LMFDB - Embedded newform 81.10.c.f.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,10,Mod(28,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("81.28");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	81.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$41.7179027293$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 14x^{2} + 196 $ x^4 + 14*x^2 + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$-1.87083 + 3.24037i$ of defining polynomial
Character	$\chi$	$=$	81.55
Dual form			81.10.c.f.28.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-11.2250 + 19.4422i) q^{2} +(4.00000 + 6.92820i) q^{4} +(246.949 + 427.729i) q^{5} +(381.500 - 660.777i) q^{7} -11674.0 q^{8} -11088.0 q^{10} +(28444.1 - 49266.6i) q^{11} +(36507.5 + 63232.8i) q^{13} +(8564.65 + 14834.4i) q^{14} +(128992. - 223421. i) q^{16} +168240. q^{17} -598129. q^{19} +(-1975.60 + 3421.83i) q^{20} +(638568. + 1.10603e6i) q^{22} +(-1.20020e6 - 2.07880e6i) q^{23} +(854594. - 1.48020e6i) q^{25} -1.63918e6 q^{26} +6104.00 q^{28} +(2.32689e6 - 4.03029e6i) q^{29} +(912050. + 1.57972e6i) q^{31} +(-92673.4 - 160515. i) q^{32} +(-1.88849e6 + 3.27096e6i) q^{34} +376845. q^{35} +1.42722e7 q^{37} +(6.71398e6 - 1.16290e7i) q^{38} +(-2.88288e6 - 4.99329e6i) q^{40} +(-1.49122e7 - 2.58286e7i) q^{41} +(-3.87845e6 + 6.71768e6i) q^{43} +455105. q^{44} +5.38887e7 q^{46} +(-1.54952e7 + 2.68384e7i) q^{47} +(1.98857e7 + 3.44431e7i) q^{49} +(1.91856e7 + 3.32304e7i) q^{50} +(-292060. + 505863. i) q^{52} +9.90123e6 q^{53} +2.80970e7 q^{55} +(-4.45362e6 + 7.71390e6i) q^{56} +(5.22386e7 + 9.04799e7i) q^{58} +(6.26049e7 + 1.08435e8i) q^{59} +(7.63832e7 - 1.32300e8i) q^{61} -4.09509e7 q^{62} +1.36249e8 q^{64} +(-1.80310e7 + 3.12306e7i) q^{65} +(1.60376e8 + 2.77779e8i) q^{67} +(672960. + 1.16560e6i) q^{68} +(-4.23007e6 + 7.32670e6i) q^{70} +1.09152e8 q^{71} +6.64640e7 q^{73} +(-1.60205e8 + 2.77483e8i) q^{74} +(-2.39252e6 - 4.14396e6i) q^{76} +(-2.17028e7 - 3.75904e7i) q^{77} +(5.76787e7 - 9.99025e7i) q^{79} +1.27418e8 q^{80} +6.69554e8 q^{82} +(3.07319e8 - 5.32293e8i) q^{83} +(4.15467e7 + 7.19611e7i) q^{85} +(-8.70710e7 - 1.50811e8i) q^{86} +(-3.32055e8 + 5.75137e8i) q^{88} -3.37797e8 q^{89} +5.57104e7 q^{91} +(9.60157e6 - 1.66304e7i) q^{92} +(-3.47865e8 - 6.02520e8i) q^{94} +(-1.47708e8 - 2.55837e8i) q^{95} +(1.17653e8 - 2.03782e8i) q^{97} -8.92867e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{4} + 1526 q^{7} - 44352 q^{10} + 146030 q^{13} + 515968 q^{16} - 2392516 q^{19} + 2554272 q^{22} + 3418378 q^{25} + 24416 q^{28} + 3648200 q^{31} - 7553952 q^{34} + 57088700 q^{37} - 11531520 q^{40}+ \cdots + 470613686 q^{97}+O(q^{100}) $ 4 * q + 16 * q^4 + 1526 * q^7 - 44352 * q^10 + 146030 * q^13 + 515968 * q^16 - 2392516 * q^19 + 2554272 * q^22 + 3418378 * q^25 + 24416 * q^28 + 3648200 * q^31 - 7553952 * q^34 + 57088700 * q^37 - 11531520 * q^40 - 15513808 * q^43 + 215554752 * q^46 + 79542876 * q^49 - 1168240 * q^52 + 112387968 * q^55 + 208954368 * q^58 + 305532986 * q^61 + 544995328 * q^64 + 641504138 * q^67 - 16920288 * q^70 + 265855940 * q^73 - 9570064 * q^76 + 230714906 * q^79 + 2678215680 * q^82 + 166186944 * q^85 - 1328221440 * q^88 + 222841780 * q^91 - 1391461344 * q^94 + 470613686 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−11.2250	+	19.4422i	−0.496078	+	0.859233i	−0.999990	−	0.00452240i	$-0.998560\pi$
$2$	−11.2250	+	19.4422i	−0.496078	+	0.859233i	0.503911	+	0.863755i	$0.331894\pi$
$3$		0			0
$3$		0			0
$4$	4.00000	+	6.92820i	0.00781250	+	0.0135316i
$5$	246.949	+	427.729i	0.176703	+	0.306058i	0.940749	−	0.339103i	$-0.110124\pi$
$5$	246.949	+	427.729i	0.176703	+	0.306058i	−0.764047	+	0.645161i	$0.776790\pi$
$6$		0			0
$7$	381.500	−	660.777i	0.0600556	−	0.104019i	−0.834434	−	0.551107i	$-0.814206\pi$
$7$	381.500	−	660.777i	0.0600556	−	0.104019i	0.894490	+	0.447088i	$0.147539\pi$
$8$	−11674.0			−1.00766
$9$		0			0
$10$	−11088.0			−0.350633
$11$	28444.1	−	49266.6i	0.585767	−	1.01458i	−0.409012	−	0.912529i	$-0.634127\pi$
$11$	28444.1	−	49266.6i	0.585767	−	1.01458i	0.994779	−	0.102049i	$-0.0325399\pi$
$12$		0			0
$13$	36507.5	+	63232.8i	0.354517	+	0.614041i	0.987035	−	0.160504i	$-0.0513120\pi$
$13$	36507.5	+	63232.8i	0.354517	+	0.614041i	−0.632518	+	0.774545i	$0.717979\pi$
$14$	8564.65	+	14834.4i	0.0595845	+	0.103203i
$15$		0			0
$16$	128992.	−	223421.i	0.492065	−	0.852282i
$17$	168240.			0.488550			0.244275	−	0.969706i	$-0.421450\pi$
$17$	168240.			0.488550			0.244275	+	0.969706i	$0.421450\pi$
$18$		0			0
$19$	−598129.			−1.05294			−0.526470	−	0.850194i	$-0.676485\pi$
$19$	−598129.			−1.05294			−0.526470	+	0.850194i	$0.676485\pi$
$20$	−1975.60	+	3421.83i	−0.00276098	+	0.00478215i
$21$		0			0
$22$	638568.	+	1.10603e6i	0.581173	+	1.00662i
$23$	−1.20020e6	−	2.07880e6i	−0.894287	−	1.54895i	−0.834684	−	0.550729i	$-0.814350\pi$
$23$	−1.20020e6	−	2.07880e6i	−0.894287	−	1.54895i	−0.0596032	−	0.998222i	$-0.518984\pi$
$24$		0			0
$25$	854594.	−	1.48020e6i	0.437552	−	0.757863i
$26$	−1.63918e6			−0.703473
$27$		0			0
$28$	6104.00			0.00187674
$29$	2.32689e6	−	4.03029e6i	0.610921	−	1.05815i	−0.380164	−	0.924919i	$-0.624133\pi$
$29$	2.32689e6	−	4.03029e6i	0.610921	−	1.05815i	0.991085	−	0.133228i	$-0.0425341\pi$
$30$		0			0
$31$	912050.	+	1.57972e6i	0.177374	+	0.307222i	0.940980	−	0.338461i	$-0.109906\pi$
$31$	912050.	+	1.57972e6i	0.177374	+	0.307222i	−0.763606	+	0.645682i	$0.776573\pi$
$32$	−92673.4	−	160515.i	−0.0156236	−	0.0270608i
$33$		0			0
$34$	−1.88849e6	+	3.27096e6i	−0.242359	+	0.419778i
