LMFDB - Embedded newform 3.71.b.a.2.8

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			2.8
Character	$\chi$	$=$	3.2
Dual form			3.71.b.a.2.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60562e10i q^{2} +(-2.92624e15 + 4.99459e16i) q^{3} +5.01667e20 q^{4} -2.60973e24i q^{5} +(1.30140e27 + 7.62467e25i) q^{6} -1.01844e29 q^{7} -4.38332e31i q^{8} +(-2.48603e33 - 2.92308e32i) q^{9} +O(q^{10})$	\(q-2.60562e10i q^{2} +(-2.92624e15 + 4.99459e16i) q^{3} +5.01667e20 q^{4} -2.60973e24i q^{5} +(1.30140e27 + 7.62467e25i) q^{6} -1.01844e29 q^{7} -4.38332e31i q^{8} +(-2.48603e33 - 2.92308e32i) q^{9} -6.79996e34 q^{10} -4.70197e36i q^{11} +(-1.46800e36 + 2.50562e37i) q^{12} -1.37324e39 q^{13} +2.65368e39i q^{14} +(1.30345e41 + 7.63669e39i) q^{15} -5.49864e41 q^{16} +6.87821e42i q^{17} +(-7.61642e42 + 6.47765e43i) q^{18} -6.24957e44 q^{19} -1.30921e45i q^{20} +(2.98021e44 - 5.08671e45i) q^{21} -1.22515e47 q^{22} +3.46526e47i q^{23} +(2.18929e48 + 1.28267e47i) q^{24} +1.65965e48 q^{25} +3.57814e49i q^{26} +(2.18743e49 - 1.23312e50i) q^{27} -5.10920e49 q^{28} +1.62210e51i q^{29} +(1.98983e50 - 3.39630e51i) q^{30} +1.22793e52 q^{31} -3.74218e52i q^{32} +(2.34844e53 + 1.37591e52i) q^{33} +1.79220e53 q^{34} +2.65786e53i q^{35} +(-1.24716e54 - 1.46641e53i) q^{36} +1.02932e55 q^{37} +1.62840e55i q^{38} +(4.01843e54 - 6.85877e55i) q^{39} -1.14393e56 q^{40} +2.23727e56i q^{41} +(-1.32540e56 - 7.76530e54i) q^{42} -2.49786e57 q^{43} -2.35882e57i q^{44} +(-7.62843e56 + 6.48786e57i) q^{45} +9.02916e57 q^{46} +1.61135e57i q^{47} +(1.60903e57 - 2.74634e58i) q^{48} -1.33131e59 q^{49} -4.32441e58i q^{50} +(-3.43538e59 - 2.01273e58i) q^{51} -6.88909e59 q^{52} +1.79448e60i q^{53} +(-3.21303e60 - 5.69960e59i) q^{54} -1.22708e61 q^{55} +4.46417e60i q^{56} +(1.82878e60 - 3.12141e61i) q^{57} +4.22658e61 q^{58} +7.30410e61i q^{59} +(6.53898e61 + 3.83107e60i) q^{60} +4.29273e62 q^{61} -3.19953e62i q^{62} +(2.53188e62 + 2.97699e61i) q^{63} -1.62423e63 q^{64} +3.58378e63i q^{65} +(3.58509e62 - 6.11914e63i) q^{66} +7.14909e63 q^{67} +3.45057e63i q^{68} +(-1.73076e64 - 1.01402e63i) q^{69} +6.92538e63 q^{70} -1.89621e64i q^{71} +(-1.28128e64 + 1.08971e65i) q^{72} -8.11385e64 q^{73} -2.68200e65i q^{74} +(-4.85654e63 + 8.28927e64i) q^{75} -3.13520e65 q^{76} +4.78869e65i q^{77} +(-1.78713e66 - 1.04705e65i) q^{78} +3.31577e66 q^{79} +1.43499e66i q^{80} +(6.09490e66 + 1.45337e66i) q^{81} +5.82948e66 q^{82} -7.13816e66i q^{83} +(1.49507e65 - 2.55183e66i) q^{84} +1.79503e67 q^{85} +6.50848e67i q^{86} +(-8.10174e67 - 4.74667e66i) q^{87} -2.06102e68 q^{88} +1.36368e68i q^{89} +(1.69049e68 + 1.98768e67i) q^{90} +1.39857e68 q^{91} +1.73841e68i q^{92} +(-3.59323e67 + 6.13303e68i) q^{93} +4.19856e67 q^{94} +1.63097e69i q^{95} +(1.86907e69 + 1.09505e68i) q^{96} +1.43149e69 q^{97} +3.46889e69i q^{98} +(-1.37442e69 + 1.16892e70i) 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 $

$2$		−	2.60562e10i		−	0.758335i	−0.925328	−	0.379167i	$-0.876210\pi$
$2$		−	2.60562e10i		−	0.758335i	0.925328	−	0.379167i	$-0.123790\pi$
$3$	−2.92624e15	+	4.99459e16i	−0.0584879	+	0.998288i
$3$	−2.92624e15	+	4.99459e16i	−0.0584879	+	0.998288i
$4$	5.01667e20			0.424928
$5$		−	2.60973e24i		−	0.896696i	−0.893859	−	0.448348i	$-0.852013\pi$
$5$		−	2.60973e24i		−	0.896696i	0.893859	−	0.448348i	$-0.147987\pi$
$6$	1.30140e27	+	7.62467e25i	0.757037	+	0.0443534i
$7$	−1.01844e29			−0.268847			−0.134424	−	0.990924i	$-0.542918\pi$
$7$	−1.01844e29			−0.268847			−0.134424	+	0.990924i	$0.542918\pi$
$8$		−	4.38332e31i		−	1.08057i
$9$	−2.48603e33	−	2.92308e32i	−0.993158	−	0.116776i
$10$	−6.79996e34			−0.679996
$11$		−	4.70197e36i		−	1.67315i	−0.547851	−	0.836576i	$-0.684554\pi$
$11$		−	4.70197e36i		−	1.67315i	0.547851	−	0.836576i	$-0.315446\pi$
$12$	−1.46800e36	+	2.50562e37i	−0.0248532	+	0.424201i
$13$	−1.37324e39			−1.41166			−0.705829	−	0.708383i	$-0.749425\pi$
$13$	−1.37324e39			−1.41166			−0.705829	+	0.708383i	$0.749425\pi$
$14$			2.65368e39i			0.203876i
$15$	1.30345e41	+	7.63669e39i	0.895161	+	0.0524459i
$16$	−5.49864e41			−0.394508
$17$			6.87821e42i			0.591239i	0.955306	+	0.295620i	$0.0955261\pi$
$17$			6.87821e42i			0.591239i	−0.955306	+	0.295620i	$0.904474\pi$
$18$	−7.61642e42	+	6.47765e43i	−0.0885550	+	0.753147i
$19$	−6.24957e44			−1.09515			−0.547576	−	0.836756i	$-0.684449\pi$
$19$	−6.24957e44			−1.09515			−0.547576	+	0.836756i	$0.684449\pi$
$20$		−	1.30921e45i		−	0.381031i
$21$	2.98021e44	−	5.08671e45i	0.0157243	−	0.268387i
$22$	−1.22515e47			−1.26881
$23$			3.46526e47i			0.757290i	0.925542	+	0.378645i	$0.123610\pi$
$23$			3.46526e47i			0.757290i	−0.925542	+	0.378645i	$0.876390\pi$
$24$	2.18929e48	+	1.28267e47i	1.07872	+	0.0632005i
$25$	1.65965e48			0.195937
$26$			3.57814e49i			1.07051i
$27$	2.18743e49	−	1.23312e50i	0.174663	−	0.984628i
$28$	−5.10920e49			−0.114241
$29$			1.62210e51i			1.06206i	0.847353	+	0.531030i	$0.178195\pi$
$29$			1.62210e51i			1.06206i	−0.847353	+	0.531030i	$0.821805\pi$
$30$	1.98983e50	−	3.39630e51i	0.0397715	−	0.678832i
$31$	1.22793e52			0.778961			0.389481	−	0.921035i	$-0.372655\pi$
$31$	1.22793e52			0.778961			0.389481	+	0.921035i	$0.372655\pi$
$32$		−	3.74218e52i		−	0.781404i
$33$	2.34844e53	+	1.37591e52i	1.67029	+	0.0978592i
$34$	1.79220e53			0.448357
$35$			2.65786e53i			0.241074i
$36$	−1.24716e54	−	1.46641e53i	−0.422021	−	0.0496212i
$37$	1.02932e55			1.33502			0.667510	−	0.744601i	$-0.267360\pi$
$37$	1.02932e55			1.33502			0.667510	+	0.744601i	$0.267360\pi$
$38$			1.62840e55i			0.830492i
$39$	4.01843e54	−	6.85877e55i	0.0825649	−	1.40924i
$40$	−1.14393e56			−0.968945
$41$			2.23727e56i			0.798516i	0.916839	+	0.399258i	$0.130732\pi$
$41$			2.23727e56i			0.798516i	−0.916839	+	0.399258i	$0.869268\pi$
$42$	−1.32540e56	−	7.76530e54i	−0.203527	−	0.0119243i
$43$	−2.49786e57			−1.68334			−0.841672	−	0.539989i	$-0.818428\pi$
$43$	−2.49786e57			−1.68334			−0.841672	+	0.539989i	$0.818428\pi$
$44$		−	2.35882e57i		−	0.710969i
$45$	−7.62843e56	+	6.48786e57i	−0.104712	+	0.890561i
$46$	9.02916e57			0.574279
$47$			1.61135e57i			0.0482797i	0.999709	+	0.0241399i	$0.00768470\pi$
$47$			1.61135e57i			0.0482797i	−0.999709	+	0.0241399i	$0.992315\pi$
$48$	1.60903e57	−	2.74634e58i	0.0230740	−	0.393833i
$49$	−1.33131e59			−0.927721
$50$		−	4.32441e58i		−	0.148586i
$51$	−3.43538e59	−	2.01273e58i	−0.590227	−	0.0345803i
$52$	−6.88909e59			−0.599853
$53$			1.79448e60i			0.802203i	0.916034	+	0.401101i	$0.131373\pi$
$53$			1.79448e60i			0.802203i	−0.916034	+	0.401101i	$0.868627\pi$
$54$	−3.21303e60	−	5.69960e59i	−0.746678	−	0.132453i
$55$	−1.22708e61			−1.50031
$56$			4.46417e60i			0.290509i
$57$	1.82878e60	−	3.12141e61i	0.0640532	−	1.09328i
$58$	4.22658e61			0.805396
$59$			7.30410e61i			0.765150i	0.923924	+	0.382575i	$0.124963\pi$
$59$			7.30410e61i			0.765150i	−0.923924	+	0.382575i	$0.875037\pi$
$60$	6.53898e61	+	3.83107e60i	0.380379	+	0.0222857i
$61$	4.29273e62			1.40020			0.700099	−	0.714045i	$-0.253139\pi$
$61$	4.29273e62			1.40020			0.700099	+	0.714045i	$0.253139\pi$
$62$		−	3.19953e62i		−	0.590714i
$63$	2.53188e62	+	2.97699e61i	0.267008	+	0.0313948i
$64$	−1.62423e63			−0.987074
$65$			3.58378e63i			1.26583i
$66$	3.58509e62	−	6.11914e63i	0.0742100	−	1.26664i
$67$	7.14909e63			0.874244			0.437122	−	0.899402i	$-0.355998\pi$
$67$	7.14909e63			0.874244			0.437122	+	0.899402i	$0.355998\pi$
$68$			3.45057e63i			0.251234i
$69$	−1.73076e64	−	1.01402e63i	−0.755994	−	0.0442923i
$70$	6.92538e63			0.182815
$71$		−	1.89621e64i		−	0.304681i	−0.988328	−	0.152340i	$-0.951319\pi$
$71$		−	1.89621e64i		−	0.304681i	0.988328	−	0.152340i	$-0.0486810\pi$
$72$	−1.28128e64	+	1.08971e65i	−0.126185	+	1.07318i
$73$	−8.11385e64			−0.493091			−0.246545	−	0.969131i	$-0.579295\pi$
$73$	−8.11385e64			−0.493091			−0.246545	+	0.969131i	$0.579295\pi$
$74$		−	2.68200e65i		−	1.01239i
$75$	−4.85654e63	+	8.28927e64i	−0.0114599	+	0.195601i
