LMFDB - Embedded newform 3.72.a.b.1.5

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			1.5
Root			$9.35614e9$ 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)

$f(q)$	$=$	$q+4.39862e10 q^{2} -5.00315e16 q^{3} -4.26395e20 q^{4} +4.61068e24 q^{5} -2.20070e27 q^{6} -1.72926e30 q^{7} -1.22615e32 q^{8} +2.50316e33 q^{9} +O(q^{10})$	\(q+4.39862e10 q^{2} -5.00315e16 q^{3} -4.26395e20 q^{4} +4.61068e24 q^{5} -2.20070e27 q^{6} -1.72926e30 q^{7} -1.22615e32 q^{8} +2.50316e33 q^{9} +2.02806e35 q^{10} -3.29988e36 q^{11} +2.13332e37 q^{12} -5.27741e39 q^{13} -7.60636e40 q^{14} -2.30679e41 q^{15} -4.38658e42 q^{16} +2.19409e42 q^{17} +1.10104e44 q^{18} +1.32889e45 q^{19} -1.96597e45 q^{20} +8.65175e46 q^{21} -1.45149e47 q^{22} +4.12260e47 q^{23} +6.13462e48 q^{24} -2.10933e49 q^{25} -2.32133e50 q^{26} -1.25237e50 q^{27} +7.37347e50 q^{28} +9.84606e51 q^{29} -1.01467e52 q^{30} -1.36951e53 q^{31} +9.65676e52 q^{32} +1.65098e53 q^{33} +9.65097e52 q^{34} -7.97306e54 q^{35} -1.06733e54 q^{36} -3.72709e55 q^{37} +5.84529e55 q^{38} +2.64037e56 q^{39} -5.65339e56 q^{40} -1.73242e57 q^{41} +3.80558e57 q^{42} +1.55004e58 q^{43} +1.40705e57 q^{44} +1.15412e58 q^{45} +1.81338e58 q^{46} -2.62885e59 q^{47} +2.19467e59 q^{48} +1.98581e60 q^{49} -9.27814e59 q^{50} -1.09774e59 q^{51} +2.25026e60 q^{52} +3.04834e61 q^{53} -5.50869e60 q^{54} -1.52147e61 q^{55} +2.12033e62 q^{56} -6.64865e61 q^{57} +4.33091e62 q^{58} -6.79021e62 q^{59} +9.83606e61 q^{60} -6.01505e62 q^{61} -6.02397e63 q^{62} -4.32860e63 q^{63} +1.46052e64 q^{64} -2.43324e64 q^{65} +7.26205e63 q^{66} -5.52019e63 q^{67} -9.35549e62 q^{68} -2.06260e64 q^{69} -3.50705e65 q^{70} +7.86618e65 q^{71} -3.06925e65 q^{72} +1.87540e66 q^{73} -1.63941e66 q^{74} +1.05533e66 q^{75} -5.66633e65 q^{76} +5.70635e66 q^{77} +1.16140e67 q^{78} +1.89457e66 q^{79} -2.02251e67 q^{80} +6.26579e66 q^{81} -7.62025e67 q^{82} -1.25922e68 q^{83} -3.68906e67 q^{84} +1.01162e67 q^{85} +6.81803e68 q^{86} -4.92614e68 q^{87} +4.04615e68 q^{88} -3.41547e67 q^{89} +5.07656e68 q^{90} +9.12600e69 q^{91} -1.75786e68 q^{92} +6.85188e69 q^{93} -1.15633e70 q^{94} +6.12709e69 q^{95} -4.83143e69 q^{96} +1.31172e70 q^{97} +8.73484e70 q^{98} -8.26012e69 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.39862e10	0.905215	0.452608	−	0.891710i	$-0.350494\pi$
$2$	4.39862e10	0.905215	0.452608	+	0.891710i	$0.350494\pi$
$3$	−5.00315e16	−0.577350
$3$	−5.00315e16	−0.577350
$4$	−4.26395e20	−0.180585
$5$	4.61068e24	0.708484	0.354242	−	0.935154i	$-0.384739\pi$
$5$	4.61068e24	0.708484	0.354242	+	0.935154i	$0.384739\pi$
$6$	−2.20070e27	−0.522626
$7$	−1.72926e30	−1.72536	−0.862680	−	0.505751i	$-0.831216\pi$
$7$	−1.72926e30	−1.72536	−0.862680	+	0.505751i	$0.831216\pi$
$8$	−1.22615e32	−1.06868
$9$	2.50316e33	0.333333
$10$	2.02806e35	0.641330
$11$	−3.29988e36	−0.354045	−0.177022	−	0.984207i	$-0.556646\pi$
$11$	−3.29988e36	−0.354045	−0.177022	+	0.984207i	$0.556646\pi$
$12$	2.13332e37	0.104261
$13$	−5.27741e39	−1.50464	−0.752318	−	0.658800i	$-0.771064\pi$
$13$	−5.27741e39	−1.50464	−0.752318	+	0.658800i	$0.771064\pi$
$14$	−7.60636e40	−1.56182
$15$	−2.30679e41	−0.409043
$16$	−4.38658e42	−0.786804
$17$	2.19409e42	0.0457423	0.0228711	−	0.999738i	$-0.492719\pi$
$17$	2.19409e42	0.0457423	0.0228711	+	0.999738i	$0.492719\pi$
$18$	1.10104e44	0.301738
$19$	1.32889e45	0.534240	0.267120	−	0.963663i	$-0.413928\pi$
$19$	1.32889e45	0.534240	0.267120	+	0.963663i	$0.413928\pi$
$20$	−1.96597e45	−0.127942
$21$	8.65175e46	0.996137
$22$	−1.45149e47	−0.320487
$23$	4.12260e47	0.187860	0.0939298	−	0.995579i	$-0.470057\pi$
$23$	4.12260e47	0.187860	0.0939298	+	0.995579i	$0.470057\pi$
$24$	6.13462e48	0.617005
$25$	−2.10933e49	−0.498051
$26$	−2.32133e50	−1.36202
$27$	−1.25237e50	−0.192450
$28$	7.37347e50	0.311575
$29$	9.84606e51	1.19711	0.598554	−	0.801082i	$-0.295742\pi$
$29$	9.84606e51	1.19711	0.598554	+	0.801082i	$0.295742\pi$
$30$	−1.01467e52	−0.370272
$31$	−1.36951e53	−1.56036	−0.780182	−	0.625553i	$-0.784873\pi$
$31$	−1.36951e53	−1.56036	−0.780182	+	0.625553i	$0.784873\pi$
$32$	9.65676e52	0.356457
$33$	1.65098e53	0.204408
$34$	9.65097e52	0.0414066
$35$	−7.97306e54	−1.22239
$36$	−1.06733e54	−0.0601951
$37$	−3.72709e55	−0.794711	−0.397355	−	0.917665i	$-0.630072\pi$
$37$	−3.72709e55	−0.794711	−0.397355	+	0.917665i	$0.630072\pi$
$38$	5.84529e55	0.483603
$39$	2.64037e56	0.868702
$40$	−5.65339e56	−0.757145
$41$	−1.73242e57	−0.965662	−0.482831	−	0.875713i	$-0.660392\pi$
$41$	−1.73242e57	−0.965662	−0.482831	+	0.875713i	$0.660392\pi$
$42$	3.80558e57	0.901718
$43$	1.55004e58	1.59299	0.796493	−	0.604647i	$-0.206686\pi$
$43$	1.55004e58	1.59299	0.796493	+	0.604647i	$0.206686\pi$
$44$	1.40705e57	0.0639353
$45$	1.15412e58	0.236161
$46$	1.81338e58	0.170053
$47$	−2.62885e59	−1.14893	−0.574463	−	0.818530i	$-0.694789\pi$
$47$	−2.62885e59	−1.14893	−0.574463	+	0.818530i	$0.694789\pi$
$48$	2.19467e59	0.454261
$49$	1.98581e60	1.97687
$50$	−9.27814e59	−0.450843
$51$	−1.09774e59	−0.0264093
$52$	2.25026e60	0.271715
$53$	3.04834e61	1.87184	0.935922	−	0.352208i	$-0.114569\pi$
$53$	3.04834e61	1.87184	0.935922	+	0.352208i	$0.114569\pi$
$54$	−5.50869e60	−0.174209
$55$	−1.52147e61	−0.250835
$56$	2.12033e62	1.84386
$57$	−6.64865e61	−0.308444
$58$	4.33091e62	1.08364
$59$	−6.79021e62	−0.926055	−0.463027	−	0.886344i	$-0.653237\pi$
$59$	−6.79021e62	−0.926055	−0.463027	+	0.886344i	$0.653237\pi$
$60$	9.83606e61	0.0738672
$61$	−6.01505e62	−0.251206	−0.125603	−	0.992081i	$-0.540087\pi$
$61$	−6.01505e62	−0.251206	−0.125603	+	0.992081i	$0.540087\pi$
$62$	−6.02397e63	−1.41246
$63$	−4.32860e63	−0.575120
$64$	1.46052e64	1.10947
$65$	−2.43324e64	−1.06601
$66$	7.26205e63	0.185033
$67$	−5.52019e63	−0.0824705	−0.0412352	−	0.999149i	$-0.513129\pi$
$67$	−5.52019e63	−0.0824705	−0.0412352	+	0.999149i	$0.513129\pi$
$68$	−9.35549e62	−0.00826038
$69$	−2.06260e64	−0.108461
$70$	−3.50705e65	−1.10653
$71$	7.86618e65	1.50000	0.750002	−	0.661435i	$-0.230052\pi$
$71$	7.86618e65	1.50000	0.750002	+	0.661435i	$0.230052\pi$
$72$	−3.06925e65	−0.356228
$73$	1.87540e66	1.33393	0.666964	−	0.745090i	$-0.267594\pi$
$73$	1.87540e66	1.33393	0.666964	+	0.745090i	$0.267594\pi$
