LMFDB - Embedded newform 3.71.b.a.2.9

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			2.9
Character	$\chi$	$=$	3.2
Dual form			3.71.b.a.2.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.54812e10i q^{2} +(3.84365e16 - 3.20279e16i) q^{3} +9.40925e20 q^{4} +2.49363e24i q^{5} +(-4.95830e26 - 5.95043e26i) q^{6} -4.12745e29 q^{7} -3.28436e31i q^{8} +(4.51579e32 - 2.46209e33i) q^{9} +O(q^{10})$	\(q-1.54812e10i q^{2} +(3.84365e16 - 3.20279e16i) q^{3} +9.40925e20 q^{4} +2.49363e24i q^{5} +(-4.95830e26 - 5.95043e26i) q^{6} -4.12745e29 q^{7} -3.28436e31i q^{8} +(4.51579e32 - 2.46209e33i) q^{9} +3.86044e34 q^{10} -2.08775e36i q^{11} +(3.61659e37 - 3.01359e37i) q^{12} +9.30805e38 q^{13} +6.38978e39i q^{14} +(7.98659e40 + 9.58466e40i) q^{15} +6.02391e41 q^{16} -1.16995e42i q^{17} +(-3.81160e43 - 6.99097e42i) q^{18} -1.28125e44 q^{19} +2.34632e45i q^{20} +(-1.58645e46 + 1.32194e46i) q^{21} -3.23209e46 q^{22} -2.85673e47i q^{23} +(-1.05191e48 - 1.26239e48i) q^{24} +2.25213e48 q^{25} -1.44100e49i q^{26} +(-6.14984e49 - 1.09097e50i) q^{27} -3.88362e50 q^{28} +6.67334e50i q^{29} +(1.48382e51 - 1.23642e51i) q^{30} +1.17156e52 q^{31} -4.81006e52i q^{32} +(-6.68664e52 - 8.02460e52i) q^{33} -1.81123e52 q^{34} -1.02923e54i q^{35} +(4.24901e53 - 2.31664e54i) q^{36} -1.02228e55 q^{37} +1.98352e54i q^{38} +(3.57769e55 - 2.98118e55i) q^{39} +8.18998e55 q^{40} +4.80829e56i q^{41} +(2.04651e56 + 2.45601e56i) q^{42} -1.37465e57 q^{43} -1.96442e57i q^{44} +(6.13954e57 + 1.12607e57i) q^{45} -4.42256e57 q^{46} -4.51793e58i q^{47} +(2.31538e58 - 1.92933e58i) q^{48} +2.68549e58 q^{49} -3.48656e58i q^{50} +(-3.74712e58 - 4.49690e58i) q^{51} +8.75818e59 q^{52} -1.76470e60i q^{53} +(-1.68895e60 + 9.52067e59i) q^{54} +5.20609e60 q^{55} +1.35560e61i q^{56} +(-4.92467e60 + 4.10357e60i) q^{57} +1.03311e61 q^{58} -1.74714e62i q^{59} +(7.51478e61 + 9.01844e61i) q^{60} -3.49951e62 q^{61} -1.81372e62i q^{62} +(-1.86387e62 + 1.01621e63i) q^{63} -3.34753e61 q^{64} +2.32109e63i q^{65} +(-1.24230e63 + 1.03517e63i) q^{66} +8.78273e63 q^{67} -1.10084e63i q^{68} +(-9.14953e63 - 1.09803e64i) q^{69} -1.59338e64 q^{70} -7.60044e64i q^{71} +(-8.08637e64 - 1.48314e64i) q^{72} +2.57532e65 q^{73} +1.58261e65i q^{74} +(8.65640e64 - 7.21310e64i) q^{75} -1.20556e65 q^{76} +8.61709e65i q^{77} +(-4.61521e65 - 5.53869e65i) q^{78} -1.03334e66 q^{79} +1.50214e66i q^{80} +(-5.85794e66 - 2.22365e66i) q^{81} +7.44380e66 q^{82} -2.08734e67i q^{83} +(-1.49273e67 + 1.24384e67i) q^{84} +2.91744e66 q^{85} +2.12812e67i q^{86} +(2.13733e67 + 2.56500e67i) q^{87} -6.85692e67 q^{88} -1.88367e68i q^{89} +(1.74329e67 - 9.50472e67i) q^{90} -3.84185e68 q^{91} -2.68797e68i q^{92} +(4.50309e68 - 3.75228e68i) q^{93} -6.99429e68 q^{94} -3.19496e68i q^{95} +(-1.54056e69 - 1.84882e69i) q^{96} -6.36018e69 q^{97} -4.15745e68i q^{98} +(-5.14022e69 - 9.42784e68i) 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 $

$2$		−	1.54812e10i		−	0.450561i	−0.974294	−	0.225281i	$-0.927670\pi$
$2$		−	1.54812e10i		−	0.450561i	0.974294	−	0.225281i	$-0.0723299\pi$
$3$	3.84365e16	−	3.20279e16i	0.768246	−	0.640155i
$3$	3.84365e16	−	3.20279e16i	0.768246	−	0.640155i
$4$	9.40925e20			0.796994
$5$			2.49363e24i			0.856806i	0.903588	+	0.428403i	$0.140924\pi$
$5$			2.49363e24i			0.856806i	−0.903588	+	0.428403i	$0.859076\pi$
$6$	−4.95830e26	−	5.95043e26i	−0.288429	−	0.346142i
$7$	−4.12745e29			−1.08956			−0.544779	−	0.838580i	$-0.683387\pi$
$7$	−4.12745e29			−1.08956			−0.544779	+	0.838580i	$0.683387\pi$
$8$		−	3.28436e31i		−	0.809656i
$9$	4.51579e32	−	2.46209e33i	0.180404	−	0.983593i
$10$	3.86044e34			0.386044
$11$		−	2.08775e36i		−	0.742908i	−0.928451	−	0.371454i	$-0.878859\pi$
$11$		−	2.08775e36i		−	0.742908i	0.928451	−	0.371454i	$-0.121141\pi$
$12$	3.61659e37	−	3.01359e37i	0.612288	−	0.510200i
$13$	9.30805e38			0.956845			0.478422	−	0.878130i	$-0.341209\pi$
$13$	9.30805e38			0.956845			0.478422	+	0.878130i	$0.341209\pi$
$14$			6.38978e39i			0.490913i
$15$	7.98659e40	+	9.58466e40i	0.548488	+	0.658237i
$16$	6.02391e41			0.432194
$17$		−	1.16995e42i		−	0.100567i	−0.998735	−	0.0502836i	$-0.983987\pi$
$17$		−	1.16995e42i		−	0.100567i	0.998735	−	0.0502836i	$-0.0160125\pi$
$18$	−3.81160e43	−	6.99097e42i	−0.443169	−	0.0812830i
$19$	−1.28125e44			−0.224521			−0.112261	−	0.993679i	$-0.535809\pi$
$19$	−1.28125e44			−0.224521			−0.112261	+	0.993679i	$0.535809\pi$
$20$			2.34632e45i			0.682869i
$21$	−1.58645e46	+	1.32194e46i	−0.837049	+	0.697486i
$22$	−3.23209e46			−0.334726
$23$		−	2.85673e47i		−	0.624303i	−0.950032	−	0.312152i	$-0.898950\pi$
$23$		−	2.85673e47i		−	0.624303i	0.950032	−	0.312152i	$-0.101050\pi$
$24$	−1.05191e48	−	1.26239e48i	−0.518305	−	0.622015i
$25$	2.25213e48			0.265884
$26$		−	1.44100e49i		−	0.431117i
$27$	−6.14984e49	−	1.09097e50i	−0.491057	−	0.871127i
$28$	−3.88362e50			−0.868372
$29$			6.67334e50i			0.436931i	0.975845	+	0.218466i	$0.0701052\pi$
$29$			6.67334e50i			0.436931i	−0.975845	+	0.218466i	$0.929895\pi$
$30$	1.48382e51	−	1.23642e51i	0.296576	−	0.247128i
$31$	1.17156e52			0.743202			0.371601	−	0.928393i	$-0.378809\pi$
$31$	1.17156e52			0.743202			0.371601	+	0.928393i	$0.378809\pi$
$32$		−	4.81006e52i		−	1.00439i
$33$	−6.68664e52	−	8.02460e52i	−0.475576	−	0.570736i
$34$	−1.81123e52			−0.0453117
$35$		−	1.02923e54i		−	0.933540i
$36$	4.24901e53	−	2.31664e54i	0.143781	−	0.783918i
$37$	−1.02228e55			−1.32590			−0.662948	−	0.748665i	$-0.730695\pi$
$37$	−1.02228e55			−1.32590			−0.662948	+	0.748665i	$0.730695\pi$
$38$			1.98352e54i			0.101161i
$39$	3.57769e55	−	2.98118e55i	0.735092	−	0.612529i
$40$	8.18998e55			0.693718
$41$			4.80829e56i			1.71615i	0.513522	+	0.858076i	$0.328340\pi$
$41$			4.80829e56i			1.71615i	−0.513522	+	0.858076i	$0.671660\pi$
$42$	2.04651e56	+	2.45601e56i	0.314260	+	0.377142i
$43$	−1.37465e57			−0.926397			−0.463198	−	0.886255i	$-0.653298\pi$
$43$	−1.37465e57			−0.926397			−0.463198	+	0.886255i	$0.653298\pi$
$44$		−	1.96442e57i		−	0.592093i
$45$	6.13954e57	+	1.12607e57i	0.842748	+	0.154571i
$46$	−4.42256e57			−0.281287
$47$		−	4.51793e58i		−	1.35368i	−0.736132	−	0.676838i	$-0.763350\pi$
$47$		−	4.51793e58i		−	1.35368i	0.736132	−	0.676838i	$-0.236650\pi$
$48$	2.31538e58	−	1.92933e58i	0.332032	−	0.276671i
$49$	2.68549e58			0.187137
$50$		−	3.48656e58i		−	0.119797i
$51$	−3.74712e58	−	4.49690e58i	−0.0643786	−	0.0772604i
$52$	8.75818e59			0.762600
$53$		−	1.76470e60i		−	0.788887i	−0.918920	−	0.394443i	$-0.870937\pi$
$53$		−	1.76470e60i		−	0.788887i	0.918920	−	0.394443i	$-0.129063\pi$
$54$	−1.68895e60	+	9.52067e59i	−0.392496	+	0.221251i
$55$	5.20609e60			0.636528
$56$			1.35560e61i			0.882168i
$57$	−4.92467e60	+	4.10357e60i	−0.172487	+	0.143728i
$58$	1.03311e61			0.196864
$59$		−	1.74714e62i		−	1.83024i	−0.403185	−	0.915119i	$-0.632097\pi$
$59$		−	1.74714e62i		−	1.83024i	0.403185	−	0.915119i	$-0.367903\pi$
$60$	7.51478e61	+	9.01844e61i	0.437142	+	0.524611i
$61$	−3.49951e62			−1.14147			−0.570733	−	0.821136i	$-0.693341\pi$
$61$	−3.49951e62			−1.14147			−0.570733	+	0.821136i	$0.693341\pi$
$62$		−	1.81372e62i		−	0.334858i
$63$	−1.86387e62	+	1.01621e63i	−0.196560	+	1.07168i
$64$	−3.34753e61			−0.0203435
$65$			2.32109e63i			0.819830i
$66$	−1.24230e63	+	1.03517e63i	−0.257152	+	0.214276i
$67$	8.78273e63			1.07402			0.537009	−	0.843577i	$-0.319554\pi$
$67$	8.78273e63			1.07402			0.537009	+	0.843577i	$0.319554\pi$
$68$		−	1.10084e63i		−	0.0801515i
$69$	−9.14953e63	−	1.09803e64i	−0.399651	−	0.479618i
$70$	−1.59338e64			−0.420617
$71$		−	7.60044e64i		−	1.22123i	−0.791929	−	0.610614i	$-0.790923\pi$
$71$		−	7.60044e64i		−	1.22123i	0.791929	−	0.610614i	$-0.209077\pi$
$72$	−8.08637e64	−	1.48314e64i	−0.796372	−	0.146065i
$73$	2.57532e65			1.56506			0.782529	−	0.622614i	$-0.213929\pi$
$73$	2.57532e65			1.56506			0.782529	+	0.622614i	$0.213929\pi$
$74$			1.58261e65i			0.597398i
$75$	8.65640e64	−	7.21310e64i	0.204265	−	0.170207i
