LMFDB - Embedded newform 4.37.b.b.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,37,Mod(3,4)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 37, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 37);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 37 $
Character orbit:	$[\chi]$	$=$	4.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:	$32.8365034637$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + \cdots + 51\!\cdots\!00 $ x^16 + 6516989503065492x^14 + 17034486537407810917043361888198x^12 + 23072686962604400610679579162976738904788666844x^10 + 17414437736843557770548667414205720006669176493316634162548145x^8 + 7290100998556943999917076003638299976059510807819390063090897454035549344520x^6 + 1580065913442518903241377790659954072974637079040446265806555551201513339370568669874480400x^4 + 153535410141602761164144701301723551659810917407928334524859080419500779864196136193775339243188420422400*x^2 + 5156239739885100544994334306227490882529912274563409421561999152540966086224689966448180302613961864037075159771136000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{240}\cdot 3^{24}\cdot 5^{6}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.4
Root			$-4.46418e7i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.37.b.b.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-210329. + 156464. i) q^{2} -7.14268e8i q^{3} +(1.97575e10 - 6.58180e10i) q^{4} +8.84656e11 q^{5} +(1.11757e14 + 1.50232e14i) q^{6} -1.08208e15i q^{7} +(6.14256e15 + 1.69348e16i) q^{8} -3.60085e17 q^{9} +O(q^{10})$	\(q+(-210329. + 156464. i) q^{2} -7.14268e8i q^{3} +(1.97575e10 - 6.58180e10i) q^{4} +8.84656e11 q^{5} +(1.11757e14 + 1.50232e14i) q^{6} -1.08208e15i q^{7} +(6.14256e15 + 1.69348e16i) q^{8} -3.60085e17 q^{9} +(-1.86069e17 + 1.38417e17i) q^{10} +6.19426e18i q^{11} +(-4.70117e19 - 1.41122e19i) q^{12} -1.29480e20 q^{13} +(1.69307e20 + 2.27594e20i) q^{14} -6.31882e20i q^{15} +(-3.94165e21 - 2.60080e21i) q^{16} +1.60201e22 q^{17} +(7.57364e22 - 5.63403e22i) q^{18} -7.21971e22i q^{19} +(1.74786e22 - 5.82263e22i) q^{20} -7.72898e23 q^{21} +(-9.69179e23 - 1.30284e24i) q^{22} +5.50534e24i q^{23} +(1.20960e25 - 4.38744e24i) q^{24} -1.37693e25 q^{25} +(2.72334e25 - 2.02589e25i) q^{26} +1.49989e26i q^{27} +(-7.12206e25 - 2.13793e25i) q^{28} -2.40170e26 q^{29} +(9.88667e25 + 1.32903e26i) q^{30} -3.47564e26i q^{31} +(1.23598e27 - 6.97018e25i) q^{32} +4.42437e27 q^{33} +(-3.36950e27 + 2.50657e27i) q^{34} -9.57272e26i q^{35} +(-7.11437e27 + 2.37000e28i) q^{36} -4.85919e26 q^{37} +(1.12963e28 + 1.51852e28i) q^{38} +9.24832e28i q^{39} +(5.43405e27 + 1.49815e28i) q^{40} +1.61141e28 q^{41} +(1.62563e29 - 1.20931e29i) q^{42} +2.17024e29i q^{43} +(4.07694e29 + 1.22383e29i) q^{44} -3.18551e29 q^{45} +(-8.61387e29 - 1.15793e30i) q^{46} -3.68245e28i q^{47} +(-1.85767e30 + 2.81540e30i) q^{48} +1.48082e30 q^{49} +(2.89609e30 - 2.15440e30i) q^{50} -1.14427e31i q^{51} +(-2.55819e30 + 8.52208e30i) q^{52} +5.88414e30 q^{53} +(-2.34679e31 - 3.15471e31i) q^{54} +5.47979e30i q^{55} +(1.83249e31 - 6.64677e30i) q^{56} -5.15681e31 q^{57} +(5.05148e31 - 3.75780e31i) q^{58} +7.36347e31i q^{59} +(-4.15892e31 - 1.24844e31i) q^{60} +2.36737e32 q^{61} +(5.43812e31 + 7.31029e31i) q^{62} +3.89642e32i q^{63} +(-2.49056e32 + 2.08046e32i) q^{64} -1.14545e32 q^{65} +(-9.30575e32 + 6.92254e32i) q^{66} -3.51092e32i q^{67} +(3.16517e32 - 1.05441e33i) q^{68} +3.93229e33 q^{69} +(1.49779e32 + 2.01343e32i) q^{70} +7.98310e32i q^{71} +(-2.21184e33 - 6.09796e33i) q^{72} -4.73322e33 q^{73} +(1.02203e32 - 7.60289e31i) q^{74} +9.83497e33i q^{75} +(-4.75187e33 - 1.42643e33i) q^{76} +6.70271e33 q^{77} +(-1.44703e34 - 1.94519e34i) q^{78} -8.69667e32i q^{79} +(-3.48700e33 - 2.30081e33i) q^{80} +5.30858e34 q^{81} +(-3.38927e33 + 2.52128e33i) q^{82} -2.72310e34i q^{83} +(-1.52705e34 + 5.08706e34i) q^{84} +1.41723e34 q^{85} +(-3.39564e34 - 4.56465e34i) q^{86} +1.71546e35i q^{87} +(-1.04899e35 + 3.80487e34i) q^{88} +4.88377e34 q^{89} +(6.70007e34 - 4.98418e34i) q^{90} +1.40108e35i q^{91} +(3.62350e35 + 1.08772e35i) q^{92} -2.48254e35 q^{93} +(5.76171e33 + 7.74528e33i) q^{94} -6.38696e34i q^{95} +(-4.97858e34 - 8.82819e35i) q^{96} -1.09730e35 q^{97} +(-3.11461e35 + 2.31696e35i) q^{98} -2.23046e36i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 177228 q^{2} - 5610707696 q^{4} + 5816089539360 q^{5} - 217628996575488 q^{6} + 11\!\cdots\!28 q^{8}+ \cdots - 93\!\cdots\!68 q^{9}+O(q^{10}) $ 16 * q + 177228 * q^2 - 5610707696 * q^4 + 5816089539360 * q^5 - 217628996575488 * q^6 + 11897560228206528 * q^8 - 935184460817545968 * q^9	$ 16 q + 177228 q^{2} - 5610707696 q^{4} + 5816089539360 q^{5} - 217628996575488 q^{6} + 11\!\cdots\!28 q^{8}+ \cdots + 10\!\cdots\!28 q^{98}+O(q^{100}) $ 16 * q + 177228 * q^2 - 5610707696 * q^4 + 5816089539360 * q^5 - 217628996575488 * q^6 + 11897560228206528 * q^8 - 935184460817545968 * q^9 - 2378142919315561000 * q^10 - 42882825786868930560 * q^12 + 194612014165659174176 * q^13 + 360192888461659120128 * q^14 - 22854023522524990832384 * q^16 + 41803218917907805318176 * q^17 + 138204474036544564333068 * q^18 + 104592026972614096023840 * q^20 - 175281296641396774711296 * q^21 - 4320007363229839528400640 * q^22 + 5118364442017682383085568 * q^24 + 61061610541832160307690800 * q^25 - 70158486911796111631798440 * q^26 - 303534200373547502486016000 * q^28 - 95320519344473743554877152 * q^29 + 361206724962468787334008320 * q^30 + 4662427702586163916855016448 * q^32 - 877278707167997370072668160 * q^33 - 9018225886246079564307746920 * q^34 - 927455191590908629268766192 * q^36 - 30841755082751179145922114784 * q^37 + 78752216997100984306444174080 * q^38 - 138122339194153338361474460800 * q^40 + 99165040763128472781035553312 * q^41 - 193406458925326074258433843200 * q^42 + 303084904999663560614745692160 * q^44 + 1511424637230487714612565241120 * q^45 - 919681205391808405630032112128 * q^46 - 1511312501851283767715389931520 * q^48 - 11342315683204385026834539108848 * q^49 + 11057816114707215621338245966500 * q^50 + 16094442403868561017575461524256 * q^52 + 20911545776251998404629518049056 * q^53 - 42689634574575573966970327785984 * q^54 - 18346492780981997297263940026368 * q^56 - 17591710635767034592583231047680 * q^57 + 33019206317228013320629044602456 * q^58 - 69704584574466315130190074982400 * q^60 + 216576725773383276684585233875232 * q^61 + 406820870675021165265665434183680 * q^62 - 266111502464782094817164314013696 * q^64 - 2065823886943449026422930314993600 * q^65 - 816784109200805225218136599695360 * q^66 + 3502994508232801473127246422490656 * q^68 + 3923547517779842564469076002041856 * q^69 + 312094823977274793710809307489280 * q^70 - 1875458138040165128132392402132032 * q^72 - 13529699358917711874787838251408864 * q^73 + 7683713356825244783786618034273240 * q^74 - 15736875982808342938482824299100160 * q^76 + 22639774155764461736245527294259200 * q^77 - 18389491597233550087389536189698560 * q^78 + 67235988583903584940074904608207360 * q^80 - 40716877106976112078739817594850800 * q^81 + 43227843112149006015980010857549336 * q^82 - 37119022564017857733030089777086464 * q^84 - 206886985961236391219562146270052800 * q^85 + 102108696026625816655543232864792832 * q^86 + 39749581676781586144951142033940480 * q^88 + 461506837768868190077604450557625888 * q^89 - 361659211507857840778210819426233000 * q^90 - 17511543929609412714530045318983680 * q^92 - 231978818535002459544922699145134080 * q^93 - 696830931593880576023589572144120832 * q^94 + 1050073689946737522972596709346639872 * q^96 + 451372245708940284684446048339288096 * q^97 + 1035415270688230597220229005750452428 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−210329.	+	156464.i	−0.802343	+	0.596863i
$2$	−210329.	+	156464.i	−0.802343	+	0.596863i
$3$		−	7.14268e8i		−	1.84365i	−0.387605	−	0.921826i	$-0.626697\pi$
$3$		−	7.14268e8i		−	1.84365i	0.387605	−	0.921826i	$-0.373303\pi$
$4$	1.97575e10	−	6.58180e10i	0.287509	−	0.957778i
$5$	8.84656e11			0.231907			0.115954	−	0.993255i	$-0.463008\pi$
$5$	8.84656e11			0.231907			0.115954	+	0.993255i	$0.463008\pi$
$6$	1.11757e14	+	1.50232e14i	1.10041	+	1.47924i
$7$		−	1.08208e15i		−	0.664502i	−0.943191	−	0.332251i	$-0.892192\pi$
$7$		−	1.08208e15i		−	0.664502i	0.943191	−	0.332251i	$-0.107808\pi$
$8$	6.14256e15	+	1.69348e16i	0.340981	+	0.940070i
$9$	−3.60085e17			−2.39905
$10$	−1.86069e17	+	1.38417e17i	−0.186069	+	0.138417i
$11$			6.19426e18i			1.11409i	0.830481	+	0.557046i	$0.188065\pi$
$11$			6.19426e18i			1.11409i	−0.830481	+	0.557046i	$0.811935\pi$
$12$	−4.70117e19	−	1.41122e19i	−1.76581	−	0.530067i
$13$	−1.29480e20			−1.15139			−0.575693	−	0.817666i	$-0.695268\pi$
$13$	−1.29480e20			−1.15139			−0.575693	+	0.817666i	$0.695268\pi$
$14$	1.69307e20	+	2.27594e20i	0.396617	+	0.533159i
$15$		−	6.31882e20i		−	0.427556i
$16$	−3.94165e21	−	2.60080e21i	−0.834677	−	0.550740i
$17$	1.60201e22			1.13916			0.569580	−	0.821936i	$-0.307106\pi$
$17$	1.60201e22			1.13916			0.569580	+	0.821936i	$0.307106\pi$
$18$	7.57364e22	−	5.63403e22i	1.92486	−	1.43190i
$19$		−	7.21971e22i		−	0.693354i	−0.937985	−	0.346677i	$-0.887310\pi$
$19$		−	7.21971e22i		−	0.693354i	0.937985	−	0.346677i	$-0.112690\pi$
$20$	1.74786e22	−	5.82263e22i	0.0666755	−	0.222116i
$21$	−7.72898e23			−1.22511
