi$
$654$	−1.68386e56	−0.0321339
$655$	7.97203e56	0.147442
$656$	−2.96056e57	−0.530695
$657$	5.01618e57	0.871532
$658$	−2.69089e55	−0.00453175
$659$	−6.74103e57	−1.10046	−0.550231	−	0.835012i	$-0.685460\pi$
$659$	−6.74103e57	−1.10046	−0.550231	+	0.835012i	$0.685460\pi$
$660$	2.65944e57	0.420862
$661$	9.42263e57	1.44558	0.722790	−	0.691068i	$-0.242859\pi$
$661$	9.42263e57	1.44558	0.722790	+	0.691068i	$0.242859\pi$
$662$	2.88586e56	0.0429226
$663$	−4.00523e57	−0.577564
$664$	−1.25880e57	−0.176000
$665$	2.67046e56	0.0362028
$666$	2.03716e56	0.0267795
$667$	1.34142e58	1.70995
$668$	4.16957e57	0.515434
$669$	−1.96639e57	−0.235741
$670$	−2.01211e56	−0.0233947
$671$	−9.88079e57	−1.11424
$672$	7.63112e55	0.00834676
$673$	−7.22539e57	−0.766571	−0.383285	−	0.923630i	$-0.625207\pi$
$673$	−7.22539e57	−0.766571	−0.383285	+	0.923630i	$0.625207\pi$
$674$	2.68861e56	0.0276694
$675$	8.29113e57	0.827725
$676$	−1.30242e58	−1.26137
$677$	−9.31845e57	−0.875540	−0.437770	−	0.899087i	$-0.644232\pi$
$677$	−9.31845e57	−0.875540	−0.437770	+	0.899087i	$0.644232\pi$
$678$	6.20224e56	0.0565380
$679$	−6.44167e56	−0.0569729
$680$	3.30562e56	0.0283674
$681$	7.11157e56	0.0592175
$682$	1.58161e56	0.0127796
$683$	1.54469e58	1.21121	0.605603	−	0.795767i	$-0.292932\pi$
$683$	1.54469e58	1.21121	0.605603	+	0.795767i	$0.292932\pi$
$684$	−8.27821e57	−0.629921
$685$	−1.18900e57	−0.0878064
$686$	−1.22768e56	−0.00879915
$687$	4.14622e57	0.288429
$688$	−7.25728e56	−0.0490017
$689$	1.43028e58	0.937401
$690$	−3.11136e56	−0.0197945
$691$	1.40721e58	0.869078	0.434539	−	0.900653i	$-0.356911\pi$
$691$	1.40721e58	0.869078	0.434539	+	0.900653i	$0.356911\pi$
$692$	2.69543e57	0.161604
$693$	−1.29424e57	−0.0753326
$694$	−1.08586e57	−0.0613627
$695$	−6.80814e57	−0.373542
$696$	1.66720e57	0.0888175
$697$	−6.27738e57	−0.324718
$698$	−4.80423e56	−0.0241317
$699$	−5.04130e57	−0.245901
$700$	−1.38450e57	−0.0655817
$701$	−2.16291e58	−0.994991	−0.497495	−	0.867467i	$-0.665747\pi$
$701$	−2.16291e58	−0.994991	−0.497495	+	0.867467i	$0.665747\pi$
$702$	−1.87100e57	−0.0835919
$703$	−1.97765e58	−0.858153
$704$	3.63969e58	1.53400
$705$	−6.77722e57	−0.277443
$706$	2.02182e57	0.0803982
$707$	3.50798e57	0.135506
$708$	−1.84332e58	−0.691702
$709$	−1.27581e58	−0.465090	−0.232545	−	0.972586i	$-0.574705\pi$
$709$	−1.27581e58	−0.465090	−0.232545	+	0.972586i	$0.574705\pi$
$710$	−3.64175e56	−0.0128978
$711$	−3.70407e57	−0.127454
$712$	2.27843e57	0.0761722
$713$	6.12798e57	0.199059
$714$	5.36637e55	0.00169382
$715$	3.27303e58	1.00387
$716$	4.49049e58	1.33837
$717$	−9.43563e57	−0.273293
$718$	2.07109e57	0.0582973
$719$	2.41677e58	0.661138	0.330569	−	0.943782i	$-0.392759\pi$
$719$	2.41677e58	0.661138	0.330569	+	0.943782i	$0.392759\pi$
$720$	−9.53987e57	−0.253645
$721$	4.60005e56	0.0118875
$722$	−2.42238e56	−0.00608458
