LMFDB - Embedded newform 1.64.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,64,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, 64, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 64);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 64 $
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:	$25.1360966918$
Analytic rank:	$0$
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} - 2 x^{4} + \cdots - 35\!\cdots\!34 $ x^5 - 2x^4 - 5096287552528786x^3 + 574038763744383494840x^2 + 3502610791787684740809332695881x - 35880030333954415007358004861309901934
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{37}\cdot 3^{17}\cdot 5^{3}\cdot 7^{2}\cdot 13 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73795e7$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.14986e9 q^{2} +2.06926e15 q^{3} -7.90120e18 q^{4} -9.56939e21 q^{5} -2.37936e24 q^{6} -1.15073e26 q^{7} +1.96908e28 q^{8} +3.13728e30 q^{9} +O(q^{10})$	\(q-1.14986e9 q^{2} +2.06926e15 q^{3} -7.90120e18 q^{4} -9.56939e21 q^{5} -2.37936e24 q^{6} -1.15073e26 q^{7} +1.96908e28 q^{8} +3.13728e30 q^{9} +1.10034e31 q^{10} -2.43908e32 q^{11} -1.63496e34 q^{12} +1.25036e35 q^{13} +1.32317e35 q^{14} -1.98016e37 q^{15} +5.02341e37 q^{16} +7.86280e38 q^{17} -3.60742e39 q^{18} -2.70961e39 q^{19} +7.56097e40 q^{20} -2.38116e41 q^{21} +2.80460e41 q^{22} +3.63454e42 q^{23} +4.07454e43 q^{24} -1.68470e43 q^{25} -1.43774e44 q^{26} +4.12346e45 q^{27} +9.09213e44 q^{28} +3.93841e45 q^{29} +2.27690e46 q^{30} +1.18807e47 q^{31} -2.39378e47 q^{32} -5.04710e47 q^{33} -9.04110e47 q^{34} +1.10118e48 q^{35} -2.47883e49 q^{36} +1.80510e49 q^{37} +3.11567e48 q^{38} +2.58732e50 q^{39} -1.88429e50 q^{40} +3.23583e50 q^{41} +2.73799e50 q^{42} +8.59653e50 q^{43} +1.92717e51 q^{44} -3.00219e52 q^{45} -4.17920e51 q^{46} +1.26451e52 q^{47} +1.03947e53 q^{48} -1.61010e53 q^{49} +1.93716e52 q^{50} +1.62702e54 q^{51} -9.87934e53 q^{52} -5.19617e53 q^{53} -4.74139e54 q^{54} +2.33405e54 q^{55} -2.26588e54 q^{56} -5.60690e54 q^{57} -4.52860e54 q^{58} -4.37498e55 q^{59} +1.56456e56 q^{60} +2.79669e56 q^{61} -1.36611e56 q^{62} -3.61016e56 q^{63} -1.88077e56 q^{64} -1.19652e57 q^{65} +5.80344e56 q^{66} +1.12890e57 q^{67} -6.21256e57 q^{68} +7.52080e57 q^{69} -1.26620e57 q^{70} +1.56870e58 q^{71} +6.17756e58 q^{72} -9.21857e58 q^{73} -2.07560e58 q^{74} -3.48607e58 q^{75} +2.14092e58 q^{76} +2.80672e58 q^{77} -2.97505e59 q^{78} -4.18902e59 q^{79} -4.80710e59 q^{80} +4.94170e60 q^{81} -3.72075e59 q^{82} -3.28273e60 q^{83} +1.88140e60 q^{84} -7.52422e60 q^{85} -9.88478e59 q^{86} +8.14959e60 q^{87} -4.80275e60 q^{88} -3.02241e61 q^{89} +3.45209e61 q^{90} -1.43882e61 q^{91} -2.87172e61 q^{92} +2.45843e62 q^{93} -1.45400e61 q^{94} +2.59294e61 q^{95} -4.95335e62 q^{96} +5.45642e61 q^{97} +1.85138e62 q^{98} -7.65208e62 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 507315096 q^{2} + 953245351116252 q^{3} + 67\!\cdots\!40 q^{4}+ \cdots + 63\!\cdots\!85 q^{9}+O(q^{10}) $ 5 * q + 507315096 * q^2 + 953245351116252 * q^3 + 6772922881670488640 * q^4 - 501184199539643271930 * q^5 + 1068627718494014524169760 * q^6 + 376817877722086399439439256 * q^7 + 7373083738744782322804569600 * q^8 + 637396295620644432934325521785 * q^9	$ 5 q + 507315096 q^{2} + 953245351116252 q^{3} + 67\!\cdots\!40 q^{4}+ \cdots - 12\!\cdots\!80 q^{99}+O(q^{100}) $ 5 * q + 507315096 * q^2 + 953245351116252 * q^3 + 6772922881670488640 * q^4 - 501184199539643271930 * q^5 + 1068627718494014524169760 * q^6 + 376817877722086399439439256 * q^7 + 7373083738744782322804569600 * q^8 + 637396295620644432934325521785 * q^9 + 34805720696971516624169126640720 * q^10 - 540229094938924469136867622360140 * q^11 - 2623634227414171572600561756413184 * q^12 + 108181792532202432266404872185866462 * q^13 - 54084971043930392944098441496816320 * q^14 - 348660153327675947104166235548634360 * q^15 - 15159504282791660159626289035944325120 * q^16 + 233526732797217220125532397644743920826 * q^17 - 878288957740682168785729261423496761608 * q^18 - 7865422683256304571013031795593188000500 * q^19 + 119732404991815793713722982154585901682560 * q^20 + 129742883997422764536533691448958694051360 * q^21 + 522423012385730886331292903044579480248672 * q^22 + 15741757721943761462993254761236931413817672 * q^23 + 81420550986598778904562391448937582504396800 * q^24 + 292140347366023827983252525250222472224504275 * q^25 + 1839051975856323981143175281915543784076214160 * q^26 + 5995620820889371589085528605465633389174051800 * q^27 + 20537937802314435233418391499696666641793064448 * q^28 + 50794057939113445336173371211400804999575041550 * q^29 + 119599751674209323591694650465650283116522069440 * q^30 + 159433862626305294394996530486509737703620382560 * q^31 - 288839096991246799804118797555409689201302994944 * q^32 - 1985039125536508051580230500373193506662510782736 * q^33 - 7795229014190619843231021275250308444731969968720 * q^34 - 10557440874563511263423843961508717076049161308080 * q^35 - 37204859885919911089599455494799964973968364182720 * q^36 - 17147796860746064343272909856513075508644081479834 * q^37 + 96961175243860213325076480378784661216846555556000 * q^38 + 492167917497720661901422065953515470410075070510120 * q^39 + 896446641636036625169137129815741762131481186432000 * q^40 + 1559678150469731047687963466434444190641664714862210 * q^41 + 2081496056204279968289878006271140331858037130897152 * q^42 - 2983480654504430801847803264567818556163926831907308 * q^43 - 18694374606435020769086358744659889563339255880625920 * q^44 - 42915794659164783458146544031317844487388645901128610 * q^45 - 51138823220473279961598851250008086980240261547467840 * q^46 - 48803318103437656200328895986865036348129901500078064 * q^47 + 105030731921033071573566542229505770762259930957135872 * q^48 + 339954400631541607259125157882259489058114941961211565 * q^49 + 1145766254187619060443643128490826898486806978223935400 * q^50 + 1573856653389132533580410794526319320841950113639520760 * q^51 + 1100089067926371487906797270480194411314440787489242496 * q^52 - 692620923468041120314769654783046236221069399596219498 * q^53 - 12241254713499812360048511900337793888058128715691896000 * q^54 - 20518321028364082359377216700393318257347660689712574760 * q^55 - 23023175950768775440489799736204099376922285452382515200 * q^56 - 17165930318654624911621905238013222730357511047458838000 * q^57 + 24263146187335234519264617757094026741989307665448630800 * q^58 + 105022627362831482575423381645924825912298204628844229700 * q^59 + 348815801318717337128814346317462318028682012888660421120 * q^60 + 392008741666961324913019363738714690637509013784647052910 * q^61 + 517886811617172418873631635177191658868452247595279666432 * q^62 - 688525987399009316135147212418376806290326301310285121288 * q^63 - 2180009675566773867746832715393348298244228612034924380160 * q^64 - 1790351395436014012859210003100506705478557202772387149660 * q^65 - 5560362505883676488751771192389016447628360456591147025280 * q^66 - 4772918882566263586387384393016421637717756025307890516324 * q^67 - 1217235811705845972574871765837936700542360337637019524992 * q^68 + 17361351448150889077637265817219083285785250426768721895520 * q^69 + 40370459686415885897530019946258677235420585269803429288320 * q^70 + 50262977800159315724835086683846685501725736129988791785560 * q^71 + 61741978698481390141302726420710704640623611541551890419200 * q^72 - 29866935912976824238577353448611378509570684111927150030878 * q^73 - 141849784351445213753933251006028603295768815102096738143920 * q^74 - 201957285133938827818209142762872334198535626872978135872700 * q^75 - 459524449626729728237506845156327517313622138193176308998400 * q^76 - 584903691091230632807084878932757448595860972050144651202208 * q^77 - 22402086294347989122673287092781322891691396539029809599296 * q^78 + 585575205089660590838265168880022777028257388453771607481200 * q^79 + 1073190252220259266057147746504064677993096991374081580523520 * q^80 + 4533130095818971466699734318425466519486071025110491052925005 * q^81 + 3942135409805155170887010182148436012685330945941771799686512 * q^82 + 2788245690403819754860784912585317051147818763920351702275532 * q^83 - 126919894267453303311398867974653650894429551428194565150720 * q^84 - 12285625873772156133384209670234539029240309631211205889028180 * q^85 - 25827853637025878857294346599932142285683441775204060440193440 * q^86 - 16639728321686122963829124023195021859110126733857984457365400 * q^87 - 37714047968515707622032367000426709169856663409503596568012800 * q^88 + 3261564182425241052169353984916675793465907809562936240181650 * q^89 + 3967145115564708643943604045640844654494980994165877917975440 * q^90 + 108036910334048530340065483166305935475510347360713558662966160 * q^91 + 166995545147622332685032938656047356744592976712074780741106176 * q^92 + 379916756753184270638361497392906589593938589120992563130336384 * q^93 - 20439950593005273708597610879292286110217691498870249996014720 * q^94 + 135646904668873700623162464290893387798407178357502623630425000 * q^95 - 903336283885608238754961378979276328179547455316018655408291840 * q^96 - 171116727826062583131545726181696338626852935879476361892307414 * q^97 - 1942373455669362555509787890732368496523562886191617825973826472 * q^98 - 126634984461121539221842595814731567513779549557792846854185980 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.14986e9	−0.378616	−0.189308	−	0.981918i	$-0.560624\pi$
$2$	−1.14986e9	−0.378616	−0.189308	+	0.981918i	$0.560624\pi$
$3$	2.06926e15	1.93418	0.967088	−	0.254444i	$-0.0818925\pi$
$3$	2.06926e15	1.93418	0.967088	+	0.254444i	$0.0818925\pi$
$4$	−7.90120e18	−0.856650
$5$	−9.56939e21	−0.919029	−0.459514	−	0.888170i	$-0.651977\pi$
$5$	−9.56939e21	−0.919029	−0.459514	+	0.888170i	$0.651977\pi$
$6$	−2.37936e24	−0.732310
$7$	−1.15073e26	−0.275667	−0.137833	−	0.990455i	$-0.544014\pi$
$7$	−1.15073e26	−0.275667	−0.137833	+	0.990455i	$0.544014\pi$
$8$	1.96908e28	0.702958
$9$	3.13728e30	2.74103
$10$	1.10034e31	0.347959
$11$	−2.43908e32	−0.383139	−0.191570	−	0.981479i	$-0.561358\pi$
$11$	−2.43908e32	−0.383139	−0.191570	+	0.981479i	$0.561358\pi$
$12$	−1.63496e34	−1.65691
$13$	1.25036e35	1.01817	0.509084	−	0.860717i	$-0.329984\pi$
$13$	1.25036e35	1.01817	0.509084	+	0.860717i	$0.329984\pi$
$14$	1.32317e35	0.104372
$15$	−1.98016e37	−1.77756
$16$	5.02341e37	0.590499
$17$	7.86280e38	1.36910	0.684552	−	0.728964i	$-0.259998\pi$
$17$	7.86280e38	1.36910	0.684552	+	0.728964i	$0.259998\pi$
$18$	−3.60742e39	−1.03780
$19$	−2.70961e39	−0.141961	−0.0709805	−	0.997478i	$-0.522613\pi$
$19$	−2.70961e39	−0.141961	−0.0709805	+	0.997478i	$0.522613\pi$
$20$	7.56097e40	0.787286
$21$	−2.38116e41	−0.533188
$22$	2.80460e41	0.145063
$23$	3.63454e42	0.463471	0.231735	−	0.972779i	$-0.425560\pi$
$23$	3.63454e42	0.463471	0.231735	+	0.972779i	$0.425560\pi$
$24$	4.07454e43	1.35964
$25$	−1.68470e43	−0.155386
$26$	−1.43774e44	−0.385495
$27$	4.12346e45	3.36746
$28$	9.09213e44	0.236150
$29$	3.93841e45	0.338675	0.169338	−	0.985558i	$-0.445837\pi$
$29$	3.93841e45	0.338675	0.169338	+	0.985558i	$0.445837\pi$
$30$	2.27690e46	0.673014
$31$	1.18807e47	1.25011	0.625055	−	0.780581i	$-0.285076\pi$
$31$	1.18807e47	1.25011	0.625055	+	0.780581i	$0.285076\pi$
$32$	−2.39378e47	−0.926530
$33$	−5.04710e47	−0.741058
$34$	−9.04110e47	−0.518365
$35$	1.10118e48	0.253346
$36$	−2.47883e49	−2.34811
$37$	1.80510e49	0.721350	0.360675	−	0.932692i	$-0.382546\pi$
$37$	1.80510e49	0.721350	0.360675	+	0.932692i	$0.382546\pi$
$38$	3.11567e48	0.0537487
$39$	2.58732e50	1.96932
$40$	−1.88429e50	−0.646038
$41$	3.23583e50	0.509677	0.254838	−	0.966984i	$-0.417978\pi$
$41$	3.23583e50	0.509677	0.254838	+	0.966984i	$0.417978\pi$
$42$	2.73799e50	0.201873
$43$	8.59653e50	0.302042	0.151021	−	0.988531i	$-0.451744\pi$
$43$	8.59653e50	0.302042	0.151021	+	0.988531i	$0.451744\pi$
$44$	1.92717e51	0.328216
$45$	−3.00219e52	−2.51909
$46$	−4.17920e51	−0.175477
$47$	1.26451e52	0.269674	0.134837	−	0.990868i	$-0.456949\pi$
$47$	1.26451e52	0.269674	0.134837	+	0.990868i	$0.456949\pi$
$48$	1.03947e53	1.14213
$49$	−1.61010e53	−0.924008
$50$	1.93716e52	0.0588315
$51$	1.62702e54	2.64809
$52$	−9.87934e53	−0.872213
$53$	−5.19617e53	−0.251764	−0.125882	−	0.992045i	$-0.540176\pi$
$53$	−5.19617e53	−0.251764	−0.125882	+	0.992045i	$0.540176\pi$
$54$	−4.74139e54	−1.27498
$55$	2.33405e54	0.352116
$56$	−2.26588e54	−0.193782
$57$	−5.60690e54	−0.274577
$58$	−4.52860e54	−0.128228
$59$	−4.37498e55	−0.722999	−0.361500	−	0.932372i	$-0.617735\pi$
$59$	−4.37498e55	−0.722999	−0.361500	+	0.932372i	$0.617735\pi$
$60$	1.56456e56	1.52275
$61$	2.79669e56	1.61716	0.808582	−	0.588383i	$-0.200235\pi$
$61$	2.79669e56	1.61716	0.808582	+	0.588383i	$0.200235\pi$
$62$	−1.36611e56	−0.473312
$63$	−3.61016e56	−0.755612
$64$	−1.88077e56	−0.239700
$65$	−1.19652e57	−0.935726
$66$	5.80344e56	0.280577
$67$	1.12890e57	0.339860	0.169930	−	0.985456i	$-0.445646\pi$
$67$	1.12890e57	0.339860	0.169930	+	0.985456i	$0.445646\pi$
$68$	−6.21256e57	−1.17284
$69$	7.52080e57	0.896433
$70$	−1.26620e57	−0.0959208
$71$	1.56870e58	0.760154	0.380077	−	0.924955i	$-0.375897\pi$
$71$	1.56870e58	0.760154	0.380077	+	0.924955i	$0.375897\pi$
$72$	6.17756e58	1.92683
$73$	−9.21857e58	−1.86206	−0.931030	−	0.364943i	$-0.881088\pi$
$73$	−9.21857e58	−1.86206	−0.931030	+	0.364943i	$0.881088\pi$
$74$	−2.07560e58	−0.273115
$75$	−3.48607e58	−0.300543
$76$	2.14092e58	0.121611
$77$	2.80672e58	0.105619
$78$	−2.97505e59	−0.745615
$79$	−4.18902e59	−0.702844	−0.351422	−	0.936217i	$-0.614302\pi$
$79$	−4.18902e59	−0.702844	−0.351422	+	0.936217i	$0.614302\pi$
$80$	−4.80710e59	−0.542685
$81$	4.94170e60	3.77223
$82$	−3.72075e59	−0.192972
$83$	−3.28273e60	−1.16218	−0.581092	−	0.813838i	$-0.697374\pi$
$83$	−3.28273e60	−1.16218	−0.581092	+	0.813838i	$0.697374\pi$
$84$	1.88140e60	0.456755
$85$	−7.52422e60	−1.25825
$86$	−9.88478e59	−0.114358
$87$	8.14959e60	0.655057
$88$	−4.80275e60	−0.269331
$89$	−3.02241e61	−1.18732	−0.593660	−	0.804716i	$-0.702317\pi$
$89$	−3.02241e61	−1.18732	−0.593660	+	0.804716i	$0.702317\pi$
$90$	3.45209e61	0.953768
$91$	−1.43882e61	−0.280675
$92$	−2.87172e61	−0.397032
$93$	2.45843e62	2.41793
$94$	−1.45400e61	−0.102103
$95$	2.59294e61	0.130466
$96$	−4.95335e62	−1.79207
$97$	5.45642e61	0.142429	0.0712145	−	0.997461i	$-0.477313\pi$
$97$	5.45642e61	0.142429	0.0712145	+	0.997461i	$0.477313\pi$
$98$	1.85138e62	0.349844
$99$	−7.65208e62	−1.05020
$100$	1.33111e62	0.133111
$101$	7.79995e62	0.570123	0.285061	−	0.958509i	$-0.407986\pi$
$101$	7.79995e62	0.570123	0.285061	+	0.958509i	$0.407986\pi$
$102$	−1.87084e63	−1.00261
$103$	2.40638e63	0.948401	0.474200	−	0.880417i	$-0.342737\pi$
$103$	2.40638e63	0.948401	0.474200	+	0.880417i	$0.342737\pi$
$104$	2.46206e63	0.715729
$105$	2.27862e63	0.490015
$106$	5.97486e62	0.0953219
$107$	9.53357e63	1.13153	0.565766	−	0.824566i	$-0.308581\pi$
$107$	9.53357e63	1.13153	0.565766	+	0.824566i	$0.308581\pi$
$108$	−3.25802e64	−2.88474
$109$	−4.35388e63	−0.288365	−0.144182	−	0.989551i	$-0.546055\pi$
$109$	−4.35388e63	−0.288365	−0.144182	+	0.989551i	$0.546055\pi$
$110$	−2.68383e63	−0.133317
$111$	3.73521e64	1.39522
$112$	−5.78057e63	−0.162781
$113$	−3.09629e64	−0.658978	−0.329489	−	0.944159i	$-0.606877\pi$
$113$	−3.09629e64	−0.658978	−0.329489	+	0.944159i	$0.606877\pi$
$114$	6.44713e63	0.103959
$115$	−3.47803e64	−0.425943
$116$	−3.11181e64	−0.290126
$117$	3.92273e65	2.79083
$118$	5.03060e64	0.273739
$119$	−9.04794e64	−0.377416
$120$	−3.89909e65	−1.24955
$121$	−3.45774e65	−0.853204
$122$	−3.21579e65	−0.612285
