LMFDB - Embedded newform 1.72.a.a.1.4

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			1.4
Root			$-6.56883e8$ 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)

$f(q)$	$=$	$q+2.67914e10 q^{2} -1.17507e16 q^{3} -1.64340e21 q^{4} +8.36674e24 q^{5} -3.14817e26 q^{6} +1.48756e30 q^{7} -1.07289e32 q^{8} -7.37139e33 q^{9} +O(q^{10})$	\(q+2.67914e10 q^{2} -1.17507e16 q^{3} -1.64340e21 q^{4} +8.36674e24 q^{5} -3.14817e26 q^{6} +1.48756e30 q^{7} -1.07289e32 q^{8} -7.37139e33 q^{9} +2.24157e35 q^{10} -3.47448e36 q^{11} +1.93111e37 q^{12} -1.64342e39 q^{13} +3.98539e40 q^{14} -9.83148e40 q^{15} +1.00597e42 q^{16} +5.97317e43 q^{17} -1.97490e44 q^{18} +3.55600e45 q^{19} -1.37499e46 q^{20} -1.74798e46 q^{21} -9.30861e46 q^{22} -5.06398e46 q^{23} +1.26071e48 q^{24} +2.76508e49 q^{25} -4.40296e49 q^{26} +1.74860e50 q^{27} -2.44466e51 q^{28} +1.18691e52 q^{29} -2.63399e51 q^{30} +7.49852e52 q^{31} +2.80279e53 q^{32} +4.08274e52 q^{33} +1.60030e54 q^{34} +1.24460e55 q^{35} +1.21142e55 q^{36} +3.49033e55 q^{37} +9.52704e55 q^{38} +1.93113e55 q^{39} -8.97656e56 q^{40} +7.21461e56 q^{41} -4.68309e56 q^{42} -1.81549e58 q^{43} +5.70997e57 q^{44} -6.16745e58 q^{45} -1.35671e57 q^{46} +2.91771e59 q^{47} -1.18208e58 q^{48} +1.20831e60 q^{49} +7.40803e59 q^{50} -7.01887e59 q^{51} +2.70080e60 q^{52} -1.18625e61 q^{53} +4.68474e60 q^{54} -2.90701e61 q^{55} -1.59598e62 q^{56} -4.17854e61 q^{57} +3.17991e62 q^{58} -4.39679e61 q^{59} +1.61571e62 q^{60} +4.52558e63 q^{61} +2.00896e63 q^{62} -1.09654e64 q^{63} +5.13380e63 q^{64} -1.37501e64 q^{65} +1.09382e63 q^{66} -2.83379e64 q^{67} -9.81633e64 q^{68} +5.95051e62 q^{69} +3.33447e65 q^{70} -3.34571e65 q^{71} +7.90865e65 q^{72} +1.11523e66 q^{73} +9.35109e65 q^{74} -3.24915e65 q^{75} -5.84395e66 q^{76} -5.16850e66 q^{77} +5.17377e65 q^{78} -2.62189e67 q^{79} +8.41666e66 q^{80} +5.33005e67 q^{81} +1.93290e67 q^{82} -2.45906e67 q^{83} +2.87264e67 q^{84} +4.99760e68 q^{85} -4.86394e68 q^{86} -1.39470e68 q^{87} +3.72772e68 q^{88} -7.46683e68 q^{89} -1.65235e69 q^{90} -2.44469e69 q^{91} +8.32216e67 q^{92} -8.81126e68 q^{93} +7.81694e69 q^{94} +2.97522e70 q^{95} -3.29347e69 q^{96} -3.60320e70 q^{97} +3.23724e70 q^{98} +2.56117e70 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.67914e10	0.551354	0.275677	−	0.961250i	$-0.411098\pi$
$2$	2.67914e10	0.551354	0.275677	+	0.961250i	$0.411098\pi$
$3$	−1.17507e16	−0.135599	−0.0677997	−	0.997699i	$-0.521598\pi$
$3$	−1.17507e16	−0.135599	−0.0677997	+	0.997699i	$0.521598\pi$
$4$	−1.64340e21	−0.696009
$5$	8.36674e24	1.28565	0.642823	−	0.766015i	$-0.277763\pi$
$5$	8.36674e24	1.28565	0.642823	+	0.766015i	$0.277763\pi$
$6$	−3.14817e26	−0.0747633
$7$	1.48756e30	1.48421	0.742104	−	0.670285i	$-0.233828\pi$
$7$	1.48756e30	1.48421	0.742104	+	0.670285i	$0.233828\pi$
$8$	−1.07289e32	−0.935101
$9$	−7.37139e33	−0.981613
$10$	2.24157e35	0.708846
$11$	−3.47448e36	−0.372777	−0.186389	−	0.982476i	$-0.559678\pi$
$11$	−3.47448e36	−0.372777	−0.186389	+	0.982476i	$0.559678\pi$
$12$	1.93111e37	0.0943784
$13$	−1.64342e39	−0.468554	−0.234277	−	0.972170i	$-0.575272\pi$
$13$	−1.64342e39	−0.468554	−0.234277	+	0.972170i	$0.575272\pi$
$14$	3.98539e40	0.818324
$15$	−9.83148e40	−0.174333
$16$	1.00597e42	0.180436
$17$	5.97317e43	1.24528	0.622642	−	0.782507i	$-0.286059\pi$
$17$	5.97317e43	1.24528	0.622642	+	0.782507i	$0.286059\pi$
$18$	−1.97490e44	−0.541216
$19$	3.55600e45	1.42958	0.714792	−	0.699338i	$-0.246522\pi$
$19$	3.55600e45	1.42958	0.714792	+	0.699338i	$0.246522\pi$
$20$	−1.37499e46	−0.894820
$21$	−1.74798e46	−0.201258
$22$	−9.30861e46	−0.205532
$23$	−5.06398e46	−0.0230756	−0.0115378	−	0.999933i	$-0.503673\pi$
$23$	−5.06398e46	−0.0230756	−0.0115378	+	0.999933i	$0.503673\pi$
$24$	1.26071e48	0.126799
$25$	2.76508e49	0.652885
$26$	−4.40296e49	−0.258339
$27$	1.74860e50	0.268706
$28$	−2.44466e51	−1.03302
$29$	1.18691e52	1.44308	0.721539	−	0.692374i	$-0.243435\pi$
$29$	1.18691e52	1.44308	0.721539	+	0.692374i	$0.243435\pi$
$30$	−2.63399e51	−0.0961191
$31$	7.49852e52	0.854350	0.427175	−	0.904169i	$-0.359509\pi$
$31$	7.49852e52	0.854350	0.427175	+	0.904169i	$0.359509\pi$
$32$	2.80279e53	1.03459
$33$	4.08274e52	0.0505483
$34$	1.60030e54	0.686592
$35$	1.24460e55	1.90816
$36$	1.21142e55	0.683211
$37$	3.49033e55	0.744227	0.372114	−	0.928187i	$-0.378633\pi$
$37$	3.49033e55	0.744227	0.372114	+	0.928187i	$0.378633\pi$
$38$	9.52704e55	0.788207
$39$	1.93113e55	0.0635357
$40$	−8.97656e56	−1.20221
$41$	7.21461e56	0.402148	0.201074	−	0.979576i	$-0.435557\pi$
$41$	7.21461e56	0.402148	0.201074	+	0.979576i	$0.435557\pi$
$42$	−4.68309e56	−0.110964
$43$	−1.81549e58	−1.86579	−0.932895	−	0.360149i	$-0.882726\pi$
$43$	−1.81549e58	−1.86579	−0.932895	+	0.360149i	$0.882726\pi$
$44$	5.70997e57	0.259456
$45$	−6.16745e58	−1.26201
$46$	−1.35671e57	−0.0127228
$47$	2.91771e59	1.27517	0.637584	−	0.770381i	$-0.279934\pi$
$47$	2.91771e59	1.27517	0.637584	+	0.770381i	$0.279934\pi$
$48$	−1.18208e58	−0.0244671
$49$	1.20831e60	1.20287
$50$	7.40803e59	0.359971
$51$	−7.01887e59	−0.168860
$52$	2.70080e60	0.326118
$53$	−1.18625e61	−0.728424	−0.364212	−	0.931316i	$-0.618662\pi$
$53$	−1.18625e61	−0.728424	−0.364212	+	0.931316i	$0.618662\pi$
$54$	4.68474e60	0.148152
$55$	−2.90701e61	−0.479259
$56$	−1.59598e62	−1.38788
$57$	−4.17854e61	−0.193851
$58$	3.17991e62	0.795647
$59$	−4.39679e61	−0.0599639	−0.0299819	−	0.999550i	$-0.509545\pi$
$59$	−4.39679e61	−0.0599639	−0.0299819	+	0.999550i	$0.509545\pi$
$60$	1.61571e62	0.121337
$61$	4.52558e63	1.89001	0.945007	−	0.327051i	$-0.106055\pi$
$61$	4.52558e63	1.89001	0.945007	+	0.327051i	$0.106055\pi$
$62$	2.00896e63	0.471049
$63$	−1.09654e64	−1.45692
$64$	5.13380e63	0.389987
$65$	−1.37501e64	−0.602395
$66$	1.09382e63	0.0278700
$67$	−2.83379e64	−0.423362	−0.211681	−	0.977339i	$-0.567894\pi$
$67$	−2.83379e64	−0.423362	−0.211681	+	0.977339i	$0.567894\pi$
$68$	−9.81633e64	−0.866728
$69$	5.95051e62	0.00312904
$70$	3.33447e65	1.05207
$71$	−3.34571e65	−0.637994	−0.318997	−	0.947756i	$-0.603346\pi$
$71$	−3.34571e65	−0.637994	−0.318997	+	0.947756i	$0.603346\pi$
$72$	7.90865e65	0.917908
$73$	1.11523e66	0.793240	0.396620	−	0.917983i	$-0.370183\pi$
