LMFDB - Embedded newform 1.66.a.a.1.5

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			1.5
Root			$-1.84762e8$ 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)

$f(q)$	$=$	$q+8.07662e9 q^{2} +2.82746e15 q^{3} +2.83384e19 q^{4} -4.30990e22 q^{5} +2.28363e25 q^{6} -4.31488e27 q^{7} -6.90965e28 q^{8} -2.30651e30 q^{9} +O(q^{10})$	\(q+8.07662e9 q^{2} +2.82746e15 q^{3} +2.83384e19 q^{4} -4.30990e22 q^{5} +2.28363e25 q^{6} -4.31488e27 q^{7} -6.90965e28 q^{8} -2.30651e30 q^{9} -3.48095e32 q^{10} -3.09454e33 q^{11} +8.01256e34 q^{12} -1.30257e36 q^{13} -3.48497e37 q^{14} -1.21861e38 q^{15} -1.60357e39 q^{16} +1.01238e40 q^{17} -1.86288e40 q^{18} +6.77371e41 q^{19} -1.22136e42 q^{20} -1.22002e43 q^{21} -2.49934e43 q^{22} +2.44678e44 q^{23} -1.95368e44 q^{24} -8.52980e44 q^{25} -1.05204e46 q^{26} -3.56474e46 q^{27} -1.22277e47 q^{28} +6.24422e46 q^{29} -9.84224e47 q^{30} -4.23499e48 q^{31} -1.04022e49 q^{32} -8.74970e48 q^{33} +8.17660e49 q^{34} +1.85967e50 q^{35} -6.53627e49 q^{36} -6.58889e50 q^{37} +5.47087e51 q^{38} -3.68296e51 q^{39} +2.97799e51 q^{40} -3.22294e51 q^{41} -9.85361e52 q^{42} -7.33033e52 q^{43} -8.76942e52 q^{44} +9.94083e52 q^{45} +1.97617e54 q^{46} +4.96764e53 q^{47} -4.53403e54 q^{48} +1.00799e55 q^{49} -6.88920e54 q^{50} +2.86246e55 q^{51} -3.69126e55 q^{52} -1.14911e56 q^{53} -2.87911e56 q^{54} +1.33372e56 q^{55} +2.98143e56 q^{56} +1.91524e57 q^{57} +5.04323e56 q^{58} -7.39266e56 q^{59} -3.45334e57 q^{60} +1.27879e58 q^{61} -3.42044e58 q^{62} +9.95231e57 q^{63} -2.48535e58 q^{64} +5.61394e58 q^{65} -7.06680e58 q^{66} -1.92730e59 q^{67} +2.86892e59 q^{68} +6.91818e59 q^{69} +1.50199e60 q^{70} -1.96706e60 q^{71} +1.59372e59 q^{72} -4.77567e60 q^{73} -5.32160e60 q^{74} -2.41177e60 q^{75} +1.91956e61 q^{76} +1.33526e61 q^{77} -2.97459e61 q^{78} +1.98178e61 q^{79} +6.91122e61 q^{80} -7.70322e61 q^{81} -2.60304e61 q^{82} +3.39503e62 q^{83} -3.45732e62 q^{84} -4.36325e62 q^{85} -5.92043e62 q^{86} +1.76553e62 q^{87} +2.13822e62 q^{88} +8.38014e62 q^{89} +8.02883e62 q^{90} +5.62042e63 q^{91} +6.93378e63 q^{92} -1.19743e64 q^{93} +4.01217e63 q^{94} -2.91940e64 q^{95} -2.94118e64 q^{96} +1.21487e64 q^{97} +8.14112e64 q^{98} +7.13759e63 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	8.07662e9	1.32970	0.664852	−	0.746975i	$-0.268495\pi$
$2$	8.07662e9	1.32970	0.664852	+	0.746975i	$0.268495\pi$
$3$	2.82746e15	0.880960	0.440480	−	0.897763i	$-0.354808\pi$
$3$	2.82746e15	0.880960	0.440480	+	0.897763i	$0.354808\pi$
$4$	2.83384e19	0.768113
$5$	−4.30990e22	−0.827832	−0.413916	−	0.910315i	$-0.635839\pi$
$5$	−4.30990e22	−0.827832	−0.413916	+	0.910315i	$0.635839\pi$
$6$	2.28363e25	1.17142
$7$	−4.31488e27	−1.47667	−0.738333	−	0.674436i	$-0.764387\pi$
$7$	−4.31488e27	−1.47667	−0.738333	+	0.674436i	$0.764387\pi$
$8$	−6.90965e28	−0.308341
$9$	−2.30651e30	−0.223910
$10$	−3.48095e32	−1.10077
$11$	−3.09454e33	−0.441910	−0.220955	−	0.975284i	$-0.570917\pi$
$11$	−3.09454e33	−0.441910	−0.220955	+	0.975284i	$0.570917\pi$
$12$	8.01256e34	0.676676
$13$	−1.30257e36	−0.815908	−0.407954	−	0.913002i	$-0.633758\pi$
$13$	−1.30257e36	−0.815908	−0.407954	+	0.913002i	$0.633758\pi$
$14$	−3.48497e37	−1.96353
$15$	−1.21861e38	−0.729287
$16$	−1.60357e39	−1.17812
$17$	1.01238e40	1.03694	0.518469	−	0.855096i	$-0.326502\pi$
$17$	1.01238e40	1.03694	0.518469	+	0.855096i	$0.326502\pi$
$18$	−1.86288e40	−0.297734
$19$	6.77371e41	1.86782	0.933909	−	0.357512i	$-0.116375\pi$
$19$	6.77371e41	1.86782	0.933909	+	0.357512i	$0.116375\pi$
$20$	−1.22136e42	−0.635869
$21$	−1.22002e43	−1.30088
$22$	−2.49934e43	−0.587610
$23$	2.44678e44	1.35656	0.678282	−	0.734801i	$-0.262725\pi$
$23$	2.44678e44	1.35656	0.678282	+	0.734801i	$0.262725\pi$
$24$	−1.95368e44	−0.271636
$25$	−8.52980e44	−0.314694
$26$	−1.05204e46	−1.08492
$27$	−3.56474e46	−1.07822
$28$	−1.22277e47	−1.13425
$29$	6.24422e46	0.185158	0.0925792	−	0.995705i	$-0.470489\pi$
$29$	6.24422e46	0.185158	0.0925792	+	0.995705i	$0.470489\pi$
$30$	−9.84224e47	−0.969735
$31$	−4.23499e48	−1.43746	−0.718732	−	0.695287i	$-0.755277\pi$
$31$	−4.23499e48	−1.43746	−0.718732	+	0.695287i	$0.755277\pi$
$32$	−1.04022e49	−1.25820
$33$	−8.74970e48	−0.389305
$34$	8.17660e49	1.37882
$35$	1.85967e50	1.22243
$36$	−6.53627e49	−0.171988
$37$	−6.58889e50	−0.711633	−0.355817	−	0.934556i	$-0.615797\pi$
$37$	−6.58889e50	−0.711633	−0.355817	+	0.934556i	$0.615797\pi$
$38$	5.47087e51	2.48364
$39$	−3.68296e51	−0.718782
$40$	2.97799e51	0.255255
$41$	−3.22294e51	−0.123816	−0.0619079	−	0.998082i	$-0.519719\pi$
$41$	−3.22294e51	−0.123816	−0.0619079	+	0.998082i	$0.519719\pi$
$42$	−9.85361e52	−1.72979
$43$	−7.33033e52	−0.598961	−0.299481	−	0.954102i	$-0.596813\pi$
$43$	−7.33033e52	−0.598961	−0.299481	+	0.954102i	$0.596813\pi$
$44$	−8.76942e52	−0.339437
$45$	9.94083e52	0.185360
$46$	1.97617e54	1.80383
$47$	4.96764e53	0.225408	0.112704	−	0.993629i	$-0.464049\pi$
$47$	4.96764e53	0.225408	0.112704	+	0.993629i	$0.464049\pi$
$48$	−4.53403e54	−1.03787
$49$	1.00799e55	1.18054
$50$	−6.88920e54	−0.418450
$51$	2.86246e55	0.913501
$52$	−3.69126e55	−0.626710
$53$	−1.14911e56	−1.05050	−0.525249	−	0.850948i	$-0.676028\pi$
$53$	−1.14911e56	−1.05050	−0.525249	+	0.850948i	$0.676028\pi$
$54$	−2.87911e56	−1.43371
$55$	1.33372e56	0.365827
$56$	2.98143e56	0.455317
$57$	1.91524e57	1.64547
$58$	5.04323e56	0.246206
$59$	−7.39266e56	−0.207067	−0.103533	−	0.994626i	$-0.533015\pi$
$59$	−7.39266e56	−0.207067	−0.103533	+	0.994626i	$0.533015\pi$
$60$	−3.45334e57	−0.560174
$61$	1.27879e58	1.21222	0.606109	−	0.795381i	$-0.292729\pi$
$61$	1.27879e58	1.21222	0.606109	+	0.795381i	$0.292729\pi$
$62$	−3.42044e58	−1.91140
$63$	9.95231e57	0.330640
$64$	−2.48535e58	−0.494923
$65$	5.61394e58	0.675435
$66$	−7.06680e58	−0.517660
$67$	−1.92730e59	−0.866000	−0.433000	−	0.901394i	$-0.642545\pi$
$67$	−1.92730e59	−0.866000	−0.433000	+	0.901394i	$0.642545\pi$
$68$	2.86892e59	0.796486
$69$	6.91818e59	1.19508
$70$	1.50199e60	1.62547
$71$	−1.96706e60	−1.34252	−0.671259	−	0.741223i	$-0.734246\pi$
$71$	−1.96706e60	−1.34252	−0.671259	+	0.741223i	$0.734246\pi$