$22$	−9.69179e23	−	1.30284e24i	−0.664961	−	0.893885i
$23$			5.50534e24i			1.69700i	0.529192	+	0.848502i	$0.322495\pi$
$23$			5.50534e24i			1.69700i	−0.529192	+	0.848502i	$0.677505\pi$
$24$	1.20960e25	−	4.38744e24i	1.73316	−	0.628650i
$25$	−1.37693e25			−0.946219
$26$	2.72334e25	−	2.02589e25i	0.923807	−	0.687219i
$27$			1.49989e26i			2.57936i
$28$	−7.12206e25	−	2.13793e25i	−0.636445	−	0.191051i
$29$	−2.40170e26			−1.14118			−0.570591	−	0.821234i	$-0.693286\pi$
$29$	−2.40170e26			−1.14118			−0.570591	+	0.821234i	$0.693286\pi$
$30$	9.88667e25	+	1.32903e26i	0.255192	+	0.343047i
$31$		−	3.47564e26i		−	0.497192i	−0.968607	−	0.248596i	$-0.920031\pi$
$31$		−	3.47564e26i		−	0.497192i	0.968607	−	0.248596i	$-0.0799691\pi$
$32$	1.23598e27	−	6.97018e25i	0.998414	−	0.0563047i
$33$	4.42437e27			2.05400
$34$	−3.36950e27	+	2.50657e27i	−0.913997	+	0.679922i
$35$		−	9.57272e26i		−	0.154103i
$36$	−7.11437e27	+	2.37000e28i	−0.689750	+	2.29776i
$37$	−4.85919e26			−0.0287696			−0.0143848	−	0.999897i	$-0.504579\pi$
$37$	−4.85919e26			−0.0287696			−0.0143848	+	0.999897i	$0.504579\pi$
$38$	1.12963e28	+	1.51852e28i	0.413837	+	0.556308i
$39$			9.24832e28i			2.12275i
$40$	5.43405e27	+	1.49815e28i	0.0790759	+	0.218009i
$41$	1.61141e28			0.150348			0.0751738	−	0.997170i	$-0.476049\pi$
$41$	1.61141e28			0.150348			0.0751738	+	0.997170i	$0.476049\pi$
$42$	1.62563e29	−	1.20931e29i	0.982959	−	0.731223i
$43$			2.17024e29i			0.859162i	0.903028	+	0.429581i	$0.141339\pi$
$43$			2.17024e29i			0.859162i	−0.903028	+	0.429581i	$0.858661\pi$
$44$	4.07694e29	+	1.22383e29i	1.06705	+	0.320312i
$45$	−3.18551e29			−0.556357
$46$	−8.61387e29	−	1.15793e30i	−1.01288	−	1.36158i
$47$		−	3.68245e28i		−	0.0294019i	−0.999892	−	0.0147010i	$-0.995320\pi$
$47$		−	3.68245e28i		−	0.0294019i	0.999892	−	0.0147010i	$-0.00467963\pi$
$48$	−1.85767e30	+	2.81540e30i	−1.01537	+	1.53885i
$49$	1.48082e30			0.558437
$50$	2.89609e30	−	2.15440e30i	0.759192	−	0.564763i
$51$		−	1.14427e31i		−	2.10021i
$52$	−2.55819e30	+	8.52208e30i	−0.331034	+	1.10277i
$53$	5.88414e30			0.540403			0.270201	−	0.962804i	$-0.412910\pi$
$53$	5.88414e30			0.540403			0.270201	+	0.962804i	$0.412910\pi$
$54$	−2.34679e31	−	3.15471e31i	−1.53953	−	2.06953i
$55$			5.47979e30i			0.258366i
$56$	1.83249e31	−	6.64677e30i	0.624679	−	0.226582i
$57$	−5.15681e31			−1.27830
$58$	5.05148e31	−	3.75780e31i	0.915620	−	0.681129i
$59$			7.36347e31i			0.981175i	0.871392	+	0.490587i	$0.163218\pi$
$59$			7.36347e31i			0.981175i	−0.871392	+	0.490587i	$0.836782\pi$
$60$	−4.15892e31	−	1.24844e31i	−0.409504	−	0.122926i
$61$	2.36737e32			1.73113			0.865563	−	0.500800i	$-0.166961\pi$
$61$	2.36737e32			1.73113			0.865563	+	0.500800i	$0.166961\pi$
$62$	5.43812e31	+	7.31029e31i	0.296755	+	0.398918i
$63$			3.89642e32i			1.59417i
$64$	−2.49056e32	+	2.08046e32i	−0.767464	+	0.641092i
$65$	−1.14545e32			−0.267015
$66$	−9.30575e32	+	6.92254e32i	−1.64801	+	1.22596i
$67$		−	3.51092e32i		−	0.474323i	−0.971470	−	0.237162i	$-0.923783\pi$
$67$		−	3.51092e32i		−	0.474323i	0.971470	−	0.237162i	$-0.0762171\pi$
$68$	3.16517e32	−	1.05441e33i	0.327519	−	1.09106i
$69$	3.93229e33			3.12868
$70$	1.49779e32	+	2.01343e32i	0.0919783	+	0.123643i
$71$			7.98310e32i			0.379770i	0.981806	+	0.189885i	$0.0608116\pi$
$71$			7.98310e32i			0.379770i	−0.981806	+	0.189885i	$0.939188\pi$
$72$	−2.21184e33	−	6.09796e33i	−0.818030	−	2.25528i
$73$	−4.73322e33			−1.36567			−0.682834	−	0.730574i	$-0.739253\pi$
$73$	−4.73322e33			−1.36567			−0.682834	+	0.730574i	$0.739253\pi$
$74$	1.02203e32	−	7.60289e31i	0.0230831	−	0.0171715i
$75$			9.83497e33i			1.74450i
$76$	−4.75187e33	−	1.42643e33i	−0.664079	−	0.199346i
$77$	6.70271e33			0.740317
$78$	−1.44703e34	−	1.94519e34i	−1.26699	−	1.70318i
$79$		−	8.69667e32i		−	0.0605432i	−0.999542	−	0.0302716i	$-0.990363\pi$
$79$		−	8.69667e32i		−	0.0605432i	0.999542	−	0.0302716i	$-0.00963723\pi$
$80$	−3.48700e33	−	2.30081e33i	−0.193568	−	0.127721i
$81$	5.30858e34			2.35639
$82$	−3.38927e33	+	2.52128e33i	−0.120630	+	0.0897369i
$83$		−	2.72310e34i		−	0.779217i	−0.920980	−	0.389609i	$-0.872610\pi$
$83$		−	2.72310e34i		−	0.779217i	0.920980	−	0.389609i	$-0.127390\pi$
$84$	−1.52705e34	+	5.08706e34i	−0.352231	+	1.17338i
$85$	1.41723e34			0.264179
$86$	−3.39564e34	−	4.56465e34i	−0.512802	−	0.689343i
$87$			1.71546e35i			2.10394i
$88$	−1.04899e35	+	3.80487e34i	−1.04733	+	0.379884i
$89$	4.88377e34			0.397864			0.198932	−	0.980013i	$-0.436253\pi$
$89$	4.88377e34			0.397864			0.198932	+	0.980013i	$0.436253\pi$
$90$	6.70007e34	−	4.98418e34i	0.446389	−	0.332069i
$91$			1.40108e35i			0.765098i
$92$	3.62350e35	+	1.08772e35i	1.62535	+	0.487905i
$93$	−2.48254e35			−0.916648
$94$	5.76171e33	+	7.74528e33i	0.0175489	+	0.0235904i
$95$		−	6.38696e34i		−	0.160794i
$96$	−4.97858e34	−	8.82819e35i	−0.103806	−	1.84073i
$97$	−1.09730e35			−0.189860			−0.0949302	−	0.995484i	$-0.530263\pi$
$97$	−1.09730e35			−0.189860			−0.0949302	+	0.995484i	$0.530263\pi$
$98$	−3.11461e35	+	2.31696e35i	−0.448058	+	0.333310i
$99$		−	2.23046e36i		−	2.67276i
$100$	−2.72047e35	+	9.06268e35i	−0.272047	+	0.906268i
$101$	−8.78256e35			−0.734237			−0.367119	−	0.930174i	$-0.619656\pi$
$101$	−8.78256e35			−0.734237			−0.367119	+	0.930174i	$0.619656\pi$
$102$	1.79036e36	+	2.40673e36i	1.25354	+	1.68509i
$103$		−	1.85754e36i		−	1.09111i	−0.838075	−	0.545555i	$-0.816319\pi$
$103$		−	1.85754e36i		−	1.09111i	0.838075	−	0.545555i	$-0.183681\pi$
$104$	−7.95336e35	−	2.19271e36i	−0.392600	−	1.08238i
$105$	−6.83749e35			−0.284112
$106$	−1.23761e36	+	9.20656e35i	−0.433588	+	0.322546i
$107$			4.43494e36i			1.31214i	0.754701	+	0.656069i	$0.227782\pi$
$107$			4.43494e36i			1.31214i	−0.754701	+	0.656069i	$0.772218\pi$
$108$	9.87199e36	+	2.96341e36i	2.47046	+	0.741591i
$109$	−3.77436e36			−0.800140			−0.400070	−	0.916485i	$-0.631014\pi$
$109$	−3.77436e36			−0.800140			−0.400070	+	0.916485i	$0.631014\pi$
$110$	−8.57390e35	−	1.15256e36i	−0.154209	−	0.207298i
$111$			3.47077e35i			0.0530410i
$112$	−2.81428e36	+	4.26520e36i	−0.365968	+	0.554644i
$113$	−1.58014e37			−1.75098			−0.875492	−	0.483232i	$-0.839463\pi$
$113$	−1.58014e37			−1.75098			−0.875492	+	0.483232i	$0.839463\pi$
$114$	1.08463e37	−	8.06856e36i	1.02564	−	0.762972i
$115$			4.87033e36i			0.393547i
$116$	−4.74516e36	+	1.58075e37i	−0.328101	+	1.09300i
$117$	4.66236e37			2.76223
$118$	−1.15212e37	−	1.54875e37i	−0.585627	−	0.787239i
$119$		−	1.73351e37i		−	0.756974i
$120$	1.07008e37	−	3.88137e36i	0.401933	−	0.145788i
$121$	−7.45622e36			−0.241203
$122$	−4.97927e37	+	3.70408e37i	−1.38896	+	1.03324i
$123$		−	1.15098e37i		−	0.277189i
$124$	−2.28759e37	−	6.86699e36i	−0.476199	−	0.142947i
$125$	−2.50545e37			−0.451342
$126$	−6.09649e37	−	8.19532e37i	−0.951503	−	1.27907i
$127$			5.99696e37i			0.811829i	0.913911	+	0.405914i	$0.133047\pi$
$127$			5.99696e37i			0.811829i	−0.913911	+	0.405914i	$0.866953\pi$
$128$	1.98322e37	−	8.27266e37i	0.233126	−	0.972447i
$129$	1.55013e38			1.58400
$130$	2.40922e37	−	1.79221e37i	0.214237	−	0.159371i
$131$			7.62375e37i			0.590589i	0.955406	+	0.295295i	$0.0954178\pi$
$131$			7.62375e37i			0.590589i	−0.955406	+	0.295295i	$0.904582\pi$
$132$	8.74144e37	−	2.91203e38i	0.590544	−	1.96727i
$133$	−7.81234e37			−0.460735
$134$	5.49333e37	+	7.38450e37i	0.283106	+	0.380570i
$135$			1.32689e38i			0.598173i
$136$	9.84045e37	+	2.71297e38i	0.388432	+	1.07089i
$137$	2.18854e38			0.757152			0.378576	−	0.925570i	$-0.376414\pi$
$137$	2.18854e38			0.757152			0.378576	+	0.925570i	$0.376414\pi$
$138$	−8.27076e38	+	6.15261e38i	−2.51028	+	1.86739i
$139$			2.96571e38i			0.790427i	0.918589	+	0.395214i	$0.129329\pi$
$139$			2.96571e38i			0.790427i	−0.918589	+	0.395214i	$0.870671\pi$
$140$	−6.30057e37	−	1.89133e37i	−0.147596	−	0.0443060i
$141$	−2.63026e37			−0.0542069
$142$	−1.24907e38	−	1.67908e38i	−0.226671	−	0.304706i
$143$		−	8.02030e38i		−	1.28275i
$144$	1.41933e39	+	9.36507e38i	2.00243	+	1.32125i
$145$	−2.12468e38			−0.264648
$146$	9.95535e38	−	7.40578e38i	1.09573	−	0.815116i
$147$		−	1.05771e39i		−	1.02956i
$148$	−9.60055e36	+	3.19822e37i	−0.00827152	+	0.0275548i
$149$	−4.69873e38			−0.358615			−0.179307	−	0.983793i	$-0.557386\pi$
$149$	−4.69873e38			−0.358615			−0.179307	+	0.983793i	$0.557386\pi$
$150$	−1.53882e39	−	2.06859e39i	−1.04123	−	1.39969i
$151$			2.81845e38i			0.169209i	0.996415	+	0.0846047i	$0.0269628\pi$
$151$			2.81845e38i			0.169209i	−0.996415	+	0.0846047i	$0.973037\pi$
$152$	1.22264e39	−	4.43475e38i	0.651802	−	0.236420i
$153$	−5.76859e39			−2.73290
$154$	−1.40978e39	+	1.04873e39i	−0.593988	+	0.441868i
$155$		−	3.07474e38i		−	0.115302i
$156$	6.08706e39	+	1.82724e39i	2.03313	+	0.610312i
$157$	1.48945e39			0.443437			0.221718	−	0.975111i	$-0.428833\pi$
$157$	1.48945e39			0.443437			0.221718	+	0.975111i	$0.428833\pi$
$158$	1.36072e38	+	1.82917e38i	0.0361360	+	0.0485764i
$159$		−	4.20286e39i		−	0.996314i
$160$	1.09341e39	−	6.16621e37i	0.231539	−	0.0130575i
$161$	5.95724e39			1.12766
$162$	−1.11655e40	+	8.30601e39i	−1.89064	+	1.40644i
$163$			5.09595e39i			0.772411i	0.922413	+	0.386205i	$0.126214\pi$
$163$			5.09595e39i			0.772411i	−0.922413	+	0.386205i	$0.873786\pi$
$164$	3.18374e38	−	1.06060e39i	0.0432264	−	0.144000i
$165$	3.91404e39			0.476337
$166$	4.26068e39	+	5.72749e39i	0.465086	+	0.625200i
$167$		−	3.99110e39i		−	0.391018i	−0.980702	−	0.195509i	$-0.937364\pi$
