LMFDB - Embedded newform 1.72.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, 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("1.1");

S:= CuspForms(chi, 72);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 72 $
Character orbit:	$[\chi]$	$=$	1.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:	$31.9246160561$
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 - 11\!\cdots\!68 $ x^6 - 3x^5 - 18795872470415627868x^4 - 3619866001951210071877967584x^3 + 86589594972295987044342709087705454976x^2 + 35564509575256206574563332087691180650482000128*x - 11608057594368249332625196663730471558406093241461869568
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{55}\cdot 3^{20}\cdot 5^{6}\cdot 7^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.88052e9$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.81063e10 q^{2} -8.58335e16 q^{3} +1.01516e21 q^{4} +8.21398e23 q^{5} +4.98747e27 q^{6} -4.94216e29 q^{7} +7.82125e31 q^{8} -1.42084e32 q^{9} +O(q^{10})$	\(q-5.81063e10 q^{2} -8.58335e16 q^{3} +1.01516e21 q^{4} +8.21398e23 q^{5} +4.98747e27 q^{6} -4.94216e29 q^{7} +7.82125e31 q^{8} -1.42084e32 q^{9} -4.77284e34 q^{10} -1.31046e37 q^{11} -8.71347e37 q^{12} -1.82494e39 q^{13} +2.87171e40 q^{14} -7.05035e40 q^{15} -6.94162e42 q^{16} -9.13260e43 q^{17} +8.25597e42 q^{18} -2.40031e45 q^{19} +8.33850e44 q^{20} +4.24203e46 q^{21} +7.61459e47 q^{22} -1.18414e48 q^{23} -6.71325e48 q^{24} -4.16770e49 q^{25} +1.06040e50 q^{26} +6.56759e50 q^{27} -5.01709e50 q^{28} +4.89616e51 q^{29} +4.09670e51 q^{30} -3.46134e52 q^{31} +2.18678e53 q^{32} +1.12481e54 q^{33} +5.30662e54 q^{34} -4.05948e53 q^{35} -1.44238e53 q^{36} +4.69217e55 q^{37} +1.39473e56 q^{38} +1.56641e56 q^{39} +6.42436e55 q^{40} -2.90342e57 q^{41} -2.46489e57 q^{42} -7.18207e57 q^{43} -1.33032e58 q^{44} -1.16707e56 q^{45} +6.88059e58 q^{46} -1.61927e59 q^{47} +5.95823e59 q^{48} -7.60275e59 q^{49} +2.42169e60 q^{50} +7.83882e60 q^{51} -1.85260e60 q^{52} -2.34415e61 q^{53} -3.81618e61 q^{54} -1.07641e61 q^{55} -3.86539e61 q^{56} +2.06027e62 q^{57} -2.84498e62 q^{58} +2.94632e62 q^{59} -7.15723e61 q^{60} +2.30321e63 q^{61} +2.01126e63 q^{62} +7.02201e61 q^{63} +3.68387e63 q^{64} -1.49900e63 q^{65} -6.53586e64 q^{66} -1.82113e64 q^{67} -9.27105e64 q^{68} +1.01639e65 q^{69} +2.35882e64 q^{70} +1.03608e66 q^{71} -1.11127e64 q^{72} -9.40991e64 q^{73} -2.72645e66 q^{74} +3.57728e66 q^{75} -2.43670e66 q^{76} +6.47650e66 q^{77} -9.10181e66 q^{78} -3.07092e67 q^{79} -5.70183e66 q^{80} -5.53049e67 q^{81} +1.68707e68 q^{82} +1.15515e68 q^{83} +4.30634e67 q^{84} -7.50150e67 q^{85} +4.17323e68 q^{86} -4.20254e68 q^{87} -1.02494e69 q^{88} -1.27226e69 q^{89} +6.78144e66 q^{90} +9.01913e68 q^{91} -1.20209e69 q^{92} +2.97099e69 q^{93} +9.40896e69 q^{94} -1.97161e69 q^{95} -1.87699e70 q^{96} +2.40529e70 q^{97} +4.41768e70 q^{98} +1.86195e69 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 66157336440 q^{2} + 89\!\cdots\!40 q^{3}+ \cdots + 28\!\cdots\!42 q^{9}+O(q^{10}) $ 6 * q + 66157336440 * q^2 + 89896952777770440 * q^3 + 8215211164782426312768 * q^4 - 4278141122384906054186220 * q^5 - 3844185387092474097708129888 * q^6 + 339238077991027352510892027600 * q^7 + 261748255411117464004338054151680 * q^8 + 28987747971890967878679507858381342 * q^9	$ 6 q + 66157336440 q^{2} + 89\!\cdots\!40 q^{3}+ \cdots - 14\!\cdots\!96 q^{99}+O(q^{100}) $ 6 * q + 66157336440 * q^2 + 89896952777770440 * q^3 + 8215211164782426312768 * q^4 - 4278141122384906054186220 * q^5 - 3844185387092474097708129888 * q^6 + 339238077991027352510892027600 * q^7 + 261748255411117464004338054151680 * q^8 + 28987747971890967878679507858381342 * q^9 - 263398563778288244573047848548292720 * q^10 - 7282201071395957974463753532023511528 * q^11 + 541210468937914072607016891134121050880 * q^12 + 1979976617302538140528908237391294561380 * q^13 - 128017496622836040959531046300766482377664 * q^14 + 1384527570467769328220186624774837086552560 * q^15 + 3676888394993384085040045713048320116002816 * q^16 + 31832108800317870559262101483836997103387820 * q^17 + 976142520820390022814071543254815896584170840 * q^18 - 2134599176603329812909260431734119625520534680 * q^19 - 1002259534476043660011780426984126177063212160 * q^20 + 84959027471295034369736212294538752678486836672 * q^21 - 1485722316536652800011319935933937121116600101920 * q^22 + 964854402645396933763118399083810192495520292720 * q^23 + 26174405694167952285079299527486641934970354984960 * q^24 - 19281402740175290596320190755488341912491573055350 * q^25 - 25489031065287762421766150549142637053582510650928 * q^26 + 512562833403212721097503677963237444718074155383120 * q^27 + 1359669743900832828937216228217468952624925402529280 * q^28 - 1317039720567844349957114876746978985654238312884220 * q^29 + 143339222293502384515474601773595895115677772364794560 * q^30 + 207186478465068422331238247449690908034655530755715392 * q^31 + 1088184206695308121738071837188209251978669942775971840 * q^32 + 3691362947608430538982225244260639132989887834164526880 * q^33 + 14816033950170870833607759912486854048128229988725590896 * q^34 + 23051745539129054008487744498480782457434321413678307680 * q^35 + 170434058245258338832832617243164934895140508181403488576 * q^36 + 204469200012514149249942417779481789241448706895708248660 * q^37 + 214562893987288214244615314981415065648734184296060185120 * q^38 - 59592640589388524102808790877963748287382610795162303056 * q^39 + 68960371201928160764899098042432251971214776224924902400 * q^40 - 2919734046508252424588883022005626663089526220940467621348 * q^41 - 30671294643397208367759780874400134513517016912238240615680 * q^42 - 20040916369245642405547102129405243305810023246036805945000 * q^43 - 97782453551268367387376497569051770607699386454832461475584 * q^44 - 125260483937857526052956293044059264550801286160703506832540 * q^45 - 153046715682271793176047221192835149722125813975592551106368 * q^46 + 808817457363531455346008899794487365168024913483463537549280 * q^47 + 2609198603968928396969404046103782910615054495128256557137920 * q^48 + 2781254770563189488685819613146286428997272420256410557714358 * q^49 + 7006022579700627712942214090063761901402175546735980199443400 * q^50 + 5207384206251438333593957907132920357364678014965573534558992 * q^51 - 14725121811173026783809130229242035456081751221768853161600 * q^52 - 25679718795007592157741622782050324347181366369160532409346060 * q^53 - 137149233644558648010083562893383635363635093434709473900255680 * q^54 - 117204222076916896957422109693993993787887100230247369516318640 * q^55 - 399675884388383438003206851384376896886023450279264479189790720 * q^56 - 782227658930786946913543064710323069676066812613811573724368160 * q^57 + 448079701387471532953636422287948168832061908600051366602252880 * q^58 + 2574973077571448260016144269589718601018514468483198670599207160 * q^59 + 8123589807705373813616392838803767380183688475255335181392775680 * q^60 + 475826432092865634978052553570578668506543772710052231981685572 * q^61 + 11448364903088694797640723309684276673600813166292613065633204480 * q^62 + 12651716130374230363535487627387763606235866258941468391309842960 * q^63 - 24713081846841456807546154884737687683145557071081015591709704192 * q^64 - 64361385967902296711263719440079272798609683319753125480723589640 * q^65 - 190230440842560220491451696290153136784050133308916444591791337856 * q^66 - 144659082341179727176864823539854352180542085255822335340299697080 * q^67 + 103906765022280475409201312234853190364811728527577591423200525440 * q^68 - 324178142584238303283610175482820308872990835336256741226468985536 * q^69 + 149058995123458688341122966890772635236709780299529720693195383680 * q^70 + 1235687217541473731844866277247085329953553172066626000767894890832 * q^71 + 4756831008242737873947724915842925231281989210351278910206749980160 * q^72 + 2367941808342149806657639366589641208779949871411828605636295901020 * q^73 + 9011435259578808279041169928582984111943617430403441524175408617616 * q^74 - 13222323962608659927909870888644111847952601354444631362060975848200 * q^75 - 18582782951953033569252470264774735316811316464954475202007848157440 * q^76 - 1325886884597236605670798015501090754589875143123368772240211064000 * q^77 - 82734460874562257213604869472472902109931833071258216779579101108800 * q^78 - 60094699780856590551494040309517729660578378792856107127665085175520 * q^79 + 44547588558087884776699653673631630698194001426805365604181595054080 * q^80 + 90431879106172356691623372809945513347962349100492777817548343419766 * q^81 + 131880025121092502946065745838775597252029739409272681579129156984880 * q^82 + 478198003543301822300844025982176525658793260101595969531167537027560 * q^83 + 357830150741096835660154046759297297209098846217256694071293018761216 * q^84 + 211578728369556023050184481668102823215907914559259741440636420213480 * q^85 + 1059998024210927691622156922996285506825265712550377293381092088317152 * q^86 + 37277468187846628282172211514267021090427372083464347850766486010160 * q^87 - 4443462717687788793413327377388585733175808835000327093394681148835840 * q^88 - 4779569984649315840943802647699331383415548856834721435179426845446660 * q^89 - 8627488862261215164556279664276659138357576658847574866996794738453040 * q^90 - 78452933928526481195247745840882105733919101509887292910721637755168 * q^91 - 3933588954885781964901938276884159688714299191002877628906051305530880 * q^92 + 7624909019792303887861325379837512501943653991471804221089819053530880 * q^93 + 31015980122032090056194424797719170840226576067548731364883132813755776 * q^94 + 8322227458201878249902498709514623471463205177085801654971437001319600 * q^95 + 166002069551604543422134778398052912195595330234015359484477454750973952 * q^96 + 90247623387797693983114581554183210926698820590955654168827969225413580 * q^97 - 169139078685664146344588160185862842690193055977419515754924822957831880 * q^98 - 148347266170563325638880362653524309583634182291703142145633675457993096 * 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 $

$2$	−5.81063e10	−1.19580	−0.597900	−	0.801571i	$-0.703998\pi$
$2$	−5.81063e10	−1.19580	−0.597900	+	0.801571i	$0.703998\pi$
$3$	−8.58335e16	−0.990495	−0.495247	−	0.868752i	$-0.664923\pi$
$3$	−8.58335e16	−0.990495	−0.495247	+	0.868752i	$0.664923\pi$
$4$	1.01516e21	0.429937
$5$	8.21398e23	0.126217	0.0631086	−	0.998007i	$-0.479899\pi$
$5$	8.21398e23	0.126217	0.0631086	+	0.998007i	$0.479899\pi$
$6$	4.98747e27	1.18443
$7$	−4.94216e29	−0.493102	−0.246551	−	0.969130i	$-0.579297\pi$
$7$	−4.94216e29	−0.493102	−0.246551	+	0.969130i	$0.579297\pi$
$8$	7.82125e31	0.681681
$9$	−1.42084e32	−0.0189206
$10$	−4.77284e34	−0.150931
$11$	−1.31046e37	−1.40599	−0.702996	−	0.711194i	$-0.748155\pi$
$11$	−1.31046e37	−1.40599	−0.702996	+	0.711194i	$0.748155\pi$
$12$	−8.71347e37	−0.425850
$13$	−1.82494e39	−0.520306	−0.260153	−	0.965567i	$-0.583773\pi$
$13$	−1.82494e39	−0.520306	−0.260153	+	0.965567i	$0.583773\pi$
$14$	2.87171e40	0.589651
$15$	−7.05035e40	−0.125017
$16$	−6.94162e42	−1.24509
$17$	−9.13260e43	−1.90396	−0.951980	−	0.306162i	$-0.900955\pi$
$17$	−9.13260e43	−1.90396	−0.951980	+	0.306162i	$0.900955\pi$
$18$	8.25597e42	0.0226253
$19$	−2.40031e45	−0.964973	−0.482487	−	0.875903i	$-0.660266\pi$
$19$	−2.40031e45	−0.964973	−0.482487	+	0.875903i	$0.660266\pi$
$20$	8.33850e44	0.0542654
$21$	4.24203e46	0.488415
$22$	7.61459e47	1.68128
$23$	−1.18414e48	−0.539590	−0.269795	−	0.962918i	$-0.586956\pi$
$23$	−1.18414e48	−0.539590	−0.269795	+	0.962918i	$0.586956\pi$
$24$	−6.71325e48	−0.675202
$25$	−4.16770e49	−0.984069
$26$	1.06040e50	0.622182
$27$	6.56759e50	1.00924
$28$	−5.01709e50	−0.212003
$29$	4.89616e51	0.595287	0.297644	−	0.954677i	$-0.403799\pi$
$29$	4.89616e51	0.595287	0.297644	+	0.954677i	$0.403799\pi$
$30$	4.09670e51	0.149496
$31$	−3.46134e52	−0.394370	−0.197185	−	0.980366i	$-0.563180\pi$
$31$	−3.46134e52	−0.394370	−0.197185	+	0.980366i	$0.563180\pi$
$32$	2.18678e53	0.807198
$33$	1.12481e54	1.39263
$34$	5.30662e54	2.27675
$35$	−4.05948e53	−0.0622379
$36$	−1.44238e53	−0.00813467
$37$	4.69217e55	1.00049	0.500245	−	0.865884i	$-0.333243\pi$
$37$	4.69217e55	1.00049	0.500245	+	0.865884i	$0.333243\pi$
$38$	1.39473e56	1.15391
$39$	1.56641e56	0.515360
$40$	6.42436e55	0.0860399
$41$	−2.90342e57	−1.61839	−0.809195	−	0.587541i	$-0.800096\pi$
$41$	−2.90342e57	−1.61839	−0.809195	+	0.587541i	$0.800096\pi$
$42$	−2.46489e57	−0.584046
$43$	−7.18207e57	−0.738107	−0.369053	−	0.929408i	$-0.620318\pi$
$43$	−7.18207e57	−0.738107	−0.369053	+	0.929408i	$0.620318\pi$
$44$	−1.33032e58	−0.604488
$45$	−1.16707e56	−0.00238811
$46$	6.88059e58	0.645242
$47$	−1.61927e59	−0.707692	−0.353846	−	0.935304i	$-0.615126\pi$
$47$	−1.61927e59	−0.707692	−0.353846	+	0.935304i	$0.615126\pi$
$48$	5.95823e59	1.23326
$49$	−7.60275e59	−0.756851
$50$	2.42169e60	1.17675
$51$	7.83882e60	1.88586
$52$	−1.85260e60	−0.223699
$53$	−2.34415e61	−1.43943	−0.719716	−	0.694269i	$-0.755728\pi$
$53$	−2.34415e61	−1.43943	−0.719716	+	0.694269i	$0.755728\pi$
$54$	−3.81618e61	−1.20684
$55$	−1.07641e61	−0.177460
$56$	−3.86539e61	−0.336138
$57$	2.06027e62	0.955801
$58$	−2.84498e62	−0.711844
$59$	2.94632e62	0.401822	0.200911	−	0.979609i	$-0.435610\pi$
$59$	2.94632e62	0.401822	0.200911	+	0.979609i	$0.435610\pi$
$60$	−7.15723e61	−0.0537496
$61$	2.30321e63	0.961889	0.480945	−	0.876751i	$-0.340294\pi$
$61$	2.30321e63	0.961889	0.480945	+	0.876751i	$0.340294\pi$
$62$	2.01126e63	0.471587
$63$	7.02201e61	0.00932980
$64$	3.68387e63	0.279844
$65$	−1.49900e63	−0.0656716
$66$	−6.53586e64	−1.66530
$67$	−1.82113e64	−0.272074	−0.136037	−	0.990704i	$-0.543437\pi$
$67$	−1.82113e64	−0.272074	−0.136037	+	0.990704i	$0.543437\pi$
$68$	−9.27105e64	−0.818582
$69$	1.01639e65	0.534461
$70$	2.35882e64	0.0744241
$71$	1.03608e66	1.97570	0.987849	−	0.155417i	$-0.0496722\pi$
$71$	1.03608e66	1.97570	0.987849	+	0.155417i	$0.0496722\pi$
$72$	−1.11127e64	−0.0128978
$73$	−9.40991e64	−0.0669305	−0.0334653	−	0.999440i	$-0.510654\pi$
$73$	−9.40991e64	−0.0669305	−0.0334653	+	0.999440i	$0.510654\pi$
$74$	−2.72645e66	−1.19638
$75$	3.57728e66	0.974715
$76$	−2.43670e66	−0.414878
$77$	6.47650e66	0.693297
$78$	−9.10181e66	−0.616267
$79$	−3.07092e67	−1.32284	−0.661420	−	0.750016i	$-0.730046\pi$
$79$	−3.07092e67	−1.32284	−0.661420	+	0.750016i	$0.730046\pi$
$80$	−5.70183e66	−0.157152
$81$	−5.53049e67	−0.980721
$82$	1.68707e68	1.93527
$83$	1.15515e68	0.861718	0.430859	−	0.902419i	$-0.358211\pi$
$83$	1.15515e68	0.861718	0.430859	+	0.902419i	$0.358211\pi$
$84$	4.30634e67	0.209987
$85$	−7.50150e67	−0.240312
$86$	4.17323e68	0.882628
$87$	−4.20254e68	−0.589629
$88$	−1.02494e69	−0.958438
$89$	−1.27226e69	−0.796581	−0.398290	−	0.917259i	$-0.630396\pi$
$89$	−1.27226e69	−0.796581	−0.398290	+	0.917259i	$0.630396\pi$
$90$	6.78144e66	0.00285570
$91$	9.01913e68	0.256564
$92$	−1.20209e69	−0.231990
$93$	2.97099e69	0.390621
$94$	9.40896e69	0.846258
$95$	−1.97161e69	−0.121796
$96$	−1.87699e70	−0.799526
$97$	2.40529e70	0.709203	0.354602	−	0.935017i	$-0.384617\pi$
$97$	2.40529e70	0.709203	0.354602	+	0.935017i	$0.384617\pi$
$98$	4.41768e70	0.905042
$99$	1.86195e69	0.0266022
$100$	−4.23088e70	−0.423088
$101$	3.61517e70	0.253933	0.126967	−	0.991907i	$-0.459476\pi$
$101$	3.61517e70	0.253933	0.126967	+	0.991907i	$0.459476\pi$
$102$	−4.55485e71	−2.25511
$103$	−2.08762e69	−0.00731021	−0.00365510	−	0.999993i	$-0.501163\pi$
$103$	−2.08762e69	−0.00731021	−0.00365510	+	0.999993i	$0.501163\pi$
$104$	−1.42733e71	−0.354683
$105$	3.48440e70	0.0616463
$106$	1.36210e72	1.72127
$107$	1.06271e72	0.962256	0.481128	−	0.876650i	$-0.340227\pi$
$107$	1.06271e72	0.962256	0.481128	+	0.876650i	$0.340227\pi$
$108$	6.66715e71	0.433907
$109$	−2.19267e72	−1.02881	−0.514403	−	0.857549i	$-0.671986\pi$
$109$	−2.19267e72	−1.02881	−0.514403	+	0.857549i	$0.671986\pi$
$110$	6.25461e71	0.212207
$111$	−4.02745e72	−0.990979
$112$	3.43066e72	0.613957
$113$	1.04172e72	0.135978	0.0679888	−	0.997686i	$-0.478342\pi$
$113$	1.04172e72	0.135978	0.0679888	+	0.997686i	$0.478342\pi$
