LMFDB - Embedded newform 3.72.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,72,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, 72, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 72);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 72 $
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:	$95.7738481683$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 27\!\cdots\!00 $ x^6 - 3x^5 - 327712249929578892882x^4 - 247064970776889197907293537206x^3 + 25021443441555202497465421340907628615965x^2 + 14077016837018585361473224499724917623325562275625*x - 279259064416593965218586682187488478036140359478345093745500
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{49}\cdot 3^{29}\cdot 5^{7}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.55163e10$ 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)

$f(q)$	$=$	$q+8.09473e10 q^{2} -5.00315e16 q^{3} +4.19128e21 q^{4} +7.59856e24 q^{5} -4.04992e27 q^{6} +1.03665e30 q^{7} +1.48142e32 q^{8} +2.50316e33 q^{9} +O(q^{10})$	\(q+8.09473e10 q^{2} -5.00315e16 q^{3} +4.19128e21 q^{4} +7.59856e24 q^{5} -4.04992e27 q^{6} +1.03665e30 q^{7} +1.48142e32 q^{8} +2.50316e33 q^{9} +6.15083e35 q^{10} +1.84599e37 q^{11} -2.09696e38 q^{12} +3.63924e39 q^{13} +8.39143e40 q^{14} -3.80167e41 q^{15} +2.09527e42 q^{16} -6.76951e43 q^{17} +2.02624e44 q^{18} -2.13387e45 q^{19} +3.18477e46 q^{20} -5.18653e46 q^{21} +1.49428e48 q^{22} +4.23025e47 q^{23} -7.41175e48 q^{24} +1.53864e49 q^{25} +2.94586e50 q^{26} -1.25237e50 q^{27} +4.34490e51 q^{28} +3.95427e51 q^{29} -3.07735e52 q^{30} -1.84438e52 q^{31} -1.80183e53 q^{32} -9.23577e53 q^{33} -5.47974e54 q^{34} +7.87707e54 q^{35} +1.04914e55 q^{36} +7.59903e55 q^{37} -1.72731e56 q^{38} -1.82077e56 q^{39} +1.12566e57 q^{40} -1.64875e57 q^{41} -4.19836e57 q^{42} -4.45136e57 q^{43} +7.73706e58 q^{44} +1.90204e58 q^{45} +3.42428e58 q^{46} +1.38140e59 q^{47} -1.04830e59 q^{48} +7.01241e58 q^{49} +1.24549e60 q^{50} +3.38689e60 q^{51} +1.52531e61 q^{52} +1.74264e61 q^{53} -1.01376e61 q^{54} +1.40269e62 q^{55} +1.53571e62 q^{56} +1.06761e62 q^{57} +3.20087e62 q^{58} -1.37996e63 q^{59} -1.59339e63 q^{60} +4.64940e62 q^{61} -1.49298e63 q^{62} +2.59490e63 q^{63} -1.95326e64 q^{64} +2.76529e64 q^{65} -7.47610e64 q^{66} +3.89158e63 q^{67} -2.83729e65 q^{68} -2.11646e64 q^{69} +6.37627e65 q^{70} +7.57891e65 q^{71} +3.70821e65 q^{72} -1.83450e66 q^{73} +6.15121e66 q^{74} -7.69806e65 q^{75} -8.94366e66 q^{76} +1.91365e67 q^{77} -1.47386e67 q^{78} +6.44832e66 q^{79} +1.59211e67 q^{80} +6.26579e66 q^{81} -1.33462e68 q^{82} +8.97347e67 q^{83} -2.17382e68 q^{84} -5.14385e68 q^{85} -3.60326e68 q^{86} -1.97838e68 q^{87} +2.73468e69 q^{88} +2.67603e69 q^{89} +1.53965e69 q^{90} +3.77263e69 q^{91} +1.77302e69 q^{92} +9.22774e68 q^{93} +1.11821e70 q^{94} -1.62143e70 q^{95} +9.01481e69 q^{96} -5.40339e69 q^{97} +5.67635e69 q^{98} +4.62080e70 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 72903656826 q^{2} - 30\!\cdots\!42 q^{3}+ \cdots + 15\!\cdots\!94 q^{9}+O(q^{10}) $ 6 * q - 72903656826 * q^2 - 300189270593998242 * q^3 + 10314006409421274045732 * q^4 + 10108593794701196744004900 * q^5 + 3647482594372016835002549982 * q^6 + 599480901407450839419869685888 * q^7 - 366478583494279643287721499310632 * q^8 + 15018933029959449607893431916515094 * q^9	$ 6 q - 72903656826 q^{2} - 30\!\cdots\!42 q^{3}+ \cdots + 55\!\cdots\!36 q^{99}+O(q^{100}) $ 6 * q - 72903656826 * q^2 - 300189270593998242 * q^3 + 10314006409421274045732 * q^4 + 10108593794701196744004900 * q^5 + 3647482594372016835002549982 * q^6 + 599480901407450839419869685888 * q^7 - 366478583494279643287721499310632 * q^8 + 15018933029959449607893431916515094 * q^9 + 542868868744970666737312582578468900 * q^10 + 22151081175113604333940540682999237064 * q^11 - 516025676824332508905200786034172600524 * q^12 - 3733792306574713187109013147800580842876 * q^13 - 32830507140759982684754962229979568501632 * q^14 - 505748566327061510308971264776339106564300 * q^15 + 21946377025014017232533669358468876656094480 * q^16 + 29728537162009030546400351590681521887294796 * q^17 - 182489189918140015151617170203501982470855274 * q^18 - 3400191903952978211629854680984130031529265672 * q^19 + 67862977310829773665490051450873586512770090200 * q^20 - 29992955754755873599156504803112485841094034816 * q^21 + 944165659732727247119333482328915476491852443592 * q^22 - 241048097798755219551674687627695903843789894224 * q^23 + 18335489777911581603442307001776299015793269984824 * q^24 + 147233544111014179651192740252202252138516733666250 * q^25 + 365811593583549796821577322473046008640162770663812 * q^26 - 751420425227272520651160327198275815599672767077458 * q^27 + 7184703440899560087451639062714257068053559172254464 * q^28 + 14043556001266662709861160370005828332436911172303796 * q^29 - 27160568289456952381721411384929474444132225608612300 * q^30 - 270783306371944339515858500277888580308160694590498224 * q^31 - 1125690872219692784327995632757361168637025492519761312 * q^32 - 1108252816804299721415203709279850747171688230559540248 * q^33 - 14624984721002826287006157938202770657423642866907848116 * q^34 + 1330179995756585937201666471865883862092414077711430400 * q^35 + 25817561922278439824339062712693846594436309019304046468 * q^36 - 35792724481179188252370374519670456030630938465810079852 * q^37 - 40096713421645845706764919843501793548783513747008434184 * q^38 + 186807398176690903032688790342604890157893721294537037332 * q^39 - 2479587661237177399988484749809178898031295693356625910000 * q^40 + 477389693785559225342921822791522325133674715121487806716 * q^41 + 1642560998635964995488184749898337758134027879087997021824 * q^42 + 11648760938240913572137172567293471863701640091329944903880 * q^43 + 74878798041661318901325225719624262581993699901301979154096 * q^44 + 25303382204946822552840415428929959629608562926007476660100 * q^45 - 22722764972174503220374661680362423965849207035012290901584 * q^46 - 74847986304767650251381147705131168308416847087017595772160 * q^47 - 1098011151886639823988203119437140867642137257944093284317360 * q^48 - 688653477285391597239303104103354245619646953145790225785290 * q^49 - 15161902343877042722978992840348999467045739232226501266733750 * q^50 - 1487364647748343570766109334072688855147129111496091826624772 * q^51 - 9233127809375467425363213342738333025041297615633059381760744 * q^52 + 54557017276559944552388010917280252208764745473331764291919716 * q^53 + 9130216135469344816922031758794829019895633468152138165404718 * q^54 - 23377768702274474935917895870707480727711321830514284596005200 * q^55 + 52410231138004746064340786054323553480340549752421553548034560 * q^56 + 170116854587877109514295582543857751828315219056921303453158104 * q^57 - 6869577034896111059681057797577176576414351550513678648728908 * q^58 - 2982562673835141937005021578485268051001526328776278691712555448 * q^59 - 3395289609879173678404575975976528237976459801298749688163571400 * q^60 + 2024766122758654206628711672366353464571765836352692052196097220 * q^61 + 6190527473014961587199547234678103673640494648116320147386047056 * q^62 + 1500593918496371285775305974945167898072787838438228726231798912 * q^63 + 45446447421689003372958411079333884263847638574085838786019075648 * q^64 + 48520756571856116218224136414427408842784606511438543051271531800 * q^65 - 47238066785844754909978749266876448249150867465391889442842027544 * q^66 - 35831986821500503360634896265657012310045332669260449034581275784 * q^67 + 185089183911227350024079142251468478888729548294423879590659066312 * q^68 + 12060008776046513765968603659742476293934666629048669377736992368 * q^69 - 344172356460367114079337658836072099942116692861986486268441785600 * q^70 - 51113783482860556737395980857143689650967786833886125865998410928 * q^71 - 917352883735831416728537588310564568722018780050793374149470446568 * q^72 - 1956710326081635365311373308078888669483174388894330237696366066724 * q^73 + 5709348546681615596063021572004447539391345291333750996512485900948 * q^74 - 7366321702275768652418713145914811812464675260129281903805785788750 * q^75 - 23809271474859754704092582776426668087720715729896871772596110280752 * q^76 + 18917631699413080007630569020425573902563798951131161813579745527296 * q^77 - 18302119242112323501394112685535398871026762720686772677565583503084 * q^78 + 48402596803386404034053884911414009193830041621338105095759924707760 * q^79 + 263392522337449869178773130835490329512120616670537417787135845410400 * q^80 + 37594724893067822275537345166051581993240166680863991649157588304806 * q^81 - 304020075917296666161317294537198008494062493274925376834937204559364 * q^82 + 231863714798237849378047661016738227772765340915812707253802255256568 * q^83 - 359461814226304716526488880176552818520355782596793385427234465442048 * q^84 - 153432496682031145548917546056875902159222382871180623315806512428600 * q^85 + 232789528332961926178362349658049178503816504422806394312074365597384 * q^86 - 702620805427701021731731825948244137787180874181672925287922318987772 * q^87 + 5297065653948252699139641997691020789333729718805571695420136408677408 * q^88 + 4386397294164484419236854507748631162668647776406659364039350285963708 * q^89 + 1358885197288426841258681446071983205212433617120516879514014376596100 * q^90 + 10645224502890544811266185738918008251735428747945615198269035910167296 * q^91 + 3494882087686348167672392093650816456059296420998691954341908970318368 * q^92 + 13547707204804187951296675402664208391644243687789646939851889160020368 * q^93 + 212140324104529926314570388896027999493814139075827826098897565498112 * q^94 - 32230267438252135206013682642661075145567906057502744951334901038078000 * q^95 + 56320053640991875947605433538589148930174287383392714581574101597935584 * q^96 + 97296789347912261411847519869140120543815674831725660650989227379865996 * q^97 + 262411331100552434262334793443846407592764783361237538614096838440889526 * q^98 + 55447600785037781851022576825288562814422347406938226617866090606707336 * 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 $

$2$	8.09473e10	1.66586	0.832928	−	0.553381i	$-0.186663\pi$
$2$	8.09473e10	1.66586	0.832928	+	0.553381i	$0.186663\pi$
$3$	−5.00315e16	−0.577350
$3$	−5.00315e16	−0.577350
$4$	4.19128e21	1.77508
$5$	7.59856e24	1.16760	0.583802	−	0.811896i	$-0.301564\pi$
$5$	7.59856e24	1.16760	0.583802	+	0.811896i	$0.301564\pi$
$6$	−4.04992e27	−0.961783
$7$	1.03665e30	1.03432	0.517158	−	0.855890i	$-0.326990\pi$
$7$	1.03665e30	1.03432	0.517158	+	0.855890i	$0.326990\pi$
$8$	1.48142e32	1.29117
$9$	2.50316e33	0.333333
$10$	6.15083e35	1.94506
$11$	1.84599e37	1.98056	0.990282	−	0.139075i	$-0.0444131\pi$
$11$	1.84599e37	1.98056	0.990282	+	0.139075i	$0.0444131\pi$
$12$	−2.09696e38	−1.02484
$13$	3.63924e39	1.03758	0.518790	−	0.854902i	$-0.326383\pi$
$13$	3.63924e39	1.03758	0.518790	+	0.854902i	$0.326383\pi$
$14$	8.39143e40	1.72302
$15$	−3.80167e41	−0.674117
$16$	2.09527e42	0.375821
$17$	−6.76951e43	−1.41130	−0.705652	−	0.708559i	$-0.749346\pi$
$17$	−6.76951e43	−1.41130	−0.705652	+	0.708559i	$0.749346\pi$
$18$	2.02624e44	0.555285
$19$	−2.13387e45	−0.857858	−0.428929	−	0.903338i	$-0.641109\pi$
$19$	−2.13387e45	−0.857858	−0.428929	+	0.903338i	$0.641109\pi$
$20$	3.18477e46	2.07259
$21$	−5.18653e46	−0.597162
$22$	1.49428e48	3.29933
$23$	4.23025e47	0.192765	0.0963825	−	0.995344i	$-0.469273\pi$
$23$	4.23025e47	0.192765	0.0963825	+	0.995344i	$0.469273\pi$
$24$	−7.41175e48	−0.745456
$25$	1.53864e49	0.363301
$26$	2.94586e50	1.72846
$27$	−1.25237e50	−0.192450
$28$	4.34490e51	1.83599
$29$	3.95427e51	0.480770	0.240385	−	0.970678i	$-0.422726\pi$
$29$	3.95427e51	0.480770	0.240385	+	0.970678i	$0.422726\pi$
$30$	−3.07735e52	−1.12298
$31$	−1.84438e52	−0.210141	−0.105071	−	0.994465i	$-0.533507\pi$
$31$	−1.84438e52	−0.210141	−0.105071	+	0.994465i	$0.533507\pi$
$32$	−1.80183e53	−0.665103
$33$	−9.23577e53	−1.14348
$34$	−5.47974e54	−2.35103
$35$	7.87707e54	1.20767
$36$	1.04914e55	0.591692
$37$	7.59903e55	1.62031	0.810153	−	0.586219i	$-0.199384\pi$
$37$	7.59903e55	1.62031	0.810153	+	0.586219i	$0.199384\pi$
$38$	−1.72731e56	−1.42907
$39$	−1.82077e56	−0.599047
$40$	1.12566e57	1.50757
$41$	−1.64875e57	−0.919026	−0.459513	−	0.888171i	$-0.651976\pi$
$41$	−1.64875e57	−0.919026	−0.459513	+	0.888171i	$0.651976\pi$
$42$	−4.19836e57	−0.994786
$43$	−4.45136e57	−0.457470	−0.228735	−	0.973489i	$-0.573459\pi$
$43$	−4.45136e57	−0.457470	−0.228735	+	0.973489i	$0.573459\pi$
$44$	7.73706e58	3.51565
$45$	1.90204e58	0.389202
$46$	3.42428e58	0.321119
$47$	1.38140e59	0.603736	0.301868	−	0.953350i	$-0.402390\pi$
$47$	1.38140e59	0.603736	0.301868	+	0.953350i	$0.402390\pi$
$48$	−1.04830e59	−0.216981
$49$	7.01241e58	0.0698082
$50$	1.24549e60	0.605208
$51$	3.38689e60	0.814817
$52$	1.52531e61	1.84178
$53$	1.74264e61	1.07007	0.535036	−	0.844829i	$-0.320298\pi$
$53$	1.74264e61	1.07007	0.535036	+	0.844829i	$0.320298\pi$
$54$	−1.01376e61	−0.320594
$55$	1.40269e62	2.31252
$56$	1.53571e62	1.33547
$57$	1.06761e62	0.495285
$58$	3.20087e62	0.800894
$59$	−1.37996e63	−1.88201	−0.941004	−	0.338395i	$-0.890116\pi$
$59$	−1.37996e63	−1.88201	−0.941004	+	0.338395i	$0.890116\pi$
$60$	−1.59339e63	−1.19661
$61$	4.64940e62	0.194172	0.0970862	−	0.995276i	$-0.469048\pi$
$61$	4.64940e62	0.194172	0.0970862	+	0.995276i	$0.469048\pi$
$62$	−1.49298e63	−0.350065
$63$	2.59490e63	0.344772
$64$	−1.95326e64	−1.48379
$65$	2.76529e64	1.21148
$66$	−7.47610e64	−1.90487
$67$	3.89158e63	0.0581393	0.0290697	−	0.999577i	$-0.490746\pi$
$67$	3.89158e63	0.0581393	0.0290697	+	0.999577i	$0.490746\pi$
$68$	−2.83729e65	−2.50517
$69$	−2.11646e64	−0.111293
$70$	6.37627e65	2.01181
$71$	7.57891e65	1.44522	0.722612	−	0.691254i	$-0.242941\pi$
$71$	7.57891e65	1.44522	0.722612	+	0.691254i	$0.242941\pi$
$72$	3.70821e65	0.430389
$73$	−1.83450e66	−1.30484	−0.652419	−	0.757858i	$-0.726246\pi$
$73$	−1.83450e66	−1.30484	−0.652419	+	0.757858i	$0.726246\pi$
$74$	6.15121e66	2.69920
$75$	−7.69806e65	−0.209752
$76$	−8.94366e66	−1.52276
$77$	1.91365e67	2.04853
$78$	−1.47386e67	−0.997926
$79$	6.44832e66	0.277770	0.138885	−	0.990309i	$-0.455648\pi$
$79$	6.44832e66	0.277770	0.138885	+	0.990309i	$0.455648\pi$
$80$	1.59211e67	0.438811
$81$	6.26579e66	0.111111
$82$	−1.33462e68	−1.53096
$83$	8.97347e67	0.669404	0.334702	−	0.942324i	$-0.391364\pi$
$83$	8.97347e67	0.669404	0.334702	+	0.942324i	$0.391364\pi$
$84$	−2.17382e68	−1.06001
$85$	−5.14385e68	−1.64785
$86$	−3.60326e68	−0.762080
$87$	−1.97838e68	−0.277573
$88$	2.73468e69	2.55724
$89$	2.67603e69	1.67550	0.837752	−	0.546051i	$-0.183870\pi$
$89$	2.67603e69	1.67550	0.837752	+	0.546051i	$0.183870\pi$
$90$	1.53965e69	0.648354
$91$	3.77263e69	1.07318
$92$	1.77302e69	0.342173
$93$	9.22774e68	0.121325
$94$	1.11821e70	1.00574
$95$	−1.62143e70	−1.00164
$96$	9.01481e69	0.383997
$97$	−5.40339e69	−0.159320	−0.0796599	−	0.996822i	$-0.525383\pi$
$97$	−5.40339e69	−0.159320	−0.0796599	+	0.996822i	$0.525383\pi$
$98$	5.67635e69	0.116290
$99$	4.62080e70	0.660188
$100$	6.44888e70	0.644888
$101$	−1.03525e71	−0.727170	−0.363585	−	0.931561i	$-0.618447\pi$
$101$	−1.03525e71	−0.727170	−0.363585	+	0.931561i	$0.618447\pi$
$102$	2.74160e71	1.35737
$103$	−7.03177e70	−0.246231	−0.123116	−	0.992392i	$-0.539289\pi$
$103$	−7.03177e70	−0.246231	−0.123116	+	0.992392i	$0.539289\pi$
$104$	5.39122e71	1.33969
$105$	−3.94102e71	−0.697250
$106$	1.41062e72	1.78259
$107$	1.09664e72	0.992983	0.496492	−	0.868042i	$-0.334621\pi$
$107$	1.09664e72	0.992983	0.496492	+	0.868042i	$0.334621\pi$
$108$	−5.24902e71	−0.341614
$109$	2.99950e72	1.40737	0.703684	−	0.710513i	$-0.251537\pi$
$109$	2.99950e72	1.40737	0.703684	+	0.710513i	$0.251537\pi$
$110$	1.13544e73	3.85232
$111$	−3.80191e72	−0.935484
$112$	2.17207e72	0.388718
$113$	−1.06159e73	−1.38571	−0.692853	−	0.721079i	$-0.743646\pi$
$113$	−1.06159e73	−1.38571	−0.692853	+	0.721079i	$0.743646\pi$
$114$	8.64201e72	0.825073
