LMFDB - Embedded newform 126.8.g.j.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,8,Mod(37,126)]

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, 2]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, 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:	$39.3605132110$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 1111x^{4} + 2838x^{3} + 1231236x^{2} + 959040x + 746496 $ x^6 - x^5 + 1111x^4 + 2838x^3 + 1231236x^2 + 959040x + 746496
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$17.0987 + 29.6158i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.8.g.j.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-270.204 + 468.008i) q^{5} +(659.910 + 622.946i) q^{7} -512.000 q^{8} +(2161.63 + 3744.06i) q^{10} +(338.422 + 586.164i) q^{11} +6647.80 q^{13} +(6955.54 - 2080.21i) q^{14} +(-2048.00 + 3547.24i) q^{16} +(-17575.9 - 30442.3i) q^{17} +(-10974.1 + 19007.6i) q^{19} +34586.2 q^{20} +5414.75 q^{22} +(-39175.3 + 67853.6i) q^{23} +(-106958. - 185257. i) q^{25} +(26591.2 - 46057.3i) q^{26} +(13410.0 - 56510.2i) q^{28} -73873.3 q^{29} +(-56981.5 - 98694.8i) q^{31} +(16384.0 + 28377.9i) q^{32} -281214. q^{34} +(-469854. + 140520. i) q^{35} +(-55212.8 + 95631.3i) q^{37} +(87792.5 + 152061. i) q^{38} +(138345. - 239620. i) q^{40} -162278. q^{41} +398919. q^{43} +(21659.0 - 37514.5i) q^{44} +(313402. + 542829. i) q^{46} +(80171.0 - 138860. i) q^{47} +(47419.7 + 822177. i) q^{49} -1.71133e6 q^{50} +(-212730. - 368458. i) q^{52} +(285179. + 493944. i) q^{53} -365772. q^{55} +(-337874. - 318948. i) q^{56} +(-295493. + 511809. i) q^{58} +(-1.28729e6 - 2.22966e6i) q^{59} +(1.29277e6 - 2.23915e6i) q^{61} -911704. q^{62} +262144. q^{64} +(-1.79626e6 + 3.11122e6i) q^{65} +(-468389. - 811274. i) q^{67} +(-1.12486e6 + 1.94831e6i) q^{68} +(-905863. + 3.81733e6i) q^{70} -3.67843e6 q^{71} +(-2.06289e6 - 3.57304e6i) q^{73} +(441702. + 765051. i) q^{74} +1.40468e6 q^{76} +(-141820. + 597634. i) q^{77} +(-3.69473e6 + 6.39946e6i) q^{79} +(-1.10676e6 - 1.91696e6i) q^{80} +(-649114. + 1.12430e6i) q^{82} -6.43368e6 q^{83} +1.89963e7 q^{85} +(1.59568e6 - 2.76379e6i) q^{86} +(-173272. - 300116. i) q^{88} +(-3.18608e6 + 5.51845e6i) q^{89} +(4.38695e6 + 4.14122e6i) q^{91} +5.01444e6 q^{92} +(-641368. - 1.11088e6i) q^{94} +(-5.93048e6 - 1.02719e7i) q^{95} -1.59546e7 q^{97} +(5.88589e6 + 2.96017e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 24 q^{2} - 192 q^{4} - 718 q^{5} - 1471 q^{7} - 3072 q^{8} + 5744 q^{10} + 208 q^{11} + 19394 q^{13} - 4504 q^{14} - 12288 q^{16} - 19244 q^{17} - 25419 q^{19} + 91904 q^{20} + 3328 q^{22} - 67400 q^{23}+ \cdots + 20461248 q^{98}+O(q^{100}) $ 6 * q + 24 * q^2 - 192 * q^4 - 718 * q^5 - 1471 * q^7 - 3072 * q^8 + 5744 * q^10 + 208 * q^11 + 19394 * q^13 - 4504 * q^14 - 12288 * q^16 - 19244 * q^17 - 25419 * q^19 + 91904 * q^20 + 3328 * q^22 - 67400 * q^23 - 93931 * q^25 + 77576 * q^26 + 58112 * q^28 + 33476 * q^29 + 78449 * q^31 + 98304 * q^32 - 307904 * q^34 - 602072 * q^35 - 496599 * q^37 + 203352 * q^38 + 367616 * q^40 + 1953168 * q^41 + 697470 * q^43 + 13312 * q^44 + 539200 * q^46 + 701328 * q^47 + 959673 * q^49 - 1502896 * q^50 - 620608 * q^52 + 2917374 * q^53 - 3275696 * q^55 + 753152 * q^56 + 133904 * q^58 - 492040 * q^59 + 3649370 * q^61 + 1255184 * q^62 + 1572864 * q^64 - 2707764 * q^65 - 3647153 * q^67 - 1231616 * q^68 - 503936 * q^70 + 3541216 * q^71 - 6183557 * q^73 + 3972792 * q^74 + 3253632 * q^76 + 13092290 * q^77 - 12453589 * q^79 - 2940928 * q^80 + 7812672 * q^82 + 11611120 * q^83 + 38154616 * q^85 + 2789880 * q^86 - 106496 * q^88 - 8292612 * q^89 + 366581 * q^91 + 8627200 * q^92 - 5610624 * q^94 - 8691056 * q^95 - 55949528 * q^97 + 20461248 * q^98

Character values

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

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	−270.204	+	468.008i	−0.966712	+	1.67440i	−0.261771	+	0.965130i	$0.584306\pi$
$5$	−270.204	+	468.008i	−0.966712	+	1.67440i	−0.704942	+	0.709265i	$0.749027\pi$
$6$		0			0
$7$	659.910	+	622.946i	0.727180	+	0.686447i
$7$	659.910	+	622.946i	0.727180	+	0.686447i
$8$	−512.000			−0.353553
$9$		0			0
$10$	2161.63	+	3744.06i	0.683569	+	1.18398i
$11$	338.422	+	586.164i	0.0766627	+	0.132784i	0.901808	−	0.432137i	$-0.142240\pi$
$11$	338.422	+	586.164i	0.0766627	+	0.132784i	−0.825145	+	0.564920i	$0.808907\pi$
$12$		0			0
$13$	6647.80			0.839220			0.419610	−	0.907704i	$-0.362167\pi$
$13$	6647.80			0.839220			0.419610	+	0.907704i	$0.362167\pi$
$14$	6955.54	−	2080.21i	0.677458	−	0.202609i
$15$		0			0
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	−17575.9	−	30442.3i	−0.867652	−	1.50282i	−0.864390	−	0.502822i	$-0.832295\pi$
$17$	−17575.9	−	30442.3i	−0.867652	−	1.50282i	−0.00326212	−	0.999995i	$-0.501038\pi$
$18$		0			0
$19$	−10974.1	+	19007.6i	−0.367054	+	0.635756i	−0.989104	−	0.147222i	$-0.952967\pi$
$19$	−10974.1	+	19007.6i	−0.367054	+	0.635756i	0.622049	+	0.782978i	$0.286300\pi$
$20$	34586.2			0.966712
$21$		0			0
$22$	5414.75			0.108417
$23$	−39175.3	+	67853.6i	−0.671374	+	1.16285i	0.306140	+	0.951986i	$0.400962\pi$
$23$	−39175.3	+	67853.6i	−0.671374	+	1.16285i	−0.977515	+	0.210868i	$0.932371\pi$
$24$		0			0
$25$	−106958.	−	185257.i	−1.36907	−	2.37129i
$26$	26591.2	−	46057.3i	0.296709	−	0.513915i
$27$		0			0
$28$	13410.0	−	56510.2i	0.115446	−	0.486490i
$29$	−73873.3			−0.562464			−0.281232	−	0.959640i	$-0.590743\pi$
$29$	−73873.3			−0.562464			−0.281232	+	0.959640i	$0.590743\pi$
$30$		0			0
$31$	−56981.5	−	98694.8i	−0.343533	−	0.595016i	0.641553	−	0.767078i	$-0.278290\pi$
$31$	−56981.5	−	98694.8i	−0.343533	−	0.595016i	−0.985086	+	0.172062i	$0.944957\pi$
$32$	16384.0	+	28377.9i	0.0883883	+	0.153093i
$33$		0			0
$34$	−281214.			−1.22705
$35$	−469854.	+	140520.i	−1.85236	+	0.553989i
$36$		0			0
$37$	−55212.8	+	95631.3i	−0.179198	+	0.310380i	−0.941606	−	0.336716i	$-0.890684\pi$
$37$	−55212.8	+	95631.3i	−0.179198	+	0.310380i	0.762408	+	0.647097i	$0.224017\pi$
$38$	87792.5	+	152061.i	0.259546	+	0.449548i
$39$		0			0
$40$	138345.	−	239620.i	0.341784	−	0.591988i
$41$	−162278.			−0.367720			−0.183860	−	0.982952i	$-0.558859\pi$
$41$	−162278.			−0.367720			−0.183860	+	0.982952i	$0.558859\pi$
$42$		0			0
$43$	398919.			0.765147			0.382574	−	0.923925i	$-0.375038\pi$
$43$	398919.			0.765147			0.382574	+	0.923925i	$0.375038\pi$
$44$	21659.0	−	37514.5i	0.0383313	−	0.0663918i
$45$		0			0
$46$	313402.	+	542829.i	0.474733	+	0.822262i
$47$	80171.0	−	138860.i	0.112635	−	0.195090i	−0.804197	−	0.594363i	$-0.797404\pi$
$47$	80171.0	−	138860.i	0.112635	−	0.195090i	0.916832	+	0.399273i	$0.130737\pi$
$48$		0			0
$49$	47419.7	+	822177.i	0.0575801	+	0.998341i
$50$	−1.71133e6			−1.93615
$51$		0			0
$52$	−212730.	−	368458.i	−0.209805	−	0.363393i
$53$	285179.	+	493944.i	0.263119	+	0.455735i	0.967069	−	0.254514i	$-0.0819155\pi$
$53$	285179.	+	493944.i	0.263119	+	0.455735i	−0.703950	+	0.710249i	$0.748582\pi$
$54$		0			0
$55$	−365772.			−0.296443
$56$	−337874.	−	318948.i	−0.257097	−	0.242696i
$57$		0			0
$58$	−295493.	+	511809.i	−0.198861	+	0.344437i
$59$	−1.28729e6	−	2.22966e6i	−0.816011	−	1.41337i	−0.908600	−	0.417668i	$-0.862848\pi$
$59$	−1.28729e6	−	2.22966e6i	−0.816011	−	1.41337i	0.0925891	−	0.995704i	$-0.470486\pi$
$60$		0			0
$61$	1.29277e6	−	2.23915e6i	0.729235	−	1.26307i	−0.227971	−	0.973668i	$-0.573209\pi$
$61$	1.29277e6	−	2.23915e6i	0.729235	−	1.26307i	0.957207	−	0.289405i	$-0.0934574\pi$
$62$	−911704.			−0.485828
$63$		0			0
$64$	262144.			0.125000
$65$	−1.79626e6	+	3.11122e6i	−0.811285	+	1.40519i
$66$		0			0
$67$	−468389.	−	811274.i	−0.190259	−	0.329538i	0.755077	−	0.655636i	$-0.227599\pi$