$114$	−1.19715e73	−1.14295
$115$	−9.72649e71	−0.0681056
$116$	4.97038e72	0.255936
$117$	2.59294e71	0.00984451
$118$	−1.71200e73	−0.480499
$119$	4.51348e73	0.938846
$120$	−5.51425e72	−0.0852221
$121$	8.48579e73	0.976813
$122$	−1.33831e74	−1.15023
$123$	2.49211e74	1.60301
$124$	−3.51381e73	−0.169554
$125$	−6.90209e73	−0.250424
$126$	−4.08023e72	−0.0111566
$127$	−9.00746e74	−1.86024	−0.930122	−	0.367250i	$-0.880299\pi$
$127$	−9.00746e74	−1.86024	−0.930122	+	0.367250i	$0.880299\pi$
$128$	−7.30394e74	−1.14184
$129$	6.16462e74	0.731091
$130$	8.71013e73	0.0785300
$131$	1.62220e75	1.11423	0.557113	−	0.830437i	$-0.311909\pi$
$131$	1.62220e75	1.11423	0.557113	+	0.830437i	$0.311909\pi$
$132$	1.14186e75	0.598742
$133$	1.18627e75	0.475830
$134$	1.05819e75	0.325345
$135$	5.39461e74	0.127383
$136$	−7.14283e75	−1.29789
$137$	−8.11932e74	−0.113747	−0.0568735	−	0.998381i	$-0.518113\pi$
$137$	−8.11932e74	−0.113747	−0.0568735	+	0.998381i	$0.518113\pi$
$138$	−5.90585e75	−0.639109
$139$	1.06544e76	0.892289	0.446144	−	0.894961i	$-0.352797\pi$
$139$	1.06544e76	0.892289	0.446144	+	0.894961i	$0.352797\pi$
$140$	−4.12102e74	−0.0267584
$141$	1.38987e76	0.700965
$142$	−6.02026e76	−2.36254
$143$	2.39150e76	0.731546
$144$	9.86291e74	0.0235579
$145$	4.02170e75	0.0751355
$146$	5.46775e75	0.0800355
$147$	6.52571e76	0.749656
$148$	4.76330e76	0.430147
$149$	2.24854e77	1.59878	0.799390	−	0.600813i	$-0.205156\pi$
$149$	2.24854e77	1.59878	0.799390	+	0.600813i	$0.205156\pi$
$150$	−2.07862e77	−1.16556
$151$	−7.68875e76	−0.340545	−0.170272	−	0.985397i	$-0.554465\pi$
$151$	−7.68875e76	−0.340545	−0.170272	+	0.985397i	$0.554465\pi$
$152$	−1.87734e77	−0.657804
$153$	1.29759e76	0.0360241
$154$	−3.76325e77	−0.829045
$155$	−2.84314e76	−0.0497763
$156$	1.59015e77	0.221572
$157$	−1.70370e78	−1.89215	−0.946074	−	0.323951i	$-0.894989\pi$
$157$	−1.70370e78	−1.89215	−0.946074	+	0.323951i	$0.894989\pi$
$158$	1.78440e78	1.58185
$159$	2.01206e78	1.42575
$160$	1.79621e77	0.101882
$161$	5.85220e77	0.266073
$162$	3.21357e78	1.17275
$163$	−4.84879e78	−1.42224	−0.711121	−	0.703070i	$-0.751812\pi$
$163$	−4.84879e78	−1.42224	−0.711121	+	0.703070i	$0.751812\pi$
$164$	−2.94744e78	−0.695805
$165$	9.23918e77	0.175774
$166$	−6.71213e78	−1.03044
$167$	7.09429e78	0.879983	0.439992	−	0.898002i	$-0.354981\pi$
$167$	7.09429e78	0.879983	0.439992	+	0.898002i	$0.354981\pi$
$168$	3.31780e78	0.332943
$169$	−8.97167e78	−0.729282
$170$	4.35884e78	0.287366
$171$	3.41046e77	0.0182579
$172$	−7.29094e78	−0.317339
$173$	−3.49843e79	−1.23947	−0.619736	−	0.784810i	$-0.712760\pi$
$173$	−3.49843e79	−1.23947	−0.619736	+	0.784810i	$0.712760\pi$
$174$	2.44194e79	0.705078
$175$	2.05974e79	0.485246
$176$	9.09670e79	1.75059
$177$	−2.52893e79	−0.398003
$178$	7.39262e79	0.952551
$179$	−6.20344e79	−0.655164	−0.327582	−	0.944823i	$-0.606234\pi$
$179$	−6.20344e79	−0.655164	−0.327582	+	0.944823i	$0.606234\pi$
$180$	−1.18477e77	−0.00102674
$181$	−1.51926e80	−1.08154	−0.540772	−	0.841169i	$-0.681868\pi$
$181$	−1.51926e80	−1.08154	−0.540772	+	0.841169i	$0.681868\pi$
$182$	−5.24068e79	−0.306799
$183$	−1.97693e80	−0.952746
$184$	−9.26144e79	−0.367829
$185$	3.85414e79	0.126279
$186$	−1.72633e80	−0.467105
$187$	1.19679e81	2.67695
$188$	−1.64381e80	−0.304263
$189$	−3.24581e80	−0.497656
$190$	1.14563e80	0.145644
$191$	9.05932e80	0.955896	0.477948	−	0.878388i	$-0.341381\pi$
$191$	9.05932e80	0.955896	0.477948	+	0.878388i	$0.341381\pi$
$192$	−3.16199e80	−0.277184
$193$	5.08974e80	0.371032	0.185516	−	0.982641i	$-0.440604\pi$
$193$	5.08974e80	0.371032	0.185516	+	0.982641i	$0.440604\pi$
$194$	−1.39762e81	−0.848065
$195$	1.28664e80	0.0650473
$196$	−7.71801e80	−0.325398
$197$	−3.08696e81	−1.08638	−0.543189	−	0.839611i	$-0.682783\pi$
$197$	−3.08696e81	−1.08638	−0.543189	+	0.839611i	$0.682783\pi$
$198$	−1.08191e80	−0.0318110
$199$	5.05608e81	1.24317	0.621584	−	0.783347i	$-0.286489\pi$
$199$	5.05608e81	1.24317	0.621584	+	0.783347i	$0.286489\pi$
$200$	−3.25966e81	−0.670822
$201$	1.56314e81	0.269487
$202$	−2.10064e81	−0.303653
$203$	−2.41976e81	−0.293537
$204$	7.95766e81	0.810801
$205$	−2.38486e81	−0.204269
$206$	1.21304e80	0.00874154
$207$	1.68247e80	0.0102094
$208$	1.26680e82	0.647828
$209$	3.14551e82	1.35674
$210$	−2.02465e81	−0.0737167
$211$	−1.95726e81	−0.0602035	−0.0301018	−	0.999547i	$-0.509583\pi$
$211$	−1.95726e81	−0.0602035	−0.0301018	+	0.999547i	$0.509583\pi$
$212$	−2.37968e82	−0.618865
$213$	−8.89300e82	−1.95692
$214$	−6.17502e82	−1.15067
$215$	−5.89934e81	−0.0931618
$216$	5.13667e82	0.687977
$217$	1.71065e82	0.194465
$218$	1.27408e83	1.23025
$219$	8.07686e81	0.0662943
$220$	−1.09273e82	−0.0762968
$221$	1.66664e83	0.990641
$222$	2.34020e83	1.18501
$223$	−3.37730e83	−1.45796	−0.728982	−	0.684533i	$-0.760006\pi$
$223$	−3.37730e83	−1.45796	−0.728982	+	0.684533i	$0.760006\pi$
$224$	−1.08074e83	−0.398031
$225$	5.92162e81	0.0186192
$226$	−6.05307e82	−0.162602
$227$	−1.84535e83	−0.423800	−0.211900	−	0.977291i	$-0.567965\pi$
$227$	−1.84535e83	−0.423800	−0.211900	+	0.977291i	$0.567965\pi$
$228$	2.09151e83	0.410934
$229$	−2.13879e83	−0.359756	−0.179878	−	0.983689i	$-0.557570\pi$
$229$	−2.13879e83	−0.359756	−0.179878	+	0.983689i	$0.557570\pi$
$230$	5.65170e82	0.0814407
$231$	−5.55900e83	−0.686707
$232$	3.82941e83	0.405796
$233$	−2.17611e83	−0.197945	−0.0989727	−	0.995090i	$-0.531556\pi$
$233$	−2.17611e83	−0.197945	−0.0989727	+	0.995090i	$0.531556\pi$
$234$	−1.50666e82	−0.0117721
$235$	−1.33006e83	−0.0893229
$236$	2.99099e83	0.172758
$237$	2.63588e84	1.31027
$238$	−2.62262e84	−1.12267
$239$	2.02144e84	0.745652	0.372826	−	0.927901i	$-0.378389\pi$
$239$	2.02144e84	0.745652	0.372826	+	0.927901i	$0.378389\pi$
$240$	4.89408e83	0.155658
$241$	4.45899e84	1.22358	0.611789	−	0.791021i	$-0.290450\pi$
$241$	4.45899e84	1.22358	0.611789	+	0.791021i	$0.290450\pi$
$242$	−4.93078e84	−1.16807
$243$	−1.84897e83	−0.0378361
$244$	2.33813e84	0.413552
$245$	−6.24489e83	−0.0955276
$246$	−1.44807e85	−1.91687
$247$	4.38042e84	0.502081
$248$	−2.70720e84	−0.268835
$249$	−9.91503e84	−0.853527
$250$	4.01055e84	0.299457
$251$	−8.10257e83	−0.0525056	−0.0262528	−	0.999655i	$-0.508357\pi$
$251$	−8.10257e83	−0.0525056	−0.0262528	+	0.999655i	$0.508357\pi$
$252$	7.12847e82	0.00401122
$253$	1.55176e85	0.758660
$254$	5.23390e85	2.22448
$255$	6.43880e84	0.238028
$256$	3.37422e85	1.08556
$257$	−5.93554e85	−1.66278	−0.831389	−	0.555691i	$-0.812454\pi$
$257$	−5.93554e85	−1.66278	−0.831389	+	0.555691i	$0.812454\pi$
$258$	−3.58203e85	−0.874238
$259$	−2.31895e85	−0.493343
$260$	−1.52172e84	−0.0282346
$261$	−6.95665e83	−0.0112632
$262$	−9.42600e85	−1.33239
$263$	5.10954e85	0.630888	0.315444	−	0.948944i	$-0.397847\pi$
$263$	5.10954e85	0.630888	0.315444	+	0.948944i	$0.397847\pi$
$264$	8.79743e85	0.949328
$265$	−1.92548e85	−0.181681
$266$	−6.89300e85	−0.568997
$267$	1.09202e86	0.789009
$268$	−1.84874e85	−0.116974
$269$	−4.25430e85	−0.235842	−0.117921	−	0.993023i	$-0.537623\pi$
$269$	−4.25430e85	−0.235842	−0.117921	+	0.993023i	$0.537623\pi$
$270$	−3.13461e85	−0.152324
$271$	−3.56327e86	−1.51858	−0.759292	−	0.650750i	$-0.774455\pi$
$271$	−3.56327e86	−1.51858	−0.759292	+	0.650750i	$0.774455\pi$
$272$	6.33950e86	2.37060
$273$	−7.74143e85	−0.254125
$274$	4.71784e85	0.136019
$275$	5.46159e86	1.38359
$276$	1.03180e86	0.229785
$277$	−4.43177e86	−0.868051	−0.434026	−	0.900901i	$-0.642907\pi$
$277$	−4.43177e86	−0.868051	−0.434026	+	0.900901i	$0.642907\pi$
$278$	−6.19090e86	−1.06700
$279$	4.91800e84	0.00746173
$280$	−3.17502e85	−0.0424264
$281$	9.46279e85	0.111415	0.0557076	−	0.998447i	$-0.482259\pi$
$281$	9.46279e85	0.111415	0.0557076	+	0.998447i	$0.482259\pi$
$282$	−8.07604e86	−0.838214
$283$	−1.17860e87	−1.07881	−0.539407	−	0.842045i	$-0.681351\pi$
$283$	−1.17860e87	−1.07881	−0.539407	+	0.842045i	$0.681351\pi$
$284$	1.05178e87	0.849425
$285$	1.69230e86	0.120639
$286$	−1.38961e87	−0.874782
$287$	1.43492e87	0.798031
$288$	−3.10706e85	−0.0152727
$289$	6.03966e87	2.62506
$290$	−2.33686e86	−0.0898470
$291$	−2.06454e87	−0.702462
