LMFDB - Embedded newform 1.64.a.a.1.5

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			1.5
Root			$-6.41810e7$ 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)

$f(q)$	$=$	$q+4.72250e9 q^{2} +8.02316e14 q^{3} +1.30786e19 q^{4} +1.36438e22 q^{5} +3.78894e24 q^{6} +4.00095e26 q^{7} +1.82063e28 q^{8} -5.00850e29 q^{9} +O(q^{10})$	\(q+4.72250e9 q^{2} +8.02316e14 q^{3} +1.30786e19 q^{4} +1.36438e22 q^{5} +3.78894e24 q^{6} +4.00095e26 q^{7} +1.82063e28 q^{8} -5.00850e29 q^{9} +6.44329e31 q^{10} -8.56884e32 q^{11} +1.04932e34 q^{12} +2.07398e35 q^{13} +1.88945e36 q^{14} +1.09467e37 q^{15} -3.46497e37 q^{16} -5.37140e38 q^{17} -2.36526e39 q^{18} -4.25177e39 q^{19} +1.78442e41 q^{20} +3.21003e41 q^{21} -4.04663e42 q^{22} +7.22439e42 q^{23} +1.46072e43 q^{24} +7.77338e43 q^{25} +9.79436e44 q^{26} -1.32014e45 q^{27} +5.23268e45 q^{28} +6.34966e45 q^{29} +5.16956e46 q^{30} +1.09199e47 q^{31} -3.31556e47 q^{32} -6.87492e47 q^{33} -2.53664e48 q^{34} +5.45883e48 q^{35} -6.55041e48 q^{36} -2.36747e49 q^{37} -2.00790e49 q^{38} +1.66399e50 q^{39} +2.48403e50 q^{40} +2.67628e50 q^{41} +1.51594e51 q^{42} -2.12019e51 q^{43} -1.12068e52 q^{44} -6.83350e51 q^{45} +3.41171e52 q^{46} -3.01357e52 q^{47} -2.78000e52 q^{48} -1.41752e52 q^{49} +3.67097e53 q^{50} -4.30956e53 q^{51} +2.71247e54 q^{52} -1.69213e52 q^{53} -6.23436e54 q^{54} -1.16912e55 q^{55} +7.28424e54 q^{56} -3.41127e54 q^{57} +2.99863e55 q^{58} -7.40118e54 q^{59} +1.43167e56 q^{60} -2.87222e56 q^{61} +5.15693e56 q^{62} -2.00388e56 q^{63} -1.24619e57 q^{64} +2.82970e57 q^{65} -3.24668e57 q^{66} -2.05697e57 q^{67} -7.02504e57 q^{68} +5.79624e57 q^{69} +2.57793e58 q^{70} +2.18652e58 q^{71} -9.11860e57 q^{72} -1.91991e58 q^{73} -1.11804e59 q^{74} +6.23671e58 q^{75} -5.56072e58 q^{76} -3.42835e59 q^{77} +7.85818e59 q^{78} -1.43780e59 q^{79} -4.72755e59 q^{80} -4.85917e59 q^{81} +1.26387e60 q^{82} +2.96542e60 q^{83} +4.19827e60 q^{84} -7.32865e60 q^{85} -1.00126e61 q^{86} +5.09444e60 q^{87} -1.56007e61 q^{88} -3.32533e60 q^{89} -3.22712e61 q^{90} +8.29790e61 q^{91} +9.44848e61 q^{92} +8.76123e61 q^{93} -1.42316e62 q^{94} -5.80104e61 q^{95} -2.66013e62 q^{96} -5.80025e61 q^{97} -6.69425e61 q^{98} +4.29170e62 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.72250e9	1.55499	0.777493	−	0.628891i	$-0.216491\pi$
$2$	4.72250e9	1.55499	0.777493	+	0.628891i	$0.216491\pi$
$3$	8.02316e14	0.749939	0.374970	−	0.927037i	$-0.377653\pi$
$3$	8.02316e14	0.749939	0.374970	+	0.927037i	$0.377653\pi$
$4$	1.30786e19	1.41798
$5$	1.36438e22	1.31033	0.655166	−	0.755485i	$-0.272599\pi$
$5$	1.36438e22	1.31033	0.655166	+	0.755485i	$0.272599\pi$
$6$	3.78894e24	1.16615
$7$	4.00095e26	0.958463	0.479231	−	0.877689i	$-0.340915\pi$
$7$	4.00095e26	0.958463	0.479231	+	0.877689i	$0.340915\pi$
$8$	1.82063e28	0.649959
$9$	−5.00850e29	−0.437591
$10$	6.44329e31	2.03755
$11$	−8.56884e32	−1.34602	−0.673012	−	0.739632i	$-0.735000\pi$
$11$	−8.56884e32	−1.34602	−0.673012	+	0.739632i	$0.735000\pi$
$12$	1.04932e34	1.06340
$13$	2.07398e35	1.68884	0.844421	−	0.535680i	$-0.179945\pi$
$13$	2.07398e35	1.68884	0.844421	+	0.535680i	$0.179945\pi$
$14$	1.88945e36	1.49040
$15$	1.09467e37	0.982669
$16$	−3.46497e37	−0.407306
$17$	−5.37140e38	−0.935291	−0.467645	−	0.883916i	$-0.654898\pi$
$17$	−5.37140e38	−0.935291	−0.467645	+	0.883916i	$0.654898\pi$
$18$	−2.36526e39	−0.680448
$19$	−4.25177e39	−0.222757	−0.111379	−	0.993778i	$-0.535527\pi$
$19$	−4.25177e39	−0.222757	−0.111379	+	0.993778i	$0.535527\pi$
$20$	1.78442e41	1.85803
$21$	3.21003e41	0.718789
$22$	−4.04663e42	−2.09305
$23$	7.22439e42	0.921243	0.460621	−	0.887597i	$-0.347627\pi$
$23$	7.22439e42	0.921243	0.460621	+	0.887597i	$0.347627\pi$
$24$	1.46072e43	0.487430
$25$	7.77338e43	0.716967
$26$	9.79436e44	2.62613
$27$	−1.32014e45	−1.07811
$28$	5.23268e45	1.35908
$29$	6.34966e45	0.546027	0.273013	−	0.962010i	$-0.411980\pi$
$29$	6.34966e45	0.546027	0.273013	+	0.962010i	$0.411980\pi$
$30$	5.16956e46	1.52804
$31$	1.09199e47	1.14902	0.574508	−	0.818499i	$-0.305193\pi$
$31$	1.09199e47	1.14902	0.574508	+	0.818499i	$0.305193\pi$
$32$	−3.31556e47	−1.28331
$33$	−6.87492e47	−1.00944
$34$	−2.53664e48	−1.45436
$35$	5.45883e48	1.25590
$36$	−6.55041e48	−0.620497
$37$	−2.36747e49	−0.946087	−0.473043	−	0.881039i	$-0.656845\pi$
$37$	−2.36747e49	−0.946087	−0.473043	+	0.881039i	$0.656845\pi$
$38$	−2.00790e49	−0.346384
$39$	1.66399e50	1.26653
$40$	2.48403e50	0.851662
$41$	2.67628e50	0.421542	0.210771	−	0.977535i	$-0.432403\pi$
$41$	2.67628e50	0.421542	0.210771	+	0.977535i	$0.432403\pi$
$42$	1.51594e51	1.11771
$43$	−2.12019e51	−0.744936	−0.372468	−	0.928045i	$-0.621488\pi$
$43$	−2.12019e51	−0.744936	−0.372468	+	0.928045i	$0.621488\pi$
$44$	−1.12068e52	−1.90864
$45$	−6.83350e51	−0.573389
$46$	3.41171e52	1.43252
$47$	−3.01357e52	−0.642686	−0.321343	−	0.946963i	$-0.604134\pi$
$47$	−3.01357e52	−0.642686	−0.321343	+	0.946963i	$0.604134\pi$
$48$	−2.78000e52	−0.305454
$49$	−1.41752e52	−0.0813493
$50$	3.67097e53	1.11487
$51$	−4.30956e53	−0.701411
$52$	2.71247e54	2.39475
$53$	−1.69213e52	−0.00819867	−0.00409934	−	0.999992i	$-0.501305\pi$
$53$	−1.69213e52	−0.00819867	−0.00409934	+	0.999992i	$0.501305\pi$
$54$	−6.23436e54	−1.67644
$55$	−1.16912e55	−1.76374
$56$	7.28424e54	0.622962
$57$	−3.41127e54	−0.167054
$58$	2.99863e55	0.849064
$59$	−7.40118e54	−0.122310	−0.0611551	−	0.998128i	$-0.519478\pi$
$59$	−7.40118e54	−0.122310	−0.0611551	+	0.998128i	$0.519478\pi$
$60$	1.43167e56	1.39341
$61$	−2.87222e56	−1.66084	−0.830420	−	0.557137i	$-0.811900\pi$
$61$	−2.87222e56	−1.66084	−0.830420	+	0.557137i	$0.811900\pi$
$62$	5.15693e56	1.78670
$63$	−2.00388e56	−0.419415
$64$	−1.24619e57	−1.58823
$65$	2.82970e57	2.21294
$66$	−3.24668e57	−1.56966
$67$	−2.05697e57	−0.619258	−0.309629	−	0.950857i	$-0.600205\pi$
$67$	−2.05697e57	−0.619258	−0.309629	+	0.950857i	$0.600205\pi$
$68$	−7.02504e57	−1.32623
$69$	5.79624e57	0.690876
$70$	2.57793e58	1.95291
$71$	2.18652e58	1.05954	0.529768	−	0.848142i	$-0.322279\pi$
$71$	2.18652e58	1.05954	0.529768	+	0.848142i	$0.322279\pi$
$72$	−9.11860e57	−0.284416
