LMFDB - Embedded newform 2.50.a.b.1.1

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			1.1
Root			$3.00244e8$ 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)

$f(q)$	$=$	$q+1.67772e7 q^{2} -6.77152e11 q^{3} +2.81475e14 q^{4} -2.33026e17 q^{5} -1.13607e19 q^{6} -5.15430e20 q^{7} +4.72237e21 q^{8} +2.19235e23 q^{9} +O(q^{10})$	\(q+1.67772e7 q^{2} -6.77152e11 q^{3} +2.81475e14 q^{4} -2.33026e17 q^{5} -1.13607e19 q^{6} -5.15430e20 q^{7} +4.72237e21 q^{8} +2.19235e23 q^{9} -3.90952e24 q^{10} -5.21317e25 q^{11} -1.90601e26 q^{12} +1.37568e27 q^{13} -8.64748e27 q^{14} +1.57794e29 q^{15} +7.92282e28 q^{16} -9.93263e29 q^{17} +3.67815e30 q^{18} +1.85532e31 q^{19} -6.55909e31 q^{20} +3.49024e32 q^{21} -8.74625e32 q^{22} -2.69345e33 q^{23} -3.19776e33 q^{24} +3.65374e34 q^{25} +2.30801e34 q^{26} +1.35867e34 q^{27} -1.45081e35 q^{28} -3.88028e34 q^{29} +2.64734e36 q^{30} -8.58347e35 q^{31} +1.32923e36 q^{32} +3.53011e37 q^{33} -1.66642e37 q^{34} +1.20108e38 q^{35} +6.17091e37 q^{36} +2.50854e38 q^{37} +3.11271e38 q^{38} -9.31545e38 q^{39} -1.10043e39 q^{40} +2.12382e38 q^{41} +5.85566e39 q^{42} -3.48149e39 q^{43} -1.46738e40 q^{44} -5.10874e40 q^{45} -4.51886e40 q^{46} +2.11562e40 q^{47} -5.36495e40 q^{48} +8.74461e39 q^{49} +6.12996e41 q^{50} +6.72589e41 q^{51} +3.87220e41 q^{52} -2.52544e42 q^{53} +2.27947e41 q^{54} +1.21480e43 q^{55} -2.43405e42 q^{56} -1.25633e43 q^{57} -6.51003e41 q^{58} -4.29058e43 q^{59} +4.44150e43 q^{60} -1.42312e43 q^{61} -1.44007e43 q^{62} -1.13000e44 q^{63} +2.23007e43 q^{64} -3.20569e44 q^{65} +5.92254e44 q^{66} +2.95546e44 q^{67} -2.79579e44 q^{68} +1.82387e45 q^{69} +2.01509e45 q^{70} -2.56483e45 q^{71} +1.03531e45 q^{72} -5.17938e45 q^{73} +4.20863e45 q^{74} -2.47414e46 q^{75} +5.22226e45 q^{76} +2.68703e46 q^{77} -1.56287e46 q^{78} +1.28546e46 q^{79} -1.84622e46 q^{80} -6.16630e46 q^{81} +3.56318e45 q^{82} +8.58374e46 q^{83} +9.82416e46 q^{84} +2.31456e47 q^{85} -5.84097e46 q^{86} +2.62754e46 q^{87} -2.46185e47 q^{88} +6.95931e47 q^{89} -8.57104e47 q^{90} -7.09067e47 q^{91} -7.58138e47 q^{92} +5.81231e47 q^{93} +3.54942e47 q^{94} -4.32337e48 q^{95} -9.00089e47 q^{96} +7.53593e48 q^{97} +1.46710e47 q^{98} -1.14291e49 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−6.77152e11	−1.38425	−0.692126	−	0.721777i	$-0.743326\pi$
$3$	−6.77152e11	−1.38425	−0.692126	+	0.721777i	$0.743326\pi$
$4$	2.81475e14	0.500000
$5$	−2.33026e17	−1.74839	−0.874196	−	0.485573i	$-0.838611\pi$
$5$	−2.33026e17	−1.74839	−0.874196	+	0.485573i	$0.838611\pi$
$6$	−1.13607e19	−0.978814
$7$	−5.15430e20	−1.01688	−0.508438	−	0.861099i	$-0.669777\pi$
$7$	−5.15430e20	−1.01688	−0.508438	+	0.861099i	$0.669777\pi$
$8$	4.72237e21	0.353553
$9$	2.19235e23	0.916153
$10$	−3.90952e24	−1.23630
$11$	−5.21317e25	−1.59581	−0.797905	−	0.602783i	$-0.794058\pi$
$11$	−5.21317e25	−1.59581	−0.797905	+	0.602783i	$0.794058\pi$
$12$	−1.90601e26	−0.692126
$13$	1.37568e27	0.702920	0.351460	−	0.936203i	$-0.385685\pi$
$13$	1.37568e27	0.702920	0.351460	+	0.936203i	$0.385685\pi$
$14$	−8.64748e27	−0.719040
$15$	1.57794e29	2.42021
$16$	7.92282e28	0.250000
$17$	−9.93263e29	−0.709685	−0.354843	−	0.934926i	$-0.615466\pi$
$17$	−9.93263e29	−0.709685	−0.354843	+	0.934926i	$0.615466\pi$
$18$	3.67815e30	0.647818
$19$	1.85532e31	0.868871	0.434436	−	0.900703i	$-0.356948\pi$
$19$	1.85532e31	0.868871	0.434436	+	0.900703i	$0.356948\pi$
$20$	−6.55909e31	−0.874196
$21$	3.49024e32	1.40761
$22$	−8.74625e32	−1.12841
$23$	−2.69345e33	−1.16944	−0.584718	−	0.811236i	$-0.698795\pi$
$23$	−2.69345e33	−1.16944	−0.584718	+	0.811236i	$0.698795\pi$
$24$	−3.19776e33	−0.489407
$25$	3.65374e34	2.05687
$26$	2.30801e34	0.497039
$27$	1.35867e34	0.116065
$28$	−1.45081e35	−0.508438
$29$	−3.88028e34	−0.0575588	−0.0287794	−	0.999586i	$-0.509162\pi$
$29$	−3.88028e34	−0.0575588	−0.0287794	+	0.999586i	$0.509162\pi$
$30$	2.64734e36	1.71135
$31$	−8.58347e35	−0.248486	−0.124243	−	0.992252i	$-0.539650\pi$
$31$	−8.58347e35	−0.248486	−0.124243	+	0.992252i	$0.539650\pi$
$32$	1.32923e36	0.176777
$33$	3.53011e37	2.20900
$34$	−1.66642e37	−0.501823
$35$	1.20108e38	1.77790
$36$	6.17091e37	0.458077
$37$	2.50854e38	0.951652	0.475826	−	0.879539i	$-0.342149\pi$
$37$	2.50854e38	0.951652	0.475826	+	0.879539i	$0.342149\pi$
$38$	3.11271e38	0.614385
$39$	−9.31545e38	−0.973018
$40$	−1.10043e39	−0.618150
$41$	2.12382e38	0.0651498	0.0325749	−	0.999469i	$-0.489629\pi$
$41$	2.12382e38	0.0651498	0.0325749	+	0.999469i	$0.489629\pi$
$42$	5.85566e39	0.995332
$43$	−3.48149e39	−0.332497	−0.166249	−	0.986084i	$-0.553165\pi$
$43$	−3.48149e39	−0.332497	−0.166249	+	0.986084i	$0.553165\pi$
$44$	−1.46738e40	−0.797905
$45$	−5.10874e40	−1.60179
$46$	−4.51886e40	−0.826916
$47$	2.11562e40	0.228581	0.114290	−	0.993447i	$-0.463541\pi$
$47$	2.11562e40	0.228581	0.114290	+	0.993447i	$0.463541\pi$
$48$	−5.36495e40	−0.346063
$49$	8.74461e39	0.0340358
$50$	6.12996e41	1.45443
$51$	6.72589e41	0.982383
$52$	3.87220e41	0.351460
$53$	−2.52544e42	−1.43740	−0.718701	−	0.695319i	$-0.755263\pi$
$53$	−2.52544e42	−1.43740	−0.718701	+	0.695319i	$0.755263\pi$
$54$	2.27947e41	0.0820703
$55$	1.21480e43	2.79010
$56$	−2.43405e42	−0.359520
$57$	−1.25633e43	−1.20274
$58$	−6.51003e41	−0.0407002
$59$	−4.29058e43	−1.76458	−0.882290	−	0.470707i	$-0.843999\pi$
$59$	−4.29058e43	−1.76458	−0.882290	+	0.470707i	$0.843999\pi$
$60$	4.44150e43	1.21011
$61$	−1.42312e43	−0.258619	−0.129309	−	0.991604i	$-0.541276\pi$
$61$	−1.42312e43	−0.258619	−0.129309	+	0.991604i	$0.541276\pi$
$62$	−1.44007e43	−0.175706
$63$	−1.13000e44	−0.931614
$64$	2.23007e43	0.125000
$65$	−3.20569e44	−1.22898
$66$	5.92254e44	1.56200
$67$	2.95546e44	0.539254	0.269627	−	0.962965i	$-0.413100\pi$
$67$	2.95546e44	0.539254	0.269627	+	0.962965i	$0.413100\pi$
$68$	−2.79579e44	−0.354843
$69$	1.82387e45	1.61879
$70$	2.01509e45	1.25716
$71$	−2.56483e45	−1.13039	−0.565197	−	0.824956i	$-0.691200\pi$
$71$	−2.56483e45	−1.13039	−0.565197	+	0.824956i	$0.691200\pi$
$72$	1.03531e45	0.323909
$73$	−5.17938e45	−1.15576	−0.577880	−	0.816122i	$-0.696120\pi$