$76$	−3.13520e65			−0.465361
$77$			4.78869e65i			0.449823i
$78$	−1.78713e66	−	1.04705e65i	−1.06868	−	0.0626119i
$79$	3.31577e66			1.26951			0.634755	−	0.772713i	$-0.281101\pi$
$79$	3.31577e66			1.26951			0.634755	+	0.772713i	$0.281101\pi$
$80$			1.43499e66i			0.353754i
$81$	6.09490e66	+	1.45337e66i	0.972727	+	0.231953i
$82$	5.82948e66			0.605543
$83$		−	7.13816e66i		−	0.485125i	−0.970136	−	0.242562i	$-0.922012\pi$
$83$		−	7.13816e66i		−	0.485125i	0.970136	−	0.242562i	$-0.0779879\pi$
$84$	1.49507e65	−	2.55183e66i	0.00668171	−	0.114045i
$85$	1.79503e67			0.530161
$86$			6.50848e67i			1.27654i
$87$	−8.10174e67	−	4.74667e66i	−1.06024	−	0.0621176i
$88$	−2.06102e68			−1.80796
$89$			1.36368e68i			0.805493i	0.915311	+	0.402747i	$0.131944\pi$
$89$			1.36368e68i			0.805493i	−0.915311	+	0.402747i	$0.868056\pi$
$90$	1.69049e68	+	1.98768e67i	0.675343	+	0.0794069i
$91$	1.39857e68			0.379520
$92$			1.73841e68i			0.321794i
$93$	−3.59323e67	+	6.13303e68i	−0.0455598	+	0.777628i
$94$	4.19856e67			0.0366122
$95$			1.63097e69i			0.982018i
$96$	1.86907e69	+	1.09505e68i	0.780066	+	0.0457027i
$97$	1.43149e69			0.415699			0.207849	−	0.978161i	$-0.433354\pi$
$97$	1.43149e69			0.415699			0.207849	+	0.978161i	$0.433354\pi$
$98$			3.46889e69i			0.703523i
$99$	−1.37442e69	+	1.16892e70i	−0.195383	+	1.66170i
$100$	8.32591e68			0.0832591
$101$			1.00810e70i			0.711631i	0.934556	+	0.355816i	$0.115797\pi$
$101$			1.00810e70i			0.711631i	−0.934556	+	0.355816i	$0.884203\pi$
$102$	−5.24441e68	+	8.95130e69i	−0.0262235	+	0.447590i
$103$	−1.28863e70			−0.457958			−0.228979	−	0.973431i	$-0.573539\pi$
$103$	−1.28863e70			−0.457958			−0.228979	+	0.973431i	$0.573539\pi$
$104$			6.01936e70i			1.52540i
$105$	−1.32749e70	−	7.77755e68i	−0.240662	−	0.0140999i
$106$	4.67574e70			0.608338
$107$			1.89135e71i			1.77150i	0.464167	+	0.885748i	$0.346354\pi$
$107$			1.89135e71i			1.77150i	−0.464167	+	0.885748i	$0.653646\pi$
$108$	1.09736e70	−	6.18613e70i	0.0742194	−	0.418396i
$109$	−7.88841e70			−0.386422			−0.193211	−	0.981157i	$-0.561890\pi$
$109$	−7.88841e70			−0.386422			−0.193211	+	0.981157i	$0.561890\pi$
$110$			3.19732e71i			1.13774i
$111$	−3.01202e70	+	5.14101e71i	−0.0780826	+	1.33274i
$112$	5.60006e70			0.106062
$113$		−	8.56101e71i		−	1.18790i	−0.804502	−	0.593950i	$-0.797568\pi$
$113$		−	8.56101e71i		−	1.18790i	0.804502	−	0.593950i	$-0.202432\pi$
$114$	−8.13319e71	−	4.76509e70i	−0.829070	−	0.0485737i
$115$	9.04340e71			0.679059
$116$			8.13755e71i			0.451299i
$117$	3.41392e72	+	4.01408e71i	1.40200	+	0.164847i
$118$	1.90317e72			0.580240
$119$		−	7.00507e71i		−	0.158953i
$120$	3.34741e71	−	5.71345e72i	0.0566716	−	0.967286i
$121$	−1.42110e73			−1.79944
$122$		−	1.11852e73i		−	1.06182i
$123$	−1.11743e73	−	6.54680e71i	−0.797149	−	0.0467036i
$124$	6.16014e72			0.331003
$125$		−	2.64365e73i		−	1.07239i
$126$	7.75690e71	−	6.59712e72i	0.0238078	−	0.202482i
$127$	−2.67571e73			−0.622743			−0.311372	−	0.950288i	$-0.600788\pi$
$127$	−2.67571e73			−0.622743			−0.311372	+	0.950288i	$0.600788\pi$
$128$		−	1.85851e72i		−	0.0328712i
$129$	7.30935e72	−	1.24758e74i	0.0984553	−	1.68046i
$130$	9.33798e73			0.959921
$131$			1.79396e73i			0.141032i	0.997511	+	0.0705160i	$0.0224646\pi$
$131$			1.79396e73i			0.141032i	−0.997511	+	0.0705160i	$0.977535\pi$
$132$	1.17813e74	+	6.90247e72i	0.709752	+	0.0415831i
$133$	6.36484e73			0.294429
$134$		−	1.86278e74i		−	0.662970i
$135$	−3.21810e74	−	5.70859e73i	−0.882912	−	0.156620i
$136$	3.01494e74			0.638877
$137$			4.94189e74i			0.810351i	0.914239	+	0.405175i	$0.132790\pi$
$137$			4.94189e74i			0.810351i	−0.914239	+	0.405175i	$0.867210\pi$
$138$	−2.64215e73	+	4.50969e74i	−0.0335884	+	0.573296i
$139$	−1.52835e75			−1.50905			−0.754527	−	0.656269i	$-0.772134\pi$
$139$	−1.52835e75			−1.50905			−0.754527	+	0.656269i	$0.772134\pi$
$140$			1.33336e74i			0.102439i
$141$	−8.04803e73	−	4.71520e72i	−0.0481971	−	0.00282378i
$142$	−4.94081e74			−0.231050
$143$			6.45693e75i			2.36192i
$144$	1.36698e75	+	1.60729e74i	0.391809	+	0.0460689i
$145$	4.23325e75			0.952344
$146$			2.11416e75i			0.373928i
$147$	3.89574e74	−	6.64936e75i	0.0542605	−	0.926133i
$148$	5.16373e75			0.567288
$149$			1.43017e76i			1.24127i	0.784099	+	0.620636i	$0.213126\pi$
$149$			1.43017e76i			1.24127i	−0.784099	+	0.620636i	$0.786874\pi$
$150$	2.15987e75	+	1.26543e74i	0.148331	+	0.00869047i
$151$	−2.32662e76			−1.26629			−0.633143	−	0.774035i	$-0.718236\pi$
$151$	−2.32662e76			−1.26629			−0.633143	+	0.774035i	$0.718236\pi$
$152$			2.73939e76i			1.18339i
$153$	2.01055e75	−	1.70994e76i	0.0690423	−	0.587194i
$154$	1.24775e76			0.341116
$155$		−	3.20457e76i		−	0.698491i
$156$	2.01591e75	−	3.44082e76i	0.0350842	−	0.598826i
$157$	4.84557e76			0.674306			0.337153	−	0.941450i	$-0.390536\pi$
$157$	4.84557e76			0.674306			0.337153	+	0.941450i	$0.390536\pi$
$158$		−	8.63963e76i		−	0.962714i
$159$	−8.96271e76	−	5.25109e75i	−0.800830	−	0.0469192i
$160$	−9.76607e76			−0.700681
$161$		−	3.52918e76i		−	0.203595i
$162$	3.78693e76	−	1.58810e77i	0.175898	−	0.737653i
$163$	4.44485e76			0.166453			0.0832263	−	0.996531i	$-0.473478\pi$
$163$	4.44485e76			0.166453			0.0832263	+	0.996531i	$0.473478\pi$
$164$			1.12236e77i			0.339312i
$165$	3.59075e76	−	6.12879e77i	0.0877499	−	1.49774i
$166$	−1.85993e77			−0.367887
$167$			2.11028e77i			0.338270i	0.985593	+	0.169135i	$0.0540974\pi$
$167$			2.11028e77i			0.338270i	−0.985593	+	0.169135i	$0.945903\pi$
$168$	−2.22967e77	−	1.30632e76i	−0.290012	−	0.0169913i
$169$	9.39477e77			0.992776
$170$		−	4.67715e77i		−	0.402040i
$171$	1.55366e78	+	1.82680e77i	1.08766	+	0.127887i
$172$	−1.25309e78			−0.715300
$173$			9.62878e77i			0.448702i	0.974508	+	0.224351i	$0.0720262\pi$
$173$			9.62878e77i			0.448702i	−0.974508	+	0.224351i	$0.927974\pi$
$174$	−1.23680e77	+	2.11101e78i	−0.0471060	+	0.804018i
$175$	−1.69026e77			−0.0526771
$176$			2.58544e78i			0.660072i
$177$	−3.64810e78	−	2.13736e77i	−0.763840	−	0.0447520i
$178$	3.55323e78			0.610834
$179$			7.42316e78i			1.04890i	0.851442	+	0.524449i	$0.175728\pi$
$179$			7.42316e78i			1.04890i	−0.851442	+	0.524449i	$0.824272\pi$
$180$	−3.82693e77	+	3.25474e78i	−0.0444952	+	0.378424i
$181$	−1.64443e79			−1.57495			−0.787473	−	0.616350i	$-0.788611\pi$
$181$	−1.64443e79			−1.57495			−0.787473	+	0.616350i	$0.788611\pi$
$182$		−	3.64414e78i		−	0.287804i
$183$	−1.25616e78	+	2.14404e79i	−0.0818947	+	1.39780i
$184$	1.51894e79			0.818307
$185$		−	2.68623e79i		−	1.19711i
$186$	1.59803e79	+	9.36259e77i	0.589702	+	0.0345496i
$187$	3.23411e79			0.989233
$188$			8.08360e77i			0.0205154i
$189$	−2.22777e78	+	1.25586e79i	−0.0469578	+	0.264715i
$190$	4.24968e79			0.744698
$191$		−	2.73220e79i		−	0.398424i	−0.979956	−	0.199212i	$-0.936162\pi$
$191$		−	2.73220e79i		−	0.398424i	0.979956	−	0.199212i	$-0.0638382\pi$
$192$	4.75290e78	−	8.11238e79i	0.0577319	−	0.985384i
$193$	−1.50607e80			−1.52525			−0.762624	−	0.646842i	$-0.776089\pi$
$193$	−1.50607e80			−1.52525			−0.762624	+	0.646842i	$0.776089\pi$
$194$		−	3.72993e79i		−	0.315239i
$195$	−1.78995e80	−	1.04870e79i	−1.26366	−	0.0740356i
$196$	−6.67875e79			−0.394215
$197$		−	3.51956e80i		−	1.73848i	−0.494388	−	0.869241i	$-0.664608\pi$
$197$		−	3.51956e80i		−	1.73848i	0.494388	−	0.869241i	$-0.335392\pi$
$198$	3.04577e80	+	3.58121e79i	1.26013	+	0.148166i
$199$	−1.15871e80			−0.401899			−0.200950	−	0.979602i	$-0.564403\pi$
$199$	−1.15871e80			−0.401899			−0.200950	+	0.979602i	$0.564403\pi$
$200$		−	7.27478e79i		−	0.211724i
$201$	−2.09200e79	+	3.57068e80i	−0.0511327	+	0.872747i
$202$	2.62672e80			0.539655
$203$		−	1.65202e80i		−	0.285532i
$204$	−1.72342e80	−	1.00972e79i	−0.250804	−	0.0146942i
$205$	5.83867e80			0.716026
$206$			3.35768e80i			0.347285i
$207$	1.01292e80	−	8.61475e80i	0.0884330	−	0.752109i
$208$	7.55095e80			0.556910
$209$			2.93853e81i			1.83236i
$210$	−2.02653e79	+	3.45894e80i	−0.0106925	+	0.182502i
