LMFDB - Embedded newform 2.72.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,72,Mod(1,2)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 72, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 72);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 72 $
Character orbit:	$[\chi]$	$=$	2.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:	$63.8492321122$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 63394039540968776880 $ x^2 - x - 63394039540968776880
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{6}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$7.96204e9$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.43597e10 q^{2} -9.23668e16 q^{3} +1.18059e21 q^{4} +8.49883e24 q^{5} -3.17370e27 q^{6} -9.92557e29 q^{7} +4.05648e31 q^{8} +1.02216e33 q^{9} +O(q^{10})$	\(q+3.43597e10 q^{2} -9.23668e16 q^{3} +1.18059e21 q^{4} +8.49883e24 q^{5} -3.17370e27 q^{6} -9.92557e29 q^{7} +4.05648e31 q^{8} +1.02216e33 q^{9} +2.92018e35 q^{10} +7.28736e36 q^{11} -1.09047e38 q^{12} -2.66530e39 q^{13} -3.41040e40 q^{14} -7.85010e41 q^{15} +1.39380e42 q^{16} +3.09524e43 q^{17} +3.51211e43 q^{18} -3.31510e45 q^{19} +1.00336e46 q^{20} +9.16793e46 q^{21} +2.50392e47 q^{22} +3.26296e48 q^{23} -3.74684e48 q^{24} +2.98785e49 q^{25} -9.15789e49 q^{26} +5.99212e50 q^{27} -1.17180e51 q^{28} -1.26107e52 q^{29} -2.69727e52 q^{30} +8.89879e52 q^{31} +4.78905e52 q^{32} -6.73110e53 q^{33} +1.06352e54 q^{34} -8.43557e54 q^{35} +1.20675e54 q^{36} -6.86465e55 q^{37} -1.13906e56 q^{38} +2.46185e56 q^{39} +3.44754e56 q^{40} +1.41861e57 q^{41} +3.15008e57 q^{42} -1.16574e58 q^{43} +8.60340e57 q^{44} +8.68716e57 q^{45} +1.12114e59 q^{46} -2.61051e59 q^{47} -1.28741e59 q^{48} -1.93567e58 q^{49} +1.02662e60 q^{50} -2.85898e60 q^{51} -3.14663e60 q^{52} -1.32728e61 q^{53} +2.05888e61 q^{54} +6.19341e61 q^{55} -4.02629e61 q^{56} +3.06205e62 q^{57} -4.33301e62 q^{58} -6.93098e62 q^{59} -9.26776e62 q^{60} -3.89181e63 q^{61} +3.05760e63 q^{62} -1.01455e63 q^{63} +1.64550e63 q^{64} -2.26519e64 q^{65} -2.31279e64 q^{66} -4.41133e64 q^{67} +3.65422e64 q^{68} -3.01389e65 q^{69} -2.89844e65 q^{70} -5.78179e65 q^{71} +4.14637e64 q^{72} -6.21903e65 q^{73} -2.35868e66 q^{74} -2.75978e66 q^{75} -3.91377e66 q^{76} -7.23312e66 q^{77} +8.45885e66 q^{78} +4.06300e67 q^{79} +1.18456e67 q^{80} -6.30231e67 q^{81} +4.87431e67 q^{82} -1.39648e67 q^{83} +1.08236e68 q^{84} +2.63059e68 q^{85} -4.00545e68 q^{86} +1.16481e69 q^{87} +2.95610e68 q^{88} +1.62547e69 q^{89} +2.98488e68 q^{90} +2.64546e69 q^{91} +3.85222e69 q^{92} -8.21953e69 q^{93} -8.96965e69 q^{94} -2.81744e70 q^{95} -4.42349e69 q^{96} +2.89197e69 q^{97} -6.65091e68 q^{98} +7.44884e69 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 68719476736 q^{2} - 73\!\cdots\!24 q^{3}+ \cdots - 61\!\cdots\!06 q^{9}+O(q^{10}) $ 2 * q + 68719476736 * q^2 - 73290552574846824 * q^3 + 2361183241434822606848 * q^4 + 4017561682270957567057500 * q^5 - 2518244211317885610315743232 * q^6 - 291238690173693964386145313552 * q^7 + 81129638414606681695789005144064 * q^8 - 6123404334975269213441745958191606 * q^9	$ 2 q + 68719476736 q^{2} - 73\!\cdots\!24 q^{3}+ \cdots - 25\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q + 68719476736 * q^2 - 73290552574846824 * q^3 + 2361183241434822606848 * q^4 + 4017561682270957567057500 * q^5 - 2518244211317885610315743232 * q^6 - 291238690173693964386145313552 * q^7 + 81129638414606681695789005144064 * q^8 - 6123404334975269213441745958191606 * q^9 + 138042368280132046088925515612160000 * q^10 + 8684021980716172090887525376850576904 * q^11 - 86526212247613054049400939322986725376 * q^12 - 1127526476847602121775517379388630880564 * q^13 - 10006885197007137092408662697676044763136 * q^14 - 870495707981432852912957098986798794190000 * q^15 + 2787593149816327892691964784081045188247552 * q^16 - 25310632831657129209270924115310927130954012 * q^17 - 210398570871227281924223539932585048573739008 * q^18 - 1515676621589311845828943656442220865774179720 * q^19 + 4743099657804439236107998378673316959354880000 * q^20 + 105057783932094120306762036640883833267054319424 * q^21 + 298380723239368814309358888863546426251303452672 * q^22 + 2203172021093641748810865503399372374910614063056 * q^23 - 2973018014802021769638859222271266932256426426368 * q^24 + 7608631123084092334620703396661508984732192968750 * q^25 - 38741514747476418312368452783630352849904496279552 * q^26 + 319648868947993055224983298099305125670447984140400 * q^27 - 343833957247777367123869889228909979682409491202048 * q^28 - 9698728689773075098486688545271532504346978353044820 * q^29 - 29910004776708962227849032598394684454226278481920000 * q^30 - 40152449056044233071756067933578167284289756136602176 * q^31 + 95780971304118053647396689196894323976171195136475136 * q^32 - 646467126733774659938188551326031765296979936890156448 * q^33 - 869666722024249947512519672631665319191092726559932416 * q^34 - 11578366136761156330569053956326057915336741584188620000 * q^35 - 7229239848136475225980096433630422626902243870395858944 * q^36 - 111302567218665505327715068364071188329715510661736133092 * q^37 - 52078252168302895367845656117167986656871260949011496960 * q^38 + 275519833227064980098009665274252977678408104840329524368 * q^39 + 162971663295510861461624602883383361666170966864035840000 * q^40 + 1293621751110559774763864122730511857252280974968281452724 * q^41 + 3609757969428628252091459480215598083336921089452940460032 * q^42 - 1570188515420028543133617556744083017145937257828102471224 * q^43 + 10252283584559329897127946035166644058616193652784990519296 * q^44 + 40708357615001912362112184537766135586032750500530146327500 * q^45 + 75700414224475307717463313812439049417335506592825614532608 * q^46 - 385166682154840572374711553898575384547395544426269119145312 * q^47 - 102152121151948219322231568723224690516220791896645696487424 * q^48 - 532035159715732504433438538355987707216238966761163005601134 * q^49 + 261430574727791417880321677225418373371479456953139200000000 * q^50 - 3932264303948319406691865647256788003255613422904957101311056 * q^51 - 1331148310703303321462704136062500237146241665952236108251136 * q^52 - 3099963518619652809000040240867303977580091183911870344857604 * q^53 + 10983051506680160776211401499861875800637953324417157378867200 * q^54 + 55675237030386993027088191557939523809594236008364091073990000 * q^55 - 11814044813067727683888054041578488163711785849542367105777664 * q^56 + 340530979210937295973262581310223186047069690231491850122484640 * q^57 - 333245780282818297674818451146232380367769998901979551377653760 * q^58 - 1634769282638530993938532031464170850734659495713497861208919640 * q^59 - 1027699938713350202229687163482744574649131800509079418306560000 * q^60 - 4880654092824262768274295733939273946937692231886071744774910356 * q^61 - 1379627644400128417380751464514180229965133097556173235859488768 * q^62 - 6025861853395026499121119084837033105792949783823904688557137744 * q^63 + 3291009114642412084309938365114701009965471731267159726697218048 * q^64 - 29543075418903360367582342730855024802992366467179006798718215000 * q^65 - 22212441338085195704544329675415390923261412452090927107868196864 * q^66 - 134179938663497929036082688157452363116312631094129088359318071272 * q^67 - 29881521036109411547967908356077030399545155480627042485522137088 * q^68 - 321605797179791219242936222377661308526135728863885795131895787072 * q^69 - 397829631188024238423499614496638648471785935450346828762972160000 * q^70 - 1460877510745740582710287713995347696234833946793802259869191016336 * q^71 - 248394789781489341122389789834951197865628377698933413906472763392 * q^72 - 3294544566820717164014310852275588208456751477490323839459061757324 * q^73 - 3824327089320080209166799848240719802335879866208768081693146873856 * q^74 - 3184606446584112229377097409458775389197568519591749999600534375000 * q^75 - 