LMFDB - Embedded newform 3.72.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,72,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

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

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 72);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 72 $
Character orbit:	$[\chi]$	$=$	3.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:	$95.7738481683$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2 x^{4} + \cdots - 10\!\cdots\!54 $ x^5 - 2x^4 - 11794880527205841026x^3 - 1576914464895109132006308600x^2 + 21982147283297468753929167380086357881x - 10487125185557323126488817758602332290924256254
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{36}\cdot 3^{20}\cdot 5^{4}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.23970e9$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.27630e10 q^{2} +5.00315e16 q^{3} +4.48853e21 q^{4} -1.31164e24 q^{5} -4.14076e27 q^{6} -1.62984e30 q^{7} -1.76066e32 q^{8} +2.50316e33 q^{9} +O(q^{10})$	\(q-8.27630e10 q^{2} +5.00315e16 q^{3} +4.48853e21 q^{4} -1.31164e24 q^{5} -4.14076e27 q^{6} -1.62984e30 q^{7} -1.76066e32 q^{8} +2.50316e33 q^{9} +1.08555e35 q^{10} -4.64381e36 q^{11} +2.24568e38 q^{12} +2.03686e39 q^{13} +1.34891e41 q^{14} -6.56235e40 q^{15} +3.97348e42 q^{16} +3.84131e43 q^{17} -2.07169e44 q^{18} +2.58249e45 q^{19} -5.88734e45 q^{20} -8.15436e46 q^{21} +3.84336e47 q^{22} -2.47461e48 q^{23} -8.80884e48 q^{24} -4.06312e49 q^{25} -1.68577e50 q^{26} +1.25237e50 q^{27} -7.31560e51 q^{28} +8.82779e50 q^{29} +5.43119e51 q^{30} +1.59171e53 q^{31} +8.68663e52 q^{32} -2.32337e53 q^{33} -3.17918e54 q^{34} +2.13777e54 q^{35} +1.12355e55 q^{36} -7.30878e55 q^{37} -2.13734e56 q^{38} +1.01907e56 q^{39} +2.30935e56 q^{40} +3.13071e57 q^{41} +6.74879e57 q^{42} +1.90602e56 q^{43} -2.08439e58 q^{44} -3.28324e57 q^{45} +2.04806e59 q^{46} -2.89170e59 q^{47} +1.98799e59 q^{48} +1.65187e60 q^{49} +3.36276e60 q^{50} +1.92187e60 q^{51} +9.14251e60 q^{52} +2.13586e61 q^{53} -1.03650e61 q^{54} +6.09102e60 q^{55} +2.86960e62 q^{56} +1.29206e62 q^{57} -7.30615e61 q^{58} +5.88472e62 q^{59} -2.94553e62 q^{60} +8.43530e62 q^{61} -1.31735e64 q^{62} -4.07975e63 q^{63} -1.65714e64 q^{64} -2.67163e63 q^{65} +1.92289e64 q^{66} -5.85854e64 q^{67} +1.72418e65 q^{68} -1.23808e65 q^{69} -1.76928e65 q^{70} +2.84685e65 q^{71} -4.40720e65 q^{72} -6.50923e65 q^{73} +6.04896e66 q^{74} -2.03284e66 q^{75} +1.15916e67 q^{76} +7.56869e66 q^{77} -8.43415e66 q^{78} -2.83385e67 q^{79} -5.21178e66 q^{80} +6.26579e66 q^{81} -2.59107e68 q^{82} +1.64358e68 q^{83} -3.66011e68 q^{84} -5.03842e67 q^{85} -1.57748e67 q^{86} +4.41668e67 q^{87} +8.17616e68 q^{88} +2.05248e69 q^{89} +2.71731e68 q^{90} -3.31976e69 q^{91} -1.11074e70 q^{92} +7.96357e69 q^{93} +2.39326e70 q^{94} -3.38730e69 q^{95} +4.34605e69 q^{96} -5.94592e70 q^{97} -1.36713e71 q^{98} -1.16242e70 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 25051277688 q^{2} + 25\!\cdots\!35 q^{3}+ \cdots + 12\!\cdots\!45 q^{9}+O(q^{10}) $ 5 * q - 25051277688 * q^2 + 250157725494998535 * q^3 + 1907299462927273154624 * q^4 + 1422573866433399534277830 * q^5 - 1253354129434737111087637416 * q^6 - 1261222231854515600228814346952 * q^7 - 151958919976138936299686009691648 * q^8 + 12515777524966208006577859930429245 * q^9	$ 5 q - 25051277688 q^{2} + 25\!\cdots\!35 q^{3}+ \cdots + 33\!\cdots\!88 q^{99}+O(q^{100}) $ 5 * q - 25051277688 * q^2 + 250157725494998535 * q^3 + 1907299462927273154624 * q^4 + 1422573866433399534277830 * q^5 - 1253354129434737111087637416 * q^6 - 1261222231854515600228814346952 * q^7 - 151958919976138936299686009691648 * q^8 + 12515777524966208006577859930429245 * q^9 - 308853354401574193552393248717551760 * q^10 + 1357894937151168401938494740936725812 * q^11 + 95425139096743786553920018696741695168 * q^12 - 3732312012481108743024076959256483425602 * q^13 + 178792454794792302794525709930294541693632 * q^14 + 71173568555121014264963983054791626595810 * q^15 - 2761767053096261549691112453399712883798016 * q^16 - 277325542902069263625709674624672840731910 * q^17 - 62707243651831565917830179941990275506237112 * q^18 + 2937432205918421125744856768913127977845719948 * q^19 - 24911205133324082416992380941498137854677077120 * q^20 - 63100896972890262121533046345756354145644343064 * q^21 + 981344865457378177927521236701073576051567611680 * q^22 - 4228346897979680919198407557464543114207597141624 * q^23 - 7602739557981482671404075764718702187632312347136 * q^24 + 19633070396484105587134362494981426945191834668275 * q^25 - 163733269614894222914401413204168398319516301314000 * q^26 + 626183687689393767209300272665229846333060639231215 * q^27 - 5768362424640263225567110092226485193092350431463936 * q^28 - 3697116438725251267139482122013539208885912739684274 * q^29 - 15452410529719698927278278181356603942084949997334320 * q^30 + 74551273173252500835223325068153865117486542141504384 * q^31 - 639756106869108826481408208267665768107401476101865472 * q^32 + 67937581787782054618912973363008350989516300927337084 * q^33 - 6217683238533672509931589234500437242788961796499134832 * q^34 - 13153074146721234298498045726570273336863567981003778800 * q^35 + 4774267150297056921454723864735495027586024236315315776 * q^36 - 160060519909409459305929258566699075666754182654348019002 * q^37 - 91685642067030133239673763998240213415299939628290081056 * q^38 - 186733336775986949394712651065025829961603412074954298614 * q^39 + 755753872880123511491678719028119895299413298470522117120 * q^40 + 2279706853693741369685932186247543106805520151549660884994 * q^41 + 8945262765426517501413121912547804713065475672808851765824 * q^42 + 6754858585968454689741824956150275855563744863320129251092 * q^43 + 10256422900727914711051439828948913719762767210529399343360 * q^44 + 3560923605022284438744581203359299419628800805488597427670 * q^45 + 215917478684214015835970415365801427523995942249450992649024 * q^46 - 468036949346743446524224540083033087921443712918743092678704 * q^47 - 138175472869917128113923965027114211523442937794848631181312 * q^48 - 1155203275623883178356241428680618202323141234160855611430803 * q^49 - 662361288254569744891489750838385910624551591076930373305800 * q^50 - 13875025406809456447127343535570692796264334304266755550370 * q^51 + 4686563330803028488195038486432142239675010588344800750934400 * q^52 + 16850153365054699278877708172474268895458775724356533295576086 * q^53 - 3137340288800574070947321989342157748567014121664790760526184 * q^54 + 69903604802785515177733563130194024072223641855144712529201880 * q^55 + 263561757691935735991107069426454954646910606378160826135654400 * q^56 + 146964271885661680599941817303782740393713518895988426056055236 * q^57 - 393766572647074503603427367357535096204856933671806739961414992 * q^58 - 390335442004059371501204897784396685449449222429047305160362108 * q^59 - 1246346083098336838245443167057803985933179433056389614496403840 * q^60 + 725074488292223066537782289903828567460896102224114882556804878 * q^61 - 9988959008617311972392577438833349328275372968547435398535343104 * q^62 - 3157035372686493241148598970419764570521041257808979169543482248 * q^63 - 2023851072198628197882474312831161597933729151994298498048327680 * q^64 + 13140351800845565438471290641483435252971725075901777919813259620 * q^65 + 49098199893802616037233646095483883838218857898857856047009777760 * q^66 + 66714375177521017736160888158122274402157076957263686329132696540 * q^67 + 122874398781837608005594402142092581637778609572473879627701828736 * q^68 - 211550728520485918988863794593760397778492966928452183274813504168 * q^69 - 293285886544485684750990625097245178785454325664385364335258966400 * q^70 + 182228903943633461999697286426491914806644676121035292409010095000 * q^71 - 380376807071099648078549525700513940155076932645648351218946289152 * q^72 - 3126186443395793129070092762366126842796181422188167587986966103774 * q^73 - 