LMFDB - Embedded newform 3.33.b.a.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,33,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, 33, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 33);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 33 $
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:	$19.4599965427$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 954745942 x^{8} + \cdots + 31\!\cdots\!00 $ x^10 + 954745942x^8 + 302468338607088448x^6 + 37939920124077893929140224x^4 + 1938513915962148831841211918581760x^2 + 31225030372218346257929044634944667648000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{61}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.1
Root			$-21147.4i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.33.b.a.2.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-126884. i q^{2} +(2.43525e7 - 3.54961e7i) q^{3} -1.18046e10 q^{4} -1.55775e11i q^{5} +(-4.50390e12 - 3.08995e12i) q^{6} +3.32502e12 q^{7} +9.52859e14i q^{8} +(-6.66929e14 - 1.72884e15i) q^{9} +O(q^{10})$	\(q-126884. i q^{2} +(2.43525e7 - 3.54961e7i) q^{3} -1.18046e10 q^{4} -1.55775e11i q^{5} +(-4.50390e12 - 3.08995e12i) q^{6} +3.32502e12 q^{7} +9.52859e14i q^{8} +(-6.66929e14 - 1.72884e15i) q^{9} -1.97653e16 q^{10} +8.04343e15i q^{11} +(-2.87473e17 + 4.19019e17i) q^{12} -2.41567e17 q^{13} -4.21893e17i q^{14} +(-5.52939e18 - 3.79350e18i) q^{15} +7.02023e19 q^{16} -3.34404e19i q^{17} +(-2.19363e20 + 8.46228e19i) q^{18} +1.91351e20 q^{19} +1.83886e21i q^{20} +(8.09727e19 - 1.18025e20i) q^{21} +1.02058e21 q^{22} -4.15623e21i q^{23} +(3.38228e22 + 2.32045e22i) q^{24} -9.82656e20 q^{25} +3.06510e22i q^{26} +(-7.76085e22 - 1.84282e22i) q^{27} -3.92507e22 q^{28} -1.41638e23i q^{29} +(-4.81336e23 + 7.01593e23i) q^{30} +9.52452e23 q^{31} -4.81506e24i q^{32} +(2.85511e23 + 1.95878e23i) q^{33} -4.24306e24 q^{34} -5.17954e23i q^{35} +(7.87286e24 + 2.04083e25i) q^{36} -2.23716e25 q^{37} -2.42794e25i q^{38} +(-5.88276e24 + 8.57468e24i) q^{39} +1.48431e26 q^{40} +7.36493e25i q^{41} +(-1.49756e25 - 1.02742e25i) q^{42} -9.07044e25 q^{43} -9.49498e25i q^{44} +(-2.69309e26 + 1.03891e26i) q^{45} -5.27360e26 q^{46} +7.60578e26i q^{47} +(1.70960e27 - 2.49191e27i) q^{48} -1.09337e27 q^{49} +1.24684e26i q^{50} +(-1.18700e27 - 8.14357e26i) q^{51} +2.85161e27 q^{52} +1.49734e27i q^{53} +(-2.33825e27 + 9.84730e27i) q^{54} +1.25296e27 q^{55} +3.16828e27i q^{56} +(4.65987e27 - 6.79220e27i) q^{57} -1.79716e28 q^{58} -1.18656e28i q^{59} +(6.52725e28 + 4.47810e28i) q^{60} +1.17230e28 q^{61} -1.20851e29i q^{62} +(-2.21756e27 - 5.74844e27i) q^{63} -3.09439e29 q^{64} +3.76300e28i q^{65} +(2.48538e28 - 3.62268e28i) q^{66} +2.96407e29 q^{67} +3.94752e29i q^{68} +(-1.47530e29 - 1.01215e29i) q^{69} -6.57202e28 q^{70} -5.78696e29i q^{71} +(1.64734e30 - 6.35490e29i) q^{72} -6.43863e29 q^{73} +2.83860e30i q^{74} +(-2.39302e28 + 3.48805e28i) q^{75} -2.25882e30 q^{76} +2.67446e28i q^{77} +(1.08799e30 + 7.46429e29i) q^{78} -1.65635e30 q^{79} -1.09357e31i q^{80} +(-2.54409e30 + 2.30603e30i) q^{81} +9.34493e30 q^{82} -1.50351e29i q^{83} +(-9.55854e29 + 1.39325e30i) q^{84} -5.20916e30 q^{85} +1.15090e31i q^{86} +(-5.02759e30 - 3.44924e30i) q^{87} -7.66426e30 q^{88} -1.77465e31i q^{89} +(1.31821e31 + 3.41711e31i) q^{90} -8.03215e29 q^{91} +4.90628e31i q^{92} +(2.31946e31 - 3.38084e31i) q^{93} +9.65054e31 q^{94} -2.98075e31i q^{95} +(-1.70916e32 - 1.17259e32i) q^{96} +1.01305e31 q^{97} +1.38732e32i q^{98} +(1.39058e31 - 5.36440e30i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9}+O(q^{10}) $ 10 * q - 21387150 * q^3 - 25792034864 * q^4 - 2424530788848 * q^6 - 5568062418940 * q^7 - 790123604155542 * q^9	$ 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9} - 70\!\cdots\!40 q^{10}+ \cdots - 33\!\cdots\!60 q^{99}+O(q^{100}) $ 10 * q - 21387150 * q^3 - 25792034864 * q^4 - 2424530788848 * q^6 - 5568062418940 * q^7 - 790123604155542 * q^9 - 7003812786596640 * q^10 - 279007424380502640 * q^12 + 567697557679805780 * q^13 - 20342205597863242080 * q^15 + 93452609752238437504 * q^16 - 546532439317269948000 * q^18 + 571007688520350419876 * q^19 - 202809296674597359852 * q^21 - 7726803521259943913760 * q^22 + 40966888307328818303616 * q^24 - 68909708350780834128950 * q^25 - 72967926462080465281230 * q^27 + 205937256056975756717600 * q^28 - 1107420825536697507876000 * q^30 + 2337947500037502285593540 * q^31 + 2522449071689961111334560 * q^33 - 6060358314194999366692224 * q^34 + 19880961335883894024618192 * q^36 - 35307903416851790686359340 * q^37 - 31624005377757923978634972 * q^39 + 103824872020641394026996480 * q^40 - 141365101025586253616004960 * q^42 + 20133134465218107006792740 * q^43 + 324508325822765233105320000 * q^45 - 1081312096716791246752963776 * q^46 + 3981901930430244196770990720 * q^48 - 2767041101974767237639509154 * q^49 + 1958591008210563208705802112 * q^51 - 5054272042223836449280397920 * q^52 + 8609682620485865645134310448 * q^54 - 11870374622399979665591304000 * q^55 + 40568829971233106153298510900 * q^57 - 126691224865576416891245282400 * q^58 + 279833341447916827662753642240 * q^60 - 196667345182223458343232398380 * q^61 + 349775312774222889759843110340 * q^63 - 738816306154787409411488427008 * q^64 + 939413077861687418842822458720 * q^66 - 442550741350999501345614861340 * q^67 + 1096443581430237499419700598208 * q^69 - 3084260511067452830890360584000 * q^70 + 5478956649034785201935062114560 * q^72 - 4530286149796751043896742263020 * q^73 + 5689646867484953837977805651250 * q^75 - 10804853453030293252172855440096 * q^76 + 9245617327241370897996048982560 * q^78 - 2115110787448996851533482223164 * q^79 - 454653247801524309158818752630 * q^81 + 6754240700896495824250705604160 * q^82 - 10589261014798101343390846457952 * q^84 + 8783873758902640422771709896960 * q^85 - 12893796544943502316879779198240 * q^87 + 15416255855088684041150976480000 * q^88 - 76437416541013126109366518121760 * q^90 + 59544256621898576615810233543816 * q^91 - 105131728169400940473110940107820 * q^93 + 301803894289991891760064059517056 * q^94 - 522680019947351351608967407401984 * q^96 + 390148965222370670128665882607700 * q^97 - 333895893109019690643343683610560 * 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 $

$2$		−	126884.i		−	1.93610i	−0.250758	−	0.968050i	$-0.580680\pi$
$2$		−	126884.i		−	1.93610i	0.250758	−	0.968050i	$-0.419320\pi$
$3$	2.43525e7	−	3.54961e7i	0.565723	−	0.824595i
$3$	2.43525e7	−	3.54961e7i	0.565723	−	0.824595i
$4$	−1.18046e10			−2.74848
$5$		−	1.55775e11i		−	1.02088i	−0.859912	−	0.510442i	$-0.829482\pi$
$5$		−	1.55775e11i		−	1.02088i	0.859912	−	0.510442i	$-0.170518\pi$
$6$	−4.50390e12	−	3.08995e12i	−1.59650	−	1.09530i
$7$	3.32502e12			0.100052			0.0500260	−	0.998748i	$-0.484070\pi$
$7$	3.32502e12			0.100052			0.0500260	+	0.998748i	$0.484070\pi$
$8$			9.52859e14i			3.38524i
$9$	−6.66929e14	−	1.72884e15i	−0.359915	−	0.932985i
$10$	−1.97653e16			−1.97653
$11$			8.04343e15i			0.175048i	0.996162	+	0.0875242i	$0.0278955\pi$
$11$			8.04343e15i			0.175048i	−0.996162	+	0.0875242i	$0.972104\pi$
$12$	−2.87473e17	+	4.19019e17i	−1.55488	+	2.26639i
$13$	−2.41567e17			−0.363031			−0.181515	−	0.983388i	$-0.558100\pi$
$13$	−2.41567e17			−0.363031			−0.181515	+	0.983388i	$0.558100\pi$
$14$		−	4.21893e17i		−	0.193711i
$15$	−5.52939e18	−	3.79350e18i	−0.841816	−	0.577538i
$16$	7.02023e19			3.80567
$17$		−	3.34404e19i		−	0.687208i	−0.939115	−	0.343604i	$-0.888352\pi$
$17$		−	3.34404e19i		−	0.687208i	0.939115	−	0.343604i	$-0.111648\pi$
$18$	−2.19363e20	+	8.46228e19i	−1.80635	+	0.696831i
$19$	1.91351e20			0.663395			0.331697	−	0.943386i	$-0.392379\pi$
$19$	1.91351e20			0.663395			0.331697	+	0.943386i	$0.392379\pi$
$20$			1.83886e21i			2.80588i
$21$	8.09727e19	−	1.18025e20i	0.0566018	−	0.0825025i
$22$	1.02058e21			0.338911
$23$		−	4.15623e21i		−	0.677726i	−0.940836	−	0.338863i	$-0.889958\pi$
$23$		−	4.15623e21i		−	0.677726i	0.940836	−	0.338863i	$-0.110042\pi$
$24$	3.38228e22	+	2.32045e22i	2.79145	+	1.91511i
$25$	−9.82656e20			−0.0422048
$26$			3.06510e22i			0.702864i
$27$	−7.76085e22	−	1.84282e22i	−0.972947	−	0.231027i
$28$	−3.92507e22			−0.274991
$29$		−	1.41638e23i		−	0.565993i	−0.959121	−	0.282997i	$-0.908671\pi$
$29$		−	1.41638e23i		−	0.565993i	0.959121	−	0.282997i	$-0.0913285\pi$
$30$	−4.81336e23	+	7.01593e23i	−1.11817	+	1.62984i
$31$	9.52452e23			1.30935			0.654675	−	0.755910i	$-0.272805\pi$
$31$	9.52452e23			1.30935			0.654675	+	0.755910i	$0.272805\pi$
$32$		−	4.81506e24i		−	3.98293i