$72$	1.59372e59	0.0690407
$73$	−4.77567e60	−1.32142	−0.660711	−	0.750640i	$-0.729745\pi$
$73$	−4.77567e60	−1.32142	−0.660711	+	0.750640i	$0.729745\pi$
$74$	−5.32160e60	−0.946262
$75$	−2.41177e60	−0.277233
$76$	1.91956e61	1.43469
$77$	1.33526e61	0.652554
$78$	−2.97459e61	−0.955768
$79$	1.98178e61	0.420896	0.210448	−	0.977605i	$-0.432508\pi$
$79$	1.98178e61	0.420896	0.210448	+	0.977605i	$0.432508\pi$
$80$	6.91122e61	0.975282
$81$	−7.70322e61	−0.725954
$82$	−2.60304e61	−0.164638
$83$	3.39503e62	1.44812	0.724062	−	0.689735i	$-0.242273\pi$
$83$	3.39503e62	1.44812	0.724062	+	0.689735i	$0.242273\pi$
$84$	−3.45732e62	−0.999225
$85$	−4.36325e62	−0.858411
$86$	−5.92043e62	−0.796441
$87$	1.76553e62	0.163117
$88$	2.13822e62	0.136259
$89$	8.38014e62	0.369893	0.184947	−	0.982749i	$-0.440789\pi$
$89$	8.38014e62	0.369893	0.184947	+	0.982749i	$0.440789\pi$
$90$	8.02883e62	0.246474
$91$	5.62042e63	1.20482
$92$	6.93378e63	1.04199
$93$	−1.19743e64	−1.26635
$94$	4.01217e63	0.299726
$95$	−2.91940e64	−1.54624
$96$	−2.94118e64	−1.10843
$97$	1.21487e64	0.326925	0.163462	−	0.986550i	$-0.447734\pi$
$97$	1.21487e64	0.326925	0.163462	+	0.986550i	$0.447734\pi$
$98$	8.14112e64	1.56977
$99$	7.13759e63	0.0989481
$100$	−2.41721e64	−0.241721
$101$	−1.81750e65	−1.31532	−0.657659	−	0.753316i	$-0.728453\pi$
$101$	−1.81750e65	−1.31532	−0.657659	+	0.753316i	$0.728453\pi$
$102$	2.31190e65	1.21469
$103$	7.22881e64	0.276603	0.138302	−	0.990390i	$-0.455836\pi$
$103$	7.22881e64	0.276603	0.138302	+	0.990390i	$0.455836\pi$
$104$	9.00029e64	0.251578
$105$	5.25815e65	1.07691
$106$	−9.28092e65	−1.39685
$107$	5.97733e65	0.663032	0.331516	−	0.943450i	$-0.392440\pi$
$107$	5.97733e65	0.663032	0.331516	+	0.943450i	$0.392440\pi$
$108$	−1.01019e66	−0.828191
$109$	−2.74427e66	−1.66750	−0.833748	−	0.552145i	$-0.813810\pi$
$109$	−2.74427e66	−1.66750	−0.833748	+	0.552145i	$0.813810\pi$
$110$	1.07719e66	0.486442
$111$	−1.86298e66	−0.626920
$112$	6.91920e66	1.73968
$113$	−2.24114e66	−0.422105	−0.211052	−	0.977475i	$-0.567689\pi$
$113$	−2.24114e66	−0.422105	−0.211052	+	0.977475i	$0.567689\pi$
$114$	1.54687e67	2.18799
$115$	−1.05454e67	−1.12301
$116$	1.76951e66	0.142223
$117$	3.00439e66	0.182690
$118$	−5.97077e66	−0.275337
$119$	−4.36829e67	−1.53121
$120$	8.42016e66	0.224869
$121$	−3.94609e67	−0.804715
$122$	1.03283e68	1.61189
$123$	−9.11273e66	−0.109077
$124$	−1.20013e68	−1.10413
$125$	1.53583e68	1.08835
$126$	8.03811e67	0.439654
$127$	−1.73979e68	−0.735996	−0.367998	−	0.929827i	$-0.619957\pi$
$127$	−1.73979e68	−0.735996	−0.367998	+	0.929827i	$0.619957\pi$
$128$	1.83041e68	0.600102
$129$	−2.07262e68	−0.527661
$130$	4.53417e68	0.898129
$131$	8.44046e68	1.30331	0.651657	−	0.758514i	$-0.274074\pi$
$131$	8.44046e68	1.30331	0.651657	+	0.758514i	$0.274074\pi$
$132$	−2.47952e68	−0.299030
$133$	−2.92277e69	−2.75814
$134$	−1.55661e69	−1.15152
$135$	1.53637e69	0.892581
$136$	−6.99518e68	−0.319731
$137$	2.24176e69	0.807552	0.403776	−	0.914858i	$-0.367697\pi$
$137$	2.24176e69	0.807552	0.403776	+	0.914858i	$0.367697\pi$
$138$	5.58755e69	1.58910
$139$	−1.48500e69	−0.333999	−0.167000	−	0.985957i	$-0.553408\pi$
$139$	−1.48500e69	−0.333999	−0.167000	+	0.985957i	$0.553408\pi$
$140$	5.27000e69	0.938965
$141$	1.40458e69	0.198575
$142$	−1.58872e70	−1.78515
$143$	4.03085e69	0.360558
$144$	3.69864e69	0.263792
$145$	−2.69120e69	−0.153280
$146$	−3.85713e70	−1.75710
$147$	2.85004e70	1.04001
$148$	−1.86718e70	−0.546615
$149$	4.50509e70	1.05962	0.529809	−	0.848117i	$-0.322264\pi$
$149$	4.50509e70	1.05962	0.529809	+	0.848117i	$0.322264\pi$
$150$	−1.94789e70	−0.368637
$151$	3.20539e70	0.488799	0.244400	−	0.969675i	$-0.421409\pi$
$151$	3.20539e70	0.488799	0.244400	+	0.969675i	$0.421409\pi$
$152$	−4.68040e70	−0.575925
$153$	−2.33506e70	−0.232181
$154$	1.07844e71	0.867703
$155$	1.82524e71	1.18998
$156$	−1.04369e71	−0.552106
$157$	−1.50496e71	−0.646825	−0.323412	−	0.946258i	$-0.604830\pi$
$157$	−1.50496e71	−0.646825	−0.323412	+	0.946258i	$0.604830\pi$
$158$	1.60061e71	0.559667
$159$	−3.24906e71	−0.925447
$160$	4.48325e71	1.04158
$161$	−1.05576e72	−2.00319
$162$	−6.22160e71	−0.965304
$163$	6.37252e71	0.809495	0.404748	−	0.914428i	$-0.367359\pi$
$163$	6.37252e71	0.809495	0.404748	+	0.914428i	$0.367359\pi$
$164$	−9.13327e70	−0.0951046
$165$	3.77103e71	0.322279
$166$	2.74204e72	1.92558
$167$	9.46317e71	0.546703	0.273351	−	0.961914i	$-0.411868\pi$
$167$	9.46317e71	0.546703	0.273351	+	0.961914i	$0.411868\pi$
$168$	8.42988e71	0.401116
$169$	−8.52012e71	−0.334293
$170$	−3.52404e72	−1.14143
$171$	−1.56236e72	−0.418223
$172$	−2.07730e72	−0.460070
$173$	−3.57942e72	−0.656620	−0.328310	−	0.944570i	$-0.606479\pi$
$173$	−3.57942e72	−0.656620	−0.328310	+	0.944570i	$0.606479\pi$
$174$	1.42595e72	0.216898
$175$	3.68050e72	0.464698
$176$	4.96231e72	0.520621
$177$	−2.09025e72	−0.182417
$178$	6.76833e72	0.491848
$179$	−1.63064e73	−0.987720	−0.493860	−	0.869542i	$-0.664414\pi$
$179$	−1.63064e73	−0.987720	−0.493860	+	0.869542i	$0.664414\pi$
$180$	2.81707e72	0.142377
$181$	−1.71573e73	−0.724262	−0.362131	−	0.932127i	$-0.617951\pi$
$181$	−1.71573e73	−0.724262	−0.362131	+	0.932127i	$0.617951\pi$
$182$	4.53940e73	1.60206
$183$	3.61574e73	1.06792
$184$	−1.69064e73	−0.418285
$185$	2.83975e73	0.589113
$186$	−9.67116e73	−1.68387
$187$	−3.13285e73	−0.458234
$188$	1.40775e73	0.173139
$189$	1.53814e74	1.59216
$190$	−2.35789e74	−2.05604
$191$	−1.11944e74	−0.823028	−0.411514	−	0.911403i	$-0.635000\pi$
$191$	−1.11944e74	−0.823028	−0.411514	+	0.911403i	$0.635000\pi$
$192$	−7.02722e73	−0.436007
$193$	2.09216e74	1.09643	0.548216	−	0.836337i	$-0.315307\pi$
$193$	2.09216e74	1.09643	0.548216	+	0.836337i	$0.315307\pi$
$194$	9.81203e73	0.434713
$195$	1.58732e74	0.595031
$196$	2.85647e74	0.906790
$197$	1.49494e74	0.402227	0.201114	−	0.979568i	$-0.435544\pi$
$197$	1.49494e74	0.402227	0.201114	+	0.979568i	$0.435544\pi$
$198$	5.76476e73	0.131572
$199$	−1.87896e74	−0.364077	−0.182038	−	0.983291i	$-0.558270\pi$
$199$	−1.87896e74	−0.364077	−0.182038	+	0.983291i	$0.558270\pi$
$200$	5.89379e73	0.0970331
