LMFDB - Embedded newform 3.68.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,68,Mod(1,3)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 68, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 68);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 68 $
Character orbit:	$[\chi]$	$=$	3.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:	$85.2871055790$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} + \cdots - 17\!\cdots\!00 $ x^5 - x^4 - 189398708752260728x^3 + 10367208713972597963236992x^2 + 3357934964760116559921767608965120*x - 178120650251916997056936485095832786534400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{40}\cdot 3^{20}\cdot 5^{3}\cdot 7^{2}\cdot 11\cdot 17 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$5.25899e7$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.77536e9 q^{2} +5.55906e15 q^{3} -1.14219e20 q^{4} +1.87613e23 q^{5} -3.21056e25 q^{6} +3.73645e28 q^{7} +1.51195e30 q^{8} +3.09032e31 q^{9} +O(q^{10})$	\(q-5.77536e9 q^{2} +5.55906e15 q^{3} -1.14219e20 q^{4} +1.87613e23 q^{5} -3.21056e25 q^{6} +3.73645e28 q^{7} +1.51195e30 q^{8} +3.09032e31 q^{9} -1.08353e33 q^{10} -1.19107e35 q^{11} -6.34951e35 q^{12} -2.41304e37 q^{13} -2.15793e38 q^{14} +1.04295e39 q^{15} +8.12372e39 q^{16} +2.68293e40 q^{17} -1.78477e41 q^{18} -8.49620e42 q^{19} -2.14290e43 q^{20} +2.07711e44 q^{21} +6.87885e44 q^{22} +2.56434e45 q^{23} +8.40502e45 q^{24} -3.25640e46 q^{25} +1.39362e47 q^{26} +1.71793e47 q^{27} -4.26774e48 q^{28} -8.53400e48 q^{29} -6.02342e48 q^{30} +9.91932e49 q^{31} -2.70042e50 q^{32} -6.62122e50 q^{33} -1.54949e50 q^{34} +7.01006e51 q^{35} -3.52973e51 q^{36} -1.57434e52 q^{37} +4.90686e52 q^{38} -1.34142e53 q^{39} +2.83661e53 q^{40} +1.78297e54 q^{41} -1.19961e54 q^{42} -5.13445e54 q^{43} +1.36043e55 q^{44} +5.79783e54 q^{45} -1.48100e55 q^{46} -1.02776e56 q^{47} +4.51603e55 q^{48} +9.77728e56 q^{49} +1.88069e56 q^{50} +1.49145e56 q^{51} +2.75616e57 q^{52} -9.83914e57 q^{53} -9.92163e56 q^{54} -2.23460e58 q^{55} +5.64932e58 q^{56} -4.72309e58 q^{57} +4.92869e58 q^{58} -2.18323e59 q^{59} -1.19125e59 q^{60} +5.16004e59 q^{61} -5.72876e59 q^{62} +1.15468e60 q^{63} +3.60738e59 q^{64} -4.52718e60 q^{65} +3.82399e60 q^{66} +8.46980e60 q^{67} -3.06442e60 q^{68} +1.42553e61 q^{69} -4.04856e61 q^{70} +2.04432e61 q^{71} +4.67240e61 q^{72} -1.75945e62 q^{73} +9.09236e61 q^{74} -1.81025e62 q^{75} +9.70430e62 q^{76} -4.45037e63 q^{77} +7.74721e62 q^{78} -1.13903e62 q^{79} +1.52412e63 q^{80} +9.55005e62 q^{81} -1.02973e64 q^{82} +1.01962e64 q^{83} -2.37246e64 q^{84} +5.03352e63 q^{85} +2.96533e64 q^{86} -4.74410e64 q^{87} -1.80084e65 q^{88} -2.83149e65 q^{89} -3.34846e64 q^{90} -9.01621e65 q^{91} -2.92897e65 q^{92} +5.51421e65 q^{93} +5.93569e65 q^{94} -1.59400e66 q^{95} -1.50118e66 q^{96} -4.28149e66 q^{97} -5.64673e66 q^{98} -3.68078e66 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 16255223088 q^{2} + 27\!\cdots\!15 q^{3}+ \cdots + 15\!\cdots\!45 q^{9}+O(q^{10}) $ 5 * q - 16255223088 * q^2 + 27795302832777615 * q^3 + 187725942510165022976 * q^4 - 78587975159033653413210 * q^5 - 90363769669063698103515024 * q^6 + 2897133779647323835395360808 * q^7 - 446560396075670111196535861248 * q^8 + 154515771913163061809603209017645 * q^9	$ 5 q - 16255223088 q^{2} + 27\!\cdots\!15 q^{3}+ \cdots - 33\!\cdots\!28 q^{99}+O(q^{100}) $ 5 * q - 16255223088 * q^2 + 27795302832777615 * q^3 + 187725942510165022976 * q^4 - 78587975159033653413210 * q^5 - 90363769669063698103515024 * q^6 + 2897133779647323835395360808 * q^7 - 446560396075670111196535861248 * q^8 + 154515771913163061809603209017645 * q^9 - 3359687674843328387731353730265760 * q^10 - 107218677940017498877929099247513932 * q^11 + 1043579884327727512139439968474696448 * q^12 + 18720658700128270654310089005018371278 * q^13 - 61671302560002915461244055855418861952 * q^14 - 436875313712028989080558866721926658830 * q^15 + 19828810558474760279626207936836822695936 * q^16 + 155634077783406813100849154582687160437850 * q^17 - 502337668612598026687246628668502560677552 * q^18 - 6330823499631802877762269921902501094783988 * q^19 + 8806685958461200090592049790099809534328320 * q^20 + 16105342150473395769449245566105034350142584 * q^21 - 1285334407460495219610552944494458560199940800 * q^22 - 3096470811979061341218583695224599825546419864 * q^23 - 2482456288409673438086642069250837537616072704 * q^24 - 128510195883326013861116838537875526813134026525 * q^25 - 309893301421656093037055250012280159780714544160 * q^26 + 858962534553352218394101882942702121170179203335 * q^27 - 1758216414458764947454106710991446824456120252416 * q^28 - 17195448123638013107201791699494703244624614194066 * q^29 - 18676707269164160844617717039655071934318585792480 * q^30 - 167299848682287535534976349940903215242774636120144 * q^31 - 661581347508711830434048681313730640500855508303872 * q^32 - 596035124534567832987517244399918779918082194046436 * q^33 - 3668629124130223548817939535033459308602451741777248 * q^34 - 597313366964957875633721976544849058693729215396560 * q^35 + 5801323783016844061209039192798206302504038362882304 * q^36 + 30043361009726020519419208243072073319518814491934358 * q^37 + 260485037699007543111228693866771891318790849526359744 * q^38 + 104069275559827645019221591022442107451411644015468394 * q^39 + 1115094440991577594559320173651217718577849903091507200 * q^40 - 808437303878393630827363118778237447937170861730235454 * q^41 - 342834506149426883197674031813537074530930837280160896 * q^42 - 4736429276246859157617871173658532851277246462721149228 * q^43 + 7015258532306255548162192439376864244003799076792468480 * q^44 - 2428616328958113717945826873336511479963953561073218090 * q^45 + 12527540911364294799696045411504819449186256978468080256 * q^46 + 108290076402229329642983829719434835232002632660130515056 * q^47 + 110229558857316837304648760016604589737407028314290454528 * q^48 + 880181676573802609519730686079181363021552872382740232333 * q^49 + 1052494889081109131658159592164188937755980711801220679600 * q^50 + 865179264617971813637134219389277404805805348251015745550 * q^51 + 2308777474667263284772763232859451620790190619345360422400 * q^52 + 3245226878182367959789303611224433348480161481518744370966 * q^53 - 2792525524679729749647164642126896980230414112629707719696 * q^54 - 51262912349629136715335621059095130466245073679837843274920 * q^55 - 47772133165991162191839606887952190261990284108568121671680 * q^56 - 35193431270626188960239511075559223006610539094694893365724 * q^57 - 84493666334602655307554841072065967874913257934429532582432 * q^58 - 179624529165245332659094970865033289643789158511842592792412 * q^59 + 48956900633719888068348132839178395661941003500967791311360 * q^60 + 584907690374744349731719712847344294312321913116060488567102 * q^61 + 3025719874056683992201295546200663430948598802434153503920896 * q^62 + 89530572459581180641513960803016595914572442189036802691432 * q^63 - 4499392031332841330291967248952523929085218266739063232921600 * q^64 - 4475515698809998982184518632813763939217510489440113220535420 * q^65 - 7145251819350648004204211437078044590913023079552444513038400 * q^66 + 1344914323542783268647242614869504266340689501787079942327420 * q^67 + 19365780359678204058695683499114787965920302224535027287671296 * q^68 - 17213468786362961074546343099951406673447837437328506826108872 * q^69 + 31668988367649764945620440396543964676121485136652812185168640 * q^70 + 208099792629824800554470944953685171609425458107698538896812280 * q^71 - 13800124861096000027311301435875177780070484438004484020744192 * q^72 - 252414514587179259177941988046481265295589404121206374617470334 * q^73 - 358084904219721857079108717596560064061662918994206334990793632 * q^74 - 714395962335323550124996935032662148018445244009738166967247575 * q^75 - 