909089362115793434062323439709786862714999800511985114251226742928 * q^74 + 982272846973530587229764561497340393007528047854257425826667195425 * q^75 + 17344875012173690040537707411833679809662138514060794984773183596288 * q^76 + 10495163179741456456758662728922622402868815939129112668959031953376 * q^77 - 8191828462944258702008436357306371395699406819716356341809714998000 * q^78 - 27301301517941598101728732493241199802996555070508118978972462370800 * q^79 + 17453171390087969064834561314810599922914790489604475485575264133120 * q^80 + 31328937410889851896281120971709651661033472234053326374297990254005 * q^81 - 211476001448904287369943798857320633308142594733381306800142859557424 * q^82 - 118340201116022360513322067378331477940966167749075029048364461271476 * q^83 - 288600084795764628291001658833202352097198631523538446517373245066752 * q^84 - 353749028745389735175606474209594334673616946227279830960229574948180 * q^85 - 598599366027984305586625758611411918350192525004808831847227328355808 * q^86 - 184972447840335595586879350012403335749718574814304198079640398507718 * q^87 + 884266222865559755895490832763056324497872985335575213438267918764032 * q^88 + 922002192851420225703931949240660524744080828362964363768621192185298 * q^89 - 773107974305929069152539888281824938594397222395836929970148461044240 * q^90 - 8079212959404027614418440109956770906886889649154860574373249888569776 * q^91 - 13670577861982746620628593404236014523694130242253442181460174526039552 * q^92 + 3729915385955429492528971192901332630862445897595761204245366555215488 * q^93 - 13436976700690544599208201928250305890032773609106302404839902759345024 * q^94 - 61508953507577523131201535405733284550943470497632040479599939746271320 * q^95 - 32007986513182294493504227608086345487918910401219597611766423881416704 * q^96 - 149876371240369823947413564997445008107894647331408877752554402308756310 * q^97 - 164242038075013607742967230335294726637154516016956449921881670478527288 * q^98 + 3399022187132399007137561865025534669344410724594880911844979606234388 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−8.27630e10	−1.70322	−0.851611	−	0.524174i	$-0.824374\pi$
$2$	−8.27630e10	−1.70322	−0.851611	+	0.524174i	$0.824374\pi$
$3$	5.00315e16	0.577350
$3$	5.00315e16	0.577350
$4$	4.48853e21	1.90097
$5$	−1.31164e24	−0.201549	−0.100774	−	0.994909i	$-0.532132\pi$
$5$	−1.31164e24	−0.201549	−0.100774	+	0.994909i	$0.532132\pi$
$6$	−4.14076e27	−0.983356
$7$	−1.62984e30	−1.62617	−0.813084	−	0.582146i	$-0.802213\pi$
$7$	−1.62984e30	−1.62617	−0.813084	+	0.582146i	$0.802213\pi$
$8$	−1.76066e32	−1.53455
$9$	2.50316e33	0.333333
$10$	1.08555e35	0.343282
$11$	−4.64381e36	−0.498235	−0.249118	−	0.968473i	$-0.580141\pi$
$11$	−4.64381e36	−0.498235	−0.249118	+	0.968473i	$0.580141\pi$
$12$	2.24568e38	1.09752
$13$	2.03686e39	0.580727	0.290363	−	0.956916i	$-0.406224\pi$
$13$	2.03686e39	0.580727	0.290363	+	0.956916i	$0.406224\pi$
$14$	1.34891e41	2.76973
$15$	−6.56235e40	−0.116364
$16$	3.97348e42	0.712708
$17$	3.84131e43	0.800835	0.400417	−	0.916333i	$-0.368865\pi$
$17$	3.84131e43	0.800835	0.400417	+	0.916333i	$0.368865\pi$
$18$	−2.07169e44	−0.567741
$19$	2.58249e45	1.03821	0.519105	−	0.854710i	$-0.326265\pi$
$19$	2.58249e45	1.03821	0.519105	+	0.854710i	$0.326265\pi$
$20$	−5.88734e45	−0.383137
$21$	−8.15436e46	−0.938869
$22$	3.84336e47	0.848606
$23$	−2.47461e48	−1.12763	−0.563817	−	0.825900i	$-0.690668\pi$
$23$	−2.47461e48	−1.12763	−0.563817	+	0.825900i	$0.690668\pi$
$24$	−8.80884e48	−0.885971
$25$	−4.06312e49	−0.959378
$26$	−1.68577e50	−0.989107
$27$	1.25237e50	0.192450
$28$	−7.31560e51	−3.09129
$29$	8.82779e50	0.107331	0.0536653	−	0.998559i	$-0.482910\pi$
$29$	8.82779e50	0.107331	0.0536653	+	0.998559i	$0.482910\pi$
$30$	5.43119e51	0.198194
$31$	1.59171e53	1.81353	0.906763	−	0.421641i	$-0.138546\pi$
$31$	1.59171e53	1.81353	0.906763	+	0.421641i	$0.138546\pi$
$32$	8.68663e52	0.320647
$33$	−2.32337e53	−0.287656
$34$	−3.17918e54	−1.36400
$35$	2.13777e54	0.327752
$36$	1.12355e55	0.633656
$37$	−7.30878e55	−1.55842	−0.779208	−	0.626765i	$-0.784379\pi$
$37$	−7.30878e55	−1.55842	−0.779208	+	0.626765i	$0.784379\pi$
$38$	−2.13734e56	−1.76830
$39$	1.01907e56	0.335283
$40$	2.30935e56	0.309286
$41$	3.13071e57	1.74508	0.872542	−	0.488540i	$-0.162470\pi$
$41$	3.13071e57	1.74508	0.872542	+	0.488540i	$0.162470\pi$
$42$	6.74879e57	1.59910
$43$	1.90602e56	0.0195883	0.00979416	−	0.999952i	$-0.496882\pi$
$43$	1.90602e56	0.0195883	0.00979416	+	0.999952i	$0.496882\pi$
$44$	−2.08439e58	−0.947129
$45$	−3.28324e57	−0.0671829
$46$	2.04806e59	1.92061
$47$	−2.89170e59	−1.26380	−0.631902	−	0.775048i	$-0.717725\pi$
$47$	−2.89170e59	−1.26380	−0.631902	+	0.775048i	$0.717725\pi$
$48$	1.98799e59	0.411482
$49$	1.65187e60	1.64442
$50$	3.36276e60	1.63403
$51$	1.92187e60	0.462362
$52$	9.14251e60	1.10394
$53$	2.13586e61	1.31153	0.655766	−	0.754964i	$-0.272346\pi$
$53$	2.13586e61	1.31153	0.655766	+	0.754964i	$0.272346\pi$
$54$	−1.03650e61	−0.327785
$55$	6.09102e60	0.100419
$56$	2.86960e62	2.49543
$57$	1.29206e62	0.599411
$58$	−7.30615e61	−0.182808
$59$	5.88472e62	0.802564	0.401282	−	0.915955i	$-0.368565\pi$
$59$	5.88472e62	0.802564	0.401282	+	0.915955i	$0.368565\pi$
$60$	−2.94553e62	−0.221204
$61$	8.43530e62	0.352283	0.176141	−	0.984365i	$-0.443638\pi$
$61$	8.43530e62	0.352283	0.176141	+	0.984365i	$0.443638\pi$
$62$	−1.31735e64	−3.08884
$63$	−4.07975e63	−0.542056
$64$	−1.65714e64	−1.25884
$65$	−2.67163e63	−0.117045
$66$	1.92289e64	0.489943
$67$	−5.85854e64	−0.875254	−0.437627	−	0.899157i	$-0.644181\pi$
$67$	−5.85854e64	−0.875254	−0.437627	+	0.899157i	$0.644181\pi$
$68$	1.72418e65	1.52236
$69$	−1.23808e65	−0.651040
$70$	−1.76928e65	−0.558235
$71$	2.84685e65	0.542867	0.271433	−	0.962457i	$-0.412502\pi$
$71$	2.84685e65	0.542867	0.271433	+	0.962457i	$0.412502\pi$
$72$	−4.40720e65	−0.511516
$73$	−6.50923e65	−0.462986	−0.231493	−	0.972837i	$-0.574361\pi$
$73$	−6.50923e65	−0.462986	−0.231493	+	0.972837i	$0.574361\pi$
$74$	6.04896e66	2.65433
$75$	−2.03284e66	−0.553897
$76$	1.15916e67	1.97360
$77$	7.56869e66	0.810215
$78$	−8.43415e66	−0.571061
$79$	−2.83385e67	−1.22072	−0.610359	−	0.792125i	$-0.708975\pi$
$79$	−2.83385e67	−1.22072	−0.610359	+	0.792125i	$0.708975\pi$
$80$	−5.21178e66	−0.143645
$81$	6.26579e66	0.111111
$82$	−2.59107e68	−2.97227
$83$	1.64358e68	1.22608	0.613039	−	0.790052i	$-0.289947\pi$
$83$	1.64358e68	1.22608	0.613039	+	0.790052i	$0.289947\pi$
$84$	−3.66011e68	−1.78476
$85$	−5.03842e67	−0.161407
$86$	−1.57748e67	−0.0333633
$87$	4.41668e67	0.0619673
$88$	8.17616e68	0.764565
$89$	2.05248e69	1.28509	0.642545	−	0.766248i	$-0.277879\pi$
$89$	2.05248e69	1.28509	0.642545	+	0.766248i	$0.277879\pi$
$90$	2.71731e68	0.114427
$91$	−3.31976e69	−0.944360
$92$	−1.11074e70	−2.14360
$93$	7.96357e69	1.04704
$94$	2.39326e70	2.15254
$95$	−3.38730e69	−0.209250
$96$	4.34605e69	0.185126
$97$	−5.94592e70	−1.75316	−0.876582	−	0.481253i	$-0.840182\pi$
$97$	−5.94592e70	−1.75316	−0.876582	+	0.481253i	$0.840182\pi$
$98$	−1.36713e71	−2.80082
$99$	−1.16242e70	−0.166078
$100$	−1.82375e71	−1.82375
$101$	−1.63433e71	−1.14797	−0.573986	−	0.818865i	$-0.694604\pi$
$101$	−1.63433e71	−1.14797	−0.573986	+	0.818865i	$0.694604\pi$
$102$	−1.59060e71	−0.787505
$103$	4.50773e71	1.57847	0.789234	−	0.614092i	$-0.210478\pi$
$103$	4.50773e71	1.57847	0.789234	+	0.614092i	$0.210478\pi$
$104$	−3.58621e71	−0.891153
$105$	1.06956e71	0.189228
$106$	−1.76770e72	−2.23383
$107$	1.00057e72	0.905986	0.452993	−	0.891514i	$-0.350356\pi$
$107$	1.00057e72	0.905986	0.452993	+	0.891514i	$0.350356\pi$
$108$	5.62129e71	0.365841
$109$	−1.00540e72	−0.471737	−0.235868	−	0.971785i	$-0.575793\pi$
$109$	−1.00540e72	−0.471737	−0.235868	+	0.971785i	$0.575793\pi$
$110$	−5.04111e71	−0.171035
$111$	−3.65669e72	−0.899752
$112$	−6.47615e72	−1.15898
$113$	2.84619e72	0.371517	0.185759	−	0.982595i	$-0.440526\pi$
$113$	2.84619e72	0.371517	0.185759	+	0.982595i	$0.440526\pi$
$114$	−1.06935e73	−1.02093
$115$	3.24580e72	0.227273
