LMFDB - Embedded newform 3.71.b.a.2.4

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			2.4
Character	$\chi$	$=$	3.2
Dual form			3.71.b.a.2.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.67615e10i q^{2} +(-4.93039e16 - 8.50161e15i) q^{3} -1.00605e21 q^{4} +4.28418e24i q^{5} +(-3.97548e26 + 2.30553e27i) q^{6} -1.75590e29 q^{7} -8.16202e30i q^{8} +(2.35860e33 + 8.38326e32i) q^{9} +O(q^{10})$	\(q-4.67615e10i q^{2} +(-4.93039e16 - 8.50161e15i) q^{3} -1.00605e21 q^{4} +4.28418e24i q^{5} +(-3.97548e26 + 2.30553e27i) q^{6} -1.75590e29 q^{7} -8.16202e30i q^{8} +(2.35860e33 + 8.38326e32i) q^{9} +2.00335e35 q^{10} -2.13277e36i q^{11} +(4.96020e37 + 8.55301e36i) q^{12} -1.41672e39 q^{13} +8.21087e39i q^{14} +(3.64225e40 - 2.11227e41i) q^{15} -1.56940e42 q^{16} -1.47869e43i q^{17} +(3.92014e43 - 1.10292e44i) q^{18} -5.25675e44 q^{19} -4.31009e45i q^{20} +(8.65729e45 + 1.49280e45i) q^{21} -9.97316e46 q^{22} -2.67086e47i q^{23} +(-6.93903e46 + 4.02420e47i) q^{24} -9.88390e48 q^{25} +6.62481e49i q^{26} +(-1.09161e50 - 6.13847e49i) q^{27} +1.76652e50 q^{28} -1.32661e51i q^{29} +(-9.87730e51 - 1.70317e51i) q^{30} +2.33257e52 q^{31} +6.37514e52i q^{32} +(-1.81320e52 + 1.05154e53i) q^{33} -6.91459e53 q^{34} -7.52261e53i q^{35} +(-2.37286e54 - 8.43394e53i) q^{36} -9.09223e54 q^{37} +2.45814e55i q^{38} +(6.98501e55 + 1.20444e55i) q^{39} +3.49676e55 q^{40} -1.39332e56i q^{41} +(6.98056e55 - 4.04828e56i) q^{42} +1.81142e57 q^{43} +2.14567e57i q^{44} +(-3.59154e57 + 1.01047e58i) q^{45} -1.24893e58 q^{46} +3.74738e58i q^{47} +(7.73775e58 + 1.33424e58i) q^{48} -1.12672e59 q^{49} +4.62186e59i q^{50} +(-1.25713e59 + 7.29054e59i) q^{51} +1.42529e60 q^{52} +1.66464e60i q^{53} +(-2.87044e60 + 5.10454e60i) q^{54} +9.13719e60 q^{55} +1.43317e60i q^{56} +(2.59178e61 + 4.46908e60i) q^{57} -6.20342e61 q^{58} -1.05505e62i q^{59} +(-3.66427e61 + 2.12504e62i) q^{60} -2.28536e62 q^{61} -1.09075e63i q^{62} +(-4.14147e62 - 1.47202e62i) q^{63} +1.12829e63 q^{64} -6.06951e63i q^{65} +(4.91716e63 + 8.47879e62i) q^{66} -1.70930e63 q^{67} +1.48763e64i q^{68} +(-2.27066e63 + 1.31684e64i) q^{69} -3.51769e64 q^{70} +3.89119e64i q^{71} +(6.84243e63 - 1.92509e64i) q^{72} -3.18042e64 q^{73} +4.25166e65i q^{74} +(4.87315e65 + 8.40290e64i) q^{75} +5.28853e65 q^{76} +3.74494e65i q^{77} +(5.63216e65 - 3.26629e66i) q^{78} -4.58513e66 q^{79} -6.72359e66i q^{80} +(4.86021e66 + 3.95455e66i) q^{81} -6.51538e66 q^{82} +7.08053e66i q^{83} +(-8.70963e66 - 1.50183e66i) q^{84} +6.33499e67 q^{85} -8.47047e67i q^{86} +(-1.12783e67 + 6.54070e67i) q^{87} -1.74077e67 q^{88} +2.22533e68i q^{89} +(4.72510e68 + 1.67946e68i) q^{90} +2.48763e68 q^{91} +2.68701e68i q^{92} +(-1.15005e69 - 1.98306e68i) q^{93} +1.75233e69 q^{94} -2.25209e69i q^{95} +(5.41989e68 - 3.14319e69i) q^{96} +4.55086e69 q^{97} +5.26869e69i q^{98} +(1.78796e69 - 5.03036e69i) 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 $

$2$		−	4.67615e10i		−	1.36094i	−0.732777	−	0.680469i	$-0.761776\pi$
$2$		−	4.67615e10i		−	1.36094i	0.732777	−	0.680469i	$-0.238224\pi$
$3$	−4.93039e16	−	8.50161e15i	−0.985457	−	0.169925i
$3$	−4.93039e16	−	8.50161e15i	−0.985457	−	0.169925i
$4$	−1.00605e21			−0.852154
$5$			4.28418e24i			1.47203i	0.676963	+	0.736017i	$0.263296\pi$
$5$			4.28418e24i			1.47203i	−0.676963	+	0.736017i	$0.736704\pi$
$6$	−3.97548e26	+	2.30553e27i	−0.231257	+	1.34115i
$7$	−1.75590e29			−0.463521			−0.231760	−	0.972773i	$-0.574449\pi$
$7$	−1.75590e29			−0.463521			−0.231760	+	0.972773i	$0.574449\pi$
$8$		−	8.16202e30i		−	0.201209i
$9$	2.35860e33	+	8.38326e32i	0.942251	+	0.334908i
$10$	2.00335e35			2.00335
$11$		−	2.13277e36i		−	0.758928i	−0.925207	−	0.379464i	$-0.876108\pi$
$11$		−	2.13277e36i		−	0.758928i	0.925207	−	0.379464i	$-0.123892\pi$
$12$	4.96020e37	+	8.55301e36i	0.839761	+	0.144802i
$13$	−1.41672e39			−1.45636			−0.728179	−	0.685387i	$-0.759633\pi$
$13$	−1.41672e39			−1.45636			−0.728179	+	0.685387i	$0.759633\pi$
$14$			8.21087e39i			0.630823i
$15$	3.64225e40	−	2.11227e41i	0.250135	−	1.45063i
$16$	−1.56940e42			−1.12599
$17$		−	1.47869e43i		−	1.27106i	−0.772077	−	0.635530i	$-0.780782\pi$
$17$		−	1.47869e43i		−	1.27106i	0.772077	−	0.635530i	$-0.219218\pi$
$18$	3.92014e43	−	1.10292e44i	0.455789	−	1.28235i
$19$	−5.25675e44			−0.921173			−0.460587	−	0.887615i	$-0.652361\pi$
$19$	−5.25675e44			−0.921173			−0.460587	+	0.887615i	$0.652361\pi$
$20$		−	4.31009e45i		−	1.25440i
$21$	8.65729e45	+	1.49280e45i	0.456780	+	0.0787638i
$22$	−9.97316e46			−1.03285
$23$		−	2.67086e47i		−	0.583683i	−0.956467	−	0.291841i	$-0.905732\pi$
$23$		−	2.67086e47i		−	0.583683i	0.956467	−	0.291841i	$-0.0942679\pi$
$24$	−6.93903e46	+	4.02420e47i	−0.0341905	+	0.198283i
$25$	−9.88390e48			−1.16688
$26$			6.62481e49i			1.98201i
$27$	−1.09161e50	−	6.13847e49i	−0.871639	−	0.490149i
$28$	1.76652e50			0.394991
$29$		−	1.32661e51i		−	0.868585i	−0.900772	−	0.434293i	$-0.856998\pi$
$29$		−	1.32661e51i		−	0.868585i	0.900772	−	0.434293i	$-0.143002\pi$
$30$	−9.87730e51	−	1.70317e51i	−1.97421	−	0.340419i
$31$	2.33257e52			1.47971			0.739853	−	0.672768i	$-0.234895\pi$
$31$	2.33257e52			1.47971			0.739853	+	0.672768i	$0.234895\pi$
$32$			6.37514e52i			1.33119i
$33$	−1.81320e52	+	1.05154e53i	−0.128961	+	0.747891i
$34$	−6.91459e53			−1.72983
$35$		−	7.52261e53i		−	0.682318i
$36$	−2.37286e54	−	8.43394e53i	−0.802943	−	0.285393i
$37$	−9.09223e54			−1.17926			−0.589631	−	0.807673i	$-0.700727\pi$
$37$	−9.09223e54			−1.17926			−0.589631	+	0.807673i	$0.700727\pi$
$38$			2.45814e55i			1.25366i
$39$	6.98501e55	+	1.20444e55i	1.43518	+	0.247472i
$40$	3.49676e55			0.296187
$41$		−	1.39332e56i		−	0.497298i	−0.968594	−	0.248649i	$-0.920013\pi$
$41$		−	1.39332e56i		−	0.497298i	0.968594	−	0.248649i	$-0.0799865\pi$
$42$	6.98056e55	−	4.04828e56i	0.107193	−	0.621649i
$43$	1.81142e57			1.22074			0.610370	−	0.792116i	$-0.291021\pi$
$43$	1.81142e57			1.22074			0.610370	+	0.792116i	$0.291021\pi$
$44$			2.14567e57i			0.646723i
$45$	−3.59154e57	+	1.01047e58i	−0.492995	+	1.38703i
$46$	−1.24893e58			−0.794356
$47$			3.74738e58i			1.12280i	0.827545	+	0.561400i	$0.189737\pi$
$47$			3.74738e58i			1.12280i	−0.827545	+	0.561400i	$0.810263\pi$
$48$	7.73775e58	+	1.33424e58i	1.10961	+	0.191333i
$49$	−1.12672e59			−0.785149
$50$			4.62186e59i			1.58806i
$51$	−1.25713e59	+	7.29054e59i	−0.215985	+	1.25257i
$52$	1.42529e60			1.24104
$53$			1.66464e60i			0.744158i	0.928201	+	0.372079i	$0.121355\pi$
$53$			1.66464e60i			0.744158i	−0.928201	+	0.372079i	$0.878645\pi$
$54$	−2.87044e60	+	5.10454e60i	−0.667063	+	1.18625i
$55$	9.13719e60			1.11717
$56$			1.43317e60i			0.0932647i
$57$	2.59178e61	+	4.46908e60i	0.907777	+	0.156530i
$58$	−6.20342e61			−1.18209
$59$		−	1.05505e62i		−	1.10523i	−0.833435	−	0.552617i	$-0.813629\pi$
$59$		−	1.05505e62i		−	1.10523i	0.833435	−	0.552617i	$-0.186371\pi$
$60$	−3.66427e61	+	2.12504e62i	−0.213154	+	1.23616i
$61$	−2.28536e62			−0.745435			−0.372717	−	0.927945i	$-0.621574\pi$
$61$	−2.28536e62			−0.745435			−0.372717	+	0.927945i	$0.621574\pi$
$62$		−	1.09075e63i		−	2.01379i
$63$	−4.14147e62	−	1.47202e62i	−0.436753	−	0.155237i
$64$	1.12829e63			0.685681
$65$		−	6.06951e63i		−	2.14381i
$66$	4.91716e63	+	8.47879e62i	1.01783	+	0.175508i
$67$	−1.70930e63			−0.209026			−0.104513	−	0.994524i	$-0.533328\pi$
$67$	−1.70930e63			−0.209026			−0.104513	+	0.994524i	$0.533328\pi$
$68$			1.48763e64i			1.08314i
$69$	−2.27066e63	+	1.31684e64i	−0.0991822	+	0.575194i
$70$	−3.51769e64			−0.928593
$71$			3.89119e64i			0.625231i	0.949880	+	0.312615i	$0.101205\pi$
$71$			3.89119e64i			0.625231i	−0.949880	+	0.312615i	$0.898795\pi$
$72$	6.84243e63	−	1.92509e64i	0.0673865	−	0.189590i
$73$	−3.18042e64			−0.193279			−0.0966393	−	0.995319i	$-0.530809\pi$
$73$	−3.18042e64			−0.193279			−0.0966393	+	0.995319i	$0.530809\pi$
$74$			4.25166e65i			1.60490i