$167$		−	3.99110e39i		−	0.391018i	0.980702	−	0.195509i	$-0.0626359\pi$
$168$	−4.74758e39	−	1.30889e40i	−0.417739	−	1.15169i
$169$	4.11874e39			0.325689
$170$	−2.98085e39	+	2.21745e39i	−0.211963	+	0.157679i
$171$			2.59971e40i			1.66339i
$172$	1.42841e40	+	4.28785e39i	0.822886	+	0.247017i
$173$	−1.39597e40			−0.724515			−0.362258	−	0.932078i	$-0.617994\pi$
$173$	−1.39597e40			−0.724515			−0.362258	+	0.932078i	$0.617994\pi$
$174$	−2.68408e40	−	3.60812e40i	−1.25576	−	1.68808i
$175$			1.48995e40i			0.628764i
$176$	1.61100e40	−	2.44156e40i	0.613576	−	0.929907i
$177$	5.25949e40			1.80894
$178$	−1.02720e40	+	7.64134e39i	−0.319224	+	0.237471i
$179$			3.03632e40i			0.853087i	0.904467	+	0.426543i	$0.140269\pi$
$179$			3.03632e40i			0.853087i	−0.904467	+	0.426543i	$0.859731\pi$
$180$	−6.29377e39	+	2.09664e40i	−0.159958	+	0.532867i
$181$	−3.77785e40			−0.869021			−0.434511	−	0.900667i	$-0.643079\pi$
$181$	−3.77785e40			−0.869021			−0.434511	+	0.900667i	$0.643079\pi$
$182$	−2.19218e40	−	2.94688e40i	−0.456659	−	0.613871i
$183$		−	1.69094e41i		−	3.19159i
$184$	−9.32318e40	+	3.38169e40i	−1.59530	+	0.578646i
$185$	−4.29871e38			−0.00667187
$186$	5.22151e40	−	3.88428e40i	0.735466	−	0.547113i
$187$			9.92327e40i			1.26913i
$188$	−2.42372e39	−	7.27561e38i	−0.0281605	−	0.00845333i
$189$	1.62301e41			1.71399
$190$	9.99330e39	+	1.34337e40i	0.0959719	+	0.129012i
$191$		−	8.46505e40i		−	0.739654i	−0.929101	−	0.369827i	$-0.879417\pi$
$191$		−	8.46505e40i		−	0.739654i	0.929101	−	0.369827i	$-0.120583\pi$
$192$	1.48601e41	+	1.77893e41i	1.18195	+	1.41494i
$193$	−2.43474e41			−1.76369			−0.881843	−	0.471543i	$-0.843697\pi$
$193$	−2.43474e41			−1.76369			−0.881843	+	0.471543i	$0.843697\pi$
$194$	2.30795e40	−	1.71688e40i	0.152333	−	0.113321i
$195$			8.18158e40i			0.492282i
$196$	2.92574e40	−	9.74649e40i	0.160556	−	0.534859i
$197$	−1.73126e41			−0.866901			−0.433451	−	0.901177i	$-0.642704\pi$
$197$	−1.73126e41			−0.866901			−0.433451	+	0.901177i	$0.642704\pi$
$198$	3.48987e41	+	4.69131e41i	1.59527	+	2.14447i
$199$			2.95433e41i			1.23340i	0.787199	+	0.616699i	$0.211530\pi$
$199$			2.95433e41i			1.23340i	−0.787199	+	0.616699i	$0.788470\pi$
$200$	−8.45788e40	−	2.33180e41i	−0.322642	−	0.889512i
$201$	−2.50774e41			−0.874487
$202$	1.84723e41	−	1.37415e41i	0.589110	−	0.438239i
$203$			2.59884e41i			0.758318i
$204$	−7.53132e41	−	2.26078e41i	−2.01154	−	0.603831i
$205$	1.42554e40			0.0348667
$206$	2.90638e41	+	3.90695e41i	0.651242	+	0.875444i
$207$		−	1.98239e42i		−	4.07120i
$208$	5.10363e41	+	3.36750e41i	0.961035	+	0.634115i
$209$	4.47208e41			0.772461
$210$	1.43813e41	−	1.06982e41i	0.227955	−	0.169576i
$211$			3.60639e40i			0.0524794i	0.999656	+	0.0262397i	$0.00835331\pi$
$211$			3.60639e40i			0.0524794i	−0.999656	+	0.0262397i	$0.991647\pi$
$212$	1.16256e41	−	3.87282e41i	0.155371	−	0.517586i
$213$	5.70207e41			0.700164
$214$	−6.93908e41	−	9.32798e41i	−0.783166	−	1.05278i
$215$			1.91991e41i			0.199246i
$216$	−2.54004e42	+	9.21318e41i	−2.42478	+	0.879513i
$217$	−3.76093e41			−0.330385
$218$	7.93858e41	−	5.90551e41i	0.641987	−	0.477574i
$219$			3.38079e42i			2.51782i
$220$	3.60669e41	+	1.08267e41i	0.247457	+	0.0742827i
$221$	−2.07428e42			−1.31161
$222$	−5.43050e40	−	7.30005e40i	−0.0316582	−	0.0425571i
$223$		−	6.05387e41i		−	0.325496i	−0.986668	−	0.162748i	$-0.947964\pi$
$223$		−	6.05387e41i		−	0.325496i	0.986668	−	0.162748i	$-0.0520357\pi$
$224$	−7.54232e40	−	1.33743e42i	−0.0374146	−	0.663448i
$225$	4.95811e42			2.27003
$226$	3.32349e42	−	2.47234e42i	1.40489	−	1.04510i
$227$			4.84852e42i			1.89297i	0.322750	+	0.946484i	$0.395393\pi$
$227$			4.84852e42i			1.89297i	−0.322750	+	0.946484i	$0.604607\pi$
$228$	−1.01886e42	+	3.39411e42i	−0.367524	+	1.22433i
$229$	3.41662e42			1.13909			0.569545	−	0.821960i	$-0.307120\pi$
$229$	3.41662e42			1.13909			0.569545	+	0.821960i	$0.307120\pi$
$230$	−7.62031e41	−	1.02437e42i	−0.234894	−	0.315760i
$231$		−	4.78754e42i		−	1.36489i
$232$	−1.47526e42	−	4.06723e42i	−0.389121	−	1.07279i
$233$	−3.75680e42			−0.917090			−0.458545	−	0.888671i	$-0.651629\pi$
$233$	−3.75680e42			−0.917090			−0.458545	+	0.888671i	$0.651629\pi$
$234$	−9.80632e42	+	7.29492e42i	−2.21626	+	1.64867i
$235$		−	3.25770e40i		−	0.00681852i
$236$	4.84649e42	+	1.45484e42i	0.939747	+	0.282097i
$237$	−6.21176e41			−0.111621
$238$	2.71232e42	+	3.64608e42i	0.451810	+	0.607353i
$239$		−	5.44846e41i		−	0.0841611i	−0.999114	−	0.0420806i	$-0.986601\pi$
$239$		−	5.44846e41i		−	0.0841611i	0.999114	−	0.0420806i	$-0.0133986\pi$
$240$	−1.64340e42	+	2.49066e42i	−0.235472	+	0.356871i
$241$	−1.46388e42			−0.194626			−0.0973128	−	0.995254i	$-0.531025\pi$
$241$	−1.46388e42			−0.194626			−0.0973128	+	0.995254i	$0.531025\pi$
$242$	1.56826e42	−	1.16663e42i	0.193527	−	0.143965i
$243$		−	1.54049e43i		−	1.76501i
$244$	4.67733e42	−	1.55815e43i	0.497715	−	1.65803i
$245$	1.31002e42			0.129506
$246$	1.80087e42	+	2.42085e42i	0.165444	+	0.222400i
$247$			9.34805e42i			0.798318i
$248$	5.88592e42	−	2.13493e42i	0.467395	−	0.169533i
$249$	−1.94503e43			−1.43661
$250$	5.26971e42	−	3.92013e42i	0.362131	−	0.269389i
$251$		−	2.11987e42i		−	0.135576i	−0.997700	−	0.0677878i	$-0.978406\pi$
$251$		−	2.11987e42i		−	0.135576i	0.997700	−	0.0677878i	$-0.0215941\pi$
$252$	2.56454e43	+	7.69835e42i	1.52686	+	0.458340i
$253$	−3.41015e43			−1.89062
$254$	−9.38309e42	−	1.26134e43i	−0.484550	−	0.651365i
$255$		−	1.01228e43i		−	0.487055i
$256$	8.77245e42	+	2.05029e43i	0.393370	+	0.919380i
$257$	1.01174e43			0.422933			0.211467	−	0.977385i	$-0.432176\pi$
$257$	1.01174e43			0.422933			0.211467	+	0.977385i	$0.432176\pi$
$258$	−3.26039e43	+	2.42540e43i	−1.27091	+	0.945428i
$259$			5.25806e41i			0.0191174i
$260$	−2.26312e42	+	7.53911e42i	−0.0767692	+	0.255741i
$261$	8.64816e43			2.73775
$262$	−1.19284e43	−	1.60350e43i	−0.352501	−	0.473855i
$263$			3.03188e43i			0.836581i	0.908313	+	0.418291i	$0.137371\pi$
$263$			3.03188e43i			0.836581i	−0.908313	+	0.418291i	$0.862629\pi$
$264$	2.71769e43	+	7.49258e43i	0.700374	+	1.93090i
$265$	5.20544e42			0.125323
$266$	1.64316e43	−	1.22235e43i	0.369668	−	0.274996i
$267$		−	3.48832e43i		−	0.733523i
$268$	−2.31082e43	−	6.93670e42i	−0.454296	−	0.136372i
$269$	−1.04106e44			−1.91397			−0.956985	−	0.290139i	$-0.906298\pi$
$269$	−1.04106e44			−1.91397			−0.956985	+	0.290139i	$0.906298\pi$
$270$	−2.07610e43	−	2.79084e43i	−0.357027	−	0.479940i
$271$			9.92001e43i			1.59612i	0.602580	+	0.798059i	$0.294139\pi$
$271$			9.92001e43i			1.59612i	−0.602580	+	0.798059i	$0.705861\pi$
$272$	−6.31456e43	−	4.16650e43i	−0.950830	−	0.627381i
$273$	1.00075e44			1.41057
$274$	−4.60313e43	+	3.42427e43i	−0.607496	+	0.451916i
$275$		−	8.52907e43i		−	1.05418i
$276$	7.76922e43	−	2.58815e44i	0.899526	−	2.99658i
$277$	2.92104e43			0.316885			0.158442	−	0.987368i	$-0.449353\pi$
$277$	2.92104e43			0.316885			0.158442	+	0.987368i	$0.449353\pi$
$278$	−4.64026e43	−	6.23776e43i	−0.471777	−	0.634194i
$279$			1.25152e44i			1.19279i
$280$	1.62112e43	−	5.88010e42i	0.144867	−	0.0525461i
$281$	8.15415e42			0.0683384			0.0341692	−	0.999416i	$-0.489121\pi$
$281$	8.15415e42			0.0683384			0.0341692	+	0.999416i	$0.489121\pi$
$282$	5.53221e42	−	4.11541e42i	0.0434925	−	0.0323541i
$283$		−	9.43649e43i		−	0.696073i	−0.937481	−	0.348037i	$-0.886849\pi$
$283$		−	9.43649e43i		−	0.696073i	0.937481	−	0.348037i	$-0.113151\pi$
$284$	5.25431e43	+	1.57726e43i	0.363736	+	0.109188i
$285$	−4.56200e43			−0.296448
$286$	1.25489e44	+	1.68691e44i	0.765626	+	1.02921i
$287$		−	1.74368e43i		−	0.0999063i
$288$	−4.45056e44	+	2.50986e43i	−2.39524	+	0.135078i
$289$	5.88733e43			0.297685
$290$	4.46883e43	−	3.32436e43i	0.212339	−	0.157959i
$291$			7.83767e43i			0.350036i
$292$	−9.35166e43	+	3.11531e44i	−0.392642	+	1.30801i
$293$	4.20097e44			1.65856			0.829282	−	0.558831i	$-0.188750\pi$
$293$	4.20097e44			1.65856			0.829282	+	0.558831i	$0.188750\pi$
$294$	1.65493e44	+	2.22467e44i	0.614508	+	0.826063i
$295$			6.51414e43i			0.227542i
$296$	−2.98479e42	−	8.22895e42i	−0.00980986	−	0.0270454i
$297$	−9.29073e44			−2.87365
$298$	9.88282e43	−	7.35183e43i	0.287732	−	0.214044i
$299$		−	7.12828e44i		−	1.95391i
$300$	6.47318e44	+	1.94314e44i	1.67084	+	0.501560i
$301$	2.34838e44			0.570915
$302$	−4.40985e43	−	5.92802e43i	−0.100995	−	0.135764i
$303$			6.27311e44i			1.35368i
$304$	−1.87770e44	+	2.84576e44i	−0.381858	+	0.578726i
$305$	2.09431e44			0.401461
$306$	1.21331e45	−	9.02577e44i	2.19273	−	1.63117i
$307$			4.94152e44i			0.842112i	0.907035	+	0.421056i	$0.138340\pi$
$307$			4.94152e44i			0.842112i	−0.907035	+	0.421056i	$0.861660\pi$
$308$	1.32429e44	−	4.41159e44i	0.212848	−	0.709059i
$309$	−1.32678e45			−2.01162
$310$	4.81086e43	+	6.46709e43i	0.0688197	+	0.0925120i
$311$		−	1.16623e45i		−	1.57434i	−0.616735	−	0.787171i	$-0.711545\pi$
$311$		−	1.16623e45i		−	1.57434i	0.616735	−	0.787171i	$-0.288455\pi$
$312$	−1.56618e45	+	5.68084e44i	−1.99554	+	0.723818i
$313$	1.18676e44			0.142746			0.0713730	−	0.997450i	$-0.477262\pi$
$313$	1.18676e44			0.142746			0.0713730	+	0.997450i	$0.477262\pi$
$314$	−3.13275e44	+	2.33045e44i	−0.355788	+	0.264671i
$315$			3.44699e44i			0.369700i
$316$	−5.72398e43	−	1.71825e43i	−0.0579870	−	0.0174067i
$317$	−1.14476e45			−1.09559			−0.547796	−	0.836612i	$-0.684533\pi$
$317$	−1.14476e45			−1.09559			−0.547796	+	0.836612i	$0.684533\pi$
