LMFDB - Embedded newform 126.9.n.b.73.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,9,Mod(19,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("126.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	126.n (of order $6$, degree $2$, 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:	$51.3297048677$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 1771 x^{10} + 26038 x^{9} + 2442597 x^{8} + 26522276 x^{7} + 1175865280 x^{6} + \cdots + 36\!\cdots\!00 $ x^12 - 2x^11 + 1771x^10 + 26038x^9 + 2442597x^8 + 26522276x^7 + 1175865280x^6 + 6901058684x^5 + 370996492174x^4 + 1285719886320x^3 + 55526550982200x^2 - 240706289358000*x + 3600954063202500
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{10}\cdot 7^{3} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.3
Root			$-9.54988 - 16.5409i$ of defining polynomial
Character	$\chi$	$=$	126.73
Dual form			126.9.n.b.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(492.158 - 284.147i) q^{5} +(-1740.97 + 1653.43i) q^{7} +1448.15 q^{8} +O(q^{10})$	\(q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(492.158 - 284.147i) q^{5} +(-1740.97 + 1653.43i) q^{7} +1448.15 q^{8} +(-5568.13 - 3214.76i) q^{10} +(2955.55 - 5119.16i) q^{11} +25179.6i q^{13} +(26048.7 + 7704.68i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(-104275. - 60203.1i) q^{17} +(83372.9 - 48135.4i) q^{19} +72741.7i q^{20} -66876.5 q^{22} +(-16926.5 - 29317.5i) q^{23} +(-33833.0 + 58600.6i) q^{25} +(246709. - 142438. i) q^{26} +(-71863.4 - 298808. i) q^{28} +1.22707e6 q^{29} +(45522.3 + 26282.3i) q^{31} +(-92681.9 + 160530. i) q^{32} +1.36224e6i q^{34} +(-387011. + 1.30844e6i) q^{35} +(-987561. - 1.71051e6i) q^{37} +(-943257. - 544590. i) q^{38} +(712720. - 411489. i) q^{40} -1.61935e6i q^{41} +3.53140e6 q^{43} +(378310. + 655253. i) q^{44} +(-191501. + 331690. i) q^{46} +(4.62311e6 - 2.66916e6i) q^{47} +(297119. - 5.75714e6i) q^{49} +765555. q^{50} +(-2.79119e6 - 1.61150e6i) q^{52} +(4.32074e6 - 7.48374e6i) q^{53} -3.35925e6i q^{55} +(-2.52119e6 + 2.39443e6i) q^{56} +(-6.94133e6 - 1.20227e7i) q^{58} +(-1.61840e7 - 9.34384e6i) q^{59} +(-2.03359e7 + 1.17409e7i) q^{61} -594701. i q^{62} +2.09715e6 q^{64} +(7.15473e6 + 1.23924e7i) q^{65} +(1.83650e6 - 3.18091e6i) q^{67} +(1.33472e7 - 7.70600e6i) q^{68} +(1.50093e7 - 3.60974e6i) q^{70} -4.94930e7 q^{71} +(2.86830e6 + 1.65601e6i) q^{73} +(-1.11730e7 + 1.93522e7i) q^{74} +1.23227e7i q^{76} +(3.31868e6 + 1.37991e7i) q^{77} +(-3.73482e7 - 6.46889e7i) q^{79} +(-8.06351e6 - 4.65547e6i) q^{80} +(-1.58663e7 + 9.16044e6i) q^{82} -2.45717e7i q^{83} -6.84262e7 q^{85} +(-1.99766e7 - 3.46005e7i) q^{86} +(4.28009e6 - 7.41334e6i) q^{88} +(3.07386e7 - 1.77469e7i) q^{89} +(-4.16329e7 - 4.38369e7i) q^{91} +4.33317e6 q^{92} +(-5.23046e7 - 3.01981e7i) q^{94} +(2.73551e7 - 4.73804e7i) q^{95} -7.41535e7i q^{97} +(-5.80890e7 + 2.96561e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 768 q^{4} - 1674 q^{5} - 1308 q^{7}+O(q^{10}) $ 12 * q - 768 * q^4 - 1674 * q^5 - 1308 * q^7	$ 12 q - 768 q^{4} - 1674 q^{5} - 1308 q^{7} + 17664 q^{10} - 10302 q^{11} - 56832 q^{14} - 98304 q^{16} - 173178 q^{17} + 405978 q^{19} - 941568 q^{22} - 158934 q^{23} + 838668 q^{25} - 1958400 q^{26} - 255744 q^{28} + 4355256 q^{29} + 4520250 q^{31} + 5270790 q^{35} + 134214 q^{37} - 1278720 q^{38} - 2260992 q^{40} - 12961896 q^{43} - 1318656 q^{44} + 2345472 q^{46} - 18385002 q^{47} - 3659172 q^{49} - 2970624 q^{50} - 3369984 q^{52} + 16540506 q^{53} - 4325376 q^{56} + 9176064 q^{58} - 31163922 q^{59} - 85390158 q^{61} + 25165824 q^{64} + 46506264 q^{65} - 37750362 q^{67} + 22166784 q^{68} + 92031744 q^{70} - 45506424 q^{71} + 9414786 q^{73} - 58837248 q^{74} + 100614066 q^{77} + 59730294 q^{79} + 27426816 q^{80} - 93259776 q^{82} - 64652220 q^{85} + 15144960 q^{86} + 60260352 q^{88} - 323014482 q^{89} - 266861424 q^{91} + 40687104 q^{92} - 443440128 q^{94} + 175918350 q^{95} - 472166400 q^{98}+O(q^{100}) $ 12 * q - 768 * q^4 - 1674 * q^5 - 1308 * q^7 + 17664 * q^10 - 10302 * q^11 - 56832 * q^14 - 98304 * q^16 - 173178 * q^17 + 405978 * q^19 - 941568 * q^22 - 158934 * q^23 + 838668 * q^25 - 1958400 * q^26 - 255744 * q^28 + 4355256 * q^29 + 4520250 * q^31 + 5270790 * q^35 + 134214 * q^37 - 1278720 * q^38 - 2260992 * q^40 - 12961896 * q^43 - 1318656 * q^44 + 2345472 * q^46 - 18385002 * q^47 - 3659172 * q^49 - 2970624 * q^50 - 3369984 * q^52 + 16540506 * q^53 - 4325376 * q^56 + 9176064 * q^58 - 31163922 * q^59 - 85390158 * q^61 + 25165824 * q^64 + 46506264 * q^65 - 37750362 * q^67 + 22166784 * q^68 + 92031744 * q^70 - 45506424 * q^71 + 9414786 * q^73 - 58837248 * q^74 + 100614066 * q^77 + 59730294 * q^79 + 27426816 * q^80 - 93259776 * q^82 - 64652220 * q^85 + 15144960 * q^86 + 60260352 * q^88 - 323014482 * q^89 - 266861424 * q^91 + 40687104 * q^92 - 443440128 * q^94 + 175918350 * q^95 - 472166400 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−5.65685	−	9.79796i	−0.353553	−	0.612372i
$2$	−5.65685	−	9.79796i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−64.0000	+	110.851i	−0.250000	+	0.433013i
$5$	492.158	−	284.147i	0.787452	−	0.454636i	−0.0516126	−	0.998667i	$-0.516436\pi$
$5$	492.158	−	284.147i	0.787452	−	0.454636i	0.839065	+	0.544031i	$0.183103\pi$
$6$		0			0
$7$	−1740.97	+	1653.43i	−0.725100	+	0.688644i
$7$	−1740.97	+	1653.43i	−0.725100	+	0.688644i
$8$	1448.15			0.353553
$9$		0			0
$10$	−5568.13	−	3214.76i	−0.556813	−	0.321476i
$11$	2955.55	−	5119.16i	0.201868	−	0.349646i	−0.747262	−	0.664529i	$-0.768632\pi$
$11$	2955.55	−	5119.16i	0.201868	−	0.349646i	0.949130	+	0.314883i	$0.101965\pi$
$12$		0			0
$13$			25179.6i			0.881609i	0.897603	+	0.440805i	$0.145307\pi$
$13$			25179.6i			0.881609i	−0.897603	+	0.440805i	$0.854693\pi$
$14$	26048.7	+	7704.68i	0.678068	+	0.200559i
$15$		0			0
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	−104275.	−	60203.1i	−1.24849	−	0.720814i	−0.277679	−	0.960674i	$-0.589565\pi$
$17$	−104275.	−	60203.1i	−1.24849	−	0.720814i	−0.970808	+	0.239860i	$0.922899\pi$
$18$		0			0
$19$	83372.9	−	48135.4i	0.639750	−	0.369360i	−0.144768	−	0.989466i	$-0.546244\pi$
$19$	83372.9	−	48135.4i	0.639750	−	0.369360i	0.784518	+	0.620106i	$0.212910\pi$
$20$			72741.7i			0.454636i
$21$		0			0
$22$	−66876.5			−0.285485
$23$	−16926.5	−	29317.5i	−0.0604860	−	0.104765i	0.834197	−	0.551467i	$-0.185932\pi$
$23$	−16926.5	−	29317.5i	−0.0604860	−	0.104765i	−0.894683	+	0.446702i	$0.852598\pi$
$24$		0			0
$25$	−33833.0	+	58600.6i	−0.0866126	+	0.150017i
$26$	246709.	−	142438.i	0.539873	−	0.311696i
$27$		0			0
$28$	−71863.4	−	298808.i	−0.116916	−	0.486138i
$29$	1.22707e6			1.73491			0.867453	−	0.497519i	$-0.165756\pi$
$29$	1.22707e6			1.73491			0.867453	+	0.497519i	$0.165756\pi$
$30$		0			0
$31$	45522.3	+	26282.3i	0.0492921	+	0.0284588i	0.524444	−	0.851445i	$-0.324273\pi$
$31$	45522.3	+	26282.3i	0.0492921	+	0.0284588i	−0.475151	+	0.879904i	$0.657607\pi$
$32$	−92681.9	+	160530.i	−0.0883883	+	0.153093i
$33$		0			0
$34$			1.36224e6i			1.01939i
$35$	−387011.	+	1.30844e6i	−0.257900	+	0.871930i
$36$		0			0
$37$	−987561.	−	1.71051e6i	−0.526935	−	0.912678i	−0.999507	−	0.0313860i	$-0.990008\pi$
$37$	−987561.	−	1.71051e6i	−0.526935	−	0.912678i	0.472573	−	0.881292i	$-0.343325\pi$
$38$	−943257.	−	544590.i	−0.452372	−	0.261177i
$39$		0			0
$40$	712720.	−	411489.i	0.278406	−	0.160738i
$41$		−	1.61935e6i		−	0.573068i	−0.958070	−	0.286534i	$-0.907497\pi$
$41$		−	1.61935e6i		−	0.573068i	0.958070	−	0.286534i	$-0.0925031\pi$
$42$		0			0
$43$	3.53140e6			1.03294			0.516468	−	0.856306i	$-0.327246\pi$
$43$	3.53140e6			1.03294			0.516468	+	0.856306i	$0.327246\pi$
$44$	378310.	+	655253.i	0.100934	+	0.174823i
$45$		0			0
$46$	−191501.	+	331690.i	−0.0427701	+	0.0740799i
$47$	4.62311e6	−	2.66916e6i	0.947422	−	0.546994i	0.0551425	−	0.998478i	$-0.482439\pi$
$47$	4.62311e6	−	2.66916e6i	0.947422	−	0.546994i	0.892279	+	0.451484i	$0.149105\pi$
$48$		0			0
$49$	297119.	−	5.75714e6i	0.0515402	−	0.998671i
$50$	765555.			0.122489
$51$		0			0
$52$	−2.79119e6	−	1.61150e6i	−0.381748	−	0.220402i
$53$	4.32074e6	−	7.48374e6i	0.547589	−	0.948452i	−0.450850	−	0.892600i	$-0.648879\pi$