$116$	3.96238e72	0.204032
$117$	5.09858e72	0.193576
$118$	−4.87037e73	−1.36695
$119$	−6.26074e73	−1.30229
$120$	1.15540e73	0.178566
$121$	−6.53072e73	−0.751762
$122$	−6.98131e73	−0.600016
$123$	1.56634e74	1.00752
$124$	7.14444e74	3.44745
$125$	1.08844e74	0.394910
$126$	3.37653e74	0.923242
$127$	2.46968e74	0.510045	0.255022	−	0.966935i	$-0.417917\pi$
$127$	2.46968e74	0.510045	0.255022	+	0.966935i	$0.417917\pi$
$128$	1.16639e75	1.82344
$129$	9.53611e72	0.0113093
$130$	2.21112e74	0.199353
$131$	−6.59495e74	−0.452981	−0.226491	−	0.974013i	$-0.572725\pi$
$131$	−6.59495e74	−0.452981	−0.226491	+	0.974013i	$0.572725\pi$
$132$	−1.04285e75	−0.546825
$133$	−4.20905e75	−1.68831
$134$	4.84870e75	1.49075
$135$	−1.64266e74	−0.0387881
$136$	−6.76323e75	−1.22892
$137$	3.57199e75	0.500414	0.250207	−	0.968192i	$-0.419501\pi$
$137$	3.57199e75	0.500414	0.250207	+	0.968192i	$0.419501\pi$
$138$	1.02468e76	1.10887
$139$	5.00635e75	0.419272	0.209636	−	0.977779i	$-0.432772\pi$
$139$	5.00635e75	0.419272	0.209636	+	0.977779i	$0.432772\pi$
$140$	9.59545e75	0.623046
$141$	−1.44676e76	−0.729657
$142$	−2.35614e76	−0.924623
$143$	−9.45880e75	−0.289339
$144$	9.94624e75	0.237569
$145$	−1.15789e75	−0.0216323
$146$	5.38723e76	0.788568
$147$	8.26454e76	0.949409
$148$	−3.28057e77	−2.96250
$149$	−9.89462e76	−0.703536	−0.351768	−	0.936087i	$-0.614419\pi$
$149$	−9.89462e76	−0.703536	−0.351768	+	0.936087i	$0.614419\pi$
$150$	1.68244e77	0.943410
$151$	−2.11236e77	−0.935590	−0.467795	−	0.883837i	$-0.654952\pi$
$151$	−2.11236e77	−0.935590	−0.467795	+	0.883837i	$0.654952\pi$
$152$	−4.54688e77	−1.59318
$153$	9.61540e76	0.266945
$154$	−6.26408e77	−1.37998
$155$	−2.08775e77	−0.365514
$156$	4.57414e77	0.637362
$157$	−1.14195e78	−1.26827	−0.634133	−	0.773224i	$-0.718643\pi$
$157$	−1.14195e78	−1.26827	−0.634133	+	0.773224i	$0.718643\pi$
$158$	2.34538e78	2.07915
$159$	1.06860e78	0.757214
$160$	−1.13937e77	−0.0646260
$161$	4.03323e78	1.83372
$162$	−5.18575e77	−0.189247
$163$	−7.25392e77	−0.212771	−0.106386	−	0.994325i	$-0.533928\pi$
$163$	−7.25392e77	−0.212771	−0.106386	+	0.994325i	$0.533928\pi$
$164$	1.40523e79	3.31735
$165$	3.04743e77	0.0579768
$166$	−1.36028e79	−2.08828
$167$	−3.73060e78	−0.462747	−0.231374	−	0.972865i	$-0.574322\pi$
$167$	−3.73060e78	−0.462747	−0.231374	+	0.972865i	$0.574322\pi$
$168$	1.43570e79	1.44074
$169$	−8.15327e78	−0.662756
$170$	4.16995e78	0.274912
$171$	6.46437e78	0.346070
$172$	8.55522e77	0.0372367
$173$	−4.39763e79	−1.55805	−0.779027	−	0.626991i	$-0.784286\pi$
$173$	−4.39763e79	−1.55805	−0.779027	+	0.626991i	$0.784286\pi$
$174$	−3.65538e78	−0.105544
$175$	6.62226e79	1.56011
$176$	−1.84521e79	−0.355096
$177$	2.94422e79	0.463361
$178$	−1.69869e80	−2.18879
$179$	−8.51182e79	−0.898959	−0.449480	−	0.893291i	$-0.648391\pi$
$179$	−8.51182e79	−0.898959	−0.449480	+	0.893291i	$0.648391\pi$
$180$	−1.47369e79	−0.127712
$181$	−3.39462e78	−0.0241658	−0.0120829	−	0.999927i	$-0.503846\pi$
$181$	−3.39462e78	−0.0241658	−0.0120829	+	0.999927i	$0.503846\pi$
$182$	2.74753e80	1.60846
$183$	4.22031e79	0.203391
$184$	4.35694e80	1.73041
$185$	9.58650e79	0.314097
$186$	−6.59089e80	−1.78334
$187$	−1.78383e80	−0.399004
$188$	−1.29795e81	−2.40245
$189$	−2.04116e80	−0.312956
$190$	2.80343e80	0.356399
$191$	−1.66344e81	−1.75518	−0.877592	−	0.479408i	$-0.840852\pi$
$191$	−1.66344e81	−1.75518	−0.877592	+	0.479408i	$0.840852\pi$
$192$	−8.29094e80	−0.726792
$193$	−1.03434e81	−0.754016	−0.377008	−	0.926210i	$-0.623047\pi$
$193$	−1.03434e81	−0.754016	−0.377008	+	0.926210i	$0.623047\pi$
$194$	4.92102e81	2.98603
$195$	−1.33666e80	−0.0675758
$196$	7.41445e81	3.12600
$197$	−4.64267e81	−1.63387	−0.816934	−	0.576731i	$-0.804328\pi$
$197$	−4.64267e81	−1.63387	−0.816934	+	0.576731i	$0.804328\pi$
$198$	9.62053e80	0.282869
$199$	4.16852e81	1.02494	0.512469	−	0.858706i	$-0.328731\pi$
$199$	4.16852e81	1.02494	0.512469	+	0.858706i	$0.328731\pi$
$200$	7.15377e81	1.47221
$201$	−2.93112e81	−0.505328
$202$	1.35262e82	1.95525
$203$	−1.43879e81	−0.174538
$204$	8.62636e81	0.878935
$205$	−4.10637e81	−0.351719
$206$	−3.73073e82	−2.68848
$207$	−6.19433e81	−0.375878
$208$	8.09342e81	0.413889
$209$	−1.19926e82	−0.517273
$210$	−8.85200e81	−0.322297
$211$	−4.43417e82	−1.36391	−0.681954	−	0.731395i	$-0.738870\pi$
$211$	−4.43417e82	−1.36391	−0.681954	+	0.731395i	$0.738870\pi$
$212$	9.58687e82	2.49318
$213$	1.42432e82	0.313424
$214$	−8.28099e82	−1.54310
$215$	−2.50001e80	−0.00394800
$216$	−2.20499e82	−0.295324
$217$	−2.59424e83	−2.94910
$218$	8.32102e82	0.803473
$219$	−3.25667e82	−0.267305
$220$	2.73397e82	0.190893
$221$	7.82421e82	0.465066
$222$	3.02639e83	1.53248
$223$	3.10989e83	1.34252	0.671262	−	0.741220i	$-0.265752\pi$
$223$	3.10989e83	1.34252	0.671262	+	0.741220i	$0.265752\pi$
$224$	−1.41578e83	−0.521426
$225$	−1.01706e83	−0.319793
$226$	−2.35559e83	−0.632776
$227$	−1.26381e83	−0.290244	−0.145122	−	0.989414i	$-0.546357\pi$
$227$	−1.26381e83	−0.290244	−0.145122	+	0.989414i	$0.546357\pi$
$228$	5.79945e83	1.13946
$229$	−8.06014e83	−1.35576	−0.677880	−	0.735173i	$-0.737101\pi$
$229$	−8.06014e83	−1.35576	−0.677880	+	0.735173i	$0.737101\pi$
$230$	−2.68632e83	−0.387097
$231$	3.78673e83	0.467778
$232$	−1.55427e83	−0.164704
$233$	3.72113e81	0.00338485	0.00169242	−	0.999999i	$-0.499461\pi$
$233$	3.72113e81	0.00338485	0.00169242	+	0.999999i	$0.499461\pi$
$234$	−4.21973e83	−0.329702
$235$	3.79288e83	0.254718
$236$	2.64138e84	1.52565
$237$	−1.41782e84	−0.704782
$238$	5.18157e84	2.21809
$239$	2.67567e83	0.0986977	0.0493489	−	0.998782i	$-0.484285\pi$
$239$	2.67567e83	0.0986977	0.0493489	+	0.998782i	$0.484285\pi$
$240$	−2.60753e83	−0.0829337
$241$	−1.52935e84	−0.419664	−0.209832	−	0.977737i	$-0.567292\pi$
$241$	−1.52935e84	−0.419664	−0.209832	+	0.977737i	$0.567292\pi$
$242$	5.40502e84	1.28042
$243$	3.13487e83	0.0641500
$244$	3.78621e84	0.669678
$245$	−2.16666e84	−0.331432
$246$	−1.29635e85	−1.71604
$247$	5.26016e84	0.602917
$248$	−2.80245e85	−2.78294
$249$	8.22308e84	0.707877
$250$	−9.00824e84	−0.672620
$251$	1.17561e85	0.761809	0.380904	−	0.924614i	$-0.375613\pi$
$251$	1.17561e85	0.761809	0.380904	+	0.924614i	$0.375613\pi$
$252$	−1.83121e85	−1.03043
$253$	1.14916e85	0.561827
$254$	−2.04398e85	−0.868719
$255$	−2.52080e84	−0.0931885
$256$	−5.74061e85	−1.84688
$257$	−4.48086e85	−1.25526	−0.627632	−	0.778510i	$-0.715976\pi$
$257$	−4.48086e85	−1.25526	−0.627632	+	0.778510i	$0.715976\pi$
$258$	−7.89237e83	−0.0192623
$259$	1.19122e86	2.53425
$260$	−1.19917e85	−0.222498
$261$	2.20973e84	0.0357768
$262$	5.45818e85	0.771528
$263$	5.67296e85	0.700456	0.350228	−	0.936665i	$-0.386104\pi$
$263$	5.67296e85	0.700456	0.350228	+	0.936665i	$0.386104\pi$
$264$	4.09066e85	0.441422
$265$	−2.80148e85	−0.264338
$266$	3.48354e86	2.87556
$267$	1.02689e86	0.741947
$268$	−2.62962e86	−1.66383
$269$	2.08453e86	1.15558	0.577792	−	0.816184i	$-0.303914\pi$
$269$	2.08453e86	1.15558	0.577792	+	0.816184i	$0.303914\pi$
$270$	1.35951e85	0.0660647
$271$	−3.22985e86	−1.37649	−0.688244	−	0.725479i	$-0.741618\pi$
$271$	−3.22985e86	−1.37649	−0.688244	+	0.725479i	$0.741618\pi$
$272$	1.52634e86	0.570761
$273$	−1.66093e86	−0.545226
$274$	−2.95628e86	−0.852317
$275$	1.88684e86	0.477996
$276$	−5.55718e86	−1.23761
$277$	−2.90954e86	−0.569892	−0.284946	−	0.958544i	$-0.591976\pi$
$277$	−2.90954e86	−0.569892	−0.284946	+	0.958544i	$0.591976\pi$
$278$	−4.14341e86	−0.714114
$279$	3.98430e86	0.604509
$280$	−3.76388e86	−0.502951
$281$	1.34892e87	1.58822	0.794110	−	0.607773i	$-0.207937\pi$
$281$	1.34892e87	1.58822	0.794110	+	0.607773i	$0.207937\pi$
$282$	1.19738e87	1.24277
$283$	−1.10082e85	−0.0100763	−0.00503813	−	0.999987i	$-0.501604\pi$
$283$	−1.10082e85	−0.0100763	−0.00503813	+	0.999987i	$0.501604\pi$
$284$	1.27782e87	1.03197
$285$	−1.69472e86	−0.120811
$286$	7.82838e86	0.492808
$287$	−5.10257e87	−2.83780
$288$	2.17440e86	0.106882
$289$	−8.25204e86	−0.358664
$290$	9.58305e85	0.0368447
$291$	−2.97484e87	−1.01219
$292$	−2.92169e87	−0.880121
$293$	1.75585e87	0.468474	0.234237	−	0.972179i	$-0.424741\pi$
