LMFDB - Embedded newform 3.71.b.a.2.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,71,Mod(2,3)]

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([1]))

N = Newforms(chi, 71, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 71);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 71 $
Character orbit:	$[\chi]$	$=$	3.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$93.0951693564$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.13
Character	$\chi$	$=$	3.2
Dual form			3.71.b.a.2.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.12481e10i q^{2} +(-4.22339e16 - 2.68226e16i) q^{3} +1.05407e21 q^{4} -2.30186e23i q^{5} +(3.01705e26 - 4.75053e26i) q^{6} +8.16038e28 q^{7} +2.51358e31i q^{8} +(1.06425e33 + 2.26565e33i) q^{9} +O(q^{10})$	\(q+1.12481e10i q^{2} +(-4.22339e16 - 2.68226e16i) q^{3} +1.05407e21 q^{4} -2.30186e23i q^{5} +(3.01705e26 - 4.75053e26i) q^{6} +8.16038e28 q^{7} +2.51358e31i q^{8} +(1.06425e33 + 2.26565e33i) q^{9} +2.58917e33 q^{10} -4.04914e36i q^{11} +(-4.45175e37 - 2.82729e37i) q^{12} +4.37303e38 q^{13} +9.17891e38i q^{14} +(-6.17419e39 + 9.72166e39i) q^{15} +9.61696e41 q^{16} +1.30296e42i q^{17} +(-2.54843e43 + 1.19708e43i) q^{18} +2.51212e44 q^{19} -2.42632e44i q^{20} +(-3.44645e45 - 2.18883e45i) q^{21} +4.55453e46 q^{22} -4.75985e46i q^{23} +(6.74208e47 - 1.06158e48i) q^{24} +8.41734e48 q^{25} +4.91885e48i q^{26} +(1.58232e49 - 1.24233e50i) q^{27} +8.60162e49 q^{28} +1.88864e51i q^{29} +(-1.09351e50 - 6.94483e49i) q^{30} -1.77389e52 q^{31} +4.04924e52i q^{32} +(-1.08609e53 + 1.71011e53i) q^{33} -1.46559e52 q^{34} -1.87841e52i q^{35} +(1.12179e54 + 2.38815e54i) q^{36} -1.27479e54 q^{37} +2.82567e54i q^{38} +(-1.84690e55 - 1.17296e55i) q^{39} +5.78592e54 q^{40} -1.52657e56i q^{41} +(2.46203e55 - 3.87661e55i) q^{42} +6.99393e56 q^{43} -4.26808e57i q^{44} +(5.21521e56 - 2.44976e56i) q^{45} +5.35395e56 q^{46} +4.05361e58i q^{47} +(-4.06162e58 - 2.57952e58i) q^{48} -1.36844e59 q^{49} +9.46795e58i q^{50} +(3.49489e58 - 5.50292e58i) q^{51} +4.60948e59 q^{52} -4.34236e60i q^{53} +(1.39739e60 + 1.77982e59i) q^{54} -9.32056e59 q^{55} +2.05118e60i q^{56} +(-1.06097e61 - 6.73817e60i) q^{57} -2.12437e61 q^{58} +1.21751e62i q^{59} +(-6.50804e60 + 1.02473e61i) q^{60} +1.58134e62 q^{61} -1.99530e62i q^{62} +(8.68468e61 + 1.84885e62i) q^{63} +6.79905e62 q^{64} -1.00661e62i q^{65} +(-1.92356e63 - 1.22164e63i) q^{66} +1.73797e63 q^{67} +1.37342e63i q^{68} +(-1.27672e63 + 2.01027e63i) q^{69} +2.11286e62 q^{70} -5.86914e63i q^{71} +(-5.69489e64 + 2.67508e64i) q^{72} +9.24306e64 q^{73} -1.43390e64i q^{74} +(-3.55497e65 - 2.25775e65i) q^{75} +2.64796e65 q^{76} -3.30425e65i q^{77} +(1.31936e65 - 2.07742e65i) q^{78} +3.24910e66 q^{79} -2.21369e65i q^{80} +(-4.00053e66 + 4.82243e66i) q^{81} +1.71711e66 q^{82} +5.01953e66i q^{83} +(-3.63280e66 - 2.30718e66i) q^{84} +2.99924e65 q^{85} +7.86688e66i q^{86} +(5.06583e67 - 7.97648e67i) q^{87} +1.01778e68 q^{88} -2.40569e68i q^{89} +(2.75552e66 + 5.86614e66i) q^{90} +3.56856e67 q^{91} -5.01722e67i q^{92} +(7.49185e68 + 4.75805e68i) q^{93} -4.55956e68 q^{94} -5.78256e67i q^{95} +(1.08611e69 - 1.71015e69i) q^{96} +4.56772e69 q^{97} -1.53925e69i q^{98} +(9.17393e69 - 4.30930e69i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 57\!\cdots\!10 q^{3}+ \cdots - 31\!\cdots\!82 q^{9}+O(q^{10}) $ 22 * q - 57760946614928610 * q^3 - 12924724784889679105472 * q^4 - 2542746418602623176312578240 * q^6 + 3460300354929279082139211020 * q^7 - 3187627653443587997840864868739482 * q^9	$ 22 q - 57\!\cdots\!10 q^{3}+ \cdots - 21\!\cdots\!80 q^{99}+O(q^{100}) $ 22 * q - 57760946614928610 * q^3 - 12924724784889679105472 * q^4 - 2542746418602623176312578240 * q^6 + 3460300354929279082139211020 * q^7 - 3187627653443587997840864868739482 * q^9 - 204904054456738768728763726683461760 * q^10 + 168216518978261501059545818584280696640 * q^12 - 1425273500899614630088058291006011908100 * q^13 - 225789500492205687292660149319768298715840 * q^15 + 7791108876170200924142434286561643963000832 * q^16 - 159240712078782992086911930584730978792685440 * q^18 + 2012529521265601397979311193864856923750823676 * q^19 - 5316334525000974787771605720411010154937122916 * q^21 - 177999664576757911046568099334764110597720653440 * q^22 + 2221044214363105865421794285118261395337437583360 * q^24 - 47913993180689593092577485889381363779493774325690 * q^25 - 327350510975933028532160361074129063579708328041490 * q^27 + 199622305967867855771313967200368144722234985321600 * q^28 + 19529370934845391692884101303550253186745064711003520 * q^30 + 12388430374073163692752061441697409777651574405007404 * q^31 + 91609538538011962010378972773658529100477255901421120 * q^33 + 605761954772905142742127812440233067564260993651653120 * q^34 + 903849673866118209515044215587923561361275075218434112 * q^36 - 2942122339532414491328953596359839081620064777882528420 * q^37 - 83642273913756481299940648535011188445494335818507646004 * q^39 + 272642123044960747425938890972217844718938356564315934720 * q^40 + 1560147154093916143029768098476489647357578674968337342080 * q^42 - 4545359228128189931707988293083620465330530163336481972580 * q^43 - 13684191484560547979485162889557225553655737227535310368640 * q^45 + 34824945738150746982031713560272687284036228683298922087680 * q^46 + 187018310806180504680614747073364302422042767094159794882560 * q^48 + 537429667187009430823177633570141302055322425376808156541794 * q^49 + 93003444735225900297901054333392923286830613776157770499840 * q^51 - 256980181653870794210710907095882776189154704275967737138560 * q^52 + 563860949077651296335542553968680463677661322067851314468800 * q^54 - 3516118540339332578884347645630886351467431915082786354698880 * q^55 + 62619566495727497029128246919971991949893526891401194293093580 * q^57 + 116675137250817318744043251484707490614825810469582794383621760 * q^58 - 289520688194704548710930657842220413516071423272166989563023360 * q^60 - 1004518379975789938184755460502459521248398274882979931600708676 * q^61 + 2259750912371699320668016184778015293200259463243321554460021420 * q^63 - 6990282608978901236062382909358427229318771679854621867713298432 * q^64 + 9802144175872303219237439174047894300074716767326740733265952640 * q^66 - 9530737568144236105810003684427263525901520593033925660073496260 * q^67 + 68660923095126616358914910008665108044130343377859227725343530880 * q^69 - 186825484366209931701114245951001364013348939360625786570907971840 * q^70 + 800859191695150280430684829106757981081528103077118327934086410240 * q^72 - 498564607593670758195755796246723418636521686724391030404386208820 * q^73 + 2109806600351472862056557154002428953234561707550117711339382623630 * q^75 - 5263274864463875706518271175142614969672638525330024503218962553216 * q^76 + 12308167524701892969963937648343555852922730564344320620076689564800 * q^78 - 17307670437682441097149414568687707748355067787533584779481303522964 * q^79 + 13169506853202980530135359556542777642532240836639689883271737852342 * q^81 - 39431820989895068684167150578955043187025954212565254141576902204160 * q^82 + 138763489413867144231869861916118201044140663071190925822310630686336 * q^84 - 61037539079877371876604729964700889725410552523647838067356520814080 * q^85 - 149627312260702067527556548128053547148656320722965526646581032129600 * q^87 + 423107204692289659768926623144292819592688368886126043795359525621760 * q^88 - 954822316211616625813572408526438784570624253142422549351495971955840 * q^90 + 1351237435163715752950727836854267043101210025128484375869461920848568 * q^91 - 1419126662189890378883596636164605113800863195507982624574295260938180 * q^93 + 10138980254856605941232671681032460690110853357766177455228626662453760 * q^94 - 12383253221007478242150050518024370091385337450937902244753056045137920 * q^96 + 5943877415032019678068302054256035030995353737176853716379501144663980 * q^97 - 21983160871333538547745741193506138170867254293489738303957813119108480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			1.12481e10i			0.327364i	0.986513	+	0.163682i	$0.0523371\pi$
$2$			1.12481e10i			0.327364i	−0.986513	+	0.163682i	$0.947663\pi$
$3$	−4.22339e16	−	2.68226e16i	−0.844145	−	0.536114i
$3$	−4.22339e16	−	2.68226e16i	−0.844145	−	0.536114i
$4$	1.05407e21			0.892833
$5$		−	2.30186e23i		−	0.0790913i	−0.999218	−	0.0395457i	$-0.987409\pi$
$5$		−	2.30186e23i		−	0.0790913i	0.999218	−	0.0395457i	$-0.0125911\pi$
$6$	3.01705e26	−	4.75053e26i	0.175505	−	0.276343i
$7$	8.16038e28			0.215416			0.107708	−	0.994183i	$-0.465649\pi$
$7$	8.16038e28			0.215416			0.107708	+	0.994183i	$0.465649\pi$
$8$			2.51358e31i			0.619646i
$9$	1.06425e33	+	2.26565e33i	0.425163	+	0.905117i
$10$	2.58917e33			0.0258917
$11$		−	4.04914e36i		−	1.44085i	−0.693533	−	0.720425i	$-0.743947\pi$
$11$		−	4.04914e36i		−	1.44085i	0.693533	−	0.720425i	$-0.256053\pi$
$12$	−4.45175e37	−	2.82729e37i	−0.753681	−	0.478660i
$13$	4.37303e38			0.449537			0.224768	−	0.974412i	$-0.427837\pi$
$13$	4.37303e38			0.449537			0.224768	+	0.974412i	$0.427837\pi$
$14$			9.17891e38i			0.0705196i