$211$	−3.80904e81			−1.70188			−0.850941	−	0.525261i	$-0.823968\pi$
$211$	−3.80904e81			−1.70188			−0.850941	+	0.525261i	$0.823968\pi$
$212$			9.00233e80i			0.340879i
$213$	9.47081e80	+	5.54878e79i	0.304159	+	0.0178201i
$214$	4.92814e81			1.34339
$215$			6.51874e81i			1.50945i
$216$	−5.40515e81	−	9.58821e80i	−1.06396	−	0.188737i
$217$	−1.25058e81			−0.209422
$218$			2.05542e81i			0.293038i
$219$	2.37431e80	−	4.05253e81i	0.0288399	−	0.492247i
$220$	−6.15588e81			−0.637523
$221$		−	9.44543e81i		−	0.834627i
$222$	1.33955e82	+	7.84819e80i	1.01066	+	0.0592128i
$223$	1.32630e82			0.855013			0.427506	−	0.904012i	$-0.359392\pi$
$223$	1.32630e82			0.855013			0.427506	+	0.904012i	$0.359392\pi$
$224$			3.81120e81i			0.210078i
$225$	−4.12594e81	−	4.85128e80i	−0.194596	−	0.0228806i
$226$	−2.23067e82			−0.900825
$227$		−	3.26514e82i		−	1.12979i	−0.825164	−	0.564894i	$-0.808917\pi$
$227$		−	3.26514e82i		−	1.12979i	0.825164	−	0.564894i	$-0.191083\pi$
$228$	9.17436e80	−	1.56590e82i	0.0272180	−	0.464564i
$229$	−4.68849e81			−0.119341			−0.0596707	−	0.998218i	$-0.519005\pi$
$229$	−4.68849e81			−0.119341			−0.0596707	+	0.998218i	$0.519005\pi$
$230$		−	2.35637e82i		−	0.514954i
$231$	−2.39175e82	−	1.40129e81i	−0.449053	−	0.0263092i
$232$	7.11021e82			1.14763
$233$		−	2.43176e81i		−	0.0337647i	−0.999857	−	0.0168823i	$-0.994626\pi$
$233$		−	2.43176e81i		−	0.0337647i	0.999857	−	0.0168823i	$-0.00537407\pi$
$234$	1.04592e82	−	8.89537e82i	0.125009	−	1.06318i
$235$	4.20518e81			0.0432922
$236$			3.66422e82i			0.325134i
$237$	−9.70274e81	+	1.65609e83i	−0.0742510	+	1.26734i
$238$	−1.82525e82			−0.120540
$239$		−	2.79624e83i		−	1.59459i	−0.603592	−	0.797294i	$-0.706264\pi$
$239$		−	2.79624e83i		−	1.59459i	0.603592	−	0.797294i	$-0.293736\pi$
$240$	−7.16721e82	−	4.19914e81i	−0.353148	−	0.0206903i
$241$	−2.99233e83			−1.27472			−0.637358	−	0.770568i	$-0.719973\pi$
$241$	−2.99233e83			−1.27472			−0.637358	+	0.770568i	$0.719973\pi$
$242$			3.70285e83i			1.36458i
$243$	−9.04250e82	+	3.00162e83i	−0.288449	+	0.957495i
$244$	2.15352e83			0.594984
$245$			3.47437e83i			0.831883i
$246$	−1.70585e82	+	2.91158e83i	−0.0354169	+	0.604506i
$247$	8.58217e83			1.54598
$248$		−	5.38243e83i		−	0.841724i
$249$	3.56522e83	+	2.08880e82i	0.484294	+	0.0283739i
$250$	−6.88834e83			−0.813232
$251$			3.24104e83i			0.332739i	0.986063	+	0.166370i	$0.0532045\pi$
$251$			3.24104e83i			0.332739i	−0.986063	+	0.166370i	$0.946796\pi$
$252$	1.27016e83	+	1.49346e82i	0.113459	+	0.0133405i
$253$	1.62936e84			1.26706
$254$			6.97188e83i			0.472248i
$255$	−5.25268e82	+	8.96541e83i	−0.0310080	+	0.529254i
$256$	−1.96598e84			−1.01200
$257$		−	2.87742e84i		−	1.29224i	−0.763236	−	0.646120i	$-0.776390\pi$
$257$		−	2.87742e84i		−	1.29224i	0.763236	−	0.646120i	$-0.223610\pi$
$258$	−3.25072e84	−	1.90454e83i	−1.27435	−	0.0746621i
$259$	−1.04830e84			−0.358917
$260$			1.79786e84i			0.537885i
$261$	4.74153e83	−	4.03260e84i	0.124023	−	1.05479i
$262$	4.67438e83			0.106950
$263$			8.97874e83i			0.179789i	0.995951	+	0.0898947i	$0.0286531\pi$
$263$			8.97874e83i			0.179789i	−0.995951	+	0.0898947i	$0.971347\pi$
$264$	6.03105e83	−	1.02940e85i	0.105744	−	1.80487i
$265$	4.68312e84			0.719332
$266$		−	1.65844e84i		−	0.223276i
$267$	−6.81102e84	−	3.99045e83i	−0.804114	−	0.0471116i
$268$	3.58646e84			0.371491
$269$		−	2.08138e84i		−	0.189244i	−0.995513	−	0.0946219i	$-0.969836\pi$
$269$		−	2.08138e84i		−	0.189244i	0.995513	−	0.0946219i	$-0.0301642\pi$
$270$	−1.48744e84	+	8.38514e84i	−0.118770	+	0.669543i
$271$	2.30026e85			1.61381			0.806905	−	0.590681i	$-0.201141\pi$
$271$	2.30026e85			1.61381			0.806905	+	0.590681i	$0.201141\pi$
$272$		−	3.78208e84i		−	0.233248i
$273$	−4.09255e83	+	6.98528e84i	−0.0221974	+	0.378871i
$274$	1.28767e85			0.614517
$275$		−	7.80362e84i		−	0.327832i
$276$	−8.68263e84	−	5.08700e83i	−0.321243	−	0.0188211i
$277$	−5.27583e85			−1.71988			−0.859941	−	0.510393i	$-0.829500\pi$
$277$	−5.27583e85			−1.71988			−0.859941	+	0.510393i	$0.829500\pi$
$278$			3.98230e85i			1.14437i
$279$	−3.05268e85	−	3.58934e84i	−0.773632	−	0.0909637i
$280$	1.16503e85			0.260498
$281$			8.62121e85i			1.70156i	0.525523	+	0.850779i	$0.323870\pi$
$281$			8.62121e85i			1.70156i	−0.525523	+	0.850779i	$0.676130\pi$
$282$	−1.22860e83	+	2.09701e84i	−0.00214137	+	0.0365495i
$283$	2.26337e85			0.348522			0.174261	−	0.984699i	$-0.444246\pi$
$283$	2.26337e85			0.348522			0.174261	+	0.984699i	$0.444246\pi$
$284$		−	9.51267e84i		−	0.129467i
$285$	−8.14602e85	−	4.77261e84i	−0.980337	−	0.0574362i
$286$	1.68243e86			1.79112
$287$		−	2.27854e85i		−	0.214679i
$288$	−1.09387e85	+	9.30317e85i	−0.0912489	+	0.776058i
$289$	8.80297e85			0.650436
$290$		−	1.10302e86i		−	0.722196i
$291$	−4.18890e84	+	7.14972e85i	−0.0243134	+	0.414987i
$292$	−4.07045e85			−0.209528
$293$		−	2.58022e85i		−	0.117839i	−0.998263	−	0.0589196i	$-0.981234\pi$
$293$		−	2.58022e85i		−	0.117839i	0.998263	−	0.0589196i	$-0.0187656\pi$
$294$	−1.73257e86	−	1.01508e85i	−0.702319	−	0.0411476i
$295$	1.90617e86			0.686107
$296$		−	4.51182e86i		−	1.44259i
$297$	−5.79807e86	−	1.02852e86i	−1.64743	−	0.292239i
$298$	3.72647e86			0.941300
$299$		−	4.75864e86i		−	1.06903i
$300$	−2.43636e84	+	4.15845e85i	−0.00486965	+	0.0831166i
$301$	2.54394e86			0.452563
$302$			6.06228e86i			0.960269i
$303$	−5.03504e86	−	2.94994e85i	−0.710413	−	0.0416218i
$304$	3.43641e86			0.432046
$305$		−	1.12029e87i		−	1.25555i
$306$	−4.45546e86	−	5.23873e85i	−0.445290	−	0.0523572i
$307$	6.01078e86			0.535905			0.267952	−	0.963432i	$-0.413653\pi$
$307$	6.01078e86			0.535905			0.267952	+	0.963432i	$0.413653\pi$
$308$			2.40233e86i			0.191142i
$309$	3.77084e85	−	6.43618e86i	0.0267850	−	0.457174i
$310$	−8.34990e86			−0.529690
$311$			3.39634e87i			1.92485i	0.271545	+	0.962426i	$0.412465\pi$
$311$			3.39634e87i			1.92485i	−0.271545	+	0.962426i	$0.587535\pi$
$312$	−3.00642e87	−	1.76141e86i	−1.52279	−	0.0892174i
$313$	3.22029e87			1.45829			0.729143	−	0.684361i	$-0.239919\pi$
$313$	3.22029e87			1.45829			0.729143	+	0.684361i	$0.239919\pi$
$314$		−	1.26257e87i		−	0.511350i
$315$	7.76913e85	−	6.60753e86i	0.0281516	−	0.239425i
$316$	1.66341e87			0.539451
$317$			5.30407e87i			1.54005i	0.638012	+	0.770026i	$0.279757\pi$
$317$			5.30407e87i			1.54005i	−0.638012	+	0.770026i	$0.720243\pi$
$318$	−1.36824e86	+	2.33534e87i	−0.0355805	+	0.607297i
$319$	7.62707e87			1.77699
$320$			4.23881e87i			0.885105i
$321$	−9.44653e87	−	5.53455e86i	−1.76846	−	0.103611i
$322$	−9.19570e86			−0.154394
$323$		−	4.29859e87i		−	0.647496i
$324$	3.05761e87	+	7.29107e86i	0.413339	+	0.0985635i
$325$	−2.27910e87			−0.276596
$326$		−	1.15816e87i		−	0.126227i
$327$	2.30834e86	−	3.93994e87i	0.0226010	−	0.385761i
$328$	9.80669e87			0.862855
$329$		−	1.64107e86i		−	0.0129799i
$330$	−1.59693e88	−	9.35612e86i	−1.13579	−	0.0665438i
$331$	7.79167e86			0.0498483			0.0249242	−	0.999689i	$-0.492066\pi$
$331$	7.79167e86			0.0498483			0.0249242	+	0.999689i	$0.492066\pi$
$332$		−	3.58098e87i		−	0.206143i
$333$	−2.55891e88	−	3.00877e87i	−1.32589	−	0.155898i
$334$	5.49858e87			0.256522
$335$		−	1.86572e88i		−	0.783931i
$336$	−1.63871e86	+	2.79700e87i	−0.00620337	+	0.105881i
$337$	6.00446e87			0.204846			0.102423	−	0.994741i	$-0.467340\pi$
$337$	6.00446e87			0.204846			0.102423	+	0.994741i	$0.467340\pi$
$338$		−	2.44792e88i		−	0.752857i
$339$	4.27587e88	+	2.50516e87i	1.18587	+	0.0694778i
$340$	9.00504e87			0.225281
$341$		−	5.77370e88i		−	1.30332i
$342$	4.75994e87	−	4.04825e88i	0.0969812	−	0.824810i
$343$	2.81737e88			0.518263
$344$			1.09489e89i			1.81898i
$345$	−2.64632e87	+	4.51681e88i	−0.0397167	+	0.677896i
$346$	2.50889e88			0.340266
$347$		−	7.03674e88i		−	0.862660i	−0.902194	−	0.431330i	$-0.858044\pi$
$347$		−	7.03674e88i		−	0.862660i	0.902194	−	0.431330i	$-0.141956\pi$
$348$	−4.06437e88	−	2.38124e87i	−0.450526	−	0.0263955i
$349$	−5.69606e88			−0.571064			−0.285532	−	0.958369i	$-0.592170\pi$