$293$	1.75585e87	0.468474	0.234237	+	0.972179i	$0.424741\pi$
$294$	−6.83998e87	−1.61705
$295$	−7.71865e86	−0.161756
$296$	1.28682e88	2.39146
$297$	−5.81576e86	−0.0958854
$298$	8.18908e87	1.19828
$299$	−5.04043e87	−0.654848
$300$	−9.12448e87	−1.05294
$301$	−3.10651e86	−0.0318539
$302$	1.74825e88	1.59352
$303$	−8.17682e87	−0.662782
$304$	1.02615e88	0.739941
$305$	−1.10641e87	−0.0710022
$306$	−7.95799e87	−0.454666
$307$	−2.36029e87	−0.120103	−0.0600515	−	0.998195i	$-0.519126\pi$
$307$	−2.36029e87	−0.120103	−0.0600515	+	0.998195i	$0.519126\pi$
$308$	3.39723e88	1.54019
$309$	2.25528e88	0.911329
$310$	1.72789e88	0.622551
$311$	1.20155e88	0.386144	0.193072	−	0.981185i	$-0.438155\pi$
$311$	1.20155e88	0.386144	0.193072	+	0.981185i	$0.438155\pi$
$312$	−1.79424e88	−0.514507
$313$	2.53520e88	0.648916	0.324458	−	0.945900i	$-0.394818\pi$
$313$	2.53520e88	0.648916	0.324458	+	0.945900i	$0.394818\pi$
$314$	9.45114e88	2.16014
$315$	5.35117e87	0.109251
$316$	−1.27198e89	−2.32054
$317$	−1.14518e89	−1.86754	−0.933768	−	0.357879i	$-0.883500\pi$
$317$	−1.14518e89	−1.86754	−0.933768	+	0.357879i	$0.883500\pi$
$318$	−8.84408e88	−1.28970
$319$	−4.09946e87	−0.0534759
$320$	2.17358e88	0.253718
$321$	5.00599e88	0.523071
$322$	−3.33802e89	−3.12324
$323$	9.92014e88	0.831435
$324$	2.81242e88	0.211219
$325$	−8.27601e88	−0.557137
$326$	6.00356e88	0.362397
$327$	−5.03019e88	−0.272357
$328$	−5.51211e89	−2.67791
$329$	4.71302e89	2.05516
$330$	−2.52215e88	−0.0987473
$331$	3.59221e89	1.26319	0.631594	−	0.775299i	$-0.282401\pi$
$331$	3.59221e89	1.26319	0.631594	+	0.775299i	$0.282401\pi$
$332$	7.37725e89	2.33073
$333$	−1.82950e89	−0.519472
$334$	3.08756e89	0.788162
$335$	7.68431e88	0.176406
$336$	−3.24012e89	−0.669139
$337$	−2.11747e89	−0.393510	−0.196755	−	0.980453i	$-0.563040\pi$
$337$	−2.11747e89	−0.393510	−0.196755	+	0.980453i	$0.563040\pi$
$338$	6.74789e89	1.12882
$339$	1.42399e89	0.214496
$340$	−2.26151e89	−0.306830
$341$	−7.39160e89	−0.903563
$342$	−5.35011e89	−0.589435
$343$	−1.05506e90	−1.04794
$344$	−3.35585e88	−0.0300592
$345$	1.62392e89	0.131216
$346$	3.63961e90	2.65371
$347$	1.36922e90	0.901106	0.450553	−	0.892750i	$-0.351227\pi$
$347$	1.36922e90	0.901106	0.450553	+	0.892750i	$0.351227\pi$
$348$	1.98244e89	0.117798
$349$	1.57916e90	0.847469	0.423735	−	0.905786i	$-0.360719\pi$
$349$	1.57916e90	0.847469	0.423735	+	0.905786i	$0.360719\pi$
$350$	−5.48078e90	−2.65722
$351$	2.55090e89	0.111761
$352$	−4.03391e89	−0.159758
$353$	−3.09741e90	−1.10917	−0.554584	−	0.832128i	$-0.687123\pi$
$353$	−3.09741e90	−1.10917	−0.554584	+	0.832128i	$0.687123\pi$
$354$	−2.43672e90	−0.789206
$355$	−3.73405e89	−0.109414
$356$	9.21262e90	2.44291
$357$	−3.13234e90	−0.751879
$358$	7.04464e90	1.53113
$359$	−1.53488e89	−0.0302149	−0.0151075	−	0.999886i	$-0.504809\pi$
$359$	−1.53488e89	−0.0302149	−0.0151075	+	0.999886i	$0.504809\pi$
$360$	5.78066e89	0.103095
$361$	4.81882e89	0.0778816
$362$	2.80949e89	0.0411597
$363$	−3.26742e90	−0.434030
$364$	−1.49009e91	−1.79520
$365$	8.53778e89	0.0933143
$366$	−3.49286e90	−0.346419
$367$	−1.43528e91	−1.29209	−0.646043	−	0.763301i	$-0.723577\pi$
$367$	−1.43528e91	−1.29209	−0.646043	+	0.763301i	$0.723577\pi$
$368$	−9.83281e90	−0.803674
$369$	7.83666e90	0.581694
$370$	−7.93407e90	−0.534977
$371$	−3.48112e91	−2.13277
$372$	3.57447e91	1.99039
$373$	−1.57191e91	−0.795726	−0.397863	−	0.917445i	$-0.630248\pi$
$373$	−1.57191e91	−0.795726	−0.397863	+	0.917445i	$0.630248\pi$
$374$	1.47635e91	0.679593
$375$	5.44562e90	0.228001
$376$	5.09130e91	1.93937
$377$	1.79810e90	0.0623297
$378$	1.68933e91	0.533034
$379$	1.25401e90	0.0360255	0.0180127	−	0.999838i	$-0.494266\pi$
$379$	1.25401e90	0.0360255	0.0180127	+	0.999838i	$0.494266\pi$
$380$	−1.52040e91	−0.397777
$381$	1.23562e91	0.294474
$382$	1.37671e92	2.98947
$383$	4.18409e90	0.0828026	0.0414013	−	0.999143i	$-0.486818\pi$
$383$	4.18409e90	0.0828026	0.0414013	+	0.999143i	$0.486818\pi$
$384$	5.83565e91	1.05276
$385$	−9.92741e90	−0.163298
$386$	8.56054e91	1.28426
$387$	4.77106e89	0.00652944
$388$	−2.66884e92	−3.33271
$389$	−3.27265e91	−0.372982	−0.186491	−	0.982457i	$-0.559712\pi$
$389$	−3.27265e91	−0.372982	−0.186491	+	0.982457i	$0.559712\pi$
$390$	1.10626e91	0.115097
$391$	−9.50574e91	−0.903049
$392$	−2.90837e92	−2.52345
$393$	−3.29955e91	−0.261529
$394$	3.84242e92	2.78284
$395$	3.71700e91	0.246034
$396$	−5.21755e91	−0.315710
$397$	1.63217e92	0.903029	0.451515	−	0.892264i	$-0.350884\pi$
$397$	1.63217e92	0.903029	0.451515	+	0.892264i	$0.350884\pi$
$398$	−3.44999e92	−1.74570
$399$	−2.10585e92	−0.974744
$400$	−1.61447e92	−0.683756
$401$	3.12425e91	0.121093	0.0605467	−	0.998165i	$-0.480716\pi$
$401$	3.12425e91	0.121093	0.0605467	+	0.998165i	$0.480716\pi$
$402$	2.42588e92	0.860686
$403$	3.24209e92	1.05316
$404$	−7.33575e92	−2.18226
$405$	−8.21847e90	−0.0223943
$406$	1.19079e92	0.297276
$407$	3.39406e92	0.776458
$408$	−3.38375e92	−0.709516
$409$	−4.44073e92	−0.853644	−0.426822	−	0.904336i	$-0.640367\pi$
$409$	−4.44073e92	−0.853644	−0.426822	+	0.904336i	$0.640367\pi$
$410$	3.39856e92	0.599056
$411$	1.78712e92	0.288914
$412$	2.02331e93	3.00062
$413$	−9.59118e92	−1.30510
$414$	5.12661e92	0.640204
$415$	−2.15579e92	−0.247115
$416$	1.76934e92	0.186208
$417$	2.50476e92	0.242067
$418$	9.92543e92	0.881031
$419$	−6.55398e92	−0.534450	−0.267225	−	0.963634i	$-0.586107\pi$
$419$	−6.55398e92	−0.534450	−0.267225	+	0.963634i	$0.586107\pi$
$420$	4.80075e92	0.359716
$421$	−1.96180e93	−1.35096	−0.675478	−	0.737380i	$-0.736063\pi$
$421$	−1.96180e93	−1.35096	−0.675478	+	0.737380i	$0.736063\pi$
$422$	3.66985e93	2.32304
$423$	−7.23838e92	−0.421268
$424$	−3.76051e93	−2.01261
$425$	−1.56077e93	−0.768303
$426$	−1.17881e93	−0.533831
$427$	−1.37482e93	−0.572871
$428$	4.49107e93	1.72225
$429$	−4.73238e92	−0.167050
$430$	2.06909e91	0.00672432
$431$	−5.42941e92	−0.162484	−0.0812418	−	0.996694i	$-0.525889\pi$
$431$	−5.42941e92	−0.162484	−0.0812418	+	0.996694i	$0.525889\pi$
$432$	4.97626e92	0.137161
$433$	−2.86336e93	−0.727035	−0.363517	−	0.931587i	$-0.618424\pi$
$433$	−2.86336e93	−0.727035	−0.363517	+	0.931587i	$0.618424\pi$
$434$	2.14707e94	5.02297
$435$	−5.79310e91	−0.0124894
$436$	−4.51279e93	−0.896756
$437$	−6.39065e93	−1.17072
$438$	2.69532e93	0.455280
$439$	−2.68753e93	−0.418662	−0.209331	−	0.977845i	$-0.567129\pi$
$439$	−2.68753e93	−0.418662	−0.209331	+	0.977845i	$0.567129\pi$
$440$	−1.07242e93	−0.154097
$441$	4.13488e93	0.548141
$442$	−6.47555e93	−0.792111
$443$	−1.56129e94	−1.76259	−0.881296	−	0.472565i	$-0.843328\pi$
$443$	−1.56129e94	−1.76259	−0.881296	+	0.472565i	$0.843328\pi$
$444$	−1.64132e94	−1.71040
$445$	−2.69212e93	−0.259008
$446$	−2.57384e94	−2.28662
$447$	−4.95043e93	−0.406187
$448$	2.70088e94	2.04709
$449$	1.26225e94	0.883891	0.441946	−	0.897042i	$-0.354288\pi$
$449$	1.26225e94	0.883891	0.441946	+	0.897042i	$0.354288\pi$
$450$	8.41752e93	0.544678
$451$	−1.45384e94	−0.869462
$452$	1.27752e94	0.706242
$453$	−1.05685e94	−0.540163
$454$	1.04597e94	0.494350
$455$	4.35434e93	0.190335
$456$	−2.27487e94	−0.919825
$457$	−8.89356e93	−0.332698	−0.166349	−	0.986067i	$-0.553198\pi$
$457$	−8.89356e93	−0.332698	−0.166349	+	0.986067i	$0.553198\pi$
$458$	6.67081e94	2.30916
$459$	4.81073e93	0.154121
$460$	1.45689e94	0.432039
$461$	4.93930e94	1.35607	0.678036	−	0.735029i	$-0.262831\pi$
$461$	4.93930e94	1.35607	0.678036	+	0.735029i	$0.262831\pi$
$462$	−3.13401e94	−0.796729
$463$	7.06043e94	1.66229	0.831143	−	0.556059i	$-0.187687\pi$
$463$	7.06043e94	1.66229	0.831143	+	0.556059i	$0.187687\pi$
$464$	3.50771e93	0.0764953
$465$	−1.04453e94	−0.211029
$466$	−3.07971e92	−0.00576515
$467$	−9.06267e93	−0.157220	−0.0786099	−	0.996905i	$-0.525048\pi$
$467$	−9.06267e93	−0.157220	−0.0786099	+	0.996905i	$0.525048\pi$
$468$	2.28851e94	0.367981
$469$	9.54851e94	1.42331
$470$	−3.13910e94	−0.433841
$471$	−5.71336e94	−0.732233
$472$	−1.03610e95	−1.23157
$473$	−8.85120e92	−0.00975959
$474$	1.17343e95	1.20040
$475$	−1.04930e95	−0.996037
