LMFDB - Embedded newform 3.44.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,44,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 44, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 44);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 44 $
Character orbit:	$[\chi]$	$=$	3.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$35.1331186037$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 908401710x + 974756489742 $ x^3 - x^2 - 908401710*x + 974756489742
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{5}\cdot 5\cdot 11 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-30662.1$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.56260e6 q^{2} +1.04604e10 q^{3} +1.20212e13 q^{4} -1.29230e15 q^{5} +4.77264e16 q^{6} -9.66721e17 q^{7} +1.47149e19 q^{8} +1.09419e20 q^{9} +O(q^{10})$	\(q+4.56260e6 q^{2} +1.04604e10 q^{3} +1.20212e13 q^{4} -1.29230e15 q^{5} +4.77264e16 q^{6} -9.66721e17 q^{7} +1.47149e19 q^{8} +1.09419e20 q^{9} -5.89624e21 q^{10} -4.14867e22 q^{11} +1.25746e23 q^{12} +6.85476e23 q^{13} -4.41076e24 q^{14} -1.35179e25 q^{15} -3.86016e25 q^{16} -1.87770e26 q^{17} +4.99235e26 q^{18} -3.67577e27 q^{19} -1.55350e28 q^{20} -1.01122e28 q^{21} -1.89287e29 q^{22} +2.38175e29 q^{23} +1.53923e29 q^{24} +5.33166e29 q^{25} +3.12755e30 q^{26} +1.14456e30 q^{27} -1.16211e31 q^{28} +4.15139e31 q^{29} -6.16767e31 q^{30} -3.15649e31 q^{31} -3.05557e32 q^{32} -4.33966e32 q^{33} -8.56717e32 q^{34} +1.24929e33 q^{35} +1.31535e33 q^{36} -6.10581e32 q^{37} -1.67711e34 q^{38} +7.17033e33 q^{39} -1.90160e34 q^{40} -4.47211e34 q^{41} -4.61381e34 q^{42} -2.07163e35 q^{43} -4.98720e35 q^{44} -1.41402e35 q^{45} +1.08670e36 q^{46} +1.73685e36 q^{47} -4.03787e35 q^{48} -1.24926e36 q^{49} +2.43262e36 q^{50} -1.96414e36 q^{51} +8.24025e36 q^{52} -1.34883e37 q^{53} +5.22217e36 q^{54} +5.36132e37 q^{55} -1.42252e37 q^{56} -3.84499e37 q^{57} +1.89411e38 q^{58} -7.90833e37 q^{59} -1.62501e38 q^{60} +1.04129e38 q^{61} -1.44018e38 q^{62} -1.05778e38 q^{63} -1.05459e39 q^{64} -8.85840e38 q^{65} -1.98001e39 q^{66} +2.71441e39 q^{67} -2.25722e39 q^{68} +2.49140e39 q^{69} +5.70002e39 q^{70} +6.41305e39 q^{71} +1.61008e39 q^{72} +4.03967e39 q^{73} -2.78583e39 q^{74} +5.57711e39 q^{75} -4.41872e40 q^{76} +4.01061e40 q^{77} +3.27153e40 q^{78} -6.03727e40 q^{79} +4.98848e40 q^{80} +1.19725e40 q^{81} -2.04044e41 q^{82} +2.83283e41 q^{83} -1.21561e41 q^{84} +2.42654e41 q^{85} -9.45200e41 q^{86} +4.34250e41 q^{87} -6.10471e41 q^{88} -7.96312e41 q^{89} -6.45160e41 q^{90} -6.62665e41 q^{91} +2.86315e42 q^{92} -3.30180e41 q^{93} +7.92454e42 q^{94} +4.75019e42 q^{95} -3.19623e42 q^{96} -2.28074e41 q^{97} -5.69989e42 q^{98} -4.53944e42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 4857024 q^{2} + 31381059609 q^{3} - 1781058029568 q^{4} - 507753321105270 q^{5} + 50\!\cdots\!72 q^{6}+ \cdots + 32\!\cdots\!27 q^{9}+O(q^{10}) $ 3 * q + 4857024 * q^2 + 31381059609 * q^3 - 1781058029568 * q^4 - 507753321105270 * q^5 + 50806186555447872 * q^6 - 1633169303707089288 * q^7 + 11196260694472851456 * q^8 + 328256967394537077627 * q^9	$ 3 q + 4857024 q^{2} + 31381059609 q^{3} - 1781058029568 q^{4} - 507753321105270 q^{5} + 50\!\cdots\!72 q^{6}+ \cdots - 30\!\cdots\!80 q^{99}+O(q^{100}) $ 3 * q + 4857024 * q^2 + 31381059609 * q^3 - 1781058029568 * q^4 - 507753321105270 * q^5 + 50806186555447872 * q^6 - 1633169303707089288 * q^7 + 11196260694472851456 * q^8 + 328256967394537077627 * q^9 - 2286850690696789595520 * q^10 - 27750966261606959036820 * q^11 - 18630496064320497506304 * q^12 - 994786398159560287290750 * q^13 - 9473256819232835003171328 * q^14 - 5311279078757398544679810 * q^15 + 23637690650696707825729536 * q^16 - 160517621023312837046953482 * q^17 + 531450656267494684974734016 * q^18 - 3227133683900578441639486764 * q^19 - 19920520041146285724571791360 * q^20 - 17083527757073731207537789464 * q^21 - 172470540148626161048719521024 * q^22 + 114780279514038504224277444504 * q^23 + 117116841417052096124312813568 * q^24 + 1825420275602850437617559193525 * q^25 + 1775037275334840765729836075136 * q^26 + 3433683820292512484657849089281 * q^27 - 8483554335441104836174737260544 * q^28 - 28241588775620253186792106789758 * q^29 - 23921265947212925347314706450560 * q^30 - 56947467162250619768506214477136 * q^31 - 290372748061904590918491662450688 * q^32 - 290284908820945289887889881934460 * q^33 - 1778246324363072918021693922216576 * q^34 - 3641689125493658442558484764497520 * q^35 - 194881569179893810108620559091712 * q^36 - 7771759793894794226158134990367878 * q^37 - 11984574206649783949969526048471808 * q^38 - 10405817086289189756233396954772250 * q^39 - 75089135561625836440773237699379200 * q^40 - 150622420768399427659977962302801266 * q^41 - 99093612311903777628193716002563584 * q^42 - 503269829459862138385119574866599988 * q^43 - 589156491500651091472842134125289472 * q^44 - 55557855123506843126788989142931430 * q^45 + 1201666039209211956008162792803812864 * q^46 + 517590816657574666863303783889459536 * q^47 + 247258593109538461886425117709303808 * q^48 + 1183207682852736238558590379440977403 * q^49 + 5363972694460023429439963707950510400 * q^50 - 1679071011209150572675116916830702846 * q^51 + 19510568225567423700598614061466308608 * q^52 + 3147649955233970731028729152905020634 * q^53 + 5559161574524140052760934938338653248 * q^54 + 72798121427511388475535050768468313960 * q^55 + 64659225918940531158350848060065054720 * q^56 - 33756958166898605235556353943083505092 * q^57 + 165860584701603780784654252956514011264 * q^58 - 178011039218636820023529236138863835076 * q^59 - 208375675617830241670577713556023726080 * q^60 - 123533499732384273913895969461615945518 * q^61 - 685215538112102475249420816230843667456 * q^62 - 178699734292245610143928973763292053192 * q^63 - 971015593402068342273570470768658087936 * q^64 - 2575578837917643212594035173081316043940 * q^65 - 1804102767066821759775567080792024239872 * q^66 + 1292774342372783673662410484960847098148 * q^67 - 2717789569206669919054906507790539296768 * q^68 + 1200642264455907951127749596978071146312 * q^69 + 1868357626946632141981582698458836116480 * q^70 + 22400468745595901369803420176388102887816 * q^71 + 1225083527242103952511819425579970658304 * q^72 + 31313509370447648548173493799361498480654 * q^73 + 12824367911381949889146580637796075349632 * q^74 + 19094540826723419331062786999031330610575 * q^75 - 45893435926810400921777338109031978491904 * q^76 + 15925552922292610065970442499593057720544 * q^77 + 18567516848493194501297063421213806260608 * q^78 - 43825544899857898915807551182364364018080 * q^79 + 51052771545930899482561003058120286535680 * q^80 + 35917545547686059365808220080151141317043 * q^81 - 207555016724016234735599639977066643719296 * q^82 + 89911369720242570860406785197345580904468 * q^83 - 88740974765555897390939203171014875922432 * q^84 - 609771200949453596987959942886782705526220 * q^85 - 1052084075872403200090705454196607607512320 * q^86 - 295416993606868163734131771553363142894874 * q^87 - 866229044996425850996432449444164589584384 * q^88 + 65289466052051143331840751197428752211806 * q^89 - 250224890870743552579783277069120057143680 * q^90 + 1361620777581018817929645459439738348447824 * q^91 + 3753917639661643691216268373890598977257472 * q^92 - 595690620533385591184229099131314527866608 * q^93 + 7862327422462694583153035384185107177477120 * q^94 + 9328236864095865156237338173319138974757400 * q^95 - 3037401505253255729894648973244849050353664 * q^96 + 6130807410554375967448029821362307484893478 * q^97 - 2033290778553828878915746018754102329738560 * q^98 - 3036482675767738016566552437404420497075380 * 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 $

