LMFDB - Embedded newform 2.66.a.b.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2,66,Mod(1,2)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2.1"); S:= CuspForms(chi, 66); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 66, names="a")

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 66 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$53.5144712945$
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} - 4862367805520722608042x + 130125819203569060903952569933488 $ x^3 - x^2 - 4862367805520722608042*x + 130125819203569060903952569933488
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{8}\cdot 5^{3}\cdot 7\cdot 11\cdot 13 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-8.04922e10$ 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)

$f(q)$	$=$	\(q+4.29497e9 q^{2} -5.99699e13 q^{3} +1.84467e19 q^{4} +6.16250e22 q^{5} -2.57569e23 q^{6} -2.55894e27 q^{7} +7.92282e28 q^{8} -1.02975e31 q^{9} +2.64677e32 q^{10} +8.24813e33 q^{11} -1.10625e33 q^{12} +2.22949e36 q^{13} -1.09906e37 q^{14} -3.69564e36 q^{15} +3.40282e38 q^{16} +8.10668e39 q^{17} -4.42272e40 q^{18} -2.71144e41 q^{19} +1.13678e42 q^{20} +1.53459e41 q^{21} +3.54255e43 q^{22} -1.66211e44 q^{23} -4.75130e42 q^{24} +1.08714e45 q^{25} +9.57560e45 q^{26} +1.23529e45 q^{27} -4.72041e46 q^{28} +5.45865e47 q^{29} -1.58727e46 q^{30} +1.86521e48 q^{31} +1.46150e48 q^{32} -4.94639e47 q^{33} +3.48179e49 q^{34} -1.57695e50 q^{35} -1.89955e50 q^{36} +2.14819e50 q^{37} -1.16455e51 q^{38} -1.33702e50 q^{39} +4.88244e51 q^{40} -7.22402e51 q^{41} +6.59102e50 q^{42} +1.76640e53 q^{43} +1.52151e53 q^{44} -6.34581e53 q^{45} -7.13870e53 q^{46} +2.08814e54 q^{47} -2.04067e52 q^{48} -1.99016e54 q^{49} +4.66921e54 q^{50} -4.86156e53 q^{51} +4.11269e55 q^{52} +1.83129e56 q^{53} +5.30553e54 q^{54} +5.08291e56 q^{55} -2.02740e56 q^{56} +1.62605e55 q^{57} +2.34447e57 q^{58} +3.10277e57 q^{59} -6.81726e55 q^{60} +1.43214e58 q^{61} +8.01103e57 q^{62} +2.63505e58 q^{63} +6.27710e57 q^{64} +1.37393e59 q^{65} -2.12446e57 q^{66} -3.92071e59 q^{67} +1.49542e59 q^{68} +9.96764e57 q^{69} -6.77293e59 q^{70} -1.24089e60 q^{71} -8.15848e59 q^{72} -2.06411e60 q^{73} +9.22642e59 q^{74} -6.51954e58 q^{75} -5.00172e60 q^{76} -2.11065e61 q^{77} -5.74248e59 q^{78} -2.95663e61 q^{79} +2.09699e61 q^{80} +1.06001e62 q^{81} -3.10269e61 q^{82} +2.09374e62 q^{83} +2.83082e60 q^{84} +4.99574e62 q^{85} +7.58665e62 q^{86} -3.27355e61 q^{87} +6.53484e62 q^{88} +1.03182e63 q^{89} -2.72550e63 q^{90} -5.70513e63 q^{91} -3.06605e63 q^{92} -1.11857e62 q^{93} +8.96850e63 q^{94} -1.67092e64 q^{95} -8.76461e61 q^{96} -1.75639e64 q^{97} -8.54768e63 q^{98} -8.49348e64 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 12884901888 q^{2} + 29\!\cdots\!12 q^{3} + 55\!\cdots\!48 q^{4} + 39\!\cdots\!50 q^{5} + 12\!\cdots\!52 q^{6} + 42\!\cdots\!64 q^{7} + 23\!\cdots\!08 q^{8} + 85\!\cdots\!19 q^{9} + 16\!\cdots\!00 q^{10}+ \cdots - 11\!\cdots\!32 q^{99}+O(q^{100}) $ 3 * q + 12884901888 * q^2 + 2984558598211212 * q^3 + 55340232221128654848 * q^4 + 3918092878575519628050 * q^5 + 12818581572312759640522752 * q^6 + 4292799991821220115501533464 * q^7 + 237684487542793012780631851008 * q^8 + 8506531680020675520627594612519 * q^9 + 16828080776172355868680834252800 * q^10 - 196390756437727241578921135931484 * q^11 + 55055388634191561739553936183918592 * q^12 + 594291588159789125437621076340076842 * q^13 + 18437435573141207874896428865729593344 * q^14 + 223941641190704507876888119858515088200 * q^15 + 1020847100762815390390123822295304634368 * q^16 - 4543147667338787792770556318133924095946 * q^17 + 36535275368076737964923292255914897178624 * q^18 - 76776862412732416183497479026519297722180 * q^19 + 72276056588106564515257853777772596428800 * q^20 + 26265549620028199801130322543173760738908256 * q^21 - 843491876136739963149757681788894276747264 * q^22 - 246585175089558483596492707518472201143440568 * q^23 + 236461093652422865070549025538001393766367232 * q^24 + 193546046773561655726447442157501687259788125 * q^25 + 2552462935434195116011024210920949410516959232 * q^26 + 104360942861770930686026372969796096727969655160 * q^27 + 79188182808748503812617821365498978591859277824 * q^28 + 531967266741361557870395008315736313563375166810 * q^29 + 961822025126642360531008869043250450941555507200 * q^30 + 6029738539523787679291490893311596271283256878176 * q^31 + 4384504911992708754611054498148849058967797628928 * q^32 + 2499511318103852899572045391368179633250062699664 * q^33 - 19512670652118780922233564618111375740234436182016 * q^34 - 213108430526997938381296997393828498022497121759600 * q^35 + 156917812856243951977707135387804545941392750280704 * q^36 - 1620332873097169620543940609594653833354625777112206 * q^37 - 329754113152177381507182807317346300429650393825280 * q^38 - 8058443520000240583429939491235801869291744868819032 * q^39 + 310423299329763037155946574982683353386702392524800 * q^40 + 36703565948034838377558864834222924936123775941865086 * q^41 + 112809676629486344743608439156862850418939754264395776 * q^42 + 198917478867600910841699694521456326480823486676005892 * q^43 - 3622770022448980965784454393608075694631072137478144 * q^44 - 216645431861240266977838791183480248608297455718819350 * q^45 - 1059075262688087558126288639094331419796211044479664128 * q^46 - 1550246333207342372432412618727579166713397594577369456 * q^47 + 1015592664013549396640628797450384791428965526166044672 * q^48 + 11478891131098122565712354085801141363063646718069629611 * q^49 + 831273941162533628784702886329321427845609852764160000 * q^50 + 57291625837763827945225305750991869614936958866433005016 * q^51 + 10962744831942027583350274961369683759440818354805276672 * q^52 + 388195149550139617029551617840486557495245907961121867682 * q^53 + 448226836571030795939966116098772631235082277392597647360 * q^54 + 895742624805791195861557775792485861196137895636425392600 * q^55 + 340110655393244246564124854911588175773439730088258043904 * q^56 + 1787627119006620995570153951692449536429396987788043658480 * q^57 + 2284782013196656381564957967317735508914297564827494645760 * q^58 + 9942474367718630997051455369033666316253859457002364589620 * q^59 + 4130994142491419196768924286426707496331233310792692531200 * q^60 + 30901057913347435136984168017635112365997774001894406985146 * q^61 + 25897529830685471496604689837855131122717132244132976132096 * q^62 + 138514635870008809143798247361228813659466120862088577199672 * q^63 + 18831305206160042291507368269622999248307066333392103538688 * q^64 + 135257076450309235113689373768740271196683349960342621544700 * q^65 + 10735319367237900935256707351753852219862293485006350188544 * q^66 + 17100824266138937068734192820846019367859612644204005842764 * q^67 - 83806282308469157168381879308291088089874694774757823348736 * q^68 - 2698212859345134110276706952535684126822641673823538886031072 * q^69 - 915293739615344190407093781869490631239425810211611974041600 * q^70 - 2069639192653675666961611875517343804017024313729705648459304 * q^71 + 673956874377416123142046667556464802058411395147118499856384 * q^72 - 1495815738901851328847860331660544347506225395356711624209698 * q^73 - 6959276698586061750400954649175342030699151683015510092414976 * q^74 - 19630994079897599350490393185253943873910057323490546919647500 * q^75 - 1416283131710085324764265346521471853851939190193097938042880 * q^76 - 42888418275967578631586680891050882789238717944468360701613792 * q^77 - 34610751375064155217963549622116647652943710894353552582377472 * q^78 + 6108958390094940959359012430413819561677141119540814251420400 * q^79 + 1333257918537750964014423391473836769119497617178970868940800 * q^80 + 199173830104428424071020062682585715958512675590259821728258923 * q^81 + 157640615393388866300261024777871924174114506678342141614227456 * q^82 + 205502582077300871012959214620783777968329728364540523725320572 * q^83 + 484513871795979359952379751208331756506686143559856395120541696 * q^84 + 1563497203971321203580713284666021364588991577456628214456792900 * q^85 + 854344066339117026044912021022845292527435646422137054043308032 * q^86 + 2751581088715129276210795138032395912793526337910098768398145640 * q^87 - 15559678767347559076570726605750196549932937615885444394778624 * q^88 - 1130441655406023955699836505406122255346035459613687451813849330 * q^89 - 930485044671823356668126364893220803234587086552337279981977600 * q^90 - 13758542132769965346791751406178617412263818701689332035952867504 * q^91 - 4548693617247945110936908742766500507009973420754158766824357888 * q^92 - 16692928740948609788490018454765087545603973049886739588798586496 * q^93 - 6658257301869454276672264167812669654284974473754868755229310976 * q^94 - 8930271988344088631293827502889147672196124499832288756967215000 * q^95 + 4361937277995710759452032949925210861803188041994594131915046912 * q^96 - 74357502639901786600354059238491465614418207375045893147311856346 * q^97 + 49301462002410884986734171741687880113831225020606791430078201856 * q^98 - 116077555785702594445847201289530245195179661533809750801608233132 * q^99

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 $

$2$	4.29497e9	0.707107
$2$	4.29497e9	0.707107
$3$	−5.99699e13	−0.0186850	−0.00934248	−	0.999956i	$-0.502974\pi$
$3$	−5.99699e13	−0.0186850	−0.00934248	+	0.999956i	$0.502974\pi$
$4$	1.84467e19	0.500000
$5$	6.16250e22	1.18367	0.591837	−	0.806058i	$-0.298403\pi$
$5$	6.16250e22	1.18367	0.591837	+	0.806058i	$0.298403\pi$
$6$	−2.57569e23	−0.0132123
$7$	−2.55894e27	−0.875736	−0.437868	−	0.899039i	$-0.644266\pi$
$7$	−2.55894e27	−0.875736	−0.437868	+	0.899039i	$0.644266\pi$
$8$	7.92282e28	0.353553
$9$	−1.02975e31	−0.999651
$10$	2.64677e32	0.836983
$11$	8.24813e33	1.17786	0.588930	−	0.808184i	$-0.299550\pi$
$11$	8.24813e33	1.17786	0.588930	+	0.808184i	$0.299550\pi$
$12$	−1.10625e33	−0.00934248
$13$	2.22949e36	1.39652	0.698260	−	0.715844i	$-0.253958\pi$
$13$	2.22949e36	1.39652	0.698260	+	0.715844i	$0.253958\pi$
$14$	−1.09906e37	−0.619239
$15$	−3.69564e36	−0.0221169
$16$	3.40282e38	0.250000
$17$	8.10668e39	0.830334	0.415167	−	0.909745i	$-0.363723\pi$
$17$	8.10668e39	0.830334	0.415167	+	0.909745i	$0.363723\pi$
$18$	−4.42272e40	−0.706860
$19$	−2.71144e41	−0.747666	−0.373833	−	0.927496i	$-0.621957\pi$
$19$	−2.71144e41	−0.747666	−0.373833	+	0.927496i	$0.621957\pi$
$20$	1.13678e42	0.591837
$21$	1.53459e41	0.0163631
$22$	3.54255e43	0.832872
$23$	−1.66211e44	−0.921519	−0.460760	−	0.887525i	$-0.652423\pi$
$23$	−1.66211e44	−0.921519	−0.460760	+	0.887525i	$0.652423\pi$
$24$	−4.75130e42	−0.00660613
$25$	1.08714e45	0.401082
$26$	9.57560e45	0.987489
$27$	1.23529e45	0.0373634
$28$	−4.72041e46	−0.437868
$29$	5.45865e47	1.61864	0.809320	−	0.587368i	$-0.199836\pi$
$29$	5.45865e47	1.61864	0.809320	+	0.587368i	$0.199836\pi$
$30$	−1.58727e46	−0.0156390
$31$	1.86521e48	0.633101	0.316551	−	0.948576i	$-0.397475\pi$
$31$	1.86521e48	0.633101	0.316551	+	0.948576i	$0.397475\pi$
$32$	1.46150e48	0.176777
$33$	−4.94639e47	−0.0220083
$34$	3.48179e49	0.587135
$35$	−1.57695e50	−1.03659
$36$	−1.89955e50	−0.499825
$37$	2.14819e50	0.232016	0.116008	−	0.993248i	$-0.462990\pi$
$37$	2.14819e50	0.232016	0.116008	+	0.993248i	$0.462990\pi$
$38$	−1.16455e51	−0.528680
$39$	−1.33702e50	−0.0260939
$40$	4.88244e51	0.418492
$41$	−7.22402e51	−0.277526	−0.138763	−	0.990326i	$-0.544313\pi$
$41$	−7.22402e51	−0.277526	−0.138763	+	0.990326i	$0.544313\pi$
$42$	6.59102e50	0.0115705
$43$	1.76640e53	1.44333	0.721664	−	0.692243i	$-0.243377\pi$
$43$	1.76640e53	1.44333	0.721664	+	0.692243i	$0.243377\pi$
$44$	1.52151e53	0.588930
$45$	−6.34581e53	−1.18326
$46$	−7.13870e53	−0.651613
$47$	2.08814e54	0.947501	0.473751	−	0.880659i	$-0.342900\pi$
$47$	2.08814e54	0.947501	0.473751	+	0.880659i	$0.342900\pi$
$48$	−2.04067e52	−0.00467124
$49$	−1.99016e54	−0.233086
$50$	4.66921e54	0.283608
$51$	−4.86156e53	−0.0155148
$52$	4.11269e55	0.698260
$53$	1.83129e56	1.67414	0.837068	−	0.547099i	$-0.184268\pi$
$53$	1.83129e56	1.67414	0.837068	+	0.547099i	$0.184268\pi$
$54$	5.30553e54	0.0264199
$55$	5.08291e56	1.39420
$56$	−2.02740e56	−0.309620
$57$	1.62605e55	0.0139701
$58$	2.34447e57	1.14455
$59$	3.10277e57	0.869078	0.434539	−	0.900653i	$-0.356911\pi$
$59$	3.10277e57	0.869078	0.434539	+	0.900653i	$0.356911\pi$
$60$	−6.81726e55	−0.0110584
$61$	1.43214e58	1.35758	0.678792	−	0.734331i	$-0.262504\pi$
$61$	1.43214e58	1.35758	0.678792	+	0.734331i	$0.262504\pi$
$62$	8.01103e57	0.447670
$63$	2.63505e58	0.875431
$64$	6.27710e57	0.125000
$65$	1.37393e59	1.65302
$66$	−2.12446e57	−0.0155622
$67$	−3.92071e59	−1.76171	−0.880854	−	0.473387i	$-0.843031\pi$
$67$	−3.92071e59	−1.76171	−0.880854	+	0.473387i	$0.843031\pi$
$68$	1.49542e59	0.415167
$69$	9.96764e57	0.0172186
$70$	−6.77293e59	−0.732977
$71$	−1.24089e60	−0.846911	−0.423456	−	0.905917i	$-0.639183\pi$
$71$	−1.24089e60	−0.846911	−0.423456	+	0.905917i	$0.639183\pi$
$72$	−8.15848e59	−0.353430
$73$	−2.06411e60	−0.571136	−0.285568	−	0.958358i	$-0.592182\pi$
$73$	−2.06411e60	−0.571136	−0.285568	+	0.958358i	$0.592182\pi$
$74$	9.22642e59	0.164060
$75$	−6.51954e58	−0.00749421
$76$	−5.00172e60	−0.373833
$77$	−2.11065e61	−1.03149
$78$	−5.74248e59	−0.0184512
$79$	−2.95663e61	−0.627938	−0.313969	−	0.949433i	$-0.601659\pi$
$79$	−2.95663e61	−0.627938	−0.313969	+	0.949433i	$0.601659\pi$
$80$	2.09699e61	0.295918
$81$	1.06001e62	0.998953
$82$	−3.10269e61	−0.196240
$83$	2.09374e62	0.893068	0.446534	−	0.894767i	$-0.352658\pi$
$83$	2.09374e62	0.893068	0.446534	+	0.894767i	$0.352658\pi$
$84$	2.83082e60	0.00818155
$85$	4.99574e62	0.982844
$86$	7.58665e62	1.02059
$87$	−3.27355e61	−0.0302442
$88$	6.53484e62	0.416436
$89$	1.03182e63	0.455437	0.227718	−	0.973727i	$-0.426873\pi$
$89$	1.03182e63	0.455437	0.227718	+	0.973727i	$0.426873\pi$
$90$	−2.72550e63	−0.836691
$91$	−5.70513e63	−1.22298
$92$	−3.06605e63	−0.460760
$93$	−1.11857e62	−0.0118295
$94$	8.96850e63	0.669985
$95$	−1.67092e64	−0.884993
$96$	−8.76461e61	−0.00330307
$97$	−1.75639e64	−0.472650	−0.236325	−	0.971674i	$-0.575943\pi$
$97$	−1.75639e64	−0.472650	−0.236325	+	0.971674i	$0.575943\pi$
$98$	−8.54768e63	−0.164817
$99$	−8.49348e64	−1.17745
$100$	2.00541e64	0.200541
$101$	2.33908e65	1.69278	0.846391	−	0.532562i	$-0.178771\pi$
$101$	2.33908e65	1.69278	0.846391	+	0.532562i	$0.178771\pi$
$102$	−2.08803e63	−0.0109706
$103$	−3.35019e65	−1.28192	−0.640959	−	0.767575i	$-0.721463\pi$
$103$	−3.35019e65	−1.28192	−0.640959	+	0.767575i	$0.721463\pi$
$104$	1.76639e65	0.493744
$105$	9.45692e63	0.0193686
$106$	7.86532e65	1.18379
$107$	1.42240e66	1.57779	0.788894	−	0.614529i	$-0.210654\pi$
$107$	1.42240e66	1.57779	0.788894	+	0.614529i	$0.210654\pi$
$108$	2.27871e64	0.0186817
$109$	−1.30058e66	−0.790270	−0.395135	−	0.918623i	$-0.629302\pi$
$109$	−1.30058e66	−0.790270	−0.395135	+	0.918623i	$0.629302\pi$
$110$	2.18309e66	0.985849
$111$	−1.28827e64	−0.00433520
$112$	−8.70761e65	−0.218934
$113$	−8.42496e66	−1.58679	−0.793393	−	0.608709i	$-0.791688\pi$
$113$	−8.42496e66	−1.58679	−0.793393	+	0.608709i	$0.791688\pi$
$114$	6.98382e64	0.00987837
$115$	−1.02427e67	−1.09078
$116$	1.00694e67	0.809320
$117$	−2.29581e67	−1.39603
$118$	1.33263e67	0.614531
$119$	−2.07445e67	−0.727154
$120$	−2.92799e65	−0.00781950
$121$	1.89946e67	0.387352
$122$	6.15100e67	0.959956
$123$	4.33223e65	0.00518556
$124$	3.44071e67	0.316551
$125$	−1.00040e68	−0.708923
$126$	1.13175e68	0.619023
$127$	1.18694e68	0.502120	0.251060	−	0.967972i	$-0.419221\pi$
$127$	1.18694e68	0.502120	0.251060	+	0.967972i	$0.419221\pi$