$73$	−1.91991e58	−0.387803	−0.193902	−	0.981021i	$-0.562114\pi$
$73$	−1.91991e58	−0.387803	−0.193902	+	0.981021i	$0.562114\pi$
$74$	−1.11804e59	−1.47115
$75$	6.23671e58	0.537682
$76$	−5.56072e58	−0.315866
$77$	−3.42835e59	−1.29011
$78$	7.85818e59	1.96944
$79$	−1.43780e59	−0.241237	−0.120618	−	0.992699i	$-0.538488\pi$
$79$	−1.43780e59	−0.241237	−0.120618	+	0.992699i	$0.538488\pi$
$80$	−4.72755e59	−0.533705
$81$	−4.85917e59	−0.370923
$82$	1.26387e60	0.655492
$83$	2.96542e60	1.04985	0.524924	−	0.851149i	$-0.324094\pi$
$83$	2.96542e60	1.04985	0.524924	+	0.851149i	$0.324094\pi$
$84$	4.19827e60	1.01923
$85$	−7.32865e60	−1.22554
$86$	−1.00126e61	−1.15837
$87$	5.09444e60	0.409487
$88$	−1.56007e61	−0.874861
$89$	−3.32533e60	−0.130632	−0.0653161	−	0.997865i	$-0.520806\pi$
$89$	−3.32533e60	−0.130632	−0.0653161	+	0.997865i	$0.520806\pi$
$90$	−3.22712e61	−0.891612
$91$	8.29790e61	1.61869
$92$	9.44848e61	1.30631
$93$	8.76123e61	0.861692
$94$	−1.42316e62	−0.999368
$95$	−5.80104e61	−0.291886
$96$	−2.66013e62	−0.962408
$97$	−5.80025e61	−0.151404	−0.0757020	−	0.997130i	$-0.524120\pi$
$97$	−5.80025e61	−0.151404	−0.0757020	+	0.997130i	$0.524120\pi$
$98$	−6.69425e61	−0.126497
$99$	4.29170e62	0.589008
$100$	1.01665e63	1.01665
$101$	−1.95277e63	−1.42734	−0.713671	−	0.700481i	$-0.752969\pi$
$101$	−1.95277e63	−1.42734	−0.713671	+	0.700481i	$0.752969\pi$
$102$	−2.03519e63	−1.09069
$103$	1.61718e63	0.637363	0.318682	−	0.947862i	$-0.396760\pi$
$103$	1.61718e63	0.637363	0.318682	+	0.947862i	$0.396760\pi$
$104$	3.77594e63	1.09768
$105$	4.37971e63	0.941851
$106$	−7.99107e61	−0.0127488
$107$	2.02228e63	0.240023	0.120011	−	0.992773i	$-0.461707\pi$
$107$	2.02228e63	0.240023	0.120011	+	0.992773i	$0.461707\pi$
$108$	−1.72656e64	−1.52874
$109$	2.99199e64	1.98164	0.990821	−	0.135180i	$-0.0431613\pi$
$109$	2.99199e64	1.98164	0.990821	+	0.135180i	$0.0431613\pi$
$110$	−5.52115e64	−2.74259
$111$	−1.89946e64	−0.709508
$112$	−1.38632e64	−0.390387
$113$	8.58568e64	1.82727	0.913637	−	0.406531i	$-0.133262\pi$
$113$	8.58568e64	1.82727	0.913637	+	0.406531i	$0.133262\pi$
$114$	−1.61097e64	−0.259767
$115$	9.85683e64	1.20713
$116$	8.30447e64	0.774257
$117$	−1.03875e65	−0.739022
$118$	−3.49520e64	−0.190191
$119$	−2.14907e65	−0.896441
$120$	1.99298e65	0.638695
$121$	3.28986e65	0.811779
$122$	−1.35640e66	−2.58259
$123$	2.14723e65	0.316131
$124$	1.42817e66	1.62929
$125$	−4.18681e65	−0.370866
$126$	−9.46329e65	−0.652184
$127$	1.13001e66	0.607104	0.303552	−	0.952815i	$-0.401827\pi$
$127$	1.13001e66	0.607104	0.303552	+	0.952815i	$0.401827\pi$
$128$	−2.82704e66	−1.18636
$129$	−1.70106e66	−0.558657
$130$	1.33633e67	3.44110
$131$	4.17132e66	0.843776	0.421888	−	0.906648i	$-0.361368\pi$
$131$	4.17132e66	0.843776	0.421888	+	0.906648i	$0.361368\pi$
$132$	−8.99143e66	−1.43136
$133$	−1.70111e66	−0.213504
$134$	−9.71403e66	−0.962938
$135$	−1.80118e67	−1.41268
$136$	−9.77932e66	−0.607901
$137$	1.55906e67	0.769422	0.384711	−	0.923037i	$-0.374301\pi$
$137$	1.55906e67	0.769422	0.384711	+	0.923037i	$0.374301\pi$
$138$	2.73727e67	1.07430
$139$	−2.06837e67	−0.646640	−0.323320	−	0.946290i	$-0.604799\pi$
$139$	−2.06837e67	−0.646640	−0.323320	+	0.946290i	$0.604799\pi$
$140$	7.13938e67	1.78085
$141$	−2.41784e67	−0.481976
$142$	1.03258e68	1.64757
$143$	−1.77716e68	−2.27322
$144$	1.73543e67	0.178233
$145$	8.66337e67	0.715476
$146$	−9.06678e67	−0.603029
$147$	−1.13730e67	−0.0610071
$148$	−3.09632e68	−1.34154
$149$	2.12773e68	0.745675	0.372838	−	0.927897i	$-0.378385\pi$
$149$	2.12773e68	0.745675	0.372838	+	0.927897i	$0.378385\pi$
$150$	2.94528e68	0.836089
$151$	−2.22182e68	−0.511606	−0.255803	−	0.966729i	$-0.582340\pi$
$151$	−2.22182e68	−0.511606	−0.255803	+	0.966729i	$0.582340\pi$
$152$	−7.74089e67	−0.144783
$153$	2.69026e68	0.409275
$154$	−1.61904e69	−2.00611
$155$	1.48989e69	1.50559
$156$	2.17626e69	1.79592
$157$	3.83578e68	0.258830	0.129415	−	0.991591i	$-0.458690\pi$
$157$	3.83578e68	0.258830	0.129415	+	0.991591i	$0.458690\pi$
$158$	−6.78998e68	−0.375120
$159$	−1.35762e67	−0.00614851
$160$	−4.52370e69	−1.68157
$161$	2.89044e69	0.882977
$162$	−2.29474e69	−0.576781
$163$	−7.56737e69	−1.56688	−0.783439	−	0.621468i	$-0.786537\pi$
$163$	−7.56737e69	−1.56688	−0.783439	+	0.621468i	$0.786537\pi$
$164$	3.50020e69	0.597740
$165$	−9.38003e69	−1.32270
$166$	1.40042e70	1.63250
$167$	1.31868e70	1.27225	0.636124	−	0.771587i	$-0.280537\pi$
$167$	1.31868e70	1.27225	0.636124	+	0.771587i	$0.280537\pi$
$168$	5.84427e69	0.467184
$169$	2.79329e70	1.85219
$170$	−3.46095e70	−1.90570
$171$	2.12950e69	0.0974765
$172$	−2.77291e70	−1.05631
$173$	−4.13644e70	−1.31273	−0.656364	−	0.754445i	$-0.727906\pi$
$173$	−4.13644e70	−1.31273	−0.656364	+	0.754445i	$0.727906\pi$
$174$	2.40585e70	0.636747
$175$	3.11009e70	0.687186
$176$	2.96908e70	0.548243
$177$	−5.93809e69	−0.0917252
$178$	−1.57039e70	−0.203131
$179$	−1.07726e71	−1.16802	−0.584009	−	0.811747i	$-0.698517\pi$
$179$	−1.07726e71	−1.16802	−0.584009	+	0.811747i	$0.698517\pi$
$180$	−8.93726e70	−0.813056
$181$	8.24880e70	0.630254	0.315127	−	0.949049i	$-0.397953\pi$
$181$	8.24880e70	0.630254	0.315127	+	0.949049i	$0.397953\pi$
$182$	3.91868e71	2.51705
$183$	−2.30443e71	−1.24553
$184$	1.31529e71	0.598770
$185$	−3.23014e71	−1.23969
$186$	4.13749e71	1.33992
$187$	4.60267e71	1.25892
$188$	−3.94133e71	−0.911318
$189$	−5.28182e71	−1.03332
$190$	−2.73954e71	−0.453878
$191$	2.79537e70	0.0392544	0.0196272	−	0.999807i	$-0.493752\pi$
$191$	2.79537e70	0.0392544	0.0196272	+	0.999807i	$0.493752\pi$
$192$	−9.99836e71	−1.19108
$193$	−2.20841e71	−0.223370	−0.111685	−	0.993744i	$-0.535625\pi$
$193$	−2.20841e71	−0.223370	−0.111685	+	0.993744i	$0.535625\pi$
$194$	−2.73917e71	−0.235431
$195$	2.27032e72	1.65957
$196$	−1.85392e71	−0.115352
$197$	2.04182e72	1.08226	0.541130	−	0.840939i	$-0.317997\pi$
$197$	2.04182e72	1.08226	0.541130	+	0.840939i	$0.317997\pi$
$198$	2.02675e72	0.915899
$199$	−5.99449e71	−0.231143	−0.115571	−	0.993299i	$-0.536870\pi$
$199$	−5.99449e71	−0.231143	−0.115571	+	0.993299i	$0.536870\pi$
$200$	1.41524e72	0.466000
$201$	−1.65034e72	−0.464406