$292$	−9.55257e85	−0.0287759
$293$	2.53018e87	0.675074	0.337537	−	0.941312i	$-0.390406\pi$
$293$	2.53018e87	0.675074	0.337537	+	0.941312i	$0.390406\pi$
$294$	−3.79185e87	−0.896439
$295$	2.42010e86	0.0507169
$296$	3.66986e87	0.682015
$297$	−8.60655e87	−1.41898
$298$	−1.30655e88	−1.91182
$299$	2.16098e87	0.280752
$300$	3.63151e87	0.419066
$301$	3.54949e87	0.363962
$302$	4.46765e87	0.407223
$303$	−3.10302e87	−0.251519
$304$	1.66621e88	1.20148
$305$	1.89186e87	0.121407
$306$	−7.53984e86	−0.0430776
$307$	−1.36905e88	−0.696639	−0.348319	−	0.937376i	$-0.613248\pi$
$307$	−1.36905e88	−0.696639	−0.348319	+	0.937376i	$0.613248\pi$
$308$	6.57468e87	0.298074
$309$	1.79188e86	0.00724072
$310$	1.65204e87	0.0595225
$311$	−2.51407e87	−0.0807948	−0.0403974	−	0.999184i	$-0.512862\pi$
$311$	−2.51407e87	−0.0807948	−0.0403974	+	0.999184i	$0.512862\pi$
$312$	1.22512e88	0.351311
$313$	−4.83943e88	−1.23871	−0.619356	−	0.785110i	$-0.712606\pi$
$313$	−4.83943e88	−1.23871	−0.619356	+	0.785110i	$0.712606\pi$
$314$	9.89956e88	2.26263
$315$	5.76787e85	0.00117758
$316$	−3.11748e88	−0.568738
$317$	2.08012e88	0.339222	0.169611	−	0.985511i	$-0.445749\pi$
$317$	2.08012e88	0.339222	0.169611	+	0.985511i	$0.445749\pi$
$318$	−1.16913e89	−1.70491
$319$	−6.41621e88	−0.836969
$320$	3.02593e87	0.0353211
$321$	−9.12161e88	−0.953110
$322$	−3.40050e88	−0.318170
$323$	2.19211e89	1.83727
$324$	−5.61433e88	−0.421648
$325$	7.60578e88	0.512017
$326$	2.81745e89	1.70072
$327$	1.88205e89	1.01903
$328$	−2.27084e89	−1.10323
$329$	8.00268e88	0.348964
$330$	−5.36855e88	−0.210190
$331$	−1.92075e89	−0.675425	−0.337712	−	0.941249i	$-0.609653\pi$
$331$	−1.92075e89	−0.675425	−0.337712	+	0.941249i	$0.609653\pi$
$332$	1.17266e89	0.370484
$333$	−6.66681e87	−0.0189299
$334$	−4.12223e89	−1.05228
$335$	−1.49588e88	−0.0343404
$336$	−2.94465e89	−0.608121
$337$	−4.69540e89	−0.872593	−0.436296	−	0.899803i	$-0.643710\pi$
$337$	−4.69540e89	−0.872593	−0.436296	+	0.899803i	$0.643710\pi$
$338$	5.21311e89	0.872075
$339$	−8.94147e88	−0.134685
$340$	−7.61522e88	−0.103319
$341$	4.53594e89	0.554481
$342$	−1.98169e88	−0.0218328
$343$	8.72193e89	0.866306
$344$	−5.61727e89	−0.503154
$345$	8.34858e88	0.0674582
$346$	2.03281e90	1.48216
$347$	−5.24760e89	−0.345354	−0.172677	−	0.984979i	$-0.555242\pi$
$347$	−5.24760e89	−0.345354	−0.172677	+	0.984979i	$0.555242\pi$
$348$	−4.26625e89	−0.253503
$349$	5.29943e89	0.284398	0.142199	−	0.989838i	$-0.454583\pi$
$349$	5.29943e89	0.284398	0.142199	+	0.989838i	$0.454583\pi$
$350$	−1.19684e90	−0.580257
$351$	−1.19854e90	−0.525111
$352$	−2.86568e90	−1.13491
$353$	3.64789e90	1.30629	0.653146	−	0.757232i	$-0.273449\pi$
$353$	3.64789e90	1.30629	0.653146	+	0.757232i	$0.273449\pi$
$354$	1.46947e90	0.475931
$355$	8.51032e89	0.249367
$356$	−1.29154e90	−0.342479
$357$	−3.87407e90	−0.929922
$358$	3.60459e90	0.783445
$359$	−8.84489e90	−1.74116	−0.870581	−	0.492025i	$-0.836257\pi$
$359$	−8.84489e90	−1.74116	−0.870581	+	0.492025i	$0.836257\pi$
$360$	−9.12797e87	−0.00162793
$361$	−4.25855e89	−0.0688265
$362$	8.82788e90	1.29331
$363$	−7.28364e90	−0.967528
$364$	9.15586e89	0.110306
$365$	−7.72929e88	−0.00844778
$366$	1.14872e91	1.13929
$367$	9.18997e90	0.827311	0.413656	−	0.910433i	$-0.364252\pi$
$367$	9.18997e90	0.827311	0.413656	+	0.910433i	$0.364252\pi$
$368$	8.21983e90	0.671839
$369$	4.12529e89	0.0306209
$370$	−2.23950e90	−0.151004
$371$	1.15851e91	0.709787
$372$	3.01603e90	0.167943
$373$	−1.55715e91	−0.788256	−0.394128	−	0.919055i	$-0.628953\pi$
$373$	−1.55715e91	−0.788256	−0.394128	+	0.919055i	$0.628953\pi$
$374$	−6.95410e91	−3.20110
$375$	5.92431e90	0.248043
$376$	−1.26647e91	−0.482421
$377$	−8.93518e90	−0.309731
$378$	1.88602e91	0.595097
$379$	1.72223e91	0.494764	0.247382	−	0.968918i	$-0.420430\pi$
$379$	1.72223e91	0.494764	0.247382	+	0.968918i	$0.420430\pi$
$380$	−2.00150e90	−0.0523647
$381$	7.73141e91	1.84256
$382$	−5.26403e91	−1.14306
$383$	8.49003e90	0.168017	0.0840084	−	0.996465i	$-0.473228\pi$
$383$	8.49003e90	0.168017	0.0840084	+	0.996465i	$0.473228\pi$
$384$	6.26923e91	1.13098
$385$	5.31978e90	0.0875060
$386$	−2.95746e91	−0.443680
$387$	1.02046e90	0.0139654
$388$	2.44175e91	0.304913
$389$	−6.46320e91	−0.736608	−0.368304	−	0.929705i	$-0.620061\pi$
$389$	−6.46320e91	−0.736608	−0.368304	+	0.929705i	$0.620061\pi$
$390$	−7.47621e90	−0.0777836
$391$	1.08143e92	1.02736
$392$	−5.94630e91	−0.515931
$393$	−1.39239e92	−1.10363
$394$	1.79372e92	1.29909
$395$	−2.52245e91	−0.166965
$396$	1.89018e90	0.0114373
$397$	−1.13512e92	−0.628025	−0.314013	−	0.949419i	$-0.601673\pi$
$397$	−1.13512e92	−0.628025	−0.314013	+	0.949419i	$0.601673\pi$
$398$	−2.93790e92	−1.48658
$399$	−1.01822e92	−0.471307
$400$	2.89305e92	1.22526
$401$	1.60541e92	0.622242	0.311121	−	0.950370i	$-0.399296\pi$
$401$	1.60541e92	0.622242	0.311121	+	0.950370i	$0.399296\pi$
$402$	−9.08284e91	−0.322253
$403$	6.31672e91	0.205193
$404$	3.66997e91	0.109175
$405$	−4.54274e91	−0.123784
$406$	1.40603e92	0.351012
$407$	−6.14889e92	−1.40668
$408$	6.13094e92	1.28556
$409$	5.68799e92	1.09341	0.546703	−	0.837327i	$-0.315883\pi$
$409$	5.68799e92	1.09341	0.546703	+	0.837327i	$0.315883\pi$
$410$	1.38576e92	0.244264
$411$	6.96910e91	0.112666
$412$	−2.11927e90	−0.00314293
$413$	−1.45612e92	−0.198139
$414$	−9.77620e90	−0.0122084
$415$	9.48836e91	0.108764
$416$	−3.99073e92	−0.419990
$417$	−9.14508e92	−0.883807
$418$	−1.82774e93	−1.62239
$419$	−3.37192e92	−0.274966	−0.137483	−	0.990504i	$-0.543901\pi$
$419$	−3.37192e92	−0.274966	−0.137483	+	0.990504i	$0.543901\pi$
$420$	3.53722e91	0.0265040
$421$	5.83161e92	0.401582	0.200791	−	0.979634i	$-0.435649\pi$
$421$	5.83161e92	0.401582	0.200791	+	0.979634i	$0.435649\pi$
$422$	1.13729e92	0.0719914
$423$	2.30072e91	0.0133900
$424$	−1.83341e93	−0.981234
$425$	3.80619e93	1.87363
$426$	5.16740e93	2.34008
$427$	−1.13829e93	−0.474309
$428$	1.07882e93	0.413709
$429$	−2.05271e93	−0.724592
$430$	3.42789e92	0.111403
$431$	3.72454e93	1.11463	0.557314	−	0.830302i	$-0.311832\pi$
$431$	3.72454e93	1.11463	0.557314	+	0.830302i	$0.311832\pi$
$432$	−4.55897e93	−1.25659
$433$	−4.58058e93	−1.16305	−0.581527	−	0.813527i	$-0.697544\pi$
$433$	−4.58058e93	−1.16305	−0.581527	+	0.813527i	$0.697544\pi$
$434$	−9.93995e92	−0.232541
$435$	−3.45196e92	−0.0744213
$436$	−2.22592e93	−0.442322
$437$	2.84230e93	0.520690
$438$	−4.69316e92	−0.0792747
$439$	3.98274e93	0.620429	0.310214	−	0.950667i	$-0.399599\pi$
$439$	3.98274e93	0.620429	0.310214	+	0.950667i	$0.399599\pi$
$440$	−8.41885e92	−0.120971
$441$	1.08023e92	0.0143201
$442$	−9.68423e93	−1.18461
$443$	7.81031e93	0.881731	0.440866	−	0.897573i	$-0.354672\pi$
$443$	7.81031e93	0.881731	0.440866	+	0.897573i	$0.354672\pi$
$444$	−4.08851e93	−0.426058
$445$	−1.04503e93	−0.100542
$446$	1.96242e94	1.74343
$447$	−1.93000e94	−1.58358
$448$	−1.82063e93	−0.137991
$449$	−1.00757e94	−0.705557	−0.352779	−	0.935707i	$-0.614763\pi$
$449$	−1.00757e94	−0.705557	−0.352779	+	0.935707i	$0.614763\pi$
$450$	−3.44083e92	−0.0222648
$451$	3.80481e94	2.27544
$452$	1.05752e93	0.0584618
$453$	6.59952e93	0.337308
$454$	1.07226e94	0.506779
$455$	7.40830e92	0.0323828
$456$	1.61139e94	0.651551
$457$	−4.53389e94	−1.69608	−0.848039	−	0.529934i	$-0.822217\pi$
$457$	−4.53389e94	−1.69608	−0.848039	+	0.529934i	$0.822217\pi$
$458$	1.24277e94	0.430196
$459$	−5.99792e94	−1.92154
$460$	−9.87394e92	−0.0292811
$461$	−6.89026e93	−0.189170	−0.0945851	−	0.995517i	$-0.530152\pi$
$461$	−6.89026e93	−0.189170	−0.0945851	+	0.995517i	$0.530152\pi$
$462$	3.23013e94	0.821164
$463$	−1.41586e94	−0.333347	−0.166673	−	0.986012i	$-0.553303\pi$
$463$	−1.41586e94	−0.333347	−0.166673	+	0.986012i	$0.553303\pi$
$464$	−3.39872e94	−0.741187
$465$	2.44036e93	0.0493031
$466$	1.26446e94	0.236703
$467$	−1.93772e94	−0.336156	−0.168078	−	0.985774i	$-0.553756\pi$
$467$	−1.93772e94	−0.336156	−0.168078	+	0.985774i	$0.553756\pi$
$468$	2.63225e92	0.00423252
$469$	9.00034e93	0.134160
$470$	7.72850e93	0.106812
$471$	1.46234e95	1.87416
$472$	2.30439e94	0.273915
$473$	9.41180e94	1.03777
$474$	−1.53161e95	−1.56682
