LMFDB - Embedded newform 1.66.a.a.1.4

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			1.4
Root			$-1.76800e8$ 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)

$f(q)$	$=$	$q+7.69444e9 q^{2} -5.56240e15 q^{3} +2.23108e19 q^{4} +6.36641e22 q^{5} -4.27995e25 q^{6} +1.82854e27 q^{7} -1.12205e29 q^{8} +2.06393e31 q^{9} +O(q^{10})$	\(q+7.69444e9 q^{2} -5.56240e15 q^{3} +2.23108e19 q^{4} +6.36641e22 q^{5} -4.27995e25 q^{6} +1.82854e27 q^{7} -1.12205e29 q^{8} +2.06393e31 q^{9} +4.89860e32 q^{10} -6.60418e31 q^{11} -1.24102e35 q^{12} -2.71546e36 q^{13} +1.40696e37 q^{14} -3.54126e38 q^{15} -1.68648e39 q^{16} +2.66707e39 q^{17} +1.58808e41 q^{18} -5.18513e41 q^{19} +1.42040e42 q^{20} -1.01711e43 q^{21} -5.08155e41 q^{22} -9.69847e43 q^{23} +6.24130e44 q^{24} +1.34262e45 q^{25} -2.08940e46 q^{26} -5.75053e46 q^{27} +4.07962e46 q^{28} +8.81829e46 q^{29} -2.72480e48 q^{30} -1.18148e48 q^{31} -8.83687e48 q^{32} +3.67351e47 q^{33} +2.05216e49 q^{34} +1.16412e50 q^{35} +4.60480e50 q^{36} +4.45413e50 q^{37} -3.98967e51 q^{38} +1.51045e52 q^{39} -7.14345e51 q^{40} -1.11431e52 q^{41} -7.82606e52 q^{42} -1.95096e53 q^{43} -1.47345e51 q^{44} +1.31398e54 q^{45} -7.46243e53 q^{46} -1.87891e54 q^{47} +9.38088e54 q^{48} -5.19477e54 q^{49} +1.03307e55 q^{50} -1.48353e55 q^{51} -6.05843e55 q^{52} +1.20429e56 q^{53} -4.42471e56 q^{54} -4.20450e54 q^{55} -2.05171e56 q^{56} +2.88418e57 q^{57} +6.78518e56 q^{58} +1.90217e57 q^{59} -7.90084e57 q^{60} -3.82531e57 q^{61} -9.09084e57 q^{62} +3.77397e58 q^{63} -5.77461e57 q^{64} -1.72878e59 q^{65} +2.82656e57 q^{66} +2.48352e59 q^{67} +5.95046e58 q^{68} +5.39468e59 q^{69} +8.95727e59 q^{70} -8.10901e59 q^{71} -2.31583e60 q^{72} -2.44135e60 q^{73} +3.42720e60 q^{74} -7.46818e60 q^{75} -1.15685e61 q^{76} -1.20760e59 q^{77} +1.16221e62 q^{78} -5.39042e61 q^{79} -1.07368e62 q^{80} +1.07262e62 q^{81} -8.57399e61 q^{82} +2.95526e62 q^{83} -2.26925e62 q^{84} +1.69797e62 q^{85} -1.50116e63 q^{86} -4.90509e62 q^{87} +7.41024e60 q^{88} +1.30157e63 q^{89} +1.01103e64 q^{90} -4.96533e63 q^{91} -2.16381e63 q^{92} +6.57188e63 q^{93} -1.44571e64 q^{94} -3.30107e64 q^{95} +4.91543e64 q^{96} -1.88312e64 q^{97} -3.99708e64 q^{98} -1.36306e63 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	7.69444e9	1.26678	0.633391	−	0.773832i	$-0.281662\pi$
$2$	7.69444e9	1.26678	0.633391	+	0.773832i	$0.281662\pi$
$3$	−5.56240e15	−1.73309	−0.866546	−	0.499097i	$-0.833665\pi$
$3$	−5.56240e15	−1.73309	−0.866546	+	0.499097i	$0.833665\pi$
$4$	2.23108e19	0.604737
$5$	6.36641e22	1.22284	0.611420	−	0.791306i	$-0.290599\pi$
$5$	6.36641e22	1.22284	0.611420	+	0.791306i	$0.290599\pi$
$6$	−4.27995e25	−2.19545
$7$	1.82854e27	0.625774	0.312887	−	0.949790i	$-0.398704\pi$
$7$	1.82854e27	0.625774	0.312887	+	0.949790i	$0.398704\pi$
$8$	−1.12205e29	−0.500712
$9$	2.06393e31	2.00361
$10$	4.89860e32	1.54907
$11$	−6.60418e31	−0.00943098	−0.00471549	−	0.999989i	$-0.501501\pi$
$11$	−6.60418e31	−0.00943098	−0.00471549	+	0.999989i	$0.501501\pi$
$12$	−1.24102e35	−1.04806
$13$	−2.71546e36	−1.70092	−0.850462	−	0.526036i	$-0.823678\pi$
$13$	−2.71546e36	−1.70092	−0.850462	+	0.526036i	$0.823678\pi$
$14$	1.40696e37	0.792720
$15$	−3.54126e38	−2.11929
$16$	−1.68648e39	−1.23903
$17$	2.66707e39	0.273177	0.136589	−	0.990628i	$-0.456386\pi$
$17$	2.66707e39	0.273177	0.136589	+	0.990628i	$0.456386\pi$
$18$	1.58808e41	2.53813
$19$	−5.18513e41	−1.42978	−0.714888	−	0.699239i	$-0.753522\pi$
$19$	−5.18513e41	−1.42978	−0.714888	+	0.699239i	$0.753522\pi$
$20$	1.42040e42	0.739496
$21$	−1.01711e43	−1.08452
$22$	−5.08155e41	−0.0119470
$23$	−9.69847e43	−0.537711	−0.268855	−	0.963181i	$-0.586645\pi$
$23$	−9.69847e43	−0.537711	−0.268855	+	0.963181i	$0.586645\pi$
$24$	6.24130e44	0.867781
$25$	1.34262e45	0.495338
$26$	−2.08940e46	−2.15470
$27$	−5.75053e46	−1.73934
$28$	4.07962e46	0.378429
$29$	8.81829e46	0.261487	0.130743	−	0.991416i	$-0.458264\pi$
$29$	8.81829e46	0.261487	0.130743	+	0.991416i	$0.458264\pi$
$30$	−2.72480e48	−2.68468
$31$	−1.18148e48	−0.401026	−0.200513	−	0.979691i	$-0.564261\pi$
$31$	−1.18148e48	−0.401026	−0.200513	+	0.979691i	$0.564261\pi$
$32$	−8.83687e48	−1.06887
$33$	3.67351e47	0.0163448
$34$	2.05216e49	0.346056
$35$	1.16412e50	0.765222
$36$	4.60480e50	1.21166
$37$	4.45413e50	0.481068	0.240534	−	0.970641i	$-0.422677\pi$
$37$	4.45413e50	0.481068	0.240534	+	0.970641i	$0.422677\pi$
$38$	−3.98967e51	−1.81121
$39$	1.51045e52	2.94786
$40$	−7.14345e51	−0.612291
$41$	−1.11431e52	−0.428086	−0.214043	−	0.976824i	$-0.568663\pi$
$41$	−1.11431e52	−0.428086	−0.214043	+	0.976824i	$0.568663\pi$
$42$	−7.82606e52	−1.37386
$43$	−1.95096e53	−1.59413	−0.797066	−	0.603892i	$-0.793616\pi$
$43$	−1.95096e53	−1.59413	−0.797066	+	0.603892i	$0.793616\pi$
$44$	−1.47345e51	−0.00570326
$45$	1.31398e54	2.45009
$46$	−7.46243e53	−0.681162
$47$	−1.87891e54	−0.852561	−0.426280	−	0.904591i	$-0.640176\pi$
$47$	−1.87891e54	−0.852561	−0.426280	+	0.904591i	$0.640176\pi$
$48$	9.38088e54	2.14735
$49$	−5.19477e54	−0.608407
$50$	1.03307e55	0.627486
$51$	−1.48353e55	−0.473442
$52$	−6.05843e55	−1.02861
$53$	1.20429e56	1.10095	0.550474	−	0.834852i	$-0.314447\pi$
$53$	1.20429e56	1.10095	0.550474	+	0.834852i	$0.314447\pi$
$54$	−4.42471e56	−2.20337
$55$	−4.20450e54	−0.0115326
$56$	−2.05171e56	−0.313333
$57$	2.88418e57	2.47793
$58$	6.78518e56	0.331247
$59$	1.90217e57	0.532794	0.266397	−	0.963863i	$-0.414167\pi$
$59$	1.90217e57	0.532794	0.266397	+	0.963863i	$0.414167\pi$
$60$	−7.90084e57	−1.28162
$61$	−3.82531e57	−0.362616	−0.181308	−	0.983426i	$-0.558033\pi$
$61$	−3.82531e57	−0.362616	−0.181308	+	0.983426i	$0.558033\pi$
$62$	−9.09084e57	−0.508012
$63$	3.77397e58	1.25381
$64$	−5.77461e57	−0.114993
$65$	−1.72878e59	−2.07996
$66$	2.82656e57	0.0207052
$67$	2.48352e59	1.11593	0.557963	−	0.829866i	$-0.311583\pi$
$67$	2.48352e59	1.11593	0.557963	+	0.829866i	$0.311583\pi$
$68$	5.95046e58	0.165200
$69$	5.39468e59	0.931902
$70$	8.95727e59	0.969369
$71$	−8.10901e59	−0.553441	−0.276721	−	0.960950i	$-0.589248\pi$
$71$	−8.10901e59	−0.553441	−0.276721	+	0.960950i	$0.589248\pi$