$76$	−1.20556e65			−0.178942
$77$			8.61709e65i			0.809442i
$78$	−4.61521e65	−	5.53869e65i	−0.275982	−	0.331204i
$79$	−1.03334e66			−0.395635			−0.197818	−	0.980239i	$-0.563385\pi$
$79$	−1.03334e66			−0.395635			−0.197818	+	0.980239i	$0.563385\pi$
$80$			1.50214e66i			0.370307i
$81$	−5.85794e66	−	2.22365e66i	−0.934909	−	0.354888i
$82$	7.44380e66			0.773232
$83$		−	2.08734e67i		−	1.41860i	−0.704907	−	0.709300i	$-0.749011\pi$
$83$		−	2.08734e67i		−	1.41860i	0.704907	−	0.709300i	$-0.250989\pi$
$84$	−1.49273e67	+	1.24384e67i	−0.667123	+	0.555892i
$85$	2.91744e66			0.0861666
$86$			2.12812e67i			0.417399i
$87$	2.13733e67	+	2.56500e67i	0.279704	+	0.335671i
$88$	−6.85692e67			−0.601500
$89$		−	1.88367e68i		−	1.11264i	−0.830969	−	0.556319i	$-0.812213\pi$
$89$		−	1.88367e68i		−	1.11264i	0.830969	−	0.556319i	$-0.187787\pi$
$90$	1.74329e67	−	9.50472e67i	0.0696437	−	0.379710i
$91$	−3.84185e68			−1.04254
$92$		−	2.68797e68i		−	0.497566i
$93$	4.50309e68	−	3.75228e68i	0.570962	−	0.475764i
$94$	−6.99429e68			−0.609914
$95$		−	3.19496e68i		−	0.192371i
$96$	−1.54056e69	−	1.84882e69i	−0.642963	−	0.771616i
$97$	−6.36018e69			−1.84697			−0.923483	−	0.383640i	$-0.874670\pi$
$97$	−6.36018e69			−1.84697			−0.923483	+	0.383640i	$0.874670\pi$
$98$		−	4.15745e68i		−	0.0843168i
$99$	−5.14022e69	−	9.42784e68i	−0.730719	−	0.134023i
$100$	2.11908e69			0.211908
$101$		−	1.13183e70i		−	0.798973i	−0.916739	−	0.399487i	$-0.869188\pi$
$101$		−	1.13183e70i		−	0.798973i	0.916739	−	0.399487i	$-0.130812\pi$
$102$	−6.96173e68	+	5.80098e68i	−0.0348106	+	0.0290065i
$103$	−4.58796e70			−1.63048			−0.815242	−	0.579121i	$-0.803396\pi$
$103$	−4.58796e70			−1.63048			−0.815242	+	0.579121i	$0.803396\pi$
$104$		−	3.05710e70i		−	0.774715i
$105$	−3.29642e70	−	3.95602e70i	−0.597610	−	0.717188i
$106$	−2.73196e70			−0.355442
$107$		−	1.83984e71i		−	1.72325i	−0.507546	−	0.861625i	$-0.669447\pi$
$107$		−	1.83984e71i		−	1.72325i	0.507546	−	0.861625i	$-0.330553\pi$
$108$	−5.78654e70	−	1.02652e71i	−0.391370	−	0.694284i
$109$	−2.36635e70			−0.115918			−0.0579591	−	0.998319i	$-0.518459\pi$
$109$	−2.36635e70			−0.115918			−0.0579591	+	0.998319i	$0.518459\pi$
$110$		−	8.05963e70i		−	0.286795i
$111$	−3.92929e71	+	3.27415e71i	−1.01861	+	0.848779i
$112$	−2.48634e71			−0.470901
$113$			3.01386e71i			0.418194i	0.977895	+	0.209097i	$0.0670525\pi$
$113$			3.01386e71i			0.418194i	−0.977895	+	0.209097i	$0.932948\pi$
$114$	6.35281e70	+	7.62397e70i	0.0647584	+	0.0777162i
$115$	7.12364e71			0.534906
$116$			6.27911e71i			0.348232i
$117$	4.20332e71	−	2.29172e72i	0.172618	−	0.941145i
$118$	−2.70478e72			−0.824634
$119$			4.82893e71i			0.109574i
$120$	3.14794e72	−	2.62308e72i	0.532946	−	0.444087i
$121$	3.53876e72			0.448088
$122$			5.41765e72i			0.514300i
$123$	1.54000e73	+	1.84814e73i	1.09860	+	1.31843i
$124$	1.10235e73			0.592328
$125$			2.67379e73i			1.08462i
$126$	1.57322e73	+	2.88549e72i	0.482858	+	0.0885625i
$127$	5.01279e73			1.16667			0.583337	−	0.812230i	$-0.301747\pi$
$127$	5.01279e73			1.16667			0.583337	+	0.812230i	$0.301747\pi$
$128$		−	5.62689e73i		−	0.995221i
$129$	−5.28369e73	+	4.40273e73i	−0.711700	+	0.593037i
$130$	3.59331e73			0.369384
$131$			2.11349e74i			1.66152i	0.556634	+	0.830758i	$0.312093\pi$
$131$			2.11349e74i			1.66152i	−0.556634	+	0.830758i	$0.687907\pi$
$132$	−6.29163e73	−	7.55054e73i	−0.379031	−	0.454873i
$133$	5.28829e73			0.244629
$134$		−	1.35967e74i		−	0.483911i
$135$	2.72048e74	−	1.53354e74i	0.746387	−	0.420740i
$136$	−3.84255e73			−0.0814249
$137$			6.97429e74i			1.14362i	0.820388	+	0.571808i	$0.193758\pi$
$137$			6.97429e74i			1.14362i	−0.820388	+	0.571808i	$0.806242\pi$
$138$	−1.69988e74	+	1.41645e74i	−0.216098	+	0.180067i
$139$	−4.01160e74			−0.396095			−0.198047	−	0.980192i	$-0.563460\pi$
$139$	−4.01160e74			−0.396095			−0.198047	+	0.980192i	$0.563460\pi$
$140$		−	9.68432e74i		−	0.744026i
$141$	−1.44700e75	−	1.73654e75i	−0.866562	−	1.03996i
$142$	−1.17664e75			−0.550238
$143$		−	1.94329e75i		−	0.710847i
$144$	2.72027e74	−	1.48314e75i	0.0779695	−	0.425103i
$145$	−1.66408e75			−0.374365
$146$		−	3.98689e75i		−	0.705155i
$147$	1.03221e75	−	8.60106e74i	0.143767	−	0.119797i
$148$	−9.61889e75			−1.05673
$149$			9.05025e75i			0.785491i	0.919647	+	0.392746i	$0.128475\pi$
$149$			9.05025e75i			0.785491i	−0.919647	+	0.392746i	$0.871525\pi$
$150$	−1.11667e75	−	1.34011e75i	−0.0766888	−	0.0920337i
$151$	−1.13347e76			−0.616906			−0.308453	−	0.951240i	$-0.599811\pi$
$151$	−1.13347e76			−0.616906			−0.308453	+	0.951240i	$0.599811\pi$
$152$			4.20807e75i			0.181785i
$153$	−2.88053e75	−	5.28326e74i	−0.0989172	−	0.0181427i
$154$	1.33403e76			0.364703
$155$			2.92145e76i			0.636779i
$156$	3.36634e76	−	2.80506e76i	0.585864	−	0.488182i
$157$	8.20448e76			1.14173			0.570865	−	0.821044i	$-0.306608\pi$
$157$	8.20448e76			1.14173			0.570865	+	0.821044i	$0.306608\pi$
$158$			1.59973e76i			0.178258i
$159$	−5.65196e76	−	6.78288e76i	−0.505010	−	0.606059i
$160$	1.19945e77			0.860564
$161$			1.17910e77i			0.680215i
$162$	−3.44247e76	+	9.06878e76i	−0.159899	+	0.421234i
$163$	2.74214e77			1.02689			0.513445	−	0.858122i	$-0.328369\pi$
$163$	2.74214e77			1.02689			0.513445	+	0.858122i	$0.328369\pi$
$164$			4.52424e77i			1.36776i
$165$	2.00104e77	−	1.66740e77i	0.489010	−	0.407476i
$166$	−3.23145e77			−0.639166
$167$			1.20047e76i			0.0192431i	0.999954	+	0.00962154i	$0.00306268\pi$
$167$			1.20047e76i			0.0192431i	−0.999954	+	0.00962154i	$0.996937\pi$
$168$	4.34171e77	+	5.21046e77i	0.564724	+	0.677722i
$169$	−7.99147e76			−0.0844485
$170$		−	4.51653e76i		−	0.0388233i
$171$	−5.78584e76	+	3.15454e77i	−0.0405044	+	0.220837i
$172$	−1.29344e78			−0.738333
$173$		−	2.70878e78i		−	1.26229i	−0.775664	−	0.631146i	$-0.782585\pi$
$173$		−	2.70878e78i		−	1.26229i	0.775664	−	0.631146i	$-0.217415\pi$
$174$	3.97092e77	−	3.30884e77i	0.151240	−	0.126024i
$175$	−9.29555e77			−0.289696
$176$		−	1.25764e78i		−	0.321081i
$177$	−5.59573e78	−	6.71540e78i	−1.17164	−	1.40607i
$178$	−2.91614e78			−0.501311
$179$			9.74597e77i			0.137711i	0.997627	+	0.0688555i	$0.0219348\pi$
$179$			9.74597e77i			0.137711i	−0.997627	+	0.0688555i	$0.978065\pi$
$180$	5.77684e78	+	1.05955e78i	0.671665	+	0.123192i
$181$	4.60514e78			0.441055			0.220527	−	0.975381i	$-0.429222\pi$
$181$	4.60514e78			0.441055			0.220527	+	0.975381i	$0.429222\pi$
$182$			5.94764e78i			0.469727i
$183$	−1.34509e79	+	1.12082e79i	−0.876926	+	0.730715i
$184$	−9.38253e78			−0.505471
$185$		−	2.54919e79i		−	1.13604i
$186$	−5.80897e78	−	6.97131e78i	−0.214361	−	0.257253i
$187$	−2.44257e78			−0.0747122
$188$		−	4.25103e79i		−	1.07887i
$189$	2.53832e79	+	4.50293e79i	0.535035	+	0.949144i
$190$	−4.94617e78			−0.0866749
$191$			5.86966e79i			0.855943i	0.903792	+	0.427972i	$0.140772\pi$
$191$			5.86966e79i			0.855943i	−0.903792	+	0.427972i	$0.859228\pi$
$192$	−1.28667e78	+	1.07214e78i	−0.0156288	+	0.0130230i
$193$	1.37980e80			1.39736			0.698682	−	0.715433i	$-0.253770\pi$
$193$	1.37980e80			1.39736			0.698682	+	0.715433i	$0.253770\pi$
$194$			9.84630e79i			0.832171i
$195$	7.43396e79	+	8.92145e79i	0.524818	+	0.629831i
$196$	2.52684e79			0.149147
$197$			2.00196e79i			0.0988865i	0.998777	+	0.0494433i	$0.0157447\pi$
$197$			2.00196e79i			0.0988865i	−0.998777	+	0.0494433i	$0.984255\pi$
$198$	−1.45954e79	+	7.95767e79i	−0.0603858	+	0.329234i
$199$	1.65570e80			0.574279			0.287140	−	0.957889i	$-0.407296\pi$
$199$	1.65570e80			0.574279			0.287140	+	0.957889i	$0.407296\pi$
$200$		−	7.39679e79i		−	0.215275i
$201$	3.37578e80	−	2.81293e80i	0.825110	−	0.687538i
$202$	−1.75220e80			−0.359987
$203$		−	2.75439e80i		−	0.476062i
$204$	−3.52576e79	−	4.23124e79i	−0.0513094	−	0.0615761i
$205$	−1.19901e81			−1.47041
$206$			7.10269e80i			0.734633i
$207$	−7.03352e80	−	1.29004e80i	−0.614060	−	0.112627i
$208$	5.60709e80			0.413543
$209$			2.67493e80i			0.166798i