$349$	−5.69606e88			−0.571064			−0.285532	+	0.958369i	$0.592170\pi$
$350$			4.40418e87i			0.0399469i
$351$	−3.00387e88	+	1.69337e89i	−0.246565	+	1.38996i
$352$	−1.75956e89			−1.30741
$353$			3.87102e88i			0.260442i	0.991485	+	0.130221i	$0.0415687\pi$
$353$			3.87102e88i			0.260442i	−0.991485	+	0.130221i	$0.958431\pi$
$354$	−5.56914e87	+	9.50556e88i	−0.0339370	+	0.579247i
$355$	−4.94860e88			−0.273206
$356$			6.84112e88i			0.342277i
$357$	3.49875e88	+	2.04985e87i	0.158681	+	0.00929684i
$358$	1.93419e89			0.795415
$359$			2.86837e88i			0.106986i	0.998568	+	0.0534932i	$0.0170356\pi$
$359$			2.86837e88i			0.106986i	−0.998568	+	0.0534932i	$0.982964\pi$
$360$	2.84384e89	+	3.34379e88i	0.962316	+	0.113149i
$361$	6.49209e88			0.199357
$362$			4.28476e89i			1.19434i
$363$	4.15848e88	−	7.09781e89i	0.105245	−	1.79636i
$364$	7.01615e88			0.161269
$365$			2.11749e89i			0.442152i
$366$	5.58656e89	+	3.27307e88i	1.06000	+	0.0621036i
$367$	−6.02960e89			−1.03986			−0.519932	−	0.854208i	$-0.674043\pi$
$367$	−6.02960e89			−1.03986			−0.519932	+	0.854208i	$0.674043\pi$
$368$		−	1.90542e89i		−	0.298757i
$369$	6.53971e88	−	5.56192e89i	0.0932472	−	0.793053i
$370$	−6.99930e89			−0.907808
$371$		−	1.82758e89i		−	0.215670i
$372$	−1.80260e88	+	3.07674e89i	−0.0193597	+	0.330436i
$373$	−1.08256e90			−1.05838			−0.529191	−	0.848503i	$-0.677505\pi$
$373$	−1.08256e90			−1.05838			−0.529191	+	0.848503i	$0.677505\pi$
$374$		−	8.42686e89i		−	0.750170i
$375$	1.32039e90	+	7.73596e88i	1.07056	+	0.0627220i
$376$	7.06306e88			0.0521697
$377$		−	2.22754e90i		−	1.49926i
$378$	3.27229e89	+	5.80473e88i	0.200742	+	0.0356098i
$379$	−1.90809e90			−1.06715			−0.533576	−	0.845752i	$-0.679152\pi$
$379$	−1.90809e90			−1.06715			−0.533576	+	0.845752i	$0.679152\pi$
$380$			8.18202e89i			0.417287i
$381$	7.82978e88	−	1.33641e90i	0.0364230	−	0.621677i
$382$	−7.11908e89			−0.302139
$383$			8.34446e89i			0.323177i	0.986858	+	0.161589i	$0.0516618\pi$
$383$			8.34446e89i			0.323177i	−0.986858	+	0.161589i	$0.948338\pi$
$384$	9.28250e88	+	5.43845e87i	0.0328150	+	0.00192257i
$385$	1.24972e90			0.403354
$386$			3.92425e90i			1.15665i
$387$	6.20976e90	+	7.30144e89i	1.67183	+	0.196573i
$388$	7.18133e89			0.176642
$389$		−	2.93246e90i		−	0.659169i	−0.944126	−	0.329584i	$-0.893091\pi$
$389$		−	2.93246e90i		−	0.659169i	0.944126	−	0.329584i	$-0.106909\pi$
$390$	−2.73252e89	+	4.66394e90i	−0.0561438	+	0.958278i
$391$	−2.38348e90			−0.447739
$392$			5.83558e90i			1.00247i
$393$	−8.96010e89	−	5.24957e88i	−0.140791	−	0.00824867i
$394$	−9.17063e90			−1.31835
$395$		−	8.65326e90i		−	1.13836i
$396$	−6.89500e89	+	5.86409e90i	−0.0830239	+	0.706105i
$397$	9.51658e90			1.04909			0.524545	−	0.851383i	$-0.324235\pi$
$397$	9.51658e90			1.04909			0.524545	+	0.851383i	$0.324235\pi$
$398$			3.01916e90i			0.304774i
$399$	−1.86251e89	+	3.17898e90i	−0.0172205	+	0.293925i
$400$	−9.12581e89			−0.0772986
$401$			1.53235e91i			1.18934i	0.803970	+	0.594670i	$0.202717\pi$
$401$			1.53235e91i			1.18934i	−0.803970	+	0.594670i	$0.797283\pi$
$402$	9.30382e90	+	5.45094e89i	0.661835	+	0.0387757i
$403$	−1.68625e91			−1.09963
$404$			5.05730e90i			0.302392i
$405$	3.79290e90	−	1.59060e91i	0.207992	−	0.872240i
$406$	−4.30454e90			−0.216529
$407$		−	4.83980e91i		−	2.23369i
$408$	−8.82245e89	+	1.50584e91i	−0.0373666	+	0.637783i
$409$	2.93270e91			1.14012			0.570061	−	0.821602i	$-0.306920\pi$
$409$	2.93270e91			1.14012			0.570061	+	0.821602i	$0.306920\pi$
$410$		−	1.52134e91i		−	0.542988i
$411$	−2.46827e91	−	1.44612e90i	−0.808964	−	0.0473957i
$412$	−6.46463e90			−0.194599
$413$		−	7.43882e90i		−	0.205709i
$414$	−2.24468e91	−	2.63929e90i	−0.570350	−	0.0670618i
$415$	−1.86287e91			−0.435009
$416$			5.13891e91i			1.10307i
$417$	4.47232e90	−	7.63348e91i	0.0882614	−	1.50647i
$418$	7.65668e91			1.38954
$419$		−	7.89580e91i		−	1.31797i	−0.752156	−	0.658985i	$-0.770986\pi$
$419$		−	7.89580e91i		−	1.31797i	0.752156	−	0.658985i	$-0.229014\pi$
$420$	−6.65959e90	−	3.90174e89i	−0.102264	−	0.00599146i
$421$	2.25424e91			0.318513			0.159256	−	0.987237i	$-0.449090\pi$
$421$	2.25424e91			0.318513			0.159256	+	0.987237i	$0.449090\pi$
$422$			9.92490e91i			1.29060i
$423$	4.71009e89	−	4.00586e90i	0.00563789	−	0.0479494i
$424$	7.86581e91			0.866839
$425$			1.14154e91i			0.115846i
$426$	1.44580e90	−	2.46773e91i	0.0135136	−	0.230655i
$427$	−4.37191e91			−0.376440
$428$			9.48828e91i			0.752758i
$429$	−3.22497e92	−	1.88945e91i	−2.35787	−	0.138144i
$430$	1.69854e92			1.14467
$431$			1.13420e92i			0.704672i	0.935874	+	0.352336i	$0.114613\pi$
$431$			1.13420e92i			0.704672i	−0.935874	+	0.352336i	$0.885387\pi$
$432$	−1.20279e91	+	6.78046e91i	−0.0689061	+	0.388444i
$433$	−1.63205e92			−0.862299			−0.431149	−	0.902281i	$-0.641892\pi$
$433$	−1.63205e92			−0.862299			−0.431149	+	0.902281i	$0.641892\pi$
$434$			3.25854e91i			0.158812i
$435$	−1.23875e91	+	2.11433e92i	−0.0557006	+	0.950713i
$436$	−3.95735e91			−0.164202
$437$		−	2.16564e92i		−	0.829347i
$438$	−1.05594e92	−	6.18654e90i	−0.373288	−	0.0218703i
$439$	6.01356e92			1.96279			0.981394	−	0.192006i	$-0.0614994\pi$
$439$	6.01356e92			1.96279			0.981394	+	0.192006i	$0.0614994\pi$
$440$			5.37871e92i			1.62119i
$441$	3.30968e92	+	3.89153e91i	0.921374	+	0.108335i
$442$	−2.46112e92			−0.632927
$443$		−	5.93314e92i		−	1.40979i	−0.709312	−	0.704894i	$-0.750994\pi$
$443$		−	5.93314e92i		−	1.40979i	0.709312	−	0.704894i	$-0.249006\pi$
$444$	−1.51103e91	+	2.57907e92i	−0.0331795	+	0.566317i
$445$	3.55883e92			0.722282
$446$		−	3.45584e92i		−	0.648386i
$447$	−7.14309e92	−	4.18501e91i	−1.23915	−	0.0725995i
$448$	1.65419e92			0.265372
$449$		−	2.47825e92i		−	0.367725i	−0.982952	−	0.183862i	$-0.941140\pi$
$449$		−	2.47825e92i		−	0.367725i	0.982952	−	0.183862i	$-0.0588601\pi$
$450$	−1.26406e91	+	1.07506e92i	−0.0173512	+	0.147569i
$451$	1.05196e93			1.33604
$452$		−	4.29477e92i		−	0.504772i
$453$	6.80824e91	−	1.16205e93i	0.0740625	−	1.26412i
$454$	−8.50771e92			−0.856757
$455$		−	3.64988e92i		−	0.340314i
$456$	−1.36821e93	−	8.01612e91i	−1.18137	−	0.0692141i
$457$	−1.98334e93			−1.58610			−0.793050	−	0.609157i	$-0.791508\pi$
$457$	−1.98334e93			−1.58610			−0.793050	+	0.609157i	$0.791508\pi$
$458$			1.22164e92i			0.0905007i
$459$	8.48163e92	+	1.50456e92i	0.582151	+	0.103268i
$460$	4.53677e92			0.288551
$461$			9.46231e92i			0.557782i	0.960323	+	0.278891i	$0.0899668\pi$
$461$			9.46231e92i			0.557782i	−0.960323	+	0.278891i	$0.910033\pi$
$462$	−3.65122e91	+	6.23200e92i	−0.0199512	+	0.340532i
$463$	4.93689e92			0.250103			0.125052	−	0.992150i	$-0.460090\pi$
$463$	4.93689e92			0.250103			0.125052	+	0.992150i	$0.460090\pi$
$464$		−	8.91936e92i		−	0.418991i
$465$	1.60055e93	+	9.37736e91i	0.697295	+	0.0408533i
$466$	−6.33623e91			−0.0256049
$467$		−	3.21353e93i		−	1.20473i	−0.798219	−	0.602367i	$-0.794224\pi$
$467$		−	3.21353e93i		−	1.20473i	0.798219	−	0.602367i	$-0.205776\pi$
$468$	1.71265e93	+	2.01373e92i	0.595749	+	0.0700482i
$469$	−7.28095e92			−0.235038
$470$		−	1.09571e92i		−	0.0328300i
$471$	−1.41793e92	+	2.42017e93i	−0.0394388	+	0.673152i
$472$	3.20163e93			0.826800
$473$			1.17449e94i			2.81649i
$474$	4.31514e93	+	2.52817e92i	0.961066	+	0.0563071i
$475$	−1.03721e93			−0.214581
$476$		−	3.51421e92i		−	0.0675436i
$477$	5.24541e92	−	4.46114e93i	0.0936777	−	0.796714i
$478$	−7.28594e93			−1.20923
$479$			6.82878e93i			1.05342i	0.850046	+	0.526709i	$0.176574\pi$
$479$			6.82878e93i			1.05342i	−0.850046	+	0.526709i	$0.823426\pi$
$480$	2.85779e92	−	4.87775e93i	0.0409814	−	0.699482i
$481$	−1.41350e94			−1.88459
$482$			7.79688e93i			0.966662i
$483$	1.76268e93	+	1.03272e92i	0.203247	+	0.0119079i
$484$	−7.12919e93			−0.764632
$485$		−	3.73581e93i		−	0.372755i
$486$	7.82109e93	+	2.35613e93i	0.726102	+	0.218741i
$487$	1.24980e94			1.07976			0.539880	−	0.841742i	$-0.318470\pi$
$487$	1.24980e94			1.07976			0.539880	+	0.841742i	$0.318470\pi$
