LMFDB - Embedded newform 1.72.a.a.1.5

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			1.5
Root			$-2.55796e9$ 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)

$f(q)$	$=$	$q+7.24174e10 q^{2} -1.51457e17 q^{3} +2.88309e21 q^{4} -9.47506e24 q^{5} -1.09681e28 q^{6} +1.67109e28 q^{7} +3.77951e31 q^{8} +1.54297e34 q^{9} +O(q^{10})$	\(q+7.24174e10 q^{2} -1.51457e17 q^{3} +2.88309e21 q^{4} -9.47506e24 q^{5} -1.09681e28 q^{6} +1.67109e28 q^{7} +3.77951e31 q^{8} +1.54297e34 q^{9} -6.86158e35 q^{10} -8.90916e36 q^{11} -4.36663e38 q^{12} +2.84313e39 q^{13} +1.21016e39 q^{14} +1.43506e42 q^{15} -4.07048e42 q^{16} +3.55424e43 q^{17} +1.11738e45 q^{18} +2.02500e45 q^{19} -2.73174e46 q^{20} -2.53097e45 q^{21} -6.45178e47 q^{22} +2.53104e48 q^{23} -5.72432e48 q^{24} +4.74250e49 q^{25} +2.05892e50 q^{26} -1.19957e51 q^{27} +4.81789e49 q^{28} -9.84748e51 q^{29} +1.03923e53 q^{30} +2.46058e52 q^{31} -3.84015e53 q^{32} +1.34935e54 q^{33} +2.57389e54 q^{34} -1.58336e53 q^{35} +4.44851e55 q^{36} +2.16700e55 q^{37} +1.46645e56 q^{38} -4.30611e56 q^{39} -3.58111e56 q^{40} +2.82335e56 q^{41} -1.83286e56 q^{42} -6.60728e56 q^{43} -2.56859e58 q^{44} -1.46197e59 q^{45} +1.83292e59 q^{46} +2.68047e59 q^{47} +6.16502e59 q^{48} -1.00425e60 q^{49} +3.43440e60 q^{50} -5.38313e60 q^{51} +8.19701e60 q^{52} +8.64627e60 q^{53} -8.68694e61 q^{54} +8.44148e61 q^{55} +6.31589e59 q^{56} -3.06699e62 q^{57} -7.13129e62 q^{58} +1.09467e63 q^{59} +4.13741e63 q^{60} -2.05081e63 q^{61} +1.78189e63 q^{62} +2.57843e62 q^{63} -1.81982e64 q^{64} -2.69388e64 q^{65} +9.77165e64 q^{66} -1.19221e65 q^{67} +1.02472e65 q^{68} -3.83344e65 q^{69} -1.14663e64 q^{70} +7.43700e65 q^{71} +5.83166e65 q^{72} +1.10274e66 q^{73} +1.56928e66 q^{74} -7.18284e66 q^{75} +5.83824e66 q^{76} -1.48880e65 q^{77} -3.11837e67 q^{78} -2.10485e67 q^{79} +3.85680e67 q^{80} +6.58138e67 q^{81} +2.04459e67 q^{82} +4.06877e67 q^{83} -7.29702e66 q^{84} -3.36766e68 q^{85} -4.78482e67 q^{86} +1.49147e69 q^{87} -3.36723e68 q^{88} +1.73494e69 q^{89} -1.05872e70 q^{90} +4.75112e67 q^{91} +7.29723e69 q^{92} -3.72672e69 q^{93} +1.94113e70 q^{94} -1.91869e70 q^{95} +5.81616e70 q^{96} +1.20371e70 q^{97} -7.27248e70 q^{98} -1.37465e71 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	7.24174e10	1.49031	0.745157	−	0.666889i	$-0.232375\pi$
$2$	7.24174e10	1.49031	0.745157	+	0.666889i	$0.232375\pi$
$3$	−1.51457e17	−1.74777	−0.873884	−	0.486134i	$-0.838407\pi$
$3$	−1.51457e17	−1.74777	−0.873884	+	0.486134i	$0.838407\pi$
$4$	2.88309e21	1.22104
$5$	−9.47506e24	−1.45595	−0.727975	−	0.685603i	$-0.759538\pi$
$5$	−9.47506e24	−1.45595	−0.727975	+	0.685603i	$0.759538\pi$
$6$	−1.09681e28	−2.60472
$7$	1.67109e28	0.0166732	0.00833659	−	0.999965i	$-0.497346\pi$
$7$	1.67109e28	0.0166732	0.00833659	+	0.999965i	$0.497346\pi$
$8$	3.77951e31	0.329413
$9$	1.54297e34	2.05469
$10$	−6.86158e35	−2.16982
$11$	−8.90916e36	−0.955865	−0.477932	−	0.878397i	$-0.658614\pi$
$11$	−8.90916e36	−0.955865	−0.477932	+	0.878397i	$0.658614\pi$
$12$	−4.36663e38	−2.13409
$13$	2.84313e39	0.810603	0.405301	−	0.914183i	$-0.367167\pi$
$13$	2.84313e39	0.810603	0.405301	+	0.914183i	$0.367167\pi$
$14$	1.21016e39	0.0248483
$15$	1.43506e42	2.54466
$16$	−4.07048e42	−0.730107
$17$	3.55424e43	0.740986	0.370493	−	0.928835i	$-0.379189\pi$
$17$	3.55424e43	0.740986	0.370493	+	0.928835i	$0.379189\pi$
$18$	1.11738e45	3.06214
$19$	2.02500e45	0.814088	0.407044	−	0.913409i	$-0.366560\pi$
$19$	2.02500e45	0.814088	0.407044	+	0.913409i	$0.366560\pi$
$20$	−2.73174e46	−1.77777
$21$	−2.53097e45	−0.0291409
$22$	−6.45178e47	−1.42454
$23$	2.53104e48	1.15335	0.576676	−	0.816973i	$-0.304350\pi$
$23$	2.53104e48	1.15335	0.576676	+	0.816973i	$0.304350\pi$
$24$	−5.72432e48	−0.575738
$25$	4.74250e49	1.11979
$26$	2.05892e50	1.20805
$27$	−1.19957e51	−1.84336
$28$	4.81789e49	0.0203586
$29$	−9.84748e51	−1.19728	−0.598641	−	0.801018i	$-0.704292\pi$
$29$	−9.84748e51	−1.19728	−0.598641	+	0.801018i	$0.704292\pi$
$30$	1.03923e53	3.79235
$31$	2.46058e52	0.280348	0.140174	−	0.990127i	$-0.455234\pi$
$31$	2.46058e52	0.280348	0.140174	+	0.990127i	$0.455234\pi$
$32$	−3.84015e53	−1.41750
$33$	1.34935e54	1.67063
$34$	2.57389e54	1.10430
$35$	−1.58336e53	−0.0242753
$36$	4.44851e55	2.50886
$37$	2.16700e55	0.462059	0.231030	−	0.972947i	$-0.425791\pi$
$37$	2.16700e55	0.462059	0.231030	+	0.972947i	$0.425791\pi$
$38$	1.46645e56	1.21325
$39$	−4.30611e56	−1.41675
$40$	−3.58111e56	−0.479609
$41$	2.82335e56	0.157376	0.0786878	−	0.996899i	$-0.474927\pi$
$41$	2.82335e56	0.157376	0.0786878	+	0.996899i	$0.474927\pi$
$42$	−1.83286e56	−0.0434290
$43$	−6.60728e56	−0.0679036	−0.0339518	−	0.999423i	$-0.510809\pi$
$43$	−6.60728e56	−0.0679036	−0.0339518	+	0.999423i	$0.510809\pi$
$44$	−2.56859e58	−1.16715
$45$	−1.46197e59	−2.99153
$46$	1.83292e59	1.71886
$47$	2.68047e59	1.17149	0.585743	−	0.810496i	$-0.300803\pi$
$47$	2.68047e59	1.17149	0.585743	+	0.810496i	$0.300803\pi$
$48$	6.16502e59	1.27606
$49$	−1.00425e60	−0.999722
$50$	3.43440e60	1.66884
$51$	−5.38313e60	−1.29507
$52$	8.19701e60	0.989775
$53$	8.64627e60	0.530927	0.265464	−	0.964121i	$-0.414475\pi$
$53$	8.64627e60	0.530927	0.265464	+	0.964121i	$0.414475\pi$
$54$	−8.68694e61	−2.74719
$55$	8.44148e61	1.39169
$56$	6.31589e59	0.00549237
$57$	−3.06699e62	−1.42284
$58$	−7.13129e62	−1.78433
$59$	1.09467e63	1.49292	0.746460	−	0.665430i	$-0.231752\pi$
$59$	1.09467e63	1.49292	0.746460	+	0.665430i	$0.231752\pi$
$60$	4.13741e63	3.10713
$61$	−2.05081e63	−0.856477	−0.428239	−	0.903666i	$-0.640866\pi$
$61$	−2.05081e63	−0.856477	−0.428239	+	0.903666i	$0.640866\pi$
$62$	1.78189e63	0.417807
$63$	2.57843e62	0.0342583
$64$	−1.81982e64	−1.38242
$65$	−2.69388e64	−1.18020
$66$	9.77165e64	2.48976
$67$	−1.19221e65	−1.78114	−0.890569	−	0.454848i	$-0.849693\pi$
$67$	−1.19221e65	−1.78114	−0.890569	+	0.454848i	$0.849693\pi$
$68$	1.02472e65	0.904771
$69$	−3.83344e65	−2.01579
$70$	−1.14663e64	−0.0361779
$71$	7.43700e65	1.41816	0.709082	−	0.705126i	$-0.249110\pi$
$71$	7.43700e65	1.41816	0.709082	+	0.705126i	$0.249110\pi$
$72$	5.83166e65	0.676844
