LMFDB - Embedded newform 1.72.a.a.1.6

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			1.6
Root			$-3.27721e9$ 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)

$f(q)$	$=$	$q+8.96793e10 q^{2} +1.38884e17 q^{3} +5.68119e21 q^{4} +3.52866e24 q^{5} +1.24550e28 q^{6} -7.32344e29 q^{7} +2.97736e32 q^{8} +1.17794e34 q^{9} +O(q^{10})$	\(q+8.96793e10 q^{2} +1.38884e17 q^{3} +5.68119e21 q^{4} +3.52866e24 q^{5} +1.24550e28 q^{6} -7.32344e29 q^{7} +2.97736e32 q^{8} +1.17794e34 q^{9} +3.16448e35 q^{10} -9.42557e36 q^{11} +7.89027e38 q^{12} -1.70901e39 q^{13} -6.56761e40 q^{14} +4.90076e41 q^{15} +1.32864e43 q^{16} +4.40535e43 q^{17} +1.05636e45 q^{18} -2.77676e45 q^{19} +2.00470e46 q^{20} -1.01711e47 q^{21} -8.45278e47 q^{22} -2.74500e48 q^{23} +4.13508e49 q^{24} -2.99002e49 q^{25} -1.53262e50 q^{26} +5.93020e50 q^{27} -4.16059e51 q^{28} +5.21767e51 q^{29} +4.39496e52 q^{30} +3.99836e52 q^{31} +4.88506e53 q^{32} -1.30906e54 q^{33} +3.95069e54 q^{34} -2.58420e54 q^{35} +6.69207e55 q^{36} +7.75221e55 q^{37} -2.49017e56 q^{38} -2.37354e56 q^{39} +1.05061e57 q^{40} +2.31324e56 q^{41} -9.12137e57 q^{42} +1.24224e58 q^{43} -5.35485e58 q^{44} +4.15654e58 q^{45} -2.46170e59 q^{46} +1.88922e59 q^{47} +1.84527e60 q^{48} -4.68197e59 q^{49} -2.68143e60 q^{50} +6.11834e60 q^{51} -9.70919e60 q^{52} -6.17450e60 q^{53} +5.31816e61 q^{54} -3.32597e61 q^{55} -2.18045e62 q^{56} -3.85648e62 q^{57} +4.67917e62 q^{58} +6.18742e62 q^{59} +2.78421e63 q^{60} -2.16263e63 q^{61} +3.58570e63 q^{62} -8.62654e63 q^{63} +1.24372e64 q^{64} -6.03051e63 q^{65} -1.17396e65 q^{66} +9.22803e64 q^{67} +2.50277e65 q^{68} -3.81237e65 q^{69} -2.31749e65 q^{70} -7.54805e65 q^{71} +3.50713e66 q^{72} -1.91877e66 q^{73} +6.95213e66 q^{74} -4.15266e66 q^{75} -1.57753e67 q^{76} +6.90276e66 q^{77} -2.12857e67 q^{78} +5.68363e65 q^{79} +4.68832e67 q^{80} -6.09560e66 q^{81} +2.07449e67 q^{82} +2.08423e68 q^{83} -5.77840e68 q^{84} +1.55450e68 q^{85} +1.11403e69 q^{86} +7.24652e68 q^{87} -2.80633e69 q^{88} -2.05657e69 q^{89} +3.72755e69 q^{90} +1.25158e69 q^{91} -1.55949e70 q^{92} +5.55309e69 q^{93} +1.69424e70 q^{94} -9.79824e69 q^{95} +6.78457e70 q^{96} +9.59744e69 q^{97} -4.19876e70 q^{98} -1.11027e71 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	8.96793e10	1.84556	0.922778	−	0.385332i	$-0.125913\pi$
$2$	8.96793e10	1.84556	0.922778	+	0.385332i	$0.125913\pi$
$3$	1.38884e17	1.60269	0.801343	−	0.598206i	$-0.204119\pi$
$3$	1.38884e17	1.60269	0.801343	+	0.598206i	$0.204119\pi$
$4$	5.68119e21	2.40608
$5$	3.52866e24	0.542219	0.271110	−	0.962548i	$-0.412609\pi$
$5$	3.52866e24	0.542219	0.271110	+	0.962548i	$0.412609\pi$
$6$	1.24550e28	2.95785
$7$	−7.32344e29	−0.730693	−0.365346	−	0.930872i	$-0.619049\pi$
$7$	−7.32344e29	−0.730693	−0.365346	+	0.930872i	$0.619049\pi$
$8$	2.97736e32	2.59499
$9$	1.17794e34	1.56860
$10$	3.16448e35	1.00070
$11$	−9.42557e36	−1.01127	−0.505635	−	0.862747i	$-0.668742\pi$
$11$	−9.42557e36	−1.01127	−0.505635	+	0.862747i	$0.668742\pi$
$12$	7.89027e38	3.85618
$13$	−1.70901e39	−0.487253	−0.243627	−	0.969869i	$-0.578337\pi$
$13$	−1.70901e39	−0.487253	−0.243627	+	0.969869i	$0.578337\pi$
$14$	−6.56761e40	−1.34853
$15$	4.90076e41	0.869007
$16$	1.32864e43	2.38313
$17$	4.40535e43	0.918426	0.459213	−	0.888326i	$-0.348131\pi$
$17$	4.40535e43	0.918426	0.459213	+	0.888326i	$0.348131\pi$
$18$	1.05636e45	2.89494
$19$	−2.77676e45	−1.11631	−0.558155	−	0.829737i	$-0.688491\pi$
$19$	−2.77676e45	−1.11631	−0.558155	+	0.829737i	$0.688491\pi$
$20$	2.00470e46	1.30462
$21$	−1.01711e47	−1.17107
$22$	−8.45278e47	−1.86636
$23$	−2.74500e48	−1.25085	−0.625424	−	0.780285i	$-0.715074\pi$
$23$	−2.74500e48	−1.25085	−0.625424	+	0.780285i	$0.715074\pi$
$24$	4.13508e49	4.15896
$25$	−2.99002e49	−0.705998
$26$	−1.53262e50	−0.899253
$27$	5.93020e50	0.911288
$28$	−4.16059e51	−1.75810
$29$	5.21767e51	0.634378	0.317189	−	0.948362i	$-0.397261\pi$
$29$	5.21767e51	0.634378	0.317189	+	0.948362i	$0.397261\pi$
$30$	4.39496e52	1.60380
$31$	3.99836e52	0.455556	0.227778	−	0.973713i	$-0.426854\pi$
$31$	3.99836e52	0.455556	0.227778	+	0.973713i	$0.426854\pi$
$32$	4.88506e53	1.80321
$33$	−1.30906e54	−1.62075
$34$	3.95069e54	1.69501
$35$	−2.58420e54	−0.396196
$36$	6.69207e55	3.77417
$37$	7.75221e55	1.65297	0.826484	−	0.562960i	$-0.190337\pi$
$37$	7.75221e55	1.65297	0.826484	+	0.562960i	$0.190337\pi$
$38$	−2.49017e56	−2.06021
$39$	−2.37354e56	−0.780913
$40$	1.05061e57	1.40706
$41$	2.31324e56	0.128942	0.0644708	−	0.997920i	$-0.479464\pi$
$41$	2.31324e56	0.128942	0.0644708	+	0.997920i	$0.479464\pi$
$42$	−9.12137e57	−2.16128
$43$	1.24224e58	1.27666	0.638332	−	0.769761i	$-0.279625\pi$
$43$	1.24224e58	1.27666	0.638332	+	0.769761i	$0.279625\pi$
$44$	−5.35485e58	−2.43320
$45$	4.15654e58	0.850526
$46$	−2.46170e59	−2.30851
$47$	1.88922e59	0.825676	0.412838	−	0.910805i	$-0.364538\pi$
$47$	1.88922e59	0.825676	0.412838	+	0.910805i	$0.364538\pi$
$48$	1.84527e60	3.81941
$49$	−4.68197e59	−0.466088
$50$	−2.68143e60	−1.30296
$51$	6.11834e60	1.47195
$52$	−9.70919e60	−1.17237
$53$	−6.17450e60	−0.379148	−0.189574	−	0.981866i	$-0.560711\pi$
$53$	−6.17450e60	−0.379148	−0.189574	+	0.981866i	$0.560711\pi$
$54$	5.31816e61	1.68183
$55$	−3.32597e61	−0.548331
$56$	−2.18045e62	−1.89614
$57$	−3.85648e62	−1.78909
$58$	4.67917e62	1.17078
$59$	6.18742e62	0.843847	0.421923	−	0.906632i	$-0.361355\pi$
$59$	6.18742e62	0.843847	0.421923	+	0.906632i	$0.361355\pi$
$60$	2.78421e63	2.09090
$61$	−2.16263e63	−0.903179	−0.451589	−	0.892226i	$-0.649143\pi$
$61$	−2.16263e63	−0.903179	−0.451589	+	0.892226i	$0.649143\pi$
$62$	3.58570e63	0.840754
$63$	−8.62654e63	−1.14616
$64$	1.24372e64	0.944789
$65$	−6.03051e63	−0.264198
$66$	−1.17396e65	−2.99118
$67$	9.22803e64	1.37865	0.689324	−	0.724453i	$-0.257908\pi$
$67$	9.22803e64	1.37865	0.689324	+	0.724453i	$0.257908\pi$
$68$	2.50277e65	2.20980
$69$	−3.81237e65	−2.00471
$70$	−2.31749e65	−0.731202
$71$	−7.54805e65	−1.43934	−0.719670	−	0.694316i	$-0.755707\pi$
$71$	−7.54805e65	−1.43934	−0.719670	+	0.694316i	$0.755707\pi$
$72$	3.50713e66	4.07051