$67$	−468389.	−	811274.i	−0.190259	−	0.329538i	−0.945336	+	0.326098i	$0.894266\pi$
$68$	−1.12486e6	+	1.94831e6i	−0.433826	+	0.751409i
$69$		0			0
$70$	−905863.	+	3.81733e6i	−0.315660	+	1.33020i
$71$	−3.67843e6			−1.21972			−0.609858	−	0.792511i	$-0.708773\pi$
$71$	−3.67843e6			−1.21972			−0.609858	+	0.792511i	$0.708773\pi$
$72$		0			0
$73$	−2.06289e6	−	3.57304e6i	−0.620650	−	1.07500i	−0.989365	−	0.145455i	$-0.953535\pi$
$73$	−2.06289e6	−	3.57304e6i	−0.620650	−	1.07500i	0.368714	−	0.929543i	$-0.379798\pi$
$74$	441702.	+	765051.i	0.126712	+	0.219472i
$75$		0			0
$76$	1.40468e6			0.367054
$77$	−141820.	+	597634.i	−0.0354014	+	0.149182i
$78$		0			0
$79$	−3.69473e6	+	6.39946e6i	−0.843117	+	1.46032i	0.0441286	+	0.999026i	$0.485949\pi$
$79$	−3.69473e6	+	6.39946e6i	−0.843117	+	1.46032i	−0.887246	+	0.461296i	$0.847384\pi$
$80$	−1.10676e6	−	1.91696e6i	−0.241678	−	0.418599i
$81$		0			0
$82$	−649114.	+	1.12430e6i	−0.130009	+	0.225182i
$83$	−6.43368e6			−1.23505			−0.617527	−	0.786549i	$-0.711865\pi$
$83$	−6.43368e6			−1.23505			−0.617527	+	0.786549i	$0.711865\pi$
$84$		0			0
$85$	1.89963e7			3.35508
$86$	1.59568e6	−	2.76379e6i	0.270520	−	0.468555i
$87$		0			0
$88$	−173272.	−	300116.i	−0.0271043	−	0.0469461i
$89$	−3.18608e6	+	5.51845e6i	−0.479062	+	0.829760i	−0.999712	−	0.0240106i	$-0.992356\pi$
$89$	−3.18608e6	+	5.51845e6i	−0.479062	+	0.829760i	0.520650	+	0.853770i	$0.325690\pi$
$90$		0			0
$91$	4.38695e6	+	4.14122e6i	0.610264	+	0.576081i
$92$	5.01444e6			0.671374
$93$		0			0
$94$	−641368.	−	1.11088e6i	−0.0796453	−	0.137950i
$95$	−5.93048e6	−	1.02719e7i	−0.709672	−	1.22919i
$96$		0			0
$97$	−1.59546e7			−1.77494			−0.887472	−	0.460861i	$-0.847541\pi$
$97$	−1.59546e7			−1.77494			−0.887472	+	0.460861i	$0.847541\pi$
$98$	5.88589e6	+	2.96017e6i	0.631714	+	0.317706i
$99$		0			0
$100$	−6.84533e6	+	1.18565e7i	−0.684533	+	1.18565i
$101$	3.21720e6	+	5.57235e6i	0.310708	+	0.538163i	0.978516	−	0.206171i	$-0.0661004\pi$
$101$	3.21720e6	+	5.57235e6i	0.310708	+	0.538163i	−0.667808	+	0.744334i	$0.732767\pi$
$102$		0			0
$103$	7.78162e6	−	1.34782e7i	0.701681	−	1.21535i	−0.266195	−	0.963919i	$-0.585766\pi$
$103$	7.78162e6	−	1.34782e7i	0.701681	−	1.21535i	0.967876	−	0.251428i	$-0.0809002\pi$
$104$	−3.40367e6			−0.296709
$105$		0			0
$106$	4.56286e6			0.372106
$107$	−6.23535e6	+	1.07999e7i	−0.492059	+	0.852272i	−0.999958	−	0.00914507i	$-0.997089\pi$
$107$	−6.23535e6	+	1.07999e7i	−0.492059	+	0.852272i	0.507899	+	0.861417i	$0.330422\pi$
$108$		0			0
$109$	−6.53171e6	−	1.13132e7i	−0.483097	−	0.836748i	0.516715	−	0.856157i	$-0.327155\pi$
$109$	−6.53171e6	−	1.13132e7i	−0.483097	−	0.836748i	−0.999812	+	0.0194096i	$0.993821\pi$
$110$	−1.46309e6	+	2.53414e6i	−0.104808	+	0.181534i
$111$		0			0
$112$	−3.56123e6	+	1.06507e6i	−0.239518	+	0.0716331i
$113$	6.21455e6			0.405168			0.202584	−	0.979265i	$-0.435066\pi$
$113$	6.21455e6			0.405168			0.202584	+	0.979265i	$0.435066\pi$
$114$		0			0
$115$	−2.11707e7	−	3.66687e7i	−1.29805	−	2.24829i
$116$	2.36395e6	+	4.09447e6i	0.140616	+	0.243554i
$117$		0			0
$118$	−2.05967e7			−1.15401
$119$	7.36541e6	−	3.10380e7i	0.400666	−	1.68842i
$120$		0			0
$121$	9.51453e6	−	1.64796e7i	0.488246	−	0.845666i
$122$	−1.03422e7	−	1.79132e7i	−0.515647	−	0.893127i
$123$		0			0
$124$	−3.64682e6	+	6.31647e6i	−0.171766	+	0.297508i
$125$	7.33830e7			3.36055
$126$		0			0
$127$	5.98610e6			0.259317			0.129659	−	0.991559i	$-0.458612\pi$
$127$	5.98610e6			0.259317			0.129659	+	0.991559i	$0.458612\pi$
$128$	1.04858e6	−	1.81619e6i	0.0441942	−	0.0765466i
$129$		0			0
$130$	1.43701e7	+	2.48898e7i	0.573665	+	0.993617i
$131$	9.86353e6	−	1.70841e7i	0.383339	−	0.663962i	−0.608199	−	0.793785i	$-0.708108\pi$
$131$	9.86353e6	−	1.70841e7i	0.383339	−	0.663962i	0.991537	+	0.129823i	$0.0414409\pi$
$132$		0			0
$133$	−1.90826e7	+	5.70708e6i	−0.703327	+	0.210346i
$134$	−7.49423e6			−0.269067
$135$		0			0
$136$	8.99884e6	+	1.55865e7i	0.306761	+	0.531326i
$137$	1.47037e7	+	2.54676e7i	0.488546	+	0.846187i	0.999913	−	0.0131753i	$-0.00419396\pi$
$137$	1.47037e7	+	2.54676e7i	0.488546	+	0.846187i	−0.511367	+	0.859363i	$0.670861\pi$
$138$		0			0
$139$	3.84080e7			1.21303			0.606513	−	0.795073i	$-0.292568\pi$
$139$	3.84080e7			1.21303			0.606513	+	0.795073i	$0.292568\pi$
$140$	2.28238e7	+	2.15453e7i	0.702974	+	0.663597i
$141$		0			0
$142$	−1.47137e7	+	2.54849e7i	−0.431235	+	0.746920i
$143$	2.24976e6	+	3.89670e6i	0.0643369	+	0.111435i
$144$		0			0
$145$	1.99609e7	−	3.45733e7i	0.543741	−	0.941787i
$146$	−3.30063e7			−0.877732
$147$		0			0
$148$	7.06723e6			0.179198
$149$	−2.03665e6	+	3.52758e6i	−0.0504387	+	0.0873624i	−0.890142	−	0.455682i	$-0.849395\pi$
$149$	−2.03665e6	+	3.52758e6i	−0.0504387	+	0.0873624i	0.839704	+	0.543045i	$0.182729\pi$
$150$		0			0
$151$	2.23327e7	+	3.86814e7i	0.527865	+	0.914289i	0.999472	+	0.0324802i	$0.0103406\pi$
$151$	2.23327e7	+	3.86814e7i	0.527865	+	0.914289i	−0.471608	+	0.881809i	$0.656326\pi$
$152$	5.61872e6	−	9.73191e6i	0.129773	−	0.224774i
$153$		0			0
$154$	3.57325e6	+	3.37310e6i	0.0788389	+	0.0744228i
$155$	6.15866e7			1.32839
$156$		0			0
$157$	3.40899e7	+	5.90454e7i	0.703034	+	1.21769i	0.967396	+	0.253268i	$0.0815054\pi$
$157$	3.40899e7	+	5.90454e7i	0.703034	+	1.21769i	−0.264362	+	0.964424i	$0.585161\pi$
$158$	2.95579e7	+	5.11957e7i	0.596174	+	1.03260i
$159$		0			0
$160$	−1.77081e7			−0.341784
$161$	−6.81213e7	+	2.03732e7i	−1.28645	+	0.384741i
$162$		0			0
$163$	−1.02401e6	+	1.77364e6i	−0.0185203	+	0.0320781i	−0.875137	−	0.483875i	$-0.839229\pi$
$163$	−1.02401e6	+	1.77364e6i	−0.0185203	+	0.0320781i	0.856617	+	0.515953i	$0.172562\pi$
$164$	5.19291e6	+	8.99438e6i	0.0919300	+	0.159227i
$165$		0			0
$166$	−2.57347e7	+	4.45738e7i	−0.436658	+	0.756313i
$167$	3.34977e7			0.556553			0.278277	−	0.960501i	$-0.410237\pi$
$167$	3.34977e7			0.556553			0.278277	+	0.960501i	$0.410237\pi$
$168$		0			0
$169$	−1.85553e7			−0.295709
$170$	7.59852e7	−	1.31610e8i	1.18620	−	2.05456i
$171$		0			0
$172$	−1.27654e7	−	2.21103e7i	−0.191287	−	0.331319i
$173$	2.97722e7	−	5.15669e7i	0.437168	−	0.757198i	−0.560301	−	0.828289i	$-0.689315\pi$
$173$	2.97722e7	−	5.15669e7i	0.437168	−	0.757198i	0.997470	+	0.0710908i	$0.0226480\pi$
$174$		0			0
$175$	4.48224e7	−	1.88882e8i	0.632210	−	2.66415i
$176$	−2.77235e6			−0.0383313
$177$		0			0
$178$	2.54886e7	+	4.41476e7i	0.338748	+	0.586729i
$179$	−2.48179e7	−	4.29858e7i	−0.323429	−	0.560195i	0.657764	−	0.753224i	$-0.271502\pi$
$179$	−2.48179e7	−	4.29858e7i	−0.323429	−	0.560195i	−0.981193	+	0.193029i	$0.938169\pi$
$180$		0			0
$181$	−1.25232e8			−1.56978			−0.784892	−	0.619633i	$-0.787281\pi$
$181$	−1.25232e8			−1.56978			−0.784892	+	0.619633i	$0.787281\pi$
$182$	4.62390e7	−	1.38288e7i	0.568537	−	0.170034i
$183$		0			0
$184$	2.00577e7	−	3.47410e7i	0.237367	−	0.411131i
$185$	−2.98375e7	−	5.16800e7i	−0.346466	−	0.600097i
$186$		0			0
$187$	1.18961e7	−	2.06047e7i	0.133033	−	0.230420i
$188$	−1.02619e7			−0.112635
$189$		0			0
$190$	−9.48877e7			−1.00363
$191$	−8.51812e7	+	1.47538e8i	−0.884560	+	1.53210i	−0.0383425	+	0.999265i	$0.512208\pi$
$191$	−8.51812e7	+	1.47538e8i	−0.884560	+	1.53210i	−0.846217	+	0.532838i	$0.821126\pi$
$192$		0			0
$193$	4.03341e7	+	6.98608e7i	0.403852	+	0.699492i	0.994187	−	0.107666i	$-0.0343377\pi$
$193$	4.03341e7	+	6.98608e7i	0.403852	+	0.699492i	−0.590335	+	0.807158i	$0.701004\pi$
$194$	−6.38184e7	+	1.10537e8i	−0.627538	+	1.08693i
$195$		0			0
$196$	4.40522e7	−	2.89379e7i	0.417899	−	0.274518i
$197$	−6.88422e7			−0.641539			−0.320769	−	0.947157i	$-0.603941\pi$
$197$	−6.88422e7			−0.641539			−0.320769	+	0.947157i	$0.603941\pi$
$198$		0			0
$199$	7.99422e7	+	1.38464e8i	0.719102	+	1.24552i	0.961356	+	0.275308i	$0.0887798\pi$
