LMFDB - Embedded newform 1.66.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,66,Mod(1,1)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 66, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 66);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 66 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$26.7572356472$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} + \cdots - 10\!\cdots\!36 $ x^5 - x^4 - 64723040936454512x^3 - 84407031146177217128088x^2 + 970644106288906308951592802733936*x - 10693396258963037598644570162849209944336
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{40}\cdot 3^{12}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.10736e8$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.09073e10 q^{2} +4.46080e15 q^{3} +8.20747e19 q^{4} +5.92338e22 q^{5} -4.86551e25 q^{6} -3.00901e27 q^{7} -4.92803e29 q^{8} +9.59772e30 q^{9} +O(q^{10})$	\(q-1.09073e10 q^{2} +4.46080e15 q^{3} +8.20747e19 q^{4} +5.92338e22 q^{5} -4.86551e25 q^{6} -3.00901e27 q^{7} -4.92803e29 q^{8} +9.59772e30 q^{9} -6.46079e32 q^{10} -6.29370e33 q^{11} +3.66119e35 q^{12} -7.76509e35 q^{13} +3.28200e37 q^{14} +2.64231e38 q^{15} +2.34711e39 q^{16} -6.14603e39 q^{17} -1.04685e41 q^{18} -5.04866e41 q^{19} +4.86160e42 q^{20} -1.34226e43 q^{21} +6.86470e43 q^{22} +1.38261e43 q^{23} -2.19830e45 q^{24} +7.98141e44 q^{25} +8.46958e45 q^{26} -3.13741e45 q^{27} -2.46963e47 q^{28} -2.65506e47 q^{29} -2.88203e48 q^{30} +5.51921e48 q^{31} -7.41928e48 q^{32} -2.80750e49 q^{33} +6.70363e49 q^{34} -1.78235e50 q^{35} +7.87731e50 q^{36} +1.65322e50 q^{37} +5.50670e51 q^{38} -3.46385e51 q^{39} -2.91906e52 q^{40} -1.49119e52 q^{41} +1.46404e53 q^{42} -1.75296e53 q^{43} -5.16554e53 q^{44} +5.68510e53 q^{45} -1.50805e53 q^{46} +4.83829e53 q^{47} +1.04700e55 q^{48} +5.15792e53 q^{49} -8.70553e54 q^{50} -2.74162e55 q^{51} -6.37318e55 q^{52} +3.42037e55 q^{53} +3.42205e55 q^{54} -3.72800e56 q^{55} +1.48285e57 q^{56} -2.25211e57 q^{57} +2.89594e57 q^{58} -6.23597e57 q^{59} +2.16867e58 q^{60} +9.92632e57 q^{61} -6.01994e58 q^{62} -2.88796e58 q^{63} -5.66902e57 q^{64} -4.59956e58 q^{65} +3.06221e59 q^{66} +1.42843e59 q^{67} -5.04434e59 q^{68} +6.16757e58 q^{69} +1.94405e60 q^{70} -1.36610e60 q^{71} -4.72979e60 q^{72} +6.63957e60 q^{73} -1.80321e60 q^{74} +3.56035e60 q^{75} -4.14368e61 q^{76} +1.89378e61 q^{77} +3.77811e61 q^{78} +9.29590e58 q^{79} +1.39028e62 q^{80} -1.12862e62 q^{81} +1.62648e62 q^{82} -5.07279e61 q^{83} -1.10166e63 q^{84} -3.64053e62 q^{85} +1.91200e63 q^{86} -1.18437e63 q^{87} +3.10156e63 q^{88} -5.42076e62 q^{89} -6.20088e63 q^{90} +2.33652e63 q^{91} +1.13478e63 q^{92} +2.46201e64 q^{93} -5.27724e63 q^{94} -2.99052e64 q^{95} -3.30960e64 q^{96} +2.04273e64 q^{97} -5.62587e63 q^{98} -6.04052e64 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 3959709648 q^{2} - 22\!\cdots\!04 q^{3}+ \cdots + 31\!\cdots\!65 q^{9}+O(q^{10}) $ 5 * q - 3959709648 * q^2 - 2231307434935404 * q^3 + 116912191997379733760 * q^4 + 26879673327548389029150 * q^5 - 33295729280564090947602240 * q^6 - 6923148241844308586296558808 * q^7 - 446887903591926627901545861120 * q^8 + 31912530537586467884680398342465 * q^9	$ 5 q - 3959709648 q^{2} - 22\!\cdots\!04 q^{3}+ \cdots - 36\!\cdots\!20 q^{99}+O(q^{100}) $ 5 * q - 3959709648 * q^2 - 2231307434935404 * q^3 + 116912191997379733760 * q^4 + 26879673327548389029150 * q^5 - 33295729280564090947602240 * q^6 - 6923148241844308586296558808 * q^7 - 446887903591926627901545861120 * q^8 + 31912530537586467884680398342465 * q^9 - 46444835254758466872049375039200 * q^10 - 5436990447821613455266185060489540 * q^11 + 195800126486592722298045722544448512 * q^12 - 2890859300726790832888435764458467514 * q^13 + 41180574237900302034722115163160949120 * q^14 + 103408365234403422747890968078751873400 * q^15 - 1473868696955444538230489908858040811520 * q^16 + 13864680686430637673540501618888491948122 * q^17 - 52766923382337010938622933627608214498704 * q^18 - 532140170263349448171574488831326440156700 * q^19 + 3499008192062174379356405538388976603788800 * q^20 - 11546436905526557006526119132251889169971040 * q^21 + 22561892587607883403404755239099221639703104 * q^22 - 94948785027142700354971234970110107282841224 * q^23 - 2324009070474316353878252433966072715423334400 * q^24 - 89368364701600219577770390611457383673793125 * q^25 - 30521938596122123780659173092206061048452902240 * q^26 - 129706546221561841046313530503436938966984152120 * q^27 - 518698434811712968791028896222612623314185598976 * q^28 - 1144597713377055966543673581436050616842314015850 * q^29 - 8898165260141424207772350064014611180432376163200 * q^30 - 4708831653623167525869999868687533742455793996640 * q^31 - 23840662820937316611832895513659338085021120462848 * q^32 - 47088400041590886495026610585051639514556983630608 * q^33 + 65410975808473083189009824374957335825741658669920 * q^34 + 431016017471985629901399384019473069677000966146800 * q^35 + 1775126313486315490006860454334179833046020355380480 * q^36 + 2530086119390649596783488597048185172700211081307582 * q^37 + 8239199056511383470655384896825357549181759120989120 * q^38 + 4961423111454378211563271585245526388719534092320280 * q^39 - 40685898216651980081843388349290441658499772853248000 * q^40 - 32007461843289961215814846894363640801437553437785390 * q^41 - 195314045299892072857192155130437414288210017195751936 * q^42 - 402059303617352898401840600044858362031212461462830244 * q^43 - 612244818796766798372650999094717302459543241837614080 * q^44 + 1043713954525992259035161696571453857355706435519522950 * q^45 + 2514856669257653110995391415101692168449088734110815360 * q^46 + 1572646433047878010336915637334684433480129688652944112 * q^47 + 24675155031348794802454414815955354749687650397068722176 * q^48 + 16734108893933327602070337185312116893972489911225126685 * q^49 - 11063577880472461941859651947553302608752466885786430000 * q^50 - 95495399267422751891095337933943462124412320320925036440 * q^51 - 183526322178405888877826050411801068824199241263844049408 * q^52 - 95621521245111298200083441902514245466096845017659053554 * q^53 - 557318597848485774743582734276566483558675400940047747200 * q^54 - 383625033771696018967747534079220095868070927508130274200 * q^55 + 1279479797562181227760971870185499697207329786220906905600 * q^56 + 3318990221727917572672253796992679057503071099524130319760 * q^57 + 8032881606980455898794762567234097793264864123190024459680 * q^58 - 2559150002019539763980782190342674875710406916414141257300 * q^59 + 15929220555559091493107654286005818307326801014009906124800 * q^60 + 3946890902136488204413925902971677716173875604816310291510 * q^61 - 92928211608041968363364267171290588248132222513261182532096 * q^62 - 68802271924921645132530256442236118351318471682753406875384 * q^63 - 69150375570305937045593462943529104399703176808647979171840 * q^64 - 203428189337486180767895923031910965130055608932610312683100 * q^65 + 326824005648317890913619314213537102979279278284539154417920 * q^66 + 479747394632655989552085275852886843492252096722130444354772 * q^67 + 420712177041165958943716953506888102330291794585554871017984 * q^68 + 2085757498496947569861287804370568246775481786853310358067680 * q^69 + 2223344131713304350953089067854023542847735414462666460473600 * q^70 - 3493409458155820303614582574535715900391996656268214500281240 * q^71 - 6018736038355998608239490168867843174641985013841657017077760 * q^72 + 733760875924726020894973106598755498748960690384116338055026 * q^73 - 15514223525339201048939769580727994056556223964900985146362080 * q^74 - 14732126168569891490987332632351786074968338319638722054452500 * q^75 - 36133342560695069070126026304846041053110806476015652787276800 * q^76 + 