$73$	−5.17938e45	−1.15576	−0.577880	+	0.816122i	$0.696120\pi$
$74$	4.20863e45	0.672920
$75$	−2.47414e46	−2.84723
$76$	5.22226e45	0.434436
$77$	2.68703e46	1.62274
$78$	−1.56287e46	−0.688027
$79$	1.28546e46	0.414185	0.207092	−	0.978321i	$-0.433600\pi$
$79$	1.28546e46	0.414185	0.207092	+	0.978321i	$0.433600\pi$
$80$	−1.84622e46	−0.437098
$81$	−6.16630e46	−1.07682
$82$	3.56318e45	0.0460679
$83$	8.58374e46	0.824638	0.412319	−	0.911040i	$-0.364719\pi$
$83$	8.58374e46	0.824638	0.412319	+	0.911040i	$0.364719\pi$
$84$	9.82416e46	0.703806
$85$	2.31456e47	1.24081
$86$	−5.84097e46	−0.235111
$87$	2.62754e46	0.0796759
$88$	−2.46185e47	−0.564204
$89$	6.95931e47	1.20924	0.604618	−	0.796516i	$-0.293326\pi$
$89$	6.95931e47	1.20924	0.604618	+	0.796516i	$0.293326\pi$
$90$	−8.57104e47	−1.13264
$91$	−7.09067e47	−0.714782
$92$	−7.58138e47	−0.584718
$93$	5.81231e47	0.343967
$94$	3.54942e47	0.161631
$95$	−4.32337e48	−1.51913
$96$	−9.00089e47	−0.244703
$97$	7.53593e48	1.58939	0.794693	−	0.607011i	$-0.207632\pi$
$97$	7.53593e48	1.58939	0.794693	+	0.607011i	$0.207632\pi$
$98$	1.46710e47	0.0240670
$99$	−1.14291e49	−1.46201
$100$	1.02844e49	1.02844
$101$	2.43523e49	1.90839	0.954195	−	0.299185i	$-0.0967147\pi$
$101$	2.43523e49	1.90839	0.954195	+	0.299185i	$0.0967147\pi$
$102$	1.12842e49	0.694650
$103$	4.35062e48	0.210882	0.105441	−	0.994426i	$-0.466375\pi$
$103$	4.35062e48	0.210882	0.105441	+	0.994426i	$0.466375\pi$
$104$	6.49647e48	0.248520
$105$	−8.13316e49	−2.46106
$106$	−4.23699e49	−1.01640
$107$	4.63551e49	0.883477	0.441739	−	0.897144i	$-0.354362\pi$
$107$	4.63551e49	0.883477	0.441739	+	0.897144i	$0.354362\pi$
$108$	3.82431e48	0.0580325
$109$	−3.16577e49	−0.383293	−0.191646	−	0.981464i	$-0.561383\pi$
$109$	−3.16577e49	−0.383293	−0.191646	+	0.981464i	$0.561383\pi$
$110$	2.03810e50	1.97290
$111$	−1.69866e50	−1.31733
$112$	−4.08366e49	−0.254219
$113$	−2.77559e50	−1.38974	−0.694869	−	0.719136i	$-0.744538\pi$
$113$	−2.77559e50	−1.38974	−0.694869	+	0.719136i	$0.744538\pi$
$114$	−2.10778e50	−0.850463
$115$	6.27643e50	2.04463
$116$	−1.09220e49	−0.0287794
$117$	3.01597e50	0.643982
$118$	−7.19839e50	−1.24775
$119$	5.11958e50	0.721661
$120$	7.45160e50	0.855675
$121$	1.65053e51	1.54661
$122$	−2.38760e50	−0.182871
$123$	−1.43815e50	−0.0901837
$124$	−2.41603e50	−0.124243
$125$	−4.37479e51	−1.84783
$126$	−1.89583e51	−0.658750
$127$	−1.11605e51	−0.319516	−0.159758	−	0.987156i	$-0.551071\pi$
$127$	−1.11605e51	−0.319516	−0.159758	+	0.987156i	$0.551071\pi$
$128$	3.74144e50	0.0883883
$129$	2.35750e51	0.460260
$130$	−5.37826e51	−0.869019
$131$	3.32081e51	0.444730	0.222365	−	0.974963i	$-0.428622\pi$
$131$	3.32081e51	0.444730	0.222365	+	0.974963i	$0.428622\pi$
$132$	9.93637e51	1.10450
$133$	−9.56287e51	−0.883534
$134$	4.95845e51	0.381310
$135$	−3.16605e51	−0.202927
$136$	−4.69055e51	−0.250912
$137$	2.87128e52	1.28358	0.641788	−	0.766882i	$-0.278193\pi$
$137$	2.87128e52	1.28358	0.641788	+	0.766882i	$0.278193\pi$
$138$	3.05995e52	1.14466
$139$	−2.07847e52	−0.651450	−0.325725	−	0.945465i	$-0.605608\pi$
$139$	−2.07847e52	−0.651450	−0.325725	+	0.945465i	$0.605608\pi$
$140$	3.38075e52	0.888948
$141$	−1.43260e52	−0.316414
$142$	−4.30308e52	−0.799309
$143$	−7.17166e52	−1.12173
$144$	1.73696e52	0.229038
$145$	9.04205e51	0.100635
$146$	−8.68956e52	−0.817246
$147$	−5.92142e51	−0.0471142
$148$	7.06090e52	0.475826
$149$	2.65487e53	1.51698	0.758489	−	0.651686i	$-0.225938\pi$
$149$	2.65487e53	1.51698	0.758489	+	0.651686i	$0.225938\pi$
$150$	−4.15091e53	−2.01330
$151$	−2.97824e52	−0.122751	−0.0613754	−	0.998115i	$-0.519549\pi$
$151$	−2.97824e52	−0.122751	−0.0613754	+	0.998115i	$0.519549\pi$
$152$	8.76150e52	0.307192
$153$	−2.17758e53	−0.650180
$154$	4.50808e53	1.14745
$155$	2.00017e53	0.434450
$156$	−2.62206e53	−0.486509
$157$	−7.16451e52	−0.113670	−0.0568349	−	0.998384i	$-0.518101\pi$
$157$	−7.16451e52	−0.113670	−0.0568349	+	0.998384i	$0.518101\pi$
$158$	2.15664e53	0.292873
$159$	1.71011e54	1.98973
$160$	−3.09744e53	−0.309075
$161$	1.38828e54	1.18917
$162$	−1.03453e54	−0.761424
$163$	−8.62792e53	−0.546147	−0.273074	−	0.961993i	$-0.588040\pi$
$163$	−8.62792e53	−0.546147	−0.273074	+	0.961993i	$0.588040\pi$
$164$	5.97802e52	0.0325749
$165$	−8.22606e54	−3.86220
$166$	1.44011e54	0.583107
$167$	1.80874e53	0.0632154	0.0316077	−	0.999500i	$-0.489937\pi$
$167$	1.80874e53	0.0632154	0.0316077	+	0.999500i	$0.489937\pi$
$168$	1.64822e54	0.497666
$169$	−1.93773e54	−0.505904
$170$	3.88318e54	0.877383
$171$	4.06751e54	0.796019
$172$	−9.79953e53	−0.166249
$173$	8.09453e54	1.19141	0.595706	−	0.803202i	$-0.296872\pi$
$173$	8.09453e54	1.19141	0.595706	+	0.803202i	$0.296872\pi$
$174$	4.40827e53	0.0563394
$175$	−1.88325e55	−2.09158
$176$	−4.13030e54	−0.398953
$177$	2.90537e55	2.44262
$178$	1.16758e55	0.855058
$179$	−9.52961e54	−0.608381	−0.304191	−	0.952611i	$-0.598386\pi$
$179$	−9.52961e54	−0.608381	−0.304191	+	0.952611i	$0.598386\pi$
$180$	−1.43798e55	−0.800897
$181$	1.57599e55	0.766354	0.383177	−	0.923675i	$-0.374830\pi$
$181$	1.57599e55	0.766354	0.383177	+	0.923675i	$0.374830\pi$
$182$	−1.18962e55	−0.505427
$183$	9.63667e54	0.357993
$184$	−1.27194e55	−0.413458
$185$	−5.84553e55	−1.66386
$186$	9.75143e54	0.243221
$187$	5.17805e55	1.13252
$188$	5.95494e54	0.114290
$189$	−7.00298e54	−0.118024
$190$	−7.25341e55	−1.07419
$191$	−1.13259e56	−1.47487	−0.737435	−	0.675419i	$-0.763963\pi$
$191$	−1.13259e56	−1.47487	−0.737435	+	0.675419i	$0.763963\pi$
$192$	−1.51010e55	−0.173031
$193$	5.85668e55	0.590878	0.295439	−	0.955362i	$-0.404534\pi$
$193$	5.85668e55	0.590878	0.295439	+	0.955362i	$0.404534\pi$
$194$	1.26432e56	1.12387
$195$	2.17074e56	1.70122
$196$	2.46139e54	0.0170179
$197$	6.36238e55	0.388327	0.194163	−	0.980969i	$-0.437801\pi$
$197$	6.36238e55	0.388327	0.194163	+	0.980969i	$0.437801\pi$
$198$	−1.91748e56	−1.03379
$199$	−1.38808e56	−0.661475	−0.330738	−	0.943723i	$-0.607298\pi$
$199$	−1.38808e56	−0.661475	−0.330738	+	0.943723i	$0.607298\pi$
$200$	1.72543e56	0.727215
$201$	−2.00130e56	−0.746463
$202$	4.08565e56	1.34944
$203$	2.00001e55	0.0585302