$210$	−6.12438e80	+	5.10325e80i	−0.323137	+	0.269260i
$211$	1.96454e81			0.877758			0.438879	−	0.898546i	$-0.355376\pi$
$211$	1.96454e81			0.877758			0.438879	+	0.898546i	$0.355376\pi$
$212$		−	1.66045e81i		−	0.628738i
$213$	−2.43426e81	−	2.92135e81i	−0.781775	−	0.938203i
$214$	−2.84829e81			−0.776430
$215$		−	3.42788e81i		−	0.793742i
$216$	−3.58314e81	+	2.01983e81i	−0.705314	+	0.397588i
$217$	−4.83557e81			−0.809762
$218$			3.66339e80i			0.0522282i
$219$	9.89863e81	−	8.24821e81i	1.20235	−	1.00188i
$220$	4.89854e81			0.507309
$221$		−	1.08900e81i		−	0.0962272i
$222$	5.06877e81	+	6.08300e81i	0.382427	+	0.458948i
$223$	−1.15896e81			−0.0747133			−0.0373566	−	0.999302i	$-0.511894\pi$
$223$	−1.15896e81			−0.0747133			−0.0373566	+	0.999302i	$0.511894\pi$
$224$			1.98533e82i			1.09434i
$225$	1.01701e81	−	5.54493e81i	0.0479665	−	0.261522i
$226$	4.66581e81			0.188422
$227$			4.38854e82i			1.51850i	0.650799	+	0.759250i	$0.274434\pi$
$227$			4.38854e82i			1.51850i	−0.650799	+	0.759250i	$0.725566\pi$
$228$	−4.63375e81	+	3.86115e81i	−0.137472	+	0.114551i
$229$	1.29871e82			0.330574			0.165287	−	0.986245i	$-0.447145\pi$
$229$	1.29871e82			0.330574			0.165287	+	0.986245i	$0.447145\pi$
$230$		−	1.10282e82i		−	0.241008i
$231$	2.75988e82	+	3.31211e82i	0.518168	+	0.621850i
$232$	2.19176e82			0.353764
$233$			7.40972e81i			0.102883i	0.998676	+	0.0514416i	$0.0163816\pi$
$233$			7.40972e81i			0.102883i	−0.998676	+	0.0514416i	$0.983618\pi$
$234$	−3.54785e82	−	6.50723e81i	−0.424044	−	0.0777752i
$235$	1.12661e83			1.15984
$236$		−	1.64393e83i		−	1.45869i
$237$	−3.97180e82	+	3.30957e82i	−0.303945	+	0.253268i
$238$	7.47575e81			0.0493698
$239$		−	1.71471e82i		−	0.0977832i	−0.998804	−	0.0488916i	$-0.984431\pi$
$239$		−	1.71471e82i		−	0.0977832i	0.998804	−	0.0488916i	$-0.0155689\pi$
$240$	4.81105e82	+	5.77371e82i	0.237054	+	0.284487i
$241$	−1.33494e83			−0.568678			−0.284339	−	0.958724i	$-0.591774\pi$
$241$	−1.33494e83			−0.568678			−0.284339	+	0.958724i	$0.591774\pi$
$242$		−	5.47842e82i		−	0.201891i
$243$	−2.96378e83	+	1.02148e83i	−0.945423	+	0.325846i
$244$	−3.29278e83			−0.909742
$245$			6.69662e82i			0.160340i
$246$	2.86114e83	−	2.38410e83i	0.594033	−	0.494988i
$247$	−1.19259e83			−0.214832
$248$		−	3.84783e83i		−	0.601738i
$249$	−6.68532e83	−	8.02301e83i	−0.908123	−	1.08983i
$250$	4.13934e83			0.488686
$251$			3.33310e83i			0.342190i	0.985255	+	0.171095i	$0.0547305\pi$
$251$			3.33310e83i			0.342190i	−0.985255	+	0.171095i	$0.945269\pi$
$252$	−1.75376e83	+	9.56181e83i	−0.156657	+	0.854124i
$253$	−5.96415e83			−0.463800
$254$		−	7.76039e83i		−	0.525659i
$255$	1.12136e83	−	9.34394e82i	0.0661971	−	0.0551600i
$256$	−9.10629e83			−0.468751
$257$		−	1.24937e84i		−	0.561088i	−0.959841	−	0.280544i	$-0.909485\pi$
$257$		−	1.24937e84i		−	0.561088i	0.959841	−	0.280544i	$-0.0905148\pi$
$258$	6.81594e83	+	8.17977e83i	0.267200	+	0.320665i
$259$	4.21941e84			1.44464
$260$			2.18397e84i			0.653400i
$261$	1.64303e84	+	3.01354e83i	0.429762	+	0.0788240i
$262$	3.27193e84			0.748615
$263$			7.32562e84i			1.46688i	0.679757	+	0.733438i	$0.262085\pi$
$263$			7.32562e84i			1.46688i	−0.679757	+	0.733438i	$0.737915\pi$
$264$	−2.63556e84	+	2.19613e84i	−0.462100	+	0.385053i
$265$	4.40051e84			0.675923
$266$		−	8.18689e83i		−	0.110220i
$267$	−6.03299e84	−	7.24016e84i	−0.712260	−	0.854779i
$268$	8.26389e84			0.855986
$269$			3.85603e84i			0.350599i	0.984515	+	0.175300i	$0.0560894\pi$
$269$			3.85603e84i			0.350599i	−0.984515	+	0.175300i	$0.943911\pi$
$270$	−2.37411e84	−	4.21163e84i	−0.189569	−	0.336293i
$271$	−4.36074e84			−0.305939			−0.152970	−	0.988231i	$-0.548884\pi$
$271$	−4.36074e84			−0.305939			−0.152970	+	0.988231i	$0.548884\pi$
$272$		−	7.04770e83i		−	0.0434646i
$273$	−1.47667e85	+	1.23047e85i	−0.800926	+	0.667386i
$274$	1.07970e85			0.515269
$275$		−	4.70189e84i		−	0.197528i
$276$	−8.60902e84	−	1.03316e85i	−0.318519	−	0.382253i
$277$	6.78783e84			0.221278			0.110639	−	0.993861i	$-0.464710\pi$
$277$	6.78783e84			0.221278			0.110639	+	0.993861i	$0.464710\pi$
$278$			6.21042e84i			0.178465i
$279$	5.29053e84	−	2.88449e85i	0.134076	−	0.731008i
$280$	−3.38037e85			−0.755846
$281$			5.12653e84i			0.101182i	0.998719	+	0.0505909i	$0.0161105\pi$
$281$			5.12653e84i			0.101182i	−0.998719	+	0.0505909i	$0.983890\pi$
$282$	−2.68836e85	+	2.24013e85i	−0.468564	+	0.390439i
$283$	4.99892e84			0.0769752			0.0384876	−	0.999259i	$-0.487746\pi$
$283$	4.99892e84			0.0769752			0.0384876	+	0.999259i	$0.487746\pi$
$284$		−	7.15144e85i		−	0.973311i
$285$	−1.02328e85	−	1.22803e85i	−0.123147	−	0.147788i
$286$	−3.00844e85			−0.320280
$287$		−	1.98460e86i		−	1.86985i
$288$	−1.18428e86	−	2.17212e85i	−0.987907	−	0.181195i
$289$	1.33971e86			0.989886
$290$			2.57620e85i			0.168674i
$291$	−2.44463e86	+	2.03703e86i	−1.41892	+	1.18234i
$292$	2.42318e86			1.24734
$293$			3.33931e86i			1.52507i	0.646947	+	0.762535i	$0.276046\pi$
$293$			3.33931e86i			1.52507i	−0.646947	+	0.762535i	$0.723954\pi$
$294$	−1.33154e85	−	1.59798e85i	−0.0539758	−	0.0647761i
$295$	4.35673e86			1.56816
$296$			3.35753e86i			1.07352i
$297$	−2.27768e86	+	1.28393e86i	−0.647167	+	0.364810i
$298$	1.40109e86			0.353912
$299$		−	2.65906e86i		−	0.597361i
$300$	8.14502e85	−	6.78698e85i	0.162798	−	0.135654i
$301$	5.67381e86			1.00936
$302$			1.75475e86i			0.277954i
$303$	−3.62501e86	−	4.35035e86i	−0.511467	−	0.613808i
$304$	−7.71812e85			−0.0970368
$305$		−	8.72649e86i		−	0.978014i
$306$	−8.17911e84	+	4.45939e85i	−0.00817440	+	0.0445683i
$307$	1.67312e87			1.49171			0.745855	−	0.666108i	$-0.232041\pi$
$307$	1.67312e87			1.49171			0.745855	+	0.666108i	$0.232041\pi$
$308$			8.10804e86i			0.645120i
$309$	−1.76345e87	+	1.46943e87i	−1.25261	+	1.04376i
$310$	4.52275e86			0.286908
$311$			9.31437e85i			0.0527886i	0.999652	+	0.0263943i	$0.00840254\pi$
$311$			9.31437e85i			0.0527886i	−0.999652	+	0.0263943i	$0.991597\pi$
$312$	−9.79125e86	−	1.17504e87i	−0.495938	−	0.595172i
$313$	3.05324e85			0.0138264			0.00691320	−	0.999976i	$-0.497799\pi$
$313$	3.05324e85			0.0138264			0.00691320	+	0.999976i	$0.497799\pi$
$314$		−	1.27015e87i		−	0.514419i
$315$	−2.53406e87	−	4.64780e86i	−0.918223	−	0.168414i
$316$	−9.72295e86			−0.315319
$317$			2.80316e86i			0.0813905i	0.999172	+	0.0406952i	$0.0129573\pi$
$317$			2.80316e86i			0.0813905i	−0.999172	+	0.0406952i	$0.987043\pi$
$318$	−1.05007e87	+	8.74990e86i	−0.273067	+	0.227538i
$319$	1.39323e87			0.324600
$320$		−	8.34750e85i		−	0.0174304i
$321$	−5.89263e87	−	7.07171e87i	−1.10315	−	1.32388i
$322$	1.82539e87			0.306478
$323$			1.49900e86i			0.0225795i
$324$	−5.51188e87	−	2.09229e87i	−0.745117	−	0.282843i
$325$	2.09629e87			0.254410
$326$		−	4.24516e87i		−	0.462677i
$327$	−9.09542e86	+	7.57893e86i	−0.0890536	+	0.0742055i
$328$	1.57921e88			1.38949
$329$			1.86475e88i			1.47491i
$330$	−2.58133e87	−	3.09784e87i	−0.183593	−	0.220329i
$331$	2.18933e88			1.40065			0.700327	−	0.713822i	$-0.253038\pi$
$331$	2.18933e88			1.40065			0.700327	+	0.713822i	$0.253038\pi$
$332$		−	1.96403e88i		−	1.13062i
$333$	−4.61640e87	+	2.51694e88i	−0.239197	+	1.30414i
$334$	1.85847e86			0.00867019
$335$			2.19009e88i			0.920224i
$336$	−9.55663e87	+	7.96323e87i	−0.361768	+	0.301450i
$337$	−1.32293e86			−0.00451326			−0.00225663	−	0.999997i	$-0.500718\pi$
$337$	−1.32293e86			−0.00451326			−0.00225663	+	0.999997i	$0.500718\pi$
$338$			1.23717e87i			0.0380492i
$339$	9.65278e87	+	1.15842e88i	0.267709	+	0.321276i
$340$	2.74509e87			0.0686743
$341$		−	2.44594e88i		−	0.552131i
$342$	4.88360e87	+	8.95716e86i	0.0995008	+	0.0182497i
$343$	4.81462e88			0.885661
$344$			4.51485e88i			0.750063i
$345$	2.73808e88	−	2.28156e88i	0.410940	−	0.342423i
$346$	−4.19350e88			−0.568740
$347$		−	9.79363e88i		−	1.20064i	−0.799761	−	0.600319i	$-0.795040\pi$
$347$		−	9.79363e88i		−	1.20064i	0.799761	−	0.600319i	$-0.204960\pi$
$348$	2.01107e88	+	2.41347e88i	0.222922	+	0.267528i