$318$	6.57596e44	+	8.83984e44i	0.594663	+	0.799386i
$319$		−	1.48768e45i		−	1.27138i
$320$	−2.20329e44	+	1.84049e44i	−0.177981	+	0.148674i
$321$	3.16773e45			2.41912
$322$	−1.25298e45	+	9.32093e44i	−0.904772	+	0.673060i
$323$		−	1.15661e45i		−	0.789841i
$324$	1.04884e45	−	3.49400e45i	0.677485	−	2.25690i
$325$	1.78284e45			1.08946
$326$	−7.97333e44	−	1.07183e45i	−0.461023	−	0.619739i
$327$			2.69590e45i			1.47518i
$328$	9.89818e43	+	2.72889e44i	0.0512656	+	0.141337i
$329$	−3.98472e43			−0.0195376
$330$	−8.23238e44	+	6.12407e44i	−0.382186	+	0.284308i
$331$			2.55493e45i			1.12325i	0.827393	+	0.561623i	$0.189823\pi$
$331$			2.55493e45i			1.12325i	−0.827393	+	0.561623i	$0.810177\pi$
$332$	−1.79229e45	−	5.38017e44i	−0.746317	−	0.224032i
$333$	1.74972e44			0.0690196
$334$	6.24464e44	+	8.39447e44i	0.233384	+	0.313731i
$335$		−	3.10596e44i		−	0.109999i
$336$	3.04649e45	+	2.01015e45i	1.02257	+	0.674718i
$337$	−4.07177e45			−1.29552			−0.647761	−	0.761844i	$-0.724294\pi$
$337$	−4.07177e45			−1.29552			−0.647761	+	0.761844i	$0.724294\pi$
$338$	−8.66292e44	+	6.44434e44i	−0.261315	+	0.194392i
$339$			1.12864e46i			3.22820i
$340$	2.80009e44	−	9.32791e44i	0.0759541	−	0.253025i
$341$	2.15290e45			0.553917
$342$	−4.06761e45	−	5.46795e45i	−0.992817	−	1.33461i
$343$		−	4.47177e45i		−	1.03558i
$344$	−3.67525e45	+	1.33308e45i	−0.807673	+	0.292958i
$345$	3.47872e45			0.725564
$346$	2.93615e45	−	2.18420e45i	0.581310	−	0.432436i
$347$		−	4.62887e45i		−	0.870051i	−0.900418	−	0.435026i	$-0.856739\pi$
$347$		−	4.62887e45i		−	0.870051i	0.900418	−	0.435026i	$-0.143261\pi$
$348$	1.12908e46	+	3.38932e45i	2.01511	+	0.604903i
$349$	7.77526e45			1.31782			0.658912	−	0.752220i	$-0.271017\pi$
$349$	7.77526e45			1.31782			0.658912	+	0.752220i	$0.271017\pi$
$350$	−2.33124e45	−	3.13381e45i	−0.375286	−	0.504485i
$351$		−	1.94205e46i		−	2.96984i
$352$	4.31751e44	+	7.65596e45i	0.0627286	+	1.11233i
$353$	−1.28246e46			−1.77051			−0.885257	−	0.465103i	$-0.846017\pi$
$353$	−1.28246e46			−1.77051			−0.885257	+	0.465103i	$0.846017\pi$
$354$	−1.10623e46	+	8.22922e45i	−1.45139	+	1.07969i
$355$			7.06229e44i			0.0880715i
$356$	9.64911e44	−	3.21440e45i	0.114390	−	0.381066i
$357$	−1.23819e46			−1.39560
$358$	−4.75075e45	−	6.38628e45i	−0.509176	−	0.684469i
$359$		−	3.32204e45i		−	0.338613i	−0.985563	−	0.169307i	$-0.945847\pi$
$359$		−	3.32204e45i		−	0.338613i	0.985563	−	0.169307i	$-0.0541529\pi$
$360$	−1.95672e45	−	5.39460e45i	−0.189707	−	0.523015i
$361$	5.63008e45			0.519260
$362$	7.94593e45	−	5.91098e45i	0.697253	−	0.518686i
$363$			5.32574e45i			0.444693i
$364$	9.22161e45	+	2.76818e45i	0.732794	+	0.219973i
$365$	−4.18727e45			−0.316708
$366$	2.64571e46	+	3.55654e46i	1.90494	+	2.56075i
$367$			1.90567e46i			1.30634i	0.757209	+	0.653172i	$0.226562\pi$
$367$			1.90567e46i			1.30634i	−0.757209	+	0.653172i	$0.773438\pi$
$368$	1.43183e46	−	2.17001e46i	0.934608	−	1.41645i
$369$	−5.80244e45			−0.360692
$370$	9.04146e43	−	6.72594e43i	0.00535313	−	0.00398219i
$371$		−	6.36714e45i		−	0.359099i
$372$	−4.90487e45	+	1.63396e46i	−0.263545	+	0.877945i
$373$	−2.75814e46			−1.41207			−0.706036	−	0.708175i	$-0.749519\pi$
$373$	−2.75814e46			−1.41207			−0.706036	+	0.708175i	$0.749519\pi$
$374$	−1.55264e46	−	2.08716e46i	−0.757496	−	1.01828i
$375$			1.78957e46i			0.832118i
$376$	6.23616e44	−	2.26197e44i	0.0276399	−	0.0100255i
$377$	3.10971e46			1.31394
$378$	−3.41367e46	+	2.53943e46i	−1.37521	+	1.02302i
$379$			7.10849e45i			0.273068i	0.990635	+	0.136534i	$0.0435963\pi$
$379$			7.10849e45i			0.273068i	−0.990635	+	0.136534i	$0.956404\pi$
$380$	−4.20377e45	−	1.26190e45i	−0.154005	−	0.0462297i
$381$	4.28344e46			1.49673
$382$	1.32448e46	+	1.78045e46i	0.441472	+	0.593457i
$383$		−	2.26690e46i		−	0.720866i	−0.932785	−	0.360433i	$-0.882629\pi$
$383$		−	2.26690e46i		−	0.720866i	0.932785	−	0.360433i	$-0.117371\pi$
$384$	−5.90890e46	−	1.41655e46i	−1.79285	−	0.429803i
$385$	5.92960e45			0.171685
$386$	5.12098e46	−	3.80949e46i	1.41508	−	1.05268i
$387$		−	7.81469e46i		−	2.06117i
$388$	−2.16799e45	+	7.22221e45i	−0.0545866	+	0.181844i
$389$	−8.79753e45			−0.211479			−0.105740	−	0.994394i	$-0.533721\pi$
$389$	−8.79753e45			−0.211479			−0.105740	+	0.994394i	$0.533721\pi$
$390$	−1.28012e46	−	1.72083e46i	−0.293825	−	0.394979i
$391$			8.81960e46i			1.93316i
$392$	9.09606e45	+	2.50775e46i	0.190416	+	0.524970i
$393$	5.44540e46			1.08884
$394$	3.64135e46	−	2.70880e46i	0.695552	−	0.517421i
$395$		−	7.69356e44i		−	0.0140404i
$396$	−1.46804e47	−	4.40683e46i	−2.55991	−	0.768445i
$397$	4.64455e45			0.0773953			0.0386976	−	0.999251i	$-0.487679\pi$
$397$	4.64455e45			0.0773953			0.0386976	+	0.999251i	$0.487679\pi$
$398$	−4.62246e46	−	6.21382e46i	−0.736169	−	0.989608i
$399$			5.58010e46i			0.849435i
$400$	5.42737e46	+	3.58112e46i	0.789787	+	0.521121i
$401$	−1.31213e47			−1.82549			−0.912746	−	0.408528i	$-0.866042\pi$
$401$	−1.31213e47			−1.82549			−0.912746	+	0.408528i	$0.866042\pi$
$402$	5.27451e46	−	3.92371e46i	0.701639	−	0.521949i
$403$			4.50024e46i			0.572459i
$404$	−1.73521e46	+	5.78051e46i	−0.211100	+	0.703236i
$405$	4.69626e46			0.546465
$406$	−4.06625e46	−	5.46613e46i	−0.452612	−	0.608431i
$407$		−	3.00991e45i		−	0.0320519i
$408$	1.93779e47	−	7.02872e46i	1.97435	−	0.716132i
$409$	−4.55215e46			−0.443810			−0.221905	−	0.975068i	$-0.571227\pi$
$409$	−4.55215e46			−0.443810			−0.221905	+	0.975068i	$0.571227\pi$
$410$	−2.99834e45	+	2.23046e45i	−0.0279751	+	0.0208106i
$411$		−	1.56320e47i		−	1.39593i
$412$	−1.22260e47	−	3.67003e46i	−1.04504	−	0.313704i
$413$	7.96789e46			0.651993
$414$	3.10172e47	+	4.16954e47i	2.42995	+	3.26650i
$415$		−	2.40901e46i		−	0.180706i
$416$	−1.60034e47	+	9.02496e45i	−1.14956	+	0.0648284i
$417$	2.11831e47			1.45727
$418$	−9.40610e46	+	6.99720e46i	−0.619779	+	0.461053i
$419$			3.48144e46i			0.219739i	0.993946	+	0.109869i	$0.0350432\pi$
$419$			3.48144e46i			0.219739i	−0.993946	+	0.109869i	$0.964957\pi$
$420$	−1.35092e46	+	4.50030e46i	−0.0816849	+	0.272116i
$421$	−1.95656e47			−1.13348			−0.566742	−	0.823896i	$-0.691796\pi$
$421$	−1.95656e47			−1.13348			−0.566742	+	0.823896i	$0.691796\pi$
$422$	−5.64270e45	−	7.58530e45i	−0.0313230	−	0.0421065i
$423$			1.32599e46i			0.0705367i
$424$	3.61437e46	+	9.96468e46i	0.184267	+	0.508016i
$425$	−2.20586e47			−1.07789
$426$	−1.19931e47	+	8.92169e46i	−0.561772	+	0.417902i
$427$		−	2.56169e47i		−	1.15034i
$428$	2.91899e47	+	8.76233e46i	1.25674	+	0.377252i
$429$	−5.72865e47			−2.36494
$430$	−3.00397e46	−	4.03814e46i	−0.118922	−	0.159864i
$431$			2.21426e47i			0.840692i	0.907364	+	0.420346i	$0.138091\pi$
$431$			2.21426e47i			0.840692i	−0.907364	+	0.420346i	$0.861909\pi$
$432$	3.90092e47	−	5.91205e47i	1.42056	−	2.15293i
$433$	4.00496e47			1.39900			0.699498	−	0.714635i	$-0.253407\pi$
$433$	4.00496e47			1.39900			0.699498	+	0.714635i	$0.253407\pi$
$434$	7.91034e46	−	5.88450e46i	0.265082	−	0.197194i
$435$			1.51759e47i			0.487919i
$436$	−7.45718e46	+	2.48421e47i	−0.230048	+	0.766356i
$437$	3.97469e47			1.17662
$438$	−5.28972e47	−	7.11079e47i	−1.50279	−	2.02015i
$439$		−	4.90828e47i		−	1.33835i	−0.743107	−	0.669173i	$-0.766649\pi$
$439$		−	4.90828e47i		−	1.33835i	0.743107	−	0.669173i	$-0.233351\pi$
$440$	−9.27992e46	+	3.36600e46i	−0.242882	+	0.0880979i
$441$	−5.33222e47			−1.33972
$442$	4.36281e47	−	3.24550e47i	1.05236	−	0.782853i
$443$		−	1.37062e47i		−	0.317432i	−0.987324	−	0.158716i	$-0.949265\pi$
$443$		−	1.37062e47i		−	0.317432i	0.987324	−	0.158716i	$-0.0507354\pi$
$444$	2.28439e46	+	6.85737e45i	0.0508015	+	0.0152498i
$445$	4.32046e46			0.0922676
$446$	9.47212e46	+	1.27331e47i	0.194276	+	0.261159i
$447$			3.35616e47i			0.661160i
$448$	2.25123e47	+	2.69500e47i	0.426007	+	0.509982i
$449$	7.80613e47			1.41906			0.709532	−	0.704674i	$-0.248907\pi$
$449$	7.80613e47			1.41906			0.709532	+	0.704674i	$0.248907\pi$
$450$	−1.04284e48	+	7.75766e47i	−1.82134	+	1.35490i
$451$			9.98149e46i			0.167501i
$452$	−3.12195e47	+	1.04001e48i	−0.503425	+	1.67705i
$453$	2.01313e47			0.311963
$454$	−7.58618e47	−	1.01979e48i	−1.12984	−	1.51881i
$455$			1.23947e47i			0.177432i
$456$	−3.16760e47	−	8.73296e47i	−0.435877	−	1.20169i
$457$	4.96948e47			0.657385			0.328692	−	0.944437i	$-0.393392\pi$
$457$	4.96948e47			0.657385			0.328692	+	0.944437i	$0.393392\pi$
$458$	−7.18616e47	+	5.34578e47i	−0.913941	+	0.679880i
$459$			2.40284e48i			2.93831i
$460$	3.20555e47	+	9.62255e46i	0.376931	+	0.113149i
$461$	8.70832e47			0.984731			0.492366	−	0.870389i	$-0.336132\pi$
$461$	8.70832e47			0.984731			0.492366	+	0.870389i	$0.336132\pi$
$462$	7.49077e47	+	1.00696e48i	0.814650	+	1.09511i
$463$		−	1.80782e48i		−	1.89102i	−0.325587	−	0.945512i	$-0.605562\pi$
$463$		−	1.80782e48i		−	1.89102i	0.325587	−	0.945512i	$-0.394438\pi$
$464$	9.46666e47	+	6.24634e47i	0.952518	+	0.628495i
$465$	−2.19619e47			−0.212577
$466$	7.90166e47	−	5.87804e47i	0.735821	−	0.547377i
$467$			7.26554e47i			0.650975i	0.945546	+	0.325487i	$0.105528\pi$
$467$			7.26554e47i			0.650975i	−0.945546	+	0.325487i	$0.894472\pi$
$468$	9.21166e47	−	3.06867e48i	0.794168	−	2.64561i
$469$	−3.79911e47			−0.315189
$470$	5.09713e45	+	6.85191e45i	0.00406972	+	0.00547079i
$471$		−	1.06387e48i		−	0.817543i
$472$	−1.24699e48	+	4.52306e47i	−0.922373	+	0.334562i
$473$	−1.34430e48			−0.957186