$475$	1.00038e95	0.949601
$476$	4.58190e94	0.403644
$477$	3.33065e93	0.0272350
$478$	−1.17459e95	−0.891650
$479$	−6.54779e94	−0.461513	−0.230757	−	0.973012i	$-0.574120\pi$
$479$	−6.54779e94	−0.461513	−0.230757	+	0.973012i	$0.574120\pi$
$480$	−1.54175e94	−0.100914
$481$	−8.56291e94	−0.520560
$482$	−2.59096e95	−1.46315
$483$	−5.02315e94	−0.263544
$484$	8.61443e94	0.419968
$485$	1.97570e94	0.0895137
$486$	1.07437e94	0.0452444
$487$	−3.64011e94	−0.142507	−0.0712535	−	0.997458i	$-0.522700\pi$
$487$	−3.64011e94	−0.142507	−0.0712535	+	0.997458i	$0.522700\pi$
$488$	1.80140e95	0.655702
$489$	4.16188e95	1.40872
$490$	3.62867e94	0.114232
$491$	−1.09388e95	−0.320315	−0.160158	−	0.987091i	$-0.551200\pi$
$491$	−1.09388e95	−0.320315	−0.160158	+	0.987091i	$0.551200\pi$
$492$	2.52989e95	0.689191
$493$	−4.47146e95	−1.13340
$494$	−2.54530e95	−0.600389
$495$	1.52940e93	0.00335766
$496$	2.40273e95	0.491027
$497$	−5.12046e95	−0.974220
$498$	5.76126e95	1.02065
$499$	9.59700e95	1.58331	0.791655	−	0.610968i	$-0.209220\pi$
$499$	9.59700e95	1.58331	0.791655	+	0.610968i	$0.209220\pi$
$500$	−7.00673e94	−0.107666
$501$	−6.08928e95	−0.871619
$502$	4.70810e94	0.0627862
$503$	2.01802e95	0.250763	0.125381	−	0.992109i	$-0.459985\pi$
$503$	2.01802e95	0.250763	0.125381	+	0.992109i	$0.459985\pi$
$504$	5.49209e93	0.00635995
$505$	2.96949e94	0.0320507
$506$	−9.01672e95	−0.907205
$507$	7.70070e95	0.722350
$508$	−9.14401e95	−0.799788
$509$	−1.72870e96	−1.41006	−0.705032	−	0.709176i	$-0.749067\pi$
$509$	−1.72870e96	−1.41006	−0.705032	+	0.709176i	$0.749067\pi$
$510$	−3.74135e95	−0.284634
$511$	4.65053e94	0.0330036
$512$	−2.36041e95	−0.156280
$513$	−1.57643e96	−0.973885
$514$	3.44892e96	1.98835
$515$	−1.71477e93	−0.000922674 0
$516$	6.25807e95	0.314323
$517$	2.12198e96	0.995009
$518$	1.34745e96	0.589939
$519$	3.00283e96	1.22769
$520$	−1.17240e95	−0.0447671
$521$	−3.28823e96	−1.17280	−0.586399	−	0.810023i	$-0.699455\pi$
$521$	−3.28823e96	−1.17280	−0.586399	+	0.810023i	$0.699455\pi$
$522$	4.04225e94	0.0134685
$523$	−3.55612e95	−0.110705	−0.0553523	−	0.998467i	$-0.517628\pi$
$523$	−3.55612e95	−0.110705	−0.0553523	+	0.998467i	$0.517628\pi$
$524$	1.64679e96	0.479047
$525$	−1.76795e96	−0.480634
$526$	−2.96896e96	−0.754416
$527$	3.16110e96	0.750864
$528$	−7.80801e96	−1.73395
$529$	−3.41370e96	−0.708842
$530$	1.11882e96	0.217254
$531$	−4.18625e94	−0.00760272
$532$	1.20426e96	0.204577
$533$	5.29856e96	0.842057
$534$	−6.34534e96	−0.943496
$535$	8.72908e95	0.121453
$536$	−1.42435e96	−0.185467
$537$	5.32463e96	0.648936
$538$	2.47201e96	0.282020
$539$	9.96309e96	1.06413
$540$	5.47639e95	0.0547666
$541$	−1.70942e97	−1.60084	−0.800418	−	0.599442i	$-0.795389\pi$
$541$	−1.70942e97	−1.60084	−0.800418	+	0.599442i	$0.795389\pi$
$542$	2.07048e97	1.81592
$543$	1.30404e97	1.07126
$544$	−1.99710e97	−1.53687
$545$	−1.80106e96	−0.129853
$546$	4.49826e96	0.303883
$547$	3.59428e96	0.227542	0.113771	−	0.993507i	$-0.463707\pi$
$547$	3.59428e96	0.227542	0.113771	+	0.993507i	$0.463707\pi$
$548$	−8.24241e95	−0.0489040
$549$	−3.27249e95	−0.0181995
$550$	−3.17353e97	−1.65450
$551$	−1.17523e97	−0.574436
$552$	7.94941e96	0.364332
$553$	1.51770e97	0.652295
$554$	2.57514e97	1.03802
$555$	−3.30814e96	−0.125079
$556$	1.08160e97	0.383628
$557$	−4.18618e97	−1.39302	−0.696511	−	0.717546i	$-0.745265\pi$
$557$	−4.18618e97	−1.39302	−0.696511	+	0.717546i	$0.745265\pi$
$558$	−2.85767e95	−0.00892273
$559$	1.31068e97	0.384041
$560$	2.81794e96	0.0774919
$561$	−1.02725e98	−2.65151
$562$	−5.49848e96	−0.133230
$563$	5.80855e97	1.32136	0.660678	−	0.750669i	$-0.270269\pi$
$563$	5.80855e97	1.32136	0.660678	+	0.750669i	$0.270269\pi$
$564$	1.41094e97	0.301371
$565$	8.55669e95	0.0171627
$566$	6.84838e97	1.29004
$567$	2.73326e97	0.483596
$568$	8.10341e97	1.34680
$569$	−3.17381e97	−0.495559	−0.247780	−	0.968816i	$-0.579701\pi$
$569$	−3.17381e97	−0.495559	−0.247780	+	0.968816i	$0.579701\pi$
$570$	−9.83336e96	−0.144260
$571$	5.58896e97	0.770459	0.385229	−	0.922821i	$-0.374122\pi$
$571$	5.58896e97	0.770459	0.385229	+	0.922821i	$0.374122\pi$
$572$	2.42776e97	0.314519
$573$	−7.77592e97	−0.946810
$574$	−8.33778e97	−0.954285
$575$	4.93513e97	0.530994
$576$	−5.23418e95	−0.00529482
$577$	−1.47965e97	−0.140740	−0.0703702	−	0.997521i	$-0.522418\pi$
$577$	−1.47965e97	−0.140740	−0.0703702	+	0.997521i	$0.522418\pi$
$578$	−3.50942e98	−3.13905
$579$	−4.36870e97	−0.367505
$580$	4.08266e96	0.0323035
$581$	−5.70892e97	−0.424915
$582$	1.19963e98	0.840004
$583$	3.07190e98	2.02383
$584$	−7.35972e96	−0.0456253
$585$	2.12984e95	0.00124255
$586$	−1.47019e98	−0.807253
$587$	2.03024e98	1.04929	0.524643	−	0.851322i	$-0.324199\pi$
$587$	2.03024e98	1.04929	0.524643	+	0.851322i	$0.324199\pi$
$588$	6.62464e97	0.322305
$589$	8.30830e97	0.380556
$590$	−1.40623e97	−0.0606472
$591$	2.64965e98	1.07605
$592$	−3.25712e98	−1.24570
$593$	−3.47815e98	−1.25287	−0.626436	−	0.779473i	$-0.715487\pi$
$593$	−3.47815e98	−1.25287	−0.626436	+	0.779473i	$0.715487\pi$
$594$	5.00095e98	1.69681
$595$	3.70736e97	0.118498
$596$	2.28263e98	0.687374
$597$	−4.33981e98	−1.23135
$598$	−1.25566e98	−0.335723
$599$	−4.81059e98	−1.21212	−0.606060	−	0.795419i	$-0.707251\pi$
$599$	−4.81059e98	−1.21212	−0.606060	+	0.795419i	$0.707251\pi$
$600$	2.79788e98	0.664445
$601$	2.45043e98	0.548527	0.274264	−	0.961655i	$-0.411566\pi$
$601$	2.45043e98	0.548527	0.274264	+	0.961655i	$0.411566\pi$
$602$	−2.06248e98	−0.435225
$603$	2.58754e96	0.00514780
$604$	−7.80531e97	−0.146413
$605$	6.97021e97	0.123291
$606$	1.80305e98	0.300767
$607$	−3.96904e98	−0.624435	−0.312218	−	0.950011i	$-0.601072\pi$
$607$	−3.96904e98	−0.624435	−0.312218	+	0.950011i	$0.601072\pi$
$608$	−5.24895e98	−0.778925
$609$	2.07696e98	0.290747
$610$	−1.09929e98	−0.145178
$611$	2.95506e98	0.368216
$612$	1.31727e97	0.0154881
$613$	3.24961e96	0.00360566	0.00180283	−	0.999998i	$-0.499426\pi$
$613$	3.24961e96	0.00360566	0.00180283	+	0.999998i	$0.499426\pi$
$614$	7.95506e98	0.833041
$615$	2.04701e98	0.202327
$616$	5.06543e98	0.472608
$617$	−8.86270e98	−0.780626	−0.390313	−	0.920682i	$-0.627633\pi$
$617$	−8.86270e98	−0.780626	−0.390313	+	0.920682i	$0.627633\pi$
$618$	−1.04119e97	−0.00865845
$619$	1.44608e99	1.13547	0.567735	−	0.823212i	$-0.307820\pi$
$619$	1.44608e99	1.13547	0.567735	+	0.823212i	$0.307820\pi$
$620$	−2.88624e97	−0.0214007
$621$	−7.77693e98	−0.544574
$622$	1.46083e98	0.0966144
$623$	6.28770e98	0.392795
$624$	−1.08734e99	−0.641670
$625$	1.70839e99	0.952461
$626$	2.81202e99	1.48125
$627$	−2.69990e99	−1.34385
$628$	−1.72953e99	−0.813504
$629$	−4.28517e99	−1.90489
$630$	−3.35150e96	−0.00140815
$631$	8.94550e98	0.355273	0.177636	−	0.984096i	$-0.443155\pi$
$631$	8.94550e98	0.355273	0.177636	+	0.984096i	$0.443155\pi$
$632$	−2.40184e99	−0.901755
$633$	1.67999e98	0.0596313
$634$	−1.20868e99	−0.405642
$635$	−7.39871e98	−0.234795
$636$	2.04256e99	0.612982
$637$	1.38745e99	0.393794
$638$	3.72822e99	1.00085
$639$	−1.47210e98	−0.0373814
$640$	−5.99945e98	−0.144119
$641$	4.95257e99	1.12557	0.562783	−	0.826605i	$-0.309731\pi$
$641$	4.95257e99	1.12557	0.562783	+	0.826605i	$0.309731\pi$
$642$	5.30023e99	1.13973
$643$	6.10234e99	1.24167	0.620836	−	0.783941i	$-0.286793\pi$
$643$	6.10234e99	1.24167	0.620836	+	0.783941i	$0.286793\pi$
$644$	5.94092e98	0.114395
$645$	5.06360e98	0.0922762
$646$	−1.27375e100	−2.19701
$647$	1.24941e99	0.203987	0.101993	−	0.994785i	$-0.467478\pi$
$647$	1.24941e99	0.203987	0.101993	+	0.994785i	$0.467478\pi$
$648$	−4.32553e99	−0.668539
$649$	−3.86103e99	−0.564959
$650$	−4.41944e99	−0.612270
$651$	−1.46831e99	−0.192616
$652$	−4.92229e99	−0.611474
$653$	8.87380e99	1.04398	0.521989	−	0.852952i	$-0.325190\pi$
$653$	8.87380e99	1.04398	0.521989	+	0.852952i	$0.325190\pi$
$654$	−1.09359e100	−1.21855
$655$	1.33247e99	0.140634
$656$	2.01544e100	2.01504
$657$	1.33700e97	0.00126637
$658$	−4.65006e99	−0.417291
$659$	−3.05838e99	−0.260052	−0.130026	−	0.991511i	$-0.541506\pi$
$659$	−3.05838e99	−0.260052	−0.130026	+	0.991511i	$0.541506\pi$
$660$	9.37925e98	0.0755715
$661$	−1.06511e100	−0.813288	−0.406644	−	0.913587i	$-0.633301\pi$