$204$	1.89317e56	0.491191
$205$	−4.94905e55	−0.113907
$206$	7.29914e55	0.149116
$207$	−5.90498e56	−1.07138
$208$	1.08993e56	0.175730
$209$	−9.67210e56	−1.38655
$210$	−1.36452e57	−1.74023
$211$	5.64284e55	0.0640586	0.0320293	−	0.999487i	$-0.489803\pi$
$211$	5.64284e55	0.0640586	0.0320293	+	0.999487i	$0.489803\pi$
$212$	−7.10849e56	−0.718701
$213$	1.73678e57	1.56475
$214$	7.77710e56	0.624713
$215$	8.11277e56	0.581336
$216$	6.41613e55	0.0410352
$217$	4.42418e56	0.252679
$218$	−5.31129e56	−0.271029
$219$	3.50722e57	1.59986
$220$	3.41937e57	1.39505
$221$	−1.36641e57	−0.498852
$222$	−2.84988e57	−0.931490
$223$	−6.70689e57	−1.96360	−0.981798	−	0.189928i	$-0.939174\pi$
$223$	−6.70689e57	−1.96360	−0.981798	+	0.189928i	$0.939174\pi$
$224$	−6.85124e56	−0.179760
$225$	8.01028e57	1.88441
$226$	−4.65666e57	−0.982694
$227$	1.77430e57	0.336042	0.168021	−	0.985783i	$-0.446262\pi$
$227$	1.77430e57	0.336042	0.168021	+	0.985783i	$0.446262\pi$
$228$	−3.53626e57	−0.601368
$229$	1.42321e57	0.217420	0.108710	−	0.994074i	$-0.465328\pi$
$229$	1.42321e57	0.217420	0.108710	+	0.994074i	$0.465328\pi$
$230$	1.05301e58	1.44577
$231$	−1.81952e58	−2.24628
$232$	−1.83241e56	−0.0203501
$233$	6.14657e57	0.614346	0.307173	−	0.951654i	$-0.400617\pi$
$233$	6.14657e57	0.614346	0.307173	+	0.951654i	$0.400617\pi$
$234$	5.05996e57	0.455364
$235$	−4.92994e57	−0.399649
$236$	−1.20769e58	−0.882290
$237$	−8.70449e57	−0.573336
$238$	8.58922e57	0.510292
$239$	−1.87389e58	−1.00460	−0.502301	−	0.864693i	$-0.667513\pi$
$239$	−1.87389e58	−1.00460	−0.502301	+	0.864693i	$0.667513\pi$
$240$	1.25017e58	0.605054
$241$	1.41041e58	0.616491	0.308245	−	0.951307i	$-0.400258\pi$
$241$	1.41041e58	0.616491	0.308245	+	0.951307i	$0.400258\pi$
$242$	2.76912e58	1.09362
$243$	3.85039e58	1.37452
$244$	−4.00572e57	−0.129309
$245$	−2.03772e57	−0.0595080
$246$	−2.41281e57	−0.0637695
$247$	2.55233e58	0.610747
$248$	−4.05343e57	−0.0878529
$249$	−5.81249e58	−1.14151
$250$	−7.33968e58	−1.30661
$251$	2.19883e58	0.354965	0.177482	−	0.984124i	$-0.443205\pi$
$251$	2.19883e58	0.354965	0.177482	+	0.984124i	$0.443205\pi$
$252$	−3.18067e58	−0.465807
$253$	1.40414e59	1.86620
$254$	−1.87242e58	−0.225932
$255$	−1.56731e59	−1.71759
$256$	6.27710e57	0.0625000
$257$	−1.39270e58	−0.126036	−0.0630180	−	0.998012i	$-0.520073\pi$
$257$	−1.39270e58	−0.126036	−0.0630180	+	0.998012i	$0.520073\pi$
$258$	3.95522e58	0.325453
$259$	−1.29298e59	−0.967712
$260$	−9.02322e58	−0.614489
$261$	−8.50692e57	−0.0527327
$262$	5.57139e58	0.314472
$263$	1.50291e59	0.772710	0.386355	−	0.922350i	$-0.373734\pi$
$263$	1.50291e59	0.772710	0.386355	+	0.922350i	$0.373734\pi$
$264$	1.66705e59	0.781001
$265$	5.88493e59	2.51314
$266$	−1.60438e59	−0.624753
$267$	−4.71250e59	−1.67389
$268$	8.31889e58	0.269627
$269$	4.46165e59	1.31997	0.659986	−	0.751278i	$-0.270562\pi$
$269$	4.46165e59	1.31997	0.659986	+	0.751278i	$0.270562\pi$
$270$	−5.31174e58	−0.143491
$271$	−1.87553e59	−0.462782	−0.231391	−	0.972861i	$-0.574328\pi$
$271$	−1.87553e59	−0.462782	−0.231391	+	0.972861i	$0.574328\pi$
$272$	−7.86944e58	−0.177421
$273$	4.80146e59	0.989438
$274$	4.81721e59	0.907626
$275$	−1.90476e60	−3.28238
$276$	5.13374e59	0.809397
$277$	−5.17979e59	−0.747408	−0.373704	−	0.927548i	$-0.621912\pi$
$277$	−5.17979e59	−0.747408	−0.373704	+	0.927548i	$0.621912\pi$
$278$	−3.48709e59	−0.460645
$279$	−1.88180e59	−0.227651
$280$	5.67196e59	0.628581
$281$	−1.19166e60	−1.21017	−0.605085	−	0.796161i	$-0.706861\pi$
$281$	−1.19166e60	−1.21017	−0.605085	+	0.796161i	$0.706861\pi$
$282$	−2.40350e59	−0.223738
$283$	2.07435e60	1.77058	0.885288	−	0.465044i	$-0.153961\pi$
$283$	2.07435e60	1.77058	0.885288	+	0.465044i	$0.153961\pi$
$284$	−7.21936e59	−0.565197
$285$	2.92758e60	2.10285
$286$	−1.20321e60	−0.793180
$287$	−1.09468e59	−0.0662492
$288$	2.91413e59	0.161955
$289$	−9.72261e59	−0.496347
$290$	1.51700e59	0.0711599
$291$	−5.10297e60	−2.20011
$292$	−1.45787e60	−0.577880
$293$	4.37111e60	1.59344	0.796719	−	0.604350i	$-0.206567\pi$
$293$	4.37111e60	1.59344	0.796719	+	0.604350i	$0.206567\pi$
$294$	−9.93450e58	−0.0333147
$295$	9.99814e60	3.08518
$296$	1.18462e60	0.336460
$297$	−7.08297e59	−0.185218
$298$	4.45413e60	1.07267
$299$	−3.70533e60	−0.822020
$300$	−6.96408e60	−1.42362
$301$	1.79447e60	0.338108
$302$	−4.99666e59	−0.0867979
$303$	−1.64902e61	−2.64169
$304$	1.46994e60	0.217218
$305$	3.31623e60	0.452167
$306$	−3.65337e60	−0.459747
$307$	−4.69486e60	−0.545421	−0.272711	−	0.962096i	$-0.587920\pi$
$307$	−4.69486e60	−0.545421	−0.272711	+	0.962096i	$0.587920\pi$
$308$	7.56330e60	0.811370
$309$	−2.94603e60	−0.291914
$310$	3.35573e60	0.307203
$311$	−1.13490e61	−0.960127	−0.480063	−	0.877234i	$-0.659386\pi$
$311$	−1.13490e61	−0.960127	−0.480063	+	0.877234i	$0.659386\pi$
$312$	−4.39910e60	−0.344014
$313$	2.24105e61	1.62037	0.810186	−	0.586173i	$-0.199366\pi$
$313$	2.24105e61	1.62037	0.810186	+	0.586173i	$0.199366\pi$
$314$	−1.20201e60	−0.0803767
$315$	2.63320e61	1.62883
$316$	3.61824e60	0.207092
$317$	−1.97282e61	−1.04505	−0.522523	−	0.852625i	$-0.675009\pi$
$317$	−1.97282e61	−1.04505	−0.522523	+	0.852625i	$0.675009\pi$
$318$	2.86908e61	1.40695
$319$	2.02286e60	0.0918530
$320$	−5.19665e60	−0.218549
$321$	−3.13895e61	−1.22296
$322$	2.32915e61	0.840871
$323$	−1.84282e61	−0.616625
$324$	−1.73566e61	−0.538408
$325$	5.02638e61	1.44582
$326$	−1.44752e61	−0.386184
$327$	2.14371e61	0.530574
$328$	1.00295e60	0.0230339
$329$	−1.09045e61	−0.232438
$330$	−1.38010e62	−2.73099
$331$	−8.48788e60	−0.155960	−0.0779801	−	0.996955i	$-0.524847\pi$
$331$	−8.48788e60	−0.155960	−0.0779801	+	0.996955i	$0.524847\pi$
$332$	2.41611e61	0.412319
$333$	5.49959e61	0.871859
$334$	3.03456e60	0.0447000
$335$	−6.88699e61	−0.942826
$336$	2.76526e61	0.351903
$337$	−1.13716e62	−1.34552	−0.672760	−	0.739861i	$-0.734891\pi$
$337$	−1.13716e62	−1.34552	−0.672760	+	0.739861i	$0.734891\pi$
$338$	−3.25097e61	−0.357728
$339$	1.87949e62	1.92375
$340$	6.51490e61	0.620404
$341$	4.47471e61	0.396536
$342$	6.82414e61	0.562871
$343$	1.27919e62	0.982265
$344$	−1.64409e61	−0.117556