$115$	3.21438e72	0.225073
$116$	1.65735e73	0.853404
$117$	9.10958e72	0.345860
$118$	−1.11704e74	−3.13516
$119$	−7.01763e73	−1.45973
$120$	−5.63186e73	−0.870398
$121$	2.53895e74	2.92263
$122$	3.76356e73	0.323463
$123$	8.24895e73	0.530600
$124$	−7.73034e73	−0.373017
$125$	−2.04897e74	−0.743413
$126$	2.10050e74	0.574340
$127$	−5.36800e74	−1.10861	−0.554307	−	0.832312i	$-0.687017\pi$
$127$	−5.36800e74	−1.10861	−0.554307	+	0.832312i	$0.687017\pi$
$128$	−1.15567e75	−1.80667
$129$	2.22709e74	0.264121
$130$	2.23843e75	2.01816
$131$	−5.69097e74	−0.390890	−0.195445	−	0.980715i	$-0.562615\pi$
$131$	−5.69097e74	−0.390890	−0.195445	+	0.980715i	$0.562615\pi$
$132$	−3.87097e75	−2.02976
$133$	−2.21208e75	−0.887296
$134$	3.15012e74	0.0968517
$135$	−9.51618e74	−0.224706
$136$	−1.00285e76	−1.82223
$137$	−1.21672e76	−1.70455	−0.852277	−	0.523090i	$-0.824779\pi$
$137$	−1.21672e76	−1.70455	−0.852277	+	0.523090i	$0.824779\pi$
$138$	−1.71322e75	−0.185398
$139$	4.97130e75	0.416337	0.208168	−	0.978093i	$-0.433250\pi$
$139$	4.97130e75	0.416337	0.208168	+	0.978093i	$0.433250\pi$
$140$	3.30150e76	2.14371
$141$	−6.91138e75	−0.348567
$142$	6.13492e76	2.40754
$143$	6.71799e76	2.05499
$144$	5.24480e75	0.125274
$145$	3.00467e76	0.561349
$146$	−1.48498e77	−2.17367
$147$	−3.50842e75	−0.0403038
$148$	3.18497e77	2.87617
$149$	−1.87555e77	−1.33357	−0.666784	−	0.745251i	$-0.732330\pi$
$149$	−1.87555e77	−1.33357	−0.666784	+	0.745251i	$0.732330\pi$
$150$	−6.23137e76	−0.349417
$151$	6.89444e76	0.305364	0.152682	−	0.988275i	$-0.451209\pi$
$151$	6.89444e76	0.305364	0.152682	+	0.988275i	$0.451209\pi$
$152$	−3.16115e77	−1.10764
$153$	−1.69451e77	−0.470435
$154$	1.54905e78	3.41255
$155$	−1.40147e77	−0.245362
$156$	−7.63135e77	−1.06335
$157$	−6.16646e77	−0.684854	−0.342427	−	0.939544i	$-0.611249\pi$
$157$	−6.16646e77	−0.684854	−0.342427	+	0.939544i	$0.611249\pi$
$158$	5.21974e77	0.462725
$159$	−8.71867e77	−0.617806
$160$	−1.36913e78	−0.776577
$161$	4.38530e77	0.199380
$162$	5.07199e77	0.185095
$163$	6.27226e78	1.83977	0.919887	−	0.392184i	$-0.128280\pi$
$163$	6.27226e78	1.83977	0.919887	+	0.392184i	$0.128280\pi$
$164$	−6.91037e78	−1.63134
$165$	−7.01785e78	−1.33513
$166$	7.26378e78	1.11513
$167$	6.69392e78	0.830320	0.415160	−	0.909748i	$-0.363726\pi$
$167$	6.69392e78	0.830320	0.415160	+	0.909748i	$0.363726\pi$
$168$	−7.68341e78	−0.771036
$169$	9.41981e77	0.0765710
$170$	−4.16381e79	−2.74507
$171$	−5.34141e78	−0.285953
$172$	−1.86569e79	−0.812045
$173$	−1.92433e79	−0.681777	−0.340889	−	0.940104i	$-0.610728\pi$
$173$	−1.92433e79	−0.681777	−0.340889	+	0.940104i	$0.610728\pi$
$174$	−1.60145e79	−0.462396
$175$	1.59504e79	0.375768
$176$	3.86785e79	0.744338
$177$	6.90418e79	1.08658
$178$	2.16617e80	2.79115
$179$	−1.10175e80	−1.16360	−0.581798	−	0.813334i	$-0.697650\pi$
$179$	−1.10175e80	−1.16360	−0.581798	+	0.813334i	$0.697650\pi$
$180$	7.97197e79	0.690863
$181$	−3.57667e79	−0.254618	−0.127309	−	0.991863i	$-0.540634\pi$
$181$	−3.57667e79	−0.254618	−0.127309	+	0.991863i	$0.540634\pi$
$182$	3.05384e80	1.78777
$183$	−2.32617e79	−0.112106
$184$	6.26676e79	0.248892
$185$	5.77416e80	1.89188
$186$	7.46961e79	0.202110
$187$	−1.24964e81	−2.79518
$188$	5.78985e80	1.07168
$189$	−1.29827e80	−0.199054
$190$	−1.31251e81	−1.66859
$191$	−2.20499e80	−0.232660	−0.116330	−	0.993211i	$-0.537113\pi$
$191$	−2.20499e80	−0.232660	−0.116330	+	0.993211i	$0.537113\pi$
$192$	9.77247e80	0.856665
$193$	−3.61963e80	−0.263864	−0.131932	−	0.991259i	$-0.542118\pi$
$193$	−3.61963e80	−0.263864	−0.131932	+	0.991259i	$0.542118\pi$
$194$	−4.37390e80	−0.265404
$195$	−1.38352e81	−0.699450
$196$	2.93910e80	0.123915
$197$	−2.77557e81	−0.976788	−0.488394	−	0.872623i	$-0.662417\pi$
$197$	−2.77557e81	−0.976788	−0.488394	+	0.872623i	$0.662417\pi$
$198$	3.74041e81	1.09978
$199$	−1.40489e81	−0.345429	−0.172714	−	0.984972i	$-0.555254\pi$
$199$	−1.40489e81	−0.345429	−0.172714	+	0.984972i	$0.555254\pi$
$200$	2.27937e81	0.469082
$201$	−1.94702e80	−0.0335667
$202$	−8.38005e81	−1.21136
$203$	4.09920e81	0.497268
$204$	1.41954e82	1.44636
$205$	−1.25281e82	−1.07306
$206$	−5.69203e81	−0.410186
$207$	1.05890e81	0.0642550
$208$	7.62520e81	0.389944
$209$	−3.93910e82	−1.69904
$210$	−3.19015e82	−1.16152
$211$	−1.05750e82	−0.325276	−0.162638	−	0.986686i	$-0.552000\pi$
$211$	−1.05750e82	−0.325276	−0.162638	+	0.986686i	$0.552000\pi$
$212$	7.30387e82	1.89946
$213$	−3.79185e82	−0.834401
$214$	8.87704e82	1.65417
$215$	−3.38239e82	−0.534145
$216$	−1.85528e82	−0.248485
$217$	−1.91199e82	−0.217352
$218$	2.42801e83	2.34447
$219$	9.17830e82	0.753349
$220$	5.87905e83	4.10489
$221$	−2.46359e83	−1.46434
$222$	−3.07754e83	−1.55838
$223$	1.94708e83	0.840546	0.420273	−	0.907398i	$-0.361934\pi$
$223$	1.94708e83	0.840546	0.420273	+	0.907398i	$0.361934\pi$
$224$	−1.86787e83	−0.687926
$225$	3.85146e82	0.121100
$226$	−8.59326e83	−2.30839
$227$	−3.59988e83	−0.826743	−0.413371	−	0.910562i	$-0.635649\pi$
$227$	−3.59988e83	−0.826743	−0.413371	+	0.910562i	$0.635649\pi$
$228$	4.47465e83	0.879168
$229$	1.26233e83	0.212331	0.106165	−	0.994348i	$-0.466143\pi$
$229$	1.26233e83	0.212331	0.106165	+	0.994348i	$0.466143\pi$
$230$	2.60195e83	0.374940
$231$	−9.57429e83	−1.18272
$232$	5.85792e83	0.620754
$233$	−9.85273e83	−0.896234	−0.448117	−	0.893975i	$-0.647905\pi$
$233$	−9.85273e83	−0.896234	−0.448117	+	0.893975i	$0.647905\pi$
$234$	7.37396e83	0.576153
$235$	1.04967e84	0.704925
$236$	−5.78382e84	−3.34071
$237$	−3.22620e83	−0.160370
$238$	−5.68059e84	−2.43171
$239$	3.19988e84	1.18034	0.590171	−	0.807278i	$-0.299060\pi$
$239$	3.19988e84	1.18034	0.590171	+	0.807278i	$0.299060\pi$
$240$	−7.96555e83	−0.253348
$241$	−1.30522e83	−0.0358161	−0.0179080	−	0.999840i	$-0.505701\pi$
$241$	−1.30522e83	−0.0358161	−0.0179080	+	0.999840i	$0.505701\pi$
$242$	2.05521e85	4.86868
$243$	−3.13487e83	−0.0641500
$244$	1.94869e84	0.344671
$245$	5.32842e83	0.0815084
$246$	6.67730e84	0.883903
$247$	−7.76566e84	−0.890096
$248$	−2.73230e84	−0.271327
$249$	−4.48957e84	−0.386480
$250$	−1.65859e85	−1.23842
$251$	1.37585e85	0.891570	0.445785	−	0.895140i	$-0.352925\pi$
$251$	1.37585e85	0.891570	0.445785	+	0.895140i	$0.352925\pi$
$252$	1.08760e85	0.611996
$253$	7.80900e84	0.381783
$254$	−4.34525e85	−1.84679
$255$	2.57355e85	0.951384
$256$	−4.74282e85	−1.52587
$257$	−1.37641e84	−0.0385586	−0.0192793	−	0.999814i	$-0.506137\pi$
$257$	−1.37641e84	−0.0385586	−0.0192793	+	0.999814i	$0.506137\pi$
$258$	1.80277e85	0.439987
$259$	7.87755e85	1.67591
$260$	1.15901e86	2.15048
$261$	9.89815e84	0.160257
$262$	−4.60668e85	−0.651167
$263$	3.68940e85	0.455541	0.227770	−	0.973715i	$-0.426856\pi$
$263$	3.68940e85	0.455541	0.227770	+	0.973715i	$0.426856\pi$
$264$	−1.36820e86	−1.47642
$265$	1.32415e86	1.24942
$266$	−1.79062e86	−1.47811
$267$	−1.33886e86	−0.967353
$268$	1.63107e85	0.103202
$269$	−5.65675e85	−0.313589	−0.156795	−	0.987631i	$-0.550116\pi$
$269$	−5.65675e85	−0.313589	−0.156795	+	0.987631i	$0.550116\pi$
$270$	−7.70309e85	−0.374327
$271$	9.90355e85	0.422067	0.211033	−	0.977479i	$-0.432317\pi$
$271$	9.90355e85	0.422067	0.211033	+	0.977479i	$0.432317\pi$
$272$	−1.41840e86	−0.530398
$273$	−1.88750e86	−0.619603
$274$	−9.84903e86	−2.83954
$275$	2.84031e86	0.719541
$276$	−8.87068e85	−0.197553
$277$	4.96677e86	0.972842	0.486421	−	0.873725i	$-0.338302\pi$
$277$	4.96677e86	0.972842	0.486421	+	0.873725i	$0.338302\pi$
$278$	4.02413e86	0.693557
$279$	−4.61678e85	−0.0700471
$280$	1.16692e87	1.55931
$281$	−9.77083e86	−1.15042	−0.575211	−	0.818005i	$-0.695080\pi$
$281$	−9.77083e86	−1.15042	−0.575211	+	0.818005i	$0.695080\pi$
$282$	−5.59457e86	−0.580662
$283$	−1.60657e87	−1.47056	−0.735278	−	0.677766i	$-0.762948\pi$
$283$	−1.60657e87	−1.47056	−0.735278	+	0.677766i	$0.762948\pi$
$284$	3.17653e87	2.56538
$285$	8.11229e86	0.578297
$286$	5.43803e87	3.42332
$287$	−1.70918e87	−0.950563
$288$	−4.51025e86	−0.221701
$289$	2.28186e87	0.991779
$290$	2.43220e87	0.935127
$291$	2.70340e86	0.0919833
$292$	−7.68892e87	−2.31619