$488$		−	1.88164e94i		−	1.51302i
$489$	−1.30067e92	+	2.22002e93i	−0.00973547	+	0.166168i
$490$	9.05287e93			0.630846
$491$		−	6.48093e92i		−	0.0420518i	−0.999779	−	0.0210259i	$-0.993307\pi$
$491$		−	6.48093e92i		−	0.0420518i	0.999779	−	0.0210259i	$-0.00669325\pi$
$492$	−5.60575e93	−	3.28431e92i	−0.338731	−	0.0198457i
$493$	−1.11572e94			−0.627931
$494$		−	2.23619e94i		−	1.17237i
$495$	3.05057e94	+	3.58686e93i	1.49004	+	0.175199i
$496$	−6.75197e93			−0.307306
$497$			1.93119e93i			0.0819126i
$498$	5.44262e92	−	9.28961e93i	0.0215169	−	0.367257i
$499$	−2.87502e94			−1.05955			−0.529776	−	0.848137i	$-0.677724\pi$
$499$	−2.87502e94			−1.05955			−0.529776	+	0.848137i	$0.677724\pi$
$500$		−	1.32623e94i		−	0.455689i
$501$	−1.05400e94	−	6.17519e92i	−0.337691	−	0.0197847i
$502$	8.44491e93			0.252328
$503$			2.23362e93i			0.0622485i	0.999516	+	0.0311243i	$0.00990876\pi$
$503$			2.23362e93i			0.0622485i	−0.999516	+	0.0311243i	$0.990091\pi$
$504$	1.30491e93	−	1.10981e94i	0.0339244	−	0.288522i
$505$	2.63086e94			0.638117
$506$		−	4.24548e94i		−	0.960857i
$507$	−2.74914e93	+	4.69230e94i	−0.0580654	+	0.991077i
$508$	−1.34231e94			−0.264621
$509$		−	1.74347e91i		−	0.000320842i	−1.00000		0.000160421i	$-0.999949\pi$
$509$		−	1.74347e91i		−	0.000320842i	1.00000		0.000160421i	$-5.10636e-5\pi$
$510$	2.33605e94	+	1.36865e93i	0.401352	+	0.0235145i
$511$	8.26350e93			0.132566
$512$			4.90319e94i			0.734564i
$513$	−1.36705e94	+	7.70645e94i	−0.191283	+	1.07832i
$514$	−7.49745e94			−0.979951
$515$			3.36297e94i			0.410649i
$516$	3.66686e93	−	6.25869e94i	0.0418364	−	0.714076i
$517$	7.57651e93			0.0807793
$518$			2.73147e94i			0.272179i
$519$	−4.80918e94	−	2.81761e93i	−0.447934	−	0.0262436i
$520$	1.57089e95			1.36782
$521$			1.82799e95i			1.48817i	0.668083	+	0.744087i	$0.267115\pi$
$521$			1.82799e95i			1.48817i	−0.668083	+	0.744087i	$0.732885\pi$
$522$	−1.05074e95	−	1.23546e94i	−0.799886	−	0.0940507i
$523$	5.33987e94			0.380164			0.190082	−	0.981768i	$-0.439125\pi$
$523$	5.33987e94			0.380164			0.190082	+	0.981768i	$0.439125\pi$
$524$			8.99971e93i			0.0599285i
$525$	4.94611e92	−	8.44216e93i	0.00308098	−	0.0525869i
$526$	2.33952e94			0.136341
$527$			8.44599e94i			0.460552i
$528$	−1.29132e95	−	7.56562e93i	−0.658942	−	0.0386062i
$529$	8.93058e94			0.426512
$530$		−	1.22024e95i		−	0.545494i
$531$	2.13504e94	−	1.81582e95i	0.0893508	−	0.759915i
$532$	3.19303e94			0.125111
$533$		−	3.07231e95i		−	1.12723i
$534$	−1.03976e94	+	1.77469e95i	−0.0357264	+	0.609788i
$535$	4.93591e95			1.58849
$536$		−	3.13368e95i		−	0.944684i
$537$	−3.70756e95	−	2.17220e94i	−1.04710	−	0.0613478i
$538$	−5.42328e94			−0.143510
$539$			6.25979e95i			1.55222i
$540$	−1.61441e95	−	2.86381e94i	−0.375174	−	0.0665522i
$541$	−2.29465e95			−0.499819			−0.249910	−	0.968269i	$-0.580401\pi$
$541$	−2.29465e95			−0.499819			−0.249910	+	0.968269i	$0.580401\pi$
$542$		−	5.99361e95i		−	1.22381i
$543$	4.81200e94	−	8.21326e95i	0.0921153	−	1.57225i
$544$	2.57395e95			0.461996
$545$			2.05866e95i			0.346503i
$546$	1.82010e95	+	1.06636e94i	0.287311	+	0.0168330i
$547$	−8.20683e94			−0.121512			−0.0607560	−	0.998153i	$-0.519351\pi$
$547$	−8.20683e94			−0.121512			−0.0607560	+	0.998153i	$0.519351\pi$
$548$			2.47918e95i			0.344341i
$549$	−1.06719e96	−	1.25480e95i	−1.39062	−	0.163509i
$550$	−2.03332e95			−0.248607
$551$		−	1.01375e96i		−	1.16312i
$552$	−4.44478e94	+	7.58647e95i	−0.0478611	+	0.816906i
$553$	−3.37693e95			−0.341305
$554$			1.37468e96i			1.30425i
$555$	1.34166e96	+	7.86056e94i	1.19506	+	0.0700163i
$556$	−7.66722e95			−0.641239
$557$		−	2.83275e95i		−	0.222472i	−0.993794	−	0.111236i	$-0.964519\pi$
$557$		−	2.83275e95i		−	0.222472i	0.993794	−	0.111236i	$-0.0354810\pi$
$558$	−9.35246e94	+	7.95412e95i	−0.0689809	+	0.586672i
$559$	3.43017e96			2.37630
$560$		−	1.46146e95i		−	0.0951057i
$561$	−9.46379e94	+	1.61531e96i	−0.0578582	+	0.987539i
$562$	2.24636e96			1.29035
$563$			1.44661e96i			0.780832i	0.920638	+	0.390416i	$0.127669\pi$
$563$			1.44661e96i			0.780832i	−0.920638	+	0.390416i	$0.872331\pi$
$564$	−4.03743e94	−	2.36546e93i	−0.0204803	−	0.00119990i
$565$	−2.23419e96			−1.06518
$566$		−	5.89748e95i		−	0.264297i
$567$	−6.20732e95	−	1.48018e95i	−0.261515	−	0.0623601i
$568$	−8.31172e95			−0.329230
$569$		−	3.44920e96i		−	1.28466i	−0.766427	−	0.642331i	$-0.777967\pi$
$569$		−	3.44920e96i		−	1.28466i	0.766427	−	0.642331i	$-0.222033\pi$
$570$	−1.24356e95	+	2.12254e96i	−0.0435559	+	0.743424i
$571$	−5.72117e96			−1.88461			−0.942304	−	0.334760i	$-0.891345\pi$
$571$	−5.72117e96			−1.88461			−0.942304	+	0.334760i	$0.891345\pi$
$572$			3.23923e96i			1.00365i
$573$	1.36462e96	+	7.99508e94i	0.397742	+	0.0233030i
$574$	−5.93700e95			−0.162799
$575$			5.75113e95i			0.148381i
$576$	4.03789e96	+	4.74776e95i	0.980320	+	0.115266i
$577$	−6.91555e96			−1.58006			−0.790030	−	0.613068i	$-0.789935\pi$
$577$	−6.91555e96			−1.58006			−0.790030	+	0.613068i	$0.789935\pi$
$578$		−	2.29372e96i		−	0.493249i
$579$	4.40713e95	−	7.52222e96i	0.0892086	−	1.52264i
$580$	2.12368e96			0.404678
$581$			7.26982e95i			0.130425i
$582$	1.86295e96	+	1.09147e95i	0.314699	+	0.0184377i
$583$	8.43760e96			1.34221
$584$			3.55656e96i			0.532820i
$585$	1.04757e96	−	8.90939e96i	0.147818	−	1.25717i
$586$	−6.72306e95			−0.0893615
$587$		−	6.50426e96i		−	0.814449i	−0.913328	−	0.407225i	$-0.866497\pi$
$587$		−	6.50426e96i		−	0.814449i	0.913328	−	0.407225i	$-0.133503\pi$
$588$	1.95436e95	−	3.33576e96i	0.0230568	−	0.393540i
$589$	−7.67407e96			−0.853081
$590$		−	4.96676e96i		−	0.520299i
$591$	1.75788e97	+	1.02991e96i	1.73551	+	0.101680i
$592$	−5.65983e96			−0.526676
$593$		−	1.45875e96i		−	0.127958i	−0.997951	−	0.0639789i	$-0.979621\pi$
$593$		−	1.45875e96i		−	0.127958i	0.997951	−	0.0639789i	$-0.0203790\pi$
$594$	−2.67993e96	+	1.51076e97i	−0.221615	+	1.24931i
$595$	−1.82813e96			−0.142533
$596$			7.17467e96i			0.527452i
$597$	3.39067e95	−	5.78729e96i	0.0235063	−	0.401211i
$598$	−1.23992e97			−0.810686
$599$			3.75295e95i			0.0231438i	0.999933	+	0.0115719i	$0.00368353\pi$
$599$			3.75295e95i			0.0231438i	−0.999933	+	0.0115719i	$0.996316\pi$
$600$	3.63346e96	+	2.12878e95i	0.211362	+	0.0123833i
$601$	−4.24927e96			−0.233189			−0.116595	−	0.993180i	$-0.537198\pi$
$601$	−4.24927e96			−0.233189			−0.116595	+	0.993180i	$0.537198\pi$
$602$		−	6.62853e96i		−	0.343194i
$603$	−1.77728e97	−	2.08973e96i	−0.868263	−	0.102090i
$604$	−1.16719e97			−0.538081
$605$			3.70869e97i			1.61355i
$606$	−7.68642e95	+	1.31194e97i	−0.0315633	+	0.538731i
$607$	4.25777e97			1.65036			0.825179	−	0.564872i	$-0.191074\pi$
$607$	4.25777e97			1.65036			0.825179	+	0.564872i	$0.191074\pi$
$608$			2.33870e97i			0.855756i
$609$	8.25117e96	+	4.83422e95i	0.285043	+	0.0167002i
$610$	−2.91904e97			−0.952129
$611$		−	2.21277e96i		−	0.0681544i
$612$	1.00863e96	−	8.57821e96i	0.0293380	−	0.249515i
$613$	2.57654e97			0.707816			0.353908	−	0.935280i	$-0.384853\pi$
$613$	2.57654e97			0.707816			0.353908	+	0.935280i	$0.384853\pi$
$614$		−	1.56618e97i		−	0.406395i
$615$	−1.70854e96	+	2.91618e97i	−0.0418789	+	0.714800i
$616$	2.09904e97			0.486066
$617$		−	1.87781e97i		−	0.410839i	−0.978674	−	0.205419i	$-0.934144\pi$
$617$		−	1.87781e97i		−	0.410839i	0.978674	−	0.205419i	$-0.0658558\pi$
$618$	−1.67702e97	−	9.82538e95i	−0.346691	−	0.0203120i
$619$	−2.47745e97			−0.483985			−0.241992	−	0.970278i	$-0.577801\pi$
$619$	−2.47745e97			−0.483985			−0.241992	+	0.970278i	$0.577801\pi$
$620$		−	1.60763e97i		−	0.296809i
$621$	4.27307e97	+	7.58002e96i	0.745649	+	0.132271i
$622$	8.84956e97			1.45968
$623$		−	1.38883e97i		−	0.216555i
$624$	−2.20959e96	+	3.77139e97i	−0.0325725	+	0.555957i
$625$	−5.49343e97			−0.765672
$626$		−	8.39084e97i		−	1.10587i
$627$	−1.46767e98	−	8.59884e96i	−1.82922	−	0.107171i
$628$	2.43086e97			0.286532
$629$			7.07984e97i			0.789316i
$630$	−1.72167e97	−	2.02434e96i	−0.181564	−	0.0213483i