$73$	−1.91877e66	−1.36478	−0.682388	−	0.730990i	$-0.739059\pi$
$73$	−1.91877e66	−1.36478	−0.682388	+	0.730990i	$0.739059\pi$
$74$	6.95213e66	3.05065
$75$	−4.15266e66	−1.13149
$76$	−1.57753e67	−2.68593
$77$	6.90276e66	0.738928
$78$	−2.12857e67	−1.44122
$79$	5.68363e65	0.0244830	0.0122415	−	0.999925i	$-0.496103\pi$
$79$	5.68363e65	0.0244830	0.0122415	+	0.999925i	$0.496103\pi$
$80$	4.68832e67	1.29218
$81$	−6.09560e66	−0.108093
$82$	2.07449e67	0.237969
$83$	2.08423e68	1.55480	0.777400	−	0.629007i	$-0.216538\pi$
$83$	2.08423e68	1.55480	0.777400	+	0.629007i	$0.216538\pi$
$84$	−5.77840e68	−2.81769
$85$	1.55450e68	0.497988
$86$	1.11403e69	2.35615
$87$	7.24652e68	1.01671
$88$	−2.80633e69	−2.62424
$89$	−2.05657e69	−1.28765	−0.643825	−	0.765172i	$-0.722654\pi$
$89$	−2.05657e69	−1.28765	−0.643825	+	0.765172i	$0.722654\pi$
$90$	3.72755e69	1.56969
$91$	1.25158e69	0.356032
$92$	−1.55949e70	−3.00963
$93$	5.55309e69	0.730113
$94$	1.69424e70	1.52383
$95$	−9.79824e69	−0.605285
$96$	6.78457e70	2.88997
$97$	9.59744e69	0.282982	0.141491	−	0.989940i	$-0.454810\pi$
$97$	9.59744e69	0.282982	0.141491	+	0.989940i	$0.454810\pi$
$98$	−4.19876e70	−0.860192
$99$	−1.11027e71	−1.58628
$100$	−1.69869e71	−1.69869
$101$	−4.05941e70	−0.285138	−0.142569	−	0.989785i	$-0.545536\pi$
$101$	−4.05941e70	−0.285138	−0.142569	+	0.989785i	$0.545536\pi$
$102$	5.48688e71	2.71656
$103$	1.17675e71	0.412062	0.206031	−	0.978545i	$-0.433945\pi$
$103$	1.17675e71	0.412062	0.206031	+	0.978545i	$0.433945\pi$
$104$	−5.08832e71	−1.26442
$105$	−3.58904e71	−0.634977
$106$	−5.53725e71	−0.699739
$107$	6.29491e71	0.569988	0.284994	−	0.958529i	$-0.408008\pi$
$107$	6.29491e71	0.569988	0.284994	+	0.958529i	$0.408008\pi$
$108$	3.36906e72	2.19263
$109$	−1.17937e72	−0.553361	−0.276680	−	0.960962i	$-0.589234\pi$
$109$	−1.17937e72	−0.553361	−0.276680	+	0.960962i	$0.589234\pi$
$110$	−2.98270e72	−1.01197
$111$	1.07666e73	2.64919
$112$	−9.73022e72	−1.74134
$113$	8.53761e72	1.11443	0.557213	−	0.830369i	$-0.311871\pi$
$113$	8.53761e72	1.11443	0.557213	+	0.830369i	$0.311871\pi$
$114$	−3.45846e73	−3.30187
$115$	−9.68618e72	−0.678234
$116$	2.96426e73	1.52636
$117$	−2.01310e73	−0.764305
$118$	5.54884e73	1.55737
$119$	−3.22624e73	−0.671087
$120$	1.45913e74	2.25507
$121$	1.96924e72	0.0226683
$122$	−1.93943e74	−1.66687
$123$	3.21272e73	0.206653
$124$	2.27154e74	1.09610
$125$	−2.54952e74	−0.925025
$126$	−7.73622e74	−2.11531
$127$	4.11099e74	0.849013	0.424507	−	0.905425i	$-0.360448\pi$
$127$	4.11099e74	0.849013	0.424507	+	0.905425i	$0.360448\pi$
$128$	−3.80898e73	−0.0595463
$129$	1.72528e75	2.04609
$130$	−5.40811e74	−0.487592
$131$	4.43848e74	0.304862	0.152431	−	0.988314i	$-0.451290\pi$
$131$	4.43848e74	0.304862	0.152431	+	0.988314i	$0.451290\pi$
$132$	−7.43703e75	−3.89965
$133$	2.03354e75	0.815680
$134$	8.27563e75	2.54437
$135$	2.09257e75	0.494118
$136$	1.31163e76	2.38331
$137$	−1.26482e75	−0.177194	−0.0885972	−	0.996068i	$-0.528238\pi$
$137$	−1.26482e75	−0.177194	−0.0885972	+	0.996068i	$0.528238\pi$
$138$	−3.41891e76	−3.69981
$139$	1.77096e75	0.148314	0.0741571	−	0.997247i	$-0.476373\pi$
$139$	1.77096e75	0.148314	0.0741571	+	0.997247i	$0.476373\pi$
$140$	−1.46813e76	−0.953278
$141$	2.62383e76	1.32330
$142$	−6.76904e76	−2.65638
$143$	1.61084e76	0.492745
$144$	1.56505e77	3.73818
$145$	1.84114e76	0.343972
$146$	−1.72074e77	−2.51877
$147$	−6.50252e76	−0.746992
$148$	4.40418e77	3.97717
$149$	−9.31325e76	−0.662199	−0.331100	−	0.943596i	$-0.607420\pi$
$149$	−9.31325e76	−0.662199	−0.331100	+	0.943596i	$0.607420\pi$
$150$	−3.72408e77	−2.08823
$151$	2.38736e77	1.05739	0.528695	−	0.848812i	$-0.322681\pi$
$151$	2.38736e77	1.05739	0.528695	+	0.848812i	$0.322681\pi$
$152$	−8.26740e77	−2.89682
$153$	5.18922e77	1.44064
$154$	6.19035e77	1.36373
$155$	1.41089e77	0.247011
$156$	−1.34845e78	−1.87894
$157$	1.31020e77	0.145512	0.0727559	−	0.997350i	$-0.476821\pi$
$157$	1.31020e77	0.145512	0.0727559	+	0.997350i	$0.476821\pi$
$158$	5.09704e76	0.0451847
$159$	−8.57541e77	−0.607655
$160$	1.72377e78	0.977734
$161$	2.01029e78	0.913985
$162$	−5.46649e77	−0.199492
$163$	1.36178e78	0.399436	0.199718	−	0.979853i	$-0.435997\pi$
$163$	1.36178e78	0.399436	0.199718	+	0.979853i	$0.435997\pi$
$164$	1.31419e78	0.310244
$165$	−4.61924e78	−0.878801
$166$	1.86913e79	2.86947
$167$	−1.39531e79	−1.73075	−0.865376	−	0.501123i	$-0.832920\pi$
$167$	−1.39531e79	−1.73075	−0.865376	+	0.501123i	$0.832920\pi$
$168$	−3.02830e79	−3.03892
$169$	−9.38136e78	−0.762585
$170$	1.39407e79	0.919065
$171$	−3.27084e79	−1.75104
$172$	7.05742e79	3.07175
$173$	1.13225e79	0.401148	0.200574	−	0.979679i	$-0.435719\pi$
$173$	1.13225e79	0.401148	0.200574	+	0.979679i	$0.435719\pi$
$174$	6.49863e79	1.87639
$175$	2.18972e79	0.515868
$176$	−1.25232e80	−2.40999
$177$	8.59335e79	1.35242
$178$	−1.84432e80	−2.37643
$179$	−1.47161e80	−1.55421	−0.777105	−	0.629371i	$-0.783313\pi$
$179$	−1.47161e80	−1.55421	−0.777105	+	0.629371i	$0.783313\pi$
$180$	2.36141e80	2.04643
$181$	2.67947e80	1.90748	0.953738	−	0.300640i	$-0.0972003\pi$
$181$	2.67947e80	1.90748	0.953738	+	0.300640i	$0.0972003\pi$
$182$	1.12241e80	0.657078
$183$	−3.00356e80	−1.44751
$184$	−8.17285e80	−3.24594
$185$	2.73550e80	0.896272
$186$	4.97997e80	1.34746
$187$	−4.15230e80	−0.928777
$188$	1.07330e81	1.98664
$189$	−4.34294e80	−0.665871
$190$	−8.78699e80	−1.11709
$191$	4.34884e80	0.458869	0.229434	−	0.973324i	$-0.426312\pi$
$191$	4.34884e80	0.458869	0.229434	+	0.973324i	$0.426312\pi$
$192$	1.72734e81	1.51420
$193$	2.99218e80	0.218124	0.109062	−	0.994035i	$-0.465215\pi$
$193$	2.99218e80	0.218124	0.109062	+	0.994035i	$0.465215\pi$
$194$	8.60692e80	0.522259
$195$	−8.37542e80	−0.423426
$196$	−2.65992e81	−1.12144
$197$	3.51236e81	1.23608	0.618042	−	0.786145i	$-0.287926\pi$
$197$	3.51236e81	1.23608	0.618042	+	0.786145i	$0.287926\pi$
$198$	−9.95683e81	−2.92757
$199$	1.32417e81	0.325580	0.162790	−	0.986661i	$-0.447951\pi$
$199$	1.32417e81	0.325580	0.162790	+	0.986661i	$0.447951\pi$
$200$	−8.90235e81	−1.83206
$201$	1.28163e82	2.20954
$202$	−3.64045e81	−0.526237
$203$	−3.82113e81	−0.463535
$204$	3.47595e82	3.54162