$661$	−1.06511e100	−0.813288	−0.406644	+	0.913587i	$0.633301\pi$
$662$	1.11608e100	0.807673
$663$	−1.43054e100	−0.981224
$664$	9.03469e99	0.587417
$665$	9.74404e98	0.0600580
$666$	3.87384e98	0.0226363
$667$	−5.79773e99	−0.321211
$668$	7.20184e99	0.378337
$669$	2.89885e100	1.44411
$670$	8.69198e98	0.0410642
$671$	−3.01827e100	−1.35241
$672$	9.27637e99	0.394248
$673$	2.22303e100	0.896210	0.448105	−	0.893981i	$-0.352099\pi$
$673$	2.22303e100	0.896210	0.448105	+	0.893981i	$0.352099\pi$
$674$	2.72833e100	1.04345
$675$	−2.73717e100	−0.993157
$676$	−9.10768e99	−0.313545
$677$	−1.40813e99	−0.0459987	−0.0229994	−	0.999735i	$-0.507322\pi$
$677$	−1.40813e99	−0.0459987	−0.0229994	+	0.999735i	$0.507322\pi$
$678$	5.19556e99	0.161056
$679$	−1.18873e100	−0.349709
$680$	−5.86711e99	−0.163816
$681$	1.58393e100	0.419771
$682$	−2.63567e100	−0.663048
$683$	−6.57835e100	−1.57102	−0.785511	−	0.618848i	$-0.787600\pi$
$683$	−6.57835e100	−1.57102	−0.785511	+	0.618848i	$0.787600\pi$
$684$	3.46216e98	0.00784974
$685$	−6.66920e98	−0.0143568
$686$	−5.06799e100	−1.03593
$687$	1.83580e100	0.356337
$688$	4.98551e100	0.919010
$689$	4.27792e100	0.748945
$690$	−4.85105e99	−0.0806665
$691$	2.58241e100	0.407900	0.203950	−	0.978981i	$-0.434622\pi$
$691$	2.58241e100	0.407900	0.203950	+	0.978981i	$0.434622\pi$
$692$	−3.55147e100	−0.532895
$693$	−9.20205e98	−0.0131176
$694$	3.04918e100	0.412974
$695$	8.75154e99	0.112622
$696$	−3.28691e100	−0.401939
$697$	2.65158e101	3.08135
$698$	−3.07930e100	−0.340083
$699$	1.86783e100	0.196064
$700$	2.09097e100	0.208625
$701$	−1.52891e101	−1.45008	−0.725039	−	0.688708i	$-0.758178\pi$
$701$	−1.52891e101	−1.45008	−0.725039	+	0.688708i	$0.758178\pi$
$702$	6.96429e100	0.627928
$703$	−1.12627e101	−0.965445
$704$	−4.82756e100	−0.393458
$705$	1.14164e100	0.0884739
$706$	−2.11966e101	−1.56206
$707$	−1.78667e100	−0.125215
$708$	−2.56727e100	−0.171116
$709$	3.38243e100	0.214431	0.107215	−	0.994236i	$-0.465807\pi$
$709$	3.38243e100	0.214431	0.107215	+	0.994236i	$0.465807\pi$
$710$	−4.94503e100	−0.298193
$711$	4.36328e99	0.0250290
$712$	−9.95064e100	−0.543014
$713$	4.09870e100	0.212798
$714$	2.25108e101	1.11200
$715$	1.96438e100	0.0923337
$716$	−6.29748e100	−0.281679
$717$	−1.73507e101	−0.738564
$718$	5.13944e101	2.08208
$719$	2.95265e101	1.13851	0.569255	−	0.822161i	$-0.307232\pi$
$719$	2.95265e101	1.13851	0.569255	+	0.822161i	$0.307232\pi$
$720$	8.10138e98	0.00297341
$721$	1.03174e99	0.00360468
$722$	2.47449e100	0.0823028
$723$	−3.82731e101	−1.21195
$724$	−1.54230e101	−0.464995
$725$	−2.04057e101	−0.585804
$726$	4.23226e101	1.15697
$727$	−7.11114e101	−1.85126	−0.925631	−	0.378427i	$-0.876465\pi$
$727$	−7.11114e101	−1.85126	−0.925631	+	0.378427i	$0.876465\pi$
$728$	7.05408e100	0.174895
$729$	4.31181e101	1.01820
$730$	4.49120e99	0.0101019
$731$	6.55909e101	1.40533
$732$	−2.00690e101	−0.409621
$733$	2.78211e101	0.540982	0.270491	−	0.962722i	$-0.412814\pi$
$733$	2.78211e101	0.540982	0.270491	+	0.962722i	$0.412814\pi$
$734$	−5.33995e101	−0.989298
$735$	5.36020e100	0.0946195
$736$	−2.58945e101	−0.435556
$737$	2.38652e101	0.382533
$738$	−2.39705e100	−0.0366165
$739$	−1.04939e102	−1.52778	−0.763889	−	0.645348i	$-0.776713\pi$
$739$	−1.04939e102	−1.52778	−0.763889	+	0.645348i	$0.776713\pi$
$740$	3.91257e100	0.0542920
$741$	−3.75987e101	−0.497309
$742$	−6.73170e101	−0.848763
$743$	−4.99542e99	−0.00600440	−0.00300220	−	0.999995i	$-0.500956\pi$
$743$	−4.99542e99	−0.00600440	−0.00300220	+	0.999995i	$0.500956\pi$
$744$	2.32368e101	0.266279
$745$	1.84695e101	0.201794
$746$	9.04804e101	0.942597
$747$	−1.64128e100	−0.0163042
$748$	1.21493e102	1.15092
$749$	−5.25209e101	−0.474490
$750$	−3.44240e101	−0.296610
$751$	2.01462e102	1.65567	0.827837	−	0.560968i	$-0.189571\pi$
$751$	2.01462e102	1.65567	0.827837	+	0.560968i	$0.189571\pi$
$752$	1.12403e102	0.881141
$753$	6.95472e100	0.0520065
$754$	5.19190e101	0.370377
$755$	−6.31552e100	−0.0429826
$756$	−3.29502e101	−0.213961
$757$	−1.65826e102	−1.02743	−0.513713	−	0.857962i	$-0.671730\pi$
$757$	−1.65826e102	−1.02743	−0.513713	+	0.857962i	$0.671730\pi$
$758$	−1.00072e102	−0.591639
$759$	−1.33193e102	−0.751448
$760$	−1.54205e101	−0.0830262
$761$	2.04868e102	1.05273	0.526367	−	0.850257i	$-0.323554\pi$
$761$	2.04868e102	1.05273	0.526367	+	0.850257i	$0.323554\pi$
$762$	−4.49244e102	−2.20334
$763$	1.08366e102	0.507306
$764$	9.19665e101	0.410975
$765$	1.06584e100	0.00454686
$766$	−4.93324e101	−0.200914
$767$	−5.37685e101	−0.209070
$768$	−2.89621e102	−1.07524
$769$	−8.80005e101	−0.311961	−0.155980	−	0.987760i	$-0.549854\pi$
$769$	−8.80005e101	−0.311961	−0.155980	+	0.987760i	$0.549854\pi$
$770$	−3.09113e101	−0.104640
$771$	5.09468e102	1.64697
$772$	5.16690e101	0.159520
$773$	−1.44639e101	−0.0426494	−0.0213247	−	0.999773i	$-0.506788\pi$
$773$	−1.44639e101	−0.0426494	−0.0213247	+	0.999773i	$0.506788\pi$
$774$	−5.92949e100	−0.0166999
$775$	1.44258e102	0.388087
$776$	1.88124e102	0.483451
$777$	1.99043e102	0.488654
$778$	3.75552e102	0.880836
$779$	6.96912e102	1.56170
$780$	1.30615e101	0.0279662
$781$	−1.35774e103	−2.77782
$782$	−6.28377e102	−1.22851
$783$	3.21560e102	0.600785
$784$	5.27754e102	0.942348
$785$	−1.39941e102	−0.238822
$786$	8.09066e102	1.31973
$787$	−9.54689e102	−1.48854	−0.744268	−	0.667882i	$-0.767201\pi$
$787$	−9.54689e102	−1.48854	−0.744268	+	0.667882i	$0.767201\pi$
$788$	−3.13376e102	−0.467074
$789$	−4.38569e102	−0.624891
$790$	1.46570e102	0.199657
$791$	−5.14836e101	−0.0670508
$792$	1.45628e101	0.0181343
$793$	−4.20322e102	−0.500477
$794$	6.59574e102	0.750993
$795$	1.65270e102	0.179954
$796$	5.13273e102	0.534484
$797$	−1.66544e103	−1.65866	−0.829332	−	0.558756i	$-0.811279\pi$
$797$	−1.66544e103	−1.65866	−0.829332	+	0.558756i	$0.811279\pi$
$798$	5.91650e102	0.563589
$799$	1.47881e103	1.34742
$800$	−9.11382e102	−0.794339
$801$	1.80767e101	0.0150718
$802$	−9.32842e102	−0.744077
$803$	1.23313e102	0.0941038
$804$	1.58684e102	0.115863
$805$	4.80699e101	0.0335830
$806$	−3.67041e102	−0.245370
$807$	3.65161e102	0.233600
$808$	2.82751e102	0.173102
$809$	1.09237e103	0.640025	0.320012	−	0.947413i	$-0.396313\pi$
$809$	1.09237e103	0.640025	0.320012	+	0.947413i	$0.396313\pi$
$810$	2.63962e102	0.148021
$811$	5.76421e102	0.309385	0.154693	−	0.987963i	$-0.450561\pi$
$811$	5.76421e102	0.309385	0.154693	+	0.987963i	$0.450561\pi$
$812$	−2.45644e102	−0.126202
$813$	3.05848e103	1.50415
$814$	3.57289e103	1.68211
$815$	−3.98279e102	−0.179511
$816$	−5.44141e103	−2.34807
$817$	1.72392e103	0.712253
$818$	−3.30508e103	−1.30749
$819$	−1.28147e101	−0.00485435
$820$	−2.42102e102	−0.0878226
$821$	−3.60032e103	−1.25072	−0.625359	−	0.780337i	$-0.715048\pi$
$821$	−3.60032e103	−1.25072	−0.625359	+	0.780337i	$0.715048\pi$
$822$	−4.04948e102	−0.134726
$823$	−1.85040e103	−0.589619	−0.294809	−	0.955556i	$-0.595256\pi$
$823$	−1.85040e103	−0.589619	−0.294809	+	0.955556i	$0.595256\pi$
$824$	−1.63278e101	−0.00498323
$825$	−4.68787e103	−1.37044
$826$	8.46098e102	0.236935
$827$	2.11952e103	0.568581	0.284290	−	0.958738i	$-0.408242\pi$
$827$	2.11952e103	0.568581	0.284290	+	0.958738i	$0.408242\pi$
$828$	1.70797e101	0.00438939
$829$	2.75559e103	0.678466	0.339233	−	0.940702i	$-0.389832\pi$
$829$	2.75559e103	0.678466	0.339233	+	0.940702i	$0.389832\pi$
$830$	−5.51333e102	−0.130059
$831$	3.80394e103	0.859800
$832$	−6.72283e102	−0.145604
$833$	6.94329e103	1.44101
$834$	5.31387e103	1.05686
$835$	5.82724e102	0.111069
$836$	3.19320e103	0.583315
$837$	−2.27326e103	−0.398012
$838$	1.95930e103	0.328804
$839$	−7.25333e103	−1.16678	−0.583389	−	0.812193i	$-0.698274\pi$
$839$	−7.25333e103	−1.16678	−0.583389	+	0.812193i	$0.698274\pi$
$840$	2.72523e102	0.0420232
$841$	−4.36761e103	−0.645633
$842$	−3.38853e103	−0.480212
$843$	−8.12224e102	−0.110356
$844$	−1.98693e102	−0.0258837
$845$	−7.36932e102	−0.0920479
$846$	−1.33686e102	−0.0160117
$847$	−4.19381e103	−0.481668
$848$	1.62722e104	1.79222
$849$	1.01163e104	1.06856
$850$	−2.21164e104	−2.24048
$851$	−5.55618e103	−0.539854
$852$	−9.02782e103	−0.841351
