LMFDB - Embedded newform 1.64.a.a.1.4

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			1.4
Root			$-3.39250e7$ 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)

$f(q)$	$=$	$q+2.54406e9 q^{2} -9.84533e14 q^{3} -2.75111e18 q^{4} -1.69176e22 q^{5} -2.50471e24 q^{6} +1.59356e26 q^{7} -3.04638e28 q^{8} -1.75256e29 q^{9} +O(q^{10})$	\(q+2.54406e9 q^{2} -9.84533e14 q^{3} -2.75111e18 q^{4} -1.69176e22 q^{5} -2.50471e24 q^{6} +1.59356e26 q^{7} -3.04638e28 q^{8} -1.75256e29 q^{9} -4.30395e31 q^{10} +8.86905e32 q^{11} +2.70856e33 q^{12} +7.82830e34 q^{13} +4.05413e35 q^{14} +1.66560e37 q^{15} -5.21275e37 q^{16} -5.03105e38 q^{17} -4.45863e38 q^{18} +8.03315e39 q^{19} +4.65423e40 q^{20} -1.56892e41 q^{21} +2.25634e42 q^{22} -1.14581e43 q^{23} +2.99927e43 q^{24} +1.77786e44 q^{25} +1.99157e44 q^{26} +1.29940e45 q^{27} -4.38407e44 q^{28} +2.15529e46 q^{29} +4.23738e46 q^{30} -6.36423e46 q^{31} +1.48364e47 q^{32} -8.73187e47 q^{33} -1.27993e48 q^{34} -2.69593e48 q^{35} +4.82150e47 q^{36} -1.05964e49 q^{37} +2.04368e49 q^{38} -7.70722e49 q^{39} +5.15376e50 q^{40} +8.54270e50 q^{41} -3.99142e50 q^{42} -3.25759e51 q^{43} -2.43998e51 q^{44} +2.96492e51 q^{45} -2.91501e52 q^{46} +1.11016e52 q^{47} +5.13212e52 q^{48} -1.48857e53 q^{49} +4.52300e53 q^{50} +4.95324e53 q^{51} -2.15365e53 q^{52} -5.90596e53 q^{53} +3.30577e54 q^{54} -1.50043e55 q^{55} -4.85461e54 q^{56} -7.90890e54 q^{57} +5.48320e55 q^{58} +2.16563e55 q^{59} -4.58224e55 q^{60} +1.72006e56 q^{61} -1.61910e56 q^{62} -2.79282e55 q^{63} +8.58238e56 q^{64} -1.32436e57 q^{65} -2.22144e57 q^{66} -2.22054e57 q^{67} +1.38410e57 q^{68} +1.12809e58 q^{69} -6.85863e57 q^{70} +2.30418e58 q^{71} +5.33898e57 q^{72} +1.23249e58 q^{73} -2.69579e58 q^{74} -1.75036e59 q^{75} -2.21001e58 q^{76} +1.41334e59 q^{77} -1.96077e59 q^{78} +8.71843e58 q^{79} +8.81873e59 q^{80} -1.07871e60 q^{81} +2.17332e60 q^{82} -1.10737e60 q^{83} +4.31626e59 q^{84} +8.51136e60 q^{85} -8.28752e60 q^{86} -2.12196e61 q^{87} -2.70185e61 q^{88} +4.52990e61 q^{89} +7.54295e60 q^{90} +1.24749e61 q^{91} +3.15225e61 q^{92} +6.26579e61 q^{93} +2.82432e61 q^{94} -1.35902e62 q^{95} -1.46069e62 q^{96} +2.14118e62 q^{97} -3.78702e62 q^{98} -1.55436e62 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.54406e9	0.837690	0.418845	−	0.908058i	$-0.362435\pi$
$2$	2.54406e9	0.837690	0.418845	+	0.908058i	$0.362435\pi$
$3$	−9.84533e14	−0.920260	−0.460130	−	0.887851i	$-0.652197\pi$
$3$	−9.84533e14	−0.920260	−0.460130	+	0.887851i	$0.652197\pi$
$4$	−2.75111e18	−0.298276
$5$	−1.69176e22	−1.62474	−0.812371	−	0.583141i	$-0.801824\pi$
$5$	−1.69176e22	−1.62474	−0.812371	+	0.583141i	$0.801824\pi$
$6$	−2.50471e24	−0.770893
$7$	1.59356e26	0.381752	0.190876	−	0.981614i	$-0.438867\pi$
$7$	1.59356e26	0.381752	0.190876	+	0.981614i	$0.438867\pi$
$8$	−3.04638e28	−1.08755
$9$	−1.75256e29	−0.153121
$10$	−4.30395e31	−1.36103
$11$	8.86905e32	1.39318	0.696591	−	0.717469i	$-0.254699\pi$
$11$	8.86905e32	1.39318	0.696591	+	0.717469i	$0.254699\pi$
$12$	2.70856e33	0.274492
$13$	7.82830e34	0.637458	0.318729	−	0.947846i	$-0.396744\pi$
$13$	7.82830e34	0.637458	0.318729	+	0.947846i	$0.396744\pi$
$14$	4.05413e35	0.319790
$15$	1.66560e37	1.49519
$16$	−5.21275e37	−0.612755
$17$	−5.03105e38	−0.876028	−0.438014	−	0.898968i	$-0.644318\pi$
$17$	−5.03105e38	−0.876028	−0.438014	+	0.898968i	$0.644318\pi$
$18$	−4.45863e38	−0.128268
$19$	8.03315e39	0.420870	0.210435	−	0.977608i	$-0.432512\pi$
$19$	8.03315e39	0.420870	0.210435	+	0.977608i	$0.432512\pi$
$20$	4.65423e40	0.484622
$21$	−1.56892e41	−0.351311
$22$	2.25634e42	1.16705
$23$	−1.14581e43	−1.46112	−0.730559	−	0.682850i	$-0.760740\pi$
$23$	−1.14581e43	−1.46112	−0.730559	+	0.682850i	$0.760740\pi$
$24$	2.99927e43	1.00083
$25$	1.77786e44	1.63979
$26$	1.99157e44	0.533992
$27$	1.29940e45	1.06117
$28$	−4.38407e44	−0.113868
$29$	2.15529e46	1.85340	0.926701	−	0.375800i	$-0.122632\pi$
$29$	2.15529e46	1.85340	0.926701	+	0.375800i	$0.122632\pi$
$30$	4.23738e46	1.25250
$31$	−6.36423e46	−0.669657	−0.334828	−	0.942279i	$-0.608678\pi$
$31$	−6.36423e46	−0.669657	−0.334828	+	0.942279i	$0.608678\pi$
$32$	1.48364e47	0.574254
$33$	−8.73187e47	−1.28209
$34$	−1.27993e48	−0.733840
$35$	−2.69593e48	−0.620249
$36$	4.82150e47	0.0456723
$37$	−1.05964e49	−0.423451	−0.211725	−	0.977329i	$-0.567908\pi$
$37$	−1.05964e49	−0.423451	−0.211725	+	0.977329i	$0.567908\pi$
$38$	2.04368e49	0.352558
$39$	−7.70722e49	−0.586628
$40$	5.15376e50	1.76699
$41$	8.54270e50	1.34556	0.672781	−	0.739842i	$-0.265100\pi$
$41$	8.54270e50	1.34556	0.672781	+	0.739842i	$0.265100\pi$
$42$	−3.99142e50	−0.294290
$43$	−3.25759e51	−1.14456	−0.572282	−	0.820057i	$-0.693942\pi$
$43$	−3.25759e51	−1.14456	−0.572282	+	0.820057i	$0.693942\pi$
$44$	−2.43998e51	−0.415553
$45$	2.96492e51	0.248782
$46$	−2.91501e52	−1.22396
$47$	1.11016e52	0.236757	0.118379	−	0.992969i	$-0.462230\pi$
$47$	1.11016e52	0.236757	0.118379	+	0.992969i	$0.462230\pi$
$48$	5.13212e52	0.563894
$49$	−1.48857e53	−0.854265
$50$	4.52300e53	1.37363
$51$	4.95324e53	0.806174
$52$	−2.15365e53	−0.190139
$53$	−5.90596e53	−0.286155	−0.143077	−	0.989712i	$-0.545700\pi$
$53$	−5.90596e53	−0.286155	−0.143077	+	0.989712i	$0.545700\pi$
$54$	3.30577e54	0.888932
$55$	−1.50043e55	−2.26356
$56$	−4.85461e54	−0.415175
$57$	−7.90890e54	−0.387310
$58$	5.48320e55	1.55258
$59$	2.16563e55	0.357887	0.178944	−	0.983859i	$-0.442732\pi$
$59$	2.16563e55	0.357887	0.178944	+	0.983859i	$0.442732\pi$
$60$	−4.58224e55	−0.445978
$61$	1.72006e56	0.994612	0.497306	−	0.867575i	$-0.334323\pi$
$61$	1.72006e56	0.994612	0.497306	+	0.867575i	$0.334323\pi$
$62$	−1.61910e56	−0.560965
$63$	−2.79282e55	−0.0584543
$64$	8.58238e56	1.09380
$65$	−1.32436e57	−1.03571
$66$	−2.22144e57	−1.07399
$67$	−2.22054e57	−0.668501	−0.334251	−	0.942484i	$-0.608483\pi$
$67$	−2.22054e57	−0.668501	−0.334251	+	0.942484i	$0.608483\pi$
$68$	1.38410e57	0.261298
$69$	1.12809e58	1.34461
$70$	−6.85863e57	−0.519576
$71$	2.30418e58	1.11655	0.558276	−	0.829656i	$-0.311463\pi$
$71$	2.30418e58	1.11655	0.558276	+	0.829656i	$0.311463\pi$
$72$	5.33898e57	0.166527
