LMFDB - Embedded newform 3.72.a.a.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3,72,Mod(1,3)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 72 $
Character orbit:	$[\chi]$	$=$	3.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			1.2
Root			$9.01834e8$ 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)

$f(q)$	$=$	\(q-2.66543e10 q^{2} +5.00315e16 q^{3} -1.65073e21 q^{4} +1.17208e25 q^{5} -1.33355e27 q^{6} -5.64464e29 q^{7} +1.06935e32 q^{8} +2.50316e33 q^{9} -3.12409e35 q^{10} +8.53757e36 q^{11} -8.25887e37 q^{12} -4.54617e39 q^{13} +1.50454e40 q^{14} +5.86408e41 q^{15} +1.04741e42 q^{16} -1.14257e43 q^{17} -6.67198e43 q^{18} -2.21661e45 q^{19} -1.93479e46 q^{20} -2.82410e46 q^{21} -2.27563e47 q^{22} -3.03260e48 q^{23} +5.35011e48 q^{24} +9.50248e49 q^{25} +1.21175e50 q^{26} +1.25237e50 q^{27} +9.31779e50 q^{28} -8.42951e51 q^{29} -1.56303e52 q^{30} +7.18088e51 q^{31} -2.80411e53 q^{32} +4.27148e53 q^{33} +3.04543e53 q^{34} -6.61595e54 q^{35} -4.13204e54 q^{36} -2.81397e55 q^{37} +5.90821e55 q^{38} -2.27452e56 q^{39} +1.25336e57 q^{40} -1.27729e57 q^{41} +7.52743e56 q^{42} +1.83917e57 q^{43} -1.40932e58 q^{44} +2.93389e58 q^{45} +8.08318e58 q^{46} +2.64330e59 q^{47} +5.24038e58 q^{48} -6.85906e59 q^{49} -2.53282e60 q^{50} -5.71645e59 q^{51} +7.50452e60 q^{52} +2.81914e61 q^{53} -3.33809e60 q^{54} +1.00067e62 q^{55} -6.03608e61 q^{56} -1.10900e62 q^{57} +2.24683e62 q^{58} -5.46158e62 q^{59} -9.68003e62 q^{60} +2.38496e63 q^{61} -1.91401e62 q^{62} -1.41294e63 q^{63} +5.00100e63 q^{64} -5.32847e64 q^{65} -1.13853e64 q^{66} +1.16046e65 q^{67} +1.88608e64 q^{68} -1.51726e65 q^{69} +1.76343e65 q^{70} -6.39177e64 q^{71} +2.67674e65 q^{72} -1.87573e66 q^{73} +7.50044e65 q^{74} +4.75424e66 q^{75} +3.65903e66 q^{76} -4.81915e66 q^{77} +6.06257e66 q^{78} -2.89824e67 q^{79} +1.22765e67 q^{80} +6.26579e66 q^{81} +3.40454e67 q^{82} -2.14602e68 q^{83} +4.66183e67 q^{84} -1.33918e68 q^{85} -4.90217e67 q^{86} -4.21742e68 q^{87} +9.12963e68 q^{88} -1.37561e69 q^{89} -7.82007e68 q^{90} +2.56615e69 q^{91} +5.00601e69 q^{92} +3.59270e68 q^{93} -7.04553e69 q^{94} -2.59804e70 q^{95} -1.40294e70 q^{96} -6.37285e70 q^{97} +1.82823e70 q^{98} +2.13709e70 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 25051277688 q^{2} + 25\!\cdots\!35 q^{3} + 19\!\cdots\!24 q^{4} + 14\!\cdots\!30 q^{5} - 12\!\cdots\!16 q^{6} - 12\!\cdots\!52 q^{7} - 15\!\cdots\!48 q^{8} + 12\!\cdots\!45 q^{9} - 30\!\cdots\!60 q^{10}+ \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

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 $

$2$	−2.66543e10	−0.548532	−0.274266	−	0.961654i	$-0.588435\pi$
$2$	−2.66543e10	−0.548532	−0.274266	+	0.961654i	$0.588435\pi$
$3$	5.00315e16	0.577350
$3$	5.00315e16	0.577350
$4$	−1.65073e21	−0.699113
$5$	1.17208e25	1.80103	0.900515	−	0.434825i	$-0.143190\pi$
$5$	1.17208e25	1.80103	0.900515	+	0.434825i	$0.143190\pi$
$6$	−1.33355e27	−0.316695
$7$	−5.64464e29	−0.563191	−0.281595	−	0.959533i	$-0.590864\pi$
$7$	−5.64464e29	−0.563191	−0.281595	+	0.959533i	$0.590864\pi$
$8$	1.06935e32	0.932018
$9$	2.50316e33	0.333333
$10$	−3.12409e35	−0.987923
$11$	8.53757e36	0.915997	0.457998	−	0.888953i	$-0.348567\pi$
$11$	8.53757e36	0.915997	0.457998	+	0.888953i	$0.348567\pi$
$12$	−8.25887e37	−0.403633
$13$	−4.54617e39	−1.29616	−0.648078	−	0.761574i	$-0.724427\pi$
$13$	−4.54617e39	−1.29616	−0.648078	+	0.761574i	$0.724427\pi$
$14$	1.50454e40	0.308928
$15$	5.86408e41	1.03983
$16$	1.04741e42	0.187871
$17$	−1.14257e43	−0.238202	−0.119101	−	0.992882i	$-0.538001\pi$
$17$	−1.14257e43	−0.238202	−0.119101	+	0.992882i	$0.538001\pi$
$18$	−6.67198e43	−0.182844
$19$	−2.21661e45	−0.891120	−0.445560	−	0.895252i	$-0.646995\pi$
$19$	−2.21661e45	−0.891120	−0.445560	+	0.895252i	$0.646995\pi$
$20$	−1.93479e46	−1.25912
$21$	−2.82410e46	−0.325158
$22$	−2.27563e47	−0.502454
$23$	−3.03260e48	−1.38190	−0.690950	−	0.722902i	$-0.742808\pi$
$23$	−3.03260e48	−1.38190	−0.690950	+	0.722902i	$0.742808\pi$
$24$	5.35011e48	0.538101
$25$	9.50248e49	2.24371
$26$	1.21175e50	0.710983
$27$	1.25237e50	0.192450
$28$	9.31779e50	0.393734
$29$	−8.42951e51	−1.02488	−0.512441	−	0.858723i	$-0.671259\pi$
$29$	−8.42951e51	−1.02488	−0.512441	+	0.858723i	$0.671259\pi$
$30$	−1.56303e52	−0.570378
$31$	7.18088e51	0.0818158	0.0409079	−	0.999163i	$-0.486975\pi$
$31$	7.18088e51	0.0818158	0.0409079	+	0.999163i	$0.486975\pi$
$32$	−2.80411e53	−1.03507
$33$	4.27148e53	0.528851
$34$	3.04543e53	0.130662
$35$	−6.61595e54	−1.01432
$36$	−4.13204e54	−0.233038
$37$	−2.81397e55	−0.600010	−0.300005	−	0.953938i	$-0.596988\pi$
$37$	−2.81397e55	−0.600010	−0.300005	+	0.953938i	$0.596988\pi$
$38$	5.90821e55	0.488808
$39$	−2.27452e56	−0.748336
$40$	1.25336e57	1.67859
$41$	−1.27729e57	−0.711974	−0.355987	−	0.934491i	$-0.615855\pi$
$41$	−1.27729e57	−0.711974	−0.355987	+	0.934491i	$0.615855\pi$
$42$	7.52743e56	0.178360
$43$	1.83917e57	0.189013	0.0945065	−	0.995524i	$-0.469873\pi$
$43$	1.83917e57	0.189013	0.0945065	+	0.995524i	$0.469873\pi$
$44$	−1.40932e58	−0.640385
$45$	2.93389e58	0.600343
$46$	8.08318e58	0.758017
$47$	2.64330e59	1.15524	0.577621	−	0.816305i	$-0.303981\pi$
$47$	2.64330e59	1.15524	0.577621	+	0.816305i	$0.303981\pi$
$48$	5.24038e58	0.108467
$49$	−6.85906e59	−0.682816
$50$	−2.53282e60	−1.23075
$51$	−5.71645e59	−0.137526
$52$	7.50452e60	0.906159
$53$	2.81914e61	1.73110	0.865552	−	0.500818i	$-0.166967\pi$
$53$	2.81914e61	1.73110	0.865552	+	0.500818i	$0.166967\pi$
$54$	−3.33809e60	−0.105565
$55$	1.00067e62	1.64974
$56$	−6.03608e61	−0.524904
$57$	−1.10900e62	−0.514489
$58$	2.24683e62	0.562180
$59$	−5.46158e62	−0.744856	−0.372428	−	0.928061i	$-0.621475\pi$
$59$	−5.46158e62	−0.744856	−0.372428	+	0.928061i	$0.621475\pi$
$60$	−9.68003e62	−0.726955
$61$	2.38496e63	0.996028	0.498014	−	0.867169i	$-0.334063\pi$
$61$	2.38496e63	0.996028	0.498014	+	0.867169i	$0.334063\pi$
$62$	−1.91401e62	−0.0448786
$63$	−1.41294e63	−0.187730
$64$	5.00100e63	0.379899
$65$	−5.32847e64	−2.33442
$66$	−1.13853e64	−0.290092
$67$	1.16046e65	1.73370	0.866851	−	0.498567i	$-0.166140\pi$
$67$	1.16046e65	1.73370	0.866851	+	0.498567i	$0.166140\pi$
$68$	1.88608e64	0.166530
$69$	−1.51726e65	−0.797841