1789395119165616187416055863991190774635411515666290423769627361280 * q^76 - 6253614148334332819110227681464586033924531964755455804402474941504 * q^77 + 9466789384876945852702739096358587279675046525044436872190360551424 * q^78 + 32545937316211131695260490720524848524451973434380542886241294936160 * q^79 + 5599663712231541868723715427304950721493954977805868890975109120000 * q^80 - 14696790322123460114208775627144901209272992806663832631738624054318 * q^81 + 44448504915312847302911380237722229185910137671134107814183600914432 * q^82 + 29029289096582559444238889025865399025664140946681211932408984041976 * q^83 + 124030339401370609190995696547481222376098869028264558454981080907776 * q^84 + 515189414072415878332203587875687294826517223054383338648578942155000 * q^85 - 53951266578270514369163302115098086401206462253116960829150888722432 * q^86 + 1220360737986859838823441297151020036222068694550765089326808848685840 * q^87 + 352265781639999779838716580389548817134634070037714508800371015548928 * q^88 + 3892840256317115370330682179701204942142442453315338735392476328046420 * q^89 + 1398728517042446180581839536582579433906499662277636873109656043520000 * q^90 + 3723923831232087792375243174156474165096790899907919377283839137781664 * q^91 + 2601046427102197195248330727233686361926270850206227221189229484703744 * q^92 - 10683042981025141340950338658167930386609577245004285723682658026015488 * q^93 - 13234226426910936531546457451421780620973501002295527600190740093730816 * q^94 - 36238128778010894690559462260868212446184933626918861697256245230950000 * q^95 - 3509920156517179589395358987240212171415117269690520628101025242284032 * q^96 - 57797943272861961641603344152467986900234375803899254441558412075626172 * q^97 - 18280588890409662105806348248520070466174156498880209215855482804109312 * q^98 - 2531090145827533343099848313526915248178613009899410920700202513213912 * 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 $

$2$	3.43597e10	0.707107
$2$	3.43597e10	0.707107
$3$	−9.23668e16	−1.06589	−0.532944	−	0.846151i	$-0.678914\pi$
$3$	−9.23668e16	−1.06589	−0.532944	+	0.846151i	$0.678914\pi$
$4$	1.18059e21	0.500000
$5$	8.49883e24	1.30594	0.652971	−	0.757383i	$-0.273522\pi$
$5$	8.49883e24	1.30594	0.652971	+	0.757383i	$0.273522\pi$
$6$	−3.17370e27	−0.753696
$7$	−9.92557e29	−0.990318	−0.495159	−	0.868802i	$-0.664890\pi$
$7$	−9.92557e29	−0.990318	−0.495159	+	0.868802i	$0.664890\pi$
$8$	4.05648e31	0.353553
$9$	1.02216e33	0.136116
$10$	2.92018e35	0.923441
$11$	7.28736e36	0.781862	0.390931	−	0.920420i	$-0.372153\pi$
$11$	7.28736e36	0.781862	0.390931	+	0.920420i	$0.372153\pi$
$12$	−1.09047e38	−0.532944
$13$	−2.66530e39	−0.759900	−0.379950	−	0.925007i	$-0.624059\pi$
$13$	−2.66530e39	−0.759900	−0.379950	+	0.925007i	$0.624059\pi$
$14$	−3.41040e40	−0.700261
$15$	−7.85010e41	−1.39199
$16$	1.39380e42	0.250000
$17$	3.09524e43	0.645295	0.322647	−	0.946519i	$-0.395427\pi$
$17$	3.09524e43	0.645295	0.322647	+	0.946519i	$0.395427\pi$
$18$	3.51211e43	0.0962486
$19$	−3.31510e45	−1.33273	−0.666367	−	0.745624i	$-0.732151\pi$
$19$	−3.31510e45	−1.33273	−0.666367	+	0.745624i	$0.732151\pi$
$20$	1.00336e46	0.652971
$21$	9.16793e46	1.05557
$22$	2.50392e47	0.552860
$23$	3.26296e48	1.48687	0.743436	−	0.668807i	$-0.233195\pi$
$23$	3.26296e48	1.48687	0.743436	+	0.668807i	$0.233195\pi$
$24$	−3.74684e48	−0.376848
$25$	2.98785e49	0.705486
$26$	−9.15789e49	−0.537331
$27$	5.99212e50	0.920803
$28$	−1.17180e51	−0.495159
$29$	−1.26107e52	−1.53324	−0.766621	−	0.642100i	$-0.778063\pi$
$29$	−1.26107e52	−1.53324	−0.766621	+	0.642100i	$0.778063\pi$
$30$	−2.69727e52	−0.984284
$31$	8.89879e52	1.01389	0.506945	−	0.861978i	$-0.330775\pi$
$31$	8.89879e52	1.01389	0.506945	+	0.861978i	$0.330775\pi$
$32$	4.78905e52	0.176777
$33$	−6.73110e53	−0.833377
$34$	1.06352e54	0.456292
$35$	−8.43557e54	−1.29330
$36$	1.20675e54	0.0680580
$37$	−6.86465e55	−1.46372	−0.731858	−	0.681457i	$-0.761347\pi$
$37$	−6.86465e55	−1.46372	−0.731858	+	0.681457i	$0.761347\pi$
$38$	−1.13906e56	−0.942385
$39$	2.46185e56	0.809968
$40$	3.44754e56	0.461720
$41$	1.41861e57	0.790745	0.395372	−	0.918521i	$-0.370616\pi$
$41$	1.41861e57	0.790745	0.395372	+	0.918521i	$0.370616\pi$
$42$	3.15008e57	0.746399
$43$	−1.16574e58	−1.19804	−0.599020	−	0.800734i	$-0.704443\pi$
$43$	−1.16574e58	−1.19804	−0.599020	+	0.800734i	$0.704443\pi$
$44$	8.60340e57	0.390931
$45$	8.68716e57	0.177760
$46$	1.12114e59	1.05138
$47$	−2.61051e59	−1.14091	−0.570456	−	0.821328i	$-0.693233\pi$
$47$	−2.61051e59	−1.14091	−0.570456	+	0.821328i	$0.693233\pi$
$48$	−1.28741e59	−0.266472
$49$	−1.93567e58	−0.0192695
$50$	1.02662e60	0.498854
$51$	−2.85898e60	−0.687811
$52$	−3.14663e60	−0.379950
$53$	−1.32728e61	−0.815024	−0.407512	−	0.913200i	$-0.633604\pi$
$53$	−1.32728e61	−0.815024	−0.407512	+	0.913200i	$0.633604\pi$
$54$	2.05888e61	0.651106
$55$	6.19341e61	1.02107
$56$	−4.02629e61	−0.350130
$57$	3.06205e62	1.42054
$58$	−4.33301e62	−1.08417
$59$	−6.93098e62	−0.945253	−0.472627	−	0.881263i	$-0.656694\pi$
$59$	−6.93098e62	−0.945253	−0.472627	+	0.881263i	$0.656694\pi$
$60$	−9.26776e62	−0.695994
$61$	−3.89181e63	−1.62533	−0.812667	−	0.582728i	$-0.801985\pi$
$61$	−3.89181e63	−1.62533	−0.812667	+	0.582728i	$0.801985\pi$
$62$	3.05760e63	0.716929
$63$	−1.01455e63	−0.134798
$64$	1.64550e63	0.125000
$65$	−2.26519e64	−0.992386
$66$	−2.31279e64	−0.589286
$67$	−4.41133e64	−0.659044	−0.329522	−	0.944148i	$-0.606888\pi$
$67$	−4.41133e64	−0.659044	−0.329522	+	0.944148i	$0.606888\pi$
$68$	3.65422e64	0.322647
$69$	−3.01389e65	−1.58484
$70$	−2.89844e65	−0.914500
$71$	−5.78179e65	−1.10253	−0.551266	−	0.834330i	$-0.685855\pi$
$71$	−5.78179e65	−1.10253	−0.551266	+	0.834330i	$0.685855\pi$
$72$	4.14637e64	0.0481243
$73$	−6.21903e65	−0.442345	−0.221172	−	0.975235i	$-0.570988\pi$
$73$	−6.21903e65	−0.442345	−0.221172	+	0.975235i	$0.570988\pi$
$74$	−2.35868e66	−1.03500
$75$	−2.75978e66	−0.751969
$76$	−3.91377e66	−0.666367
$77$	−7.23312e66	−0.774292
$78$	8.45885e66	0.572734
$79$	4.06300e67	1.75019	0.875095	−	0.483950i	$-0.160798\pi$
$79$	4.06300e67	1.75019	0.875095	+	0.483950i	$0.160798\pi$
$80$	1.18456e67	0.326486
$81$	−6.30231e67	−1.11759
$82$	4.87431e67	0.559141
$83$	−1.39648e67	−0.104175	−0.0520874	−	0.998643i	$-0.516587\pi$
$83$	−1.39648e67	−0.104175	−0.0520874	+	0.998643i	$0.516587\pi$
$84$	1.08236e68	0.527784
$85$	2.63059e68	0.842718
$86$	−4.00545e68	−0.847142
$87$	1.16481e69	1.63426
$88$	2.95610e68	0.276430
$89$	1.62547e69	1.01773	0.508866	−	0.860845i	$-0.330065\pi$
$89$	1.62547e69	1.01773	0.508866	+	0.860845i	$0.330065\pi$
$90$	2.98488e68	0.125695
$91$	2.64546e69	0.752543
$92$	3.85222e69	0.743436
$93$	−8.21953e69	−1.08069
$94$	−8.96965e69	−0.806746
$95$	−2.81744e70	−1.74047
$96$	−4.42349e69	−0.188424
$97$	2.89197e69	0.0852702	0.0426351	−	0.999091i	$-0.486425\pi$
$97$	2.89197e69	0.0852702	0.0426351	+	0.999091i	$0.486425\pi$
$98$	−6.65091e68	−0.0136256
$99$	7.44884e69	0.106424
$100$	3.52743e70	0.352743
$101$	−2.42494e71	−1.70331	−0.851653	−	0.524106i	$-0.824399\pi$
$101$	−2.42494e71	−1.70331	−0.851653	+	0.524106i	$0.824399\pi$
$102$	−9.82337e70	−0.486356
$103$	3.03301e70	0.106207	0.0531034	−	0.998589i	$-0.483089\pi$
$103$	3.03301e70	0.106207	0.0531034	+	0.998589i	$0.483089\pi$
$104$	−1.08117e71	−0.268665
$105$	7.79167e71	1.37851
$106$	−4.56051e71	−0.576309
$107$	1.08526e72	0.982673	0.491337	−	0.870970i	$-0.336508\pi$
$107$	1.08526e72	0.982673	0.491337	+	0.870970i	$0.336508\pi$
$108$	7.07424e71	0.460402
$109$	−2.27024e72	−1.06520	−0.532600	−	0.846367i	$-0.678785\pi$
$109$	−2.27024e72	−1.06520	−0.532600	+	0.846367i	$0.678785\pi$
$110$	2.12804e72	0.722003
$111$	6.34066e72	1.56016
$112$	−1.38342e72	−0.247580
$113$	−8.35978e72	−1.09121	−0.545607	−	0.838041i	$-0.683701\pi$
$113$	−8.35978e72	−1.09121	−0.545607	+	0.838041i	$0.683701\pi$
$114$	1.05211e73	1.00448
$115$	2.77313e73	1.94177
$116$	−1.48881e73	−0.766621
$117$	−2.72436e72	−0.103435
$118$	−2.38147e73	−0.668395
$119$	−3.07220e73	−0.639047