$15$	−6.17419e39	+	9.72166e39i	−0.0424020	+	0.0667646i
$16$	9.61696e41			0.689983
$17$			1.30296e42i			0.112001i	0.998431	+	0.0560003i	$0.0178348\pi$
$17$			1.30296e42i			0.112001i	−0.998431	+	0.0560003i	$0.982165\pi$
$18$	−2.54843e43	+	1.19708e43i	−0.296303	+	0.139183i
$19$	2.51212e44			0.440215			0.220107	−	0.975476i	$-0.429359\pi$
$19$	2.51212e44			0.440215			0.220107	+	0.975476i	$0.429359\pi$
$20$		−	2.42632e44i		−	0.0706153i
$21$	−3.44645e45	−	2.18883e45i	−0.181843	−	0.115488i
$22$	4.55453e46			0.471683
$23$		−	4.75985e46i		−	0.104020i	−0.998647	−	0.0520102i	$-0.983437\pi$
$23$		−	4.75985e46i		−	0.104020i	0.998647	−	0.0520102i	$-0.0165628\pi$
$24$	6.74208e47	−	1.06158e48i	0.332201	−	0.523071i
$25$	8.41734e48			0.993745
$26$			4.91885e48i			0.147162i
$27$	1.58232e49	−	1.24233e50i	0.126346	−	0.991986i
$28$	8.60162e49			0.192331
$29$			1.88864e51i			1.23657i	0.785953	+	0.618287i	$0.212173\pi$
$29$			1.88864e51i			1.23657i	−0.785953	+	0.618287i	$0.787827\pi$
$30$	−1.09351e50	−	6.94483e49i	−0.0218563	−	0.0138809i
$31$	−1.77389e52			−1.12530			−0.562650	−	0.826695i	$-0.690218\pi$
$31$	−1.77389e52			−1.12530			−0.562650	+	0.826695i	$0.690218\pi$
$32$			4.04924e52i			0.845521i
$33$	−1.08609e53	+	1.71011e53i	−0.772460	+	1.21629i
$34$	−1.46559e52			−0.0366650
$35$		−	1.87841e52i		−	0.0170376i
$36$	1.12179e54	+	2.38815e54i	0.379600	+	0.808118i
$37$	−1.27479e54			−0.165340			−0.0826698	−	0.996577i	$-0.526345\pi$
$37$	−1.27479e54			−0.165340			−0.0826698	+	0.996577i	$0.526345\pi$
$38$			2.82567e54i			0.144111i
$39$	−1.84690e55	−	1.17296e55i	−0.379474	−	0.241003i
$40$	5.78592e54			0.0490086
$41$		−	1.52657e56i		−	0.544856i	−0.962176	−	0.272428i	$-0.912173\pi$
$41$		−	1.52657e56i		−	0.544856i	0.962176	−	0.272428i	$-0.0878266\pi$
$42$	2.46203e55	−	3.87661e55i	0.0378066	−	0.0595288i
$43$	6.99393e56			0.471330			0.235665	−	0.971834i	$-0.424273\pi$
$43$	6.99393e56			0.471330			0.235665	+	0.971834i	$0.424273\pi$
$44$		−	4.26808e57i		−	1.28644i
$45$	5.21521e56	−	2.44976e56i	0.0715869	−	0.0336267i
$46$	5.35395e56			0.0340526
$47$			4.05361e58i			1.21455i	0.794490	+	0.607277i	$0.207738\pi$
$47$			4.05361e58i			1.21455i	−0.794490	+	0.607277i	$0.792262\pi$
$48$	−4.06162e58	−	2.57952e58i	−0.582446	−	0.369910i
$49$	−1.36844e59			−0.953596
$50$			9.46795e58i			0.325316i
$51$	3.49489e58	−	5.50292e58i	0.0600451	−	0.0945447i
$52$	4.60948e59			0.401361
$53$		−	4.34236e60i		−	1.94120i	−0.240696	−	0.970600i	$-0.577376\pi$
$53$		−	4.34236e60i		−	1.94120i	0.240696	−	0.970600i	$-0.422624\pi$
$54$	1.39739e60	+	1.77982e59i	0.324741	+	0.0413612i
$55$	−9.32056e59			−0.113959
$56$			2.05118e60i			0.133482i
$57$	−1.06097e61	−	6.73817e60i	−0.371605	−	0.236005i
$58$	−2.12437e61			−0.404810
$59$			1.21751e62i			1.27542i	0.770277	+	0.637709i	$0.220118\pi$
$59$			1.21751e62i			1.27542i	−0.770277	+	0.637709i	$0.779882\pi$
$60$	−6.50804e60	+	1.02473e61i	−0.0378579	+	0.0596096i
$61$	1.58134e62			0.515799			0.257899	−	0.966172i	$-0.416970\pi$
$61$	1.58134e62			0.515799			0.257899	+	0.966172i	$0.416970\pi$
$62$		−	1.99530e62i		−	0.368383i
$63$	8.68468e61	+	1.84885e62i	0.0915872	+	0.194977i
$64$	6.79905e62			0.413190
$65$		−	1.00661e62i		−	0.0355545i
$66$	−1.92356e63	−	1.22164e63i	−0.398169	−	0.252876i
$67$	1.73797e63			0.212532			0.106266	−	0.994338i	$-0.466110\pi$
$67$	1.73797e63			0.212532			0.106266	+	0.994338i	$0.466110\pi$
$68$			1.37342e63i			0.0999977i
$69$	−1.27672e63	+	2.01027e63i	−0.0557668	+	0.0878084i
$70$	2.11286e62			0.00557749
$71$		−	5.86914e63i		−	0.0943045i	−0.998888	−	0.0471522i	$-0.984985\pi$
$71$		−	5.86914e63i		−	0.0943045i	0.998888	−	0.0471522i	$-0.0150146\pi$
$72$	−5.69489e64	+	2.67508e64i	−0.560852	+	0.263451i
$73$	9.24306e64			0.561715			0.280857	−	0.959750i	$-0.409381\pi$
$73$	9.24306e64			0.561715			0.280857	+	0.959750i	$0.409381\pi$
$74$		−	1.43390e64i		−	0.0541262i
$75$	−3.55497e65	−	2.25775e65i	−0.838865	−	0.532761i
$76$	2.64796e65			0.393038
$77$		−	3.30425e65i		−	0.310383i
$78$	1.31936e65	−	2.07742e65i	0.0788958	−	0.124226i
$79$	3.24910e66			1.24398			0.621991	−	0.783024i	$-0.286324\pi$
$79$	3.24910e66			1.24398			0.621991	+	0.783024i	$0.286324\pi$
$80$		−	2.21369e65i		−	0.0545717i
$81$	−4.00053e66	+	4.82243e66i	−0.638472	+	0.769645i
$82$	1.71711e66			0.178366
$83$			5.01953e66i			0.341138i	0.985346	+	0.170569i	$0.0545605\pi$
$83$			5.01953e66i			0.341138i	−0.985346	+	0.170569i	$0.945439\pi$
$84$	−3.63280e66	−	2.30718e66i	−0.162355	−	0.103111i
$85$	2.99924e65			0.00885827
$86$			7.86688e66i			0.154297i
$87$	5.06583e67	−	7.97648e67i	0.662944	−	1.04385i
$88$	1.01778e68			0.892817
$89$		−	2.40569e68i		−	1.42098i	−0.703705	−	0.710492i	$-0.748473\pi$
$89$		−	2.40569e68i		−	1.42098i	0.703705	−	0.710492i	$-0.251527\pi$
$90$	2.75552e66	+	5.86614e66i	0.0110082	+	0.0234350i
$91$	3.56856e67			0.0968376
$92$		−	5.01722e67i		−	0.0928729i
$93$	7.49185e68	+	4.75805e68i	0.949917	+	0.603289i
$94$	−4.55956e68			−0.397601
$95$		−	5.78256e67i		−	0.0348172i
$96$	1.08611e69	−	1.71015e69i	0.453296	−	0.713743i
$97$	4.56772e69			1.32644			0.663222	−	0.748423i	$-0.269189\pi$
$97$	4.56772e69			1.32644			0.663222	+	0.748423i	$0.269189\pi$
$98$		−	1.53925e69i		−	0.312173i
$99$	9.17393e69	−	4.30930e69i	1.30414	−	0.612597i
$100$	8.87248e69			0.887248
$101$		−	2.35412e70i		−	1.66180i	−0.556419	−	0.830902i	$-0.687825\pi$
$101$		−	2.35412e70i		−	1.66180i	0.556419	−	0.830902i	$-0.312175\pi$
$102$	6.18977e68	+	3.93110e68i	0.0309506	+	0.0196566i
$103$	3.00658e70			1.06849			0.534245	−	0.845330i	$-0.320596\pi$
$103$	3.00658e70			1.06849			0.534245	+	0.845330i	$0.320596\pi$
$104$			1.09920e70i			0.278554i
$105$	−5.03838e68	+	7.93324e68i	−0.00913409	+	0.0143822i
$106$	4.88435e70			0.635480
$107$		−	1.07506e71i		−	1.00693i	−0.864016	−	0.503464i	$-0.832059\pi$
$107$		−	1.07506e71i		−	1.00693i	0.864016	−	0.503464i	$-0.167941\pi$
$108$	1.66788e70	−	1.30950e71i	0.112806	−	0.885678i
$109$	3.79626e71			1.85964			0.929819	−	0.368017i	$-0.119963\pi$
$109$	3.79626e71			1.85964			0.929819	+	0.368017i	$0.119963\pi$
$110$		−	1.04839e70i		−	0.0373060i
$111$	5.38392e70	+	3.41931e70i	0.139571	+	0.0886409i
$112$	7.84780e70			0.148634
$113$		−	7.25560e71i		−	1.00676i	−0.864064	−	0.503382i	$-0.832089\pi$
$113$		−	7.25560e71i		−	1.00676i	0.864064	−	0.503382i	$-0.167911\pi$
$114$	7.57919e70	−	1.19339e71i	0.0772597	−	0.121650i
$115$	−1.09565e70			−0.00822712
$116$			1.99076e72i			1.10405i
$117$	4.65400e71	+	9.90775e71i	0.191127	+	0.406883i
$118$	−1.36947e72			−0.417526
$119$			1.06327e71i			0.0241268i
$120$	−2.44362e71	−	1.55193e71i	−0.0413704	−	0.0262742i
$121$	−8.49807e72			−1.07605
$122$			1.77871e72i			0.168854i
$123$	−4.09466e72	+	6.44730e72i	−0.292105	+	0.459938i
$124$	−1.86981e73			−1.00470
$125$		−	3.88731e72i		−	0.157688i
$126$	−2.07962e72	+	9.76866e71i	−0.0638285	+	0.0299824i
$127$	−3.44078e73			−0.800804			−0.400402	−	0.916340i	$-0.631129\pi$
$127$	−3.44078e73			−0.800804			−0.400402	+	0.916340i	$0.631129\pi$
$128$			5.54527e73i			0.980785i
$129$	−2.95381e73	−	1.87596e73i	−0.397871	−	0.252687i
$130$	1.13225e72			0.0116393
$131$			6.66359e73i			0.523857i	0.965087	+	0.261928i	$0.0843584\pi$
$131$			6.66359e73i			0.523857i	−0.965087	+	0.261928i	$0.915642\pi$
$132$	−1.14481e74	+	1.80258e74i	−0.689678	+	1.08594i
$133$	2.04999e73			0.0948295
$134$			1.95490e73i			0.0695755i
$135$	−2.85967e73	−	3.64228e72i	−0.0784575	−	0.00999289i
$136$	−3.27510e73			−0.0694006
$137$		−	8.01060e74i		−	1.31355i	−0.754088	−	0.656773i	$-0.771921\pi$
$137$		−	8.01060e74i		−	1.31355i	0.754088	−	0.656773i	$-0.228079\pi$
$138$	−2.26118e73	−	1.43607e73i	−0.0287453	−	0.0182561i
$139$	1.38867e75			1.37114			0.685568	−	0.728008i	$-0.259554\pi$
$139$	1.38867e75			1.37114			0.685568	+	0.728008i	$0.259554\pi$
$140$		−	1.97997e73i		−	0.0152117i
$141$	1.08728e75	−	1.71200e75i	0.651139	−	1.02526i
$142$	6.60169e73			0.0308719
$143$		−	1.77070e75i		−	0.647715i
$144$	1.02348e75	+	2.17886e75i	0.293355	+	0.624515i
$145$	4.34739e74			0.0978022
$146$			1.03967e75i			0.183885i
$147$	5.77947e75	+	3.67053e75i	0.804974	+	0.511236i
$148$	−1.34371e75			−0.147621
$149$		−	1.68760e76i		−	1.46470i	−0.680926	−	0.732352i	$-0.738423\pi$
$149$		−	1.68760e76i		−	1.46470i	0.680926	−	0.732352i	$-0.261577\pi$
$150$	2.53955e75	−	3.99869e75i	0.174407	−	0.274614i
$151$	2.07357e76			1.12856			0.564282	−	0.825582i	$-0.309153\pi$
$151$	2.07357e76			1.12856			0.564282	+	0.825582i	$0.309153\pi$
$152$			6.31442e75i			0.272777i
$153$	−2.95206e75	+	1.38668e75i	−0.101374	+	0.0476185i
$154$	3.71667e75			0.101608
$155$			4.08326e75i			0.0890015i
$156$	−1.94677e76	−	1.23638e76i	−0.338807	−	0.215175i
$157$	−1.12310e77			−1.56290			−0.781448	−	0.623971i	$-0.785518\pi$
$157$	−1.12310e77			−1.56290			−0.781448	+	0.623971i	$0.785518\pi$
$158$			3.65463e76i			0.407235i
$159$	−1.16473e77	+	1.83395e77i	−1.04071	+	1.63866i
$160$	9.32079e75			0.0668734
$161$		−	3.88422e75i		−	0.0224077i
$162$	−5.42434e76	−	4.49986e76i	−0.251954	−	0.209013i
$163$	−5.88820e76			−0.220504			−0.110252	−	0.993904i	$-0.535166\pi$
$163$	−5.88820e76			−0.220504			−0.110252	+	0.993904i	$0.535166\pi$
$164$		−	1.60911e77i		−	0.486465i