$631$	−9.73213e97			−0.970913			−0.485457	−	0.874261i	$-0.661347\pi$
$631$	−9.73213e97			−0.970913			−0.485457	+	0.874261i	$0.661347\pi$
$632$		−	1.45341e98i		−	1.37180i
$633$	1.11462e97	−	1.90246e98i	0.0995396	−	1.69897i
$634$	1.38204e98			1.16788
$635$			6.98288e97i			0.558411i
$636$	−4.49629e97	−	2.63430e96i	−0.340295	−	0.0199373i
$637$	1.82821e98			1.30962
$638$		−	1.98732e98i		−	1.34755i
$639$	−5.54277e96	+	4.71404e97i	−0.0355793	+	0.302596i
$640$	−4.85021e96			−0.0294755
$641$			9.78372e97i			0.562954i	0.959568	+	0.281477i	$0.0908243\pi$
$641$			9.78372e97i			0.562954i	−0.959568	+	0.281477i	$0.909176\pi$
$642$	−1.44209e97	+	2.46140e98i	−0.0785719	+	1.34109i
$643$	−1.86748e97			−0.0963546			−0.0481773	−	0.998839i	$-0.515341\pi$
$643$	−1.86748e97			−0.0963546			−0.0481773	+	0.998839i	$0.515341\pi$
$644$		−	1.77047e97i		−	0.0865134i
$645$	−3.25585e98	−	1.90754e97i	−1.50686	−	0.0882844i
$646$	−1.12005e98			−0.491019
$647$			2.89862e98i			1.20376i	0.798585	+	0.601882i	$0.205582\pi$
$647$			2.89862e98i			1.20376i	−0.798585	+	0.601882i	$0.794418\pi$
$648$	6.37059e97	−	2.67159e98i	0.250642	−	1.05110i
$649$	3.43436e98			1.28021
$650$			5.93846e97i			0.209752i
$651$	3.65951e96	−	6.24615e97i	0.0122486	−	0.209063i
$652$	2.22983e97			0.0707304
$653$			5.85695e98i			1.76080i	0.474232	+	0.880400i	$0.342726\pi$
$653$			5.85695e98i			1.76080i	−0.474232	+	0.880400i	$0.657274\pi$
$654$	−1.02660e98	−	6.01466e96i	−0.292536	−	0.0171392i
$655$	4.68175e97			0.126463
$656$		−	1.23019e98i		−	0.315021i
$657$	2.01713e98	+	2.37174e97i	0.489717	+	0.0575810i
$658$	−4.27600e96			−0.00984309
$659$			4.77430e98i			1.04213i	0.853518	+	0.521063i	$0.174464\pi$
$659$			4.77430e98i			1.04213i	−0.853518	+	0.521063i	$0.825536\pi$
$660$	1.80136e97	−	3.07461e98i	0.0372874	−	0.636432i
$661$	2.52313e98			0.495324			0.247662	−	0.968846i	$-0.420338\pi$
$661$	2.52313e98			0.495324			0.247662	+	0.968846i	$0.420338\pi$
$662$		−	2.03021e97i		−	0.0378017i
$663$	4.71761e98	+	2.76396e97i	0.833198	+	0.0488156i
$664$	−3.12889e98			−0.524212
$665$		−	1.66105e98i		−	0.264013i
$666$	−7.83970e97	+	6.66754e98i	−0.118223	+	1.00547i
$667$	−5.62102e98			−0.804287
$668$			1.05866e98i			0.143740i
$669$	−3.88108e97	+	6.62434e98i	−0.0500079	+	0.853549i
$670$	−4.86135e98			−0.594482
$671$		−	2.01843e99i		−	2.34275i
$672$	−1.90354e98	−	1.11525e97i	−0.209719	−	0.0122870i
$673$	−7.24676e98			−0.757908			−0.378954	−	0.925415i	$-0.623716\pi$
$673$	−7.24676e98			−0.757908			−0.378954	+	0.925415i	$0.623716\pi$
$674$		−	1.56453e98i		−	0.155342i
$675$	3.63036e97	−	2.04654e98i	0.0342230	−	0.192925i
$676$	4.71304e98			0.421859
$677$		−	4.27488e98i		−	0.363347i	−0.983359	−	0.181673i	$-0.941849\pi$
$677$		−	4.27488e98i		−	0.363347i	0.983359	−	0.181673i	$-0.0581513\pi$
$678$	6.52749e97	−	1.11413e99i	0.0526874	−	0.899283i
$679$	−1.45790e98			−0.111760
$680$		−	7.86818e98i		−	0.572878i
$681$	1.63080e99	+	9.55459e97i	1.12785	+	0.0660789i
$682$	−1.50441e99			−0.988354
$683$			1.50254e99i			0.937781i	0.883256	+	0.468890i	$0.155346\pi$
$683$			1.50254e99i			0.937781i	−0.883256	+	0.468890i	$0.844654\pi$
$684$	7.79421e98	+	9.16443e97i	0.462177	+	0.0543428i
$685$	1.28970e99			0.726638
$686$		−	7.34100e98i		−	0.393017i
$687$	1.37197e97	−	2.34171e98i	0.00698003	−	0.119137i
$688$	1.37348e99			0.664092
$689$		−	2.46426e99i		−	1.13244i
$690$	1.17691e99	+	6.89529e97i	0.514072	+	0.0301186i
$691$	−1.32500e99			−0.550153			−0.275076	−	0.961422i	$-0.588703\pi$
$691$	−1.32500e99			−0.550153			−0.275076	+	0.961422i	$0.588703\pi$
$692$			4.83044e98i			0.190666i
$693$	1.39977e98	−	1.19048e99i	0.0525283	−	0.446745i
$694$	−1.83351e99			−0.654186
$695$			3.98858e99i			1.35316i
$696$	−2.08062e98	+	3.55126e99i	−0.0671226	+	1.14567i
$697$	−1.53884e99			−0.472114
$698$			1.48418e99i			0.433057i
$699$	1.21456e98	+	7.11591e96i	0.0337069	+	0.00197483i
$700$	−8.47947e97			−0.0223840
$701$		−	3.85352e99i		−	0.967669i	−0.875160	−	0.483834i	$-0.839244\pi$
$701$		−	3.85352e99i		−	0.967669i	0.875160	−	0.483834i	$-0.160756\pi$
$702$	4.41226e99	+	7.82693e98i	1.05405	+	0.186979i
$703$	−6.43278e99			−1.46205
$704$			7.63709e99i			1.65152i
$705$	−1.23054e97	+	2.10032e98i	−0.00253207	+	0.0432181i
$706$	1.00864e99			0.197502
$707$		−	1.02669e99i		−	0.191320i
$708$	−1.83013e99	−	1.07224e98i	−0.324577	−	0.0190164i
$709$	−5.23902e99			−0.884365			−0.442183	−	0.896925i	$-0.645796\pi$
$709$	−5.23902e99			−0.884365			−0.442183	+	0.896925i	$0.645796\pi$
$710$			1.28942e99i			0.207182i
$711$	−8.24310e99	−	9.69225e98i	−1.26082	−	0.148248i
$712$	5.97745e99			0.870394
$713$			4.25512e99i			0.589899i
$714$	5.34114e97	−	9.11640e98i	0.00705012	−	0.120333i
$715$	1.68508e100			2.11792
$716$			3.72395e99i			0.445706i
$717$	1.39661e100	+	8.18248e98i	1.59186	+	0.0932641i
$718$	7.47387e98			0.0811316
$719$		−	8.31250e99i		−	0.859450i	−0.902960	−	0.429725i	$-0.858611\pi$
$719$		−	8.31250e99i		−	0.859450i	0.902960	−	0.429725i	$-0.141389\pi$
$720$	4.19460e98	−	3.56744e99i	0.0413098	−	0.351333i
$721$	1.31240e99			0.123121
$722$		−	1.69159e99i		−	0.151180i
$723$	8.75629e98	−	1.49455e100i	0.0745555	−	1.27253i
$724$	−8.24956e99			−0.669239
$725$			2.69212e99i			0.208097i
$726$	−1.84942e100	−	1.08354e99i	−1.36224	−	0.0798113i
$727$	1.05912e99			0.0743428			0.0371714	−	0.999309i	$-0.488165\pi$
$727$	1.05912e99			0.0743428			0.0371714	+	0.999309i	$0.488165\pi$
$728$		−	6.13038e99i		−	0.410099i
$729$	−1.47273e100	−	5.39471e99i	−0.938985	−	0.343957i
$730$	5.51738e99			0.335300
$731$		−	1.71808e100i		−	0.995258i
$732$	−6.30172e98	+	1.07560e100i	−0.0347994	+	0.593965i
$733$	−3.42595e99			−0.180361			−0.0901803	−	0.995925i	$-0.528744\pi$
$733$	−3.42595e99			−0.180361			−0.0901803	+	0.995925i	$0.528744\pi$
$734$			1.57108e100i			0.788565i
$735$	−1.73530e100	−	1.01668e99i	−0.830459	−	0.0486551i
$736$	1.29676e100			0.591749
$737$		−	3.36148e100i		−	1.46274i
$738$	−1.44923e100	−	1.70400e99i	−0.601400	−	0.0707126i
$739$	1.15846e100			0.458486			0.229243	−	0.973369i	$-0.426375\pi$
$739$	1.15846e100			0.458486			0.229243	+	0.973369i	$0.426375\pi$
$740$		−	1.34759e100i		−	0.508685i
$741$	−2.51135e99	+	4.28644e100i	−0.0904211	+	1.54333i
$742$	−4.76198e99			−0.163550
$743$			1.11144e100i			0.364148i	0.983285	+	0.182074i	$0.0582811\pi$
$743$			1.11144e100i			0.364148i	−0.983285	+	0.182074i	$0.941719\pi$
$744$	2.68830e100	+	1.57503e99i	0.840283	+	0.0492307i
$745$	3.73234e100			1.11304
$746$			2.82074e100i			0.802608i
$747$	−2.08654e99	+	1.77457e100i	−0.0566507	+	0.481806i
$748$	1.62244e100			0.420353
$749$		−	1.92624e100i		−	0.476262i
$750$	2.01570e99	−	3.44044e100i	0.0475642	−	0.811840i
$751$	4.42170e99			0.0995844			0.0497922	−	0.998760i	$-0.484144\pi$
$751$	4.42170e99			0.0995844			0.0497922	+	0.998760i	$0.484144\pi$
$752$		−	8.86022e98i		−	0.0190467i
$753$	−1.61877e100	−	9.48406e98i	−0.332169	−	0.0194612i
$754$	−5.80412e100			−1.13694
$755$			6.07184e100i			1.13547i
$756$	−1.11760e99	+	6.30023e99i	−0.0199537	+	0.112485i
$757$	5.96362e99			0.101661			0.0508305	−	0.998707i	$-0.483813\pi$
$757$	5.96362e99			0.101661			0.0508305	+	0.998707i	$0.483813\pi$
$758$			4.97175e100i			0.809259i
$759$	−4.76789e99	+	8.13796e100i	−0.0741078	+	1.26489i
$760$	7.14906e100			1.06114
$761$			1.48842e100i			0.210990i	0.994420	+	0.105495i	$0.0336427\pi$
$761$			1.48842e100i			0.210990i	−0.994420	+	0.105495i	$0.966357\pi$
$762$	−3.48217e100	−	2.04014e99i	−0.471439	−	0.0276208i
$763$	8.03391e99			0.103889
$764$		−	1.37065e100i		−	0.169301i
$765$	−4.46249e100	−	5.24699e99i	−0.526534	−	0.0619099i
$766$	2.17425e100			0.245077
$767$		−	1.00303e101i		−	1.08013i
$768$	5.75294e99	−	9.81928e100i	0.0591898	−	1.01027i
$769$	−1.03233e101			−1.01484			−0.507420	−	0.861699i	$-0.669401\pi$
$769$	−1.03233e101			−1.01484			−0.507420	+	0.861699i	$0.669401\pi$
$770$		−	3.25629e100i		−	0.305877i
