LMFDB - Embedded newform 162.10.c.g.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,10,Mod(55,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("162.55");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not 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:	$83.4358054585$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	162.55
Dual form			162.10.c.g.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00000 - 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(-217.500 - 376.721i) q^{5} +(1263.50 - 2188.45i) q^{7} -4096.00 q^{8} +O(q^{10})$	\(q+(8.00000 - 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(-217.500 - 376.721i) q^{5} +(1263.50 - 2188.45i) q^{7} -4096.00 q^{8} -6960.00 q^{10} +(-4561.50 + 7900.75i) q^{11} +(39590.0 + 68571.9i) q^{13} +(-20216.0 - 35015.1i) q^{14} +(-32768.0 + 56755.8i) q^{16} +437976. q^{17} +116966. q^{19} +(-55680.0 + 96440.6i) q^{20} +(72984.0 + 126412. i) q^{22} +(-130551. - 226121. i) q^{23} +(881950. - 1.52758e6i) q^{25} +1.26688e6 q^{26} -646912. q^{28} +(-198075. + 343076. i) q^{29} +(2.94127e6 + 5.09442e6i) q^{31} +(524288. + 908093. i) q^{32} +(3.50381e6 - 6.06877e6i) q^{34} -1.09924e6 q^{35} -8.98625e6 q^{37} +(935728. - 1.62073e6i) q^{38} +(890880. + 1.54305e6i) q^{40} +(8.72478e6 + 1.51118e7i) q^{41} +(1.60473e7 - 2.77948e7i) q^{43} +2.33549e6 q^{44} -4.17763e6 q^{46} +(1.04829e7 - 1.81569e7i) q^{47} +(1.69839e7 + 2.94170e7i) q^{49} +(-1.41112e7 - 2.44413e7i) q^{50} +(1.01350e7 - 1.75544e7i) q^{52} -4.06690e7 q^{53} +3.96850e6 q^{55} +(-5.17530e6 + 8.96388e6i) q^{56} +(3.16920e6 + 5.48922e6i) q^{58} +(-4.21915e7 - 7.30779e7i) q^{59} +(7.40192e7 - 1.28205e8i) q^{61} +9.41205e7 q^{62} +1.67772e7 q^{64} +(1.72216e7 - 2.98288e7i) q^{65} +(-7.74696e7 - 1.34181e8i) q^{67} +(-5.60609e7 - 9.71004e7i) q^{68} +(-8.79396e6 + 1.52316e7i) q^{70} -1.68344e8 q^{71} +4.18698e8 q^{73} +(-7.18900e7 + 1.24517e8i) q^{74} +(-1.49716e7 - 2.59317e7i) q^{76} +(1.15269e7 + 1.99652e7i) q^{77} +(-1.05299e8 + 1.82383e8i) q^{79} +2.85082e7 q^{80} +2.79193e8 q^{82} +(3.88197e8 - 6.72377e8i) q^{83} +(-9.52598e7 - 1.64995e8i) q^{85} +(-2.56757e8 - 4.44716e8i) q^{86} +(1.86839e7 - 3.23615e7i) q^{88} -3.70838e8 q^{89} +2.00088e8 q^{91} +(-3.34211e7 + 5.78870e7i) q^{92} +(-1.67726e8 - 2.90510e8i) q^{94} +(-2.54401e7 - 4.40636e7i) q^{95} +(-1.54921e8 + 2.68331e8i) q^{97} +5.43486e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 16 q^{2} - 256 q^{4} - 435 q^{5} + 2527 q^{7} - 8192 q^{8}+O(q^{10}) $ 2 * q + 16 * q^2 - 256 * q^4 - 435 * q^5 + 2527 * q^7 - 8192 * q^8	\( 2 q + 16 q^{2} - 256 q^{4} - 435 q^{5} + 2527 q^{7} - 8192 q^{8} - 13920 q^{10} - 9123 q^{11} + 79180 q^{13} - 40432 q^{14} - 65536 q^{16} + 875952 q^{17} + 233932 q^{19} - 111360 q^{20} + 145968 q^{22} - 261102 q^{23} + 1763900 q^{25} + 2533760 q^{26} - 1293824 q^{28} - 396150 q^{29} + 5882533 q^{31} + 1048576 q^{32} + 7007616 q^{34} - 2198490 q^{35} - 17972492 q^{37} + 1871456 q^{38} + 1781760 q^{40} + 17449566 q^{41} + 32094646 q^{43} + 4670976 q^{44} - 8355264 q^{46} + 20965782 q^{47} + 33967878 q^{49} - 28222400 q^{50} + 20270080 q^{52} - 81338094 q^{53} + 7937010 q^{55} - 10350592 q^{56} + 6338400 q^{58} - 84383076 q^{59} + 148038424 q^{61} + 188241056 q^{62} + 33554432 q^{64} + 34443300 q^{65} - 154939106 q^{67} - 112121856 q^{68} - 17587920 q^{70} - 336687120 q^{71} + 837395986 q^{73} - 143779936 q^{74} - 29943296 q^{76} + 23053821 q^{77} - 210598040 q^{79} + 57016320 q^{80} + 558386112 q^{82} + 776394525 q^{83} - 190519560 q^{85} - 513514336 q^{86} + 37367808 q^{88} - 741675492 q^{89} + 400175720 q^{91} - 66842112 q^{92} - 335452512 q^{94} - 50880210 q^{95} - 309841967 q^{97} + 1086972096 q^{98}+O(q^{100}) \) 2 * q + 16 * q^2 - 256 * q^4 - 435 * q^5 + 2527 * q^7 - 8192 * q^8 - 13920 * q^10 - 9123 * q^11 + 79180 * q^13 - 40432 * q^14 - 65536 * q^16 + 875952 * q^17 + 233932 * q^19 - 111360 * q^20 + 145968 * q^22 - 261102 * q^23 + 1763900 * q^25 + 2533760 * q^26 - 1293824 * q^28 - 396150 * q^29 + 5882533 * q^31 + 1048576 * q^32 + 7007616 * q^34 - 2198490 * q^35 - 17972492 * q^37 + 1871456 * q^38 + 1781760 * q^40 + 17449566 * q^41 + 32094646 * q^43 + 4670976 * q^44 - 8355264 * q^46 + 20965782 * q^47 + 33967878 * q^49 - 28222400 * q^50 + 20270080 * q^52 - 81338094 * q^53 + 7937010 * q^55 - 10350592 * q^56 + 6338400 * q^58 - 84383076 * q^59 + 148038424 * q^61 + 188241056 * q^62 + 33554432 * q^64 + 34443300 * q^65 - 154939106 * q^67 - 112121856 * q^68 - 17587920 * q^70 - 336687120 * q^71 + 837395986 * q^73 - 143779936 * q^74 - 29943296 * q^76 + 23053821 * q^77 - 210598040 * q^79 + 57016320 * q^80 + 558386112 * q^82 + 776394525 * q^83 - 190519560 * q^85 - 513514336 * q^86 + 37367808 * q^88 - 741675492 * q^89 + 400175720 * q^91 - 66842112 * q^92 - 335452512 * q^94 - 50880210 * q^95 - 309841967 * q^97 + 1086972096 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	−217.500	−	376.721i	−0.155630	−	0.269560i	0.777658	−	0.628688i	$-0.216408\pi$
$5$	−217.500	−	376.721i	−0.155630	−	0.269560i	−0.933288	+	0.359128i	$0.883074\pi$
$6$		0			0
$7$	1263.50	−	2188.45i	0.198900	−	0.344504i	−0.749272	−	0.662262i	$-0.769597\pi$
$7$	1263.50	−	2188.45i	0.198900	−	0.344504i	0.948172	+	0.317758i	$0.102930\pi$
$8$	−4096.00			−0.353553
$9$		0			0
$10$	−6960.00			−0.220095
$11$	−4561.50	+	7900.75i	−0.0939378	+	0.162705i	−0.909165	−	0.416436i	$-0.863279\pi$
$11$	−4561.50	+	7900.75i	−0.0939378	+	0.162705i	0.815227	+	0.579142i	$0.196612\pi$
$12$		0			0
$13$	39590.0	+	68571.9i	0.384450	+	0.665888i	0.991693	−	0.128629i	$-0.0410576\pi$
$13$	39590.0	+	68571.9i	0.384450	+	0.665888i	−0.607242	+	0.794517i	$0.707724\pi$
$14$	−20216.0	−	35015.1i	−0.140643	−	0.243601i
$15$		0			0
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	437976.			1.27183			0.635917	−	0.771758i	$-0.280622\pi$
$17$	437976.			1.27183			0.635917	+	0.771758i	$0.280622\pi$
$18$		0			0
$19$	116966.			0.205906			0.102953	−	0.994686i	$-0.467171\pi$
$19$	116966.			0.205906			0.102953	+	0.994686i	$0.467171\pi$
$20$	−55680.0	+	96440.6i	−0.0778152	+	0.134780i
$21$		0			0
$22$	72984.0	+	126412.i	0.0664241	+	0.115050i
$23$	−130551.	−	226121.i	−0.0972758	−	0.168487i	0.813280	−	0.581872i	$-0.197680\pi$
$23$	−130551.	−	226121.i	−0.0972758	−	0.168487i	−0.910556	+	0.413385i	$0.864346\pi$
$24$		0			0
$25$	881950.	−	1.52758e6i	0.451558	−	0.782122i
$26$	1.26688e6			0.543695
$27$		0			0
$28$	−646912.			−0.198900
$29$	−198075.	+	343076.i	−0.0520042	+	0.0900740i	−0.890856	−	0.454286i	$-0.849894\pi$
$29$	−198075.	+	343076.i	−0.0520042	+	0.0900740i	0.838851	+	0.544360i	$0.183228\pi$
$30$		0			0
$31$	2.94127e6	+	5.09442e6i	0.572014	+	0.990758i	0.996359	+	0.0852569i	$0.0271711\pi$
$31$	2.94127e6	+	5.09442e6i	0.572014	+	0.990758i	−0.424345	+	0.905501i	$0.639496\pi$
$32$	524288.	+	908093.i	0.0883883	+	0.153093i
$33$		0			0
$34$	3.50381e6	−	6.06877e6i	0.449661	−	0.778836i
$35$	−1.09924e6			−0.123819
$36$		0			0
$37$	−8.98625e6			−0.788262			−0.394131	−	0.919054i	$-0.628954\pi$
$37$	−8.98625e6			−0.788262			−0.394131	+	0.919054i	$0.628954\pi$
$38$	935728.	−	1.62073e6i	0.0727987	−	0.126091i
$39$		0			0
$40$	890880.	+	1.54305e6i	0.0550236	+	0.0953037i
$41$	8.72478e6	+	1.51118e7i	0.482200	+	0.835195i	0.999791	−	0.0204330i	$-0.00650449\pi$
$41$	8.72478e6	+	1.51118e7i	0.482200	+	0.835195i	−0.517591	+	0.855628i	$0.673171\pi$
$42$		0			0
$43$	1.60473e7	−	2.77948e7i	0.715805	−	1.23981i	−0.246844	−	0.969055i	$-0.579393\pi$
$43$	1.60473e7	−	2.77948e7i	0.715805	−	1.23981i	0.962648	−	0.270755i	$-0.0872733\pi$
$44$	2.33549e6			0.0939378
$45$		0			0
$46$	−4.17763e6			−0.137569
$47$	1.04829e7	−	1.81569e7i	0.313358	−	0.542752i	−0.665729	−	0.746193i	$-0.731879\pi$
$47$	1.04829e7	−	1.81569e7i	0.313358	−	0.542752i	0.979087	+	0.203442i	$0.0652127\pi$
$48$		0			0
$49$	1.69839e7	+	2.94170e7i	0.420878	+	0.728982i
$50$	−1.41112e7	−	2.44413e7i	−0.319300	−	0.553044i
$51$		0			0
$52$	1.01350e7	−	1.75544e7i	0.192225	−	0.332944i
$53$	−4.06690e7			−0.707983			−0.353991	−	0.935249i	$-0.615176\pi$