$165$	3.93644e76	+	2.50002e76i	0.0961978	+	0.0610949i
$166$	−5.64604e76			−0.111676
$167$			4.54499e77i			0.728545i	0.931292	+	0.364272i	$0.118682\pi$
$167$			4.54499e77i			0.728545i	−0.931292	+	0.364272i	$0.881318\pi$
$168$	5.50179e76	−	8.66292e76i	0.0715615	−	0.112678i
$169$	−7.55079e77			−0.797917
$170$			3.37359e75i			0.00289988i
$171$	2.67353e77	+	5.69159e77i	0.187163	+	0.398446i
$172$	7.37210e77			0.420819
$173$			2.54449e77i			0.118573i	0.998241	+	0.0592866i	$0.0188826\pi$
$173$			2.54449e77i			0.118573i	−0.998241	+	0.0592866i	$0.981117\pi$
$174$	8.97206e77	+	5.69813e77i	0.341718	+	0.217024i
$175$	6.86887e77			0.214069
$176$		−	3.89404e78i		−	0.994162i
$177$	3.26568e78	−	5.14202e78i	0.683770	−	1.07664i
$178$	2.70595e78			0.465179
$179$		−	3.43333e78i		−	0.485131i	−0.970135	−	0.242565i	$-0.922011\pi$
$179$		−	3.43333e78i		−	0.485131i	0.970135	−	0.242565i	$-0.0779889\pi$
$180$	5.49720e77	−	2.58222e77i	0.0639151	−	0.0300230i
$181$	1.14573e79			1.09732			0.548660	−	0.836046i	$-0.315138\pi$
$181$	1.14573e79			1.09732			0.548660	+	0.836046i	$0.315138\pi$
$182$			4.01397e77i			0.0317012i
$183$	−6.67861e78	−	4.24156e78i	−0.435409	−	0.276527i
$184$	1.19643e78			0.0644558
$185$			2.93438e77i			0.0130769i
$186$	−5.35192e78	+	8.42694e78i	−0.197495	+	0.310969i
$187$	5.27588e78			0.161376
$188$			4.27279e79i			1.08439i
$189$	1.29123e78	−	1.01379e79i	0.0272171	−	0.213690i
$190$	6.50431e77			0.0113979
$191$			1.51764e79i			0.221311i	0.993859	+	0.110655i	$0.0352950\pi$
$191$			1.51764e79i			0.221311i	−0.993859	+	0.110655i	$0.964705\pi$
$192$	−2.87151e79	−	1.82368e79i	−0.348792	−	0.221517i
$193$	−1.13363e80			−1.14806			−0.574032	−	0.818833i	$-0.694621\pi$
$193$	−1.13363e80			−1.14806			−0.574032	+	0.818833i	$0.694621\pi$
$194$			5.13784e79i			0.434230i
$195$	−2.69999e78	+	4.25131e78i	−0.0190613	+	0.0300131i
$196$	−1.44244e80			−0.851401
$197$		−	1.20336e80i		−	0.594400i	−0.954815	−	0.297200i	$-0.903947\pi$
$197$		−	1.20336e80i		−	0.594400i	0.954815	−	0.297200i	$-0.0960528\pi$
$198$	4.84716e79	+	1.03190e80i	0.200542	+	0.426928i
$199$	−2.08792e80			−0.724196			−0.362098	−	0.932140i	$-0.617939\pi$
$199$	−2.08792e80			−0.724196			−0.362098	+	0.932140i	$0.617939\pi$
$200$			2.11577e80i			0.615769i
$201$	−7.34014e79	−	4.66170e79i	−0.179408	−	0.113942i
$202$	2.64795e80			0.544015
$203$			1.54120e80i			0.266378i
$204$	3.68386e79	−	5.80047e79i	0.0536102	−	0.0844126i
$205$	−3.51395e79			−0.0430934
$206$			3.38185e80i			0.349785i
$207$	1.07841e80	−	5.06567e79i	0.0941506	−	0.0442257i
$208$	4.20553e80			0.310173
$209$		−	1.01719e81i		−	0.634284i
$210$	−8.92343e78	−	5.66724e78i	−0.00470822	−	0.00299017i
$211$	3.92120e81			1.75199			0.875997	−	0.482316i	$-0.160204\pi$
$211$	3.92120e81			1.75199			0.875997	+	0.482316i	$0.160204\pi$
$212$		−	4.57716e81i		−	1.73317i
$213$	−1.57426e80	+	2.47877e80i	−0.0505580	+	0.0796067i
$214$	1.20924e81			0.329632
$215$		−	1.60991e80i		−	0.0372782i
$216$	3.12270e81	+	3.97729e80i	0.614680	+	0.0782899i
$217$	−1.44756e81			−0.242408
$218$			4.27009e81i			0.608779i
$219$	−3.90371e81	−	2.47923e81i	−0.474169	−	0.301143i
$220$	−9.82453e80			−0.101746
$221$			5.69790e80i			0.0503484i
$222$	−3.84609e80	+	6.05591e80i	−0.0290178	+	0.0456904i
$223$	−1.62520e82			−1.04770			−0.523850	−	0.851811i	$-0.675505\pi$
$223$	−1.62520e82			−1.04770			−0.523850	+	0.851811i	$0.675505\pi$
$224$			3.30434e81i			0.182139i
$225$	8.95816e81	+	1.90707e82i	0.422504	+	0.899455i
$226$	8.16121e81			0.329579
$227$		−	1.50734e82i		−	0.521562i	−0.965398	−	0.260781i	$-0.916020\pi$
$227$		−	1.50734e82i		−	0.521562i	0.965398	−	0.260781i	$-0.0839801\pi$
$228$	−1.11833e82	−	7.10251e81i	−0.331782	−	0.210713i
$229$	−2.06913e82			−0.526678			−0.263339	−	0.964703i	$-0.584824\pi$
$229$	−2.06913e82			−0.526678			−0.263339	+	0.964703i	$0.584824\pi$
$230$		−	1.23240e80i		−	0.00269326i
$231$	−8.86287e81	+	1.39551e82i	−0.166401	+	0.262008i
$232$	−4.74726e82			−0.766237
$233$			9.45562e82i			1.31290i	0.754368	+	0.656452i	$0.227944\pi$
$233$			9.45562e82i			1.31290i	−0.754368	+	0.656452i	$0.772056\pi$
$234$	−1.11444e82	+	5.23488e81i	−0.133199	+	0.0625680i
$235$	9.33084e81			0.0960607
$236$			1.28334e83i			1.13873i
$237$	−1.37222e83	−	8.71492e82i	−1.05010	−	0.666917i
$238$	−1.19598e81			−0.00789824
$239$		−	2.81848e83i		−	1.60727i	−0.595123	−	0.803634i	$-0.702897\pi$
$239$		−	2.81848e83i		−	1.60727i	0.595123	−	0.803634i	$-0.297103\pi$
$240$	−5.93770e81	+	9.34928e81i	−0.0292566	+	0.0460664i
$241$	3.81914e83			1.62693			0.813464	−	0.581615i	$-0.197579\pi$
$241$	3.81914e83			1.62693			0.813464	+	0.581615i	$0.197579\pi$
$242$		−	9.55875e82i		−	0.352260i
$243$	2.98308e83	−	9.63653e82i	0.951581	−	0.307398i
$244$	1.66684e83			0.460522
$245$			3.14997e82i			0.0754212i
$246$	−7.25202e82	−	4.60573e82i	−0.150567	−	0.0956247i
$247$	1.09856e83			0.197893
$248$		−	4.45883e83i		−	0.697287i
$249$	1.34637e83	−	2.11994e83i	0.182889	−	0.287970i
$250$	4.37250e82			0.0516214
$251$			1.57526e84i			1.61723i	0.588337	+	0.808616i	$0.299783\pi$
$251$			1.57526e84i			1.61723i	−0.588337	+	0.808616i	$0.700217\pi$
$252$	9.15427e82	+	1.94882e83i	0.0817720	+	0.174082i
$253$	−1.92733e83			−0.149878
$254$		−	3.87023e83i		−	0.262154i
$255$	−1.26670e82	−	8.04475e81i	−0.00747767	−	0.00474905i
$256$	1.78950e83			0.0921157
$257$		−	2.37602e84i		−	1.06707i	−0.845779	−	0.533533i	$-0.820864\pi$
$257$		−	2.37602e84i		−	1.06707i	0.845779	−	0.533533i	$-0.179136\pi$
$258$	2.11010e83	−	3.32249e83i	0.0827206	−	0.130249i
$259$	−1.04027e83			−0.0356169
$260$		−	1.06104e83i		−	0.0317442i
$261$	−4.27900e84	+	2.00999e84i	−1.11924	+	0.525745i
$262$	−7.49530e83			−0.171492
$263$			4.76137e84i			0.953412i	0.879063	+	0.476706i	$0.158169\pi$
$263$			4.76137e84i			0.953412i	−0.879063	+	0.476706i	$0.841831\pi$
$264$	−4.29850e84	−	2.72996e84i	−0.753667	−	0.478652i
$265$	−9.99551e83			−0.153532
$266$			2.30586e83i			0.0310438i
$267$	−6.45269e84	+	1.01602e85i	−0.761809	+	1.19952i
$268$	1.83195e84			0.189756
$269$			4.45918e84i			0.405439i	0.979237	+	0.202719i	$0.0649779\pi$
$269$			4.45918e84i			0.405439i	−0.979237	+	0.202719i	$0.935022\pi$
$270$	4.09689e82	−	3.21660e83i	0.00327132	−	0.0256842i
$271$	7.41306e84			0.520083			0.260041	−	0.965597i	$-0.416264\pi$
$271$	7.41306e84			0.520083			0.260041	+	0.965597i	$0.416264\pi$
$272$			1.25305e84i			0.0772784i
$273$	−1.50714e84	−	9.57181e83i	−0.0817450	−	0.0519160i
$274$	9.01044e84			0.430008
$275$		−	3.40830e85i		−	1.43184i
$276$	−1.34575e84	+	2.11897e84i	−0.0497905	+	0.0783982i
$277$	3.18093e85			1.03696			0.518481	−	0.855089i	$-0.326498\pi$
$277$	3.18093e85			1.03696			0.518481	+	0.855089i	$0.326498\pi$
$278$			1.56200e85i			0.448861i
$279$	−1.88787e85	−	4.01902e85i	−0.478436	−	1.01853i
$280$	4.72153e83			0.0105573
$281$		−	2.57759e85i		−	0.508737i	−0.967107	−	0.254369i	$-0.918132\pi$
$281$		−	2.57759e85i		−	0.508737i	0.967107	−	0.254369i	$-0.0818676\pi$
$282$	1.92568e85	+	1.22299e85i	0.335633	+	0.213160i
$283$	6.89321e85			1.06144			0.530721	−	0.847547i	$-0.321921\pi$
$283$	6.89321e85			1.06144			0.530721	+	0.847547i	$0.321921\pi$
$284$		−	6.18649e84i		−	0.0841981i
$285$	−1.55103e84	+	2.44220e84i	−0.0186660	+	0.0293908i
$286$	1.99171e85			0.212039
$287$		−	1.24574e85i		−	0.117371i
$288$	−9.17416e85	+	4.30941e85i	−0.765295	+	0.359485i
$289$	1.33642e86			0.987456
$290$			4.89001e84i			0.0320170i
$291$	−1.92913e86	−	1.22518e86i	−1.11971	−	0.711125i
$292$	9.74284e85			0.501517
$293$			2.82171e86i			1.28868i	0.764738	+	0.644341i	$0.222868\pi$
$293$			2.82171e86i			1.28868i	−0.764738	+	0.644341i	$0.777132\pi$
$294$	−4.12866e85	+	6.50084e85i	−0.167360	+	0.263520i
$295$	2.80254e85			0.100875
$296$		−	3.20428e85i		−	0.102452i
$297$	−5.03037e86	−	6.40703e85i	−1.42930	−	0.182046i
$298$	1.89824e86			0.479492
$299$		−	2.08150e85i		−	0.0467610i
$300$	−3.74719e86	−	2.37983e86i	−0.748966	−	0.475666i
$301$	5.70731e85			0.101532
$302$			2.33239e86i			0.369451i
$303$	−6.31436e86	+	9.94235e86i	−0.890917	+	1.40280i
$304$	2.41590e86			0.303741
$305$		−	3.64002e85i		−	0.0407952i
$306$	−1.55976e85	−	3.32052e85i	−0.0155886	−	0.0331861i
$307$	4.09468e86			0.365070			0.182535	−	0.983199i	$-0.441570\pi$
$307$	4.09468e86			0.365070			0.182535	+	0.983199i	$0.441570\pi$
$308$		−	3.48291e86i		−	0.277120i
$309$	−1.26980e87	−	8.06445e86i	−0.901961	−	0.572833i
$310$	−4.59291e85			−0.0291359
$311$			9.33742e86i			0.529192i	0.964359	+	0.264596i	$0.0852386\pi$
$311$			9.33742e86i			0.529192i	−0.964359	+	0.264596i	$0.914761\pi$
$312$	2.94833e86	−	4.64234e86i	0.149336	−	0.235140i
$313$	3.10134e87			1.40442			0.702211	−	0.711969i	$-0.252196\pi$
$313$	3.10134e87			1.40442			0.702211	+	0.711969i	$0.252196\pi$
$314$		−	1.26328e87i		−	0.511636i
$315$	4.25581e85	−	1.99909e85i	0.0154210	−	0.00724375i
$316$	3.42478e87			1.11067
$317$		−	3.85445e87i		−	1.11915i	−0.828780	−	0.559575i	$-0.810965\pi$
$317$		−	3.85445e87i		−	1.11915i	0.828780	−	0.559575i	$-0.189035\pi$
$318$	−2.06285e87	−	1.31011e87i	−0.536437	−	0.340690i
$319$	7.64738e87			1.78172
$320$		−	1.56505e86i		−	0.0326797i
$321$	−2.88358e87	+	4.54038e87i	−0.539829	+	0.849994i