$205$	8.16263e80	0.0699147
$206$	1.05530e82	0.760484
$207$	−3.23343e82	−1.96208
$208$	−2.27065e82	−1.16119
$209$	2.61725e82	1.12889
$210$	−3.21862e82	−1.17189
$211$	4.99936e82	1.53776	0.768878	−	0.639396i	$-0.220815\pi$
$211$	4.99936e82	1.53776	0.768878	+	0.639396i	$0.220815\pi$
$212$	−3.50785e82	−0.912259
$213$	−1.04831e83	−2.30681
$214$	5.64523e82	1.05194
$215$	4.38346e82	0.692232
$216$	1.76563e83	2.36479
$217$	−2.92818e82	−0.332871
$218$	−1.05765e83	−1.02126
$219$	−2.66487e83	−2.18731
$220$	−1.88954e83	−1.31933
$221$	−7.52878e82	−0.447506
$222$	9.65541e83	4.88923
$223$	3.30848e83	1.42825	0.714127	−	0.700016i	$-0.246824\pi$
$223$	3.30848e83	1.42825	0.714127	+	0.700016i	$0.246824\pi$
$224$	−3.57754e83	−1.31759
$225$	−3.52205e83	−1.10743
$226$	7.65646e83	2.05674
$227$	1.77204e83	0.406963	0.203482	−	0.979079i	$-0.434774\pi$
$227$	1.77204e83	0.406963	0.203482	+	0.979079i	$0.434774\pi$
$228$	−2.19094e84	−4.30470
$229$	6.88941e82	0.115884	0.0579419	−	0.998320i	$-0.481546\pi$
$229$	6.88941e82	0.115884	0.0579419	+	0.998320i	$0.481546\pi$
$230$	−8.68650e83	−1.25172
$231$	9.58685e83	1.18427
$232$	1.55349e84	1.64621
$233$	−6.50771e83	−0.591961	−0.295981	−	0.955194i	$-0.595646\pi$
$233$	−6.50771e83	−0.591961	−0.295981	+	0.955194i	$0.595646\pi$
$234$	−1.80533e84	−1.41057
$235$	6.66644e83	0.447697
$236$	3.51519e84	2.03036
$237$	7.89366e82	0.0392385
$238$	−2.89326e84	−1.23853
$239$	3.58095e84	1.32091	0.660454	−	0.750866i	$-0.270364\pi$
$239$	3.58095e84	1.32091	0.660454	+	0.750866i	$0.270364\pi$
$240$	6.51134e84	2.07096
$241$	−5.65183e84	−1.55090	−0.775450	−	0.631409i	$-0.782477\pi$
$241$	−5.65183e84	−1.55090	−0.775450	+	0.631409i	$0.782477\pi$
$242$	1.76600e83	0.0418355
$243$	−5.29984e84	−1.08453
$244$	−1.22863e85	−2.17312
$245$	−1.65211e84	−0.252722
$246$	2.88114e84	0.381390
$247$	4.74549e84	0.543926
$248$	1.19045e85	1.18217
$249$	2.89467e85	2.49185
$250$	−2.28639e85	−1.70719
$251$	−1.10729e85	−0.717535	−0.358767	−	0.933427i	$-0.616803\pi$
$251$	−1.10729e85	−0.717535	−0.358767	+	0.933427i	$0.616803\pi$
$252$	−4.90090e85	−2.75776
$253$	2.58732e85	1.26494
$254$	3.68671e85	1.56690
$255$	2.15896e85	0.798119
$256$	−3.27825e85	−1.05468
$257$	−4.79699e85	−1.34383	−0.671913	−	0.740630i	$-0.734527\pi$
$257$	−4.79699e85	−1.34383	−0.671913	+	0.740630i	$0.734527\pi$
$258$	1.54722e86	3.77617
$259$	−5.67729e85	−1.20781
$260$	−3.42604e85	−0.635681
$261$	6.14608e85	0.995085
$262$	3.98040e85	0.562640
$263$	−3.95482e85	−0.488312	−0.244156	−	0.969736i	$-0.578511\pi$
$263$	−3.95482e85	−0.488312	−0.244156	+	0.969736i	$0.578511\pi$
$264$	−3.89755e86	−4.20583
$265$	−2.17877e85	−0.205581
$266$	1.82367e86	1.50538
$267$	−2.85625e86	−2.06370
$268$	5.24262e86	3.31713
$269$	−1.28994e86	−0.715093	−0.357547	−	0.933895i	$-0.616387\pi$
$269$	−1.28994e86	−0.715093	−0.357547	+	0.933895i	$0.616387\pi$
$270$	1.87660e86	0.911922
$271$	−7.31308e85	−0.311667	−0.155833	−	0.987783i	$-0.549806\pi$
$271$	−7.31308e85	−0.311667	−0.155833	+	0.987783i	$0.549806\pi$
$272$	5.85313e86	2.18873
$273$	1.73825e86	0.570608
$274$	−1.13429e86	−0.327022
$275$	2.81826e86	0.713955
$276$	−2.16588e87	−4.82350
$277$	3.58591e86	0.702373	0.351186	−	0.936306i	$-0.385778\pi$
$277$	3.58591e86	0.702373	0.351186	+	0.936306i	$0.385778\pi$
$278$	1.58818e86	0.273722
$279$	4.70981e86	0.714585
$280$	−7.69408e86	−1.02813
$281$	1.47500e86	0.173667	0.0868337	−	0.996223i	$-0.472325\pi$
$281$	1.47500e86	0.173667	0.0868337	+	0.996223i	$0.472325\pi$
$282$	2.35304e87	2.44222
$283$	6.70839e86	0.614045	0.307022	−	0.951702i	$-0.400667\pi$
$283$	6.70839e86	0.614045	0.307022	+	0.951702i	$0.400667\pi$
$284$	−4.28819e87	−3.46316
$285$	−1.36082e87	−0.970081
$286$	1.44459e87	0.909388
$287$	−1.69409e86	−0.0942167
$288$	5.75428e87	2.82851
$289$	−3.60057e86	−0.156494
$290$	1.65112e87	0.634819
$291$	1.33293e87	0.453531
$292$	−1.09009e88	−3.28376
$293$	2.88023e87	0.768469	0.384234	−	0.923236i	$-0.374465\pi$
$293$	2.88023e87	0.768469	0.384234	+	0.923236i	$0.374465\pi$
$294$	−5.83141e87	−1.37862
$295$	2.18333e87	0.457550
$296$	2.30811e88	4.28944
$297$	−5.58955e87	−0.921558
$298$	−8.35205e87	−1.22213
$299$	4.69122e87	0.609479
$300$	−2.35921e88	−2.72246
$301$	−9.09750e87	−0.932849
$302$	2.14096e88	1.95147
$303$	−5.63788e87	−0.456986
$304$	−3.68931e88	−2.66031
$305$	−7.63120e87	−0.489721
$306$	4.65366e88	2.65879
$307$	3.26615e88	1.66197	0.830986	−	0.556293i	$-0.187777\pi$
$307$	3.26615e88	1.66197	0.830986	+	0.556293i	$0.187777\pi$
$308$	3.92159e88	1.77792
$309$	1.63432e88	0.660406
$310$	1.26527e88	0.455873
$311$	−3.08266e88	−0.990675	−0.495337	−	0.868701i	$-0.664956\pi$
$311$	−3.08266e88	−0.990675	−0.495337	+	0.868701i	$0.664956\pi$
$312$	−7.06687e88	−2.02647
$313$	−3.74021e88	−0.957354	−0.478677	−	0.877991i	$-0.658883\pi$
$313$	−3.74021e88	−0.957354	−0.478677	+	0.877991i	$0.658883\pi$
$314$	1.17497e88	0.268550
$315$	−3.04402e88	−0.621473
$316$	3.22898e87	0.0589079
$317$	4.62803e88	0.754731	0.377366	−	0.926064i	$-0.376830\pi$
$317$	4.62803e88	0.754731	0.377366	+	0.926064i	$0.376830\pi$
$318$	−7.69036e88	−1.12146
$319$	−4.91795e88	−0.641527
$320$	4.38868e88	0.512283
$321$	8.74264e88	0.913511
$322$	1.80281e89	1.68681
$323$	−1.22326e89	−1.02525
$324$	−3.46303e88	−0.260081
$325$	5.10996e88	0.344000
$326$	1.22123e89	0.737181
$327$	−1.63795e89	−0.886863
$328$	6.88733e88	0.334603
$329$	−1.38356e89	−0.603315
$330$	−4.14250e89	−1.62188
$331$	−8.92965e88	−0.314008	−0.157004	−	0.987598i	$-0.550184\pi$
$331$	−8.92965e88	−0.314008	−0.157004	+	0.987598i	$0.550184\pi$
$332$	1.18409e90	3.74097
$333$	9.13161e89	2.59285
$334$	−1.25130e90	−3.19420
$335$	3.25626e89	0.747530
$336$	−1.35137e90	−2.79081
$337$	−9.67451e88	−0.179791	−0.0898954	−	0.995951i	$-0.528653\pi$
$337$	−9.67451e88	−0.179791	−0.0898954	+	0.995951i	$0.528653\pi$
$338$	−8.41314e89	−1.40739
$339$	1.18574e90	1.78607
$340$	8.83142e89	1.19820
$341$	−3.76868e89	−0.460690
$342$	−2.93326e90	−3.23165
$343$	1.07854e90	1.07126
$344$	3.69860e90	3.31294
$345$	−1.34526e90	−1.08700
$346$	1.01539e90	0.740341
$347$	−1.96223e90	−1.29138	−0.645690	−	0.763600i	$-0.723430\pi$
