LMFDB - Embedded newform 3.71.b.a.2.6

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			2.6
Character	$\chi$	$=$	3.2
Dual form			3.71.b.a.2.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.74673e10i q^{2} +(-7.56180e15 - 4.94568e16i) q^{3} -2.23206e20 q^{4} +1.07403e24i q^{5} +(-1.85301e27 + 2.83320e26i) q^{6} +6.73954e29 q^{7} -3.58706e31i q^{8} +(-2.38879e33 + 7.47965e32i) q^{9} +O(q^{10})$	\(q-3.74673e10i q^{2} +(-7.56180e15 - 4.94568e16i) q^{3} -2.23206e20 q^{4} +1.07403e24i q^{5} +(-1.85301e27 + 2.83320e26i) q^{6} +6.73954e29 q^{7} -3.58706e31i q^{8} +(-2.38879e33 + 7.47965e32i) q^{9} +4.02409e34 q^{10} +9.56510e35i q^{11} +(1.68784e36 + 1.10391e37i) q^{12} +9.40335e38 q^{13} -2.52512e40i q^{14} +(5.31179e40 - 8.12158e39i) q^{15} -1.60749e42 q^{16} +1.38452e43i q^{17} +(2.80242e43 + 8.95016e43i) q^{18} -4.21700e44 q^{19} -2.39729e44i q^{20} +(-5.09631e45 - 3.33316e46i) q^{21} +3.58378e46 q^{22} +7.41679e47i q^{23} +(-1.77405e48 + 2.71247e47i) q^{24} +7.31680e48 q^{25} -3.52318e49i q^{26} +(5.50556e49 + 1.12486e50i) q^{27} -1.50431e50 q^{28} +6.56664e50i q^{29} +(-3.04294e50 - 1.99018e51i) q^{30} +2.15139e52 q^{31} +1.78798e52i q^{32} +(4.73059e52 - 7.23294e51i) q^{33} +5.18742e53 q^{34} +7.23844e53i q^{35} +(5.33194e53 - 1.66951e53i) q^{36} +4.93106e54 q^{37} +1.57999e55i q^{38} +(-7.11063e54 - 4.65060e55i) q^{39} +3.85260e55 q^{40} -5.23895e55i q^{41} +(-1.24884e57 + 1.90945e56i) q^{42} +1.48232e57 q^{43} -2.13499e56i q^{44} +(-8.03335e56 - 2.56563e57i) q^{45} +2.77887e58 q^{46} +1.27739e58i q^{47} +(1.21555e58 + 7.95014e58i) q^{48} +3.10710e59 q^{49} -2.74141e59i q^{50} +(6.84738e59 - 1.04695e59i) q^{51} -2.09889e59 q^{52} +3.94947e60i q^{53} +(4.21455e60 - 2.06278e60i) q^{54} -1.02732e60 q^{55} -2.41752e61i q^{56} +(3.18881e60 + 2.08559e61i) q^{57} +2.46034e61 q^{58} +9.57573e61i q^{59} +(-1.18563e61 + 1.81279e60i) q^{60} -2.37768e61 q^{61} -8.06068e62i q^{62} +(-1.60994e63 + 5.04094e62i) q^{63} -1.22788e63 q^{64} +1.00994e63i q^{65} +(-2.70999e62 - 1.77242e63i) q^{66} -8.71513e63 q^{67} -3.09033e63i q^{68} +(3.66811e64 - 5.60843e63i) q^{69} +2.71205e64 q^{70} +4.27746e64i q^{71} +(2.68300e64 + 8.56876e64i) q^{72} +1.50425e65 q^{73} -1.84754e65i q^{74} +(-5.53282e64 - 3.61865e65i) q^{75} +9.41260e64 q^{76} +6.44644e65i q^{77} +(-1.74245e66 + 2.66416e65i) q^{78} -2.81029e66 q^{79} -1.72649e66i q^{80} +(5.14688e66 - 3.57347e66i) q^{81} -1.96289e66 q^{82} +1.40793e66i q^{83} +(1.13753e66 + 7.43982e66i) q^{84} -1.48701e67 q^{85} -5.55387e67i q^{86} +(3.24765e67 - 4.96556e66i) q^{87} +3.43106e67 q^{88} -8.71916e67i q^{89} +(-9.61271e67 + 3.00988e67i) q^{90} +6.33743e68 q^{91} -1.65547e68i q^{92} +(-1.62684e68 - 1.06401e69i) q^{93} +4.78603e68 q^{94} -4.52917e68i q^{95} +(8.84276e68 - 1.35203e68i) q^{96} -5.94495e69 q^{97} -1.16415e70i q^{98} +(-7.15436e68 - 2.28491e69i) 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 $

$2$		−	3.74673e10i		−	1.09044i	−0.838292	−	0.545221i	$-0.816446\pi$
$2$		−	3.74673e10i		−	1.09044i	0.838292	−	0.545221i	$-0.183554\pi$
$3$	−7.56180e15	−	4.94568e16i	−0.151141	−	0.988512i
$3$	−7.56180e15	−	4.94568e16i	−0.151141	−	0.988512i
$4$	−2.23206e20			−0.189063
$5$			1.07403e24i			0.369033i	0.982829	+	0.184516i	$0.0590719\pi$
$5$			1.07403e24i			0.369033i	−0.982829	+	0.184516i	$0.940928\pi$
$6$	−1.85301e27	+	2.83320e26i	−1.07791	+	0.164810i
$7$	6.73954e29			1.77909			0.889547	−	0.456844i	$-0.151020\pi$
$7$	6.73954e29			1.77909			0.889547	+	0.456844i	$0.151020\pi$
$8$		−	3.58706e31i		−	0.884279i
$9$	−2.38879e33	+	7.47965e32i	−0.954313	+	0.298809i
$10$	4.02409e34			0.402409
$11$			9.56510e35i			0.340365i	0.985413	+	0.170183i	$0.0544358\pi$
$11$			9.56510e35i			0.340365i	−0.985413	+	0.170183i	$0.945564\pi$
$12$	1.68784e36	+	1.10391e37i	0.0285751	+	0.186891i
$13$	9.40335e38			0.966641			0.483321	−	0.875443i	$-0.339431\pi$
$13$	9.40335e38			0.966641			0.483321	+	0.875443i	$0.339431\pi$
$14$		−	2.52512e40i		−	1.94000i
$15$	5.31179e40	−	8.12158e39i	0.364793	−	0.0557759i
$16$	−1.60749e42			−1.15332
$17$			1.38452e43i			1.19011i	0.803686	+	0.595054i	$0.202869\pi$
$17$			1.38452e43i			1.19011i	−0.803686	+	0.595054i	$0.797131\pi$
$18$	2.80242e43	+	8.95016e43i	0.325834	+	1.04062i
$19$	−4.21700e44			−0.738971			−0.369485	−	0.929237i	$-0.620466\pi$
$19$	−4.21700e44			−0.738971			−0.369485	+	0.929237i	$0.620466\pi$
$20$		−	2.39729e44i		−	0.0697705i
$21$	−5.09631e45	−	3.33316e46i	−0.268893	−	1.75866i
$22$	3.58378e46			0.371149
$23$			7.41679e47i			1.62085i	0.585845	+	0.810423i	$0.300763\pi$
$23$			7.41679e47i			1.62085i	−0.585845	+	0.810423i	$0.699237\pi$
$24$	−1.77405e48	+	2.71247e47i	−0.874121	+	0.133651i
$25$	7.31680e48			0.863815
$26$		−	3.52318e49i		−	1.05407i
$27$	5.50556e49	+	1.12486e50i	0.439612	+	0.898188i
$28$	−1.50431e50			−0.336361
$29$			6.56664e50i			0.429945i	0.976620	+	0.214973i	$0.0689663\pi$
$29$			6.56664e50i			0.429945i	−0.976620	+	0.214973i	$0.931034\pi$
$30$	−3.04294e50	−	1.99018e51i	−0.0608203	−	0.397786i
$31$	2.15139e52			1.36477			0.682386	−	0.730992i	$-0.260942\pi$
$31$	2.15139e52			1.36477			0.682386	+	0.730992i	$0.260942\pi$
$32$			1.78798e52i			0.373347i
$33$	4.73059e52	−	7.23294e51i	0.336455	−	0.0514431i
$34$	5.18742e53			1.29774
$35$			7.23844e53i			0.656544i
$36$	5.33194e53	−	1.66951e53i	0.180425	−	0.0564937i
$37$	4.93106e54			0.639559			0.319779	−	0.947492i	$-0.396391\pi$
$37$	4.93106e54			0.639559			0.319779	+	0.947492i	$0.396391\pi$
$38$			1.57999e55i			0.805804i
$39$	−7.11063e54	−	4.65060e55i	−0.146099	−	0.955537i
$40$	3.85260e55			0.326328
$41$		−	5.23895e55i		−	0.186986i	−0.995620	−	0.0934930i	$-0.970197\pi$
$41$		−	5.23895e55i		−	0.186986i	0.995620	−	0.0934930i	$-0.0298033\pi$
$42$	−1.24884e57	+	1.90945e56i	−1.91771	+	0.293213i
$43$	1.48232e57			0.998958			0.499479	−	0.866326i	$-0.333525\pi$
$43$	1.48232e57			0.998958			0.499479	+	0.866326i	$0.333525\pi$
$44$		−	2.13499e56i		−	0.0643505i
$45$	−8.03335e56	−	2.56563e57i	−0.110270	−	0.352173i
$46$	2.77887e58			1.76744
$47$			1.27739e58i			0.382735i	0.981518	+	0.191367i	$0.0612922\pi$
$47$			1.27739e58i			0.382735i	−0.981518	+	0.191367i	$0.938708\pi$
$48$	1.21555e58	+	7.95014e58i	0.174313	+	1.14007i
$49$	3.10710e59			2.16517
$50$		−	2.74141e59i		−	0.941940i
$51$	6.84738e59	−	1.04695e59i	1.17644	−	0.179874i
$52$	−2.09889e59			−0.182756
$53$			3.94947e60i			1.76556i	0.469782	+	0.882782i	$0.344332\pi$
$53$			3.94947e60i			1.76556i	−0.469782	+	0.882782i	$0.655668\pi$
$54$	4.21455e60	−	2.06278e60i	0.979421	−	0.479371i
$55$	−1.02732e60			−0.125606
$56$		−	2.41752e61i		−	1.57322i
$57$	3.18881e60	+	2.08559e61i	0.111689	+	0.730481i
$58$	2.46034e61			0.468830
$59$			9.57573e61i			1.00312i	0.865124	+	0.501558i	$0.167240\pi$
$59$			9.57573e61i			1.00312i	−0.865124	+	0.501558i	$0.832760\pi$
$60$	−1.18563e61	+	1.81279e60i	−0.0689689	+	0.0105452i
$61$	−2.37768e61			−0.0775549			−0.0387774	−	0.999248i	$-0.512346\pi$
$61$	−2.37768e61			−0.0775549			−0.0387774	+	0.999248i	$0.512346\pi$
$62$		−	8.06068e62i		−	1.48820i
$63$	−1.60994e63	+	5.04094e62i	−1.69781	+	0.531609i
$64$	−1.22788e63			−0.746205
$65$			1.00994e63i			0.356722i
$66$	−2.70999e62	−	1.77242e63i	−0.0560957	−	0.366885i
$67$	−8.71513e63			−1.06575			−0.532875	−	0.846194i	$-0.678889\pi$
$67$	−8.71513e63			−1.06575			−0.532875	+	0.846194i	$0.678889\pi$
$68$		−	3.09033e63i		−	0.225005i
$69$	3.66811e64	−	5.60843e63i	1.60223	−	0.244976i
$70$	2.71205e64			0.715923
$71$			4.27746e64i			0.687296i	0.939098	+	0.343648i	$0.111663\pi$
$71$			4.27746e64i			0.687296i	−0.939098	+	0.343648i	$0.888337\pi$
$72$	2.68300e64	+	8.56876e64i	0.264231	+	0.843879i
$73$	1.50425e65			0.914156			0.457078	−	0.889427i	$-0.348896\pi$
$73$	1.50425e65			0.914156			0.457078	+	0.889427i	$0.348896\pi$
$74$		−	1.84754e65i		−	0.697401i
$75$	−5.53282e64	−	3.61865e65i	−0.130558	−	0.853892i
$76$	9.41260e64			0.139712
$77$			6.44644e65i			0.605542i
$78$	−1.74245e66	+	2.66416e65i	−1.04196	+	0.159312i
$79$	−2.81029e66			−1.07598			−0.537988	−	0.842952i	$-0.680815\pi$
$79$	−2.81029e66			−1.07598			−0.537988	+	0.842952i	$0.680815\pi$
$80$		−	1.72649e66i		−	0.425612i
$81$	5.14688e66	−	3.57347e66i	0.821426	−	0.570314i
$82$	−1.96289e66			−0.203897
$83$			1.40793e66i			0.0956856i	0.998855	+	0.0478428i	$0.0152346\pi$
$83$			1.40793e66i			0.0956856i	−0.998855	+	0.0478428i	$0.984765\pi$
$84$	1.13753e66	+	7.43982e66i	0.0508378	+	0.332497i
$85$	−1.48701e67			−0.439189
$86$		−	5.55387e67i		−	1.08931i