25871798846989842274158113588872654076768674584213145553762784 * q^77 + 152853676099484832021645784710928259514016680275865958517430912 * q^78 + 59699536569481886874118825694486111435856996884515844586586000 * q^79 + 219177295509817100053456351931646916206927220422985017075302400 * q^80 - 65583962416587044196237908629906173582326728520698989687871395 * q^81 - 142296434381269688499177453649327032329978008843889237410699296 * q^82 + 209047534837132969695050943022419892956201321886275074830990116 * q^83 - 1354709036605046757778457263098823484206949849923331537372897280 * q^84 - 1670550938011517784167531235760024383135110452768829071189193700 * q^85 - 1010926193522040357819139524349238009908059943237053024421679040 * q^86 - 13125541831432259160108322296931402049512991915132402846472360 * q^87 + 3795986156893622389528985077855302896604937707291737426546933760 * q^88 + 1493974679319648583095502764787645056501586744645243776851520450 * q^89 + 11168691266815947461428091063256972957381716390895407392159178400 * q^90 + 2617522707396973663766320817347076504527878438540996722544653360 * q^91 + 5247747536363486457856850601737389388282095910031013129592297472 * q^92 + 18739223210125935355706186663397055877109210120967221009013809792 * q^93 - 12861091983377738108305257044091193029406256915207083515703514880 * q^94 - 82117654407511305658368168133560153272734117033702557537140601000 * q^95 - 56452805466036872845515504865736329476063459354106526340942397440 * q^96 - 31085940707578182510537462951801111142341367310530261899829858838 * q^97 - 46798198452208171360777266613142082443922483732249545388761625936 * q^98 - 36017030678524367090996061767134771004855794650938085175529135220 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.09073e10	−1.79573	−0.897864	−	0.440273i	$-0.854882\pi$
$2$	−1.09073e10	−1.79573	−0.897864	+	0.440273i	$0.854882\pi$
$3$	4.46080e15	1.38986	0.694932	−	0.719075i	$-0.255434\pi$
$3$	4.46080e15	1.38986	0.694932	+	0.719075i	$0.255434\pi$
$4$	8.20747e19	2.22464
$5$	5.92338e22	1.13774	0.568872	−	0.822426i	$-0.307380\pi$
$5$	5.92338e22	1.13774	0.568872	+	0.822426i	$0.307380\pi$
$6$	−4.86551e25	−2.49582
$7$	−3.00901e27	−1.02976	−0.514881	−	0.857262i	$-0.672164\pi$
$7$	−3.00901e27	−1.02976	−0.514881	+	0.857262i	$0.672164\pi$
$8$	−4.92803e29	−2.19912
$9$	9.59772e30	0.931723
$10$	−6.46079e32	−2.04308
$11$	−6.29370e33	−0.898761	−0.449380	−	0.893341i	$-0.648355\pi$
$11$	−6.29370e33	−0.898761	−0.449380	+	0.893341i	$0.648355\pi$
$12$	3.66119e35	3.09195
$13$	−7.76509e35	−0.486393	−0.243197	−	0.969977i	$-0.578196\pi$
$13$	−7.76509e35	−0.486393	−0.243197	+	0.969977i	$0.578196\pi$
$14$	3.28200e37	1.84917
$15$	2.64231e38	1.58131
$16$	2.34711e39	1.72438
$17$	−6.14603e39	−0.629513	−0.314756	−	0.949173i	$-0.601923\pi$
$17$	−6.14603e39	−0.629513	−0.314756	+	0.949173i	$0.601923\pi$
$18$	−1.04685e41	−1.67312
$19$	−5.04866e41	−1.39214	−0.696072	−	0.717972i	$-0.745071\pi$
$19$	−5.04866e41	−1.39214	−0.696072	+	0.717972i	$0.745071\pi$
$20$	4.86160e42	2.53107
$21$	−1.34226e43	−1.43123
$22$	6.86470e43	1.61393
$23$	1.38261e43	0.0766560	0.0383280	−	0.999265i	$-0.487797\pi$
$23$	1.38261e43	0.0766560	0.0383280	+	0.999265i	$0.487797\pi$
$24$	−2.19830e45	−3.05648
$25$	7.98141e44	0.294462
$26$	8.46958e45	0.873430
$27$	−3.13741e45	−0.0948962
$28$	−2.46963e47	−2.29085
$29$	−2.65506e47	−0.787299	−0.393650	−	0.919261i	$-0.628788\pi$
$29$	−2.65506e47	−0.787299	−0.393650	+	0.919261i	$0.628788\pi$
$30$	−2.88203e48	−2.83960
$31$	5.51921e48	1.87336	0.936682	−	0.350182i	$-0.113880\pi$
$31$	5.51921e48	1.87336	0.936682	+	0.350182i	$0.113880\pi$
$32$	−7.41928e48	−0.897403
$33$	−2.80750e49	−1.24916
$34$	6.70363e49	1.13043
$35$	−1.78235e50	−1.17161
$36$	7.87731e50	2.07275
$37$	1.65322e50	0.178556	0.0892780	−	0.996007i	$-0.471544\pi$
$37$	1.65322e50	0.178556	0.0892780	+	0.996007i	$0.471544\pi$
$38$	5.50670e51	2.49991
$39$	−3.46385e51	−0.676021
$40$	−2.91906e52	−2.50204
$41$	−1.49119e52	−0.572873	−0.286437	−	0.958099i	$-0.592471\pi$
$41$	−1.49119e52	−0.572873	−0.286437	+	0.958099i	$0.592471\pi$
$42$	1.46404e53	2.57010
$43$	−1.75296e53	−1.43234	−0.716171	−	0.697925i	$-0.754107\pi$
$43$	−1.75296e53	−1.43234	−0.716171	+	0.697925i	$0.754107\pi$
$44$	−5.16554e53	−1.99942
$45$	5.68510e53	1.06006
$46$	−1.50805e53	−0.137653
$47$	4.83829e53	0.219539	0.109769	−	0.993957i	$-0.464989\pi$
$47$	4.83829e53	0.219539	0.109769	+	0.993957i	$0.464989\pi$
$48$	1.04700e55	2.39666
$49$	5.15792e53	0.0604090
$50$	−8.70553e54	−0.528774
$51$	−2.74162e55	−0.874937
$52$	−6.37318e55	−1.08205
$53$	3.42037e55	0.312685	0.156342	−	0.987703i	$-0.450030\pi$
$53$	3.42037e55	0.312685	0.156342	+	0.987703i	$0.450030\pi$
$54$	3.42205e55	0.170408
$55$	−3.72800e56	−1.02256
$56$	1.48285e57	2.26457
$57$	−2.25211e57	−1.93489
$58$	2.89594e57	1.41378
$59$	−6.23597e57	−1.74668	−0.873340	−	0.487111i	$-0.838051\pi$
$59$	−6.23597e57	−1.74668	−0.873340	+	0.487111i	$0.838051\pi$
$60$	2.16867e58	3.51785
$61$	9.92632e57	0.940954	0.470477	−	0.882412i	$-0.344082\pi$
$61$	9.92632e57	0.940954	0.470477	+	0.882412i	$0.344082\pi$
$62$	−6.01994e58	−3.36405
$63$	−2.88796e58	−0.959452
$64$	−5.66902e57	−0.112891
$65$	−4.59956e58	−0.553391
$66$	3.06221e59	2.24314
$67$	1.42843e59	0.641842	0.320921	−	0.947106i	$-0.396008\pi$
$67$	1.42843e59	0.641842	0.320921	+	0.947106i	$0.396008\pi$
$68$	−5.04434e59	−1.40044
$69$	6.16757e58	0.106541
$70$	1.94405e60	2.10389
$71$	−1.36610e60	−0.932368	−0.466184	−	0.884688i	$-0.654371\pi$
$71$	−1.36610e60	−0.932368	−0.466184	+	0.884688i	$0.654371\pi$
$72$	−4.72979e60	−2.04897
$73$	6.63957e60	1.83716	0.918579	−	0.395236i	$-0.129337\pi$
$73$	6.63957e60	1.83716	0.918579	+	0.395236i	$0.129337\pi$
$74$	−1.80321e60	−0.320638
$75$	3.56035e60	0.409262
$76$	−4.14368e61	−3.09702
$77$	1.89378e61	0.925509
$78$	3.77811e61	1.21395
$79$	9.29590e58	0.00197429	0.000987145	−	1.00000i	$-0.499686\pi$
$79$	9.29590e58	0.00197429	0.000987145		1.00000i	$0.499686\pi$
$80$	1.39028e62	1.96191
$81$	−1.12862e62	−1.06362
$82$	1.62648e62	1.02872
$83$	−5.07279e61	−0.216376	−0.108188	−	0.994130i	$-0.534505\pi$
$83$	−5.07279e61	−0.216376	−0.108188	+	0.994130i	$0.534505\pi$
$84$	−1.10166e63	−3.18397
$85$	−3.64053e62	−0.716225
$86$	1.91200e63	2.57210
$87$	−1.18437e63	−1.09424
$88$	3.10156e63	1.97648
$89$	−5.42076e62	−0.239268	−0.119634	−	0.992818i	$-0.538172\pi$
$89$	−5.42076e62	−0.239268	−0.119634	+	0.992818i	$0.538172\pi$
$90$	−6.20088e63	−1.90358
$91$	2.33652e63	0.500869
$92$	1.13478e63	0.170532
$93$	2.46201e64	2.60372
$94$	−5.27724e63	−0.394232
$95$	−2.99052e64	−1.58390
$96$	−3.30960e64	−1.24727
$97$	2.04273e64	0.549706	0.274853	−	0.961486i	$-0.411371\pi$
$97$	2.04273e64	0.549706	0.274853	+	0.961486i	$0.411371\pi$
$98$	−5.62587e63	−0.108478
$99$	−6.04052e64	−0.837396
$100$	6.55072e64	0.655072
$101$	1.56124e64	0.112986	0.0564932	−	0.998403i	$-0.482008\pi$
$101$	1.56124e64	0.112986	0.0564932	+	0.998403i	$0.482008\pi$
$102$	2.99036e65	1.57115
$103$	8.00101e64	0.306150	0.153075	−	0.988215i	$-0.451082\pi$
$103$	8.00101e64	0.306150	0.153075	+	0.988215i	$0.451082\pi$
$104$	3.82666e65	1.06964
$105$	−7.95071e65	−1.62837
$106$	−3.73068e65	−0.561497
$107$	−1.19579e66	−1.32643	−0.663213	−	0.748431i	$-0.730808\pi$
$107$	−1.19579e66	−1.32643	−0.663213	+	0.748431i	$0.730808\pi$
$108$	−2.57502e65	−0.211110
$109$	7.19665e65	0.437290	0.218645	−	0.975805i	$-0.429836\pi$
$109$	7.19665e65	0.437290	0.218645	+	0.975805i	$0.429836\pi$
$110$	4.06623e66	1.83624
$111$	7.37469e65	0.248169
$112$	−7.06247e66	−1.77570
$113$	−8.36303e66	−1.57512	−0.787561	−	0.616237i	$-0.788657\pi$
$113$	−8.36303e66	−1.57512	−0.787561	+	0.616237i	$0.788657\pi$
$114$	2.45643e67	3.47454
$115$	8.18975e65	0.0872149
$116$	−2.17914e67	−1.75146
$117$	−7.45272e66	−0.453184
$118$	6.80173e67	3.13656
$119$	1.84934e67	0.648248