$75$	4.87315e65	+	8.40290e64i	1.14991	+	0.198283i
$76$	5.28853e65			0.784982
$77$			3.74494e65i			0.351779i
$78$	5.63216e65	−	3.26629e66i	0.336794	−	1.95319i
$79$	−4.58513e66			−1.75551			−0.877754	−	0.479111i	$-0.840959\pi$
$79$	−4.58513e66			−1.75551			−0.877754	+	0.479111i	$0.840959\pi$
$80$		−	6.72359e66i		−	1.65749i
$81$	4.86021e66	+	3.95455e66i	0.775674	+	0.631134i
$82$	−6.51538e66			−0.676792
$83$			7.08053e66i			0.481208i	0.970623	+	0.240604i	$0.0773455\pi$
$83$			7.08053e66i			0.481208i	−0.970623	+	0.240604i	$0.922655\pi$
$84$	−8.70963e66	−	1.50183e66i	−0.389247	−	0.0671188i
$85$	6.33499e67			1.87104
$86$		−	8.47047e67i		−	1.66135i
$87$	−1.12783e67	+	6.54070e67i	−0.147594	+	0.855954i
$88$	−1.74077e67			−0.152703
$89$			2.22533e68i			1.31445i	0.753694	+	0.657225i	$0.228270\pi$
$89$			2.22533e68i			1.31445i	−0.753694	+	0.657225i	$0.771730\pi$
$90$	4.72510e68	+	1.67946e68i	1.88766	+	0.670936i
$91$	2.48763e68			0.675052
$92$			2.68701e68i			0.497387i
$93$	−1.15005e69	−	1.98306e68i	−1.45819	−	0.251439i
$94$	1.75233e69			1.52806
$95$		−	2.25209e69i		−	1.35600i
$96$	5.41989e68	−	3.14319e69i	0.226203	−	1.31183i
$97$	4.55086e69			1.32155			0.660774	−	0.750585i	$-0.270228\pi$
$97$	4.55086e69			1.32155			0.660774	+	0.750585i	$0.270228\pi$
$98$			5.26869e69i			1.06854i
$99$	1.78796e69	−	5.03036e69i	0.254171	−	0.715100i
$100$	9.94365e69			0.994365
$101$		−	2.30795e70i		−	1.62921i	−0.580014	−	0.814607i	$-0.696953\pi$
$101$		−	2.30795e70i		−	1.62921i	0.580014	−	0.814607i	$-0.303047\pi$
$102$	3.40916e70	+	5.87851e69i	1.70468	+	0.293942i
$103$	2.95919e70			1.05165			0.525824	−	0.850593i	$-0.323757\pi$
$103$	2.95919e70			1.05165			0.525824	+	0.850593i	$0.323757\pi$
$104$			1.15633e70i			0.293033i
$105$	−6.39543e69	+	3.70894e70i	−0.115943	+	0.672395i
$106$	7.78411e70			1.01275
$107$			1.40966e71i			1.32033i	0.751121	+	0.660165i	$0.229514\pi$
$107$			1.40966e71i			1.32033i	−0.751121	+	0.660165i	$0.770486\pi$
$108$	1.09821e71	+	6.17558e70i	0.742770	+	0.417682i
$109$	2.10261e69			0.0102999			0.00514993	−	0.999987i	$-0.498361\pi$
$109$	2.10261e69			0.0102999			0.00514993	+	0.999987i	$0.498361\pi$
$110$		−	4.27268e71i		−	1.52040i
$111$	4.48283e71	+	7.72986e70i	1.16211	+	0.200386i
$112$	2.75571e71			0.521919
$113$		−	5.93393e71i		−	0.823374i	−0.911325	−	0.411687i	$-0.864940\pi$
$113$		−	5.93393e71i		−	0.823374i	0.911325	−	0.411687i	$-0.135060\pi$
$114$	2.08981e71	−	1.21196e72i	0.213028	−	1.23543i
$115$	1.14424e72			0.859201
$116$			1.33463e72i			0.740169i
$117$	−3.34149e72	−	1.18768e72i	−1.37225	−	0.487745i
$118$	−4.93359e72			−1.50416
$119$			2.59644e72i			0.589162i
$120$	−1.72404e72	−	2.97281e71i	−0.291880	−	0.0503296i
$121$	3.34875e72			0.424029
$122$			1.06867e73i			1.01449i
$123$	−1.18455e72	+	6.86963e72i	−0.0845033	+	0.490066i
$124$	−2.34667e73			−1.26094
$125$		−	6.05599e72i		−	0.245660i
$126$	−6.88338e72	+	1.93662e73i	−0.211267	+	0.594394i
$127$	3.70877e73			0.863177			0.431588	−	0.902071i	$-0.357953\pi$
$127$	3.70877e73			0.863177			0.431588	+	0.902071i	$0.357953\pi$
$128$			2.25037e73i			0.398021i
$129$	−8.93101e73	−	1.54000e73i	−1.20299	−	0.207434i
$130$	−2.83819e74			−2.91759
$131$		−	1.15855e74i		−	0.910796i	−0.890288	−	0.455398i	$-0.849497\pi$
$131$		−	1.15855e74i		−	0.910796i	0.890288	−	0.455398i	$-0.150503\pi$
$132$	1.82416e73	−	1.05790e74i	0.109894	−	0.637318i
$133$	9.23034e73			0.426983
$134$			7.99293e73i			0.284471i
$135$	2.62983e74	−	4.67667e74i	0.721516	−	1.28308i
$136$	−1.20691e74			−0.255749
$137$			1.06870e75i			1.75242i	0.481934	+	0.876208i	$0.339935\pi$
$137$			1.06870e75i			1.75242i	−0.481934	+	0.876208i	$0.660065\pi$
$138$	6.15773e74	+	1.06179e74i	0.782804	+	0.134981i
$139$	7.90368e74			0.780389			0.390195	−	0.920732i	$-0.372408\pi$
$139$	7.90368e74			0.780389			0.390195	+	0.920732i	$0.372408\pi$
$140$			7.56809e74i			0.581440i
$141$	3.18587e74	−	1.84760e75i	0.190792	−	1.10647i
$142$	1.81958e75			0.850901
$143$			3.02155e75i			1.10527i
$144$	−3.70158e75	−	1.31567e75i	−1.06096	−	0.377102i
$145$	5.68343e75			1.27859
$146$			1.48721e75i			0.263040i
$147$	5.55516e75	+	9.57890e74i	0.773730	+	0.133416i
$148$	9.14720e75			1.00491
$149$		−	1.21346e76i		−	1.05319i	−0.850117	−	0.526594i	$-0.823469\pi$
$149$		−	1.21346e76i		−	1.05319i	0.850117	−	0.526594i	$-0.176531\pi$
$150$	3.92932e75	−	2.27876e76i	0.269851	−	1.56496i
$151$	−2.22129e76			−1.20896			−0.604480	−	0.796620i	$-0.706619\pi$
$151$	−2.22129e76			−1.20896			−0.604480	+	0.796620i	$0.706619\pi$
$152$			4.29057e75i			0.185349i
$153$	1.23963e76	−	3.48765e76i	0.425687	−	1.19766i
$154$	1.75119e76			0.478749
$155$			9.99316e76i			2.17818i
$156$	−7.02724e76	−	1.21173e76i	−1.22299	−	0.210884i
$157$	3.63789e75			0.0506246			0.0253123	−	0.999680i	$-0.491942\pi$
$157$	3.63789e75			0.0506246			0.0253123	+	0.999680i	$0.491942\pi$
$158$			2.14407e77i			2.38914i
$159$	1.41521e76	−	8.20734e76i	0.126451	−	0.733336i
$160$	−2.73123e77			−1.95956
$161$			4.68977e76i			0.270549i
$162$	1.84921e77	−	2.27271e77i	0.858935	−	1.05564i
$163$	−3.66830e77			−1.37372			−0.686860	−	0.726790i	$-0.741011\pi$
$163$	−3.66830e77			−1.37372			−0.686860	+	0.726790i	$0.741011\pi$
$164$			1.40175e77i			0.423774i
$165$	−4.50499e77	−	7.76808e76i	−1.10092	−	0.189835i
$166$	3.31096e77			0.654894
$167$			3.68267e77i			0.590319i	0.955448	+	0.295159i	$0.0953727\pi$
$167$			3.68267e77i			0.590319i	−0.955448	+	0.295159i	$0.904627\pi$
$168$	1.21843e76	−	7.06610e76i	0.0158480	−	0.0919083i
$169$	1.06079e78			1.12098
$170$		−	2.96234e78i		−	2.54637i
$171$	−1.23986e78	−	4.40687e77i	−0.867976	−	0.308508i
$172$	−1.82237e78			−1.04026
$173$			2.35375e78i			1.09685i	0.836201	+	0.548423i	$0.184772\pi$
$173$			2.35375e78i			1.09685i	−0.836201	+	0.548423i	$0.815228\pi$
$174$	3.05853e78	+	5.27390e77i	1.16490	+	0.200867i
$175$	1.73552e78			0.540875
$176$			3.34717e78i			0.854543i
$177$	−8.96966e77	+	5.20184e78i	−0.187807	+	1.08916i
$178$	1.04060e79			1.78889
$179$			3.49531e78i			0.493889i	0.969030	+	0.246945i	$0.0794266\pi$
$179$			3.49531e78i			0.493889i	−0.969030	+	0.246945i	$0.920573\pi$
$180$	3.61325e78	−	1.01658e79i	0.420108	−	1.18196i
$181$	6.41960e78			0.614834			0.307417	−	0.951575i	$-0.400535\pi$
$181$	6.41960e78			0.614834			0.307417	+	0.951575i	$0.400535\pi$
$182$		−	1.16325e79i		−	0.918704i
$183$	1.12677e79	+	1.94292e78i	0.734594	+	0.126668i
$184$	−2.17996e78			−0.117442
$185$		−	3.89528e79i		−	1.73591i
$186$	−9.27309e78	+	5.37780e79i	−0.342193	+	1.98450i
$187$	−3.15371e79			−0.964642
$188$		−	3.77003e79i		−	0.956798i
$189$	1.91676e79	+	1.07786e79i	0.404023	+	0.227194i
$190$	−1.05311e80			−1.84543
$191$			2.90982e78i			0.0424324i	0.999775	+	0.0212162i	$0.00675384\pi$
$191$			2.90982e78i			0.0424324i	−0.999775	+	0.0212162i	$0.993246\pi$
$192$	−5.56292e79	−	9.59229e78i	−0.675709	−	0.116514i
$193$	9.53087e79			0.965221			0.482611	−	0.875835i	$-0.339689\pi$
$193$	9.53087e79			0.965221			0.482611	+	0.875835i	$0.339689\pi$
$194$		−	2.12805e80i		−	1.79855i
$195$	−5.16006e79	+	2.99251e80i	−0.364287	+	2.11263i
$196$	1.13353e80			0.669067
$197$			3.72987e80i			1.84237i	0.389128	+	0.921184i	$0.372776\pi$
$197$			3.72987e80i			1.84237i	−0.389128	+	0.921184i	$0.627224\pi$
$198$	−2.35227e80	−	8.36076e79i	−0.973208	−	0.345911i
$199$	−4.68250e79			−0.162413			−0.0812064	−	0.996697i	$-0.525877\pi$
$199$	−4.68250e79			−0.162413			−0.0812064	+	0.996697i	$0.525877\pi$
$200$			8.06726e79i			0.234788i
$201$	8.42751e79	+	1.45318e79i	0.205986	+	0.0355187i
$202$	−1.07923e81			−2.21726
$203$			2.32939e80i			0.402607i
$204$	1.26473e80	−	7.33462e80i	0.184052	−	1.06739i
$205$	5.96925e80			0.732039
$206$		−	1.38376e81i		−	1.43123i
$207$	2.23905e80	−	6.29949e80i	0.195480	−	0.549975i
$208$	2.22340e81			1.63984
$209$			1.12114e81i			0.699104i
$210$	1.73436e81	+	2.99060e80i	0.915089	+	0.157791i
