LMFDB - Embedded newform 3.72.a.b.1.2

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			1.2
Root			$-1.03374e10$ 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)

$f(q)$	$=$	$q-7.41748e10 q^{2} -5.00315e16 q^{3} +3.14071e21 q^{4} -1.28474e25 q^{5} +3.71108e27 q^{6} -1.80308e28 q^{7} -5.78216e31 q^{8} +2.50316e33 q^{9} +O(q^{10})$	\(q-7.41748e10 q^{2} -5.00315e16 q^{3} +3.14071e21 q^{4} -1.28474e25 q^{5} +3.71108e27 q^{6} -1.80308e28 q^{7} -5.78216e31 q^{8} +2.50316e33 q^{9} +9.52956e35 q^{10} +9.59386e36 q^{11} -1.57135e38 q^{12} -3.58027e39 q^{13} +1.33743e39 q^{14} +6.42777e41 q^{15} -3.12690e42 q^{16} +3.97167e43 q^{17} -1.85671e44 q^{18} +1.44036e45 q^{19} -4.03501e46 q^{20} +9.02110e44 q^{21} -7.11622e47 q^{22} -7.47202e46 q^{23} +2.89290e48 q^{24} +1.22705e50 q^{25} +2.65565e50 q^{26} -1.25237e50 q^{27} -5.66297e49 q^{28} +8.56644e51 q^{29} -4.76779e52 q^{30} -1.40114e53 q^{31} +3.68464e53 q^{32} -4.79996e53 q^{33} -2.94598e54 q^{34} +2.31650e53 q^{35} +7.86170e54 q^{36} -1.84621e55 q^{37} -1.06838e56 q^{38} +1.79126e56 q^{39} +7.42859e56 q^{40} -1.60402e57 q^{41} -6.69138e55 q^{42} -1.56429e58 q^{43} +3.01316e58 q^{44} -3.21591e58 q^{45} +5.54236e57 q^{46} +7.88181e57 q^{47} +1.56444e59 q^{48} -1.00420e60 q^{49} -9.10162e60 q^{50} -1.98709e60 q^{51} -1.12446e61 q^{52} +2.82435e61 q^{53} +9.28941e60 q^{54} -1.23257e62 q^{55} +1.04257e60 q^{56} -7.20634e61 q^{57} -6.35414e62 q^{58} -1.10211e63 q^{59} +2.01878e63 q^{60} +7.22029e62 q^{61} +1.03930e64 q^{62} -4.51340e61 q^{63} -1.99476e64 q^{64} +4.59973e64 q^{65} +3.56036e64 q^{66} -3.01419e64 q^{67} +1.24739e65 q^{68} +3.73837e63 q^{69} -1.71826e64 q^{70} -5.43039e65 q^{71} -1.44736e65 q^{72} -2.36329e66 q^{73} +1.36942e66 q^{74} -6.13912e66 q^{75} +4.52376e66 q^{76} -1.72985e65 q^{77} -1.32867e67 q^{78} +1.15832e67 q^{79} +4.01727e67 q^{80} +6.26579e66 q^{81} +1.18978e68 q^{82} +1.12047e68 q^{83} +2.83327e66 q^{84} -5.10258e68 q^{85} +1.16031e69 q^{86} -4.28592e68 q^{87} -5.54732e68 q^{88} -1.53088e69 q^{89} +2.38540e69 q^{90} +6.45552e67 q^{91} -2.34675e68 q^{92} +7.01014e69 q^{93} -5.84632e68 q^{94} -1.85049e70 q^{95} -1.84348e70 q^{96} +3.69629e70 q^{97} +7.44863e70 q^{98} +2.40149e70 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−7.41748e10	−1.52648	−0.763241	−	0.646114i	$-0.776393\pi$
$2$	−7.41748e10	−1.52648	−0.763241	+	0.646114i	$0.776393\pi$
$3$	−5.00315e16	−0.577350
$3$	−5.00315e16	−0.577350
$4$	3.14071e21	1.33014
$5$	−1.28474e25	−1.97416	−0.987078	−	0.160242i	$-0.948772\pi$
$5$	−1.28474e25	−1.97416	−0.987078	+	0.160242i	$0.948772\pi$
$6$	3.71108e27	0.881314
$7$	−1.80308e28	−0.0179902	−0.00899508	−	0.999960i	$-0.502863\pi$
$7$	−1.80308e28	−0.0179902	−0.00899508	+	0.999960i	$0.502863\pi$
$8$	−5.78216e31	−0.503959
$9$	2.50316e33	0.333333
$10$	9.52956e35	3.01351
$11$	9.59386e36	1.02933	0.514663	−	0.857392i	$-0.327917\pi$
$11$	9.59386e36	1.02933	0.514663	+	0.857392i	$0.327917\pi$
$12$	−1.57135e38	−0.767959
$13$	−3.58027e39	−1.02077	−0.510383	−	0.859947i	$-0.670496\pi$
$13$	−3.58027e39	−1.02077	−0.510383	+	0.859947i	$0.670496\pi$
$14$	1.33743e39	0.0274617
$15$	6.42777e41	1.13978
$16$	−3.12690e42	−0.560860
$17$	3.97167e43	0.828012	0.414006	−	0.910274i	$-0.364129\pi$
$17$	3.97167e43	0.828012	0.414006	+	0.910274i	$0.364129\pi$
$18$	−1.85671e44	−0.508827
$19$	1.44036e45	0.579052	0.289526	−	0.957170i	$-0.406502\pi$
$19$	1.44036e45	0.579052	0.289526	+	0.957170i	$0.406502\pi$
$20$	−4.03501e46	−2.62591
$21$	9.02110e44	0.0103866
$22$	−7.11622e47	−1.57125
$23$	−7.47202e46	−0.0340487	−0.0170243	−	0.999855i	$-0.505419\pi$
$23$	−7.47202e46	−0.0340487	−0.0170243	+	0.999855i	$0.505419\pi$
$24$	2.89290e48	0.290961
$25$	1.22705e50	2.89729
$26$	2.65565e50	1.55818
$27$	−1.25237e50	−0.192450
$28$	−5.66297e49	−0.0239295
$29$	8.56644e51	1.04153	0.520765	−	0.853700i	$-0.325647\pi$
$29$	8.56644e51	1.04153	0.520765	+	0.853700i	$0.325647\pi$
$30$	−4.76779e52	−1.73985
$31$	−1.40114e53	−1.59640	−0.798202	−	0.602390i	$-0.794215\pi$
$31$	−1.40114e53	−1.59640	−0.798202	+	0.602390i	$0.794215\pi$
$32$	3.68464e53	1.36010
$33$	−4.79996e53	−0.594282
$34$	−2.94598e54	−1.26394
$35$	2.31650e53	0.0355154
$36$	7.86170e54	0.443381
$37$	−1.84621e55	−0.393658	−0.196829	−	0.980438i	$-0.563064\pi$
$37$	−1.84621e55	−0.393658	−0.196829	+	0.980438i	$0.563064\pi$
$38$	−1.06838e56	−0.883912
$39$	1.79126e56	0.589340
$40$	7.42859e56	0.994894
$41$	−1.60402e57	−0.894095	−0.447048	−	0.894510i	$-0.647525\pi$
$41$	−1.60402e57	−0.894095	−0.447048	+	0.894510i	$0.647525\pi$
$42$	−6.69138e55	−0.0158550
$43$	−1.56429e58	−1.60764	−0.803818	−	0.594876i	$-0.797201\pi$
$43$	−1.56429e58	−1.60764	−0.803818	+	0.594876i	$0.797201\pi$
$44$	3.01316e58	1.36915
$45$	−3.21591e58	−0.658052
$46$	5.54236e57	0.0519746
$47$	7.88181e57	0.0344470	0.0172235	−	0.999852i	$-0.494517\pi$
$47$	7.88181e57	0.0344470	0.0172235	+	0.999852i	$0.494517\pi$
$48$	1.56444e59	0.323813
$49$	−1.00420e60	−0.999676
$50$	−9.10162e60	−4.42266
$51$	−1.98709e60	−0.478053
$52$	−1.12446e61	−1.35777
$53$	2.82435e61	1.73431	0.867153	−	0.498042i	$-0.165947\pi$
$53$	2.82435e61	1.73431	0.867153	+	0.498042i	$0.165947\pi$
$54$	9.28941e60	0.293771
$55$	−1.23257e62	−2.03205
$56$	1.04257e60	0.00906631
$57$	−7.20634e61	−0.334316
$58$	−6.35414e62	−1.58987
$59$	−1.10211e63	−1.50307	−0.751537	−	0.659691i	$-0.770687\pi$
$59$	−1.10211e63	−1.50307	−0.751537	+	0.659691i	$0.770687\pi$
$60$	2.01878e63	1.51607
$61$	7.22029e62	0.301540	0.150770	−	0.988569i	$-0.451825\pi$
$61$	7.22029e62	0.301540	0.150770	+	0.988569i	$0.451825\pi$
$62$	1.03930e64	2.43688
$63$	−4.51340e61	−0.00599672
$64$	−1.99476e64	−1.51531
$65$	4.59973e64	2.01515
$66$	3.56036e64	0.907160
$67$	−3.01419e64	−0.450314	−0.225157	−	0.974322i	$-0.572290\pi$
$67$	−3.01419e64	−0.450314	−0.225157	+	0.974322i	$0.572290\pi$
$68$	1.24739e65	1.10137
$69$	3.73837e63	0.0196580
$70$	−1.71826e64	−0.0542136
$71$	−5.43039e65	−1.03552	−0.517761	−	0.855525i	$-0.673234\pi$
$71$	−5.43039e65	−1.03552	−0.517761	+	0.855525i	$0.673234\pi$
$72$	−1.44736e65	−0.167986
$73$	−2.36329e66	−1.68095	−0.840477	−	0.541846i	$-0.817725\pi$