$74$	−1.63941e66	−0.719384
$75$	1.05533e66	0.287550
$76$	−5.66633e65	−0.0964760
$77$	5.70635e66	0.610855
$78$	1.16140e67	0.786363
$79$	1.89457e66	0.0816109	0.0408055	−	0.999167i	$-0.487008\pi$
$79$	1.89457e66	0.0816109	0.0408055	+	0.999167i	$0.487008\pi$
$80$	−2.02251e67	−0.557438
$81$	6.26579e66	0.111111
$82$	−7.62025e67	−0.874132
$83$	−1.25922e68	−0.939355	−0.469678	−	0.882838i	$-0.655630\pi$
$83$	−1.25922e68	−0.939355	−0.469678	+	0.882838i	$0.655630\pi$
$84$	−3.68906e67	−0.179888
$85$	1.01162e67	0.0324076
$86$	6.81803e68	1.44200
$87$	−4.92614e68	−0.691151
$88$	4.04615e68	0.378362
$89$	−3.41547e67	−0.0213848	−0.0106924	−	0.999943i	$-0.503404\pi$
$89$	−3.41547e67	−0.0213848	−0.0106924	+	0.999943i	$0.503404\pi$
$90$	5.07656e68	0.213777
$91$	9.12600e69	2.59604
$92$	−1.75786e68	−0.0339247
$93$	6.85188e69	0.900876
$94$	−1.15633e70	−1.04003
$95$	6.12709e69	0.378501
$96$	−4.83143e69	−0.205801
$97$	1.31172e70	0.386761	0.193381	−	0.981124i	$-0.438055\pi$
$97$	1.31172e70	0.386761	0.193381	+	0.981124i	$0.438055\pi$
$98$	8.73484e70	1.78949
$99$	−8.26012e69	−0.118015
$100$	8.99407e69	0.0899407
$101$	−4.78853e70	−0.336352	−0.168176	−	0.985757i	$-0.553788\pi$
$101$	−4.78853e70	−0.336352	−0.168176	+	0.985757i	$0.553788\pi$
$102$	−4.82853e69	−0.0239061
$103$	1.58722e71	0.555798	0.277899	−	0.960610i	$-0.410362\pi$
$103$	1.58722e71	0.555798	0.277899	+	0.960610i	$0.410362\pi$
$104$	6.47090e71	1.60798
$105$	3.98905e71	0.705747
$106$	1.34085e72	1.69442
$107$	5.01353e71	0.453962	0.226981	−	0.973899i	$-0.427115\pi$
$107$	5.01353e71	0.453962	0.226981	+	0.973899i	$0.427115\pi$
$108$	5.34003e70	0.0347537
$109$	1.22527e72	0.574900	0.287450	−	0.957796i	$-0.407192\pi$
$109$	1.22527e72	0.574900	0.287450	+	0.957796i	$0.407192\pi$
$110$	−6.69237e71	−0.227060
$111$	1.86472e72	0.458826
$112$	7.58553e72	1.35752
$113$	1.13644e73	1.48341	0.741705	−	0.670726i	$-0.234017\pi$
$113$	1.13644e73	1.48341	0.741705	+	0.670726i	$0.234017\pi$
$114$	−2.92449e72	−0.279208
$115$	1.90080e72	0.133095
$116$	−4.19831e72	−0.216180
$117$	−1.32102e73	−0.501545
$118$	−2.98676e73	−0.838279
$119$	−3.79415e72	−0.0789219
$120$	2.82848e73	0.437138
$121$	−7.59829e73	−0.874652
$122$	−2.64579e73	−0.227395
$123$	8.66755e73	0.557526
$124$	5.83953e73	0.281779
$125$	−2.92524e74	−1.06134
$126$	−1.90399e74	−0.520607
$127$	3.93807e74	0.813300	0.406650	−	0.913584i	$-0.366697\pi$
$127$	3.93807e74	0.813300	0.406650	+	0.913584i	$0.366697\pi$
$128$	4.14412e74	0.647856
$129$	−7.75508e74	−0.919711
$130$	−1.07029e75	−0.964969
$131$	−2.14908e75	−1.47612	−0.738059	−	0.674736i	$-0.764257\pi$
$131$	−2.14908e75	−1.47612	−0.738059	+	0.674736i	$0.764257\pi$
$132$	−7.03971e73	−0.0369131
$133$	−2.29800e75	−0.921757
$134$	−2.42812e74	−0.0746535
$135$	−5.77427e74	−0.136348
$136$	−2.69028e74	−0.0488840
$137$	−8.79951e75	−1.23276	−0.616380	−	0.787449i	$-0.711401\pi$
$137$	−8.79951e75	−1.23276	−0.616380	+	0.787449i	$0.711401\pi$
$138$	−9.07261e74	−0.0981804
$139$	7.22831e75	0.605357	0.302678	−	0.953093i	$-0.402119\pi$
$139$	7.22831e75	0.605357	0.302678	+	0.953093i	$0.402119\pi$
$140$	3.39967e75	0.220746
$141$	1.31526e76	0.663333
$142$	3.46004e76	1.35783
$143$	1.74148e76	0.532709
$144$	−1.09803e76	−0.262268
$145$	4.53970e76	0.848132
$146$	8.24917e76	1.20749
$147$	−9.93532e76	−1.14134
$148$	1.58921e76	0.143513
$149$	7.34373e75	0.0522161	0.0261080	−	0.999659i	$-0.491689\pi$
$149$	7.34373e75	0.0522161	0.0261080	+	0.999659i	$0.491689\pi$
$150$	4.64199e76	0.260294
$151$	3.57797e77	1.58473	0.792364	−	0.610048i	$-0.208850\pi$
$151$	3.57797e77	1.58473	0.792364	+	0.610048i	$0.208850\pi$
$152$	−1.62942e77	−0.570934
$153$	5.49215e75	0.0152474
$154$	2.51001e77	0.552955
$155$	−6.31438e77	−1.10549
$156$	−1.12584e77	−0.156875
$157$	7.55825e77	0.839428	0.419714	−	0.907656i	$-0.362130\pi$
$157$	7.55825e77	0.839428	0.419714	+	0.907656i	$0.362130\pi$
$158$	8.33349e76	0.0738755
$159$	−1.52513e78	−1.08071
$160$	4.45242e77	0.252544
$161$	−7.12905e77	−0.324125
$162$	2.75608e77	0.100579
$163$	−3.45980e77	−0.101483	−0.0507413	−	0.998712i	$-0.516158\pi$
$163$	−3.45980e77	−0.101483	−0.0507413	+	0.998712i	$0.516158\pi$
$164$	7.38694e77	0.174384
$165$	7.61215e77	0.144820
$166$	−5.53884e78	−0.850319
$167$	−1.36563e79	−1.69394	−0.846969	−	0.531642i	$-0.821575\pi$
$167$	−1.36563e79	−1.69394	−0.846969	+	0.531642i	$0.821575\pi$
$168$	−1.06083e79	−1.06456
$169$	1.55490e79	1.26393
$170$	4.44976e77	0.0293359
$171$	3.32642e78	0.178080
$172$	−6.60928e78	−0.287670
$173$	−4.26945e79	−1.51264	−0.756320	−	0.654202i	$-0.773005\pi$
$173$	−4.26945e79	−1.51264	−0.756320	+	0.654202i	$0.773005\pi$
$174$	−2.16682e79	−0.625640
$175$	3.64757e79	0.859317
$176$	1.44752e79	0.278564
$177$	3.39725e79	0.534658
$178$	−1.50234e78	−0.0193579
$179$	1.16788e80	1.23343	0.616714	−	0.787187i	$-0.288463\pi$
$179$	1.16788e80	1.23343	0.616714	+	0.787187i	$0.288463\pi$
$180$	−4.92113e78	−0.0426472
$181$	2.50000e79	0.177972	0.0889859	−	0.996033i	$-0.471637\pi$
$181$	2.50000e79	0.177972	0.0889859	+	0.996033i	$0.471637\pi$
$182$	4.01418e80	2.34997
$183$	3.00942e79	0.145034
$184$	−5.05493e79	−0.200763
$185$	−1.71844e80	−0.563040
$186$	3.01388e80	0.815487
$187$	−7.24024e78	−0.0161948
$188$	1.12093e80	0.207479
$189$	2.16567e80	0.332046
$190$	2.69508e80	0.342625
$191$	−1.75479e81	−1.85157	−0.925787	−	0.378046i	$-0.876596\pi$
$191$	−1.75479e81	−1.85157	−0.925787	+	0.378046i	$0.876596\pi$
$192$	−7.30719e80	−0.640555
$193$	−2.22924e81	−1.62507	−0.812536	−	0.582911i	$-0.801914\pi$
$193$	−2.22924e81	−1.62507	−0.812536	+	0.582911i	$0.801914\pi$
$194$	5.76974e80	0.350102
$195$	1.21739e81	0.615461
$196$	−8.46740e80	−0.356993
$197$	4.61130e81	1.62283	0.811413	−	0.584473i	$-0.198699\pi$
$197$	4.61130e81	1.62283	0.811413	+	0.584473i	$0.198699\pi$
$198$	−3.63331e80	−0.106829
$199$	−4.10653e81	−1.00970	−0.504848	−	0.863208i	$-0.668452\pi$
$199$	−4.10653e81	−1.00970	−0.504848	+	0.863208i	$0.668452\pi$
$200$	2.58635e81	0.532259
$201$	2.76184e80	0.0476143
$202$	−2.10630e81	−0.304471
$203$	−1.70264e82	−2.06544
$204$	4.68070e79	0.00476913
$205$	−7.98762e81	−0.684156
$206$	6.98160e81	0.503117
