LMFDB - Embedded newform 3.38.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,38,Mod(1,3)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 38, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 38);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 38 $
Character orbit:	$[\chi]$	$=$	3.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:	$26.0142114374$
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} - 2495042360x + 9241471873200 $ x^3 - x^2 - 2495042360*x + 9241471873200
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{5}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$47984.3$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-679444. q^{2} -3.87420e8 q^{3} +3.24205e11 q^{4} -1.35264e13 q^{5} +2.63231e14 q^{6} -4.10476e15 q^{7} -1.26897e17 q^{8} +1.50095e17 q^{9} +O(q^{10})$	\(q-679444. q^{2} -3.87420e8 q^{3} +3.24205e11 q^{4} -1.35264e13 q^{5} +2.63231e14 q^{6} -4.10476e15 q^{7} -1.26897e17 q^{8} +1.50095e17 q^{9} +9.19042e18 q^{10} +1.15138e19 q^{11} -1.25604e20 q^{12} +4.10734e20 q^{13} +2.78896e21 q^{14} +5.24040e21 q^{15} +4.16612e22 q^{16} -2.52734e22 q^{17} -1.01981e23 q^{18} +8.17932e23 q^{19} -4.38533e24 q^{20} +1.59027e24 q^{21} -7.82302e24 q^{22} -7.67235e24 q^{23} +4.91626e25 q^{24} +1.10204e26 q^{25} -2.79071e26 q^{26} -5.81497e25 q^{27} -1.33079e27 q^{28} +7.52830e26 q^{29} -3.56056e27 q^{30} -3.41837e27 q^{31} -1.08658e28 q^{32} -4.46070e27 q^{33} +1.71718e28 q^{34} +5.55226e28 q^{35} +4.86615e28 q^{36} -4.82934e28 q^{37} -5.55739e29 q^{38} -1.59127e29 q^{39} +1.71646e30 q^{40} +5.14552e29 q^{41} -1.08050e30 q^{42} +1.56506e30 q^{43} +3.73285e30 q^{44} -2.03024e30 q^{45} +5.21293e30 q^{46} -1.18810e31 q^{47} -1.61404e31 q^{48} -1.71303e30 q^{49} -7.48772e31 q^{50} +9.79142e30 q^{51} +1.33162e32 q^{52} -4.07740e31 q^{53} +3.95095e31 q^{54} -1.55741e32 q^{55} +5.20883e32 q^{56} -3.16884e32 q^{57} -5.11506e32 q^{58} +6.63304e31 q^{59} +1.69897e33 q^{60} -1.38461e33 q^{61} +2.32259e33 q^{62} -6.16103e32 q^{63} +1.65684e33 q^{64} -5.55574e33 q^{65} +3.03080e33 q^{66} +3.53054e33 q^{67} -8.19376e33 q^{68} +2.97243e33 q^{69} -3.77245e34 q^{70} -6.34947e33 q^{71} -1.90466e34 q^{72} +4.38920e34 q^{73} +3.28127e34 q^{74} -4.26951e34 q^{75} +2.65178e35 q^{76} -4.72616e34 q^{77} +1.08118e35 q^{78} +2.43750e34 q^{79} -5.63525e35 q^{80} +2.25284e34 q^{81} -3.49610e35 q^{82} +4.41573e35 q^{83} +5.15574e35 q^{84} +3.41857e35 q^{85} -1.06337e36 q^{86} -2.91662e35 q^{87} -1.46108e36 q^{88} +1.79925e36 q^{89} +1.37943e36 q^{90} -1.68596e36 q^{91} -2.48742e36 q^{92} +1.32435e36 q^{93} +8.07247e36 q^{94} -1.10637e37 q^{95} +4.20964e36 q^{96} -4.46953e36 q^{97} +1.16391e36 q^{98} +1.72817e36 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 310908 q^{2} - 1162261467 q^{3} + 338476600848 q^{4} - 9628717886790 q^{5} + 120452129394012 q^{6} - 46\!\cdots\!44 q^{7}+ \cdots + 45\!\cdots\!63 q^{9}+O(q^{10}) $ 3 * q - 310908 * q^2 - 1162261467 * q^3 + 338476600848 * q^4 - 9628717886790 * q^5 + 120452129394012 * q^6 - 4621884343701744 * q^7 - 93383909093911488 * q^8 + 450283905890997363 * q^9	$ 3 q - 310908 q^{2} - 1162261467 q^{3} + 338476600848 q^{4} - 9628717886790 q^{5} + 120452129394012 q^{6} - 46\!\cdots\!44 q^{7}+ \cdots + 34\!\cdots\!20 q^{99}+O(q^{100}) $ 3 * q - 310908 * q^2 - 1162261467 * q^3 + 338476600848 * q^4 - 9628717886790 * q^5 + 120452129394012 * q^6 - 4621884343701744 * q^7 - 93383909093911488 * q^8 + 450283905890997363 * q^9 + 10698950136741797880 * q^10 + 22673303357139628620 * q^11 - 131132770215589974672 * q^12 - 168270000203795091510 * q^13 + 797101803583223694528 * q^14 + 3730362592143228440310 * q^15 + 32071173863897028608256 * q^16 - 27168549617785276146906 * q^17 - 46665622870919402711868 * q^18 + 582035599719143813745204 * q^19 - 4066256929972106412494880 * q^20 + 1790612692538373730632816 * q^21 - 4486408000290444592999152 * q^22 - 17157197763697459349569272 * q^23 + 36178839725894735603677632 * q^24 - 24896488591542260192608275 * q^25 - 618603181238074545425686344 * q^26 - 174449211009120179071170507 * q^27 - 2033429672978753784958610688 * q^28 + 111201150055901033185229778 * q^29 - 4144992493763124201408763320 * q^30 - 11859842025407507592851987736 * q^31 - 27281435223830339470718352384 * q^32 - 8784102273868376561238795180 * q^33 - 18783445175675019452330905464 * q^34 + 47739964986924083632994534880 * q^35 + 50803521960848503410923854608 * q^36 + 60344578140045347560278093666 * q^37 - 372452605565029151271789397776 * q^38 + 65191245762984394008603948390 * q^39 + 1732463594119923393272610326400 * q^40 + 2087364862188523841295969725934 * q^41 - 308813570526994475930424384192 * q^42 + 2483325896102099669944761791244 * q^43 + 4284309379683814482835899511872 * q^44 - 1445218899595437120383607511590 * q^45 - 4327236604482200607954371165856 * q^46 - 11791379189662012541191082473632 * q^47 - 12425029861155006269057528957184 * q^48 - 22445324860908932271245865545973 * q^49 - 96691457712658313260807892933700 * q^50 + 10525652778343134781834358357034 * q^51 + 43220201443333906987967057359584 * q^52 - 115357757368640109037215455345382 * q^53 + 18079218432141178878219826663452 * q^54 - 129419469300146958823045789059480 * q^55 + 630552391741804501615596905794560 * q^56 - 225492516658598958982491855084756 * q^57 + 580965936186746161132050423512088 * q^58 + 1091721381032593697748326986744236 * q^59 + 1575351248209432222688802119596320 * q^60 + 294380981976352085651508270601002 * q^61 + 248838835694853996733454208986592 * q^62 - 693720044952823401986519854167024 * q^63 - 1064135955800023765084313699610624 * q^64 - 7515875365146923444942971038019860 * q^65 + 1738126381326036186247137444425328 * q^66 + 3824374619785575741360273276519444 * q^67 - 21329399470876894544665401157365216 * q^68 + 6647049947481376149267749297614008 * q^69 - 43059062291480572688803543269144960 * q^70 - 22149353642418626281921550104284744 * q^71 - 14016423778058764430102498387802048 * q^72 + 32759279450923542889398870347665278 * q^73 + 46478870171568672595185044851456728 * q^74 + 9645409784518223707985532085946475 * q^75 + 347061692957154720144564653376455616 * q^76 - 61122141948697926808926153780754368 * q^77 + 239659546972210465807272116553102216 * q^78 + 74649348023552719727334936629819640 * q^79 - 618088038723375449595358546989335040 * q^80 + 67585198634817523235520443624317923 * q^81 + 103937675337495441364448738414881512 * q^82 - 317656267631459020909914460046822604 * q^83 + 787792318252538877979265797505586432 * q^84 + 210972517320554825185658741373302580 * q^85 - 2655243937093032975138251645354123760 * q^86 - 43081603932019555612226948170121442 * q^87 - 1353962196634819912991147659264835328 * q^88 - 1604427814888922862357874180114447026 * q^89 + 1605855018835039028277517574319663480 * q^90 + 459759011513895387754487414763335904 * q^91 - 5426885178857894678398508472745540224 * q^92 + 4594745796946127015893929993303122904 * q^93 + 15155501875748762861069416648677456000 * q^94 - 10713376656166940710475311057833316200 * q^95 + 10569386975038174570781705261883595776 * q^96 + 2690787195739502167683294096108844614 * q^97 - 1675640263817086437903041451354198300 * q^98 + 3403141198368098368991272474406443020 * 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 $

