LMFDB - Embedded newform 3.72.a.b.1.4

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			1.4
Root			$3.35353e9$ 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)

$f(q)$	$=$	$q+7.97054e9 q^{2} -5.00315e16 q^{3} -2.29765e21 q^{4} -4.57364e24 q^{5} -3.98779e26 q^{6} +9.29524e29 q^{7} -3.71335e31 q^{8} +2.50316e33 q^{9} +O(q^{10})$	\(q+7.97054e9 q^{2} -5.00315e16 q^{3} -2.29765e21 q^{4} -4.57364e24 q^{5} -3.98779e26 q^{6} +9.29524e29 q^{7} -3.71335e31 q^{8} +2.50316e33 q^{9} -3.64544e34 q^{10} -1.92623e36 q^{11} +1.14955e38 q^{12} -4.14371e38 q^{13} +7.40881e39 q^{14} +2.28826e41 q^{15} +5.12921e42 q^{16} -3.53245e43 q^{17} +1.99515e43 q^{18} -4.04277e45 q^{19} +1.05087e46 q^{20} -4.65055e46 q^{21} -1.53531e46 q^{22} -3.13511e48 q^{23} +1.85784e48 q^{24} -2.14334e49 q^{25} -3.30276e48 q^{26} -1.25237e50 q^{27} -2.13572e51 q^{28} -6.13666e51 q^{29} +1.82387e51 q^{30} +1.45158e52 q^{31} +1.28561e53 q^{32} +9.63722e52 q^{33} -2.81555e53 q^{34} -4.25131e54 q^{35} -5.75138e54 q^{36} -6.20710e55 q^{37} -3.22231e55 q^{38} +2.07316e55 q^{39} +1.69835e56 q^{40} +2.78018e57 q^{41} -3.70674e56 q^{42} -1.70252e57 q^{43} +4.42581e57 q^{44} -1.14485e58 q^{45} -2.49885e58 q^{46} +1.72342e59 q^{47} -2.56622e59 q^{48} -1.40510e59 q^{49} -1.70836e59 q^{50} +1.76734e60 q^{51} +9.52081e59 q^{52} +1.89331e60 q^{53} -9.98205e59 q^{54} +8.80989e60 q^{55} -3.45165e61 q^{56} +2.02266e62 q^{57} -4.89125e61 q^{58} +3.04131e62 q^{59} -5.25764e62 q^{60} -1.73950e63 q^{61} +1.15699e62 q^{62} +2.32674e63 q^{63} -1.10863e64 q^{64} +1.89519e63 q^{65} +7.68139e62 q^{66} +1.89865e64 q^{67} +8.11634e64 q^{68} +1.56854e65 q^{69} -3.38853e64 q^{70} -9.78234e65 q^{71} -9.29508e64 q^{72} +2.89986e65 q^{73} -4.94740e65 q^{74} +1.07235e66 q^{75} +9.28889e66 q^{76} -1.79048e66 q^{77} +1.65242e65 q^{78} -1.48560e66 q^{79} -2.34592e67 q^{80} +6.26579e66 q^{81} +2.21595e67 q^{82} -1.28470e68 q^{83} +1.06854e68 q^{84} +1.61562e68 q^{85} -1.35700e67 q^{86} +3.07027e68 q^{87} +7.15276e67 q^{88} +4.41961e68 q^{89} -9.12511e67 q^{90} -3.85168e68 q^{91} +7.20339e69 q^{92} -7.26250e68 q^{93} +1.37366e69 q^{94} +1.84902e70 q^{95} -6.43213e69 q^{96} +2.25437e70 q^{97} -1.11994e69 q^{98} -4.82165e69 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	7.97054e9	0.164030	0.0820150	−	0.996631i	$-0.473864\pi$
$2$	7.97054e9	0.164030	0.0820150	+	0.996631i	$0.473864\pi$
$3$	−5.00315e16	−0.577350
$3$	−5.00315e16	−0.577350
$4$	−2.29765e21	−0.973094
$5$	−4.57364e24	−0.702793	−0.351396	−	0.936227i	$-0.614293\pi$
$5$	−4.57364e24	−0.702793	−0.351396	+	0.936227i	$0.614293\pi$
$6$	−3.98779e26	−0.0947027
$7$	9.29524e29	0.927428	0.463714	−	0.885985i	$-0.346516\pi$
$7$	9.29524e29	0.927428	0.463714	+	0.885985i	$0.346516\pi$
$8$	−3.71335e31	−0.323647
$9$	2.50316e33	0.333333
$10$	−3.64544e34	−0.115279
$11$	−1.92623e36	−0.206665	−0.103333	−	0.994647i	$-0.532951\pi$
$11$	−1.92623e36	−0.206665	−0.103333	+	0.994647i	$0.532951\pi$
$12$	1.14955e38	0.561816
$13$	−4.14371e38	−0.118141	−0.0590705	−	0.998254i	$-0.518814\pi$
$13$	−4.14371e38	−0.118141	−0.0590705	+	0.998254i	$0.518814\pi$
$14$	7.40881e39	0.152126
$15$	2.28826e41	0.405758
$16$	5.12921e42	0.920006
$17$	−3.53245e43	−0.736443	−0.368222	−	0.929738i	$-0.620033\pi$
$17$	−3.53245e43	−0.736443	−0.368222	+	0.929738i	$0.620033\pi$
$18$	1.99515e43	0.0546766
$19$	−4.04277e45	−1.62527	−0.812636	−	0.582771i	$-0.801968\pi$
$19$	−4.04277e45	−1.62527	−0.812636	+	0.582771i	$0.801968\pi$
$20$	1.05087e46	0.683883
$21$	−4.65055e46	−0.535451
$22$	−1.53531e46	−0.0338993
$23$	−3.13511e48	−1.42861	−0.714306	−	0.699834i	$-0.753258\pi$
$23$	−3.13511e48	−1.42861	−0.714306	+	0.699834i	$0.753258\pi$
$24$	1.85784e48	0.186857
$25$	−2.14334e49	−0.506082
$26$	−3.30276e48	−0.0193786
$27$	−1.25237e50	−0.192450
$28$	−2.13572e51	−0.902475
$29$	−6.13666e51	−0.746111	−0.373055	−	0.927809i	$-0.621690\pi$
$29$	−6.13666e51	−0.746111	−0.373055	+	0.927809i	$0.621690\pi$
$30$	1.82387e51	0.0665564
$31$	1.45158e52	0.165387	0.0826937	−	0.996575i	$-0.473648\pi$
$31$	1.45158e52	0.165387	0.0826937	+	0.996575i	$0.473648\pi$
$32$	1.28561e53	0.474555
$33$	9.63722e52	0.119318
$34$	−2.81555e53	−0.120799
$35$	−4.25131e54	−0.651790
$36$	−5.75138e54	−0.324365
$37$	−6.20710e55	−1.32351	−0.661755	−	0.749720i	$-0.730188\pi$
$37$	−6.20710e55	−1.32351	−0.661755	+	0.749720i	$0.730188\pi$
$38$	−3.22231e55	−0.266593
$39$	2.07316e55	0.0682087
$40$	1.69835e56	0.227456
$41$	2.78018e57	1.54969	0.774846	−	0.632150i	$-0.217827\pi$
$41$	2.78018e57	1.54969	0.774846	+	0.632150i	$0.217827\pi$
$42$	−3.70674e56	−0.0878300
$43$	−1.70252e57	−0.174970	−0.0874848	−	0.996166i	$-0.527883\pi$
$43$	−1.70252e57	−0.174970	−0.0874848	+	0.996166i	$0.527883\pi$
$44$	4.42581e57	0.201105
$45$	−1.14485e58	−0.234264
$46$	−2.49885e58	−0.234335
$47$	1.72342e59	0.753213	0.376606	−	0.926373i	$-0.377091\pi$
$47$	1.72342e59	0.753213	0.376606	+	0.926373i	$0.377091\pi$
$48$	−2.56622e59	−0.531166
$49$	−1.40510e59	−0.139877
$50$	−1.70836e59	−0.0830127
$51$	1.76734e60	0.425186
$52$	9.52081e59	0.114962
$53$	1.89331e60	0.116260	0.0581299	−	0.998309i	$-0.481486\pi$
$53$	1.89331e60	0.116260	0.0581299	+	0.998309i	$0.481486\pi$
$54$	−9.98205e59	−0.0315676
$55$	8.80989e60	0.145243
$56$	−3.45165e61	−0.300159
$57$	2.02266e62	0.938352
$58$	−4.89125e61	−0.122384
$59$	3.04131e62	0.414777	0.207389	−	0.978259i	$-0.433504\pi$
$59$	3.04131e62	0.414777	0.207389	+	0.978259i	$0.433504\pi$
$60$	−5.25764e62	−0.394840
$61$	−1.73950e63	−0.726466	−0.363233	−	0.931698i	$-0.618327\pi$
$61$	−1.73950e63	−0.726466	−0.363233	+	0.931698i	$0.618327\pi$
$62$	1.15699e62	0.0271285
$63$	2.32674e63	0.309143
$64$	−1.10863e64	−0.842165
$65$	1.89519e63	0.0830286
$66$	7.68139e62	0.0195718
$67$	1.89865e64	0.283654	0.141827	−	0.989891i	$-0.454702\pi$
$67$	1.89865e64	0.283654	0.141827	+	0.989891i	$0.454702\pi$
$68$	8.11634e64	0.716629
$69$	1.56854e65	0.824810
$70$	−3.38853e64	−0.106913
$71$	−9.78234e65	−1.86540	−0.932699	−	0.360657i	$-0.882553\pi$
$71$	−9.78234e65	−1.86540	−0.932699	+	0.360657i	$0.882553\pi$
$72$	−9.29508e64	−0.107882
$73$	2.89986e65	0.206260	0.103130	−	0.994668i	$-0.467114\pi$
$73$	2.89986e65	0.206260	0.103130	+	0.994668i	$0.467114\pi$