$293$	1.74289e87	0.465018	0.232509	−	0.972594i	$-0.425306\pi$
$293$	1.74289e87	0.465018	0.232509	+	0.972594i	$0.425306\pi$
$294$	−2.83997e86	−0.0671403
$295$	−1.04857e88	−2.19744
$296$	1.12573e88	2.09208
$297$	−2.31186e87	−0.381160
$298$	−1.51820e88	−2.22153
$299$	1.53949e87	0.200009
$300$	−3.22647e87	−0.372326
$301$	−4.61452e87	−0.473169
$302$	5.58086e87	0.508692
$303$	5.17951e87	0.419832
$304$	−4.47105e87	−0.322401
$305$	3.53287e87	0.226717
$306$	−1.37166e88	−0.783677
$307$	−3.34383e88	−1.70150	−0.850751	−	0.525569i	$-0.823852\pi$
$307$	−3.34383e88	−1.70150	−0.850751	+	0.525569i	$0.823852\pi$
$308$	8.02065e88	3.63629
$309$	3.51810e87	0.142162
$310$	−1.13445e88	−0.408738
$311$	−2.61401e88	−0.840066	−0.420033	−	0.907509i	$-0.637981\pi$
$311$	−2.61401e88	−0.840066	−0.420033	+	0.907509i	$0.637981\pi$
$312$	−2.69731e88	−0.773469
$313$	3.17000e88	0.811400	0.405700	−	0.914006i	$-0.367028\pi$
$313$	3.17000e88	0.811400	0.405700	+	0.914006i	$0.367028\pi$
$314$	−4.99158e88	−1.14087
$315$	1.97175e88	0.402557
$316$	2.70267e88	0.493063
$317$	6.30501e88	1.02821	0.514106	−	0.857727i	$-0.328124\pi$
$317$	6.30501e88	1.02821	0.514106	+	0.857727i	$0.328124\pi$
$318$	−7.05753e88	−1.02918
$319$	7.29954e88	0.952195
$320$	−1.48420e89	−1.73248
$321$	−5.48668e88	−0.573299
$322$	3.54978e88	0.332138
$323$	1.44453e89	1.21070
$324$	2.62617e88	0.197231
$325$	5.59948e88	0.376954
$326$	5.07723e89	3.06480
$327$	−1.50069e89	−0.812544
$328$	−2.44248e89	−1.18662
$329$	1.43204e89	0.624453
$330$	−5.68076e89	−2.22414
$331$	−1.52866e89	−0.537549	−0.268775	−	0.963203i	$-0.586619\pi$
$331$	−1.52866e89	−0.537549	−0.268775	+	0.963203i	$0.586619\pi$
$332$	3.76103e89	1.18824
$333$	1.90215e89	0.540102
$334$	5.41854e89	1.38319
$335$	2.95704e88	0.0678837
$336$	−1.08672e89	−0.224426
$337$	6.20666e89	1.15344	0.576722	−	0.816941i	$-0.304332\pi$
$337$	6.20666e89	1.15344	0.576722	+	0.816941i	$0.304332\pi$
$338$	7.62508e88	0.127556
$339$	5.31128e89	0.800037
$340$	−2.15593e90	−2.92505
$341$	−3.40471e89	−0.416198
$342$	−4.32373e89	−0.476356
$343$	−9.68650e89	−0.962112
$344$	−6.59432e89	−0.590671
$345$	−1.60820e89	−0.129946
$346$	−1.55769e90	−1.13574
$347$	−2.25155e90	−1.48179	−0.740893	−	0.671623i	$-0.765598\pi$
$347$	−2.25155e90	−1.48179	−0.740893	+	0.671623i	$0.765598\pi$
$348$	−8.29196e89	−0.492713
$349$	1.04948e90	0.563213	0.281606	−	0.959530i	$-0.409133\pi$
$349$	1.04948e90	0.563213	0.281606	+	0.959530i	$0.409133\pi$
$350$	1.29114e90	0.625975
$351$	−4.55766e89	−0.199682
$352$	−3.32615e90	−1.31728
$353$	3.88135e90	1.38989	0.694946	−	0.719062i	$-0.255428\pi$
$353$	3.88135e90	1.38989	0.694946	+	0.719062i	$0.255428\pi$
$354$	5.58874e90	1.81008
$355$	5.75888e90	1.68745
$356$	1.12160e91	2.97415
$357$	3.51103e90	0.842778
$358$	−8.91840e90	−1.93838
$359$	1.60113e90	0.315190	0.157595	−	0.987504i	$-0.449626\pi$
$359$	1.60113e90	0.315190	0.157595	+	0.987504i	$0.449626\pi$
$360$	2.81771e90	0.502524
$361$	−1.63396e90	−0.264080
$362$	−2.89522e90	−0.424157
$363$	−1.27028e91	−1.68738
$364$	1.58121e91	1.90498
$365$	−1.39396e91	−1.52354
$366$	−1.88297e90	−0.186752
$367$	−1.59612e91	−1.43688	−0.718438	−	0.695591i	$-0.755143\pi$
$367$	−1.59612e91	−1.43688	−0.718438	+	0.695591i	$0.755143\pi$
$368$	8.86354e89	0.0724452
$369$	−4.12708e90	−0.306342
$370$	4.67403e91	3.15159
$371$	1.80651e91	1.10679
$372$	3.86761e90	0.215361
$373$	−6.83531e90	−0.346015	−0.173007	−	0.984921i	$-0.555348\pi$
$373$	−6.83531e90	−0.346015	−0.173007	+	0.984921i	$0.555348\pi$
$374$	−1.01155e92	−4.65636
$375$	1.02513e91	0.429209
$376$	2.04643e91	0.779523
$377$	1.43905e91	0.498837
$378$	−1.05091e91	−0.331595
$379$	6.66619e90	0.191508	0.0957538	−	0.995405i	$-0.469474\pi$
$379$	6.66619e90	0.191508	0.0957538	+	0.995405i	$0.469474\pi$
$380$	−6.79589e91	−1.77799
$381$	2.68569e91	0.640059
$382$	−1.78488e91	−0.387578
$383$	−1.62606e91	−0.321795	−0.160898	−	0.986971i	$-0.551439\pi$
$383$	−1.62606e91	−0.321795	−0.160898	+	0.986971i	$0.551439\pi$
$384$	5.78199e91	1.04308
$385$	1.45410e92	2.39187
$386$	−2.93000e91	−0.439559
$387$	−1.11425e91	−0.152490
$388$	−2.26471e91	−0.282805
$389$	−4.19375e91	−0.477960	−0.238980	−	0.971025i	$-0.576813\pi$
$389$	−4.19375e91	−0.477960	−0.238980	+	0.971025i	$0.576813\pi$
$390$	−1.11992e92	−1.16518
$391$	−2.86367e91	−0.272050
$392$	1.03883e91	0.0901340
$393$	2.84728e91	0.225681
$394$	−2.24675e92	−1.62719
$395$	4.89979e91	0.324325
$396$	1.93671e92	1.17188
$397$	7.94566e91	0.439609	0.219805	−	0.975544i	$-0.429458\pi$
$397$	7.94566e91	0.439609	0.219805	+	0.975544i	$0.429458\pi$
$398$	−1.13722e92	−0.575434
$399$	1.10674e92	0.512280
$400$	3.22387e91	0.136536
$401$	3.06655e92	1.18857	0.594284	−	0.804255i	$-0.297435\pi$
$401$	3.06655e92	1.18857	0.594284	+	0.804255i	$0.297435\pi$
$402$	−1.57606e91	−0.0559174
$403$	−6.71215e91	−0.218038
$404$	−4.33902e92	−1.29078
$405$	4.76109e91	0.129734
$406$	3.31820e92	0.828376
$407$	1.40277e93	3.20912
$408$	5.01739e92	1.05206
$409$	1.13654e92	0.218478	0.109239	−	0.994016i	$-0.465159\pi$
$409$	1.13654e92	0.218478	0.109239	+	0.994016i	$0.465159\pi$
$410$	−1.01412e93	−1.78756
$411$	6.08744e92	0.984125
$412$	−2.94721e92	−0.437079
$413$	−1.43054e93	−1.94659
$414$	8.57149e91	0.107040
$415$	6.81854e92	0.781599
$416$	−6.55727e92	−0.690097
$417$	−2.48722e92	−0.240372
$418$	−3.18860e93	−2.83036
$419$	1.63357e93	1.33211	0.666055	−	0.745902i	$-0.267981\pi$
$419$	1.63357e93	1.33211	0.666055	+	0.745902i	$0.267981\pi$
$420$	−1.65179e93	−1.23767
$421$	−5.83317e92	−0.401689	−0.200845	−	0.979623i	$-0.564369\pi$
$421$	−5.83317e92	−0.401689	−0.200845	+	0.979623i	$0.564369\pi$
$422$	−8.56015e92	−0.541863
$423$	3.45787e92	0.201245
$424$	2.58157e93	1.38164
$425$	−1.04158e93	−0.512728
$426$	−3.06940e93	−1.38999
$427$	4.81981e92	0.200836
$428$	4.59635e93	1.76262
$429$	−3.36111e93	−1.18645
$430$	−2.73796e93	−0.889808
$431$	1.52684e92	0.0456932	0.0228466	−	0.999739i	$-0.492727\pi$
$431$	1.52684e92	0.0456932	0.0228466	+	0.999739i	$0.492727\pi$
$432$	−2.62405e92	−0.0723268
$433$	7.06740e93	1.79448	0.897241	−	0.441541i	$-0.145568\pi$
$433$	7.06740e93	1.79448	0.897241	+	0.441541i	$0.145568\pi$
$434$	−1.54770e93	−0.362078
$435$	−1.50328e93	−0.324095
$436$	1.25717e94	2.49819
$437$	−9.02682e92	−0.165365
$438$	7.42958e93	1.25497
$439$	−3.91121e93	−0.609285	−0.304642	−	0.952467i	$-0.598537\pi$
$439$	−3.91121e93	−0.609285	−0.304642	+	0.952467i	$0.598537\pi$
$440$	2.07796e94	2.98584
$441$	1.75531e92	0.0232694
$442$	−1.99421e94	−2.43938
$443$	−6.51372e93	−0.735355	−0.367677	−	0.929953i	$-0.619847\pi$
$443$	−6.51372e93	−0.735355	−0.367677	+	0.929953i	$0.619847\pi$
$444$	−1.59349e94	−1.66056
$445$	2.03340e94	1.95633
$446$	1.57611e94	1.40023
$447$	9.38365e93	0.769936
$448$	−2.02485e94	−1.53470
$449$	7.51651e93	0.526346	0.263173	−	0.964749i	$-0.415231\pi$
$449$	7.51651e93	0.526346	0.263173	+	0.964749i	$0.415231\pi$
$450$	3.11765e93	0.201736
$451$	−3.04357e94	−1.82019
$452$	−4.44941e94	−2.45973
$453$	−3.44939e93	−0.176302
$454$	−2.91401e94	−1.37723
$455$	2.86665e94	1.25306
$456$	1.58157e94	0.639495
$457$	8.10540e93	0.303214	0.151607	−	0.988441i	$-0.451555\pi$
$457$	8.10540e93	0.303214	0.151607	+	0.988441i	$0.451555\pi$
$458$	1.02182e94	0.353713
$459$	8.47792e93	0.271606
$460$	1.34724e94	0.399522
$461$	6.73106e94	1.84799	0.923997	−	0.382400i	$-0.124902\pi$
$461$	6.73106e94	1.84799	0.923997	+	0.382400i	$0.124902\pi$
$462$	−7.75013e94	−1.97024
$463$	2.40928e94	0.567234	0.283617	−	0.958938i	$-0.408466\pi$
$463$	2.40928e94	0.567234	0.283617	+	0.958938i	$0.408466\pi$
$464$	8.28528e93	0.180684
$465$	7.01175e93	0.141660
$466$	−7.97552e94	−1.49300
$467$	1.45676e94	0.252720	0.126360	−	0.991984i	$-0.459671\pi$
$467$	1.45676e94	0.252720	0.126360	+	0.991984i	$0.459671\pi$
$468$	3.81808e94	0.613928
$469$	4.03421e93	0.0601344
$470$	8.49678e94	1.17430
$471$	3.08517e94	0.395401
$472$	−2.04430e95	−2.42999
$473$	−8.21717e94	−0.906049
$474$	−2.61152e94	−0.267154
$475$	−3.28326e94	−0.311661
$476$	−2.94129e95	−2.59114
$477$	4.36209e94	0.356691
$478$	2.59021e95	1.96628