$73$	−2.36329e66	−1.68095	−0.840477	+	0.541846i	$0.817725\pi$
$74$	1.36942e66	0.600912
$75$	−6.13912e66	−1.67275
$76$	4.52376e66	0.770223
$77$	−1.72985e65	−0.0185178
$78$	−1.32867e67	−0.899616
$79$	1.15832e67	0.498963	0.249481	−	0.968380i	$-0.419740\pi$
$79$	1.15832e67	0.498963	0.249481	+	0.968380i	$0.419740\pi$
$80$	4.01727e67	1.10723
$81$	6.26579e66	0.111111
$82$	1.18978e68	1.36482
$83$	1.12047e68	0.835848	0.417924	−	0.908482i	$-0.362758\pi$
$83$	1.12047e68	0.835848	0.417924	+	0.908482i	$0.362758\pi$
$84$	2.83327e66	0.0138157
$85$	−5.10258e68	−1.63462
$86$	1.16031e69	2.45403
$87$	−4.28592e68	−0.601327
$88$	−5.54732e68	−0.518738
$89$	−1.53088e69	−0.958511	−0.479256	−	0.877675i	$-0.659093\pi$
$89$	−1.53088e69	−0.958511	−0.479256	+	0.877675i	$0.659093\pi$
$90$	2.38540e69	1.00450
$91$	6.45552e67	0.0183638
$92$	−2.34675e68	−0.0452896
$93$	7.01014e69	0.921684
$94$	−5.84632e68	−0.0525828
$95$	−1.85049e70	−1.14314
$96$	−1.84348e70	−0.785255
$97$	3.69629e70	1.08986	0.544928	−	0.838483i	$-0.316557\pi$
$97$	3.69629e70	1.08986	0.544928	+	0.838483i	$0.316557\pi$
$98$	7.44863e70	1.52599
$99$	2.40149e70	0.343109
$100$	3.85381e71	3.85381
$101$	−2.94874e70	−0.207123	−0.103561	−	0.994623i	$-0.533024\pi$
$101$	−2.94874e70	−0.207123	−0.103561	+	0.994623i	$0.533024\pi$
$102$	1.47392e71	0.729738
$103$	4.50031e71	1.57587	0.787936	−	0.615758i	$-0.211150\pi$
$103$	4.50031e71	1.57587	0.787936	+	0.615758i	$0.211150\pi$
$104$	2.07017e71	0.514425
$105$	−1.15898e70	−0.0205048
$106$	−2.09496e72	−2.64739
$107$	8.36876e71	0.757770	0.378885	−	0.925444i	$-0.376308\pi$
$107$	8.36876e71	0.757770	0.378885	+	0.925444i	$0.376308\pi$
$108$	−3.93333e71	−0.255986
$109$	9.20192e71	0.431755	0.215878	−	0.976420i	$-0.430739\pi$
$109$	9.20192e71	0.431755	0.215878	+	0.976420i	$0.430739\pi$
$110$	9.14252e72	3.10189
$111$	9.23686e71	0.227279
$112$	5.63806e70	0.0100900
$113$	−7.06372e72	−0.922038	−0.461019	−	0.887390i	$-0.652516\pi$
$113$	−7.06372e72	−0.922038	−0.461019	+	0.887390i	$0.652516\pi$
$114$	5.34528e72	0.510327
$115$	9.59964e71	0.0672174
$116$	2.69047e73	1.38538
$117$	−8.96196e72	−0.340255
$118$	8.17491e73	2.29441
$119$	−7.16125e71	−0.0148961
$120$	−3.71664e73	−0.574402
$121$	5.16999e72	0.0595126
$122$	−5.35563e73	−0.460296
$123$	8.02518e73	0.516206
$124$	−4.40059e74	−2.12345
$125$	−1.03233e75	−3.74554
$126$	3.34780e72	0.00915388
$127$	3.50843e74	0.724571	0.362285	−	0.932067i	$-0.381997\pi$
$127$	3.50843e74	0.724571	0.362285	+	0.932067i	$0.381997\pi$
$128$	6.09596e74	0.952989
$129$	7.82639e74	0.928169
$130$	−3.41184e75	−3.07609
$131$	4.03851e74	0.277390	0.138695	−	0.990335i	$-0.455709\pi$
$131$	4.03851e74	0.277390	0.138695	+	0.990335i	$0.455709\pi$
$132$	−1.50753e75	−0.790481
$133$	−2.59709e73	−0.0104172
$134$	2.23577e75	0.687396
$135$	1.60897e75	0.379926
$136$	−2.29648e75	−0.417284
$137$	5.44716e75	0.763116	0.381558	−	0.924345i	$-0.375388\pi$
$137$	5.44716e75	0.763116	0.381558	+	0.924345i	$0.375388\pi$
$138$	−2.77293e74	−0.0300076
$139$	−8.26848e75	−0.692469	−0.346234	−	0.938148i	$-0.612540\pi$
$139$	−8.26848e75	−0.692469	−0.346234	+	0.938148i	$0.612540\pi$
$140$	7.27546e74	0.0472406
$141$	−3.94339e74	−0.0198880
$142$	4.02798e76	1.58071
$143$	−3.43486e76	−1.05070
$144$	−7.82712e75	−0.186953
$145$	−1.10057e77	−2.05614
$146$	1.75297e77	2.56595
$147$	5.02417e76	0.577163
$148$	−5.79841e76	−0.523622
$149$	2.72922e75	0.0194056	0.00970278	−	0.999953i	$-0.496911\pi$
$149$	2.72922e75	0.0194056	0.00970278	+	0.999953i	$0.496911\pi$
$150$	4.55368e77	2.55342
$151$	−6.97288e76	−0.308838	−0.154419	−	0.988005i	$-0.549351\pi$
$151$	−6.97288e76	−0.308838	−0.154419	+	0.988005i	$0.549351\pi$
$152$	−8.32838e76	−0.291819
$153$	9.94171e76	0.276004
$154$	1.28311e76	0.0282670
$155$	1.80011e78	3.15155
$156$	5.62585e77	0.783907
$157$	−8.28864e77	−0.920546	−0.460273	−	0.887777i	$-0.652248\pi$
$157$	−8.28864e77	−0.920546	−0.460273	+	0.887777i	$0.652248\pi$
$158$	−8.59184e77	−0.761657
$159$	−1.41307e78	−1.00130
$160$	−4.73382e78	−2.68505
$161$	1.34727e75	0.000612541 0
$162$	−4.64763e77	−0.169609
$163$	−3.54530e78	−1.03990	−0.519952	−	0.854195i	$-0.674050\pi$
$163$	−3.54530e78	−1.03990	−0.519952	+	0.854195i	$0.674050\pi$
$164$	−5.03778e78	−1.18928
$165$	6.16671e78	1.17320
$166$	−8.31105e78	−1.27591
$167$	5.22595e78	0.648232	0.324116	−	0.946017i	$-0.394933\pi$
$167$	5.22595e78	0.648232	0.324116	+	0.946017i	$0.394933\pi$
$168$	−5.21614e76	−0.00523444
$169$	5.16245e77	0.0419641
$170$	3.78483e79	2.49522
$171$	3.60544e78	0.193017
$172$	−4.91299e79	−2.13839
$173$	−3.00307e79	−1.06397	−0.531984	−	0.846754i	$-0.678553\pi$
$173$	−3.00307e79	−1.06397	−0.531984	+	0.846754i	$0.678553\pi$
$174$	3.17907e79	0.917914
$175$	−2.21247e78	−0.0521227
$176$	−2.99990e79	−0.577308
$177$	5.51405e79	0.867800
$178$	1.13553e80	1.46315
$179$	−3.07420e79	−0.324675	−0.162338	−	0.986735i	$-0.551903\pi$
$179$	−3.07420e79	−0.324675	−0.162338	+	0.986735i	$0.551903\pi$
$180$	−1.01003e80	−0.875304
$181$	1.59878e80	1.13815	0.569073	−	0.822287i	$-0.307302\pi$
$181$	1.59878e80	1.13815	0.569073	+	0.822287i	$0.307302\pi$
$182$	−4.78837e78	−0.0280319
$183$	−3.61242e79	−0.174094
$184$	4.32044e78	0.0171591
$185$	2.37190e80	0.777142
$186$	−5.19976e80	−1.40693
$187$	3.81036e80	0.852294
$188$	2.47545e79	0.0458195
$189$	2.25812e78	0.00346221
$190$	1.37260e81	1.74498
$191$	1.23648e81	1.30467	0.652337	−	0.757929i	$-0.273789\pi$
$191$	1.23648e81	1.30467	0.652337	+	0.757929i	$0.273789\pi$
$192$	9.98009e80	0.874864
$193$	6.51318e80	0.474797	0.237399	−	0.971412i	$-0.423705\pi$
$193$	6.51318e80	0.474797	0.237399	+	0.971412i	$0.423705\pi$
$194$	−2.74171e81	−1.66365
$195$	−2.30131e81	−1.16345
$196$	−3.15391e81	−1.32971
$197$	−2.07691e81	−0.730915	−0.365458	−	0.930828i	$-0.619087\pi$
$197$	−2.07691e81	−0.730915	−0.365458	+	0.930828i	$0.619087\pi$
$198$	−1.78130e81	−0.523749
$199$	−2.04805e80	−0.0503566	−0.0251783	−	0.999683i	$-0.508015\pi$
$199$	−2.04805e80	−0.0503566	−0.0251783	+	0.999683i	$0.508015\pi$
$200$	−7.09500e81	−1.46012
$201$	1.50805e81	0.259989
$202$	2.18722e81	0.316169
$203$	−1.54460e80	−0.0187373
$204$	−6.24088e81	−0.635879
$205$	2.06076e82	1.76508