$322$	4.36902e85			0.00733548
$323$			3.27320e86i			0.0493043i
$324$	−4.21684e87	+	5.08318e87i	−0.570049	+	0.687164i
$325$	3.68093e87			0.446725
$326$		−	6.62314e86i		−	0.0721851i
$327$	−1.60331e88	−	1.01826e88i	−1.56981	−	0.996978i
$328$	3.83716e87			0.337617
$329$			3.30790e87i			0.261635i
$330$	−2.81206e86	+	4.42776e86i	−0.0200003	+	0.0314917i
$331$	6.86763e87			0.439366			0.219683	−	0.975571i	$-0.429498\pi$
$331$	6.86763e87			0.439366			0.219683	+	0.975571i	$0.429498\pi$
$332$			5.29094e87i			0.304579i
$333$	−1.35669e87	−	2.88822e87i	−0.0702963	−	0.149652i
$334$	−5.11227e87			−0.238499
$335$		−	4.00057e86i		−	0.0168095i
$336$	−3.31443e87	−	2.10499e87i	−0.125468	−	0.0796846i
$337$	−2.11842e88			−0.722711			−0.361356	−	0.932428i	$-0.617686\pi$
$337$	−2.11842e88			−0.722711			−0.361356	+	0.932428i	$0.617686\pi$
$338$		−	8.49324e87i		−	0.261209i
$339$	−1.94614e88	+	3.06432e88i	−0.539741	+	0.849856i
$340$	3.16141e86			0.00790895
$341$			7.18275e88i			1.62139i
$342$	−6.40198e87	+	3.00722e87i	−0.130437	+	0.0612705i
$343$	−2.28775e88			−0.420837
$344$			1.75798e88i			0.292058i
$345$	4.62736e86	+	2.93882e86i	0.00694488	+	0.00441067i
$346$	−2.86208e87			−0.0388166
$347$		−	7.19244e88i		−	0.881749i	−0.897569	−	0.440874i	$-0.854668\pi$
$347$		−	7.19244e88i		−	0.881749i	0.897569	−	0.440874i	$-0.145332\pi$
$348$	5.33975e88	−	8.40777e88i	0.591898	−	0.931981i
$349$	4.01456e88			0.402484			0.201242	−	0.979542i	$-0.435502\pi$
$349$	4.01456e88			0.402484			0.201242	+	0.979542i	$0.435502\pi$
$350$			7.72621e87i			0.0700785i
$351$	6.91953e87	−	5.43275e88i	0.0567973	−	0.445934i
$352$	1.63960e89			1.21827
$353$		−	9.88819e88i		−	0.665277i	−0.943054	−	0.332638i	$-0.892061\pi$
$353$		−	9.88819e88i		−	0.665277i	0.943054	−	0.332638i	$-0.107939\pi$
$354$	5.78382e88	+	3.67329e88i	0.352453	+	0.223842i
$355$	−1.35099e87			−0.00745867
$356$		−	2.53577e89i		−	1.26870i
$357$	2.85196e87	−	4.49059e87i	0.0129347	−	0.0203665i
$358$	3.86185e88			0.158814
$359$			2.80770e89i			1.04724i	0.851953	+	0.523618i	$0.175418\pi$
$359$			2.80770e89i			1.04724i	−0.851953	+	0.523618i	$0.824582\pi$
$360$	6.15766e87	+	1.31088e88i	0.0208367	+	0.0443585i
$361$	−2.62543e89			−0.806211
$362$			1.28874e89i			0.359223i
$363$	3.58907e89	+	2.27940e89i	0.908342	+	0.576885i
$364$	3.76151e88			0.0864598
$365$		−	2.12762e88i		−	0.0444268i
$366$	4.77097e88	−	7.51220e88i	0.0905251	−	0.142537i
$367$	−6.65935e89			−1.14847			−0.574235	−	0.818691i	$-0.694700\pi$
$367$	−6.65935e89			−1.14847			−0.574235	+	0.818691i	$0.694700\pi$
$368$		−	4.57753e88i		−	0.0717723i
$369$	3.45867e89	−	1.62465e89i	0.493158	−	0.231653i
$370$	−3.30063e87			−0.00428092
$371$		−	3.54353e89i		−	0.418167i
$372$	7.89694e89	+	5.01532e89i	0.848117	+	0.538636i
$373$	−1.82559e90			−1.78482			−0.892409	−	0.451227i	$-0.850987\pi$
$373$	−1.82559e90			−1.78482			−0.892409	+	0.451227i	$0.850987\pi$
$374$			5.93439e88i			0.0528287i
$375$	−1.04268e89	+	1.64176e89i	−0.0845387	+	0.133112i
$376$	−1.01891e90			−0.752593
$377$			8.25909e89i			0.555885i
$378$	1.14033e89	+	1.45240e88i	0.0699545	+	0.00890989i
$379$	−2.51153e90			−1.40464			−0.702321	−	0.711861i	$-0.747853\pi$
$379$	−2.51153e90			−1.40464			−0.702321	+	0.711861i	$0.747853\pi$
$380$		−	6.09523e88i		−	0.0310859i
$381$	1.45317e90	+	9.22906e89i	0.675995	+	0.429322i
$382$	−1.70707e89			−0.0724492
$383$			1.55268e90i			0.601345i	0.953727	+	0.300672i	$0.0972111\pi$
$383$			1.55268e90i			0.601345i	−0.953727	+	0.300672i	$0.902789\pi$
$384$	1.48739e90	−	2.34198e90i	0.525813	−	0.827925i
$385$	−7.60593e88			−0.0245486
$386$		−	1.27512e90i		−	0.375835i
$387$	7.44329e89	+	1.58458e90i	0.200392	+	0.426609i
$388$	4.81470e90			1.18429
$389$		−	1.16489e90i		−	0.261847i	−0.991392	−	0.130924i	$-0.958206\pi$
$389$		−	1.16489e90i		−	0.261847i	0.991392	−	0.130924i	$-0.0417943\pi$
$390$	−4.78194e88	−	3.03699e88i	−0.00982523	−	0.00623997i
$391$	6.20191e88			0.0116503
$392$		−	3.43970e90i		−	0.590891i
$393$	1.78735e90	−	2.81429e90i	0.280847	−	0.442211i
$394$	1.35356e90			0.194585
$395$		−	7.47897e89i		−	0.0983882i
$396$	9.66997e90	−	4.54230e90i	1.16438	−	0.546946i
$397$	−7.51773e90			−0.828742			−0.414371	−	0.910108i	$-0.635998\pi$
$397$	−7.51773e90			−0.828742			−0.414371	+	0.910108i	$0.635998\pi$
$398$		−	2.34852e90i		−	0.237076i
$399$	−8.65790e89	−	5.49860e89i	−0.0800499	−	0.0508395i
$400$	8.09492e90			0.685667
$401$			2.48785e91i			1.93095i	0.260495	+	0.965475i	$0.416114\pi$
$401$			2.48785e91i			1.93095i	−0.260495	+	0.965475i	$0.583886\pi$
$402$	5.24355e89	−	8.25630e89i	0.0373004	−	0.0587318i
$403$	−7.75730e90			−0.505864
$404$		−	2.48141e91i		−	1.48371i
$405$	1.11006e90	+	9.20867e89i	0.0608722	+	0.0504976i
$406$	−1.73357e90			−0.0872027
$407$			5.16179e90i			0.238230i
$408$	1.38320e90	+	8.78469e89i	0.0585842	+	0.0372067i
$409$	−4.34812e91			−1.69039			−0.845193	−	0.534461i	$-0.820515\pi$
$409$	−4.34812e91			−1.69039			−0.845193	+	0.534461i	$0.820515\pi$
$410$		−	3.95254e89i		−	0.0141072i
$411$	−2.14865e91	+	3.38319e91i	−0.704211	+	1.10882i
$412$	3.16915e91			0.953983
$413$			9.93535e90i			0.274746i
$414$	5.69794e89	+	1.21302e90i	0.0144779	+	0.0308216i
$415$	1.15543e90			0.0269810
$416$			1.77075e91i			0.380093i
$417$	−5.86489e91	−	3.72477e91i	−1.15744	−	0.735086i
$418$	1.14415e91			0.207642
$419$		−	9.14147e90i		−	0.152590i	−0.997085	−	0.0762949i	$-0.975691\pi$
$419$		−	9.14147e90i		−	0.152590i	0.997085	−	0.0762949i	$-0.0243090\pi$
$420$	−5.31081e89	+	8.36220e89i	−0.00815521	+	0.0128409i
$421$	3.42789e91			0.484343			0.242172	−	0.970233i	$-0.422140\pi$
$421$	3.42789e91			0.484343			0.242172	+	0.970233i	$0.422140\pi$
$422$			4.41062e91i			0.573540i
$423$	−9.18405e91	+	4.31405e91i	−1.09931	+	0.516384i
$424$	1.09149e92			1.20286
$425$			1.09675e91i			0.111300i
$426$	−2.78815e90	−	1.77075e90i	−0.0260604	−	0.0165509i
$427$	1.29043e91			0.111112
$428$		−	1.13318e92i		−	0.899019i
$429$	−4.74949e91	+	7.47836e91i	−0.347249	+	0.546766i
$430$	1.81085e90			0.0122035
$431$		−	1.74261e92i		−	1.08267i	−0.840808	−	0.541333i	$-0.817920\pi$
$431$		−	1.74261e92i		−	1.08267i	0.840808	−	0.541333i	$-0.182080\pi$
$432$	1.52171e91	−	1.19474e92i	0.0871768	−	0.684454i
$433$	1.67440e92			0.884671			0.442336	−	0.896850i	$-0.354150\pi$
$433$	1.67440e92			0.884671			0.442336	+	0.896850i	$0.354150\pi$
$434$		−	1.62824e91i		−	0.0793558i
$435$	−1.83607e91	−	1.16608e91i	−0.0825593	−	0.0524332i
$436$	4.00153e92			1.66035
$437$		−	1.19573e91i		−	0.0457914i
$438$	2.78868e91	−	4.39095e91i	0.0985835	−	0.155226i
$439$	2.07182e91			0.0676230			0.0338115	−	0.999428i	$-0.489235\pi$
$439$	2.07182e91			0.0676230			0.0338115	+	0.999428i	$0.489235\pi$
$440$		−	2.34280e91i		−	0.0706141i
$441$	−1.45637e92	−	3.10041e92i	−0.405434	−	0.863115i
$442$	−6.40908e90			−0.0164822
$443$			5.21055e92i			1.23809i	0.785355	+	0.619046i	$0.212481\pi$
$443$			5.21055e92i			1.23809i	−0.785355	+	0.619046i	$0.787519\pi$
$444$	5.67503e91	+	3.60419e91i	0.124613	+	0.0791415i
$445$	−5.53756e91			−0.112388
$446$		−	1.82805e92i		−	0.342979i
$447$	−4.52658e92	+	7.12739e92i	−0.785249	+	1.23642i
$448$	5.54828e91			0.0890078
$449$			9.00414e92i			1.33604i	0.744142	+	0.668022i	$0.232859\pi$
$449$			9.00414e92i			1.33604i	−0.744142	+	0.668022i	$0.767141\pi$
$450$	−2.14510e92	+	1.00763e92i	−0.294449	+	0.138313i
$451$	−6.18129e92			−0.785056
$452$		−	7.64792e92i		−	0.898872i
$453$	−8.75751e92	−	5.56187e92i	−0.952672	−	0.605039i
$454$	1.69548e92			0.170741
$455$		−	8.21433e90i		−	0.00765902i
$456$	1.69369e92	−	2.66683e92i	0.146240	−	0.230264i
$457$	2.29745e92			0.183729			0.0918647	−	0.995772i	$-0.470717\pi$
$457$	2.29745e92			0.183729			0.0918647	+	0.995772i	$0.470717\pi$
$458$		−	2.32738e92i		−	0.172416i
$459$	1.61871e92	+	2.06170e91i	0.111103	+	0.0141508i
$460$	−1.15489e91			−0.00734544
$461$			6.76318e92i			0.398674i	0.979931	+	0.199337i	$0.0638789\pi$
$461$			6.76318e92i			0.398674i	−0.979931	+	0.199337i	$0.936121\pi$
$462$	−1.56970e92	−	9.96908e91i	−0.0857721	−	0.0544736i
$463$	−4.59443e92			−0.232754			−0.116377	−	0.993205i	$-0.537128\pi$
$463$	−4.59443e92			−0.232754			−0.116377	+	0.993205i	$0.537128\pi$
$464$			1.81630e93i			0.853214i
$465$	1.09524e92	−	1.72452e92i	0.0477150	−	0.0751302i
$466$	−1.06358e93			−0.429798
$467$		−	1.73821e93i		−	0.651645i	−0.945431	−	0.325822i	$-0.894359\pi$
$467$		−	1.73821e93i		−	0.651645i	0.945431	−	0.325822i	$-0.105641\pi$
$468$	4.90564e92	+	1.04435e93i	0.170644	+	0.363279i
$469$	1.41825e92			0.0457830
$470$			1.04955e92i			0.0314468i
$471$	4.74328e93	+	3.01244e93i	1.31931	+	0.837890i
$472$	−3.06031e93			−0.790307
$473$		−	2.83194e93i		−	0.679117i
$474$	9.80268e92	−	1.54349e93i	0.218325	−	0.343766i
$475$	2.11454e93			0.437461
$476$			1.12076e92i			0.0215412i
$477$	9.83826e93	−	4.62136e93i	1.75701	−	0.825327i
$478$	3.17027e93			0.526162
$479$		−	9.63868e93i		−	1.48688i	−0.668805	−	0.743438i	$-0.733194\pi$
$479$		−	9.63868e93i		−	1.48688i	0.668805	−	0.743438i	$-0.266806\pi$
$480$	−3.93654e92	−	2.50008e92i	−0.0564509	−	0.0358518i
$481$	−5.57468e92			−0.0743262
$482$			4.29582e93i			0.532598i
$483$	−1.04185e92	+	1.64046e92i	−0.0120131	+	0.0189154i
$484$	−8.95756e93			−0.960732