$53$	−4.06690e7			−0.707983			−0.353991	+	0.935249i	$0.615176\pi$
$54$		0			0
$55$	3.96850e6			0.0584783
$56$	−5.17530e6	+	8.96388e6i	−0.0703217	+	0.121801i
$57$		0			0
$58$	3.16920e6	+	5.48922e6i	0.0367725	+	0.0636919i
$59$	−4.21915e7	−	7.30779e7i	−0.453306	−	0.785149i	0.545283	−	0.838252i	$-0.316422\pi$
$59$	−4.21915e7	−	7.30779e7i	−0.453306	−	0.785149i	−0.998589	+	0.0531032i	$0.983089\pi$
$60$		0			0
$61$	7.40192e7	−	1.28205e8i	0.684479	−	1.18555i	−0.289121	−	0.957293i	$-0.593363\pi$
$61$	7.40192e7	−	1.28205e8i	0.684479	−	1.18555i	0.973600	−	0.228260i	$-0.0733036\pi$
$62$	9.41205e7			0.808950
$63$		0			0
$64$	1.67772e7			0.125000
$65$	1.72216e7	−	2.98288e7i	0.119664	−	0.207265i
$66$		0			0
$67$	−7.74696e7	−	1.34181e8i	−0.469672	−	0.813495i	0.529727	−	0.848168i	$-0.322294\pi$
$67$	−7.74696e7	−	1.34181e8i	−0.469672	−	0.813495i	−0.999399	+	0.0346729i	$0.988961\pi$
$68$	−5.60609e7	−	9.71004e7i	−0.317958	−	0.550720i
$69$		0			0
$70$	−8.79396e6	+	1.52316e7i	−0.0437767	+	0.0758235i
$71$	−1.68344e8			−0.786202			−0.393101	−	0.919495i	$-0.628598\pi$
$71$	−1.68344e8			−0.786202			−0.393101	+	0.919495i	$0.628598\pi$
$72$		0			0
$73$	4.18698e8			1.72563			0.862816	−	0.505519i	$-0.168699\pi$
$73$	4.18698e8			1.72563			0.862816	+	0.505519i	$0.168699\pi$
$74$	−7.18900e7	+	1.24517e8i	−0.278693	+	0.482710i
$75$		0			0
$76$	−1.49716e7	−	2.59317e7i	−0.0514764	−	0.0891598i
$77$	1.15269e7	+	1.99652e7i	0.0373684	+	0.0647240i
$78$		0			0
$79$	−1.05299e8	+	1.82383e8i	−0.304160	+	0.526821i	−0.977074	−	0.212900i	$-0.931709\pi$
$79$	−1.05299e8	+	1.82383e8i	−0.304160	+	0.526821i	0.672914	+	0.739721i	$0.265042\pi$
$80$	2.85082e7			0.0778152
$81$		0			0
$82$	2.79193e8			0.681934
$83$	3.88197e8	−	6.72377e8i	0.897844	−	1.55511i	0.0675999	−	0.997713i	$-0.478466\pi$
$83$	3.88197e8	−	6.72377e8i	0.897844	−	1.55511i	0.830244	−	0.557400i	$-0.188201\pi$
$84$		0			0
$85$	−9.52598e7	−	1.64995e8i	−0.197936	−	0.342835i
$86$	−2.56757e8	−	4.44716e8i	−0.506150	−	0.876678i
$87$		0			0
$88$	1.86839e7	−	3.23615e7i	0.0332120	−	0.0575249i
$89$	−3.70838e8			−0.626511			−0.313256	−	0.949669i	$-0.601420\pi$
$89$	−3.70838e8			−0.626511			−0.313256	+	0.949669i	$0.601420\pi$
$90$		0			0
$91$	2.00088e8			0.305868
$92$	−3.34211e7	+	5.78870e7i	−0.0486379	+	0.0842433i
$93$		0			0
$94$	−1.67726e8	−	2.90510e8i	−0.221578	−	0.383784i
$95$	−2.54401e7	−	4.40636e7i	−0.0320452	−	0.0555039i
$96$		0			0
$97$	−1.54921e8	+	2.68331e8i	−0.177680	+	0.307750i	−0.941085	−	0.338169i	$-0.890192\pi$
$97$	−1.54921e8	+	2.68331e8i	−0.177680	+	0.307750i	0.763406	+	0.645919i	$0.223526\pi$
$98$	5.43486e8			0.595211
$99$		0			0
$100$	−4.51558e8			−0.451558
$101$	8.79828e8	−	1.52391e9i	0.841301	−	1.45718i	−0.0474933	−	0.998872i	$-0.515123\pi$
$101$	8.79828e8	−	1.52391e9i	0.841301	−	1.45718i	0.888795	−	0.458305i	$-0.151543\pi$
$102$		0			0
$103$	6.67014e6	+	1.15530e7i	0.00583939	+	0.0101141i	0.868930	−	0.494934i	$-0.164808\pi$
$103$	6.67014e6	+	1.15530e7i	0.00583939	+	0.0101141i	−0.863091	+	0.505049i	$0.831475\pi$
$104$	−1.62161e8	−	2.80870e8i	−0.135924	−	0.235427i
$105$		0			0
$106$	−3.25352e8	+	5.63527e8i	−0.250310	+	0.433549i
$107$	1.02477e8			0.0755787			0.0377894	−	0.999286i	$-0.487968\pi$
$107$	1.02477e8			0.0755787			0.0377894	+	0.999286i	$0.487968\pi$
$108$		0			0
$109$	−6.48714e8			−0.440184			−0.220092	−	0.975479i	$-0.570636\pi$
$109$	−6.48714e8			−0.440184			−0.220092	+	0.975479i	$0.570636\pi$
$110$	3.17480e7	−	5.49892e7i	0.0206752	−	0.0358105i
$111$		0			0
$112$	8.28047e7	+	1.43422e8i	0.0497249	+	0.0861261i
$113$	−1.53626e9	−	2.66087e9i	−0.886360	−	1.53522i	−0.844146	−	0.536113i	$-0.819892\pi$
$113$	−1.53626e9	−	2.66087e9i	−0.886360	−	1.53522i	−0.0422141	−	0.999109i	$-0.513441\pi$
$114$		0			0
$115$	−5.67897e7	+	9.83626e7i	−0.0302781	+	0.0524433i
$116$	1.01414e8			0.0520042
$117$		0			0
$118$	−1.35013e9			−0.641071
$119$	5.53383e8	−	9.58487e8i	0.252967	−	0.438152i
$120$		0			0
$121$	1.13736e9	+	1.96996e9i	0.482351	+	0.835457i
$122$	−1.18431e9	−	2.05128e9i	−0.484000	−	0.838312i
$123$		0			0
$124$	7.52964e8	−	1.30417e9i	0.286007	−	0.495379i
$125$	−1.61691e9			−0.592365
$126$		0			0
$127$	−3.34109e9			−1.13965			−0.569825	−	0.821766i	$-0.692989\pi$
$127$	−3.34109e9			−1.13965			−0.569825	+	0.821766i	$0.692989\pi$
$128$	1.34218e8	−	2.32472e8i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−2.75546e8	−	4.77260e8i	−0.0846154	−	0.146558i
$131$	−2.42532e9	−	4.20078e9i	−0.719530	−	1.24626i	−0.961186	−	0.275900i	$-0.911024\pi$
$131$	−2.42532e9	−	4.20078e9i	−0.719530	−	1.24626i	0.241656	−	0.970362i	$-0.422309\pi$
$132$		0			0
$133$	1.47787e8	−	2.55974e8i	0.0409546	−	0.0709354i
$134$	−2.47903e9			−0.664216
$135$		0			0
$136$	−1.79395e9			−0.449661
$137$	1.95010e9	−	3.37768e9i	0.472950	−	0.819173i	−0.526571	−	0.850131i	$-0.676522\pi$
$137$	1.95010e9	−	3.37768e9i	0.472950	−	0.819173i	0.999521	+	0.0309579i	$0.00985580\pi$
$138$		0			0
$139$	2.67183e9	+	4.62774e9i	0.607074	+	1.05148i	0.991720	+	0.128419i	$0.0409901\pi$
$139$	2.67183e9	+	4.62774e9i	0.607074	+	1.05148i	−0.384646	+	0.923064i	$0.625677\pi$
$140$	1.40703e8	+	2.43705e8i	0.0309548	+	0.0536153i
$141$		0			0
$142$	−1.34675e9	+	2.33264e9i	−0.277964	+	0.481448i
$143$	−7.22359e8			−0.144458
$144$		0			0
$145$	1.72325e8			0.0323737
$146$	3.34958e9	−	5.80165e9i	0.610103	−	1.05673i
$147$		0			0
$148$	1.15024e9	+	1.99227e9i	0.197065	+	0.341327i
$149$	−2.97014e9	−	5.14443e9i	−0.493672	−	0.855065i	0.506302	−	0.862357i	$-0.331012\pi$
$149$	−2.97014e9	−	5.14443e9i	−0.493672	−	0.855065i	−0.999973	+	0.00729170i	$0.997679\pi$
$150$		0			0
$151$	−6.23896e8	+	1.08062e9i	−0.0976598	+	0.169152i	−0.910716	−	0.413034i	$-0.864469\pi$
$151$	−6.23896e8	+	1.08062e9i	−0.0976598	+	0.169152i	0.813056	+	0.582186i	$0.197802\pi$
$152$	−4.79093e8			−0.0727987
$153$		0			0
$154$	3.68861e8			0.0528469
$155$	1.27945e9	−	2.21607e9i	0.178045	−	0.308384i
$156$		0			0
$157$	−2.56222e9	−	4.43790e9i	−0.336564	−	0.582947i	0.647220	−	0.762304i	$-0.275932\pi$
$157$	−2.56222e9	−	4.43790e9i	−0.336564	−	0.582947i	−0.983784	+	0.179357i	$0.942598\pi$
$158$	1.68478e9	+	2.91813e9i	0.215074	+	0.372519i
$159$		0			0
$160$	2.28065e8	−	3.95021e8i	0.0275118	−	0.0476519i
$161$	−6.59805e8			−0.0773925
$162$		0			0
$163$	1.17910e10			1.30830			0.654151	−	0.756364i	$-0.273026\pi$
$163$	1.17910e10			1.30830			0.654151	+	0.756364i	$0.273026\pi$
$164$	2.23354e9	−	3.86861e9i	0.241100	−	0.417598i
$165$		0			0
$166$	−6.21116e9	−	1.07580e10i	−0.634872	−	1.09963i
$167$	−5.20376e9	−	9.01318e9i	−0.517718	−	0.896714i	−0.999788	−	0.0205811i	$-0.993448\pi$
$167$	−5.20376e9	−	9.01318e9i	−0.517718	−	0.896714i	0.482070	−	0.876133i	$-0.339885\pi$
$168$		0			0
$169$	2.16751e9	−	3.75424e9i	0.204396	−	0.354024i
$170$	−3.04831e9			−0.279924
$171$		0			0
$172$	−8.21623e9			−0.715805
$173$	−1.75185e9	+	3.03429e9i	−0.148693	+	0.257543i	−0.930744	−	0.365670i	$-0.880840\pi$
$173$	−1.75185e9	+	3.03429e9i	−0.148693	+	0.257543i	0.782052	+	0.623213i	$0.214173\pi$
$174$		0			0
$175$	−2.22869e9	−	3.86020e9i	−0.179630	−	0.311128i
$176$	−2.98942e8	−	5.17784e8i	−0.0234845	−	0.0406763i
$177$		0			0
$178$	−2.96670e9	+	5.13848e9i	−0.221505	+	0.383658i
$179$	1.89515e10			1.37976			0.689882	−	0.723922i	$-0.257662\pi$
$179$	1.89515e10			1.37976			0.689882	+	0.723922i	$0.257662\pi$
$180$		0			0
$181$	2.02932e10			1.40539			0.702695	−	0.711492i	$-0.251980\pi$
$181$	2.02932e10			1.40539			0.702695	+	0.711492i	$0.251980\pi$
$182$	1.60070e9	−	2.77250e9i	0.108141	−	0.187305i
$183$		0			0
$184$	5.34737e8	+	9.26191e8i	0.0343922	+	0.0595690i
$185$	1.95451e9	+	3.38531e9i	0.122677	+	0.212484i
$186$		0			0
$187$	−1.99783e9	+	3.46034e9i	−0.119473	+	0.206934i
$188$	−5.36724e9			−0.313358
$189$		0			0
$190$	−8.14083e8			−0.0453187
$191$	−5.95826e9	+	1.03200e10i	−0.323943	+	0.561087i	−0.981298	−	0.192495i	$-0.938342\pi$
$191$	−5.95826e9	+	1.03200e10i	−0.323943	+	0.561087i	0.657354	+	0.753581i	$0.271675\pi$
$192$		0			0
$193$	2.51484e9	+	4.35583e9i	0.130467	+	0.225976i	0.923857	−	0.382738i	$-0.125019\pi$