$474$	1.30652e47	−	9.71917e46i	0.0895580	−	0.0666222i
$475$			9.94104e47i			0.656065i
$476$	−1.14096e48	−	3.42498e47i	−0.725013	−	0.217637i
$477$	−2.11879e48			−1.29645
$478$	8.52488e46	+	1.14597e47i	0.0502326	+	0.0675261i
$479$			1.39029e48i			0.788982i	0.918900	+	0.394491i	$0.129079\pi$
$479$			1.39029e48i			0.788982i	−0.918900	+	0.394491i	$0.870921\pi$
$480$	−4.40433e46	−	7.80991e47i	−0.0240734	−	0.426878i
$481$	6.29166e46			0.0331249
$482$	3.07898e47	−	2.29045e47i	0.156157	−	0.116165i
$483$		−	4.25507e48i		−	2.07902i
$484$	−1.47316e47	+	4.90753e47i	−0.0693480	+	0.231018i
$485$	−9.70733e46			−0.0440300
$486$	2.41031e48	+	3.24011e48i	1.05347	+	1.41614i
$487$		−	3.97047e48i		−	1.67233i	−0.548480	−	0.836163i	$-0.684793\pi$
$487$		−	3.97047e48i		−	1.67233i	0.548480	−	0.836163i	$-0.315207\pi$
$488$	1.45417e48	+	4.00909e48i	0.590281	+	1.62738i
$489$	3.63988e48			1.42406
$490$	−2.75536e47	+	2.04971e47i	−0.103908	+	0.0772971i
$491$		−	4.46359e47i		−	0.162262i	−0.996703	−	0.0811312i	$-0.974147\pi$
$491$		−	4.46359e47i		−	0.162262i	0.996703	−	0.0811312i	$-0.0258533\pi$
$492$	−7.57551e47	−	2.27405e47i	−0.265485	−	0.0796943i
$493$	−3.84755e48			−1.29999
$494$	−1.46263e48	−	1.96617e48i	−0.476486	−	0.640525i
$495$		−	1.97319e48i		−	0.619833i
$496$	−9.03942e47	+	1.36997e48i	−0.273823	+	0.414994i
$497$	8.63838e47			0.252358
$498$	4.09097e48	−	3.04327e48i	1.15265	−	0.857456i
$499$			5.95694e48i			1.61888i	0.587206	+	0.809438i	$0.300228\pi$
$499$			5.95694e48i			1.61888i	−0.587206	+	0.809438i	$0.699772\pi$
$500$	−4.95015e47	+	1.64904e48i	−0.129765	+	0.432286i
$501$	−2.85072e48			−0.720901
$502$	3.31683e47	+	4.45870e47i	0.0809200	+	0.108778i
$503$			5.90539e48i			1.39003i	0.718994	+	0.695016i	$0.244603\pi$
$503$			5.90539e48i			1.39003i	−0.718994	+	0.695016i	$0.755397\pi$
$504$	−6.59851e48	+	2.39340e48i	−1.49864	+	0.543583i
$505$	−7.76954e47			−0.170275
$506$	7.17255e48	−	5.33566e48i	1.51693	−	1.12844i
$507$		−	2.94188e48i		−	0.600458i
$508$	3.94708e48	+	1.18485e48i	0.777551	+	0.233408i
$509$	−2.14889e48			−0.408595			−0.204298	−	0.978909i	$-0.565491\pi$
$509$	−2.14889e48			−0.408595			−0.204298	+	0.978909i	$0.565491\pi$
$510$	1.58386e48	+	2.12913e48i	0.290705	+	0.390785i
$511$			5.12174e48i			0.907489i
$512$	−5.05306e48	−	2.93978e48i	−0.864362	−	0.502870i
$513$	1.08288e49			1.78841
$514$	−2.12798e48	+	1.58301e48i	−0.339337	+	0.252433i
$515$		−	1.64328e48i		−	0.253036i
$516$	3.06267e48	−	1.02027e49i	0.455414	−	1.51712i
$517$	2.28101e47			0.0327565
$518$	−8.22697e46	−	1.10592e47i	−0.0114105	−	0.0153387i
$519$			9.97100e48i			1.33575i
$520$	−7.03599e47	−	1.93979e48i	−0.0910469	−	0.251013i
$521$	5.15369e48			0.644227			0.322114	−	0.946701i	$-0.395607\pi$
$521$	5.15369e48			0.644227			0.322114	+	0.946701i	$0.395607\pi$
$522$	−1.81896e49	+	1.35313e49i	−2.19662	+	1.63406i
$523$		−	4.67519e48i		−	0.545467i	−0.962090	−	0.272733i	$-0.912072\pi$
$523$		−	4.67519e48i		−	0.545467i	0.962090	−	0.272733i	$-0.0879277\pi$
$524$	5.01780e48	+	1.50626e48i	0.565653	+	0.169800i
$525$	1.06423e49			1.15922
$526$	−4.74380e48	−	6.37693e48i	−0.499324	−	0.671225i
$527$		−	5.56800e48i		−	0.566381i
$528$	−1.74393e49	−	1.15069e49i	−1.71442	−	1.13122i
$529$	−1.97842e49			−1.87982
$530$	−1.09486e48	+	8.14464e47i	−0.100552	+	0.0748008i
$531$		−	2.65147e49i		−	2.35389i
$532$	−1.54352e48	+	5.14192e48i	−0.132466	+	0.441282i
$533$	−2.08645e48			−0.173108
$534$	5.45797e48	+	7.33697e48i	0.437813	+	0.588538i
$535$			3.92339e48i			0.304294i
$536$	5.94567e48	−	2.15660e48i	0.445897	−	0.161735i
$537$	2.16875e49			1.57280
$538$	2.18966e49	−	1.62888e49i	1.53566	−	1.14238i
$539$			9.17262e48i			0.622151i
$540$	8.73331e48	+	2.62160e48i	0.572916	+	0.171980i
$541$	1.80924e49			1.14801			0.574003	−	0.818853i	$-0.305390\pi$
$541$	1.80924e49			1.14801			0.574003	+	0.818853i	$0.305390\pi$
$542$	−1.55212e49	−	2.08647e49i	−0.952663	−	1.28063i
$543$			2.69840e49i			1.60217i
$544$	1.98005e49	−	1.11663e48i	1.13735	−	0.0641400i
$545$	−3.33901e48			−0.185558
$546$	−2.10486e49	+	1.56581e49i	−1.13176	+	0.841919i
$547$		−	1.44140e48i		−	0.0749914i	−0.999297	−	0.0374957i	$-0.988062\pi$
$547$		−	1.44140e48i		−	0.0749914i	0.999297	−	0.0374957i	$-0.0119381\pi$
$548$	4.32400e48	−	1.44045e49i	0.217688	−	0.725184i
$549$	−8.52453e49			−4.15306
$550$	1.33449e49	+	1.79391e49i	0.629198	+	0.845811i
$551$			1.73396e49i			0.791243i
$552$	2.41543e49	+	6.65925e49i	1.06682	+	2.94118i
$553$	−9.41053e47			−0.0402311
$554$	−6.14381e48	+	4.57038e48i	−0.254251	+	0.189137i
$555$			3.07044e47i			0.0123006i
$556$	1.95197e49	+	5.85949e48i	0.757053	+	0.227255i
$557$	−9.88492e48			−0.371176			−0.185588	−	0.982628i	$-0.559419\pi$
$557$	−9.88492e48			−0.371176			−0.185588	+	0.982628i	$0.559419\pi$
$558$	−1.95818e49	−	2.63232e49i	−0.711931	−	0.957025i
$559$		−	2.81001e49i		−	0.989227i
$560$	−2.48967e48	+	3.77323e48i	−0.0848706	+	0.128626i
$561$	7.08788e49			2.33983
$562$	−1.71506e48	+	1.27583e48i	−0.0548309	+	0.0407887i
$563$		−	1.54659e49i		−	0.478877i	−0.970912	−	0.239439i	$-0.923037\pi$
$563$		−	1.54659e49i		−	0.478877i	0.970912	−	0.239439i	$-0.0769634\pi$
$564$	−5.19674e47	+	1.73118e48i	−0.0155850	+	0.0519182i
$565$	−1.39788e49			−0.406066
$566$	1.47647e49	+	1.98477e49i	0.415460	+	0.558490i
$567$		−	5.74433e49i		−	1.56583i
$568$	−1.35192e49	+	4.90367e48i	−0.357011	+	0.129494i
$569$	3.71061e49			0.949345			0.474673	−	0.880162i	$-0.342566\pi$
$569$	3.71061e49			0.949345			0.474673	+	0.880162i	$0.342566\pi$
$570$	9.59524e48	−	7.13789e48i	0.237853	−	0.176939i
$571$		−	2.71045e49i		−	0.651017i	−0.945539	−	0.325508i	$-0.894465\pi$
$571$		−	2.71045e49i		−	0.651017i	0.945539	−	0.325508i	$-0.105535\pi$
$572$	−5.27880e49	−	1.58461e49i	−1.22859	−	0.368803i
$573$	−6.04631e49			−1.36366
$574$	2.72823e48	+	3.66747e48i	0.0596304	+	0.0801591i
$575$		−	7.58046e49i		−	1.60574i
$576$	8.96814e49	−	7.49142e49i	1.84119	−	1.53801i
$577$	−7.36078e48			−0.146473			−0.0732367	−	0.997315i	$-0.523333\pi$
$577$	−7.36078e48			−0.146473			−0.0732367	+	0.997315i	$0.523333\pi$
$578$	−1.23828e49	+	9.21156e48i	−0.238846	+	0.177677i
$579$			1.73906e50i			3.25162i
$580$	−4.19783e48	+	1.39842e49i	−0.0760889	+	0.253474i
$581$	−2.94663e49			−0.517792
$582$	−1.22631e49	−	1.64849e49i	−0.208924	−	0.280849i
$583$			3.64479e49i			0.602059i
$584$	−2.90741e49	−	8.01561e49i	−0.465666	−	1.28382i
$585$	4.12458e49			0.640582
$586$	−8.83587e49	+	6.57300e49i	−1.33074	+	0.989935i
$587$		−	3.21694e49i		−	0.469848i	−0.972014	−	0.234924i	$-0.924516\pi$
$587$		−	3.21694e49i		−	0.469848i	0.972014	−	0.234924i	$-0.0754841\pi$
$588$	−6.96161e49	−	2.08976e49i	−0.986093	−	0.296009i
$589$	−2.50931e49			−0.344730
$590$	−1.01923e49	−	1.37012e49i	−0.135811	−	0.182566i
$591$			1.23658e50i			1.59826i
$592$	1.91532e48	+	1.26378e48i	0.0240133	+	0.0158446i
$593$	2.77965e49			0.338070			0.169035	−	0.985610i	$-0.445935\pi$
$593$	2.77965e49			0.338070			0.169035	+	0.985610i	$0.445935\pi$
$594$	1.95411e50	−	1.45366e50i	2.30565	−	1.71517i
$595$		−	1.53356e49i		−	0.175548i
$596$	−9.28352e48	+	3.09261e49i	−0.103105	+	0.343473i
$597$	2.11018e50			2.27395
$598$	1.11532e50	+	1.49929e50i	1.16621	+	1.56770i
$599$		−	2.12300e49i		−	0.215411i	−0.994183	−	0.107705i	$-0.965650\pi$
$599$		−	2.12300e49i		−	0.215411i	0.994183	−	0.107705i	$-0.0343503\pi$
$600$	−1.66553e50	+	6.04119e49i	−1.63995	+	0.594840i
$601$	−2.90392e49			−0.277488			−0.138744	−	0.990328i	$-0.544306\pi$
$601$	−2.90392e49			−0.277488			−0.138744	+	0.990328i	$0.544306\pi$
$602$	−4.93934e49	+	3.67437e49i	−0.458070	+	0.340758i
$603$			1.26423e50i			1.13793i
$604$	1.85504e49	+	5.56854e48i	0.162065	+	0.0486493i
$605$	−6.59619e48			−0.0559366
$606$	−9.81515e49	−	1.31942e50i	−0.807960	−	1.08611i
$607$		−	2.45384e50i		−	1.96087i	−0.196839	−	0.980436i	$-0.563068\pi$
$607$		−	2.45384e50i		−	1.96087i	0.196839	−	0.980436i	$-0.436932\pi$
$608$	−5.03227e48	−	8.92339e49i	−0.0390391	−	0.692254i
$609$	1.85627e50			1.39807
$610$	−4.40494e49	+	3.27683e49i	−0.322109	+	0.239617i
$611$			4.76802e48i			0.0338530i
$612$	−1.13973e50	+	3.79677e50i	−0.785735	+	2.61751i
$613$	−2.07905e50			−1.39180			−0.695898	−	0.718141i	$-0.744993\pi$
$613$	−2.07905e50			−1.39180			−0.695898	+	0.718141i	$0.744993\pi$
$614$	−7.73171e49	−	1.03935e50i	−0.502626	−	0.675663i
$615$		−	1.01822e49i		−	0.0642820i
$616$	4.11718e49	+	1.13509e50i	0.252434	+	0.695950i
$617$	2.32916e50			1.38697			0.693485	−	0.720471i	$-0.256074\pi$
$617$	2.32916e50			1.38697			0.693485	+	0.720471i	$0.256074\pi$
$618$	2.79061e50	−	2.07594e50i	1.61401	−	1.20066i
$619$			1.77577e50i			0.997595i	0.866719	+	0.498797i	$0.166225\pi$
$619$			1.77577e50i			0.997595i	−0.866719	+	0.498797i	$0.833775\pi$
$620$	−2.02373e49	−	6.07492e48i	−0.110434	−	0.0331505i
$621$	−8.25741e50			−4.37719
$622$	1.82474e50	+	2.45293e50i	0.939666	+	1.26316i
$623$		−	5.28465e49i		−	0.264382i
$624$	2.40530e50	−	3.64536e50i	1.16909	−	1.77181i
$625$	1.78205e50			0.841550
$626$	−2.49610e49	+	1.85685e49i	−0.114531	+	0.0851998i
$627$		−	3.19427e50i		−	1.42415i
$628$	2.94278e49	−	9.80325e49i	0.127492	−	0.424714i
$629$	−7.78448e48			−0.0327731
$630$	−5.39330e49	−	7.25004e49i	−0.220660	−	0.296627i
$631$			9.00402e49i			0.358021i	0.983847	+	0.179010i	$0.0572895\pi$
$631$			9.00402e49i			0.358021i	−0.983847	+	0.179010i	$0.942710\pi$
$632$	1.47276e49	−	5.34199e48i	0.0569149	−	0.0206441i