$87$	3.24765e67	−	4.96556e66i	0.425006	−	0.0649823i
$88$	3.43106e67			0.300978
$89$		−	8.71916e67i		−	0.515020i	−0.966276	−	0.257510i	$-0.917098\pi$
$89$		−	8.71916e67i		−	0.515020i	0.966276	−	0.257510i	$-0.0829021\pi$
$90$	−9.61271e67	+	3.00988e67i	−0.384024	+	0.120243i
$91$	6.33743e68			1.71975
$92$		−	1.65547e68i		−	0.306442i
$93$	−1.62684e68	−	1.06401e69i	−0.206273	−	1.34909i
$94$	4.78603e68			0.417350
$95$		−	4.52917e68i		−	0.272704i
$96$	8.84276e68	−	1.35203e68i	0.369058	−	0.0564279i
$97$	−5.94495e69			−1.72639			−0.863193	−	0.504875i	$-0.831539\pi$
$97$	−5.94495e69			−1.72639			−0.863193	+	0.504875i	$0.831539\pi$
$98$		−	1.16415e70i		−	2.36100i
$99$	−7.15436e68	−	2.28491e69i	−0.101704	−	0.324815i
$100$	−1.63315e69			−0.163315
$101$		−	6.40697e69i		−	0.452277i	−0.974095	−	0.226139i	$-0.927390\pi$
$101$		−	6.40697e69i		−	0.452277i	0.974095	−	0.226139i	$-0.0726102\pi$
$102$	−3.92262e69	−	2.56553e70i	−0.196142	−	1.28284i
$103$	1.41045e70			0.501251			0.250625	−	0.968084i	$-0.419364\pi$
$103$	1.41045e70			0.501251			0.250625	+	0.968084i	$0.419364\pi$
$104$		−	3.37304e70i		−	0.854781i
$105$	3.57990e70	−	5.47357e69i	0.649002	−	0.0992305i
$106$	1.47976e71			1.92525
$107$		−	1.78393e71i		−	1.67088i	−0.549578	−	0.835442i	$-0.685212\pi$
$107$		−	1.78393e71i		−	1.67088i	0.549578	−	0.835442i	$-0.314788\pi$
$108$	−1.22887e70	−	2.51076e70i	−0.0831144	−	0.169814i
$109$	7.39284e70			0.362146			0.181073	−	0.983470i	$-0.442043\pi$
$109$	7.39284e70			0.362146			0.181073	+	0.983470i	$0.442043\pi$
$110$			3.84908e70i			0.136966i
$111$	−3.72877e70	−	2.43875e71i	−0.0966634	−	0.632212i
$112$	−1.08337e72			−2.05186
$113$		−	8.68793e71i		−	1.20551i	−0.797926	−	0.602755i	$-0.794070\pi$
$113$		−	8.68793e71i		−	1.20551i	0.797926	−	0.602755i	$-0.205930\pi$
$114$	7.81414e71	−	1.19476e71i	0.796547	−	0.121790i
$115$	−7.96583e71			−0.598145
$116$		−	1.46572e71i		−	0.0812868i
$117$	−2.24627e72	+	7.03338e71i	−0.922478	+	0.288841i
$118$	3.58777e72			1.09384
$119$			9.33101e72i			2.11731i
$120$	−2.91326e71	−	1.90537e72i	−0.0493215	−	0.322579i
$121$	6.98256e72			0.884151
$122$			8.90852e71i			0.0845691i
$123$	−2.59101e72	+	3.96159e71i	−0.184838	+	0.0282612i
$124$	−4.80204e72			−0.258028
$125$			1.69558e73i			0.687809i
$126$	1.88870e73	+	6.03200e73i	0.579689	+	1.85136i
$127$	−4.17415e73			−0.971490			−0.485745	−	0.874101i	$-0.661452\pi$
$127$	−4.17415e73			−0.971490			−0.485745	+	0.874101i	$0.661452\pi$
$128$			6.71142e73i			1.18704i
$129$	−1.12090e73	−	7.33110e73i	−0.150983	−	0.987482i
$130$	3.78399e73			0.388985
$131$			4.79654e73i			0.377079i	0.982066	+	0.188540i	$0.0603754\pi$
$131$			4.79654e73i			0.377079i	−0.982066	+	0.188540i	$0.939625\pi$
$132$	−1.05590e73	+	1.61444e72i	−0.0636113	+	0.00972599i
$133$	−2.84206e74			−1.31470
$134$			3.26532e74i			1.16214i
$135$	−1.20813e74	+	5.91311e73i	−0.331461	+	0.162231i
$136$	4.96636e74			1.05239
$137$		−	3.85815e74i		−	0.632643i	−0.948652	−	0.316322i	$-0.897552\pi$
$137$		−	3.85815e74i		−	0.632643i	0.948652	−	0.316322i	$-0.102448\pi$
$138$	−2.10133e74	−	1.37434e75i	−0.267132	−	1.74713i
$139$	−2.92083e73			−0.0288395			−0.0144198	−	0.999896i	$-0.504590\pi$
$139$	−2.92083e73			−0.0288395			−0.0144198	+	0.999896i	$0.504590\pi$
$140$		−	1.61567e74i		−	0.124128i
$141$	6.31755e74	−	9.65936e73i	0.378338	−	0.0578468i
$142$	1.60265e75			0.749457
$143$			8.99440e74i			0.329011i
$144$	3.83996e75	−	1.20235e75i	1.10063	−	0.344622i
$145$	−7.05275e74			−0.158664
$146$		−	5.63602e75i		−	0.996834i
$147$	−2.34953e75	−	1.53667e76i	−0.327246	−	2.14030i
$148$	−1.10064e75			−0.120917
$149$			7.65280e75i			0.664204i	0.943244	+	0.332102i	$0.107758\pi$
$149$			7.65280e75i			0.664204i	−0.943244	+	0.332102i	$0.892242\pi$
$150$	−1.35581e76	+	2.07300e75i	−0.931119	+	0.142365i
$151$	−1.71428e76			−0.933016			−0.466508	−	0.884517i	$-0.654488\pi$
$151$	−1.71428e76			−0.933016			−0.466508	+	0.884517i	$0.654488\pi$
$152$			1.51266e76i			0.653456i
$153$	−1.03557e76	−	3.30733e76i	−0.355615	−	1.13574i
$154$	2.41530e76			0.660308
$155$			2.31065e76i			0.503646i
$156$	1.58714e75	+	1.03804e76i	0.0276219	+	0.180657i
$157$	4.83802e76			0.673256			0.336628	−	0.941638i	$-0.390714\pi$
$157$	4.83802e76			0.673256			0.336628	+	0.941638i	$0.390714\pi$
$158$			1.05294e77i			1.17329i
$159$	1.95328e77	−	2.98651e76i	1.74528	−	0.266849i
$160$	−1.92033e76			−0.137777
$161$			4.99857e77i			2.88364i
$162$	−1.33888e77	−	1.92840e77i	−0.621895	−	0.895718i
$163$	−2.68918e77			−1.00706			−0.503528	−	0.863979i	$-0.667965\pi$
$163$	−2.68918e77			−1.00706			−0.503528	+	0.863979i	$0.667965\pi$
$164$			1.16937e76i			0.0353521i
$165$	7.76837e75	+	5.08078e76i	0.0189842	+	0.124163i
$166$	5.27512e76			0.104340
$167$		−	2.52508e76i		−	0.0404761i	−0.999795	−	0.0202380i	$-0.993558\pi$
$167$		−	2.52508e76i		−	0.0404761i	0.999795	−	0.0202380i	$-0.00644241\pi$
$168$	−1.19563e78	+	1.82808e77i	−1.55514	+	0.237777i
$169$	−6.20825e76			−0.0656046
$170$			5.57142e77i			0.478910i
$171$	1.00735e78	−	3.15417e77i	0.705209	−	0.220811i
$172$	−3.30864e77			−0.188866
$173$		−	1.78943e78i		−	0.833877i	−0.908935	−	0.416938i	$-0.863103\pi$
$173$		−	1.78943e78i		−	0.833877i	0.908935	−	0.416938i	$-0.136897\pi$
$174$	−1.86046e77	−	1.21681e78i	−0.0708594	−	0.463445i
$175$	4.93118e78			1.53681
$176$		−	1.53758e78i		−	0.392550i
$177$	4.73585e78	−	7.24098e77i	0.991593	−	0.151612i
$178$	−3.26683e78			−0.561600
$179$		−	3.48527e78i		−	0.492471i	−0.969210	−	0.246235i	$-0.920806\pi$
$179$		−	3.48527e78i		−	0.492471i	0.969210	−	0.246235i	$-0.0791937\pi$
$180$	1.79309e77	+	5.72664e77i	0.0208480	+	0.0665828i
$181$	−1.09292e79			−1.04674			−0.523371	−	0.852105i	$-0.675326\pi$
$181$	−1.09292e79			−1.04674			−0.523371	+	0.852105i	$0.675326\pi$
$182$		−	2.37446e79i		−	1.87528i
$183$	1.79795e77	+	1.17592e78i	0.0117217	+	0.0766639i
$184$	2.66045e79			1.43328
$185$			5.29610e78i			0.236018i
$186$	−3.98655e79	+	6.09533e78i	−1.47111	+	0.224928i
$187$	−1.32431e79			−0.405072
$188$		−	2.85121e78i		−	0.0723610i
$189$	3.71049e79	+	7.58105e79i	0.782111	+	1.59796i
$190$	−1.69696e79			−0.297368
$191$		−	1.08457e80i		−	1.58158i	−0.612088	−	0.790789i	$-0.709670\pi$
$191$		−	1.08457e80i		−	1.58158i	0.612088	−	0.790789i	$-0.290330\pi$
$192$	9.28502e78	+	6.07272e79i	0.112782	+	0.737633i
$193$	−5.69826e79			−0.577080			−0.288540	−	0.957468i	$-0.593170\pi$
$193$	−5.69826e79			−0.577080			−0.288540	+	0.957468i	$0.593170\pi$
$194$			2.22741e80i			1.88252i
$195$	4.99486e79	−	7.63701e78i	0.352624	−	0.0539153i
$196$	−6.93525e79			−0.409354
$197$			9.63743e79i			0.476040i	0.971260	+	0.238020i	$0.0764983\pi$
$197$			9.63743e79i			0.476040i	−0.971260	+	0.238020i	$0.923502\pi$
$198$	−8.56092e79	+	2.68055e79i	−0.354192	+	0.110903i
$199$	5.16960e80			1.79308			0.896540	−	0.442963i	$-0.146073\pi$
$199$	5.16960e80			1.79308			0.896540	+	0.442963i	$0.146073\pi$
$200$		−	2.62458e80i		−	0.763854i
$201$	6.59021e79	+	4.31022e80i	0.161078	+	1.05351i
$202$	−2.40052e80			−0.493182
$203$			4.42561e80i			0.764913i
$204$	−1.52838e80	+	2.33685e79i	−0.222421	+	0.0340075i
$205$	5.62677e79			0.0690039
$206$		−	5.28458e80i		−	0.546585i
$207$	−5.54750e80	−	1.77172e81i	−0.484323	−	1.54679i
$208$	−1.51158e81			−1.11484
$209$		−	4.03360e80i		−	0.251520i
$210$	−2.05080e80	−	1.34129e81i	−0.108205	−	0.707698i
$211$	2.13952e81			0.955938			0.477969	−	0.878377i	$-0.341373\pi$
$211$	2.13952e81			0.955938			0.477969	+	0.878377i	$0.341373\pi$
$212$		−	8.81547e80i		−	0.333803i
$213$	2.11550e81	−	3.23453e80i	0.679401	−	0.103878i
$214$	−6.68392e81			−1.82200
$215$			1.59206e81i			0.368648i
$216$	4.03495e81	−	1.97488e81i	0.794249	−	0.388740i
$217$	1.44994e82			2.42806
$218$		−	2.76990e81i		−	0.394899i
$219$	−1.13749e81	−	7.43955e81i	−0.138166	−	0.903655i
$220$	2.29304e80			0.0237475
$221$			1.30191e82i			1.15041i
$222$	−9.13732e81	+	1.39707e81i	−0.689390	+	0.105406i
$223$	6.95888e81			0.448610			0.224305	−	0.974519i	$-0.427989\pi$
$223$	6.95888e81			0.448610			0.224305	+	0.974519i	$0.427989\pi$
$224$			1.20501e82i			0.664219i
$225$	−1.74783e82	+	5.47271e81i	−0.824350	+	0.258116i
$226$	−3.25513e82			−1.31454
$227$			7.59143e81i			0.262675i	0.991338	+	0.131337i	$0.0419271\pi$
$227$			7.59143e81i			0.262675i	−0.991338	+	0.131337i	$0.958073\pi$
$228$	−7.11762e80	−	4.65517e81i	−0.0211162	−	0.138107i
$229$	−3.55819e82			−0.905705			−0.452853	−	0.891585i	$-0.649594\pi$
$229$	−3.55819e82			−0.905705			−0.452853	+	0.891585i	$0.649594\pi$