$74$	−4.94740e65	−0.217095
$75$	1.07235e66	0.292187
$76$	9.28889e66	1.58154
$77$	−1.79048e66	−0.191667
$78$	1.65242e65	0.0111883
$79$	−1.48560e66	−0.0639940	−0.0319970	−	0.999488i	$-0.510187\pi$
$79$	−1.48560e66	−0.0639940	−0.0319970	+	0.999488i	$0.510187\pi$
$80$	−2.34592e67	−0.646574
$81$	6.26579e66	0.111111
$82$	2.21595e67	0.254196
$83$	−1.28470e68	−0.958365	−0.479183	−	0.877715i	$-0.659067\pi$
$83$	−1.28470e68	−0.958365	−0.479183	+	0.877715i	$0.659067\pi$
$84$	1.06854e68	0.521044
$85$	1.61562e68	0.517567
$86$	−1.35700e67	−0.0287003
$87$	3.07027e68	0.430767
$88$	7.15276e67	0.0668865
$89$	4.41961e68	0.276719	0.138359	−	0.990382i	$-0.455817\pi$
$89$	4.41961e68	0.276719	0.138359	+	0.990382i	$0.455817\pi$
$90$	−9.12511e67	−0.0384263
$91$	−3.85168e68	−0.109567
$92$	7.20339e69	1.39017
$93$	−7.26250e68	−0.0954864
$94$	1.37366e69	0.123549
$95$	1.84902e70	1.14223
$96$	−6.43213e69	−0.273985
$97$	2.25437e70	0.664704	0.332352	−	0.943155i	$-0.392158\pi$
$97$	2.25437e70	0.664704	0.332352	+	0.943155i	$0.392158\pi$
$98$	−1.11994e69	−0.0229440
$99$	−4.82165e69	−0.0688885
$100$	4.92466e70	0.492466
$101$	2.00566e71	1.40879	0.704397	−	0.709806i	$-0.251217\pi$
$101$	2.00566e71	1.40879	0.704397	+	0.709806i	$0.251217\pi$
$102$	1.40867e70	0.0697432
$103$	4.91193e71	1.72001	0.860004	−	0.510287i	$-0.170461\pi$
$103$	4.91193e71	1.72001	0.860004	+	0.510287i	$0.170461\pi$
$104$	1.53870e70	0.0382359
$105$	2.12700e71	0.376311
$106$	1.50907e70	0.0190701
$107$	1.79474e72	1.62509	0.812547	−	0.582896i	$-0.198081\pi$
$107$	1.79474e72	1.62509	0.812547	+	0.582896i	$0.198081\pi$
$108$	2.87751e71	0.187272
$109$	8.60617e71	0.403803	0.201901	−	0.979406i	$-0.435288\pi$
$109$	8.60617e71	0.403803	0.201901	+	0.979406i	$0.435288\pi$
$110$	7.02196e70	0.0238242
$111$	3.10551e72	0.764129
$112$	4.76772e72	0.853240
$113$	−2.57394e72	−0.335980	−0.167990	−	0.985789i	$-0.553728\pi$
$113$	−2.57394e72	−0.335980	−0.167990	+	0.985789i	$0.553728\pi$
$114$	1.61217e72	0.153918
$115$	1.43389e73	1.00402
$116$	1.40999e73	0.726036
$117$	−1.03724e72	−0.0393803
$118$	2.42409e72	0.0680359
$119$	−3.28350e73	−0.682998
$120$	−8.49712e72	−0.131322
$121$	−8.31618e73	−0.957289
$122$	−1.38648e73	−0.119162
$123$	−1.39097e74	−0.894715
$124$	−3.33524e73	−0.160937
$125$	2.91730e74	1.05846
$126$	1.85454e73	0.0507087
$127$	−4.50539e74	−0.930465	−0.465233	−	0.885188i	$-0.654029\pi$
$127$	−4.50539e74	−0.930465	−0.465233	+	0.885188i	$0.654029\pi$
$128$	−3.91921e74	−0.612695
$129$	8.51798e73	0.101019
$130$	1.51057e73	0.0136192
$131$	−2.52319e75	−1.73308	−0.866541	−	0.499106i	$-0.833662\pi$
$131$	−2.52319e75	−1.73308	−0.866541	+	0.499106i	$0.833662\pi$
$132$	−2.21430e74	−0.116108
$133$	−3.75785e75	−1.50732
$134$	1.51333e74	0.0465278
$135$	5.72788e74	0.135253
$136$	1.31172e75	0.238347
$137$	−5.99515e75	−0.839886	−0.419943	−	0.907551i	$-0.637950\pi$
$137$	−5.99515e75	−0.839886	−0.419943	+	0.907551i	$0.637950\pi$
$138$	1.25021e75	0.135293
$139$	1.81712e76	1.52180	0.760902	−	0.648867i	$-0.224757\pi$
$139$	1.81712e76	1.52180	0.760902	+	0.648867i	$0.224757\pi$
$140$	9.76804e75	0.634253
$141$	−8.62255e75	−0.434868
$142$	−7.79706e75	−0.305981
$143$	7.98174e74	0.0244156
$144$	1.28392e76	0.306669
$145$	2.80669e76	0.524361
$146$	2.31135e75	0.0338329
$147$	7.02993e75	0.0807580
$148$	1.42618e77	1.28790
$149$	2.30471e77	1.63872	0.819359	−	0.573281i	$-0.194329\pi$
$149$	2.30471e77	1.63872	0.819359	+	0.573281i	$0.194329\pi$
$150$	8.54719e75	0.0479274
$151$	−2.21496e77	−0.981034	−0.490517	−	0.871432i	$-0.663192\pi$
$151$	−2.21496e77	−0.981034	−0.490517	+	0.871432i	$0.663192\pi$
$152$	1.50122e77	0.526014
$153$	−8.84227e76	−0.245481
$154$	−1.42711e76	−0.0314392
$155$	−6.63903e76	−0.116233
$156$	−4.76341e76	−0.0663735
$157$	9.07880e77	1.00830	0.504151	−	0.863615i	$-0.331805\pi$
$157$	9.07880e77	1.00830	0.504151	+	0.863615i	$0.331805\pi$
$158$	−1.18410e76	−0.0104969
$159$	−9.47254e76	−0.0671226
$160$	−5.87994e77	−0.333514
$161$	−2.91416e78	−1.32493
$162$	4.99417e76	0.0182255
$163$	4.87835e77	0.143091	0.0715456	−	0.997437i	$-0.477207\pi$
$163$	4.87835e77	0.143091	0.0715456	+	0.997437i	$0.477207\pi$
$164$	−6.38788e78	−1.50800
$165$	−4.40772e77	−0.0838560
$166$	−1.02398e78	−0.157201
$167$	3.53760e77	0.0438807	0.0219403	−	0.999759i	$-0.493016\pi$
$167$	3.53760e77	0.0438807	0.0219403	+	0.999759i	$0.493016\pi$
$168$	1.72691e78	0.173297
$169$	−1.21304e79	−0.986043
$170$	1.28773e78	0.0848965
$171$	−1.01197e79	−0.541758
$172$	3.91181e78	0.170262
$173$	2.26507e79	0.802499	0.401249	−	0.915969i	$-0.368576\pi$
$173$	2.26507e79	0.802499	0.401249	+	0.915969i	$0.368576\pi$
$174$	2.44717e78	0.0706587
$175$	−1.99229e79	−0.469355
$176$	−9.88003e78	−0.190133
$177$	−1.52162e79	−0.239472
$178$	3.52267e78	0.0453901
$179$	7.12435e79	0.752423	0.376212	−	0.926534i	$-0.377227\pi$
$179$	7.12435e79	0.752423	0.376212	+	0.926534i	$0.377227\pi$
$180$	2.63048e79	0.227961
$181$	2.07166e80	1.47479	0.737393	−	0.675463i	$-0.236056\pi$
$181$	2.07166e80	1.47479	0.737393	+	0.675463i	$0.236056\pi$
$182$	−3.07000e78	−0.0179723
$183$	8.70299e79	0.419425
$184$	1.16417e80	0.462365
$185$	2.83891e80	0.930154
$186$	−5.78861e78	−0.0156626
$187$	6.80431e79	0.152197
$188$	−3.95983e80	−0.732947
$189$	−1.16411e80	−0.178484
$190$	1.47377e80	0.187360
$191$	−2.65055e80	−0.279674	−0.139837	−	0.990175i	$-0.544658\pi$
$191$	−2.65055e80	−0.279674	−0.139837	+	0.990175i	$0.544658\pi$
$192$	5.54664e80	0.486224
$193$	−2.06528e81	−1.50555	−0.752773	−	0.658280i	$-0.771284\pi$
$193$	−2.06528e81	−1.50555	−0.752773	+	0.658280i	$0.771284\pi$
$194$	1.79685e80	0.109031
$195$	−9.48191e79	−0.0479366
$196$	3.22843e80	0.136114
$197$	−7.80157e80	−0.274556	−0.137278	−	0.990533i	$-0.543835\pi$
$197$	−7.80157e80	−0.274556	−0.137278	+	0.990533i	$0.543835\pi$
$198$	−3.84312e79	−0.0112998
$199$	−2.60932e81	−0.641570	−0.320785	−	0.947152i	$-0.603947\pi$
$199$	−2.60932e81	−0.641570	−0.320785	+	0.947152i	$0.603947\pi$
$200$	7.95897e80	0.163792
$201$	−9.49924e80	−0.163768
$202$	1.59862e81	0.231084
$203$	−5.70418e81	−0.691964
$204$	−4.06073e81	−0.413746
$205$	−1.27155e82	−1.08911
$206$	3.91507e81	0.282133
$207$	−7.84766e81	−0.476204