$206$	−3.33809e82	−2.40554
$207$	−1.87036e80	−0.0113496
$208$	1.11951e82	0.572507
$209$	1.38186e82	0.596034
$210$	8.59671e80	0.0313002
$211$	−1.79862e82	−0.553239	−0.276620	−	0.960980i	$-0.589214\pi$
$211$	−1.79862e82	−0.553239	−0.276620	+	0.960980i	$0.589214\pi$
$212$	8.87049e82	2.30688
$213$	2.71691e82	0.597859
$214$	−6.20751e82	−1.15672
$215$	2.00971e83	3.17372
$216$	7.24139e81	0.0969870
$217$	2.52638e81	0.0287196
$218$	−6.82550e82	−0.659066
$219$	1.18239e83	0.970500
$220$	−3.87114e83	−2.70292
$221$	−1.42196e83	−0.845206
$222$	−6.85142e82	−0.346936
$223$	1.34688e82	0.0581440	0.0290720	−	0.999577i	$-0.490745\pi$
$223$	1.34688e82	0.0581440	0.0290720	+	0.999577i	$0.490745\pi$
$224$	−6.64372e81	−0.0244685
$225$	3.07150e83	0.965763
$226$	5.23950e83	1.40747
$227$	1.00861e83	0.231635	0.115818	−	0.993271i	$-0.463051\pi$
$227$	1.00861e83	0.231635	0.115818	+	0.993271i	$0.463051\pi$
$228$	−2.26330e83	−0.444689
$229$	−3.46235e83	−0.582386	−0.291193	−	0.956664i	$-0.594052\pi$
$229$	−3.46235e83	−0.582386	−0.291193	+	0.956664i	$0.594052\pi$
$230$	−7.12051e82	−0.102606
$231$	8.65472e81	0.0106912
$232$	−4.95325e83	−0.524888
$233$	9.74231e83	0.886190	0.443095	−	0.896475i	$-0.353880\pi$
$233$	9.74231e83	0.886190	0.443095	+	0.896475i	$0.353880\pi$
$234$	6.64752e83	0.519394
$235$	−1.01261e83	−0.0680038
$236$	−3.46143e84	−1.99930
$237$	−5.79527e83	−0.288076
$238$	5.31184e82	0.0227386
$239$	−1.00875e84	−0.372097	−0.186049	−	0.982541i	$-0.559568\pi$
$239$	−1.00875e84	−0.372097	−0.186049	+	0.982541i	$0.559568\pi$
$240$	−2.00990e84	−0.639257
$241$	−5.41291e84	−1.48534	−0.742670	−	0.669657i	$-0.766441\pi$
$241$	−5.41291e84	−1.48534	−0.742670	+	0.669657i	$0.766441\pi$
$242$	−3.83483e83	−0.0908449
$243$	−3.13487e83	−0.0641500
$244$	2.26769e84	0.401092
$245$	1.29014e85	1.97352
$246$	−5.95266e84	−0.787979
$247$	−5.15687e84	−0.591077
$248$	8.10163e84	0.804522
$249$	−5.60588e84	−0.482577
$250$	7.65732e85	5.71750
$251$	−2.12652e85	−1.37801	−0.689006	−	0.724756i	$-0.741953\pi$
$251$	−2.12652e85	−1.37801	−0.689006	+	0.724756i	$0.741953\pi$
$252$	−1.41753e83	−0.00797651
$253$	−7.16856e83	−0.0350472
$254$	−2.60237e85	−1.10604
$255$	2.55290e85	0.943750
$256$	1.88328e84	0.0605893
$257$	−1.45680e85	−0.408107	−0.204053	−	0.978960i	$-0.565412\pi$
$257$	−1.45680e85	−0.408107	−0.204053	+	0.978960i	$0.565412\pi$
$258$	−5.80521e85	−1.41683
$259$	3.32886e83	0.00708197
$260$	1.44464e86	2.68044
$261$	2.14431e85	0.347176
$262$	−2.99556e85	−0.423430
$263$	−1.16201e86	−1.43477	−0.717385	−	0.696677i	$-0.754661\pi$
$263$	−1.16201e86	−1.43477	−0.717385	+	0.696677i	$0.754661\pi$
$264$	2.77541e85	0.299494
$265$	−3.62857e86	−3.42379
$266$	1.92638e84	0.0159017
$267$	7.65925e85	0.553397
$268$	−9.46673e85	−0.598983
$269$	1.07362e86	0.595174	0.297587	−	0.954695i	$-0.403818\pi$
$269$	1.07362e86	0.595174	0.297587	+	0.954695i	$0.403818\pi$
$270$	−1.19345e86	−0.579950
$271$	−3.24003e85	−0.138083	−0.0690414	−	0.997614i	$-0.521994\pi$
$271$	−3.24003e85	−0.138083	−0.0690414	+	0.997614i	$0.521994\pi$
$272$	−1.24190e86	−0.464399
$273$	−3.22979e84	−0.0106023
$274$	−4.04042e86	−1.16488
$275$	1.17721e87	2.98226
$276$	1.17412e85	0.0261480
$277$	4.79772e86	0.939730	0.469865	−	0.882738i	$-0.344303\pi$
$277$	4.79772e86	0.939730	0.469865	+	0.882738i	$0.344303\pi$
$278$	6.13313e86	1.05704
$279$	−3.50728e86	−0.532134
$280$	−1.33944e85	−0.0178983
$281$	−5.53471e86	−0.651659	−0.325830	−	0.945429i	$-0.605644\pi$
$281$	−5.53471e86	−0.651659	−0.325830	+	0.945429i	$0.605644\pi$
$282$	2.92500e85	0.0303587
$283$	−1.95256e87	−1.78725	−0.893625	−	0.448814i	$-0.851847\pi$
$283$	−1.95256e87	−1.78725	−0.893625	+	0.448814i	$0.851847\pi$
$284$	−1.70553e87	−1.37739
$285$	9.25830e86	0.659992
$286$	2.54780e87	1.60388
$287$	2.89219e85	0.0160849
$288$	9.22324e86	0.453367
$289$	−7.23355e86	−0.314397
$290$	8.16344e87	3.13866
$291$	−1.84931e87	−0.629229
$292$	−7.42243e87	−2.23591
$293$	1.67943e87	0.448086	0.224043	−	0.974579i	$-0.428074\pi$
$293$	1.67943e87	0.448086	0.224043	+	0.974579i	$0.428074\pi$
$294$	−3.72667e87	−0.881029
$295$	1.41593e88	2.96730
$296$	1.06751e87	0.198388
$297$	−1.20150e87	−0.198094
$298$	−2.02439e86	−0.0296222
$299$	2.67518e86	0.0347557
$300$	−1.92812e88	−2.22500
$301$	2.82055e86	0.0289216
$302$	5.17212e87	0.471435
$303$	1.47530e87	0.119582
$304$	−4.50386e87	−0.324767
$305$	−9.27622e87	−0.595287
$306$	−7.37424e87	−0.421315
$307$	3.62562e88	1.84489	0.922444	−	0.386131i	$-0.126189\pi$
$307$	3.62562e88	1.84489	0.922444	+	0.386131i	$0.126189\pi$
$308$	−5.43297e86	−0.0246313
$309$	−2.25157e88	−0.909830
$310$	−1.33523e89	−4.81078
$311$	7.58148e87	0.243647	0.121823	−	0.992552i	$-0.461126\pi$
$311$	7.58148e87	0.243647	0.121823	+	0.992552i	$0.461126\pi$
$312$	−1.03574e88	−0.297003
$313$	−1.55437e88	−0.397860	−0.198930	−	0.980014i	$-0.563747\pi$
$313$	−1.55437e88	−0.397860	−0.198930	+	0.980014i	$0.563747\pi$
$314$	6.14808e88	1.40520
$315$	5.79856e86	0.0118385
$316$	3.63796e88	0.663693
$317$	1.38647e88	0.226103	0.113051	−	0.993589i	$-0.463937\pi$
$317$	1.38647e88	0.226103	0.113051	+	0.993589i	$0.463937\pi$
$318$	1.04814e89	1.52847
$319$	8.21852e88	1.07207
$320$	2.56275e89	2.99146
$321$	−4.18702e88	−0.437498
$322$	−9.99333e85	−0.000935032 0
$323$	5.72063e88	0.479462
$324$	1.96791e88	0.147794
$325$	−4.39317e89	−2.95746
$326$	2.62972e89	1.58739
$327$	−4.60386e88	−0.249274
$328$	9.27471e88	0.450587
$329$	−1.42116e86	−0.000619708 0
$330$	−4.57415e89	−1.79087
$331$	−2.48596e89	−0.874179	−0.437089	−	0.899418i	$-0.643991\pi$
$331$	−2.48596e89	−0.874179	−0.437089	+	0.899418i	$0.643991\pi$
$332$	3.51907e89	1.11180
$333$	−4.62134e88	−0.131219
$334$	−3.87634e89	−0.989514
$335$	3.87247e89	0.888991
$336$	−2.82081e87	−0.00582545
$337$	6.20222e89	1.15262	0.576310	−	0.817231i	$-0.304492\pi$
$337$	6.20222e89	1.15262	0.576310	+	0.817231i	$0.304492\pi$
$338$	−3.82923e88	−0.0640573
$339$	3.53409e89	0.532339
$340$	−1.60257e90	−2.17429
$341$	−1.34424e90	−1.64322
$342$	−2.67433e89	−0.294637
$343$	3.62190e88	0.0359745
$344$	9.04498e89	0.810183
$345$	−4.80285e88	−0.0388080
$346$	2.22752e90	1.62413
$347$	1.28300e90	0.844366	0.422183	−	0.906511i	$-0.361264\pi$