$123$	6.69579e65	0.985804
$124$	−9.38717e65	−1.07091
$125$	1.19873e66	1.06183
$126$	4.15116e65	0.286087
$127$	−1.71483e66	−0.921308	−0.460654	−	0.887580i	$-0.652385\pi$
$127$	−1.71483e66	−0.921308	−0.460654	+	0.887580i	$0.652385\pi$
$128$	2.42413e66	1.01728
$129$	1.77885e66	0.584201
$130$	1.37583e66	0.354281
$131$	−4.29490e66	−0.868774	−0.434387	−	0.900726i	$-0.643035\pi$
$131$	−4.29490e66	−0.868774	−0.434387	+	0.900726i	$0.643035\pi$
$132$	3.98781e66	0.634828
$133$	3.11803e65	0.0391339
$134$	−1.29808e66	−0.128676
$135$	−3.94590e67	−3.09480
$136$	1.54825e67	0.962422
$137$	2.53921e67	1.25315	0.626573	−	0.779363i	$-0.284457\pi$
$137$	2.53921e67	1.25315	0.626573	+	0.779363i	$0.284457\pi$
$138$	−8.64785e66	−0.339404
$139$	1.60697e67	0.502390	0.251195	−	0.967937i	$-0.419176\pi$
$139$	1.60697e67	0.502390	0.251195	+	0.967937i	$0.419176\pi$
$140$	−8.70062e66	−0.217029
$141$	2.61660e67	0.521597
$142$	−1.80378e67	−0.287807
$143$	−3.04973e67	−0.390100
$144$	1.57598e68	1.61858
$145$	−3.76881e67	−0.311252
$146$	1.06000e68	0.705006
$147$	−3.33171e68	−1.78719
$148$	−1.42624e68	−0.617944
$149$	−1.60985e68	−0.564181	−0.282091	−	0.959388i	$-0.591028\pi$
$149$	−1.60985e68	−0.564181	−0.282091	+	0.959388i	$0.591028\pi$
$150$	4.00849e67	0.113791
$151$	−2.49704e68	−0.574979	−0.287490	−	0.957784i	$-0.592821\pi$
$151$	−2.49704e68	−0.574979	−0.287490	+	0.957784i	$0.592821\pi$
$152$	−5.33545e67	−0.0997925
$153$	2.46678e69	3.75276
$154$	−3.22733e67	−0.0399890
$155$	−1.13691e69	−1.14889
$156$	−2.04429e69	−1.68701
$157$	1.93952e69	1.30875	0.654373	−	0.756172i	$-0.272933\pi$
$157$	1.93952e69	1.30875	0.654373	+	0.756172i	$0.272933\pi$
$158$	4.81678e68	0.266108
$159$	−1.07522e69	−0.486956
$160$	2.29070e69	0.851508
$161$	−4.18236e68	−0.127763
$162$	−5.68225e69	−1.42823
$163$	−3.46413e69	−0.717274	−0.358637	−	0.933477i	$-0.616758\pi$
$163$	−3.46413e69	−0.717274	−0.358637	+	0.933477i	$0.616758\pi$
$164$	−2.55670e69	−0.436614
$165$	4.82976e69	0.681054
$166$	3.77467e69	0.440021
$167$	1.46319e70	1.41166	0.705831	−	0.708380i	$-0.250574\pi$
$167$	1.46319e70	1.41166	0.705831	+	0.708380i	$0.250574\pi$
$168$	−4.68869e69	−0.374808
$169$	5.52965e68	0.0366662
$170$	8.65178e69	0.476392
$171$	−8.50082e69	−0.389120
$172$	−6.79229e69	−0.258744
$173$	6.95687e69	0.220781	0.110390	−	0.993888i	$-0.464790\pi$
$173$	6.95687e69	0.220781	0.110390	+	0.993888i	$0.464790\pi$
$174$	−9.37087e69	−0.248015
$175$	1.93863e69	0.0428347
$176$	−1.22525e70	−0.226243
$177$	−9.05298e70	−1.39841
$178$	3.47534e70	0.449538
$179$	−7.72748e70	−0.837852	−0.418926	−	0.908020i	$-0.637593\pi$
$179$	−7.72748e70	−0.837852	−0.418926	+	0.908020i	$0.637593\pi$
$180$	2.37209e71	2.15798
$181$	−2.40823e71	−1.84002	−0.920011	−	0.391892i	$-0.871821\pi$
$181$	−2.40823e71	−1.84002	−0.920011	+	0.391892i	$0.871821\pi$
$182$	1.65444e70	0.106268
$183$	5.78708e71	3.12788
$184$	7.15670e70	0.325800
$185$	−1.72737e71	−0.662941
$186$	−2.82684e71	−0.915468
$187$	−1.91780e71	−0.524557
$188$	−9.99113e70	−0.231016
$189$	−4.74497e71	−0.928297
$190$	−2.98151e70	−0.0493966
$191$	1.08495e72	1.52356	0.761780	−	0.647836i	$-0.224326\pi$
$191$	1.08495e72	1.52356	0.761780	+	0.647836i	$0.224326\pi$
$192$	−3.89181e71	−0.463621
$193$	1.08691e71	0.109936	0.0549679	−	0.998488i	$-0.482494\pi$
$193$	1.08691e71	0.109936	0.0549679	+	0.998488i	$0.482494\pi$
$194$	−6.27410e70	−0.0539259
$195$	−2.47591e72	−1.80986
$196$	1.27217e72	0.791551
$197$	1.84925e72	0.980186	0.490093	−	0.871670i	$-0.336963\pi$
$197$	1.84925e72	0.980186	0.490093	+	0.871670i	$0.336963\pi$
$198$	8.79880e71	0.397622
$199$	1.80760e72	0.696997	0.348498	−	0.937309i	$-0.386692\pi$
$199$	1.80760e72	0.696997	0.348498	+	0.937309i	$0.386692\pi$
$200$	−3.31730e71	−0.109230
$201$	2.33599e72	0.657349
$202$	−8.96883e71	−0.215858
$203$	−4.53203e71	−0.0933615
$204$	−1.28554e73	−2.26848
$205$	−3.09650e72	−0.468408
$206$	−2.76700e72	−0.359080
$207$	1.14026e73	1.27039
$208$	6.28107e72	0.601227
$209$	6.60897e71	0.0543908
$210$	−2.62009e72	−0.185528
$211$	−1.54379e73	−0.941221	−0.470611	−	0.882341i	$-0.655966\pi$
$211$	−1.54379e73	−0.941221	−0.470611	+	0.882341i	$0.655966\pi$
$212$	4.10560e72	0.215674
$213$	3.24605e73	1.47027
$214$	−1.09622e73	−0.428416
$215$	−8.22636e72	−0.277585
$216$	8.11942e73	2.36718
$217$	−1.36714e73	−0.344614
$218$	5.00635e72	0.109180
$219$	−1.90756e74	−3.60155
$220$	−1.84418e73	−0.301640
$221$	9.83133e73	1.39398
$222$	−4.29496e73	−0.528252
$223$	2.35527e73	0.251442	0.125721	−	0.992066i	$-0.459876\pi$
$223$	2.35527e73	0.251442	0.125721	+	0.992066i	$0.459876\pi$
$224$	2.75459e73	0.255413
$225$	−5.28536e73	−0.425917
$226$	3.56030e73	0.249500
$227$	2.46957e74	1.50594	0.752968	−	0.658057i	$-0.228622\pi$
$227$	2.46957e74	1.50594	0.752968	+	0.658057i	$0.228622\pi$
$228$	4.43012e73	0.235217
$229$	−2.99938e74	−1.38744	−0.693719	−	0.720245i	$-0.744029\pi$
$229$	−2.99938e74	−1.38744	−0.693719	+	0.720245i	$0.744029\pi$
$230$	3.99924e73	0.161269
$231$	5.80783e73	0.204285
$232$	7.75504e73	0.238074
$233$	4.83092e74	1.29514	0.647572	−	0.762004i	$-0.275784\pi$
$233$	4.83092e74	1.29514	0.647572	+	0.762004i	$0.275784\pi$
$234$	−4.51058e74	−1.05665
$235$	−1.21006e74	−0.247838
$236$	3.45676e74	0.619357
$237$	−8.66818e74	−1.35942
$238$	1.04038e74	0.142896
$239$	−6.21166e74	−0.747608	−0.373804	−	0.927508i	$-0.621947\pi$
$239$	−6.21166e74	−0.747608	−0.373804	+	0.927508i	$0.621947\pi$
$240$	−9.94714e74	−1.04965
$241$	−3.17493e74	−0.293898	−0.146949	−	0.989144i	$-0.546945\pi$
$241$	−3.17493e74	−0.293898	−0.146949	+	0.989144i	$0.546945\pi$
$242$	3.97591e74	0.323037
$243$	5.50611e75	3.92869
$244$	−2.20972e75	−1.38534
$245$	1.54077e75	0.849190
$246$	−7.69920e74	−0.373241
$247$	−3.38799e74	−0.144540
$248$	2.33941e75	0.878775
$249$	−6.79282e75	−2.24787
$250$	−1.37837e75	−0.402027
$251$	3.82426e75	0.983615	0.491807	−	0.870704i	$-0.336336\pi$
$251$	3.82426e75	0.983615	0.491807	+	0.870704i	$0.336336\pi$
$252$	2.85246e75	0.647294
$253$	−8.86493e74	−0.177574
$254$	1.97182e75	0.348822
$255$	−1.55696e76	−2.43367
$256$	−1.05270e75	−0.145461
$257$	7.62665e75	0.932052	0.466026	−	0.884771i	$-0.345685\pi$
$257$	7.62665e75	0.932052	0.466026	+	0.884771i	$0.345685\pi$
$258$	−2.04542e75	−0.221188
$259$	−2.07717e75	−0.198852
$260$	9.45393e75	0.801589
$261$	1.23559e76	0.928320
$262$	4.93852e75	0.328932
$263$	1.28572e76	0.759521	0.379760	−	0.925085i	$-0.376006\pi$
$263$	1.28572e76	0.759521	0.379760	+	0.925085i	$0.376006\pi$
$264$	−9.93814e75	−0.520933
$265$	4.97242e75	0.231378
$266$	−3.58529e74	−0.0148167
$267$	−6.25415e76	−2.29648
$268$	−8.91968e75	−0.291141
$269$	3.17052e76	0.920310	0.460155	−	0.887838i	$-0.347794\pi$
$269$	3.17052e76	0.920310	0.460155	+	0.887838i	$0.347794\pi$
$270$	4.53722e76	1.17174
$271$	−5.69145e76	−1.30825	−0.654125	−	0.756387i	$-0.726963\pi$
$271$	−5.69145e76	−1.30825	−0.654125	+	0.756387i	$0.726963\pi$
$272$	3.94980e76	0.808454
$273$	−2.97730e76	−0.542875
$274$	−2.91973e76	−0.474461
$275$	4.10911e75	0.0595344
$276$	−5.94234e76	−0.767929
$277$	−3.83488e76	−0.442221	−0.221110	−	0.975249i	$-0.570968\pi$
$277$	−3.83488e76	−0.442221	−0.221110	+	0.975249i	$0.570968\pi$
$278$	−1.84778e76	−0.190213
$279$	3.72731e77	3.42659
$280$	2.16831e76	0.178091
$281$	9.26162e76	0.679888	0.339944	−	0.940446i	$-0.389592\pi$
$281$	9.26162e76	0.679888	0.339944	+	0.940446i	$0.389592\pi$
$282$	−3.00871e76	−0.197485
$283$	−2.27051e77	−1.33306	−0.666532	−	0.745477i	$-0.732222\pi$
$283$	−2.27051e77	−1.33306	−0.666532	+	0.745477i	$0.732222\pi$
$284$	−1.23946e77	−0.651186
$285$	5.36546e76	0.252345
$286$	3.50675e76	0.147698
$287$	−3.72356e76	−0.140501
$288$	−7.50995e77	−2.53965
$289$	2.88412e77	0.874444
$290$	4.33360e76	0.117845
$291$	1.12908e77	0.275482
$292$	7.28378e77	1.59513
$293$	−7.85286e77	−1.54418	−0.772090	−	0.635513i	$-0.780788\pi$