$476$	−2.81015e95	−2.47561
$477$	5.34639e94	0.437178
$478$	−2.21447e94	−0.168104
$479$	−1.81852e95	−1.28176	−0.640880	−	0.767641i	$-0.721430\pi$
$479$	−1.81852e95	−1.28176	−0.640880	+	0.767641i	$0.721430\pi$
$480$	−5.70046e93	−0.0373118
$481$	−1.48870e95	−0.905015
$482$	1.26574e95	0.714782
$483$	2.01789e95	1.05870
$484$	−2.93133e95	−1.42907
$485$	7.79892e94	0.353348
$486$	−2.59451e94	−0.109262
$487$	6.61058e94	0.258798	0.129399	−	0.991593i	$-0.458695\pi$
$487$	6.61058e94	0.258798	0.129399	+	0.991593i	$0.458695\pi$
$488$	−1.48517e95	−0.540595
$489$	−3.62925e94	−0.122844
$490$	1.79319e95	0.564502
$491$	5.04693e95	1.47786	0.738931	−	0.673781i	$-0.235331\pi$
$491$	5.04693e95	1.47786	0.738931	+	0.673781i	$0.235331\pi$
$492$	7.03058e95	1.91527
$493$	3.39103e94	0.0859540
$494$	−4.35347e95	−1.02690
$495$	1.52468e94	0.0334729
$496$	6.32462e95	1.29251
$497$	−4.63992e95	−0.882793
$498$	−6.80567e95	−1.20567
$499$	2.97625e95	0.491021	0.245511	−	0.969394i	$-0.421044\pi$
$499$	2.97625e95	0.491021	0.245511	+	0.969394i	$0.421044\pi$
$500$	4.88549e95	0.750711
$501$	−1.86648e95	−0.267167
$502$	−9.72969e95	−1.29753
$503$	−6.53298e95	−0.811798	−0.405899	−	0.913918i	$-0.633041\pi$
$503$	−6.53298e95	−0.811798	−0.405899	+	0.913918i	$0.633041\pi$
$504$	7.18304e95	0.831811
$505$	2.14366e95	0.231372
$506$	−9.51081e95	−0.956917
$507$	−4.07921e95	−0.382642
$508$	1.10852e96	0.969578
$509$	2.06565e95	0.168490	0.0842452	−	0.996445i	$-0.473152\pi$
$509$	2.06565e95	0.168490	0.0842452	+	0.996445i	$0.473152\pi$
$510$	2.08629e95	0.158721
$511$	1.06090e96	0.752894
$512$	1.99703e96	1.32221
$513$	3.23422e95	0.199804
$514$	3.70849e96	2.13799
$515$	−5.91252e95	−0.318138
$516$	4.28031e94	0.0214986
$517$	1.34285e96	0.629672
$518$	−9.85887e96	−4.31639
$519$	−2.20020e96	−0.899543
$520$	4.70382e95	0.179611
$521$	2.25325e96	0.803654	0.401827	−	0.915716i	$-0.368375\pi$
$521$	2.25325e96	0.803654	0.401827	+	0.915716i	$0.368375\pi$
$522$	−1.82884e95	−0.0609359
$523$	3.86411e95	0.120293	0.0601464	−	0.998190i	$-0.480843\pi$
$523$	3.86411e95	0.120293	0.0601464	+	0.998190i	$0.480843\pi$
$524$	−2.96016e96	−0.861103
$525$	3.31322e96	0.900730
$526$	−4.69511e96	−1.19303
$527$	6.11425e96	1.45233
$528$	−9.23187e95	−0.205015
$529$	1.30780e96	0.271559
$530$	2.31859e96	0.450226
$531$	1.47304e96	0.267521
$532$	−1.88925e97	−3.20941
$533$	6.37682e96	1.01342
$534$	−8.49883e96	−1.26370
$535$	−1.31238e96	−0.182600
$536$	1.03149e97	1.34312
$537$	−4.25860e96	−0.519014
$538$	−1.72522e97	−1.96822
$539$	−7.67096e96	−0.819310
$540$	−7.37312e95	−0.0737348
$541$	1.09095e97	1.02165	0.510825	−	0.859685i	$-0.329340\pi$
$541$	1.09095e97	1.02165	0.510825	+	0.859685i	$0.329340\pi$
$542$	2.67312e97	2.34447
$543$	−1.69838e95	−0.0139521
$544$	3.33680e96	0.256785
$545$	1.31873e96	0.0950780
$546$	1.37463e97	0.928642
$547$	−4.26238e96	−0.269837	−0.134919	−	0.990857i	$-0.543077\pi$
$547$	−4.26238e96	−0.269837	−0.134919	+	0.990857i	$0.543077\pi$
$548$	1.60330e97	0.951271
$549$	2.11149e96	0.117428
$550$	−1.56160e97	−0.814134
$551$	2.27977e96	0.111432
$552$	2.17984e97	0.999051
$553$	4.61873e97	1.98509
$554$	2.40802e97	0.970653
$555$	4.79627e96	0.181344
$556$	2.24712e97	0.797023
$557$	−1.57602e97	−0.524449	−0.262225	−	0.965007i	$-0.584456\pi$
$557$	−1.57602e97	−0.524449	−0.262225	+	0.965007i	$0.584456\pi$
$558$	−3.29752e97	−1.02961
$559$	3.88229e95	0.0113755
$560$	8.49439e96	0.233592
$561$	−8.92480e96	−0.230365
$562$	−1.11640e98	−2.70509
$563$	−7.36686e97	−1.67585	−0.837923	−	0.545788i	$-0.816230\pi$
$563$	−7.36686e97	−1.67585	−0.837923	+	0.545788i	$0.816230\pi$
$564$	−6.49384e97	−1.38705
$565$	−3.73318e96	−0.0748788
$566$	9.11076e95	0.0171621
$567$	−1.02123e97	−0.180685
$568$	−5.01233e97	−0.833055
$569$	−3.73954e96	−0.0583893	−0.0291946	−	0.999574i	$-0.509294\pi$
$569$	−3.73954e96	−0.0583893	−0.0291946	+	0.999574i	$0.509294\pi$
$570$	1.40260e97	0.205767
$571$	−6.30034e96	−0.0868524	−0.0434262	−	0.999057i	$-0.513827\pi$
$571$	−6.30034e96	−0.0868524	−0.0434262	+	0.999057i	$0.513827\pi$
$572$	−4.24561e97	−0.550023
$573$	−8.32245e97	−1.01336
$574$	4.22304e98	4.83340
$575$	1.00546e98	1.08183
$576$	−4.14809e97	−0.419614
$577$	−9.11194e97	−0.866701	−0.433351	−	0.901225i	$-0.642669\pi$
$577$	−9.11194e97	−0.866701	−0.433351	+	0.901225i	$0.642669\pi$
$578$	6.82963e97	0.610885
$579$	−5.17498e97	−0.435331
$580$	−5.19723e96	−0.0411223
$581$	−2.67878e98	−1.99381
$582$	2.46206e98	1.72398
$583$	−9.91853e97	−0.653452
$584$	1.14605e98	0.710474
$585$	−6.68750e96	−0.0390149
$586$	−1.45319e98	−0.797916
$587$	−1.87146e98	−0.967227	−0.483614	−	0.875282i	$-0.660676\pi$
$587$	−1.87146e98	−0.967227	−0.483614	+	0.875282i	$0.660676\pi$
$588$	3.70956e98	1.80479
$589$	4.11057e98	1.88282
$590$	6.38819e97	0.275506
$591$	−2.32280e98	−0.943314
$592$	−2.90413e98	−1.11070
$593$	−7.95555e97	−0.286569	−0.143284	−	0.989682i	$-0.545766\pi$
$593$	−7.95555e97	−0.286569	−0.143284	+	0.989682i	$0.545766\pi$
$594$	4.81330e97	0.163314
$595$	8.21184e97	0.262475
$596$	−4.44123e98	−1.33740
$597$	2.08558e98	0.591749
$598$	4.17161e98	1.11535
$599$	1.38081e98	0.347922	0.173961	−	0.984753i	$-0.444343\pi$
$599$	1.38081e98	0.347922	0.173961	+	0.984753i	$0.444343\pi$
$600$	3.57914e98	0.849981
$601$	−6.80788e97	−0.152394	−0.0761970	−	0.997093i	$-0.524278\pi$
$601$	−6.80788e97	−0.152394	−0.0761970	+	0.997093i	$0.524278\pi$
$602$	2.57104e97	0.0542543
$603$	−1.46648e98	−0.291751
$604$	−9.48138e98	−1.77853
$605$	8.56596e97	0.151517
$606$	6.76738e98	1.12887
$607$	−2.30083e98	−0.361981	−0.180991	−	0.983485i	$-0.557930\pi$
$607$	−2.30083e98	−0.361981	−0.180991	+	0.983485i	$0.557930\pi$
$608$	2.24331e98	0.332899
$609$	−7.19850e97	−0.100769
$610$	9.15698e97	0.120932
$611$	−5.88999e98	−0.733925
$612$	4.31590e98	0.507453
$613$	7.42749e98	0.824129	0.412064	−	0.911155i	$-0.364808\pi$
$613$	7.42749e98	0.824129	0.412064	+	0.911155i	$0.364808\pi$
$614$	1.95345e98	0.204562
$615$	−2.05448e98	−0.203065
$616$	−1.33259e99	−1.24331
$617$	1.98937e99	1.75223	0.876115	−	0.482102i	$-0.160126\pi$
$617$	1.98937e99	1.75223	0.876115	+	0.482102i	$0.160126\pi$
$618$	−1.86654e99	−1.55220
$619$	1.66616e99	1.30827	0.654135	−	0.756378i	$-0.273033\pi$
$619$	1.66616e99	1.30827	0.654135	+	0.756378i	$0.273033\pi$
$620$	−9.37094e98	−0.694829
$621$	−3.09912e98	−0.217013
$622$	−9.94440e98	−0.657688
$623$	−3.34522e99	−2.08977
$624$	4.04926e98	0.238959
$625$	1.57804e99	0.879784
$626$	−2.09821e99	−1.10525
$627$	−6.00008e98	−0.298648
$628$	−5.12569e99	−2.41093
$629$	−2.80753e99	−1.24803
$630$	−4.42879e98	−0.186078
$631$	3.31380e99	1.31609	0.658043	−	0.752980i	$-0.271385\pi$
$631$	3.31380e99	1.31609	0.658043	+	0.752980i	$0.271385\pi$
$632$	4.98944e99	1.87325
$633$	−2.21848e99	−0.787453
$634$	9.47783e99	3.18083
$635$	−3.23933e98	−0.102799
$636$	4.79646e99	1.43944
$637$	3.36462e99	0.954962
$638$	3.39284e98	0.0910813
$639$	7.12611e98	0.180956
$640$	−1.52989e99	−0.367512
$641$	−4.71728e99	−1.07209	−0.536045	−	0.844189i	$-0.680082\pi$
$641$	−4.71728e99	−1.07209	−0.536045	+	0.844189i	$0.680082\pi$
$642$	−4.14310e99	−0.890907
$643$	5.29762e98	0.107793	0.0538966	−	0.998547i	$-0.482836\pi$
$643$	5.29762e98	0.107793	0.0538966	+	0.998547i	$0.482836\pi$
$644$	1.81033e100	3.48585
$645$	−1.25080e97	−0.00227938
$646$	−8.21021e99	−1.41612
$647$	1.03238e100	1.68553	0.842764	−	0.538283i	$-0.180927\pi$
$647$	1.03238e100	1.68553	0.842764	+	0.538283i	$0.180927\pi$
$648$	−1.10319e99	−0.170505
$649$	−2.73276e99	−0.399866
$650$	6.84948e99	0.948928
$651$	−1.29794e100	−1.70266
$652$	−3.25595e99	−0.404471
$653$	−1.44262e100	−1.69721	−0.848603	−	0.529030i	$-0.822556\pi$
$653$	−1.44262e100	−1.69721	−0.848603	+	0.529030i	$0.822556\pi$
$654$	4.16314e99	0.463885
$655$	8.65021e98	0.0912978
$656$	1.24398e100	1.24373
$657$	−1.62936e99	−0.154329
$658$	−3.90064e100	−3.50039
$659$	2.23730e100	1.90236	0.951178	−	0.308644i	$-0.0998752\pi$
$659$	2.23730e100	1.90236	0.951178	+	0.308644i	$0.0998752\pi$
$660$	1.36785e99	0.110212
$661$	7.29918e99	0.557343	0.278671	−	0.960387i	$-0.410106\pi$