$479$	−1.30586e95	−0.920420	−0.460210	−	0.887810i	$-0.652226\pi$
$479$	−1.30586e95	−0.920420	−0.460210	+	0.887810i	$0.652226\pi$
$480$	6.84996e94	0.448357
$481$	2.76547e95	1.68120
$482$	−1.05654e94	−0.0596644
$483$	−2.19404e94	−0.115112
$484$	1.06415e96	5.18790
$485$	−4.10580e94	−0.186023
$486$	−2.53759e94	−0.106865
$487$	−2.74082e95	−1.07301	−0.536503	−	0.843898i	$-0.680255\pi$
$487$	−2.74082e95	−1.07301	−0.536503	+	0.843898i	$0.680255\pi$
$488$	6.88769e94	0.250709
$489$	−3.13811e95	−1.06219
$490$	4.31321e94	0.135781
$491$	−3.69071e94	−0.108073	−0.0540365	−	0.998539i	$-0.517209\pi$
$491$	−3.69071e94	−0.108073	−0.0540365	+	0.998539i	$0.517209\pi$
$492$	3.45737e95	0.941856
$493$	−2.67685e95	−0.678513
$494$	−6.28610e95	−1.48277
$495$	3.51114e95	0.770839
$496$	−3.86449e94	−0.0789756
$497$	7.85670e95	1.49482
$498$	−3.63418e95	−0.643821
$499$	−6.69681e95	−1.10484	−0.552419	−	0.833567i	$-0.686295\pi$
$499$	−6.69681e95	−1.10484	−0.552419	+	0.833567i	$0.686295\pi$
$500$	−8.58781e95	−1.31961
$501$	−3.34907e95	−0.479385
$502$	1.11372e96	1.48523
$503$	−4.64828e95	−0.577602	−0.288801	−	0.957389i	$-0.593257\pi$
$503$	−4.64828e95	−0.577602	−0.288801	+	0.957389i	$0.593257\pi$
$504$	3.84413e95	0.445158
$505$	−7.86639e95	−0.849047
$506$	6.32117e95	0.635996
$507$	−4.71288e94	−0.0442083
$508$	−2.24988e96	−1.96788
$509$	−2.35898e96	−1.92417	−0.962083	−	0.272758i	$-0.912064\pi$
$509$	−2.35898e96	−1.92417	−0.962083	+	0.272758i	$0.912064\pi$
$510$	2.08322e96	1.58487
$511$	−1.90174e96	−1.34961
$512$	−1.11044e96	−0.735208
$513$	2.67239e95	0.165095
$514$	−1.11416e95	−0.0642331
$515$	−5.34313e95	−0.287501
$516$	9.33435e95	0.468834
$517$	2.55006e96	1.19574
$518$	6.37667e96	2.79182
$519$	9.62771e95	0.393624
$520$	4.09655e96	1.56423
$521$	−2.25201e95	−0.0803215	−0.0401607	−	0.999193i	$-0.512787\pi$
$521$	−2.25201e95	−0.0803215	−0.0401607	+	0.999193i	$0.512787\pi$
$522$	8.01229e95	0.266965
$523$	6.44928e95	0.200771	0.100386	−	0.994949i	$-0.467992\pi$
$523$	6.44928e95	0.200771	0.100386	+	0.994949i	$0.467992\pi$
$524$	−2.38524e96	−0.693860
$525$	−7.98021e95	−0.216950
$526$	2.98647e96	0.758865
$527$	1.24856e96	0.296573
$528$	−1.93515e96	−0.429744
$529$	−4.63694e96	−0.962842
$530$	1.07186e97	2.08136
$531$	−3.45427e96	−0.627336
$532$	−9.27147e96	−1.57502
$533$	−6.00019e96	−0.953562
$534$	−1.08377e97	−1.61147
$535$	8.33292e96	1.15941
$536$	5.76504e95	0.0750676
$537$	5.51224e96	0.671802
$538$	−4.57899e96	−0.522395
$539$	1.29448e96	0.138260
$540$	−3.98850e96	−0.398870
$541$	−3.30152e96	−0.309179	−0.154590	−	0.987979i	$-0.549406\pi$
$541$	−3.30152e96	−0.309179	−0.154590	+	0.987979i	$0.549406\pi$
$542$	8.01666e96	0.703103
$543$	1.78946e96	0.147004
$544$	1.21975e97	0.938662
$545$	2.27918e97	1.64325
$546$	−1.52788e97	−1.03217
$547$	−1.71718e97	−1.08709	−0.543545	−	0.839380i	$-0.682918\pi$
$547$	−1.71718e97	−1.08709	−0.543545	+	0.839380i	$0.682918\pi$
$548$	−5.09962e97	−3.02572
$549$	1.16382e96	0.0647242
$550$	2.29916e97	1.19865
$551$	−8.43790e96	−0.412432
$552$	−3.13536e96	−0.143698
$553$	6.68467e96	0.287302
$554$	4.02047e97	1.62061
$555$	−2.88890e97	−1.09228
$556$	2.08361e97	0.739030
$557$	1.26148e97	0.419779	0.209890	−	0.977725i	$-0.432690\pi$
$557$	1.26148e97	0.419779	0.209890	+	0.977725i	$0.432690\pi$
$558$	−3.73716e96	−0.116688
$559$	−1.61996e97	−0.474662
$560$	1.65046e97	0.453869
$561$	6.25216e97	1.61380
$562$	−7.90922e97	−1.91644
$563$	1.27403e97	0.289823	0.144912	−	0.989445i	$-0.453710\pi$
$563$	1.27403e97	0.289823	0.144912	+	0.989445i	$0.453710\pi$
$564$	−2.89675e97	−0.618733
$565$	−8.06653e97	−1.61796
$566$	−1.30048e98	−2.44973
$567$	6.49545e96	0.114924
$568$	1.12275e98	1.86603
$569$	6.31265e97	0.985659	0.492829	−	0.870126i	$-0.335963\pi$
$569$	6.31265e97	0.985659	0.492829	+	0.870126i	$0.335963\pi$
$570$	6.56668e97	0.963359
$571$	−4.55268e97	−0.627604	−0.313802	−	0.949488i	$-0.601603\pi$
$571$	−4.55268e97	−0.627604	−0.313802	+	0.949488i	$0.601603\pi$
$572$	2.81570e98	3.64777
$573$	1.10319e97	0.134326
$574$	−1.38354e98	−1.58350
$575$	6.50884e96	0.0700317
$576$	−4.88932e97	−0.494596
$577$	−1.54224e98	−1.46694	−0.733469	−	0.679723i	$-0.762100\pi$
$577$	−1.54224e98	−1.46694	−0.733469	+	0.679723i	$0.762100\pi$
$578$	1.84710e98	1.65216
$579$	1.81096e97	0.152342
$580$	1.25934e98	0.996438
$581$	9.30237e97	0.692375
$582$	2.18833e97	0.153231
$583$	3.21689e98	2.11935
$584$	−2.71766e98	−1.68476
$585$	6.92196e97	0.403828
$586$	1.41082e98	0.774654
$587$	−3.03248e98	−1.56727	−0.783637	−	0.621220i	$-0.786638\pi$
$587$	−3.03248e98	−1.56727	−0.783637	+	0.621220i	$0.786638\pi$
$588$	−1.47048e97	−0.0715423
$589$	3.93568e97	0.180271
$590$	−8.48792e98	−3.66062
$591$	1.38866e98	0.563949
$592$	1.59220e98	0.608945
$593$	−4.38798e97	−0.158060	−0.0790302	−	0.996872i	$-0.525182\pi$
$593$	−4.38798e97	−0.158060	−0.0790302	+	0.996872i	$0.525182\pi$
$594$	−1.87139e98	−0.634957
$595$	−5.33239e98	−1.70439
$596$	−7.86094e98	−2.36719
$597$	7.02888e97	0.199433
$598$	1.24617e98	0.333186
$599$	−1.67839e98	−0.422904	−0.211452	−	0.977388i	$-0.567819\pi$
$599$	−1.67839e98	−0.422904	−0.211452	+	0.977388i	$0.567819\pi$
$600$	−1.14040e98	−0.270825
$601$	5.66573e98	1.26827	0.634135	−	0.773222i	$-0.281356\pi$
$601$	5.66573e98	1.26827	0.634135	+	0.773222i	$0.281356\pi$
$602$	−3.73533e98	−0.788231
$603$	9.74122e96	0.0193798
$604$	2.88965e98	0.542044
$605$	1.92924e99	3.41248
$606$	4.19267e98	0.699379
$607$	−2.75702e97	−0.0433752	−0.0216876	−	0.999765i	$-0.506904\pi$
$607$	−2.75702e97	−0.0433752	−0.0216876	+	0.999765i	$0.506904\pi$
$608$	3.84487e98	0.570564
$609$	−2.05090e98	−0.287098
$610$	2.85976e98	0.377677
$611$	5.02726e98	0.626424
$612$	−7.10219e98	−0.835058
$613$	5.64289e98	0.626116	0.313058	−	0.949734i	$-0.398647\pi$
$613$	5.64289e98	0.626116	0.313058	+	0.949734i	$0.398647\pi$
$614$	−2.70674e99	−2.83446
$615$	6.26801e98	0.619531
$616$	2.83491e99	2.64499
$617$	9.19226e98	0.809653	0.404826	−	0.914394i	$-0.367332\pi$
$617$	9.19226e98	0.809653	0.404826	+	0.914394i	$0.367332\pi$
$618$	2.84781e98	0.236821
$619$	−1.49758e99	−1.17590	−0.587951	−	0.808896i	$-0.700065\pi$
$619$	−1.49758e99	−1.17590	−0.587951	+	0.808896i	$0.700065\pi$
$620$	−5.87394e98	−0.435536
$621$	−5.29783e97	−0.0370976
$622$	−2.11597e99	−1.39943
$623$	2.77411e99	1.73300
$624$	−3.81500e98	−0.225135
$625$	−2.20856e99	−1.23131
$626$	2.56603e99	1.35168
$627$	1.97079e99	0.980943
$628$	−2.58454e99	−1.21567
$629$	−5.14417e99	−2.28674
$630$	1.59608e99	0.670602
$631$	−7.21240e98	−0.286443	−0.143221	−	0.989691i	$-0.545746\pi$
$631$	−7.21240e98	−0.286443	−0.143221	+	0.989691i	$0.545746\pi$
$632$	9.55264e98	0.358647
$633$	5.29082e98	0.187798
$634$	5.10374e99	1.71285
$635$	−4.07890e99	−1.29442
$636$	−3.65424e99	−1.09665
$637$	2.55198e98	0.0724315
$638$	5.90878e99	1.58622
$639$	1.89712e99	0.481741
$640$	−8.78141e99	−2.10948
$641$	−1.12772e98	−0.0256295	−0.0128147	−	0.999918i	$-0.504079\pi$
$641$	−1.12772e98	−0.0256295	−0.0128147	+	0.999918i	$0.504079\pi$
$642$	−4.44132e99	−0.955034
$643$	−9.14079e99	−1.85992	−0.929960	−	0.367660i	$-0.880159\pi$
$643$	−9.14079e99	−1.85992	−0.929960	+	0.367660i	$0.880159\pi$
$644$	1.83800e99	0.353914
$645$	1.69226e99	0.308389
$646$	1.16931e100	2.01685
$647$	1.13923e100	1.85998	0.929990	−	0.367584i	$-0.119815\pi$
$647$	1.13923e100	1.85998	0.929990	+	0.367584i	$0.119815\pi$
$648$	9.28223e98	0.143463
$649$	−2.54740e100	−3.72744
$650$	4.53263e99	0.627951
$651$	9.56597e98	0.125488
$652$	2.62888e100	3.26574
$653$	8.91827e99	1.04921	0.524606	−	0.851345i	$-0.324213\pi$
$653$	8.91827e99	1.04921	0.524606	+	0.851345i	$0.324213\pi$
$654$	−1.21477e100	−1.35358
$655$	−4.32431e99	−0.456405
$656$	−3.45458e99	−0.345389
$657$	−4.59204e99	−0.434946
$658$	1.15920e100	1.04025
$659$	−1.20200e100	−1.02205	−0.511024	−	0.859566i	$-0.670734\pi$
$659$	−1.20200e100	−1.02205	−0.511024	+	0.859566i	$0.670734\pi$
$660$	−2.94138e100	−2.36996
$661$	5.35859e99	0.409165	0.204583	−	0.978849i	$-0.434416\pi$
$661$	5.35859e99	0.409165	0.204583	+	0.978849i	$0.434416\pi$