$199$	7.99422e7	+	1.38464e8i	0.719102	+	1.24552i	−0.242255	+	0.970213i	$0.577887\pi$
$200$	5.47626e7	+	9.48517e7i	0.484038	+	0.838378i
$201$		0			0
$202$	5.14752e7			0.439408
$203$	−4.87497e7	−	4.60191e7i	−0.409012	−	0.386102i
$204$		0			0
$205$	4.38483e7	−	7.59476e7i	0.355480	−	0.615709i
$206$	−6.22530e7	−	1.07825e8i	−0.496164	−	0.859380i
$207$		0			0
$208$	−1.36147e7	+	2.35813e7i	−0.104903	+	0.181697i
$209$	−1.48555e7			−0.112557
$210$		0			0
$211$	−2.11016e8			−1.54642			−0.773208	−	0.634152i	$-0.781349\pi$
$211$	−2.11016e8			−1.54642			−0.773208	+	0.634152i	$0.781349\pi$
$212$	1.82515e7	−	3.16124e7i	0.131559	−	0.227868i
$213$		0			0
$214$	4.98828e7	+	8.63995e7i	0.347938	+	0.602647i
$215$	−1.07790e8	+	1.86697e8i	−0.739678	+	1.28116i
$216$		0			0
$217$	2.38789e7	−	1.00626e8i	0.158637	−	0.668500i
$218$	−1.04507e8			−0.683202
$219$		0			0
$220$	1.17047e7	+	2.02732e7i	0.0741108	+	0.128364i
$221$	−1.16841e8	−	2.02374e8i	−0.728151	−	1.26119i
$222$		0			0
$223$	1.54881e7			0.0935259			0.0467629	−	0.998906i	$-0.485109\pi$
$223$	1.54881e7			0.0935259			0.0467629	+	0.998906i	$0.485109\pi$
$224$	−6.86594e6	+	2.89332e7i	−0.0408162	+	0.172000i
$225$		0			0
$226$	2.48582e7	−	4.30557e7i	0.143249	−	0.248114i
$227$	1.12793e8	+	1.95363e8i	0.640017	+	1.10854i	0.985428	+	0.170091i	$0.0544062\pi$
$227$	1.12793e8	+	1.95363e8i	0.640017	+	1.10854i	−0.345411	+	0.938452i	$0.612260\pi$
$228$		0			0
$229$	−2.94394e7	+	5.09905e7i	−0.161996	+	0.280585i	−0.935584	−	0.353103i	$-0.885126\pi$
$229$	−2.94394e7	+	5.09905e7i	−0.161996	+	0.280585i	0.773588	+	0.633688i	$0.218460\pi$
$230$	−3.38731e8			−1.83572
$231$		0			0
$232$	3.78231e7			0.198861
$233$	−1.85008e7	+	3.20443e7i	−0.0958173	+	0.165960i	−0.909949	−	0.414719i	$-0.863880\pi$
$233$	−1.85008e7	+	3.20443e7i	−0.0958173	+	0.165960i	0.814132	+	0.580680i	$0.197213\pi$
$234$		0			0
$235$	4.33251e7	+	7.50413e7i	0.217772	+	0.377192i
$236$	−8.23868e7	+	1.42698e8i	−0.408005	+	0.706686i
$237$		0			0
$238$	−1.85576e8	−	1.75181e8i	−0.892282	−	0.842302i
$239$	3.52275e8			1.66913			0.834564	−	0.550911i	$-0.185720\pi$
$239$	3.52275e8			1.66913			0.834564	+	0.550911i	$0.185720\pi$
$240$		0			0
$241$	−5.05482e7	−	8.75520e7i	−0.232619	−	0.402909i	0.725959	−	0.687738i	$-0.241396\pi$
$241$	−5.05482e7	−	8.75520e7i	−0.232619	−	0.402909i	−0.958578	+	0.284830i	$0.908063\pi$
$242$	−7.61162e7	−	1.31837e8i	−0.345242	−	0.597976i
$243$		0			0
$244$	−1.65475e8			−0.729235
$245$	−3.97598e8	−	1.99963e8i	−1.72728	−	0.868697i
$246$		0			0
$247$	−7.29534e7	+	1.26359e8i	−0.308039	+	0.533540i
$248$	2.91745e7	+	5.05318e7i	0.121457	+	0.210370i
$249$		0			0
$250$	2.93532e8	−	5.08412e8i	1.18813	−	2.05791i
$251$	−9.75552e7			−0.389397			−0.194698	−	0.980863i	$-0.562373\pi$
$251$	−9.75552e7			−0.389397			−0.194698	+	0.980863i	$0.562373\pi$
$252$		0			0
$253$	−5.30311e7			−0.205877
$254$	2.39444e7	−	4.14729e7i	0.0916824	−	0.158799i
$255$		0			0
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	−8.75026e7	+	1.51559e8i	−0.321555	+	0.556949i	−0.980809	−	0.194971i	$-0.937539\pi$
$257$	−8.75026e7	+	1.51559e8i	−0.321555	+	0.556949i	0.659254	+	0.751920i	$0.270872\pi$
$258$		0			0
$259$	−9.60086e7	+	2.87135e7i	−0.343369	+	0.102692i
$260$	2.29922e8			0.811285
$261$		0			0
$262$	−7.89082e7	−	1.36673e8i	−0.271061	−	0.469492i
$263$	−3.04800e7	−	5.27930e7i	−0.103317	−	0.178950i	0.809733	−	0.586799i	$-0.199612\pi$
$263$	−3.04800e7	−	5.27930e7i	−0.103317	−	0.178950i	−0.913049	+	0.407849i	$0.866279\pi$
$264$		0			0
$265$	−3.08226e8			−1.01744
$266$	−3.67907e7	+	1.55037e8i	−0.119854	+	0.505067i
$267$		0			0
$268$	−2.99769e7	+	5.19215e7i	−0.0951295	+	0.164769i
$269$	−5.40032e7	−	9.35362e7i	−0.169156	−	0.292986i	0.768968	−	0.639288i	$-0.220771\pi$
$269$	−5.40032e7	−	9.35362e7i	−0.169156	−	0.292986i	−0.938123	+	0.346302i	$0.887437\pi$
$270$		0			0
$271$	−2.86823e7	+	4.96791e7i	−0.0875429	+	0.151629i	−0.906472	−	0.422266i	$-0.861235\pi$
$271$	−2.86823e7	+	4.96791e7i	−0.0875429	+	0.151629i	0.818929	+	0.573895i	$0.194568\pi$
$272$	1.43981e8			0.433826
$273$		0			0
$274$	2.35260e8			0.690909
$275$	7.23940e7	−	1.25390e8i	0.209913	−	0.363579i
$276$		0			0
$277$	1.96515e8	+	3.40374e8i	0.555542	+	0.962226i	0.997861	+	0.0653689i	$0.0208224\pi$
$277$	1.96515e8	+	3.40374e8i	0.555542	+	0.962226i	−0.442319	+	0.896858i	$0.645844\pi$
$278$	1.53632e8	−	2.66099e8i	0.428870	−	0.742824i
$279$		0			0
$280$	2.40565e8	−	7.19464e7i	0.654907	−	0.195865i
$281$	−1.85300e8			−0.498198			−0.249099	−	0.968478i	$-0.580135\pi$
$281$	−1.85300e8			−0.498198			−0.249099	+	0.968478i	$0.580135\pi$
$282$		0			0
$283$	2.04039e8	+	3.53406e8i	0.535132	+	0.926875i	0.999157	+	0.0410533i	$0.0130713\pi$
$283$	2.04039e8	+	3.53406e8i	0.535132	+	0.926875i	−0.464025	+	0.885822i	$0.653595\pi$
$284$	1.17710e8	+	2.03879e8i	0.304929	+	0.528152i
$285$		0			0
$286$	3.59962e7			0.0909861
$287$	−1.07089e8	−	1.01091e8i	−0.267398	−	0.252420i
$288$		0			0
$289$	−4.12653e8	+	7.14736e8i	−1.00564	+	1.74182i
$290$	−1.59687e8	−	2.76586e8i	−0.384483	−	0.665944i
$291$		0			0
$292$	−1.32025e8	+	2.28674e8i	−0.310325	+	0.537499i
$293$	2.80589e8			0.651679			0.325839	−	0.945425i	$-0.394353\pi$
$293$	2.80589e8			0.651679			0.325839	+	0.945425i	$0.394353\pi$
$294$		0			0
$295$	1.39133e9			3.15539
$296$	2.82689e7	−	4.89632e7i	0.0633561	−	0.109736i
$297$		0			0
$298$	1.62932e7	+	2.82206e7i	0.0356655	+	0.0617745i
$299$	−2.60429e8	+	4.51077e8i	−0.563431	+	0.975891i
$300$		0			0
$301$	2.63251e8	+	2.48505e8i	0.556400	+	0.525233i
$302$	3.57324e8			0.746514
$303$		0			0
$304$	−4.49498e7	−	7.78553e7i	−0.0917635	−	0.158939i
$305$	6.98626e8	+	1.21006e9i	1.40992	+	2.44206i
$306$		0			0
$307$	−6.07300e8			−1.19790			−0.598948	−	0.800788i	$-0.704414\pi$
$307$	−6.07300e8			−1.19790			−0.598948	+	0.800788i	$0.704414\pi$
$308$	3.76625e7	−	1.12638e7i	0.0734482	−	0.0219663i
$309$		0			0
$310$	2.46346e8	−	4.26684e8i	0.469656	−	0.813469i
$311$	−4.72511e8	−	8.18413e8i	−0.890739	−	1.54281i	−0.838991	−	0.544145i	$-0.816854\pi$
$311$	−4.72511e8	−	8.18413e8i	−0.890739	−	1.54281i	−0.0517476	−	0.998660i	$-0.516479\pi$
$312$		0			0
$313$	−6.12314e7	+	1.06056e8i	−0.112867	+	0.195492i	−0.916925	−	0.399059i	$-0.869337\pi$
$313$	−6.12314e7	+	1.06056e8i	−0.112867	+	0.195492i	0.804058	+	0.594551i	$0.202670\pi$
$314$	5.45438e8			0.994241
$315$		0			0
$316$	4.72926e8			0.843117
$317$	5.53647e8	−	9.58945e8i	0.976170	−	1.69078i	0.300151	−	0.953892i	$-0.402963\pi$
$317$	5.53647e8	−	9.58945e8i	0.976170	−	1.69078i	0.676019	−	0.736885i	$-0.263704\pi$
$318$		0			0
$319$	−2.50003e7	−	4.33018e7i	−0.0431200	−	0.0746860i
$320$	−7.08325e7	+	1.22685e8i	−0.120839	+	0.209299i
$321$		0			0
$322$	−1.31336e8	+	5.53451e8i	−0.219223	+	0.923812i
$323$	7.71515e8			1.27390
$324$		0			0
$325$	−7.11037e8	−	1.23155e9i	−1.14895	−	1.99004i
$326$	8.19208e6	+	1.41891e7i	0.0130958	+	0.0226826i
$327$		0			0
$328$	8.30866e7			0.130009
$329$	1.39408e8	−	4.16931e7i	0.215825	−	0.0645474i
$330$		0			0
$331$	−2.85435e8	+	4.94388e8i	−0.432622	+	0.749324i	−0.997098	−	0.0761256i	$-0.975745\pi$
$331$	−2.85435e8	+	4.94388e8i	−0.432622	+	0.749324i	0.564476	+	0.825450i	$0.309078\pi$
$332$	2.05878e8	+	3.56591e8i	0.308764	+	0.534794i
$333$		0			0
$334$	1.33991e8	−	2.32079e8i	0.196771	−	0.340818i
$335$	5.06243e8			0.735703
$336$		0			0
$337$	−3.47533e8			−0.494643			−0.247322	−	0.968933i	$-0.579550\pi$
$337$	−3.47533e8			−0.494643			−0.247322	+	0.968933i	$0.579550\pi$
$338$	−7.42212e7	+	1.28555e8i	−0.104549	+	0.181084i
$339$		0			0
$340$	−6.07882e8	−	1.05288e9i	−0.838770	−	1.45279i
$341$	3.85676e7	−	6.68010e7i	0.0526722	−	0.0912310i