$73$	1.11523e66	0.793240	0.396620	+	0.917983i	$0.370183\pi$
$74$	9.35109e65	0.410333
$75$	−3.24915e65	−0.0885309
$76$	−5.84395e66	−0.995002
$77$	−5.16850e66	−0.553278
$78$	5.17377e65	0.0350307
$79$	−2.62189e67	−1.12941	−0.564707	−	0.825291i	$-0.691011\pi$
$79$	−2.62189e67	−1.12941	−0.564707	+	0.825291i	$0.691011\pi$
$80$	8.41666e66	0.231977
$81$	5.33005e67	0.945176
$82$	1.93290e67	0.221726
$83$	−2.45906e67	−0.183441	−0.0917206	−	0.995785i	$-0.529237\pi$
$83$	−2.45906e67	−0.183441	−0.0917206	+	0.995785i	$0.529237\pi$
$84$	2.87264e67	0.140077
$85$	4.99760e68	1.60099
$86$	−4.86394e68	−1.02871
$87$	−1.39470e68	−0.195680
$88$	3.72772e68	0.348584
$89$	−7.46683e68	−0.467510	−0.233755	−	0.972296i	$-0.575101\pi$
$89$	−7.46683e68	−0.467510	−0.233755	+	0.972296i	$0.575101\pi$
$90$	−1.65235e69	−0.695813
$91$	−2.44469e69	−0.695432
$92$	8.32216e67	0.0160608
$93$	−8.81126e68	−0.115849
$94$	7.81694e69	0.703069
$95$	2.97522e70	1.83794
$96$	−3.29347e69	−0.140289
$97$	−3.60320e70	−1.06241	−0.531205	−	0.847243i	$-0.678261\pi$
$97$	−3.60320e70	−1.06241	−0.531205	+	0.847243i	$0.678261\pi$
$98$	3.23724e70	0.663208
$99$	2.56117e70	0.365923
$100$	−4.54414e70	−0.454414
$101$	−2.29583e71	−1.61262	−0.806310	−	0.591494i	$-0.798538\pi$
$101$	−2.29583e71	−1.61262	−0.806310	+	0.591494i	$0.798538\pi$
$102$	−1.88045e70	−0.0931015
$103$	1.20793e71	0.422981	0.211490	−	0.977380i	$-0.432168\pi$
$103$	1.20793e71	0.422981	0.211490	+	0.977380i	$0.432168\pi$
$104$	1.76320e71	0.438146
$105$	−1.46249e71	−0.258746
$106$	−3.17814e71	−0.401620
$107$	1.09733e72	0.993606	0.496803	−	0.867863i	$-0.334507\pi$
$107$	1.09733e72	0.993606	0.496803	+	0.867863i	$0.334507\pi$
$108$	−2.87365e71	−0.187021
$109$	2.59483e72	1.21750	0.608749	−	0.793363i	$-0.291672\pi$
$109$	2.59483e72	1.21750	0.608749	+	0.793363i	$0.291672\pi$
$110$	−7.78828e71	−0.264242
$111$	−4.10137e71	−0.100917
$112$	1.49644e72	0.267805
$113$	−1.10654e73	−1.44438	−0.722191	−	0.691694i	$-0.756865\pi$
$113$	−1.10654e73	−1.44438	−0.722191	+	0.691694i	$0.756865\pi$
$114$	−1.11949e72	−0.106880
$115$	−4.23690e71	−0.0296671
$116$	−1.95058e73	−1.00439
$117$	1.21143e73	0.459939
$118$	−1.17796e72	−0.0330613
$119$	8.88546e73	1.84826
$120$	1.05480e73	0.163019
$121$	−7.48002e73	−0.861037
$122$	1.21247e74	1.04207
$123$	−8.47764e72	−0.0545310
$124$	−1.23231e74	−0.594635
$125$	−1.22999e74	−0.446267
$126$	−2.93778e74	−0.803277
$127$	4.59115e74	0.948177	0.474089	−	0.880477i	$-0.342778\pi$
$127$	4.59115e74	0.948177	0.474089	+	0.880477i	$0.342778\pi$
$128$	−5.24249e74	−0.819565
$129$	2.13332e74	0.253000
$130$	−3.68384e74	−0.332133
$131$	−4.32910e74	−0.297349	−0.148675	−	0.988886i	$-0.547501\pi$
$131$	−4.32910e74	−0.297349	−0.148675	+	0.988886i	$0.547501\pi$
$132$	−6.70959e73	−0.0351821
$133$	5.28977e75	2.12180
$134$	−7.59213e74	−0.233423
$135$	1.46301e75	0.345460
$136$	−6.40853e75	−1.16447
$137$	6.89360e75	0.965753	0.482877	−	0.875688i	$-0.339592\pi$
$137$	6.89360e75	0.965753	0.482877	+	0.875688i	$0.339592\pi$
$138$	1.59423e73	0.00172521
$139$	−5.17084e75	−0.433047	−0.216524	−	0.976277i	$-0.569472\pi$
$139$	−5.17084e75	−0.433047	−0.216524	+	0.976277i	$0.569472\pi$
$140$	−2.04539e76	−1.32810
$141$	−3.42850e75	−0.172912
$142$	−8.96362e75	−0.351761
$143$	5.71003e75	0.174666
$144$	−7.41537e75	−0.177119
$145$	9.93059e76	1.85529
$146$	2.98787e76	0.437356
$147$	−1.41985e76	−0.163109
$148$	−5.73603e76	−0.517989
$149$	1.51522e76	0.107737	0.0538685	−	0.998548i	$-0.482845\pi$
$149$	1.51522e76	0.107737	0.0538685	+	0.998548i	$0.482845\pi$
$150$	−8.70493e75	−0.0488119
$151$	2.97727e77	1.31867	0.659336	−	0.751849i	$-0.270838\pi$
$151$	2.97727e77	1.31867	0.659336	+	0.751849i	$0.270838\pi$
$152$	−3.81518e77	−1.33681
$153$	−4.40306e77	−1.22239
$154$	−1.38471e77	−0.305052
$155$	6.27382e77	1.09839
$156$	−3.17362e76	−0.0442214
$157$	−3.15755e77	−0.350682	−0.175341	−	0.984508i	$-0.556103\pi$
$157$	−3.15755e77	−0.350682	−0.175341	+	0.984508i	$0.556103\pi$
$158$	−7.02442e77	−0.622707
$159$	1.39393e77	0.0987738
$160$	2.34502e78	1.33011
$161$	−7.53298e76	−0.0342490
$162$	1.42799e78	0.521127
$163$	1.41844e78	0.416056	0.208028	−	0.978123i	$-0.433296\pi$
$163$	1.41844e78	0.416056	0.208028	+	0.978123i	$0.433296\pi$
$164$	−1.18565e78	−0.279898
$165$	3.41593e77	0.0649873
$166$	−6.58817e77	−0.101141
$167$	−1.28690e79	−1.59629	−0.798143	−	0.602468i	$-0.794184\pi$
$167$	−1.28690e79	−1.59629	−0.798143	+	0.602468i	$0.794184\pi$
$168$	1.87539e78	0.188196
$169$	−9.60123e78	−0.780457
$170$	1.33893e79	0.882714
$171$	−2.62127e79	−1.40330
$172$	2.98358e79	1.29861
$173$	1.50433e79	0.532973	0.266487	−	0.963839i	$-0.414137\pi$
$173$	1.50433e79	0.532973	0.266487	+	0.963839i	$0.414137\pi$
$174$	−3.73660e78	−0.107889
$175$	4.11322e79	0.969017
$176$	−3.49521e78	−0.0672625
$177$	5.16652e77	0.00813106
$178$	−2.00047e79	−0.257764
$179$	−1.18460e79	−0.125109	−0.0625546	−	0.998042i	$-0.519925\pi$
$179$	−1.18460e79	−0.125109	−0.0625546	+	0.998042i	$0.519925\pi$
$180$	1.01356e80	0.878367
$181$	−2.24548e80	−1.59853	−0.799264	−	0.600980i	$-0.794777\pi$
$181$	−2.24548e80	−1.59853	−0.799264	+	0.600980i	$0.794777\pi$
$182$	−6.54967e79	−0.383429
$183$	−5.31785e79	−0.256285
$184$	5.43307e78	0.0215781
$185$	2.92027e80	0.956813
$186$	−2.36066e79	−0.0638740
$187$	−2.07536e80	−0.464213
$188$	−4.79497e80	−0.887528
$189$	2.60115e80	0.398815
$190$	7.97103e80	1.01335
$191$	1.22084e81	1.28817	0.644085	−	0.764954i	$-0.277238\pi$
$191$	1.22084e81	1.28817	0.644085	+	0.764954i	$0.277238\pi$
$192$	−6.03256e79	−0.0528820
$193$	3.41838e79	0.0249193	0.0124597	−	0.999922i	$-0.496034\pi$
$193$	3.41838e79	0.0249193	0.0124597	+	0.999922i	$0.496034\pi$
$194$	−9.65349e80	−0.585764
$195$	1.61573e80	0.0816844
$196$	−1.98575e81	−0.837208
$197$	−1.42985e81	−0.503198	−0.251599	−	0.967832i	$-0.580956\pi$
$197$	−1.42985e81	−0.503198	−0.251599	+	0.967832i	$0.580956\pi$
$198$	6.86174e80	0.201753
$199$	−9.11570e80	−0.224133	−0.112067	−	0.993701i	$-0.535747\pi$
$199$	−9.11570e80	−0.224133	−0.112067	+	0.993701i	$0.535747\pi$
$200$	−2.96661e81	−0.610514
$201$	3.32989e80	0.0574077
$202$	−6.15086e81	−0.889124
$203$	1.76561e82	2.14183
$204$	1.15348e81	0.117528
$205$	6.03628e81	0.517020