$347$	1.28300e90	0.844366	0.422183	+	0.906511i	$0.361264\pi$
$348$	−1.34609e90	−0.799852
$349$	−2.49310e90	−1.33794	−0.668970	−	0.743290i	$-0.733264\pi$
$349$	−2.49310e90	−1.33794	−0.668970	+	0.743290i	$0.733264\pi$
$350$	1.64110e89	0.0795644
$351$	4.48381e89	0.196447
$352$	3.53500e90	1.39999
$353$	−4.90622e90	−1.75689	−0.878446	−	0.477841i	$-0.841420\pi$
$353$	−4.90622e90	−1.75689	−0.878446	+	0.477841i	$0.841420\pi$
$354$	−4.09003e90	−1.32468
$355$	6.97666e90	2.04428
$356$	−4.80807e90	−1.27496
$357$	3.58288e88	0.00860025
$358$	2.28028e90	0.495611
$359$	9.68489e90	1.90652	0.953261	−	0.302149i	$-0.0977039\pi$
$359$	9.68489e90	1.90652	0.953261	+	0.302149i	$0.0977039\pi$
$360$	1.85949e90	0.331631
$361$	−4.11273e90	−0.664698
$362$	−1.18589e91	−1.73736
$363$	−2.58663e89	−0.0343596
$364$	2.02749e89	0.0244265
$365$	3.03623e91	3.31847
$366$	2.67951e90	0.265752
$367$	−9.72236e89	−0.0875238	−0.0437619	−	0.999042i	$-0.513934\pi$
$367$	−9.72236e89	−0.0875238	−0.0437619	+	0.999042i	$0.513934\pi$
$368$	2.33643e89	0.0190965
$369$	−4.01512e90	−0.298032
$370$	−1.75935e91	−1.18629
$371$	−5.09254e89	−0.0312005
$372$	2.20168e91	1.22597
$373$	7.09847e90	0.359337	0.179668	−	0.983727i	$-0.442498\pi$
$373$	7.09847e90	0.359337	0.179668	+	0.983727i	$0.442498\pi$
$374$	−2.82633e91	−1.30101
$375$	5.16493e91	2.16249
$376$	−4.55739e89	−0.0173599
$377$	−3.06701e91	−1.06316
$378$	−1.67496e89	−0.00528500
$379$	4.74171e90	0.136221	0.0681103	−	0.997678i	$-0.478303\pi$
$379$	4.74171e90	0.136221	0.0681103	+	0.997678i	$0.478303\pi$
$380$	−5.81187e91	−1.52054
$381$	−1.75532e91	−0.418331
$382$	−9.17155e91	−1.99156
$383$	−7.74364e91	−1.53246	−0.766230	−	0.642567i	$-0.777869\pi$
$383$	−7.74364e91	−1.53246	−0.766230	+	0.642567i	$0.777869\pi$
$384$	−3.04990e91	−0.550209
$385$	2.22242e90	0.0365569
$386$	−4.83113e91	−0.724769
$387$	−3.91567e91	−0.535879
$388$	1.16090e92	1.44967
$389$	9.47720e91	1.08011	0.540056	−	0.841629i	$-0.318403\pi$
$389$	9.47720e91	1.08011	0.540056	+	0.841629i	$0.318403\pi$
$390$	1.70699e92	1.77598
$391$	−2.96764e90	−0.0281927
$392$	5.80644e91	0.503796
$393$	−2.02053e91	−0.160151
$394$	1.54054e92	1.11573
$395$	−1.48815e92	−0.985030
$396$	7.54240e91	0.456384
$397$	3.39074e92	1.87599	0.937996	−	0.346645i	$-0.112679\pi$
$397$	3.39074e92	1.87599	0.937996	+	0.346645i	$0.112679\pi$
$398$	1.51914e91	0.0768684
$399$	1.29936e90	0.00601440
$400$	−3.83686e92	−1.62497
$401$	1.13718e92	0.440762	0.220381	−	0.975414i	$-0.429270\pi$
$401$	1.13718e92	0.440762	0.220381	+	0.975414i	$0.429270\pi$
$402$	−1.11859e92	−0.396869
$403$	5.01647e92	1.62955
$404$	−9.26114e91	−0.275503
$405$	−8.04993e91	−0.219351
$406$	1.14570e91	0.0286021
$407$	−1.77122e92	−0.405203
$408$	1.14897e92	0.240919
$409$	4.39695e92	0.845228	0.422614	−	0.906310i	$-0.361113\pi$
$409$	4.39695e92	0.845228	0.422614	+	0.906310i	$0.361113\pi$
$410$	−1.52856e93	−2.69437
$411$	−2.72530e92	−0.440585
$412$	1.41342e93	2.09614
$413$	1.98720e91	0.0270405
$414$	1.38734e91	0.0173249
$415$	−1.43951e93	−1.65009
$416$	−1.31920e93	−1.38835
$417$	4.13685e92	0.399797
$418$	−1.02499e93	−0.909834
$419$	1.08422e93	0.884133	0.442067	−	0.896982i	$-0.354245\pi$
$419$	1.08422e93	0.884133	0.442067	+	0.896982i	$0.354245\pi$
$420$	−3.64003e91	−0.0272744
$421$	1.06458e93	0.733098	0.366549	−	0.930399i	$-0.380539\pi$
$421$	1.06458e93	0.733098	0.366549	+	0.930399i	$0.380539\pi$
$422$	1.33412e93	0.844509
$423$	1.97294e91	0.0114823
$424$	−1.63309e93	−0.874020
$425$	4.87344e93	2.39899
$426$	−2.01526e93	−0.912621
$427$	−1.30188e91	−0.00542476
$428$	2.62839e93	1.00794
$429$	1.71851e93	0.606623
$430$	−1.49070e94	−4.84463
$431$	−8.33246e92	−0.249362	−0.124681	−	0.992197i	$-0.539791\pi$
$431$	−8.33246e92	−0.249362	−0.124681	+	0.992197i	$0.539791\pi$
$432$	3.91603e92	0.107938
$433$	−7.23024e92	−0.183583	−0.0917915	−	0.995778i	$-0.529259\pi$
$433$	−7.23024e92	−0.183583	−0.0917915	+	0.995778i	$0.529259\pi$
$434$	−1.87394e92	−0.0438399
$435$	5.50631e93	1.18711
$436$	2.89006e93	0.574297
$437$	−1.07624e92	−0.0197160
$438$	−8.77037e93	−1.48145
$439$	1.59243e93	0.248067	0.124033	−	0.992278i	$-0.460417\pi$
$439$	1.59243e93	0.248067	0.124033	+	0.992278i	$0.460417\pi$
$440$	7.12689e93	1.02407
$441$	−2.51367e93	−0.333225
$442$	1.05474e94	1.29019
$443$	1.37333e94	1.55039	0.775197	−	0.631720i	$-0.217651\pi$
$443$	1.37333e94	1.55039	0.775197	+	0.631720i	$0.217651\pi$
$444$	2.90103e93	0.302313
$445$	1.96679e94	1.89225
$446$	−9.99043e92	−0.0887558
$447$	−1.36547e92	−0.0112038
$448$	3.59671e92	0.0272607
$449$	1.04434e94	0.731305	0.365652	−	0.930752i	$-0.380846\pi$
$449$	1.04434e94	0.731305	0.365652	+	0.930752i	$0.380846\pi$
$450$	−2.27828e94	−1.47422
$451$	−1.53888e94	−0.920316
$452$	−2.21851e94	−1.22644
$453$	3.48864e93	0.178308
$454$	−7.48133e93	−0.353587
$455$	−8.29368e92	−0.0362529
$456$	4.16682e93	0.168482
$457$	−1.33750e94	−0.500342	−0.250171	−	0.968202i	$-0.580487\pi$
$457$	−1.33750e94	−0.500342	−0.250171	+	0.968202i	$0.580487\pi$
$458$	2.56819e94	0.889002
$459$	−4.97399e93	−0.159351
$460$	3.01497e93	0.0894088
$461$	−1.64596e94	−0.451895	−0.225948	−	0.974139i	$-0.572548\pi$
$461$	−1.64596e94	−0.451895	−0.225948	+	0.974139i	$0.572548\pi$
$462$	−6.41962e92	−0.0163200
$463$	−4.44222e93	−0.104586	−0.0522931	−	0.998632i	$-0.516653\pi$
$463$	−4.44222e93	−0.104586	−0.0522931	+	0.998632i	$0.516653\pi$
$464$	−2.67864e94	−0.584152
$465$	−9.00623e94	−1.81955
$466$	−7.22634e94	−1.35275
$467$	5.62422e94	0.975693	0.487847	−	0.872929i	$-0.337783\pi$
$467$	5.62422e94	0.975693	0.487847	+	0.872929i	$0.337783\pi$
$468$	−2.81470e94	−0.452589
$469$	5.43484e92	0.00810123
$470$	7.51102e93	0.103807
$471$	4.14693e94	0.531478
$472$	6.37260e94	0.757488
$473$	−1.50076e95	−1.65478
$474$	4.29863e94	0.439743
$475$	1.76739e95	1.67768
$476$	−2.24914e93	−0.0198139
$477$	7.06980e94	0.578102
$478$	7.48235e94	0.567999
$479$	2.30115e94	0.162194	0.0810970	−	0.996706i	$-0.474158\pi$
$479$	2.30115e94	0.162194	0.0810970	+	0.996706i	$0.474158\pi$
$480$	2.36841e95	1.55022
$481$	6.60991e94	0.401833
$482$	4.01502e95	2.26734
$483$	−6.74059e91	−0.000353651 0
$484$	1.62375e94	0.0791604