$342$		0			0
$343$	−4.80879e8	+	5.72103e8i	−0.643437	+	0.765499i
$344$	−2.04247e8			−0.270520
$345$		0			0
$346$	−2.38177e8	−	4.12535e8i	−0.309125	−	0.535420i
$347$	9.03031e7	+	1.56409e8i	0.116024	+	0.200960i	0.918189	−	0.396143i	$-0.129652\pi$
$347$	9.03031e7	+	1.56409e8i	0.116024	+	0.200960i	−0.802164	+	0.597103i	$0.796318\pi$
$348$		0			0
$349$	−4.21856e8			−0.531222			−0.265611	−	0.964080i	$-0.585574\pi$
$349$	−4.21856e8			−0.531222			−0.265611	+	0.964080i	$0.585574\pi$
$350$	−1.12933e9	−	1.06607e9i	−1.40793	−	1.32907i
$351$		0			0
$352$	−1.10894e7	+	1.92074e7i	−0.0135522	+	0.0234731i
$353$	2.45274e8	+	4.24828e8i	0.296784	+	0.514045i	0.975398	−	0.220450i	$-0.0707525\pi$
$353$	2.45274e8	+	4.24828e8i	0.296784	+	0.514045i	−0.678614	+	0.734495i	$0.737419\pi$
$354$		0			0
$355$	9.93928e8	−	1.72153e9i	1.17911	−	2.04229i
$356$	4.07818e8			0.479062
$357$		0			0
$358$	−3.97086e8			−0.457397
$359$	5.36048e8	−	9.28462e8i	0.611467	−	1.05909i	−0.379526	−	0.925181i	$-0.623913\pi$
$359$	5.36048e8	−	9.28462e8i	0.611467	−	1.05909i	0.990993	−	0.133911i	$-0.0427536\pi$
$360$		0			0
$361$	2.06076e8	+	3.56933e8i	0.230543	+	0.399312i
$362$	−5.00927e8	+	8.67632e8i	−0.555002	+	0.961292i
$363$		0			0
$364$	8.91473e7	−	3.75668e8i	0.0968843	−	0.408272i
$365$	2.22961e9			2.39996
$366$		0			0
$367$	−1.35304e8	−	2.34353e8i	−0.142882	−	0.247480i	0.785698	−	0.618610i	$-0.212304\pi$
$367$	−1.35304e8	−	2.34353e8i	−0.142882	−	0.247480i	−0.928581	+	0.371130i	$0.878970\pi$
$368$	−1.60462e8	−	2.77928e8i	−0.167844	−	0.290714i
$369$		0			0
$370$	−4.77399e8			−0.489977
$371$	−1.19508e8	+	5.03610e8i	−0.121504	+	0.512019i
$372$		0			0
$373$	−3.30141e8	+	5.71821e8i	−0.329396	+	0.570531i	−0.982392	−	0.186831i	$-0.940178\pi$
$373$	−3.30141e8	+	5.71821e8i	−0.329396	+	0.570531i	0.652996	+	0.757361i	$0.273512\pi$
$374$	−9.51689e7	−	1.64837e8i	−0.0940685	−	0.162931i
$375$		0			0
$376$	−4.10476e7	+	7.10965e7i	−0.0398226	+	0.0689748i
$377$	−4.91095e8			−0.472031
$378$		0			0
$379$	−1.97748e8			−0.186584			−0.0932922	−	0.995639i	$-0.529739\pi$
$379$	−1.97748e8			−0.186584			−0.0932922	+	0.995639i	$0.529739\pi$
$380$	−3.79551e8	+	6.57401e8i	−0.354836	+	0.614594i
$381$		0			0
$382$	6.81450e8	+	1.18031e9i	0.625478	+	1.08336i
$383$	−5.42851e8	+	9.40246e8i	−0.493725	+	0.855157i	−0.999974	−	0.00723074i	$-0.997698\pi$
$383$	−5.42851e8	+	9.40246e8i	−0.493725	+	0.855157i	0.506249	+	0.862387i	$0.331032\pi$
$384$		0			0
$385$	−2.41377e8	−	2.27856e8i	−0.215567	−	0.203493i
$386$	6.45346e8			0.571133
$387$		0			0
$388$	5.10547e8	+	8.84294e8i	0.443736	+	0.768574i
$389$	2.92406e8	+	5.06463e8i	0.251862	+	0.436238i	0.964039	−	0.265762i	$-0.0856236\pi$
$389$	2.92406e8	+	5.06463e8i	0.251862	+	0.436238i	−0.712176	+	0.702001i	$0.752290\pi$
$390$		0			0
$391$	2.75416e9			2.33008
$392$	−2.42789e7	−	4.20954e8i	−0.0203576	−	0.352967i
$393$		0			0
$394$	−2.75369e8	+	4.76953e8i	−0.226818	+	0.392861i
$395$	−1.99667e9	−	3.45833e9i	−1.63010	−	2.82342i
$396$		0			0
$397$	−7.91480e8	+	1.37088e9i	−0.634853	+	1.09960i	0.351694	+	0.936115i	$0.385606\pi$
$397$	−7.91480e8	+	1.37088e9i	−0.634853	+	1.09960i	−0.986546	+	0.163482i	$0.947727\pi$
$398$	1.27907e9			1.01696
$399$		0			0
$400$	8.76202e8			0.684533
$401$	−4.75005e8	+	8.22733e8i	−0.367869	+	0.637168i	−0.989232	−	0.146355i	$-0.953246\pi$
$401$	−4.75005e8	+	8.22733e8i	−0.367869	+	0.637168i	0.621363	+	0.783523i	$0.286579\pi$
$402$		0			0
$403$	−3.78801e8	−	6.56103e8i	−0.288300	−	0.499349i
$404$	2.05901e8	−	3.56630e8i	0.155354	−	0.269081i
$405$		0			0
$406$	−5.13828e8	+	1.53672e8i	−0.381046	+	0.113960i
$407$	−7.47408e7			−0.0549512
$408$		0			0
$409$	3.44514e8	+	5.96716e8i	0.248986	+	0.431257i	0.963245	−	0.268625i	$-0.0865692\pi$
$409$	3.44514e8	+	5.96716e8i	0.248986	+	0.431257i	−0.714258	+	0.699882i	$0.753236\pi$
$410$	−3.50787e8	−	6.07580e8i	−0.251362	−	0.435372i
$411$		0			0
$412$	−9.96048e8			−0.701681
$413$	5.39459e8	−	2.27329e9i	0.376819	−	1.58792i
$414$		0			0
$415$	1.73841e9	−	3.01101e9i	1.19394	−	2.06797i
$416$	1.08918e8	+	1.88651e8i	0.0741773	+	0.128479i
$417$		0			0
$418$	−5.94218e7	+	1.02922e8i	−0.0397950	+	0.0689270i
$419$	−1.41673e9			−0.940887			−0.470443	−	0.882430i	$-0.655906\pi$
$419$	−1.41673e9			−0.940887			−0.470443	+	0.882430i	$0.655906\pi$
$420$		0			0
$421$	−2.86813e9			−1.87332			−0.936660	−	0.350240i	$-0.886100\pi$
$421$	−2.86813e9			−1.87332			−0.936660	+	0.350240i	$0.886100\pi$
$422$	−8.44063e8	+	1.46196e9i	−0.546741	+	0.946983i
$423$		0			0
$424$	−1.46012e8	−	2.52900e8i	−0.0930266	−	0.161127i
$425$	−3.75977e9	+	6.51211e9i	−2.37575	+	4.11491i
$426$		0			0
$427$	2.24798e9	−	6.72309e8i	1.39732	−	0.417899i
$428$	7.98124e8			0.492059
$429$		0			0
$430$	8.62317e8	+	1.49358e9i	0.523031	+	0.905916i
$431$	6.54074e8	+	1.13289e9i	0.393511	+	0.681580i	0.992910	−	0.118870i	$-0.0379271\pi$
$431$	6.54074e8	+	1.13289e9i	0.393511	+	0.681580i	−0.599399	+	0.800450i	$0.704594\pi$
$432$		0			0
$433$	−1.57896e8			−0.0934678			−0.0467339	−	0.998907i	$-0.514881\pi$
$433$	−1.57896e8			−0.0934678			−0.0467339	+	0.998907i	$0.514881\pi$
$434$	−6.01643e8	−	5.67942e8i	−0.353284	−	0.333496i
$435$		0			0
$436$	−4.18029e8	+	7.24048e8i	−0.241548	+	0.418374i
$437$	−8.59824e8	−	1.48926e9i	−0.492861	−	0.853661i
$438$		0			0
$439$	−1.19764e9	+	2.07438e9i	−0.675619	+	1.17021i	0.300669	+	0.953729i	$0.402790\pi$
$439$	−1.19764e9	+	2.07438e9i	−0.675619	+	1.17021i	−0.976288	+	0.216478i	$0.930543\pi$
$440$	1.87275e8			0.104808
$441$		0			0
$442$	−1.86945e9			−1.02976
$443$	2.02980e7	−	3.51571e7i	0.0110928	−	0.0192132i	−0.860426	−	0.509576i	$-0.829802\pi$
$443$	2.02980e7	−	3.51571e7i	0.0110928	−	0.0192132i	0.871519	+	0.490363i	$0.163136\pi$
$444$		0			0
$445$	−1.72179e9	−	2.98222e9i	−0.926231	−	1.60428i
$446$	6.19525e7	−	1.07305e8i	0.0330664	−	0.0572727i
$447$		0			0
$448$	1.72991e8	+	1.63302e8i	0.0908974	+	0.0858059i
$449$	−1.72734e9			−0.900568			−0.450284	−	0.892885i	$-0.648677\pi$
$449$	−1.72734e9			−0.900568			−0.450284	+	0.892885i	$0.648677\pi$
$450$		0			0
$451$	−5.49186e7	−	9.51217e7i	−0.0281904	−	0.0488272i
$452$	−1.98866e8	−	3.44446e8i	−0.101292	−	0.175443i
$453$		0			0
$454$	1.80469e9			0.905121
$455$	−3.12349e9	+	9.34150e8i	−1.55454	+	0.464919i
$456$		0			0
$457$	1.29712e9	−	2.24668e9i	0.635731	−	1.10112i	−0.350629	−	0.936514i	$-0.614032\pi$
$457$	1.29712e9	−	2.24668e9i	0.635731	−	1.10112i	0.986360	−	0.164604i	$-0.0526345\pi$
$458$	2.35515e8	+	4.07924e8i	0.114548	+	0.198404i
$459$		0			0
$460$	−1.35492e9	+	2.34679e9i	−0.649026	+	1.12415i
$461$	−1.29682e9			−0.616493			−0.308246	−	0.951307i	$-0.599742\pi$
$461$	−1.29682e9			−0.616493			−0.308246	+	0.951307i	$0.599742\pi$
$462$		0			0
$463$	4.47444e8			0.209510			0.104755	−	0.994498i	$-0.466594\pi$
$463$	4.47444e8			0.209510			0.104755	+	0.994498i	$0.466594\pi$
$464$	1.51293e8	−	2.62046e8i	0.0703080	−	0.121777i
$465$		0			0
$466$	1.48006e8	+	2.56354e8i	0.0677531	+	0.117352i
$467$	−2.04121e8	+	3.53548e8i	−0.0927425	+	0.160635i	−0.908664	−	0.417528i	$-0.862897\pi$
$467$	−2.04121e8	+	3.53548e8i	−0.0927425	+	0.160635i	0.815922	+	0.578162i	$0.196230\pi$
$468$		0			0
$469$	1.96285e8	−	8.27149e8i	0.0878582	−	0.370236i
$470$	6.93202e8			0.307976
$471$		0			0
$472$	6.59095e8	+	1.14159e9i	0.288503	+	0.499702i
$473$	1.35003e8	+	2.33832e8i	0.0586582	+	0.101599i
$474$		0			0
$475$	4.69507e9			2.01009
$476$	−1.95599e9	+	5.84983e8i	−0.831272	+	0.248610i
$477$		0			0
$478$	1.40910e9	−	2.44064e9i	0.590126	−	1.02213i
$479$	−1.88014e8	−	3.25649e8i	−0.0781655	−	0.135387i	0.824293	−	0.566163i	$-0.191573\pi$
$479$	−1.88014e8	−	3.25649e8i	−0.0781655	−	0.135387i	−0.902458	+	0.430777i	$0.858240\pi$
$480$		0			0