$128$	2.69599e67	0.0883883
$129$	−1.05931e67	−0.0269686
$130$	5.90096e68	1.16886
$131$	−4.63257e68	−0.715327	−0.357664	−	0.933850i	$-0.616427\pi$
$131$	−4.63257e68	−0.715327	−0.357664	+	0.933850i	$0.616427\pi$
$132$	−9.12449e66	−0.0110041
$133$	6.93840e68	0.654759
$134$	−1.68393e69	−1.24572
$135$	7.61247e67	0.0442261
$136$	6.42277e68	0.293567
$137$	−1.52289e69	−0.548592	−0.274296	−	0.961645i	$-0.588445\pi$
$137$	−1.52289e69	−0.548592	−0.274296	+	0.961645i	$0.588445\pi$
$138$	4.28107e67	0.0121754
$139$	−7.46844e69	−1.67977	−0.839883	−	0.542767i	$-0.817377\pi$
$139$	−7.46844e69	−1.67977	−0.839883	+	0.542767i	$0.817377\pi$
$140$	−2.90895e69	−0.518293
$141$	−1.25226e68	−0.0177040
$142$	−5.32959e69	−0.598857
$143$	1.83892e70	1.64490
$144$	−3.50404e69	−0.249913
$145$	3.36389e70	1.91594
$146$	−8.86528e69	−0.403854
$147$	1.19350e68	0.00435520
$148$	3.96272e69	0.116008
$149$	2.05458e70	0.483247	0.241623	−	0.970370i	$-0.422320\pi$
$149$	2.05458e70	0.483247	0.241623	+	0.970370i	$0.422320\pi$
$150$	−2.80012e68	−0.00529921
$151$	7.39852e70	1.12822	0.564111	−	0.825699i	$-0.309219\pi$
$151$	7.39852e70	1.12822	0.564111	+	0.825699i	$0.309219\pi$
$152$	−2.14822e70	−0.264340
$153$	−8.34781e70	−0.830044
$154$	−9.06515e70	−0.729376
$155$	1.14944e71	0.749385
$156$	−2.46637e69	−0.0130470
$157$	−3.66951e71	−1.57714	−0.788569	−	0.614947i	$-0.789178\pi$
$157$	−3.66951e71	−1.57714	−0.788569	+	0.614947i	$0.789178\pi$
$158$	−1.26986e71	−0.444019
$159$	−1.09822e70	−0.0312812
$160$	9.00650e70	0.209246
$161$	4.25323e71	0.807008
$162$	4.55269e71	0.706366
$163$	−1.29796e72	−1.64878	−0.824391	−	0.566020i	$-0.808482\pi$
$163$	−1.29796e72	−1.64878	−0.824391	+	0.566020i	$0.808482\pi$
$164$	−1.33260e71	−0.138763
$165$	−3.04822e70	−0.0260506
$166$	8.99254e71	0.631494
$167$	−1.14607e72	−0.662102	−0.331051	−	0.943613i	$-0.607403\pi$
$167$	−1.14607e72	−0.662102	−0.331051	+	0.943613i	$0.607403\pi$
$168$	1.21583e70	0.00578523
$169$	2.42194e72	0.950268
$170$	2.14565e72	0.694976
$171$	2.79209e72	0.747405
$172$	3.25844e72	0.721664
$173$	−3.50711e72	−0.643355	−0.321678	−	0.946849i	$-0.604247\pi$
$173$	−3.50711e72	−0.643355	−0.321678	+	0.946849i	$0.604247\pi$
$174$	−1.40598e71	−0.0213859
$175$	−2.78191e72	−0.351242
$176$	2.80669e72	0.294465
$177$	−1.86073e71	−0.0162387
$178$	4.43163e72	0.322042
$179$	−1.06620e73	−0.645825	−0.322912	−	0.946429i	$-0.604662\pi$
$179$	−1.06620e73	−0.645825	−0.322912	+	0.946429i	$0.604662\pi$
$180$	−1.17059e73	−0.591630
$181$	−2.21946e73	−0.936899	−0.468450	−	0.883490i	$-0.655187\pi$
$181$	−2.21946e73	−0.936899	−0.468450	+	0.883490i	$0.655187\pi$
$182$	−2.45034e73	−0.864780
$183$	−8.58854e71	−0.0253664
$184$	−1.31686e73	−0.325806
$185$	1.32382e73	0.274631
$186$	−4.80420e71	−0.00836470
$187$	6.68649e73	0.978017
$188$	3.85194e73	0.473751
$189$	−3.16103e72	−0.0327205
$190$	−7.17657e73	−0.625784
$191$	2.06223e74	1.51619	0.758093	−	0.652147i	$-0.226131\pi$
$191$	2.06223e74	1.51619	0.758093	+	0.652147i	$0.226131\pi$
$192$	−3.76437e71	−0.00233562
$193$	1.31472e74	0.689002	0.344501	−	0.938786i	$-0.388048\pi$
$193$	1.31472e74	0.689002	0.344501	+	0.938786i	$0.388048\pi$
$194$	−7.54364e73	−0.334214
$195$	−8.23941e72	−0.0308867
$196$	−3.67120e73	−0.116543
$197$	2.75458e74	0.741144	0.370572	−	0.928804i	$-0.379162\pi$
$197$	2.75458e74	0.741144	0.370572	+	0.928804i	$0.379162\pi$
$198$	−3.64792e74	−0.832581
$199$	−4.16712e74	−0.807441	−0.403721	−	0.914882i	$-0.632283\pi$
$199$	−4.16712e74	−0.807441	−0.403721	+	0.914882i	$0.632283\pi$
$200$	8.61318e73	0.141804
$201$	2.35125e73	0.0329175
$202$	1.00463e75	1.19698
$203$	−1.39683e75	−1.41750
$204$	−8.96800e72	−0.00775738
$205$	−4.45180e74	−0.328500
$206$	−1.43890e75	−0.906452
$207$	1.71155e75	0.921198
$208$	7.58657e74	0.349130
$209$	−2.23643e75	−0.880646
$210$	4.06172e73	0.0136956
$211$	−5.05562e75	−1.46081	−0.730406	−	0.683013i	$-0.760669\pi$
$211$	−5.05562e75	−1.46081	−0.730406	+	0.683013i	$0.760669\pi$
$212$	3.37813e75	0.837068
$213$	7.44162e73	0.0158245
$214$	6.10916e75	1.11566
$215$	1.08855e76	1.70843
$216$	9.78697e73	0.0132100
$217$	−4.77296e75	−0.554430
$218$	−5.58594e75	−0.558805
$219$	1.23784e74	0.0106717
$220$	9.37632e75	0.697100
$221$	1.80738e76	1.15958
$222$	−5.53307e73	−0.00306545
$223$	−7.22797e75	−0.346025	−0.173013	−	0.984920i	$-0.555350\pi$
$223$	−7.22797e75	−0.346025	−0.173013	+	0.984920i	$0.555350\pi$
$224$	−3.73989e75	−0.154810
$225$	−1.11947e76	−0.400942
$226$	−3.61849e76	−1.12203
$227$	−1.73716e76	−0.466659	−0.233329	−	0.972398i	$-0.574962\pi$
$227$	−1.73716e76	−0.466659	−0.233329	+	0.972398i	$0.574962\pi$
$228$	2.99953e74	0.00698506
$229$	−5.62633e76	−1.13651	−0.568253	−	0.822854i	$-0.692380\pi$
$229$	−5.62633e76	−1.13651	−0.568253	+	0.822854i	$0.692380\pi$
$230$	−4.39922e76	−0.771296
$231$	1.26575e75	0.0192734
$232$	4.32479e76	0.572276
$233$	1.25542e77	1.44451	0.722257	−	0.691625i	$-0.243105\pi$
$233$	1.25542e77	1.44451	0.722257	+	0.691625i	$0.243105\pi$
$234$	−9.86043e76	−0.987144
$235$	1.28682e77	1.12153
$236$	5.72360e76	0.434539
$237$	1.77309e75	0.0117330
$238$	−8.90969e76	−0.514175
$239$	4.21882e74	0.00212451	0.00106226	−	0.999999i	$-0.499662\pi$
$239$	4.21882e74	0.00212451	0.00106226	+	0.999999i	$0.499662\pi$
$240$	−1.25756e75	−0.00552922
$241$	2.44072e77	0.937484	0.468742	−	0.883335i	$-0.344707\pi$
$241$	2.44072e77	0.937484	0.468742	+	0.883335i	$0.344707\pi$
$242$	8.15813e76	0.273899
$243$	−1.90816e76	−0.0560288
$244$	2.64184e77	0.678792
$245$	−1.22644e77	−0.275897
$246$	1.86068e75	0.00366675
$247$	−6.04513e77	−1.04413
$248$	1.47777e77	0.223835
$249$	−1.25561e76	−0.0166869
$250$	−4.29669e77	−0.501284
$251$	2.88535e76	0.0295667	0.0147834	−	0.999891i	$-0.495294\pi$
$251$	2.88535e76	0.0295667	0.0147834	+	0.999891i	$0.495294\pi$
$252$	4.86082e77	0.437715
$253$	−1.37093e78	−1.08542
$254$	5.09787e77	0.355053
$255$	−2.99594e76	−0.0183644
$256$	1.15792e77	0.0625000
$257$	−1.45937e78	−0.693967	−0.346983	−	0.937871i	$-0.612794\pi$
$257$	−1.45937e78	−0.693967	−0.346983	+	0.937871i	$0.612794\pi$
$258$	−4.54970e76	−0.0190696
$259$	−5.49709e77	−0.203184
$260$	2.53444e78	0.826512
$261$	−5.62102e78	−1.61807
$262$	−1.98967e78	−0.505813
$263$	5.84583e78	1.31306	0.656529	−	0.754301i	$-0.272024\pi$
$263$	5.84583e78	1.31306	0.656529	+	0.754301i	$0.272024\pi$
$264$	−3.91894e76	−0.00778110
$265$	1.12853e79	1.98163
$266$	2.98002e78	0.462984
$267$	−6.18780e76	−0.00850982
$268$	−7.23244e78	−0.880854
$269$	1.53999e79	1.66176	0.830882	−	0.556448i	$-0.187836\pi$
$269$	1.53999e79	1.66176	0.830882	+	0.556448i	$0.187836\pi$
$270$	3.26953e77	0.0312726
$271$	−1.36371e79	−1.15670	−0.578350	−	0.815789i	$-0.696303\pi$
$271$	−1.36371e79	−1.15670	−0.578350	+	0.815789i	$0.696303\pi$
$272$	2.75856e78	0.207584
$273$	3.42136e77	0.0228514
$274$	−6.54075e78	−0.387913
$275$	8.96684e78	0.472419
$276$	1.83870e77	0.00860928
$277$	−1.89058e79	−0.787049	−0.393525	−	0.919314i	$-0.628744\pi$
$277$	−1.89058e79	−0.787049	−0.393525	+	0.919314i	$0.628744\pi$
$278$	−3.20767e79	−1.18777
$279$	−1.92069e79	−0.632880
$280$	−1.24938e79	−0.366488
$281$	−1.33349e78	−0.0348364	−0.0174182	−	0.999848i	$-0.505545\pi$
$281$	−1.33349e78	−0.0348364	−0.0174182	+	0.999848i	$0.505545\pi$
$282$	−5.37840e77	−0.0125186
$283$	3.16363e79	0.656337	0.328169	−	0.944619i	$-0.393569\pi$
$283$	3.16363e79	0.656337	0.328169	+	0.944619i	$0.393569\pi$
$284$	−2.28904e79	−0.423456
$285$	1.00205e78	0.0165361
$286$	7.89808e79	1.16312
$287$	1.84858e79	0.243040
$288$	−1.50497e79	−0.176715
$289$	−2.96009e79	−0.310545
$290$	1.44478e80	1.35477
$291$	1.05331e78	0.00883145
$292$	−3.80761e79	−0.285568
$293$	−3.30606e79	−0.221878	−0.110939	−	0.993827i	$-0.535386\pi$
$293$	−3.30606e79	−0.221878	−0.110939	+	0.993827i	$0.535386\pi$
$294$	5.12603e77	0.00307959