$347$	−1.96223e90	−1.29138	−0.645690	+	0.763600i	$0.723430\pi$
$348$	4.11689e90	2.44628
$349$	−1.63278e90	−0.876245	−0.438122	−	0.898915i	$-0.644356\pi$
$349$	−1.63278e90	−0.876245	−0.438122	+	0.898915i	$0.644356\pi$
$350$	1.96373e90	0.952063
$351$	−1.01347e90	−0.444028
$352$	−4.60445e90	−1.82353
$353$	9.94976e89	0.356296	0.178148	−	0.984004i	$-0.442989\pi$
$353$	9.94976e89	0.356296	0.178148	+	0.984004i	$0.442989\pi$
$354$	7.70646e90	2.49597
$355$	−2.66345e90	−0.780438
$356$	−1.16838e91	−3.09819
$357$	−4.48073e90	−1.07554
$358$	−1.31973e91	−2.86838
$359$	7.92810e90	1.56069	0.780344	−	0.625351i	$-0.215044\pi$
$359$	7.92810e90	1.56069	0.780344	+	0.625351i	$0.215044\pi$
$360$	1.23755e91	2.20711
$361$	1.52301e90	0.246148
$362$	2.40293e91	3.52035
$363$	2.73496e89	0.0363301
$364$	7.11047e90	0.856641
$365$	−6.77069e90	−0.740008
$366$	−2.69357e91	−2.67146
$367$	1.04017e91	0.936394	0.468197	−	0.883624i	$-0.344904\pi$
$367$	1.04017e91	0.936394	0.468197	+	0.883624i	$0.344904\pi$
$368$	−3.64712e91	−2.98093
$369$	2.72484e90	0.202258
$370$	2.45317e91	1.65412
$371$	4.52186e90	0.277041
$372$	3.15482e91	1.75671
$373$	1.05380e91	0.533451	0.266726	−	0.963772i	$-0.414058\pi$
$373$	1.05380e91	0.533451	0.266726	+	0.963772i	$0.414058\pi$
$374$	−3.72375e91	−1.71411
$375$	−3.54089e91	−1.48252
$376$	5.62490e91	2.14262
$377$	−8.91703e90	−0.309102
$378$	−3.89472e91	−1.22890
$379$	−1.44514e91	−0.415162	−0.207581	−	0.978218i	$-0.566559\pi$
$379$	−1.44514e91	−0.415162	−0.207581	+	0.978218i	$0.566559\pi$
$380$	−5.56656e91	−1.45636
$381$	5.70952e91	1.36070
$382$	3.90000e91	0.846868
$383$	−6.98913e91	−1.38314	−0.691570	−	0.722309i	$-0.743081\pi$
$383$	−6.98913e91	−1.38314	−0.691570	+	0.722309i	$0.743081\pi$
$384$	−5.29007e90	−0.0954340
$385$	2.43575e91	0.400661
$386$	2.68336e91	0.402559
$387$	1.46328e92	2.00258
$388$	5.45249e91	0.680877
$389$	7.91353e91	0.901903	0.450951	−	0.892549i	$-0.351085\pi$
$389$	7.91353e91	0.901903	0.450951	+	0.892549i	$0.351085\pi$
$390$	−7.51102e91	−0.781457
$391$	−1.20927e92	−1.14881
$392$	−1.39399e92	−1.20950
$393$	6.16435e91	0.488598
$394$	3.14986e92	2.28126
$395$	2.00556e90	0.0132751
$396$	−6.30766e92	−3.81671
$397$	−3.43801e92	−1.90215	−0.951074	−	0.308962i	$-0.900018\pi$
$397$	−3.43801e92	−1.90215	−0.951074	+	0.308962i	$0.900018\pi$
$398$	1.18750e92	0.600877
$399$	2.82427e92	1.30728
$400$	−3.97266e92	−1.68249
$401$	1.54868e92	0.600256	0.300128	−	0.953899i	$-0.402971\pi$
$401$	1.54868e92	0.600256	0.300128	+	0.953899i	$0.402971\pi$
$402$	1.14935e93	4.07783
$403$	−6.83322e91	−0.221971
$404$	−2.30623e92	−0.686063
$405$	−2.15093e91	−0.0586102
$406$	−3.42676e92	−0.855480
$407$	−7.30691e92	−1.67160
$408$	1.82165e93	3.81970
$409$	−3.32967e92	−0.640064	−0.320032	−	0.947407i	$-0.603694\pi$
$409$	−3.32967e92	−0.640064	−0.320032	+	0.947407i	$0.603694\pi$
$410$	7.32019e91	0.129031
$411$	−1.75664e92	−0.283987
$412$	6.68534e92	0.991454
$413$	−4.53132e92	−0.616593
$414$	−2.89972e93	−3.62113
$415$	7.35456e92	0.843042
$416$	−8.34859e92	−0.878618
$417$	2.45958e92	0.237701
$418$	2.34713e93	2.08343
$419$	1.01601e93	0.828511	0.414255	−	0.910161i	$-0.364042\pi$
$419$	1.01601e93	0.828511	0.414255	+	0.910161i	$0.364042\pi$
$420$	−2.03900e93	−1.52780
$421$	−1.95970e93	−1.34951	−0.674753	−	0.738044i	$-0.735750\pi$
$421$	−1.95970e93	−1.34951	−0.674753	+	0.738044i	$0.735750\pi$
$422$	4.48339e93	2.83801
$423$	2.22538e93	1.29516
$424$	−1.83837e93	−0.983887
$425$	−1.31721e93	−0.648407
$426$	−9.40112e93	−4.25735
$427$	1.58379e93	0.659946
$428$	3.57626e93	1.37143
$429$	2.23720e93	0.789715
$430$	3.93105e93	1.27755
$431$	−2.39031e93	−0.715338	−0.357669	−	0.933848i	$-0.616428\pi$
$431$	−2.39031e93	−0.715338	−0.357669	+	0.933848i	$0.616428\pi$
$432$	7.87909e93	2.17172
$433$	3.73828e93	0.949188	0.474594	−	0.880205i	$-0.342595\pi$
$433$	3.73828e93	0.949188	0.474594	+	0.880205i	$0.342595\pi$
$434$	−2.62597e93	−0.614333
$435$	2.55705e93	0.551279
$436$	−6.70021e93	−1.33143
$437$	7.62220e93	1.39633
$438$	−2.38983e94	−4.03680
$439$	1.41081e93	0.219775	0.109888	−	0.993944i	$-0.464951\pi$
$439$	1.41081e93	0.219775	0.109888	+	0.993944i	$0.464951\pi$
$440$	−9.90259e93	−1.42291
$441$	−5.51506e93	−0.731106
$442$	−6.75175e93	−0.825897
$443$	−1.52815e94	−1.72517	−0.862587	−	0.505909i	$-0.831157\pi$
$443$	−1.52815e94	−1.72517	−0.862587	+	0.505909i	$0.831157\pi$
$444$	6.11671e94	6.37415
$445$	−7.25694e93	−0.698189
$446$	2.96702e94	2.63592
$447$	−1.29346e94	−1.06130
$448$	−9.10834e93	−0.690350
$449$	−6.58554e93	−0.461154	−0.230577	−	0.973054i	$-0.574061\pi$
$449$	−6.58554e93	−0.461154	−0.230577	+	0.973054i	$0.574061\pi$
$450$	−3.15855e94	−2.04382
$451$	−2.18036e93	−0.130395
$452$	4.85038e94	2.68140
$453$	3.31566e94	1.69466
$454$	1.58915e94	0.751073
$455$	4.41641e93	0.193048
$456$	−1.14821e95	−4.64269
$457$	−5.94864e93	−0.222532	−0.111266	−	0.993791i	$-0.535491\pi$
$457$	−5.94864e93	−0.222532	−0.111266	+	0.993791i	$0.535491\pi$
$458$	6.17838e93	0.213870
$459$	2.61246e94	0.836950
$460$	−5.50290e94	−1.63188
$461$	−1.65335e94	−0.453924	−0.226962	−	0.973904i	$-0.572879\pi$
$461$	−1.65335e94	−0.453924	−0.226962	+	0.973904i	$0.572879\pi$
$462$	8.59741e94	2.18564
$463$	−4.37845e94	−1.03085	−0.515425	−	0.856935i	$-0.672366\pi$
$463$	−4.37845e94	−1.03085	−0.515425	+	0.856935i	$0.672366\pi$
$464$	6.93241e94	1.51180
$465$	1.95950e94	0.395881
$466$	−5.83607e94	−1.09250
$467$	8.26716e94	1.43419	0.717095	−	0.696975i	$-0.245471\pi$
$467$	8.26716e94	1.43419	0.717095	+	0.696975i	$0.245471\pi$
$468$	−1.14368e95	−1.83898
$469$	−6.75809e94	−1.00737
$470$	5.97841e94	0.826251
$471$	1.81965e94	0.233210
$472$	1.84222e95	2.18978
$473$	−1.17089e95	−1.29105
$474$	7.07898e93	0.0724168
$475$	8.30255e94	0.788113
$476$	−1.83289e95	−1.61469
$477$	−7.27316e94	−0.594731
$478$	3.21137e95	2.43781
$479$	−5.41589e94	−0.381732	−0.190866	−	0.981616i	$-0.561130\pi$
$479$	−5.41589e94	−0.381732	−0.190866	+	0.981616i	$0.561130\pi$
$480$	2.39405e95	1.56700
$481$	−1.32486e95	−0.805414
$482$	−5.06852e95	−2.86227
$483$	2.79197e95	1.46483
$484$	1.11876e94	0.0545416