$33$	2.85511e23	+	1.95878e23i	0.144344	+	0.0990290i
$34$	−4.24306e24			−1.33050
$35$		−	5.17954e23i		−	0.102142i
$36$	7.87286e24	+	2.04083e25i	0.989219	+	2.56429i
$37$	−2.23716e25			−1.81330			−0.906649	−	0.421886i	$-0.861368\pi$
$37$	−2.23716e25			−1.81330			−0.906649	+	0.421886i	$0.861368\pi$
$38$		−	2.42794e25i		−	1.28440i
$39$	−5.88276e24	+	8.57468e24i	−0.205375	+	0.299353i
$40$	1.48431e26			3.45593
$41$			7.36493e25i			1.15512i	0.816349	+	0.577559i	$0.195995\pi$
$41$			7.36493e25i			1.15512i	−0.816349	+	0.577559i	$0.804005\pi$
$42$	−1.49756e25	−	1.02742e25i	−0.159733	−	0.109587i
$43$	−9.07044e25			−0.663947			−0.331973	−	0.943289i	$-0.607714\pi$
$43$	−9.07044e25			−0.663947			−0.331973	+	0.943289i	$0.607714\pi$
$44$		−	9.49498e25i		−	0.481118i
$45$	−2.69309e26	+	1.03891e26i	−0.952470	+	0.367431i
$46$	−5.27360e26			−1.31214
$47$			7.60578e26i			1.34146i	0.741701	+	0.670730i	$0.234019\pi$
$47$			7.60578e26i			1.34146i	−0.741701	+	0.670730i	$0.765981\pi$
$48$	1.70960e27	−	2.49191e27i	2.15296	−	3.13814i
$49$	−1.09337e27			−0.989990
$50$			1.24684e26i			0.0817127i
$51$	−1.18700e27	−	8.14357e26i	−0.566669	−	0.388770i
$52$	2.85161e27			0.997784
$53$			1.49734e27i			0.386283i	0.981171	+	0.193141i	$0.0618676\pi$
$53$			1.49734e27i			0.386283i	−0.981171	+	0.193141i	$0.938132\pi$
$54$	−2.33825e27	+	9.84730e27i	−0.447292	+	1.88372i
$55$	1.25296e27			0.178704
$56$			3.16828e27i			0.338700i
$57$	4.65987e27	−	6.79220e27i	0.375298	−	0.547032i
$58$	−1.79716e28			−1.09582
$59$		−	1.18656e28i		−	0.550373i	−0.961391	−	0.275187i	$-0.911260\pi$
$59$		−	1.18656e28i		−	0.550373i	0.961391	−	0.275187i	$-0.0887397\pi$
$60$	6.52725e28	+	4.47810e28i	2.31372	+	1.58735i
$61$	1.17230e28			0.318978			0.159489	−	0.987200i	$-0.449015\pi$
$61$	1.17230e28			0.318978			0.159489	+	0.987200i	$0.449015\pi$
$62$		−	1.20851e29i		−	2.53503i
$63$	−2.21756e27	−	5.74844e27i	−0.0360102	−	0.0933471i
$64$	−3.09439e29			−3.90567
$65$			3.76300e28i			0.370612i
$66$	2.48538e28	−	3.62268e28i	0.191730	−	0.279465i
$67$	2.96407e29			1.79759			0.898796	−	0.438367i	$-0.144443\pi$
$67$	2.96407e29			1.79759			0.898796	+	0.438367i	$0.144443\pi$
$68$			3.94752e29i			1.88878i
$69$	−1.47530e29	−	1.01215e29i	−0.558849	−	0.383405i
$70$	−6.57202e28			−0.197756
$71$		−	5.78696e29i		−	1.38777i	−0.720086	−	0.693885i	$-0.755898\pi$
$71$		−	5.78696e29i		−	1.38777i	0.720086	−	0.693885i	$-0.244102\pi$
$72$	1.64734e30	−	6.35490e29i	3.15838	−	1.21840i
$73$	−6.43863e29			−0.989982			−0.494991	−	0.868898i	$-0.664829\pi$
$73$	−6.43863e29			−0.989982			−0.494991	+	0.868898i	$0.664829\pi$
$74$			2.83860e30i			3.51073i
$75$	−2.39302e28	+	3.48805e28i	−0.0238762	+	0.0348019i
$76$	−2.25882e30			−1.82333
$77$			2.67446e28i			0.0175140i
$78$	1.08799e30	+	7.46429e29i	0.579578	+	0.397626i
$79$	−1.65635e30			−0.719646			−0.359823	−	0.933021i	$-0.617163\pi$
$79$	−1.65635e30			−0.719646			−0.359823	+	0.933021i	$0.617163\pi$
$80$		−	1.09357e31i		−	3.88515i
$81$	−2.54409e30	+	2.30603e30i	−0.740923	+	0.671590i
$82$	9.34493e30			2.23643
$83$		−	1.50351e29i		−	0.0296386i	−0.999890	−	0.0148193i	$-0.995283\pi$
$83$		−	1.50351e29i		−	0.0296386i	0.999890	−	0.0148193i	$-0.00471730\pi$
$84$	−9.55854e29	+	1.39325e30i	−0.155569	+	0.226757i
$85$	−5.20916e30			−0.701560
$86$			1.15090e31i			1.28547i
$87$	−5.02759e30	−	3.44924e30i	−0.466715	−	0.320196i
$88$	−7.66426e30			−0.592581
$89$		−	1.77465e31i		−	1.14518i	−0.819843	−	0.572589i	$-0.805939\pi$
$89$		−	1.77465e31i		−	1.14518i	0.819843	−	0.572589i	$-0.194061\pi$
$90$	1.31821e31	+	3.41711e31i	0.711384	+	1.84408i
$91$	−8.03215e29			−0.0363220
$92$			4.90628e31i			1.86272i
$93$	2.31946e31	−	3.38084e31i	0.740730	−	1.07968i
$94$	9.65054e31			2.59720
$95$		−	2.98075e31i		−	0.677249i
$96$	−1.70916e32	−	1.17259e32i	−3.28430	−	2.25323i
$97$	1.01305e31			0.164924			0.0824619	−	0.996594i	$-0.473722\pi$
$97$	1.01305e31			0.164924			0.0824619	+	0.996594i	$0.473722\pi$
$98$			1.38732e32i			1.91672i
$99$	1.39058e31	−	5.36440e30i	0.163318	−	0.0630025i
$100$	1.15999e31			0.115999
$101$		−	1.40760e32i		−	1.20043i	−0.799839	−	0.600215i	$-0.795082\pi$
$101$		−	1.40760e32i		−	1.20043i	0.799839	−	0.600215i	$-0.204918\pi$
$102$	−1.03329e32	+	1.50612e32i	−0.752697	+	1.09713i
$103$	−1.47630e32			−0.919979			−0.459990	−	0.887924i	$-0.652147\pi$
$103$	−1.47630e32			−0.919979			−0.459990	+	0.887924i	$0.652147\pi$
$104$		−	2.30179e32i		−	1.22895i
$105$	−1.83854e31	−	1.26135e31i	−0.0842255	−	0.0577839i
$106$	1.89988e32			0.747882
$107$			1.62737e32i			0.551245i	0.961266	+	0.275623i	$0.0888840\pi$
$107$			1.62737e32i			0.551245i	−0.961266	+	0.275623i	$0.911116\pi$
$108$	9.16141e32	+	2.17539e32i	2.67413	+	0.634974i
$109$	−4.61894e30			−0.0116337			−0.00581685	−	0.999983i	$-0.501852\pi$
$109$	−4.61894e30			−0.0116337			−0.00581685	+	0.999983i	$0.501852\pi$
$110$		−	1.58981e32i		−	0.345989i
$111$	−5.44805e32	+	7.94105e32i	−1.02582	+	1.49524i
$112$	2.33424e32			0.380766
$113$		−	5.42686e32i		−	0.767880i	−0.923358	−	0.383940i	$-0.874567\pi$
$113$		−	5.42686e32i		−	0.767880i	0.923358	−	0.383940i	$-0.125433\pi$
$114$	−8.61823e32	−	5.91264e32i	−1.05911	−	0.726614i
$115$	−6.47435e32			−0.691880
$116$			1.67198e33i			1.55562i
$117$	1.61108e32	+	4.17630e32i	0.130660	+	0.338702i
$118$	−1.50556e33			−1.06558
$119$		−	1.11190e32i		−	0.0687566i
$120$	3.61468e33	−	5.26873e33i	1.95510	−	2.84975i
$121$	2.04668e33			0.969358
$122$		−	1.48746e33i		−	0.617572i
$123$	2.61426e33	+	1.79355e33i	0.952505	+	0.653477i
$124$	−1.12434e34			−3.59873
$125$		−	3.47384e33i		−	0.977798i
$126$	−7.29386e32	+	2.81373e32i	−0.180729	+	0.0697194i
$127$	6.20104e33			1.35396			0.676979	−	0.736002i	$-0.263289\pi$
$127$	6.20104e33			1.35396			0.676979	+	0.736002i	$0.263289\pi$
$128$			1.85824e34i			3.57884i
$129$	−2.20888e33	+	3.21966e33i	−0.375610	+	0.547487i
$130$	4.77465e33			0.717543
$131$			1.97429e33i			0.262464i	0.991352	+	0.131232i	$0.0418933\pi$
$131$			1.97429e33i			0.262464i	−0.991352	+	0.131232i	$0.958107\pi$
$132$	−3.37035e33	−	2.31227e33i	−0.396727	−	0.272179i
$133$	6.36245e32			0.0663740
$134$		−	3.76093e34i		−	3.48032i
$135$	−2.87065e33	+	1.20894e34i	−0.235852	+	0.993267i
$136$	3.18640e34			2.32636
$137$		−	8.44351e33i		−	0.548269i	−0.961691	−	0.274135i	$-0.911609\pi$
$137$		−	8.44351e33i		−	0.548269i	0.961691	−	0.274135i	$-0.0883914\pi$
$138$	−1.28425e34	+	1.87192e34i	−0.742311	+	1.08199i
$139$	−1.01447e34			−0.522399			−0.261199	−	0.965285i	$-0.584118\pi$
$139$	−1.01447e34			−0.522399			−0.261199	+	0.965285i	$0.584118\pi$
$140$			6.11426e33i			0.280734i
$141$	2.69976e34	+	1.85220e34i	1.10616	+	0.758895i
$142$	−7.34275e34			−2.68686
$143$		−	1.94303e33i		−	0.0635480i
$144$	−4.68200e34	−	1.21369e35i	−1.36972	−	3.55064i
$145$	−2.20636e34			−0.577814
$146$			8.16960e34i			1.91670i
$147$	−2.66264e34	+	3.88105e34i	−0.560060	+	0.816341i
$148$	2.64089e35			4.98382
$149$		−	7.22722e34i		−	1.22459i	−0.790629	−	0.612295i	$-0.790246\pi$
$149$		−	7.22722e34i		−	1.22459i	0.790629	−	0.612295i	$-0.209754\pi$
$150$	4.42578e33	+	3.03636e33i	0.0673799	+	0.0462267i
$151$	−5.85291e34			−0.801199			−0.400600	−	0.916253i	$-0.631198\pi$
$151$	−5.85291e34			−0.801199			−0.400600	+	0.916253i	$0.631198\pi$
$152$			1.82330e35i			2.24575i
$153$	−5.78131e34	+	2.23024e34i	−0.641155	+	0.247336i
$154$	3.39347e33			0.0339088
$155$		−	1.48368e35i		−	1.33670i
$156$	6.94439e34	−	1.01221e35i	0.564469	−	0.822768i
$157$	9.18249e34			0.673854			0.336927	−	0.941531i	$-0.390612\pi$
$157$	9.18249e34			0.673854			0.336927	+	0.941531i	$0.390612\pi$
$158$			2.10165e35i			1.39331i
$159$	5.31496e34	+	3.64639e34i	0.318527	+	0.218529i
$160$	−7.50065e35			−4.06611
$161$		−	1.38196e34i		−	0.0678079i
$162$	2.92599e35	+	3.22805e35i	1.30027	+	1.43450i
$163$	2.23688e35			0.900827			0.450413	−	0.892820i	$-0.351277\pi$
$163$	2.23688e35			0.900827			0.450413	+	0.892820i	$0.351277\pi$
$164$		−	8.69403e35i		−	3.17482i
$165$	3.05128e34	−	4.44753e34i	0.101097	−	0.147359i
$166$	−1.90772e34			−0.0573833
$167$		−	4.51876e35i		−	1.23468i	−0.786695	−	0.617342i	$-0.788210\pi$
$167$		−	4.51876e35i		−	1.23468i	0.786695	−	0.617342i	$-0.211790\pi$
$168$	1.12462e35	+	7.71556e34i	0.279290	+	0.191610i
$169$	−3.84425e35			−0.868209
$170$			6.60960e35i			1.35829i
$171$	−1.27617e35	−	3.30814e35i	−0.238766	−	0.618937i
$172$	1.07073e36			1.82485
$173$			7.43665e35i			1.15515i	0.816336	+	0.577577i	$0.196002\pi$
$173$			7.43665e35i			1.15515i	−0.816336	+	0.577577i	$0.803998\pi$
$174$	−4.37654e35	+	6.37922e35i	−0.619930	+	0.903608i
$175$	−3.26736e33			−0.00422268