$295$	1.91208e80	1.02870
$296$	1.70197e79	0.0820299
$297$	1.01888e79	0.0440088
$298$	8.82435e79	0.341707
$299$	−3.70566e80	−1.28692
$300$	−1.20264e78	−0.00374711
$301$	−4.52012e80	−1.26398
$302$	3.17764e80	0.797773
$303$	−1.40274e79	−0.0316296
$304$	−9.22655e79	−0.186917
$305$	8.82558e80	1.60694
$306$	−3.58536e80	−0.586930
$307$	−9.91773e80	−1.46021	−0.730105	−	0.683335i	$-0.760529\pi$
$307$	−9.91773e80	−1.46021	−0.730105	+	0.683335i	$0.760529\pi$
$308$	−3.89345e80	−0.515747
$309$	2.00911e79	0.0239526
$310$	4.93680e80	0.529895
$311$	−1.10103e80	−0.106436	−0.0532178	−	0.998583i	$-0.516948\pi$
$311$	−1.10103e80	−0.106436	−0.0532178	+	0.998583i	$0.516948\pi$
$312$	−1.05930e79	−0.00922560
$313$	−5.96098e80	−0.467871	−0.233936	−	0.972252i	$-0.575161\pi$
$313$	−5.96098e80	−0.467871	−0.233936	+	0.972252i	$0.575161\pi$
$314$	−1.57604e81	−1.11520
$315$	1.62385e81	1.03622
$316$	−5.45402e80	−0.313969
$317$	1.48481e81	0.771337	0.385669	−	0.922637i	$-0.373971\pi$
$317$	1.48481e81	0.771337	0.385669	+	0.922637i	$0.373971\pi$
$318$	−4.71682e79	−0.0221191
$319$	4.50237e81	1.90653
$320$	3.86826e80	0.147959
$321$	−8.53011e79	−0.0294809
$322$	1.82675e81	0.570641
$323$	−2.19808e81	−0.620813
$324$	1.95536e81	0.499476
$325$	2.42376e81	0.560120
$326$	−5.57469e81	−1.16587
$327$	7.79956e79	0.0147662
$328$	−5.72346e80	−0.0981202
$329$	−5.34343e81	−0.829761
$330$	−1.30920e80	−0.0184205
$331$	2.52352e81	0.321808	0.160904	−	0.986970i	$-0.448559\pi$
$331$	2.52352e81	0.321808	0.160904	+	0.986970i	$0.448559\pi$
$332$	3.86227e81	0.446534
$333$	−2.21209e81	−0.231935
$334$	−4.92232e81	−0.468177
$335$	−2.41614e82	−2.08529
$336$	5.22194e79	0.00409078
$337$	−1.43364e82	−1.01969	−0.509847	−	0.860265i	$-0.670298\pi$
$337$	−1.43364e82	−1.01969	−0.509847	+	0.860265i	$0.670298\pi$
$338$	1.04022e82	0.671941
$339$	5.05244e80	0.0296491
$340$	9.21551e81	0.491422
$341$	1.53845e82	0.745704
$342$	1.19919e82	0.528495
$343$	2.69417e82	1.07986
$344$	1.39949e82	0.510294
$345$	6.14256e80	0.0203811
$346$	−1.50629e82	−0.454921
$347$	−1.89767e82	−0.521809	−0.260905	−	0.965365i	$-0.584021\pi$
$347$	−1.89767e82	−0.521809	−0.260905	+	0.965365i	$0.584021\pi$
$348$	−6.03862e80	−0.0151221
$349$	3.16407e82	0.721804	0.360902	−	0.932604i	$-0.382469\pi$
$349$	3.16407e82	0.721804	0.360902	+	0.932604i	$0.382469\pi$
$350$	−1.19482e82	−0.248366
$351$	2.75407e81	0.0521788
$352$	1.20547e82	0.208218
$353$	2.60873e82	0.410914	0.205457	−	0.978666i	$-0.434132\pi$
$353$	2.60873e82	0.410914	0.205457	+	0.978666i	$0.434132\pi$
$354$	−7.99176e80	−0.0114825
$355$	−7.64700e82	−1.00247
$356$	1.90337e82	0.227718
$357$	1.24404e81	0.0135868
$358$	−4.57929e82	−0.456667
$359$	1.09989e83	1.00180	0.500898	−	0.865506i	$-0.333003\pi$
$359$	1.09989e83	1.00180	0.500898	+	0.865506i	$0.333003\pi$
$360$	−5.02767e82	−0.418346
$361$	−5.79987e82	−0.440995
$362$	−9.53249e82	−0.662488
$363$	−1.13910e81	−0.00723766
$364$	−1.05241e83	−0.611492
$365$	−1.27201e83	−0.676038
$366$	−3.68875e81	−0.0179368
$367$	3.48544e83	1.55100	0.775499	−	0.631349i	$-0.217498\pi$
$367$	3.48544e83	1.55100	0.775499	+	0.631349i	$0.217498\pi$
$368$	−5.65586e82	−0.230380
$369$	7.43890e82	0.277429
$370$	5.68578e82	0.194193
$371$	−4.68615e83	−1.46610
$372$	−2.06339e81	−0.00591474
$373$	−1.04070e83	−0.273393	−0.136696	−	0.990613i	$-0.543649\pi$
$373$	−1.04070e83	−0.273393	−0.136696	+	0.990613i	$0.543649\pi$
$374$	2.87183e83	0.691562
$375$	5.99940e81	0.0132462
$376$	1.65440e83	0.334992
$377$	1.21700e84	2.26046
$378$	−1.35765e82	−0.0231369
$379$	−5.07951e83	−0.794415	−0.397207	−	0.917729i	$-0.630021\pi$
$379$	−5.07951e83	−0.794415	−0.397207	+	0.917729i	$0.630021\pi$
$380$	−3.08231e83	−0.442496
$381$	−7.11806e81	−0.00938210
$382$	8.85720e83	1.07211
$383$	1.28354e84	1.42709	0.713543	−	0.700611i	$-0.247089\pi$
$383$	1.28354e84	1.42709	0.713543	+	0.700611i	$0.247089\pi$
$384$	−1.61678e81	−0.00165153
$385$	−1.30069e84	−1.22095
$386$	5.64667e83	0.487198
$387$	−1.81895e84	−1.44282
$388$	−3.23997e83	−0.236325
$389$	−9.01988e83	−0.605116	−0.302558	−	0.953131i	$-0.597841\pi$
$389$	−9.01988e83	−0.605116	−0.302558	+	0.953131i	$0.597841\pi$
$390$	−3.53880e82	−0.0218402
$391$	−1.34742e84	−0.765169
$392$	−1.57677e83	−0.0824083
$393$	2.77815e82	0.0133659
$394$	1.18308e84	0.524068
$395$	−1.82203e84	−0.743274
$396$	−1.56677e84	−0.588724
$397$	1.49859e84	0.518790	0.259395	−	0.965771i	$-0.416477\pi$
$397$	1.49859e84	0.518790	0.259395	+	0.965771i	$0.416477\pi$
$398$	−1.78976e84	−0.570947
$399$	−4.16095e82	−0.0122341
$400$	3.69933e83	0.100271
$401$	3.35632e84	0.838824	0.419412	−	0.907796i	$-0.362236\pi$
$401$	3.35632e84	0.838824	0.419412	+	0.907796i	$0.362236\pi$
$402$	1.00985e83	0.0232762
$403$	4.15848e84	0.884139
$404$	4.31485e84	0.846391
$405$	6.53228e84	1.18243
$406$	−5.99936e84	−1.00233
$407$	1.77186e84	0.273282
$408$	−3.85173e82	−0.00548530
$409$	1.09506e83	0.0144022	0.00720111	−	0.999974i	$-0.497708\pi$
$409$	1.09506e83	0.0144022	0.00720111	+	0.999974i	$0.497708\pi$
$410$	−1.91203e84	−0.232285
$411$	9.13273e82	0.0102504
$412$	−6.18001e84	−0.640959
$413$	−7.93979e84	−0.761084
$414$	7.35104e84	0.651385
$415$	1.29027e85	1.05710
$416$	3.25841e84	0.246872
$417$	4.47881e83	0.0313864
$418$	−9.60540e84	−0.622710
$419$	−2.41999e85	−1.45164	−0.725819	−	0.687886i	$-0.758539\pi$
$419$	−2.41999e85	−1.45164	−0.725819	+	0.687886i	$0.758539\pi$
$420$	1.74449e83	0.00968429
$421$	1.93571e85	0.994652	0.497326	−	0.867564i	$-0.334315\pi$
$421$	1.93571e85	0.994652	0.497326	+	0.867564i	$0.334315\pi$
$422$	−2.17137e85	−1.03295
$423$	−2.15026e85	−0.947170
$424$	1.45089e85	0.591896
$425$	8.81306e84	0.333032
$426$	3.19615e83	0.0111896
$427$	−3.66476e85	−1.18889
$428$	2.62386e85	0.788894
$429$	−1.10280e84	−0.0307350
$430$	4.67527e85	1.20804
$431$	−4.95409e85	−1.18701	−0.593503	−	0.804832i	$-0.702256\pi$
$431$	−4.95409e85	−1.18701	−0.593503	+	0.804832i	$0.702256\pi$
$432$	4.20347e83	0.00934085
$433$	3.73826e85	0.770572	0.385286	−	0.922797i	$-0.374103\pi$
$433$	3.73826e85	0.770572	0.385286	+	0.922797i	$0.374103\pi$
$434$	−2.04997e85	−0.392041
$435$	−2.01732e84	−0.0357993
$436$	−2.39915e85	−0.395135
$437$	4.50670e85	0.688989
$438$	5.31650e83	0.00754600
$439$	−5.95537e84	−0.0784896	−0.0392448	−	0.999230i	$-0.512495\pi$
$439$	−5.95537e84	−0.0784896	−0.0392448	+	0.999230i	$0.512495\pi$
$440$	4.02710e85	0.492924
$441$	2.04936e85	0.233004
$442$	7.76263e85	0.819946
$443$	6.36424e85	0.624633	0.312317	−	0.949978i	$-0.398895\pi$
$443$	6.36424e85	0.624633	0.312317	+	0.949978i	$0.398895\pi$
$444$	−2.37644e83	−0.00216760
$445$	6.35858e85	0.539088
$446$	−3.10439e85	−0.244677
$447$	−1.23213e84	−0.00902945
$448$	−1.60627e85	−0.109467
$449$	−1.44527e86	−0.916099	−0.458049	−	0.888927i	$-0.651452\pi$
$449$	−1.44527e86	−0.916099	−0.458049	+	0.888927i	$0.651452\pi$
$450$	−4.80810e85	−0.283509
$451$	−5.95847e85	−0.326886
$452$	−1.55413e86	−0.793393
$453$	−4.43688e84	−0.0210808
$454$	−7.46105e85	−0.329978
$455$	−3.51579e86	−1.44761
$456$	1.28829e84	0.00493918
$457$	3.55013e86	1.26756	0.633779	−	0.773514i	$-0.281503\pi$
$457$	3.55013e86	1.26756	0.633779	+	0.773514i	$0.281503\pi$
$458$	−2.41649e86	−0.803631
$459$	1.00141e85	0.0310241
$460$	−1.88945e86	−0.545389
$461$	7.06618e86	1.90066	0.950331	−	0.311242i	$-0.100745\pi$
$461$	7.06618e86	1.90066	0.950331	+	0.311242i	$0.100745\pi$
$462$	5.43636e84	0.0136284
$463$	−4.99355e86	−1.16688	−0.583441	−	0.812156i	$-0.698294\pi$
$463$	−4.99355e86	−1.16688	−0.583441	+	0.812156i	$0.698294\pi$
$464$	1.85748e86	0.404660
$465$	−6.89316e84	−0.0140022
$466$	5.39199e86	1.02143
$467$	−3.76528e86	−0.665271	−0.332636	−	0.943055i	$-0.607938\pi$
$467$	−3.76528e86	−0.665271	−0.332636	+	0.943055i	$0.607938\pi$
$468$	−4.23502e86	−0.698016
$469$	1.00329e87	1.54279
$470$	5.52684e86	0.793043