$2$	4.56260e6	1.53839	0.769196	−	0.639013i	$-0.220657\pi$
$2$	4.56260e6	1.53839	0.769196	+	0.639013i	$0.220657\pi$
$3$	1.04604e10	0.577350
$3$	1.04604e10	0.577350
$4$	1.20212e13	1.36665
$5$	−1.29230e15	−1.21201	−0.606007	−	0.795459i	$-0.707230\pi$
$5$	−1.29230e15	−1.21201	−0.606007	+	0.795459i	$0.707230\pi$
$6$	4.77264e16	0.888191
$7$	−9.66721e17	−0.654174	−0.327087	−	0.944994i	$-0.606067\pi$
$7$	−9.66721e17	−0.654174	−0.327087	+	0.944994i	$0.606067\pi$
$8$	1.47149e19	0.564055
$9$	1.09419e20	0.333333
$10$	−5.89624e21	−1.86455
$11$	−4.14867e22	−1.69031	−0.845155	−	0.534521i	$-0.820492\pi$
$11$	−4.14867e22	−1.69031	−0.845155	+	0.534521i	$0.820492\pi$
$12$	1.25746e23	0.789037
$13$	6.85476e23	0.769503	0.384752	−	0.923020i	$-0.374287\pi$
$13$	6.85476e23	0.769503	0.384752	+	0.923020i	$0.374287\pi$
$14$	−4.41076e24	−1.00638
$15$	−1.35179e25	−0.699757
$16$	−3.86016e25	−0.498914
$17$	−1.87770e26	−0.659134	−0.329567	−	0.944132i	$-0.606903\pi$
$17$	−1.87770e26	−0.659134	−0.329567	+	0.944132i	$0.606903\pi$
$18$	4.99235e26	0.512798
$19$	−3.67577e27	−1.18072	−0.590359	−	0.807141i	$-0.701014\pi$
$19$	−3.67577e27	−1.18072	−0.590359	+	0.807141i	$0.701014\pi$
$20$	−1.55350e28	−1.65640
$21$	−1.01122e28	−0.377688
$22$	−1.89287e29	−2.60036
$23$	2.38175e29	1.25820	0.629098	−	0.777326i	$-0.283424\pi$
$23$	2.38175e29	1.25820	0.629098	+	0.777326i	$0.283424\pi$
$24$	1.53923e29	0.325657
$25$	5.33166e29	0.468978
$26$	3.12755e30	1.18380
$27$	1.14456e30	0.192450
$28$	−1.16211e31	−0.894028
$29$	4.15139e31	1.50188	0.750942	−	0.660368i	$-0.229600\pi$
$29$	4.15139e31	1.50188	0.750942	+	0.660368i	$0.229600\pi$
$30$	−6.16767e31	−1.07650
$31$	−3.15649e31	−0.272225	−0.136112	−	0.990693i	$-0.543461\pi$
$31$	−3.15649e31	−0.272225	−0.136112	+	0.990693i	$0.543461\pi$
$32$	−3.05557e32	−1.33158
$33$	−4.33966e32	−0.975901
$34$	−8.56717e32	−1.01401
$35$	1.24929e33	0.792868
$36$	1.31535e33	0.455551
$37$	−6.10581e32	−0.117329	−0.0586646	−	0.998278i	$-0.518684\pi$
$37$	−6.10581e32	−0.117329	−0.0586646	+	0.998278i	$0.518684\pi$
$38$	−1.67711e34	−1.81641
$39$	7.17033e33	0.444273
$40$	−1.90160e34	−0.683642
$41$	−4.47211e34	−0.945496	−0.472748	−	0.881198i	$-0.656738\pi$
$41$	−4.47211e34	−0.945496	−0.472748	+	0.881198i	$0.656738\pi$
$42$	−4.61381e34	−0.581032
$43$	−2.07163e35	−1.57304	−0.786520	−	0.617565i	$-0.788119\pi$
$43$	−2.07163e35	−1.57304	−0.786520	+	0.617565i	$0.788119\pi$
$44$	−4.98720e35	−2.31007
$45$	−1.41402e35	−0.404005
$46$	1.08670e36	1.93560
$47$	1.73685e36	1.94831	0.974155	−	0.225883i	$-0.0725266\pi$
$47$	1.73685e36	1.94831	0.974155	+	0.225883i	$0.0725266\pi$
$48$	−4.03787e35	−0.288048
$49$	−1.24926e36	−0.572056
$50$	2.43262e36	0.721472
$51$	−1.96414e36	−0.380551
$52$	8.24025e36	1.05164
$53$	−1.34883e37	−1.14294	−0.571472	−	0.820622i	$-0.693627\pi$
$53$	−1.34883e37	−1.14294	−0.571472	+	0.820622i	$0.693627\pi$
$54$	5.22217e36	0.296064
$55$	5.36132e37	2.04868
$56$	−1.42252e37	−0.368990
$57$	−3.84499e37	−0.681687
$58$	1.89411e38	2.31049
$59$	−7.90833e37	−0.667985	−0.333992	−	0.942576i	$-0.608396\pi$
$59$	−7.90833e37	−0.667985	−0.333992	+	0.942576i	$0.608396\pi$
$60$	−1.62501e38	−0.956324
$61$	1.04129e38	0.429517	0.214759	−	0.976667i	$-0.431103\pi$
$61$	1.04129e38	0.429517	0.214759	+	0.976667i	$0.431103\pi$
$62$	−1.44018e38	−0.418789
$63$	−1.05778e38	−0.218058
$64$	−1.05459e39	−1.54958
$65$	−8.85840e38	−0.932649
$66$	−1.98001e39	−1.50132
$67$	2.71441e39	1.48959	0.744796	−	0.667292i	$-0.232547\pi$
$67$	2.71441e39	1.48959	0.744796	+	0.667292i	$0.232547\pi$
$68$	−2.25722e39	−0.900806
$69$	2.49140e39	0.726420
$70$	5.70002e39	1.21974
$71$	6.41305e39	1.01160	0.505801	−	0.862650i	$-0.331197\pi$
$71$	6.41305e39	1.01160	0.505801	+	0.862650i	$0.331197\pi$
$72$	1.61008e39	0.188018
$73$	4.03967e39	0.350675	0.175337	−	0.984508i	$-0.443898\pi$
$73$	4.03967e39	0.350675	0.175337	+	0.984508i	$0.443898\pi$
$74$	−2.78583e39	−0.180498
$75$	5.57711e39	0.270765
$76$	−4.41872e40	−1.61363
$77$	4.01061e40	1.10576
$78$	3.27153e40	0.683466
$79$	−6.03727e40	−0.959087	−0.479543	−	0.877518i	$-0.659198\pi$
$79$	−6.03727e40	−0.959087	−0.479543	+	0.877518i	$0.659198\pi$
$80$	4.98848e40	0.604691
$81$	1.19725e40	0.111111
$82$	−2.04044e41	−1.45454
$83$	2.83283e41	1.55612	0.778058	−	0.628193i	$-0.216205\pi$
$83$	2.83283e41	1.55612	0.778058	+	0.628193i	$0.216205\pi$
$84$	−1.21561e41	−0.516168
$85$	2.42654e41	0.798879
$86$	−9.45200e41	−2.41995
$87$	4.34250e41	0.867113
$88$	−6.10471e41	−0.953427
$89$	−7.96312e41	−0.975434	−0.487717	−	0.873002i	$-0.662170\pi$
$89$	−7.96312e41	−0.975434	−0.487717	+	0.873002i	$0.662170\pi$
$90$	−6.45160e41	−0.621518
$91$	−6.62665e41	−0.503389
$92$	2.86315e42	1.71952
$93$	−3.30180e41	−0.157169
$94$	7.92454e42	2.99726
$95$	4.75019e42	1.43105
$96$	−3.19623e42	−0.768789
$97$	−2.28074e41	−0.0439018	−0.0219509	−	0.999759i	$-0.506988\pi$
$97$	−2.28074e41	−0.0439018	−0.0219509	+	0.999759i	$0.506988\pi$
$98$	−5.69989e42	−0.880047
$99$	−4.53944e42	−0.563437
$100$	6.40930e42	0.640930
$101$	−1.22069e41	−0.00985585	−0.00492793	−	0.999988i	$-0.501569\pi$
$101$	−1.22069e41	−0.00985585	−0.00492793	+	0.999988i	$0.501569\pi$
$102$	−8.96156e42	−0.585437
$103$	−1.54032e43	−0.815851	−0.407926	−	0.913015i	$-0.633748\pi$
$103$	−1.54032e43	−0.815851	−0.407926	+	0.913015i	$0.633748\pi$
$104$	1.00867e43	0.434042
$105$	1.30680e43	0.457763
$106$	−6.15415e43	−1.75830
$107$	−3.88129e43	−0.906201	−0.453100	−	0.891459i	$-0.649682\pi$
$107$	−3.88129e43	−0.906201	−0.453100	+	0.891459i	$0.649682\pi$
$108$	1.37590e43	0.263012
$109$	−6.58075e43	−1.03182	−0.515912	−	0.856642i	$-0.672547\pi$
$109$	−6.58075e43	−1.03182	−0.515912	+	0.856642i	$0.672547\pi$
$110$	2.44616e44	3.15167
$111$	−6.38689e42	−0.0677400
$112$	3.73170e43	0.326377
$113$	1.24527e43	0.0899655	0.0449828	−	0.998988i	$-0.485677\pi$
$113$	1.24527e43	0.0899655	0.0449828	+	0.998988i	$0.485677\pi$
$114$	−1.75431e44	−1.04870
$115$	−3.07794e44	−1.52495
$116$	4.99046e44	2.05255
$117$	7.50041e43	0.256501
$118$	−3.60825e44	−1.02762
$119$	1.81521e44	0.431188
$120$	−1.98914e44	−0.394701
$121$	1.11875e45	1.85715
$122$	4.75099e44	0.660767
$123$	−4.67799e44	−0.545882
$124$	−3.79448e44	−0.372037
$125$	7.80163e44	0.643606
$126$	−4.82621e44	−0.335459
$127$	5.22881e44	0.306636	0.153318	−	0.988177i	$-0.451004\pi$
$127$	5.22881e44	0.306636	0.153318	+	0.988177i	$0.451004\pi$
$128$	−2.12396e45	−1.05228
$129$	−2.16699e45	−0.908195
$130$	−4.04173e45	−1.43478
$131$	−1.97998e45	−0.596112	−0.298056	−	0.954548i	$-0.596338\pi$
$131$	−1.97998e45	−0.596112	−0.298056	+	0.954548i	$0.596338\pi$
$132$	−5.21679e45	−1.33372
$133$	3.55345e45	0.772395
$134$	1.23848e46	2.29158
$135$	−1.47911e45	−0.233252
$136$	−2.76300e45	−0.371787
$137$	7.04963e45	0.810352	0.405176	−	0.914239i	$-0.367210\pi$
$137$	7.04963e45	0.810352	0.405176	+	0.914239i	$0.367210\pi$
$138$	1.13673e46	1.11752
$139$	−1.36482e46	−1.14884	−0.574419	−	0.818562i	$-0.694772\pi$
$139$	−1.36482e46	−1.14884	−0.574419	+	0.818562i	$0.694772\pi$