$349$	−1.05684e89			−1.05955			−0.529774	−	0.848139i	$-0.677723\pi$
$349$	−1.05684e89			−1.05955			−0.529774	+	0.848139i	$0.677723\pi$
$350$			1.43906e88i			0.130526i
$351$	−5.72430e88	−	1.01548e89i	−0.469865	−	0.833533i
$352$	−1.00422e89			−0.746167
$353$			7.36022e88i			0.495195i	0.968863	+	0.247597i	$0.0796410\pi$
$353$			7.36022e88i			0.495195i	−0.968863	+	0.247597i	$0.920359\pi$
$354$	−1.03962e89	+	8.66285e88i	−0.633522	+	0.527894i
$355$	1.89527e89			1.04635
$356$		−	1.77239e89i		−	0.886766i
$357$	1.54661e88	+	1.85607e88i	0.0701443	+	0.0841797i
$358$	1.50879e88			0.0620473
$359$		−	1.77655e89i		−	0.662632i	−0.943520	−	0.331316i	$-0.892507\pi$
$359$		−	1.77655e89i		−	0.662632i	0.943520	−	0.331316i	$-0.107493\pi$
$360$	3.69842e88	−	2.01644e89i	0.125149	−	0.682336i
$361$	−3.09235e89			−0.949590
$362$		−	7.12930e88i		−	0.198722i
$363$	1.36018e89	−	1.13339e89i	0.344242	−	0.286846i
$364$	−3.61489e89			−0.830897
$365$			6.42189e89i			1.34095i
$366$	1.73516e89	+	2.08236e89i	0.329232	+	0.395109i
$367$	−5.55416e89			−0.957868			−0.478934	−	0.877851i	$-0.658977\pi$
$367$	−5.55416e89			−0.957868			−0.478934	+	0.877851i	$0.658977\pi$
$368$		−	1.72087e89i		−	0.269820i
$369$	1.18384e90	+	2.17132e89i	1.68800	+	0.309600i
$370$	−3.94645e89			−0.511854
$371$			7.28370e89i			0.859538i
$372$	4.23707e89	−	3.53061e89i	0.455053	−	0.379181i
$373$	1.70227e90			1.66425			0.832126	−	0.554587i	$-0.187124\pi$
$373$	1.70227e90			1.66425			0.832126	+	0.554587i	$0.187124\pi$
$374$			3.78139e88i			0.0336624i
$375$	8.56359e89	+	1.02771e90i	0.694323	+	0.833252i
$376$	−1.48385e90			−1.09601
$377$			6.21158e89i			0.418075i
$378$	6.97107e89	−	3.92961e89i	0.427648	−	0.241066i
$379$	−5.03165e89			−0.281409			−0.140705	−	0.990052i	$-0.544937\pi$
$379$	−5.03165e89			−0.281409			−0.140705	+	0.990052i	$0.544937\pi$
$380$		−	3.00622e89i		−	0.153319i
$381$	1.92674e90	−	1.60549e90i	0.896293	−	0.746852i
$382$	9.08692e89			0.385655
$383$			1.55646e90i			0.602810i	0.953496	+	0.301405i	$0.0974556\pi$
$383$			1.55646e90i			0.602810i	−0.953496	+	0.301405i	$0.902544\pi$
$384$	−1.80218e90	−	2.16278e90i	−0.637095	−	0.764574i
$385$	−2.14879e90			−0.693534
$386$		−	2.13609e90i		−	0.629598i
$387$	−6.20764e89	+	3.38451e90i	−0.167125	+	0.911197i
$388$	−5.98445e90			−1.47202
$389$		−	2.84920e90i		−	0.640452i	−0.947341	−	0.320226i	$-0.896241\pi$
$389$		−	2.84920e90i		−	0.640452i	0.947341	−	0.320226i	$-0.103759\pi$
$390$	1.38114e90	−	1.15086e90i	0.283778	−	0.236463i
$391$	−3.34225e89			−0.0627844
$392$		−	8.82010e89i		−	0.151517i
$393$	6.76907e90	+	8.12352e90i	1.06363	+	1.27645i
$394$	3.09927e89			0.0445545
$395$		−	2.57677e90i		−	0.338982i
$396$	−4.83657e90	−	8.87089e89i	−0.582379	−	0.106816i
$397$	−1.55866e91			−1.71823			−0.859117	−	0.511779i	$-0.828987\pi$
$397$	−1.55866e91			−1.71823			−0.859117	+	0.511779i	$0.828987\pi$
$398$		−	2.56321e90i		−	0.258748i
$399$	2.03263e90	−	1.69373e90i	0.187935	−	0.156600i
$400$	1.35666e90			0.114914
$401$		−	8.89096e90i		−	0.690074i	−0.938589	−	0.345037i	$-0.887866\pi$
$401$		−	8.89096e90i		−	0.690074i	0.938589	−	0.345037i	$-0.112134\pi$
$402$	−4.35474e90	−	5.22610e90i	−0.309778	−	0.371763i
$403$	1.09050e91			0.711129
$404$		−	1.06496e91i		−	0.636777i
$405$	5.54496e90	−	1.46076e91i	0.304070	−	0.801035i
$406$	−4.26411e90			−0.214495
$407$			2.13427e91i			0.985019i
$408$	−1.47694e90	+	1.23069e90i	−0.0625544	+	0.0521246i
$409$	4.04782e91			1.57364			0.786821	−	0.617182i	$-0.211726\pi$
$409$	4.04782e91			1.57364			0.786821	+	0.617182i	$0.211726\pi$
$410$			1.85621e91i			0.662510i
$411$	2.23372e91	+	2.68067e91i	0.732091	+	0.878578i
$412$	−4.31692e91			−1.29949
$413$			7.21124e91i			1.99415i
$414$	−1.99713e90	+	1.08887e91i	−0.0507452	+	0.276672i
$415$	5.20506e91			1.21546
$416$		−	4.47722e91i		−	0.961042i
$417$	−1.54192e91	+	1.28483e91i	−0.304298	+	0.253562i
$418$	4.14110e90			0.0751530
$419$			1.48631e91i			0.248096i	0.992276	+	0.124048i	$0.0395876\pi$
$419$			1.48631e91i			0.248096i	−0.992276	+	0.124048i	$0.960412\pi$
$420$	−3.10169e91	−	3.72232e91i	−0.476292	−	0.571595i
$421$	1.16066e92			1.63996			0.819980	−	0.572392i	$-0.193985\pi$
$421$	1.16066e92			1.63996			0.819980	+	0.572392i	$0.193985\pi$
$422$		−	3.04134e91i		−	0.395484i
$423$	−1.11235e92	−	2.04020e91i	−1.33147	−	0.244208i
$424$	−5.79589e91			−0.638727
$425$		−	2.63489e90i		−	0.0267393i
$426$	−4.52259e91	+	3.76853e91i	−0.422718	+	0.352237i
$427$	1.44441e92			1.24369
$428$		−	1.73115e92i		−	1.37342i
$429$	−6.22396e91	−	7.46933e91i	−0.455052	−	0.546106i
$430$	−5.30676e91			−0.357629
$431$			1.44620e92i			0.898510i	0.893404	+	0.449255i	$0.148311\pi$
$431$			1.44620e92i			0.898510i	−0.893404	+	0.449255i	$0.851689\pi$
$432$	−3.70461e91	−	6.57192e91i	−0.212232	−	0.376496i
$433$	4.86986e91			0.257300			0.128650	−	0.991690i	$-0.458936\pi$
$433$	4.86986e91			0.257300			0.128650	+	0.991690i	$0.458936\pi$
$434$			7.48603e91i			0.364847i
$435$	−6.39616e91	+	5.32972e91i	−0.287604	+	0.239652i
$436$	−2.22656e91			−0.0923861
$437$			3.66018e91i			0.140169i
$438$	−1.27692e92	−	1.53242e92i	−0.451408	−	0.541733i
$439$	−2.36710e92			−0.772605			−0.386303	−	0.922372i	$-0.626248\pi$
$439$	−2.36710e92			−0.772605			−0.386303	+	0.922372i	$0.626248\pi$
$440$		−	1.70986e92i		−	0.515369i
$441$	1.21271e91	−	6.61190e91i	0.0337603	−	0.184067i
$442$	−1.68590e91			−0.0433563
$443$		−	4.49640e92i		−	1.06840i	−0.845358	−	0.534201i	$-0.820613\pi$
$443$		−	4.49640e92i		−	1.06840i	0.845358	−	0.534201i	$-0.179387\pi$
$444$	−3.69717e92	+	3.08073e92i	−0.811830	+	0.676472i
$445$	4.69717e92			0.953314
$446$			1.79420e91i			0.0336629i
$447$	2.89861e92	+	3.47860e92i	0.502836	+	0.603450i
$448$	1.38167e91			0.0221654
$449$			7.29055e92i			1.08178i	0.841094	+	0.540889i	$0.181912\pi$
$449$			7.29055e92i			1.08178i	−0.841094	+	0.540889i	$0.818088\pi$
$450$	−8.58420e91	−	1.57445e91i	−0.117832	−	0.0216119i
$451$	1.00385e93			1.27494
$452$			2.83582e92i			0.333298i
$453$	−4.35668e92	+	3.63029e92i	−0.473935	+	0.394915i
$454$	6.79397e92			0.684178
$455$		−	9.58017e92i		−	0.893252i
$456$	1.34776e92	+	1.61744e92i	0.116370	+	0.139656i
$457$	7.87907e92			0.630097			0.315049	−	0.949076i	$-0.397979\pi$
$457$	7.87907e92			0.630097			0.315049	+	0.949076i	$0.397979\pi$
$458$		−	2.01055e92i		−	0.148944i
$459$	−1.27639e92	+	7.19503e91i	−0.0876069	+	0.0493843i
$460$	6.70281e92			0.426317
$461$			2.26033e93i			1.33242i	0.745766	+	0.666208i	$0.232084\pi$
$461$			2.26033e93i			1.33242i	−0.745766	+	0.666208i	$0.767916\pi$
$462$	5.12754e92	−	4.27261e92i	0.280182	−	0.233466i
$463$	−2.49294e93			−1.26292			−0.631462	−	0.775407i	$-0.717545\pi$
$463$	−2.49294e93			−1.26292			−0.631462	+	0.775407i	$0.717545\pi$
$464$			4.01996e92i			0.188839i
$465$	9.35680e92	+	1.12290e93i	0.407637	+	0.489203i
$466$	1.14711e92			0.0463552
$467$		−	2.67357e93i		−	1.00231i	−0.865358	−	0.501154i	$-0.832909\pi$
$467$		−	2.67357e93i		−	1.00231i	0.865358	−	0.501154i	$-0.167091\pi$
$468$	3.95500e92	−	2.15634e93i	0.137576	−	0.750087i
$469$	−3.62503e93			−1.17021
$470$		−	1.74412e93i		−	0.522578i
$471$	3.15352e93	−	2.62773e93i	0.877129	−	0.730884i
$472$	−5.73823e93			−1.48186
$473$			2.86993e93i			0.688227i
$474$	5.12361e92	+	6.14881e92i	0.114113	+	0.136946i
$475$	−2.88553e92			−0.0596966
$476$			4.54366e92i			0.0873298i
$477$	−4.34483e93	−	7.96899e92i	−0.775943	−	0.142318i
$478$	−2.65457e92			−0.0440574
$479$			7.50443e92i			0.115764i	0.998323	+	0.0578821i	$0.0184348\pi$
$479$			7.50443e92i			0.115764i	−0.998323	+	0.0578821i	$0.981565\pi$
$480$	4.61027e93	−	3.84159e93i	0.661125	−	0.550894i
$481$	−9.51543e93			−1.26868
$482$			2.06665e93i			0.256224i
$483$	3.77642e93	+	4.53206e93i	0.435443	+	0.522572i
$484$	3.32971e93			0.357123
$485$		−	1.58599e94i		−	1.58249i
$486$	1.58138e93	+	4.58828e93i	0.146813	+	0.425971i
$487$	−2.15681e93			−0.186336			−0.0931682	−	0.995650i	$-0.529699\pi$