$73$	1.23249e58	0.248951	0.124475	−	0.992223i	$-0.460275\pi$
$73$	1.23249e58	0.248951	0.124475	+	0.992223i	$0.460275\pi$
$74$	−2.69579e58	−0.354720
$75$	−1.75036e59	−1.50903
$76$	−2.21001e58	−0.125535
$77$	1.41334e59	0.531850
$78$	−1.96077e59	−0.491412
$79$	8.71843e58	0.146280	0.0731400	−	0.997322i	$-0.476698\pi$
$79$	8.71843e58	0.146280	0.0731400	+	0.997322i	$0.476698\pi$
$80$	8.81873e59	0.995570
$81$	−1.07871e60	−0.823433
$82$	2.17332e60	1.12716
$83$	−1.10737e60	−0.392041	−0.196021	−	0.980600i	$-0.562802\pi$
$83$	−1.10737e60	−0.392041	−0.196021	+	0.980600i	$0.562802\pi$
$84$	4.31626e59	0.104788
$85$	8.51136e60	1.42332
$86$	−8.28752e60	−0.958789
$87$	−2.12196e61	−1.70561
$88$	−2.70185e61	−1.51516
$89$	4.52990e61	1.77952	0.889762	−	0.456425i	$-0.150870\pi$
$89$	4.52990e61	1.77952	0.889762	+	0.456425i	$0.150870\pi$
$90$	7.54295e60	0.208402
$91$	1.24749e61	0.243351
$92$	3.15225e61	0.435816
$93$	6.26579e61	0.616259
$94$	2.82432e61	0.198329
$95$	−1.35902e62	−0.683805
$96$	−1.46069e62	−0.528463
$97$	2.14118e62	0.558913	0.279456	−	0.960158i	$-0.409846\pi$
$97$	2.14118e62	0.558913	0.279456	+	0.960158i	$0.409846\pi$
$98$	−3.78702e62	−0.715609
$99$	−1.55436e62	−0.213325
$100$	−4.89110e62	−0.489110
$101$	5.59834e61	0.0409200	0.0204600	−	0.999791i	$-0.493487\pi$
$101$	5.59834e61	0.0409200	0.0204600	+	0.999791i	$0.493487\pi$
$102$	1.26014e63	0.675323
$103$	1.88637e63	0.743454	0.371727	−	0.928342i	$-0.378766\pi$
$103$	1.88637e63	0.743454	0.371727	+	0.928342i	$0.378766\pi$
$104$	−2.38480e63	−0.693269
$105$	2.65424e63	0.570790
$106$	−1.50252e63	−0.239709
$107$	1.23542e64	1.46631	0.733154	−	0.680063i	$-0.238047\pi$
$107$	1.23542e64	1.46631	0.733154	+	0.680063i	$0.238047\pi$
$108$	−3.57480e63	−0.316522
$109$	−1.18914e64	−0.787587	−0.393793	−	0.919199i	$-0.628837\pi$
$109$	−1.18914e64	−0.787587	−0.393793	+	0.919199i	$0.628837\pi$
$110$	−3.81720e64	−1.89616
$111$	1.04325e64	0.389685
$112$	−8.30685e63	−0.233921
$113$	2.40110e64	0.511022	0.255511	−	0.966806i	$-0.417756\pi$
$113$	2.40110e64	0.511022	0.255511	+	0.966806i	$0.417756\pi$
$114$	−2.01207e64	−0.324445
$115$	1.93844e65	2.37394
$116$	−5.92945e64	−0.552825
$117$	−1.37196e64	−0.0976083
$118$	5.50950e64	0.299798
$119$	−8.01731e64	−0.334426
$120$	−5.07405e65	−1.62609
$121$	3.81336e65	0.940954
$122$	4.37594e65	0.833177
$123$	−8.41057e65	−1.23827
$124$	1.75087e65	0.199743
$125$	−1.17351e66	−1.03949
$126$	−7.10512e64	−0.0489665
$127$	2.34022e66	1.25730	0.628651	−	0.777687i	$-0.283607\pi$
$127$	2.34022e66	1.25730	0.628651	+	0.777687i	$0.283607\pi$
$128$	8.14997e65	0.342013
$129$	3.20720e66	1.05330
$130$	−3.36926e66	−0.867600
$131$	2.18093e64	0.00441159	0.00220579	−	0.999998i	$-0.499298\pi$
$131$	2.18093e64	0.00441159	0.00220579	+	0.999998i	$0.499298\pi$
$132$	2.40224e66	0.382417
$133$	1.28013e66	0.160668
$134$	−5.64919e66	−0.559997
$135$	−2.19828e67	−1.72413
$136$	1.53265e67	0.952726
$137$	−3.44835e67	−1.70182	−0.850909	−	0.525312i	$-0.823948\pi$
$137$	−3.44835e67	−1.70182	−0.850909	+	0.525312i	$0.823948\pi$
$138$	2.86992e67	1.12636
$139$	2.95724e67	0.924528	0.462264	−	0.886742i	$-0.347037\pi$
$139$	2.95724e67	0.924528	0.462264	+	0.886742i	$0.347037\pi$
$140$	7.41682e66	0.185005
$141$	−1.09299e67	−0.217878
$142$	5.86198e67	0.935323
$143$	6.94296e67	0.888095
$144$	9.13567e66	0.0938257
$145$	−3.64625e68	−3.01130
$146$	3.13553e67	0.208544
$147$	1.46555e68	0.786147
$148$	2.91518e67	0.126305
$149$	1.45208e68	0.508889	0.254444	−	0.967087i	$-0.418107\pi$
$149$	1.45208e68	0.508889	0.254444	+	0.967087i	$0.418107\pi$
$150$	−4.45304e68	−1.26410
$151$	1.10687e68	0.254872	0.127436	−	0.991847i	$-0.459325\pi$
$151$	1.10687e68	0.254872	0.127436	+	0.991847i	$0.459325\pi$
$152$	−2.44721e68	−0.457718
$153$	8.81724e67	0.134138
$154$	3.59563e68	0.445525
$155$	1.07668e69	1.08802
$156$	2.12034e68	0.174977
$157$	1.88317e66	0.00127072	0.000635360	−	1.00000i	$-0.499798\pi$
$157$	1.88317e66	0.00127072	0.000635360		1.00000i	$0.499798\pi$
$158$	2.21802e68	0.122537
$159$	5.81462e68	0.263337
$160$	−2.50997e69	−0.933014
$161$	−1.82592e69	−0.557785
$162$	−2.74432e69	−0.689781
$163$	−3.00371e69	−0.621941	−0.310970	−	0.950420i	$-0.600654\pi$
$163$	−3.00371e69	−0.621941	−0.310970	+	0.950420i	$0.600654\pi$
$164$	−2.35019e69	−0.401349
$165$	1.47723e70	2.08307
$166$	−2.81721e69	−0.328409
$167$	2.97039e69	0.286579	0.143290	−	0.989681i	$-0.454232\pi$
$167$	2.97039e69	0.286579	0.143290	+	0.989681i	$0.454232\pi$
$168$	4.77952e69	0.382069
$169$	−8.95281e69	−0.593647
$170$	2.16534e70	1.19230
$171$	−1.40786e69	−0.0644440
$172$	8.96199e69	0.341396
$173$	−2.38452e70	−0.756743	−0.378371	−	0.925654i	$-0.623516\pi$
$173$	−2.38452e70	−0.756743	−0.378371	+	0.925654i	$0.623516\pi$
$174$	−5.39839e70	−1.42877
$175$	2.83314e70	0.625993
$176$	−4.62321e70	−0.853679
$177$	−2.13213e70	−0.329349
$178$	1.15244e71	1.49069
$179$	−7.15882e69	−0.0776195	−0.0388097	−	0.999247i	$-0.512357\pi$
$179$	−7.15882e69	−0.0776195	−0.0388097	+	0.999247i	$0.512357\pi$
$180$	−8.15683e69	−0.0742058
$181$	−4.39429e70	−0.335748	−0.167874	−	0.985808i	$-0.553690\pi$
$181$	−4.39429e70	−0.335748	−0.167874	+	0.985808i	$0.553690\pi$
$182$	3.17369e70	0.203853
$183$	−1.69346e71	−0.915302
$184$	3.49057e71	1.58904
$185$	1.79266e71	0.687999
$186$	1.59406e71	0.516234
$187$	−4.46207e71	−1.22047
$188$	−3.05417e70	−0.0706190
$189$	2.07068e71	0.405104
$190$	−3.45743e71	−0.572816
$191$	−7.65031e71	−1.07431	−0.537153	−	0.843485i	$-0.680500\pi$
$191$	−7.65031e71	−1.07431	−0.537153	+	0.843485i	$0.680500\pi$
$192$	−8.44964e71	−1.00658
$193$	2.52559e70	0.0255451	0.0127726	−	0.999918i	$-0.495934\pi$
$193$	2.52559e70	0.0255451	0.0127726	+	0.999918i	$0.495934\pi$
$194$	5.44731e71	0.468196
$195$	1.30388e72	0.953119
$196$	4.09522e71	0.254807
$197$	3.17310e72	1.68189	0.840945	−	0.541120i	$-0.182000\pi$
$197$	3.17310e72	1.68189	0.840945	+	0.541120i	$0.182000\pi$
$198$	−3.95439e71	−0.178700
$199$	8.06783e70	0.0311089	0.0155545	−	0.999879i	$-0.495049\pi$
$199$	8.06783e70	0.0311089	0.0155545	+	0.999879i	$0.495049\pi$
$200$	−5.41605e72	−1.78336
