LMFDB - Embedded newform 3.72.a.b.1.1

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			1.1
Root			$-1.38952e10$ 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)

$f(q)$	$=$	$q-9.55218e10 q^{2} -5.00315e16 q^{3} +6.76322e21 q^{4} +1.07436e25 q^{5} +4.77910e27 q^{6} +6.00629e29 q^{7} -4.20491e32 q^{8} +2.50316e33 q^{9} +O(q^{10})$	\(q-9.55218e10 q^{2} -5.00315e16 q^{3} +6.76322e21 q^{4} +1.07436e25 q^{5} +4.77910e27 q^{6} +6.00629e29 q^{7} -4.20491e32 q^{8} +2.50316e33 q^{9} -1.02625e36 q^{10} -5.00889e36 q^{11} -3.38375e38 q^{12} -1.84599e39 q^{13} -5.73732e40 q^{14} -5.37518e41 q^{15} +2.41968e43 q^{16} +4.60184e43 q^{17} -2.39106e44 q^{18} -3.59368e45 q^{19} +7.26612e46 q^{20} -3.00504e46 q^{21} +4.78458e47 q^{22} -3.60035e47 q^{23} +2.10378e49 q^{24} +7.30729e49 q^{25} +1.76332e50 q^{26} -1.25237e50 q^{27} +4.06219e51 q^{28} +2.60359e51 q^{29} +5.13447e52 q^{30} -6.00487e52 q^{31} -1.31847e54 q^{32} +2.50603e53 q^{33} -4.39576e54 q^{34} +6.45291e54 q^{35} +1.69294e55 q^{36} -9.09423e54 q^{37} +3.43275e56 q^{38} +9.23578e55 q^{39} -4.51758e57 q^{40} +2.33340e57 q^{41} +2.87047e57 q^{42} +9.88722e57 q^{43} -3.38763e58 q^{44} +2.68929e58 q^{45} +3.43911e58 q^{46} +8.25094e58 q^{47} -1.21060e60 q^{48} -6.43769e59 q^{49} -6.98005e60 q^{50} -2.30237e60 q^{51} -1.24848e61 q^{52} -5.19654e59 q^{53} +1.19628e61 q^{54} -5.38134e61 q^{55} -2.52559e62 q^{56} +1.79798e62 q^{57} -2.48699e62 q^{58} -1.73450e62 q^{59} -3.63535e63 q^{60} +3.56730e63 q^{61} +5.73596e63 q^{62} +1.50347e63 q^{63} +6.88091e64 q^{64} -1.98326e64 q^{65} -2.39380e64 q^{66} -1.11521e65 q^{67} +3.11233e65 q^{68} +1.80131e64 q^{69} -6.16393e65 q^{70} +2.19894e65 q^{71} -1.05255e66 q^{72} +1.58732e66 q^{73} +8.68697e65 q^{74} -3.65595e66 q^{75} -2.43049e67 q^{76} -3.00849e66 q^{77} -8.82218e66 q^{78} +4.62485e66 q^{79} +2.59960e68 q^{80} +6.26579e66 q^{81} -2.22891e68 q^{82} +2.07787e68 q^{83} -2.03238e68 q^{84} +4.94403e68 q^{85} -9.44445e68 q^{86} -1.30262e68 q^{87} +2.10619e69 q^{88} +1.63858e69 q^{89} -2.56885e69 q^{90} -1.10876e69 q^{91} -2.43499e69 q^{92} +3.00433e69 q^{93} -7.88144e69 q^{94} -3.86090e70 q^{95} +6.59649e70 q^{96} +1.45726e70 q^{97} +6.14940e70 q^{98} -1.25380e70 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.55218e10	−1.96579	−0.982896	−	0.184163i	$-0.941043\pi$
$2$	−9.55218e10	−1.96579	−0.982896	+	0.184163i	$0.941043\pi$
$3$	−5.00315e16	−0.577350
$3$	−5.00315e16	−0.577350
$4$	6.76322e21	2.86434
$5$	1.07436e25	1.65087	0.825437	−	0.564494i	$-0.190929\pi$
$5$	1.07436e25	1.65087	0.825437	+	0.564494i	$0.190929\pi$
$6$	4.77910e27	1.13495
$7$	6.00629e29	0.599275	0.299638	−	0.954053i	$-0.403134\pi$
$7$	6.00629e29	0.599275	0.299638	+	0.954053i	$0.403134\pi$
$8$	−4.20491e32	−3.66490
$9$	2.50316e33	0.333333
$10$	−1.02625e36	−3.24527
$11$	−5.00889e36	−0.537404	−0.268702	−	0.963223i	$-0.586595\pi$
$11$	−5.00889e36	−0.537404	−0.268702	+	0.963223i	$0.586595\pi$
$12$	−3.38375e38	−1.65373
$13$	−1.84599e39	−0.526309	−0.263154	−	0.964754i	$-0.584763\pi$
$13$	−1.84599e39	−0.526309	−0.263154	+	0.964754i	$0.584763\pi$
$14$	−5.73732e40	−1.17805
$15$	−5.37518e41	−0.953132
$16$	2.41968e43	4.34009
$17$	4.60184e43	0.959389	0.479695	−	0.877435i	$-0.340747\pi$
$17$	4.60184e43	0.959389	0.479695	+	0.877435i	$0.340747\pi$
$18$	−2.39106e44	−0.655264
$19$	−3.59368e45	−1.44473	−0.722366	−	0.691511i	$-0.756945\pi$
$19$	−3.59368e45	−1.44473	−0.722366	+	0.691511i	$0.756945\pi$
$20$	7.26612e46	4.72866
$21$	−3.00504e46	−0.345992
$22$	4.78458e47	1.05643
$23$	−3.60035e47	−0.164061	−0.0820306	−	0.996630i	$-0.526141\pi$
$23$	−3.60035e47	−0.164061	−0.0820306	+	0.996630i	$0.526141\pi$
$24$	2.10378e49	2.11593
$25$	7.30729e49	1.72538
$26$	1.76332e50	1.03461
$27$	−1.25237e50	−0.192450
$28$	4.06219e51	1.71653
$29$	2.60359e51	0.316551	0.158275	−	0.987395i	$-0.449407\pi$
$29$	2.60359e51	0.316551	0.158275	+	0.987395i	$0.449407\pi$
$30$	5.13447e52	1.87366
$31$	−6.00487e52	−0.684169	−0.342084	−	0.939669i	$-0.611133\pi$
$31$	−6.00487e52	−0.684169	−0.342084	+	0.939669i	$0.611133\pi$
$32$	−1.31847e54	−4.86681
$33$	2.50603e53	0.310271
$34$	−4.39576e54	−1.88596
$35$	6.45291e54	0.989328
$36$	1.69294e55	0.954779
$37$	−9.09423e54	−0.193912	−0.0969560	−	0.995289i	$-0.530911\pi$
$37$	−9.09423e54	−0.193912	−0.0969560	+	0.995289i	$0.530911\pi$
$38$	3.43275e56	2.84004
$39$	9.23578e55	0.303864
$40$	−4.51758e57	−6.05028
$41$	2.33340e57	1.30066	0.650328	−	0.759654i	$-0.274632\pi$
$41$	2.33340e57	1.30066	0.650328	+	0.759654i	$0.274632\pi$
$42$	2.87047e57	0.680147
$43$	9.88722e57	1.01612	0.508059	−	0.861322i	$-0.330363\pi$
$43$	9.88722e57	1.01612	0.508059	+	0.861322i	$0.330363\pi$
$44$	−3.38763e58	−1.53931
$45$	2.68929e58	0.550291
$46$	3.43911e58	0.322510
$47$	8.25094e58	0.360603	0.180301	−	0.983611i	$-0.442293\pi$
$47$	8.25094e58	0.360603	0.180301	+	0.983611i	$0.442293\pi$
$48$	−1.21060e60	−2.50575
$49$	−6.43769e59	−0.640869
$50$	−6.98005e60	−3.39175
$51$	−2.30237e60	−0.553904
$52$	−1.24848e61	−1.50753
$53$	−5.19654e59	−0.0319096	−0.0159548	−	0.999873i	$-0.505079\pi$
$53$	−5.19654e59	−0.0319096	−0.0159548	+	0.999873i	$0.505079\pi$
$54$	1.19628e61	0.378317
$55$	−5.38134e61	−0.887187
$56$	−2.52559e62	−2.19628
$57$	1.79798e62	0.834116
$58$	−2.48699e62	−0.622273
$59$	−1.73450e62	−0.236553	−0.118276	−	0.992981i	$-0.537737\pi$
$59$	−1.73450e62	−0.236553	−0.118276	+	0.992981i	$0.537737\pi$
$60$	−3.63535e63	−2.73009
$61$	3.56730e63	1.48981	0.744904	−	0.667172i	$-0.232495\pi$
$61$	3.56730e63	1.48981	0.744904	+	0.667172i	$0.232495\pi$
$62$	5.73596e63	1.34493
$63$	1.50347e63	0.199758
$64$	6.88091e64	5.22705
$65$	−1.98326e64	−0.868869
$66$	−2.39380e64	−0.609927
$67$	−1.11521e65	−1.66611	−0.833053	−	0.553194i	$-0.813409\pi$
$67$	−1.11521e65	−1.66611	−0.833053	+	0.553194i	$0.813409\pi$
$68$	3.11233e65	2.74801
$69$	1.80131e64	0.0947208
$70$	−6.16393e65	−1.94481
$71$	2.19894e65	0.419316	0.209658	−	0.977775i	$-0.432765\pi$
$71$	2.19894e65	0.419316	0.209658	+	0.977775i	$0.432765\pi$
$72$	−1.05255e66	−1.22163
$73$	1.58732e66	1.12903	0.564513	−	0.825424i	$-0.309064\pi$