$487$	−2.15681e93			−0.186336			−0.0931682	+	0.995650i	$0.529699\pi$
$488$			1.14936e94i			0.924195i
$489$	1.05399e94	−	8.78252e93i	0.788905	−	0.657369i
$490$	1.03671e93			0.0722431
$491$		−	1.19973e94i		−	0.778448i	−0.921143	−	0.389224i	$-0.872743\pi$
$491$		−	1.19973e94i		−	0.778448i	0.921143	−	0.389224i	$-0.127257\pi$
$492$	1.44902e94	+	1.73896e94i	0.875581	+	1.05078i
$493$	7.80750e92			0.0439410
$494$			1.84627e93i			0.0967949i
$495$	2.35096e93	−	1.28178e94i	0.114832	−	0.626084i
$496$	7.05740e93			0.321208
$497$			3.13704e94i			1.33060i
$498$	−1.24206e94	+	1.03497e94i	−0.491037	+	0.409165i
$499$	−2.45053e94			−0.903112			−0.451556	−	0.892243i	$-0.649131\pi$
$499$	−2.45053e94			−0.903112			−0.451556	+	0.892243i	$0.649131\pi$
$500$			2.51583e94i			0.864433i
$501$	3.84485e92	+	4.61419e92i	0.0123185	+	0.0147834i
$502$	5.16002e93			0.154178
$503$			4.38755e93i			0.122276i	0.998129	+	0.0611382i	$0.0194730\pi$
$503$			4.38755e93i			0.122276i	−0.998129	+	0.0611382i	$0.980527\pi$
$504$	3.33761e94	+	6.12161e93i	0.867694	+	0.159146i
$505$	2.82236e94			0.684565
$506$			9.23321e93i			0.208970i
$507$	−3.07164e93	+	2.55950e93i	−0.0648772	+	0.0540601i
$508$	4.71666e94			0.929833
$509$		−	6.53053e94i		−	1.20178i	−0.799331	−	0.600891i	$-0.794812\pi$
$509$		−	6.53053e94i		−	1.20178i	0.799331	−	0.600891i	$-0.205188\pi$
$510$	−1.44655e93	−	1.73600e93i	−0.0248529	−	0.0298259i
$511$	−1.06295e95			−1.70522
$512$		−	5.23330e94i		−	0.784019i
$513$	7.87947e93	+	1.39780e94i	0.110253	+	0.195586i
$514$	−1.93417e94			−0.252804
$515$		−	1.14407e95i		−	1.39701i
$516$	−4.97155e94	+	4.14264e94i	−0.567221	+	0.472647i
$517$	−9.43232e94			−1.00566
$518$		−	6.53214e94i		−	0.650900i
$519$	−8.67565e94	−	1.04116e95i	−0.808062	−	0.969750i
$520$	7.62327e94			0.663780
$521$			1.16959e95i			0.952171i	0.879399	+	0.476085i	$0.157945\pi$
$521$			1.16959e95i			0.952171i	−0.879399	+	0.476085i	$0.842055\pi$
$522$	4.66531e93	−	2.54361e94i	0.0355151	−	0.193634i
$523$	6.32830e94			0.450535			0.225267	−	0.974297i	$-0.427674\pi$
$523$	6.32830e94			0.450535			0.225267	+	0.974297i	$0.427674\pi$
$524$			1.98863e95i			1.32422i
$525$	−3.57289e94	+	2.97717e94i	−0.222558	+	0.185451i
$526$	1.13409e95			0.660917
$527$		−	1.37068e94i		−	0.0747418i
$528$	−4.02797e94	−	4.83395e94i	−0.205541	−	0.246669i
$529$	1.27777e95			0.610246
$530$		−	6.81250e94i		−	0.304545i
$531$	−4.30161e95	−	7.88971e94i	−1.80021	−	0.330182i
$532$	4.97588e94			0.194968
$533$			4.47558e95i			1.64209i
$534$	−1.12086e95	+	9.33978e94i	−0.385130	+	0.320917i
$535$	4.58789e95			1.47649
$536$		−	2.88456e95i		−	0.869585i
$537$	3.12143e94	+	3.74601e94i	0.0881564	+	0.105796i
$538$	5.96959e94			0.157966
$539$		−	5.60663e94i		−	0.139026i
$540$	2.55977e95	−	1.44295e95i	0.594866	−	0.335328i
$541$	2.43697e95			0.530818			0.265409	−	0.964136i	$-0.414493\pi$
$541$	2.43697e95			0.530818			0.265409	+	0.964136i	$0.414493\pi$
$542$			6.75094e94i			0.137844i
$543$	1.77006e95	−	1.47493e95i	0.338839	−	0.282343i
$544$	−5.62755e94			−0.101008
$545$		−	5.90080e94i		−	0.0993193i
$546$	1.90491e95	+	2.28607e95i	0.300698	+	0.360866i
$547$	2.51866e95			0.372917			0.186459	−	0.982463i	$-0.440299\pi$
$547$	2.51866e95			0.372917			0.186459	+	0.982463i	$0.440299\pi$
$548$			6.56228e95i			0.911455i
$549$	−1.58030e95	+	8.61609e95i	−0.205925	+	1.12274i
$550$	−7.27907e94			−0.0889983
$551$		−	8.55020e94i		−	0.0981003i
$552$	−3.60632e95	+	3.00503e95i	−0.388326	+	0.323580i
$553$	4.26506e95			0.431068
$554$		−	1.05084e95i		−	0.0996996i
$555$	−8.16453e95	−	9.79820e95i	−0.727238	−	0.872754i
$556$	−3.77461e95			−0.315685
$557$		−	1.15192e96i		−	0.904667i	−0.891849	−	0.452334i	$-0.850592\pi$
$557$		−	1.15192e96i		−	0.904667i	0.891849	−	0.452334i	$-0.149408\pi$
$558$	−4.46553e95	−	8.19036e94i	−0.329364	−	0.0604096i
$559$	−1.27953e96			−0.886418
$560$		−	6.20002e95i		−	0.403471i
$561$	−9.38841e94	+	7.82306e94i	−0.0573974	+	0.0478274i
$562$	7.93648e94			0.0455887
$563$		−	1.90991e96i		−	1.03091i	−0.856917	−	0.515454i	$-0.827623\pi$
$563$		−	1.90991e96i		−	1.03091i	0.856917	−	0.515454i	$-0.172377\pi$
$564$	−1.36152e96	−	1.63395e96i	−0.690645	−	0.828839i
$565$	−7.51547e95			−0.358311
$566$		−	7.73891e94i		−	0.0346820i
$567$	2.41784e96	+	9.17800e95i	1.01864	+	0.386671i
$568$	−2.49626e96			−0.988775
$569$			3.96704e96i			1.47753i	0.673961	+	0.738767i	$0.264592\pi$
$569$			3.96704e96i			1.47753i	−0.673961	+	0.738767i	$0.735408\pi$
$570$	−1.90114e95	+	1.58416e95i	−0.0665877	+	0.0554854i
$571$	4.44634e96			1.46467			0.732334	−	0.680946i	$-0.238431\pi$
$571$	4.44634e96			1.46467			0.732334	+	0.680946i	$0.238431\pi$
$572$		−	1.82849e96i		−	0.566541i
$573$	1.87993e96	+	2.25609e96i	0.547936	+	0.657575i
$574$	−3.07239e96			−0.842482
$575$		−	6.43373e95i		−	0.165992i
$576$	−1.51167e94	+	8.24189e94i	−0.00367004	+	0.0200097i
$577$	−1.73203e96			−0.395732			−0.197866	−	0.980229i	$-0.563401\pi$
$577$	−1.73203e96			−0.395732			−0.197866	+	0.980229i	$0.563401\pi$
$578$		−	2.07402e96i		−	0.446005i
$579$	5.30346e96	−	4.41920e96i	1.07352	−	0.894529i
$580$	−1.56578e96			−0.298367
$581$			8.61539e96i			1.54565i
$582$	3.15357e96	+	3.78458e96i	0.532718	+	0.639312i
$583$	−3.68425e96			−0.586070
$584$		−	8.45826e96i		−	1.26716i
$585$	5.71471e96	+	1.04815e96i	0.806378	+	0.147900i
$586$	5.16964e96			0.687138
$587$			1.18368e97i			1.48218i	0.671405	+	0.741090i	$0.265691\pi$
$587$			1.18368e97i			1.48218i	−0.671405	+	0.741090i	$0.734309\pi$
$588$	9.71230e95	−	8.09295e95i	0.114582	−	0.0954774i
$589$	−1.50106e96			−0.166864
$590$		−	6.74472e96i		−	0.706551i
$591$	6.41186e95	+	7.69483e95i	0.0633027	+	0.0759692i
$592$	−6.15812e96			−0.573045
$593$			1.34936e97i			1.18362i	0.806078	+	0.591810i	$0.201586\pi$
$593$			1.34936e97i			1.18362i	−0.806078	+	0.591810i	$0.798414\pi$
$594$	1.98768e96	+	3.52611e96i	0.164369	+	0.291589i
$595$	−1.20416e96			−0.0938835
$596$			8.51561e96i			0.626032i
$597$	6.36393e96	−	5.30286e96i	0.441188	−	0.367628i
$598$	−4.11654e96			−0.269148
$599$		−	1.63551e97i		−	1.00859i	−0.863531	−	0.504295i	$-0.831752\pi$
$599$		−	1.63551e97i		−	1.00859i	0.863531	−	0.504295i	$-0.168248\pi$
$600$	−2.36904e96	−	2.84307e96i	−0.137809	−	0.165384i
$601$	3.06474e96			0.168185			0.0840924	−	0.996458i	$-0.473201\pi$
$601$	3.06474e96			0.168185			0.0840924	+	0.996458i	$0.473201\pi$
$602$		−	8.78372e96i		−	0.454780i
$603$	3.96609e96	−	2.16238e97i	0.193757	−	1.05640i
$604$	−1.06651e97			−0.491670
$605$			8.82436e96i			0.383924i
$606$	−6.73486e96	+	5.61194e96i	−0.276558	+	0.230447i
$607$	−2.64456e97			−1.02506			−0.512529	−	0.858670i	$-0.671291\pi$
$607$	−2.64456e97			−1.02506			−0.512529	+	0.858670i	$0.671291\pi$
$608$			6.16287e96i			0.225506i
$609$	−8.82173e96	−	1.05869e97i	−0.304753	−	0.365733i
$610$	−1.35096e97			−0.440655
$611$		−	4.20531e97i		−	1.29526i
$612$	−2.71036e96	−	4.97115e95i	−0.0788365	−	0.0144596i
$613$	4.19655e97			1.15286			0.576429	−	0.817147i	$-0.304446\pi$
$613$	4.19655e97			1.15286			0.576429	+	0.817147i	$0.304446\pi$
$614$		−	2.59019e97i		−	0.672107i
$615$	−4.60858e97	+	3.84019e97i	−1.12964	+	0.941289i
$616$	2.83016e97			0.655370
$617$		−	3.95625e97i		−	0.865573i	−0.901497	−	0.432786i	$-0.857530\pi$
$617$		−	3.95625e97i		−	0.865573i	0.901497	−	0.432786i	$-0.142470\pi$
$618$	2.27485e97	+	2.73003e97i	0.470279	+	0.564379i
$619$	−1.57665e97			−0.308008			−0.154004	−	0.988070i	$-0.549217\pi$
$619$	−1.57665e97			−0.308008			−0.154004	+	0.988070i	$0.549217\pi$
$620$			2.74886e97i			0.507510i
$621$	−3.11661e97	+	1.75685e97i	−0.543847	+	0.306568i
$622$	1.44197e96			0.0237845
$623$			7.77474e97i			1.21228i
$624$	2.15517e97	−	1.79583e97i	0.317703	−	0.264731i
$625$	−4.75981e97			−0.663421
$626$		−	4.72677e95i		−	0.00622964i
$627$	8.56724e96	+	1.02815e97i	0.106777	+	0.128142i
$628$	7.71980e97			0.909952
$629$			1.19602e97i			0.133342i
$630$	−7.19534e96	+	3.92303e97i	−0.0758809	+	0.413716i