$211$	−1.44785e81			−0.646902			−0.323451	−	0.946245i	$-0.604843\pi$
$211$	−1.44785e81			−0.646902			−0.323451	+	0.946245i	$0.604843\pi$
$212$		−	1.67471e81i		−	0.634137i
$213$	3.30814e80	−	1.91851e81i	0.106242	−	0.616138i
$214$	6.59178e81			1.79689
$215$			7.76046e81i			1.79697i
$216$	−5.01023e80	+	8.90976e80i	−0.0986225	+	0.175382i
$217$	−4.09577e81			−0.685875
$218$		−	9.83213e79i		−	0.0140175i
$219$	1.56807e81	+	2.70387e80i	0.190468	+	0.0328429i
$220$	−9.19243e81			−0.951999
$221$			2.09490e82i			1.85112i
$222$	3.61460e81	−	2.09624e82i	0.272713	−	1.58156i
$223$	2.39353e82			1.54301			0.771505	−	0.636223i	$-0.219504\pi$
$223$	2.39353e82			1.54301			0.771505	+	0.636223i	$0.219504\pi$
$224$		−	1.11941e82i		−	0.617034i
$225$	−2.33122e82	−	8.28592e81i	−1.09950	−	0.390798i
$226$	−2.77480e82			−1.12056
$227$			1.04666e82i			0.362160i	0.983468	+	0.181080i	$0.0579593\pi$
$227$			1.04666e82i			0.362160i	−0.983468	+	0.181080i	$0.942041\pi$
$228$	−2.60745e82	−	4.49610e81i	−0.773566	−	0.133388i
$229$	−7.49785e81			−0.190851			−0.0954256	−	0.995437i	$-0.530421\pi$
$229$	−7.49785e81			−0.190851			−0.0954256	+	0.995437i	$0.530421\pi$
$230$		−	5.35066e82i		−	1.16932i
$231$	3.18380e81	−	1.84640e82i	0.0597760	−	0.346663i
$232$	−1.08278e82			−0.174767
$233$		−	5.20495e81i		−	0.0722702i	−0.999347	−	0.0361351i	$-0.988495\pi$
$233$		−	5.20495e81i		−	0.0722702i	0.999347	−	0.0361351i	$-0.0115047\pi$
$234$	−5.55375e82	+	1.56253e83i	−0.663791	+	1.86755i
$235$	−1.60544e83			−1.65280
$236$			1.06143e83i			0.941830i
$237$	2.26065e83	+	3.89809e82i	1.72998	+	0.298305i
$238$	1.21413e83			0.801814
$239$		−	1.97118e83i		−	1.12409i	−0.827108	−	0.562043i	$-0.810016\pi$
$239$		−	1.97118e83i		−	1.12409i	0.827108	−	0.562043i	$-0.189984\pi$
$240$	−5.71613e82	+	3.31499e83i	−0.281649	+	1.63339i
$241$	1.68879e83			0.719415			0.359708	−	0.933065i	$-0.382876\pi$
$241$	1.68879e83			0.719415			0.359708	+	0.933065i	$0.382876\pi$
$242$		−	1.56593e83i		−	0.577077i
$243$	−2.06007e83	−	2.36295e83i	−0.657148	−	0.753762i
$244$	2.29917e83			0.635225
$245$		−	4.82706e83i		−	1.15577i
$246$	3.21234e83	+	5.53912e82i	0.666949	+	0.115004i
$247$	7.44737e83			1.34156
$248$		−	1.90385e83i		−	0.297731i
$249$	6.01959e82	−	3.49098e83i	0.0817692	−	0.474210i
$250$	−2.83187e83			−0.334328
$251$			1.06788e84i			1.09633i	0.836370	+	0.548166i	$0.184674\pi$
$251$			1.06788e84i			1.09633i	−0.836370	+	0.548166i	$0.815326\pi$
$252$	4.16651e83	+	1.48092e83i	0.372181	+	0.132285i
$253$	−5.69633e83			−0.442973
$254$		−	1.73428e84i		−	1.17473i
$255$	−3.12340e84	−	5.38576e83i	−1.84383	−	0.317937i
$256$	2.38436e84			1.22736
$257$		−	5.43962e83i		−	0.244292i	−0.992512	−	0.122146i	$-0.961022\pi$
$257$		−	5.43962e83i		−	0.244292i	0.992512	−	0.122146i	$-0.0389776\pi$
$258$	−7.20126e83	+	4.17628e84i	−0.282305	+	1.63719i
$259$	1.59651e84			0.546612
$260$			6.10620e84i			1.82685i
$261$	1.11213e84	−	3.12894e84i	0.290896	−	0.818426i
$262$	−5.41757e84			−1.23954
$263$			4.54075e84i			0.909235i	0.890687	+	0.454617i	$0.150224\pi$
$263$			4.54075e84i			0.909235i	−0.890687	+	0.454617i	$0.849776\pi$
$264$	8.58269e83	+	1.47994e83i	0.150483	+	0.0259481i
$265$	−7.13163e84			−1.09543
$266$		−	4.31625e84i		−	0.581098i
$267$	1.89189e84	−	1.09717e85i	0.223358	−	1.29533i
$268$	1.71963e84			0.178122
$269$		−	5.83689e84i		−	0.530704i	−0.964152	−	0.265352i	$-0.914512\pi$
$269$		−	5.83689e84i		−	0.530704i	0.964152	−	0.265352i	$-0.0854881\pi$
$270$	−2.18688e85	−	1.22975e85i	−1.74620	−	0.981939i
$271$	−1.48814e85			−1.04405			−0.522023	−	0.852931i	$-0.674822\pi$
$271$	−1.48814e85			−1.04405			−0.522023	+	0.852931i	$0.674822\pi$
$272$			2.32066e85i			1.43120i
$273$	−1.22650e85	−	2.11489e84i	−0.665235	−	0.114708i
$274$	4.99741e85			2.38493
$275$			2.10801e85i			0.885581i
$276$	2.28439e84	−	1.32480e85i	0.0845185	−	0.490154i
$277$	5.42144e85			1.76735			0.883675	−	0.468101i	$-0.155062\pi$
$277$	5.42144e85			1.76735			0.883675	+	0.468101i	$0.155062\pi$
$278$		−	3.69588e85i		−	1.06206i
$279$	5.50161e85	+	1.95545e85i	1.39426	+	0.495565i
$280$	−6.13997e84			−0.137289
$281$			2.97484e85i			0.587142i	0.955937	+	0.293571i	$0.0948437\pi$
$281$			2.97484e85i			0.587142i	−0.955937	+	0.293571i	$0.905156\pi$
$282$	−8.63967e85	−	1.48976e85i	−1.50584	−	0.259656i
$283$	5.73533e85			0.883147			0.441573	−	0.897225i	$-0.354420\pi$
$283$	5.73533e85			0.883147			0.441573	+	0.897225i	$0.354420\pi$
$284$		−	3.91472e85i		−	0.532793i
$285$	−1.91464e85	+	1.11037e86i	−0.230418	+	1.33628i
$286$	1.41292e86			1.50420
$287$			2.44654e85i			0.230508i
$288$	−5.34444e85	+	1.50364e86i	−0.445826	+	1.25432i
$289$	−8.33138e85			−0.615591
$290$		−	2.65766e86i		−	1.74008i
$291$	−2.24376e86	−	3.86897e85i	−1.30233	−	0.224564i
$292$	3.19965e85			0.164703
$293$		−	3.32264e86i		−	1.51746i	−0.651407	−	0.758728i	$-0.725821\pi$
$293$		−	3.32264e86i		−	1.51746i	0.651407	−	0.758728i	$-0.274179\pi$
$294$	4.47924e85	−	2.59767e86i	0.181571	−	1.05300i
$295$	4.52005e86			1.62694
$296$			7.42109e85i			0.237278i
$297$	−1.30919e86	+	2.32816e86i	−0.371988	+	0.661511i
$298$	−5.67432e86			−1.43332
$299$			3.78387e86i			0.850050i
$300$	−4.90261e86	−	8.45371e85i	−0.979904	−	0.168968i
$301$	−3.18068e86			−0.565838
$302$			1.03871e87i			1.64532i
$303$	−1.96213e86	+	1.13791e87i	−0.276844	+	1.60552i
$304$	8.24993e86			1.03723
$305$		−	9.79089e86i		−	1.09731i
$306$	−1.63088e87	−	5.79668e86i	−1.62994	−	0.579334i
$307$	−6.78391e85			−0.0604835			−0.0302417	−	0.999543i	$-0.509628\pi$
$307$	−6.78391e85			−0.0604835			−0.0302417	+	0.999543i	$0.509628\pi$
$308$		−	3.76758e86i		−	0.299770i
$309$	−1.45900e87	−	2.51579e86i	−1.03635	−	0.178701i
$310$	4.67295e87			2.96437
$311$			1.32515e87i			0.751017i	0.926819	+	0.375509i	$0.122532\pi$
$311$			1.32515e87i			0.751017i	−0.926819	+	0.375509i	$0.877468\pi$
$312$	9.83069e85	−	5.70118e86i	0.0497936	−	0.288771i
$313$	1.29243e87			0.585267			0.292634	−	0.956225i	$-0.405468\pi$
$313$	1.29243e87			0.585267			0.292634	+	0.956225i	$0.405468\pi$
$314$		−	1.70113e86i		−	0.0688970i
$315$	6.30640e86	−	1.77428e87i	0.228514	−	0.642915i
$316$	4.61285e87			1.49596
$317$		−	5.06907e87i		−	1.47182i	−0.677081	−	0.735908i	$-0.736755\pi$
$317$		−	5.06907e87i		−	1.47182i	0.677081	−	0.735908i	$-0.263245\pi$
$318$	−3.83787e87	−	6.61775e86i	−0.998025	−	0.172092i
$319$	−2.82935e87			−0.659194
$320$			4.83381e87i			1.00935i
$321$	1.19844e87	−	6.95018e87i	0.224357	−	1.30113i
$322$	2.19301e87			0.368201
$323$			7.77312e87i			1.17087i
$324$	−4.88959e87	−	3.97846e87i	−0.660994	−	0.537823i
$325$	1.40028e88			1.69940
$326$			1.71535e88i			1.86955i
$327$	−1.03667e86	−	1.78756e85i	−0.0101501	−	0.00175020i
$328$	−1.13723e87			−0.100061
$329$		−	6.58003e87i		−	0.520441i
$330$	−3.63247e87	+	2.10660e88i	−0.258353	+	1.49829i
$331$	−1.25624e88			−0.803695			−0.401848	−	0.915707i	$-0.631632\pi$
$331$	−1.25624e88			−0.803695			−0.401848	+	0.915707i	$0.631632\pi$
$332$		−	7.12334e87i		−	0.410063i
$333$	−2.14449e88	−	7.62225e87i	−1.11116	−	0.394943i
$334$	1.72207e88			0.803387
$335$		−	7.32295e87i		−	0.307693i
$336$	−1.35867e88	−	2.34280e87i	−0.514328	−	0.0886870i
$337$	−5.30861e87			−0.181106			−0.0905532	−	0.995892i	$-0.528864\pi$
$337$	−5.30861e87			−0.181106			−0.0905532	+	0.995892i	$0.528864\pi$
$338$		−	4.96043e88i		−	1.52558i
$339$	−5.04480e87	+	2.92566e88i	−0.139912	+	0.811399i
$340$	−6.37329e88			−1.59442
$341$		−	4.97484e88i		−	1.12299i
$342$	−2.06072e88	+	5.79776e88i	−0.419860	+	1.18126i
$343$	4.49819e88			0.827453
$344$		−	1.47848e88i		−	0.245624i
$345$	−5.64158e88	−	9.72792e87i	−0.846705	−	0.146000i
$346$	1.10065e89			1.49274
$347$			1.03658e89i			1.27078i	0.772190	+	0.635391i	$0.219161\pi$
$347$			1.03658e89i			1.27078i	−0.772190	+	0.635391i	$0.780839\pi$
$348$	1.13465e88	−	6.58024e88i	0.125773	−	0.729404i
$349$	−9.34084e88			−0.936475			−0.468237	−	0.883603i	$-0.655111\pi$