$201$	2.18619e72	0.615195
$202$	1.42425e71	0.0342783
$203$	3.43460e72	0.707540
$204$	−1.36269e72	−0.240462
$205$	−1.44522e73	−2.18619
$206$	4.79904e72	0.622783
$207$	2.00810e72	0.223728
$208$	−4.08069e72	−0.390606
$209$	7.12464e72	0.586348
$210$	6.75255e72	0.478145
$211$	−1.70718e72	−0.104084	−0.0520418	−	0.998645i	$-0.516573\pi$
$211$	−1.70718e72	−0.104084	−0.0520418	+	0.998645i	$0.516573\pi$
$212$	1.62480e72	0.0853531
$213$	−2.26854e73	−1.02752
$214$	3.14298e73	1.22831
$215$	5.51107e73	1.85962
$216$	−3.95848e73	−1.15408
$217$	−1.01418e73	−0.255643
$218$	−3.02525e73	−0.659753
$219$	−1.21343e73	−0.229100
$220$	4.12786e73	0.675166
$221$	−3.93846e73	−0.558431
$222$	2.65409e73	0.326435
$223$	−1.54395e74	−1.64827	−0.824136	−	0.566391i	$-0.808339\pi$
$223$	−1.54395e74	−1.64827	−0.824136	+	0.566391i	$0.808339\pi$
$224$	2.36427e73	0.219223
$225$	−3.11582e73	−0.251086
$226$	6.10855e73	0.428078
$227$	2.89225e73	0.176369	0.0881843	−	0.996104i	$-0.471894\pi$
$227$	2.89225e73	0.176369	0.0881843	+	0.996104i	$0.471894\pi$
$228$	2.17583e73	0.115525
$229$	3.67482e74	1.69988	0.849940	−	0.526879i	$-0.176638\pi$
$229$	3.67482e74	1.69988	0.849940	+	0.526879i	$0.176638\pi$
$230$	4.93151e74	1.98862
$231$	−1.39148e74	−0.489440
$232$	−6.56585e74	−2.01567
$233$	−1.84654e74	−0.495047	−0.247523	−	0.968882i	$-0.579617\pi$
$233$	−1.84654e74	−0.495047	−0.247523	+	0.968882i	$0.579617\pi$
$234$	−3.49035e73	−0.0817654
$235$	−1.87813e74	−0.384670
$236$	−5.95789e73	−0.106749
$237$	−8.58358e73	−0.134616
$238$	−2.03965e74	−0.280145
$239$	9.41567e74	1.13323	0.566614	−	0.823983i	$-0.308253\pi$
$239$	9.41567e74	1.13323	0.566614	+	0.823983i	$0.308253\pi$
$240$	−8.68233e74	−0.916183
$241$	1.39238e74	0.128890	0.0644451	−	0.997921i	$-0.479472\pi$
$241$	1.39238e74	0.128890	0.0644451	+	0.997921i	$0.479472\pi$
$242$	9.70143e74	0.788228
$243$	−4.25218e74	−0.303399
$244$	−4.73208e74	−0.296669
$245$	2.51831e75	1.38796
$246$	−2.13970e75	−1.03728
$247$	6.28859e74	0.268287
$248$	1.93879e75	0.728287
$249$	1.09024e75	0.360780
$250$	−2.98548e75	−0.870771
$251$	2.56608e75	0.660007	0.330003	−	0.943980i	$-0.392950\pi$
$251$	2.56608e75	0.660007	0.330003	+	0.943980i	$0.392950\pi$
$252$	7.68337e73	0.0174355
$253$	−1.01622e76	−2.03560
$254$	5.95367e75	1.05323
$255$	−8.37971e75	−1.30983
$256$	−5.84244e75	−0.807301
$257$	8.56043e75	1.04617	0.523085	−	0.852281i	$-0.324781\pi$
$257$	8.56043e75	1.04617	0.523085	+	0.852281i	$0.324781\pi$
$258$	8.15933e75	0.882336
$259$	−1.68860e75	−0.161653
$260$	3.64347e75	0.308926
$261$	−3.77729e75	−0.283795
$262$	5.54841e73	0.00369554
$263$	6.11957e75	0.361506	0.180753	−	0.983529i	$-0.442147\pi$
$263$	6.11957e75	0.361506	0.180753	+	0.983529i	$0.442147\pi$
$264$	2.66006e76	1.39434
$265$	9.99150e75	0.464928
$266$	3.25674e75	0.134590
$267$	−4.45984e76	−1.63762
$268$	6.10895e75	0.199398
$269$	−3.88727e76	−1.12836	−0.564180	−	0.825652i	$-0.690808\pi$
$269$	−3.88727e76	−1.12836	−0.564180	+	0.825652i	$0.690808\pi$
$270$	−5.59258e76	−1.44429
$271$	3.99908e76	0.919237	0.459618	−	0.888116i	$-0.347986\pi$
$271$	3.99908e76	0.919237	0.459618	+	0.888116i	$0.347986\pi$
$272$	2.62256e76	0.536791
$273$	−1.22819e76	−0.223946
$274$	−8.77282e76	−1.42560
$275$	1.57680e77	2.28452
$276$	−3.10349e76	−0.401065
$277$	8.95270e75	0.103238	0.0516192	−	0.998667i	$-0.483562\pi$
$277$	8.95270e75	0.103238	0.0516192	+	0.998667i	$0.483562\pi$
$278$	7.52340e76	0.774467
$279$	1.11537e76	0.102539
$280$	8.21285e76	0.674553
$281$	−1.02715e77	−0.754021	−0.377010	−	0.926209i	$-0.623048\pi$
$281$	−1.02715e77	−0.754021	−0.377010	+	0.926209i	$0.623048\pi$
$282$	−2.78063e76	−0.182514
$283$	−1.44978e77	−0.851195	−0.425597	−	0.904913i	$-0.639936\pi$
$283$	−1.44978e77	−0.851195	−0.425597	+	0.904913i	$0.639936\pi$
$284$	−6.33906e76	−0.333040
$285$	1.33800e77	0.629278
$286$	1.76633e77	0.743948
$287$	1.36133e77	0.513671
$288$	−2.60017e76	−0.0879303
$289$	−7.67087e76	−0.232575
$290$	−9.27629e77	−2.52253
$291$	−2.10806e77	−0.514345
$292$	−3.39072e76	−0.0742561
$293$	7.30204e77	1.43587	0.717934	−	0.696112i	$-0.245088\pi$
$293$	7.30204e77	1.43587	0.717934	+	0.696112i	$0.245088\pi$
$294$	3.72844e77	0.658547
$295$	−3.66374e77	−0.581474
$296$	3.22806e77	0.460525
$297$	1.15245e78	1.47840
$298$	3.69418e77	0.426291
$299$	−8.96973e77	−0.931401
$300$	4.81545e77	0.450108
$301$	−5.19118e77	−0.436940
$302$	2.81594e77	0.213504
$303$	−5.51175e76	−0.0376571
$304$	−4.18748e77	−0.257890
$305$	−2.90994e78	−1.61599
$306$	2.24316e77	0.112366
$307$	1.16301e77	0.0525685	0.0262842	−	0.999655i	$-0.491633\pi$
$307$	1.16301e77	0.0525685	0.0262842	+	0.999655i	$0.491633\pi$
$308$	−3.88826e77	−0.158638
$309$	−1.85719e78	−0.684171
$310$	2.73913e78	0.911423
$311$	−1.09750e78	−0.329953	−0.164977	−	0.986297i	$-0.552755\pi$
$311$	−1.09750e78	−0.329953	−0.164977	+	0.986297i	$0.552755\pi$
$312$	2.34792e78	0.637988
$313$	4.21242e78	1.03487	0.517434	−	0.855723i	$-0.326887\pi$
$313$	4.21242e78	1.03487	0.517434	+	0.855723i	$0.326887\pi$
$314$	4.79090e75	0.00106447
$315$	4.72480e77	0.0949731
$316$	−2.39854e77	−0.0436318
$317$	−3.47405e78	−0.572096	−0.286048	−	0.958215i	$-0.592342\pi$
$317$	−3.47405e78	−0.572096	−0.286048	+	0.958215i	$0.592342\pi$
$318$	1.47928e78	0.220595
$319$	1.91154e79	2.58212
$320$	−1.45194e79	−1.77715
$321$	−1.21631e79	−1.34938
$322$	−4.64526e78	−0.467250
$323$	−4.04152e78	−0.368694
$324$	2.96766e78	0.245610
$325$	1.39176e79	1.04530
$326$	−7.64164e78	−0.520993
$327$	1.17075e79	0.724785
$328$	−2.60244e79	−1.46337
$329$	1.76911e78	0.0903825
$330$	3.75816e79	1.74496
$331$	−4.43371e79	−1.87148	−0.935741	−	0.352687i	$-0.885268\pi$
$331$	−4.43371e79	−1.87148	−0.935741	+	0.352687i	$0.885268\pi$
$332$	3.04649e78	0.116937
$333$	1.85708e78	0.0648392
$334$	7.55686e78	0.240064
$335$	3.75663e79	1.08614
$336$	8.17836e78	0.215268
$337$	7.26234e79	1.74074	0.870372	−	0.492396i	$-0.163879\pi$
$337$	7.26234e79	1.74074	0.870372	+	0.492396i	$0.163879\pi$
$338$	−2.27765e79	−0.497292
$339$	−2.36396e79	−0.470273
$340$	−2.34157e79	−0.424542
$341$	−5.64447e79	−0.932954
$342$	−3.58169e78	−0.0539840
$343$	−5.14894e79	−0.707870