$72$	−2.31583e60	−1.00323
$73$	−2.44135e60	−0.675518	−0.337759	−	0.941233i	$-0.609669\pi$
$73$	−2.44135e60	−0.675518	−0.337759	+	0.941233i	$0.609669\pi$
$74$	3.42720e60	0.609409
$75$	−7.46818e60	−0.858467
$76$	−1.15685e61	−0.864638
$77$	−1.20760e59	−0.00590166
$78$	1.16221e62	3.73429
$79$	−5.39042e61	−1.14483	−0.572416	−	0.819963i	$-0.693994\pi$
$79$	−5.39042e61	−1.14483	−0.572416	+	0.819963i	$0.693994\pi$
$80$	−1.07368e62	−1.51514
$81$	1.07262e62	1.01084
$82$	−8.57399e61	−0.542291
$83$	2.95526e62	1.26054	0.630271	−	0.776375i	$-0.282944\pi$
$83$	2.95526e62	1.26054	0.630271	+	0.776375i	$0.282944\pi$
$84$	−2.26925e62	−0.655852
$85$	1.69797e62	0.334052
$86$	−1.50116e63	−2.01942
$87$	−4.90509e62	−0.453181
$88$	7.41024e60	0.00472221
$89$	1.30157e63	0.574503	0.287252	−	0.957855i	$-0.407258\pi$
$89$	1.30157e63	0.574503	0.287252	+	0.957855i	$0.407258\pi$
$90$	1.01103e64	3.10373
$91$	−4.96533e63	−1.06439
$92$	−2.16381e63	−0.325173
$93$	6.57188e63	0.695014
$94$	−1.44571e64	−1.08001
$95$	−3.30107e64	−1.74839
$96$	4.91543e64	1.85245
$97$	−1.88312e64	−0.506752	−0.253376	−	0.967368i	$-0.581541\pi$
$97$	−1.88312e64	−0.506752	−0.253376	+	0.967368i	$0.581541\pi$
$98$	−3.99708e64	−0.770719
$99$	−1.36306e63	−0.0188960
$100$	2.99549e64	0.299549
$101$	1.93492e65	1.40029	0.700147	−	0.713999i	$-0.253118\pi$
$101$	1.93492e65	1.40029	0.700147	+	0.713999i	$0.253118\pi$
$102$	−1.14149e65	−0.599747
$103$	6.56312e63	0.0251131	0.0125565	−	0.999921i	$-0.496003\pi$
$103$	6.56312e63	0.0251131	0.0125565	+	0.999921i	$0.496003\pi$
$104$	3.04689e65	0.851674
$105$	−6.47532e65	−1.32620
$106$	9.26636e65	1.39466
$107$	−2.60336e65	−0.288776	−0.144388	−	0.989521i	$-0.546121\pi$
$107$	−2.60336e65	−0.288776	−0.144388	+	0.989521i	$0.546121\pi$
$108$	−1.28299e66	−1.05185
$109$	−7.08454e65	−0.430478	−0.215239	−	0.976561i	$-0.569053\pi$
$109$	−7.08454e65	−0.430478	−0.215239	+	0.976561i	$0.569053\pi$
$110$	−3.23512e64	−0.0146093
$111$	−2.47757e66	−0.833736
$112$	−3.08379e66	−0.775353
$113$	9.27922e66	1.74768	0.873840	−	0.486214i	$-0.161622\pi$
$113$	9.27922e66	1.74768	0.873840	+	0.486214i	$0.161622\pi$
$114$	2.21921e67	3.13900
$115$	−6.17445e66	−0.657534
$116$	1.96744e66	0.158131
$117$	−5.60452e67	−3.40799
$118$	1.46361e67	0.674933
$119$	4.87684e66	0.170947
$120$	3.97347e67	1.06116
$121$	−4.90327e67	−0.999911
$122$	−2.94336e67	−0.459356
$123$	6.19824e67	0.741912
$124$	−2.63599e67	−0.242515
$125$	−8.70854e67	−0.617120
$126$	2.90386e68	1.58830
$127$	−3.13148e68	−1.32474	−0.662368	−	0.749179i	$-0.730448\pi$
$127$	−3.13148e68	−1.32474	−0.662368	+	0.749179i	$0.730448\pi$
$128$	2.81591e68	0.923197
$129$	1.08520e69	2.76278
$130$	−1.33020e69	−2.63485
$131$	−1.75019e68	−0.270252	−0.135126	−	0.990828i	$-0.543144\pi$
$131$	−1.75019e68	−0.270252	−0.135126	+	0.990828i	$0.543144\pi$
$132$	8.19592e66	0.00988427
$133$	−9.48121e68	−0.894717
$134$	1.91092e69	1.41364
$135$	−3.66103e69	−2.12694
$136$	−2.99259e68	−0.136783
$137$	1.86067e69	0.670271	0.335135	−	0.942170i	$-0.391218\pi$
$137$	1.86067e69	0.670271	0.335135	+	0.942170i	$0.391218\pi$
$138$	4.15090e69	1.18052
$139$	−2.01831e68	−0.0453948	−0.0226974	−	0.999742i	$-0.507225\pi$
$139$	−2.01831e68	−0.0453948	−0.0226974	+	0.999742i	$0.507225\pi$
$140$	2.59726e69	0.462758
$141$	1.04513e70	1.47757
$142$	−6.23943e69	−0.701089
$143$	1.79334e68	0.0160414
$144$	−3.48077e70	−2.48253
$145$	5.61409e69	0.319756
$146$	−1.87848e70	−0.855734
$147$	2.88954e70	1.05442
$148$	9.93754e69	0.290920
$149$	6.22808e70	1.46488	0.732438	−	0.680834i	$-0.238383\pi$
$149$	6.22808e70	1.46488	0.732438	+	0.680834i	$0.238383\pi$
$150$	−5.74634e70	−1.08749
$151$	−8.46222e70	−1.29043	−0.645214	−	0.764002i	$-0.723232\pi$
$151$	−8.46222e70	−1.29043	−0.645214	+	0.764002i	$0.723232\pi$
$152$	5.81799e70	0.715907
$153$	5.50464e70	0.547341
$154$	−9.29180e68	−0.00747612
$155$	−7.52180e70	−0.490390
$156$	3.36994e71	1.78268
$157$	3.56741e71	1.53326	0.766628	−	0.642091i	$-0.221933\pi$
$157$	3.56741e71	1.53326	0.766628	+	0.642091i	$0.221933\pi$
$158$	−4.14762e71	−1.45025
$159$	−6.69877e71	−1.90804
$160$	−5.62592e71	−1.30706
$161$	−1.77340e71	−0.336485
$162$	8.25317e71	1.28051
$163$	4.70096e71	0.597158	0.298579	−	0.954385i	$-0.403487\pi$
$163$	4.70096e71	0.597158	0.298579	+	0.954385i	$0.403487\pi$
$164$	−2.48612e71	−0.258879
$165$	2.33871e70	0.0199870
$166$	2.27390e72	1.59683
$167$	−2.51276e72	−1.45166	−0.725832	−	0.687872i	$-0.758545\pi$
$167$	−2.51276e72	−1.45166	−0.725832	+	0.687872i	$0.758545\pi$
$168$	1.14125e72	0.543035
$169$	4.82505e72	1.89314
$170$	1.30649e72	0.423172
$171$	−1.07017e73	−2.86471
$172$	−4.35277e72	−0.964030
$173$	6.07054e72	1.11360	0.556800	−	0.830647i	$-0.312029\pi$
$173$	6.07054e72	1.11360	0.556800	+	0.830647i	$0.312029\pi$
$174$	−3.77419e72	−0.574081
$175$	2.45503e72	0.309970
$176$	1.11378e71	0.0116853
$177$	−1.05806e73	−0.923380
$178$	1.00148e73	0.727770
$179$	1.50731e73	0.913019	0.456509	−	0.889719i	$-0.349099\pi$
$179$	1.50731e73	0.913019	0.456509	+	0.889719i	$0.349099\pi$
$180$	2.93160e73	1.48166
$181$	−3.08872e73	−1.30384	−0.651921	−	0.758287i	$-0.726037\pi$
$181$	−3.08872e73	−1.30384	−0.651921	+	0.758287i	$0.726037\pi$
$182$	−3.82054e73	−1.34836
$183$	2.12779e73	0.628447
$184$	1.08822e73	0.269238
$185$	2.83568e73	0.588270
$186$	5.05669e73	0.880432
$187$	−1.76138e71	−0.00257633
$188$	−4.19201e73	−0.515575
$189$	−1.05151e74	−1.08844
$190$	−2.53999e74	−2.21483
$191$	1.07944e74	0.793619	0.396810	−	0.917901i	$-0.370117\pi$
$191$	1.07944e74	0.793619	0.396810	+	0.917901i	$0.370117\pi$
$192$	3.21207e73	0.199294
$193$	1.82335e73	0.0955561	0.0477780	−	0.998858i	$-0.484786\pi$
$193$	1.82335e73	0.0955561	0.0477780	+	0.998858i	$0.484786\pi$
$194$	−1.44895e74	−0.641945
$195$	9.61615e74	3.60476
$196$	−1.15900e74	−0.367926
$197$	2.66005e74	0.715710	0.357855	−	0.933777i	$-0.383508\pi$
$197$	2.66005e74	0.715710	0.357855	+	0.933777i	$0.383508\pi$
$198$	−1.04879e73	−0.0239371
$199$	−8.37150e74	−1.62210	−0.811051	−	0.584975i	$-0.801104\pi$
$199$	−8.37150e74	−1.62210	−0.811051	+	0.584975i	$0.801104\pi$
$200$	−1.50649e74	−0.248022
$201$	−1.38143e75	−1.93400