$207$	1.03195e81	0.0626199
$208$	2.31498e82	1.18385
$209$	−4.38519e81	−0.189145
$210$	1.75463e82	0.638853
$211$	−3.40940e82	−1.04870	−0.524350	−	0.851503i	$-0.675692\pi$
$211$	−3.40940e82	−1.04870	−0.524350	+	0.851503i	$0.675692\pi$
$212$	−1.29980e82	−0.338027
$213$	−3.93557e82	−0.866028
$214$	2.20526e82	0.410933
$215$	7.14673e82	1.12860
$216$	1.53559e82	0.205668
$217$	2.36824e83	2.69219
$218$	5.38952e82	0.520409
$219$	−9.38291e82	−0.770143
$220$	6.48747e81	0.0452971
$221$	−1.15791e82	−0.0688255
$222$	8.20221e82	0.415337
$223$	2.11970e82	0.0915063	0.0457531	−	0.998953i	$-0.485431\pi$
$223$	2.11970e82	0.0915063	0.0457531	+	0.998953i	$0.485431\pi$
$224$	−1.66990e83	−0.615017
$225$	−5.27997e82	−0.166017
$226$	4.99877e83	1.34281
$227$	−4.37536e83	−1.00484	−0.502418	−	0.864625i	$-0.667556\pi$
$227$	−4.37536e83	−1.00484	−0.502418	+	0.864625i	$0.667556\pi$
$228$	2.83495e82	0.0557004
$229$	−5.70136e83	−0.959000	−0.479500	−	0.877542i	$-0.659182\pi$
$229$	−5.70136e83	−0.959000	−0.479500	+	0.877542i	$0.659182\pi$
$230$	8.36091e82	0.120480
$231$	−2.85498e83	−0.352677
$232$	−1.20728e84	−1.27933
$233$	1.43087e83	0.130156	0.0650782	−	0.997880i	$-0.479270\pi$
$233$	1.43087e83	0.130156	0.0650782	+	0.997880i	$0.479270\pi$
$234$	−5.81066e83	−0.454007
$235$	−1.21208e84	−0.813995
$236$	2.89531e83	0.167232
$237$	−9.47881e82	−0.0471181
$238$	−1.66890e83	−0.0714413
$239$	−1.67713e84	−0.618646	−0.309323	−	0.950957i	$-0.600102\pi$
$239$	−1.67713e84	−0.618646	−0.309323	+	0.950957i	$0.600102\pi$
$240$	1.01189e84	0.321837
$241$	4.90215e84	1.34518	0.672591	−	0.740014i	$-0.265181\pi$
$241$	4.90215e84	1.34518	0.672591	+	0.740014i	$0.265181\pi$
$242$	−3.34220e84	−0.791749
$243$	−3.13487e83	−0.0641500
$244$	2.56479e83	0.0453641
$245$	9.15594e84	1.40058
$246$	3.81253e84	0.504681
$247$	−7.01310e84	−0.803838
$248$	1.67923e85	1.66754
$249$	6.30008e84	0.542337
$250$	−1.28670e85	−0.960745
$251$	−1.44085e85	−0.933687	−0.466843	−	0.884340i	$-0.654609\pi$
$251$	−1.44085e85	−0.933687	−0.466843	+	0.884340i	$0.654609\pi$
$252$	1.84570e84	0.103858
$253$	−1.36041e84	−0.0665107
$254$	1.73221e85	0.736212
$255$	−5.06131e83	−0.0187106
$256$	−1.62570e85	−0.523025
$257$	4.14406e85	1.16092	0.580458	−	0.814290i	$-0.302874\pi$
$257$	4.14406e85	1.16092	0.580458	+	0.814290i	$0.302874\pi$
$258$	−3.41117e85	−0.832537
$259$	6.44511e85	1.37116
$260$	1.03752e85	0.192506
$261$	2.46462e85	0.399036
$262$	−9.45298e85	−1.33620
$263$	−3.75588e85	−0.463748	−0.231874	−	0.972746i	$-0.574486\pi$
$263$	−3.75588e85	−0.463748	−0.231874	+	0.972746i	$0.574486\pi$
$264$	−2.02435e85	−0.218447
$265$	1.40549e86	1.32617
$266$	−1.01080e86	−0.834388
$267$	1.70881e84	0.0123465
$268$	2.35378e84	0.0148930
$269$	−6.52419e85	−0.361677	−0.180838	−	0.983513i	$-0.557881\pi$
$269$	−6.52419e85	−0.361677	−0.180838	+	0.983513i	$0.557881\pi$
$270$	−2.53988e85	−0.123424
$271$	−1.92776e86	−0.821565	−0.410783	−	0.911733i	$-0.634744\pi$
$271$	−1.92776e86	−0.821565	−0.410783	+	0.911733i	$0.634744\pi$
$272$	−9.62454e84	−0.0359902
$273$	−4.56588e86	−1.49882
$274$	−3.87057e86	−1.11591
$275$	6.96053e85	0.176332
$276$	8.79483e84	0.0195864
$277$	−1.44338e85	−0.0282715	−0.0141357	−	0.999900i	$-0.504500\pi$
$277$	−1.44338e85	−0.0282715	−0.0141357	+	0.999900i	$0.504500\pi$
$278$	3.17946e86	0.547978
$279$	−3.42810e86	−0.520121
$280$	9.77617e86	1.30635
$281$	7.41111e86	0.872587	0.436294	−	0.899804i	$-0.356291\pi$
$281$	7.41111e86	0.872587	0.436294	+	0.899804i	$0.356291\pi$
$282$	5.78531e86	0.600459
$283$	6.24790e86	0.571894	0.285947	−	0.958245i	$-0.407692\pi$
$283$	6.24790e86	0.571894	0.285947	+	0.958245i	$0.407692\pi$
$284$	−3.35410e86	−0.270879
$285$	−3.06548e86	−0.218527
$286$	7.66012e86	0.482216
$287$	2.99580e87	1.66612
$288$	2.41724e86	0.118819
$289$	−2.29596e87	−0.997908
$290$	1.99684e87	0.767742
$291$	−6.56271e86	−0.223297
$292$	−7.99661e86	−0.240888
$293$	2.16658e87	0.578061	0.289031	−	0.957320i	$-0.406667\pi$
$293$	2.16658e87	0.578061	0.289031	+	0.957320i	$0.406667\pi$
$294$	−4.37017e87	−1.03316
$295$	−3.13075e87	−0.656095
$296$	4.56998e87	0.849295
$297$	4.13267e86	0.0681359
$298$	3.23023e86	0.0472668
$299$	−2.17567e87	−0.282660
$300$	−4.49987e86	−0.0519273
$301$	−2.68042e88	−2.74847
$302$	1.57381e88	1.43452
$303$	2.39578e87	0.194193
$304$	−5.82929e87	−0.420342
$305$	−2.77335e87	−0.177975
$306$	2.41579e86	0.0138022
$307$	−5.57566e87	−0.283716	−0.141858	−	0.989887i	$-0.545308\pi$
$307$	−5.57566e87	−0.283716	−0.141858	+	0.989887i	$0.545308\pi$
$308$	−2.43316e87	−0.110311
$309$	−7.94113e87	−0.320890
$310$	−2.77746e88	−1.00071
$311$	3.90643e88	1.25541	0.627706	−	0.778451i	$-0.283994\pi$
$311$	3.90643e88	1.25541	0.627706	+	0.778451i	$0.283994\pi$
$312$	−3.23749e88	−0.928368
$313$	3.92299e88	1.00414	0.502069	−	0.864827i	$-0.332572\pi$
$313$	3.92299e88	1.00414	0.502069	+	0.864827i	$0.332572\pi$
$314$	3.32459e88	0.759863
$315$	−1.99578e88	−0.407463
$316$	−8.07834e86	−0.0147377
$317$	7.81578e88	1.27458	0.637292	−	0.770622i	$-0.280054\pi$
$317$	7.81578e88	1.27458	0.637292	+	0.770622i	$0.280054\pi$
$318$	−6.70847e88	−0.978275
$319$	−3.24908e88	−0.423830
$320$	6.73397e88	0.786044
$321$	−2.50834e88	−0.262095
$322$	−3.13580e88	−0.293403
$323$	2.91571e87	0.0244374
$324$	−2.67170e87	−0.0200650
$325$	1.11318e89	0.749386
$326$	−1.52184e88	−0.0918636
$327$	−6.13024e88	−0.331919
$328$	2.12420e89	1.03199
$329$	4.54597e89	1.98231
$330$	3.34830e88	0.131093
$331$	−1.74254e89	−0.612757	−0.306379	−	0.951910i	$-0.599117\pi$
$331$	−1.74254e89	−0.612757	−0.306379	+	0.951910i	$0.599117\pi$
$332$	5.36926e88	0.169634
$333$	−9.32949e88	−0.264904
$334$	−6.00688e89	−1.53338
$335$	−2.54518e88	−0.0584290
$336$	−3.79516e89	−0.783764
$337$	5.13205e89	0.953739	0.476870	−	0.878974i	$-0.341771\pi$
$337$	5.13205e89	0.953739	0.476870	+	0.878974i	$0.341771\pi$
$338$	6.83940e89	1.14413
$339$	−5.68578e89	−0.856448
$340$	−4.31352e87	−0.00585235
$341$	4.51923e89	0.552438
$342$	1.46317e89	0.161201
$343$	−1.69690e90	−1.68544
$344$	−1.90058e90	−1.70240
$345$	−9.51000e88	−0.0768427
$346$	−1.87797e90	−1.36927
$347$	−1.01985e89	−0.0671179	−0.0335590	−	0.999437i	$-0.510684\pi$