$208$	−2.12540e81	−0.108690
$209$	7.78731e81	0.335888
$210$	1.69533e81	0.0617263
$211$	4.85541e82	1.49348	0.746739	−	0.665117i	$-0.231618\pi$
$211$	4.85541e82	1.49348	0.746739	+	0.665117i	$0.231618\pi$
$212$	−4.35018e81	−0.113132
$213$	4.89426e82	1.07699
$214$	1.43051e82	0.266564
$215$	7.78673e81	0.122967
$216$	4.65047e81	0.0622858
$217$	1.34928e82	0.153385
$218$	6.85959e81	0.0662357
$219$	−1.45085e82	−0.119084
$220$	−2.02421e82	−0.141335
$221$	1.46374e82	0.0870041
$222$	2.47526e82	0.125340
$223$	2.25536e83	0.973628	0.486814	−	0.873506i	$-0.338159\pi$
$223$	2.25536e83	0.973628	0.486814	+	0.873506i	$0.338159\pi$
$224$	1.19501e83	0.440116
$225$	−5.36512e82	−0.168694
$226$	−2.05157e82	−0.0551108
$227$	1.37056e83	0.314761	0.157380	−	0.987538i	$-0.449695\pi$
$227$	1.37056e83	0.314761	0.157380	+	0.987538i	$0.449695\pi$
$228$	−4.64737e83	−0.913105
$229$	−7.57490e83	−1.27414	−0.637070	−	0.770806i	$-0.719854\pi$
$229$	−7.57490e83	−1.27414	−0.637070	+	0.770806i	$0.719854\pi$
$230$	1.14289e83	0.164689
$231$	8.95803e82	0.110659
$232$	2.27876e83	0.241476
$233$	−1.61573e84	−1.46972	−0.734859	−	0.678220i	$-0.762752\pi$
$233$	−1.61573e84	−1.46972	−0.734859	+	0.678220i	$0.762752\pi$
$234$	−8.26733e81	−0.00645955
$235$	−7.88232e83	−0.529353
$236$	−6.98789e83	−0.403617
$237$	7.43267e82	0.0369469
$238$	−2.61713e83	−0.112032
$239$	1.48356e84	0.547240	0.273620	−	0.961838i	$-0.411779\pi$
$239$	1.48356e84	0.547240	0.273620	+	0.961838i	$0.411779\pi$
$240$	1.17370e84	0.373300
$241$	−2.45592e84	−0.673921	−0.336961	−	0.941519i	$-0.609399\pi$
$241$	−2.45592e84	−0.673921	−0.336961	+	0.941519i	$0.609399\pi$
$242$	−6.62845e83	−0.157024
$243$	−3.13487e83	−0.0641500
$244$	3.99677e84	0.706920
$245$	6.42643e83	0.0983045
$246$	−1.10868e84	−0.146760
$247$	1.67521e84	0.192011
$248$	−5.39024e83	−0.0535270
$249$	6.42758e84	0.553312
$250$	2.32525e84	0.173620
$251$	2.92095e85	1.89281	0.946405	−	0.322981i	$-0.104685\pi$
$251$	2.92095e85	1.89281	0.946405	+	0.322981i	$0.104685\pi$
$252$	−5.34605e84	−0.300825
$253$	6.03894e84	0.295245
$254$	−3.59104e84	−0.152624
$255$	−8.08318e84	−0.298817
$256$	2.30529e85	0.741665
$257$	−8.01422e84	−0.224510	−0.112255	−	0.993679i	$-0.535807\pi$
$257$	−8.01422e84	−0.224510	−0.112255	+	0.993679i	$0.535807\pi$
$258$	6.78930e83	0.0165701
$259$	−5.76965e85	−1.22746
$260$	−4.35448e84	−0.0807946
$261$	−1.53610e85	−0.248704
$262$	−2.01112e85	−0.284277
$263$	1.39849e86	1.72675	0.863377	−	0.504559i	$-0.168345\pi$
$263$	1.39849e86	1.72675	0.863377	+	0.504559i	$0.168345\pi$
$264$	−3.57864e84	−0.0386170
$265$	−8.65934e84	−0.0817065
$266$	−2.99521e85	−0.247246
$267$	−2.21120e85	−0.159764
$268$	−4.36244e85	−0.276022
$269$	−2.31756e86	−1.28477	−0.642383	−	0.766383i	$-0.722054\pi$
$269$	−2.31756e86	−1.28477	−0.642383	+	0.766383i	$0.722054\pi$
$270$	4.56543e84	0.0221855
$271$	−2.23430e86	−0.952206	−0.476103	−	0.879389i	$-0.657951\pi$
$271$	−2.23430e86	−0.952206	−0.476103	+	0.879389i	$0.657951\pi$
$272$	−1.81187e86	−0.677532
$273$	1.92705e85	0.0632587
$274$	−4.77846e85	−0.137766
$275$	4.12857e85	0.104590
$276$	−3.60397e86	−0.802617
$277$	5.39578e86	1.05687	0.528436	−	0.848973i	$-0.322779\pi$
$277$	5.39578e86	1.05687	0.528436	+	0.848973i	$0.322779\pi$
$278$	1.44835e86	0.249621
$279$	3.63354e85	0.0551291
$280$	1.57866e86	0.210949
$281$	8.52295e86	1.00350	0.501748	−	0.865014i	$-0.332690\pi$
$281$	8.52295e86	1.00350	0.501748	+	0.865014i	$0.332690\pi$
$282$	−6.87264e85	−0.0713313
$283$	−7.02537e86	−0.643059	−0.321529	−	0.946900i	$-0.604197\pi$
$283$	−7.02537e86	−0.643059	−0.321529	+	0.946900i	$0.604197\pi$
$284$	2.24764e87	1.81521
$285$	−9.25093e86	−0.659467
$286$	6.36188e84	0.00400490
$287$	2.58424e87	1.43723
$288$	3.21809e86	0.158185
$289$	−1.05295e87	−0.457652
$290$	2.23709e86	0.0860109
$291$	−1.12790e87	−0.383767
$292$	−6.66288e86	−0.200711
$293$	9.34044e86	0.249211	0.124605	−	0.992206i	$-0.460233\pi$
$293$	9.34044e86	0.249211	0.124605	+	0.992206i	$0.460233\pi$
$294$	5.60324e85	0.0132467
$295$	−1.39099e87	−0.291502
$296$	2.30491e87	0.428350
$297$	2.41235e86	0.0397728
$298$	1.83698e87	0.268799
$299$	1.29910e87	0.168778
$300$	−2.46388e87	−0.284325
$301$	−1.58254e87	−0.162272
$302$	−1.76544e87	−0.160919
$303$	−1.00346e88	−0.813368
$304$	−2.07362e88	−1.49526
$305$	7.95585e87	0.510555
$306$	−7.04777e86	−0.0402662
$307$	−1.65158e88	−0.840403	−0.420201	−	0.907431i	$-0.638041\pi$
$307$	−1.65158e88	−0.840403	−0.420201	+	0.907431i	$0.638041\pi$
$308$	4.11390e87	0.186510
$309$	−2.45751e88	−0.993047
$310$	−5.29167e86	−0.0190657
$311$	4.69774e88	1.50971	0.754857	−	0.655889i	$-0.227706\pi$
$311$	4.69774e88	1.50971	0.754857	+	0.655889i	$0.227706\pi$
$312$	−7.69837e86	−0.0220755
$313$	−3.60840e88	−0.923614	−0.461807	−	0.886980i	$-0.652799\pi$
$313$	−3.60840e88	−0.923614	−0.461807	+	0.886980i	$0.652799\pi$
$314$	7.23630e87	0.165392
$315$	−1.06417e88	−0.217263
$316$	3.41338e87	0.0622721
$317$	1.15766e89	1.88789	0.943946	−	0.330101i	$-0.107083\pi$
$317$	1.15766e89	1.88789	0.943946	+	0.330101i	$0.107083\pi$
$318$	−7.55013e86	−0.0110101
$319$	1.18206e88	0.154195
$320$	5.07048e88	0.591868
$321$	−8.97938e88	−0.938248
$322$	−2.32274e88	−0.217329
$323$	1.42809e89	1.19692
$324$	−1.43966e88	−0.108122
$325$	8.88139e87	0.0597891
$326$	3.88831e87	0.0234712
$327$	−4.30580e88	−0.233136
$328$	−1.03238e89	−0.501553
$329$	1.60196e89	0.698551
$330$	−3.51320e87	−0.0137549
$331$	3.24351e89	1.14057	0.570284	−	0.821448i	$-0.306833\pi$
$331$	3.24351e89	1.14057	0.570284	+	0.821448i	$0.306833\pi$
$332$	2.95181e89	0.932580
$333$	−1.55373e89	−0.441170
$334$	2.81966e87	0.00719775
$335$	−8.68375e88	−0.199350
$336$	−2.38537e89	−0.492618
$337$	−8.10661e89	−1.50653	−0.753265	−	0.657717i	$-0.771522\pi$
$337$	−8.10661e89	−1.50653	−0.753265	+	0.657717i	$0.771522\pi$
$338$	−9.66856e88	−0.161741
$339$	1.28778e89	0.193978
$340$	−3.71213e89	−0.503641
$341$	−2.79609e88	−0.0341798
$342$	−8.06594e88	−0.0888645
$343$	−1.06434e90	−1.05715
$344$	6.32206e88	0.0566283
$345$	−7.17396e89	−0.579670
$346$	1.80538e89	0.131634
$347$	2.76963e90	1.82274	0.911372	−	0.411584i	$-0.135024\pi$
$347$	2.76963e90	1.82274	0.911372	+	0.411584i	$0.135024\pi$