$633$	2.57593e49			0.0967536
$634$	2.40777e50	−	1.79114e50i	0.879041	−	0.653918i
$635$			5.30525e49i			0.188269i
$636$	−2.76624e50	−	8.30379e49i	−0.954247	−	0.286450i
$637$	−1.91737e50			−0.642977
$638$	2.32768e50	+	3.12902e50i	0.758841	+	1.02009i
$639$		−	2.87459e50i		−	0.911088i
$640$	1.75446e49	−	7.31846e49i	0.0540636	−	0.225517i
$641$	4.65547e49			0.139482			0.0697411	−	0.997565i	$-0.477783\pi$
$641$	4.65547e49			0.139482			0.0697411	+	0.997565i	$0.477783\pi$
$642$	−6.66268e50	+	4.95637e50i	−1.94097	+	1.44389i
$643$		−	4.29584e50i		−	1.21689i	−0.793597	−	0.608444i	$-0.791794\pi$
$643$		−	4.29584e50i		−	1.21689i	0.793597	−	0.608444i	$-0.208206\pi$
$644$	1.17700e50	−	3.92093e50i	0.324214	−	1.08005i
$645$	1.37133e50			0.367340
$646$	1.80967e50	+	2.43268e50i	0.471427	+	0.633724i
$647$			2.15910e50i			0.547010i	0.961871	+	0.273505i	$0.0881831\pi$
$647$			2.15910e50i			0.547010i	−0.961871	+	0.273505i	$0.911817\pi$
$648$	3.26083e50	+	8.98997e50i	0.803485	+	2.21518i
$649$	−4.56113e50			−1.09312
$650$	−3.74984e50	+	2.78951e50i	−0.874123	+	0.650260i
$651$			2.68631e50i			0.609114i
$652$	3.35405e50	+	1.00683e50i	0.739798	+	0.222075i
$653$	5.38075e50			1.15453			0.577266	−	0.816556i	$-0.304120\pi$
$653$	5.38075e50			1.15453			0.577266	+	0.816556i	$0.304120\pi$
$654$	−4.21812e50	−	5.67028e50i	−0.880480	−	1.18360i
$655$			6.74440e49i			0.136962i
$656$	−6.35161e49	−	4.19095e49i	−0.125492	−	0.0828025i
$657$	1.70436e51			3.27631
$658$	8.38105e48	−	6.23466e48i	0.0156759	−	0.0116613i
$659$			5.76436e50i			1.04909i	0.851382	+	0.524546i	$0.175765\pi$
$659$			5.76436e50i			1.04909i	−0.851382	+	0.524546i	$0.824235\pi$
$660$	7.73317e49	−	2.57614e50i	0.136951	−	0.456225i
$661$	−8.17417e50			−1.40870			−0.704348	−	0.709854i	$-0.748761\pi$
$661$	−8.17417e50			−1.40870			−0.704348	+	0.709854i	$0.748761\pi$
$662$	−3.99754e50	−	5.37377e50i	−0.670424	−	0.901229i
$663$			1.48159e51i			2.41816i
$664$	4.61152e50	−	1.67268e50i	0.732519	−	0.265698i
$665$	−6.91123e49			−0.106848
$666$	−3.68018e49	+	2.73768e49i	−0.0553774	+	0.0411952i
$667$		−	1.32222e51i		−	1.93659i
$668$	−2.62686e50	−	7.88542e49i	−0.374508	−	0.112421i
$669$	−4.32408e50			−0.600101
$670$	4.85970e49	+	6.53274e49i	0.0656543	+	0.0882570i
$671$			1.46641e51i			1.92863i
$672$	−9.55284e50	+	5.38724e49i	−1.22317	+	0.0689794i
$673$	−1.40655e51			−1.75342			−0.876709	−	0.481022i	$-0.840266\pi$
$673$	−1.40655e51			−1.75342			−0.876709	+	0.481022i	$0.840266\pi$
$674$	8.56412e50	−	6.37085e50i	1.03945	−	0.773249i
$675$		−	2.06525e51i		−	2.44064i
$676$	8.13760e49	−	2.71087e50i	0.0936388	−	0.311938i
$677$	2.08440e50			0.233553			0.116776	−	0.993158i	$-0.462744\pi$
$677$	2.08440e50			0.233553			0.116776	+	0.993158i	$0.462744\pi$
$678$	−1.76592e51	−	2.37386e51i	−1.92680	−	2.59013i
$679$			1.18737e50i			0.126163i
$680$	8.70541e49	+	2.40005e50i	0.0900801	+	0.248347i
$681$	3.46314e51			3.48997
$682$	−4.52818e50	+	3.36851e50i	−0.444432	+	0.330613i
$683$			1.80161e51i			1.72222i	0.508418	+	0.861110i	$0.330230\pi$
$683$			1.80161e51i			1.72222i	−0.508418	+	0.861110i	$0.669770\pi$
$684$	1.71108e51	+	5.13637e50i	1.59316	+	0.478241i
$685$	1.93610e50			0.175589
$686$	6.99672e50	+	9.40546e50i	0.618102	+	0.830894i
$687$		−	2.44038e51i		−	2.10008i
$688$	5.64435e50	−	8.55432e50i	0.473175	−	0.717123i
$689$	−7.61876e50			−0.622212
$690$	−7.31678e50	+	5.44295e50i	−0.582152	+	0.433062i
$691$		−	2.04610e51i		−	1.58607i	−0.609177	−	0.793035i	$-0.708500\pi$
$691$		−	2.04610e51i		−	1.58607i	0.609177	−	0.793035i	$-0.291500\pi$
$692$	−2.75810e50	+	9.18802e50i	−0.208305	+	0.693925i
$693$	−2.41354e51			−1.77606
$694$	7.24252e50	+	9.73588e50i	0.519301	+	0.698080i
$695$			2.62363e50i			0.183306i
$696$	−2.90510e51	+	1.05373e51i	−1.97785	+	0.717404i
$697$	2.58149e50			0.171270
$698$	−1.63537e51	+	1.21655e51i	−1.05735	+	0.786560i
$699$			2.68336e51i			1.69079i
$700$	9.80658e50	+	2.94378e50i	0.602217	+	0.180776i
$701$	1.92653e50			0.115306			0.0576528	−	0.998337i	$-0.481638\pi$
$701$	1.92653e50			0.115306			0.0576528	+	0.998337i	$0.481638\pi$
$702$	3.03862e51	+	4.08471e51i	1.77259	+	2.38283i
$703$			3.50820e49i			0.0199475i
$704$	−1.28869e51	−	1.54272e51i	−0.714236	−	0.855026i
$705$	−2.32687e49			−0.0125710
$706$	2.69739e51	−	2.00659e51i	1.42056	−	1.05675i
$707$			9.50347e50i			0.487902i
$708$	1.03914e51	−	3.46169e51i	0.520089	−	1.73257i
$709$	−3.86868e51			−1.88769			−0.943844	−	0.330391i	$-0.892819\pi$
$709$	−3.86868e51			−1.88769			−0.943844	+	0.330391i	$0.892819\pi$
$710$	−1.10499e50	−	1.48541e50i	−0.0525666	−	0.0706636i
$711$			3.13154e50i			0.145246i
$712$	2.99989e50	+	8.27057e50i	0.135664	+	0.374021i
$713$	1.91345e51			0.843736
$714$	2.60428e51	−	1.93732e51i	1.11975	−	0.832980i
$715$		−	7.09521e50i		−	0.297479i
$716$	1.99845e51	+	5.99901e50i	0.817068	+	0.245271i
$717$	−3.89166e50			−0.155164
$718$	5.19779e50	+	6.98722e50i	0.202106	+	0.271684i
$719$		−	2.73011e51i		−	1.03529i	−0.855597	−	0.517643i	$-0.826810\pi$
$719$		−	2.73011e51i		−	1.03529i	0.855597	−	0.517643i	$-0.173190\pi$
$720$	1.25562e51	+	8.28487e50i	0.464378	+	0.306408i
$721$	−2.01001e51			−0.725044
$722$	−1.18417e51	+	8.80905e50i	−0.416625	+	0.309927i
$723$			1.04561e51i			0.358822i
$724$	−7.46409e50	+	2.48650e51i	−0.249852	+	0.832329i
$725$	3.30697e51			1.07981
$726$	−8.33287e50	−	1.12016e51i	−0.265421	−	0.356797i
$727$		−	2.89403e51i		−	0.899257i	−0.893216	−	0.449629i	$-0.851556\pi$
$727$		−	2.89403e51i		−	0.899257i	0.893216	−	0.449629i	$-0.148444\pi$
$728$	−2.37270e51	+	8.60621e50i	−0.719246	+	0.260884i
$729$	−3.03535e51			−0.897663
$730$	8.80706e50	−	6.55157e50i	0.254109	−	0.189031i
$731$			3.47674e51i			0.978723i
$732$	−1.11294e52	−	3.34087e51i	−3.05684	−	0.917613i
$733$	7.89670e50			0.211629			0.105814	−	0.994386i	$-0.466255\pi$
$733$	7.89670e50			0.211629			0.105814	+	0.994386i	$0.466255\pi$
$734$	−2.98168e51	−	4.00818e51i	−0.779709	−	1.04814i
$735$		−	9.35706e50i		−	0.238763i
$736$	3.83732e50	+	6.80446e51i	0.0955493	+	1.69431i
$737$	2.17476e51			0.528440
$738$	1.22042e51	−	9.07873e50i	0.289398	−	0.215283i
$739$		−	2.27200e51i		−	0.525786i	−0.964825	−	0.262893i	$-0.915323\pi$
$739$		−	2.27200e51i		−	0.525786i	0.964825	−	0.262893i	$-0.0846767\pi$
$740$	−8.49318e48	+	2.82933e49i	−0.00191822	+	0.00639017i
$741$	6.67702e51			1.47182
$742$	9.96228e50	+	1.33920e51i	0.214333	+	0.288120i
$743$		−	6.02538e51i		−	1.26528i	−0.774447	−	0.632639i	$-0.781972\pi$
$743$		−	6.02538e51i		−	1.26528i	0.774447	−	0.632639i	$-0.218028\pi$
$744$	−1.52491e51	−	4.20413e51i	−0.312559	−	0.861713i
$745$	−4.15676e50			−0.0831653
$746$	5.80118e51	−	4.31549e51i	1.13297	−	0.842814i
$747$			9.80548e51i			1.86938i
$748$	6.53130e51	+	1.96059e51i	1.21554	+	0.364887i
$749$	4.79897e51			0.871918
$750$	−2.80003e51	−	3.76398e51i	−0.496660	−	0.667644i
$751$		−	3.01091e51i		−	0.521410i	−0.965419	−	0.260705i	$-0.916045\pi$
$751$		−	3.01091e51i		−	0.521410i	0.965419	−	0.260705i	$-0.0839550\pi$
$752$	−9.57732e49	+	1.45149e50i	−0.0161928	+	0.0245411i
$753$	−1.51415e51			−0.249954
$754$	−6.54064e51	+	4.86558e51i	−1.05423	+	0.784243i
$755$			2.49336e50i			0.0392409i
$756$	3.20666e51	−	1.06823e52i	0.492789	−	1.64162i
$757$	−3.25156e51			−0.487940			−0.243970	−	0.969783i	$-0.578450\pi$
$757$	−3.25156e51			−0.487940			−0.243970	+	0.969783i	$0.578450\pi$
$758$	−1.11222e51	−	1.49512e51i	−0.162984	−	0.219095i
$759$			2.43576e52i			3.48564i
$760$	1.08162e51	−	3.92323e50i	0.151157	−	0.0548276i
$761$	4.88593e50			0.0666843			0.0333421	−	0.999444i	$-0.489385\pi$
$761$	4.88593e50			0.0666843			0.0333421	+	0.999444i	$0.489385\pi$
$762$	−9.00934e51	+	6.70204e51i	−1.20089	+	0.893342i
$763$			4.08417e51i			0.531695i
$764$	−5.57152e51	−	1.67248e51i	−0.708424	−	0.212658i
$765$	−5.10322e51			−0.633780
$766$	3.54688e51	+	4.76796e51i	0.430258	+	0.578382i
$767$		−	9.53419e51i		−	1.12971i
$768$	1.46445e52	−	6.26588e51i	1.69502	−	0.725237i
$769$	2.41255e51			0.272774			0.136387	−	0.990656i	$-0.456451\pi$
$769$	2.41255e51			0.272774			0.136387	+	0.990656i	$0.456451\pi$
$770$	−1.24717e51	+	9.27768e50i	−0.137750	+	0.102472i
$771$		−	7.22652e51i		−	0.779741i
$772$	−4.81044e51	+	1.60250e52i	−0.507076	+	1.68922i
$773$	1.12085e50			0.0115429			0.00577146	−	0.999983i	$-0.498163\pi$
$773$	1.12085e50			0.0115429			0.00577146	+	0.999983i	$0.498163\pi$
$774$	1.22272e52	+	1.64366e52i	1.23024	+	1.65377i
$775$			4.78571e51i			0.470452i
$776$	−6.74024e50	−	1.85826e51i	−0.0647387	−	0.178482i
$777$	3.75566e50			0.0352459
$778$	1.85038e51	−	1.37650e51i	0.169679	−	0.126224i
$779$		−	1.16339e51i		−	0.104244i
$780$	5.38495e51	+	1.61647e51i	0.471497	+	0.141536i
$781$	−4.94494e51			−0.423099
$782$	−1.37995e52	−	1.85502e52i	−1.15383	−	1.55106i
$783$		−	3.60229e52i		−	2.94352i
$784$	−5.83689e51	−	3.85133e51i	−0.466114	−	0.307554i
$785$	1.31765e51			0.102836
$786$	−1.14533e52	+	8.52010e51i	−0.873624	+	0.649888i
$787$		−	2.00865e52i		−	1.49747i	−0.662867	−	0.748737i	$-0.730661\pi$
$787$		−	2.00865e52i		−	1.49747i	0.662867	−	0.748737i	$-0.269339\pi$
$788$	−3.42053e51	+	1.13948e52i	−0.249242	+	0.830299i
$789$	2.16557e52			1.54236
$790$	1.20377e50	+	1.61818e50i	0.00838020	+	0.0112652i
$791$			1.70984e52i			1.16353i
$792$	3.77724e52	−	1.37007e52i	2.51259	−	0.911361i
$793$	−3.06526e52			−1.99319
$794$	−9.76886e50	+	7.26705e50i	−0.0620976	+	0.0461944i