$70$	1.76343e65	0.556389
$71$	−6.39177e64	−0.121885	−0.0609424	−	0.998141i	$-0.519411\pi$
$71$	−6.39177e64	−0.121885	−0.0609424	+	0.998141i	$0.519411\pi$
$72$	2.67674e65	0.310673
$73$	−1.87573e66	−1.33416	−0.667082	−	0.744985i	$-0.732457\pi$
$73$	−1.87573e66	−1.33416	−0.667082	+	0.744985i	$0.732457\pi$
$74$	7.50044e65	0.329125
$75$	4.75424e66	1.29541
$76$	3.65903e66	0.622993
$77$	−4.81915e66	−0.515881
$78$	6.06257e66	0.410486
$79$	−2.89824e67	−1.24845	−0.624226	−	0.781243i	$-0.714586\pi$
$79$	−2.89824e67	−1.24845	−0.624226	+	0.781243i	$0.714586\pi$
$80$	1.22765e67	0.338361
$81$	6.26579e66	0.111111
$82$	3.40454e67	0.390541
$83$	−2.14602e68	−1.60089	−0.800444	−	0.599408i	$-0.795403\pi$
$83$	−2.14602e68	−1.60089	−0.800444	+	0.599408i	$0.795403\pi$
$84$	4.66183e67	0.227322
$85$	−1.33918e68	−0.429009
$86$	−4.90217e67	−0.103680
$87$	−4.21742e68	−0.591716
$88$	9.12963e68	0.853725
$89$	−1.37561e69	−0.861289	−0.430645	−	0.902522i	$-0.641714\pi$
$89$	−1.37561e69	−0.861289	−0.430645	+	0.902522i	$0.641714\pi$
$90$	−7.82007e68	−0.329308
$91$	2.56615e69	0.729983
$92$	5.00601e69	0.966104
$93$	3.59270e68	0.0472364
$94$	−7.04553e69	−0.633687
$95$	−2.59804e70	−1.60493
$96$	−1.40294e70	−0.597599
$97$	−6.37285e70	−1.87904	−0.939522	−	0.342489i	$-0.888730\pi$
$97$	−6.37285e70	−1.87904	−0.939522	+	0.342489i	$0.888730\pi$
$98$	1.82823e70	0.374547
$99$	2.13709e70	0.305332
$100$	−1.56861e71	−1.56861
$101$	7.51365e70	0.527767	0.263884	−	0.964555i	$-0.414997\pi$
$101$	7.51365e70	0.527767	0.263884	+	0.964555i	$0.414997\pi$
$102$	1.52368e70	0.0754375
$103$	−2.62181e71	−0.918080	−0.459040	−	0.888416i	$-0.651806\pi$
$103$	−2.62181e71	−0.918080	−0.459040	+	0.888416i	$0.651806\pi$
$104$	−4.86144e71	−1.20804
$105$	−3.31006e71	−0.585620
$106$	−7.51422e71	−0.949567
$107$	−1.92338e72	−1.74157	−0.870786	−	0.491663i	$-0.836389\pi$
$107$	−1.92338e72	−1.74157	−0.870786	+	0.491663i	$0.836389\pi$
$108$	−2.06732e71	−0.134544
$109$	3.99771e72	1.87573	0.937867	−	0.346996i	$-0.112798\pi$
$109$	3.99771e72	1.87573	0.937867	+	0.346996i	$0.112798\pi$
$110$	−2.66721e72	−0.904934
$111$	−1.40787e72	−0.346416
$112$	−5.91228e71	−0.105807
$113$	−8.23328e72	−1.07470	−0.537351	−	0.843358i	$-0.680575\pi$
$113$	−8.23328e72	−1.07470	−0.537351	+	0.843358i	$0.680575\pi$
$114$	2.95597e72	0.282213
$115$	−3.55444e73	−2.48885
$116$	1.39149e73	0.716507
$117$	−1.13798e73	−0.432052
$118$	1.45575e73	0.408577
$119$	6.44938e72	0.134153
$120$	6.27074e73	0.969136
$121$	−1.39821e73	−0.160950
$122$	−6.35694e73	−0.546354
$123$	−6.39050e73	−0.411058
$124$	−1.18537e73	−0.0571985
$125$	6.17370e74	2.23996
$126$	3.76609e73	0.102976
$127$	4.68633e74	0.967833	0.483917	−	0.875114i	$-0.339214\pi$
$127$	4.68633e74	0.967833	0.483917	+	0.875114i	$0.339214\pi$
$128$	5.28803e74	0.826684
$129$	9.20165e73	0.109127
$130$	1.42026e75	1.28050
$131$	−2.29152e74	−0.157396	−0.0786978	−	0.996899i	$-0.525076\pi$
$131$	−2.29152e74	−0.157396	−0.0786978	+	0.996899i	$0.525076\pi$
$132$	−7.05107e74	−0.369726
$133$	1.25120e75	0.501871
$134$	−3.09312e75	−0.950991
$135$	1.46787e75	0.346608
$136$	−1.22180e75	−0.222009
$137$	5.42895e75	0.760563	0.380282	−	0.924871i	$-0.375827\pi$
$137$	5.42895e75	0.760563	0.380282	+	0.924871i	$0.375827\pi$
$138$	4.04414e75	0.437641
$139$	−1.35813e76	−1.13741	−0.568703	−	0.822543i	$-0.692554\pi$
$139$	−1.35813e76	−1.13741	−0.568703	+	0.822543i	$0.692554\pi$
$140$	1.09212e76	0.709126
$141$	1.32248e76	0.666979
$142$	1.70368e75	0.0668577
$143$	−3.88133e76	−1.18727
$144$	2.62184e75	0.0626236
$145$	−9.88004e76	−1.84584
$146$	4.99962e76	0.731831
$147$	−3.43169e76	−0.394224
$148$	4.64511e76	0.419474
$149$	−7.20958e76	−0.512622	−0.256311	−	0.966594i	$-0.582507\pi$
$149$	−7.20958e76	−0.512622	−0.256311	+	0.966594i	$0.582507\pi$
$150$	−1.26721e77	−0.710572
$151$	−2.97397e77	−1.31721	−0.658605	−	0.752489i	$-0.728853\pi$
$151$	−2.97397e77	−1.31721	−0.658605	+	0.752489i	$0.728853\pi$
$152$	−2.37032e77	−0.830540
$153$	−2.86003e76	−0.0794007
$154$	1.28451e77	0.282977
$155$	8.41654e76	0.147353
$156$	3.75463e77	0.523171
$157$	1.07623e77	0.119527	0.0597637	−	0.998213i	$-0.480965\pi$
$157$	1.07623e77	0.119527	0.0597637	+	0.998213i	$0.480965\pi$
$158$	7.72504e77	0.684817
$159$	1.41046e78	0.999454
$160$	−3.28663e78	−1.86419
$161$	1.71179e78	0.778274
$162$	−1.67010e77	−0.0609480
$163$	1.02722e78	0.301304	0.150652	−	0.988587i	$-0.451863\pi$
$163$	1.02722e78	0.301304	0.150652	+	0.988587i	$0.451863\pi$
$164$	2.10847e78	0.497750
$165$	5.00650e78	0.952476
$166$	5.72005e78	0.878138
$167$	5.80096e78	0.719557	0.359778	−	0.933038i	$-0.382852\pi$
$167$	5.80096e78	0.719557	0.359778	+	0.933038i	$0.382852\pi$
$168$	−3.01994e78	−0.303053
$169$	8.36564e78	0.680019
$170$	3.56948e78	0.235325
$171$	−5.54852e78	−0.297040
$172$	−3.03598e78	−0.132141
$173$	−3.03896e79	−1.07668	−0.538341	−	0.842727i	$-0.680949\pi$
$173$	−3.03896e79	−1.07668	−0.538341	+	0.842727i	$0.680949\pi$
$174$	1.12412e79	0.324575
$175$	−5.36380e79	−1.26364
$176$	8.94238e78	0.172089
$177$	−2.73251e79	−0.430043
$178$	3.66658e79	0.472445
$179$	9.44353e79	0.997360	0.498680	−	0.866786i	$-0.333818\pi$
$179$	9.44353e79	0.997360	0.498680	+	0.866786i	$0.333818\pi$
$180$	−4.84307e79	−0.419708
$181$	−3.00455e79	−0.213890	−0.106945	−	0.994265i	$-0.534107\pi$
$181$	−3.00455e79	−0.213890	−0.106945	+	0.994265i	$0.534107\pi$
$182$	−6.83989e79	−0.400419
$183$	1.19323e80	0.575057
$184$	−3.24290e80	−1.28796
$185$	−3.29819e80	−1.08064
$186$	−9.57609e78	−0.0259107
$187$	−9.75476e79	−0.218192
$188$	−4.36338e80	−0.807644
$189$	−7.06916e79	−0.108386
$190$	6.92488e80	0.880358
$191$	−4.35536e80	−0.459557	−0.229779	−	0.973243i	$-0.573800\pi$
$191$	−4.35536e80	−0.459557	−0.229779	+	0.973243i	$0.573800\pi$
$192$	2.50208e80	0.219335
$193$	1.39857e81	1.01953	0.509766	−	0.860313i	$-0.329732\pi$
$193$	1.39857e81	1.01953	0.509766	+	0.860313i	$0.329732\pi$
$194$	1.69864e81	1.03072
$195$	−2.66591e81	−1.34778
$196$	1.13225e81	0.477365
$197$	−4.10013e81	−1.44293	−0.721467	−	0.692448i	$-0.756532\pi$
$197$	−4.10013e81	−1.44293	−0.721467	+	0.692448i	$0.756532\pi$
$198$	−5.69625e80	−0.167485
$199$	7.67215e81	1.88640	0.943198	−	0.332230i	$-0.107801\pi$
$199$	7.67215e81	1.88640	0.943198	+	0.332230i	$0.107801\pi$