$73$	1.58732e66	1.12903	0.564513	+	0.825424i	$0.309064\pi$
$74$	8.68697e65	0.381190
$75$	−3.65595e66	−0.996151
$76$	−2.43049e67	−4.13820
$77$	−3.00849e66	−0.322053
$78$	−8.82218e66	−0.597334
$79$	4.62485e66	0.199221	0.0996107	−	0.995026i	$-0.468240\pi$
$79$	4.62485e66	0.199221	0.0996107	+	0.995026i	$0.468240\pi$
$80$	2.59960e68	7.16494
$81$	6.26579e66	0.111111
$82$	−2.22891e68	−2.55682
$83$	2.07787e68	1.55005	0.775025	−	0.631930i	$-0.217737\pi$
$83$	2.07787e68	1.55005	0.775025	+	0.631930i	$0.217737\pi$
$84$	−2.03238e68	−0.991036
$85$	4.94403e68	1.58383
$86$	−9.44445e68	−1.99748
$87$	−1.30262e68	−0.182761
$88$	2.10619e69	1.96953
$89$	1.63858e69	1.02594	0.512971	−	0.858406i	$-0.328545\pi$
$89$	1.63858e69	1.02594	0.512971	+	0.858406i	$0.328545\pi$
$90$	−2.56885e69	−1.08176
$91$	−1.10876e69	−0.315404
$92$	−2.43499e69	−0.469927
$93$	3.00433e69	0.395005
$94$	−7.88144e69	−0.708870
$95$	−3.86090e70	−2.38507
$96$	6.59649e70	2.80985
$97$	1.45726e70	0.429677	0.214838	−	0.976650i	$-0.431078\pi$
$97$	1.45726e70	0.429677	0.214838	+	0.976650i	$0.431078\pi$
$98$	6.14940e70	1.25982
$99$	−1.25380e70	−0.179135
$100$	4.94208e71	4.94208
$101$	−1.45756e70	−0.102381	−0.0511903	−	0.998689i	$-0.516301\pi$
$101$	−1.45756e70	−0.102381	−0.0511903	+	0.998689i	$0.516301\pi$
$102$	2.19927e71	1.08886
$103$	−3.12473e71	−1.09419	−0.547093	−	0.837072i	$-0.684265\pi$
$103$	−3.12473e71	−1.09419	−0.547093	+	0.837072i	$0.684265\pi$
$104$	7.76222e71	1.92887
$105$	−3.22849e71	−0.571189
$106$	4.96383e70	0.0627276
$107$	−1.70184e71	−0.154097	−0.0770485	−	0.997027i	$-0.524550\pi$
$107$	−1.70184e71	−0.154097	−0.0770485	+	0.997027i	$0.524550\pi$
$108$	−8.47004e71	−0.551242
$109$	−3.05749e72	−1.43458	−0.717290	−	0.696775i	$-0.754618\pi$
$109$	−3.05749e72	−1.43458	−0.717290	+	0.696775i	$0.754618\pi$
$110$	5.14035e72	1.74402
$111$	4.54998e71	0.111955
$112$	1.45333e73	2.60091
$113$	1.29429e73	1.68946	0.844730	−	0.535193i	$-0.179761\pi$
$113$	1.29429e73	1.68946	0.844730	+	0.535193i	$0.179761\pi$
$114$	−1.71746e73	−1.63970
$115$	−3.86806e72	−0.270844
$116$	1.76087e73	0.906708
$117$	−4.62080e72	−0.175436
$118$	1.65683e73	0.465014
$119$	2.76400e73	0.574938
$120$	2.26021e74	3.49313
$121$	−6.17832e73	−0.711196
$122$	−3.40755e74	−2.92865
$123$	−1.16744e74	−0.750934
$124$	−4.06123e74	−1.95969
$125$	3.30056e74	1.19752
$126$	−1.43614e74	−0.392683
$127$	2.10261e73	0.0434238	0.0217119	−	0.999764i	$-0.493088\pi$
$127$	2.10261e73	0.0434238	0.0217119	+	0.999764i	$0.493088\pi$
$128$	−3.45962e75	−5.40848
$129$	−4.94673e74	−0.586656
$130$	1.89444e75	1.70802
$131$	1.40662e75	0.966153	0.483077	−	0.875578i	$-0.339519\pi$
$131$	1.40662e75	0.966153	0.483077	+	0.875578i	$0.339519\pi$
$132$	1.69488e75	0.888720
$133$	−2.15847e75	−0.865792
$134$	1.06527e76	3.27522
$135$	−1.34549e75	−0.317711
$136$	−1.93503e76	−3.51606
$137$	−1.63089e75	−0.228477	−0.114239	−	0.993453i	$-0.536443\pi$
$137$	−1.63089e75	−0.228477	−0.114239	+	0.993453i	$0.536443\pi$
$138$	−1.72064e75	−0.186201
$139$	−8.34063e75	−0.698511	−0.349256	−	0.937028i	$-0.613565\pi$
$139$	−8.34063e75	−0.698511	−0.349256	+	0.937028i	$0.613565\pi$
$140$	4.36425e76	2.83377
$141$	−4.12807e75	−0.208194
$142$	−2.10046e76	−0.824287
$143$	9.24637e75	0.282841
$144$	6.05684e76	1.44670
$145$	2.79719e76	0.522586
$146$	−1.51624e77	−2.21943
$147$	3.22088e76	0.370006
$148$	−6.15063e76	−0.555429
$149$	−1.22812e77	−0.873228	−0.436614	−	0.899649i	$-0.643822\pi$
$149$	−1.22812e77	−0.873228	−0.436614	+	0.899649i	$0.643822\pi$
$150$	3.49223e77	1.95823
$151$	−2.17660e77	−0.964043	−0.482021	−	0.876159i	$-0.660097\pi$
$151$	−2.17660e77	−0.964043	−0.482021	+	0.876159i	$0.660097\pi$
$152$	1.51111e78	5.29479
$153$	1.15191e77	0.319796
$154$	2.87376e77	0.633089
$155$	−6.45138e77	−1.12948
$156$	6.24636e77	0.870370
$157$	1.34612e78	1.49501	0.747506	−	0.664255i	$-0.231251\pi$
$157$	1.34612e78	1.49501	0.747506	+	0.664255i	$0.231251\pi$
$158$	−4.41774e77	−0.391628
$159$	2.59991e76	0.0184230
$160$	−1.41650e79	−8.03449
$161$	−2.16247e77	−0.0983178
$162$	−5.98519e77	−0.218421
$163$	−1.43941e78	−0.422207	−0.211103	−	0.977464i	$-0.567706\pi$
$163$	−1.43941e78	−0.422207	−0.211103	+	0.977464i	$0.567706\pi$
$164$	1.57813e79	3.72552
$165$	2.69237e78	0.512218
$166$	−1.98482e79	−3.04708
$167$	8.33788e78	1.03424	0.517119	−	0.855913i	$-0.327004\pi$
$167$	8.33788e78	1.03424	0.517119	+	0.855913i	$0.327004\pi$
$168$	1.26359e79	1.26802
$169$	−8.89438e78	−0.722999
$170$	−4.72262e79	−3.11348
$171$	−8.99555e78	−0.481577
$172$	6.68695e79	2.91050
$173$	3.97555e79	1.40851	0.704256	−	0.709946i	$-0.251281\pi$
$173$	3.97555e79	1.40851	0.704256	+	0.709946i	$0.251281\pi$
$174$	1.24428e79	0.359270
$175$	4.38897e79	1.03398
$176$	−1.21199e80	−2.33238
$177$	8.67798e78	0.136574
$178$	−1.56520e80	−2.01679
$179$	1.00778e80	1.06435	0.532175	−	0.846634i	$-0.321375\pi$
$179$	1.00778e80	1.06435	0.532175	+	0.846634i	$0.321375\pi$
$180$	1.81882e80	1.57622
$181$	1.71533e79	0.122112	0.0610558	−	0.998134i	$-0.480553\pi$
$181$	1.71533e79	0.122112	0.0610558	+	0.998134i	$0.480553\pi$
$182$	1.05910e80	0.620018
$183$	−1.78477e80	−0.860141
$184$	1.51391e80	0.601268
$185$	−9.77046e79	−0.320124
$186$	−2.86979e80	−0.776498
$187$	−2.30501e80	−0.515580
$188$	5.58029e80	1.03289
$189$	−7.52209e79	−0.115331
$190$	3.68800e81	4.68855
$191$	1.04157e81	1.09902	0.549510	−	0.835487i	$-0.314815\pi$
$191$	1.04157e81	1.09902	0.549510	+	0.835487i	$0.314815\pi$
$192$	−3.44262e81	−3.01784
$193$	1.06215e81	0.774286	0.387143	−	0.922020i	$-0.373462\pi$
$193$	1.06215e81	0.774286	0.387143	+	0.922020i	$0.373462\pi$
$194$	−1.39200e81	−0.844655
$195$	9.92253e80	0.501642
$196$	−4.35396e81	−1.83567
$197$	−1.09026e81	−0.383688	−0.191844	−	0.981425i	$-0.561447\pi$
$197$	−1.09026e81	−0.383688	−0.191844	+	0.981425i	$0.561447\pi$
$198$	1.19766e81	0.352142
$199$	3.82995e81	0.941691	0.470845	−	0.882216i	$-0.343949\pi$
$199$	3.82995e81	0.941691	0.470845	+	0.882216i	$0.343949\pi$
$200$	−3.07265e82	−6.32336
$201$	5.57958e81	0.961926
$202$	1.39229e81	0.201259
$203$	1.56379e81	0.189701
$204$	−1.55715e82	−1.58657
$205$	2.50691e82	2.14722
$206$	2.98480e82	2.15094
