LMFDB - Embedded newform 2.50.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,50,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 50, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 50);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 50 $
Character orbit:	$[\chi]$	$=$	2.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:	$30.4132410198$
Analytic rank:	$0$
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} - 104434803447206332x + 4289992005756109702361620 $ x^3 - x^2 - 104434803447206332*x + 4289992005756109702361620
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$4.17763e7$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.67772e7 q^{2} +7.94355e11 q^{3} +2.81475e14 q^{4} -5.65262e16 q^{5} +1.33271e19 q^{6} -4.38546e20 q^{7} +4.72237e21 q^{8} +3.91700e23 q^{9} +O(q^{10})$	\(q+1.67772e7 q^{2} +7.94355e11 q^{3} +2.81475e14 q^{4} -5.65262e16 q^{5} +1.33271e19 q^{6} -4.38546e20 q^{7} +4.72237e21 q^{8} +3.91700e23 q^{9} -9.48353e23 q^{10} +5.68225e25 q^{11} +2.23591e26 q^{12} +1.61873e27 q^{13} -7.35759e27 q^{14} -4.49019e28 q^{15} +7.92282e28 q^{16} +2.39583e30 q^{17} +6.57164e30 q^{18} -9.22680e30 q^{19} -1.59107e31 q^{20} -3.48361e32 q^{21} +9.53324e32 q^{22} -1.45988e33 q^{23} +3.75123e33 q^{24} -1.45684e34 q^{25} +2.71577e34 q^{26} +1.21060e35 q^{27} -1.23440e35 q^{28} +1.26757e36 q^{29} -7.53328e35 q^{30} -2.70852e36 q^{31} +1.32923e36 q^{32} +4.51372e37 q^{33} +4.01954e37 q^{34} +2.47894e37 q^{35} +1.10254e38 q^{36} -7.30159e37 q^{37} -1.54800e38 q^{38} +1.28584e39 q^{39} -2.66938e38 q^{40} +1.21786e39 q^{41} -5.84453e39 q^{42} -1.71091e40 q^{43} +1.59941e40 q^{44} -2.21413e40 q^{45} -2.44928e40 q^{46} -1.04023e41 q^{47} +6.29353e40 q^{48} -6.46007e40 q^{49} -2.44416e41 q^{50} +1.90314e42 q^{51} +4.55631e41 q^{52} -1.17198e41 q^{53} +2.03105e42 q^{54} -3.21196e42 q^{55} -2.07098e42 q^{56} -7.32935e42 q^{57} +2.12663e43 q^{58} -8.71601e42 q^{59} -1.26388e43 q^{60} -2.61290e43 q^{61} -4.54414e43 q^{62} -1.71779e44 q^{63} +2.23007e43 q^{64} -9.15004e43 q^{65} +7.57277e44 q^{66} +3.87604e44 q^{67} +6.74368e44 q^{68} -1.15966e45 q^{69} +4.15897e44 q^{70} +2.06352e44 q^{71} +1.84975e45 q^{72} +4.21892e44 q^{73} -1.22500e45 q^{74} -1.15724e46 q^{75} -2.59711e45 q^{76} -2.49193e46 q^{77} +2.15728e46 q^{78} +8.65650e45 q^{79} -4.47847e45 q^{80} +2.43119e45 q^{81} +2.04322e46 q^{82} +1.57334e47 q^{83} -9.80550e46 q^{84} -1.35427e47 q^{85} -2.87044e47 q^{86} +1.00690e48 q^{87} +2.68337e47 q^{88} -2.35938e47 q^{89} -3.71470e47 q^{90} -7.09886e47 q^{91} -4.10921e47 q^{92} -2.15153e48 q^{93} -1.74522e48 q^{94} +5.21556e47 q^{95} +1.05588e48 q^{96} +1.57542e48 q^{97} -1.08382e48 q^{98} +2.22574e49 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 50331648 q^{2} - 16203614388 q^{3} + 844424930131968 q^{4} - 10\!\cdots\!30 q^{5}+ \cdots + 38\!\cdots\!99 q^{9}+O(q^{10}) $ 3 * q + 50331648 * q^2 - 16203614388 * q^3 + 844424930131968 * q^4 - 101813016401840430 * q^5 - 271851538568183808 * q^6 - 125479179230203797096 * q^7 + 14167099448608935641088 * q^8 + 389432931519696922052199 * q^9	$ 3 q + 50331648 q^{2} - 16203614388 q^{3} + 844424930131968 q^{4} - 10\!\cdots\!30 q^{5}+ \cdots + 17\!\cdots\!68 q^{99}+O(q^{100}) $ 3 * q + 50331648 * q^2 - 16203614388 * q^3 + 844424930131968 * q^4 - 101813016401840430 * q^5 - 271851538568183808 * q^6 - 125479179230203797096 * q^7 + 14167099448608935641088 * q^8 + 389432931519696922052199 * q^9 - 1708138967785219691642880 * q^10 - 25860036791834065092767004 * q^11 - 4560911982490750474518528 * q^12 + 2945123797958353151076283242 * q^13 - 2105191293447842827899764736 * q^14 + 87846213583565151681178171080 * q^15 + 237684487542793012780631851008 * q^16 + 3910755572889939740390354668854 * q^17 + 6533600409619163515804905897984 * q^18 + 14590272981610371514592320211580 * q^19 - 28657816420549672374145992622080 * q^20 - 109864176920553355284360667668384 * q^21 - 433859423024547146219412063780864 * q^22 - 4953158032634305739950894912759608 * q^23 - 76519405487235538713099840258048 * q^24 + 39451396326519132102111422427450525 * q^25 + 49410978105087649819887436428214272 * q^26 + 196120894647932767255303897131684600 * q^27 - 35319249051493843857725179325054976 * q^28 + 937305925294643190481854503019954330 * q^29 + 1473814900073606599827889310694113280 * q^30 + 2414809991776326638635666091994140256 * q^31 + 3987683987354747618711421180841033728 * q^32 + 84513992666209345011409783180743651984 * q^33 + 65611590969578263251512904595972030464 * q^34 + 300439012903055674136683294221406953360 * q^35 + 109615625329869184043978320110151532544 * q^36 + 309377978155169809207437071391240173874 * q^37 + 244784161311441230740562508130843361280 * q^38 + 360871814296103457146322338824042742568 * q^39 - 480798376175908692150280133755042529280 * q^40 - 1143109642820632592659114174552039005954 * q^41 - 1843215026858338481130460343376694738944 * q^42 - 17579019372148890319048762066144112105148 * q^43 - 7278953253718200774306659587057331994624 * q^44 - 114813225075613761568802306330842527416790 * q^45 - 83100202195640796409195993344669099491328 * q^46 - 218573936001854642959028674713638582342256 * q^47 - 1283782594050935875866038049574767034368 * q^48 + 373628008074429359506251920014708170372651 * q^49 + 661884597671618007409657390132581787238400 * q^50 + 2241123510744223933356304325509677976541016 * q^51 + 828978652440326199960612616642419335626752 * q^52 + 740200780025011930130058449331923084936802 * q^53 + 3290362611621611989719960627820052978073600 * q^54 + 3200488473448119911679443277764576117207640 * q^55 - 592558670294707341071328602175181544226816 * q^56 - 20594915296543361145254552753753824314692880 * q^57 + 15725383966748092449643217077738426104545280 * q^58 - 53014363316602767635595514099864508327238540 * q^59 + 24726510922553313824338061789606248427028480 * q^60 - 124730102606725385116407342714381742110559494 * q^61 + 40513788830989655702944515329261561809207296 * q^62 - 468292624427612329618287149072325587596605768 * q^63 + 66902235595591869424607154817945084517941248 * q^64 - 421321721827999315000625667485604880336092420 * q^65 + 1417909509983410082474944396936503289964396544 * q^66 + 1111804215897361218882144911380577470099878924 * q^67 + 1100779833800263951475494327194015485053108224 * q^68 + 770909887444909922528222240570561038770401568 * q^69 + 5040530214301352105016749150744096280422645760 * q^70 - 4013080456871179368491803943114613092268032424 * q^71 + 1839045023134286552449577775805156054221717504 * q^72 - 10015638764428635672946257750737669286684666018 * q^73 + 5190501165152565405751960553138256904961654784 * q^74 - 38646070268253498119014909069282536501398301900 * q^75 + 4106796747700892799440257160412915334360596480 * q^76 - 23360330575813840356220747501745396153372866272 * q^77 + 6054424376757615658890593484076151085295730688 * q^78 + 36077368003505469428776991593224667583970712560 * q^79 - 8066458209552474124482754264517239602916884480 * q^80 - 14427585993163108762153736521422002728666768917 * q^81 - 19178197389284602263681972875121261643315544064 * q^82 + 150749458884727999220762915504103393007529125692 * q^83 - 30924016640048146099037657360264977001327099904 * q^84 + 566911972337878875844467446456481028710158526660 * q^85 - 294927005074726317042989995716306055916282707968 * q^86 + 1072056267743755243448622937355132996639037778920 * q^87 - 122120570991533057521910078130531663257517686784 * q^88 + 542251936064510107856207107418847041962289942670 * q^89 - 1926246276750188410412295154610712544457407856640 * q^90 - 1459783720923935217191336434024489699257545191344 * q^91 - 1394190041879939899769105566678075930691499982848 * q^92 - 2368291579513879043404530519265491460552020418176 * q^93 - 3667062136273291745526503225864452641889814839296 * q^94 - 2813579016011586836853932078889401271258883877400 * q^95 - 21538297877432866191553707421934574685271359488 * q^96 + 4343844254337968328695747517284119056283595359014 * q^97 + 6268437795114445441178041812501482151306766319616 * q^98 + 17595360353038055002493296165642581030249046200468 * 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 $