$201$	−5.44936e74	−0.762911
$202$	−1.46793e75	−1.74898
$203$	−2.69431e74	−0.273417
$204$	8.11175e74	0.701672
$205$	1.38905e74	0.102499
$206$	5.83844e74	0.367800
$207$	−5.64352e74	−0.303749
$208$	2.08876e75	0.961234
$209$	−2.09615e75	−0.825407
$210$	4.24681e75	1.43198
$211$	2.09402e74	0.0605063	0.0302532	−	0.999542i	$-0.490369\pi$
$211$	2.09402e74	0.0605063	0.0302532	+	0.999542i	$0.490369\pi$
$212$	−3.25639e75	−0.806901
$213$	−5.56178e75	−1.18270
$214$	4.82766e75	0.881636
$215$	3.15930e75	0.495839
$216$	2.46311e75	0.332458
$217$	1.82735e76	2.12265
$218$	−2.21644e76	−2.21728
$219$	−1.35030e76	−1.16412
$220$	3.77953e75	0.280997
$221$	−1.31869e76	−0.846047
$222$	−1.50466e76	−0.833619
$223$	−2.42481e75	−0.116083	−0.0580416	−	0.998314i	$-0.518486\pi$
$223$	−2.42481e75	−0.116083	−0.0580416	+	0.998314i	$0.518486\pi$
$224$	4.48842e76	1.85795
$225$	1.96741e75	0.0704632
$226$	−1.81009e76	−0.561274
$227$	5.23296e76	1.40575	0.702873	−	0.711315i	$-0.251900\pi$
$227$	5.23296e76	1.40575	0.702873	+	0.711315i	$0.251900\pi$
$228$	5.42748e76	1.26391
$229$	−1.29972e75	−0.0262541	−0.0131270	−	0.999914i	$-0.504179\pi$
$229$	−1.29972e75	−0.0262541	−0.0131270	+	0.999914i	$0.504179\pi$
$230$	−8.51711e76	−1.49327
$231$	3.77539e76	0.574873
$232$	−4.31454e75	−0.0570920
$233$	−1.38880e77	−1.59799	−0.798994	−	0.601338i	$-0.794634\pi$
$233$	−1.38880e77	−1.59799	−0.798994	+	0.601338i	$0.794634\pi$
$234$	2.42653e76	0.242924
$235$	−2.14100e76	−0.186600
$236$	−2.09496e76	−0.159051
$237$	5.60341e76	0.370793
$238$	−3.52810e77	−2.03606
$239$	2.72255e77	1.37102	0.685511	−	0.728062i	$-0.259579\pi$
$239$	2.72255e77	1.37102	0.685511	+	0.728062i	$0.259579\pi$
$240$	1.95412e77	0.859184
$241$	3.63695e77	1.39696	0.698479	−	0.715631i	$-0.253861\pi$
$241$	3.63695e77	1.39696	0.698479	+	0.715631i	$0.253861\pi$
$242$	−3.18711e77	−1.07003
$243$	1.49400e77	0.438679
$244$	3.62389e77	0.931121
$245$	−4.34432e77	−0.977291
$246$	−7.36001e76	−0.145040
$247$	−8.82321e77	−1.52397
$248$	2.92623e77	0.443230
$249$	9.59932e77	1.27574
$250$	1.24043e78	1.44718
$251$	−1.80617e78	−1.85081	−0.925406	−	0.378978i	$-0.876275\pi$
$251$	−1.80617e78	−1.85081	−0.925406	+	0.378978i	$0.876275\pi$
$252$	2.82032e77	0.253969
$253$	−7.57166e77	−0.599480
$254$	−1.40516e78	−0.978657
$255$	−1.23369e78	−0.756225
$256$	2.39529e78	1.29288
$257$	−2.54177e77	−0.120868	−0.0604338	−	0.998172i	$-0.519248\pi$
$257$	−2.54177e77	−0.120868	−0.0604338	+	0.998172i	$0.519248\pi$
$258$	−1.67398e78	−0.701632
$259$	2.84303e78	1.05084
$260$	1.59090e78	0.518810
$261$	−1.44024e77	−0.0414589
$262$	6.81704e78	1.73302
$263$	1.62486e77	0.0364968	0.0182484	−	0.999833i	$-0.494191\pi$
$263$	1.62486e77	0.0364968	0.0182484	+	0.999833i	$0.494191\pi$
$264$	6.04574e77	0.120039
$265$	4.95255e78	0.869636
$266$	−2.36061e79	−3.66751
$267$	2.36945e78	0.325861
$268$	−5.46165e78	−0.665185
$269$	−8.33021e78	−0.898891	−0.449445	−	0.893308i	$-0.648378\pi$
$269$	−8.33021e78	−0.898891	−0.449445	+	0.893308i	$0.648378\pi$
$270$	1.24087e79	1.18687
$271$	3.64165e78	0.308885	0.154442	−	0.988002i	$-0.450642\pi$
$271$	3.64165e78	0.308885	0.154442	+	0.988002i	$0.450642\pi$
$272$	−1.62342e79	−1.22163
$273$	1.58915e79	1.06140
$274$	1.81058e79	1.07381
$275$	2.63958e78	0.139066
$276$	1.96050e79	0.917955
$277$	−2.55025e79	−1.06167	−0.530836	−	0.847475i	$-0.678122\pi$
$277$	−2.55025e79	−1.06167	−0.530836	+	0.847475i	$0.678122\pi$
$278$	−1.19938e79	−0.444120
$279$	9.76804e78	0.321863
$280$	−1.28497e79	−0.376926
$281$	3.90687e79	1.02064	0.510321	−	0.859984i	$-0.329526\pi$
$281$	3.90687e79	1.02064	0.510321	+	0.859984i	$0.329526\pi$
$282$	1.13443e79	0.264046
$283$	4.89050e78	0.101460	0.0507299	−	0.998712i	$-0.483845\pi$
$283$	4.89050e78	0.101460	0.0507299	+	0.998712i	$0.483845\pi$
$284$	−5.57431e79	−1.03121
$285$	−8.25450e79	−1.36217
$286$	3.25557e79	0.479436
$287$	1.39066e79	0.182835
$288$	2.39928e79	0.281725
$289$	7.17196e78	0.0752416
$290$	−2.17358e79	−0.203817
$291$	3.43499e79	0.288007
$292$	−1.35335e80	−1.01500
$293$	−8.90054e79	−0.597336	−0.298668	−	0.954357i	$-0.596542\pi$
$293$	−8.90054e79	−0.597336	−0.298668	+	0.954357i	$0.596542\pi$
$294$	2.30187e80	1.38291
$295$	3.18616e79	0.171416
$296$	4.55270e79	0.219426
$297$	1.10312e80	0.476474
$298$	3.63859e80	1.40898
$299$	−3.18710e80	−1.10683
$300$	−6.83456e79	−0.212946
$301$	3.16295e80	0.884466
$302$	2.58887e80	0.649958
$303$	−5.13892e80	−1.15874
$304$	−1.08621e81	−2.20050
$305$	−5.51148e80	−1.00351
$306$	−1.88594e80	−0.308732
$307$	2.64643e80	0.389639	0.194820	−	0.980839i	$-0.437588\pi$
$307$	2.64643e80	0.389639	0.194820	+	0.980839i	$0.437588\pi$
$308$	3.78390e80	0.501235
$309$	2.04392e80	0.243676
$310$	1.47418e81	1.58232
$311$	6.77375e80	0.654812	0.327406	−	0.944884i	$-0.393826\pi$
$311$	6.77375e80	0.654812	0.327406	+	0.944884i	$0.393826\pi$
$312$	2.54480e80	0.221630
$313$	5.03991e80	0.395578	0.197789	−	0.980245i	$-0.436624\pi$
$313$	5.03991e80	0.395578	0.197789	+	0.980245i	$0.436624\pi$
$314$	−1.21550e81	−0.860086
$315$	−4.28935e80	−0.273715
$316$	5.61604e80	0.323296
$317$	6.95762e80	0.361439	0.180719	−	0.983535i	$-0.442157\pi$
$317$	6.95762e80	0.361439	0.180719	+	0.983535i	$0.442157\pi$
$318$	−2.62415e81	−1.23057
$319$	−1.93230e80	−0.0818234
$320$	1.07116e81	0.409713
$321$	1.69007e81	0.584104
$322$	−8.52695e81	−2.66365
$323$	6.85756e81	1.93681
$324$	−2.18297e81	−0.557615
$325$	1.11106e81	0.256761
$326$	5.14685e81	1.07639
$327$	−7.75931e81	−1.46900
$328$	2.22694e80	0.0381775
$329$	−2.14347e81	−0.332852
$330$	3.04572e81	0.428536
$331$	−6.41852e81	−0.818511	−0.409256	−	0.912420i	$-0.634212\pi$
$331$	−6.41852e81	−0.818511	−0.409256	+	0.912420i	$0.634212\pi$
$332$	9.62096e81	1.11232
$333$	1.51973e81	0.159342
$334$	7.64305e81	0.726953
$335$	8.30646e81	0.716902
$336$	1.95638e82	1.53259
$337$	−2.56545e82	−1.82470	−0.912351	−	0.409408i	$-0.865735\pi$
$337$	−2.56545e82	−1.82470	−0.912351	+	0.409408i	$0.865735\pi$
$338$	−6.88138e81	−0.444511
$339$	−6.33675e81	−0.371857
$340$	−1.23647e82	−0.659357
$341$	1.31053e82	0.635230
$342$	−1.26186e82	−0.556113
$343$	−6.65152e81	−0.266601