$348$	−7.05441e89	−0.419177
$349$	−2.21675e90	−1.18963	−0.594817	−	0.803861i	$-0.702775\pi$
$349$	−2.21675e90	−1.18963	−0.594817	+	0.803861i	$0.702775\pi$
$350$	−1.58796e89	−0.0769883
$351$	5.18945e88	0.0227362
$352$	−2.47639e89	−0.0980741
$353$	−4.39981e89	−0.157555	−0.0787774	−	0.996892i	$-0.525102\pi$
$353$	−4.39981e89	−0.157555	−0.0787774	+	0.996892i	$0.525102\pi$
$354$	−1.21281e89	−0.0392805
$355$	4.47409e90	1.31099
$356$	−1.01547e90	−0.269273
$357$	1.64278e90	0.394329
$358$	5.67849e89	0.123420
$359$	7.63083e89	0.150217	0.0751085	−	0.997175i	$-0.476070\pi$
$359$	7.63083e89	0.150217	0.0751085	+	0.997175i	$0.476070\pi$
$360$	4.25124e89	0.0758188
$361$	1.01566e91	1.64151
$362$	1.65123e90	0.241909
$363$	4.16071e90	0.552691
$364$	8.84982e89	0.106619
$365$	−1.32629e90	−0.144958
$366$	6.93675e89	0.0687983
$367$	−7.55309e90	−0.679954	−0.339977	−	0.940434i	$-0.610419\pi$
$367$	−7.55309e90	−0.679954	−0.339977	+	0.940434i	$0.610419\pi$
$368$	−1.60806e91	−1.31433
$369$	6.95921e90	0.516564
$370$	2.26276e90	0.152573
$371$	1.75988e90	0.107823
$372$	1.66867e90	0.0929173
$373$	−8.66729e90	−0.438753	−0.219376	−	0.975640i	$-0.570402\pi$
$373$	−8.66729e90	−0.438753	−0.219376	+	0.975640i	$0.570402\pi$
$374$	5.42340e89	0.0249649
$375$	−1.45957e91	−0.611104
$376$	−6.39966e90	−0.243775
$377$	2.54285e90	0.0881462
$378$	−9.27856e89	−0.0292767
$379$	4.02723e91	1.15695	0.578474	−	0.815701i	$-0.303648\pi$
$379$	4.02723e91	1.15695	0.578474	+	0.815701i	$0.303648\pi$
$380$	−4.24841e91	−1.11150
$381$	2.25412e91	0.537204
$382$	−2.11263e90	−0.0458749
$383$	−9.02959e91	−1.78695	−0.893473	−	0.449117i	$-0.851739\pi$
$383$	−9.02959e91	−1.78695	−0.893473	+	0.449117i	$0.851739\pi$
$384$	1.96084e91	0.353740
$385$	8.18901e90	0.134702
$386$	−1.64614e91	−0.246955
$387$	−4.26168e90	−0.0583232
$388$	−5.17976e91	−0.646820
$389$	−1.18149e92	−1.34654	−0.673269	−	0.739397i	$-0.735111\pi$
$389$	−1.18149e92	−1.34654	−0.673269	+	0.739397i	$0.735111\pi$
$390$	−7.55760e89	−0.00786303
$391$	1.10746e92	1.05209
$392$	5.21762e90	0.0452707
$393$	1.26239e92	1.00060
$394$	−6.21827e90	−0.0450354
$395$	6.79459e90	0.0449745
$396$	1.10785e91	0.0670350
$397$	3.17980e92	1.75928	0.879642	−	0.475636i	$-0.157782\pi$
$397$	3.17980e92	1.75928	0.879642	+	0.475636i	$0.157782\pi$
$398$	−2.07977e91	−0.105237
$399$	1.88011e92	0.870254
$400$	−1.09936e92	−0.465599
$401$	2.32170e92	0.899871	0.449935	−	0.893061i	$-0.351447\pi$
$401$	2.32170e92	0.899871	0.449935	+	0.893061i	$0.351447\pi$
$402$	−7.57141e90	−0.0268628
$403$	−6.01495e90	−0.0195390
$404$	−4.60830e92	−1.37089
$405$	−2.86575e91	−0.0780881
$406$	−4.54654e91	−0.113503
$407$	1.19563e92	0.273524
$408$	−6.56274e91	−0.137610
$409$	7.00984e92	1.34751	0.673753	−	0.738957i	$-0.264681\pi$
$409$	7.00984e92	1.34751	0.673753	+	0.738957i	$0.264681\pi$
$410$	−1.01350e92	−0.178647
$411$	2.99947e92	0.484908
$412$	−1.12859e93	−1.67373
$413$	2.82697e92	0.384676
$414$	−6.25501e91	−0.0781117
$415$	5.87578e92	0.673532
$416$	−5.32722e91	−0.0560644
$417$	−9.09134e92	−0.878614
$418$	6.20691e91	0.0550956
$419$	−6.81804e92	−0.555983	−0.277992	−	0.960584i	$-0.589669\pi$
$419$	−6.81804e92	−0.555983	−0.277992	+	0.960584i	$0.589669\pi$
$420$	−4.88710e92	−0.366186
$421$	−1.79290e93	−1.23465	−0.617323	−	0.786710i	$-0.711783\pi$
$421$	−1.79290e93	−1.23465	−0.617323	+	0.786710i	$0.711783\pi$
$422$	3.87003e92	0.244975
$423$	4.31399e92	0.251071
$424$	−7.03053e91	−0.0376271
$425$	7.57125e92	0.372701
$426$	3.90099e92	0.176658
$427$	−1.61691e93	−0.673745
$428$	−4.12370e93	−1.58137
$429$	−3.99339e91	−0.0140964
$430$	6.20645e91	0.0201703
$431$	3.86882e93	1.15781	0.578903	−	0.815397i	$-0.303481\pi$
$431$	3.86882e93	1.15781	0.578903	+	0.815397i	$0.303481\pi$
$432$	−6.42365e92	−0.177055
$433$	3.48433e93	0.884707	0.442353	−	0.896841i	$-0.354144\pi$
$433$	3.48433e93	0.884707	0.442353	+	0.896841i	$0.354144\pi$
$434$	1.07545e92	0.0251597
$435$	−1.40423e93	−0.302740
$436$	−1.97740e93	−0.392938
$437$	1.26745e94	2.32188
$438$	−1.15640e92	−0.0195334
$439$	3.20217e93	0.498832	0.249416	−	0.968396i	$-0.419761\pi$
$439$	3.20217e93	0.498832	0.249416	+	0.968396i	$0.419761\pi$
$440$	−3.27142e92	−0.0470074
$441$	−3.51718e92	−0.0466257
$442$	1.16668e92	0.0142713
$443$	1.37314e94	1.55018	0.775090	−	0.631850i	$-0.217704\pi$
$443$	1.37314e94	1.55018	0.775090	+	0.631850i	$0.217704\pi$
$444$	−7.13538e93	−0.743570
$445$	−2.02137e93	−0.194476
$446$	1.79764e93	0.159704
$447$	−1.15308e94	−0.946114
$448$	−1.03050e94	−0.781048
$449$	8.82823e93	0.618200	0.309100	−	0.951030i	$-0.399972\pi$
$449$	8.82823e93	0.618200	0.309100	+	0.951030i	$0.399972\pi$
$450$	−4.27629e92	−0.0276709
$451$	−5.35526e93	−0.320268
$452$	5.91402e93	0.326940
$453$	1.10818e94	0.566400
$454$	1.09241e93	0.0516302
$455$	1.76162e93	0.0770030
$456$	−7.51084e93	−0.303694
$457$	−1.32298e94	−0.494914	−0.247457	−	0.968899i	$-0.579595\pi$
$457$	−1.32298e94	−0.494914	−0.247457	+	0.968899i	$0.579595\pi$
$458$	−6.03760e93	−0.208997
$459$	4.42392e93	0.141729
$460$	−3.29457e94	−0.977004
$461$	−1.46928e94	−0.403388	−0.201694	−	0.979449i	$-0.564645\pi$
$461$	−1.46928e94	−0.403388	−0.201694	+	0.979449i	$0.564645\pi$
$462$	7.14004e92	0.0181514
$463$	6.21821e93	0.146400	0.0731998	−	0.997317i	$-0.476679\pi$
$463$	6.21821e93	0.146400	0.0731998	+	0.997317i	$0.476679\pi$
$464$	−3.14762e94	−0.686427
$465$	3.32161e93	0.0671071
$466$	−1.28783e94	−0.241078
$467$	8.14155e93	0.141240	0.0706200	−	0.997503i	$-0.477502\pi$
$467$	8.14155e93	0.141240	0.0706200	+	0.997503i	$0.477502\pi$
$468$	2.38321e93	0.0383208
$469$	1.76484e94	0.263069
$470$	−6.28264e93	−0.0868297
$471$	−4.54226e94	−0.582144
$472$	−1.12935e94	−0.134241
$473$	3.27945e93	0.0361602
$474$	5.92424e92	0.00606040
$475$	8.66504e94	0.822522
$476$	7.54434e94	0.664621
$477$	4.73926e93	0.0387532
$478$	1.18247e94	0.0897638
$479$	−3.39082e94	−0.238998	−0.119499	−	0.992834i	$-0.538129\pi$
$479$	−3.39082e94	−0.238998	−0.119499	+	0.992834i	$0.538129\pi$
$480$	2.94183e94	0.192554
$481$	2.57204e94	0.156361
$482$	−1.95750e94	−0.110543
$483$	1.45800e95	0.764952
$484$	1.91077e95	0.931533
$485$	−1.03107e95	−0.467149
$486$	−2.49866e93	−0.0105225
$487$	3.97365e94	0.155565	0.0777824	−	0.996970i	$-0.475216\pi$