$120$	−1.30214e68	−3.47749
$121$	−9.42636e66	−0.192229
$122$	−1.08269e68	−1.68970
$123$	−6.65192e67	−0.796216
$124$	4.52988e68	4.16756
$125$	−1.13277e68	−0.802722
$126$	3.14997e68	1.72292
$127$	−3.26601e68	−1.38165	−0.690823	−	0.723024i	$-0.742752\pi$
$127$	−3.26601e68	−1.38165	−0.690823	+	0.723024i	$0.742752\pi$
$128$	3.35557e68	1.10012
$129$	−7.81960e68	−1.99076
$130$	5.01686e68	0.993740
$131$	5.38623e68	0.831702	0.415851	−	0.909433i	$-0.363484\pi$
$131$	5.38623e68	0.831702	0.415851	+	0.909433i	$0.363484\pi$
$132$	−2.30425e69	−2.77892
$133$	1.51915e69	1.43358
$134$	−1.55803e69	−1.15257
$135$	−1.85841e68	−0.107968
$136$	3.02878e69	1.38437
$137$	4.98213e68	0.179472	0.0897360	−	0.995966i	$-0.471398\pi$
$137$	4.98213e68	0.179472	0.0897360	+	0.995966i	$0.471398\pi$
$138$	−6.72712e68	−0.191319
$139$	5.13109e69	1.15406	0.577030	−	0.816723i	$-0.304211\pi$
$139$	5.13109e69	1.15406	0.577030	+	0.816723i	$0.304211\pi$
$140$	−1.46286e70	−2.60640
$141$	2.15827e69	0.305129
$142$	1.49004e70	1.67428
$143$	4.88712e69	0.437151
$144$	2.25269e70	1.60665
$145$	−1.57270e70	−0.895745
$146$	−7.24194e70	−3.29904
$147$	2.30085e69	0.0839603
$148$	1.35688e70	0.397223
$149$	−2.08556e70	−0.490534	−0.245267	−	0.969456i	$-0.578876\pi$
$149$	−2.08556e70	−0.490534	−0.245267	+	0.969456i	$0.578876\pi$
$150$	−3.88337e70	−0.734924
$151$	9.77832e70	1.49112	0.745562	−	0.666437i	$-0.232181\pi$
$151$	9.77832e70	1.49112	0.745562	+	0.666437i	$0.232181\pi$
$152$	2.48800e71	3.06149
$153$	−5.89879e70	−0.586531
$154$	−2.06559e71	−1.66196
$155$	3.26924e71	2.13141
$156$	−2.84295e71	−1.50390
$157$	−3.04629e71	−1.30928	−0.654639	−	0.755941i	$-0.727179\pi$
$157$	−3.04629e71	−1.30928	−0.654639	+	0.755941i	$0.727179\pi$
$158$	−1.01393e69	−0.00354529
$159$	1.52576e71	0.434589
$160$	−4.39473e71	−1.02102
$161$	−4.16029e70	−0.0789374
$162$	1.23101e72	1.90996
$163$	5.37470e71	0.682742	0.341371	−	0.939929i	$-0.389109\pi$
$163$	5.37470e71	0.682742	0.341371	+	0.939929i	$0.389109\pi$
$164$	−1.22389e72	−1.27444
$165$	−1.66299e72	−1.42122
$166$	5.53303e71	0.388553
$167$	−5.14205e71	−0.297065	−0.148532	−	0.988908i	$-0.547455\pi$
$167$	−5.14205e71	−0.297065	−0.148532	+	0.988908i	$0.547455\pi$
$168$	6.61470e72	3.14745
$169$	−1.94573e72	−0.763422
$170$	3.97082e72	1.28614
$171$	−4.84557e72	−1.29709
$172$	−1.43874e73	−3.18644
$173$	8.39501e72	1.54001	0.770003	−	0.638040i	$-0.220254\pi$
$173$	8.39501e72	1.54001	0.770003	+	0.638040i	$0.220254\pi$
$174$	1.29182e73	1.96496
$175$	−2.40161e72	−0.303226
$176$	−1.47720e73	−1.54981
$177$	−2.78174e73	−2.42765
$178$	5.91257e72	0.429661
$179$	1.43234e73	0.867606	0.433803	−	0.901008i	$-0.357171\pi$
$179$	1.43234e73	0.867606	0.433803	+	0.901008i	$0.357171\pi$
$180$	4.66603e73	2.35826
$181$	2.48051e73	1.04710	0.523548	−	0.851996i	$-0.324608\pi$
$181$	2.48051e73	1.04710	0.523548	+	0.851996i	$0.324608\pi$
$182$	−2.54850e73	−0.899425
$183$	4.42794e73	1.30780
$184$	−6.81356e72	−0.168576
$185$	9.79265e72	0.203151
$186$	−2.68538e74	−4.67557
$187$	3.86813e73	0.565781
$188$	3.97101e73	0.488395
$189$	9.44048e72	0.0977204
$190$	3.26183e74	2.84426
$191$	−2.55448e74	−1.87810	−0.939048	−	0.343787i	$-0.888290\pi$
$191$	−2.55448e74	−1.87810	−0.939048	+	0.343787i	$0.888290\pi$
$192$	−2.52884e73	−0.156903
$193$	2.50811e74	1.31442	0.657209	−	0.753708i	$-0.271737\pi$
$193$	2.50811e74	1.31442	0.657209	+	0.753708i	$0.271737\pi$
$194$	−2.22806e74	−0.987122
$195$	−2.05177e74	−0.769139
$196$	4.23335e73	0.134388
$197$	3.05152e74	0.821039	0.410520	−	0.911852i	$-0.365347\pi$
$197$	3.05152e74	0.821039	0.410520	+	0.911852i	$0.365347\pi$
$198$	6.58855e74	1.50374
$199$	−4.46747e74	−0.865639	−0.432820	−	0.901481i	$-0.642481\pi$
$199$	−4.46747e74	−0.865639	−0.432820	+	0.901481i	$0.642481\pi$
$200$	−3.93327e74	−0.647558
$201$	6.37195e74	0.892073
$202$	−1.70289e74	−0.202893
$203$	7.98910e74	0.810731
$204$	−2.25018e75	−1.94642
$205$	−8.83291e74	−0.651783
$206$	−8.72691e74	−0.549763
$207$	1.32699e74	0.0714221
$208$	−1.82255e75	−0.838729
$209$	3.17748e75	1.25120
$210$	8.67204e75	2.92411
$211$	−3.78137e75	−1.09262	−0.546310	−	0.837583i	$-0.683968\pi$
$211$	−3.78137e75	−1.09262	−0.546310	+	0.837583i	$0.683968\pi$
$212$	2.80726e75	0.695611
$213$	−6.09392e75	−1.29586
$214$	1.30428e76	2.38190
$215$	−1.03834e76	−1.62964
$216$	1.54613e75	0.208688
$217$	−1.66073e76	−1.92912
$218$	−7.84957e75	−0.785253
$219$	2.96178e76	2.55340
$220$	−3.05975e76	−2.27483
$221$	4.77245e75	0.306191
$222$	−8.04376e75	−0.445643
$223$	7.53916e75	0.360923	0.180462	−	0.983582i	$-0.442241\pi$
$223$	7.53916e75	0.360923	0.180462	+	0.983582i	$0.442241\pi$
$224$	2.23247e76	0.924112
$225$	7.66034e75	0.274357
$226$	9.12177e76	2.82849
$227$	1.68747e76	0.453310	0.226655	−	0.973975i	$-0.427221\pi$
$227$	1.68747e76	0.453310	0.226655	+	0.973975i	$0.427221\pi$
$228$	−1.84841e77	−4.30444
$229$	−3.67980e76	−0.743312	−0.371656	−	0.928370i	$-0.621210\pi$
$229$	−3.67980e76	−0.743312	−0.371656	+	0.928370i	$0.621210\pi$
$230$	−8.93277e75	−0.156614
$231$	8.44778e76	1.28633
$232$	1.30842e77	1.73137
$233$	3.35750e76	0.386321	0.193161	−	0.981167i	$-0.438126\pi$
$233$	3.35750e76	0.386321	0.193161	+	0.981167i	$0.438126\pi$
$234$	8.12887e76	0.813795
$235$	2.86590e76	0.249779
$236$	−5.11815e77	−3.88573
$237$	4.14672e74	0.00274400
$238$	−2.01713e77	−1.16408
$239$	−1.52398e77	−0.767444	−0.383722	−	0.923449i	$-0.625358\pi$
$239$	−1.52398e77	−0.767444	−0.383722	+	0.923449i	$0.625358\pi$
$240$	6.20178e77	2.72679
$241$	1.54178e77	0.592202	0.296101	−	0.955157i	$-0.404314\pi$
$241$	1.54178e77	0.592202	0.296101	+	0.955157i	$0.404314\pi$
$242$	1.02816e77	0.345191
$243$	−4.71137e77	−1.38339
$244$	8.14700e77	2.09328
$245$	3.05523e76	0.0687300
$246$	7.25542e77	1.42979
$247$	3.92033e77	0.677129
$248$	−2.71989e78	−4.11975
$249$	−2.26287e77	−0.300733
$250$	1.23554e78	1.44147
$251$	−1.76296e77	−0.180654	−0.0903270	−	0.995912i	$-0.528791\pi$
$251$	−1.76296e77	−0.180654	−0.0903270	+	0.995912i	$0.528791\pi$
$252$	−2.37029e78	−2.13444
$253$	−8.70176e76	−0.0688954
$254$	3.56232e78	2.48106
$255$	−1.62397e78	−0.995455
$256$	−3.45085e78	−1.86263
$257$	2.52232e78	1.19943	0.599714	−	0.800215i	$-0.295281\pi$
$257$	2.52232e78	1.19943	0.599714	+	0.800215i	$0.295281\pi$
$258$	8.52904e78	3.57486
$259$	−4.97455e77	−0.183870
$260$	−3.77508e78	−1.23110
$261$	−2.54826e78	−0.733545
$262$	−5.87490e78	−1.49351
$263$	1.00671e78	0.226121	0.113061	−	0.993588i	$-0.463935\pi$
$263$	1.00671e78	0.226121	0.113061	+	0.993588i	$0.463935\pi$
$264$	1.38354e79	2.74704
$265$	2.02601e78	0.355755
$266$	−1.65697e79	−2.57431
$267$	−2.41810e78	−0.332551
$268$	1.17238e79	1.42787
$269$	−6.96749e78	−0.751843	−0.375921	−	0.926652i	$-0.622674\pi$
$269$	−6.96749e78	−0.751843	−0.375921	+	0.926652i	$0.622674\pi$
$270$	2.02701e78	0.193880
$271$	−1.10528e77	−0.00937496	−0.00468748	−	0.999989i	$-0.501492\pi$
$271$	−1.10528e77	−0.00937496	−0.00468748	+	0.999989i	$0.501492\pi$
$272$	−1.44254e79	−1.08552
$273$	1.04228e79	0.696140
$274$	−5.43414e78	−0.322283
$275$	−5.02327e78	−0.264651
$276$	5.06201e78	0.237016
$277$	1.88681e79	0.785481	0.392740	−	0.919649i	$-0.371527\pi$
$277$	1.88681e79	0.785481	0.392740	+	0.919649i	$0.371527\pi$
$278$	−5.59661e79	−2.07238
$279$	5.29719e79	1.74545
$280$	8.78348e79	2.57650
$281$	3.18846e79	0.832962	0.416481	−	0.909144i	$-0.363263\pi$
$281$	3.18846e79	0.832962	0.416481	+	0.909144i	$0.363263\pi$
$282$	−2.35408e79	−0.547929
$283$	1.43491e79	0.297690	0.148845	−	0.988861i	$-0.452444\pi$
$283$	1.43491e79	0.297690	0.148845	+	0.988861i	$0.452444\pi$
$284$	−1.12123e80	−2.07418
$285$	−1.33401e80	−2.20141
$286$	−5.33050e79	−0.785005
$287$	4.48701e79	0.589923
$288$	−7.12082e79	−0.836131
$289$	−5.75454e79	−0.603714
$290$	1.71538e80	1.60852
$291$	9.11223e79	0.764016
$292$	5.44941e80	4.08702
$293$	−2.42856e80	−1.62986	−0.814931	−	0.579558i	$-0.803225\pi$