$140$	1.50180e46	1.08357
$141$	1.81680e46	1.12486
$142$	2.92601e46	1.55624
$143$	−2.84382e46	−1.30070
$144$	−4.22375e45	−0.166305
$145$	−5.36483e46	−1.82030
$146$	1.84314e46	0.539475
$147$	−1.30677e46	−0.330277
$148$	−7.33991e45	−0.160348
$149$	−6.34924e46	−1.20010	−0.600049	−	0.799963i	$-0.704852\pi$
$149$	−6.34924e46	−1.20010	−0.600049	+	0.799963i	$0.704852\pi$
$150$	2.54461e46	0.416542
$151$	7.57341e45	0.107470	0.0537350	−	0.998555i	$-0.482887\pi$
$151$	7.57341e45	0.107470	0.0537350	+	0.998555i	$0.482887\pi$
$152$	−5.40884e46	−0.665989
$153$	−2.05456e46	−0.219711
$154$	1.82988e47	1.70109
$155$	4.07913e46	0.329940
$156$	8.61959e46	0.607166
$157$	−1.59997e47	−0.982358	−0.491179	−	0.871059i	$-0.663434\pi$
$157$	−1.59997e47	−0.982358	−0.491179	+	0.871059i	$0.663434\pi$
$158$	−2.75456e47	−1.47545
$159$	−1.41092e47	−0.659879
$160$	3.94871e47	1.61389
$161$	−2.30249e47	−0.823080
$162$	5.46258e46	0.170933
$163$	2.01881e47	0.553430	0.276715	−	0.960952i	$-0.410754\pi$
$163$	2.01881e47	0.553430	0.276715	+	0.960952i	$0.410754\pi$
$164$	−5.37601e47	−1.29216
$165$	5.60813e47	1.18281
$166$	1.29251e48	2.39392
$167$	−2.04593e47	−0.333033	−0.166517	−	0.986039i	$-0.553252\pi$
$167$	−2.04593e47	−0.333033	−0.166517	+	0.986039i	$0.553252\pi$
$168$	−1.48800e47	−0.213036
$169$	−3.23653e47	−0.407865
$170$	1.10713e48	1.22899
$171$	−4.02199e47	−0.393572
$172$	−2.49034e48	−2.14980
$173$	3.51004e47	0.267498	0.133749	−	0.991015i	$-0.457298\pi$
$173$	3.51004e47	0.267498	0.133749	+	0.991015i	$0.457298\pi$
$174$	1.98131e48	1.33396
$175$	−5.15423e47	−0.306793
$176$	1.60146e48	0.843320
$177$	−8.27239e47	−0.385661
$178$	−3.63325e48	−1.50060
$179$	−2.04481e48	−0.748708	−0.374354	−	0.927286i	$-0.622136\pi$
$179$	−2.04481e48	−0.748708	−0.374354	+	0.927286i	$0.622136\pi$
$180$	−1.69982e48	−0.552134
$181$	−3.20223e48	−0.923345	−0.461672	−	0.887051i	$-0.652750\pi$
$181$	−3.20223e48	−0.923345	−0.461672	+	0.887051i	$0.652750\pi$
$182$	−3.02347e48	−0.774410
$183$	1.08923e48	0.247982
$184$	3.50472e48	0.709692
$185$	7.89053e47	0.142205
$186$	−1.50648e48	−0.241788
$187$	7.78995e48	1.11414
$188$	2.08790e49	2.66266
$189$	−1.10647e48	−0.125896
$190$	2.16732e49	2.20151
$191$	−3.02200e48	−0.274206	−0.137103	−	0.990557i	$-0.543779\pi$
$191$	−3.02200e48	−0.274206	−0.137103	+	0.990557i	$0.543779\pi$
$192$	−1.10314e49	−0.894650
$193$	−1.79481e49	−1.30178	−0.650888	−	0.759174i	$-0.725603\pi$
$193$	−1.79481e49	−1.30178	−0.650888	+	0.759174i	$0.725603\pi$
$194$	−1.04061e48	−0.0675383
$195$	−9.26620e48	−0.538465
$196$	−1.50177e49	−0.781802
$197$	2.54943e49	1.18965	0.594825	−	0.803855i	$-0.297221\pi$
$197$	2.54943e49	1.18965	0.594825	+	0.803855i	$0.297221\pi$
$198$	−2.07116e49	−0.866787
$199$	−2.22144e49	−0.834244	−0.417122	−	0.908851i	$-0.636961\pi$
$199$	−2.22144e49	−0.834244	−0.417122	+	0.908851i	$0.636961\pi$
$200$	7.84546e48	0.264529
$201$	2.83937e49	0.860016
$202$	−5.56950e47	−0.0151622
$203$	−4.01323e49	−0.982494
$204$	−2.36113e49	−0.520081
$205$	5.77930e49	1.14595
$206$	−7.02786e49	−1.25510
$207$	2.60609e49	0.419399
$208$	−2.64605e49	−0.383916
$209$	1.52496e50	1.99578
$210$	5.96242e49	0.704219
$211$	−1.11346e50	−1.18741	−0.593706	−	0.804682i	$-0.702336\pi$
$211$	−1.11346e50	−1.18741	−0.593706	+	0.804682i	$0.702336\pi$
$212$	−1.62145e50	−1.56201
$213$	6.70827e49	0.584049
$214$	−1.77087e50	−1.39409
$215$	2.67716e50	1.90655
$216$	1.68420e49	0.108552
$217$	3.05145e49	0.178083
$218$	−3.00253e50	−1.58735
$219$	4.22564e49	0.202462
$220$	6.44495e50	2.79983
$221$	−1.28712e50	−0.507206
$222$	−2.91408e49	−0.104211
$223$	8.11200e49	0.263374	0.131687	−	0.991291i	$-0.457961\pi$
$223$	8.11200e49	0.263374	0.131687	+	0.991291i	$0.457961\pi$
$224$	2.95388e50	0.871086
$225$	5.83385e49	0.156326
$226$	5.68165e49	0.138402
$227$	−3.50053e50	−0.775492	−0.387746	−	0.921766i	$-0.626746\pi$
$227$	−3.50053e50	−0.775492	−0.387746	+	0.921766i	$0.626746\pi$
$228$	−4.62213e50	−0.931630
$229$	5.91349e50	1.08488	0.542439	−	0.840095i	$-0.317501\pi$
$229$	5.91349e50	1.08488	0.542439	+	0.840095i	$0.317501\pi$
$230$	−1.40434e51	−2.34597
$231$	4.19524e50	0.638409
$232$	6.10870e50	0.847144
$233$	−9.65662e50	−1.22088	−0.610440	−	0.792063i	$-0.709007\pi$
$233$	−9.65662e50	−1.22088	−0.610440	+	0.792063i	$0.709007\pi$
$234$	3.42214e50	0.394599
$235$	−2.24453e51	−2.36138
$236$	−9.50676e50	−0.912902
$237$	−6.31520e50	−0.553729
$238$	8.28207e50	0.663337
$239$	2.10427e51	1.54009	0.770047	−	0.637987i	$-0.220233\pi$
$239$	2.10427e51	1.54009	0.770047	+	0.637987i	$0.220233\pi$
$240$	5.21813e50	0.349119
$241$	−1.35652e51	−0.829965	−0.414982	−	0.909829i	$-0.636212\pi$
$241$	−1.35652e51	−0.829965	−0.414982	+	0.909829i	$0.636212\pi$
$242$	5.10440e51	2.85702
$243$	1.25237e50	0.0641500
$244$	1.25176e51	0.587001
$245$	1.61442e51	0.693340
$246$	−2.13438e51	−0.839781
$247$	−2.51965e51	−0.908566
$248$	−4.64473e50	−0.153550
$249$	2.96324e51	0.898424
$250$	3.55957e51	0.990119
$251$	1.64213e51	0.419201	0.209601	−	0.977787i	$-0.432784\pi$
$251$	1.64213e51	0.419201	0.209601	+	0.977787i	$0.432784\pi$
$252$	−1.27157e51	−0.298009
$253$	−9.88112e51	−2.12674
$254$	2.38570e51	0.471727
$255$	2.53825e51	0.461233
$256$	−4.14504e50	−0.0692420
$257$	−6.10196e50	−0.0937362	−0.0468681	−	0.998901i	$-0.514924\pi$
$257$	−6.10196e50	−0.0937362	−0.0468681	+	0.998901i	$0.514924\pi$
$258$	−9.88712e51	−1.39716
$259$	5.90262e50	0.0767537
$260$	−1.06489e52	−1.27461
$261$	4.54241e51	0.500628
$262$	−9.03384e51	−0.917054
$263$	2.81731e51	0.263504	0.131752	−	0.991283i	$-0.457940\pi$
$263$	2.81731e51	0.263504	0.131752	+	0.991283i	$0.457940\pi$
$264$	−6.38574e51	−0.550462
$265$	1.74309e52	1.38526
$266$	1.62129e52	1.18825
$267$	−8.32970e51	−0.563167
$268$	3.26305e52	2.03575
$269$	−6.28193e51	−0.361759	−0.180880	−	0.983505i	$-0.557894\pi$
$269$	−6.28193e51	−0.361759	−0.180880	+	0.983505i	$0.557894\pi$
$270$	−6.74860e51	−0.358833
$271$	−3.10633e52	−1.52549	−0.762743	−	0.646702i	$-0.776148\pi$
$271$	−3.10633e52	−1.52549	−0.762743	+	0.646702i	$0.776148\pi$
$272$	7.24821e51	0.328851
$273$	−6.93171e51	−0.290632
$274$	3.21646e52	1.24664
$275$	−2.21193e52	−0.792718
$276$	2.99496e52	0.992763
$277$	−3.49544e52	−1.07198	−0.535991	−	0.844224i	$-0.680062\pi$
$277$	−3.49544e52	−1.07198	−0.535991	+	0.844224i	$0.680062\pi$
$278$	−6.22714e52	−1.76736
$279$	−3.45380e51	−0.0907416
$280$	1.83831e52	0.447221
$281$	2.62712e52	0.591962	0.295981	−	0.955194i	$-0.404353\pi$
$281$	2.62712e52	0.591962	0.295981	+	0.955194i	$0.404353\pi$
$282$	8.28935e52	1.73047
$283$	7.08487e52	1.37064	0.685320	−	0.728242i	$-0.259662\pi$
$283$	7.08487e52	1.37064	0.685320	+	0.728242i	$0.259662\pi$
$284$	7.70925e52	1.38251
$285$	4.96887e52	0.826215
$286$	−1.29752e53	−2.00099
$287$	4.32328e52	0.618519
$288$	−3.34337e52	−0.443860
$289$	−4.58954e52	−0.565543
$290$	−2.44776e53	−2.80034
$291$	−2.38573e51	−0.0253467
$292$	4.85617e52	0.479250
$293$	−9.78673e52	−0.897395	−0.448698	−	0.893684i	$-0.648112\pi$
$293$	−9.78673e52	−0.897395	−0.448698	+	0.893684i	$0.648112\pi$
$294$	−5.96229e52	−0.508095
$295$	1.02199e53	0.809607
$296$	−8.98461e51	−0.0661801
$297$	−4.74841e52	−0.325300
$298$	−2.89690e53	−1.84622
$299$	1.63264e53	0.968186
$300$	6.70435e52	0.370041
$301$	2.00269e53	1.02904
$302$	3.45544e52	0.165331
$303$	−1.27688e51	−0.00569028
$304$	1.41891e53	0.589077
$305$	−1.34566e53	−0.520581