$202$	−9.22195e72	−2.21950
$203$	2.54047e72	0.523346
$204$	−5.63630e72	−0.994590
$205$	3.65148e72	0.552359
$206$	7.63715e72	0.991091
$207$	−3.61833e72	−0.403127
$208$	−7.18629e72	−0.687875
$209$	3.64328e72	0.299836
$210$	2.06832e73	1.46457
$211$	−2.24768e73	−1.37037	−0.685183	−	0.728371i	$-0.740278\pi$
$211$	−2.24768e73	−1.37037	−0.685183	+	0.728371i	$0.740278\pi$
$212$	−2.21307e71	−0.0116256
$213$	1.75428e73	0.794588
$214$	9.55021e72	0.373232
$215$	−2.89275e73	−0.976112
$216$	−2.40348e73	−0.700725
$217$	4.36901e73	1.10129
$218$	1.41297e74	3.08143
$219$	−1.54038e73	−0.290829
$220$	−1.52904e74	−2.50095
$221$	−1.11402e74	−1.57956
$222$	−8.97021e73	−1.10327
$223$	1.34223e74	1.43293	0.716464	−	0.697624i	$-0.245759\pi$
$223$	1.34223e74	1.43293	0.716464	+	0.697624i	$0.245759\pi$
$224$	−1.32654e74	−1.23001
$225$	−3.89329e73	−0.313738
$226$	4.05458e74	2.84139
$227$	8.28902e73	0.505462	0.252731	−	0.967537i	$-0.418671\pi$
$227$	8.28902e73	0.505462	0.252731	+	0.967537i	$0.418671\pi$
$228$	−4.46146e73	−0.236880
$229$	−1.94712e74	−0.900688	−0.450344	−	0.892855i	$-0.648699\pi$
$229$	−1.94712e74	−0.900688	−0.450344	+	0.892855i	$0.648699\pi$
$230$	4.65488e74	1.87708
$231$	−2.75062e74	−0.967507
$232$	1.15604e74	0.354895
$233$	1.85040e74	0.496083	0.248041	−	0.968749i	$-0.420213\pi$
$233$	1.85040e74	0.496083	0.248041	+	0.968749i	$0.420213\pi$
$234$	−4.90550e74	−1.14917
$235$	−4.11166e74	−0.842131
$236$	−9.67970e73	−0.173434
$237$	−1.15357e74	−0.180913
$238$	−1.01490e75	−1.39395
$239$	1.17037e75	1.40861	0.704303	−	0.709900i	$-0.251260\pi$
$239$	1.17037e75	1.40861	0.704303	+	0.709900i	$0.251260\pi$
$240$	−3.79299e74	−0.400246
$241$	1.07492e75	0.995035	0.497517	−	0.867454i	$-0.334245\pi$
$241$	1.07492e75	0.995035	0.497517	+	0.867454i	$0.334245\pi$
$242$	1.55363e75	1.26231
$243$	1.12112e75	0.799936
$244$	−3.75646e75	−2.35505
$245$	−1.93404e74	−0.106595
$246$	1.01403e75	0.491579
$247$	−8.81809e74	−0.376202
$248$	1.98811e75	0.746814
$249$	2.37921e75	0.787323
$250$	−1.97722e75	−0.576692
$251$	3.30820e75	0.850882	0.425441	−	0.904986i	$-0.360119\pi$
$251$	3.30820e75	0.850882	0.425441	+	0.904986i	$0.360119\pi$
$252$	−2.62079e75	−0.594723
$253$	−6.19046e75	−1.24001
$254$	5.33644e75	0.944039
$255$	−5.87989e75	−0.919081
$256$	−1.85665e75	−0.256549
$257$	−3.83510e75	−0.468688	−0.234344	−	0.972154i	$-0.575294\pi$
$257$	−3.83510e75	−0.468688	−0.234344	+	0.972154i	$0.575294\pi$
$258$	−8.03327e75	−0.868704
$259$	−9.47215e75	−0.906789
$260$	3.70085e76	3.13792
$261$	−3.18023e75	−0.238936
$262$	1.96990e76	1.31206
$263$	1.43118e76	0.845448	0.422724	−	0.906258i	$-0.361074\pi$
$263$	1.43118e76	0.845448	0.422724	+	0.906258i	$0.361074\pi$
$264$	−1.25167e76	−0.656092
$265$	−2.30871e74	−0.0107430
$266$	−8.03350e75	−0.331996
$267$	−2.66797e75	−0.0979662
$268$	−2.69023e76	−0.878098
$269$	4.09775e75	0.118946	0.0594728	−	0.998230i	$-0.481058\pi$
$269$	4.09775e75	0.118946	0.0594728	+	0.998230i	$0.481058\pi$
$270$	−8.50605e76	−2.19669
$271$	−1.28815e76	−0.296097	−0.148049	−	0.988980i	$-0.547299\pi$
$271$	−1.28815e76	−0.296097	−0.148049	+	0.988980i	$0.547299\pi$
$272$	1.86118e76	0.380949
$273$	6.65754e76	1.21392
$274$	7.36265e76	1.19644
$275$	−6.66088e76	−0.965055
$276$	7.58067e76	0.979651
$277$	4.42046e76	0.509747	0.254874	−	0.966974i	$-0.417966\pi$
$277$	4.42046e76	0.509747	0.254874	+	0.966974i	$0.417966\pi$
$278$	−9.76789e76	−1.00552
$279$	−5.46924e76	−0.502799
$280$	9.93849e76	0.816286
$281$	−3.12493e76	−0.229399	−0.114699	−	0.993400i	$-0.536591\pi$
$281$	−3.12493e76	−0.229399	−0.114699	+	0.993400i	$0.536591\pi$
$282$	−1.14182e77	−0.749466
$283$	2.35005e77	1.37976	0.689881	−	0.723923i	$-0.257663\pi$
$283$	2.35005e77	1.37976	0.689881	+	0.723923i	$0.257663\pi$
$284$	2.85966e77	1.50241
$285$	−4.65427e76	−0.218896
$286$	−8.39264e77	−3.53483
$287$	1.07077e77	0.404032
$288$	1.66060e77	0.561567
$289$	−4.13043e76	−0.125231
$290$	4.09127e77	1.11256
$291$	−4.65364e76	−0.113544
$292$	−2.51098e77	−0.549899
$293$	−4.60913e77	−0.906335	−0.453167	−	0.891425i	$-0.649706\pi$
$293$	−4.60913e77	−0.906335	−0.453167	+	0.891425i	$0.649706\pi$
$294$	−5.37091e76	−0.0948652
$295$	−1.00980e77	−0.160267
$296$	−4.31029e77	−0.614918
$297$	1.13121e78	1.45116
$298$	1.00482e78	1.15951
$299$	1.49832e78	1.55583
$300$	8.15674e77	0.762425
$301$	−8.48279e77	−0.713993
$302$	−1.04926e78	−0.795541
$303$	−1.56674e78	−1.07042
$304$	1.47323e77	0.0907302
$305$	−3.91881e78	−2.17625
$306$	1.27048e78	0.636417
$307$	3.47715e77	0.157168	0.0785841	−	0.996907i	$-0.474960\pi$
$307$	3.47715e77	0.157168	0.0785841	+	0.996907i	$0.474960\pi$
$308$	−4.48380e78	−1.82936
$309$	1.29749e78	0.477984
$310$	7.03602e78	2.34117
$311$	−1.27935e78	−0.384626	−0.192313	−	0.981334i	$-0.561599\pi$
$311$	−1.27935e78	−0.384626	−0.192313	+	0.981334i	$0.561599\pi$
$312$	3.02950e78	0.823193
$313$	2.55012e77	0.0626490	0.0313245	−	0.999509i	$-0.490027\pi$
$313$	2.55012e77	0.0626490	0.0313245	+	0.999509i	$0.490027\pi$
$314$	1.81145e78	0.402478
$315$	−2.73405e78	−0.549572
$316$	−1.88043e78	−0.342070
$317$	8.57182e78	1.41158	0.705791	−	0.708420i	$-0.250592\pi$
$317$	8.57182e78	1.41158	0.705791	+	0.708420i	$0.250592\pi$
$318$	−6.41137e76	−0.00956085
$319$	−5.44093e78	−0.734965
$320$	−1.70027e79	−2.08111
$321$	1.62251e78	0.180002
$322$	1.36501e79	1.37302
$323$	2.28380e78	0.208343
$324$	−6.35511e78	−0.525963
$325$	1.61218e79	1.21084
$326$	−3.57369e79	−2.43648
$327$	2.40052e79	1.48611
$328$	4.87251e78	0.273985
$329$	−1.20572e79	−0.615991
$330$	−4.42971e79	−2.05677
$331$	−1.19633e78	−0.0504973	−0.0252486	−	0.999681i	$-0.508038\pi$
$331$	−1.19633e78	−0.0504973	−0.0252486	+	0.999681i	$0.508038\pi$
$332$	3.87836e79	1.48867
$333$	1.18575e79	0.413999
$334$	6.22748e79	1.97833
$335$	−2.80649e79	−0.811433
$336$	−1.11227e79	−0.292767
$337$	−6.02075e79	−1.44314	−0.721571	−	0.692340i	$-0.756580\pi$
$337$	−6.02075e79	−1.44314	−0.721571	+	0.692340i	$0.756580\pi$
$338$	1.31913e80	2.88013
$339$	6.88843e79	1.37034
$340$	−9.58484e79	−1.73780
$341$	−9.35711e79	−1.54660
$342$	1.00565e79	0.151575
$343$	−7.53887e79	−1.03643
$344$	−3.86008e79	−0.484178