$206$	3.23622e81	0.233212
$207$	3.73285e80	0.0226513
$208$	−1.65323e81	−0.0845442
$209$	−1.23553e82	−0.532916
$210$	−3.91823e81	−0.142661
$211$	−2.21435e82	−0.681113	−0.340556	−	0.940224i	$-0.610615\pi$
$211$	−2.21435e82	−0.681113	−0.340556	+	0.940224i	$0.610615\pi$
$212$	1.94949e82	0.506989
$213$	3.93143e81	0.0865116
$214$	2.93991e82	0.547829
$215$	−1.51897e83	−2.39875
$216$	−1.87605e82	−0.251267
$217$	1.11545e83	1.26803
$218$	6.95192e82	0.671273
$219$	−1.31047e82	−0.107563
$220$	4.77738e82	0.333568
$221$	−9.81643e82	−0.583483
$222$	−1.09882e82	−0.0556409
$223$	2.01661e83	0.870562	0.435281	−	0.900295i	$-0.356649\pi$
$223$	2.01661e83	0.870562	0.435281	+	0.900295i	$0.356649\pi$
$224$	4.16932e83	1.53554
$225$	−2.03825e83	−0.640881
$226$	−2.96457e83	−0.796366
$227$	−1.46236e83	−0.335843	−0.167921	−	0.985800i	$-0.553705\pi$
$227$	−1.46236e83	−0.335843	−0.167921	+	0.985800i	$0.553705\pi$
$228$	6.86703e82	0.134922
$229$	−4.81835e83	−0.810473	−0.405237	−	0.914212i	$-0.632811\pi$
$229$	−4.81835e83	−0.810473	−0.405237	+	0.914212i	$0.632811\pi$
$230$	−1.13513e82	−0.0163571
$231$	6.07333e82	0.0750242
$232$	−1.27342e84	−1.34942
$233$	−1.88929e81	−0.00171855	−0.000859277	−	1.00000i	$-0.500274\pi$
$233$	−1.88929e81	−0.00171855	−0.000859277		1.00000i	$0.500274\pi$
$234$	3.24559e83	0.253589
$235$	2.44117e84	1.63941
$236$	7.22570e82	0.0417354
$237$	3.08090e83	0.153148
$238$	2.38054e84	1.01904
$239$	−1.27611e84	−0.470721	−0.235360	−	0.971908i	$-0.575627\pi$
$239$	−1.27611e84	−0.470721	−0.235360	+	0.971908i	$0.575627\pi$
$240$	−9.89014e82	−0.0314560
$241$	5.41160e83	0.148498	0.0742491	−	0.997240i	$-0.476344\pi$
$241$	5.41160e83	0.148498	0.0742491	+	0.997240i	$0.476344\pi$
$242$	−2.00400e84	−0.474737
$243$	−1.93942e84	−0.396871
$244$	−7.43735e84	−1.31547
$245$	1.01097e85	1.54647
$246$	−2.27128e83	−0.0300659
$247$	−5.84401e84	−0.669837
$248$	−8.04506e84	−0.798904
$249$	2.88956e83	0.0248745
$250$	−3.29530e84	−0.246051
$251$	8.14610e84	0.527877	0.263938	−	0.964540i	$-0.414978\pi$
$251$	8.14610e84	0.527877	0.263938	+	0.964540i	$0.414978\pi$
$252$	1.80206e85	1.01403
$253$	1.75947e83	0.00860206
$254$	1.23003e85	0.522781
$255$	−5.87251e84	−0.217094
$256$	−2.61672e85	−0.841857
$257$	2.13634e85	0.598472	0.299236	−	0.954179i	$-0.403268\pi$
$257$	2.13634e85	0.598472	0.299236	+	0.954179i	$0.403268\pi$
$258$	5.71546e84	0.139493
$259$	5.19209e85	1.10459
$260$	2.25969e85	0.419272
$261$	−8.74919e85	−1.41654
$262$	−1.15983e85	−0.163945
$263$	−1.10338e86	−1.36237	−0.681186	−	0.732110i	$-0.738536\pi$
$263$	−1.10338e86	−1.36237	−0.681186	+	0.732110i	$0.738536\pi$
$264$	−4.38031e84	−0.0472678
$265$	−9.92508e85	−0.936495
$266$	1.41721e86	1.16986
$267$	8.77402e84	0.0633941
$268$	4.65706e85	0.294664
$269$	−4.36355e85	−0.241899	−0.120949	−	0.992659i	$-0.538594\pi$
$269$	−4.36355e85	−0.241899	−0.120949	+	0.992659i	$0.538594\pi$
$270$	3.91961e85	0.190471
$271$	2.29128e86	0.976490	0.488245	−	0.872706i	$-0.337637\pi$
$271$	2.29128e86	0.976490	0.488245	+	0.872706i	$0.337637\pi$
$272$	6.00881e85	0.224694
$273$	2.87267e85	0.0943001
$274$	1.84689e86	0.532472
$275$	−9.60719e85	−0.243381
$276$	−9.77909e83	−0.00217784
$277$	−1.04127e86	−0.203954	−0.101977	−	0.994787i	$-0.532517\pi$
$277$	−1.04127e86	−0.203954	−0.101977	+	0.994787i	$0.532517\pi$
$278$	−1.38534e86	−0.238763
$279$	−5.52745e86	−0.838641
$280$	−1.33532e87	−1.78433
$281$	1.15640e87	1.36155	0.680774	−	0.732494i	$-0.261644\pi$
$281$	1.15640e87	1.36155	0.680774	+	0.732494i	$0.261644\pi$
$282$	−9.18543e85	−0.0953358
$283$	1.09780e85	0.0100486	0.00502428	−	0.999987i	$-0.498401\pi$
$283$	1.09780e85	0.0100486	0.00502428	+	0.999987i	$0.498401\pi$
$284$	5.49835e86	0.444049
$285$	−3.49608e86	−0.249223
$286$	1.52980e86	0.0963030
$287$	1.07322e87	0.596871
$288$	−2.06605e87	−1.01556
$289$	1.26710e87	0.550730
$290$	2.66055e87	1.02292
$291$	4.23400e86	0.144062
$292$	−1.83278e87	−0.552102
$293$	2.85103e87	0.760680	0.380340	−	0.924847i	$-0.375807\pi$
$293$	2.85103e87	0.760680	0.380340	+	0.924847i	$0.375807\pi$
$294$	−3.80398e86	−0.0899306
$295$	−3.67868e86	−0.0770923
$296$	−3.74473e87	−0.695928
$297$	−6.07547e86	−0.100167
$298$	4.05950e86	0.0594012
$299$	8.32225e85	0.0108122
$300$	5.33966e86	0.0616182
$301$	−2.70065e88	−2.76922
$302$	7.97652e87	0.727055
$303$	2.69776e87	0.218670
$304$	3.57722e87	0.257949
$305$	3.78644e88	2.42989
$306$	−1.17964e88	−0.673968
$307$	−1.36551e88	−0.694838	−0.347419	−	0.937710i	$-0.612942\pi$
$307$	−1.36551e88	−0.694838	−0.347419	+	0.937710i	$0.612942\pi$
$308$	8.49393e87	0.385086
$309$	−1.41940e87	−0.0573559
$310$	1.68085e88	0.605603
$311$	4.31495e88	1.38670	0.693350	−	0.720601i	$-0.256134\pi$
$311$	4.31495e88	1.38670	0.693350	+	0.720601i	$0.256134\pi$
$312$	−2.07188e87	−0.0594123
$313$	−3.92534e88	−1.00474	−0.502369	−	0.864653i	$-0.667538\pi$
$313$	−3.92534e88	−1.00474	−0.502369	+	0.864653i	$0.667538\pi$
$314$	−8.45953e87	−0.193350
$315$	−9.17446e88	−1.87308
$316$	4.30883e88	0.786082
$317$	−3.50094e88	−0.570927	−0.285464	−	0.958390i	$-0.592148\pi$
$317$	−3.50094e88	−0.570927	−0.285464	+	0.958390i	$0.592148\pi$
$318$	3.73453e87	0.0544594
$319$	−4.12390e88	−0.537946
$320$	4.29532e88	0.501385
$321$	−1.28944e88	−0.134732
$322$	−2.01819e87	−0.0188833
$323$	2.12406e89	1.78024
$324$	−8.75942e88	−0.657851
$325$	−4.54419e88	−0.305912
$326$	3.80020e88	0.229394
$327$	−3.04910e88	−0.165092
$328$	−7.74045e88	−0.376049
$329$	4.34027e89	1.89261
$330$	9.15174e87	0.0358310
$331$	−9.05874e88	−0.318547	−0.159274	−	0.987234i	$-0.550915\pi$
$331$	−9.05874e88	−0.318547	−0.159274	+	0.987234i	$0.550915\pi$
$332$	4.04123e88	0.127677
$333$	−2.57286e89	−0.730543
$334$	−3.44779e89	−0.880119
$335$	−2.37096e89	−0.544294
$336$	−1.75841e88	−0.0363142
$337$	7.10802e89	1.32095	0.660476	−	0.750847i	$-0.270354\pi$
$337$	7.10802e89	1.32095	0.660476	+	0.750847i	$0.270354\pi$
$338$	−2.57231e89	−0.430308
$339$	1.30026e89	0.195857
$340$	−8.21307e89	−1.11430
$341$	−2.60535e89	−0.318482
$342$	−7.02275e89	−0.773714
$343$	3.03148e89	0.301102
$344$	1.94781e90	1.74470
$345$	4.97864e87	0.00402284
$346$	4.03030e89	0.293857
$347$	2.40600e90	1.58343	0.791715	−	0.610890i	$-0.209188\pi$