$35$	376845.			0.0424479
$36$		0			0
$37$	1.42722e7			1.25194			0.625968	−	0.779848i	$-0.284704\pi$
$37$	1.42722e7			1.25194			0.625968	+	0.779848i	$0.284704\pi$
$38$	6.71398e6	−	1.16290e7i	0.522341	−	0.904721i
$39$		0			0
$40$	−2.88288e6	−	4.99329e6i	−0.178056	−	0.308402i
$41$	−1.49122e7	−	2.58286e7i	−0.824163	−	1.42749i	−0.902558	−	0.430569i	$-0.858313\pi$
$41$	−1.49122e7	−	2.58286e7i	−0.824163	−	1.42749i	0.0783949	−	0.996922i	$-0.475021\pi$
$42$		0			0
$43$	−3.87845e6	+	6.71768e6i	−0.173002	+	0.299648i	−0.939468	−	0.342637i	$-0.888680\pi$
$43$	−3.87845e6	+	6.71768e6i	−0.173002	+	0.299648i	0.766466	+	0.642285i	$0.222013\pi$
$44$	455105.			0.0183052
$45$		0			0
$46$	5.38887e7			1.77455
$47$	−1.54952e7	+	2.68384e7i	−0.463186	+	0.802262i	−0.999118	−	0.0419996i	$-0.986627\pi$
$47$	−1.54952e7	+	2.68384e7i	−0.463186	+	0.802262i	0.535932	+	0.844261i	$0.319961\pi$
$48$		0			0
$49$	1.98857e7	+	3.44431e7i	0.492787	+	0.853532i
$50$	1.91856e7	+	3.32304e7i	0.434121	+	0.751919i
$51$		0			0
$52$	−292060.	+	505863.i	−0.00553933	+	0.00959440i
$53$	9.90123e6			0.172365			0.0861823	−	0.996279i	$-0.472533\pi$
$53$	9.90123e6			0.172365			0.0861823	+	0.996279i	$0.472533\pi$
$54$		0			0
$55$	2.80970e7			0.414026
$56$	−4.45362e6	+	7.71390e6i	−0.0605156	+	0.104816i
$57$		0			0
$58$	5.22386e7	+	9.04799e7i	0.606130	+	1.04985i
$59$	6.26049e7	+	1.08435e8i	0.672627	+	1.16502i	0.977157	+	0.212521i	$0.0681674\pi$
$59$	6.26049e7	+	1.08435e8i	0.672627	+	1.16502i	−0.304530	+	0.952503i	$0.598499\pi$
$60$		0			0
$61$	7.63832e7	−	1.32300e8i	0.706340	−	1.22342i	−0.259866	−	0.965645i	$-0.583678\pi$
$61$	7.63832e7	−	1.32300e8i	0.706340	−	1.22342i	0.966206	−	0.257772i	$-0.0829884\pi$
$62$	−4.09509e7			−0.351966
$63$		0			0
$64$	1.36249e8			1.01513
$65$	−1.80310e7	+	3.12306e7i	−0.125288	+	0.217005i
$66$		0			0
$67$	1.60376e8	+	2.77779e8i	0.972306	+	1.68408i	0.688554	+	0.725185i	$0.258246\pi$
$67$	1.60376e8	+	2.77779e8i	0.972306	+	1.68408i	0.283752	+	0.958898i	$0.408421\pi$
$68$	672960.	+	1.16560e6i	0.00381680	+	0.00661088i
$69$		0			0
$70$	−4.23007e6	+	7.32670e6i	−0.0210575	+	0.0364726i
$71$	1.09152e8			0.509763			0.254881	−	0.966972i	$-0.417964\pi$
$71$	1.09152e8			0.509763			0.254881	+	0.966972i	$0.417964\pi$
$72$		0			0
$73$	6.64640e7			0.273926			0.136963	−	0.990576i	$-0.456266\pi$
$73$	6.64640e7			0.273926			0.136963	+	0.990576i	$0.456266\pi$
$74$	−1.60205e8	+	2.77483e8i	−0.621059	+	1.07571i
$75$		0			0
$76$	−2.39252e6	−	4.14396e6i	−0.00822609	−	0.0142480i
$77$	−2.17028e7	−	3.75904e7i	−0.0703571	−	0.121862i
$78$		0			0
$79$	5.76787e7	−	9.99025e7i	0.166607	−	0.288572i	−0.770618	−	0.637298i	$-0.780052\pi$
$79$	5.76787e7	−	9.99025e7i	0.166607	−	0.288572i	0.937225	+	0.348726i	$0.113385\pi$