$349$	−9.34084e88			−0.936475			−0.468237	+	0.883603i	$0.655111\pi$
$350$		−	8.11554e88i		−	0.736098i
$351$	1.54651e89	+	8.69651e88i	1.26942	+	0.713832i
$352$	1.35967e89			1.01028
$353$			2.01080e89i			1.35286i	0.736505	+	0.676432i	$0.236475\pi$
$353$			2.01080e89i			1.35286i	−0.736505	+	0.676432i	$0.763525\pi$
$354$	2.43246e89	+	4.19435e88i	1.48228	+	0.255594i
$355$	−1.66706e89			−0.920361
$356$		−	2.23878e89i		−	1.12011i
$357$	2.20739e88	−	1.28015e89i	0.100113	−	0.580594i
$358$	1.63446e89			0.672153
$359$			2.38934e89i			0.891193i	0.895234	+	0.445597i	$0.147008\pi$
$359$			2.38934e89i			0.891193i	−0.895234	+	0.445597i	$0.852992\pi$
$360$	8.24746e88	+	2.93142e88i	0.279082	+	0.0991953i
$361$	−4.93165e88			−0.151440
$362$		−	3.00190e89i		−	0.836751i
$363$	−1.65107e89	−	2.84698e88i	−0.417862	−	0.0720531i
$364$	−2.50267e89			−0.575248
$365$		−	1.36255e89i		−	0.284513i
$366$	9.08539e88	−	5.26895e89i	0.172387	−	0.999738i
$367$	−2.48564e89			−0.428672			−0.214336	−	0.976760i	$-0.568759\pi$
$367$	−2.48564e89			−0.428672			−0.214336	+	0.976760i	$0.568759\pi$
$368$			4.19164e89i			0.657219i
$369$	1.16806e89	−	3.28629e89i	0.166549	−	0.468579i
$370$	−1.82149e90			−2.36247
$371$		−	2.92295e89i		−	0.344933i
$372$	1.15700e90	+	1.99505e89i	1.24260	+	0.214265i
$373$	2.54408e89			0.248726			0.124363	−	0.992237i	$-0.460311\pi$
$373$	2.54408e89			0.248726			0.124363	+	0.992237i	$0.460311\pi$
$374$			1.47472e90i			1.31282i
$375$	−5.14856e88	+	2.98584e89i	−0.0417438	+	0.242087i
$376$	3.05862e89			0.225918
$377$			1.87944e90i			1.26497i
$378$	5.04021e89	−	8.96308e89i	0.309197	−	0.549850i
$379$	−2.48882e90			−1.39194			−0.695970	−	0.718071i	$-0.745025\pi$
$379$	−2.48882e90			−1.39194			−0.695970	+	0.718071i	$0.745025\pi$
$380$			2.26570e90i			1.15552i
$381$	−1.82857e90	−	3.15305e89i	−0.850624	−	0.146675i
$382$	1.36067e89			0.0577480
$383$		−	1.58279e90i		−	0.613009i	−0.951869	−	0.306505i	$-0.900841\pi$
$383$		−	1.58279e90i		−	0.613009i	0.951869	−	0.306505i	$-0.0991595\pi$
$384$	1.91318e89	−	1.10952e90i	0.0676336	−	0.392232i
$385$	−1.60440e90			−0.517830
$386$		−	4.45678e90i		−	1.31361i
$387$	4.27242e90	+	1.51856e90i	1.15024	+	0.408835i
$388$	−4.57838e90			−1.12616
$389$		−	4.84674e90i		−	1.08947i	−0.838610	−	0.544733i	$-0.816631\pi$
$389$		−	4.84674e90i		−	1.08947i	0.838610	−	0.544733i	$-0.183369\pi$
$390$	1.39934e91	+	2.41292e90i	2.87516	+	0.495772i
$391$	−3.94938e90			−0.741895
$392$			9.19628e89i			0.157979i
$393$	−9.84957e89	+	5.71213e90i	−0.154767	+	0.897550i
$394$	1.74414e91			2.50735
$395$		−	1.96435e91i		−	2.58417i
$396$	−1.79877e90	+	5.06077e90i	−0.216593	+	0.609376i
$397$	−5.01246e90			−0.552565			−0.276282	−	0.961076i	$-0.589103\pi$
$397$	−5.01246e90			−0.552565			−0.276282	+	0.961076i	$0.589103\pi$
$398$			2.18961e90i			0.221034i
$399$	−4.55092e90	−	7.84728e89i	−0.420773	−	0.0725551i
$400$	1.55118e91			1.31390
$401$			8.94213e90i			0.694045i	0.937857	+	0.347023i	$0.112807\pi$
$401$			8.94213e90i			0.694045i	−0.937857	+	0.347023i	$0.887193\pi$
$402$	6.79528e89	−	3.94083e90i	0.0483388	−	0.280334i
$403$	−3.30461e91			−2.15498
$404$			2.32190e91i			1.38834i
$405$	−1.69420e91	+	2.08220e91i	−0.929051	+	1.14182i
$406$	1.08926e91			0.547924
$407$			1.93916e91i			0.894974i
$408$	5.95055e90	+	1.02607e90i	0.252030	+	0.0434581i
$409$	2.05971e91			0.800739			0.400369	−	0.916354i	$-0.368882\pi$
$409$	2.05971e91			0.800739			0.400369	+	0.916354i	$0.368882\pi$
$410$		−	2.79131e91i		−	0.996261i
$411$	9.08569e90	−	5.26912e91i	0.297779	−	1.72693i
$412$	−2.97708e91			−0.896166
$413$			1.85257e91i			0.512299i
$414$	−2.94574e91	−	1.04701e91i	−0.748483	−	0.266036i
$415$	−3.03343e91			−0.708354
$416$		−	9.03181e91i		−	1.93869i
$417$	−3.89683e91	−	6.71940e90i	−0.769040	−	0.132608i
$418$	5.24264e91			0.951438
$419$			6.27916e91i			1.04812i	0.851681	+	0.524060i	$0.175583\pi$
$419$			6.27916e91i			1.04812i	−0.851681	+	0.524060i	$0.824417\pi$
$420$	6.43410e90	−	3.73137e91i	0.0988012	−	0.572984i
$421$	−5.53194e91			−0.781635			−0.390818	−	0.920468i	$-0.627808\pi$
$421$	−5.53194e91			−0.781635			−0.390818	+	0.920468i	$0.627808\pi$
$422$			6.77038e91i			0.880395i
$423$	−3.14152e91	+	8.83856e91i	−0.376034	+	1.05796i
$424$	1.35868e91			0.149732
$425$			1.46153e92i			1.48318i
$426$	−8.97124e91	−	1.54694e91i	−0.838526	−	0.144589i
$427$	4.01287e91			0.345525
$428$		−	1.41818e92i		−	1.12512i
$429$	2.56880e91	−	1.48974e92i	0.187813	−	1.08920i
$430$	3.62891e92			2.44557
$431$		−	3.00391e91i		−	0.186630i	−0.995637	−	0.0933152i	$-0.970254\pi$
$431$		−	3.00391e91i		−	0.186630i	0.995637	−	0.0933152i	$-0.0297464\pi$
$432$	1.71317e92	+	9.63369e91i	0.981454	+	0.551902i
$433$	2.30229e92			1.21642			0.608211	−	0.793775i	$-0.291887\pi$
$433$	2.30229e92			1.21642			0.608211	+	0.793775i	$0.291887\pi$
$434$			1.91524e92i			0.933434i
$435$	−2.80215e92	−	4.83183e91i	−1.25999	−	0.217264i
$436$	−2.11532e90			−0.00877707
$437$			1.40400e92i			0.537673i
$438$	1.26437e91	−	7.33253e91i	0.0446971	−	0.259215i
$439$	1.26162e91			0.0411786			0.0205893	−	0.999788i	$-0.493446\pi$
$439$	1.26162e91			0.0411786			0.0205893	+	0.999788i	$0.493446\pi$
$440$		−	7.45779e91i		−	0.224785i
$441$	−2.65747e92	−	9.44555e91i	−0.739807	−	0.262952i
$442$	9.79607e92			2.51926
$443$		−	4.85832e92i		−	1.15440i	−0.816603	−	0.577200i	$-0.804145\pi$
$443$		−	4.85832e92i		−	1.15440i	0.816603	−	0.577200i	$-0.195855\pi$
$444$	−4.50993e92	−	7.77659e91i	−0.990298	−	0.170760i
$445$	−9.53372e92			−1.93492
$446$		−	1.11925e93i		−	2.09994i
$447$	−1.03164e92	+	5.98283e92i	−0.178963	+	1.03787i
$448$	−1.98117e92			−0.317827
$449$		−	2.19912e92i		−	0.326307i	−0.986601	−	0.163154i	$-0.947833\pi$
$449$		−	2.19912e92i		−	0.326307i	0.986601	−	0.163154i	$-0.0521666\pi$
$450$	−3.87462e92	+	1.09011e93i	−0.531853	+	1.49635i
$451$	−2.97164e92			−0.377413
$452$			5.96981e92i			0.701641i
$453$	1.09518e93	+	1.88845e92i	1.19138	+	0.205432i
$454$	4.89434e92			0.492878
$455$			1.06575e93i			0.993699i
$456$	3.64767e91	−	2.11542e92i	0.0314954	−	0.182653i
$457$	−1.02874e93			−0.822693			−0.411346	−	0.911479i	$-0.634941\pi$
$457$	−1.02874e93			−0.822693			−0.411346	+	0.911479i	$0.634941\pi$
$458$			3.50611e92i			0.259737i
$459$	−9.07691e92	+	1.61416e93i	−0.623008	+	1.10790i
$460$	−1.15116e93			−0.732171
$461$		−	2.35636e93i		−	1.38902i	−0.719481	−	0.694512i	$-0.755620\pi$
$461$		−	2.35636e93i		−	1.38902i	0.719481	−	0.694512i	$-0.244380\pi$
$462$	−8.63406e92	−	1.48879e92i	−0.471787	−	0.0813515i
$463$	6.47047e92			0.327794			0.163897	−	0.986477i	$-0.447594\pi$
$463$	6.47047e92			0.327794			0.163897	+	0.986477i	$0.447594\pi$
$464$			2.08197e93i			0.978016i
$465$	8.49580e92	−	4.92702e93i	0.370127	−	2.14650i
$466$	−2.43391e92			−0.0983554
$467$		−	2.09812e93i		−	0.786575i	−0.919415	−	0.393288i	$-0.871338\pi$
$467$		−	2.09812e93i		−	0.786575i	0.919415	−	0.393288i	$-0.128662\pi$
$468$	3.36169e93	+	1.19486e93i	1.16937	+	0.415634i
$469$	3.00136e92			0.0968878
$470$			7.50730e93i			2.24936i
$471$	−1.79362e92	−	3.09279e91i	−0.0498884	−	0.00860239i
$472$	−8.61138e92			−0.222384
$473$		−	3.86335e93i		−	0.926454i
$474$	1.82281e93	−	1.05711e94i	0.405975	−	2.35439i
$475$	5.19572e93			1.07490
$476$		−	2.61214e93i		−	0.502057i
$477$	−1.39551e93	+	3.92623e93i	−0.249224	+	0.701184i
$478$	−9.21752e93			−1.52981
$479$			5.68106e93i			0.876367i	0.898885	+	0.438184i	$0.144378\pi$
$479$			5.68106e93i			0.876367i	−0.898885	+	0.438184i	$0.855622\pi$
$480$	1.34660e94	+	2.32198e93i	1.93106	+	0.332978i
$481$	1.28812e94			1.71743
$482$		−	7.89704e93i		−	0.979080i
$483$	3.98706e92	−	2.31224e93i	0.0459730	−	0.266614i
$484$	−3.36900e93			−0.361338
$485$			1.94967e94i			1.94537i
$486$	−1.10495e94	+	9.63321e93i	−1.02582	+	0.894338i
$487$	−6.53582e93			−0.564659			−0.282330	−	0.959317i	$-0.591107\pi$