$306$	−9.37411e52	−0.338002
$307$	3.49196e53	1.17380	0.586899	−	0.809660i	$-0.300348\pi$
$307$	3.49196e53	1.17380	0.586899	+	0.809660i	$0.300348\pi$
$308$	4.82123e53	1.51119
$309$	−1.61123e53	−0.471032
$310$	1.86114e53	0.507578
$311$	1.85544e53	0.472170	0.236085	−	0.971732i	$-0.424136\pi$
$311$	1.85544e53	0.472170	0.236085	+	0.971732i	$0.424136\pi$
$312$	1.05510e53	0.250594
$313$	7.17292e53	1.59035	0.795175	−	0.606380i	$-0.207379\pi$
$313$	7.17292e53	1.59035	0.795175	+	0.606380i	$0.207379\pi$
$314$	−7.30002e53	−1.51125
$315$	1.36696e53	0.264289
$316$	−7.25752e53	−1.31074
$317$	−7.25321e52	−0.122393	−0.0611964	−	0.998126i	$-0.519492\pi$
$317$	−7.25321e52	−0.122393	−0.0611964	+	0.998126i	$0.519492\pi$
$318$	−6.43746e53	−1.01515
$319$	−1.72227e54	−2.53865
$320$	1.36284e54	1.87811
$321$	−4.05996e53	−0.523195
$322$	−1.05053e54	−1.26622
$323$	6.90198e53	0.778251
$324$	1.43924e53	0.151850
$325$	3.65473e53	0.360880
$326$	9.21103e53	0.851393
$327$	−6.88370e53	−0.595724
$328$	−6.58064e53	−0.533311
$329$	−1.67905e54	−1.27453
$330$	2.55876e54	1.81962
$331$	−6.34311e53	−0.422669	−0.211334	−	0.977414i	$-0.567781\pi$
$331$	−6.34311e53	−0.422669	−0.211334	+	0.977414i	$0.567781\pi$
$332$	3.40540e54	2.12667
$333$	−6.68091e52	−0.0391097
$334$	−9.33477e53	−0.512336
$335$	−3.50783e54	−1.80541
$336$	3.90349e53	0.188434
$337$	2.65467e54	1.20218	0.601088	−	0.799183i	$-0.294734\pi$
$337$	2.65467e54	1.20218	0.601088	+	0.799183i	$0.294734\pi$
$338$	−1.47670e54	−0.627456
$339$	1.30259e53	0.0519416
$340$	2.91700e54	1.09179
$341$	1.30952e54	0.460145
$342$	−1.83507e54	−0.605469
$343$	3.31883e54	1.02840
$344$	−3.04837e54	−0.887280
$345$	−3.21963e54	−0.880431
$346$	1.60149e54	0.411518
$347$	−3.14107e54	−0.758567	−0.379284	−	0.925280i	$-0.623830\pi$
$347$	−3.14107e54	−0.758567	−0.379284	+	0.925280i	$0.623830\pi$
$348$	5.22020e54	1.18504
$349$	−1.66164e54	−0.354643	−0.177321	−	0.984153i	$-0.556743\pi$
$349$	−1.66164e54	−0.354643	−0.177321	+	0.984153i	$0.556743\pi$
$350$	−2.35167e54	−0.471969
$351$	7.84570e53	0.148091
$352$	1.26766e55	2.25079
$353$	6.16284e54	1.02950	0.514748	−	0.857342i	$-0.327886\pi$
$353$	6.16284e54	1.02950	0.514748	+	0.857342i	$0.327886\pi$
$354$	−3.77436e54	−0.593298
$355$	−8.28757e54	−1.22608
$356$	−9.57262e54	−1.33308
$357$	1.89877e54	0.248947
$358$	−9.32964e54	−1.15181
$359$	5.63280e54	0.654929	0.327464	−	0.944864i	$-0.393806\pi$
$359$	5.63280e54	0.654929	0.327464	+	0.944864i	$0.393806\pi$
$360$	−2.08071e54	−0.227881
$361$	3.81948e54	0.394094
$362$	−1.46105e55	−1.42047
$363$	1.17025e55	1.07223
$364$	−7.96602e54	−0.687958
$365$	−5.22046e54	−0.425023
$366$	4.96971e54	0.381494
$367$	−6.57731e54	−0.476132	−0.238066	−	0.971249i	$-0.576514\pi$
$367$	−6.57731e54	−0.476132	−0.238066	+	0.971249i	$0.576514\pi$
$368$	−9.19396e54	−0.627732
$369$	−4.89334e54	−0.315165
$370$	3.60013e54	0.218767
$371$	1.30394e55	0.747685
$372$	−3.96916e54	−0.214795
$373$	−1.12137e55	−0.572807	−0.286404	−	0.958109i	$-0.592460\pi$
$373$	−1.12137e55	−0.572807	−0.286404	+	0.958109i	$0.592460\pi$
$374$	3.55424e55	1.71399
$375$	8.16078e54	0.371586
$376$	2.55575e55	1.09895
$377$	2.84568e55	1.15570
$378$	−5.04838e54	−0.193677
$379$	3.17152e54	0.114954	0.0574771	−	0.998347i	$-0.481694\pi$
$379$	3.17152e54	0.114954	0.0574771	+	0.998347i	$0.481694\pi$
$380$	5.71030e55	1.95574
$381$	5.46952e54	0.177036
$382$	−1.37882e55	−0.421837
$383$	2.67653e55	0.774102	0.387051	−	0.922058i	$-0.373494\pi$
$383$	2.67653e55	0.774102	0.387051	+	0.922058i	$0.373494\pi$
$384$	−2.22174e55	−0.607535
$385$	−5.18290e55	−1.34019
$386$	−8.18899e55	−2.00264
$387$	−2.26675e55	−0.524346
$388$	−2.74172e54	−0.0599985
$389$	−4.96399e55	−1.02781	−0.513907	−	0.857846i	$-0.671802\pi$
$389$	−4.96399e55	−1.02781	−0.513907	+	0.857846i	$0.671802\pi$
$390$	−4.22779e55	−0.828371
$391$	−4.47221e55	−0.829320
$392$	−1.83827e55	−0.322671
$393$	−2.07113e55	−0.344165
$394$	1.16320e56	1.83015
$395$	7.80195e55	1.16243
$396$	−5.45695e55	−0.770022
$397$	1.17506e56	1.57060	0.785300	−	0.619116i	$-0.212509\pi$
$397$	1.17506e56	1.57060	0.785300	+	0.619116i	$0.212509\pi$
$398$	−1.01355e56	−1.28339
$399$	3.71703e55	0.445942
$400$	−2.05811e55	−0.233980
$401$	−1.22312e54	−0.0131785	−0.00658926	−	0.999978i	$-0.502097\pi$
$401$	−1.22312e54	−0.0131785	−0.00658926	+	0.999978i	$0.502097\pi$
$402$	1.29549e56	1.32304
$403$	−2.16370e55	−0.209478
$404$	−1.46741e54	−0.0134695
$405$	−1.54721e55	−0.134668
$406$	−1.83108e56	−1.51146
$407$	2.53310e55	0.198323
$408$	−2.89020e55	−0.214652
$409$	1.58299e56	1.11539	0.557696	−	0.830045i	$-0.311686\pi$
$409$	1.58299e56	1.11539	0.557696	+	0.830045i	$0.311686\pi$
$410$	2.63686e56	1.76293
$411$	7.37416e55	0.467857
$412$	−1.85165e56	−1.11498
$413$	7.64515e55	0.436978
$414$	1.18905e56	0.645200
$415$	−3.66086e56	−1.88603
$416$	−2.09452e56	−1.02466
$417$	−1.42765e56	−0.663282
$418$	6.95776e56	3.07029
$419$	8.93668e55	0.374606	0.187303	−	0.982302i	$-0.440025\pi$
$419$	8.93668e55	0.374606	0.187303	+	0.982302i	$0.440025\pi$
$420$	1.57093e56	0.625602
$421$	−2.19258e56	−0.829641	−0.414821	−	0.909903i	$-0.636156\pi$
$421$	−2.19258e56	−0.829641	−0.414821	+	0.909903i	$0.636156\pi$
$422$	−5.08027e56	−1.82671
$423$	1.90044e56	0.649436
$424$	−1.98478e56	−0.644683
$425$	−1.00112e56	−0.309119
$426$	3.06071e56	0.898497
$427$	−1.00664e56	−0.280979
$428$	−4.66577e56	−1.23846
$429$	−2.97473e56	−0.750959
$430$	1.22148e57	2.93302
$431$	3.47761e55	0.0794364	0.0397182	−	0.999211i	$-0.487354\pi$
$431$	3.47761e55	0.0794364	0.0397182	+	0.999211i	$0.487354\pi$
$432$	−4.41819e55	−0.0960161
$433$	2.55606e56	0.528545	0.264272	−	0.964448i	$-0.414868\pi$
$433$	2.55606e56	0.528545	0.264272	+	0.964448i	$0.414868\pi$
$434$	1.39225e56	0.273961
$435$	−5.61180e56	−1.05095
$436$	−7.91085e56	−1.41014
$437$	−8.75478e56	−1.48557
$438$	1.92799e56	0.311466
$439$	−6.27063e56	−0.964548	−0.482274	−	0.876020i	$-0.660189\pi$
$439$	−6.27063e56	−0.964548	−0.482274	+	0.876020i	$0.660189\pi$
$440$	7.88911e56	1.15557
$441$	−1.36693e56	−0.190685
$442$	−5.87259e56	−0.780281
$443$	−2.70311e55	−0.0342124	−0.0171062	−	0.999854i	$-0.505445\pi$
$443$	−2.70311e55	−0.0342124	−0.0171062	+	0.999854i	$0.505445\pi$
$444$	−7.67781e55	−0.0925771
$445$	1.02907e57	1.18224
$446$	3.70118e56	0.405173
$447$	−6.64152e56	−0.692877
$448$	1.01949e57	1.01370
$449$	1.72989e57	1.63954	0.819768	−	0.572696i	$-0.194102\pi$
$449$	1.72989e57	1.63954	0.819768	+	0.572696i	$0.194102\pi$
$450$	2.66175e56	0.240491
$451$	1.85533e57	1.59818
$452$	1.49696e56	0.122952
$453$	7.92205e55	0.0620478
$454$	−1.59715e57	−1.19301
$455$	8.56360e56	0.610115
$456$	−5.65784e56	−0.384509
$457$	−9.95087e56	−0.645153	−0.322577	−	0.946543i	$-0.604549\pi$
$457$	−9.95087e56	−0.645153	−0.322577	+	0.946543i	$0.604549\pi$
$458$	2.69809e57	1.66897
$459$	−2.14914e56	−0.126850
$460$	−3.70005e57	−2.08408
$461$	−1.80262e57	−0.969025	−0.484512	−	0.874784i	$-0.661003\pi$
$461$	−1.80262e57	−0.969025	−0.484512	+	0.874784i	$0.661003\pi$
$462$	1.91412e57	0.982124
$463$	2.20081e57	1.07793	0.538965	−	0.842328i	$-0.318815\pi$
$463$	2.20081e57	1.07793	0.538965	+	0.842328i	$0.318815\pi$
$464$	−1.60250e57	−0.749311
$465$	4.26691e56	0.190491
$466$	−4.40593e57	−1.87819
$467$	3.37955e57	1.37577	0.687885	−	0.725820i	$-0.258539\pi$
$467$	3.37955e57	1.37577	0.687885	+	0.725820i	$0.258539\pi$
$468$	9.01640e56	0.350548
$469$	−2.62408e57	−0.974453