$293$	−7.85286e77	−1.54418	−0.772090	+	0.635513i	$0.780788\pi$
$294$	3.83099e77	0.676660
$295$	4.18659e77	0.664457
$296$	3.55438e77	0.507078
$297$	−1.00574e78	−1.29021
$298$	1.85110e77	0.213608
$299$	4.54448e77	0.471891
$300$	2.75442e77	0.257460
$301$	−9.89227e76	−0.0832628
$302$	2.87124e77	0.217697
$303$	1.61401e78	1.10272
$304$	−1.36115e77	−0.0838278
$305$	−2.67626e78	−1.48622
$306$	−2.83645e78	−1.42085
$307$	−2.46188e78	−1.11278	−0.556388	−	0.830923i	$-0.687813\pi$
$307$	−2.46188e78	−1.11278	−0.556388	+	0.830923i	$0.687813\pi$
$308$	−2.21764e77	−0.0904783
$309$	4.97943e78	1.83437
$310$	1.30728e78	0.434987
$311$	−4.46651e78	−1.34281	−0.671407	−	0.741089i	$-0.734310\pi$
$311$	−4.46651e78	−1.34281	−0.671407	+	0.741089i	$0.734310\pi$
$312$	5.09465e78	1.38435
$313$	2.75654e78	0.677201	0.338601	−	0.940930i	$-0.390046\pi$
$313$	2.75654e78	0.677201	0.338601	+	0.940930i	$0.390046\pi$
$314$	−2.23017e78	−0.495512
$315$	3.45470e78	0.694429
$316$	3.30983e78	0.602092
$317$	−1.07470e79	−1.76978	−0.884888	−	0.465803i	$-0.845766\pi$
$317$	−1.07470e79	−1.76978	−0.884888	+	0.465803i	$0.845766\pi$
$318$	1.23635e78	0.184369
$319$	−9.60609e77	−0.129760
$320$	1.79979e78	0.220291
$321$	1.97274e79	2.18858
$322$	4.80912e77	0.0483733
$323$	−2.13051e78	−0.194359
$324$	−3.90453e79	−3.23148
$325$	−2.10648e78	−0.158209
$326$	3.98326e78	0.271571
$327$	−9.00932e78	−0.557748
$328$	6.37162e78	0.358281
$329$	−1.45510e78	−0.0743402
$330$	−5.55354e78	−0.257858
$331$	2.07542e79	0.876041	0.438021	−	0.898965i	$-0.355680\pi$
$331$	2.07542e79	0.876041	0.438021	+	0.898965i	$0.355680\pi$
$332$	2.59375e79	0.995584
$333$	5.66309e79	1.97724
$334$	−1.68246e79	−0.534478
$335$	−1.08029e79	−0.312341
$336$	−1.19615e79	−0.314847
$337$	−2.57458e79	−0.617114	−0.308557	−	0.951206i	$-0.599846\pi$
$337$	−2.57458e79	−0.617114	−0.308557	+	0.951206i	$0.599846\pi$
$338$	−6.35831e77	−0.0138824
$339$	−6.40704e79	−1.27458
$340$	5.94504e79	1.07788
$341$	−2.89780e79	−0.478966
$342$	9.77473e78	0.147327
$343$	3.85794e79	0.530385
$344$	1.69273e79	0.212322
$345$	−7.19695e79	−0.823848
$346$	−7.99941e78	−0.0835912
$347$	−4.77104e78	−0.0455234	−0.0227617	−	0.999741i	$-0.507246\pi$
$347$	−4.77104e78	−0.0455234	−0.0227617	+	0.999741i	$0.507246\pi$
$348$	−6.43915e79	−0.561155
$349$	−2.34138e80	−1.86411	−0.932053	−	0.362323i	$-0.881984\pi$
$349$	−2.34138e80	−1.86411	−0.932053	+	0.362323i	$0.881984\pi$
$350$	−2.22914e78	−0.0162179
$351$	5.15580e80	3.42864
$352$	5.83862e79	0.354990
$353$	−7.30803e79	−0.406347	−0.203173	−	0.979143i	$-0.565126\pi$
$353$	−7.30803e79	−0.406347	−0.203173	+	0.979143i	$0.565126\pi$
$354$	1.04096e80	0.529459
$355$	−1.50115e80	−0.698604
$356$	2.38806e80	1.01712
$357$	−1.87226e80	−0.729989
$358$	8.88549e79	0.317224
$359$	3.10624e80	1.01569	0.507844	−	0.861449i	$-0.330443\pi$
$359$	3.10624e80	1.01569	0.507844	+	0.861449i	$0.330443\pi$
$360$	−5.91155e80	−1.77081
$361$	−3.56973e80	−0.979847
$362$	2.76912e80	0.696662
$363$	−7.15496e80	−1.65025
$364$	1.13684e80	0.240440
$365$	8.82161e80	1.71129
$366$	−6.65432e80	−1.18427
$367$	−2.95687e80	−0.482893	−0.241447	−	0.970414i	$-0.577622\pi$
$367$	−2.95687e80	−0.482893	−0.241447	+	0.970414i	$0.577622\pi$
$368$	1.82578e80	0.273679
$369$	1.01517e81	1.39704
$370$	1.98623e80	0.251000
$371$	5.97938e79	0.0694029
$372$	−1.94245e81	−2.07132
$373$	6.53601e80	0.640449	0.320224	−	0.947342i	$-0.396242\pi$
$373$	6.53601e80	0.640449	0.320224	+	0.947342i	$0.396242\pi$
$374$	2.20520e80	0.198606
$375$	2.48049e81	2.05377
$376$	2.48992e80	0.189569
$377$	4.92442e80	0.344828
$378$	5.45604e80	0.351468
$379$	−1.70057e81	−1.00800	−0.503998	−	0.863705i	$-0.668138\pi$
$379$	−1.70057e81	−1.00800	−0.503998	+	0.863705i	$0.668138\pi$
$380$	−2.04873e80	−0.111764
$381$	−3.54844e81	−1.78197
$382$	−1.24754e81	−0.576844
$383$	−4.22264e81	−1.79814	−0.899068	−	0.437808i	$-0.855755\pi$
$383$	−4.22264e81	−1.79814	−0.899068	+	0.437808i	$0.855755\pi$
$384$	5.01616e81	1.96761
$385$	−2.68586e80	−0.0970667
$386$	−1.24979e80	−0.0416235
$387$	2.69697e81	0.827906
$388$	−4.31123e80	−0.122012
$389$	1.74537e81	0.455487	0.227744	−	0.973721i	$-0.426865\pi$
$389$	1.74537e81	0.455487	0.227744	+	0.973721i	$0.426865\pi$
$390$	2.84694e81	0.685241
$391$	2.85776e81	0.634539
$392$	−3.17041e81	−0.649538
$393$	−8.88726e81	−1.68036
$394$	−2.12637e81	−0.371114
$395$	4.00864e81	0.645934
$396$	6.04606e81	0.899651
$397$	1.07185e82	1.47310	0.736551	−	0.676382i	$-0.236453\pi$
$397$	1.07185e82	1.47310	0.736551	+	0.676382i	$0.236453\pi$
$398$	−2.07848e81	−0.263894
$399$	6.45201e80	0.0756918
$400$	−8.46291e80	−0.0917551
$401$	−1.05350e82	−1.05582	−0.527908	−	0.849301i	$-0.677024\pi$
$401$	−1.05350e82	−1.05582	−0.527908	+	0.849301i	$0.677024\pi$
$402$	−2.68606e81	−0.248883
$403$	1.48551e82	1.27282
$404$	−6.16290e81	−0.488396
$405$	−4.72890e82	−3.46679
$406$	5.21119e80	0.0353482
$407$	−4.40278e81	−0.276377
$408$	3.20373e82	1.86149
$409$	−4.74020e81	−0.254984	−0.127492	−	0.991840i	$-0.540693\pi$
$409$	−4.74020e81	−0.254984	−0.127492	+	0.991840i	$0.540693\pi$
$410$	3.56053e81	0.177347
$411$	5.25430e82	2.42380
$412$	−1.90133e82	−0.812447
$413$	5.03441e81	0.199307
$414$	−1.31113e82	−0.480989
$415$	3.14137e82	1.06808
$416$	−2.99308e82	−0.943363
$417$	3.32524e82	0.971710
$418$	−7.59937e80	−0.0205932
$419$	−4.38377e82	−1.10181	−0.550904	−	0.834569i	$-0.685717\pi$
$419$	−4.38377e82	−1.10181	−0.550904	+	0.834569i	$0.685717\pi$
$420$	−1.80038e82	−0.419771
$421$	−1.14158e82	−0.246956	−0.123478	−	0.992347i	$-0.539405\pi$
$421$	−1.14158e82	−0.246956	−0.123478	+	0.992347i	$0.539405\pi$
$422$	1.77514e82	0.356362
$423$	3.96712e82	0.739185
$424$	−1.02317e82	−0.176979
$425$	−1.32464e82	−0.212739
$426$	−3.73249e82	−0.556669
$427$	−3.21823e82	−0.445798
$428$	−7.53266e82	−0.969326
$429$	−6.31069e82	−0.754522
$430$	9.45914e81	0.105098
$431$	1.31107e83	1.35391	0.676956	−	0.736023i	$-0.263299\pi$
$431$	1.31107e83	1.35391	0.676956	+	0.736023i	$0.263299\pi$
$432$	2.07138e83	1.98848
$433$	−5.01725e82	−0.447813	−0.223907	−	0.974611i	$-0.571881\pi$
$433$	−5.01725e82	−0.447813	−0.223907	+	0.974611i	$0.571881\pi$
$434$	1.57202e82	0.130476
$435$	−7.79866e82	−0.602017
$436$	3.44009e82	0.247028
$437$	−9.84819e81	−0.0657947
$438$	2.19343e83	1.36360
$439$	6.75059e82	0.390579	0.195290	−	0.980746i	$-0.437435\pi$
$439$	6.75059e82	0.390579	0.195290	+	0.980746i	$0.437435\pi$
$440$	4.59594e82	0.247523
$441$	−5.05133e83	−2.53274
$442$	−1.13046e83	−0.527782
$443$	2.29536e83	0.998005	0.499002	−	0.866601i	$-0.333700\pi$
$443$	2.29536e83	0.998005	0.499002	+	0.866601i	$0.333700\pi$
$444$	−2.95127e83	−1.19521
$445$	2.89226e83	1.09118
$446$	−2.70822e82	−0.0951999
$447$	−3.33120e83	−1.09122
$448$	2.16426e82	0.0660772
$449$	2.84021e83	0.808333	0.404167	−	0.914685i	$-0.367562\pi$
$449$	2.84021e83	0.808333	0.404167	+	0.914685i	$0.367562\pi$
$450$	6.07741e82	0.161259
$451$	−7.89246e82	−0.195277
$452$	2.44644e83	0.564514
$453$	−5.16704e83	−1.11211
$454$	−2.83965e83	−0.570172
$455$	1.37687e83	0.257948
$456$	−1.10404e83	−0.193016
$457$	−3.53890e83	−0.577442	−0.288721	−	0.957413i	$-0.593230\pi$
$457$	−3.53890e83	−0.577442	−0.288721	+	0.957413i	$0.593230\pi$
$458$	3.44886e83	0.525307
$459$	3.24219e84	4.61040
$460$	2.74806e83	0.364884
$461$	−9.02523e83	−1.11913	−0.559563	−	0.828788i	$-0.689031\pi$
$461$	−9.02523e83	−1.11913	−0.559563	+	0.828788i	$0.689031\pi$
$462$	−6.67818e82	−0.0773456
$463$	−1.17555e84	−1.27187	−0.635933	−	0.771744i	$-0.719385\pi$
$463$	−1.17555e84	−1.27187	−0.635933	+	0.771744i	$0.719385\pi$
$464$	1.97842e83	0.199987
$465$	−2.35256e84	−2.22215
$466$	−5.55487e83	−0.490363
$467$	1.78581e84	1.47351	0.736757	−	0.676157i	$-0.236356\pi$
$467$	1.78581e84	1.47351	0.736757	+	0.676157i	$0.236356\pi$
$468$	−3.09943e84	−2.39077
$469$	−1.29906e83	−0.0936881