$73$	1.10274e66	0.784352	0.392176	−	0.919890i	$-0.371722\pi$
$73$	1.10274e66	0.784352	0.392176	+	0.919890i	$0.371722\pi$
$74$	1.56928e66	0.688614
$75$	−7.18284e66	−1.95714
$76$	5.83824e66	0.994031
$77$	−1.48880e65	−0.0159373
$78$	−3.11837e67	−2.11140
$79$	−2.10485e67	−0.906691	−0.453346	−	0.891335i	$-0.649770\pi$
$79$	−2.10485e67	−0.906691	−0.453346	+	0.891335i	$0.649770\pi$
$80$	3.85680e67	1.06300
$81$	6.58138e67	1.16707
$82$	2.04459e67	0.234539
$83$	4.06877e67	0.303522	0.151761	−	0.988417i	$-0.451506\pi$
$83$	4.06877e67	0.303522	0.151761	+	0.988417i	$0.451506\pi$
$84$	−7.29702e66	−0.0355820
$85$	−3.36766e68	−1.07884
$86$	−4.78482e67	−0.101198
$87$	1.49147e69	2.09257
$88$	−3.36723e68	−0.314875
$89$	1.73494e69	1.08627	0.543136	−	0.839645i	$-0.317237\pi$
$89$	1.73494e69	1.08627	0.543136	+	0.839645i	$0.317237\pi$
$90$	−1.05872e70	−4.45832
$91$	4.75112e67	0.0135153
$92$	7.29723e69	1.40828
$93$	−3.72672e69	−0.489984
$94$	1.94113e70	1.74588
$95$	−1.91869e70	−1.18527
$96$	5.81616e70	2.47747
$97$	1.20371e70	0.354917	0.177458	−	0.984128i	$-0.443213\pi$
$97$	1.20371e70	0.354917	0.177458	+	0.984128i	$0.443213\pi$
$98$	−7.27248e70	−1.48990
$99$	−1.37465e71	−1.96401
$100$	1.36731e71	1.36731
$101$	1.36306e71	0.957427	0.478713	−	0.877971i	$-0.341103\pi$
$101$	1.36306e71	0.957427	0.478713	+	0.877971i	$0.341103\pi$
$102$	−3.89832e71	−1.93006
$103$	−3.00530e70	−0.105237	−0.0526183	−	0.998615i	$-0.516757\pi$
$103$	−3.00530e70	−0.105237	−0.0526183	+	0.998615i	$0.516757\pi$
$104$	1.07456e71	0.267023
$105$	2.39811e70	0.0424276
$106$	6.26140e71	0.791249
$107$	1.28426e72	1.16286	0.581431	−	0.813595i	$-0.302493\pi$
$107$	1.28426e72	1.16286	0.581431	+	0.813595i	$0.302493\pi$
$108$	−3.45846e72	−2.25081
$109$	1.08885e72	0.510889	0.255444	−	0.966824i	$-0.417778\pi$
$109$	1.08885e72	0.510889	0.255444	+	0.966824i	$0.417778\pi$
$110$	6.11310e72	2.07406
$111$	−3.28207e72	−0.807573
$112$	−6.80213e70	−0.0121732
$113$	9.44011e72	1.23223	0.616116	−	0.787656i	$-0.288705\pi$
$113$	9.44011e72	1.23223	0.616116	+	0.787656i	$0.288705\pi$
$114$	−2.22103e73	−2.12047
$115$	−2.39818e73	−1.67922
$116$	−2.83912e73	−1.46192
$117$	4.38686e73	1.66554
$118$	7.92731e73	2.22492
$119$	5.93944e71	0.0123546
$120$	5.42383e73	0.838246
$121$	−7.49900e72	−0.0863223
$122$	−1.48514e74	−1.27642
$123$	−4.27615e73	−0.275056
$124$	7.09408e73	0.342315
$125$	−4.80706e73	−0.174411
$126$	1.86723e73	0.0510556
$127$	1.15758e74	0.239067	0.119533	−	0.992830i	$-0.461860\pi$
$127$	1.15758e74	0.239067	0.119533	+	0.992830i	$0.461860\pi$
$128$	−4.11135e74	−0.642732
$129$	1.00072e74	0.118680
$130$	−1.95084e75	−1.75886
$131$	1.25286e75	0.860542	0.430271	−	0.902700i	$-0.358418\pi$
$131$	1.25286e75	0.860542	0.430271	+	0.902700i	$0.358418\pi$
$132$	3.89030e75	2.03990
$133$	3.38394e73	0.0135734
$134$	−8.63367e75	−2.65445
$135$	1.13660e76	2.68384
$136$	1.34333e75	0.244091
$137$	1.18462e76	1.65959	0.829793	−	0.558072i	$-0.188459\pi$
$137$	1.18462e76	1.65959	0.829793	+	0.558072i	$0.188459\pi$
$138$	−2.77607e76	−3.00416
$139$	4.72365e74	0.0395596	0.0197798	−	0.999804i	$-0.493703\pi$
$139$	4.72365e74	0.0395596	0.0197798	+	0.999804i	$0.493703\pi$
$140$	−4.56498e74	−0.0296410
$141$	−4.05976e76	−2.04749
$142$	5.38568e76	2.11351
$143$	−2.53299e76	−0.774827
$144$	−6.28062e76	−1.50015
$145$	9.33055e76	1.74318
$146$	7.98574e76	1.16893
$147$	1.52100e77	1.74728
$148$	6.24766e76	0.564191
$149$	−2.66004e77	−1.89136	−0.945682	−	0.325092i	$-0.894605\pi$
$149$	−2.66004e77	−1.89136	−0.945682	+	0.325092i	$0.894605\pi$
$150$	−5.20162e77	−2.91675
$151$	2.28316e77	1.01124	0.505621	−	0.862756i	$-0.331263\pi$
$151$	2.28316e77	1.01124	0.505621	+	0.862756i	$0.331263\pi$
$152$	7.65349e76	0.268171
$153$	5.48407e77	1.52250
$154$	−1.07815e76	−0.0237516
$155$	−2.33142e77	−0.408173
$156$	−1.24149e78	−1.72990
$157$	1.23189e78	1.36815	0.684075	−	0.729412i	$-0.260206\pi$
$157$	1.23189e78	1.36815	0.684075	+	0.729412i	$0.260206\pi$
$158$	−1.52428e78	−1.35125
$159$	−1.30953e78	−0.927938
$160$	3.63856e78	2.06381
$161$	4.22959e76	0.0192300
$162$	4.76606e78	1.73931
$163$	1.10845e78	0.325128	0.162564	−	0.986698i	$-0.448024\pi$
$163$	1.10845e78	0.325128	0.162564	+	0.986698i	$0.448024\pi$
$164$	8.13996e77	0.192161
$165$	−1.27852e79	−2.43236
$166$	2.94650e78	0.452344
$167$	−3.23560e78	−0.401347	−0.200674	−	0.979658i	$-0.564313\pi$
$167$	−3.23560e78	−0.401347	−0.200674	+	0.979658i	$0.564313\pi$
$168$	−9.56583e76	−0.00959938
$169$	−4.21866e78	−0.342923
$170$	−2.43877e79	−1.60781
$171$	3.12450e79	1.67270
$172$	−1.90494e78	−0.0829127
$173$	−3.53659e79	−1.25299	−0.626495	−	0.779425i	$-0.715511\pi$
$173$	−3.53659e79	−1.25299	−0.626495	+	0.779425i	$0.715511\pi$
$174$	1.08008e80	3.11859
$175$	7.92513e77	0.0186705
$176$	3.62646e79	0.697884
$177$	−1.65795e80	−2.60928
$178$	1.25640e80	1.61889
$179$	1.28237e80	1.35435	0.677173	−	0.735824i	$-0.263205\pi$
$179$	1.28237e80	1.35435	0.677173	+	0.735824i	$0.263205\pi$
$180$	−4.21499e80	−3.65277
$181$	2.08947e79	0.148746	0.0743732	−	0.997230i	$-0.476304\pi$
$181$	2.08947e79	0.148746	0.0743732	+	0.997230i	$0.476304\pi$
$182$	3.44063e78	0.0201421
$183$	3.10609e80	1.49692
$184$	9.56611e79	0.379929
$185$	−2.05325e80	−0.672736
$186$	−2.69879e80	−0.730230
$187$	−3.16653e80	−0.708283
$188$	7.72804e80	1.43043
$189$	−2.00458e79	−0.0307347
$190$	−1.38947e81	−1.76643
$191$	1.30165e81	1.37344	0.686722	−	0.726920i	$-0.259049\pi$
$191$	1.30165e81	1.37344	0.686722	+	0.726920i	$0.259049\pi$
$192$	2.75624e81	2.41614
$193$	−2.08949e81	−1.52320	−0.761599	−	0.648049i	$-0.775585\pi$
$193$	−2.08949e81	−1.52320	−0.761599	+	0.648049i	$0.775585\pi$
$194$	8.71697e80	0.528937
$195$	4.08007e81	2.06271
$196$	−2.89533e81	−1.22070
$197$	−4.76108e81	−1.67554	−0.837770	−	0.546023i	$-0.816141\pi$
$197$	−4.76108e81	−1.67554	−0.837770	+	0.546023i	$0.816141\pi$
$198$	−9.95488e81	−2.92699
$199$	−3.08009e81	−0.757321	−0.378660	−	0.925536i	$-0.623615\pi$
$199$	−3.08009e81	−0.757321	−0.378660	+	0.925536i	$0.623615\pi$
$200$	1.79243e81	0.368874
$201$	1.80568e82	3.11302
$202$	9.87091e81	1.42687
$203$	−1.64560e80	−0.0199625
$204$	−1.55201e82	−1.58133
$205$	−2.67514e81	−0.229131