$347$	2.40600e90	1.58343	0.791715	+	0.610890i	$0.209188\pi$
$348$	2.29206e89	0.136195
$349$	−2.47727e90	−1.32945	−0.664723	−	0.747090i	$-0.731450\pi$
$349$	−2.47727e90	−1.32945	−0.664723	+	0.747090i	$0.731450\pi$
$350$	1.10199e90	0.534272
$351$	−2.87369e89	−0.125903
$352$	−9.73823e89	−0.385670
$353$	−2.04104e90	−0.730886	−0.365443	−	0.930834i	$-0.619082\pi$
$353$	−2.04104e90	−0.730886	−0.365443	+	0.930834i	$0.619082\pi$
$354$	1.38418e88	0.00448310
$355$	−2.79927e90	−0.820234
$356$	1.22710e90	0.325391
$357$	−1.04410e90	−0.250623
$358$	−3.17371e89	−0.0689794
$359$	−6.21950e90	−1.22434	−0.612171	−	0.790725i	$-0.709704\pi$
$359$	−6.21950e90	−1.22434	−0.612171	+	0.790725i	$0.709704\pi$
$360$	6.61697e90	1.18010
$361$	6.45780e90	1.04371
$362$	−6.01596e90	−0.881355
$363$	8.78952e89	0.116756
$364$	4.01761e90	0.484026
$365$	9.33088e90	1.01983
$366$	−1.42473e90	−0.141304
$367$	2.10281e90	0.189302	0.0946510	−	0.995511i	$-0.469826\pi$
$367$	2.10281e90	0.189302	0.0946510	+	0.995511i	$0.469826\pi$
$368$	−5.09419e88	−0.00416368
$369$	−5.31817e90	−0.394754
$370$	7.82382e90	0.527543
$371$	−1.76462e91	−1.08113
$372$	1.44805e90	0.0806321
$373$	1.20278e91	0.608867	0.304434	−	0.952534i	$-0.401533\pi$
$373$	1.20278e91	0.608867	0.304434	+	0.952534i	$0.401533\pi$
$374$	−5.56019e90	−0.255946
$375$	1.44531e90	0.0605135
$376$	−3.13036e91	−1.19241
$377$	−1.95060e91	−0.676160
$378$	6.96884e90	0.219888
$379$	4.95585e91	1.42373	0.711863	−	0.702319i	$-0.247852\pi$
$379$	4.95585e91	1.42373	0.711863	+	0.702319i	$0.247852\pi$
$380$	−4.88948e91	−1.27922
$381$	−5.39491e90	−0.128572
$382$	3.27080e91	0.710238
$383$	2.54928e90	0.0504500	0.0252250	−	0.999682i	$-0.491970\pi$
$383$	2.54928e90	0.0504500	0.0252250	+	0.999682i	$0.491970\pi$
$384$	6.16027e90	0.111133
$385$	−4.32435e91	−0.711320
$386$	9.15833e89	0.0137394
$387$	1.33827e92	1.83148
$388$	5.92152e91	0.739447
$389$	8.52718e90	0.0971840	0.0485920	−	0.998819i	$-0.484527\pi$
$389$	8.52718e90	0.0971840	0.0485920	+	0.998819i	$0.484527\pi$
$390$	4.32876e90	0.0450370
$391$	−3.02480e90	−0.0287357
$392$	−1.29638e92	−1.12481
$393$	5.08698e90	0.0403204
$394$	−3.83077e91	−0.277441
$395$	−2.19367e92	−1.45203
$396$	−4.20904e91	−0.254685
$397$	1.80733e92	0.999943	0.499972	−	0.866042i	$-0.333344\pi$
$397$	1.80733e92	0.999943	0.499972	+	0.866042i	$0.333344\pi$
$398$	−2.44222e91	−0.123577
$399$	−6.21584e91	−0.287714
$400$	2.78157e91	0.117804
$401$	−2.07567e92	−0.804513	−0.402256	−	0.915527i	$-0.631774\pi$
$401$	−2.07567e92	−0.804513	−0.402256	+	0.915527i	$0.631774\pi$
$402$	8.92125e90	0.0316520
$403$	−1.23232e92	−0.400309
$404$	3.77298e92	1.12240
$405$	4.45951e92	1.21516
$406$	4.73030e92	1.18090
$407$	−1.21271e92	−0.277431
$408$	7.53044e91	0.157901
$409$	−5.70567e92	−1.09680	−0.548402	−	0.836215i	$-0.684764\pi$
$409$	−5.70567e92	−1.09680	−0.548402	+	0.836215i	$0.684764\pi$
$410$	1.61720e92	0.285061
$411$	−8.10044e91	−0.130956
$412$	−1.98512e92	−0.294398
$413$	−6.54050e91	−0.0889988
$414$	1.00008e91	0.0124889
$415$	−2.05743e92	−0.235840
$416$	−4.60617e92	−0.484760
$417$	6.07608e91	0.0587210
$418$	−3.31015e92	−0.293825
$419$	1.16282e93	0.948232	0.474116	−	0.880462i	$-0.342768\pi$
$419$	1.16282e93	0.948232	0.474116	+	0.880462i	$0.342768\pi$
$420$	2.40347e92	0.180089
$421$	−1.65335e93	−1.13854	−0.569272	−	0.822149i	$-0.692775\pi$
$421$	−1.65335e93	−1.13854	−0.569272	+	0.822149i	$0.692775\pi$
$422$	−5.93256e92	−0.375535
$423$	−2.15075e93	−1.25172
$424$	1.27271e93	0.681150
$425$	1.65163e93	0.813027
$426$	1.05328e92	0.0476985
$427$	6.73208e93	2.80517
$428$	−1.80336e93	−0.691558
$429$	−6.70966e91	−0.0236846
$430$	−4.06954e93	−1.32256
$431$	−4.60718e92	−0.137877	−0.0689385	−	0.997621i	$-0.521961\pi$
$431$	−4.60718e92	−0.137877	−0.0689385	+	0.997621i	$0.521961\pi$
$432$	1.75903e92	0.0484842
$433$	4.52525e93	1.14901	0.574504	−	0.818502i	$-0.305195\pi$
$433$	4.52525e93	1.14901	0.574504	+	0.818502i	$0.305195\pi$
$434$	2.98845e93	0.699135
$435$	−1.16691e93	−0.251576
$436$	−4.26435e93	−0.847389
$437$	−1.80075e92	−0.0329885
$438$	−3.51094e92	−0.0593052
$439$	−1.10687e94	−1.72427	−0.862137	−	0.506675i	$-0.830875\pi$
$439$	−1.10687e94	−1.72427	−0.862137	+	0.506675i	$0.830875\pi$
$440$	3.11888e93	0.448156
$441$	−8.90695e93	−1.18075
$442$	−2.62996e93	−0.321706
$443$	1.36463e94	1.54058	0.770288	−	0.637696i	$-0.220112\pi$
$443$	1.36463e94	1.54058	0.770288	+	0.637696i	$0.220112\pi$
$444$	6.74021e92	0.0702390
$445$	−6.24730e93	−0.601052
$446$	5.40279e93	0.479988
$447$	−1.78049e92	−0.0146091
$448$	7.63685e93	0.578821
$449$	1.96709e94	1.37746	0.688732	−	0.725016i	$-0.258168\pi$
$449$	1.96709e94	1.37746	0.688732	+	0.725016i	$0.258168\pi$
$450$	−5.46075e93	−0.353352
$451$	−2.50670e93	−0.149911
$452$	1.81849e94	1.00530
$453$	−3.49849e93	−0.178811
$454$	−3.91786e93	−0.185168
$455$	−2.04541e94	−0.894079
$456$	4.48309e93	0.181270
$457$	−1.48423e94	−0.555233	−0.277617	−	0.960692i	$-0.589544\pi$
$457$	−1.48423e94	−0.555233	−0.277617	+	0.960692i	$0.589544\pi$
$458$	−1.29090e94	−0.446858
$459$	1.04447e94	0.334615
$460$	6.96294e92	0.0206485
$461$	−3.51720e94	−0.965638	−0.482819	−	0.875720i	$-0.660387\pi$
$461$	−3.51720e94	−0.965638	−0.482819	+	0.875720i	$0.660387\pi$
$462$	1.62713e93	0.0413649
$463$	2.60052e93	0.0612259	0.0306129	−	0.999531i	$-0.490254\pi$
$463$	2.60052e93	0.0612259	0.0306129	+	0.999531i	$0.490254\pi$
$464$	1.19399e94	0.260384
$465$	−7.37216e93	−0.148941
$466$	−5.06167e91	−0.000947533 0
$467$	3.99075e94	0.692317	0.346159	−	0.938176i	$-0.387486\pi$
$467$	3.99075e94	0.692317	0.346159	+	0.938176i	$0.387486\pi$
$468$	−1.99087e94	−0.320121
$469$	−4.21544e94	−0.628358
$470$	6.54024e94	0.903898
$471$	3.71034e93	0.0475522
$472$	4.71725e93	0.0560723
$473$	6.30786e94	0.695524
$474$	8.25416e93	0.0844387
$475$	9.83262e94	0.933354
$476$	−1.46024e95	−1.28640
$477$	8.74434e94	0.715030
$478$	−3.41888e94	−0.259534
$479$	−4.08012e94	−0.287582	−0.143791	−	0.989608i	$-0.545929\pi$
$479$	−4.08012e94	−0.287582	−0.143791	+	0.989608i	$0.545929\pi$
$480$	−2.75556e94	−0.180362
$481$	−5.73609e94	−0.348711
$482$	1.44984e94	0.0818751
$483$	8.85175e92	0.00464415
$484$	1.22927e95	0.599289
$485$	−3.01471e95	−1.36588