$345$	−4.25009e62	−2.83029
$346$	1.35804e62	0.842456
$347$	1.85460e62	1.07196	0.535979	−	0.844231i	$-0.319943\pi$
$347$	1.85460e62	1.07196	0.535979	+	0.844231i	$0.319943\pi$
$348$	7.39586e60	0.0398380
$349$	1.74990e62	0.878598	0.439299	−	0.898341i	$-0.355227\pi$
$349$	1.74990e62	0.878598	0.439299	+	0.898341i	$0.355227\pi$
$350$	−3.15957e62	−1.47897
$351$	1.86909e61	0.0815843
$352$	−6.92949e61	−0.282102
$353$	−4.46780e62	−1.69673	−0.848367	−	0.529409i	$-0.822414\pi$
$353$	−4.46780e62	−1.69673	−0.848367	+	0.529409i	$0.822414\pi$
$354$	4.87440e62	1.72720
$355$	5.97672e62	1.97637
$356$	1.95887e62	0.604618
$357$	−3.46673e62	−0.998961
$358$	−1.59880e62	−0.430190
$359$	−6.15371e62	−1.54640	−0.773202	−	0.634160i	$-0.781346\pi$
$359$	−6.15371e62	−1.54640	−0.773202	+	0.634160i	$0.781346\pi$
$360$	−2.41253e62	−0.566320
$361$	−1.11739e62	−0.245063
$362$	2.64408e62	0.541894
$363$	−1.11766e63	−2.14090
$364$	−1.99585e62	−0.357391
$365$	1.20693e63	2.02072
$366$	1.61676e62	0.253140
$367$	1.78399e62	0.261261	0.130631	−	0.991431i	$-0.458300\pi$
$367$	1.78399e62	0.261261	0.130631	+	0.991431i	$0.458300\pi$
$368$	−2.13397e62	−0.292359
$369$	4.65615e61	0.0596872
$370$	−9.80718e62	−1.17653
$371$	1.30169e63	1.46166
$372$	1.63602e62	0.171983
$373$	−6.15312e61	−0.0605661	−0.0302830	−	0.999541i	$-0.509641\pi$
$373$	−6.15312e61	−0.0605661	−0.0302830	+	0.999541i	$0.509641\pi$
$374$	8.68733e62	0.800814
$375$	2.96240e63	2.55786
$376$	9.99073e61	0.0808156
$377$	−5.33802e61	−0.0404592
$378$	−1.17491e62	−0.0834553
$379$	−1.93924e63	−1.29113	−0.645567	−	0.763704i	$-0.723379\pi$
$379$	−1.93924e63	−1.29113	−0.645567	+	0.763704i	$0.723379\pi$
$380$	−1.21692e63	−0.759564
$381$	7.55736e62	0.442291
$382$	−1.90016e63	−1.04289
$383$	4.92299e61	0.0253430	0.0126715	−	0.999920i	$-0.495966\pi$
$383$	4.92299e61	0.0253430	0.0126715	+	0.999920i	$0.495966\pi$
$384$	−2.53352e62	−0.122352
$385$	−6.26146e63	−2.83719
$386$	9.82589e62	0.417814
$387$	−7.63264e62	−0.304619
$388$	2.12118e63	0.794693
$389$	1.52402e63	0.536075	0.268038	−	0.963408i	$-0.413625\pi$
$389$	1.52402e63	0.536075	0.268038	+	0.963408i	$0.413625\pi$
$390$	3.64189e63	1.20294
$391$	2.67530e63	0.829931
$392$	4.12952e61	0.0120335
$393$	−2.24869e63	−0.615619
$394$	1.06743e63	0.274588
$395$	−2.99545e63	−0.724157
$396$	−3.21700e63	−0.731003
$397$	−4.22139e63	−0.901753	−0.450877	−	0.892586i	$-0.648889\pi$
$397$	−4.22139e63	−0.901753	−0.450877	+	0.892586i	$0.648889\pi$
$398$	−2.32881e63	−0.467734
$399$	6.47551e63	1.22303
$400$	2.89479e63	0.514218
$401$	7.10002e63	1.18638	0.593188	−	0.805064i	$-0.297869\pi$
$401$	7.10002e63	1.18638	0.593188	+	0.805064i	$0.297869\pi$
$402$	−3.35762e63	−0.527829
$403$	−1.18081e63	−0.174665
$404$	6.85458e63	0.954195
$405$	1.43691e64	1.88270
$406$	3.35546e62	0.0413871
$407$	−1.30774e64	−1.51866
$408$	3.17621e63	0.347325
$409$	−4.19928e63	−0.432468	−0.216234	−	0.976342i	$-0.569377\pi$
$409$	−4.19928e63	−0.432468	−0.216234	+	0.976342i	$0.569377\pi$
$410$	−8.30312e62	−0.0805447
$411$	−1.94429e64	−1.77679
$412$	1.22459e63	0.105441
$413$	2.21149e64	1.79436
$414$	−9.90691e63	−0.757582
$415$	−2.00023e64	−1.44179
$416$	1.82859e63	0.124260
$417$	1.40744e64	0.901771
$418$	−1.62271e64	−0.980442
$419$	2.50397e64	1.42687	0.713436	−	0.700720i	$-0.247138\pi$
$419$	2.50397e64	1.42687	0.713436	+	0.700720i	$0.247138\pi$
$420$	−2.28928e64	−1.23053
$421$	−2.02007e63	−0.102437	−0.0512184	−	0.998687i	$-0.516310\pi$
$421$	−2.02007e63	−0.102437	−0.0512184	+	0.998687i	$0.516310\pi$
$422$	9.46712e62	0.0452963
$423$	4.63818e63	0.209415
$424$	−1.19261e64	−0.508199
$425$	−3.62913e64	−1.45973
$426$	2.91383e64	1.10644
$427$	7.33518e63	0.262983
$428$	1.30478e64	0.441739
$429$	4.85630e64	1.55275
$430$	1.36110e64	0.411066
$431$	−6.45676e64	−1.84213	−0.921067	−	0.389403i	$-0.872681\pi$
$431$	−6.45676e64	−1.84213	−0.921067	+	0.389403i	$0.872681\pi$
$432$	1.07645e63	0.0290162
$433$	5.64458e64	1.43773	0.718867	−	0.695148i	$-0.244661\pi$
$433$	5.64458e64	1.43773	0.718867	+	0.695148i	$0.244661\pi$
$434$	7.42254e63	0.178671
$435$	−6.12283e63	−0.139305
$436$	−8.91086e63	−0.191646
$437$	−4.99721e64	−1.01609
$438$	5.88415e64	1.13127
$439$	4.39799e64	0.799602	0.399801	−	0.916602i	$-0.369079\pi$
$439$	4.39799e64	0.799602	0.399801	+	0.916602i	$0.369079\pi$
$440$	5.73675e64	0.986450
$441$	1.91712e63	0.0311820
$442$	−2.29246e64	−0.352741
$443$	5.44392e64	0.792538	0.396269	−	0.918134i	$-0.370305\pi$
$443$	5.44392e64	0.792538	0.396269	+	0.918134i	$0.370305\pi$
$444$	−4.78130e64	−0.658663
$445$	−1.62170e65	−2.11422
$446$	−1.12523e65	−1.38847
$447$	−1.79775e65	−2.09988
$448$	−1.14945e64	−0.127109
$449$	6.51981e64	0.682652	0.341326	−	0.939945i	$-0.389124\pi$
$449$	6.51981e64	0.682652	0.341326	+	0.939945i	$0.389124\pi$
$450$	1.34390e65	1.33248
$451$	−1.10718e64	−0.103967
$452$	−7.81258e64	−0.694869
$453$	2.01672e64	0.169918
$454$	2.97678e64	0.237617
$455$	1.65231e65	1.24972
$456$	−5.93286e64	−0.425232
$457$	1.64423e65	1.11691	0.558453	−	0.829536i	$-0.311395\pi$
$457$	1.64423e65	1.11691	0.558453	+	0.829536i	$0.311395\pi$
$458$	2.38775e64	0.153739
$459$	−1.34951e64	−0.0823696
$460$	1.76666e65	1.02232
$461$	7.21325e64	0.395784	0.197892	−	0.980224i	$-0.436590\pi$
$461$	7.21325e64	0.395784	0.197892	+	0.980224i	$0.436590\pi$
$462$	−3.05265e65	−1.58836
$463$	1.94522e65	0.959916	0.479958	−	0.877291i	$-0.340652\pi$
$463$	1.94522e65	0.959916	0.479958	+	0.877291i	$0.340652\pi$
$464$	−3.07427e63	−0.0143897
$465$	−1.35442e65	−0.601388
$466$	1.03122e65	0.434408
$467$	−7.84448e64	−0.313545	−0.156773	−	0.987635i	$-0.550109\pi$
$467$	−7.84448e64	−0.313545	−0.156773	+	0.987635i	$0.550109\pi$
$468$	8.48921e64	0.321991
$469$	−1.52334e65	−0.548354
$470$	−8.27106e64	−0.282595
$471$	4.85146e64	0.157348
$472$	−2.02617e65	−0.623873
$473$	1.81496e65	0.530603
$474$	−1.46037e65	−0.405410
$475$	6.77886e65	1.78716
$476$	1.44103e65	0.360831
$477$	−5.53665e65	−1.31688
$478$	−3.14386e65	−0.710362
$479$	−3.87609e65	−0.832097	−0.416048	−	0.909342i	$-0.636585\pi$
$479$	−3.87609e65	−0.832097	−0.416048	+	0.909342i	$0.636585\pi$