$2$	−679444.	−1.83273	−0.916366	−	0.400342i	$-0.868891\pi$
$2$	−679444.	−1.83273	−0.916366	+	0.400342i	$0.868891\pi$
$3$	−3.87420e8	−0.577350
$3$	−3.87420e8	−0.577350
$4$	3.24205e11	2.35890
$5$	−1.35264e13	−1.58576	−0.792879	−	0.609379i	$-0.791419\pi$
$5$	−1.35264e13	−1.58576	−0.792879	+	0.609379i	$0.791419\pi$
$6$	2.63231e14	1.05813
$7$	−4.10476e15	−0.952740	−0.476370	−	0.879245i	$-0.658048\pi$
$7$	−4.10476e15	−0.952740	−0.476370	+	0.879245i	$0.658048\pi$
$8$	−1.26897e17	−2.49051
$9$	1.50095e17	0.333333
$10$	9.19042e18	2.90627
$11$	1.15138e19	0.624390	0.312195	−	0.950018i	$-0.398936\pi$
$11$	1.15138e19	0.624390	0.312195	+	0.950018i	$0.398936\pi$
$12$	−1.25604e20	−1.36191
$13$	4.10734e20	1.01300	0.506499	−	0.862241i	$-0.330940\pi$
$13$	4.10734e20	1.01300	0.506499	+	0.862241i	$0.330940\pi$
$14$	2.78896e21	1.74612
$15$	5.24040e21	0.915538
$16$	4.16612e22	2.20552
$17$	−2.52734e22	−0.435871	−0.217936	−	0.975963i	$-0.569932\pi$
$17$	−2.52734e22	−0.435871	−0.217936	+	0.975963i	$0.569932\pi$
$18$	−1.01981e23	−0.610910
$19$	8.17932e23	1.80209	0.901043	−	0.433730i	$-0.142803\pi$
$19$	8.17932e23	1.80209	0.901043	+	0.433730i	$0.142803\pi$
$20$	−4.38533e24	−3.74065
$21$	1.59027e24	0.550065
$22$	−7.82302e24	−1.14434
$23$	−7.67235e24	−0.493132	−0.246566	−	0.969126i	$-0.579302\pi$
$23$	−7.67235e24	−0.493132	−0.246566	+	0.969126i	$0.579302\pi$
$24$	4.91626e25	1.43789
$25$	1.10204e26	1.51463
$26$	−2.79071e26	−1.85655
$27$	−5.81497e25	−0.192450
$28$	−1.33079e27	−2.24742
$29$	7.52830e26	0.664253	0.332127	−	0.943235i	$-0.392234\pi$
$29$	7.52830e26	0.664253	0.332127	+	0.943235i	$0.392234\pi$
$30$	−3.56056e27	−1.67793
$31$	−3.41837e27	−0.878270	−0.439135	−	0.898421i	$-0.644715\pi$
$31$	−3.41837e27	−0.878270	−0.439135	+	0.898421i	$0.644715\pi$
$32$	−1.08658e28	−1.55163
$33$	−4.46070e27	−0.360492
$34$	1.71718e28	0.798834
$35$	5.55226e28	1.51081
$36$	4.86615e28	0.786301
$37$	−4.82934e28	−0.470063	−0.235031	−	0.971988i	$-0.575519\pi$
$37$	−4.82934e28	−0.470063	−0.235031	+	0.971988i	$0.575519\pi$
$38$	−5.55739e29	−3.30274
$39$	−1.59127e29	−0.584854
$40$	1.71646e30	3.94934
$41$	5.14552e29	0.749770	0.374885	−	0.927071i	$-0.377682\pi$
$41$	5.14552e29	0.749770	0.374885	+	0.927071i	$0.377682\pi$
$42$	−1.08050e30	−1.00812
$43$	1.56506e30	0.944853	0.472426	−	0.881370i	$-0.343378\pi$
$43$	1.56506e30	0.944853	0.472426	+	0.881370i	$0.343378\pi$
$44$	3.73285e30	1.47288
$45$	−2.03024e30	−0.528586
$46$	5.21293e30	0.903779
$47$	−1.18810e31	−1.38370	−0.691851	−	0.722040i	$-0.743204\pi$
$47$	−1.18810e31	−1.38370	−0.691851	+	0.722040i	$0.743204\pi$
$48$	−1.61404e31	−1.27336
$49$	−1.71303e30	−0.0922862
$50$	−7.48772e31	−2.77590
$51$	9.79142e30	0.251650
$52$	1.33162e32	2.38956
$53$	−4.07740e31	−0.514375	−0.257188	−	0.966361i	$-0.582796\pi$
$53$	−4.07740e31	−0.514375	−0.257188	+	0.966361i	$0.582796\pi$
$54$	3.95095e31	0.352709
$55$	−1.55741e32	−0.990131
$56$	5.20883e32	2.37280
$57$	−3.16884e32	−1.04043
$58$	−5.11506e32	−1.21740
$59$	6.63304e31	0.115067	0.0575335	−	0.998344i	$-0.481676\pi$
$59$	6.63304e31	0.115067	0.0575335	+	0.998344i	$0.481676\pi$
$60$	1.69897e33	2.15967
$61$	−1.38461e33	−1.29636	−0.648182	−	0.761486i	$-0.724470\pi$
$61$	−1.38461e33	−1.29636	−0.648182	+	0.761486i	$0.724470\pi$
$62$	2.32259e33	1.60963
$63$	−6.16103e32	−0.317580
$64$	1.65684e33	0.638192
$65$	−5.55574e33	−1.60637
$66$	3.03080e33	0.660684
$67$	3.53054e33	0.582716	0.291358	−	0.956614i	$-0.405893\pi$
$67$	3.53054e33	0.582716	0.291358	+	0.956614i	$0.405893\pi$
$68$	−8.19376e33	−1.02818
$69$	2.97243e33	0.284710
$70$	−3.77245e34	−2.76892
$71$	−6.34947e33	−0.358474	−0.179237	−	0.983806i	$-0.557363\pi$
$71$	−6.34947e33	−0.358474	−0.179237	+	0.983806i	$0.557363\pi$
$72$	−1.90466e34	−0.830169
$73$	4.38920e34	1.48222	0.741110	−	0.671384i	$-0.234300\pi$
$73$	4.38920e34	1.48222	0.741110	+	0.671384i	$0.234300\pi$
$74$	3.28127e34	0.861499
$75$	−4.26951e34	−0.874470
$76$	2.65178e35	4.25095
$77$	−4.72616e34	−0.594881
$78$	1.08118e35	1.07188
$79$	2.43750e34	0.190916	0.0954582	−	0.995433i	$-0.469568\pi$
$79$	2.43750e34	0.190916	0.0954582	+	0.995433i	$0.469568\pi$
$80$	−5.63525e35	−3.49743
$81$	2.25284e34	0.111111
$82$	−3.49610e35	−1.37413
$83$	4.41573e35	1.38694	0.693471	−	0.720485i	$-0.256081\pi$
$83$	4.41573e35	1.38694	0.693471	+	0.720485i	$0.256081\pi$
$84$	5.15574e35	1.29755
$85$	3.41857e35	0.691186
$86$	−1.06337e36	−1.73166
$87$	−2.91662e35	−0.383507
$88$	−1.46108e36	−1.55505
$89$	1.79925e36	1.55374	0.776868	−	0.629663i	$-0.216807\pi$
$89$	1.79925e36	1.55374	0.776868	+	0.629663i	$0.216807\pi$
$90$	1.37943e36	0.968756
$91$	−1.68596e36	−0.965123
$92$	−2.48742e36	−1.16325
$93$	1.32435e36	0.507070
$94$	8.07247e36	2.53595
$95$	−1.10637e37	−2.85767
$96$	4.20964e36	0.895832
$97$	−4.46953e36	−0.785208	−0.392604	−	0.919708i	$-0.628426\pi$
$97$	−4.46953e36	−0.785208	−0.392604	+	0.919708i	$0.628426\pi$
$98$	1.16391e36	0.169136
$99$	1.72817e36	0.208130
$100$	3.57286e37	3.57286
$101$	1.71365e37	1.42553	0.712767	−	0.701401i	$-0.247442\pi$
$101$	1.71365e37	1.42553	0.712767	+	0.701401i	$0.247442\pi$
$102$	−6.65272e36	−0.461207
$103$	−2.35646e37	−1.36387	−0.681934	−	0.731414i	$-0.738861\pi$
$103$	−2.35646e37	−1.36387	−0.681934	+	0.731414i	$0.738861\pi$
$104$	−5.21210e37	−2.52288
$105$	−2.15106e37	−0.872269
$106$	2.77037e37	0.942712
$107$	−4.25420e37	−1.21680	−0.608399	−	0.793631i	$-0.708188\pi$
$107$	−4.25420e37	−1.21680	−0.608399	+	0.793631i	$0.708188\pi$
$108$	−1.88525e37	−0.453971
$109$	−1.62022e37	−0.328991	−0.164496	−	0.986378i	$-0.552600\pi$
$109$	−1.62022e37	−0.328991	−0.164496	+	0.986378i	$0.552600\pi$
$110$	1.05817e38	1.81464
$111$	1.87099e37	0.271391
$112$	−1.71009e38	−2.10129
$113$	−3.47825e37	−0.362585	−0.181292	−	0.983429i	$-0.558028\pi$
$113$	−3.47825e37	−0.362585	−0.181292	+	0.983429i	$0.558028\pi$
$114$	2.15305e38	1.90684
$115$	1.03779e38	0.781989
$116$	2.44071e38	1.56691
$117$	6.16489e37	0.337666
$118$	−4.50678e37	−0.210887
$119$	1.03741e38	0.415272
$120$	−6.64993e38	−2.28015
$121$	−2.07471e38	−0.610137
$122$	9.40768e38	2.37589
$123$	−1.99348e38	−0.432880
$124$	−1.10825e39	−2.07176
$125$	−5.06483e38	−0.816074
$126$	4.18608e38	0.582039
$127$	4.21818e38	0.506706	0.253353	−	0.967374i	$-0.418467\pi$
$127$	4.21818e38	0.506706	0.253353	+	0.967374i	$0.418467\pi$
$128$	3.67655e38	0.381994
$129$	−6.06336e38	−0.545511
$130$	3.77482e39	2.94404
$131$	−1.15197e39	−0.779691	−0.389845	−	0.920880i	$-0.627472\pi$
$131$	−1.15197e39	−0.779691	−0.389845	+	0.920880i	$0.627472\pi$
$132$	−1.44618e39	−0.850365
$133$	−3.35742e39	−1.71692
$134$	−2.39880e39	−1.06796
$135$	7.86556e38	0.305179
$136$	3.20712e39	1.08554
$137$	−2.75856e39	−0.815365	−0.407683	−	0.913124i	$-0.633663\pi$
$137$	−2.75856e39	−0.815365	−0.407683	+	0.913124i	$0.633663\pi$
$138$	−2.01960e39	−0.521797
$139$	−2.82157e39	−0.637847	−0.318923	−	0.947780i	$-0.603321\pi$
$139$	−2.82157e39	−0.637847	−0.318923	+	0.947780i	$0.603321\pi$
$140$	1.80007e40	3.56387
$141$	4.60294e39	0.798880
$142$	4.31411e39	0.656987
$143$	4.72912e39	0.632505
$144$	6.25312e39	0.735175
$145$	−1.01831e40	−1.05334
$146$	−2.98222e40	−2.71651
$147$	6.63662e38	0.0532815
$148$	−1.56570e40	−1.10883