$207$	−9.01223e80	−0.0546871
$208$	−4.46671e82	−2.28423
$209$	1.80004e82	0.776405
$210$	3.08391e82	1.12284
$211$	5.70488e81	0.175477	0.0877383	−	0.996144i	$-0.472036\pi$
$211$	5.70488e81	0.175477	0.0877383	+	0.996144i	$0.472036\pi$
$212$	−3.51454e81	−0.0913998
$213$	−1.10016e82	−0.242092
$214$	1.62563e82	0.302923
$215$	1.06224e83	1.67748
$216$	5.26609e82	0.705310
$217$	−3.60670e82	−0.410005
$218$	2.92057e83	2.82008
$219$	−7.94162e82	−0.651843
$220$	−3.63952e83	−2.54120
$221$	−8.49496e82	−0.504935
$222$	−4.34622e82	−0.220080
$223$	3.59928e83	1.55379	0.776897	−	0.629628i	$-0.216793\pi$
$223$	3.59928e83	1.55379	0.776897	+	0.629628i	$0.216793\pi$
$224$	−7.91909e83	−2.91656
$225$	1.82913e83	0.575128
$226$	−1.23633e84	−3.32113
$227$	6.98511e83	1.60419	0.802094	−	0.597198i	$-0.203719\pi$
$227$	6.98511e83	1.60419	0.802094	+	0.597198i	$0.203719\pi$
$228$	1.21601e84	2.38919
$229$	1.01227e84	1.70270	0.851349	−	0.524600i	$-0.175785\pi$
$229$	1.01227e84	1.70270	0.851349	+	0.524600i	$0.175785\pi$
$230$	3.69484e83	0.532424
$231$	1.50519e83	0.185937
$232$	−1.09479e84	−1.16013
$233$	−3.33538e83	−0.303396	−0.151698	−	0.988427i	$-0.548474\pi$
$233$	−3.33538e83	−0.303396	−0.151698	+	0.988427i	$0.548474\pi$
$234$	4.41387e83	0.344871
$235$	8.86446e83	0.595310
$236$	−1.17308e84	−0.677567
$237$	−2.31389e83	−0.115021
$238$	−2.64022e84	−1.13021
$239$	−4.53746e84	−1.67374	−0.836869	−	0.547402i	$-0.815617\pi$
$239$	−4.53746e84	−1.67374	−0.836869	+	0.547402i	$0.815617\pi$
$240$	−1.30062e85	−4.13668
$241$	−3.25077e84	−0.892032	−0.446016	−	0.895025i	$-0.647158\pi$
$241$	−3.25077e84	−0.892032	−0.446016	+	0.895025i	$0.647158\pi$
$242$	5.90164e84	1.39806
$243$	−3.13487e83	−0.0641500
$244$	2.41264e85	4.26731
$245$	−6.91639e84	−1.05799
$246$	1.11516e85	1.47618
$247$	6.63391e84	0.760375
$248$	2.52499e85	2.50741
$249$	−1.03959e85	−0.894922
$250$	−3.15275e85	−2.35407
$251$	−1.91946e84	−0.124383	−0.0621917	−	0.998064i	$-0.519809\pi$
$251$	−1.91946e84	−0.124383	−0.0621917	+	0.998064i	$0.519809\pi$
$252$	1.01683e85	0.572175
$253$	1.80337e84	0.0881673
$254$	−2.00845e84	−0.0853620
$255$	−2.47357e85	−0.914425
$256$	1.67999e86	5.40489
$257$	−3.04149e85	−0.852042	−0.426021	−	0.904713i	$-0.640085\pi$
$257$	−3.04149e85	−0.852042	−0.426021	+	0.904713i	$0.640085\pi$
$258$	4.72520e85	1.15324
$259$	−5.46226e84	−0.116207
$260$	−1.34132e86	−2.48873
$261$	6.51719e84	0.105517
$262$	−1.34363e86	−1.89926
$263$	1.25294e85	0.154704	0.0773518	−	0.997004i	$-0.475354\pi$
$263$	1.25294e85	0.154704	0.0773518	+	0.997004i	$0.475354\pi$
$264$	−1.05376e86	−1.13711
$265$	−5.58295e84	−0.0526787
$266$	2.06181e86	1.70197
$267$	−8.19808e85	−0.592328
$268$	−7.54244e86	−4.77229
$269$	−1.50122e84	−0.00832219	−0.00416109	−	0.999991i	$-0.501325\pi$
$269$	−1.50122e84	−0.00832219	−0.00416109	+	0.999991i	$0.501325\pi$
$270$	1.28524e86	0.624553
$271$	−1.67332e86	−0.713129	−0.356564	−	0.934271i	$-0.616052\pi$
$271$	−1.67332e86	−0.713129	−0.356564	+	0.934271i	$0.616052\pi$
$272$	1.11350e87	4.16383
$273$	5.54728e85	0.182098
$274$	1.55785e86	0.449139
$275$	−3.66014e86	−0.927229
$276$	1.21827e86	0.271312
$277$	7.73635e86	1.51532	0.757660	−	0.652649i	$-0.226342\pi$
$277$	7.73635e86	1.51532	0.757660	+	0.652649i	$0.226342\pi$
$278$	7.96711e86	1.37313
$279$	−1.50311e86	−0.228056
$280$	−2.71339e87	−3.62578
$281$	−1.47974e87	−1.74226	−0.871129	−	0.491055i	$-0.836611\pi$
$281$	−1.47974e87	−1.74226	−0.871129	+	0.491055i	$0.836611\pi$
$282$	3.94321e86	0.409266
$283$	1.06238e87	0.972439	0.486219	−	0.873837i	$-0.338376\pi$
$283$	1.06238e87	0.972439	0.486219	+	0.873837i	$0.338376\pi$
$284$	1.48719e87	1.20106
$285$	1.93167e87	1.37702
$286$	−8.83229e86	−0.556006
$287$	1.40151e87	0.779451
$288$	−3.30032e87	−1.62227
$289$	−1.83077e86	−0.0795719
$290$	−2.67192e87	−1.02729
$291$	−7.29092e86	−0.248074
$292$	1.07354e88	3.23391
$293$	2.21777e87	0.591719	0.295860	−	0.955231i	$-0.404394\pi$
$293$	2.21777e87	0.591719	0.295860	+	0.955231i	$0.404394\pi$
$294$	−3.07664e87	−0.727355
$295$	−1.86347e87	−0.390519
$296$	3.82404e87	0.710667
$297$	6.27297e86	0.103424
$298$	1.17312e88	1.71658
$299$	6.64621e86	0.0863469
$300$	−2.47260e88	−2.85331
$301$	5.93856e87	0.608934
$302$	2.07912e88	1.89511
$303$	7.29240e86	0.0591094
$304$	−8.69557e88	−6.27026
$305$	3.83256e88	2.45949
$306$	−1.10033e88	−0.628653
$307$	−8.90381e86	−0.0453068	−0.0226534	−	0.999743i	$-0.507211\pi$
$307$	−8.90381e86	−0.0453068	−0.0226534	+	0.999743i	$0.507211\pi$
$308$	−2.03471e88	−0.922469
$309$	1.56335e88	0.631728
$310$	6.16247e88	2.22032
$311$	−5.49061e88	−1.76452	−0.882260	−	0.470762i	$-0.843979\pi$
$311$	−5.49061e88	−1.76452	−0.882260	+	0.470762i	$0.843979\pi$
$312$	−3.88356e88	−1.11363
$313$	−8.29393e87	−0.212293	−0.106147	−	0.994350i	$-0.533851\pi$
$313$	−8.29393e87	−0.212293	−0.106147	+	0.994350i	$0.533851\pi$
$314$	−1.28583e89	−2.93888
$315$	1.61526e88	0.329776
$316$	3.12789e88	0.570637
$317$	3.10820e88	0.506880	0.253440	−	0.967351i	$-0.418438\pi$
$317$	3.10820e88	0.506880	0.253440	+	0.967351i	$0.418438\pi$
$318$	−2.48348e87	−0.0362158
$319$	−1.30411e88	−0.170116
$320$	7.39256e89	8.62920
$321$	8.51456e87	0.0889679
$322$	2.06563e88	0.193272
$323$	−1.65376e89	−1.38606
$324$	4.23769e88	0.318260
$325$	−1.34892e89	−0.908085
$326$	1.37495e89	0.829971
$327$	1.52971e89	0.828255
$328$	−9.81173e89	−4.76677
$329$	4.95575e88	0.216100
$330$	−2.57180e89	−1.00691
$331$	−1.46459e89	−0.515018	−0.257509	−	0.966276i	$-0.582902\pi$
$331$	−1.46459e89	−0.515018	−0.257509	+	0.966276i	$0.582902\pi$
$332$	1.40531e90	4.43987
$333$	−2.27643e88	−0.0646373
$334$	−7.96449e89	−2.03310
$335$	−1.19814e90	−2.75053
$336$	−7.27124e89	−1.50163
$337$	5.01090e89	0.931224	0.465612	−	0.884989i	$-0.345834\pi$
$337$	5.01090e89	0.931224	0.465612	+	0.884989i	$0.345834\pi$
$338$	8.49607e89	1.42127
$339$	−6.47555e89	−0.975410
$340$	3.34375e90	4.53662
$341$	3.00777e89	0.367675
$342$	8.59271e89	0.946680
$343$	−9.90014e89	−0.983332
$344$	−4.15749e90	−3.72397
$345$	1.93525e89	0.156372
$346$	−3.79751e90	−2.76884
$347$	2.84608e90	1.87306	0.936528	−	0.350594i	$-0.114020\pi$