$120$	−3.18438e73	−0.492142
$121$	−3.37665e73	−0.388692
$122$	−1.33722e74	−1.14928
$123$	−1.31032e74	−0.842845
$124$	1.05058e74	0.506945
$125$	−1.06007e74	−0.384618
$126$	−3.48597e73	−0.0953167
$127$	7.45002e74	1.53860	0.769299	−	0.638889i	$-0.220606\pi$
$127$	7.45002e74	1.53860	0.769299	+	0.638889i	$0.220606\pi$
$128$	5.65391e73	0.0883883
$129$	1.07676e75	1.27698
$130$	−7.78314e74	−0.701723
$131$	−1.03505e75	−0.710933	−0.355467	−	0.934689i	$-0.615678\pi$
$131$	−1.03505e75	−0.710933	−0.355467	+	0.934689i	$0.615678\pi$
$132$	−7.94668e74	−0.416688
$133$	3.29042e75	1.31983
$134$	−1.51572e75	−0.466014
$135$	5.09260e75	1.20252
$136$	1.25558e75	0.228146
$137$	5.98104e75	0.837909	0.418955	−	0.908007i	$-0.362397\pi$
$137$	5.98104e75	0.837909	0.418955	+	0.908007i	$0.362397\pi$
$138$	−1.03556e76	−1.12065
$139$	3.86691e75	0.323846	0.161923	−	0.986803i	$-0.448230\pi$
$139$	3.86691e75	0.323846	0.161923	+	0.986803i	$0.448230\pi$
$140$	−9.95896e75	−0.646649
$141$	2.41125e76	1.21608
$142$	−1.98661e76	−0.779607
$143$	−1.94230e76	−0.594137
$144$	1.42468e75	0.0340290
$145$	−1.07176e77	−2.00233
$146$	−2.13684e76	−0.312785
$147$	1.78792e75	0.0205391
$148$	−8.10435e76	−0.731858
$149$	2.70209e77	1.92126	0.960631	−	0.277828i	$-0.0896144\pi$
$149$	2.70209e77	1.92126	0.960631	+	0.277828i	$0.0896144\pi$
$150$	−9.48254e76	−0.531722
$151$	1.79093e77	0.793228	0.396614	−	0.917985i	$-0.370185\pi$
$151$	1.79093e77	0.793228	0.396614	+	0.917985i	$0.370185\pi$
$152$	−1.34476e77	−0.471192
$153$	3.16383e76	0.0878349
$154$	−2.48528e77	−0.547507
$155$	7.56293e77	1.32408
$156$	2.90644e77	0.404984
$157$	6.39482e76	0.0710217	0.0355108	−	0.999369i	$-0.488694\pi$
$157$	6.39482e76	0.0710217	0.0355108	+	0.999369i	$0.488694\pi$
$158$	1.39604e78	1.23757
$159$	1.22597e78	0.868724
$160$	4.07013e77	0.230860
$161$	−3.23867e78	−1.47248
$162$	−2.16546e78	−0.790254
$163$	−2.53862e78	−0.744625	−0.372312	−	0.928108i	$-0.621435\pi$
$163$	−2.53862e78	−0.744625	−0.372312	+	0.928108i	$0.621435\pi$
$164$	1.67480e78	0.395372
$165$	−5.72065e78	−1.08834
$166$	−4.79827e77	−0.0736627
$167$	3.67379e78	0.455700	0.227850	−	0.973696i	$-0.426830\pi$
$167$	3.67379e78	0.455700	0.227850	+	0.973696i	$0.426830\pi$
$168$	3.71895e78	0.373200
$169$	−5.19826e78	−0.422552
$170$	9.03865e78	0.595891
$171$	−3.38856e78	−0.181406
$172$	−1.37626e79	−0.599020
$173$	−3.95908e79	−1.40268	−0.701339	−	0.712828i	$-0.747414\pi$
$173$	−3.95908e79	−1.40268	−0.701339	+	0.712828i	$0.747414\pi$
$174$	4.00226e79	1.15560
$175$	−2.96561e79	−0.698656
$176$	1.01571e79	0.195465
$177$	6.40192e79	1.00753
$178$	5.58507e79	0.719646
$179$	−6.45436e79	−0.681664	−0.340832	−	0.940124i	$-0.610709\pi$
$179$	−6.45436e79	−0.681664	−0.340832	+	0.940124i	$0.610709\pi$
$180$	1.02560e79	0.0888799
$181$	1.27704e80	0.909108	0.454554	−	0.890719i	$-0.349799\pi$
$181$	1.27704e80	0.909108	0.454554	+	0.890719i	$0.349799\pi$
$182$	9.08972e79	0.532128
$183$	3.59474e80	1.73242
$184$	1.32361e80	0.525688
$185$	−5.83415e80	−1.91153
$186$	−2.82421e80	−0.764165
$187$	2.25561e80	0.504531
$188$	−3.08195e80	−0.570456
$189$	−5.94752e80	−0.911888
$190$	−9.68067e80	−1.23070
$191$	7.68172e80	0.810539	0.405269	−	0.914197i	$-0.367178\pi$
$191$	7.68172e80	0.810539	0.405269	+	0.914197i	$0.367178\pi$
$192$	−1.51990e80	−0.133236
$193$	−1.27166e81	−0.927015	−0.463508	−	0.886093i	$-0.653409\pi$
$193$	−1.27166e81	−0.927015	−0.463508	+	0.886093i	$0.653409\pi$
$194$	9.93673e79	0.0602951
$195$	2.09228e81	1.05777
$196$	−2.28524e79	−0.00963475
$197$	−1.74454e81	−0.613946	−0.306973	−	0.951718i	$-0.599316\pi$
$197$	−1.74454e81	−0.613946	−0.306973	+	0.951718i	$0.599316\pi$
$198$	2.55940e80	0.0752531
$199$	2.36803e81	0.582242	0.291121	−	0.956686i	$-0.405972\pi$
$199$	2.36803e81	0.582242	0.291121	+	0.956686i	$0.405972\pi$
$200$	1.21202e81	0.249427
$201$	4.07461e81	0.702467
$202$	−8.33204e81	−1.20442
$203$	1.25168e82	1.51840
$204$	−3.37528e81	−0.343906
$205$	1.20565e82	1.03267
$206$	1.04213e81	0.0750996
$207$	3.33526e81	0.202387
$208$	−3.71488e81	−0.189975
$209$	−2.41583e82	−1.04201
$210$	2.67720e82	0.974755
$211$	−5.10102e82	−1.56902	−0.784512	−	0.620114i	$-0.787086\pi$
$211$	−5.10102e82	−1.56902	−0.784512	+	0.620114i	$0.787086\pi$
$212$	−1.56698e82	−0.407512
$213$	5.34045e82	1.17517
$214$	3.72892e82	0.694855
$215$	−9.90742e82	−1.56457
$216$	2.43069e82	0.325553
$217$	−8.83255e82	−1.00407
$218$	−7.80048e82	−0.753210
$219$	5.74432e82	0.471490
$220$	7.31188e82	0.510533
$221$	−8.24974e82	−0.490359
$222$	2.17863e83	1.10320
$223$	−1.54284e83	−0.666038	−0.333019	−	0.942920i	$-0.608067\pi$
$223$	−1.54284e83	−0.666038	−0.333019	+	0.942920i	$0.608067\pi$
$224$	−4.75340e82	−0.175065
$225$	3.05406e82	0.0960280
$226$	−2.87240e83	−0.771605
$227$	−1.70944e82	−0.0392586	−0.0196293	−	0.999807i	$-0.506249\pi$
$227$	−1.70944e82	−0.0392586	−0.0196293	+	0.999807i	$0.506249\pi$
$228$	3.61503e83	0.710272
$229$	9.55862e83	1.60781	0.803907	−	0.594756i	$-0.202751\pi$
$229$	9.55862e83	1.60781	0.803907	+	0.594756i	$0.202751\pi$
$230$	9.52841e83	1.37304
$231$	6.68100e83	0.825308
$232$	−5.11551e83	−0.542083
$233$	7.73687e83	0.703769	0.351884	−	0.936043i	$-0.385541\pi$
$233$	7.73687e83	0.703769	0.351884	+	0.936043i	$0.385541\pi$
$234$	−9.36082e82	−0.0731393
$235$	−2.21863e84	−1.48996
$236$	−8.18266e83	−0.472627
$237$	−3.75287e84	−1.86551
$238$	−1.05560e84	−0.451874
$239$	−4.19002e83	−0.154558	−0.0772788	−	0.997010i	$-0.524623\pi$
$239$	−4.19002e83	−0.154558	−0.0772788	+	0.997010i	$0.524623\pi$
$240$	−1.09414e84	−0.347997
$241$	5.94373e84	1.63100	0.815500	−	0.578757i	$-0.196462\pi$
$241$	5.94373e84	1.63100	0.815500	+	0.578757i	$0.196462\pi$
$242$	−1.16021e84	−0.274847
$243$	1.32149e84	0.270420
$244$	−4.59464e84	−0.812667
$245$	−1.64509e83	−0.0251649
$246$	−4.50224e84	−0.595981
$247$	8.83572e84	1.01274
$248$	3.60978e84	0.358464
$249$	1.28988e84	0.111039
$250$	−3.64238e84	−0.271966
$251$	−3.58077e84	−0.232038	−0.116019	−	0.993247i	$-0.537013\pi$
$251$	−3.58077e84	−0.232038	−0.116019	+	0.993247i	$0.537013\pi$
$252$	−1.19777e84	−0.0673991
$253$	2.37784e85	1.16253
$254$	2.55981e85	1.08795
$255$	−2.42980e85	−0.898242
$256$	1.94267e84	0.0625000
$257$	−3.64352e85	−1.02069	−0.510346	−	0.859969i	$-0.670483\pi$
$257$	−3.64352e85	−1.02069	−0.510346	+	0.859969i	$0.670483\pi$
$258$	3.69971e85	0.902958
$259$	6.81355e85	1.44955
$260$	−2.67427e85	−0.496193
$261$	−1.28902e85	−0.208699
$262$	−3.55639e85	−0.502706
$263$	2.38509e85	0.294493	0.147247	−	0.989100i	$-0.452959\pi$
$263$	2.38509e85	0.294493	0.147247	+	0.989100i	$0.452959\pi$
$264$	−2.73046e85	−0.294643
$265$	−1.12804e86	−1.06438
$266$	1.13058e86	0.933261
$267$	−1.50139e86	−1.08479
$268$	−5.20798e85	−0.329522
$269$	−3.04581e86	−1.68849	−0.844243	−	0.535961i	$-0.819949\pi$
$269$	−3.04581e86	−1.68849	−0.844243	+	0.535961i	$0.819949\pi$
$270$	1.74980e86	0.850307
$271$	1.64028e86	0.699049	0.349525	−	0.936927i	$-0.386343\pi$
$271$	1.64028e86	0.699049	0.349525	+	0.936927i	$0.386343\pi$
$272$	4.31414e85	0.161324
$273$	−2.44352e86	−0.802126
$274$	2.05507e86	0.592491
$275$	2.17735e86	0.551593
$276$	−3.55817e86	−0.792419
$277$	2.66441e86	0.521879	0.260940	−	0.965355i	$-0.415968\pi$
$277$	2.66441e86	0.521879	0.260940	+	0.965355i	$0.415968\pi$
$278$	1.32866e86	0.228994
$279$	9.09598e85	0.138007
$280$	−3.42187e86	−0.457250
$281$	1.09637e87	1.29087	0.645435	−	0.763815i	$-0.276676\pi$
$281$	1.09637e87	1.29087	0.645435	+	0.763815i	$0.276676\pi$
$282$	8.28498e86	0.859901
$283$	1.69440e86	0.155095	0.0775474	−	0.996989i	$-0.475291\pi$
$283$	1.69440e86	0.155095	0.0775474	+	0.996989i	$0.475291\pi$
$284$	−6.82593e86	−0.551266
$285$	2.60238e87	1.85515
$286$	−6.67369e86	−0.420118
$287$	−1.40805e87	−0.783089
$288$	4.89517e85	0.0240621
$289$	−1.34272e87	−0.583595
$290$	−3.68255e87	−1.41586
$291$	−2.67122e86	−0.0908884
$292$	−7.34213e86	−0.221172
$293$	−5.46726e85	−0.0145871	−0.00729355	−	0.999973i	$-0.502322\pi$
$293$	−5.46726e85	−0.0145871	−0.00729355	+	0.999973i	$0.502322\pi$