$631$	1.71786e98			1.71380			0.856899	−	0.515485i	$-0.172388\pi$
$631$	1.71786e98			1.71380			0.856899	+	0.515485i	$0.172388\pi$
$632$			3.39386e97i			0.320329i
$633$	7.55100e97	−	6.29201e97i	0.674334	−	0.561901i
$634$	4.33962e96			0.0366714
$635$			1.25001e98i			0.999613i
$636$	−5.31807e97	−	6.38218e97i	−0.402490	−	0.483026i
$637$	2.49966e97			0.179061
$638$		−	2.15688e97i		−	0.146252i
$639$	−1.87129e98	−	3.43220e97i	−1.20119	−	0.220314i
$640$	1.40314e98			0.852710
$641$		−	2.94358e98i		−	1.69373i	−0.531807	−	0.846866i	$-0.678487\pi$
$641$		−	2.94358e98i		−	1.69373i	0.531807	−	0.846866i	$-0.321513\pi$
$642$	−1.09478e98	+	9.12248e97i	−0.596489	+	0.497035i
$643$	2.32906e98			1.20170			0.600850	−	0.799362i	$-0.294829\pi$
$643$	2.32906e98			1.20170			0.600850	+	0.799362i	$0.294829\pi$
$644$			1.10945e98i			0.542127i
$645$	−1.09788e98	−	1.31756e98i	−0.508118	−	0.609789i
$646$	2.32063e96			0.0101734
$647$			5.20402e97i			0.216117i	0.994145	+	0.108059i	$0.0344634\pi$
$647$			5.20402e97i			0.216117i	−0.994145	+	0.108059i	$0.965537\pi$
$648$	−7.30326e97	+	1.92396e98i	−0.287337	+	0.756955i
$649$	−3.64760e98			−1.35970
$650$		−	3.24531e97i		−	0.114627i
$651$	−1.85863e98	+	1.54873e98i	−0.622096	+	0.518373i
$652$	2.58015e98			0.818426
$653$			1.22745e98i			0.369014i	0.982831	+	0.184507i	$0.0590688\pi$
$653$			1.22745e98i			0.369014i	−0.982831	+	0.184507i	$0.940931\pi$
$654$	1.17331e97	+	1.40808e97i	0.0334342	+	0.0401241i
$655$	−5.27026e98			−1.42360
$656$			2.89647e98i			0.741712i
$657$	1.16296e98	−	6.34065e98i	0.282342	−	1.53938i
$658$	2.88686e98			0.664537
$659$		−	6.82522e98i		−	1.48980i	−0.667178	−	0.744898i	$-0.732498\pi$
$659$		−	6.82522e98i		−	1.48980i	0.667178	−	0.744898i	$-0.267502\pi$
$660$	1.88283e98	−	1.56890e98i	0.389738	−	0.324756i
$661$	−3.27395e98			−0.642720			−0.321360	−	0.946957i	$-0.604140\pi$
$661$	−3.27395e98			−0.642720			−0.321360	+	0.946957i	$0.604140\pi$
$662$		−	3.38934e98i		−	0.631081i
$663$	−3.48784e97	−	4.18574e97i	−0.0616003	−	0.0739262i
$664$	−6.85557e98			−1.14858
$665$			1.31870e98i			0.209599i
$666$	3.89652e98	+	7.14672e97i	0.587596	+	0.107773i
$667$	1.90639e98			0.272777
$668$			1.12955e97i			0.0153366i
$669$	−4.45463e97	+	3.71190e97i	−0.0573982	+	0.0478280i
$670$	3.39052e98			0.414618
$671$			7.30611e98i			0.848004i
$672$	6.35859e98	+	7.63091e98i	0.700545	+	0.840720i
$673$	−3.94455e98			−0.412544			−0.206272	−	0.978495i	$-0.566133\pi$
$673$	−3.94455e98			−0.412544			−0.206272	+	0.978495i	$0.566133\pi$
$674$			2.04805e96i			0.00203350i
$675$	−1.38502e98	−	2.45701e98i	−0.130564	−	0.231619i
$676$	−7.51937e97			−0.0673050
$677$			6.31271e97i			0.0536552i	0.999640	+	0.0268276i	$0.00854052\pi$
$677$			6.31271e97i			0.0536552i	−0.999640	+	0.0268276i	$0.991459\pi$
$678$	1.79338e98	−	1.49436e98i	0.144755	−	0.120619i
$679$	2.62513e99			2.01238
$680$		−	9.58190e97i		−	0.0697653i
$681$	1.40556e99	+	1.68680e99i	0.972075	+	1.16658i
$682$	−3.78660e98			−0.248769
$683$			2.29940e99i			1.43513i	0.696494	+	0.717563i	$0.254742\pi$
$683$			2.29940e99i			1.43513i	−0.696494	+	0.717563i	$0.745258\pi$
$684$	−5.44404e97	+	2.96819e98i	−0.0322818	+	0.176006i
$685$	−1.73913e99			−0.979856
$686$		−	7.45359e98i		−	0.399045i
$687$	4.99178e98	−	4.15949e98i	0.253963	−	0.211619i
$688$	−8.28078e98			−0.400383
$689$		−	1.64259e99i		−	0.754842i
$690$	−3.53212e98	−	4.23887e98i	−0.154283	−	0.185154i
$691$	−3.03620e99			−1.26066			−0.630331	−	0.776326i	$-0.717081\pi$
$691$	−3.03620e99			−1.26066			−0.630331	+	0.776326i	$0.717081\pi$
$692$		−	2.54876e99i		−	1.00604i
$693$	2.12160e99	+	3.89129e98i	0.796161	+	0.146026i
$694$	−1.51617e99			−0.540961
$695$		−	1.00034e99i		−	0.339376i
$696$	8.42437e98	−	7.01976e98i	0.271778	−	0.226464i
$697$	5.62548e98			0.172589
$698$			1.63612e99i			0.477391i
$699$	2.37318e98	+	2.84804e98i	0.0658611	+	0.0790396i
$700$	−8.74641e98			−0.230886
$701$			3.97406e96i			0.000997938i	1.00000		0.000498969i	$0.000158827\pi$
$701$			3.97406e96i			0.000997938i	−1.00000		0.000498969i	$0.999841\pi$
$702$	−1.57208e99	+	8.86189e98i	−0.375558	+	0.211703i
$703$	1.30979e99			0.297692
$704$			6.98880e97i			0.0151133i
$705$	4.33028e99	−	3.60829e99i	0.891040	−	0.742475i
$706$	1.13945e99			0.223116
$707$			4.67156e99i			0.870528i
$708$	−5.26516e99	−	6.31869e99i	−0.933787	−	1.12063i
$709$	−9.04620e99			−1.52703			−0.763516	−	0.645789i	$-0.776528\pi$
$709$	−9.04620e99			−1.52703			−0.763516	+	0.645789i	$0.776528\pi$
$710$		−	2.93410e99i		−	0.471447i
$711$	−4.66634e98	+	2.54417e99i	−0.0713741	+	0.389144i
$712$	−6.18663e99			−0.900854
$713$		−	3.34685e99i		−	0.463983i
$714$	2.87342e98	−	2.39433e98i	0.0379281	−	0.0316043i
$715$	4.84585e99			0.609058
$716$			9.17022e98i			0.109755i
$717$	−5.49186e98	−	6.59075e98i	−0.0625964	−	0.0751216i
$718$	−2.75031e99			−0.298556
$719$			4.42669e97i			0.00457687i	0.999997	+	0.00228843i	$0.000728431\pi$
$719$			4.42669e97i			0.00457687i	−0.999997	+	0.00228843i	$0.999272\pi$
$720$	3.69840e99	+	6.78335e98i	0.364231	+	0.0668047i
$721$	1.89366e100			1.77651
$722$			4.78732e99i			0.427849i
$723$	−5.13106e99	+	4.27554e99i	−0.436884	+	0.364042i
$724$	4.33309e99			0.351518
$725$			1.50292e99i			0.116173i
$726$	−1.75462e99	−	2.10571e99i	−0.129242	−	0.155102i
$727$	1.27207e100			0.892910			0.446455	−	0.894806i	$-0.352686\pi$
$727$	1.27207e100			0.892910			0.446455	+	0.894806i	$0.352686\pi$
$728$			1.26180e100i			0.844097i
$729$	−8.12014e99	+	1.34186e100i	−0.517726	+	0.855547i
$730$	9.94185e99			0.604181
$731$			1.60828e99i			0.0931652i
$732$	−1.26563e100	+	1.05461e100i	−0.698905	+	0.582376i
$733$	1.57972e100			0.831651			0.415825	−	0.909444i	$-0.363493\pi$
$733$	1.57972e100			0.831651			0.415825	+	0.909444i	$0.363493\pi$
$734$			8.59849e99i			0.431579i
$735$	2.14479e99	+	2.57395e99i	0.102643	+	0.123181i
$736$	−1.37410e100			−0.627042
$737$		−	1.83362e100i		−	0.797896i
$738$	3.36146e99	−	1.83273e100i	0.139494	−	0.760546i
$739$	3.34212e100			1.32272			0.661358	−	0.750070i	$-0.269980\pi$
$739$	3.34212e100			1.32272			0.661358	+	0.750070i	$0.269980\pi$
$740$		−	2.39860e100i		−	0.905414i
$741$	−4.58391e99	+	3.81963e99i	−0.165044	+	0.137526i
$742$	1.12760e100			0.387275
$743$		−	1.11059e99i		−	0.0363868i	−0.999834	−	0.0181934i	$-0.994209\pi$
$743$		−	1.11059e99i		−	0.0363868i	0.999834	−	0.0181934i	$-0.00579146\pi$
$744$	−1.23238e100	−	1.47897e100i	−0.385206	−	0.462283i
$745$	−2.25680e100			−0.673013
$746$		−	2.63531e100i		−	0.749847i
$747$	−5.13921e100	−	9.42598e99i	−1.39532	−	0.255921i
$748$	−2.29828e99			−0.0595452
$749$			7.59385e100i			1.87758i
$750$	1.59102e100	−	1.32574e100i	0.375431	−	0.312835i
$751$	−4.80520e100			−1.08222			−0.541108	−	0.840953i	$-0.681995\pi$
$751$	−4.80520e100			−1.08222			−0.541108	+	0.840953i	$0.681995\pi$
$752$		−	2.72156e100i		−	0.585051i
$753$	1.06752e100	+	1.28113e100i	0.219055	+	0.262886i
$754$	9.61625e99			0.188369
$755$		−	2.82647e100i		−	0.528568i
$756$	2.38836e100	+	4.23692e100i	0.426420	+	0.756462i
$757$	−3.78772e100			−0.645688			−0.322844	−	0.946452i	$-0.604639\pi$
$757$	−3.78772e100			−0.645688			−0.322844	+	0.946452i	$0.604639\pi$
$758$			7.78959e99i			0.126792i
$759$	−2.29241e100	+	1.91019e100i	−0.356312	+	0.296904i
$760$	−1.04934e100			−0.155754
$761$		−	7.26745e100i		−	1.03019i	−0.857132	−	0.515097i	$-0.827756\pi$
$761$		−	7.26745e100i		−	1.03019i	0.857132	−	0.515097i	$-0.172244\pi$
$762$	−2.48549e100	−	2.98283e100i	−0.336503	−	0.403835i
$763$	9.76699e99			0.126300
$764$			5.52291e100i			0.682182i
$765$	1.31745e99	−	7.18298e99i	0.0155448	−	0.0847528i
$766$	2.40958e100			0.271603
$767$		−	1.62625e101i		−	1.75125i
$768$	−3.50014e100	+	2.91656e100i	−0.360116	+	0.300074i
$769$	5.05887e100			0.497315			0.248658	−	0.968591i	$-0.420011\pi$
$769$	5.05887e100			0.497315			0.248658	+	0.968591i	$0.420011\pi$
$770$			3.32657e100i			0.312480i
$771$	−4.00146e100	−	4.80213e100i	−0.359183	−	0.431053i