$2$	1.67772e7	0.707107
$2$	1.67772e7	0.707107
$3$	7.94355e11	1.62384	0.811921	−	0.583767i	$-0.198422\pi$
$3$	7.94355e11	1.62384	0.811921	+	0.583767i	$0.198422\pi$
$4$	2.81475e14	0.500000
$5$	−5.65262e16	−0.424116	−0.212058	−	0.977257i	$-0.568017\pi$
$5$	−5.65262e16	−0.424116	−0.212058	+	0.977257i	$0.568017\pi$
$6$	1.33271e19	1.14823
$7$	−4.38546e20	−0.865194	−0.432597	−	0.901587i	$-0.642403\pi$
$7$	−4.38546e20	−0.865194	−0.432597	+	0.901587i	$0.642403\pi$
$8$	4.72237e21	0.353553
$9$	3.91700e23	1.63686
$10$	−9.48353e23	−0.299895
$11$	5.68225e25	1.73940	0.869700	−	0.493580i	$-0.164312\pi$
$11$	5.68225e25	1.73940	0.869700	+	0.493580i	$0.164312\pi$
$12$	2.23591e26	0.811921
$13$	1.61873e27	0.827106	0.413553	−	0.910480i	$-0.364288\pi$
$13$	1.61873e27	0.827106	0.413553	+	0.910480i	$0.364288\pi$
$14$	−7.35759e27	−0.611785
$15$	−4.49019e28	−0.688698
$16$	7.92282e28	0.250000
$17$	2.39583e30	1.71182	0.855910	−	0.517124i	$-0.172997\pi$
$17$	2.39583e30	1.71182	0.855910	+	0.517124i	$0.172997\pi$
$18$	6.57164e30	1.15744
$19$	−9.22680e30	−0.432104	−0.216052	−	0.976382i	$-0.569318\pi$
$19$	−9.22680e30	−0.432104	−0.216052	+	0.976382i	$0.569318\pi$
$20$	−1.59107e31	−0.212058
$21$	−3.48361e32	−1.40494
$22$	9.53324e32	1.22994
$23$	−1.45988e33	−0.633849	−0.316925	−	0.948451i	$-0.602650\pi$
$23$	−1.45988e33	−0.633849	−0.316925	+	0.948451i	$0.602650\pi$
$24$	3.75123e33	0.574115
$25$	−1.45684e34	−0.820125
$26$	2.71577e34	0.584852
$27$	1.21060e35	1.03416
$28$	−1.23440e35	−0.432597
$29$	1.26757e36	1.88027	0.940135	−	0.340802i	$-0.110699\pi$
$29$	1.26757e36	1.88027	0.940135	+	0.340802i	$0.110699\pi$
$30$	−7.53328e35	−0.486983
$31$	−2.70852e36	−0.784099	−0.392049	−	0.919944i	$-0.628234\pi$
$31$	−2.70852e36	−0.784099	−0.392049	+	0.919944i	$0.628234\pi$
$32$	1.32923e36	0.176777
$33$	4.51372e37	2.82451
$34$	4.01954e37	1.21044
$35$	2.47894e37	0.366943
$36$	1.10254e38	0.818431
$37$	−7.30159e37	−0.276997	−0.138499	−	0.990363i	$-0.544228\pi$
$37$	−7.30159e37	−0.276997	−0.138499	+	0.990363i	$0.544228\pi$
$38$	−1.54800e38	−0.305544
$39$	1.28584e39	1.34309
$40$	−2.66938e38	−0.149948
$41$	1.21786e39	0.373587	0.186793	−	0.982399i	$-0.440191\pi$
$41$	1.21786e39	0.373587	0.186793	+	0.982399i	$0.440191\pi$
$42$	−5.84453e39	−0.993441
$43$	−1.71091e40	−1.63400	−0.816998	−	0.576640i	$-0.804363\pi$
$43$	−1.71091e40	−1.63400	−0.816998	+	0.576640i	$0.804363\pi$
$44$	1.59941e40	0.869700
$45$	−2.21413e40	−0.694220
$46$	−2.44928e40	−0.448199
$47$	−1.04023e41	−1.12392	−0.561958	−	0.827166i	$-0.689952\pi$
$47$	−1.04023e41	−1.12392	−0.561958	+	0.827166i	$0.689952\pi$
$48$	6.29353e40	0.405960
$49$	−6.46007e40	−0.251439
$50$	−2.44416e41	−0.579916
$51$	1.90314e42	2.77973
$52$	4.55631e41	0.413553
$53$	−1.17198e41	−0.0667057	−0.0333528	−	0.999444i	$-0.510619\pi$
$53$	−1.17198e41	−0.0667057	−0.0333528	+	0.999444i	$0.510619\pi$
$54$	2.03105e42	0.731264
$55$	−3.21196e42	−0.737708
$56$	−2.07098e42	−0.305892
$57$	−7.32935e42	−0.701668
$58$	2.12663e43	1.32955
$59$	−8.71601e42	−0.358462	−0.179231	−	0.983807i	$-0.557361\pi$
$59$	−8.71601e42	−0.358462	−0.179231	+	0.983807i	$0.557361\pi$
$60$	−1.26388e43	−0.344349
$61$	−2.61290e43	−0.474834	−0.237417	−	0.971408i	$-0.576301\pi$
$61$	−2.61290e43	−0.474834	−0.237417	+	0.971408i	$0.576301\pi$
$62$	−4.54414e43	−0.554441
$63$	−1.71779e44	−1.41620
$64$	2.23007e43	0.125000
$65$	−9.15004e43	−0.350789
$66$	7.57277e44	1.99723
$67$	3.87604e44	0.707222	0.353611	−	0.935393i	$-0.384954\pi$
$67$	3.87604e44	0.707222	0.353611	+	0.935393i	$0.384954\pi$
$68$	6.74368e44	0.855910
$69$	−1.15966e45	−1.02927
$70$	4.15897e44	0.259468
$71$	2.06352e44	0.0909449	0.0454724	−	0.998966i	$-0.485521\pi$
$71$	2.06352e44	0.0909449	0.0454724	+	0.998966i	$0.485521\pi$
$72$	1.84975e45	0.578718
$73$	4.21892e44	0.0941438	0.0470719	−	0.998892i	$-0.485011\pi$
$73$	4.21892e44	0.0941438	0.0470719	+	0.998892i	$0.485011\pi$
$74$	−1.22500e45	−0.195867
$75$	−1.15724e46	−1.33175
$76$	−2.59711e45	−0.216052
$77$	−2.49193e46	−1.50492
$78$	2.15728e46	0.949707
$79$	8.65650e45	0.278919	0.139460	−	0.990228i	$-0.455463\pi$
$79$	8.65650e45	0.278919	0.139460	+	0.990228i	$0.455463\pi$
$80$	−4.47847e45	−0.106029
$81$	2.43119e45	0.0424557
$82$	2.04322e46	0.264166
$83$	1.57334e47	1.51150	0.755750	−	0.654860i	$-0.227272\pi$
$83$	1.57334e47	1.51150	0.755750	+	0.654860i	$0.227272\pi$
$84$	−9.80550e46	−0.702469
$85$	−1.35427e47	−0.726011
$86$	−2.87044e47	−1.15541
$87$	1.00690e48	3.05326
$88$	2.68337e47	0.614971
$89$	−2.35938e47	−0.409962	−0.204981	−	0.978766i	$-0.565713\pi$
$89$	−2.35938e47	−0.409962	−0.204981	+	0.978766i	$0.565713\pi$
$90$	−3.71470e47	−0.490887
$91$	−7.09886e47	−0.715607
$92$	−4.10921e47	−0.316925
$93$	−2.15153e48	−1.27325
$94$	−1.74522e48	−0.794729
$95$	5.21556e47	0.183262
$96$	1.05588e48	0.287057
$97$	1.57542e48	0.332269	0.166135	−	0.986103i	$-0.446871\pi$
$97$	1.57542e48	0.332269	0.166135	+	0.986103i	$0.446871\pi$
$98$	−1.08382e48	−0.177794
$99$	2.22574e49	2.84716
$100$	−4.10063e48	−0.410063
$101$	−2.10004e49	−1.64571	−0.822857	−	0.568248i	$-0.807621\pi$
$101$	−2.10004e49	−1.64571	−0.822857	+	0.568248i	$0.807621\pi$
$102$	3.19294e49	1.96556
$103$	−3.08538e49	−1.49554	−0.747769	−	0.663960i	$-0.768875\pi$
$103$	−3.08538e49	−1.49554	−0.747769	+	0.663960i	$0.768875\pi$
$104$	7.64421e48	0.292426
$105$	1.96915e49	0.595857
$106$	−1.96626e48	−0.0471680
$107$	−1.65194e49	−0.314842	−0.157421	−	0.987532i	$-0.550318\pi$
$107$	−1.65194e49	−0.314842	−0.157421	+	0.987532i	$0.550318\pi$
$108$	3.40754e49	0.517082
$109$	−9.19427e49	−1.11319	−0.556593	−	0.830785i	$-0.687892\pi$
$109$	−9.19427e49	−1.11319	−0.556593	+	0.830785i	$0.687892\pi$
$110$	−5.38878e49	−0.521638
$111$	−5.80005e49	−0.449800
$112$	−3.47452e49	−0.216298
$113$	6.93766e49	0.347369	0.173685	−	0.984801i	$-0.444433\pi$
$113$	6.93766e49	0.347369	0.173685	+	0.984801i	$0.444433\pi$
$114$	−1.22966e50	−0.496154
$115$	8.25217e49	0.268826
$116$	3.56789e50	0.940135
$117$	6.34055e50	1.35386
$118$	−1.46230e50	−0.253471
$119$	−1.05068e51	−1.48106
$120$	−2.12043e50	−0.243491
$121$	2.16161e51	2.02552
$122$	−4.38372e50	−0.335758
$123$	9.67409e50	0.606646
$124$	−7.62381e50	−0.392049
$125$	1.82760e51	0.771945
$126$	−2.88197e51	−1.00141
$127$	−3.58918e51	−1.02755	−0.513776	−	0.857924i	$-0.671754\pi$
$127$	−3.58918e51	−1.02755	−0.513776	+	0.857924i	$0.671754\pi$
$128$	3.74144e50	0.0883883
$129$	−1.35907e52	−2.65335
$130$	−1.53512e51	−0.248045
$131$	8.30864e51	1.11271	0.556357	−	0.830944i	$-0.312199\pi$
$131$	8.30864e51	1.11271	0.556357	+	0.830944i	$0.312199\pi$
$132$	1.27050e52	1.41226
$133$	4.04638e51	0.373854
$134$	6.50292e51	0.500081
$135$	−6.84308e51	−0.438605
$136$	1.13140e52	0.605220
$137$	1.87006e52	0.835989	0.417995	−	0.908449i	$-0.362733\pi$
$137$	1.87006e52	0.835989	0.417995	+	0.908449i	$0.362733\pi$