$294$	6.14323e85	0.0145233
$295$	−5.89052e87	−1.23445
$296$	−2.78463e87	−0.517502
$297$	4.36667e87	0.719941
$298$	9.28430e87	1.35854
$299$	−8.69675e87	−1.12987
$300$	−3.25817e87	−0.375984
$301$	1.15706e88	1.18644
$302$	6.15360e87	0.560897
$303$	2.23984e88	1.81553
$304$	−4.62057e87	−0.333183
$305$	−3.30759e88	−2.12259
$306$	1.08708e87	0.0621087
$307$	1.78937e88	0.910515	0.455257	−	0.890360i	$-0.349547\pi$
$307$	1.78937e88	0.910515	0.455257	+	0.890360i	$0.349547\pi$
$308$	−8.53936e87	−0.387146
$309$	−2.80150e87	−0.113205
$310$	2.59860e88	0.936268
$311$	−5.36276e87	−0.172343	−0.0861716	−	0.996280i	$-0.527463\pi$
$311$	−5.36276e87	−0.172343	−0.0861716	+	0.996280i	$0.527463\pi$
$312$	9.98645e87	0.286367
$313$	−1.38977e88	−0.355728	−0.177864	−	0.984055i	$-0.556919\pi$
$313$	−1.38977e88	−0.355728	−0.177864	+	0.984055i	$0.556919\pi$
$314$	2.19724e87	0.0502199
$315$	−8.62250e87	−0.176039
$316$	4.79675e88	0.875095
$317$	4.28637e88	0.699013	0.349507	−	0.936934i	$-0.386349\pi$
$317$	4.28637e88	0.699013	0.349507	+	0.936934i	$0.386349\pi$
$318$	4.21240e88	0.614281
$319$	−9.18988e88	−1.19878
$320$	1.39849e88	0.163243
$321$	−1.00242e89	−1.04742
$322$	−1.11280e89	−1.04120
$323$	−1.02610e89	−0.860006
$324$	−7.44046e88	−0.558794
$325$	−7.96351e88	−0.536099
$326$	−8.72262e88	−0.526529
$327$	2.09695e89	1.13538
$328$	5.75457e88	0.279570
$329$	2.59108e89	1.12987
$330$	−1.96560e89	−0.769574
$331$	4.90355e89	1.72432	0.862159	−	0.506638i	$-0.169112\pi$
$331$	4.90355e89	1.72432	0.862159	+	0.506638i	$0.169112\pi$
$332$	−1.64867e88	−0.0520874
$333$	−7.01676e88	−0.199235
$334$	1.26230e89	0.322229
$335$	−3.74912e89	−0.860674
$336$	1.27782e89	0.263892
$337$	1.44761e89	0.269024	0.134512	−	0.990912i	$-0.457053\pi$
$337$	1.44761e89	0.269024	0.134512	+	0.990912i	$0.457053\pi$
$338$	−1.78611e89	−0.298789
$339$	7.72166e89	1.16311
$340$	3.10566e89	0.421359
$341$	6.48487e89	0.792722
$342$	−1.16430e89	−0.128274
$343$	1.01626e90	1.00940
$344$	−4.72880e89	−0.423571
$345$	−2.56145e90	−2.06971
$346$	−1.36033e90	−0.991843
$347$	−2.12882e90	−1.40101	−0.700506	−	0.713646i	$-0.747042\pi$
$347$	−2.12882e90	−1.40101	−0.700506	+	0.713646i	$0.747042\pi$
$348$	1.37517e90	0.817132
$349$	2.29118e90	1.22958	0.614789	−	0.788691i	$-0.289241\pi$
$349$	2.29118e90	1.22958	0.614789	+	0.788691i	$0.289241\pi$
$350$	−1.01898e90	−0.494024
$351$	−1.59708e90	−0.699718
$352$	3.48995e89	0.138215
$353$	−1.51281e90	−0.541728	−0.270864	−	0.962618i	$-0.587309\pi$
$353$	−1.51281e90	−0.541728	−0.270864	+	0.962618i	$0.587309\pi$
$354$	2.19968e90	0.712434
$355$	−4.91385e90	−1.43984
$356$	1.91902e90	0.508866
$357$	2.83770e90	0.681152
$358$	−2.21770e90	−0.482010
$359$	8.53921e89	0.168099	0.0840494	−	0.996462i	$-0.473215\pi$
$359$	8.53921e89	0.168099	0.0840494	+	0.996462i	$0.473215\pi$
$360$	3.52393e89	0.0628476
$361$	4.80250e90	0.776178
$362$	4.38788e90	0.642836
$363$	3.11891e90	0.414302
$364$	3.12321e90	0.376272
$365$	−5.28545e90	−0.577677
$366$	1.23514e91	1.22501
$367$	−1.26788e91	−1.14139	−0.570694	−	0.821163i	$-0.693326\pi$
$367$	−1.26788e91	−1.14139	−0.570694	+	0.821163i	$0.693326\pi$
$368$	4.54790e90	0.371718
$369$	1.45005e90	0.107633
$370$	−2.00460e91	−1.35166
$371$	1.31740e91	0.807134
$372$	−9.70391e90	−0.540346
$373$	1.05124e90	0.0532156	0.0266078	−	0.999646i	$-0.491529\pi$
$373$	1.05124e90	0.0532156	0.0266078	+	0.999646i	$0.491529\pi$
$374$	7.75023e90	0.356757
$375$	9.79155e90	0.409960
$376$	−1.05895e91	−0.403373
$377$	3.36113e91	1.16511
$378$	−2.04355e91	−0.644802
$379$	2.47534e91	0.711120	0.355560	−	0.934653i	$-0.384290\pi$
$379$	2.47534e91	0.711120	0.355560	+	0.934653i	$0.384290\pi$
$380$	−3.32625e91	−0.870237
$381$	−6.88134e91	−1.63997
$382$	2.63942e91	0.573137
$383$	−1.08516e91	−0.214751	−0.107376	−	0.994219i	$-0.534245\pi$
$383$	−1.08516e91	−0.214751	−0.107376	+	0.994219i	$0.534245\pi$
$384$	−5.22234e90	−0.0942120
$385$	−6.14731e91	−1.01118
$386$	−4.36940e91	−0.655499
$387$	−1.19157e91	−0.163072
$388$	3.41424e90	0.0426351
$389$	−1.55093e91	−0.176759	−0.0883796	−	0.996087i	$-0.528169\pi$
$389$	−1.55093e91	−0.176759	−0.0883796	+	0.996087i	$0.528169\pi$
$390$	7.18903e91	0.747958
$391$	1.00996e92	0.959470
$392$	−7.85201e89	−0.00681280
$393$	9.56039e91	0.757775
$394$	−5.99420e91	−0.434125
$395$	3.45308e92	2.28565
$396$	8.79404e90	0.0532120
$397$	4.58855e90	0.0253871	0.0126935	−	0.999919i	$-0.495959\pi$
$397$	4.58855e90	0.0253871	0.0126935	+	0.999919i	$0.495959\pi$
$398$	8.13650e91	0.411707
$399$	−3.03926e92	−1.40679
$400$	4.16445e91	0.176372
$401$	2.98868e92	1.15839	0.579194	−	0.815190i	$-0.303367\pi$
$401$	2.98868e92	1.15839	0.579194	+	0.815190i	$0.303367\pi$
$402$	1.40002e92	0.496719
$403$	−2.37179e92	−0.770455
$404$	−2.86287e92	−0.851653
$405$	−5.35623e92	−1.45951
$406$	4.30075e92	1.07367
$407$	−5.00252e92	−1.14442
$408$	−1.15974e92	−0.243178
$409$	−2.50889e92	−0.482286	−0.241143	−	0.970490i	$-0.577522\pi$
$409$	−2.50889e92	−0.482286	−0.241143	+	0.970490i	$0.577522\pi$
$410$	4.14259e92	0.730206
$411$	−5.52450e92	−0.893117
$412$	3.58075e91	0.0531034
$413$	6.87939e92	0.936102
$414$	1.14599e92	0.143109
$415$	−1.18685e92	−0.136046
$416$	−1.27642e92	−0.134333
$417$	−3.57174e92	−0.345184
$418$	−8.30073e92	−0.736815
$419$	1.22637e92	0.100006	0.0500029	−	0.998749i	$-0.484077\pi$
$419$	1.22637e92	0.100006	0.0500029	+	0.998749i	$0.484077\pi$
$420$	9.19878e92	0.689256
$421$	1.39807e93	0.962750	0.481375	−	0.876515i	$-0.340137\pi$
$421$	1.39807e93	0.962750	0.481375	+	0.876515i	$0.340137\pi$
$422$	−1.75270e93	−1.10947
$423$	−2.66836e92	−0.155296
$424$	−5.38410e92	−0.288155
$425$	9.24812e92	0.455246
$426$	1.83497e93	0.830974
$427$	3.86284e93	1.60960
$428$	1.28125e93	0.491337
$429$	1.79404e93	0.633283
$430$	−3.40416e93	−1.10632
$431$	−1.49285e93	−0.446758	−0.223379	−	0.974732i	$-0.571709\pi$
$431$	−1.49285e93	−0.446758	−0.223379	+	0.974732i	$0.571709\pi$
$432$	8.35179e92	0.230201
$433$	−2.86723e93	−0.728019	−0.364010	−	0.931395i	$-0.618592\pi$
$433$	−2.86723e93	−0.728019	−0.364010	+	0.931395i	$0.618592\pi$
$434$	−3.03484e93	−0.709988
$435$	9.89953e93	2.13425
$436$	−2.68023e93	−0.532600
$437$	−1.08170e94	−1.98160
$438$	1.97373e93	0.333394
$439$	−1.36801e93	−0.213107	−0.106553	−	0.994307i	$-0.533982\pi$
$439$	−1.36801e93	−0.213107	−0.106553	+	0.994307i	$0.533982\pi$
$440$	2.51234e93	0.361002
$441$	−1.97856e91	−0.00262289
$442$	−2.83459e93	−0.346736
$443$	−3.14720e93	−0.355297	−0.177649	−	0.984094i	$-0.556849\pi$
$443$	−3.14720e93	−0.355297	−0.177649	+	0.984094i	$0.556849\pi$
$444$	7.48573e93	0.780079
$445$	1.38146e94	1.32910
$446$	−5.30117e93	−0.470960
$447$	−2.49583e94	−2.04785
$448$	−1.63326e93	−0.123790
$449$	−6.32716e93	−0.443061	−0.221531	−	0.975153i	$-0.571105\pi$
$449$	−6.32716e93	−0.443061	−0.221531	+	0.975153i	$0.571105\pi$
$450$	1.04937e93	0.0679020
$451$	1.03379e94	0.618253
$452$	−9.86949e93	−0.545607
$453$	−1.65423e94	−0.845492
$454$	−5.87358e92	−0.0277600
$455$	2.24833e94	0.982778
$456$	1.24211e94	0.502238
$457$	5.24008e93	0.196026	0.0980129	−	0.995185i	$-0.468751\pi$
$457$	5.24008e93	0.196026	0.0980129	+	0.995185i	$0.468751\pi$
$458$	3.28432e94	1.13690
$459$	1.85471e94	0.594189
$460$	3.27394e94	0.970884
$461$	9.61738e93	0.264043	0.132021	−	0.991247i	$-0.457853\pi$
$461$	9.61738e93	0.264043	0.132021	+	0.991247i	$0.457853\pi$
$462$	2.29557e94	0.583581
$463$	−5.03886e94	−1.18633	−0.593167	−	0.805079i	$-0.702123\pi$
$463$	−5.03886e94	−1.18633	−0.593167	+	0.805079i	$0.702123\pi$
$464$	−1.75768e94	−0.383310
$465$	−6.98564e94	−1.41132
$466$	2.65837e94	0.497640
$467$	9.93231e94	1.72306	0.861531	−	0.507705i	$-0.169506\pi$
$467$	9.93231e94	1.72306	0.861531	+	0.507705i	$0.169506\pi$
$468$	−3.21635e93	−0.0517173
$469$	4.37850e94	0.652663
$470$	−7.62316e94	−1.05356
$471$	−5.90669e93	−0.0757011
$472$	−2.81154e94	−0.334198
$473$	−8.49516e94	−0.936701
$474$	−1.28947e95	−1.31911
$475$	−9.90501e94	−0.940225
$476$	−3.62702e94	−0.319524
$477$	−1.35670e94	−0.110938
$478$	−1.43968e94	−0.109289