$470$	−1.02409e58	−3.63273
$471$	−1.67363e57	−0.567164
$472$	−1.16370e57	−0.376780
$473$	8.59450e57	2.65893
$474$	−2.88137e57	−0.851853
$475$	−1.95980e57	−0.553730
$476$	2.18210e57	0.589284
$477$	−1.47587e57	−0.380981
$478$	9.60095e57	2.36927
$479$	1.37561e57	0.324551	0.162275	−	0.986746i	$-0.448117\pi$
$479$	1.37561e57	0.324551	0.162275	+	0.986746i	$0.448117\pi$
$480$	4.13049e57	0.931783
$481$	−4.18539e56	−0.0902852
$482$	−6.18925e57	−1.27681
$483$	−2.40849e57	−0.475205
$484$	1.34487e58	2.53808
$485$	2.94739e56	0.0532096
$486$	5.71405e56	0.0986879
$487$	4.03185e57	0.666242	0.333121	−	0.942884i	$-0.391898\pi$
$487$	4.03185e57	0.666242	0.333121	+	0.942884i	$0.391898\pi$
$488$	1.53224e57	0.242271
$489$	2.11175e57	0.319523
$490$	7.36596e57	1.06663
$491$	−1.20430e58	−1.66910	−0.834552	−	0.550929i	$-0.814274\pi$
$491$	−1.20430e58	−1.66910	−0.834552	+	0.550929i	$0.814274\pi$
$492$	−5.62350e57	−0.746031
$493$	−7.79504e57	−0.989942
$494$	−1.14962e58	−1.39773
$495$	5.86630e57	0.682893
$496$	1.21846e57	0.135817
$497$	−6.19963e57	−0.661764
$498$	1.35201e58	1.38213
$499$	−1.80912e58	−1.77135	−0.885675	−	0.464305i	$-0.846304\pi$
$499$	−1.80912e58	−1.77135	−0.885675	+	0.464305i	$0.846304\pi$
$500$	9.37850e57	0.879586
$501$	−2.14012e57	−0.192277
$502$	7.49238e57	0.644896
$503$	1.83848e58	1.51617	0.758084	−	0.652157i	$-0.226136\pi$
$503$	1.83848e58	1.51617	0.758084	+	0.652157i	$0.226136\pi$
$504$	−1.55650e57	−0.122997
$505$	1.57749e56	0.0119454
$506$	−4.50836e58	−3.27177
$507$	−3.38553e57	−0.235481
$508$	6.28566e57	0.419065
$509$	2.58706e58	1.65338	0.826691	−	0.562656i	$-0.190220\pi$
$509$	2.58706e58	1.65338	0.826691	+	0.562656i	$0.190220\pi$
$510$	1.15810e58	0.709558
$511$	−3.90523e57	−0.229402
$512$	1.67913e58	0.945760
$513$	−4.20714e57	−0.227229
$514$	−2.78408e57	−0.144203
$515$	1.99055e58	0.988823
$516$	−2.60499e58	−1.24119
$517$	−7.20561e58	−3.29325
$518$	2.69313e57	0.118077
$519$	3.67163e57	0.154440
$520$	−1.30350e58	−0.526065
$521$	−1.15962e58	−0.449059	−0.224530	−	0.974467i	$-0.572085\pi$
$521$	−1.15962e58	−0.449059	−0.224530	+	0.974467i	$0.572085\pi$
$522$	2.07252e58	0.770162
$523$	4.11381e58	1.46709	0.733547	−	0.679639i	$-0.237863\pi$
$523$	4.11381e58	1.46709	0.733547	+	0.679639i	$0.237863\pi$
$524$	−2.38017e58	−0.814677
$525$	−5.39151e57	−0.177127
$526$	1.28543e58	0.405372
$527$	5.92693e57	0.179433
$528$	1.67518e58	0.486891
$529$	2.08934e58	0.583059
$530$	7.95300e58	2.13108
$531$	−8.65321e57	−0.222662
$532$	4.27167e58	1.05559
$533$	−3.06553e58	−0.727562
$534$	−3.80051e58	−0.866372
$535$	5.01578e58	1.09833
$536$	3.99422e58	0.840211
$537$	−2.13894e58	−0.432267
$538$	−2.86619e58	−0.556527
$539$	5.18279e58	0.966952
$540$	−1.77807e58	−0.318775
$541$	−7.75327e58	−1.33581	−0.667903	−	0.744248i	$-0.732808\pi$
$541$	−7.75327e58	−1.33581	−0.667903	+	0.744248i	$0.732808\pi$
$542$	−1.41729e59	−2.34680
$543$	−3.34965e58	−0.533093
$544$	5.73743e58	0.877690
$545$	8.50429e58	1.25059
$546$	−3.16266e58	−0.447106
$547$	2.55610e58	0.347416	0.173708	−	0.984797i	$-0.444425\pi$
$547$	2.55610e58	0.347416	0.173708	+	0.984797i	$0.444425\pi$
$548$	8.47449e58	1.10747
$549$	1.13937e58	0.143172
$550$	−1.00922e59	−1.21951
$551$	−1.52595e59	−1.77330
$552$	3.66606e58	0.409741
$553$	5.83636e58	0.627410
$554$	−1.59483e59	−1.64913
$555$	8.25377e57	0.0821019
$556$	−1.64068e59	−1.57006
$557$	5.65846e58	0.520969	0.260484	−	0.965478i	$-0.416118\pi$
$557$	5.65846e58	0.520969	0.260484	+	0.965478i	$0.416118\pi$
$558$	−1.57583e58	−0.139596
$559$	−1.42005e59	−1.21046
$560$	−4.82247e58	−0.395573
$561$	8.14856e58	0.643249
$562$	1.19865e59	0.910670
$563$	1.84272e59	1.34750	0.673751	−	0.738958i	$-0.264682\pi$
$563$	1.84272e59	1.34750	0.673751	+	0.738958i	$0.264682\pi$
$564$	2.18402e59	1.53729
$565$	−1.60926e58	−0.109039
$566$	3.23254e59	2.10858
$567$	−1.15741e58	−0.0726860
$568$	9.43670e58	0.570599
$569$	−2.36928e59	−1.37944	−0.689719	−	0.724077i	$-0.742266\pi$
$569$	−2.36928e59	−1.37944	−0.689719	+	0.724077i	$0.742266\pi$
$570$	2.26709e59	1.27104
$571$	2.07972e59	1.12287	0.561433	−	0.827522i	$-0.310250\pi$
$571$	2.07972e59	1.12287	0.561433	+	0.827522i	$0.310250\pi$
$572$	−3.41861e59	−1.77760
$573$	−3.16112e58	−0.158313
$574$	1.97254e59	0.951525
$575$	1.26987e59	0.590066
$576$	−1.15392e59	−0.516527
$577$	2.08396e59	0.898688	0.449344	−	0.893359i	$-0.351658\pi$
$577$	2.08396e59	0.898688	0.449344	+	0.893359i	$0.351658\pi$
$578$	−2.09402e59	−0.870027
$579$	−1.87743e59	−0.751581
$580$	−6.44917e59	−2.48772
$581$	−2.73856e59	−1.01797
$582$	−1.08851e58	−0.0389932
$583$	5.59584e59	1.93193
$584$	5.94431e58	0.197800
$585$	−9.69277e58	−0.310883
$586$	−4.46529e59	−1.38055
$587$	2.73977e58	0.0816574	0.0408287	−	0.999166i	$-0.487000\pi$
$587$	2.73977e58	0.0816574	0.0408287	+	0.999166i	$0.487000\pi$
$588$	−1.57090e59	−0.451373
$589$	1.16025e59	0.321421
$590$	4.66294e59	1.24549
$591$	2.66679e59	0.686845
$592$	2.35694e58	0.0585372
$593$	2.35256e58	0.0563462	0.0281731	−	0.999603i	$-0.491031\pi$
$593$	2.35256e58	0.0563462	0.0281731	+	0.999603i	$0.491031\pi$
$594$	−2.16651e59	−0.500440
$595$	−2.34579e59	−0.522606
$596$	−7.63254e59	−1.64012
$597$	−2.32370e59	−0.481651
$598$	7.44906e59	1.48945
$599$	−1.14383e59	−0.220641	−0.110320	−	0.993896i	$-0.535188\pi$
$599$	−1.14383e59	−0.220641	−0.110320	+	0.993896i	$0.535188\pi$
$600$	8.20663e58	0.152726
$601$	1.46354e59	0.262787	0.131393	−	0.991330i	$-0.458055\pi$
$601$	1.46354e59	0.262787	0.131393	+	0.991330i	$0.458055\pi$
$602$	9.13745e59	1.58307
$603$	2.97008e59	0.496531
$604$	9.10414e58	0.146874
$605$	−1.44576e60	−2.25089
$606$	−5.82589e57	−0.00875389
$607$	−5.45219e59	−0.790705	−0.395352	−	0.918530i	$-0.629378\pi$
$607$	−5.45219e59	−0.790705	−0.395352	+	0.918530i	$0.629378\pi$
$608$	1.12316e60	1.57222
$609$	−4.19798e59	−0.567243
$610$	−6.13970e59	−0.800858
$611$	1.19057e60	1.49923
$612$	−2.46982e59	−0.300269
$613$	−1.00661e60	−1.18158	−0.590790	−	0.806826i	$-0.701184\pi$
$613$	−1.00661e60	−1.18158	−0.590790	+	0.806826i	$0.701184\pi$
$614$	1.59324e60	1.80576
$615$	6.04535e59	0.661617
$616$	5.90155e59	0.623708
$617$	−1.26792e60	−1.29408	−0.647038	−	0.762458i	$-0.723992\pi$
$617$	−1.26792e60	−1.29408	−0.647038	+	0.762458i	$0.723992\pi$
$618$	−7.35139e59	−0.724632
$619$	−8.28879e59	−0.789119	−0.394559	−	0.918870i	$-0.629103\pi$
$619$	−8.28879e59	−0.789119	−0.394559	+	0.918870i	$0.629103\pi$
$620$	4.90360e59	0.450914
$621$	2.72606e59	0.242140
$622$	8.46562e59	0.726382
$623$	7.69811e59	0.638104
$624$	−2.76786e59	−0.221654
$625$	−1.61434e60	−1.24904
$626$	3.27271e60	2.44658
$627$	1.59516e60	1.15226
$628$	−1.92336e60	−1.34254
$629$	1.14649e59	0.0773356
$630$	6.23690e59	0.406581
$631$	2.76062e60	1.73930	0.869650	−	0.493668i	$-0.164344\pi$
$631$	2.76062e60	1.73930	0.869650	+	0.493668i	$0.164344\pi$
$632$	−8.88375e59	−0.540977
$633$	−1.16472e60	−0.685553
$634$	−3.30935e59	−0.188288
$635$	−6.75719e59	−0.371647
$636$	−1.69610e60	−0.901825
$637$	−8.56341e59	−0.440199
$638$	−7.85805e60	−3.90544
$639$	7.01709e59	0.337201
$640$	2.74479e60	1.27538
$641$	−2.57952e60	−1.15902	−0.579510	−	0.814965i	$-0.696756\pi$
$641$	−2.57952e60	−1.15902	−0.579510	+	0.814965i	$0.696756\pi$
$642$	−1.85240e60	−0.804880
$643$	−9.94946e59	−0.418084	−0.209042	−	0.977907i	$-0.567035\pi$
$643$	−9.94946e59	−0.418084	−0.209042	+	0.977907i	$0.567035\pi$
$644$	−2.76787e60	−1.12486