$486$	−5.19598e94	−0.218816
$487$	3.27689e93	0.0128287	0.00641436	−	0.999979i	$-0.497958\pi$
$487$	3.27689e93	0.0128287	0.00641436	+	0.999979i	$0.497958\pi$
$488$	−4.85543e95	−1.76735
$489$	−1.66676e94	−0.0564169
$490$	2.70852e95	0.852650
$491$	4.34752e95	1.27306	0.636530	−	0.771252i	$-0.280369\pi$
$491$	4.34752e95	1.27306	0.636530	+	0.771252i	$0.280369\pi$
$492$	1.39322e94	0.0379541
$493$	7.08963e95	1.79704
$494$	−1.56569e95	−0.369318
$495$	2.14287e95	0.470447
$496$	7.54326e94	0.154156
$497$	−4.97694e95	−0.946915
$498$	7.74153e93	0.0137147
$499$	−1.09615e95	−0.180843	−0.0904214	−	0.995904i	$-0.528821\pi$
$499$	−1.09615e95	−0.180843	−0.0904214	+	0.995904i	$0.528821\pi$
$500$	2.02136e95	0.310605
$501$	1.51220e95	0.216455
$502$	2.18245e95	0.291047
$503$	−9.58026e95	−1.19046	−0.595229	−	0.803556i	$-0.702938\pi$
$503$	−9.58026e95	−1.19046	−0.595229	+	0.803556i	$0.702938\pi$
$504$	1.17646e96	1.36236
$505$	−1.92087e96	−2.07326
$506$	4.71386e93	0.00474278
$507$	1.12821e95	0.105829
$508$	−7.54511e95	−0.659939
$509$	−1.05726e96	−0.862381	−0.431190	−	0.902261i	$-0.641906\pi$
$509$	−1.05726e96	−0.862381	−0.431190	+	0.902261i	$0.641906\pi$
$510$	−1.57333e95	−0.119696
$511$	1.65898e96	1.17733
$512$	5.36791e95	0.355403
$513$	6.21803e95	0.384137
$514$	5.72355e95	0.329970
$515$	1.01064e96	0.543803
$516$	−3.50590e95	−0.176090
$517$	−1.01375e96	−0.475353
$518$	1.39103e96	0.609019
$519$	−1.76768e95	−0.0722709
$520$	1.47523e96	0.563300
$521$	−1.96717e96	−0.701621	−0.350811	−	0.936446i	$-0.614094\pi$
$521$	−1.96717e96	−0.701621	−0.350811	+	0.936446i	$0.614094\pi$
$522$	−2.34403e96	−0.781017
$523$	3.87755e96	1.20711	0.603556	−	0.797320i	$-0.293750\pi$
$523$	3.87755e96	1.20711	0.603556	+	0.797320i	$0.293750\pi$
$524$	7.11446e95	0.206958
$525$	−4.83331e95	−0.131398
$526$	−2.95611e96	−0.751150
$527$	4.47900e96	1.06391
$528$	4.10710e94	0.00912076
$529$	−4.81332e96	−0.999468
$530$	−2.65907e96	−0.516340
$531$	3.24105e95	0.0588613
$532$	−8.69323e96	−1.47679
$533$	−1.18566e96	−0.188428
$534$	2.35068e95	0.0349526
$535$	9.18111e96	1.27743
$536$	3.04033e96	0.395887
$537$	1.39198e95	0.0169647
$538$	−1.16906e96	−0.133372
$539$	−4.19826e96	−0.448403
$540$	−2.40431e96	−0.240443
$541$	4.26840e96	0.399726	0.199863	−	0.979824i	$-0.435950\pi$
$541$	4.26840e96	0.399726	0.199863	+	0.979824i	$0.435950\pi$
$542$	6.13866e96	0.538392
$543$	2.63859e96	0.216759
$544$	1.67415e97	1.28835
$545$	2.17103e97	1.56527
$546$	7.69630e95	0.0519928
$547$	−2.17204e97	−1.37505	−0.687524	−	0.726162i	$-0.741302\pi$
$547$	−2.17204e97	−1.37505	−0.687524	+	0.726162i	$0.741302\pi$
$548$	−1.13290e97	−0.672172
$549$	−3.33598e97	−1.85526
$550$	−2.57390e96	−0.134189
$551$	4.22066e97	2.06300
$552$	−6.38421e94	−0.00292597
$553$	−3.90023e97	−1.67628
$554$	−2.78972e96	−0.112451
$555$	−3.43151e96	−0.129743
$556$	8.49777e96	0.301405
$557$	−3.72064e97	−1.23811	−0.619054	−	0.785348i	$-0.712484\pi$
$557$	−3.72064e97	−1.23811	−0.619054	+	0.785348i	$0.712484\pi$
$558$	−1.48088e97	−0.462388
$559$	2.98361e97	0.874224
$560$	1.25203e97	0.344302
$561$	2.43869e96	0.0629470
$562$	3.09815e97	0.750695
$563$	6.76595e97	1.53915	0.769575	−	0.638557i	$-0.220468\pi$
$563$	6.76595e97	1.53915	0.769575	+	0.638557i	$0.220468\pi$
$564$	5.63440e96	0.120348
$565$	−9.25813e97	−1.85696
$566$	2.94116e95	0.00554032
$567$	7.92877e97	1.40284
$568$	3.58956e97	0.596589
$569$	−3.33386e97	−0.520550	−0.260275	−	0.965535i	$-0.583813\pi$
$569$	−3.33386e97	−0.520550	−0.260275	+	0.965535i	$0.583813\pi$
$570$	−9.36649e96	−0.137410
$571$	−3.04740e97	−0.420095	−0.210047	−	0.977691i	$-0.567362\pi$
$571$	−3.04740e97	−0.420095	−0.210047	+	0.977691i	$0.567362\pi$
$572$	−9.38388e96	−0.121569
$573$	−1.43456e97	−0.174675
$574$	2.87530e97	0.329087
$575$	−1.40023e96	−0.0150657
$576$	−3.78432e97	−0.382816
$577$	−1.43220e97	−0.136226	−0.0681131	−	0.997678i	$-0.521698\pi$
$577$	−1.43220e97	−0.136226	−0.0681131	+	0.997678i	$0.521698\pi$
$578$	3.39475e97	0.303647
$579$	−4.01683e95	−0.00337905
$580$	−1.63200e98	−1.29130
$581$	−3.65800e97	−0.272265
$582$	1.13435e97	0.0794293
$583$	4.12161e97	0.271540
$584$	−1.19652e98	−0.741760
$585$	1.01357e98	0.591319
$586$	7.63832e97	0.419404
$587$	1.13425e97	0.0586215	0.0293108	−	0.999570i	$-0.490669\pi$
$587$	1.13425e97	0.0586215	0.0293108	+	0.999570i	$0.490669\pi$
$588$	2.33339e97	0.113525
$589$	2.66648e98	1.22136
$590$	−9.85571e96	−0.0425052
$591$	1.68017e97	0.0682334
$592$	3.51116e97	0.134286
$593$	−4.87454e98	−1.75587	−0.877933	−	0.478783i	$-0.841078\pi$
$593$	−4.87454e98	−1.75587	−0.877933	+	0.478783i	$0.841078\pi$
$594$	−1.62770e97	−0.0552276
$595$	7.43423e98	2.37621
$596$	−2.49013e97	−0.0749858
$597$	1.07116e97	0.0303923
$598$	2.22965e96	0.00596134
$599$	2.87843e98	0.725277	0.362638	−	0.931930i	$-0.381876\pi$
$599$	2.87843e98	0.725277	0.362638	+	0.931930i	$0.381876\pi$
$600$	3.48596e97	0.0827853
$601$	−6.71527e98	−1.50321	−0.751605	−	0.659613i	$-0.770720\pi$
$601$	−6.71527e98	−1.50321	−0.751605	+	0.659613i	$0.770720\pi$
$602$	−7.23541e98	−1.52682
$603$	2.08890e98	0.415578
$604$	−4.89286e98	−0.917806
$605$	−6.25834e98	−1.10699
$606$	7.22767e97	0.120565
$607$	−8.73461e97	−0.137418	−0.0687092	−	0.997637i	$-0.521888\pi$
$607$	−8.73461e97	−0.137418	−0.0687092	+	0.997637i	$0.521888\pi$
$608$	9.96674e98	1.47903
$609$	−2.07470e98	−0.290430
$610$	1.01444e99	1.33973
$611$	−4.79502e98	−0.597486
$612$	7.23600e98	0.850791
$613$	−1.31148e98	−0.145518	−0.0727589	−	0.997350i	$-0.523180\pi$
$613$	−1.31148e98	−0.145518	−0.0727589	+	0.997350i	$0.523180\pi$
$614$	−3.65840e98	−0.383102
$615$	−7.09303e97	−0.0701076
$616$	5.54521e98	0.517371
$617$	7.66289e98	0.674947	0.337473	−	0.941335i	$-0.390428\pi$
$617$	7.66289e98	0.674947	0.337473	+	0.941335i	$0.390428\pi$
$618$	−3.80277e97	−0.0316234
$619$	9.61404e98	0.754897	0.377448	−	0.926031i	$-0.376802\pi$
$619$	9.61404e98	0.754897	0.377448	+	0.926031i	$0.376802\pi$
$620$	−1.03104e99	−0.764490
$621$	−8.85487e96	−0.00620055
$622$	1.15604e99	0.764563
$623$	−1.11074e99	−0.693882
$624$	1.94265e97	0.0114641
$625$	−2.20015e99	−1.22663
$626$	−1.05165e99	−0.553967
$627$	1.45182e98	0.0722631
$628$	5.18914e98	0.244077
$629$	2.08484e99	0.926774
$630$	−2.45797e99	−1.03273