$487$	3.97365e94	0.155565	0.0777824	+	0.996970i	$0.475216\pi$
$488$	6.45936e94	0.235118
$489$	−2.44071e94	−0.0826138
$490$	5.12221e93	0.0161249
$491$	−9.76191e94	−0.285852	−0.142926	−	0.989733i	$-0.545651\pi$
$491$	−9.76191e94	−0.285852	−0.142926	+	0.989733i	$0.545651\pi$
$492$	3.19596e95	0.870642
$493$	2.16774e95	0.549468
$494$	1.33523e94	0.0314956
$495$	2.20525e94	0.0484143
$496$	7.44548e94	0.152157
$497$	−9.09292e95	−1.73002
$498$	5.12313e94	0.0907598
$499$	−2.55677e95	−0.421815	−0.210908	−	0.977506i	$-0.567642\pi$
$499$	−2.55677e95	−0.421815	−0.210908	+	0.977506i	$0.567642\pi$
$500$	−6.70295e95	−1.02998
$501$	−1.76991e94	−0.0253345
$502$	2.32816e95	0.310478
$503$	−1.16607e96	−1.44898	−0.724489	−	0.689286i	$-0.757924\pi$
$503$	−1.16607e96	−1.44898	−0.724489	+	0.689286i	$0.757924\pi$
$504$	−8.64001e94	−0.100053
$505$	−9.17316e95	−0.990090
$506$	4.81336e94	0.0484290
$507$	6.06901e95	0.569292
$508$	1.03518e96	0.905431
$509$	1.43124e95	0.116743	0.0583716	−	0.998295i	$-0.481409\pi$
$509$	1.43124e95	0.116743	0.0583716	+	0.998295i	$0.481409\pi$
$510$	−6.44273e94	−0.0490150
$511$	2.69549e95	0.191292
$512$	1.10914e96	0.734351
$513$	5.06303e95	0.312784
$514$	−6.38777e94	−0.0368264
$515$	−2.24654e96	−1.20881
$516$	−1.95714e95	−0.0983008
$517$	−3.31971e95	−0.155663
$518$	−4.59872e95	−0.201340
$519$	−1.13325e96	−0.463323
$520$	−7.03748e94	−0.0268719
$521$	4.13964e96	1.47647	0.738233	−	0.674546i	$-0.235660\pi$
$521$	4.13964e96	1.47647	0.738233	+	0.674546i	$0.235660\pi$
$522$	−1.22436e95	−0.0407948
$523$	−3.42682e96	−1.06680	−0.533398	−	0.845865i	$-0.679085\pi$
$523$	−3.42682e96	−1.06680	−0.533398	+	0.845865i	$0.679085\pi$
$524$	5.79742e96	1.68645
$525$	9.96773e95	0.270982
$526$	1.11467e96	0.283240
$527$	−5.12765e95	−0.121798
$528$	4.94313e95	0.109774
$529$	5.01301e96	1.04093
$530$	−6.90197e94	−0.0134023
$531$	7.61288e95	0.138259
$532$	8.63425e96	1.46677
$533$	−1.15202e96	−0.183082
$534$	−1.76244e95	−0.0262060
$535$	−8.20852e96	−1.14210
$536$	−7.05034e95	−0.0918037
$537$	−3.56442e96	−0.434412
$538$	−1.84722e96	−0.210740
$539$	2.70655e95	0.0289077
$540$	−1.31607e96	−0.131613
$541$	−3.47000e96	−0.324958	−0.162479	−	0.986712i	$-0.551949\pi$
$541$	−3.47000e96	−0.324958	−0.162479	+	0.986712i	$0.551949\pi$
$542$	−1.78086e96	−0.156190
$543$	−1.03648e97	−0.851469
$544$	−4.54137e96	−0.349483
$545$	−3.93616e96	−0.283790
$546$	1.53597e95	0.0103763
$547$	−1.63692e97	−1.03628	−0.518140	−	0.855296i	$-0.673375\pi$
$547$	−1.63692e97	−1.03628	−0.518140	+	0.855296i	$0.673375\pi$
$548$	1.37748e97	0.817288
$549$	−4.35424e96	−0.242155
$550$	3.29070e95	0.0171558
$551$	2.48091e97	1.21263
$552$	−5.82454e96	−0.266947
$553$	−1.38090e96	−0.0593498
$554$	4.30073e96	0.173359
$555$	−1.42035e97	−0.537024
$556$	−4.17512e97	−1.48086
$557$	5.23036e97	1.74049	0.870246	−	0.492617i	$-0.163960\pi$
$557$	5.23036e97	1.74049	0.870246	+	0.492617i	$0.163960\pi$
$558$	2.89613e95	0.00904282
$559$	7.05476e95	0.0206711
$560$	−2.18059e97	−0.599651
$561$	−3.40430e96	−0.0878712
$562$	6.79326e96	0.164603
$563$	−3.11953e97	−0.709645	−0.354822	−	0.934934i	$-0.615459\pi$
$563$	−3.11953e97	−0.709645	−0.354822	+	0.934934i	$0.615459\pi$
$564$	1.98116e97	0.423167
$565$	1.17723e97	0.236124
$566$	−5.59960e96	−0.105481
$567$	5.82420e96	0.103048
$568$	3.63252e97	0.603729
$569$	3.65222e97	0.570257	0.285129	−	0.958489i	$-0.407964\pi$
$569$	3.65222e97	0.570257	0.285129	+	0.958489i	$0.407964\pi$
$570$	−7.37349e96	−0.108172
$571$	6.38294e97	0.879912	0.439956	−	0.898019i	$-0.354994\pi$
$571$	6.38294e97	0.879912	0.439956	+	0.898019i	$0.354994\pi$
$572$	−1.83393e96	−0.0237587
$573$	1.32611e97	0.161470
$574$	2.05978e97	0.235748
$575$	6.71961e97	0.722996
$576$	−2.77507e97	−0.280722
$577$	4.49734e97	0.427774	0.213887	−	0.976858i	$-0.431388\pi$
$577$	4.49734e97	0.427774	0.213887	+	0.976858i	$0.431388\pi$
$578$	−8.39260e96	−0.0750686
$579$	1.03329e98	0.869228
$580$	−6.44880e97	−0.510253
$581$	−1.19416e98	−0.888815
$582$	−8.98994e96	−0.0629493
$583$	−3.64696e96	−0.0240269
$584$	−1.07682e97	−0.0667554
$585$	4.74394e96	0.0276762
$586$	7.44484e96	0.0408780
$587$	−1.49727e98	−0.773835	−0.386918	−	0.922114i	$-0.626460\pi$
$587$	−1.49727e98	−0.773835	−0.386918	+	0.922114i	$0.626460\pi$
$588$	−1.61523e97	−0.0785852
$589$	−5.86842e97	−0.268800
$590$	−1.10869e97	−0.0478151
$591$	3.90324e97	0.158515
$592$	−3.18375e98	−1.21764
$593$	−3.72172e96	−0.0134061	−0.00670304	−	0.999978i	$-0.502134\pi$
$593$	−3.72172e96	−0.0134061	−0.00670304	+	0.999978i	$0.502134\pi$
$594$	1.92277e96	0.00652393
$595$	1.50175e98	0.480006
$596$	−5.29543e98	−1.59463
$597$	1.30549e98	0.370411
$598$	1.03545e97	0.0276846
$599$	−4.23873e98	−1.06803	−0.534015	−	0.845475i	$-0.679317\pi$
$599$	−4.23873e98	−1.06803	−0.534015	+	0.845475i	$0.679317\pi$
$600$	−3.98200e97	−0.0945653
$601$	4.00322e98	0.896118	0.448059	−	0.894004i	$-0.352115\pi$
$601$	4.00322e98	0.896118	0.448059	+	0.894004i	$0.352115\pi$
$602$	−1.26137e97	−0.0266174
$603$	4.75261e97	0.0945514
$604$	5.08921e98	0.954639
$605$	3.80352e98	0.672776
$606$	−7.99813e97	−0.133417
$607$	−1.30028e98	−0.204568	−0.102284	−	0.994755i	$-0.532615\pi$
$607$	−1.30028e98	−0.204568	−0.102284	+	0.994755i	$0.532615\pi$
$608$	−5.19745e98	−0.771282
$609$	2.85389e98	0.399506
$610$	6.34125e97	0.0837463
$611$	−7.14136e97	−0.0889853
$612$	2.03165e98	0.238876
$613$	3.81210e98	0.422978	0.211489	−	0.977380i	$-0.432169\pi$
$613$	3.81210e98	0.422978	0.211489	+	0.977380i	$0.432169\pi$
$614$	−1.31640e98	−0.137851
$615$	6.36178e98	0.628799
$616$	6.64866e97	0.0620325
$617$	1.31432e98	0.115766	0.0578828	−	0.998323i	$-0.481565\pi$
$617$	1.31432e98	0.115766	0.0578828	+	0.998323i	$0.481565\pi$
$618$	−1.95877e98	−0.162890
$619$	1.31528e99	1.03277	0.516383	−	0.856358i	$-0.327278\pi$
$619$	1.31528e99	1.03277	0.516383	+	0.856358i	$0.327278\pi$
$620$	1.52542e98	0.113106
$621$	3.92631e98	0.274937
$622$	3.74435e98	0.247638
$623$	4.10813e98	0.256637
$624$	1.06337e98	0.0627524
$625$	−4.26529e98	−0.237798
$626$	−2.87609e98	−0.151500
$627$	−3.89611e98	−0.193925
$628$	−2.08599e99	−0.981173
$629$	2.19263e99	0.974690
$630$	−8.48201e97	−0.0356377