$485$	−4.74878e95	−2.15155
$486$	2.32528e94	0.0979238
$487$	−3.71658e95	−1.45501	−0.727504	−	0.686103i	$-0.759320\pi$
$487$	−3.71658e95	−1.45501	−0.727504	+	0.686103i	$0.759320\pi$
$488$	−4.17488e94	−0.151964
$489$	1.77377e95	0.600389
$490$	−9.56958e95	−3.01254
$491$	1.33840e95	0.391915	0.195958	−	0.980612i	$-0.437218\pi$
$491$	1.33840e95	0.391915	0.195958	+	0.980612i	$0.437218\pi$
$492$	2.52048e95	0.686629
$493$	3.40231e95	0.862398
$494$	3.82510e95	0.902268
$495$	−3.08530e95	−0.677350
$496$	4.38124e95	0.895359
$497$	9.79144e93	0.0186292
$498$	4.15815e95	0.736645
$499$	−4.75122e95	−0.783856	−0.391928	−	0.919996i	$-0.628192\pi$
$499$	−4.75122e95	−0.783856	−0.391928	+	0.919996i	$0.628192\pi$
$500$	−3.24227e96	−4.98212
$501$	−2.61462e95	−0.374257
$502$	1.57734e96	2.10351
$503$	1.16638e96	1.44936	0.724679	−	0.689087i	$-0.241988\pi$
$503$	1.16638e96	1.44936	0.724679	+	0.689087i	$0.241988\pi$
$504$	2.60972e93	0.00302210
$505$	3.78837e95	0.408892
$506$	5.31726e94	0.0534989
$507$	−2.58285e94	−0.0242280
$508$	1.10190e96	0.963784
$509$	1.38620e96	1.13069	0.565346	−	0.824854i	$-0.308743\pi$
$509$	1.38620e96	1.13069	0.565346	+	0.824854i	$0.308743\pi$
$510$	−1.89361e96	−1.44062
$511$	4.26121e94	0.0302407
$512$	−1.57906e96	−1.04548
$513$	−1.80386e95	−0.111439
$514$	1.08058e96	0.622967
$515$	−5.78174e96	−3.11101
$516$	2.45805e96	1.23460
$517$	7.56170e94	0.0354573
$518$	−2.46918e94	−0.0108105
$519$	1.50248e96	0.614282
$520$	−2.65963e96	−1.01555
$521$	1.27377e96	0.454309	0.227154	−	0.973859i	$-0.427058\pi$
$521$	1.27377e96	0.454309	0.227154	+	0.973859i	$0.427058\pi$
$522$	−1.59054e96	−0.529958
$523$	4.46663e95	0.139050	0.0695249	−	0.997580i	$-0.477852\pi$
$523$	4.46663e95	0.139050	0.0695249	+	0.997580i	$0.477852\pi$
$524$	1.26838e96	0.368968
$525$	1.10693e95	0.0300931
$526$	8.61921e96	2.19015
$527$	−5.56488e96	−1.32184
$528$	1.50090e96	0.333309
$529$	−4.81030e96	−0.998841
$530$	2.69148e97	5.22635
$531$	−2.75876e96	−0.501024
$532$	−8.15670e94	−0.0138564
$533$	5.74283e96	0.912662
$534$	−5.68123e96	−0.844750
$535$	−1.07517e97	−1.49596
$536$	1.74286e96	0.226940
$537$	1.53807e96	0.187451
$538$	−7.96353e96	−0.908521
$539$	−9.63416e96	−1.02899
$540$	5.05332e96	0.505357
$541$	3.74729e96	0.350925	0.175462	−	0.984486i	$-0.443858\pi$
$541$	3.74729e96	0.350925	0.175462	+	0.984486i	$0.443858\pi$
$542$	2.40329e96	0.210781
$543$	−7.99892e96	−0.657109
$544$	1.46342e97	1.12618
$545$	−1.18221e97	−0.852352
$546$	2.39569e95	0.0161842
$547$	−1.30252e97	−0.824580	−0.412290	−	0.911053i	$-0.635271\pi$
$547$	−1.30252e97	−0.824580	−0.412290	+	0.911053i	$0.635271\pi$
$548$	1.71080e97	1.01505
$549$	1.80735e96	0.100513
$550$	−8.73196e97	−4.55236
$551$	1.23387e97	0.603100
$552$	−2.16158e95	−0.00990683
$553$	−2.08855e95	−0.00897643
$554$	−3.55870e97	−1.43448
$555$	−1.18670e97	−0.448683
$556$	−2.59689e97	−0.921084
$557$	5.55355e97	1.84804	0.924020	−	0.382343i	$-0.124883\pi$
$557$	5.55355e97	1.84804	0.924020	+	0.382343i	$0.124883\pi$
$558$	2.60152e97	0.812293
$559$	5.60058e97	1.64102
$560$	−7.24346e95	−0.0199192
$561$	−1.90638e97	−0.492072
$562$	4.10536e97	0.994745
$563$	−2.77712e97	−0.631751	−0.315876	−	0.948801i	$-0.602298\pi$
$563$	−2.77712e97	−0.631751	−0.315876	+	0.948801i	$0.602298\pi$
$564$	−1.23851e96	−0.0264539
$565$	9.07507e97	1.82025
$566$	1.44831e98	2.72820
$567$	−1.12977e95	−0.00199891
$568$	3.13994e97	0.521861
$569$	−6.74674e97	−1.05344	−0.526719	−	0.850040i	$-0.676578\pi$
$569$	−6.74674e97	−1.05344	−0.526719	+	0.850040i	$0.676578\pi$
$570$	−6.86732e97	−1.00746
$571$	7.58495e97	1.04561	0.522806	−	0.852451i	$-0.324885\pi$
$571$	7.58495e97	1.04561	0.522806	+	0.852451i	$0.324885\pi$
$572$	−1.07879e98	−1.39759
$573$	−6.18629e97	−0.753254
$574$	−2.14527e96	−0.0245533
$575$	−9.16855e96	−0.0986488
$576$	−4.99319e97	−0.505103
$577$	1.12905e98	1.07392	0.536958	−	0.843609i	$-0.319573\pi$
$577$	1.12905e98	1.07392	0.536958	+	0.843609i	$0.319573\pi$
$578$	5.36547e97	0.479921
$579$	−3.25864e97	−0.274124
$580$	−3.45657e98	−2.73496
$581$	−2.02030e96	−0.0150370
$582$	1.37172e98	0.960506
$583$	2.70965e98	1.78517
$584$	1.36649e98	0.847133
$585$	1.15138e98	0.671717
$586$	−1.24571e98	−0.683994
$587$	−3.81225e97	−0.197028	−0.0985141	−	0.995136i	$-0.531409\pi$
$587$	−3.81225e97	−0.197028	−0.0985141	+	0.995136i	$0.531409\pi$
$588$	1.57795e98	0.767711
$589$	−2.01815e98	−0.924401
$590$	−1.05027e99	−4.52953
$591$	1.03911e98	0.421994
$592$	5.77290e97	0.220787
$593$	1.59145e98	0.573260	0.286630	−	0.958041i	$-0.407465\pi$
$593$	1.59145e98	0.573260	0.286630	+	0.958041i	$0.407465\pi$
$594$	8.91213e97	0.302387
$595$	9.20037e96	0.0294072
$596$	8.57171e96	0.0258122
$597$	1.02467e97	0.0290734
$598$	−1.98431e97	−0.0530540
$599$	2.51450e98	0.633576	0.316788	−	0.948496i	$-0.397396\pi$
$599$	2.51450e98	0.633576	0.316788	+	0.948496i	$0.397396\pi$
$600$	3.54974e98	0.842998
$601$	−1.72408e98	−0.385935	−0.192968	−	0.981205i	$-0.561811\pi$
$601$	−1.72408e98	−0.385935	−0.192968	+	0.981205i	$0.561811\pi$
$602$	−2.09214e97	−0.0441483
$603$	−7.54500e97	−0.150105
$604$	−2.18998e98	−0.410799
$605$	−6.64211e97	−0.117487
$606$	−1.09430e98	−0.182540
$607$	2.59202e98	0.407794	0.203897	−	0.978992i	$-0.434639\pi$
$607$	2.59202e98	0.407794	0.203897	+	0.978992i	$0.434639\pi$
$608$	5.30721e98	0.787570
$609$	7.72787e96	0.0108180
$610$	6.88062e98	0.908695
$611$	−2.82190e97	−0.0351624
$612$	3.12241e98	0.367125
$613$	−3.25273e98	−0.360912	−0.180456	−	0.983583i	$-0.557757\pi$
$613$	−3.25273e98	−0.360912	−0.180456	+	0.983583i	$0.557757\pi$
$614$	−2.68930e99	−2.81619
$615$	−1.03103e99	−1.01907
$616$	1.00023e97	0.00933219
$617$	−1.27158e99	−1.12000	−0.560002	−	0.828491i	$-0.689200\pi$
$617$	−1.27158e99	−1.12000	−0.560002	+	0.828491i	$0.689200\pi$
$618$	1.67010e99	1.38884
$619$	−1.34260e99	−1.05421	−0.527107	−	0.849799i	$-0.676723\pi$
$619$	−1.34260e99	−1.05421	−0.527107	+	0.849799i	$0.676723\pi$
$620$	5.65363e99	4.19201
$621$	9.35772e96	0.00655267
$622$	−5.62355e98	−0.371922
$623$	2.76031e97	0.0172438
$624$	−5.60110e98	−0.330537
$625$	8.06609e99	4.49700
$626$	1.15295e99	0.607326
$627$	−6.91366e98	−0.344120
$628$	−2.60323e99	−1.22446