$193$	2.51484e9	+	4.35583e9i	0.130467	+	0.225976i	−0.793389	+	0.608714i	$0.791686\pi$
$194$	2.47874e9	+	4.29330e9i	0.125638	+	0.217612i
$195$		0			0
$196$	4.34789e9	−	7.53076e9i	0.210439	−	0.364491i
$197$	5.95780e8			0.0281831			0.0140915	−	0.999901i	$-0.495514\pi$
$197$	5.95780e8			0.0281831			0.0140915	+	0.999901i	$0.495514\pi$
$198$		0			0
$199$	1.94694e10			0.880065			0.440032	−	0.897982i	$-0.354967\pi$
$199$	1.94694e10			0.880065			0.440032	+	0.897982i	$0.354967\pi$
$200$	−3.61247e9	+	6.25698e9i	−0.159650	+	0.276522i
$201$		0			0
$202$	−1.40772e10	−	2.43825e10i	−0.594890	−	1.03038i
$203$	5.00536e8	+	8.66953e8i	0.0206872	+	0.0358314i
$204$		0			0
$205$	3.79528e9	−	6.57362e9i	0.150090	−	0.259963i
$206$	2.13445e8			0.00825815
$207$		0			0
$208$	−5.18914e9			−0.192225
$209$	−5.33540e8	+	9.24119e8i	−0.0193423	+	0.0335019i
$210$		0			0
$211$	1.04724e10	+	1.81388e10i	0.363728	+	0.629996i	0.988571	−	0.150755i	$-0.0481703\pi$
$211$	1.04724e10	+	1.81388e10i	0.363728	+	0.629996i	−0.624843	+	0.780750i	$0.714837\pi$
$212$	5.20564e9	+	9.01643e9i	0.176996	+	0.306565i
$213$		0			0
$214$	8.19816e8	−	1.41996e9i	0.0267211	−	0.0462823i
$215$	−1.39612e10			−0.445604
$216$		0			0
$217$	1.48652e10			0.455094
$218$	−5.18971e9	+	8.98885e9i	−0.155629	+	0.269557i
$219$		0			0
$220$	−5.07969e8	−	8.79827e8i	−0.0146196	−	0.0253219i
$221$	1.73395e10	+	3.00328e10i	0.488957	+	0.846898i
$222$		0			0
$223$	1.87120e10	−	3.24102e10i	0.506697	−	0.877626i	−0.493273	−	0.869875i	$-0.664199\pi$
$223$	1.87120e10	−	3.24102e10i	0.506697	−	0.877626i	0.999970	−	0.00775082i	$-0.00246719\pi$
$224$	2.64975e9			0.0703217
$225$		0			0
$226$	−4.91602e10			−1.25350
$227$	−7.69356e9	+	1.33256e10i	−0.192314	+	0.333098i	−0.946017	−	0.324118i	$-0.894933\pi$
$227$	−7.69356e9	+	1.33256e10i	−0.192314	+	0.333098i	0.753703	+	0.657216i	$0.228266\pi$
$228$		0			0
$229$	3.56977e10	+	6.18302e10i	0.857789	+	1.48573i	0.874033	+	0.485867i	$0.161496\pi$
$229$	3.56977e10	+	6.18302e10i	0.857789	+	1.48573i	−0.0162434	+	0.999868i	$0.505171\pi$
$230$	9.08635e8	+	1.57380e9i	0.0214099	+	0.0370830i
$231$		0			0
$232$	8.11315e8	−	1.40524e9i	0.0183863	−	0.0318460i
$233$	−4.39177e10			−0.976199			−0.488099	−	0.872788i	$-0.662310\pi$
$233$	−4.39177e10			−0.976199			−0.488099	+	0.872788i	$0.662310\pi$
$234$		0			0
$235$	−9.12012e9			−0.195072
$236$	−1.08010e10	+	1.87079e10i	−0.226653	+	0.392574i
$237$		0			0
$238$	−8.85412e9	−	1.53358e10i	−0.178875	−	0.309820i
$239$	3.84772e10	+	6.66445e10i	0.762804	+	1.32122i	0.941400	+	0.337293i	$0.109511\pi$
$239$	3.84772e10	+	6.66445e10i	0.762804	+	1.32122i	−0.178596	+	0.983923i	$0.557155\pi$
$240$		0			0
$241$	1.13548e10	−	1.96671e10i	0.216822	−	0.375546i	−0.737013	−	0.675879i	$-0.763764\pi$
$241$	1.13548e10	−	1.96671e10i	0.216822	−	0.375546i	0.953835	+	0.300333i	$0.0970977\pi$
$242$	3.63955e10			0.682148
$243$		0			0
$244$	−3.78978e10			−0.684479
$245$	7.38801e9	−	1.27964e10i	0.131003	−	0.226903i
$246$		0			0
$247$	4.63068e9	+	8.02058e9i	0.0791606	+	0.137110i
$248$	−1.20474e10	−	2.08668e10i	−0.202238	−	0.350286i
$249$		0			0
$250$	−1.29352e10	+	2.24045e10i	−0.209433	+	0.362748i
$251$	8.27276e10			1.31558			0.657792	−	0.753199i	$-0.271490\pi$
$251$	8.27276e10			1.31558			0.657792	+	0.753199i	$0.271490\pi$
$252$		0			0
$253$	2.38203e9			0.0365515
$254$	−2.67287e10	+	4.62955e10i	−0.402927	+	0.697890i
$255$		0			0
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	4.39895e10	+	7.61921e10i	0.628999	+	1.08946i	0.987753	+	0.156026i	$0.0498685\pi$
$257$	4.39895e10	+	7.61921e10i	0.628999	+	1.08946i	−0.358754	+	0.933432i	$0.616798\pi$
$258$		0			0
$259$	−1.13541e10	+	1.96659e10i	−0.156785	+	0.271560i
$260$	−8.81748e9			−0.119664
$261$		0			0
$262$	−7.76103e10			−1.01757
$263$	−7.53686e10	+	1.30542e11i	−0.971381	+	1.68248i	−0.279987	+	0.960004i	$0.590330\pi$
$263$	−7.53686e10	+	1.30542e11i	−0.971381	+	1.68248i	−0.691394	+	0.722478i	$0.743003\pi$
$264$		0			0
$265$	8.84552e9	+	1.53209e10i	0.110184	+	0.190844i
$266$	−2.36458e9	−	4.09558e9i	−0.0289593	−	0.0501589i
$267$		0			0
$268$	−1.98322e10	+	3.43504e10i	−0.234836	+	0.406748i
$269$	−6.86181e10			−0.799012			−0.399506	−	0.916731i	$-0.630818\pi$
$269$	−6.86181e10			−0.799012			−0.399506	+	0.916731i	$0.630818\pi$
$270$		0			0
$271$	2.35686e10			0.265444			0.132722	−	0.991153i	$-0.457628\pi$
$271$	2.35686e10			0.265444			0.132722	+	0.991153i	$0.457628\pi$
$272$	−1.43516e10	+	2.48577e10i	−0.158979	+	0.275360i
$273$		0			0
$274$	−3.12017e10	−	5.40429e10i	−0.334426	−	0.579243i
$275$	8.04603e9	+	1.39361e10i	0.0848368	+	0.146942i
$276$		0			0
$277$	−6.14274e10	+	1.06395e11i	−0.626907	+	1.08583i	0.361262	+	0.932464i	$0.382346\pi$
$277$	−6.14274e10	+	1.06395e11i	−0.626907	+	1.08583i	−0.988169	+	0.153370i	$0.950987\pi$
$278$	8.54984e10			0.858532
$279$		0			0
$280$	4.50251e9			0.0437767
$281$	1.74582e10	−	3.02384e10i	0.167040	−	0.289322i	−0.770338	−	0.637636i	$-0.779912\pi$
$281$	1.74582e10	−	3.02384e10i	0.167040	−	0.289322i	0.937378	+	0.348314i	$0.113246\pi$
$282$		0			0
$283$	3.80823e10	+	6.59604e10i	0.352926	+	0.611286i	0.986761	−	0.162183i	$-0.0518534\pi$
$283$	3.80823e10	+	6.59604e10i	0.352926	+	0.611286i	−0.633835	+	0.773469i	$0.718520\pi$
$284$	2.15480e10	+	3.73222e10i	0.196550	+	0.340435i
$285$		0			0
$286$	−5.77887e9	+	1.00093e10i	−0.0510735	+	0.0884620i
$287$	4.40951e10			0.383638
$288$		0			0
$289$	7.32351e10			0.617560
$290$	1.37860e9	−	2.38781e9i	0.0114458	−	0.0198248i
$291$		0			0
$292$	−5.35933e10	−	9.28264e10i	−0.431408	−	0.747220i
$293$	8.86616e10	+	1.53566e11i	0.702799	+	1.21728i	0.967480	+	0.252948i	$0.0814002\pi$
$293$	8.86616e10	+	1.53566e11i	0.702799	+	1.21728i	−0.264680	+	0.964336i	$0.585266\pi$
$294$		0			0
$295$	−1.83533e10	+	3.17889e10i	−0.141096	+	0.244386i
$296$	3.68077e10			0.278693
$297$		0			0
$298$	−9.50444e10			−0.698158
$299$	1.03370e10	−	1.79043e10i	0.0747955	−	0.129550i
$300$		0			0
$301$	−4.05516e10	−	7.02374e10i	−0.284747	−	0.493196i
$302$	9.98234e9	+	1.72899e10i	0.0690559	+	0.119608i
$303$		0			0
$304$	−3.83274e9	+	6.63850e9i	−0.0257382	+	0.0445799i
$305$	−6.43967e10			−0.426103
$306$		0			0
$307$	1.91554e11			1.23075			0.615374	−	0.788235i	$-0.289005\pi$
$307$	1.91554e11			1.23075			0.615374	+	0.788235i	$0.289005\pi$
$308$	2.95089e9	−	5.11109e9i	0.0186842	−	0.0323620i
$309$		0			0
$310$	−2.04712e10	−	3.54572e10i	−0.125897	−	0.218060i
$311$	−7.64523e10	−	1.32419e11i	−0.463414	−	0.802656i	0.535715	−	0.844399i	$-0.320042\pi$
$311$	−7.64523e10	−	1.32419e11i	−0.463414	−	0.802656i	−0.999128	+	0.0417431i	$0.986709\pi$
$312$		0			0
$313$	6.19002e9	−	1.07214e10i	0.0364538	−	0.0631398i	−0.847223	−	0.531238i	$-0.821727\pi$
$313$	6.19002e9	−	1.07214e10i	0.0364538	−	0.0631398i	0.883677	+	0.468098i	$0.155060\pi$
$314$	−8.19911e10			−0.475974
$315$		0			0
$316$	5.39131e10			0.304160
$317$	3.01474e10	−	5.22168e10i	0.167681	−	0.290432i	−0.769923	−	0.638136i	$-0.779706\pi$
$317$	3.01474e10	−	5.22168e10i	0.167681	−	0.290432i	0.937604	+	0.347705i	$0.113039\pi$
$318$		0			0
$319$	−1.80704e9	−	3.12988e9i	−0.00977033	−	0.0169227i
$320$	−3.64904e9	−	6.32033e9i	−0.0194538	−	0.0336950i
$321$		0			0
$322$	−5.27844e9	+	9.14252e9i	−0.0273624	+	0.0473930i
$323$	5.12283e10			0.261878
$324$		0			0
$325$	1.39666e11			0.694407
$326$	9.43283e10	−	1.63381e11i	0.462555	−	0.801168i
$327$		0			0
$328$	−3.57367e10	−	6.18978e10i	−0.170483	−	0.295286i
$329$	−2.64903e10	−	4.58825e10i	−0.124654	−	0.215906i
$330$		0			0
$331$	3.72517e10	−	6.45219e10i	0.170577	−	0.295448i	−0.768045	−	0.640396i	$-0.778770\pi$
$331$	3.72517e10	−	6.45219e10i	0.170577	−	0.295448i	0.938622	+	0.344948i	$0.112104\pi$
$332$	−1.98757e11			−0.897844
$333$		0			0
$334$	−1.66520e11			−0.732164
$335$	−3.36993e10	+	5.83688e10i	−0.146190	+	0.253209i
$336$		0			0
$337$	9.63304e10	+	1.66849e11i	0.406845	+	0.704676i	0.994534	−	0.104411i	$-0.0332956\pi$
$337$	9.63304e10	+	1.66849e11i	0.406845	+	0.704676i	−0.587689	+	0.809087i	$0.699962\pi$
$338$	−3.46802e10	−	6.00679e10i	−0.144530	−	0.250333i