$481$	−3.67043e8	+	6.35738e8i	−0.150387	+	0.260477i
$482$	−8.08771e8			−0.328973
$483$		0			0
$484$	−1.21786e9			−0.488246
$485$	4.31100e9	−	7.46688e9i	1.71586	−	2.97196i
$486$		0			0
$487$	1.96697e9	+	3.40689e9i	0.771696	+	1.33662i	0.936633	+	0.350312i	$0.113924\pi$
$487$	1.96697e9	+	3.40689e9i	0.771696	+	1.33662i	−0.164938	+	0.986304i	$0.552742\pi$
$488$	−6.61900e8	+	1.14644e9i	−0.257824	+	0.446564i
$489$		0			0
$490$	−2.97578e9	+	1.95479e9i	−1.14265	+	0.750608i
$491$	4.06838e9			1.55109			0.775543	−	0.631295i	$-0.217476\pi$
$491$	4.06838e9			1.55109			0.775543	+	0.631295i	$0.217476\pi$
$492$		0			0
$493$	1.29839e9	+	2.24887e9i	0.488023	+	0.845280i
$494$	5.83627e8	+	1.01087e9i	0.217817	+	0.377270i
$495$		0			0
$496$	4.66792e8			0.171766
$497$	−2.42743e9	−	2.29146e9i	−0.886952	−	0.837270i
$498$		0			0
$499$	−1.26756e9	+	2.19549e9i	−0.456687	+	0.791004i	−0.998783	−	0.0493117i	$-0.984297\pi$
$499$	−1.26756e9	+	2.19549e9i	−0.456687	+	0.791004i	0.542097	+	0.840316i	$0.317631\pi$
$500$	−2.34825e9	−	4.06730e9i	−0.840137	−	1.45516i
$501$		0			0
$502$	−3.90221e8	+	6.75882e8i	−0.137673	+	0.238456i
$503$	1.65400e9			0.579492			0.289746	−	0.957104i	$-0.406429\pi$
$503$	1.65400e9			0.579492			0.289746	+	0.957104i	$0.406429\pi$
$504$		0			0
$505$	−3.47720e9			−1.20146
$506$	−2.12124e8	+	3.67410e8i	−0.0727886	+	0.126074i
$507$		0			0
$508$	−1.91555e8	−	3.31783e8i	−0.0648293	−	0.112288i
$509$	−6.05650e8	+	1.04902e9i	−0.203568	+	0.352590i	−0.949676	−	0.313235i	$-0.898587\pi$
$509$	−6.05650e8	+	1.04902e9i	−0.203568	+	0.352590i	0.746108	+	0.665825i	$0.231920\pi$
$510$		0			0
$511$	8.64485e8	−	3.64296e9i	0.286605	−	1.20776i
$512$	−1.34218e8			−0.0441942
$513$		0			0
$514$	7.00021e8	+	1.21247e9i	0.227374	+	0.393823i
$515$	4.20526e9	+	7.28372e9i	1.35665	+	2.34978i
$516$		0			0
$517$	1.08526e8			0.0345397
$518$	−1.85101e8	+	7.80021e8i	−0.0585134	+	0.246577i
$519$		0			0
$520$	9.19687e8	−	1.59294e9i	0.286833	−	0.496809i
$521$	−4.39174e8	−	7.60671e8i	−0.136052	−	0.235649i	0.789947	−	0.613175i	$-0.210108\pi$
$521$	−4.39174e8	−	7.60671e8i	−0.136052	−	0.235649i	−0.925999	+	0.377527i	$0.876775\pi$
$522$		0			0
$523$	1.35133e9	−	2.34057e9i	0.413052	−	0.715427i	−0.582170	−	0.813067i	$-0.697796\pi$
$523$	1.35133e9	−	2.34057e9i	0.413052	−	0.715427i	0.995222	+	0.0976400i	$0.0311294\pi$
$524$	−1.26253e9			−0.383339
$525$		0			0
$526$	−4.87680e8			−0.146112
$527$	−2.00300e9	+	3.46929e9i	−0.596133	+	1.03253i
$528$		0			0
$529$	−1.36699e9	−	2.36770e9i	−0.401487	−	0.695395i
$530$	−1.23291e9	+	2.13546e9i	−0.359720	+	0.623053i
$531$		0			0
$532$	9.26963e8	+	8.75040e8i	0.266914	+	0.251963i
$533$	−1.07879e9			−0.308598
$534$		0			0
$535$	−3.36964e9	−	5.83638e9i	−0.951360	−	1.64780i
$536$	2.39815e8	+	4.15372e8i	0.0672667	+	0.116509i
$537$		0			0
$538$	−8.64051e8			−0.239222
$539$	−4.65882e8	+	3.06038e8i	−0.128149	+	0.0841812i
$540$		0			0
$541$	7.16665e8	−	1.24130e9i	0.194592	−	0.337044i	−0.752174	−	0.658964i	$-0.770995\pi$
$541$	7.16665e8	−	1.24130e9i	0.194592	−	0.337044i	0.946767	+	0.321920i	$0.104328\pi$
$542$	2.29458e8	+	3.97433e8i	0.0619022	+	0.107218i
$543$		0			0
$544$	5.75926e8	−	9.97533e8i	0.153381	−	0.265663i
$545$	7.05958e9			1.86806
$546$		0			0
$547$	−6.58354e8			−0.171990			−0.0859952	−	0.996296i	$-0.527407\pi$
$547$	−6.58354e8			−0.171990			−0.0859952	+	0.996296i	$0.527407\pi$
$548$	9.41039e8	−	1.62993e9i	0.244273	−	0.423094i
$549$		0			0
$550$	−5.79152e8	−	1.00312e9i	−0.148431	−	0.257089i
$551$	8.10691e8	−	1.40416e9i	0.206455	−	0.357590i
$552$		0			0
$553$	−6.42471e9	+	1.92145e9i	−1.61553	+	0.483161i
$554$	3.14424e9			0.785655
$555$		0			0
$556$	−1.22906e9	−	2.12879e9i	−0.303257	−	0.525256i
$557$	−2.72877e9	−	4.72637e9i	−0.669074	−	1.15887i	−0.978163	−	0.207837i	$-0.933358\pi$
$557$	−2.72877e9	−	4.72637e9i	−0.669074	−	1.15887i	0.309089	−	0.951033i	$-0.399976\pi$
$558$		0			0
$559$	2.65193e9			0.642127
$560$	4.63802e8	−	1.95447e9i	0.111603	−	0.470296i
$561$		0			0
$562$	−7.41198e8	+	1.28379e9i	−0.176140	+	0.305083i
$563$	−1.50153e9	−	2.60072e9i	−0.354612	−	0.614207i	0.632439	−	0.774610i	$-0.282054\pi$
$563$	−1.50153e9	−	2.60072e9i	−0.354612	−	0.614207i	−0.987052	+	0.160403i	$0.948721\pi$
$564$		0			0
$565$	−1.67920e9	+	2.90846e9i	−0.391681	+	0.678412i
$566$	3.26462e9			0.756790
$567$		0			0
$568$	1.88336e9			0.431235
$569$	−1.62201e9	+	2.80941e9i	−0.369115	+	0.639326i	−0.989427	−	0.145029i	$-0.953672\pi$
$569$	−1.62201e9	+	2.80941e9i	−0.369115	+	0.639326i	0.620313	+	0.784355i	$0.287006\pi$
$570$		0			0
$571$	−2.44038e9	−	4.22686e9i	−0.548569	−	0.950149i	−0.998373	−	0.0570221i	$-0.981839\pi$
$571$	−2.44038e9	−	4.22686e9i	−0.548569	−	0.950149i	0.449804	−	0.893127i	$-0.351494\pi$
$572$	1.43985e8	−	2.49389e8i	0.0321684	−	0.0557174i
$573$		0			0
$574$	−1.12873e9	+	3.37573e8i	−0.249115	+	0.0745034i
$575$	1.67605e10			3.67662
$576$		0			0
$577$	−3.55569e9	−	6.15863e9i	−0.770563	−	1.33465i	−0.937255	−	0.348645i	$-0.886642\pi$
$577$	−3.55569e9	−	6.15863e9i	−0.770563	−	1.33465i	0.166692	−	0.986009i	$-0.446691\pi$
$578$	3.30122e9	+	5.71788e9i	0.711095	+	1.23165i
$579$		0			0
$580$	−2.55499e9			−0.543741
$581$	−4.24565e9	−	4.00783e9i	−0.898106	−	0.847800i
$582$		0			0
$583$	−1.93022e8	+	3.34323e8i	−0.0403428	+	0.0698758i
$584$	1.05620e9	+	1.82940e9i	0.219433	+	0.380069i
$585$		0			0
$586$	1.12235e9	−	1.94398e9i	0.230403	−	0.399070i
$587$	−1.89582e9			−0.386869			−0.193434	−	0.981113i	$-0.561963\pi$
$587$	−1.89582e9			−0.386869			−0.193434	+	0.981113i	$0.561963\pi$
$588$		0			0
$589$	2.50128e9			0.504380
$590$	5.56532e9	−	9.63942e9i	1.11560	−	1.93227i
$591$		0			0
$592$	−2.26152e8	−	3.91706e8i	−0.0447995	−	0.0775951i
$593$	−1.07277e9	+	1.85810e9i	−0.211260	+	0.365912i	−0.952109	−	0.305759i	$-0.901090\pi$
$593$	−1.07277e9	+	1.85810e9i	−0.211260	+	0.365912i	0.740849	+	0.671671i	$0.234423\pi$
$594$		0			0
$595$	1.25359e10	+	1.18337e10i	2.43975	+	2.30309i
$596$	2.60691e8			0.0504387
$597$		0			0
$598$	2.08343e9	+	3.60861e9i	0.398406	+	0.690059i
$599$	−3.73799e9	−	6.47439e9i	−0.710631	−	1.23085i	−0.964621	−	0.263642i	$-0.915076\pi$
$599$	−3.73799e9	−	6.47439e9i	−0.710631	−	1.23085i	0.253990	−	0.967207i	$-0.418257\pi$
$600$		0			0
$601$	1.83935e9			0.345623			0.172812	−	0.984955i	$-0.444715\pi$
$601$	1.83935e9			0.345623			0.172812	+	0.984955i	$0.444715\pi$
$602$	2.77470e9	−	8.29834e8i	0.518355	−	0.155026i
$603$		0			0
$604$	1.42930e9	−	2.47561e9i	0.263932	−	0.457144i
$605$	5.14173e9	+	8.90574e9i	0.943986	+	1.63503i
$606$		0			0
$607$	−2.18208e9	+	3.77948e9i	−0.396014	+	0.685916i	−0.993230	−	0.116164i	$-0.962940\pi$
$607$	−2.18208e9	+	3.77948e9i	−0.396014	+	0.685916i	0.597216	+	0.802080i	$0.296274\pi$
$608$	−7.19197e8			−0.129773
$609$		0			0
$610$	1.11780e10			1.99393
$611$	5.32961e8	−	9.23115e8i	0.0945259	−	0.163724i
$612$		0			0
$613$	1.25453e9	+	2.17290e9i	0.219972	+	0.381003i	0.954799	−	0.297251i	$-0.0960699\pi$
$613$	1.25453e9	+	2.17290e9i	0.219972	+	0.381003i	−0.734827	+	0.678255i	$0.762737\pi$
$614$	−2.42920e9	+	4.20750e9i	−0.423520	+	0.733558i
$615$		0			0
$616$	7.26120e7	−	3.05989e8i	0.0125163	−	0.0527439i
$617$	1.26023e9			0.215999			0.108000	−	0.994151i	$-0.465555\pi$
$617$	1.26023e9			0.215999			0.108000	+	0.994151i	$0.465555\pi$
$618$		0			0
$619$	1.67673e9	+	2.90418e9i	0.284148	+	0.492159i	0.972402	−	0.233311i	$-0.0749559\pi$
$619$	1.67673e9	+	2.90418e9i	0.284148	+	0.492159i	−0.688254	+	0.725470i	$0.741623\pi$
$620$	−1.97077e9	−	3.41348e9i	−0.332097	−	0.575209i
$621$		0			0
$622$	−7.56017e9			−1.25970
$623$	−5.54023e9	+	1.65693e9i	−0.917951	+	0.274533i
$624$		0			0
$625$	−1.14723e10	+	1.98706e10i	−1.87962	+	3.25559i