$479$	−2.60784e94	−0.183810	−0.0919051	−	0.995768i	$-0.529296\pi$
$479$	−2.60784e94	−0.183810	−0.0919051	+	0.995768i	$0.529296\pi$
$480$	−3.75945e94	−0.246071
$481$	1.82963e95	1.11228
$482$	2.04225e95	1.15329
$483$	2.99146e95	1.56949
$484$	−3.98645e94	−0.194346
$485$	2.45784e94	0.111358
$486$	4.54059e94	0.191216
$487$	−2.12388e95	−0.831481	−0.415740	−	0.909483i	$-0.636478\pi$
$487$	−2.12388e95	−0.831481	−0.415740	+	0.909483i	$0.636478\pi$
$488$	−1.57871e95	−0.574642
$489$	2.34484e95	0.793686
$490$	−5.65250e93	−0.0177942
$491$	4.85894e94	0.142282	0.0711408	−	0.997466i	$-0.477336\pi$
$491$	4.85894e94	0.142282	0.0711408	+	0.997466i	$0.477336\pi$
$492$	−1.54696e95	−0.421422
$493$	−3.90332e95	−0.989393
$494$	3.03593e95	0.716118
$495$	6.33065e94	0.138984
$496$	1.24031e95	0.253473
$497$	5.73875e95	1.09186
$498$	4.43201e94	0.0785162
$499$	3.56506e95	0.588163	0.294081	−	0.955780i	$-0.404986\pi$
$499$	3.56506e95	0.588163	0.294081	+	0.955780i	$0.404986\pi$
$500$	−1.25151e95	−0.192309
$501$	−3.39336e95	−0.485725
$502$	−1.23034e95	−0.164076
$503$	2.65606e95	0.330046	0.165023	−	0.986290i	$-0.447230\pi$
$503$	2.65606e95	0.330046	0.165023	+	0.986290i	$0.447230\pi$
$504$	−4.11551e94	−0.0476584
$505$	−2.06092e96	−2.22442
$506$	8.17018e95	0.822031
$507$	4.80146e95	0.450392
$508$	8.79543e95	0.769299
$509$	−1.69802e96	−1.38503	−0.692517	−	0.721402i	$-0.743498\pi$
$509$	−1.69802e96	−1.38503	−0.692517	+	0.721402i	$0.743498\pi$
$510$	−8.34872e95	−0.635153
$511$	6.17274e95	0.438062
$512$	6.67496e94	0.0441942
$513$	−1.98644e96	−1.22718
$514$	−1.25190e96	−0.721739
$515$	2.57770e95	0.138700
$516$	1.27121e96	0.638488
$517$	−1.90237e96	−0.892035
$518$	2.34112e96	1.02498
$519$	3.65688e96	1.49510
$520$	−9.18871e95	−0.350861
$521$	−6.03019e95	−0.215076	−0.107538	−	0.994201i	$-0.534297\pi$
$521$	−6.03019e95	−0.215076	−0.107538	+	0.994201i	$0.534297\pi$
$522$	−4.42902e95	−0.147572
$523$	8.32790e95	0.259254	0.129627	−	0.991563i	$-0.458622\pi$
$523$	8.32790e95	0.259254	0.129627	+	0.991563i	$0.458622\pi$
$524$	−1.22197e96	−0.355467
$525$	2.73924e96	0.744688
$526$	8.19511e95	0.208238
$527$	2.75439e96	0.654258
$528$	−9.38179e95	−0.208344
$529$	5.83101e96	1.21079
$530$	−3.87590e96	−0.752627
$531$	−7.08456e95	−0.128664
$532$	3.88464e96	0.659915
$533$	−3.78102e96	−0.600887
$534$	−5.15875e96	−0.767061
$535$	9.22343e96	1.28331
$536$	−1.78945e96	−0.233007
$537$	5.96169e96	0.726578
$538$	−1.04653e97	−1.19394
$539$	−1.41059e95	−0.0150661
$540$	6.01228e96	0.601258
$541$	−1.08118e97	−1.01250	−0.506251	−	0.862386i	$-0.668969\pi$
$541$	−1.08118e97	−1.01250	−0.506251	+	0.862386i	$0.668969\pi$
$542$	5.63595e96	0.494302
$543$	−1.17956e97	−0.969006
$544$	1.48233e96	0.114073
$545$	−1.92944e97	−1.39109
$546$	−8.39589e96	−0.567189
$547$	−2.08862e97	−1.32224	−0.661120	−	0.750280i	$-0.729919\pi$
$547$	−2.08862e97	−1.32224	−0.661120	+	0.750280i	$0.729919\pi$
$548$	7.06117e96	0.418955
$549$	−3.97805e96	−0.221234
$550$	7.48133e96	0.390035
$551$	4.18057e97	2.04340
$552$	−1.22258e97	−0.560325
$553$	−4.03276e97	−1.73325
$554$	9.15486e96	0.369024
$555$	5.38882e97	2.03748
$556$	4.56524e96	0.161923
$557$	4.66202e97	1.55137	0.775683	−	0.631122i	$-0.217405\pi$
$557$	4.66202e97	1.55137	0.775683	+	0.631122i	$0.217405\pi$
$558$	3.12536e96	0.0975855
$559$	3.10704e97	0.910391
$560$	−1.17575e97	−0.323325
$561$	−2.08344e97	−0.537773
$562$	3.76710e97	0.912783
$563$	−7.60373e97	−1.72973	−0.864866	−	0.502004i	$-0.832596\pi$
$563$	−7.60373e97	−1.72973	−0.864866	+	0.502004i	$0.832596\pi$
$564$	2.84670e97	0.608042
$565$	−7.10484e97	−1.42506
$566$	5.82191e96	0.109669
$567$	6.25540e97	1.10677
$568$	−2.34537e97	−0.389804
$569$	−9.94344e97	−1.55257	−0.776285	−	0.630382i	$-0.782898\pi$
$569$	−9.94344e97	−1.55257	−0.776285	+	0.630382i	$0.782898\pi$
$570$	8.94172e97	1.31179
$571$	7.87685e97	1.08585	0.542926	−	0.839780i	$-0.317316\pi$
$571$	7.87685e97	1.08585	0.542926	+	0.839780i	$0.317316\pi$
$572$	−2.29306e97	−0.297068
$573$	−7.09535e97	−0.863943
$574$	−4.83803e97	−0.553727
$575$	9.74923e97	1.04897
$576$	1.68197e96	0.0170145
$577$	−7.78316e97	−0.740311	−0.370156	−	0.928970i	$-0.620696\pi$
$577$	−7.78316e97	−0.740311	−0.370156	+	0.928970i	$0.620696\pi$
$578$	−4.61355e97	−0.412664
$579$	1.17459e98	0.988094
$580$	−1.26531e98	−1.00116
$581$	1.38609e97	0.103166
$582$	−9.17824e96	−0.0642678
$583$	−9.67240e97	−0.637236
$584$	−2.52274e97	−0.156393
$585$	−2.31539e97	−0.135080
$586$	−1.87854e96	−0.0103146
$587$	2.03623e98	1.05238	0.526192	−	0.850366i	$-0.323619\pi$
$587$	2.03623e98	1.05238	0.526192	+	0.850366i	$0.323619\pi$
$588$	2.11080e96	0.0102696
$589$	−2.95004e98	−1.35125
$590$	−2.02397e98	−0.872886
$591$	1.61138e98	0.654397
$592$	−9.56792e97	−0.365929
$593$	4.59659e98	1.65575	0.827874	−	0.560914i	$-0.189550\pi$
$593$	4.59659e98	1.65575	0.827874	+	0.560914i	$0.189550\pi$
$594$	1.50038e98	0.509075
$595$	−2.61101e98	−0.834559
$596$	3.19006e98	0.960631
$597$	−2.18728e98	−0.620604
$598$	−2.98818e98	−0.798942
$599$	7.92205e98	1.99611	0.998057	−	0.0623109i	$-0.0198470\pi$
$599$	7.92205e98	1.99611	0.998057	+	0.0623109i	$0.0198470\pi$
$600$	−1.11950e98	−0.265861
$601$	4.61672e98	1.03345	0.516725	−	0.856151i	$-0.327151\pi$
$601$	4.61672e98	1.03345	0.516725	+	0.856151i	$0.327151\pi$
$602$	3.97564e98	0.838940
$603$	−4.50908e97	−0.0897065
$604$	2.11436e98	0.396614
$605$	−2.86976e98	−0.507610
$606$	7.69604e98	1.28378
$607$	−4.46919e98	−0.703122	−0.351561	−	0.936165i	$-0.614349\pi$
$607$	−4.46919e98	−0.703122	−0.351561	+	0.936165i	$0.614349\pi$
$608$	−1.58762e98	−0.235596
$609$	−1.15614e99	−1.61844
$610$	−1.13648e99	−1.50090
$611$	6.95779e98	0.866979
$612$	3.73519e97	0.0439175
$613$	−1.34335e99	−1.49053	−0.745265	−	0.666768i	$-0.767677\pi$
$613$	−1.34335e99	−1.49053	−0.745265	+	0.666768i	$0.767677\pi$
$614$	6.14822e98	0.643831
$615$	−1.11362e99	−1.10071
$616$	−2.93410e98	−0.273754
$617$	2.42572e98	0.213657	0.106828	−	0.994277i	$-0.465930\pi$
$617$	2.42572e98	0.213657	0.106828	+	0.994277i	$0.465930\pi$
$618$	−9.62586e97	−0.0800477
$619$	3.25711e98	0.255749	0.127875	−	0.991790i	$-0.459185\pi$
$619$	3.25711e98	0.255749	0.127875	+	0.991790i	$0.459185\pi$
$620$	8.92874e98	0.662041
$621$	1.95520e99	1.36912
$622$	−1.84263e98	−0.121865
$623$	−1.61337e99	−1.00788
$624$	3.43132e98	0.202492
$625$	−2.16634e99	−1.20778
$626$	−4.77520e98	−0.251538
$627$	2.23142e99	1.11067
$628$	7.54967e97	0.0355108
$629$	−2.12478e99	−0.944528
$630$	−2.96267e98	−0.124478
$631$	−1.04677e99	−0.415726	−0.207863	−	0.978158i	$-0.566651\pi$
$631$	−1.04677e99	−0.415726	−0.207863	+	0.978158i	$0.566651\pi$
$632$	1.64815e99	0.618786
$633$	4.71165e99	1.67240
$634$	1.47278e99	0.494277
$635$	6.33164e99	2.00932
$636$	1.44737e99	0.434362
$637$	5.15913e97	0.0146429
$638$	−3.15762e99	−0.847668
$639$	−5.90991e98	−0.150072
$640$	4.80516e98	0.115430
$641$	1.46238e99	0.332354	0.166177	−	0.986096i	$-0.446858\pi$
$641$	1.46238e99	0.332354	0.166177	+	0.986096i	$0.446858\pi$
$642$	−3.44428e99	−0.740637
$643$	−9.14057e99	−1.85988	−0.929938	−	0.367717i	$-0.880140\pi$
$643$	−9.14057e99	−1.85988	−0.929938	+	0.367717i	$0.880140\pi$
$644$	−3.82355e99	−0.736238
$645$	9.15117e99	1.66766
$646$	−3.52566e99	−0.608116
$647$	4.52649e99	0.739026	0.369513	−	0.929226i	$-0.379525\pi$
$647$	4.52649e99	0.739026	0.369513	+	0.929226i	$0.379525\pi$
$648$	−2.55652e99	−0.395127
$649$	−5.05085e99	−0.739057
$650$	−2.73624e99	−0.379079
$651$	8.15835e99	1.07023
$652$	−2.99707e99	−0.372312
$653$	−1.37490e100	−1.61753	−0.808764	−	0.588133i	$-0.799863\pi$
$653$	−1.37490e100	−1.61753	−0.808764	+	0.588133i	$0.799863\pi$
$654$	7.20506e99	0.802837
$655$	−8.79668e99	−0.928438
$656$	1.97725e99	0.197686
$657$	−6.35684e98	−0.0602103
$658$	8.90289e99	0.798936
$659$	3.10956e99	0.264403	0.132201	−	0.991223i	$-0.457795\pi$
$659$	3.10956e99	0.264403	0.132201	+	0.991223i	$0.457795\pi$
$660$	−6.75375e99	−0.544171
$661$	−1.25822e100	−0.960737	−0.480368	−	0.877067i	$-0.659497\pi$
$661$	−1.25822e100	−0.960737	−0.480368	+	0.877067i	$0.659497\pi$