$470$	1.39139e83	0.0938356
$471$	4.01337e84	2.53134
$472$	−8.61469e83	−0.508238
$473$	−2.09676e83	−0.115724
$474$	9.96717e83	0.514700
$475$	4.56487e82	0.0220587
$476$	7.14896e83	0.323313
$477$	−1.63018e84	−0.690093
$478$	7.14253e83	0.283056
$479$	−4.37337e84	−1.62274	−0.811368	−	0.584536i	$-0.801277\pi$
$479$	−4.37337e84	−1.62274	−0.811368	+	0.584536i	$0.801277\pi$
$480$	4.74006e84	1.64697
$481$	2.25702e84	0.734455
$482$	3.65071e83	0.111275
$483$	−8.65440e83	−0.247117
$484$	2.73203e84	0.730897
$485$	−5.22146e83	−0.130896
$486$	−6.33125e84	−1.48746
$487$	4.62469e84	1.01841	0.509203	−	0.860647i	$-0.329940\pi$
$487$	4.62469e84	1.01841	0.509203	+	0.860647i	$0.329940\pi$
$488$	5.50691e84	1.13680
$489$	−7.16819e84	−1.38733
$490$	−1.77166e84	−0.321517
$491$	−1.06620e85	−1.81455	−0.907277	−	0.420533i	$-0.861843\pi$
$491$	−1.06620e85	−1.81455	−0.907277	+	0.420533i	$0.861843\pi$
$492$	−5.29047e84	−0.844489
$493$	3.09669e84	0.463681
$494$	3.89571e83	0.0547252
$495$	7.32258e84	0.965162
$496$	5.96816e84	0.738189
$497$	−1.80515e84	−0.209549
$498$	7.81077e84	0.851078
$499$	−8.87919e84	−0.908252	−0.454126	−	0.890938i	$-0.650048\pi$
$499$	−8.87919e84	−0.908252	−0.454126	+	0.890938i	$0.650048\pi$
$500$	−9.47141e84	−0.909619
$501$	3.02772e85	2.73040
$502$	−4.39735e84	−0.372412
$503$	1.82243e84	0.144964	0.0724818	−	0.997370i	$-0.476908\pi$
$503$	1.82243e84	0.144964	0.0724818	+	0.997370i	$0.476908\pi$
$504$	−7.10869e84	−0.531163
$505$	−7.46408e84	−0.523959
$506$	1.01934e84	0.0672323
$507$	1.14423e84	0.0709189
$508$	1.35493e85	0.789239
$509$	−1.57331e85	−0.861401	−0.430700	−	0.902495i	$-0.641733\pi$
$509$	−1.57331e85	−0.861401	−0.430700	+	0.902495i	$0.641733\pi$
$510$	1.79028e85	0.921426
$511$	1.06081e85	0.513308
$512$	−2.11482e85	−0.962210
$513$	−1.11730e85	−0.478048
$514$	−8.76956e84	−0.352890
$515$	−2.30276e85	−0.871608
$516$	−1.40550e85	−0.500456
$517$	−3.08424e84	−0.103323
$518$	2.38845e84	0.0752886
$519$	1.43956e85	0.427029
$520$	−2.35604e85	−0.657776
$521$	2.23640e85	0.587707	0.293853	−	0.955850i	$-0.405062\pi$
$521$	2.23640e85	0.587707	0.293853	+	0.955850i	$0.405062\pi$
$522$	−1.42075e85	−0.351477
$523$	8.37853e85	1.95148	0.975741	−	0.218927i	$-0.0702555\pi$
$523$	8.37853e85	1.95148	0.975741	+	0.218927i	$0.0702555\pi$
$524$	3.39348e85	0.744235
$525$	4.01152e84	0.0828497
$526$	−1.47839e85	−0.287567
$527$	9.34155e85	1.71153
$528$	−2.53536e85	−0.437594
$529$	−4.82871e85	−0.785195
$530$	−5.71757e84	−0.0876036
$531$	−1.37255e86	−1.98176
$532$	−2.46362e84	−0.0335241
$533$	4.04596e85	0.518937
$534$	7.19138e85	0.869486
$535$	−9.12305e85	−1.03991
$536$	2.22290e85	0.238907
$537$	−1.59902e86	−1.62055
$538$	−3.64565e85	−0.348444
$539$	3.92716e85	0.354024
$540$	3.11773e86	2.65116
$541$	1.46553e86	1.17565	0.587827	−	0.808986i	$-0.299983\pi$
$541$	1.46553e86	1.17565	0.587827	+	0.808986i	$0.299983\pi$
$542$	6.54436e85	0.495324
$543$	−4.98326e86	−3.55893
$544$	−1.88218e86	−1.26852
$545$	4.16640e85	0.265016
$546$	3.42347e85	0.205541
$547$	1.03373e83	0.000585878 0	0.000292939	−	1.00000i	$-0.499907\pi$
$547$	1.03373e83	0.000585878 0	0.000292939		1.00000i	$0.499907\pi$
$548$	−2.00628e86	−1.07351
$549$	8.77400e86	4.43270
$550$	−4.72489e84	−0.0225407
$551$	−1.06716e85	−0.0480787
$552$	1.48091e86	0.630155
$553$	4.82042e85	0.193751
$554$	4.40956e85	0.167432
$555$	−3.57437e86	−1.28224
$556$	−1.26970e86	−0.430372
$557$	−1.52548e86	−0.488616	−0.244308	−	0.969698i	$-0.578561\pi$
$557$	−1.52548e86	−0.488616	−0.244308	+	0.969698i	$0.578561\pi$
$558$	−4.28587e86	−1.29736
$559$	1.07488e86	0.307529
$560$	5.53166e85	0.149600
$561$	−3.96843e86	−1.01459
$562$	−1.06495e86	−0.257417
$563$	6.23004e86	1.42389	0.711945	−	0.702235i	$-0.247814\pi$
$563$	6.23004e86	1.42389	0.711945	+	0.702235i	$0.247814\pi$
$564$	−2.06743e86	−0.446826
$565$	2.96296e86	0.605620
$566$	2.61076e86	0.504719
$567$	−5.68655e86	−1.03988
$568$	3.08890e86	0.534356
$569$	−2.01891e86	−0.330431	−0.165216	−	0.986257i	$-0.552832\pi$
$569$	−2.01891e86	−0.330431	−0.165216	+	0.986257i	$0.552832\pi$
$570$	−6.16951e85	−0.0955417
$571$	−8.80331e86	−1.29006	−0.645028	−	0.764159i	$-0.723154\pi$
$571$	−8.80331e86	−1.29006	−0.645028	+	0.764159i	$0.723154\pi$
$572$	2.40965e86	0.334179
$573$	2.24505e87	2.94683
$574$	4.28157e85	0.0531959
$575$	−6.12309e85	−0.0720167
$576$	−5.90051e86	−0.657024
$577$	4.21339e86	0.444215	0.222107	−	0.975022i	$-0.428706\pi$
$577$	4.21339e86	0.444215	0.222107	+	0.975022i	$0.428706\pi$
$578$	−3.31633e86	−0.331079
$579$	2.24910e86	0.212635
$580$	2.97782e86	0.266634
$581$	3.77752e86	0.320375
$582$	−1.29828e86	−0.104302
$583$	1.26739e86	0.0964607
$584$	−1.81521e87	−1.30895
$585$	−3.75381e87	−2.56486
$586$	9.02967e86	0.584651
$587$	−1.93457e87	−1.18709	−0.593545	−	0.804801i	$-0.702272\pi$
$587$	−1.93457e87	−1.18709	−0.593545	+	0.804801i	$0.702272\pi$
$588$	2.63245e87	1.53100
$589$	−3.21921e86	−0.177467
$590$	−4.81398e86	−0.251574
$591$	3.82657e87	1.89585
$592$	9.06773e86	0.425956
$593$	−3.07531e87	−1.36983	−0.684914	−	0.728624i	$-0.740160\pi$
$593$	−3.07531e87	−1.36983	−0.684914	+	0.728624i	$0.740160\pi$
$594$	1.15646e87	0.488493
$595$	8.65833e86	0.346856
$596$	1.27198e87	0.483306
$597$	3.74040e87	1.34811
$598$	−5.22550e86	−0.178666
$599$	−3.29040e87	−1.06734	−0.533672	−	0.845692i	$-0.679188\pi$
$599$	−3.29040e87	−1.06734	−0.533672	+	0.845692i	$0.679188\pi$
$600$	−6.86437e86	−0.211269
$601$	−3.89130e87	−1.13645	−0.568224	−	0.822874i	$-0.692369\pi$
$601$	−3.89130e87	−1.13645	−0.568224	+	0.822874i	$0.692369\pi$
$602$	1.13747e86	0.0315247
$603$	3.54168e87	0.931568
$604$	1.97296e87	0.492556
$605$	3.30885e87	0.784119
$606$	−1.85589e87	−0.417507
$607$	−3.00692e87	−0.642212	−0.321106	−	0.947043i	$-0.604055\pi$
$607$	−3.00692e87	−0.642212	−0.321106	+	0.947043i	$0.604055\pi$
$608$	6.48621e86	0.131531
$609$	−9.37796e86	−0.180577
$610$	3.07732e87	0.562707
$611$	1.58109e87	0.274574
$612$	−1.94905e88	−3.21480
$613$	7.23158e87	1.13300	0.566498	−	0.824063i	$-0.308298\pi$
$613$	7.23158e87	1.13300	0.566498	+	0.824063i	$0.308298\pi$
$614$	2.83081e87	0.421315
$615$	−6.40746e87	−0.905982
$616$	5.52666e86	0.0742455
$617$	−6.75048e87	−0.861691	−0.430846	−	0.902426i	$-0.641785\pi$
$617$	−6.75048e87	−0.861691	−0.430846	+	0.902426i	$0.641785\pi$
$618$	−5.72564e87	−0.694523
$619$	7.11084e87	0.819720	0.409860	−	0.912149i	$-0.365578\pi$
$619$	7.11084e87	0.819720	0.409860	+	0.912149i	$0.365578\pi$
$620$	8.98295e87	0.984194
$621$	1.49869e88	1.56072
$622$	5.13585e87	0.508411
$623$	3.47797e87	0.327304
$624$	1.29972e88	1.16288
$625$	−9.64457e87	−0.820470
$626$	−3.16963e87	−0.256399
$627$	1.36757e87	0.105201
$628$	−1.53245e88	−1.12114
$629$	1.41931e88	0.987603
$630$	−3.97241e87	−0.262922
$631$	−1.17327e88	−0.738708	−0.369354	−	0.929289i	$-0.620421\pi$
$631$	−1.17327e88	−0.738708	−0.369354	+	0.929289i	$0.620421\pi$
$632$	−8.24853e87	−0.494070
$633$	−3.19451e88	−1.82049
$634$	1.23575e88	0.670066
$635$	1.64099e88	0.846709
$636$	8.49556e87	0.417150
$637$	−2.01320e88	−0.940795
$638$	1.10456e87	0.0491291
$639$	4.92145e88	2.08361
$640$	−2.31975e88	−0.934914
$641$	−5.85075e87	−0.224483	−0.112241	−	0.993681i	$-0.535803\pi$
$641$	−5.85075e87	−0.224483	−0.112241	+	0.993681i	$0.535803\pi$
$642$	−2.26837e88	−0.828631
$643$	−3.09879e88	−1.07782	−0.538910	−	0.842363i	$-0.681164\pi$
$643$	−3.09879e88	−1.07782	−0.538910	+	0.842363i	$0.681164\pi$
$644$	3.30457e87	0.109448
$645$	−1.70225e88	−0.536898
$646$	2.44979e87	0.0735875
$647$	3.14549e88	0.899919	0.449959	−	0.893049i	$-0.351438\pi$
$647$	3.14549e88	0.899919	0.449959	+	0.893049i	$0.351438\pi$
$648$	9.73061e88	2.65172
$649$	1.06709e88	0.277009
$650$	2.42215e87	0.0599004
$651$	−2.82898e88	−0.666543
$652$	2.73708e88	0.614452
$653$	1.00332e88	0.214622	0.107311	−	0.994226i	$-0.465776\pi$
$653$	1.00332e88	0.214622	0.107311	+	0.994226i	$0.465776\pi$