$202$	1.48881e75	1.77387
$203$	1.61246e74	0.163632
$204$	−3.30989e74	−0.286308
$205$	−7.09416e74	−0.523481
$206$	5.04995e73	0.0318128
$207$	−2.00169e75	−1.07736
$208$	4.57958e75	2.10750
$209$	3.42436e73	0.0134842
$210$	−4.98239e75	−1.68001
$211$	4.64754e75	1.34290	0.671450	−	0.741050i	$-0.265672\pi$
$211$	4.64754e75	1.34290	0.671450	+	0.741050i	$0.265672\pi$
$212$	2.68688e75	0.665784
$213$	4.51056e75	0.959165
$214$	−2.00314e75	−0.365817
$215$	−1.24206e76	−1.94937
$216$	6.45240e75	0.870912
$217$	−2.16038e75	−0.250951
$218$	−5.45116e75	−0.545321
$219$	1.35798e76	1.17073
$220$	−9.38059e73	−0.00697418
$221$	−7.24234e75	−0.464654
$222$	−1.90635e76	−1.05616
$223$	−2.05561e76	−0.984087	−0.492044	−	0.870571i	$-0.663750\pi$
$223$	−2.05561e76	−0.984087	−0.492044	+	0.870571i	$0.663750\pi$
$224$	−1.61586e76	−0.668870
$225$	2.77106e76	0.992464
$226$	7.13983e76	2.21393
$227$	−6.07971e75	−0.163321	−0.0816606	−	0.996660i	$-0.526022\pi$
$227$	−6.07971e75	−0.163321	−0.0816606	+	0.996660i	$0.526022\pi$
$228$	6.43485e76	1.49850
$229$	−1.28178e76	−0.258918	−0.129459	−	0.991585i	$-0.541324\pi$
$229$	−1.28178e76	−0.258918	−0.129459	+	0.991585i	$0.541324\pi$
$230$	−4.75089e76	−0.832953
$231$	6.71716e74	0.0102281
$232$	−9.89458e75	−0.130930
$233$	1.53244e77	1.76326	0.881628	−	0.471945i	$-0.156448\pi$
$233$	1.53244e77	1.76326	0.881628	+	0.471945i	$0.156448\pi$
$234$	−4.31236e77	−4.31718
$235$	−1.19619e77	−1.04255
$236$	4.24390e76	0.322200
$237$	2.99837e77	1.98410
$238$	3.75246e76	0.216553
$239$	−9.89282e76	−0.498182	−0.249091	−	0.968480i	$-0.580132\pi$
$239$	−9.89282e76	−0.498182	−0.249091	+	0.968480i	$0.580132\pi$
$240$	5.97226e77	2.62587
$241$	−1.95874e77	−0.752354	−0.376177	−	0.926548i	$-0.622762\pi$
$241$	−1.95874e77	−0.752354	−0.376177	+	0.926548i	$0.622762\pi$
$242$	−3.77279e77	−1.26667
$243$	−4.26677e75	−0.0125284
$244$	−8.53459e76	−0.219287
$245$	−3.30721e77	−0.743984
$246$	4.76920e77	0.939841
$247$	1.40800e78	2.43194
$248$	1.32568e77	0.200799
$249$	−1.64383e78	−2.18464
$250$	−6.70073e77	−0.781757
$251$	1.01010e77	0.103506	0.0517531	−	0.998660i	$-0.483519\pi$
$251$	1.01010e77	0.103506	0.0517531	+	0.998660i	$0.483519\pi$
$252$	8.42004e77	0.758223
$253$	6.40505e75	0.00507114
$254$	−2.40950e78	−1.67815
$255$	−9.44479e77	−0.578944
$256$	2.37973e78	1.28448
$257$	−4.05414e78	−1.92785	−0.963923	−	0.266183i	$-0.914238\pi$
$257$	−4.05414e78	−1.92785	−0.963923	+	0.266183i	$0.914238\pi$
$258$	8.35004e78	3.49984
$259$	8.14454e77	0.301040
$260$	−3.85705e78	−1.25783
$261$	1.82003e78	0.523917
$262$	−1.34667e78	−0.342350
$263$	3.09616e78	0.695444	0.347722	−	0.937598i	$-0.386955\pi$
$263$	3.09616e78	0.695444	0.347722	+	0.937598i	$0.386955\pi$
$264$	−4.12187e76	−0.00818402
$265$	7.66703e78	1.34628
$266$	−7.29526e78	−1.13341
$267$	−7.23986e78	−0.995667
$268$	5.54093e78	0.674842
$269$	−1.10328e79	−1.19052	−0.595258	−	0.803534i	$-0.702950\pi$
$269$	−1.10328e79	−1.19052	−0.595258	+	0.803534i	$0.702950\pi$
$270$	−2.81695e79	−2.69437
$271$	1.37650e79	1.16755	0.583775	−	0.811915i	$-0.301575\pi$
$271$	1.37650e79	1.16755	0.583775	+	0.811915i	$0.301575\pi$
$272$	−4.49797e78	−0.338475
$273$	2.76192e79	1.84469
$274$	1.43168e79	0.849087
$275$	−8.86689e76	−0.00467153
$276$	1.20360e79	0.563555
$277$	1.54069e79	0.641392	0.320696	−	0.947182i	$-0.396083\pi$
$277$	1.54069e79	0.641392	0.320696	+	0.947182i	$0.396083\pi$
$278$	−1.55297e78	−0.0575053
$279$	−2.43849e79	−0.803498
$280$	−1.30621e79	−0.383156
$281$	−5.34712e79	−1.39690	−0.698449	−	0.715659i	$-0.746126\pi$
$281$	−5.34712e79	−1.39690	−0.698449	+	0.715659i	$0.746126\pi$
$282$	8.04165e79	1.87175
$283$	−9.25172e79	−1.91939	−0.959695	−	0.281043i	$-0.909320\pi$
$283$	−9.25172e79	−1.91939	−0.959695	+	0.281043i	$0.909320\pi$
$284$	−1.80919e79	−0.334686
$285$	1.83619e80	3.03012
$286$	1.37988e78	0.0203209
$287$	−2.03756e79	−0.267885
$288$	−1.82387e80	−2.14159
$289$	−8.82058e79	−0.925374
$290$	4.31973e79	0.405062
$291$	1.04746e80	0.878248
$292$	−5.44686e79	−0.408511
$293$	−1.15528e80	−0.775337	−0.387669	−	0.921799i	$-0.626720\pi$
$293$	−1.15528e80	−0.775337	−0.387669	+	0.921799i	$0.626720\pi$
$294$	2.22334e80	1.33573
$295$	1.21100e80	0.651522
$296$	−4.99777e79	−0.240877
$297$	3.79776e78	0.0164037
$298$	4.79216e80	1.85568
$299$	2.63358e80	0.914605
$300$	−1.66621e80	−0.519147
$301$	−3.56741e80	−0.997567
$302$	−6.51120e80	−1.63469
$303$	−1.07628e81	−2.42684
$304$	8.74463e80	1.77154
$305$	−2.43535e80	−0.443422
$306$	4.23551e80	0.693361
$307$	1.91973e80	0.282647	0.141323	−	0.989963i	$-0.454864\pi$
$307$	1.91973e80	0.282647	0.141323	+	0.989963i	$0.454864\pi$
$308$	−2.69426e78	−0.00356895
$309$	−3.65067e79	−0.0435233
$310$	−5.78760e80	−0.621218
$311$	1.25133e81	1.20965	0.604825	−	0.796358i	$-0.293243\pi$
$311$	1.25133e81	1.20965	0.604825	+	0.796358i	$0.293243\pi$
$312$	−1.69480e81	−1.47603
$313$	8.06493e80	0.633009	0.316504	−	0.948591i	$-0.397491\pi$
$313$	8.06493e80	0.633009	0.316504	+	0.948591i	$0.397491\pi$
$314$	2.74492e81	1.94230
$315$	2.40266e81	1.53320
$316$	−1.20265e81	−0.692322
$317$	−2.97272e80	−0.154429	−0.0772144	−	0.997015i	$-0.524603\pi$
$317$	−2.97272e80	−0.154429	−0.0772144	+	0.997015i	$0.524603\pi$
$318$	−5.15432e81	−2.41708
$319$	−5.82376e78	−0.00246608
$320$	−3.67635e80	−0.140619
$321$	1.44809e81	0.500476
$322$	−1.36453e81	−0.426254
$323$	−1.38291e81	−0.390583
$324$	2.39310e81	0.611290
$325$	−3.64583e81	−0.842533
$326$	3.61712e81	0.756469
$327$	3.94071e81	0.746058
$328$	1.25031e81	0.214348
$329$	−3.43566e81	−0.533511
$330$	1.79951e80	0.0253192
$331$	−1.10080e82	−1.40378	−0.701892	−	0.712283i	$-0.747661\pi$
$331$	−1.10080e82	−1.40378	−0.701892	+	0.712283i	$0.747661\pi$
$332$	6.59343e81	0.762296
$333$	9.19300e81	0.963872
$334$	−1.93343e82	−1.83894
$335$	1.58111e82	1.36460
$336$	1.71533e82	1.34376
$337$	6.66720e81	0.474211	0.237105	−	0.971484i	$-0.423801\pi$
$337$	6.66720e81	0.474211	0.237105	+	0.971484i	$0.423801\pi$
$338$	3.71260e82	2.39820
$339$	−5.16147e82	−3.02889
$340$	3.78831e81	0.202014
$341$	7.80272e79	0.00378206
$342$	−8.23438e82	−3.62896
$343$	−2.51115e82	−1.00650