$347$	2.84608e90	1.87306	0.936528	+	0.350594i	$0.114020\pi$
$348$	−8.80988e89	−0.523488
$349$	2.84264e90	1.52553	0.762763	−	0.646678i	$-0.223842\pi$
$349$	2.84264e90	1.52553	0.762763	+	0.646678i	$0.223842\pi$
$350$	−4.19242e90	−2.03259
$351$	2.31186e89	0.101288
$352$	6.60405e90	2.61545
$353$	−1.37033e90	−0.490709	−0.245355	−	0.969433i	$-0.578904\pi$
$353$	−1.37033e90	−0.490709	−0.245355	+	0.969433i	$0.578904\pi$
$354$	−8.28936e89	−0.268476
$355$	2.36244e90	0.692237
$356$	1.10821e91	2.93864
$357$	−1.38287e90	−0.331941
$358$	−9.62652e90	−2.09229
$359$	−4.99398e90	−0.983091	−0.491546	−	0.870852i	$-0.663568\pi$
$359$	−4.99398e90	−0.983091	−0.491546	+	0.870852i	$0.663568\pi$
$360$	−1.13082e91	−2.01676
$361$	6.72720e90	1.08725
$362$	−1.63851e90	−0.240046
$363$	3.09111e90	0.410609
$364$	−7.49877e90	−0.903422
$365$	1.70535e91	1.86388
$366$	1.70485e91	1.69086
$367$	1.36496e90	0.122878	0.0614392	−	0.998111i	$-0.480431\pi$
$367$	1.36496e90	0.122878	0.0614392	+	0.998111i	$0.480431\pi$
$368$	−8.71168e90	−0.712040
$369$	5.84086e90	0.433552
$370$	9.33291e90	0.629297
$371$	−3.12120e89	−0.0191226
$372$	2.03189e91	1.13143
$373$	2.56069e91	1.29627	0.648133	−	0.761527i	$-0.275550\pi$
$373$	2.56069e91	1.29627	0.648133	+	0.761527i	$0.275550\pi$
$374$	2.20179e91	1.01352
$375$	−1.65132e91	−0.691387
$376$	−3.46944e91	−1.32157
$377$	−4.80620e90	−0.166604
$378$	7.18523e90	0.226716
$379$	−1.49876e91	−0.430565	−0.215283	−	0.976552i	$-0.569067\pi$
$379$	−1.49876e91	−0.430565	−0.215283	+	0.976552i	$0.569067\pi$
$380$	−2.61122e92	−6.83164
$381$	−1.05197e90	−0.0250707
$382$	−9.94929e91	−2.16044
$383$	5.42897e91	1.07439	0.537194	−	0.843459i	$-0.319484\pi$
$383$	5.42897e91	1.07439	0.537194	+	0.843459i	$0.319484\pi$
$384$	1.73090e92	3.12259
$385$	−3.23219e91	−0.531669
$386$	−1.01458e92	−1.52209
$387$	2.47493e91	0.338706
$388$	9.85580e91	1.23074
$389$	1.65261e92	1.88348	0.941738	−	0.336346i	$-0.109191\pi$
$389$	1.65261e92	1.88348	0.941738	+	0.336346i	$0.109191\pi$
$390$	−9.47818e91	−0.986123
$391$	−1.65682e91	−0.157399
$392$	2.70699e92	2.34872
$393$	−7.03754e91	−0.557809
$394$	1.04143e92	0.754250
$395$	4.96875e91	0.328890
$396$	−8.47975e91	−0.513102
$397$	−3.13621e92	−1.73517	−0.867585	−	0.497289i	$-0.834329\pi$
$397$	−3.13621e92	−1.73517	−0.867585	+	0.497289i	$0.834329\pi$
$398$	−3.65843e92	−1.85117
$399$	1.07992e92	0.499865
$400$	1.76813e93	7.48832
$401$	−3.00867e92	−1.16614	−0.583069	−	0.812423i	$-0.698148\pi$
$401$	−3.00867e92	−1.16614	−0.583069	+	0.812423i	$0.698148\pi$
$402$	−5.32972e92	−1.89095
$403$	1.10849e92	0.360084
$404$	−9.85780e91	−0.293252
$405$	6.73170e91	0.183430
$406$	−1.49376e92	−0.372913
$407$	4.55520e91	0.104209
$408$	9.68126e92	2.03000
$409$	−1.70808e92	−0.328345	−0.164173	−	0.986432i	$-0.552495\pi$
$409$	−1.70808e92	−0.328345	−0.164173	+	0.986432i	$0.552495\pi$
$410$	−2.39464e93	−4.22098
$411$	8.15957e91	0.131911
$412$	−2.11332e93	−3.13411
$413$	−1.04179e92	−0.141760
$414$	8.60864e91	0.107503
$415$	2.23237e93	2.55894
$416$	2.43388e93	2.56145
$417$	4.17294e92	0.403286
$418$	−1.71943e93	−1.52625
$419$	3.30468e92	0.269483	0.134741	−	0.990881i	$-0.456980\pi$
$419$	3.30468e92	0.269483	0.134741	+	0.990881i	$0.456980\pi$
$420$	−2.18350e93	−1.63608
$421$	2.08496e92	0.143577	0.0717883	−	0.997420i	$-0.477129\pi$
$421$	2.08496e92	0.143577	0.0717883	+	0.997420i	$0.477129\pi$
$422$	−5.44940e92	−0.344950
$423$	2.06534e92	0.120201
$424$	2.18510e92	0.116945
$425$	3.36270e93	1.65532
$426$	1.05089e93	0.475902
$427$	2.14262e93	0.892805
$428$	−1.15099e93	−0.441386
$429$	−4.62610e92	−0.163298
$430$	−1.01467e94	−3.29758
$431$	4.93852e93	1.47793	0.738964	−	0.673745i	$-0.235315\pi$
$431$	4.93852e93	1.47793	0.738964	+	0.673745i	$0.235315\pi$
$432$	−3.03033e93	−0.835250
$433$	−2.61242e93	−0.663320	−0.331660	−	0.943399i	$-0.607609\pi$
$433$	−2.61242e93	−0.663320	−0.331660	+	0.943399i	$0.607609\pi$
$434$	3.44518e93	0.805985
$435$	−1.39948e93	−0.301715
$436$	−2.06785e94	−4.10912
$437$	1.29385e93	0.237024
$438$	7.58598e93	1.28139
$439$	9.98877e93	1.55604	0.778022	−	0.628237i	$-0.216223\pi$
$439$	9.98877e93	1.55604	0.778022	+	0.628237i	$0.216223\pi$
$440$	2.26280e94	3.25145
$441$	−1.61146e93	−0.213623
$442$	8.11453e93	0.992597
$443$	−5.42510e93	−0.612457	−0.306229	−	0.951958i	$-0.599067\pi$
$443$	−5.42510e93	−0.612457	−0.306229	+	0.951958i	$0.599067\pi$
$444$	3.07725e93	0.320677
$445$	1.76042e94	1.69370
$446$	−3.43810e94	−3.05443
$447$	6.14447e93	0.504159
$448$	4.13287e94	3.13244
$449$	−1.15678e94	−0.810037	−0.405019	−	0.914308i	$-0.632735\pi$
$449$	−1.15678e94	−0.810037	−0.405019	+	0.914308i	$0.632735\pi$
$450$	−1.74721e94	−1.13058
$451$	−1.16877e94	−0.698978
$452$	8.75359e94	4.83918
$453$	1.08898e94	0.556590
$454$	−6.67230e94	−3.15350
$455$	−1.19120e94	−0.520692
$456$	−7.56032e94	−3.05695
$457$	3.82365e94	1.43038	0.715192	−	0.698928i	$-0.246339\pi$
$457$	3.82365e94	1.43038	0.715192	+	0.698928i	$0.246339\pi$
$458$	−9.66940e94	−3.34715
$459$	−5.76320e93	−0.184635
$460$	−2.61606e94	−0.775790
$461$	4.00920e94	1.10072	0.550358	−	0.834929i	$-0.314491\pi$
$461$	4.00920e94	1.10072	0.550358	+	0.834929i	$0.314491\pi$
$462$	−1.43779e94	−0.365514
$463$	1.93405e94	0.455347	0.227673	−	0.973738i	$-0.426888\pi$
$463$	1.93405e94	0.455347	0.227673	+	0.973738i	$0.426888\pi$
$464$	6.29985e94	1.37386
$465$	3.22772e94	0.652104
$466$	3.18601e94	0.596414
$467$	−2.68390e94	−0.465604	−0.232802	−	0.972524i	$-0.574789\pi$
$467$	−2.68390e94	−0.465604	−0.232802	+	0.972524i	$0.574789\pi$
$468$	−3.12515e94	−0.502508
$469$	−6.69830e94	−0.998455
$470$	−8.46749e94	−1.17026
$471$	−6.73483e94	−0.863146
$472$	7.29341e94	0.866942
$473$	−4.95240e94	−0.546066
$474$	2.21026e94	0.226106
$475$	−2.62601e95	−2.49272
$476$	1.86936e95	1.64682
$477$	−1.30077e93	−0.0106365
$478$	4.33427e95	3.29022
$479$	−5.38319e94	−0.379428	−0.189714	−	0.981839i	$-0.560756\pi$
$479$	−5.38319e94	−0.379428	−0.189714	+	0.981839i	$0.560756\pi$
$480$	7.08699e95	4.63872
$481$	1.67879e94	0.102058
$482$	3.10519e95	1.75355
$483$	1.08192e94	0.0567638
$484$	−4.17853e95	−2.03711
$485$	1.56562e95	0.709342
$486$	2.99448e94	0.126106