$149$	1.60101e40	1.00103	0.500515	−	0.865728i	$-0.333144\pi$
$149$	1.60101e40	1.00103	0.500515	+	0.865728i	$0.333144\pi$
$150$	2.90090e40	1.60267
$151$	4.57788e39	0.223661	0.111831	−	0.993727i	$-0.464329\pi$
$151$	4.57788e39	0.223661	0.111831	+	0.993727i	$0.464329\pi$
$152$	−1.03793e41	−4.48811
$153$	−3.79340e39	−0.145290
$154$	3.21116e40	1.09026
$155$	4.62382e40	1.39272
$156$	−5.15897e40	−1.37961
$157$	1.29011e40	0.306538	0.153269	−	0.988185i	$-0.451020\pi$
$157$	1.29011e40	0.306538	0.153269	+	0.988185i	$0.451020\pi$
$158$	−1.65614e40	−0.349899
$159$	1.57967e40	0.296975
$160$	1.46975e41	2.46050
$161$	3.14932e40	0.469827
$162$	−1.53068e40	−0.203637
$163$	2.27947e40	0.270622	0.135311	−	0.990803i	$-0.456797\pi$
$163$	2.27947e40	0.270622	0.135311	+	0.990803i	$0.456797\pi$
$164$	1.66821e41	1.76864
$165$	6.03372e40	0.571652
$166$	−3.00024e41	−2.54189
$167$	−1.07603e41	−0.815773	−0.407887	−	0.913033i	$-0.633734\pi$
$167$	−1.07603e41	−0.815773	−0.407887	+	0.913033i	$0.633734\pi$
$168$	−2.01801e41	−1.36994
$169$	4.30125e39	0.0261632
$170$	−2.32273e41	−1.26676
$171$	1.22767e41	0.600695
$172$	5.07400e41	2.22882
$173$	1.88646e40	0.0744379	0.0372189	−	0.999307i	$-0.488150\pi$
$173$	1.88646e40	0.0744379	0.0372189	+	0.999307i	$0.488150\pi$
$174$	1.98168e41	0.702865
$175$	−4.52360e41	−1.44305
$176$	4.79680e41	1.37711
$177$	−2.56978e40	−0.0664339
$178$	−1.22249e42	−2.84758
$179$	7.34863e41	1.54321	0.771605	−	0.636102i	$-0.219454\pi$
$179$	7.34863e41	1.54321	0.771605	+	0.636102i	$0.219454\pi$
$180$	−6.58214e41	−1.24688
$181$	−1.09361e42	−1.86986	−0.934932	−	0.354827i	$-0.884540\pi$
$181$	−1.09361e42	−1.86986	−0.934932	+	0.354827i	$0.884540\pi$
$182$	1.14552e42	1.76881
$183$	5.36428e41	0.748456
$184$	9.73601e41	1.22815
$185$	6.53236e41	0.745406
$186$	−8.99820e41	−0.929322
$187$	−2.90994e41	−0.272153
$188$	−3.85188e42	−3.26402
$189$	2.38691e41	0.183355
$190$	7.51714e42	5.23734
$191$	−7.94715e41	−0.502451	−0.251226	−	0.967929i	$-0.580834\pi$
$191$	−7.94715e41	−0.502451	−0.251226	+	0.967929i	$0.580834\pi$
$192$	−6.41894e41	−0.368460
$193$	−2.53002e42	−1.31921	−0.659604	−	0.751613i	$-0.729276\pi$
$193$	−2.53002e42	−1.31921	−0.659604	+	0.751613i	$0.729276\pi$
$194$	3.03680e42	1.43908
$195$	2.15241e42	0.927437
$196$	−5.55373e41	−0.217694
$197$	1.05535e42	0.376507	0.188253	−	0.982121i	$-0.439717\pi$
$197$	1.05535e42	0.376507	0.188253	+	0.982121i	$0.439717\pi$
$198$	−1.17419e42	−0.381446
$199$	3.73817e42	1.10631	0.553155	−	0.833078i	$-0.313424\pi$
$199$	3.73817e42	1.10631	0.553155	+	0.833078i	$0.313424\pi$
$200$	−1.39845e43	−3.77219
$201$	−1.36780e42	−0.336431
$202$	−1.16433e43	−2.61262
$203$	−3.09019e42	−0.632861
$204$	3.17443e42	0.593619
$205$	−6.96003e42	−1.18895
$206$	1.60109e43	2.49960
$207$	−1.15158e42	−0.164377
$208$	1.71116e43	2.23419
$209$	9.41754e42	1.12520
$210$	1.46153e43	1.59864
$211$	−1.65439e43	−1.65735	−0.828673	−	0.559733i	$-0.810904\pi$
$211$	−1.65439e43	−1.65735	−0.828673	+	0.559733i	$0.810904\pi$
$212$	−1.32192e43	−1.21336
$213$	2.45991e42	0.206965
$214$	2.89049e43	2.23006
$215$	−2.11696e43	−1.49831
$216$	7.37904e42	0.479298
$217$	1.40316e43	0.836763
$218$	1.10085e43	0.602953
$219$	−1.70047e43	−0.855760
$220$	−5.04920e43	−2.33562
$221$	−1.03806e43	−0.441536
$222$	−1.27123e43	−0.497387
$223$	−3.53484e42	−0.127271	−0.0636355	−	0.997973i	$-0.520269\pi$
$223$	−3.53484e42	−0.127271	−0.0636355	+	0.997973i	$0.520269\pi$
$224$	4.46016e43	1.47830
$225$	1.65410e43	0.504876
$226$	2.36327e43	0.664520
$227$	2.48280e43	0.643374	0.321687	−	0.946846i	$-0.395750\pi$
$227$	2.48280e43	0.643374	0.321687	+	0.946846i	$0.395750\pi$
$228$	−1.02735e44	−2.45429
$229$	4.70012e43	1.03551	0.517753	−	0.855530i	$-0.326769\pi$
$229$	4.70012e43	1.03551	0.517753	+	0.855530i	$0.326769\pi$
$230$	−7.05122e43	−1.43317
$231$	1.83101e43	0.343455
$232$	−9.55320e43	−1.65433
$233$	8.79333e43	1.40627	0.703135	−	0.711056i	$-0.251783\pi$
$233$	8.79333e43	1.40627	0.703135	+	0.711056i	$0.251783\pi$
$234$	−4.18870e43	−0.618851
$235$	1.60707e44	2.19422
$236$	2.15047e43	0.271432
$237$	−9.44337e42	−0.110226
$238$	−7.04863e43	−0.761082
$239$	−1.13232e44	−1.13137	−0.565687	−	0.824620i	$-0.691389\pi$
$239$	−1.13232e44	−1.13137	−0.565687	+	0.824620i	$0.691389\pi$
$240$	2.18321e44	2.01924
$241$	−1.33612e44	−1.14428	−0.572139	−	0.820157i	$-0.693886\pi$
$241$	−1.33612e44	−1.14428	−0.572139	+	0.820157i	$0.693886\pi$
$242$	1.40965e44	1.11822
$243$	−8.72796e42	−0.0641500
$244$	−4.48899e44	−3.05800
$245$	2.31711e43	0.146344
$246$	1.35446e44	0.793353
$247$	3.35952e44	1.82551
$248$	4.33782e44	2.18734
$249$	−1.71075e44	−0.800751
$250$	3.44127e44	1.49564
$251$	9.12839e41	0.00368494	0.00184247	−	0.999998i	$-0.499414\pi$
$251$	9.12839e41	0.00368494	0.00184247	+	0.999998i	$0.499414\pi$
$252$	−1.99744e44	−0.749141
$253$	−8.83383e43	−0.307907
$254$	−2.86601e44	−0.928655
$255$	−1.32443e44	−0.399056
$256$	−4.77515e44	−1.33828
$257$	−5.59665e44	−1.45937	−0.729685	−	0.683784i	$-0.760333\pi$
$257$	−5.59665e44	−1.45937	−0.729685	+	0.683784i	$0.760333\pi$
$258$	4.11971e44	0.999775
$259$	1.98233e44	0.447848
$260$	−1.80120e45	−3.78927
$261$	1.12996e44	0.221418
$262$	7.82700e44	1.42896
$263$	−5.30358e44	−0.902376	−0.451188	−	0.892429i	$-0.649000\pi$
$263$	−5.30358e44	−0.902376	−0.451188	+	0.892429i	$0.649000\pi$
$264$	5.66051e44	0.897807
$265$	5.51526e44	0.815675
$266$	2.28118e45	3.14665
$267$	−6.97068e44	−0.897050
$268$	1.14462e45	1.37457
$269$	−2.65460e44	−0.297565	−0.148783	−	0.988870i	$-0.547536\pi$
$269$	−2.65460e44	−0.297565	−0.148783	+	0.988870i	$0.547536\pi$
$270$	−5.34421e44	−0.559311
$271$	−5.19245e44	−0.507505	−0.253753	−	0.967269i	$-0.581665\pi$
$271$	−5.19245e44	−0.507505	−0.253753	+	0.967269i	$0.581665\pi$
$272$	−1.05292e45	−0.961324
$273$	6.53177e44	0.557214
$274$	1.87429e45	1.49435
$275$	1.26887e45	0.945718
$276$	9.63677e44	0.671604
$277$	−2.01890e45	−1.31595	−0.657975	−	0.753040i	$-0.728587\pi$
$277$	−2.01890e45	−1.31595	−0.657975	+	0.753040i	$0.728587\pi$
$278$	1.91710e45	1.16900
$279$	−5.13079e44	−0.292757
$280$	−7.04567e45	−3.76269
$281$	1.74726e45	0.873555	0.436778	−	0.899570i	$-0.356120\pi$
$281$	1.74726e45	0.873555	0.436778	+	0.899570i	$0.356120\pi$
$282$	−3.12744e45	−1.46413
$283$	1.44699e45	0.634477	0.317238	−	0.948346i	$-0.397244\pi$
$283$	1.44699e45	0.634477	0.317238	+	0.948346i	$0.397244\pi$
$284$	−2.05853e45	−0.845607
$285$	4.28629e45	1.64988
$286$	−3.21318e45	−1.15921
$287$	−2.11212e45	−0.714336
$288$	−1.63090e45	−0.517209
$289$	−2.72335e45	−0.810016
$290$	6.91882e45	1.93050
$291$	1.73159e45	0.453340
$292$	1.42300e46	3.49641
$293$	−5.22491e45	−1.20511	−0.602557	−	0.798076i	$-0.705851\pi$
$293$	−5.22491e45	−1.20511	−0.602557	+	0.798076i	$0.705851\pi$
$294$	−4.50921e44	−0.0976506
$295$	−8.97211e44	−0.182468
$296$	6.12830e45	1.17069
$297$	−6.69527e44	−0.120164
$298$	−1.08779e46	−1.83462
$299$	−3.15129e45	−0.499542
$300$	−1.38420e46	−2.06279
$301$	−6.42420e45	−0.900199
$302$	−3.11041e45	−0.409911
$303$	−6.63904e45	−0.823032
$304$	3.40760e46	3.97454
$305$	1.87288e46	2.05572
$306$	2.57740e45	0.266278
$307$	1.87097e46	1.81973	0.909865	−	0.414904i	$-0.136185\pi$
$307$	1.87097e46	1.81973	0.909865	+	0.414904i	$0.136185\pi$
$308$	−1.53225e46	−1.40327
$309$	9.12943e45	0.787429