$345$	7.90829e79	0.905277
$346$	−1.95343e80	−2.04127
$347$	1.32734e80	1.26650	0.633248	−	0.773949i	$-0.281721\pi$
$347$	1.32734e80	1.26650	0.633248	+	0.773949i	$0.281721\pi$
$348$	6.66281e79	0.580646
$349$	−5.81469e79	−0.462941	−0.231471	−	0.972842i	$-0.574354\pi$
$349$	−5.81469e79	−0.462941	−0.231471	+	0.972842i	$0.574354\pi$
$350$	1.46874e80	1.06857
$351$	−2.73795e80	−1.82075
$352$	2.84105e80	1.72737
$353$	2.98209e80	1.65813	0.829064	−	0.559154i	$-0.188874\pi$
$353$	2.98209e80	1.65813	0.829064	+	0.559154i	$0.188874\pi$
$354$	−2.80426e79	−0.142632
$355$	2.98325e80	1.38834
$356$	−4.34907e79	−0.185234
$357$	−1.72424e80	−0.672277
$358$	−5.08735e80	−1.81625
$359$	−3.44639e80	−1.12691	−0.563455	−	0.826147i	$-0.690528\pi$
$359$	−3.44639e80	−1.12691	−0.563455	+	0.826147i	$0.690528\pi$
$360$	−1.24413e80	−0.372680
$361$	−3.46237e80	−0.950379
$362$	3.89549e80	0.980037
$363$	2.63951e80	0.608785
$364$	1.08525e81	2.29528
$365$	−2.61950e80	−0.508151
$366$	−1.08827e81	−1.93678
$367$	9.05746e80	1.47920	0.739598	−	0.673049i	$-0.235016\pi$
$367$	9.05746e80	1.47920	0.739598	+	0.673049i	$0.235016\pi$
$368$	−2.50323e80	−0.375227
$369$	−1.34042e80	−0.184463
$370$	−1.52543e81	−1.92770
$371$	−6.77013e78	−0.00785812
$372$	1.14585e81	1.22187
$373$	1.52085e80	0.149024	0.0745121	−	0.997220i	$-0.476260\pi$
$373$	1.52085e80	0.149024	0.0745121	+	0.997220i	$0.476260\pi$
$374$	2.17361e81	1.95761
$375$	−3.35914e80	−0.278127
$376$	−5.48659e80	−0.417720
$377$	1.31691e81	0.922153
$378$	−2.49434e81	−1.60681
$379$	1.67737e81	0.994248	0.497124	−	0.867680i	$-0.334389\pi$
$379$	1.67737e81	0.994248	0.497124	+	0.867680i	$0.334389\pi$
$380$	−7.58695e80	−0.413889
$381$	9.06622e80	0.455291
$382$	1.32011e80	0.0610401
$383$	−1.23141e81	−0.524372	−0.262186	−	0.965017i	$-0.584443\pi$
$383$	−1.23141e81	−0.524372	−0.262186	+	0.965017i	$0.584443\pi$
$384$	−2.26818e81	−0.889701
$385$	−4.67759e81	−1.69048
$386$	−1.04292e81	−0.347337
$387$	1.06190e81	0.325977
$388$	−7.58592e80	−0.214688
$389$	1.48659e81	0.387954	0.193977	−	0.981006i	$-0.437861\pi$
$389$	1.48659e81	0.387954	0.193977	+	0.981006i	$0.437861\pi$
$390$	1.07216e82	2.58061
$391$	−3.88051e81	−0.861630
$392$	−2.58078e80	−0.0528738
$393$	3.34672e81	0.632781
$394$	9.64249e81	1.68290
$395$	−1.96170e81	−0.316100
$396$	5.61294e81	0.835203
$397$	−1.33902e82	−1.84029	−0.920146	−	0.391576i	$-0.871930\pi$
$397$	−1.33902e82	−1.84029	−0.920146	+	0.391576i	$0.871930\pi$
$398$	−2.83090e81	−0.359424
$399$	−1.36483e81	−0.160115
$400$	−2.69345e81	−0.292025
$401$	−5.92318e81	−0.593618	−0.296809	−	0.954937i	$-0.595923\pi$
$401$	−5.92318e81	−0.593618	−0.296809	+	0.954937i	$0.595923\pi$
$402$	−7.79373e81	−0.722145
$403$	2.26477e82	1.94051
$404$	−2.55395e82	−2.02395
$405$	−6.62977e81	−0.486032
$406$	1.19974e82	0.813796
$407$	2.02865e82	1.27345
$408$	−7.84611e81	−0.455889
$409$	−1.97907e82	−1.06457	−0.532287	−	0.846564i	$-0.678667\pi$
$409$	−1.97907e82	−1.06457	−0.532287	+	0.846564i	$0.678667\pi$
$410$	1.72441e82	0.858912
$411$	1.25086e82	0.577020
$412$	2.11505e82	0.903771
$413$	−2.96118e81	−0.117230
$414$	−1.70876e82	−0.626858
$415$	4.04597e82	1.37565
$416$	−6.87641e82	−2.16732
$417$	−1.65949e82	−0.484941
$418$	1.72054e82	0.466241
$419$	5.68402e81	0.142861	0.0714306	−	0.997446i	$-0.477244\pi$
$419$	5.68402e81	0.142861	0.0714306	+	0.997446i	$0.477244\pi$
$420$	5.72804e82	1.33553
$421$	6.48979e82	1.40393	0.701964	−	0.712212i	$-0.252307\pi$
$421$	6.48979e82	1.40393	0.701964	+	0.712212i	$0.252307\pi$
$422$	−1.06147e83	−2.13090
$423$	1.50935e82	0.281234
$424$	−3.08073e80	−0.00532880
$425$	−4.17539e82	−0.670573
$426$	8.28459e82	1.23557
$427$	−1.14916e83	−1.59185
$428$	2.64486e82	0.340348
$429$	−1.42585e83	−1.70478
$430$	−1.36610e83	−1.51784
$431$	1.31954e83	1.36266	0.681331	−	0.731976i	$-0.261401\pi$
$431$	1.31954e83	1.36266	0.681331	+	0.731976i	$0.261401\pi$
$432$	4.57425e82	0.439119
$433$	−4.32188e82	−0.385748	−0.192874	−	0.981224i	$-0.561781\pi$
$433$	−4.32188e82	−0.385748	−0.192874	+	0.981224i	$0.561781\pi$
$434$	2.06326e83	1.71249
$435$	6.95077e82	0.536563
$436$	3.91310e83	2.80994
$437$	−3.07164e82	−0.205213
$438$	−7.27443e82	−0.452235
$439$	−3.04529e81	−0.0176196	−0.00880982	−	0.999961i	$-0.502804\pi$
$439$	−3.04529e81	−0.0176196	−0.00880982	+	0.999961i	$0.502804\pi$
$440$	−2.12853e83	−1.14636
$441$	7.09966e81	0.0355977
$442$	−5.26095e83	−2.45619
$443$	1.28926e83	0.560560	0.280280	−	0.959918i	$-0.409573\pi$
$443$	1.28926e83	0.560560	0.280280	+	0.959918i	$0.409573\pi$
$444$	−2.48423e83	−1.00607
$445$	−4.53703e82	−0.171171
$446$	6.33869e83	2.22819
$447$	1.70712e83	0.559211
$448$	−4.98593e83	−1.52226
$449$	−4.12515e83	−1.17403	−0.587017	−	0.809575i	$-0.699698\pi$
$449$	−4.12515e83	−1.17403	−0.587017	+	0.809575i	$0.699698\pi$
$450$	−1.83861e83	−0.487859
$451$	−2.29327e83	−0.567405
$452$	1.12289e84	2.59104
$453$	−1.78261e83	−0.383674
$454$	3.91448e83	0.785987
$455$	1.13215e84	2.12102
$456$	−6.21064e82	−0.108579
$457$	−9.82972e83	−1.60391	−0.801957	−	0.597382i	$-0.796208\pi$
$457$	−9.82972e83	−1.60391	−0.801957	+	0.597382i	$0.796208\pi$
$458$	−9.19525e83	−1.40056
$459$	7.09100e83	1.00834
$460$	1.28913e84	1.71170
$461$	−1.38498e84	−1.71737	−0.858685	−	0.512504i	$-0.828718\pi$
$461$	−1.38498e84	−1.71737	−0.858685	+	0.512504i	$0.828718\pi$
$462$	−1.29898e84	−1.50446
$463$	7.43768e83	0.804705	0.402352	−	0.915485i	$-0.368193\pi$
$463$	7.43768e83	0.804705	0.402352	+	0.915485i	$0.368193\pi$
$464$	−2.20014e83	−0.222400
$465$	1.19537e84	1.12910
$466$	8.73851e83	0.771402
$467$	4.43713e83	0.366118	0.183059	−	0.983102i	$-0.441400\pi$
$467$	4.43713e83	0.366118	0.183059	+	0.983102i	$0.441400\pi$
$468$	−1.35854e84	−1.04792
$469$	−8.22984e83	−0.593536
$470$	−1.94173e84	−1.30950
$471$	3.07751e83	0.194107
$472$	−1.34748e83	−0.0794967
$473$	1.81676e84	1.00270
$474$	−5.44772e83	−0.281317
$475$	−3.30506e83	−0.159710
$476$	−2.81068e84	−1.27114
$477$	8.47502e81	0.00358766
$478$	5.52707e84	2.19036
$479$	3.88526e84	1.44162	0.720811	−	0.693132i	$-0.243770\pi$
$479$	3.88526e84	1.44162	0.720811	+	0.693132i	$0.243770\pi$
$480$	−3.62944e84	−1.26107