$293$	−2.42856e80	−1.62986	−0.814931	+	0.579558i	$0.803225\pi$
$294$	−2.50959e79	−0.150770
$295$	−3.69380e80	−1.98728
$296$	−8.14712e79	−0.392666
$297$	1.97459e79	0.0852889
$298$	2.27477e80	0.880866
$299$	−1.07361e79	−0.0372849
$300$	2.92215e80	0.910462
$301$	5.27466e80	1.47497
$302$	−1.06655e81	−2.67765
$303$	6.96440e79	0.157036
$304$	−1.18498e81	−2.40059
$305$	5.87974e80	1.07057
$306$	6.43396e80	1.05325
$307$	−2.51887e80	−0.370859	−0.185430	−	0.982658i	$-0.559368\pi$
$307$	−2.51887e80	−0.370859	−0.185430	+	0.982658i	$0.559368\pi$
$308$	1.55431e81	2.05893
$309$	3.56909e80	0.425508
$310$	−3.56584e81	−3.82743
$311$	−6.94191e80	−0.671068	−0.335534	−	0.942028i	$-0.608917\pi$
$311$	−6.94191e80	−0.671068	−0.335534	+	0.942028i	$0.608917\pi$
$312$	1.70700e81	1.48665
$313$	3.26598e80	0.256343	0.128172	−	0.991752i	$-0.459089\pi$
$313$	3.26598e80	0.256343	0.128172	+	0.991752i	$0.459089\pi$
$314$	3.32266e81	2.35111
$315$	−1.71065e81	−1.09161
$316$	7.62959e78	0.00439209
$317$	2.76472e81	1.43623	0.718117	−	0.695922i	$-0.245004\pi$
$317$	2.76472e81	1.43623	0.718117	+	0.695922i	$0.245004\pi$
$318$	−1.66418e81	−0.780404
$319$	1.67102e81	0.707594
$320$	−3.35798e80	−0.128441
$321$	−5.33420e81	−1.84355
$322$	4.53773e80	0.141750
$323$	3.10292e81	0.876372
$324$	−9.26312e81	−2.36616
$325$	−6.19764e80	−0.143224
$326$	−5.86232e81	−1.22602
$327$	3.21029e81	0.607773
$328$	7.34865e81	1.25982
$329$	−1.45584e81	−0.226073
$330$	1.81386e82	2.55212
$331$	1.53451e81	0.195687	0.0978434	−	0.995202i	$-0.468806\pi$
$331$	1.53451e81	0.195687	0.0978434	+	0.995202i	$0.468806\pi$
$332$	−4.16348e81	−0.481359
$333$	1.58671e81	0.166365
$334$	5.60857e81	0.533448
$335$	8.46114e81	0.730252
$336$	−3.15043e82	−2.46799
$337$	5.02558e81	0.357449	0.178725	−	0.983899i	$-0.442803\pi$
$337$	5.02558e81	0.357449	0.178725	+	0.983899i	$0.442803\pi$
$338$	2.12226e82	1.37090
$339$	−3.73058e82	−2.18921
$340$	−2.98795e82	−1.59334
$341$	−3.47363e82	−1.68371
$342$	5.28518e82	2.32923
$343$	2.41398e82	0.967555
$344$	8.63863e82	3.14989
$345$	3.65329e81	0.121217
$346$	−9.15665e82	−2.76543
$347$	1.18019e82	0.324523	0.162261	−	0.986748i	$-0.448121\pi$
$347$	1.18019e82	0.324523	0.162261	+	0.986748i	$0.448121\pi$
$348$	−9.72070e82	−2.43429
$349$	1.90414e82	0.434384	0.217192	−	0.976129i	$-0.430310\pi$
$349$	1.90414e82	0.434384	0.217192	+	0.976129i	$0.430310\pi$
$350$	2.61950e82	0.544511
$351$	2.43623e81	0.0461568
$352$	4.66948e82	0.806551
$353$	−7.23948e82	−1.14033	−0.570164	−	0.821531i	$-0.693120\pi$
$353$	−7.23948e82	−1.14033	−0.570164	+	0.821531i	$0.693120\pi$
$354$	3.03412e83	4.35940
$355$	−8.09195e82	−1.06080
$356$	−4.44908e82	−0.532286
$357$	8.24956e82	0.900977
$358$	−1.56229e83	−1.55799
$359$	7.54818e82	0.687500	0.343750	−	0.939061i	$-0.388303\pi$
$359$	7.54818e82	0.687500	0.343750	+	0.939061i	$0.388303\pi$
$360$	−2.80164e83	−2.33121
$361$	1.23372e83	0.938065
$362$	−2.70555e83	−1.88030
$363$	−4.20491e82	−0.267173
$364$	1.91769e83	1.11425
$365$	3.93287e83	2.09022
$366$	−4.82966e83	−2.34845
$367$	8.29730e82	0.369224	0.184612	−	0.982811i	$-0.440897\pi$
$367$	8.29730e82	0.369224	0.184612	+	0.982811i	$0.440897\pi$
$368$	3.24514e82	0.132184
$369$	−1.43121e83	−0.533759
$370$	−1.06811e83	−0.364804
$371$	−1.02919e83	−0.321991
$372$	2.02069e84	5.79234
$373$	−1.35550e83	−0.356092	−0.178046	−	0.984022i	$-0.556978\pi$
$373$	−1.35550e83	−0.356092	−0.178046	+	0.984022i	$0.556978\pi$
$374$	−4.21907e83	−1.01599
$375$	−5.05305e83	−1.11567
$376$	−2.38432e83	−0.482792
$377$	2.06168e83	0.382937
$378$	−1.02970e83	−0.175479
$379$	−3.17092e83	−0.495919	−0.247959	−	0.968770i	$-0.579760\pi$
$379$	−3.17092e83	−0.495919	−0.247959	+	0.968770i	$0.579760\pi$
$380$	−2.45446e84	−3.52362
$381$	−1.45690e84	−1.92030
$382$	2.78623e84	3.37255
$383$	1.04053e84	1.15689	0.578447	−	0.815720i	$-0.303659\pi$
$383$	1.04053e84	1.15689	0.578447	+	0.815720i	$0.303659\pi$
$384$	1.49685e84	1.52902
$385$	1.12176e84	1.05299
$386$	−2.73566e84	−2.36034
$387$	−1.68244e84	−1.33455
$388$	1.67657e84	1.22290
$389$	−7.00058e83	−0.469647	−0.234824	−	0.972038i	$-0.575451\pi$
$389$	−7.00058e83	−0.469647	−0.234824	+	0.972038i	$0.575451\pi$
$390$	2.23792e84	1.38116
$391$	−8.49758e82	−0.0482559
$392$	−2.54184e83	−0.132847
$393$	2.40269e84	1.15595
$394$	−3.32837e84	−1.47436
$395$	5.50632e81	0.00224624
$396$	−4.95774e84	−1.86290
$397$	1.12932e84	0.390954	0.195477	−	0.980708i	$-0.437374\pi$
$397$	1.12932e84	0.390954	0.195477	+	0.980708i	$0.437374\pi$
$398$	4.87279e84	1.55445
$399$	6.77661e84	1.99248
$400$	1.87332e84	0.507766
$401$	−2.71761e84	−0.679196	−0.339598	−	0.940571i	$-0.610291\pi$
$401$	−2.71761e84	−0.679196	−0.339598	+	0.940571i	$0.610291\pi$
$402$	−6.95005e84	−1.60192
$403$	−4.28572e84	−0.911191
$404$	1.28139e84	0.251354
$405$	−6.68525e84	−1.21012
$406$	−8.71391e84	−1.45585
$407$	−1.04049e84	−0.160479
$408$	1.35108e85	1.92409
$409$	−4.67812e84	−0.615267	−0.307634	−	0.951505i	$-0.599537\pi$
$409$	−4.67812e84	−0.615267	−0.307634	+	0.951505i	$0.599537\pi$
$410$	9.63428e84	1.17043
$411$	2.22243e84	0.249442
$412$	6.56681e84	0.681075
$413$	1.87641e85	1.79866
$414$	−1.44739e84	−0.128255
$415$	−3.00481e84	−0.246181
$416$	5.76114e84	0.436491
$417$	2.28888e85	1.60399
$418$	−3.46576e85	−2.24682
$419$	−2.65850e85	−1.59471	−0.797355	−	0.603511i	$-0.793768\pi$
$419$	−2.65850e85	−1.59471	−0.797355	+	0.603511i	$0.793768\pi$
$420$	−6.52553e85	−3.62254
$421$	2.53204e85	1.30108	0.650538	−	0.759474i	$-0.274544\pi$
$421$	2.53204e85	1.30108	0.650538	+	0.759474i	$0.274544\pi$
$422$	4.12444e85	1.96205
$423$	4.64365e84	0.204549
$424$	−1.68557e85	−0.687632
$425$	−4.90540e84	−0.185368
$426$	6.64679e85	2.32702
$427$	−2.98683e85	−0.968958
$428$	−9.81444e85	−2.95082
$429$	2.18005e85	0.607581
$430$	1.13255e86	2.92639
$431$	−5.90856e85	−1.41570	−0.707849	−	0.706364i	$-0.750334\pi$
$431$	−5.90856e85	−1.41570	−0.707849	+	0.706364i	$0.750334\pi$
$432$	−7.36384e84	−0.163637
$433$	1.55299e85	0.320120	0.160060	−	0.987107i	$-0.448831\pi$
$433$	1.55299e85	0.320120	0.160060	+	0.987107i	$0.448831\pi$
$434$	1.81140e86	3.46417
$435$	−7.01549e85	−1.24496
$436$	5.90663e85	0.972812
$437$	−6.98034e84	−0.106716
$438$	−3.23049e86	−4.58522
$439$	−6.75030e85	−0.889664	−0.444832	−	0.895614i	$-0.646737\pi$
$439$	−6.75030e85	−0.889664	−0.444832	+	0.895614i	$0.646737\pi$
$440$	1.83717e86	2.24873
$441$	4.95043e84	0.0562845
$442$	−5.20543e85	−0.549835
$443$	1.83465e86	1.80066	0.900329	−	0.435209i	$-0.143326\pi$
$443$	1.83465e86	1.80066	0.900329	+	0.435209i	$0.143326\pi$
$444$	6.05276e85	0.552086
$445$	−3.21093e85	−0.272226
$446$	−8.22316e85	−0.648120
$447$	−9.30328e85	−0.681776
$448$	1.70581e85	0.116251
$449$	−1.79552e85	−0.113811	−0.0569054	−	0.998380i	$-0.518123\pi$
$449$	−1.79552e85	−0.113811	−0.0569054	+	0.998380i	$0.518123\pi$
$450$	−8.35533e85	−0.492671
$451$	9.38513e85	0.514876
$452$	−6.86393e86	−3.50408
$453$	4.36192e86	2.07246
$454$	−1.84057e86	−0.814022
$455$	1.38401e86	0.569861
$456$	1.10985e87	4.25506
$457$	−3.17076e86	−1.13211	−0.566053	−	0.824369i	$-0.691530\pi$
$457$	−3.17076e86	−1.13211	−0.566053	+	0.824369i	$0.691530\pi$
$458$	4.01365e86	1.33479
$459$	1.92826e85	0.0597383
$460$	6.72171e85	0.194022
$461$	4.28801e85	0.115339	0.0576694	−	0.998336i	$-0.481633\pi$
$461$	4.28801e85	0.115339	0.0576694	+	0.998336i	$0.481633\pi$
$462$	−9.21421e86	−2.30990
$463$	−5.18691e86	−1.21207	−0.606033	−	0.795439i	$-0.707240\pi$
$463$	−5.18691e86	−1.21207	−0.606033	+	0.795439i	$0.707240\pi$
$464$	−6.23172e86	−1.35761
$465$	1.45834e87	2.96237
$466$	−3.66211e86	−0.693728
$467$	−4.87986e86	−0.862201	−0.431101	−	0.902304i	$-0.641875\pi$
$467$	−4.87986e86	−0.862201	−0.431101	+	0.902304i	$0.641875\pi$
$468$	−6.11680e86	−1.00817
$469$	−4.29816e86	−0.660944
$470$	−3.12591e86	−0.448535
$471$	−1.35889e87	−1.81972