$471$	2.20060e85	0.0294688
$472$	2.45827e86	0.307266
$473$	1.45695e87	1.70004
$474$	7.61536e84	0.00829649
$475$	−2.94770e86	−0.299876
$476$	−3.82668e86	−0.363577
$477$	−1.88576e87	−1.67355
$478$	1.81197e84	0.00150226
$479$	−1.87445e87	−1.45201	−0.726005	−	0.687690i	$-0.758625\pi$
$479$	−1.87445e87	−1.45201	−0.726005	+	0.687690i	$0.758625\pi$
$480$	−5.40119e84	−0.00390975
$481$	4.78938e86	0.324014
$482$	1.04828e87	0.662901
$483$	−2.55066e85	−0.0150789
$484$	3.50389e86	0.193676
$485$	−1.08238e87	−0.559463
$486$	−8.19549e85	−0.0396184
$487$	−1.55783e87	−0.704415	−0.352207	−	0.935922i	$-0.614569\pi$
$487$	−1.55783e87	−0.704415	−0.352207	+	0.935922i	$0.614569\pi$
$488$	1.13466e87	0.479978
$489$	7.78384e85	0.0308075
$490$	−5.26751e86	−0.195089
$491$	−1.38973e87	−0.481705	−0.240853	−	0.970562i	$-0.577427\pi$
$491$	−1.38973e87	−0.481705	−0.240853	+	0.970562i	$0.577427\pi$
$492$	7.99156e84	0.00259278
$493$	4.42515e87	1.34401
$494$	−2.59637e87	−0.738312
$495$	−5.23411e87	−1.39371
$496$	6.34699e86	0.158275
$497$	3.17537e87	0.741671
$498$	−5.39281e85	−0.0117995
$499$	6.72159e87	1.37786	0.688929	−	0.724829i	$-0.258081\pi$
$499$	6.72159e87	1.37786	0.688929	+	0.724829i	$0.258081\pi$
$500$	−1.84542e87	−0.354461
$501$	6.87295e85	0.0123714
$502$	1.23925e86	0.0209068
$503$	−5.91204e87	−0.934927	−0.467463	−	0.884012i	$-0.654832\pi$
$503$	−5.91204e87	−0.934927	−0.467463	+	0.884012i	$0.654832\pi$
$504$	2.08771e87	0.309511
$505$	1.44146e88	2.00370
$506$	−5.88809e87	−0.767508
$507$	−1.45244e86	−0.0177557
$508$	2.18952e87	0.251060
$509$	4.26210e87	0.458454	0.229227	−	0.973373i	$-0.426380\pi$
$509$	4.26210e87	0.458454	0.229227	+	0.973373i	$0.426380\pi$
$510$	−1.28675e86	−0.0129856
$511$	5.28192e87	0.500165
$512$	4.97323e86	0.0441942
$513$	−3.34941e86	−0.0279354
$514$	−6.26794e87	−0.490709
$515$	−2.06456e88	−1.51737
$516$	−1.95408e86	−0.0134843
$517$	1.72233e88	1.11602
$518$	−2.36098e87	−0.143673
$519$	2.10321e86	0.0120211
$520$	1.08854e88	0.584432
$521$	−2.84292e88	−1.43397	−0.716983	−	0.697091i	$-0.754478\pi$
$521$	−2.84292e88	−1.43397	−0.716983	+	0.697091i	$0.754478\pi$
$522$	−2.41421e88	−1.14415
$523$	−2.96021e88	−1.31831	−0.659155	−	0.752007i	$-0.729086\pi$
$523$	−2.96021e88	−1.31831	−0.659155	+	0.752007i	$0.729086\pi$
$524$	−8.54558e87	−0.357664
$525$	1.66831e86	0.00656295
$526$	2.51076e88	0.928472
$527$	1.51207e88	0.525686
$528$	−1.68317e86	−0.00550207
$529$	−4.90588e87	−0.150802
$530$	4.84700e88	1.40122
$531$	−3.19506e88	−0.868775
$532$	1.27991e88	0.327379
$533$	−1.61059e88	−0.387570
$534$	−2.65764e86	−0.00601735
$535$	8.76553e88	1.86759
$536$	−3.10631e88	−0.622858
$537$	6.39398e86	0.0120672
$538$	6.61422e88	1.17505
$539$	−1.64151e88	−0.274542
$540$	1.40425e87	0.0221130
$541$	1.13474e89	1.68262	0.841308	−	0.540555i	$-0.181786\pi$
$541$	1.13474e89	1.68262	0.841308	+	0.540555i	$0.181786\pi$
$542$	−5.85710e88	−0.817911
$543$	1.33100e87	0.0175059
$544$	1.18479e88	0.146784
$545$	−8.01482e88	−0.935422
$546$	1.46946e87	0.0161584
$547$	2.38093e88	0.246694	0.123347	−	0.992364i	$-0.460637\pi$
$547$	2.38093e88	0.246694	0.123347	+	0.992364i	$0.460637\pi$
$548$	−2.80923e88	−0.274296
$549$	−1.47474e89	−1.35711
$550$	3.85123e88	0.334050
$551$	−1.48008e89	−1.21020
$552$	7.89718e86	0.00608768
$553$	7.56584e88	0.549908
$554$	−8.11997e88	−0.556528
$555$	−7.93895e86	−0.00513146
$556$	−1.37768e89	−0.839883
$557$	9.44222e88	0.542976	0.271488	−	0.962442i	$-0.412484\pi$
$557$	9.44222e88	0.542976	0.271488	+	0.962442i	$0.412484\pi$
$558$	−8.24932e88	−0.447514
$559$	3.93819e89	2.01564
$560$	−5.36607e88	−0.259146
$561$	−4.00988e87	−0.0182742
$562$	−5.72728e87	−0.0246330
$563$	8.69509e88	0.352981	0.176491	−	0.984302i	$-0.443525\pi$
$563$	8.69509e88	0.352981	0.176491	+	0.984302i	$0.443525\pi$
$564$	−2.31001e87	−0.00885202
$565$	−5.19188e89	−1.87824
$566$	1.35877e89	0.464101
$567$	−2.71249e89	−0.874819
$568$	−9.83136e88	−0.299428
$569$	4.74930e89	1.36609	0.683047	−	0.730374i	$-0.260654\pi$
$569$	4.74930e89	1.36609	0.683047	+	0.730374i	$0.260654\pi$
$570$	4.30378e87	0.0116928
$571$	6.64779e89	1.70610	0.853048	−	0.521832i	$-0.174751\pi$
$571$	6.64779e89	1.70610	0.853048	+	0.521832i	$0.174751\pi$
$572$	3.39220e89	0.822452
$573$	−1.23672e88	−0.0283299
$574$	7.93960e88	0.171855
$575$	−1.80694e89	−0.369605
$576$	−6.46382e88	−0.124956
$577$	−4.40512e89	−0.804904	−0.402452	−	0.915441i	$-0.631842\pi$
$577$	−4.40512e89	−0.804904	−0.402452	+	0.915441i	$0.631842\pi$
$578$	−1.27135e89	−0.219589
$579$	−7.88435e87	−0.0128740
$580$	6.20529e89	0.957970
$581$	−5.35775e89	−0.782092
$582$	4.52391e87	0.00624478
$583$	1.51047e90	1.97190
$584$	−1.63536e89	−0.201927
$585$	−1.41479e90	−1.65245
$586$	−1.41994e89	−0.156891
$587$	−8.05465e88	−0.0841993	−0.0420996	−	0.999113i	$-0.513405\pi$
$587$	−8.05465e88	−0.0841993	−0.0420996	+	0.999113i	$0.513405\pi$
$588$	2.20161e87	0.00217760
$589$	−5.05741e89	−0.473349
$590$	8.21233e89	0.727404
$591$	−1.65192e88	−0.0138483
$592$	7.30992e88	0.0580039
$593$	−1.76930e90	−1.32900	−0.664498	−	0.747290i	$-0.731355\pi$
$593$	−1.76930e90	−1.32900	−0.664498	+	0.747290i	$0.731355\pi$
$594$	4.37607e88	0.0311189
$595$	−1.27838e90	−0.860713
$596$	3.79003e89	0.241623
$597$	2.49902e88	0.0150870
$598$	−1.59157e90	−0.909990
$599$	−1.22753e90	−0.664752	−0.332376	−	0.943147i	$-0.607850\pi$
$599$	−1.22753e90	−0.664752	−0.332376	+	0.943147i	$0.607850\pi$
$600$	−5.16531e87	−0.00264960
$601$	2.40139e90	1.16692	0.583462	−	0.812141i	$-0.301698\pi$
$601$	2.40139e90	1.16692	0.583462	+	0.812141i	$0.301698\pi$
$602$	−1.94138e90	−0.893766
$603$	4.03734e90	1.76109
$604$	1.36479e90	0.564111
$605$	1.17054e90	0.458498
$606$	−6.02474e88	−0.0223655
$607$	1.94700e90	0.685067	0.342533	−	0.939506i	$-0.388715\pi$
$607$	1.94700e90	0.685067	0.342533	+	0.939506i	$0.388715\pi$
$608$	−3.96277e89	−0.132170
$609$	8.37680e88	0.0264860
$610$	3.79056e90	1.13627
$611$	4.65550e90	1.32320
$612$	−1.53990e90	−0.415022
$613$	−2.45284e90	−0.626908	−0.313454	−	0.949603i	$-0.601486\pi$
$613$	−2.45284e90	−0.626908	−0.313454	+	0.949603i	$0.601486\pi$
$614$	−4.25963e90	−1.03252
$615$	2.66974e88	0.00613801
$616$	−1.67223e90	−0.364688
$617$	1.74358e88	0.00360724	0.00180362	−	0.999998i	$-0.499426\pi$
$617$	1.74358e88	0.00360724	0.00180362	+	0.999998i	$0.499426\pi$
$618$	8.62905e88	0.0169370
$619$	6.02420e88	0.0112190	0.00560949	−	0.999984i	$-0.498214\pi$
$619$	6.02420e88	0.0112190	0.00560949	+	0.999984i	$0.498214\pi$
$620$	2.12034e90	0.374693
$621$	−2.05318e89	−0.0344311
$622$	−4.72889e89	−0.0752613
$623$	−2.64036e90	−0.398842
$624$	−4.54966e88	−0.00652348
$625$	−9.11166e90	−1.24022
$626$	−2.56022e90	−0.330835
$627$	1.34118e89	0.0164548
$628$	−6.76905e90	−0.788569
$629$	1.74147e90	0.192650
$630$	6.97439e90	0.732721
$631$	−1.14551e91	−1.14300	−0.571500	−	0.820602i	$-0.693638\pi$
$631$	−1.14551e91	−1.14300	−0.571500	+	0.820602i	$0.693638\pi$
$632$	−2.34249e90	−0.222010
$633$	3.03185e89	0.0272952
$634$	6.37720e90	0.545418
$635$	7.31452e90	0.594346
$636$	−2.02586e89	−0.0156406
$637$	−4.43705e90	−0.325509
$638$	1.93375e91	1.34812
$639$	1.27780e91	0.846615
$640$	1.66141e90	0.104623
$641$	−7.44725e90	−0.445769	−0.222884	−	0.974845i	$-0.571547\pi$
$641$	−7.44725e90	−0.445769	−0.222884	+	0.974845i	$0.571547\pi$
$642$	−3.66365e89	−0.0208462
$643$	−6.61650e90	−0.357908	−0.178954	−	0.983857i	$-0.557271\pi$
$643$	−6.61650e90	−0.357908	−0.178954	+	0.983857i	$0.557271\pi$
$644$	7.84582e90	0.403504
$645$	−6.52800e89	−0.0319220
$646$	−9.44066e90	−0.438981
$647$	−1.44244e91	−0.637837	−0.318919	−	0.947782i	$-0.603320\pi$
$647$	−1.44244e91	−0.637837	−0.318919	+	0.947782i	$0.603320\pi$
$648$	8.39823e90	0.353183
$649$	2.55920e91	1.02365
$650$	1.04100e91	0.396064
$651$	2.86234e89	0.0103595
$652$	−2.39431e91	−0.824391