$347$	−1.01985e89	−0.0671179	−0.0335590	+	0.999437i	$0.510684\pi$
$348$	2.10048e89	0.124812
$349$	−1.18931e90	−0.638255	−0.319127	−	0.947712i	$-0.603390\pi$
$349$	−1.18931e90	−0.638255	−0.319127	+	0.947712i	$0.603390\pi$
$350$	1.60443e90	0.777867
$351$	6.60925e89	0.289567
$352$	−3.18662e89	−0.126202
$353$	4.04773e90	1.44947	0.724735	−	0.689028i	$-0.241962\pi$
$353$	4.04773e90	1.44947	0.724735	+	0.689028i	$0.241962\pi$
$354$	1.49432e90	0.483981
$355$	3.62684e90	1.06273
$356$	1.45634e88	0.00386178
$357$	1.89827e89	0.0455656
$358$	5.13704e90	1.11652
$359$	−4.95846e88	−0.00976098	−0.00488049	−	0.999988i	$-0.501554\pi$
$359$	−4.95846e88	−0.00976098	−0.00488049	+	0.999988i	$0.501554\pi$
$360$	−1.41513e90	−0.252382
$361$	−4.42141e90	−0.714587
$362$	1.09966e90	0.161103
$363$	3.80154e90	0.504981
$364$	−3.89128e90	−0.468806
$365$	8.64687e90	0.945066
$366$	1.32373e90	0.131287
$367$	1.33486e91	1.20168	0.600841	−	0.799369i	$-0.294832\pi$
$367$	1.33486e91	1.20168	0.600841	+	0.799369i	$0.294832\pi$
$368$	−1.80841e90	−0.147809
$369$	−4.33651e90	−0.321887
$370$	−7.55879e90	−0.509672
$371$	−5.27136e91	−3.22960
$372$	−2.92161e90	−0.162685
$373$	1.99463e91	1.00972	0.504858	−	0.863202i	$-0.331545\pi$
$373$	1.99463e91	1.00972	0.504858	+	0.863202i	$0.331545\pi$
$374$	−3.18471e89	−0.0146598
$375$	1.46354e91	0.612768
$376$	3.22337e91	1.22784
$377$	−5.19617e91	−1.80121
$378$	9.52595e90	0.300573
$379$	2.76472e91	0.794254	0.397127	−	0.917764i	$-0.370007\pi$
$379$	2.76472e91	0.794254	0.397127	+	0.917764i	$0.370007\pi$
$380$	−2.61256e90	−0.0683516
$381$	−1.97028e91	−0.469559
$382$	−7.71866e91	−1.67607
$383$	5.93168e91	1.17387	0.586937	−	0.809633i	$-0.300334\pi$
$383$	5.93168e91	1.17387	0.586937	+	0.809633i	$0.300334\pi$
$384$	−2.07337e91	−0.374040
$385$	2.63102e91	0.432780
$386$	−9.80559e91	−1.47104
$387$	3.87999e91	0.530995
$388$	−5.59309e90	−0.0698434
$389$	1.35208e91	0.154096	0.0770478	−	0.997027i	$-0.475451\pi$
$389$	1.35208e91	0.154096	0.0770478	+	0.997027i	$0.475451\pi$
$390$	5.35484e91	0.557125
$391$	9.04536e89	0.00859313
$392$	−2.43490e92	−2.11264
$393$	1.07522e92	0.852237
$394$	2.02834e92	1.46901
$395$	8.73524e90	0.0578200
$396$	3.52207e90	0.0213118
$397$	−1.25353e92	−0.693541	−0.346770	−	0.937950i	$-0.612722\pi$
$397$	−1.25353e92	−0.693541	−0.346770	+	0.937950i	$0.612722\pi$
$398$	−1.80631e92	−0.913993
$399$	1.14972e92	0.532177
$400$	9.25273e91	0.391868
$401$	3.81605e92	1.47907	0.739536	−	0.673117i	$-0.235045\pi$
$401$	3.81605e92	1.47907	0.739536	+	0.673117i	$0.235045\pi$
$402$	1.21483e91	0.0431012
$403$	7.22747e92	2.34778
$404$	2.04181e91	0.0607402
$405$	2.88895e91	0.0787204
$406$	−7.48927e92	−1.86967
$407$	1.22990e92	0.281363
$408$	1.34599e91	0.0282232
$409$	−3.52403e92	−0.677427	−0.338713	−	0.940890i	$-0.609992\pi$
$409$	−3.52403e92	−0.677427	−0.338713	+	0.940890i	$0.609992\pi$
$410$	−3.51345e92	−0.619309
$411$	4.40253e92	0.711734
$412$	−6.76785e91	−0.100369
$413$	1.17420e93	1.59778
$414$	4.53917e91	0.0566845
$415$	−5.80587e92	−0.665518
$416$	−5.09627e92	−0.536338
$417$	−3.61644e92	−0.349503
$418$	−1.92888e92	−0.171217
$419$	−1.85270e93	−1.51080	−0.755399	−	0.655265i	$-0.772557\pi$
$419$	−1.85270e93	−1.51080	−0.755399	+	0.655265i	$0.772557\pi$
$420$	−1.70091e92	−0.127447
$421$	2.39044e93	1.64613	0.823064	−	0.567949i	$-0.192263\pi$
$421$	2.39044e93	1.64613	0.823064	+	0.567949i	$0.192263\pi$
$422$	−1.49967e93	−0.949299
$423$	−6.58042e92	−0.382975
$424$	−3.73772e93	−2.00041
$425$	−4.62805e91	−0.0227820
$426$	−1.73111e93	−0.783942
$427$	1.04016e93	0.433421
$428$	−2.13774e92	−0.0819788
$429$	−8.71291e92	−0.307559
$430$	3.14358e93	1.02163
$431$	3.09247e93	0.925470	0.462735	−	0.886497i	$-0.346868\pi$
$431$	3.09247e93	0.925470	0.462735	+	0.886497i	$0.346868\pi$
$432$	5.49361e92	0.151420
$433$	−1.20416e93	−0.305748	−0.152874	−	0.988246i	$-0.548853\pi$
$433$	−1.20416e93	−0.305748	−0.152874	+	0.988246i	$0.548853\pi$
$434$	1.04170e94	2.43701
$435$	−2.27128e93	−0.489669
$436$	−5.22451e92	−0.103819
$437$	5.47849e92	0.100362
$438$	−4.12719e93	−0.697145
$439$	6.16345e93	0.960137	0.480069	−	0.877231i	$-0.340612\pi$
$439$	6.16345e93	0.960137	0.480069	+	0.877231i	$0.340612\pi$
$440$	1.86555e93	0.268063
$441$	4.97079e93	0.658955
$442$	−5.09321e92	−0.0623019
$443$	7.31036e93	0.825289	0.412645	−	0.910892i	$-0.364605\pi$
$443$	7.31036e93	0.825289	0.412645	+	0.910892i	$0.364605\pi$
$444$	−7.95108e92	−0.0828573
$445$	−1.57476e92	−0.0151508
$446$	9.32374e92	0.0828329
$447$	−3.67418e92	−0.0301470
$448$	−2.52561e94	−1.91424
$449$	3.65350e93	0.255838	0.127919	−	0.991785i	$-0.459170\pi$
$449$	3.65350e93	0.255838	0.127919	+	0.991785i	$0.459170\pi$
$450$	−2.32246e93	−0.150281
$451$	5.71677e93	0.341888
$452$	−4.84572e93	−0.267882
$453$	−1.79011e94	−0.914943
$454$	−1.92455e94	−0.909594
$455$	4.20771e94	1.83925
$456$	8.15225e93	0.329629
$457$	−1.33731e94	−0.500272	−0.250136	−	0.968211i	$-0.580475\pi$
$457$	−1.33731e94	−0.500272	−0.250136	+	0.968211i	$0.580475\pi$
$458$	−2.50781e94	−0.868102
$459$	−2.74781e92	−0.00880310
$460$	−8.10492e92	−0.0240351
$461$	5.31170e94	1.45831	0.729156	−	0.684347i	$-0.239913\pi$
$461$	5.31170e94	1.45831	0.729156	+	0.684347i	$0.239913\pi$
$462$	−1.25580e94	−0.319249
$463$	−4.99489e94	−1.17598	−0.587991	−	0.808867i	$-0.700081\pi$
$463$	−4.99489e94	−1.17598	−0.587991	+	0.808867i	$0.700081\pi$
$464$	−4.31905e94	−0.941890
$465$	3.15918e94	0.638256
$466$	6.29387e93	0.117820
$467$	1.10529e94	0.191747	0.0958733	−	0.995394i	$-0.469436\pi$
$467$	1.10529e94	0.191747	0.0958733	+	0.995394i	$0.469436\pi$
$468$	5.63275e93	0.0905717
$469$	9.54584e93	0.142291
$470$	−5.33148e94	−0.736841
$471$	−3.78151e94	−0.484644
$472$	8.32582e94	0.989660
$473$	−5.11494e94	−0.563988
$474$	−4.16937e93	−0.0426520
$475$	−2.80307e94	−0.266079
$476$	1.61781e93	0.0142521
$477$	7.63046e94	0.623948
$478$	−7.37708e94	−0.560008
$479$	−1.20022e95	−0.845961	−0.422981	−	0.906139i	$-0.639016\pi$
$479$	−1.20022e95	−0.845961	−0.422981	+	0.906139i	$0.639016\pi$
$480$	−2.22762e94	−0.145806
$481$	1.96694e95	1.19575
$482$	2.15627e95	1.21768
$483$	3.56677e94	0.187134
$484$	3.23987e94	0.157949
$485$	6.04790e94	0.274014
$486$	−1.37891e94	−0.0580696