$629$	−7.33252e98	−0.325953
$630$	−4.30107e97	−0.0180712
$631$	2.91634e98	0.115823	0.0579117	−	0.998322i	$-0.481556\pi$
$631$	2.91634e98	0.115823	0.0579117	+	0.998322i	$0.481556\pi$
$632$	−6.69761e98	−0.251457
$633$	8.99879e98	0.319413
$634$	−1.02841e99	−0.345142
$635$	−4.50743e99	−1.43042
$636$	−4.43804e99	−1.33188
$637$	3.59530e99	1.02044
$638$	−6.09607e99	−1.63650
$639$	−1.35931e99	−0.345174
$640$	−7.83174e99	−1.88135
$641$	−2.41429e99	−0.548693	−0.274347	−	0.961631i	$-0.588462\pi$
$641$	−2.41429e99	−0.548693	−0.274347	+	0.961631i	$0.588462\pi$
$642$	3.10571e99	0.667833
$643$	7.51971e99	1.53007	0.765035	−	0.643988i	$-0.222721\pi$
$643$	7.51971e99	1.53007	0.765035	+	0.643988i	$0.222721\pi$
$644$	4.23138e96	0.000814768 0
$645$	−1.00549e100	−1.83235
$646$	−4.24326e99	−0.731890
$647$	−8.23099e98	−0.134385	−0.0671924	−	0.997740i	$-0.521404\pi$
$647$	−8.23099e98	−0.134385	−0.0671924	+	0.997740i	$0.521404\pi$
$648$	−3.62298e98	−0.0559955
$649$	−1.05735e100	−1.54715
$650$	3.25862e100	4.51450
$651$	−1.26399e98	−0.0165812
$652$	−1.11348e100	−1.38322
$653$	1.21547e100	1.42997	0.714986	−	0.699139i	$-0.246433\pi$
$653$	1.21547e100	1.42997	0.714986	+	0.699139i	$0.246433\pi$
$654$	3.41490e99	0.380512
$655$	−5.18845e99	−0.547610
$656$	5.01562e99	0.501462
$657$	−5.91569e99	−0.560318
$658$	1.05414e97	0.000945973 0
$659$	−1.02237e100	−0.869310	−0.434655	−	0.900597i	$-0.643130\pi$
$659$	−1.02237e100	−0.869310	−0.434655	+	0.900597i	$0.643130\pi$
$660$	1.93679e100	1.56053
$661$	1.38098e100	1.05448	0.527238	−	0.849717i	$-0.323227\pi$
$661$	1.38098e100	1.05448	0.527238	+	0.849717i	$0.323227\pi$
$662$	1.84396e100	1.33442
$663$	7.11430e99	0.487980
$664$	−6.47873e99	−0.421233
$665$	3.33659e98	0.0205653
$666$	3.42787e99	0.200304
$667$	−6.40086e98	−0.0354627
$668$	1.64132e100	0.862243
$669$	−6.73863e98	−0.0335695
$670$	−2.87239e100	−1.35703
$671$	6.92704e99	0.310383
$672$	3.32396e98	0.0141269
$673$	1.76128e100	0.710058	0.355029	−	0.934855i	$-0.384471\pi$
$673$	1.76128e100	0.710058	0.355029	+	0.934855i	$0.384471\pi$
$674$	−4.60049e100	−1.75945
$675$	−1.53672e100	−0.557584
$676$	1.62138e99	0.0558183
$677$	−5.25010e100	−1.71502	−0.857512	−	0.514465i	$-0.827991\pi$
$677$	−5.25010e100	−1.71502	−0.857512	+	0.514465i	$0.827991\pi$
$678$	−2.62140e100	−0.812605
$679$	−6.66472e98	−0.0196067
$680$	2.95039e100	0.823784
$681$	−5.04622e99	−0.133735
$682$	9.97085e100	2.50834
$683$	−2.06092e100	−0.492182	−0.246091	−	0.969247i	$-0.579146\pi$
$683$	−2.06092e100	−0.492182	−0.246091	+	0.969247i	$0.579146\pi$
$684$	1.13237e100	0.256741
$685$	−6.99821e100	−1.50651
$686$	−2.68653e99	−0.0549144
$687$	1.73227e100	0.336241
$688$	4.89138e100	0.901659
$689$	−1.01119e101	−1.77032
$690$	3.56250e99	0.0592396
$691$	9.03663e100	1.42737	0.713684	−	0.700468i	$-0.247025\pi$
$691$	9.03663e100	1.42737	0.713684	+	0.700468i	$0.247025\pi$
$692$	−9.43178e100	−1.41523
$693$	−4.33009e98	−0.00617258
$694$	−9.51663e100	−1.28891
$695$	1.06229e101	1.36704
$696$	2.47819e100	0.303044
$697$	−6.37065e100	−0.740321
$698$	1.84925e101	2.04234
$699$	−4.87423e100	−0.511642
$700$	−6.94874e99	−0.0693308
$701$	−4.28600e100	−0.406502	−0.203251	−	0.979127i	$-0.565151\pi$
$701$	−4.28600e100	−0.406502	−0.203251	+	0.979127i	$0.565151\pi$
$702$	−3.32586e100	−0.299872
$703$	−2.65920e100	−0.227949
$704$	−1.91374e101	−1.55975
$705$	5.06625e99	0.0392620
$706$	3.63918e101	2.68186
$707$	5.31682e98	0.00372617
$708$	1.73180e101	1.15430
$709$	−1.74835e100	−0.110837	−0.0554187	−	0.998463i	$-0.517649\pi$
$709$	−1.74835e100	−0.110837	−0.0554187	+	0.998463i	$0.517649\pi$
$710$	−5.17492e101	−3.12056
$711$	2.89946e100	0.166321
$712$	8.85182e100	0.483051
$713$	1.04694e100	0.0543554
$714$	−2.65760e99	−0.0131281
$715$	4.41291e101	2.07425
$716$	−9.65518e100	−0.431865
$717$	5.04691e100	0.214830
$718$	−7.18375e101	−2.91027
$719$	2.40688e101	0.928066	0.464033	−	0.885818i	$-0.346402\pi$
$719$	2.40688e101	0.928066	0.464033	+	0.885818i	$0.346402\pi$
$720$	1.00558e101	0.369075
$721$	−8.11443e99	−0.0283502
$722$	3.05061e101	1.01465
$723$	2.70816e101	0.857562
$724$	5.02130e101	1.51390
$725$	1.05114e102	3.01761
$726$	1.91862e100	0.0524493
$727$	1.35006e101	0.351464	0.175732	−	0.984438i	$-0.443771\pi$
$727$	1.35006e101	0.351464	0.175732	+	0.984438i	$0.443771\pi$
$728$	−3.73268e99	−0.00925459
$729$	1.56842e100	0.0370370
$730$	−2.25211e102	−5.06558
$731$	−6.21285e101	−1.33114
$732$	−1.13456e101	−0.231571
$733$	4.53101e101	0.881056	0.440528	−	0.897739i	$-0.354791\pi$
$733$	4.53101e101	0.881056	0.440528	+	0.897739i	$0.354791\pi$
$734$	7.21154e100	0.133603
$735$	−6.45477e101	−1.13941
$736$	−2.75318e100	−0.0463096
$737$	−2.89178e101	−0.463520
$738$	2.97821e101	0.454940
$739$	−8.32551e101	−1.21209	−0.606043	−	0.795432i	$-0.707244\pi$
$739$	−8.32551e101	−1.21209	−0.606043	+	0.795432i	$0.707244\pi$
$740$	7.44947e101	1.03371
$741$	2.58006e101	0.341259
$742$	3.77738e100	0.0476269
$743$	−2.12768e101	−0.255743	−0.127871	−	0.991791i	$-0.540814\pi$
$743$	−2.12768e101	−0.255743	−0.127871	+	0.991791i	$0.540814\pi$
$744$	−4.05337e101	−0.464491
$745$	−3.50635e100	−0.0383096
$746$	−5.26528e101	−0.548520
$747$	2.80471e101	0.278616
$748$	1.19673e102	1.13367
$749$	−1.50896e100	−0.0136324
$750$	−3.83107e102	−3.30100
$751$	−5.67991e101	−0.466792	−0.233396	−	0.972382i	$-0.574984\pi$
$751$	−5.67991e101	−0.466792	−0.233396	+	0.972382i	$0.574984\pi$
$752$	−2.46456e100	−0.0193200
$753$	1.06393e102	0.795595
$754$	2.27495e102	1.62289
$755$	8.95836e101	0.609694
$756$	7.09212e99	0.00460524
$757$	8.22337e101	0.509502	0.254751	−	0.967007i	$-0.418006\pi$
$757$	8.22337e101	0.509502	0.254751	+	0.967007i	$0.418006\pi$
$758$	−3.51715e101	−0.207938
$759$	3.58654e100	0.0202345
$760$	1.06998e102	0.576096
$761$	−1.04658e102	−0.537794	−0.268897	−	0.963169i	$-0.586659\pi$
$761$	−1.04658e102	−0.537794	−0.268897	+	0.963169i	$0.586659\pi$
$762$	1.30201e102	0.638575
$763$	−1.65918e100	−0.00776735
$764$	3.88343e102	1.73540
$765$	−1.27725e102	−0.544875
$766$	5.74383e102	2.33927
$767$	3.94586e102	1.53429
$768$	−9.42233e100	−0.0349812
$769$	−9.38676e101	−0.332760	−0.166380	−	0.986062i	$-0.553208\pi$