$344$	5.06500e81	0.184684
$345$	−2.98167e82	−0.989324
$346$	−2.89096e82	−0.873110
$347$	2.56415e82	0.705075	0.352538	−	0.935798i	$-0.385319\pi$
$347$	2.56415e82	0.705075	0.352538	+	0.935798i	$0.385319\pi$
$348$	5.00323e81	0.125292
$349$	4.48163e82	1.02237	0.511186	−	0.859470i	$-0.329206\pi$
$349$	4.48163e82	1.02237	0.511186	+	0.859470i	$0.329206\pi$
$350$	2.97260e82	0.617911
$351$	4.64332e82	0.879725
$352$	3.21900e82	0.556013
$353$	−2.99910e82	−0.472404	−0.236202	−	0.971704i	$-0.575903\pi$
$353$	−2.99910e82	−0.472404	−0.236202	+	0.971704i	$0.575903\pi$
$354$	−1.68821e82	−0.242561
$355$	8.47782e82	1.11138
$356$	2.37480e82	0.284120
$357$	−1.23512e83	−1.34894
$358$	−1.31700e83	−1.31337
$359$	−2.10675e83	−1.91886	−0.959430	−	0.281945i	$-0.909020\pi$
$359$	−2.10675e83	−1.91886	−0.959430	+	0.281945i	$0.909020\pi$
$360$	−6.86877e81	−0.0571541
$361$	3.27314e83	2.48874
$362$	−1.38573e83	−0.963054
$363$	−1.11574e83	−0.708922
$364$	1.59274e83	0.925441
$365$	2.05827e83	1.09392
$366$	2.92030e83	1.42001
$367$	−3.92372e83	−1.74603	−0.873014	−	0.487694i	$-0.837838\pi$
$367$	−3.92372e83	−1.74603	−0.873014	+	0.487694i	$0.837838\pi$
$368$	−3.92358e83	−1.59819
$369$	7.43373e81	0.0277236
$370$	2.29356e83	0.783346
$371$	4.95827e83	1.55124
$372$	−3.39331e83	−0.972698
$373$	1.26657e83	0.332730	0.166365	−	0.986064i	$-0.446797\pi$
$373$	1.26657e83	0.332730	0.166365	+	0.986064i	$0.446797\pi$
$374$	−2.53028e83	−0.609315
$375$	4.34249e83	0.958789
$376$	−3.43246e82	−0.0695026
$377$	−8.13353e82	−0.151072
$378$	1.24230e84	2.11711
$379$	−4.28255e83	−0.669773	−0.334887	−	0.942258i	$-0.608698\pi$
$379$	−4.28255e83	−0.669773	−0.334887	+	0.942258i	$0.608698\pi$
$380$	−8.27311e83	−1.18769
$381$	−4.91919e83	−0.648383
$382$	−9.04126e83	−1.09438
$383$	−9.73624e83	−1.08251	−0.541254	−	0.840859i	$-0.682050\pi$
$383$	−9.73624e83	−1.08251	−0.541254	+	0.840859i	$0.682050\pi$
$384$	5.17543e83	0.528666
$385$	−5.75483e83	−0.540205
$386$	1.68976e84	1.45793
$387$	1.69075e83	0.134113
$388$	3.44274e83	0.251115
$389$	−1.68070e84	−1.12753	−0.563766	−	0.825934i	$-0.690648\pi$
$389$	−1.68070e84	−1.12753	−0.563766	+	0.825934i	$0.690648\pi$
$390$	1.28202e84	0.791215
$391$	2.47707e84	1.40667
$392$	−6.96483e83	−0.364010
$393$	2.38651e84	1.14817
$394$	1.20741e84	0.534843
$395$	−8.54128e83	−0.348431
$396$	2.02268e83	0.0760033
$397$	−1.50384e84	−0.520608	−0.260304	−	0.965527i	$-0.583823\pi$
$397$	−1.50384e84	−0.520608	−0.260304	+	0.965527i	$0.583823\pi$
$398$	−1.51757e84	−0.484115
$399$	−8.26403e84	−2.42981
$400$	1.36781e84	0.370746
$401$	3.50343e84	0.875592	0.437796	−	0.899074i	$-0.355759\pi$
$401$	3.50343e84	0.875592	0.437796	+	0.899074i	$0.355759\pi$
$402$	−4.40124e84	−1.01445
$403$	5.51636e84	1.17284
$404$	−5.15051e84	−1.01031
$405$	3.32001e84	0.600968
$406$	−2.17609e84	−0.363564
$407$	2.03896e84	0.314478
$408$	−1.97786e84	−0.281670
$409$	6.85305e84	0.901315	0.450657	−	0.892697i	$-0.351190\pi$
$409$	6.85305e84	0.901315	0.450657	+	0.892697i	$0.351190\pi$
$410$	1.12189e84	0.136293
$411$	6.33849e84	0.711421
$412$	2.04853e84	0.212463
$413$	3.18984e84	0.305768
$414$	−4.55806e84	−0.403896
$415$	−1.46322e85	−1.19880
$416$	1.35496e85	1.02658
$417$	−4.19878e84	−0.294240
$418$	−1.69298e85	−1.09755
$419$	−3.91256e84	−0.234696	−0.117348	−	0.993091i	$-0.537439\pi$
$419$	−3.91256e84	−0.234696	−0.117348	+	0.993091i	$0.537439\pi$
$420$	1.49007e85	0.827191
$421$	1.58534e85	0.814620	0.407310	−	0.913290i	$-0.366467\pi$
$421$	1.58534e85	0.814620	0.407310	+	0.913290i	$0.366467\pi$
$422$	1.69126e84	0.0804555
$423$	−1.14579e84	−0.0504711
$424$	7.93994e84	0.323912
$425$	−8.63539e84	−0.326318
$426$	−4.49204e85	−1.57265
$427$	−5.51784e85	−1.79004
$428$	1.69388e85	0.509283
$429$	1.13971e85	0.317637
$430$	2.55165e85	0.659320
$431$	−3.17940e85	−0.761788	−0.380894	−	0.924619i	$-0.624384\pi$
$431$	−3.17940e85	−0.761788	−0.380894	+	0.924619i	$0.624384\pi$
$432$	5.71630e85	1.27026
$433$	−7.88778e84	−0.162592	−0.0812958	−	0.996690i	$-0.525906\pi$
$433$	−7.88778e84	−0.162592	−0.0812958	+	0.996690i	$0.525906\pi$
$434$	1.47588e86	2.82250
$435$	−7.60926e84	−0.135034
$436$	−7.77680e85	−1.28083
$437$	1.65738e86	2.53382
$438$	−1.09059e86	−1.54793
$439$	−3.47928e85	−0.458556	−0.229278	−	0.973361i	$-0.573637\pi$
$439$	−3.47928e85	−0.458556	−0.229278	+	0.973361i	$0.573637\pi$
$440$	−9.21552e84	−0.112800
$441$	−2.32493e85	−0.264335
$442$	−1.06506e86	−1.12499
$443$	−7.49927e85	−0.736034	−0.368017	−	0.929819i	$-0.619963\pi$
$443$	−7.49927e85	−0.736034	−0.368017	+	0.929819i	$0.619963\pi$
$444$	−5.27939e85	−0.481546
$445$	−3.61176e85	−0.306209
$446$	−1.95843e85	−0.154356
$447$	1.27380e86	0.933481
$448$	1.07240e86	0.730836
$449$	−3.20820e85	−0.203355	−0.101678	−	0.994817i	$-0.532421\pi$
$449$	−3.20820e85	−0.203355	−0.101678	+	0.994817i	$0.532421\pi$
$450$	1.58900e85	0.0936952
$451$	9.97350e84	0.0547155
$452$	−6.35103e85	−0.324224
$453$	9.06313e85	0.430612
$454$	4.22646e86	1.86923
$455$	−2.42235e86	−0.997392
$456$	−1.32336e86	−0.507367
$457$	4.78632e86	1.70893	0.854467	−	0.519505i	$-0.173884\pi$
$457$	4.78632e86	1.70893	0.854467	+	0.519505i	$0.173884\pi$
$458$	−1.04973e85	−0.0349101
$459$	−3.60887e86	−1.11804
$460$	−2.98839e86	−0.862597
$461$	−2.70244e86	−0.726902	−0.363451	−	0.931613i	$-0.618402\pi$
$461$	−2.70244e86	−0.726902	−0.363451	+	0.931613i	$0.618402\pi$
$462$	3.04924e86	0.764411
$463$	3.44950e86	0.806073	0.403036	−	0.915184i	$-0.367955\pi$
$463$	3.44950e86	0.806073	0.403036	+	0.915184i	$0.367955\pi$
$464$	−1.00130e86	−0.218138
$465$	5.16079e86	1.04832
$466$	−1.12169e87	−2.12485
$467$	−3.82062e86	−0.675048	−0.337524	−	0.941317i	$-0.609589\pi$
$467$	−3.82062e86	−0.675048	−0.337524	+	0.941317i	$0.609589\pi$
$468$	8.51394e85	0.140327
$469$	8.31606e86	1.27879
$470$	−1.72921e86	−0.248123
$471$	−4.25522e86	−0.569827
$472$	5.10807e85	0.0638472
$473$	2.26840e86	0.264687
$474$	4.52566e86	0.493044
$475$	−5.77784e86	−0.587791
$476$	−1.23790e87	−1.17614
$477$	2.65043e86	0.235217
$478$	2.19890e87	1.82305
$479$	−6.10105e86	−0.472607	−0.236304	−	0.971679i	$-0.575936\pi$