$80$	1.27418e8			0.347797
$81$		0			0
$82$	6.69554e8			1.63540
$83$	3.07319e8	−	5.32293e8i	0.710785	−	1.23112i	−0.253777	−	0.967263i	$-0.581673\pi$
$83$	3.07319e8	−	5.32293e8i	0.710785	−	1.23112i	0.964563	−	0.263854i	$-0.0849937\pi$
$84$		0			0
$85$	4.15467e7	+	7.19611e7i	0.0863280	+	0.149525i
$86$	−8.70710e7	−	1.50811e8i	−0.171645	−	0.297298i
$87$		0			0
$88$	−3.32055e8	+	5.75137e8i	−0.590253	+	1.02235i
$89$	−3.37797e8			−0.570691			−0.285345	−	0.958425i	$-0.592108\pi$
$89$	−3.37797e8			−0.570691			−0.285345	+	0.958425i	$0.592108\pi$
$90$		0			0
$91$	5.57104e7			0.0851629
$92$	9.60157e6	−	1.66304e7i	0.0139732	−	0.0242024i
$93$		0			0
$94$	−3.47865e8	−	6.02520e8i	−0.459553	−	0.795970i
$95$	−1.47708e8	−	2.55837e8i	−0.186057	−	0.322261i
$96$		0			0
$97$	1.17653e8	−	2.03782e8i	0.134937	−	0.233718i	−0.790636	−	0.612286i	$-0.790250\pi$
$97$	1.17653e8	−	2.03782e8i	0.134937	−	0.233718i	0.925573	+	0.378568i	$0.123583\pi$
$98$	−8.92867e8			−0.977843
$99$		0			0
$100$	1.36735e7			0.0136735
$101$	4.58085e8	−	7.93426e8i	0.438026	−	0.758683i	−0.559511	−	0.828823i	$-0.689011\pi$
$101$	4.58085e8	−	7.93426e8i	0.438026	−	0.758683i	0.997537	+	0.0701397i	$0.0223445\pi$
$102$		0			0
$103$	−5.03997e7	−	8.72949e7i	−0.0441225	−	0.0764225i	0.843121	−	0.537724i	$-0.180716\pi$
$103$	−5.03997e7	−	8.72949e7i	−0.0441225	−	0.0764225i	−0.887243	+	0.461302i	$0.847383\pi$
$104$	−4.26187e8	−	7.38178e8i	−0.357232	−	0.618744i
$105$		0			0
$106$	−1.11141e8	+	1.92502e8i	−0.0855063	+	0.148101i
$107$	1.50887e9			1.11282			0.556411	−	0.830907i	$-0.312178\pi$
$107$	1.50887e9			1.11282			0.556411	+	0.830907i	$0.312178\pi$
$108$		0			0
$109$	−2.26733e9			−1.53849			−0.769247	−	0.638951i	$-0.779369\pi$
$109$	−2.26733e9			−1.53849			−0.769247	+	0.638951i	$0.779369\pi$
$110$	−3.15388e8	+	5.46268e8i	−0.205389	+	0.355745i
$111$		0			0
$112$	−9.84209e7	−	1.70470e8i	−0.0591025	−	0.102369i
$113$	−5.79808e8	−	1.00426e9i	−0.334527	−	0.579418i	0.648867	−	0.760902i	$-0.275243\pi$
$113$	−5.79808e8	−	1.00426e9i	−0.334527	−	0.579418i	−0.983394	+	0.181484i	$0.941910\pi$
$114$		0			0
$115$	5.92776e8	−	1.02672e9i	0.316046	−	0.547407i
$116$	3.72303e7			0.0190913
$117$		0			0
$118$	−2.81095e9			−1.33470
$119$	6.41835e7	−	1.11169e8i	0.0293401	−	0.0508186i
$120$		0			0
$121$	−4.39157e8	−	7.60643e8i	−0.186246	−	0.322587i
$122$	1.71480e9	+	2.97012e9i	0.700800	+	1.21382i
$123$		0			0
$124$	−7.29640e6	+	1.26377e7i	−0.00277148	+	0.00480034i
$125$	1.80881e9			0.662672
$126$		0			0
$127$	−2.61195e9			−0.890938			−0.445469	−	0.895297i	$-0.646963\pi$
$127$	−2.61195e9			−0.890938			−0.445469	+	0.895297i	$0.646963\pi$
$128$	−1.48194e9	+	2.56680e9i	−0.487962	+	0.845175i
$129$		0			0
$130$	−4.04795e8	−	7.01126e8i	−0.124305	−	0.215303i