$631$	−3.45492e99	−1.37213	−0.686066	−	0.727539i	$-0.740664\pi$
$631$	−3.45492e99	−1.37213	−0.686066	+	0.727539i	$0.740664\pi$
$632$	2.81299e99	1.05612
$633$	2.60201e98	0.0923585
$634$	−9.37951e98	−0.314783
$635$	3.84130e99	1.21902
$636$	−2.29078e98	−0.0687474
$637$	−1.98577e99	−0.563610
$638$	−1.10485e99	−0.296599
$639$	2.46625e99	0.626263
$640$	−4.38625e99	−1.05367
$641$	6.76561e99	1.53761	0.768807	−	0.639481i	$-0.220851\pi$
$641$	6.76561e99	1.53761	0.768807	+	0.639481i	$0.220851\pi$
$642$	−3.45459e98	−0.0742853
$643$	8.73473e98	0.177730	0.0888649	−	0.996044i	$-0.471676\pi$
$643$	8.73473e98	0.177730	0.0888649	+	0.996044i	$0.471676\pi$
$644$	1.23797e98	0.0238376
$645$	1.78489e99	0.325268
$646$	5.69066e99	0.981540
$647$	9.77030e98	0.159517	0.0797583	−	0.996814i	$-0.474585\pi$
$647$	9.77030e98	0.159517	0.0797583	+	0.996814i	$0.474585\pi$
$648$	−5.71853e99	−0.883836
$649$	1.52766e98	0.0223531
$650$	−1.21745e99	−0.168666
$651$	−1.31073e99	−0.171944
$652$	−2.33107e99	−0.289578
$653$	−3.54694e99	−0.417288	−0.208644	−	0.977992i	$-0.566905\pi$
$653$	−3.54694e99	−0.417288	−0.208644	+	0.977992i	$0.566905\pi$
$654$	−8.16896e98	−0.0910242
$655$	−3.62205e99	−0.382286
$656$	7.25765e98	0.0725621
$657$	−8.22082e99	−0.778654
$658$	1.16282e100	1.04350
$659$	−1.47560e100	−1.25469	−0.627347	−	0.778740i	$-0.715859\pi$
$659$	−1.47560e100	−1.25469	−0.627347	+	0.778740i	$0.715859\pi$
$660$	−5.61374e98	−0.0452317
$661$	−4.37153e99	−0.333796	−0.166898	−	0.985974i	$-0.553375\pi$
$661$	−4.37153e99	−0.333796	−0.166898	+	0.985974i	$0.553375\pi$
$662$	−2.42697e99	−0.175633
$663$	1.15350e99	0.0791199
$664$	2.63829e99	0.171536
$665$	4.42582e100	2.72788
$666$	−6.89305e99	−0.402788
$667$	−6.01050e98	−0.0332999
$668$	2.11490e100	1.11103
$669$	−2.36965e99	−0.118048
$670$	−6.35214e99	−0.300099
$671$	−1.57240e100	−0.704554
$672$	−4.89923e99	−0.208218
$673$	−5.37613e98	−0.0216738	−0.0108369	−	0.999941i	$-0.503450\pi$
$673$	−5.37613e98	−0.0216738	−0.0108369	+	0.999941i	$0.503450\pi$
$674$	1.90434e100	0.728313
$675$	4.83501e99	0.175434
$676$	1.57787e100	0.543205
$677$	−9.63742e99	−0.314820	−0.157410	−	0.987533i	$-0.550314\pi$
$677$	−9.63742e99	−0.314820	−0.157410	+	0.987533i	$0.550314\pi$
$678$	3.48357e99	0.107987
$679$	−5.35999e100	−1.57684
$680$	−5.36185e100	−1.49709
$681$	1.71837e99	0.0455401
$682$	−6.98009e99	−0.175596
$683$	−4.22963e100	−1.01011	−0.505053	−	0.863088i	$-0.668527\pi$
$683$	−4.22963e100	−1.01011	−0.505053	+	0.863088i	$0.668527\pi$
$684$	4.30780e100	0.976707
$685$	5.76770e100	1.24162
$686$	8.12177e99	0.166014
$687$	5.66188e99	0.109900
$688$	−1.82632e100	−0.336656
$689$	1.94951e100	0.341306
$690$	1.33385e98	0.00221801
$691$	−4.96329e99	−0.0783969	−0.0391985	−	0.999231i	$-0.512480\pi$
$691$	−4.96329e99	−0.0783969	−0.0391985	+	0.999231i	$0.512480\pi$
$692$	−2.47222e100	−0.370954
$693$	3.80990e100	0.543105
$694$	6.44601e100	0.873031
$695$	−4.32631e100	−0.556746
$696$	1.49635e100	0.182981
$697$	4.30941e100	0.500788
$698$	−6.63695e100	−0.732995
$699$	2.22004e97	0.000233035 0
$700$	−6.75968e100	−0.674444
$701$	1.64375e101	1.55900	0.779500	−	0.626403i	$-0.215473\pi$
$701$	1.64375e101	1.55900	0.779500	+	0.626403i	$0.215473\pi$
$702$	−7.69901e99	−0.0694172
$703$	1.24116e101	1.06393
$704$	−1.78373e100	−0.145378
$705$	−2.86854e100	−0.222304
$706$	−5.46824e100	−0.402977
$707$	−3.41520e101	−2.39346
$708$	−8.49068e98	−0.00565929
$709$	−1.01077e101	−0.640784	−0.320392	−	0.947285i	$-0.603815\pi$
$709$	−1.01077e101	−0.640784	−0.320392	+	0.947285i	$0.603815\pi$
$710$	−7.49963e100	−0.452240
$711$	1.93270e101	1.10865
$712$	8.01105e100	0.437169
$713$	−3.79724e99	−0.0197147
$714$	−2.79729e100	−0.138182
$715$	4.77744e100	0.224559
$716$	1.94678e100	0.0870770
$717$	1.49952e100	0.0638295
$718$	−1.66629e101	−0.675046
$719$	4.27913e100	0.164999	0.0824993	−	0.996591i	$-0.473710\pi$
$719$	4.27913e100	0.164999	0.0824993	+	0.996591i	$0.473710\pi$
$720$	−6.20425e100	−0.227712
$721$	1.79687e101	0.627791
$722$	1.73014e101	0.575453
$723$	−6.35899e99	−0.0201363
$724$	3.69023e101	1.11259
$725$	3.28190e101	0.942164
$726$	2.35484e100	0.0643740
$727$	−1.41850e101	−0.369280	−0.184640	−	0.982806i	$-0.559112\pi$
$727$	−1.41850e101	−0.369280	−0.184640	+	0.982806i	$0.559112\pi$
$728$	2.62287e101	0.650299
$729$	−3.77469e101	−0.891361
$730$	2.49987e101	0.562285
$731$	−1.08442e102	−2.32344
$732$	8.73938e100	0.178376
$733$	−4.26839e101	−0.829990	−0.414995	−	0.909824i	$-0.636217\pi$
$733$	−4.26839e101	−0.829990	−0.414995	+	0.909824i	$0.636217\pi$
$734$	5.63373e100	0.104372
$735$	−1.18795e101	−0.209700
$736$	−1.41933e100	−0.0238737
$737$	9.84594e100	0.157820
$738$	−1.42481e101	−0.217649
$739$	4.06155e101	0.591309	0.295655	−	0.955295i	$-0.404462\pi$
$739$	4.06155e101	0.591309	0.295655	+	0.955295i	$0.404462\pi$
$740$	−4.79919e101	−0.665950
$741$	6.86710e100	0.0908296
$742$	−4.72768e101	−0.596087
$743$	5.86566e101	0.705041	0.352520	−	0.935804i	$-0.385325\pi$
$743$	5.86566e101	0.705041	0.352520	+	0.935804i	$0.385325\pi$
$744$	9.45348e100	0.108331
$745$	1.26775e101	0.138512
$746$	3.22242e101	0.335702
$747$	1.81267e101	0.180068
$748$	3.41066e101	0.323096
$749$	1.63235e102	1.47472
$750$	3.87220e100	0.0333644
$751$	−1.52292e102	−1.25158	−0.625790	−	0.779991i	$-0.715223\pi$
$751$	−1.52292e102	−1.25158	−0.625790	+	0.779991i	$0.715223\pi$
$752$	2.93511e101	0.230087
$753$	−9.57220e100	−0.0715798
$754$	−5.22592e101	−0.372804
$755$	2.49101e102	1.69534
$756$	−4.27474e101	−0.277578
$757$	−2.57564e102	−1.59581	−0.797907	−	0.602781i	$-0.794059\pi$
$757$	−2.57564e102	−1.59581	−0.797907	+	0.602781i	$0.794059\pi$
$758$	1.32774e102	0.784977
$759$	−2.06749e99	−0.00116643
$760$	−3.19207e102	−1.71866
$761$	1.01313e102	0.520607	0.260303	−	0.965527i	$-0.416177\pi$
$761$	1.01313e102	0.520607	0.260303	+	0.965527i	$0.416177\pi$
$762$	−1.44537e101	−0.0708889
$763$	3.85997e102	1.80702
$764$	−2.00633e102	−0.896577
$765$	−3.68392e102	−1.57156
$766$	6.82989e100	0.0278158
$767$	7.22578e100	0.0280963
$768$	3.07482e101	0.114155
$769$	1.90299e102	0.674609	0.337304	−	0.941396i	$-0.390485\pi$
$769$	1.90299e102	0.674609	0.337304	+	0.941396i	$0.390485\pi$
$770$	−1.15855e102	−0.392189