$723$	2.69621e58	0.658291
$724$	−4.30754e58	−1.02232
$725$	−4.53944e58	−1.04730
$726$	−2.22994e57	−0.0500141
$727$	−4.92924e58	−1.07479	−0.537396	−	0.843330i	$-0.680592\pi$
$727$	−4.92924e58	−1.07479	−0.537396	+	0.843330i	$0.680592\pi$
$728$	6.25805e56	0.0132662
$729$	3.22819e58	0.665342
$730$	1.69966e57	0.0340599
$731$	−1.53878e57	−0.0299828
$732$	−2.37547e58	−0.450062
$733$	4.81159e58	0.886456	0.443228	−	0.896409i	$-0.353833\pi$
$733$	4.81159e58	0.886456	0.443228	+	0.896409i	$0.353833\pi$
$734$	−6.60720e56	−0.0118372
$735$	−1.54098e58	−0.268477
$736$	−1.29178e58	−0.218873
$737$	−9.46682e58	−1.55999
$738$	−1.09904e57	−0.0176139
$739$	9.13074e58	1.42330	0.711648	−	0.702537i	$-0.247949\pi$
$739$	9.13074e58	1.42330	0.711648	+	0.702537i	$0.247949\pi$
$740$	−2.28598e58	−0.346595
$741$	6.80746e58	1.00395
$742$	−1.91634e56	−0.00274911
$743$	1.50391e57	0.0209870	0.0104935	−	0.999945i	$-0.496660\pi$
$743$	1.50391e57	0.0209870	0.0104935	+	0.999945i	$0.496660\pi$
$744$	7.61627e56	0.0103394
$745$	3.10594e58	0.410194
$746$	−7.59183e56	−0.00975439
$747$	7.70285e58	0.962895
$748$	7.76461e58	0.944358
$749$	6.56431e57	0.0776804
$750$	2.34056e57	0.0269503
$751$	−1.25195e59	−1.40272	−0.701358	−	0.712809i	$-0.747423\pi$
$751$	−1.25195e59	−1.40272	−0.701358	+	0.712809i	$0.747423\pi$
$752$	−9.33204e58	−1.01745
$753$	−4.21933e57	−0.0447658
$754$	1.02438e58	0.105767
$755$	−4.43126e58	−0.445261
$756$	−8.30208e57	−0.0811876
$757$	1.29607e58	0.123357	0.0616784	−	0.998096i	$-0.480355\pi$
$757$	1.29607e58	0.123357	0.0616784	+	0.998096i	$0.480355\pi$
$758$	−1.98189e57	−0.0183595
$759$	−1.46387e59	−1.31991
$760$	−5.61837e57	−0.0493096
$761$	6.14300e58	0.524801	0.262401	−	0.964959i	$-0.415486\pi$
$761$	6.14300e58	0.524801	0.262401	+	0.964959i	$0.415486\pi$
$762$	2.45023e57	0.0203765
$763$	−9.19557e57	−0.0744433
$764$	1.85481e59	1.46179
$765$	−2.02277e58	−0.155198
$766$	−4.74916e57	−0.0354754
$767$	−2.26862e59	−1.64989
$768$	8.66991e58	0.613917
$769$	1.38280e59	0.953388	0.476694	−	0.879069i	$-0.341835\pi$
$769$	1.38280e59	0.953388	0.476694	+	0.879069i	$0.341835\pi$
$770$	−4.38534e56	−0.00294404
$771$	7.61272e58	0.497651
$772$	−2.75287e58	−0.175239
$773$	1.19232e59	0.739119	0.369560	−	0.929207i	$-0.379509\pi$
$773$	1.19232e59	0.739119	0.369560	+	0.929207i	$0.379509\pi$
$774$	−2.69409e56	−0.00162638
$775$	−2.07375e58	−0.121919
$776$	1.35526e58	0.0775992
$777$	−7.43336e57	−0.0414529
$778$	−1.15557e58	−0.0627646
$779$	1.06693e59	0.564440
$780$	7.86880e58	0.405480
$781$	−1.71342e59	−0.860036
$782$	−9.08405e57	−0.0444162
$783$	−2.72205e59	−1.29652
$784$	−2.12189e59	−0.984565
$785$	9.31098e58	0.420889
$786$	−2.72283e57	−0.0119911
$787$	2.56981e59	1.10260	0.551301	−	0.834307i	$-0.314132\pi$
$787$	2.56981e59	1.10260	0.551301	+	0.834307i	$0.314132\pi$
$788$	−3.90703e59	−1.63327
$789$	1.51227e59	0.615957