$487$	−1.50831e95	−0.590488	−0.295244	−	0.955422i	$-0.595401\pi$
$487$	−1.50831e95	−0.590488	−0.295244	+	0.955422i	$0.595401\pi$
$488$	−1.50002e96	−5.45999
$489$	7.20160e94	0.243761
$490$	6.60666e95	2.07980
$491$	4.29858e95	1.25873	0.629365	−	0.777110i	$-0.283315\pi$
$491$	4.29858e95	1.25873	0.629365	+	0.777110i	$0.283315\pi$
$492$	−7.89563e95	−2.15093
$493$	1.19813e95	0.303696
$494$	−6.33683e95	−1.49474
$495$	−1.34703e95	−0.295729
$496$	−1.45299e96	−2.96935
$497$	1.32075e95	0.251285
$498$	9.93034e95	1.75923
$499$	7.16654e95	1.18233	0.591167	−	0.806549i	$-0.298668\pi$
$499$	7.16654e95	1.18233	0.591167	+	0.806549i	$0.298668\pi$
$500$	2.23224e96	3.43010
$501$	−4.17157e95	−0.597118
$502$	1.83350e95	0.244512
$503$	−3.57817e95	−0.444629	−0.222315	−	0.974975i	$-0.571361\pi$
$503$	−3.57817e95	−0.444629	−0.222315	+	0.974975i	$0.571361\pi$
$504$	−6.32195e95	−0.732094
$505$	−1.56594e95	−0.169017
$506$	−1.72261e95	−0.173318
$507$	4.45000e95	0.417424
$508$	1.42204e95	0.124380
$509$	−2.71480e95	−0.221440	−0.110720	−	0.993852i	$-0.535316\pi$
$509$	−2.71480e95	−0.221440	−0.110720	+	0.993852i	$0.535316\pi$
$510$	2.36280e96	1.79757
$511$	9.53393e95	0.676597
$512$	−7.87872e96	−5.21641
$513$	4.50061e95	0.278039
$514$	2.90529e96	1.67494
$515$	−3.35708e96	−1.80636
$516$	−3.34558e96	−1.68038
$517$	−4.13280e95	−0.193790
$518$	5.21765e95	0.228438
$519$	−1.98903e96	−0.813204
$520$	8.33940e96	3.18432
$521$	1.50372e96	0.536325	0.268162	−	0.963374i	$-0.413584\pi$
$521$	1.50372e96	0.536325	0.268162	+	0.963374i	$0.413584\pi$
$522$	−6.22533e95	−0.207424
$523$	7.87904e95	0.245281	0.122640	−	0.992451i	$-0.460864\pi$
$523$	7.87904e95	0.245281	0.122640	+	0.992451i	$0.460864\pi$
$524$	9.51329e96	2.76739
$525$	−2.19587e96	−0.596969
$526$	−1.19683e96	−0.304115
$527$	−2.76334e96	−0.656384
$528$	6.06378e96	1.34660
$529$	−4.68626e96	−0.973084
$530$	5.33293e95	0.103555
$531$	−4.34173e95	−0.0788509
$532$	−1.45982e97	−2.47992
$533$	−4.30744e96	−0.684546
$534$	7.83095e96	1.16439
$535$	−1.82838e96	−0.254395
$536$	4.68937e97	6.10611
$537$	−5.04209e96	−0.614503
$538$	1.43399e95	0.0163597
$539$	3.22457e96	0.344406
$540$	−9.09986e96	−0.910031
$541$	7.34710e96	0.688039	0.344020	−	0.938962i	$-0.388211\pi$
$541$	7.34710e96	0.688039	0.344020	+	0.938962i	$0.388211\pi$
$542$	1.59838e97	1.40186
$543$	−8.58204e95	−0.0705012
$544$	−6.06737e97	−4.66917
$545$	−3.28484e97	−2.36831
$546$	−5.29886e96	−0.357968
$547$	−8.45815e96	−0.535458	−0.267729	−	0.963494i	$-0.586273\pi$
$547$	−8.45815e96	−0.535458	−0.267729	+	0.963494i	$0.586273\pi$
$548$	−1.10300e97	−0.654436
$549$	8.92950e96	0.496603
$550$	3.49623e97	1.82274
$551$	−9.35648e96	−0.457331
$552$	−7.57434e96	−0.347142
$553$	2.77782e96	0.119388
$554$	−7.38990e97	−2.97880
$555$	4.88831e96	0.184824
$556$	−5.64095e97	−2.00077
$557$	1.44839e97	0.481976	0.240988	−	0.970528i	$-0.422529\pi$
$557$	1.44839e97	0.481976	0.240988	+	0.970528i	$0.422529\pi$
$558$	1.43580e97	0.448311
$559$	−1.82517e97	−0.534792
$560$	1.56140e98	4.29377
$561$	1.15323e97	0.297670
$562$	1.41348e98	3.42491
$563$	1.44653e97	0.329062	0.164531	−	0.986372i	$-0.447389\pi$
$563$	1.44653e97	0.329062	0.164531	+	0.986372i	$0.447389\pi$
$564$	−2.79191e97	−0.596338
$565$	1.39053e98	2.78909
$566$	−1.01481e98	−1.91161
$567$	3.76342e96	0.0665861
$568$	−9.24632e97	−1.53675
$569$	8.43929e97	1.31771	0.658856	−	0.752269i	$-0.271041\pi$
$569$	8.43929e97	1.31771	0.658856	+	0.752269i	$0.271041\pi$
$570$	−1.84517e98	−2.70694
$571$	4.71117e97	0.649451	0.324726	−	0.945808i	$-0.394728\pi$
$571$	4.71117e97	0.649451	0.324726	+	0.945808i	$0.394728\pi$
$572$	6.25353e97	0.810151
$573$	−5.21115e97	−0.634519
$574$	−1.33875e98	−1.53224
$575$	−2.63088e97	−0.283069
$576$	1.72240e98	1.74235
$577$	1.71982e97	0.163585	0.0817923	−	0.996649i	$-0.473936\pi$
$577$	1.71982e97	0.163585	0.0817923	+	0.996649i	$0.473936\pi$
$578$	1.74878e97	0.156422
$579$	−5.31410e97	−0.447034
$580$	1.89180e98	1.49686
$581$	1.24803e98	0.928906
$582$	6.96441e97	0.487662
$583$	2.60289e96	0.0171483
$584$	−6.67454e98	−4.13776
$585$	−4.96440e97	−0.289623
$586$	−2.11845e98	−1.16320
$587$	−1.64628e98	−0.850849	−0.425424	−	0.904994i	$-0.639875\pi$
$587$	−1.64628e98	−0.850849	−0.425424	+	0.904994i	$0.639875\pi$
$588$	2.17835e98	1.05982
$589$	2.15796e98	0.988440
$590$	1.78002e98	0.767679
$591$	5.45472e97	0.221522
$592$	−2.20051e98	−0.841595
$593$	3.82413e98	1.37750	0.688748	−	0.725000i	$-0.258160\pi$
$593$	3.82413e98	1.37750	0.688748	+	0.725000i	$0.258160\pi$
$594$	−5.99205e97	−0.203309
$595$	2.96953e98	0.949150
$596$	−8.30604e98	−2.50122
$597$	−1.91618e98	−0.543686
$598$	−6.34857e97	−0.169740
$599$	−5.76759e98	−1.45326	−0.726628	−	0.687031i	$-0.758914\pi$
$599$	−5.76759e98	−1.45326	−0.726628	+	0.687031i	$0.758914\pi$
$600$	1.53729e99	3.65079
$601$	8.69962e98	1.94741	0.973703	−	0.227821i	$-0.0731600\pi$
$601$	8.69962e98	1.94741	0.973703	+	0.227821i	$0.0731600\pi$
$602$	−5.67261e98	−1.19704
$603$	−2.79155e98	−0.555368
$604$	−1.47208e99	−2.76134
$605$	−6.63772e98	−1.17410
$606$	−6.96582e97	−0.116197
$607$	2.72040e98	0.427991	0.213995	−	0.976835i	$-0.431352\pi$
$607$	2.72040e98	0.427991	0.213995	+	0.976835i	$0.431352\pi$
$608$	4.73815e99	7.03124
$609$	−7.82390e97	−0.109524
$610$	−3.66092e99	−4.83484
$611$	−1.52312e98	−0.189788
$612$	7.79064e98	0.916005
$613$	−8.03567e97	−0.0891610	−0.0445805	−	0.999006i	$-0.514195\pi$
$613$	−8.03567e97	−0.0891610	−0.0445805	+	0.999006i	$0.514195\pi$
$614$	8.50507e97	0.0890637
$615$	−1.25424e99	−1.23970
$616$	1.26504e99	1.18029
$617$	−7.76940e98	−0.684328	−0.342164	−	0.939640i	$-0.611160\pi$
$617$	−7.76940e98	−0.684328	−0.342164	+	0.939640i	$0.611160\pi$
$618$	−1.49334e99	−1.24185
$619$	1.67971e99	1.31892	0.659458	−	0.751741i	$-0.270786\pi$
$619$	1.67971e99	1.31892	0.659458	+	0.751741i	$0.270786\pi$
$620$	−4.36321e99	−3.23520
$621$	4.50896e97	0.0315736
$622$	5.24473e99	3.46868
$623$	9.84180e98	0.614821
$624$	2.23476e99	1.31880
$625$	4.51226e98	0.251567
$626$	7.92251e98	0.417325
$627$	−9.00587e98	−0.448258
$628$	9.10408e99	4.28222
$629$	−4.18502e98	−0.186037
$630$	−1.54293e99	−0.648271