$479$	−6.10105e86	−0.472607	−0.236304	+	0.971679i	$0.575936\pi$
$480$	1.26762e87	0.917591
$481$	8.58248e86	0.580628
$482$	2.93743e87	1.85754
$483$	−2.98511e87	−1.76473
$484$	−1.11826e87	−0.618112
$485$	−5.23596e86	−0.270639
$486$	1.20665e87	0.583313
$487$	−2.58271e87	−1.16784	−0.583922	−	0.811810i	$-0.698483\pi$
$487$	−2.58271e87	−1.16784	−0.583922	+	0.811810i	$0.698483\pi$
$488$	−8.83602e86	−0.373777
$489$	1.80181e87	0.713133
$490$	−3.50874e87	−1.29951
$491$	−1.59135e87	−0.551590	−0.275795	−	0.961216i	$-0.588941\pi$
$491$	−1.59135e87	−0.551590	−0.275795	+	0.961216i	$0.588941\pi$
$492$	−2.58240e86	−0.0837833
$493$	6.32152e86	0.191998
$494$	−7.12618e87	−2.02643
$495$	−3.07623e86	−0.0819124
$496$	6.79109e87	1.69350
$497$	8.48761e87	1.98245
$498$	7.75301e87	1.69635
$499$	6.17736e86	0.126630	0.0633148	−	0.997994i	$-0.479833\pi$
$499$	6.17736e86	0.126630	0.0633148	+	0.997994i	$0.479833\pi$
$500$	4.35228e87	0.835973
$501$	2.67568e87	0.481623
$502$	−1.45877e88	−2.46103
$503$	−6.30784e87	−0.997520	−0.498760	−	0.866740i	$-0.666211\pi$
$503$	−6.30784e87	−0.997520	−0.498760	+	0.866740i	$0.666211\pi$
$504$	−6.87670e86	−0.101950
$505$	7.83327e87	1.08886
$506$	−6.11535e87	−0.797130
$507$	−2.40903e87	−0.294499
$508$	−4.93028e87	−0.565328
$509$	3.55481e87	0.382374	0.191187	−	0.981554i	$-0.438766\pi$
$509$	3.55481e87	0.382374	0.191187	+	0.981554i	$0.438766\pi$
$510$	−9.96408e87	−1.00556
$511$	2.06064e88	1.95130
$512$	1.25928e88	1.11905
$513$	−2.41465e88	−2.01391
$514$	−2.05289e87	−0.160718
$515$	−3.11555e87	−0.228981
$516$	−5.87347e87	−0.405303
$517$	−1.53725e87	−0.0996101
$518$	2.29621e88	1.39731
$519$	−1.01207e88	−0.578456
$520$	−3.87904e87	−0.208265
$521$	7.83300e86	0.0395096	0.0197548	−	0.999805i	$-0.493711\pi$
$521$	7.83300e86	0.0395096	0.0197548	+	0.999805i	$0.493711\pi$
$522$	−1.16322e87	−0.0551280
$523$	7.66258e87	0.341248	0.170624	−	0.985336i	$-0.445422\pi$
$523$	7.66258e87	0.341248	0.170624	+	0.985336i	$0.445422\pi$
$524$	2.39189e88	1.00109
$525$	1.04065e88	0.409380
$526$	1.31234e87	0.0485300
$527$	−4.28741e88	−1.49056
$528$	1.40307e88	0.458646
$529$	2.73355e88	0.840267
$530$	3.99999e88	1.15636
$531$	1.70512e87	0.0463643
$532$	−8.28266e88	−2.11856
$533$	4.19809e87	0.101022
$534$	1.91372e88	0.433299
$535$	−2.57617e88	−0.548879
$536$	1.33170e88	0.267023
$537$	−4.61056e88	−0.870141
$538$	−6.72800e88	−1.19526
$539$	−3.11925e88	−0.521694
$540$	4.35382e88	0.685603
$541$	4.26881e88	0.632989	0.316494	−	0.948594i	$-0.397494\pi$
$541$	4.26881e88	0.632989	0.316494	+	0.948594i	$0.397494\pi$
$542$	2.94123e88	0.410725
$543$	−4.85116e88	−0.638045
$544$	−1.05310e89	−1.30468
$545$	1.18275e89	1.38041
$546$	1.28350e89	1.41135
$547$	1.09284e89	1.13232	0.566162	−	0.824294i	$-0.308428\pi$
$547$	1.09284e89	1.13232	0.566162	+	0.824294i	$0.308428\pi$
$548$	6.35278e88	0.620291
$549$	−2.94955e88	−0.271428
$550$	2.13189e88	0.184917
$551$	4.22966e88	0.345842
$552$	−4.78022e88	−0.368492
$553$	−8.55114e88	−0.621523
$554$	−2.05974e89	−1.41171
$555$	8.02928e88	0.518985
$556$	−4.20825e88	−0.256549
$557$	−2.58989e89	−1.48932	−0.744659	−	0.667445i	$-0.767388\pi$
$557$	−2.58989e89	−1.48932	−0.744659	+	0.667445i	$0.767388\pi$
$558$	7.88928e88	0.427982
$559$	9.54825e88	0.488697
$560$	−2.98211e89	−1.44017
$561$	−8.85801e88	−0.403685
$562$	3.15543e89	1.35715
$563$	2.05127e88	0.0832720	0.0416360	−	0.999133i	$-0.486743\pi$
$563$	2.05127e88	0.0832720	0.0416360	+	0.999133i	$0.486743\pi$
$564$	3.98035e88	0.152528
$565$	9.65910e88	0.349432
$566$	3.94987e88	0.134912
$567$	3.32385e89	1.07199
$568$	1.35917e89	0.413954
$569$	−4.82021e88	−0.138649	−0.0693246	−	0.997594i	$-0.522084\pi$
$569$	−4.82021e88	−0.138649	−0.0693246	+	0.997594i	$0.522084\pi$
$570$	−6.66685e89	−1.81129
$571$	2.85877e89	0.733679	0.366839	−	0.930284i	$-0.380440\pi$
$571$	2.85877e89	0.733679	0.366839	+	0.930284i	$0.380440\pi$
$572$	1.14228e89	0.276949
$573$	−3.16516e89	−0.725055
$574$	1.12318e89	0.243116
$575$	−2.08705e89	−0.426903
$576$	5.73247e88	0.110818
$577$	7.19222e89	1.31416	0.657081	−	0.753820i	$-0.271791\pi$
$577$	7.19222e89	1.31416	0.657081	+	0.753820i	$0.271791\pi$
$578$	5.79252e88	0.100049
$579$	5.91549e89	0.965912
$580$	−7.62642e88	−0.117736
$581$	−1.46491e90	−2.13839
$582$	2.77431e89	0.382965
$583$	3.55596e89	0.464226
$584$	3.29982e89	0.407449
$585$	−1.29486e89	−0.151237
$586$	−7.18863e89	−0.794280
$587$	−1.35875e90	−1.42037	−0.710183	−	0.704017i	$-0.751388\pi$
$587$	−1.35875e90	−1.42037	−0.710183	+	0.704017i	$0.751388\pi$
$588$	8.07655e89	0.798845
$589$	−2.86866e90	−2.68492
$590$	2.57334e89	0.227933
$591$	4.22689e89	0.354346
$592$	1.05657e90	0.838386
$593$	1.95497e90	1.46846	0.734232	−	0.678898i	$-0.237542\pi$
$593$	1.95497e90	1.46846	0.734232	+	0.678898i	$0.237542\pi$
$594$	8.90951e89	0.633570
$595$	1.88269e90	1.26759
$596$	1.27667e90	0.813907
$597$	−5.31270e89	−0.320737
$598$	−2.57410e90	−1.47176
$599$	1.37765e90	0.746051	0.373026	−	0.927821i	$-0.378320\pi$
$599$	1.37765e90	0.746051	0.373026	+	0.927821i	$0.378320\pi$
$600$	1.66645e89	0.0854823
$601$	−3.62620e90	−1.76210	−0.881051	−	0.473022i	$-0.843163\pi$
$601$	−3.62620e90	−1.76210	−0.881051	+	0.473022i	$0.843163\pi$
$602$	2.55459e90	1.17608
$603$	4.44533e89	0.193906
$604$	9.08356e89	0.375453
$605$	1.70073e90	0.666169
$606$	−4.15052e90	−1.54078
$607$	3.08451e90	1.08531	0.542655	−	0.839956i	$-0.317419\pi$
$607$	3.08451e90	1.08531	0.542655	+	0.839956i	$0.317419\pi$
$608$	−7.04615e90	−2.35009
$609$	−7.61805e89	−0.240870
$610$	−4.45141e90	−1.33438
$611$	−6.47068e89	−0.183912
$612$	−6.61718e89	−0.178341
$613$	4.99238e90	1.27597	0.637987	−	0.770047i	$-0.279767\pi$
$613$	4.99238e90	1.27597	0.637987	+	0.770047i	$0.279767\pi$
$614$	2.13742e90	0.518105
$615$	3.92750e89	0.0902973
$616$	−9.22616e89	−0.201209
$617$	8.87952e90	1.83705	0.918526	−	0.395360i	$-0.129380\pi$
$617$	8.87952e90	1.83705	0.918526	+	0.395360i	$0.129380\pi$
$618$	1.65080e90	0.324017
$619$	−2.19932e90	−0.409584	−0.204792	−	0.978806i	$-0.565652\pi$
$619$	−2.19932e90	−0.409584	−0.204792	+	0.978806i	$0.565652\pi$
$620$	5.17243e90	0.914038
$621$	−8.72214e90	−1.46267