$626$	4.89851e8	+	8.48447e8i	0.0798094	+	0.138234i
$627$		0			0
$628$	2.18175e9	−	3.77891e9i	0.351517	−	0.608846i
$629$	3.88165e9			0.621926
$630$		0			0
$631$	8.67026e9			1.37382			0.686910	−	0.726743i	$-0.258967\pi$
$631$	8.67026e9			1.37382			0.686910	+	0.726743i	$0.258967\pi$
$632$	1.89170e9	−	3.27653e9i	0.298087	−	0.516302i
$633$		0			0
$634$	−4.42918e9	−	7.67156e9i	−0.690256	−	1.19556i
$635$	−1.61747e9	+	2.80154e9i	−0.250685	+	0.434199i
$636$		0			0
$637$	3.15237e8	+	5.46566e9i	0.0483224	+	0.837828i
$638$	−4.00005e8			−0.0609808
$639$		0			0
$640$	5.66660e8	+	9.81483e8i	0.0854461	+	0.147997i
$641$	2.88292e9	+	4.99337e9i	0.432345	+	0.748843i	0.997075	−	0.0764328i	$-0.0243531\pi$
$641$	2.88292e9	+	4.99337e9i	0.432345	+	0.748843i	−0.564730	+	0.825276i	$0.691020\pi$
$642$		0			0
$643$	2.51024e9			0.372371			0.186186	−	0.982515i	$-0.440387\pi$
$643$	2.51024e9			0.372371			0.186186	+	0.982515i	$0.440387\pi$
$644$	3.30908e9	+	3.12372e9i	0.488210	+	0.460863i
$645$		0			0
$646$	3.08606e9	−	5.34521e9i	0.450392	−	0.780102i
$647$	−3.91464e9	−	6.78036e9i	−0.568234	−	0.984210i	−0.996741	−	0.0806713i	$-0.974294\pi$
$647$	−3.91464e9	−	6.78036e9i	−0.568234	−	0.984210i	0.428507	−	0.903538i	$-0.359040\pi$
$648$		0			0
$649$	8.71297e8	−	1.50913e9i	0.125115	−	0.216706i
$650$	−1.13766e10			−1.62486
$651$		0			0
$652$	1.31073e8			0.0185203
$653$	2.72632e9	−	4.72212e9i	0.383160	−	0.663653i	−0.608352	−	0.793668i	$-0.708169\pi$
$653$	2.72632e9	−	4.72212e9i	0.383160	−	0.663653i	0.991512	+	0.130014i	$0.0415023\pi$
$654$		0			0
$655$	5.33034e9	+	9.23241e9i	0.741157	+	1.28372i
$656$	3.32346e8	−	5.75641e8i	0.0459650	−	0.0796137i
$657$		0			0
$658$	2.68774e8	−	1.13262e9i	0.0367788	−	0.154986i
$659$	7.30618e9			0.994470			0.497235	−	0.867616i	$-0.334349\pi$
$659$	7.30618e9			0.994470			0.497235	+	0.867616i	$0.334349\pi$
$660$		0			0
$661$	−5.63349e9	−	9.75749e9i	−0.758704	−	1.31411i	−0.943512	−	0.331339i	$-0.892500\pi$
$661$	−5.63349e9	−	9.75749e9i	−0.758704	−	1.31411i	0.184808	−	0.982775i	$-0.440834\pi$
$662$	2.28348e9	+	3.95510e9i	0.305910	+	0.529852i
$663$		0			0
$664$	3.29404e9			0.436658
$665$	2.48525e9	−	1.04729e10i	0.327714	−	1.38099i
$666$		0			0
$667$	2.89401e9	−	5.01257e9i	0.377624	−	0.654063i
$668$	−1.07192e9	−	1.85663e9i	−0.139138	−	0.240995i
$669$		0			0
$670$	2.02497e9	−	3.50736e9i	0.260110	−	0.450524i
$671$	1.75001e9			0.223621
$672$		0			0
$673$	−4.40416e9			−0.556943			−0.278471	−	0.960445i	$-0.589828\pi$
$673$	−4.40416e9			−0.556943			−0.278471	+	0.960445i	$0.589828\pi$
$674$	−1.39013e9	+	2.40778e9i	−0.174883	+	0.302906i
$675$		0			0
$676$	5.93770e8	+	1.02844e9i	0.0739273	+	0.128046i
$677$	−4.28255e9	+	7.41760e9i	−0.530447	+	0.918761i	0.468922	+	0.883240i	$0.344643\pi$
$677$	−4.28255e9	+	7.41760e9i	−0.530447	+	0.918761i	−0.999369	+	0.0355218i	$0.988691\pi$
$678$		0			0
$679$	−1.05286e10	−	9.93885e9i	−1.29070	−	1.21841i
$680$	−9.72611e9			−1.18620
$681$		0			0
$682$	−3.08540e8	−	5.34408e8i	−0.0372449	−	0.0645101i
$683$	−5.18466e9	−	8.98010e9i	−0.622656	−	1.07847i	−0.988989	−	0.147988i	$-0.952720\pi$
$683$	−5.18466e9	−	8.98010e9i	−0.622656	−	1.07847i	0.366333	−	0.930484i	$-0.380613\pi$
$684$		0			0
$685$	−1.58921e10			−1.88914
$686$	2.04013e9	+	5.62004e9i	0.241281	+	0.664668i
$687$		0			0
$688$	−8.16986e8	+	1.41506e9i	−0.0956434	+	0.165659i
$689$	1.89581e9	+	3.28364e9i	0.220815	+	0.382462i
$690$		0			0
$691$	6.88286e9	−	1.19215e10i	0.793589	−	1.37454i	−0.130142	−	0.991495i	$-0.541543\pi$
$691$	6.88286e9	−	1.19215e10i	0.793589	−	1.37454i	0.923731	−	0.383041i	$-0.125123\pi$
$692$	−3.81084e9			−0.437168
$693$		0			0
$694$	1.44485e9			0.164083
$695$	−1.03780e10	+	1.79753e10i	−1.17265	+	2.03109i
$696$		0			0
$697$	2.85218e9	+	4.94013e9i	0.319053	+	0.552616i
$698$	−1.68743e9	+	2.92271e9i	−0.187815	+	0.325305i
$699$		0			0
$700$	−1.19032e10	+	3.55993e9i	−1.31166	+	0.392282i
$701$	−1.60131e10			−1.75575			−0.877874	−	0.478891i	$-0.841039\pi$
$701$	−1.60131e10			−1.75575			−0.877874	+	0.478891i	$0.841039\pi$
$702$		0			0
$703$	−1.21182e9	−	2.09893e9i	−0.131551	−	0.227853i
$704$	8.87152e7	+	1.53659e8i	0.00958283	+	0.0165980i
$705$		0			0
$706$	3.92439e9			0.419716
$707$	−1.34821e9	+	5.68139e9i	−0.143480	+	0.604626i
$708$		0			0
$709$	−9.47418e9	+	1.64098e10i	−0.998343	+	1.72918i	−0.449344	+	0.893359i	$0.648342\pi$
$709$	−9.47418e9	+	1.64098e10i	−0.998343	+	1.72918i	−0.549000	+	0.835822i	$0.684991\pi$
$710$	−7.95143e9	−	1.37723e10i	−0.833760	−	1.44411i
$711$		0			0
$712$	1.63127e9	−	2.82545e9i	0.169374	−	0.293364i
$713$	8.92906e9			0.922556
$714$		0			0
$715$	−2.43158e9			−0.248781
$716$	−1.58834e9	+	2.75109e9i	−0.161714	+	0.280098i
$717$		0			0
$718$	−4.28838e9	−	7.42770e9i	−0.432372	−	0.748891i
$719$	4.22087e9	−	7.31076e9i	0.423497	−	0.733519i	−0.572782	−	0.819708i	$-0.694136\pi$
$719$	4.22087e9	−	7.31076e9i	0.423497	−	0.733519i	0.996279	+	0.0861893i	$0.0274690\pi$
$720$		0			0
$721$	1.35313e10	−	4.04685e9i	1.34452	−	0.402109i
$722$	3.29721e9			0.326036
$723$		0			0
$724$	4.00742e9	+	6.94105e9i	0.392446	+	0.679736i
$725$	7.90136e9	+	1.36856e10i	0.770050	+	1.33377i
$726$		0			0
$727$	−1.46028e9			−0.140950			−0.0704752	−	0.997514i	$-0.522452\pi$
$727$	−1.46028e9			−0.140950			−0.0704752	+	0.997514i	$0.522452\pi$
$728$	−2.24612e9	−	2.12030e9i	−0.215761	−	0.203675i
$729$		0			0
$730$	8.91845e9	−	1.54472e10i	0.848515	−	1.46967i
$731$	−7.01135e9	−	1.21440e10i	−0.663882	−	1.14988i
$732$		0			0
$733$	−1.59745e9	+	2.76686e9i	−0.149818	+	0.259492i	−0.931160	−	0.364611i	$-0.881202\pi$
$733$	−1.59745e9	+	2.76686e9i	−0.149818	+	0.259492i	0.781342	+	0.624103i	$0.214535\pi$
$734$	−2.16486e9			−0.202066
$735$		0			0
$736$	−2.56739e9			−0.237367
$737$	3.17026e8	−	5.49105e8i	0.0291715	−	0.0505265i
$738$		0			0
$739$	5.44510e9	+	9.43118e9i	0.496307	+	0.859628i	0.999991	−	0.00425955i	$-0.00135586\pi$
$739$	5.44510e9	+	9.43118e9i	0.496307	+	0.859628i	−0.503684	+	0.863888i	$0.668023\pi$
$740$	−1.90960e9	+	3.30752e9i	−0.173233	+	0.300049i
$741$		0			0
$742$	3.01108e9	+	2.84242e9i	0.270588	+	0.255431i
$743$	−1.23102e10			−1.10105			−0.550523	−	0.834820i	$-0.685572\pi$
$743$	−1.23102e10			−1.10105			−0.550523	+	0.834820i	$0.685572\pi$
$744$		0			0
$745$	−1.10062e9	−	1.90633e9i	−0.0975194	−	0.168909i
$746$	2.64113e9	+	4.57457e9i	0.232918	+	0.403426i
$747$		0			0
$748$	−1.52270e9			−0.133033
$749$	−1.08425e10	+	3.24270e9i	−0.942855	+	0.281982i
$750$		0			0
$751$	1.06396e9	−	1.84283e9i	0.0916612	−	0.158762i	−0.816549	−	0.577276i	$-0.804116\pi$
$751$	1.06396e9	−	1.84283e9i	0.0916612	−	0.158762i	0.908210	+	0.418514i	$0.137449\pi$
$752$	3.28380e8	+	5.68772e8i	0.0281588	+	0.0487726i
$753$		0			0
$754$	−1.96438e9	+	3.40240e9i	−0.166888	+	0.289059i
$755$	−2.41376e10			−2.04117
$756$		0			0
$757$	−1.35668e10			−1.13669			−0.568344	−	0.822791i	$-0.692416\pi$
$757$	−1.35668e10			−1.13669			−0.568344	+	0.822791i	$0.692416\pi$
$758$	−7.90993e8	+	1.37004e9i	−0.0659675	+	0.114259i
$759$		0			0
$760$	3.03641e9	+	5.25921e9i	0.250907	+	0.434583i
$761$	4.19117e9	−	7.25933e9i	0.344738	−	0.597104i	−0.640568	−	0.767902i	$-0.721301\pi$
$761$	4.19117e9	−	7.25933e9i	0.344738	−	0.597104i	0.985306	+	0.170797i	$0.0546343\pi$
$762$		0			0
$763$	2.73720e9	−	1.15346e10i	0.223085	−	0.940086i
$764$	1.09032e10			0.884560
$765$		0			0
$766$	4.34281e9	+	7.52197e9i	0.349116	+	0.604687i
$767$	−8.55767e9	−	1.48223e10i	−0.684813	−	1.18613i
$768$		0			0
$769$	2.02485e10			1.60565			0.802823	−	0.596218i	$-0.203330\pi$
$769$	2.02485e10			1.60565			0.802823	+	0.596218i	$0.203330\pi$
$770$	−2.54414e9	+	7.60882e8i	−0.200828	+	0.0600620i
$771$		0			0