$631$	−1.16693e99	−0.463449	−0.231725	−	0.972781i	$-0.574437\pi$
$631$	−1.16693e99	−0.463449	−0.231725	+	0.972781i	$0.574437\pi$
$632$	−1.94471e99	−0.730126
$633$	−2.85424e98	−0.101311
$634$	−2.96901e99	−0.996420
$635$	2.25896e98	0.0716871
$636$	1.75838e98	0.0527697
$637$	1.18839e99	0.337295
$638$	1.24571e99	0.334412
$639$	5.50428e98	0.139772
$640$	−3.71687e100	−8.92871
$641$	−3.57448e99	−0.812367	−0.406184	−	0.913791i	$-0.633141\pi$
$641$	−3.57448e99	−0.812367	−0.406184	+	0.913791i	$0.633141\pi$
$642$	−8.13326e98	−0.174892
$643$	8.56174e99	1.74210	0.871049	−	0.491197i	$-0.163440\pi$
$643$	8.56174e99	1.74210	0.871049	+	0.491197i	$0.163440\pi$
$644$	−1.46253e99	−0.281615
$645$	−5.31456e99	−0.968495
$646$	1.57970e100	2.72471
$647$	1.00942e99	0.164804	0.0824021	−	0.996599i	$-0.473741\pi$
$647$	1.00942e99	0.164804	0.0824021	+	0.996599i	$0.473741\pi$
$648$	−2.63471e99	−0.407211
$649$	8.68793e98	0.127125
$650$	1.28851e100	1.78511
$651$	1.80449e99	0.236717
$652$	−9.73507e99	−1.20934
$653$	−1.34187e99	−0.157867	−0.0789336	−	0.996880i	$-0.525152\pi$
$653$	−1.34187e99	−0.157867	−0.0789336	+	0.996880i	$0.525152\pi$
$654$	−1.46121e100	−1.62818
$655$	1.51121e100	1.59500
$656$	5.64608e100	5.64496
$657$	3.97332e99	0.376342
$658$	−4.73382e99	−0.424808
$659$	−2.12505e100	−1.80691	−0.903456	−	0.428681i	$-0.858979\pi$
$659$	−2.12505e100	−1.80691	−0.903456	+	0.428681i	$0.858979\pi$
$660$	1.82091e100	1.46716
$661$	3.11310e98	0.0237707	0.0118853	−	0.999929i	$-0.496217\pi$
$661$	3.11310e98	0.0237707	0.0118853	+	0.999929i	$0.496217\pi$
$662$	1.39900e100	1.01242
$663$	4.25016e99	0.291524
$664$	−8.73724e100	−5.68078
$665$	−2.31897e100	−1.42931
$666$	2.17448e99	0.127063
$667$	−9.37382e98	−0.0519337
$668$	5.63909e100	2.96241
$669$	−1.80078e100	−0.897083
$670$	1.14448e101	5.40697
$671$	−1.78682e100	−0.800630
$672$	3.96204e100	1.68388
$673$	−3.81530e99	−0.153813	−0.0769067	−	0.997038i	$-0.524504\pi$
$673$	−3.81530e99	−0.153813	−0.0769067	+	0.997038i	$0.524504\pi$
$674$	−4.78650e100	−1.83059
$675$	−9.15141e99	−0.332050
$676$	−6.01547e100	−2.07091
$677$	2.80988e100	0.917890	0.458945	−	0.888465i	$-0.348228\pi$
$677$	2.80988e100	0.917890	0.458945	+	0.888465i	$0.348228\pi$
$678$	6.18556e100	1.91745
$679$	8.75276e99	0.257494
$680$	−2.07892e101	−5.80458
$681$	−3.49476e100	−0.926178
$682$	−2.87308e100	−0.722773
$683$	−1.40913e99	−0.0336524	−0.0168262	−	0.999858i	$-0.505356\pi$
$683$	−1.40913e99	−0.0336524	−0.0168262	+	0.999858i	$0.505356\pi$
$684$	−6.08389e100	−1.37940
$685$	−1.75215e100	−0.377187
$686$	9.45679e100	1.93303
$687$	−5.06455e100	−0.983053
$688$	2.39239e101	4.41004
$689$	9.59277e98	0.0167943
$690$	−1.84859e100	−0.307395
$691$	3.17608e98	0.00501673	0.00250837	−	0.999997i	$-0.499202\pi$
$691$	3.17608e98	0.00501673	0.00250837	+	0.999997i	$0.499202\pi$
$692$	2.68875e101	4.03445
$693$	−7.53071e99	−0.107351
$694$	−2.71862e101	−3.68204
$695$	−8.96082e100	−1.15315
$696$	5.47738e100	0.669799
$697$	1.07379e101	1.24784
$698$	−2.71534e101	−2.99887
$699$	1.66874e100	0.175166
$700$	2.96836e101	2.96167
$701$	3.63428e100	0.344690	0.172345	−	0.985037i	$-0.444866\pi$
$701$	3.63428e100	0.344690	0.172345	+	0.985037i	$0.444866\pi$
$702$	−2.20833e100	−0.199111
$703$	3.26818e100	0.280151
$704$	−3.44657e101	−2.80904
$705$	−4.43503e100	−0.343702
$706$	1.30897e101	0.964632
$707$	−8.75453e99	−0.0613541
$708$	5.86911e100	0.391193
$709$	6.07104e100	0.384877	0.192438	−	0.981309i	$-0.438360\pi$
$709$	6.07104e100	0.384877	0.192438	+	0.981309i	$0.438360\pi$
$710$	−2.25665e101	−1.36079
$711$	1.15767e100	0.0664072
$712$	−6.89008e101	−3.75997
$713$	2.16196e100	0.112246
$714$	1.32094e101	0.652526
$715$	9.93391e100	0.466934
$716$	6.81586e101	3.04866
$717$	2.27016e101	0.966334
$718$	4.77034e101	1.93255
$719$	1.70041e101	0.655659	0.327829	−	0.944737i	$-0.393683\pi$
$719$	1.70041e101	0.655659	0.327829	+	0.944737i	$0.393683\pi$
$720$	6.50721e101	2.38831
$721$	−1.87680e101	−0.655718
$722$	−6.42594e101	−2.13730
$723$	1.62641e101	0.515015
$724$	1.16011e101	0.349769
$725$	1.90252e101	0.546172
$726$	−2.95268e101	−0.807173
$727$	−1.84223e101	−0.479591	−0.239796	−	0.970823i	$-0.577080\pi$
$727$	−1.84223e101	−0.479591	−0.239796	+	0.970823i	$0.577080\pi$
$728$	4.66222e101	1.15592
$729$	1.56842e100	0.0370370
$730$	−1.62898e102	−3.66400
$731$	4.54994e101	0.974853
$732$	−1.20708e102	−2.46373
$733$	1.27148e101	0.247240	0.123620	−	0.992330i	$-0.460550\pi$
$733$	1.27148e101	0.247240	0.123620	+	0.992330i	$0.460550\pi$
$734$	−1.30384e101	−0.241553
$735$	3.46038e101	0.610833
$736$	4.74693e101	0.798455
$737$	5.58598e101	0.895372
$738$	−5.57930e101	−0.852273
$739$	8.41381e101	1.22494	0.612470	−	0.790494i	$-0.290176\pi$
$739$	8.41381e101	1.22494	0.612470	+	0.790494i	$0.290176\pi$
$740$	−6.60798e101	−0.916943
$741$	−3.31905e101	−0.439003
$742$	2.98142e100	0.0375911
$743$	1.57115e102	1.88849	0.944244	−	0.329245i	$-0.106794\pi$
$743$	1.57115e102	1.88849	0.944244	+	0.329245i	$0.106794\pi$
$744$	−1.26329e102	−1.44765
$745$	−1.31944e102	−1.44159
$746$	−2.44602e102	−2.54819
$747$	5.20123e101	0.516683
$748$	−1.55893e102	−1.47680
$749$	−1.02217e101	−0.0923465
$750$	1.57737e102	1.35912
$751$	−6.59365e101	−0.541886	−0.270943	−	0.962595i	$-0.587336\pi$
$751$	−6.59365e101	−0.541886	−0.270943	+	0.962595i	$0.587336\pi$
$752$	1.99646e102	1.56505
$753$	9.60336e100	0.0718128
$754$	4.59097e101	0.327508
$755$	−2.33844e102	−1.59151
$756$	−5.08736e101	−0.330345
$757$	−1.67667e102	−1.03883	−0.519413	−	0.854523i	$-0.673849\pi$
$757$	−1.67667e102	−1.03883	−0.519413	+	0.854523i	$0.673849\pi$
$758$	1.43164e102	0.846401
$759$	−9.02256e100	−0.0509034
$760$	1.62347e103	8.74103
$761$	−3.20762e102	−1.64827	−0.824133	−	0.566396i	$-0.808337\pi$
$761$	−3.20762e102	−1.64827	−0.824133	+	0.566396i	$0.808337\pi$
$762$	1.00486e101	0.0492838
$763$	−1.83642e102	−0.859708
$764$	7.04439e102	3.14796
$765$	1.23757e102	0.527944
$766$	−5.18585e102	−2.11202
$767$	3.20187e101	0.124500
$768$	−8.40523e102	−3.12051
$769$	1.18875e102	0.421411	0.210705	−	0.977550i	$-0.432424\pi$
$769$	1.18875e102	0.421411	0.210705	+	0.977550i	$0.432424\pi$