$344$	2.18908e82	0.798202
$345$	3.43448e82	1.13957
$346$	4.67094e82	1.41069
$347$	−2.67024e82	−0.734248	−0.367124	−	0.930172i	$-0.619658\pi$
$347$	−2.67024e82	−0.734248	−0.367124	+	0.930172i	$0.619658\pi$
$348$	−1.09437e82	−0.274055
$349$	9.03770e81	0.206173	0.103086	−	0.994672i	$-0.467128\pi$
$349$	9.03770e81	0.206173	0.103086	+	0.994672i	$0.467128\pi$
$350$	1.88900e82	0.392664
$351$	1.56154e83	2.95849
$352$	5.83603e80	0.0100805
$353$	−5.79038e82	−0.912072	−0.456036	−	0.889961i	$-0.650731\pi$
$353$	−5.79038e82	−0.912072	−0.456036	+	0.889961i	$0.650731\pi$
$354$	−8.14120e82	−1.16972
$355$	−5.16253e82	−0.676770
$356$	2.90391e82	0.347423
$357$	−2.71270e82	−0.296268
$358$	1.15979e83	1.15660
$359$	−8.10181e82	−0.737926	−0.368963	−	0.929444i	$-0.620287\pi$
$359$	−8.10181e82	−0.737926	−0.368963	+	0.929444i	$0.620287\pi$
$360$	−1.47436e83	−1.22679
$361$	1.37338e83	1.04426
$362$	−2.37660e83	−1.65168
$363$	2.72740e83	1.73294
$364$	−1.10781e83	−0.643679
$365$	−1.55426e83	−0.826051
$366$	1.63722e83	0.796106
$367$	−2.23295e82	−0.0993645	−0.0496823	−	0.998765i	$-0.515821\pi$
$367$	−2.23295e82	−0.0993645	−0.0496823	+	0.998765i	$0.515821\pi$
$368$	1.63563e83	0.666240
$369$	−2.29986e83	−0.857716
$370$	2.18190e83	0.745210
$371$	2.20210e83	0.688945
$372$	1.46624e83	0.420301
$373$	−3.67990e83	−0.966717	−0.483358	−	0.875423i	$-0.660583\pi$
$373$	−3.67990e83	−0.966717	−0.483358	+	0.875423i	$0.660583\pi$
$374$	−1.35529e81	−0.00326365
$375$	4.84404e83	1.06953
$376$	2.10823e83	0.426888
$377$	−2.39458e83	−0.444769
$378$	−8.09075e83	−1.37881
$379$	−2.08921e83	−0.326744	−0.163372	−	0.986565i	$-0.552237\pi$
$379$	−2.08921e83	−0.326744	−0.163372	+	0.986565i	$0.552237\pi$
$380$	−7.36497e83	−1.05731
$381$	1.74186e84	2.29589
$382$	8.30565e83	1.00534
$383$	−6.21778e83	−0.691314	−0.345657	−	0.938361i	$-0.612344\pi$
$383$	−6.21778e83	−0.691314	−0.345657	+	0.938361i	$0.612344\pi$
$384$	−1.56632e84	−1.59999
$385$	−7.68808e81	−0.00721679
$386$	1.40297e83	0.121049
$387$	−4.02665e84	−3.19402
$388$	−4.20139e83	−0.306452
$389$	1.44566e84	0.969850	0.484925	−	0.874556i	$-0.338847\pi$
$389$	1.44566e84	0.969850	0.484925	+	0.874556i	$0.338847\pi$
$390$	7.39909e84	4.56645
$391$	−2.58665e83	−0.146890
$392$	5.82880e83	0.304637
$393$	9.73528e83	0.468371
$394$	2.04676e84	0.906648
$395$	−3.43176e84	−1.39995
$396$	−3.04109e82	−0.0114271
$397$	−2.56097e84	−0.886569	−0.443285	−	0.896381i	$-0.646187\pi$
$397$	−2.56097e84	−0.886569	−0.443285	+	0.896381i	$0.646187\pi$
$398$	−6.44140e84	−2.05485
$399$	5.27383e84	1.55063
$400$	−2.26430e84	−0.613739
$401$	−8.35388e82	−0.0208783	−0.0104392	−	0.999946i	$-0.503323\pi$
$401$	−8.35388e82	−0.0208783	−0.0104392	+	0.999946i	$0.503323\pi$
$402$	−1.06293e85	−2.44996
$403$	3.20827e84	0.682114
$404$	4.31698e84	0.846809
$405$	6.82872e84	1.23609
$406$	1.24070e84	0.207286
$407$	−2.94159e82	−0.00453695
$408$	1.66460e84	0.237058
$409$	6.47461e84	0.851541	0.425771	−	0.904831i	$-0.360003\pi$
$409$	6.47461e84	0.851541	0.425771	+	0.904831i	$0.360003\pi$
$410$	−5.45856e84	−0.663136
$411$	−1.03498e85	−1.16164
$412$	1.46429e83	0.0151868
$413$	3.47819e84	0.333409
$414$	−1.54019e85	−1.36478
$415$	1.88144e85	1.54144
$416$	2.39962e85	1.81807
$417$	1.12266e84	0.0786734
$418$	2.63485e83	0.0170815
$419$	−1.03548e85	−0.621133	−0.310567	−	0.950552i	$-0.600519\pi$
$419$	−1.03548e85	−0.621133	−0.310567	+	0.950552i	$0.600519\pi$
$420$	−1.44470e85	−0.802002
$421$	−2.49789e85	−1.28353	−0.641765	−	0.766902i	$-0.721797\pi$
$421$	−2.49789e85	−1.28353	−0.641765	+	0.766902i	$0.721797\pi$
$422$	3.57602e85	1.70116
$423$	−3.87793e85	−1.70820
$424$	−1.35128e85	−0.551258
$425$	3.58086e84	0.135315
$426$	3.47062e85	1.21505
$427$	−6.99473e84	−0.226916
$428$	−5.80832e84	−0.174634
$429$	−9.97529e83	−0.0278012
$430$	−9.55699e85	−2.46943
$431$	5.31382e85	1.27320	0.636599	−	0.771195i	$-0.280341\pi$
$431$	5.31382e85	1.27320	0.636599	+	0.771195i	$0.280341\pi$
$432$	9.69816e85	2.15510
$433$	4.06333e85	0.837578	0.418789	−	0.908083i	$-0.362455\pi$
$433$	4.06333e85	0.837578	0.418789	+	0.908083i	$0.362455\pi$
$434$	−1.66229e85	−0.317901
$435$	−3.12278e85	−0.554167
$436$	−1.58062e85	−0.260326
$437$	5.02879e85	0.768806
$438$	1.04489e86	1.48307
$439$	−6.80579e85	−0.896977	−0.448489	−	0.893789i	$-0.648038\pi$
$439$	−6.80579e85	−0.896977	−0.448489	+	0.893789i	$0.648038\pi$
$440$	4.71766e83	0.00577451
$441$	−1.07216e86	−1.21901
$442$	−5.57257e85	−0.588616
$443$	4.98621e85	0.489384	0.244692	−	0.969601i	$-0.421313\pi$
$443$	4.98621e85	0.489384	0.244692	+	0.969601i	$0.421313\pi$
$444$	−5.52766e85	−0.504191
$445$	8.28633e85	0.702526
$446$	−1.58168e86	−1.24662
$447$	−3.46431e86	−2.53876
$448$	−1.05591e85	−0.0719600
$449$	2.19217e86	1.38953	0.694765	−	0.719237i	$-0.255508\pi$
$449$	2.19217e86	1.38953	0.694765	+	0.719237i	$0.255508\pi$
$450$	2.13218e86	1.25724
$451$	7.35911e83	0.00403727
$452$	2.07027e86	1.05689
$453$	4.70703e86	2.23643
$454$	−4.67800e85	−0.206892
$455$	−3.16113e86	−1.30158
$456$	−3.23620e86	−1.24073
$457$	5.33189e86	1.90373	0.951864	−	0.306520i	$-0.0991648\pi$
$457$	5.33189e86	1.90373	0.951864	+	0.306520i	$0.0991648\pi$
$458$	−9.86260e85	−0.327992
$459$	−1.53371e86	−0.475150
$460$	−1.37757e86	−0.397635
$461$	−6.25225e86	−1.68173	−0.840865	−	0.541245i	$-0.817953\pi$
$461$	−6.25225e86	−1.68173	−0.840865	+	0.541245i	$0.817953\pi$
$462$	5.16847e84	0.0129568
$463$	9.64512e85	0.225385	0.112693	−	0.993630i	$-0.464052\pi$
$463$	9.64512e85	0.225385	0.112693	+	0.993630i	$0.464052\pi$
$464$	−1.48719e86	−0.323990
$465$	4.18393e86	0.849891
$466$	1.17912e87	2.23366
$467$	5.11330e86	0.903447	0.451723	−	0.892158i	$-0.350809\pi$
$467$	5.11330e86	0.903447	0.451723	+	0.892158i	$0.350809\pi$
$468$	−1.25042e87	−2.06093
$469$	4.54120e86	0.698318
$470$	−9.20402e86	−1.32068
$471$	−1.98434e87	−2.65727
$472$	−2.13433e86	−0.266776
$473$	1.28845e85	0.0150342
$474$	2.30707e87	2.51342
$475$	−6.96165e86	−0.708223
$476$	1.08806e86	0.103378
$477$	2.48557e87	2.20587
$478$	−7.61197e86	−0.631088
$479$	−1.99037e86	−0.154180	−0.0770901	−	0.997024i	$-0.524563\pi$
$479$	−1.99037e86	−0.154180	−0.0770901	+	0.997024i	$0.524563\pi$