3167576238289455647607470438405921376289304779045740803124282368 * q^76 - 2715616264867565296962962180641800513550454260043685733361085024 * q^77 - 1722715631772832981701583674878761695633721340944383480275395680 * q^78 - 3431503850832591202644393930474874375763697022794649483222945280 * q^79 - 8322155504340769679256255462767373452465836703993138541717749760 * q^80 + 4775024753984126184465953508872070059599675694871715649184269205 * q^81 - 6362169783346643199240774371522649930233919884701663896646628064 * q^82 - 2753559226275970537111940225815871118779223599597864793376534836 * q^83 - 9774031537088362109664563191733058527530044006822089118438893568 * q^84 - 100223085545462292798863671541625307722645907180923010395975039060 * q^85 - 287767761108017143223082018540844348985876033069110036187064944832 * q^86 - 95590537588367238050824370796559187863343340269759771352286126518 * q^87 - 475509956271309169302126186902650458005506404316097446988140167168 * q^88 - 953231813381767774308665680609247777419192406201469535932206722638 * q^89 - 103824946893111374784083486264977336654984096886031891078875867040 * q^90 - 1826343975172985917715752368227201077015187248090890361406237190544 * q^91 - 3132766731772277225542233484759817592417648594742828753496091850752 * q^92 - 930029991600410615305341159302088161126938972921803642822874755312 * q^93 - 4377709041417318550457656800988375516480152699177767581662212342016 * q^94 - 3334812729598028343033336500168508357868459521335461166424246211800 * q^95 - 3677770780504345932935680810193675103543675932078897134851043885056 * q^96 - 11968150959482375162440074477550294838351889417758320270285978711190 * q^97 - 17297597363568888846780657367452226513119832175100344485603054876848 * q^98 - 3313395357082126364699797809873297365206219515646735115126034266028 * 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 $

$2$	−5.77536e9	−0.475416	−0.237708	−	0.971337i	$-0.576396\pi$
$2$	−5.77536e9	−0.475416	−0.237708	+	0.971337i	$0.576396\pi$
$3$	5.55906e15	0.577350
$3$	5.55906e15	0.577350
$4$	−1.14219e20	−0.773979
$5$	1.87613e23	0.720722	0.360361	−	0.932813i	$-0.382654\pi$
$5$	1.87613e23	0.720722	0.360361	+	0.932813i	$0.382654\pi$
$6$	−3.21056e25	−0.274482
$7$	3.73645e28	1.82673	0.913366	−	0.407140i	$-0.133474\pi$
$7$	3.73645e28	1.82673	0.913366	+	0.407140i	$0.133474\pi$
$8$	1.51195e30	0.843379
$9$	3.09032e31	0.333333
$10$	−1.08353e33	−0.342643
$11$	−1.19107e35	−1.54626	−0.773129	−	0.634249i	$-0.781309\pi$
$11$	−1.19107e35	−1.54626	−0.773129	+	0.634249i	$0.781309\pi$
$12$	−6.34951e35	−0.446857
$13$	−2.41304e37	−1.16269	−0.581343	−	0.813658i	$-0.697473\pi$
$13$	−2.41304e37	−1.16269	−0.581343	+	0.813658i	$0.697473\pi$
$14$	−2.15793e38	−0.868458
$15$	1.04295e39	0.416109
$16$	8.12372e39	0.373023
$17$	2.68293e40	0.161648	0.0808239	−	0.996728i	$-0.474245\pi$
$17$	2.68293e40	0.161648	0.0808239	+	0.996728i	$0.474245\pi$
$18$	−1.78477e41	−0.158472
$19$	−8.49620e42	−1.23305	−0.616523	−	0.787337i	$-0.711459\pi$
$19$	−8.49620e42	−1.23305	−0.616523	+	0.787337i	$0.711459\pi$
$20$	−2.14290e43	−0.557824
$21$	2.07711e44	1.05466
$22$	6.87885e44	0.735116
$23$	2.56434e45	0.618149	0.309074	−	0.951038i	$-0.399981\pi$
$23$	2.56434e45	0.618149	0.309074	+	0.951038i	$0.399981\pi$
$24$	8.40502e45	0.486925
$25$	−3.25640e46	−0.480560
$26$	1.39362e47	0.552760
$27$	1.71793e47	0.192450
$28$	−4.26774e48	−1.41385
$29$	−8.53400e48	−0.872610	−0.436305	−	0.899799i	$-0.643713\pi$
$29$	−8.53400e48	−0.872610	−0.436305	+	0.899799i	$0.643713\pi$
$30$	−6.02342e48	−0.197825
$31$	9.91932e49	1.08609	0.543044	−	0.839704i	$-0.317272\pi$
$31$	9.91932e49	1.08609	0.543044	+	0.839704i	$0.317272\pi$
$32$	−2.70042e50	−1.02072
$33$	−6.62122e50	−0.892732
$34$	−1.54949e50	−0.0768500
$35$	7.01006e51	1.31657
$36$	−3.52973e51	−0.257993
$37$	−1.57434e52	−0.459557	−0.229779	−	0.973243i	$-0.573800\pi$
$37$	−1.57434e52	−0.459557	−0.229779	+	0.973243i	$0.573800\pi$
$38$	4.90686e52	0.586210
$39$	−1.34142e53	−0.671277
$40$	2.83661e53	0.607842
$41$	1.78297e54	1.67064	0.835322	−	0.549762i	$-0.185281\pi$
$41$	1.78297e54	1.67064	0.835322	+	0.549762i	$0.185281\pi$
$42$	−1.19961e54	−0.501405
$43$	−5.13445e54	−0.975665	−0.487833	−	0.872937i	$-0.662212\pi$
$43$	−5.13445e54	−0.975665	−0.487833	+	0.872937i	$0.662212\pi$
$44$	1.36043e55	1.19677
$45$	5.79783e54	0.240241
$46$	−1.48100e55	−0.293878
$47$	−1.02776e56	−0.992234	−0.496117	−	0.868256i	$-0.665241\pi$
$47$	−1.02776e56	−0.992234	−0.496117	+	0.868256i	$0.665241\pi$
$48$	4.51603e55	0.215365
$49$	9.77728e56	2.33695
$50$	1.88069e56	0.228466
$51$	1.49145e56	0.0933274
$52$	2.75616e57	0.899895
$53$	−9.83914e57	−1.69713	−0.848566	−	0.529089i	$-0.822534\pi$
$53$	−9.83914e57	−1.69713	−0.848566	+	0.529089i	$0.822534\pi$
$54$	−9.92163e56	−0.0914939
$55$	−2.23460e58	−1.11442
$56$	5.64932e58	1.54063
$57$	−4.72309e58	−0.711900
$58$	4.92869e58	0.414853
$59$	−2.18323e59	−1.03647	−0.518235	−	0.855238i	$-0.673411\pi$
$59$	−2.18323e59	−1.03647	−0.518235	+	0.855238i	$0.673411\pi$
$60$	−1.19125e59	−0.322060
$61$	5.16004e59	0.801869	0.400934	−	0.916107i	$-0.368686\pi$
$61$	5.16004e59	0.801869	0.400934	+	0.916107i	$0.368686\pi$
$62$	−5.72876e59	−0.516344
$63$	1.15468e60	0.608911
$64$	3.60738e59	0.112244
$65$	−4.52718e60	−0.837973
$66$	3.82399e60	0.424420
$67$	8.46980e60	0.568025	0.284012	−	0.958821i	$-0.408334\pi$
$67$	8.46980e60	0.568025	0.284012	+	0.958821i	$0.408334\pi$
$68$	−3.06442e60	−0.125112
$69$	1.42553e61	0.356888
$70$	−4.04856e61	−0.625917
$71$	2.04432e61	0.196514	0.0982572	−	0.995161i	$-0.468673\pi$
$71$	2.04432e61	0.196514	0.0982572	+	0.995161i	$0.468673\pi$
$72$	4.67240e61	0.281126
$73$	−1.75945e62	−0.666899	−0.333449	−	0.942768i	$-0.608213\pi$
$73$	−1.75945e62	−0.666899	−0.333449	+	0.942768i	$0.608213\pi$
$74$	9.09236e61	0.218481
$75$	−1.81025e62	−0.277451
$76$	9.70430e62	0.954352
$77$	−4.45037e63	−2.82460
$78$	7.74721e62	0.319136
$79$	−1.13903e62	−0.0306216	−0.0153108	−	0.999883i	$-0.504874\pi$
$79$	−1.13903e62	−0.0306216	−0.0153108	+	0.999883i	$0.504874\pi$
$80$	1.52412e63	0.268846
$81$	9.55005e62	0.111111
$82$	−1.02973e64	−0.794251
$83$	1.01962e64	0.523987	0.261993	−	0.965070i	$-0.415620\pi$
$83$	1.01962e64	0.523987	0.261993	+	0.965070i	$0.415620\pi$
$84$	−2.37246e64	−0.816288
$85$	5.03352e63	0.116503
$86$	2.96533e64	0.463847
$87$	−4.74410e64	−0.503801
$88$	−1.80084e65	−1.30408
$89$	−2.83149e65	−1.40427	−0.702133	−	0.712045i	$-0.747769\pi$
$89$	−2.83149e65	−1.40427	−0.702133	+	0.712045i	$0.747769\pi$
$90$	−3.34846e64	−0.114214
$91$	−9.01621e65	−2.12392
$92$	−2.92897e65	−0.478434
$93$	5.51421e65	0.627053
$94$	5.93569e65	0.471724
$95$	−1.59400e66	−0.888683
$96$	−1.50118e66	−0.589313
$97$	−4.28149e66	−1.18780	−0.593898	−	0.804541i	$-0.702412\pi$
$97$	−4.28149e66	−1.18780	−0.593898	+	0.804541i	$0.702412\pi$
$98$	−5.64673e66	−1.11102
$99$	−3.68078e66	−0.515419
$100$	3.71944e66	0.371944
$101$	−1.33778e66	−0.0958558	−0.0479279	−	0.998851i	$-0.515262\pi$
$101$	−1.33778e66	−0.0958558	−0.0479279	+	0.998851i	$0.515262\pi$
$102$	−8.61369e65	−0.0443694
$103$	−2.08606e67	−0.774962	−0.387481	−	0.921878i	$-0.626655\pi$
$103$	−2.08606e67	−0.774962	−0.387481	+	0.921878i	$0.626655\pi$
$104$	−3.64840e67	−0.980585
$105$	3.89694e67	0.760119
$106$	5.68246e67	0.806845
$107$	−1.93149e67	−0.200233	−0.100116	−	0.994976i	$-0.531922\pi$
$107$	−1.93149e67	−0.200233	−0.100116	+	0.994976i	$0.531922\pi$
$108$	−1.96220e67	−0.148952
$109$	−2.27440e68	−1.26788	−0.633942	−	0.773381i	$-0.718564\pi$
$109$	−2.27440e68	−1.26788	−0.633942	+	0.773381i	$0.718564\pi$
$110$	1.29056e68	0.529814
$111$	−8.75183e67	−0.265326
$112$	3.03539e68	0.681413
$113$	1.17878e69	1.96473	0.982367	−	0.186964i	$-0.0598648\pi$
$113$	1.17878e69	1.96473	0.982367	+	0.186964i	$0.0598648\pi$
$114$	2.72776e68	0.338449
$115$	4.81103e68	0.445513
$116$	9.74747e68	0.675382
$117$	−7.45706e68	−0.387562
$118$	1.26089e69	0.492755