$795$		−	3.71808e51i		−	0.231052i
$796$	1.94448e52	+	5.83701e51i	1.18132	+	0.354613i
$797$	−2.76118e52			−1.64000			−0.820002	−	0.572360i	$-0.806028\pi$
$797$	−2.76118e52			−1.64000			−0.820002	+	0.572360i	$0.806028\pi$
$798$	−8.73086e51	−	1.17366e52i	−0.506996	−	0.681539i
$799$		−	5.89933e50i		−	0.0334935i
$800$	−1.70185e52	+	9.59745e50i	−0.944718	+	0.0532766i
$801$	−1.75857e52			−0.954497
$802$	2.75981e52	−	2.05302e52i	1.46467	−	1.08957i
$803$		−	2.93188e52i		−	1.52148i
$804$	−4.95466e51	+	1.65054e52i	−0.251423	+	0.837564i
$805$	5.27010e51			0.261513
$806$	−7.04125e51	−	9.46533e51i	−0.341680	−	0.459309i
$807$			7.43597e52i			3.52869i
$808$	−5.39474e51	−	1.48731e52i	−0.250361	−	0.690235i
$809$	−8.53752e51			−0.387488			−0.193744	−	0.981052i	$-0.562063\pi$
$809$	−8.53752e51			−0.387488			−0.193744	+	0.981052i	$0.562063\pi$
$810$	−9.87763e51	+	7.34796e51i	−0.438452	+	0.326164i
$811$			3.26137e52i			1.41587i	0.706276	+	0.707937i	$0.250374\pi$
$811$			3.26137e52i			1.41587i	−0.706276	+	0.707937i	$0.749626\pi$
$812$	1.71051e52	+	5.13466e51i	0.726300	+	0.218024i
$813$	7.08555e52			2.94268
$814$	4.70943e50	+	6.33073e50i	0.0191306	+	0.0257167i
$815$			4.50816e51i			0.179128i
$816$	−2.97600e52	+	4.51029e52i	−1.15667	+	1.75300i
$817$	1.56685e52			0.595704
$818$	9.57451e51	−	7.12248e51i	0.356088	−	0.264894i
$819$		−	5.04507e52i		−	1.83551i
$820$	2.81652e50	−	9.38264e50i	0.0100245	−	0.0333945i
$821$	1.39242e52			0.484833			0.242417	−	0.970172i	$-0.422060\pi$
$821$	1.39242e52			0.484833			0.242417	+	0.970172i	$0.422060\pi$
$822$	2.44585e52	+	3.28787e52i	0.833176	+	1.12001i
$823$		−	1.13968e52i		−	0.379827i	−0.981801	−	0.189914i	$-0.939179\pi$
$823$		−	1.13968e52i		−	0.379827i	0.981801	−	0.189914i	$-0.0608208\pi$
$824$	3.14571e52	−	1.14101e52i	1.02572	−	0.372047i
$825$	−6.09204e52			−1.94353
$826$	−1.67588e52	+	1.24669e52i	−0.523122	+	0.389150i
$827$			4.62352e52i			1.41213i	0.708149	+	0.706063i	$0.249530\pi$
$827$			4.62352e52i			1.41213i	−0.708149	+	0.706063i	$0.750470\pi$
$828$	−1.30477e53	−	3.91670e52i	−3.89930	−	1.17051i
$829$	3.44192e52			1.00651			0.503256	−	0.864137i	$-0.332135\pi$
$829$	3.44192e52			1.00651			0.503256	+	0.864137i	$0.332135\pi$
$830$	3.76923e51	+	5.06686e51i	0.107857	+	0.144988i
$831$		−	2.08641e52i		−	0.584225i
$832$	3.22477e52	−	2.69377e52i	0.883647	−	0.738144i
$833$	2.37230e52			0.636149
$834$	−4.45543e52	+	3.31439e52i	−1.16923	+	0.869791i
$835$		−	3.53075e51i		−	0.0906799i
$836$	8.83571e51	−	2.94343e52i	0.222090	−	0.739846i
$837$	5.21308e52			1.28244
$838$	−5.44720e51	−	7.32249e51i	−0.131154	−	0.176306i
$839$			4.95084e51i			0.116671i	0.998297	+	0.0583356i	$0.0185794\pi$
$839$			4.95084e51i			0.116671i	−0.998297	+	0.0583356i	$0.981421\pi$
$840$	−4.19997e51	−	1.15792e52i	−0.0968767	−	0.267085i
$841$	1.33894e52			0.302297
$842$	4.11522e52	−	3.06131e52i	0.909443	−	0.676534i
$843$		−	5.82425e51i		−	0.125992i
$844$	2.37365e51	+	7.12533e50i	0.0502636	+	0.0150883i
$845$	3.64367e51			0.0755297
$846$	−2.07470e51	−	2.78896e51i	−0.0421007	−	0.0565947i
$847$			8.06825e51i			0.160280i
$848$	−2.31932e52	−	1.53035e52i	−0.451061	−	0.297622i
$849$	−6.74019e52			−1.28332
$850$	4.63957e52	−	3.45137e52i	0.864842	−	0.643355i
$851$		−	2.67515e51i		−	0.0488220i
$852$	1.12659e52	−	3.75299e52i	0.201304	−	0.670602i
$853$	−7.16842e52			−1.25413			−0.627063	−	0.778969i	$-0.715743\pi$
$853$	−7.16842e52			−1.25413			−0.627063	+	0.778969i	$0.715743\pi$
$854$	4.00812e52	+	5.38799e52i	0.686593	+	0.922965i
$855$			2.29985e52i			0.385753i
$856$	−7.51048e52	+	2.72419e52i	−1.23350	+	0.447414i
$857$	−3.30307e52			−0.531206			−0.265603	−	0.964082i	$-0.585571\pi$
$857$	−3.30307e52			−0.531206			−0.265603	+	0.964082i	$0.585571\pi$
$858$	1.20490e53	−	8.96328e52i	1.89750	−	1.41155i
$859$			3.95083e52i			0.609272i	0.952469	+	0.304636i	$0.0985349\pi$
$859$			3.95083e52i			0.609272i	−0.952469	+	0.304636i	$0.901465\pi$
$860$	1.26365e52	+	3.79327e51i	0.190833	+	0.0572851i
$861$	−1.24546e52			−0.184192
$862$	−3.46451e52	−	4.65723e52i	−0.501778	−	0.674524i
$863$		−	7.83387e52i		−	1.11117i	−0.831458	−	0.555587i	$-0.812494\pi$
$863$		−	7.83387e52i		−	1.11117i	0.831458	−	0.555587i	$-0.187506\pi$
$864$	1.04545e52	+	1.85383e53i	0.145230	+	2.57527i
$865$	−1.23496e52			−0.168020
$866$	−8.42361e52	+	6.26632e52i	−1.12247	+	0.835008i
$867$		−	4.20514e52i		−	0.548828i
$868$	−7.43066e51	+	2.47537e52i	−0.0949887	+	0.316435i
$869$	5.38695e51			0.0674508
$870$	−2.37448e52	−	3.19194e52i	−0.291221	−	0.391479i
$871$			4.54592e52i			0.546129i
$872$	−2.31842e52	−	6.39180e52i	−0.272832	−	0.752188i
$873$	3.95121e52			0.455485
$874$	−8.35995e52	+	6.21897e52i	−0.944057	+	0.702283i
$875$			2.71111e52i			0.299918i
$876$	2.22517e53	+	6.67959e52i	2.41151	+	0.723896i
$877$	6.41883e52			0.681495			0.340748	−	0.940155i	$-0.389320\pi$
$877$	6.41883e52			0.681495			0.340748	+	0.940155i	$0.389320\pi$
$878$	7.67969e52	+	1.03236e53i	0.798808	+	1.07381i
$879$		−	3.00062e53i		−	3.05781i
$880$	1.42518e52	−	2.15994e52i	0.142293	−	0.215652i
$881$	−5.07542e52			−0.496484			−0.248242	−	0.968698i	$-0.579853\pi$
$881$	−5.07542e52			−0.496484			−0.248242	+	0.968698i	$0.579853\pi$
$882$	1.12152e53	−	8.34301e52i	1.07491	−	0.799628i
$883$		−	9.26717e52i		−	0.870271i	−0.900365	−	0.435136i	$-0.856700\pi$
$883$		−	9.26717e52i		−	0.870271i	0.900365	−	0.435136i	$-0.143300\pi$
$884$	−4.09825e52	+	1.36525e53i	−0.377101	+	1.25623i
$885$	4.65284e52			0.419507
$886$	2.14453e52	+	2.88282e52i	0.189463	+	0.254689i
$887$			1.55086e53i			1.34260i	0.741183	+	0.671302i	$0.234265\pi$
$887$			1.55086e53i			1.34260i	−0.741183	+	0.671302i	$0.765735\pi$
$888$	−5.87768e51	+	2.13194e51i	−0.0498623	+	0.0180860i
$889$	6.48922e52			0.539462
$890$	−9.08719e51	+	6.75996e51i	−0.0740303	+	0.0550711i
$891$			3.28827e53i			2.62524i
$892$	−3.98453e52	−	1.19609e52i	−0.311753	−	0.0935831i
$893$	−2.65863e51			−0.0203859
$894$	−5.25118e52	−	7.05899e52i	−0.394622	−	0.530477i
$895$			2.68610e52i			0.197837i
$896$	−8.95171e52	−	2.14601e52i	−0.646193	−	0.154913i
$897$	−5.09151e53			−3.60232
$898$	−1.64186e53	+	1.22138e53i	−1.13858	+	0.846986i
$899$			8.34744e52i			0.567386i
$900$	9.79599e52	−	3.26333e53i	0.652654	−	2.17418i
$901$	9.42645e52			0.615605
$902$	−1.56174e52	−	2.09940e52i	−0.0999752	−	0.134393i
$903$		−	1.67737e53i		−	1.05257i
$904$	−9.70608e52	−	2.67593e53i	−0.597052	−	1.64605i
$905$	−3.34210e52			−0.201532
$906$	−4.23420e52	+	3.14982e52i	−0.250302	+	0.186199i
$907$			1.95504e53i			1.13299i	0.824066	+	0.566493i	$0.191700\pi$
$907$			1.95504e53i			1.13299i	−0.824066	+	0.566493i	$0.808300\pi$
$908$	3.19120e53	+	9.57945e52i	1.81304	+	0.544246i
$909$	3.16247e53			1.76147
$910$	−1.93933e52	−	2.60697e52i	−0.105902	−	0.142361i
$911$		−	2.92281e53i		−	1.56484i	−0.622750	−	0.782421i	$-0.713985\pi$
$911$		−	2.92281e53i		−	1.56484i	0.622750	−	0.782421i	$-0.286015\pi$
$912$	2.03263e53	+	1.34118e53i	1.06697	+	0.704013i
$913$	1.68676e53			0.868120
$914$	−1.04523e53	+	7.77545e52i	−0.527448	+	0.392368i
$915$		−	1.49590e53i		−	0.740153i
$916$	6.75038e52	−	2.24875e53i	0.327499	−	1.09099i
$917$	8.24954e52			0.392448
$918$	−3.75958e53	−	5.05389e53i	−1.75377	−	2.35753i
$919$		−	1.04711e53i		−	0.478976i	−0.970899	−	0.239488i	$-0.923020\pi$
$919$		−	1.04711e53i		−	0.478976i	0.970899	−	0.239488i	$-0.0769796\pi$
$920$	−8.24780e52	+	2.99163e52i	−0.369962	+	0.134192i
$921$	3.52957e53			1.55256
$922$	−1.83162e53	+	1.36254e53i	−0.790092	+	0.587749i
$923$		−	1.03365e53i		−	0.437262i
$924$	−3.15106e53	−	9.45897e52i	−1.30726	−	0.392418i
$925$	6.69077e51			0.0272223
$926$	2.82859e53	+	3.80238e53i	1.12868	+	1.51725i
$927$			6.68872e53i			2.61763i
$928$	−2.96845e53	+	1.67403e52i	−1.13937	+	0.0642539i
$929$	2.29761e53			0.864953			0.432477	−	0.901645i	$-0.357640\pi$
$929$	2.29761e53			0.864953			0.432477	+	0.901645i	$0.357640\pi$
$930$	4.61924e52	−	3.43625e52i	0.170560	−	0.126879i
$931$		−	1.06911e53i		−	0.387195i
$932$	−7.42250e52	+	2.47265e53i	−0.263672	+	0.878368i
$933$	−8.33004e53			−2.90254
$934$	−1.13680e53	−	1.52816e53i	−0.388543	−	0.522305i
$935$			8.77868e52i			0.294320i
$936$	2.86388e53	+	7.89561e53i	0.941868	+	2.59669i
$937$	1.30930e53			0.422402			0.211201	−	0.977443i	$-0.432262\pi$
$937$	1.30930e53			0.422402			0.211201	+	0.977443i	$0.432262\pi$
$938$	7.99065e52	−	5.94424e52i	0.252890	−	0.188124i
$939$		−	8.47663e52i		−	0.263174i
$940$	−2.14416e51	−	6.43641e50i	−0.00653063	−	0.00196039i
$941$	−4.51966e52			−0.135049			−0.0675247	−	0.997718i	$-0.521510\pi$
$941$	−4.51966e52			−0.135049			−0.0675247	+	0.997718i	$0.521510\pi$
$942$	1.66457e53	+	2.23762e53i	0.487961	+	0.655950i
$943$			8.87135e52i			0.255140i
$944$	1.91509e53	−	2.90242e53i	0.540372	−	0.818964i
$945$	1.43580e53			0.397487
$946$	2.82746e53	−	2.10335e53i	0.767992	−	0.571309i
$947$		−	4.34143e52i		−	0.115700i	−0.998325	−	0.0578500i	$-0.981575\pi$
$947$		−	4.34143e52i		−	0.115700i	0.998325	−	0.0578500i	$-0.0184245\pi$
$948$	−1.22729e52	+	4.08845e52i	−0.0320920	+	0.106908i
$949$	6.12855e53			1.57241
$950$	−1.55541e53	−	2.09089e53i	−0.391581	−	0.526389i
$951$			8.17668e53i			2.01989i
$952$	2.93566e53	−	1.06482e53i	0.711609	−	0.258114i
$953$	−5.50064e53			−1.30840			−0.654201	−	0.756321i	$-0.726995\pi$
$953$	−5.50064e53			−1.30840			−0.654201	+	0.756321i	$0.726995\pi$