$770$	3.08745e102	1.04515
$771$	1.52171e102	0.491927
$772$	7.18356e102	2.21782
$773$	1.74221e102	0.513721	0.256861	−	0.966448i	$-0.417312\pi$
$773$	1.74221e102	0.513721	0.256861	+	0.966448i	$0.417312\pi$
$774$	−2.36409e102	−0.665825
$775$	−4.38793e102	−1.18045
$776$	−6.12766e102	−1.57472
$777$	2.73285e101	0.0670919
$778$	−1.57860e103	−3.70252
$779$	−8.38551e102	−1.87910
$780$	6.71083e102	1.43687
$781$	−1.10142e102	−0.225342
$782$	1.58263e102	0.309413
$783$	−3.26065e101	−0.0609203
$784$	−1.55772e103	−2.78143
$785$	1.44621e103	2.46808
$786$	6.72238e102	1.09654
$787$	7.19935e101	0.112251	0.0561255	−	0.998424i	$-0.482125\pi$
$787$	7.19935e101	0.112251	0.0561255	+	0.998424i	$0.482125\pi$
$788$	−7.37365e102	−1.09901
$789$	−6.26864e101	−0.0893181
$790$	−4.74624e102	−0.646528
$791$	7.77391e102	1.01245
$792$	5.27213e102	0.656511
$793$	−6.58520e102	−0.784099
$794$	2.99576e103	3.41098
$795$	2.79323e101	0.0304140
$796$	2.59028e103	2.69732
$797$	6.43676e102	0.641058	0.320529	−	0.947239i	$-0.396139\pi$
$797$	6.43676e102	0.641058	0.320529	+	0.947239i	$0.396139\pi$
$798$	−1.03156e103	−0.982630
$799$	3.79695e102	0.345959
$800$	−9.63441e103	−8.39712
$801$	4.10162e102	0.341981
$802$	2.87394e103	2.29238
$803$	−7.95073e102	−0.606743
$804$	3.77360e103	2.75528
$805$	−2.32327e102	−0.162310
$806$	−1.05885e103	−0.707850
$807$	7.51082e100	0.00480482
$808$	6.12890e102	0.375214
$809$	1.14977e103	0.673659	0.336829	−	0.941566i	$-0.390645\pi$
$809$	1.14977e103	0.673659	0.336829	+	0.941566i	$0.390645\pi$
$810$	−6.43024e102	−0.360586
$811$	−2.63210e103	−1.41274	−0.706370	−	0.707843i	$-0.749669\pi$
$811$	−2.63210e103	−1.41274	−0.706370	+	0.707843i	$0.749669\pi$
$812$	1.05763e103	0.543368
$813$	8.37185e102	0.411725
$814$	−4.35121e102	−0.204853
$815$	−1.54644e103	−0.697010
$816$	−5.57100e103	−2.40399
$817$	−3.55316e103	−1.46802
$818$	1.63159e103	0.645459
$819$	−2.77539e102	−0.105135
$820$	1.69548e104	6.15036
$821$	2.49077e102	0.0865270	0.0432635	−	0.999064i	$-0.486224\pi$
$821$	2.49077e102	0.0865270	0.0432635	+	0.999064i	$0.486224\pi$
$822$	−7.79417e102	−0.259310
$823$	−3.58748e103	−1.14313	−0.571565	−	0.820557i	$-0.693663\pi$
$823$	−3.58748e103	−1.14313	−0.571565	+	0.820557i	$0.693663\pi$
$824$	1.31392e104	4.01008
$825$	1.83122e103	0.535336
$826$	9.95138e102	0.278671
$827$	1.11811e103	0.299942	0.149971	−	0.988690i	$-0.452082\pi$
$827$	1.11811e103	0.299942	0.149971	+	0.988690i	$0.452082\pi$
$828$	−6.09517e102	−0.156642
$829$	4.01077e103	0.987510	0.493755	−	0.869601i	$-0.335624\pi$
$829$	4.01077e103	0.987510	0.493755	+	0.869601i	$0.335624\pi$
$830$	−2.13240e104	−5.03034
$831$	−3.87062e103	−0.874871
$832$	−1.27021e104	−2.75104
$833$	−2.96252e103	−0.614843
$834$	−3.98607e103	−0.792775
$835$	8.95786e103	1.70740
$836$	1.21741e104	2.22389
$837$	7.52030e102	0.131668
$838$	−3.15668e103	−0.529747
$839$	4.23627e103	0.681451	0.340725	−	0.940163i	$-0.389327\pi$
$839$	4.23627e103	0.681451	0.340725	+	0.940163i	$0.389327\pi$
$840$	1.35755e104	2.09335
$841$	−6.08698e103	−0.899796
$842$	−1.99159e103	−0.282242
$843$	7.40339e103	1.00589
$844$	3.85834e103	0.502624
$845$	−9.55575e103	−1.19358
$846$	−1.97285e103	−0.236290
$847$	−3.71088e103	−0.426202
$848$	−1.25740e103	−0.138490
$849$	−5.31526e103	−0.561438
$850$	−3.21211e104	−3.25401
$851$	3.27424e102	0.0318134
$852$	−7.44064e103	−0.693433
$853$	−3.58616e103	−0.320582	−0.160291	−	0.987070i	$-0.551243\pi$
$853$	−3.58616e103	−0.320582	−0.160291	+	0.987070i	$0.551243\pi$
$854$	−2.04667e104	−1.75507
$855$	−9.66444e103	−0.795023
$856$	7.15607e103	0.564750
$857$	−2.72681e103	−0.206460	−0.103230	−	0.994658i	$-0.532918\pi$
$857$	−2.72681e103	−0.206460	−0.103230	+	0.994658i	$0.532918\pi$
$858$	4.41893e103	0.321010
$859$	1.95296e104	1.36125	0.680623	−	0.732634i	$-0.261709\pi$
$859$	1.95296e104	1.36125	0.680623	+	0.732634i	$0.261709\pi$
$860$	7.18418e104	4.80488
$861$	−7.01197e103	−0.450016
$862$	−4.71736e104	−2.90530
$863$	−1.74167e101	−0.00102939	−0.000514697	−	1.00000i	$-0.500164\pi$
$863$	−1.74167e101	−0.00102939	−0.000514697		1.00000i	$0.500164\pi$
$864$	1.65120e104	0.936618
$865$	4.27116e104	2.32527
$866$	2.49543e104	1.30395
$867$	9.15961e102	0.0459409
$868$	−2.43929e104	−1.17439
$869$	−2.31654e103	−0.107063
$870$	1.33680e104	0.593109
$871$	2.05867e104	0.876886
$872$	1.28565e105	5.25759
$873$	3.64776e103	0.143226
$874$	−1.23591e104	−0.465941
$875$	1.98241e104	0.717643
$876$	−5.37110e104	−1.86710
$877$	4.04745e103	0.135113	0.0675563	−	0.997715i	$-0.478480\pi$
$877$	4.04745e103	0.135113	0.0675563	+	0.997715i	$0.478480\pi$
$878$	−9.54145e104	−3.05886
$879$	−1.10958e104	−0.341629
$880$	−1.30211e105	−3.85047
$881$	−5.92170e103	−0.168191	−0.0840954	−	0.996458i	$-0.526800\pi$
$881$	−5.92170e103	−0.168191	−0.0840954	+	0.996458i	$0.526800\pi$
$882$	1.53929e104	0.419939
$883$	6.43768e104	1.68704	0.843518	−	0.537101i	$-0.180481\pi$
$883$	6.43768e104	1.68704	0.843518	+	0.537101i	$0.180481\pi$
$884$	−5.74533e104	−1.44630
$885$	9.32325e103	0.225466
$886$	5.18215e104	1.20396
$887$	−1.64578e104	−0.367353	−0.183677	−	0.982987i	$-0.558800\pi$
$887$	−1.64578e104	−0.367353	−0.183677	+	0.982987i	$0.558800\pi$
$888$	−1.91323e104	−0.410304
$889$	1.26289e103	0.0260228
$890$	−1.68159e105	−3.32946
$891$	−3.13846e103	−0.0597116
$892$	2.43427e105	4.45059
$893$	−2.96513e104	−0.520974
$894$	−5.86930e104	−0.991071
$895$	1.08272e105	1.75711
$896$	−2.07795e105	−3.24117
$897$	−3.32520e103	−0.0498524
$898$	1.10497e105	1.59236
$899$	−1.56342e104	−0.216574
$900$	1.23708e105	1.64736
$901$	−2.39137e103	−0.0306137
$902$	1.11643e105	1.37405
$903$	−2.97115e104	−0.351568
$904$	−5.44238e105	−6.19170
$905$	1.84287e104	0.201591
$906$	−1.04022e105	−1.09414
$907$	−1.48880e105	−1.50583	−0.752916	−	0.658117i	$-0.771353\pi$
$907$	−1.48880e105	−1.50583	−0.752916	+	0.658117i	$0.771353\pi$
$908$	4.72418e105	4.59493
$909$	−3.64850e103	−0.0341269
$910$	1.13786e105	1.02357
$911$	1.62254e104	0.140376	0.0701882	−	0.997534i	$-0.477640\pi$
$911$	1.62254e104	0.140376	0.0701882	+	0.997534i	$0.477640\pi$
$912$	4.35053e105	3.62014
$913$	−1.04078e105	−0.833004