$230$			2.98458e82i			0.652242i
$231$	3.18820e82	−	4.87467e81i	0.598586	−	0.0915221i
$232$	2.35550e82			0.380192
$233$			3.22793e82i			0.448194i	0.974567	+	0.224097i	$0.0719433\pi$
$233$			3.22793e82i			0.448194i	−0.974567	+	0.224097i	$0.928057\pi$
$234$	2.63522e82	+	8.41615e82i	0.314964	+	1.00591i
$235$	−1.37195e82			−0.141242
$236$		−	2.13736e82i		−	0.189652i
$237$	2.12509e82	+	1.38988e83i	0.162624	+	1.06362i
$238$	3.49608e83			2.30881
$239$		−	3.24392e83i		−	1.84988i	−0.380116	−	0.924939i	$-0.624116\pi$
$239$		−	3.24392e83i		−	1.84988i	0.380116	−	0.924939i	$-0.375884\pi$
$240$	−8.53866e82	+	1.30554e82i	−0.420723	+	0.0643273i
$241$	−2.13929e83			−0.911326			−0.455663	−	0.890152i	$-0.650598\pi$
$241$	−2.13929e83			−0.911326			−0.455663	+	0.890152i	$0.650598\pi$
$242$		−	2.61618e83i		−	0.964115i
$243$	−2.15652e83	−	2.27526e83i	−0.687914	−	0.725792i
$244$	5.30713e81			0.0146628
$245$			3.33711e83i			0.799020i
$246$	1.48430e82	+	9.70783e82i	0.0308172	+	0.201555i
$247$	−3.96539e83			−0.714319
$248$		−	7.71718e83i		−	1.20684i
$249$	6.96315e82	−	1.06465e82i	0.0945864	−	0.0144620i
$250$	6.35288e83			0.750015
$251$		−	1.84142e84i		−	1.89048i	−0.326376	−	0.945240i	$-0.605828\pi$
$251$		−	1.84142e84i		−	1.89048i	0.326376	−	0.945240i	$-0.394172\pi$
$252$	3.59348e83	−	1.12517e83i	0.320993	−	0.100508i
$253$	−7.09423e83			−0.551680
$254$			1.56394e84i			1.05935i
$255$	1.12445e83	+	7.35427e83i	0.0663793	+	0.434144i
$256$	1.06496e84			0.548193
$257$			2.78141e84i			1.24912i	0.780976	+	0.624562i	$0.214722\pi$
$257$			2.78141e84i			1.24912i	−0.780976	+	0.624562i	$0.785278\pi$
$258$	−2.74676e84	+	4.19972e83i	−1.07679	+	0.164638i
$259$	3.32331e84			1.13783
$260$		−	2.25426e83i		−	0.0674430i
$261$	−4.91162e83	−	1.56863e84i	−0.128472	−	0.410302i
$262$	1.79713e84			0.411183
$263$			2.55167e84i			0.510944i	0.966817	+	0.255472i	$0.0822308\pi$
$263$			2.55167e84i			0.510944i	−0.966817	+	0.255472i	$0.917769\pi$
$264$	−2.59450e83	−	1.69689e84i	−0.0454901	−	0.297521i
$265$	−4.24184e84			−0.651551
$266$			1.06484e85i			1.43360i
$267$	−4.31222e84	+	6.59326e83i	−0.509104	+	0.0778406i
$268$	1.94527e84			0.201494
$269$			1.62397e85i			1.47655i	0.674500	+	0.738275i	$0.264359\pi$
$269$			1.62397e85i			1.47655i	−0.674500	+	0.738275i	$0.735641\pi$
$270$	2.21548e84	+	4.52654e84i	0.176904	+	0.361439i
$271$	−1.84202e84			−0.129231			−0.0646157	−	0.997910i	$-0.520582\pi$
$271$	−1.84202e84			−0.129231			−0.0646157	+	0.997910i	$0.520582\pi$
$272$		−	2.22560e85i		−	1.37257i
$273$	−4.79224e84	−	3.13429e85i	−0.259924	−	1.69999i
$274$	−1.44554e85			−0.689861
$275$			6.99859e84i			0.294013i
$276$	−8.18744e84	+	1.25184e84i	−0.302922	+	0.0463159i
$277$	4.99183e85			1.62730			0.813650	−	0.581355i	$-0.197477\pi$
$277$	4.99183e85			1.62730			0.813650	+	0.581355i	$0.197477\pi$
$278$			1.09436e84i			0.0314478i
$279$	−5.13923e85	+	1.60917e85i	−1.30242	+	0.407806i
$280$	2.59648e85			0.580568
$281$		−	8.02187e85i		−	1.58327i	−0.610995	−	0.791634i	$-0.709231\pi$
$281$		−	8.02187e85i		−	1.58327i	0.610995	−	0.791634i	$-0.290769\pi$
$282$	−3.61910e84	−	2.36702e85i	−0.0630786	−	0.412555i
$283$	1.22156e86			1.88101			0.940505	−	0.339780i	$-0.110353\pi$
$283$	1.22156e86			1.88101			0.940505	+	0.339780i	$0.110353\pi$
$284$		−	9.54757e84i		−	0.129942i
$285$	−2.23998e85	+	3.42487e84i	−0.269572	+	0.0412167i
$286$	3.36996e85			0.358768
$287$		−	3.53081e85i		−	0.332665i
$288$	−1.33734e85	−	4.27111e85i	−0.111559	−	0.356290i
$289$	−5.63496e85			−0.416358
$290$			2.64247e85i			0.173014i
$291$	4.49546e85	+	2.94018e86i	0.260927	+	1.70655i
$292$	−3.35758e85			−0.172833
$293$		−	2.05294e86i		−	0.937582i	−0.883309	−	0.468791i	$-0.844690\pi$
$293$		−	2.05294e86i		−	0.937582i	0.883309	−	0.468791i	$-0.155310\pi$
$294$	−5.75750e86	+	8.80305e85i	−2.33387	+	0.356843i
$295$	−1.02846e86			−0.370183
$296$		−	1.76880e86i		−	0.565549i
$297$	−1.07594e86	+	5.26612e85i	−0.305712	+	0.149629i
$298$	2.86730e86			0.724275
$299$			6.97427e86i			1.56678i
$300$	1.23496e85	+	8.07706e85i	0.0246836	+	0.161439i
$301$	9.99018e86			1.77724
$302$			6.42295e86i			1.01740i
$303$	−3.16868e86	+	4.84483e85i	−0.447081	+	0.0683575i
$304$	6.77878e86			0.852268
$305$		−	2.55369e85i		−	0.0286203i
$306$	−1.23917e87	+	3.88001e86i	−1.23845	+	0.387777i
$307$	1.48515e87			1.32412			0.662058	−	0.749453i	$-0.269683\pi$
$307$	1.48515e87			1.32412			0.662058	+	0.749453i	$0.269683\pi$
$308$		−	1.43888e86i		−	0.114486i
$309$	−1.06656e86	−	6.97564e86i	−0.0757594	−	0.495493i
$310$	8.65739e86			0.549196
$311$		−	1.60180e87i		−	0.907808i	−0.891051	−	0.453904i	$-0.850031\pi$
$311$		−	1.60180e87i		−	0.907808i	0.891051	−	0.453904i	$-0.149969\pi$
$312$	−1.66820e87	+	2.55063e86i	−0.844962	+	0.129192i
$313$	−2.72246e87			−1.23285			−0.616423	−	0.787415i	$-0.711419\pi$
$313$	−2.72246e87			−1.23285			−0.616423	+	0.787415i	$0.711419\pi$
$314$		−	1.81268e87i		−	0.734146i
$315$	−5.41410e86	−	1.72911e87i	−0.196181	−	0.626548i
$316$	6.27274e86			0.203427
$317$			4.70724e87i			1.36676i	0.730063	+	0.683380i	$0.239491\pi$
$317$			4.70724e87i			1.36676i	−0.730063	+	0.683380i	$0.760509\pi$
$318$	−1.11897e87	−	7.31842e87i	−0.290983	−	1.90313i
$319$	−6.28106e86			−0.146339
$320$		−	1.31878e87i		−	0.275374i
$321$	−8.82276e87	+	1.34898e87i	−1.65169	+	0.252539i
$322$	1.87283e88			3.14444
$323$		−	5.83851e87i		−	0.879455i
$324$	−1.14882e87	+	7.97621e86i	−0.155301	+	0.107825i
$325$	6.88024e87			0.834999
$326$			1.00756e88i			1.09814i
$327$	−5.59032e86	−	3.65626e87i	−0.0547350	−	0.357986i
$328$	−1.87924e87			−0.165348
$329$			8.60901e87i			0.680921i
$330$	1.90363e87	−	2.91060e86i	0.135393	−	0.0207011i
$331$	−2.84891e86			−0.0182263			−0.00911317	−	0.999958i	$-0.502901\pi$
$331$	−2.84891e86			−0.0182263			−0.00911317	+	0.999958i	$0.502901\pi$
$332$		−	3.14258e86i		−	0.0180906i
$333$	−1.17793e88	+	3.68826e87i	−0.610339	+	0.191106i
$334$	−9.46079e86			−0.0441368
$335$		−	9.36028e87i		−	0.393297i
$336$	8.19227e87	+	5.35802e88i	0.310120	+	2.02829i
$337$	−3.03137e88			−1.03417			−0.517086	−	0.855933i	$-0.672983\pi$
$337$	−3.03137e88			−1.03417			−0.517086	+	0.855933i	$0.672983\pi$
$338$			2.32606e87i			0.0715380i
$339$	−4.29677e88	+	6.56964e87i	−1.19166	+	0.182202i
$340$	3.31910e87			0.0830344
$341$			2.05783e88i			0.464521i
$342$	−1.18178e88	−	3.77428e88i	−0.240782	−	0.768989i
$343$	1.12690e89			2.07295
$344$		−	5.31719e88i		−	0.883358i
$345$	6.02360e87	+	3.93964e88i	0.0904041	+	0.591274i
$346$	−6.70452e88			−0.909294
$347$			7.95172e88i			0.974831i	0.873170	+	0.487416i	$0.162060\pi$
$347$			7.95172e88i			0.974831i	−0.873170	+	0.487416i	$0.837940\pi$
$348$	−7.24896e87	+	1.10835e87i	−0.0803530	+	0.0122857i
$349$	3.95452e88			0.396464			0.198232	−	0.980155i	$-0.436480\pi$
$349$	3.95452e88			0.396464			0.198232	+	0.980155i	$0.436480\pi$
$350$		−	1.84758e89i		−	1.67580i
$351$	5.17707e88	+	1.05775e89i	0.424947	+	0.868225i
$352$	−1.71022e88			−0.127074
$353$		−	1.92807e89i		−	1.29720i	−0.761129	−	0.648601i	$-0.775355\pi$
$353$		−	1.92807e89i		−	1.29720i	0.761129	−	0.648601i	$-0.224645\pi$
$354$	−2.71300e88	−	1.77439e89i	−0.165324	−	1.08127i
$355$	−4.59411e88			−0.253635
$356$			1.94617e88i			0.0973713i
$357$	4.61482e89	−	7.05593e88i	2.09299	−	0.320012i
$358$	−1.30584e89			−0.537011
$359$			8.63288e87i			0.0321996i	0.999870	+	0.0160998i	$0.00512494\pi$
$359$			8.63288e87i			0.0321996i	−0.999870	+	0.0160998i	$0.994875\pi$
$360$	−9.20307e88	+	2.88161e88i	−0.311419	+	0.0975097i
$361$	−1.47820e89			−0.453923
$362$			4.09489e89i			1.14141i
$363$	−5.28007e88	−	3.45335e89i	−0.133631	−	0.873994i
$364$	−1.41455e89			−0.325140
$365$			1.61561e89i			0.337354i
$366$	4.40587e88	−	6.73645e87i	0.0835976	−	0.0127818i
$367$	−3.37495e89			−0.582043			−0.291022	−	0.956716i	$-0.593995\pi$
$367$	−3.37495e89			−0.582043			−0.291022	+	0.956716i	$0.593995\pi$
$368$		−	1.19224e90i		−	1.86935i
$369$	3.91855e88	+	1.25148e89i	0.0558731	+	0.178443i
$370$	1.98430e89			0.257364
$371$			2.66176e90i			3.14110i
$372$	3.63121e88	+	2.37494e89i	0.0389985	+	0.255064i
$373$	−1.82806e90			−1.78723			−0.893616	−	0.448832i	$-0.851840\pi$
$373$	−1.82806e90			−1.78723			−0.893616	+	0.448832i	$0.851840\pi$
$374$			4.96181e89i			0.441707i
$375$	8.38579e89	−	1.28216e89i	0.679907	−	0.103956i
$376$	4.58207e89			0.338444
$377$			6.17484e89i			0.415603i
$378$	2.84041e90	−	1.39022e90i	1.74248	−	0.852846i
$379$	1.23841e90			0.692614			0.346307	−	0.938121i	$-0.387436\pi$
$379$	1.23841e90			0.692614			0.346307	+	0.938121i	$0.387436\pi$