$310$	−3.14163e46	−2.55249
$311$	6.28962e45	0.481457	0.240728	−	0.970593i	$-0.422614\pi$
$311$	6.28962e45	0.481457	0.240728	+	0.970593i	$0.422614\pi$
$312$	2.01927e46	1.45658
$313$	−2.39735e46	−1.62990	−0.814950	−	0.579532i	$-0.803236\pi$
$313$	−2.39735e46	−1.62990	−0.814950	+	0.579532i	$0.803236\pi$
$314$	−8.76559e45	−0.561801
$315$	8.33365e45	0.503605
$316$	7.90250e45	0.450354
$317$	−2.60716e46	−1.40143	−0.700716	−	0.713440i	$-0.747136\pi$
$317$	−2.60716e46	−1.40143	−0.700716	+	0.713440i	$0.747136\pi$
$318$	−1.07330e46	−0.544275
$319$	8.66797e45	0.414753
$320$	−2.24111e46	−1.01202
$321$	1.64817e46	0.702518
$322$	−2.13979e46	−0.861067
$323$	−2.06719e46	−0.785477
$324$	7.30383e45	0.262100
$325$	4.52643e46	1.53431
$326$	−1.54877e46	−0.495977
$327$	6.27707e45	0.189943
$328$	−6.52953e46	−1.86731
$329$	4.87687e46	1.31831
$330$	−4.09957e46	−1.04769
$331$	−2.64270e46	−0.638601	−0.319300	−	0.947654i	$-0.603448\pi$
$331$	−2.64270e46	−0.638601	−0.319300	+	0.947654i	$0.603448\pi$
$332$	1.43160e47	3.27166
$333$	−7.24858e45	−0.156688
$334$	7.31102e46	1.49509
$335$	−4.77554e46	−0.924047
$336$	6.62525e46	1.21318
$337$	1.28332e46	0.222425	0.111212	−	0.993797i	$-0.464527\pi$
$337$	1.28332e46	0.222425	0.111212	+	0.993797i	$0.464527\pi$
$338$	−2.92246e45	−0.0479501
$339$	1.34754e46	0.209338
$340$	1.10832e47	1.63044
$341$	−3.93586e46	−0.548383
$342$	−8.34134e46	−1.10091
$343$	8.32247e46	1.04066
$344$	−1.98602e47	−2.35316
$345$	−4.02062e46	−0.451481
$346$	−1.28174e46	−0.136425
$347$	−1.41659e47	−1.42938	−0.714692	−	0.699440i	$-0.753433\pi$
$347$	−1.41659e47	−1.42938	−0.714692	+	0.699440i	$0.753433\pi$
$348$	−9.45583e46	−0.904656
$349$	−1.75631e47	−1.59342	−0.796712	−	0.604359i	$-0.793429\pi$
$349$	−1.75631e47	−1.59342	−0.796712	+	0.604359i	$0.793429\pi$
$350$	3.07353e47	2.64472
$351$	−2.38841e46	−0.194951
$352$	−1.25107e47	−0.968820
$353$	−1.54052e47	−1.13197	−0.565987	−	0.824414i	$-0.691505\pi$
$353$	−1.54052e47	−1.13197	−0.565987	+	0.824414i	$0.691505\pi$
$354$	1.74602e46	0.121756
$355$	8.58854e46	0.568453
$356$	5.83328e47	3.66512
$357$	−4.01915e46	−0.239757
$358$	−4.99298e47	−2.82829
$359$	−1.07520e47	−0.578421	−0.289210	−	0.957266i	$-0.593393\pi$
$359$	−1.07520e47	−0.578421	−0.289210	+	0.957266i	$0.593393\pi$
$360$	2.57632e47	1.31645
$361$	4.63005e47	2.24751
$362$	7.43049e47	3.42696
$363$	8.03784e46	0.352263
$364$	−5.46599e47	−2.27663
$365$	−5.93700e47	−2.35044
$366$	−3.64473e47	−1.37172
$367$	3.17956e47	1.13774	0.568872	−	0.822426i	$-0.307380\pi$
$367$	3.17956e47	1.13774	0.568872	+	0.822426i	$0.307380\pi$
$368$	−3.19639e47	−1.08762
$369$	7.72315e46	0.249923
$370$	−4.43837e47	−1.36613
$371$	1.67368e47	0.490066
$372$	4.29361e47	1.19613
$373$	−1.78361e45	−0.00472811	−0.00236405	−	0.999997i	$-0.500753\pi$
$373$	−1.78361e45	−0.00472811	−0.00236405	+	0.999997i	$0.500753\pi$
$374$	1.97714e47	0.498784
$375$	1.96222e47	0.471160
$376$	1.50767e48	3.44612
$377$	3.09212e47	0.672887
$378$	−1.62177e47	−0.336040
$379$	−1.48349e47	−0.292724	−0.146362	−	0.989231i	$-0.546756\pi$
$379$	−1.48349e47	−0.292724	−0.146362	+	0.989231i	$0.546756\pi$
$380$	−3.58690e48	−6.74097
$381$	−1.63421e47	−0.292547
$382$	5.39964e47	0.920858
$383$	1.02517e48	1.66579	0.832893	−	0.553434i	$-0.186683\pi$
$383$	1.02517e48	1.66579	0.832893	+	0.553434i	$0.186683\pi$
$384$	−1.42437e47	−0.220544
$385$	6.39279e47	0.943338
$386$	1.71901e48	2.41775
$387$	2.34907e47	0.314951
$388$	−1.44905e48	−1.85223
$389$	−7.18903e47	−0.876198	−0.438099	−	0.898927i	$-0.644348\pi$
$389$	−7.18903e47	−0.876198	−0.438099	+	0.898927i	$0.644348\pi$
$390$	−1.46244e48	−1.69974
$391$	1.93906e47	0.214942
$392$	2.17379e47	0.229839
$393$	4.46297e47	0.450155
$394$	−7.17054e47	−0.690036
$395$	−3.29706e47	−0.302747
$396$	5.60281e47	0.490959
$397$	−1.97535e48	−1.65204	−0.826020	−	0.563641i	$-0.809400\pi$
$397$	−1.97535e48	−1.65204	−0.826020	+	0.563641i	$0.809400\pi$
$398$	−2.53988e48	−2.02757
$399$	1.30073e48	0.991264
$400$	4.59121e48	3.34055
$401$	−1.19337e48	−0.829093	−0.414547	−	0.910028i	$-0.636060\pi$
$401$	−1.19337e48	−0.829093	−0.414547	+	0.910028i	$0.636060\pi$
$402$	9.29346e47	0.616588
$403$	−1.40404e48	−0.889685
$404$	5.55575e48	3.36270
$405$	−3.04728e47	−0.176195
$406$	2.09961e48	1.15986
$407$	−5.56043e47	−0.293503
$408$	−1.24250e48	−0.626736
$409$	2.67926e48	1.29162	0.645808	−	0.763500i	$-0.276521\pi$
$409$	2.67926e48	1.29162	0.645808	+	0.763500i	$0.276521\pi$
$410$	4.72895e48	2.17903
$411$	1.06872e48	0.470751
$412$	−7.63978e48	−3.21723
$413$	−2.72271e47	−0.109629
$414$	7.82434e47	0.301260
$415$	−5.97289e48	−2.19935
$416$	−4.46295e48	−1.57179
$417$	1.09313e48	0.368261
$418$	−6.39869e48	−2.06220
$419$	1.24117e48	0.382711	0.191356	−	0.981521i	$-0.438712\pi$
$419$	1.24117e48	0.382711	0.191356	+	0.981521i	$0.438712\pi$
$420$	−6.97385e48	−2.05760
$421$	2.08519e48	0.588743	0.294372	−	0.955691i	$-0.404890\pi$
$421$	2.08519e48	0.588743	0.294372	+	0.955691i	$0.404890\pi$
$422$	1.12407e49	3.03747
$423$	−1.78327e48	−0.461234
$424$	5.17412e48	1.28105
$425$	−2.78522e48	−0.660182
$426$	−1.67137e48	−0.379312
$427$	5.68351e48	1.23510
$428$	−1.37924e49	−2.87031
$429$	−1.83216e48	−0.365177
$430$	1.43836e49	2.74599
$431$	6.66174e48	1.21831	0.609155	−	0.793051i	$-0.291509\pi$
$431$	6.66174e48	1.21831	0.609155	+	0.793051i	$0.291509\pi$
$432$	−2.42259e48	−0.424453
$433$	−9.73853e47	−0.163481	−0.0817405	−	0.996654i	$-0.526048\pi$
$433$	−9.73853e47	−0.163481	−0.0817405	+	0.996654i	$0.526048\pi$
$434$	−9.53370e48	−1.53356
$435$	3.94513e48	0.608149
$436$	−5.25285e48	−0.776059
$437$	−6.27546e48	−0.888667
$438$	1.15537e49	1.56838
$439$	6.18878e48	0.805400	0.402700	−	0.915332i	$-0.368072\pi$
$439$	6.18878e48	0.805400	0.402700	+	0.915332i	$0.368072\pi$
$440$	1.97631e49	2.46593
$441$	−2.57116e47	−0.0307621
$442$	7.05305e48	0.809217
$443$	−3.09041e48	−0.340054	−0.170027	−	0.985439i	$-0.554385\pi$
$443$	−3.09041e48	−0.340054	−0.170027	+	0.985439i	$0.554385\pi$
$444$	6.06584e48	0.640185
$445$	−2.43374e49	−2.46385
$446$	2.40172e48	0.233253
$447$	−6.20262e48	−0.577945
$448$	−6.80094e48	−0.608031
$449$	−6.87278e48	−0.589624	−0.294812	−	0.955555i	$-0.595257\pi$
$449$	−6.87278e48	−0.589624	−0.294812	+	0.955555i	$0.595257\pi$
$450$	−1.12387e49	−0.925301
$451$	5.92448e48	0.468149
$452$	−1.12767e49	−0.855302
$453$	−1.77357e48	−0.129131
$454$	−1.68692e49	−1.17913
$455$	2.28050e49	1.53045
$456$	4.02117e49	2.59121
$457$	−5.99870e48	−0.371200	−0.185600	−	0.982625i	$-0.559423\pi$
$457$	−5.99870e48	−0.371200	−0.185600	+	0.982625i	$0.559423\pi$
$458$	−3.19347e49	−1.89780
$459$	1.46964e48	0.0838834
$460$	3.36458e49	1.84464
$461$	−2.03325e48	−0.107084	−0.0535420	−	0.998566i	$-0.517051\pi$
$461$	−2.03325e48	−0.107084	−0.0535420	+	0.998566i	$0.517051\pi$
$462$	−1.24407e49	−0.629461
$463$	3.27311e49	1.59115	0.795577	−	0.605853i	$-0.207168\pi$
$463$	3.27311e49	1.59115	0.795577	+	0.605853i	$0.207168\pi$
$464$	3.13638e49	1.46503
$465$	−1.79136e49	−0.804089
$466$	−5.97457e49	−2.57731
$467$	−1.94246e48	−0.0805358	−0.0402679	−	0.999189i	$-0.512821\pi$
$467$	−1.94246e48	−0.0805358	−0.0402679	+	0.999189i	$0.512821\pi$
$468$	1.99869e49	0.796521
$469$	−1.44920e49	−0.555177
$470$	−1.09191e50	−4.02141
$471$	−4.99816e48	−0.176980
$472$	−8.41715e48	−0.286575