$53$	4.32074e6	−	7.48374e6i	0.547589	−	0.948452i	0.998439	−	0.0558524i	$-0.0177876\pi$
$54$		0			0
$55$		−	3.35925e6i		−	0.367106i
$56$	−2.52119e6	+	2.39443e6i	−0.256362	+	0.243472i
$57$		0			0
$58$	−6.94133e6	−	1.20227e7i	−0.613382	−	1.06241i
$59$	−1.61840e7	−	9.34384e6i	−1.33560	−	0.771112i	−0.349452	−	0.936954i	$-0.613632\pi$
$59$	−1.61840e7	−	9.34384e6i	−1.33560	−	0.771112i	−0.986152	+	0.165842i	$0.946966\pi$
$60$		0			0
$61$	−2.03359e7	+	1.17409e7i	−1.46874	+	0.847975i	−0.999386	−	0.0350379i	$-0.988845\pi$
$61$	−2.03359e7	+	1.17409e7i	−1.46874	+	0.847975i	−0.469349	+	0.883013i	$0.655511\pi$
$62$		−	594701.i		−	0.0402468i
$63$		0			0
$64$	2.09715e6			0.125000
$65$	7.15473e6	+	1.23924e7i	0.400811	+	0.694225i
$66$		0			0
$67$	1.83650e6	−	3.18091e6i	0.0911363	−	0.157853i	−0.816853	−	0.576846i	$-0.804283\pi$
$67$	1.83650e6	−	3.18091e6i	0.0911363	−	0.157853i	0.907990	+	0.418993i	$0.137617\pi$
$68$	1.33472e7	−	7.70600e6i	0.624243	−	0.360407i
$69$		0			0
$70$	1.50093e7	−	3.60974e6i	0.625127	−	0.150343i
$71$	−4.94930e7			−1.94765			−0.973824	−	0.227302i	$-0.927010\pi$
$71$	−4.94930e7			−1.94765			−0.973824	+	0.227302i	$0.927010\pi$
$72$		0			0
$73$	2.86830e6	+	1.65601e6i	0.101003	+	0.0583139i	0.549650	−	0.835395i	$-0.314761\pi$
$73$	2.86830e6	+	1.65601e6i	0.101003	+	0.0583139i	−0.448648	+	0.893709i	$0.648094\pi$
$74$	−1.11730e7	+	1.93522e7i	−0.372599	+	0.645361i
$75$		0			0
$76$			1.23227e7i			0.369360i
$77$	3.31868e6	+	1.37991e7i	0.0944067	+	0.392543i
$78$		0			0
$79$	−3.73482e7	−	6.46889e7i	−0.958873	−	1.66082i	−0.725245	−	0.688490i	$-0.758274\pi$
$79$	−3.73482e7	−	6.46889e7i	−0.958873	−	1.66082i	−0.233627	−	0.972326i	$-0.575060\pi$
$80$	−8.06351e6	−	4.65547e6i	−0.196863	−	0.113659i
$81$		0			0
$82$	−1.58663e7	+	9.16044e6i	−0.350931	+	0.202610i
$83$		−	2.45717e7i		−	0.517753i	−0.965910	−	0.258876i	$-0.916648\pi$
$83$		−	2.45717e7i		−	0.517753i	0.965910	−	0.258876i	$-0.0833522\pi$
$84$		0			0
$85$	−6.84262e7			−1.31083
$86$	−1.99766e7	−	3.46005e7i	−0.365198	−	0.632542i
$87$		0			0
$88$	4.28009e6	−	7.41334e6i	0.0713711	−	0.123618i
$89$	3.07386e7	−	1.77469e7i	0.489919	−	0.282855i	−0.234622	−	0.972087i	$-0.575385\pi$
$89$	3.07386e7	−	1.77469e7i	0.489919	−	0.282855i	0.724541	+	0.689232i	$0.242052\pi$
$90$		0			0
$91$	−4.16329e7	−	4.38369e7i	−0.607115	−	0.639255i
$92$	4.33317e6			0.0604860
$93$		0			0
$94$	−5.23046e7	−	3.01981e7i	−0.669928	−	0.386783i
$95$	2.73551e7	−	4.73804e7i	0.335849	−	0.581707i
$96$		0			0
$97$		−	7.41535e7i		−	0.837616i	−0.908075	−	0.418808i	$-0.862448\pi$
$97$		−	7.41535e7i		−	0.837616i	0.908075	−	0.418808i	$-0.137552\pi$
$98$	−5.80890e7	+	2.96561e7i	−0.629781	+	0.321522i
$99$		0			0
$100$	−4.33063e6	−	7.50087e6i	−0.0433063	−	0.0750087i
$101$	−8.06054e7	−	4.65376e7i	−0.774602	−	0.447217i	0.0599117	−	0.998204i	$-0.480918\pi$
$101$	−8.06054e7	−	4.65376e7i	−0.774602	−	0.447217i	−0.834514	+	0.550987i	$0.814251\pi$
$102$		0			0
$103$	1.75131e8	−	1.01112e8i	1.55602	−	0.898368i	0.558387	−	0.829580i	$-0.311420\pi$
$103$	1.75131e8	−	1.01112e8i	1.55602	−	0.898368i	0.997631	−	0.0687872i	$-0.0219130\pi$
$104$			3.64640e7i			0.311696i
$105$		0			0
$106$	−9.77672e7			−0.774408
$107$	−8.72092e7	−	1.51051e8i	−0.665315	−	1.15236i	−0.979200	−	0.202898i	$-0.934964\pi$
$107$	−8.72092e7	−	1.51051e8i	−0.665315	−	1.15236i	0.313885	−	0.949461i	$-0.398369\pi$
$108$		0			0
$109$	−1.40611e7	+	2.43546e7i	−0.0996127	+	0.172534i	−0.911524	−	0.411246i	$-0.865094\pi$
$109$	−1.40611e7	+	2.43546e7i	−0.0996127	+	0.172534i	0.811912	+	0.583780i	$0.198427\pi$
$110$	−3.29138e7	+	1.90028e7i	−0.224805	+	0.129791i
$111$		0			0
$112$	3.77225e7	+	1.11576e7i	0.239733	+	0.0709083i
$113$	−1.08325e7			−0.0664380			−0.0332190	−	0.999448i	$-0.510576\pi$
$113$	−1.08325e7			−0.0664380			−0.0332190	+	0.999448i	$0.510576\pi$
$114$		0			0
$115$	−1.66610e7	−	9.61922e6i	−0.0952597	−	0.0549982i
$116$	−7.85322e7	+	1.36022e8i	−0.433727	+	0.751236i
$117$		0			0
$118$			2.11427e8i			1.09052i
$119$	2.81081e8	−	6.76000e7i	1.40166	−	0.337100i
$120$		0			0
$121$	8.97089e7	+	1.55380e8i	0.418499	+	0.724861i
$122$	2.30074e8	+	1.32833e8i	1.03855	+	0.599609i
$123$		0			0
$124$	−5.82685e6	+	3.36414e6i	−0.0246461	+	0.0142294i
$125$			2.60444e8i			1.06678i
$126$		0			0
$127$	−1.46298e8			−0.562371			−0.281186	−	0.959653i	$-0.590728\pi$
$127$	−1.46298e8			−0.562371			−0.281186	+	0.959653i	$0.590728\pi$
$128$	−1.18633e7	−	2.05478e7i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	8.09465e7	−	1.40203e8i	0.283416	−	0.490891i
$131$	1.71536e8	−	9.90363e7i	0.582465	−	0.336286i	−0.179647	−	0.983731i	$-0.557496\pi$
$131$	1.71536e8	−	9.90363e7i	0.582465	−	0.336286i	0.762112	+	0.647445i	$0.224162\pi$
$132$		0			0
$133$	−6.55607e7	+	2.21654e8i	−0.209526	+	0.708383i
$134$	−4.15552e7			−0.128886
$135$		0			0
$136$	−1.51006e8	−	8.71834e7i	−0.441407	−	0.254846i
$137$	8.12797e7	−	1.40781e8i	0.230728	−	0.399632i	−0.727295	−	0.686325i	$-0.759223\pi$
$137$	8.12797e7	−	1.40781e8i	0.230728	−	0.399632i	0.958022	+	0.286693i	$0.0925560\pi$
$138$		0			0
$139$		−	4.08667e8i		−	1.09474i	−0.836892	−	0.547369i	$-0.815630\pi$
$139$		−	4.08667e8i		−	1.09474i	0.836892	−	0.547369i	$-0.184370\pi$
$140$	−1.20274e8	−	1.26641e8i	−0.313082	−	0.329656i
$141$		0			0
$142$	2.79975e8	+	4.84931e8i	0.688598	+	1.19269i
$143$	1.28899e8	+	7.44197e7i	0.308251	+	0.177969i
$144$		0			0
$145$	6.03910e8	−	3.48668e8i	1.36616	−	0.788750i
$146$		−	3.74713e7i		−	0.0824683i
$147$		0			0
$148$	2.52816e8			0.526935
$149$	−8.81970e7	−	1.52762e8i	−0.178940	−	0.309934i	0.762577	−	0.646897i	$-0.223934\pi$
$149$	−8.81970e7	−	1.52762e8i	−0.178940	−	0.309934i	−0.941518	+	0.336963i	$0.890600\pi$
$150$		0			0
$151$	−2.65985e8	+	4.60699e8i	−0.511622	+	0.886155i	0.488287	+	0.872683i	$0.337622\pi$
$151$	−2.65985e8	+	4.60699e8i	−0.511622	+	0.886155i	−0.999909	+	0.0134724i	$0.995711\pi$
$152$	1.20737e8	−	6.97075e7i	0.226186	−	0.130588i
$153$		0			0
$154$	1.16430e8	−	1.10576e8i	0.207005	−	0.196597i
$155$	2.98722e7			0.0517536
$156$		0			0
$157$	4.92648e8	+	2.84430e8i	0.810845	+	0.468142i	0.847249	−	0.531196i	$-0.178257\pi$
$157$	4.92648e8	+	2.84430e8i	0.810845	+	0.468142i	−0.0364042	+	0.999337i	$0.511590\pi$
$158$	−4.22546e8	+	7.31872e8i	−0.678026	+	1.17437i
$159$		0			0
$160$			1.05341e8i			0.160738i
$161$	7.79429e7	+	2.30540e7i	0.116004	+	0.0343117i
$162$		0			0
$163$	5.17985e7	+	8.97177e7i	0.0733782	+	0.127095i	0.900380	−	0.435105i	$-0.143289\pi$
$163$	5.17985e7	+	8.97177e7i	0.0733782	+	0.127095i	−0.827002	+	0.562199i	$0.809955\pi$
$164$	1.79507e8	+	1.03639e8i	0.248146	+	0.143267i
$165$		0			0
$166$	−2.40752e8	+	1.38998e8i	−0.317057	+	0.183053i
$167$		−	2.24426e8i		−	0.288541i	−0.989538	−	0.144270i	$-0.953917\pi$
$167$		−	2.24426e8i		−	0.288541i	0.989538	−	0.144270i	$-0.0460835\pi$
$168$		0			0
$169$	1.81716e8			0.222765
$170$	3.87077e8	+	6.70437e8i	0.463449	+	0.802717i
$171$		0			0
$172$	−2.26010e8	+	3.91460e8i	−0.258234	+	0.447274i
$173$	4.86992e8	−	2.81165e8i	0.543672	−	0.313889i	−0.202894	−	0.979201i	$-0.565035\pi$
$173$	4.86992e8	−	2.81165e8i	0.543672	−	0.313889i	0.746566	+	0.665311i	$0.231701\pi$
$174$		0			0
$175$	−3.79899e7	−	1.57962e8i	−0.0405057	−	0.168423i
$176$	−9.68475e7			−0.100934
$177$		0			0
$178$	−3.47768e8	−	2.00784e8i	−0.346425	−	0.200009i
$179$	4.49466e8	−	7.78498e8i	0.437809	−	0.758307i	−0.559711	−	0.828688i	$-0.689088\pi$
$179$	4.49466e8	−	7.78498e8i	0.437809	−	0.758307i	0.997520	+	0.0703804i	$0.0224213\pi$
$180$		0			0
$181$			1.85029e9i			1.72396i	0.506945	+	0.861979i	$0.330775\pi$
$181$			1.85029e9i			1.72396i	−0.506945	+	0.861979i	$0.669225\pi$
$182$	−1.94001e8	+	6.55896e8i	−0.176815	+	0.597791i
$183$		0			0
$184$	−2.45121e7	−	4.24563e7i	−0.0213850	−	0.0370400i
$185$	−9.72071e8	−	5.61225e8i	−0.829872	−	0.479127i
$186$		0			0
$187$	−6.16379e8	+	3.55867e8i	−0.504059	+	0.291019i
$188$			6.83304e8i			0.546994i
$189$		0			0
$190$	−6.18975e8			−0.474962
$191$	4.24840e8	+	7.35844e8i	0.319221	+	0.552907i	0.980326	−	0.197386i	$-0.0632454\pi$
$191$	4.24840e8	+	7.35844e8i	0.319221	+	0.552907i	−0.661105	+	0.750294i	$0.729912\pi$