$772$	2.58139e9	−	4.47109e9i	0.201926	−	0.349746i
$773$	1.08122e10	+	1.87272e10i	0.841947	+	1.45829i	0.888247	+	0.459367i	$0.151924\pi$
$773$	1.08122e10	+	1.87272e10i	0.841947	+	1.45829i	−0.0463002	+	0.998928i	$0.514743\pi$
$774$		0			0
$775$	−1.21893e10	+	2.11125e10i	−0.940638	+	1.62923i
$776$	8.16876e9			0.627538
$777$		0			0
$778$	4.67850e9			0.356187
$779$	1.78085e9	−	3.08453e9i	0.134973	−	0.233780i
$780$		0			0
$781$	−1.24486e9	−	2.15616e9i	−0.0935066	−	0.161958i
$782$	1.10166e10	−	1.90814e10i	0.823806	−	1.42687i
$783$		0			0
$784$	−3.01357e9	−	1.51561e9i	−0.223345	−	0.112326i
$785$	−3.68449e10			−2.71853
$786$		0			0
$787$	6.63279e9	+	1.14883e10i	0.485048	+	0.840128i	0.999852	−	0.0171798i	$-0.00546878\pi$
$787$	6.63279e9	+	1.14883e10i	0.485048	+	0.840128i	−0.514804	+	0.857308i	$0.672135\pi$
$788$	2.20295e9	+	3.81562e9i	0.160385	+	0.277794i
$789$		0			0
$790$	−3.19466e10			−2.30532
$791$	4.10105e9	+	3.87133e9i	0.294630	+	0.278127i
$792$		0			0
$793$	8.59409e9	−	1.48854e10i	0.611989	−	1.06000i
$794$	6.33184e9	+	1.09671e10i	0.448909	+	0.777533i
$795$		0			0
$796$	5.11630e9	−	8.86169e9i	0.359551	−	0.622760i
$797$	6.98382e9			0.488640			0.244320	−	0.969695i	$-0.421435\pi$
$797$	6.98382e9			0.488640			0.244320	+	0.969695i	$0.421435\pi$
$798$		0			0
$799$	−5.63630e9			−0.390913
$800$	3.50481e9	−	6.07051e9i	0.242019	−	0.419189i
$801$		0			0
$802$	3.80004e9	+	6.58186e9i	0.260123	+	0.450545i
$803$	1.39626e9	−	2.41839e9i	0.0951614	−	0.164824i
$804$		0			0
$805$	8.87186e9	−	3.73862e10i	0.599417	−	2.52596i
$806$	−6.06082e9			−0.407717
$807$		0			0
$808$	−1.64721e9	−	2.85304e9i	−0.109852	−	0.190269i
$809$	4.95232e9	+	8.57767e9i	0.328843	+	0.569573i	0.982283	−	0.187406i	$-0.0600079\pi$
$809$	4.95232e9	+	8.57767e9i	0.328843	+	0.569573i	−0.653439	+	0.756979i	$0.726675\pi$
$810$		0			0
$811$	−1.09986e10			−0.724046			−0.362023	−	0.932169i	$-0.617914\pi$
$811$	−1.09986e10			−0.724046			−0.362023	+	0.932169i	$0.617914\pi$
$812$	−9.90644e8	+	4.17459e9i	−0.0649339	+	0.273633i
$813$		0			0
$814$	−2.98963e8	+	5.17820e8i	−0.0194282	+	0.0336506i
$815$	−5.53384e8	−	9.58489e8i	−0.0358076	−	0.0620205i
$816$		0			0
$817$	−4.37776e9	+	7.58251e9i	−0.280850	+	0.486447i
$818$	5.51223e9			0.352120
$819$		0			0
$820$	−5.61259e9			−0.355480
$821$	−3.23026e9	+	5.59497e9i	−0.203721	+	0.352855i	−0.949725	−	0.313087i	$-0.898637\pi$
$821$	−3.23026e9	+	5.59497e9i	−0.203721	+	0.352855i	0.746003	+	0.665942i	$0.231970\pi$
$822$		0			0
$823$	−6.01171e9	−	1.04126e10i	−0.375923	−	0.651117i	0.614542	−	0.788884i	$-0.289341\pi$
$823$	−6.01171e9	−	1.04126e10i	−0.375923	−	0.651117i	−0.990465	+	0.137767i	$0.956008\pi$
$824$	−3.98419e9	+	6.90082e9i	−0.248082	+	0.429690i
$825$		0			0
$826$	−1.35920e10	−	1.28306e10i	−0.839175	−	0.792169i
$827$	2.82746e10			1.73831			0.869156	−	0.494538i	$-0.164663\pi$
$827$	2.82746e10			1.73831			0.869156	+	0.494538i	$0.164663\pi$
$828$		0			0
$829$	−3.16275e9	−	5.47804e9i	−0.192807	−	0.333952i	0.753372	−	0.657594i	$-0.228426\pi$
$829$	−3.16275e9	−	5.47804e9i	−0.192807	−	0.333952i	−0.946179	+	0.323642i	$0.895093\pi$
$830$	−1.39073e10	−	2.40881e10i	−0.844245	−	1.46228i
$831$		0			0
$832$	1.74268e9			0.104903
$833$	2.41955e10	−	1.58940e10i	1.45036	−	0.952745i
$834$		0			0
$835$	−9.05121e9	+	1.56772e10i	−0.538027	+	0.931890i
$836$	4.75375e8	+	8.23373e8i	0.0281393	+	0.0487388i
$837$		0			0
$838$	−5.66691e9	+	9.81538e9i	−0.332654	+	0.576173i
$839$	1.89113e10			1.10549			0.552744	−	0.833351i	$-0.313581\pi$
$839$	1.89113e10			1.10549			0.552744	+	0.833351i	$0.313581\pi$
$840$		0			0
$841$	−1.17926e10			−0.683635
$842$	−1.14725e10	+	1.98710e10i	−0.662319	+	1.14717i
$843$		0			0
$844$	6.75251e9	+	1.16957e10i	0.386604	+	0.669618i
$845$	5.01372e9	−	8.68402e9i	0.285866	−	0.495134i
$846$		0			0
$847$	1.65447e10	−	4.94805e9i	0.935548	−	0.279796i
$848$	−2.33619e9			−0.131559
$849$		0			0
$850$	3.00782e10	+	5.20969e10i	1.67991	+	2.90968i
$851$	−4.32595e9	−	7.49277e9i	−0.240618	−	0.416763i
$852$		0			0
$853$	2.21338e10			1.22105			0.610526	−	0.791996i	$-0.290958\pi$
$853$	2.21338e10			1.22105			0.610526	+	0.791996i	$0.290958\pi$
$854$	4.33404e9	−	1.82637e10i	0.238117	−	1.00343i
$855$		0			0
$856$	3.19250e9	−	5.52957e9i	0.173969	−	0.301324i
$857$	−7.79400e9	−	1.34996e10i	−0.422988	−	0.732636i	0.573243	−	0.819386i	$-0.305685\pi$
$857$	−7.79400e9	−	1.34996e10i	−0.422988	−	0.732636i	−0.996230	+	0.0867498i	$0.972352\pi$
$858$		0			0
$859$	1.23240e10	−	2.13458e10i	0.663400	−	1.14904i	−0.316316	−	0.948654i	$-0.602446\pi$
$859$	1.23240e10	−	2.13458e10i	0.663400	−	1.14904i	0.979716	−	0.200389i	$-0.0642205\pi$
$860$	1.37971e10			0.739678
$861$		0			0
$862$	1.04652e10			0.556508
$863$	−1.11714e10	+	1.93494e10i	−0.591654	+	1.02478i	0.402355	+	0.915484i	$0.368192\pi$
$863$	−1.11714e10	+	1.93494e10i	−0.591654	+	1.02478i	−0.994010	+	0.109292i	$0.965142\pi$
$864$		0			0
$865$	1.60891e10	+	2.78672e10i	0.845232	+	1.46399i
$866$	−6.31582e8	+	1.09393e9i	−0.0330459	+	0.0572371i
$867$		0			0
$868$	−6.34139e9	+	1.89653e9i	−0.329128	+	0.0984332i
$869$	−5.00151e9			−0.258543
$870$		0			0
$871$	−3.11376e9	−	5.39318e9i	−0.159669	−	0.276555i
$872$	3.34423e9	+	5.79238e9i	0.170800	+	0.295835i
$873$		0			0
$874$	−1.37572e10			−0.697011
$875$	4.84262e10	+	4.57136e10i	2.44372	+	2.30684i
$876$		0			0
$877$	6.90962e7	−	1.19678e8i	0.00345904	−	0.00599123i	−0.864291	−	0.502993i	$-0.832232\pi$
$877$	6.90962e7	−	1.19678e8i	0.00345904	−	0.00599123i	0.867750	+	0.497001i	$0.165566\pi$
$878$	9.58115e9	+	1.65950e10i	0.477735	+	0.827461i
$879$		0			0
$880$	7.49101e8	−	1.29748e9i	0.0370554	−	0.0641818i
$881$	−1.53707e10			−0.757320			−0.378660	−	0.925536i	$-0.623615\pi$
$881$	−1.53707e10			−0.757320			−0.378660	+	0.925536i	$0.623615\pi$
$882$		0			0
$883$	−1.20807e10			−0.590515			−0.295257	−	0.955418i	$-0.595405\pi$
$883$	−1.20807e10			−0.590515			−0.295257	+	0.955418i	$0.595405\pi$
$884$	−7.47781e9	+	1.29519e10i	−0.364076	+	0.630597i
$885$		0			0
$886$	−1.62384e8	−	2.81257e8i	−0.00784377	−	0.0135858i
$887$	7.18701e9	−	1.24483e10i	0.345793	−	0.598930i	−0.639705	−	0.768621i	$-0.720943\pi$
$887$	7.18701e9	−	1.24483e10i	0.345793	−	0.598930i	0.985497	+	0.169690i	$0.0542767\pi$
$888$		0			0
$889$	3.95029e9	+	3.72902e9i	0.188570	+	0.178008i
$890$	−2.75486e10			−1.30989
$891$		0			0
$892$	−4.95620e8	−	8.58439e8i	−0.0233815	−	0.0404979i
$893$	1.75960e9	+	3.04772e9i	0.0826866	+	0.143217i
$894$		0			0
$895$	2.68236e10			1.25065
$896$	1.82335e9	−	5.45314e8i	0.0846823	−	0.0253261i
$897$		0			0
$898$	−6.90938e9	+	1.19674e10i	−0.318399	+	0.551483i
$899$	4.20941e9	+	7.29091e9i	0.193225	+	0.334675i
$900$		0			0
$901$	1.00245e10	−	1.73630e10i	0.456591	−	0.790839i
$902$	−8.78697e8			−0.0398672
$903$		0			0
$904$	−3.18185e9			−0.143249
$905$	3.38382e10	−	5.86095e10i	1.51753	−	2.62844i
$906$		0			0
$907$	1.12941e10	+	1.95619e10i	0.502603	+	0.870533i	0.999995	+	0.00300772i	$0.000957390\pi$
$907$	1.12941e10	+	1.95619e10i	0.502603	+	0.870533i	−0.497393	+	0.867525i	$0.665709\pi$
$908$	7.21875e9	−	1.25032e10i	0.320009	−	0.554271i
$909$		0			0
$910$	−6.02200e9	+	2.53768e10i	−0.264908	+	1.11633i
$911$	4.00994e10			1.75721			0.878606	−	0.477548i	$-0.158474\pi$
$911$	4.00994e10			1.75721			0.878606	+	0.477548i	$0.158474\pi$
$912$		0			0
$913$	−2.17730e9	−	3.77119e9i	−0.0946826	−	0.163995i
$914$	−1.03770e10	−	1.79734e10i	−0.449530	−	0.778608i
$915$		0			0
$916$	3.76824e9			0.161996
$917$	1.71515e10	−	5.12955e9i	0.734531	−	0.219678i
$918$		0			0
$919$	−2.21264e9	+	3.83241e9i	−0.0940387	+	0.162880i	−0.909207	−	0.416344i	$-0.863311\pi$
$919$	−2.21264e9	+	3.83241e9i	−0.0940387	+	0.162880i	0.815168	+	0.579224i	$0.196644\pi$