$485$		−	1.05143e93i		−	0.104910i
$486$	1.08393e93	+	3.35542e93i	0.100631	+	0.311514i
$487$	−1.38125e94			−1.19332			−0.596661	−	0.802493i	$-0.703506\pi$
$487$	−1.38125e94			−1.19332			−0.596661	+	0.802493i	$0.703506\pi$
$488$			3.97482e93i			0.319613i
$489$	2.48682e93	+	1.57937e93i	0.186138	+	0.118215i
$490$	−3.54313e92			−0.0246902
$491$			1.48757e94i			0.965219i	0.875836	+	0.482609i	$0.160311\pi$
$491$			1.48757e94i			0.965219i	−0.875836	+	0.482609i	$0.839689\pi$
$492$	−4.31606e93	+	6.79591e93i	−0.260801	+	0.410647i
$493$	−2.46083e93			−0.138497
$494$			1.23568e93i			0.0647830i
$495$	−9.91940e92	−	2.11171e93i	−0.0484511	−	0.103146i
$496$	−1.70595e94			−0.776438
$497$		−	4.78944e92i		−	0.0203147i
$498$	2.38454e93	+	1.51442e93i	0.0942710	+	0.0598712i
$499$	4.91040e93			0.180966			0.0904832	−	0.995898i	$-0.471159\pi$
$499$	4.91040e93			0.180966			0.0904832	+	0.995898i	$0.471159\pi$
$500$		−	4.09750e93i		−	0.140789i
$501$	1.21908e94	−	1.91953e94i	0.390583	−	0.614998i
$502$	−1.77188e94			−0.529424
$503$			3.13005e94i			0.872311i	0.899871	+	0.436155i	$0.143660\pi$
$503$			3.13005e94i			0.872311i	−0.899871	+	0.436155i	$0.856340\pi$
$504$	−4.64725e93	+	2.18296e93i	−0.120817	+	0.0567516i
$505$	−5.41885e93			−0.131434
$506$		−	2.16789e93i		−	0.0490647i
$507$	3.18899e94	+	2.02532e94i	0.673558	+	0.427774i
$508$	−3.62682e94			−0.714984
$509$		−	7.12471e94i		−	1.31113i	−0.755140	−	0.655563i	$-0.772431\pi$
$509$		−	7.12471e94i		−	1.31113i	0.755140	−	0.655563i	$-0.227569\pi$
$510$	9.04885e91	−	1.42480e92i	0.00155467	−	0.00244792i
$511$	7.54269e93			0.121003
$512$			6.74798e94i			1.01094i
$513$	3.97498e93	−	3.12089e94i	0.0556195	−	0.436687i
$514$	2.67259e94			0.349319
$515$		−	6.92074e93i		−	0.0845083i
$516$	−3.11353e94	−	1.97739e94i	−0.355233	−	0.225607i
$517$	1.64136e95			1.74999
$518$		−	1.17011e93i		−	0.0116597i
$519$	6.82498e93	−	1.07464e94i	0.0635688	−	0.100093i
$520$	2.53020e93			0.0220312
$521$		−	1.70370e95i		−	1.38699i	−0.720463	−	0.693493i	$-0.756071\pi$
$521$		−	1.70370e95i		−	1.38699i	0.720463	−	0.693493i	$-0.243929\pi$
$522$	−2.26086e94	−	4.81308e94i	−0.172110	−	0.366400i
$523$	1.65735e95			1.17993			0.589964	−	0.807430i	$-0.299142\pi$
$523$	1.65735e95			1.17993			0.589964	+	0.807430i	$0.299142\pi$
$524$			7.02389e94i			0.467716i
$525$	−2.90099e94	−	1.84241e94i	−0.180705	−	0.114765i
$526$	−5.35566e94			−0.312113
$527$		−	2.31132e94i		−	0.126034i
$528$	−1.04448e95	+	1.64461e95i	−0.532984	+	0.839217i
$529$	2.07121e95			0.989180
$530$		−	1.12431e94i		−	0.0502609i
$531$	−2.75845e95	+	1.29574e95i	−1.15440	+	0.542261i
$532$	2.16083e94			0.0846669
$533$		−	6.67574e94i		−	0.244933i
$534$	−1.14283e95	−	7.25808e94i	−0.392679	−	0.249389i
$535$	−2.47463e94			−0.0796394
$536$			4.36854e94i			0.131695i
$537$	−9.20908e94	+	1.45003e95i	−0.260085	+	0.409521i
$538$	−5.01575e94			−0.132726
$539$			5.54102e95i			1.37399i
$540$	−3.01430e94	−	3.83922e93i	−0.0700494	−	0.00892198i
$541$	−9.54225e94			−0.207848			−0.103924	−	0.994585i	$-0.533140\pi$
$541$	−9.54225e94			−0.207848			−0.103924	+	0.994585i	$0.533140\pi$
$542$			8.33832e94i			0.170257i
$543$	−4.83887e95	−	3.07315e95i	−0.926297	−	0.588288i
$544$	−5.27602e94			−0.0946988
$545$		−	8.73846e94i		−	0.147081i
$546$	1.07665e94	−	1.69526e94i	0.0169954	−	0.0267604i
$547$	−4.66764e95			−0.691100			−0.345550	−	0.938400i	$-0.612308\pi$
$547$	−4.66764e95			−0.691100			−0.345550	+	0.938400i	$0.612308\pi$
$548$		−	8.44374e95i		−	1.17278i
$549$	1.68294e95	+	3.58275e95i	0.219299	+	0.466858i
$550$	3.83371e95			0.468732
$551$			4.74450e95i			0.544358i
$552$	−5.05298e94	−	3.20913e94i	−0.0544101	−	0.0345557i
$553$	2.65138e95			0.267974
$554$			3.57796e95i			0.339464i
$555$	7.87077e93	−	1.23930e94i	0.00701073	−	0.0110388i
$556$	1.46376e96			1.22420
$557$		−	1.56831e96i		−	1.23169i	−0.787868	−	0.615844i	$-0.788815\pi$
$557$		−	1.56831e96i		−	1.23169i	0.787868	−	0.615844i	$-0.211185\pi$
$558$	4.52065e95	−	2.12350e95i	0.333430	−	0.156623i
$559$	3.05847e95			0.211880
$560$		−	1.80645e94i		−	0.0117556i
$561$	−2.22821e95	−	1.41513e95i	−0.136225	−	0.0865159i
$562$	2.89932e95			0.166542
$563$			3.30600e96i			1.78447i	0.451574	+	0.892234i	$0.350863\pi$
$563$			3.30600e96i			1.78447i	−0.451574	+	0.892234i	$0.649137\pi$
$564$	1.14607e96	−	1.80457e96i	0.581359	−	0.915386i
$565$	−1.67014e95			−0.0796264
$566$			7.75358e95i			0.347478i
$567$	−3.26459e95	+	3.93529e95i	−0.137537	+	0.165794i
$568$	1.47526e95			0.0584353
$569$		−	4.10695e96i		−	1.52964i	−0.644241	−	0.764822i	$-0.722827\pi$
$569$		−	4.10695e96i		−	1.52964i	0.644241	−	0.764822i	$-0.277173\pi$
$570$	−2.74702e94	−	1.74463e94i	−0.00962149	−	0.00611058i
$571$	−6.40982e95			−0.211146			−0.105573	−	0.994412i	$-0.533668\pi$
$571$	−6.40982e95			−0.211146			−0.105573	+	0.994412i	$0.533668\pi$
$572$		−	1.86644e96i		−	0.578301i
$573$	4.07072e95	−	6.40960e95i	0.118648	−	0.186818i
$574$	1.40122e95			0.0384230
$575$		−	4.00653e95i		−	0.103370i
$576$	7.23589e95	+	1.54043e96i	0.175673	+	0.373985i
$577$	−3.17496e96			−0.725412			−0.362706	−	0.931904i	$-0.618147\pi$
$577$	−3.17496e96			−0.725412			−0.362706	+	0.931904i	$0.618147\pi$
$578$			1.50322e96i			0.323258i
$579$	4.78777e96	+	3.04069e96i	0.969132	+	0.615493i
$580$	4.58246e95			0.0873210
$581$			4.09613e95i			0.0734867i
$582$	1.37810e96	−	2.16991e96i	0.232797	−	0.366553i
$583$	−1.75828e97			−2.79698
$584$			2.32332e96i			0.348064i
$585$	2.28063e95	−	1.07129e95i	0.0321809	−	0.0151165i
$586$	−3.17390e96			−0.421868
$587$			1.02244e97i			1.28028i	0.768258	+	0.640141i	$0.221124\pi$
$587$			1.02244e97i			1.28028i	−0.768258	+	0.640141i	$0.778876\pi$
$588$	6.09197e96	+	3.86899e96i	0.718707	+	0.456448i
$589$	−4.45624e96			−0.495374
$590$			3.15234e95i			0.0330227i
$591$	−3.22773e96	+	5.08227e96i	−0.318666	+	0.501760i
$592$	−1.22596e96			−0.114081
$593$			8.12941e96i			0.713091i	0.934278	+	0.356545i	$0.116045\pi$
$593$			8.12941e96i			0.713091i	−0.934278	+	0.356545i	$0.883955\pi$
$594$	7.20672e95	−	5.65824e96i	0.0595953	−	0.467903i
$595$	2.44749e94			0.00190822
$596$		−	1.77885e97i		−	1.30774i
$597$	8.81810e96	+	5.60035e96i	0.611327	+	0.388252i
$598$	2.34130e95			0.0153079
$599$		−	2.67750e97i		−	1.65117i	−0.564281	−	0.825583i	$-0.690846\pi$
$599$		−	2.67750e97i		−	1.65117i	0.564281	−	0.825583i	$-0.309154\pi$
$600$	5.67504e96	−	8.93571e96i	0.330123	−	0.519799i
$601$	7.56183e96			0.414974			0.207487	−	0.978238i	$-0.433472\pi$
$601$	7.56183e96			0.414974			0.207487	+	0.978238i	$0.433472\pi$
$602$			6.41967e95i			0.0332380i
$603$	1.84964e96	+	3.93764e96i	0.0903609	+	0.192367i
$604$	2.18569e97			1.00762
$605$			1.95614e96i			0.0851062i
$606$	−1.11833e97	−	7.10248e96i	−0.459228	−	0.291654i
$607$	4.67720e96			0.181293			0.0906466	−	0.995883i	$-0.471107\pi$
$607$	4.67720e96			0.181293			0.0906466	+	0.995883i	$0.471107\pi$
$608$			1.01722e97i			0.372211i
$609$	4.13391e96	−	6.50911e96i	0.142809	−	0.224862i
$610$	4.09435e95			0.0133549
$611$			1.77266e97i			0.545987i
$612$	−3.11168e96	+	1.46166e96i	−0.0905096	+	0.0425154i
$613$	−7.43240e96			−0.204180			−0.102090	−	0.994775i	$-0.532553\pi$
$613$	−7.43240e96			−0.204180			−0.102090	+	0.994775i	$0.532553\pi$
$614$			4.60576e96i			0.119511i
$615$	1.48408e96	+	9.42534e95i	0.0363771	+	0.0231030i
$616$	8.30550e96			0.192327
$617$		−	1.68196e97i		−	0.367990i	−0.982927	−	0.183995i	$-0.941097\pi$
$617$		−	1.68196e97i		−	0.367990i	0.982927	−	0.183995i	$-0.0589030\pi$
$618$	9.07101e96	−	1.42829e97i	0.187525	−	0.295270i
$619$	2.76239e97			0.539651			0.269825	−	0.962909i	$-0.413034\pi$
$619$	2.76239e97			0.539651			0.269825	+	0.962909i	$0.413034\pi$
$620$			4.30404e96i			0.0794635i
$621$	−5.91331e96	−	7.53160e95i	−0.103187	−	0.0131426i
$622$	−1.05029e97			−0.173239
$623$		−	1.96313e97i		−	0.306103i
$624$	−1.77616e97	−	1.12803e97i	−0.261831	−	0.166288i
$625$	7.04029e97			0.981273
$626$			3.48843e97i			0.459758i
$627$	−2.72838e97	+	4.29601e97i	−0.340049	+	0.535428i
$628$	−1.18383e98			−1.39540
$629$		−	1.66100e96i		−	0.0185181i
$630$	2.24861e95	+	4.78699e95i	0.00237134	+	0.00504828i
$631$	−2.59882e96			−0.0259267			−0.0129634	−	0.999916i	$-0.504126\pi$
$631$	−2.59882e96			−0.0259267			−0.0129634	+	0.999916i	$0.504126\pi$
$632$			8.16686e97i			0.770828i
$633$	−1.65607e98	−	1.05177e98i	−1.47894	−	0.939269i
$634$	4.33554e97			0.366369
$635$			7.92019e96i			0.0633366i
$636$	−1.22771e98	+	1.93311e98i	−0.929176	+	1.46305i
$637$	−5.98425e97			−0.428676
$638$			8.60188e97i			0.583270i
$639$	1.32974e97	−	6.24623e96i	0.0853565	−	0.0400948i
$640$	1.27644e97			0.0775716
$641$		−	6.94168e97i		−	0.399423i	−0.979855	−	0.199712i	$-0.935999\pi$
$641$		−	6.94168e97i		−	0.399423i	0.979855	−	0.199712i	$-0.0640006\pi$
$642$	−5.10709e97	−	3.24349e97i	−0.278258	−	0.176721i
$643$	3.20781e98			1.65510			0.827550	−	0.561392i	$-0.189734\pi$
$643$	3.20781e98			1.65510			0.827550	+	0.561392i	$0.189734\pi$
$644$		−	4.09424e96i		−	0.0200063i
$645$	−4.31819e96	+	6.79926e96i	−0.0199853	+	0.0314682i
$646$	−3.68175e96			−0.0161405
$647$		−	4.60243e98i		−	1.91134i	−0.294444	−	0.955669i	$-0.595134\pi$
$647$		−	4.60243e98i		−	1.91134i	0.294444	−	0.955669i	$-0.404866\pi$