$138$	−1.94559e52	−0.727805
$139$	7.10289e51	0.222624	0.111312	−	0.993785i	$-0.464495\pi$
$139$	7.10289e51	0.222624	0.111312	+	0.993785i	$0.464495\pi$
$140$	6.97759e51	0.183471
$141$	−8.26315e52	−1.82506
$142$	3.46200e51	0.0643077
$143$	9.19800e52	1.43867
$144$	3.10337e52	0.409216
$145$	−7.16508e52	−0.797453
$146$	7.07818e51	0.0665697
$147$	−5.13159e52	−0.408298
$148$	−2.05522e52	−0.138499
$149$	−1.54238e53	−0.881308	−0.440654	−	0.897677i	$-0.645253\pi$
$149$	−1.54238e53	−0.881308	−0.440654	+	0.897677i	$0.645253\pi$
$150$	−1.94153e53	−0.941692
$151$	−2.11963e52	−0.0873626	−0.0436813	−	0.999046i	$-0.513909\pi$
$151$	−2.11963e52	−0.0873626	−0.0436813	+	0.999046i	$0.513909\pi$
$152$	−4.35723e52	−0.152772
$153$	9.38449e53	2.80201
$154$	−4.18077e53	−1.06414
$155$	1.53102e53	0.332549
$156$	3.61932e53	0.671544
$157$	2.10086e53	0.333316	0.166658	−	0.986015i	$-0.446702\pi$
$157$	2.10086e53	0.333316	0.166658	+	0.986015i	$0.446702\pi$
$158$	1.45232e53	0.197226
$159$	−9.30971e52	−0.108319
$160$	−7.51362e52	−0.0749739
$161$	6.40226e53	0.548403
$162$	4.07886e52	0.0300207
$163$	−2.57326e54	−1.62887	−0.814436	−	0.580253i	$-0.802954\pi$
$163$	−2.57326e54	−1.62887	−0.814436	+	0.580253i	$0.802954\pi$
$164$	3.42796e53	0.186793
$165$	−2.55144e54	−1.19792
$166$	2.63962e54	1.06879
$167$	3.95831e53	0.138343	0.0691713	−	0.997605i	$-0.477964\pi$
$167$	3.95831e53	0.138343	0.0691713	+	0.997605i	$0.477964\pi$
$168$	−1.64509e54	−0.496721
$169$	−1.20995e54	−0.315896
$170$	−2.27210e54	−0.513367
$171$	−3.61414e54	−0.707294
$172$	−4.81580e54	−0.816998
$173$	8.07344e54	1.18831	0.594154	−	0.804351i	$-0.297487\pi$
$173$	8.07344e54	1.18831	0.594154	+	0.804351i	$0.297487\pi$
$174$	1.68930e55	2.15898
$175$	6.38890e54	0.709568
$176$	4.50194e54	0.434850
$177$	−6.92361e54	−0.582086
$178$	−3.95839e54	−0.289887
$179$	1.08682e55	0.693841	0.346921	−	0.937894i	$-0.387227\pi$
$179$	1.08682e55	0.693841	0.346921	+	0.937894i	$0.387227\pi$
$180$	−6.23223e54	−0.347110
$181$	−9.05176e54	−0.440158	−0.220079	−	0.975482i	$-0.570631\pi$
$181$	−9.05176e54	−0.440158	−0.220079	+	0.975482i	$0.570631\pi$
$182$	−1.19099e55	−0.506010
$183$	−2.07557e55	−0.771055
$184$	−6.89410e54	−0.224100
$185$	4.12731e54	0.117479
$186$	−3.60966e55	−0.900325
$187$	1.36137e56	2.97754
$188$	−2.92800e55	−0.561958
$189$	−5.30905e55	−0.894752
$190$	8.75026e54	0.129586
$191$	−9.68165e55	−1.26076	−0.630379	−	0.776287i	$-0.717101\pi$
$191$	−9.68165e55	−1.26076	−0.630379	+	0.776287i	$0.717101\pi$
$192$	1.77147e55	0.202980
$193$	−5.34429e55	−0.539183	−0.269591	−	0.962975i	$-0.586889\pi$
$193$	−5.34429e55	−0.539183	−0.269591	+	0.962975i	$0.586889\pi$
$194$	2.64312e55	0.234950
$195$	−7.26838e55	−0.569626
$196$	−1.81835e55	−0.125720
$197$	2.48206e56	1.51492	0.757461	−	0.652880i	$-0.226439\pi$
$197$	2.48206e56	1.51492	0.757461	+	0.652880i	$0.226439\pi$
$198$	3.73417e56	2.01325
$199$	5.78065e55	0.275471	0.137736	−	0.990469i	$-0.456018\pi$
$199$	5.78065e55	0.275471	0.137736	+	0.990469i	$0.456018\pi$
$200$	−6.87971e55	−0.289958
$201$	3.07895e56	1.14842
$202$	−3.52329e56	−1.16370
$203$	−5.55887e56	−1.62680
$204$	5.35687e56	1.38986
$205$	−6.88408e55	−0.158444
$206$	−5.17641e56	−1.05750
$207$	−5.71836e56	−1.03752
$208$	1.28249e56	0.206776
$209$	−5.24290e56	−0.751602
$210$	3.30369e56	0.421335
$211$	5.32965e54	0.00605032	0.00302516	−	0.999995i	$-0.499037\pi$
$211$	5.32965e54	0.00605032	0.00302516	+	0.999995i	$0.499037\pi$
$212$	−3.29884e55	−0.0333528
$213$	1.63916e56	0.147680
$214$	−2.77150e56	−0.222627
$215$	9.67115e56	0.693004
$216$	5.71691e56	0.365632
$217$	1.18781e57	0.678397
$218$	−1.54254e57	−0.787142
$219$	3.35132e56	0.152875
$220$	−9.04087e56	−0.368854
$221$	3.87820e57	1.41586
$222$	−9.73088e56	−0.318056
$223$	4.37480e57	1.28082	0.640412	−	0.768032i	$-0.278764\pi$
$223$	4.37480e57	1.28082	0.640412	+	0.768032i	$0.278764\pi$
$224$	−5.82928e56	−0.152946
$225$	−5.70642e57	−1.34243
$226$	1.16395e57	0.245627
$227$	2.82668e57	0.535357	0.267679	−	0.963508i	$-0.413743\pi$
$227$	2.82668e57	0.535357	0.267679	+	0.963508i	$0.413743\pi$
$228$	−2.06303e57	−0.350834
$229$	−7.37233e57	−1.12625	−0.563126	−	0.826371i	$-0.690401\pi$
$229$	−7.37233e57	−1.12625	−0.563126	+	0.826371i	$0.690401\pi$
$230$	1.38448e57	0.190089
$231$	−1.97948e58	−2.44375
$232$	5.98592e57	0.664776
$233$	5.28015e57	0.527747	0.263874	−	0.964557i	$-0.415000\pi$
$233$	5.28015e57	0.527747	0.263874	+	0.964557i	$0.415000\pi$
$234$	1.06377e58	0.957322
$235$	5.88005e57	0.476671
$236$	−2.45334e57	−0.179231
$237$	6.87633e57	0.452921
$238$	−1.76276e58	−1.04727
$239$	−1.17485e58	−0.629845	−0.314923	−	0.949117i	$-0.601979\pi$
$239$	−1.17485e58	−0.629845	−0.314923	+	0.949117i	$0.601979\pi$
$240$	−3.55749e57	−0.172174
$241$	2.71621e58	1.18726	0.593631	−	0.804738i	$-0.297694\pi$
$241$	2.71621e58	1.18726	0.593631	+	0.804738i	$0.297694\pi$
$242$	3.62658e58	1.43226
$243$	−2.70384e58	−0.965222
$244$	−7.35466e57	−0.237417
$245$	3.65163e57	0.106639
$246$	1.62304e58	0.428963
$247$	−1.49357e58	−0.357395
$248$	−1.27906e58	−0.277221
$249$	1.24979e59	2.45444
$250$	3.06621e58	0.545847
$251$	−3.65004e58	−0.589239	−0.294620	−	0.955615i	$-0.595193\pi$
$251$	−3.65004e58	−0.589239	−0.294620	+	0.955615i	$0.595193\pi$
$252$	−4.83514e58	−0.708102
$253$	−8.29542e58	−1.10252
$254$	−6.02165e58	−0.726590
$255$	−1.07577e59	−1.17893
$256$	6.27710e57	0.0625000
$257$	−9.35018e57	−0.0846172	−0.0423086	−	0.999105i	$-0.513471\pi$
$257$	−9.35018e57	−0.0846172	−0.0423086	+	0.999105i	$0.513471\pi$
$258$	−2.28015e59	−1.87620
$259$	3.20209e58	0.239656
$260$	−2.57551e58	−0.175394
$261$	4.96506e59	3.07774
$262$	1.39396e59	0.786807
$263$	−8.31210e58	−0.427361	−0.213681	−	0.976904i	$-0.568545\pi$
$263$	−8.31210e58	−0.427361	−0.213681	+	0.976904i	$0.568545\pi$
$264$	2.13155e59	0.998616
$265$	6.62478e57	0.0282910
$266$	6.78870e58	0.264354
$267$	−1.87419e59	−0.665713
$268$	1.09101e59	0.353611
$269$	−4.44312e59	−1.31449	−0.657244	−	0.753678i	$-0.728278\pi$
$269$	−4.44312e59	−1.31449	−0.657244	+	0.753678i	$0.728278\pi$
$270$	−1.14808e59	−0.310141
$271$	6.43014e59	1.58662	0.793309	−	0.608819i	$-0.208356\pi$
$271$	6.43014e59	1.58662	0.793309	+	0.608819i	$0.208356\pi$
$272$	1.89818e59	0.427955
$273$	−5.63901e59	−1.16203
$274$	3.13743e59	0.591134
$275$	−8.27811e59	−1.42653
$276$	−3.26417e59	−0.514636
$277$	1.24422e60	1.79533	0.897663	−	0.440682i	$-0.145263\pi$
$277$	1.24422e60	1.79533	0.897663	+	0.440682i	$0.145263\pi$
$278$	1.19167e59	0.157419
$279$	−1.06093e60	−1.28346
$280$	1.17064e59	0.129734
$281$	8.54992e59	0.868275	0.434137	−	0.900847i	$-0.357053\pi$
$281$	8.54992e59	0.868275	0.434137	+	0.900847i	$0.357053\pi$
$282$	−1.38633e60	−1.29051
$283$	−1.94873e60	−1.66335	−0.831677	−	0.555260i	$-0.812619\pi$
$283$	−1.94873e60	−1.66335	−0.831677	+	0.555260i	$0.812619\pi$
$284$	5.80828e58	0.0454724
$285$	4.14301e59	0.297589
$286$	1.54317e60	1.01729
$287$	−5.34086e59	−0.323225
$288$	5.20659e59	0.289359
$289$	3.78119e60	1.93033
$290$	−1.20210e60	−0.563884
$291$	1.25145e60	0.539553
$292$	1.18752e59	0.0470719
$293$	−1.71967e60	−0.626887	−0.313443	−	0.949607i	$-0.601483\pi$
$293$	−1.71967e60	−0.626887	−0.313443	+	0.949607i	$0.601483\pi$
$294$	−8.60937e59	−0.288710
$295$	4.92683e59	0.152030
$296$	−3.44808e59	−0.0979333
$297$	6.87895e60	1.79882
$298$	−2.58768e60	−0.623179
$299$	−2.36315e60	−0.524260
$300$	−3.25735e60	−0.665877
$301$	7.50315e60	1.41372
$302$	−3.55615e59	−0.0617747
$303$	−1.66818e61	−2.67238
$304$	−7.31023e59	−0.108026
$305$	1.47697e60	0.201385