$662$	1.68485e100	1.21928
$663$	7.62002e99	0.522668
$664$	−5.66480e98	−0.0368314
$665$	2.79647e100	1.72362
$666$	−2.41094e99	−0.140881
$667$	−4.11482e100	−2.27973
$668$	4.33724e99	0.227850
$669$	1.42507e100	0.709921
$670$	−1.28819e100	−0.608588
$671$	−2.83610e100	−1.27079
$672$	4.39056e99	0.186600
$673$	2.29817e100	0.926504	0.463252	−	0.886227i	$-0.346683\pi$
$673$	2.29817e100	0.926504	0.463252	+	0.886227i	$0.346683\pi$
$674$	4.97396e99	0.190229
$675$	1.79035e100	0.649614
$676$	−6.13702e99	−0.211276
$677$	3.08782e100	1.00868	0.504341	−	0.863505i	$-0.331735\pi$
$677$	3.08782e100	1.00868	0.504341	+	0.863505i	$0.331735\pi$
$678$	2.65314e100	0.822444
$679$	−2.87044e99	−0.0844446
$680$	1.06710e100	0.297946
$681$	1.57895e99	0.0418453
$682$	2.22818e100	0.560539
$683$	−3.93569e100	−0.939908	−0.469954	−	0.882691i	$-0.655730\pi$
$683$	−3.93569e100	−0.939908	−0.469954	+	0.882691i	$0.655730\pi$
$684$	−4.00050e99	−0.0907032
$685$	5.08319e100	1.09426
$686$	3.49185e100	0.713755
$687$	−8.82899e100	−1.71375
$688$	−1.62480e100	−0.299510
$689$	3.53761e100	0.619337
$690$	−8.80109e100	−1.46350
$691$	−1.07645e101	−1.70029	−0.850144	−	0.526551i	$-0.823485\pi$
$691$	−1.07645e101	−1.70029	−0.850144	+	0.526551i	$0.823485\pi$
$692$	−4.67406e100	−0.701339
$693$	−7.39340e99	−0.105394
$694$	−7.31456e100	−0.990666
$695$	3.28642e100	0.422924
$696$	4.72503e100	0.577799
$697$	4.39094e100	0.510263
$698$	7.87243e100	0.869444
$699$	−7.14630e100	−0.750138
$700$	−3.50117e100	−0.349328
$701$	−1.05775e101	−1.00322	−0.501608	−	0.865095i	$-0.667258\pi$
$701$	−1.05775e101	−1.00322	−0.501608	+	0.865095i	$0.667258\pi$
$702$	−5.48752e100	−0.494776
$703$	2.27570e101	1.95074
$704$	1.19914e100	0.0977327
$705$	2.04928e101	1.58813
$706$	−5.19796e100	−0.383060
$707$	2.40689e101	1.68681
$708$	7.55806e100	0.503767
$709$	−2.61898e101	−1.66031	−0.830157	−	0.557530i	$-0.811749\pi$
$709$	−2.61898e101	−1.66031	−0.830157	+	0.557530i	$0.811749\pi$
$710$	−1.68838e101	−1.01812
$711$	4.15304e100	0.238229
$712$	6.59369e100	0.359823
$713$	2.90364e101	1.50752
$714$	9.75025e100	0.481647
$715$	−1.65073e101	−0.775909
$716$	−7.61996e100	−0.340832
$717$	3.87019e100	0.164741
$718$	2.93405e100	0.118864
$719$	1.36856e101	0.527701	0.263851	−	0.964564i	$-0.415007\pi$
$719$	1.36856e101	0.527701	0.263851	+	0.964564i	$0.415007\pi$
$720$	1.21081e100	0.0444399
$721$	−3.01043e100	−0.105179
$722$	1.65013e101	0.548841
$723$	−5.49003e101	−1.73846
$724$	1.50766e101	0.454554
$725$	−3.76789e101	−1.08168
$726$	1.07165e101	0.292956
$727$	−5.37911e101	−1.40036	−0.700178	−	0.713968i	$-0.746896\pi$
$727$	−5.37911e101	−1.40036	−0.700178	+	0.713968i	$0.746896\pi$
$728$	1.07313e101	0.266064
$729$	3.51209e101	0.829351
$730$	−1.81607e101	−0.408479
$731$	−3.60825e101	−0.773089
$732$	4.24392e101	0.866212
$733$	3.01940e101	0.587123	0.293562	−	0.955940i	$-0.405159\pi$
$733$	3.01940e101	0.587123	0.293562	+	0.955940i	$0.405159\pi$
$734$	−4.35641e101	−0.807083
$735$	1.51952e100	0.0268229
$736$	1.56265e101	0.262844
$737$	−3.21470e101	−0.515281
$738$	4.98232e100	0.0761080
$739$	3.82116e101	0.556311	0.278156	−	0.960536i	$-0.410277\pi$
$739$	3.82116e101	0.556311	0.278156	+	0.960536i	$0.410277\pi$
$740$	−6.88775e101	−0.955765
$741$	−8.16127e101	−1.07947
$742$	4.52657e101	0.570730
$743$	−3.37540e101	−0.405716	−0.202858	−	0.979208i	$-0.565023\pi$
$743$	−3.37540e101	−0.405716	−0.202858	+	0.979208i	$0.565023\pi$
$744$	−3.33424e101	−0.382083
$745$	2.29646e102	2.50906
$746$	3.61204e100	0.0376291
$747$	−1.42743e100	−0.0141799
$748$	2.66296e101	0.252266
$749$	−1.07718e102	−0.973159
$750$	3.36435e101	0.289885
$751$	1.25387e102	1.03047	0.515233	−	0.857050i	$-0.327705\pi$
$751$	1.25387e102	1.03047	0.515233	+	0.857050i	$0.327705\pi$
$752$	−3.63852e101	−0.285228
$753$	3.30744e101	0.247327
$754$	1.15488e102	0.823858
$755$	1.52208e102	1.03591
$756$	−7.02159e101	−0.455944
$757$	2.17114e101	0.134519	0.0672597	−	0.997736i	$-0.478574\pi$
$757$	2.17114e101	0.134519	0.0672597	+	0.997736i	$0.478574\pi$
$758$	8.50521e101	0.502838
$759$	−2.19633e102	−1.23912
$760$	−1.14289e102	−0.615350
$761$	−1.75196e102	−0.900262	−0.450131	−	0.892963i	$-0.648623\pi$
$761$	−1.75196e102	−0.900262	−0.450131	+	0.892963i	$0.648623\pi$
$762$	−2.36441e102	−1.15964
$763$	2.25334e102	1.05489
$764$	9.06897e101	0.405269
$765$	2.68889e101	0.114707
$766$	−3.72857e101	−0.151852
$767$	1.84731e102	0.718298
$768$	−1.79438e101	−0.0666180
$769$	1.18064e102	0.418537	0.209268	−	0.977858i	$-0.432892\pi$
$769$	1.18064e102	0.418537	0.209268	+	0.977858i	$0.432892\pi$
$770$	−2.11220e102	−0.715013
$771$	3.36540e102	1.08794
$772$	−1.50131e102	−0.463508
$773$	−4.33078e102	−1.27701	−0.638505	−	0.769618i	$-0.720447\pi$
$773$	−4.33078e102	−1.27701	−0.638505	+	0.769618i	$0.720447\pi$
$774$	−4.09421e101	−0.115310
$775$	2.65883e102	0.715285
$776$	1.17312e101	0.0301476
$777$	−6.29346e102	−1.54505
$778$	−5.32896e101	−0.124988
$779$	−4.70283e102	−1.05385
$780$	2.47013e102	0.528886
$781$	−4.21340e102	−0.862027
$782$	3.47021e102	0.678448
$783$	−7.55649e102	−1.41181
$784$	−2.69793e100	−0.00481737
$785$	5.43485e101	0.0927502
$786$	3.28493e102	0.535828
$787$	1.11611e103	1.74022	0.870109	−	0.492859i	$-0.164048\pi$
$787$	1.11611e103	1.74022	0.870109	+	0.492859i	$0.164048\pi$
$788$	−2.05959e102	−0.306973
$789$	−2.20303e102	−0.313897
$790$	1.18647e103	1.61620
$791$	8.29755e102	1.08065
$792$	3.02161e101	0.0376265
$793$	1.03728e103	1.23509
$794$	1.57661e101	0.0179514
$795$	1.04193e103	1.13450
$796$	2.79568e102	0.291121
$797$	−1.22357e103	−1.21859	−0.609295	−	0.792944i	$-0.708547\pi$
$797$	−1.22357e103	−1.21859	−0.609295	+	0.792944i	$0.708547\pi$
$798$	−1.04428e103	−0.994751
$799$	−8.08017e102	−0.736224
$800$	1.43090e102	0.124713
$801$	1.66149e102	0.138530
$802$	1.02690e103	0.819104
$803$	−4.53203e102	−0.345853
$804$	4.81045e102	0.351233
$805$	−2.75249e103	−1.92297
$806$	−8.14942e102	−0.544794
$807$	2.81332e103	1.79974
$808$	−9.83673e102	−0.602210
$809$	−5.54240e102	−0.324732	−0.162366	−	0.986731i	$-0.551913\pi$
$809$	−5.54240e102	−0.324732	−0.162366	+	0.986731i	$0.551913\pi$
$810$	−1.84039e103	−1.03203
$811$	−7.50156e102	−0.402635	−0.201317	−	0.979526i	$-0.564522\pi$
$811$	−7.50156e102	−0.402635	−0.201317	+	0.979526i	$0.564522\pi$
$812$	1.47773e103	0.759199
$813$	−1.51507e103	−0.745108
$814$	−1.71885e103	−0.809230
$815$	−2.15753e103	−0.972437
$816$	−3.98483e102	−0.171953
$817$	3.86454e103	1.59667
$818$	−8.62048e102	−0.341027
$819$	2.70408e102	0.102433
$820$	1.42338e103	0.516333
$821$	4.87066e103	1.69202	0.846011	−	0.533165i	$-0.178998\pi$
$821$	4.87066e103	1.69202	0.846011	+	0.533165i	$0.178998\pi$
$822$	−1.89820e103	−0.631529
$823$	4.47328e101	0.0142538	0.00712692	−	0.999975i	$-0.497731\pi$
$823$	4.47328e101	0.0142538	0.00712692	+	0.999975i	$0.497731\pi$
$824$	1.23034e102	0.0375498
$825$	−2.01115e103	−0.587936
$826$	2.36374e103	0.661924
$827$	2.50293e103	0.671434	0.335717	−	0.941963i	$-0.391021\pi$
$827$	2.50293e103	0.671434	0.335717	+	0.941963i	$0.391021\pi$
$828$	3.93758e102	0.101194
$829$	−4.43213e103	−1.09126	−0.545629	−	0.838027i	$-0.683709\pi$
$829$	−4.43213e103	−1.09126	−0.545629	+	0.838027i	$0.683709\pi$
$830$	−4.07797e102	−0.0961993
$831$	−2.46103e103	−0.556265
$832$	−4.38576e102	−0.0949875
$833$	−5.99137e101	−0.0124345
$834$	−1.22724e103	−0.244082
$835$	3.12229e103	0.595118
$836$	−2.85211e103	−0.521007
$837$	5.33226e103	0.933593
$838$	4.21379e102	0.0707148
$839$	9.25434e103	1.48866	0.744330	−	0.667812i	$-0.232769\pi$
$839$	9.25434e103	1.48866	0.744330	+	0.667812i	$0.232769\pi$
$840$	3.16068e103	0.487377
$841$	9.13816e103	1.35083
$842$	4.80372e103	0.680767
$843$	−1.01268e104	−1.37592
$844$	−6.02222e103	−0.784512
$845$	−4.41791e103	−0.551828
$846$	−9.16841e102	−0.109811
$847$	3.35152e103	0.384929
$848$	−1.84996e103	−0.203756
$849$	−1.56506e103	−0.165314
$850$	3.17763e103	0.321908
$851$	−2.23991e104	−2.17636
$852$	6.30490e103	0.587587
$853$	−1.23930e104	−1.10786	−0.553931	−	0.832563i	$-0.686873\pi$