$622$	5.47090e90	0.870706
$623$	−3.61593e90	−0.546209
$624$	5.90588e90	0.846809
$625$	−4.30726e90	−0.586274
$626$	4.07055e90	0.526001
$627$	−5.92679e90	−0.727151
$628$	−4.26481e90	−0.496835
$629$	−6.67045e90	−0.737920
$630$	−3.46434e90	−0.363960
$631$	1.14120e91	1.13870	0.569348	−	0.822096i	$-0.307196\pi$
$631$	1.14120e91	1.13870	0.569348	+	0.822096i	$0.307196\pi$
$632$	−1.36934e90	−0.129780
$633$	5.92076e89	0.0533036
$634$	5.61941e90	0.480606
$635$	7.49832e90	0.609281
$636$	−9.20731e90	−0.710848
$637$	−1.31297e91	−0.963215
$638$	−1.56065e90	−0.108801
$639$	4.53703e90	0.300604
$640$	−7.88891e90	−0.496784
$641$	3.27620e90	0.196103	0.0980516	−	0.995181i	$-0.468739\pi$
$641$	3.27620e90	0.196103	0.0980516	+	0.995181i	$0.468739\pi$
$642$	1.36500e91	0.776686
$643$	−2.16180e91	−1.16939	−0.584695	−	0.811253i	$-0.698786\pi$
$643$	−2.16180e91	−1.16939	−0.584695	+	0.811253i	$0.698786\pi$
$644$	−2.99184e91	−1.53868
$645$	8.93280e90	0.436814
$646$	5.53859e91	2.57539
$647$	−1.42216e91	−0.628867	−0.314433	−	0.949280i	$-0.601815\pi$
$647$	−1.42216e91	−0.628867	−0.314433	+	0.949280i	$0.601815\pi$
$648$	5.32266e90	0.223842
$649$	2.28769e90	0.0915048
$650$	8.97365e90	0.341417
$651$	5.16675e91	1.86997
$652$	1.80587e91	0.621784
$653$	2.24492e91	0.735397	0.367698	−	0.929945i	$-0.380146\pi$
$653$	2.24492e91	0.735397	0.367698	+	0.929945i	$0.380146\pi$
$654$	−6.26690e91	−1.95333
$655$	−3.63776e91	−1.07893
$656$	5.16820e90	0.145869
$657$	1.10151e91	0.295880
$658$	−1.73120e91	−0.442595
$659$	−3.65576e91	−0.889615	−0.444807	−	0.895626i	$-0.646728\pi$
$659$	−3.65576e91	−0.889615	−0.444807	+	0.895626i	$0.646728\pi$
$660$	1.06865e91	0.247547
$661$	−5.31927e91	−1.17302	−0.586509	−	0.809943i	$-0.699498\pi$
$661$	−5.31927e91	−1.17302	−0.586509	+	0.809943i	$0.699498\pi$
$662$	−5.18399e91	−1.08838
$663$	−3.72855e91	−0.745333
$664$	−2.34585e91	−0.446516
$665$	1.25969e92	2.28328
$666$	1.22743e91	0.211878
$667$	1.52783e91	0.251179
$668$	2.68171e91	0.419929
$669$	−6.85605e90	−0.102265
$670$	6.70882e91	0.953268
$671$	−3.95728e91	−0.535692
$672$	1.26908e92	1.63678
$673$	1.15641e92	1.42109	0.710545	−	0.703651i	$-0.248448\pi$
$673$	1.15641e92	1.42109	0.710545	+	0.703651i	$0.248448\pi$
$674$	−2.07202e92	−2.42631
$675$	3.04065e91	0.339308
$676$	−2.41446e91	−0.256775
$677$	6.02999e90	0.0611202	0.0305601	−	0.999533i	$-0.490271\pi$
$677$	6.02999e90	0.0611202	0.0305601	+	0.999533i	$0.490271\pi$
$678$	−5.11795e91	−0.494460
$679$	−5.24201e91	−0.482758
$680$	3.01486e91	0.264684
$681$	1.47960e92	1.23841
$682$	1.05847e92	0.844668
$683$	−2.61306e92	−1.98828	−0.994138	−	0.108123i	$-0.965516\pi$
$683$	−2.61306e92	−1.98828	−0.994138	+	0.108123i	$0.965516\pi$
$684$	−4.42748e91	−0.321243
$685$	−9.66176e91	−0.668518
$686$	−5.37218e91	−0.354501
$687$	−3.67491e90	−0.0231288
$688$	1.17547e92	0.705645
$689$	1.49679e92	0.857111
$690$	−2.40818e92	−1.31551
$691$	7.16720e91	0.373519	0.186760	−	0.982406i	$-0.440201\pi$
$691$	7.16720e91	0.373519	0.186760	+	0.982406i	$0.440201\pi$
$692$	−1.01435e92	−0.504358
$693$	−3.07978e91	−0.146113
$694$	2.07097e92	0.937542
$695$	6.40020e91	0.276495
$696$	−1.21992e91	−0.0502957
$697$	−3.26283e91	−0.128389
$698$	3.61964e92	1.35945
$699$	−3.92679e92	−1.40776
$700$	1.04299e92	0.356940
$701$	−5.13430e91	−0.167744	−0.0838718	−	0.996477i	$-0.526729\pi$
$701$	−5.13430e91	−0.167744	−0.0838718	+	0.996477i	$0.526729\pi$
$702$	3.75023e92	1.16977
$703$	−4.46312e92	−1.32920
$704$	7.69100e91	0.218711
$705$	−6.05360e91	−0.164387
$706$	−2.42226e92	−0.628157
$707$	7.84231e92	1.94229
$708$	−5.92341e91	−0.140117
$709$	1.93775e92	0.437820	0.218910	−	0.975745i	$-0.429750\pi$
$709$	1.93775e92	0.437820	0.218910	+	0.975745i	$0.429750\pi$
$710$	6.84721e92	1.47781
$711$	−4.57099e91	−0.0942429
$712$	−5.79039e91	−0.114053
$713$	−1.03621e93	−1.95001
$714$	−9.97558e92	−1.79369
$715$	−1.73726e92	−0.298482
$716$	−4.62096e92	−0.758680
$717$	7.69792e92	1.20782
$718$	−1.70154e93	−2.55152
$719$	5.01688e92	0.719026	0.359513	−	0.933140i	$-0.382943\pi$
$719$	5.01688e92	0.719026	0.359513	+	0.933140i	$0.382943\pi$
$720$	−1.59408e92	−0.218375
$721$	−3.11915e92	−0.408451
$722$	2.64359e93	3.30929
$723$	1.02833e93	1.23066
$724$	−4.86210e92	−0.556315
$725$	−5.32620e91	−0.0582683
$726$	−9.01143e92	−0.942656
$727$	7.41150e92	0.741374	0.370687	−	0.928758i	$-0.379122\pi$
$727$	7.41150e92	0.741374	0.370687	+	0.928758i	$0.379122\pi$
$728$	−3.88352e92	−0.371497
$729$	1.21594e93	1.11241
$730$	1.66239e93	1.45458
$731$	−7.42107e92	−0.621086
$732$	1.02464e93	0.820280
$733$	1.44495e93	1.10656	0.553280	−	0.832995i	$-0.313376\pi$
$733$	1.44495e93	1.10656	0.553280	+	0.832995i	$0.313376\pi$
$734$	−3.16904e93	−2.32170
$735$	−1.22834e93	−0.860954
$736$	−2.54519e93	−1.70683
$737$	5.96410e92	0.382694
$738$	6.00395e91	0.0368642
$739$	−2.36880e93	−1.39182	−0.695912	−	0.718127i	$-0.745000\pi$
$739$	−2.36880e93	−1.39182	−0.695912	+	0.718127i	$0.745000\pi$
$740$	8.04738e92	0.452505
$741$	−2.49473e93	−1.34255
$742$	4.00460e93	2.06268
$743$	1.77150e93	0.873384	0.436692	−	0.899611i	$-0.356150\pi$
$743$	1.77150e93	0.873384	0.436692	+	0.899611i	$0.356150\pi$
$744$	8.27380e92	0.390467
$745$	−1.94165e93	−0.877186
$746$	1.02296e93	0.442433
$747$	−7.83067e92	−0.324250
$748$	−8.87797e92	−0.351975
$749$	−2.57915e93	−0.979077
$750$	3.50727e93	1.27491
$751$	5.24778e93	1.82675	0.913373	−	0.407125i	$-0.133469\pi$
$751$	5.24778e93	1.82675	0.913373	+	0.407125i	$0.133469\pi$
$752$	−7.96594e92	−0.265557
$753$	−5.10687e93	−1.63049
$754$	−6.56914e92	−0.200882
$755$	−1.38149e93	−0.404644
$756$	4.35884e93	1.22296
$757$	4.85964e93	1.30614	0.653068	−	0.757300i	$-0.273482\pi$
$757$	4.85964e93	1.30614	0.653068	+	0.757300i	$0.273482\pi$
$758$	−3.45885e93	−0.890600
$759$	−2.14086e93	−0.528117
$760$	2.01721e93	0.476769
$761$	−2.49197e92	−0.0564342	−0.0282171	−	0.999602i	$-0.508983\pi$
$761$	−2.49197e92	−0.0564342	−0.0282171	+	0.999602i	$0.508983\pi$
$762$	−3.97304e93	−0.862157
$763$	1.18412e94	2.46234
$764$	−3.17230e93	−0.632179
$765$	1.00639e93	0.192207
$766$	−7.86360e93	−1.43942
$767$	9.62944e92	0.168947