$206$	−2.17636e81	−0.156836
$207$	3.90532e82	2.36978
$208$	−1.15729e82	−0.591827
$209$	−1.80410e82	−0.778158
$210$	1.73665e81	0.0632305
$211$	−1.91357e82	−0.588595	−0.294298	−	0.955714i	$-0.595086\pi$
$211$	−1.91357e82	−0.588595	−0.294298	+	0.955714i	$0.595086\pi$
$212$	2.49280e82	0.648282
$213$	−1.12638e83	−2.47862
$214$	9.30026e82	1.73303
$215$	6.26044e81	0.0988642
$216$	−4.53377e82	−0.607228
$217$	4.11185e80	0.00467430
$218$	7.88514e82	0.761385
$219$	−1.67017e83	−1.37087
$220$	2.43375e83	1.69931
$221$	1.01052e83	0.600645
$222$	−2.37679e83	−1.20354
$223$	−1.45604e83	−0.628568	−0.314284	−	0.949329i	$-0.601764\pi$
$223$	−1.45604e83	−0.628568	−0.314284	+	0.949329i	$0.601764\pi$
$224$	−6.41722e81	−0.0236343
$225$	7.31752e83	2.30083
$226$	6.83628e83	1.83641
$227$	−7.14905e83	−1.64184	−0.820920	−	0.571044i	$-0.806539\pi$
$227$	−7.14905e83	−1.64184	−0.820920	+	0.571044i	$0.806539\pi$
$228$	−8.84241e83	−1.73734
$229$	5.74972e83	0.967135	0.483568	−	0.875307i	$-0.339341\pi$
$229$	5.74972e83	0.967135	0.483568	+	0.875307i	$0.339341\pi$
$230$	−1.73670e84	−2.50257
$231$	2.25488e82	0.0278547
$232$	−3.72187e83	−0.394400
$233$	−5.12625e83	−0.466299	−0.233150	−	0.972441i	$-0.574903\pi$
$233$	−5.12625e83	−0.466299	−0.233150	+	0.972441i	$0.574903\pi$
$234$	3.17684e84	2.48218
$235$	−2.53976e84	−1.70563
$236$	3.15603e84	1.82291
$237$	3.18794e84	1.58469
$238$	4.30119e82	0.0184122
$239$	2.77202e84	1.02252	0.511259	−	0.859427i	$-0.329179\pi$
$239$	2.77202e84	1.02252	0.511259	+	0.859427i	$0.329179\pi$
$240$	−5.84139e84	−1.85788
$241$	−3.62149e84	−0.993763	−0.496881	−	0.867818i	$-0.665522\pi$
$241$	−3.62149e84	−0.993763	−0.496881	+	0.867818i	$0.665522\pi$
$242$	−5.43058e83	−0.128647
$243$	−9.59835e83	−0.196415
$244$	−5.91266e84	−1.04579
$245$	9.51529e84	1.45555
$246$	−3.09667e84	−0.409920
$247$	5.75733e84	0.659902
$248$	9.29980e83	0.0923504
$249$	−6.16242e84	−0.530487
$250$	−3.48114e84	−0.259927
$251$	−1.83355e84	−0.118816	−0.0594080	−	0.998234i	$-0.518921\pi$
$251$	−1.83355e84	−0.118816	−0.0594080	+	0.998234i	$0.518921\pi$
$252$	7.43384e83	0.0418306
$253$	−2.25495e85	−1.10245
$254$	8.38290e84	0.356285
$255$	5.10055e85	1.88556
$256$	1.31959e85	0.424543
$257$	2.37866e85	0.666356	0.333178	−	0.942864i	$-0.391879\pi$
$257$	2.37866e85	0.666356	0.333178	+	0.942864i	$0.391879\pi$
$258$	7.24693e84	0.176870
$259$	3.62124e83	0.00770400
$260$	−7.76671e85	−1.44106
$261$	−1.51943e86	−2.46005
$262$	9.07289e85	1.28248
$263$	8.47455e85	1.04638	0.523188	−	0.852217i	$-0.324743\pi$
$263$	8.47455e85	1.04638	0.523188	+	0.852217i	$0.324743\pi$
$264$	5.09989e85	0.550328
$265$	−8.19238e85	−0.773004
$266$	2.45056e84	0.0202287
$267$	−2.62768e86	−1.89855
$268$	−3.43725e86	−2.17483
$269$	1.63487e86	0.906313	0.453157	−	0.891431i	$-0.350298\pi$
$269$	1.63487e86	0.906313	0.453157	+	0.891431i	$0.350298\pi$
$270$	8.23092e86	3.99977
$271$	1.41373e86	0.602498	0.301249	−	0.953546i	$-0.402597\pi$
$271$	1.41373e86	0.602498	0.301249	+	0.953546i	$0.402597\pi$
$272$	−1.44675e86	−0.540999
$273$	−7.19589e84	−0.0236217
$274$	8.57872e86	2.47330
$275$	−4.22517e86	−1.07037
$276$	−1.10521e87	−2.46135
$277$	−3.86108e86	−0.756271	−0.378136	−	0.925750i	$-0.623435\pi$
$277$	−3.86108e86	−0.756271	−0.378136	+	0.925750i	$0.623435\pi$
$278$	3.42074e85	0.0589563
$279$	3.79659e86	0.576030
$280$	−5.98434e84	−0.00799661
$281$	−9.63170e85	−0.113404	−0.0567020	−	0.998391i	$-0.518058\pi$
$281$	−9.63170e85	−0.113404	−0.0567020	+	0.998391i	$0.518058\pi$
$282$	−2.93997e87	−3.05140
$283$	1.98988e87	1.82141	0.910705	−	0.413057i	$-0.135539\pi$
$283$	1.98988e87	1.82141	0.910705	+	0.413057i	$0.135539\pi$
$284$	2.14415e87	1.73163
$285$	2.90599e87	2.07158
$286$	−1.83433e87	−1.15474
$287$	4.71806e84	0.00262395
$288$	−5.92522e87	−2.91253
$289$	−1.03751e87	−0.450940
$290$	6.75693e87	2.59789
$291$	−1.82310e87	−0.620312
$292$	3.17930e87	0.957722
$293$	−2.37010e87	−0.632362	−0.316181	−	0.948699i	$-0.602401\pi$
$293$	−2.37010e87	−0.632362	−0.316181	+	0.948699i	$0.602401\pi$
$294$	1.10147e88	2.60400
$295$	−1.03721e88	−2.17362
$296$	8.19020e86	0.152208
$297$	1.06871e88	1.76200
$298$	−1.92633e88	−2.81873
$299$	7.19610e87	0.934910
$300$	−2.07088e88	−2.38973
$301$	−1.10413e85	−0.00113217
$302$	1.65341e88	1.50707
$303$	−2.06444e88	−1.67336
$304$	−8.24271e87	−0.594371
$305$	1.94315e88	1.24699
$306$	3.97142e88	2.26900
$307$	1.16534e88	0.592980	0.296490	−	0.955036i	$-0.404184\pi$
$307$	1.16534e88	0.592980	0.296490	+	0.955036i	$0.404184\pi$
$308$	−4.29234e86	−0.0194600
$309$	4.55173e87	0.183929
$310$	−1.68835e88	−0.608306
$311$	−1.08311e88	−0.348079	−0.174040	−	0.984739i	$-0.555682\pi$
$311$	−1.08311e88	−0.348079	−0.174040	+	0.984739i	$0.555682\pi$
$312$	−1.62750e88	−0.466695
$313$	−2.68969e88	−0.688460	−0.344230	−	0.938885i	$-0.611860\pi$
$313$	−2.68969e88	−0.688460	−0.344230	+	0.938885i	$0.611860\pi$
$314$	8.92101e88	2.03897
$315$	−2.44308e87	−0.0498784
$316$	−6.06847e88	−1.10710
$317$	−1.03867e89	−1.69385	−0.846923	−	0.531716i	$-0.821547\pi$
$317$	−1.03867e89	−1.69385	−0.846923	+	0.531716i	$0.821547\pi$
$318$	−9.48330e88	−1.38292
$319$	8.77328e88	1.14444
$320$	1.72429e89	2.01273
$321$	−1.94510e89	−2.03241
$322$	3.06296e87	0.0286588
$323$	7.19732e88	0.603228
$324$	1.89747e89	1.42504
$325$	1.34836e89	0.907706
$326$	8.02707e88	0.484543
$327$	−1.64913e89	−0.892915
$328$	1.06709e88	0.0518416
$329$	4.47930e87	0.0195324
$330$	−9.25869e89	−3.62497
$331$	4.90097e89	1.72341	0.861704	−	0.507411i	$-0.169397\pi$
$331$	4.90097e89	1.72341	0.861704	+	0.507411i	$0.169397\pi$
$332$	1.17306e89	0.370612
$333$	3.34361e89	0.949391
$334$	−2.34314e89	−0.598133
$335$	1.12963e90	2.59325
$336$	1.03023e88	0.0212759
$337$	−8.91968e89	−1.65763	−0.828815	−	0.559522i	$-0.810985\pi$
$337$	−8.91968e89	−1.65763	−0.828815	+	0.559522i	$0.810985\pi$
$338$	−3.05505e89	−0.511063
$339$	−1.42977e90	−2.15365
$340$	−9.70927e89	−1.31730
$341$	−2.19217e89	−0.267975
$342$	2.26268e90	2.49285
$343$	−3.35683e88	−0.0333417
$344$	−2.49723e88	−0.0223683
$345$	3.63220e90	2.93489
$346$	−2.56110e90	−1.86735
$347$	−5.77290e89	−0.379925	−0.189962	−	0.981791i	$-0.560837\pi$