$176$			5.64667e35i			0.666177i
$177$	−4.21183e35	−	2.88957e35i	−0.453835	−	0.311359i
$178$	−2.25175e36			−2.21718
$179$			4.96136e35i			0.446634i	0.974746	+	0.223317i	$0.0716885\pi$
$179$			4.96136e35i			0.446634i	−0.974746	+	0.223317i	$0.928311\pi$
$180$	3.17910e36	−	1.22639e36i	2.61785	−	1.00988i
$181$	4.85520e34			0.0365890			0.0182945	−	0.999833i	$-0.494176\pi$
$181$	4.85520e34			0.0365890			0.0182945	+	0.999833i	$0.494176\pi$
$182$			1.01915e35i			0.0703230i
$183$	2.85484e35	−	4.16120e35i	0.180453	−	0.263027i
$184$	3.96030e36			2.29426
$185$			3.48492e36i			1.85117i
$186$	−4.28975e36	−	2.94303e36i	−2.09038	−	1.43413i
$187$	2.68975e35			0.120295
$188$		−	8.97835e36i		−	3.68698i
$189$	−2.58050e35	−	6.12743e34i	−0.0973454	−	0.0231148i
$190$	−3.78211e36			−1.31122
$191$			1.68963e36i			0.538588i	0.963058	+	0.269294i	$0.0867903\pi$
$191$			1.68963e36i			0.538588i	−0.963058	+	0.269294i	$0.913210\pi$
$192$	−7.53562e36	+	1.09839e37i	−2.20953	+	3.22060i
$193$	−8.05571e34			−0.0217364			−0.0108682	−	0.999941i	$-0.503460\pi$
$193$	−8.05571e34			−0.0217364			−0.0108682	+	0.999941i	$0.503460\pi$
$194$		−	1.28540e36i		−	0.319309i
$195$	1.33572e36	+	9.16384e35i	0.305605	+	0.209664i
$196$	1.29069e37			2.72097
$197$		−	7.79570e35i		−	0.151494i	−0.997127	−	0.0757470i	$-0.975866\pi$
$197$		−	7.79570e35i		−	0.151494i	0.997127	−	0.0757470i	$-0.0241341\pi$
$198$	−6.80658e35	−	1.76443e36i	−0.121979	−	0.316199i
$199$	4.39580e36			0.726755			0.363378	−	0.931642i	$-0.381623\pi$
$199$	4.39580e36			0.726755			0.363378	+	0.931642i	$0.381623\pi$
$200$		−	9.36333e35i		−	0.142873i
$201$	7.21825e36	−	1.05213e37i	1.01694	−	1.48229i
$202$	−1.78602e37			−2.32415
$203$		−	4.70949e35i		−	0.0566288i
$204$	1.40122e37	+	9.61320e36i	1.55748	+	1.06853i
$205$	1.14727e37			1.17924
$206$			1.87319e37i			1.78117i
$207$	−7.18545e36	+	2.77191e36i	−0.632308	+	0.243923i
$208$	−1.69585e37			−1.38158
$209$			1.53911e36i			0.116126i
$210$	−1.60045e36	+	2.33281e36i	−0.111875	+	0.163069i
$211$	−1.68904e37			−1.09426			−0.547131	−	0.837047i	$-0.684280\pi$
$211$	−1.68904e37			−1.09426			−0.547131	+	0.837047i	$0.684280\pi$
$212$		−	1.76755e37i		−	1.06169i
$213$	−2.05415e37	−	1.40927e37i	−1.14435	−	0.785093i
$214$	2.06487e37			1.06727
$215$			1.41294e37i			0.677813i
$216$	1.75595e37	−	7.39500e37i	0.782082	−	3.29366i
$217$	3.16693e36			0.131003
$218$			5.86070e35i			0.0225240i
$219$	−1.56797e37	+	2.28546e37i	−0.560056	+	0.816335i
$220$	−1.47908e37			−0.491166
$221$			8.07808e36i			0.249478i
$222$	1.00759e38	+	6.91271e37i	2.89493	+	1.98610i
$223$	−2.51740e36			−0.0673091			−0.0336545	−	0.999434i	$-0.510715\pi$
$223$	−2.51740e36			−0.0673091			−0.0336545	+	0.999434i	$0.510715\pi$
$224$		−	1.60102e37i		−	0.398500i
$225$	6.55362e35	+	1.69886e36i	0.0151901	+	0.0393764i
$226$	−6.88583e37			−1.48669
$227$		−	7.35476e37i		−	1.47963i	−0.672808	−	0.739817i	$-0.734912\pi$
$227$		−	7.35476e37i		−	1.47963i	0.672808	−	0.739817i	$-0.265088\pi$
$228$	−5.50081e37	+	8.01795e37i	−1.03150	+	1.50351i
$229$	−6.11670e37			−1.06942			−0.534712	−	0.845034i	$-0.679580\pi$
$229$	−6.11670e37			−1.06942			−0.534712	+	0.845034i	$0.679580\pi$
$230$			8.21493e37i			1.33955i
$231$	9.49330e35	+	6.51298e35i	0.0144419	+	0.00990805i
$232$	1.34961e38			1.91602
$233$		−	7.46496e37i		−	0.989311i	−0.869089	−	0.494655i	$-0.835294\pi$
$233$		−	7.46496e37i		−	0.989311i	0.869089	−	0.494655i	$-0.164706\pi$
$234$	5.29907e37	−	2.04421e37i	0.655762	−	0.252971i
$235$	1.18479e38			1.36948
$236$			1.40069e38i			1.51269i
$237$	−4.03363e37	+	5.87940e37i	−0.407120	+	0.593417i
$238$	−1.41083e37			−0.133120
$239$		−	1.61751e38i		−	1.42719i	−0.700560	−	0.713594i	$-0.747066\pi$
$239$		−	1.61751e38i		−	1.42719i	0.700560	−	0.713594i	$-0.252934\pi$
$240$	−3.88176e38	−	2.66313e38i	−3.20368	−	2.19792i
$241$	1.97739e38			1.52693			0.763464	−	0.645850i	$-0.223497\pi$
$241$	1.97739e38			1.52693			0.763464	+	0.645850i	$0.223497\pi$
$242$		−	2.59692e38i		−	1.87677i
$243$	1.99000e37	+	1.46463e38i	0.134633	+	0.990896i
$244$	−1.38385e38			−0.876704
$245$			1.70320e38i			1.01066i
$246$	2.27573e38	−	3.31709e38i	1.26520	−	1.84415i
$247$	−4.62239e37			−0.240833
$248$			9.07553e38i			4.43246i
$249$	−5.33689e36	−	3.66143e36i	−0.0244398	−	0.0167672i
$250$	−4.40775e38			−1.89311
$251$		−	1.24466e38i		−	0.501502i	−0.968052	−	0.250751i	$-0.919322\pi$
$251$		−	1.24466e38i		−	0.501502i	0.968052	−	0.250751i	$-0.0806775\pi$
$252$	2.61775e37	+	6.78582e37i	0.0989735	+	0.256563i
$253$	3.34303e37			0.118635
$254$		−	7.86815e38i		−	2.62140i
$255$	−1.26856e38	+	1.84905e38i	−0.396889	+	0.578503i
$256$	1.02878e39			3.02332
$257$			3.50815e38i			0.968608i	0.874900	+	0.484304i	$0.160927\pi$
$257$			3.50815e38i			0.968608i	−0.874900	+	0.484304i	$0.839073\pi$
$258$	4.08524e38	+	2.80272e38i	1.05999	+	0.727219i
$259$	−7.43861e37			−0.181424
$260$		−	4.44208e38i		−	1.01862i
$261$	−2.44869e38	+	9.44624e37i	−0.528063	+	0.203709i
$262$	2.50506e38			0.508156
$263$			2.03930e38i			0.389214i	0.980881	+	0.194607i	$0.0623431\pi$
$263$			2.03930e38i			0.389214i	−0.980881	+	0.194607i	$0.937657\pi$
$264$	−1.86644e38	+	2.72051e38i	−0.335236	+	0.488639i
$265$	2.33247e38			0.394350
$266$		−	8.07295e37i		−	0.128507i
$267$	−6.29932e38	−	4.32172e38i	−0.944308	−	0.647853i
$268$	−3.49898e39			−4.94065
$269$			4.26655e38i			0.567598i	0.958884	+	0.283799i	$0.0915948\pi$
$269$			4.26655e38i			0.567598i	−0.958884	+	0.283799i	$0.908405\pi$
$270$	1.53396e39	+	3.64240e38i	1.92306	+	0.456633i
$271$	1.15745e39			1.36771			0.683854	−	0.729619i	$-0.260303\pi$
$271$	1.15745e39			1.36771			0.683854	+	0.729619i	$0.260303\pi$
$272$		−	2.34759e39i		−	2.61529i
$273$	−1.95603e37	+	2.85110e37i	−0.0205482	+	0.0299509i
$274$	−1.07135e39			−1.06150
$275$		−	7.90393e36i		−	0.00738788i
$276$	1.74154e39	+	1.19480e39i	1.53599	+	1.05378i
$277$	6.87913e38			0.572608			0.286304	−	0.958139i	$-0.407573\pi$
$277$	6.87913e38			0.572608			0.286304	+	0.958139i	$0.407573\pi$
$278$			1.28720e39i			1.01142i
$279$	−6.35218e38	−	1.64664e39i	−0.471255	−	1.22160i
$280$	4.93538e38			0.345773
$281$		−	1.16221e39i		−	0.769099i	−0.923104	−	0.384549i	$-0.874357\pi$
$281$		−	1.16221e39i		−	0.769099i	0.923104	−	0.384549i	$-0.125643\pi$
$282$	2.35015e39	−	3.42557e39i	1.46930	−	2.14164i
$283$	−1.02580e37			−0.00606010			−0.00303005	−	0.999995i	$-0.500964\pi$
$283$	−1.02580e37			−0.00606010			−0.00303005	+	0.999995i	$0.500964\pi$
$284$			6.83130e39i			3.81426i
$285$	−1.05805e39	−	7.25889e38i	−0.558457	−	0.383136i
$286$	−2.46539e38			−0.123035
$287$			2.44886e38i			0.115572i
$288$	−8.32448e39	+	3.21131e39i	−3.71601	+	1.43351i
$289$	1.24965e39			0.527745
$290$			2.79952e39i			1.11871i
$291$	2.46703e38	−	3.59593e38i	0.0933011	−	0.135995i
$292$	7.60057e39			2.72095
$293$			1.53092e39i			0.518884i	0.965759	+	0.259442i	$0.0835387\pi$
$293$			1.53092e39i			0.518884i	−0.965759	+	0.259442i	$0.916461\pi$
$294$	4.92444e39	+	3.37847e39i	1.58052	+	1.08433i
$295$	−1.84836e39			−0.561868
$296$		−	2.13170e40i		−	6.13844i
$297$	1.48226e38	−	6.24239e38i	0.0404410	−	0.170313i
$298$	−9.17020e39			−2.37093
$299$			1.00401e39i			0.246035i
$300$	2.82487e38	−	4.11752e38i	0.0656234	−	0.0956523i
$301$	−3.01594e38			−0.0664293
$302$			7.42642e39i			1.55120i
$303$	−4.99643e39	−	3.42786e39i	−0.989869	−	0.679111i
$304$	1.34332e40			2.52466
$305$		−	1.82614e39i		−	0.325639i
$306$	2.82982e39	+	7.33557e39i	0.478868	+	1.24134i
$307$	−2.33912e39			−0.375697			−0.187849	−	0.982198i	$-0.560151\pi$
$307$	−2.33912e39			−0.375697			−0.187849	+	0.982198i	$0.560151\pi$
$308$		−	3.15710e38i		−	0.0481368i
$309$	−3.59515e39	+	5.24028e39i	−0.520453	+	0.758610i
$310$	−1.88255e40			−2.58798
$311$			4.01877e39i			0.524719i	0.964970	+	0.262360i	$0.0845007\pi$
$311$			4.01877e39i			0.524719i	−0.964970	+	0.262360i	$0.915499\pi$
$312$	−8.17047e39	−	5.60544e39i	−1.01338	−	0.695243i
$313$	1.23219e40			1.45200			0.726001	−	0.687694i	$-0.241377\pi$
$313$	1.23219e40			1.45200			0.726001	+	0.687694i	$0.241377\pi$
$314$		−	1.16511e40i		−	1.30465i
$315$	−8.95460e38	+	3.45439e38i	−0.0952966	+	0.0367623i
$316$	1.95526e40			1.97793
$317$			5.36512e39i			0.515978i	0.966148	+	0.257989i	$0.0830599\pi$
$317$			5.36512e39i			0.515978i	−0.966148	+	0.257989i	$0.916940\pi$
$318$	4.62670e39	−	6.74385e39i	0.423094	−	0.616700i
$319$	1.13925e39			0.0990763
$320$			4.82028e40i			3.98724i
$321$	5.77652e39	+	3.96305e39i	0.454554	+	0.311852i
$322$	−1.75348e39			−0.131283
$323$		−	6.39883e39i		−	0.455890i
$324$	3.00321e40	−	2.72218e40i	2.03641	−	1.84585i
$325$	2.37377e38			0.0153216