$920$	1.08394e10	+	1.87744e10i	0.458931	+	0.794891i
$921$		0			0
$922$	−5.18730e9	+	8.98466e9i	−0.217963	+	0.377523i
$923$	−2.44535e10			−1.02361
$924$		0			0
$925$	2.36219e10			0.981336
$926$	1.78977e9	−	3.09998e9i	0.0740730	−	0.128298i
$927$		0			0
$928$	−1.21034e9	−	2.09637e9i	−0.0497152	−	0.0861093i
$929$	1.43849e10	−	2.49153e10i	0.588641	−	1.01956i	−0.405769	−	0.913976i	$-0.632996\pi$
$929$	1.43849e10	−	2.49153e10i	0.588641	−	1.01956i	0.994411	−	0.105581i	$-0.0336703\pi$
$930$		0			0
$931$	−1.61480e10	−	8.12129e9i	−0.655837	−	0.329838i
$932$	2.36810e9			0.0958173
$933$		0			0
$934$	1.63297e9	+	2.82838e9i	0.0655788	+	0.113586i
$935$	6.42876e9	+	1.11349e10i	0.257209	+	0.445500i
$936$		0			0
$937$	−3.85301e10			−1.53007			−0.765036	−	0.643988i	$-0.777279\pi$
$937$	−3.85301e10			−1.53007			−0.765036	+	0.643988i	$0.777279\pi$
$938$	−4.94552e9	−	4.66850e9i	−0.195660	−	0.184700i
$939$		0			0
$940$	2.77281e9	−	4.80264e9i	0.108886	−	0.188596i
$941$	1.98576e10	+	3.43943e10i	0.776895	+	1.34562i	0.933723	+	0.357995i	$0.116540\pi$
$941$	1.98576e10	+	3.43943e10i	0.776895	+	1.34562i	−0.156829	+	0.987626i	$0.550127\pi$
$942$		0			0
$943$	6.35730e9	−	1.10112e10i	0.246878	−	0.427605i
$944$	1.05455e10			0.408005
$945$		0			0
$946$	2.16005e9			0.0829553
$947$	1.22182e10	−	2.11625e10i	0.467500	−	0.809734i	−0.531810	−	0.846864i	$-0.678488\pi$
$947$	1.22182e10	−	2.11625e10i	0.467500	−	0.809734i	0.999310	+	0.0371293i	$0.0118213\pi$
$948$		0			0
$949$	−1.37137e10	−	2.37528e10i	−0.520863	−	0.902160i
$950$	1.87803e10	−	3.25284e10i	0.710672	−	1.23092i
$951$		0			0
$952$	−3.77109e9	+	1.58915e10i	−0.141657	+	0.596945i
$953$	−2.13072e10			−0.797445			−0.398722	−	0.917072i	$-0.630546\pi$
$953$	−2.13072e10			−0.797445			−0.398722	+	0.917072i	$0.630546\pi$
$954$		0			0
$955$	−4.60327e10	−	7.97310e10i	−1.71023	−	2.96221i
$956$	−1.12728e10	−	1.95251e10i	−0.417282	−	0.722754i
$957$		0			0
$958$	−3.00822e9			−0.110543
$959$	−6.16181e9	+	2.59660e10i	−0.225602	+	0.950691i
$960$		0			0
$961$	7.26253e9	−	1.25791e10i	0.263971	−	0.457211i
$962$	2.93635e9	+	5.08590e9i	0.106339	+	0.184185i
$963$		0			0
$964$	−3.23508e9	+	5.60333e9i	−0.116310	+	0.201454i
$965$	−4.35938e10			−1.56164
$966$		0			0
$967$	−2.39953e10			−0.853363			−0.426681	−	0.904402i	$-0.640317\pi$
$967$	−2.39953e10			−0.853363			−0.426681	+	0.904402i	$0.640317\pi$
$968$	−4.87144e9	+	8.43758e9i	−0.172621	+	0.298988i
$969$		0			0
$970$	−3.44880e10	−	5.97350e10i	−1.21330	−	2.10149i
$971$	1.42414e10	−	2.46668e10i	0.499212	−	0.864661i	−0.500787	−	0.865570i	$-0.666956\pi$
$971$	1.42414e10	−	2.46668e10i	0.499212	−	0.864661i	1.00000		0.000909327i	$0.000289448\pi$
$972$		0			0
$973$	2.53459e10	+	2.39261e10i	0.882088	+	0.832679i
$974$	3.14715e10			1.09134
$975$		0			0
$976$	5.29520e9	+	9.17155e9i	0.182309	+	0.315768i
$977$	−2.37646e10	−	4.11615e10i	−0.815266	−	1.41208i	−0.909137	−	0.416498i	$-0.863257\pi$
$977$	−2.37646e10	−	4.11615e10i	−0.815266	−	1.41208i	0.0938706	−	0.995584i	$-0.470076\pi$
$978$		0			0
$979$	−4.31296e9			−0.146905
$980$	1.64007e9	+	2.84359e10i	0.0556634	+	0.965109i
$981$		0			0
$982$	1.62735e10	−	2.81865e10i	0.548392	−	0.949842i
$983$	4.95134e9	+	8.57597e9i	0.166259	+	0.287969i	0.937102	−	0.349057i	$-0.113498\pi$
$983$	4.95134e9	+	8.57597e9i	0.166259	+	0.287969i	−0.770843	+	0.637026i	$0.780165\pi$
$984$		0			0
$985$	1.86015e10	−	3.22187e10i	0.620184	−	1.07419i
$986$	2.07742e10			0.690168
$987$		0			0
$988$	9.33803e9			0.308039
$989$	−1.56278e10	+	2.70681e10i	−0.513700	+	0.889755i
$990$		0			0
$991$	−9.34663e8	−	1.61888e9i	−0.0305069	−	0.0528394i	0.850369	−	0.526187i	$-0.176379\pi$
$991$	−9.34663e8	−	1.61888e9i	−0.0305069	−	0.0528394i	−0.880876	+	0.473348i	$0.843045\pi$
$992$	1.86717e9	−	3.23403e9i	0.0607286	−	0.105185i
$993$		0			0
$994$	−2.55855e10	+	7.65190e9i	−0.826306	+	0.247125i
$995$	−8.64029e10			−2.78066
$996$		0			0
$997$	−7.70789e9	−	1.33505e10i	−0.246322	−	0.426642i	0.716181	−	0.697915i	$-0.245889\pi$
$997$	−7.70789e9	−	1.33505e10i	−0.246322	−	0.426642i	−0.962502	+	0.271273i	$0.912555\pi$
$998$	1.01405e10	+	1.75639e10i	0.322926	+	0.559324i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.8.g.j.37.1	yes	6
3.2	odd	2		126.8.g.i.37.3	✓	6
7.4	even	3	inner	126.8.g.j.109.1	yes	6
21.11	odd	6		126.8.g.i.109.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.8.g.i.37.3	✓	6	3.2	odd	2
126.8.g.i.109.3	yes	6	21.11	odd	6
126.8.g.j.37.1	yes	6	1.1	even	1	trivial
126.8.g.j.109.1	yes	6	7.4	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-270.204 + 468.008i) q^{5} +(659.910 + 622.946i) q^{7} -512.000 q^{8} +(2161.63 + 3744.06i) q^{10} +(338.422 + 586.164i) q^{11} +6647.80 q^{13} +(6955.54 - 2080.21i) q^{14} +(-2048.00 + 3547.24i) q^{16} +(-17575.9 - 30442.3i) q^{17} +(-10974.1 + 19007.6i) q^{19} +34586.2 q^{20} +5414.75 q^{22} +(-39175.3 + 67853.6i) q^{23} +(-106958. - 185257. i) q^{25} +(26591.2 - 46057.3i) q^{26} +(13410.0 - 56510.2i) q^{28} -73873.3 q^{29} +(-56981.5 - 98694.8i) q^{31} +(16384.0 + 28377.9i) q^{32} -281214. q^{34} +(-469854. + 140520. i) q^{35} +(-55212.8 + 95631.3i) q^{37} +(87792.5 + 152061. i) q^{38} +(138345. - 239620. i) q^{40} -162278. q^{41} +398919. q^{43} +(21659.0 - 37514.5i) q^{44} +(313402. + 542829. i) q^{46} +(80171.0 - 138860. i) q^{47} +(47419.7 + 822177. i) q^{49} -1.71133e6 q^{50} +(-212730. - 368458. i) q^{52} +(285179. + 493944. i) q^{53} -365772. q^{55} +(-337874. - 318948. i) q^{56} +(-295493. + 511809. i) q^{58} +(-1.28729e6 - 2.22966e6i) q^{59} +(1.29277e6 - 2.23915e6i) q^{61} -911704. q^{62} +262144. q^{64} +(-1.79626e6 + 3.11122e6i) q^{65} +(-468389. - 811274. i) q^{67} +(-1.12486e6 + 1.94831e6i) q^{68} +(-905863. + 3.81733e6i) q^{70} -3.67843e6 q^{71} +(-2.06289e6 - 3.57304e6i) q^{73} +(441702. + 765051. i) q^{74} +1.40468e6 q^{76} +(-141820. + 597634. i) q^{77} +(-3.69473e6 + 6.39946e6i) q^{79} +(-1.10676e6 - 1.91696e6i) q^{80} +(-649114. + 1.12430e6i) q^{82} -6.43368e6 q^{83} +1.89963e7 q^{85} +(1.59568e6 - 2.76379e6i) q^{86} +(-173272. - 300116. i) q^{88} +(-3.18608e6 + 5.51845e6i) q^{89} +(4.38695e6 + 4.14122e6i) q^{91} +5.01444e6 q^{92} +(-641368. - 1.11088e6i) q^{94} +(-5.93048e6 - 1.02719e7i) q^{95} -1.59546e7 q^{97} +(5.88589e6 + 2.96017e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 24 q^{2} - 192 q^{4} - 718 q^{5} - 1471 q^{7} - 3072 q^{8} + 5744 q^{10} + 208 q^{11} + 19394 q^{13} - 4504 q^{14} - 12288 q^{16} - 19244 q^{17} - 25419 q^{19} + 91904 q^{20} + 3328 q^{22} - 67400 q^{23}+ \cdots + 20461248 q^{98}+O(q^{100}) \) 6 * q + 24 * q^2 - 192 * q^4 - 718 * q^5 - 1471 * q^7 - 3072 * q^8 + 5744 * q^10 + 208 * q^11 + 19394 * q^13 - 4504 * q^14 - 12288 * q^16 - 19244 * q^17 - 25419 * q^19 + 91904 * q^20 + 3328 * q^22 - 67400 * q^23 - 93931 * q^25 + 77576 * q^26 + 58112 * q^28 + 33476 * q^29 + 78449 * q^31 + 98304 * q^32 - 307904 * q^34 - 602072 * q^35 - 496599 * q^37 + 203352 * q^38 + 367616 * q^40 + 1953168 * q^41 + 697470 * q^43 + 13312 * q^44 + 539200 * q^46 + 701328 * q^47 + 959673 * q^49 - 1502896 * q^50 - 620608 * q^52 + 2917374 * q^53 - 3275696 * q^55 + 753152 * q^56 + 133904 * q^58 - 492040 * q^59 + 3649370 * q^61 + 1255184 * q^62 + 1572864 * q^64 - 2707764 * q^65 - 3647153 * q^67 - 1231616 * q^68 - 503936 * q^70 + 3541216 * q^71 - 6183557 * q^73 + 3972792 * q^74 + 3253632 * q^76 + 13092290 * q^77 - 12453589 * q^79 - 2940928 * q^80 + 7812672 * q^82 + 11611120 * q^83 + 38154616 * q^85 + 2789880 * q^86 - 106496 * q^88 - 8292612 * q^89 + 366581 * q^91 + 8627200 * q^92 - 5610624 * q^94 - 8691056 * q^95 - 55949528 * q^97 + 20461248 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more