$661$	7.29918e99	0.557343	0.278671	+	0.960387i	$0.410106\pi$
$662$	−2.97302e100	−2.15149
$663$	3.91457e99	0.268506
$664$	−2.89378e100	−1.88147
$665$	5.52077e99	0.340276
$666$	1.51415e100	0.884777
$667$	−2.18453e99	−0.121030
$668$	−1.67449e100	−0.879667
$669$	1.55593e100	0.775107
$670$	−6.35976e99	−0.300459
$671$	−3.91720e99	−0.175520
$672$	−7.08339e99	−0.301045
$673$	4.23066e100	1.70559	0.852793	−	0.522248i	$-0.174907\pi$
$673$	4.23066e100	1.70559	0.852793	+	0.522248i	$0.174907\pi$
$674$	1.75248e100	0.670236
$675$	−5.08852e99	−0.184632
$676$	−3.65962e100	−1.25988
$677$	−3.80823e100	−1.24401	−0.622007	−	0.783011i	$-0.713683\pi$
$677$	−3.80823e100	−1.24401	−0.622007	+	0.783011i	$0.713683\pi$
$678$	−1.17854e100	−0.365334
$679$	9.69092e100	2.85094
$680$	8.87093e99	0.247687
$681$	−6.32303e99	−0.167572
$682$	6.11751e100	1.53897
$683$	1.41337e99	0.0337537	0.0168768	−	0.999858i	$-0.494628\pi$
$683$	1.41337e99	0.0337537	0.0168768	+	0.999858i	$0.494628\pi$
$684$	2.90155e100	0.657868
$685$	−4.68517e99	−0.100858
$686$	8.73203e100	1.78488
$687$	−4.03261e100	−0.782748
$688$	7.57353e98	0.0139607
$689$	4.35044e100	0.761642
$690$	−1.34401e100	−0.223491
$691$	−3.94804e100	−0.623607	−0.311804	−	0.950147i	$-0.600933\pi$
$691$	−3.94804e100	−0.623607	−0.311804	+	0.950147i	$0.600933\pi$
$692$	−1.97389e101	−2.96181
$693$	1.89456e100	0.270072
$694$	−1.13321e101	−1.53478
$695$	−6.56654e99	−0.0845038
$696$	−7.77626e99	−0.0950917
$697$	1.20260e101	1.39752
$698$	−1.30696e101	−1.44343
$699$	1.86174e98	0.00195424
$700$	2.97242e101	2.96572
$701$	−1.34811e101	−1.27860	−0.639299	−	0.768958i	$-0.720776\pi$
$701$	−1.34811e101	−1.27860	−0.639299	+	0.768958i	$0.720776\pi$
$702$	−2.11120e100	−0.190354
$703$	−1.88748e101	−1.61796
$704$	7.69546e100	0.627199
$705$	1.89764e100	0.147062
$706$	2.56351e101	1.88916
$707$	2.66371e101	1.86680
$708$	1.32152e101	0.880833
$709$	1.12193e101	0.711254	0.355627	−	0.934628i	$-0.384267\pi$
$709$	1.12193e101	0.711254	0.355627	+	0.934628i	$0.384267\pi$
$710$	3.09041e100	0.186357
$711$	−7.09357e100	−0.406906
$712$	−3.61371e101	−1.97203
$713$	−3.93886e101	−2.04499
$714$	2.59242e101	1.28062
$715$	1.24066e100	0.0583158
$716$	−3.82056e101	−1.70889
$717$	1.33868e100	0.0569832
$718$	1.27031e100	0.0514628
$719$	−5.31513e100	−0.204945	−0.102473	−	0.994736i	$-0.532675\pi$
$719$	−5.31513e100	−0.204945	−0.102473	+	0.994736i	$0.532675\pi$
$720$	−1.30459e100	−0.0478818
$721$	−7.34689e101	−2.56686
$722$	−3.98820e100	−0.132650
$723$	−7.65158e100	−0.242293
$724$	−1.52368e100	−0.0459384
$725$	−3.58684e100	−0.102971
$726$	2.70421e101	0.739249
$727$	−2.12328e101	−0.552759	−0.276380	−	0.961049i	$-0.589135\pi$
$727$	−2.12328e101	−0.552759	−0.276380	+	0.961049i	$0.589135\pi$
$728$	5.84496e101	1.44916
$729$	1.56842e100	0.0370370
$730$	−7.06612e100	−0.158935
$731$	7.32161e99	0.0156870
$732$	1.89430e101	0.386639
$733$	1.73914e101	0.338176	0.169088	−	0.985601i	$-0.445918\pi$
$733$	1.73914e101	0.338176	0.169088	+	0.985601i	$0.445918\pi$
$734$	1.18788e102	2.20071
$735$	−1.08401e101	−0.191352
$736$	−2.14960e101	−0.361572
$737$	2.72060e101	0.436082
$738$	−6.48585e101	−0.990755
$739$	−7.18574e101	−1.04615	−0.523075	−	0.852287i	$-0.675215\pi$
$739$	−7.18574e101	−1.04615	−0.523075	+	0.852287i	$0.675215\pi$
$740$	4.30293e101	0.597088
$741$	2.63174e101	0.348094
$742$	2.88108e102	3.63259
$743$	9.36903e101	1.12614	0.563069	−	0.826410i	$-0.309620\pi$
$743$	9.36903e101	1.12614	0.563069	+	0.826410i	$0.309620\pi$
$744$	−1.40211e102	−1.60673
$745$	1.29782e101	0.141797
$746$	1.30096e102	1.35530
$747$	4.11413e101	0.408693
$748$	−8.00679e101	−0.758493
$749$	−1.63077e102	−1.47329
$750$	−4.50696e101	−0.388337
$751$	−5.13495e101	−0.422006	−0.211003	−	0.977485i	$-0.567673\pi$
$751$	−5.13495e101	−0.422006	−0.211003	+	0.977485i	$0.567673\pi$
$752$	−1.14901e102	−0.900723
$753$	5.88175e101	0.439830
$754$	−1.48816e101	−0.106161
$755$	2.77066e101	0.188567
$756$	−9.16182e101	−0.594920
$757$	−3.50586e101	−0.217216	−0.108608	−	0.994085i	$-0.534639\pi$
$757$	−3.50586e101	−0.217216	−0.108608	+	0.994085i	$0.534639\pi$
$758$	−1.03786e101	−0.0613594
$759$	5.74944e101	0.324371
$760$	5.96387e101	0.321104
$761$	−1.05001e102	−0.539557	−0.269779	−	0.962922i	$-0.586951\pi$
$761$	−1.05001e102	−0.539557	−0.269779	+	0.962922i	$0.586951\pi$
$762$	−1.02263e102	−0.501555
$763$	1.63865e102	0.767124
$764$	−7.46641e102	−3.33655
$765$	−1.26120e101	−0.0538024
$766$	−3.46287e101	−0.141031
$767$	1.19864e102	0.466071
$768$	−2.87211e102	−1.06630
$769$	2.15812e102	0.765050	0.382525	−	0.923945i	$-0.375055\pi$
$769$	2.15812e102	0.765050	0.382525	+	0.923945i	$0.375055\pi$
$770$	8.21622e101	0.278132
$771$	−2.24184e102	−0.724727
$772$	−4.64269e102	−1.43336
$773$	3.49930e102	1.03183	0.515916	−	0.856639i	$-0.327451\pi$
$773$	3.49930e102	1.03183	0.515916	+	0.856639i	$0.327451\pi$
$774$	−3.94867e100	−0.0111211
$775$	−6.46731e102	−1.73986
$776$	1.04687e103	2.69031
$777$	5.95984e102	1.46315
$778$	2.70854e102	0.635272
$779$	8.08503e102	1.81176
$780$	−5.99963e101	−0.128459
$781$	−1.32202e102	−0.270475
$782$	7.86724e102	1.53809
$783$	1.10556e101	0.0206558
$784$	6.56365e102	1.17199
$785$	1.49783e102	0.255617
$786$	2.73081e102	0.445442
$787$	−9.36346e102	−1.45993	−0.729967	−	0.683482i	$-0.760465\pi$
$787$	−9.36346e102	−1.45993	−0.729967	+	0.683482i	$0.760465\pi$
$788$	−2.08388e103	−3.10593
$789$	2.83827e102	0.404408
$790$	−3.07630e102	−0.419051
$791$	−4.63884e102	−0.604149
$792$	2.04662e102	0.254855
$793$	1.71815e102	0.204580
$794$	−1.35083e103	−1.53806
$795$	−1.40162e102	−0.152615
$796$	1.87105e103	1.94837
$797$	9.13288e102	0.909573	0.454786	−	0.890601i	$-0.349716\pi$
$797$	9.13288e102	0.909573	0.454786	+	0.890601i	$0.349716\pi$
$798$	1.74287e103	1.66021
$799$	−1.11079e103	−1.01210
$800$	−3.52948e102	−0.307622
$801$	5.13768e102	0.428363
$802$	−2.58572e102	−0.206249
$803$	3.02276e102	0.230676
$804$	−1.31564e103	−0.960612
$805$	−5.29015e102	−0.369585
$806$	−2.68325e103	−1.79377
$807$	1.04292e103	0.667177
$808$	2.87750e103	1.76162
$809$	−6.62764e102	−0.388317	−0.194159	−	0.980970i	$-0.562198\pi$
$809$	−6.62764e102	−0.388317	−0.194159	+	0.980970i	$0.562198\pi$
$810$	6.80185e101	0.0381425
$811$	1.94214e103	1.04241	0.521206	−	0.853431i	$-0.325482\pi$
$811$	1.94214e103	1.04241	0.521206	+	0.853431i	$0.325482\pi$
$812$	−6.45807e102	−0.331790
$813$	−1.61594e103	−0.794716
$814$	−2.80903e103	−1.32248
$815$	9.51455e101	0.0428838
$816$	7.63650e102	0.329529
$817$	4.92227e101	0.0203368
$818$	3.67528e103	1.45395
$819$	−8.30988e102	−0.314787
$820$	−1.84316e103	−0.668607
$821$	−1.93712e103	−0.672936	−0.336468	−	0.941695i	$-0.609232\pi$
$821$	−1.93712e103	−0.672936	−0.336468	+	0.941695i	$0.609232\pi$
$822$	−1.47907e103	−0.492085
$823$	3.09538e103	0.986324	0.493162	−	0.869937i	$-0.335841\pi$
$823$	3.09538e103	0.986324	0.493162	+	0.869937i	$0.335841\pi$
$824$	−7.93656e103	−2.42223
$825$	9.44015e102	0.275971
$826$	7.93795e103	2.22288
$827$	−1.04573e103	−0.280526	−0.140263	−	0.990114i	$-0.544795\pi$
$827$	−1.04573e103	−0.280526	−0.140263	+	0.990114i	$0.544795\pi$
$828$	−2.78034e103	−0.714532
$829$	−6.78277e102	−0.167002	−0.0835010	−	0.996508i	$-0.526610\pi$
$829$	−6.78277e102	−0.167002	−0.0835010	+	0.996508i	$0.526610\pi$
$830$	1.78419e103	0.420891
$831$	−1.45569e103	−0.329027
$832$	−3.37537e103	−0.731043
$833$	6.34533e103	1.31691
$834$	−2.07301e103	−0.412294
$835$	4.89321e102	0.0932661
$836$	−5.38291e103	−0.983319
$837$	1.99341e103	0.349013
$838$	5.42427e103	0.910287
$839$	−6.49133e103	−1.04420	−0.522100	−	0.852884i	$-0.674851\pi$
$839$	−6.49133e103	−1.04420	−0.522100	+	0.852884i	$0.674851\pi$
$840$	−1.88313e103	−0.290379
$841$	−6.68692e103	−0.988480
$842$	1.62365e104	2.30098
$843$	6.74884e103	0.916960
$844$	−1.99029e104	−2.59274
$845$	1.06942e103	0.133578
$846$	5.99070e103	0.717513
$847$	1.06440e104	1.22249
$848$	8.48679e103	0.934740
$849$	−5.50760e101	−0.00581754
$850$	1.29174e104	1.30859
$851$	1.80864e104	1.75732
$852$	6.39312e103	0.595809