$200$	1.01614e82	2.09118
$201$	5.80596e81	1.00095
$202$	−2.00271e81	−0.289497
$203$	4.75815e81	0.577204
$204$	9.43633e80	0.0961462
$205$	−1.49709e82	−1.28229
$206$	6.98826e81	0.503596
$207$	−7.59107e81	−0.460634
$208$	−4.76173e81	−0.243510
$209$	−1.89245e82	−0.816263
$210$	8.82273e81	0.321231
$211$	−1.49794e82	−0.460753	−0.230377	−	0.973102i	$-0.573996\pi$
$211$	−1.49794e82	−0.460753	−0.230377	+	0.973102i	$0.573996\pi$
$212$	−4.65365e82	−1.21024
$213$	−3.19790e81	−0.0703702
$214$	5.12663e82	0.955308
$215$	2.15565e82	0.340418
$216$	1.33922e82	0.179367
$217$	−4.05334e81	−0.0460779
$218$	−1.06556e83	−1.02890
$219$	−9.38457e82	−0.770279
$220$	−1.65184e83	−1.15335
$221$	5.19432e82	0.308747
$222$	3.75258e82	0.190020
$223$	−1.90079e83	−0.820560	−0.410280	−	0.911960i	$-0.634569\pi$
$223$	−1.90079e83	−0.820560	−0.410280	+	0.911960i	$0.634569\pi$
$224$	1.58282e83	0.582942
$225$	2.37862e83	0.747903
$226$	2.19452e83	0.589509
$227$	−2.84560e82	−0.0653515	−0.0326758	−	0.999466i	$-0.510403\pi$
$227$	−2.84560e82	−0.0653515	−0.0326758	+	0.999466i	$0.510403\pi$
$228$	1.83067e83	0.359685
$229$	−4.55513e83	−0.766199	−0.383099	−	0.923707i	$-0.625143\pi$
$229$	−4.55513e83	−0.766199	−0.383099	+	0.923707i	$0.625143\pi$
$230$	9.47410e83	1.36521
$231$	−2.41109e83	−0.297844
$232$	−9.01408e83	−0.955208
$233$	2.07830e83	0.189048	0.0945241	−	0.995523i	$-0.469867\pi$
$233$	2.07830e83	0.189048	0.0945241	+	0.995523i	$0.469867\pi$
$234$	3.03320e83	0.236994
$235$	3.09815e84	2.08062
$236$	9.01561e83	0.520738
$237$	−1.45003e84	−0.720795
$238$	−1.71904e83	−0.0735874
$239$	−1.64164e84	−0.605553	−0.302777	−	0.953062i	$-0.597914\pi$
$239$	−1.64164e84	−0.605553	−0.302777	+	0.953062i	$0.597914\pi$
$240$	6.14213e83	0.195353
$241$	4.79724e84	1.31640	0.658198	−	0.752845i	$-0.271319\pi$
$241$	4.79724e84	1.31640	0.658198	+	0.752845i	$0.271319\pi$
$242$	3.72682e83	0.0882863
$243$	3.13487e83	0.0641500
$244$	−3.93693e84	−0.696336
$245$	−8.03935e84	−1.22977
$246$	1.70334e84	0.225479
$247$	1.00771e85	1.15503
$248$	7.67885e83	0.0762538
$249$	−1.07369e85	−0.924273
$250$	−1.64555e85	−1.22869
$251$	4.82130e84	0.312426	0.156213	−	0.987723i	$-0.450071\pi$
$251$	4.82130e84	0.312426	0.156213	+	0.987723i	$0.450071\pi$
$252$	2.33239e84	0.131245
$253$	−2.58910e85	−1.26582
$254$	−1.24911e85	−0.530888
$255$	−6.70012e84	−0.247689
$256$	−2.59031e85	−0.833362
$257$	−9.38779e84	−0.262989	−0.131494	−	0.991317i	$-0.541978\pi$
$257$	−9.38779e84	−0.262989	−0.131494	+	0.991317i	$0.541978\pi$
$258$	−2.45263e84	−0.0598595
$259$	1.58838e85	0.337920
$260$	8.79587e85	1.63202
$261$	−2.11004e85	−0.341627
$262$	6.10788e84	0.0863365
$263$	1.13976e85	0.140729	0.0703646	−	0.997521i	$-0.477584\pi$
$263$	1.13976e85	0.140729	0.0703646	+	0.997521i	$0.477584\pi$
$264$	4.56769e85	0.492898
$265$	3.30425e86	3.11777
$266$	−3.33497e85	−0.275292
$267$	−6.88237e85	−0.497266
$268$	−1.91561e86	−1.21205
$269$	7.11649e85	0.394512	0.197256	−	0.980352i	$-0.436797\pi$
$269$	7.11649e85	0.394512	0.197256	+	0.980352i	$0.436797\pi$
$270$	−3.91250e85	−0.190126
$271$	−1.39607e86	−0.594971	−0.297486	−	0.954726i	$-0.596148\pi$
$271$	−1.39607e86	−0.594971	−0.297486	+	0.954726i	$0.596148\pi$
$272$	−1.19674e85	−0.0447512
$273$	1.28388e86	0.421456
$274$	−1.44705e86	−0.417193
$275$	8.11281e86	2.05523
$276$	2.50459e86	0.557781
$277$	−5.24273e86	−1.02689	−0.513447	−	0.858121i	$-0.671632\pi$
$277$	−5.24273e86	−1.02689	−0.513447	+	0.858121i	$0.671632\pi$
$278$	3.61999e86	0.623903
$279$	1.79748e85	0.0272719
$280$	−7.07475e86	−0.945368
$281$	−5.97430e86	−0.703417	−0.351708	−	0.936110i	$-0.614399\pi$
$281$	−5.97430e86	−0.703417	−0.351708	+	0.936110i	$0.614399\pi$
$282$	−3.52499e86	−0.365859
$283$	−3.07474e86	−0.281443	−0.140721	−	0.990049i	$-0.544942\pi$
$283$	−3.07474e86	−0.281443	−0.140721	+	0.990049i	$0.544942\pi$
$284$	1.05511e86	0.0852112
$285$	−1.29984e87	−0.926609
$286$	1.03454e87	0.651258
$287$	7.20986e86	0.400977
$288$	−7.01911e86	−0.345024
$289$	−2.17022e87	−0.943260
$290$	2.63345e87	1.01250
$291$	−3.18843e87	−1.08487
$292$	3.09633e87	0.932730
$293$	−2.34379e87	−0.625342	−0.312671	−	0.949861i	$-0.601224\pi$
$293$	−2.34379e87	−0.625342	−0.312671	+	0.949861i	$0.601224\pi$
$294$	9.14693e86	0.216245
$295$	−6.40139e87	−1.34151
$296$	−3.00911e87	−0.559220
$297$	1.06922e87	0.176284
$298$	1.92166e87	0.281190
$299$	1.37867e88	1.79116
$300$	−7.84798e87	−0.905635
$301$	−1.03814e87	−0.106450
$302$	7.92690e87	0.722532
$303$	3.75920e87	0.304707
$304$	−2.32171e87	−0.167415
$305$	2.79536e88	1.79388
$306$	7.62320e86	0.0435538
$307$	1.94400e88	0.989197	0.494599	−	0.869121i	$-0.335315\pi$
$307$	1.94400e88	0.989197	0.494599	+	0.869121i	$0.335315\pi$
$308$	7.95512e87	0.360659
$309$	−1.31173e88	−0.530054
$310$	−2.24337e87	−0.0808277
$311$	1.39238e88	0.447471	0.223735	−	0.974650i	$-0.428175\pi$
$311$	1.39238e88	0.447471	0.223735	+	0.974650i	$0.428175\pi$
$312$	−2.43225e88	−0.697462
$313$	−6.56054e88	−1.67925	−0.839625	−	0.543167i	$-0.817225\pi$
$313$	−6.56054e88	−1.67925	−0.839625	+	0.543167i	$0.817225\pi$
$314$	−2.86862e87	−0.0655647
$315$	−1.65607e88	−0.338108
$316$	4.78422e88	0.872809
$317$	1.11779e89	1.82287	0.911434	−	0.411446i	$-0.134976\pi$
$317$	1.11779e89	1.82287	0.911434	+	0.411446i	$0.134976\pi$
$318$	−3.75948e88	−0.548233
$319$	−7.19676e88	−0.938788
$320$	5.86156e88	0.684209
$321$	−9.62297e88	−1.00550
$322$	−4.56266e88	−0.426908
$323$	2.53263e88	0.212267
$324$	−1.03431e88	−0.0776792
$325$	−4.31999e89	−2.90820
$326$	−2.73799e88	−0.165275
$327$	2.00012e89	1.08296
$328$	−1.36587e89	−0.663573
$329$	−1.49205e89	−0.650621
$330$	−1.33445e89	−0.522464
$331$	3.66213e89	1.28778	0.643888	−	0.765120i	$-0.277320\pi$
$331$	3.66213e89	1.28778	0.643888	+	0.765120i	$0.277320\pi$
$332$	3.54250e89	1.11920
$333$	−7.04381e88	−0.200003
$334$	−1.54620e89	−0.394700
$335$	1.36015e90	3.12245
$336$	−2.95800e88	−0.0610878
$337$	−3.46322e89	−0.643605	−0.321802	−	0.946807i	$-0.604289\pi$
$337$	−3.46322e89	−0.643605	−0.321802	+	0.946807i	$0.604289\pi$
$338$	−2.22980e89	−0.373012
$339$	−4.11924e89	−0.620480
$340$	2.21063e89	0.299926
$341$	6.13072e88	0.0749430
$342$	1.47892e89	0.162936
$343$	9.54187e89	0.947747
$344$	1.96671e89	0.176163