$914$	−3.65241e105	−2.81184
$915$	−1.91749e105	−1.41998
$916$	6.84622e105	4.87710
$917$	8.44858e104	0.578991
$918$	5.50511e104	0.362953
$919$	−1.30392e105	−0.827085	−0.413543	−	0.910485i	$-0.635709\pi$
$919$	−1.30392e105	−0.827085	−0.413543	+	0.910485i	$0.635709\pi$
$920$	1.62648e105	0.992617
$921$	4.45471e103	0.0261579
$922$	−3.82966e105	−2.16378
$923$	−4.05922e104	−0.220690
$924$	1.01800e105	0.532587
$925$	−6.64541e104	−0.334573
$926$	−1.84744e105	−0.895117
$927$	−7.82168e104	−0.364728
$928$	−3.43274e105	−1.54059
$929$	5.94344e104	0.256732	0.128366	−	0.991727i	$-0.459027\pi$
$929$	5.94344e104	0.256732	0.128366	+	0.991727i	$0.459027\pi$
$930$	−3.08318e105	−1.28190
$931$	2.31350e105	0.925884
$932$	−2.25579e105	−0.869029
$933$	2.74704e105	1.01875
$934$	2.56371e105	0.915281
$935$	−2.47641e105	−0.851158
$936$	1.94300e105	0.642956
$937$	−2.33357e105	−0.743473	−0.371736	−	0.928338i	$-0.621238\pi$
$937$	−2.33357e105	−0.743473	−0.371736	+	0.928338i	$0.621238\pi$
$938$	6.39833e105	1.96276
$939$	4.14958e104	0.122568
$940$	5.99523e105	1.70517
$941$	−3.62971e105	−0.994124	−0.497062	−	0.867715i	$-0.665588\pi$
$941$	−3.62971e105	−0.994124	−0.497062	+	0.867715i	$0.665588\pi$
$942$	6.43323e105	1.69676
$943$	−8.40105e104	−0.213387
$944$	−4.19694e105	−1.02666
$945$	−8.08141e104	−0.190396
$946$	4.73062e105	1.07345
$947$	−7.90504e105	−1.72775	−0.863873	−	0.503710i	$-0.831968\pi$
$947$	−7.90504e105	−1.72775	−0.863873	+	0.503710i	$0.831968\pi$
$948$	−1.56493e105	−0.329458
$949$	−2.93018e105	−0.594216
$950$	2.50841e106	4.90016
$951$	−1.55508e105	−0.292647
$952$	−1.16224e106	−2.10709
$953$	2.10689e105	0.367997	0.183999	−	0.982927i	$-0.441096\pi$
$953$	2.10689e105	0.367997	0.183999	+	0.982927i	$0.441096\pi$
$954$	1.24252e104	0.0209092
$955$	1.11902e106	1.81434
$956$	−3.06879e106	−4.79415
$957$	6.52466e104	0.0982165
$958$	5.14212e105	0.745876
$959$	−9.79558e104	−0.136921
$960$	−3.69861e106	−4.98207
$961$	−4.09752e105	−0.531913
$962$	−1.60361e105	−0.200624
$963$	−4.25997e104	−0.0513657
$964$	−2.19857e106	−2.55508
$965$	1.14113e106	1.27825
$966$	−1.03347e105	−0.111586
$967$	4.51617e105	0.470035	0.235018	−	0.971991i	$-0.424485\pi$
$967$	4.51617e105	0.470035	0.235018	+	0.971991i	$0.424485\pi$
$968$	2.59792e106	2.60646
$969$	8.27400e105	0.800242
$970$	−1.49551e106	−1.39442
$971$	1.82300e106	1.63872	0.819358	−	0.573283i	$-0.194330\pi$
$971$	1.82300e106	1.63872	0.819358	+	0.573283i	$0.194330\pi$
$972$	−2.12018e105	−0.183747
$973$	−5.00963e105	−0.418600
$974$	1.44076e106	1.16078
$975$	6.74885e105	0.524283
$976$	8.63172e106	6.46590
$977$	2.39068e106	1.72689	0.863443	−	0.504446i	$-0.168303\pi$
$977$	2.39068e106	1.72689	0.863443	+	0.504446i	$0.168303\pi$
$978$	−6.87910e105	−0.479184
$979$	−8.20748e105	−0.551346
$980$	−4.67771e106	−3.03045
$981$	−7.65338e105	−0.478193
$982$	−4.10608e106	−2.47440
$983$	−3.22254e106	−1.87304	−0.936522	−	0.350609i	$-0.885975\pi$
$983$	−3.22254e106	−1.87304	−0.936522	+	0.350609i	$0.885975\pi$
$984$	4.90896e106	2.75210
$985$	−1.17133e106	−0.633420
$986$	−1.14448e106	−0.597002
$987$	−2.47944e105	−0.124766
$988$	4.48666e106	2.17797
$989$	−3.55974e105	−0.166706
$990$	1.28671e106	0.581342
$991$	1.35266e106	0.589624	0.294812	−	0.955555i	$-0.404743\pi$
$991$	1.35266e106	0.589624	0.294812	+	0.955555i	$0.404743\pi$
$992$	7.91721e106	3.32972
$993$	7.32757e105	0.297346
$994$	−1.26160e106	−0.493975
$995$	4.11473e106	1.55461
$996$	−7.03098e106	−2.56336
$997$	−4.30649e106	−1.51511	−0.757556	−	0.652770i	$-0.773607\pi$
$997$	−4.30649e106	−1.51511	−0.757556	+	0.652770i	$0.773607\pi$
$998$	−6.84560e106	−2.32422
$999$	1.13893e105	0.0373184

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.72.a.b.1.1	✓	6	1.1	even	1	trivial
9.72.a.c.1.6		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)

\(f(q)\)	\(=\)	\(q-9.55218e10 q^{2} -5.00315e16 q^{3} +6.76322e21 q^{4} +1.07436e25 q^{5} +4.77910e27 q^{6} +6.00629e29 q^{7} -4.20491e32 q^{8} +2.50316e33 q^{9} +O(q^{10})\)	\(q-9.55218e10 q^{2} -5.00315e16 q^{3} +6.76322e21 q^{4} +1.07436e25 q^{5} +4.77910e27 q^{6} +6.00629e29 q^{7} -4.20491e32 q^{8} +2.50316e33 q^{9} -1.02625e36 q^{10} -5.00889e36 q^{11} -3.38375e38 q^{12} -1.84599e39 q^{13} -5.73732e40 q^{14} -5.37518e41 q^{15} +2.41968e43 q^{16} +4.60184e43 q^{17} -2.39106e44 q^{18} -3.59368e45 q^{19} +7.26612e46 q^{20} -3.00504e46 q^{21} +4.78458e47 q^{22} -3.60035e47 q^{23} +2.10378e49 q^{24} +7.30729e49 q^{25} +1.76332e50 q^{26} -1.25237e50 q^{27} +4.06219e51 q^{28} +2.60359e51 q^{29} +5.13447e52 q^{30} -6.00487e52 q^{31} -1.31847e54 q^{32} +2.50603e53 q^{33} -4.39576e54 q^{34} +6.45291e54 q^{35} +1.69294e55 q^{36} -9.09423e54 q^{37} +3.43275e56 q^{38} +9.23578e55 q^{39} -4.51758e57 q^{40} +2.33340e57 q^{41} +2.87047e57 q^{42} +9.88722e57 q^{43} -3.38763e58 q^{44} +2.68929e58 q^{45} +3.43911e58 q^{46} +8.25094e58 q^{47} -1.21060e60 q^{48} -6.43769e59 q^{49} -6.98005e60 q^{50} -2.30237e60 q^{51} -1.24848e61 q^{52} -5.19654e59 q^{53} +1.19628e61 q^{54} -5.38134e61 q^{55} -2.52559e62 q^{56} +1.79798e62 q^{57} -2.48699e62 q^{58} -1.73450e62 q^{59} -3.63535e63 q^{60} +3.56730e63 q^{61} +5.73596e63 q^{62} +1.50347e63 q^{63} +6.88091e64 q^{64} -1.98326e64 q^{65} -2.39380e64 q^{66} -1.11521e65 q^{67} +3.11233e65 q^{68} +1.80131e64 q^{69} -6.16393e65 q^{70} +2.19894e65 q^{71} -1.05255e66 q^{72} +1.58732e66 q^{73} +8.68697e65 q^{74} -3.65595e66 q^{75} -2.43049e67 q^{76} -3.00849e66 q^{77} -8.82218e66 q^{78} +4.62485e66 q^{79} +2.59960e68 q^{80} +6.26579e66 q^{81} -2.22891e68 q^{82} +2.07787e68 q^{83} -2.03238e68 q^{84} +4.94403e68 q^{85} -9.44445e68 q^{86} -1.30262e68 q^{87} +2.10619e69 q^{88} +1.63858e69 q^{89} -2.56885e69 q^{90} -1.10876e69 q^{91} -2.43499e69 q^{92} +3.00433e69 q^{93} -7.88144e69 q^{94} -3.86090e70 q^{95} +6.59649e70 q^{96} +1.45726e70 q^{97} +6.14940e70 q^{98} -1.25380e70 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 72903656826 q^{2} - 30\!\cdots\!42 q^{3}+ \cdots + 15\!\cdots\!94 q^{9}+O(q^{10}) \) 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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