$654$	1.03594e88	0.211172
$655$	4.10995e88	0.798428
$656$	1.62549e88	0.300963
$657$	−2.89212e89	−5.10397
$658$	1.67316e87	0.0281464
$659$	3.87613e88	0.621595	0.310798	−	0.950476i	$-0.399404\pi$
$659$	3.87613e88	0.621595	0.310798	+	0.950476i	$0.399404\pi$
$660$	−3.81609e88	−0.583425
$661$	5.13511e88	0.748521	0.374261	−	0.927324i	$-0.377897\pi$
$661$	5.13511e88	0.748521	0.374261	+	0.927324i	$0.377897\pi$
$662$	−2.38644e88	−0.331683
$663$	2.03436e89	2.69620
$664$	−6.46395e88	−0.816966
$665$	−2.98376e87	−0.0359652
$666$	−6.51175e88	−0.748616
$667$	1.43143e88	0.156966
$668$	−1.15609e89	−1.20930
$669$	4.87367e88	0.486332
$670$	1.24218e88	0.118257
$671$	−6.82135e88	−0.619599
$672$	5.69996e88	0.494014
$673$	1.51230e89	1.25073	0.625366	−	0.780332i	$-0.284950\pi$
$673$	1.51230e89	1.25073	0.625366	+	0.780332i	$0.284950\pi$
$674$	2.96040e88	0.233649
$675$	−6.94677e88	−0.523256
$676$	−4.36909e87	−0.0314101
$677$	9.60349e87	0.0659001	0.0329500	−	0.999457i	$-0.489510\pi$
$677$	9.60349e87	0.0659001	0.0329500	+	0.999457i	$0.489510\pi$
$678$	7.36718e88	0.482576
$679$	−6.27885e87	−0.0392629
$680$	−1.48158e89	−0.884493
$681$	5.11018e89	2.91274
$682$	3.33205e88	0.181344
$683$	−1.20923e89	−0.628431	−0.314215	−	0.949352i	$-0.601741\pi$
$683$	−1.20923e89	−0.628431	−0.314215	+	0.949352i	$0.601741\pi$
$684$	6.71666e88	0.333339
$685$	−2.42987e89	−1.15168
$686$	−4.43609e88	−0.200812
$687$	−6.20650e89	−2.68355
$688$	4.31839e88	0.178355
$689$	−6.49708e88	−0.256338
$690$	8.27547e88	0.311922
$691$	−5.63672e88	−0.202987	−0.101494	−	0.994836i	$-0.532362\pi$
$691$	−5.63672e88	−0.202987	−0.101494	+	0.994836i	$0.532362\pi$
$692$	−5.49676e88	−0.189132
$693$	8.80546e88	0.289504
$694$	5.48602e87	0.0172359
$695$	−1.53777e89	−0.461711
$696$	1.60472e89	0.460477
$697$	2.54427e89	0.697800
$698$	2.69225e89	0.705780
$699$	9.99643e89	2.50504
$700$	−1.53175e88	−0.0366943
$701$	−3.32347e89	−0.761158	−0.380579	−	0.924748i	$-0.624275\pi$
$701$	−3.32347e89	−0.761158	−0.380579	+	0.924748i	$0.624275\pi$
$702$	−5.92844e89	−1.29814
$703$	−4.89111e88	−0.102404
$704$	4.58736e88	0.0918383
$705$	−2.50393e89	−0.479363
$706$	8.40319e88	0.153849
$707$	−8.97562e88	−0.157164
$708$	7.15294e89	1.19794
$709$	3.99117e89	0.639357	0.319678	−	0.947526i	$-0.396425\pi$
$709$	3.99117e89	0.639357	0.319678	+	0.947526i	$0.396425\pi$
$710$	1.72611e89	0.264503
$711$	−1.31421e90	−1.92652
$712$	−5.95136e89	−0.834635
$713$	4.31808e89	0.579389
$714$	2.15283e89	0.276386
$715$	2.91841e89	0.358513
$716$	6.10563e89	0.717745
$717$	−1.28536e90	−1.44600
$718$	−3.57174e89	−0.384556
$719$	2.39039e89	0.246325	0.123162	−	0.992387i	$-0.460696\pi$
$719$	2.39039e89	0.246325	0.123162	+	0.992387i	$0.460696\pi$
$720$	−1.50812e90	−1.48752
$721$	−2.76909e89	−0.261442
$722$	4.10468e89	0.370986
$723$	−6.56975e89	−0.568451
$724$	1.90279e90	1.57626
$725$	−6.63501e88	−0.0526253
$726$	8.22719e89	0.624810
$727$	−6.96567e88	−0.0506558	−0.0253279	−	0.999679i	$-0.508063\pi$
$727$	−6.96567e88	−0.0506558	−0.0253279	+	0.999679i	$0.508063\pi$
$728$	−2.83316e89	−0.197303
$729$	5.73751e90	3.82654
$730$	−1.01436e90	−0.647921
$731$	6.75928e89	0.413526
$732$	−4.57249e90	−2.67950
$733$	−1.46414e90	−0.821880	−0.410940	−	0.911662i	$-0.634799\pi$
$733$	−1.46414e90	−0.821880	−0.410940	+	0.911662i	$0.634799\pi$
$734$	3.39998e89	0.182831
$735$	3.18825e90	1.64248
$736$	−8.70027e89	−0.429419
$737$	−2.75348e89	−0.130214
$738$	−1.16730e90	−0.528942
$739$	−3.24476e90	−1.40891	−0.704454	−	0.709749i	$-0.748808\pi$
$739$	−3.24476e90	−1.40891	−0.704454	+	0.709749i	$0.748808\pi$
$740$	1.36483e90	0.567909
$741$	−7.01064e89	−0.279566
$742$	−6.87543e88	−0.0262771
$743$	1.23913e90	0.453909	0.226955	−	0.973905i	$-0.427123\pi$
$743$	1.23913e90	0.453909	0.226955	+	0.973905i	$0.427123\pi$
$744$	4.84084e90	1.69970
$745$	1.54053e90	0.518499
$746$	−7.51548e89	−0.242484
$747$	−1.02988e91	−3.18558
$748$	1.51529e90	0.449362
$749$	−1.09705e90	−0.311925
$750$	−2.85221e90	−0.777591
$751$	−2.90019e90	−0.758172	−0.379086	−	0.925361i	$-0.623762\pi$
$751$	−2.90019e90	−0.758172	−0.379086	+	0.925361i	$0.623762\pi$
$752$	6.35214e89	0.159242
$753$	7.91339e90	1.90248
$754$	−5.66239e89	−0.130558
$755$	2.38952e90	0.528423
$756$	3.74910e90	0.795226
$757$	5.88673e90	1.19772	0.598858	−	0.800855i	$-0.295621\pi$
$757$	5.88673e90	1.19772	0.598858	+	0.800855i	$0.295621\pi$
$758$	1.95541e90	0.381643
$759$	−1.83439e90	−0.343459
$760$	5.10570e89	0.0917122
$761$	6.18701e90	1.06626	0.533131	−	0.846033i	$-0.321015\pi$
$761$	6.18701e90	1.06626	0.533131	+	0.846033i	$0.321015\pi$
$762$	4.08020e90	0.674683
$763$	5.01013e89	0.0794926
$764$	−8.57242e90	−1.30516
$765$	−2.36056e91	−3.44889
$766$	4.85543e90	0.680804
$767$	−5.47030e90	−0.736135
$768$	−2.17831e90	−0.281346
$769$	−7.95075e88	−0.00985663	−0.00492832	−	0.999988i	$-0.501569\pi$
$769$	−7.95075e88	−0.00985663	−0.00492832	+	0.999988i	$0.501569\pi$
$770$	3.08835e89	0.0367510
$771$	1.57815e91	1.80275
$772$	−8.58791e89	−0.0941765
$773$	−2.44555e90	−0.257468	−0.128734	−	0.991679i	$-0.541091\pi$
$773$	−2.44555e90	−0.257468	−0.128734	+	0.991679i	$0.541091\pi$
$774$	−3.10113e90	−0.313459
$775$	−2.00153e90	−0.194249
$776$	1.07441e90	0.100121
$777$	−4.29822e90	−0.384615
$778$	−2.00693e90	−0.172455
$779$	−8.76786e89	−0.0723542
$780$	1.95627e91	1.55041
$781$	−3.82619e90	−0.291245
$782$	−3.28602e90	−0.240247
$783$	1.62398e91	1.14048
$784$	−8.08818e90	−0.545625
$785$	−1.85600e91	−1.20278
$786$	1.02191e91	0.636212
$787$	1.22272e91	0.731345	0.365673	−	0.930744i	$-0.380839\pi$
$787$	1.22272e91	0.731345	0.365673	+	0.930744i	$0.380839\pi$
$788$	−1.46113e91	−0.839676
$789$	2.66049e91	1.46905
$790$	−4.60936e90	−0.244561
$791$	3.56299e90	0.181658
$792$	−1.50676e91	−0.738244
$793$	3.49687e91	1.64655
$794$	−1.23247e91	−0.557740
$795$	1.02892e91	0.447526
$796$	−1.42822e91	−0.597082
$797$	−3.33569e91	−1.34044	−0.670222	−	0.742161i	$-0.733801\pi$
$797$	−3.33569e91	−1.34044	−0.670222	+	0.742161i	$0.733801\pi$
$798$	−7.41889e89	−0.0286581
$799$	9.94258e90	0.369212
$800$	4.03279e90	0.143970
$801$	−9.48213e91	−3.25448
$802$	1.21138e91	0.399749
$803$	2.24848e91	0.713428
$804$	−1.84572e91	−0.563118
$805$	4.00227e90	0.117418
$806$	−1.70813e91	−0.481911
$807$	6.56064e91	1.78004
$808$	1.53587e91	0.400772
$809$	5.41859e91	1.35990	0.679952	−	0.733257i	$-0.262001\pi$
$809$	5.41859e91	1.35990	0.679952	+	0.733257i	$0.262001\pi$
$810$	5.43757e91	1.31258
$811$	−4.10679e91	−0.953556	−0.476778	−	0.879024i	$-0.658195\pi$
$811$	−4.10679e91	−0.953556	−0.476778	+	0.879024i	$0.658195\pi$
$812$	3.58085e90	0.0799781
$813$	−1.17771e92	−2.53038
$814$	5.06256e90	0.104641
$815$	3.31496e91	0.659195
$816$	8.17318e91	1.56369
$817$	−2.32933e90	−0.0428781
$818$	5.45056e90	0.0965410
$819$	−4.51399e91	−0.769340
$820$	2.44660e91	0.401261
$821$	7.47546e91	1.17986	0.589928	−	0.807456i	$-0.299156\pi$
$821$	7.47546e91	1.17986	0.589928	+	0.807456i	$0.299156\pi$
$822$	−6.04169e91	−0.917690
$823$	−1.00127e92	−1.46372	−0.731859	−	0.681456i	$-0.761347\pi$
$823$	−1.00127e92	−1.46372	−0.731859	+	0.681456i	$0.761347\pi$
$824$	4.73836e91	0.666685
$825$	8.50282e90	0.115150
$826$	−5.78886e90	−0.0754608
$827$	7.70914e91	0.967348	0.483674	−	0.875248i	$-0.339302\pi$
$827$	7.70914e91	0.967348	0.483674	+	0.875248i	$0.339302\pi$
$828$	−9.00939e91	−1.08828
$829$	8.89462e90	0.103433	0.0517166	−	0.998662i	$-0.483531\pi$
$829$	8.89462e90	0.103433	0.0517166	+	0.998662i	$0.483531\pi$
$830$	−3.61213e91	−0.404392
$831$	−7.93537e91	−0.855332
$832$	−2.35164e91	−0.244054
$833$	−1.26599e92	−1.26506
$834$	−3.82355e91	−0.367905
$835$	−1.40018e92	−1.29736
$836$	−5.22188e90	−0.0465939
$837$	4.89895e92	4.20970
$838$	5.04071e91	0.417162
$839$	1.70386e91	0.135810	0.0679049	−	0.997692i	$-0.478369\pi$
$839$	1.70386e91	0.135810	0.0679049	+	0.997692i	$0.478369\pi$