$648$	−1.21216e98	−	1.00557e98i	−0.476907	−	0.395627i
$649$	4.92987e98			1.83769
$650$			4.14037e97i			0.146242i
$651$	6.11363e97	+	3.88275e97i	0.204628	+	0.129958i
$652$	−6.20658e97			−0.196873
$653$			4.23868e98i			1.27429i	0.770743	+	0.637147i	$0.219885\pi$
$653$			4.23868e98i			1.27429i	−0.770743	+	0.637147i	$0.780115\pi$
$654$	1.14535e98	−	1.80343e98i	0.326375	−	0.513898i
$655$	1.53386e97			0.0414325
$656$		−	1.46810e98i		−	0.375941i
$657$	9.83692e97	+	2.09415e98i	0.238820	+	0.508417i
$658$	−3.72077e97			−0.0856499
$659$		−	4.42082e98i		−	0.964968i	−0.875905	−	0.482484i	$-0.839735\pi$
$659$		−	4.42082e98i		−	0.964968i	0.875905	−	0.482484i	$-0.160265\pi$
$660$	4.14928e97	+	2.63520e97i	0.0858885	+	0.0545475i
$661$	−6.76804e97			−0.132865			−0.0664327	−	0.997791i	$-0.521162\pi$
$661$	−6.76804e97			−0.132865			−0.0664327	+	0.997791i	$0.521162\pi$
$662$			7.72481e97i			0.143833i
$663$	1.52833e97	−	2.40645e97i	0.0269925	−	0.0425013i
$664$	−1.26170e98			−0.211384
$665$		−	4.71879e96i		−	0.00750020i
$666$	3.24871e97	−	1.52603e97i	0.0489906	−	0.0230125i
$667$	8.98965e97			0.128629
$668$			4.79074e98i			0.650469i
$669$	6.86386e98	+	4.35922e98i	0.884411	+	0.561687i
$670$	4.49990e96			0.00550282
$671$		−	6.40306e98i		−	0.743189i
$672$	8.86309e97	−	1.39555e98i	0.0976474	−	0.153752i
$673$	−1.85832e99			−1.94354			−0.971770	−	0.235930i	$-0.924186\pi$
$673$	−1.85832e99			−1.94354			−0.971770	+	0.235930i	$0.924186\pi$
$674$		−	2.38283e98i		−	0.236590i
$675$	1.33189e98	−	1.04571e99i	0.125556	−	0.985781i
$676$	−7.95906e98			−0.712406
$677$			1.40840e99i			1.19708i	0.801093	+	0.598539i	$0.204252\pi$
$677$			1.40840e99i			1.19708i	−0.801093	+	0.598539i	$0.795748\pi$
$678$	−3.44680e98	−	2.18905e98i	−0.278212	−	0.176692i
$679$	3.72743e98			0.285738
$680$			7.53884e96i			0.00548899i
$681$	−4.04308e98	+	6.36609e98i	−0.279617	+	0.440275i
$682$	−8.07926e98			−0.530785
$683$			2.28741e99i			1.42764i	0.700329	+	0.713820i	$0.253037\pi$
$683$			2.28741e99i			1.42764i	−0.700329	+	0.713820i	$0.746963\pi$
$684$	2.81809e98	+	5.99933e98i	0.167105	+	0.355746i
$685$	−1.84393e98			−0.103890
$686$		−	2.57329e98i		−	0.137767i
$687$	8.73873e98	+	5.54994e98i	0.444593	+	0.282360i
$688$	6.72604e98			0.325210
$689$		−	1.89893e99i		−	0.872641i
$690$	−3.30563e96	+	5.20492e96i	−0.00144390	+	0.00227351i
$691$	−3.08509e99			−1.28096			−0.640481	−	0.767974i	$-0.721265\pi$
$691$	−3.08509e99			−1.28096			−0.640481	+	0.767974i	$0.721265\pi$
$692$			2.68207e98i			0.105866i
$693$	7.48627e98	−	3.51655e98i	0.280933	−	0.131963i
$694$	8.09017e98			0.288653
$695$		−	3.19652e98i		−	0.108445i
$696$	2.00495e99	+	1.27334e99i	0.646816	+	0.410791i
$697$	1.98906e98			0.0610241
$698$			4.51564e98i			0.131759i
$699$	2.53625e99	−	3.99348e99i	0.703866	−	1.10828i
$700$	7.24028e98			0.191128
$701$		−	1.85280e99i		−	0.465261i	−0.972565	−	0.232631i	$-0.925267\pi$
$701$		−	1.85280e99i		−	0.465261i	0.972565	−	0.232631i	$-0.0747333\pi$
$702$	6.11084e98	+	7.78319e97i	0.145983	+	0.0185934i
$703$	−3.20242e98			−0.0727849
$704$		−	2.75303e99i		−	0.595344i
$705$	−3.94078e98	−	2.50278e98i	−0.0810892	−	0.0514995i
$706$	1.11224e99			0.217788
$707$		−	1.92105e99i		−	0.357980i
$708$	3.44226e99	−	5.42006e99i	0.610492	−	0.961258i
$709$	−3.35670e99			−0.566624			−0.283312	−	0.959028i	$-0.591433\pi$
$709$	−3.35670e99			−0.566624			−0.283312	+	0.959028i	$0.591433\pi$
$710$		−	1.51962e97i		−	0.00244170i
$711$	3.45785e99	+	7.36131e99i	0.528896	+	1.12595i
$712$	6.04689e99			0.880506
$713$			8.44347e98i			0.117054i
$714$	5.05109e97	+	3.20793e97i	0.00666726	+	0.00423436i
$715$	−4.07591e98			−0.0512287
$716$		−	3.61897e99i		−	0.433141i
$717$	−7.55990e99	+	1.19035e100i	−0.861679	+	1.35677i
$718$	−3.15814e99			−0.342828
$719$			5.92577e99i			0.612680i	0.951922	+	0.306340i	$0.0991044\pi$
$719$			5.92577e99i			0.612680i	−0.951922	+	0.306340i	$0.900896\pi$
$720$	5.01544e98	−	2.35592e98i	0.0493937	−	0.0232019i
$721$	2.45349e99			0.230170
$722$		−	2.95312e99i		−	0.263925i
$723$	−1.61297e100	−	1.02439e100i	−1.37336	−	0.872220i
$724$	1.20768e100			0.979723
$725$			1.58974e100i			1.22884i
$726$	−2.56391e99	+	4.03703e99i	−0.188852	+	0.297359i
$727$	−1.40387e100			−0.985424			−0.492712	−	0.870193i	$-0.663994\pi$
$727$	−1.40387e100			−0.985424			−0.492712	+	0.870193i	$0.663994\pi$
$728$			8.96986e98i			0.0600050i
$729$	−1.51835e100	−	3.93153e99i	−0.968073	−	0.250667i
$730$	2.39318e98			0.0145437
$731$			9.11284e98i			0.0527893i
$732$	−7.03972e99	−	4.47091e99i	−0.388748	−	0.246892i
$733$	1.36041e100			0.716196			0.358098	−	0.933684i	$-0.383425\pi$
$733$	1.36041e100			0.716196			0.358098	+	0.933684i	$0.383425\pi$
$734$		−	7.49054e99i		−	0.375968i
$735$	8.44904e98	−	1.33035e99i	0.0404344	−	0.0636664i
$736$	1.92738e99			0.0879515
$737$		−	7.03730e99i		−	0.306227i
$738$	1.82743e99	+	3.89036e99i	0.0758348	+	0.161442i
$739$	7.96485e99			0.315226			0.157613	−	0.987501i	$-0.449620\pi$
$739$	7.96485e99			0.315226			0.157613	+	0.987501i	$0.449620\pi$
$740$			3.09304e98i			0.0116755i
$741$	−4.63964e99	−	2.94662e99i	−0.167050	−	0.106093i
$742$	3.98582e99			0.136893
$743$			2.47695e100i			0.811537i	0.913976	+	0.405769i	$0.132996\pi$
$743$			2.47695e100i			0.811537i	−0.913976	+	0.405769i	$0.867004\pi$
$744$	−1.19597e100	+	1.88314e100i	−0.373826	+	0.588612i
$745$	−3.88462e99			−0.115845
$746$		−	2.05345e100i		−	0.584286i
$747$	−1.13725e100	+	5.34203e99i	−0.308769	+	0.145039i
$748$	5.56115e99			0.144082
$749$		−	8.77286e99i		−	0.216909i
$750$	−1.84668e99	−	1.17282e99i	−0.0435760	−	0.0276750i
$751$	5.27348e100			1.18768			0.593840	−	0.804583i	$-0.297611\pi$
$751$	5.27348e100			1.18768			0.593840	+	0.804583i	$0.297611\pi$
$752$			3.89834e100i			0.838021i
$753$	4.22526e100	−	6.65294e100i	0.867021	−	1.36518i
$754$	−9.28995e99			−0.181977
$755$		−	4.77308e99i		−	0.0892596i
$756$	1.36105e99	−	1.06861e100i	0.0243003	−	0.190790i
$757$	6.74395e100			1.14963			0.574815	−	0.818283i	$-0.305074\pi$
$757$	6.74395e100			1.14963			0.574815	+	0.818283i	$0.305074\pi$
$758$		−	2.82500e100i		−	0.459829i
$759$	8.13986e99	+	5.16960e99i	0.126519	+	0.0803517i
$760$	1.45349e99			0.0215743
$761$		−	1.00554e101i		−	1.42540i	−0.701469	−	0.712700i	$-0.747472\pi$
$761$		−	1.00554e101i		−	1.42540i	0.701469	−	0.712700i	$-0.252528\pi$
$762$	−1.03810e100	+	1.63455e100i	−0.140545	+	0.221296i
$763$	3.09789e100			0.400597
$764$			1.59970e100i			0.197593i
$765$	3.19194e98	+	6.79522e98i	0.00376621	+	0.00801777i
$766$	−1.74647e100			−0.196859
$767$			5.32421e100i			0.573347i
$768$	−7.55777e99	−	4.79992e99i	−0.0777591	−	0.0493845i
$769$	−2.79122e100			−0.274392			−0.137196	−	0.990544i	$-0.543809\pi$
$769$	−2.79122e100			−0.274392			−0.137196	+	0.990544i	$0.543809\pi$
$770$		−	8.55526e98i		−	0.00803633i
$771$	−6.37312e100	+	1.00349e101i	−0.572069	+	0.900759i
$772$	−1.19493e101			−1.02503
$773$			2.28495e100i			0.187325i	0.995604	+	0.0936623i	$0.0298574\pi$
$773$			2.28495e100i			0.187325i	−0.995604	+	0.0936623i	$0.970143\pi$
$774$	−1.78236e100	+	8.37232e99i	−0.139657	+	0.0656013i
$775$	−1.49315e101			−1.11826
$776$			1.14813e101i			0.821925i
$777$	4.39348e99	+	2.79029e99i	0.0300658	+	0.0190947i
$778$	1.31028e100			0.0857194
$779$		−	3.83493e100i		−	0.239854i
$780$	−2.84599e99	+	4.48118e99i	−0.0170185	+	0.0267967i
$781$	−2.37650e100			−0.135879
$782$			6.97600e98i			0.00381391i
$783$	2.34632e101	+	2.98844e100i	1.22666	+	0.156236i
$784$	−1.31603e101			−0.657965
$785$			2.58522e100i			0.123612i
$786$	3.16556e100	+	2.01044e100i	0.144764	+	0.0919393i
$787$	−1.87839e101			−0.821617			−0.410808	−	0.911722i	$-0.634754\pi$
$787$	−1.87839e101			−0.821617			−0.410808	+	0.911722i	$0.634754\pi$
$788$		−	1.26843e101i		−	0.530700i
$789$	1.27712e101	−	2.01091e101i	0.511138	−	0.804819i
$790$	8.41245e99			0.0322088
$791$		−	5.92084e100i		−	0.216874i
$792$	1.08318e101	+	2.30594e101i	0.379593	+	0.808103i
$793$	6.91524e100			0.231871
$794$		−	8.45606e100i		−	0.271300i
$795$	4.22150e100	+	2.68106e100i	0.129604	+	0.0823108i
$796$	−2.20082e101			−0.646586
$797$			3.00247e101i			0.844184i	0.906553	+	0.422092i	$0.138704\pi$
$797$			3.00247e101i			0.844184i	−0.906553	+	0.422092i	$0.861296\pi$
$798$	6.18491e99	−	9.73853e99i	0.0166430	−	0.0262055i
$799$	−5.28170e100			−0.136031
$800$			3.40839e101i			0.840232i
$801$	5.45044e101	−	2.56025e101i	1.28616	−	0.604150i
$802$	−2.79837e101			−0.632124
$803$		−	3.74264e101i		−	0.809347i
$804$	−7.73703e100	−	4.91376e100i	−0.160182	−	0.101731i
$805$	−8.94092e98			−0.00177226
$806$		−	8.72552e100i		−	0.165602i
$807$	1.19607e101	−	1.88329e101i	0.217362	−	0.342249i
$808$	5.91726e101			1.02973
$809$		−	6.14405e101i		−	1.02390i	−0.859016	−	0.511949i	$-0.828924\pi$
$809$		−	6.14405e101i		−	1.02390i	0.859016	−	0.511949i	$-0.171076\pi$
$810$	−1.03580e100	+	1.24861e100i	−0.0165311	+	0.0199274i
$811$	8.21044e101			1.25498			0.627490	−	0.778625i	$-0.284082\pi$
$811$	8.21044e101			1.25498			0.627490	+	0.778625i	$0.284082\pi$
$812$			1.62454e101i			0.237831i
$813$	−3.13083e101	−	1.98838e101i	−0.439026	−	0.278824i
$814$	−5.80605e100			−0.0779878
$815$			1.35538e100i			0.0174400i