$485$	3.38661e94	0.153438
$486$	−4.75286e95	−2.00156
$487$	3.32841e95	1.30304	0.651521	−	0.758631i	$-0.274131\pi$
$487$	3.32841e95	1.30304	0.651521	+	0.758631i	$0.274131\pi$
$488$	−6.43893e95	−2.34374
$489$	1.89130e95	0.640170
$490$	−1.48160e95	−0.466413
$491$	1.65994e95	0.486069	0.243035	−	0.970018i	$-0.421857\pi$
$491$	1.65994e95	0.486069	0.243035	+	0.970018i	$0.421857\pi$
$492$	1.82521e95	0.497223
$493$	2.29857e95	0.582629
$494$	4.25572e95	1.00385
$495$	−3.91777e95	−0.860111
$496$	5.31238e95	1.08565
$497$	5.52777e95	1.05172
$498$	2.59592e96	4.59886
$499$	−3.67945e95	−0.607034	−0.303517	−	0.952826i	$-0.598161\pi$
$499$	−3.67945e95	−0.607034	−0.303517	+	0.952826i	$0.598161\pi$
$500$	−1.44843e96	−2.22568
$501$	−1.93786e96	−2.77385
$502$	−9.93006e95	−1.32425
$503$	8.12299e94	0.100937	0.0504687	−	0.998726i	$-0.483928\pi$
$503$	8.12299e94	0.100937	0.0504687	+	0.998726i	$0.483928\pi$
$504$	−2.56843e96	−2.97429
$505$	−1.43243e95	−0.154607
$506$	2.32029e96	2.33453
$507$	−1.30292e96	−1.22218
$508$	2.33553e96	2.04279
$509$	1.02853e96	0.838950	0.419475	−	0.907767i	$-0.362214\pi$
$509$	1.02853e96	0.838950	0.419475	+	0.907767i	$0.362214\pi$
$510$	1.93614e96	1.47297
$511$	1.40520e96	0.997232
$512$	−2.84997e96	−1.88693
$513$	−1.64667e96	−1.01728
$514$	−4.30191e96	−2.48011
$515$	4.15236e95	0.223428
$516$	9.80164e96	4.92305
$517$	−1.78070e96	−0.834982
$518$	−5.09135e96	−2.22909
$519$	1.57251e96	0.642914
$520$	−1.79550e96	−0.685592
$521$	−7.31210e95	−0.260797	−0.130399	−	0.991462i	$-0.541626\pi$
$521$	−7.31210e95	−0.260797	−0.130399	+	0.991462i	$0.541626\pi$
$522$	5.51176e96	1.83649
$523$	−5.73676e94	−0.0178590	−0.00892950	−	0.999960i	$-0.502842\pi$
$523$	−5.73676e94	−0.0178590	−0.00892950	+	0.999960i	$0.502842\pi$
$524$	2.52159e96	0.733522
$525$	3.04118e96	0.826774
$526$	−3.54665e96	−0.901207
$527$	1.76142e96	0.418394
$528$	−1.73927e97	−3.86246
$529$	2.71914e96	0.564619
$530$	−1.95391e96	−0.379412
$531$	7.28839e96	1.32366
$532$	1.15529e97	1.96259
$533$	−3.95334e95	−0.0628272
$534$	−2.56146e97	−3.80867
$535$	2.22126e96	0.309058
$536$	2.74751e97	3.57758
$537$	−2.04383e97	−2.49091
$538$	−1.15681e97	−1.31974
$539$	4.41303e96	0.471341
$540$	1.18883e97	1.18889
$541$	−1.10887e97	−1.03843	−0.519217	−	0.854642i	$-0.673776\pi$
$541$	−1.10887e97	−1.03843	−0.519217	+	0.854642i	$0.673776\pi$
$542$	−6.55832e96	−0.575199
$543$	3.72136e97	3.05708
$544$	2.15204e97	1.65611
$545$	−4.16159e96	−0.300043
$546$	1.55885e97	1.05309
$547$	−5.26057e96	−0.333030	−0.166515	−	0.986039i	$-0.553251\pi$
$547$	−5.26057e96	−0.333030	−0.166515	+	0.986039i	$0.553251\pi$
$548$	−7.18571e96	−0.426343
$549$	−2.54744e97	−1.41673
$550$	2.52740e97	1.31764
$551$	−1.44882e97	−0.708162
$552$	−1.13508e98	−5.20222
$553$	−4.16237e95	−0.0178895
$554$	3.21582e97	1.29627
$555$	3.79917e97	1.43644
$556$	1.00611e97	0.356855
$557$	−2.33015e97	−0.775399	−0.387700	−	0.921786i	$-0.626730\pi$
$557$	−2.33015e97	−0.775399	−0.387700	+	0.921786i	$0.626730\pi$
$558$	4.22372e97	1.31881
$559$	−2.12300e97	−0.622058
$560$	−3.43347e97	−0.944186
$561$	−5.76689e97	−1.48854
$562$	1.32277e97	0.320513
$563$	8.06940e97	1.83566	0.917832	−	0.396970i	$-0.129938\pi$
$563$	8.06940e97	1.83566	0.917832	+	0.396970i	$0.129938\pi$
$564$	1.49065e98	3.18396
$565$	3.01263e97	0.604264
$566$	6.01604e97	1.13325
$567$	4.46408e96	0.0789829
$568$	−2.24732e98	−3.73508
$569$	2.37950e97	0.371535	0.185767	−	0.982594i	$-0.440523\pi$
$569$	2.37950e97	0.371535	0.185767	+	0.982594i	$0.440523\pi$
$570$	−1.22037e98	−1.79034
$571$	−1.21157e98	−1.67019	−0.835097	−	0.550103i	$-0.814588\pi$
$571$	−1.21157e98	−1.67019	−0.835097	+	0.550103i	$0.814588\pi$
$572$	9.15146e97	1.18558
$573$	6.03985e97	0.735422
$574$	−1.51924e97	−0.173882
$575$	8.20760e97	0.883096
$576$	1.46503e98	1.48200
$577$	−1.11248e98	−1.05816	−0.529079	−	0.848572i	$-0.677463\pi$
$577$	−1.11248e98	−1.05816	−0.529079	+	0.848572i	$0.677463\pi$
$578$	−3.22896e97	−0.288818
$579$	4.15566e97	0.349583
$580$	1.04599e98	0.827623
$581$	−1.52638e98	−1.13608
$582$	1.19536e98	0.837017
$583$	5.81982e97	0.383421
$584$	−5.71286e98	−3.54159
$585$	−7.10355e97	−0.414421
$586$	2.58297e98	1.41825
$587$	1.10969e97	0.0573523	0.0286761	−	0.999589i	$-0.490871\pi$
$587$	1.10969e97	0.0573523	0.0286761	+	0.999589i	$0.490871\pi$
$588$	−3.69420e98	−1.79732
$589$	−1.11025e98	−0.508542
$590$	1.95800e98	0.844434
$591$	4.87811e98	1.98105
$592$	1.02999e99	3.93924
$593$	2.59277e98	0.933948	0.466974	−	0.884271i	$-0.345344\pi$
$593$	2.59277e98	0.933948	0.466974	+	0.884271i	$0.345344\pi$
$594$	−5.01267e98	−1.70079
$595$	−1.13843e98	−0.363876
$596$	−5.29103e98	−1.59330
$597$	1.83906e98	0.521803
$598$	4.20705e98	1.12483
$599$	1.27153e98	0.320386	0.160193	−	0.987086i	$-0.448788\pi$
$599$	1.27153e98	0.320386	0.160193	+	0.987086i	$0.448788\pi$
$600$	−1.23640e99	−2.93622
$601$	−7.29168e98	−1.63224	−0.816120	−	0.577882i	$-0.803879\pi$
$601$	−7.29168e98	−1.63224	−0.816120	+	0.577882i	$0.803879\pi$
$602$	−8.15857e98	−1.72163
$603$	1.08700e99	2.16255
$604$	1.35630e99	2.54416
$605$	6.94879e96	0.0122912
$606$	−5.05601e98	−0.843393
$607$	1.00909e98	0.158757	0.0793783	−	0.996845i	$-0.474706\pi$
$607$	1.00909e98	0.158757	0.0793783	+	0.996845i	$0.474706\pi$
$608$	−1.35646e99	−2.01294
$609$	−5.30695e98	−0.742901
$610$	−6.84361e98	−0.903808
$611$	−3.22870e98	−0.402313
$612$	2.94810e99	3.46630
$613$	−1.57887e99	−1.75186	−0.875929	−	0.482441i	$-0.839750\pi$
$613$	−1.57887e99	−1.75186	−0.875929	+	0.482441i	$0.839750\pi$
$614$	2.92906e99	3.06726
$615$	1.13366e98	0.112051
$616$	2.05520e99	1.91751
$617$	−1.73396e99	−1.52727	−0.763634	−	0.645649i	$-0.776587\pi$
$617$	−1.73396e99	−1.52727	−0.763634	+	0.645649i	$0.776587\pi$
$618$	1.46565e99	1.21882
$619$	−9.36745e98	−0.735535	−0.367768	−	0.929918i	$-0.619878\pi$
$619$	−9.36745e98	−0.735535	−0.367768	+	0.929918i	$0.619878\pi$
$620$	8.01551e98	0.594328
$621$	−1.62784e99	−1.13988
$622$	−2.76450e99	−1.82835
$623$	1.50612e99	0.940877
$624$	−3.15358e99	−1.86102
$625$	3.66681e98	0.204431
$626$	−3.35420e99	−1.76685
$627$	3.63495e99	1.80926
$628$	7.44347e98	0.350113