$306$	1.57446e61	1.98132
$307$	−4.30346e59	−0.0499951	−0.0249976	−	0.999688i	$-0.507958\pi$
$307$	−4.30346e59	−0.0499951	−0.0249976	+	0.999688i	$0.507958\pi$
$308$	−7.01416e60	−0.752460
$309$	−2.45089e61	−2.42852
$310$	2.56863e60	0.235148
$311$	−4.46188e59	−0.0377475	−0.0188737	−	0.999822i	$-0.506008\pi$
$311$	−4.46188e59	−0.0377475	−0.0188737	+	0.999822i	$0.506008\pi$
$312$	6.07222e60	0.474854
$313$	3.50202e60	0.253211	0.126605	−	0.991953i	$-0.459592\pi$
$313$	3.50202e60	0.253211	0.126605	+	0.991953i	$0.459592\pi$
$314$	3.52466e60	0.235690
$315$	9.71000e60	0.600635
$316$	2.43659e60	0.139460
$317$	8.94498e59	0.0473836	0.0236918	−	0.999719i	$-0.492458\pi$
$317$	8.94498e59	0.0473836	0.0236918	+	0.999719i	$0.492458\pi$
$318$	−1.56191e60	−0.0765934
$319$	7.20264e61	3.27054
$320$	−1.26058e60	−0.0530145
$321$	−1.31223e61	−0.511253
$322$	1.07412e61	0.387779
$323$	−2.21059e61	−0.739684
$324$	6.84319e59	0.0212278
$325$	−2.35822e61	−0.678330
$326$	−4.31721e61	−1.15179
$327$	−7.30351e61	−1.80764
$328$	5.75116e60	0.132083
$329$	4.56191e61	0.972405
$330$	−4.28060e61	−0.847058
$331$	2.61998e61	0.481407	0.240704	−	0.970599i	$-0.422622\pi$
$331$	2.61998e61	0.481407	0.240704	+	0.970599i	$0.422622\pi$
$332$	4.42855e61	0.755750
$333$	−2.86003e61	−0.453406
$334$	6.64094e60	0.0978230
$335$	−2.19098e61	−0.299944
$336$	−2.76000e61	−0.351235
$337$	1.36805e62	1.61872	0.809358	−	0.587316i	$-0.199815\pi$
$337$	1.36805e62	1.61872	0.809358	+	0.587316i	$0.199815\pi$
$338$	−2.02997e61	−0.223372
$339$	5.51096e61	0.564073
$340$	−3.81195e61	−0.363005
$341$	−1.53905e62	−1.36386
$342$	−6.06352e61	−0.500133
$343$	1.41003e62	1.08274
$344$	−8.07956e61	−0.577705
$345$	6.55515e61	0.436531
$346$	1.35450e62	0.840261
$347$	−7.99219e61	−0.461949	−0.230974	−	0.972960i	$-0.574191\pi$
$347$	−7.99219e61	−0.461949	−0.230974	+	0.972960i	$0.574191\pi$
$348$	2.83417e62	1.52663
$349$	−1.83544e62	−0.921548	−0.460774	−	0.887517i	$-0.652428\pi$
$349$	−1.83544e62	−0.921548	−0.460774	+	0.887517i	$0.652428\pi$
$350$	1.07188e62	0.501740
$351$	1.95963e62	0.855362
$352$	7.55301e61	0.307486
$353$	1.40284e61	0.0532756	0.0266378	−	0.999645i	$-0.491520\pi$
$353$	1.40284e61	0.0532756	0.0266378	+	0.999645i	$0.491520\pi$
$354$	−1.16159e62	−0.411597
$355$	−1.16643e61	−0.0385712
$356$	−6.64108e61	−0.204981
$357$	−8.34616e62	−2.40500
$358$	1.82339e62	0.490620
$359$	−5.18325e62	−1.30253	−0.651265	−	0.758850i	$-0.725761\pi$
$359$	−5.18325e62	−1.30253	−0.651265	+	0.758850i	$0.725761\pi$
$360$	−1.04559e62	−0.245444
$361$	−3.70826e62	−0.813286
$362$	−1.51863e62	−0.311238
$363$	1.71708e63	3.28912
$364$	−1.99815e62	−0.357803
$365$	−2.38480e61	−0.0399279
$366$	−3.48223e62	−0.545218
$367$	1.17851e62	0.172590	0.0862948	−	0.996270i	$-0.472497\pi$
$367$	1.17851e62	0.172590	0.0862948	+	0.996270i	$0.472497\pi$
$368$	−1.15664e62	−0.158462
$369$	4.77034e62	0.611510
$370$	6.92448e61	0.0830702
$371$	5.13969e61	0.0577134
$372$	−6.05601e62	−0.636626
$373$	−1.26964e63	−1.24972	−0.624860	−	0.780737i	$-0.714844\pi$
$373$	−1.26964e63	−1.24972	−0.624860	+	0.780737i	$0.714844\pi$
$374$	2.28401e63	2.10544
$375$	1.45176e63	1.25352
$376$	−4.91237e62	−0.397364
$377$	2.05184e63	1.55518
$378$	−8.90711e62	−0.632685
$379$	−8.52756e61	−0.0567759	−0.0283880	−	0.999597i	$-0.509037\pi$
$379$	−8.52756e61	−0.0567759	−0.0283880	+	0.999597i	$0.509037\pi$
$380$	1.46805e62	0.0916311
$381$	−2.85108e63	−1.66858
$382$	−1.62431e63	−0.891491
$383$	2.26804e63	1.16756	0.583781	−	0.811911i	$-0.301573\pi$
$383$	2.26804e63	1.16756	0.583781	+	0.811911i	$0.301573\pi$
$384$	2.97203e62	0.143529
$385$	1.40859e63	0.638261
$386$	−8.96623e62	−0.381260
$387$	−6.70165e63	−2.67463
$388$	4.43443e62	0.166135
$389$	−3.69467e62	−0.129960	−0.0649802	−	0.997887i	$-0.520698\pi$
$389$	−3.69467e62	−0.129960	−0.0649802	+	0.997887i	$0.520698\pi$
$390$	−1.21943e63	−0.402786
$391$	−3.49764e63	−1.08504
$392$	−3.05068e62	−0.0888972
$393$	6.60001e63	1.80687
$394$	4.16421e63	1.07121
$395$	−4.89319e62	−0.118294
$396$	6.26490e63	1.42358
$397$	−6.48767e63	−1.38587	−0.692933	−	0.721002i	$-0.743682\pi$
$397$	−6.48767e63	−1.38587	−0.692933	+	0.721002i	$0.743682\pi$
$398$	9.69832e62	0.194787
$399$	3.21426e63	0.607079
$400$	−1.15422e63	−0.205031
$401$	6.26348e63	1.04659	0.523297	−	0.852150i	$-0.324702\pi$
$401$	6.26348e63	1.04659	0.523297	+	0.852150i	$0.324702\pi$
$402$	5.16562e63	0.812053
$403$	−4.38435e63	−0.648532
$404$	−5.91110e63	−0.822857
$405$	−1.37426e62	−0.0180061
$406$	−9.32624e63	−1.15032
$407$	−4.14895e63	−0.481809
$408$	8.98734e63	0.982782
$409$	4.09059e63	0.421274	0.210637	−	0.977564i	$-0.432446\pi$
$409$	4.09059e63	0.421274	0.210637	+	0.977564i	$0.432446\pi$
$410$	−1.15496e63	−0.112037
$411$	1.48549e64	1.35751
$412$	−8.68458e63	−0.747769
$413$	3.82238e63	0.310139
$414$	−9.59382e63	−0.733640
$415$	−8.89347e63	−0.641052
$416$	2.15165e63	0.146213
$417$	5.64221e63	0.361507
$418$	−8.79613e63	−0.531463
$419$	4.65451e63	0.265235	0.132617	−	0.991167i	$-0.457662\pi$
$419$	4.65451e63	0.265235	0.132617	+	0.991167i	$0.457662\pi$
$420$	5.54268e63	0.297929
$421$	−6.78354e63	−0.343990	−0.171995	−	0.985098i	$-0.555021\pi$
$421$	−6.78354e63	−0.343990	−0.171995	+	0.985098i	$0.555021\pi$
$422$	8.94167e61	0.00427822
$423$	−4.07460e64	−1.83970
$424$	−5.53454e62	−0.0235840
$425$	−3.49034e64	−1.40391
$426$	2.75006e63	0.104426
$427$	1.14588e64	0.410824
$428$	−4.64981e63	−0.157421
$429$	7.30648e64	2.33617
$430$	1.62255e64	0.490028
$431$	5.56035e64	1.58639	0.793193	−	0.608971i	$-0.208417\pi$
$431$	5.56035e64	1.58639	0.793193	+	0.608971i	$0.208417\pi$
$432$	9.59138e63	0.258541
$433$	3.47009e64	0.883869	0.441934	−	0.897047i	$-0.354292\pi$
$433$	3.47009e64	0.883869	0.441934	+	0.897047i	$0.354292\pi$
$434$	1.99282e64	0.479699
$435$	−5.69162e64	−1.29494
$436$	−2.58796e64	−0.556593
$437$	1.34701e64	0.273889
$438$	5.62258e63	0.108099
$439$	−4.09271e64	−0.744099	−0.372049	−	0.928213i	$-0.621345\pi$
$439$	−4.09271e64	−0.744099	−0.372049	+	0.928213i	$0.621345\pi$
$440$	−1.51681e64	−0.260819
$441$	−2.53041e64	−0.411572
$442$	6.50654e64	1.00116
$443$	−1.21785e65	−1.77298	−0.886488	−	0.462751i	$-0.846862\pi$
$443$	−1.21785e65	−1.77298	−0.886488	+	0.462751i	$0.846862\pi$
$444$	−1.63257e64	−0.224900
$445$	1.33367e64	0.173871
$446$	7.33970e64	0.905679
$447$	−1.22520e65	−1.43110
$448$	−9.77991e63	−0.108149
$449$	5.54542e64	0.580629	0.290315	−	0.956931i	$-0.406240\pi$
$449$	5.54542e64	0.580629	0.290315	+	0.956931i	$0.406240\pi$
$450$	−9.57379e64	−0.949243
$451$	6.92016e64	0.649817
$452$	1.95278e64	0.173685
$453$	−1.68374e64	−0.141863
$454$	4.74239e64	0.378555
$455$	4.01272e64	0.303500
$456$	−3.46119e64	−0.248077
$457$	−1.52223e65	−1.03403	−0.517014	−	0.855977i	$-0.672956\pi$
$457$	−1.52223e65	−1.03403	−0.517014	+	0.855977i	$0.672956\pi$
$458$	−1.23687e65	−0.796380
$459$	2.90040e65	1.77030
$460$	2.32278e64	0.134413
$461$	1.88013e65	1.03161	0.515806	−	0.856706i	$-0.327493\pi$
$461$	1.88013e65	1.03161	0.515806	+	0.856706i	$0.327493\pi$
$462$	−3.32101e65	−1.72799
$463$	3.45913e65	1.70699	0.853497	−	0.521098i	$-0.174477\pi$
$463$	3.45913e65	1.70699	0.853497	+	0.521098i	$0.174477\pi$
$464$	1.00427e65	0.470067
$465$	1.21618e65	0.540007
$466$	8.85861e64	0.373174
$467$	−1.96639e65	−0.785970	−0.392985	−	0.919545i	$-0.628558\pi$
$467$	−1.96639e65	−0.785970	−0.392985	+	0.919545i	$0.628558\pi$
$468$	1.78471e65	0.676929
$469$	−1.69982e65	−0.611884
$470$	9.86509e64	0.337057
$471$	1.66883e65	0.541252
$472$	−4.11602e64	−0.126736
$473$	−9.72185e65	−2.84217