$772$	1.29829e101			1.11369
$773$			1.66422e101i			1.36436i	0.731185	+	0.682180i	$0.238968\pi$
$773$			1.66422e101i			1.36436i	−0.731185	+	0.682180i	$0.761032\pi$
$774$	5.23962e100	+	9.61015e99i	0.410550	+	0.0753003i
$775$	2.63851e100			0.197606
$776$			2.08891e101i			1.49541i
$777$	1.62179e101	−	1.35139e101i	1.10984	−	0.924794i
$778$	−4.41089e100			−0.288563
$779$		−	6.16062e100i		−	0.385312i
$780$	6.99479e100	+	8.39441e100i	0.418277	+	0.501972i
$781$	−1.58678e101			−0.907260
$782$			5.17419e99i			0.0282883i
$783$	7.28042e100	−	4.10399e100i	0.380623	−	0.214558i
$784$	1.61771e100			0.0808797
$785$			2.04590e101i			0.978240i
$786$	1.25762e101	−	1.04793e101i	0.575121	−	0.479230i
$787$	−2.61330e101			−1.14307			−0.571536	−	0.820577i	$-0.693652\pi$
$787$	−2.61330e101			−1.14307			−0.571536	+	0.820577i	$0.693652\pi$
$788$			1.88369e100i			0.0788120i
$789$	2.34624e101	+	2.81571e101i	0.939027	+	1.12692i
$790$	−3.98914e100			−0.152732
$791$		−	1.24396e101i		−	0.455647i
$792$	−3.09644e100	+	1.68823e101i	−0.108513	+	0.591631i
$793$	−3.25736e101			−1.09221
$794$			2.41298e101i			0.774170i
$795$	1.69140e101	−	1.40939e101i	0.519275	−	0.432695i
$796$	1.55789e101			0.457697
$797$		−	5.13585e101i		−	1.44401i	−0.691886	−	0.722007i	$-0.743220\pi$
$797$		−	5.13585e101i		−	1.44401i	0.691886	−	0.722007i	$-0.256780\pi$
$798$	−2.62209e100	−	3.14676e100i	−0.0705581	−	0.0846763i
$799$	−5.28577e100			−0.136135
$800$		−	1.08329e101i		−	0.267051i
$801$	−4.63775e101	−	8.50623e100i	−1.09438	−	0.200724i
$802$	−1.37642e101			−0.310921
$803$		−	5.37662e101i		−	1.16269i
$804$	3.17635e101	−	2.64675e101i	0.657608	−	0.547964i
$805$	−2.94025e101			−0.582812
$806$		−	1.68822e101i		−	0.320407i
$807$	1.23501e101	+	1.48213e101i	0.224438	+	0.269346i
$808$	−3.71733e101			−0.646894
$809$			2.67843e100i			0.0446356i	0.999751	+	0.0223178i	$0.00710457\pi$
$809$			2.67843e100i			0.0446356i	−0.999751	+	0.0223178i	$0.992895\pi$
$810$	−2.26142e101	−	8.58426e100i	−0.360916	−	0.137002i
$811$	1.49582e101			0.228638			0.114319	−	0.993444i	$-0.463531\pi$
$811$	1.49582e101			0.228638			0.114319	+	0.993444i	$0.463531\pi$
$812$		−	2.59167e101i		−	0.379419i
$813$	−1.67612e101	+	1.39665e101i	−0.235037	+	0.195848i
$814$	3.30410e101			0.443811
$815$			6.83790e101i			0.879846i
$816$	−2.25723e100	−	2.70889e100i	−0.0278241	−	0.0333915i
$817$	1.76127e101			0.207996
$818$		−	6.26650e101i		−	0.709022i
$819$	−1.73490e101	+	9.45897e101i	−0.188078	+	1.02543i
$820$	−1.12818e102			−1.17191
$821$			8.70511e101i			0.866490i	0.901276	+	0.433245i	$0.142632\pi$
$821$			8.70511e101i			0.866490i	−0.901276	+	0.433245i	$0.857368\pi$
$822$	4.15000e101	−	3.45806e101i	0.395853	−	0.329852i
$823$	8.75629e101			0.800435			0.400217	−	0.916420i	$-0.368935\pi$
$823$	8.75629e101			0.800435			0.400217	+	0.916420i	$0.368935\pi$
$824$			1.50685e102i			1.32013i
$825$	−1.50592e101	−	1.80724e101i	−0.126448	−	0.151750i
$826$	1.11638e102			0.898487
$827$		−	6.07172e101i		−	0.468402i	−0.972188	−	0.234201i	$-0.924753\pi$
$827$		−	6.07172e101i		−	0.468402i	0.972188	−	0.234201i	$-0.0752474\pi$
$828$	−6.61802e101	−	1.21383e101i	−0.489402	−	0.0897627i
$829$	1.70770e102			1.21060			0.605302	−	0.795996i	$-0.293052\pi$
$829$	1.70770e102			1.21060			0.605302	+	0.795996i	$0.293052\pi$
$830$		−	8.05804e101i		−	0.547641i
$831$	2.60901e101	−	2.17400e101i	0.169996	−	0.141652i
$832$	−3.11589e100			−0.0194655
$833$		−	3.14190e100i		−	0.0188199i
$834$	1.98907e101	+	2.38707e101i	0.114245	+	0.137105i
$835$	−2.99353e100			−0.0164876
$836$			2.51691e101i			0.132937i
$837$	−7.20493e101	−	1.27814e102i	−0.364955	−	0.647423i
$838$	2.30098e101			0.111782
$839$			3.34300e102i			1.55764i	0.627246	+	0.778821i	$0.284182\pi$
$839$			3.34300e102i			1.55764i	−0.627246	+	0.778821i	$0.715818\pi$
$840$	−1.29930e102	+	1.08266e102i	−0.580676	+	0.483859i
$841$	1.88737e102			0.809091
$842$		−	1.79684e102i		−	0.738903i
$843$	1.64192e101	+	1.97046e101i	0.0647721	+	0.0777326i
$844$	1.84848e102			0.699568
$845$		−	1.99278e101i		−	0.0723559i
$846$	−3.15847e101	+	1.72205e102i	−0.110031	+	0.599907i
$847$	−1.46061e102			−0.488218
$848$		−	1.06304e102i		−	0.340952i
$849$	1.92141e101	−	1.60105e101i	0.0591359	−	0.0492760i
$850$	−4.07911e100			−0.0120477
$851$			2.92038e102i			0.827761i
$852$	−2.29046e102	−	2.74877e102i	−0.623070	−	0.747742i
$853$	5.58140e102			1.45723			0.728614	−	0.684925i	$-0.240165\pi$
$853$	5.58140e102			1.45723			0.728614	+	0.684925i	$0.240165\pi$
$854$		−	2.23611e102i		−	0.560360i
$855$	−7.86627e101	−	1.44278e101i	−0.189215	−	0.0347044i
$856$	−6.04269e102			−1.39524
$857$		−	5.96954e102i		−	1.32316i	−0.749875	−	0.661580i	$-0.769886\pi$
$857$		−	5.96954e102i		−	1.32316i	0.749875	−	0.661580i	$-0.230114\pi$
$858$	−1.15634e102	+	9.63542e101i	−0.246054	+	0.205029i
$859$	−7.35196e102			−1.50190			−0.750952	−	0.660357i	$-0.770405\pi$
$859$	−7.35196e102			−1.50190			−0.750952	+	0.660357i	$0.770405\pi$
$860$		−	3.22538e102i		−	0.632608i
$861$	−6.35626e102	−	7.62811e102i	−1.19699	−	1.43650i
$862$	2.23888e102			0.404834
$863$			8.42231e102i			1.46236i	0.682186	+	0.731178i	$0.261029\pi$
$863$			8.42231e102i			1.46236i	−0.682186	+	0.731178i	$0.738971\pi$
$864$	−5.24763e102	+	2.95811e102i	−0.874949	+	0.493211i
$865$	6.75469e102			1.08154
$866$		−	7.53911e101i		−	0.115929i
$867$	5.14937e102	−	4.29080e102i	0.760476	−	0.633680i
$868$	−4.54991e102			−0.645375
$869$			2.15736e102i			0.293921i
$870$	8.25103e101	+	9.90201e101i	0.107978	+	0.129583i
$871$	8.17501e102			1.02767
$872$			7.77193e101i			0.0938538i
$873$	−2.87212e102	+	1.56593e103i	−0.333199	+	1.81666i
$874$	5.66639e101			0.0631548
$875$		−	1.10359e103i		−	1.18175i
$876$	9.31386e102	−	7.76094e102i	0.958266	−	0.798493i
$877$	−8.68994e102			−0.859075			−0.429537	−	0.903049i	$-0.641323\pi$
$877$	−8.68994e102			−0.859075			−0.429537	+	0.903049i	$0.641323\pi$
$878$			3.66454e102i			0.348106i
$879$	1.06951e103	+	1.28351e103i	0.976281	+	1.17163i
$880$	3.13610e102			0.275104
$881$			7.63406e102i			0.643574i	0.946812	+	0.321787i	$0.104284\pi$
$881$			7.63406e102i			0.643574i	−0.946812	+	0.321787i	$0.895716\pi$
$882$	−1.02360e102	−	1.87741e101i	−0.0829334	−	0.0152111i
$883$	4.94769e102			0.385282			0.192641	−	0.981269i	$-0.438295\pi$
$883$	4.94769e102			0.385282			0.192641	+	0.981269i	$0.438295\pi$
$884$		−	1.02467e102i		−	0.0766926i
$885$	1.67457e103	−	1.39537e103i	1.20473	−	1.00386i
$886$	−6.96096e102			−0.481381
$887$		−	9.71255e102i		−	0.645664i	−0.946456	−	0.322832i	$-0.895365\pi$
$887$		−	9.71255e102i		−	0.645664i	0.946456	−	0.322832i	$-0.104635\pi$
$888$	1.07535e103	+	1.29052e103i	0.687219	+	0.824728i
$889$	−2.06901e103			−1.27116
$890$		−	7.27177e102i		−	0.429526i
$891$	−4.64243e102	+	1.22299e103i	−0.263649	+	0.694551i
$892$	−1.09049e102			−0.0595460
$893$			5.78859e102i			0.303929i
$894$	5.38529e102	−	4.48739e102i	0.271891	−	0.226558i
$895$	−2.43029e102			−0.117992
$896$			2.32247e103i			1.08435i
$897$	−8.51642e102	−	1.02205e103i	−0.382403	−	0.458920i
$898$	1.12866e103			0.487408
$899$			7.81824e102i			0.324728i
$900$	9.56932e101	−	5.21736e102i	0.0382290	−	0.208431i
$901$	−2.06461e102			−0.0793362
$902$		−	1.55408e103i		−	0.574440i
$903$	2.18082e103	−	1.81720e103i	0.775439	−	0.646149i
$904$	9.89860e102			0.338594
$905$			1.14835e103i			0.377898i
$906$	5.62011e102	+	6.74466e102i	0.177934	+	0.213537i
$907$	−3.35218e103			−1.02111			−0.510554	−	0.859846i	$-0.670560\pi$
$907$	−3.35218e103			−1.02111			−0.510554	+	0.859846i	$0.670560\pi$
$908$			4.12929e103i			1.21024i
$909$	−2.78666e103	−	5.11109e102i	−0.785864	−	0.144138i
$910$	−1.48312e103			−0.402465
$911$		−	1.74094e103i		−	0.454613i	−0.973823	−	0.227306i	$-0.927008\pi$
$911$		−	1.74094e103i		−	0.454613i	0.973823	−	0.227306i	$-0.0729919\pi$
$912$	−2.96658e102	+	2.47196e102i	−0.0745481	+	0.0621185i
$913$	−4.35785e103			−1.05389
$914$		−	1.21977e103i		−	0.283898i