$645$	2.80040e60	1.10074
$646$	3.14910e60	1.19726
$647$	−9.07848e59	−0.333865	−0.166933	−	0.985968i	$-0.553386\pi$
$647$	−9.07848e59	−0.333865	−0.166933	+	0.985968i	$0.553386\pi$
$648$	1.76174e59	0.0626727
$649$	3.28091e60	1.12910
$650$	1.66751e60	0.555175
$651$	3.19192e59	0.102816
$652$	2.42686e60	0.756346
$653$	3.98516e60	1.20175	0.600873	−	0.799344i	$-0.294820\pi$
$653$	3.98516e60	1.20175	0.600873	+	0.799344i	$0.294820\pi$
$654$	−3.14075e60	−0.916457
$655$	2.55872e60	0.722496
$656$	1.72631e60	0.471722
$657$	4.42017e59	0.116892
$658$	−7.66082e60	−1.96073
$659$	7.30688e60	1.81007	0.905035	−	0.425337i	$-0.139844\pi$
$659$	7.30688e60	1.81007	0.905035	+	0.425337i	$0.139844\pi$
$660$	6.74165e60	1.61648
$661$	6.34402e59	0.147243	0.0736213	−	0.997286i	$-0.476544\pi$
$661$	6.34402e59	0.147243	0.0736213	+	0.997286i	$0.476544\pi$
$662$	−2.89410e60	−0.650231
$663$	−1.34637e60	−0.292835
$664$	4.16847e60	0.877734
$665$	−4.59211e60	−0.936153
$666$	−3.04823e59	−0.0601661
$667$	9.88758e60	1.88966
$668$	−2.45946e60	−0.455140
$669$	8.48544e59	0.152059
$670$	−1.60048e61	−2.77742
$671$	−4.31998e60	−0.726018
$672$	3.08987e60	0.502922
$673$	−1.08068e61	−1.70363	−0.851814	−	0.523845i	$-0.824497\pi$
$673$	−1.08068e61	−1.70363	−0.851814	+	0.523845i	$0.824497\pi$
$674$	1.21122e61	1.84942
$675$	6.10241e59	0.0902548
$676$	−3.89070e60	−0.557409
$677$	−7.78512e60	−1.08046	−0.540230	−	0.841517i	$-0.681663\pi$
$677$	−7.78512e60	−1.08046	−0.540230	+	0.841517i	$0.681663\pi$
$678$	5.94321e59	0.0799066
$679$	2.20484e59	0.0287194
$680$	3.57062e60	0.450612
$681$	−3.66167e60	−0.447731
$682$	5.97483e60	0.707883
$683$	−1.04731e61	−1.20235	−0.601174	−	0.799118i	$-0.705300\pi$
$683$	−1.04731e61	−1.20235	−0.601174	+	0.799118i	$0.705300\pi$
$684$	−4.83491e60	−0.537877
$685$	−9.11022e60	−0.982158
$686$	1.51425e61	1.58208
$687$	6.18572e60	0.626355
$688$	7.99682e60	0.784812
$689$	−9.24589e60	−0.879499
$690$	−1.46899e61	−1.35445
$691$	9.34628e60	0.835335	0.417668	−	0.908600i	$-0.362848\pi$
$691$	9.34628e60	0.835335	0.417668	+	0.908600i	$0.362848\pi$
$692$	4.21949e60	0.365577
$693$	4.38837e60	0.368586
$694$	−1.43314e61	−1.16697
$695$	1.76376e61	1.39241
$696$	6.38992e60	0.489099
$697$	8.39727e60	0.623208
$698$	−7.58141e60	−0.545580
$699$	−1.01012e61	−0.704875
$700$	−6.19600e60	−0.419280
$701$	1.17846e61	0.773356	0.386678	−	0.922215i	$-0.373623\pi$
$701$	1.17846e61	0.773356	0.386678	+	0.922215i	$0.373623\pi$
$702$	3.57968e60	0.227822
$703$	2.24436e60	0.138533
$704$	4.37515e61	2.61927
$705$	−2.34785e61	−1.36334
$706$	2.81185e61	1.58377
$707$	1.18006e59	0.00644745
$708$	−9.94440e60	−0.527064
$709$	−2.12559e61	−1.09291	−0.546457	−	0.837487i	$-0.684024\pi$
$709$	−2.12559e61	−1.09291	−0.546457	+	0.837487i	$0.684024\pi$
$710$	−3.78128e61	−1.88619
$711$	−6.60592e60	−0.319696
$712$	−1.17176e61	−0.550198
$713$	−7.51798e60	−0.342512
$714$	8.66333e60	0.382978
$715$	3.67506e61	1.57647
$716$	−2.45810e61	−1.02322
$717$	2.20114e61	0.889173
$718$	2.57002e61	1.00754
$719$	−2.58349e61	−0.982960	−0.491480	−	0.870889i	$-0.663544\pi$
$719$	−2.58349e61	−0.982960	−0.491480	+	0.870889i	$0.663544\pi$
$720$	5.45835e60	0.201564
$721$	1.48906e61	0.533709
$722$	1.74267e61	0.606271
$723$	−1.41897e61	−0.479180
$724$	−3.84947e61	−1.26189
$725$	2.21338e61	0.704350
$726$	5.33938e61	1.64950
$727$	−7.14277e59	−0.0214228	−0.0107114	−	0.999943i	$-0.503410\pi$
$727$	−7.14277e59	−0.0214228	−0.0107114	+	0.999943i	$0.503410\pi$
$728$	−9.75101e60	−0.283939
$729$	1.31002e60	0.0370370
$730$	−2.38188e61	−0.653852
$731$	3.88988e61	1.03684
$732$	1.30938e61	0.338905
$733$	−5.72283e61	−1.43839	−0.719193	−	0.694811i	$-0.755488\pi$
$733$	−5.72283e61	−1.43839	−0.719193	+	0.694811i	$0.755488\pi$
$734$	−3.00096e61	−0.732479
$735$	1.68874e61	0.400300
$736$	−7.27761e61	−1.67539
$737$	−1.12612e62	−2.51787
$738$	−2.23263e61	−0.484848
$739$	−5.83871e61	−1.23158	−0.615788	−	0.787912i	$-0.711162\pi$
$739$	−5.83871e61	−1.23158	−0.615788	+	0.787912i	$0.711162\pi$
$740$	9.48536e60	0.194344
$741$	−2.63565e61	−0.524561
$742$	5.94935e61	1.15023
$743$	9.77520e61	1.83597	0.917987	−	0.396611i	$-0.129814\pi$
$743$	9.77520e61	1.83597	0.917987	+	0.396611i	$0.129814\pi$
$744$	−4.85855e60	−0.0886520
$745$	8.20510e61	1.45454
$746$	−5.11635e61	−0.881202
$747$	3.09966e61	0.518705
$748$	9.36445e61	1.52264
$749$	3.75212e61	0.592813
$750$	3.72344e61	0.571645
$751$	−2.27440e61	−0.339319	−0.169659	−	0.985503i	$-0.554267\pi$
$751$	−2.27440e61	−0.339319	−0.169659	+	0.985503i	$0.554267\pi$
$752$	−6.70452e61	−0.972040
$753$	1.71773e61	0.242026
$754$	1.29837e62	1.77793
$755$	−9.78710e60	−0.130255
$756$	−1.33011e61	−0.172056
$757$	−2.28350e61	−0.287104	−0.143552	−	0.989643i	$-0.545852\pi$
$757$	−2.28350e61	−0.287104	−0.143552	+	0.989643i	$0.545852\pi$
$758$	1.44704e61	0.176845
$759$	−1.03360e62	−1.22788
$760$	6.98984e61	0.807188
$761$	8.53778e61	0.958462	0.479231	−	0.877689i	$-0.340916\pi$
$761$	8.53778e61	0.958462	0.479231	+	0.877689i	$0.340916\pi$
$762$	2.49552e61	0.272351
$763$	6.36175e61	0.674993
$764$	−3.63281e61	−0.374745
$765$	2.65510e61	0.266293
$766$	1.22119e62	1.19087
$767$	−5.42097e61	−0.514016
$768$	−4.33586e60	−0.0399769
$769$	−1.13257e62	−1.01542	−0.507712	−	0.861527i	$-0.669509\pi$
$769$	−1.13257e62	−1.01542	−0.507712	+	0.861527i	$0.669509\pi$
$770$	−2.36475e62	−2.06174
$771$	−6.38287e60	−0.0541186
$772$	−2.15758e62	−1.77907
$773$	2.18119e62	1.74918	0.874588	−	0.484866i	$-0.161132\pi$
$773$	2.18119e62	1.74918	0.874588	+	0.484866i	$0.161132\pi$
$774$	−1.03423e62	−0.806651
$775$	−1.68293e61	−0.127667
$776$	−3.35607e60	−0.0247630
$777$	6.17434e60	0.0443138
$778$	−2.26487e62	−1.58118
$779$	1.64385e62	1.11636
$780$	−1.11391e62	−0.735894
$781$	−2.66056e62	−1.70992
$782$	−2.04049e62	−1.27582
$783$	4.75152e61	0.289038
$784$	4.82236e61	0.285407
$785$	2.06764e62	1.19063
$786$	−9.44972e61	−0.529461
$787$	3.94168e61	0.214894	0.107447	−	0.994211i	$-0.465732\pi$
$787$	3.94168e61	0.214894	0.107447	+	0.994211i	$0.465732\pi$
$788$	3.06472e62	1.62584
$789$	2.94701e61	0.152134
$790$	3.55972e62	1.78827
$791$	−1.20383e61	−0.0588531
$792$	−6.67971e61	−0.317809
$793$	7.13781e61	0.330515
$794$	5.36134e62	2.41620
$795$	1.82333e62	0.799783
$796$	−2.67043e62	−1.14012
$797$	−1.85308e62	−0.770087	−0.385043	−	0.922898i	$-0.625814\pi$
$797$	−1.85308e62	−0.770087	−0.385043	+	0.922898i	$0.625814\pi$
$798$	1.69593e62	0.686034
$799$	−3.26127e62	−1.28420
$800$	−1.62913e62	−0.624482
$801$	−8.71316e61	−0.325145
$802$	−5.58062e60	−0.0202737
$803$	−1.67593e62	−0.592749
$804$	3.41326e62	1.17534
$805$	2.97551e62	0.997584
$806$	−9.87209e61	−0.322259
$807$	−6.57113e61	−0.208862
$808$	−1.79622e60	−0.00555924
$809$	2.89492e62	0.872455	0.436228	−	0.899836i	$-0.356314\pi$
$809$	2.89492e62	0.872455	0.436228	+	0.899836i	$0.356314\pi$
$810$	−7.05928e61	−0.207173
$811$	−3.86441e62	−1.10442	−0.552211	−	0.833704i	$-0.686216\pi$
$811$	−3.86441e62	−1.10442	−0.552211	+	0.833704i	$0.686216\pi$
$812$	−4.82439e62	−1.34273
$813$	−3.24933e62	−0.880740
$814$	1.15575e62	0.305098
$815$	−2.60891e62	−0.670765
$816$	7.58189e61	0.189862
$817$	7.61482e62	1.85732
$818$	7.22255e62	1.71591
$819$	−7.25081e61	−0.167796
$820$	6.94741e62	1.56612
$821$	−7.00271e62	−1.53776	−0.768880	−	0.639394i	$-0.779185\pi$
$821$	−7.00271e62	−1.53776	−0.768880	+	0.639394i	$0.779185\pi$
$822$	3.36453e62	0.719748