$474$	1.15366e65	0.320263
$475$	1.34419e65	0.354379
$476$	−2.95741e65	−0.740529
$477$	−4.59066e64	−0.109188
$478$	−1.97107e65	−0.445368
$479$	5.20394e64	0.111715	0.0558576	−	0.998439i	$-0.482211\pi$
$479$	5.20394e64	0.111715	0.0558576	+	0.998439i	$0.482211\pi$
$480$	−5.96848e64	−0.121746
$481$	−1.18193e65	−0.229106
$482$	4.55705e65	0.839521
$483$	5.08567e65	0.890519
$484$	6.08439e65	1.01276
$485$	−8.90528e64	−0.140921
$486$	−4.53629e65	−0.682515
$487$	1.99942e65	0.286051	0.143026	−	0.989719i	$-0.454317\pi$
$487$	1.99942e65	0.286051	0.143026	+	0.989719i	$0.454317\pi$
$488$	−1.23391e65	−0.167879
$489$	−2.04408e66	−2.64503
$490$	6.12642e64	0.0754055
$491$	−3.18295e65	−0.372677	−0.186339	−	0.982486i	$-0.559662\pi$
$491$	−3.18295e65	−0.372677	−0.186339	+	0.982486i	$0.559662\pi$
$492$	2.72302e65	0.303323
$493$	3.03688e66	3.21869
$494$	−2.50579e65	−0.252717
$495$	−1.25813e66	−1.20753
$496$	−2.14591e65	−0.196025
$497$	−9.04947e64	−0.0786849
$498$	2.09679e66	1.73555
$499$	6.39909e65	0.504260	0.252130	−	0.967693i	$-0.418869\pi$
$499$	6.39909e65	0.504260	0.252130	+	0.967693i	$0.418869\pi$
$500$	5.14424e65	0.385972
$501$	3.14430e65	0.224647
$502$	−6.12375e65	−0.416655
$503$	1.03311e66	0.669471	0.334735	−	0.942312i	$-0.391353\pi$
$503$	1.03311e66	0.669471	0.334735	+	0.942312i	$0.391353\pi$
$504$	−8.11202e65	−0.500703
$505$	1.18708e66	0.697974
$506$	−1.39174e66	−0.779598
$507$	−9.61133e65	−0.512966
$508$	−1.01026e66	−0.513776
$509$	−1.63284e66	−0.791333	−0.395666	−	0.918394i	$-0.629486\pi$
$509$	−1.63284e66	−0.791333	−0.395666	+	0.918394i	$0.629486\pi$
$510$	−1.80485e66	−0.833627
$511$	−1.85019e65	−0.0814526
$512$	1.05312e65	0.0441942
$513$	−1.11700e66	−0.446866
$514$	−1.56870e65	−0.0598334
$515$	1.74405e66	0.634281
$516$	−3.82545e66	−1.32668
$517$	−5.91088e66	−1.95494
$518$	5.37221e65	0.169463
$519$	6.41318e66	1.92963
$520$	−4.32098e65	−0.124023
$521$	3.93193e66	1.07667	0.538334	−	0.842732i	$-0.319054\pi$
$521$	3.93193e66	1.07667	0.538334	+	0.842732i	$0.319054\pi$
$522$	8.32999e66	2.17629
$523$	−2.10835e66	−0.525596	−0.262798	−	0.964851i	$-0.584645\pi$
$523$	−2.10835e66	−0.525596	−0.262798	+	0.964851i	$0.584645\pi$
$524$	2.33867e66	0.556357
$525$	5.07505e66	1.15223
$526$	−1.39454e66	−0.302190
$527$	−6.48917e66	−1.34224
$528$	3.57614e66	0.706128
$529$	−3.17348e66	−0.598235
$530$	1.11145e65	0.0200047
$531$	−3.41406e66	−0.586753
$532$	1.13895e66	0.186927
$533$	1.97137e66	0.308996
$534$	−3.14437e66	−0.470730
$535$	9.33781e65	0.133530
$536$	1.83041e66	0.250041
$537$	8.63324e66	1.12669
$538$	−7.45431e66	−0.929484
$539$	−3.67077e66	−0.437354
$540$	−1.92615e66	−0.219303
$541$	−8.41780e66	−0.915937	−0.457968	−	0.888968i	$-0.651423\pi$
$541$	−8.41780e66	−0.915937	−0.457968	+	0.888968i	$0.651423\pi$
$542$	1.07880e67	1.12191
$543$	−7.19031e66	−0.714746
$544$	3.18461e66	0.302610
$545$	5.19717e66	0.472120
$546$	−9.46069e66	−0.821681
$547$	5.67745e66	0.471481	0.235740	−	0.971816i	$-0.424248\pi$
$547$	5.67745e66	0.471481	0.235740	+	0.971816i	$0.424248\pi$
$548$	5.26374e66	0.417995
$549$	−1.02347e67	−0.777238
$550$	−1.38884e67	−1.00871
$551$	−1.16956e67	−0.812472
$552$	−5.47636e66	−0.363902
$553$	−3.79628e66	−0.241319
$554$	2.08746e67	1.26949
$555$	3.27855e66	0.190767
$556$	1.99929e66	0.111312
$557$	2.68265e67	1.42926	0.714631	−	0.699502i	$-0.246595\pi$
$557$	2.68265e67	1.42926	0.714631	+	0.699502i	$0.246595\pi$
$558$	−1.77994e67	−0.907544
$559$	−2.76950e67	−1.35149
$560$	1.96402e66	0.0917357
$561$	1.08141e68	4.83506
$562$	1.43444e67	0.613963
$563$	−2.46352e67	−1.00949	−0.504744	−	0.863269i	$-0.668413\pi$
$563$	−2.46352e67	−1.00949	−0.504744	+	0.863269i	$0.668413\pi$
$564$	−2.32587e67	−0.912531
$565$	−3.92160e66	−0.147325
$566$	−3.26943e67	−1.17617
$567$	−1.06619e66	−0.0367324
$568$	9.74467e65	0.0321539
$569$	−2.62664e67	−0.830137	−0.415069	−	0.909790i	$-0.636242\pi$
$569$	−2.62664e67	−0.830137	−0.415069	+	0.909790i	$0.636242\pi$
$570$	6.95081e66	0.210427
$571$	5.51879e67	1.60051	0.800257	−	0.599658i	$-0.204697\pi$
$571$	5.51879e67	1.60051	0.800257	+	0.599658i	$0.204697\pi$
$572$	2.58901e67	0.719334
$573$	−7.69066e67	−2.04727
$574$	−8.96048e66	−0.228555
$575$	2.12681e67	0.519836
$576$	8.73520e66	0.204608
$577$	−4.65003e66	−0.104387	−0.0521937	−	0.998637i	$-0.516621\pi$
$577$	−4.65003e66	−0.104387	−0.0521937	+	0.998637i	$0.516621\pi$
$578$	6.34379e67	1.36495
$579$	−4.24526e67	−0.875548
$580$	−2.01679e67	−0.398726
$581$	−6.89981e67	−1.30774
$582$	2.09958e67	0.381521
$583$	−6.65951e66	−0.116028
$584$	1.99233e66	0.0332848
$585$	−3.58407e67	−0.574193
$586$	−2.88513e67	−0.443276
$587$	−9.45616e67	−1.39342	−0.696709	−	0.717354i	$-0.745353\pi$
$587$	−9.45616e67	−1.39342	−0.696709	+	0.717354i	$0.745353\pi$
$588$	−1.44441e67	−0.204149
$589$	2.49910e67	0.338812
$590$	8.26585e66	0.107501
$591$	1.97164e68	2.45999
$592$	−5.78492e66	−0.0692493
$593$	−9.11419e67	−1.04684	−0.523418	−	0.852076i	$-0.675343\pi$
$593$	−9.11419e67	−1.04684	−0.523418	+	0.852076i	$0.675343\pi$
$594$	1.15410e68	1.27196
$595$	5.93912e67	0.628140
$596$	−4.34141e67	−0.440654
$597$	4.59188e67	0.447321
$598$	−3.96471e67	−0.370708
$599$	1.33989e68	1.20258	0.601289	−	0.799032i	$-0.294654\pi$
$599$	1.33989e68	1.20258	0.601289	+	0.799032i	$0.294654\pi$
$600$	−5.46493e67	−0.470846
$601$	1.90045e68	1.57193	0.785963	−	0.618274i	$-0.212168\pi$
$601$	1.90045e68	1.57193	0.785963	+	0.618274i	$0.212168\pi$
$602$	1.25882e68	0.999654
$603$	1.51825e68	1.15762
$604$	−5.96624e66	−0.0436813
$605$	−1.22188e68	−0.859054
$606$	−2.79874e68	−1.88966
$607$	−2.65855e68	−1.72394	−0.861968	−	0.506962i	$-0.830768\pi$
$607$	−2.65855e68	−1.72394	−0.861968	+	0.506962i	$0.830768\pi$
$608$	−1.22645e67	−0.0763859
$609$	−4.41572e68	−2.64166
$610$	2.47795e67	0.142401
$611$	−1.68385e68	−0.929597
$612$	2.64150e68	1.40101
$613$	3.75059e68	1.91125	0.955627	−	0.294580i	$-0.0951798\pi$
$613$	3.75059e68	1.91125	0.955627	+	0.294580i	$0.0951798\pi$
$614$	−7.22001e66	−0.0353519
$615$	−5.46840e67	−0.257288
$616$	−1.17678e68	−0.532069
$617$	1.14520e68	0.497617	0.248809	−	0.968553i	$-0.419961\pi$
$617$	1.14520e68	0.497617	0.248809	+	0.968553i	$0.419961\pi$
$618$	−4.11191e68	−1.71722
$619$	4.65278e68	1.86763	0.933817	−	0.357750i	$-0.116456\pi$
$619$	4.65278e68	1.86763	0.933817	+	0.357750i	$0.116456\pi$
$620$	4.30945e67	0.166274
$621$	−1.76734e68	−0.655504
$622$	−7.48579e66	−0.0266915
$623$	1.03470e68	0.354697
$624$	1.01875e68	0.335772
$625$	1.55479e68	0.492731
$626$	5.87541e67	0.179047
$627$	−4.16472e68	−1.22048
$628$	5.91340e67	0.166658
$629$	−1.74934e68	−0.474170
$630$	1.62907e68	0.424713
$631$	4.71150e67	0.118152	0.0590758	−	0.998253i	$-0.481185\pi$
$631$	4.71150e67	0.118152	0.0590758	+	0.998253i	$0.481185\pi$
$632$	4.08792e67	0.0986129
$633$	4.23363e66	0.00982476
$634$	1.50072e67	0.0335052
$635$	2.02883e68	0.435802
$636$	−2.62045e67	−0.0541597
$637$	−1.04571e68	−0.207967
$638$	1.20840e69	2.31262
$639$	8.08279e67	0.148864
$640$	−2.11490e67	−0.0374869
$641$	−1.14710e69	−1.95694	−0.978471	−	0.206383i	$-0.933831\pi$
$641$	−1.14710e69	−1.95694	−0.978471	+	0.206383i	$0.933831\pi$
$642$	−2.20155e68	−0.361511
$643$	5.88590e68	0.930345	0.465173	−	0.885220i	$-0.345992\pi$
$643$	5.88590e68	0.930345	0.465173	+	0.885220i	$0.345992\pi$
$644$	1.80208e68	0.274201
$645$	7.68233e68	1.12533
$646$	−3.70875e68	−0.523036
$647$	−8.23336e68	−1.11795	−0.558975	−	0.829185i	$-0.688805\pi$
$647$	−8.23336e68	−1.11795	−0.558975	+	0.829185i	$0.688805\pi$
$648$	1.14810e67	0.0150103
$649$	−4.95266e68	−0.623510