$339$		0			0
$340$	−2.43865e10	+	4.22387e10i	−0.0989679	+	0.171417i
$341$	−5.36663e10			−0.214935
$342$		0			0
$343$	1.87810e11			0.732649
$344$	−6.57298e10	+	1.13847e11i	−0.253075	+	0.438339i
$345$		0			0
$346$	2.80296e10	+	4.85487e10i	0.105141	+	0.182110i
$347$	−2.64418e11	−	4.57985e11i	−0.979056	−	1.69577i	−0.665843	−	0.746092i	$-0.731928\pi$
$347$	−2.64418e11	−	4.57985e11i	−0.979056	−	1.69577i	−0.313213	−	0.949683i	$-0.601405\pi$
$348$		0			0
$349$	9.74080e10	−	1.68716e11i	0.351464	−	0.608753i	−0.635043	−	0.772477i	$-0.719017\pi$
$349$	9.74080e10	−	1.68716e11i	0.351464	−	0.608753i	0.986506	+	0.163724i	$0.0523508\pi$
$350$	−7.13180e10			−0.254035
$351$		0			0
$352$	−9.56616e9			−0.0332120
$353$	4.21962e10	−	7.30859e10i	0.144639	−	0.250523i	−0.784599	−	0.620004i	$-0.787131\pi$
$353$	4.21962e10	−	7.30859e10i	0.144639	−	0.250523i	0.929238	+	0.369481i	$0.120464\pi$
$354$		0			0
$355$	3.66147e10	+	6.34186e10i	0.122357	+	0.211928i
$356$	4.74672e10	+	8.22157e10i	0.156628	+	0.271287i
$357$		0			0
$358$	1.51612e11	−	2.62600e11i	0.487820	−	0.844930i
$359$	2.49683e11			0.793347			0.396674	−	0.917960i	$-0.370164\pi$
$359$	2.49683e11			0.793347			0.396674	+	0.917960i	$0.370164\pi$
$360$		0			0
$361$	−3.09007e11			−0.957603
$362$	1.62345e11	−	2.81191e11i	0.496880	−	0.860622i
$363$		0			0
$364$	−2.56112e10	−	4.43600e10i	−0.0764671	−	0.132445i
$365$	−9.10668e10	−	1.57732e11i	−0.268561	−	0.465161i
$366$		0			0
$367$	2.76662e11	−	4.79193e11i	0.796073	−	1.37884i	−0.126083	−	0.992020i	$-0.540241\pi$
$367$	2.76662e11	−	4.79193e11i	0.796073	−	1.37884i	0.922156	−	0.386819i	$-0.126426\pi$
$368$	1.71116e10			0.0486379
$369$		0			0
$370$	6.25443e10			0.173492
$371$	−5.13853e10	+	8.90020e10i	−0.140818	+	0.243903i
$372$		0			0
$373$	6.52761e10	+	1.13062e11i	0.174608	+	0.302430i	0.940026	−	0.341104i	$-0.110801\pi$
$373$	6.52761e10	+	1.13062e11i	0.174608	+	0.302430i	−0.765417	+	0.643534i	$0.777467\pi$
$374$	3.19652e10	+	5.53654e10i	0.0844804	+	0.146324i
$375$		0			0
$376$	−4.29379e10	+	7.43707e10i	−0.110789	+	0.191892i
$377$	−3.13672e10			−0.0799722
$378$		0			0
$379$	−3.21465e11			−0.800307			−0.400154	−	0.916448i	$-0.631043\pi$
$379$	−3.21465e11			−0.800307			−0.400154	+	0.916448i	$0.631043\pi$
$380$	−6.51267e9	+	1.12803e10i	−0.0160226	+	0.0277519i
$381$		0			0
$382$	9.53321e10	+	1.65120e11i	0.229063	+	0.396748i
$383$	−3.40111e11	−	5.89090e11i	−0.807656	−	1.39890i	−0.914483	−	0.404624i	$-0.867402\pi$
$383$	−3.40111e11	−	5.89090e11i	−0.807656	−	1.39890i	0.106827	−	0.994278i	$-0.465931\pi$
$384$		0			0
$385$	5.01421e9	−	8.68486e9i	0.0116313	−	0.0201460i
$386$	8.04748e10			0.184509
$387$		0			0
$388$	7.93195e10			0.177680
$389$	3.97293e11	−	6.88132e11i	0.879707	−	1.52370i	0.0280452	−	0.999607i	$-0.491072\pi$
$389$	3.97293e11	−	6.88132e11i	0.879707	−	1.52370i	0.851662	−	0.524091i	$-0.175595\pi$
$390$		0			0
$391$	−5.71782e10	−	9.90356e10i	−0.123719	−	0.214287i
$392$	−6.95662e10	−	1.20492e11i	−0.148803	−	0.257734i
$393$		0			0
$394$	4.76624e9	−	8.25538e9i	0.00996422	−	0.0172585i
$395$	9.16101e10			0.189346
$396$		0			0
$397$	1.97913e11			0.399868			0.199934	−	0.979809i	$-0.435927\pi$
$397$	1.97913e11			0.399868			0.199934	+	0.979809i	$0.435927\pi$
$398$	1.55756e11	−	2.69777e11i	0.311150	−	0.538928i
$399$		0			0
$400$	5.77995e10	+	1.00112e11i	0.112890	+	0.195531i
$401$	4.78238e10	+	8.28332e10i	0.0923622	+	0.159976i	0.908505	−	0.417875i	$-0.137225\pi$
$401$	4.78238e10	+	8.28332e10i	0.0923622	+	0.159976i	−0.816142	+	0.577851i	$0.803892\pi$
$402$		0			0
$403$	−2.32889e11	+	4.03376e11i	−0.439822	+	0.761794i
$404$	−4.50472e11			−0.841301
$405$		0			0
$406$	1.60171e10			0.0292562
$407$	4.09908e10	−	7.09981e10i	0.0740476	−	0.128254i
$408$		0			0
$409$	−1.41102e11	−	2.44395e11i	−0.249332	−	0.431855i	0.714009	−	0.700137i	$-0.246878\pi$
$409$	−1.41102e11	−	2.44395e11i	−0.249332	−	0.431855i	−0.963341	+	0.268282i	$0.913544\pi$
$410$	−6.07245e10	−	1.05178e11i	−0.106130	−	0.183822i
$411$		0			0
$412$	1.70756e9	−	2.95757e9i	0.00291970	−	0.00505706i
$413$	−2.13236e11			−0.360650
$414$		0			0
$415$	−3.37732e11			−0.558927
$416$	−4.15131e10	+	7.19028e10i	−0.0679619	+	0.117713i
$417$		0			0
$418$	8.53665e9	+	1.47859e10i	0.0136771	+	0.0236894i
$419$	7.62515e10	+	1.32072e11i	0.120861	+	0.209337i	0.920107	−	0.391666i	$-0.128101\pi$
$419$	7.62515e10	+	1.32072e11i	0.120861	+	0.209337i	−0.799247	+	0.601003i	$0.794768\pi$
$420$		0			0
$421$	5.38287e10	−	9.32340e10i	0.0835111	−	0.144645i	−0.821245	−	0.570576i	$-0.806720\pi$
$421$	5.38287e10	−	9.32340e10i	0.0835111	−	0.144645i	0.904756	+	0.425931i	$0.140053\pi$
$422$	3.35118e11			0.514390
$423$		0			0
$424$	1.66580e11			0.250310
$425$	3.86273e11	−	6.69044e11i	0.574307	−	0.994729i
$426$		0			0
$427$	−1.87047e11	−	3.23974e11i	−0.272285	−	0.471612i
$428$	−1.31171e10	−	2.27194e10i	−0.0188947	−	0.0327265i
$429$		0			0
$430$	−1.11689e11	+	1.93452e11i	−0.157545	+	0.272875i
$431$	7.77462e10			0.108525			0.0542627	−	0.998527i	$-0.482719\pi$
$431$	7.77462e10			0.108525			0.0542627	+	0.998527i	$0.482719\pi$
$432$		0			0
$433$	1.20952e11			0.165356			0.0826778	−	0.996576i	$-0.473653\pi$
$433$	1.20952e11			0.165356			0.0826778	+	0.996576i	$0.473653\pi$
$434$	1.18921e11	−	2.05978e11i	0.160900	−	0.278687i
$435$		0			0
$436$	8.30354e10	+	1.43822e11i	0.110046	+	0.190605i
$437$	−1.52700e10	−	2.64485e10i	−0.0200297	−	0.0346924i
$438$		0			0
$439$	−5.15966e11	+	8.93679e11i	−0.663026	+	1.14839i	0.316791	+	0.948495i	$0.397395\pi$
$439$	−5.15966e11	+	8.93679e11i	−0.663026	+	1.14839i	−0.979817	+	0.199899i	$0.935939\pi$
$440$	−1.62550e10			−0.0206752
$441$		0			0
$442$	5.54863e11			0.691489
$443$	−3.10258e11	+	5.37382e11i	−0.382742	+	0.662928i	−0.991453	−	0.130464i	$-0.958353\pi$
$443$	−3.10258e11	+	5.37382e11i	−0.382742	+	0.662928i	0.608711	+	0.793392i	$0.291687\pi$
$444$		0			0
$445$	8.06572e10	+	1.39702e11i	0.0975042	+	0.168882i
$446$	−2.99392e11	−	5.18563e11i	−0.358289	−	0.620575i
$447$		0			0
$448$	2.11980e10	−	3.67160e10i	0.0248625	−	0.0430630i
$449$	−7.51040e11			−0.872076			−0.436038	−	0.899928i	$-0.643619\pi$
$449$	−7.51040e11			−0.872076			−0.436038	+	0.899928i	$0.643619\pi$
$450$		0			0
$451$	−1.59192e11			−0.181187
$452$	−3.93281e11	+	6.81183e11i	−0.443180	+	0.767611i
$453$		0			0
$454$	1.23097e11	+	2.13210e11i	0.135987	+	0.235536i
$455$	−4.35191e10	−	7.53773e10i	−0.0476024	−	0.0824497i
$456$		0			0
$457$	−6.66852e11	+	1.15502e12i	−0.715165	+	1.23870i	0.247731	+	0.968829i	$0.420315\pi$
$457$	−6.66852e11	+	1.15502e12i	−0.715165	+	1.23870i	−0.962896	+	0.269874i	$0.913018\pi$
$458$	1.14233e12			1.21310
$459$		0			0
$460$	2.90763e10			0.0302781
$461$	−2.63950e11	+	4.57174e11i	−0.272187	+	0.471441i	−0.969421	−	0.245402i	$-0.921080\pi$
$461$	−2.63950e11	+	4.57174e11i	−0.272187	+	0.471441i	0.697235	+	0.716843i	$0.254413\pi$
$462$		0			0
$463$	−5.43728e11	−	9.41765e11i	−0.549879	−	0.952419i	−0.998282	−	0.0585873i	$-0.981340\pi$
$463$	−5.43728e11	−	9.41765e11i	−0.549879	−	0.952419i	0.448403	−	0.893831i	$-0.351993\pi$
$464$	−1.29810e10	−	2.24838e10i	−0.0130011	−	0.0225185i
$465$		0			0
$466$	−3.51342e11	+	6.08542e11i	−0.345138	+	0.597797i
$467$	−8.01186e11			−0.779484			−0.389742	−	0.920924i	$-0.627436\pi$
$467$	−8.01186e11			−0.779484			−0.389742	+	0.920924i	$0.627436\pi$
$468$		0			0
$469$	−3.91531e11			−0.373670
$470$	−7.29609e10	+	1.26372e11i	−0.0689684	+	0.119457i
$471$		0			0
$472$	1.72817e11	+	2.99327e11i	0.160268	+	0.277592i
$473$	1.46400e11	+	2.53572e11i	0.134482	+	0.232930i
$474$		0			0
$475$	1.03158e11	−	1.78675e11i	0.0929785	−	0.161043i
$476$	−2.83332e11			−0.252967
$477$		0			0
$478$	1.23127e12			1.07877
$479$	1.94899e11	−	3.37575e11i	0.169161	−	0.292995i	−0.768964	−	0.639292i	$-0.779228\pi$
$479$	1.94899e11	−	3.37575e11i	0.169161	−	0.292995i	0.938125	+	0.346297i	$0.112561\pi$
$480$		0			0
$481$	−3.55765e11	−	6.16204e11i	−0.303048	−	0.524894i
$482$	−1.81677e11	−	3.14673e11i	−0.153316	−	0.265551i
$483$		0			0
$484$	2.91164e11	−	5.04311e11i	0.241176	−	0.417729i
$485$	1.34781e11			0.110609