$347$	−5.77290e89	−0.379925	−0.189962	+	0.981791i	$0.560837\pi$
$348$	4.30003e90	2.55511
$349$	−4.84482e89	−0.260001	−0.130000	−	0.991514i	$-0.541498\pi$
$349$	−4.84482e89	−0.260001	−0.130000	+	0.991514i	$0.541498\pi$
$350$	5.73917e88	0.0278249
$351$	−3.41052e90	−1.49423
$352$	3.42125e90	1.35494
$353$	1.42739e90	0.511141	0.255570	−	0.966790i	$-0.417737\pi$
$353$	1.42739e90	0.511141	0.255570	+	0.966790i	$0.417737\pi$
$354$	−1.20064e91	−3.88864
$355$	−7.04660e90	−2.06478
$356$	5.00198e90	1.32638
$357$	−8.99568e88	−0.0215930
$358$	9.28657e90	2.01840
$359$	5.48300e90	1.07936	0.539679	−	0.841871i	$-0.318546\pi$
$359$	5.48300e90	1.07936	0.539679	+	0.841871i	$0.318546\pi$
$360$	−5.52553e90	−0.985451
$361$	−2.08676e90	−0.337261
$362$	1.51314e90	0.221679
$363$	1.13577e90	0.150871
$364$	1.36979e89	0.0165027
$365$	−1.04485e91	−1.14198
$366$	2.24934e91	2.23089
$367$	7.78300e90	0.700651	0.350325	−	0.936628i	$-0.386071\pi$
$367$	7.78300e90	0.700651	0.350325	+	0.936628i	$0.386071\pi$
$368$	−1.03026e91	−0.842070
$369$	4.35633e90	0.323359
$370$	−1.48691e91	−1.00259
$371$	1.44487e89	0.00885225
$372$	−1.07445e91	−0.598288
$373$	2.21940e91	1.12350	0.561748	−	0.827308i	$-0.310129\pi$
$373$	2.21940e91	1.12350	0.561748	+	0.827308i	$0.310129\pi$
$374$	−2.29312e91	−1.05556
$375$	7.28061e90	0.304830
$376$	1.01309e91	0.385903
$377$	−2.79977e91	−0.970520
$378$	−1.45166e90	−0.0458044
$379$	2.32494e91	0.667912	0.333956	−	0.942589i	$-0.391616\pi$
$379$	2.32494e91	0.667912	0.333956	+	0.942589i	$0.391616\pi$
$380$	−5.53177e91	−1.44726
$381$	−1.75323e91	−0.417834
$382$	9.42623e91	2.04686
$383$	−3.10566e91	−0.614608	−0.307304	−	0.951611i	$-0.599427\pi$
$383$	−3.10566e91	−0.614608	−0.307304	+	0.951611i	$0.599427\pi$
$384$	6.22691e91	1.12335
$385$	1.41064e90	0.0232039
$386$	−1.51316e92	−2.27004
$387$	−1.01948e91	−0.139521
$388$	3.47041e91	0.433366
$389$	1.00254e92	1.14259	0.571293	−	0.820746i	$-0.306442\pi$
$389$	1.00254e92	1.14259	0.571293	+	0.820746i	$0.306442\pi$
$390$	2.95468e92	3.07409
$391$	8.99594e91	0.854617
$392$	−3.79556e91	−0.329322
$393$	−1.89754e92	−1.50403
$394$	−3.44785e92	−2.49708
$395$	1.99436e92	1.32010
$396$	−3.96325e92	−2.39813
$397$	1.85194e91	0.102462	0.0512310	−	0.998687i	$-0.483686\pi$
$397$	1.85194e91	0.102462	0.0512310	+	0.998687i	$0.483686\pi$
$398$	−2.23052e92	−1.12865
$399$	−5.12521e90	−0.0237232
$400$	−1.93043e92	−0.817568
$401$	3.21121e90	0.0124464	0.00622319	−	0.999981i	$-0.498019\pi$
$401$	3.21121e90	0.0124464	0.00622319	+	0.999981i	$0.498019\pi$
$402$	1.30763e93	4.63937
$403$	6.99576e91	0.227251
$404$	3.92982e92	1.16905
$405$	−6.23589e92	−1.69920
$406$	−1.19170e91	−0.0297504
$407$	−1.93062e92	−0.441666
$408$	−2.03456e92	−0.426614
$409$	9.69922e92	1.86449	0.932243	−	0.361832i	$-0.117849\pi$
$409$	9.69922e92	1.86449	0.932243	+	0.361832i	$0.117849\pi$
$410$	−1.93726e92	−0.341477
$411$	−1.79419e93	−2.90057
$412$	−8.66456e91	−0.128498
$413$	1.82929e91	0.0248917
$414$	2.82813e93	3.53172
$415$	−3.85518e92	−0.441914
$416$	−1.09180e93	−1.14903
$417$	−7.15428e91	−0.0691411
$418$	−1.30648e93	−1.15970
$419$	−3.16261e92	−0.257898	−0.128949	−	0.991651i	$-0.541160\pi$
$419$	−3.16261e92	−0.257898	−0.128949	+	0.991651i	$0.541160\pi$
$420$	6.91397e91	0.0518057
$421$	−1.25234e92	−0.0862399	−0.0431199	−	0.999070i	$-0.513730\pi$
$421$	−1.25234e92	−0.0862399	−0.0431199	+	0.999070i	$0.513730\pi$
$422$	−1.38575e93	−0.877192
$423$	4.13588e93	2.40705
$424$	3.26787e92	0.174895
$425$	1.68560e93	0.829750
$426$	−8.15697e93	−3.69393
$427$	−3.42708e91	−0.0142802
$428$	3.70263e93	1.41990
$429$	3.83639e93	1.35422
$430$	4.53364e92	0.147339
$431$	1.34309e93	0.401940	0.200970	−	0.979597i	$-0.435591\pi$
$431$	1.34309e93	0.401940	0.200970	+	0.979597i	$0.435591\pi$
$432$	4.88281e93	1.34585
$433$	−6.54613e92	−0.166213	−0.0831064	−	0.996541i	$-0.526484\pi$
$433$	−6.54613e92	−0.166213	−0.0831064	+	0.996541i	$0.526484\pi$
$434$	2.97769e91	0.00696617
$435$	−1.41317e94	−3.04668
$436$	3.13924e93	0.623814
$437$	5.12535e93	0.938929
$438$	−1.20949e94	−2.04302
$439$	7.68243e93	1.19676	0.598382	−	0.801211i	$-0.295811\pi$
$439$	7.68243e93	1.19676	0.598382	+	0.801211i	$0.295811\pi$
$440$	3.19047e93	0.458442
$441$	−1.54952e94	−2.05412
$442$	7.31790e93	0.895150
$443$	5.19510e93	0.586492	0.293246	−	0.956037i	$-0.405265\pi$
$443$	5.19510e93	0.586492	0.293246	+	0.956037i	$0.405265\pi$
$444$	−9.46250e93	−0.986076
$445$	−1.64386e94	−1.58156
$446$	−1.05443e94	−0.936763
$447$	4.02880e94	3.30567
$448$	−3.04107e92	−0.0230493
$449$	−2.36537e93	−0.165636	−0.0828180	−	0.996565i	$-0.526392\pi$
$449$	−2.36537e93	−0.165636	−0.0828180	+	0.996565i	$0.526392\pi$
$450$	5.29915e94	3.42896
$451$	−2.51537e93	−0.150430
$452$	2.72167e94	1.50460
$453$	−3.45800e94	−1.76742
$454$	−5.17716e94	−2.44686
$455$	−4.50171e92	−0.0196776
$456$	−1.15917e94	−0.468701
$457$	−2.52913e93	−0.0946119	−0.0473060	−	0.998880i	$-0.515064\pi$
$457$	−2.52913e93	−0.0946119	−0.0473060	+	0.998880i	$0.515064\pi$
$458$	4.16380e94	1.44134
$459$	−4.26355e94	−1.36591
$460$	−6.91417e94	−2.05039
$461$	3.36399e94	0.923573	0.461787	−	0.886991i	$-0.347209\pi$
$461$	3.36399e94	0.923573	0.461787	+	0.886991i	$0.347209\pi$
$462$	1.63293e93	0.0415123
$463$	3.22637e94	0.759608	0.379804	−	0.925067i	$-0.375991\pi$
$463$	3.22637e94	0.759608	0.379804	+	0.925067i	$0.375991\pi$
$464$	4.00840e94	0.874144
$465$	3.53108e94	0.713392
$466$	−3.71229e94	−0.694932
$467$	−3.75409e93	−0.0651261	−0.0325630	−	0.999470i	$-0.510367\pi$
$467$	−3.75409e93	−0.0651261	−0.0325630	+	0.999470i	$0.510367\pi$
$468$	1.26477e95	2.03369
$469$	−1.99229e93	−0.0296972
$470$	−1.83923e95	−2.54192
$471$	−1.86578e95	−2.39121
$472$	4.13731e94	0.491788
$473$	5.88653e93	0.0649066
$474$	2.30862e95	2.36168
$475$	9.60355e94	0.911609
$476$	1.71239e93	0.0150854
$477$	1.33409e95	1.09089
$478$	2.00742e95	1.52387
$479$	4.52883e94	0.319209	0.159604	−	0.987181i	$-0.448978\pi$
$479$	4.52883e94	0.319209	0.159604	+	0.987181i	$0.448978\pi$
$480$	−5.51084e95	−3.60707
$481$	6.16107e94	0.374547
$482$	−2.62259e95	−1.48102
$483$	−6.40600e93	−0.0336096
$484$	−2.16203e94	−0.105403