$790$	−1.25507e57	−0.00498096
$791$	3.38704e58	0.130979
$792$	2.72294e58	0.102606
$793$	−2.92355e59	−1.07352
$794$	2.36338e58	0.0845693
$795$	−4.82645e58	−0.168307
$796$	3.00240e59	1.02035
$797$	5.39123e59	1.78563	0.892816	−	0.450421i	$-0.148726\pi$
$797$	5.39123e59	1.78563	0.892816	+	0.450421i	$0.148726\pi$
$798$	−9.12091e56	−0.00294428
$799$	−1.97870e59	−0.622547
$800$	4.37145e58	0.134054
$801$	−1.39422e59	−0.416738
$802$	−1.63775e58	−0.0477171
$803$	7.99677e59	2.27115
$804$	−2.27595e59	−0.630106
$805$	−1.69911e58	−0.0458571
$806$	4.67969e57	0.0123126
$807$	−2.82722e59	−0.725190
$808$	−7.38042e58	−0.184565
$809$	−4.68209e59	−1.14155	−0.570775	−	0.821106i	$-0.693357\pi$
$809$	−4.68209e59	−1.14155	−0.570775	+	0.821106i	$0.693357\pi$
$810$	4.05946e56	0.000964995 0
$811$	5.03719e58	0.116751	0.0583756	−	0.998295i	$-0.481408\pi$
$811$	5.03719e58	0.116751	0.0583756	+	0.998295i	$0.481408\pi$
$812$	4.54543e58	0.102725
$813$	−1.01945e59	−0.224652
$814$	3.24763e58	0.0697856
$815$	−2.34425e59	−0.491217
$816$	1.86106e59	0.380288
$817$	2.61539e58	0.0521175
$818$	−5.06983e58	−0.0985259
$819$	−3.82942e58	−0.0725793
$820$	1.23327e59	0.227969
$821$	−7.92919e59	−1.42953	−0.714766	−	0.699363i	$-0.753467\pi$
$821$	−7.92919e59	−1.42953	−0.714766	+	0.699363i	$0.753467\pi$
$822$	4.06102e57	0.00714106
$823$	5.91534e58	0.101457	0.0507287	−	0.998712i	$-0.483846\pi$
$823$	5.91534e58	0.101457	0.0507287	+	0.998712i	$0.483846\pi$
$824$	−9.67802e57	−0.0161912
$825$	4.95383e59	0.808416
$826$	3.03958e57	0.00483864
$827$	9.18303e59	1.42601	0.713006	−	0.701158i	$-0.247333\pi$
$827$	9.18303e59	1.42601	0.713006	+	0.701158i	$0.247333\pi$
$828$	5.26711e59	0.797903
$829$	−6.10924e59	−0.902858	−0.451429	−	0.892307i	$-0.649086\pi$
$829$	−6.10924e59	−0.902858	−0.451429	+	0.892307i	$0.649086\pi$
$830$	2.61000e58	0.0376304
$831$	5.07236e59	0.713493
$832$	1.07692e60	1.47793
$833$	−4.49912e59	−0.602428
$834$	2.32531e58	0.0303792
$835$	−1.73164e59	−0.220743
$836$	−1.31971e60	−1.64153
$837$	−1.24351e59	−0.150931
$838$	6.26037e58	0.0741476
$839$	−1.07495e60	−1.24242	−0.621210	−	0.783644i	$-0.713359\pi$
$839$	−1.07495e60	−1.24242	−0.621210	+	0.783644i	$0.713359\pi$
$840$	−2.11177e57	−0.00238189
$841$	5.81851e59	0.640463
$842$	−2.55945e58	−0.0274947
$843$	4.78649e58	0.0501825
$844$	−3.34016e59	−0.341780
$845$	5.40902e59	0.540202
$846$	−3.46429e58	−0.0337693
$847$	−1.21777e59	−0.115866
$848$	−6.64589e59	−0.617217
$849$	−3.81130e59	−0.345514
$850$	3.07410e58	0.0272038
$851$	1.25830e60	1.08700
$852$	−4.11928e59	−0.347384
$853$	−7.04560e59	−0.580047	−0.290023	−	0.957020i	$-0.593663\pi$
$853$	−7.04560e59	−0.580047	−0.290023	+	0.957020i	$0.593663\pi$
$854$	3.91709e57	0.00314830
$855$	3.43799e59	0.269773
$856$	−1.38106e59	−0.105804
$857$	1.18884e60	0.889234	0.444617	−	0.895721i	$-0.353340\pi$