$487$	3.76721e95	1.47483	0.737415	−	0.675440i	$-0.236046\pi$
$487$	3.76721e95	1.47483	0.737415	+	0.675440i	$0.236046\pi$
$488$	7.37535e94	0.268460
$489$	1.73099e94	0.0585910
$490$	4.02735e95	1.26782
$491$	−4.34178e95	−1.27138	−0.635690	−	0.771945i	$-0.719284\pi$
$491$	−4.34178e95	−1.27138	−0.635690	+	0.771945i	$0.719284\pi$
$492$	−3.69580e94	−0.100681
$493$	2.16031e94	0.0547585
$494$	−3.08480e95	−0.727646
$495$	−3.80848e94	−0.0836116
$496$	6.00747e95	1.22770
$497$	−1.36027e96	−2.58805
$498$	2.77117e95	0.490932
$499$	−8.40522e95	−1.38669	−0.693345	−	0.720606i	$-0.743864\pi$
$499$	−8.40522e95	−1.38669	−0.693345	+	0.720606i	$0.743864\pi$
$500$	1.24731e95	0.191663
$501$	6.83245e95	0.977996
$502$	−6.33775e95	−0.845187
$503$	−5.37816e95	−0.668298	−0.334149	−	0.942520i	$-0.608449\pi$
$503$	−5.37816e95	−0.668298	−0.334149	+	0.942520i	$0.608449\pi$
$504$	5.30752e95	0.614621
$505$	−2.20784e95	−0.238300
$506$	−5.98394e94	−0.0602065
$507$	−7.77939e95	−0.729731
$508$	−1.67917e95	−0.146870
$509$	1.52037e96	1.24014	0.620068	−	0.784548i	$-0.287105\pi$
$509$	1.52037e96	1.24014	0.620068	+	0.784548i	$0.287105\pi$
$510$	−2.22628e94	−0.0169371
$511$	−3.24305e96	−2.30150
$512$	−1.69359e96	−1.12131
$513$	−1.66426e95	−0.102815
$514$	1.82282e96	1.05088
$515$	7.31818e95	0.393774
$516$	3.30673e95	0.166086
$517$	8.67490e95	0.406771
$518$	2.83496e96	1.24120
$519$	2.13607e96	0.873323
$520$	2.98352e96	1.13923
$521$	−3.55898e96	−1.26936	−0.634682	−	0.772773i	$-0.718869\pi$
$521$	−3.55898e96	−1.26936	−0.634682	+	0.772773i	$0.718869\pi$
$522$	1.08409e96	0.361214
$523$	3.55764e96	1.10752	0.553760	−	0.832676i	$-0.313192\pi$
$523$	3.55764e96	1.10752	0.553760	+	0.832676i	$0.313192\pi$
$524$	9.16356e95	0.266565
$525$	−1.82494e96	−0.496127
$526$	−1.65207e96	−0.419792
$527$	−3.00483e95	−0.0713746
$528$	−7.24216e95	−0.160829
$529$	−4.64593e96	−0.964709
$530$	6.18222e96	1.20047
$531$	−1.69969e96	−0.308685
$532$	9.79855e95	0.166456
$533$	9.14267e96	1.45297
$534$	7.51642e94	0.0111763
$535$	2.31158e96	0.321624
$536$	6.76858e95	0.0881349
$537$	−5.84306e96	−0.712120
$538$	−2.86974e96	−0.327395
$539$	−6.55294e96	−0.699899
$540$	2.46212e95	0.0246224
$541$	−1.31600e97	−1.23241	−0.616203	−	0.787587i	$-0.711330\pi$
$541$	−1.31600e97	−1.23241	−0.616203	+	0.787587i	$0.711330\pi$
$542$	−8.47947e96	−0.743693
$543$	−1.25079e96	−0.102752
$544$	2.11878e95	0.0163052
$545$	5.64935e96	0.407307
$546$	−2.00836e97	−1.35676
$547$	1.62334e97	1.02768	0.513842	−	0.857885i	$-0.328222\pi$
$547$	1.62334e97	1.02768	0.513842	+	0.857885i	$0.328222\pi$
$548$	3.75207e96	0.222618
$549$	−1.50566e96	−0.0837353
$550$	3.06168e96	0.159619
$551$	1.30843e97	0.639544
$552$	2.52906e96	0.115910
$553$	−3.27620e96	−0.140808
$554$	−6.34888e95	−0.0255918
$555$	8.59764e96	0.325071
$556$	−3.08212e96	−0.109319
$557$	−3.48766e95	−0.0116058	−0.00580289	−	0.999983i	$-0.501847\pi$
$557$	−3.48766e95	−0.0116058	−0.00580289	+	0.999983i	$0.501847\pi$
$558$	−1.50789e97	−0.470822
$559$	−8.18018e97	−2.39687
$560$	3.49744e97	0.961780
$561$	3.62240e95	0.00935008
$562$	3.25987e97	0.789879
$563$	−1.05933e97	−0.240980	−0.120490	−	0.992715i	$-0.538447\pi$
$563$	−1.05933e97	−0.240980	−0.120490	+	0.992715i	$0.538447\pi$
$564$	−5.60818e96	−0.119788
$565$	5.23976e97	1.05097
$566$	2.74822e97	0.517687
$567$	−1.08352e97	−0.191707
$568$	−9.64512e97	−1.60303
$569$	8.98716e97	1.40326	0.701628	−	0.712543i	$-0.252457\pi$
$569$	8.98716e97	1.40326	0.701628	+	0.712543i	$0.252457\pi$
$570$	−1.34839e97	−0.197814
$571$	−7.97488e97	−1.09937	−0.549683	−	0.835373i	$-0.685252\pi$
$571$	−7.97488e97	−1.09937	−0.549683	+	0.835373i	$0.685252\pi$
$572$	−7.42559e96	−0.0961994
$573$	8.77949e97	1.06901
$574$	1.31774e98	1.50819
$575$	−8.69592e96	−0.0935637
$576$	3.65590e97	0.369825
$577$	1.38077e98	1.31335	0.656676	−	0.754173i	$-0.271962\pi$
$577$	1.38077e98	1.31335	0.656676	+	0.754173i	$0.271962\pi$
$578$	−1.00990e98	−0.903321
$579$	1.11532e98	0.938236
$580$	−1.93571e97	−0.153160
$581$	2.17752e98	1.62073
$582$	−2.88669e97	−0.202132
$583$	−1.00592e98	−0.662716
$584$	−2.29952e98	−1.42555
$585$	−6.09079e97	−0.355337
$586$	9.52996e97	0.523270
$587$	−1.63974e98	−0.847466	−0.423733	−	0.905787i	$-0.639281\pi$
$587$	−1.63974e98	−0.847466	−0.423733	+	0.905787i	$0.639281\pi$
$588$	4.23637e97	0.206110
$589$	−1.81993e98	−0.833609
$590$	−1.37710e98	−0.593907
$591$	−2.30710e98	−0.936939
$592$	1.63492e98	0.625281
$593$	−4.11092e98	−1.48080	−0.740402	−	0.672164i	$-0.765365\pi$
$593$	−4.11092e98	−1.48080	−0.740402	+	0.672164i	$0.765365\pi$
$594$	1.81780e97	0.0616777
$595$	−1.74936e97	−0.0559148
$596$	−3.13133e96	−0.00942946
$597$	2.05456e98	0.582949
$598$	−9.56993e97	−0.255869
$599$	2.49324e98	0.628219	0.314110	−	0.949387i	$-0.398294\pi$
$599$	2.49324e98	0.628219	0.314110	+	0.949387i	$0.398294\pi$
$600$	−1.29399e98	−0.307300
$601$	4.62414e98	1.03511	0.517556	−	0.855650i	$-0.326842\pi$
$601$	4.62414e98	1.03511	0.517556	+	0.855650i	$0.326842\pi$
$602$	−1.17901e99	−2.48796
$603$	−1.38179e97	−0.0274902
$604$	−1.52563e98	−0.286179
$605$	−3.50333e98	−0.619677
$606$	1.05381e98	0.175786
$607$	1.06500e99	1.67553	0.837763	−	0.546034i	$-0.183863\pi$
$607$	1.06500e99	1.67553	0.837763	+	0.546034i	$0.183863\pi$
$608$	1.28328e98	0.190434
$609$	8.51857e98	1.19248
$610$	−1.21989e98	−0.161106
$611$	1.38735e99	1.72872
$612$	−2.34182e96	−0.00275346
$613$	1.04947e99	1.16445	0.582227	−	0.813027i	$-0.302182\pi$
$613$	1.04947e99	1.16445	0.582227	+	0.813027i	$0.302182\pi$
$614$	−2.45252e98	−0.256824
$615$	3.99633e98	0.394998
$616$	−6.99685e98	−0.652810
$617$	−5.32463e98	−0.468993	−0.234496	−	0.972117i	$-0.575344\pi$
$617$	−5.32463e98	−0.468993	−0.234496	+	0.972117i	$0.575344\pi$
$618$	−3.49300e98	−0.290475
$619$	−8.75915e98	−0.687771	−0.343885	−	0.939012i	$-0.611743\pi$
$619$	−8.75915e98	−0.687771	−0.343885	+	0.939012i	$0.611743\pi$
$620$	2.69242e98	0.199636
$621$	−5.16302e97	−0.0361536
$622$	1.71829e99	1.13642
$623$	5.90623e97	0.0368965
$624$	−1.15822e99	−0.683498
$625$	−4.55401e98	−0.253894
$626$	1.72558e99	0.908962
$627$	2.19398e98	0.109203
$628$	−3.22280e98	−0.151588
$629$	−8.17758e97	−0.0363519
$630$	−8.77869e98	−0.368842