$771$	−2.51034e101	−0.0811525
$772$	−5.61778e100	−0.0173441
$773$	−5.00659e102	−1.47628	−0.738142	−	0.674646i	$-0.764296\pi$
$773$	−5.00659e102	−1.47628	−0.738142	+	0.674646i	$0.764296\pi$
$774$	3.58540e102	1.00980
$775$	2.07340e102	0.557792
$776$	3.86582e102	0.993461
$777$	−6.10104e101	−0.149781
$778$	2.28455e101	0.0535828
$779$	2.56552e102	0.574904
$780$	−2.65529e101	−0.0568530
$781$	1.16246e102	0.237829
$782$	−8.10386e100	−0.0158435
$783$	2.07543e102	0.387763
$784$	1.21552e102	0.217042
$785$	−2.64184e102	−0.450852
$786$	1.36287e101	0.0222308
$787$	1.35053e102	0.210573	0.105286	−	0.994442i	$-0.466424\pi$
$787$	1.35053e102	0.210573	0.105286	+	0.994442i	$0.466424\pi$
$788$	2.34982e102	0.350230
$789$	1.29654e102	0.184737
$790$	−5.87715e102	−0.800581
$791$	−1.64605e103	−2.14376
$792$	−2.74784e102	−0.342175
$793$	−7.43743e102	−0.885574
$794$	4.84210e102	0.551323
$795$	1.16626e102	0.126988
$796$	1.49808e102	0.155998
$797$	−5.25327e102	−0.523190	−0.261595	−	0.965178i	$-0.584248\pi$
$797$	−5.25327e102	−0.523190	−0.261595	+	0.965178i	$0.584248\pi$
$798$	−1.66531e102	−0.158633
$799$	1.74279e103	1.58795
$800$	7.74993e102	0.675466
$801$	5.50409e102	0.458914
$802$	−5.56101e102	−0.443571
$803$	−3.87486e102	−0.295702
$804$	−5.47236e101	−0.0399562
$805$	−6.30265e101	−0.0440321
$806$	−3.30157e102	−0.220712
$807$	5.12746e101	0.0328013
$808$	2.46317e103	1.50796
$809$	−7.55509e102	−0.442657	−0.221328	−	0.975199i	$-0.571039\pi$
$809$	−7.55509e102	−0.442657	−0.221328	+	0.975199i	$0.571039\pi$
$810$	1.19477e103	0.669985
$811$	3.04981e103	1.63694	0.818470	−	0.574549i	$-0.194822\pi$
$811$	3.04981e103	1.63694	0.818470	+	0.574549i	$0.194822\pi$
$812$	−2.90160e103	−1.49073
$813$	−2.69240e102	−0.132412
$814$	−3.24902e102	−0.152963
$815$	1.18677e103	0.534900
$816$	−7.06075e101	−0.0304684
$817$	−6.45588e103	−2.66730
$818$	−1.52863e103	−0.604727
$819$	1.80208e103	0.682645
$820$	−9.92004e102	−0.359850
$821$	1.72051e103	0.597688	0.298844	−	0.954302i	$-0.403399\pi$
$821$	1.72051e103	0.597688	0.298844	+	0.954302i	$0.403399\pi$
$822$	−2.17022e102	−0.0722029
$823$	2.37532e103	0.756882	0.378441	−	0.925625i	$-0.376460\pi$
$823$	2.37532e103	0.756882	0.378441	+	0.925625i	$0.376460\pi$
$824$	−1.29597e103	−0.395530
$825$	1.12891e102	0.0330023
$826$	−1.75229e102	−0.0490699
$827$	−2.95808e103	−0.793533	−0.396766	−	0.917920i	$-0.629868\pi$
$827$	−2.95808e103	−0.793533	−0.396766	+	0.917920i	$0.629868\pi$
$828$	−6.13459e101	−0.0157655
$829$	2.93212e103	0.721930	0.360965	−	0.932579i	$-0.382447\pi$
$829$	2.93212e103	0.721930	0.360965	+	0.932579i	$0.382447\pi$
$830$	−5.51215e102	−0.130032
$831$	1.22357e102	0.0276561
$832$	−8.43700e102	−0.182730
$833$	7.21746e103	1.49791
$834$	1.62787e102	0.0323761
$835$	−1.07672e104	−2.05226
$836$	2.03047e103	0.370914
$837$	1.31119e103	0.229569
$838$	3.11536e103	0.522812
$839$	8.86310e103	1.42573	0.712863	−	0.701304i	$-0.247398\pi$
$839$	8.86310e103	1.42573	0.712863	+	0.701304i	$0.247398\pi$
$840$	1.56909e103	0.241954
$841$	7.32276e103	1.08247
$842$	−4.42955e103	−0.627741
$843$	−1.35884e103	−0.184625
$844$	3.63907e103	0.474060
$845$	−8.03310e103	−1.00339
$846$	−5.76217e103	−0.690142
$847$	−1.11270e104	−1.27796
$848$	−1.19333e103	−0.131434
$849$	−1.28999e101	−0.00136258
$850$	4.42494e103	0.448266
$851$	−1.76750e102	−0.0171735
$852$	−6.46092e102	−0.0602128
$853$	4.83418e103	0.432148	0.216074	−	0.976377i	$-0.430675\pi$
$853$	4.83418e103	0.432148	0.216074	+	0.976377i	$0.430675\pi$
$854$	1.80362e104	1.54664
$855$	−2.19315e104	−1.80414
$856$	−1.17731e104	−0.929123
$857$	−2.35431e104	−1.78256	−0.891282	−	0.453449i	$-0.850193\pi$
$857$	−2.35431e104	−1.78256	−0.891282	+	0.453449i	$0.850193\pi$
$858$	−1.79761e102	−0.0130586
$859$	5.03546e103	0.350980	0.175490	−	0.984481i	$-0.443849\pi$
$859$	5.03546e103	0.350980	0.175490	+	0.984481i	$0.443849\pi$
$860$	2.49628e104	1.66955
$861$	−1.26110e103	−0.0809353
$862$	−1.23433e103	−0.0760191
$863$	2.60129e104	1.53747	0.768733	−	0.639569i	$-0.220887\pi$
$863$	2.60129e104	1.53747	0.768733	+	0.639569i	$0.220887\pi$
$864$	4.90096e103	0.277999
$865$	1.25863e104	0.685215
$866$	1.21238e104	0.633510
$867$	−1.48893e103	−0.0746787
$868$	−1.83314e104	−0.882561
$869$	9.10971e103	0.421020
$870$	−3.12632e103	−0.138707
$871$	4.65711e103	0.198368
$872$	−2.78395e104	−1.13848
$873$	2.65606e104	1.04288
$874$	−4.82447e102	−0.0181884
$875$	−1.82968e104	−0.662352
$876$	2.15364e103	0.0748647
$877$	−2.37137e104	−0.791614	−0.395807	−	0.918334i	$-0.629535\pi$
$877$	−2.37137e104	−0.791614	−0.395807	+	0.918334i	$0.629535\pi$
$878$	−2.96546e104	−0.950686
$879$	−3.35015e103	−0.103148
$880$	−2.92435e103	−0.0864758
$881$	5.29095e104	1.50276	0.751378	−	0.659872i	$-0.229389\pi$
$881$	5.29095e104	1.50276	0.751378	+	0.659872i	$0.229389\pi$
$882$	−2.38630e104	−0.651013
$883$	−5.63190e104	−1.47588	−0.737939	−	0.674868i	$-0.764201\pi$
$883$	−5.63190e104	−1.47588	−0.737939	+	0.674868i	$0.764201\pi$
$884$	1.61324e104	0.406109
$885$	4.32270e102	0.0104537
$886$	3.65604e104	0.849403
$887$	−3.47630e104	−0.775942	−0.387971	−	0.921672i	$-0.626824\pi$
$887$	−3.47630e104	−0.775942	−0.387971	+	0.921672i	$0.626824\pi$
$888$	4.40030e103	0.0943675
$889$	6.82962e104	1.40729
$890$	−1.67374e104	−0.331393
$891$	−1.85191e104	−0.352340
$892$	−3.31411e104	−0.605919
$893$	1.03754e105	1.82296
$894$	−4.77018e102	−0.00805477
$895$	−9.91124e103	−0.160846
$896$	−7.79852e104	−1.21640
$897$	−9.77919e101	−0.00146613
$898$	5.27012e104	0.759470
$899$	8.90009e104	1.23289
$900$	3.34966e104	0.446058
$901$	−7.08569e104	−0.907094
$902$	−6.71580e103	−0.0826543
$903$	3.17344e104	0.375504
$904$	1.18719e105	1.35064
$905$	−1.87874e105	−2.05514
$906$	−9.37295e103	−0.0985882
$907$	−7.38168e104	−0.746615	−0.373307	−	0.927708i	$-0.621776\pi$
$907$	−7.38168e104	−0.746615	−0.373307	+	0.927708i	$0.621776\pi$
$908$	2.40324e104	0.233749
$909$	1.69235e105	1.58297
$910$	−5.47994e104	−0.492954
$911$	−2.12753e105	−1.84066	−0.920328	−	0.391147i	$-0.872078\pi$
$911$	−2.12753e105	−1.84066	−0.920328	+	0.391147i	$0.872078\pi$
$912$	−4.20347e103	−0.0349777
$913$	8.54395e103	0.0683826
$914$	−3.97645e104	−0.306130
$915$	−4.44931e104	−0.329491