$486$		0			0
$487$	−1.90992e12			−1.53863			−0.769317	−	0.638868i	$-0.779403\pi$
$487$	−1.90992e12			−1.53863			−0.769317	+	0.638868i	$0.779403\pi$
$488$	−3.03183e11	+	5.25128e11i	−0.242000	+	0.419156i
$489$		0			0
$490$	−1.18208e11	−	2.04743e11i	−0.0926329	−	0.160445i
$491$	1.94209e11	+	3.36380e11i	0.150800	+	0.261194i	0.931522	−	0.363685i	$-0.118482\pi$
$491$	1.94209e11	+	3.36380e11i	0.150800	+	0.261194i	−0.780721	+	0.624879i	$0.785148\pi$
$492$		0			0
$493$	−8.67521e10	+	1.50259e11i	−0.0661407	+	0.114559i
$494$	1.48182e11			0.111950
$495$		0			0
$496$	−3.85518e11			−0.286007
$497$	−2.12702e11	+	3.68411e11i	−0.156375	+	0.270850i
$498$		0			0
$499$	2.59022e10	+	4.48639e10i	0.0187018	+	0.0323925i	0.875225	−	0.483716i	$-0.160713\pi$
$499$	2.59022e10	+	4.48639e10i	0.0187018	+	0.0323925i	−0.856523	+	0.516109i	$0.827380\pi$
$500$	2.06964e11	+	3.58472e11i	0.148091	+	0.256502i
$501$		0			0
$502$	6.61821e11	−	1.14631e12i	0.465129	−	0.805628i
$503$	9.91895e11			0.690891			0.345446	−	0.938439i	$-0.387728\pi$
$503$	9.91895e11			0.690891			0.345446	+	0.938439i	$0.387728\pi$
$504$		0			0
$505$	−7.65450e11			−0.523728
$506$	1.90563e10	−	3.30064e10i	0.0129229	−	0.0223831i
$507$		0			0
$508$	4.27659e11	+	7.40728e11i	0.284912	+	0.493483i
$509$	1.37321e12	+	2.37847e12i	0.906792	+	1.57061i	0.818494	+	0.574515i	$0.194809\pi$
$509$	1.37321e12	+	2.37847e12i	0.906792	+	1.57061i	0.0882981	+	0.996094i	$0.471857\pi$
$510$		0			0
$511$	5.29025e11	−	9.16298e11i	0.343227	−	0.594487i
$512$	−6.87195e10			−0.0441942
$513$		0			0
$514$	1.40766e12			0.889539
$515$	2.90151e9	−	5.02557e9i	0.00181757	−	0.00314813i
$516$		0			0
$517$	9.56354e10	+	1.65645e11i	0.0588723	+	0.101970i
$518$	1.81666e11	+	3.14655e11i	0.110864	+	0.192022i
$519$		0			0
$520$	−7.05399e10	+	1.22179e11i	−0.0423077	+	0.0732791i
$521$	5.16949e11			0.307382			0.153691	−	0.988119i	$-0.450884\pi$
$521$	5.16949e11			0.307382			0.153691	+	0.988119i	$0.450884\pi$
$522$		0			0
$523$	−3.12202e11			−0.182464			−0.0912322	−	0.995830i	$-0.529081\pi$
$523$	−3.12202e11			−0.182464			−0.0912322	+	0.995830i	$0.529081\pi$
$524$	−6.20883e11	+	1.07540e12i	−0.359765	+	0.623131i
$525$		0			0
$526$	1.20590e12	+	2.08868e12i	0.686870	+	1.18969i
$527$	1.28820e12	+	2.23124e12i	0.727507	+	1.26008i
$528$		0			0
$529$	8.66489e11	−	1.50080e12i	0.481075	−	0.833246i
$530$	2.83057e11			0.155823
$531$		0			0
$532$	−7.56667e10			−0.0409546
$533$	−6.90828e11	+	1.19655e12i	−0.370764	+	0.642182i
$534$		0			0
$535$	−2.22888e10	−	3.86052e10i	−0.0117623	−	0.0203730i
$536$	3.17315e11	+	5.49606e11i	0.166054	+	0.287614i
$537$		0			0
$538$	−5.48945e11	+	9.50800e11i	−0.282494	+	0.489293i
$539$	−3.09889e11			−0.158145
$540$		0			0
$541$	−1.35533e12			−0.680234			−0.340117	−	0.940383i	$-0.610467\pi$
$541$	−1.35533e12			−0.680234			−0.340117	+	0.940383i	$0.610467\pi$
$542$	1.88549e11	−	3.26576e11i	0.0938485	−	0.162550i
$543$		0			0
$544$	2.29626e11	+	3.97723e11i	0.112415	+	0.194709i
$545$	1.41095e11	+	2.44384e11i	0.0685060	+	0.118656i
$546$		0			0
$547$	1.38459e12	−	2.39818e12i	0.661269	−	1.14535i	−0.319014	−	0.947750i	$-0.603352\pi$
$547$	1.38459e12	−	2.39818e12i	0.661269	−	1.14535i	0.980283	−	0.197601i	$-0.0633150\pi$
$548$	−9.98453e11			−0.472950
$549$		0			0
$550$	2.57473e11			0.119977
$551$	−2.31680e10	+	4.01282e10i	−0.0107080	+	0.0185467i
$552$		0			0
$553$	2.66091e11	+	4.60882e11i	0.120995	+	0.209569i
$554$	9.82838e11	+	1.70233e12i	0.443290	+	0.767801i
$555$		0			0
$556$	6.83987e11	−	1.18470e12i	0.303537	−	0.525741i
$557$	8.90709e11			0.392091			0.196046	−	0.980595i	$-0.437190\pi$
$557$	8.90709e11			0.392091			0.196046	+	0.980595i	$0.437190\pi$
$558$		0			0
$559$	2.54125e12			1.10077
$560$	3.60201e10	−	6.23886e10i	0.0154774	−	0.0268077i
$561$		0			0
$562$	−2.79331e11	−	4.83815e11i	−0.118115	−	0.204581i
$563$	−1.13743e10	−	1.97009e10i	−0.00477132	−	0.00826417i	0.863630	−	0.504126i	$-0.168185\pi$
$563$	−1.13743e10	−	1.97009e10i	−0.00477132	−	0.00826417i	−0.868401	+	0.495862i	$0.834852\pi$
$564$		0			0
$565$	−6.68271e11	+	1.15748e12i	−0.275889	+	0.477854i
$566$	1.21863e12			0.499113
$567$		0			0
$568$	6.89535e11			0.277964
$569$	−2.16886e12	+	3.75658e12i	−0.867415	+	1.50241i	−0.00278521	+	0.999996i	$0.500887\pi$
$569$	−2.16886e12	+	3.75658e12i	−0.867415	+	1.50241i	−0.864629	+	0.502410i	$0.832447\pi$
$570$		0			0
$571$	−1.24039e12	−	2.14841e12i	−0.488308	−	0.845775i	0.511601	−	0.859223i	$-0.329053\pi$
$571$	−1.24039e12	−	2.14841e12i	−0.488308	−	0.845775i	−0.999910	+	0.0134481i	$0.995719\pi$
$572$	9.24620e10	+	1.60149e11i	0.0361145	+	0.0625521i
$573$		0			0
$574$	3.52760e11	−	6.10999e11i	0.135636	−	0.234929i
$575$	−4.60558e11			−0.175703
$576$		0			0
$577$	−1.50387e12			−0.564831			−0.282415	−	0.959292i	$-0.591136\pi$
$577$	−1.50387e12			−0.564831			−0.282415	+	0.959292i	$0.591136\pi$
$578$	5.85881e11	−	1.01478e12i	0.218340	−	0.378177i
$579$		0			0
$580$	−2.20576e10	−	3.82049e10i	−0.00809344	−	0.0140182i
$581$	−9.80974e11	−	1.69910e12i	−0.357162	−	0.618623i
$582$		0			0
$583$	1.85512e11	−	3.21316e11i	0.0665064	−	0.115192i
$584$	−1.71499e12			−0.610103
$585$		0			0
$586$	2.83717e12			0.993908
$587$	−9.03834e11	+	1.56549e12i	−0.314208	+	0.544224i	−0.979269	−	0.202565i	$-0.935072\pi$
$587$	−9.03834e11	+	1.56549e12i	−0.314208	+	0.544224i	0.665061	+	0.746789i	$0.268406\pi$
$588$		0			0
$589$	3.44028e11	+	5.95874e11i	0.117781	+	0.204003i
$590$	2.93653e11	+	5.08622e11i	0.0997701	+	0.172807i
$591$		0			0
$592$	2.94461e11	−	5.10022e11i	0.0985327	−	0.170664i
$593$	4.13005e12			1.37154			0.685771	−	0.727818i	$-0.259465\pi$
$593$	4.13005e12			1.37154			0.685771	+	0.727818i	$0.259465\pi$
$594$		0			0
$595$	−4.81443e11			−0.157477
$596$	−7.60355e11	+	1.31697e12i	−0.246836	+	0.427532i
$597$		0			0
$598$	−1.65392e11	−	2.86468e11i	−0.0528884	−	0.0916054i
$599$	8.11617e11	+	1.40576e12i	0.257591	+	0.446160i	0.965596	−	0.260047i	$-0.0837380\pi$
$599$	8.11617e11	+	1.40576e12i	0.257591	+	0.446160i	−0.708005	+	0.706207i	$0.750405\pi$
$600$		0			0
$601$	−9.39652e11	+	1.62753e12i	−0.293787	+	0.508853i	−0.974702	−	0.223509i	$-0.928249\pi$
$601$	−9.39652e11	+	1.62753e12i	−0.293787	+	0.508853i	0.680915	+	0.732362i	$0.261582\pi$
$602$	−1.29765e12			−0.402693
$603$		0			0
$604$	3.19435e11			0.0976598
$605$	4.94751e11	−	8.56934e11i	0.150137	−	0.260045i
$606$		0			0
$607$	−2.71746e11	−	4.70678e11i	−0.0812483	−	0.140726i	0.822538	−	0.568710i	$-0.192557\pi$
$607$	−2.71746e11	−	4.70678e11i	−0.0812483	−	0.140726i	−0.903786	+	0.427984i	$0.859224\pi$
$608$	6.13239e10	+	1.06216e11i	0.0181997	+	0.0315227i
$609$		0			0
$610$	−5.15174e11	+	8.92307e11i	−0.150650	+	0.260934i
$611$	1.66007e12			0.481882
$612$		0			0
$613$	3.90638e12			1.11738			0.558692	−	0.829375i	$-0.311303\pi$
$613$	3.90638e12			1.11738			0.558692	+	0.829375i	$0.311303\pi$
$614$	1.53244e12	−	2.65426e12i	0.435135	−	0.753677i
$615$		0			0
$616$	−4.72142e10	−	8.17774e10i	−0.0132117	−	0.0228834i
$617$	−2.08225e12	−	3.60656e12i	−0.578428	−	1.00187i	−0.995660	−	0.0930667i	$-0.970333\pi$
$617$	−2.08225e12	−	3.60656e12i	−0.578428	−	1.00187i	0.417232	−	0.908800i	$-0.363000\pi$
$618$		0			0
$619$	−1.21483e12	+	2.10415e12i	−0.332589	+	0.576060i	−0.983019	−	0.183506i	$-0.941255\pi$
$619$	−1.21483e12	+	2.10415e12i	−0.332589	+	0.576060i	0.650430	+	0.759566i	$0.274589\pi$
$620$	−6.55079e11			−0.178045
$621$		0			0
$622$	−2.44647e12			−0.655366
$623$	−4.68553e11	+	8.11558e11i	−0.124613	+	0.215836i
$624$		0			0
$625$	−1.37088e12	−	2.37444e12i	−0.359368	−	0.622444i
$626$	−9.90403e10	−	1.71543e11i	−0.0257767	−	0.0446466i
$627$		0			0
$628$	−6.55929e11	+	1.13610e12i	−0.168282	+	0.291473i
$629$	−3.93576e12			−1.00254
$630$		0			0
$631$	−1.52098e12			−0.381936			−0.190968	−	0.981596i	$-0.561163\pi$
$631$	−1.52098e12			−0.381936			−0.190968	+	0.981596i	$0.561163\pi$
$632$	4.31305e11	−	7.47042e11i	0.107537	−	0.186259i
$633$		0			0
$634$	−4.82358e11	−	8.35469e11i	−0.118568	−	0.205366i
$635$	7.26687e11	+	1.25866e12i	0.177364	+	0.307203i
$636$		0			0