$119$	1.00246e69	0.295287
$120$	1.57689e69	0.350937
$121$	8.25296e69	1.39091
$122$	−2.98011e69	−0.381222
$123$	9.91161e69	0.964546
$124$	−1.13298e70	−0.840610
$125$	−1.88226e70	−1.06707
$126$	−6.66870e69	−0.289486
$127$	−3.05307e70	−1.01698	−0.508490	−	0.861068i	$-0.669796\pi$
$127$	−3.05307e70	−1.01698	−0.508490	+	0.861068i	$0.669796\pi$
$128$	3.77677e70	0.967358
$129$	−2.85427e70	−0.563300
$130$	2.61461e70	0.398386
$131$	−2.43570e69	−0.0287102	−0.0143551	−	0.999897i	$-0.504570\pi$
$131$	−2.43570e69	−0.0287102	−0.0143551	+	0.999897i	$0.504570\pi$
$132$	7.56271e70	0.690956
$133$	−3.17456e71	−2.25244
$134$	−4.89161e70	−0.270048
$135$	3.22305e70	0.138703
$136$	4.05645e70	0.136330
$137$	−1.63181e71	−0.429071	−0.214536	−	0.976716i	$-0.568824\pi$
$137$	−1.63181e71	−0.429071	−0.214536	+	0.976716i	$0.568824\pi$
$138$	−8.23296e70	−0.169671
$139$	−3.17547e71	−0.513822	−0.256911	−	0.966435i	$-0.582705\pi$
$139$	−3.17547e71	−0.513822	−0.256911	+	0.966435i	$0.582705\pi$
$140$	−8.00684e71	−1.01899
$141$	−5.71339e71	−0.572867
$142$	−1.18067e71	−0.0934262
$143$	2.87410e72	1.79781
$144$	2.51049e71	0.124341
$145$	−1.60109e72	−0.628909
$146$	1.01614e72	0.317055
$147$	5.43525e72	1.34924
$148$	1.79819e72	0.355688
$149$	5.57287e72	0.879709	0.439855	−	0.898069i	$-0.355030\pi$
$149$	5.57287e72	0.879709	0.439855	+	0.898069i	$0.355030\pi$
$150$	1.04549e72	0.131905
$151$	8.67737e71	0.0876315	0.0438158	−	0.999040i	$-0.486049\pi$
$151$	8.67737e71	0.0876315	0.0438158	+	0.999040i	$0.486049\pi$
$152$	−1.28458e73	−1.03993
$153$	8.29109e71	0.0538826
$154$	2.57025e73	1.34286
$155$	1.86099e73	0.782768
$156$	1.53216e73	0.519555
$157$	−1.95325e73	−0.534710	−0.267355	−	0.963598i	$-0.586150\pi$
$157$	−1.95325e73	−0.534710	−0.267355	+	0.963598i	$0.586150\pi$
$158$	6.57831e71	0.0145580
$159$	−5.46964e73	−0.979840
$160$	−5.06633e73	−0.735655
$161$	9.58152e73	1.12919
$162$	−5.51550e72	−0.0528240
$163$	−6.75372e73	−0.526330	−0.263165	−	0.964751i	$-0.584766\pi$
$163$	−6.75372e73	−0.526330	−0.263165	+	0.964751i	$0.584766\pi$
$164$	−2.03649e74	−1.29304
$165$	−1.24223e74	−0.643412
$166$	−5.88864e73	−0.249112
$167$	−3.07961e74	−1.06535	−0.532677	−	0.846319i	$-0.678814\pi$
$167$	−3.07961e74	−1.06535	−0.532677	+	0.846319i	$0.678814\pi$
$168$	3.14049e74	0.889481
$169$	1.51548e74	0.351840
$170$	−2.90704e73	−0.0553875
$171$	−2.62560e74	−0.411015
$172$	5.86453e74	0.755145
$173$	1.26343e73	0.0133970	0.00669851	−	0.999978i	$-0.497868\pi$
$173$	1.26343e73	0.0133970	0.00669851	+	0.999978i	$0.497868\pi$
$174$	2.73989e74	0.239515
$175$	−1.21674e75	−0.877854
$176$	−9.67591e74	−0.576790
$177$	−1.21367e75	−0.598407
$178$	1.63529e75	0.667611
$179$	1.02108e75	0.345528	0.172764	−	0.984963i	$-0.444730\pi$
$179$	1.02108e75	0.345528	0.172764	+	0.984963i	$0.444730\pi$
$180$	−6.62224e74	−0.185941
$181$	5.54911e75	1.29417	0.647085	−	0.762418i	$-0.275988\pi$
$181$	5.54911e75	1.29417	0.647085	+	0.762418i	$0.275988\pi$
$182$	5.20718e75	1.00974
$183$	2.86850e75	0.462959
$184$	3.87715e75	0.521333
$185$	−2.95366e75	−0.331213
$186$	−3.18465e75	−0.298111
$187$	−3.19555e75	−0.249949
$188$	1.17390e76	0.767969
$189$	6.41894e75	0.351555
$190$	9.20591e75	0.422495
$191$	−5.83177e75	−0.224483	−0.112241	−	0.993681i	$-0.535803\pi$
$191$	−5.83177e75	−0.224483	−0.112241	+	0.993681i	$0.535803\pi$
$192$	2.00537e75	0.0648041
$193$	−3.51258e76	−0.953798	−0.476899	−	0.878958i	$-0.658239\pi$
$193$	−3.51258e76	−0.953798	−0.476899	+	0.878958i	$0.658239\pi$
$194$	2.47271e76	0.564697
$195$	−2.51669e76	−0.483804
$196$	−1.11675e77	−1.80875
$197$	−6.33821e76	−0.865661	−0.432831	−	0.901475i	$-0.642485\pi$
$197$	−6.33821e76	−0.865661	−0.432831	+	0.901475i	$0.642485\pi$
$198$	2.12578e76	0.245039
$199$	1.76627e76	0.171981	0.0859904	−	0.996296i	$-0.472595\pi$
$199$	1.76627e76	0.171981	0.0859904	+	0.996296i	$0.472595\pi$
$200$	−4.92351e76	−0.405294
$201$	4.70841e76	0.327949
$202$	7.72616e75	0.0455714
$203$	−3.18869e77	−1.59402
$204$	−1.70353e76	−0.0722335
$205$	3.34507e77	1.20407
$206$	1.20478e77	0.368430
$207$	7.92461e76	0.206050
$208$	−1.96029e77	−0.433709
$209$	1.01196e78	1.90661
$210$	−2.25062e77	−0.361373
$211$	−1.38499e78	−1.89664	−0.948321	−	0.317313i	$-0.897219\pi$
$211$	−1.38499e78	−1.89664	−0.948321	+	0.317313i	$0.897219\pi$
$212$	1.12382e78	1.31355
$213$	1.13645e77	0.113458
$214$	1.11550e77	0.0951939
$215$	−9.63290e77	−0.703183
$216$	2.59742e77	0.162308
$217$	3.70630e78	1.98399
$218$	1.31355e78	0.602773
$219$	−9.78087e77	−0.385034
$220$	2.55234e78	0.862539
$221$	−6.47401e77	−0.187946
$222$	5.05450e77	0.126140
$223$	−1.26136e78	−0.270786	−0.135393	−	0.990792i	$-0.543230\pi$
$223$	−1.26136e78	−0.270786	−0.135393	+	0.990792i	$0.543230\pi$
$224$	−1.00900e79	−1.86458
$225$	−1.00633e78	−0.160187
$226$	−6.80786e78	−0.934067
$227$	1.07871e79	1.27656	0.638278	−	0.769806i	$-0.279647\pi$
$227$	1.07871e79	1.27656	0.638278	+	0.769806i	$0.279647\pi$
$228$	5.39468e78	0.550995
$229$	9.21353e78	0.812713	0.406357	−	0.913715i	$-0.366799\pi$
$229$	9.21353e78	0.812713	0.406357	+	0.913715i	$0.366799\pi$
$230$	−2.77854e78	−0.211804
$231$	−2.47399e79	−1.63078
$232$	−1.29030e79	−0.735940
$233$	−1.37622e79	−0.679616	−0.339808	−	0.940495i	$-0.610362\pi$
$233$	−1.37622e79	−0.679616	−0.339808	+	0.940495i	$0.610362\pi$
$234$	4.30672e78	0.184253
$235$	−1.92821e79	−0.715125
$236$	2.49367e79	0.802207
$237$	−6.33194e77	−0.0176794
$238$	−5.78958e78	−0.140384
$239$	1.52312e79	0.320926	0.160463	−	0.987042i	$-0.448701\pi$
$239$	1.52312e79	0.320926	0.160463	+	0.987042i	$0.448701\pi$
$240$	8.47265e78	0.155218
$241$	−2.52271e79	−0.402065	−0.201033	−	0.979585i	$-0.564430\pi$
$241$	−2.52271e79	−0.402065	−0.201033	+	0.979585i	$0.564430\pi$
$242$	−4.76638e79	−0.661263
$243$	5.30893e78	0.0641500
$244$	−5.89375e79	−0.620630
$245$	1.83434e80	1.68429
$246$	−5.72431e79	−0.458561
$247$	2.05017e80	1.43365
$248$	1.49975e80	0.915984
$249$	5.66810e79	0.302524
$250$	1.08707e80	0.507304
$251$	3.11981e80	1.27367	0.636836	−	0.770999i	$-0.280243\pi$
$251$	3.11981e80	1.27367	0.636836	+	0.770999i	$0.280243\pi$
$252$	−1.31887e80	−0.471284
$253$	−3.05430e80	−0.955817
$254$	1.76326e80	0.483489
$255$	2.79816e79	0.0672631
$256$	−2.71358e80	−0.572142
$257$	−7.80617e80	−1.44437	−0.722185	−	0.691700i	$-0.756862\pi$
$257$	−7.80617e80	−1.44437	−0.722185	+	0.691700i	$0.756862\pi$
$258$	1.64844e80	0.267802
$259$	−5.88243e80	−0.839488
$260$	5.17091e80	0.648574
$261$	−2.63728e80	−0.290870
$262$	1.40671e79	0.0136493
$263$	7.00843e80	0.598554	0.299277	−	0.954166i	$-0.403255\pi$
$263$	7.00843e80	0.598554	0.299277	+	0.954166i	$0.403255\pi$
$264$	−1.00110e81	−0.752912
$265$	−1.84595e81	−1.22316
$266$	1.83342e81	1.07085
$267$	−1.57404e81	−0.810754
$268$	−9.67413e80	−0.439639
$269$	1.69674e81	0.680636	0.340318	−	0.940310i	$-0.389465\pi$
$269$	1.69674e81	0.680636	0.340318	+	0.940310i	$0.389465\pi$
$270$	−1.86143e80	−0.0659417
$271$	8.15736e80	0.255316	0.127658	−	0.991818i	$-0.459254\pi$
$271$	8.15736e80	0.255316	0.127658	+	0.991818i	$0.459254\pi$
$272$	2.17953e80	0.0602984
$273$	−5.01217e81	−1.22624
$274$	9.42426e80	0.203987
$275$	3.87860e81	0.743070
$276$	−1.62823e81	−0.276224
$277$	−3.62914e81	−0.545421	−0.272711	−	0.962096i	$-0.587920\pi$
$277$	−3.62914e81	−0.545421	−0.272711	+	0.962096i	$0.587920\pi$
$278$	1.83395e81	0.244279
$279$	3.06538e81	0.362029
$280$	1.05989e82	1.11036
$281$	8.52742e81	0.792786	0.396393	−	0.918081i	$-0.370262\pi$
$281$	8.52742e81	0.792786	0.396393	+	0.918081i	$0.370262\pi$
$282$	3.29969e81	0.272350
$283$	−3.42923e81	−0.251392	−0.125696	−	0.992069i	$-0.540116\pi$
$283$	−3.42923e81	−0.251392	−0.125696	+	0.992069i	$0.540116\pi$
$284$	−2.33501e81	−0.152098
$285$	−8.86113e81	−0.513082
$286$	−1.65990e82	−0.854710
$287$	6.66196e82	3.05182
$288$	−8.34514e81	−0.340240
$289$	−2.68274e82	−0.973870
$290$	9.24687e81	0.298994
$291$	−2.38011e82	−0.685774
$292$	2.00962e82	0.516166