$853$	−6.68838e103	−0.597903	−0.298951	−	0.954268i	$-0.596637\pi$
$853$	−6.68838e103	−0.597903	−0.298951	+	0.954268i	$0.596637\pi$
$854$	6.61416e103	0.567179
$855$	2.80134e101	0.00230446
$856$	8.31172e103	0.655952
$857$	−3.19123e103	−0.241624	−0.120812	−	0.992675i	$-0.538550\pi$
$857$	−3.19123e103	−0.241624	−0.120812	+	0.992675i	$0.538550\pi$
$858$	1.19275e104	0.866467
$859$	9.18231e103	0.640022	0.320011	−	0.947414i	$-0.396313\pi$
$859$	9.18231e103	0.640022	0.320011	+	0.947414i	$0.396313\pi$
$860$	−5.98877e102	−0.0400537
$861$	−1.23164e104	−0.790445
$862$	−2.16420e104	−1.33287
$863$	2.50272e104	1.47921	0.739604	−	0.673042i	$-0.235013\pi$
$863$	2.50272e104	1.47921	0.739604	+	0.673042i	$0.235013\pi$
$864$	1.43619e104	0.814653
$865$	−2.87361e103	−0.156443
$866$	2.66160e104	1.39078
$867$	−5.18405e104	−2.60011
$868$	1.73658e103	0.0836075
$869$	4.02432e104	1.85990
$870$	2.00581e103	0.0889930
$871$	3.32345e103	0.141561
$872$	−1.71494e104	−0.701318
$873$	−3.41753e102	−0.0134186
$874$	−1.65156e104	−0.622641
$875$	3.41113e103	0.123484
$876$	8.19930e102	0.0285024
$877$	4.91519e104	1.64079	0.820397	−	0.571794i	$-0.193752\pi$
$877$	4.91519e104	1.64079	0.820397	+	0.571794i	$0.193752\pi$
$878$	−2.31422e104	−0.741908
$879$	−2.17174e104	−0.668657
$880$	7.47201e103	0.220954
$881$	−3.01600e104	−0.856618	−0.428309	−	0.903632i	$-0.640891\pi$
$881$	−3.01600e104	−0.856618	−0.428309	+	0.903632i	$0.640891\pi$
$882$	−6.27681e102	−0.0171240
$883$	5.98872e102	0.0156938	0.00784692	−	0.999969i	$-0.497502\pi$
$883$	5.98872e102	0.0156938	0.00784692	+	0.999969i	$0.497502\pi$
$884$	1.69191e104	0.425913
$885$	−2.07726e103	−0.0502348
$886$	−4.53829e104	−1.05437
$887$	−8.85897e104	−1.97740	−0.988700	−	0.149905i	$-0.952103\pi$
$887$	−8.85897e104	−1.97740	−0.988700	+	0.149905i	$0.952103\pi$
$888$	−3.14997e104	−0.675532
$889$	4.45163e104	0.917290
$890$	6.07228e103	0.120228
$891$	7.24748e104	1.37889
$892$	−3.42850e104	−0.626833
$893$	3.88675e104	0.682904
$894$	1.12145e105	1.89365
$895$	−5.09549e103	−0.0826929
$896$	3.60973e104	0.563041
$897$	−1.85484e104	−0.278083
$898$	5.85465e104	0.843705
$899$	−1.69473e104	−0.234763
$900$	6.01139e102	0.00800508
$901$	2.14081e105	2.74062
$902$	−2.21084e105	−2.72097
$903$	−3.04665e104	−0.360502
$904$	8.14757e103	0.0926934
$905$	−1.24792e104	−0.136509
$906$	−3.83474e104	−0.403352
$907$	−1.37429e105	−1.39002	−0.695008	−	0.719002i	$-0.744599\pi$
$907$	−1.37429e105	−1.39002	−0.695008	+	0.719002i	$0.744599\pi$
$908$	−1.87332e104	−0.182207
$909$	−5.13657e102	−0.00480458
$910$	−4.30469e103	−0.0387233
$911$	−2.56820e104	−0.222191	−0.111095	−	0.993810i	$-0.535436\pi$
$911$	−2.56820e104	−0.222191	−0.111095	+	0.993810i	$0.535436\pi$
$912$	−1.43016e105	−1.19006
$913$	−1.51377e105	−1.21157
$914$	2.63447e105	2.02817
$915$	−1.62385e104	−0.120253
$916$	−2.17121e104	−0.154672
$917$	−8.01717e104	−0.549427
$918$	3.48517e105	2.29778
$919$	9.66972e104	0.613357	0.306679	−	0.951813i	$-0.400782\pi$
$919$	9.66972e104	0.613357	0.306679	+	0.951813i	$0.400782\pi$
$920$	−7.60733e103	−0.0464263
$921$	1.17510e105	0.690017
$922$	4.00367e104	0.226210
$923$	−1.89077e105	−1.02797
$924$	−5.64327e104	−0.295241
$925$	−1.95555e105	−0.984551
$926$	8.22707e104	0.398616
$927$	2.96617e101	0.000138314 0
$928$	1.07068e105	0.480515
$929$	−5.01785e104	−0.216750	−0.108375	−	0.994110i	$-0.534565\pi$
$929$	−5.01785e104	−0.216750	−0.108375	+	0.994110i	$0.534565\pi$
$930$	−1.41800e104	−0.0589567
$931$	1.82490e105	0.730341
$932$	−2.20910e104	−0.0851040
$933$	2.15791e104	0.0800268
$934$	1.12593e105	0.401975
$935$	9.83040e104	0.337877
$936$	2.02800e103	0.00671082
$937$	−3.80885e105	−1.21350	−0.606748	−	0.794895i	$-0.707526\pi$
$937$	−3.80885e105	−1.21350	−0.606748	+	0.794895i	$0.707526\pi$
$938$	−5.22976e104	−0.160428
$939$	4.15385e105	1.22694
$940$	−1.35023e104	−0.0384032
$941$	4.25058e104	0.116417	0.0582085	−	0.998304i	$-0.481461\pi$
$941$	4.25058e104	0.116417	0.0582085	+	0.998304i	$0.481461\pi$
$942$	−8.49714e105	−2.24112
$943$	3.43805e105	0.873267
$944$	−2.04522e105	−0.500305
$945$	−2.66610e104	−0.0628127
$946$	−5.46885e105	−1.24097
$947$	2.66864e105	0.583264	0.291632	−	0.956531i	$-0.405802\pi$
$947$	2.66864e105	0.583264	0.291632	+	0.956531i	$0.405802\pi$
$948$	2.67584e105	0.563331
$949$	1.71725e104	0.0348243
$950$	−5.81283e105	−1.13553
$951$	−1.78544e105	−0.335997
$952$	3.53010e105	0.639994
$953$	4.58379e105	0.800620	0.400310	−	0.916380i	$-0.368902\pi$
$953$	4.58379e105	0.800620	0.400310	+	0.916380i	$0.368902\pi$
$954$	−1.93532e104	−0.0325675
$955$	7.44131e104	0.120651
$956$	2.05209e105	0.320583
$957$	5.50725e105	0.829013
$958$	3.80468e105	0.551877
$959$	4.01270e104	0.0560888
$960$	−2.59726e104	−0.0349853
$961$	−6.50528e105	−0.844472
$962$	4.97559e105	0.622486
$963$	−1.50994e104	−0.0182065
$964$	4.52659e105	0.526062
$965$	4.18070e104	0.0468306
$966$	2.91877e105	0.315146
$967$	1.94973e105	0.202925	0.101463	−	0.994839i	$-0.467648\pi$
$967$	1.94973e105	0.202925	0.101463	+	0.994839i	$0.467648\pi$
$968$	6.63694e105	0.665875
$969$	−1.88156e106	−1.81981
$970$	−1.14801e105	−0.107040
$971$	−5.10660e105	−0.459039	−0.229519	−	0.973304i	$-0.573715\pi$
$971$	−5.10660e105	−0.459039	−0.229519	+	0.973304i	$0.573715\pi$
$972$	−1.87700e104	−0.0162672
$973$	−5.26560e105	−0.439989
$974$	2.11513e105	0.170410
$975$	−6.52830e105	−0.507150
$976$	−1.59880e106	−1.19764
$977$	−5.02326e105	−0.362851	−0.181426	−	0.983405i	$-0.558071\pi$
$977$	−5.02326e105	−0.362851	−0.181426	+	0.983405i	$0.558071\pi$
$978$	−2.41832e106	−1.68455
$979$	1.66724e106	1.11999
$980$	−6.33956e104	−0.0410708
$981$	3.11544e104	0.0194657
$982$	6.35614e105	0.383033
$983$	3.07562e106	1.78765	0.893825	−	0.448416i	$-0.148012\pi$
$983$	3.07562e106	1.78765	0.893825	+	0.448416i	$0.148012\pi$
$984$	1.94914e106	1.09274
$985$	−2.53563e105	−0.137120
$986$	2.59820e106	1.35532
$987$	−6.86898e105	−0.345647
$988$	4.44683e105	0.215863
$989$	8.50456e105	0.398275
$990$	−8.88679e103	−0.00401509
$991$	−4.03271e106	−1.75785	−0.878926	−	0.476958i	$-0.841739\pi$
$991$	−4.03271e106	−1.75785	−0.878926	+	0.476958i	$0.841739\pi$
$992$	−7.56917e105	−0.318335
$993$	1.64865e106	0.669005
$994$	2.97531e106	1.16497
$995$	4.15306e105	0.156909
$996$	−1.00653e106	−0.366963
$997$	−2.83608e106	−0.997791	−0.498896	−	0.866662i	$-0.666261\pi$
$997$	−2.83608e106	−0.997791	−0.498896	+	0.866662i	$0.666261\pi$
$998$	−5.57646e106	−1.89332
$999$	3.08162e106	1.00973

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.72.a.a.1.2	✓	6
3.2	odd	2		9.72.a.b.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.72.a.a.1.2	✓	6	1.1	even	1	trivial
9.72.a.b.1.5		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 72 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-5.81063e10 q^{2} -8.58335e16 q^{3} +1.01516e21 q^{4} +8.21398e23 q^{5} +4.98747e27 q^{6} -4.94216e29 q^{7} +7.82125e31 q^{8} -1.42084e32 q^{9} +O(q^{10})\)	\(q-5.81063e10 q^{2} -8.58335e16 q^{3} +1.01516e21 q^{4} +8.21398e23 q^{5} +4.98747e27 q^{6} -4.94216e29 q^{7} +7.82125e31 q^{8} -1.42084e32 q^{9} -4.77284e34 q^{10} -1.31046e37 q^{11} -8.71347e37 q^{12} -1.82494e39 q^{13} +2.87171e40 q^{14} -7.05035e40 q^{15} -6.94162e42 q^{16} -9.13260e43 q^{17} +8.25597e42 q^{18} -2.40031e45 q^{19} +8.33850e44 q^{20} +4.24203e46 q^{21} +7.61459e47 q^{22} -1.18414e48 q^{23} -6.71325e48 q^{24} -4.16770e49 q^{25} +1.06040e50 q^{26} +6.56759e50 q^{27} -5.01709e50 q^{28} +4.89616e51 q^{29} +4.09670e51 q^{30} -3.46134e52 q^{31} +2.18678e53 q^{32} +1.12481e54 q^{33} +5.30662e54 q^{34} -4.05948e53 q^{35} -1.44238e53 q^{36} +4.69217e55 q^{37} +1.39473e56 q^{38} +1.56641e56 q^{39} +6.42436e55 q^{40} -2.90342e57 q^{41} -2.46489e57 q^{42} -7.18207e57 q^{43} -1.33032e58 q^{44} -1.16707e56 q^{45} +6.88059e58 q^{46} -1.61927e59 q^{47} +5.95823e59 q^{48} -7.60275e59 q^{49} +2.42169e60 q^{50} +7.83882e60 q^{51} -1.85260e60 q^{52} -2.34415e61 q^{53} -3.81618e61 q^{54} -1.07641e61 q^{55} -3.86539e61 q^{56} +2.06027e62 q^{57} -2.84498e62 q^{58} +2.94632e62 q^{59} -7.15723e61 q^{60} +2.30321e63 q^{61} +2.01126e63 q^{62} +7.02201e61 q^{63} +3.68387e63 q^{64} -1.49900e63 q^{65} -6.53586e64 q^{66} -1.82113e64 q^{67} -9.27105e64 q^{68} +1.01639e65 q^{69} +2.35882e64 q^{70} +1.03608e66 q^{71} -1.11127e64 q^{72} -9.40991e64 q^{73} -2.72645e66 q^{74} +3.57728e66 q^{75} -2.43670e66 q^{76} +6.47650e66 q^{77} -9.10181e66 q^{78} -3.07092e67 q^{79} -5.70183e66 q^{80} -5.53049e67 q^{81} +1.68707e68 q^{82} +1.15515e68 q^{83} +4.30634e67 q^{84} -7.50150e67 q^{85} +4.17323e68 q^{86} -4.20254e68 q^{87} -1.02494e69 q^{88} -1.27226e69 q^{89} +6.78144e66 q^{90} +9.01913e68 q^{91} -1.20209e69 q^{92} +2.97099e69 q^{93} +9.40896e69 q^{94} -1.97161e69 q^{95} -1.87699e70 q^{96} +2.40529e70 q^{97} +4.41768e70 q^{98} +1.86195e69 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 66157336440 q^{2} + 89\!