$480$	3.12936e87	2.26525
$481$	−1.20950e87	−0.818261
$482$	−1.50714e87	−0.953068
$483$	9.86438e86	0.583160
$484$	−1.09396e87	−0.604683
$485$	−1.19887e87	−0.619677
$486$	−3.28304e85	−0.0158707
$487$	5.95350e86	0.269204	0.134602	−	0.990900i	$-0.457024\pi$
$487$	5.95350e86	0.269204	0.134602	+	0.990900i	$0.457024\pi$
$488$	4.29220e86	0.181566
$489$	−2.61486e87	−1.03493
$490$	−2.54471e87	−0.942466
$491$	−5.25079e87	−1.82002	−0.910010	−	0.414587i	$-0.863926\pi$
$491$	−5.25079e87	−1.82002	−0.910010	+	0.414587i	$0.863926\pi$
$492$	1.38288e87	0.448662
$493$	2.35190e86	0.0714323
$494$	1.08338e88	3.08074
$495$	−8.67777e85	−0.0231068
$496$	1.99255e87	0.496883
$497$	−1.48276e87	−0.346329
$498$	−1.26484e88	−2.76746
$499$	7.37774e87	1.51236	0.756181	−	0.654363i	$-0.227063\pi$
$499$	7.37774e87	1.51236	0.756181	+	0.654363i	$0.227063\pi$
$500$	−1.94295e87	−0.373195
$501$	1.39770e88	2.51587
$502$	7.77212e86	0.131120
$503$	1.28406e87	0.203061	0.101530	−	0.994832i	$-0.467626\pi$
$503$	1.28406e87	0.203061	0.101530	+	0.994832i	$0.467626\pi$
$504$	−4.23459e87	−0.627796
$505$	1.23185e88	1.71234
$506$	4.92832e85	0.00642403
$507$	−2.68389e88	−3.28099
$508$	−6.98660e87	−0.801116
$509$	2.60784e87	0.280513	0.140257	−	0.990115i	$-0.455207\pi$
$509$	2.60784e87	0.280513	0.140257	+	0.990115i	$0.455207\pi$
$510$	−7.26723e87	−0.733395
$511$	−4.46410e87	−0.422722
$512$	7.92179e87	0.703963
$513$	2.98173e88	2.48687
$514$	−3.11943e88	−2.44216
$515$	4.17835e86	0.0307093
$516$	2.42118e88	1.67075
$517$	1.24087e86	0.00804049
$518$	6.26677e87	0.381352
$519$	−3.37668e88	−1.92997
$520$	1.93978e88	1.04146
$521$	−1.32543e88	−0.668548	−0.334274	−	0.942476i	$-0.608491\pi$
$521$	−1.32543e88	−0.668548	−0.334274	+	0.942476i	$0.608491\pi$
$522$	1.40041e88	0.663688
$523$	5.46812e87	0.243519	0.121760	−	0.992560i	$-0.461146\pi$
$523$	5.46812e87	0.243519	0.121760	+	0.992560i	$0.461146\pi$
$524$	−3.90483e87	−0.163431
$525$	−1.36558e88	−0.537207
$526$	2.38232e88	0.880975
$527$	−3.15110e87	−0.109551
$528$	−6.19531e86	−0.0202516
$529$	−2.31259e88	−0.710867
$530$	5.89935e88	1.70545
$531$	3.92594e88	1.06751
$532$	−2.11534e88	−0.541068
$533$	3.02587e88	0.728142
$534$	−5.57066e88	−1.26129
$535$	−1.65741e88	−0.353128
$536$	−2.78663e88	−0.558758
$537$	−8.38428e88	−1.58235
$538$	−8.48909e88	−1.50813
$539$	3.43072e86	0.00573787
$540$	−8.16806e88	−1.28624
$541$	6.12366e88	0.908029	0.454015	−	0.890994i	$-0.349991\pi$
$541$	6.12366e88	0.908029	0.454015	+	0.890994i	$0.349991\pi$
$542$	1.05914e89	1.47903
$543$	1.71807e89	2.25968
$544$	−2.35686e88	−0.291991
$545$	−4.51031e88	−0.526406
$546$	2.12514e89	2.33683
$547$	−3.21753e88	−0.333376	−0.166688	−	0.986010i	$-0.553307\pi$
$547$	−3.21753e88	−0.333376	−0.166688	+	0.986010i	$0.553307\pi$
$548$	4.15131e88	0.405337
$549$	−7.89516e88	−0.726541
$550$	−6.82257e86	−0.00591781
$551$	−4.57240e88	−0.373867
$552$	−6.05311e88	−0.466615
$553$	−9.85658e88	−0.716406
$554$	1.18548e89	0.812503
$555$	−1.57732e89	−1.01953
$556$	−4.50301e87	−0.0274519
$557$	−2.75914e88	−0.158664	−0.0793322	−	0.996848i	$-0.525279\pi$
$557$	−2.75914e88	−0.158664	−0.0793322	+	0.996848i	$0.525279\pi$
$558$	−1.87628e89	−1.01786
$559$	5.29777e89	2.71150
$560$	−1.96327e89	−0.948133
$561$	9.79752e86	0.00446502
$562$	−4.11431e89	−1.76957
$563$	−1.72931e89	−0.702020	−0.351010	−	0.936372i	$-0.614162\pi$
$563$	−1.72931e89	−0.702020	−0.351010	+	0.936372i	$0.614162\pi$
$564$	2.33176e89	0.893539
$565$	5.90753e89	2.13713
$566$	−7.11868e89	−2.43145
$567$	1.96132e89	0.632556
$568$	9.09873e88	0.277115
$569$	−3.33657e89	−0.959735	−0.479867	−	0.877341i	$-0.659315\pi$
$569$	−3.33657e89	−0.959735	−0.479867	+	0.877341i	$0.659315\pi$
$570$	1.41284e90	3.83850
$571$	−6.14714e88	−0.157761	−0.0788805	−	0.996884i	$-0.525135\pi$
$571$	−6.14714e88	−0.157761	−0.0788805	+	0.996884i	$0.525135\pi$
$572$	4.00110e87	0.00970081
$573$	−6.00425e89	−1.37542
$574$	−1.56779e89	−0.339352
$575$	−1.30213e89	−0.266349
$576$	−1.19184e89	−0.230402
$577$	6.35935e89	1.16198	0.580991	−	0.813910i	$-0.302665\pi$
$577$	6.35935e89	1.16198	0.580991	+	0.813910i	$0.302665\pi$
$578$	−6.78694e89	−1.17225
$579$	−1.01422e89	−0.165607
$580$	1.25255e89	0.193368
$581$	5.40380e89	0.788815
$582$	8.05965e89	1.11255
$583$	−7.95338e87	−0.0103830
$584$	2.73932e89	0.338240
$585$	−3.56807e90	−4.16742
$586$	−8.88925e89	−0.982183
$587$	1.85837e90	1.94265	0.971323	−	0.237762i	$-0.0764139\pi$
$587$	1.85837e90	1.94265	0.971323	+	0.237762i	$0.0764139\pi$
$588$	6.44681e89	0.637649
$589$	6.12614e89	0.573377
$590$	9.31796e89	0.825336
$591$	−1.47962e90	−1.24039
$592$	−7.51180e89	−0.596058
$593$	−2.24950e90	−1.68970	−0.844850	−	0.535004i	$-0.820310\pi$
$593$	−2.24950e90	−1.68970	−0.844850	+	0.535004i	$0.820310\pi$
$594$	2.92216e88	0.0207799
$595$	3.10480e89	0.209041
$596$	1.38954e90	0.885864
$597$	4.65657e90	2.81125
$598$	2.02639e90	1.15861
$599$	9.74495e89	0.527725	0.263863	−	0.964560i	$-0.415003\pi$
$599$	9.74495e89	0.527725	0.263863	+	0.964560i	$0.415003\pi$
$600$	8.37969e89	0.429845
$601$	−2.26000e90	−1.09822	−0.549108	−	0.835751i	$-0.685033\pi$
$601$	−2.26000e90	−1.09822	−0.549108	+	0.835751i	$0.685033\pi$
$602$	−2.74492e90	−1.26370
$603$	5.12579e90	2.23588
$604$	−1.88799e90	−0.780369
$605$	−3.12163e90	−1.22273
$606$	−8.28139e90	−3.07428
$607$	−3.77122e90	−1.32693	−0.663467	−	0.748206i	$-0.730916\pi$
$607$	−3.77122e90	−1.32693	−0.663467	+	0.748206i	$0.730916\pi$
$608$	4.58204e90	1.52824
$609$	−8.96914e89	−0.283589
$610$	−1.87387e90	−0.561719
$611$	5.10211e90	1.45014
$612$	1.22813e90	0.330997
$613$	−2.13613e90	−0.545962	−0.272981	−	0.962019i	$-0.588010\pi$
$613$	−2.13613e90	−0.545962	−0.272981	+	0.962019i	$0.588010\pi$
$614$	1.47713e90	0.358052
$615$	3.94606e90	0.907240
$616$	1.35499e88	0.00295504
$617$	1.72839e89	0.0357581	0.0178790	−	0.999840i	$-0.494309\pi$
$617$	1.72839e89	0.0357581	0.0178790	+	0.999840i	$0.494309\pi$
$618$	−2.80898e89	−0.0551345
$619$	2.38513e90	0.444186	0.222093	−	0.975025i	$-0.428711\pi$
$619$	2.38513e90	0.444186	0.222093	+	0.975025i	$0.428711\pi$
$620$	−1.67818e90	−0.296557