$662$	−1.23741e100	−0.895480
$663$	1.23257e100	0.845437
$664$	1.32934e100	0.864312
$665$	−1.68086e100	−1.03601
$666$	1.53974e100	0.899732
$667$	1.67276e99	0.0926756
$668$	2.80561e100	1.47388
$669$	−9.74155e99	−0.485289
$670$	2.39364e99	0.113085
$671$	8.58274e99	0.384571
$672$	9.34523e99	0.397174
$673$	2.42021e100	0.975703	0.487852	−	0.872927i	$-0.337781\pi$
$673$	2.42021e100	0.975703	0.487852	+	0.872927i	$0.337781\pi$
$674$	5.02412e100	1.92147
$675$	−1.92694e99	−0.0699173
$676$	3.94811e99	0.135919
$677$	2.92966e99	0.0957016	0.0478508	−	0.998854i	$-0.484763\pi$
$677$	2.92966e99	0.0957016	0.0478508	+	0.998854i	$0.484763\pi$
$678$	4.29934e100	1.33275
$679$	−5.60144e99	−0.164787
$680$	−7.62018e100	−2.12764
$681$	1.80108e100	0.477320
$682$	−2.75602e100	−0.693326
$683$	−1.39931e100	−0.334178	−0.167089	−	0.985942i	$-0.553437\pi$
$683$	−1.39931e100	−0.334178	−0.167089	+	0.985942i	$0.553437\pi$
$684$	−2.23874e100	−0.507588
$685$	−9.24533e100	−1.99025
$686$	−7.84096e100	−1.60274
$687$	−6.31563e99	−0.122589
$688$	−9.32683e99	−0.171927
$689$	6.34186e100	1.11028
$690$	−1.30180e100	−0.216472
$691$	1.43018e100	0.225902	0.112951	−	0.993601i	$-0.463970\pi$
$691$	1.43018e100	0.225902	0.112951	+	0.993601i	$0.463970\pi$
$692$	−8.06540e100	−1.21021
$693$	4.79016e100	0.682842
$694$	−1.82257e101	−2.46844
$695$	3.77747e100	0.486117
$696$	−2.93081e100	−0.358393
$697$	1.11612e101	1.29702
$698$	8.49528e100	0.938231
$699$	4.92947e100	0.517441
$700$	6.68525e100	0.667017
$701$	1.19790e101	1.13614	0.568070	−	0.822980i	$-0.307690\pi$
$701$	1.19790e101	1.13614	0.568070	+	0.822980i	$0.307690\pi$
$702$	−3.68930e100	−0.332642
$703$	−1.62153e101	−1.38999
$704$	−3.60570e101	−2.93873
$705$	−5.25165e100	−0.406988
$706$	3.14185e101	2.31536
$707$	−1.07319e101	−0.752123
$708$	2.89373e101	1.92876
$709$	−2.54319e101	−1.61227	−0.806135	−	0.591732i	$-0.798445\pi$
$709$	−2.54319e101	−1.61227	−0.806135	+	0.591732i	$0.798445\pi$
$710$	4.66165e101	2.81105
$711$	1.61412e100	0.0925899
$712$	3.96431e101	2.16336
$713$	−7.80221e99	−0.0405079
$714$	2.84208e101	1.40395
$715$	5.10470e101	2.39942
$716$	−4.61776e101	−2.06547
$717$	−1.60095e101	−0.681471
$718$	1.29607e101	0.525062
$719$	−4.25555e101	−1.64089	−0.820446	−	0.571724i	$-0.806275\pi$
$719$	−4.25555e101	−1.64089	−0.820446	+	0.571724i	$0.806275\pi$
$720$	3.98529e100	0.146270
$721$	−7.28950e100	−0.254681
$722$	−1.32264e101	−0.439919
$723$	6.53021e99	0.0206784
$724$	−1.49908e101	−0.451966
$725$	6.08420e100	0.174664
$726$	−1.02826e102	−2.81094
$727$	1.96540e101	0.511658	0.255829	−	0.966722i	$-0.417652\pi$
$727$	1.96540e101	0.511658	0.255829	+	0.966722i	$0.417652\pi$
$728$	5.58883e101	1.38566
$729$	1.56842e100	0.0370370
$730$	−1.12837e102	−2.53799
$731$	3.01336e101	0.645630
$732$	−9.74962e100	−0.198996
$733$	4.65487e101	0.905141	0.452571	−	0.891729i	$-0.350507\pi$
$733$	4.65487e101	0.905141	0.452571	+	0.891729i	$0.350507\pi$
$734$	−1.29201e102	−2.39363
$735$	−2.66589e100	−0.0470589
$736$	−7.62218e100	−0.128208
$737$	7.18380e100	0.115149
$738$	−3.34076e101	−0.510322
$739$	6.55112e101	0.953757	0.476879	−	0.878969i	$-0.341768\pi$
$739$	6.55112e101	0.953757	0.476879	+	0.878969i	$0.341768\pi$
$740$	2.42011e102	3.35823
$741$	3.88528e101	0.513897
$742$	1.46232e102	1.84376
$743$	−2.79549e101	−0.336013	−0.168006	−	0.985786i	$-0.553733\pi$
$743$	−2.79549e101	−0.336013	−0.168006	+	0.985786i	$0.553733\pi$
$744$	1.36701e101	0.156651
$745$	−1.42514e102	−1.55708
$746$	−5.53300e101	−0.576411
$747$	2.24620e101	0.223135
$748$	−5.23761e102	−4.96166
$749$	1.13684e102	1.02706
$750$	8.29816e101	0.715001
$751$	1.51149e102	1.24219	0.621093	−	0.783737i	$-0.286689\pi$
$751$	1.51149e102	1.24219	0.621093	+	0.783737i	$0.286689\pi$
$752$	2.89442e101	0.226897
$753$	−6.88361e101	−0.514748
$754$	1.16487e102	0.830991
$755$	5.23878e101	0.356544
$756$	−5.44142e101	−0.353336
$757$	−1.76935e102	−1.09625	−0.548126	−	0.836396i	$-0.684659\pi$
$757$	−1.76935e102	−1.09625	−0.548126	+	0.836396i	$0.684659\pi$
$758$	5.39610e101	0.319024
$759$	−3.90696e101	−0.220423
$760$	−2.40202e102	−1.29328
$761$	1.85265e102	0.952004	0.476002	−	0.879444i	$-0.342086\pi$
$761$	1.85265e102	0.952004	0.476002	+	0.879444i	$0.342086\pi$
$762$	2.17400e102	1.06625
$763$	3.10944e102	1.45566
$764$	−9.24173e101	−0.412990
$765$	−1.28759e102	−0.549282
$766$	−1.31625e102	−0.536064
$767$	−5.02202e102	−1.95273
$768$	2.37290e102	0.880962
$769$	3.11758e102	1.10518	0.552589	−	0.833454i	$-0.313640\pi$
$769$	3.11758e102	1.10518	0.552589	+	0.833454i	$0.313640\pi$
$770$	1.17705e103	3.98451
$771$	6.88638e100	0.0222618
$772$	−1.51709e102	−0.468379
$773$	−8.15788e101	−0.240550	−0.120275	−	0.992741i	$-0.538378\pi$
$773$	−8.15788e101	−0.240550	−0.120275	+	0.992741i	$0.538378\pi$
$774$	−9.01952e101	−0.254027
$775$	−2.83784e101	−0.0763446
$776$	−8.00466e101	−0.205708
$777$	−3.94126e102	−0.967585
$778$	−3.39472e102	−0.796212
$779$	3.51822e102	0.788394
$780$	−5.79872e102	−1.24158
$781$	1.39906e103	2.86236
$782$	−2.31807e102	−0.453196
$783$	−4.95220e101	−0.0925242
$784$	1.46929e101	0.0262354
$785$	−4.68562e102	−0.799639
$786$	2.30479e102	0.375952
$787$	−7.44955e102	−1.16152	−0.580761	−	0.814074i	$-0.697245\pi$
$787$	−7.44955e102	−1.16152	−0.580761	+	0.814074i	$0.697245\pi$
$788$	−1.16332e103	−1.73387
$789$	−1.84587e102	−0.263006
$790$	3.96625e102	0.540279
$791$	−1.10050e103	−1.43326
$792$	6.84532e102	0.852413
$793$	1.69203e102	0.201469
$794$	6.43180e102	0.732326
$795$	−6.62493e102	−0.721354
$796$	−5.88829e102	−0.613162
$797$	−5.34875e102	−0.532699	−0.266350	−	0.963876i	$-0.585818\pi$
$797$	−5.34875e102	−0.532699	−0.266350	+	0.963876i	$0.585818\pi$
$798$	8.95876e102	0.853386
$799$	−9.35143e102	−0.852055
$800$	−2.77236e102	−0.241633
$801$	6.69851e102	0.558501
$802$	2.48229e103	1.97998
$803$	−3.38647e103	−2.58432
$804$	−8.16049e101	−0.0595836
$805$	3.33220e102	0.232797
$806$	−5.43331e102	−0.363220
$807$	2.83016e102	0.181051
$808$	−1.53363e103	−0.938897
$809$	−6.34520e102	−0.371769	−0.185884	−	0.982572i	$-0.559515\pi$
$809$	−6.34520e102	−0.371769	−0.185884	+	0.982572i	$0.559515\pi$
$810$	3.85398e102	0.216118
$811$	−4.13813e102	−0.222108	−0.111054	−	0.993814i	$-0.535423\pi$
$811$	−4.13813e102	−0.222108	−0.111054	+	0.993814i	$0.535423\pi$
$812$	1.71809e103	0.882688
$813$	−4.95490e102	−0.243680
$814$	1.13551e104	5.34593
$815$	4.76601e103	2.14813
$816$	7.09646e102	0.306226
$817$	9.49864e102	0.392445
$818$	9.19997e102	0.363952
$819$	9.44347e102	0.357728
$820$	−5.25089e103	−1.90476
$821$	6.59788e101	0.0229204	0.0114602	−	0.999934i	$-0.496352\pi$
$821$	6.59788e101	0.0229204	0.0114602	+	0.999934i	$0.496352\pi$
$822$	4.92762e103	1.63941
$823$	−5.99799e103	−1.91122	−0.955612	−	0.294628i	$-0.904804\pi$
$823$	−5.99799e103	−1.91122	−0.955612	+	0.294628i	$0.904804\pi$
$824$	−1.04170e103	−0.317926
$825$	−1.42105e103	−0.415427
$826$	−1.15799e104	−3.24274
$827$	4.58671e103	1.23043	0.615213	−	0.788361i	$-0.289070\pi$
$827$	4.58671e103	1.23043	0.615213	+	0.788361i	$0.289070\pi$
$828$	4.43814e102	0.114058
$829$	−1.62819e103	−0.400885	−0.200442	−	0.979706i	$-0.564238\pi$
$829$	−1.62819e103	−0.400885	−0.200442	+	0.979706i	$0.564238\pi$
$830$	5.51942e103	1.30203
$831$	−2.48495e103	−0.561670
$832$	−7.10838e103	−1.53955
$833$	−4.74706e102	−0.0985206
$834$	−2.01334e103	−0.400425
$835$	5.08641e103	0.969486
$836$	−1.65099e104	−3.01593
$837$	2.30985e102	0.0404417
$838$	1.32233e104	2.21911
$839$	−1.51975e103	−0.244469	−0.122234	−	0.992501i	$-0.539006\pi$
$839$	−1.51975e103	−0.244469	−0.122234	+	0.992501i	$0.539006\pi$
$840$	−5.83828e103	−0.900265
$841$	−5.20122e103	−0.768860
$842$	−4.72179e103	−0.669157
$843$	4.88850e103	0.664196
$844$	−4.43227e103	−0.577390
$845$	7.15770e102	0.0894047
$846$	2.79905e103	0.335246
$847$	2.63201e104	3.02292
$848$	3.65130e103	0.402156
$849$	8.03793e103	0.849026
$850$	−8.43134e103	−0.854132
$851$	3.21458e103	0.312338
$852$	−1.58927e104	−1.48113
$853$	2.32517e103	0.207857	0.103929	−	0.994585i	$-0.466859\pi$