$480$	2.09744e65	0.427838
$481$	3.45095e65	0.668935
$482$	2.36627e65	0.435925
$483$	−9.40079e65	−1.64611
$484$	4.64582e65	0.773305
$485$	−1.75607e66	−2.77887
$486$	6.45988e65	0.971933
$487$	8.09553e65	1.15821	0.579103	−	0.815255i	$-0.303403\pi$
$487$	8.09553e65	1.15821	0.579103	+	0.815255i	$0.303403\pi$
$488$	−6.72049e64	−0.0914355
$489$	5.84241e65	0.756005
$490$	−3.41872e64	−0.0420785
$491$	−1.15921e66	−1.35727	−0.678634	−	0.734477i	$-0.737428\pi$
$491$	−1.15921e66	−1.35727	−0.678634	+	0.734477i	$0.737428\pi$
$492$	−4.04803e64	−0.0450919
$493$	3.85414e64	0.0408486
$494$	4.28210e65	0.431863
$495$	2.66327e66	2.55616
$496$	−6.80052e64	−0.0621214
$497$	1.32199e66	1.14947
$498$	−9.75175e65	−0.807167
$499$	1.98775e66	1.56638	0.783191	−	0.621781i	$-0.213591\pi$
$499$	1.98775e66	1.56638	0.783191	+	0.621781i	$0.213591\pi$
$500$	−1.23139e66	−0.923915
$501$	−1.22479e65	−0.0875061
$502$	3.68902e65	0.250998
$503$	−1.31100e66	−0.849548	−0.424774	−	0.905300i	$-0.639646\pi$
$503$	−1.31100e66	−0.849548	−0.424774	+	0.905300i	$0.639646\pi$
$504$	−5.33629e65	−0.329375
$505$	−5.67472e66	−3.33661
$506$	2.35576e66	1.31960
$507$	1.31213e66	0.700299
$508$	−3.14141e65	−0.159758
$509$	7.52616e65	0.364744	0.182372	−	0.983230i	$-0.441623\pi$
$509$	7.52616e65	0.364744	0.182372	+	0.983230i	$0.441623\pi$
$510$	−2.62950e66	−1.21452
$511$	2.66961e66	1.17526
$512$	1.05312e65	0.0441942
$513$	2.52076e65	0.100846
$514$	−2.33656e65	−0.0891210
$515$	−1.01381e66	−0.368704
$516$	6.63576e65	0.230130
$517$	−1.10291e66	−0.364772
$518$	−2.16925e66	−0.684275
$519$	−5.48123e66	−1.64922
$520$	−1.51384e66	−0.434510
$521$	2.28801e66	0.626519	0.313260	−	0.949667i	$-0.398579\pi$
$521$	2.28801e66	0.626519	0.313260	+	0.949667i	$0.398579\pi$
$522$	−1.42722e65	−0.0372877
$523$	3.63925e65	0.0907237	0.0453618	−	0.998971i	$-0.485556\pi$
$523$	3.63925e65	0.0907237	0.0453618	+	0.998971i	$0.485556\pi$
$524$	9.34724e65	0.222365
$525$	1.27524e67	2.89528
$526$	2.52146e66	0.546389
$527$	8.52564e65	0.176347
$528$	2.79684e66	0.552251
$529$	1.94992e66	0.367581
$530$	9.87327e66	1.77706
$531$	−9.40644e66	−1.61663
$532$	−2.69171e66	−0.441767
$533$	2.92170e65	0.0457951
$534$	−7.90627e66	−1.18362
$535$	−1.08019e67	−1.54466
$536$	1.39568e66	0.190655
$537$	6.45299e66	0.842153
$538$	7.48541e66	0.933362
$539$	−4.55871e65	−0.0543147
$540$	−8.91163e65	−0.101464
$541$	−1.63939e67	−1.78382	−0.891908	−	0.452218i	$-0.850633\pi$
$541$	−1.63939e67	−1.78382	−0.891908	+	0.452218i	$0.850633\pi$
$542$	−3.14662e66	−0.327236
$543$	−1.06719e67	−1.06083
$544$	−1.32027e66	−0.125456
$545$	7.37707e66	0.670146
$546$	8.05552e66	0.699638
$547$	1.43390e67	1.19078	0.595388	−	0.803439i	$-0.296999\pi$
$547$	1.43390e67	1.19078	0.595388	+	0.803439i	$0.296999\pi$
$548$	8.08194e66	0.641788
$549$	−3.11997e66	−0.236934
$550$	−3.19565e67	−2.32099
$551$	−7.19915e65	−0.0500112
$552$	8.61299e66	0.572330
$553$	−6.62563e66	−0.421174
$554$	−8.69024e66	−0.528497
$555$	3.95831e67	2.30320
$556$	−5.85037e66	−0.325725
$557$	1.82851e67	0.974193	0.487097	−	0.873348i	$-0.338056\pi$
$557$	1.82851e67	0.974193	0.487097	+	0.873348i	$0.338056\pi$
$558$	−3.15713e66	−0.160973
$559$	−4.78942e66	−0.233719
$560$	9.51597e66	0.444474
$561$	−3.50632e67	−1.56770
$562$	−1.99927e67	−0.855720
$563$	−2.90085e67	−1.18869	−0.594346	−	0.804209i	$-0.702589\pi$
$563$	−2.90085e67	−1.18869	−0.594346	+	0.804209i	$0.702589\pi$
$564$	−4.03240e66	−0.158207
$565$	6.46783e67	2.42981
$566$	3.48018e67	1.25199
$567$	3.17830e67	1.09499
$568$	−1.21121e67	−0.399654
$569$	−4.00130e66	−0.126459	−0.0632296	−	0.997999i	$-0.520140\pi$
$569$	−4.00130e66	−0.126459	−0.0632296	+	0.997999i	$0.520140\pi$
$570$	4.91166e67	1.48694
$571$	−4.01640e67	−1.16480	−0.582401	−	0.812902i	$-0.697887\pi$
$571$	−4.01640e67	−1.16480	−0.582401	+	0.812902i	$0.697887\pi$
$572$	−2.01864e67	−0.560863
$573$	7.66932e67	2.04159
$574$	−1.83657e66	−0.0468453
$575$	−9.84116e67	−2.40538
$576$	4.88910e66	0.114519
$577$	−4.66796e67	−1.04790	−0.523950	−	0.851749i	$-0.675542\pi$
$577$	−4.66796e67	−1.04790	−0.523950	+	0.851749i	$0.675542\pi$
$578$	−1.63118e67	−0.350970
$579$	−3.96586e67	−0.817924
$580$	2.54511e66	0.0503177
$581$	−4.42432e67	−0.838554
$582$	−8.56136e67	−1.55571
$583$	1.31656e68	2.29382
$584$	−2.44589e67	−0.408623
$585$	−7.02799e67	−1.12593
$586$	7.33351e67	1.12673
$587$	2.48745e67	0.366539	0.183270	−	0.983063i	$-0.441332\pi$
$587$	2.48745e67	0.366539	0.183270	+	0.983063i	$0.441332\pi$
$588$	−1.66673e66	−0.0235571
$589$	−1.59251e67	−0.215902
$590$	1.67741e68	2.18155
$591$	−4.30830e67	−0.537542
$592$	1.98747e67	0.237913
$593$	4.14071e66	0.0475592	0.0237796	−	0.999717i	$-0.492430\pi$
$593$	4.14071e66	0.0475592	0.0237796	+	0.999717i	$0.492430\pi$
$594$	−1.18833e67	−0.130969
$595$	−1.19299e68	−1.26175
$596$	7.47279e67	0.758489
$597$	9.39940e67	0.915649
$598$	−6.21650e67	−0.581256
$599$	2.10487e68	1.88915	0.944577	−	0.328291i	$-0.106473\pi$
$599$	2.10487e68	1.88915	0.944577	+	0.328291i	$0.106473\pi$
$600$	−1.16838e68	−1.00665
$601$	1.59794e68	1.32171	0.660854	−	0.750514i	$-0.270194\pi$
$601$	1.59794e68	1.32171	0.660854	+	0.750514i	$0.270194\pi$
$602$	3.01061e67	0.239079
$603$	6.47941e67	0.494039
$604$	−8.38300e66	−0.0613754
$605$	−3.84615e68	−2.70408
$606$	−2.76660e68	−1.86796
$607$	2.59164e68	1.68055	0.840275	−	0.542160i	$-0.182393\pi$
$607$	2.59164e68	1.68055	0.840275	+	0.542160i	$0.182393\pi$
$608$	2.46614e67	0.153596
$609$	−1.35431e67	−0.0810205
$610$	5.56371e67	0.319730
$611$	2.91042e67	0.160674
$612$	−6.12934e67	−0.325090
$613$	−5.81382e67	−0.296265	−0.148132	−	0.988968i	$-0.547326\pi$
$613$	−5.81382e67	−0.296265	−0.148132	+	0.988968i	$0.547326\pi$
$614$	−7.87666e67	−0.385671
$615$	3.35125e67	0.157676
$616$	1.26891e68	0.573725
$617$	−3.39743e68	−1.47626	−0.738131	−	0.674657i	$-0.764291\pi$
$617$	−3.39743e68	−1.47626	−0.738131	+	0.674657i	$0.764291\pi$
$618$	−4.94262e67	−0.206414
$619$	3.60992e67	0.144903	0.0724514	−	0.997372i	$-0.476918\pi$
$619$	3.60992e67	0.144903	0.0724514	+	0.997372i	$0.476918\pi$
$620$	5.62997e67	0.217225