$380$			1.01094e89i			0.0515583i
$381$	3.15641e89	+	2.06440e90i	0.146832	+	0.960329i
$382$	−4.06360e90			−1.72462
$383$		−	1.59350e90i		−	0.617156i	−0.951199	−	0.308578i	$-0.900147\pi$
$383$		−	1.59350e90i		−	0.617156i	0.951199	−	0.308578i	$-0.0998532\pi$
$384$	3.31925e90	−	5.07504e89i	1.17340	−	0.179410i
$385$	−6.92364e89			−0.223465
$386$			2.13498e90i			0.629272i
$387$	−3.54097e90	+	1.10873e90i	−0.953318	+	0.298498i
$388$	1.32695e90			0.326396
$389$		−	3.53522e90i		−	0.794657i	−0.917676	−	0.397329i	$-0.869937\pi$
$389$		−	3.53522e90i		−	0.794657i	0.917676	−	0.397329i	$-0.130063\pi$
$390$	−2.86138e89	−	1.87144e90i	−0.0587915	−	0.384516i
$391$	−1.02687e91			−1.92898
$392$		−	1.11454e91i		−	1.91462i
$393$	2.37221e90	−	3.62705e89i	0.372747	−	0.0569920i
$394$	3.61088e90			0.519094
$395$		−	3.01832e90i		−	0.397070i
$396$	1.59690e89	+	5.10005e89i	0.0192285	+	0.0614106i
$397$	3.96451e90			0.437040			0.218520	−	0.975832i	$-0.429877\pi$
$397$	3.96451e90			0.437040			0.218520	+	0.975832i	$0.429877\pi$
$398$		−	1.93691e91i		−	1.95525i
$399$	2.14911e90	+	1.40559e91i	0.198704	+	1.29959i
$400$	−1.17617e91			−0.996253
$401$			2.23372e91i			1.73371i	0.498563	+	0.866854i	$0.333861\pi$
$401$			2.23372e91i			1.73371i	−0.498563	+	0.866854i	$0.666139\pi$
$402$	1.61492e91	−	2.46917e90i	1.14879	−	0.175647i
$403$	2.02303e91			1.31925
$404$			1.43008e90i			0.0855089i
$405$	3.83800e90	+	5.52789e90i	0.210465	+	0.303133i
$406$	1.65816e91			0.834093
$407$			4.71661e90i			0.217684i
$408$	−3.75546e90	−	2.45620e91i	−0.159059	−	1.04030i
$409$	−2.96339e91			−1.15205			−0.576027	−	0.817431i	$-0.695398\pi$
$409$	−2.96339e91			−1.15205			−0.576027	+	0.817431i	$0.695398\pi$
$410$		−	2.10820e90i		−	0.0752448i
$411$	−1.90812e91	+	2.91745e90i	−0.625376	+	0.0956182i
$412$	−3.14821e90			−0.0947680
$413$			6.45360e91i			1.78464i
$414$	−6.63815e91	+	2.07850e91i	−1.68669	+	0.528126i
$415$	−1.51215e90			−0.0353111
$416$			1.68130e91i			0.360892i
$417$	2.20867e89	+	1.44455e90i	0.00435883	+	0.0285082i
$418$	−1.51128e91			−0.274268
$419$			5.73588e90i			0.0957435i	0.998853	+	0.0478718i	$0.0152439\pi$
$419$			5.73588e90i			0.0957435i	−0.998853	+	0.0478718i	$0.984756\pi$
$420$	−7.99057e90	+	1.22173e90i	−0.122702	+	0.0187608i
$421$	5.52037e91			0.780000			0.390000	−	0.920815i	$-0.372475\pi$
$421$	5.52037e91			0.780000			0.390000	+	0.920815i	$0.372475\pi$
$422$		−	8.01619e91i		−	1.04240i
$423$	−9.55442e90	−	3.05142e91i	−0.114365	−	0.365249i
$424$	1.41670e92			1.56125
$425$			1.01302e92i			1.02803i
$426$	−1.21189e91	−	7.92619e91i	−0.113273	−	0.740847i
$427$	−1.60245e91			−0.137977
$428$			3.98185e91i			0.315903i
$429$	4.44834e91	−	6.80139e90i	0.325232	−	0.0497270i
$430$	5.96500e91			0.401989
$431$			1.88079e92i			1.16852i	0.811567	+	0.584259i	$0.198615\pi$
$431$			1.88079e92i			1.16852i	−0.811567	+	0.584259i	$0.801385\pi$
$432$	−8.85013e91	−	1.80820e92i	−0.507012	−	1.03590i
$433$	8.12054e91			0.429051			0.214525	−	0.976718i	$-0.431180\pi$
$433$	8.12054e91			0.429051			0.214525	+	0.976718i	$0.431180\pi$
$434$		−	5.43253e92i		−	2.64765i
$435$	5.33315e90	+	3.48806e91i	0.0239806	+	0.156841i
$436$	−1.65013e91			−0.0684685
$437$		−	3.12766e92i		−	1.19776i
$438$	−2.78740e92	+	4.26185e91i	−0.985383	+	0.150662i
$439$	2.15018e92			0.701806			0.350903	−	0.936412i	$-0.385875\pi$
$439$	2.15018e92			0.701806			0.350903	+	0.936412i	$0.385875\pi$
$440$			3.68505e91i			0.111071i
$441$	−7.42223e92	+	2.32400e92i	−2.06625	+	0.646973i
$442$	4.87791e92			1.25445
$443$			6.12999e92i			1.45656i	0.685279	+	0.728281i	$0.259680\pi$
$443$			6.12999e92i			1.45656i	−0.685279	+	0.728281i	$0.740320\pi$
$444$	8.32286e90	+	5.44343e91i	0.0182755	+	0.119528i
$445$	9.36461e91			0.190059
$446$		−	2.60730e92i		−	0.489183i
$447$	3.78483e92	−	5.78690e91i	0.656573	−	0.100388i
$448$	−8.27537e92			−1.32757
$449$		−	6.85161e92i		−	1.01665i	−0.861166	−	0.508324i	$-0.830265\pi$
$449$		−	6.85161e92i		−	1.01665i	0.861166	−	0.508324i	$-0.169735\pi$
$450$	2.05048e92	+	6.54865e92i	0.281460	+	0.898905i
$451$	5.01110e91			0.0636436
$452$			1.93920e92i			0.227917i
$453$	1.29631e92	+	8.47829e92i	0.141017	+	0.922298i
$454$	2.84430e92			0.286432
$455$			6.80656e92i			0.634642i
$456$	7.48115e92	−	1.14385e92i	0.645950	−	0.0987639i
$457$	1.14924e92			0.0919057			0.0459529	−	0.998944i	$-0.485368\pi$
$457$	1.14924e92			0.0919057			0.0459529	+	0.998944i	$0.485368\pi$
$458$			1.33316e93i			0.987619i
$459$	−1.55739e93	+	7.62254e92i	−1.06894	+	0.523186i
$460$	1.77802e92			0.113087
$461$		−	1.66396e91i		−	0.00980866i	−0.999988	−	0.00490433i	$-0.998439\pi$
$461$		−	1.66396e91i		−	0.00980866i	0.999988	−	0.00490433i	$-0.00156110\pi$
$462$	−1.82641e92	−	1.19453e93i	−0.0997995	−	0.652723i
$463$	3.91041e92			0.198101			0.0990507	−	0.995082i	$-0.468419\pi$
$463$	3.91041e92			0.198101			0.0990507	+	0.995082i	$0.468419\pi$
$464$		−	1.05558e93i		−	0.495864i
$465$	1.14277e93	−	1.74727e92i	0.497860	−	0.0761214i
$466$	1.20942e93			0.488730
$467$		−	1.16552e93i		−	0.436946i	−0.975843	−	0.218473i	$-0.929892\pi$
$467$		−	1.16552e93i		−	0.436946i	0.975843	−	0.218473i	$-0.0701075\pi$
$468$	5.01381e92	−	1.56989e92i	0.174407	−	0.0546092i
$469$	−5.87360e93			−1.89607
$470$			5.14032e92i			0.154016i
$471$	−3.65842e92	−	2.39273e93i	−0.101756	−	0.665522i
$472$	3.43488e93			0.887036
$473$			1.41786e93i			0.340011i
$474$	5.20750e93	−	7.96212e92i	1.15981	−	0.177332i
$475$	−3.08549e93			−0.638334
$476$		−	2.08274e93i		−	0.400306i
$477$	−2.95407e93	−	9.43447e93i	−0.527566	−	1.68490i
$478$	−1.21541e94			−2.01718
$479$		−	2.30295e93i		−	0.355257i	−0.984098	−	0.177628i	$-0.943158\pi$
$479$		−	2.30295e93i		−	0.355257i	0.984098	−	0.177628i	$-0.0568425\pi$
$480$	1.45212e92	+	9.49735e92i	0.0208237	+	0.136194i
$481$	4.63685e93			0.618224
$482$			8.01535e93i			0.993748i
$483$	2.47213e94	−	3.77982e93i	2.85051	−	0.435835i
$484$	−1.55855e93			−0.167160
$485$		−	6.38504e93i		−	0.637093i
$486$	−8.52480e93	+	8.07990e93i	−0.791434	+	0.750130i
$487$	1.78355e93			0.154089			0.0770443	−	0.997028i	$-0.475452\pi$
$487$	1.78355e93			0.154089			0.0770443	+	0.997028i	$0.475452\pi$
$488$			8.52889e92i			0.0685802i
$489$	2.03350e93	+	1.32998e94i	0.152207	+	0.995487i
$490$	1.25032e94			0.871285
$491$		−	1.05458e93i		−	0.0684269i	−0.999415	−	0.0342135i	$-0.989107\pi$
$491$		−	1.05458e93i		−	0.0684269i	0.999415	−	0.0342135i	$-0.0108926\pi$
$492$	5.78331e92	−	8.84251e91i	0.0349460	−	0.00534315i
$493$	−9.09163e93			−0.511682
$494$			1.48572e94i			0.778924i
$495$	2.45405e93	−	7.68398e92i	0.119867	−	0.0375322i
$496$	−3.45834e94			−1.57402
$497$			2.88281e94i			1.22276i
$498$	−3.98894e92	−	2.60890e93i	−0.0157700	−	0.103141i
$499$	3.61226e93			0.133125			0.0665625	−	0.997782i	$-0.478797\pi$
$499$	3.61226e93			0.133125			0.0665625	+	0.997782i	$0.478797\pi$
$500$		−	3.78464e93i		−	0.130039i
$501$	−1.24882e93	+	1.90942e92i	−0.0400111	+	0.00611759i
$502$	−6.89929e94			−2.06146
$503$		−	5.80394e94i		−	1.61750i	−0.588154	−	0.808749i	$-0.700145\pi$
$503$		−	5.80394e94i		−	1.61750i	0.588154	−	0.808749i	$-0.299855\pi$
$504$	1.80822e94	+	5.77495e94i	0.470091	+	1.50134i
$505$	6.88126e93			0.166905
$506$			2.65802e94i			0.601575i
$507$	4.69456e92	+	3.07040e93i	0.00991553	+	0.0648510i
$508$	9.31697e93			0.183673
$509$		−	7.93157e94i		−	1.45961i	−0.683655	−	0.729805i	$-0.739611\pi$
$509$		−	7.93157e94i		−	1.45961i	0.683655	−	0.729805i	$-0.260389\pi$
$510$	2.75545e94	−	4.21300e93i	0.473408	−	0.0723828i
$511$	1.01380e95			1.62637
$512$			3.93334e94i			0.589268i
$513$	−2.32169e94	−	4.74353e94i	−0.324860	−	0.663734i
$514$	1.04212e95			1.36210
$515$			1.51486e94i			0.184978i
$516$	2.50193e93	+	1.63635e94i	0.0285453	+	0.186696i
$517$	−1.22183e94			−0.130270
$518$		−	1.24515e95i		−	1.24074i
$519$	−8.84996e94	+	1.35313e94i	−0.824298	+	0.126033i
$520$	3.62274e94			0.315442
$521$		−	1.22143e95i		−	0.994372i	−0.867644	−	0.497186i	$-0.834367\pi$
$521$		−	1.22143e95i		−	0.994372i	0.867644	−	0.497186i	$-0.165633\pi$
$522$	−5.87725e94	+	1.84025e94i	−0.447411	+	0.140091i
$523$	−4.52157e94			−0.321907			−0.160953	−	0.986962i	$-0.551457\pi$
$523$	−4.52157e94			−0.321907			−0.160953	+	0.986962i	$0.551457\pi$
$524$		−	1.07062e94i		−	0.0712917i
$525$	−3.72886e94	−	2.43881e95i	−0.232274	−	1.51915i
$526$	9.56041e94			0.557154
$527$			2.97864e95i			1.62423i
$528$	−7.60438e94	+	1.16269e94i	−0.388040	+	0.0593303i
$529$	−3.40701e95			−1.62714
$530$			1.58930e95i			0.710479i