$653$	4.47335e91	1.46539	0.732697	−	0.680555i	$-0.238261\pi$
$653$	4.47335e91	1.46539	0.732697	+	0.680555i	$0.238261\pi$
$654$	3.34988e89	0.0104413
$655$	−2.85482e91	−0.846714
$656$	−2.45821e90	−0.0693815
$657$	2.12551e91	0.570937
$658$	−2.29498e91	−0.586730
$659$	−4.58143e91	−1.11487	−0.557437	−	0.830220i	$-0.688215\pi$
$659$	−4.58143e91	−1.11487	−0.557437	+	0.830220i	$0.688215\pi$
$660$	−5.62297e89	−0.0130253
$661$	−1.32901e90	−0.0293076	−0.0146538	−	0.999893i	$-0.504665\pi$
$661$	−1.32901e90	−0.0293076	−0.0146538	+	0.999893i	$0.504665\pi$
$662$	1.08384e91	0.227553
$663$	−1.08388e90	−0.0216667
$664$	1.65883e91	0.315747
$665$	4.27579e91	0.775020
$666$	−9.50086e90	−0.164003
$667$	−9.07286e91	−1.49161
$668$	−2.11412e91	−0.331051
$669$	4.33460e89	0.00646547
$670$	−1.03772e92	−1.47452
$671$	1.18125e92	1.59904
$672$	2.24281e89	0.00289262
$673$	−7.07428e91	−0.869346	−0.434673	−	0.900588i	$-0.643136\pi$
$673$	−7.07428e91	−0.869346	−0.434673	+	0.900588i	$0.643136\pi$
$674$	−6.15746e91	−0.721032
$675$	1.34293e90	0.0149858
$676$	4.46770e91	0.475134
$677$	6.67838e91	0.676923	0.338462	−	0.940980i	$-0.390093\pi$
$677$	6.67838e91	0.676923	0.338462	+	0.940980i	$0.390093\pi$
$678$	2.17001e90	0.0209650
$679$	4.49449e91	0.413917
$680$	3.95803e91	0.347488
$681$	1.04177e90	0.00871951
$682$	6.60760e91	0.527293
$683$	4.87503e91	0.370940	0.185470	−	0.982650i	$-0.440619\pi$
$683$	4.87503e91	0.370940	0.185470	+	0.982650i	$0.440619\pi$
$684$	5.15050e91	0.373703
$685$	−9.38479e91	−0.649353
$686$	1.15714e92	0.763575
$687$	3.37410e90	0.0212356
$688$	6.01076e91	0.360832
$689$	4.08284e92	2.33796
$690$	2.63821e90	0.0144116
$691$	−3.71186e92	−1.93444	−0.967219	−	0.253942i	$-0.918273\pi$
$691$	−3.71186e92	−1.93444	−0.967219	+	0.253942i	$0.918273\pi$
$692$	−6.46947e91	−0.321678
$693$	2.17343e92	1.03113
$694$	−8.15041e91	−0.368975
$695$	−4.60243e92	−1.98829
$696$	−2.59357e90	−0.0106930
$697$	−5.85628e91	−0.230439
$698$	1.35896e92	0.510393
$699$	−7.52874e90	−0.0269907
$700$	−5.13172e91	−0.175621
$701$	−2.74620e92	−0.897215	−0.448607	−	0.893729i	$-0.648080\pi$
$701$	−2.74620e92	−0.897215	−0.448607	+	0.893729i	$0.648080\pi$
$702$	1.18286e91	0.0368960
$703$	−5.82469e91	−0.173470
$704$	5.17744e91	0.147232
$705$	−7.71703e90	−0.0209558
$706$	1.12044e92	0.290560
$707$	−5.98557e92	−1.48243
$708$	−3.43243e90	−0.00811935
$709$	1.02253e92	0.231034	0.115517	−	0.993306i	$-0.463148\pi$
$709$	1.02253e92	0.231034	0.115517	+	0.993306i	$0.463148\pi$
$710$	−3.28436e92	−0.708851
$711$	3.04458e92	0.627719
$712$	8.17491e91	0.161021
$713$	−3.10018e92	−0.583415
$714$	5.34313e90	0.00960735
$715$	1.13323e93	1.94703
$716$	−1.96679e92	−0.322912
$717$	−2.53002e88	−3.96964e−5 0
$718$	4.72399e92	0.708377
$719$	7.48312e92	1.07249	0.536246	−	0.844062i	$-0.319842\pi$
$719$	7.48312e92	1.07249	0.536246	+	0.844062i	$0.319842\pi$
$720$	−2.15937e92	−0.295815
$721$	8.57293e92	1.12262
$722$	−2.49102e92	−0.311831
$723$	−1.46370e91	−0.0175169
$724$	−4.09417e92	−0.468450
$725$	5.93429e92	0.649208
$726$	−4.89242e90	−0.00511780
$727$	−1.16463e93	−1.16498	−0.582491	−	0.812837i	$-0.697922\pi$
$727$	−1.16463e93	−1.16498	−0.582491	+	0.812837i	$0.697922\pi$
$728$	−4.52007e92	−0.432390
$729$	−1.09077e93	−0.997906
$730$	−5.46323e92	−0.478031
$731$	1.43197e93	1.19845
$732$	−1.58431e91	−0.0126832
$733$	1.03316e93	0.791202	0.395601	−	0.918422i	$-0.370536\pi$
$733$	1.03316e93	0.791202	0.395601	+	0.918422i	$0.370536\pi$
$734$	1.49699e93	1.09672
$735$	7.35493e90	0.00515513
$736$	−2.42917e92	−0.162903
$737$	−3.23386e93	−2.07505
$738$	3.19498e92	0.196172
$739$	1.38903e93	0.816145	0.408073	−	0.912950i	$-0.366201\pi$
$739$	1.38903e93	0.816145	0.408073	+	0.912950i	$0.366201\pi$
$740$	2.44202e92	0.137315
$741$	3.62526e91	0.0195096
$742$	−2.01269e93	−1.03669
$743$	−9.21979e92	−0.454553	−0.227277	−	0.973830i	$-0.572982\pi$
$743$	−9.21979e92	−0.454553	−0.227277	+	0.973830i	$0.572982\pi$
$744$	−8.86219e90	−0.00418235
$745$	1.26613e93	0.572006
$746$	−4.46976e92	−0.193318
$747$	−2.15602e93	−0.892756
$748$	1.23344e93	0.489008
$749$	−3.63983e93	−1.38173
$750$	2.57672e91	0.00936648
$751$	−1.44158e93	−0.501811	−0.250906	−	0.968012i	$-0.580728\pi$
$751$	−1.44158e93	−0.501811	−0.250906	+	0.968012i	$0.580728\pi$
$752$	7.10558e92	0.236875
$753$	−1.73034e90	−0.000552453 0
$754$	5.22698e93	1.59839
$755$	4.55934e93	1.33545
$756$	−5.83107e91	−0.0163603
$757$	−4.15048e92	−0.111553	−0.0557766	−	0.998443i	$-0.517763\pi$
$757$	−4.15048e92	−0.111553	−0.0557766	+	0.998443i	$0.517763\pi$
$758$	−2.18163e93	−0.561736
$759$	8.22144e91	0.0202810
$760$	−1.32384e93	−0.312892
$761$	−3.28716e93	−0.744423	−0.372212	−	0.928148i	$-0.621400\pi$
$761$	−3.28716e93	−0.744423	−0.372212	+	0.928148i	$0.621400\pi$
$762$	−3.05718e91	−0.00663415
$763$	3.32810e93	0.692068
$764$	3.80414e93	0.758093
$765$	−5.14434e93	−0.982501
$766$	5.51277e93	1.00910
$767$	6.91760e93	1.21369
$768$	−6.94404e90	−0.00116781
$769$	8.33371e93	1.34348	0.671741	−	0.740786i	$-0.265547\pi$
$769$	8.33371e93	1.34348	0.671741	+	0.740786i	$0.265547\pi$
$770$	−5.58640e93	−0.863343
$771$	8.75182e91	0.0129667
$772$	2.42523e93	0.344501
$773$	−1.30793e93	−0.178135	−0.0890676	−	0.996026i	$-0.528389\pi$
$773$	−1.30793e93	−0.178135	−0.0890676	+	0.996026i	$0.528389\pi$
$774$	−7.81232e93	−1.02023
$775$	2.02774e93	0.253926
$776$	−1.39156e93	−0.167107
$777$	3.29660e91	0.00379650
$778$	−3.87401e93	−0.427882
$779$	1.95875e93	0.207497
$780$	−1.51990e92	−0.0154433
$781$	−1.02350e94	−0.997542
$782$	−5.78711e93	−0.541056
$783$	6.74301e92	0.0604779
$784$	−6.77217e92	−0.0582714
$785$	−2.26134e94	−1.86682
$786$	1.19320e92	0.00945110
$787$	−8.71435e93	−0.662303	−0.331151	−	0.943578i	$-0.607437\pi$
$787$	−8.71435e93	−0.662303	−0.331151	+	0.943578i	$0.607437\pi$
$788$	5.08130e93	0.370572
$789$	−3.50573e92	−0.0245345
$790$	−7.82554e93	−0.525574
$791$	2.15590e94	1.38961
$792$	−6.72923e93	−0.416291
$793$	3.19295e94	1.89589
$794$	6.43640e93	0.366840
$795$	−6.76778e92	−0.0370267
$796$	−7.68698e93	−0.403721
$797$	−4.61864e92	−0.0232873	−0.0116436	−	0.999932i	$-0.503706\pi$
$797$	−4.61864e92	−0.0232873	−0.0116436	+	0.999932i	$0.503706\pi$
$798$	−1.78711e92	−0.00865084
$799$	1.69279e94	0.786743
$800$	1.58885e93	0.0709020
$801$	−1.06251e94	−0.455278
$802$	1.44153e94	0.593138
$803$	−1.70250e94	−0.672718
$804$	4.33729e92	0.0164587
$805$	2.62105e94	0.955234
$806$	1.78605e94	0.625181
$807$	−9.23532e92	−0.0310500
$808$	1.85321e94	0.598489
$809$	2.29584e93	0.0712222	0.0356111	−	0.999366i	$-0.488662\pi$
$809$	2.29584e93	0.0712222	0.0356111	+	0.999366i	$0.488662\pi$
$810$	2.80559e94	0.836107
$811$	−2.52337e94	−0.722443	−0.361221	−	0.932480i	$-0.617640\pi$
$811$	−2.52337e94	−0.722443	−0.361221	+	0.932480i	$0.617640\pi$
$812$	−2.57670e94	−0.708751
$813$	8.17817e92	0.0216129
$814$	7.61007e93	0.193239
$815$	−7.99867e94	−1.95162
$816$	−1.65430e92	−0.00387869
$817$	−4.78950e94	−1.07913
$818$	4.70324e92	0.0101839
$819$	5.87484e94	1.22256
$820$	−8.21212e93	−0.164250
$821$	4.18490e94	0.804513	0.402256	−	0.915527i	$-0.368226\pi$
$821$	4.18490e94	0.804513	0.402256	+	0.915527i	$0.368226\pi$
$822$	3.92248e92	0.00724814
$823$	−3.08588e94	−0.548130	−0.274065	−	0.961711i	$-0.588368\pi$
$823$	−3.08588e94	−0.548130	−0.274065	+	0.961711i	$0.588368\pi$
$824$	−2.65430e94	−0.453226
$825$	−5.37740e92	−0.00882713
$826$	−3.41011e94	−0.538167
$827$	−3.35046e94	−0.508365	−0.254183	−	0.967156i	$-0.581806\pi$
$827$	−3.35046e94	−0.508365	−0.254183	+	0.967156i	$0.581806\pi$
$828$	3.15725e94	0.460599
$829$	−1.17006e94	−0.164129	−0.0820647	−	0.996627i	$-0.526151\pi$
$829$	−1.17006e94	−0.164129	−0.0820647	+	0.996627i	$0.526151\pi$
$830$	5.54165e94	0.747483
$831$	1.13378e93	0.0147060
$832$	1.39948e94	0.174565
$833$	−1.61336e94	−0.193539
$834$	1.92364e93	0.0221935