$293$	7.13908e82	1.63522	0.817612	−	0.575770i	$-0.195298\pi$
$293$	7.13908e82	1.63522	0.817612	+	0.575770i	$0.195298\pi$
$294$	−3.13905e82	−0.641450
$295$	−4.09602e82	−0.747007
$296$	−2.38032e82	−0.387581
$297$	−2.04617e82	−0.297577
$298$	−3.21853e82	−0.418228
$299$	−6.18786e82	−0.718713
$300$	2.06766e82	0.214742
$301$	−1.91846e83	−1.78228
$302$	−5.01149e81	−0.0416615
$303$	−7.43680e81	−0.0553424
$304$	−6.90208e82	−0.459955
$305$	9.68090e82	0.577924
$306$	−4.78840e81	−0.0256167
$307$	7.69803e82	0.369185	0.184593	−	0.982815i	$-0.440903\pi$
$307$	7.69803e82	0.369185	0.184593	+	0.982815i	$0.440903\pi$
$308$	5.08317e83	2.18618
$309$	−1.15966e83	−0.447425
$310$	−1.07479e83	−0.372141
$311$	−4.70941e83	−1.46384	−0.731920	−	0.681390i	$-0.761376\pi$
$311$	−4.70941e83	−1.46384	−0.731920	+	0.681390i	$0.761376\pi$
$312$	−2.02817e83	−0.566141
$313$	2.60650e83	0.653617	0.326808	−	0.945091i	$-0.394027\pi$
$313$	2.60650e83	0.653617	0.326808	+	0.945091i	$0.394027\pi$
$314$	1.12807e83	0.254210
$315$	2.16633e83	0.438855
$316$	1.30099e82	0.0237005
$317$	7.13368e83	1.16904	0.584519	−	0.811380i	$-0.301283\pi$
$317$	7.13368e83	1.16904	0.584519	+	0.811380i	$0.301283\pi$
$318$	3.15891e83	0.465832
$319$	1.01646e84	1.34928
$320$	6.76792e82	0.0808967
$321$	−1.07372e83	−0.115604
$322$	−5.53367e83	−0.536836
$323$	−2.27947e83	−0.199319
$324$	−1.09080e83	−0.0859977
$325$	7.85783e83	0.558741
$326$	3.90052e83	0.250226
$327$	−1.26435e84	−0.732013
$328$	2.69575e84	1.40899
$329$	−3.84018e84	−1.81255
$330$	7.17431e83	0.305888
$331$	−4.92501e84	−1.89745	−0.948723	−	0.316110i	$-0.897623\pi$
$331$	−4.92501e84	−1.89745	−0.948723	+	0.316110i	$0.897623\pi$
$332$	−1.16460e84	−0.405555
$333$	−4.86520e83	−0.153186
$334$	1.77859e84	0.506487
$335$	1.58904e84	0.409388
$336$	1.68739e84	0.393414
$337$	−6.11915e84	−1.29148	−0.645742	−	0.763555i	$-0.723452\pi$
$337$	−6.11915e84	−1.29148	−0.645742	+	0.763555i	$0.723452\pi$
$338$	−8.75242e83	−0.167270
$339$	6.55289e84	1.13434
$340$	−5.74924e83	−0.0901710
$341$	−1.18146e85	−1.67937
$342$	1.51638e84	0.195403
$343$	2.08998e85	2.44225
$344$	−7.76303e84	−0.822855
$345$	2.67448e84	0.257217
$346$	−7.29678e82	−0.00636916
$347$	−1.93404e85	−1.53260	−0.766299	−	0.642485i	$-0.777904\pi$
$347$	−1.93404e85	−1.53260	−0.766299	+	0.642485i	$0.777904\pi$
$348$	5.41868e84	0.389932
$349$	−2.36125e85	−1.54344	−0.771719	−	0.635963i	$-0.780603\pi$
$349$	−2.36125e85	−1.54344	−0.771719	+	0.635963i	$0.780603\pi$
$350$	7.02710e84	0.417346
$351$	−4.14543e84	−0.223759
$352$	3.21638e85	1.57830
$353$	1.87959e85	0.838709	0.419354	−	0.907823i	$-0.362256\pi$
$353$	1.87959e85	0.838709	0.419354	+	0.907823i	$0.362256\pi$
$354$	7.00938e84	0.284492
$355$	3.83541e84	0.141632
$356$	3.23410e85	1.08687
$357$	5.57274e84	0.170484
$358$	−5.89710e84	−0.164269
$359$	−3.34371e85	−0.848329	−0.424164	−	0.905585i	$-0.639432\pi$
$359$	−3.34371e85	−0.848329	−0.424164	+	0.905585i	$0.639432\pi$
$360$	8.76603e84	0.202614
$361$	2.47076e85	0.520403
$362$	−3.20481e85	−0.615270
$363$	4.58787e85	0.803044
$364$	1.02982e86	1.64387
$365$	−3.30095e85	−0.480649
$366$	−1.65666e85	−0.220098
$367$	−1.25268e86	−1.51889	−0.759443	−	0.650574i	$-0.774529\pi$
$367$	−1.25268e86	−1.51889	−0.759443	+	0.650574i	$0.774529\pi$
$368$	2.08320e85	0.230584
$369$	5.50993e85	0.556881
$370$	1.70584e85	0.157464
$371$	−3.67635e86	−3.10021
$372$	−6.29829e85	−0.485326
$373$	5.31628e85	0.374422	0.187211	−	0.982320i	$-0.440055\pi$
$373$	5.31628e85	0.374422	0.187211	+	0.982320i	$0.440055\pi$
$374$	1.84554e85	0.118830
$375$	−1.04636e86	−0.616074
$376$	−1.55392e86	−0.836829
$377$	2.05929e86	1.01457
$378$	−3.70717e85	−0.167135
$379$	2.29046e86	0.945167	0.472584	−	0.881286i	$-0.343321\pi$
$379$	2.29046e86	0.945167	0.472584	+	0.881286i	$0.343321\pi$
$380$	1.82065e86	0.687822
$381$	−1.69722e86	−0.587154
$382$	3.36806e85	0.106723
$383$	−1.47199e86	−0.427313	−0.213657	−	0.976909i	$-0.568537\pi$
$383$	−1.47199e86	−0.427313	−0.213657	+	0.976909i	$0.568537\pi$
$384$	2.09953e86	0.558504
$385$	−8.34947e86	−2.03575
$386$	2.02864e86	0.453451
$387$	−1.58671e86	−0.325222
$388$	4.89028e86	0.919329
$389$	4.89559e86	0.844294	0.422147	−	0.906527i	$-0.361277\pi$
$389$	4.89559e86	0.844294	0.422147	+	0.906527i	$0.361277\pi$
$390$	1.45348e86	0.230008
$391$	6.87993e85	0.0999223
$392$	1.47827e87	1.97093
$393$	−1.35402e85	−0.0165758
$394$	3.66054e86	0.411549
$395$	−2.13697e85	−0.0220697
$396$	4.20415e86	0.398924
$397$	−8.06951e86	−0.703664	−0.351832	−	0.936063i	$-0.614441\pi$
$397$	−8.06951e86	−0.703664	−0.351832	+	0.936063i	$0.614441\pi$
$398$	−1.02009e86	−0.0817625
$399$	−1.76476e87	−1.30045
$400$	−2.64541e86	−0.179260
$401$	2.27883e87	1.42028	0.710142	−	0.704059i	$-0.248631\pi$
$401$	2.27883e87	1.42028	0.710142	+	0.704059i	$0.248631\pi$
$402$	−2.71928e86	−0.155912
$403$	−2.39357e87	−1.26278
$404$	1.52800e86	0.0741904
$405$	1.79171e86	0.0800802
$406$	1.84158e87	0.757825
$407$	1.87514e87	0.710594
$408$	2.25500e86	0.0787103
$409$	−4.79690e87	−1.54252	−0.771259	−	0.636522i	$-0.780373\pi$
$409$	−4.79690e87	−1.54252	−0.771259	+	0.636522i	$0.780373\pi$
$410$	−1.93190e87	−0.572434
$411$	−9.07130e86	−0.247724
$412$	2.38269e87	0.599805
$413$	−8.15753e87	−1.89335
$414$	−4.57675e86	−0.0979593
$415$	1.91293e87	0.377649
$416$	6.51622e87	1.18678
$417$	−1.76526e87	−0.296655
$418$	−5.84441e87	−0.906432
$419$	4.08589e87	0.584947	0.292474	−	0.956274i	$-0.405522\pi$
$419$	4.08589e87	0.584947	0.292474	+	0.956274i	$0.405522\pi$
$420$	−4.45105e87	−0.588317
$421$	2.45984e87	0.300232	0.150116	−	0.988668i	$-0.452035\pi$
$421$	2.45984e87	0.300232	0.150116	+	0.988668i	$0.452035\pi$
$422$	7.99883e87	0.901694
$423$	−3.17611e87	−0.330745
$424$	−1.48763e88	−1.43133
$425$	−8.73668e86	−0.0776815
$426$	−6.56341e86	−0.0539396
$427$	1.92802e88	1.46480
$428$	2.20613e87	0.154976
$429$	1.59773e88	1.03797
$430$	5.56334e87	0.334305
$431$	8.37838e86	0.0465770	0.0232885	−	0.999729i	$-0.492586\pi$
$431$	8.37838e86	0.0465770	0.0232885	+	0.999729i	$0.492586\pi$
$432$	1.39559e87	0.0717883
$433$	3.36183e87	0.160041	0.0800206	−	0.996793i	$-0.474501\pi$
$433$	3.36183e87	0.160041	0.0800206	+	0.996793i	$0.474501\pi$
$434$	−2.14052e88	−0.943222
$435$	−8.90055e87	−0.363101
$436$	2.59780e88	0.981316
$437$	−2.17871e88	−0.762206
$438$	5.64880e87	0.183052
$439$	5.49250e88	1.64895	0.824477	−	0.565895i	$-0.191469\pi$
$439$	5.49250e88	1.64895	0.824477	+	0.565895i	$0.191469\pi$
$440$	−3.37860e88	−0.939880
$441$	3.02149e88	0.778983
$442$	3.73897e87	0.0893525
$443$	8.19409e87	0.181542	0.0907708	−	0.995872i	$-0.471067\pi$
$443$	8.19409e87	0.181542	0.0907708	+	0.995872i	$0.471067\pi$
$444$	9.99627e87	0.205357
$445$	−5.31224e88	−1.01209
$446$	7.28480e87	0.128736
$447$	3.09799e88	0.507900
$448$	1.34788e88	0.205040
$449$	6.77299e88	0.956154	0.478077	−	0.878318i	$-0.341334\pi$
$449$	6.77299e88	0.956154	0.478077	+	0.878318i	$0.341334\pi$
$450$	5.81192e87	0.0761554
$451$	−2.12363e89	−2.58325
$452$	−1.34639e89	−1.52066
$453$	4.82380e87	0.0505941
$454$	−6.22996e88	−0.606896
$455$	−1.69156e89	−1.53075
$456$	−7.14108e88	−0.600401
$457$	2.04125e89	1.59479	0.797393	−	0.603460i	$-0.206212\pi$
$457$	2.04125e89	1.59479	0.797393	+	0.603460i	$0.206212\pi$
$458$	−5.32114e88	−0.386377
$459$	4.60907e87	0.0311091
$460$	−5.49512e88	−0.344818
$461$	8.64910e88	0.504650	0.252325	−	0.967643i	$-0.418805\pi$
$461$	8.64910e88	0.504650	0.252325	+	0.967643i	$0.418805\pi$
$462$	1.42882e89	0.775301
$463$	2.91494e89	1.47118	0.735592	−	0.677425i	$-0.236904\pi$
$463$	2.91494e89	1.47118	0.735592	+	0.677425i	$0.236904\pi$
$464$	−6.93279e88	−0.325504
$465$	1.03454e89	0.451931
$466$	7.94815e88	0.323101
$467$	−3.42007e89	−1.29396	−0.646979	−	0.762508i	$-0.723968\pi$
$467$	−3.42007e89	−1.29396	−0.646979	+	0.762508i	$0.723968\pi$
$468$	8.51739e88	0.299965
$469$	3.16470e89	1.03763
$470$	1.11361e89	0.339982
$471$	−1.08582e89	−0.308715