$131$	1.63443e9	+	2.83092e9i	0.484893	+	0.839859i	0.999849	−	0.0173572i	$-0.00552526\pi$
$131$	1.63443e9	+	2.83092e9i	0.484893	+	0.839859i	−0.514956	+	0.857216i	$0.672192\pi$
$132$		0			0
$133$	−2.28186e8	+	3.95230e8i	−0.0632349	+	0.109526i
$134$	−7.20087e9			−1.92936
$135$		0			0
$136$	−1.96403e9			−0.492292
$137$	2.83442e7	−	4.90936e7i	0.00687419	−	0.0119064i	−0.862568	−	0.505941i	$-0.831145\pi$
$137$	2.83442e7	−	4.90936e7i	0.00687419	−	0.0119064i	0.869442	+	0.494035i	$0.164479\pi$
$138$		0			0
$139$	−3.39949e9	−	5.88808e9i	−0.772408	−	1.33785i	−0.936240	−	0.351362i	$-0.885719\pi$
$139$	−3.39949e9	−	5.88808e9i	−0.772408	−	1.33785i	0.163832	−	0.986488i	$-0.447615\pi$
$140$	1.50738e6	+	2.61086e6i	0.000331624	+	0.000574390i
$141$		0			0
$142$	−1.22523e9	+	2.12215e9i	−0.252882	+	0.438005i
$143$	4.15369e9			0.830657
$144$		0			0
$145$	2.29850e9			0.431805
$146$	−7.46056e8	+	1.29221e9i	−0.135889	+	0.235366i
$147$		0			0
$148$	5.70887e7	+	9.88805e7i	0.00978076	+	0.0169408i
$149$	−7.29746e8	−	1.26396e9i	−0.121292	−	0.210085i	0.798985	−	0.601351i	$-0.205371\pi$
$149$	−7.29746e8	−	1.26396e9i	−0.121292	−	0.210085i	−0.920278	+	0.391266i	$0.872037\pi$
$150$		0			0
$151$	−2.47961e9	+	4.29481e9i	−0.388139	+	0.672276i	−0.992199	−	0.124663i	$-0.960215\pi$
$151$	−2.47961e9	+	4.29481e9i	−0.388139	+	0.672276i	0.604061	+	0.796938i	$0.293548\pi$
$152$	6.98254e9			1.06100
$153$		0			0
$154$	9.74455e8			0.139611
$155$	−4.50460e8	+	7.80220e8i	−0.0626850	+	0.108574i
$156$		0			0
$157$	−2.84547e9	−	4.92851e9i	−0.373772	−	0.647391i	0.616371	−	0.787456i	$-0.288602\pi$
$157$	−2.84547e9	−	4.92851e9i	−0.373772	−	0.647391i	−0.990142	+	0.140065i	$0.955269\pi$
$158$	1.29488e9	+	2.24281e9i	0.165300	+	0.286309i
$159$		0			0
$160$	4.57713e7	−	7.92782e7i	0.00552145	−	0.00956343i
$161$	−1.83150e9			−0.214828
$162$		0			0
$163$	7.88882e9			0.875322			0.437661	−	0.899140i	$-0.355807\pi$
$163$	7.88882e9			0.875322			0.437661	+	0.899140i	$0.355807\pi$
$164$	1.19297e8	−	2.06629e8i	0.0128775	−	0.0223046i
$165$		0			0
$166$	6.89930e9	+	1.19499e10i	0.705211	+	1.22146i
$167$	−4.62504e9	−	8.01081e9i	−0.460142	−	0.796989i	0.538826	−	0.842417i	$-0.318868\pi$
$167$	−4.62504e9	−	8.01081e9i	−0.460142	−	0.796989i	−0.998968	+	0.0454285i	$0.985535\pi$
$168$		0			0
$169$	2.63665e9	−	4.56682e9i	0.248635	−	0.430649i
$170$	−1.86544e9			−0.171302
$171$		0			0
$172$	−6.20552e7			−0.00540630
$173$	9.27127e9	−	1.60583e10i	0.786922	−	1.36299i	−0.140922	−	0.990021i	$-0.545007\pi$
$173$	9.27127e9	−	1.60583e10i	0.786922	−	1.36299i	0.927844	−	0.372969i	$-0.121660\pi$
$174$		0			0
$175$	−6.52056e8	−	1.12939e9i	−0.0525549	−	0.0910278i
$176$	−7.33812e9	−	1.27100e10i	−0.576471	−	0.998477i
$177$		0			0
$178$	3.79176e9	−	6.56752e9i	0.283107	−	0.490356i