$487$	−6.53582e93			−0.564659			−0.282330	+	0.959317i	$0.591107\pi$
$488$			1.86531e93i			0.149988i
$489$	1.80861e94	+	3.11864e93i	1.35374	+	0.233429i
$490$	−2.25721e94			−1.57293
$491$			4.85344e93i			0.314918i	0.987526	+	0.157459i	$0.0503303\pi$
$491$			4.85344e93i			0.314918i	−0.987526	+	0.157459i	$0.949670\pi$
$492$	1.19171e93	−	6.91116e93i	0.0720098	−	0.417611i
$493$	−1.96165e94			−1.10402
$494$		−	3.48250e94i		−	1.82578i
$495$	2.15510e94	+	7.65994e93i	1.05265	+	0.374148i
$496$	−3.66073e94			−1.66613
$497$		−	6.83256e93i		−	0.289807i
$498$	−1.63244e94	−	2.81485e93i	−0.645370	−	0.111283i
$499$	−4.12758e94			−1.52116			−0.760582	−	0.649242i	$-0.775086\pi$
$499$	−4.12758e94			−1.52116			−0.760582	+	0.649242i	$0.775086\pi$
$500$			6.09260e93i			0.209340i
$501$	3.13086e93	−	1.81570e94i	0.100310	−	0.581734i
$502$	4.99356e94			1.49204
$503$		−	2.11905e94i		−	0.590556i	−0.955411	−	0.295278i	$-0.904588\pi$
$503$		−	2.11905e94i		−	0.590556i	0.955411	−	0.295278i	$-0.0954123\pi$
$504$	−1.20146e93	+	3.38028e93i	−0.0312350	+	0.0878787i
$505$	9.88767e94			2.39826
$506$			2.66369e94i			0.602859i
$507$	−5.23014e94	−	9.01846e93i	−1.10467	−	0.190482i
$508$	−3.73119e94			−0.735560
$509$		−	3.33454e94i		−	0.613640i	−0.951768	−	0.306820i	$-0.900735\pi$
$509$		−	3.33454e94i		−	0.613640i	0.951768	−	0.306820i	$-0.0992650\pi$
$510$	−2.51846e94	+	1.46055e95i	−0.432693	+	2.50934i
$511$	5.58450e93			0.0895887
$512$		−	8.49285e94i		−	1.27234i
$513$	5.73833e94	+	3.22684e94i	0.802930	+	0.451512i
$514$	−2.54365e94			−0.332466
$515$			1.26777e95i			1.54806i
$516$	8.98501e94	+	1.54931e94i	1.02513	+	0.176766i
$517$	7.99230e94			0.852124
$518$		−	7.46551e94i		−	0.743905i
$519$	2.00106e94	−	1.16049e95i	0.186382	−	1.08090i
$520$	−4.95394e94			−0.431354
$521$			3.90509e94i			0.317915i	0.987285	+	0.158957i	$0.0508132\pi$
$521$			3.90509e94i			0.317915i	−0.987285	+	0.158957i	$0.949187\pi$
$522$	−1.46314e95	−	5.20048e94i	−1.11383	−	0.395891i
$523$	2.17152e95			1.54599			0.772993	−	0.634415i	$-0.218759\pi$
$523$	2.17152e95			1.54599			0.772993	+	0.634415i	$0.218759\pi$
$524$			1.16556e95i			0.776138i
$525$	−8.55678e94	−	1.47547e94i	−0.533009	−	0.0919082i
$526$	2.12332e95			1.23741
$527$		−	3.44916e95i		−	1.88079i
$528$	2.84563e94	−	1.65029e95i	0.145208	−	0.842116i
$529$	1.38052e95			0.659315
$530$			3.33486e95i			1.49081i
$531$	8.84479e94	−	2.48845e95i	0.370151	−	1.04141i
$532$	−9.28615e94			−0.363855
$533$			1.97395e95i			0.724243i
$534$	−5.13055e95	−	8.84675e94i	−1.76287	−	0.303976i
$535$	−6.03924e95			−1.94357
$536$			1.39513e94i			0.0420579i
$537$	2.97157e94	−	1.72332e95i	0.0839241	−	0.486706i
$538$	−2.72942e95			−0.722255
$539$			2.40303e95i			0.595871i
$540$	−2.64573e95	+	4.70494e95i	−0.614843	+	1.09338i
$541$	1.77318e95			0.386233			0.193117	−	0.981176i	$-0.438140\pi$
$541$	1.77318e95			0.386233			0.193117	+	0.981176i	$0.438140\pi$
$542$			6.95878e95i			1.42088i
$543$	−3.16511e95	−	5.45769e94i	−0.605892	−	0.104476i
$544$	9.42687e95			1.69202
$545$			9.00797e93i			0.0151618i
$546$	−9.88952e94	+	5.73530e95i	−0.156111	+	0.905343i
$547$	−8.66089e94			−0.128235			−0.0641174	−	0.997942i	$-0.520423\pi$
$547$	−8.66089e94			−0.128235			−0.0641174	+	0.997942i	$0.520423\pi$
$548$		−	1.07516e96i		−	1.49333i
$549$	−5.39024e95	−	1.91587e95i	−0.702387	−	0.249652i
$550$	9.85737e95			1.20522
$551$			6.97365e95i			0.800118i
$552$	1.07481e95	+	1.85332e94i	0.115734	+	0.0199564i
$553$	8.05104e95			0.813715
$554$		−	2.53514e96i		−	2.40525i
$555$	−3.31161e95	+	1.92053e96i	−0.294975	+	1.71067i
$556$	−7.95147e95			−0.665012
$557$		−	1.93338e96i		−	1.51839i	−0.650861	−	0.759197i	$-0.725592\pi$
$557$		−	1.93338e96i		−	1.51839i	0.650861	−	0.759197i	$-0.274408\pi$
$558$	9.14400e95	−	2.57263e96i	0.674433	−	1.89750i
$559$	−2.56628e96			−1.77783
$560$			1.18060e96i			0.768282i
$561$	1.55491e96	+	2.68117e95i	0.950613	+	0.163917i
$562$	1.39108e96			0.799064
$563$			3.03118e96i			1.63613i	0.575125	+	0.818066i	$0.304953\pi$
$563$			3.03118e96i			1.63613i	−0.575125	+	0.818066i	$0.695047\pi$
$564$	−3.20513e95	+	1.85877e96i	−0.162584	+	0.942883i
$565$	2.54221e96			1.21203
$566$		−	2.68192e96i		−	1.20191i
$567$	−8.53405e95	−	6.94381e95i	−0.359541	−	0.292544i
$568$	3.17600e95			0.125802
$569$			1.06144e96i			0.395336i	0.980269	+	0.197668i	$0.0633369\pi$
$569$			1.06144e96i			0.395336i	−0.980269	+	0.197668i	$0.936663\pi$
$570$	5.19225e96	+	8.95313e95i	1.81859	+	0.313585i
$571$	−2.60220e96			−0.857190			−0.428595	−	0.903497i	$-0.640991\pi$
$571$	−2.60220e96			−0.857190			−0.428595	+	0.903497i	$0.640991\pi$
$572$		−	3.03982e96i		−	0.941860i
$573$	2.47381e94	−	1.43466e95i	0.00721033	−	0.0418154i
$574$	1.14404e96			0.313707
$575$			2.63985e96i			0.681090i
$576$	2.66119e96	+	9.45876e95i	0.646084	+	0.229640i
$577$	−4.10802e96			−0.938597			−0.469298	−	0.883040i	$-0.655493\pi$
$577$	−4.10802e96			−0.938597			−0.469298	+	0.883040i	$0.655493\pi$
$578$			3.89588e96i			0.837782i
$579$	−4.69910e96	−	8.10277e95i	−0.951184	−	0.164015i
$580$	−5.71779e96			−1.08955
$581$		−	1.24327e96i		−	0.223050i
$582$	−1.80919e96	+	1.04921e97i	−0.305618	+	1.77239i
$583$	3.55030e96			0.564762
$584$			2.59586e95i			0.0388895i
$585$	5.08822e96	−	1.43155e97i	0.717977	−	2.02001i
$586$	−1.55371e97			−2.06516
$587$			8.35912e96i			1.04671i	0.852114	+	0.523356i	$0.175320\pi$
$587$			8.35912e96i			1.04671i	−0.852114	+	0.523356i	$0.824680\pi$
$588$	−5.58874e96	−	9.63682e95i	−0.659337	−	0.113691i
$589$	−1.22617e97			−1.36307
$590$		−	2.11364e97i		−	2.21417i
$591$	3.17099e96	−	1.83897e97i	0.313064	−	1.81557i
$592$	1.42693e97			1.32783
$593$			6.31904e96i			0.554289i	0.960828	+	0.277145i	$0.0893881\pi$
$593$			6.31904e96i			0.554289i	−0.960828	+	0.277145i	$0.910612\pi$
$594$	1.08868e97	+	6.12199e96i	0.900276	+	0.506252i
$595$	−1.11236e97			−0.867267
$596$			1.22080e97i			0.897478i
$597$	2.30866e96	+	3.98088e95i	0.160051	+	0.0275980i
$598$	1.76939e97			1.15687
$599$			2.23963e97i			1.38114i	0.723267	+	0.690568i	$0.242640\pi$
$599$			2.23963e97i			1.38114i	−0.723267	+	0.690568i	$0.757360\pi$
$600$	6.85847e95	−	3.97748e96i	0.0398964	−	0.231374i
$601$	−1.54495e97			−0.847829			−0.423914	−	0.905702i	$-0.639344\pi$
$601$	−1.54495e97			−0.847829			−0.423914	+	0.905702i	$0.639344\pi$
$602$			1.48733e97i			0.770071i
$603$	−4.03155e96	−	1.43295e96i	−0.196955	−	0.0700043i
$604$	2.23472e97			1.03022
$605$			1.43467e97i			0.624185i
$606$	5.32103e97	+	9.17520e96i	2.18501	+	0.376768i
$607$	−4.03778e96			−0.156509			−0.0782543	−	0.996933i	$-0.524935\pi$
$607$	−4.03778e96			−0.156509			−0.0782543	+	0.996933i	$0.524935\pi$
$608$		−	3.35125e97i		−	1.22626i
$609$	1.98036e96	−	1.14848e97i	0.0684130	−	0.396752i
$610$	−4.57837e97			−1.49337
$611$		−	5.30900e97i		−	1.63520i
$612$	−1.24712e97	+	3.50873e97i	−0.362751	+	1.02059i
$613$	6.79324e97			1.86621			0.933105	−	0.359605i	$-0.117088\pi$
$613$	6.79324e97			1.86621			0.933105	+	0.359605i	$0.117088\pi$
$614$			3.17226e96i			0.0823143i
$615$	−2.94307e97	−	5.07482e96i	−0.721393	−	0.124392i
$616$	3.05663e96			0.0707812
$617$			6.49728e96i			0.142151i	0.997471	+	0.0710756i	$0.0226432\pi$
$617$			6.49728e96i			0.142151i	−0.997471	+	0.0710756i	$0.977357\pi$
$618$	−1.17642e97	+	6.82250e97i	−0.243202	+	1.41041i
$619$	3.00911e97			0.587848			0.293924	−	0.955829i	$-0.405039\pi$
$619$	3.00911e97			0.587848			0.293924	+	0.955829i	$0.405039\pi$
$620$		−	1.00536e98i		−	1.85614i
$621$	−1.63950e97	+	2.91554e97i	−0.286091	+	0.508760i
$622$	6.19658e97			1.02209
$623$		−	3.90746e97i		−	0.609275i
$624$	−1.09623e98	−	1.89025e97i	−1.61599	−	0.278650i
$625$	−5.77749e97			−0.805265
$626$		−	6.04358e97i		−	0.796513i
$627$	9.53154e96	−	5.52769e97i	0.118795	−	0.688937i
$628$	−3.65988e96			−0.0431400
$629$			1.34446e98i			1.49891i
$630$	−8.29682e97	−	2.94897e97i	−0.874968	−	0.310993i
$631$	7.09493e97			0.707816			0.353908	−	0.935280i	$-0.384853\pi$