$472$	3.07311e87	3.84116
$473$	1.10326e87	1.28733
$474$	−4.52293e84	−0.00492747
$475$	−4.02954e86	−0.409934
$476$	1.51784e87	1.44212
$477$	3.28277e86	0.291335
$478$	1.66224e87	1.37812
$479$	−2.24879e87	−1.74198	−0.870992	−	0.491297i	$-0.836523\pi$
$479$	−2.24879e87	−1.74198	−0.870992	+	0.491297i	$0.836523\pi$
$480$	−1.96040e87	−1.41907
$481$	−1.28374e86	−0.0868484
$482$	−1.68166e87	−1.06343
$483$	−1.85582e86	−0.109712
$484$	−7.73666e86	−0.427641
$485$	1.20999e87	0.625425
$486$	5.13881e87	2.48418
$487$	2.82778e86	0.127866	0.0639329	−	0.997954i	$-0.479636\pi$
$487$	2.82778e86	0.127866	0.0639329	+	0.997954i	$0.479636\pi$
$488$	−4.89172e87	−2.06927
$489$	2.39755e87	0.948919
$490$	−3.33242e86	−0.123420
$491$	−4.22797e86	−0.146549	−0.0732746	−	0.997312i	$-0.523345\pi$
$491$	−4.22797e86	−0.146549	−0.0732746	+	0.997312i	$0.523345\pi$
$492$	−5.45954e87	−1.77129
$493$	1.63181e87	0.495615
$494$	−4.27600e87	−1.21594
$495$	−3.57803e87	−0.952742
$496$	1.29542e88	3.23040
$497$	4.11061e87	0.960117
$498$	2.46817e87	0.540035
$499$	−4.51309e87	−0.925137	−0.462569	−	0.886583i	$-0.653072\pi$
$499$	−4.51309e87	−0.925137	−0.462569	+	0.886583i	$0.653072\pi$
$500$	−9.29715e87	−1.78577
$501$	−2.29377e87	−0.412880
$502$	1.92291e87	0.324406
$503$	8.39544e87	1.32765	0.663826	−	0.747887i	$-0.268932\pi$
$503$	8.39544e87	1.32765	0.663826	+	0.747887i	$0.268932\pi$
$504$	1.42320e88	2.10995
$505$	9.24784e86	0.128550
$506$	9.49123e86	0.123717
$507$	−8.67952e87	−1.06105
$508$	−2.68057e88	−3.07366
$509$	1.14263e88	1.22907	0.614537	−	0.788888i	$-0.289343\pi$
$509$	1.14263e88	1.22907	0.614537	+	0.788888i	$0.289343\pi$
$510$	1.77130e88	1.78757
$511$	−1.99785e88	−1.89184
$512$	2.52595e88	2.24466
$513$	1.58397e87	0.132109
$514$	−2.75116e88	−2.15385
$515$	4.73930e87	0.348321
$516$	−6.41792e88	−4.42873
$517$	−3.04508e87	−0.197313
$518$	5.42587e87	0.330181
$519$	3.74485e88	2.14040
$520$	2.26668e88	1.21697
$521$	7.88978e87	0.397959	0.198980	−	0.980004i	$-0.436237\pi$
$521$	7.88978e87	0.397959	0.198980	+	0.980004i	$0.436237\pi$
$522$	2.77945e88	1.31725
$523$	3.41308e88	1.51999	0.759996	−	0.649928i	$-0.225201\pi$
$523$	3.41308e88	1.51999	0.759996	+	0.649928i	$0.225201\pi$
$524$	4.42073e88	1.85024
$525$	−1.07131e88	−0.421443
$526$	−1.09804e88	−0.406052
$527$	−3.39212e88	−1.17931
$528$	−6.58951e88	−2.15402
$529$	−3.23407e88	−0.994124
$530$	−2.20982e88	−0.638840
$531$	−5.98511e88	−1.62742
$532$	1.24683e89	3.18919
$533$	1.15792e88	0.278642
$534$	2.63748e88	0.597170
$535$	−7.08314e88	−1.50913
$536$	−7.03936e88	−1.41149
$537$	6.38939e88	1.20585
$538$	7.59962e88	1.35011
$539$	−3.24624e87	−0.0542933
$540$	−1.52528e88	−0.240189
$541$	−9.95703e88	−1.47645	−0.738225	−	0.674554i	$-0.764336\pi$
$541$	−9.95703e88	−1.47645	−0.738225	+	0.674554i	$0.764336\pi$
$542$	1.20555e87	0.0168349
$543$	1.10650e89	1.45532
$544$	4.55991e88	0.564927
$545$	4.26285e88	0.497524
$546$	−1.13684e89	−1.25008
$547$	−1.51189e89	−1.56651	−0.783254	−	0.621702i	$-0.786441\pi$
$547$	−1.51189e89	−1.56651	−0.783254	+	0.621702i	$0.786441\pi$
$548$	4.08907e88	0.399261
$549$	9.52700e88	0.876708
$550$	5.47900e88	0.475241
$551$	1.34045e89	1.09603
$552$	−3.03940e88	−0.234297
$553$	−2.79714e86	−0.00203305
$554$	−2.05799e89	−1.41051
$555$	4.36831e88	0.282352
$556$	4.21133e89	2.56737
$557$	1.51675e89	0.872211	0.436105	−	0.899896i	$-0.356357\pi$
$557$	1.51675e89	0.872211	0.436105	+	0.899896i	$0.356357\pi$
$558$	−5.77778e89	−3.13436
$559$	1.36119e89	0.696681
$560$	−4.18337e89	−2.02030
$561$	1.72550e89	0.786359
$562$	−3.47773e89	−1.49577
$563$	1.72968e88	0.0702171	0.0351085	−	0.999384i	$-0.488822\pi$
$563$	1.72968e88	0.0702171	0.0351085	+	0.999384i	$0.488822\pi$
$564$	1.77139e89	0.678803
$565$	−4.95374e89	−1.79209
$566$	−1.56509e89	−0.534571
$567$	3.39602e89	1.09527
$568$	6.73220e89	2.05039
$569$	−4.01985e89	−1.15627	−0.578137	−	0.815940i	$-0.696220\pi$
$569$	−4.01985e89	−1.15627	−0.578137	+	0.815940i	$0.696220\pi$
$570$	1.45504e90	3.95314
$571$	−3.66352e88	−0.0940211	−0.0470106	−	0.998894i	$-0.514969\pi$
$571$	−3.66352e88	−0.0940211	−0.0470106	+	0.998894i	$0.514969\pi$
$572$	4.01109e89	0.972504
$573$	−1.13950e90	−2.61030
$574$	−4.89409e89	−1.05934
$575$	1.10352e88	0.0225723
$576$	−5.44097e88	−0.105183
$577$	4.81630e89	0.880034	0.440017	−	0.897989i	$-0.354972\pi$
$577$	4.81630e89	0.880034	0.440017	+	0.897989i	$0.354972\pi$
$578$	6.27663e89	1.08411
$579$	1.11882e90	1.82686
$580$	−1.29079e90	−1.99271
$581$	1.52641e89	0.222816
$582$	−9.93895e89	−1.37197
$583$	−2.15268e89	−0.281029
$584$	−3.27200e90	−4.04013
$585$	−4.41453e89	−0.515607
$586$	2.64889e90	2.92679
$587$	2.68476e89	0.280651	0.140325	−	0.990105i	$-0.455185\pi$
$587$	2.68476e89	0.280651	0.140325	+	0.990105i	$0.455185\pi$
$588$	1.88841e89	0.186782
$589$	−2.78646e90	−2.60799
$590$	4.02892e90	3.56861
$591$	1.36122e90	1.14113
$592$	3.88029e89	0.307899
$593$	6.86027e89	0.515304	0.257652	−	0.966238i	$-0.417051\pi$
$593$	6.86027e89	0.515304	0.257652	+	0.966238i	$0.417051\pi$
$594$	−2.15374e89	−0.153156
$595$	1.09544e90	0.737541
$596$	−1.71172e90	−1.09126
$597$	−1.99285e90	−1.20312
$598$	1.17102e89	0.0669536
$599$	−1.15766e90	−0.626918	−0.313459	−	0.949602i	$-0.601488\pi$
$599$	−1.15766e90	−0.626918	−0.313459	+	0.949602i	$0.601488\pi$
$600$	−1.75455e90	−0.900018
$601$	3.48416e90	1.69308	0.846540	−	0.532325i	$-0.178681\pi$
$601$	3.48416e90	1.69308	0.846540	+	0.532325i	$0.178681\pi$
$602$	−5.75321e90	−2.64865
$603$	1.37097e90	0.598019
$604$	8.02553e90	3.31721
$605$	−5.58359e89	−0.218708
$606$	−7.59625e89	−0.281993
$607$	−2.71680e90	−0.955927	−0.477963	−	0.878380i	$-0.658625\pi$
$607$	−2.71680e90	−0.955927	−0.477963	+	0.878380i	$0.658625\pi$
$608$	3.74575e90	1.24931
$609$	3.56378e90	1.12681
$610$	−6.41318e90	−1.92244
$611$	−3.75697e89	−0.106782
$612$	−4.84141e90	−1.30482
$613$	−2.26615e90	−0.579193	−0.289597	−	0.957149i	$-0.593521\pi$
$613$	−2.26615e90	−0.579193	−0.289597	+	0.957149i	$0.593521\pi$
$614$	2.74740e90	0.665962
$615$	−3.94019e90	−0.905890
$616$	−9.33261e90	−2.03531
$617$	3.42657e90	0.708912	0.354456	−	0.935073i	$-0.384666\pi$
$617$	3.42657e90	0.708912	0.354456	+	0.935073i	$0.384666\pi$
$618$	−3.89290e90	−0.764096
$619$	3.94976e90	0.735572	0.367786	−	0.929910i	$-0.380116\pi$
$619$	3.94976e90	0.735572	0.367786	+	0.929910i	$0.380116\pi$
$620$	2.68322e91	4.74162
$621$	−4.33782e88	−0.00727436
$622$	7.57172e90	1.20506
$623$	1.63111e90	0.246389
$624$	−8.13005e90	−1.16572
$625$	−8.87318e90	−1.20775
$626$	−3.56228e90	−0.460323
$627$	1.41741e91	1.73900
$628$	−2.50023e91	−2.91267
$629$	−1.01607e90	−0.112403
$630$	1.86585e91	1.96024
$631$	1.71736e91	1.71359	0.856797	−	0.515655i	$-0.172451\pi$
$631$	1.71736e91	1.71359	0.856797	+	0.515655i	$0.172451\pi$
$632$	−4.58105e88	−0.00434170
$633$	−1.68679e91	−1.51859
$634$	−3.01555e91	−2.57909
$635$	−1.93458e91	−1.57196
$636$	1.25226e91	0.966805
$637$	−4.00517e89	−0.0293825
$638$	−1.82262e91	−1.27065
$639$	−1.31115e91	−0.868708
$640$	1.98763e91	1.25166
$641$	2.79928e91	1.67556	0.837782	−	0.546005i	$-0.183852\pi$
$641$	2.79928e91	1.67556	0.837782	+	0.546005i	$0.183852\pi$
$642$	5.81815e91	3.31052
$643$	1.83708e91	0.993738	0.496869	−	0.867826i	$-0.334483\pi$
$643$	1.83708e91	0.993738	0.496869	+	0.867826i	$0.334483\pi$
$644$	−3.41455e90	−0.175607
$645$	−4.63185e91	−2.26498
$646$	−3.38443e91	−1.57373
$647$	−1.63697e91	−0.723854	−0.361927	−	0.932206i	$-0.617881\pi$
$647$	−1.63697e91	−0.723854	−0.361927	+	0.932206i	$0.617881\pi$
$648$	5.56188e91	2.33902
$649$	3.92473e91	1.56985
$650$	6.75992e90	0.257192
$651$	−7.40821e91	−2.68121
$652$	4.41127e91	1.51886
$653$	−3.73141e91	−1.22235	−0.611173	−	0.791497i	$-0.709302\pi$
$653$	−3.73141e91	−1.22235	−0.611173	+	0.791497i	$0.709302\pi$
$654$	−3.50154e91	−1.09140
$655$	3.19047e91	0.946264
$656$	−3.49999e91	−0.987853