$621$	−3.65950e67	−0.135731
$622$	−1.90405e68	−0.678912
$623$	−3.58704e68	−1.22964
$624$	−7.38046e67	−0.243254
$625$	3.70404e68	1.17386
$626$	3.75985e68	1.14578
$627$	6.54948e68	1.91934
$628$	−2.01663e67	−0.0568349
$629$	−2.49164e68	−0.675373
$630$	4.41777e68	1.15175
$631$	−1.97407e68	−0.495044	−0.247522	−	0.968882i	$-0.579616\pi$
$631$	−1.97407e68	−0.495044	−0.247522	+	0.968882i	$0.579616\pi$
$632$	6.07040e67	0.146436
$633$	−3.82106e67	−0.0886733
$634$	−3.30984e68	−0.738959
$635$	2.60069e68	0.558640
$636$	4.81352e68	0.994864
$637$	1.20298e67	0.0239245
$638$	3.39379e67	0.0649498
$639$	−5.62301e68	−1.03561
$640$	−8.71853e67	−0.154537
$641$	−8.01714e67	−0.136772	−0.0683861	−	0.997659i	$-0.521785\pi$
$641$	−8.01714e67	−0.136772	−0.0683861	+	0.997659i	$0.521785\pi$
$642$	−5.26628e68	−0.864760
$643$	1.38094e67	0.0218276	0.0109138	−	0.999940i	$-0.496526\pi$
$643$	1.38094e67	0.0218276	0.0109138	+	0.999940i	$0.496526\pi$
$644$	3.90767e68	0.594586
$645$	−5.49357e68	−0.804715
$646$	−3.09174e68	−0.436020
$647$	−3.29500e67	−0.0447405	−0.0223702	−	0.999750i	$-0.507121\pi$
$647$	−3.29500e67	−0.0447405	−0.0223702	+	0.999750i	$0.507121\pi$
$648$	−2.91195e68	−0.380712
$649$	2.23675e69	2.81593
$650$	8.43287e68	1.02235
$651$	−2.99584e68	−0.349771
$652$	−2.42854e68	−0.273074
$653$	−1.29443e69	−1.40186	−0.700929	−	0.713231i	$-0.747231\pi$
$653$	−1.29443e69	−1.40186	−0.700929	+	0.713231i	$0.747231\pi$
$654$	3.59655e68	0.375172
$655$	−7.73833e68	−0.777563
$656$	1.68266e67	0.0162874
$657$	−1.13550e69	−1.05885
$658$	−1.82948e68	−0.164359
$659$	−1.29161e69	−1.11799	−0.558995	−	0.829171i	$-0.688813\pi$
$659$	−1.29161e69	−1.11799	−0.558995	+	0.829171i	$0.688813\pi$
$660$	−2.31543e69	−1.93110
$661$	9.63417e68	0.774245	0.387123	−	0.922028i	$-0.373469\pi$
$661$	9.63417e68	0.774245	0.387123	+	0.922028i	$0.373469\pi$
$662$	−1.42403e68	−0.110280
$663$	9.25269e68	0.690536
$664$	4.05356e68	0.291554
$665$	2.22840e69	1.54476
$666$	9.22677e68	0.616497
$667$	1.04513e68	0.0673114
$668$	5.09116e67	0.0316077
$669$	4.54158e69	2.71811
$670$	−1.15545e69	−0.666679
$671$	7.41896e68	0.412706
$672$	4.63933e68	0.248833
$673$	8.62520e68	0.446067	0.223034	−	0.974811i	$-0.428404\pi$
$673$	8.62520e68	0.446067	0.223034	+	0.974811i	$0.428404\pi$
$674$	−1.90784e69	−0.951426
$675$	4.96422e68	0.238731
$676$	−5.45421e68	−0.252952
$677$	−2.63131e69	−1.17693	−0.588464	−	0.808524i	$-0.700267\pi$
$677$	−2.63131e69	−1.17693	−0.588464	+	0.808524i	$0.700267\pi$
$678$	3.15327e69	1.36030
$679$	−3.88425e69	−1.61621
$680$	1.09302e69	0.438692
$681$	−1.20147e69	−0.465167
$682$	7.50732e68	0.280393
$683$	1.91092e69	0.688551	0.344275	−	0.938869i	$-0.388125\pi$
$683$	1.91092e69	0.688551	0.344275	+	0.938869i	$0.388125\pi$
$684$	1.14490e69	0.398010
$685$	−6.69082e69	−2.24420
$686$	2.14612e69	0.694566
$687$	−9.63727e68	−0.300964
$688$	−2.75832e68	−0.0831243
$689$	−3.47420e69	−1.01038
$690$	−7.13047e69	−2.00132
$691$	−3.63593e69	−0.984926	−0.492463	−	0.870333i	$-0.663903\pi$
$691$	−3.63593e69	−0.984926	−0.492463	+	0.870333i	$0.663903\pi$
$692$	2.27841e69	0.595706
$693$	5.89090e69	1.48668
$694$	3.11150e69	0.757989
$695$	4.84337e69	1.13899
$696$	1.24082e68	0.0281697
$697$	−2.10951e68	−0.0462358
$698$	2.93585e69	0.621263
$699$	−4.16216e69	−0.850409
$700$	−5.30087e69	−1.04579
$701$	8.99753e69	1.71408	0.857041	−	0.515248i	$-0.172300\pi$
$701$	8.99753e69	1.71408	0.857041	+	0.515248i	$0.172300\pi$
$702$	3.13582e68	0.0576888
$703$	4.65414e69	0.826863
$704$	−1.16258e69	−0.199476
$705$	3.33832e69	0.553215
$706$	−7.49573e69	−1.19977
$707$	−1.25519e70	−1.94060
$708$	8.17789e69	1.22131
$709$	−7.36602e69	−1.06267	−0.531337	−	0.847160i	$-0.678310\pi$
$709$	−7.36602e69	−1.06267	−0.531337	+	0.847160i	$0.678310\pi$
$710$	1.00273e70	1.39751
$711$	2.81817e69	0.379457
$712$	3.28644e69	0.427529
$713$	2.31191e69	0.290588
$714$	−5.81621e69	−0.706372
$715$	1.67118e70	1.96122
$716$	−2.68235e69	−0.304191
$717$	1.26890e70	1.39062
$718$	−1.03242e70	−1.09347
$719$	−7.15587e69	−0.732495	−0.366247	−	0.930518i	$-0.619358\pi$
$719$	−7.15587e69	−0.732495	−0.366247	+	0.930518i	$0.619358\pi$
$720$	−4.04756e69	−0.400449
$721$	−2.24244e69	−0.214441
$722$	−1.87466e69	−0.173285
$723$	−9.55058e69	−0.853378
$724$	4.43603e69	0.383177
$725$	−1.41775e69	−0.118391
$726$	−1.87512e70	−1.51384
$727$	−1.60013e69	−0.124900	−0.0624501	−	0.998048i	$-0.519891\pi$
$727$	−1.60013e69	−0.124900	−0.0624501	+	0.998048i	$0.519891\pi$
$728$	−3.34848e69	−0.252714
$729$	−1.13171e70	−0.825866
$730$	2.02489e70	1.42887
$731$	3.45804e69	0.235968
$732$	2.71248e69	0.178997
$733$	2.09305e69	0.133577	0.0667887	−	0.997767i	$-0.478725\pi$
$733$	2.09305e69	0.133577	0.0667887	+	0.997767i	$0.478725\pi$
$734$	2.99304e69	0.184739
$735$	1.37984e69	0.0823740
$736$	−3.58021e69	−0.206729
$737$	−1.54073e70	−0.860546
$738$	7.81173e68	0.0422052
$739$	2.82972e70	1.47895	0.739477	−	0.673182i	$-0.235073\pi$
$739$	2.82972e70	1.47895	0.739477	+	0.673182i	$0.235073\pi$
$740$	−1.64537e70	−0.831930
$741$	−1.72831e70	−0.845427
$742$	2.18387e70	1.03355
$743$	3.69750e70	1.69310	0.846550	−	0.532310i	$-0.178676\pi$
$743$	3.69750e70	1.69310	0.846550	+	0.532310i	$0.178676\pi$
$744$	2.74478e69	0.121611
$745$	−6.18653e70	−2.65227
$746$	−1.03232e69	−0.0428267
$747$	1.88186e70	0.755495
$748$	1.45749e70	0.566261
$749$	−2.38928e70	−0.898386
$750$	4.97007e70	1.80868
$751$	3.61337e70	1.27272	0.636361	−	0.771391i	$-0.280439\pi$
$751$	3.61337e70	1.27272	0.636361	+	0.771391i	$0.280439\pi$
$752$	1.67617e69	0.0571452
$753$	−1.48894e70	−0.491361
$754$	−8.95572e68	−0.0286090
$755$	6.94006e69	0.214616
$756$	−1.97116e69	−0.0590118
$757$	3.99376e70	1.15753	0.578766	−	0.815493i	$-0.303534\pi$
$757$	3.99376e70	1.15753	0.578766	+	0.815493i	$0.303534\pi$
$758$	−3.25351e70	−0.912969
$759$	−9.50816e70	−2.58329
$760$	−2.04165e70	−0.537093
$761$	6.65810e70	1.69600	0.848000	−	0.529996i	$-0.177807\pi$
$761$	6.65810e70	1.69600	0.848000	+	0.529996i	$0.177807\pi$
$762$	1.26791e70	0.312747
$763$	1.63173e70	0.389761
$764$	−3.18794e70	−0.737435
$765$	5.07432e70	1.13677