$485$	−1.14052e95	−0.516741
$486$	−6.95087e94	−0.292720
$487$	2.24802e95	0.880078	0.440039	−	0.897979i	$-0.354965\pi$
$487$	2.24802e95	0.880078	0.440039	+	0.897979i	$0.354965\pi$
$488$	−7.75105e94	−0.282135
$489$	−1.67881e95	−0.568248
$490$	6.89072e95	2.16922
$491$	−3.12115e95	−0.913949	−0.456974	−	0.889480i	$-0.651067\pi$
$491$	−3.12115e95	−0.913949	−0.456974	+	0.889480i	$0.651067\pi$
$492$	−1.23285e95	−0.335853
$493$	−3.50003e95	−0.887169
$494$	4.16931e95	0.983461
$495$	1.30249e96	2.85950
$496$	−1.00158e95	−0.204684
$497$	1.24279e94	0.0236453
$498$	−4.46266e95	−0.790592
$499$	−7.56923e94	−0.124877	−0.0624385	−	0.998049i	$-0.519888\pi$
$499$	−7.56923e94	−0.124877	−0.0624385	+	0.998049i	$0.519888\pi$
$500$	−1.38592e95	−0.212962
$501$	4.90053e95	0.701462
$502$	−1.32781e95	−0.177073
$503$	−4.88429e95	−0.606930	−0.303465	−	0.952843i	$-0.598143\pi$
$503$	−4.88429e95	−0.606930	−0.303465	+	0.952843i	$0.598143\pi$
$504$	9.74520e93	0.0112851
$505$	−1.29151e96	−1.39397
$506$	−1.63297e96	−1.64299
$507$	6.38945e95	0.599351
$508$	3.33741e95	0.291909
$509$	−2.25448e96	−1.83893	−0.919465	−	0.393173i	$-0.871377\pi$
$509$	−2.25448e96	−1.83893	−0.919465	+	0.393173i	$0.871377\pi$
$510$	3.69368e96	2.81008
$511$	1.84277e94	0.0130776
$512$	1.92638e96	1.27543
$513$	−2.42912e96	−1.50066
$514$	1.72256e96	0.993080
$515$	2.84754e95	0.153219
$516$	2.88516e95	0.144912
$517$	−2.38808e96	−1.11978
$518$	2.62241e94	0.0114814
$519$	5.35640e96	2.18994
$520$	−1.01816e96	−0.388773
$521$	4.78442e96	1.70643	0.853217	−	0.521555i	$-0.174648\pi$
$521$	4.78442e96	1.70643	0.853217	+	0.521555i	$0.174648\pi$
$522$	−1.10033e97	−3.66624
$523$	−3.42392e96	−1.06589	−0.532947	−	0.846149i	$-0.678915\pi$
$523$	−3.42392e96	−1.06589	−0.532947	+	0.846149i	$0.678915\pi$
$524$	3.61211e96	1.05075
$525$	−1.20031e95	−0.0326317
$526$	6.13705e96	1.55943
$527$	8.74550e95	0.207734
$528$	−5.49251e96	−1.21974
$529$	1.59030e96	0.330220
$530$	−5.93271e96	−1.15202
$531$	1.68904e97	3.06749
$532$	9.75621e94	0.0165737
$533$	8.02715e95	0.127569
$534$	−1.90290e97	−2.82944
$535$	−1.21684e97	−1.69307
$536$	−4.50597e96	−0.586730
$537$	−1.94223e97	−2.36708
$538$	1.18393e97	1.35069
$539$	8.94699e96	0.955599
$540$	3.27691e97	3.27707
$541$	1.73275e97	1.62268	0.811338	−	0.584577i	$-0.198739\pi$
$541$	1.73275e97	1.62268	0.811338	+	0.584577i	$0.198739\pi$
$542$	1.02378e97	0.897911
$543$	−3.16464e96	−0.259974
$544$	−1.36488e97	−1.05035
$545$	−1.03169e97	−0.743829
$546$	−5.21107e95	−0.0352037
$547$	1.22668e97	0.776571	0.388286	−	0.921539i	$-0.373067\pi$
$547$	1.22668e97	0.776571	0.388286	+	0.921539i	$0.373067\pi$
$548$	3.41537e97	2.02641
$549$	−3.16433e97	−1.75980
$550$	−3.05976e97	−1.59519
$551$	−1.99411e97	−0.974693
$552$	−1.44885e97	−0.664028
$553$	−3.51738e95	−0.0151174
$554$	−2.79610e97	−1.12708
$555$	3.10978e97	1.17579
$556$	1.36187e96	0.0483038
$557$	−1.54227e96	−0.0513216	−0.0256608	−	0.999671i	$-0.508169\pi$
$557$	−1.54227e96	−0.0513216	−0.0256608	+	0.999671i	$0.508169\pi$
$558$	2.74939e97	0.858465
$559$	−1.87854e96	−0.0550428
$560$	6.44505e95	0.0177236
$561$	4.79592e97	1.23791
$562$	−6.97502e96	−0.169008
$563$	5.62328e97	1.27921	0.639605	−	0.768704i	$-0.279098\pi$
$563$	5.62328e97	1.27921	0.639605	+	0.768704i	$0.279098\pi$
$564$	−1.17046e98	−2.50006
$565$	−8.94455e97	−1.79407
$566$	1.44102e98	2.71447
$567$	1.09980e96	0.0194588
$568$	2.81082e97	0.467162
$569$	−3.69796e97	−0.577400	−0.288700	−	0.957420i	$-0.593223\pi$
$569$	−3.69796e97	−0.577400	−0.288700	+	0.957420i	$0.593223\pi$
$570$	2.10444e98	3.08731
$571$	−2.02641e97	−0.279348	−0.139674	−	0.990198i	$-0.544605\pi$
$571$	−2.02641e97	−0.279348	−0.139674	+	0.990198i	$0.544605\pi$
$572$	−7.30284e97	−0.946091
$573$	−1.97144e98	−2.40046
$574$	3.41669e95	0.00391051
$575$	1.20035e98	1.29151
$576$	−2.80792e98	−2.84044
$577$	−4.59828e97	−0.437375	−0.218688	−	0.975795i	$-0.570178\pi$
$577$	−4.59828e97	−0.437375	−0.218688	+	0.975795i	$0.570178\pi$
$578$	−7.51336e97	−0.672042
$579$	3.16468e98	2.66220
$580$	2.69008e98	2.12849
$581$	6.79926e95	0.00506068
$582$	−1.32024e98	−0.924460
$583$	−7.70310e97	−0.507495
$584$	4.16781e97	0.258376
$585$	−4.15657e98	−2.42494
$586$	−1.71636e98	−0.942418
$587$	1.85598e98	0.959223	0.479611	−	0.877481i	$-0.340778\pi$
$587$	1.85598e98	0.959223	0.479611	+	0.877481i	$0.340778\pi$
$588$	4.38517e98	2.13350
$589$	4.98267e97	0.228228
$590$	−7.51117e98	−3.23937
$591$	7.21098e98	2.92846
$592$	−8.82074e97	−0.337353
$593$	−4.87530e97	−0.175614	−0.0878071	−	0.996138i	$-0.527986\pi$
$593$	−4.87530e97	−0.175614	−0.0878071	+	0.996138i	$0.527986\pi$
$594$	7.73934e98	2.62594
$595$	−5.62765e96	−0.0179877
$596$	−7.66913e98	−2.30942
$597$	4.66501e98	1.32362
$598$	5.21122e98	1.39331
$599$	−3.09432e98	−0.779673	−0.389837	−	0.920884i	$-0.627469\pi$
$599$	−3.09432e98	−0.779673	−0.389837	+	0.920884i	$0.627469\pi$
$600$	−2.71476e98	−0.644707
$601$	1.44772e98	0.324072	0.162036	−	0.986785i	$-0.448194\pi$
$601$	1.44772e98	0.324072	0.162036	+	0.986785i	$0.448194\pi$
$602$	−7.99584e95	−0.00168729
$603$	−1.83954e99	−3.65969
$604$	6.58256e98	1.23476
$605$	7.10535e97	0.125681
$606$	−1.49501e99	−2.49383
$607$	5.83468e98	0.917949	0.458975	−	0.888449i	$-0.348217\pi$
$607$	5.83468e98	0.917949	0.458975	+	0.888449i	$0.348217\pi$
$608$	−7.77628e98	−1.15397
$609$	2.49237e97	0.0348898
$610$	1.40718e99	1.85840
$611$	7.62094e98	0.949610
$612$	1.58111e99	1.85903
$613$	−1.11545e99	−1.23766	−0.618830	−	0.785525i	$-0.712393\pi$
$613$	−1.11545e99	−1.23766	−0.618830	+	0.785525i	$0.712393\pi$
$614$	8.43908e98	0.883726
$615$	4.05167e98	0.400468
$616$	−5.62693e96	−0.00524996
$617$	1.79065e99	1.57720	0.788600	−	0.614907i	$-0.210806\pi$
$617$	1.79065e99	1.57720	0.788600	+	0.614907i	$0.210806\pi$
$618$	3.29624e98	0.274112
$619$	−1.57443e99	−1.23624	−0.618122	−	0.786082i	$-0.712106\pi$
$619$	−1.57443e99	−1.23624	−0.618122	+	0.786082i	$0.712106\pi$
$620$	−6.72168e98	−0.498394
$621$	−3.03616e99	−2.12604
$622$	−7.84358e98	−0.518747
$623$	2.89923e97	0.0181116
$624$	1.75280e99	1.03438
$625$	−1.55306e99	−0.865858
$626$	−1.94780e99	−1.02602
$627$	2.73243e99	1.36004