$345$	−1.77834e90	−1.43694
$346$	8.10012e89	0.590595
$347$	1.37806e89	0.0906925	0.0453462	−	0.998971i	$-0.485561\pi$
$347$	1.37806e89	0.0906925	0.0453462	+	0.998971i	$0.485561\pi$
$348$	6.96183e89	0.413676
$349$	7.56700e89	0.406089	0.203045	−	0.979170i	$-0.434916\pi$
$349$	7.56700e89	0.406089	0.203045	+	0.979170i	$0.434916\pi$
$350$	1.42968e90	0.693145
$351$	−5.69348e89	−0.249445
$352$	−2.39402e90	−0.948122
$353$	−1.58919e90	−0.569081	−0.284540	−	0.958664i	$-0.591841\pi$
$353$	−1.58919e90	−0.569081	−0.284540	+	0.958664i	$0.591841\pi$
$354$	7.28332e89	0.235892
$355$	−7.49164e89	−0.219518
$356$	2.27076e90	0.602138
$357$	3.22673e89	0.0774534
$358$	−2.51711e90	−0.547084
$359$	−1.85515e90	−0.365197	−0.182598	−	0.983188i	$-0.558451\pi$
$359$	−1.85515e90	−0.365197	−0.182598	+	0.983188i	$0.558451\pi$
$360$	3.13735e90	0.559531
$361$	−1.27401e90	−0.205905
$362$	8.00841e89	0.117325
$363$	−6.99546e89	−0.0929246
$364$	−4.23603e90	−0.510340
$365$	−2.19850e91	−2.40287
$366$	−3.18047e90	−0.315437
$367$	1.33204e91	1.19915	0.599573	−	0.800320i	$-0.295337\pi$
$367$	1.33204e91	1.19915	0.599573	+	0.800320i	$0.295337\pi$
$368$	−3.17639e90	−0.259619
$369$	−3.19727e90	−0.237325
$370$	8.79109e90	0.592763
$371$	−1.59130e91	−0.974942
$372$	−5.93059e89	−0.0330235
$373$	−9.13925e90	−0.462644	−0.231322	−	0.972877i	$-0.574305\pi$
$373$	−9.13925e90	−0.462644	−0.231322	+	0.972877i	$0.574305\pi$
$374$	2.60006e90	0.119685
$375$	3.08880e91	1.29324
$376$	2.82661e91	1.07671
$377$	3.83220e91	1.32841
$378$	1.88423e90	0.0594533
$379$	−1.67606e91	−0.481501	−0.240751	−	0.970587i	$-0.577394\pi$
$379$	−1.67606e91	−0.481501	−0.240751	+	0.970587i	$0.577394\pi$
$380$	4.28866e91	1.12203
$381$	2.34464e91	0.558779
$382$	1.16089e91	0.252082
$383$	−7.05333e91	−1.39585	−0.697923	−	0.716173i	$-0.745892\pi$
$383$	−7.05333e91	−1.39585	−0.697923	+	0.716173i	$0.745892\pi$
$384$	2.64568e91	0.477286
$385$	−5.64841e91	−0.929117
$386$	−3.72780e91	−0.559246
$387$	4.60373e90	0.0630043
$388$	1.05199e92	1.31366
$389$	4.07181e90	0.0464063	0.0232031	−	0.999731i	$-0.492614\pi$
$389$	4.07181e90	0.0464063	0.0232031	+	0.999731i	$0.492614\pi$
$390$	7.10580e91	0.739298
$391$	3.46495e91	0.329172
$392$	−7.33472e91	−0.636397
$393$	−1.14648e91	−0.0908724
$394$	1.09286e92	0.791496
$395$	−3.39696e92	−2.24850
$396$	−3.52776e91	−0.213462
$397$	−6.00990e91	−0.332510	−0.166255	−	0.986083i	$-0.553167\pi$
$397$	−6.00990e91	−0.332510	−0.166255	+	0.986083i	$0.553167\pi$
$398$	−2.04496e92	−1.03475
$399$	6.25992e91	0.289755
$400$	9.95304e91	0.421528
$401$	−7.89990e91	−0.306194	−0.153097	−	0.988211i	$-0.548925\pi$
$401$	−7.89990e91	−0.306194	−0.153097	+	0.988211i	$0.548925\pi$
$402$	−1.54754e92	−0.549055
$403$	−3.26455e91	−0.106046
$404$	−1.24030e92	−0.368969
$405$	7.34399e91	0.200114
$406$	−1.26825e92	−0.316615
$407$	−2.40245e92	−0.549607
$408$	−6.11287e91	−0.128177
$409$	7.09304e92	1.36350	0.681749	−	0.731586i	$-0.261219\pi$
$409$	7.09304e92	1.36350	0.681749	+	0.731586i	$0.261219\pi$
$410$	3.99038e92	0.703375
$411$	2.71619e92	0.439111
$412$	4.32791e92	0.641841
$413$	3.08286e92	0.419496
$414$	2.02334e92	0.252672
$415$	−2.51530e93	−2.88325
$416$	1.27480e93	1.34161
$417$	−6.79492e92	−0.656681
$418$	5.04418e92	0.447747
$419$	−3.36861e92	−0.274696	−0.137348	−	0.990523i	$-0.543858\pi$
$419$	−3.36861e92	−0.274696	−0.137348	+	0.990523i	$0.543858\pi$
$420$	5.46403e92	0.409414
$421$	8.90463e92	0.613199	0.306599	−	0.951839i	$-0.400809\pi$
$421$	8.90463e92	0.613199	0.306599	+	0.951839i	$0.400809\pi$
$422$	3.99266e92	0.252738
$423$	6.61659e92	0.385080
$424$	3.01464e93	1.61342
$425$	−1.08572e93	−0.534456
$426$	8.52377e91	0.0386003
$427$	−1.34622e93	−0.560954
$428$	3.17499e93	1.21755
$429$	−1.94189e93	−0.685473
$430$	−5.74573e92	−0.186730
$431$	−1.82524e93	−0.546231	−0.273115	−	0.961981i	$-0.588054\pi$
$431$	−1.82524e93	−0.546231	−0.273115	+	0.961981i	$0.588054\pi$
$432$	1.31175e92	0.0361558
$433$	−2.34465e93	−0.595330	−0.297665	−	0.954670i	$-0.596208\pi$
$433$	−2.34465e93	−0.595330	−0.297665	+	0.954670i	$0.596208\pi$
$434$	1.08039e92	0.0252752
$435$	−4.94314e93	−1.06570
$436$	−6.59916e93	−1.31135
$437$	6.72209e93	1.23144
$438$	2.50139e93	0.422523
$439$	−1.29845e93	−0.202271	−0.101135	−	0.994873i	$-0.532248\pi$
$439$	−1.29845e93	−0.202271	−0.101135	+	0.994873i	$0.532248\pi$
$440$	1.07006e94	1.53758
$441$	−1.71693e93	−0.227605
$442$	−1.38451e93	−0.169358
$443$	−5.84909e93	−0.660322	−0.330161	−	0.943925i	$-0.607103\pi$
$443$	−5.84909e93	−0.660322	−0.330161	+	0.943925i	$0.607103\pi$
$444$	2.32402e93	0.242184
$445$	−1.61232e94	−1.55121
$446$	5.06641e93	0.450104
$447$	−3.60706e93	−0.295962
$448$	−2.82288e93	−0.213956
$449$	−1.25515e94	−0.878926	−0.439463	−	0.898261i	$-0.644831\pi$
$449$	−1.25515e94	−0.878926	−0.439463	+	0.898261i	$0.644831\pi$
$450$	−6.34004e93	−0.410249
$451$	−1.09050e94	−0.652166
$452$	1.35910e94	0.751338
$453$	−1.48792e94	−0.760491
$454$	7.58474e92	0.0358474
$455$	3.00773e94	1.31472
$456$	−1.18591e94	−0.479512
$457$	4.54711e94	1.70102	0.850511	−	0.525957i	$-0.176293\pi$
$457$	4.54711e94	1.70102	0.850511	+	0.525957i	$0.176293\pi$
$458$	1.21414e94	0.420285
$459$	−1.43092e93	−0.0458420
$460$	5.86743e94	1.73998
$461$	−1.20833e94	−0.331745	−0.165872	−	0.986147i	$-0.553044\pi$
$461$	−1.20833e94	−0.331745	−0.165872	+	0.986147i	$0.553044\pi$
$462$	6.42660e93	0.163377
$463$	3.82107e94	0.899621	0.449810	−	0.893124i	$-0.351492\pi$
$463$	3.82107e94	0.899621	0.449810	+	0.893124i	$0.351492\pi$
$464$	−8.82920e93	−0.192545
$465$	4.21092e93	0.0850742
$466$	−5.53955e93	−0.103699
$467$	5.41330e94	0.939102	0.469551	−	0.882905i	$-0.344416\pi$
$467$	5.41330e94	0.939102	0.469551	+	0.882905i	$0.344416\pi$
$468$	1.87850e94	0.302053
$469$	−6.55037e94	−0.976405
$470$	−8.25790e94	−1.14129
$471$	5.38455e93	0.0690092
$472$	−5.84033e94	−0.694219
$473$	1.57020e94	0.173135
$474$	3.86496e94	0.395379
$475$	−2.10633e95	−1.99941
$476$	−1.06462e94	−0.0937882
$477$	7.05675e94	0.577035
$478$	4.37567e94	0.332165
$479$	1.66649e95	1.17460	0.587302	−	0.809368i	$-0.300190\pi$
$479$	1.66649e95	1.17460	0.587302	+	0.809368i	$0.300190\pi$
$480$	−1.64435e95	−1.07629
$481$	1.27928e95	0.777706
$482$	−1.27867e95	−0.722085