$631$	7.09493e97			0.707816			0.353908	+	0.935280i	$0.384853\pi$
$632$			3.74239e97i			0.353225i
$633$	7.13849e97	+	1.23091e97i	0.637495	+	0.109925i
$634$	−2.37037e98			−2.00305
$635$			1.58891e98i			1.27063i
$636$	−1.42377e97	+	8.25696e97i	−0.107756	+	0.624915i
$637$	1.59625e98			1.14346
$638$			1.32305e98i			0.897122i
$639$	−3.26209e97	+	9.17777e97i	−0.209395	+	0.589124i
$640$	−9.64101e97			−0.585900
$641$			7.58856e97i			0.436645i	0.975877	+	0.218323i	$0.0700585\pi$
$641$			7.58856e97i			0.436645i	−0.975877	+	0.218323i	$0.929942\pi$
$642$	−3.25001e98	−	5.60408e97i	−1.77076	−	0.305336i
$643$	1.28425e98			0.662624			0.331312	−	0.943521i	$-0.392509\pi$
$643$	1.28425e98			0.662624			0.331312	+	0.943521i	$0.392509\pi$
$644$		−	4.71812e97i		−	0.230549i
$645$	6.59764e97	−	3.82621e98i	0.305350	−	1.77084i
$646$	3.63483e98			1.59348
$647$		−	1.29437e98i		−	0.537537i	−0.963205	−	0.268768i	$-0.913383\pi$
$647$		−	1.29437e98i		−	0.537537i	0.963205	−	0.268768i	$-0.0866167\pi$
$648$	3.22771e97	−	3.96691e97i	0.126990	−	0.156073i
$649$	−2.25019e98			−0.838793
$650$		−	6.54790e98i		−	2.31278i
$651$	2.01938e98	+	3.48206e97i	0.675900	+	0.116547i
$652$	3.69047e98			1.17062
$653$			3.26500e98i			0.981570i	0.871281	+	0.490785i	$0.163290\pi$
$653$			3.26500e98i			0.981570i	−0.871281	+	0.490785i	$0.836710\pi$
$654$	−8.35889e95	+	4.84763e96i	−0.00238192	+	0.0138136i
$655$	4.96346e98			1.34072
$656$			2.18668e98i			0.559951i
$657$	−7.50133e97	−	2.66622e97i	−0.182117	−	0.0647305i
$658$	−3.07692e98			−0.708288
$659$		−	1.07077e98i		−	0.233725i	−0.993148	−	0.116862i	$-0.962716\pi$
$659$		−	1.07077e98i		−	0.233725i	0.993148	−	0.116862i	$-0.0372836\pi$
$660$	4.53223e98	+	7.81504e97i	0.938154	+	0.161768i
$661$	−1.60477e98			−0.315038			−0.157519	−	0.987516i	$-0.550349\pi$
$661$	−1.60477e98			−0.315038			−0.157519	+	0.987516i	$0.550349\pi$
$662$			5.87435e98i			1.09378i
$663$	1.78100e98	−	1.03287e99i	0.314551	−	1.82420i
$664$	5.77914e97			0.0968235
$665$			3.95445e98i			0.628533i
$666$	−3.56428e98	+	1.00280e99i	−0.537494	+	1.51222i
$667$	−3.54318e98			−0.506978
$668$		−	3.70494e98i		−	0.503042i
$669$	−1.18010e99	−	2.03489e98i	−1.52057	−	0.262196i
$670$	−3.42432e98			−0.418751
$671$			4.87414e98i			0.565731i
$672$	−9.51681e97	+	5.51914e98i	−0.104850	+	0.608061i
$673$	1.46060e99			1.52758			0.763790	−	0.645465i	$-0.223336\pi$
$673$	1.46060e99			1.52758			0.763790	+	0.645465i	$0.223336\pi$
$674$			2.48238e98i			0.246475i
$675$	1.07894e99	+	6.06720e98i	1.01710	+	0.571947i
$676$	−1.06721e99			−0.955245
$677$		−	1.45576e99i		−	1.23733i	−0.785655	−	0.618664i	$-0.787674\pi$
$677$		−	1.45576e99i		−	1.23733i	0.785655	−	0.618664i	$-0.212326\pi$
$678$	1.36808e99	+	2.35902e98i	1.10426	+	0.190411i
$679$	−7.99088e98			−0.612565
$680$		−	5.17063e98i		−	0.376471i
$681$	8.89830e97	−	5.16045e98i	0.0615401	−	0.356893i
$682$	−2.32631e99			−1.52832
$683$		−	1.89429e98i		−	0.118228i	−0.998251	−	0.0591141i	$-0.981172\pi$
$683$		−	1.89429e98i		−	0.118228i	0.998251	−	0.0591141i	$-0.0188276\pi$
$684$	1.24735e99	+	4.43351e98i	0.739650	+	0.262896i
$685$	−4.57852e99			−2.57962
$686$		−	2.10342e99i		−	1.12611i
$687$	3.69674e98	+	6.37438e97i	0.188076	+	0.0324304i
$688$	−2.84284e99			−1.37454
$689$		−	2.35834e99i		−	1.08376i
$690$	−4.54892e98	+	2.63809e99i	−0.198697	+	1.15231i
$691$	3.61198e99			1.49973			0.749867	−	0.661589i	$-0.230118\pi$
$691$	3.61198e99			1.49973			0.749867	+	0.661589i	$0.230118\pi$
$692$		−	2.36798e99i		−	0.934682i
$693$	−3.13948e98	+	8.83282e98i	−0.117813	+	0.331464i
$694$	4.84720e99			1.72946
$695$			3.38608e99i			1.14876i
$696$	5.33853e98	+	9.20537e97i	0.172226	+	0.0296974i
$697$	−2.06030e99			−0.632095
$698$			4.36792e99i			1.27448i
$699$	−4.42505e97	+	2.56625e98i	−0.0122805	+	0.0712192i
$700$	−1.74601e99			−0.460909
$701$			4.31481e99i			1.08351i	0.840538	+	0.541753i	$0.182239\pi$
$701$			4.31481e99i			1.08351i	−0.840538	+	0.541753i	$0.817761\pi$
$702$	4.06662e99	−	7.23173e99i	0.971482	−	1.72760i
$703$	4.77956e99			1.08630
$704$		−	2.40639e99i		−	0.520383i
$705$	7.91547e99	+	1.36489e99i	1.62876	+	0.280852i
$706$	9.40281e99			1.84117
$707$			4.05253e99i			0.755174i
$708$	9.02389e98	−	5.23329e99i	0.160041	−	0.928133i
$709$	−5.40229e99			−0.911926			−0.455963	−	0.889999i	$-0.650705\pi$
$709$	−5.40229e99			−0.911926			−0.455963	+	0.889999i	$0.650705\pi$
$710$			7.79541e99i			1.25256i
$711$	−1.08145e100	−	3.84383e99i	−1.65413	−	0.587933i
$712$	1.81632e99			0.264480
$713$		−	6.22997e99i		−	0.863679i
$714$	−5.98616e99	−	1.03221e99i	−0.790153	−	0.136248i
$715$	−1.29449e100			−1.62700
$716$		−	3.51644e99i		−	0.420870i
$717$	−1.67582e99	+	9.71868e99i	−0.191010	+	1.10774i
$718$	1.11729e100			1.21286
$719$		−	6.54802e99i		−	0.677016i	−0.940964	−	0.338508i	$-0.890078\pi$
$719$		−	6.54802e99i		−	0.677016i	0.940964	−	0.338508i	$-0.109922\pi$
$720$	5.63656e99	−	1.58583e100i	0.555107	−	1.56177i
$721$	−5.19606e99			−0.487461
$722$			2.30611e99i			0.206100i
$723$	−8.32641e99	−	1.43574e99i	−0.708953	−	0.122247i
$724$	−6.45841e99			−0.523933
$725$			1.31121e100i			1.01354i
$726$	−1.33129e99	+	7.72064e99i	−0.0980598	+	0.568685i
$727$	5.74768e99			0.403448			0.201724	−	0.979442i	$-0.435346\pi$
$727$	5.74768e99			0.403448			0.201724	+	0.979442i	$0.435346\pi$
$728$		−	2.03041e99i		−	0.135827i
$729$	8.14809e99	+	1.34016e100i	0.519508	+	0.854466i
$730$	−6.37148e99			−0.387204
$731$		−	2.67853e100i		−	1.55163i
$732$	−1.13358e100	−	1.95467e99i	−0.625987	−	0.107941i
$733$	−2.02698e99			−0.106712			−0.0533558	−	0.998576i	$-0.516992\pi$
$733$	−2.02698e99			−0.106712			−0.0533558	+	0.998576i	$0.516992\pi$
$734$			1.16232e100i			0.583397i
$735$	−4.10378e99	+	2.37993e100i	−0.196393	+	1.13896i
$736$	1.70271e100			0.776993
$737$			3.64554e99i			0.158635i
$738$	−1.53672e100	−	5.46201e99i	−0.637708	−	0.226663i
$739$	3.12492e99			0.123676			0.0618378	−	0.998086i	$-0.480304\pi$
$739$	3.12492e99			0.123676			0.0618378	+	0.998086i	$0.480304\pi$
$740$			3.91883e100i			1.47927i
$741$	−3.67184e100	−	6.33146e99i	−1.32205	−	0.227964i
$742$	−1.36681e100			−0.469432
$743$		−	1.73630e100i		−	0.568873i	−0.958695	−	0.284436i	$-0.908194\pi$
$743$		−	1.73630e100i		−	0.568873i	0.958695	−	0.284436i	$-0.0918065\pi$
$744$	−1.61858e99	+	9.38673e99i	−0.0505919	+	0.293401i
$745$	5.19868e100			1.55033
$746$		−	1.18965e100i		−	0.338501i
$747$	−5.93579e99	+	1.67002e100i	−0.161160	+	0.453419i
$748$	3.17278e100			0.822024
$749$		−	2.47523e100i		−	0.612000i
$750$	1.39622e100	+	2.40755e99i	0.329466	+	0.0568107i
$751$	1.28783e100			0.290041			0.145020	−	0.989429i	$-0.453675\pi$
$751$	1.28783e100			0.290041			0.145020	+	0.989429i	$0.453675\pi$
$752$		−	5.88112e100i		−	1.26426i
$753$	9.07869e99	−	5.26507e100i	0.186294	−	1.08039i
$754$	8.78853e100			1.72155
$755$		−	9.51641e100i		−	1.77963i
$756$	−1.92835e100	−	1.08437e100i	−0.344289	−	0.193604i
$757$	−3.61479e100			−0.616207			−0.308104	−	0.951353i	$-0.599694\pi$
$757$	−3.61479e100			−0.616207			−0.308104	+	0.951353i	$0.599694\pi$
$758$			1.16381e101i			1.89435i
$759$	2.80852e100	+	4.84280e99i	0.436531	+	0.0752722i
$760$	−1.83816e100			−0.272840
$761$		−	9.18222e100i		−	1.30162i	−0.759240	−	0.650811i	$-0.774429\pi$
$761$		−	9.18222e100i		−	1.30162i	0.759240	−	0.650811i	$-0.225571\pi$
$762$	−1.47441e100	+	8.55067e100i	−0.199616	+	1.15765i
$763$	−3.69198e98			−0.00477420
$764$		−	2.92741e99i		−	0.0361590i
$765$	1.49417e101	+	5.31079e100i	1.76299	+	0.626626i
$766$	−7.40137e100			−0.834268
$767$			1.49472e101i			1.60962i
$768$	−1.17558e101	−	2.02709e100i	−1.20951	−	0.208560i
$769$	1.18589e101			1.16580			0.582899	−	0.812544i	$-0.301918\pi$
$769$	1.18589e101			1.16580			0.582899	+	0.812544i	$0.301918\pi$
$770$			7.50242e100i			0.704735i
$771$	−4.62455e99	+	2.68195e100i	−0.0415113	+	0.240739i
$772$	−9.58849e100			−0.822517