$531$	−7.16231e94	−	2.28744e95i	−0.299740	−	0.957287i
$532$	6.34366e94			0.248561
$533$		−	4.92636e94i		−	0.180748i
$534$	2.47032e94	+	1.61567e95i	0.0848806	+	0.555148i
$535$	1.91599e95			0.616611
$536$			3.12617e95i			0.942422i
$537$	−1.72370e95	+	2.63549e94i	−0.486814	+	0.0744324i
$538$	6.08458e95			1.61009
$539$			2.97197e95i			0.736950i
$540$	2.69662e94	−	1.31984e94i	0.0626670	−	0.0306719i
$541$	3.52145e95			0.767039			0.383520	−	0.923533i	$-0.374712\pi$
$541$	3.52145e95			0.767039			0.383520	+	0.923533i	$0.374712\pi$
$542$			6.90153e94i			0.140919i
$543$	8.26447e94	+	5.40525e95i	0.158205	+	1.03472i
$544$	−2.47549e95			−0.444323
$545$			7.94011e94i			0.133644i
$546$	−1.17433e96	+	1.79552e95i	−1.85374	+	0.283431i
$547$	9.52447e95			1.41021			0.705106	−	0.709102i	$-0.250900\pi$
$547$	9.52447e95			1.41021			0.705106	+	0.709102i	$0.250900\pi$
$548$			8.61162e94i			0.119609i
$549$	5.67979e94	−	1.77842e94i	0.0740116	−	0.0231741i
$550$	2.62218e95			0.320604
$551$		−	2.76915e95i		−	0.317717i
$552$	−2.01178e95	−	1.31577e96i	−0.216627	−	1.41682i
$553$	−1.89400e96			−1.91426
$554$		−	1.87030e96i		−	1.77448i
$555$	2.61928e95	−	4.00480e94i	0.233307	−	0.0356719i
$556$	6.51947e93			0.00545249
$557$			1.40954e96i			1.10699i	0.832851	+	0.553497i	$0.186707\pi$
$557$			1.40954e96i			1.10699i	−0.832851	+	0.553497i	$0.813293\pi$
$558$	6.02911e95	+	1.92553e96i	0.444689	+	1.42021i
$559$	1.39388e96			0.965634
$560$		−	1.16357e96i		−	0.757204i
$561$	1.00141e95	+	6.54959e95i	0.0612228	+	0.400418i
$562$	−3.00558e96			−1.72646
$563$		−	1.95346e96i		−	1.05442i	−0.849736	−	0.527208i	$-0.823239\pi$
$563$		−	1.95346e96i		−	1.05442i	0.849736	−	0.527208i	$-0.176761\pi$
$564$	−1.41012e95	+	2.15603e94i	−0.0715297	+	0.0109367i
$565$	9.33107e95			0.444873
$566$		−	4.57687e96i		−	2.05113i
$567$	3.46876e96	−	2.40835e96i	1.46139	−	1.01464i
$568$	1.53435e96			0.607762
$569$			2.31100e96i			0.860739i	0.902653	+	0.430369i	$0.141617\pi$
$569$			2.31100e96i			0.860739i	−0.902653	+	0.430369i	$0.858383\pi$
$570$	1.28320e95	+	8.39260e95i	0.0449444	+	0.293952i
$571$	6.42257e95			0.211566			0.105783	−	0.994389i	$-0.466265\pi$
$571$	6.42257e95			0.211566			0.105783	+	0.994389i	$0.466265\pi$
$572$		−	2.00761e95i		−	0.0622039i
$573$	−5.36395e96	+	8.20133e95i	−1.56341	+	0.239041i
$574$	−1.32290e96			−0.362752
$575$			5.42671e96i			1.40011i
$576$	2.93316e96	−	9.18415e95i	0.712113	−	0.222973i
$577$	−1.41993e96			−0.324424			−0.162212	−	0.986756i	$-0.551863\pi$
$577$	−1.41993e96			−0.324424			−0.162212	+	0.986756i	$0.551863\pi$
$578$			2.11127e96i			0.454014i
$579$	4.30891e95	+	2.81818e96i	0.0872203	+	0.570451i
$580$	1.57422e95			0.0299975
$581$			9.48877e95i			0.170234i
$582$	1.10161e97	−	1.68433e96i	1.86090	−	0.284526i
$583$	−3.77771e96			−0.600937
$584$		−	5.39585e96i		−	0.808369i
$585$	−7.55404e95	−	2.41255e96i	−0.106592	−	0.340425i
$586$	−7.69181e96			−1.02238
$587$			1.55094e97i			1.94205i	0.238973	+	0.971026i	$0.423189\pi$
$587$			1.55094e97i			1.94205i	−0.238973	+	0.971026i	$0.576811\pi$
$588$	5.24430e95	+	3.42995e96i	0.0618701	+	0.404652i
$589$	−9.07241e96			−1.00853
$590$			3.85336e96i			0.403663i
$591$	4.76636e96	−	7.28763e95i	0.470571	−	0.0719490i
$592$	−7.92664e96			−0.737615
$593$			3.07126e96i			0.269403i	0.990886	+	0.134702i	$0.0430076\pi$
$593$			3.07126e96i			0.269403i	−0.990886	+	0.134702i	$0.956992\pi$
$594$	1.97307e96	+	4.03126e96i	0.163161	+	0.333361i
$595$	−1.00218e97			−0.781358
$596$		−	1.70815e96i		−	0.125576i
$597$	−3.90915e96	−	2.55672e97i	−0.271007	−	1.77248i
$598$	2.61307e97			1.70848
$599$			1.12034e97i			0.690893i	0.938438	+	0.345447i	$0.112273\pi$
$599$			1.12034e97i			0.690893i	−0.938438	+	0.345447i	$0.887727\pi$
$600$	−1.29803e97	+	1.98466e96i	−0.755079	+	0.115449i
$601$	6.51749e96			0.357663			0.178831	−	0.983880i	$-0.442768\pi$
$601$	6.51749e96			0.357663			0.178831	+	0.983880i	$0.442768\pi$
$602$		−	3.74305e97i		−	1.93798i
$603$	2.08186e97	−	6.51861e96i	1.01706	−	0.318456i
$604$	3.82639e96			0.176399
$605$			7.49945e96i			0.326281i
$606$	1.81522e96	+	1.18722e97i	0.0745399	+	0.487516i
$607$	−8.71897e96			−0.337957			−0.168978	−	0.985620i	$-0.554047\pi$
$607$	−8.71897e96			−0.337957			−0.168978	+	0.985620i	$0.554047\pi$
$608$		−	7.53989e96i		−	0.275892i
$609$	2.18877e97	−	3.34656e96i	0.756126	−	0.115610i
$610$	−9.56799e95			−0.0312088
$611$			1.20117e97i			0.369967i
$612$	2.31146e96	+	7.38216e96i	0.0672336	+	0.214726i
$613$	3.08337e96			0.0847050			0.0423525	−	0.999103i	$-0.486515\pi$
$613$	3.08337e96			0.0847050			0.0423525	+	0.999103i	$0.486515\pi$
$614$		−	5.56444e97i		−	1.44387i
$615$	−4.25485e95	−	2.78282e96i	−0.0104293	−	0.0682112i
$616$	2.31238e97			0.535468
$617$		−	3.48898e97i		−	0.763339i	−0.924299	−	0.381669i	$-0.875349\pi$
$617$		−	3.48898e97i		−	0.763339i	0.924299	−	0.381669i	$-0.124651\pi$
$618$	−2.61358e97	+	3.99609e96i	−0.540306	+	0.0826112i
$619$	−2.02151e97			−0.394916			−0.197458	−	0.980311i	$-0.563269\pi$
$619$	−2.02151e97			−0.394916			−0.197458	+	0.980311i	$0.563269\pi$
$620$		−	5.15752e96i		−	0.0952208i
$621$	−8.34286e97	+	4.08335e97i	−1.45582	+	0.712543i
$622$	−6.00150e97			−0.989911
$623$		−	5.87631e97i		−	0.916269i
$624$	1.14303e97	+	7.47579e97i	0.168498	+	1.10204i
$625$	4.37647e97			0.609991
$626$			1.02003e98i			1.34435i
$627$	−1.99489e97	+	3.05013e96i	−0.248631	+	0.0380149i
$628$	−1.07988e97			−0.127288
$629$			6.82715e97i			0.761144i
$630$	−6.47853e97	+	2.02852e97i	−0.683214	+	0.213924i
$631$	8.63445e97			0.861404			0.430702	−	0.902494i	$-0.358266\pi$
$631$	8.63445e97			0.861404			0.430702	+	0.902494i	$0.358266\pi$
$632$			1.00807e98i			0.951464i
$633$	−1.61786e97	−	1.05814e98i	−0.144481	−	0.944957i
$634$	1.76368e98			1.49037
$635$		−	4.48315e97i		−	0.358511i
$636$	−4.35985e97	+	6.66608e96i	−0.329968	+	0.0504512i
$637$	2.92172e98			2.09295
$638$			2.35334e97i			0.159574i
$639$	−3.19939e97	−	1.02180e98i	−0.205370	−	0.655896i
$640$	−7.20824e97			−0.438057
$641$			1.78330e98i			1.02611i	0.858357	+	0.513054i	$0.171486\pi$
$641$			1.78330e98i			1.02611i	−0.858357	+	0.513054i	$0.828514\pi$
$642$	5.05425e97	+	3.30565e98i	0.275379	+	1.80107i
$643$	−1.54596e98			−0.797652			−0.398826	−	0.917027i	$-0.630582\pi$
$643$	−1.54596e98			−0.797652			−0.398826	+	0.917027i	$0.630582\pi$
$644$		−	1.11571e98i		−	0.545189i
$645$	7.87380e97	−	1.20388e97i	0.364413	−	0.0557177i
$646$	−2.18753e98			−0.958994
$647$			7.33049e96i			0.0304427i	0.999884	+	0.0152214i	$0.00484529\pi$
$647$			7.33049e96i			0.0304427i	−0.999884	+	0.0152214i	$0.995155\pi$
$648$	−1.28183e98	−	1.84622e98i	−0.504317	−	0.726371i
$649$	−9.15928e97			−0.341426
$650$		−	2.57784e98i		−	0.910518i
$651$	−1.09642e98	−	7.17093e98i	−0.366978	−	2.40016i
$652$	6.00241e97			0.190397
$653$		−	1.43275e98i		−	0.430734i	−0.976533	−	0.215367i	$-0.930905\pi$
$653$		−	1.43275e98i		−	0.430734i	0.976533	−	0.215367i	$-0.0690948\pi$
$654$	−1.36990e98	+	2.09454e97i	−0.390363	+	0.0596854i
$655$	−5.15161e97			−0.139155
$656$			8.42156e97i			0.215654i
$657$	−3.59335e98	+	1.12513e98i	−0.872391	+	0.273158i
$658$	3.22556e98			0.742504
$659$			2.16793e98i			0.473211i	0.971606	+	0.236605i	$0.0760349\pi$
$659$			2.16793e98i			0.473211i	−0.971606	+	0.236605i	$0.923965\pi$
$660$	−1.73395e96	−	1.13406e97i	−0.00358921	−	0.0234746i
$661$	8.01711e98			1.57386			0.786931	−	0.617041i	$-0.211669\pi$
$661$	8.01711e98			1.57386			0.786931	+	0.617041i	$0.211669\pi$
$662$			1.06741e97i			0.0198748i
$663$	6.43884e98	−	9.84480e97i	1.13719	−	0.173873i
$664$	5.05032e97			0.0846128
$665$		−	3.05245e98i		−	0.485166i
$666$	1.38189e98	+	4.41338e98i	0.208390	+	0.665539i
$667$	−4.87034e98			−0.696875
$668$			5.63614e96i			0.00765253i
$669$	−5.26217e97	−	3.44164e98i	−0.0678032	−	0.443456i
$670$	−3.50704e98			−0.428867
$671$		−	2.27427e97i		−	0.0263970i
$672$	5.95961e98	−	9.11207e97i	0.656588	−	0.100391i
$673$	1.53899e97			0.0160956			0.00804781	−	0.999968i	$-0.497438\pi$
$673$	1.53899e97			0.0160956			0.00804781	+	0.999968i	$0.497438\pi$
$674$			1.13577e99i			1.12770i
$675$	4.02830e98	+	8.23038e98i	0.379743	+	0.775868i
$676$	1.38572e97			0.0124034
$677$		−	8.33012e98i		−	0.708024i	−0.935241	−	0.354012i	$-0.884817\pi$
$677$		−	8.33012e98i		−	0.708024i	0.935241	−	0.354012i	$-0.115183\pi$
$678$	2.46147e98	+	1.60988e99i	0.198680	+	1.29944i
$679$	−4.00662e99			−3.07140
$680$			5.33400e98i			0.388366i
$681$	3.75448e98	−	5.74049e97i	0.259657	−	0.0397009i
$682$	7.71012e98			0.506533