$192$		0			0
$193$	1.28117e9	−	2.21906e9i	0.923377	−	1.59934i	0.129227	−	0.991615i	$-0.458750\pi$
$193$	1.28117e9	−	2.21906e9i	0.923377	−	1.59934i	0.794150	−	0.607721i	$-0.207916\pi$
$194$	−7.26553e8	+	4.19476e8i	−0.512933	+	0.296142i
$195$		0			0
$196$	6.19170e8	+	4.01393e8i	0.419552	+	0.271985i
$197$	5.98729e8			0.397526			0.198763	−	0.980048i	$-0.436308\pi$
$197$	5.98729e8			0.397526			0.198763	+	0.980048i	$0.436308\pi$
$198$		0			0
$199$	1.86878e9	+	1.07894e9i	1.19164	+	0.687994i	0.958679	−	0.284492i	$-0.0918248\pi$
$199$	1.86878e9	+	1.07894e9i	1.19164	+	0.687994i	0.232962	+	0.972486i	$0.425158\pi$
$200$	−4.89955e7	+	8.48627e7i	−0.0306222	+	0.0530392i
$201$		0			0
$202$			1.05302e9i			0.632460i
$203$	−2.13628e9	+	2.02887e9i	−1.25798	+	1.19473i
$204$		0			0
$205$	−4.60135e8	−	7.96977e8i	−0.260537	−	0.451263i
$206$	−1.98138e9	−	1.14395e9i	−1.10027	−	0.635242i
$207$		0			0
$208$	3.57273e8	−	2.06272e8i	0.190874	−	0.110201i
$209$		−	5.69066e8i		−	0.298248i
$210$		0			0
$211$	−8.51078e8			−0.429378			−0.214689	−	0.976682i	$-0.568874\pi$
$211$	−8.51078e8			−0.429378			−0.214689	+	0.976682i	$0.568874\pi$
$212$	5.53055e8	+	9.57919e8i	0.273795	+	0.474226i
$213$		0			0
$214$	−9.86659e8	+	1.70894e9i	−0.470448	+	0.814841i
$215$	1.73801e9	−	1.00344e9i	0.813388	−	0.469610i
$216$		0			0
$217$	−1.22709e8	+	2.95115e7i	−0.0553397	+	0.0133092i
$218$	3.18167e8			0.140874
$219$		0			0
$220$	3.72377e8	+	2.14992e8i	0.158961	+	0.0917764i
$221$	1.51589e9	−	2.62560e9i	0.635476	−	1.10068i
$222$		0			0
$223$		−	2.16526e9i		−	0.875571i	−0.899079	−	0.437785i	$-0.855763\pi$
$223$		−	2.16526e9i		−	0.875571i	0.899079	−	0.437785i	$-0.144237\pi$
$224$	−1.04069e8	−	4.32720e8i	−0.0413362	−	0.171876i
$225$		0			0
$226$	6.12781e7	+	1.06137e8i	0.0234894	+	0.0406848i
$227$	−3.02401e8	−	1.74591e8i	−0.113888	−	0.0657535i	0.441974	−	0.897028i	$-0.354278\pi$
$227$	−3.02401e8	−	1.74591e8i	−0.113888	−	0.0657535i	−0.555862	+	0.831275i	$0.687612\pi$
$228$		0			0
$229$	−2.78484e9	+	1.60783e9i	−1.01265	+	0.584653i	−0.911966	−	0.410266i	$-0.865436\pi$
$229$	−2.78484e9	+	1.60783e9i	−1.01265	+	0.584653i	−0.100682	+	0.994919i	$0.532103\pi$
$230$			2.17658e8i			0.0777792i
$231$		0			0
$232$	1.77698e9			0.613382
$233$	1.60950e9	+	2.78774e9i	0.546095	+	0.945864i	0.998537	+	0.0540705i	$0.0172196\pi$
$233$	1.60950e9	+	2.78774e9i	0.546095	+	0.945864i	−0.452442	+	0.891794i	$0.649447\pi$
$234$		0			0
$235$	1.51687e9	−	2.62729e9i	0.497366	−	0.861463i
$236$	2.07155e9	−	1.19601e9i	0.667802	−	0.385556i
$237$		0			0
$238$	−2.25237e9	−	2.37161e9i	−0.701993	−	0.739156i
$239$	−2.29096e9			−0.702143			−0.351071	−	0.936349i	$-0.614183\pi$
$239$	−2.29096e9			−0.702143			−0.351071	+	0.936349i	$0.614183\pi$
$240$		0			0
$241$	−4.75785e9	−	2.74695e9i	−1.41040	−	0.814296i	−0.414975	−	0.909833i	$-0.636210\pi$
$241$	−4.75785e9	−	2.74695e9i	−1.41040	−	0.814296i	−0.995426	+	0.0955370i	$0.969543\pi$
$242$	1.01494e9	−	1.75793e9i	0.295923	−	0.512554i
$243$		0			0
$244$		−	3.00568e9i		−	0.847975i
$245$	−1.48965e9	−	2.91785e9i	−0.413446	−	0.809838i
$246$		0			0
$247$	1.21203e9	+	2.09930e9i	0.325631	+	0.564010i
$248$	6.59233e7	+	3.80608e7i	0.0174274	+	0.0100617i
$249$		0			0
$250$	2.55182e9	−	1.47330e9i	0.653267	−	0.377164i
$251$		−	4.73267e9i		−	1.19237i	−0.802846	−	0.596186i	$-0.796682\pi$
$251$		−	4.73267e9i		−	1.19237i	0.802846	−	0.596186i	$-0.203318\pi$
$252$		0			0
$253$	−2.00108e8			−0.0488408
$254$	8.27585e8	+	1.43342e9i	0.198828	+	0.344381i
$255$		0			0
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	−2.26889e9	+	1.30994e9i	−0.520093	+	0.300276i	−0.736973	−	0.675923i	$-0.763745\pi$
$257$	−2.26889e9	+	1.30994e9i	−0.520093	+	0.300276i	0.216880	+	0.976198i	$0.430412\pi$
$258$		0			0
$259$	4.54751e9	+	1.34506e9i	1.01059	+	0.298912i
$260$	−1.83161e9			−0.400811
$261$		0			0
$262$	−1.94071e9	−	1.12047e9i	−0.411865	−	0.237790i
$263$	−9.08331e8	+	1.57328e9i	−0.189855	+	0.328838i	−0.945202	−	0.326487i	$-0.894135\pi$
$263$	−9.08331e8	+	1.57328e9i	−0.189855	+	0.328838i	0.755347	+	0.655325i	$0.227468\pi$
$264$		0			0
$265$		−	4.91091e9i		−	0.995814i
$266$	2.54262e9	−	6.11501e8i	0.507873	−	0.122143i
$267$		0			0
$268$	2.35072e8	+	4.07156e8i	0.0455682	+	0.0789264i
$269$	1.79083e9	+	1.03394e9i	0.342016	+	0.197463i	0.661163	−	0.750242i	$-0.270063\pi$
$269$	1.79083e9	+	1.03394e9i	0.342016	+	0.197463i	−0.319147	+	0.947705i	$0.603396\pi$
$270$		0			0
$271$	−1.44467e9	+	8.34079e8i	−0.267850	+	0.154643i	−0.627910	−	0.778286i	$-0.716089\pi$
$271$	−1.44467e9	+	8.34079e8i	−0.267850	+	0.154643i	0.360060	+	0.932929i	$0.382756\pi$
$272$			1.97274e9i			0.360407i
$273$		0			0
$274$	−1.83915e9			−0.326298
$275$	1.99991e8	+	3.46394e8i	0.0349686	+	0.0605675i
$276$		0			0
$277$	9.76261e8	−	1.69093e9i	0.165824	−	0.287215i	−0.771124	−	0.636685i	$-0.780305\pi$
$277$	9.76261e8	−	1.69093e9i	0.165824	−	0.287215i	0.936948	+	0.349470i	$0.113638\pi$
$278$	−4.00410e9	+	2.31177e9i	−0.670387	+	0.387048i
$279$		0			0
$280$	−5.60451e8	+	1.89482e9i	−0.0911813	+	0.308274i
$281$	3.24189e9			0.519963			0.259982	−	0.965614i	$-0.416283\pi$
$281$	3.24189e9			0.519963			0.259982	+	0.965614i	$0.416283\pi$
$282$		0			0
$283$	−9.76907e9	−	5.64018e9i	−1.52303	−	0.879320i	−0.999629	−	0.0272318i	$-0.991331\pi$
$283$	−9.76907e9	−	5.64018e9i	−1.52303	−	0.879320i	−0.523398	−	0.852088i	$-0.675336\pi$
$284$	3.16755e9	−	5.48636e9i	0.486912	−	0.843357i
$285$		0			0
$286$		−	1.68393e9i		−	0.251686i
$287$	2.67749e9	+	2.81924e9i	0.394639	+	0.415531i
$288$		0			0
$289$	3.76095e9	+	6.51416e9i	0.539146	+	0.933828i
$290$	−6.83246e9	−	3.94472e9i	−0.966018	−	0.557731i
$291$		0			0
$292$	−3.67142e8	+	2.11970e8i	−0.0505013	+	0.0291570i
$293$			2.00624e9i			0.272215i	0.990694	+	0.136108i	$0.0434593\pi$
$293$			2.00624e9i			0.272215i	−0.990694	+	0.136108i	$0.956541\pi$
$294$		0			0
$295$	−1.06201e10			−1.40230
$296$	−1.43014e9	−	2.47708e9i	−0.186300	−	0.322680i
$297$		0			0
$298$	−9.97835e8	+	1.72830e9i	−0.126530	+	0.219156i
$299$	7.38204e8	−	4.26202e8i	0.0923616	−	0.0533250i
$300$		0			0
$301$	−6.14805e9	+	5.83894e9i	−0.748982	+	0.711325i
$302$	6.01855e9			0.723543
$303$		0			0
$304$	−1.36598e9	−	7.88650e8i	−0.159938	−	0.0923400i
$305$	−6.67230e9	+	1.15568e10i	−0.771039	+	1.33548i
$306$		0			0
$307$			6.67089e9i			0.750983i	0.926826	+	0.375491i	$0.122526\pi$
$307$			6.67089e9i			0.750983i	−0.926826	+	0.375491i	$0.877474\pi$
$308$	−1.74204e9	−	5.15262e8i	−0.193578	−	0.0572565i
$309$		0			0
$310$	−1.68983e8	−	2.92687e8i	−0.0182976	−	0.0316925i
$311$	−4.72509e9	−	2.72803e9i	−0.505090	−	0.291614i	0.225723	−	0.974192i	$-0.427526\pi$
$311$	−4.72509e9	−	2.72803e9i	−0.505090	−	0.291614i	−0.730813	+	0.682578i	$0.760859\pi$
$312$		0			0
$313$	1.45428e10	−	8.39632e9i	1.51521	−	0.874805i	0.515366	−	0.856970i	$-0.327656\pi$
$313$	1.45428e10	−	8.39632e9i	1.51521	−	0.874805i	0.999841	−	0.0178355i	$-0.00567750\pi$
$314$		−	6.43592e9i		−	0.662052i
$315$		0			0
$316$	9.56113e9			0.958873
$317$	−4.76107e9	−	8.24642e9i	−0.471485	−	0.816636i	0.527983	−	0.849255i	$-0.322948\pi$
$317$	−4.76107e9	−	8.24642e9i	−0.471485	−	0.816636i	−0.999468	+	0.0326192i	$0.989615\pi$
$318$		0			0
$319$	3.62666e9	−	6.28155e9i	0.350222	−	0.606603i
$320$	1.03213e9	−	5.95900e8i	0.0984315	−	0.0568295i
$321$		0			0
$322$	−2.15030e8	−	8.94094e8i	−0.0200021	−	0.0831687i
$323$	−1.15916e10			−1.06496
$324$		0			0
$325$	−1.47554e9	−	8.51904e8i	−0.132257	−	0.0763585i
$326$	5.86033e8	−	1.01504e9i	0.0518862	−	0.0898695i
$327$		0			0
$328$		−	2.34507e9i		−	0.202610i
$329$	−3.63541e9	+	1.22909e10i	−0.310291	+	1.04906i
$330$		0			0
$331$	−2.57258e9	−	4.45585e9i	−0.214317	−	0.371209i	0.738744	−	0.673986i	$-0.235419\pi$
$331$	−2.57258e9	−	4.45585e9i	−0.214317	−	0.371209i	−0.953061	+	0.302778i	$0.902086\pi$
$332$	2.72380e9	+	1.57259e9i	0.224193	+	0.129438i
$333$		0			0
$334$	−2.19892e9	+	1.26954e9i	−0.176694	+	0.102015i
$335$		−	2.08735e9i		−	0.165735i
$336$		0			0
$337$	8.86100e9			0.687010			0.343505	−	0.939151i	$-0.388386\pi$
$337$	8.86100e9			0.687010			0.343505	+	0.939151i	$0.388386\pi$
$338$	−1.02794e9	−	1.78045e9i	−0.0787593	−	0.136415i