$629$	3.41513e99	1.51813
$630$	−2.72985e99	−1.14696
$631$	−4.79167e99	−1.90303	−0.951513	−	0.307610i	$-0.900471\pi$
$631$	−4.79167e99	−1.90303	−0.951513	+	0.307610i	$0.900471\pi$
$632$	1.69222e98	0.0635332
$633$	6.94332e99	2.46454
$634$	4.15038e99	1.39290
$635$	1.45063e99	0.460351
$636$	−4.87185e99	−1.46206
$637$	8.00152e98	0.227103
$638$	−4.41039e99	−1.18397
$639$	−8.89112e99	−2.25775
$640$	−1.34406e98	−0.0322872
$641$	1.45823e98	0.0331411	0.0165705	−	0.999863i	$-0.494725\pi$
$641$	1.45823e98	0.0331411	0.0165705	+	0.999863i	$0.494725\pi$
$642$	7.84033e99	1.68594
$643$	−8.69884e97	−0.0176999	−0.00884997	−	0.999961i	$-0.502817\pi$
$643$	−8.69884e97	−0.0176999	−0.00884997	+	0.999961i	$0.502817\pi$
$644$	1.14208e100	2.19912
$645$	6.08793e99	1.10943
$646$	−1.09701e100	−1.89215
$647$	4.99099e99	0.814863	0.407432	−	0.913236i	$-0.366424\pi$
$647$	4.99099e99	0.814863	0.407432	+	0.913236i	$0.366424\pi$
$648$	−1.81488e99	−0.280501
$649$	−5.83200e99	−0.853357
$650$	4.58257e99	0.634871
$651$	−4.06677e99	−0.533488
$652$	7.73653e99	0.961074
$653$	9.21261e99	1.08384	0.541920	−	0.840430i	$-0.317698\pi$
$653$	9.21261e99	1.08384	0.541920	+	0.840430i	$0.317698\pi$
$654$	−1.46891e100	−1.63676
$655$	1.56619e99	0.165302
$656$	3.07346e99	0.307285
$657$	−2.26019e100	−2.14079
$658$	−1.24077e100	−1.11345
$659$	−6.46631e98	−0.0549825	−0.0274912	−	0.999622i	$-0.508752\pi$
$659$	−6.46631e98	−0.0549825	−0.0274912	+	0.999622i	$0.508752\pi$
$660$	−2.62428e100	−2.11446
$661$	9.22693e99	0.704540	0.352270	−	0.935899i	$-0.385410\pi$
$661$	9.22693e99	0.704540	0.352270	+	0.935899i	$0.385410\pi$
$662$	−8.00805e99	−0.579520
$663$	−1.04563e100	−0.717211
$664$	6.20551e100	4.03470
$665$	7.17568e99	0.442277
$666$	8.18916e100	4.78524
$667$	−1.43225e100	−0.793509
$668$	−7.92700e100	−4.16432
$669$	4.59495e100	2.28904
$670$	2.92019e100	1.37961
$671$	2.03841e100	0.913358
$672$	−4.96864e100	−2.11168
$673$	−4.29183e100	−1.73024	−0.865122	−	0.501561i	$-0.832759\pi$
$673$	−4.29183e100	−1.73024	−0.865122	+	0.501561i	$0.832759\pi$
$674$	−8.67603e99	−0.331814
$675$	−1.77314e100	−0.643367
$676$	−5.32973e100	−1.83484
$677$	−1.48734e100	−0.485863	−0.242931	−	0.970043i	$-0.578109\pi$
$677$	−1.48734e100	−0.485863	−0.242931	+	0.970043i	$0.578109\pi$
$678$	1.06336e101	3.29630
$679$	−7.02863e99	−0.206773
$680$	4.62831e100	1.29228
$681$	2.46108e100	0.652234
$682$	−3.37973e100	−0.850230
$683$	−3.63310e100	−0.867645	−0.433822	−	0.900998i	$-0.642835\pi$
$683$	−3.63310e100	−0.867645	−0.433822	+	0.900998i	$0.642835\pi$
$684$	−1.85823e101	−4.21315
$685$	−4.46314e99	−0.0960782
$686$	9.67227e100	1.97707
$687$	9.56831e99	0.185725
$688$	1.65049e101	3.04246
$689$	1.05523e100	0.184741
$690$	−1.20642e101	−2.00611
$691$	4.83899e99	0.0764335	0.0382168	−	0.999269i	$-0.487832\pi$
$691$	4.83899e99	0.0764335	0.0382168	+	0.999269i	$0.487832\pi$
$692$	6.43251e100	0.965193
$693$	8.13101e100	1.15908
$694$	−1.75971e101	−2.38331
$695$	6.24911e99	0.0804188
$696$	2.15755e101	2.63835
$697$	1.01906e100	0.118423
$698$	−1.46427e101	−1.61716
$699$	−9.03819e100	−0.948728
$700$	1.24402e101	1.24122
$701$	8.08128e100	0.766462	0.383231	−	0.923653i	$-0.374811\pi$
$701$	8.08128e100	0.766462	0.383231	+	0.923653i	$0.374811\pi$
$702$	−9.08876e100	−0.819478
$703$	−2.15260e101	−1.84523
$704$	−1.17228e101	−0.955437
$705$	9.25863e100	0.717518
$706$	8.92287e100	0.657564
$707$	2.97289e100	0.208348
$708$	4.88205e101	3.25403
$709$	2.33325e101	1.47918	0.739588	−	0.673060i	$-0.235021\pi$
$709$	2.33325e101	1.47918	0.739588	+	0.673060i	$0.235021\pi$
$710$	−2.38857e101	−1.44034
$711$	6.69495e99	0.0384040
$712$	−6.12314e101	−3.34145
$713$	−1.09755e101	−0.569831
$714$	−4.01829e101	−1.98497
$715$	5.68410e100	0.267176
$716$	−8.36049e101	−3.73955
$717$	4.97337e101	2.11700
$718$	7.10986e101	2.88034
$719$	1.67032e101	0.644055	0.322028	−	0.946730i	$-0.395636\pi$
$719$	1.67032e101	0.644055	0.322028	+	0.946730i	$0.395636\pi$
$720$	5.52254e101	2.02691
$721$	−8.61786e100	−0.301091
$722$	1.36582e101	0.454281
$723$	−7.84950e101	−2.48561
$724$	1.52226e102	4.58953
$725$	−1.56009e101	−0.447869
$726$	2.45270e100	0.0670492
$727$	−2.35455e101	−0.612966	−0.306483	−	0.951876i	$-0.599152\pi$
$727$	−2.35455e101	−0.612966	−0.306483	+	0.951876i	$0.599152\pi$
$728$	3.72640e101	0.923902
$729$	−6.90290e101	−1.63006
$730$	−6.07191e101	−1.36573
$731$	5.47252e101	1.17252
$732$	−1.70638e102	−3.48282
$733$	5.81904e101	1.13152	0.565758	−	0.824572i	$-0.308584\pi$
$733$	5.81904e101	1.13152	0.565758	+	0.824572i	$0.308584\pi$
$734$	9.32816e101	1.72817
$735$	−2.29452e101	−0.405034
$736$	−1.34095e102	−2.25554
$737$	−8.69795e101	−1.39419
$738$	2.44362e101	0.373278
$739$	−5.36578e101	−0.781188	−0.390594	−	0.920563i	$-0.627730\pi$
$739$	−5.36578e101	−0.781188	−0.390594	+	0.920563i	$0.627730\pi$
$740$	1.55409e102	2.15650
$741$	6.59074e101	0.871741
$742$	4.05517e101	0.511294
$743$	−1.03782e102	−1.24744	−0.623720	−	0.781648i	$-0.714379\pi$
$743$	−1.03782e102	−1.24744	−0.623720	+	0.781648i	$0.714379\pi$
$744$	1.65335e102	1.89464
$745$	−3.28633e101	−0.359057
$746$	9.45041e101	0.984515
$747$	2.45509e102	2.43886
$748$	−2.35900e102	−2.23471
$749$	−4.61004e101	−0.416486
$750$	−3.17544e102	−2.73608
$751$	1.87214e102	1.53858	0.769290	−	0.638899i	$-0.220610\pi$
$751$	1.87214e102	1.53858	0.769290	+	0.638899i	$0.220610\pi$
$752$	2.51010e102	1.96769
$753$	−1.53785e102	−1.14998
$754$	−7.99673e101	−0.570466
$755$	8.42417e101	0.573338
$756$	−2.46731e102	−1.60214
$757$	1.70450e102	1.05607	0.528037	−	0.849221i	$-0.322928\pi$
$757$	1.70450e102	1.05607	0.528037	+	0.849221i	$0.322928\pi$
$758$	−1.29599e102	−0.766205
$759$	3.59338e102	2.02731
$760$	−2.91729e102	−1.57071
$761$	−3.00350e102	−1.54338	−0.771688	−	0.636001i	$-0.780587\pi$
$761$	−3.00350e102	−1.54338	−0.771688	+	0.636001i	$0.780587\pi$
$762$	5.12025e102	2.51125
$763$	8.63702e101	0.404337
$764$	2.47066e102	1.10407
$765$	1.83110e102	0.781145
$766$	−6.26780e102	−2.55266
$767$	−1.05743e102	−0.411167
$768$	−4.55296e102	−1.69033
$769$	−2.51240e102	−0.890645	−0.445322	−	0.895370i	$-0.646911\pi$