$816$	3.36102e100	−	5.29214e100i	0.0414301	−	0.0652343i
$817$	1.75696e101			0.207487
$818$		−	4.89083e101i		−	0.553372i
$819$	3.79784e100	+	8.08510e100i	0.0411718	+	0.0876494i
$820$	−3.70395e100			−0.0384752
$821$			2.21747e101i			0.220723i	0.993892	+	0.110361i	$0.0352008\pi$
$821$			2.21747e101i			0.220723i	−0.993892	+	0.110361i	$0.964799\pi$
$822$	−3.80546e101	−	2.41684e101i	−0.362989	−	0.230533i
$823$	−4.70014e101			−0.429652			−0.214826	−	0.976652i	$-0.568918\pi$
$823$	−4.70014e101			−0.429652			−0.214826	+	0.976652i	$0.568918\pi$
$824$			7.55730e101i			0.662085i
$825$	−9.14195e101	+	1.43946e102i	−0.767628	+	1.20868i
$826$	−1.11754e101			−0.0899420
$827$			2.11486e102i			1.63150i	0.578401	+	0.815752i	$0.303677\pi$
$827$			2.11486e102i			1.63150i	−0.578401	+	0.815752i	$0.696323\pi$
$828$	1.13672e101	−	5.33957e100i	0.0840608	−	0.0394861i
$829$	−1.10453e102			−0.783015			−0.391508	−	0.920175i	$-0.628046\pi$
$829$	−1.10453e102			−0.783015			−0.391508	+	0.920175i	$0.628046\pi$
$830$			1.29964e100i			0.00883263i
$831$	−1.34343e102	−	8.53209e101i	−0.875346	−	0.555930i
$832$	2.97325e101			0.185744
$833$		−	1.78303e101i		−	0.106803i
$834$	4.18968e101	−	6.59692e101i	0.240641	−	0.378904i
$835$	1.04619e101			0.0576216
$836$		−	1.07219e102i		−	0.566309i
$837$	−2.80687e101	+	2.20376e102i	−0.142177	+	1.11628i
$838$	1.02825e101			0.0499524
$839$		−	1.12988e102i		−	0.526458i	−0.964733	−	0.263229i	$-0.915213\pi$
$839$		−	1.12988e102i		−	0.526458i	0.964733	−	0.263229i	$-0.0847875\pi$
$840$	−1.99408e100	−	1.26644e100i	−0.00891186	−	0.00565990i
$841$	−1.23427e102			−0.529114
$842$			3.85574e101i			0.158557i
$843$	−6.91378e101	+	1.08862e102i	−0.272741	+	0.429448i
$844$	4.13322e102			1.56424
$845$			1.73809e101i			0.0631083i
$846$	−4.85251e101	−	1.03304e102i	−0.169045	−	0.359876i
$847$	−6.93474e101			−0.231799
$848$		−	4.17603e102i		−	1.33940i
$849$	−2.91127e102	−	1.84894e102i	−0.896011	−	0.569054i
$850$	−1.23364e101			−0.0364356
$851$			6.06778e100i			0.0171987i
$852$	−1.65938e101	+	2.61280e101i	−0.0451398	+	0.0710754i
$853$	4.93867e102			1.28942			0.644709	−	0.764428i	$-0.276979\pi$
$853$	4.93867e102			1.28942			0.644709	+	0.764428i	$0.276979\pi$
$854$			1.45150e101i			0.0363740i
$855$	1.31012e101	−	6.15409e100i	0.0315136	−	0.0148030i
$856$	2.70224e102			0.623939
$857$			7.32326e102i			1.62321i	0.584205	+	0.811606i	$0.301407\pi$
$857$			7.32326e102i			1.62321i	−0.584205	+	0.811606i	$0.698593\pi$
$858$	−8.41177e101	−	5.34229e101i	−0.178992	−	0.113677i
$859$	4.77330e102			0.975120			0.487560	−	0.873089i	$-0.337887\pi$
$859$	4.77330e102			0.975120			0.487560	+	0.873089i	$0.337887\pi$
$860$		−	1.69696e101i		−	0.0332832i
$861$	−3.34140e101	+	5.26124e101i	−0.0629242	+	0.0990781i
$862$	1.96011e102			0.354426
$863$		−	5.62344e102i		−	0.976391i	−0.872734	−	0.488196i	$-0.837655\pi$
$863$		−	5.62344e102i		−	0.976391i	0.872734	−	0.488196i	$-0.162345\pi$
$864$	5.03050e102	+	6.40719e101i	0.838745	+	0.106828i
$865$	5.85705e100			0.00937811
$866$			1.88339e102i			0.289610i
$867$	−5.64421e102	−	3.58462e102i	−0.833556	−	0.529389i
$868$	−1.52584e102			−0.216430
$869$		−	1.31560e103i		−	1.79239i
$870$	1.31163e101	−	2.06524e101i	0.0171647	−	0.0270270i
$871$	7.60021e101			0.0955411
$872$			9.54221e102i			1.15232i
$873$	4.86119e102	+	1.03488e103i	0.563955	+	1.20059i
$874$	1.34498e101			0.0149905
$875$		−	3.17219e101i		−	0.0339686i
$876$	−4.11478e102	−	2.61328e102i	−0.423353	−	0.268870i
$877$	−1.88382e103			−1.86231			−0.931156	−	0.364621i	$-0.881199\pi$
$877$	−1.88382e103			−1.86231			−0.931156	+	0.364621i	$0.881199\pi$
$878$			2.33042e101i			0.0221374i
$879$	7.56856e102	−	1.19172e103i	0.690880	−	1.08783i
$880$	−8.96354e101			−0.0786296
$881$			7.61615e102i			0.642065i	0.947068	+	0.321032i	$0.104030\pi$
$881$			7.61615e102i			0.642065i	−0.947068	+	0.321032i	$0.895970\pi$
$882$	3.48739e102	−	1.63814e102i	0.282553	−	0.132725i
$883$	−1.22362e103			−0.952845			−0.476423	−	0.879216i	$-0.658067\pi$
$883$	−1.22362e103			−0.952845			−0.476423	+	0.879216i	$0.658067\pi$
$884$			6.00599e101i			0.0449527i
$885$	−1.18362e102	−	7.51715e101i	−0.0851528	−	0.0540803i
$886$	−5.86090e102			−0.405307
$887$			1.57787e103i			1.04892i	0.851434	+	0.524462i	$0.175734\pi$
$887$			1.57787e103i			1.04892i	−0.851434	+	0.524462i	$0.824266\pi$
$888$	−8.59471e101	+	1.35329e102i	−0.0549259	+	0.0864843i
$889$	−2.80780e102			−0.172506
$890$		−	6.22873e101i		−	0.0367916i
$891$	1.95267e103	+	1.61987e103i	1.10894	+	0.919943i
$892$	−1.71308e103			−0.935421
$893$			1.01832e103i			0.534665i
$894$	−8.01699e102	−	5.09157e102i	−0.404761	−	0.257062i
$895$	−7.90304e101			−0.0383696
$896$			4.52515e102i			0.211277i
$897$	−5.58312e101	+	8.79097e101i	−0.0250692	+	0.0394731i
$898$	−1.01280e103			−0.437373
$899$		−	3.35025e103i		−	1.39152i
$900$	9.44253e102	+	2.01019e103i	0.377225	+	0.803063i
$901$	5.65794e102			0.217416
$902$		−	6.95281e102i		−	0.256999i
$903$	−2.41042e102	−	1.53085e102i	−0.0857081	−	0.0544329i
$904$	1.82375e103			0.623837
$905$		−	2.63732e102i		−	0.0867885i
$906$	6.25607e102	−	9.85057e102i	0.198068	−	0.311871i
$907$	6.49851e102			0.197951			0.0989757	−	0.995090i	$-0.468443\pi$
$907$	6.49851e102			0.197951			0.0989757	+	0.995090i	$0.468443\pi$
$908$		−	1.58884e103i		−	0.465668i
$909$	5.33360e103	−	2.50537e103i	1.50413	−	0.706538i
$910$	9.23960e100			0.00250729
$911$		−	1.13670e103i		−	0.296826i	−0.988925	−	0.148413i	$-0.952583\pi$
$911$		−	1.13670e103i		−	0.296826i	0.988925	−	0.148413i	$-0.0474165\pi$
$912$	−1.02033e103	−	6.48007e102i	−0.256401	−	0.162840i
$913$	2.03248e103			0.491528
$914$			2.58420e102i			0.0601464i
$915$	−9.76349e101	+	1.53732e102i	−0.0218709	+	0.0344371i
$916$	−2.18101e103			−0.470235
$917$			5.43774e102i			0.112847i
$918$	−2.31904e101	+	1.82075e102i	−0.00463248	+	0.0363711i
$919$	4.72182e103			0.907960			0.453980	−	0.891012i	$-0.350004\pi$
$919$	4.72182e103			0.907960			0.453980	+	0.891012i	$0.350004\pi$
$920$		−	2.75401e101i		−	0.00509790i
$921$	−1.72934e103	−	1.09830e103i	−0.308173	−	0.195719i
$922$	−7.60732e102			−0.130512
$923$		−	2.56659e102i		−	0.0423933i
$924$	−9.34209e102	+	1.47097e103i	−0.148568	+	0.233930i
$925$	−1.07303e103			−0.164305
$926$		−	5.16788e102i		−	0.0761952i
$927$	3.19976e103	+	6.81186e103i	0.454283	+	0.967108i
$928$	−7.64757e103			−1.04555
$929$		−	4.10693e103i		−	0.540714i	−0.962760	−	0.270357i	$-0.912858\pi$
$929$		−	4.10693e103i		−	0.540714i	0.962760	−	0.270357i	$-0.0871417\pi$
$930$	1.93976e102	+	1.23194e102i	0.0245949	+	0.0156202i
$931$	−3.43770e103			−0.419787
$932$			9.96690e103i			1.17220i
$933$	2.50454e103	−	3.94356e103i	0.283707	−	0.446715i
$934$	1.95516e103			0.213325
$935$		−	1.21443e102i		−	0.0127634i
$936$	−2.49039e103	+	1.16982e103i	−0.252123	+	0.118431i
$937$	7.03711e103			0.686291			0.343146	−	0.939282i	$-0.388508\pi$
$937$	7.03711e103			0.686291			0.343146	+	0.939282i	$0.388508\pi$
$938$			1.59527e102i			0.0149877i
$939$	−1.30982e104	−	8.31861e103i	−1.18554	−	0.752931i
$940$	9.83537e102			0.0857661
$941$		−	9.60260e103i		−	0.806775i	−0.915029	−	0.403387i	$-0.867833\pi$
$941$		−	9.60260e103i		−	0.806775i	0.915029	−	0.403387i	$-0.132167\pi$
$942$	−3.38844e103	+	5.33531e103i	−0.274295	+	0.431895i
$943$	−7.26624e102			−0.0566761
$944$			1.17088e104i			0.880016i
$945$	−2.33360e102	−	2.97224e101i	−0.0169010	−	0.00215263i
$946$	3.18541e103			0.222318
$947$			1.83912e104i			1.23698i	0.785795	+	0.618488i	$0.212254\pi$
$947$			1.83912e104i			1.23698i	−0.785795	+	0.618488i	$0.787746\pi$
$948$	−1.44642e104	−	9.18615e103i	−0.937566	−	0.595445i
$949$	4.04202e103			0.252511
$950$			2.37847e103i			0.143209i
$951$	−1.03386e104	+	1.62788e104i	−0.599992	+	0.944725i
$952$	−2.67261e102			−0.0149500
$953$			9.09493e103i			0.490397i	0.969473	+	0.245198i	$0.0788531\pi$
$953$			9.09493e103i			0.490397i	−0.969473	+	0.245198i	$0.921147\pi$
$954$	5.19817e103	+	1.10662e104i	0.270183	+	0.575183i
$955$	3.49341e102			0.0175038
$956$		−	2.97088e104i		−	1.43502i
$957$	−3.22979e104	−	2.05123e104i	−1.50403	−	0.955204i
$958$	1.08417e104			0.486750
$959$		−	6.53695e103i		−	0.282959i
$960$	−4.19787e102	+	6.60981e102i	−0.0175201	+	0.0275864i
$961$	6.61745e103			0.266301
$962$		−	6.27048e102i		−	0.0243317i
$963$	2.43570e104	−	1.14413e104i	0.911388	−	0.428109i
$964$	4.02564e104			1.45258
$965$			2.60946e103i			0.0908019i
$966$	−1.84521e102	−	1.17189e102i	−0.00619222	−	0.00393266i
$967$	3.01861e104			0.976967			0.488484	−	0.872573i	$-0.337550\pi$
$967$	3.01861e104			0.976967			0.488484	+	0.872573i	$0.337550\pi$
$968$		−	2.13606e104i		−	0.666769i
$969$	8.77959e102	−	1.38240e103i	0.0264327	−	0.0416200i
$970$	1.18266e103			0.0343438
$971$			2.40546e103i			0.0673790i	0.999432	+	0.0336895i	$0.0107257\pi$
$971$			2.40546e103i			0.0673790i	−0.999432	+	0.0336895i	$0.989274\pi$
$972$	3.14438e104	−	1.01576e104i	0.849603	−	0.274455i
$973$	1.13321e104			0.295365
$974$		−	1.55365e104i		−	0.390651i
$975$	−1.55460e104	−	9.87322e103i	−0.377101	−	0.239495i
$976$	1.52077e104			0.355892
$977$		−	2.34159e104i		−	0.528690i	−0.964428	−	0.264345i	$-0.914844\pi$
$977$		−	2.34159e104i		−	0.528690i	0.964428	−	0.264345i	$-0.0851557\pi$