$481$	−4.91009e84	−1.59779
$482$	5.07629e84	1.54727
$483$	2.31905e84	0.662179
$484$	4.30267e84	1.15109
$485$	−7.91377e83	−0.198389
$486$	5.29449e84	1.24389
$487$	−6.87945e84	−1.51493	−0.757463	−	0.652878i	$-0.773561\pi$
$487$	−6.87945e84	−1.51493	−0.757463	+	0.652878i	$0.773561\pi$
$488$	−5.22924e84	−1.07948
$489$	−6.07143e84	−1.17506
$490$	−9.13352e83	−0.165753
$491$	−7.22668e84	−1.22991	−0.614953	−	0.788564i	$-0.710825\pi$
$491$	−7.22668e84	−1.22991	−0.614953	+	0.788564i	$0.710825\pi$
$492$	2.80827e84	0.448269
$493$	−3.41066e84	−0.510694
$494$	−4.16434e84	−0.584988
$495$	5.85552e84	0.771795
$496$	−3.78372e84	−0.468000
$497$	8.74817e84	1.01553
$498$	1.12358e85	1.22428
$499$	1.29645e85	1.32613	0.663067	−	0.748560i	$-0.269255\pi$
$499$	1.29645e85	1.32613	0.663067	+	0.748560i	$0.269255\pi$
$500$	−5.47575e84	−0.525883
$501$	1.05800e85	0.954109
$502$	1.56229e85	1.32311
$503$	−1.26653e85	−1.00745	−0.503724	−	0.863865i	$-0.668037\pi$
$503$	−1.26653e85	−1.00745	−0.503724	+	0.863865i	$0.668037\pi$
$504$	−3.64831e84	−0.272602
$505$	−2.66433e85	−1.87029
$506$	−2.92344e85	−1.92821
$507$	2.24110e85	1.38903
$508$	1.47789e85	0.860864
$509$	1.58987e85	0.870467	0.435233	−	0.900318i	$-0.356666\pi$
$509$	1.58987e85	0.870467	0.435233	+	0.900318i	$0.356666\pi$
$510$	−2.77678e85	−1.42916
$511$	−7.68148e84	−0.371695
$512$	1.73068e85	0.787433
$513$	5.61293e84	0.240156
$514$	−1.81113e85	−0.728804
$515$	2.20646e85	0.835157
$516$	−2.22475e85	−0.792166
$517$	2.58228e85	0.865070
$518$	−4.47322e85	−1.41004
$519$	−3.31873e85	−0.984466
$520$	5.15183e85	1.43832
$521$	−3.41495e84	−0.0897420	−0.0448710	−	0.998993i	$-0.514288\pi$
$521$	−3.41495e84	−0.0897420	−0.0448710	+	0.998993i	$0.514288\pi$
$522$	−1.50186e85	−0.371543
$523$	−2.46994e85	−0.575286	−0.287643	−	0.957738i	$-0.592872\pi$
$523$	−2.46994e85	−0.575286	−0.287643	+	0.957738i	$0.592872\pi$
$524$	5.45549e85	1.19646
$525$	2.49528e85	0.515348
$526$	6.75872e85	1.31466
$527$	−5.86553e85	−1.07466
$528$	2.38214e85	0.411149
$529$	−9.30521e84	−0.151312
$530$	−1.09029e84	−0.0167052
$531$	3.70688e84	0.0535218
$532$	−2.22482e85	−0.302746
$533$	5.55056e85	0.711918
$534$	−1.25995e85	−0.152336
$535$	2.75916e85	0.314509
$536$	−3.74498e85	−0.402493
$537$	−8.64303e85	−0.875943
$538$	1.93516e85	0.184959
$539$	1.21465e85	0.109498
$540$	−2.35569e86	−2.00315
$541$	−2.40272e86	−1.92748	−0.963740	−	0.266842i	$-0.914020\pi$
$541$	−2.40272e86	−1.92748	−0.963740	+	0.266842i	$0.914020\pi$
$542$	−6.08329e85	−0.460427
$543$	6.61815e85	0.472652
$544$	1.78092e86	1.20027
$545$	4.08222e86	2.59661
$546$	3.14402e86	1.88763
$547$	−2.76159e86	−1.56516	−0.782579	−	0.622551i	$-0.786096\pi$
$547$	−2.76159e86	−1.56516	−0.782579	+	0.622551i	$0.786096\pi$
$548$	2.03903e86	1.09103
$549$	1.43855e86	0.726769
$550$	−3.14560e86	−1.50065
$551$	−2.69973e85	−0.121631
$552$	1.05528e86	0.449042
$553$	−5.75255e85	−0.231217
$554$	2.08756e86	0.792650
$555$	−2.59159e86	−0.929690
$556$	−2.70514e86	−0.916926
$557$	3.40659e86	1.09114	0.545571	−	0.838065i	$-0.316313\pi$
$557$	3.40659e86	1.09114	0.545571	+	0.838065i	$0.316313\pi$
$558$	−2.58284e86	−0.781846
$559$	−4.39724e86	−1.25808
$560$	−1.89147e86	−0.511536
$561$	3.69280e86	0.944116
$562$	−1.47575e86	−0.356712
$563$	−6.77865e86	−1.54928	−0.774638	−	0.632405i	$-0.782068\pi$
$563$	−6.77865e86	−1.54928	−0.774638	+	0.632405i	$0.782068\pi$
$564$	−3.16219e86	−0.683434
$565$	1.17141e87	2.39433
$566$	1.10981e87	2.14551
$567$	−1.94413e86	−0.355516
$568$	3.98084e86	0.688656
$569$	−7.28196e86	−1.19182	−0.595912	−	0.803050i	$-0.703209\pi$
$569$	−7.28196e86	−1.19182	−0.595912	+	0.803050i	$0.703209\pi$
$570$	−2.19798e86	−0.340381
$571$	1.03258e87	1.51316	0.756579	−	0.653902i	$-0.226869\pi$
$571$	1.03258e87	1.51316	0.756579	+	0.653902i	$0.226869\pi$
$572$	−2.32428e87	−3.22339
$573$	2.24277e85	0.0294384
$574$	5.05670e86	0.628265
$575$	5.61579e86	0.660501
$576$	6.24152e86	0.694995
$577$	−3.16007e85	−0.0333164	−0.0166582	−	0.999861i	$-0.505303\pi$
$577$	−3.16007e85	−0.0333164	−0.0166582	+	0.999861i	$0.505303\pi$
$578$	−1.95059e86	−0.194733
$579$	−1.77184e86	−0.167514
$580$	1.13305e87	1.01453
$581$	1.18645e87	1.00624
$582$	−2.19768e86	−0.176559
$583$	1.44996e85	0.0110356
$584$	−3.49545e86	−0.252056
$585$	−1.41726e87	−0.968363
$586$	−2.17666e87	−1.40934
$587$	−1.43853e87	−0.882711	−0.441356	−	0.897332i	$-0.645502\pi$
$587$	−1.43853e87	−0.882711	−0.441356	+	0.897332i	$0.645502\pi$
$588$	−1.48743e86	−0.0865070
$589$	−4.64290e86	−0.255951
$590$	−4.76880e86	−0.249213
$591$	1.63819e87	0.811629
$592$	8.20323e86	0.385346
$593$	−2.93573e87	−1.30765	−0.653827	−	0.756644i	$-0.726838\pi$
$593$	−2.93573e87	−1.30765	−0.653827	+	0.756644i	$0.726838\pi$
$594$	5.34212e87	2.25653
$595$	−2.93216e87	−1.17463
$596$	2.78278e87	1.05736
$597$	−4.80948e86	−0.173343
$598$	7.07583e87	2.41930
$599$	−1.56895e87	−0.508938	−0.254469	−	0.967081i	$-0.581901\pi$
$599$	−1.56895e87	−0.508938	−0.254469	+	0.967081i	$0.581901\pi$
$600$	1.13547e87	0.349472
$601$	4.83029e86	0.141068	0.0705338	−	0.997509i	$-0.477530\pi$
$601$	4.83029e86	0.141068	0.0705338	+	0.997509i	$0.477530\pi$
$602$	−4.00599e87	−1.11025
$603$	1.03023e87	0.270982
$604$	−2.90583e87	−0.725450
$605$	4.48862e87	1.06370
$606$	−7.39892e87	−1.66449
$607$	4.23483e87	0.904465	0.452232	−	0.891900i	$-0.350628\pi$
$607$	4.23483e87	0.904465	0.452232	+	0.891900i	$0.350628\pi$
$608$	1.40970e87	0.285867
$609$	2.03826e87	0.392478
$610$	−1.85066e88	−3.38404
$611$	−6.25009e87	−1.08540
$612$	3.51849e87	0.580345
$613$	5.92849e87	0.928836	0.464418	−	0.885616i	$-0.346263\pi$
$613$	5.92849e87	0.928836	0.464418	+	0.885616i	$0.346263\pi$
$614$	1.64208e87	0.244394
$615$	2.92964e87	0.414236
$616$	−6.24175e87	−0.838521
$617$	−1.01610e87	−0.129704	−0.0648522	−	0.997895i	$-0.520658\pi$
$617$	−1.01610e87	−0.129704	−0.0648522	+	0.997895i	$0.520658\pi$
$618$	6.12741e87	0.743258
$619$	1.56773e88	1.80724	0.903622	−	0.428330i	$-0.140898\pi$
$619$	1.56773e88	1.80724	0.903622	+	0.428330i	$0.140898\pi$
$620$	1.94857e88	2.13490
$621$	−9.53720e87	−0.993197
$622$	−6.04174e87	−0.598088