$683$			4.93620e98i			0.308084i	0.988064	+	0.154042i	$0.0492290\pi$
$683$			4.93620e98i			0.308084i	−0.988064	+	0.154042i	$0.950771\pi$
$684$	−2.24848e98	+	7.04030e97i	−0.133329	+	0.0417472i
$685$	4.14375e98			0.233466
$686$		−	4.22217e99i		−	2.26043i
$687$	2.69063e98	+	1.75977e99i	0.136889	+	0.895301i
$688$	−2.38282e99			−1.15212
$689$			3.71383e99i			1.70667i
$690$	1.47608e99	−	2.25688e98i	0.644750	−	0.0985804i
$691$	1.52452e98			0.0632998			0.0316499	−	0.999499i	$-0.489924\pi$
$691$	1.52452e98			0.0632998			0.0316499	+	0.999499i	$0.489924\pi$
$692$			3.99413e98i			0.157655i
$693$	−4.82171e98	−	1.53992e99i	−0.180941	−	0.577877i
$694$	2.97929e99			1.06300
$695$		−	3.13705e97i		−	0.0106427i
$696$	−1.78118e98	−	1.16495e99i	−0.0574625	−	0.375824i
$697$	7.25342e98			0.222533
$698$		−	1.48165e99i		−	0.432321i
$699$	1.59643e99	−	2.44090e98i	0.443046	−	0.0677404i
$700$	−1.10067e99			−0.290553
$701$		−	3.87093e99i		−	0.972042i	−0.873947	−	0.486021i	$-0.838448\pi$
$701$		−	3.87093e99i		−	0.972042i	0.873947	−	0.486021i	$-0.161552\pi$
$702$	3.96309e99	−	1.93971e99i	0.946749	−	0.463380i
$703$	−2.07943e99			−0.472615
$704$		−	1.17448e99i		−	0.253983i
$705$	1.03744e98	+	6.78522e98i	0.0213474	+	0.139619i
$706$	−7.22394e99			−1.41452
$707$		−	4.31800e99i		−	0.804643i
$708$	−1.05707e99	+	1.61623e98i	−0.187474	+	0.0286642i
$709$	9.32705e99			1.57444			0.787220	−	0.616673i	$-0.211520\pi$
$709$	9.32705e99			1.57444			0.787220	+	0.616673i	$0.211520\pi$
$710$			1.72129e99i			0.276574i
$711$	6.71320e99	−	2.10200e99i	1.02682	−	0.321511i
$712$	−3.12762e99			−0.455422
$713$			1.59564e100i			2.21209i
$714$	−2.64367e99	−	1.72905e100i	−0.348955	−	2.28228i
$715$	−9.66022e98			−0.121416
$716$			7.77934e98i			0.0931081i
$717$	−1.60434e100	+	2.45299e99i	−1.82863	+	0.279592i
$718$	3.23451e98			0.0351118
$719$		−	1.22951e99i		−	0.127122i	−0.997978	−	0.0635610i	$-0.979754\pi$
$719$		−	1.22951e99i		−	0.127122i	0.997978	−	0.0635610i	$-0.0202457\pi$
$720$	1.29135e99	+	4.12422e99i	0.127177	+	0.406167i
$721$	9.50579e99			0.891772
$722$			5.53842e99i			0.494976i
$723$	1.61769e99	+	1.05803e100i	0.137738	+	0.900857i
$724$	2.43947e99			0.197900
$725$			4.80468e99i			0.371393i
$726$	−1.29388e100	+	1.97830e99i	−0.953040	+	0.145717i
$727$	−6.23831e99			−0.437887			−0.218944	−	0.975737i	$-0.570261\pi$
$727$	−6.23831e99			−0.437887			−0.218944	+	0.975737i	$0.570261\pi$
$728$		−	2.27327e100i		−	1.52074i
$729$	−9.62201e99	+	1.23860e100i	−0.613483	+	0.789708i
$730$	6.05324e99			0.367864
$731$			2.05230e100i			1.18887i
$732$	−4.01315e97	−	2.62474e98i	−0.00221614	−	0.0144943i
$733$	1.63823e100			0.862452			0.431226	−	0.902244i	$-0.358081\pi$
$733$	1.63823e100			0.862452			0.431226	+	0.902244i	$0.358081\pi$
$734$			1.26450e100i			0.634684i
$735$	1.65043e100	−	2.52346e99i	0.789841	−	0.120764i
$736$	−1.32610e100			−0.605138
$737$		−	8.33611e99i		−	0.362745i
$738$	4.68894e99	−	1.46817e99i	0.194582	−	0.0609263i
$739$	−2.58809e100			−1.02429			−0.512145	−	0.858899i	$-0.671149\pi$
$739$	−2.58809e100			−1.02429			−0.512145	+	0.858899i	$0.671149\pi$
$740$		−	1.18212e99i		−	0.0446223i
$741$	2.99855e99	+	1.96115e100i	0.107963	+	0.706114i
$742$	9.97290e100			3.42519
$743$		−	3.25238e100i		−	1.06560i	−0.846242	−	0.532799i	$-0.821140\pi$
$743$		−	3.25238e100i		−	1.06560i	0.846242	−	0.532799i	$-0.178860\pi$
$744$	−3.81667e100	+	5.83558e99i	−1.19298	+	0.182403i
$745$	−8.21932e99			−0.245113
$746$			6.84924e100i			1.94887i
$747$	−1.05308e99	−	3.36324e99i	−0.0285917	−	0.0913140i
$748$	2.95593e99			0.0765841
$749$		−	1.20229e101i		−	2.97266i
$750$	−4.80392e99	−	3.14193e100i	−0.113358	−	0.741399i
$751$	−2.15441e100			−0.485210			−0.242605	−	0.970125i	$-0.578002\pi$
$751$	−2.15441e100			−0.485210			−0.242605	+	0.970125i	$0.578002\pi$
$752$		−	2.05339e100i		−	0.441415i
$753$	−9.10706e100	+	1.39244e100i	−1.86876	+	0.285729i
$754$	2.31355e100			0.453191
$755$		−	1.84118e100i		−	0.344314i
$756$	−8.28205e99	−	1.69214e100i	−0.147868	−	0.302115i
$757$	−3.19520e100			−0.544681			−0.272340	−	0.962201i	$-0.587798\pi$
$757$	−3.19520e100			−0.544681			−0.272340	+	0.962201i	$0.587798\pi$
$758$		−	4.63997e100i		−	0.755255i
$759$	5.36452e99	+	3.50858e100i	0.0833813	+	0.545342i
$760$	−1.62464e100			−0.241147
$761$			2.01704e100i			0.285925i	0.989728	+	0.142962i	$0.0456628\pi$
$761$			2.01704e100i			0.285925i	−0.989728	+	0.142962i	$0.954337\pi$
$762$	7.73476e100	−	1.18262e100i	1.04718	−	0.160111i
$763$	4.98243e100			0.644292
$764$			2.42083e100i			0.299018i
$765$	3.55216e100	−	1.11223e100i	0.419124	−	0.131234i
$766$	−5.97042e100			−0.672973
$767$			9.00440e100i			0.969654i
$768$	−8.05300e99	−	5.26694e100i	−0.0828542	−	0.541895i
$769$	−4.20089e98			−0.00412971			−0.00206486	−	0.999998i	$-0.500657\pi$
$769$	−4.20089e98			−0.00412971			−0.00206486	+	0.999998i	$0.500657\pi$
$770$			2.59410e100i			0.243675i
$771$	1.37560e101	−	2.10325e100i	1.23477	−	0.188793i
$772$	1.27189e100			0.109105
$773$		−	4.81153e100i		−	0.394458i	−0.980357	−	0.197229i	$-0.936806\pi$
$773$		−	4.81153e100i		−	0.394458i	0.980357	−	0.197229i	$-0.0631942\pi$
$774$	4.15410e100	+	1.32670e101i	0.325494	+	1.03954i
$775$	1.57413e101			1.17891
$776$			2.13249e101i			1.52661i
$777$	−2.51302e100	−	1.64360e101i	−0.171973	−	1.12476i
$778$	−1.32455e101			−0.866527
$779$			2.20926e100i			0.138177i
$780$	−1.11488e100	+	1.70463e99i	−0.0666682	+	0.0101934i
$781$	−4.09144e100			−0.233932
$782$			3.84740e101i			2.10344i
$783$	−7.38656e100	+	3.61530e100i	−0.386172	+	0.189009i
$784$	−4.99464e101			−2.49713
$785$			5.19617e100i			0.248454i
$786$	−1.35896e100	−	8.88804e100i	−0.0621465	−	0.406459i
$787$	1.22010e101			0.533679			0.266840	−	0.963741i	$-0.414021\pi$
$787$	1.22010e101			0.533679			0.266840	+	0.963741i	$0.414021\pi$
$788$		−	2.15113e100i		−	0.0900015i
$789$	1.26197e101	−	1.92952e100i	0.505074	−	0.0772244i
$790$	−1.13088e101			−0.432982
$791$		−	5.85527e101i		−	2.14472i
$792$	−8.19610e100	+	2.56632e100i	−0.287227	+	0.0899350i
$793$	−2.23582e100			−0.0749677
$794$		−	1.48539e101i		−	0.476567i
$795$	3.20759e100	+	2.09788e101i	0.0984759	+	0.644066i
$796$	−1.15389e101			−0.339005
$797$			7.77697e100i			0.218660i	0.994006	+	0.109330i	$0.0348705\pi$
$797$			7.77697e100i			0.218660i	−0.994006	+	0.109330i	$0.965129\pi$
$798$	5.26637e101	−	8.05213e100i	1.41713	−	0.216676i
$799$	−1.76857e101			−0.455496
$800$			1.30823e101i			0.322502i
$801$	6.52163e100	+	2.08283e101i	0.153893	+	0.491491i
$802$	8.36914e101			1.89051
$803$			1.43883e101i			0.311147i
$804$	−1.47098e100	−	9.62069e100i	−0.0304540	−	0.199179i
$805$	−5.36860e101			−1.06416
$806$		−	7.57974e101i		−	1.43856i
$807$	8.03164e101	−	1.22801e101i	1.45959	−	0.223167i
$808$	−2.29822e101			−0.399939
$809$		−	8.91757e101i		−	1.48610i	−0.669236	−	0.743050i	$-0.733378\pi$
$809$		−	8.91757e101i		−	1.48610i	0.669236	−	0.743050i	$-0.266622\pi$
$810$	2.07115e101	−	1.43799e101i	0.330549	−	0.229499i
$811$	4.01682e101			0.613977			0.306989	−	0.951713i	$-0.400679\pi$
$811$	4.01682e101			0.613977			0.306989	+	0.951713i	$0.400679\pi$
$812$		−	9.87824e100i		−	0.144617i
$813$	1.39290e100	+	9.11002e100i	0.0195321	+	0.127747i
$814$	1.76719e101			0.237371
$815$		−	2.88825e101i		−	0.371636i
$816$	−1.10071e102	+	1.68296e101i	−1.35681	+	0.207452i
$817$	−6.25095e101			−0.738200
$818$			1.11030e102i			1.25625i
$819$	−1.51388e102	+	4.74017e101i	−1.64118	+	0.513875i
$820$	−1.25593e100			−0.0130461
$821$		−	4.66174e100i		−	0.0464021i	−0.999731	−	0.0232011i	$-0.992614\pi$
$821$		−	4.66174e100i		−	0.0464021i	0.999731	−	0.0232011i	$-0.00738579\pi$
$822$	1.09309e101	+	7.14919e101i	0.104266	+	0.681936i
$823$	−1.18842e102			−1.08636			−0.543182	−	0.839615i	$-0.682781\pi$
$823$	−1.18842e102			−1.08636			−0.543182	+	0.839615i	$0.682781\pi$
$824$		−	5.05938e101i		−	0.443246i
$825$	3.46128e101	−	5.29220e100i	0.290635	−	0.0444373i
$826$	2.41799e102			1.94604
$827$			7.49819e99i			0.00578447i	0.999996	+	0.00289223i	$0.000920628\pi$
$827$			7.49819e99i			0.00578447i	−0.999996	+	0.00289223i	$0.999079\pi$
$828$	1.23824e101	+	3.95459e101i	0.0915676	+	0.292442i
$829$	6.46738e101			0.458479			0.229240	−	0.973370i	$-0.426376\pi$
$829$	6.46738e101			0.458479			0.229240	+	0.973370i	$0.426376\pi$
$830$			5.66561e100i			0.0385047i
$831$	−3.77472e101	−	2.46880e102i	−0.245951	−	1.60861i
$832$	−1.15462e102			−0.721313
$833$			4.30184e102i			2.57679i
$834$	5.41233e100	−	8.27530e99i	0.0310865	−	0.00475305i
$835$	2.71200e100			0.0149370