$483$	8.56436e94	0.449337
$484$	2.30807e94	0.112522
$485$	−7.46947e95	−3.38421
$486$	−8.35577e93	−0.0351884
$487$	−8.93387e94	−0.349753	−0.174877	−	0.984590i	$-0.555953\pi$
$487$	−8.93387e94	−0.349753	−0.174877	+	0.984590i	$0.555953\pi$
$488$	2.55035e95	0.928316
$489$	5.13936e94	0.173958
$490$	2.14283e95	0.674570
$491$	1.04088e95	0.304793	0.152397	−	0.988319i	$-0.451301\pi$
$491$	1.04088e95	0.304793	0.152397	+	0.988319i	$0.451301\pi$
$492$	1.05490e95	0.287376
$493$	9.63130e94	0.244129
$494$	−2.68598e95	−0.633571
$495$	2.50483e95	0.549913
$496$	7.52136e93	0.0153708
$497$	3.60792e94	0.0686444
$498$	2.86183e95	0.506993
$499$	6.10274e95	1.00683	0.503414	−	0.864045i	$-0.332077\pi$
$499$	6.10274e95	1.00683	0.503414	+	0.864045i	$0.332077\pi$
$500$	−1.01911e96	−1.56598
$501$	2.90231e95	0.415436
$502$	−1.28508e95	−0.171376
$503$	−4.60428e95	−0.572135	−0.286068	−	0.958209i	$-0.592348\pi$
$503$	−4.60428e95	−0.572135	−0.286068	+	0.958209i	$0.592348\pi$
$504$	−1.51092e95	−0.174968
$505$	8.80658e95	0.950525
$506$	6.90107e95	0.694341
$507$	4.18546e95	0.392609
$508$	−7.73587e95	−0.676624
$509$	1.93136e96	1.57537	0.787684	−	0.616080i	$-0.211280\pi$
$509$	1.93136e96	1.57537	0.787684	+	0.616080i	$0.211280\pi$
$510$	1.78587e95	0.135865
$511$	1.05878e96	0.751388
$512$	−5.58171e95	−0.369559
$513$	−2.77601e95	−0.171496
$514$	2.50225e95	0.144258
$515$	−3.07297e96	−1.65349
$516$	−1.51895e95	−0.0762918
$517$	2.25674e96	1.05820
$518$	−4.23372e95	−0.185360
$519$	−1.52044e96	−0.621623
$520$	−5.69798e96	−2.17572
$521$	1.05273e96	0.375473	0.187737	−	0.982219i	$-0.439885\pi$
$521$	1.05273e96	0.375473	0.187737	+	0.982219i	$0.439885\pi$
$522$	5.62416e95	0.187393
$523$	3.70201e96	1.15246	0.576232	−	0.817286i	$-0.304522\pi$
$523$	3.70201e96	1.15246	0.576232	+	0.817286i	$0.304522\pi$
$524$	3.78269e95	0.110037
$525$	−2.68359e96	−0.729561
$526$	−3.03795e95	−0.0771945
$527$	−8.20464e94	−0.0194887
$528$	4.47401e95	0.0993556
$529$	4.38077e96	0.909650
$530$	−8.80724e96	−1.71020
$531$	−1.36712e96	−0.248285
$532$	−2.06539e96	−0.350864
$533$	5.80680e96	0.922829
$534$	1.83445e96	0.272766
$535$	−2.25435e97	−3.13662
$536$	1.24093e97	1.61584
$537$	4.72475e96	0.575826
$538$	−1.89685e96	−0.216402
$539$	−5.85597e96	−0.625457
$540$	−2.42306e96	−0.242318
$541$	−1.68062e96	−0.157386	−0.0786931	−	0.996899i	$-0.525075\pi$
$541$	−1.68062e96	−0.157386	−0.0786931	+	0.996899i	$0.525075\pi$
$542$	3.72111e96	0.326361
$543$	−1.50322e96	−0.123489
$544$	3.20388e96	0.246556
$545$	4.68563e97	3.37825
$546$	−3.42210e96	−0.231182
$547$	1.99192e97	1.26102	0.630510	−	0.776181i	$-0.282846\pi$
$547$	1.99192e97	1.26102	0.630510	+	0.776181i	$0.282846\pi$
$548$	−8.96174e96	−0.531719
$549$	5.96992e96	0.332009
$550$	−2.16241e97	−1.12736
$551$	1.86849e97	0.913293
$552$	−1.62247e97	−0.743602
$553$	1.63595e97	0.703117
$554$	1.39741e97	0.563285
$555$	−1.65014e97	−0.623905
$556$	2.24191e97	0.795174
$557$	−3.63517e97	−1.20967	−0.604833	−	0.796353i	$-0.706760\pi$
$557$	−3.63517e97	−1.20967	−0.604833	+	0.796353i	$0.706760\pi$
$558$	−4.79107e95	−0.0149595
$559$	−8.36119e96	−0.244990
$560$	−6.92964e96	−0.190562
$561$	−4.88046e96	−0.125973
$562$	1.59241e97	0.385847
$563$	5.00417e97	1.13837	0.569186	−	0.822209i	$-0.307258\pi$
$563$	5.00417e97	1.13837	0.569186	+	0.822209i	$0.307258\pi$
$564$	−2.18307e97	−0.466293
$565$	−9.65004e97	−1.93557
$566$	8.19551e96	0.154381
$567$	−3.53681e96	−0.0625768
$568$	−6.83502e96	−0.113599
$569$	−5.59658e97	−0.873850	−0.436925	−	0.899498i	$-0.643933\pi$
$569$	−5.59658e97	−0.873850	−0.436925	+	0.899498i	$0.643933\pi$
$570$	3.46462e97	0.508275
$571$	−4.63127e97	−0.638438	−0.319219	−	0.947681i	$-0.603421\pi$
$571$	−4.63127e97	−0.638438	−0.319219	+	0.947681i	$0.603421\pi$
$572$	6.40703e97	0.830038
$573$	−2.17906e97	−0.265326
$574$	−1.92174e97	−0.219949
$575$	−2.88172e98	−3.10058
$576$	1.25183e97	0.126633
$577$	−1.03762e97	−0.0986952	−0.0493476	−	0.998782i	$-0.515714\pi$
$577$	−1.03762e97	−0.0986952	−0.0493476	+	0.998782i	$0.515714\pi$
$578$	5.78458e97	0.517408
$579$	6.99728e97	0.588627
$580$	1.63093e98	1.29045
$581$	1.21135e98	0.901605
$582$	8.49854e97	0.595084
$583$	2.40686e98	1.58569
$584$	−2.00581e98	−1.24346
$585$	−1.33380e98	−0.778138
$586$	6.24719e97	0.343020
$587$	1.24398e98	0.642924	0.321462	−	0.946923i	$-0.395826\pi$
$587$	1.24398e98	0.642924	0.321462	+	0.946923i	$0.395826\pi$
$588$	5.66481e97	0.275607
$589$	−1.59172e97	−0.0729077
$590$	1.70625e98	0.735860
$591$	−2.05136e98	−0.833079
$592$	−2.94739e97	−0.112724
$593$	−4.18089e98	−1.50601	−0.753004	−	0.658016i	$-0.771396\pi$
$593$	−4.18089e98	−1.50601	−0.753004	+	0.658016i	$0.771396\pi$
$594$	−2.84992e97	−0.0966972
$595$	7.55917e97	0.241614
$596$	1.19011e98	0.358381
$597$	3.83850e98	1.08911
$598$	−3.67475e98	−0.982508
$599$	−1.21681e98	−0.306598	−0.153299	−	0.988180i	$-0.548990\pi$
$599$	−1.21681e98	−0.306598	−0.153299	+	0.988180i	$0.548990\pi$
$600$	5.08393e98	1.20734
$601$	1.56457e98	0.350227	0.175114	−	0.984548i	$-0.443971\pi$
$601$	1.56457e98	0.350227	0.175114	+	0.984548i	$0.443971\pi$
$602$	2.76710e97	0.0583914
$603$	2.90481e98	0.577901
$604$	4.90923e98	0.920878
$605$	−1.63881e98	−0.289876
$606$	−1.00199e98	−0.167141
$607$	−1.57108e98	−0.247172	−0.123586	−	0.992334i	$-0.539439\pi$
$607$	−1.57108e98	−0.247172	−0.123586	+	0.992334i	$0.539439\pi$
$608$	6.21561e98	0.922373
$609$	2.38058e98	0.333249
$610$	−7.45082e98	−0.983999
$611$	−1.20169e99	−1.49737
$612$	4.72114e97	0.0555100
$613$	6.33736e98	0.703172	0.351586	−	0.936156i	$-0.385642\pi$
$613$	6.33736e98	0.703172	0.351586	+	0.936156i	$0.385642\pi$
$614$	−5.18158e98	−0.542607
$615$	−7.49016e98	−0.740329
$616$	−5.15334e98	−0.480810
$617$	−2.08291e99	−1.83462	−0.917312	−	0.398169i	$-0.869646\pi$
$617$	−2.08291e99	−1.83462	−0.917312	+	0.398169i	$0.869646\pi$
$618$	3.49633e98	0.290751
$619$	−2.41506e98	−0.189631	−0.0948157	−	0.995495i	$-0.530226\pi$
$619$	−2.41506e98	−0.189631	−0.0948157	+	0.995495i	$0.530226\pi$
$620$	−1.38935e98	−0.103016
$621$	−3.79793e98	−0.265947
$622$	−3.71130e98	−0.245452
$623$	7.76480e98	0.485070
$624$	−2.38237e98	−0.140590
$625$	3.21159e99	1.79052
$626$	1.74866e99	0.921122
$627$	−9.46820e98	−0.471270
$628$	−1.77657e98	−0.0835631