$623$	−1.33045e87	−0.125206
$624$	−5.76568e87	−0.515864
$625$	−1.41403e88	−1.20293
$626$	1.20429e87	0.0974183
$627$	2.92306e87	0.224859
$628$	5.01666e87	0.367017
$629$	1.27167e88	0.884866
$630$	−1.29116e88	−0.854577
$631$	−5.69991e87	−0.358875	−0.179438	−	0.983769i	$-0.557428\pi$
$631$	−5.69991e87	−0.358875	−0.179438	+	0.983769i	$0.557428\pi$
$632$	−2.61769e87	−0.156794
$633$	−1.80335e88	−1.02769
$634$	4.04804e88	2.19499
$635$	1.54176e88	0.795507
$636$	−1.77558e86	−0.00871848
$637$	−2.93992e87	−0.137386
$638$	−2.56948e88	−1.14286
$639$	−1.09512e88	−0.463644
$640$	−3.85716e88	−1.55453
$641$	−3.75954e88	−1.44247	−0.721236	−	0.692690i	$-0.756426\pi$
$641$	−3.75954e88	−1.44247	−0.721236	+	0.692690i	$0.756426\pi$
$642$	7.66229e87	0.279902
$643$	5.08063e88	1.76714	0.883572	−	0.468296i	$-0.155132\pi$
$643$	5.08063e88	1.76714	0.883572	+	0.468296i	$0.155132\pi$
$644$	3.78029e88	1.25205
$645$	−2.32090e88	−0.732025
$646$	1.07852e88	0.323970
$647$	−1.87849e88	−0.537433	−0.268716	−	0.963219i	$-0.586599\pi$
$647$	−1.87849e88	−0.537433	−0.268716	+	0.963219i	$0.586599\pi$
$648$	−8.84674e87	−0.241085
$649$	6.34196e87	0.164632
$650$	7.61353e88	1.88285
$651$	3.50533e88	0.825900
$652$	−9.89705e88	−2.22181
$653$	6.60139e87	0.141211	0.0706057	−	0.997504i	$-0.477507\pi$
$653$	6.60139e87	0.141211	0.0706057	+	0.997504i	$0.477507\pi$
$654$	1.13365e89	2.31088
$655$	5.69127e88	1.10563
$656$	−9.27325e87	−0.171696
$657$	9.61588e87	0.169699
$658$	−5.69399e88	−0.957857
$659$	−4.59134e88	−0.736289	−0.368145	−	0.929768i	$-0.620007\pi$
$659$	−4.59134e88	−0.736289	−0.368145	+	0.929768i	$0.620007\pi$
$660$	−1.22678e89	−1.87556
$661$	−1.18619e89	−1.72906	−0.864529	−	0.502583i	$-0.832383\pi$
$661$	−1.18619e89	−1.72906	−0.864529	+	0.502583i	$0.832383\pi$
$662$	−5.64965e87	−0.0785226
$663$	−8.93795e88	−1.18457
$664$	5.39893e88	0.682359
$665$	−2.32097e88	−0.279761
$666$	5.59969e88	0.643763
$667$	4.58724e88	0.503023
$668$	1.72465e89	1.80403
$669$	1.07690e89	1.07461
$670$	−1.32537e89	−1.26177
$671$	2.46116e89	2.23553
$672$	−1.06431e89	−0.922432
$673$	4.18096e88	0.345781	0.172890	−	0.984941i	$-0.444689\pi$
$673$	4.18096e88	0.345781	0.172890	+	0.984941i	$0.444689\pi$
$674$	−2.84330e89	−2.24407
$675$	−1.02619e89	−0.772967
$676$	3.65323e89	2.62637
$677$	−1.54143e89	−1.05774	−0.528872	−	0.848702i	$-0.677385\pi$
$677$	−1.54143e89	−1.05774	−0.528872	+	0.848702i	$0.677385\pi$
$678$	3.25306e89	2.13087
$679$	−2.32065e88	−0.145115
$680$	−1.33427e89	−0.796552
$681$	6.65041e88	0.379066
$682$	−4.41889e89	−2.40495
$683$	1.37735e89	0.715800	0.357900	−	0.933760i	$-0.383493\pi$
$683$	1.37735e89	0.715800	0.357900	+	0.933760i	$0.383493\pi$
$684$	2.78508e88	0.138220
$685$	2.12715e89	1.00820
$686$	−3.56023e89	−1.61164
$687$	−1.56220e89	−0.675461
$688$	7.34641e88	0.303416
$689$	−3.50944e87	−0.0138463
$690$	3.73469e89	1.40769
$691$	−1.04508e89	−0.376349	−0.188175	−	0.982136i	$-0.560257\pi$
$691$	−1.04508e89	−0.376349	−0.188175	+	0.982136i	$0.560257\pi$
$692$	−5.40988e89	−1.86143
$693$	1.71709e89	0.564542
$694$	6.26836e89	1.96938
$695$	−2.82205e89	−0.847313
$696$	9.27507e88	0.266150
$697$	−1.43754e89	−0.394264
$698$	−2.74599e89	−0.719867
$699$	1.48461e89	0.372032
$700$	4.06756e89	0.974419
$701$	1.99798e89	0.457588	0.228794	−	0.973475i	$-0.426522\pi$
$701$	1.99798e89	0.457588	0.228794	+	0.973475i	$0.426522\pi$
$702$	−1.29299e90	−2.83124
$703$	1.00660e89	0.210747
$704$	1.06784e90	2.13780
$705$	−3.29885e89	−0.631548
$706$	1.40829e90	2.57837
$707$	−7.81294e89	−1.36805
$708$	−7.76619e88	−0.130065
$709$	−5.01550e89	−0.803449	−0.401724	−	0.915761i	$-0.631589\pi$
$709$	−5.01550e89	−0.803449	−0.401724	+	0.915761i	$0.631589\pi$
$710$	1.40884e90	2.15886
$711$	7.20119e88	0.105563
$712$	−6.05419e88	−0.0849056
$713$	7.88897e89	1.05852
$714$	−8.14270e89	−1.04538
$715$	−2.42473e90	−2.97867
$716$	−1.40890e90	−1.65623
$717$	9.39007e89	1.05637
$718$	−1.62756e90	−1.75233
$719$	8.38497e89	0.864055	0.432028	−	0.901860i	$-0.357798\pi$
$719$	8.38497e89	0.864055	0.432028	+	0.901860i	$0.357798\pi$
$720$	2.36779e89	0.233544
$721$	6.47028e89	0.610889
$722$	−1.63510e90	−1.47783
$723$	8.62424e89	0.746216
$724$	1.07883e90	0.893690
$725$	4.93583e89	0.391483
$726$	1.24651e90	0.946653
$727$	1.03681e90	0.753988	0.376994	−	0.926216i	$-0.376958\pi$
$727$	1.03681e90	0.753988	0.376994	+	0.926216i	$0.376958\pi$
$728$	1.51074e90	1.05208
$729$	1.45566e90	0.970827
$730$	−1.23706e90	−0.790168
$731$	1.13884e90	0.696732
$732$	−3.01387e90	−1.76614
$733$	−3.18443e90	−1.78754	−0.893771	−	0.448523i	$-0.851950\pi$
$733$	−3.18443e90	−1.78754	−0.893771	+	0.448523i	$0.851950\pi$
$734$	4.27738e90	2.30013
$735$	−1.55172e89	−0.0799394
$736$	−2.39529e90	−1.18224
$737$	1.76259e90	0.833536
$738$	−6.33011e89	−0.286837
$739$	−3.22969e89	−0.140236	−0.0701181	−	0.997539i	$-0.522338\pi$
$739$	−3.22969e89	−0.140236	−0.0701181	+	0.997539i	$0.522338\pi$
$740$	−4.22457e90	−1.75786
$741$	−7.07490e89	−0.282128
$742$	−3.19719e88	−0.0122193
$743$	−2.59061e90	−0.948974	−0.474487	−	0.880262i	$-0.657366\pi$
$743$	−2.59061e90	−0.948974	−0.474487	+	0.880262i	$0.657366\pi$
$744$	1.59509e90	0.560065
$745$	2.90304e90	0.977081
$746$	7.18218e89	0.231731
$747$	−1.48523e90	−0.459404
$748$	6.01964e90	1.78513
$749$	8.09105e89	0.230053
$750$	−1.58635e90	−0.432484
$751$	−5.64788e90	−1.47648	−0.738240	−	0.674538i	$-0.764343\pi$
$751$	−5.64788e90	−1.47648	−0.738240	+	0.674538i	$0.764343\pi$
$752$	1.04419e90	0.261770
$753$	2.65422e90	0.638110
$754$	6.21909e90	1.43394
$755$	−3.03142e90	−0.670374
$756$	−6.90788e90	−1.46524
$757$	−2.35445e90	−0.479037	−0.239519	−	0.970892i	$-0.576990\pi$
$757$	−2.35445e90	−0.479037	−0.239519	+	0.970892i	$0.576990\pi$
$758$	7.92139e90	1.54604
$759$	−4.96671e90	−0.929936
$760$	−1.05615e90	−0.189714
$761$	5.15918e89	0.0889128	0.0444564	−	0.999011i	$-0.485844\pi$
$761$	5.15918e89	0.0889128	0.0444564	+	0.999011i	$0.485844\pi$
$762$	4.28152e90	0.707972
$763$	1.19708e91	1.89933
$764$	3.65595e89	0.0556621
$765$	3.67055e90	0.536285
$766$	−5.81531e90	−0.815392
$767$	−1.53499e90	−0.206563
$768$	−1.48962e90	−0.192397