$857$	1.18884e60	0.889234	0.444617	+	0.895721i	$0.353340\pi$
$858$	−1.11790e59	−0.0816418
$859$	2.54870e60	1.81744	0.908718	−	0.417410i	$-0.137062\pi$
$859$	2.54870e60	1.81744	0.908718	+	0.417410i	$0.137062\pi$
$860$	3.02315e58	0.0210495
$861$	4.01026e58	0.0272651
$862$	4.35756e58	0.0289297
$863$	−1.01594e60	−0.658640	−0.329320	−	0.944218i	$-0.606819\pi$
$863$	−1.01594e60	−0.658640	−0.329320	+	0.944218i	$0.606819\pi$
$864$	2.62132e59	0.165954
$865$	−1.11943e59	−0.0692095
$866$	−1.09954e59	−0.0663890
$867$	−6.78679e59	−0.400196
$868$	2.07649e58	0.0119584
$869$	−5.90501e59	−0.332135
$870$	−3.45677e58	−0.0189901
$871$	−2.80106e60	−1.50297
$872$	1.93465e59	0.101395
$873$	−8.29309e59	−0.424546
$874$	1.54396e59	0.0772064
$875$	1.27818e59	0.0624347
$876$	1.92253e60	0.917357
$877$	−3.07649e59	−0.143405	−0.0717023	−	0.997426i	$-0.522843\pi$
$877$	−3.07649e59	−0.143405	−0.0717023	+	0.997426i	$0.522843\pi$
$878$	−2.14132e57	−0.000975087 0
$879$	−1.39566e60	−0.620881
$880$	−1.52084e60	−0.660981
$881$	1.76559e60	0.749694	0.374847	−	0.927087i	$-0.377695\pi$
$881$	1.76559e60	0.749694	0.374847	+	0.927087i	$0.377695\pi$
$882$	−7.87701e58	−0.0326780
$883$	1.02366e60	0.414918	0.207459	−	0.978244i	$-0.433481\pi$
$883$	1.02366e60	0.414918	0.207459	+	0.978244i	$0.433481\pi$
$884$	2.29741e60	0.909843
$885$	7.65542e59	0.296232
$886$	7.86015e58	0.0297193
$887$	−4.52674e59	−0.167244	−0.0836221	−	0.996498i	$-0.526649\pi$
$887$	−4.52674e59	−0.167244	−0.0836221	+	0.996498i	$0.526649\pi$
$888$	1.56390e59	0.0564604
$889$	1.33807e59	0.0472055
$890$	−4.72410e58	−0.0162864
$891$	1.90994e59	0.0643468
$892$	1.12793e60	0.371366
$893$	3.36309e60	1.08214
$894$	−1.06083e59	−0.0333600
$895$	−1.86493e60	−0.573178
$896$	−5.83335e58	−0.0175228
$897$	−4.33133e60	−1.27167
$898$	4.52652e58	0.0129897
$899$	6.80829e59	0.190970
$900$	−1.78242e60	−0.488696
$901$	−1.40915e60	−0.377658
$902$	−1.75208e59	−0.0459007
$903$	9.83043e57	0.00251752
$904$	−7.12599e59	−0.178399
$905$	1.78895e60	0.437826
$906$	1.51349e59	0.0362119
$907$	−6.39985e60	−1.49699	−0.748497	−	0.663138i	$-0.769224\pi$
$907$	−6.39985e60	−1.49699	−0.748497	+	0.663138i	$0.769224\pi$
$908$	−4.07921e59	−0.0932860
$909$	4.51622e60	1.00975
$910$	−1.29754e58	−0.00283644
$911$	−3.60826e60	−0.771208	−0.385604	−	0.922664i	$-0.626007\pi$
$911$	−3.60826e60	−0.771208	−0.385604	+	0.922664i	$0.626007\pi$
$912$	−3.16314e60	−0.661035
$913$	1.22798e61	2.50924
$914$	2.37697e59	0.0474927
$915$	9.86547e59	0.192746
$916$	−2.37828e60	−0.454366
$917$	−1.48694e59	−0.0277793
$918$	1.84337e59	0.0336773
$919$	6.99835e60	1.25034	0.625170	−	0.780489i	$-0.285030\pi$
$919$	6.99835e60	1.25034	0.625170	+	0.780489i	$0.285030\pi$
$920$	3.57475e59	0.0624591
$921$	4.98479e60	0.851775
$922$	1.35694e59	0.0226765
$923$	−5.06969e60	−0.828603
$924$	−4.96037e59	−0.0792937