$344$	9.92387e79	1.24477
$345$	−1.90845e80	−2.18464
$346$	−6.06637e79	−0.633916
$347$	4.96199e79	0.473454	0.236727	−	0.971576i	$-0.423925\pi$
$347$	4.96199e79	0.473454	0.236727	+	0.971576i	$0.423925\pi$
$348$	5.83774e79	0.508743
$349$	4.97595e79	0.396164	0.198082	−	0.980185i	$-0.436529\pi$
$349$	4.97595e79	0.396164	0.198082	+	0.980185i	$0.436529\pi$
$350$	7.20768e79	0.524388
$351$	1.01721e80	0.676453
$352$	1.31585e80	0.800040
$353$	1.92495e80	1.07033	0.535163	−	0.844749i	$-0.320250\pi$
$353$	1.92495e80	1.07033	0.535163	+	0.844749i	$0.320250\pi$
$354$	−5.42429e79	−0.275892
$355$	−3.89813e80	−1.81411
$356$	−1.24623e80	−0.530789
$357$	7.89331e79	0.307759
$358$	−1.82125e79	−0.0650210
$359$	5.20149e80	1.70080	0.850398	−	0.526140i	$-0.176361\pi$
$359$	5.20149e80	1.70080	0.850398	+	0.526140i	$0.176361\pi$
$360$	−9.03230e79	−0.270564
$361$	−2.99783e80	−0.822869
$362$	−1.11794e80	−0.281253
$363$	−3.75438e80	−0.865923
$364$	−3.43198e79	−0.0725858
$365$	−2.08508e80	−0.404481
$366$	−4.30826e80	−0.766739
$367$	6.58558e80	1.07551	0.537753	−	0.843103i	$-0.319273\pi$
$367$	6.58558e80	1.07551	0.537753	+	0.843103i	$0.319273\pi$
$368$	5.97281e80	0.895307
$369$	−1.49716e80	−0.206034
$370$	4.56063e80	0.576329
$371$	−9.41153e79	−0.109240
$372$	−1.72379e80	−0.183815
$373$	3.59988e80	0.352744	0.176372	−	0.984324i	$-0.443564\pi$
$373$	3.59988e80	0.352744	0.176372	+	0.984324i	$0.443564\pi$
$374$	−1.13518e81	−1.02237
$375$	1.15536e81	0.956603
$376$	−3.38198e80	−0.257486
$377$	1.68723e81	1.18147
$378$	5.26795e80	0.339352
$379$	−8.36060e80	−0.495567	−0.247784	−	0.968815i	$-0.579702\pi$
$379$	−8.36060e80	−0.495567	−0.247784	+	0.968815i	$0.579702\pi$
$380$	3.73881e80	0.203963
$381$	−2.30403e81	−1.15705
$382$	−1.94629e81	−0.899935
$383$	1.93079e81	0.822193	0.411097	−	0.911592i	$-0.365146\pi$
$383$	1.93079e81	0.822193	0.411097	+	0.911592i	$0.365146\pi$
$384$	−8.02392e80	−0.314741
$385$	−2.39104e81	−0.864119
$386$	6.42527e79	0.0213989
$387$	5.70913e80	0.175257
$388$	−5.89063e80	−0.166710
$389$	−5.18176e81	−1.35227	−0.676137	−	0.736776i	$-0.736347\pi$
$389$	−5.18176e81	−1.35227	−0.676137	+	0.736776i	$0.736347\pi$
$390$	3.31715e81	0.798418
$391$	5.76462e81	1.27998
$392$	4.53476e81	0.929058
$393$	−2.14719e79	−0.00405981
$394$	8.07257e81	1.40890
$395$	−1.47495e81	−0.237667
$396$	4.27621e80	0.0636298
$397$	−4.30808e81	−0.592083	−0.296041	−	0.955175i	$-0.595667\pi$
$397$	−4.30808e81	−0.592083	−0.296041	+	0.955175i	$0.595667\pi$
$398$	2.05251e80	0.0260596
$399$	−1.26033e81	−0.147856
$400$	−9.26754e81	−1.00479
$401$	−1.60082e82	−1.60434	−0.802168	−	0.597098i	$-0.796320\pi$
$401$	−1.60082e82	−1.60434	−0.802168	+	0.597098i	$0.796320\pi$
$402$	5.56182e81	0.515343
$403$	−4.98211e81	−0.426878
$404$	−1.54017e80	−0.0122055
$405$	1.82493e82	1.33787
$406$	8.73784e81	0.592699
$407$	−9.39798e81	−0.589944
$408$	−1.50895e82	−0.876756
$409$	2.24771e82	1.20908	0.604541	−	0.796574i	$-0.293357\pi$
$409$	2.24771e82	1.20908	0.604541	+	0.796574i	$0.293357\pi$
$410$	−3.67674e82	−1.83135
$411$	3.39501e82	1.56612
$412$	−5.18961e81	−0.221754
$413$	3.45107e81	0.136624
$414$	5.10874e81	0.187414
$415$	1.87340e82	0.636966
$416$	1.16144e82	0.366063
$417$	−2.91150e82	−0.850806
$418$	1.81255e82	0.491177
$419$	1.12509e82	0.282779	0.141389	−	0.989954i	$-0.454843\pi$
$419$	1.12509e82	0.282779	0.141389	+	0.989954i	$0.454843\pi$
$420$	−7.30210e81	−0.170253
$421$	−8.89409e81	−0.192405	−0.0962023	−	0.995362i	$-0.530670\pi$
$421$	−8.89409e81	−0.192405	−0.0962023	+	0.995362i	$0.530670\pi$
$422$	−4.34318e81	−0.0871897
$423$	−1.94563e81	−0.0362525
$424$	1.79918e82	0.311208
$425$	−8.94452e82	−1.43650
$426$	−5.77132e82	−0.860741
$427$	2.74103e82	0.379695
$428$	−3.39877e82	−0.437365
$429$	−6.83557e82	−0.817279
$430$	1.40205e83	1.55779
$431$	1.55724e83	1.60813	0.804063	−	0.594544i	$-0.202667\pi$
$431$	1.55724e83	1.60813	0.804063	+	0.594544i	$0.202667\pi$
$432$	−6.77346e82	−0.650238
$433$	−1.61378e83	−1.44037	−0.720185	−	0.693782i	$-0.755943\pi$
$433$	−1.61378e83	−1.44037	−0.720185	+	0.693782i	$0.755943\pi$
$434$	−2.58014e82	−0.214149
$435$	3.58985e83	2.77118
$436$	3.27146e82	0.234918
$437$	−9.20445e82	−0.614940
$438$	−3.08704e82	−0.191914
$439$	−2.41284e83	−1.39603	−0.698016	−	0.716082i	$-0.745934\pi$
$439$	−2.41284e83	−1.39603	−0.698016	+	0.716082i	$0.745934\pi$
$440$	4.57090e83	2.46174
$441$	2.60881e82	0.130806
$442$	−1.00197e83	−0.467792
$443$	1.04534e83	0.454506	0.227253	−	0.973836i	$-0.427025\pi$
$443$	1.04534e83	0.454506	0.227253	+	0.973836i	$0.427025\pi$
$444$	−2.87009e82	−0.116234
$445$	−7.66353e83	−2.89127
$446$	−3.92790e83	−1.38074
$447$	−1.42962e83	−0.468310
$448$	1.36766e83	0.417561
$449$	4.96606e83	1.41336	0.706678	−	0.707535i	$-0.250193\pi$
$449$	4.96606e83	1.41336	0.706678	+	0.707535i	$0.250193\pi$
$450$	−7.92684e82	−0.210332
$451$	7.57657e83	1.87461
$452$	−6.60569e82	−0.152426
$453$	−1.08975e83	−0.234549
$454$	7.35807e82	0.147742
$455$	−2.11046e83	−0.395383
$456$	2.40936e83	0.421219
$457$	−1.18034e83	−0.192596	−0.0962979	−	0.995353i	$-0.530700\pi$
$457$	−1.18034e83	−0.192596	−0.0962979	+	0.995353i	$0.530700\pi$
$458$	9.34897e83	1.42397
$459$	−6.53737e83	−0.929616
$460$	−5.33286e83	−0.708089
$461$	7.43360e83	0.921764	0.460882	−	0.887461i	$-0.347533\pi$
$461$	7.43360e83	0.921764	0.460882	+	0.887461i	$0.347533\pi$
$462$	−3.54001e83	−0.409999
$463$	8.96271e83	0.969701	0.484851	−	0.874597i	$-0.338874\pi$
$463$	8.96271e83	0.969701	0.484851	+	0.874597i	$0.338874\pi$
$464$	−1.12350e84	−1.13568
$465$	−1.06002e84	−1.00126
$466$	−4.69771e83	−0.414696
$467$	2.08627e84	1.72143	0.860714	−	0.509090i	$-0.170018\pi$
$467$	2.08627e84	1.72143	0.860714	+	0.509090i	$0.170018\pi$
$468$	3.77441e82	0.0291142
$469$	−3.53857e83	−0.255202
$470$	−4.77808e83	−0.322234
$471$	−1.85404e81	−0.00116939
$472$	−6.59734e83	−0.389221
$473$	−2.88917e84	−1.59459
$474$	−2.18372e83	−0.112766
$475$	1.42818e84	0.690137
$476$	2.20565e83	0.0997511
$477$	1.03506e83	0.0438163
$478$	2.39541e84	0.949293
$479$	2.82456e84	1.04805	0.524026	−	0.851702i	$-0.324430\pi$