$769$	3.98793e90	0.494388	0.247194	−	0.968966i	$-0.420492\pi$
$769$	3.98793e90	0.494388	0.247194	+	0.968966i	$0.420492\pi$
$770$	−2.20899e91	−2.62867
$771$	−3.07697e90	−0.351488
$772$	−2.88829e90	−0.316735
$773$	−5.31617e90	−0.559687	−0.279843	−	0.960046i	$-0.590282\pi$
$773$	−5.31617e90	−0.559687	−0.279843	+	0.960046i	$0.590282\pi$
$774$	5.01481e90	0.506890
$775$	8.48846e90	0.823807
$776$	−1.05601e90	−0.0984065
$777$	−7.59966e90	−0.680037
$778$	7.02043e90	0.603263
$779$	−1.13789e90	−0.0939014
$780$	2.96926e91	2.35325
$781$	−1.87360e91	−1.42616
$782$	−1.83257e91	−1.33982
$783$	−8.38245e90	−0.588675
$784$	4.91168e89	0.0331340
$785$	5.23348e90	0.339153
$786$	1.58048e91	0.983966
$787$	2.94356e91	1.76063	0.880315	−	0.474389i	$-0.157331\pi$
$787$	2.94356e91	1.76063	0.880315	+	0.474389i	$0.157331\pi$
$788$	2.67041e91	1.53463
$789$	1.14826e91	0.634035
$790$	−9.26414e90	−0.491532
$791$	3.43509e91	1.75137
$792$	7.81359e90	0.382831
$793$	−5.95693e91	−2.80490
$794$	−6.32352e91	−2.86163
$795$	−1.85232e89	−0.00805658
$796$	−7.83995e90	−0.327757
$797$	−4.20154e90	−0.168838	−0.0844192	−	0.996430i	$-0.526903\pi$
$797$	−4.20154e90	−0.168838	−0.0844192	+	0.996430i	$0.526903\pi$
$798$	−6.44541e90	−0.248977
$799$	1.61871e91	0.601098
$800$	−2.57731e91	−0.920094
$801$	1.66549e90	0.0571634
$802$	−2.79722e91	−0.923069
$803$	1.64514e91	0.521992
$804$	−2.15841e91	−0.658520
$805$	3.94367e91	1.15699
$806$	1.06954e92	3.01746
$807$	3.28769e90	0.0892020
$808$	−3.55527e91	−0.927714
$809$	1.39812e91	0.350886	0.175443	−	0.984490i	$-0.443864\pi$
$809$	1.39812e91	0.350886	0.175443	+	0.984490i	$0.443864\pi$
$810$	−3.13091e91	−0.755774
$811$	−3.59866e90	−0.0835571	−0.0417786	−	0.999127i	$-0.513302\pi$
$811$	−3.59866e90	−0.0835571	−0.0417786	+	0.999127i	$0.513302\pi$
$812$	3.32258e91	0.742096
$813$	−1.03351e91	−0.222055
$814$	9.58030e91	1.98021
$815$	−1.03248e92	−2.05313
$816$	1.49325e91	0.285689
$817$	9.01457e90	0.165940
$818$	−9.34613e91	−1.65540
$819$	−4.15600e91	−0.708325
$820$	4.77562e91	0.783237
$821$	−2.87760e91	−0.454173	−0.227087	−	0.973875i	$-0.572920\pi$
$821$	−2.87760e91	−0.454173	−0.227087	+	0.973875i	$0.572920\pi$
$822$	5.90717e91	0.897258
$823$	1.30669e92	1.91020	0.955098	−	0.296290i	$-0.0957496\pi$
$823$	1.30669e92	1.91020	0.955098	+	0.296290i	$0.0957496\pi$
$824$	2.94429e91	0.414260
$825$	−5.34414e91	−0.723733
$826$	−1.39841e91	−0.182291
$827$	−6.67625e91	−0.837740	−0.418870	−	0.908046i	$-0.637574\pi$
$827$	−6.67625e91	−0.837740	−0.418870	+	0.908046i	$0.637574\pi$
$828$	−4.73227e91	−0.571628
$829$	−1.02129e92	−1.18763	−0.593814	−	0.804603i	$-0.702378\pi$
$829$	−1.02129e92	−1.18763	−0.593814	+	0.804603i	$0.702378\pi$
$830$	1.91071e92	2.13912
$831$	3.54661e91	0.382280
$832$	−2.58457e92	−2.68227
$833$	7.61409e90	0.0760853
$834$	−7.83693e91	−0.754077
$835$	1.79919e92	1.66707
$836$	4.76489e91	0.425163
$837$	−1.44158e92	−1.23876
$838$	2.68428e91	0.222147
$839$	−5.22788e91	−0.416700	−0.208350	−	0.978054i	$-0.566809\pi$
$839$	−5.22788e91	−0.416700	−0.208350	+	0.978054i	$0.566809\pi$
$840$	7.97382e91	0.612165
$841$	−9.49120e91	−0.701855
$842$	3.06480e92	2.18309
$843$	−2.50718e91	−0.172035
$844$	−2.93965e92	−1.94316
$845$	3.81112e92	2.42698
$846$	7.12788e91	0.437314
$847$	1.31626e92	0.778060
$848$	5.86318e89	0.00333936
$849$	1.88548e92	1.03474
$850$	−1.97183e92	−1.04273
$851$	−1.71035e92	−0.871575
$852$	2.29436e92	1.12671
$853$	2.86871e91	0.135766	0.0678832	−	0.997693i	$-0.478375\pi$
$853$	2.86871e91	0.135766	0.0678832	+	0.997693i	$0.478375\pi$
$854$	−5.42691e92	−2.47531
$855$	2.90545e91	0.127726
$856$	3.68182e91	0.156005
$857$	1.42668e92	0.582679	0.291340	−	0.956620i	$-0.405899\pi$
$857$	1.42668e92	0.582679	0.291340	+	0.956620i	$0.405899\pi$
$858$	−6.73355e92	−2.65091
$859$	−2.36785e92	−0.898608	−0.449304	−	0.893379i	$-0.648328\pi$
$859$	−2.36785e92	−0.898608	−0.449304	+	0.893379i	$0.648328\pi$
$860$	−3.78331e92	−1.38411
$861$	8.59095e91	0.303000
$862$	6.23152e92	2.11892
$863$	3.48284e92	1.14181	0.570905	−	0.821016i	$-0.306592\pi$
$863$	3.48284e92	1.14181	0.570905	+	0.821016i	$0.306592\pi$
$864$	4.37701e92	1.38355
$865$	−5.64369e92	−1.72011
$866$	−2.04100e92	−0.599833
$867$	−3.31391e91	−0.0939159
$868$	5.71405e92	1.56161
$869$	1.23202e92	0.324711
$870$	3.28250e92	0.834349
$871$	−4.26612e92	−1.04583
$872$	5.44729e92	1.28799
$873$	2.90506e91	0.0662530
$874$	−1.45058e92	−0.319104
$875$	−1.67512e92	−0.355462
$876$	−2.01460e92	−0.412391
$877$	7.38143e92	1.45765	0.728825	−	0.684700i	$-0.240067\pi$
$877$	7.38143e92	1.45765	0.728825	+	0.684700i	$0.240067\pi$
$878$	−1.43814e91	−0.0273983
$879$	−3.69798e92	−0.679696
$880$	4.05096e92	0.718380
$881$	−4.66751e92	−0.798627	−0.399313	−	0.916814i	$-0.630751\pi$
$881$	−4.66751e92	−0.798627	−0.399313	+	0.916814i	$0.630751\pi$
$882$	3.35281e91	0.0553540
$883$	−5.66714e92	−0.902821	−0.451410	−	0.892316i	$-0.649079\pi$
$883$	−5.66714e92	−0.902821	−0.451410	+	0.892316i	$0.649079\pi$
$884$	−1.45698e93	−2.23979
$885$	−8.10183e91	−0.120190
$886$	6.08851e92	0.871664
$887$	4.96787e91	0.0686398	0.0343199	−	0.999411i	$-0.489073\pi$
$887$	4.96787e91	0.0686398	0.0343199	+	0.999411i	$0.489073\pi$
$888$	−3.45821e92	−0.461151
$889$	4.52110e92	0.581887
$890$	−2.14261e92	−0.266169
$891$	4.16375e92	0.499271
$892$	1.75545e93	2.03187
$893$	1.28130e92	0.143163
$894$	8.06184e92	0.869566
$895$	−1.46979e93	−1.53049
$896$	−1.13109e93	−1.13709
$897$	1.20213e93	1.16678
$898$	−1.94810e93	−1.82561
$899$	6.93378e92	0.627393
$900$	−5.09188e92	−0.444876
$901$	9.08910e90	0.00766814
$902$	−1.08299e93	−0.882308
$903$	−6.80588e92	−0.535452
$904$	1.56313e93	1.18765
$905$	1.12545e93	0.825842
$906$	−8.41835e92	−0.596608
$907$	1.79893e93	1.23136	0.615680	−	0.787997i	$-0.288882\pi$
$907$	1.79893e93	1.23136	0.615680	+	0.787997i	$0.288882\pi$
$908$	1.08409e93	0.716737
$909$	9.78044e92	0.624592
$910$	5.34658e93	3.29816
$911$	−8.99801e92	−0.536188	−0.268094	−	0.963393i	$-0.586394\pi$
$911$	−8.99801e92	−0.536188	−0.268094	+	0.963393i	$0.586394\pi$
$912$	1.18199e92	0.0680421
$913$	−2.54102e93	−1.41312
$914$	−4.64208e93	−2.49406
$915$	−3.14412e93	−1.63206