$326$		−	2.83825e40i		−	1.74409i
$327$	−1.12483e38	+	1.63954e38i	−0.00658146	+	0.00959310i
$328$	−7.01774e40			−3.91035
$329$			2.52894e39i			0.134216i
$330$	−5.64321e39	−	3.87159e39i	−0.285301	−	0.195734i
$331$	5.34455e39			0.257432			0.128716	−	0.991681i	$-0.458914\pi$
$331$	5.34455e39			0.257432			0.128716	+	0.991681i	$0.458914\pi$
$332$			1.77484e39i			0.0814611i
$333$	1.49203e40	+	3.86769e40i	0.652633	+	1.69178i
$334$	−5.73359e40			−2.39047
$335$		−	4.61726e40i		−	1.83513i
$336$	5.68447e39	−	8.28566e39i	0.215408	−	0.313977i
$337$	4.61200e40			1.66652			0.833261	−	0.552880i	$-0.186471\pi$
$337$	4.61200e40			1.66652			0.833261	+	0.552880i	$0.186471\pi$
$338$			4.87774e40i			1.68094i
$339$	−1.92632e40	−	1.32158e40i	−0.633190	−	0.434408i
$340$	6.14923e40			1.92823
$341$			7.66098e39i			0.229200i
$342$	−4.19751e40	+	1.61926e40i	−1.19832	+	0.462274i
$343$	−7.30774e39			−0.199103
$344$		−	8.64286e40i		−	2.24762i
$345$	−1.57667e40	+	2.29814e40i	−0.391412	+	0.570521i
$346$	9.43594e40			2.23649
$347$		−	4.15967e40i		−	0.941428i	−0.882286	−	0.470714i	$-0.843996\pi$
$347$		−	4.15967e40i		−	0.941428i	0.882286	−	0.470714i	$-0.156004\pi$
$348$	5.93490e40	+	4.07170e40i	1.28276	+	0.880052i
$349$	−7.90833e40			−1.63259			−0.816296	−	0.577633i	$-0.803976\pi$
$349$	−7.90833e40			−1.63259			−0.816296	+	0.577633i	$0.803976\pi$
$350$			4.14576e38i			0.00817552i
$351$	1.87476e40	+	4.45165e39i	0.353210	+	0.0838700i
$352$	3.87296e40			0.697205
$353$			7.60658e40i			1.30856i	0.756251	+	0.654281i	$0.227029\pi$
$353$			7.60658e40i			1.30856i	−0.756251	+	0.654281i	$0.772971\pi$
$354$	−3.66641e40	+	5.34415e40i	−0.602822	+	0.878671i
$355$	−9.01462e40			−1.41675
$356$			2.09491e41i			3.14750i
$357$	−3.94681e39	−	2.70776e39i	−0.0566964	−	0.0388972i
$358$	6.29518e40			0.864728
$359$		−	7.81716e40i		−	1.02692i	−0.858113	−	0.513461i	$-0.828363\pi$
$359$		−	7.81716e40i		−	1.02692i	0.858113	−	0.513461i	$-0.171637\pi$
$360$	−9.89932e40	−	2.56614e41i	−1.24384	−	3.22434i
$361$	−4.65834e40			−0.559907
$362$		−	6.16048e39i		−	0.0708399i
$363$	4.98418e40	−	7.26492e40i	0.548388	−	0.799328i
$364$	9.48167e39			0.0998303
$365$			1.00297e41i			1.01066i
$366$	−5.27990e40	−	3.62234e40i	−0.509247	−	0.349375i
$367$	−4.95255e40			−0.457269			−0.228635	−	0.973512i	$-0.573426\pi$
$367$	−4.95255e40			−0.457269			−0.228635	+	0.973512i	$0.573426\pi$
$368$		−	2.91777e41i		−	2.57920i
$369$	1.27328e41	−	4.91188e40i	1.07771	−	0.415744i
$370$	4.42182e41			3.58405
$371$			4.97868e39i			0.0386484i
$372$	−2.73804e41	+	3.99096e41i	−2.03588	+	2.96749i
$373$	2.76216e41			1.96747			0.983733	−	0.179637i	$-0.0574922\pi$
$373$	2.76216e41			1.96747			0.983733	+	0.179637i	$0.0574922\pi$
$374$		−	3.41287e40i		−	0.232903i
$375$	−1.23308e41	−	8.45967e40i	−0.806288	−	0.553163i
$376$	−7.24724e41			−4.54116
$377$			3.42150e40i			0.205473i
$378$	−7.77474e39	+	3.27425e40i	−0.0447525	+	0.188470i
$379$	−1.91209e41			−1.05507			−0.527536	−	0.849533i	$-0.676884\pi$
$379$	−1.91209e41			−1.05507			−0.527536	+	0.849533i	$0.676884\pi$
$380$			3.51867e41i			1.86141i
$381$	1.51011e41	−	2.20113e41i	0.765966	−	1.11647i
$382$	2.14387e41			1.04276
$383$		−	1.72630e41i		−	0.805258i	−0.915363	−	0.402629i	$-0.868097\pi$
$383$		−	1.72630e41i		−	0.805258i	0.915363	−	0.402629i	$-0.131903\pi$
$384$	6.59603e41	+	4.52529e41i	2.95110	+	2.02463i
$385$	4.16613e39			0.0178797
$386$			1.02214e40i			0.0420838i
$387$	6.04934e40	+	1.56814e41i	0.238964	+	0.619453i
$388$	−1.19587e41			−0.453290
$389$			1.60668e41i			0.584435i	0.956352	+	0.292218i	$0.0943932\pi$
$389$			1.60668e41i			0.584435i	−0.956352	+	0.292218i	$0.905607\pi$
$390$	1.16275e41	−	1.69481e41i	0.405930	−	0.591682i
$391$	−1.38986e41			−0.465739
$392$		−	1.04183e42i		−	3.35135i
$393$	7.00795e40	+	4.80789e40i	0.216426	+	0.148482i
$394$	−9.89152e40			−0.293308
$395$			2.58017e41i			0.734675i
$396$	−1.64153e41	+	6.33248e40i	−0.448876	+	0.173161i
$397$	2.38838e41			0.627272			0.313636	−	0.949543i	$-0.398453\pi$
$397$	2.38838e41			0.627272			0.313636	+	0.949543i	$0.398453\pi$
$398$		−	5.57757e41i		−	1.40707i
$399$	1.54942e40	−	2.25842e40i	0.0375493	−	0.0547317i
$400$	−6.89847e40			−0.160618
$401$			8.57887e41i			1.91920i	0.281367	+	0.959600i	$0.409212\pi$
$401$			8.57887e41i			1.91920i	−0.281367	+	0.959600i	$0.590788\pi$
$402$	−1.33499e42	−	9.15882e41i	−2.86985	−	1.96890i
$403$	−2.30081e41			−0.475335
$404$			1.66162e42i			3.29936i
$405$	3.59221e41	+	3.96305e41i	0.685616	+	0.756396i
$406$	−5.97560e40			−0.109639
$407$		−	1.79944e41i		−	0.317415i
$408$	7.75968e41	−	1.13105e42i	1.31608	−	1.91831i
$409$	−9.77762e41			−1.59463			−0.797316	−	0.603562i	$-0.793747\pi$
$409$	−9.77762e41			−1.59463			−0.797316	+	0.603562i	$0.793747\pi$
$410$		−	1.45570e42i		−	2.28313i
$411$	−2.99712e41	−	2.05621e41i	−0.452100	−	0.310168i
$412$	1.74272e42			2.52855
$413$		−	3.94534e40i		−	0.0550660i
$414$	3.51712e41	+	9.11721e41i	0.472260	+	1.22421i
$415$	−2.34209e40			−0.0302576
$416$			1.16316e42i			1.44593i
$417$	−2.47049e41	+	3.60097e41i	−0.295533	+	0.430768i
$418$	1.95289e41			0.224832
$419$		−	1.18838e42i		−	1.31683i	−0.752655	−	0.658415i	$-0.771227\pi$
$419$		−	1.18838e42i		−	1.31683i	0.752655	−	0.658415i	$-0.228773\pi$
$420$	2.17033e41	+	1.48898e41i	0.231492	+	0.158818i
$421$	1.14010e42			1.17066			0.585330	−	0.810795i	$-0.300965\pi$
$421$	1.14010e42			1.17066			0.585330	+	0.810795i	$0.300965\pi$
$422$			2.14313e42i			2.11860i
$423$	1.31492e42	−	5.07252e41i	1.25156	−	0.482812i
$424$	−1.42675e42			−1.30766
$425$			3.28604e40i			0.0290035i
$426$	−1.78814e42	+	2.60639e42i	−1.52002	+	2.21557i
$427$	3.89791e40			0.0319144
$428$		−	1.92105e42i		−	1.51509i
$429$	−6.89699e40	−	4.73176e40i	−0.0524014	−	0.0359506i
$430$	1.79280e42			1.31231
$431$		−	2.63310e42i		−	1.85708i	−0.371232	−	0.928540i	$-0.621064\pi$
$431$		−	2.63310e42i		−	1.85708i	0.371232	−	0.928540i	$-0.378936\pi$
$432$	−5.44830e42	−	1.29370e42i	−3.70272	−	0.879214i
$433$	5.65819e41			0.370571			0.185285	−	0.982685i	$-0.440679\pi$
$433$	5.65819e41			0.370571			0.185285	+	0.982685i	$0.440679\pi$
$434$		−	4.01833e41i		−	0.253635i
$435$	−5.37304e41	+	7.83171e41i	−0.326883	+	0.476462i
$436$	5.45249e40			0.0319750
$437$		−	7.95296e41i		−	0.449600i
$438$	2.89989e42	+	1.98950e42i	1.58051	+	1.08432i
$439$	−6.38160e41			−0.335349			−0.167675	−	0.985842i	$-0.553626\pi$
$439$	−6.38160e41			−0.335349			−0.167675	+	0.985842i	$0.553626\pi$
$440$			1.19390e42i			0.604956i
$441$	7.29202e41	+	1.89027e42i	0.356312	+	0.923646i
$442$	1.02498e42			0.483014
$443$			1.79266e42i			0.814778i	0.913255	+	0.407389i	$0.133561\pi$
$443$			1.79266e42i			0.814778i	−0.913255	+	0.407389i	$0.866439\pi$
$444$	6.43122e42	−	9.37412e42i	2.81946	−	4.10963i
$445$	−2.76445e42			−1.16909
$446$			3.19418e41i			0.130317i
$447$	−2.56538e42	−	1.76001e42i	−1.00979	−	0.692779i
$448$	−1.02889e42			−0.390770
$449$		−	1.62816e42i		−	0.596701i	−0.954456	−	0.298351i	$-0.903564\pi$
$449$		−	1.62816e42i		−	0.596701i	0.954456	−	0.298351i	$-0.0964365\pi$
$450$	2.15558e41	−	8.31552e40i	0.0762367	−	0.0294096i
$451$	−5.92393e41			−0.202202
$452$			6.40621e42i			2.11051i
$453$	−1.42533e42	+	2.07756e42i	−0.453257	+	0.660665i
$454$	−9.33203e42			−2.86472
$455$			1.25120e41i			0.0370805i
$456$	6.47201e42	+	4.44020e42i	1.85183	+	1.27047i
$457$	3.30431e42			0.912897			0.456448	−	0.889750i	$-0.349121\pi$
$457$	3.30431e42			0.912897			0.456448	+	0.889750i	$0.349121\pi$
$458$			7.76113e42i			2.07051i
$459$	−6.16247e41	+	2.59526e42i	−0.158764	+	0.668617i
$460$	7.64273e42			1.90162
$461$		−	2.06354e42i		−	0.495904i	−0.968772	−	0.247952i	$-0.920242\pi$
$461$		−	2.06354e42i		−	0.495904i	0.968772	−	0.247952i	$-0.0797576\pi$
$462$	8.26395e40	−	1.20455e41i	0.0191830	−	0.0279610i
$463$	4.33983e42			0.973144			0.486572	−	0.873640i	$-0.338247\pi$
$463$	4.33983e42			0.973144			0.486572	+	0.873640i	$0.338247\pi$
$464$		−	9.94330e42i		−	2.15399i
$465$	−5.26648e42	−	3.61313e42i	−1.10223	−	0.756200i
$466$	−9.47186e42			−1.91540
$467$			7.09797e42i			1.38696i	0.720475	+	0.693481i	$0.243924\pi$
$467$			7.09797e42i			1.38696i	−0.720475	+	0.693481i	$0.756076\pi$
$468$	−1.90182e42	−	4.92998e42i	−0.359117	−	0.930917i
$469$	9.85559e41			0.179853
$470$		−	1.50331e43i		−	2.65144i
$471$	2.23617e42	−	3.25943e42i	0.381215	−	0.555657i
$472$	1.13062e43			1.86314
$473$		−	7.29575e41i		−	0.116223i
$474$	7.46004e42	+	5.11804e42i	1.14891	+	0.788226i
$475$	−1.88032e41			−0.0279984
$476$			1.31256e42i			0.188976i
$477$	2.58866e42	−	9.98618e41i	0.360396	−	0.139029i
$478$	−2.05237e43			−2.76318