$472$	−3.30093e89	−0.874138
$473$	6.11548e89	1.50863
$474$	3.65692e87	0.00840507
$475$	2.76671e89	0.592553
$476$	−1.14500e89	−0.228546
$477$	−3.04061e89	−0.565711
$478$	−8.79656e88	−0.152573
$479$	3.81978e89	0.617729	0.308865	−	0.951106i	$-0.400051\pi$
$479$	3.81978e89	0.617729	0.308865	+	0.951106i	$0.400051\pi$
$480$	−2.81641e89	−0.424731
$481$	3.79894e89	0.534321
$482$	1.45696e89	0.191149
$483$	5.32643e89	0.651939
$484$	−9.42647e89	−1.07654
$485$	−8.03263e89	−0.856070
$486$	−3.06610e88	−0.0304980
$487$	3.07933e89	0.285914	0.142957	−	0.989729i	$-0.454339\pi$
$487$	3.07933e89	0.285914	0.142957	+	0.989729i	$0.454339\pi$
$488$	7.80172e89	0.676279
$489$	−3.75443e89	−0.303877
$490$	−1.05940e90	−0.800739
$491$	1.21836e90	0.860096	0.430048	−	0.902806i	$-0.358497\pi$
$491$	1.21836e90	0.860096	0.430048	+	0.902806i	$0.358497\pi$
$492$	−1.13210e90	−0.746539
$493$	−2.28961e89	−0.141055
$494$	−1.18405e90	−0.681579
$495$	−6.90562e89	−0.371474
$496$	8.05818e89	0.405136
$497$	7.63850e89	0.358979
$498$	−3.27353e89	−0.143825
$499$	−4.26981e90	−1.75404	−0.877021	−	0.480452i	$-0.840473\pi$
$499$	−4.26981e90	−1.75404	−0.877021	+	0.480452i	$0.840473\pi$
$500$	2.14990e90	0.825892
$501$	−1.71197e90	−0.615082
$502$	−1.80180e90	−0.605525
$503$	8.97832e89	0.282272	0.141136	−	0.989990i	$-0.454925\pi$
$503$	8.97832e89	0.282272	0.141136	+	0.989990i	$0.454925\pi$
$504$	1.74582e90	0.513542
$505$	−2.50985e89	−0.0690854
$506$	1.76397e90	0.454411
$507$	8.42463e89	0.203135
$508$	3.48720e90	0.787122
$509$	6.18367e90	1.30677	0.653387	−	0.757024i	$-0.273348\pi$
$509$	6.18367e90	1.30677	0.653387	+	0.757024i	$0.273348\pi$
$510$	−1.61604e89	−0.0319780
$511$	−6.57408e90	−1.21825
$512$	−4.00635e90	−0.695352
$513$	−1.45958e90	−0.237300
$514$	4.50834e90	0.686677
$515$	−3.91373e90	−0.558532
$516$	3.26013e90	0.435983
$517$	1.22413e91	1.53425
$518$	3.39731e90	0.399106
$519$	7.02350e88	0.00773477
$520$	−6.84487e90	−0.706729
$521$	1.22625e91	1.18718	0.593590	−	0.804768i	$-0.297710\pi$
$521$	1.22625e91	1.18718	0.593590	+	0.804768i	$0.297710\pi$
$522$	1.52312e90	0.138284
$523$	6.71745e89	0.0572002	0.0286001	−	0.999591i	$-0.490895\pi$
$523$	6.71745e89	0.0572002	0.0286001	+	0.999591i	$0.490895\pi$
$524$	2.78204e89	0.0222211
$525$	−6.76392e90	−0.506829
$526$	−4.04762e90	−0.284562
$527$	2.66128e90	0.175564
$528$	−5.37890e90	−0.333010
$529$	−1.06335e91	−0.617892
$530$	1.06610e91	0.581510
$531$	−6.74687e90	−0.345490
$532$	3.62596e91	1.74335
$533$	−4.30237e91	−1.94243
$534$	9.09066e90	0.385446
$535$	−3.62372e90	−0.144312
$536$	1.28059e91	0.479060
$537$	5.67624e90	0.199490
$538$	−9.79931e90	−0.323586
$539$	−1.16454e92	−3.61353
$540$	−3.68134e90	−0.107353
$541$	6.11627e90	0.167640	0.0838202	−	0.996481i	$-0.473288\pi$
$541$	6.11627e90	0.167640	0.0838202	+	0.996481i	$0.473288\pi$
$542$	−4.71117e90	−0.121381
$543$	3.08479e91	0.747190
$544$	−7.24502e90	−0.164997
$545$	−4.26707e91	−0.913792
$546$	2.89471e91	0.582976
$547$	2.29837e91	0.435357	0.217678	−	0.976021i	$-0.430152\pi$
$547$	2.29837e91	0.435357	0.217678	+	0.976021i	$0.430152\pi$
$548$	1.86383e91	0.332092
$549$	1.59461e91	0.267290
$550$	−2.24003e91	−0.353268
$551$	7.25066e91	1.07597
$552$	2.15533e91	0.300992
$553$	−4.25593e90	−0.0559375
$554$	2.09596e91	0.259302
$555$	−1.64196e91	−0.191226
$556$	3.62700e91	0.397687
$557$	−3.52766e91	−0.364198	−0.182099	−	0.983280i	$-0.558289\pi$
$557$	−3.52766e91	−0.364198	−0.182099	+	0.983280i	$0.558289\pi$
$558$	−1.77037e91	−0.172115
$559$	1.23896e92	1.13439
$560$	5.69478e91	0.491109
$561$	−1.77642e91	−0.144308
$562$	−4.92489e91	−0.376903
$563$	−4.76483e91	−0.343571	−0.171785	−	0.985134i	$-0.554954\pi$
$563$	−4.76483e91	−0.343571	−0.171785	+	0.985134i	$0.554954\pi$
$564$	6.52579e91	0.443387
$565$	2.21154e92	1.41603
$566$	1.98050e91	0.119516
$567$	3.56833e91	0.202970
$568$	3.09091e91	0.165736
$569$	1.28188e92	0.648017	0.324008	−	0.946054i	$-0.394969\pi$
$569$	1.28188e92	0.648017	0.324008	+	0.946054i	$0.394969\pi$
$570$	5.11762e91	0.243927
$571$	−2.62224e92	−1.17859	−0.589296	−	0.807917i	$-0.700595\pi$
$571$	−2.62224e92	−1.17859	−0.589296	+	0.807917i	$0.700595\pi$
$572$	−3.28277e92	−1.39147
$573$	−3.24192e91	−0.129605
$574$	−3.84752e92	−1.45088
$575$	−8.35052e91	−0.297058
$576$	1.11479e91	0.0374147
$577$	−4.45730e92	−1.41150	−0.705752	−	0.708459i	$-0.749391\pi$
$577$	−4.45730e92	−1.41150	−0.705752	+	0.708459i	$0.749391\pi$
$578$	1.54938e92	0.462994
$579$	−1.95266e92	−0.550675
$580$	1.82875e92	0.486762
$581$	3.80974e92	0.957183
$582$	1.37460e92	0.326028
$583$	1.17191e93	2.62420
$584$	−2.66019e92	−0.562448
$585$	−1.39904e92	−0.279324
$586$	−4.12308e92	−0.777412
$587$	−1.37226e92	−0.244377	−0.122188	−	0.992507i	$-0.538991\pi$
$587$	−1.37226e92	−0.244377	−0.122188	+	0.992507i	$0.538991\pi$
$588$	−6.20809e92	−1.04428
$589$	−8.42766e92	−1.33920
$590$	2.36560e92	0.355139
$591$	−3.52345e92	−0.499790
$592$	−1.27895e92	−0.171426
$593$	1.35912e93	1.72158	0.860789	−	0.508963i	$-0.169971\pi$
$593$	1.35912e93	1.72158	0.860789	+	0.508963i	$0.169971\pi$
$594$	1.18173e92	0.141473
$595$	1.88075e92	0.212820
$596$	−6.36529e92	−0.680877
$597$	9.81882e91	0.0992931
$598$	3.57371e92	0.341688
$599$	−6.75829e92	−0.610996	−0.305498	−	0.952193i	$-0.598823\pi$
$599$	−6.75829e92	−0.610996	−0.305498	+	0.952193i	$0.598823\pi$
$600$	−2.73701e92	−0.233997
$601$	−3.17076e92	−0.256370	−0.128185	−	0.991750i	$-0.540915\pi$
$601$	−3.17076e92	−0.256370	−0.128185	+	0.991750i	$0.540915\pi$
$602$	1.10798e93	0.847324
$603$	2.61743e92	0.189342
$604$	−9.91122e91	−0.0678250
$605$	1.54836e93	1.00246
$606$	4.29502e91	0.0263107
$607$	9.12938e92	0.529200	0.264600	−	0.964358i	$-0.414760\pi$
$607$	9.12938e92	0.529200	0.264600	+	0.964358i	$0.414760\pi$
$608$	2.29433e93	1.25860
$609$	−1.77261e93	−0.920310
$610$	−5.59107e92	−0.274755
$611$	2.48003e93	1.15366
$612$	−9.47001e91	−0.0417040
$613$	3.04124e93	1.26801	0.634007	−	0.773327i	$-0.281409\pi$
$613$	3.04124e93	1.26801	0.634007	+	0.773327i	$0.281409\pi$
$614$	−4.44589e92	−0.175517
$615$	1.85955e93	0.695170
$616$	−6.72873e93	−2.38221
$617$	1.14078e93	0.382514	0.191257	−	0.981540i	$-0.438744\pi$
$617$	1.14078e93	0.382514	0.191257	+	0.981540i	$0.438744\pi$
$618$	6.69743e92	0.212713
$619$	−2.14763e93	−0.646135	−0.323067	−	0.946376i	$-0.604714\pi$
$619$	−2.14763e93	−0.646135	−0.323067	+	0.946376i	$0.604714\pi$
$620$	−2.12561e93	−0.605846
$621$	4.40534e92	0.118963
$622$	2.71986e93	0.695934
$623$	−1.05797e94	−2.56522
$624$	−1.08974e93	−0.250402
$625$	−1.32474e93	−0.288502
$626$	−1.50535e93	−0.310740
$627$	5.62553e93	1.10078
$628$	2.23098e93	0.413855
$629$	−4.22383e92	−0.0742864
$630$	−1.25113e93	−0.208639
$631$	1.13735e94	1.79850	0.899251	−	0.437433i	$-0.144112\pi$
$631$	1.13735e94	1.79850	0.899251	+	0.437433i	$0.144112\pi$
$632$	−1.72216e92	−0.0258256
$633$	−7.69926e93	−1.09503
$634$	−4.11996e93	−0.555780
$635$	−5.72796e93	−0.732960
$636$	6.24738e93	0.758376
$637$	−2.35930e94	−2.71714
$638$	−5.87041e93	−0.641469
$639$	6.31760e92	0.0655048
$640$	7.08572e93	0.697196
$641$	1.62732e94	1.51960	0.759798	−	0.650159i	$-0.225298\pi$
$641$	1.62732e94	1.51960	0.759798	+	0.650159i	$0.225298\pi$
$642$	6.20115e92	0.0549602
$643$	1.59984e94	1.34589	0.672945	−	0.739692i	$-0.265029\pi$
$643$	1.59984e94	1.34589	0.672945	+	0.739692i	$0.265029\pi$
$644$	−1.09439e94	−0.873971
$645$	−5.35498e93	−0.405983
$646$	1.31647e93	0.0947596
$647$	1.12621e94	0.769707	0.384854	−	0.922978i	$-0.374252\pi$
$647$	1.12621e94	0.769707	0.384854	+	0.922978i	$0.374252\pi$
$648$	1.44392e93	0.0937088
$649$	2.60038e94	1.60265
$650$	−4.53818e93	−0.265634
$651$	2.06036e94	1.14546
$652$	7.71404e93	0.407369
$653$	−3.37557e94	−1.69338	−0.846691	−	0.532084i	$-0.821409\pi$
$653$	−3.37557e94	−1.69338	−0.846691	+	0.532084i	$0.821409\pi$
$654$	7.30210e93	0.348011
$655$	−4.56969e92	−0.0206921
$656$	1.44843e94	0.623189
$657$	−5.43724e93	−0.222300
$658$	2.21784e94	0.861714