$769$	−2.51240e102	−0.890645	−0.445322	+	0.895370i	$0.646911\pi$
$770$	2.18437e102	0.739443
$771$	−6.66226e102	−2.15373
$772$	1.69991e102	0.524822
$773$	3.28414e102	0.968389	0.484194	−	0.874960i	$-0.339113\pi$
$773$	3.28414e102	0.968389	0.484194	+	0.874960i	$0.339113\pi$
$774$	1.31226e103	3.69586
$775$	−1.19552e102	−0.321622
$776$	2.85750e102	0.734337
$777$	−7.88486e102	−1.93574
$778$	7.09680e102	1.66451
$779$	−6.42330e101	−0.143939
$780$	−4.75823e102	−1.01880
$781$	7.11447e102	1.45556
$782$	−1.08446e103	−2.12019
$783$	3.09418e102	0.578100
$784$	−6.22065e102	−1.11075
$785$	4.62324e101	0.0788994
$786$	5.52814e102	0.901735
$787$	1.06832e103	1.66571	0.832856	−	0.553490i	$-0.186704\pi$
$787$	1.06832e103	1.66571	0.832856	+	0.553490i	$0.186704\pi$
$788$	1.99544e103	2.97411
$789$	−5.49261e102	−0.782610
$790$	1.79857e101	0.0245000
$791$	−6.25247e102	−0.814303
$792$	−3.30567e103	−4.11639
$793$	3.69595e102	0.440077
$794$	−3.08318e103	−3.51052
$795$	−3.02597e102	−0.329482
$796$	7.52284e102	0.783372
$797$	−1.10629e102	−0.110179	−0.0550896	−	0.998481i	$-0.517544\pi$
$797$	−1.10629e102	−0.110179	−0.0550896	+	0.998481i	$0.517544\pi$
$798$	2.53278e103	2.41266
$799$	8.32270e102	0.758322
$800$	−1.46064e103	−1.27306
$801$	−2.42251e103	−2.01981
$802$	1.38884e103	1.10781
$803$	1.80855e103	1.38016
$804$	7.28117e103	5.31632
$805$	7.09362e102	0.495580
$806$	−6.12798e102	−0.409660
$807$	−1.79152e103	−1.14607
$808$	−1.20863e103	−0.739930
$809$	−1.41431e103	−0.828650	−0.414325	−	0.910129i	$-0.635982\pi$
$809$	−1.41431e103	−0.828650	−0.414325	+	0.910129i	$0.635982\pi$
$810$	−1.92894e102	−0.108168
$811$	1.43878e103	0.772244	0.386122	−	0.922448i	$-0.373814\pi$
$811$	1.43878e103	0.772244	0.386122	+	0.922448i	$0.373814\pi$
$812$	−2.17086e103	−1.11530
$813$	−1.01567e103	−0.499504
$814$	−6.55278e103	−3.08503
$815$	4.80526e102	0.216582
$816$	8.12907e103	3.50784
$817$	−3.44941e103	−1.42515
$818$	−2.98602e103	−1.18127
$819$	1.47428e103	0.558472
$820$	4.63735e102	0.168220
$821$	2.19205e103	0.761497	0.380749	−	0.924679i	$-0.375666\pi$
$821$	2.19205e103	0.761497	0.380749	+	0.924679i	$0.375666\pi$
$822$	−1.57534e103	−0.524114
$823$	3.12031e103	0.994267	0.497134	−	0.867674i	$-0.334386\pi$
$823$	3.12031e103	0.994267	0.497134	+	0.867674i	$0.334386\pi$
$824$	3.50361e103	1.06930
$825$	3.91412e103	1.14425
$826$	−4.06366e103	−1.13796
$827$	2.11225e103	0.566629	0.283314	−	0.959027i	$-0.408566\pi$
$827$	2.11225e103	0.566629	0.283314	+	0.959027i	$0.408566\pi$
$828$	−1.83697e104	−4.72091
$829$	−1.96211e103	−0.483100	−0.241550	−	0.970388i	$-0.577656\pi$
$829$	−1.96211e103	−0.483100	−0.241550	+	0.970388i	$0.577656\pi$
$830$	6.59552e103	1.55588
$831$	4.98026e103	1.12568
$832$	−2.12553e103	−0.460351
$833$	−2.06257e103	−0.428067
$834$	2.20573e103	0.438690
$835$	−4.92357e103	−0.938447
$836$	1.48691e104	2.71620
$837$	2.37111e103	0.415143
$838$	9.11146e103	1.52906
$839$	−2.16449e103	−0.348182	−0.174091	−	0.984730i	$-0.555699\pi$
$839$	−2.16449e103	−0.348182	−0.174091	+	0.984730i	$0.555699\pi$
$840$	−1.06859e104	−1.64776
$841$	−4.04243e103	−0.597565
$842$	−1.75744e104	−2.49059
$843$	2.04855e103	0.278334
$844$	2.84023e104	3.69996
$845$	−3.31037e103	−0.413488
$846$	1.99571e104	2.39028
$847$	−1.44216e102	−0.0165635
$848$	−8.20369e103	−0.903559
$849$	9.31690e103	0.984121
$850$	−1.18126e104	−1.19667
$851$	−2.12798e104	−2.06761
$852$	−5.95562e104	−5.55036
$853$	1.07783e104	0.963519	0.481759	−	0.876304i	$-0.339998\pi$
$853$	1.07783e104	0.963519	0.481759	+	0.876304i	$0.339998\pi$
$854$	1.42033e104	1.21797
$855$	−1.15417e104	−0.949450
$856$	1.87422e104	1.47911
$857$	1.55866e104	1.18014	0.590070	−	0.807352i	$-0.299100\pi$
$857$	1.55866e104	1.18014	0.590070	+	0.807352i	$0.299100\pi$
$858$	2.00630e104	1.45746
$859$	−2.36353e104	−1.64742	−0.823709	−	0.567013i	$-0.808099\pi$
$859$	−2.36353e104	−1.64742	−0.823709	+	0.567013i	$0.808099\pi$
$860$	2.49033e104	1.66556
$861$	−2.35282e103	−0.151000
$862$	−2.14361e104	−1.32020
$863$	−6.21883e102	−0.0367557	−0.0183779	−	0.999831i	$-0.505850\pi$
$863$	−6.21883e102	−0.0367557	−0.0183779	+	0.999831i	$0.505850\pi$
$864$	2.89694e104	1.64324
$865$	3.99532e103	0.217510
$866$	3.35247e104	1.75178
$867$	−5.00062e103	−0.250810
$868$	−1.66355e104	−0.800915
$869$	−5.35715e102	−0.0247589
$870$	2.29315e104	1.01742
$871$	−1.57708e104	−0.671751
$872$	−3.51140e104	−1.43597
$873$	1.13052e104	0.443886
$874$	6.83553e104	2.57701
$875$	1.86713e104	0.675909
$876$	−1.51396e105	−5.26283
$877$	−6.60072e103	−0.220346	−0.110173	−	0.993912i	$-0.535141\pi$
$877$	−6.60072e103	−0.220346	−0.110173	+	0.993912i	$0.535141\pi$
$878$	1.26521e104	0.405607
$879$	4.00018e104	1.23161
$880$	−4.41901e104	−1.30674
$881$	5.29232e104	1.50315	0.751574	−	0.659649i	$-0.229295\pi$
$881$	5.29232e104	1.50315	0.751574	+	0.659649i	$0.229295\pi$
$882$	−4.94587e104	−1.34930
$883$	−7.90261e103	−0.207093	−0.103547	−	0.994625i	$-0.533019\pi$
$883$	−7.90261e103	−0.207093	−0.103547	+	0.994625i	$0.533019\pi$
$884$	−4.27724e104	−1.07673
$885$	3.03231e104	0.733309
$886$	−1.37043e105	−3.18391
$887$	1.25748e104	0.280680	0.140340	−	0.990103i	$-0.455180\pi$
$887$	1.25748e104	0.280680	0.140340	+	0.990103i	$0.455180\pi$
$888$	3.20560e105	6.87463
$889$	−3.01066e104	−0.620368
$890$	−6.50797e104	−1.28855
$891$	5.74545e103	0.109312
$892$	1.87961e105	3.43649
$893$	−5.24591e104	−0.921710
$894$	−1.15997e105	−1.95868
$895$	−5.19281e104	−0.842723
$896$	2.78948e103	0.0435100
$897$	6.51537e104	0.976803
$898$	−5.90587e104	−0.851086
$899$	2.08621e104	0.288995
$900$	−2.00094e105	−2.66456
$901$	−2.72009e104	−0.348219
$902$	−1.95533e104	−0.240651
$903$	−1.26350e105	−1.49506
$904$	2.54195e105	2.89193
$905$	9.45494e104	1.03427
$906$	2.97346e105	3.12760
$907$	8.04063e104	0.813264	0.406632	−	0.913592i	$-0.366703\pi$
$907$	8.04063e104	0.813264	0.406632	+	0.913592i	$0.366703\pi$
$908$	1.00673e105	0.979185
$909$	−4.78172e104	−0.447267
$910$	3.96060e104	0.356280
$911$	−1.22988e105	−1.06404	−0.532022	−	0.846730i	$-0.678568\pi$
$911$	−1.22988e105	−1.06404	−0.532022	+	0.846730i	$0.678568\pi$
$912$	−5.12387e105	−4.26364