$339$		0			0
$340$	4.37928e9	−	7.58513e9i	0.327708	−	0.567607i
$341$	2.69087e8	−	1.55357e8i	0.0199010	−	0.0114898i
$342$		0			0
$343$	9.00177e9	+	1.05142e10i	0.650356	+	0.759629i
$344$	5.11402e9			0.365198
$345$		0			0
$346$	−5.50968e9	−	3.18102e9i	−0.384434	−	0.221953i
$347$	6.65626e9	−	1.15290e10i	0.459106	−	0.795194i	−0.539808	−	0.841788i	$-0.681503\pi$
$347$	6.65626e9	−	1.15290e10i	0.459106	−	0.795194i	0.998914	+	0.0465938i	$0.0148367\pi$
$348$		0			0
$349$			1.58409e10i			1.06777i	0.845557	+	0.533884i	$0.179268\pi$
$349$			1.58409e10i			1.06777i	−0.845557	+	0.533884i	$0.820732\pi$
$350$	−1.33280e9	+	1.26579e9i	−0.0888166	+	0.0843511i
$351$		0			0
$352$	5.47852e8	+	9.48908e8i	0.0356856	+	0.0618092i
$353$	−2.64000e9	−	1.52420e9i	−0.170022	−	0.0981621i	0.412574	−	0.910924i	$-0.364630\pi$
$353$	−2.64000e9	−	1.52420e9i	−0.170022	−	0.0981621i	−0.582596	+	0.812762i	$0.697963\pi$
$354$		0			0
$355$	−2.43584e10	+	1.40633e10i	−1.53368	+	0.885471i
$356$			4.54322e9i			0.282855i
$357$		0			0
$358$	−1.01703e10			−0.619155
$359$	1.53081e10	+	2.65144e10i	0.921602	+	1.59626i	0.796937	+	0.604062i	$0.206452\pi$
$359$	1.53081e10	+	2.65144e10i	0.921602	+	1.59626i	0.124665	+	0.992199i	$0.460215\pi$
$360$		0			0
$361$	−3.85775e9	+	6.68183e9i	−0.227146	+	0.393429i
$362$	1.81291e10	−	1.04668e10i	1.05570	−	0.609511i
$363$		0			0
$364$	7.52388e9	−	1.80949e9i	0.428584	−	0.103075i
$365$	1.88221e9			0.106046
$366$		0			0
$367$	1.40867e10	+	8.13298e9i	0.776508	+	0.448317i	0.835191	−	0.549960i	$-0.185357\pi$
$367$	1.40867e10	+	8.13298e9i	0.776508	+	0.448317i	−0.0586833	+	0.998277i	$0.518690\pi$
$368$	−2.77323e8	+	4.80338e8i	−0.0151215	+	0.0261912i
$369$		0			0
$370$			1.26991e10i			0.677588i
$371$	4.85161e9	+	2.01730e10i	0.256089	+	1.06482i
$372$		0			0
$373$	7.41142e9	+	1.28370e10i	0.382883	+	0.663173i	0.991473	−	0.130312i	$-0.0415980\pi$
$373$	7.41142e9	+	1.28370e10i	0.382883	+	0.663173i	−0.608590	+	0.793485i	$0.708265\pi$
$374$	6.97353e9	+	4.02617e9i	0.356424	+	0.205781i
$375$		0			0
$376$	6.69499e9	−	3.86535e9i	0.334964	−	0.193392i
$377$			3.08971e10i			1.52951i
$378$		0			0
$379$	2.49929e10			1.21132			0.605661	−	0.795723i	$-0.292909\pi$
$379$	2.49929e10			1.21132			0.605661	+	0.795723i	$0.292909\pi$
$380$	3.50145e9	+	6.06469e9i	0.167924	+	0.290853i
$381$		0			0
$382$	4.80651e9	−	8.32513e9i	0.225723	−	0.390964i
$383$	2.14081e10	−	1.23600e10i	0.994907	−	0.574410i	0.0881693	−	0.996106i	$-0.471898\pi$
$383$	2.14081e10	−	1.23600e10i	0.994907	−	0.574410i	0.906737	+	0.421696i	$0.138565\pi$
$384$		0			0
$385$	5.55429e9	+	5.84833e9i	0.252805	+	0.266188i
$386$	−2.89897e10			−1.30585
$387$		0			0
$388$	8.22001e9	+	4.74583e9i	0.362698	+	0.209404i
$389$	3.75530e9	−	6.50436e9i	0.164001	−	0.284058i	−0.772299	−	0.635259i	$-0.780893\pi$
$389$	3.75530e9	−	6.50436e9i	0.164001	−	0.284058i	0.936300	+	0.351201i	$0.114227\pi$
$390$		0			0
$391$			4.07610e9i			0.174397i
$392$	4.30274e8	−	8.33723e9i	0.0182222	−	0.353083i
$393$		0			0
$394$	−3.38693e9	−	5.86633e9i	−0.140547	−	0.243434i
$395$	−3.67624e10	−	2.12248e10i	−1.51013	−	0.871876i
$396$		0			0
$397$	3.43170e9	−	1.98129e9i	0.138149	−	0.0797603i	−0.429333	−	0.903146i	$-0.641251\pi$
$397$	3.43170e9	−	1.98129e9i	0.138149	−	0.0797603i	0.567481	+	0.823386i	$0.307918\pi$
$398$		−	2.44136e10i		−	0.972971i
$399$		0			0
$400$	1.10864e9			0.0433063
$401$	1.48221e10	+	2.56727e10i	0.573236	+	0.992874i	0.996231	+	0.0867417i	$0.0276455\pi$
$401$	1.48221e10	+	2.56727e10i	0.573236	+	0.992874i	−0.422995	+	0.906132i	$0.639021\pi$
$402$		0			0
$403$	−6.61779e8	+	1.14624e9i	−0.0250895	+	0.0434564i
$404$	1.03175e10	−	5.95681e9i	0.387301	−	0.223608i
$405$		0			0
$406$	3.19634e10	+	9.45415e9i	1.17638	+	0.347951i
$407$	−1.16751e10			−0.425485
$408$		0			0
$409$	−1.61493e10	−	9.32380e9i	−0.577113	−	0.333196i	0.182872	−	0.983137i	$-0.441460\pi$
$409$	−1.61493e10	−	9.32380e9i	−0.577113	−	0.333196i	−0.759985	+	0.649941i	$0.774794\pi$
$410$	−5.20583e9	+	9.01676e9i	−0.184228	+	0.319091i
$411$		0			0
$412$			2.58847e10i			0.898368i
$413$	4.36252e10	−	1.04919e10i	1.49947	−	0.360622i
$414$		0			0
$415$	−6.98197e9	−	1.20931e10i	−0.235389	−	0.407705i
$416$	−4.04208e9	−	2.33370e9i	−0.134968	−	0.0779240i
$417$		0			0
$418$	−5.57569e9	+	3.21912e9i	−0.182639	+	0.105447i
$419$		−	1.52395e9i		−	0.0494441i	−0.999694	−	0.0247221i	$-0.992130\pi$
$419$		−	1.52395e9i		−	0.0494441i	0.999694	−	0.0247221i	$-0.00787008\pi$
$420$		0			0
$421$	−2.02402e10			−0.644298			−0.322149	−	0.946689i	$-0.604405\pi$
$421$	−2.02402e10			−0.644298			−0.322149	+	0.946689i	$0.604405\pi$
$422$	4.81443e9	+	8.33883e9i	0.151808	+	0.262939i
$423$		0			0
$424$	6.25710e9	−	1.08376e10i	0.193602	−	0.335328i
$425$	7.05587e9	−	4.07371e9i	0.216269	−	0.124863i
$426$		0			0
$427$	1.59912e10	−	5.40645e10i	0.481028	−	1.62630i
$428$	2.23255e10			0.665315
$429$		0			0
$430$	−1.96633e10	−	1.13526e10i	−0.575152	−	0.332064i
$431$	3.19684e9	−	5.53708e9i	0.0926427	−	0.160462i	−0.815980	−	0.578081i	$-0.803802\pi$
$431$	3.19684e9	−	5.53708e9i	0.0926427	−	0.160462i	0.908622	+	0.417619i	$0.137135\pi$
$432$		0			0
$433$			3.18824e10i			0.906984i	0.891260	+	0.453492i	$0.149822\pi$
$433$			3.18824e10i			0.906984i	−0.891260	+	0.453492i	$0.850178\pi$
$434$	9.83298e8	+	1.03535e9i	0.0277157	+	0.0291830i
$435$		0			0
$436$	−1.79983e9	−	3.11739e9i	−0.0498063	−	0.0862671i
$437$	−2.82242e9	−	1.62952e9i	−0.0773919	−	0.0446822i
$438$		0			0
$439$	−7.29008e9	+	4.20893e9i	−0.196279	+	0.113322i	−0.594919	−	0.803786i	$-0.702816\pi$
$439$	−7.29008e9	+	4.20893e9i	−0.196279	+	0.113322i	0.398640	+	0.917108i	$0.369482\pi$
$440$		−	4.86471e9i		−	0.129791i
$441$		0			0
$442$	−3.43007e10			−0.898699
$443$	−1.90612e10	−	3.30150e10i	−0.494921	−	0.857229i	0.505062	−	0.863083i	$-0.331470\pi$
$443$	−1.90612e10	−	3.30150e10i	−0.494921	−	0.857229i	−0.999983	+	0.00585447i	$0.998136\pi$
$444$		0			0
$445$	1.00855e10	−	1.74686e10i	0.257192	−	0.445469i
$446$	−2.12152e10	+	1.22486e10i	−0.536175	+	0.309561i
$447$		0			0
$448$	−3.65107e9	+	3.46750e9i	−0.0906375	+	0.0860804i
$449$	1.76118e10			0.433330			0.216665	−	0.976246i	$-0.430482\pi$
$449$	1.76118e10			0.433330			0.216665	+	0.976246i	$0.430482\pi$
$450$		0			0
$451$	−8.28973e9	−	4.78608e9i	−0.200371	−	0.115684i
$452$	6.93283e8	−	1.20080e9i	0.0166095	−	0.0287685i
$453$		0			0
$454$			3.95054e9i			0.0929894i
$455$	−3.29461e10	−	9.74479e9i	−0.768702	−	0.227367i
$456$		0			0
$457$	2.74598e10	+	4.75617e10i	0.629553	+	1.09042i	0.987642	+	0.156730i	$0.0500952\pi$
$457$	2.74598e10	+	4.75617e10i	0.629553	+	1.09042i	−0.358089	+	0.933688i	$0.616571\pi$
$458$	3.15069e10	+	1.81905e10i	0.716050	+	0.413412i
$459$		0			0
$460$	2.13261e9	−	1.23126e9i	0.0476298	−	0.0274991i
$461$			3.01948e10i			0.668542i	0.942477	+	0.334271i	$0.108490\pi$
$461$			3.01948e10i			0.668542i	−0.942477	+	0.334271i	$0.891510\pi$
$462$		0			0
$463$	−1.01407e10			−0.220670			−0.110335	−	0.993894i	$-0.535192\pi$
$463$	−1.01407e10			−0.220670			−0.110335	+	0.993894i	$0.535192\pi$
$464$	−1.00521e10	−	1.74108e10i	−0.216863	−	0.375618i
$465$		0			0
$466$	1.82094e10	−	3.15397e10i	0.386147	−	0.668827i
$467$	−6.06931e10	+	3.50412e10i	−1.27606	+	0.736735i	−0.976122	−	0.217223i	$-0.930300\pi$
$467$	−6.06931e10	+	3.50412e10i	−1.27606	+	0.736735i	−0.299941	+	0.953958i	$0.596967\pi$
$468$		0			0
$469$	2.06214e9	+	8.57438e9i	0.0426213	+	0.177219i
$470$	−3.43228e10			−0.703382
$471$		0			0
$472$	−2.34369e10	−	1.35313e10i	−0.472208	−	0.272629i
$473$	1.04372e10	−	1.80778e10i	0.208517	−	0.361162i
$474$		0			0
$475$			6.51427e9i			0.127965i
$476$	−1.04956e10	+	3.54845e10i	−0.204447	+	0.691212i
$477$		0			0
$478$	1.29596e10	+	2.24467e10i	0.248245	+	0.429973i
$479$	−4.26270e10	−	2.46107e10i	−0.809735	−	0.467501i	0.0371288	−	0.999310i	$-0.488179\pi$
$479$	−4.26270e10	−	2.46107e10i	−0.809735	−	0.467501i	−0.846864	+	0.531810i	$0.821512\pi$
$480$		0			0
$481$	4.30699e10	−	2.48664e10i	0.804625	−	0.464551i
$482$			6.21563e10i			1.15159i
$483$		0			0
$484$	−2.29655e10			−0.418499
$485$	−2.10705e10	−	3.64952e10i	−0.380810	−	0.659583i
$486$		0			0