\cdots\!40 q^{3}+ \cdots + 28\!\cdots\!42 q^{9}+O(q^{10}) \) 6 * q + 66157336440 * q^2 + 89896952777770440 * q^3 + 8215211164782426312768 * q^4 - 4278141122384906054186220 * q^5 - 3844185387092474097708129888 * q^6 + 339238077991027352510892027600 * q^7 + 261748255411117464004338054151680 * q^8 + 28987747971890967878679507858381342 * q^9	\( 6 q + 66157336440 q^{2} + 89\!\cdots\!40 q^{3}+ \cdots - 14\!\cdots\!96 q^{99}+O(q^{100}) \) 6 * q + 66157336440 * q^2 + 89896952777770440 * q^3 + 8215211164782426312768 * q^4 - 4278141122384906054186220 * q^5 - 3844185387092474097708129888 * q^6 + 339238077991027352510892027600 * q^7 + 261748255411117464004338054151680 * q^8 + 28987747971890967878679507858381342 * q^9 - 263398563778288244573047848548292720 * q^10 - 7282201071395957974463753532023511528 * q^11 + 541210468937914072607016891134121050880 * q^12 + 1979976617302538140528908237391294561380 * q^13 - 128017496622836040959531046300766482377664 * q^14 + 1384527570467769328220186624774837086552560 * q^15 + 3676888394993384085040045713048320116002816 * q^16 + 31832108800317870559262101483836997103387820 * q^17 + 976142520820390022814071543254815896584170840 * q^18 - 2134599176603329812909260431734119625520534680 * q^19 - 1002259534476043660011780426984126177063212160 * q^20 + 84959027471295034369736212294538752678486836672 * q^21 - 1485722316536652800011319935933937121116600101920 * q^22 + 964854402645396933763118399083810192495520292720 * q^23 + 26174405694167952285079299527486641934970354984960 * q^24 - 19281402740175290596320190755488341912491573055350 * q^25 - 25489031065287762421766150549142637053582510650928 * q^26 + 512562833403212721097503677963237444718074155383120 * q^27 + 1359669743900832828937216228217468952624925402529280 * q^28 - 1317039720567844349957114876746978985654238312884220 * q^29 + 143339222293502384515474601773595895115677772364794560 * q^30 + 207186478465068422331238247449690908034655530755715392 * q^31 + 1088184206695308121738071837188209251978669942775971840 * q^32 + 3691362947608430538982225244260639132989887834164526880 * q^33 + 14816033950170870833607759912486854048128229988725590896 * q^34 + 23051745539129054008487744498480782457434321413678307680 * q^35 + 170434058245258338832832617243164934895140508181403488576 * q^36 + 204469200012514149249942417779481789241448706895708248660 * q^37 + 214562893987288214244615314981415065648734184296060185120 * q^38 - 59592640589388524102808790877963748287382610795162303056 * q^39 + 68960371201928160764899098042432251971214776224924902400 * q^40 - 2919734046508252424588883022005626663089526220940467621348 * q^41 - 30671294643397208367759780874400134513517016912238240615680 * q^42 - 20040916369245642405547102129405243305810023246036805945000 * q^43 - 97782453551268367387376497569051770607699386454832461475584 * q^44 - 125260483937857526052956293044059264550801286160703506832540 * q^45 - 153046715682271793176047221192835149722125813975592551106368 * q^46 + 808817457363531455346008899794487365168024913483463537549280 * q^47 + 2609198603968928396969404046103782910615054495128256557137920 * q^48 + 2781254770563189488685819613146286428997272420256410557714358 * q^49 + 7006022579700627712942214090063761901402175546735980199443400 * q^50 + 5207384206251438333593957907132920357364678014965573534558992 * q^51 - 14725121811173026783809130229242035456081751221768853161600 * q^52 - 25679718795007592157741622782050324347181366369160532409346060 * q^53 - 137149233644558648010083562893383635363635093434709473900255680 * q^54 - 117204222076916896957422109693993993787887100230247369516318640 * q^55 - 399675884388383438003206851384376896886023450279264479189790720 * q^56 - 782227658930786946913543064710323069676066812613811573724368160 * q^57 + 448079701387471532953636422287948168832061908600051366602252880 * q^58 + 2574973077571448260016144269589718601018514468483198670599207160 * q^59 + 8123589807705373813616392838803767380183688475255335181392775680 * q^60 + 475826432092865634978052553570578668506543772710052231981685572 * q^61 + 11448364903088694797640723309684276673600813166292613065633204480 * q^62 + 12651716130374230363535487627387763606235866258941468391309842960 * q^63 - 24713081846841456807546154884737687683145557071081015591709704192 * q^64 - 64361385967902296711263719440079272798609683319753125480723589640 * q^65 - 190230440842560220491451696290153136784050133308916444591791337856 * q^66 - 144659082341179727176864823539854352180542085255822335340299697080 * q^67 + 103906765022280475409201312234853190364811728527577591423200525440 * q^68 - 324178142584238303283610175482820308872990835336256741226468985536 * q^69 + 149058995123458688341122966890772635236709780299529720693195383680 * q^70 + 1235687217541473731844866277247085329953553172066626000767894890832 * q^71 + 4756831008242737873947724915842925231281989210351278910206749980160 * q^72 + 2367941808342149806657639366589641208779949871411828605636295901020 * q^73 + 9011435259578808279041169928582984111943617430403441524175408617616 * q^74 - 13222323962608659927909870888644111847952601354444631362060975848200 * q^75 - 18582782951953033569252470264774735316811316464954475202007848157440 * q^76 - 1325886884597236605670798015501090754589875143123368772240211064000 * q^77 - 82734460874562257213604869472472902109931833071258216779579101108800 * q^78 - 60094699780856590551494040309517729660578378792856107127665085175520 * q^79 + 44547588558087884776699653673631630698194001426805365604181595054080 * q^80 + 90431879106172356691623372809945513347962349100492777817548343419766 * q^81 + 131880025121092502946065745838775597252029739409272681579129156984880 * q^82 + 478198003543301822300844025982176525658793260101595969531167537027560 * q^83 + 357830150741096835660154046759297297209098846217256694071293018761216 * q^84 + 211578728369556023050184481668102823215907914559259741440636420213480 * q^85 + 1059998024210927691622156922996285506825265712550377293381092088317152 * q^86 + 37277468187846628282172211514267021090427372083464347850766486010160 * q^87 - 4443462717687788793413327377388585733175808835000327093394681148835840 * q^88 - 4779569984649315840943802647699331383415548856834721435179426845446660 * q^89 - 8627488862261215164556279664276659138357576658847574866996794738453040 * q^90 - 78452933928526481195247745840882105733919101509887292910721637755168 * q^91 - 3933588954885781964901938276884159688714299191002877628906051305530880 * q^92 + 7624909019792303887861325379837512501943653991471804221089819053530880 * q^93 + 31015980122032090056194424797719170840226576067548731364883132813755776 * q^94 + 8322227458201878249902498709514623471463205177085801654971437001319600 * q^95 + 166002069551604543422134778398052912195595330234015359484477454750973952 * q^96 + 90247623387797693983114581554183210926698820590955654168827969225413580 * q^97 - 169139078685664146344588160185862842690193055977419515754924822957831880 * q^98 - 148347266170563325638880362653524309583634182291703142145633675457993096 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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