$479$	2.82456e84	1.04805	0.524026	+	0.851702i	$0.324430\pi$
$480$	2.47114e84	0.858616
$481$	−8.29516e83	−0.269932
$482$	3.54229e83	0.107970
$483$	1.79768e84	0.513307
$484$	−1.04910e84	−0.280664
$485$	−3.62238e84	−0.908090
$486$	−1.08178e84	−0.254154
$487$	−1.40116e84	−0.308550	−0.154275	−	0.988028i	$-0.549304\pi$
$487$	−1.40116e84	−0.308550	−0.154275	+	0.988028i	$0.549304\pi$
$488$	−5.23997e84	−1.08169
$489$	2.95726e84	0.572347
$490$	6.40674e84	1.16268
$491$	−9.53280e84	−1.62238	−0.811192	−	0.584780i	$-0.801181\pi$
$491$	−9.53280e84	−1.62238	−0.811192	+	0.584780i	$0.801181\pi$
$492$	2.31384e84	0.369346
$493$	−1.08434e85	−1.62363
$494$	1.59986e84	0.224741
$495$	2.62961e84	0.346599
$496$	3.31751e84	0.410336
$497$	3.67186e84	0.426246
$498$	2.77364e84	0.302222
$499$	9.33185e83	0.0954554	0.0477277	−	0.998860i	$-0.484802\pi$
$499$	9.33185e83	0.0954554	0.0477277	+	0.998860i	$0.484802\pi$
$500$	3.22845e84	0.310056
$501$	−2.92445e84	−0.263727
$502$	6.52828e84	0.552881
$503$	1.86028e85	1.47975	0.739873	−	0.672747i	$-0.234886\pi$
$503$	1.86028e85	1.47975	0.739873	+	0.672747i	$0.234886\pi$
$504$	8.50801e83	0.0635721
$505$	−9.47107e83	−0.0664845
$506$	−2.58534e85	−1.70520
$507$	8.81434e84	0.546310
$508$	−6.43821e84	−0.375023
$509$	1.08331e85	0.593119	0.296559	−	0.955014i	$-0.404161\pi$
$509$	1.08331e85	0.593119	0.296559	+	0.955014i	$0.404161\pi$
$510$	−2.13185e85	−1.09723
$511$	1.96405e84	0.0950375
$512$	−2.23806e85	−1.01828
$513$	1.04383e85	0.446615
$514$	2.17783e85	0.876366
$515$	−3.19129e85	−1.20792
$516$	−8.82338e84	−0.314173
$517$	9.84607e84	0.329846
$518$	−4.29591e84	−0.135415
$519$	2.34764e85	0.696400
$520$	4.03452e85	1.12638
$521$	−1.60719e84	−0.0422356	−0.0211178	−	0.999777i	$-0.506723\pi$
$521$	−1.60719e84	−0.0422356	−0.0211178	+	0.999777i	$0.506723\pi$
$522$	−9.60966e84	−0.237732
$523$	−4.89922e85	−1.14110	−0.570550	−	0.821263i	$-0.693270\pi$
$523$	−4.89922e85	−1.14110	−0.570550	+	0.821263i	$0.693270\pi$
$524$	−5.99997e82	−0.00131587
$525$	−2.78932e85	−0.576076
$526$	1.55686e85	0.302829
$527$	3.20188e85	0.586638
$528$	4.55170e85	0.785607
$529$	6.97907e85	1.13486
$530$	2.54190e85	0.389465
$531$	−3.79541e84	−0.0548000
$532$	−3.52179e84	−0.0479234
$533$	6.68748e85	0.857740
$534$	−1.13461e86	−1.37182
$535$	−2.09004e86	−2.38237
$536$	6.76462e85	0.727030
$537$	7.04809e84	0.0714301
$538$	−9.88946e85	−0.945216
$539$	−1.32022e86	−1.19015
$540$	6.04772e85	0.514267
$541$	1.88800e85	0.151457	0.0757284	−	0.997128i	$-0.475872\pi$
$541$	1.88800e85	0.151457	0.0757284	+	0.997128i	$0.475872\pi$
$542$	1.01739e86	0.770035
$543$	4.32632e85	0.308976
$544$	−7.46427e85	−0.503062
$545$	2.01174e86	1.27963
$546$	−3.12461e85	−0.187597
$547$	−5.20458e85	−0.294975	−0.147487	−	0.989064i	$-0.547119\pi$
$547$	−5.20458e85	−0.294975	−0.147487	+	0.989064i	$0.547119\pi$
$548$	9.48679e85	0.507612
$549$	−3.01452e85	−0.152296
$550$	4.01147e86	1.91372
$551$	1.73138e86	0.780040
$552$	−3.43658e86	−1.46233
$553$	1.38934e85	0.0558427
$554$	2.27762e85	0.0864817
$555$	−1.76493e86	−0.633138
$556$	−8.13569e85	−0.275764
$557$	−3.49609e86	−1.11981	−0.559905	−	0.828557i	$-0.689162\pi$
$557$	−3.49609e86	−1.11981	−0.559905	+	0.828557i	$0.689162\pi$
$558$	2.83758e85	0.0858955
$559$	−2.55014e86	−0.729612
$560$	1.40532e86	0.380061
$561$	4.39305e86	1.12315
$562$	−2.61313e86	−0.631635
$563$	3.12313e86	0.713799	0.356899	−	0.934143i	$-0.383834\pi$
$563$	3.12313e86	0.713799	0.356899	+	0.934143i	$0.383834\pi$
$564$	3.00694e85	0.0649879
$565$	−4.06209e86	−0.830279
$566$	−3.68833e86	−0.713037
$567$	−1.71900e86	−0.314347
$568$	−7.01942e86	−1.21431
$569$	9.57453e86	1.56704	0.783522	−	0.621365i	$-0.213421\pi$
$569$	9.57453e86	1.56704	0.783522	+	0.621365i	$0.213421\pi$
$570$	3.40396e86	0.527140
$571$	1.18863e87	1.74184	0.870922	−	0.491421i	$-0.163522\pi$
$571$	1.18863e87	1.74184	0.870922	+	0.491421i	$0.163522\pi$
$572$	−1.91009e86	−0.264898
$573$	7.53199e86	0.988642
$574$	3.46332e86	0.430297
$575$	−2.03709e87	−2.39592
$576$	−1.50412e86	−0.167484
$577$	6.90737e86	0.728240	0.364120	−	0.931352i	$-0.381370\pi$
$577$	6.90737e86	0.728240	0.364120	+	0.931352i	$0.381370\pi$
$578$	−1.95152e86	−0.194825
$579$	−2.48653e85	−0.0235082
$580$	1.00312e87	0.898199
$581$	−1.76466e86	−0.149663
$582$	−5.36305e86	−0.430862
$583$	−5.23803e86	−0.398665
$584$	−3.75464e86	−0.270747
$585$	2.32103e86	0.158588
$586$	1.85769e87	1.20281
$587$	−2.29584e87	−1.40878	−0.704388	−	0.709815i	$-0.748779\pi$
$587$	−2.29584e87	−1.40878	−0.704388	+	0.709815i	$0.748779\pi$
$588$	−4.03188e86	−0.234489
$589$	−5.11248e86	−0.281838
$590$	−9.32078e86	−0.487095
$591$	−3.12402e87	−1.54778
$592$	5.52362e86	0.259472
$593$	1.89673e87	0.844856	0.422428	−	0.906396i	$-0.361178\pi$
$593$	1.89673e87	0.844856	0.422428	+	0.906396i	$0.361178\pi$
$594$	2.93190e87	1.23844
$595$	1.35634e87	0.543355
$596$	−3.99483e86	−0.151789
$597$	−7.94305e85	−0.0286283
$598$	−2.28196e87	−0.780225
$599$	3.88204e87	1.25926	0.629630	−	0.776895i	$-0.283206\pi$
$599$	3.88204e87	1.25926	0.629630	+	0.776895i	$0.283206\pi$
$600$	5.33228e87	1.64115
$601$	1.33959e87	0.391225	0.195613	−	0.980681i	$-0.437330\pi$
$601$	1.33959e87	0.391225	0.195613	+	0.980681i	$0.437330\pi$
$602$	−1.32067e87	−0.366020
$603$	3.89164e86	0.102362
$604$	−3.04512e86	−0.0760222
$605$	−6.45130e87	−1.52881
$606$	−1.40222e86	−0.0315450
$607$	−3.65491e87	−0.780608	−0.390304	−	0.920686i	$-0.627630\pi$
$607$	−3.65491e87	−0.780608	−0.390304	+	0.920686i	$0.627630\pi$
$608$	1.19183e87	0.241686
$609$	−3.38148e87	−0.651121
$610$	−7.40306e87	−1.35370
$611$	8.69067e86	0.150923
$612$	−2.42572e86	−0.0400102
$613$	9.00256e86	0.141046	0.0705231	−	0.997510i	$-0.477533\pi$
$613$	9.00256e86	0.141046	0.0705231	+	0.997510i	$0.477533\pi$
$614$	2.95878e86	0.0440361
$615$	1.42287e88	2.01187
$616$	−4.30558e87	−0.578415
$617$	1.99271e87	0.254368	0.127184	−	0.991879i	$-0.459406\pi$
$617$	1.99271e87	0.254368	0.127184	+	0.991879i	$0.459406\pi$
$618$	−4.72481e87	−0.573123
$619$	1.64027e88	1.89087	0.945433	−	0.325818i	$-0.105640\pi$
$619$	1.64027e88	1.89087	0.945433	+	0.325818i	$0.105640\pi$
$620$	−2.96206e87	−0.324530