$915$	−2.79491e103	−	3.35416e103i	−0.626080	−	0.751355i
$916$	1.22199e103			0.263466
$917$		−	8.72332e103i		−	1.81032i
$918$	1.11388e102	+	1.97600e102i	0.0222507	+	0.0394723i
$919$	−3.33857e103			−0.641974			−0.320987	−	0.947084i	$-0.604015\pi$
$919$	−3.33857e103			−0.641974			−0.320987	+	0.947084i	$0.604015\pi$
$920$		−	2.33966e103i		−	0.433090i
$921$	6.43090e103	−	5.35867e103i	1.14600	−	0.954926i
$922$	3.49926e103			0.600335
$923$		−	7.07453e103i		−	1.16852i
$924$	2.59684e103	+	3.11645e103i	0.412977	+	0.495611i
$925$	−2.30230e103			−0.352535
$926$			3.85937e103i			0.569025i
$927$	−2.07182e103	+	1.12959e104i	−0.294145	+	1.60373i
$928$	3.20991e103			0.438848
$929$			1.46418e104i			1.92772i	0.266403	+	0.963862i	$0.414165\pi$
$929$			1.46418e104i			1.92772i	−0.266403	+	0.963862i	$0.585835\pi$
$930$	1.73839e103	−	1.44854e103i	0.220416	−	0.183666i
$931$	−3.44077e102			−0.0420163
$932$			6.97199e102i			0.0819973i
$933$	2.98320e102	+	3.58012e102i	0.0337929	+	0.0405546i
$934$	−4.13901e103			−0.451602
$935$		−	6.09088e102i		−	0.0640138i
$936$	−7.52683e103	−	1.38052e103i	−0.762004	−	0.139762i
$937$	7.88360e103			0.768846			0.384423	−	0.923157i	$-0.374400\pi$
$937$	7.88360e103			0.768846			0.384423	+	0.923157i	$0.374400\pi$
$938$			5.61197e103i			0.527249i
$939$	1.17356e102	−	9.77890e101i	0.0106221	−	0.00885104i
$940$	1.06005e104			0.924383
$941$			1.67900e104i			1.41063i	0.708892	+	0.705317i	$0.249195\pi$
$941$			1.67900e104i			1.41063i	−0.708892	+	0.705317i	$0.750805\pi$
$942$	−4.06803e103	−	4.88202e103i	−0.329308	−	0.395201i
$943$	1.37360e104			1.07140
$944$		−	1.05246e104i		−	0.791018i
$945$	−1.12287e104	+	6.32963e103i	−0.813232	+	0.458421i
$946$	4.44299e103			0.310089
$947$		−	1.04680e104i		−	0.704065i	−0.935988	−	0.352033i	$-0.885491\pi$
$947$		−	1.04680e104i		−	0.704065i	0.935988	−	0.352033i	$-0.114509\pi$
$948$	−3.73716e103	+	3.11406e103i	−0.242243	+	0.201853i
$949$	2.39712e104			1.49752
$950$			4.46715e102i			0.0268970i
$951$	8.97794e102	+	1.07744e103i	0.0521025	+	0.0625279i
$952$	1.58599e103			0.0887172
$953$		−	1.04090e104i		−	0.561252i	−0.959817	−	0.280626i	$-0.909458\pi$
$953$		−	1.04090e104i		−	0.561252i	0.959817	−	0.280626i	$-0.0905420\pi$
$954$	−1.23369e103	+	6.72631e103i	−0.0641231	+	0.349610i
$955$	−1.46368e104			−0.733377
$956$		−	1.61341e103i		−	0.0779327i
$957$	5.35508e103	−	4.46222e103i	0.249372	−	0.207794i
$958$	1.16177e103			0.0521589
$959$		−	2.87860e104i		−	1.24604i
$960$	−2.67353e102	−	3.20849e102i	−0.0111581	−	0.0133908i
$961$	−1.11239e104			−0.447651
$962$			1.47310e104i			0.571617i
$963$	−4.52985e104	−	8.30833e103i	−1.69498	−	0.310881i
$964$	−1.25608e104			−0.453233
$965$			3.44071e104i			1.19727i
$966$	7.01616e103	−	5.84634e103i	0.235451	−	0.196194i
$967$	3.75886e104			1.21655			0.608274	−	0.793727i	$-0.291862\pi$
$967$	3.75886e104			1.21655			0.608274	+	0.793727i	$0.291862\pi$
$968$		−	1.16225e104i		−	0.362797i
$969$	4.80099e102	+	5.76164e102i	0.0144544	+	0.0173466i
$970$	−2.45531e104			−0.713009
$971$		−	2.49458e104i		−	0.698755i	−0.936982	−	0.349378i	$-0.886393\pi$
$971$		−	2.49458e104i		−	0.698755i	0.936982	−	0.349378i	$-0.113607\pi$
$972$	−2.78869e104	+	9.61139e103i	−0.753497	+	0.259697i
$973$	1.65577e104			0.431568
$974$			3.33899e103i			0.0839560i
$975$	8.05742e103	−	6.71399e103i	0.195449	−	0.162862i
$976$	−2.10807e104			−0.493335
$977$		−	3.37599e104i		−	0.762240i	−0.924526	−	0.381120i	$-0.875538\pi$
$977$		−	3.37599e104i		−	0.762240i	0.924526	−	0.381120i	$-0.124462\pi$
$978$	−1.35964e104	−	1.63169e104i	−0.296185	−	0.355450i
$979$	−3.93263e104			−0.826587
$980$			6.30101e103i			0.127790i
$981$	−1.06859e103	+	5.82615e103i	−0.0209121	+	0.114016i
$982$	−1.85732e104			−0.350739
$983$			5.67680e104i			1.03450i	0.855834	+	0.517250i	$0.173044\pi$
$983$			5.67680e104i			1.03450i	−0.855834	+	0.517250i	$0.826956\pi$
$984$	6.06995e104	−	5.05790e104i	1.06747	−	0.889491i
$985$	−4.99215e103			−0.0847265
$986$		−	1.20869e103i		−	0.0197981i
$987$	5.97242e104	+	7.16747e104i	0.944170	+	1.13309i
$988$	−1.12214e104			−0.171220
$989$			3.92702e104i			0.578352i
$990$	−1.98435e104	−	3.63956e103i	−0.282089	−	0.0517388i
$991$	6.60727e104			0.906659			0.453330	−	0.891343i	$-0.350236\pi$
$991$	6.60727e104			0.906659			0.453330	+	0.891343i	$0.350236\pi$
$992$		−	5.63529e104i		−	0.746462i
$993$	8.41501e104	−	7.01196e104i	1.07605	−	0.896635i
$994$	4.85651e104			0.599516
$995$			4.12870e104i			0.492046i
$996$	−6.29038e104	−	7.54905e104i	−0.723769	−	0.868591i
$997$	−9.86067e104			−1.09541			−0.547704	−	0.836672i	$-0.684498\pi$
$997$	−9.86067e104			−1.09541			−0.547704	+	0.836672i	$0.684498\pi$
$998$			3.79371e104i			0.406907i
$999$	6.28686e104	+	1.11528e105i	0.651091	+	1.15502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.71.b.a.2.9	✓	22
3.2	odd	2	inner	3.71.b.a.2.14	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.71.b.a.2.9	✓	22	1.1	even	1	trivial
3.71.b.a.2.14	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)

\(f(q)\)	\(=\)	\(q-1.54812e10i q^{2} +(3.84365e16 - 3.20279e16i) q^{3} +9.40925e20 q^{4} +2.49363e24i q^{5} +(-4.95830e26 - 5.95043e26i) q^{6} -4.12745e29 q^{7} -3.28436e31i q^{8} +(4.51579e32 - 2.46209e33i) q^{9} +O(q^{10})\)	\(q-1.54812e10i q^{2} +(3.84365e16 - 3.20279e16i) q^{3} +9.40925e20 q^{4} +2.49363e24i q^{5} +(-4.95830e26 - 5.95043e26i) q^{6} -4.12745e29 q^{7} -3.28436e31i q^{8} +(4.51579e32 - 2.46209e33i) q^{9} +3.86044e34 q^{10} -2.08775e36i q^{11} +(3.61659e37 - 3.01359e37i) q^{12} +9.30805e38 q^{13} +6.38978e39i q^{14} +(7.98659e40 + 9.58466e40i) q^{15} +6.02391e41 q^{16} -1.16995e42i q^{17} +(-3.81160e43 - 6.99097e42i) q^{18} -1.28125e44 q^{19} +2.34632e45i q^{20} +(-1.58645e46 + 1.32194e46i) q^{21} -3.23209e46 q^{22} -2.85673e47i q^{23} +(-1.05191e48 - 1.26239e48i) q^{24} +2.25213e48 q^{25} -1.44100e49i q^{26} +(-6.14984e49 - 1.09097e50i) q^{27} -3.88362e50 q^{28} +6.67334e50i q^{29} +(1.48382e51 - 1.23642e51i) q^{30} +1.17156e52 q^{31} -4.81006e52i q^{32} +(-6.68664e52 - 8.02460e52i) q^{33} -1.81123e52 q^{34} -1.02923e54i q^{35} +(4.24901e53 - 2.31664e54i) q^{36} -1.02228e55 q^{37} +1.98352e54i q^{38} +(3.57769e55 - 2.98118e55i) q^{39} +8.18998e55 q^{40} +4.80829e56i q^{41} +(2.04651e56 + 2.45601e56i) q^{42} -1.37465e57 q^{43} -1.96442e57i q^{44} +(6.13954e57 + 1.12607e57i) q^{45} -4.42256e57 q^{46} -4.51793e58i q^{47} +(2.31538e58 - 1.92933e58i) q^{48} +2.68549e58 q^{49} -3.48656e58i q^{50} +(-3.74712e58 - 4.49690e58i) q^{51} +8.75818e59 q^{52} -1.76470e60i q^{53} +(-1.68895e60 + 9.52067e59i) q^{54} +5.20609e60 q^{55} +1.35560e61i q^{56} +(-4.92467e60 + 4.10357e60i) q^{57} +1.03311e61 q^{58} -1.74714e62i q^{59} +(7.51478e61 + 9.01844e61i) q^{60} -3.49951e62 q^{61} -1.81372e62i q^{62} +(-1.86387e62 + 1.01621e63i) q^{63} -3.34753e61 q^{64} +2.32109e63i q^{65} +(-1.24230e63 + 1.03517e63i) q^{66} +8.78273e63 q^{67} -1.10084e63i q^{68} +(-9.14953e63 - 1.09803e64i) q^{69} -1.59338e64 q^{70} -7.60044e64i q^{71} +(-8.08637e64 - 1.48314e64i) q^{72} +2.57532e65 q^{73} +1.58261e65i q^{74} +(8.65640e64 - 7.21310e64i) q^{75} -1.20556e65 q^{76} +8.61709e65i q^{77} +(-4.61521e65 - 5.53869e65i) q^{78} -1.03334e66 q^{79} +1.50214e66i q^{80} +(-5.85794e66 - 2.22365e66i) q^{81} +7.44380e66 q^{82} -2.08734e67i q^{83} +(-1.49273e67 + 1.24384e67i) q^{84} +2.91744e66 q^{85} +2.12812e67i q^{86} +(2.13733e67 + 2.56500e67i) q^{87} -6.85692e67 q^{88} -1.88367e68i q^{89} +(1.74329e67 - 9.50472e67i) q^{90} -3.84185e68 q^{91} -2.68797e68i q^{92} +(4.50309e68 - 3.75228e68i) q^{93} -6.99429e68 q^{94} -3.19496e68i q^{95} +(-1.54056e69 - 1.84882e69i) q^{96} -6.36018e69 q^{97} -4.15745e68i q^{98} +(-5.14022e69 - 9.42784e68i) 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

Fields

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Groups

Database

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