$823$	−6.16948e62	−1.28574	−0.642868	−	0.765977i	$-0.722256\pi$
$823$	−6.16948e62	−1.28574	−0.642868	+	0.765977i	$0.722256\pi$
$824$	−2.26656e62	−0.460185
$825$	−2.31376e62	−0.457676
$826$	3.48817e62	0.672244
$827$	−1.18524e62	−0.222555	−0.111277	−	0.993789i	$-0.535494\pi$
$827$	−1.18524e62	−0.222555	−0.111277	+	0.993789i	$0.535494\pi$
$828$	3.13283e62	0.573172
$829$	5.09313e62	0.907951	0.453976	−	0.891014i	$-0.350005\pi$
$829$	5.09313e62	0.907951	0.453976	+	0.891014i	$0.350005\pi$
$830$	−1.67030e63	−2.90146
$831$	−3.65636e62	−0.618909
$832$	−7.22896e62	−1.19241
$833$	2.34574e62	0.377061
$834$	−6.51381e62	−1.02039
$835$	2.64396e62	0.403641
$836$	1.83318e63	2.72754
$837$	−3.61280e61	−0.0523897
$838$	4.07745e62	0.576291
$839$	−1.03721e63	−1.42884	−0.714422	−	0.699715i	$-0.753310\pi$
$839$	−1.03721e63	−1.42884	−0.714422	+	0.699715i	$0.753310\pi$
$840$	1.92294e62	0.258203
$841$	9.59365e62	1.25565
$842$	−1.00039e63	−1.27631
$843$	2.74806e62	0.341769
$844$	−1.33851e63	−1.62278
$845$	4.18257e62	0.494338
$846$	8.67095e62	0.999088
$847$	−1.08152e63	−1.21490
$848$	5.20669e62	0.570231
$849$	7.41102e62	0.791340
$850$	−4.56773e62	−0.475547
$851$	−1.45425e62	−0.147623
$852$	8.06415e62	0.798192
$853$	6.46285e62	0.623764	0.311882	−	0.950121i	$-0.399041\pi$
$853$	6.46285e62	0.623764	0.311882	+	0.950121i	$0.399041\pi$
$854$	−4.59289e62	−0.432256
$855$	5.19761e62	0.477015
$856$	−5.71126e62	−0.511147
$857$	−3.89227e62	−0.339715	−0.169858	−	0.985469i	$-0.554331\pi$
$857$	−3.89227e62	−0.339715	−0.169858	+	0.985469i	$0.554331\pi$
$858$	−1.35725e63	−1.15527
$859$	5.04634e62	0.418913	0.209456	−	0.977818i	$-0.432831\pi$
$859$	5.04634e62	0.418913	0.209456	+	0.977818i	$0.432831\pi$
$860$	3.21827e63	2.60558
$861$	4.52231e62	0.357102
$862$	1.58669e62	0.122204
$863$	9.68552e62	0.727597	0.363799	−	0.931478i	$-0.381480\pi$
$863$	9.68552e62	0.727597	0.363799	+	0.931478i	$0.381480\pi$
$864$	−3.49729e62	−0.256263
$865$	−4.53602e62	−0.324212
$866$	1.16623e63	0.813109
$867$	−4.80082e62	−0.326516
$868$	3.66820e62	0.243377
$869$	2.50466e63	1.62115
$870$	−2.56044e63	−1.61678
$871$	1.86066e63	1.14625
$872$	−9.68348e62	−0.582005
$873$	−2.49556e61	−0.0146339
$874$	−3.99445e63	−2.28540
$875$	−7.54200e62	−0.421031
$876$	5.07972e62	0.276695
$877$	−6.26532e61	−0.0333006	−0.0166503	−	0.999861i	$-0.505300\pi$
$877$	−6.26532e61	−0.0333006	−0.0166503	+	0.999861i	$0.505300\pi$
$878$	−2.86104e63	−1.48385
$879$	−1.02373e63	−0.518111
$880$	−2.06956e63	−1.02212
$881$	−3.44233e61	−0.0165909	−0.00829546	−	0.999966i	$-0.502641\pi$
$881$	−3.44233e61	−0.0165909	−0.00829546	+	0.999966i	$0.502641\pi$
$882$	−6.23676e62	−0.293349
$883$	3.56652e62	0.163715	0.0818576	−	0.996644i	$-0.473915\pi$
$883$	3.56652e62	0.163715	0.0818576	+	0.996644i	$0.473915\pi$
$884$	−1.54727e63	−0.693173
$885$	1.06904e63	0.467427
$886$	−1.23332e62	−0.0526321
$887$	−1.11406e63	−0.464035	−0.232017	−	0.972712i	$-0.574533\pi$
$887$	−1.11406e63	−0.464035	−0.232017	+	0.972712i	$0.574533\pi$
$888$	−9.39822e61	−0.0382091
$889$	−5.05481e62	−0.200593
$890$	4.69524e63	1.81875
$891$	−4.96700e62	−0.187812
$892$	9.75159e62	0.359941
$893$	−6.38425e63	−2.30040
$894$	−3.03026e63	−1.06592
$895$	2.64250e63	0.907445
$896$	2.05328e63	0.688375
$897$	1.70780e63	0.558983
$898$	7.89277e63	2.52225
$899$	−1.31038e63	−0.408850
$900$	7.01299e62	0.213643
$901$	2.53269e63	0.753353
$902$	8.46513e63	2.45863
$903$	2.09488e63	0.594118
$904$	1.83239e62	0.0507455
$905$	4.13824e63	1.11911
$906$	3.61451e62	0.0954539
$907$	−4.75180e63	−1.22547	−0.612734	−	0.790289i	$-0.709930\pi$
$907$	−4.75180e63	−1.22547	−0.612734	+	0.790289i	$0.709930\pi$
$908$	−4.20805e63	−1.05983
$909$	−1.33566e61	−0.00328528
$910$	3.90723e63	0.938596
$911$	−4.95250e63	−1.16193	−0.580964	−	0.813929i	$-0.697324\pi$
$911$	−4.95250e63	−1.16193	−0.580964	+	0.813929i	$0.697324\pi$
$912$	1.48423e63	0.340104
$913$	−1.17525e64	−2.63032
$914$	−4.54018e63	−0.992499
$915$	−1.40761e63	−0.300558
$916$	7.10873e63	1.48265
$917$	1.91409e63	0.389961
$918$	−9.80565e62	−0.195146
$919$	−2.19827e63	−0.427364	−0.213682	−	0.976903i	$-0.568546\pi$
$919$	−2.19827e63	−0.427364	−0.213682	+	0.976903i	$0.568546\pi$
$920$	−4.52914e63	−0.860156
$921$	3.65271e63	0.677693
$922$	−8.22464e63	−1.49074
$923$	4.39599e63	0.778431
$924$	5.04318e63	0.872483
$925$	−3.25541e62	−0.0550248
$926$	1.00414e64	1.65828
$927$	−1.68540e63	−0.271950
$928$	−1.26848e64	−1.99988
$929$	−8.33744e62	−0.128438	−0.0642192	−	0.997936i	$-0.520456\pi$
$929$	−8.33744e62	−0.128438	−0.0642192	+	0.997936i	$0.520456\pi$
$930$	1.94682e63	0.293050
$931$	4.59201e63	0.675437
$932$	−1.16084e64	−1.66852
$933$	1.94085e63	0.272607
$934$	1.54195e64	2.11647
$935$	−1.00669e64	−1.35035
$936$	1.10367e63	0.144681
$937$	1.31192e64	1.68077	0.840383	−	0.541993i	$-0.182330\pi$
$937$	1.31192e64	1.68077	0.840383	+	0.541993i	$0.182330\pi$
$938$	−1.19726e64	−1.49909
$939$	7.50313e63	0.918189
$940$	−2.69819e64	−3.22718
$941$	1.09648e64	1.28181	0.640905	−	0.767620i	$-0.278559\pi$
$941$	1.09648e64	1.28181	0.640905	+	0.767620i	$0.278559\pi$
$942$	−7.63608e63	−0.872522
$943$	−1.06515e64	−1.18962
$944$	3.05274e63	0.333267
$945$	1.42989e63	0.152588
$946$	3.92132e64	4.09047
$947$	4.97351e62	0.0507152	0.0253576	−	0.999678i	$-0.491928\pi$
$947$	4.97351e62	0.0507152	0.0253576	+	0.999678i	$0.491928\pi$
$948$	−7.59162e63	−0.756755
$949$	2.76910e63	0.269845
$950$	−8.94176e63	−0.851855
$951$	−7.58711e62	−0.0706635
$952$	2.67105e63	0.243214
$953$	−1.25621e64	−1.11832	−0.559160	−	0.829060i	$-0.688876\pi$
$953$	−1.25621e64	−1.11832	−0.559160	+	0.829060i	$0.688876\pi$
$954$	−6.73381e63	−0.586099
$955$	3.90533e63	0.332342
$956$	2.52959e64	2.10477
$957$	−1.80156e64	−1.46569
$958$	6.27636e63	0.499286
$959$	−6.81502e63	−0.530112
$960$	1.42558e64	1.08433
$961$	−1.24484e64	−0.925894
$962$	−1.90962e63	−0.138894
$963$	−4.24686e63	−0.302067
$964$	−1.63070e64	−1.13427
$965$	2.31943e64	1.57777
$966$	−1.09890e64	−0.731052
$967$	−1.92657e63	−0.125347	−0.0626737	−	0.998034i	$-0.519963\pi$
$967$	−1.92657e63	−0.125347	−0.0626737	+	0.998034i	$0.519963\pi$
$968$	1.64622e64	1.04753
$969$	7.21971e63	0.449323
$970$	1.34478e63	0.0818573
$971$	1.82399e64	1.08595	0.542973	−	0.839750i	$-0.317299\pi$
$971$	1.82399e64	1.08595	0.542973	+	0.839750i	$0.317299\pi$
$972$	1.50550e63	0.0876708
$973$	1.31940e64	0.751540
$974$	1.83957e64	1.02494
$975$	3.82298e63	0.208354
$976$	−4.01956e63	−0.214292
$977$	−2.86004e64	−1.49155	−0.745776	−	0.666197i	$-0.767921\pi$
$977$	−2.86004e64	−1.49155	−0.745776	+	0.666197i	$0.767921\pi$
$978$	9.63507e63	0.491552
$979$	3.30364e64	1.64879
$980$	1.94073e64	0.947554
$981$	−7.20059e63	−0.343941
$982$	−5.49475e64	−2.56774
$983$	2.49132e64	1.13901	0.569507	−	0.821986i	$-0.307134\pi$
$983$	2.49132e64	1.13901	0.569507	+	0.821986i	$0.307134\pi$
$984$	−6.88359e63	−0.307907
$985$	−3.29462e64	−1.44187
$986$	−3.55656e64	−1.52292
$987$	−1.75634e64	−0.735852
$988$	−3.02893e64	−1.24169
$989$	−4.93411e64	−1.97919
$990$	2.67656e64	1.05056
$991$	2.27461e63	0.0873620	0.0436810	−	0.999046i	$-0.486091\pi$
$991$	2.27461e63	0.0873620	0.0436810	+	0.999046i	$0.486091\pi$
$992$	9.64487e63	0.362490
$993$	−6.63512e63	−0.244028
$994$	−2.82864e64	−1.01805
$995$	2.87076e64	1.01111
$996$	3.56217e64	1.22783
$997$	3.04681e64	1.02778	0.513890	−	0.857856i	$-0.328204\pi$
$997$	3.04681e64	1.02778	0.513890	+	0.857856i	$0.328204\pi$