$836$			9.00324e100i			0.0475531i
$837$	1.18446e102	+	2.42002e102i	0.599970	+	1.22582i
$838$	2.14908e101			0.104403
$839$			3.16527e102i			1.47483i	0.675440	+	0.737415i	$0.263954\pi$
$839$			3.16527e102i			1.47483i	−0.675440	+	0.737415i	$0.736046\pi$
$840$	−1.96340e101	−	1.28413e102i	−0.0877475	−	0.573899i
$841$	1.90150e102			0.815147
$842$		−	2.06833e102i		−	0.850544i
$843$	−3.96736e102	+	6.06598e101i	−1.56508	+	0.239296i
$844$	−4.77554e101			−0.180733
$845$		−	6.66783e100i		−	0.0242103i
$846$	−1.14328e102	+	3.57978e101i	−0.398282	+	0.124708i
$847$	4.70592e102			1.57299
$848$		−	6.34874e102i		−	2.03626i
$849$	−9.23723e101	−	6.04147e102i	−0.284297	−	1.85940i
$850$	3.79553e102			1.12101
$851$			3.65727e102i			1.03663i
$852$	−4.72192e101	+	7.21968e100i	−0.128450	+	0.0196396i
$853$	−5.41555e101			−0.141392			−0.0706962	−	0.997498i	$-0.522522\pi$
$853$	−5.41555e101			−0.141392			−0.0706962	+	0.997498i	$0.522522\pi$
$854$			6.00393e101i			0.150456i
$855$	3.38766e101	+	1.08192e102i	0.0814865	+	0.260245i
$856$	−6.39908e102			−1.47753
$857$			2.60836e101i			0.0578148i	0.999582	+	0.0289074i	$0.00920280\pi$
$857$			2.60836e101i			0.0578148i	−0.999582	+	0.0289074i	$0.990797\pi$
$858$	−2.54830e101	−	1.66667e102i	−0.0542244	−	0.354646i
$859$	−1.06634e102			−0.217839			−0.108919	−	0.994051i	$-0.534739\pi$
$859$	−1.06634e102			−0.217839			−0.108919	+	0.994051i	$0.534739\pi$
$860$		−	3.55357e101i		−	0.0696977i
$861$	−1.74622e102	+	2.66993e101i	−0.328844	+	0.0502793i
$862$	7.04680e102			1.27420
$863$		−	7.06229e102i		−	1.22622i	−0.789999	−	0.613109i	$-0.789919\pi$
$863$		−	7.06229e102i		−	1.22622i	0.789999	−	0.613109i	$-0.210081\pi$
$864$	−2.01122e102	+	9.84380e101i	−0.335336	+	0.164128i
$865$	1.92190e102			0.307728
$866$		−	3.04255e102i		−	0.467855i
$867$	4.26105e101	+	2.78687e102i	0.0629286	+	0.411575i
$868$	−3.23635e102			−0.459056
$869$		−	2.68807e102i		−	0.366225i
$870$	1.30688e102	−	1.99819e101i	0.171026	−	0.0261494i
$871$	−8.19514e102			−1.03020
$872$		−	2.65186e102i		−	0.320238i
$873$	1.42013e103	−	4.44662e102i	1.64751	−	0.515859i
$874$	−1.17185e103			−1.30608
$875$			1.14274e103i			1.22368i
$876$	2.53894e101	+	1.66055e102i	0.0261221	+	0.170848i
$877$	1.27965e103			1.26504			0.632520	−	0.774544i	$-0.282020\pi$
$877$	1.27965e103			1.26504			0.632520	+	0.774544i	$0.282020\pi$
$878$		−	8.05615e102i		−	0.765279i
$879$	−1.01532e103	+	1.55239e102i	−0.926812	+	0.141707i
$880$	1.65140e102			0.144864
$881$			2.03421e103i			1.71490i	0.514567	+	0.857450i	$0.327953\pi$
$881$			2.03421e103i			1.71490i	−0.514567	+	0.857450i	$0.672047\pi$
$882$	8.70741e102	+	2.78091e103i	0.705487	+	2.25313i
$883$	4.77812e100			0.00372077			0.00186038	−	0.999998i	$-0.499408\pi$
$883$	4.77812e100			0.00372077			0.00186038	+	0.999998i	$0.499408\pi$
$884$		−	2.90595e102i		−	0.217500i
$885$	7.77701e101	+	5.08643e102i	0.0559497	+	0.365930i
$886$	2.29674e103			1.58830
$887$		−	1.96441e103i		−	1.30589i	−0.757407	−	0.652943i	$-0.773534\pi$
$887$		−	1.96441e103i		−	1.30589i	0.757407	−	0.652943i	$-0.226466\pi$
$888$	−8.74794e102	+	1.33754e102i	−0.559052	+	0.0854774i
$889$	−2.81319e103			−1.72837
$890$		−	3.50867e102i		−	0.207249i
$891$	3.41806e102	+	4.92305e102i	0.194115	+	0.279585i
$892$	−1.55326e102			−0.0848156
$893$		−	5.38674e102i		−	0.282830i
$894$	−2.16820e102	−	1.41807e103i	−0.109467	−	0.715955i
$895$	3.74328e102			0.181738
$896$			4.52319e103i			2.11186i
$897$	3.44925e103	−	5.27380e102i	1.54878	−	0.236804i
$898$	−2.56711e103			−1.10860
$899$			1.41274e103i			0.586777i
$900$	3.90127e102	−	1.22154e102i	0.155854	−	0.0488001i
$901$	−5.46812e103			−2.10121
$902$		−	1.87752e102i		−	0.0693996i
$903$	−7.55438e102	−	4.94082e103i	−0.268613	−	1.75682i
$904$	−3.11642e103			−1.06601
$905$		−	1.17383e103i		−	0.386282i
$906$	3.17659e103	−	4.85691e102i	1.00571	−	0.153771i
$907$	2.06701e103			0.629632			0.314816	−	0.949153i	$-0.398057\pi$
$907$	2.06701e103			0.629632			0.314816	+	0.949153i	$0.398057\pi$
$908$		−	1.69445e102i		−	0.0496621i
$909$	4.79219e102	+	1.53049e103i	0.135144	+	0.431614i
$910$	2.55023e103			0.692040
$911$		−	7.29561e103i		−	1.90510i	−0.304377	−	0.952552i	$-0.598448\pi$
$911$		−	7.29561e103i		−	1.90510i	0.304377	−	0.952552i	$-0.401552\pi$
$912$	−5.12598e102	−	3.35257e103i	−0.128812	−	0.842478i
$913$	−1.34669e102			−0.0325681
$914$		−	4.30588e102i		−	0.100218i
$915$	−1.26297e102	+	1.93105e101i	−0.0282915	+	0.00432569i
$916$	7.94210e102			0.171235
$917$			3.23264e103i			0.670859i
$918$	2.85596e103	+	5.83512e103i	0.570503	+	1.16562i
$919$	1.02760e104			1.97596			0.987982	−	0.154568i	$-0.0493985\pi$
$919$	1.02760e104			1.97596			0.987982	+	0.154568i	$0.0493985\pi$
$920$			2.85739e103i			0.528927i
$921$	−1.12304e103	−	7.34505e103i	−0.200128	−	1.30890i
$922$	−6.23439e101			−0.0106958
$923$			4.02225e103i			0.664369i
$924$	−7.11626e102	+	1.08806e102i	−0.113170	+	0.0173034i
$925$	3.60796e103			0.552460
$926$		−	1.46512e103i		−	0.216018i
$927$	−3.36928e103	+	1.05497e103i	−0.478350	+	0.149778i
$928$	−1.17410e103			−0.160519
$929$		−	5.83401e103i		−	0.768099i	−0.923313	−	0.384050i	$-0.874529\pi$
$929$		−	5.83401e103i		−	0.768099i	0.923313	−	0.384050i	$-0.125471\pi$
$930$	−6.54655e102	−	4.28167e103i	−0.0830059	−	0.542887i
$931$	−1.31026e104			−1.60000
$932$		−	7.20493e102i		−	0.0847370i
$933$	−7.92197e103	+	1.21125e103i	−0.897379	+	0.137207i
$934$	−4.36687e103			−0.476464
$935$		−	1.42234e103i		−	0.149485i
$936$	2.52292e103	+	8.05750e103i	0.255416	+	0.815729i
$937$	−3.69929e103			−0.360771			−0.180386	−	0.983596i	$-0.557735\pi$
$937$	−3.69929e103			−0.360771			−0.180386	+	0.983596i	$0.557735\pi$
$938$			2.20068e104i			2.06755i
$939$	2.05867e103	+	1.34644e104i	0.186333	+	1.21868i
$940$	3.06228e102			0.0267036
$941$		−	8.37545e103i		−	0.703674i	−0.936061	−	0.351837i	$-0.885557\pi$
$941$		−	8.37545e103i		−	0.703674i	0.936061	−	0.351837i	$-0.114443\pi$
$942$	−8.96492e103	+	1.37071e103i	−0.725713	+	0.110959i
$943$	3.88562e103			0.303075
$944$		−	1.53929e104i		−	1.15691i
$945$	−8.14224e103	+	3.98517e103i	−0.589700	+	0.288624i
$946$	5.31233e103			0.370762
$947$			1.34182e104i			0.902494i	0.892399	+	0.451247i	$0.149021\pi$
$947$			1.34182e104i			0.902494i	−0.892399	+	0.451247i	$0.850979\pi$
$948$	−4.74332e102	−	3.10230e103i	−0.0307462	−	0.201090i
$949$	1.41450e104			0.883661
$950$			1.15605e104i			0.696066i
$951$	2.32805e104	−	3.55952e103i	1.35106	−	0.206573i
$952$	3.34709e104			1.87230
$953$		−	1.44176e104i		−	0.777392i	−0.921366	−	0.388696i	$-0.872926\pi$
$953$		−	1.44176e104i		−	0.777392i	0.921366	−	0.388696i	$-0.127074\pi$
$954$	−3.53484e104	+	1.10681e104i	−1.83729	+	0.575280i
$955$	1.16486e104			0.583654
$956$			7.24062e103i			0.349743i
$957$	4.74961e102	+	3.10641e103i	0.0221177	+	0.144657i
$958$	−8.62854e103			−0.387387
$959$		−	2.60021e104i		−	1.12553i
$960$	−6.52227e103	+	9.97236e102i	−0.272211	+	0.0416203i
$961$	2.14353e104			0.862603
$962$		−	1.73730e104i		−	0.674137i
$963$	1.33432e104	+	4.26145e104i	0.499275	+	1.59455i
$964$	4.77503e103			0.172298
$965$		−	6.12008e103i		−	0.212962i
$966$	−1.41620e104	−	9.26242e104i	−0.475253	−	3.10831i
$967$	−3.39129e104			−1.09758			−0.548792	−	0.835959i	$-0.684912\pi$
$967$	−3.39129e104			−1.09758			−0.548792	+	0.835959i	$0.684912\pi$
$968$		−	2.50469e104i		−	0.781837i
$969$	−2.88754e104	+	4.41497e103i	−0.869352	+	0.132921i
$970$	−2.39230e104			−0.694712
$971$			3.72372e104i			1.04305i	0.853237	+	0.521523i	$0.174636\pi$
$971$			3.72372e104i			1.04305i	−0.853237	+	0.521523i	$0.825364\pi$
$972$	4.81349e103	+	5.07853e103i	0.130059	+	0.137221i
$973$	−1.96850e103			−0.0513082
$974$		−	6.68246e103i		−	0.168025i
$975$	−5.20270e103	−	3.40275e104i	−0.126202	−	0.825407i
$976$	3.82210e103			0.0894454
$977$			2.47114e104i			0.557941i	0.960300	+	0.278970i	$0.0899931\pi$
$977$			2.47114e104i			0.557941i	−0.960300	+	0.278970i	$0.910007\pi$
$978$	4.98308e104	−	7.61899e103i	1.08552	−	0.165973i
$979$	8.33996e103			0.175295
$980$		−	7.44864e103i		−	0.151065i
$981$	−1.76600e104	+	5.52959e103i	−0.345601	+	0.108213i
$982$	−3.95122e103			−0.0746156
$983$		−	5.18570e104i		−	0.945006i	−0.881329	−	0.472503i	$-0.843351\pi$
$983$		−	5.18570e104i		−	0.945006i	0.881329	−	0.472503i	$-0.156649\pi$
$984$	1.42105e103	+	9.29413e103i	0.0249908	+	0.163448i
$985$	−1.03509e104			−0.175674
$986$			3.40639e104i			0.557959i
$987$	4.25774e104	−	6.50996e103i	0.673099	−	0.102915i
$988$	8.85100e103			0.135051
$989$			1.09941e105i			1.61916i