$473$	1.80198e49	0.589956
$474$	6.41624e48	0.202014
$475$	9.01390e49	2.72949
$476$	3.36334e49	0.979586
$477$	−6.11997e48	−0.171458
$478$	7.69345e49	2.07351
$479$	−1.26170e49	−0.327152	−0.163576	−	0.986531i	$-0.552303\pi$
$479$	−1.26170e49	−0.327152	−0.163576	+	0.986531i	$0.552303\pi$
$480$	−5.69412e49	−1.42057
$481$	−1.98357e49	−0.476172
$482$	9.07822e49	2.09715
$483$	−1.22011e49	−0.271255
$484$	−6.72631e49	−1.43926
$485$	6.04566e49	1.24515
$486$	5.93016e48	0.117570
$487$	6.52218e48	0.124482	0.0622410	−	0.998061i	$-0.480175\pi$
$487$	6.52218e48	0.124482	0.0622410	+	0.998061i	$0.480175\pi$
$488$	1.75704e50	3.22860
$489$	−8.83112e48	−0.156244
$490$	−1.57434e49	−0.268208
$491$	−3.63594e49	−0.596498	−0.298249	−	0.954488i	$-0.596403\pi$
$491$	−3.63594e49	−0.596498	−0.298249	+	0.954488i	$0.596403\pi$
$492$	−6.46297e49	−1.02112
$493$	−1.90265e49	−0.289529
$494$	−2.28261e50	−3.34566
$495$	−2.33759e49	−0.330044
$496$	−1.42413e50	−1.93705
$497$	2.60631e49	0.341533
$498$	1.16236e50	1.46756
$499$	7.84299e48	0.0954161	0.0477081	−	0.998861i	$-0.484808\pi$
$499$	7.84299e48	0.0954161	0.0477081	+	0.998861i	$0.484808\pi$
$500$	−1.64204e50	−1.92504
$501$	4.16876e49	0.470987
$502$	−6.20223e47	−0.00675351
$503$	1.60037e50	1.67963	0.839814	−	0.542875i	$-0.182664\pi$
$503$	1.60037e50	1.67963	0.839814	+	0.542875i	$0.182664\pi$
$504$	7.81818e49	0.790935
$505$	−2.31795e50	−2.26055
$506$	6.00209e49	0.564311
$507$	−1.66639e48	−0.0151053
$508$	1.36755e50	1.19527
$509$	−1.73622e50	−1.46327	−0.731635	−	0.681696i	$-0.761243\pi$
$509$	−1.73622e50	−1.46327	−0.731635	+	0.681696i	$0.761243\pi$
$510$	8.99873e49	0.731363
$511$	−1.80166e50	−1.41217
$512$	2.73915e50	2.07072
$513$	−4.75625e49	−0.346812
$514$	3.80261e50	2.67463
$515$	3.18745e50	2.16276
$516$	−1.96577e50	−1.28681
$517$	−1.36796e50	−0.863969
$518$	−1.34688e50	−0.820785
$519$	−7.30852e48	−0.0429767
$520$	7.05009e50	4.00067
$521$	−3.53919e50	−1.93824	−0.969118	−	0.246598i	$-0.920687\pi$
$521$	−3.53919e50	−1.93824	−0.969118	+	0.246598i	$0.920687\pi$
$522$	−7.67743e49	−0.405799
$523$	−1.14063e50	−0.581921	−0.290961	−	0.956735i	$-0.593975\pi$
$523$	−1.14063e50	−0.581921	−0.290961	+	0.956735i	$0.593975\pi$
$524$	−3.73475e50	−1.83922
$525$	1.75253e50	0.833143
$526$	3.60349e50	1.65381
$527$	8.63938e49	0.382813
$528$	−1.85838e50	−0.795073
$529$	−1.83199e50	−0.756820
$530$	−3.74731e50	−1.49491
$531$	9.95584e48	0.0383556
$532$	−1.08849e51	−4.05005
$533$	2.11344e50	0.759515
$534$	4.73619e50	1.64405
$535$	5.75440e50	1.92955
$536$	−4.48016e50	−1.45126
$537$	−2.84701e50	−0.890973
$538$	1.80365e50	0.545358
$539$	−1.97235e49	−0.0576226
$540$	2.55006e50	0.719888
$541$	5.03224e50	1.37281	0.686407	−	0.727217i	$-0.259187\pi$
$541$	5.03224e50	1.37281	0.686407	+	0.727217i	$0.259187\pi$
$542$	3.52798e50	0.930121
$543$	4.23688e50	1.07957
$544$	2.74615e50	0.676309
$545$	2.19158e50	0.521701
$546$	−4.43797e50	−1.02122
$547$	−7.51701e50	−1.67217	−0.836083	−	0.548603i	$-0.815160\pi$
$547$	−7.51701e50	−1.67217	−0.836083	+	0.548603i	$0.815160\pi$
$548$	−8.94340e50	−1.92337
$549$	−2.07823e50	−0.432121
$550$	−8.62125e50	−1.73325
$551$	6.15763e50	1.19704
$552$	−3.77193e50	−0.709072
$553$	−1.00054e50	−0.181894
$554$	1.37173e51	2.41178
$555$	−2.53077e50	−0.430360
$556$	−9.14767e50	−1.50462
$557$	4.20191e50	0.668537	0.334268	−	0.942478i	$-0.391511\pi$
$557$	4.20191e50	0.668537	0.334268	+	0.942478i	$0.391511\pi$
$558$	3.48609e50	0.536544
$559$	6.42822e50	0.957133
$560$	2.31314e51	3.33214
$561$	1.12737e50	0.157128
$562$	−1.18716e51	−1.60099
$563$	−8.89971e50	−1.16137	−0.580685	−	0.814128i	$-0.697215\pi$
$563$	−8.89971e50	−1.16137	−0.580685	+	0.814128i	$0.697215\pi$
$564$	1.49230e51	1.88448
$565$	4.70481e50	0.574971
$566$	−9.83147e50	−1.16283
$567$	−9.24738e49	−0.105860
$568$	8.05731e50	0.892782
$569$	−1.72128e51	−1.84618	−0.923092	−	0.384579i	$-0.874347\pi$
$569$	−1.72128e51	−1.84618	−0.923092	+	0.384579i	$0.874347\pi$
$570$	−2.91229e51	−3.02378
$571$	6.69419e50	0.672868	0.336434	−	0.941707i	$-0.390779\pi$
$571$	6.69419e50	0.672868	0.336434	+	0.941707i	$0.390779\pi$
$572$	1.53321e51	1.49202
$573$	3.07889e50	0.290090
$574$	1.43506e51	1.30919
$575$	−8.45521e50	−0.746912
$576$	2.48683e50	0.212731
$577$	2.04906e51	1.69747	0.848737	−	0.528815i	$-0.177364\pi$
$577$	2.04906e51	1.69747	0.848737	+	0.528815i	$0.177364\pi$
$578$	1.85037e51	1.48454
$579$	9.80181e50	0.761645
$580$	−3.30140e51	−2.48474
$581$	−1.81255e51	−1.32139
$582$	−1.17652e51	−0.830850
$583$	−4.69466e50	−0.321171
$584$	−5.56978e51	−3.69148
$585$	−8.33887e50	−0.535456
$586$	3.55004e51	2.20865
$587$	1.81661e51	1.09511	0.547554	−	0.836770i	$-0.315559\pi$
$587$	1.81661e51	1.09511	0.547554	+	0.836770i	$0.315559\pi$
$588$	2.15163e50	0.125686
$589$	−2.79600e51	−1.58272
$590$	6.09605e50	0.334415
$591$	−4.08866e50	−0.217376
$592$	−2.01196e51	−1.03674
$593$	−4.63037e50	−0.231262	−0.115631	−	0.993292i	$-0.536889\pi$
$593$	−4.63037e50	−0.231262	−0.115631	+	0.993292i	$0.536889\pi$
$594$	4.54906e50	0.220228
$595$	−1.40324e51	−0.658520
$596$	5.19055e51	2.36133
$597$	−1.44824e51	−0.638729
$598$	2.14113e51	0.915526
$599$	−5.00284e50	−0.207406	−0.103703	−	0.994608i	$-0.533069\pi$
$599$	−5.00284e50	−0.207406	−0.103703	+	0.994608i	$0.533069\pi$
$600$	5.41790e51	2.17787
$601$	3.80150e51	1.48176	0.740880	−	0.671638i	$-0.234409\pi$
$601$	3.80150e51	1.48176	0.740880	+	0.671638i	$0.234409\pi$
$602$	4.36488e51	1.64982
$603$	5.29915e50	0.194239
$604$	1.48417e51	0.527596
$605$	2.80633e51	0.967530
$606$	4.51086e51	1.50840
$607$	2.17471e51	0.705360	0.352680	−	0.935744i	$-0.385270\pi$
$607$	2.17471e51	0.705360	0.352680	+	0.935744i	$0.385270\pi$
$608$	−8.88749e51	−2.79617
$609$	1.19720e51	0.365382
$610$	−1.27252e52	−3.76758
$611$	−4.87992e51	−1.40169
$612$	−1.22984e51	−0.342726
$613$	1.29111e51	0.349095	0.174548	−	0.984649i	$-0.444154\pi$
$613$	1.29111e51	0.349095	0.174548	+	0.984649i	$0.444154\pi$
$614$	−1.27122e52	−3.33508
$615$	2.69646e51	0.686443
$616$	5.99737e51	1.48156
$617$	−4.63240e50	−0.111053	−0.0555265	−	0.998457i	$-0.517684\pi$
$617$	−4.63240e50	−0.111053	−0.0555265	+	0.998457i	$0.517684\pi$
$618$	−6.20293e51	−1.44315
$619$	2.35900e51	0.532660	0.266330	−	0.963882i	$-0.414189\pi$
$619$	2.35900e51	0.532660	0.266330	+	0.963882i	$0.414189\pi$
$620$	1.49907e52	3.28530
$621$	4.46145e50	0.0949034
$622$	−4.27344e51	−0.882381
$623$	−7.38552e51	−1.48031
$624$	−6.62940e51	−1.28991
$625$	−1.16749e51	−0.220532
$626$	1.62886e52	2.98717
$627$	−3.64855e51	−0.649637
$628$	4.18261e51	0.723093
$629$	1.22054e51	0.204887
$630$	−5.66225e51	−0.922973
$631$	−1.06497e52	−1.68576	−0.842880	−	0.538101i	$-0.819142\pi$
$631$	−1.06497e52	−1.68576	−0.842880	+	0.538101i	$0.819142\pi$
$632$	−3.09312e51	−0.475479
$633$	6.40946e51	0.956869
$634$	1.77142e52	2.56845
$635$	−5.70567e51	−0.803512
$636$	5.12137e51	0.700535
$637$	−7.03598e50	−0.0934857
$638$	−5.88940e51	−0.760131
$639$	−9.53021e50	−0.119491
$640$	−4.97304e51	−0.605749
$641$	1.54062e52	1.82314	0.911572	−	0.411141i	$-0.134870\pi$
$641$	1.54062e52	1.82314	0.911572	+	0.411141i	$0.134870\pi$
$642$	−1.11984e52	−1.28753
$643$	−1.17010e52	−1.30713	−0.653565	−	0.756871i	$-0.726727\pi$
$643$	−1.17010e52	−1.30713	−0.653565	+	0.756871i	$0.726727\pi$
$644$	1.02103e52	1.10828