$998$	−8.25426e64	−2.72503
$999$	−6.98847e62	−0.0225800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.44.a.a.1.3	✓	3
3.2	odd	2		9.44.a.a.1.1		3

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 44 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+4.56260e6 q^{2} +1.04604e10 q^{3} +1.20212e13 q^{4} -1.29230e15 q^{5} +4.77264e16 q^{6} -9.66721e17 q^{7} +1.47149e19 q^{8} +1.09419e20 q^{9} +O(q^{10})\)	\(q+4.56260e6 q^{2} +1.04604e10 q^{3} +1.20212e13 q^{4} -1.29230e15 q^{5} +4.77264e16 q^{6} -9.66721e17 q^{7} +1.47149e19 q^{8} +1.09419e20 q^{9} -5.89624e21 q^{10} -4.14867e22 q^{11} +1.25746e23 q^{12} +6.85476e23 q^{13} -4.41076e24 q^{14} -1.35179e25 q^{15} -3.86016e25 q^{16} -1.87770e26 q^{17} +4.99235e26 q^{18} -3.67577e27 q^{19} -1.55350e28 q^{20} -1.01122e28 q^{21} -1.89287e29 q^{22} +2.38175e29 q^{23} +1.53923e29 q^{24} +5.33166e29 q^{25} +3.12755e30 q^{26} +1.14456e30 q^{27} -1.16211e31 q^{28} +4.15139e31 q^{29} -6.16767e31 q^{30} -3.15649e31 q^{31} -3.05557e32 q^{32} -4.33966e32 q^{33} -8.56717e32 q^{34} +1.24929e33 q^{35} +1.31535e33 q^{36} -6.10581e32 q^{37} -1.67711e34 q^{38} +7.17033e33 q^{39} -1.90160e34 q^{40} -4.47211e34 q^{41} -4.61381e34 q^{42} -2.07163e35 q^{43} -4.98720e35 q^{44} -1.41402e35 q^{45} +1.08670e36 q^{46} +1.73685e36 q^{47} -4.03787e35 q^{48} -1.24926e36 q^{49} +2.43262e36 q^{50} -1.96414e36 q^{51} +8.24025e36 q^{52} -1.34883e37 q^{53} +5.22217e36 q^{54} +5.36132e37 q^{55} -1.42252e37 q^{56} -3.84499e37 q^{57} +1.89411e38 q^{58} -7.90833e37 q^{59} -1.62501e38 q^{60} +1.04129e38 q^{61} -1.44018e38 q^{62} -1.05778e38 q^{63} -1.05459e39 q^{64} -8.85840e38 q^{65} -1.98001e39 q^{66} +2.71441e39 q^{67} -2.25722e39 q^{68} +2.49140e39 q^{69} +5.70002e39 q^{70} +6.41305e39 q^{71} +1.61008e39 q^{72} +4.03967e39 q^{73} -2.78583e39 q^{74} +5.57711e39 q^{75} -4.41872e40 q^{76} +4.01061e40 q^{77} +3.27153e40 q^{78} -6.03727e40 q^{79} +4.98848e40 q^{80} +1.19725e40 q^{81} -2.04044e41 q^{82} +2.83283e41 q^{83} -1.21561e41 q^{84} +2.42654e41 q^{85} -9.45200e41 q^{86} +4.34250e41 q^{87} -6.10471e41 q^{88} -7.96312e41 q^{89} -6.45160e41 q^{90} -6.62665e41 q^{91} +2.86315e42 q^{92} -3.30180e41 q^{93} +7.92454e42 q^{94} +4.75019e42 q^{95} -3.19623e42 q^{96} -2.28074e41 q^{97} -5.69989e42 q^{98} -4.53944e42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 4857024 q^{2} + 31381059609 q^{3} - 1781058029568 q^{4} - 507753321105270 q^{5} + 50\!\cdots\!72 q^{6}+ \cdots + 32\!\cdots\!27 q^{9}+O(q^{10}) \) 3 * q + 4857024 * q^2 + 31381059609 * q^3 - 1781058029568 * q^4 - 507753321105270 * q^5 + 50806186555447872 * q^6 - 1633169303707089288 * q^7 + 11196260694472851456 * q^8 + 328256967394537077627 * q^9	\( 3 q + 4857024 q^{2} + 31381059609 q^{3} - 1781058029568 q^{4} - 507753321105270 q^{5} + 50\!\cdots\!72 q^{6}+ \cdots - 30\!\cdots\!80 q^{99}+O(q^{100}) \) 3 * q + 4857024 * q^2 + 31381059609 * q^3 - 1781058029568 * q^4 - 507753321105270 * q^5 + 50806186555447872 * q^6 - 1633169303707089288 * q^7 + 11196260694472851456 * q^8 + 328256967394537077627 * q^9 - 2286850690696789595520 * q^10 - 27750966261606959036820 * q^11 - 18630496064320497506304 * q^12 - 994786398159560287290750 * q^13 - 9473256819232835003171328 * q^14 - 5311279078757398544679810 * q^15 + 23637690650696707825729536 * q^16 - 160517621023312837046953482 * q^17 + 531450656267494684974734016 * q^18 - 3227133683900578441639486764 * q^19 - 19920520041146285724571791360 * q^20 - 17083527757073731207537789464 * q^21 - 172470540148626161048719521024 * q^22 + 114780279514038504224277444504 * q^23 + 117116841417052096124312813568 * q^24 + 1825420275602850437617559193525 * q^25 + 1775037275334840765729836075136 * q^26 + 3433683820292512484657849089281 * q^27 - 8483554335441104836174737260544 * q^28 - 28241588775620253186792106789758 * q^29 - 23921265947212925347314706450560 * q^30 - 56947467162250619768506214477136 * q^31 - 290372748061904590918491662450688 * q^32 - 290284908820945289887889881934460 * q^33 - 1778246324363072918021693922216576 * q^34 - 3641689125493658442558484764497520 * q^35 - 194881569179893810108620559091712 * q^36 - 7771759793894794226158134990367878 * q^37 - 11984574206649783949969526048471808 * q^38 - 10405817086289189756233396954772250 * q^39 - 75089135561625836440773237699379200 * q^40 - 150622420768399427659977962302801266 * q^41 - 99093612311903777628193716002563584 * q^42 - 503269829459862138385119574866599988 * q^43 - 589156491500651091472842134125289472 * q^44 - 55557855123506843126788989142931430 * q^45 + 1201666039209211956008162792803812864 * q^46 + 517590816657574666863303783889459536 * q^47 + 247258593109538461886425117709303808 * q^48 + 1183207682852736238558590379440977403 * q^49 + 5363972694460023429439963707950510400 * q^50 - 1679071011209150572675116916830702846 * q^51 + 19510568225567423700598614061466308608 * q^52 + 3147649955233970731028729152905020634 * q^53 + 5559161574524140052760934938338653248 * q^54 + 72798121427511388475535050768468313960 * q^55 + 64659225918940531158350848060065054720 * q^56 - 33756958166898605235556353943083505092 * q^57 + 165860584701603780784654252956514011264 * q^58 - 178011039218636820023529236138863835076 * q^59 - 208375675617830241670577713556023726080 * q^60 - 123533499732384273913895969461615945518 * q^61 - 685215538112102475249420816230843667456 * q^62 - 178699734292245610143928973763292053192 * q^63 - 971015593402068342273570470768658087936 * q^64 - 2575578837917643212594035173081316043940 * q^65 - 1804102767066821759775567080792024239872 * q^66 + 1292774342372783673662410484960847098148 * q^67 - 2717789569206669919054906507790539296768 * q^68 + 1200642264455907951127749596978071146312 * q^69 + 1868357626946632141981582698458836116480 * q^70 + 22400468745595901369803420176388102887816 * q^71 + 1225083527242103952511819425579970658304 * q^72 + 31313509370447648548173493799361498480654 * q^73 + 12824367911381949889146580637796075349632 * q^74 + 19094540826723419331062786999031330610575 * q^75 - 45893435926810400921777338109031978491904 * q^76 + 15925552922292610065970442499593057720544 * q^77 + 18567516848493194501297063421213806260608 * q^78 - 43825544899857898915807551182364364018080 * q^79 + 51052771545930899482561003058120286535680 * q^80 + 35917545547686059365808220080151141317043 * q^81 - 207555016724016234735599639977066643719296 * q^82 + 89911369720242570860406785197345580904468 * q^83 - 88740974765555897390939203171014875922432 * q^84 - 609771200949453596987959942886782705526220 * q^85 - 1052084075872403200090705454196607607512320 * q^86 - 295416993606868163734131771553363142894874 * q^87 - 866229044996425850996432449444164589584384 * q^88 + 65289466052051143331840751197428752211806 * q^89 - 250224890870743552579783277069120057143680 * q^90 + 1361620777581018817929645459439738348447824 * q^91 + 3753917639661643691216268373890598977257472 * q^92 - 595690620533385591184229099131314527866608 * q^93 + 7862327422462694583153035384185107177477120 * q^94 + 9328236864095865156237338173319138974757400 * q^95 - 3037401505253255729894648973244849050353664 * q^96 + 6130807410554375967448029821362307484893478 * q^97 - 2033290778553828878915746018754102329738560 * q^98 - 3036482675767738016566552437404420497075380 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more