$621$	−1.48887e88	−1.55050
$622$	−2.79211e87	−0.276399
$623$	7.21869e87	0.679337
$624$	4.01758e87	0.359459
$625$	5.77379e86	0.0491180
$626$	1.07167e88	0.866898
$627$	−7.01445e87	−0.539592
$628$	−5.18081e84	−0.000379026 0
$629$	5.33109e87	0.370955
$630$	1.20202e87	0.0795580
$631$	2.29325e87	0.144387	0.0721934	−	0.997391i	$-0.477000\pi$
$631$	2.29325e87	0.144387	0.0721934	+	0.997391i	$0.477000\pi$
$632$	−2.65597e87	−0.159087
$633$	1.68078e87	0.0957840
$634$	−8.83819e87	−0.479239
$635$	−3.95910e88	−2.04279
$636$	−1.59967e87	−0.0785471
$637$	−1.16530e88	−0.544559
$638$	4.86308e88	2.16302
$639$	−4.03822e87	−0.170967
$640$	−1.37878e88	−0.555682
$641$	1.08867e88	0.417706	0.208853	−	0.977947i	$-0.433027\pi$
$641$	1.08867e88	0.417706	0.208853	+	0.977947i	$0.433027\pi$
$642$	−3.09437e88	−1.13037
$643$	2.35352e88	0.818600	0.409300	−	0.912400i	$-0.365773\pi$
$643$	2.35352e88	0.818600	0.409300	+	0.912400i	$0.365773\pi$
$644$	5.02331e87	0.166374
$645$	−5.42583e88	−1.71134
$646$	−1.02819e88	−0.308851
$647$	5.67683e88	1.62413	0.812065	−	0.583567i	$-0.198343\pi$
$647$	5.67683e88	1.62413	0.812065	+	0.583567i	$0.198343\pi$
$648$	3.28618e88	0.895527
$649$	1.92071e88	0.498602
$650$	3.54074e88	0.875634
$651$	9.98494e87	0.235258
$652$	8.26355e87	0.185510
$653$	−6.10331e88	−1.30557	−0.652785	−	0.757543i	$-0.726400\pi$
$653$	−6.10331e88	−1.30557	−0.652785	+	0.757543i	$0.726400\pi$
$654$	2.97846e88	0.607145
$655$	−3.68961e86	−0.00716770
$656$	−4.45309e88	−0.824500
$657$	−2.16002e87	−0.0381196
$658$	4.50073e87	0.0757125
$659$	4.53598e88	0.727413	0.363706	−	0.931514i	$-0.381511\pi$
$659$	4.53598e88	0.727413	0.363706	+	0.931514i	$0.381511\pi$
$660$	−4.06402e88	−0.621329
$661$	−2.88478e88	−0.420501	−0.210251	−	0.977648i	$-0.567428\pi$
$661$	−2.88478e88	−0.420501	−0.210251	+	0.977648i	$0.567428\pi$
$662$	−1.12797e89	−1.56772
$663$	3.87754e88	0.513902
$664$	3.37347e88	0.426366
$665$	−2.16568e88	−0.261044
$666$	4.72454e87	0.0543151
$667$	−2.46955e89	−2.70804
$668$	−8.17187e87	−0.0854797
$669$	1.52007e89	1.51684
$670$	9.55710e88	0.909850
$671$	1.52553e89	1.38568
$672$	−2.32770e88	−0.201742
$673$	−4.58578e88	−0.379261	−0.189631	−	0.981856i	$-0.560729\pi$
$673$	−4.58578e88	−0.379261	−0.189631	+	0.981856i	$0.560729\pi$
$674$	1.84759e89	1.45820
$675$	2.31016e89	1.74010
$676$	2.46302e88	0.177071
$677$	−2.36254e89	−1.62120	−0.810600	−	0.585600i	$-0.800859\pi$
$677$	−2.36254e89	−1.62120	−0.810600	+	0.585600i	$0.800859\pi$
$678$	−6.01407e88	−0.393943
$679$	3.41211e88	0.213366
$680$	−2.59289e89	−1.54794
$681$	−2.84751e88	−0.162305
$682$	−1.43599e89	−0.781526
$683$	2.85240e88	0.148238	0.0741188	−	0.997249i	$-0.476386\pi$
$683$	2.85240e88	0.148238	0.0741188	+	0.997249i	$0.476386\pi$
$684$	3.87318e87	0.0192221
$685$	5.83379e89	2.76502
$686$	−1.30992e89	−0.592975
$687$	−3.61798e89	−1.56433
$688$	1.69810e89	0.701338
$689$	−4.62337e88	−0.182412
$690$	−4.85523e89	−1.83005
$691$	2.68324e89	0.966276	0.483138	−	0.875544i	$-0.339497\pi$
$691$	2.68324e89	0.966276	0.483138	+	0.875544i	$0.339497\pi$
$692$	6.56007e88	0.225718
$693$	−2.47697e88	−0.0814374
$694$	1.26236e89	0.396608
$695$	−5.00295e89	−1.50212
$696$	6.46430e89	1.85494
$697$	−4.29788e89	−1.17875
$698$	1.26591e89	0.331862
$699$	1.81798e89	0.455572
$700$	−7.79428e88	−0.186719
$701$	−3.19036e89	−0.730672	−0.365336	−	0.930876i	$-0.619046\pi$
$701$	−3.19036e89	−0.730672	−0.365336	+	0.930876i	$0.619046\pi$
$702$	2.58785e89	0.566657
$703$	−8.51223e88	−0.178218
$704$	7.61176e89	1.52386
$705$	1.84908e89	0.353996
$706$	4.89720e89	0.896601
$707$	8.92132e87	0.0156213
$708$	5.86574e88	0.0982370
$709$	2.81601e89	0.451106	0.225553	−	0.974231i	$-0.427581\pi$
$709$	2.81601e89	0.451106	0.225553	+	0.974231i	$0.427581\pi$
$710$	−9.91709e89	−1.51966
$711$	−1.52796e88	−0.0223985
$712$	−1.37998e90	−1.93532
$713$	7.29218e89	0.978447
$714$	2.00811e89	0.257806
$715$	−1.17458e90	−1.44293
$716$	1.96947e88	0.0231520
$717$	−9.27003e89	−1.04286
$718$	1.32329e90	1.42474
$719$	−3.41292e89	−0.351695	−0.175847	−	0.984417i	$-0.556267\pi$
$719$	−3.41292e89	−0.351695	−0.175847	+	0.984417i	$0.556267\pi$
$720$	−1.54554e89	−0.152443
$721$	3.00605e89	0.283815
$722$	−7.62668e89	−0.689309
$723$	−1.37084e89	−0.118612
$724$	1.20892e89	0.100146
$725$	3.83181e90	3.03919
$726$	−9.55138e89	−0.725375
$727$	−1.71525e90	−1.24737	−0.623683	−	0.781678i	$-0.714364\pi$
$727$	−1.71525e90	−1.24737	−0.623683	+	0.781678i	$0.714364\pi$
$728$	−3.80033e89	−0.264657
$729$	1.65330e90	1.10264
$730$	−5.30458e89	−0.338830
$731$	1.63891e90	1.00267
$732$	4.65889e89	0.273013
$733$	2.18440e90	1.22618	0.613092	−	0.790011i	$-0.289925\pi$
$733$	2.18440e90	1.22618	0.613092	+	0.790011i	$0.289925\pi$
$734$	1.67541e90	0.900940
$735$	−2.47936e90	−1.27729
$736$	−1.69997e90	−0.839052
$737$	−1.96941e90	−0.931343
$738$	−3.80888e89	−0.172592
$739$	−1.54735e90	−0.671875	−0.335938	−	0.941884i	$-0.609053\pi$
$739$	−1.54735e90	−0.671875	−0.335938	+	0.941884i	$0.609053\pi$
$740$	−4.93180e89	−0.205214
$741$	−6.19132e89	−0.246894
$742$	−2.39435e89	−0.0915093
$743$	2.46406e90	0.902617	0.451309	−	0.892368i	$-0.350957\pi$
$743$	2.46406e90	0.902617	0.451309	+	0.892368i	$0.350957\pi$
$744$	−1.90880e90	−0.670214
$745$	−2.45658e90	−0.826813
$746$	9.15831e89	0.295490
$747$	1.94073e89	0.0600298
$748$	1.22756e90	0.364036
$749$	1.96872e90	0.559766
$750$	2.93931e90	0.801336
$751$	−1.27632e90	−0.333657	−0.166829	−	0.985986i	$-0.553353\pi$
$751$	−1.27632e90	−0.333657	−0.166829	+	0.985986i	$0.553353\pi$
$752$	−5.78698e89	−0.145074
$753$	−2.52639e90	−0.607378
$754$	4.29242e90	0.989702
$755$	−1.87256e90	−0.414101
$756$	−5.69668e89	−0.120833
$757$	1.74981e90	0.356016	0.178008	−	0.984029i	$-0.443035\pi$
$757$	1.74981e90	0.356016	0.178008	+	0.984029i	$0.443035\pi$
$758$	−2.12699e90	−0.415131
$759$	1.00051e91	1.87328
$760$	4.14010e90	0.743673
$761$	−8.36501e90	−1.44162	−0.720809	−	0.693134i	$-0.756229\pi$
$761$	−8.36501e90	−1.44162	−0.720809	+	0.693134i	$0.756229\pi$
$762$	−5.86159e90	−0.969245
$763$	−1.89497e90	−0.300663
$764$	2.10469e90	0.320440
$765$	−1.49167e90	−0.217940