$631$	−3.58663e99	−1.42444	−0.712221	−	0.701956i	$-0.752311\pi$
$631$	−3.58663e99	−1.42444	−0.712221	+	0.701956i	$0.752311\pi$
$632$	5.51653e97	0.0207114
$633$	−2.42924e99	−0.862260
$634$	9.22717e98	0.309671
$635$	2.06060e99	0.653924
$636$	2.17646e98	0.0653166
$637$	5.82233e97	0.0165252
$638$	9.42168e97	0.0252926
$639$	−2.44867e99	−0.621799
$640$	1.79251e99	0.430598
$641$	−1.34304e99	−0.305232	−0.152616	−	0.988286i	$-0.548770\pi$
$641$	−1.34304e99	−0.305232	−0.152616	+	0.988286i	$0.548770\pi$
$642$	−7.15705e98	−0.153901
$643$	−8.80678e99	−1.79196	−0.895979	−	0.444096i	$-0.853525\pi$
$643$	−8.80678e99	−1.79196	−0.895979	+	0.444096i	$0.853525\pi$
$644$	6.69573e99	1.28929
$645$	−3.89582e98	−0.0709953
$646$	1.13826e99	0.196331
$647$	−8.67749e99	−1.41675	−0.708373	−	0.705838i	$-0.750570\pi$
$647$	−8.67749e99	−1.41675	−0.708373	+	0.705838i	$0.750570\pi$
$648$	−2.32670e98	−0.0359607
$649$	−5.85827e98	−0.0857201
$650$	7.07895e97	0.00980720
$651$	−6.75067e98	−0.0885568
$652$	−1.12088e99	−0.139241
$653$	−4.90696e99	−0.577290	−0.288645	−	0.957436i	$-0.593205\pi$
$653$	−4.90696e99	−0.577290	−0.288645	+	0.957436i	$0.593205\pi$
$654$	−3.43196e98	−0.0382412
$655$	1.15402e100	1.21800
$656$	1.42601e100	1.42573
$657$	7.25880e98	0.0687534
$658$	1.27685e99	0.114583
$659$	1.50960e100	1.28360	0.641799	−	0.766873i	$-0.278188\pi$
$659$	1.50960e100	1.28360	0.641799	+	0.766873i	$0.278188\pi$
$660$	1.01274e99	0.0815998
$661$	−1.88783e100	−1.44149	−0.720743	−	0.693202i	$-0.756199\pi$
$661$	−1.88783e100	−1.44149	−0.720743	+	0.693202i	$0.756199\pi$
$662$	2.58525e99	0.187087
$663$	−7.32334e98	−0.0502318
$664$	4.77055e99	0.310172
$665$	1.71871e100	1.05934
$666$	−1.23841e99	−0.0723651
$667$	1.92391e100	1.06590
$668$	−8.12817e98	−0.0427000
$669$	−1.12839e100	−0.562125
$670$	−6.92142e98	−0.0326994
$671$	3.35068e99	0.150135
$672$	−5.97882e99	−0.254101
$673$	−4.10856e100	−1.65636	−0.828180	−	0.560462i	$-0.810624\pi$
$673$	−4.10856e100	−1.65636	−0.828180	+	0.560462i	$0.810624\pi$
$674$	−6.46141e99	−0.247116
$675$	2.68425e99	0.0973956
$676$	2.78714e100	0.959512
$677$	1.17960e100	0.385332	0.192666	−	0.981264i	$-0.438287\pi$
$677$	1.17960e100	0.385332	0.192666	+	0.981264i	$0.438287\pi$
$678$	1.02643e99	0.0318182
$679$	2.09549e100	0.616465
$680$	−5.99934e99	−0.167509
$681$	−6.85713e99	−0.181727
$682$	−2.22863e98	−0.00560652
$683$	−7.83273e100	−1.87059	−0.935295	−	0.353870i	$-0.884866\pi$
$683$	−7.83273e100	−1.87059	−0.935295	+	0.353870i	$0.884866\pi$
$684$	2.32515e100	0.527181
$685$	2.74197e100	0.590265
$686$	−8.48335e99	−0.173405
$687$	3.78984e100	0.735625
$688$	−8.73259e99	−0.160973
$689$	−7.84534e98	−0.0137350
$690$	−5.71803e99	−0.0950832
$691$	−1.06559e101	−1.68313	−0.841567	−	0.540153i	$-0.818366\pi$
$691$	−1.06559e101	−1.68313	−0.841567	+	0.540153i	$0.818366\pi$
$692$	−5.20434e100	−0.780907
$693$	−4.48184e99	−0.0638891
$694$	2.20755e100	0.298985
$695$	−8.31087e100	−1.06951
$696$	−1.14010e100	−0.139416
$697$	−9.82083e100	−1.14126
$698$	−1.76687e100	−0.195136
$699$	8.08375e100	0.848542
$700$	4.57759e100	0.456727
$701$	−9.33290e100	−0.885171	−0.442585	−	0.896726i	$-0.645939\pi$
$701$	−9.33290e100	−0.885171	−0.442585	+	0.896726i	$0.645939\pi$
$702$	4.13627e98	0.00372942
$703$	2.50939e101	2.15107
$704$	2.13547e100	0.174046
$705$	3.94365e100	0.305622
$706$	−3.50689e99	−0.0258437
$707$	1.86431e101	1.30656
$708$	3.49615e100	0.233028
$709$	1.43537e101	0.909959	0.454980	−	0.890502i	$-0.349647\pi$
$709$	1.43537e101	0.909959	0.454980	+	0.890502i	$0.349647\pi$
$710$	3.56610e100	0.215041
$711$	−3.71868e99	−0.0213313
$712$	−1.64115e100	−0.0895590
$713$	−4.55087e100	−0.236274
$714$	1.30939e100	0.0646818
$715$	−3.65056e99	−0.0171591
$716$	−1.63693e101	−0.732179
$717$	−7.42246e100	−0.315949
$718$	6.08219e99	0.0246401
$719$	−8.28580e100	−0.319491	−0.159746	−	0.987158i	$-0.551067\pi$
$719$	−8.28580e100	−0.319491	−0.159746	+	0.987158i	$0.551067\pi$
$720$	−5.87219e100	−0.215525
$721$	4.56576e101	1.59518
$722$	8.09539e100	0.269257
$723$	1.22873e101	0.389089
$724$	−4.75996e101	−1.43511
$725$	1.31530e101	0.377594
$726$	3.31632e100	0.0906579
$727$	−1.09830e101	−0.285924	−0.142962	−	0.989728i	$-0.545663\pi$
$727$	−1.09830e101	−0.285924	−0.142962	+	0.989728i	$0.545663\pi$
$728$	1.43026e100	0.0354611
$729$	1.56842e100	0.0370370
$730$	−1.05713e100	−0.0237775
$731$	6.01408e100	0.128855
$732$	−1.99964e101	−0.408140
$733$	−2.61177e101	−0.507861	−0.253930	−	0.967223i	$-0.581723\pi$
$733$	−2.61177e101	−0.507861	−0.253930	+	0.967223i	$0.581723\pi$
$734$	−6.02022e100	−0.111533
$735$	−3.21524e100	−0.0567562
$736$	−4.03054e101	−0.677955
$737$	−3.65723e100	−0.0586215
$738$	5.54687e100	0.0847320
$739$	5.56353e101	0.809977	0.404988	−	0.914322i	$-0.367276\pi$
$739$	5.56353e101	0.809977	0.404988	+	0.914322i	$0.367276\pi$
$740$	−6.52282e101	−0.905127
$741$	−8.38132e100	−0.110858
$742$	1.40272e100	0.0176861
$743$	−1.83886e101	−0.221027	−0.110513	−	0.993875i	$-0.535250\pi$
$743$	−1.83886e101	−0.221027	−0.110513	+	0.993875i	$0.535250\pi$
$744$	2.69682e100	0.0309038
$745$	−1.05409e102	−1.15168
$746$	−6.90830e100	−0.0719686
$747$	−3.21582e101	−0.319455
$748$	−1.56339e101	−0.148102
$749$	1.66826e102	1.50716
$750$	−1.16336e101	−0.100239
$751$	−4.12921e101	−0.339351	−0.169676	−	0.985500i	$-0.554272\pi$
$751$	−4.12921e101	−0.339351	−0.169676	+	0.985500i	$0.554272\pi$
$752$	8.83979e101	0.692961
$753$	−1.46140e102	−1.09281
$754$	2.02679e100	0.0144586
$755$	1.01304e102	0.689464
$756$	2.67471e101	0.173681
$757$	8.18442e101	0.507089	0.253544	−	0.967324i	$-0.418404\pi$
$757$	8.18442e101	0.507089	0.253544	+	0.967324i	$0.418404\pi$
$758$	3.20992e101	0.189774
$759$	−3.02137e101	−0.170460
$760$	−6.86605e101	−0.369679
$761$	3.41716e102	1.75594	0.877970	−	0.478715i	$-0.158897\pi$
$761$	3.41716e102	1.75594	0.877970	+	0.478715i	$0.158897\pi$
$762$	1.79665e101	0.0881176
$763$	7.99964e101	0.374498
$764$	6.09005e101	0.272149
$765$	4.04414e101	0.172522
$766$	−7.19707e101	−0.293113
$767$	−1.26023e101	−0.0490022
$768$	−1.15337e102	−0.428200
$769$	−2.92182e102	−1.03578	−0.517890	−	0.855447i	$-0.673282\pi$
$769$	−2.92182e102	−1.03578	−0.517890	+	0.855447i	$0.673282\pi$
$770$	6.52708e100	0.0220952