$631$	−4.59111e99	−1.82337	−0.911687	−	0.410885i	$-0.865220\pi$
$631$	−4.59111e99	−1.82337	−0.911687	+	0.410885i	$0.865220\pi$
$632$	−2.32302e98	−0.0872163
$633$	1.70578e99	0.605467
$634$	3.43787e99	1.15377
$635$	1.81572e99	0.576210
$636$	6.50308e98	0.195160
$637$	−1.04799e100	−2.97446
$638$	−1.42915e99	−0.383657
$639$	1.96903e99	0.500001
$640$	1.91072e99	0.458995
$641$	6.96176e98	0.158219	0.0791096	−	0.996866i	$-0.474792\pi$
$641$	6.96176e98	0.158219	0.0791096	+	0.996866i	$0.474792\pi$
$642$	−1.10333e99	−0.237252
$643$	−1.02997e99	−0.209573	−0.104786	−	0.994495i	$-0.533416\pi$
$643$	−1.02997e99	−0.209573	−0.104786	+	0.994495i	$0.533416\pi$
$644$	3.03979e98	0.0585323
$645$	−3.57562e99	−0.651600
$646$	1.28251e98	0.0221211
$647$	3.61045e99	0.589467	0.294734	−	0.955579i	$-0.404769\pi$
$647$	3.61045e99	0.589467	0.294734	+	0.955579i	$0.404769\pi$
$648$	−7.68280e98	−0.118743
$649$	2.24069e99	0.327865
$650$	4.89645e99	0.678355
$651$	−1.18487e100	−1.55434
$652$	1.47524e98	0.0183263
$653$	2.97885e99	0.350454	0.175227	−	0.984528i	$-0.443934\pi$
$653$	2.97885e99	0.350454	0.175227	+	0.984528i	$0.443934\pi$
$654$	−2.69646e99	−0.300458
$655$	−9.90871e99	−1.04581
$656$	7.59938e99	0.759787
$657$	4.69442e99	0.444642
$658$	1.99960e100	1.79442
$659$	2.98836e99	0.254097	0.127049	−	0.991896i	$-0.459450\pi$
$659$	2.98836e99	0.254097	0.127049	+	0.991896i	$0.459450\pi$
$660$	−3.24578e98	−0.0261523
$661$	−6.06399e99	−0.463027	−0.231514	−	0.972832i	$-0.574368\pi$
$661$	−6.06399e99	−0.463027	−0.231514	+	0.972832i	$0.574368\pi$
$662$	−7.66477e99	−0.554677
$663$	5.79321e98	0.0397364
$664$	1.54399e100	1.00387
$665$	−1.05953e100	−0.653050
$666$	−4.10369e99	−0.239795
$667$	4.05914e99	0.224888
$668$	5.82297e99	0.305900
$669$	−1.06052e99	−0.0528312
$670$	−1.11953e99	−0.0528908
$671$	1.98490e99	0.0889381
$672$	8.35479e99	0.355080
$673$	1.07220e100	0.432257	0.216129	−	0.976365i	$-0.430657\pi$
$673$	1.07220e100	0.432257	0.216129	+	0.976365i	$0.430657\pi$
$674$	2.25740e100	0.863339
$675$	2.64165e99	0.0958499
$676$	−6.63000e99	−0.228247
$677$	2.72768e100	0.891036	0.445518	−	0.895273i	$-0.353020\pi$
$677$	2.72768e100	0.891036	0.445518	+	0.895273i	$0.353020\pi$
$678$	−2.50096e100	−0.775269
$679$	−2.26829e100	−0.667302
$680$	−1.24040e99	−0.0346335
$681$	2.18906e100	0.580143
$682$	1.98784e100	0.500076
$683$	1.87111e100	0.446853	0.223426	−	0.974721i	$-0.428276\pi$
$683$	1.87111e100	0.446853	0.223426	+	0.974721i	$0.428276\pi$
$684$	−1.41837e99	−0.0321587
$685$	−4.05717e100	−0.873390
$686$	−7.46401e100	−1.52569
$687$	2.85248e100	0.553679
$688$	−6.79936e100	−1.25337
$689$	−1.60873e101	−2.81644
$690$	−4.18309e99	−0.0695592
$691$	3.20344e100	0.505994	0.252997	−	0.967467i	$-0.418584\pi$
$691$	3.20344e100	0.505994	0.252997	+	0.967467i	$0.418584\pi$
$692$	1.82047e100	0.273161
$693$	1.42839e100	0.203618
$694$	−4.48592e99	−0.0607562
$695$	3.33274e100	0.428885
$696$	6.04018e100	0.738622
$697$	−3.80108e99	−0.0441716
$698$	−5.23134e100	−0.577758
$699$	−7.15888e99	−0.0751459
$700$	−1.55531e100	−0.155180
$701$	−7.24062e100	−0.686730	−0.343365	−	0.939202i	$-0.611567\pi$
$701$	−7.24062e100	−0.686730	−0.343365	+	0.939202i	$0.611567\pi$
$702$	2.90716e100	0.262121
$703$	−4.95290e100	−0.424567
$704$	−4.81953e100	−0.392803
$705$	6.06422e100	0.469961
$706$	1.78044e101	1.31208
$707$	8.28062e100	0.580328
$708$	−1.44857e100	−0.0965514
$709$	3.06069e101	1.94034	0.970169	−	0.242430i	$-0.0779444\pi$
$709$	3.06069e101	1.94034	0.970169	+	0.242430i	$0.0779444\pi$
$710$	1.59531e101	0.961998
$711$	4.74240e99	0.0272036
$712$	4.18788e99	0.0228536
$713$	−5.64596e100	−0.293129
$714$	8.34978e99	0.0412466
$715$	8.02942e100	0.377415
$716$	−4.97976e100	−0.222739
$717$	8.39096e100	0.357175
$718$	−2.18104e99	−0.00883579
$719$	3.61868e101	1.39532	0.697660	−	0.716429i	$-0.254224\pi$
$719$	3.61868e101	1.39532	0.697660	+	0.716429i	$0.254224\pi$
$720$	−5.06266e100	−0.185813
$721$	−2.74472e101	−0.958951
$722$	−1.94481e101	−0.646855
$723$	−2.45262e101	−0.776641
$724$	−1.06599e100	−0.0321391
$725$	−2.07686e101	−0.596221
$726$	1.67216e101	0.457116
$727$	−1.47122e101	−0.383007	−0.191504	−	0.981492i	$-0.561336\pi$
$727$	−1.47122e101	−0.383007	−0.191504	+	0.981492i	$0.561336\pi$
$728$	−1.11899e102	−2.77434
$729$	1.56842e100	0.0370370
$730$	3.80343e101	0.855488
$731$	3.40092e100	0.0728668
$732$	−1.28320e100	−0.0261910
$733$	8.02367e101	1.56021	0.780103	−	0.625651i	$-0.215167\pi$
$733$	8.02367e101	1.56021	0.780103	+	0.625651i	$0.215167\pi$
$734$	5.87153e101	1.08778
$735$	−4.58086e101	−0.808624
$736$	3.98110e100	0.0669639
$737$	1.82160e100	0.0291982
$738$	−1.90747e101	−0.291377
$739$	−2.26756e101	−0.330127	−0.165064	−	0.986283i	$-0.552783\pi$
$739$	−2.26756e101	−0.330127	−0.165064	+	0.986283i	$0.552783\pi$
$740$	7.32736e100	0.101677
$741$	3.50876e101	0.464096
$742$	−2.31867e102	−2.92349
$743$	1.17329e102	1.41027	0.705136	−	0.709073i	$-0.250886\pi$
$743$	1.17329e102	1.41027	0.705136	+	0.709073i	$0.250886\pi$
$744$	−8.40144e101	−0.962752
$745$	3.38596e100	0.0369942
$746$	8.77363e101	0.914010
$747$	−3.15203e101	−0.313118
$748$	3.08720e99	0.00292454
$749$	−8.66968e101	−0.783247
$750$	6.43758e101	0.554687
$751$	−2.77147e101	−0.227767	−0.113884	−	0.993494i	$-0.536329\pi$
$751$	−2.77147e101	−0.227767	−0.113884	+	0.993494i	$0.536329\pi$
$752$	1.15317e102	0.903979
$753$	7.20879e101	0.539064
$754$	−2.28560e102	−1.63049
$755$	1.64969e102	1.12275
$756$	−9.23430e100	−0.0599626
$757$	1.92905e102	1.19520	0.597600	−	0.801795i	$-0.296121\pi$
$757$	1.92905e102	1.19520	0.597600	+	0.801795i	$0.296121\pi$
$758$	1.21610e102	0.718971
$759$	6.80635e100	0.0384000
$760$	−7.51274e101	−0.404497
$761$	−2.32233e102	−1.19335	−0.596676	−	0.802482i	$-0.703512\pi$
$761$	−2.32233e102	−1.19335	−0.596676	+	0.802482i	$0.703512\pi$
$762$	−8.66650e101	−0.425052
$763$	−2.11882e102	−0.991910
$764$	7.48234e101	0.334367
$765$	2.53225e100	0.0108025
$766$	2.60912e102	1.06261
$767$	3.58347e102	1.39338
$768$	8.13365e101	0.301969
$769$	1.01090e102	0.358365	0.179182	−	0.983816i	$-0.442655\pi$
$769$	1.01090e102	0.358365	0.179182	+	0.983816i	$0.442655\pi$
$770$	1.15728e102	0.391759