$853$	1.21482e104	1.08598	0.542988	−	0.839741i	$-0.317293\pi$
$853$	1.21482e104	1.08598	0.542988	+	0.839741i	$0.317293\pi$
$854$	1.13784e104	0.975727
$855$	−8.47894e102	−0.0697500
$856$	−1.76165e104	−1.39028
$857$	−1.22652e104	−0.928658	−0.464329	−	0.885663i	$-0.653704\pi$
$857$	−1.22652e104	−0.928658	−0.464329	+	0.885663i	$0.653704\pi$
$858$	3.91666e103	0.284523
$859$	−2.30125e104	−1.60401	−0.802005	−	0.597317i	$-0.796233\pi$
$859$	−2.30125e104	−1.60401	−0.802005	+	0.597317i	$0.796233\pi$
$860$	−1.12214e102	−0.00750502
$861$	−2.55290e104	−1.63840
$862$	4.49354e103	0.276746
$863$	−2.76172e104	−1.63228	−0.816142	−	0.577851i	$-0.803892\pi$
$863$	−2.76172e104	−1.63228	−0.816142	+	0.577851i	$0.803892\pi$
$864$	1.08788e103	0.0617085
$865$	5.76812e103	0.314024
$866$	2.36980e104	1.23830
$867$	−4.12862e103	−0.207075
$868$	−1.16443e105	−5.60614
$869$	1.31599e104	0.608205
$870$	4.79455e102	0.0212723
$871$	−1.19330e104	−0.508283
$872$	1.77017e104	0.723902
$873$	−1.48836e104	−0.584388
$874$	5.28909e104	1.99400
$875$	−1.77398e104	−0.642191
$876$	−1.46177e104	−0.508138
$877$	−8.25117e103	−0.275442	−0.137721	−	0.990471i	$-0.543978\pi$
$877$	−8.25117e103	−0.275442	−0.137721	+	0.990471i	$0.543978\pi$
$878$	2.22428e104	0.713075
$879$	8.78477e103	0.270474
$880$	2.42025e103	0.0715692
$881$	1.26306e104	0.358738	0.179369	−	0.983782i	$-0.442594\pi$
$881$	1.26306e104	0.358738	0.179369	+	0.983782i	$0.442594\pi$
$882$	−3.42215e104	−0.933607
$883$	6.07815e104	1.59282	0.796409	−	0.604758i	$-0.206730\pi$
$883$	6.07815e104	1.59282	0.796409	+	0.604758i	$0.206730\pi$
$884$	3.51192e104	0.884075
$885$	−3.86176e103	−0.0933897
$886$	1.29217e105	3.00209
$887$	−7.44473e104	−1.66173	−0.830865	−	0.556475i	$-0.812154\pi$
$887$	−7.44473e104	−1.66173	−0.830865	+	0.556475i	$0.812154\pi$
$888$	6.43818e104	1.38071
$889$	−4.02519e104	−0.829419
$890$	2.22808e104	0.441149
$891$	−2.90972e103	−0.0553595
$892$	1.39588e105	2.55210
$893$	−7.46779e104	−1.31209
$894$	4.09712e104	0.691827
$895$	1.11645e104	0.181184
$896$	−1.90104e105	−2.96522
$897$	−2.52180e104	−0.378077
$898$	−1.04467e105	−1.50546
$899$	1.40513e104	0.194647
$900$	−4.56512e104	−0.607915
$901$	8.20450e104	1.05032
$902$	1.20325e105	1.48089
$903$	−1.55424e103	−0.0183909
$904$	−5.01116e104	−0.570110
$905$	4.45252e102	0.00487059
$906$	8.74677e104	0.920018
$907$	1.28660e105	1.30133	0.650663	−	0.759366i	$-0.274491\pi$
$907$	1.28660e105	1.30133	0.650663	+	0.759366i	$0.274491\pi$
$908$	−5.67264e104	−0.551744
$909$	−4.09099e104	−0.382658
$910$	−3.60378e104	−0.324182
$911$	−3.76696e103	−0.0325903	−0.0162952	−	0.999867i	$-0.505187\pi$
$911$	−3.76696e103	−0.0325903	−0.0162952	+	0.999867i	$0.505187\pi$
$912$	5.13397e104	0.427205
$913$	−7.63247e104	−0.610876
$914$	7.36058e104	0.566659
$915$	−5.53554e103	−0.0409931
$916$	−3.61782e105	−2.57725
$917$	1.07487e105	0.736624
$918$	−3.98151e104	−0.262502
$919$	9.80319e104	0.621823	0.310912	−	0.950439i	$-0.399366\pi$
$919$	9.80319e104	0.621823	0.310912	+	0.950439i	$0.399366\pi$
$920$	−5.71474e104	−0.348761
$921$	−1.18089e104	−0.0693414
$922$	−4.08791e105	−2.30969
$923$	5.79863e104	0.315257
$924$	1.69969e105	0.889230
$925$	2.96965e105	1.49511
$926$	−5.84342e105	−2.83124
$927$	1.12835e105	0.526156
$928$	7.66838e103	0.0344152
$929$	3.51816e105	1.51970	0.759850	−	0.650098i	$-0.225272\pi$
$929$	3.51816e105	1.51970	0.759850	+	0.650098i	$0.225272\pi$
$930$	8.64488e104	0.359430
$931$	4.26592e105	1.70726
$932$	1.67024e103	0.00643448
$933$	6.01155e104	0.222940
$934$	7.50054e104	0.267780
$935$	2.33975e104	0.0804188
$936$	−8.97684e104	−0.297051
$937$	−5.10802e105	−1.62741	−0.813706	−	0.581277i	$-0.802553\pi$
$937$	−5.10802e105	−1.62741	−0.813706	+	0.581277i	$0.802553\pi$
$938$	−7.90263e105	−2.42421
$939$	1.26840e105	0.374652
$940$	1.70244e105	0.484211
$941$	1.80732e104	0.0494997	0.0247499	−	0.999694i	$-0.492121\pi$
$941$	1.80732e104	0.0494997	0.0247499	+	0.999694i	$0.492121\pi$
$942$	4.72855e105	1.24716
$943$	−7.74729e105	−1.96782
$944$	2.33828e105	0.571994
$945$	2.67727e104	0.0630759
$946$	7.32552e103	0.0166228
$947$	1.64655e105	0.359874	0.179937	−	0.983678i	$-0.442411\pi$
$947$	1.64655e105	0.359874	0.179937	+	0.983678i	$0.442411\pi$
$948$	−6.36392e105	−1.33977
$949$	−1.32584e105	−0.268869
$950$	8.68430e105	1.69647
$951$	−5.72950e105	−1.07822
$952$	1.10230e106	1.99843
$953$	−1.05816e105	−0.184822	−0.0924111	−	0.995721i	$-0.529457\pi$
$953$	−1.05816e105	−0.184822	−0.0924111	+	0.995721i	$0.529457\pi$
$954$	−4.42483e105	−0.744611
$955$	2.18184e105	0.353755
$956$	1.20098e105	0.187621
$957$	−2.05103e104	−0.0308743
$958$	1.50506e106	2.18312
$959$	−5.82178e105	−0.813758
$960$	1.08747e105	0.146484
$961$	1.76320e106	2.28887
$962$	1.23209e106	1.54144
$963$	2.50457e105	0.301995
$964$	−6.86454e105	−0.797768
$965$	1.35669e105	0.151971
$966$	−1.67006e106	−1.80320
$967$	−1.82207e106	−1.89638	−0.948188	−	0.317709i	$-0.897087\pi$
$967$	−1.82207e106	−1.89638	−0.948188	+	0.317709i	$0.897087\pi$
$968$	1.14983e106	1.15361
$969$	4.96320e105	0.480029
$970$	−6.45462e105	−0.601830
$971$	1.26353e106	1.13580	0.567902	−	0.823096i	$-0.307755\pi$
$971$	1.26353e106	1.13580	0.567902	+	0.823096i	$0.307755\pi$
$972$	1.40710e105	0.121947
$973$	−8.15958e105	−0.681807
$974$	−5.47111e105	−0.440791
$975$	−4.14062e105	−0.321663
$976$	3.35175e105	0.251075
$977$	−1.55091e106	−1.12029	−0.560143	−	0.828396i	$-0.689254\pi$
$977$	−1.55091e106	−1.12029	−0.560143	+	0.828396i	$0.689254\pi$
$978$	3.00368e105	0.209230
$979$	−9.53133e105	−0.640277
$980$	−9.72510e105	−0.630041
$981$	−2.51668e105	−0.157246
$982$	−4.17699e106	−2.51713
$983$	−2.85037e105	−0.165673	−0.0828365	−	0.996563i	$-0.526398\pi$
$983$	−2.85037e105	−0.165673	−0.0828365	+	0.996563i	$0.526398\pi$
$984$	−2.75779e106	−1.54609
$985$	6.08952e105	0.329304
$986$	−2.80652e105	−0.146399
$987$	2.35800e106	1.18655
$988$	2.36104e106	1.14613
$989$	−4.71665e104	−0.0220885
$990$	−1.26187e105	−0.0570118
$991$	−2.98004e106	−1.29900	−0.649498	−	0.760363i	$-0.725021\pi$
$991$	−2.98004e106	−1.29900	−0.649498	+	0.760363i	$0.725021\pi$
$992$	1.38266e106	0.581501
$993$	1.79724e106	0.729302
$994$	3.84014e106	1.50359
$995$	−5.46761e105	−0.206575
$996$	3.69095e106	1.34565
$997$	−3.42704e106	−1.20570	−0.602852	−	0.797853i	$-0.705969\pi$
$997$	−3.42704e106	−1.20570	−0.602852	+	0.797853i	$0.705969\pi$
$998$	−2.46324e106	−0.836319
$999$	−9.15327e105	−0.299917

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.72.a.a.1.1	✓	5
3.2	odd	2		9.72.a.a.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.72.a.a.1.1	✓	5	1.1	even	1	trivial
9.72.a.a.1.5		5	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 72 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-8.27630e10 q^{2} +5.00315e16 q^{3} +4.48853e21 q^{4} -1.31164e24 q^{5} -4.14076e27 q^{6} -1.62984e30 q^{7} -1.76066e32 q^{8} +2.50316e33 q^{9} +O(q^{10})\)	\(q-8.27630e10 q^{2} +5.00315e16 q^{3} +4.48853e21 q^{4} -1.31164e24 q^{5} -4.14076e27 q^{6} -1.62984e30 q^{7} -1.76066e32 q^{8} +2.50316e33 q^{9} +1.08555e35 q^{10} -4.64381e36 q^{11} +2.24568e38 q^{12} +2.03686e39 q^{13} +1.34891e41 q^{14} -6.56235e40 q^{15} +3.97348e42 q^{16} +3.84131e43 q^{17} -2.07169e44 q^{18} +2.58249e45 q^{19} -5.88734e45 q^{20} -8.15436e46 q^{21} +3.84336e47 q^{22} -2.47461e48 q^{23} -8.80884e48 q^{24} -4.06312e49 q^{25} -1.68577e50 q^{26} +1.25237e50 q^{27} -7.31560e51 q^{28} +8.82779e50 q^{29} +5.43119e51 q^{30} +1.59171e53 q^{31} +8.68663e52 q^{32} -2.32337e53 q^{33} -3.17918e54 q^{34} +2.13777e54 q^{35} +1.12355e55 q^{36} -7.30878e55 q^{37} -2.13734e56 q^{38} +1.01907e56 q^{39} +2.30935e56 q^{40} +3.13071e57 q^{41} +6.74879e57 q^{42} +1.90602e56 q^{43} -2.08439e58 q^{44} -3.28324e57 q^{45} +2.04806e59 q^{46} -2.89170e59 q^{47} +1.98799e59 q^{48} +1.65187e60 q^{49} +3.36276e60 q^{50} +1.92187e60 q^{51} +9.14251e60 q^{52} +2.13586e61 q^{53} -1.03650e61 q^{54} +6.09102e60 q^{55} +2.86960e62 q^{56} +1.29206e62 q^{57} -7.30615e61 q^{58} +5.88472e62 q^{59} -2.94553e62 q^{60} +8.43530e62 q^{61} -1.31735e64 q^{62} -4.07975e63 q^{63} -1.65714e64 q^{64} -2.67163e63 q^{65} +1.92289e64 q^{66} -5.85854e64 q^{67} +1.72418e65 q^{68} -1.23808e65 q^{69} -1.76928e65 q^{70} +2.84685e65 q^{71} -4.40720e65 q^{72} -6.50923e65 q^{73} +6.04896e66 q^{74} -2.03284e66 q^{75} +1.15916e67 q^{76} +7.56869e66 q^{77} -8.43415e66 q^{78} -2.83385e67 q^{79} -5.21178e66 q^{80} +6.26579e66 q^{81} -2.59107e68 q^{82} +1.64358e68 q^{83} -3.66011e68 q^{84} -5.03842e67 q^{85} -1.57748e67 q^{86} +4.41668e67 q^{87} +8.17616e68 q^{88} +2.05248e69 q^{89} +2.71731e68 q^{90} -3.31976e69 q^{91} -1.11074e70 q^{92} +7.96357e69 q^{93} +2.39326e70 q^{94} -3.38730e69 q^{95} +4.34605e69 q^{96} -5.94592e70 q^{97} -1.36713e71 q^{98} -1.16242e70 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 25051277688 q^{2} + 25\!