$978$	−1.77650e103	+	2.79721e103i	−0.0386995	+	0.0609348i
$979$	−9.74097e104			−2.04742
$980$			3.32029e103i			0.0673385i
$981$	4.04017e104	+	8.60099e104i	0.790650	+	1.68319i
$982$	−1.67324e104			−0.315978
$983$			9.04228e104i			1.64780i	0.566734	+	0.823901i	$0.308207\pi$
$983$			9.04228e104i			1.64780i	−0.566734	+	0.823901i	$0.691793\pi$
$984$	−1.62058e104	−	1.02923e104i	−0.284998	−	0.181002i
$985$	−2.76997e103			−0.0470119
$986$		−	2.76798e103i		−	0.0453389i
$987$	8.87265e103	−	1.39705e104i	0.140266	−	0.220858i
$988$	1.15796e104			0.176685
$989$		−	3.32900e103i		−	0.0490280i
$990$	2.37528e103	−	1.11575e103i	0.0337663	−	0.0158611i
$991$	−4.24587e104			−0.582624			−0.291312	−	0.956628i	$-0.594092\pi$
$991$	−4.24587e104			−0.582624			−0.291312	+	0.956628i	$0.594092\pi$
$992$		−	7.18293e104i		−	0.951465i
$993$	−2.90047e104	−	1.84208e104i	−0.370889	−	0.235551i
$994$	5.38723e102			0.00665032
$995$			4.80610e103i			0.0572777i
$996$	1.41917e104	−	2.23457e104i	0.163289	−	0.257109i
$997$	−8.71298e104			−0.967913			−0.483956	−	0.875092i	$-0.660801\pi$
$997$	−8.71298e104			−0.967913			−0.483956	+	0.875092i	$0.660801\pi$
$998$			5.52329e103i			0.0592419i
$999$	−2.01712e103	+	1.58371e104i	−0.0208900	+	0.164015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.71.b.a.2.13	yes	22
3.2	odd	2	inner	3.71.b.a.2.10	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.71.b.a.2.10	✓	22	3.2	odd	2	inner
3.71.b.a.2.13	yes	22	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 71 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.12481e10i q^{2} +(-4.22339e16 - 2.68226e16i) q^{3} +1.05407e21 q^{4} -2.30186e23i q^{5} +(3.01705e26 - 4.75053e26i) q^{6} +8.16038e28 q^{7} +2.51358e31i q^{8} +(1.06425e33 + 2.26565e33i) q^{9} +O(q^{10})\)	\(q+1.12481e10i q^{2} +(-4.22339e16 - 2.68226e16i) q^{3} +1.05407e21 q^{4} -2.30186e23i q^{5} +(3.01705e26 - 4.75053e26i) q^{6} +8.16038e28 q^{7} +2.51358e31i q^{8} +(1.06425e33 + 2.26565e33i) q^{9} +2.58917e33 q^{10} -4.04914e36i q^{11} +(-4.45175e37 - 2.82729e37i) q^{12} +4.37303e38 q^{13} +9.17891e38i q^{14} +(-6.17419e39 + 9.72166e39i) q^{15} +9.61696e41 q^{16} +1.30296e42i q^{17} +(-2.54843e43 + 1.19708e43i) q^{18} +2.51212e44 q^{19} -2.42632e44i q^{20} +(-3.44645e45 - 2.18883e45i) q^{21} +4.55453e46 q^{22} -4.75985e46i q^{23} +(6.74208e47 - 1.06158e48i) q^{24} +8.41734e48 q^{25} +4.91885e48i q^{26} +(1.58232e49 - 1.24233e50i) q^{27} +8.60162e49 q^{28} +1.88864e51i q^{29} +(-1.09351e50 - 6.94483e49i) q^{30} -1.77389e52 q^{31} +4.04924e52i q^{32} +(-1.08609e53 + 1.71011e53i) q^{33} -1.46559e52 q^{34} -1.87841e52i q^{35} +(1.12179e54 + 2.38815e54i) q^{36} -1.27479e54 q^{37} +2.82567e54i q^{38} +(-1.84690e55 - 1.17296e55i) q^{39} +5.78592e54 q^{40} -1.52657e56i q^{41} +(2.46203e55 - 3.87661e55i) q^{42} +6.99393e56 q^{43} -4.26808e57i q^{44} +(5.21521e56 - 2.44976e56i) q^{45} +5.35395e56 q^{46} +4.05361e58i q^{47} +(-4.06162e58 - 2.57952e58i) q^{48} -1.36844e59 q^{49} +9.46795e58i q^{50} +(3.49489e58 - 5.50292e58i) q^{51} +4.60948e59 q^{52} -4.34236e60i q^{53} +(1.39739e60 + 1.77982e59i) q^{54} -9.32056e59 q^{55} +2.05118e60i q^{56} +(-1.06097e61 - 6.73817e60i) q^{57} -2.12437e61 q^{58} +1.21751e62i q^{59} +(-6.50804e60 + 1.02473e61i) q^{60} +1.58134e62 q^{61} -1.99530e62i q^{62} +(8.68468e61 + 1.84885e62i) q^{63} +6.79905e62 q^{64} -1.00661e62i q^{65} +(-1.92356e63 - 1.22164e63i) q^{66} +1.73797e63 q^{67} +1.37342e63i q^{68} +(-1.27672e63 + 2.01027e63i) q^{69} +2.11286e62 q^{70} -5.86914e63i q^{71} +(-5.69489e64 + 2.67508e64i) q^{72} +9.24306e64 q^{73} -1.43390e64i q^{74} +(-3.55497e65 - 2.25775e65i) q^{75} +2.64796e65 q^{76} -3.30425e65i q^{77} +(1.31936e65 - 2.07742e65i) q^{78} +3.24910e66 q^{79} -2.21369e65i q^{80} +(-4.00053e66 + 4.82243e66i) q^{81} +1.71711e66 q^{82} +5.01953e66i q^{83} +(-3.63280e66 - 2.30718e66i) q^{84} +2.99924e65 q^{85} +7.86688e66i q^{86} +(5.06583e67 - 7.97648e67i) q^{87} +1.01778e68 q^{88} -2.40569e68i q^{89} +(2.75552e66 + 5.86614e66i) q^{90} +3.56856e67 q^{91} -5.01722e67i q^{92} +(7.49185e68 + 4.75805e68i) q^{93} -4.55956e68 q^{94} -5.78256e67i q^{95} +(1.08611e69 - 1.71015e69i) q^{96} +4.56772e69 q^{97} -1.53925e69i q^{98} +(9.17393e69 - 4.30930e69i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 57\!\cdots\!10 q^{3}+ \cdots - 31\!\cdots\!82 q^{9}+O(q^{10}) \) 22 * q - 57760946614928610 * q^3 - 12924724784889679105472 * q^4 - 2542746418602623176312578240 * q^6 + 3460300354929279082139211020 * q^7 - 3187627653443587997840864868739482 * q^9	\( 22 q - 57\!\cdots\!10 q^{3}+ \cdots - 21\!\cdots\!80 q^{99}+O(q^{100}) \) 22 * q - 57760946614928610 * q^3 - 12924724784889679105472 * q^4 - 2542746418602623176312578240 * q^6 + 3460300354929279082139211020 * q^7 - 3187627653443587997840864868739482 * q^9 - 204904054456738768728763726683461760 * q^10 + 168216518978261501059545818584280696640 * q^12 - 1425273500899614630088058291006011908100 * q^13 - 225789500492205687292660149319768298715840 * q^15 + 7791108876170200924142434286561643963000832 * q^16 - 159240712078782992086911930584730978792685440 * q^18 + 2012529521265601397979311193864856923750823676 * q^19 - 5316334525000974787771605720411010154937122916 * q^21 - 177999664576757911046568099334764110597720653440 * q^22 + 2221044214363105865421794285118261395337437583360 * q^24 - 47913993180689593092577485889381363779493774325690 * q^25 - 327350510975933028532160361074129063579708328041490 * q^27 + 199622305967867855771313967200368144722234985321600 * q^28 + 19529370934845391692884101303550253186745064711003520 * q^30 + 12388430374073163692752061441697409777651574405007404 * q^31 + 91609538538011962010378972773658529100477255901421120 * q^33 + 605761954772905142742127812440233067564260993651653120 * q^34 + 903849673866118209515044215587923561361275075218434112 * q^36 - 2942122339532414491328953596359839081620064777882528420 * q^37 - 83642273913756481299940648535011188445494335818507646004 * q^39 + 272642123044960747425938890972217844718938356564315934720 * q^40 + 1560147154093916143029768098476489647357578674968337342080 * q^42 - 4545359228128189931707988293083620465330530163336481972580 * q^43 - 13684191484560547979485162889557225553655737227535310368640 * q^45 + 34824945738150746982031713560272687284036228683298922087680 * q^46 + 187018310806180504680614747073364302422042767094159794882560 * q^48 + 537429667187009430823177633570141302055322425376808156541794 * q^49 + 93003444735225900297901054333392923286830613776157770499840 * q^51 - 256980181653870794210710907095882776189154704275967737138560 * q^52 + 563860949077651296335542553968680463677661322067851314468800 * q^54 - 3516118540339332578884347645630886351467431915082786354698880 * q^55 + 62619566495727497029128246919971991949893526891401194293093580 * q^57 + 116675137250817318744043251484707490614825810469582794383621760 * q^58 - 289520688194704548710930657842220413516071423272166989563023360 * q^60 - 1004518379975789938184755460502459521248398274882979931600708676 * q^61 + 2259750912371699320668016184778015293200259463243321554460021420 * q^63 - 6990282608978901236062382909358427229318771679854621867713298432 * q^64 + 9802144175872303219237439174047894300074716767326740733265952640 * q^66 - 9530737568144236105810003684427263525901520593033925660073496260 * q^67 + 68660923095126616358914910008665108044130343377859227725343530880 * q^69 - 186825484366209931701114245951001364013348939360625786570907971840 * q^70 + 800859191695150280430684829106757981081528103077118327934086410240 * q^72 - 498564607593670758195755796246723418636521686724391030404386208820 * q^73 + 2109806600351472862056557154002428953234561707550117711339382623630 * q^75 - 5263274864463875706518271175142614969672638525330024503218962553216 * q^76 + 12308167524701892969963937648343555852922730564344320620076689564800 * q^78 - 17307670437682441097149414568687707748355067787533584779481303522964 * q^79 + 13169506853202980530135359556542777642532240836639689883271737852342 * q^81 - 39431820989895068684167150578955043187025954212565254141576902204160 * q^82 + 138763489413867144231869861916118201044140663071190925822310630686336 * q^84 - 61037539079877371876604729964700889725410552523647838067356520814080 * q^85 - 149627312260702067527556548128053547148656320722965526646581032129600 * q^87 + 423107204692289659768926623144292819592688368886126043795359525621760 * q^88 - 954822316211616625813572408526438784570624253142422549351495971955840 * q^90 + 1351237435163715752950727836854267043101210025128484375869461920848568 * q^91 - 1419126662189890378883596636164605113800863195507982624574295260938180 * q^93 + 10138980254856605941232671681032460690110853357766177455228626662453760 * q^94 - 12383253221007478242150050518024370091385337450937902244753056045137920 * q^96 + 5943877415032019678068302054256035030995353737176853716379501144663980 * q^97 - 21983160871333538547745741193506138170867254293489738303957813119108480 * q^99

Introduction

L-functions

Modular forms

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