$954$	4.45644e53	−	3.31514e53i	1.04020	−	0.773805i
$955$		−	7.48865e52i		−	0.171531i
$956$	−3.58607e52	−	1.07648e52i	−0.0806076	−	0.0241971i
$957$	−1.06260e54			−2.34399
$958$	−2.17531e53	−	2.92420e53i	−0.470914	−	0.633034i
$959$		−	2.36818e53i		−	0.503129i
$960$	1.31461e53	+	1.57374e53i	0.274103	+	0.328134i
$961$	3.67876e53			0.752801
$962$	−1.32332e52	+	9.84419e51i	−0.0265775	+	0.0197710i
$963$		−	1.59695e54i		−	3.14788i
$964$	−2.89227e52	+	9.63499e52i	−0.0559567	+	0.186408i
$965$	−2.15391e53			−0.409012
$966$	6.65765e53	+	8.94966e53i	1.24089	+	1.66808i
$967$			1.58463e53i			0.289903i	0.989439	+	0.144951i	$0.0463025\pi$
$967$			1.58463e53i			0.289903i	−0.989439	+	0.144951i	$0.953697\pi$
$968$	−4.58003e52	−	1.26270e53i	−0.0822454	−	0.226747i
$969$	−8.26127e53			−1.45619
$970$	2.04174e52	−	1.51885e52i	0.0353272	−	0.0262799i
$971$		−	1.54880e53i		−	0.263056i	−0.991312	−	0.131528i	$-0.958012\pi$
$971$		−	1.54880e53i		−	0.263056i	0.991312	−	0.131528i	$-0.0419884\pi$
$972$	−1.01392e54	−	3.04362e53i	−1.69048	−	0.507456i
$973$	3.20914e53			0.525240
$974$	6.21236e53	+	8.35108e53i	0.998150	+	1.34178i
$975$		−	1.27343e54i		−	2.00859i
$976$	−9.33133e53	−	6.15704e53i	−1.44493	−	0.953401i
$977$	1.88019e53			0.285825			0.142912	−	0.989735i	$-0.454353\pi$
$977$	1.88019e53			0.285825			0.142912	+	0.989735i	$0.454353\pi$
$978$	−7.65573e53	+	5.69510e53i	−1.14258	+	0.849966i
$979$			3.02514e53i			0.443258i
$980$	2.58827e52	−	8.62229e52i	0.0372341	−	0.124038i
$981$	1.35909e54			1.91958
$982$	6.98392e52	+	9.38825e52i	0.0968484	+	0.130190i
$983$			3.70779e53i			0.504838i	0.967618	+	0.252419i	$0.0812261\pi$
$983$			3.70779e53i			0.504838i	−0.967618	+	0.252419i	$0.918774\pi$
$984$	1.94916e53	−	7.06996e52i	0.260577	−	0.0945160i
$985$	−1.53157e53			−0.201041
$986$	8.09253e53	−	6.02003e53i	1.04304	−	0.775915i
$987$			2.84616e52i			0.0360206i
$988$	6.15270e53	+	1.84694e53i	0.764611	+	0.229524i
$989$	−1.19479e54			−1.45800
$990$	3.08733e53	+	4.15020e53i	0.369956	+	0.497319i
$991$			1.53904e54i			1.81102i	0.424324	+	0.905510i	$0.360512\pi$
$991$			1.53904e54i			1.81102i	−0.424324	+	0.905510i	$0.639488\pi$
$992$	−2.42258e52	−	4.29580e53i	−0.0279942	−	0.496403i
$993$	1.82490e54			2.07087
$994$	−1.81691e53	+	1.35160e53i	−0.202478	+	0.150623i
$995$			2.61356e53i			0.286034i
$996$	−3.84289e53	+	1.28018e54i	−0.413038	+	1.37595i
$997$	−5.75666e53			−0.607656			−0.303828	−	0.952727i	$-0.598265\pi$
$997$	−5.75666e53			−0.607656			−0.303828	+	0.952727i	$0.598265\pi$
$998$	−9.32047e53	−	1.25292e54i	−0.966247	−	1.29889i
$999$		−	7.28826e52i		−	0.0742071i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.37.b.b.3.4	yes	16
4.3	odd	2	inner	4.37.b.b.3.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.37.b.b.3.3	✓	16	4.3	odd	2	inner
4.37.b.b.3.4	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 37 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-210329. + 156464. i) q^{2} -7.14268e8i q^{3} +(1.97575e10 - 6.58180e10i) q^{4} +8.84656e11 q^{5} +(1.11757e14 + 1.50232e14i) q^{6} -1.08208e15i q^{7} +(6.14256e15 + 1.69348e16i) q^{8} -3.60085e17 q^{9} +O(q^{10})\)	\(q+(-210329. + 156464. i) q^{2} -7.14268e8i q^{3} +(1.97575e10 - 6.58180e10i) q^{4} +8.84656e11 q^{5} +(1.11757e14 + 1.50232e14i) q^{6} -1.08208e15i q^{7} +(6.14256e15 + 1.69348e16i) q^{8} -3.60085e17 q^{9} +(-1.86069e17 + 1.38417e17i) q^{10} +6.19426e18i q^{11} +(-4.70117e19 - 1.41122e19i) q^{12} -1.29480e20 q^{13} +(1.69307e20 + 2.27594e20i) q^{14} -6.31882e20i q^{15} +(-3.94165e21 - 2.60080e21i) q^{16} +1.60201e22 q^{17} +(7.57364e22 - 5.63403e22i) q^{18} -7.21971e22i q^{19} +(1.74786e22 - 5.82263e22i) q^{20} -7.72898e23 q^{21} +(-9.69179e23 - 1.30284e24i) q^{22} +5.50534e24i q^{23} +(1.20960e25 - 4.38744e24i) q^{24} -1.37693e25 q^{25} +(2.72334e25 - 2.02589e25i) q^{26} +1.49989e26i q^{27} +(-7.12206e25 - 2.13793e25i) q^{28} -2.40170e26 q^{29} +(9.88667e25 + 1.32903e26i) q^{30} -3.47564e26i q^{31} +(1.23598e27 - 6.97018e25i) q^{32} +4.42437e27 q^{33} +(-3.36950e27 + 2.50657e27i) q^{34} -9.57272e26i q^{35} +(-7.11437e27 + 2.37000e28i) q^{36} -4.85919e26 q^{37} +(1.12963e28 + 1.51852e28i) q^{38} +9.24832e28i q^{39} +(5.43405e27 + 1.49815e28i) q^{40} +1.61141e28 q^{41} +(1.62563e29 - 1.20931e29i) q^{42} +2.17024e29i q^{43} +(4.07694e29 + 1.22383e29i) q^{44} -3.18551e29 q^{45} +(-8.61387e29 - 1.15793e30i) q^{46} -3.68245e28i q^{47} +(-1.85767e30 + 2.81540e30i) q^{48} +1.48082e30 q^{49} +(2.89609e30 - 2.15440e30i) q^{50} -1.14427e31i q^{51} +(-2.55819e30 + 8.52208e30i) q^{52} +5.88414e30 q^{53} +(-2.34679e31 - 3.15471e31i) q^{54} +5.47979e30i q^{55} +(1.83249e31 - 6.64677e30i) q^{56} -5.15681e31 q^{57} +(5.05148e31 - 3.75780e31i) q^{58} +7.36347e31i q^{59} +(-4.15892e31 - 1.24844e31i) q^{60} +2.36737e32 q^{61} +(5.43812e31 + 7.31029e31i) q^{62} +3.89642e32i q^{63} +(-2.49056e32 + 2.08046e32i) q^{64} -1.14545e32 q^{65} +(-9.30575e32 + 6.92254e32i) q^{66} -3.51092e32i q^{67} +(3.16517e32 - 1.05441e33i) q^{68} +3.93229e33 q^{69} +(1.49779e32 + 2.01343e32i) q^{70} +7.98310e32i q^{71} +(-2.21184e33 - 6.09796e33i) q^{72} -4.73322e33 q^{73} +(1.02203e32 - 7.60289e31i) q^{74} +9.83497e33i q^{75} +(-4.75187e33 - 1.42643e33i) q^{76} +6.70271e33 q^{77} +(-1.44703e34 - 1.94519e34i) q^{78} -8.69667e32i q^{79} +(-3.48700e33 - 2.30081e33i) q^{80} +5.30858e34 q^{81} +(-3.38927e33 + 2.52128e33i) q^{82} -2.72310e34i q^{83} +(-1.52705e34 + 5.08706e34i) q^{84} +1.41723e34 q^{85} +(-3.39564e34 - 4.56465e34i) q^{86} +1.71546e35i q^{87} +(-1.04899e35 + 3.80487e34i) q^{88} +4.88377e34 q^{89} +(6.70007e34 - 4.98418e34i) q^{90} +1.40108e35i q^{91} +(3.62350e35 + 1.08772e35i) q^{92} -2.48254e35 q^{93} +(5.76171e33 + 7.74528e33i) q^{94} -6.38696e34i q^{95} +(-4.97858e34 - 8.82819e35i) q^{96} -1.09730e35 q^{97} +(-3.11461e35 + 2.31696e35i) q^{98} -2.23046e36i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 177228 q^{2} - 5610707696 q^{4} + 5816089539360 q^{5} - 217628996575488 q^{6} + 11\!\cdots\!28 q^{8}+ \cdots - 93\!\cdots\!68 q^{9}+O(q^{10}) \) 16 * q + 177228 * q^2 - 5610707696 * q^4 + 5816089539360 * q^5 - 217628996575488 * q^6 + 11897560228206528 * q^8 - 935184460817545968 * q^9	\( 16 q + 177228 q^{2} - 5610707696 q^{4} + 5816089539360 q^{5} - 217628996575488 q^{6} + 11\!\cdots\!28 q^{8}+ \cdots + 10\!\cdots\!28 q^{98}+O(q^{100}) \) 16 * q + 177228 * q^2 - 5610707696 * q^4 + 5816089539360 * q^5 - 217628996575488 * q^6 + 11897560228206528 * q^8 - 935184460817545968 * q^9 - 2378142919315561000 * q^10 - 42882825786868930560 * q^12 + 194612014165659174176 * q^13 + 360192888461659120128 * q^14 - 22854023522524990832384 * q^16 + 41803218917907805318176 * q^17 + 138204474036544564333068 * q^18 + 104592026972614096023840 * q^20 - 175281296641396774711296 * q^21 - 4320007363229839528400640 * q^22 + 5118364442017682383085568 * q^24 + 61061610541832160307690800 * q^25 - 70158486911796111631798440 * q^26 - 303534200373547502486016000 * q^28 - 95320519344473743554877152 * q^29 + 361206724962468787334008320 * q^30 + 4662427702586163916855016448 * q^32 - 877278707167997370072668160 * q^33 - 9018225886246079564307746920 * q^34 - 927455191590908629268766192 * q^36 - 30841755082751179145922114784 * q^37 + 78752216997100984306444174080 * q^38 - 138122339194153338361474460800 * q^40 + 99165040763128472781035553312 * q^41 - 193406458925326074258433843200 * q^42 + 303084904999663560614745692160 * q^44 + 1511424637230487714612565241120 * q^45 - 919681205391808405630032112128 * q^46 - 1511312501851283767715389931520 * q^48 - 11342315683204385026834539108848 * q^49 + 11057816114707215621338245966500 * q^50 + 16094442403868561017575461524256 * q^52 + 20911545776251998404629518049056 * q^53 - 42689634574575573966970327785984 * q^54 - 18346492780981997297263940026368 * q^56 - 17591710635767034592583231047680 * q^57 + 33019206317228013320629044602456 * q^58 - 69704584574466315130190074982400 * q^60 + 216576725773383276684585233875232 * q^61 + 406820870675021165265665434183680 * q^62 - 266111502464782094817164314013696 * q^64 - 2065823886943449026422930314993600 * q^65 - 816784109200805225218136599695360 * q^66 + 3502994508232801473127246422490656 * q^68 + 3923547517779842564469076002041856 * q^69 + 312094823977274793710809307489280 * q^70 - 1875458138040165128132392402132032 * q^72 - 13529699358917711874787838251408864 * q^73 + 7683713356825244783786618034273240 * q^74 - 15736875982808342938482824299100160 * q^76 + 22639774155764461736245527294259200 * q^77 - 18389491597233550087389536189698560 * q^78 + 67235988583903584940074904608207360 * q^80 - 40716877106976112078739817594850800 * q^81 + 43227843112149006015980010857549336 * q^82 - 37119022564017857733030089777086464 * q^84 - 206886985961236391219562146270052800 * q^85 + 102108696026625816655543232864792832 * q^86 + 39749581676781586144951142033940480 * q^88 + 461506837768868190077604450557625888 * q^89 - 361659211507857840778210819426233000 * q^90 - 17511543929609412714530045318983680 * q^92 - 231978818535002459544922699145134080 * q^93 - 696830931593880576023589572144120832 * q^94 + 1050073689946737522972596709346639872 * q^96 + 451372245708940284684446048339288096 * q^97 + 1035415270688230597220229005750452428 * q^98

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