$637$	−1.34479e12	+	2.32924e12i	−0.323613	+	0.560515i
$638$	−5.78252e10			−0.0138173
$639$		0			0
$640$	−1.16769e11			−0.0275118
$641$	3.04845e11	−	5.28006e11i	0.0713210	−	0.123532i	−0.828159	−	0.560493i	$-0.810612\pi$
$641$	3.04845e11	−	5.28006e11i	0.0713210	−	0.123532i	0.899480	+	0.436961i	$0.143945\pi$
$642$		0			0
$643$	−2.47621e12	−	4.28891e12i	−0.571265	−	0.989459i	−0.996436	−	0.0843467i	$-0.973120\pi$
$643$	−2.47621e12	−	4.28891e12i	−0.571265	−	0.989459i	0.425172	−	0.905113i	$-0.360214\pi$
$644$	8.44550e10	+	1.46280e11i	0.0193481	+	0.0335119i
$645$		0			0
$646$	4.09826e11	−	7.09840e11i	0.0925878	−	0.160367i
$647$	−3.20285e12			−0.718567			−0.359284	−	0.933228i	$-0.616979\pi$
$647$	−3.20285e12			−0.718567			−0.359284	+	0.933228i	$0.616979\pi$
$648$		0			0
$649$	7.69827e11			0.170330
$650$	1.11732e12	−	1.93526e12i	0.245510	−	0.425236i
$651$		0			0
$652$	−1.50925e12	−	2.61410e12i	−0.327075	−	0.566511i
$653$	−3.09875e12	−	5.36719e12i	−0.666925	−	1.15515i	−0.978759	−	0.205012i	$-0.934277\pi$
$653$	−3.09875e12	−	5.36719e12i	−0.666925	−	1.15515i	0.311834	−	0.950137i	$-0.399057\pi$
$654$		0			0
$655$	−1.05502e12	+	1.82734e12i	−0.223961	+	0.387912i
$656$	−1.14357e12			−0.241100
$657$		0			0
$658$	−8.47688e11			−0.176287
$659$	4.00510e12	−	6.93703e12i	0.827235	−	1.43281i	−0.0729650	−	0.997335i	$-0.523246\pi$
$659$	4.00510e12	−	6.93703e12i	0.827235	−	1.43281i	0.900200	−	0.435478i	$-0.143421\pi$
$660$		0			0
$661$	4.47408e12	+	7.74934e12i	0.911586	+	1.57891i	0.811824	+	0.583902i	$0.198475\pi$
$661$	4.47408e12	+	7.74934e12i	0.911586	+	1.57891i	0.0997618	+	0.995011i	$0.468192\pi$
$662$	−5.96028e11	−	1.03235e12i	−0.120616	−	0.208913i
$663$		0			0
$664$	−1.59006e12	+	2.75406e12i	−0.317436	+	0.549815i
$665$	−1.28574e11			−0.0254951
$666$		0			0
$667$	1.03436e11			0.0202350
$668$	−1.33216e12	+	2.30737e12i	−0.258859	+	0.448357i
$669$		0			0
$670$	5.39188e11	+	9.33901e11i	0.103372	+	0.179046i
$671$	6.75277e11	+	1.16961e12i	0.128597	+	0.222737i
$672$		0			0
$673$	−2.66277e12	+	4.61206e12i	−0.500341	+	0.866617i	0.499658	+	0.866223i	$0.333459\pi$
$673$	−2.66277e12	+	4.61206e12i	−0.500341	+	0.866617i	−1.00000		0.000394350i	$0.999874\pi$
$674$	3.08257e12			0.575366
$675$		0			0
$676$	−1.10977e12			−0.204396
$677$	5.51061e10	−	9.54466e10i	0.0100821	−	0.0174627i	−0.860940	−	0.508706i	$-0.830124\pi$
$677$	5.51061e10	−	9.54466e10i	0.0100821	−	0.0174627i	0.871022	+	0.491243i	$0.163457\pi$
$678$		0			0
$679$	3.91485e11	+	6.78072e11i	0.0706808	+	0.122423i
$680$	3.90184e11	+	6.75819e11i	0.0699809	+	0.121210i
$681$		0			0
$682$	−4.29331e11	+	7.43623e11i	−0.0759910	+	0.131620i
$683$	−3.48463e12			−0.612722			−0.306361	−	0.951915i	$-0.599111\pi$
$683$	−3.48463e12			−0.612722			−0.306361	+	0.951915i	$0.599111\pi$
$684$		0			0
$685$	−1.69659e12			−0.294421
$686$	1.50248e12	−	2.60238e12i	0.259031	−	0.448654i
$687$		0			0
$688$	1.05168e12	+	1.82156e12i	0.178951	+	0.309953i
$689$	−1.61009e12	−	2.78875e12i	−0.272184	−	0.471437i
$690$		0			0
$691$	5.50847e12	−	9.54096e12i	0.919137	−	1.59199i	0.118407	−	0.992965i	$-0.462221\pi$
$691$	5.50847e12	−	9.54096e12i	0.919137	−	1.59199i	0.800729	−	0.599026i	$-0.204446\pi$
$692$	8.96947e11			0.148693
$693$		0			0
$694$	−8.46136e12			−1.38459
$695$	1.16224e12	−	2.01307e12i	0.188958	−	0.327285i
$696$		0			0
$697$	3.82125e12	+	6.61859e12i	0.613278	+	1.06223i
$698$	−1.55853e12	−	2.69945e12i	−0.248522	−	0.430453i
$699$		0			0
$700$	−5.70544e11	+	9.88211e11i	−0.0898148	+	0.155564i
$701$	8.81897e12			1.37939			0.689695	−	0.724100i	$-0.257745\pi$
$701$	8.81897e12			1.37939			0.689695	+	0.724100i	$0.257745\pi$
$702$		0			0
$703$	−1.05109e12			−0.162308
$704$	−7.65293e10	+	1.32553e11i	−0.0117422	+	0.0203381i
$705$		0			0
$706$	−6.75139e11	−	1.16937e12i	−0.102276	−	0.177146i
$707$	−2.22333e12	−	3.85091e12i	−0.334669	−	0.579664i
$708$		0			0
$709$	9.24571e11	−	1.60140e12i	0.137414	−	0.238009i	−0.789103	−	0.614261i	$-0.789454\pi$
$709$	9.24571e11	−	1.60140e12i	0.137414	−	0.238009i	0.926517	+	0.376253i	$0.122787\pi$
$710$	1.17167e12			0.173039
$711$		0			0
$712$	1.51895e12			0.221505
$713$	7.67971e11	−	1.33016e12i	0.111286	−	0.192754i
$714$		0			0
$715$	1.57113e11	+	2.72128e11i	0.0224820	+	0.0389400i
$716$	−2.42579e12	−	4.20159e12i	−0.344941	−	0.597455i
$717$		0			0
$718$	1.99746e12	−	3.45970e12i	0.280491	−	0.485824i
$719$	−6.42135e12			−0.896078			−0.448039	−	0.894014i	$-0.647878\pi$
$719$	−6.42135e12			−0.896078			−0.448039	+	0.894014i	$0.647878\pi$
$720$		0			0
$721$	3.37109e10			0.00464581
$722$	−2.47205e12	+	4.28172e12i	−0.338564	+	0.586410i
$723$		0			0
$724$	−2.59753e12	−	4.49905e12i	−0.351347	−	0.608551i
$725$	3.49384e11	+	6.05152e11i	0.0469659	+	0.0813473i
$726$		0			0
$727$	2.82460e12	−	4.89235e12i	0.375018	−	0.649550i	−0.615312	−	0.788284i	$-0.710970\pi$
$727$	2.82460e12	−	4.89235e12i	0.375018	−	0.649550i	0.990330	+	0.138734i	$0.0443032\pi$
$728$	−8.19560e11			−0.108141
$729$		0			0
$730$	−2.91414e12			−0.379802
$731$	7.02834e12	−	1.21734e13i	0.910384	−	1.57683i
$732$		0			0
$733$	6.21547e11	+	1.07655e12i	0.0795254	+	0.137742i	0.903045	−	0.429545i	$-0.141326\pi$
$733$	6.21547e11	+	1.07655e12i	0.0795254	+	0.137742i	−0.823520	+	0.567287i	$0.807993\pi$
$734$	−4.42660e12	−	7.66709e12i	−0.562908	−	0.974986i
$735$		0			0
$736$	1.36893e11	−	2.37105e11i	0.0171961	−	0.0297845i
$737$	1.41351e12			0.176480
$738$		0			0
$739$	−2.20942e12			−0.272507			−0.136253	−	0.990674i	$-0.543506\pi$
$739$	−2.20942e12			−0.272507			−0.136253	+	0.990674i	$0.543506\pi$
$740$	5.00354e11	−	8.66639e11i	0.0613387	−	0.106242i
$741$		0			0
$742$	8.22165e11	+	1.42403e12i	0.0995730	+	0.172466i
$743$	8.34929e10	+	1.44614e11i	0.0100508	+	0.0174085i	0.871007	−	0.491271i	$-0.163467\pi$
$743$	8.34929e10	+	1.44614e11i	0.0100508	+	0.0174085i	−0.860956	+	0.508679i	$0.830134\pi$
$744$		0			0
$745$	−1.29201e12	+	2.23783e12i	−0.153661	+	0.266148i
$746$	2.08884e12			0.246933
$747$		0			0
$748$	1.02289e12			0.119473
$749$	1.29480e11	−	2.24265e11i	0.0150326	−	0.0260372i
$750$		0			0
$751$	2.48530e12	+	4.30466e12i	0.285101	+	0.493810i	0.972634	−	0.232344i	$-0.0746395\pi$
$751$	2.48530e12	+	4.30466e12i	0.285101	+	0.493810i	−0.687533	+	0.726154i	$0.741306\pi$
$752$	6.87007e11	+	1.18993e12i	0.0783395	+	0.135688i
$753$		0			0
$754$	−2.50937e11	+	4.34636e11i	−0.0282744	+	0.0489728i
$755$	5.42790e11			0.0607953
$756$		0			0
$757$	9.48178e12			1.04944			0.524721	−	0.851274i	$-0.324170\pi$
$757$	9.48178e12			1.04944			0.524721	+	0.851274i	$0.324170\pi$
$758$	−2.57172e12	+	4.45435e12i	−0.282951	+	0.490086i
$759$		0			0
$760$	1.04203e11	+	1.80484e11i	0.0113297	+	0.0196236i
$761$	−4.73532e12	−	8.20182e12i	−0.511822	−	0.886501i	−0.999906	−	0.0137048i	$-0.995637\pi$
$761$	−4.73532e12	−	8.20182e12i	−0.511822	−	0.886501i	0.488084	−	0.872796i	$-0.337696\pi$
$762$		0			0
$763$	−8.19651e11	+	1.41968e12i	−0.0875525	+	0.151645i
$764$	3.05063e12			0.323943
$765$		0			0
$766$	−1.08836e13			−1.14220
$767$	3.34073e12	−	5.78631e12i	0.348547	−	0.603702i
$768$		0			0
$769$	5.13637e12	+	8.89646e12i	0.529649	+	0.917379i	0.999402	+	0.0345810i	$0.0110097\pi$
$769$	5.13637e12	+	8.89646e12i	0.529649	+	0.917379i	−0.469753	+	0.882798i	$0.655657\pi$
$770$	−8.02273e10	−	1.38958e11i	−0.00822458	−	0.0142454i
$771$		0			0
$772$	6.43799e11	−	1.11509e12i	0.0652337	−	0.112988i
$773$	−1.13305e13			−1.14141			−0.570704	−	0.821156i	$-0.693330\pi$
$773$	−1.13305e13			−1.14141			−0.570704	+	0.821156i	$0.693330\pi$
$774$		0			0
$775$	1.03762e13			1.03319
$776$	6.34556e11	−	1.09908e12i	0.0628192	−	0.108806i
$777$		0			0
$778$	−6.35670e12	−	1.10101e13i	−0.622047	−	1.07742i
$779$	1.02050e12	+	1.76756e12i	0.0992878	+	0.171971i
$780$		0			0
$781$	7.67899e11	−	1.33004e12i	0.0738541	−	0.127919i
$782$	−1.82970e12			−0.174965
$783$		0			0
$784$	−2.22612e12			−0.210439
$785$	−1.11457e12	+	1.93049e12i	−0.104759	+	0.181448i
$786$		0			0
$787$	−3.43458e12	−	5.94886e12i	−0.319144	−	0.552774i	0.661165	−	0.750240i	$-0.270062\pi$
$787$	−3.43458e12	−	5.94886e12i	−0.319144	−	0.552774i	−0.980310	+	0.197466i	$0.936729\pi$