$771$	−2.07334e102	−0.670255
$772$	9.50537e101	0.293464
$773$	6.70202e101	0.197621	0.0988107	−	0.995106i	$-0.468496\pi$
$773$	6.70202e101	0.197621	0.0988107	+	0.995106i	$0.468496\pi$
$774$	1.70666e102	0.480665
$775$	2.88875e102	0.777140
$776$	−1.60836e102	−0.413325
$777$	−3.22459e102	−0.791641
$778$	5.94727e101	0.139490
$779$	−2.30219e102	−0.515896
$780$	−5.19089e101	−0.111143
$781$	−2.59575e102	−0.531069
$782$	3.97871e100	0.00777863
$783$	−1.23309e102	−0.230384
$784$	−8.71091e102	−1.55541
$785$	3.48487e102	0.594721
$786$	4.72947e102	0.771458
$787$	6.00076e102	0.935628	0.467814	−	0.883827i	$-0.345042\pi$
$787$	6.00076e102	0.935628	0.467814	+	0.883827i	$0.345042\pi$
$788$	−1.96623e102	−0.293059
$789$	1.87912e102	0.267745
$790$	3.84230e101	0.0523396
$791$	−1.96520e103	−2.55942
$792$	1.01281e102	0.126121
$793$	3.17439e102	0.377974
$794$	−5.51381e102	−0.627804
$795$	−7.03189e102	−0.765665
$796$	1.75100e102	0.182336
$797$	−1.51412e103	−1.50796	−0.753981	−	0.656896i	$-0.771869\pi$
$797$	−1.51412e103	−1.50796	−0.753981	+	0.656896i	$0.771869\pi$
$798$	5.05720e102	0.481734
$799$	−5.76794e101	−0.0525545
$800$	−2.03693e102	−0.177534
$801$	−8.54945e100	−0.00712827
$802$	1.67854e103	1.33888
$803$	−6.18860e102	−0.472270
$804$	−1.17763e101	−0.00859845
$805$	−3.28698e102	−0.229638
$806$	3.17909e103	2.12525
$807$	3.26415e102	0.208814
$808$	5.87146e102	0.359454
$809$	4.10348e101	0.0240425	0.0120213	−	0.999928i	$-0.496173\pi$
$809$	4.10348e101	0.0240425	0.0120213	+	0.999928i	$0.496173\pi$
$810$	1.27074e102	0.0712589
$811$	−2.03960e103	−1.09473	−0.547363	−	0.836895i	$-0.684368\pi$
$811$	−2.03960e103	−1.09473	−0.547363	+	0.836895i	$0.684368\pi$
$812$	7.25997e102	0.372989
$813$	9.64486e102	0.474331
$814$	5.40985e102	0.254694
$815$	−1.59520e102	−0.0718987
$816$	4.81531e101	0.0207789
$817$	2.05983e103	0.851038
$818$	−1.55009e103	−0.613217
$819$	2.28438e103	0.865346
$820$	3.40588e102	0.123549
$821$	2.21933e103	0.770973	0.385487	−	0.922713i	$-0.374034\pi$
$821$	2.21933e103	0.770973	0.385487	+	0.922713i	$0.374034\pi$
$822$	1.93651e103	0.644273
$823$	1.30911e103	0.417140	0.208570	−	0.978007i	$-0.433119\pi$
$823$	1.30911e103	0.417140	0.208570	+	0.978007i	$0.433119\pi$
$824$	−1.94618e103	−0.593972
$825$	−3.48246e102	−0.101806
$826$	5.16488e103	1.44633
$827$	−2.26423e103	−0.607400	−0.303700	−	0.952768i	$-0.598222\pi$
$827$	−2.26423e103	−0.607400	−0.303700	+	0.952768i	$0.598222\pi$
$828$	−4.40019e101	−0.0113082
$829$	−3.73362e103	−0.919273	−0.459636	−	0.888107i	$-0.652020\pi$
$829$	−3.73362e103	−0.919273	−0.459636	+	0.888107i	$0.652020\pi$
$830$	−2.55378e103	−0.602437
$831$	7.22145e101	0.0163225
$832$	−7.70774e103	−1.66936
$833$	4.35705e102	0.0904263
$834$	−1.59073e103	−0.316375
$835$	−6.29647e103	−1.20013
$836$	1.86982e102	0.0341568
$837$	1.71513e103	0.300292
$838$	−8.14932e103	−1.36760
$839$	−1.94596e102	−0.0313029	−0.0156515	−	0.999878i	$-0.504982\pi$
$839$	−1.94596e102	−0.0313029	−0.0156515	+	0.999878i	$0.504982\pi$
$840$	−4.89117e103	−0.754220
$841$	2.92965e103	0.433069
$842$	1.05146e104	1.49010
$843$	−3.70789e103	−0.503788
$844$	1.45375e103	0.189380
$845$	7.16913e103	0.895474
$846$	−2.89448e103	−0.346675
$847$	1.31394e104	1.50909
$848$	−1.33718e104	−1.47277
$849$	−3.12592e103	−0.330183
$850$	−2.03571e102	−0.0206226
$851$	−1.53653e103	−0.149294
$852$	1.67811e103	0.156392
$853$	1.21456e103	0.108574	0.0542872	−	0.998525i	$-0.482711\pi$
$853$	1.21456e103	0.108574	0.0542872	+	0.998525i	$0.482711\pi$
$854$	4.57526e103	0.392339
$855$	1.53371e103	0.126167
$856$	−6.14734e103	−0.485141
$857$	5.81350e103	0.440168	0.220084	−	0.975481i	$-0.429367\pi$
$857$	5.81350e103	0.440168	0.220084	+	0.975481i	$0.429367\pi$
$858$	−3.83248e103	−0.278408
$859$	1.35273e104	0.942871	0.471436	−	0.881901i	$-0.343736\pi$
$859$	1.35273e104	0.942871	0.471436	+	0.881901i	$0.343736\pi$
$860$	−3.04733e103	−0.203809
$861$	−1.49884e104	−0.961932
$862$	1.36026e104	0.837750
$863$	2.53534e104	1.49849	0.749245	−	0.662293i	$-0.230417\pi$
$863$	2.53534e104	1.49849	0.749245	+	0.662293i	$0.230417\pi$
$864$	−1.20938e103	−0.0686002
$865$	−1.96851e104	−1.07168
$866$	−5.29664e103	−0.276768
$867$	1.14870e104	0.576142
$868$	−1.00981e104	−0.486170
$869$	−6.25185e102	−0.0288939
$870$	−9.99052e103	−0.443256
$871$	2.91323e103	0.124088
$872$	−1.50237e104	−0.614387
$873$	3.28343e103	0.128920
$874$	2.40978e103	0.0908494
$875$	5.05850e104	1.83120
$876$	4.00083e103	0.139077
$877$	−2.22829e104	−0.743853	−0.371926	−	0.928262i	$-0.621303\pi$
$877$	−2.22829e104	−0.743853	−0.371926	+	0.928262i	$0.621303\pi$
$878$	2.71107e104	0.869131
$879$	−1.08397e104	−0.333744
$880$	6.67405e103	0.197358
$881$	2.18580e104	0.620820	0.310410	−	0.950603i	$-0.399534\pi$
$881$	2.18580e104	0.620820	0.310410	+	0.950603i	$0.399534\pi$
$882$	2.18647e104	0.596496
$883$	−1.05298e104	−0.275939	−0.137970	−	0.990436i	$-0.544058\pi$
$883$	−1.05298e104	−0.275939	−0.137970	+	0.990436i	$0.544058\pi$
$884$	4.93727e102	0.0124289
$885$	1.56636e104	0.378796
$886$	3.21555e104	0.747064
$887$	−2.93393e104	−0.654878	−0.327439	−	0.944872i	$-0.606186\pi$
$887$	−2.93393e104	−0.654878	−0.327439	+	0.944872i	$0.606186\pi$
$888$	−2.28643e104	−0.490340
$889$	−6.80994e104	−1.40324
$890$	−6.92679e102	−0.0137147
$891$	−2.06764e103	−0.0393383
$892$	−9.03828e102	−0.0165247
$893$	−3.49346e104	−0.613803
$894$	−1.61613e103	−0.0272895
$895$	5.38470e104	0.873864
$896$	−7.16626e104	−1.11778
$897$	1.08852e104	0.163194
$898$	1.60704e104	0.231588
$899$	−1.34843e105	−1.86792
$900$	2.25135e103	0.0299802
$901$	6.68832e103	0.0856224
$902$	2.51459e104	0.309482
$903$	1.34105e105	1.58683
$904$	−1.39345e105	−1.58530
$905$	1.15267e104	0.126090
$906$	−7.87403e104	−0.828221
$907$	−1.88000e105	−1.90151	−0.950754	−	0.309945i	$-0.899689\pi$
$907$	−1.88000e105	−1.90151	−0.950754	+	0.309945i	$0.899689\pi$
$908$	1.86563e104	0.181459
$909$	−1.19864e104	−0.112117
$910$	1.85081e105	1.66492
$911$	−7.93633e104	−0.686622	−0.343311	−	0.939222i	$-0.611548\pi$
$911$	−7.93633e104	−0.686622	−0.343311	+	0.939222i	$0.611548\pi$
$912$	2.91648e104	0.242685
$913$	4.15528e104	0.332574
$914$	−5.88231e104	−0.452854