$768$	6.77259e93	1.13898
$769$	−1.14739e94	−1.84971	−0.924854	−	0.380323i	$-0.875813\pi$
$769$	−1.14739e94	−1.84971	−0.924854	+	0.380323i	$0.875813\pi$
$770$	−4.64796e93	−0.718313
$771$	−7.18676e92	−0.106480
$772$	5.92883e93	0.842183
$773$	−9.35627e93	−1.27429	−0.637146	−	0.770743i	$-0.719885\pi$
$773$	−9.35627e93	−1.27429	−0.637146	+	0.770743i	$0.719885\pi$
$774$	1.36555e93	0.178331
$775$	3.61236e93	0.452361
$776$	−8.39431e92	−0.100804
$777$	8.03855e93	0.925752
$778$	−1.35744e94	−1.49929
$779$	−2.18312e93	−0.231265
$780$	4.49821e93	0.457051
$781$	6.08713e93	0.593273
$782$	2.00064e94	1.87046
$783$	−2.22590e93	−0.199641
$784$	−1.61637e94	−1.39082
$785$	6.48624e93	0.535462
$786$	1.92749e94	1.52672
$787$	1.93082e93	0.146745	0.0733725	−	0.997305i	$-0.476624\pi$
$787$	1.93082e93	0.146745	0.0733725	+	0.997305i	$0.476624\pi$
$788$	4.23641e93	0.308956
$789$	4.59424e92	0.0321522
$790$	−6.89847e93	−0.463311
$791$	9.67026e93	0.623307
$792$	−4.93182e92	−0.0305098
$793$	−1.66572e94	−0.989060
$794$	−1.21460e94	−0.692255
$795$	1.40031e94	0.766115
$796$	−5.32467e93	−0.279652
$797$	−2.54244e94	−1.28190	−0.640952	−	0.767581i	$-0.721460\pi$
$797$	−2.54244e94	−1.28190	−0.640952	+	0.767581i	$0.721460\pi$
$798$	−6.67455e94	−3.23093
$799$	5.02913e93	0.233734
$800$	8.87287e93	0.395949
$801$	−1.93289e93	−0.0828228
$802$	2.82959e94	1.16428
$803$	1.47785e94	0.583950
$804$	−1.54426e94	−0.586002
$805$	4.55021e94	1.65831
$806$	4.45536e94	1.55953
$807$	−2.35534e94	−0.791887
$808$	1.25583e94	0.405567
$809$	−7.36019e93	−0.228330	−0.114165	−	0.993462i	$-0.536419\pi$
$809$	−7.36019e93	−0.228330	−0.114165	+	0.993462i	$0.536419\pi$
$810$	2.68145e94	0.799110
$811$	−1.74672e94	−0.500088	−0.250044	−	0.968234i	$-0.580445\pi$
$811$	−1.74672e94	−0.500088	−0.250044	+	0.968234i	$0.580445\pi$
$812$	−7.63523e93	−0.210015
$813$	1.02966e94	0.272115
$814$	1.64679e94	0.418163
$815$	−2.74650e94	−0.670126
$816$	−4.59015e94	−1.07621
$817$	−4.96535e94	−1.11875
$818$	5.53495e94	1.19848
$819$	−1.29636e94	−0.269772
$820$	3.93635e93	0.0787306
$821$	5.13658e94	0.987465	0.493733	−	0.869614i	$-0.335632\pi$
$821$	5.13658e94	0.987465	0.493733	+	0.869614i	$0.335632\pi$
$822$	5.11936e94	0.945979
$823$	−6.92758e94	−1.23051	−0.615257	−	0.788326i	$-0.710948\pi$
$823$	−6.92758e94	−1.23051	−0.615257	+	0.788326i	$0.710948\pi$
$824$	−4.99486e93	−0.0852882
$825$	7.46331e93	0.122512
$826$	2.57632e94	0.406581
$827$	−3.37947e94	−0.512766	−0.256383	−	0.966575i	$-0.582531\pi$
$827$	−3.37947e94	−0.512766	−0.256383	+	0.966575i	$0.582531\pi$
$828$	−1.59928e94	−0.233313
$829$	3.45099e94	0.484084	0.242042	−	0.970266i	$-0.422183\pi$
$829$	3.45099e94	0.484084	0.242042	+	0.970266i	$0.422183\pi$
$830$	−1.18179e95	−1.59405
$831$	−7.21073e94	−0.935289
$832$	3.23733e94	0.403812
$833$	1.02046e95	1.22415
$834$	−3.39120e94	−0.391252
$835$	−4.07853e94	−0.452578
$836$	−5.94015e94	−0.634006
$837$	1.50966e95	1.54990
$838$	−3.16003e94	−0.312076
$839$	5.24459e94	0.498251	0.249126	−	0.968471i	$-0.419857\pi$
$839$	5.24459e94	0.498251	0.249126	+	0.968471i	$0.419857\pi$
$840$	−3.63320e94	−0.332057
$841$	−1.09830e95	−0.965716
$842$	1.28042e95	1.08320
$843$	1.10465e95	0.899145
$844$	5.93411e93	0.0464757
$845$	3.67209e94	0.276739
$846$	−9.25411e93	−0.0671117
$847$	1.70269e95	1.18830
$848$	1.84267e95	1.23761
$849$	1.38277e94	0.0893820
$850$	−6.97448e94	−0.433907
$851$	−1.61216e95	−0.965377
$852$	−1.57612e95	−0.908451
$853$	−1.64299e95	−0.911574	−0.455787	−	0.890089i	$-0.650642\pi$
$853$	−1.64299e95	−0.911574	−0.455787	+	0.890089i	$0.650642\pi$
$854$	−4.45655e95	−2.38023
$855$	6.73363e94	0.346219
$856$	−4.13013e94	−0.204440
$857$	1.65574e95	0.789069	0.394535	−	0.918881i	$-0.370906\pi$
$857$	1.65574e95	0.789069	0.394535	+	0.918881i	$0.370906\pi$
$858$	9.20499e94	0.422363
$859$	9.71170e93	0.0429060	0.0214530	−	0.999770i	$-0.493171\pi$
$859$	9.71170e93	0.0429060	0.0214530	+	0.999770i	$0.493171\pi$
$860$	8.95294e94	0.380861
$861$	3.93203e94	0.161070
$862$	−2.56788e95	−1.01295
$863$	−4.06064e95	−1.54257	−0.771283	−	0.636492i	$-0.780385\pi$
$863$	−4.06064e95	−1.54257	−0.771283	+	0.636492i	$0.780385\pi$
$864$	3.70811e95	1.35661
$865$	1.54269e95	0.543571
$866$	−6.37067e94	−0.216199
$867$	2.02784e94	0.0662848
$868$	5.17840e95	1.63044
$869$	−6.13270e94	−0.185998
$870$	−6.14572e94	−0.179555
$871$	2.51044e95	0.706576
$872$	1.89619e95	0.514158
$873$	−2.80210e94	−0.0732017
$874$	1.33860e96	3.36922
$875$	−6.62691e95	−1.60712
$876$	−3.82654e95	−0.894175
$877$	−8.19676e95	−1.84568	−0.922838	−	0.385188i	$-0.874137\pi$
$877$	−8.19676e95	−1.84568	−0.922838	+	0.385188i	$0.874137\pi$
$878$	−2.81008e95	−0.609744
$879$	−2.51659e95	−0.526229
$880$	−2.13871e95	−0.430987
$881$	9.77446e95	1.89835	0.949174	−	0.314751i	$-0.101921\pi$
$881$	9.77446e95	1.89835	0.949174	+	0.314751i	$0.101921\pi$
$882$	−1.87776e95	−0.351488
$883$	−8.10448e94	−0.146219	−0.0731093	−	0.997324i	$-0.523292\pi$
$883$	−8.10448e94	−0.146219	−0.0731093	+	0.997324i	$0.523292\pi$
$884$	−3.73696e95	−0.649860
$885$	9.00875e94	0.151011
$886$	−6.05688e95	−0.978707
$887$	−3.11613e95	−0.485398	−0.242699	−	0.970102i	$-0.578033\pi$
$887$	−3.11613e95	−0.485398	−0.242699	+	0.970102i	$0.578033\pi$
$888$	1.28726e95	0.193305
$889$	7.50698e95	1.08682
$890$	−2.91708e95	−0.407168
$891$	2.38379e95	0.320806
$892$	−6.87151e94	−0.0891650
$893$	3.36493e95	0.421021
$894$	1.02880e96	1.24125
$895$	7.02788e95	0.817666
$896$	−7.89802e95	−0.886151
$897$	−9.01140e95	−0.975075
$898$	−2.59114e95	−0.270402
$899$	−2.64442e95	−0.266159
$900$	5.57531e94	0.0541237
$901$	−1.16333e96	−1.08930
$902$	8.05522e94	0.0727554
$903$	8.94312e95	0.779179
$904$	1.54855e95	0.130152
$905$	7.39463e95	0.599567
$906$	7.31995e95	0.572587
$907$	1.19814e96	0.904212	0.452106	−	0.891964i	$-0.350673\pi$
$907$	1.19814e96	0.904212	0.452106	+	0.891964i	$0.350673\pi$
$908$	1.48293e96	1.07977
$909$	4.19209e95	0.294513
$910$	−1.95644e96	−1.32624
$911$	1.91371e96	1.25178	0.625890	−	0.779912i	$-0.284736\pi$
$911$	1.91371e96	1.25178	0.625890	+	0.779912i	$0.284736\pi$
$912$	−3.07122e96	−1.93856