$769$	−9.38676e101	−0.332760	−0.166380	+	0.986062i	$0.553208\pi$
$770$	−1.64847e101	−0.0558034
$771$	7.28859e101	0.235620
$772$	2.04560e102	0.631549
$773$	−8.71743e99	−0.00257049	−0.00128525	−	0.999999i	$-0.500409\pi$
$773$	−8.71743e99	−0.00257049	−0.00128525	+	0.999999i	$0.500409\pi$
$774$	2.90444e102	0.818008
$775$	−1.71927e103	−4.62524
$776$	−2.13725e102	−0.549243
$777$	−1.66548e100	−0.00408878
$778$	−7.02969e102	−1.64877
$779$	−2.31037e102	−0.517728
$780$	−7.22777e102	−1.54755
$781$	−5.20984e102	−1.06589
$782$	2.20124e101	0.0430356
$783$	−1.07283e102	−0.200442
$784$	3.14003e102	0.560679
$785$	1.06488e103	1.81730
$786$	1.49872e102	0.244467
$787$	8.49378e102	1.32433	0.662167	−	0.749356i	$-0.269637\pi$
$787$	8.49378e102	1.32433	0.662167	+	0.749356i	$0.269637\pi$
$788$	−6.52299e102	−0.972223
$789$	5.81373e102	0.828364
$790$	1.10383e103	1.50363
$791$	1.27365e101	0.0165876
$792$	−1.38858e102	−0.172913
$793$	−2.58506e102	−0.307802
$794$	−2.51507e103	−2.86367
$795$	1.81543e103	1.97673
$796$	−6.43235e101	−0.0669816
$797$	−1.35821e103	−1.35269	−0.676344	−	0.736585i	$-0.736437\pi$
$797$	−1.35821e103	−1.35269	−0.676344	+	0.736585i	$0.736437\pi$
$798$	−9.63799e100	−0.00918087
$799$	3.13039e101	0.0285226
$800$	4.52124e103	3.94061
$801$	−3.83204e102	−0.319504
$802$	−8.43501e102	−0.672814
$803$	−2.26731e103	−1.73025
$804$	4.73635e102	0.345823
$805$	−1.73089e100	−0.00120925
$806$	−3.72095e103	−2.48748
$807$	−5.37147e102	−0.343624
$808$	1.70501e102	0.104381
$809$	1.13372e103	0.664253	0.332127	−	0.943235i	$-0.392234\pi$
$809$	1.13372e103	0.664253	0.332127	+	0.943235i	$0.392234\pi$
$810$	5.97102e102	0.334835
$811$	8.73667e102	0.468928	0.234464	−	0.972125i	$-0.424667\pi$
$811$	8.73667e102	0.468928	0.234464	+	0.972125i	$0.424667\pi$
$812$	−4.85115e101	−0.0249233
$813$	1.62104e102	0.0797221
$814$	1.31380e103	0.618534
$815$	4.55480e103	2.05293
$816$	6.21342e102	0.268121
$817$	−2.25314e103	−0.930905
$818$	−3.26143e103	−1.29022
$819$	1.61592e101	0.00612125
$820$	6.47225e103	2.34781
$821$	−1.62977e103	−0.566167	−0.283084	−	0.959095i	$-0.591357\pi$
$821$	−1.62977e103	−0.566167	−0.283084	+	0.959095i	$0.591357\pi$
$822$	2.02149e103	0.672545
$823$	1.99863e103	0.636852	0.318426	−	0.947948i	$-0.396846\pi$
$823$	1.99863e103	0.636852	0.318426	+	0.947948i	$0.396846\pi$
$824$	−2.60215e103	−0.794175
$825$	−5.88979e103	−1.72181
$826$	−1.47400e102	−0.0412769
$827$	−4.47454e103	−1.20034	−0.600168	−	0.799874i	$-0.704900\pi$
$827$	−4.47454e103	−1.20034	−0.600168	+	0.799874i	$0.704900\pi$
$828$	−5.87428e101	−0.0150965
$829$	5.27092e103	1.29778	0.648889	−	0.760883i	$-0.275234\pi$
$829$	5.27092e103	1.29778	0.648889	+	0.760883i	$0.275234\pi$
$830$	1.06776e104	2.51884
$831$	−2.40037e103	−0.542554
$832$	7.14177e103	1.54678
$833$	−3.98835e103	−0.827744
$834$	−3.06850e103	−0.610283
$835$	−6.71401e103	−1.27971
$836$	4.34003e103	0.792811
$837$	1.75475e103	0.307228
$838$	−8.04214e103	−1.34961
$839$	1.96574e103	0.316211	0.158105	−	0.987422i	$-0.449461\pi$
$839$	1.96574e103	0.316211	0.158105	+	0.987422i	$0.449461\pi$
$840$	6.70141e101	0.0103336
$841$	5.73542e102	0.0847828
$842$	−7.89646e103	−1.11906
$843$	2.76910e103	0.376236
$844$	−5.64896e103	−0.735888
$845$	−6.63242e102	−0.0828436
$846$	−1.46342e102	−0.0175276
$847$	−9.32192e100	−0.00107064
$848$	−8.83147e103	−0.972703
$849$	9.76895e103	1.03187
$850$	−3.61486e104	−3.66201
$851$	1.37949e102	0.0134035
$852$	8.53303e103	0.795239
$853$	4.32736e103	0.386841	0.193420	−	0.981116i	$-0.438042\pi$
$853$	4.32736e103	0.386841	0.193420	+	0.981116i	$0.438042\pi$
$854$	9.65665e101	0.00828079
$855$	−4.63207e103	−0.381046
$856$	−4.83895e103	−0.381885
$857$	6.66223e103	0.504429	0.252215	−	0.967671i	$-0.418841\pi$
$857$	6.66223e103	0.504429	0.252215	+	0.967671i	$0.418841\pi$
$858$	−1.27470e104	−0.925998
$859$	−2.02986e104	−1.41485	−0.707423	−	0.706791i	$-0.750142\pi$
$859$	−2.02986e104	−1.41485	−0.707423	+	0.706791i	$0.750142\pi$
$860$	6.31194e104	4.22151
$861$	−1.44701e102	−0.00928663
$862$	6.18058e103	0.380646
$863$	1.32545e104	0.783396	0.391698	−	0.920094i	$-0.371888\pi$
$863$	1.32545e104	0.783396	0.391698	+	0.920094i	$0.371888\pi$
$864$	−4.61453e103	−0.261752
$865$	3.85817e104	2.10044
$866$	5.36302e103	0.280236
$867$	3.61906e103	0.181517
$868$	7.93463e102	0.0382012
$869$	1.11128e104	0.513596
$870$	−4.08429e104	−1.81211
$871$	1.07916e104	0.459666
$872$	−5.32069e103	−0.217587
$873$	9.25239e103	0.363286
$874$	7.98298e102	0.0300960
$875$	1.86138e103	0.0673830
$876$	3.71356e104	1.29090
$877$	−1.99467e104	−0.665864	−0.332932	−	0.942951i	$-0.608038\pi$
$877$	−1.99467e104	−0.665864	−0.332932	+	0.942951i	$0.608038\pi$
$878$	−1.18118e104	−0.378669
$879$	−8.40244e103	−0.258702
$880$	3.85411e104	1.13970
$881$	3.97784e102	0.0112980	0.00564901	−	0.999984i	$-0.498202\pi$
$881$	3.97784e102	0.0112980	0.00564901	+	0.999984i	$0.498202\pi$
$882$	1.86451e104	0.508662
$883$	5.31075e104	1.39172	0.695858	−	0.718179i	$-0.255024\pi$
$883$	5.31075e104	1.39172	0.695858	+	0.718179i	$0.255024\pi$
$884$	−4.46598e104	−1.12425
$885$	−7.08414e104	−1.71317
$886$	−1.01866e105	−2.36665
$887$	5.44582e104	1.21556	0.607778	−	0.794107i	$-0.292061\pi$
$887$	5.44582e104	1.21556	0.607778	+	0.794107i	$0.292061\pi$
$888$	−5.34090e103	−0.114539
$889$	−6.32599e102	−0.0130352
$890$	−1.45887e105	−2.88848
$891$	6.01131e103	0.114370
$892$	4.23015e103	0.0773400
$893$	1.13526e103	0.0199466
$894$	1.01284e103	0.0171024
$895$	3.94956e104	0.640959
$896$	−1.09915e103	−0.0171444
$897$	−1.33844e103	−0.0200662
$898$	−7.74640e104	−1.11632
$899$	−1.20028e105	−1.66270
$900$	9.64669e104	1.28460
$901$	1.12174e105	1.43603
$902$	1.14146e105	1.40484
$903$	−1.41116e103	−0.0166979
$904$	4.08436e104	0.464670
$905$	−2.05402e105	−2.24688
$906$	−2.58769e104	−0.272183
$907$	1.11106e105	1.12377	0.561886	−	0.827215i	$-0.310076\pi$
$907$	1.11106e105	1.12377	0.561886	+	0.827215i	$0.310076\pi$
$908$	3.16775e104	0.308108
$909$	−7.38115e103	−0.0690408
$910$	6.15182e103	0.0553394
$911$	4.79287e104	0.414661	0.207330	−	0.978271i	$-0.433522\pi$
$911$	4.79287e104	0.414661	0.207330	+	0.978271i	$0.433522\pi$