$766$	8.25940e68	0.0179202
$767$	−5.90246e70	−1.24036
$768$	−4.25055e69	−0.0865157
$769$	−5.73078e70	−1.12984	−0.564922	−	0.825144i	$-0.691094\pi$
$769$	−5.73078e70	−1.12984	−0.564922	+	0.825144i	$0.691094\pi$
$770$	−1.05050e71	−2.00619
$771$	9.43066e69	0.174466
$772$	1.64851e70	0.295439
$773$	−6.58392e70	−1.14311	−0.571553	−	0.820565i	$-0.693659\pi$
$773$	−6.58392e70	−1.14311	−0.571553	+	0.820565i	$0.693659\pi$
$774$	−1.28055e70	−0.215398
$775$	−3.13618e70	−0.511104
$776$	3.55874e70	0.561933
$777$	8.75540e70	1.33956
$778$	2.55688e70	0.379062
$779$	3.94036e69	0.0566068
$780$	6.11009e70	0.850608
$781$	1.33709e71	1.80389
$782$	4.48841e70	0.586850
$783$	−5.27201e68	−0.00668056
$784$	6.92819e68	0.00850896
$785$	1.66952e70	0.198739
$786$	−3.77267e70	−0.435308
$787$	1.47428e71	1.64892	0.824460	−	0.565920i	$-0.191479\pi$
$787$	1.47428e71	1.64892	0.824460	+	0.565920i	$0.191479\pi$
$788$	1.79085e70	0.194163
$789$	−1.01770e71	−1.06963
$790$	−5.02552e70	−0.512056
$791$	1.43062e71	1.41319
$792$	−5.39724e70	−0.516897
$793$	−1.95776e70	−0.181788
$794$	−7.08231e70	−0.637636
$795$	−3.98499e71	−3.47882
$796$	−3.90709e70	−0.330738
$797$	3.58327e70	0.294138	0.147069	−	0.989126i	$-0.453016\pi$
$797$	3.58327e70	0.294138	0.147069	+	0.989126i	$0.453016\pi$
$798$	1.08641e71	0.864815
$799$	−2.10137e70	−0.162220
$800$	4.85666e70	0.363607
$801$	1.52572e71	1.10784
$802$	1.19119e71	0.838895
$803$	2.70010e71	1.84437
$804$	−5.63315e70	−0.373231
$805$	−3.23506e71	−2.07914
$806$	−1.98107e70	−0.123507
$807$	−3.02122e71	−1.82717
$808$	1.15001e71	0.674718
$809$	4.95238e70	0.281887	0.140943	−	0.990018i	$-0.454986\pi$
$809$	4.95238e70	0.281887	0.140943	+	0.990018i	$0.454986\pi$
$810$	2.41073e71	1.33127
$811$	−3.54799e71	−1.90095	−0.950477	−	0.310796i	$-0.899404\pi$
$811$	−3.54799e71	−1.90095	−0.950477	+	0.310796i	$0.899404\pi$
$812$	5.62953e69	0.0292651
$813$	1.27002e71	0.640607
$814$	−2.19403e71	−1.07385
$815$	2.01053e71	0.954880
$816$	5.32880e70	0.245596
$817$	−6.45928e70	−0.288897
$818$	−7.04522e70	−0.305801
$819$	−1.55452e71	−0.654850
$820$	−1.39303e70	−0.0569537
$821$	−1.95327e71	−0.775095	−0.387547	−	0.921850i	$-0.626678\pi$
$821$	−1.95327e71	−0.775095	−0.387547	+	0.921850i	$0.626678\pi$
$822$	−3.26198e71	−1.25638
$823$	2.05807e71	0.769421	0.384710	−	0.923037i	$-0.374301\pi$
$823$	2.05807e71	0.769421	0.384710	+	0.923037i	$0.374301\pi$
$824$	2.05452e70	0.0745581
$825$	1.28981e72	4.54364
$826$	3.71027e71	1.26880
$827$	−8.99522e70	−0.298625	−0.149313	−	0.988790i	$-0.547706\pi$
$827$	−8.99522e70	−0.298625	−0.149313	+	0.988790i	$0.547706\pi$
$828$	−1.66210e71	−0.535691
$829$	−4.10043e71	−1.28305	−0.641526	−	0.767102i	$-0.721698\pi$
$829$	−4.10043e71	−1.28305	−0.641526	+	0.767102i	$0.721698\pi$
$830$	−3.35583e71	−1.01950
$831$	3.50750e71	1.03460
$832$	3.06787e70	0.0878650
$833$	−8.68569e69	−0.0241547
$834$	2.36129e71	0.637648
$835$	−4.21483e70	−0.110525
$836$	−2.72245e71	−0.693277
$837$	−1.16621e70	−0.0288405
$838$	4.20096e71	1.00895
$839$	−6.23847e69	−0.0145516	−0.00727579	−	0.999974i	$-0.502316\pi$
$839$	−6.23847e69	−0.0145516	−0.00727579	+	0.999974i	$0.502316\pi$
$840$	−3.84078e71	−0.870115
$841$	−4.52961e71	−0.996687
$842$	−3.38912e70	−0.0724337
$843$	8.06932e71	1.67518
$844$	1.58832e70	0.0320293
$845$	4.51540e71	0.884518
$846$	7.78157e70	0.148079
$847$	−8.50731e71	−1.57271
$848$	−2.00086e71	−0.359351
$849$	−1.40465e72	−2.45092
$850$	−6.08866e71	−1.03219
$851$	−6.75661e71	−1.11290
$852$	4.88860e71	0.782375
$853$	1.20122e72	1.86798	0.933989	−	0.357301i	$-0.116303\pi$
$853$	1.20122e72	1.86798	0.933989	+	0.357301i	$0.116303\pi$
$854$	1.23064e71	0.185957
$855$	−9.47834e71	−1.39175
$856$	2.18906e71	0.312356
$857$	3.84535e71	0.533219	0.266610	−	0.963805i	$-0.414097\pi$
$857$	3.84535e71	0.533219	0.266610	+	0.963805i	$0.414097\pi$
$858$	8.14752e71	1.09796
$859$	4.56460e71	0.597820	0.298910	−	0.954281i	$-0.403377\pi$
$859$	4.56460e71	0.597820	0.298910	+	0.954281i	$0.403377\pi$
$860$	2.28354e71	0.290668
$861$	7.41264e70	0.0917056
$862$	−1.08326e72	−1.30259
$863$	9.22876e71	1.07865	0.539323	−	0.842099i	$-0.318680\pi$
$863$	9.22876e71	1.07865	0.539323	+	0.842099i	$0.318680\pi$
$864$	1.80598e70	0.0205176
$865$	−1.88623e72	−2.08306
$866$	9.47004e71	1.01663
$867$	6.58368e71	0.687070
$868$	1.24530e71	0.126339
$869$	−6.70131e71	−0.660960
$870$	−1.02724e71	−0.0985033
$871$	4.06578e71	0.379052
$872$	−1.49499e71	−0.135514
$873$	1.65214e72	1.45612
$874$	−8.38392e71	−0.718484
$875$	2.25490e72	1.87901
$876$	9.87196e71	0.799931
$877$	1.86935e72	1.47299	0.736496	−	0.676442i	$-0.236479\pi$
$877$	1.86935e72	1.47299	0.736496	+	0.676442i	$0.236479\pi$
$878$	7.37861e71	0.565404
$879$	−2.95991e72	−2.20572
$880$	9.62466e71	0.697525
$881$	−2.06246e72	−1.45370	−0.726850	−	0.686796i	$-0.759017\pi$
$881$	−2.06246e72	−1.45370	−0.726850	+	0.686796i	$0.759017\pi$
$882$	3.21640e70	0.0220490
$883$	1.01095e72	0.674051	0.337026	−	0.941495i	$-0.390579\pi$
$883$	1.01095e72	0.674051	0.337026	+	0.941495i	$0.390579\pi$
$884$	−3.84611e71	−0.249426
$885$	−6.77026e72	−4.27066
$886$	9.13338e71	0.560409
$887$	3.84733e71	0.229631	0.114815	−	0.993387i	$-0.463372\pi$
$887$	3.84733e71	0.229631	0.114815	+	0.993387i	$0.463372\pi$
$888$	−8.02169e71	−0.465745
$889$	5.75247e71	0.324908
$890$	−2.72076e72	−1.49498
$891$	3.21460e72	1.71839
$892$	−1.88782e72	−0.981798
$893$	3.92515e71	0.198607
$894$	−3.01612e72	−1.48484
$895$	2.22064e72	1.06369
$896$	−1.92845e71	−0.0898799
$897$	2.50907e72	1.13788
$898$	1.09384e72	0.482708
$899$	3.33062e70	0.0143025
$900$	2.25469e72	0.942206
$901$	2.50843e72	1.02010
$902$	−1.85755e71	−0.0735156
$903$	−1.21513e72	−0.468027
$904$	−1.31073e72	−0.491347
$905$	−3.67247e72	−1.33989
$906$	3.38349e71	0.120150
$907$	−1.65047e72	−0.570465	−0.285232	−	0.958458i	$-0.592071\pi$
$907$	−1.65047e72	−0.570465	−0.285232	+	0.958458i	$0.592071\pi$
$908$	4.99421e71	0.168021
$909$	5.33888e72	1.74838
$910$	2.77212e72	0.883684
$911$	1.74723e72	0.542188	0.271094	−	0.962553i	$-0.412614\pi$
$911$	1.74723e72	0.542188	0.271094	+	0.962553i	$0.412614\pi$