$479$			8.21010e42i			1.06901i	0.845167	+	0.534503i	$0.179501\pi$
$479$			8.21010e42i			1.06901i	−0.845167	+	0.534503i	$0.820499\pi$
$480$	−1.82660e43	+	2.66244e43i	−2.30029	+	3.35289i
$481$	5.40423e42			0.658283
$482$		−	2.50899e43i		−	2.95629i
$483$	−4.90541e41	−	3.36541e41i	−0.0559140	−	0.0383605i
$484$	−2.41603e43			−2.66426
$485$		−	1.57807e42i		−	0.168368i
$486$	1.85839e43	−	2.52499e42i	1.91847	−	0.260663i
$487$	1.04710e43			1.04599			0.522994	−	0.852336i	$-0.324815\pi$
$487$	1.04710e43			1.04599			0.522994	+	0.852336i	$0.324815\pi$
$488$			1.11703e43i			1.07981i
$489$	5.44737e42	−	7.94006e42i	0.509618	−	0.742817i
$490$	2.16109e43			1.95675
$491$			1.85171e43i			1.62282i	0.584478	+	0.811409i	$0.301299\pi$
$491$			1.85171e43i			1.62282i	−0.584478	+	0.811409i	$0.698701\pi$
$492$	−3.08604e43	−	2.11722e43i	−2.61794	−	1.79607i
$493$	−4.73642e42			−0.388955
$494$			5.86509e42i			0.466276i
$495$	−8.35637e41	−	2.16617e42i	−0.0643183	−	0.166728i
$496$	6.68643e43			4.98296
$497$		−	1.92418e42i		−	0.138849i
$498$	−4.64578e41	+	6.77167e41i	−0.0324630	+	0.0473180i
$499$	1.43694e43			0.972367			0.486183	−	0.873857i	$-0.338389\pi$
$499$	1.43694e43			0.972367			0.486183	+	0.873857i	$0.338389\pi$
$500$			4.10074e43i			2.68746i
$501$	−1.60398e43	−	1.10043e43i	−1.01811	−	0.698489i
$502$	−1.57928e43			−0.970957
$503$		−	1.89774e43i		−	1.13018i	−0.825028	−	0.565091i	$-0.808841\pi$
$503$		−	1.89774e43i		−	1.13018i	0.825028	−	0.565091i	$-0.191159\pi$
$504$	5.47745e42	−	2.11302e42i	0.316002	−	0.121903i
$505$	−2.19268e43			−1.22550
$506$		−	4.24178e42i		−	0.229689i
$507$	−9.36171e42	+	1.36456e43i	−0.491166	+	0.715921i
$508$	−7.32011e43			−3.72133
$509$			6.72668e42i			0.331372i	0.986179	+	0.165686i	$0.0529839\pi$
$509$			6.72668e42i			0.331372i	−0.986179	+	0.165686i	$0.947016\pi$
$510$	2.34615e43	+	1.60960e43i	1.12004	+	0.768416i
$511$	−2.14086e42			−0.0990498
$512$		−	5.07256e43i		−	2.27461i
$513$	−1.48504e43	−	3.52625e42i	−0.645448	−	0.153262i
$514$	4.45129e43			1.87532
$515$			2.29969e43i			0.939192i
$516$	2.60751e43	−	3.80069e43i	1.03236	−	1.50476i
$517$	−6.11766e42			−0.234821
$518$			9.43842e42i			0.351255i
$519$	2.63972e43	+	1.81101e43i	0.952534	+	0.653497i
$520$	−3.58561e43			−1.25461
$521$		−	4.46167e43i		−	1.51389i	−0.653480	−	0.756944i	$-0.726691\pi$
$521$		−	4.46167e43i		−	1.51389i	0.653480	−	0.756944i	$-0.273309\pi$
$522$	1.19858e43	+	3.10700e43i	0.394402	+	1.02238i
$523$	−2.49127e43			−0.795049			−0.397525	−	0.917592i	$-0.630131\pi$
$523$	−2.49127e43			−0.795049			−0.397525	+	0.917592i	$0.630131\pi$
$524$		−	2.33057e43i		−	0.721377i
$525$	−7.95684e40	+	1.15978e41i	−0.00238886	+	0.00348200i
$526$	2.58755e43			0.753557
$527$		−	3.18503e43i		−	0.899797i
$528$	2.00435e43	+	1.37511e43i	0.549327	+	0.376872i
$529$	2.03347e43			0.540688
$530$		−	2.95954e43i		−	0.763501i
$531$	−2.05137e43	+	7.91352e42i	−0.513490	+	0.198088i
$532$	−7.51064e42			−0.182428
$533$		−	1.77912e43i		−	0.419344i
$534$	−5.48358e43	+	7.99284e43i	−1.25431	+	1.82827i
$535$	2.53502e43			0.562758
$536$			2.82434e44i			6.08528i
$537$	1.76109e43	+	1.20822e43i	0.368292	+	0.252671i
$538$	5.41358e43			1.09893
$539$		−	8.79446e42i		−	0.173296i
$540$	3.38870e43	−	1.42711e44i	0.648235	−	2.72998i
$541$	−3.72048e43			−0.690943			−0.345472	−	0.938429i	$-0.612281\pi$
$541$	−3.72048e43			−0.690943			−0.345472	+	0.938429i	$0.612281\pi$
$542$		−	1.46862e44i		−	2.64802i
$543$	1.18236e42	−	1.72341e42i	0.0206992	−	0.0301711i
$544$	−1.61017e44			−2.73710
$545$			7.19513e41i			0.0118767i
$546$	3.61760e42	+	2.48190e42i	0.0579880	+	0.0397833i
$547$	5.23568e43			0.815035			0.407517	−	0.913197i	$-0.366395\pi$
$547$	5.23568e43			0.815035			0.407517	+	0.913197i	$0.366395\pi$
$548$			9.96726e43i			1.50691i
$549$	−7.81839e42	−	2.02671e43i	−0.114805	−	0.297601i
$550$	−1.00288e42			−0.0143037
$551$		−	2.71025e43i		−	0.375477i
$552$	9.64433e43	−	1.40575e44i	1.29792	−	1.89184i
$553$	−5.50741e42			−0.0720021
$554$		−	8.72853e43i		−	1.10863i
$555$	1.23701e44	+	8.48667e43i	1.52646	+	1.04725i
$556$	1.19755e44			1.43580
$557$			2.62069e43i			0.305304i	0.988280	+	0.152652i	$0.0487814\pi$
$557$			2.62069e43i			0.305304i	−0.988280	+	0.152652i	$0.951219\pi$
$558$	−2.08932e44	+	8.05992e43i	−2.36515	+	0.912396i
$559$	2.19112e43			0.241033
$560$		−	3.63616e43i		−	0.388718i
$561$	6.55023e42	−	9.54758e42i	0.0680535	−	0.0991945i
$562$	−1.47466e44			−1.48905
$563$			5.31718e43i			0.521852i	0.965359	+	0.260926i	$0.0840278\pi$
$563$			5.31718e43i			0.521852i	−0.965359	+	0.260926i	$0.915972\pi$
$564$	−3.18697e44	−	2.18646e44i	−3.04027	−	2.08581i
$565$	−8.45367e43			−0.783917
$566$			1.30158e42i			0.0117330i
$567$	−8.45917e42	+	7.66760e42i	−0.0741309	+	0.0671940i
$568$	5.51416e44			4.69793
$569$			4.63087e43i			0.383589i	0.981435	+	0.191795i	$0.0614308\pi$
$569$			4.63087e43i			0.383589i	−0.981435	+	0.191795i	$0.938569\pi$
$570$	−9.21039e43	+	1.34250e44i	−0.741789	+	1.08123i
$571$	−1.68609e44			−1.32039			−0.660196	−	0.751093i	$-0.729527\pi$
$571$	−1.68609e44			−1.32039			−0.660196	+	0.751093i	$0.729527\pi$
$572$			2.29367e43i			0.174661i
$573$	5.99752e43	+	4.11467e43i	0.444117	+	0.304692i
$574$	3.10721e43			0.223759
$575$			4.08414e42i			0.0286033i
$576$	2.06374e44	+	5.34971e44i	1.40571	+	3.64393i
$577$	−1.21677e44			−0.806109			−0.403054	−	0.915176i	$-0.632051\pi$
$577$	−1.21677e44			−0.806109			−0.403054	+	0.915176i	$0.632051\pi$
$578$		−	1.58561e44i		−	1.02177i
$579$	−1.96177e42	+	2.85946e42i	−0.0122968	+	0.0179237i
$580$	2.60453e44			1.58811
$581$		−	4.99921e41i		−	0.00296540i
$582$	−4.56267e43	−	3.13027e43i	−0.263300	−	0.180640i
$583$	−1.20437e43			−0.0676182
$584$		−	6.13510e44i		−	3.35132i
$585$	6.50562e43	−	2.50965e43i	0.345776	−	0.133389i
$586$	1.94250e44			1.00461
$587$			2.36048e44i			1.18793i	0.804491	+	0.593965i	$0.202438\pi$
$587$			2.36048e44i			1.18793i	−0.804491	+	0.593965i	$0.797562\pi$
$588$	3.14315e44	−	4.58144e44i	1.53932	−	2.24370i
$589$	1.82252e44			0.868616
$590$			2.34528e44i			1.08783i
$591$	−2.76717e43	−	1.89845e43i	−0.124921	−	0.0857037i
$592$	−1.57054e45			−6.90082
$593$		−	4.30384e43i		−	0.184069i	−0.995756	−	0.0920346i	$-0.970663\pi$
$593$		−	4.30384e43i		−	0.184069i	0.995756	−	0.0920346i	$-0.0293370\pi$
$594$	−7.92061e43	−	1.88076e43i	−0.329743	−	0.0782978i
$595$	−1.73206e43			−0.0701925
$596$			8.53148e44i			3.36577i
$597$	1.07049e44	−	1.56034e44i	0.411142	−	0.599279i
$598$	1.27393e44			0.476349
$599$			5.05774e43i			0.184131i	0.995753	+	0.0920656i	$0.0293470\pi$
$599$			5.05774e43i			0.184131i	−0.995753	+	0.0920656i	$0.970653\pi$
$600$	−3.32362e43	−	2.28021e43i	−0.117813	−	0.0808266i
$601$	2.58265e44			0.891402			0.445701	−	0.895182i	$-0.352955\pi$
$601$	2.58265e44			0.891402			0.445701	+	0.895182i	$0.352955\pi$
$602$			3.82676e43i			0.128614i
$603$	−1.97682e44	−	5.12440e44i	−0.646980	−	1.67713i
$604$	6.90915e44			2.20208
$605$		−	3.18821e44i		−	0.989602i
$606$	−4.34941e44	+	6.33968e44i	−1.31483	+	1.91648i
$607$	−1.94744e44			−0.573383			−0.286691	−	0.958023i	$-0.592555\pi$
$607$	−1.94744e44			−0.573383			−0.286691	+	0.958023i	$0.592555\pi$
$608$		−	9.21365e44i		−	2.64225i
$609$	−1.67169e43	−	1.14688e43i	−0.0466958	−	0.0320362i
$610$	−2.31708e44			−0.630470
$611$		−	1.83730e44i		−	0.486992i
$612$	6.82462e44	−	2.63271e44i	1.76220	−	0.679800i
$613$	2.20047e44			0.553538			0.276769	−	0.960936i	$-0.410736\pi$
$613$	2.20047e44			0.553538			0.276769	+	0.960936i	$0.410736\pi$
$614$			2.96797e44i			0.727387i
$615$	2.79389e44	−	4.07236e44i	0.667125	−	0.972398i
$616$	−2.54838e43			−0.0592889
$617$			3.27379e44i			0.742143i	0.928604	+	0.371072i	$0.121010\pi$
$617$			3.27379e44i			0.742143i	−0.928604	+	0.371072i	$0.878990\pi$
$618$	6.64909e44	+	4.56168e44i	1.46875	+	1.00765i
$619$	−2.91495e44			−0.627453			−0.313727	−	0.949513i	$-0.601578\pi$
$619$	−2.91495e44			−0.627453			−0.313727	+	0.949513i	$0.601578\pi$
$620$			1.75143e45i			3.67388i
$621$	−7.65919e43	+	3.22559e44i	−0.156573	+	0.659391i
$622$	5.09919e44			1.01591
$623$		−	5.90075e43i		−	0.114577i
$624$	−4.12983e44	+	6.01962e44i	−0.781590	+	1.13924i
$625$	−5.64015e44			−1.04042
$626$		−	1.56345e45i		−	2.81122i
$627$	5.46326e43	+	3.74813e43i	0.0957572	+	0.0656953i
$628$	−1.08396e45			−1.85208
$629$			7.48114e44i			1.24611i
$630$	4.38307e43	+	1.13620e44i	0.0711754	+	0.184504i
$631$	−3.46134e44			−0.547992			−0.273996	−	0.961731i	$-0.588346\pi$
$631$	−3.46134e44			−0.547992			−0.273996	+	0.961731i	$0.588346\pi$
$632$		−	1.57827e45i		−	2.43617i
$633$	−4.11324e44	+	5.99544e44i	−0.619049	+	0.902323i