$487$	4.42360e10	−	7.66190e10i	0.786430	−	1.36214i	−0.141711	−	0.989908i	$-0.545260\pi$
$487$	4.42360e10	−	7.66190e10i	0.786430	−	1.36214i	0.928141	−	0.372229i	$-0.121406\pi$
$488$	−2.94495e10	+	1.70027e10i	−0.519276	+	0.299804i
$489$		0			0
$490$	−2.01622e10	+	3.11013e10i	−0.349747	+	0.539504i
$491$	−2.13831e8			−0.00367913			−0.00183957	−	0.999998i	$-0.500586\pi$
$491$	−2.13831e8			−0.00367913			−0.00183957	+	0.999998i	$0.500586\pi$
$492$		0			0
$493$	−1.27952e11	−	7.38732e10i	−2.16601	−	1.25054i
$494$	1.37126e10	−	2.37509e10i	0.230256	−	0.398815i
$495$		0			0
$496$		−	8.61219e8i		−	0.0142294i
$497$	8.61656e10	−	8.18334e10i	1.41224	−	1.34124i
$498$		0			0
$499$	−2.90208e10	−	5.02656e10i	−0.468067	−	0.810715i	0.531267	−	0.847204i	$-0.321716\pi$
$499$	−2.90208e10	−	5.02656e10i	−0.468067	−	0.810715i	−0.999334	+	0.0364889i	$0.988383\pi$
$500$	−2.88706e10	−	1.66684e10i	−0.461929	−	0.266695i
$501$		0			0
$502$	−4.63706e10	+	2.67720e10i	−0.730176	+	0.421567i
$503$		−	3.68913e10i		−	0.576304i	−0.957585	−	0.288152i	$-0.906959\pi$
$503$		−	3.68913e10i		−	0.576304i	0.957585	−	0.288152i	$-0.0930409\pi$
$504$		0			0
$505$	−5.28941e10			−0.813283
$506$	1.13198e9	+	1.96065e9i	0.0172678	+	0.0299087i
$507$		0			0
$508$	9.36306e9	−	1.62173e10i	0.140593	−	0.243514i
$509$	−9.82181e10	+	5.67062e10i	−1.46326	+	0.844811i	−0.999160	−	0.0409736i	$-0.986954\pi$
$509$	−9.82181e10	+	5.67062e10i	−1.46326	+	0.844811i	−0.464096	+	0.885785i	$0.653621\pi$
$510$		0			0
$511$	−7.73171e9	+	1.85948e9i	−0.113395	+	0.0272714i
$512$	3.03700e9			0.0441942
$513$		0			0
$514$	2.56696e10	+	1.48203e10i	0.367761	+	0.212327i
$515$	5.74615e10	−	9.95262e10i	0.816860	−	1.41484i
$516$		0			0
$517$		−	3.15553e10i		−	0.441683i
$518$	−1.25457e10	−	5.21652e10i	−0.174252	−	0.724539i
$519$		0			0
$520$	1.03612e10	+	1.79460e10i	0.141708	+	0.245446i
$521$	6.29055e10	+	3.63185e10i	0.853763	+	0.492920i	0.861919	−	0.507046i	$-0.169263\pi$
$521$	6.29055e10	+	3.63185e10i	0.853763	+	0.492920i	−0.00815564	+	0.999967i	$0.502596\pi$
$522$		0			0
$523$	−1.07742e11	+	6.22051e10i	−1.44006	+	0.831417i	−0.997853	−	0.0654973i	$-0.979137\pi$
$523$	−1.07742e11	+	6.22051e10i	−1.44006	+	0.831417i	−0.442204	+	0.896914i	$0.645803\pi$
$524$			2.53533e10i			0.336286i
$525$		0			0
$526$	2.05532e10			0.268495
$527$	−3.16455e9	−	5.48117e9i	−0.0410270	−	0.0710609i
$528$		0			0
$529$	3.85825e10	−	6.68268e10i	0.492683	−	0.853352i
$530$	−4.81169e10	+	2.77803e10i	−0.609809	+	0.352074i
$531$		0			0
$532$	−2.03747e10	−	2.14533e10i	−0.254357	−	0.267823i
$533$	4.07747e10			0.505222
$534$		0			0
$535$	−8.58413e10	−	4.95605e10i	−1.04781	−	0.604952i
$536$	2.65953e9	−	4.60645e9i	0.0322216	−	0.0558094i
$537$		0			0
$538$		−	2.33954e10i		−	0.279255i
$539$	−2.85936e10	−	1.85365e10i	−0.338777	−	0.219621i
$540$		0			0
$541$	2.79878e10	+	4.84764e10i	0.326723	+	0.565902i	0.981860	−	0.189609i	$-0.0607221\pi$
$541$	2.79878e10	+	4.84764e10i	0.326723	+	0.565902i	−0.655136	+	0.755511i	$0.727389\pi$
$542$	1.63446e10	+	9.43653e9i	0.189398	+	0.109349i
$543$		0			0
$544$	1.93288e10	−	1.11595e10i	0.220703	−	0.127423i
$545$			1.59817e10i			0.181150i
$546$		0			0
$547$	6.83882e10			0.763892			0.381946	−	0.924185i	$-0.375254\pi$
$547$	6.83882e10			0.763892			0.381946	+	0.924185i	$0.375254\pi$
$548$	1.04038e10	+	1.80199e10i	0.115364	+	0.199816i
$549$		0			0
$550$	2.26263e9	−	3.91900e9i	0.0247266	−	0.0428277i
$551$	1.02304e11	−	5.90653e10i	1.10991	−	0.640805i
$552$		0			0
$553$	1.71981e11	+	5.08685e10i	1.83899	+	0.543937i
$554$	−2.20903e10			−0.234510
$555$		0			0
$556$	4.53012e10	+	2.61547e10i	0.474035	+	0.273684i
$557$	−7.18130e10	+	1.24384e11i	−0.746075	+	1.29224i	0.203616	+	0.979051i	$0.434731\pi$
$557$	−7.18130e10	+	1.24384e11i	−0.746075	+	1.29224i	−0.949691	+	0.313189i	$0.898603\pi$
$558$		0			0
$559$			8.89195e10i			0.910646i
$560$	2.17358e10	−	5.22746e9i	0.221016	−	0.0531544i
$561$		0			0
$562$	−1.83389e10	−	3.17639e10i	−0.183835	−	0.318411i
$563$	−1.50338e10	−	8.67975e9i	−0.149635	−	0.0863920i	0.423313	−	0.905984i	$-0.360867\pi$
$563$	−1.50338e10	−	8.67975e9i	−0.149635	−	0.0863920i	−0.572948	+	0.819592i	$0.694200\pi$
$564$		0			0
$565$	−5.33132e9	+	3.07804e9i	−0.0523168	+	0.0302051i
$566$			1.27623e11i			1.24355i
$567$		0			0
$568$	−7.16736e10			−0.688598
$569$	−4.83337e10	−	8.37164e10i	−0.461106	−	0.798659i	0.537910	−	0.843002i	$-0.319214\pi$
$569$	−4.83337e10	−	8.37164e10i	−0.461106	−	0.798659i	−0.999016	+	0.0443429i	$0.985881\pi$
$570$		0			0
$571$	1.00793e10	−	1.74578e10i	0.0948165	−	0.164227i	−0.814716	−	0.579861i	$-0.803107\pi$
$571$	1.00793e10	−	1.74578e10i	0.0948165	−	0.164227i	0.909532	+	0.415634i	$0.136440\pi$
$572$	−1.64990e10	+	9.52572e9i	−0.154125	+	0.0889844i
$573$		0			0
$574$	1.24766e10	−	4.21820e10i	0.114934	−	0.388579i
$575$	2.29070e9			0.0209554
$576$		0			0
$577$	1.42798e10	+	8.24442e9i	0.128830	+	0.0743801i	0.563030	−	0.826436i	$-0.309636\pi$
$577$	1.42798e10	+	8.24442e9i	0.128830	+	0.0743801i	−0.434200	+	0.900817i	$0.642969\pi$
$578$	4.25503e10	−	7.36993e10i	0.381234	−	0.660316i
$579$		0			0
$580$			8.92589e10i			0.788750i
$581$	4.06276e10	+	4.27784e10i	0.356547	+	0.375422i
$582$		0			0
$583$	−2.55403e10	−	4.42372e10i	−0.221081	−	0.382924i
$584$	4.15374e9	+	2.39816e9i	0.0357098	+	0.0206171i
$585$		0			0
$586$	1.96571e10	−	1.13490e10i	0.166697	−	0.0962427i
$587$		−	1.98805e11i		−	1.67446i	−0.546848	−	0.837232i	$-0.684172\pi$
$587$		−	1.98805e11i		−	1.67446i	0.546848	−	0.837232i	$-0.315828\pi$
$588$		0			0
$589$	5.06043e9			0.0420462
$590$	6.00764e10	+	1.04055e11i	0.495788	+	0.858730i
$591$		0			0
$592$	−1.61802e10	+	2.80249e10i	−0.131734	+	0.228169i
$593$	−6.34438e10	+	3.66293e10i	−0.513063	+	0.296217i	−0.734092	−	0.679050i	$-0.762392\pi$
$593$	−6.34438e10	+	3.66293e10i	−0.513063	+	0.296217i	0.221029	+	0.975267i	$0.429058\pi$
$594$		0			0
$595$	1.19128e11	−	1.13138e11i	0.950484	−	0.902696i
$596$	2.25784e10			0.178940
$597$		0			0
$598$	−8.35182e9	−	4.82193e9i	−0.0653095	−	0.0377065i
$599$	5.16184e10	−	8.94057e10i	0.400956	−	0.694477i	−0.592885	−	0.805287i	$-0.702011\pi$
$599$	5.16184e10	−	8.94057e10i	0.400956	−	0.694477i	0.993842	+	0.110810i	$0.0353446\pi$
$600$		0			0
$601$			1.48749e11i			1.14014i	0.821598	+	0.570068i	$0.193083\pi$
$601$			1.48749e11i			1.14014i	−0.821598	+	0.570068i	$0.806917\pi$
$602$	9.19883e10	+	2.72083e10i	0.700401	+	0.207165i
$603$		0			0
$604$	−3.40461e10	−	5.89695e10i	−0.255811	−	0.443078i
$605$	8.83018e10	+	5.09811e10i	0.659095	+	0.380529i
$606$		0			0
$607$	−1.34656e11	+	7.77437e10i	−0.991907	+	0.572678i	−0.905844	−	0.423612i	$-0.860762\pi$
$607$	−1.34656e11	+	7.77437e10i	−0.991907	+	0.572678i	−0.0860632	+	0.996290i	$0.527429\pi$
$608$			1.78451e10i			0.130588i
$609$		0			0
$610$	1.50977e11			1.09041
$611$	6.72084e10	+	1.16408e11i	0.482235	+	0.835256i
$612$		0			0
$613$	8.43270e10	−	1.46059e11i	0.597207	−	1.03439i	−0.396024	−	0.918240i	$-0.629610\pi$
$613$	8.43270e10	−	1.46059e11i	0.597207	−	1.03439i	0.993231	−	0.116153i	$-0.0370563\pi$
$614$	6.53611e10	−	3.77362e10i	0.459881	−	0.265513i
$615$		0			0
$616$	4.80597e9	+	1.99832e10i	0.0333778	+	0.138785i
$617$	1.44523e11			0.997234			0.498617	−	0.866822i	$-0.333841\pi$
$617$	1.44523e11			0.997234			0.498617	+	0.866822i	$0.333841\pi$
$618$		0			0
$619$	−8.06793e9	−	4.65802e9i	−0.0549541	−	0.0317277i	0.472271	−	0.881453i	$-0.343434\pi$
$619$	−8.06793e9	−	4.65802e9i	−0.0549541	−	0.0317277i	−0.527225	+	0.849726i	$0.676768\pi$
$620$	−1.91182e9	+	3.31137e9i	−0.0129384	+	0.0224100i
$621$		0			0
$622$			6.17284e10i			0.412404i
$623$	−2.41715e10	+	8.17211e10i	−0.160454	+	0.542478i
$624$		0			0
$625$	6.07886e10	+	1.05289e11i	0.398384	+	0.690021i
$626$	−1.64534e11	−	9.49935e10i	−1.07141	−	0.618581i
$627$		0			0
$628$	−6.30589e10	+	3.64071e10i	−0.405423	+	0.234071i
$629$			2.37817e11i			1.51929i
$630$		0			0
$631$	7.06360e10			0.445563			0.222781	−	0.974868i	$-0.428486\pi$
$631$	7.06360e10			0.445563			0.222781	+	0.974868i	$0.428486\pi$
$632$	−5.40859e10	−	9.36796e10i	−0.339013	−	0.587187i
$633$		0			0
$634$	−5.38654e10	+	9.32976e10i	−0.333390	+	0.577449i
$635$	−7.20016e10	+	4.15701e10i	−0.442840	+	0.255674i