$621$	5.57714e90	0.935264
$622$	9.62829e90	1.53236
$623$	2.37997e90	0.359509
$624$	−2.54734e91	−3.65249
$625$	−9.18339e90	−1.24998
$626$	6.20551e90	0.801884
$627$	−1.90477e89	−0.0233693
$628$	7.95920e90	0.927216
$629$	1.18795e90	0.131417
$630$	1.84871e91	1.94224
$631$	5.66487e90	0.565244	0.282622	−	0.959231i	$-0.408796\pi$
$631$	5.66487e90	0.565244	0.282622	+	0.959231i	$0.408796\pi$
$632$	6.04833e90	0.573232
$633$	−2.58515e91	−2.32737
$634$	−2.28734e90	−0.195628
$635$	−1.99363e91	−1.61994
$636$	−1.49455e91	−1.15386
$637$	1.41062e91	1.03485
$638$	−4.48106e88	−0.00312398
$639$	−1.67364e91	−1.10888
$640$	1.79272e91	1.12892
$641$	1.34848e91	0.807161	0.403580	−	0.914944i	$-0.367766\pi$
$641$	1.34848e91	0.807161	0.403580	+	0.914944i	$0.367766\pi$
$642$	1.11423e91	0.633994
$643$	−3.26536e91	−1.76634	−0.883171	−	0.469050i	$-0.844596\pi$
$643$	−3.26536e91	−1.76634	−0.883171	+	0.469050i	$0.844596\pi$
$644$	−3.95661e90	−0.203485
$645$	6.90886e91	3.37844
$646$	−1.06407e91	−0.494783
$647$	−4.26660e90	−0.188666	−0.0943328	−	0.995541i	$-0.530072\pi$
$647$	−4.26660e90	−0.188666	−0.0943328	+	0.995541i	$0.530072\pi$
$648$	−1.20353e91	−0.506139
$649$	−1.25623e89	−0.00502477
$650$	−2.80526e91	−1.06731
$651$	1.20169e91	0.434922
$652$	1.04882e91	0.361123
$653$	3.32079e91	1.08784	0.543918	−	0.839139i	$-0.316940\pi$
$653$	3.32079e91	1.08784	0.543918	+	0.839139i	$0.316940\pi$
$654$	3.03215e91	0.945092
$655$	−1.11425e91	−0.330475
$656$	1.87926e91	0.530411
$657$	−5.03877e91	−1.35347
$658$	−2.64354e91	−0.675842
$659$	−4.45167e90	−0.108330	−0.0541648	−	0.998532i	$-0.517250\pi$
$659$	−4.45167e90	−0.108330	−0.0541648	+	0.998532i	$0.517250\pi$
$660$	5.21786e89	0.0120869
$661$	−2.71335e91	−0.598354	−0.299177	−	0.954198i	$-0.596712\pi$
$661$	−2.71335e91	−0.598354	−0.299177	+	0.954198i	$0.596712\pi$
$662$	−8.47007e91	−1.77829
$663$	4.02848e91	0.805289
$664$	−3.31595e91	−0.631169
$665$	−6.03613e91	−1.09410
$666$	7.07349e91	1.22102
$667$	−8.55240e90	−0.140604
$668$	−5.60618e91	−0.877874
$669$	1.14342e92	1.70551
$670$	1.21657e92	1.72865
$671$	2.52631e89	0.00341983
$672$	8.98804e91	1.15921
$673$	3.15118e90	0.0387243	0.0193622	−	0.999813i	$-0.493836\pi$
$673$	3.15118e90	0.0387243	0.0193622	+	0.999813i	$0.493836\pi$
$674$	5.13003e91	0.600722
$675$	−7.72077e91	−0.861564
$676$	1.07651e92	1.14485
$677$	8.74365e91	0.886260	0.443130	−	0.896457i	$-0.353868\pi$
$677$	8.74365e91	0.886260	0.443130	+	0.896457i	$0.353868\pi$
$678$	−3.97146e92	−3.83694
$679$	−3.44335e91	−0.317112
$680$	−1.90521e91	−0.167264
$681$	3.38178e91	0.283051
$682$	6.00376e89	0.00479105
$683$	1.38127e92	1.05101	0.525505	−	0.850791i	$-0.323877\pi$
$683$	1.38127e92	1.05101	0.525505	+	0.850791i	$0.323877\pi$
$684$	−2.38765e92	−1.73240
$685$	1.18458e92	0.819634
$686$	−1.93219e92	−1.27502
$687$	7.12980e91	0.448728
$688$	3.29026e92	1.97518
$689$	−3.27022e92	−1.87263
$690$	2.64264e92	1.44358
$691$	−1.00192e92	−0.522153	−0.261076	−	0.965318i	$-0.584077\pi$
$691$	−1.00192e92	−0.522153	−0.261076	+	0.965318i	$0.584077\pi$
$692$	1.35439e92	0.673434
$693$	−2.49240e90	−0.0118246
$694$	−2.05460e92	−0.930132
$695$	−1.28494e91	−0.0555106
$696$	5.50377e91	0.226913
$697$	−2.97195e91	−0.116943
$698$	6.95400e91	0.261176
$699$	−8.52404e92	−3.05589
$700$	5.47737e91	0.187450
$701$	3.27880e92	1.07122	0.535610	−	0.844465i	$-0.320082\pi$
$701$	3.27880e92	1.07122	0.535610	+	0.844465i	$0.320082\pi$
$702$	1.20151e93	3.74777
$703$	−2.30953e92	−0.687820
$704$	3.81366e89	0.00108450
$705$	6.65370e92	1.80683
$706$	−4.45537e92	−1.15540
$707$	3.53808e92	0.876268
$708$	−2.36063e92	−0.558402
$709$	1.04617e91	0.0236374	0.0118187	−	0.999930i	$-0.496238\pi$
$709$	1.04617e91	0.0236374	0.0118187	+	0.999930i	$0.496238\pi$
$710$	−3.97228e92	−0.857320
$711$	−1.11254e93	−2.29379
$712$	−1.46043e92	−0.287661
$713$	1.14586e92	0.215636
$714$	−2.08727e92	−0.375306
$715$	1.14172e91	0.0196161
$716$	3.36294e92	0.552136
$717$	5.50278e92	0.863396
$718$	−6.23389e92	−0.934791
$719$	7.52266e92	1.07816	0.539079	−	0.842255i	$-0.318772\pi$
$719$	7.52266e92	1.07816	0.539079	+	0.842255i	$0.318772\pi$
$720$	−2.21600e93	−3.03574
$721$	1.20009e91	0.0157151
$722$	1.05674e93	1.32285
$723$	1.08953e93	1.30390
$724$	−6.89120e92	−0.788481
$725$	1.18396e92	0.129524
$726$	2.09858e93	2.19525
$727$	8.53972e92	0.854231	0.427116	−	0.904197i	$-0.359530\pi$
$727$	8.53972e92	0.854231	0.427116	+	0.904197i	$0.359530\pi$
$728$	5.57136e92	0.532956
$729$	−1.08117e93	−0.989124
$730$	−1.19592e93	−1.04643
$731$	−5.20336e92	−0.435481
$732$	4.74728e92	0.380045
$733$	−5.08934e92	−0.389746	−0.194873	−	0.980828i	$-0.562430\pi$
$733$	−5.08934e92	−0.389746	−0.194873	+	0.980828i	$0.562430\pi$
$734$	−1.71813e92	−0.125873
$735$	1.83960e93	1.28939
$736$	8.57042e92	0.574742
$737$	−1.64016e91	−0.0105243
$738$	−1.76961e93	−1.08654
$739$	1.59512e92	0.0937234	0.0468617	−	0.998901i	$-0.485078\pi$
$739$	1.59512e92	0.0937234	0.0468617	+	0.998901i	$0.485078\pi$
$740$	6.32665e92	0.355748
$741$	−7.83189e93	−4.21478
$742$	1.69439e93	0.872743
$743$	−1.89948e93	−0.936481	−0.468240	−	0.883601i	$-0.655112\pi$
$743$	−1.89948e93	−0.936481	−0.468240	+	0.883601i	$0.655112\pi$
$744$	−7.37399e92	−0.348002
$745$	3.96506e93	1.79131
$746$	−2.83148e93	−1.22462
$747$	6.09944e93	2.52563
$748$	−3.92980e90	−0.00155800
$749$	−4.76035e92	−0.180709
$750$	3.72722e93	1.35486
$751$	1.38707e93	0.482839	0.241419	−	0.970421i	$-0.422387\pi$
$751$	1.38707e93	0.482839	0.241419	+	0.970421i	$0.422387\pi$
$752$	3.16874e93	1.05635
$753$	−5.61856e92	−0.179386
$754$	−1.84249e93	−0.563426
$755$	−5.38740e93	−1.57799
$756$	−2.34600e93	−0.658218
$757$	−2.02487e93	−0.544228	−0.272114	−	0.962265i	$-0.587723\pi$
$757$	−2.02487e93	−0.544228	−0.272114	+	0.962265i	$0.587723\pi$
$758$	−1.60753e93	−0.413913
$759$	−3.56275e91	−0.00878875
$760$	3.70397e93	0.875439
$761$	−2.55933e93	−0.579595	−0.289797	−	0.957088i	$-0.593588\pi$
$761$	−2.55933e93	−0.579595	−0.289797	+	0.957088i	$0.593588\pi$
$762$	1.34026e94	2.90839
$763$	−1.29544e93	−0.269382
$764$	2.40831e93	0.479931
$765$	3.50448e93	0.669310
$766$	−4.78423e93	−0.875744
$767$	−5.16527e93	−0.906242