$771$	4.00964e101	0.129621
$772$	4.74530e102	1.46504
$773$	3.15899e102	0.931485	0.465743	−	0.884920i	$-0.345787\pi$
$773$	3.15899e102	0.931485	0.465743	+	0.884920i	$0.345787\pi$
$774$	−3.39679e100	−0.00956675
$775$	−3.11124e101	−0.0836996
$776$	−8.37125e101	−0.215129
$777$	2.88664e102	0.708675
$778$	−9.41711e101	−0.220873
$779$	−1.12396e103	−2.51867
$780$	2.17861e101	0.0466468
$781$	1.88430e102	0.385513
$782$	8.82707e101	0.172574
$783$	7.68536e101	0.143589
$784$	−7.20705e101	−0.128688
$785$	−4.15232e102	−0.708628
$786$	1.00619e102	0.164128
$787$	−3.97701e102	−0.620089	−0.310045	−	0.950722i	$-0.600344\pi$
$787$	−3.97701e102	−0.620089	−0.310045	+	0.950722i	$0.600344\pi$
$788$	1.79253e102	0.267169
$789$	−6.99687e102	−0.996942
$790$	5.41566e100	0.00737716
$791$	−2.39254e102	−0.311597
$792$	1.79045e101	0.0222955
$793$	7.20798e101	0.0858253
$794$	2.53447e102	0.288575
$795$	4.33240e101	0.0471733
$796$	5.99532e102	0.624308
$797$	−1.19699e103	−1.19212	−0.596060	−	0.802940i	$-0.703268\pi$
$797$	−1.19699e103	−1.19212	−0.596060	+	0.802940i	$0.703268\pi$
$798$	1.49855e102	0.142748
$799$	−6.08790e102	−0.554698
$800$	−2.75551e102	−0.240164
$801$	1.10630e102	0.0922395
$802$	1.85052e102	0.147606
$803$	−5.58580e101	−0.0426269
$804$	2.18260e102	0.159362
$805$	1.33283e103	0.931155
$806$	−4.79424e100	−0.00320498
$807$	1.15951e103	0.741760
$808$	−7.44769e102	−0.455951
$809$	−6.85039e102	−0.401368	−0.200684	−	0.979656i	$-0.564316\pi$
$809$	−6.85039e102	−0.401368	−0.200684	+	0.979656i	$0.564316\pi$
$810$	−2.28416e101	−0.0128088
$811$	5.72392e102	0.307223	0.153611	−	0.988131i	$-0.450910\pi$
$811$	5.72392e102	0.307223	0.153611	+	0.988131i	$0.450910\pi$
$812$	1.31062e103	0.673346
$813$	1.11785e103	0.549757
$814$	9.52982e101	0.0448661
$815$	−2.23118e102	−0.100563
$816$	9.06505e102	0.391174
$817$	6.88291e102	0.284373
$818$	5.58722e102	0.221031
$819$	−9.64135e101	−0.0365224
$820$	2.92159e103	1.05981
$821$	−3.44358e103	−1.19627	−0.598133	−	0.801397i	$-0.704091\pi$
$821$	−3.44358e103	−1.19627	−0.598133	+	0.801397i	$0.704091\pi$
$822$	2.39074e102	0.0795395
$823$	1.69663e103	0.540620	0.270310	−	0.962773i	$-0.412874\pi$
$823$	1.69663e103	0.540620	0.270310	+	0.962773i	$0.412874\pi$
$824$	−1.82397e103	−0.556675
$825$	−2.06559e102	−0.0603849
$826$	2.25325e102	0.0630984
$827$	3.39184e103	0.909891	0.454946	−	0.890519i	$-0.349659\pi$
$827$	3.39184e103	0.909891	0.454946	+	0.890519i	$0.349659\pi$
$828$	1.80312e103	0.463391
$829$	−3.27072e103	−0.805300	−0.402650	−	0.915354i	$-0.631911\pi$
$829$	−3.27072e103	−0.805300	−0.402650	+	0.915354i	$0.631911\pi$
$830$	4.68332e102	0.110479
$831$	−2.69959e103	−0.610185
$832$	4.59384e102	0.0994942
$833$	4.96344e102	0.103011
$834$	−7.24630e102	−0.144119
$835$	−1.61797e102	−0.0308390
$836$	−1.78925e103	−0.326850
$837$	−1.81792e102	−0.0318288
$838$	−5.43435e102	−0.0911979
$839$	−6.58084e103	−1.05860	−0.529300	−	0.848435i	$-0.677545\pi$
$839$	−6.58084e103	−1.05860	−0.529300	+	0.848435i	$0.677545\pi$
$840$	−7.89828e102	−0.121792
$841$	−2.99898e103	−0.443319
$842$	−1.42904e103	−0.202519
$843$	−4.26417e103	−0.579369
$844$	−1.11561e104	−1.45330
$845$	5.54800e103	0.692984
$846$	3.43849e102	0.0411832
$847$	−7.73009e103	−0.887817
$848$	9.71120e102	0.106960
$849$	3.51490e103	0.371270
$850$	6.03470e102	0.0611341
$851$	1.94599e104	1.89078
$852$	−1.12453e104	−1.04801
$853$	1.05269e104	0.941043	0.470522	−	0.882388i	$-0.344066\pi$
$853$	1.05269e104	0.941043	0.470522	+	0.882388i	$0.344066\pi$
$854$	−1.28876e103	−0.110514
$855$	4.62838e103	0.380743
$856$	−6.66450e103	−0.525956
$857$	1.89752e104	1.43670	0.718352	−	0.695680i	$-0.244897\pi$
$857$	1.89752e104	1.43670	0.718352	+	0.695680i	$0.244897\pi$
$858$	−3.18295e101	−0.00231223
$859$	9.55747e103	0.666171	0.333085	−	0.942897i	$-0.391910\pi$
$859$	9.55747e103	0.666171	0.333085	+	0.942897i	$0.391910\pi$
$860$	−1.78912e103	−0.119659
$861$	−1.29294e104	−0.829784
$862$	3.08366e103	0.189915
$863$	−6.27180e103	−0.370688	−0.185344	−	0.982674i	$-0.559340\pi$
$863$	−6.27180e103	−0.370688	−0.185344	+	0.982674i	$0.559340\pi$
$864$	−1.61006e103	−0.0913282
$865$	−1.03596e104	−0.563990
$866$	2.77720e103	0.145118
$867$	5.26808e103	0.264225
$868$	−3.10018e103	−0.149258
$869$	2.86160e102	0.0132253
$870$	−1.11925e103	−0.0496584
$871$	−7.86745e102	−0.0335112
$872$	−3.19577e103	−0.130689
$873$	5.64303e103	0.221568
$874$	1.01023e104	0.380859
$875$	2.71170e104	0.981649
$876$	3.33354e103	0.115880
$877$	5.51794e104	1.84201	0.921003	−	0.389554i	$-0.127371\pi$
$877$	5.51794e104	1.84201	0.921003	+	0.389554i	$0.127371\pi$
$878$	2.55230e103	0.0818233
$879$	−4.67317e103	−0.143882
$880$	4.51877e103	0.133624
$881$	−6.99895e103	−0.198787	−0.0993936	−	0.995048i	$-0.531690\pi$
$881$	−6.99895e103	−0.198787	−0.0993936	+	0.995048i	$0.531690\pi$
$882$	−2.80339e102	−0.00764801
$883$	−5.75362e104	−1.50777	−0.753886	−	0.657005i	$-0.771823\pi$
$883$	−5.75362e104	−1.50777	−0.753886	+	0.657005i	$0.771823\pi$
$884$	−3.36318e103	−0.0846632
$885$	6.95933e103	0.168299
$886$	1.09447e104	0.254276
$887$	5.25644e104	1.17329	0.586643	−	0.809846i	$-0.300449\pi$
$887$	5.25644e104	1.17329	0.586643	+	0.809846i	$0.300449\pi$
$888$	−1.15318e104	−0.247308
$889$	−4.18787e104	−0.862940
$890$	−1.61114e103	−0.0318998
$891$	−1.20693e103	−0.0229628
$892$	−5.18204e104	−0.947432
$893$	−6.96740e104	−1.22418
$894$	−9.19070e103	−0.155191
$895$	−3.25842e104	−0.528798
$896$	−3.64300e104	−0.568231
$897$	−6.49959e103	−0.0974438
$898$	7.03658e103	0.101403
$899$	−8.90788e103	−0.123397
$900$	1.23272e104	0.164155
$901$	−6.68804e103	−0.0856187
$902$	−4.26843e103	−0.0525335
$903$	7.91767e103	0.0936877
$904$	9.55793e103	0.108739
$905$	−9.47504e104	−1.03647
$906$	8.83279e103	0.0929066
$907$	1.49060e105	1.50766	0.753830	−	0.657069i	$-0.228204\pi$
$907$	1.49060e105	1.50766	0.753830	+	0.657069i	$0.228204\pi$
$908$	−3.14908e104	−0.306292
$909$	5.02047e104	0.469598
$910$	1.40411e103	0.0126308
$911$	−2.92761e103	−0.0253286	−0.0126643	−	0.999920i	$-0.504031\pi$
$911$	−2.92761e103	−0.0253286	−0.0126643	+	0.999920i	$0.504031\pi$
$912$	1.03746e105	0.863290
$913$	2.47464e104	0.198061
$914$	−1.05449e104	−0.0811807
$915$	−3.98044e104	−0.294769