$636$		0			0
$637$	1.44963e11	+	7.48135e9i	0.880438	+	0.0454383i
$638$	−8.20618e10			−0.495289
$639$		0			0
$640$	−1.16772e10	−	6.74184e9i	−0.0696016	−	0.0401845i
$641$	8.56780e10	−	1.48399e11i	0.507501	−	0.879018i	−0.492461	−	0.870335i	$-0.663903\pi$
$641$	8.56780e10	−	1.48399e11i	0.507501	−	0.879018i	0.999962	−	0.00868351i	$-0.00276408\pi$
$642$		0			0
$643$			2.21436e11i			1.29540i	0.761894	+	0.647702i	$0.224270\pi$
$643$			2.21436e11i			1.29540i	−0.761894	+	0.647702i	$0.775730\pi$
$644$	−7.54391e9	+	7.16461e9i	−0.0438584	+	0.0416533i
$645$		0			0
$646$	6.55720e10	+	1.13574e11i	0.376520	+	0.652152i
$647$	−2.60129e11	−	1.50186e11i	−1.48447	−	0.857060i	−0.484627	−	0.874721i	$-0.661045\pi$
$647$	−2.60129e11	−	1.50186e11i	−1.48447	−	0.857060i	−0.999844	+	0.0176611i	$0.994378\pi$
$648$		0			0
$649$	−9.56653e10	+	5.52324e10i	−0.539232	+	0.311326i
$650$			1.92764e10i			0.107987i
$651$		0			0
$652$	−1.32604e10			−0.0733782
$653$	1.54212e10	+	2.67102e10i	0.0848134	+	0.146901i	0.905312	−	0.424748i	$-0.139637\pi$
$653$	1.54212e10	+	2.67102e10i	0.0848134	+	0.146901i	−0.820498	+	0.571649i	$0.806304\pi$
$654$		0			0
$655$	5.62818e10	−	9.74830e10i	0.305776	−	0.529619i
$656$	−2.29769e10	+	1.32657e10i	−0.124073	+	0.0716335i
$657$		0			0
$658$	1.40991e11	−	3.39083e10i	0.752121	−	0.180885i
$659$	5.20757e10			0.276117			0.138059	−	0.990424i	$-0.455914\pi$
$659$	5.20757e10			0.276117			0.138059	+	0.990424i	$0.455914\pi$
$660$		0			0
$661$	−3.25623e9	−	1.87999e9i	−0.0170573	−	0.00984803i	0.491447	−	0.870907i	$-0.336468\pi$
$661$	−3.25623e9	−	1.87999e9i	−0.0170573	−	0.00984803i	−0.508504	+	0.861059i	$0.669801\pi$
$662$	−2.91055e10	+	5.04121e10i	−0.151545	+	0.262484i
$663$		0			0
$664$		−	3.55836e10i		−	0.183053i
$665$	3.07161e10	+	1.27717e11i	0.157065	+	0.653076i
$666$		0			0
$667$	−2.07699e10	−	3.59745e10i	−0.104938	−	0.181757i
$668$	2.48779e10	+	1.43633e10i	0.124942	+	0.0721352i
$669$		0			0
$670$	−2.04517e10	+	1.18078e10i	−0.101492	+	0.0585963i
$671$			1.38804e11i			0.684716i
$672$		0			0
$673$	−5.59360e10			−0.272666			−0.136333	−	0.990663i	$-0.543532\pi$
$673$	−5.59360e10			−0.272666			−0.136333	+	0.990663i	$0.543532\pi$
$674$	−5.01254e10	−	8.68197e10i	−0.242895	−	0.420706i
$675$		0			0
$676$	−1.16298e10	+	2.01435e10i	−0.0556913	+	0.0964601i
$677$	5.03454e10	−	2.90669e10i	0.239665	−	0.138371i	−0.375358	−	0.926880i	$-0.622480\pi$
$677$	5.03454e10	−	2.90669e10i	0.239665	−	0.138371i	0.615023	+	0.788509i	$0.289147\pi$
$678$		0			0
$679$	1.22608e11	+	1.29099e11i	0.576819	+	0.607355i
$680$	−9.90918e10			−0.463449
$681$		0			0
$682$	−3.04437e9	−	1.75767e9i	−0.0140721	−	0.00812455i
$683$	−1.49556e11	+	2.59038e11i	−0.687259	+	1.19037i	0.285463	+	0.958390i	$0.407853\pi$
$683$	−1.49556e11	+	2.59038e11i	−0.687259	+	1.19037i	−0.972721	+	0.231977i	$0.925481\pi$
$684$		0			0
$685$		−	9.23816e10i		−	0.419588i
$686$	5.20964e10	−	1.47677e11i	0.235240	−	0.666830i
$687$		0			0
$688$	−2.89293e10	−	5.01069e10i	−0.129117	−	0.223637i
$689$	1.88438e11	+	1.08795e11i	0.836164	+	0.482760i
$690$		0			0
$691$	−1.91529e11	+	1.10579e11i	−0.840084	+	0.485022i	−0.857293	−	0.514829i	$-0.827855\pi$
$691$	−1.91529e11	+	1.10579e11i	−0.840084	+	0.485022i	0.0172091	+	0.999852i	$0.494522\pi$
$692$			7.19782e10i			0.313889i
$693$		0			0
$694$	−1.50614e11			−0.649273
$695$	−1.16122e11	−	2.01128e11i	−0.497707	−	0.862053i
$696$		0			0
$697$	−9.74901e10	+	1.68858e11i	−0.413075	+	0.715467i
$698$	1.55208e11	−	8.96095e10i	0.653872	−	0.377513i
$699$		0			0
$700$	1.99417e10	+	5.89835e9i	0.0830557	+	0.0245662i
$701$	−8.17785e10			−0.338662			−0.169331	−	0.985559i	$-0.554161\pi$
$701$	−8.17785e10			−0.338662			−0.169331	+	0.985559i	$0.554161\pi$
$702$		0			0
$703$	−1.64672e11	−	9.50732e10i	−0.674213	−	0.389257i
$704$	6.19824e9	−	1.07357e10i	0.0252335	−	0.0437057i
$705$		0			0
$706$			3.44888e10i			0.138822i
$707$	2.17278e11	−	5.22554e10i	0.869637	−	0.209148i
$708$		0			0
$709$	3.36982e10	+	5.83670e10i	0.133359	+	0.230984i	0.924969	−	0.380042i	$-0.124090\pi$
$709$	3.36982e10	+	5.83670e10i	0.133359	+	0.230984i	−0.791610	+	0.611026i	$0.790757\pi$
$710$	2.75584e11	+	1.59108e11i	1.08448	+	0.626122i
$711$		0			0
$712$	4.45143e10	−	2.57003e10i	0.173213	−	0.100004i
$713$		−	1.77947e9i		−	0.00688544i
$714$		0			0
$715$	8.45847e10			0.323644
$716$	5.75316e10	+	9.96477e10i	0.218904	+	0.379154i
$717$		0			0
$718$	1.73191e11	−	2.99976e11i	0.651671	−	1.12873i
$719$	−3.16071e11	+	1.82484e11i	−1.18269	+	0.682824i	−0.956634	−	0.291291i	$-0.905915\pi$
$719$	−3.16071e11	+	1.82484e11i	−1.18269	+	0.682824i	−0.226052	+	0.974115i	$0.572582\pi$
$720$		0			0
$721$	−1.37715e11	+	4.65600e11i	−0.509614	+	1.72295i
$722$	8.72910e10			0.321233
$723$		0			0
$724$	−2.05107e11	−	1.18419e11i	−0.746495	−	0.430989i
$725$	−4.15154e10	+	7.19068e10i	−0.150265	+	0.260266i
$726$		0			0
$727$		−	2.13030e11i		−	0.762613i	−0.924449	−	0.381306i	$-0.875474\pi$
$727$		−	2.13030e11i		−	0.762613i	0.924449	−	0.381306i	$-0.124526\pi$
$728$	−6.02908e10	−	6.34826e10i	−0.214647	−	0.226011i
$729$		0			0
$730$	−1.06474e10	−	1.84418e10i	−0.0374931	−	0.0649399i
$731$	−3.68237e11	−	2.12601e11i	−1.28961	−	0.744555i
$732$		0			0
$733$	2.17597e11	−	1.25630e11i	0.753768	−	0.435188i	−0.0732857	−	0.997311i	$-0.523349\pi$
$733$	2.17597e11	−	1.25630e11i	0.753768	−	0.435188i	0.827054	+	0.562123i	$0.190015\pi$
$734$		−	1.84028e11i		−	0.634016i
$735$		0			0
$736$	6.27511e9			0.0213850
$737$	−1.08557e10	−	1.88027e10i	−0.0367950	−	0.0637308i
$738$		0			0
$739$	1.78081e11	−	3.08445e11i	0.597089	−	1.03419i	−0.396160	−	0.918182i	$-0.629657\pi$
$739$	1.78081e11	−	3.08445e11i	0.597089	−	1.03419i	0.993248	−	0.116007i	$-0.0370094\pi$
$740$	1.24425e11	−	7.18369e10i	0.414936	−	0.239563i
$741$		0			0
$742$	1.70209e11	−	1.61652e11i	0.561523	−	0.533291i
$743$	−2.51055e11			−0.823785			−0.411893	−	0.911232i	$-0.635132\pi$
$743$	−2.51055e11			−0.823785			−0.411893	+	0.911232i	$0.635132\pi$
$744$		0			0
$745$	−8.68136e10	−	5.01219e10i	−0.281814	−	0.162705i
$746$	8.38506e10	−	1.45234e11i	0.270739	−	0.468934i
$747$		0			0
$748$		−	9.11019e10i		−	0.291019i
$749$	4.01580e11	+	1.18780e11i	1.27598	+	0.377411i
$750$		0			0
$751$	6.20249e10	+	1.07430e11i	0.194987	+	0.337728i	0.946896	−	0.321539i	$-0.104200\pi$
$751$	6.20249e10	+	1.07430e11i	0.194987	+	0.337728i	−0.751909	+	0.659267i	$0.770867\pi$
$752$	−7.57451e10	−	4.37315e10i	−0.236855	−	0.136749i
$753$		0			0
$754$	3.02728e11	−	1.74780e11i	0.936629	−	0.540763i
$755$			3.02316e11i			0.930407i
$756$		0			0
$757$	−2.18830e11			−0.666382			−0.333191	−	0.942859i	$-0.608125\pi$
$757$	−2.18830e11			−0.666382			−0.333191	+	0.942859i	$0.608125\pi$
$758$	−1.41381e11	−	2.44879e11i	−0.428267	−	0.741780i
$759$		0			0
$760$	3.96144e10	−	6.86141e10i	0.118740	−	0.205664i
$761$	−3.56127e11	+	2.05610e11i	−1.06186	+	0.613063i	−0.925945	−	0.377658i	$-0.876730\pi$
$761$	−3.56127e11	+	2.05610e11i	−1.06186	+	0.613063i	−0.135911	+	0.990721i	$0.543396\pi$
$762$		0			0
$763$	−1.57888e10	−	6.56497e10i	−0.0465854	−	0.193702i
$764$	−1.08759e11			−0.319221
$765$		0			0
$766$	−2.42205e11	−	1.39837e11i	−0.703505	−	0.406169i
$767$	2.35275e11	−	4.07507e11i	0.679819	−	1.17748i
$768$		0			0
$769$			4.43811e9i			0.0126909i	0.999980	+	0.00634545i	$0.00201983\pi$
$769$			4.43811e9i			0.0126909i	−0.999980	+	0.00634545i	$0.997980\pi$
$770$	2.58819e10	−	8.75039e10i	0.0736264	−	0.248923i
$771$		0			0
$772$	1.63990e11	+	2.84040e11i	0.461689	+	0.799668i
$773$	7.27675e10	+	4.20123e10i	0.203807	+	0.117668i	0.598430	−	0.801175i	$-0.295791\pi$
$773$	7.27675e10	+	4.20123e10i	0.203807	+	0.117668i	−0.394623	+	0.918843i	$0.629125\pi$
$774$		0			0
$775$	−3.08032e9	+	1.77842e9i	−0.00853863	+	0.00492978i
$776$		−	1.07386e11i		−	0.296142i
$777$		0			0
$778$	−8.49726e10			−0.231932
$779$	−7.79481e10	−	1.35010e11i	−0.211668	−	0.366620i
$780$		0			0
$781$	−1.46279e11	+	2.53363e11i	−0.393168	+	0.680987i
$782$	3.99375e10	−	2.30579e10i	0.106796	−	0.0616585i
$783$		0			0
$784$	−8.41218e10	+	4.29467e10i	−0.222661	+	0.113675i
$785$	3.23280e11			0.851336
$786$		0			0