$840$	4.48679e91	0.344460
$841$	−1.19719e92	−0.885299
$842$	1.31265e91	0.0935015
$843$	1.91647e92	1.31502
$844$	1.21978e92	0.806297
$845$	−5.29154e90	−0.0336973
$846$	−4.56162e91	−0.279868
$847$	3.97892e91	0.235200
$848$	−2.61025e91	−0.148666
$849$	−4.69828e92	−2.57838
$850$	1.52315e91	0.0805465
$851$	6.56069e91	0.334324
$852$	−2.56477e92	−1.25951
$853$	2.48680e91	0.117692	0.0588460	−	0.998267i	$-0.481258\pi$
$853$	2.48680e91	0.117692	0.0588460	+	0.998267i	$0.481258\pi$
$854$	3.70050e91	0.168786
$855$	8.13476e91	0.357612
$856$	1.87724e92	0.795418
$857$	1.41839e92	0.579296	0.289648	−	0.957133i	$-0.406462\pi$
$857$	1.41839e92	0.579296	0.289648	+	0.957133i	$0.406462\pi$
$858$	7.25639e91	0.285674
$859$	−3.07690e91	−0.116769	−0.0583847	−	0.998294i	$-0.518595\pi$
$859$	−3.07690e91	−0.116769	−0.0583847	+	0.998294i	$0.518595\pi$
$860$	6.49981e91	0.237793
$861$	−7.70503e91	−0.271753
$862$	−1.50754e92	−0.512613
$863$	−2.87438e91	−0.0942334	−0.0471167	−	0.998889i	$-0.515003\pi$
$863$	−2.87438e91	−0.0942334	−0.0471167	+	0.998889i	$0.515003\pi$
$864$	−9.87064e92	−3.12005
$865$	−6.65730e91	−0.202904
$866$	5.76912e91	0.169549
$867$	5.96801e92	1.69133
$868$	1.08021e92	0.295213
$869$	1.02174e92	0.269287
$870$	8.96735e91	0.227933
$871$	1.41153e92	0.346035
$872$	−8.57315e91	−0.202708
$873$	1.71183e92	0.390402
$874$	1.13240e91	0.0249109
$875$	−1.37941e92	−0.292712
$876$	1.50720e93	3.08527
$877$	7.89285e92	1.55864	0.779322	−	0.626624i	$-0.215564\pi$
$877$	7.89285e92	1.55864	0.779322	+	0.626624i	$0.215564\pi$
$878$	−7.76222e91	−0.147880
$879$	−1.62496e93	−2.98671
$880$	1.17249e92	0.207924
$881$	−1.02239e93	−1.74934	−0.874671	−	0.484717i	$-0.838923\pi$
$881$	−1.02239e93	−1.74934	−0.874671	+	0.484717i	$0.838923\pi$
$882$	5.80831e92	0.958935
$883$	−6.60718e92	−1.05258	−0.526289	−	0.850306i	$-0.676417\pi$
$883$	−6.60718e92	−1.05258	−0.526289	+	0.850306i	$0.676417\pi$
$884$	−7.76793e92	−1.19415
$885$	8.66315e92	1.28518
$886$	−2.63933e92	−0.377861
$887$	−2.71527e92	−0.375162	−0.187581	−	0.982249i	$-0.560065\pi$
$887$	−2.71527e92	−0.375162	−0.187581	+	0.982249i	$0.560065\pi$
$888$	7.35494e92	0.980778
$889$	1.97331e92	0.253974
$890$	−3.32568e92	−0.413139
$891$	−1.20532e93	−1.44529
$892$	−1.86095e92	−0.215398
$893$	−3.42633e91	−0.0382832
$894$	3.83041e92	0.413155
$895$	7.39472e92	0.770010
$896$	−2.78952e92	−0.280431
$897$	9.40371e92	0.912720
$898$	−3.26583e92	−0.306048
$899$	4.67910e92	0.423381
$900$	4.17607e92	0.364862
$901$	−4.08565e92	−0.344691
$902$	9.07521e91	0.0739351
$903$	−2.04697e92	−0.161045
$904$	−6.09685e92	−0.463234
$905$	2.30453e93	1.69103
$906$	5.94135e92	0.421063
$907$	−9.32414e92	−0.638233	−0.319116	−	0.947716i	$-0.603386\pi$
$907$	−9.32414e92	−0.638233	−0.319116	+	0.947716i	$0.603386\pi$
$908$	−1.95125e93	−1.29006
$909$	2.44706e93	1.56273
$910$	−1.58320e92	−0.0976635
$911$	6.82273e92	0.406564	0.203282	−	0.979120i	$-0.434839\pi$
$911$	6.82273e92	0.406564	0.203282	+	0.979120i	$0.434839\pi$
$912$	−2.81657e92	−0.162138
$913$	8.00683e92	0.445278
$914$	4.06923e92	0.218629
$915$	−5.53788e93	−2.87461
$916$	2.36987e93	1.18855
$917$	4.94226e92	0.239492
$918$	−3.72806e93	−1.74557
$919$	8.29916e92	0.375487	0.187744	−	0.982218i	$-0.439883\pi$
$919$	8.29916e92	0.375487	0.187744	+	0.982218i	$0.439883\pi$
$920$	−6.84853e92	−0.299420
$921$	−5.09427e93	−2.15230
$922$	1.03777e93	0.423719
$923$	1.96144e93	0.773965
$924$	−4.58888e92	−0.175001
$925$	−3.04104e92	−0.112087
$926$	1.35172e93	0.481549
$927$	7.54949e93	2.59960
$928$	−9.42767e92	−0.313793
$929$	3.38716e93	1.08978	0.544892	−	0.838506i	$-0.316571\pi$
$929$	3.38716e93	1.08978	0.544892	+	0.838506i	$0.316571\pi$
$930$	2.70511e93	0.841342
$931$	4.36274e92	0.131173
$932$	−3.81701e93	−1.10949
$933$	−9.24238e93	−2.59724
$934$	−2.05343e93	−0.557896
$935$	1.83522e93	0.482083
$936$	7.72418e93	1.96184
$937$	−3.03836e93	−0.746179	−0.373089	−	0.927795i	$-0.621702\pi$
$937$	−3.03836e93	−0.746179	−0.373089	+	0.927795i	$0.621702\pi$
$938$	1.49373e92	0.0354718
$939$	5.70400e93	1.30983
$940$	9.56091e92	0.212311
$941$	−2.32725e93	−0.499769	−0.249884	−	0.968276i	$-0.580393\pi$
$941$	−2.32725e93	−0.499769	−0.249884	+	0.968276i	$0.580393\pi$
$942$	−4.61481e93	−0.958408
$943$	1.17608e93	0.236220
$944$	−2.19773e93	−0.426930
$945$	4.54065e93	0.853132
$946$	2.41098e92	0.0438150
$947$	6.25689e93	1.09985	0.549926	−	0.835213i	$-0.314656\pi$
$947$	6.25689e93	1.09985	0.549926	+	0.835213i	$0.314656\pi$
$948$	6.84890e93	1.16455
$949$	−1.15265e94	−1.89589
$950$	−5.24895e91	−0.00835178
$951$	−2.22382e94	−3.42306
$952$	−1.78161e93	−0.265308
$953$	6.65569e93	0.958885	0.479443	−	0.877573i	$-0.340839\pi$
$953$	6.65569e93	0.958885	0.479443	+	0.877573i	$0.340839\pi$
$954$	1.87448e93	0.261280
$955$	−1.03823e94	−1.40020
$956$	4.90796e93	0.640438
$957$	−1.98775e93	−0.250978
$958$	5.02876e93	0.614394
$959$	−2.92194e93	−0.345450
$960$	3.72423e93	0.426081
$961$	5.08303e93	0.562776
$962$	−2.59525e93	−0.278077
$963$	2.99095e94	3.10156
$964$	2.50857e93	0.251768
$965$	−1.04011e93	−0.101034
$966$	9.95132e92	0.0935624
$967$	1.16513e94	1.06033	0.530165	−	0.847895i	$-0.322130\pi$
$967$	1.16513e94	1.06033	0.530165	+	0.847895i	$0.322130\pi$
$968$	−6.80857e93	−0.599766
$969$	−4.40859e93	−0.375925
$970$	6.00394e92	0.0495594
$971$	3.52112e93	0.281368	0.140684	−	0.990055i	$-0.455070\pi$
$971$	3.52112e93	0.281368	0.140684	+	0.990055i	$0.455070\pi$
$972$	−4.35049e94	−3.36551
$973$	−1.84918e93	−0.138492
$974$	−5.31774e93	−0.385585
$975$	−4.35885e93	−0.306003
$976$	1.40489e94	0.954934
$977$	1.56288e94	1.02860	0.514301	−	0.857610i	$-0.328052\pi$
$977$	1.56288e94	1.02860	0.514301	+	0.857610i	$0.328052\pi$
$978$	8.24240e93	0.525267
$979$	7.37189e93	0.454909
$980$	−1.21739e94	−0.727458
$981$	−1.36594e94	−0.790417
$982$	1.22597e94	0.687020
$983$	−2.15640e94	−1.17029	−0.585146	−	0.810928i	$-0.698963\pi$
$983$	−2.15640e94	−1.17029	−0.585146	+	0.810928i	$0.698963\pi$
$984$	1.31846e94	0.692978
$985$	−1.76962e94	−0.900819
$986$	−3.56075e93	−0.175557
$987$	−3.01099e93	−0.143787
$988$	2.67692e93	0.123820
$989$	3.12444e93	0.139987
$990$	−8.41992e93	−0.365426
$991$	1.31180e94	0.551501	0.275750	−	0.961229i	$-0.411074\pi$
$991$	1.31180e94	0.551501	0.275750	+	0.961229i	$0.411074\pi$
$992$	−2.84397e94	−1.15826
$993$	4.29459e94	1.69442
$994$	2.07566e93	0.0793387
$995$	−1.72976e94	−0.640560
$996$	5.36714e94	1.92563
$997$	−3.78877e94	−1.31705	−0.658523	−	0.752560i	$-0.728819\pi$
$997$	−3.78877e94	−1.31705	−0.658523	+	0.752560i	$0.728819\pi$
$998$	1.02098e94	0.343879
$999$	7.44323e94	2.42912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.64.a.a.1.2	✓	5
3.2	odd	2		9.64.a.c.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.64.a.a.1.2	✓	5	1.1	even	1	trivial