$916$	1.74045e105	1.23986
$917$	−2.34537e105	−1.60731
$918$	3.52611e103	0.0232477
$919$	3.76133e104	0.238584	0.119292	−	0.992859i	$-0.461938\pi$
$919$	3.76133e104	0.238584	0.119292	+	0.992859i	$0.461938\pi$
$920$	−5.32452e104	−0.324947
$921$	8.26311e104	0.485207
$922$	−1.17110e104	−0.0661677
$923$	4.05352e104	0.220380
$924$	−2.05825e104	−0.107682
$925$	1.33039e105	0.669806
$926$	4.95625e103	0.0240139
$927$	1.22953e105	0.573336
$928$	−7.88938e104	−0.354071
$929$	1.69217e105	0.730948	0.365474	−	0.930821i	$-0.380907\pi$
$929$	1.69217e105	0.730948	0.365474	+	0.930821i	$0.380907\pi$
$930$	2.64750e103	0.0110076
$931$	5.68050e104	0.227338
$932$	3.71239e105	1.43017
$933$	−2.35035e105	−0.871634
$934$	6.48925e103	0.0231676
$935$	−3.11205e104	−0.106963
$936$	3.85161e103	0.0127453
$937$	−8.56442e103	−0.0272862	−0.0136431	−	0.999907i	$-0.504343\pi$
$937$	−8.56442e103	−0.0272862	−0.0136431	+	0.999907i	$0.504343\pi$
$938$	1.40667e104	0.0431512
$939$	1.80534e105	0.533249
$940$	1.81108e105	0.515110
$941$	−5.02109e105	−1.37520	−0.687600	−	0.726089i	$-0.741336\pi$
$941$	−5.02109e105	−1.37520	−0.687600	+	0.726089i	$0.741336\pi$
$942$	−3.62043e104	−0.0954890
$943$	−8.71615e105	−2.21391
$944$	1.55995e105	0.381598
$945$	5.32421e104	0.125437
$946$	2.61390e103	0.00593135
$947$	−2.48454e105	−0.543026	−0.271513	−	0.962435i	$-0.587524\pi$
$947$	−2.48454e105	−0.543026	−0.271513	+	0.962435i	$0.587524\pi$
$948$	−1.70777e104	−0.0359528
$949$	−1.20162e104	−0.0243678
$950$	6.90651e104	0.134918
$951$	−5.79195e105	−1.08997
$952$	1.21928e105	0.221050
$953$	5.53593e105	0.966925	0.483462	−	0.875365i	$-0.339379\pi$
$953$	5.53593e105	0.966925	0.483462	+	0.875365i	$0.339379\pi$
$954$	3.77745e103	0.00635669
$955$	1.21227e105	0.196553
$956$	−3.40870e105	−0.532517
$957$	−5.91404e104	−0.0890247
$958$	−2.70267e104	−0.0392028
$959$	−5.57264e105	−0.778933
$960$	−2.53684e105	−0.341715
$961$	−7.49265e105	−0.972647
$962$	2.05006e104	0.0256479
$963$	4.49252e105	0.541698
$964$	5.64285e105	0.655789
$965$	9.44585e105	1.05809
$966$	1.16210e105	0.125475
$967$	−1.32392e106	−1.37791	−0.688956	−	0.724803i	$-0.741931\pi$
$967$	−1.32392e106	−1.37791	−0.688956	+	0.724803i	$0.741931\pi$
$968$	3.08809e105	0.309823
$969$	−7.14495e105	−0.691043
$970$	−8.21817e104	−0.0766264
$971$	1.30256e106	1.17089	0.585445	−	0.810712i	$-0.300920\pi$
$971$	1.30256e106	1.17089	0.585445	+	0.810712i	$0.300920\pi$
$972$	7.20285e104	0.0624240
$973$	1.68906e106	1.41136
$974$	3.16721e104	0.0255173
$975$	−4.44350e104	−0.0345192
$976$	−8.92225e105	−0.668353
$977$	2.04507e106	1.47724	0.738622	−	0.674120i	$-0.235477\pi$
$977$	2.04507e106	1.47724	0.738622	+	0.674120i	$0.235477\pi$
$978$	−1.94538e104	−0.0135511
$979$	−8.51318e104	−0.0571881
$980$	−1.47657e105	−0.0956596
$981$	2.15426e105	0.134601
$982$	−7.78077e104	−0.0468883
$983$	6.32814e104	0.0367812	0.0183906	−	0.999831i	$-0.494146\pi$
$983$	6.32814e104	0.0367812	0.0183906	+	0.999831i	$0.494146\pi$
$984$	5.16514e105	0.289571
$985$	3.56816e105	0.192956
$986$	1.72781e105	0.0901292
$987$	−8.01487e105	−0.403309
$988$	−3.84905e105	−0.186845
$989$	5.33759e105	0.249964
$990$	1.75771e104	0.00794140
$991$	1.69886e106	0.740531	0.370266	−	0.928926i	$-0.379267\pi$
$991$	1.69886e106	0.740531	0.370266	+	0.928926i	$0.379267\pi$
$992$	1.86618e105	0.0784854
$993$	−1.62278e106	−0.658507
$994$	−7.24755e105	−0.283775
$995$	1.19341e106	0.450891
$996$	−1.47683e106	−0.538425
$997$	6.72137e105	0.236472	0.118236	−	0.992986i	$-0.462276\pi$
$997$	6.72137e105	0.236472	0.118236	+	0.992986i	$0.462276\pi$
$998$	−2.03789e105	−0.0691903
$999$	7.77357e105	0.254710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.72.a.b.1.4	✓	6
3.2	odd	2		9.72.a.c.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.72.a.b.1.4	✓	6	1.1	even	1	trivial
9.72.a.c.1.3		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)

\(f(q)\)	\(=\)	\(q+7.97054e9 q^{2} -5.00315e16 q^{3} -2.29765e21 q^{4} -4.57364e24 q^{5} -3.98779e26 q^{6} +9.29524e29 q^{7} -3.71335e31 q^{8} +2.50316e33 q^{9} +O(q^{10})\)	\(q+7.97054e9 q^{2} -5.00315e16 q^{3} -2.29765e21 q^{4} -4.57364e24 q^{5} -3.98779e26 q^{6} +9.29524e29 q^{7} -3.71335e31 q^{8} +2.50316e33 q^{9} -3.64544e34 q^{10} -1.92623e36 q^{11} +1.14955e38 q^{12} -4.14371e38 q^{13} +7.40881e39 q^{14} +2.28826e41 q^{15} +5.12921e42 q^{16} -3.53245e43 q^{17} +1.99515e43 q^{18} -4.04277e45 q^{19} +1.05087e46 q^{20} -4.65055e46 q^{21} -1.53531e46 q^{22} -3.13511e48 q^{23} +1.85784e48 q^{24} -2.14334e49 q^{25} -3.30276e48 q^{26} -1.25237e50 q^{27} -2.13572e51 q^{28} -6.13666e51 q^{29} +1.82387e51 q^{30} +1.45158e52 q^{31} +1.28561e53 q^{32} +9.63722e52 q^{33} -2.81555e53 q^{34} -4.25131e54 q^{35} -5.75138e54 q^{36} -6.20710e55 q^{37} -3.22231e55 q^{38} +2.07316e55 q^{39} +1.69835e56 q^{40} +2.78018e57 q^{41} -3.70674e56 q^{42} -1.70252e57 q^{43} +4.42581e57 q^{44} -1.14485e58 q^{45} -2.49885e58 q^{46} +1.72342e59 q^{47} -2.56622e59 q^{48} -1.40510e59 q^{49} -1.70836e59 q^{50} +1.76734e60 q^{51} +9.52081e59 q^{52} +1.89331e60 q^{53} -9.98205e59 q^{54} +8.80989e60 q^{55} -3.45165e61 q^{56} +2.02266e62 q^{57} -4.89125e61 q^{58} +3.04131e62 q^{59} -5.25764e62 q^{60} -1.73950e63 q^{61} +1.15699e62 q^{62} +2.32674e63 q^{63} -1.10863e64 q^{64} +1.89519e63 q^{65} +7.68139e62 q^{66} +1.89865e64 q^{67} +8.11634e64 q^{68} +1.56854e65 q^{69} -3.38853e64 q^{70} -9.78234e65 q^{71} -9.29508e64 q^{72} +2.89986e65 q^{73} -4.94740e65 q^{74} +1.07235e66 q^{75} +9.28889e66 q^{76} -1.79048e66 q^{77} +1.65242e65 q^{78} -1.48560e66 q^{79} -2.34592e67 q^{80} +6.26579e66 q^{81} +2.21595e67 q^{82} -1.28470e68 q^{83} +1.06854e68 q^{84} +1.61562e68 q^{85} -1.35700e67 q^{86} +3.07027e68 q^{87} +7.15276e67 q^{88} +4.41961e68 q^{89} -9.12511e67 q^{90} -3.85168e68 q^{91} +7.20339e69 q^{92} -7.26250e68 q^{93} +1.37366e69 q^{94} +1.84902e70 q^{95} -6.43213e69 q^{96} +2.25437e70 q^{97} -1.11994e69 q^{98} -4.82165e69 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 72903656826 q^{2} - 30\!\cdots\!42 q^{3}+ \cdots + 15\!\cdots\!94 q^{9}+O(q^{10}) \) 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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