$657$	6.37247e91	1.71172
$658$	1.58793e91	0.405965
$659$	1.03260e91	0.251279	0.125640	−	0.992076i	$-0.459902\pi$
$659$	1.03260e91	0.251279	0.125640	+	0.992076i	$0.459902\pi$
$660$	−1.36489e92	−3.16170
$661$	1.92294e91	0.424052	0.212026	−	0.977264i	$-0.431994\pi$
$661$	1.92294e91	0.424052	0.212026	+	0.977264i	$0.431994\pi$
$662$	−1.67373e91	−0.351400
$663$	2.12889e91	0.425564
$664$	2.49989e91	0.475837
$665$	8.99848e91	1.63104
$666$	−1.73067e91	−0.298746
$667$	−3.67092e90	−0.0603512
$668$	−4.22032e91	−0.660862
$669$	3.36307e91	0.501634
$670$	−9.22879e91	−1.31133
$671$	−6.24733e91	−0.845693
$672$	9.95860e91	1.28439
$673$	1.05581e92	1.29747	0.648734	−	0.761015i	$-0.275299\pi$
$673$	1.05581e92	1.29747	0.648734	+	0.761015i	$0.275299\pi$
$674$	−5.48153e91	−0.641882
$675$	−2.50409e90	−0.0279433
$676$	−1.59695e92	−1.69834
$677$	−1.37277e92	−1.39145	−0.695724	−	0.718309i	$-0.744916\pi$
$677$	−1.37277e92	−1.39145	−0.695724	+	0.718309i	$0.744916\pi$
$678$	4.06904e92	3.93122
$679$	−6.14660e91	−0.566066
$680$	1.79406e92	1.57506
$681$	7.52747e91	0.630040
$682$	3.78878e92	3.02348
$683$	−1.35909e92	−1.03413	−0.517065	−	0.855946i	$-0.672976\pi$
$683$	−1.35909e92	−1.03413	−0.517065	+	0.855946i	$0.672976\pi$
$684$	−3.97698e92	−2.88556
$685$	2.95111e91	0.204193
$686$	−2.63299e92	−1.73747
$687$	−1.64149e92	−1.03310
$688$	−4.11438e92	−2.46991
$689$	−2.65594e91	−0.152088
$690$	−3.98473e91	−0.217673
$691$	−3.52140e92	−1.83518	−0.917590	−	0.397529i	$-0.869868\pi$
$691$	−3.52140e92	−1.83518	−0.917590	+	0.397529i	$0.869868\pi$
$692$	6.89018e92	3.42596
$693$	1.81760e92	0.862318
$694$	−1.28727e92	−0.582755
$695$	3.03934e92	1.31303
$696$	5.83662e92	2.40636
$697$	9.16491e91	0.360631
$698$	−2.07690e92	−0.780035
$699$	1.49772e92	0.536934
$700$	−1.97112e92	−0.674568
$701$	−1.31797e92	−0.430597	−0.215299	−	0.976548i	$-0.569072\pi$
$701$	−1.31797e92	−0.430597	−0.215299	+	0.976548i	$0.569072\pi$
$702$	−2.65725e91	−0.0828852
$703$	−8.34654e91	−0.248576
$704$	3.56791e91	0.101462
$705$	1.27842e92	0.347159
$706$	7.89629e92	2.04772
$707$	−4.69779e91	−0.116349
$708$	−2.28311e93	−5.40064
$709$	6.14299e91	0.138796	0.0693980	−	0.997589i	$-0.477892\pi$
$709$	6.14299e91	0.138796	0.0693980	+	0.997589i	$0.477892\pi$
$710$	8.82610e92	1.90490
$711$	8.92195e89	0.00183949
$712$	2.67137e92	0.526180
$713$	7.63093e91	0.143604
$714$	−8.99800e92	−1.61791
$715$	2.89483e92	0.497366
$716$	1.17559e93	1.93011
$717$	−6.79817e92	−1.06664
$718$	−8.23299e92	−1.23456
$719$	−4.30787e92	−0.617410	−0.308705	−	0.951158i	$-0.599896\pi$
$719$	−4.30787e92	−0.617410	−0.308705	+	0.951158i	$0.599896\pi$
$720$	1.33435e93	1.82795
$721$	−2.40751e92	−0.315262
$722$	−1.34565e93	−1.68451
$723$	6.87760e92	0.823080
$724$	2.03587e93	2.32941
$725$	−2.11912e92	−0.231830
$726$	4.58641e92	0.479769
$727$	9.48594e92	0.948882	0.474441	−	0.880287i	$-0.342650\pi$
$727$	9.48594e92	0.948882	0.474441	+	0.880287i	$0.342650\pi$
$728$	−1.15144e93	−1.10147
$729$	−9.39051e92	−0.859102
$730$	−4.28968e93	−3.75346
$731$	1.07737e93	0.901677
$732$	3.63422e93	2.90938
$733$	1.82856e93	1.40033	0.700163	−	0.713983i	$-0.253111\pi$
$733$	1.82856e93	1.40033	0.700163	+	0.713983i	$0.253111\pi$
$734$	−9.05008e92	−0.663026
$735$	1.36288e92	0.0955254
$736$	−1.02580e92	−0.0687913
$737$	−8.99012e92	−0.576862
$738$	1.56105e93	0.958486
$739$	−1.82418e93	−1.07183	−0.535913	−	0.844273i	$-0.680033\pi$
$739$	−1.82418e93	−1.07183	−0.535913	+	0.844273i	$0.680033\pi$
$740$	8.03729e92	0.451938
$741$	1.74878e93	0.941118
$742$	1.12256e93	0.578208
$743$	−4.24872e92	−0.209470	−0.104735	−	0.994500i	$-0.533399\pi$
$743$	−4.24872e92	−0.209470	−0.104735	+	0.994500i	$0.533399\pi$
$744$	−1.21329e94	−5.72590
$745$	−1.23536e93	−0.558102
$746$	1.47848e93	0.639444
$747$	−4.86873e92	−0.201602
$748$	3.17476e93	1.25866
$749$	3.59815e93	1.36590
$750$	5.51149e93	2.00345
$751$	−3.87442e93	−1.34868	−0.674340	−	0.738421i	$-0.735572\pi$
$751$	−3.87442e93	−1.34868	−0.674340	+	0.738421i	$0.735572\pi$
$752$	1.13560e93	0.378569
$753$	−7.86424e92	−0.251085
$754$	−2.24873e93	−0.687651
$755$	5.79207e93	1.69652
$756$	7.74825e92	0.217393
$757$	−6.09523e93	−1.63823	−0.819114	−	0.573631i	$-0.805534\pi$
$757$	−6.09523e93	−1.63823	−0.819114	+	0.573631i	$0.805534\pi$
$758$	3.45860e93	0.890535
$759$	−3.88168e92	−0.0957552
$760$	1.47374e94	3.48320
$761$	−5.86076e93	−1.32725	−0.663625	−	0.748066i	$-0.730983\pi$
$761$	−5.86076e93	−1.32725	−0.663625	+	0.748066i	$0.730983\pi$
$762$	1.58908e94	3.44834
$763$	−2.16548e93	−0.450304
$764$	−2.09658e94	−4.17809
$765$	−3.49408e93	−0.667323
$766$	−1.13493e94	−2.07747
$767$	4.84228e93	0.849573
$768$	−1.53936e94	−2.58881
$769$	−1.69848e93	−0.273813	−0.136906	−	0.990584i	$-0.543716\pi$
$769$	−1.69848e93	−0.273813	−0.136906	+	0.990584i	$0.543716\pi$
$770$	−1.22353e94	−1.89089
$771$	1.12516e94	1.66704
$772$	2.05852e94	2.92411
$773$	−3.19412e93	−0.435028	−0.217514	−	0.976057i	$-0.569795\pi$
$773$	−3.19412e93	−0.435028	−0.217514	+	0.976057i	$0.569795\pi$
$774$	1.83508e94	2.39648
$775$	4.40511e93	0.551635
$776$	−1.00667e94	−1.20887
$777$	−2.21905e93	−0.255555
$778$	7.63571e93	0.843359
$779$	7.52853e93	0.797522
$780$	−1.68399e94	−1.71106
$781$	8.59785e93	0.837976
$782$	9.26852e92	0.0866545
$783$	8.33001e92	0.0747117
$784$	1.21062e93	0.104168
$785$	−1.80443e94	−1.48962
$786$	−2.62068e94	−2.07578
$787$	−2.28522e93	−0.173680	−0.0868400	−	0.996222i	$-0.527677\pi$
$787$	−2.28522e93	−0.173680	−0.0868400	+	0.996222i	$0.527677\pi$
$788$	2.50453e94	1.82652
$789$	4.49072e93	0.314278
$790$	−6.00588e91	−0.00403363
$791$	2.51644e94	1.62200
$792$	2.97679e94	1.84153
$793$	−7.70787e93	−0.457674
$794$	−1.23178e94	−0.702047
$795$	9.03765e93	0.494452
$796$	−3.66667e94	−1.92574
$797$	3.12524e94	1.57575	0.787875	−	0.615835i	$-0.211181\pi$
$797$	3.12524e94	1.57575	0.787875	+	0.615835i	$0.211181\pi$
$798$	−7.39142e94	−3.57795
$799$	−2.97362e93	−0.138202
$800$	−5.92164e93	−0.264251
$801$	−5.20270e93	−0.222932
$802$	2.96417e94	1.21965
$803$	−4.17875e94	−1.65117
$804$	5.22976e94	1.98454
$805$	−2.46430e93	−0.0898105
$806$	4.67454e94	1.63625
$807$	−3.10806e94	−1.04496
$808$	−7.69386e93	−0.248471
$809$	−5.19331e94	−1.61108	−0.805541	−	0.592540i	$-0.798125\pi$
$809$	−5.19331e94	−1.61108	−0.805541	+	0.592540i	$0.798125\pi$
$810$	7.29177e94	2.17305
$811$	−6.77866e94	−1.94073	−0.970367	−	0.241635i	$-0.922316\pi$
$811$	−6.77866e94	−1.94073	−0.970367	+	0.241635i	$0.922316\pi$
$812$	6.55703e94	1.80358
$813$	−4.93043e92	−0.0130299
$814$	1.13489e94	0.288177
$815$	3.18364e94	0.776786
$816$	−6.43489e94	−1.50873
$817$	8.85009e94	1.99403
$818$	5.10255e94	1.10485
$819$	2.24253e94	0.466671
$820$	−7.24958e94	−1.44998
$821$	5.55656e94	1.06820	0.534101	−	0.845420i	$-0.320650\pi$
$821$	5.55656e94	1.06820	0.534101	+	0.845420i	$0.320650\pi$
$822$	−2.42406e94	−0.447930
$823$	−3.07724e94	−0.546596	−0.273298	−	0.961929i	$-0.588114\pi$
$823$	−3.07724e94	−0.546596	−0.273298	+	0.961929i	$0.588114\pi$
$824$	−3.94292e94	−0.673262
$825$	−2.24078e94	−0.367829
$826$	−2.04664e95	−3.22991
$827$	−8.43554e94	−1.27992	−0.639962	−	0.768407i	$-0.721050\pi$
$827$	−8.43554e94	−1.27992	−0.639962	+	0.768407i	$0.721050\pi$
$828$	1.08913e94	0.158888
$829$	1.11756e95	1.56765	0.783824	−	0.620984i	$-0.213267\pi$
$829$	1.11756e95	1.56765	0.783824	+	0.620984i	$0.213267\pi$
$830$	3.27742e94	0.442074
$831$	8.41669e94	1.09171
$832$	4.40205e93	0.0549094
$833$	−3.17007e93	−0.0380283
$834$	−2.49654e95	−2.88033
$835$	−3.04583e94	−0.337984
$836$	2.60791e95	2.78348
$837$	−1.73160e94	−0.177775
$838$	2.89970e95	2.86367
$839$	−9.28022e94	−0.881646	−0.440823	−	0.897594i	$-0.645313\pi$
$839$	−9.28022e94	−0.881646	−0.440823	+	0.897594i	$0.645313\pi$
$840$	3.91814e95	3.58099
$841$	−4.32351e94	−0.380160
$842$	−2.76176e95	−2.33638
$843$	1.42231e95	1.15770
$844$	−3.10355e95	−2.43069