$634$	6.80750e44			0.998986
$635$		−	9.65965e44i		−	1.38223i
$636$	−6.27413e44	−	4.30444e44i	−0.875466	−	0.600624i
$637$	2.64122e44			0.359397
$638$		−	1.44553e44i		−	0.191822i
$639$	−1.00047e45	+	3.85950e44i	−1.29477	+	0.499479i
$640$	2.89467e45			3.65358
$641$			7.50862e44i			0.924339i	0.886792	+	0.462170i	$0.152929\pi$
$641$			7.50862e44i			0.924339i	−0.886792	+	0.462170i	$0.847071\pi$
$642$	5.02848e44	−	7.32949e44i	0.603777	−	0.880062i
$643$	1.05855e45			1.23975			0.619877	−	0.784699i	$-0.287182\pi$
$643$	1.05855e45			1.23975			0.619877	+	0.784699i	$0.287182\pi$
$644$			1.63135e44i			0.186369i
$645$	5.01541e44	+	3.44088e44i	0.558921	+	0.383454i
$646$	−8.11911e44			−0.882649
$647$		−	1.91518e44i		−	0.203114i	−0.994830	−	0.101557i	$-0.967618\pi$
$647$		−	1.91518e44i		−	0.203114i	0.994830	−	0.101557i	$-0.0323825\pi$
$648$	−2.19732e45	−	2.42416e45i	−2.27349	−	2.50820i
$649$	9.54401e43			0.0963420
$650$		−	3.01194e43i		−	0.0296642i
$651$	7.71226e43	−	1.12414e44i	0.0741116	−	0.108025i
$652$	−2.64056e45			−2.47591
$653$		−	2.44920e44i		−	0.224085i	−0.993703	−	0.112043i	$-0.964261\pi$
$653$		−	2.44920e44i		−	0.224085i	0.993703	−	0.112043i	$-0.0357393\pi$
$654$	2.08032e43	+	1.42723e43i	0.0185732	+	0.0127424i
$655$	3.07544e44			0.267945
$656$			5.17035e45i			4.39600i
$657$	4.29411e44	+	1.11314e45i	0.356309	+	0.923639i
$658$	3.20883e44			0.259855
$659$		−	1.98611e45i		−	1.56977i	−0.619641	−	0.784885i	$-0.712722\pi$
$659$		−	1.98611e45i		−	1.56977i	0.619641	−	0.784885i	$-0.287278\pi$
$660$	−3.60193e44	+	5.25015e44i	−0.277864	+	0.405013i
$661$	1.20413e45			0.906668			0.453334	−	0.891341i	$-0.350234\pi$
$661$	1.20413e45			0.906668			0.453334	+	0.891341i	$0.350234\pi$
$662$		−	6.78139e44i		−	0.498415i
$663$	2.86741e44	+	1.96722e44i	0.205718	+	0.141135i
$664$	1.43264e44			0.100334
$665$		−	9.91108e43i		−	0.0677602i
$666$	4.90749e45	−	1.89315e45i	3.27546	−	1.26356i
$667$	−5.88679e44			−0.383588
$668$			5.33423e45i			3.39351i
$669$	−6.13050e43	+	8.93578e43i	−0.0380783	+	0.0555028i
$670$	−5.85858e45			−3.55300
$671$			9.42928e43i			0.0558365i
$672$	−5.68300e44	−	3.89889e44i	−0.328601	−	0.225441i
$673$	2.80548e45			1.58404			0.792019	−	0.610497i	$-0.209030\pi$
$673$	2.80548e45			1.58404			0.792019	+	0.610497i	$0.209030\pi$
$674$		−	5.85190e45i		−	3.22655i
$675$	7.62625e43	+	1.81086e43i	0.0410630	+	0.00975045i
$676$	4.53800e45			2.38626
$677$			1.47860e44i			0.0759330i	0.999279	+	0.0379665i	$0.0120880\pi$
$677$			1.47860e44i			0.0759330i	−0.999279	+	0.0379665i	$0.987912\pi$
$678$	−1.67687e45	+	2.44420e45i	−0.841056	+	1.22592i
$679$	3.36841e43			0.0165010
$680$		−	4.96360e45i		−	2.37495i
$681$	−2.61065e45	−	1.79107e45i	−1.22010	−	0.837064i
$682$	9.72058e44			0.443754
$683$			9.55001e44i			0.425866i	0.977067	+	0.212933i	$0.0683016\pi$
$683$			9.55001e44i			0.425866i	−0.977067	+	0.212933i	$0.931698\pi$
$684$	1.50648e45	+	3.90515e45i	0.656243	+	1.70114i
$685$	−1.31528e45			−0.559719
$686$			9.27236e44i			0.385482i
$687$	−1.48957e45	+	2.17119e45i	−0.604998	+	0.881842i
$688$	−6.36766e45			−2.52676
$689$		−	3.61707e44i		−	0.140233i
$690$	2.91598e45	+	2.00054e45i	1.10458	+	0.757813i
$691$	1.48087e43			0.00548112			0.00274056	−	0.999996i	$-0.499128\pi$
$691$	1.48087e43			0.00548112			0.00274056	+	0.999996i	$0.499128\pi$
$692$		−	8.77870e45i		−	3.17492i
$693$	4.62371e43	−	1.78368e43i	0.0163403	−	0.00630353i
$694$	−5.27796e45			−1.82270
$695$			1.58029e45i			0.533309i
$696$	3.28664e45	−	4.79059e45i	1.08394	−	1.57994i
$697$	2.46286e45			0.793807
$698$			1.00344e46i			3.16086i
$699$	−2.64977e45	−	1.81791e45i	−0.815781	−	0.559676i
$700$	3.85700e43			0.0116059
$701$			2.59851e45i			0.764252i	0.924110	+	0.382126i	$0.124808\pi$
$701$			2.59851e45i			0.764252i	−0.924110	+	0.382126i	$0.875192\pi$
$702$	5.64844e44	−	2.37878e45i	0.162381	−	0.683849i
$703$	−4.28081e45			−1.20293
$704$		−	2.48895e45i		−	0.683682i
$705$	2.88526e45	−	4.20554e45i	0.774744	−	1.12926i
$706$	9.65156e45			2.53351
$707$		−	4.68030e44i		−	0.120105i
$708$	4.97191e45	+	3.41104e45i	1.24736	+	0.855765i
$709$	−4.74943e45			−1.16493			−0.582467	−	0.812854i	$-0.697913\pi$
$709$	−4.74943e45			−1.16493			−0.582467	+	0.812854i	$0.697913\pi$
$710$			1.14381e46i			2.74297i
$711$	1.10467e45	+	2.86357e45i	0.259011	+	0.671419i
$712$	1.69099e46			3.87670
$713$		−	3.95861e45i		−	0.887381i
$714$	−3.43572e44	+	5.00789e44i	−0.0753089	+	0.109770i
$715$	−3.02674e44			−0.0648751
$716$		−	5.85670e45i		−	1.22757i
$717$	−5.74154e45	−	3.93905e45i	−1.17685	−	0.807393i
$718$	−9.91874e45			−1.98822
$719$			9.21397e43i			0.0180628i	0.999959	+	0.00903139i	$0.00287482\pi$
$719$			9.21397e43i			0.0180628i	−0.999959	+	0.00903139i	$0.997125\pi$
$720$	−1.89061e46	+	7.29336e45i	−3.62479	+	1.39832i
$721$	−4.90872e44			−0.0920458
$722$			5.91070e45i			1.08404i
$723$	4.81543e45	−	7.01895e45i	0.863819	−	1.25910i
$724$	−5.73139e44			−0.100564
$725$			1.39181e44i			0.0238876i
$726$	−9.21804e45	−	6.32414e45i	−1.54758	−	1.06173i
$727$	5.76530e45			0.946828			0.473414	−	0.880840i	$-0.343021\pi$
$727$	5.76530e45			0.946828			0.473414	+	0.880840i	$0.343021\pi$
$728$		−	7.65351e44i		−	0.122959i
$729$	5.68349e45	+	2.86038e45i	0.893253	+	0.449555i
$730$	1.27262e46			1.95673
$731$			3.03319e45i			0.456270i
$732$	−3.37003e45	+	4.91214e45i	−0.495972	+	0.722926i
$733$	1.34453e45			0.193601			0.0968006	−	0.995304i	$-0.469139\pi$
$733$	1.34453e45			0.193601			0.0968006	+	0.995304i	$0.469139\pi$
$734$			6.28401e45i			0.885319i
$735$	6.04568e45	+	4.14771e45i	0.833389	+	0.571756i
$736$	−2.00125e46			−2.69933
$737$			2.38413e45i			0.314666i
$738$	−6.23241e45	−	1.61559e46i	−0.804922	−	2.08655i
$739$	1.04952e46			1.32641			0.663207	−	0.748436i	$-0.269195\pi$
$739$	1.04952e46			1.32641			0.663207	+	0.748436i	$0.269195\pi$
$740$		−	4.11383e46i		−	5.08790i
$741$	−1.12567e45	+	1.64077e45i	−0.136245	+	0.198590i
$742$	6.31716e44			0.0748272
$743$			6.63876e44i			0.0769602i	0.999259	+	0.0384801i	$0.0122516\pi$
$743$			6.63876e44i			0.0769602i	−0.999259	+	0.0384801i	$0.987748\pi$
$744$	3.22146e46	+	2.21012e46i	3.65499	+	2.50755i
$745$	−1.12582e46			−1.25017
$746$		−	3.50474e46i		−	3.80921i
$747$	−2.59933e44	+	1.00274e44i	−0.0276524	+	0.0106674i
$748$	−3.17516e45			−0.330628
$749$			5.41103e44i			0.0551532i
$750$	−1.07340e46	+	1.56458e46i	−1.07098	+	1.56105i
$751$	−7.65260e45			−0.747429			−0.373715	−	0.927544i	$-0.621916\pi$
$751$	−7.65260e45			−0.747429			−0.373715	+	0.927544i	$0.621916\pi$
$752$			5.33943e46i			5.10516i
$753$	−4.41807e45	−	3.03107e45i	−0.413536	−	0.283711i
$754$	4.34134e45			0.397816
$755$			9.11734e45i			0.817932i
$756$	3.04619e45	+	7.23321e44i	0.267552	+	0.0635305i
$757$	−2.28615e45			−0.196594			−0.0982970	−	0.995157i	$-0.531340\pi$
$757$	−2.28615e45			−0.196594			−0.0982970	+	0.995157i	$0.531340\pi$
$758$			2.42614e46i			2.04272i
$759$	8.14113e44	−	1.18665e45i	0.0671145	−	0.0978257i
$760$	2.84024e46			2.29265
$761$			2.33191e45i			0.184313i	0.995745	+	0.0921566i	$0.0293760\pi$
$761$			2.33191e45i			0.184313i	−0.995745	+	0.0921566i	$0.970624\pi$
$762$	−2.79289e46	−	1.91609e46i	−2.16159	−	1.48299i
$763$	−1.53581e43			−0.00116398
$764$		−	1.99454e46i		−	1.48030i
$765$	3.47414e45	+	9.00581e45i	0.252502	+	0.654545i
$766$	−2.19040e46			−1.55906
$767$			2.86633e45i			0.199803i
$768$	2.50535e46	−	3.65178e46i	1.71036	−	2.49302i
$769$	−2.60977e45			−0.174494			−0.0872470	−	0.996187i	$-0.527807\pi$
$769$	−2.60977e45			−0.174494			−0.0872470	+	0.996187i	$0.527807\pi$
$770$		−	5.28616e44i		−	0.0346169i
$771$	1.24526e46	+	8.54323e45i	0.798710	+	0.547964i
$772$	9.50947e44			0.0597420
$773$		−	2.69029e46i		−	1.65549i	−0.561103	−	0.827746i	$-0.689623\pi$
$773$		−	2.69029e46i		−	1.65549i	0.561103	−	0.827746i	$-0.310377\pi$
$774$	1.98972e46	−	7.67567e45i	1.19932	−	0.462659i
$775$	−9.35933e44			−0.0552609
$776$			9.65294e45i			0.558306i
$777$	−1.81149e45	+	2.64042e45i	−0.102636	+	0.149602i
$778$	2.03863e46			1.13153
$779$			1.40928e46i			0.766300i
$780$	−1.57677e46	−	1.08176e46i	−0.839951	−	0.576258i
$781$	4.65470e45			0.242927
$782$			1.76351e46i			0.901716i
$783$	−2.61013e45	+	1.09923e46i	−0.130760	+	0.550682i
$784$	−7.67572e46			−3.76758
$785$		−	1.43040e46i		−	0.687927i
$786$	6.10045e45	−	8.89199e45i	0.287476	−	0.419023i
$787$	−2.82931e46			−1.30642			−0.653212	−	0.757175i	$-0.726579\pi$
$787$	−2.82931e46			−1.30642			−0.653212	+	0.757175i	$0.726579\pi$
$788$			9.20255e45i			0.416379i
$789$	7.23871e45	+	4.96620e45i	0.320944	+	0.220187i
$790$	3.27383e46			1.42240
$791$		−	1.80444e45i		−	0.0768280i