$853$	2.32517e103	0.207857	0.103929	+	0.994585i	$0.466859\pi$
$854$	3.90151e103	0.334563
$855$	−4.05870e103	−0.333880
$856$	1.62459e104	1.28211
$857$	8.54167e103	0.646731	0.323365	−	0.946274i	$-0.395186\pi$
$857$	8.54167e103	0.646731	0.323365	+	0.946274i	$0.395186\pi$
$858$	−2.72073e104	−1.97646
$859$	−1.07545e104	−0.749608	−0.374804	−	0.927104i	$-0.622290\pi$
$859$	−1.07545e104	−0.749608	−0.374804	+	0.927104i	$0.622290\pi$
$860$	−1.41766e104	−0.948148
$861$	8.55130e103	0.548808
$862$	1.23594e103	0.0761183
$863$	−3.34468e103	−0.197684	−0.0988420	−	0.995103i	$-0.531514\pi$
$863$	−3.34468e103	−0.197684	−0.0988420	+	0.995103i	$0.531514\pi$
$864$	2.25655e103	0.127999
$865$	−1.46221e104	−0.796046
$866$	5.72087e104	2.98935
$867$	−1.14165e104	−0.572604
$868$	−8.01368e103	−0.385817
$869$	1.19035e104	0.550141
$870$	−1.21687e104	−0.539896
$871$	1.41624e103	0.0603242
$872$	4.44350e104	1.81715
$873$	−1.35255e103	−0.0531066
$874$	−7.30696e103	−0.275474
$875$	−2.12407e104	−0.768923
$876$	3.84688e104	1.33725
$877$	−4.01731e104	−1.34106	−0.670532	−	0.741881i	$-0.733934\pi$
$877$	−4.01731e104	−1.34106	−0.670532	+	0.741881i	$0.733934\pi$
$878$	−3.16602e104	−1.01498
$879$	−8.71996e103	−0.268479
$880$	2.93901e104	0.869093
$881$	1.67336e104	0.475275	0.237638	−	0.971354i	$-0.423627\pi$
$881$	1.67336e104	0.475275	0.237638	+	0.971354i	$0.423627\pi$
$882$	1.42088e103	0.0387635
$883$	5.97846e104	1.56669	0.783347	−	0.621585i	$-0.213511\pi$
$883$	5.97846e104	1.56669	0.783347	+	0.621585i	$0.213511\pi$
$884$	−1.03256e105	−2.59932
$885$	5.24618e104	1.26869
$886$	−5.27268e104	−1.22499
$887$	5.67147e104	1.26592	0.632961	−	0.774184i	$-0.281839\pi$
$887$	5.67147e104	1.26592	0.632961	+	0.774184i	$0.281839\pi$
$888$	−5.63221e104	−1.20787
$889$	−5.56475e104	−1.14666
$890$	1.64598e105	3.25896
$891$	1.15666e104	0.220063
$892$	8.16076e104	1.49203
$893$	−2.94774e104	−0.517919
$894$	7.59581e104	1.28260
$895$	−8.37174e104	−1.35862
$896$	−1.19803e105	−1.86867
$897$	−7.70230e103	−0.115475
$898$	6.08441e104	0.876817
$899$	−7.29319e103	−0.101030
$900$	1.61425e104	0.214963
$901$	−1.17968e105	−1.51020
$902$	−2.46369e105	−3.03217
$903$	2.30872e104	0.273184
$904$	−1.57265e105	−1.78918
$905$	−2.71775e104	−0.297293
$906$	−2.79219e104	−0.293693
$907$	−5.37464e104	−0.543615	−0.271807	−	0.962352i	$-0.587621\pi$
$907$	−5.37464e104	−0.543615	−0.271807	+	0.962352i	$0.587621\pi$
$908$	−1.50881e105	−1.46753
$909$	−2.59139e104	−0.242390
$910$	2.32048e105	2.08741
$911$	2.02280e105	1.75005	0.875027	−	0.484074i	$-0.160843\pi$
$911$	2.02280e105	1.75005	0.875027	+	0.484074i	$0.160843\pi$
$912$	2.23693e104	0.186138
$913$	1.65649e105	1.32580
$914$	6.56110e104	0.505111
$915$	−1.76755e104	−0.130895
$916$	5.29078e104	0.376904
$917$	−5.89956e104	−0.404304
$918$	6.86264e104	0.452456
$919$	−1.34127e105	−0.850775	−0.425387	−	0.905011i	$-0.639862\pi$
$919$	−1.34127e105	−0.850775	−0.425387	+	0.905011i	$0.639862\pi$
$920$	4.76183e104	0.290607
$921$	1.67297e105	0.982362
$922$	5.44861e105	3.07849
$923$	2.75814e105	1.49954
$924$	−4.01285e105	−2.09942
$925$	1.16922e105	0.588659
$926$	1.95025e105	0.944931
$927$	−1.76016e104	−0.0820771
$928$	−7.12490e104	−0.319761
$929$	−9.89216e104	−0.427300	−0.213650	−	0.976910i	$-0.568535\pi$
$929$	−9.89216e104	−0.427300	−0.213650	+	0.976910i	$0.568535\pi$
$930$	5.67582e104	0.235985
$931$	−1.49636e104	−0.0598855
$932$	−4.12956e105	−1.59088
$933$	1.30783e105	0.485012
$934$	1.17921e105	0.420995
$935$	−9.49549e105	−3.26366
$936$	1.34951e105	0.446563
$937$	3.45321e105	1.10019	0.550095	−	0.835102i	$-0.314592\pi$
$937$	3.45321e105	1.10019	0.550095	+	0.835102i	$0.314592\pi$
$938$	3.26559e104	0.100175
$939$	−1.58600e105	−0.468462
$940$	4.39945e105	1.25130
$941$	5.44005e104	0.148995	0.0744974	−	0.997221i	$-0.476265\pi$
$941$	5.44005e104	0.148995	0.0744974	+	0.997221i	$0.476265\pi$
$942$	2.49737e105	0.658681
$943$	−6.97463e104	−0.177156
$944$	−2.89140e105	−0.707299
$945$	−9.86498e104	−0.232417
$946$	−6.65158e105	−1.50935
$947$	5.89362e105	1.28812	0.644062	−	0.764973i	$-0.277248\pi$
$947$	5.89362e105	1.28812	0.644062	+	0.764973i	$0.277248\pi$
$948$	−1.35219e105	−0.284670
$949$	−6.67619e105	−1.35387
$950$	−2.65771e105	−0.519182
$951$	−3.15450e105	−0.593638
$952$	−1.03960e106	−1.88476
$953$	3.31497e105	0.579004	0.289502	−	0.957177i	$-0.406510\pi$
$953$	3.31497e105	0.579004	0.289502	+	0.957177i	$0.406510\pi$
$954$	3.53099e105	0.594195
$955$	−1.67547e105	−0.271655
$956$	1.34116e106	2.09520
$957$	−3.65207e105	−0.549750
$958$	−1.05706e106	−1.53329
$959$	−1.26132e106	−1.76305
$960$	7.42567e105	1.00025
$961$	−7.36319e105	−0.955841
$962$	2.23857e106	2.80063
$963$	2.74507e105	0.330994
$964$	−5.47054e104	−0.0635763
$965$	−2.75040e105	−0.308089
$966$	−1.77601e105	−0.191760
$967$	4.28185e105	0.445648	0.222824	−	0.974859i	$-0.428472\pi$
$967$	4.28185e105	0.445648	0.222824	+	0.974859i	$0.428472\pi$
$968$	3.76125e106	3.77361
$969$	−7.22719e105	−0.698997
$970$	−3.32353e105	−0.309887
$971$	3.34549e105	0.300730	0.150365	−	0.988631i	$-0.451955\pi$
$971$	3.34549e105	0.300730	0.150365	+	0.988631i	$0.451955\pi$
$972$	−1.31391e105	−0.113871
$973$	5.15351e105	0.430623
$974$	−2.21862e106	−1.78747
$975$	−2.80150e105	−0.217634
$976$	9.74176e104	0.0729741
$977$	3.83131e105	0.276752	0.138376	−	0.990380i	$-0.455812\pi$
$977$	3.83131e105	0.276752	0.138376	+	0.990380i	$0.455812\pi$
$978$	−2.54022e106	−1.76946
$979$	4.93992e106	3.31844
$980$	2.23329e105	0.144684
$981$	7.50820e105	0.469123
$982$	−2.98753e105	−0.180034
$983$	−8.98586e105	−0.522288	−0.261144	−	0.965300i	$-0.584100\pi$
$983$	−8.98586e105	−0.522288	−0.261144	+	0.965300i	$0.584100\pi$
$984$	1.22201e106	0.685093
$985$	−2.10903e106	−1.14050
$986$	−2.16684e106	−1.13030
$987$	−7.16470e105	−0.360528
$988$	−3.25481e106	−1.57999
$989$	−1.88304e105	−0.0881843
$990$	2.84217e106	1.28411
$991$	−2.72131e106	−1.18621	−0.593107	−	0.805124i	$-0.702099\pi$
$991$	−2.72131e106	−1.18621	−0.593107	+	0.805124i	$0.702099\pi$
$992$	3.32326e105	0.139766
$993$	7.64814e105	0.310354
$994$	6.35978e106	2.49015
$995$	−1.06751e106	−0.403324
$996$	−1.88170e106	−0.686032
$997$	4.43498e106	1.56032	0.780160	−	0.625581i	$-0.215138\pi$
$997$	4.43498e106	1.56032	0.780160	+	0.625581i	$0.215138\pi$
$998$	−5.42089e106	−1.84050
$999$	−9.51677e105	−0.311828

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.72.a.b.1.6	✓	6
3.2	odd	2		9.72.a.c.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.72.a.b.1.6	✓	6	1.1	even	1	trivial
9.72.a.c.1.1		6	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:	\( k \)	\(=\)	\( 72 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+8.09473e10 q^{2} -5.00315e16 q^{3} +4.19128e21 q^{4} +7.59856e24 q^{5} -4.04992e27 q^{6} +1.03665e30 q^{7} +1.48142e32 q^{8} +2.50316e33 q^{9} +O(q^{10})\)	\(q+8.09473e10 q^{2} -5.00315e16 q^{3} +4.19128e21 q^{4} +7.59856e24 q^{5} -4.04992e27 q^{6} +1.03665e30 q^{7} +1.48142e32 q^{8} +2.50316e33 q^{9} +6.15083e35 q^{10} +1.84599e37 q^{11} -2.09696e38 q^{12} +3.63924e39 q^{13} +8.39143e40 q^{14} -3.80167e41 q^{15} +2.09527e42 q^{16} -6.76951e43 q^{17} +2.02624e44 q^{18} -2.13387e45 q^{19} +3.18477e46 q^{20} -5.18653e46 q^{21} +1.49428e48 q^{22} +4.23025e47 q^{23} -7.41175e48 q^{24} +1.53864e49 q^{25} +2.94586e50 q^{26} -1.25237e50 q^{27} +4.34490e51 q^{28} +3.95427e51 q^{29} -3.07735e52 q^{30} -1.84438e52 q^{31} -1.80183e53 q^{32} -9.23577e53 q^{33} -5.47974e54 q^{34} +7.87707e54 q^{35} +1.04914e55 q^{36} +7.59903e55 q^{37} -1.72731e56 q^{38} -1.82077e56 q^{39} +1.12566e57 q^{40} -1.64875e57 q^{41} -4.19836e57 q^{42} -4.45136e57 q^{43} +7.73706e58 q^{44} +1.90204e58 q^{45} +3.42428e58 q^{46} +1.38140e59 q^{47} -1.04830e59 q^{48} +7.01241e58 q^{49} +1.24549e60 q^{50} +3.38689e60 q^{51} +1.52531e61 q^{52} +1.74264e61 q^{53} -1.01376e61 q^{54} +1.40269e62 q^{55} +1.53571e62 q^{56} +1.06761e62 q^{57} +3.20087e62 q^{58} -1.37996e63 q^{59} -1.59339e63 q^{60} +4.64940e62 q^{61} -1.49298e63 q^{62} +2.59490e63 q^{63} -1.95326e64 q^{64} +2.76529e64 q^{65} -7.47610e64 q^{66} +3.89158e63 q^{67} -2.83729e65 q^{68} -2.11646e64 q^{69} +6.37627e65 q^{70} +7.57891e65 q^{71} +3.70821e65 q^{72} -1.83450e66 q^{73} +6.15121e66 q^{74} -7.69806e65 q^{75} -8.94366e66 q^{76} +1.91365e67 q^{77} -1.47386e67 q^{78} +6.44832e66 q^{79} +1.59211e67 q^{80} +6.26579e66 q^{81} -1.33462e68 q^{82} +8.97347e67 q^{83} -2.17382e68 q^{84} -5.14385e68 q^{85} -3.60326e68 q^{86} -1.97838e68 q^{87} +2.73468e69 q^{88} +2.67603e69 q^{89} +1.53965e69 q^{90} +3.77263e69 q^{91} +1.77302e69 q^{92} +9.22774e68 q^{93} +1.11821e70 q^{94} -1.62143e70 q^{95} +9.01481e69 q^{96} -5.40339e69 q^{97} +5.67635e69 q^{98} +4.62080e70 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 72903656826 q^{2} - 30\!