$853$	−1.23930e104	−1.10786	−0.553931	+	0.832563i	$0.686873\pi$
$854$	1.32726e104	1.13816
$855$	−2.87988e103	−0.236906
$856$	4.40233e103	0.347427
$857$	−1.40213e103	−0.106162	−0.0530809	−	0.998590i	$-0.516904\pi$
$857$	−1.40213e103	−0.106162	−0.0530809	+	0.998590i	$0.516904\pi$
$858$	6.16427e103	0.447799
$859$	−9.88429e103	−0.688951	−0.344475	−	0.938795i	$-0.611943\pi$
$859$	−9.88429e103	−0.688951	−0.344475	+	0.938795i	$0.611943\pi$
$860$	−1.16966e104	−0.782286
$861$	1.30057e104	0.834685
$862$	−5.12939e103	−0.315906
$863$	−2.55295e103	−0.150889	−0.0754447	−	0.997150i	$-0.524038\pi$
$863$	−2.55295e103	−0.150889	−0.0754447	+	0.997150i	$0.524038\pi$
$864$	2.86965e103	0.162777
$865$	−3.36476e104	−1.83182
$866$	−9.85174e103	−0.514787
$867$	1.24023e104	0.622047
$868$	−1.04276e104	−0.502037
$869$	2.96086e104	1.36841
$870$	3.40145e104	1.50915
$871$	1.17575e104	0.500808
$872$	−9.20918e103	−0.376605
$873$	2.95605e102	0.0116066
$874$	−3.71670e104	−1.40121
$875$	1.05218e104	0.380895
$876$	6.78169e103	0.235745
$877$	3.65526e104	1.22020	0.610102	−	0.792323i	$-0.291129\pi$
$877$	3.65526e104	1.22020	0.610102	+	0.792323i	$0.291129\pi$
$878$	−4.70043e103	−0.150689
$879$	5.04993e102	0.0155482
$880$	8.63235e103	0.255267
$881$	2.70647e104	0.768701	0.384351	−	0.923187i	$-0.374425\pi$
$881$	2.70647e104	0.768701	0.384351	+	0.923187i	$0.374425\pi$
$882$	−6.79829e101	−0.00185466
$883$	8.21961e103	0.215400	0.107700	−	0.994183i	$-0.465651\pi$
$883$	8.21961e103	0.215400	0.107700	+	0.994183i	$0.465651\pi$
$884$	−9.73957e103	−0.245180
$885$	5.44089e104	1.31578
$886$	−1.08137e104	−0.251233
$887$	−2.43864e104	−0.544326	−0.272163	−	0.962251i	$-0.587739\pi$
$887$	−2.43864e104	−0.544326	−0.272163	+	0.962251i	$0.587739\pi$
$888$	2.57208e104	0.551599
$889$	−7.39456e104	−1.52370
$890$	4.74666e104	0.939816
$891$	−4.59272e104	−0.873800
$892$	−1.82147e104	−0.333019
$893$	8.65410e104	1.52053
$894$	−8.57561e104	−1.44805
$895$	−5.48545e104	−0.890215
$896$	−5.61183e103	−0.0875326
$897$	8.03291e104	1.20432
$898$	−2.17400e104	−0.313291
$899$	−1.12220e105	−1.55454
$900$	3.60559e103	0.0480140
$901$	−4.10827e104	−0.525931
$902$	3.55208e104	0.437171
$903$	−1.06874e105	−1.26461
$904$	−3.39113e104	−0.385803
$905$	1.08534e105	1.18724
$906$	−5.68389e104	−0.597853
$907$	−5.10164e104	−0.516002	−0.258001	−	0.966145i	$-0.583064\pi$
$907$	−5.10164e104	−0.516002	−0.258001	+	0.966145i	$0.583064\pi$
$908$	−2.01815e103	−0.0196293
$909$	−2.47868e104	−0.231847
$910$	7.72520e104	0.694929
$911$	−2.03029e104	−0.175653	−0.0878267	−	0.996136i	$-0.527992\pi$
$911$	−2.03029e104	−0.175653	−0.0878267	+	0.996136i	$0.527992\pi$
$912$	4.26787e104	0.355136
$913$	−1.01767e104	−0.0814503
$914$	1.80048e104	0.138611
$915$	3.05511e105	2.26245
$916$	1.12848e105	0.803907
$917$	1.02734e105	0.704050
$918$	6.37272e104	0.420155
$919$	−1.23823e105	−0.785415	−0.392708	−	0.919663i	$-0.628462\pi$
$919$	−1.23823e105	−0.785415	−0.392708	+	0.919663i	$0.628462\pi$
$920$	1.12492e105	0.686519
$921$	−1.65278e105	−0.970506
$922$	3.30451e104	0.186706
$923$	1.54102e105	0.837814
$924$	7.88753e104	0.412654
$925$	−2.05105e105	−1.03263
$926$	−1.73134e105	−0.838865
$927$	3.10022e103	0.0144565
$928$	−6.03933e104	−0.271041
$929$	−2.11283e105	−0.912656	−0.456328	−	0.889812i	$-0.650836\pi$
$929$	−2.11283e105	−0.912656	−0.456328	+	0.889812i	$0.650836\pi$
$930$	−2.40025e105	−0.997956
$931$	6.41693e103	0.0256811
$932$	9.13408e104	0.351884
$933$	4.95341e104	0.183698
$934$	3.41272e105	1.21839
$935$	1.91701e105	0.658889
$936$	−1.10513e104	−0.0365697
$937$	−2.84835e105	−0.907481	−0.453740	−	0.891134i	$-0.649911\pi$
$937$	−2.84835e105	−0.907481	−0.453740	+	0.891134i	$0.649911\pi$
$938$	1.50444e105	0.461503
$939$	1.28368e105	0.379166
$940$	−2.61930e105	−0.744982
$941$	3.33196e105	0.912573	0.456287	−	0.889833i	$-0.349179\pi$
$941$	3.33196e105	0.912573	0.456287	+	0.889833i	$0.349179\pi$
$942$	−2.02952e104	−0.0535288
$943$	4.62887e105	1.17574
$944$	−9.66038e104	−0.236313
$945$	−5.05469e105	−1.19087
$946$	−2.91892e105	−0.662348
$947$	−2.40563e105	−0.525782	−0.262891	−	0.964826i	$-0.584676\pi$
$947$	−2.40563e105	−0.525782	−0.262891	+	0.964826i	$0.584676\pi$
$948$	−4.43060e105	−0.932753
$949$	1.65756e105	0.336138
$950$	−3.40333e105	−0.664839
$951$	−3.95918e105	−0.745070
$952$	−1.24623e105	−0.225937
$953$	−9.68498e104	−0.169161	−0.0845806	−	0.996417i	$-0.526955\pi$
$953$	−9.68498e104	−0.169161	−0.0845806	+	0.996417i	$0.526955\pi$
$954$	−4.66157e104	−0.0784449
$955$	6.52856e105	1.05852
$956$	−4.94670e104	−0.0772788
$957$	8.48840e105	1.27777
$958$	−8.96046e104	−0.129973
$959$	−5.93653e105	−0.829797
$960$	−1.29174e105	−0.173998
$961$	2.15489e104	0.0279734
$962$	6.28657e105	0.786500
$963$	1.10931e105	0.133758
$964$	7.01712e105	0.815500
$965$	−1.08076e106	−1.21063
$966$	1.02786e106	1.10980
$967$	1.39455e106	1.45142	0.725710	−	0.688001i	$-0.241511\pi$
$967$	1.39455e106	1.45142	0.725710	+	0.688001i	$0.241511\pi$
$968$	−1.36973e105	−0.137423
$969$	9.47778e105	0.916669
$970$	8.44506e104	0.0787420
$971$	−6.16683e105	−0.554344	−0.277172	−	0.960820i	$-0.589397\pi$
$971$	−6.16683e105	−0.554344	−0.277172	+	0.960820i	$0.589397\pi$
$972$	1.56013e105	0.135210
$973$	−3.83813e105	−0.320711
$974$	−7.29760e105	−0.587946
$975$	7.35564e105	0.571421
$976$	−5.42439e105	−0.406334
$977$	−4.30500e105	−0.310968	−0.155484	−	0.987838i	$-0.549694\pi$
$977$	−4.30500e105	−0.310968	−0.155484	+	0.987838i	$0.549694\pi$
$978$	8.05681e105	0.561221
$979$	1.18454e106	0.795726
$980$	−1.94218e104	−0.0125824
$981$	−2.32055e105	−0.144991
$982$	1.66952e105	0.100608
$983$	−7.46016e105	−0.433609	−0.216804	−	0.976215i	$-0.569563\pi$
$983$	−7.46016e105	−0.433609	−0.216804	+	0.976215i	$0.569563\pi$
$984$	−5.31531e105	−0.297991
$985$	−1.48266e106	−0.801778
$986$	−1.34117e106	−0.699606
$987$	−2.39330e106	−1.20431
$988$	1.04314e106	0.506372
$989$	−3.80376e106	−1.78133
$990$	2.17519e105	0.0982762
$991$	3.73382e106	1.62757	0.813783	−	0.581169i	$-0.197405\pi$
$991$	3.73382e106	1.62757	0.813783	+	0.581169i	$0.197405\pi$
$992$	4.26167e105	0.179232
$993$	−4.52926e106	−1.83793
$994$	1.97182e106	0.772059
$995$	2.01255e106	0.760374
$996$	1.52283e105	0.0555193
$997$	1.00008e106	0.351848	0.175924	−	0.984404i	$-0.443709\pi$
$997$	1.00008e106	0.351848	0.175924	+	0.984404i	$0.443709\pi$
$998$	1.22495e106	0.415894
$999$	−4.11338e106	−1.34779

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.72.a.a.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.72.a.a.1.1	✓	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 72 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q+3.43597e10 q^{2} -9.23668e16 q^{3} +1.18059e21 q^{4} +8.49883e24 q^{5} -3.17370e27 q^{6} -9.92557e29 q^{7} +4.05648e31 q^{8} +1.02216e33 q^{9} +O(q^{10})\)	\(q+3.43597e10 q^{2} -9.23668e16 q^{3} +1.18059e21 q^{4} +8.49883e24 q^{5} -3.17370e27 q^{6} -9.92557e29 q^{7} +4.05648e31 q^{8} +1.02216e33 q^{9} +2.92018e35 q^{10} +7.28736e36 q^{11} -1.09047e38 q^{12} -2.66530e39 q^{13} -3.41040e40 q^{14} -7.85010e41 q^{15} +1.39380e42 q^{16} +3.09524e43 q^{17} +3.51211e43 q^{18} -3.31510e45 q^{19} +1.00336e46 q^{20} +9.16793e46 q^{21} +2.50392e47 q^{22} +3.26296e48 q^{23} -3.74684e48 q^{24} +2.98785e49 q^{25} -9.15789e49 q^{26} +5.99212e50 q^{27} -1.17180e51 q^{28} -1.26107e52 q^{29} -2.69727e52 q^{30} +8.89879e52 q^{31} +4.78905e52 q^{32} -6.73110e53 q^{33} +1.06352e54 q^{34} -8.43557e54 q^{35} +1.20675e54 q^{36} -6.86465e55 q^{37} -1.13906e56 q^{38} +2.46185e56 q^{39} +3.44754e56 q^{40} +1.41861e57 q^{41} +3.15008e57 q^{42} -1.16574e58 q^{43} +8.60340e57 q^{44} +8.68716e57 q^{45} +1.12114e59 q^{46} -2.61051e59 q^{47} -1.28741e59 q^{48} -1.93567e58 q^{49} +1.02662e60 q^{50} -2.85898e60 q^{51} -3.14663e60 q^{52} -1.32728e61 q^{53} +2.05888e61 q^{54} +6.19341e61 q^{55} -4.02629e61 q^{56} +3.06205e62 q^{57} -4.33301e62 q^{58} -6.93098e62 q^{59} -9.26776e62 q^{60} -3.89181e63 q^{61} +3.05760e63 q^{62} -1.01455e63 q^{63} +1.64550e63 q^{64} -2.26519e64 q^{65} -2.31279e64 q^{66} -4.41133e64 q^{67} +3.65422e64 q^{68} -3.01389e65 q^{69} -2.89844e65 q^{70} -5.78179e65 q^{71} +4.14637e64 q^{72} -6.21903e65 q^{73} -2.35868e66 q^{74} -2.75978e66 q^{75} -3.91377e66 q^{76} -7.23312e66 q^{77} +8.45885e66 q^{78} +4.06300e67 q^{79} +1.18456e67 q^{80} -6.30231e67 q^{81} +4.87431e67 q^{82} -1.39648e67 q^{83} +1.08236e68 q^{84} +2.63059e68 q^{85} -4.00545e68 q^{86} +1.16481e69 q^{87} +2.95610e68 q^{88} +1.62547e69 q^{89} +2.98488e68 q^{90} +2.64546e69 q^{91} +3.85222e69 q^{92} -8.21953e69 q^{93} -8.96965e69 q^{94} -2.81744e70 q^{95} -4.42349e69 q^{96} +2.89197e69 q^{97} -6.65091e68 q^{98} +7.44884e69 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 68719476736 q^{2} - 73\!