$659$	−2.35541e94	−0.869773	−0.434887	−	0.900485i	$-0.643212\pi$
$659$	−2.35541e94	−0.869773	−0.434887	+	0.900485i	$0.643212\pi$
$660$	1.41886e94	0.497987
$661$	−1.81947e94	−0.607011	−0.303506	−	0.952830i	$-0.598157\pi$
$661$	−1.81947e94	−0.607011	−0.303506	+	0.952830i	$0.598157\pi$
$662$	2.84437e94	0.902077
$663$	−3.59894e93	−0.108510
$664$	1.54161e94	0.441919
$665$	−5.95589e94	−1.62339
$666$	2.80983e93	0.0728271
$667$	−2.18841e94	−0.539402
$668$	3.51750e94	0.824562
$669$	−7.01197e93	−0.156338
$670$	−9.17730e93	−0.194630
$671$	−6.14596e94	−1.23990
$672$	−5.60908e94	−1.07652
$673$	−2.06642e94	−0.377324	−0.188662	−	0.982042i	$-0.560415\pi$
$673$	−2.06642e94	−0.377324	−0.188662	+	0.982042i	$0.560415\pi$
$674$	3.53403e94	0.613993
$675$	−5.59425e93	−0.0924838
$676$	−1.73096e94	−0.272316
$677$	1.15680e95	1.73195	0.865977	−	0.500084i	$-0.166698\pi$
$677$	1.15680e95	1.73195	0.865977	+	0.500084i	$0.166698\pi$
$678$	−3.78453e94	−0.539284
$679$	−1.59976e95	−2.16978
$680$	7.61042e93	0.0982562
$681$	5.99664e94	0.737020
$682$	6.82335e94	0.798401
$683$	3.09764e94	0.345094	0.172547	−	0.985001i	$-0.444800\pi$
$683$	3.09764e94	0.345094	0.172547	+	0.985001i	$0.444800\pi$
$684$	2.99893e94	0.318117
$685$	−3.06148e94	−0.309241
$686$	−1.20704e95	−1.16108
$687$	5.12186e94	0.469220
$688$	−4.17109e94	−0.363946
$689$	2.37423e95	1.97323
$690$	−1.54461e94	−0.122285
$691$	−8.29204e94	−0.625384	−0.312692	−	0.949855i	$-0.601231\pi$
$691$	−8.29204e94	−0.625384	−0.312692	+	0.949855i	$0.601231\pi$
$692$	−1.44308e93	−0.0103690
$693$	−1.37530e95	−0.941533
$694$	1.11698e95	0.728622
$695$	−5.95760e94	−0.370323
$696$	−7.17285e94	−0.424895
$697$	4.78356e94	0.270056
$698$	1.36370e95	0.733776
$699$	−7.65048e94	−0.392377
$700$	1.38975e95	0.679441
$701$	2.87448e95	1.33970	0.669848	−	0.742499i	$-0.266359\pi$
$701$	2.87448e95	1.33970	0.669848	+	0.742499i	$0.266359\pi$
$702$	2.39413e94	0.106379
$703$	1.33759e95	0.566656
$704$	−4.29664e94	−0.173558
$705$	−1.07191e95	−0.412877
$706$	−1.08553e95	−0.398736
$707$	−4.99854e94	−0.175103
$708$	1.38624e95	0.463154
$709$	6.92752e94	0.220764	0.110382	−	0.993889i	$-0.464793\pi$
$709$	6.92752e94	0.220764	0.110382	+	0.993889i	$0.464793\pi$
$710$	−2.21509e94	−0.0673343
$711$	−3.51996e93	−0.0102072
$712$	−4.28107e95	−1.18433
$713$	2.54365e95	0.671364
$714$	−3.21846e94	−0.0810509
$715$	5.39218e95	1.29572
$716$	−1.16627e95	−0.267431
$717$	8.46711e94	0.185286
$718$	1.93111e95	0.403309
$719$	−3.27545e95	−0.652910	−0.326455	−	0.945213i	$-0.605854\pi$
$719$	−3.27545e95	−0.652910	−0.326455	+	0.945213i	$0.605854\pi$
$720$	4.71000e94	0.0896153
$721$	−7.79447e95	−1.41565
$722$	−1.42695e95	−0.247408
$723$	−1.40239e95	−0.232133
$724$	−6.33815e95	−1.00166
$725$	2.77901e95	0.419341
$726$	−2.64966e95	−0.381780
$727$	7.51775e95	1.03439	0.517196	−	0.855867i	$-0.326976\pi$
$727$	7.51775e95	1.03439	0.517196	+	0.855867i	$0.326976\pi$
$728$	−1.36321e96	−1.79127
$729$	2.95127e94	0.0370370
$730$	1.90642e95	0.228508
$731$	−1.37753e95	−0.157714
$732$	−3.27637e95	−0.358321
$733$	−8.34341e95	−0.871687	−0.435843	−	0.900022i	$-0.643550\pi$
$733$	−8.34341e95	−0.871687	−0.435843	+	0.900022i	$0.643550\pi$
$734$	7.23465e95	0.722104
$735$	1.01972e96	0.972425
$736$	−6.92479e95	−0.630957
$737$	−1.00881e96	−0.878312
$738$	−3.18218e95	−0.264750
$739$	2.44995e95	0.194791	0.0973954	−	0.995246i	$-0.468949\pi$
$739$	2.44995e95	0.194791	0.0973954	+	0.995246i	$0.468949\pi$
$740$	3.37365e95	0.256352
$741$	1.13970e96	0.827716
$742$	2.12322e96	1.47389
$743$	−4.11593e95	−0.273113	−0.136557	−	0.990632i	$-0.543604\pi$
$743$	−4.11593e95	−0.273113	−0.136557	+	0.990632i	$0.543604\pi$
$744$	8.33721e95	0.528844
$745$	1.04554e96	0.634026
$746$	−3.07034e95	−0.178007
$747$	3.15093e95	0.174662
$748$	3.64993e95	0.193455
$749$	−7.21690e95	−0.365771
$750$	6.04310e95	0.292892
$751$	3.36514e96	1.55979	0.779894	−	0.625912i	$-0.215273\pi$
$751$	3.36514e96	1.55979	0.779894	+	0.625912i	$0.215273\pi$
$752$	−8.34925e95	−0.370126
$753$	1.73432e96	0.735355
$754$	−1.18931e96	−0.482344
$755$	1.62799e95	0.0631579
$756$	−7.33166e95	−0.272096
$757$	1.94655e96	0.691120	0.345560	−	0.938397i	$-0.387689\pi$
$757$	1.94655e96	0.691120	0.345560	+	0.938397i	$0.387689\pi$
$758$	−1.32282e96	−0.449348
$759$	−1.69791e96	−0.551841
$760$	−2.41004e96	−0.749497
$761$	−2.64276e95	−0.0786450	−0.0393225	−	0.999227i	$-0.512520\pi$
$761$	−2.64276e95	−0.0786450	−0.0393225	+	0.999227i	$0.512520\pi$
$762$	9.80207e95	0.279143
$763$	−8.49819e96	−2.31608
$764$	6.66100e95	0.173745
$765$	1.55552e95	0.0388344
$766$	8.50128e95	0.203152
$767$	5.26823e96	1.20509
$768$	−1.50849e96	−0.330326
$769$	4.28922e96	0.899179	0.449590	−	0.893235i	$-0.351570\pi$
$769$	4.28922e96	0.899179	0.449590	+	0.893235i	$0.351570\pi$
$770$	4.82212e96	0.967829
$771$	−4.33950e96	−0.833907
$772$	4.01204e96	0.738220
$773$	−3.32391e96	−0.585648	−0.292824	−	0.956166i	$-0.594595\pi$
$773$	−3.32391e96	−0.585648	−0.292824	+	0.956166i	$0.594595\pi$
$774$	9.16381e95	0.154616
$775$	−3.23013e96	−0.521931
$776$	−6.47339e96	−1.00176
$777$	−3.27008e96	−0.484679
$778$	−2.82738e96	−0.401391
$779$	−1.51484e97	−2.05998
$780$	2.87454e96	0.374454
$781$	−2.43493e96	−0.303862
$782$	−3.97341e95	−0.0475047
$783$	−1.46608e96	−0.167934
$784$	7.94279e96	0.871736
$785$	−3.66454e96	−0.385377
$786$	7.81996e94	0.00788042
$787$	9.98437e94	0.00964200	0.00482100	−	0.999988i	$-0.498465\pi$
$787$	9.98437e94	0.00964200	0.00482100	+	0.999988i	$0.498465\pi$
$788$	7.23945e96	0.670004
$789$	3.89603e96	0.345575
$790$	1.23418e95	0.0104923
$791$	4.40444e97	3.58904
$792$	−5.56515e96	−0.434694
$793$	−1.24514e97	−0.932322
$794$	4.66043e96	0.334533
$795$	−1.02618e97	−0.706192
$796$	−2.01742e96	−0.133110
$797$	−4.26357e96	−0.269724	−0.134862	−	0.990864i	$-0.543059\pi$
$797$	−4.26357e96	−0.269724	−0.134862	+	0.990864i	$0.543059\pi$
$798$	1.01921e97	0.618255
$799$	−2.75741e96	−0.160392
$800$	8.79364e96	0.490517
$801$	−8.75019e96	−0.468089
$802$	−1.31610e97	−0.675226
$803$	2.09562e97	1.03120
$804$	−5.37791e96	−0.253826
$805$	1.79762e97	0.813833
$806$	1.38237e97	0.600346
$807$	9.43230e96	0.392965
$808$	−2.02265e96	−0.0808428
$809$	−3.39325e97	−1.30119	−0.650594	−	0.759426i	$-0.725480\pi$
$809$	−3.39325e97	−1.30119	−0.650594	+	0.759426i	$0.725480\pi$
$810$	−1.03478e96	−0.0380714
$811$	−2.89220e97	−1.02101	−0.510504	−	0.859875i	$-0.670541\pi$
$811$	−2.89220e97	−1.02101	−0.510504	+	0.859875i	$0.670541\pi$
$812$	3.64209e97	1.23374
$813$	4.53472e96	0.147407
$814$	−1.08296e97	−0.337828
$815$	−1.26709e97	−0.379338
$816$	1.21162e96	0.0348133
$817$	4.36233e97	1.20304
$818$	2.77038e97	0.733338
$819$	−2.78629e97	−0.707972
$820$	−3.82072e97	−0.931924
$821$	−5.73101e97	−1.34195	−0.670973	−	0.741482i	$-0.734123\pi$
$821$	−5.73101e97	−1.34195	−0.670973	+	0.741482i	$0.734123\pi$
$822$	5.23900e96	0.117772
$823$	5.84786e97	1.26213	0.631063	−	0.775732i	$-0.282619\pi$
$823$	5.84786e97	1.26213	0.631063	+	0.775732i	$0.282619\pi$
$824$	−3.15402e97	−0.653587
$825$	2.15614e97	0.429012
$826$	4.71127e97	0.900132
$827$	−1.64939e97	−0.302614	−0.151307	−	0.988487i	$-0.548348\pi$
$827$	−1.64939e97	−0.302614	−0.151307	+	0.988487i	$0.548348\pi$
$828$	−9.05143e96	−0.159478
$829$	−9.64766e97	−1.63247	−0.816235	−	0.577720i	$-0.803942\pi$
$829$	−9.64766e97	−1.63247	−0.816235	+	0.577720i	$0.803942\pi$
$830$	−1.10479e97	−0.179540
$831$	−2.01746e97	−0.314899
$832$	−8.70477e96	−0.130505
$833$	2.62317e97	0.377763
$834$	1.01950e97	0.141035
$835$	−5.77775e97	−0.767824
$836$	−1.15585e98	−1.47567
$837$	1.70406e97	0.209018
$838$	−2.35975e97	−0.278093
$839$	−4.06038e97	−0.459771	−0.229885	−	0.973218i	$-0.573835\pi$
$839$	−4.06038e97	−0.459771	−0.229885	+	0.973218i	$0.573835\pi$
$840$	5.89197e97	0.641069
$841$	−2.28166e97	−0.238553
$842$	−1.42065e97	−0.142735
$843$	4.74044e97	0.457715
$844$	1.58193e98	1.46796
$845$	2.84323e97	0.253578
$846$	1.83432e97	0.157241