$650$	−3.95643e68	−0.479652
$651$	9.43544e68	1.10161
$652$	−7.24308e68	−0.814436
$653$	−4.04310e68	−0.437866	−0.218933	−	0.975740i	$-0.570258\pi$
$653$	−4.04310e68	−0.437866	−0.218933	+	0.975740i	$0.570258\pi$
$654$	−1.22533e69	−1.27819
$655$	−4.69656e68	−0.471920
$656$	9.64885e67	0.0933967
$657$	1.65255e68	0.154100
$658$	7.65362e68	0.687594
$659$	−1.59048e69	−1.37669	−0.688343	−	0.725385i	$-0.741662\pi$
$659$	−1.59048e69	−1.37669	−0.688343	+	0.725385i	$0.741662\pi$
$660$	−7.18166e68	−0.598961
$661$	1.64318e69	1.32053	0.660266	−	0.751032i	$-0.270444\pi$
$661$	1.64318e69	1.32053	0.660266	+	0.751032i	$0.270444\pi$
$662$	4.39560e68	0.340406
$663$	3.08066e69	2.29913
$664$	7.42987e68	0.534396
$665$	−2.28727e68	−0.158557
$666$	−4.79834e68	−0.320607
$667$	−1.85050e69	−1.19181
$668$	1.11416e68	0.0691713
$669$	3.47515e69	2.07986
$670$	−3.67585e68	−0.212093
$671$	−1.48472e69	−0.825927
$672$	−4.63052e68	−0.248360
$673$	−1.44435e69	−0.746968	−0.373484	−	0.927637i	$-0.621837\pi$
$673$	−1.44435e69	−0.746968	−0.373484	+	0.927637i	$0.621837\pi$
$674$	2.29521e69	1.14460
$675$	−1.76365e69	−0.848144
$676$	−3.40572e68	−0.157948
$677$	4.42761e69	1.98037	0.990186	−	0.139755i	$-0.0446314\pi$
$677$	4.42761e69	1.98037	0.990186	+	0.139755i	$0.0446314\pi$
$678$	9.24586e68	0.398860
$679$	−6.90897e68	−0.287477
$680$	−6.39538e68	−0.256684
$681$	2.24539e69	0.869336
$682$	−2.58210e69	−0.964396
$683$	−6.24013e68	−0.224847	−0.112423	−	0.993660i	$-0.535861\pi$
$683$	−6.24013e68	−0.224847	−0.112423	+	0.993660i	$0.535861\pi$
$684$	−1.01729e69	−0.353647
$685$	−1.05707e69	−0.354557
$686$	2.36564e69	0.765611
$687$	−5.85624e69	−1.82885
$688$	−1.35553e69	−0.408499
$689$	−1.89712e68	−0.0551726
$690$	1.09977e69	0.308674
$691$	−1.65576e69	−0.448524	−0.224262	−	0.974529i	$-0.571997\pi$
$691$	−1.65576e69	−0.448524	−0.224262	+	0.974529i	$0.571997\pi$
$692$	2.27247e69	0.594154
$693$	−9.76089e69	−2.46335
$694$	−1.34087e69	−0.326647
$695$	−4.01499e68	−0.0944185
$696$	4.75494e69	1.07949
$697$	2.91778e69	0.639513
$698$	−3.07936e69	−0.651633
$699$	4.19431e69	0.856978
$700$	1.79832e69	0.354784
$701$	3.50945e69	0.668572	0.334286	−	0.942472i	$-0.391505\pi$
$701$	3.50945e69	0.668572	0.334286	+	0.942472i	$0.391505\pi$
$702$	3.28772e69	0.604833
$703$	6.73704e68	0.119692
$704$	1.26718e69	0.217425
$705$	4.67085e69	0.774038
$706$	2.35358e68	0.0376716
$707$	9.20966e69	1.42386
$708$	−1.94882e69	−0.291043
$709$	−7.32363e69	−1.05656	−0.528280	−	0.849070i	$-0.677163\pi$
$709$	−7.32363e69	−1.05656	−0.528280	+	0.849070i	$0.677163\pi$
$710$	−1.95694e68	−0.0272739
$711$	3.39075e69	0.456552
$712$	−1.11419e69	−0.144943
$713$	3.95412e69	0.497000
$714$	−1.40025e70	−1.70059
$715$	−5.19928e69	−0.610162
$716$	3.05914e69	0.346921
$717$	−9.33248e69	−1.02277
$718$	−8.69604e69	−0.921028
$719$	5.39270e69	0.552012	0.276006	−	0.961156i	$-0.410989\pi$
$719$	5.39270e69	0.552012	0.276006	+	0.961156i	$0.410989\pi$
$720$	−1.75422e69	−0.173555
$721$	1.35308e70	1.29393
$722$	−6.22142e69	−0.575080
$723$	2.15764e70	1.92792
$724$	−2.54784e69	−0.220079
$725$	−1.84664e70	−1.54206
$726$	2.88079e70	2.32576
$727$	1.12907e70	0.881309	0.440655	−	0.897677i	$-0.354746\pi$
$727$	1.12907e70	0.881309	0.440655	+	0.897677i	$0.354746\pi$
$728$	−3.35234e69	−0.253005
$729$	−2.20599e70	−1.60982
$730$	−4.00103e68	−0.0282333
$731$	−4.09907e70	−2.79711
$732$	−5.84221e69	−0.385528
$733$	4.27091e69	0.272567	0.136283	−	0.990670i	$-0.456484\pi$
$733$	4.27091e69	0.272567	0.136283	+	0.990670i	$0.456484\pi$
$734$	1.97721e69	0.122039
$735$	2.90069e69	0.173166
$736$	−1.94052e69	−0.112050
$737$	2.20246e70	1.23014
$738$	8.00330e69	0.432403
$739$	−2.03599e70	−1.06411	−0.532055	−	0.846710i	$-0.678580\pi$
$739$	−2.03599e70	−1.06411	−0.532055	+	0.846710i	$0.678580\pi$
$740$	1.16174e69	0.0587395
$741$	−1.18642e70	−0.580354
$742$	8.62297e68	0.0408095
$743$	1.12304e70	0.514243	0.257122	−	0.966379i	$-0.417226\pi$
$743$	1.12304e70	0.514243	0.257122	+	0.966379i	$0.417226\pi$
$744$	−1.01603e70	−0.450163
$745$	8.71849e69	0.373777
$746$	−2.13010e70	−0.883686
$747$	6.16276e70	2.47412
$748$	3.83193e70	1.48877
$749$	7.24453e69	0.272399
$750$	2.43566e70	0.886370
$751$	−1.72919e69	−0.0609066	−0.0304533	−	0.999536i	$-0.509695\pi$
$751$	−1.72919e69	−0.0609066	−0.0304533	+	0.999536i	$0.509695\pi$
$752$	−8.24159e69	−0.280979
$753$	−2.89943e70	−0.956831
$754$	3.44242e70	1.09968
$755$	1.19815e69	0.0370519
$756$	−1.49436e70	−0.447376
$757$	−1.67080e69	−0.0484256	−0.0242128	−	0.999707i	$-0.507708\pi$
$757$	−1.67080e69	−0.0484256	−0.0242128	+	0.999707i	$0.507708\pi$
$758$	−1.43069e69	−0.0401466
$759$	−6.58951e70	−1.79031
$760$	2.46298e69	0.0647930
$761$	−1.82952e70	−0.466030	−0.233015	−	0.972473i	$-0.574859\pi$
$761$	−1.82952e70	−0.466030	−0.233015	+	0.972473i	$0.574859\pi$
$762$	−4.78332e70	−1.17987
$763$	4.03211e70	0.963122
$764$	−2.72514e70	−0.630379
$765$	−5.30470e70	−1.18838
$766$	3.80513e70	0.825591
$767$	−1.41088e70	−0.296486
$768$	4.98625e69	0.101490
$769$	1.74967e70	0.344954	0.172477	−	0.985014i	$-0.444823\pi$
$769$	1.74967e70	0.344954	0.172477	+	0.985014i	$0.444823\pi$
$770$	2.36323e70	0.451318
$771$	−7.42736e69	−0.137405
$772$	−1.50428e70	−0.269591
$773$	5.68036e70	0.986229	0.493115	−	0.869964i	$-0.335858\pi$
$773$	5.68036e70	0.986229	0.493115	+	0.869964i	$0.335858\pi$
$774$	−1.12435e71	−1.89125
$775$	3.94587e70	0.643059
$776$	7.43973e69	0.117475
$777$	2.54359e70	0.389164
$778$	−6.19863e69	−0.0918958
$779$	−1.12369e70	−0.161428
$780$	−2.04587e70	−0.284813
$781$	1.17254e70	0.158190
$782$	−5.86806e70	−0.767237
$783$	1.53452e71	1.94451
$784$	−5.11819e69	−0.0628598
$785$	−1.18754e70	−0.141365
$786$	1.10730e71	1.27765
$787$	2.11456e70	0.236505	0.118252	−	0.992984i	$-0.462271\pi$
$787$	2.11456e70	0.236505	0.118252	+	0.992984i	$0.462271\pi$
$788$	6.98639e70	0.757461
$789$	−6.60276e70	−0.693967
$790$	−8.20941e69	−0.0836466
$791$	−3.04249e70	−0.300542
$792$	1.05108e71	1.00662
$793$	−4.22957e70	−0.392738
$794$	−1.08845e71	−0.979956
$795$	5.26243e69	0.0459400
$796$	1.62711e70	0.137736
$797$	1.36404e71	1.11969	0.559844	−	0.828598i	$-0.310861\pi$
$797$	1.36404e71	1.11969	0.559844	+	0.828598i	$0.310861\pi$
$798$	5.39264e70	0.429270
$799$	−2.49223e71	−1.92394
$800$	−1.93647e70	−0.144979
$801$	−9.24171e70	−0.671051
$802$	1.05084e71	0.740054
$803$	2.39730e70	0.163754
$804$	8.66648e70	0.574208
$805$	−3.61896e70	−0.232586
$806$	−7.35572e70	−0.458582
$807$	−3.52941e71	−2.13452
$808$	−9.91717e70	−0.581848
$809$	1.21224e71	0.690002	0.345001	−	0.938602i	$-0.387879\pi$
$809$	1.21224e71	0.690002	0.345001	+	0.938602i	$0.387879\pi$
$810$	−2.30562e69	−0.0127323
$811$	−2.96765e71	−1.59001	−0.795007	−	0.606600i	$-0.792533\pi$
$811$	−2.96765e71	−1.59001	−0.795007	+	0.606600i	$0.792533\pi$
$812$	−1.56468e71	−0.813399
$813$	5.10781e71	2.57642
$814$	−6.96078e70	−0.340690
$815$	1.45457e71	0.690831
$816$	1.50782e71	0.694932
$817$	1.57863e71	0.706056
$818$	6.86287e70	0.297886
$819$	−2.78062e71	−1.17135
$820$	−1.93770e70	−0.0792221
$821$	4.81615e71	1.91114	0.955570	−	0.294766i	$-0.0952416\pi$
$821$	4.81615e71	1.91114	0.955570	+	0.294766i	$0.0952416\pi$
$822$	2.49223e71	0.959908
$823$	−1.34527e71	−0.502935	−0.251468	−	0.967866i	$-0.580913\pi$
$823$	−1.34527e71	−0.502935	−0.251468	+	0.967866i	$0.580913\pi$
$824$	−1.45703e71	−0.528752
$825$	−6.57575e71	−2.31645
$826$	6.41288e70	0.219302
$827$	7.76898e70	0.257916	0.128958	−	0.991650i	$-0.458837\pi$
$827$	7.76898e70	0.257916	0.128958	+	0.991650i	$0.458837\pi$
$828$	−1.60958e71	−0.518762