$629$	3.21515e98	0.142924
$630$	4.41415e98	0.185463
$631$	−1.68388e99	−0.668757	−0.334379	−	0.942439i	$-0.608526\pi$
$631$	−1.68388e99	−0.668757	−0.334379	+	0.942439i	$0.608526\pi$
$632$	−3.09922e99	−1.16358
$633$	−7.49445e98	−0.266016
$634$	−2.97938e99	−0.999902
$635$	5.49274e99	1.74310
$636$	−2.32829e99	−0.698731
$637$	3.11825e99	0.885036
$638$	1.91824e99	0.514955
$639$	−1.59996e98	−0.0406283
$640$	6.19797e99	1.48888
$641$	7.68372e99	1.74627	0.873136	−	0.487477i	$-0.162083\pi$
$641$	7.68372e99	1.74627	0.873136	+	0.487477i	$0.162083\pi$
$642$	2.56493e99	0.551547
$643$	−6.39697e99	−1.30162	−0.650811	−	0.759240i	$-0.725571\pi$
$643$	−6.39697e99	−1.30162	−0.650811	+	0.759240i	$0.725571\pi$
$644$	−2.82571e99	−0.544101
$645$	1.07850e99	0.196540
$646$	−6.75054e98	−0.116435
$647$	1.11658e99	0.182300	0.0911502	−	0.995837i	$-0.470946\pi$
$647$	1.11658e99	0.182300	0.0911502	+	0.995837i	$0.470946\pi$
$648$	6.70030e98	0.103558
$649$	−4.66286e99	−0.682285
$650$	1.15146e100	1.59524
$651$	−2.02795e98	−0.0266031
$652$	−1.69567e99	−0.210645
$653$	−6.81378e98	−0.0801623	−0.0400811	−	0.999196i	$-0.512762\pi$
$653$	−6.81378e98	−0.0801623	−0.0400811	+	0.999196i	$0.512762\pi$
$654$	−5.33117e99	−0.594036
$655$	−2.68584e99	−0.283474
$656$	−1.33786e99	−0.133759
$657$	−4.69525e99	−0.444721
$658$	3.97694e99	0.356887
$659$	−1.13441e100	−0.964575	−0.482288	−	0.876013i	$-0.660194\pi$
$659$	−1.13441e100	−0.964575	−0.482288	+	0.876013i	$0.660194\pi$
$660$	−8.26439e99	−0.665888
$661$	8.88161e98	0.0678172	0.0339086	−	0.999425i	$-0.489204\pi$
$661$	8.88161e98	0.0678172	0.0339086	+	0.999425i	$0.489204\pi$
$662$	−9.76115e99	−0.706386
$663$	2.59880e99	0.178255
$664$	−2.29484e100	−1.49206
$665$	1.46650e100	0.903884
$666$	1.87748e99	0.109708
$667$	2.55633e100	1.41628
$668$	−9.57583e99	−0.503051
$669$	−9.50992e99	−0.473751
$670$	−3.62538e100	−1.71276
$671$	2.03617e100	0.912359
$672$	7.91907e99	0.336562
$673$	−2.21574e100	−0.893271	−0.446636	−	0.894716i	$-0.647378\pi$
$673$	−2.21574e100	−0.893271	−0.446636	+	0.894716i	$0.647378\pi$
$674$	9.23097e99	0.353038
$675$	1.19006e100	0.431802
$676$	−1.38094e100	−0.475410
$677$	8.79319e98	0.0287242	0.0143621	−	0.999897i	$-0.495428\pi$
$677$	8.79319e98	0.0287242	0.0143621	+	0.999897i	$0.495428\pi$
$678$	1.09795e100	0.340353
$679$	3.59724e100	1.05826
$680$	−1.43205e100	−0.399844
$681$	−1.42370e99	−0.0377307
$682$	−1.63410e99	−0.0411087
$683$	7.70570e100	1.84025	0.920126	−	0.391623i	$-0.128086\pi$
$683$	7.70570e100	1.84025	0.920126	+	0.391623i	$0.128086\pi$
$684$	9.15912e99	0.207664
$685$	6.36314e100	1.36980
$686$	−2.54332e100	−0.519869
$687$	−2.27900e100	−0.442365
$688$	1.92637e99	0.0355100
$689$	−1.28163e101	−2.24378
$690$	4.74004e100	0.788205
$691$	1.13910e101	1.79925	0.899625	−	0.436664i	$-0.143840\pi$
$691$	1.13910e101	1.79925	0.899625	+	0.436664i	$0.143840\pi$
$692$	5.01650e100	0.752722
$693$	−1.20631e100	−0.171960
$694$	−3.67312e99	−0.0497477
$695$	−1.59183e101	−2.04850
$696$	−4.50988e100	−0.551489
$697$	1.45940e100	0.169594
$698$	−2.01693e100	−0.222753
$699$	1.03980e100	0.109147
$700$	8.85421e100	0.883424
$701$	−7.44015e100	−0.705655	−0.352827	−	0.935688i	$-0.614780\pi$
$701$	−7.44015e100	−0.705655	−0.352827	+	0.935688i	$0.614780\pi$
$702$	1.51756e100	0.136829
$703$	6.23747e100	0.534681
$704$	4.26964e100	0.347986
$705$	1.55005e101	1.20125
$706$	4.23587e100	0.312159
$707$	−4.24118e100	−0.297234
$708$	4.51065e100	0.300648
$709$	−1.83002e101	−1.16015	−0.580075	−	0.814563i	$-0.696977\pi$
$709$	−1.83002e101	−1.16015	−0.580075	+	0.814563i	$0.696977\pi$
$710$	1.99684e100	0.120413
$711$	−7.25474e100	−0.416151
$712$	−1.47100e101	−0.802737
$713$	−2.17767e100	−0.113061
$714$	−8.60061e99	−0.0424857
$715$	−4.54921e101	−2.13832
$716$	−1.55888e101	−0.697267
$717$	−8.21337e100	−0.349616
$718$	4.94478e100	0.200322
$719$	3.61557e101	1.39412	0.697062	−	0.717011i	$-0.254490\pi$
$719$	3.61557e101	1.39412	0.697062	+	0.717011i	$0.254490\pi$
$720$	3.07300e100	0.112787
$721$	1.47992e101	0.517054
$722$	3.39578e100	0.112945
$723$	2.40013e101	0.760021
$724$	4.95971e100	0.149533
$725$	−8.01013e101	−2.29954
$726$	1.86459e100	0.0509721
$727$	6.39908e99	0.0166589	0.00832944	−	0.999965i	$-0.497349\pi$
$727$	6.39908e99	0.0166589	0.00832944	+	0.999965i	$0.497349\pi$
$728$	2.74411e101	0.680357
$729$	1.56842e100	0.0370370
$730$	5.85994e101	1.31805
$731$	−2.10138e100	−0.0450233
$732$	−1.96971e101	−0.402030
$733$	−5.85570e101	−1.13864	−0.569322	−	0.822115i	$-0.692794\pi$
$733$	−5.85570e101	−1.13864	−0.569322	+	0.822115i	$0.692794\pi$
$734$	−3.55046e101	−0.657771
$735$	−4.02221e101	−0.710009
$736$	8.50373e101	1.43037
$737$	9.90750e101	1.58807
$738$	8.52208e100	0.130180
$739$	−3.75897e100	−0.0547257	−0.0273629	−	0.999626i	$-0.508711\pi$
$739$	−3.75897e100	−0.0547257	−0.0273629	+	0.999626i	$0.508711\pi$
$740$	5.44443e101	0.755486
$741$	5.04173e101	0.666857
$742$	4.24150e101	0.534787
$743$	1.27312e102	1.53027	0.765134	−	0.643871i	$-0.222673\pi$
$743$	1.27312e102	1.53027	0.765134	+	0.643871i	$0.222673\pi$
$744$	3.84185e100	0.0440252
$745$	−8.45018e101	−0.923248
$746$	2.43600e101	0.253775
$747$	−5.37181e101	−0.533629
$748$	1.61025e101	0.152541
$749$	1.08568e102	0.980837
$750$	−8.23296e101	−0.709384
$751$	−1.12201e102	−0.922103	−0.461051	−	0.887373i	$-0.652528\pi$
$751$	−1.12201e102	−0.922103	−0.461051	+	0.887373i	$0.652528\pi$
$752$	2.76863e101	0.217036
$753$	2.41217e101	0.180379
$754$	−1.02145e102	−0.728673
$755$	−3.48572e102	−2.37233
$756$	1.16693e101	0.0757741
$757$	1.54946e102	0.960012	0.480006	−	0.877265i	$-0.340635\pi$
$757$	1.54946e102	0.960012	0.480006	+	0.877265i	$0.340635\pi$
$758$	4.46741e101	0.264119
$759$	−1.29537e102	−0.730820
$760$	−2.77820e102	−1.49583
$761$	1.07214e102	0.550931	0.275465	−	0.961311i	$-0.411168\pi$
$761$	1.07214e102	0.550931	0.275465	+	0.961311i	$0.411168\pi$
$762$	−6.24947e101	−0.306508
$763$	−2.25656e102	−1.05640
$764$	7.18954e101	0.321282
$765$	−3.35217e101	−0.143003
$766$	1.88001e102	0.765666
$767$	2.48293e102	0.965449
$768$	−1.29597e102	−0.481142
$769$	3.88378e102	1.37680	0.688398	−	0.725333i	$-0.258314\pi$
$769$	3.88378e102	1.37680	0.688398	+	0.725333i	$0.258314\pi$