$766$	4.91206e90	0.688743
$767$	1.69532e90	0.228138
$768$	5.75208e90	0.742927
$769$	5.02702e90	0.623205	0.311602	−	0.950213i	$-0.399134\pi$
$769$	5.02702e90	0.623205	0.311602	+	0.950213i	$0.399134\pi$
$770$	−6.08295e90	−0.723864
$771$	−8.42803e90	−0.962749
$772$	−6.94818e88	−0.00761950
$773$	−9.31255e90	−0.980425	−0.490213	−	0.871603i	$-0.663081\pi$
$773$	−9.31255e90	−0.980425	−0.490213	+	0.871603i	$0.663081\pi$
$774$	1.45244e90	0.146811
$775$	−1.13147e91	−1.09810
$776$	−6.52287e90	−0.607847
$777$	1.66248e90	0.148763
$778$	−1.31827e91	−1.13279
$779$	6.86248e90	0.566306
$780$	−3.58712e90	−0.284293
$781$	2.04359e91	1.55556
$782$	1.46656e91	1.07223
$783$	2.80060e91	1.96678
$784$	7.75954e90	0.523456
$785$	−3.18588e88	−0.00206459
$786$	−5.46259e88	−0.00340086
$787$	−1.11647e91	−0.667793	−0.333896	−	0.942610i	$-0.608364\pi$
$787$	−1.11647e91	−0.667793	−0.333896	+	0.942610i	$0.608364\pi$
$788$	−8.72955e90	−0.501668
$789$	−6.02492e90	−0.332679
$790$	−3.75237e90	−0.199091
$791$	3.82631e90	0.195084
$792$	4.73517e90	0.232002
$793$	1.34651e91	0.634024
$794$	−1.09600e91	−0.495982
$795$	−9.83696e90	−0.427855
$796$	−2.21955e89	−0.00927905
$797$	−3.74336e91	−1.50427	−0.752133	−	0.659011i	$-0.770975\pi$
$797$	−3.74336e91	−1.50427	−0.752133	+	0.659011i	$0.770975\pi$
$798$	−3.20637e90	−0.123858
$799$	−5.58528e90	−0.207406
$800$	2.63771e91	0.941655
$801$	−7.93894e90	−0.272482
$802$	−4.07259e91	−1.34394
$803$	1.09310e91	0.346834
$804$	−6.01446e90	−0.183498
$805$	3.08902e91	0.906256
$806$	−1.26748e91	−0.357592
$807$	3.82714e91	1.03839
$808$	−1.70547e90	−0.0445027
$809$	−4.60359e91	−1.15536	−0.577682	−	0.816262i	$-0.696042\pi$
$809$	−4.60359e91	−1.15536	−0.577682	+	0.816262i	$0.696042\pi$
$810$	4.64274e91	1.12072
$811$	6.97054e91	1.61849	0.809244	−	0.587473i	$-0.199877\pi$
$811$	6.97054e91	1.61849	0.809244	+	0.587473i	$0.199877\pi$
$812$	−9.44896e90	−0.211042
$813$	−3.93723e91	−0.845937
$814$	−2.39091e91	−0.494190
$815$	5.08157e91	1.01049
$816$	−2.58200e91	−0.493987
$817$	−2.61687e91	−0.481712
$818$	5.71831e91	1.01283
$819$	−2.18631e90	−0.0372622
$820$	3.97597e91	0.652089
$821$	2.40187e90	0.0379088	0.0189544	−	0.999820i	$-0.493966\pi$
$821$	2.40187e90	0.0379088	0.0189544	+	0.999820i	$0.493966\pi$
$822$	8.63713e91	1.31192
$823$	−1.25656e92	−1.83691	−0.918456	−	0.395523i	$-0.870563\pi$
$823$	−1.25656e92	−1.83691	−0.918456	+	0.395523i	$0.870563\pi$
$824$	−5.74660e91	−0.808545
$825$	−1.55241e92	−2.10236
$826$	8.77975e90	0.114449
$827$	1.21276e92	1.52178	0.760891	−	0.648880i	$-0.224762\pi$
$827$	1.21276e92	1.52178	0.760891	+	0.648880i	$0.224762\pi$
$828$	−5.52451e90	−0.0667326
$829$	−6.65548e91	−0.773948	−0.386974	−	0.922091i	$-0.626480\pi$
$829$	−6.65548e91	−0.773948	−0.386974	+	0.922091i	$0.626480\pi$
$830$	4.76606e91	0.533580
$831$	−8.81423e90	−0.0950062
$832$	6.71854e91	0.697253
$833$	7.48908e91	0.748360
$834$	−7.40703e91	−0.712711
$835$	−5.02520e91	−0.465617
$836$	−1.96007e91	−0.174893
$837$	−8.26970e91	−0.710621
$838$	2.86231e91	0.236881
$839$	−1.35743e92	−1.08197	−0.540984	−	0.841033i	$-0.681948\pi$
$839$	−1.35743e92	−1.08197	−0.540984	+	0.841033i	$0.681948\pi$
$840$	−8.08583e91	−0.620764
$841$	3.29299e92	2.43510
$842$	−2.26271e91	−0.161175
$843$	1.01126e92	0.693895
$844$	4.69664e90	0.0310456
$845$	1.51460e92	0.964523
$846$	−4.94980e90	−0.0303683
$847$	6.07683e91	0.359211
$848$	3.07863e91	0.175343
$849$	1.42735e92	0.783321
$850$	−2.27554e92	−1.20334
$851$	1.21414e92	0.618711
$852$	6.24101e91	0.306484
$853$	−3.81968e92	−1.80773	−0.903864	−	0.427821i	$-0.859281\pi$
$853$	−3.81968e92	−1.80773	−0.903864	+	0.427821i	$0.859281\pi$
$854$	6.97335e91	0.318067
$855$	2.38177e91	0.104705
$856$	−3.76356e92	−1.59469
$857$	1.69651e92	0.692883	0.346441	−	0.938072i	$-0.387390\pi$
$857$	1.69651e92	0.692883	0.346441	+	0.938072i	$0.387390\pi$
$858$	−1.73901e92	−0.684626
$859$	−2.92816e92	−1.11125	−0.555623	−	0.831434i	$-0.687520\pi$
$859$	−2.92816e92	−1.11125	−0.555623	+	0.831434i	$0.687520\pi$
$860$	−1.51616e92	−0.554681
$861$	−1.34028e92	−0.472711
$862$	3.96171e92	1.34711
$863$	−1.14708e92	−0.376058	−0.188029	−	0.982163i	$-0.560210\pi$
$863$	−1.14708e92	−0.376058	−0.188029	+	0.982163i	$0.560210\pi$
$864$	1.92785e92	0.609382
$865$	4.03404e92	1.22951
$866$	−4.10555e92	−1.20658
$867$	7.55222e91	0.214029
$868$	2.79012e91	0.0762522
$869$	7.73242e91	0.203795
$870$	9.13281e92	2.32139
$871$	−1.73830e92	−0.426142
$872$	3.62258e92	0.856542
$873$	−3.75256e91	−0.0855813
$874$	−2.34167e92	−0.515129
$875$	−1.87006e92	−0.396828
$876$	3.33827e91	0.0683349
$877$	3.77068e92	0.744615	0.372308	−	0.928109i	$-0.378567\pi$
$877$	3.77068e92	0.744615	0.372308	+	0.928109i	$0.378567\pi$
$878$	−6.13841e92	−1.16944
$879$	−7.18910e92	−1.32137
$880$	7.82138e92	1.38701
$881$	−7.07985e92	−1.21139	−0.605694	−	0.795698i	$-0.707104\pi$
$881$	−7.07985e92	−1.21139	−0.605694	+	0.795698i	$0.707104\pi$
$882$	6.63699e91	0.109575
$883$	−1.04734e92	−0.166850	−0.0834251	−	0.996514i	$-0.526586\pi$
$883$	−1.04734e92	−0.166850	−0.0834251	+	0.996514i	$0.526586\pi$
$884$	1.08351e92	0.166567
$885$	3.60707e92	0.535108
$886$	2.65941e92	0.380735
$887$	7.01851e92	0.969730	0.484865	−	0.874589i	$-0.338869\pi$
$887$	7.01851e92	0.969730	0.484865	+	0.874589i	$0.338869\pi$
$888$	−3.17813e92	−0.423803
$889$	3.72930e92	0.479978
$890$	−1.94965e93	−2.42198
$891$	−9.56717e92	−1.14719
$892$	4.24757e92	0.491640
$893$	8.91809e91	0.0996439
$894$	−3.63704e92	−0.392299
$895$	1.21110e92	0.126112
$896$	1.29875e92	0.130564
$897$	8.83099e92	0.857132
$898$	1.26340e93	1.18395
$899$	−1.37168e93	−1.24114
$900$	8.57196e91	0.0748930
$901$	2.97132e92	0.250680
$902$	1.92753e93	1.57034
$903$	5.11089e92	0.402098
$904$	−7.31468e92	−0.555763
$905$	7.43410e92	0.545504
$906$	−2.77239e92	−0.196479
$907$	−1.65121e93	−1.13024	−0.565122	−	0.825007i	$-0.691171\pi$
$907$	−1.65121e93	−1.13024	−0.565122	+	0.825007i	$0.691171\pi$
$908$	−7.95690e91	−0.0526065
$909$	−9.81145e90	−0.00626572
$910$	−5.36914e92	−0.331208
$911$	2.13707e93	1.27347	0.636735	−	0.771082i	$-0.280284\pi$
$911$	2.13707e93	1.27347	0.636735	+	0.771082i	$0.280284\pi$