$829$	−5.87735e70	−0.183906	−0.0919529	−	0.995763i	$-0.529311\pi$
$829$	−5.87735e70	−0.183906	−0.0919529	+	0.995763i	$0.529311\pi$
$830$	−1.49208e71	−0.453292
$831$	9.88353e71	2.91533
$832$	3.60988e70	0.103388
$833$	−1.54773e71	−0.430419
$834$	9.46606e70	0.255624
$835$	−2.23748e70	−0.0586733
$836$	−1.47575e71	−0.375801
$837$	−3.27894e71	−0.810886
$838$	7.80898e70	0.187549
$839$	−2.93145e70	−0.0683777	−0.0341888	−	0.999415i	$-0.510885\pi$
$839$	−2.93145e70	−0.0683777	−0.0341888	+	0.999415i	$0.510885\pi$
$840$	9.29907e70	0.210667
$841$	1.15226e72	2.53542
$842$	−1.13809e71	−0.243237
$843$	6.79167e71	1.40994
$844$	1.50016e69	0.00302516
$845$	6.83941e70	0.133977
$846$	−6.83604e71	−1.30086
$847$	−9.47966e71	−1.75246
$848$	−9.28541e69	−0.0166764
$849$	−1.54799e72	−2.70102
$850$	−5.85581e71	−0.992713
$851$	1.06595e71	0.175574
$852$	4.61383e70	0.0738400
$853$	−5.36884e71	−0.834889	−0.417445	−	0.908702i	$-0.637074\pi$
$853$	−5.36884e71	−0.834889	−0.417445	+	0.908702i	$0.637074\pi$
$854$	1.92246e71	0.290496
$855$	2.04294e71	0.299975
$856$	−7.80108e70	−0.111313
$857$	2.07429e71	0.287634	0.143817	−	0.989604i	$-0.454062\pi$
$857$	2.07429e71	0.287634	0.143817	+	0.989604i	$0.454062\pi$
$858$	1.22582e72	1.65192
$859$	−7.03695e71	−0.921620	−0.460810	−	0.887499i	$-0.652441\pi$
$859$	−7.03695e71	−0.921620	−0.460810	+	0.887499i	$0.652441\pi$
$860$	2.72219e71	0.346502
$861$	−4.24254e71	−0.524866
$862$	9.32871e71	1.12174
$863$	−3.68596e71	−0.430810	−0.215405	−	0.976525i	$-0.569107\pi$
$863$	−3.68596e71	−0.430810	−0.215405	+	0.976525i	$0.569107\pi$
$864$	1.60917e71	0.182816
$865$	−4.56361e71	−0.503981
$866$	5.82185e71	0.624990
$867$	3.00361e72	3.13455
$868$	3.34339e71	0.339199
$869$	4.91884e71	0.485152
$870$	−9.54895e71	−0.915659
$871$	6.27425e71	0.584947
$872$	−4.34187e71	−0.393571
$873$	6.17094e71	0.543879
$874$	2.25990e71	0.193669
$875$	−8.01488e71	−0.667882
$876$	9.43313e70	0.0764373
$877$	−1.93572e72	−1.52529	−0.762645	−	0.646817i	$-0.776100\pi$
$877$	−1.93572e72	−1.52529	−0.762645	+	0.646817i	$0.776100\pi$
$878$	−6.86643e71	−0.526157
$879$	−1.36603e72	−1.01796
$880$	−2.54478e71	−0.184427
$881$	5.95854e71	0.419982	0.209991	−	0.977703i	$-0.432657\pi$
$881$	5.95854e71	0.419982	0.209991	+	0.977703i	$0.432657\pi$
$882$	−4.24532e71	−0.291025
$883$	1.87124e72	1.24765	0.623826	−	0.781564i	$-0.285578\pi$
$883$	1.87124e72	1.24765	0.623826	+	0.781564i	$0.285578\pi$
$884$	1.09162e72	0.707928
$885$	3.91365e71	0.246872
$886$	−2.04322e72	−1.25368
$887$	−2.12365e72	−1.26752	−0.633758	−	0.773531i	$-0.718489\pi$
$887$	−2.12365e72	−1.26752	−0.633758	+	0.773531i	$0.718489\pi$
$888$	−2.73900e71	−0.159028
$889$	1.57402e72	0.889033
$890$	2.23753e71	0.122946
$891$	1.38146e71	0.0738474
$892$	1.23140e72	0.640412
$893$	9.59804e71	0.485648
$894$	−2.05554e72	−1.01194
$895$	−6.14341e71	−0.294269
$896$	−1.64080e71	−0.0764731
$897$	−1.87718e72	−0.851316
$898$	9.30367e71	0.410567
$899$	−3.43323e72	−1.47432
$900$	−1.60622e72	−0.671216
$901$	−2.80788e71	−0.114188
$902$	1.16101e72	0.459490
$903$	5.96016e72	2.29566
$904$	3.27622e71	0.122814
$905$	5.11662e71	0.186678
$906$	−2.82485e71	−0.100312
$907$	2.10319e72	0.726943	0.363471	−	0.931605i	$-0.381591\pi$
$907$	2.10319e72	0.726943	0.363471	+	0.931605i	$0.381591\pi$
$908$	7.95641e71	0.267679
$909$	−8.22587e72	−2.69381
$910$	6.73222e71	0.214607
$911$	4.91507e72	1.52521	0.762604	−	0.646866i	$-0.223921\pi$
$911$	4.91507e72	1.52521	0.762604	+	0.646866i	$0.223921\pi$
$912$	−5.80691e71	−0.175417
$913$	8.94009e72	2.62910
$914$	−2.55387e72	−0.731168
$915$	1.17324e72	0.327017
$916$	−2.07513e72	−0.563126
$917$	−3.64372e72	−0.962713
$918$	4.86607e72	1.25179
$919$	−1.76130e72	−0.441166	−0.220583	−	0.975368i	$-0.570796\pi$
$919$	−1.76130e72	−0.441166	−0.220583	+	0.975368i	$0.570796\pi$
$920$	3.89698e71	0.0950443
$921$	−3.41847e71	−0.0811842
$922$	3.15434e72	0.729459
$923$	3.34026e71	0.0752210
$924$	−5.57173e72	−1.22188
$925$	1.06372e72	0.227172
$926$	5.80345e72	1.20703
$927$	−1.20854e73	−2.44799
$928$	1.68489e72	0.332388
$929$	−4.47943e72	−0.860671	−0.430336	−	0.902669i	$-0.641605\pi$
$929$	−4.47943e72	−0.860671	−0.430336	+	0.902669i	$0.641605\pi$
$930$	2.04041e72	0.381842
$931$	5.96058e71	0.108648
$932$	1.48623e72	0.263874
$933$	−3.54431e71	−0.0612959
$934$	−3.29906e72	−0.555765
$935$	−7.69533e72	−1.26282
$936$	2.99424e72	0.478661
$937$	6.98453e72	1.08772	0.543860	−	0.839176i	$-0.316962\pi$
$937$	6.98453e72	1.08772	0.543860	+	0.839176i	$0.316962\pi$
$938$	−2.85183e72	−0.432667
$939$	2.78185e72	0.411174
$940$	1.65509e72	0.238335
$941$	−1.60971e72	−0.225840	−0.112920	−	0.993604i	$-0.536020\pi$
$941$	−1.60971e72	−0.225840	−0.112920	+	0.993604i	$0.536020\pi$
$942$	2.79983e72	0.382723
$943$	−1.77793e72	−0.236798
$944$	−6.90554e71	−0.0896156
$945$	3.00101e72	0.379479
$946$	−1.63106e73	−2.00972
$947$	−1.31016e72	−0.157307	−0.0786537	−	0.996902i	$-0.525062\pi$
$947$	−1.31016e72	−0.157307	−0.0786537	+	0.996902i	$0.525062\pi$
$948$	1.93552e72	0.226460
$949$	6.82928e71	0.0778668
$950$	2.25518e72	0.250584
$951$	7.10549e71	0.0769434
$952$	−4.96172e72	−0.523633
$953$	−4.69763e72	−0.483173	−0.241587	−	0.970379i	$-0.577668\pi$
$953$	−4.69763e72	−0.483173	−0.241587	+	0.970379i	$0.577668\pi$
$954$	−7.70185e71	−0.0772076
$955$	5.47267e72	0.534708
$956$	−3.30691e72	−0.314923
$957$	5.72145e73	5.31084
$958$	8.73076e71	0.0789945
$959$	−8.20106e72	−0.723293
$960$	−1.00135e72	−0.0860872
$961$	−4.59618e72	−0.385189
$962$	−1.98294e72	−0.162002
$963$	−6.47066e72	−0.515353
$964$	7.64546e72	0.593631
$965$	3.02093e72	0.228676
$966$	8.53233e72	0.629692
$967$	−1.35157e73	−0.972503	−0.486252	−	0.873819i	$-0.661636\pi$
$967$	−1.35157e73	−0.972503	−0.486252	+	0.873819i	$0.661636\pi$
$968$	1.02079e73	0.716128
$969$	−1.75599e73	−1.20113
$970$	−1.49406e72	−0.0996460
$971$	1.73168e73	1.12615	0.563074	−	0.826406i	$-0.309619\pi$
$971$	1.73168e73	1.12615	0.563074	+	0.826406i	$0.309619\pi$
$972$	−7.61063e72	−0.482611
$973$	−3.11495e72	−0.192613
$974$	3.35447e72	0.202269
$975$	−1.87326e73	−1.10150
$976$	−2.07015e72	−0.118709
$977$	−1.61768e72	−0.0904639	−0.0452320	−	0.998977i	$-0.514403\pi$
$977$	−1.61768e72	−0.0904639	−0.0452320	+	0.998977i	$0.514403\pi$
$978$	−3.42940e73	−1.87032
$979$	−1.34066e73	−0.713088
$980$	1.02784e72	0.0533197
$981$	−3.60139e73	−1.82213
$982$	−5.34010e72	−0.263523
$983$	−1.86672e72	−0.0898499	−0.0449249	−	0.998990i	$-0.514305\pi$
$983$	−1.86672e72	−0.0898499	−0.0449249	+	0.998990i	$0.514305\pi$
$984$	4.56846e72	0.214482
$985$	−1.40302e73	−0.642503
$986$	5.09504e73	2.27595
$987$	3.62378e73	1.57903
$988$	−4.20401e72	−0.178698
$989$	2.49773e73	1.03571
$990$	−2.11078e73	−0.853850
$991$	2.80003e73	1.10499	0.552494	−	0.833517i	$-0.313676\pi$
$991$	2.80003e73	1.10499	0.552494	+	0.833517i	$0.313676\pi$
$992$	−3.60024e72	−0.138610
$993$	2.08120e73	0.781729
$994$	−1.51825e72	−0.0556387
$995$	−3.26758e72	−0.116832
$996$	3.51784e73	1.22722
$997$	−1.83032e73	−0.623011	−0.311505	−	0.950244i	$-0.600833\pi$
$997$	−1.83032e73	−0.623011	−0.311505	+	0.950244i	$0.600833\pi$
$998$	1.07359e73	0.356566
$999$	−8.83932e72	−0.286460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.50.a.b.1.3	✓	3
4.3	odd	2		16.50.a.b.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.50.a.b.1.3	✓	3	1.1	even	1	trivial