$773$			1.15598e101i			0.947697i	0.880606	+	0.473849i	$0.157136\pi$
$773$			1.15598e101i			0.947697i	−0.880606	+	0.473849i	$0.842864\pi$
$774$	7.10101e100	−	1.99785e101i	0.556399	−	1.56541i
$775$	−2.30549e101			−1.72665
$776$		−	3.71442e100i		−	0.265908i
$777$	−7.87141e100	−	1.35729e100i	−0.538663	−	0.0928830i
$778$	−2.26641e101			−1.48270
$779$			7.32435e100i			0.458097i
$780$	5.19125e100	−	3.01060e101i	0.310428	−	1.80029i
$781$	8.29902e100			0.474505
$782$			1.84679e101i			1.00967i
$783$	−8.14333e100	+	1.44814e101i	−0.425736	+	0.757093i
$784$	1.76827e101			0.884067
$785$			1.55854e100i			0.0745212i
$786$	2.67108e101	+	4.60581e100i	1.22151	+	0.210628i
$787$	−2.13502e100			−0.0933872			−0.0466936	−	0.998909i	$-0.514868\pi$
$787$	−2.13502e100			−0.0933872			−0.0466936	+	0.998909i	$0.514868\pi$
$788$		−	3.75242e101i		−	1.56998i
$789$	3.86037e100	−	2.23877e101i	0.154502	−	0.896012i
$790$	−9.18560e101			−3.51690
$791$			1.04194e101i			0.381651i
$792$	−4.10579e100	−	1.45933e100i	−0.143885	−	0.0511415i
$793$	3.23772e101			1.08562
$794$			2.34390e101i			0.752007i
$795$	3.51617e101	+	6.06303e100i	1.07950	+	0.186140i
$796$	4.71081e100			0.138401
$797$		−	6.29559e101i		−	1.77009i	−0.465507	−	0.885044i	$-0.654128\pi$
$797$		−	6.29559e101i		−	1.77009i	0.465507	−	0.885044i	$-0.345872\pi$
$798$	−3.66950e100	+	2.12808e101i	−0.0987430	+	0.572647i
$799$	5.54122e101			1.42714
$800$		−	6.30112e101i		−	1.55335i
$801$	−1.86555e101	+	5.24866e101i	−0.440219	+	1.23854i
$802$	4.18147e101			0.944553
$803$			6.78310e100i			0.146685i
$804$	−8.47846e100	−	1.46196e100i	−0.175532	−	0.0302674i
$805$	−2.00918e101			−0.398257
$806$			1.54529e102i			2.93280i
$807$	−4.96230e100	+	2.87782e101i	−0.0901798	+	0.522986i
$808$	−1.88375e101			−0.327813
$809$		−	2.38020e101i		−	0.396657i	−0.980136	−	0.198328i	$-0.936449\pi$
$809$		−	2.38020e101i		−	0.396657i	0.980136	−	0.198328i	$-0.0635512\pi$
$810$	9.73669e101	+	7.92234e101i	1.55394	+	1.26438i
$811$	−4.71748e101			−0.721075			−0.360538	−	0.932745i	$-0.617407\pi$
$811$	−4.71748e101			−0.721075			−0.360538	+	0.932745i	$0.617407\pi$
$812$		−	2.34348e101i		−	0.343083i
$813$	7.33713e101	+	1.26516e101i	1.02886	+	0.177409i
$814$	9.06783e101			1.21800
$815$		−	1.57156e102i		−	2.02216i
$816$	1.97293e101	−	1.14418e102i	0.243196	−	1.41038i
$817$	−9.52218e101			−1.12451
$818$		−	9.63153e101i		−	1.08976i
$819$	5.86733e101	+	2.08544e101i	0.636068	+	0.226080i
$820$	−6.00534e101			−0.623810
$821$			5.37857e101i			0.535373i	0.963506	+	0.267686i	$0.0862591\pi$
$821$			5.37857e101i			0.535373i	−0.963506	+	0.267686i	$0.913741\pi$
$822$	−2.46392e102	−	4.24861e101i	−2.35025	−	0.405259i
$823$	4.86000e101			0.444265			0.222133	−	0.975016i	$-0.428698\pi$
$823$	4.86000e101			0.444265			0.222133	+	0.975016i	$0.428698\pi$
$824$		−	2.41530e101i		−	0.211601i
$825$	1.79215e101	−	1.03933e102i	0.150482	−	0.872702i
$826$	8.66291e101			0.697208
$827$			1.19480e102i			0.921728i	0.887471	+	0.460864i	$0.152460\pi$
$827$			1.19480e102i			0.921728i	−0.887471	+	0.460864i	$0.847540\pi$
$828$	−2.25259e101	+	6.33758e101i	−0.166579	+	0.468664i
$829$	4.87669e101			0.345714			0.172857	−	0.984947i	$-0.444700\pi$
$829$	4.87669e101			0.345714			0.172857	+	0.984947i	$0.444700\pi$
$830$			1.41848e102i			0.964027i
$831$	−2.67298e102	−	4.60909e101i	−1.74165	−	0.300317i
$832$	−1.59848e102			−0.998597
$833$			1.66607e102i			0.997970i
$834$	−3.14209e101	+	1.82221e102i	−0.180471	+	1.04662i
$835$	−1.57772e102			−0.868969
$836$		−	1.12792e102i		−	0.595744i
$837$	−2.54626e102	−	1.43184e102i	−1.28977	−	0.725277i
$838$	2.93623e102			1.42643
$839$		−	2.72159e102i		−	1.26810i	−0.773291	−	0.634052i	$-0.781391\pi$
$839$		−	2.72159e102i		−	1.26810i	0.773291	−	0.634052i	$-0.218609\pi$
$840$	3.02725e101	+	5.21996e100i	0.135292	+	0.0233288i
$841$	5.72817e101			0.245559
$842$			2.58682e102i			1.06376i
$843$	2.52910e101	−	1.46672e102i	0.0997701	−	0.578603i
$844$	1.45661e102			0.551261
$845$			4.54464e102i			1.65012i
$846$	4.13304e102	+	1.46902e102i	1.43982	+	0.511759i
$847$	−5.88009e101			−0.196546
$848$		−	2.61248e102i		−	0.837913i
$849$	−2.82774e102	−	4.87595e101i	−0.870303	−	0.150069i
$850$	6.83431e102			2.01852
$851$			2.42841e102i			0.688314i
$852$	−3.32814e101	+	1.93011e102i	−0.0905348	+	0.525045i
$853$	−1.56864e102			−0.409549			−0.204775	−	0.978809i	$-0.565646\pi$
$853$	−1.56864e102			−0.409549			−0.204775	+	0.978809i	$0.565646\pi$
$854$		−	1.87648e102i		−	0.470238i
$855$	1.88798e102	−	5.31178e102i	0.454134	−	1.27769i
$856$	1.15057e102			0.265663
$857$			2.71856e102i			0.602574i	0.953533	+	0.301287i	$0.0974162\pi$
$857$			2.71856e102i			0.602574i	−0.953533	+	0.301287i	$0.902584\pi$
$858$	−6.96626e102	−	1.20121e102i	−1.48233	−	0.255602i
$859$	4.66950e102			0.953916			0.476958	−	0.878926i	$-0.341739\pi$
$859$	4.66950e102			0.953916			0.476958	+	0.878926i	$0.341739\pi$
$860$		−	7.80738e102i		−	1.53130i
$861$	2.07995e101	−	1.20624e102i	0.0391690	−	0.227156i
$862$	−1.40467e102			−0.253993
$863$			2.51608e102i			0.436865i	0.975852	+	0.218432i	$0.0700943\pi$
$863$			2.51608e102i			0.436865i	−0.975852	+	0.218432i	$0.929906\pi$
$864$	3.91336e102	−	6.95917e102i	0.652482	−	1.16032i
$865$	−1.00839e103			−1.61460
$866$		−	1.07659e103i		−	1.65548i
$867$	4.10770e102	+	7.08302e101i	0.606639	+	0.104604i
$868$	4.12053e102			0.584471
$869$			9.77903e102i			1.33230i
$870$	−2.25944e102	+	1.31033e103i	−0.295683	+	1.71477i
$871$	2.42160e102			0.304416
$872$		−	1.71616e100i		−	0.00207243i
$873$	1.07337e103	+	3.81511e102i	1.24523	+	0.442597i
$874$	6.56533e102			0.731740
$875$			1.06337e102i			0.113869i
$876$	−1.57755e102	−	2.72021e101i	−0.162308	−	0.0279872i
$877$	1.25532e102			0.124099			0.0620493	−	0.998073i	$-0.480236\pi$
$877$	1.25532e102			0.124099			0.0620493	+	0.998073i	$0.480236\pi$
$878$		−	5.89954e101i		−	0.0560416i
$879$	−2.82478e102	+	1.63819e103i	−0.257854	+	1.49539i
$880$	−1.43399e103			−1.25792
$881$		−	8.14189e102i		−	0.686386i	−0.939265	−	0.343193i	$-0.888492\pi$
$881$		−	8.14189e102i		−	0.686386i	0.939265	−	0.343193i	$-0.111508\pi$
$882$	−4.41688e102	+	1.24267e103i	−0.357862	+	1.00683i
$883$	7.57968e102			0.590237			0.295119	−	0.955461i	$-0.404641\pi$
$883$	7.57968e102			0.590237			0.295119	+	0.955461i	$0.404641\pi$
$884$		−	2.10757e103i		−	1.57744i
$885$	−2.22856e103	−	3.84277e102i	−1.60328	−	0.276458i
$886$	−2.27183e103			−1.57107
$887$		−	1.28813e102i		−	0.0856313i	−0.999083	−	0.0428156i	$-0.986367\pi$
$887$		−	1.28813e102i		−	0.0856313i	0.999083	−	0.0428156i	$-0.0136328\pi$
$888$	6.30912e101	−	3.65889e102i	0.0403195	−	0.233828i
$889$	−6.51224e102			−0.400100
$890$			4.45811e103i			2.63330i
$891$	8.43415e102	−	1.03657e103i	0.478985	−	0.588680i
$892$	−2.40800e103			−1.31488
$893$		−	1.96990e103i		−	1.03429i
$894$	2.79766e103	+	4.82408e102i	1.41248	+	0.243558i
$895$	−1.49745e103			−0.727022
$896$		−	3.95144e102i		−	0.184491i
$897$	3.21690e102	−	1.86560e103i	0.144445	−	0.837688i
$898$	−1.02834e103			−0.444084
$899$		−	3.09441e103i		−	1.28525i
$900$	2.34531e103	+	8.33602e102i	0.936942	+	0.333020i
$901$	2.46149e103			0.945869
$902$			1.38958e103i			0.513636i
$903$	1.56820e103	+	2.70409e102i	0.557609	+	0.0961501i
$904$	−4.84329e102			−0.165670
$905$			2.75027e103i			0.905056i
$906$	8.83069e102	−	5.12124e103i	0.279581	−	1.62139i
$907$	−5.55658e102			−0.169259			−0.0846296	−	0.996412i	$-0.526971\pi$
$907$	−5.55658e102			−0.169259			−0.0846296	+	0.996412i	$0.526971\pi$
$908$		−	1.05299e103i		−	0.308616i
$909$	1.93481e103	−	5.44353e103i	0.545636	−	1.53513i
$910$	4.98359e103			1.35236
$911$			5.75671e103i			1.50325i	0.659591	+	0.751625i	$0.270730\pi$
$911$			5.75671e103i			1.50325i	−0.659591	+	0.751625i	$0.729270\pi$
$912$	−4.06754e103	−	7.01377e102i	−1.02215	−	0.176251i
$913$	1.51012e103			0.365202
$914$			4.81053e103i			1.11963i