$913$	−1.05061e96	−0.639940
$914$	3.86573e96	2.27238
$915$	−1.55835e96	−0.884055
$916$	−3.68319e94	−0.0201661
$917$	−3.64196e96	−1.92456
$918$	−2.91475e96	−1.48667
$919$	−1.98334e96	−0.976435	−0.488217	−	0.872722i	$-0.662353\pi$
$919$	−1.98334e96	−0.976435	−0.488217	+	0.872722i	$0.662353\pi$
$920$	7.28650e95	0.346270
$921$	7.48267e95	0.343256
$922$	−2.18266e96	−0.966565
$923$	2.56222e96	1.09537
$924$	1.06988e96	0.441568
$925$	5.62019e95	0.223947
$926$	2.78603e96	1.07184
$927$	−1.66733e95	−0.0619343
$928$	−6.49537e95	−0.232967
$929$	−1.29350e96	−0.447976	−0.223988	−	0.974592i	$-0.571908\pi$
$929$	−1.29350e96	−0.447976	−0.223988	+	0.974592i	$0.571908\pi$
$930$	4.16818e96	1.39396
$931$	6.82780e96	2.20504
$932$	−3.93565e96	−1.22744
$933$	1.91525e96	0.576863
$934$	−3.08577e96	−0.897615
$935$	1.35023e96	0.379340
$936$	−2.07593e95	−0.0563309
$937$	−3.93665e96	−1.03179	−0.515893	−	0.856653i	$-0.672540\pi$
$937$	−3.93665e96	−1.03179	−0.515893	+	0.856653i	$0.672540\pi$
$938$	6.71657e96	1.70042
$939$	1.42502e96	0.348488
$940$	−6.06725e95	−0.143330
$941$	−5.34012e96	−1.21868	−0.609338	−	0.792911i	$-0.708565\pi$
$941$	−5.34012e96	−1.21868	−0.609338	+	0.792911i	$0.708565\pi$
$942$	−3.43678e96	−0.757701
$943$	−7.88582e95	−0.167964
$944$	1.18546e96	0.243948
$945$	−6.62924e96	−1.31804
$946$	1.83210e96	0.351955
$947$	−7.99905e96	−1.48479	−0.742393	−	0.669965i	$-0.766309\pi$
$947$	−7.99905e96	−1.48479	−0.742393	+	0.669965i	$0.766309\pi$
$948$	1.58791e96	0.284811
$949$	6.22064e96	1.07816
$950$	−4.66654e96	−0.781588
$951$	1.96724e96	0.318413
$952$	3.01834e96	0.472136
$953$	−3.08161e96	−0.465863	−0.232931	−	0.972493i	$-0.574832\pi$
$953$	−3.08161e96	−0.465863	−0.232931	+	0.972493i	$0.574832\pi$
$954$	2.14065e96	0.312769
$955$	4.82466e96	0.681329
$956$	7.71527e96	1.05310
$957$	−5.46351e95	−0.0720831
$958$	−4.92759e96	−0.628428
$959$	−9.67292e96	−1.19248
$960$	3.02866e96	0.360941
$961$	9.25531e96	1.06630
$962$	6.93175e96	0.772063
$963$	−1.37868e96	−0.148460
$964$	1.03065e97	1.07302
$965$	−9.01699e96	−0.907661
$966$	−2.41096e97	−2.34657
$967$	5.72011e96	0.538324	0.269162	−	0.963095i	$-0.413253\pi$
$967$	5.72011e96	0.538324	0.269162	+	0.963095i	$0.413253\pi$
$968$	2.72661e96	0.248127
$969$	1.93895e97	1.70625
$970$	−4.22889e96	−0.359869
$971$	1.96577e96	0.161774	0.0808870	−	0.996723i	$-0.474225\pi$
$971$	1.96577e96	0.161774	0.0808870	+	0.996723i	$0.474225\pi$
$972$	4.23375e96	0.336955
$973$	6.40759e96	0.493205
$974$	−2.08596e97	−1.55289
$975$	3.14149e96	0.226197
$976$	−2.05063e97	−1.42813
$977$	5.57249e96	0.375384	0.187692	−	0.982228i	$-0.439899\pi$
$977$	5.57249e96	0.375384	0.187692	+	0.982228i	$0.439899\pi$
$978$	1.45525e97	0.948256
$979$	−2.59327e96	−0.163460
$980$	−1.23111e97	−0.750670
$981$	6.32967e96	0.373369
$982$	−1.28527e97	−0.733452
$983$	1.57897e97	0.871735	0.435867	−	0.900011i	$-0.356442\pi$
$983$	1.57897e97	0.871735	0.435867	+	0.900011i	$0.356442\pi$
$984$	6.29658e95	0.0336329
$985$	−6.44304e96	−0.332977
$986$	5.10565e96	0.255300
$987$	−6.06059e96	−0.293229
$988$	−2.50035e97	−1.17058
$989$	−1.79357e97	−0.812530
$990$	−2.48456e96	−0.108919
$991$	−3.35919e97	−1.42508	−0.712542	−	0.701629i	$-0.752456\pi$
$991$	−3.35919e97	−1.42508	−0.712542	+	0.701629i	$0.752456\pi$
$992$	4.40532e97	1.80862
$993$	−1.81481e97	−0.721076
$994$	6.85512e97	2.63607
$995$	8.09814e96	0.301395
$996$	2.72029e97	0.979911
$997$	3.08734e97	1.07644	0.538222	−	0.842803i	$-0.319096\pi$
$997$	3.08734e97	1.07644	0.538222	+	0.842803i	$0.319096\pi$
$998$	4.98922e96	0.168380
$999$	2.34877e97	0.767294

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.66.a.a.1.5	✓	5	1.1	even	1	trivial
9.66.a.b.1.1		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)

\(f(q)\)	\(=\)	\(q+8.07662e9 q^{2} +2.82746e15 q^{3} +2.83384e19 q^{4} -4.30990e22 q^{5} +2.28363e25 q^{6} -4.31488e27 q^{7} -6.90965e28 q^{8} -2.30651e30 q^{9} +O(q^{10})\)	\(q+8.07662e9 q^{2} +2.82746e15 q^{3} +2.83384e19 q^{4} -4.30990e22 q^{5} +2.28363e25 q^{6} -4.31488e27 q^{7} -6.90965e28 q^{8} -2.30651e30 q^{9} -3.48095e32 q^{10} -3.09454e33 q^{11} +8.01256e34 q^{12} -1.30257e36 q^{13} -3.48497e37 q^{14} -1.21861e38 q^{15} -1.60357e39 q^{16} +1.01238e40 q^{17} -1.86288e40 q^{18} +6.77371e41 q^{19} -1.22136e42 q^{20} -1.22002e43 q^{21} -2.49934e43 q^{22} +2.44678e44 q^{23} -1.95368e44 q^{24} -8.52980e44 q^{25} -1.05204e46 q^{26} -3.56474e46 q^{27} -1.22277e47 q^{28} +6.24422e46 q^{29} -9.84224e47 q^{30} -4.23499e48 q^{31} -1.04022e49 q^{32} -8.74970e48 q^{33} +8.17660e49 q^{34} +1.85967e50 q^{35} -6.53627e49 q^{36} -6.58889e50 q^{37} +5.47087e51 q^{38} -3.68296e51 q^{39} +2.97799e51 q^{40} -3.22294e51 q^{41} -9.85361e52 q^{42} -7.33033e52 q^{43} -8.76942e52 q^{44} +9.94083e52 q^{45} +1.97617e54 q^{46} +4.96764e53 q^{47} -4.53403e54 q^{48} +1.00799e55 q^{49} -6.88920e54 q^{50} +2.86246e55 q^{51} -3.69126e55 q^{52} -1.14911e56 q^{53} -2.87911e56 q^{54} +1.33372e56 q^{55} +2.98143e56 q^{56} +1.91524e57 q^{57} +5.04323e56 q^{58} -7.39266e56 q^{59} -3.45334e57 q^{60} +1.27879e58 q^{61} -3.42044e58 q^{62} +9.95231e57 q^{63} -2.48535e58 q^{64} +5.61394e58 q^{65} -7.06680e58 q^{66} -1.92730e59 q^{67} +2.86892e59 q^{68} +6.91818e59 q^{69} +1.50199e60 q^{70} -1.96706e60 q^{71} +1.59372e59 q^{72} -4.77567e60 q^{73} -5.32160e60 q^{74} -2.41177e60 q^{75} +1.91956e61 q^{76} +1.33526e61 q^{77} -2.97459e61 q^{78} +1.98178e61 q^{79} +6.91122e61 q^{80} -7.70322e61 q^{81} -2.60304e61 q^{82} +3.39503e62 q^{83} -3.45732e62 q^{84} -4.36325e62 q^{85} -5.92043e62 q^{86} +1.76553e62 q^{87} +2.13822e62 q^{88} +8.38014e62 q^{89} +8.02883e62 q^{90} +5.62042e63 q^{91} +6.93378e63 q^{92} -1.19743e64 q^{93} +4.01217e63 q^{94} -2.91940e64 q^{95} -2.94118e64 q^{96} +1.21487e64 q^{97} +8.14112e64 q^{98} +7.13759e63 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3959709648 q^{2} - 22\!\cdots\!04 q^{3}+ \cdots + 31\!\cdots\!65 q^{9}+O(q^{10}) \) 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

Representations

Groups

Database

Properties

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