$990$	−2.87898e103	−	9.19466e103i	−0.0409267	−	0.130708i
$991$	−1.65940e104			−0.227706			−0.113853	−	0.993498i	$-0.536319\pi$
$991$	−1.65940e104			−0.227706			−0.113853	+	0.993498i	$0.536319\pi$
$992$			3.84664e104i			0.509533i
$993$	2.15429e102	+	1.40898e103i	0.00275474	+	0.0180170i
$994$	1.08011e105			1.33335
$995$			5.55229e104i			0.661705i
$996$	−1.55422e103	+	2.37636e102i	−0.0178828	+	0.00273423i
$997$	−8.04145e104			−0.893314			−0.446657	−	0.894705i	$-0.647386\pi$
$997$	−8.04145e104			−0.893314			−0.446657	+	0.894705i	$0.647386\pi$
$998$		−	1.35341e104i		−	0.145165i
$999$	2.71483e104	+	5.54676e104i	0.281158	+	0.574444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.71.b.a.2.6	✓	22
3.2	odd	2	inner	3.71.b.a.2.17	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.71.b.a.2.6	✓	22	1.1	even	1	trivial
3.71.b.a.2.17	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)

\(f(q)\)	\(=\)	\(q-3.74673e10i q^{2} +(-7.56180e15 - 4.94568e16i) q^{3} -2.23206e20 q^{4} +1.07403e24i q^{5} +(-1.85301e27 + 2.83320e26i) q^{6} +6.73954e29 q^{7} -3.58706e31i q^{8} +(-2.38879e33 + 7.47965e32i) q^{9} +O(q^{10})\)	\(q-3.74673e10i q^{2} +(-7.56180e15 - 4.94568e16i) q^{3} -2.23206e20 q^{4} +1.07403e24i q^{5} +(-1.85301e27 + 2.83320e26i) q^{6} +6.73954e29 q^{7} -3.58706e31i q^{8} +(-2.38879e33 + 7.47965e32i) q^{9} +4.02409e34 q^{10} +9.56510e35i q^{11} +(1.68784e36 + 1.10391e37i) q^{12} +9.40335e38 q^{13} -2.52512e40i q^{14} +(5.31179e40 - 8.12158e39i) q^{15} -1.60749e42 q^{16} +1.38452e43i q^{17} +(2.80242e43 + 8.95016e43i) q^{18} -4.21700e44 q^{19} -2.39729e44i q^{20} +(-5.09631e45 - 3.33316e46i) q^{21} +3.58378e46 q^{22} +7.41679e47i q^{23} +(-1.77405e48 + 2.71247e47i) q^{24} +7.31680e48 q^{25} -3.52318e49i q^{26} +(5.50556e49 + 1.12486e50i) q^{27} -1.50431e50 q^{28} +6.56664e50i q^{29} +(-3.04294e50 - 1.99018e51i) q^{30} +2.15139e52 q^{31} +1.78798e52i q^{32} +(4.73059e52 - 7.23294e51i) q^{33} +5.18742e53 q^{34} +7.23844e53i q^{35} +(5.33194e53 - 1.66951e53i) q^{36} +4.93106e54 q^{37} +1.57999e55i q^{38} +(-7.11063e54 - 4.65060e55i) q^{39} +3.85260e55 q^{40} -5.23895e55i q^{41} +(-1.24884e57 + 1.90945e56i) q^{42} +1.48232e57 q^{43} -2.13499e56i q^{44} +(-8.03335e56 - 2.56563e57i) q^{45} +2.77887e58 q^{46} +1.27739e58i q^{47} +(1.21555e58 + 7.95014e58i) q^{48} +3.10710e59 q^{49} -2.74141e59i q^{50} +(6.84738e59 - 1.04695e59i) q^{51} -2.09889e59 q^{52} +3.94947e60i q^{53} +(4.21455e60 - 2.06278e60i) q^{54} -1.02732e60 q^{55} -2.41752e61i q^{56} +(3.18881e60 + 2.08559e61i) q^{57} +2.46034e61 q^{58} +9.57573e61i q^{59} +(-1.18563e61 + 1.81279e60i) q^{60} -2.37768e61 q^{61} -8.06068e62i q^{62} +(-1.60994e63 + 5.04094e62i) q^{63} -1.22788e63 q^{64} +1.00994e63i q^{65} +(-2.70999e62 - 1.77242e63i) q^{66} -8.71513e63 q^{67} -3.09033e63i q^{68} +(3.66811e64 - 5.60843e63i) q^{69} +2.71205e64 q^{70} +4.27746e64i q^{71} +(2.68300e64 + 8.56876e64i) q^{72} +1.50425e65 q^{73} -1.84754e65i q^{74} +(-5.53282e64 - 3.61865e65i) q^{75} +9.41260e64 q^{76} +6.44644e65i q^{77} +(-1.74245e66 + 2.66416e65i) q^{78} -2.81029e66 q^{79} -1.72649e66i q^{80} +(5.14688e66 - 3.57347e66i) q^{81} -1.96289e66 q^{82} +1.40793e66i q^{83} +(1.13753e66 + 7.43982e66i) q^{84} -1.48701e67 q^{85} -5.55387e67i q^{86} +(3.24765e67 - 4.96556e66i) q^{87} +3.43106e67 q^{88} -8.71916e67i q^{89} +(-9.61271e67 + 3.00988e67i) q^{90} +6.33743e68 q^{91} -1.65547e68i q^{92} +(-1.62684e68 - 1.06401e69i) q^{93} +4.78603e68 q^{94} -4.52917e68i q^{95} +(8.84276e68 - 1.35203e68i) q^{96} -5.94495e69 q^{97} -1.16415e70i q^{98} +(-7.15436e68 - 2.28491e69i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 57\!\cdots\!10 q^{3}+ \cdots - 31\!\cdots\!82 q^{9}+O(q^{10}) \) 22 * q - 57760946614928610 * q^3 - 12924724784889679105472 * q^4 - 2542746418602623176312578240 * q^6 + 3460300354929279082139211020 * q^7 - 3187627653443587997840864868739482 * q^9	\( 22 q - 57\!\cdots\!10 q^{3}+ \cdots - 21\!\cdots\!80 q^{99}+O(q^{100}) \) 22 * q - 57760946614928610 * q^3 - 12924724784889679105472 * q^4 - 2542746418602623176312578240 * q^6 + 3460300354929279082139211020 * q^7 - 3187627653443587997840864868739482 * q^9 - 204904054456738768728763726683461760 * q^10 + 168216518978261501059545818584280696640 * q^12 - 1425273500899614630088058291006011908100 * q^13 - 225789500492205687292660149319768298715840 * q^15 + 7791108876170200924142434286561643963000832 * q^16 - 159240712078782992086911930584730978792685440 * q^18 + 2012529521265601397979311193864856923750823676 * q^19 - 5316334525000974787771605720411010154937122916 * q^21 - 177999664576757911046568099334764110597720653440 * q^22 + 2221044214363105865421794285118261395337437583360 * q^24 - 47913993180689593092577485889381363779493774325690 * q^25 - 327350510975933028532160361074129063579708328041490 * q^27 + 199622305967867855771313967200368144722234985321600 * q^28 + 19529370934845391692884101303550253186745064711003520 * q^30 + 12388430374073163692752061441697409777651574405007404 * q^31 + 91609538538011962010378972773658529100477255901421120 * q^33 + 605761954772905142742127812440233067564260993651653120 * q^34 + 903849673866118209515044215587923561361275075218434112 * q^36 - 2942122339532414491328953596359839081620064777882528420 * q^37 - 83642273913756481299940648535011188445494335818507646004 * q^39 + 272642123044960747425938890972217844718938356564315934720 * q^40 + 1560147154093916143029768098476489647357578674968337342080 * q^42 - 4545359228128189931707988293083620465330530163336481972580 * q^43 - 13684191484560547979485162889557225553655737227535310368640 * q^45 + 34824945738150746982031713560272687284036228683298922087680 * q^46 + 187018310806180504680614747073364302422042767094159794882560 * q^48 + 537429667187009430823177633570141302055322425376808156541794 * q^49 + 93003444735225900297901054333392923286830613776157770499840 * q^51 - 256980181653870794210710907095882776189154704275967737138560 * q^52 + 563860949077651296335542553968680463677661322067851314468800 * q^54 - 3516118540339332578884347645630886351467431915082786354698880 * q^55 + 62619566495727497029128246919971991949893526891401194293093580 * q^57 + 116675137250817318744043251484707490614825810469582794383621760 * q^58 - 289520688194704548710930657842220413516071423272166989563023360 * q^60 - 1004518379975789938184755460502459521248398274882979931600708676 * q^61 + 2259750912371699320668016184778015293200259463243321554460021420 * q^63 - 6990282608978901236062382909358427229318771679854621867713298432 * q^64 + 9802144175872303219237439174047894300074716767326740733265952640 * q^66 - 9530737568144236105810003684427263525901520593033925660073496260 * q^67 + 68660923095126616358914910008665108044130343377859227725343530880 * q^69 - 186825484366209931701114245951001364013348939360625786570907971840 * q^70 + 800859191695150280430684829106757981081528103077118327934086410240 * q^72 - 498564607593670758195755796246723418636521686724391030404386208820 * q^73 + 2109806600351472862056557154002428953234561707550117711339382623630 * q^75 - 5263274864463875706518271175142614969672638525330024503218962553216 * q^76 + 12308167524701892969963937648343555852922730564344320620076689564800 * q^78 - 17307670437682441097149414568687707748355067787533584779481303522964 * q^79 + 13169506853202980530135359556542777642532240836639689883271737852342 * q^81 - 39431820989895068684167150578955043187025954212565254141576902204160 * q^82 + 138763489413867144231869861916118201044140663071190925822310630686336 * q^84 - 61037539079877371876604729964700889725410552523647838067356520814080 * q^85 - 149627312260702067527556548128053547148656320722965526646581032129600 * q^87 + 423107204692289659768926623144292819592688368886126043795359525621760 * q^88 - 954822316211616625813572408526438784570624253142422549351495971955840 * q^90 + 1351237435163715752950727836854267043101210025128484375869461920848568 * q^91 - 1419126662189890378883596636164605113800863195507982624574295260938180 * q^93 + 10138980254856605941232671681032460690110853357766177455228626662453760 * q^94 - 12383253221007478242150050518024370091385337450937902244753056045137920 * q^96 + 5943877415032019678068302054256035030995353737176853716379501144663980 * q^97 - 21983160871333538547745741193506138170867254293489738303957813119108480 * q^99

Introduction

L-functions

Modular forms

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