$915$	−8.32383e102	+	4.82729e103i	−0.186460	+	1.08135i
$916$	7.54318e102			0.162635
$917$			2.03431e103i			0.422173i
$918$	7.54805e103	+	4.24450e103i	1.50779	+	0.847876i
$919$	−3.78298e103			−0.727430			−0.363715	−	0.931510i	$-0.618492\pi$
$919$	−3.78298e103			−0.727430			−0.363715	+	0.931510i	$0.618492\pi$
$920$		−	9.33935e102i		−	0.172879i
$921$	3.34473e102	+	5.76741e101i	0.0596038	+	0.0102777i
$922$	−1.10187e104			−1.89038
$923$		−	5.51274e103i		−	0.910560i
$924$	−3.20305e102	+	1.85757e103i	−0.0509384	+	0.295410i
$925$	8.98667e103			1.37606
$926$		−	3.02569e103i		−	0.446107i
$927$	6.97956e103	+	2.48077e103i	0.990917	+	0.352205i
$928$	8.45730e103			1.15625
$929$		−	7.96269e102i		−	0.104836i	−0.998625	−	0.0524179i	$-0.983307\pi$
$929$		−	7.96269e102i		−	0.104836i	0.998625	−	0.0524179i	$-0.0166928\pi$
$930$	−2.30395e104	−	3.97276e103i	−2.92126	−	0.503720i
$931$	5.92287e103			0.723258
$932$			5.23642e102i			0.0615854i
$933$	1.12659e103	−	6.53349e103i	0.127617	−	0.740095i
$934$	−9.81114e103			−1.07048
$935$		−	1.35111e104i		−	1.41999i
$936$	−9.69384e102	+	2.72733e103i	−0.0981388	+	0.276110i
$937$	−7.10847e103			−0.693251			−0.346626	−	0.938004i	$-0.612673\pi$
$937$	−7.10847e103			−0.693251			−0.346626	+	0.938004i	$0.612673\pi$
$938$		−	1.40348e103i		−	0.131858i
$939$	−6.37217e103	−	1.09877e103i	−0.576756	−	0.0994515i
$940$	1.61515e104			1.40844
$941$		−	1.76452e103i		−	0.148249i	−0.997249	−	0.0741243i	$-0.976384\pi$
$941$		−	1.76452e103i		−	0.148249i	0.997249	−	0.0741243i	$-0.0236161\pi$
$942$	−1.44624e102	+	8.38725e102i	−0.0117073	+	0.0678950i
$943$	−3.72137e103			−0.290264
$944$			1.65580e104i			1.24448i
$945$	−4.61773e103	+	8.21177e103i	−0.334438	+	0.594735i
$946$	−1.80656e104			−1.26085
$947$		−	2.36848e103i		−	0.159302i	−0.996823	−	0.0796509i	$-0.974619\pi$
$947$		−	2.36848e103i		−	0.159302i	0.996823	−	0.0796509i	$-0.0253805\pi$
$948$	−2.27431e104	−	3.92166e103i	−1.47421	−	0.254202i
$949$	4.50577e103			0.281483
$950$		−	2.42960e104i		−	1.46288i
$951$	−4.30952e103	+	2.49925e104i	−0.250098	+	1.45041i
$952$	2.11922e103			0.118545
$953$			3.21733e104i			1.73478i	0.497630	+	0.867389i	$0.334204\pi$
$953$			3.21733e104i			1.73478i	−0.497630	+	0.867389i	$0.665796\pi$
$954$	1.83596e104	+	6.52562e103i	0.954268	+	0.339179i
$955$	−1.24662e103			−0.0624620
$956$			1.98310e104i			0.957894i
$957$	1.39498e104	+	2.40540e103i	0.649607	+	0.112013i
$958$	2.65655e104			1.19268
$959$		−	1.87654e104i		−	0.812281i
$960$	4.10952e103	−	2.38326e104i	0.171513	−	0.994667i
$961$	2.95593e104			1.18953
$962$		−	6.02343e104i		−	2.33731i
$963$	−1.18175e104	+	3.32483e104i	−0.442188	+	1.24408i
$964$	−1.69900e104			−0.613052
$965$			4.08320e104i			1.42084i
$966$	−1.08124e104	−	1.86441e103i	−0.362846	−	0.0625665i
$967$	−2.30950e104			−0.747464			−0.373732	−	0.927537i	$-0.621922\pi$
$967$	−2.30950e104			−0.747464			−0.373732	+	0.927537i	$0.621922\pi$
$968$		−	2.73326e103i		−	0.0853185i
$969$	6.60840e103	−	3.83245e104i	0.198959	−	1.15384i
$970$	9.11697e104			2.64752
$971$		−	4.65922e104i		−	1.30509i	−0.757751	−	0.652544i	$-0.773702\pi$
$971$		−	4.65922e104i		−	1.30509i	0.757751	−	0.652544i	$-0.226298\pi$
$972$	2.07253e104	+	2.37723e104i	0.559991	+	0.642321i
$973$	−1.38781e104			−0.361727
$974$			3.05625e104i			0.768467i
$975$	−6.90391e104	−	1.19046e104i	−1.67469	−	0.288771i
$976$	3.58663e104			0.839350
$977$		−	2.36720e104i		−	0.534473i	−0.963631	−	0.267237i	$-0.913889\pi$
$977$		−	2.36720e104i		−	0.534473i	0.963631	−	0.267237i	$-0.0861105\pi$
$978$	1.45832e104	−	8.45735e104i	0.317683	−	1.84236i
$979$	4.74612e104			0.997573
$980$			4.85624e104i			0.984890i
$981$	4.95922e102	+	1.76267e102i	0.00970506	+	0.00344950i
$982$	2.26954e104			0.428584
$983$		−	1.07149e104i		−	0.195261i	−0.995223	−	0.0976306i	$-0.968874\pi$
$983$		−	1.07149e104i		−	0.195261i	0.995223	−	0.0976306i	$-0.0311264\pi$
$984$	5.60700e103	+	9.66830e102i	0.0986058	+	0.0170029i
$985$	−1.59795e105			−2.71203
$986$			9.17295e104i			1.50251i
$987$	−5.59408e103	+	3.24421e104i	−0.0884359	+	0.512872i
$988$	−7.49239e104			−1.14321
$989$		−	4.83805e104i		−	0.712525i
$990$	3.58190e104	−	1.00776e105i	0.509192	−	1.43260i
$991$	−3.14935e104			−0.432159			−0.216079	−	0.976376i	$-0.569327\pi$
$991$	−3.14935e104			−0.432159			−0.216079	+	0.976376i	$0.569327\pi$
$992$			1.48705e105i			1.96977i
$993$	6.19374e104	+	1.06800e104i	0.792007	+	0.136568i
$994$	−3.19501e104			−0.394410
$995$		−	2.00607e104i		−	0.239077i
$996$	−6.05599e103	+	3.51209e104i	−0.0696800	+	0.404100i
$997$	1.45337e104			0.161453			0.0807266	−	0.996736i	$-0.474276\pi$
$997$	1.45337e104			0.161453			0.0807266	+	0.996736i	$0.474276\pi$
$998$			1.93012e105i			2.07021i
$999$	9.92518e104	+	5.58123e104i	1.02789	+	0.578014i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.71.b.a.2.4	✓	22
3.2	odd	2	inner	3.71.b.a.2.19	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.71.b.a.2.4	✓	22	1.1	even	1	trivial
3.71.b.a.2.19	yes	22	3.2	odd	2	inner

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)

\(f(q)\)	\(=\)	\(q-4.67615e10i q^{2} +(-4.93039e16 - 8.50161e15i) q^{3} -1.00605e21 q^{4} +4.28418e24i q^{5} +(-3.97548e26 + 2.30553e27i) q^{6} -1.75590e29 q^{7} -8.16202e30i q^{8} +(2.35860e33 + 8.38326e32i) q^{9} +O(q^{10})\)	\(q-4.67615e10i q^{2} +(-4.93039e16 - 8.50161e15i) q^{3} -1.00605e21 q^{4} +4.28418e24i q^{5} +(-3.97548e26 + 2.30553e27i) q^{6} -1.75590e29 q^{7} -8.16202e30i q^{8} +(2.35860e33 + 8.38326e32i) q^{9} +2.00335e35 q^{10} -2.13277e36i q^{11} +(4.96020e37 + 8.55301e36i) q^{12} -1.41672e39 q^{13} +8.21087e39i q^{14} +(3.64225e40 - 2.11227e41i) q^{15} -1.56940e42 q^{16} -1.47869e43i q^{17} +(3.92014e43 - 1.10292e44i) q^{18} -5.25675e44 q^{19} -4.31009e45i q^{20} +(8.65729e45 + 1.49280e45i) q^{21} -9.97316e46 q^{22} -2.67086e47i q^{23} +(-6.93903e46 + 4.02420e47i) q^{24} -9.88390e48 q^{25} +6.62481e49i q^{26} +(-1.09161e50 - 6.13847e49i) q^{27} +1.76652e50 q^{28} -1.32661e51i q^{29} +(-9.87730e51 - 1.70317e51i) q^{30} +2.33257e52 q^{31} +6.37514e52i q^{32} +(-1.81320e52 + 1.05154e53i) q^{33} -6.91459e53 q^{34} -7.52261e53i q^{35} +(-2.37286e54 - 8.43394e53i) q^{36} -9.09223e54 q^{37} +2.45814e55i q^{38} +(6.98501e55 + 1.20444e55i) q^{39} +3.49676e55 q^{40} -1.39332e56i q^{41} +(6.98056e55 - 4.04828e56i) q^{42} +1.81142e57 q^{43} +2.14567e57i q^{44} +(-3.59154e57 + 1.01047e58i) q^{45} -1.24893e58 q^{46} +3.74738e58i q^{47} +(7.73775e58 + 1.33424e58i) q^{48} -1.12672e59 q^{49} +4.62186e59i q^{50} +(-1.25713e59 + 7.29054e59i) q^{51} +1.42529e60 q^{52} +1.66464e60i q^{53} +(-2.87044e60 + 5.10454e60i) q^{54} +9.13719e60 q^{55} +1.43317e60i q^{56} +(2.59178e61 + 4.46908e60i) q^{57} -6.20342e61 q^{58} -1.05505e62i q^{59} +(-3.66427e61 + 2.12504e62i) q^{60} -2.28536e62 q^{61} -1.09075e63i q^{62} +(-4.14147e62 - 1.47202e62i) q^{63} +1.12829e63 q^{64} -6.06951e63i q^{65} +(4.91716e63 + 8.47879e62i) q^{66} -1.70930e63 q^{67} +1.48763e64i q^{68} +(-2.27066e63 + 1.31684e64i) q^{69} -3.51769e64 q^{70} +3.89119e64i q^{71} +(6.84243e63 - 1.92509e64i) q^{72} -3.18042e64 q^{73} +4.25166e65i q^{74} +(4.87315e65 + 8.40290e64i) q^{75} +5.28853e65 q^{76} +3.74494e65i q^{77} +(5.63216e65 - 3.26629e66i) q^{78} -4.58513e66 q^{79} -6.72359e66i q^{80} +(4.86021e66 + 3.95455e66i) q^{81} -6.51538e66 q^{82} +7.08053e66i q^{83} +(-8.70963e66 - 1.50183e66i) q^{84} +6.33499e67 q^{85} -8.47047e67i q^{86} +(-1.12783e67 + 6.54070e67i) q^{87} -1.74077e67 q^{88} +2.22533e68i q^{89} +(4.72510e68 + 1.67946e68i) q^{90} +2.48763e68 q^{91} +2.68701e68i q^{92} +(-1.15005e69 - 1.98306e68i) q^{93} +1.75233e69 q^{94} -2.25209e69i q^{95} +(5.41989e68 - 3.14319e69i) q^{96} +4.55086e69 q^{97} +5.26869e69i q^{98} +(1.78796e69 - 5.03036e69i) 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

Varieties

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