$835$	−7.06264e94	−0.783712
$836$	−4.12549e94	−0.440323
$837$	2.30408e93	0.0236548
$838$	−1.03938e95	−1.02646
$839$	1.14354e95	1.08639	0.543196	−	0.839606i	$-0.317214\pi$
$839$	1.14354e95	1.08639	0.543196	+	0.839606i	$0.317214\pi$
$840$	7.49255e92	0.00684782
$841$	1.84240e95	1.62000
$842$	8.31379e94	0.703325
$843$	7.99689e91	0.000650916 0
$844$	−9.32597e94	−0.730406
$845$	1.49252e95	1.12481
$846$	−9.23528e94	−0.669751
$847$	−4.86060e94	−0.339218
$848$	6.23155e94	0.418534
$849$	−1.89723e93	−0.0122636
$850$	3.78518e94	0.235489
$851$	−3.57053e94	−0.213807
$852$	1.37274e93	0.00791225
$853$	3.68714e94	0.204572	0.102286	−	0.994755i	$-0.467384\pi$
$853$	3.68714e94	0.204572	0.102286	+	0.994755i	$0.467384\pi$
$854$	−1.57400e95	−0.840669
$855$	1.72063e95	0.884684
$856$	1.12694e95	0.557832
$857$	2.89800e95	1.38109	0.690545	−	0.723289i	$-0.257371\pi$
$857$	2.89800e95	1.38109	0.690545	+	0.723289i	$0.257371\pi$
$858$	−4.73647e93	−0.0217329
$859$	−3.64352e95	−1.60969	−0.804847	−	0.593482i	$-0.797753\pi$
$859$	−3.64352e95	−1.60969	−0.804847	+	0.593482i	$0.797753\pi$
$860$	2.00801e95	0.854215
$861$	−1.10859e93	−0.00454119
$862$	−2.12777e95	−0.839340
$863$	−1.70592e95	−0.648049	−0.324024	−	0.946049i	$-0.605036\pi$
$863$	−1.70592e95	−0.648049	−0.324024	+	0.946049i	$0.605036\pi$
$864$	1.80538e93	0.00660498
$865$	−2.16126e95	−0.761523
$866$	1.60557e95	0.544877
$867$	1.77516e93	0.00580253
$868$	−8.80456e94	−0.277215
$869$	−2.43867e95	−0.739623
$870$	−8.66433e93	−0.0253139
$871$	−8.74121e95	−2.46026
$872$	−1.03042e95	−0.279403
$873$	1.80864e95	0.472485
$874$	1.93561e95	0.487189
$875$	2.55997e95	0.620829
$876$	2.28342e93	0.00533583
$877$	1.13332e95	0.255192	0.127596	−	0.991826i	$-0.459274\pi$
$877$	1.13332e95	0.255192	0.127596	+	0.991826i	$0.459274\pi$
$878$	−2.55781e94	−0.0555005
$879$	1.98264e93	0.00414577
$880$	1.72963e95	0.348550
$881$	3.46490e94	0.0672936	0.0336468	−	0.999434i	$-0.489288\pi$
$881$	3.46490e94	0.0672936	0.0336468	+	0.999434i	$0.489288\pi$
$882$	8.80193e94	0.164759
$883$	3.54449e95	0.639486	0.319743	−	0.947504i	$-0.396403\pi$
$883$	3.54449e95	0.639486	0.319743	+	0.947504i	$0.396403\pi$
$884$	3.33402e95	0.579789
$885$	−1.14667e94	−0.0192213
$886$	2.73342e95	0.441683
$887$	5.03084e95	0.783651	0.391825	−	0.920040i	$-0.371844\pi$
$887$	5.03084e95	0.783651	0.391825	+	0.920040i	$0.371844\pi$
$888$	−1.02067e93	−0.00153273
$889$	−3.03730e95	−0.439725
$890$	2.73099e95	0.381193
$891$	8.74306e95	1.17663
$892$	−1.33332e95	−0.173013
$893$	−5.66187e95	−0.708415
$894$	−5.29195e93	−0.00638479
$895$	−6.57045e95	−0.764445
$896$	−6.89888e94	−0.0774049
$897$	2.22228e94	0.0240461
$898$	−6.20738e95	−0.647780
$899$	1.01815e96	1.02476
$900$	−2.06506e95	−0.200471
$901$	1.48456e96	1.39009
$902$	−2.55914e95	−0.231144
$903$	2.71071e94	0.0236173
$904$	−6.67494e95	−0.561014
$905$	−1.36774e96	−1.10898
$906$	−1.90563e94	−0.0149064
$907$	1.61526e95	0.121900	0.0609502	−	0.998141i	$-0.480587\pi$
$907$	1.61526e95	0.121900	0.0609502	+	0.998141i	$0.480587\pi$
$908$	−3.20450e95	−0.233329
$909$	−2.40866e96	−1.69219
$910$	−1.51002e96	−1.02362
$911$	−1.33150e96	−0.870953	−0.435476	−	0.900200i	$-0.643420\pi$
$911$	−1.33150e96	−0.870953	−0.435476	+	0.900200i	$0.643420\pi$
$912$	5.53315e93	0.00349253
$913$	1.72694e96	1.05191
$914$	1.52477e96	0.896298
$915$	−5.29269e94	−0.0300255
$916$	−1.03787e96	−0.568253
$917$	1.18545e96	0.626438
$918$	4.30102e94	0.0219374
$919$	2.82457e96	1.39058	0.695292	−	0.718727i	$-0.255275\pi$
$919$	2.82457e96	1.39058	0.695292	+	0.718727i	$0.255275\pi$
$920$	−8.11513e95	−0.385648
$921$	5.94765e94	0.0272840
$922$	3.03490e96	1.34397
$923$	−2.76656e96	−1.18273
$924$	2.33490e94	0.00963672
$925$	2.33538e95	0.0930574
$926$	−2.14471e96	−0.825110
$927$	3.44985e96	1.28147
$928$	7.97783e95	0.286138
$929$	−5.27553e96	−1.82707	−0.913535	−	0.406761i	$-0.866658\pi$
$929$	−5.27553e96	−1.82707	−0.913535	+	0.406761i	$0.866658\pi$
$930$	−2.96059e94	−0.00990108
$931$	5.39620e95	0.174270
$932$	2.31584e96	0.722257
$933$	6.60287e93	0.00198874
$934$	−1.61718e96	−0.470418
$935$	4.12055e96	1.15765
$936$	−1.81893e96	−0.493572
$937$	1.99204e96	0.522108	0.261054	−	0.965324i	$-0.415930\pi$
$937$	1.99204e96	0.522108	0.261054	+	0.965324i	$0.415930\pi$
$938$	4.30908e96	1.09092
$939$	3.57479e94	0.00874216
$940$	2.37376e96	0.560766
$941$	−5.54541e96	−1.26552	−0.632762	−	0.774346i	$-0.718079\pi$
$941$	−5.54541e96	−1.26552	−0.632762	+	0.774346i	$0.718079\pi$
$942$	9.45151e94	0.0208376
$943$	1.20071e96	0.255745
$944$	1.05582e96	0.217270
$945$	−1.94798e95	−0.0387304
$946$	6.25757e96	1.20211
$947$	−5.59741e96	−1.03899	−0.519496	−	0.854473i	$-0.673880\pi$
$947$	−5.59741e96	−1.03899	−0.519496	+	0.854473i	$0.673880\pi$
$948$	3.27077e94	0.00586650
$949$	−4.60192e96	−0.797603
$950$	−1.26603e96	−0.212044
$951$	−8.90438e94	−0.0144124
$952$	−1.64355e96	−0.257088
$953$	−6.27181e96	−0.948142	−0.474071	−	0.880487i	$-0.657216\pi$
$953$	−6.27181e96	−0.948142	−0.474071	+	0.880487i	$0.657216\pi$
$954$	−8.09927e96	−1.18338
$955$	1.27085e97	1.79467
$956$	7.78235e93	0.00106226
$957$	−2.70006e95	−0.0356235
$958$	−8.05070e96	−1.02673
$959$	3.89697e96	0.480422
$960$	−2.31979e94	−0.00276461
$961$	−5.20079e96	−0.599183
$962$	2.05702e96	0.229113
$963$	−1.46471e97	−1.57724
$964$	4.50233e96	0.468742
$965$	8.10195e96	0.815553
$966$	−1.09550e95	−0.0106624
$967$	−4.74079e96	−0.446160	−0.223080	−	0.974800i	$-0.571611\pi$
$967$	−4.74079e96	−0.446160	−0.223080	+	0.974800i	$0.571611\pi$
$968$	1.50491e96	0.136950
$969$	1.31818e95	0.0115999
$970$	−4.64877e96	−0.395600
$971$	4.12691e96	0.339626	0.169813	−	0.985476i	$-0.445684\pi$
$971$	4.12691e96	0.339626	0.169813	+	0.985476i	$0.445684\pi$
$972$	−3.51994e95	−0.0280144
$973$	1.91113e97	1.47103
$974$	−6.69082e96	−0.498097
$975$	−1.45353e95	−0.0104658
$976$	4.87333e96	0.339396
$977$	2.07713e97	1.39923	0.699617	−	0.714518i	$-0.253354\pi$
$977$	2.07713e97	1.39923	0.699617	+	0.714518i	$0.253354\pi$
$978$	3.34313e95	0.0217842
$979$	8.51057e96	0.536440
$980$	−2.26238e96	−0.137949
$981$	1.33927e97	0.789994
$982$	−5.96884e96	−0.340617
$983$	−6.37824e96	−0.352137	−0.176069	−	0.984378i	$-0.556338\pi$
$983$	−6.37824e96	−0.352137	−0.176069	+	0.984378i	$0.556338\pi$
$984$	3.43235e94	0.00183337
$985$	1.69751e97	0.877273
$986$	1.90059e97	0.950360
$987$	3.20445e95	0.0155041
$988$	−1.11513e97	−0.522065
$989$	−2.93595e97	−1.33006
$990$	−2.24803e97	−0.985504
$991$	−2.69408e96	−0.114292	−0.0571460	−	0.998366i	$-0.518200\pi$
$991$	−2.69408e96	−0.114292	−0.0571460	+	0.998366i	$0.518200\pi$
$992$	2.72601e96	0.111918
$993$	−1.51335e95	−0.00601298
$994$	1.36381e97	0.524441
$995$	−2.56799e97	−0.955746
$996$	−2.31620e95	−0.00834347
$997$	−3.91620e97	−1.36544	−0.682719	−	0.730681i	$-0.739203\pi$
$997$	−3.91620e97	−1.36544	−0.682719	+	0.730681i	$0.739203\pi$
$998$	2.88690e97	0.974293
$999$	2.65364e95	0.00866889