16.50.a.b.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:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 50 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q+1.67772e7 q^{2} +7.94355e11 q^{3} +2.81475e14 q^{4} -5.65262e16 q^{5} +1.33271e19 q^{6} -4.38546e20 q^{7} +4.72237e21 q^{8} +3.91700e23 q^{9} +O(q^{10})\)	\(q+1.67772e7 q^{2} +7.94355e11 q^{3} +2.81475e14 q^{4} -5.65262e16 q^{5} +1.33271e19 q^{6} -4.38546e20 q^{7} +4.72237e21 q^{8} +3.91700e23 q^{9} -9.48353e23 q^{10} +5.68225e25 q^{11} +2.23591e26 q^{12} +1.61873e27 q^{13} -7.35759e27 q^{14} -4.49019e28 q^{15} +7.92282e28 q^{16} +2.39583e30 q^{17} +6.57164e30 q^{18} -9.22680e30 q^{19} -1.59107e31 q^{20} -3.48361e32 q^{21} +9.53324e32 q^{22} -1.45988e33 q^{23} +3.75123e33 q^{24} -1.45684e34 q^{25} +2.71577e34 q^{26} +1.21060e35 q^{27} -1.23440e35 q^{28} +1.26757e36 q^{29} -7.53328e35 q^{30} -2.70852e36 q^{31} +1.32923e36 q^{32} +4.51372e37 q^{33} +4.01954e37 q^{34} +2.47894e37 q^{35} +1.10254e38 q^{36} -7.30159e37 q^{37} -1.54800e38 q^{38} +1.28584e39 q^{39} -2.66938e38 q^{40} +1.21786e39 q^{41} -5.84453e39 q^{42} -1.71091e40 q^{43} +1.59941e40 q^{44} -2.21413e40 q^{45} -2.44928e40 q^{46} -1.04023e41 q^{47} +6.29353e40 q^{48} -6.46007e40 q^{49} -2.44416e41 q^{50} +1.90314e42 q^{51} +4.55631e41 q^{52} -1.17198e41 q^{53} +2.03105e42 q^{54} -3.21196e42 q^{55} -2.07098e42 q^{56} -7.32935e42 q^{57} +2.12663e43 q^{58} -8.71601e42 q^{59} -1.26388e43 q^{60} -2.61290e43 q^{61} -4.54414e43 q^{62} -1.71779e44 q^{63} +2.23007e43 q^{64} -9.15004e43 q^{65} +7.57277e44 q^{66} +3.87604e44 q^{67} +6.74368e44 q^{68} -1.15966e45 q^{69} +4.15897e44 q^{70} +2.06352e44 q^{71} +1.84975e45 q^{72} +4.21892e44 q^{73} -1.22500e45 q^{74} -1.15724e46 q^{75} -2.59711e45 q^{76} -2.49193e46 q^{77} +2.15728e46 q^{78} +8.65650e45 q^{79} -4.47847e45 q^{80} +2.43119e45 q^{81} +2.04322e46 q^{82} +1.57334e47 q^{83} -9.80550e46 q^{84} -1.35427e47 q^{85} -2.87044e47 q^{86} +1.00690e48 q^{87} +2.68337e47 q^{88} -2.35938e47 q^{89} -3.71470e47 q^{90} -7.09886e47 q^{91} -4.10921e47 q^{92} -2.15153e48 q^{93} -1.74522e48 q^{94} +5.21556e47 q^{95} +1.05588e48 q^{96} +1.57542e48 q^{97} -1.08382e48 q^{98} +2.22574e49 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 50331648 q^{2} - 16203614388 q^{3} + 844424930131968 q^{4} - 10\!\cdots\!30 q^{5}+ \cdots + 38\!\cdots\!99 q^{9}+O(q^{10}) \) 3 * q + 50331648 * q^2 - 16203614388 * q^3 + 844424930131968 * q^4 - 101813016401840430 * q^5 - 271851538568183808 * q^6 - 125479179230203797096 * q^7 + 14167099448608935641088 * q^8 + 389432931519696922052199 * q^9	\( 3 q + 50331648 q^{2} - 16203614388 q^{3} + 844424930131968 q^{4} - 10\!\cdots\!30 q^{5}+ \cdots + 17\!\cdots\!68 q^{99}+O(q^{100}) \) 3 * q + 50331648 * q^2 - 16203614388 * q^3 + 844424930131968 * q^4 - 101813016401840430 * q^5 - 271851538568183808 * q^6 - 125479179230203797096 * q^7 + 14167099448608935641088 * q^8 + 389432931519696922052199 * q^9 - 1708138967785219691642880 * q^10 - 25860036791834065092767004 * q^11 - 4560911982490750474518528 * q^12 + 2945123797958353151076283242 * q^13 - 2105191293447842827899764736 * q^14 + 87846213583565151681178171080 * q^15 + 237684487542793012780631851008 * q^16 + 3910755572889939740390354668854 * q^17 + 6533600409619163515804905897984 * q^18 + 14590272981610371514592320211580 * q^19 - 28657816420549672374145992622080 * q^20 - 109864176920553355284360667668384 * q^21 - 433859423024547146219412063780864 * q^22 - 4953158032634305739950894912759608 * q^23 - 76519405487235538713099840258048 * q^24 + 39451396326519132102111422427450525 * q^25 + 49410978105087649819887436428214272 * q^26 + 196120894647932767255303897131684600 * q^27 - 35319249051493843857725179325054976 * q^28 + 937305925294643190481854503019954330 * q^29 + 1473814900073606599827889310694113280 * q^30 + 2414809991776326638635666091994140256 * q^31 + 3987683987354747618711421180841033728 * q^32 + 84513992666209345011409783180743651984 * q^33 + 65611590969578263251512904595972030464 * q^34 + 300439012903055674136683294221406953360 * q^35 + 109615625329869184043978320110151532544 * q^36 + 309377978155169809207437071391240173874 * q^37 + 244784161311441230740562508130843361280 * q^38 + 360871814296103457146322338824042742568 * q^39 - 480798376175908692150280133755042529280 * q^40 - 1143109642820632592659114174552039005954 * q^41 - 1843215026858338481130460343376694738944 * q^42 - 17579019372148890319048762066144112105148 * q^43 - 7278953253718200774306659587057331994624 * q^44 - 114813225075613761568802306330842527416790 * q^45 - 83100202195640796409195993344669099491328 * q^46 - 218573936001854642959028674713638582342256 * q^47 - 1283782594050935875866038049574767034368 * q^48 + 373628008074429359506251920014708170372651 * q^49 + 661884597671618007409657390132581787238400 * q^50 + 2241123510744223933356304325509677976541016 * q^51 + 828978652440326199960612616642419335626752 * q^52 + 740200780025011930130058449331923084936802 * q^53 + 3290362611621611989719960627820052978073600 * q^54 + 3200488473448119911679443277764576117207640 * q^55 - 592558670294707341071328602175181544226816 * q^56 - 20594915296543361145254552753753824314692880 * q^57 + 15725383966748092449643217077738426104545280 * q^58 - 53014363316602767635595514099864508327238540 * q^59 + 24726510922553313824338061789606248427028480 * q^60 - 124730102606725385116407342714381742110559494 * q^61 + 40513788830989655702944515329261561809207296 * q^62 - 468292624427612329618287149072325587596605768 * q^63 + 66902235595591869424607154817945084517941248 * q^64 - 421321721827999315000625667485604880336092420 * q^65 + 1417909509983410082474944396936503289964396544 * q^66 + 1111804215897361218882144911380577470099878924 * q^67 + 1100779833800263951475494327194015485053108224 * q^68 + 770909887444909922528222240570561038770401568 * q^69 + 5040530214301352105016749150744096280422645760 * q^70 - 4013080456871179368491803943114613092268032424 * q^71 + 1839045023134286552449577775805156054221717504 * q^72 - 10015638764428635672946257750737669286684666018 * q^73 + 5190501165152565405751960553138256904961654784 * q^74 - 38646070268253498119014909069282536501398301900 * q^75 + 4106796747700892799440257160412915334360596480 * q^76 - 23360330575813840356220747501745396153372866272 * q^77 + 6054424376757615658890593484076151085295730688 * q^78 + 36077368003505469428776991593224667583970712560 * q^79 - 8066458209552474124482754264517239602916884480 * q^80 - 14427585993163108762153736521422002728666768917 * q^81 - 19178197389284602263681972875121261643315544064 * q^82 + 150749458884727999220762915504103393007529125692 * q^83 - 30924016640048146099037657360264977001327099904 * q^84 + 566911972337878875844467446456481028710158526660 * q^85 - 294927005074726317042989995716306055916282707968 * q^86 + 1072056267743755243448622937355132996639037778920 * q^87 - 122120570991533057521910078130531663257517686784 * q^88 + 542251936064510107856207107418847041962289942670 * q^89 - 1926246276750188410412295154610712544457407856640 * q^90 - 1459783720923935217191336434024489699257545191344 * q^91 - 1394190041879939899769105566678075930691499982848 * q^92 - 2368291579513879043404530519265491460552020418176 * q^93 - 3667062136273291745526503225864452641889814839296 * q^94 - 2813579016011586836853932078889401271258883877400 * q^95 - 21538297877432866191553707421934574685271359488 * q^96 + 4343844254337968328695747517284119056283595359014 * q^97 + 6268437795114445441178041812501482151306766319616 * q^98 + 17595360353038055002493296165642581030249046200468 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more