$912$	−9.95369e71	−0.300684
$913$	−4.47485e72	−1.31597
$914$	2.75856e72	0.789771
$915$	−2.24559e72	−0.625913
$916$	4.00597e71	0.108710
$917$	−1.71164e72	−0.452235
$918$	−2.26411e71	−0.0582441
$919$	−2.26784e72	−0.568044	−0.284022	−	0.958818i	$-0.591669\pi$
$919$	−2.26784e72	−0.568044	−0.284022	+	0.958818i	$0.591669\pi$
$920$	2.96396e72	0.722887
$921$	3.17913e72	0.755000
$922$	1.21018e72	0.279861
$923$	−3.52839e72	−0.794576
$924$	−5.12150e72	−1.12314
$925$	9.16554e72	1.95743
$926$	3.26353e72	0.678763
$927$	9.53809e71	0.193200
$928$	−5.15777e70	−0.0101751
$929$	−5.22436e72	−1.00380	−0.501901	−	0.864925i	$-0.667366\pi$
$929$	−5.22436e72	−1.00380	−0.501901	+	0.864925i	$0.667366\pi$
$930$	−2.27233e72	−0.425246
$931$	1.62240e71	0.0295728
$932$	1.73011e72	0.307173
$933$	7.68500e72	1.32906
$934$	−1.31608e72	−0.221710
$935$	−1.20662e73	−1.98009
$936$	1.42425e72	0.227682
$937$	2.17978e72	0.339464	0.169732	−	0.985490i	$-0.445710\pi$
$937$	2.17978e72	0.339464	0.169732	+	0.985490i	$0.445710\pi$
$938$	−2.55573e72	−0.387745
$939$	−1.51753e73	−2.24300
$940$	−1.38765e72	−0.199825
$941$	−6.39953e72	−0.897847	−0.448924	−	0.893570i	$-0.648192\pi$
$941$	−6.39953e72	−0.897847	−0.448924	+	0.893570i	$0.648192\pi$
$942$	8.13940e71	0.111262
$943$	−5.72040e71	−0.0761885
$944$	−3.39934e72	−0.441145
$945$	1.63188e72	0.206352
$946$	3.04500e72	0.375193
$947$	8.32607e72	0.999691	0.499845	−	0.866115i	$-0.333390\pi$
$947$	8.32607e72	0.999691	0.499845	+	0.866115i	$0.333390\pi$
$948$	−2.45010e72	−0.286668
$949$	−7.12517e72	−0.812406
$950$	1.13730e73	1.26371
$951$	1.33590e73	1.44661
$952$	2.41765e72	0.255146
$953$	1.86907e73	1.92243	0.961214	−	0.275804i	$-0.0889441\pi$
$953$	1.86907e73	1.92243	0.961214	+	0.275804i	$0.0889441\pi$
$954$	−9.28896e72	−0.931176
$955$	2.63922e73	2.57865
$956$	−5.27452e72	−0.502301
$957$	−1.36978e72	−0.127148
$958$	−6.50300e72	−0.588381
$959$	−1.47994e73	−1.30524
$960$	3.51892e72	0.302527
$961$	−1.11955e73	−0.938255
$962$	5.78973e72	0.473008
$963$	1.01627e73	0.809401
$964$	3.96994e72	0.308245
$965$	−1.36476e73	−1.03309
$966$	−1.57719e73	−1.16398
$967$	7.70074e72	0.554095	0.277047	−	0.960856i	$-0.410644\pi$
$967$	7.70074e72	0.554095	0.277047	+	0.960856i	$0.410644\pi$
$968$	7.79439e72	0.546809
$969$	1.24787e73	0.853564
$970$	−2.94619e73	−1.96496
$971$	2.89962e72	0.188569	0.0942845	−	0.995545i	$-0.469944\pi$
$971$	2.89962e72	0.188569	0.0942845	+	0.995545i	$0.469944\pi$
$972$	1.08379e73	0.687260
$973$	1.07131e73	0.662444
$974$	1.35820e73	0.818975
$975$	−3.40362e73	−2.00137
$976$	−1.12751e72	−0.0646547
$977$	1.83564e73	1.02653	0.513263	−	0.858231i	$-0.328437\pi$
$977$	1.83564e73	1.02653	0.513263	+	0.858231i	$0.328437\pi$
$978$	9.80194e72	0.534577
$979$	−3.62801e73	−1.92971
$980$	−5.73567e71	−0.0297540
$981$	−6.94048e72	−0.351155
$982$	−1.94483e73	−0.959733
$983$	−1.42481e73	−0.685799	−0.342900	−	0.939372i	$-0.611409\pi$
$983$	−1.42481e73	−0.685799	−0.342900	+	0.939372i	$0.611409\pi$
$984$	−6.79146e71	−0.0318848
$985$	−1.48260e73	−0.678947
$986$	6.46617e71	0.0288843
$987$	7.38403e72	0.321753
$988$	7.18416e72	0.305373
$989$	9.37722e72	0.388834
$990$	4.46823e73	1.80748
$991$	−1.87344e73	−0.739323	−0.369662	−	0.929166i	$-0.620526\pi$
$991$	−1.87344e73	−0.739323	−0.369662	+	0.929166i	$0.620526\pi$
$992$	−1.14094e72	−0.0439265
$993$	5.74758e72	0.215888
$994$	2.21794e73	0.812798
$995$	3.23458e73	1.15652
$996$	−1.63607e73	−0.570753
$997$	−4.87977e73	−1.66099	−0.830497	−	0.557023i	$-0.811943\pi$
$997$	−4.87977e73	−1.66099	−0.830497	+	0.557023i	$0.811943\pi$
$998$	3.33489e73	1.10760
$999$	3.40827e72	0.110453

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.50.a.b.1.1	✓	3	1.1	even	1	trivial
16.50.a.b.1.3		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)

\(f(q)\)	\(=\)	\(q+1.67772e7 q^{2} -6.77152e11 q^{3} +2.81475e14 q^{4} -2.33026e17 q^{5} -1.13607e19 q^{6} -5.15430e20 q^{7} +4.72237e21 q^{8} +2.19235e23 q^{9} +O(q^{10})\)	\(q+1.67772e7 q^{2} -6.77152e11 q^{3} +2.81475e14 q^{4} -2.33026e17 q^{5} -1.13607e19 q^{6} -5.15430e20 q^{7} +4.72237e21 q^{8} +2.19235e23 q^{9} -3.90952e24 q^{10} -5.21317e25 q^{11} -1.90601e26 q^{12} +1.37568e27 q^{13} -8.64748e27 q^{14} +1.57794e29 q^{15} +7.92282e28 q^{16} -9.93263e29 q^{17} +3.67815e30 q^{18} +1.85532e31 q^{19} -6.55909e31 q^{20} +3.49024e32 q^{21} -8.74625e32 q^{22} -2.69345e33 q^{23} -3.19776e33 q^{24} +3.65374e34 q^{25} +2.30801e34 q^{26} +1.35867e34 q^{27} -1.45081e35 q^{28} -3.88028e34 q^{29} +2.64734e36 q^{30} -8.58347e35 q^{31} +1.32923e36 q^{32} +3.53011e37 q^{33} -1.66642e37 q^{34} +1.20108e38 q^{35} +6.17091e37 q^{36} +2.50854e38 q^{37} +3.11271e38 q^{38} -9.31545e38 q^{39} -1.10043e39 q^{40} +2.12382e38 q^{41} +5.85566e39 q^{42} -3.48149e39 q^{43} -1.46738e40 q^{44} -5.10874e40 q^{45} -4.51886e40 q^{46} +2.11562e40 q^{47} -5.36495e40 q^{48} +8.74461e39 q^{49} +6.12996e41 q^{50} +6.72589e41 q^{51} +3.87220e41 q^{52} -2.52544e42 q^{53} +2.27947e41 q^{54} +1.21480e43 q^{55} -2.43405e42 q^{56} -1.25633e43 q^{57} -6.51003e41 q^{58} -4.29058e43 q^{59} +4.44150e43 q^{60} -1.42312e43 q^{61} -1.44007e43 q^{62} -1.13000e44 q^{63} +2.23007e43 q^{64} -3.20569e44 q^{65} +5.92254e44 q^{66} +2.95546e44 q^{67} -2.79579e44 q^{68} +1.82387e45 q^{69} +2.01509e45 q^{70} -2.56483e45 q^{71} +1.03531e45 q^{72} -5.17938e45 q^{73} +4.20863e45 q^{74} -2.47414e46 q^{75} +5.22226e45 q^{76} +2.68703e46 q^{77} -1.56287e46 q^{78} +1.28546e46 q^{79} -1.84622e46 q^{80} -6.16630e46 q^{81} +3.56318e45 q^{82} +8.58374e46 q^{83} +9.82416e46 q^{84} +2.31456e47 q^{85} -5.84097e46 q^{86} +2.62754e46 q^{87} -2.46185e47 q^{88} +6.95931e47 q^{89} -8.57104e47 q^{90} -7.09067e47 q^{91} -7.58138e47 q^{92} +5.81231e47 q^{93} +3.54942e47 q^{94} -4.32337e48 q^{95} -9.00089e47 q^{96} +7.53593e48 q^{97} +1.46710e47 q^{98} -1.14291e49 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 50331648 q^{2} - 16203614388 q^{3} + 844424930131968 q^{4} - 10\!\cdots\!30 q^{5}+ \cdots + 38\!\cdots\!99 q^{9}+O(q^{10}) \) 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