$912$	4.12271e92	0.237326
$913$	−9.82130e92	−0.546185
$914$	−3.00286e92	−0.161336
$915$	2.86493e93	1.48713
$916$	−1.01098e93	−0.507034
$917$	3.47545e90	0.00168413
$918$	−1.66315e93	−0.778730
$919$	−2.31977e93	−1.04956	−0.524779	−	0.851238i	$-0.675852\pi$
$919$	−2.31977e93	−1.04956	−0.524779	+	0.851238i	$0.675852\pi$
$920$	−5.90522e93	−2.58178
$921$	−1.14502e92	−0.0483767
$922$	1.89115e93	0.772152
$923$	1.80378e93	0.711755
$924$	3.82812e92	0.145988
$925$	−1.88389e93	−0.694370
$926$	2.28017e93	0.812309
$927$	−3.30598e92	−0.113838
$928$	3.19768e93	1.06432
$929$	7.42194e92	0.238794	0.119397	−	0.992847i	$-0.461904\pi$
$929$	7.42194e92	0.238794	0.119397	+	0.992847i	$0.461904\pi$
$930$	−2.69677e93	−0.838747
$931$	−1.19579e93	−0.359534
$932$	5.08003e92	0.147661
$933$	1.08053e93	0.303643
$934$	5.30760e93	1.44202
$935$	7.54877e93	1.98294
$936$	4.17952e92	0.106154
$937$	−3.23775e93	−0.795144	−0.397572	−	0.917571i	$-0.630147\pi$
$937$	−3.23775e93	−0.795144	−0.397572	+	0.917571i	$0.630147\pi$
$938$	−9.00235e92	−0.213780
$939$	−4.14727e93	−0.952348
$940$	5.16694e92	0.114738
$941$	8.51382e93	1.82832	0.914158	−	0.405357i	$-0.132853\pi$
$941$	8.51382e93	1.82832	0.914158	+	0.405357i	$0.132853\pi$
$942$	−4.71680e90	−0.000979589 0
$943$	−9.78830e93	−1.96602
$944$	−1.12889e93	−0.219297
$945$	−3.50311e93	−0.658190
$946$	−7.35024e93	−1.33577
$947$	−6.01031e93	−1.05651	−0.528254	−	0.849087i	$-0.677153\pi$
$947$	−6.01031e93	−1.05651	−0.528254	+	0.849087i	$0.677153\pi$
$948$	2.36144e92	0.0401526
$949$	9.64831e92	0.158696
$950$	3.63339e93	0.578121
$951$	3.42031e93	0.526477
$952$	2.44238e93	0.363705
$953$	2.35944e93	0.339924	0.169962	−	0.985451i	$-0.445636\pi$
$953$	2.35944e93	0.339924	0.169962	+	0.985451i	$0.445636\pi$
$954$	2.63325e92	0.0367045
$955$	1.29425e94	1.74547
$956$	−2.59035e93	−0.338015
$957$	−1.88197e94	−2.37623
$958$	7.18587e93	0.877942
$959$	−5.49517e93	−0.649673
$960$	1.42948e94	1.63544
$961$	−4.98172e93	−0.551560
$962$	−2.11034e93	−0.226119
$963$	−2.16515e93	−0.224523
$964$	−3.83058e92	−0.0384448
$965$	−4.27270e92	−0.0415042
$966$	4.57341e93	0.429992
$967$	1.61123e94	1.46630	0.733150	−	0.680067i	$-0.238049\pi$
$967$	1.61123e94	1.46630	0.733150	+	0.680067i	$0.238049\pi$
$968$	−1.16170e94	−1.02334
$969$	3.97901e93	0.339294
$970$	−9.21555e93	−0.760697
$971$	2.23086e94	1.78265	0.891326	−	0.453363i	$-0.149776\pi$
$971$	2.23086e94	1.78265	0.891326	+	0.453363i	$0.149776\pi$
$972$	1.16982e93	0.0904966
$973$	4.71255e93	0.352940
$974$	−3.56464e93	−0.258469
$975$	−1.37024e94	−0.961945
$976$	−8.96624e93	−0.609454
$977$	−2.74680e94	−1.80779	−0.903895	−	0.427755i	$-0.859305\pi$
$977$	−2.74680e94	−1.80779	−0.903895	+	0.427755i	$0.859305\pi$
$978$	7.52345e93	0.479450
$979$	4.01759e94	2.47920
$980$	−6.92815e93	−0.413996
$981$	2.08404e93	0.120596
$982$	−2.42521e94	−1.35905
$983$	−3.40980e93	−0.185052	−0.0925259	−	0.995710i	$-0.529494\pi$
$983$	−3.40980e93	−0.185052	−0.0925259	+	0.995710i	$0.529494\pi$
$984$	2.56218e94	1.34668
$985$	−5.36814e94	−2.73264
$986$	−2.75863e94	−1.36010
$987$	−1.74175e93	−0.0831755
$988$	−1.73006e93	−0.0800235
$989$	3.73257e94	1.67234
$990$	6.68989e93	0.290342
$991$	1.50057e94	0.630865	0.315432	−	0.948948i	$-0.397850\pi$
$991$	1.50057e94	0.630865	0.315432	+	0.948948i	$0.397850\pi$
$992$	−9.44221e93	−0.384553
$993$	4.36514e94	1.72225
$994$	9.34145e93	0.357062
$995$	−1.36489e93	−0.0505440
$996$	−2.99937e93	−0.107612
$997$	−3.28573e93	−0.114218	−0.0571090	−	0.998368i	$-0.518188\pi$
$997$	−3.28573e93	−0.114218	−0.0571090	+	0.998368i	$0.518188\pi$
$998$	2.37408e93	0.0799620
$999$	−1.37690e94	−0.449354

Twists

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

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

\(f(q)\)	\(=\)	\(q+2.54406e9 q^{2} -9.84533e14 q^{3} -2.75111e18 q^{4} -1.69176e22 q^{5} -2.50471e24 q^{6} +1.59356e26 q^{7} -3.04638e28 q^{8} -1.75256e29 q^{9} +O(q^{10})\)	\(q+2.54406e9 q^{2} -9.84533e14 q^{3} -2.75111e18 q^{4} -1.69176e22 q^{5} -2.50471e24 q^{6} +1.59356e26 q^{7} -3.04638e28 q^{8} -1.75256e29 q^{9} -4.30395e31 q^{10} +8.86905e32 q^{11} +2.70856e33 q^{12} +7.82830e34 q^{13} +4.05413e35 q^{14} +1.66560e37 q^{15} -5.21275e37 q^{16} -5.03105e38 q^{17} -4.45863e38 q^{18} +8.03315e39 q^{19} +4.65423e40 q^{20} -1.56892e41 q^{21} +2.25634e42 q^{22} -1.14581e43 q^{23} +2.99927e43 q^{24} +1.77786e44 q^{25} +1.99157e44 q^{26} +1.29940e45 q^{27} -4.38407e44 q^{28} +2.15529e46 q^{29} +4.23738e46 q^{30} -6.36423e46 q^{31} +1.48364e47 q^{32} -8.73187e47 q^{33} -1.27993e48 q^{34} -2.69593e48 q^{35} +4.82150e47 q^{36} -1.05964e49 q^{37} +2.04368e49 q^{38} -7.70722e49 q^{39} +5.15376e50 q^{40} +8.54270e50 q^{41} -3.99142e50 q^{42} -3.25759e51 q^{43} -2.43998e51 q^{44} +2.96492e51 q^{45} -2.91501e52 q^{46} +1.11016e52 q^{47} +5.13212e52 q^{48} -1.48857e53 q^{49} +4.52300e53 q^{50} +4.95324e53 q^{51} -2.15365e53 q^{52} -5.90596e53 q^{53} +3.30577e54 q^{54} -1.50043e55 q^{55} -4.85461e54 q^{56} -7.90890e54 q^{57} +5.48320e55 q^{58} +2.16563e55 q^{59} -4.58224e55 q^{60} +1.72006e56 q^{61} -1.61910e56 q^{62} -2.79282e55 q^{63} +8.58238e56 q^{64} -1.32436e57 q^{65} -2.22144e57 q^{66} -2.22054e57 q^{67} +1.38410e57 q^{68} +1.12809e58 q^{69} -6.85863e57 q^{70} +2.30418e58 q^{71} +5.33898e57 q^{72} +1.23249e58 q^{73} -2.69579e58 q^{74} -1.75036e59 q^{75} -2.21001e58 q^{76} +1.41334e59 q^{77} -1.96077e59 q^{78} +8.71843e58 q^{79} +8.81873e59 q^{80} -1.07871e60 q^{81} +2.17332e60 q^{82} -1.10737e60 q^{83} +4.31626e59 q^{84} +8.51136e60 q^{85} -8.28752e60 q^{86} -2.12196e61 q^{87} -2.70185e61 q^{88} +4.52990e61 q^{89} +7.54295e60 q^{90} +1.24749e61 q^{91} +3.15225e61 q^{92} +6.26579e61 q^{93} +2.82432e61 q^{94} -1.35902e62 q^{95} -1.46069e62 q^{96} +2.14118e62 q^{97} -3.78702e62 q^{98} -1.55436e62 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 507315096 q^{2} + 953245351116252 q^{3} + 67\!\cdots\!40 q^{4}+ \cdots + 63\!\cdots\!85 q^{9}+O(q^{10}) \) 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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