$845$	−1.15253e95	−0.868579
$846$	−5.06495e94	−0.367315
$847$	2.83640e94	0.197950
$848$	8.02797e94	0.539188
$849$	6.40084e94	0.413749
$850$	5.35044e94	0.332870
$851$	2.28576e93	0.0136874
$852$	−5.00157e95	−2.88283
$853$	1.20372e95	0.667853	0.333926	−	0.942599i	$-0.391626\pi$
$853$	1.20372e95	0.667853	0.333926	+	0.942599i	$0.391626\pi$
$854$	3.25782e95	1.73999
$855$	−2.87021e95	−1.47576
$856$	5.89291e95	2.91697
$857$	−1.68193e95	−0.801549	−0.400774	−	0.916177i	$-0.631259\pi$
$857$	−1.68193e95	−0.801549	−0.400774	+	0.916177i	$0.631259\pi$
$858$	−2.37783e95	−1.09105
$859$	1.81782e95	0.803106	0.401553	−	0.915836i	$-0.368471\pi$
$859$	1.81782e95	0.803106	0.401553	+	0.915836i	$0.368471\pi$
$860$	−8.52218e95	−3.62536
$861$	2.00157e95	0.819913
$862$	6.44462e95	2.54221
$863$	3.05606e94	0.116094	0.0580471	−	0.998314i	$-0.481513\pi$
$863$	3.05606e94	0.116094	0.0580471	+	0.998314i	$0.481513\pi$
$864$	2.32773e94	0.0851601
$865$	4.97268e95	1.75213
$866$	−1.69389e95	−0.574849
$867$	−2.56699e95	−0.839080
$868$	−1.36304e96	−4.29159
$869$	−5.85057e92	−0.00177441
$870$	7.65197e95	2.23562
$871$	−1.10919e95	−0.312188
$872$	−3.54653e95	−0.961653
$873$	1.96056e95	0.512173
$874$	7.61364e94	0.191633
$875$	3.40850e95	0.826612
$876$	2.43087e96	5.68040
$877$	−3.29968e95	−0.742992	−0.371496	−	0.928434i	$-0.621155\pi$
$877$	−3.29968e95	−0.742992	−0.371496	+	0.928434i	$0.621155\pi$
$878$	7.36272e95	1.59759
$879$	−1.08333e96	−2.26529
$880$	−8.75003e95	−1.76329
$881$	3.35880e95	0.652330	0.326165	−	0.945313i	$-0.394244\pi$
$881$	3.35880e95	0.652330	0.326165	+	0.945313i	$0.394244\pi$
$882$	−5.39956e94	−0.101072
$883$	−3.89135e95	−0.702065	−0.351032	−	0.936363i	$-0.614169\pi$
$883$	−3.89135e95	−0.702065	−0.351032	+	0.936363i	$0.614169\pi$
$884$	3.91697e95	0.681164
$885$	−1.64773e96	−2.76204
$886$	−2.00110e96	−3.23349
$887$	8.02150e94	0.124951	0.0624753	−	0.998047i	$-0.480101\pi$
$887$	8.02150e94	0.124951	0.0624753	+	0.998047i	$0.480101\pi$
$888$	−3.63427e95	−0.545753
$889$	9.82745e95	1.42277
$890$	3.50224e95	0.488844
$891$	7.10320e95	0.955936
$892$	6.18775e95	0.802924
$893$	−2.44269e95	−0.305630
$894$	1.01473e96	1.22428
$895$	8.48430e95	0.987114
$896$	−1.00969e96	−1.13287
$897$	−4.78917e94	−0.0518210
$898$	1.95842e95	0.204373
$899$	−1.46539e96	−1.47490
$900$	6.28720e95	0.610346
$901$	−2.10217e95	−0.196839
$902$	−1.02366e96	−0.924577
$903$	2.35292e96	2.05001
$904$	4.12133e96	3.46388
$905$	1.46930e96	1.19133
$906$	−4.75765e96	−3.72157
$907$	9.19484e94	0.0693917	0.0346958	−	0.999398i	$-0.488954\pi$
$907$	9.19484e94	0.0693917	0.0346958	+	0.999398i	$0.488954\pi$
$908$	1.38499e96	1.00845
$909$	1.49844e95	0.105272
$910$	−1.50958e96	−1.02332
$911$	−1.26977e96	−0.830570	−0.415285	−	0.909691i	$-0.636318\pi$
$911$	−1.26977e96	−0.830570	−0.415285	+	0.909691i	$0.636318\pi$
$912$	−5.28595e96	−3.33649
$913$	3.19267e95	0.194470
$914$	3.45843e96	2.03295
$915$	2.62284e96	1.48794
$916$	−3.02019e96	−1.65360
$917$	−1.62072e96	−0.856455
$918$	−2.10320e95	−0.107274
$919$	−7.89845e94	−0.0388855	−0.0194427	−	0.999811i	$-0.506189\pi$
$919$	−7.89845e94	−0.0388855	−0.0194427	+	0.999811i	$0.506189\pi$
$920$	−4.03593e95	−0.191796
$921$	−1.12362e96	−0.515444
$922$	−4.67704e95	−0.207117
$923$	1.06079e96	0.453497
$924$	6.93349e96	2.86163
$925$	1.31950e95	0.0525780
$926$	5.65750e96	2.17654
$927$	7.67915e95	0.285247
$928$	1.96987e96	0.706525
$929$	−3.07843e96	−1.06615	−0.533076	−	0.846067i	$-0.678964\pi$
$929$	−3.07843e96	−1.06615	−0.533076	+	0.846067i	$0.678964\pi$
$930$	−1.59065e97	−5.31961
$931$	−2.60406e95	−0.0840981
$932$	2.75566e96	0.859426
$933$	−3.09665e96	−0.932693
$934$	5.32259e96	1.54828
$935$	2.29124e96	0.643714
$936$	3.67273e96	0.996606
$937$	−5.21997e96	−1.36814	−0.684071	−	0.729415i	$-0.739792\pi$
$937$	−5.21997e96	−1.36814	−0.684071	+	0.729415i	$0.739792\pi$
$938$	4.68811e96	1.18688
$939$	1.45689e96	0.356283
$940$	2.35218e96	0.555668
$941$	−2.77584e96	−0.633477	−0.316739	−	0.948513i	$-0.602588\pi$
$941$	−2.77584e96	−0.633477	−0.316739	+	0.948513i	$0.602588\pi$
$942$	1.48217e97	3.26772
$943$	−2.06174e95	−0.0439141
$944$	−1.46365e97	−3.01195
$945$	5.59196e95	0.111181
$946$	−1.20335e97	−2.31170
$947$	5.99294e96	1.11241	0.556206	−	0.831045i	$-0.312257\pi$
$947$	5.99294e96	1.11241	0.556206	+	0.831045i	$0.312257\pi$
$948$	3.40341e94	0.00610440
$949$	−5.15568e96	−0.893582
$950$	4.39513e96	0.736130
$951$	1.23329e97	1.99617
$952$	−9.11362e96	−1.42558
$953$	−7.84394e96	−1.18581	−0.592905	−	0.805273i	$-0.702019\pi$
$953$	−7.84394e96	−1.18581	−0.592905	+	0.805273i	$0.702019\pi$
$954$	−3.58060e96	−0.523159
$955$	−1.51311e97	−2.13679
$956$	−1.25080e97	−1.70729
$957$	7.45408e96	0.983459
$958$	2.45281e97	3.12813
$959$	−1.49913e96	−0.184813
$960$	−1.49793e96	−0.178515
$961$	2.17819e97	2.50949
$962$	1.40021e96	0.155956
$963$	−1.14769e97	−1.23586
$964$	1.26542e97	1.31744
$965$	1.48565e97	1.49547
$966$	2.02419e96	0.197013
$967$	−9.17776e96	−0.863727	−0.431863	−	0.901939i	$-0.642144\pi$
$967$	−9.17776e96	−0.863727	−0.431863	+	0.901939i	$0.642144\pi$
$968$	4.64534e96	0.422735
$969$	1.38415e97	1.21804
$970$	−1.31977e97	−1.12309
$971$	1.48138e97	1.21910	0.609552	−	0.792746i	$-0.291349\pi$
$971$	1.48138e97	1.21910	0.609552	+	0.792746i	$0.291349\pi$
$972$	−3.86684e97	−3.07753
$973$	−1.54395e97	−1.18841
$974$	−3.08433e96	−0.229612
$975$	−2.76465e96	−0.199062
$976$	2.32981e97	1.62257
$977$	−2.55083e97	−1.71834	−0.859169	−	0.511692i	$-0.829019\pi$
$977$	−2.55083e97	−1.71834	−0.859169	+	0.511692i	$0.829019\pi$
$978$	−2.61507e97	−1.70400
$979$	3.41167e96	0.215045
$980$	2.50757e96	0.152900
$981$	6.90715e96	0.407433
$982$	4.61155e96	0.263162
$983$	−1.22356e97	−0.675516	−0.337758	−	0.941233i	$-0.609669\pi$
$983$	−1.22356e97	−0.675516	−0.337758	+	0.941233i	$0.609669\pi$
$984$	3.27809e97	1.75097
$985$	1.80753e97	0.934133
$986$	−1.77986e97	−0.889990
$987$	−6.49423e96	−0.314210
$988$	3.21760e97	1.50637
$989$	−2.42366e96	−0.109798
$990$	3.90265e97	1.71087
$991$	1.04643e97	0.443931	0.221966	−	0.975054i	$-0.428753\pi$
$991$	1.04643e97	0.443931	0.221966	+	0.975054i	$0.428753\pi$
$992$	−4.09486e97	−1.68116
$993$	6.84517e96	0.271978
$994$	−4.48355e97	−1.72411
$995$	−2.64626e97	−0.984876
$996$	−1.85725e97	−0.669024
$997$	5.92859e96	0.206709	0.103354	−	0.994645i	$-0.467042\pi$
$997$	5.92859e96	0.206709	0.103354	+	0.994645i	$0.467042\pi$
$998$	4.92254e97	1.66130
$999$	−5.18682e95	−0.0169443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.66.a.a.1.1	✓	5
3.2	odd	2		9.66.a.b.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.66.a.a.1.1	✓	5	1.1	even	1	trivial
9.66.a.b.1.5		5	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:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 66 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-1.09073e10 q^{2} +4.46080e15 q^{3} +8.20747e19 q^{4} +5.92338e22 q^{5} -4.86551e25 q^{6} -3.00901e27 q^{7} -4.92803e29 q^{8} +9.59772e30 q^{9} +O(q^{10})\)	\(q-1.09073e10 q^{2} +4.46080e15 q^{3} +8.20747e19 q^{4} +5.92338e22 q^{5} -4.86551e25 q^{6} -3.00901e27 q^{7} -4.92803e29 q^{8} +9.59772e30 q^{9} -6.46079e32 q^{10} -6.29370e33 q^{11} +3.66119e35 q^{12} -7.76509e35 q^{13} +3.28200e37 q^{14} +2.64231e38 q^{15} +2.34711e39 q^{16} -6.14603e39 q^{17} -1.04685e41 q^{18} -5.04866e41 q^{19} +4.86160e42 q^{20} -1.34226e43 q^{21} +6.86470e43 q^{22} +1.38261e43 q^{23} -2.19830e45 q^{24} +7.98141e44 q^{25} +8.46958e45 q^{26} -3.13741e45 q^{27} -2.46963e47 q^{28} -2.65506e47 q^{29} -2.88203e48 q^{30} +5.51921e48 q^{31} -7.41928e48 q^{32} -2.80750e49 q^{33} +6.70363e49 q^{34} -1.78235e50 q^{35} +7.87731e50 q^{36} +1.65322e50 q^{37} +5.50670e51 q^{38} -3.46385e51 q^{39} -2.91906e52 q^{40} -1.49119e52 q^{41} +1.46404e53 q^{42} -1.75296e53 q^{43} -5.16554e53 q^{44} +5.68510e53 q^{45} -1.50805e53 q^{46} +4.83829e53 q^{47} +1.04700e55 q^{48} +5.15792e53 q^{49} -8.70553e54 q^{50} -2.74162e55 q^{51} -6.37318e55 q^{52} +3.42037e55 q^{53} +3.42205e55 q^{54} -3.72800e56 q^{55} +1.48285e57 q^{56} -2.25211e57 q^{57} +2.89594e57 q^{58} -6.23597e57 q^{59} +2.16867e58 q^{60} +9.92632e57 q^{61} -6.01994e58 q^{62} -2.88796e58 q^{63} -5.66902e57 q^{64} -4.59956e58 q^{65} +3.06221e59 q^{66} +1.42843e59 q^{67} -5.04434e59 q^{68} +6.16757e58 q^{69} +1.94405e60 q^{70} -1.36610e60 q^{71} -4.72979e60 q^{72} +6.63957e60 q^{73} -1.80321e60 q^{74} +3.56035e60 q^{75} -4.14368e61 q^{76} +1.89378e61 q^{77} +3.77811e61 q^{78} +9.29590e58 q^{79} +1.39028e62 q^{80} -1.12862e62 q^{81} +1.62648e62 q^{82} -5.07279e61 q^{83} -1.10166e63 q^{84} -3.64053e62 q^{85} +1.91200e63 q^{86} -1.18437e63 q^{87} +3.10156e63 q^{88} -5.42076e62 q^{89} -6.20088e63 q^{90} +2.33652e63 q^{91} +1.13478e63 q^{92} +2.46201e64 q^{93} -5.27724e63 q^{94} -2.99052e64 q^{95} -3.30960e64 q^{96} +2.04273e64 q^{97} -5.62587e63 q^{98} -6.04052e64 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3959709648 q^{2} - 22\!