$768$	−1.32370e94	−2.22613
$769$	2.46450e93	0.397304	0.198652	−	0.980070i	$-0.436344\pi$
$769$	2.46450e93	0.397304	0.198652	+	0.980070i	$0.436344\pi$
$770$	−5.91554e91	−0.00914210
$771$	2.25508e94	3.34113
$772$	4.06806e92	0.0577863
$773$	−1.11858e94	−1.52347	−0.761735	−	0.647889i	$-0.775652\pi$
$773$	−1.11858e94	−1.52347	−0.761735	+	0.647889i	$0.775652\pi$
$774$	−3.09828e94	−4.04612
$775$	−1.58628e93	−0.198643
$776$	2.11295e93	0.253737
$777$	−4.53032e93	−0.521730
$778$	1.11235e94	1.22859
$779$	5.77785e93	0.612067
$780$	2.14544e94	2.17993
$781$	5.35534e91	0.00521949
$782$	−1.99028e93	−0.186078
$783$	−5.07099e93	−0.454816
$784$	8.76088e93	0.753834
$785$	2.27116e94	1.87493
$786$	7.49075e93	0.593325
$787$	−5.14732e93	−0.391203	−0.195602	−	0.980683i	$-0.562666\pi$
$787$	−5.14732e93	−0.391203	−0.195602	+	0.980683i	$0.562666\pi$
$788$	5.93479e93	0.432816
$789$	−1.72221e94	−1.20527
$790$	−2.64055e94	−1.77343
$791$	1.69674e94	1.09365
$792$	1.52942e92	0.00946146
$793$	1.03875e94	0.616783
$794$	−1.97052e94	−1.12309
$795$	−4.26471e94	−2.33323
$796$	−1.86775e94	−0.980945
$797$	1.71138e93	0.0862880	0.0431440	−	0.999069i	$-0.486263\pi$
$797$	1.71138e93	0.0862880	0.0431440	+	0.999069i	$0.486263\pi$
$798$	4.05792e94	1.96431
$799$	−5.01119e93	−0.232900
$800$	−1.18645e94	−0.529452
$801$	2.68635e94	1.15108
$802$	−6.42784e92	−0.0264483
$803$	1.61231e92	0.00637080
$804$	−3.08209e94	−1.16956
$805$	−1.12902e94	−0.411468
$806$	2.46858e94	0.864090
$807$	6.13687e94	2.06328
$808$	−2.17109e94	−0.701145
$809$	−4.00552e94	−1.24260	−0.621300	−	0.783572i	$-0.713395\pi$
$809$	−4.00552e94	−1.24260	−0.621300	+	0.783572i	$0.713395\pi$
$810$	5.25431e94	1.56586
$811$	1.51220e94	0.432944	0.216472	−	0.976289i	$-0.430545\pi$
$811$	1.51220e94	0.432944	0.216472	+	0.976289i	$0.430545\pi$
$812$	3.59753e93	0.0989541
$813$	−7.65667e94	−2.02347
$814$	−2.26339e92	−0.00574732
$815$	2.99282e94	0.730229
$816$	2.50195e94	0.586609
$817$	1.01160e95	2.27925
$818$	4.98184e94	1.07872
$819$	−1.02481e95	−2.13263
$820$	−1.58277e94	−0.316568
$821$	−6.13335e94	−1.17909	−0.589543	−	0.807737i	$-0.700692\pi$
$821$	−6.13335e94	−1.17909	−0.589543	+	0.807737i	$0.700692\pi$
$822$	−7.96357e94	−1.47155
$823$	6.29274e93	0.111775	0.0558876	−	0.998437i	$-0.482201\pi$
$823$	6.29274e93	0.111775	0.0558876	+	0.998437i	$0.482201\pi$
$824$	−7.36416e92	−0.0125744
$825$	4.93212e92	0.00809619
$826$	2.67627e94	0.422356
$827$	1.31042e94	0.198830	0.0994150	−	0.995046i	$-0.468303\pi$
$827$	1.31042e94	0.198830	0.0994150	+	0.995046i	$0.468303\pi$
$828$	−4.46595e94	−0.651520
$829$	2.97591e94	0.417443	0.208722	−	0.977975i	$-0.433070\pi$
$829$	2.97591e94	0.417443	0.208722	+	0.977975i	$0.433070\pi$
$830$	1.44766e95	1.95267
$831$	−8.56995e94	−1.11159
$832$	1.56807e94	0.195595
$833$	−1.38548e94	−0.166203
$834$	8.63826e93	0.0996620
$835$	−1.59973e95	−1.77515
$836$	7.64003e92	0.00815438
$837$	6.79415e94	0.697522
$838$	−7.96741e94	−0.786840
$839$	1.23639e95	1.17460	0.587302	−	0.809368i	$-0.300190\pi$
$839$	1.23639e95	1.17460	0.587302	+	0.809368i	$0.300190\pi$
$840$	7.26565e94	0.664045
$841$	−1.05952e95	−0.931625
$842$	−1.92199e95	−1.62595
$843$	2.97429e95	2.42095
$844$	1.03691e95	0.812101
$845$	3.07183e95	2.31501
$846$	−2.98385e95	−2.16391
$847$	−8.96582e94	−0.625719
$848$	−2.03102e95	−1.36411
$849$	5.14618e95	3.32648
$850$	2.75527e94	0.171415
$851$	−4.31983e94	−0.258676
$852$	1.00634e95	0.580042
$853$	4.72798e94	0.262320	0.131160	−	0.991361i	$-0.458130\pi$
$853$	4.72798e94	0.262320	0.131160	+	0.991361i	$0.458130\pi$
$854$	−5.38205e94	−0.287453
$855$	−6.81317e95	−3.50308
$856$	2.92111e94	0.144594
$857$	−3.75717e95	−1.79054	−0.895271	−	0.445521i	$-0.853018\pi$
$857$	−3.75717e95	−1.79054	−0.895271	+	0.445521i	$0.853018\pi$
$858$	−7.67542e93	−0.0352181
$859$	−2.87427e95	−1.26984	−0.634921	−	0.772577i	$-0.718967\pi$
$859$	−2.87427e95	−1.26984	−0.634921	+	0.772577i	$0.718967\pi$
$860$	−2.77115e95	−1.17886
$861$	1.13337e95	0.464270
$862$	4.08869e95	1.61286
$863$	−8.10537e94	−0.307909	−0.153954	−	0.988078i	$-0.549201\pi$
$863$	−8.10537e94	−0.307909	−0.153954	+	0.988078i	$0.549201\pi$
$864$	5.08167e95	1.85913
$865$	3.86476e95	1.36175
$866$	3.12650e95	1.06103
$867$	4.90636e95	1.60376
$868$	−4.82000e94	−0.151760
$869$	3.55993e93	0.0107969
$870$	−2.40281e95	−0.702009
$871$	−6.74390e95	−1.89811
$872$	7.94923e94	0.215546
$873$	−3.88661e95	−1.01533
$874$	3.86937e95	0.973909
$875$	−1.59239e95	−0.386178
$876$	3.02976e95	0.707986
$877$	3.33882e95	0.751806	0.375903	−	0.926659i	$-0.377333\pi$
$877$	3.33882e95	0.751806	0.375903	+	0.926659i	$0.377333\pi$
$878$	−5.23667e95	−1.13627
$879$	6.42615e95	1.34373
$880$	7.09080e93	0.0142892
$881$	−6.50620e95	−1.26360	−0.631801	−	0.775130i	$-0.717684\pi$
$881$	−6.50620e95	−1.26360	−0.631801	+	0.775130i	$0.717684\pi$
$882$	−8.24969e95	−1.54422
$883$	5.79206e95	1.04498	0.522492	−	0.852644i	$-0.325002\pi$
$883$	5.79206e95	1.04498	0.522492	+	0.852644i	$0.325002\pi$
$884$	−1.61583e95	−0.280993
$885$	−6.73607e95	−1.12915
$886$	3.83661e95	0.619943
$887$	4.38872e95	0.683628	0.341814	−	0.939768i	$-0.388959\pi$
$887$	4.38872e95	0.683628	0.341814	+	0.939768i	$0.388959\pi$
$888$	2.77996e95	0.417462
$889$	−5.72603e95	−0.828985
$890$	6.37587e95	0.889947
$891$	−7.08375e93	−0.00953318
$892$	−4.58625e95	−0.595114
$893$	9.74240e95	1.21897
$894$	−2.66559e96	−3.21606
$895$	9.59617e95	1.11648
$896$	5.14899e95	0.577713
$897$	−1.46491e96	−1.58510
$898$	1.68675e96	1.76023
$899$	−1.04187e95	−0.104863
$900$	6.18248e95	0.600179
$901$	3.21194e95	0.300754
$902$	5.66242e93	0.00511434
$903$	1.98434e96	1.72888
$904$	−1.04118e96	−0.875085
$905$	−1.96641e96	−1.59439
$906$	3.62179e96	2.83307
$907$	−2.30624e96	−1.74048	−0.870239	−	0.492630i	$-0.836036\pi$
$907$	−2.30624e96	−1.74048	−0.870239	+	0.492630i	$0.836036\pi$
$908$	−1.35644e95	−0.0987664
$909$	3.99354e96	2.80564
$910$	−2.43231e96	−1.64882
$911$	−9.24387e95	−0.604654	−0.302327	−	0.953204i	$-0.597763\pi$
$911$	−9.24387e95	−0.604654	−0.302327	+	0.953204i	$0.597763\pi$
$912$	−4.86411e96	−3.07023
$913$	−1.95171e94	−0.0118882
$914$	4.10259e96	2.41161