\cdots\!35 q^{3}+ \cdots + 12\!\cdots\!45 q^{9}+O(q^{10}) \) 5 * q - 25051277688 * q^2 + 250157725494998535 * q^3 + 1907299462927273154624 * q^4 + 1422573866433399534277830 * q^5 - 1253354129434737111087637416 * q^6 - 1261222231854515600228814346952 * q^7 - 151958919976138936299686009691648 * q^8 + 12515777524966208006577859930429245 * q^9	\( 5 q - 25051277688 q^{2} + 25\!\cdots\!35 q^{3}+ \cdots + 33\!\cdots\!88 q^{99}+O(q^{100}) \) 5 * q - 25051277688 * q^2 + 250157725494998535 * q^3 + 1907299462927273154624 * q^4 + 1422573866433399534277830 * q^5 - 1253354129434737111087637416 * q^6 - 1261222231854515600228814346952 * q^7 - 151958919976138936299686009691648 * q^8 + 12515777524966208006577859930429245 * q^9 - 308853354401574193552393248717551760 * q^10 + 1357894937151168401938494740936725812 * q^11 + 95425139096743786553920018696741695168 * q^12 - 3732312012481108743024076959256483425602 * q^13 + 178792454794792302794525709930294541693632 * q^14 + 71173568555121014264963983054791626595810 * q^15 - 2761767053096261549691112453399712883798016 * q^16 - 277325542902069263625709674624672840731910 * q^17 - 62707243651831565917830179941990275506237112 * q^18 + 2937432205918421125744856768913127977845719948 * q^19 - 24911205133324082416992380941498137854677077120 * q^20 - 63100896972890262121533046345756354145644343064 * q^21 + 981344865457378177927521236701073576051567611680 * q^22 - 4228346897979680919198407557464543114207597141624 * q^23 - 7602739557981482671404075764718702187632312347136 * q^24 + 19633070396484105587134362494981426945191834668275 * q^25 - 163733269614894222914401413204168398319516301314000 * q^26 + 626183687689393767209300272665229846333060639231215 * q^27 - 5768362424640263225567110092226485193092350431463936 * q^28 - 3697116438725251267139482122013539208885912739684274 * q^29 - 15452410529719698927278278181356603942084949997334320 * q^30 + 74551273173252500835223325068153865117486542141504384 * q^31 - 639756106869108826481408208267665768107401476101865472 * q^32 + 67937581787782054618912973363008350989516300927337084 * q^33 - 6217683238533672509931589234500437242788961796499134832 * q^34 - 13153074146721234298498045726570273336863567981003778800 * q^35 + 4774267150297056921454723864735495027586024236315315776 * q^36 - 160060519909409459305929258566699075666754182654348019002 * q^37 - 91685642067030133239673763998240213415299939628290081056 * q^38 - 186733336775986949394712651065025829961603412074954298614 * q^39 + 755753872880123511491678719028119895299413298470522117120 * q^40 + 2279706853693741369685932186247543106805520151549660884994 * q^41 + 8945262765426517501413121912547804713065475672808851765824 * q^42 + 6754858585968454689741824956150275855563744863320129251092 * q^43 + 10256422900727914711051439828948913719762767210529399343360 * q^44 + 3560923605022284438744581203359299419628800805488597427670 * q^45 + 215917478684214015835970415365801427523995942249450992649024 * q^46 - 468036949346743446524224540083033087921443712918743092678704 * q^47 - 138175472869917128113923965027114211523442937794848631181312 * q^48 - 1155203275623883178356241428680618202323141234160855611430803 * q^49 - 662361288254569744891489750838385910624551591076930373305800 * q^50 - 13875025406809456447127343535570692796264334304266755550370 * q^51 + 4686563330803028488195038486432142239675010588344800750934400 * q^52 + 16850153365054699278877708172474268895458775724356533295576086 * q^53 - 3137340288800574070947321989342157748567014121664790760526184 * q^54 + 69903604802785515177733563130194024072223641855144712529201880 * q^55 + 263561757691935735991107069426454954646910606378160826135654400 * q^56 + 146964271885661680599941817303782740393713518895988426056055236 * q^57 - 393766572647074503603427367357535096204856933671806739961414992 * q^58 - 390335442004059371501204897784396685449449222429047305160362108 * q^59 - 1246346083098336838245443167057803985933179433056389614496403840 * q^60 + 725074488292223066537782289903828567460896102224114882556804878 * q^61 - 9988959008617311972392577438833349328275372968547435398535343104 * q^62 - 3157035372686493241148598970419764570521041257808979169543482248 * q^63 - 2023851072198628197882474312831161597933729151994298498048327680 * q^64 + 13140351800845565438471290641483435252971725075901777919813259620 * q^65 + 49098199893802616037233646095483883838218857898857856047009777760 * q^66 + 66714375177521017736160888158122274402157076957263686329132696540 * q^67 + 122874398781837608005594402142092581637778609572473879627701828736 * q^68 - 211550728520485918988863794593760397778492966928452183274813504168 * q^69 - 293285886544485684750990625097245178785454325664385364335258966400 * q^70 + 182228903943633461999697286426491914806644676121035292409010095000 * q^71 - 380376807071099648078549525700513940155076932645648351218946289152 * q^72 - 3126186443395793129070092762366126842796181422188167587986966103774 * q^73 - 909089362115793434062323439709786862714999800511985114251226742928 * q^74 + 982272846973530587229764561497340393007528047854257425826667195425 * q^75 + 17344875012173690040537707411833679809662138514060794984773183596288 * q^76 + 10495163179741456456758662728922622402868815939129112668959031953376 * q^77 - 8191828462944258702008436357306371395699406819716356341809714998000 * q^78 - 27301301517941598101728732493241199802996555070508118978972462370800 * q^79 + 17453171390087969064834561314810599922914790489604475485575264133120 * q^80 + 31328937410889851896281120971709651661033472234053326374297990254005 * q^81 - 211476001448904287369943798857320633308142594733381306800142859557424 * q^82 - 118340201116022360513322067378331477940966167749075029048364461271476 * q^83 - 288600084795764628291001658833202352097198631523538446517373245066752 * q^84 - 353749028745389735175606474209594334673616946227279830960229574948180 * q^85 - 598599366027984305586625758611411918350192525004808831847227328355808 * q^86 - 184972447840335595586879350012403335749718574814304198079640398507718 * q^87 + 884266222865559755895490832763056324497872985335575213438267918764032 * q^88 + 922002192851420225703931949240660524744080828362964363768621192185298 * q^89 - 773107974305929069152539888281824938594397222395836929970148461044240 * q^90 - 8079212959404027614418440109956770906886889649154860574373249888569776 * q^91 - 13670577861982746620628593404236014523694130242253442181460174526039552 * q^92 + 3729915385955429492528971192901332630862445897595761204245366555215488 * q^93 - 13436976700690544599208201928250305890032773609106302404839902759345024 * q^94 - 61508953507577523131201535405733284550943470497632040479599939746271320 * q^95 - 32007986513182294493504227608086345487918910401219597611766423881416704 * q^96 - 149876371240369823947413564997445008107894647331408877752554402308756310 * q^97 - 164242038075013607742967230335294726637154516016956449921881670478527288 * q^98 + 3399022187132399007137561865025534669344410724594880911844979606234388 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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