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.66.a.b.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.66.a.b.1.2	✓	3	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 66 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q+4.29497e9 q^{2} -5.99699e13 q^{3} +1.84467e19 q^{4} +6.16250e22 q^{5} -2.57569e23 q^{6} -2.55894e27 q^{7} +7.92282e28 q^{8} -1.02975e31 q^{9} +2.64677e32 q^{10} +8.24813e33 q^{11} -1.10625e33 q^{12} +2.22949e36 q^{13} -1.09906e37 q^{14} -3.69564e36 q^{15} +3.40282e38 q^{16} +8.10668e39 q^{17} -4.42272e40 q^{18} -2.71144e41 q^{19} +1.13678e42 q^{20} +1.53459e41 q^{21} +3.54255e43 q^{22} -1.66211e44 q^{23} -4.75130e42 q^{24} +1.08714e45 q^{25} +9.57560e45 q^{26} +1.23529e45 q^{27} -4.72041e46 q^{28} +5.45865e47 q^{29} -1.58727e46 q^{30} +1.86521e48 q^{31} +1.46150e48 q^{32} -4.94639e47 q^{33} +3.48179e49 q^{34} -1.57695e50 q^{35} -1.89955e50 q^{36} +2.14819e50 q^{37} -1.16455e51 q^{38} -1.33702e50 q^{39} +4.88244e51 q^{40} -7.22402e51 q^{41} +6.59102e50 q^{42} +1.76640e53 q^{43} +1.52151e53 q^{44} -6.34581e53 q^{45} -7.13870e53 q^{46} +2.08814e54 q^{47} -2.04067e52 q^{48} -1.99016e54 q^{49} +4.66921e54 q^{50} -4.86156e53 q^{51} +4.11269e55 q^{52} +1.83129e56 q^{53} +5.30553e54 q^{54} +5.08291e56 q^{55} -2.02740e56 q^{56} +1.62605e55 q^{57} +2.34447e57 q^{58} +3.10277e57 q^{59} -6.81726e55 q^{60} +1.43214e58 q^{61} +8.01103e57 q^{62} +2.63505e58 q^{63} +6.27710e57 q^{64} +1.37393e59 q^{65} -2.12446e57 q^{66} -3.92071e59 q^{67} +1.49542e59 q^{68} +9.96764e57 q^{69} -6.77293e59 q^{70} -1.24089e60 q^{71} -8.15848e59 q^{72} -2.06411e60 q^{73} +9.22642e59 q^{74} -6.51954e58 q^{75} -5.00172e60 q^{76} -2.11065e61 q^{77} -5.74248e59 q^{78} -2.95663e61 q^{79} +2.09699e61 q^{80} +1.06001e62 q^{81} -3.10269e61 q^{82} +2.09374e62 q^{83} +2.83082e60 q^{84} +4.99574e62 q^{85} +7.58665e62 q^{86} -3.27355e61 q^{87} +6.53484e62 q^{88} +1.03182e63 q^{89} -2.72550e63 q^{90} -5.70513e63 q^{91} -3.06605e63 q^{92} -1.11857e62 q^{93} +8.96850e63 q^{94} -1.67092e64 q^{95} -8.76461e61 q^{96} -1.75639e64 q^{97} -8.54768e63 q^{98} -8.49348e64 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 12884901888 q^{2} + 29\!\cdots\!12 q^{3} + 55\!\cdots\!48 q^{4} + 39\!\cdots\!50 q^{5} + 12\!\cdots\!52 q^{6} + 42\!\cdots\!64 q^{7} + 23\!\cdots\!08 q^{8} + 85\!\cdots\!19 q^{9} + 16\!\cdots\!00 q^{10}+ \cdots - 11\!\cdots\!32 q^{99}+O(q^{100}) \) 3 * q + 12884901888 * q^2 + 2984558598211212 * q^3 + 55340232221128654848 * q^4 + 3918092878575519628050 * q^5 + 12818581572312759640522752 * q^6 + 4292799991821220115501533464 * q^7 + 237684487542793012780631851008 * q^8 + 8506531680020675520627594612519 * q^9 + 16828080776172355868680834252800 * q^10 - 196390756437727241578921135931484 * q^11 + 55055388634191561739553936183918592 * q^12 + 594291588159789125437621076340076842 * q^13 + 18437435573141207874896428865729593344 * q^14 + 223941641190704507876888119858515088200 * q^15 + 1020847100762815390390123822295304634368 * q^16 - 4543147667338787792770556318133924095946 * q^17 + 36535275368076737964923292255914897178624 * q^18 - 76776862412732416183497479026519297722180 * q^19 + 72276056588106564515257853777772596428800 * q^20 + 26265549620028199801130322543173760738908256 * q^21 - 843491876136739963149757681788894276747264 * q^22 - 246585175089558483596492707518472201143440568 * q^23 + 236461093652422865070549025538001393766367232 * q^24 + 193546046773561655726447442157501687259788125 * q^25 + 2552462935434195116011024210920949410516959232 * q^26 + 104360942861770930686026372969796096727969655160 * q^27 + 79188182808748503812617821365498978591859277824 * q^28 + 531967266741361557870395008315736313563375166810 * q^29 + 961822025126642360531008869043250450941555507200 * q^30 + 6029738539523787679291490893311596271283256878176 * q^31 + 4384504911992708754611054498148849058967797628928 * q^32 + 2499511318103852899572045391368179633250062699664 * q^33 - 19512670652118780922233564618111375740234436182016 * q^34 - 213108430526997938381296997393828498022497121759600 * q^35 + 156917812856243951977707135387804545941392750280704 * q^36 - 1620332873097169620543940609594653833354625777112206 * q^37 - 329754113152177381507182807317346300429650393825280 * q^38 - 8058443520000240583429939491235801869291744868819032 * q^39 + 310423299329763037155946574982683353386702392524800 * q^40 + 36703565948034838377558864834222924936123775941865086 * q^41 + 112809676629486344743608439156862850418939754264395776 * q^42 + 198917478867600910841699694521456326480823486676005892 * q^43 - 3622770022448980965784454393608075694631072137478144 * q^44 - 216645431861240266977838791183480248608297455718819350 * q^45 - 1059075262688087558126288639094331419796211044479664128 * q^46 - 1550246333207342372432412618727579166713397594577369456 * q^47 + 1015592664013549396640628797450384791428965526166044672 * q^48 + 11478891131098122565712354085801141363063646718069629611 * q^49 + 831273941162533628784702886329321427845609852764160000 * q^50 + 57291625837763827945225305750991869614936958866433005016 * q^51 + 10962744831942027583350274961369683759440818354805276672 * q^52 + 388195149550139617029551617840486557495245907961121867682 * q^53 + 448226836571030795939966116098772631235082277392597647360 * q^54 + 895742624805791195861557775792485861196137895636425392600 * q^55 + 340110655393244246564124854911588175773439730088258043904 * q^56 + 1787627119006620995570153951692449536429396987788043658480 * q^57 + 2284782013196656381564957967317735508914297564827494645760 * q^58 + 9942474367718630997051455369033666316253859457002364589620 * q^59 + 4130994142491419196768924286426707496331233310792692531200 * q^60 + 30901057913347435136984168017635112365997774001894406985146 * q^61 + 25897529830685471496604689837855131122717132244132976132096 * q^62 + 138514635870008809143798247361228813659466120862088577199672 * q^63 + 18831305206160042291507368269622999248307066333392103538688 * q^64 + 135257076450309235113689373768740271196683349960342621544700 * q^65 + 10735319367237900935256707351753852219862293485006350188544 * q^66 + 17100824266138937068734192820846019367859612644204005842764 * q^67 - 83806282308469157168381879308291088089874694774757823348736 * q^68 - 2698212859345134110276706952535684126822641673823538886031072 * q^69 - 915293739615344190407093781869490631239425810211611974041600 * q^70 - 2069639192653675666961611875517343804017024313729705648459304 * q^71 + 673956874377416123142046667556464802058411395147118499856384 * q^72 - 1495815738901851328847860331660544347506225395356711624209698 * q^73 - 6959276698586061750400954649175342030699151683015510092414976 * q^74 - 19630994079897599350490393185253943873910057323490546919647500 * q^75 - 1416283131710085324764265346521471853851939190193097938042880 * q^76 - 42888418275967578631586680891050882789238717944468360701613792 * q^77 - 34610751375064155217963549622116647652943710894353552582377472 * q^78 + 6108958390094940959359012430413819561677141119540814251420400 * q^79 + 1333257918537750964014423391473836769119497617178970868940800 * q^80 + 199173830104428424071020062682585715958512675590259821728258923 * q^81 + 157640615393388866300261024777871924174114506678342141614227456 * q^82 + 205502582077300871012959214620783777968329728364540523725320572 * q^83 + 484513871795979359952379751208331756506686143559856395120541696 * q^84 + 1563497203971321203580713284666021364588991577456628214456792900 * q^85 + 854344066339117026044912021022845292527435646422137054043308032 * q^86 + 2751581088715129276210795138032395912793526337910098768398145640 * q^87 - 15559678767347559076570726605750196549932937615885444394778624 * q^88 - 1130441655406023955699836505406122255346035459613687451813849330 * q^89 - 930485044671823356668126364893220803234587086552337279981977600 * q^90 - 13758542132769965346791751406178617412263818701689332035952867504 * q^91 - 4548693617247945110936908742766500507009973420754158766824357888 * q^92 - 16692928740948609788490018454765087545603973049886739588798586496 * q^93 - 6658257301869454276672264167812669654284974473754868755229310976 * q^94 - 8930271988344088631293827502889147672196124499832288756967215000 * q^95 + 4361937277995710759452032949925210861803188041994594131915046912 * q^96 - 74357502639901786600354059238491465614418207375045893147311856346 * q^97 + 49301462002410884986734171741687880113831225020606791430078201856 * q^98 - 116077555785702594445847201289530245195179661533809750801608233132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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