$787$	−1.50839e11	−	8.70868e10i	−0.393200	−	0.227014i	0.290345	−	0.956922i	$-0.406230\pi$
$787$	−1.50839e11	−	8.70868e10i	−0.393200	−	0.227014i	−0.683546	+	0.729908i	$0.739563\pi$
$788$	−3.83187e10	+	6.63699e10i	−0.0993815	+	0.172134i
$789$		0			0
$790$			4.80262e11i			1.23302i
$791$	1.88591e10	−	1.79109e10i	0.0481742	−	0.0457521i
$792$		0			0
$793$	−2.95632e11	−	5.12050e11i	−0.747582	−	1.29485i
$794$	−3.88252e10	−	2.24158e10i	−0.0976860	−	0.0563990i
$795$		0			0
$796$	−2.39204e11	+	1.38104e11i	−0.595820	+	0.343997i
$797$		−	2.85416e11i		−	0.707368i	−0.935365	−	0.353684i	$-0.884929\pi$
$797$		−	2.85416e11i		−	0.707368i	0.935365	−	0.353684i	$-0.115071\pi$
$798$		0			0
$799$	−6.42766e11			−1.57712
$800$	−6.27142e9	−	1.08624e10i	−0.0153111	−	0.0265196i
$801$		0			0
$802$	1.67693e11	−	2.90453e11i	0.405339	−	0.702068i
$803$	1.69548e10	−	9.78886e9i	0.0407784	−	0.0235434i
$804$		0			0
$805$	4.49109e10	−	1.08011e10i	0.106947	−	0.0257208i
$806$	1.49744e10			0.0354820
$807$		0			0
$808$	−1.16729e11	−	6.73936e10i	−0.273863	−	0.158115i
$809$	−2.92767e10	+	5.07088e10i	−0.0683484	+	0.118383i	−0.898174	−	0.439639i	$-0.855106\pi$
$809$	−2.92767e10	+	5.07088e10i	−0.0683484	+	0.118383i	0.829826	+	0.558022i	$0.188440\pi$
$810$		0			0
$811$		−	3.15833e11i		−	0.730086i	−0.930991	−	0.365043i	$-0.881054\pi$
$811$		−	3.15833e11i		−	0.730086i	0.930991	−	0.365043i	$-0.118946\pi$
$812$	−8.81811e10	−	3.66657e11i	−0.202839	−	0.843404i
$813$		0			0
$814$	6.60446e10	+	1.14393e11i	0.150432	+	0.260555i
$815$	5.09861e10	+	2.94368e10i	0.115564	+	0.0667207i
$816$		0			0
$817$	2.94423e11	−	1.69985e11i	0.660821	−	0.381525i
$818$			2.10974e11i			0.471210i
$819$		0			0
$820$	1.17794e11			0.260537
$821$	1.56329e11	+	2.70770e11i	0.344086	+	0.595975i	0.985187	−	0.171481i	$-0.0548553\pi$
$821$	1.56329e11	+	2.70770e11i	0.344086	+	0.595975i	−0.641101	+	0.767457i	$0.721522\pi$
$822$		0			0
$823$	5.10476e10	−	8.84170e10i	0.111269	−	0.192724i	−0.805013	−	0.593257i	$-0.797842\pi$
$823$	5.10476e10	−	8.84170e10i	0.111269	−	0.192724i	0.916282	+	0.400533i	$0.131175\pi$
$824$	2.53617e11	−	1.46426e11i	0.550136	−	0.317621i
$825$		0			0
$826$	−3.49580e11	−	3.68087e11i	−0.750977	−	0.790734i
$827$	4.47639e11			0.956986			0.478493	−	0.878091i	$-0.341183\pi$
$827$	4.47639e11			0.956986			0.478493	+	0.878091i	$0.341183\pi$
$828$		0			0
$829$	1.86546e11	+	1.07702e11i	0.394973	+	0.228038i	0.684313	−	0.729189i	$-0.260102\pi$
$829$	1.86546e11	+	1.07702e11i	0.394973	+	0.228038i	−0.289340	+	0.957226i	$0.593436\pi$
$830$	−7.89920e10	+	1.36818e11i	−0.166445	+	0.288291i
$831$		0			0
$832$			5.28055e10i			0.110201i
$833$	−3.77580e11	+	5.82437e11i	−0.784203	+	1.20968i
$834$		0			0
$835$	−6.37700e10	−	1.10453e11i	−0.131181	−	0.227212i
$836$	6.30817e10	+	3.64202e10i	0.129145	+	0.0745620i
$837$		0			0
$838$	−1.49316e10	+	8.62076e9i	−0.0302782	+	0.0174811i
$839$		−	7.41073e11i		−	1.49559i	−0.663929	−	0.747796i	$-0.731112\pi$
$839$		−	7.41073e11i		−	1.49559i	0.663929	−	0.747796i	$-0.268888\pi$
$840$		0			0
$841$	1.00544e12			2.00990
$842$	1.14496e11	+	1.98313e11i	0.227794	+	0.394550i
$843$		0			0
$844$	5.44690e10	−	9.43431e10i	0.107344	−	0.185926i
$845$	8.94331e10	−	5.16342e10i	0.175417	−	0.101277i
$846$		0			0
$847$	−4.13091e11	−	1.22184e11i	−0.802624	−	0.237400i
$848$	−1.41582e11			−0.273795
$849$		0			0
$850$	−7.98281e10	−	4.60888e10i	−0.152926	−	0.0882916i
$851$	−3.34318e10	+	5.79056e10i	−0.0637444	+	0.110408i
$852$		0			0
$853$			6.71696e11i			1.26875i	0.773025	+	0.634376i	$0.218743\pi$
$853$			6.71696e11i			1.26875i	−0.773025	+	0.634376i	$0.781257\pi$
$854$	−6.20182e11	+	1.49154e11i	−1.16597	+	0.280416i
$855$		0			0
$856$	−1.26292e11	−	2.18745e11i	−0.235224	−	0.407420i
$857$	−6.38087e11	−	3.68399e11i	−1.18292	−	0.682961i	−0.226234	−	0.974073i	$-0.572641\pi$
$857$	−6.38087e11	−	3.68399e11i	−1.18292	−	0.682961i	−0.956689	+	0.291112i	$0.905975\pi$
$858$		0			0
$859$	1.28267e10	−	7.40553e9i	0.0235583	−	0.0136014i	−0.488175	−	0.872746i	$-0.662337\pi$
$859$	1.28267e10	−	7.40553e9i	0.0235583	−	0.0136014i	0.511733	+	0.859145i	$0.329004\pi$
$860$			2.56880e11i			0.469610i
$861$		0			0
$862$	−7.23362e10			−0.131017
$863$	1.53636e11	+	2.66105e11i	0.276980	+	0.479744i	0.970633	−	0.240566i	$-0.0773330\pi$
$863$	1.53636e11	+	2.66105e11i	0.276980	+	0.479744i	−0.693653	+	0.720310i	$0.744000\pi$
$864$		0			0
$865$	1.59785e11	−	2.76755e11i	0.285411	−	0.494346i
$866$	3.12382e11	−	1.80354e11i	0.555412	−	0.320667i
$867$		0			0
$868$	4.58198e9	−	1.54912e10i	0.00807187	−	0.0272901i
$869$	−4.41538e11			−0.774263
$870$		0			0
$871$	8.00942e10	+	4.62424e10i	0.139164	+	0.0803466i
$872$	−2.03627e10	+	3.52692e10i	−0.0352184	+	0.0610001i
$873$		0			0
$874$			3.68719e10i			0.0631902i
$875$	−4.30627e11	−	4.53425e11i	−0.734631	−	0.773522i
$876$		0			0
$877$	9.02694e10	+	1.56351e11i	0.152596	+	0.264303i	0.932181	−	0.361993i	$-0.117903\pi$
$877$	9.02694e10	+	1.56351e11i	0.152596	+	0.264303i	−0.779585	+	0.626296i	$0.784570\pi$
$878$	8.24778e10	+	4.76186e10i	0.138790	+	0.0801306i
$879$		0			0
$880$	−4.76642e10	+	2.75190e10i	−0.0794807	+	0.0458882i
$881$			6.42949e11i			1.06727i	0.845716	+	0.533633i	$0.179174\pi$
$881$			6.42949e11i			1.06727i	−0.845716	+	0.533633i	$0.820826\pi$
$882$		0			0
$883$	−3.92563e11			−0.645754			−0.322877	−	0.946441i	$-0.604650\pi$
$883$	−3.92563e11			−0.645754			−0.322877	+	0.946441i	$0.604650\pi$
$884$	1.94034e11	+	3.36077e11i	0.317738	+	0.550339i
$885$		0			0
$886$	−2.15653e11	+	3.73522e11i	−0.349962	+	0.606152i
$887$	3.07716e11	−	1.77660e11i	0.497113	−	0.287008i	−0.230407	−	0.973094i	$-0.574006\pi$
$887$	3.07716e11	−	1.77660e11i	0.497113	−	0.287008i	0.727521	+	0.686086i	$0.240673\pi$
$888$		0			0
$889$	2.54699e11	−	2.41894e11i	0.407775	−	0.387273i
$890$	−2.28209e11			−0.363724
$891$		0			0
$892$	2.40022e11	+	1.38577e11i	0.379133	+	0.218893i
$893$	2.56962e11	−	4.45071e11i	0.404076	−	0.699879i
$894$		0			0
$895$		−	5.10858e11i		−	0.796174i
$896$	5.46280e10	+	1.61579e10i	0.0847585	+	0.0250699i
$897$		0			0
$898$	−9.96275e10	−	1.72560e11i	−0.153205	−	0.265359i
$899$	5.58589e10	+	3.22501e10i	0.0855172	+	0.0493734i
$900$		0			0
$901$	−9.01089e11	+	5.20244e11i	−1.36732	+	0.789420i
$902$			1.08297e11i			0.163602i
$903$		0			0
$904$	−1.56872e10			−0.0234894
$905$	5.25756e11	+	9.10636e11i	0.783773	+	1.35753i
$906$		0			0
$907$	−2.88507e11	+	4.99710e11i	−0.426312	+	0.738395i	−0.996542	−	0.0830907i	$-0.973521\pi$
$907$	−2.88507e11	+	4.99710e11i	−0.426312	+	0.738395i	0.570230	+	0.821485i	$0.306854\pi$
$908$	3.87073e10	−	2.23477e10i	0.0569442	−	0.0328767i
$909$		0			0
$910$	9.08920e10	+	3.77929e11i	0.132544	+	0.551118i
$911$	−5.83597e11			−0.847305			−0.423652	−	0.905825i	$-0.639252\pi$
$911$	−5.83597e11			−0.847305			−0.423652	+	0.905825i	$0.639252\pi$
$912$		0			0
$913$	−1.25786e11	−	7.26228e10i	−0.181030	−	0.104518i
$914$	3.10672e11	−	5.38099e11i	0.445161	−	0.771042i
$915$		0			0
$916$		−	4.11604e11i		−	0.584653i
$917$	−1.34888e11	+	4.56042e11i	−0.190764	+	0.644952i
$918$		0			0
$919$	3.96096e11	+	6.86059e11i	0.555314	+	0.961833i	0.997879	+	0.0650961i	$0.0207354\pi$
$919$	3.96096e11	+	6.86059e11i	0.555314	+	0.961833i	−0.442565	+	0.896737i	$0.645931\pi$
$920$	−2.41277e10	−	1.39301e10i	−0.0336794	−	0.0194448i
$921$		0			0
$922$	2.95848e11	−	1.70808e11i	0.409397	−	0.236365i
$923$		−	1.24622e12i		−	1.71707i
$924$		0			0
$925$	1.33649e11			0.182557
$926$	5.73643e10	+	9.93578e10i	0.0780185	+	0.135132i
$927$		0			0
$928$	−1.13727e11	+	1.96981e11i	−0.153345	+	0.265602i
$929$	5.67196e11	−	3.27471e11i	0.761501	−	0.439653i	−0.0683336	−	0.997663i	$-0.521768\pi$
$929$	5.67196e11	−	3.27471e11i	0.761501	−	0.439653i	0.829834	+	0.558010i	$0.188435\pi$
$930$		0			0
$931$	−2.52350e11	−	4.94291e11i	−0.335896	−	0.657937i
$932$	−4.12033e11			−0.546095
$933$		0			0
$934$	6.86664e11	+	3.96446e11i	0.902313	+	0.520950i
$935$	−2.02237e11	+	3.50285e11i	−0.264615	+	0.458327i
$936$		0			0
$937$			1.23429e11i			0.160125i	0.996790	+	0.0800627i	$0.0255120\pi$
$937$			1.23429e11i			0.160125i	−0.996790	+	0.0800627i	$0.974488\pi$
$938$	7.23462e10	−	6.87088e10i	0.0934554	−	0.0887566i
$939$		0			0