\cdots\!42 q^{3}+ \cdots + 15\!\cdots\!94 q^{9}+O(q^{10}) \) 6 * q - 72903656826 * q^2 - 300189270593998242 * q^3 + 10314006409421274045732 * q^4 + 10108593794701196744004900 * q^5 + 3647482594372016835002549982 * q^6 + 599480901407450839419869685888 * q^7 - 366478583494279643287721499310632 * q^8 + 15018933029959449607893431916515094 * q^9	\( 6 q - 72903656826 q^{2} - 30\!\cdots\!42 q^{3}+ \cdots + 55\!\cdots\!36 q^{99}+O(q^{100}) \) 6 * q - 72903656826 * q^2 - 300189270593998242 * q^3 + 10314006409421274045732 * q^4 + 10108593794701196744004900 * q^5 + 3647482594372016835002549982 * q^6 + 599480901407450839419869685888 * q^7 - 366478583494279643287721499310632 * q^8 + 15018933029959449607893431916515094 * q^9 + 542868868744970666737312582578468900 * q^10 + 22151081175113604333940540682999237064 * q^11 - 516025676824332508905200786034172600524 * q^12 - 3733792306574713187109013147800580842876 * q^13 - 32830507140759982684754962229979568501632 * q^14 - 505748566327061510308971264776339106564300 * q^15 + 21946377025014017232533669358468876656094480 * q^16 + 29728537162009030546400351590681521887294796 * q^17 - 182489189918140015151617170203501982470855274 * q^18 - 3400191903952978211629854680984130031529265672 * q^19 + 67862977310829773665490051450873586512770090200 * q^20 - 29992955754755873599156504803112485841094034816 * q^21 + 944165659732727247119333482328915476491852443592 * q^22 - 241048097798755219551674687627695903843789894224 * q^23 + 18335489777911581603442307001776299015793269984824 * q^24 + 147233544111014179651192740252202252138516733666250 * q^25 + 365811593583549796821577322473046008640162770663812 * q^26 - 751420425227272520651160327198275815599672767077458 * q^27 + 7184703440899560087451639062714257068053559172254464 * q^28 + 14043556001266662709861160370005828332436911172303796 * q^29 - 27160568289456952381721411384929474444132225608612300 * q^30 - 270783306371944339515858500277888580308160694590498224 * q^31 - 1125690872219692784327995632757361168637025492519761312 * q^32 - 1108252816804299721415203709279850747171688230559540248 * q^33 - 14624984721002826287006157938202770657423642866907848116 * q^34 + 1330179995756585937201666471865883862092414077711430400 * q^35 + 25817561922278439824339062712693846594436309019304046468 * q^36 - 35792724481179188252370374519670456030630938465810079852 * q^37 - 40096713421645845706764919843501793548783513747008434184 * q^38 + 186807398176690903032688790342604890157893721294537037332 * q^39 - 2479587661237177399988484749809178898031295693356625910000 * q^40 + 477389693785559225342921822791522325133674715121487806716 * q^41 + 1642560998635964995488184749898337758134027879087997021824 * q^42 + 11648760938240913572137172567293471863701640091329944903880 * q^43 + 74878798041661318901325225719624262581993699901301979154096 * q^44 + 25303382204946822552840415428929959629608562926007476660100 * q^45 - 22722764972174503220374661680362423965849207035012290901584 * q^46 - 74847986304767650251381147705131168308416847087017595772160 * q^47 - 1098011151886639823988203119437140867642137257944093284317360 * q^48 - 688653477285391597239303104103354245619646953145790225785290 * q^49 - 15161902343877042722978992840348999467045739232226501266733750 * q^50 - 1487364647748343570766109334072688855147129111496091826624772 * q^51 - 9233127809375467425363213342738333025041297615633059381760744 * q^52 + 54557017276559944552388010917280252208764745473331764291919716 * q^53 + 9130216135469344816922031758794829019895633468152138165404718 * q^54 - 23377768702274474935917895870707480727711321830514284596005200 * q^55 + 52410231138004746064340786054323553480340549752421553548034560 * q^56 + 170116854587877109514295582543857751828315219056921303453158104 * q^57 - 6869577034896111059681057797577176576414351550513678648728908 * q^58 - 2982562673835141937005021578485268051001526328776278691712555448 * q^59 - 3395289609879173678404575975976528237976459801298749688163571400 * q^60 + 2024766122758654206628711672366353464571765836352692052196097220 * q^61 + 6190527473014961587199547234678103673640494648116320147386047056 * q^62 + 1500593918496371285775305974945167898072787838438228726231798912 * q^63 + 45446447421689003372958411079333884263847638574085838786019075648 * q^64 + 48520756571856116218224136414427408842784606511438543051271531800 * q^65 - 47238066785844754909978749266876448249150867465391889442842027544 * q^66 - 35831986821500503360634896265657012310045332669260449034581275784 * q^67 + 185089183911227350024079142251468478888729548294423879590659066312 * q^68 + 12060008776046513765968603659742476293934666629048669377736992368 * q^69 - 344172356460367114079337658836072099942116692861986486268441785600 * q^70 - 51113783482860556737395980857143689650967786833886125865998410928 * q^71 - 917352883735831416728537588310564568722018780050793374149470446568 * q^72 - 1956710326081635365311373308078888669483174388894330237696366066724 * q^73 + 5709348546681615596063021572004447539391345291333750996512485900948 * q^74 - 7366321702275768652418713145914811812464675260129281903805785788750 * q^75 - 23809271474859754704092582776426668087720715729896871772596110280752 * q^76 + 18917631699413080007630569020425573902563798951131161813579745527296 * q^77 - 18302119242112323501394112685535398871026762720686772677565583503084 * q^78 + 48402596803386404034053884911414009193830041621338105095759924707760 * q^79 + 263392522337449869178773130835490329512120616670537417787135845410400 * q^80 + 37594724893067822275537345166051581993240166680863991649157588304806 * q^81 - 304020075917296666161317294537198008494062493274925376834937204559364 * q^82 + 231863714798237849378047661016738227772765340915812707253802255256568 * q^83 - 359461814226304716526488880176552818520355782596793385427234465442048 * q^84 - 153432496682031145548917546056875902159222382871180623315806512428600 * q^85 + 232789528332961926178362349658049178503816504422806394312074365597384 * q^86 - 702620805427701021731731825948244137787180874181672925287922318987772 * q^87 + 5297065653948252699139641997691020789333729718805571695420136408677408 * q^88 + 4386397294164484419236854507748631162668647776406659364039350285963708 * q^89 + 1358885197288426841258681446071983205212433617120516879514014376596100 * q^90 + 10645224502890544811266185738918008251735428747945615198269035910167296 * q^91 + 3494882087686348167672392093650816456059296420998691954341908970318368 * q^92 + 13547707204804187951296675402664208391644243687789646939851889160020368 * q^93 + 212140324104529926314570388896027999493814139075827826098897565498112 * q^94 - 32230267438252135206013682642661075145567906057502744951334901038078000 * q^95 + 56320053640991875947605433538589148930174287383392714581574101597935584 * q^96 + 97296789347912261411847519869140120543815674831725660650989227379865996 * q^97 + 262411331100552434262334793443846407592764783361237538614096838440889526 * q^98 + 55447600785037781851022576825288562814422347406938226617866090606707336 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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