$915$	1.38755e104	0.102754
$916$	2.43103e104	0.173181
$917$	3.71631e105	2.54683
$918$	−1.20866e103	−0.00796870
$919$	2.77242e105	1.75856	0.879282	−	0.476302i	$-0.158023\pi$
$919$	2.77242e105	1.75856	0.879282	+	0.476302i	$0.158023\pi$
$920$	−2.33067e104	−0.142237
$921$	2.78959e104	0.163803
$922$	2.33642e105	1.32009
$923$	−4.15130e105	−2.25696
$924$	1.21735e104	0.0636883
$925$	7.86166e104	0.395806
$926$	−2.19706e105	−1.06452
$927$	3.97307e104	0.185266
$928$	9.50811e104	0.426718
$929$	2.18445e104	0.0943594	0.0471797	−	0.998886i	$-0.484977\pi$
$929$	2.18445e104	0.0943594	0.0471797	+	0.998886i	$0.484977\pi$
$930$	1.38961e105	0.577759
$931$	2.63893e105	1.05612
$932$	−6.10117e103	−0.0235043
$933$	−1.95445e105	−0.724812
$934$	4.86176e104	0.173572
$935$	−3.33824e103	−0.0114738
$936$	1.61977e105	0.535994
$937$	−4.05744e105	−1.29270	−0.646348	−	0.763043i	$-0.723704\pi$
$937$	−4.05744e105	−1.29270	−0.646348	+	0.763043i	$0.723704\pi$
$938$	4.19885e104	0.128804
$939$	−1.96273e105	−0.579740
$940$	5.16825e104	0.146996
$941$	2.38583e105	0.653444	0.326722	−	0.945120i	$-0.394056\pi$
$941$	2.38583e105	0.653444	0.326722	+	0.945120i	$0.394056\pi$
$942$	−1.66334e105	−0.438707
$943$	−7.14207e104	−0.181409
$944$	2.97858e105	0.728623
$945$	9.98520e104	0.235249
$946$	−2.24987e105	−0.510531
$947$	−1.47147e105	−0.321609	−0.160804	−	0.986986i	$-0.551409\pi$
$947$	−1.47147e105	−0.321609	−0.160804	+	0.986986i	$0.551409\pi$
$948$	4.04172e103	0.00850883
$949$	−9.89724e105	−2.00708
$950$	−1.23296e105	−0.240859
$951$	−3.91036e105	−0.735882
$952$	4.65220e104	0.0843425
$953$	−7.15366e105	−1.24948	−0.624741	−	0.780832i	$-0.714796\pi$
$953$	−7.15366e105	−1.24948	−0.624741	+	0.780832i	$0.714796\pi$
$954$	3.35635e105	0.564807
$955$	−8.09078e105	−1.31181
$956$	7.15121e104	0.111718
$957$	1.62557e105	0.244698
$958$	−5.27932e105	−0.765777
$959$	1.52166e106	2.12695
$960$	−3.36911e105	−0.453823
$961$	1.10523e106	1.43473
$962$	8.65182e105	1.08241
$963$	1.25496e105	0.151321
$964$	−2.09025e105	−0.242920
$965$	−1.02783e106	−1.15134
$966$	1.56889e105	0.169396
$967$	5.15730e105	0.536763	0.268382	−	0.963313i	$-0.413511\pi$
$967$	5.15730e105	0.536763	0.268382	+	0.963313i	$0.413511\pi$
$968$	9.31665e105	0.934727
$969$	−1.45877e104	−0.0141089
$970$	2.66024e105	0.248042
$971$	−1.27513e106	−1.14623	−0.573114	−	0.819476i	$-0.694265\pi$
$971$	−1.27513e106	−1.14623	−0.573114	+	0.819476i	$0.694265\pi$
$972$	1.33669e104	0.0115846
$973$	−1.24996e106	−1.04446
$974$	1.65705e106	1.33504
$975$	−5.56940e105	−0.432658
$976$	2.63855e105	0.197650
$977$	1.72982e106	1.24952	0.624762	−	0.780815i	$-0.285196\pi$
$977$	1.72982e106	1.24952	0.624762	+	0.780815i	$0.285196\pi$
$978$	7.61398e104	0.0530375
$979$	1.12707e104	0.00757118
$980$	−3.90405e105	−0.252924
$981$	3.06705e105	0.191633
$982$	−1.90979e106	−1.15087
$983$	2.51479e106	1.46168	0.730839	−	0.682550i	$-0.239129\pi$
$983$	2.51479e106	1.46168	0.730839	+	0.682550i	$0.239129\pi$
$984$	−1.06277e106	−0.595819
$985$	2.12612e106	1.14975
$986$	9.50241e104	0.0495682
$987$	−2.27442e106	−1.14449
$988$	2.99035e105	0.145161
$989$	6.39019e105	0.299258
$990$	−1.67521e105	−0.0756865
$991$	4.22320e106	1.84089	0.920444	−	0.390874i	$-0.127827\pi$
$991$	4.22320e106	1.84089	0.920444	+	0.390874i	$0.127827\pi$
$992$	−1.32251e106	−0.556203
$993$	8.71819e105	0.353776
$994$	−5.98330e106	−2.34274
$995$	−1.89339e106	−0.715354
$996$	−2.68632e105	−0.0979381
$997$	3.24866e106	1.14295	0.571473	−	0.820621i	$-0.306372\pi$
$997$	3.24866e106	1.14295	0.571473	+	0.820621i	$0.306372\pi$
$998$	−3.69714e106	−1.25525
$999$	4.66769e105	0.152942

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.72.a.b.1.5	✓	6
3.2	odd	2		9.72.a.c.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.72.a.b.1.5	✓	6	1.1	even	1	trivial
9.72.a.c.1.2		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)

\(f(q)\)	\(=\)	\(q+4.39862e10 q^{2} -5.00315e16 q^{3} -4.26395e20 q^{4} +4.61068e24 q^{5} -2.20070e27 q^{6} -1.72926e30 q^{7} -1.22615e32 q^{8} +2.50316e33 q^{9} +O(q^{10})\)	\(q+4.39862e10 q^{2} -5.00315e16 q^{3} -4.26395e20 q^{4} +4.61068e24 q^{5} -2.20070e27 q^{6} -1.72926e30 q^{7} -1.22615e32 q^{8} +2.50316e33 q^{9} +2.02806e35 q^{10} -3.29988e36 q^{11} +2.13332e37 q^{12} -5.27741e39 q^{13} -7.60636e40 q^{14} -2.30679e41 q^{15} -4.38658e42 q^{16} +2.19409e42 q^{17} +1.10104e44 q^{18} +1.32889e45 q^{19} -1.96597e45 q^{20} +8.65175e46 q^{21} -1.45149e47 q^{22} +4.12260e47 q^{23} +6.13462e48 q^{24} -2.10933e49 q^{25} -2.32133e50 q^{26} -1.25237e50 q^{27} +7.37347e50 q^{28} +9.84606e51 q^{29} -1.01467e52 q^{30} -1.36951e53 q^{31} +9.65676e52 q^{32} +1.65098e53 q^{33} +9.65097e52 q^{34} -7.97306e54 q^{35} -1.06733e54 q^{36} -3.72709e55 q^{37} +5.84529e55 q^{38} +2.64037e56 q^{39} -5.65339e56 q^{40} -1.73242e57 q^{41} +3.80558e57 q^{42} +1.55004e58 q^{43} +1.40705e57 q^{44} +1.15412e58 q^{45} +1.81338e58 q^{46} -2.62885e59 q^{47} +2.19467e59 q^{48} +1.98581e60 q^{49} -9.27814e59 q^{50} -1.09774e59 q^{51} +2.25026e60 q^{52} +3.04834e61 q^{53} -5.50869e60 q^{54} -1.52147e61 q^{55} +2.12033e62 q^{56} -6.64865e61 q^{57} +4.33091e62 q^{58} -6.79021e62 q^{59} +9.83606e61 q^{60} -6.01505e62 q^{61} -6.02397e63 q^{62} -4.32860e63 q^{63} +1.46052e64 q^{64} -2.43324e64 q^{65} +7.26205e63 q^{66} -5.52019e63 q^{67} -9.35549e62 q^{68} -2.06260e64 q^{69} -3.50705e65 q^{70} +7.86618e65 q^{71} -3.06925e65 q^{72} +1.87540e66 q^{73} -1.63941e66 q^{74} +1.05533e66 q^{75} -5.66633e65 q^{76} +5.70635e66 q^{77} +1.16140e67 q^{78} +1.89457e66 q^{79} -2.02251e67 q^{80} +6.26579e66 q^{81} -7.62025e67 q^{82} -1.25922e68 q^{83} -3.68906e67 q^{84} +1.01162e67 q^{85} +6.81803e68 q^{86} -4.92614e68 q^{87} +4.04615e68 q^{88} -3.41547e67 q^{89} +5.07656e68 q^{90} +9.12600e69 q^{91} -1.75786e68 q^{92} +6.85188e69 q^{93} -1.15633e70 q^{94} +6.12709e69 q^{95} -4.83143e69 q^{96} +1.31172e70 q^{97} +8.73484e70 q^{98} -8.26012e69 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 72903656826 q^{2} - 30\!\cdots\!42 q^{3}+ \cdots + 15\!\cdots\!94 q^{9}+O(q^{10}) \) 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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