\cdots\!04 q^{3}+ \cdots + 31\!\cdots\!65 q^{9}+O(q^{10}) \) 5 * q - 3959709648 * q^2 - 2231307434935404 * q^3 + 116912191997379733760 * q^4 + 26879673327548389029150 * q^5 - 33295729280564090947602240 * q^6 - 6923148241844308586296558808 * q^7 - 446887903591926627901545861120 * q^8 + 31912530537586467884680398342465 * q^9	\( 5 q - 3959709648 q^{2} - 22\!\cdots\!04 q^{3}+ \cdots - 36\!\cdots\!20 q^{99}+O(q^{100}) \) 5 * q - 3959709648 * q^2 - 2231307434935404 * q^3 + 116912191997379733760 * q^4 + 26879673327548389029150 * q^5 - 33295729280564090947602240 * q^6 - 6923148241844308586296558808 * q^7 - 446887903591926627901545861120 * q^8 + 31912530537586467884680398342465 * q^9 - 46444835254758466872049375039200 * q^10 - 5436990447821613455266185060489540 * q^11 + 195800126486592722298045722544448512 * q^12 - 2890859300726790832888435764458467514 * q^13 + 41180574237900302034722115163160949120 * q^14 + 103408365234403422747890968078751873400 * q^15 - 1473868696955444538230489908858040811520 * q^16 + 13864680686430637673540501618888491948122 * q^17 - 52766923382337010938622933627608214498704 * q^18 - 532140170263349448171574488831326440156700 * q^19 + 3499008192062174379356405538388976603788800 * q^20 - 11546436905526557006526119132251889169971040 * q^21 + 22561892587607883403404755239099221639703104 * q^22 - 94948785027142700354971234970110107282841224 * q^23 - 2324009070474316353878252433966072715423334400 * q^24 - 89368364701600219577770390611457383673793125 * q^25 - 30521938596122123780659173092206061048452902240 * q^26 - 129706546221561841046313530503436938966984152120 * q^27 - 518698434811712968791028896222612623314185598976 * q^28 - 1144597713377055966543673581436050616842314015850 * q^29 - 8898165260141424207772350064014611180432376163200 * q^30 - 4708831653623167525869999868687533742455793996640 * q^31 - 23840662820937316611832895513659338085021120462848 * q^32 - 47088400041590886495026610585051639514556983630608 * q^33 + 65410975808473083189009824374957335825741658669920 * q^34 + 431016017471985629901399384019473069677000966146800 * q^35 + 1775126313486315490006860454334179833046020355380480 * q^36 + 2530086119390649596783488597048185172700211081307582 * q^37 + 8239199056511383470655384896825357549181759120989120 * q^38 + 4961423111454378211563271585245526388719534092320280 * q^39 - 40685898216651980081843388349290441658499772853248000 * q^40 - 32007461843289961215814846894363640801437553437785390 * q^41 - 195314045299892072857192155130437414288210017195751936 * q^42 - 402059303617352898401840600044858362031212461462830244 * q^43 - 612244818796766798372650999094717302459543241837614080 * q^44 + 1043713954525992259035161696571453857355706435519522950 * q^45 + 2514856669257653110995391415101692168449088734110815360 * q^46 + 1572646433047878010336915637334684433480129688652944112 * q^47 + 24675155031348794802454414815955354749687650397068722176 * q^48 + 16734108893933327602070337185312116893972489911225126685 * q^49 - 11063577880472461941859651947553302608752466885786430000 * q^50 - 95495399267422751891095337933943462124412320320925036440 * q^51 - 183526322178405888877826050411801068824199241263844049408 * q^52 - 95621521245111298200083441902514245466096845017659053554 * q^53 - 557318597848485774743582734276566483558675400940047747200 * q^54 - 383625033771696018967747534079220095868070927508130274200 * q^55 + 1279479797562181227760971870185499697207329786220906905600 * q^56 + 3318990221727917572672253796992679057503071099524130319760 * q^57 + 8032881606980455898794762567234097793264864123190024459680 * q^58 - 2559150002019539763980782190342674875710406916414141257300 * q^59 + 15929220555559091493107654286005818307326801014009906124800 * q^60 + 3946890902136488204413925902971677716173875604816310291510 * q^61 - 92928211608041968363364267171290588248132222513261182532096 * q^62 - 68802271924921645132530256442236118351318471682753406875384 * q^63 - 69150375570305937045593462943529104399703176808647979171840 * q^64 - 203428189337486180767895923031910965130055608932610312683100 * q^65 + 326824005648317890913619314213537102979279278284539154417920 * q^66 + 479747394632655989552085275852886843492252096722130444354772 * q^67 + 420712177041165958943716953506888102330291794585554871017984 * q^68 + 2085757498496947569861287804370568246775481786853310358067680 * q^69 + 2223344131713304350953089067854023542847735414462666460473600 * q^70 - 3493409458155820303614582574535715900391996656268214500281240 * q^71 - 6018736038355998608239490168867843174641985013841657017077760 * q^72 + 733760875924726020894973106598755498748960690384116338055026 * q^73 - 15514223525339201048939769580727994056556223964900985146362080 * q^74 - 14732126168569891490987332632351786074968338319638722054452500 * q^75 - 36133342560695069070126026304846041053110806476015652787276800 * q^76 + 25871798846989842274158113588872654076768674584213145553762784 * q^77 + 152853676099484832021645784710928259514016680275865958517430912 * q^78 + 59699536569481886874118825694486111435856996884515844586586000 * q^79 + 219177295509817100053456351931646916206927220422985017075302400 * q^80 - 65583962416587044196237908629906173582326728520698989687871395 * q^81 - 142296434381269688499177453649327032329978008843889237410699296 * q^82 + 209047534837132969695050943022419892956201321886275074830990116 * q^83 - 1354709036605046757778457263098823484206949849923331537372897280 * q^84 - 1670550938011517784167531235760024383135110452768829071189193700 * q^85 - 1010926193522040357819139524349238009908059943237053024421679040 * q^86 - 13125541831432259160108322296931402049512991915132402846472360 * q^87 + 3795986156893622389528985077855302896604937707291737426546933760 * q^88 + 1493974679319648583095502764787645056501586744645243776851520450 * q^89 + 11168691266815947461428091063256972957381716390895407392159178400 * q^90 + 2617522707396973663766320817347076504527878438540996722544653360 * q^91 + 5247747536363486457856850601737389388282095910031013129592297472 * q^92 + 18739223210125935355706186663397055877109210120967221009013809792 * q^93 - 12861091983377738108305257044091193029406256915207083515703514880 * q^94 - 82117654407511305658368168133560153272734117033702557537140601000 * q^95 - 56452805466036872845515504865736329476063459354106526340942397440 * q^96 - 31085940707578182510537462951801111142341367310530261899829858838 * q^97 - 46798198452208171360777266613142082443922483732249545388761625936 * q^98 - 36017030678524367090996061767134771004855794650938085175529135220 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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