$912$	2.25335e104	0.187505
$913$	1.07496e105	0.860360
$914$	9.92084e104	0.763763
$915$	4.64104e104	0.343689
$916$	−1.08742e105	−0.774658
$917$	−7.28177e102	−0.00499028
$918$	3.68945e104	0.243246
$919$	−2.57767e105	−1.63504	−0.817518	−	0.575903i	$-0.804651\pi$
$919$	−2.57767e105	−1.63504	−0.817518	+	0.575903i	$0.804651\pi$
$920$	−5.55066e103	−0.0338748
$921$	−1.81395e105	−1.06515
$922$	1.22089e105	0.689809
$923$	1.94422e105	1.05703
$924$	2.71820e103	0.0142209
$925$	−2.26539e105	−1.14054
$926$	3.29500e104	0.159649
$927$	1.12650e105	0.525290
$928$	3.15643e105	1.41659
$929$	−3.79615e105	−1.63978	−0.819891	−	0.572520i	$-0.805966\pi$
$929$	−3.79615e105	−1.63978	−0.819891	+	0.572520i	$0.805966\pi$
$930$	6.68035e105	2.77750
$931$	−1.44641e105	−0.578865
$932$	3.05978e105	1.17876
$933$	−3.79313e104	−0.140669
$934$	−4.17176e105	−1.48938
$935$	−4.89534e105	−1.68256
$936$	5.18195e104	0.171475
$937$	−1.63570e105	−0.521134	−0.260567	−	0.965456i	$-0.583909\pi$
$937$	−1.63570e105	−0.521134	−0.260567	+	0.965456i	$0.583909\pi$
$938$	−4.03128e103	−0.0123664
$939$	7.77676e104	0.229705
$940$	−3.18032e104	−0.0904549
$941$	7.87522e104	0.215690	0.107845	−	0.994168i	$-0.465605\pi$
$941$	7.87522e104	0.215690	0.107845	+	0.994168i	$0.465605\pi$
$942$	−3.07598e105	−0.811290
$943$	1.19853e104	0.0304427
$944$	3.44620e105	0.843014
$945$	−2.90111e103	−0.00683494
$946$	1.11319e106	2.52599
$947$	7.23496e105	1.58129	0.790646	−	0.612274i	$-0.209745\pi$
$947$	7.23496e105	1.58129	0.790646	+	0.612274i	$0.209745\pi$
$948$	−1.82013e105	−0.383183
$949$	8.46122e105	1.71586
$950$	−1.31096e106	−2.56095
$951$	−6.93672e104	−0.130541
$952$	4.14075e103	0.00750701
$953$	5.29029e105	0.924020	0.462010	−	0.886875i	$-0.347128\pi$
$953$	5.29029e105	0.924020	0.462010	+	0.886875i	$0.347128\pi$
$954$	−5.24401e105	−0.882462
$955$	−1.58856e106	−2.57563
$956$	−3.16818e105	−0.494943
$957$	−4.11185e105	−0.618962
$958$	−1.70687e105	−0.247586
$959$	−9.82169e103	−0.0137286
$960$	−1.28219e106	−1.72712
$961$	1.19287e106	1.54850
$962$	−4.90289e105	−0.613390
$963$	2.09483e105	0.252590
$964$	−1.70004e106	−1.97572
$965$	−8.36776e105	−0.937324
$966$	4.99982e102	0.000539841 0
$967$	−1.52416e106	−1.58632	−0.793158	−	0.609015i	$-0.791565\pi$
$967$	−1.52416e106	−1.58632	−0.793158	+	0.609015i	$0.791565\pi$
$968$	−2.98937e104	−0.0299919
$969$	−2.86212e105	−0.276818
$970$	3.52240e106	3.28430
$971$	1.39780e106	1.25650	0.628252	−	0.778010i	$-0.283771\pi$
$971$	1.39780e106	1.25650	0.628252	+	0.778010i	$0.283771\pi$
$972$	−9.84573e104	−0.0853288
$973$	1.49088e104	0.0124576
$974$	2.75677e106	2.22104
$975$	2.19797e106	1.70749
$976$	−2.25771e105	−0.169122
$977$	1.95942e106	1.41537	0.707686	−	0.706527i	$-0.249739\pi$
$977$	1.95942e106	1.41537	0.707686	+	0.706527i	$0.249739\pi$
$978$	−1.31569e106	−0.916482
$979$	−1.46871e106	−0.986621
$980$	4.05196e106	2.62506
$981$	2.30338e105	0.143918
$982$	−9.92754e105	−0.598251
$983$	−9.68470e105	−0.562906	−0.281453	−	0.959575i	$-0.590816\pi$
$983$	−9.68470e105	−0.562906	−0.281453	+	0.959575i	$0.590816\pi$
$984$	−4.64028e105	−0.260147
$985$	2.66830e106	1.44294
$986$	−2.52365e106	−1.31643
$987$	7.11026e102	0.000357789 0
$988$	−1.61963e106	−0.786218
$989$	1.16884e105	0.0547378
$990$	2.28852e106	1.03396
$991$	−1.69772e106	−0.740033	−0.370016	−	0.929025i	$-0.620648\pi$
$991$	−1.69772e106	−0.740033	−0.370016	+	0.929025i	$0.620648\pi$
$992$	−5.16272e106	−2.17127
$993$	1.24376e106	0.504707
$994$	−7.26278e104	−0.0284372
$995$	2.63122e105	0.0994118
$996$	−1.76065e106	−0.641897
$997$	9.22649e105	0.324608	0.162304	−	0.986741i	$-0.448108\pi$
$997$	9.22649e105	0.324608	0.162304	+	0.986741i	$0.448108\pi$
$998$	3.52421e106	1.19654
$999$	2.31213e105	0.0757595

Twists

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

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

\(f(q)\)	\(=\)	\(q-7.41748e10 q^{2} -5.00315e16 q^{3} +3.14071e21 q^{4} -1.28474e25 q^{5} +3.71108e27 q^{6} -1.80308e28 q^{7} -5.78216e31 q^{8} +2.50316e33 q^{9} +O(q^{10})\)	\(q-7.41748e10 q^{2} -5.00315e16 q^{3} +3.14071e21 q^{4} -1.28474e25 q^{5} +3.71108e27 q^{6} -1.80308e28 q^{7} -5.78216e31 q^{8} +2.50316e33 q^{9} +9.52956e35 q^{10} +9.59386e36 q^{11} -1.57135e38 q^{12} -3.58027e39 q^{13} +1.33743e39 q^{14} +6.42777e41 q^{15} -3.12690e42 q^{16} +3.97167e43 q^{17} -1.85671e44 q^{18} +1.44036e45 q^{19} -4.03501e46 q^{20} +9.02110e44 q^{21} -7.11622e47 q^{22} -7.47202e46 q^{23} +2.89290e48 q^{24} +1.22705e50 q^{25} +2.65565e50 q^{26} -1.25237e50 q^{27} -5.66297e49 q^{28} +8.56644e51 q^{29} -4.76779e52 q^{30} -1.40114e53 q^{31} +3.68464e53 q^{32} -4.79996e53 q^{33} -2.94598e54 q^{34} +2.31650e53 q^{35} +7.86170e54 q^{36} -1.84621e55 q^{37} -1.06838e56 q^{38} +1.79126e56 q^{39} +7.42859e56 q^{40} -1.60402e57 q^{41} -6.69138e55 q^{42} -1.56429e58 q^{43} +3.01316e58 q^{44} -3.21591e58 q^{45} +5.54236e57 q^{46} +7.88181e57 q^{47} +1.56444e59 q^{48} -1.00420e60 q^{49} -9.10162e60 q^{50} -1.98709e60 q^{51} -1.12446e61 q^{52} +2.82435e61 q^{53} +9.28941e60 q^{54} -1.23257e62 q^{55} +1.04257e60 q^{56} -7.20634e61 q^{57} -6.35414e62 q^{58} -1.10211e63 q^{59} +2.01878e63 q^{60} +7.22029e62 q^{61} +1.03930e64 q^{62} -4.51340e61 q^{63} -1.99476e64 q^{64} +4.59973e64 q^{65} +3.56036e64 q^{66} -3.01419e64 q^{67} +1.24739e65 q^{68} +3.73837e63 q^{69} -1.71826e64 q^{70} -5.43039e65 q^{71} -1.44736e65 q^{72} -2.36329e66 q^{73} +1.36942e66 q^{74} -6.13912e66 q^{75} +4.52376e66 q^{76} -1.72985e65 q^{77} -1.32867e67 q^{78} +1.15832e67 q^{79} +4.01727e67 q^{80} +6.26579e66 q^{81} +1.18978e68 q^{82} +1.12047e68 q^{83} +2.83327e66 q^{84} -5.10258e68 q^{85} +1.16031e69 q^{86} -4.28592e68 q^{87} -5.54732e68 q^{88} -1.53088e69 q^{89} +2.38540e69 q^{90} +6.45552e67 q^{91} -2.34675e68 q^{92} +7.01014e69 q^{93} -5.84632e68 q^{94} -1.85049e70 q^{95} -1.84348e70 q^{96} +3.69629e70 q^{97} +7.44863e70 q^{98} +2.40149e70 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 72903656826 q^{2} - 30\!\cdots\!42 q^{3}+ \cdots + 15\!\cdots\!94 q^{9}+O(q^{10}) \) 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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