\cdots\!24 q^{3}+ \cdots - 61\!\cdots\!06 q^{9}+O(q^{10}) \) 2 * q + 68719476736 * q^2 - 73290552574846824 * q^3 + 2361183241434822606848 * q^4 + 4017561682270957567057500 * q^5 - 2518244211317885610315743232 * q^6 - 291238690173693964386145313552 * q^7 + 81129638414606681695789005144064 * q^8 - 6123404334975269213441745958191606 * q^9	\( 2 q + 68719476736 q^{2} - 73\!\cdots\!24 q^{3}+ \cdots - 25\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q + 68719476736 * q^2 - 73290552574846824 * q^3 + 2361183241434822606848 * q^4 + 4017561682270957567057500 * q^5 - 2518244211317885610315743232 * q^6 - 291238690173693964386145313552 * q^7 + 81129638414606681695789005144064 * q^8 - 6123404334975269213441745958191606 * q^9 + 138042368280132046088925515612160000 * q^10 + 8684021980716172090887525376850576904 * q^11 - 86526212247613054049400939322986725376 * q^12 - 1127526476847602121775517379388630880564 * q^13 - 10006885197007137092408662697676044763136 * q^14 - 870495707981432852912957098986798794190000 * q^15 + 2787593149816327892691964784081045188247552 * q^16 - 25310632831657129209270924115310927130954012 * q^17 - 210398570871227281924223539932585048573739008 * q^18 - 1515676621589311845828943656442220865774179720 * q^19 + 4743099657804439236107998378673316959354880000 * q^20 + 105057783932094120306762036640883833267054319424 * q^21 + 298380723239368814309358888863546426251303452672 * q^22 + 2203172021093641748810865503399372374910614063056 * q^23 - 2973018014802021769638859222271266932256426426368 * q^24 + 7608631123084092334620703396661508984732192968750 * q^25 - 38741514747476418312368452783630352849904496279552 * q^26 + 319648868947993055224983298099305125670447984140400 * q^27 - 343833957247777367123869889228909979682409491202048 * q^28 - 9698728689773075098486688545271532504346978353044820 * q^29 - 29910004776708962227849032598394684454226278481920000 * q^30 - 40152449056044233071756067933578167284289756136602176 * q^31 + 95780971304118053647396689196894323976171195136475136 * q^32 - 646467126733774659938188551326031765296979936890156448 * q^33 - 869666722024249947512519672631665319191092726559932416 * q^34 - 11578366136761156330569053956326057915336741584188620000 * q^35 - 7229239848136475225980096433630422626902243870395858944 * q^36 - 111302567218665505327715068364071188329715510661736133092 * q^37 - 52078252168302895367845656117167986656871260949011496960 * q^38 + 275519833227064980098009665274252977678408104840329524368 * q^39 + 162971663295510861461624602883383361666170966864035840000 * q^40 + 1293621751110559774763864122730511857252280974968281452724 * q^41 + 3609757969428628252091459480215598083336921089452940460032 * q^42 - 1570188515420028543133617556744083017145937257828102471224 * q^43 + 10252283584559329897127946035166644058616193652784990519296 * q^44 + 40708357615001912362112184537766135586032750500530146327500 * q^45 + 75700414224475307717463313812439049417335506592825614532608 * q^46 - 385166682154840572374711553898575384547395544426269119145312 * q^47 - 102152121151948219322231568723224690516220791896645696487424 * q^48 - 532035159715732504433438538355987707216238966761163005601134 * q^49 + 261430574727791417880321677225418373371479456953139200000000 * q^50 - 3932264303948319406691865647256788003255613422904957101311056 * q^51 - 1331148310703303321462704136062500237146241665952236108251136 * q^52 - 3099963518619652809000040240867303977580091183911870344857604 * q^53 + 10983051506680160776211401499861875800637953324417157378867200 * q^54 + 55675237030386993027088191557939523809594236008364091073990000 * q^55 - 11814044813067727683888054041578488163711785849542367105777664 * q^56 + 340530979210937295973262581310223186047069690231491850122484640 * q^57 - 333245780282818297674818451146232380367769998901979551377653760 * q^58 - 1634769282638530993938532031464170850734659495713497861208919640 * q^59 - 1027699938713350202229687163482744574649131800509079418306560000 * q^60 - 4880654092824262768274295733939273946937692231886071744774910356 * q^61 - 1379627644400128417380751464514180229965133097556173235859488768 * q^62 - 6025861853395026499121119084837033105792949783823904688557137744 * q^63 + 3291009114642412084309938365114701009965471731267159726697218048 * q^64 - 29543075418903360367582342730855024802992366467179006798718215000 * q^65 - 22212441338085195704544329675415390923261412452090927107868196864 * q^66 - 134179938663497929036082688157452363116312631094129088359318071272 * q^67 - 29881521036109411547967908356077030399545155480627042485522137088 * q^68 - 321605797179791219242936222377661308526135728863885795131895787072 * q^69 - 397829631188024238423499614496638648471785935450346828762972160000 * q^70 - 1460877510745740582710287713995347696234833946793802259869191016336 * q^71 - 248394789781489341122389789834951197865628377698933413906472763392 * q^72 - 3294544566820717164014310852275588208456751477490323839459061757324 * q^73 - 3824327089320080209166799848240719802335879866208768081693146873856 * q^74 - 3184606446584112229377097409458775389197568519591749999600534375000 * q^75 - 1789395119165616187416055863991190774635411515666290423769627361280 * q^76 - 6253614148334332819110227681464586033924531964755455804402474941504 * q^77 + 9466789384876945852702739096358587279675046525044436872190360551424 * q^78 + 32545937316211131695260490720524848524451973434380542886241294936160 * q^79 + 5599663712231541868723715427304950721493954977805868890975109120000 * q^80 - 14696790322123460114208775627144901209272992806663832631738624054318 * q^81 + 44448504915312847302911380237722229185910137671134107814183600914432 * q^82 + 29029289096582559444238889025865399025664140946681211932408984041976 * q^83 + 124030339401370609190995696547481222376098869028264558454981080907776 * q^84 + 515189414072415878332203587875687294826517223054383338648578942155000 * q^85 - 53951266578270514369163302115098086401206462253116960829150888722432 * q^86 + 1220360737986859838823441297151020036222068694550765089326808848685840 * q^87 + 352265781639999779838716580389548817134634070037714508800371015548928 * q^88 + 3892840256317115370330682179701204942142442453315338735392476328046420 * q^89 + 1398728517042446180581839536582579433906499662277636873109656043520000 * q^90 + 3723923831232087792375243174156474165096790899907919377283839137781664 * q^91 + 2601046427102197195248330727233686361926270850206227221189229484703744 * q^92 - 10683042981025141340950338658167930386609577245004285723682658026015488 * q^93 - 13234226426910936531546457451421780620973501002295527600190740093730816 * q^94 - 36238128778010894690559462260868212446184933626918861697256245230950000 * q^95 - 3509920156517179589395358987240212171415117269690520628101025242284032 * q^96 - 57797943272861961641603344152467986900234375803899254441558412075626172 * q^97 - 18280588890409662105806348248520070466174156498880209215855482804109312 * q^98 - 2531090145827533343099848313526915248178613009899410920700202513213912 * q^99

Introduction

L-functions

Modular forms

Varieties

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