$916$	−2.54655e93	−1.27716
$917$	1.66892e93	0.808728
$918$	3.34872e93	1.56796
$919$	−1.85074e93	−0.837348	−0.418674	−	0.908137i	$-0.637505\pi$
$919$	−1.85074e93	−0.837348	−0.418674	+	0.908137i	$0.637505\pi$
$920$	1.79456e93	0.784587
$921$	2.78977e92	0.117867
$922$	−6.54056e93	−2.67049
$923$	4.53481e93	1.78939
$924$	−3.59743e93	−1.37191
$925$	−1.84033e93	−0.678313
$926$	3.51244e93	1.25131
$927$	−8.09966e92	−0.278904
$928$	−2.10527e93	−0.700724
$929$	3.53579e93	1.13760	0.568802	−	0.822475i	$-0.307407\pi$
$929$	3.53579e93	1.13760	0.568802	+	0.822475i	$0.307407\pi$
$930$	5.64511e93	1.75574
$931$	6.02699e91	0.0181211
$932$	2.42006e93	0.703438
$933$	−1.02645e93	−0.288446
$934$	2.09543e93	0.569308
$935$	6.27980e93	1.64961
$936$	−1.89118e93	−0.480334
$937$	1.39400e93	0.342346	0.171173	−	0.985241i	$-0.445244\pi$
$937$	1.39400e93	0.342346	0.171173	+	0.985241i	$0.445244\pi$
$938$	−3.88654e93	−0.922940
$939$	2.04600e92	0.0469829
$940$	−5.37748e93	−1.19413
$941$	−4.43425e93	−0.952241	−0.476120	−	0.879380i	$-0.657957\pi$
$941$	−4.43425e93	−0.952241	−0.476120	+	0.879380i	$0.657957\pi$
$942$	1.45335e93	0.301834
$943$	1.93345e93	0.388342
$944$	2.56449e92	0.0498176
$945$	−7.20642e93	−1.35400
$946$	8.57964e93	1.55919
$947$	−7.29795e93	−1.28285	−0.641426	−	0.767185i	$-0.721657\pi$
$947$	−7.29795e93	−1.28285	−0.641426	+	0.767185i	$0.721657\pi$
$948$	−1.50870e93	−0.256532
$949$	−3.98186e93	−0.654939
$950$	−1.56081e93	−0.248346
$951$	6.87731e93	1.05860
$952$	−3.91266e93	−0.582650
$953$	−5.59234e93	−0.805689	−0.402844	−	0.915268i	$-0.631978\pi$
$953$	−5.59234e93	−0.805689	−0.402844	+	0.915268i	$0.631978\pi$
$954$	4.00232e91	0.00557877
$955$	3.81396e92	0.0514363
$956$	1.53068e94	1.99738
$957$	−4.36535e93	−0.551179
$958$	1.83481e94	2.24170
$959$	6.23772e93	0.737462
$960$	−1.36416e94	−1.56071
$961$	2.89240e93	0.320237
$962$	−2.31879e94	−2.48454
$963$	−1.01286e93	−0.105032
$964$	1.40584e94	1.41094
$965$	−3.01311e93	−0.292688
$966$	1.09517e94	1.02968
$967$	−1.35469e94	−1.23284	−0.616419	−	0.787418i	$-0.711417\pi$
$967$	−1.35469e94	−1.23284	−0.616419	+	0.787418i	$0.711417\pi$
$968$	5.98960e93	0.527623
$969$	1.83233e93	0.156244
$970$	−3.73727e93	−0.308493
$971$	1.40182e94	1.12018	0.560088	−	0.828433i	$-0.310767\pi$
$971$	1.40182e94	1.12018	0.560088	+	0.828433i	$0.310767\pi$
$972$	1.46627e94	1.13430
$973$	−8.27547e93	−0.619781
$974$	−3.24882e94	−2.35569
$975$	1.29348e94	0.908060
$976$	9.95217e93	0.676470
$977$	2.67935e94	1.76340	0.881700	−	0.471810i	$-0.156399\pi$
$977$	2.67935e94	1.76340	0.881700	+	0.471810i	$0.156399\pi$
$978$	−2.86723e94	−1.82721
$979$	2.84943e93	0.175834
$980$	−2.52946e93	−0.151149
$981$	−1.49854e94	−0.867149
$982$	−3.41280e94	−1.91249
$983$	1.93233e94	1.04868	0.524342	−	0.851508i	$-0.324311\pi$
$983$	1.93233e94	1.04868	0.524342	+	0.851508i	$0.324311\pi$
$984$	3.90930e93	0.205472
$985$	2.78582e94	1.41812
$986$	−1.61068e94	−0.794122
$987$	−9.67365e93	−0.461956
$988$	−1.15328e94	−0.533448
$989$	−1.53171e94	−0.686267
$990$	2.76527e94	1.20013
$991$	−2.43225e94	−1.02256	−0.511279	−	0.859415i	$-0.670828\pi$
$991$	−2.43225e94	−1.02256	−0.511279	+	0.859415i	$0.670828\pi$
$992$	−3.62057e94	−1.47455
$993$	−9.59833e92	−0.0378699
$994$	4.13132e94	1.57913
$995$	−8.17878e93	−0.302874
$996$	3.11167e94	1.11641
$997$	3.29728e94	1.14619	0.573097	−	0.819487i	$-0.305742\pi$
$997$	3.29728e94	1.14619	0.573097	+	0.819487i	$0.305742\pi$
$998$	6.12246e94	2.06212
$999$	3.12540e94	1.01998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.64.a.a.1.5	✓	5
3.2	odd	2		9.64.a.c.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.64.a.a.1.5	✓	5	1.1	even	1	trivial
9.64.a.c.1.1		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 64 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+4.72250e9 q^{2} +8.02316e14 q^{3} +1.30786e19 q^{4} +1.36438e22 q^{5} +3.78894e24 q^{6} +4.00095e26 q^{7} +1.82063e28 q^{8} -5.00850e29 q^{9} +O(q^{10})\)	\(q+4.72250e9 q^{2} +8.02316e14 q^{3} +1.30786e19 q^{4} +1.36438e22 q^{5} +3.78894e24 q^{6} +4.00095e26 q^{7} +1.82063e28 q^{8} -5.00850e29 q^{9} +6.44329e31 q^{10} -8.56884e32 q^{11} +1.04932e34 q^{12} +2.07398e35 q^{13} +1.88945e36 q^{14} +1.09467e37 q^{15} -3.46497e37 q^{16} -5.37140e38 q^{17} -2.36526e39 q^{18} -4.25177e39 q^{19} +1.78442e41 q^{20} +3.21003e41 q^{21} -4.04663e42 q^{22} +7.22439e42 q^{23} +1.46072e43 q^{24} +7.77338e43 q^{25} +9.79436e44 q^{26} -1.32014e45 q^{27} +5.23268e45 q^{28} +6.34966e45 q^{29} +5.16956e46 q^{30} +1.09199e47 q^{31} -3.31556e47 q^{32} -6.87492e47 q^{33} -2.53664e48 q^{34} +5.45883e48 q^{35} -6.55041e48 q^{36} -2.36747e49 q^{37} -2.00790e49 q^{38} +1.66399e50 q^{39} +2.48403e50 q^{40} +2.67628e50 q^{41} +1.51594e51 q^{42} -2.12019e51 q^{43} -1.12068e52 q^{44} -6.83350e51 q^{45} +3.41171e52 q^{46} -3.01357e52 q^{47} -2.78000e52 q^{48} -1.41752e52 q^{49} +3.67097e53 q^{50} -4.30956e53 q^{51} +2.71247e54 q^{52} -1.69213e52 q^{53} -6.23436e54 q^{54} -1.16912e55 q^{55} +7.28424e54 q^{56} -3.41127e54 q^{57} +2.99863e55 q^{58} -7.40118e54 q^{59} +1.43167e56 q^{60} -2.87222e56 q^{61} +5.15693e56 q^{62} -2.00388e56 q^{63} -1.24619e57 q^{64} +2.82970e57 q^{65} -3.24668e57 q^{66} -2.05697e57 q^{67} -7.02504e57 q^{68} +5.79624e57 q^{69} +2.57793e58 q^{70} +2.18652e58 q^{71} -9.11860e57 q^{72} -1.91991e58 q^{73} -1.11804e59 q^{74} +6.23671e58 q^{75} -5.56072e58 q^{76} -3.42835e59 q^{77} +7.85818e59 q^{78} -1.43780e59 q^{79} -4.72755e59 q^{80} -4.85917e59 q^{81} +1.26387e60 q^{82} +2.96542e60 q^{83} +4.19827e60 q^{84} -7.32865e60 q^{85} -1.00126e61 q^{86} +5.09444e60 q^{87} -1.56007e61 q^{88} -3.32533e60 q^{89} -3.22712e61 q^{90} +8.29790e61 q^{91} +9.44848e61 q^{92} +8.76123e61 q^{93} -1.42316e62 q^{94} -5.80104e61 q^{95} -2.66013e62 q^{96} -5.80025e61 q^{97} -6.69425e61 q^{98} +4.29170e62 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 507315096 q^{2} + 953245351116252 q^{3} + 67\!\cdots\!40 q^{4}+ \cdots + 63\!\cdots\!85 q^{9}+O(q^{10}) \) 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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