$771$	1.43715e101	+	8.42001e99i	1.29003	+	0.0755805i
$772$	−7.55547e100			−0.648121
$773$			1.93755e101i			1.58844i	0.607633	+	0.794218i	$0.292119\pi$
$773$			1.93755e101i			1.58844i	−0.607633	+	0.794218i	$0.707881\pi$
$774$	1.90248e100	−	1.61803e101i	0.149069	−	1.26780i
$775$	2.03794e100			0.152627
$776$		−	6.27470e100i		−	0.449193i
$777$	3.06758e99	−	5.23583e100i	0.0209923	−	0.358302i
$778$	−7.64089e100			−0.499871
$779$		−	1.39820e101i		−	0.874496i
$780$	−8.97960e100	−	5.26099e99i	−0.536965	−	0.0314598i
$781$	−8.91593e100			−0.509777
$782$			6.21044e100i			0.339536i
$783$	2.00024e101	+	3.54824e100i	1.04573	+	0.185503i
$784$	7.32041e100			0.365993
$785$		−	1.26456e101i		−	0.604648i
$786$	−1.36784e99	+	2.33466e100i	−0.00625526	+	0.106766i
$787$	2.22963e101			0.975255			0.487627	−	0.873052i	$-0.337862\pi$
$787$	2.22963e101			0.975255			0.487627	+	0.873052i	$0.337862\pi$
$788$		−	1.76565e101i		−	0.738730i
$789$	−4.48451e100	−	2.62740e99i	−0.179482	−	0.0105155i
$790$	−2.25471e101			−0.863261
$791$			8.71891e100i			0.319364i
$792$	5.12377e101	+	6.02453e100i	1.79559	+	0.211126i
$793$	−5.89496e101			−1.97660
$794$		−	2.47966e101i		−	0.795562i
$795$	−1.37039e100	+	2.33902e101i	−0.0420722	+	0.718100i
$796$	−5.81287e100			−0.170778
$797$			5.57517e101i			1.56753i	0.621056	+	0.783766i	$0.286704\pi$
$797$			5.57517e101i			1.56753i	−0.621056	+	0.783766i	$0.713296\pi$
$798$	8.28320e100	+	4.85298e99i	0.222893	+	0.0130589i
$799$	−1.10832e100			−0.0285448
$800$		−	6.21071e100i		−	0.153106i
$801$	3.98614e100	−	3.39015e101i	0.0940620	−	0.799982i
$802$	3.99273e101			0.901918
$803$			3.81510e101i			0.825016i
$804$	−1.04948e100	+	1.79129e101i	−0.0217277	+	0.370855i
$805$	−9.21020e100			−0.182563
$806$			4.39372e101i			0.833885i
$807$	1.03956e101	+	6.09062e99i	0.188920	+	0.0110685i
$808$	4.41882e101			0.768969
$809$			2.81577e99i			0.00469243i	0.999997	+	0.00234622i	$0.000746825\pi$
$809$			2.81577e99i			0.00469243i	−0.999997	+	0.00234622i	$0.999253\pi$
$810$	−4.14451e101	−	9.88285e100i	−0.661450	−	0.157727i
$811$	−9.09400e101			−1.39003			−0.695017	−	0.718994i	$-0.744603\pi$
$811$	−9.09400e101			−1.39003			−0.695017	+	0.718994i	$0.744603\pi$
$812$		−	8.28764e100i		−	0.121331i
$813$	−6.73113e100	+	1.14889e102i	−0.0943884	+	1.61105i
$814$	−1.26107e102			−1.69389
$815$		−	1.15998e101i		−	0.149257i
$816$	1.88899e101	+	1.10673e100i	0.232849	+	0.0136422i
$817$	1.56106e102			1.84352
$818$		−	7.64149e101i		−	0.864594i
$819$	−3.47688e101	−	4.08812e100i	−0.376924	−	0.0443187i
$820$	2.92907e101			0.304260
$821$		−	1.10604e102i		−	1.10093i	−0.834859	−	0.550464i	$-0.814451\pi$
$821$		−	1.10604e102i		−	1.10093i	0.834859	−	0.550464i	$-0.185549\pi$
$822$	−3.76803e100	+	6.43137e101i	−0.0359419	+	0.613465i
$823$	4.66356e101			0.426308			0.213154	−	0.977019i	$-0.431626\pi$
$823$	4.66356e101			0.426308			0.213154	+	0.977019i	$0.431626\pi$
$824$			5.64848e101i			0.494857i
$825$	3.89759e101	+	2.28353e100i	0.327271	+	0.0191742i
$826$	−1.93827e101			−0.155996
$827$		−	1.75102e102i		−	1.35082i	−0.737441	−	0.675412i	$-0.763966\pi$
$827$		−	1.75102e102i		−	1.35082i	0.737441	−	0.675412i	$-0.236034\pi$
$828$	5.08150e100	−	4.32173e101i	0.0375777	−	0.319592i
$829$	5.73382e101			0.406477			0.203238	−	0.979129i	$-0.434853\pi$
$829$	5.73382e101			0.406477			0.203238	+	0.979129i	$0.434853\pi$
$830$			4.85392e101i			0.329883i
$831$	1.54384e101	−	2.63506e102i	0.100592	−	1.71694i
$832$	2.23046e102			1.39341
$833$		−	9.15705e101i		−	0.548505i
$834$	−1.98899e102	−	1.16532e101i	−1.14241	−	0.0669317i
$835$	5.50725e101			0.303325
$836$			1.47416e102i			0.778619i
$837$	2.68602e101	−	1.51419e102i	0.136056	−	0.766987i
$838$	−2.05735e102			−0.999463
$839$			3.42154e102i			1.59424i	0.603824	+	0.797118i	$0.293643\pi$
$839$			3.42154e102i			1.59424i	−0.603824	+	0.797118i	$0.706357\pi$
$840$	−3.40915e100	+	5.81883e101i	−0.0152360	+	0.260052i
$841$	−2.98515e101			−0.127969
$842$		−	5.87369e101i		−	0.241539i
$843$	−4.30594e102	−	2.52277e101i	−1.69865	−	0.0995206i
$844$	−1.91087e102			−0.723178
$845$		−	2.45178e102i		−	0.890218i
$846$	−1.04377e101	−	1.22727e100i	−0.0363617	−	0.00427541i
$847$	1.44731e102			0.483774
$848$		−	9.86722e101i		−	0.316475i
$849$	−6.62317e100	+	1.13046e102i	−0.0203844	+	0.347926i
$850$	2.97442e101			0.0878497
$851$			3.56685e102i			1.01100i
$852$	4.75119e101	+	2.78364e100i	0.129246	+	0.00757228i
$853$	3.03608e102			0.792678			0.396339	−	0.918104i	$-0.370281\pi$
$853$	3.03608e102			0.792678			0.396339	+	0.918104i	$0.370281\pi$
$854$			1.13915e102i			0.285468i
$855$	4.76744e101	−	4.05464e102i	0.114676	−	0.975299i
$856$	8.29041e102			1.91423
$857$			3.05908e102i			0.678051i	0.940777	+	0.339026i	$0.110097\pi$
$857$			3.05908e102i			0.678051i	−0.940777	+	0.339026i	$0.889903\pi$
$858$	−4.92320e101	+	8.40305e102i	−0.104759	+	1.78806i
$859$	−2.81153e102			−0.574358			−0.287179	−	0.957877i	$-0.592717\pi$
$859$	−2.81153e102			−0.574358			−0.287179	+	0.957877i	$0.592717\pi$
$860$			3.27024e102i			0.641406i
$861$	1.13804e102	+	6.66755e100i	0.214312	+	0.0125561i
$862$	2.95531e102			0.534377
$863$		−	1.13968e102i		−	0.197882i	−0.995093	−	0.0989408i	$-0.968455\pi$
$863$		−	1.13968e102i		−	0.197882i	0.995093	−	0.0989408i	$-0.0315455\pi$
$864$	−4.61454e102	−	8.18575e101i	−0.769392	−	0.136483i
$865$	2.51285e102			0.402349
$866$			4.25251e102i			0.653911i
$867$	−2.57596e101	+	4.39672e102i	−0.0380427	+	0.649323i
$868$	−6.27376e101			−0.0889892
$869$		−	1.55906e103i		−	2.12408i
$870$	5.50915e102	+	3.22771e101i	0.720959	+	0.0422397i
$871$	−9.81742e102			−1.23413
$872$			3.45775e102i			0.417557i
$873$	−3.55874e102	−	4.18436e101i	−0.412855	−	0.0485435i
$874$	−5.64284e102			−0.628923
$875$			2.69241e102i			0.288310i
$876$	1.19111e101	−	2.03302e102i	0.0122549	−	0.209169i
$877$	9.24452e101			0.0913900			0.0456950	−	0.998955i	$-0.485450\pi$
$877$	9.24452e101			0.0913900			0.0456950	+	0.998955i	$0.485450\pi$
$878$		−	1.56690e103i		−	1.48845i
$879$	1.28871e102	+	7.55034e100i	0.117637	+	0.00689217i
$880$	6.74730e102			0.591884
$881$			1.22861e103i			1.03575i	0.855455	+	0.517877i	$0.173277\pi$
$881$			1.22861e103i			1.03575i	−0.855455	+	0.517877i	$0.826723\pi$
$882$	1.01398e102	−	8.62378e102i	0.0821544	−	0.698710i
$883$	−1.92081e103			−1.49575			−0.747877	−	0.663837i	$-0.768927\pi$
$883$	−1.92081e103			−1.49575			−0.747877	+	0.663837i	$0.768927\pi$
$884$		−	4.73846e102i		−	0.354656i
$885$	−5.57792e101	+	9.52055e102i	−0.0401290	+	0.684932i
$886$	−1.54595e103			−1.06909
$887$		−	1.57795e103i		−	1.04898i	−0.851418	−	0.524488i	$-0.824257\pi$
$887$		−	1.57795e103i		−	1.04898i	0.851418	−	0.524488i	$-0.175743\pi$
$888$	2.25347e103	+	1.32027e102i	1.44012	+	0.0843739i
$889$	2.72506e102			0.167423
$890$		−	9.27296e102i		−	0.547732i
$891$	6.83370e102	−	2.86580e103i	0.388093	−	1.62752i
$892$	6.65362e102			0.363319
$893$		−	1.00702e102i		−	0.0528736i
$894$	−1.09045e102	+	1.86122e103i	−0.0550547	+	0.939689i
$895$	1.93724e103			0.940541
$896$			1.89279e101i			0.00883735i
$897$	2.37675e103	+	1.39249e102i	1.06720	+	0.0625256i
$898$	−6.45737e102			−0.278858
$899$			1.99184e103i			0.827303i
$900$	−2.06985e102	−	2.43373e101i	−0.0826895	−	0.00972263i
$901$	−1.23428e103			−0.474294
$902$		−	2.74100e103i		−	1.01317i
$903$	−7.44417e101	+	1.27059e103i	−0.0264695	+	0.451788i
$904$	−3.75257e103			−1.28361
$905$			4.29152e103i			1.41225i
$906$	−3.02786e103	−	1.77397e102i	−0.958625	−	0.0561641i
$907$	3.25819e103			0.992480			0.496240	−	0.868186i	$-0.334714\pi$
$907$	3.25819e103			0.992480			0.496240	+	0.868186i	$0.334714\pi$
$908$		−	1.63801e103i		−	0.480079i
$909$	2.94675e102	−	2.50616e103i	0.0831012	−	0.706763i
$910$	−9.51021e102			−0.258072
$911$			6.46396e103i			1.68793i	0.536395	+	0.843967i	$0.319786\pi$
$911$			6.46396e103i			1.68793i	−0.536395	+	0.843967i	$0.680214\pi$
$912$	−1.00558e102	+	1.71635e103i	−0.0252695	+	0.431306i