$847$	3.08368e98	2.54083
$848$	−7.99305e97	−0.633070
$849$	−1.90633e97	−0.145141
$850$	5.04575e96	0.0369310
$851$	−4.03713e97	−0.284075
$852$	−1.29804e97	−0.0878139
$853$	8.43388e97	0.548574	0.274287	−	0.961648i	$-0.411558\pi$
$853$	8.43388e97	0.548574	0.274287	+	0.961648i	$0.411558\pi$
$854$	−1.11350e98	−0.696390
$855$	−4.92596e97	−0.296228
$856$	−2.92031e97	−0.168872
$857$	1.46311e98	0.813615	0.406807	−	0.913514i	$-0.366642\pi$
$857$	1.46311e98	0.813615	0.406807	+	0.913514i	$0.366642\pi$
$858$	−9.22746e97	−0.493467
$859$	5.83986e96	0.0300352	0.0150176	−	0.999887i	$-0.495220\pi$
$859$	5.83986e96	0.0300352	0.0150176	+	0.999887i	$0.495220\pi$
$860$	1.10026e98	0.544249
$861$	3.70342e98	1.76197
$862$	−4.83882e96	−0.0221435
$863$	3.12456e98	1.37539	0.687697	−	0.725998i	$-0.258622\pi$
$863$	3.12456e98	1.37539	0.687697	+	0.725998i	$0.258622\pi$
$864$	−4.63912e97	−0.196438
$865$	2.37037e96	0.00965552
$866$	−1.94158e97	−0.0760862
$867$	−1.49135e98	−0.562264
$868$	−4.23331e98	−1.53557
$869$	1.35666e97	0.0473489
$870$	5.14039e97	0.172624
$871$	−2.04380e98	−0.660434
$872$	−3.43878e98	−1.06931
$873$	−1.32311e98	−0.395932
$874$	1.25829e98	0.362365
$875$	−7.03296e98	−1.94925
$876$	1.11716e98	0.298009
$877$	−7.69315e97	−0.197523	−0.0987615	−	0.995111i	$-0.531488\pi$
$877$	−7.69315e97	−0.197523	−0.0987615	+	0.995111i	$0.531488\pi$
$878$	−3.17212e98	−0.783940
$879$	3.96866e98	0.944097
$880$	−1.81533e98	−0.415705
$881$	6.54753e98	1.44339	0.721697	−	0.692209i	$-0.243362\pi$
$881$	6.54753e98	1.44339	0.721697	+	0.692209i	$0.243362\pi$
$882$	−1.74502e98	−0.370341
$883$	4.98413e98	1.01837	0.509185	−	0.860657i	$-0.329947\pi$
$883$	4.98413e98	1.01837	0.509185	+	0.860657i	$0.329947\pi$
$884$	7.39456e97	0.145466
$885$	−2.27700e98	−0.431285
$886$	−4.73238e97	−0.0863078
$887$	−2.61814e98	−0.459781	−0.229891	−	0.973216i	$-0.573837\pi$
$887$	−2.61814e98	−0.459781	−0.229891	+	0.973216i	$0.573837\pi$
$888$	−1.32323e98	−0.223770
$889$	−1.14077e99	−1.85775
$890$	3.06801e98	0.481162
$891$	−1.13748e98	−0.171806
$892$	1.44071e98	0.209582
$893$	8.73207e98	1.22347
$894$	−1.78920e98	−0.241464
$895$	1.91568e98	0.249029
$896$	1.41117e99	1.76710
$897$	−3.43987e98	−0.414949
$898$	−3.91165e98	−0.454572
$899$	−8.46515e98	−0.947731
$900$	1.14942e98	0.123981
$901$	−2.63977e98	−0.274338
$902$	1.22648e99	1.22812
$903$	−1.06648e99	−1.02900
$904$	1.78225e99	1.65701
$905$	1.04109e99	0.932737
$906$	−2.78592e97	−0.0240533
$907$	−1.03722e98	−0.0863030	−0.0431515	−	0.999069i	$-0.513740\pi$
$907$	−1.03722e98	−0.0863030	−0.0431515	+	0.999069i	$0.513740\pi$
$908$	−1.23210e99	−0.988028
$909$	−4.13416e97	−0.0319519
$910$	9.76935e98	0.727745
$911$	1.61687e99	1.16094	0.580469	−	0.814282i	$-0.302869\pi$
$911$	1.61687e99	1.16094	0.580469	+	0.814282i	$0.302869\pi$
$912$	−3.83691e98	−0.265555
$913$	−1.21443e99	−0.810218
$914$	−1.17889e99	−0.758188
$915$	5.38167e98	0.333665
$916$	−1.05236e99	−0.629023
$917$	−9.10088e97	−0.0524458
$918$	−2.66190e97	−0.0147898
$919$	1.86340e99	0.998244	0.499122	−	0.866532i	$-0.333656\pi$
$919$	1.86340e99	0.998244	0.499122	+	0.866532i	$0.333656\pi$
$920$	7.27404e98	0.375736
$921$	4.27938e98	0.213149
$922$	−4.99517e98	−0.239919
$923$	−4.93303e98	−0.228485
$924$	2.82577e99	1.26219
$925$	5.12667e98	0.220845
$926$	−1.68348e99	−0.699425
$927$	−6.44660e98	−0.258321
$928$	2.30454e99	0.890690
$929$	−8.15833e98	−0.304141	−0.152070	−	0.988370i	$-0.548594\pi$
$929$	−8.15833e98	−0.304141	−0.152070	+	0.988370i	$0.548594\pi$
$930$	−5.97482e98	−0.214855
$931$	−8.30697e99	−2.88157
$932$	1.57190e99	0.526009
$933$	−2.61799e99	−0.845149
$934$	1.97522e99	0.615169
$935$	−5.99526e98	−0.180144
$936$	−1.12747e99	−0.326862
$937$	−3.12630e99	−0.874489	−0.437245	−	0.899343i	$-0.644046\pi$
$937$	−3.12630e99	−0.874489	−0.437245	+	0.899343i	$0.644046\pi$
$938$	−1.82773e99	−0.493306
$939$	1.44897e99	0.377366
$940$	2.20239e99	0.553492
$941$	−7.45385e98	−0.180771	−0.0903854	−	0.995907i	$-0.528810\pi$
$941$	−7.45385e98	−0.180771	−0.0903854	+	0.995907i	$0.528810\pi$
$942$	6.27101e98	0.146768
$943$	4.57213e99	1.03271
$944$	−1.77360e99	−0.386628
$945$	1.20428e99	0.253373
$946$	−3.53191e99	−0.717227
$947$	−7.61494e99	−1.49260	−0.746298	−	0.665612i	$-0.768170\pi$
$947$	−7.61494e99	−1.49260	−0.746298	+	0.665612i	$0.768170\pi$
$948$	7.23229e97	0.0136835
$949$	4.24562e99	0.775394
$950$	−1.59787e99	−0.281709
$951$	3.96566e99	0.674944
$952$	1.51567e99	0.249039
$953$	9.71747e99	1.54149	0.770745	−	0.637143i	$-0.219884\pi$
$953$	9.71747e99	1.54149	0.770745	+	0.637143i	$0.219884\pi$
$954$	1.75606e99	0.268948
$955$	−1.09412e99	−0.161790
$956$	−1.73969e99	−0.248390
$957$	5.65056e99	0.779007
$958$	−2.20606e99	−0.293679
$959$	−6.09716e99	−0.783798
$960$	3.76233e98	0.0467057
$961$	1.49800e99	0.179588
$962$	−2.19402e99	−0.254025
$963$	−5.96890e98	−0.0667442
$964$	2.88142e99	0.311190
$965$	−6.59005e99	−0.687423
$966$	−3.07620e99	−0.309943
$967$	1.25380e100	1.22023	0.610117	−	0.792312i	$-0.291123\pi$
$967$	1.25380e100	1.22023	0.610117	+	0.792312i	$0.291123\pi$
$968$	1.24781e100	1.17307
$969$	−1.26717e99	−0.115077
$970$	4.63913e99	0.406990
$971$	1.53306e100	1.29932	0.649658	−	0.760226i	$-0.274912\pi$
$971$	1.53306e100	1.29932	0.649658	+	0.760226i	$0.274912\pi$
$972$	−6.06382e98	−0.0496508
$973$	−1.18650e100	−0.938615
$974$	−1.77842e99	−0.135928
$975$	4.36822e99	0.322589
$976$	4.19187e99	0.299116
$977$	−1.53934e100	−1.06137	−0.530685	−	0.847569i	$-0.678065\pi$
$977$	−1.53934e100	−1.06137	−0.530685	+	0.847569i	$0.678065\pi$
$978$	2.16832e99	0.144468
$979$	3.37250e100	2.17136
$980$	−2.09517e100	−1.30361
$981$	−7.02862e99	−0.422628
$982$	−7.03649e99	−0.408904
$983$	4.33889e99	0.243689	0.121845	−	0.992549i	$-0.461119\pi$
$983$	4.33889e99	0.243689	0.121845	+	0.992549i	$0.461119\pi$
$984$	1.49859e100	0.813478
$985$	−1.18913e100	−0.623901
$986$	1.32233e99	0.0670600
$987$	−2.13478e100	−1.04647
$988$	−2.34169e100	−1.10961
$989$	−1.31665e100	−0.603106
$990$	3.98824e99	0.176605
$991$	4.29161e98	0.0183719	0.00918593	−	0.999958i	$-0.497076\pi$
$991$	4.29161e98	0.0183719	0.00918593	+	0.999958i	$0.497076\pi$
$992$	−2.67863e100	−1.10859
$993$	−2.73784e100	−1.09549
$994$	−4.41151e99	−0.170665
$995$	3.31376e99	0.123950
$996$	−6.47406e99	−0.234147
$997$	−3.72332e100	−1.30209	−0.651047	−	0.759037i	$-0.725670\pi$
$997$	−3.72332e100	−1.30209	−0.651047	+	0.759037i	$0.725670\pi$
$998$	2.46597e100	0.833900
$999$	−2.70459e99	−0.0884419

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.68.a.a.1.3	✓	5
3.2	odd	2		9.68.a.b.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.68.a.a.1.3	✓	5	1.1	even	1	trivial
9.68.a.b.1.3		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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 68 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-5.77536e9 q^{2} +5.55906e15 q^{3} -1.14219e20 q^{4} +1.87613e23 q^{5} -3.21056e25 q^{6} +3.73645e28 q^{7} +1.51195e30 q^{8} +3.09032e31 q^{9} +O(q^{10})\)	\(q-5.77536e9 q^{2} +5.55906e15 q^{3} -1.14219e20 q^{4} +1.87613e23 q^{5} -3.21056e25 q^{6} +3.73645e28 q^{7} +1.51195e30 q^{8} +3.09032e31 q^{9} -1.08353e33 q^{10} -1.19107e35 q^{11} -6.34951e35 q^{12} -2.41304e37 q^{13} -2.15793e38 q^{14} +1.04295e39 q^{15} +8.12372e39 q^{16} +2.68293e40 q^{17} -1.78477e41 q^{18} -8.49620e42 q^{19} -2.14290e43 q^{20} +2.07711e44 q^{21} +6.87885e44 q^{22} +2.56434e45 q^{23} +8.40502e45 q^{24} -3.25640e46 q^{25} +1.39362e47 q^{26} +1.71793e47 q^{27} -4.26774e48 q^{28} -8.53400e48 q^{29} -6.02342e48 q^{30} +9.91932e49 q^{31} -2.70042e50 q^{32} -6.62122e50 q^{33} -1.54949e50 q^{34} +7.01006e51 q^{35} -3.52973e51 q^{36} -1.57434e52 q^{37} +4.90686e52 q^{38} -1.34142e53 q^{39} +2.83661e53 q^{40} +1.78297e54 q^{41} -1.19961e54 q^{42} -5.13445e54 q^{43} +1.36043e55 q^{44} +5.79783e54 q^{45} -1.48100e55 q^{46} -1.02776e56 q^{47} +4.51603e55 q^{48} +9.77728e56 q^{49} +1.88069e56 q^{50} +1.49145e56 q^{51} +2.75616e57 q^{52} -9.83914e57 q^{53} -9.92163e56 q^{54} -2.23460e58 q^{55} +5.64932e58 q^{56} -4.72309e58 q^{57} +4.92869e58 q^{58} -2.18323e59 q^{59} -1.19125e59 q^{60} +5.16004e59 q^{61} -5.72876e59 q^{62} +1.15468e60 q^{63} +3.60738e59 q^{64} -4.52718e60 q^{65} +3.82399e60 q^{66} +8.46980e60 q^{67} -3.06442e60 q^{68} +1.42553e61 q^{69} -4.04856e61 q^{70} +2.04432e61 q^{71} +4.67240e61 q^{72} -1.75945e62 q^{73} +9.09236e61 q^{74} -1.81025e62 q^{75} +9.70430e62 q^{76} -4.45037e63 q^{77} +7.74721e62 q^{78} -1.13903e62 q^{79} +1.52412e63 q^{80} +9.55005e62 q^{81} -1.02973e64 q^{82} +1.01962e64 q^{83} -2.37246e64 q^{84} +5.03352e63 q^{85} +2.96533e64 q^{86} -4.74410e64 q^{87} -1.80084e65 q^{88} -2.83149e65 q^{89} -3.34846e64 q^{90} -9.01621e65 q^{91} -2.92897e65 q^{92} +5.51421e65 q^{93} +5.93569e65 q^{94} -1.59400e66 q^{95} -1.50118e66 q^{96} -4.28149e66 q^{97} -5.64673e66 q^{98} -3.68078e66 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 16255223088 q^{2} + 27\!