$628$	3.55164e99	1.67056
$629$	7.70204e98	0.342380
$630$	−1.76921e98	−0.0743344
$631$	−2.12772e99	−0.845030	−0.422515	−	0.906356i	$-0.638853\pi$
$631$	−2.12772e99	−0.845030	−0.422515	+	0.906356i	$0.638853\pi$
$632$	−7.95530e98	−0.298676
$633$	2.89823e99	1.02873
$634$	−7.52177e99	−2.52436
$635$	−1.09682e99	−0.348070
$636$	−3.77551e99	−1.13305
$637$	−2.85520e99	−0.810377
$638$	6.35338e99	1.70557
$639$	1.14750e100	2.91389
$640$	3.89552e99	0.935786
$641$	2.69308e99	0.612052	0.306026	−	0.952023i	$-0.401001\pi$
$641$	2.69308e99	0.612052	0.306026	+	0.952023i	$0.401001\pi$
$642$	−1.40859e100	−3.02894
$643$	4.39025e99	0.893306	0.446653	−	0.894707i	$-0.352616\pi$
$643$	4.39025e99	0.893306	0.446653	+	0.894707i	$0.352616\pi$
$644$	1.21943e98	0.0234806
$645$	−9.48185e98	−0.172792
$646$	5.21211e99	0.898999
$647$	−2.00625e99	−0.327555	−0.163777	−	0.986497i	$-0.552368\pi$
$647$	−2.00625e99	−0.327555	−0.163777	+	0.986497i	$0.552368\pi$
$648$	2.48744e99	0.384450
$649$	−9.75259e99	−1.42703
$650$	9.76444e99	1.35277
$651$	−6.22766e97	−0.00816959
$652$	3.19575e99	0.396993
$653$	−7.91688e98	−0.0931399	−0.0465700	−	0.998915i	$-0.514829\pi$
$653$	−7.91688e98	−0.0931399	−0.0465700	+	0.998915i	$0.514829\pi$
$654$	−1.19426e100	−1.33072
$655$	−1.18709e100	−1.25291
$656$	−1.14924e99	−0.114901
$657$	1.70149e100	1.61160
$658$	3.24379e98	0.0291094
$659$	−1.03753e100	−0.882204	−0.441102	−	0.897457i	$-0.645412\pi$
$659$	−1.03753e100	−0.882204	−0.441102	+	0.897457i	$0.645412\pi$
$660$	−3.68608e100	−2.96999
$661$	9.15686e99	0.699189	0.349594	−	0.936901i	$-0.386319\pi$
$661$	9.15686e99	0.699189	0.349594	+	0.936901i	$0.386319\pi$
$662$	3.54915e100	2.56842
$663$	−1.53050e100	−1.04979
$664$	1.53780e99	0.0999843
$665$	−3.20630e98	−0.0197622
$666$	2.42135e100	1.41489
$667$	−2.49244e100	−1.38089
$668$	−9.32853e99	−0.490059
$669$	2.20528e100	1.09859
$670$	8.18045e100	3.86475
$671$	1.82710e100	0.818676
$672$	9.71930e98	0.0413072
$673$	2.62528e100	1.05838	0.529188	−	0.848504i	$-0.322496\pi$
$673$	2.62528e100	1.05838	0.529188	+	0.848504i	$0.322496\pi$
$674$	−6.45940e100	−2.47039
$675$	−5.68895e100	−2.06418
$676$	−1.21628e100	−0.418722
$677$	−1.24990e100	−0.408298	−0.204149	−	0.978940i	$-0.565443\pi$
$677$	−1.24990e100	−0.408298	−0.204149	+	0.978940i	$0.565443\pi$
$678$	−1.03540e101	−3.20962
$679$	2.01151e98	0.00591759
$680$	−1.27281e100	−0.355384
$681$	1.08277e101	2.86956
$682$	−1.58751e100	−0.399367
$683$	6.03205e100	1.44055	0.720277	−	0.693686i	$-0.244015\pi$
$683$	6.03205e100	1.44055	0.720277	+	0.693686i	$0.244015\pi$
$684$	9.00821e100	2.04243
$685$	−1.12244e101	−2.41627
$686$	−2.43093e99	−0.0496896
$687$	−8.70834e100	−1.69033
$688$	2.68948e99	0.0495769
$689$	2.45825e100	0.430371
$690$	2.63034e101	4.37391
$691$	−8.14523e100	−1.28657	−0.643284	−	0.765628i	$-0.722429\pi$
$691$	−8.14523e100	−1.28657	−0.643284	+	0.765628i	$0.722429\pi$
$692$	−1.01963e101	−1.52995
$693$	−2.29716e99	−0.0327463
$694$	−4.18058e100	−0.566207
$695$	−4.47569e99	−0.0575969
$696$	5.63702e100	0.689321
$697$	1.00349e100	0.116613
$698$	−3.50849e100	−0.387483
$699$	7.76405e100	0.814983
$700$	2.28489e99	0.0227973
$701$	−8.77633e99	−0.0832383	−0.0416191	−	0.999134i	$-0.513252\pi$
$701$	−8.77633e99	−0.0832383	−0.0416191	+	0.999134i	$0.513252\pi$
$702$	−2.46981e101	−2.22688
$703$	4.38817e100	0.376157
$704$	1.62130e101	1.32140
$705$	3.84664e101	2.98104
$706$	1.03368e101	0.761760
$707$	2.27779e99	0.0159634
$708$	−4.78002e101	−3.18602
$709$	1.33405e101	0.845731	0.422866	−	0.906192i	$-0.361024\pi$
$709$	1.33405e101	0.845731	0.422866	+	0.906192i	$0.361024\pi$
$710$	−5.10296e101	−3.07717
$711$	−3.24771e101	−1.86297
$712$	6.55722e100	0.357832
$713$	6.22784e100	0.323340
$714$	−6.51443e99	−0.0321803
$715$	2.40002e101	1.12811
$716$	3.69718e101	1.65371
$717$	−4.19841e101	−1.78712
$718$	3.97064e101	1.60858
$719$	−3.22131e101	−1.24210	−0.621050	−	0.783771i	$-0.713294\pi$
$719$	−3.22131e101	−1.24210	−0.621050	+	0.783771i	$0.713294\pi$
$720$	5.95092e101	2.18414
$721$	−5.02212e98	−0.00175463
$722$	−1.51117e101	−0.502625
$723$	5.48499e101	1.73687
$724$	6.02413e100	0.181625
$725$	−4.67017e101	−1.34071
$726$	8.22497e100	0.224846
$727$	3.03114e101	0.789105	0.394552	−	0.918873i	$-0.370900\pi$
$727$	3.03114e101	0.789105	0.394552	+	0.918873i	$0.370900\pi$
$728$	1.79569e99	0.00445213
$729$	−3.48853e101	−0.823787
$730$	−7.56654e101	−1.70191
$731$	−2.34839e100	−0.0503156
$732$	8.95512e101	1.82780
$733$	−5.95165e100	−0.115730	−0.0578651	−	0.998324i	$-0.518429\pi$
$733$	−5.95165e100	−0.115730	−0.0578651	+	0.998324i	$0.518429\pi$
$734$	5.63624e101	1.04419
$735$	−1.44115e102	−2.54396
$736$	−9.71959e101	−1.63488
$737$	1.06216e102	1.70253
$738$	3.15474e101	0.481906
$739$	−9.02882e101	−1.31448	−0.657239	−	0.753682i	$-0.728276\pi$
$739$	−9.02882e101	−1.31448	−0.657239	+	0.753682i	$0.728276\pi$
$740$	−5.91969e101	−0.821435
$741$	−8.71986e101	−1.15336
$742$	1.04633e100	0.0131926
$743$	6.42826e101	0.772664	0.386332	−	0.922360i	$-0.373742\pi$
$743$	6.42826e101	0.772664	0.386332	+	0.922360i	$0.373742\pi$
$744$	−1.40852e101	−0.161407
$745$	2.52040e102	2.75373
$746$	1.60723e102	1.67436
$747$	6.27797e101	0.623646
$748$	−9.12939e101	−0.864839
$749$	2.14611e100	0.0193886
$750$	5.27242e101	0.454292
$751$	4.29708e101	0.353147	0.176574	−	0.984287i	$-0.443499\pi$
$751$	4.29708e101	0.353147	0.176574	+	0.984287i	$0.443499\pi$
$752$	−1.09108e102	−0.855311
$753$	2.77703e101	0.207663
$754$	−2.02752e102	−1.44638
$755$	−2.16331e102	−1.47232
$756$	−5.77938e100	−0.0375282
$757$	−1.69155e102	−1.04805	−0.524023	−	0.851704i	$-0.675569\pi$
$757$	−1.69155e102	−1.04805	−0.524023	+	0.851704i	$0.675569\pi$
$758$	1.68366e102	0.995399
$759$	3.41527e102	1.92682
$760$	−7.25173e101	−0.390444
$761$	1.17695e102	0.604785	0.302393	−	0.953183i	$-0.402215\pi$
$761$	1.17695e102	0.604785	0.302393	+	0.953183i	$0.402215\pi$
$762$	−1.26965e102	−0.622703
$763$	1.81956e100	0.00851814
$764$	3.75279e102	1.67702
$765$	−5.19619e102	−2.21668
$766$	−2.24904e102	−0.915958
$767$	3.11229e102	1.21016
$768$	−1.99861e102	−0.742003
$769$	5.14817e102	1.82502	0.912511	−	0.409052i	$-0.134140\pi$