$645$	8.20153e51	0.865048
$646$	1.40454e52	1.43957
$647$	5.61235e51	0.559005	0.279503	−	0.960145i	$-0.409830\pi$
$647$	5.61235e51	0.559005	0.279503	+	0.960145i	$0.409830\pi$
$648$	−2.85879e51	−0.276723
$649$	7.63718e50	0.0718466
$650$	−3.07546e52	−2.81198
$651$	−5.43614e51	−0.483106
$652$	7.39015e51	0.638371
$653$	−9.59702e51	−0.805828	−0.402914	−	0.915238i	$-0.632003\pi$
$653$	−9.59702e51	−0.805828	−0.402914	+	0.915238i	$0.632003\pi$
$654$	−4.26492e51	−0.348115
$655$	1.55820e52	1.23640
$656$	2.14369e52	1.65364
$657$	6.58796e51	0.494073
$658$	−3.31356e52	−2.41610
$659$	9.86794e51	0.699594	0.349797	−	0.936826i	$-0.386251\pi$
$659$	9.86794e51	0.699594	0.349797	+	0.936826i	$0.386251\pi$
$660$	1.95616e52	1.34847
$661$	−3.94530e51	−0.264456	−0.132228	−	0.991219i	$-0.542213\pi$
$661$	−3.94530e51	−0.264456	−0.132228	+	0.991219i	$0.542213\pi$
$662$	1.79556e52	1.17038
$663$	4.02166e51	0.254921
$664$	−5.60345e52	−3.45419
$665$	4.54137e52	2.72262
$666$	4.92501e51	0.287166
$667$	−5.77598e51	−0.327565
$668$	−3.48854e52	−1.92433
$669$	1.36947e51	0.0734799
$670$	3.24472e52	1.69353
$671$	−1.59422e52	−0.809436
$672$	−1.72796e52	−0.853495
$673$	−1.19487e52	−0.574172	−0.287086	−	0.957905i	$-0.592687\pi$
$673$	−1.19487e52	−0.574172	−0.287086	+	0.957905i	$0.592687\pi$
$674$	−8.71947e51	−0.407645
$675$	−6.40831e51	−0.291490
$676$	1.39449e51	0.0617164
$677$	−1.67874e52	−0.722924	−0.361462	−	0.932387i	$-0.617722\pi$
$677$	−1.67874e52	−0.722924	−0.361462	+	0.932387i	$0.617722\pi$
$678$	−9.15581e51	−0.383661
$679$	1.83464e52	0.748099
$680$	−4.33808e52	−1.72140
$681$	−9.61888e51	−0.371452
$682$	2.67420e52	1.00504
$683$	−1.07263e52	−0.392345	−0.196172	−	0.980569i	$-0.562851\pi$
$683$	−1.07263e52	−0.392345	−0.196172	+	0.980569i	$0.562851\pi$
$684$	3.98018e52	1.41698
$685$	3.73134e52	1.29297
$686$	−5.65465e52	−1.90726
$687$	−1.82092e52	−0.597849
$688$	6.52022e52	2.08390
$689$	−1.67473e52	−0.521061
$690$	2.73179e52	0.827444
$691$	1.11109e51	0.0327648	0.0163824	−	0.999866i	$-0.494785\pi$
$691$	1.11109e51	0.0327648	0.0163824	+	0.999866i	$0.494785\pi$
$692$	6.11599e51	0.175592
$693$	−7.09372e51	−0.198294
$694$	9.62493e52	2.61968
$695$	3.81656e52	1.01147
$696$	3.70111e52	0.955126
$697$	−1.30045e52	−0.326803
$698$	1.19332e53	2.92032
$699$	−3.40671e52	−0.811910
$700$	−1.46657e53	−3.40401
$701$	−3.38745e52	−0.765755	−0.382877	−	0.923799i	$-0.625067\pi$
$701$	−3.38745e52	−0.765755	−0.382877	+	0.923799i	$0.625067\pi$
$702$	1.62279e52	0.357294
$703$	−3.95007e52	−0.847094
$704$	1.90766e52	0.398480
$705$	−6.22612e52	−1.26683
$706$	1.04670e53	2.07460
$707$	−7.03414e52	−1.35816
$708$	−8.33135e51	−0.156711
$709$	−1.72294e52	−0.315729	−0.157865	−	0.987461i	$-0.550461\pi$
$709$	−1.72294e52	−0.315729	−0.157865	+	0.987461i	$0.550461\pi$
$710$	−5.83543e52	−1.04182
$711$	3.65856e51	0.0636388
$712$	−2.28321e53	−3.86959
$713$	2.62270e52	0.433104
$714$	2.73079e52	0.439411
$715$	−6.39680e52	−1.00300
$716$	2.38246e53	3.64029
$717$	4.38682e52	0.653199
$718$	7.30542e52	1.06009
$719$	6.83545e52	0.966680	0.483340	−	0.875433i	$-0.339423\pi$
$719$	6.83545e52	0.966680	0.483340	+	0.875433i	$0.339423\pi$
$720$	−8.45821e52	−1.16581
$721$	9.67273e52	1.29941
$722$	−3.14586e53	−4.11909
$723$	5.17642e52	0.660649
$724$	−3.54555e53	−4.41083
$725$	8.29646e52	1.00610
$726$	−5.46126e52	−0.645603
$727$	−1.43130e52	−0.164947	−0.0824736	−	0.996593i	$-0.526282\pi$
$727$	−1.43130e52	−0.164947	−0.0824736	+	0.996593i	$0.526282\pi$
$728$	2.13944e53	2.40364
$729$	3.38139e51	0.0370370
$730$	4.03386e53	4.30773
$731$	−3.95543e52	−0.411834
$732$	1.73913e53	1.76554
$733$	1.21007e53	1.19781	0.598904	−	0.800821i	$-0.295603\pi$
$733$	1.21007e53	1.19781	0.598904	+	0.800821i	$0.295603\pi$
$734$	−2.16033e53	−2.08518
$735$	−8.97695e51	−0.0844915
$736$	8.33663e52	0.765158
$737$	4.06501e52	0.363842
$738$	−5.24745e52	−0.458042
$739$	−1.58257e52	−0.134723	−0.0673613	−	0.997729i	$-0.521458\pi$
$739$	−1.58257e52	−0.134723	−0.0673613	+	0.997729i	$0.521458\pi$
$740$	2.11782e53	1.75834
$741$	−1.30155e53	−1.05396
$742$	−1.13717e53	−0.898159
$743$	1.09014e53	0.839823	0.419911	−	0.907565i	$-0.362061\pi$
$743$	1.09014e53	0.839823	0.419911	+	0.907565i	$0.362061\pi$
$744$	−1.68056e53	−1.26286
$745$	−2.16558e53	−1.58739
$746$	1.21187e51	0.00866536
$747$	6.62778e52	0.462314
$748$	−9.43417e52	−0.641984
$749$	1.74625e53	1.15929
$750$	−1.33322e53	−0.863510
$751$	6.11841e52	0.386634	0.193317	−	0.981136i	$-0.438075\pi$
$751$	6.11841e52	0.386634	0.193317	+	0.981136i	$0.438075\pi$
$752$	−4.94976e53	−3.05179
$753$	−3.53653e50	−0.00212750
$754$	−2.10093e53	−1.23322
$755$	−6.19222e52	−0.354673
$756$	7.73849e52	0.432517
$757$	1.99961e53	1.09062	0.545308	−	0.838236i	$-0.316413\pi$
$757$	1.99961e53	1.09062	0.545308	+	0.838236i	$0.316413\pi$
$758$	1.00795e53	0.536485
$759$	3.42241e52	0.177770
$760$	1.40395e54	7.11705
$761$	−1.62121e53	−0.802092	−0.401046	−	0.916058i	$-0.631353\pi$
$761$	−1.62121e53	−0.802092	−0.401046	+	0.916058i	$0.631353\pi$
$762$	1.11035e53	0.536159
$763$	6.65063e52	0.313443
$764$	−2.57651e53	−1.18523
$765$	5.13110e52	0.230395
$766$	−6.96547e53	−3.05294
$767$	2.72441e52	0.116562
$768$	1.84999e53	0.772658
$769$	−3.14345e53	−1.28165	−0.640825	−	0.767687i	$-0.721408\pi$
$769$	−3.14345e53	−1.28165	−0.640825	+	0.767687i	$0.721408\pi$
$770$	−4.34354e53	−1.72888
$771$	2.16826e53	0.842567
$772$	−8.20245e53	−3.11188
$773$	−2.85720e53	−1.05833	−0.529164	−	0.848520i	$-0.677494\pi$
$773$	−2.85720e53	−1.05833	−0.529164	+	0.848520i	$0.677494\pi$
$774$	−1.59606e53	−0.577220
$775$	−3.76717e53	−1.33025
$776$	5.67171e53	1.95557
$777$	−7.67996e52	−0.258565
$778$	4.88454e53	1.60584
$779$	4.20869e53	1.35115
$780$	6.97822e53	2.18773
$781$	−7.31068e52	−0.223828
$782$	−1.31748e53	−0.393931
$783$	−4.37768e52	−0.127836
$784$	−7.13667e52	−0.203539
$785$	−1.74506e53	−0.486095
$786$	−3.03234e53	−0.825013
$787$	3.70794e53	0.985371	0.492685	−	0.870207i	$-0.336015\pi$
$787$	3.70794e53	0.985371	0.492685	+	0.870207i	$0.336015\pi$
$788$	3.42151e53	0.888143
$789$	2.05472e53	0.520987
$790$	2.24017e53	0.554854
$791$	1.42774e53	0.345449
$792$	−2.19300e53	−0.518349
$793$	−5.68708e53	−1.31321
$794$	1.34214e54	3.02775
$795$	−2.13672e53	−0.470930
$796$	1.21193e54	2.60968
$797$	−7.44870e53	−1.56712	−0.783558	−	0.621318i	$-0.786597\pi$
$797$	−7.44870e53	−1.56712	−0.783558	+	0.621318i	$0.786597\pi$
$798$	−8.83775e53	−1.81672
$799$	3.00273e53	0.603115
$800$	−1.19745e54	−2.35014
$801$	2.70058e53	0.517912
$802$	8.10827e53	1.51951
$803$	5.05366e53	0.925483
$804$	−4.43449e53	−0.793609
$805$	−4.25989e53	−0.745032
$806$	9.53967e53	1.63055
$807$	1.02845e53	0.171799
$808$	−2.17458e54	−3.55030
$809$	−1.60117e53	−0.255499	−0.127749	−	0.991806i	$-0.540775\pi$
$809$	−1.60117e53	−0.255499	−0.127749	+	0.991806i	$0.540775\pi$
$810$	2.07046e53	0.322919
$811$	1.93099e53	0.294371	0.147185	−	0.989109i	$-0.452979\pi$
$811$	1.93099e53	0.294371	0.147185	+	0.989109i	$0.452979\pi$
$812$	−1.00186e54	−1.49286
$813$	2.01166e53	0.293008
$814$	3.77800e53	0.537911
$815$	−3.08330e53	−0.429141
$816$	4.07922e53	0.555021
$817$	1.28011e54	1.70271
$818$	−1.82041e54	−2.36719
$819$	−2.53054e53	−0.321708
$820$	−2.25648e54	−2.80463
$821$	−6.63036e53	−0.805728	−0.402864	−	0.915260i	$-0.631985\pi$