$788$	−7.62599e10	−	1.32086e11i	−0.00704577	−	0.0122036i
$789$		0			0
$790$	7.32881e11	−	1.26939e12i	0.0669440	−	0.115950i
$791$	−7.76423e12			−0.705187
$792$		0			0
$793$	1.17217e13			1.05259
$794$	1.58330e12	−	2.74236e12i	0.141375	−	0.244868i
$795$		0			0
$796$	−2.49209e12	−	4.31642e12i	−0.220016	−	0.381079i
$797$	4.17934e12	+	7.23882e12i	0.366898	+	0.635485i	0.989079	−	0.147388i	$-0.0470866\pi$
$797$	4.17934e12	+	7.23882e12i	0.366898	+	0.635485i	−0.622181	+	0.782873i	$0.713753\pi$
$798$		0			0
$799$	4.59125e12	−	7.95229e12i	0.398539	−	0.690290i
$800$	1.84958e12			0.159650
$801$		0			0
$802$	1.53036e12			0.130620
$803$	−1.90989e12	+	3.30803e12i	−0.162102	+	0.280769i
$804$		0			0
$805$	1.43508e11	+	2.48562e11i	0.0120446	+	0.0208619i
$806$	3.72623e12	+	6.45402e12i	0.311001	+	0.538670i
$807$		0			0
$808$	−3.60378e12	+	6.24192e12i	−0.297445	+	0.515190i
$809$	5.37009e12			0.440771			0.220386	−	0.975413i	$-0.429268\pi$
$809$	5.37009e12			0.440771			0.220386	+	0.975413i	$0.429268\pi$
$810$		0			0
$811$	6.15396e12			0.499529			0.249764	−	0.968307i	$-0.419647\pi$
$811$	6.15396e12			0.499529			0.249764	+	0.968307i	$0.419647\pi$
$812$	1.28137e11	−	2.21940e11i	0.0103436	−	0.0179157i
$813$		0			0
$814$	−6.55852e11	−	1.13597e12i	−0.0523596	−	0.0906895i
$815$	−2.56455e12	−	4.44193e12i	−0.203611	−	0.352665i
$816$		0			0
$817$	1.87699e12	−	3.25104e12i	0.147388	−	0.255284i
$818$	−4.51525e12			−0.352608
$819$		0			0
$820$	−1.94318e12			−0.150090
$821$	3.86872e12	−	6.70081e12i	0.297182	−	0.514735i	−0.678308	−	0.734778i	$-0.737286\pi$
$821$	3.86872e12	−	6.70081e12i	0.297182	−	0.514735i	0.975490	+	0.220043i	$0.0706198\pi$
$822$		0			0
$823$	−1.09797e13	−	1.90175e13i	−0.834244	−	1.44495i	−0.894644	−	0.446779i	$-0.852571\pi$
$823$	−1.09797e13	−	1.90175e13i	−0.834244	−	1.44495i	0.0604003	−	0.998174i	$-0.480762\pi$
$824$	−2.73209e10	−	4.73212e10i	−0.00206454	−	0.00357588i
$825$		0			0
$826$	−1.70589e12	+	2.95469e12i	−0.127509	+	0.220852i
$827$	−1.89761e12			−0.141069			−0.0705346	−	0.997509i	$-0.522471\pi$
$827$	−1.89761e12			−0.141069			−0.0705346	+	0.997509i	$0.522471\pi$
$828$		0			0
$829$	1.14625e13			0.842912			0.421456	−	0.906849i	$-0.361519\pi$
$829$	1.14625e13			0.842912			0.421456	+	0.906849i	$0.361519\pi$
$830$	−2.70185e12	+	4.67975e12i	−0.197611	+	0.342272i
$831$		0			0
$832$	6.64210e11	+	1.15045e12i	0.0480563	+	0.0832360i
$833$	7.43856e12	+	1.28840e13i	0.535286	+	0.927143i
$834$		0			0
$835$	−2.26364e12	+	3.92073e12i	−0.161145	+	0.279112i
$836$	2.73173e11			0.0193423
$837$		0			0
$838$	2.44005e12			0.170923
$839$	−1.20245e13	+	2.08270e13i	−0.837794	+	1.45110i	0.0539402	+	0.998544i	$0.482822\pi$
$839$	−1.20245e13	+	2.08270e13i	−0.837794	+	1.45110i	−0.891735	+	0.452558i	$0.850511\pi$
$840$		0			0
$841$	7.17511e12	+	1.24276e13i	0.494591	+	0.856657i
$842$	−8.61259e11	−	1.49174e12i	−0.0590513	−	0.102280i
$843$		0			0
$844$	2.68095e12	−	4.64354e12i	0.181864	−	0.314998i
$845$	−1.88574e12			−0.127241
$846$		0			0
$847$	5.74821e12			0.383758
$848$	1.33264e12	−	2.30821e12i	0.0884978	−	0.153283i
$849$		0			0
$850$	−6.18037e12	−	1.07047e13i	−0.406096	−	0.703380i
$851$	1.17316e12	+	2.03198e12i	0.0766788	+	0.132812i
$852$		0			0
$853$	−1.14279e13	+	1.97938e13i	−0.739089	+	1.28014i	0.213817	+	0.976874i	$0.431410\pi$
$853$	−1.14279e13	+	1.97938e13i	−0.739089	+	1.28014i	−0.952906	+	0.303266i	$0.901923\pi$
$854$	−5.98549e12			−0.385070
$855$		0			0
$856$	−4.19746e11			−0.0267211
$857$	−1.30882e13	+	2.26694e13i	−0.828832	+	1.43558i	0.0701229	+	0.997538i	$0.477661\pi$
$857$	−1.30882e13	+	2.26694e13i	−0.828832	+	1.43558i	−0.898955	+	0.438041i	$0.855672\pi$
$858$		0			0
$859$	1.78084e12	+	3.08450e12i	0.111598	+	0.193293i	0.916415	−	0.400230i	$-0.131070\pi$
$859$	1.78084e12	+	3.08450e12i	0.111598	+	0.193293i	−0.804817	+	0.593523i	$0.797737\pi$
$860$	1.78703e12	+	3.09523e12i	0.111401	+	0.192952i
$861$		0			0
$862$	6.21969e11	−	1.07728e12i	0.0383695	−	0.0664579i
$863$	2.73564e13			1.67884			0.839421	−	0.543481i	$-0.182894\pi$
$863$	2.73564e13			1.67884			0.839421	+	0.543481i	$0.182894\pi$
$864$		0			0
$865$	1.52411e12			0.0925643
$866$	9.67619e11	−	1.67597e12i	0.0584621	−	0.101259i
$867$		0			0
$868$	−1.90274e12	−	3.29564e12i	−0.113773	−	0.197061i
$869$	−9.60643e11	−	1.66388e12i	−0.0571443	−	0.0989769i
$870$		0			0
$871$	6.13404e12	−	1.06245e13i	0.361131	−	0.625497i
$872$	2.65713e12			0.155629
$873$		0			0
$874$	−4.88641e11			−0.0283262
$875$	−2.04296e12	+	3.53851e12i	−0.117821	+	0.204072i
$876$		0			0
$877$	5.52594e12	+	9.57121e12i	0.315434	+	0.546347i	0.979530	−	0.201300i	$-0.0645167\pi$
$877$	5.52594e12	+	9.57121e12i	0.315434	+	0.546347i	−0.664096	+	0.747647i	$0.731183\pi$
$878$	8.25545e12	+	1.42989e13i	0.468830	+	0.812037i
$879$		0			0
$880$	−1.30040e11	+	2.25236e11i	−0.00730979	+	0.0126609i
$881$	2.76007e13			1.54358			0.771789	−	0.635879i	$-0.219362\pi$
$881$	2.76007e13			1.54358			0.771789	+	0.635879i	$0.219362\pi$
$882$		0			0
$883$	2.98889e11			0.0165458			0.00827288	−	0.999966i	$-0.497367\pi$
$883$	2.98889e11			0.0165458			0.00827288	+	0.999966i	$0.497367\pi$
$884$	4.43890e12	−	7.68841e12i	0.244478	−	0.423449i
$885$		0			0
$886$	4.96412e12	+	8.59811e12i	0.270639	+	0.468761i
$887$	1.54272e13	+	2.67208e13i	0.836819	+	1.44941i	0.892540	+	0.450967i	$0.148921\pi$
$887$	1.54272e13	+	2.67208e13i	0.836819	+	1.44941i	−0.0557210	+	0.998446i	$0.517746\pi$
$888$		0			0
$889$	−4.22147e12	+	7.31179e12i	−0.226676	+	0.392614i
$890$	2.58103e12			0.137892
$891$		0			0
$892$	−9.58055e12			−0.506697
$893$	1.22614e12	−	2.12374e12i	0.0645222	−	0.111756i
$894$		0			0
$895$	−4.12195e12	−	7.13943e12i	−0.214733	−	0.371929i
$896$	−3.39168e11	−	5.87457e11i	−0.0175804	−	0.0304502i
$897$		0			0
$898$	−6.00832e12	+	1.04067e13i	−0.308325	+	0.534035i
$899$	−2.33037e12			−0.118989
$900$		0			0
$901$	−1.78121e13			−0.900436
$902$	−1.27354e12	+	2.20583e12i	−0.0640594	+	0.110954i
$903$		0			0
$904$	6.29250e12	+	1.08989e13i	0.313376	+	0.542783i
$905$	−4.41377e12	−	7.64487e12i	−0.218721	−	0.378836i
$906$		0			0
$907$	1.16873e13	−	2.02430e13i	0.573431	−	0.993211i	−0.422779	−	0.906233i	$-0.638945\pi$
$907$	1.16873e13	−	2.02430e13i	0.573431	−	0.993211i	0.996210	−	0.0869786i	$-0.0277212\pi$
$908$	3.93910e12			0.192314
$909$		0			0
$910$	−1.39261e12			−0.0673199
$911$	−1.36555e13	+	2.36521e13i	−0.656865	+	1.13772i	0.324558	+	0.945866i	$0.394784\pi$
$911$	−1.36555e13	+	2.36521e13i	−0.656865	+	1.13772i	−0.981423	+	0.191857i	$0.938549\pi$
$912$		0			0
$913$	3.54152e12	+	6.13410e12i	0.168683	+	0.292168i
$914$	1.06696e13	+	1.84803e13i	0.505698	+	0.875895i
$915$		0			0
$916$	9.13861e12	−	1.58285e13i	0.428895	−	0.742867i
$917$	−1.22576e13			−0.572457
$918$		0			0
$919$	−2.88513e13			−1.33427			−0.667137	−	0.744935i	$-0.732481\pi$
$919$	−2.88513e13			−1.33427			−0.667137	+	0.744935i	$0.732481\pi$
$920$	2.32611e11	−	4.02893e11i	0.0107049	−	0.0185415i
$921$		0			0
$922$	4.22319e12	+	7.31479e12i	0.192465	+	0.333359i
$923$	−6.66472e12	−	1.15436e13i	−0.302256	−	0.523522i
$924$		0			0
$925$	−7.92542e12	+	1.37272e13i	−0.355946	+	0.616517i
$926$	−1.73993e13			−0.777647
$927$		0			0
$928$	−4.15393e11			−0.0183863
$929$	2.47230e12	−	4.28215e12i	0.108901	−	0.188621i	−0.806425	−	0.591337i	$-0.798600\pi$
$929$	2.47230e12	−	4.28215e12i	0.108901	−	0.188621i	0.915325	+	0.402716i	$0.131934\pi$
$930$		0			0
$931$	1.98654e12	+	3.44079e12i	0.0866612	+	0.150102i
$932$	5.62147e12	+	9.73667e12i	0.244050	+	0.422706i
$933$		0			0
$934$	−6.40949e12	+	1.11016e13i	−0.275589	+	0.477335i
$935$	1.73811e12			0.0743747
$936$		0			0
$937$	−3.28563e13			−1.39248			−0.696242	−	0.717807i	$-0.745146\pi$
$937$	−3.28563e13			−1.39248			−0.696242	+	0.717807i	$0.745146\pi$
$938$	−3.13225e12	+	5.42521e12i	−0.132112	+	0.228825i
$939$		0			0
$940$	1.16737e12	+	2.02195e12i	0.0487680	+	0.0844687i
$941$	2.30259e13	+	3.98819e13i	0.957332	+	1.65815i	0.728940	+	0.684578i	$0.240013\pi$
$941$	2.30259e13	+	3.98819e13i	0.957332	+	1.65815i	0.228392	+	0.973569i	$0.426653\pi$