$940$	1.94159e11	+	3.36293e11i	0.248683	+	0.430732i
$941$	−2.90756e11	−	1.67868e11i	−0.370826	−	0.214097i	0.302993	−	0.952993i	$-0.402014\pi$
$941$	−2.90756e11	−	1.67868e11i	−0.370826	−	0.214097i	−0.673819	+	0.738896i	$0.735347\pi$
$942$		0			0
$943$	−4.74753e10	+	2.74099e10i	−0.0600373	+	0.0346626i
$944$			3.06179e11i			0.385556i
$945$		0			0
$946$	−2.36168e11			−0.294887
$947$	2.86082e11	+	4.95509e11i	0.355706	+	0.616100i	0.987238	−	0.159249i	$-0.0509072\pi$
$947$	2.86082e11	+	4.95509e11i	0.355706	+	0.616100i	−0.631533	+	0.775349i	$0.717574\pi$
$948$		0			0
$949$	−4.16978e10	+	7.22227e10i	−0.0514101	+	0.0890449i
$950$	6.38265e10	−	3.68503e10i	0.0783622	−	0.0452424i
$951$		0			0
$952$	4.07048e11	−	9.78952e10i	0.495562	−	0.119183i
$953$	5.15910e11			0.625464			0.312732	−	0.949841i	$-0.398756\pi$
$953$	5.15910e11			0.625464			0.312732	+	0.949841i	$0.398756\pi$
$954$		0			0
$955$	4.18176e11	+	2.41434e11i	0.502743	+	0.290259i
$956$	1.46621e11	−	2.53955e11i	0.175536	−	0.304037i
$957$		0			0
$958$			5.56877e11i			0.661146i
$959$	9.12661e10	+	3.79485e11i	0.107903	+	0.448662i
$960$		0			0
$961$	−4.25064e11	−	7.36232e11i	−0.498380	−	0.863220i
$962$	−4.87280e11	−	2.81331e11i	−0.568956	−	0.328487i
$963$		0			0
$964$	6.09005e11	−	3.51609e11i	0.705201	−	0.407148i
$965$		−	1.45617e12i		−	1.67920i
$966$		0			0
$967$	1.27085e12			1.45341			0.726703	−	0.686952i	$-0.241052\pi$
$967$	1.27085e12			1.45341			0.726703	+	0.686952i	$0.241052\pi$
$968$	1.29912e11	+	2.25015e11i	0.147962	+	0.256277i
$969$		0			0
$970$	−2.38386e11	+	4.12896e11i	−0.269274	+	0.466395i
$971$	−1.28913e12	+	7.44277e11i	−1.45017	+	0.837255i	−0.998490	−	0.0549264i	$-0.982508\pi$
$971$	−1.28913e12	+	7.44277e11i	−1.45017	+	0.837255i	−0.451678	+	0.892181i	$0.649174\pi$
$972$		0			0
$973$	6.75703e11	+	7.11474e11i	0.753884	+	0.793794i
$974$	−1.00095e12			−1.11218
$975$		0			0
$976$	3.33183e11	+	1.92363e11i	0.367184	+	0.211994i
$977$	−4.09875e11	+	7.09924e11i	−0.449855	+	0.779172i	−0.998376	−	0.0569648i	$-0.981858\pi$
$977$	−4.09875e11	+	7.09924e11i	−0.449855	+	0.779172i	0.548521	+	0.836137i	$0.315191\pi$
$978$		0			0
$979$		−	2.09808e11i		−	0.228397i
$980$	4.18784e11	+	2.16129e10i	0.454032	+	0.0234320i
$981$		0			0
$982$	1.20961e9	+	2.09511e9i	0.00130077	+	0.00225300i
$983$	9.98852e11	+	5.76688e11i	1.06976	+	0.617627i	0.928116	−	0.372290i	$-0.121427\pi$
$983$	9.98852e11	+	5.76688e11i	1.06976	+	0.617627i	0.141645	+	0.989917i	$0.454761\pi$
$984$		0			0
$985$	2.94669e11	−	1.70127e11i	0.313033	−	0.180730i
$986$			1.67156e12i			1.76854i
$987$		0			0
$988$	−3.10280e11			−0.325631
$989$	−5.97742e10	−	1.03532e11i	−0.0624782	−	0.108215i
$990$		0			0
$991$	3.12577e11	−	5.41399e11i	0.324087	−	0.561336i	−0.657240	−	0.753681i	$-0.728276\pi$
$991$	3.12577e11	−	5.41399e11i	0.324087	−	0.561336i	0.981327	+	0.192346i	$0.0616095\pi$
$992$	−8.43818e9	+	4.87179e9i	−0.00871369	+	0.00503085i
$993$		0			0
$994$	−1.28923e12	−	3.81328e11i	−1.32064	−	0.390619i
$995$	1.22631e12			1.25115
$996$		0			0
$997$	1.54866e11	+	8.94122e10i	0.156739	+	0.0904932i	0.576318	−	0.817226i	$-0.304489\pi$
$997$	1.54866e11	+	8.94122e10i	0.156739	+	0.0904932i	−0.419579	+	0.907719i	$0.637822\pi$
$998$	−3.28333e11	+	5.68690e11i	−0.330973	+	0.573262i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.n.b.73.3		12
3.2	odd	2		14.9.d.a.3.5	✓	12
7.5	odd	6	inner	126.9.n.b.19.3		12
12.11	even	2		112.9.s.c.17.4		12
21.2	odd	6		98.9.d.b.19.5		12
21.5	even	6		14.9.d.a.5.5	yes	12
21.11	odd	6		98.9.b.c.97.4		12
21.17	even	6		98.9.b.c.97.3		12
21.20	even	2		98.9.d.b.31.5		12
84.47	odd	6		112.9.s.c.33.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.9.d.a.3.5	✓	12	3.2	odd	2
14.9.d.a.5.5	yes	12	21.5	even	6
98.9.b.c.97.3		12	21.17	even	6
98.9.b.c.97.4		12	21.11	odd	6
98.9.d.b.19.5		12	21.2	odd	6
98.9.d.b.31.5		12	21.20	even	2
112.9.s.c.17.4		12	12.11	even	2
112.9.s.c.33.4		12	84.47	odd	6
126.9.n.b.19.3		12	7.5	odd	6	inner
126.9.n.b.73.3		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(492.158 - 284.147i) q^{5} +(-1740.97 + 1653.43i) q^{7} +1448.15 q^{8} +O(q^{10})\)	\(q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(492.158 - 284.147i) q^{5} +(-1740.97 + 1653.43i) q^{7} +1448.15 q^{8} +(-5568.13 - 3214.76i) q^{10} +(2955.55 - 5119.16i) q^{11} +25179.6i q^{13} +(26048.7 + 7704.68i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(-104275. - 60203.1i) q^{17} +(83372.9 - 48135.4i) q^{19} +72741.7i q^{20} -66876.5 q^{22} +(-16926.5 - 29317.5i) q^{23} +(-33833.0 + 58600.6i) q^{25} +(246709. - 142438. i) q^{26} +(-71863.4 - 298808. i) q^{28} +1.22707e6 q^{29} +(45522.3 + 26282.3i) q^{31} +(-92681.9 + 160530. i) q^{32} +1.36224e6i q^{34} +(-387011. + 1.30844e6i) q^{35} +(-987561. - 1.71051e6i) q^{37} +(-943257. - 544590. i) q^{38} +(712720. - 411489. i) q^{40} -1.61935e6i q^{41} +3.53140e6 q^{43} +(378310. + 655253. i) q^{44} +(-191501. + 331690. i) q^{46} +(4.62311e6 - 2.66916e6i) q^{47} +(297119. - 5.75714e6i) q^{49} +765555. q^{50} +(-2.79119e6 - 1.61150e6i) q^{52} +(4.32074e6 - 7.48374e6i) q^{53} -3.35925e6i q^{55} +(-2.52119e6 + 2.39443e6i) q^{56} +(-6.94133e6 - 1.20227e7i) q^{58} +(-1.61840e7 - 9.34384e6i) q^{59} +(-2.03359e7 + 1.17409e7i) q^{61} -594701. i q^{62} +2.09715e6 q^{64} +(7.15473e6 + 1.23924e7i) q^{65} +(1.83650e6 - 3.18091e6i) q^{67} +(1.33472e7 - 7.70600e6i) q^{68} +(1.50093e7 - 3.60974e6i) q^{70} -4.94930e7 q^{71} +(2.86830e6 + 1.65601e6i) q^{73} +(-1.11730e7 + 1.93522e7i) q^{74} +1.23227e7i q^{76} +(3.31868e6 + 1.37991e7i) q^{77} +(-3.73482e7 - 6.46889e7i) q^{79} +(-8.06351e6 - 4.65547e6i) q^{80} +(-1.58663e7 + 9.16044e6i) q^{82} -2.45717e7i q^{83} -6.84262e7 q^{85} +(-1.99766e7 - 3.46005e7i) q^{86} +(4.28009e6 - 7.41334e6i) q^{88} +(3.07386e7 - 1.77469e7i) q^{89} +(-4.16329e7 - 4.38369e7i) q^{91} +4.33317e6 q^{92} +(-5.23046e7 - 3.01981e7i) q^{94} +(2.73551e7 - 4.73804e7i) q^{95} -7.41535e7i q^{97} +(-5.80890e7 + 2.96561e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 768 q^{4} - 1674 q^{5} - 1308 q^{7}+O(q^{10}) \) 12 * q - 768 * q^4 - 1674 * q^5 - 1308 * q^7	\( 12 q - 768 q^{4} - 1674 q^{5} - 1308 q^{7} + 17664 q^{10} - 10302 q^{11} - 56832 q^{14} - 98304 q^{16} - 173178 q^{17} + 405978 q^{19} - 941568 q^{22} - 158934 q^{23} + 838668 q^{25} - 1958400 q^{26} - 255744 q^{28} + 4355256 q^{29} + 4520250 q^{31} + 5270790 q^{35} + 134214 q^{37} - 1278720 q^{38} - 2260992 q^{40} - 12961896 q^{43} - 1318656 q^{44} + 2345472 q^{46} - 18385002 q^{47} - 3659172 q^{49} - 2970624 q^{50} - 3369984 q^{52} + 16540506 q^{53} - 4325376 q^{56} + 9176064 q^{58} - 31163922 q^{59} - 85390158 q^{61} + 25165824 q^{64} + 46506264 q^{65} - 37750362 q^{67} + 22166784 q^{68} + 92031744 q^{70} - 45506424 q^{71} + 9414786 q^{73} - 58837248 q^{74} + 100614066 q^{77} + 59730294 q^{79} + 27426816 q^{80} - 93259776 q^{82} - 64652220 q^{85} + 15144960 q^{86} + 60260352 q^{88} - 323014482 q^{89} - 266861424 q^{91} + 40687104 q^{92} - 443440128 q^{94} + 175918350 q^{95} - 472166400 q^{98}+O(q^{100}) \) 12 * q - 768 * q^4 - 1674 * q^5 - 1308 * q^7 + 17664 * q^10 - 10302 * q^11 - 56832 * q^14 - 98304 * q^16 - 173178 * q^17 + 405978 * q^19 - 941568 * q^22 - 158934 * q^23 + 838668 * q^25 - 1958400 * q^26 - 255744 * q^28 + 4355256 * q^29 + 4520250 * q^31 + 5270790 * q^35 + 134214 * q^37 - 1278720 * q^38 - 2260992 * q^40 - 12961896 * q^43 - 1318656 * q^44 + 2345472 * q^46 - 18385002 * q^47 - 3659172 * q^49 - 2970624 * q^50 - 3369984 * q^52 + 16540506 * q^53 - 4325376 * q^56 + 9176064 * q^58 - 31163922 * q^59 - 85390158 * q^61 + 25165824 * q^64 + 46506264 * q^65 - 37750362 * q^67 + 22166784 * q^68 + 92031744 * q^70 - 45506424 * q^71 + 9414786 * q^73 - 58837248 * q^74 + 100614066 * q^77 + 59730294 * q^79 + 27426816 * q^80 - 93259776 * q^82 - 64652220 * q^85 + 15144960 * q^86 + 60260352 * q^88 - 323014482 * q^89 - 266861424 * q^91 + 40687104 * q^92 - 443440128 * q^94 + 175918350 * q^95 - 472166400 * q^98

Introduction

L-functions

Modular forms

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Database

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