$770$	1.50554e102	0.509650
$771$	−4.69685e101	−0.151837
$772$	−2.30867e102	−0.712767
$773$	−3.12416e102	−0.921216	−0.460608	−	0.887604i	$-0.652369\pi$
$773$	−3.12416e102	−0.921216	−0.460608	+	0.887604i	$0.652369\pi$
$774$	−1.22709e101	−0.0345599
$775$	6.82361e101	0.183571
$776$	−6.81479e102	−1.75130
$777$	7.94693e101	0.195098
$778$	−1.08531e101	−0.0254553
$779$	2.83126e102	0.634455
$780$	4.40071e102	0.942246
$781$	−5.45701e101	−0.111646
$782$	−9.23558e101	−0.180561
$783$	−1.05568e102	−0.197239
$784$	−7.18428e101	−0.128281
$785$	1.26143e102	0.215273
$786$	3.05587e101	0.0498464
$787$	5.80756e102	0.905504	0.452752	−	0.891636i	$-0.350442\pi$
$787$	5.80756e102	0.905504	0.452752	+	0.891636i	$0.350442\pi$
$788$	6.76822e102	1.00877
$789$	5.70240e101	0.0812501
$790$	9.05434e102	1.23338
$791$	4.64739e102	0.605263
$792$	2.28529e102	0.284575
$793$	−1.08424e103	−1.29101
$794$	1.60190e102	0.182392
$795$	1.65317e103	1.80005
$796$	−1.26647e103	−1.31880
$797$	1.08594e103	1.08152	0.540762	−	0.841176i	$-0.318136\pi$
$797$	1.08594e103	1.08152	0.540762	+	0.841176i	$0.318136\pi$
$798$	−1.66854e102	−0.158940
$799$	−3.02015e102	−0.275181
$800$	−2.66460e103	−2.32240
$801$	−3.44336e102	−0.287096
$802$	2.10566e102	0.167957
$803$	−1.60142e103	−1.22209
$804$	−9.58408e102	−0.699779
$805$	2.00635e103	1.40169
$806$	8.70143e101	0.0581696
$807$	3.56049e102	0.227771
$808$	8.03470e102	0.491888
$809$	−1.60385e103	−0.939704	−0.469852	−	0.882745i	$-0.655693\pi$
$809$	−1.60385e103	−0.939704	−0.469852	+	0.882745i	$0.655693\pi$
$810$	−1.95749e102	−0.109769
$811$	1.24817e103	0.669935	0.334968	−	0.942230i	$-0.391275\pi$
$811$	1.24817e103	0.669935	0.334968	+	0.942230i	$0.391275\pi$
$812$	−7.85444e102	−0.403530
$813$	−6.98473e102	−0.343507
$814$	6.40355e102	0.301477
$815$	1.20398e103	0.542658
$816$	−5.98749e101	−0.0258371
$817$	−4.07672e102	−0.168433
$818$	−1.89060e103	−0.747923
$819$	6.42347e102	0.243328
$820$	2.47129e103	0.896463
$821$	−1.65555e103	−0.575123	−0.287562	−	0.957762i	$-0.592845\pi$
$821$	−1.65555e103	−0.575123	−0.287562	+	0.957762i	$0.592845\pi$
$822$	−7.23980e102	−0.240867
$823$	−3.26754e103	−1.04118	−0.520592	−	0.853806i	$-0.674289\pi$
$823$	−3.26754e103	−1.04118	−0.520592	+	0.853806i	$0.674289\pi$
$824$	−2.80363e103	−0.855667
$825$	4.05896e103	1.18659
$826$	−8.21715e102	−0.230107
$827$	−4.83309e103	−1.29652	−0.648259	−	0.761420i	$-0.724503\pi$
$827$	−4.83309e103	−1.29652	−0.648259	+	0.761420i	$0.724503\pi$
$828$	1.25308e103	0.322035
$829$	−3.86384e103	−0.951335	−0.475668	−	0.879625i	$-0.657793\pi$
$829$	−3.86384e103	−0.951335	−0.475668	+	0.879625i	$0.657793\pi$
$830$	6.70434e103	1.58155
$831$	−2.62302e103	−0.592878
$832$	−2.27354e103	−0.492408
$833$	7.83695e102	0.162648
$834$	1.81114e103	0.360211
$835$	6.79917e103	1.29594
$836$	3.12392e103	0.570660
$837$	8.99309e101	0.0157455
$838$	8.97878e102	0.150680
$839$	5.71513e103	0.919340	0.459670	−	0.888090i	$-0.347968\pi$
$839$	5.71513e103	0.919340	0.459670	+	0.888090i	$0.347968\pi$
$840$	−3.53960e103	−0.545808
$841$	3.40827e102	0.0503820
$842$	−2.37346e103	−0.336359
$843$	−2.98904e103	−0.406118
$844$	2.47271e103	0.322118
$845$	9.80517e103	1.22473
$846$	−1.76361e103	−0.211229
$847$	7.89238e102	0.0906456
$848$	2.95281e103	0.325224
$849$	−1.53834e103	−0.162491
$850$	2.89392e103	0.293166
$851$	8.53365e103	0.829154
$852$	5.27888e102	0.0491967
$853$	9.33625e102	0.0834607	0.0417303	−	0.999129i	$-0.486713\pi$
$853$	9.33625e102	0.0834607	0.0417303	+	0.999129i	$0.486713\pi$
$854$	3.58826e103	0.307701
$855$	−6.50329e103	−0.534978
$856$	−2.05676e104	−1.62318
$857$	8.65565e103	0.655361	0.327680	−	0.944789i	$-0.393733\pi$
$857$	8.65565e103	0.655361	0.327680	+	0.944789i	$0.393733\pi$
$858$	5.17596e103	0.376004
$859$	7.70170e103	0.536821	0.268410	−	0.963305i	$-0.413502\pi$
$859$	7.70170e103	0.536821	0.268410	+	0.963305i	$0.413502\pi$
$860$	−3.55840e103	−0.237991
$861$	3.60721e103	0.231504
$862$	4.86504e103	0.299625
$863$	−1.42237e104	−0.840674	−0.420337	−	0.907368i	$-0.638088\pi$
$863$	−1.42237e104	−0.840674	−0.420337	+	0.907368i	$0.638088\pi$
$864$	−3.51177e103	−0.199200
$865$	−3.56189e104	−1.93914
$866$	6.24949e103	0.326558
$867$	−1.08580e104	−0.544591
$868$	6.69099e102	0.0322136
$869$	−2.47439e104	−1.14358
$870$	1.31756e104	0.584569
$871$	−5.27565e104	−2.24715
$872$	4.27494e104	1.74822
$873$	−1.59522e104	−0.626348
$874$	−1.79172e104	−0.675484
$875$	−3.48483e104	−1.26152
$876$	1.54914e104	0.538512
$877$	3.78992e104	1.26516	0.632579	−	0.774496i	$-0.281996\pi$
$877$	3.78992e104	1.26516	0.632579	+	0.774496i	$0.281996\pi$
$878$	3.46091e103	0.110952
$879$	−1.17263e104	−0.361041
$880$	1.04812e104	0.309938
$881$	6.08115e104	1.72719	0.863596	−	0.504184i	$-0.168207\pi$
$881$	6.08115e104	1.72719	0.863596	+	0.504184i	$0.168207\pi$
$882$	4.57635e103	0.124849
$883$	5.44040e104	1.42569	0.712847	−	0.701320i	$-0.247406\pi$
$883$	5.44040e104	1.42569	0.712847	+	0.701320i	$0.247406\pi$
$884$	−8.57443e103	−0.215849
$885$	−3.20272e104	−0.774520
$886$	1.55903e104	0.362208
$887$	−3.03898e104	−0.678328	−0.339164	−	0.940727i	$-0.610144\pi$
$887$	−3.03898e104	−0.678328	−0.339164	+	0.940727i	$0.610144\pi$
$888$	−1.50551e104	−0.322866
$889$	−2.64526e104	−0.545075
$890$	4.29752e104	0.850888
$891$	5.34946e103	0.101777
$892$	3.13769e104	0.573664
$893$	−5.85917e104	−1.02946
$894$	9.61437e103	0.162345
$895$	1.10685e105	1.79628
$896$	−2.98490e104	−0.465581
$897$	6.89771e104	1.03413
$898$	3.34552e104	0.482119
$899$	−6.05313e103	−0.0838515
$900$	−3.92646e104	−0.522868
$901$	−3.22106e104	−0.412353
$902$	2.90665e104	0.357734
$903$	−5.19400e103	−0.0614592
$904$	−8.80424e104	−1.00164
$905$	−3.52156e104	−0.385222
$906$	3.96595e104	0.417154
$907$	1.41856e105	1.43480	0.717398	−	0.696664i	$-0.245333\pi$
$907$	1.41856e105	1.43480	0.717398	+	0.696664i	$0.245333\pi$
$908$	4.69732e103	0.0456881
$909$	1.88078e104	0.175922
$910$	−8.01687e104	−0.721167
$911$	3.40379e104	0.294483	0.147241	−	0.989101i	$-0.452961\pi$
$911$	3.40379e104	0.294483	0.147241	+	0.989101i	$0.452961\pi$
$912$	−1.16159e104	−0.0966574
$913$	−1.83218e105	−1.46641
$914$	−1.21200e105	−0.933065
$915$	1.39856e105	1.03570
$916$	7.51931e104	0.535659
$917$	1.29348e104	0.0886437