$942$		0			0
$943$	2.27806e12	−	3.94571e12i	0.0938128	−	0.162489i
$944$	5.53013e12			0.226653
$945$		0			0
$946$	4.68479e12			0.190187
$947$	−1.44720e13	+	2.50663e13i	−0.584728	+	1.01278i	0.410181	+	0.912004i	$0.365466\pi$
$947$	−1.44720e13	+	2.50663e13i	−0.584728	+	1.01278i	−0.994909	+	0.100775i	$0.967868\pi$
$948$		0			0
$949$	1.65763e13	+	2.87109e13i	0.663420	+	1.14908i
$950$	−1.65053e12	−	2.85880e12i	−0.0657457	−	0.113875i
$951$		0			0
$952$	−2.26666e12	+	3.92596e12i	−0.0894374	+	0.154910i
$953$	−2.49105e13			−0.978284			−0.489142	−	0.872204i	$-0.662690\pi$
$953$	−2.49105e13			−0.978284			−0.489142	+	0.872204i	$0.662690\pi$
$954$		0			0
$955$	5.18369e12			0.201662
$956$	9.85016e12	−	1.70610e13i	0.381402	−	0.660608i
$957$		0			0
$958$	−3.11839e12	−	5.40120e12i	−0.119615	−	0.207179i
$959$	−4.92791e12	−	8.53540e12i	−0.188139	−	0.325867i
$960$		0			0
$961$	−4.08229e12	+	7.07073e12i	−0.154400	+	0.267429i
$962$	−1.13845e13			−0.428574
$963$		0			0
$964$	−5.81366e12			−0.216822
$965$	1.09395e12	−	1.89479e12i	0.0406094	−	0.0703375i
$966$		0			0
$967$	−1.99207e13	−	3.45037e13i	−0.732632	−	1.26896i	−0.955755	−	0.294165i	$-0.904959\pi$
$967$	−1.99207e13	−	3.45037e13i	−0.732632	−	1.26896i	0.223123	−	0.974790i	$-0.428375\pi$
$968$	−4.65862e12	−	8.06897e12i	−0.170537	−	0.295379i
$969$		0			0
$970$	1.07825e12	−	1.86758e12i	0.0391063	−	0.0677341i
$971$	1.76953e13			0.638809			0.319405	−	0.947618i	$-0.396517\pi$
$971$	1.76953e13			0.638809			0.319405	+	0.947618i	$0.396517\pi$
$972$		0			0
$973$	1.35034e13			0.482987
$974$	−1.52794e13	+	2.64646e13i	−0.543989	+	0.942216i
$975$		0			0
$976$	4.85092e12	+	8.40205e12i	0.171120	+	0.296388i
$977$	−1.62258e12	−	2.81039e12i	−0.0569744	−	0.0986826i	0.836131	−	0.548529i	$-0.184812\pi$
$977$	−1.62258e12	−	2.81039e12i	−0.0569744	−	0.0986826i	−0.893106	+	0.449847i	$0.851479\pi$
$978$		0			0
$979$	1.69158e12	−	2.92990e12i	0.0588531	−	0.101937i
$980$	−3.78266e12			−0.131003
$981$		0			0
$982$	6.21469e12			0.213264
$983$	2.08808e13	−	3.61665e13i	0.713272	−	1.23542i	−0.250350	−	0.968155i	$-0.580546\pi$
$983$	2.08808e13	−	3.61665e13i	0.713272	−	1.23542i	0.963622	−	0.267269i	$-0.0861211\pi$
$984$		0			0
$985$	−1.29582e11	−	2.24443e11i	−0.00438614	−	0.00759702i
$986$	1.38803e12	+	2.40414e12i	0.0467685	+	0.0810055i
$987$		0			0
$988$	1.18546e12	−	2.05327e12i	0.0395803	−	0.0685551i
$989$	−8.37998e12			−0.278522
$990$		0			0
$991$	−5.72174e13			−1.88450			−0.942251	−	0.334907i	$-0.891295\pi$
$991$	−5.72174e13			−1.88450			−0.942251	+	0.334907i	$0.891295\pi$
$992$	−3.08414e12	+	5.34189e12i	−0.101119	+	0.175143i
$993$		0			0
$994$	3.40323e12	+	5.89457e12i	0.110574	+	0.191520i
$995$	−4.23460e12	−	7.33455e12i	−0.136965	−	0.237230i
$996$		0			0
$997$	2.21014e12	−	3.82807e12i	0.0708420	−	0.122702i	−0.828429	−	0.560095i	$-0.810765\pi$
$997$	2.21014e12	−	3.82807e12i	0.0708420	−	0.122702i	0.899271	+	0.437393i	$0.144098\pi$
$998$	8.28870e11			0.0264484
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.10.c.g.55.1		2
3.2	odd	2		162.10.c.d.55.1		2
9.2	odd	6		54.10.a.c.1.1	yes	1
9.4	even	3	inner	162.10.c.g.109.1		2
9.5	odd	6		162.10.c.d.109.1		2
9.7	even	3		54.10.a.b.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.10.a.b.1.1	✓	1	9.7	even	3
54.10.a.c.1.1	yes	1	9.2	odd	6
162.10.c.d.55.1		2	3.2	odd	2
162.10.c.d.109.1		2	9.5	odd	6
162.10.c.g.55.1		2	1.1	even	1	trivial
162.10.c.g.109.1		2	9.4	even	3	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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(8.00000 - 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(-217.500 - 376.721i) q^{5} +(1263.50 - 2188.45i) q^{7} -4096.00 q^{8} +O(q^{10})\)	\(q+(8.00000 - 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(-217.500 - 376.721i) q^{5} +(1263.50 - 2188.45i) q^{7} -4096.00 q^{8} -6960.00 q^{10} +(-4561.50 + 7900.75i) q^{11} +(39590.0 + 68571.9i) q^{13} +(-20216.0 - 35015.1i) q^{14} +(-32768.0 + 56755.8i) q^{16} +437976. q^{17} +116966. q^{19} +(-55680.0 + 96440.6i) q^{20} +(72984.0 + 126412. i) q^{22} +(-130551. - 226121. i) q^{23} +(881950. - 1.52758e6i) q^{25} +1.26688e6 q^{26} -646912. q^{28} +(-198075. + 343076. i) q^{29} +(2.94127e6 + 5.09442e6i) q^{31} +(524288. + 908093. i) q^{32} +(3.50381e6 - 6.06877e6i) q^{34} -1.09924e6 q^{35} -8.98625e6 q^{37} +(935728. - 1.62073e6i) q^{38} +(890880. + 1.54305e6i) q^{40} +(8.72478e6 + 1.51118e7i) q^{41} +(1.60473e7 - 2.77948e7i) q^{43} +2.33549e6 q^{44} -4.17763e6 q^{46} +(1.04829e7 - 1.81569e7i) q^{47} +(1.69839e7 + 2.94170e7i) q^{49} +(-1.41112e7 - 2.44413e7i) q^{50} +(1.01350e7 - 1.75544e7i) q^{52} -4.06690e7 q^{53} +3.96850e6 q^{55} +(-5.17530e6 + 8.96388e6i) q^{56} +(3.16920e6 + 5.48922e6i) q^{58} +(-4.21915e7 - 7.30779e7i) q^{59} +(7.40192e7 - 1.28205e8i) q^{61} +9.41205e7 q^{62} +1.67772e7 q^{64} +(1.72216e7 - 2.98288e7i) q^{65} +(-7.74696e7 - 1.34181e8i) q^{67} +(-5.60609e7 - 9.71004e7i) q^{68} +(-8.79396e6 + 1.52316e7i) q^{70} -1.68344e8 q^{71} +4.18698e8 q^{73} +(-7.18900e7 + 1.24517e8i) q^{74} +(-1.49716e7 - 2.59317e7i) q^{76} +(1.15269e7 + 1.99652e7i) q^{77} +(-1.05299e8 + 1.82383e8i) q^{79} +2.85082e7 q^{80} +2.79193e8 q^{82} +(3.88197e8 - 6.72377e8i) q^{83} +(-9.52598e7 - 1.64995e8i) q^{85} +(-2.56757e8 - 4.44716e8i) q^{86} +(1.86839e7 - 3.23615e7i) q^{88} -3.70838e8 q^{89} +2.00088e8 q^{91} +(-3.34211e7 + 5.78870e7i) q^{92} +(-1.67726e8 - 2.90510e8i) q^{94} +(-2.54401e7 - 4.40636e7i) q^{95} +(-1.54921e8 + 2.68331e8i) q^{97} +5.43486e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 16 q^{2} - 256 q^{4} - 435 q^{5} + 2527 q^{7} - 8192 q^{8}+O(q^{10}) \) 2 * q + 16 * q^2 - 256 * q^4 - 435 * q^5 + 2527 * q^7 - 8192 * q^8	\( 2 q + 16 q^{2} - 256 q^{4} - 435 q^{5} + 2527 q^{7} - 8192 q^{8} - 13920 q^{10} - 9123 q^{11} + 79180 q^{13} - 40432 q^{14} - 65536 q^{16} + 875952 q^{17} + 233932 q^{19} - 111360 q^{20} + 145968 q^{22} - 261102 q^{23} + 1763900 q^{25} + 2533760 q^{26} - 1293824 q^{28} - 396150 q^{29} + 5882533 q^{31} + 1048576 q^{32} + 7007616 q^{34} - 2198490 q^{35} - 17972492 q^{37} + 1871456 q^{38} + 1781760 q^{40} + 17449566 q^{41} + 32094646 q^{43} + 4670976 q^{44} - 8355264 q^{46} + 20965782 q^{47} + 33967878 q^{49} - 28222400 q^{50} + 20270080 q^{52} - 81338094 q^{53} + 7937010 q^{55} - 10350592 q^{56} + 6338400 q^{58} - 84383076 q^{59} + 148038424 q^{61} + 188241056 q^{62} + 33554432 q^{64} + 34443300 q^{65} - 154939106 q^{67} - 112121856 q^{68} - 17587920 q^{70} - 336687120 q^{71} + 837395986 q^{73} - 143779936 q^{74} - 29943296 q^{76} + 23053821 q^{77} - 210598040 q^{79} + 57016320 q^{80} + 558386112 q^{82} + 776394525 q^{83} - 190519560 q^{85} - 513514336 q^{86} + 37367808 q^{88} - 741675492 q^{89} + 400175720 q^{91} - 66842112 q^{92} - 335452512 q^{94} - 50880210 q^{95} - 309841967 q^{97} + 1086972096 q^{98}+O(q^{100}) \) 2 * q + 16 * q^2 - 256 * q^4 - 435 * q^5 + 2527 * q^7 - 8192 * q^8 - 13920 * q^10 - 9123 * q^11 + 79180 * q^13 - 40432 * q^14 - 65536 * q^16 + 875952 * q^17 + 233932 * q^19 - 111360 * q^20 + 145968 * q^22 - 261102 * q^23 + 1763900 * q^25 + 2533760 * q^26 - 1293824 * q^28 - 396150 * q^29 + 5882533 * q^31 + 1048576 * q^32 + 7007616 * q^34 - 2198490 * q^35 - 17972492 * q^37 + 1871456 * q^38 + 1781760 * q^40 + 17449566 * q^41 + 32094646 * q^43 + 4670976 * q^44 - 8355264 * q^46 + 20965782 * q^47 + 33967878 * q^49 - 28222400 * q^50 + 20270080 * q^52 - 81338094 * q^53 + 7937010 * q^55 - 10350592 * q^56 + 6338400 * q^58 - 84383076 * q^59 + 148038424 * q^61 + 188241056 * q^62 + 33554432 * q^64 + 34443300 * q^65 - 154939106 * q^67 - 112121856 * q^68 - 17587920 * q^70 - 336687120 * q^71 + 837395986 * q^73 - 143779936 * q^74 - 29943296 * q^76 + 23053821 * q^77 - 210598040 * q^79 + 57016320 * q^80 + 558386112 * q^82 + 776394525 * q^83 - 190519560 * q^85 - 513514336 * q^86 + 37367808 * q^88 - 741675492 * q^89 + 400175720 * q^91 - 66842112 * q^92 - 335452512 * q^94 - 50880210 * q^95 - 309841967 * q^97 + 1086972096 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more