$769$	5.14817e102	1.82502	0.912511	+	0.409052i	$0.134140\pi$
$770$	1.02155e101	0.0345811
$771$	−3.60264e102	−1.16464
$772$	−6.02419e102	−1.85988
$773$	−1.57508e102	−0.464442	−0.232221	−	0.972663i	$-0.574599\pi$
$773$	−1.57508e102	−0.464442	−0.232221	+	0.972663i	$0.574599\pi$
$774$	−7.38281e101	−0.207930
$775$	1.16693e102	0.313932
$776$	4.54945e101	0.116914
$777$	−5.48462e100	−0.0134648
$778$	7.26010e102	1.70281
$779$	5.71727e101	0.128118
$780$	1.17632e103	2.51865
$781$	−6.62574e102	−1.35557
$782$	6.51462e102	1.27365
$783$	1.18127e103	2.20702
$784$	4.08777e102	0.729904
$785$	−1.16722e103	−1.99196
$786$	−1.37415e103	−2.24147
$787$	5.11809e102	0.798003	0.399002	−	0.916950i	$-0.369357\pi$
$787$	5.11809e102	0.798003	0.399002	+	0.916950i	$0.369357\pi$
$788$	−1.37266e103	−2.04590
$789$	−1.28353e103	−1.82882
$790$	1.44426e103	1.96736
$791$	1.57752e101	0.0205452
$792$	−5.19552e102	−0.646971
$793$	−5.83072e102	−0.694263
$794$	1.34112e102	0.152701
$795$	1.24079e103	1.35103
$796$	−8.88019e102	−0.924716
$797$	−1.17523e103	−1.17045	−0.585225	−	0.810871i	$-0.698994\pi$
$797$	−1.17523e103	−1.17045	−0.585225	+	0.810871i	$0.698994\pi$
$798$	−3.71154e101	−0.0353550
$799$	9.52704e102	0.868056
$800$	−1.82119e103	−1.58731
$801$	2.67695e103	2.23196
$802$	2.32547e101	0.0185490
$803$	−9.82448e102	−0.749735
$804$	5.20595e103	3.80111
$805$	−4.00756e101	−0.0279980
$806$	5.06614e102	0.338675
$807$	−2.47613e103	−1.58403
$808$	5.15169e102	0.315389
$809$	1.46599e103	0.858933	0.429466	−	0.903083i	$-0.358702\pi$
$809$	1.46599e103	0.858933	0.429466	+	0.903083i	$0.358702\pi$
$810$	−4.51587e103	−2.53235
$811$	2.18547e103	1.17302	0.586508	−	0.809943i	$-0.300502\pi$
$811$	2.18547e103	1.17302	0.586508	+	0.809943i	$0.300502\pi$
$812$	−4.74441e101	−0.0243749
$813$	−2.14118e103	−1.05303
$814$	−1.39810e103	−0.658222
$815$	−1.05026e103	−0.473370
$816$	2.19120e103	0.945541
$817$	−1.33797e102	−0.0552795
$818$	7.02392e103	2.77867
$819$	7.33081e101	0.0277699
$820$	−7.71266e102	−0.279777
$821$	5.04984e102	0.175426	0.0877132	−	0.996146i	$-0.472044\pi$
$821$	5.04984e102	0.175426	0.0877132	+	0.996146i	$0.472044\pi$
$822$	−1.29930e104	−4.32276
$823$	−5.32035e103	−1.69530	−0.847649	−	0.530557i	$-0.821983\pi$
$823$	−5.32035e103	−1.69530	−0.847649	+	0.530557i	$0.821983\pi$
$824$	−1.13586e102	−0.0346663
$825$	6.39931e103	1.87076
$826$	1.32472e102	0.0370965
$827$	−2.30555e103	−0.618485	−0.309243	−	0.950983i	$-0.600076\pi$
$827$	−2.30555e103	−0.618485	−0.309243	+	0.950983i	$0.600076\pi$
$828$	1.12594e104	2.89359
$829$	3.46617e103	0.853422	0.426711	−	0.904388i	$-0.359672\pi$
$829$	3.46617e103	0.853422	0.426711	+	0.904388i	$0.359672\pi$
$830$	−2.79182e103	−0.658590
$831$	5.84787e103	1.32179
$832$	−5.17398e103	−1.12059
$833$	−3.56933e103	−0.740780
$834$	−5.18094e102	−0.103042
$835$	3.06575e103	0.584342
$836$	−5.20139e103	−0.950159
$837$	−2.95163e103	−0.516783
$838$	−2.29028e103	−0.384348
$839$	7.40220e103	1.19073	0.595363	−	0.803457i	$-0.297008\pi$
$839$	7.40220e103	1.19073	0.595363	+	0.803457i	$0.297008\pi$
$840$	9.06368e101	0.0139762
$841$	2.93245e103	0.433484
$842$	−9.06912e102	−0.128524
$843$	1.45878e103	0.198204
$844$	−5.51699e103	−0.718696
$845$	3.99721e103	0.499279
$846$	2.99509e104	3.58726
$847$	−1.25315e101	−0.00143927
$848$	−3.51945e103	−0.387634
$849$	−3.01380e104	−3.18340
$850$	1.22067e104	1.23659
$851$	5.48478e103	0.532917
$852$	−3.24746e104	−3.02649
$853$	−5.40227e103	−0.482931	−0.241466	−	0.970409i	$-0.577628\pi$
$853$	−5.40227e103	−0.482931	−0.241466	+	0.970409i	$0.577628\pi$
$854$	−2.48180e102	−0.0212820
$855$	−2.96048e104	−2.43537
$856$	4.85387e103	0.383062
$857$	4.93600e103	0.373728	0.186864	−	0.982386i	$-0.440168\pi$
$857$	4.93600e103	0.373728	0.186864	+	0.982386i	$0.440168\pi$
$858$	2.77821e104	2.01821
$859$	−1.69749e104	−1.18318	−0.591588	−	0.806240i	$-0.701499\pi$
$859$	−1.69749e104	−1.18318	−0.591588	+	0.806240i	$0.701499\pi$
$860$	1.80494e103	0.120717
$861$	−7.14581e101	−0.00458606
$862$	9.72630e103	0.599018
$863$	1.04290e104	0.616393	0.308196	−	0.951323i	$-0.400275\pi$
$863$	1.04290e104	0.616393	0.308196	+	0.951323i	$0.400275\pi$
$864$	4.60651e104	2.61297
$865$	3.35094e104	1.82429
$866$	−4.74053e103	−0.247709
$867$	1.57138e104	0.788138
$868$	1.18548e102	0.00570748
$869$	1.87524e104	0.866674
$870$	−1.02338e105	−4.54051
$871$	−3.38961e104	−1.44380
$872$	4.11531e103	0.168293
$873$	1.85729e104	0.729245
$874$	3.71165e104	1.39930
$875$	−8.03301e101	−0.00290799
$876$	−4.81526e104	−1.67388
$877$	−3.66634e104	−1.22390	−0.611951	−	0.790896i	$-0.709615\pi$
$877$	−3.66634e104	−1.22390	−0.611951	+	0.790896i	$0.709615\pi$
$878$	5.56341e104	1.78355
$879$	3.58967e104	1.10522
$880$	−3.43609e104	−1.01608
$881$	−1.72680e104	−0.490452	−0.245226	−	0.969466i	$-0.578862\pi$
$881$	−1.72680e104	−0.490452	−0.245226	+	0.969466i	$0.578862\pi$
$882$	−1.12212e105	−3.06129
$883$	−8.24129e103	−0.215968	−0.107984	−	0.994153i	$-0.534440\pi$
$883$	−8.24129e103	−0.215968	−0.107984	+	0.994153i	$0.534440\pi$
$884$	2.91341e104	0.733410
$885$	1.57092e105	3.79898
$886$	3.76216e104	0.874057
$887$	−6.95317e103	−0.155201	−0.0776004	−	0.996985i	$-0.524726\pi$
$887$	−6.95317e103	−0.155201	−0.0776004	+	0.996985i	$0.524726\pi$
$888$	−1.24046e104	−0.266025
$889$	1.93442e102	0.00398601
$890$	−1.19044e105	−2.35702
$891$	−5.86346e104	−1.11557
$892$	−4.19791e104	−0.767504
$893$	5.42795e104	0.953693
$894$	2.91755e105	4.92648
$895$	−1.21505e105	−1.97186
$896$	−6.87041e102	−0.0107164
$897$	−1.08990e105	−1.63401
$898$	−1.71294e104	−0.246850
$899$	−2.42305e104	−0.335656
$900$	2.10971e105	2.80940
$901$	3.07309e104	0.393410
$902$	−1.82156e104	−0.224188
$903$	1.67228e102	0.00197877
$904$	3.56790e104	0.405913
$905$	−1.97978e104	−0.216567
$906$	−2.50419e105	−2.63401
$907$	7.86629e104	0.795630	0.397815	−	0.917466i	$-0.369769\pi$
$907$	7.86629e104	0.795630	0.397815	+	0.917466i	$0.369769\pi$
$908$	−2.06114e105	−2.00475
$909$	2.10315e105	1.96722
$910$	−3.26002e103	−0.0293259
$911$	6.04363e103	0.0522872	0.0261436	−	0.999658i	$-0.491677\pi$
$911$	6.04363e103	0.0522872	0.0261436	+	0.999658i	$0.491677\pi$