\cdots\!15 q^{3}+ \cdots + 15\!\cdots\!45 q^{9}+O(q^{10}) \) 5 * q - 16255223088 * q^2 + 27795302832777615 * q^3 + 187725942510165022976 * q^4 - 78587975159033653413210 * q^5 - 90363769669063698103515024 * q^6 + 2897133779647323835395360808 * q^7 - 446560396075670111196535861248 * q^8 + 154515771913163061809603209017645 * q^9	\( 5 q - 16255223088 q^{2} + 27\!\cdots\!15 q^{3}+ \cdots - 33\!\cdots\!28 q^{99}+O(q^{100}) \) 5 * q - 16255223088 * q^2 + 27795302832777615 * q^3 + 187725942510165022976 * q^4 - 78587975159033653413210 * q^5 - 90363769669063698103515024 * q^6 + 2897133779647323835395360808 * q^7 - 446560396075670111196535861248 * q^8 + 154515771913163061809603209017645 * q^9 - 3359687674843328387731353730265760 * q^10 - 107218677940017498877929099247513932 * q^11 + 1043579884327727512139439968474696448 * q^12 + 18720658700128270654310089005018371278 * q^13 - 61671302560002915461244055855418861952 * q^14 - 436875313712028989080558866721926658830 * q^15 + 19828810558474760279626207936836822695936 * q^16 + 155634077783406813100849154582687160437850 * q^17 - 502337668612598026687246628668502560677552 * q^18 - 6330823499631802877762269921902501094783988 * q^19 + 8806685958461200090592049790099809534328320 * q^20 + 16105342150473395769449245566105034350142584 * q^21 - 1285334407460495219610552944494458560199940800 * q^22 - 3096470811979061341218583695224599825546419864 * q^23 - 2482456288409673438086642069250837537616072704 * q^24 - 128510195883326013861116838537875526813134026525 * q^25 - 309893301421656093037055250012280159780714544160 * q^26 + 858962534553352218394101882942702121170179203335 * q^27 - 1758216414458764947454106710991446824456120252416 * q^28 - 17195448123638013107201791699494703244624614194066 * q^29 - 18676707269164160844617717039655071934318585792480 * q^30 - 167299848682287535534976349940903215242774636120144 * q^31 - 661581347508711830434048681313730640500855508303872 * q^32 - 596035124534567832987517244399918779918082194046436 * q^33 - 3668629124130223548817939535033459308602451741777248 * q^34 - 597313366964957875633721976544849058693729215396560 * q^35 + 5801323783016844061209039192798206302504038362882304 * q^36 + 30043361009726020519419208243072073319518814491934358 * q^37 + 260485037699007543111228693866771891318790849526359744 * q^38 + 104069275559827645019221591022442107451411644015468394 * q^39 + 1115094440991577594559320173651217718577849903091507200 * q^40 - 808437303878393630827363118778237447937170861730235454 * q^41 - 342834506149426883197674031813537074530930837280160896 * q^42 - 4736429276246859157617871173658532851277246462721149228 * q^43 + 7015258532306255548162192439376864244003799076792468480 * q^44 - 2428616328958113717945826873336511479963953561073218090 * q^45 + 12527540911364294799696045411504819449186256978468080256 * q^46 + 108290076402229329642983829719434835232002632660130515056 * q^47 + 110229558857316837304648760016604589737407028314290454528 * q^48 + 880181676573802609519730686079181363021552872382740232333 * q^49 + 1052494889081109131658159592164188937755980711801220679600 * q^50 + 865179264617971813637134219389277404805805348251015745550 * q^51 + 2308777474667263284772763232859451620790190619345360422400 * q^52 + 3245226878182367959789303611224433348480161481518744370966 * q^53 - 2792525524679729749647164642126896980230414112629707719696 * q^54 - 51262912349629136715335621059095130466245073679837843274920 * q^55 - 47772133165991162191839606887952190261990284108568121671680 * q^56 - 35193431270626188960239511075559223006610539094694893365724 * q^57 - 84493666334602655307554841072065967874913257934429532582432 * q^58 - 179624529165245332659094970865033289643789158511842592792412 * q^59 + 48956900633719888068348132839178395661941003500967791311360 * q^60 + 584907690374744349731719712847344294312321913116060488567102 * q^61 + 3025719874056683992201295546200663430948598802434153503920896 * q^62 + 89530572459581180641513960803016595914572442189036802691432 * q^63 - 4499392031332841330291967248952523929085218266739063232921600 * q^64 - 4475515698809998982184518632813763939217510489440113220535420 * q^65 - 7145251819350648004204211437078044590913023079552444513038400 * q^66 + 1344914323542783268647242614869504266340689501787079942327420 * q^67 + 19365780359678204058695683499114787965920302224535027287671296 * q^68 - 17213468786362961074546343099951406673447837437328506826108872 * q^69 + 31668988367649764945620440396543964676121485136652812185168640 * q^70 + 208099792629824800554470944953685171609425458107698538896812280 * q^71 - 13800124861096000027311301435875177780070484438004484020744192 * q^72 - 252414514587179259177941988046481265295589404121206374617470334 * q^73 - 358084904219721857079108717596560064061662918994206334990793632 * q^74 - 714395962335323550124996935032662148018445244009738166967247575 * q^75 - 3167576238289455647607470438405921376289304779045740803124282368 * q^76 - 2715616264867565296962962180641800513550454260043685733361085024 * q^77 - 1722715631772832981701583674878761695633721340944383480275395680 * q^78 - 3431503850832591202644393930474874375763697022794649483222945280 * q^79 - 8322155504340769679256255462767373452465836703993138541717749760 * q^80 + 4775024753984126184465953508872070059599675694871715649184269205 * q^81 - 6362169783346643199240774371522649930233919884701663896646628064 * q^82 - 2753559226275970537111940225815871118779223599597864793376534836 * q^83 - 9774031537088362109664563191733058527530044006822089118438893568 * q^84 - 100223085545462292798863671541625307722645907180923010395975039060 * q^85 - 287767761108017143223082018540844348985876033069110036187064944832 * q^86 - 95590537588367238050824370796559187863343340269759771352286126518 * q^87 - 475509956271309169302126186902650458005506404316097446988140167168 * q^88 - 953231813381767774308665680609247777419192406201469535932206722638 * q^89 - 103824946893111374784083486264977336654984096886031891078875867040 * q^90 - 1826343975172985917715752368227201077015187248090890361406237190544 * q^91 - 3132766731772277225542233484759817592417648594742828753496091850752 * q^92 - 930029991600410615305341159302088161126938972921803642822874755312 * q^93 - 4377709041417318550457656800988375516480152699177767581662212342016 * q^94 - 3334812729598028343033336500168508357868459521335461166424246211800 * q^95 - 3677770780504345932935680810193675103543675932078897134851043885056 * q^96 - 11968150959482375162440074477550294838351889417758320270285978711190 * q^97 - 17297597363568888846780657367452226513119832175100344485603054876848 * q^98 - 3313395357082126364699797809873297365206219515646735115126034266028 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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