$821$	−6.63036e53	−0.805728	−0.402864	+	0.915260i	$0.631985\pi$
$822$	−7.26138e53	−0.862761
$823$	7.44114e53	0.864455	0.432227	−	0.901765i	$-0.357728\pi$
$823$	7.44114e53	0.864455	0.432227	+	0.901765i	$0.357728\pi$
$824$	2.99029e54	3.39672
$825$	−4.91585e53	−0.546010
$826$	1.84993e53	0.200920
$827$	−9.00288e53	−0.956158	−0.478079	−	0.878317i	$-0.658667\pi$
$827$	−9.00288e53	−0.956158	−0.478079	+	0.878317i	$0.658667\pi$
$828$	−3.73348e53	−0.387751
$829$	−3.70753e53	−0.376553	−0.188276	−	0.982116i	$-0.560290\pi$
$829$	−3.70753e53	−0.376553	−0.188276	+	0.982116i	$0.560290\pi$
$830$	4.05825e54	4.03082
$831$	7.82164e53	0.759764
$832$	6.80520e53	0.646486
$833$	4.32940e52	0.0402249
$834$	−7.42722e53	−0.674924
$835$	1.45548e54	1.29362
$836$	3.05322e54	2.65425
$837$	1.98778e53	0.169023
$838$	−8.43304e53	−0.701407
$839$	−1.89366e54	−1.54066	−0.770329	−	0.637646i	$-0.779908\pi$
$839$	−1.89366e54	−1.54066	−0.770329	+	0.637646i	$0.779908\pi$
$840$	2.72964e54	2.17239
$841$	−7.17723e53	−0.558767
$842$	−1.41677e54	−1.07901
$843$	−6.76924e53	−0.504347
$844$	−5.36363e54	−3.90952
$845$	−5.81804e52	−0.0414885
$846$	1.21163e54	0.845318
$847$	8.51619e53	0.581302
$848$	−1.69869e54	−1.13447
$849$	−5.60593e53	−0.366315
$850$	1.89240e54	1.20994
$851$	3.70524e53	0.231803
$852$	7.97517e53	0.488211
$853$	1.21911e52	0.00730272	0.00365136	−	0.999993i	$-0.498838\pi$
$853$	1.21911e52	0.00730272	0.00365136	+	0.999993i	$0.498838\pi$
$854$	−3.86163e54	−2.26360
$855$	−1.66060e54	−0.952557
$856$	5.39847e54	3.03044
$857$	1.82750e54	1.00395	0.501975	−	0.864882i	$-0.332607\pi$
$857$	1.82750e54	1.00395	0.501975	+	0.864882i	$0.332607\pi$
$858$	1.24485e54	0.669271
$859$	5.92142e53	0.311568	0.155784	−	0.987791i	$-0.450210\pi$
$859$	5.92142e53	0.311568	0.155784	+	0.987791i	$0.450210\pi$
$860$	−6.86329e54	−3.53436
$861$	8.18277e53	0.412422
$862$	−4.52628e54	−2.23284
$863$	2.34693e53	0.113318	0.0566592	−	0.998394i	$-0.481955\pi$
$863$	2.34693e53	0.113318	0.0566592	+	0.998394i	$0.481955\pi$
$864$	6.31844e53	0.298611
$865$	−2.55170e53	−0.118040
$866$	6.61679e53	0.299617
$867$	1.05508e54	0.467663
$868$	4.54912e54	1.97384
$869$	2.80650e53	0.119206
$870$	−2.68049e54	−1.11457
$871$	1.45011e54	0.590290
$872$	2.05602e54	0.819355
$873$	−6.70852e53	−0.261736
$874$	4.26382e54	1.62869
$875$	2.07899e54	0.777506
$876$	−5.51300e54	−2.01866
$877$	−7.93050e53	−0.284320	−0.142160	−	0.989844i	$-0.545405\pi$
$877$	−7.93050e53	−0.284320	−0.142160	+	0.989844i	$0.545405\pi$
$878$	−4.20493e54	−1.47608
$879$	2.02424e54	0.695773
$880$	−6.48834e54	−2.18376
$881$	2.56353e54	0.844859	0.422429	−	0.906396i	$-0.361177\pi$
$881$	2.56353e54	0.844859	0.422429	+	0.906396i	$0.361177\pi$
$882$	1.74696e53	0.0563786
$883$	2.54626e54	0.804691	0.402346	−	0.915488i	$-0.368195\pi$
$883$	2.54626e54	0.804691	0.402346	+	0.915488i	$0.368195\pi$
$884$	−3.36545e54	−1.04154
$885$	3.47598e53	0.105348
$886$	2.09976e54	0.623227
$887$	2.32098e54	0.674660	0.337330	−	0.941386i	$-0.390476\pi$
$887$	2.32098e54	0.674660	0.337330	+	0.941386i	$0.390476\pi$
$888$	−2.37423e54	−0.675901
$889$	−1.73146e54	−0.482759
$890$	1.65359e55	4.51557
$891$	2.59389e53	0.0693767
$892$	−1.14601e54	−0.300220
$893$	−9.71784e54	−2.49355
$894$	4.21434e54	1.05922
$895$	−9.94004e54	−2.44716
$896$	−1.50914e54	−0.363941
$897$	1.22088e54	0.288411
$898$	4.66967e54	1.08062
$899$	−2.57345e54	−0.583394
$900$	5.36267e54	1.19095
$901$	1.03050e54	0.224201
$902$	−4.02535e54	−0.857991
$903$	2.48886e54	0.519730
$904$	4.41380e54	0.903019
$905$	1.47926e55	2.96515
$906$	1.20504e54	0.236662
$907$	−8.85168e54	−1.70330	−0.851649	−	0.524112i	$-0.824397\pi$
$907$	−8.85168e54	−1.70330	−0.851649	+	0.524112i	$0.824397\pi$
$908$	8.04937e54	1.51766
$909$	2.57210e54	0.475178
$910$	−1.54947e55	−2.80491
$911$	−3.42424e54	−0.607399	−0.303699	−	0.952768i	$-0.598222\pi$
$911$	−3.42424e54	−0.607399	−0.303699	+	0.952768i	$0.598222\pi$
$912$	−1.32017e55	−2.29470
$913$	5.08421e54	0.865992
$914$	4.07578e54	0.680309
$915$	−7.25593e54	−1.18687
$916$	1.52380e55	2.44266
$917$	4.72857e54	0.742843
$918$	−9.98538e53	−0.153736
$919$	−8.49570e54	−1.28192	−0.640962	−	0.767573i	$-0.721464\pi$
$919$	−8.49570e54	−1.28192	−0.640962	+	0.767573i	$0.721464\pi$
$920$	−1.31693e55	−1.94755
$921$	−7.24852e54	−1.05062
$922$	1.38148e54	0.196256
$923$	−2.60794e54	−0.363133
$924$	5.93624e54	0.810177
$925$	−5.32211e54	−0.711970
$926$	−2.22389e55	−2.91616
$927$	−3.53693e54	−0.454623
$928$	−8.18010e54	−1.03067
$929$	−5.60014e54	−0.691685	−0.345843	−	0.938293i	$-0.612407\pi$
$929$	−5.60014e54	−0.691685	−0.345843	+	0.938293i	$0.612407\pi$
$930$	1.21713e55	1.47368
$931$	−1.40114e54	−0.166308
$932$	2.85084e55	3.31726
$933$	−2.43673e54	−0.277969
$934$	1.31979e54	0.147601
$935$	3.93609e54	0.431569
$936$	−7.82308e54	−0.840958
$937$	9.79573e54	1.03242	0.516208	−	0.856463i	$-0.327343\pi$
$937$	9.79573e54	1.03242	0.516208	+	0.856463i	$0.327343\pi$
$938$	9.84652e54	1.01749
$939$	9.28782e54	0.941023
$940$	5.21020e55	5.17594
$941$	1.66648e54	0.162328	0.0811638	−	0.996701i	$-0.474136\pi$
$941$	1.66648e54	0.162328	0.0811638	+	0.996701i	$0.474136\pi$
$942$	3.39597e54	0.324356
$943$	−3.94783e54	−0.369736
$944$	2.76340e54	0.253783
$945$	−3.22863e54	−0.290756
$946$	−1.22435e55	−1.08123
$947$	1.77183e54	0.153443	0.0767216	−	0.997053i	$-0.475555\pi$
$947$	1.77183e54	0.153443	0.0767216	+	0.997053i	$0.475555\pi$
$948$	−3.06159e54	−0.260012
$949$	1.80279e55	1.50148
$950$	−6.12444e55	−5.00242
$951$	1.01007e55	0.809117
$952$	−1.31645e55	−1.03424
$953$	−7.66663e54	−0.590726	−0.295363	−	0.955385i	$-0.595441\pi$
$953$	−7.66663e54	−0.590726	−0.295363	+	0.955385i	$0.595441\pi$
$954$	4.15817e54	0.314237
$955$	1.07496e55	0.796766
$956$	−3.67103e55	−2.66880
$957$	−3.35815e54	−0.239458
$958$	8.57254e54	0.599581
$959$	1.13232e55	0.776831
$960$	8.68250e54	0.584288
$961$	−3.46368e54	−0.228641
$962$	1.34773e55	0.872696
$963$	−6.38533e54	−0.405599
$964$	−4.33179e55	−2.69924
$965$	3.42220e55	2.09194
$966$	8.28997e54	0.497137
$967$	−1.08091e55	−0.635915	−0.317957	−	0.948105i	$-0.602997\pi$
$967$	−1.08091e55	−0.635915	−0.317957	+	0.948105i	$0.602997\pi$
$968$	2.63275e55	1.51955
$969$	8.00871e54	0.453495
$970$	−4.10769e55	−2.28202
$971$	1.69341e55	0.923011	0.461505	−	0.887137i	$-0.347310\pi$
$971$	1.69341e55	0.923011	0.461505	+	0.887137i	$0.347310\pi$
$972$	−2.82965e54	−0.151324
$973$	1.15819e55	0.607702
$974$	−4.43145e54	−0.228142
$975$	−1.75363e55	−0.885836
$976$	−5.76846e55	−2.85916
$977$	−1.54539e55	−0.751603	−0.375802	−	0.926700i	$-0.622633\pi$
$977$	−1.54539e55	−0.751603	−0.375802	+	0.926700i	$0.622633\pi$
$978$	6.00026e54	0.286352
$979$	2.07163e55	0.970138
$980$	7.51218e54	0.345210
$981$	−2.43187e54	−0.109664
$982$	2.47042e55	1.09322
$983$	−1.30842e55	−0.568209	−0.284104	−	0.958793i	$-0.591696\pi$
$983$	−1.30842e55	−0.568209	−0.284104	+	0.958793i	$0.591696\pi$
$984$	2.52967e55	1.07809
$985$	−1.42751e55	−0.597048
$986$	1.29275e55	0.530629
$987$	−1.88940e55	−0.761126
$988$	1.08917e56	4.30620
$989$	−1.20077e55	−0.465938
$990$	1.58826e55	0.604881
$991$	−1.06749e55	−0.399025	−0.199512	−	0.979895i	$-0.563936\pi$
$991$	−1.06749e55	−0.399025	−0.199512	+	0.979895i	$0.563936\pi$
$992$	3.71434e55	1.36275
$993$	1.02384e55	0.368696
$994$	−1.77084e55	−0.625938