$912$	1.24841e105	1.03882
$913$	−3.62493e104	−0.290126
$914$	−1.83153e104	−0.141001
$915$	−2.94303e105	−2.17945
$916$	1.65770e105	1.18091
$917$	2.09364e103	0.0143480
$918$	−3.08755e105	−2.03563
$919$	1.18475e105	0.751495	0.375748	−	0.926722i	$-0.377386\pi$
$919$	1.18475e105	0.751495	0.375748	+	0.926722i	$0.377386\pi$
$920$	−9.06394e104	−0.553158
$921$	−1.76498e105	−1.03639
$922$	2.43611e105	1.37641
$923$	2.11444e105	1.14957
$924$	6.50103e103	0.0340116
$925$	1.02770e105	0.517410
$926$	2.33645e105	1.13205
$927$	−4.63708e104	−0.216229
$928$	3.78158e105	1.69715
$929$	−4.31929e105	−1.86576	−0.932878	−	0.360193i	$-0.882711\pi$
$929$	−4.31929e105	−1.86576	−0.932878	+	0.360193i	$0.882711\pi$
$930$	2.55712e105	1.06318
$931$	−2.03359e105	−0.813862
$932$	−1.47794e105	−0.569368
$933$	1.64044e105	0.608362
$934$	−2.71861e104	−0.0970583
$935$	3.00030e105	1.03122
$936$	1.65802e105	0.548651
$937$	3.09266e104	0.0985319	0.0492660	−	0.998786i	$-0.484312\pi$
$937$	3.09266e104	0.0985319	0.0492660	+	0.998786i	$0.484312\pi$
$938$	−1.44276e104	−0.0442582
$939$	4.07372e105	1.20327
$940$	−7.32237e105	−2.08263
$941$	−4.01567e105	−1.09983	−0.549915	−	0.835220i	$-0.685340\pi$
$941$	−4.01567e105	−1.09983	−0.549915	+	0.835220i	$0.685340\pi$
$942$	−1.35115e106	−3.56365
$943$	7.14602e104	0.181509
$944$	−4.45583e105	−1.08999
$945$	1.89935e104	0.0447482
$946$	4.26287e104	0.0967313
$947$	−4.43257e105	−0.968794	−0.484397	−	0.874848i	$-0.660961\pi$
$947$	−4.43257e105	−0.968794	−0.484397	+	0.874848i	$0.660961\pi$
$948$	9.19110e105	1.93496
$949$	3.13523e105	0.635798
$950$	6.95464e105	1.35858
$951$	1.57314e106	2.96045
$952$	2.24482e103	0.00406977
$953$	6.60285e104	0.115328	0.0576638	−	0.998336i	$-0.481635\pi$
$953$	6.60285e104	0.115328	0.0576638	+	0.998336i	$0.481635\pi$
$954$	9.66112e105	1.62577
$955$	−1.23332e106	−1.99967
$956$	7.99198e105	1.24853
$957$	−1.32877e106	−2.00022
$958$	3.27966e105	0.475721
$959$	1.97960e104	0.0276706
$960$	−2.61155e106	−3.51778
$961$	−7.09791e105	−0.921405
$962$	4.46168e105	0.558192
$963$	1.98157e106	2.38933
$964$	−1.04411e106	−1.21342
$965$	1.97981e106	2.21770
$966$	−4.63906e104	−0.0500889
$967$	4.78586e105	0.498104	0.249052	−	0.968490i	$-0.419881\pi$
$967$	4.78586e105	0.498104	0.249052	+	0.968490i	$0.419881\pi$
$968$	−2.83426e104	−0.0284357
$969$	−1.09008e106	−1.05430
$970$	−8.25938e105	−0.770106
$971$	1.15958e106	1.04236	0.521179	−	0.853447i	$-0.325492\pi$
$971$	1.15958e106	1.04236	0.521179	+	0.853447i	$0.325492\pi$
$972$	−2.76729e105	−0.239829
$973$	7.89363e102	0.000659585 0
$974$	1.62795e106	1.31159
$975$	−2.04218e106	−1.58646
$976$	8.34778e105	0.625320
$977$	−2.07962e106	−1.50220	−0.751099	−	0.660189i	$-0.770476\pi$
$977$	−2.07962e106	−1.50220	−0.751099	+	0.660189i	$0.770476\pi$
$978$	−1.21575e106	−0.846868
$979$	−1.54568e106	−1.03833
$980$	2.74334e106	1.77727
$981$	1.68005e106	1.04972
$982$	−2.26026e106	−1.36207
$983$	−2.86716e106	−1.66649	−0.833244	−	0.552906i	$-0.813519\pi$
$983$	−2.86716e106	−1.66649	−0.833244	+	0.552906i	$0.813519\pi$
$984$	−1.61617e105	−0.0906071
$985$	4.51115e106	2.43950
$986$	−2.53463e106	−1.32216
$987$	−6.78420e104	−0.0341381
$988$	1.65989e106	0.805764
$989$	−1.67233e105	−0.0783167
$990$	9.43230e106	4.26156
$991$	4.74717e105	0.206928	0.103464	−	0.994633i	$-0.467007\pi$
$991$	4.74717e105	0.206928	0.103464	+	0.994633i	$0.467007\pi$
$992$	−9.44900e105	−0.397394
$993$	−7.42284e106	−3.01212
$994$	8.99993e104	0.0352389
$995$	2.91841e106	1.10262
$996$	−1.77668e106	−0.647744
$997$	3.70822e106	1.30463	0.652314	−	0.757948i	$-0.273798\pi$
$997$	3.70822e106	1.30463	0.652314	+	0.757948i	$0.273798\pi$
$998$	−5.48143e105	−0.186106
$999$	−2.59946e106	−0.851743

Twists

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

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

\(f(q)\)	\(=\)	\(q+7.24174e10 q^{2} -1.51457e17 q^{3} +2.88309e21 q^{4} -9.47506e24 q^{5} -1.09681e28 q^{6} +1.67109e28 q^{7} +3.77951e31 q^{8} +1.54297e34 q^{9} +O(q^{10})\)	\(q+7.24174e10 q^{2} -1.51457e17 q^{3} +2.88309e21 q^{4} -9.47506e24 q^{5} -1.09681e28 q^{6} +1.67109e28 q^{7} +3.77951e31 q^{8} +1.54297e34 q^{9} -6.86158e35 q^{10} -8.90916e36 q^{11} -4.36663e38 q^{12} +2.84313e39 q^{13} +1.21016e39 q^{14} +1.43506e42 q^{15} -4.07048e42 q^{16} +3.55424e43 q^{17} +1.11738e45 q^{18} +2.02500e45 q^{19} -2.73174e46 q^{20} -2.53097e45 q^{21} -6.45178e47 q^{22} +2.53104e48 q^{23} -5.72432e48 q^{24} +4.74250e49 q^{25} +2.05892e50 q^{26} -1.19957e51 q^{27} +4.81789e49 q^{28} -9.84748e51 q^{29} +1.03923e53 q^{30} +2.46058e52 q^{31} -3.84015e53 q^{32} +1.34935e54 q^{33} +2.57389e54 q^{34} -1.58336e53 q^{35} +4.44851e55 q^{36} +2.16700e55 q^{37} +1.46645e56 q^{38} -4.30611e56 q^{39} -3.58111e56 q^{40} +2.82335e56 q^{41} -1.83286e56 q^{42} -6.60728e56 q^{43} -2.56859e58 q^{44} -1.46197e59 q^{45} +1.83292e59 q^{46} +2.68047e59 q^{47} +6.16502e59 q^{48} -1.00425e60 q^{49} +3.43440e60 q^{50} -5.38313e60 q^{51} +8.19701e60 q^{52} +8.64627e60 q^{53} -8.68694e61 q^{54} +8.44148e61 q^{55} +6.31589e59 q^{56} -3.06699e62 q^{57} -7.13129e62 q^{58} +1.09467e63 q^{59} +4.13741e63 q^{60} -2.05081e63 q^{61} +1.78189e63 q^{62} +2.57843e62 q^{63} -1.81982e64 q^{64} -2.69388e64 q^{65} +9.77165e64 q^{66} -1.19221e65 q^{67} +1.02472e65 q^{68} -3.83344e65 q^{69} -1.14663e64 q^{70} +7.43700e65 q^{71} +5.83166e65 q^{72} +1.10274e66 q^{73} +1.56928e66 q^{74} -7.18284e66 q^{75} +5.83824e66 q^{76} -1.48880e65 q^{77} -3.11837e67 q^{78} -2.10485e67 q^{79} +3.85680e67 q^{80} +6.58138e67 q^{81} +2.04459e67 q^{82} +4.06877e67 q^{83} -7.29702e66 q^{84} -3.36766e68 q^{85} -4.78482e67 q^{86} +1.49147e69 q^{87} -3.36723e68 q^{88} +1.73494e69 q^{89} -1.05872e70 q^{90} +4.75112e67 q^{91} +7.29723e69 q^{92} -3.72672e69 q^{93} +1.94113e70 q^{94} -1.91869e70 q^{95} +5.81616e70 q^{96} +1.20371e70 q^{97} -7.27248e70 q^{98} -1.37465e71 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 66157336440 q^{2} + 89\!\cdots\!40 q^{3}+ \cdots + 28\!\cdots\!42 q^{9}+O(q^{10}) \) 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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