$913$	−3.35634e103			−0.811687
$914$			5.16783e103i			1.20279i
$915$	5.59537e103	+	3.27823e102i	1.25340	+	0.0734347i
$916$	−2.35206e102			−0.0507115
$917$		−	1.82705e102i		−	0.0379161i
$918$	3.92031e102	−	2.20999e103i	0.0783116	−	0.441465i
$919$	−4.28133e103			−0.823257			−0.411628	−	0.911352i	$-0.635040\pi$
$919$	−4.28133e103			−0.823257			−0.411628	+	0.911352i	$0.635040\pi$
$920$		−	3.96401e103i		−	0.733772i
$921$	−1.75890e102	+	3.00214e103i	−0.0313440	+	0.534988i
$922$	2.46552e103			0.422986
$923$			2.60396e103i			0.430105i
$924$	−1.19986e103	−	7.02979e101i	−0.190815	−	0.0111795i
$925$	1.70830e103			0.261580
$926$		−	1.28637e103i		−	0.189662i
$927$	3.20357e103	+	3.76676e102i	0.454825	+	0.0534783i
$928$	6.07020e103			0.829897
$929$			7.05432e101i			0.00928763i	0.999989	+	0.00464382i	$0.00147818\pi$
$929$			7.05432e101i			0.00928763i	−0.999989	+	0.00464382i	$0.998522\pi$
$930$	2.44338e102	−	4.17043e103i	0.0309805	−	0.528783i
$931$	8.32014e103			1.01600
$932$		−	1.21993e102i		−	0.0143476i
$933$	−1.69633e104	−	9.93850e102i	−1.92156	−	0.112581i
$934$	−8.37323e103			−0.913592
$935$		−	8.44015e103i		−	0.887041i
$936$	1.75950e103	−	1.49643e104i	0.178129	−	1.51496i
$937$	−1.77126e103			−0.172742			−0.0863708	−	0.996263i	$-0.527527\pi$
$937$	−1.77126e103			−0.172742			−0.0863708	+	0.996263i	$0.527527\pi$
$938$			1.89714e103i			0.178238i
$939$	−9.42334e102	+	1.60840e104i	−0.0852921	+	1.45579i
$940$	2.10960e102			0.0183961
$941$		−	1.18373e104i		−	0.994525i	−0.867600	−	0.497263i	$-0.834339\pi$
$941$		−	1.18373e104i		−	0.994525i	0.867600	−	0.497263i	$-0.165661\pi$
$942$	6.30603e103	+	3.69459e102i	0.510475	+	0.0299078i
$943$	−7.75274e103			−0.604708
$944$		−	4.01626e103i		−	0.301858i
$945$	3.27745e103	+	5.81388e102i	0.237369	+	0.0421069i
$946$	3.06027e104			2.13584
$947$		−	1.38062e104i		−	0.928592i	−0.885680	−	0.464296i	$-0.846307\pi$
$947$		−	1.38062e104i		−	0.928592i	0.885680	−	0.464296i	$-0.153693\pi$
$948$	−4.86754e102	+	8.30806e103i	−0.0315514	+	0.538527i
$949$	1.11423e104			0.696075
$950$			2.70257e103i			0.162724i
$951$	−2.64917e104	−	1.55210e103i	−1.53742	−	0.0900745i
$952$	−3.07055e103			−0.171760
$953$		−	1.40643e104i		−	0.758343i	−0.925326	−	0.379172i	$-0.876209\pi$
$953$		−	1.40643e104i		−	0.758343i	0.925326	−	0.379172i	$-0.123791\pi$
$954$	−1.16240e104	−	1.36675e103i	−0.604176	−	0.0710391i
$955$	−7.13030e103			−0.357265
$956$		−	1.40278e104i		−	0.677585i
$957$	−2.23187e103	+	3.80941e104i	−0.103932	+	1.77394i
$958$	1.77932e104			0.798843
$959$		−	5.03304e103i		−	0.217861i
$960$	−2.11711e104	−	1.24038e103i	−0.883589	−	0.0517679i
$961$	−9.77133e103			−0.393219
$962$			3.68303e104i			1.42915i
$963$	5.52856e103	−	4.70196e104i	0.206867	−	1.75938i
$964$	−1.50115e104			−0.541663
$965$			3.93044e104i			1.36768i
$966$	2.69088e102	−	4.59287e103i	0.00903016	−	0.154129i
$967$	3.16479e104			1.02428			0.512140	−	0.858902i	$-0.328853\pi$
$967$	3.16479e104			1.02428			0.512140	+	0.858902i	$0.328853\pi$
$968$			6.22914e104i			1.94442i
$969$	2.14697e104	+	1.25787e103i	0.646388	+	0.0378707i
$970$	−9.73409e103			−0.282673
$971$			4.37118e104i			1.22441i	0.790700	+	0.612203i	$0.209717\pi$
$971$			4.37118e104i			1.22441i	−0.790700	+	0.612203i	$0.790283\pi$
$972$	−4.53632e103	+	1.50581e104i	−0.122570	+	0.406867i
$973$	1.55654e104			0.405705
$974$		−	3.25650e104i		−	0.818819i
$975$	6.66919e102	−	1.13832e104i	0.0161775	−	0.276122i
$976$	−2.36042e104			−0.552390
$977$		−	8.08532e104i		−	1.82552i	−0.408493	−	0.912761i	$-0.633946\pi$
$977$		−	8.08532e104i		−	1.82552i	0.408493	−	0.912761i	$-0.366054\pi$
$978$	5.78452e103	+	3.38905e102i	0.126011	+	0.00738275i
$979$	6.41197e104			1.34771
$980$			1.74297e104i			0.353491i
$981$	1.96108e104	+	2.30584e103i	0.383779	+	0.0451247i
$982$	−1.68868e103			−0.0318894
$983$			1.56856e104i			0.285844i	0.989734	+	0.142922i	$0.0456498\pi$
$983$			1.56856e104i			0.285844i	−0.989734	+	0.142922i	$0.954350\pi$
$984$	−2.86967e103	+	4.89804e104i	−0.0504666	+	0.861378i
$985$	−9.18509e104			−1.55889
$986$			2.90713e104i			0.476182i
$987$	8.19647e102	+	4.80216e101i	0.0129577	+	0.000759166i
$988$	4.30539e104			0.656930
$989$		−	8.65576e104i		−	1.27478i
$990$	9.34599e103	−	7.94862e104i	0.132860	−	1.12995i
$991$	−6.19444e103			−0.0850010			−0.0425005	−	0.999096i	$-0.513532\pi$
$991$	−6.19444e103			−0.0850010			−0.0425005	+	0.999096i	$0.513532\pi$
$992$		−	4.59515e104i		−	0.608683i
$993$	−2.28003e102	+	3.89162e103i	−0.00291553	+	0.0497630i
$994$	5.03194e103			0.0621172
$995$			3.02392e104i			0.360382i
$996$	1.78855e104	+	1.04788e103i	0.205790	+	0.0120569i
$997$	−1.52012e105			−1.68868			−0.844342	−	0.535804i	$-0.820009\pi$
$997$	−1.52012e105			−1.68868			−0.844342	+	0.535804i	$0.820009\pi$
$998$			7.49122e104i			0.803496i
$999$	2.25155e104	−	1.26927e105i	0.233179	−	1.31450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.71.b.a.2.8	✓	22
3.2	odd	2	inner	3.71.b.a.2.15	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.71.b.a.2.8	✓	22	1.1	even	1	trivial
3.71.b.a.2.15	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)

\(f(q)\)	\(=\)	\(q-2.60562e10i q^{2} +(-2.92624e15 + 4.99459e16i) q^{3} +5.01667e20 q^{4} -2.60973e24i q^{5} +(1.30140e27 + 7.62467e25i) q^{6} -1.01844e29 q^{7} -4.38332e31i q^{8} +(-2.48603e33 - 2.92308e32i) q^{9} +O(q^{10})\)	\(q-2.60562e10i q^{2} +(-2.92624e15 + 4.99459e16i) q^{3} +5.01667e20 q^{4} -2.60973e24i q^{5} +(1.30140e27 + 7.62467e25i) q^{6} -1.01844e29 q^{7} -4.38332e31i q^{8} +(-2.48603e33 - 2.92308e32i) q^{9} -6.79996e34 q^{10} -4.70197e36i q^{11} +(-1.46800e36 + 2.50562e37i) q^{12} -1.37324e39 q^{13} +2.65368e39i q^{14} +(1.30345e41 + 7.63669e39i) q^{15} -5.49864e41 q^{16} +6.87821e42i q^{17} +(-7.61642e42 + 6.47765e43i) q^{18} -6.24957e44 q^{19} -1.30921e45i q^{20} +(2.98021e44 - 5.08671e45i) q^{21} -1.22515e47 q^{22} +3.46526e47i q^{23} +(2.18929e48 + 1.28267e47i) q^{24} +1.65965e48 q^{25} +3.57814e49i q^{26} +(2.18743e49 - 1.23312e50i) q^{27} -5.10920e49 q^{28} +1.62210e51i q^{29} +(1.98983e50 - 3.39630e51i) q^{30} +1.22793e52 q^{31} -3.74218e52i q^{32} +(2.34844e53 + 1.37591e52i) q^{33} +1.79220e53 q^{34} +2.65786e53i q^{35} +(-1.24716e54 - 1.46641e53i) q^{36} +1.02932e55 q^{37} +1.62840e55i q^{38} +(4.01843e54 - 6.85877e55i) q^{39} -1.14393e56 q^{40} +2.23727e56i q^{41} +(-1.32540e56 - 7.76530e54i) q^{42} -2.49786e57 q^{43} -2.35882e57i q^{44} +(-7.62843e56 + 6.48786e57i) q^{45} +9.02916e57 q^{46} +1.61135e57i q^{47} +(1.60903e57 - 2.74634e58i) q^{48} -1.33131e59 q^{49} -4.32441e58i q^{50} +(-3.43538e59 - 2.01273e58i) q^{51} -6.88909e59 q^{52} +1.79448e60i q^{53} +(-3.21303e60 - 5.69960e59i) q^{54} -1.22708e61 q^{55} +4.46417e60i q^{56} +(1.82878e60 - 3.12141e61i) q^{57} +4.22658e61 q^{58} +7.30410e61i q^{59} +(6.53898e61 + 3.83107e60i) q^{60} +4.29273e62 q^{61} -3.19953e62i q^{62} +(2.53188e62 + 2.97699e61i) q^{63} -1.62423e63 q^{64} +3.58378e63i q^{65} +(3.58509e62 - 6.11914e63i) q^{66} +7.14909e63 q^{67} +3.45057e63i q^{68} +(-1.73076e64 - 1.01402e63i) q^{69} +6.92538e63 q^{70} -1.89621e64i q^{71} +(-1.28128e64 + 1.08971e65i) q^{72} -8.11385e64 q^{73} -2.68200e65i q^{74} +(-4.85654e63 + 8.28927e64i) q^{75} -3.13520e65 q^{76} +4.78869e65i q^{77} +(-1.78713e66 - 1.04705e65i) q^{78} +3.31577e66 q^{79} +1.43499e66i q^{80} +(6.09490e66 + 1.45337e66i) q^{81} +5.82948e66 q^{82} -7.13816e66i q^{83} +(1.49507e65 - 2.55183e66i) q^{84} +1.79503e67 q^{85} +6.50848e67i q^{86} +(-8.10174e67 - 4.74667e66i) q^{87} -2.06102e68 q^{88} +1.36368e68i q^{89} +(1.69049e68 + 1.98768e67i) q^{90} +1.39857e68 q^{91} +1.73841e68i q^{92} +(-3.59323e67 + 6.13303e68i) q^{93} +4.19856e67 q^{94} +1.63097e69i q^{95} +(1.86907e69 + 1.09505e68i) q^{96} +1.43149e69 q^{97} +3.46889e69i q^{98} +(-1.37442e69 + 1.16892e70i) 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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