$913$	−1.96451e105	−1.57232
$914$	−5.33470e104	−0.410695
$915$	−1.05985e105	−0.784869
$916$	3.91401e104	0.278825
$917$	−3.25050e104	−0.222761
$918$	2.34284e105	1.54464
$919$	4.12870e104	0.261886	0.130943	−	0.991390i	$-0.458199\pi$
$919$	4.12870e104	0.261886	0.130943	+	0.991390i	$0.458199\pi$
$920$	−2.88392e105	−1.76001
$921$	4.53617e105	2.66362
$922$	−1.48272e105	−0.837742
$923$	1.28997e105	0.701323
$924$	5.44647e105	2.84944
$925$	−2.31793e105	−1.16699
$926$	−3.92657e105	−1.90249
$927$	1.38614e105	0.646361
$928$	2.54886e105	1.14391
$929$	3.33237e105	1.43945	0.719723	−	0.694261i	$-0.244269\pi$
$929$	3.33237e105	1.43945	0.719723	+	0.694261i	$0.244269\pi$
$930$	1.75726e105	0.730621
$931$	1.30007e105	0.520299
$932$	−3.69716e105	−1.42430
$933$	−4.28132e105	−1.58774
$934$	7.41393e105	2.64688
$935$	−1.46521e105	−0.503601
$936$	−5.99371e105	−1.98337
$937$	2.91093e105	0.927421	0.463710	−	0.885987i	$-0.346518\pi$
$937$	2.91093e105	0.927421	0.463710	+	0.885987i	$0.346518\pi$
$938$	−6.06061e105	−1.85915
$939$	−5.19457e105	−1.53434
$940$	3.78733e105	1.07719
$941$	−3.75336e105	−1.02799	−0.513995	−	0.857793i	$-0.671835\pi$
$941$	−3.75336e105	−1.02799	−0.513995	+	0.857793i	$0.671835\pi$
$942$	1.63185e105	0.430402
$943$	−6.34984e104	−0.161286
$944$	8.22086e105	2.01100
$945$	−1.53248e105	−0.361048
$946$	−1.05004e106	−2.38271
$947$	−2.33130e105	−0.509535	−0.254768	−	0.967002i	$-0.581999\pi$
$947$	−2.33130e105	−0.509535	−0.254768	+	0.967002i	$0.581999\pi$
$948$	4.48454e104	0.0944109
$949$	3.27919e105	0.664991
$950$	7.44567e105	1.45451
$951$	6.42760e105	1.20960
$952$	−9.60566e105	−1.74147
$953$	1.04961e106	1.83328	0.916639	−	0.399717i	$-0.130892\pi$
$953$	1.04961e106	1.83328	0.916639	+	0.399717i	$0.130892\pi$
$954$	−6.52252e105	−1.09761
$955$	1.53456e105	0.248808
$956$	2.03441e106	3.17821
$957$	−6.83026e105	−1.02817
$958$	−4.85693e105	−0.704508
$959$	9.26287e104	0.129475
$960$	6.09518e105	0.821028
$961$	−6.10467e105	−0.792469
$962$	−1.18812e106	−1.48644
$963$	7.41500e105	0.894083
$964$	−3.21091e106	−3.73159
$965$	1.05584e105	0.118271
$966$	2.50382e106	2.70343
$967$	1.77776e106	1.85026	0.925129	−	0.379652i	$-0.123956\pi$
$967$	1.77776e106	1.85026	0.925129	+	0.379652i	$0.123956\pi$
$968$	5.86313e104	0.0588240
$969$	−1.69891e106	−1.64315
$970$	3.03709e105	0.283179
$971$	9.85751e105	0.886103	0.443052	−	0.896496i	$-0.353896\pi$
$971$	9.85751e105	0.886103	0.443052	+	0.896496i	$0.353896\pi$
$972$	−3.01094e106	−2.60946
$973$	−1.29695e105	−0.108372
$974$	2.98489e106	2.40484
$975$	7.09692e105	0.551323
$976$	−2.87336e106	−2.15239
$977$	−2.52963e106	−1.82726	−0.913630	−	0.406548i	$-0.866732\pi$
$977$	−2.52963e106	−1.82726	−0.913630	+	0.406548i	$0.866732\pi$
$978$	1.69610e106	1.18147
$979$	1.93843e106	1.30216
$980$	−9.38595e105	−0.608069
$981$	−1.38922e106	−0.868001
$982$	1.48862e106	0.897068
$983$	−1.38533e106	−0.805197	−0.402599	−	0.915377i	$-0.631893\pi$
$983$	−1.38533e106	−0.805197	−0.402599	+	0.915377i	$0.631893\pi$
$984$	9.56542e105	0.536263
$985$	1.23939e106	0.670229
$986$	2.06134e106	1.07527
$987$	−1.92155e106	−0.966925
$988$	2.69600e106	1.30873
$989$	−3.40996e106	−1.59691
$990$	−3.51343e106	−1.58738
$991$	−3.81072e106	−1.66108	−0.830542	−	0.556955i	$-0.811969\pi$
$991$	−3.81072e106	−1.66108	−0.830542	+	0.556955i	$0.811969\pi$
$992$	1.95322e106	0.821462
$993$	−1.24019e106	−0.503256
$994$	4.95727e106	1.94100
$995$	4.67254e105	0.176536
$996$	1.64452e107	5.99559
$997$	3.61202e106	1.27079	0.635393	−	0.772189i	$-0.280838\pi$
$997$	3.61202e106	1.27079	0.635393	+	0.772189i	$0.280838\pi$
$998$	−3.29970e106	−1.12032
$999$	4.59721e106	1.50633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.72.a.a.1.6	✓	6
3.2	odd	2		9.72.a.b.1.1		6

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

\(f(q)\)	\(=\)	\(q+8.96793e10 q^{2} +1.38884e17 q^{3} +5.68119e21 q^{4} +3.52866e24 q^{5} +1.24550e28 q^{6} -7.32344e29 q^{7} +2.97736e32 q^{8} +1.17794e34 q^{9} +O(q^{10})\)	\(q+8.96793e10 q^{2} +1.38884e17 q^{3} +5.68119e21 q^{4} +3.52866e24 q^{5} +1.24550e28 q^{6} -7.32344e29 q^{7} +2.97736e32 q^{8} +1.17794e34 q^{9} +3.16448e35 q^{10} -9.42557e36 q^{11} +7.89027e38 q^{12} -1.70901e39 q^{13} -6.56761e40 q^{14} +4.90076e41 q^{15} +1.32864e43 q^{16} +4.40535e43 q^{17} +1.05636e45 q^{18} -2.77676e45 q^{19} +2.00470e46 q^{20} -1.01711e47 q^{21} -8.45278e47 q^{22} -2.74500e48 q^{23} +4.13508e49 q^{24} -2.99002e49 q^{25} -1.53262e50 q^{26} +5.93020e50 q^{27} -4.16059e51 q^{28} +5.21767e51 q^{29} +4.39496e52 q^{30} +3.99836e52 q^{31} +4.88506e53 q^{32} -1.30906e54 q^{33} +3.95069e54 q^{34} -2.58420e54 q^{35} +6.69207e55 q^{36} +7.75221e55 q^{37} -2.49017e56 q^{38} -2.37354e56 q^{39} +1.05061e57 q^{40} +2.31324e56 q^{41} -9.12137e57 q^{42} +1.24224e58 q^{43} -5.35485e58 q^{44} +4.15654e58 q^{45} -2.46170e59 q^{46} +1.88922e59 q^{47} +1.84527e60 q^{48} -4.68197e59 q^{49} -2.68143e60 q^{50} +6.11834e60 q^{51} -9.70919e60 q^{52} -6.17450e60 q^{53} +5.31816e61 q^{54} -3.32597e61 q^{55} -2.18045e62 q^{56} -3.85648e62 q^{57} +4.67917e62 q^{58} +6.18742e62 q^{59} +2.78421e63 q^{60} -2.16263e63 q^{61} +3.58570e63 q^{62} -8.62654e63 q^{63} +1.24372e64 q^{64} -6.03051e63 q^{65} -1.17396e65 q^{66} +9.22803e64 q^{67} +2.50277e65 q^{68} -3.81237e65 q^{69} -2.31749e65 q^{70} -7.54805e65 q^{71} +3.50713e66 q^{72} -1.91877e66 q^{73} +6.95213e66 q^{74} -4.15266e66 q^{75} -1.57753e67 q^{76} +6.90276e66 q^{77} -2.12857e67 q^{78} +5.68363e65 q^{79} +4.68832e67 q^{80} -6.09560e66 q^{81} +2.07449e67 q^{82} +2.08423e68 q^{83} -5.77840e68 q^{84} +1.55450e68 q^{85} +1.11403e69 q^{86} +7.24652e68 q^{87} -2.80633e69 q^{88} -2.05657e69 q^{89} +3.72755e69 q^{90} +1.25158e69 q^{91} -1.55949e70 q^{92} +5.55309e69 q^{93} +1.69424e70 q^{94} -9.79824e69 q^{95} +6.78457e70 q^{96} +9.59744e69 q^{97} -4.19876e70 q^{98} -1.11027e71 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 66157336440 q^{2} + 89\!\cdots\!40 q^{3}+ \cdots + 28\!\cdots\!42 q^{9}+O(q^{10}) \) 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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