$915$	1.35464e96	0.768491
$916$	−2.85977e95	−0.156577
$917$	−3.20029e95	−0.169117
$918$	−1.18010e96	−0.601911
$919$	−1.74967e96	−0.861394	−0.430697	−	0.902497i	$-0.641732\pi$
$919$	−1.74967e96	−0.861394	−0.430697	+	0.902497i	$0.641732\pi$
$920$	6.92805e95	0.329236
$921$	−1.06783e96	−0.489853
$922$	−4.81075e96	−2.13038
$923$	2.20197e96	0.941362
$924$	1.49865e94	0.00618532
$925$	5.98019e95	0.238292
$926$	7.42138e95	0.285514
$927$	1.35458e95	0.0503168
$928$	−7.79262e95	−0.279495
$929$	9.02077e95	0.312416	0.156208	−	0.987724i	$-0.450073\pi$
$929$	9.02077e95	0.312416	0.156208	+	0.987724i	$0.450073\pi$
$930$	3.21930e96	1.07663
$931$	2.69356e96	0.869885
$932$	3.41900e96	1.06631
$933$	−6.96041e96	−2.09644
$934$	3.93440e96	1.14447
$935$	−1.12137e94	−0.00315044
$936$	6.28856e96	1.70642
$937$	5.66813e96	1.48561	0.742803	−	0.669511i	$-0.233496\pi$
$937$	5.66813e96	1.48561	0.742803	+	0.669511i	$0.233496\pi$
$938$	3.49420e96	0.884617
$939$	−4.48604e96	−1.09706
$940$	−2.66880e96	−0.630466
$941$	−3.88472e96	−0.886538	−0.443269	−	0.896389i	$-0.646181\pi$
$941$	−3.88472e96	−0.886538	−0.443269	+	0.896389i	$0.646181\pi$
$942$	−1.52684e97	−3.36619
$943$	1.08071e96	0.230186
$944$	−3.20797e96	−0.660147
$945$	−6.69433e96	−1.33098
$946$	9.91391e94	0.0190451
$947$	1.45061e96	0.269262	0.134631	−	0.990896i	$-0.457015\pi$
$947$	1.45061e96	0.269262	0.134631	+	0.990896i	$0.457015\pi$
$948$	6.68961e96	1.19986
$949$	6.62940e96	1.14901
$950$	−5.35660e96	−0.897164
$951$	1.65355e96	0.267639
$952$	−5.47207e95	−0.0855955
$953$	−1.02285e97	−1.54629	−0.773144	−	0.634230i	$-0.781317\pi$
$953$	−1.02285e97	−1.54629	−0.773144	+	0.634230i	$0.781317\pi$
$954$	1.91251e97	2.79435
$955$	6.87213e96	0.970470
$956$	−2.20717e96	−0.301269
$957$	3.23941e94	0.00427394
$958$	−1.53147e96	−0.195313
$959$	3.40230e96	0.419438
$960$	2.04494e96	0.243705
$961$	−7.28391e96	−0.839178
$962$	−9.30644e96	−1.03656
$963$	−5.37315e96	−0.578595
$964$	−4.37011e96	−0.454976
$965$	1.16082e96	0.116850
$966$	7.59008e96	0.738737
$967$	1.31294e97	1.23562	0.617808	−	0.786329i	$-0.288021\pi$
$967$	1.31294e97	1.23562	0.617808	+	0.786329i	$0.288021\pi$
$968$	5.50173e96	0.500668
$969$	7.69232e96	0.676915
$970$	−9.22462e96	−0.784996
$971$	−8.40882e96	−0.692006	−0.346003	−	0.938233i	$-0.612461\pi$
$971$	−8.40882e96	−0.692006	−0.346003	+	0.938233i	$0.612461\pi$
$972$	−9.51952e94	−0.00757638
$973$	−3.69055e95	−0.0284069
$974$	4.58088e96	0.341022
$975$	2.02796e97	1.46019
$976$	6.45131e96	0.449292
$977$	−8.22971e95	−0.0554385	−0.0277192	−	0.999616i	$-0.508824\pi$
$977$	−8.22971e95	−0.0554385	−0.0277192	+	0.999616i	$0.508824\pi$
$978$	−2.01199e97	−1.31103
$979$	−8.59581e94	−0.00541813
$980$	−7.37866e96	−0.449915
$981$	−1.46220e97	−0.862509
$982$	−4.04018e97	−2.30557
$983$	−1.65515e97	−0.913792	−0.456896	−	0.889520i	$-0.651039\pi$
$983$	−1.65515e97	−0.913792	−0.456896	+	0.889520i	$0.651039\pi$
$984$	−6.95475e96	−0.371485
$985$	1.69350e97	0.875199
$986$	1.80966e96	0.0904891
$987$	1.91105e97	0.924623
$988$	3.14138e97	1.47068
$989$	1.89214e97	0.857182
$990$	−6.67706e95	−0.0292712
$991$	−2.01523e97	−0.854930	−0.427465	−	0.904032i	$-0.640593\pi$
$991$	−2.01523e97	−0.854930	−0.427465	+	0.904032i	$0.640593\pi$
$992$	1.04406e97	0.428644
$993$	6.12312e97	2.43289
$994$	−1.14090e97	−0.438724
$995$	−5.32964e97	−1.98357
$996$	−3.66753e97	−1.32113
$997$	1.09099e97	0.380389	0.190194	−	0.981746i	$-0.439088\pi$
$997$	1.09099e97	0.380389	0.190194	+	0.981746i	$0.439088\pi$
$998$	5.67675e97	1.91583
$999$	−2.56136e97	−0.836744

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.66.a.a.1.4	✓	5
3.2	odd	2		9.66.a.b.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.66.a.a.1.4	✓	5	1.1	even	1	trivial
9.66.a.b.1.2		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)

\(f(q)\)	\(=\)	\(q+7.69444e9 q^{2} -5.56240e15 q^{3} +2.23108e19 q^{4} +6.36641e22 q^{5} -4.27995e25 q^{6} +1.82854e27 q^{7} -1.12205e29 q^{8} +2.06393e31 q^{9} +O(q^{10})\)	\(q+7.69444e9 q^{2} -5.56240e15 q^{3} +2.23108e19 q^{4} +6.36641e22 q^{5} -4.27995e25 q^{6} +1.82854e27 q^{7} -1.12205e29 q^{8} +2.06393e31 q^{9} +4.89860e32 q^{10} -6.60418e31 q^{11} -1.24102e35 q^{12} -2.71546e36 q^{13} +1.40696e37 q^{14} -3.54126e38 q^{15} -1.68648e39 q^{16} +2.66707e39 q^{17} +1.58808e41 q^{18} -5.18513e41 q^{19} +1.42040e42 q^{20} -1.01711e43 q^{21} -5.08155e41 q^{22} -9.69847e43 q^{23} +6.24130e44 q^{24} +1.34262e45 q^{25} -2.08940e46 q^{26} -5.75053e46 q^{27} +4.07962e46 q^{28} +8.81829e46 q^{29} -2.72480e48 q^{30} -1.18148e48 q^{31} -8.83687e48 q^{32} +3.67351e47 q^{33} +2.05216e49 q^{34} +1.16412e50 q^{35} +4.60480e50 q^{36} +4.45413e50 q^{37} -3.98967e51 q^{38} +1.51045e52 q^{39} -7.14345e51 q^{40} -1.11431e52 q^{41} -7.82606e52 q^{42} -1.95096e53 q^{43} -1.47345e51 q^{44} +1.31398e54 q^{45} -7.46243e53 q^{46} -1.87891e54 q^{47} +9.38088e54 q^{48} -5.19477e54 q^{49} +1.03307e55 q^{50} -1.48353e55 q^{51} -6.05843e55 q^{52} +1.20429e56 q^{53} -4.42471e56 q^{54} -4.20450e54 q^{55} -2.05171e56 q^{56} +2.88418e57 q^{57} +6.78518e56 q^{58} +1.90217e57 q^{59} -7.90084e57 q^{60} -3.82531e57 q^{61} -9.09084e57 q^{62} +3.77397e58 q^{63} -5.77461e57 q^{64} -1.72878e59 q^{65} +2.82656e57 q^{66} +2.48352e59 q^{67} +5.95046e58 q^{68} +5.39468e59 q^{69} +8.95727e59 q^{70} -8.10901e59 q^{71} -2.31583e60 q^{72} -2.44135e60 q^{73} +3.42720e60 q^{74} -7.46818e60 q^{75} -1.15685e61 q^{76} -1.20760e59 q^{77} +1.16221e62 q^{78} -5.39042e61 q^{79} -1.07368e62 q^{80} +1.07262e62 q^{81} -8.57399e61 q^{82} +2.95526e62 q^{83} -2.26925e62 q^{84} +1.69797e62 q^{85} -1.50116e63 q^{86} -4.90509e62 q^{87} +7.41024e60 q^{88} +1.30157e63 q^{89} +1.01103e64 q^{90} -4.96533e63 q^{91} -2.16381e63 q^{92} +6.57188e63 q^{93} -1.44571e64 q^{94} -3.30107e64 q^{95} +4.91543e64 q^{96} -1.88312e64 q^{97} -3.99708e64 q^{98} -1.36306e63 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3959709648 q^{2} - 22\!\cdots\!04 q^{3}+ \cdots + 31\!\cdots\!65 q^{9}+O(q^{10}) \) 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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