$792$	5.11152e45	+	1.32503e46i	0.213278	+	0.552869i
$793$	−2.83188e45			−0.115799
$794$		−	3.03048e46i		−	1.21446i
$795$	5.68015e45	−	8.27936e45i	0.223093	−	0.325179i
$796$	−5.18908e46			−1.99747
$797$		−	2.99617e46i		−	1.13040i	−0.824952	−	0.565202i	$-0.808798\pi$
$797$		−	2.99617e46i		−	1.13040i	0.824952	−	0.565202i	$-0.191202\pi$
$798$	−2.86558e45	−	1.96597e45i	−0.105966	−	0.0726992i
$799$	2.54340e46			0.921863
$800$			4.73155e45i			0.168099i
$801$	−3.06809e46	+	1.18357e46i	−1.06843	+	0.412166i
$802$	1.08852e47			3.71576
$803$		−	5.17886e45i		−	0.173295i
$804$	−8.52089e46	+	1.24200e47i	−2.79504	+	4.07404i
$805$	−2.15274e45			−0.0692240
$806$			2.91936e46i			0.920295i
$807$	1.51446e46	+	1.03901e46i	0.468039	+	0.321103i
$808$	1.34124e47			4.06374
$809$		−	3.61728e46i		−	1.07450i	−0.843423	−	0.537250i	$-0.819463\pi$
$809$		−	3.61728e46i		−	1.07450i	0.843423	−	0.537250i	$-0.180537\pi$
$810$	5.02849e46	−	4.55794e46i	1.46446	−	1.32742i
$811$	1.12467e46			0.321137			0.160568	−	0.987025i	$-0.448667\pi$
$811$	1.12467e46			0.321137			0.160568	+	0.987025i	$0.448667\pi$
$812$			5.55939e45i			0.155643i
$813$	2.81868e46	−	4.10850e46i	0.773744	−	1.12781i
$814$	−2.28321e46			−0.614547
$815$		−	3.48449e46i		−	0.919640i
$816$	−8.33304e46	−	5.71697e46i	−2.15656	−	1.47953i
$817$	−1.73563e46			−0.440459
$818$			1.24063e47i			3.08737i
$819$	5.35688e44	+	1.38863e45i	0.0130728	+	0.0338879i
$820$	−1.35431e47			−3.24113
$821$			3.93236e46i			0.922917i	0.887162	+	0.461458i	$0.152674\pi$
$821$			3.93236e46i			0.922917i	−0.887162	+	0.461458i	$0.847326\pi$
$822$	−2.60900e46	+	3.80287e46i	−0.600517	+	0.875311i
$823$	−7.89170e45			−0.178145			−0.0890724	−	0.996025i	$-0.528390\pi$
$823$	−7.89170e45			−0.178145			−0.0890724	+	0.996025i	$0.528390\pi$
$824$		−	1.40670e47i		−	3.11435i
$825$	−2.80559e44	−	1.92481e44i	−0.00609201	−	0.00417950i
$826$	−5.00601e45			−0.106613
$827$			6.50864e46i			1.35957i	0.733410	+	0.679786i	$0.237927\pi$
$827$			6.50864e46i			1.35957i	−0.733410	+	0.679786i	$0.762073\pi$
$828$	8.48217e46	−	3.27214e46i	1.73789	−	0.670419i
$829$	−1.21411e45			−0.0243998			−0.0121999	−	0.999926i	$-0.503883\pi$
$829$	−1.21411e45			−0.0243998			−0.0121999	+	0.999926i	$0.503883\pi$
$830$			2.97174e45i			0.0585817i
$831$	1.67524e46	−	2.44182e46i	0.323937	−	0.472169i
$832$	7.47502e46			1.41788
$833$			3.65628e46i			0.680329i
$834$	4.56907e46	+	3.13466e46i	0.834009	+	0.572182i
$835$	−7.03908e46			−1.26047
$836$		−	1.81687e46i		−	0.319171i
$837$	−7.39184e46	−	1.75520e46i	−1.27393	−	0.302496i
$838$	−1.50786e47			−2.54952
$839$		−	7.49501e45i		−	0.124331i	−0.998066	−	0.0621657i	$-0.980199\pi$
$839$		−	7.49501e45i		−	0.124331i	0.998066	−	0.0621657i	$-0.0198007\pi$
$840$	1.20189e46	−	1.75187e46i	0.195612	−	0.285123i
$841$	4.25620e46			0.679652
$842$		−	1.44661e47i		−	2.26652i
$843$	−4.12538e46	−	2.83027e46i	−0.634195	−	0.435097i
$844$	1.99385e47			3.00756
$845$			5.98836e46i			0.886341i
$846$	−6.43622e46	−	1.66842e47i	−0.934771	−	2.42315i
$847$	6.80526e45			0.0969863
$848$			1.05116e47i			1.47007i
$849$	−2.49808e44	+	3.64119e44i	−0.00342834	+	0.00499713i
$850$	4.16947e45			0.0561536
$851$			9.29814e46i			1.22892i
$852$	2.42485e47	+	1.66359e47i	3.14522	+	2.15781i
$853$	1.06310e47			1.35329			0.676644	−	0.736310i	$-0.263434\pi$
$853$	1.06310e47			1.35329			0.676644	+	0.736310i	$0.263434\pi$
$854$		−	4.94584e45i		−	0.0617894i
$855$	−5.15325e46	+	1.98795e46i	−0.631864	+	0.243752i
$856$	−1.55065e47			−1.86610
$857$			1.39444e47i			1.64705i	0.567280	+	0.823525i	$0.307996\pi$
$857$			1.39444e47i			1.64705i	−0.567280	+	0.823525i	$0.692004\pi$
$858$	−6.00385e45	+	8.75119e45i	−0.0696039	+	0.101454i
$859$	7.55142e46			0.859287			0.429643	−	0.902999i	$-0.358639\pi$
$859$	7.55142e46			0.859287			0.429643	+	0.902999i	$0.358639\pi$
$860$		−	1.66793e47i		−	1.86296i
$861$	8.69249e45	+	5.96358e45i	0.0953001	+	0.0653818i
$862$	−3.34099e47			−3.59549
$863$		−	1.85282e47i		−	1.95731i	−0.205500	−	0.978657i	$-0.565882\pi$
$863$		−	1.85282e47i		−	1.95731i	0.205500	−	0.978657i	$-0.434118\pi$
$864$	−8.87331e46	+	3.73690e47i	−0.920165	+	3.87518i
$865$	1.15844e47			1.17928
$866$		−	7.17935e46i		−	0.717462i
$867$	3.04322e46	−	4.43579e46i	0.298558	−	0.435176i
$868$	−3.73844e46			−0.360060
$869$		−	1.33227e46i		−	0.125973i
$870$	9.93721e46	+	6.81754e46i	0.922479	+	0.632877i
$871$	−7.16020e46			−0.652581
$872$		−	4.40120e45i		−	0.0393828i
$873$	−6.75633e45	−	1.75140e46i	−0.0593585	−	0.153871i
$874$	−1.00911e47			−0.870470
$875$		−	1.15506e46i		−	0.0978307i
$876$	1.85093e47	−	2.69791e47i	1.53930	−	2.24368i
$877$	1.46201e46			0.119387			0.0596935	−	0.998217i	$-0.480988\pi$
$877$	1.46201e46			0.119387			0.0596935	+	0.998217i	$0.480988\pi$
$878$			8.09725e46i			0.649270i
$879$	5.43417e46	+	3.72818e46i	0.427870	+	0.293545i
$880$	8.79608e46			0.680090
$881$			1.73634e46i			0.131832i	0.997825	+	0.0659158i	$0.0209969\pi$
$881$			1.73634e46i			0.131832i	−0.997825	+	0.0659158i	$0.979003\pi$
$882$	2.39845e47	−	9.25242e46i	1.78827	−	0.689855i
$883$	4.64621e45			0.0340195			0.0170097	−	0.999855i	$-0.494585\pi$
$883$	4.64621e45			0.0340195			0.0170097	+	0.999855i	$0.494585\pi$
$884$		−	9.53588e46i		−	0.685685i
$885$	−4.50122e46	+	6.56096e46i	−0.317862	+	0.463313i
$886$	2.27461e47			1.57749
$887$		−	2.27105e47i		−	1.54685i	−0.633887	−	0.773425i	$-0.718542\pi$
$887$		−	2.27105e47i		−	1.54685i	0.633887	−	0.773425i	$-0.281458\pi$
$888$	−7.56670e47	−	5.19122e47i	−5.06173	−	3.47266i
$889$	2.06186e46			0.135466
$890$			3.50766e47i			2.26348i
$891$	−1.85484e46	−	2.04632e46i	−0.117561	−	0.129697i
$892$	2.97170e46			0.184998
$893$			1.45537e47i			0.889918i
$894$	−2.23318e47	+	3.25507e47i	−1.34129	+	1.95506i
$895$	7.72853e46			0.455962
$896$			6.17869e46i			0.358071i
$897$	3.56383e46	+	2.44501e46i	0.202880	+	0.139188i
$898$	−2.06588e47			−1.15527
$899$		−	1.34903e47i		−	0.741084i
$900$	−7.73632e45	−	2.00544e46i	−0.0417498	−	0.108225i
$901$	5.00715e46			0.265457
$902$			7.51653e46i			0.391483i
$903$	−7.34459e45	+	1.07054e46i	−0.0375806	+	0.0547772i
$904$	5.17103e47			2.59946
$905$		−	7.56317e45i		−	0.0373531i
$906$	2.63609e47	+	1.80852e47i	1.27911	+	0.877551i
$907$	−3.42600e47			−1.63332			−0.816659	−	0.577121i	$-0.804176\pi$
$907$	−3.42600e47			−1.63332			−0.816659	+	0.577121i	$0.804176\pi$
$908$			8.68203e47i			4.06675i
$909$	−2.43351e47	+	9.38768e46i	−1.11998	+	0.432052i
$910$	1.58758e46			0.0717916
$911$		−	1.52266e47i		−	0.676565i	−0.941045	−	0.338283i	$-0.890154\pi$
$911$		−	1.52266e47i		−	0.676565i	0.941045	−	0.338283i	$-0.109846\pi$
$912$	3.27133e47	−	4.76828e47i	1.42826	−	2.08183i
$913$	1.20934e45			0.00518819
$914$		−	4.19265e47i		−	1.76746i
$915$	−6.48209e46	−	4.44711e46i	−0.268520	−	0.184222i
$916$	7.22055e47			2.93929
$917$			6.56455e45i			0.0262600i
$918$	3.29297e47	+	7.81920e46i	1.29451	+	0.307383i
$919$	−2.89180e47			−1.11717			−0.558585	−	0.829447i	$-0.688656\pi$
$919$	−2.89180e47			−1.11717			−0.558585	+	0.829447i	$0.688656\pi$
$920$		−	6.16914e47i		−	2.34218i
$921$	−5.69634e46	+	8.30296e46i	−0.212541	+	0.309798i
$922$	−2.61831e47			−0.960121
$923$			1.39794e47i			0.503803i
$924$	−1.12065e46	−	7.68835e45i	−0.0396934	−	0.0272321i
$925$	2.19836e46			0.0765298
$926$		−	5.50657e47i		−	1.88410i
$927$	9.84585e46	+	2.55228e47i	0.331114	+	0.858327i
$928$	−6.81995e47			−2.25431
$929$		−	1.59632e47i		−	0.518643i	−0.965791	−	0.259322i	$-0.916501\pi$
$929$		−	1.59632e47i		−	0.518643i	0.965791	−	0.259322i	$-0.0834990\pi$
$930$	−4.58449e47	+	6.68234e47i	−1.46408	+	2.13403i
$931$	−2.09217e47			−0.656754
$932$			8.81212e47i			2.71910i
$933$	1.42651e47	+	9.78672e46i	0.432681	+	0.296846i
$934$	9.00621e47			2.68529
$935$		−	4.18995e46i		−	0.122807i
$936$	−3.97943e47	+	1.53513e47i	−1.14659	+	0.442315i
$937$	2.42896e47			0.687998			0.343999	−	0.938970i	$-0.388218\pi$
$937$	2.42896e47			0.687998			0.343999	+	0.938970i	$0.388218\pi$
$938$		−	1.25052e47i		−	0.348213i
$939$	3.00069e47	−	4.37378e47i	0.821431	−	1.19731i
$940$	−1.39860e48			−3.76398
$941$		−	3.68592e47i		−	0.975241i	−0.873056	−	0.487620i	$-0.837865\pi$
$941$		−	3.68592e47i		−	0.975241i	0.873056	−	0.487620i	$-0.162135\pi$
$942$	−4.13570e47	−	2.83735e47i	−1.07581	−	0.738070i
$943$	3.06103e47			0.782854
$944$		−	8.32992e47i		−	2.09454i
$945$	−9.54498e45	+	4.01977e46i	−0.0235975	+	0.0993784i
$946$	−9.25716e46			−0.225019
$947$			4.58650e47i			1.09618i	0.836420	+	0.548089i	$0.184645\pi$
$947$			4.58650e47i			1.09618i	−0.836420	+	0.548089i	$0.815355\pi$
$948$	4.76156e47	−	6.94043e47i	1.11896	−	1.63100i