$925$	−4.25817e60	−0.665760
$926$	2.21658e59	0.0338968
$927$	5.92217e59	0.0885821
$928$	−1.43519e60	−0.209979
$929$	−1.28627e61	−1.84081	−0.920406	−	0.390963i	$-0.872142\pi$
$929$	−1.28627e61	−1.84081	−0.920406	+	0.390963i	$0.872142\pi$
$930$	−1.57916e58	−0.00221067
$931$	7.64690e60	1.04717
$932$	2.89170e60	0.387371
$933$	1.18559e60	0.155368
$934$	−3.83497e59	−0.0491645
$935$	−3.22469e60	−0.404436
$936$	8.05670e59	0.0988558
$937$	−1.05021e61	−1.26071	−0.630354	−	0.776308i	$-0.717090\pi$
$937$	−1.05021e61	−1.26071	−0.630354	+	0.776308i	$0.717090\pi$
$938$	3.75297e58	0.00440775
$939$	3.75546e60	0.431538
$940$	3.88743e60	0.437060
$941$	−7.41023e60	−0.815163	−0.407581	−	0.913169i	$-0.633628\pi$
$941$	−7.41023e60	−0.815163	−0.407581	+	0.913169i	$0.633628\pi$
$942$	−3.18015e59	−0.0342298
$943$	−6.78847e60	−0.714960
$944$	1.05413e61	1.08635
$945$	3.44790e59	0.0347698
$946$	−4.29490e58	−0.00423823
$947$	5.73646e60	0.553949	0.276974	−	0.960877i	$-0.410668\pi$
$947$	5.73646e60	0.553949	0.276974	+	0.960877i	$0.410668\pi$
$948$	−1.41964e60	−0.134155
$949$	2.36610e61	2.18814
$950$	−5.22488e59	−0.0472870
$951$	1.14249e61	1.01193
$952$	−6.16562e58	−0.00534465
$953$	−1.08849e61	−0.923467	−0.461733	−	0.887019i	$-0.652772\pi$
$953$	−1.08849e61	−0.923467	−0.461733	+	0.887019i	$0.652772\pi$
$954$	−2.46712e59	−0.0204856
$955$	−7.70313e60	−0.626034
$956$	5.41230e60	0.430521
$957$	−1.62639e61	−1.26628
$958$	5.23152e59	0.0398690
$959$	2.21772e59	0.0165434
$960$	−3.63405e60	−0.265357
$961$	−1.36794e61	−0.977769
$962$	9.60914e59	0.0672350
$963$	8.45098e60	0.578853
$964$	−1.54655e61	−1.03701
$965$	1.14328e60	0.0750487
$966$	5.80329e58	0.00372943
$967$	2.37432e61	1.49381	0.746906	−	0.664930i	$-0.231539\pi$
$967$	2.37432e61	1.49381	0.746906	+	0.664930i	$0.231539\pi$
$968$	2.56206e60	0.157814
$969$	−6.70691e60	−0.404469
$970$	−2.80999e59	−0.0165915
$971$	−1.71671e61	−0.992436	−0.496218	−	0.868198i	$-0.665278\pi$
$971$	−1.71671e61	−0.992436	−0.496218	+	0.868198i	$0.665278\pi$
$972$	−1.73706e61	−0.983233
$973$	1.26985e60	0.0703783
$974$	−1.79505e60	−0.0974134
$975$	1.46575e61	0.778870
$976$	1.35845e61	0.706842
$977$	3.29474e61	1.67873	0.839367	−	0.543565i	$-0.182926\pi$
$977$	3.29474e61	1.67873	0.839367	+	0.543565i	$0.182926\pi$
$978$	8.00675e59	0.0399493
$979$	−2.22265e61	−1.08599
$980$	8.83912e60	0.422936
$981$	−1.18385e61	−0.554731
$982$	1.84463e59	0.00846492
$983$	3.50912e61	1.57707	0.788535	−	0.614990i	$-0.210840\pi$
$983$	3.50912e61	1.57707	0.788535	+	0.614990i	$0.210840\pi$
$984$	−8.43716e59	−0.0371362
$985$	1.62261e61	0.699474
$986$	−1.00925e60	−0.0426112
$987$	1.26408e60	0.0522725
$988$	−3.90477e61	−1.58153
$989$	−1.66407e60	−0.0660157
$990$	−5.64575e59	−0.0219381
$991$	−1.41075e61	−0.536959	−0.268480	−	0.963285i	$-0.586521\pi$
$991$	−1.41075e61	−0.536959	−0.268480	+	0.963285i	$0.586521\pi$