$918$	3.81400e103	0.0251458
$919$	4.02731e104	0.255455	0.127727	−	0.991809i	$-0.459232\pi$
$919$	4.02731e104	0.255455	0.127727	+	0.991809i	$0.459232\pi$
$920$	−3.80093e105	−2.31965
$921$	9.72611e104	0.571113
$922$	3.22073e104	0.181973
$923$	2.90581e104	0.157982
$924$	3.98007e104	0.208226
$925$	−2.67397e105	−1.34625
$926$	−1.01848e105	−0.493471
$927$	−6.56281e104	−0.306027
$928$	2.36372e105	1.06083
$929$	8.27390e104	0.357398	0.178699	−	0.983904i	$-0.442811\pi$
$929$	8.27390e104	0.357398	0.178699	+	0.983904i	$0.442811\pi$
$930$	−1.12239e104	−0.0466659
$931$	1.52039e105	0.608471
$932$	−3.43071e104	−0.132166
$933$	6.96631e104	0.258347
$934$	−1.44288e105	−0.515128
$935$	−1.14333e105	−0.392971
$936$	−1.21689e105	−0.402680
$937$	7.68415e104	0.244816	0.122408	−	0.992480i	$-0.460938\pi$
$937$	7.68415e104	0.244816	0.122408	+	0.992480i	$0.460938\pi$
$938$	1.74595e105	0.535589
$939$	−3.28234e105	−0.969515
$940$	−5.11422e105	−1.45459
$941$	2.19253e104	0.0600502	0.0300251	−	0.999549i	$-0.490441\pi$
$941$	2.19253e104	0.0600502	0.0300251	+	0.999549i	$0.490441\pi$
$942$	−1.43521e104	−0.0378538
$943$	3.87352e105	0.983878
$944$	−5.72054e104	−0.139937
$945$	−8.28560e104	−0.195207
$946$	−4.18526e104	−0.0949703
$947$	2.29101e105	0.500728	0.250364	−	0.968152i	$-0.419450\pi$
$947$	2.29101e105	0.500728	0.250364	+	0.968152i	$0.419450\pi$
$948$	2.39362e105	0.503917
$949$	8.52740e105	1.72928
$950$	5.61427e105	1.09674
$951$	5.59246e105	1.05243
$952$	6.89663e104	0.125033
$953$	5.19182e105	0.906821	0.453410	−	0.891302i	$-0.350207\pi$
$953$	5.19182e105	0.906821	0.453410	+	0.891302i	$0.350207\pi$
$954$	−1.88093e105	−0.316522
$955$	−5.10482e105	−0.827677
$956$	2.70991e105	0.423350
$957$	−3.60065e105	−0.542009
$958$	−4.44190e105	−0.644308
$959$	−3.06444e105	−0.428342
$960$	2.93263e105	0.395028
$961$	−7.65180e105	−0.993306
$962$	−3.40983e105	−0.426597
$963$	−4.81452e105	−0.580524
$964$	−7.91896e105	−0.920309
$965$	1.63924e106	1.83621
$966$	−2.28277e105	−0.246476
$967$	8.56809e105	0.891752	0.445876	−	0.895095i	$-0.352892\pi$
$967$	8.56809e105	0.891752	0.445876	+	0.895095i	$0.352892\pi$
$968$	−1.49517e105	−0.150008
$969$	1.26711e105	0.122552
$970$	1.99093e106	1.85635
$971$	−1.91450e106	−1.72097	−0.860484	−	0.509477i	$-0.829839\pi$
$971$	−1.91450e106	−1.72097	−0.860484	+	0.509477i	$0.829839\pi$
$972$	−5.17483e104	−0.0448481
$973$	7.66614e105	0.640576
$974$	2.38126e105	0.191851
$975$	−2.16136e106	−1.67905
$976$	2.49804e105	0.187125
$977$	1.08236e106	0.781832	0.390916	−	0.920426i	$-0.372158\pi$
$977$	1.08236e106	0.781832	0.390916	+	0.920426i	$0.372158\pi$
$978$	−1.36986e105	−0.0954215
$979$	−1.17443e106	−0.788938
$980$	1.32708e106	0.859749
$981$	1.00069e106	0.625244
$982$	−2.77438e105	−0.167189
$983$	−2.33991e106	−1.36003	−0.680016	−	0.733198i	$-0.738027\pi$
$983$	−2.33991e106	−1.36003	−0.680016	+	0.733198i	$0.738027\pi$
$984$	−6.83367e105	−0.383114
$985$	−4.80567e106	−2.59877
$986$	−2.56715e105	−0.133913
$987$	−7.46494e105	−0.375636
$988$	−1.66346e106	−0.807496
$989$	−5.57747e105	−0.261197
$990$	−6.67644e105	−0.301645
$991$	−9.64403e105	−0.420382	−0.210191	−	0.977660i	$-0.567409\pi$
$991$	−9.64403e105	−0.420382	−0.210191	+	0.977660i	$0.567409\pi$
$992$	−2.01359e105	−0.0846852
$993$	1.83222e106	0.743497
$994$	−9.61665e104	−0.0376537
$995$	8.99235e106	3.39746
$996$	1.77237e106	0.646171
$997$	−3.16867e106	−1.11481	−0.557403	−	0.830242i	$-0.688202\pi$
$997$	−3.16867e106	−1.11481	−0.557403	+	0.830242i	$0.688202\pi$
$998$	−1.62664e106	−0.552278
$999$	−3.52413e105	−0.115472

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.72.a.a.1.2	✓	5
3.2	odd	2		9.72.a.a.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.72.a.a.1.2	✓	5	1.1	even	1	trivial
9.72.a.a.1.4		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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 72 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66543e10 q^{2} +5.00315e16 q^{3} -1.65073e21 q^{4} +1.17208e25 q^{5} -1.33355e27 q^{6} -5.64464e29 q^{7} +1.06935e32 q^{8} +2.50316e33 q^{9} -3.12409e35 q^{10} +8.53757e36 q^{11} -8.25887e37 q^{12} -4.54617e39 q^{13} +1.50454e40 q^{14} +5.86408e41 q^{15} +1.04741e42 q^{16} -1.14257e43 q^{17} -6.67198e43 q^{18} -2.21661e45 q^{19} -1.93479e46 q^{20} -2.82410e46 q^{21} -2.27563e47 q^{22} -3.03260e48 q^{23} +5.35011e48 q^{24} +9.50248e49 q^{25} +1.21175e50 q^{26} +1.25237e50 q^{27} +9.31779e50 q^{28} -8.42951e51 q^{29} -1.56303e52 q^{30} +7.18088e51 q^{31} -2.80411e53 q^{32} +4.27148e53 q^{33} +3.04543e53 q^{34} -6.61595e54 q^{35} -4.13204e54 q^{36} -2.81397e55 q^{37} +5.90821e55 q^{38} -2.27452e56 q^{39} +1.25336e57 q^{40} -1.27729e57 q^{41} +7.52743e56 q^{42} +1.83917e57 q^{43} -1.40932e58 q^{44} +2.93389e58 q^{45} +8.08318e58 q^{46} +2.64330e59 q^{47} +5.24038e58 q^{48} -6.85906e59 q^{49} -2.53282e60 q^{50} -5.71645e59 q^{51} +7.50452e60 q^{52} +2.81914e61 q^{53} -3.33809e60 q^{54} +1.00067e62 q^{55} -6.03608e61 q^{56} -1.10900e62 q^{57} +2.24683e62 q^{58} -5.46158e62 q^{59} -9.68003e62 q^{60} +2.38496e63 q^{61} -1.91401e62 q^{62} -1.41294e63 q^{63} +5.00100e63 q^{64} -5.32847e64 q^{65} -1.13853e64 q^{66} +1.16046e65 q^{67} +1.88608e64 q^{68} -1.51726e65 q^{69} +1.76343e65 q^{70} -6.39177e64 q^{71} +2.67674e65 q^{72} -1.87573e66 q^{73} +7.50044e65 q^{74} +4.75424e66 q^{75} +3.65903e66 q^{76} -4.81915e66 q^{77} +6.06257e66 q^{78} -2.89824e67 q^{79} +1.22765e67 q^{80} +6.26579e66 q^{81} +3.40454e67 q^{82} -2.14602e68 q^{83} +4.66183e67 q^{84} -1.33918e68 q^{85} -4.90217e67 q^{86} -4.21742e68 q^{87} +9.12963e68 q^{88} -1.37561e69 q^{89} -7.82007e68 q^{90} +2.56615e69 q^{91} +5.00601e69 q^{92} +3.59270e68 q^{93} -7.04553e69 q^{94} -2.59804e70 q^{95} -1.40294e70 q^{96} -6.37285e70 q^{97} +1.82823e70 q^{98} +2.13709e70 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 25051277688 q^{2} + 25\!\cdots\!35 q^{3} + 19\!\cdots\!24 q^{4} + 14\!\cdots\!30 q^{5} - 12\!\cdots\!16 q^{6} - 12\!\cdots\!52 q^{7} - 15\!\cdots\!48 q^{8} + 12\!\cdots\!45 q^{9} - 30\!\cdots\!60 q^{10}+ \cdots + 33\!\cdots\!88 q^{99}+O(q^{100}) \) 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

Properties

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