$916$	7.91849e104	0.564096
$917$	−6.43980e104	−0.441328
$918$	2.79828e104	0.184491
$919$	8.23043e104	0.522062	0.261031	−	0.965330i	$-0.415938\pi$
$919$	8.23043e104	0.522062	0.261031	+	0.965330i	$0.415938\pi$
$920$	4.54571e103	0.0277417
$921$	1.60457e104	0.0942196
$922$	−9.42308e104	−0.532409
$923$	5.49841e104	0.298935
$924$	−9.98093e103	−0.0522175
$925$	9.65104e104	0.485895
$926$	6.96716e103	0.0337571
$927$	−8.90413e104	−0.415203
$928$	3.32667e105	1.49299
$929$	4.14935e104	0.179235	0.0896173	−	0.995976i	$-0.471436\pi$
$929$	4.14935e104	0.179235	0.0896173	+	0.995976i	$0.471436\pi$
$930$	−1.97511e104	−0.0821194
$931$	4.29677e105	1.71960
$932$	3.10487e102	0.00119613
$933$	−5.07036e104	−0.188036
$934$	1.06918e105	0.381712
$935$	−1.73640e105	−0.596813
$936$	−1.29973e105	−0.430090
$937$	−6.06630e105	−1.93272	−0.966359	−	0.257198i	$-0.917201\pi$
$937$	−6.06630e105	−1.93272	−0.966359	+	0.257198i	$0.917201\pi$
$938$	−1.12938e105	−0.346448
$939$	4.61253e104	0.136242
$940$	−4.01183e105	−1.14105
$941$	6.73749e104	0.184530	0.0922649	−	0.995734i	$-0.470589\pi$
$941$	6.73749e104	0.184530	0.0922649	+	0.995734i	$0.470589\pi$
$942$	9.94051e103	0.0262181
$943$	−3.65346e103	−0.00927982
$944$	−4.42302e103	−0.0108197
$945$	2.17631e105	0.512734
$946$	1.68997e105	0.383480
$947$	−2.29778e104	−0.0502209	−0.0251104	−	0.999685i	$-0.507994\pi$
$947$	−2.29778e104	−0.0502209	−0.0251104	+	0.999685i	$0.507994\pi$
$948$	−5.06316e104	−0.106592
$949$	−1.83280e105	−0.371676
$950$	2.63430e105	0.514608
$951$	4.11384e104	0.0774174
$952$	−9.53308e105	−1.72831
$953$	2.30162e105	0.402009	0.201005	−	0.979590i	$-0.435579\pi$
$953$	2.30162e105	0.402009	0.201005	+	0.979590i	$0.435579\pi$
$954$	2.34273e105	0.394235
$955$	1.02144e106	1.65613
$956$	2.09717e105	0.327626
$957$	4.84586e104	0.0729452
$958$	−1.09312e105	−0.158560
$959$	1.02547e106	1.43338
$960$	−5.04729e104	−0.0679875
$961$	−2.08057e105	−0.270087
$962$	−1.53678e105	−0.192263
$963$	−8.08887e105	−0.975337
$964$	−8.89345e104	−0.103356
$965$	2.86007e104	0.0320374
$966$	2.37151e103	0.00256057
$967$	−4.70015e105	−0.489183	−0.244592	−	0.969626i	$-0.578654\pi$
$967$	−4.70015e105	−0.489183	−0.244592	+	0.969626i	$0.578654\pi$
$968$	8.02520e105	0.805157
$969$	−2.49591e105	−0.241399
$970$	−8.07683e105	−0.753086
$971$	1.49029e105	0.133964	0.0669819	−	0.997754i	$-0.478663\pi$
$971$	1.49029e105	0.133964	0.0669819	+	0.997754i	$0.478663\pi$
$972$	3.18725e105	0.276226
$973$	−7.69194e105	−0.642732
$974$	8.77924e103	0.00707317
$975$	5.33972e104	0.0414815
$976$	4.55258e105	0.341027
$977$	−1.71649e105	−0.123989	−0.0619945	−	0.998076i	$-0.519746\pi$
$977$	−1.71649e105	−0.123989	−0.0619945	+	0.998076i	$0.519746\pi$
$978$	−4.46549e104	−0.0311057
$979$	2.59433e105	0.174277
$980$	−1.66142e106	−1.07635
$981$	−1.91275e106	−1.19511
$982$	1.16476e106	0.701907
$983$	1.01872e106	0.592116	0.296058	−	0.955170i	$-0.404328\pi$
$983$	1.01872e106	0.592116	0.296058	+	0.955170i	$0.404328\pi$
$984$	9.09554e104	0.0509920
$985$	−1.19632e106	−0.646935
$986$	1.89941e106	0.990806
$987$	−5.10010e105	−0.256637
$988$	9.60407e105	0.466212
$989$	9.19358e104	0.0430543
$990$	5.74104e105	0.259383
$991$	3.89325e106	1.69706	0.848531	−	0.529146i	$-0.177488\pi$
$991$	3.89325e106	1.69706	0.848531	+	0.529146i	$0.177488\pi$
$992$	2.10168e106	0.883898
$993$	1.06446e105	0.0431949
$994$	−1.33339e106	−0.522086
$995$	−7.62687e105	−0.288156
$996$	−4.74871e104	−0.0173129
$997$	−4.52527e106	−1.59208	−0.796042	−	0.605241i	$-0.793077\pi$
$997$	−4.52527e106	−1.59208	−0.796042	+	0.605241i	$0.793077\pi$
$998$	−2.93675e105	−0.0997085
$999$	6.10319e105	0.199978

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.72.a.a.1.4	✓	6
3.2	odd	2		9.72.a.b.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.72.a.a.1.4	✓	6	1.1	even	1	trivial
9.72.a.b.1.3		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)

\(f(q)\)	\(=\)	\(q+2.67914e10 q^{2} -1.17507e16 q^{3} -1.64340e21 q^{4} +8.36674e24 q^{5} -3.14817e26 q^{6} +1.48756e30 q^{7} -1.07289e32 q^{8} -7.37139e33 q^{9} +O(q^{10})\)	\(q+2.67914e10 q^{2} -1.17507e16 q^{3} -1.64340e21 q^{4} +8.36674e24 q^{5} -3.14817e26 q^{6} +1.48756e30 q^{7} -1.07289e32 q^{8} -7.37139e33 q^{9} +2.24157e35 q^{10} -3.47448e36 q^{11} +1.93111e37 q^{12} -1.64342e39 q^{13} +3.98539e40 q^{14} -9.83148e40 q^{15} +1.00597e42 q^{16} +5.97317e43 q^{17} -1.97490e44 q^{18} +3.55600e45 q^{19} -1.37499e46 q^{20} -1.74798e46 q^{21} -9.30861e46 q^{22} -5.06398e46 q^{23} +1.26071e48 q^{24} +2.76508e49 q^{25} -4.40296e49 q^{26} +1.74860e50 q^{27} -2.44466e51 q^{28} +1.18691e52 q^{29} -2.63399e51 q^{30} +7.49852e52 q^{31} +2.80279e53 q^{32} +4.08274e52 q^{33} +1.60030e54 q^{34} +1.24460e55 q^{35} +1.21142e55 q^{36} +3.49033e55 q^{37} +9.52704e55 q^{38} +1.93113e55 q^{39} -8.97656e56 q^{40} +7.21461e56 q^{41} -4.68309e56 q^{42} -1.81549e58 q^{43} +5.70997e57 q^{44} -6.16745e58 q^{45} -1.35671e57 q^{46} +2.91771e59 q^{47} -1.18208e58 q^{48} +1.20831e60 q^{49} +7.40803e59 q^{50} -7.01887e59 q^{51} +2.70080e60 q^{52} -1.18625e61 q^{53} +4.68474e60 q^{54} -2.90701e61 q^{55} -1.59598e62 q^{56} -4.17854e61 q^{57} +3.17991e62 q^{58} -4.39679e61 q^{59} +1.61571e62 q^{60} +4.52558e63 q^{61} +2.00896e63 q^{62} -1.09654e64 q^{63} +5.13380e63 q^{64} -1.37501e64 q^{65} +1.09382e63 q^{66} -2.83379e64 q^{67} -9.81633e64 q^{68} +5.95051e62 q^{69} +3.33447e65 q^{70} -3.34571e65 q^{71} +7.90865e65 q^{72} +1.11523e66 q^{73} +9.35109e65 q^{74} -3.24915e65 q^{75} -5.84395e66 q^{76} -5.16850e66 q^{77} +5.17377e65 q^{78} -2.62189e67 q^{79} +8.41666e66 q^{80} +5.33005e67 q^{81} +1.93290e67 q^{82} -2.45906e67 q^{83} +2.87264e67 q^{84} +4.99760e68 q^{85} -4.86394e68 q^{86} -1.39470e68 q^{87} +3.72772e68 q^{88} -7.46683e68 q^{89} -1.65235e69 q^{90} -2.44469e69 q^{91} +8.32216e67 q^{92} -8.81126e68 q^{93} +7.81694e69 q^{94} +2.97522e70 q^{95} -3.29347e69 q^{96} -3.60320e70 q^{97} +3.23724e70 q^{98} +2.56117e70 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 66157336440 q^{2} + 89\!\cdots\!40 q^{3}+ \cdots + 28\!\cdots\!42 q^{9}+O(q^{10}) \) 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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