$995$	−5.05639e55	−1.75434
$996$	−5.54633e55	−1.88889
$997$	1.93192e55	0.645846	0.322923	−	0.946425i	$-0.395335\pi$
$997$	1.93192e55	0.645846	0.322923	+	0.946425i	$0.395335\pi$
$998$	−5.32887e54	−0.174872
$999$	2.80825e54	0.0904637

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.38.a.a.1.1	✓	3
3.2	odd	2		9.38.a.b.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.38.a.a.1.1	✓	3	1.1	even	1	trivial
9.38.a.b.1.3		3	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 38 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-679444. q^{2} -3.87420e8 q^{3} +3.24205e11 q^{4} -1.35264e13 q^{5} +2.63231e14 q^{6} -4.10476e15 q^{7} -1.26897e17 q^{8} +1.50095e17 q^{9} +O(q^{10})\)	\(q-679444. q^{2} -3.87420e8 q^{3} +3.24205e11 q^{4} -1.35264e13 q^{5} +2.63231e14 q^{6} -4.10476e15 q^{7} -1.26897e17 q^{8} +1.50095e17 q^{9} +9.19042e18 q^{10} +1.15138e19 q^{11} -1.25604e20 q^{12} +4.10734e20 q^{13} +2.78896e21 q^{14} +5.24040e21 q^{15} +4.16612e22 q^{16} -2.52734e22 q^{17} -1.01981e23 q^{18} +8.17932e23 q^{19} -4.38533e24 q^{20} +1.59027e24 q^{21} -7.82302e24 q^{22} -7.67235e24 q^{23} +4.91626e25 q^{24} +1.10204e26 q^{25} -2.79071e26 q^{26} -5.81497e25 q^{27} -1.33079e27 q^{28} +7.52830e26 q^{29} -3.56056e27 q^{30} -3.41837e27 q^{31} -1.08658e28 q^{32} -4.46070e27 q^{33} +1.71718e28 q^{34} +5.55226e28 q^{35} +4.86615e28 q^{36} -4.82934e28 q^{37} -5.55739e29 q^{38} -1.59127e29 q^{39} +1.71646e30 q^{40} +5.14552e29 q^{41} -1.08050e30 q^{42} +1.56506e30 q^{43} +3.73285e30 q^{44} -2.03024e30 q^{45} +5.21293e30 q^{46} -1.18810e31 q^{47} -1.61404e31 q^{48} -1.71303e30 q^{49} -7.48772e31 q^{50} +9.79142e30 q^{51} +1.33162e32 q^{52} -4.07740e31 q^{53} +3.95095e31 q^{54} -1.55741e32 q^{55} +5.20883e32 q^{56} -3.16884e32 q^{57} -5.11506e32 q^{58} +6.63304e31 q^{59} +1.69897e33 q^{60} -1.38461e33 q^{61} +2.32259e33 q^{62} -6.16103e32 q^{63} +1.65684e33 q^{64} -5.55574e33 q^{65} +3.03080e33 q^{66} +3.53054e33 q^{67} -8.19376e33 q^{68} +2.97243e33 q^{69} -3.77245e34 q^{70} -6.34947e33 q^{71} -1.90466e34 q^{72} +4.38920e34 q^{73} +3.28127e34 q^{74} -4.26951e34 q^{75} +2.65178e35 q^{76} -4.72616e34 q^{77} +1.08118e35 q^{78} +2.43750e34 q^{79} -5.63525e35 q^{80} +2.25284e34 q^{81} -3.49610e35 q^{82} +4.41573e35 q^{83} +5.15574e35 q^{84} +3.41857e35 q^{85} -1.06337e36 q^{86} -2.91662e35 q^{87} -1.46108e36 q^{88} +1.79925e36 q^{89} +1.37943e36 q^{90} -1.68596e36 q^{91} -2.48742e36 q^{92} +1.32435e36 q^{93} +8.07247e36 q^{94} -1.10637e37 q^{95} +4.20964e36 q^{96} -4.46953e36 q^{97} +1.16391e36 q^{98} +1.72817e36 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 310908 q^{2} - 1162261467 q^{3} + 338476600848 q^{4} - 9628717886790 q^{5} + 120452129394012 q^{6} - 46\!\cdots\!44 q^{7}+ \cdots + 45\!\cdots\!63 q^{9}+O(q^{10}) \) 3 * q - 310908 * q^2 - 1162261467 * q^3 + 338476600848 * q^4 - 9628717886790 * q^5 + 120452129394012 * q^6 - 4621884343701744 * q^7 - 93383909093911488 * q^8 + 450283905890997363 * q^9	\( 3 q - 310908 q^{2} - 1162261467 q^{3} + 338476600848 q^{4} - 9628717886790 q^{5} + 120452129394012 q^{6} - 46\!\cdots\!44 q^{7}+ \cdots + 34\!\cdots\!20 q^{99}+O(q^{100}) \) 3 * q - 310908 * q^2 - 1162261467 * q^3 + 338476600848 * q^4 - 9628717886790 * q^5 + 120452129394012 * q^6 - 4621884343701744 * q^7 - 93383909093911488 * q^8 + 450283905890997363 * q^9 + 10698950136741797880 * q^10 + 22673303357139628620 * q^11 - 131132770215589974672 * q^12 - 168270000203795091510 * q^13 + 797101803583223694528 * q^14 + 3730362592143228440310 * q^15 + 32071173863897028608256 * q^16 - 27168549617785276146906 * q^17 - 46665622870919402711868 * q^18 + 582035599719143813745204 * q^19 - 4066256929972106412494880 * q^20 + 1790612692538373730632816 * q^21 - 4486408000290444592999152 * q^22 - 17157197763697459349569272 * q^23 + 36178839725894735603677632 * q^24 - 24896488591542260192608275 * q^25 - 618603181238074545425686344 * q^26 - 174449211009120179071170507 * q^27 - 2033429672978753784958610688 * q^28 + 111201150055901033185229778 * q^29 - 4144992493763124201408763320 * q^30 - 11859842025407507592851987736 * q^31 - 27281435223830339470718352384 * q^32 - 8784102273868376561238795180 * q^33 - 18783445175675019452330905464 * q^34 + 47739964986924083632994534880 * q^35 + 50803521960848503410923854608 * q^36 + 60344578140045347560278093666 * q^37 - 372452605565029151271789397776 * q^38 + 65191245762984394008603948390 * q^39 + 1732463594119923393272610326400 * q^40 + 2087364862188523841295969725934 * q^41 - 308813570526994475930424384192 * q^42 + 2483325896102099669944761791244 * q^43 + 4284309379683814482835899511872 * q^44 - 1445218899595437120383607511590 * q^45 - 4327236604482200607954371165856 * q^46 - 11791379189662012541191082473632 * q^47 - 12425029861155006269057528957184 * q^48 - 22445324860908932271245865545973 * q^49 - 96691457712658313260807892933700 * q^50 + 10525652778343134781834358357034 * q^51 + 43220201443333906987967057359584 * q^52 - 115357757368640109037215455345382 * q^53 + 18079218432141178878219826663452 * q^54 - 129419469300146958823045789059480 * q^55 + 630552391741804501615596905794560 * q^56 - 225492516658598958982491855084756 * q^57 + 580965936186746161132050423512088 * q^58 + 1091721381032593697748326986744236 * q^59 + 1575351248209432222688802119596320 * q^60 + 294380981976352085651508270601002 * q^61 + 248838835694853996733454208986592 * q^62 - 693720044952823401986519854167024 * q^63 - 1064135955800023765084313699610624 * q^64 - 7515875365146923444942971038019860 * q^65 + 1738126381326036186247137444425328 * q^66 + 3824374619785575741360273276519444 * q^67 - 21329399470876894544665401157365216 * q^68 + 6647049947481376149267749297614008 * q^69 - 43059062291480572688803543269144960 * q^70 - 22149353642418626281921550104284744 * q^71 - 14016423778058764430102498387802048 * q^72 + 32759279450923542889398870347665278 * q^73 + 46478870171568672595185044851456728 * q^74 + 9645409784518223707985532085946475 * q^75 + 347061692957154720144564653376455616 * q^76 - 61122141948697926808926153780754368 * q^77 + 239659546972210465807272116553102216 * q^78 + 74649348023552719727334936629819640 * q^79 - 618088038723375449595358546989335040 * q^80 + 67585198634817523235520443624317923 * q^81 + 103937675337495441364448738414881512 * q^82 - 317656267631459020909914460046822604 * q^83 + 787792318252538877979265797505586432 * q^84 + 210972517320554825185658741373302580 * q^85 - 2655243937093032975138251645354123760 * q^86 - 43081603932019555612226948170121442 * q^87 - 1353962196634819912991147659264835328 * q^88 - 1604427814888922862357874180114447026 * q^89 + 1605855018835039028277517574319663480 * q^90 + 459759011513895387754487414763335904 * q^91 - 5426885178857894678398508472745540224 * q^92 + 4594745796946127015893929993303122904 * q^93 + 15155501875748762861069416648677456000 * q^94 - 10713376656166940710475311057833316200 * q^95 + 10569386975038174570781705261883595776 * q^96 + 2690787195739502167683294096108844614 * q^97 - 1675640263817086437903041451354198300 * q^98 + 3403141198368098368991272474406443020 * q^99

Introduction

L-functions

Modular forms

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