$992$	−6.55635e59	−0.0244441
$993$	−1.35567e61	−0.495101
$994$	6.79257e58	0.00243004
$995$	−1.24691e61	−0.436982
$996$	2.95224e61	1.01353
$997$	−1.88767e61	−0.634857	−0.317429	−	0.948282i	$-0.602819\pi$
$997$	−1.88767e61	−0.634857	−0.317429	+	0.948282i	$0.602819\pi$
$998$	1.69929e59	0.00559874
$999$	−2.55339e61	−0.824185

Twists

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

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

\(f(q)\)	\(=\)	\(q-81363.7 q^{2} +3.82217e9 q^{3} -2.19240e12 q^{4} +9.10518e13 q^{5} -3.10986e14 q^{6} -1.69829e16 q^{7} +3.57303e17 q^{8} -2.18640e19 q^{9} +O(q^{10})\)	\(q-81363.7 q^{2} +3.82217e9 q^{3} -2.19240e12 q^{4} +9.10518e13 q^{5} -3.10986e14 q^{6} -1.69829e16 q^{7} +3.57303e17 q^{8} -2.18640e19 q^{9} -7.40831e18 q^{10} -3.48555e21 q^{11} -8.37973e21 q^{12} -1.03131e23 q^{13} +1.38179e21 q^{14} +3.48015e23 q^{15} +4.79207e24 q^{16} +1.01608e25 q^{17} +1.77894e24 q^{18} -1.72697e26 q^{19} -1.99622e26 q^{20} -6.49115e25 q^{21} +2.83598e26 q^{22} +1.09881e28 q^{23} +1.36567e27 q^{24} -3.71843e28 q^{25} +8.39114e27 q^{26} -2.22974e29 q^{27} +3.72334e28 q^{28} +1.22079e30 q^{29} -2.83158e28 q^{30} +5.57694e29 q^{31} -1.17562e30 q^{32} -1.33224e31 q^{33} -8.26720e29 q^{34} -1.54633e30 q^{35} +4.79348e31 q^{36} +1.14515e32 q^{37} +1.40513e31 q^{38} -3.94185e32 q^{39} +3.25331e31 q^{40} -6.17804e32 q^{41} +5.28145e30 q^{42} -1.51443e32 q^{43} +7.64174e33 q^{44} -1.99076e33 q^{45} -8.94030e32 q^{46} -1.94739e34 q^{47} +1.83161e34 q^{48} -4.42792e34 q^{49} +3.02545e33 q^{50} +3.88362e34 q^{51} +2.26105e35 q^{52} -1.38685e35 q^{53} +1.81420e34 q^{54} -3.17366e35 q^{55} -6.06805e33 q^{56} -6.60078e35 q^{57} -9.93283e34 q^{58} +2.19974e36 q^{59} -7.62989e35 q^{60} +2.83478e36 q^{61} -4.53761e34 q^{62} +3.71315e35 q^{63} -1.04422e37 q^{64} -9.39028e36 q^{65} +1.08396e36 q^{66} +2.71602e37 q^{67} -2.22766e37 q^{68} +4.19982e37 q^{69} +1.25815e35 q^{70} +4.91576e37 q^{71} -7.81208e36 q^{72} -2.29426e38 q^{73} -9.31739e36 q^{74} -1.42125e38 q^{75} +3.78622e38 q^{76} +5.91949e37 q^{77} +3.20723e37 q^{78} +1.69414e38 q^{79} +4.36327e38 q^{80} -5.47960e37 q^{81} +5.02668e37 q^{82} -3.52307e39 q^{83} +1.42312e38 q^{84} +9.25158e38 q^{85} +1.23220e37 q^{86} +4.66608e39 q^{87} -1.24540e39 q^{88} +6.37675e39 q^{89} +1.61976e38 q^{90} +1.75147e39 q^{91} -2.40903e40 q^{92} +2.13160e39 q^{93} +1.58447e39 q^{94} -1.57244e40 q^{95} -4.49341e39 q^{96} +3.79303e40 q^{97} +3.60272e39 q^{98} +7.62083e40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 344688 q^{2} - 10820953044 q^{3} + 6271704903936 q^{4} - 212302350281550 q^{5} + 49\!\cdots\!76 q^{6}+ \cdots + 13\!\cdots\!19 q^{9}+O(q^{10}) \) 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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