9.64.a.c.1.4		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:	\( k \)	\(=\)	\( 64 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-1.14986e9 q^{2} +2.06926e15 q^{3} -7.90120e18 q^{4} -9.56939e21 q^{5} -2.37936e24 q^{6} -1.15073e26 q^{7} +1.96908e28 q^{8} +3.13728e30 q^{9} +O(q^{10})\)	\(q-1.14986e9 q^{2} +2.06926e15 q^{3} -7.90120e18 q^{4} -9.56939e21 q^{5} -2.37936e24 q^{6} -1.15073e26 q^{7} +1.96908e28 q^{8} +3.13728e30 q^{9} +1.10034e31 q^{10} -2.43908e32 q^{11} -1.63496e34 q^{12} +1.25036e35 q^{13} +1.32317e35 q^{14} -1.98016e37 q^{15} +5.02341e37 q^{16} +7.86280e38 q^{17} -3.60742e39 q^{18} -2.70961e39 q^{19} +7.56097e40 q^{20} -2.38116e41 q^{21} +2.80460e41 q^{22} +3.63454e42 q^{23} +4.07454e43 q^{24} -1.68470e43 q^{25} -1.43774e44 q^{26} +4.12346e45 q^{27} +9.09213e44 q^{28} +3.93841e45 q^{29} +2.27690e46 q^{30} +1.18807e47 q^{31} -2.39378e47 q^{32} -5.04710e47 q^{33} -9.04110e47 q^{34} +1.10118e48 q^{35} -2.47883e49 q^{36} +1.80510e49 q^{37} +3.11567e48 q^{38} +2.58732e50 q^{39} -1.88429e50 q^{40} +3.23583e50 q^{41} +2.73799e50 q^{42} +8.59653e50 q^{43} +1.92717e51 q^{44} -3.00219e52 q^{45} -4.17920e51 q^{46} +1.26451e52 q^{47} +1.03947e53 q^{48} -1.61010e53 q^{49} +1.93716e52 q^{50} +1.62702e54 q^{51} -9.87934e53 q^{52} -5.19617e53 q^{53} -4.74139e54 q^{54} +2.33405e54 q^{55} -2.26588e54 q^{56} -5.60690e54 q^{57} -4.52860e54 q^{58} -4.37498e55 q^{59} +1.56456e56 q^{60} +2.79669e56 q^{61} -1.36611e56 q^{62} -3.61016e56 q^{63} -1.88077e56 q^{64} -1.19652e57 q^{65} +5.80344e56 q^{66} +1.12890e57 q^{67} -6.21256e57 q^{68} +7.52080e57 q^{69} -1.26620e57 q^{70} +1.56870e58 q^{71} +6.17756e58 q^{72} -9.21857e58 q^{73} -2.07560e58 q^{74} -3.48607e58 q^{75} +2.14092e58 q^{76} +2.80672e58 q^{77} -2.97505e59 q^{78} -4.18902e59 q^{79} -4.80710e59 q^{80} +4.94170e60 q^{81} -3.72075e59 q^{82} -3.28273e60 q^{83} +1.88140e60 q^{84} -7.52422e60 q^{85} -9.88478e59 q^{86} +8.14959e60 q^{87} -4.80275e60 q^{88} -3.02241e61 q^{89} +3.45209e61 q^{90} -1.43882e61 q^{91} -2.87172e61 q^{92} +2.45843e62 q^{93} -1.45400e61 q^{94} +2.59294e61 q^{95} -4.95335e62 q^{96} +5.45642e61 q^{97} +1.85138e62 q^{98} -7.65208e62 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 507315096 q^{2} + 953245351116252 q^{3} + 67\!\cdots\!40 q^{4}+ \cdots + 63\!\cdots\!85 q^{9}+O(q^{10}) \) 5 * q + 507315096 * q^2 + 953245351116252 * q^3 + 6772922881670488640 * q^4 - 501184199539643271930 * q^5 + 1068627718494014524169760 * q^6 + 376817877722086399439439256 * q^7 + 7373083738744782322804569600 * q^8 + 637396295620644432934325521785 * q^9	\( 5 q + 507315096 q^{2} + 953245351116252 q^{3} + 67\!\cdots\!40 q^{4}+ \cdots - 12\!\cdots\!80 q^{99}+O(q^{100}) \) 5 * q + 507315096 * q^2 + 953245351116252 * q^3 + 6772922881670488640 * q^4 - 501184199539643271930 * q^5 + 1068627718494014524169760 * q^6 + 376817877722086399439439256 * q^7 + 7373083738744782322804569600 * q^8 + 637396295620644432934325521785 * q^9 + 34805720696971516624169126640720 * q^10 - 540229094938924469136867622360140 * q^11 - 2623634227414171572600561756413184 * q^12 + 108181792532202432266404872185866462 * q^13 - 54084971043930392944098441496816320 * q^14 - 348660153327675947104166235548634360 * q^15 - 15159504282791660159626289035944325120 * q^16 + 233526732797217220125532397644743920826 * q^17 - 878288957740682168785729261423496761608 * q^18 - 7865422683256304571013031795593188000500 * q^19 + 119732404991815793713722982154585901682560 * q^20 + 129742883997422764536533691448958694051360 * q^21 + 522423012385730886331292903044579480248672 * q^22 + 15741757721943761462993254761236931413817672 * q^23 + 81420550986598778904562391448937582504396800 * q^24 + 292140347366023827983252525250222472224504275 * q^25 + 1839051975856323981143175281915543784076214160 * q^26 + 5995620820889371589085528605465633389174051800 * q^27 + 20537937802314435233418391499696666641793064448 * q^28 + 50794057939113445336173371211400804999575041550 * q^29 + 119599751674209323591694650465650283116522069440 * q^30 + 159433862626305294394996530486509737703620382560 * q^31 - 288839096991246799804118797555409689201302994944 * q^32 - 1985039125536508051580230500373193506662510782736 * q^33 - 7795229014190619843231021275250308444731969968720 * q^34 - 10557440874563511263423843961508717076049161308080 * q^35 - 37204859885919911089599455494799964973968364182720 * q^36 - 17147796860746064343272909856513075508644081479834 * q^37 + 96961175243860213325076480378784661216846555556000 * q^38 + 492167917497720661901422065953515470410075070510120 * q^39 + 896446641636036625169137129815741762131481186432000 * q^40 + 1559678150469731047687963466434444190641664714862210 * q^41 + 2081496056204279968289878006271140331858037130897152 * q^42 - 2983480654504430801847803264567818556163926831907308 * q^43 - 18694374606435020769086358744659889563339255880625920 * q^44 - 42915794659164783458146544031317844487388645901128610 * q^45 - 51138823220473279961598851250008086980240261547467840 * q^46 - 48803318103437656200328895986865036348129901500078064 * q^47 + 105030731921033071573566542229505770762259930957135872 * q^48 + 339954400631541607259125157882259489058114941961211565 * q^49 + 1145766254187619060443643128490826898486806978223935400 * q^50 + 1573856653389132533580410794526319320841950113639520760 * q^51 + 1100089067926371487906797270480194411314440787489242496 * q^52 - 692620923468041120314769654783046236221069399596219498 * q^53 - 12241254713499812360048511900337793888058128715691896000 * q^54 - 20518321028364082359377216700393318257347660689712574760 * q^55 - 23023175950768775440489799736204099376922285452382515200 * q^56 - 17165930318654624911621905238013222730357511047458838000 * q^57 + 24263146187335234519264617757094026741989307665448630800 * q^58 + 105022627362831482575423381645924825912298204628844229700 * q^59 + 348815801318717337128814346317462318028682012888660421120 * q^60 + 392008741666961324913019363738714690637509013784647052910 * q^61 + 517886811617172418873631635177191658868452247595279666432 * q^62 - 688525987399009316135147212418376806290326301310285121288 * q^63 - 2180009675566773867746832715393348298244228612034924380160 * q^64 - 1790351395436014012859210003100506705478557202772387149660 * q^65 - 5560362505883676488751771192389016447628360456591147025280 * q^66 - 4772918882566263586387384393016421637717756025307890516324 * q^67 - 1217235811705845972574871765837936700542360337637019524992 * q^68 + 17361351448150889077637265817219083285785250426768721895520 * q^69 + 40370459686415885897530019946258677235420585269803429288320 * q^70 + 50262977800159315724835086683846685501725736129988791785560 * q^71 + 61741978698481390141302726420710704640623611541551890419200 * q^72 - 29866935912976824238577353448611378509570684111927150030878 * q^73 - 141849784351445213753933251006028603295768815102096738143920 * q^74 - 201957285133938827818209142762872334198535626872978135872700 * q^75 - 459524449626729728237506845156327517313622138193176308998400 * q^76 - 584903691091230632807084878932757448595860972050144651202208 * q^77 - 22402086294347989122673287092781322891691396539029809599296 * q^78 + 585575205089660590838265168880022777028257388453771607481200 * q^79 + 1073190252220259266057147746504064677993096991374081580523520 * q^80 + 4533130095818971466699734318425466519486071025110491052925005 * q^81 + 3942135409805155170887010182148436012685330945941771799686512 * q^82 + 2788245690403819754860784912585317051147818763920351702275532 * q^83 - 126919894267453303311398867974653650894429551428194565150720 * q^84 - 12285625873772156133384209670234539029240309631211205889028180 * q^85 - 25827853637025878857294346599932142285683441775204060440193440 * q^86 - 16639728321686122963829124023195021859110126733857984457365400 * q^87 - 37714047968515707622032367000426709169856663409503596568012800 * q^88 + 3261564182425241052169353984916675793465907809562936240181650 * q^89 + 3967145115564708643943604045640844654494980994165877917975440 * q^90 + 108036910334048530340065483166305935475510347360713558662966160 * q^91 + 166995545147622332685032938656047356744592976712074780741106176 * q^92 + 379916756753184270638361497392906589593938589120992563130336384 * q^93 - 20439950593005273708597610879292286110217691498870249996014720 * q^94 + 135646904668873700623162464290893387798407178357502623630425000 * q^95 - 903336283885608238754961378979276328179547455316018655408291840 * q^96 - 171116727826062583131545726181696338626852935879476361892307414 * q^97 - 1942373455669362555509787890732368496523562886191617825973826472 * q^98 - 126634984461121539221842595814731567513779549557792846854185980 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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