$949$	1.55536e47			0.359394
$950$			2.38583e46i			0.0542077i
$951$	1.90441e47	+	1.30654e47i	0.425473	+	0.291901i
$952$	1.05948e47			0.232757
$953$		−	4.15648e47i		−	0.897922i	−0.893551	−	0.448961i	$-0.851794\pi$
$953$		−	4.15648e47i		−	0.897922i	0.893551	−	0.448961i	$-0.148206\pi$
$954$	−1.26709e47	−	3.28460e47i	−0.269174	−	0.697763i
$955$	2.63201e47			0.549836
$956$			1.90942e48i			3.92260i
$957$	2.77437e46	−	4.04391e46i	0.0560497	−	0.0816978i
$958$	1.04173e48			2.06970
$959$		−	2.80749e46i		−	0.0548555i
$960$	1.71101e48	+	1.17386e48i	3.28786	+	2.25567i
$961$	3.78021e47			0.714400
$962$		−	6.85712e47i		−	1.27450i
$963$	2.81346e47	−	1.08534e47i	0.514304	−	0.198401i
$964$	−2.33423e48			−4.19674
$965$			1.25487e46i			0.0221903i
$966$	−4.27018e46	+	6.22419e46i	−0.0742697	+	0.108255i
$967$	−1.11802e48			−1.91261			−0.956307	−	0.292364i	$-0.905558\pi$
$967$	−1.11802e48			−1.91261			−0.956307	+	0.292364i	$0.905558\pi$
$968$			1.95020e48i			3.28151i
$969$	−2.27134e47	−	1.55828e47i	−0.375925	−	0.257908i
$970$	−2.00233e47			−0.325977
$971$			5.70842e47i			0.914131i	0.889433	+	0.457066i	$0.151100\pi$
$971$			5.70842e47i			0.914131i	−0.889433	+	0.457066i	$0.848900\pi$
$972$	−2.34912e47	−	1.72894e48i	−0.370037	−	2.72346i
$973$	−3.37314e46			−0.0522671
$974$		−	1.32861e48i		−	2.02514i
$975$	5.78073e45	−	8.42597e45i	0.00866780	−	0.0126341i
$976$	8.22979e47			1.21392
$977$			8.55388e47i			1.24122i	0.784118	+	0.620612i	$0.213116\pi$
$977$			8.55388e47i			1.24122i	−0.784118	+	0.620612i	$0.786884\pi$
$978$	−1.00747e48	−	6.91185e47i	−1.43817	−	0.986672i
$979$	1.42743e47			0.200462
$980$		−	2.01056e48i		−	2.77779i
$981$	3.08050e45	+	7.98540e45i	0.00418714	+	0.0108541i
$982$	2.34953e48			3.14194
$983$			1.24357e48i			1.63611i	0.575137	+	0.818057i	$0.304949\pi$
$983$			1.24357e48i			1.63611i	−0.575137	+	0.818057i	$0.695051\pi$
$984$	−1.70900e48	+	2.49102e48i	−2.21218	+	3.22446i
$985$	−1.21437e47			−0.154658
$986$			6.00977e47i			0.753056i
$987$	8.97676e46	+	6.15861e46i	0.110674	+	0.0759291i
$988$	5.45657e47			0.661924
$989$			3.76988e47i			0.449974i
$990$	−2.74853e47	+	1.06029e47i	−0.322803	+	0.124527i
$991$	−5.02373e47			−0.580561			−0.290281	−	0.956942i	$-0.593749\pi$
$991$	−5.02373e47			−0.580561			−0.290281	+	0.956942i	$0.593749\pi$
$992$		−	4.58612e48i		−	5.21505i
$993$	1.30153e47	−	1.89711e47i	0.145635	−	0.212277i
$994$	−2.44148e47			−0.268826
$995$		−	6.84753e47i		−	0.741933i
$996$	6.30000e46	+	4.32219e46i	0.0671725	+	0.0460845i
$997$	−8.84911e47			−0.928490			−0.464245	−	0.885707i	$-0.653674\pi$
$997$	−8.84911e47			−0.928490			−0.464245	+	0.885707i	$0.653674\pi$
$998$		−	1.82325e48i		−	1.88260i
$999$	1.73623e48	+	4.12269e47i	1.76424	+	0.418921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.33.b.a.2.1	✓	10
3.2	odd	2	inner	3.33.b.a.2.10	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.33.b.a.2.1	✓	10	1.1	even	1	trivial
3.33.b.a.2.10	yes	10	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:	\( k \)	\(=\)	\( 33 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-126884. i q^{2} +(2.43525e7 - 3.54961e7i) q^{3} -1.18046e10 q^{4} -1.55775e11i q^{5} +(-4.50390e12 - 3.08995e12i) q^{6} +3.32502e12 q^{7} +9.52859e14i q^{8} +(-6.66929e14 - 1.72884e15i) q^{9} +O(q^{10})\)	\(q-126884. i q^{2} +(2.43525e7 - 3.54961e7i) q^{3} -1.18046e10 q^{4} -1.55775e11i q^{5} +(-4.50390e12 - 3.08995e12i) q^{6} +3.32502e12 q^{7} +9.52859e14i q^{8} +(-6.66929e14 - 1.72884e15i) q^{9} -1.97653e16 q^{10} +8.04343e15i q^{11} +(-2.87473e17 + 4.19019e17i) q^{12} -2.41567e17 q^{13} -4.21893e17i q^{14} +(-5.52939e18 - 3.79350e18i) q^{15} +7.02023e19 q^{16} -3.34404e19i q^{17} +(-2.19363e20 + 8.46228e19i) q^{18} +1.91351e20 q^{19} +1.83886e21i q^{20} +(8.09727e19 - 1.18025e20i) q^{21} +1.02058e21 q^{22} -4.15623e21i q^{23} +(3.38228e22 + 2.32045e22i) q^{24} -9.82656e20 q^{25} +3.06510e22i q^{26} +(-7.76085e22 - 1.84282e22i) q^{27} -3.92507e22 q^{28} -1.41638e23i q^{29} +(-4.81336e23 + 7.01593e23i) q^{30} +9.52452e23 q^{31} -4.81506e24i q^{32} +(2.85511e23 + 1.95878e23i) q^{33} -4.24306e24 q^{34} -5.17954e23i q^{35} +(7.87286e24 + 2.04083e25i) q^{36} -2.23716e25 q^{37} -2.42794e25i q^{38} +(-5.88276e24 + 8.57468e24i) q^{39} +1.48431e26 q^{40} +7.36493e25i q^{41} +(-1.49756e25 - 1.02742e25i) q^{42} -9.07044e25 q^{43} -9.49498e25i q^{44} +(-2.69309e26 + 1.03891e26i) q^{45} -5.27360e26 q^{46} +7.60578e26i q^{47} +(1.70960e27 - 2.49191e27i) q^{48} -1.09337e27 q^{49} +1.24684e26i q^{50} +(-1.18700e27 - 8.14357e26i) q^{51} +2.85161e27 q^{52} +1.49734e27i q^{53} +(-2.33825e27 + 9.84730e27i) q^{54} +1.25296e27 q^{55} +3.16828e27i q^{56} +(4.65987e27 - 6.79220e27i) q^{57} -1.79716e28 q^{58} -1.18656e28i q^{59} +(6.52725e28 + 4.47810e28i) q^{60} +1.17230e28 q^{61} -1.20851e29i q^{62} +(-2.21756e27 - 5.74844e27i) q^{63} -3.09439e29 q^{64} +3.76300e28i q^{65} +(2.48538e28 - 3.62268e28i) q^{66} +2.96407e29 q^{67} +3.94752e29i q^{68} +(-1.47530e29 - 1.01215e29i) q^{69} -6.57202e28 q^{70} -5.78696e29i q^{71} +(1.64734e30 - 6.35490e29i) q^{72} -6.43863e29 q^{73} +2.83860e30i q^{74} +(-2.39302e28 + 3.48805e28i) q^{75} -2.25882e30 q^{76} +2.67446e28i q^{77} +(1.08799e30 + 7.46429e29i) q^{78} -1.65635e30 q^{79} -1.09357e31i q^{80} +(-2.54409e30 + 2.30603e30i) q^{81} +9.34493e30 q^{82} -1.50351e29i q^{83} +(-9.55854e29 + 1.39325e30i) q^{84} -5.20916e30 q^{85} +1.15090e31i q^{86} +(-5.02759e30 - 3.44924e30i) q^{87} -7.66426e30 q^{88} -1.77465e31i q^{89} +(1.31821e31 + 3.41711e31i) q^{90} -8.03215e29 q^{91} +4.90628e31i q^{92} +(2.31946e31 - 3.38084e31i) q^{93} +9.65054e31 q^{94} -2.98075e31i q^{95} +(-1.70916e32 - 1.17259e32i) q^{96} +1.01305e31 q^{97} +1.38732e32i q^{98} +(1.39058e31 - 5.36440e30i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9}+O(q^{10}) \) 10 * q - 21387150 * q^3 - 25792034864 * q^4 - 2424530788848 * q^6 - 5568062418940 * q^7 - 790123604155542 * q^9	\( 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9} - 70\!\cdots\!40 q^{10}+ \cdots - 33\!\cdots\!60 q^{99}+O(q^{100}) \) 10 * q - 21387150 * q^3 - 25792034864 * q^4 - 2424530788848 * q^6 - 5568062418940 * q^7 - 790123604155542 * q^9 - 7003812786596640 * q^10 - 279007424380502640 * q^12 + 567697557679805780 * q^13 - 20342205597863242080 * q^15 + 93452609752238437504 * q^16 - 546532439317269948000 * q^18 + 571007688520350419876 * q^19 - 202809296674597359852 * q^21 - 7726803521259943913760 * q^22 + 40966888307328818303616 * q^24 - 68909708350780834128950 * q^25 - 72967926462080465281230 * q^27 + 205937256056975756717600 * q^28 - 1107420825536697507876000 * q^30 + 2337947500037502285593540 * q^31 + 2522449071689961111334560 * q^33 - 6060358314194999366692224 * q^34 + 19880961335883894024618192 * q^36 - 35307903416851790686359340 * q^37 - 31624005377757923978634972 * q^39 + 103824872020641394026996480 * q^40 - 141365101025586253616004960 * q^42 + 20133134465218107006792740 * q^43 + 324508325822765233105320000 * q^45 - 1081312096716791246752963776 * q^46 + 3981901930430244196770990720 * q^48 - 2767041101974767237639509154 * q^49 + 1958591008210563208705802112 * q^51 - 5054272042223836449280397920 * q^52 + 8609682620485865645134310448 * q^54 - 11870374622399979665591304000 * q^55 + 40568829971233106153298510900 * q^57 - 126691224865576416891245282400 * q^58 + 279833341447916827662753642240 * q^60 - 196667345182223458343232398380 * q^61 + 349775312774222889759843110340 * q^63 - 738816306154787409411488427008 * q^64 + 939413077861687418842822458720 * q^66 - 442550741350999501345614861340 * q^67 + 1096443581430237499419700598208 * q^69 - 3084260511067452830890360584000 * q^70 + 5478956649034785201935062114560 * q^72 - 4530286149796751043896742263020 * q^73 + 5689646867484953837977805651250 * q^75 - 10804853453030293252172855440096 * q^76 + 9245617327241370897996048982560 * q^78 - 2115110787448996851533482223164 * q^79 - 454653247801524309158818752630 * q^81 + 6754240700896495824250705604160 * q^82 - 10589261014798101343390846457952 * q^84 + 8783873758902640422771709896960 * q^85 - 12893796544943502316879779198240 * q^87 + 15416255855088684041150976480000 * q^88 - 76437416541013126109366518121760 * q^90 + 59544256621898576615810233543816 * q^91 - 105131728169400940473110940107820 * q^93 + 301803894289991891760064059517056 * q^94 - 522680019947351351608967407401984 * q^96 + 390148965222370670128665882607700 * q^97 - 333895893109019690643343683610560 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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