$179$	−1.83931e10			−1.33911			−0.669555	−	0.742762i	$-0.733515\pi$
$179$	−1.83931e10			−1.33911			−0.669555	+	0.742762i	$0.733515\pi$
$180$		0			0
$181$	1.17014e9			0.0810375			0.0405187	−	0.999179i	$-0.487099\pi$
$181$	1.17014e9			0.0810375			0.0405187	+	0.999179i	$0.487099\pi$
$182$	−6.25348e8	+	1.08313e9i	−0.0422475	+	0.0731748i
$183$		0			0
$184$	1.40111e10	+	2.42679e10i	0.901137	+	1.56081i
$185$	3.52450e9	+	6.10462e9i	0.221220	+	0.383165i
$186$		0			0
$187$	4.78543e9	−	8.28861e9i	0.286176	−	0.495672i
$188$	−2.47922e8			−0.0144746
$189$		0			0
$190$	6.63205e9			0.369196
$191$	5.18747e9	−	8.98496e9i	0.282036	−	0.488502i	−0.689850	−	0.723953i	$-0.742323\pi$
$191$	5.18747e9	−	8.98496e9i	0.282036	−	0.488502i	0.971886	+	0.235451i	$0.0756567\pi$
$192$		0			0
$193$	5.86977e9	+	1.01667e10i	0.304518	+	0.527441i	0.977154	−	0.212533i	$-0.0681712\pi$
$193$	5.86977e9	+	1.01667e10i	0.304518	+	0.527441i	−0.672636	+	0.739974i	$0.734838\pi$
$194$	2.64131e9	+	4.57489e9i	0.133879	+	0.231885i
$195$		0			0
$196$	−1.59086e8	+	2.75545e8i	−0.00769979	+	0.0133364i
$197$	2.61163e10			1.23542			0.617708	−	0.786408i	$-0.288062\pi$
$197$	2.61163e10			1.23542			0.617708	+	0.786408i	$0.288062\pi$
$198$		0			0
$199$	2.31315e10			1.04560			0.522800	−	0.852455i	$-0.324887\pi$
$199$	2.31315e10			1.04560			0.522800	+	0.852455i	$0.324887\pi$
$200$	−9.97651e9	+	1.72798e10i	−0.440904	+	0.763668i
$201$		0			0
$202$	1.02840e10	+	1.78124e10i	0.434590	+	0.752732i
$203$	−1.77542e9	−	3.07511e9i	−0.0733785	−	0.127095i
$204$		0			0
$205$	7.36509e9	−	1.27567e10i	0.291263	−	0.504483i
$206$	2.26294e9			0.0875530
$207$		0			0
$208$	1.88367e10			0.697782
$209$	−1.70132e10	+	2.94678e10i	−0.616777	+	1.06829i
$210$		0			0
$211$	−1.28953e10	−	2.23354e10i	−0.447880	−	0.775750i	0.550368	−	0.834922i	$-0.314487\pi$
$211$	−1.28953e10	−	2.23354e10i	−0.447880	−	0.775750i	−0.998248	+	0.0591717i	$0.981154\pi$
$212$	3.96049e7	+	6.85978e7i	0.00134660	+	0.00233238i
$213$		0			0
$214$	−1.69371e10	+	2.93358e10i	−0.552047	+	0.956173i
$215$	−3.83113e9			−0.122279
$216$		0			0
$217$	1.39179e9			0.0426093
$218$	2.54507e10	−	4.40820e10i	0.763214	−	1.32193i
$219$		0			0
$220$	1.12388e8	+	1.94662e8i	0.00323458	+	0.00560246i
$221$	6.14202e9	+	1.06383e10i	0.173199	+	0.299990i
$222$		0			0
$223$	5.01684e8	−	8.68942e8i	0.0135850	−	0.0235298i	−0.859153	−	0.511719i	$-0.829009\pi$
$223$	5.01684e8	−	8.68942e8i	0.0135850	−	0.0235298i	0.872738	+	0.488189i	$0.162342\pi$
$224$	−1.41420e8			−0.00375313
$225$		0			0
$226$	2.60333e10			0.663806
$227$	−2.63956e10	+	4.57184e10i	−0.659803	+	1.14281i	0.320863	+	0.947126i	$0.396027\pi$
$227$	−2.63956e10	+	4.57184e10i	−0.659803	+	1.14281i	−0.980666	+	0.195687i	$0.937306\pi$
$228$		0			0
$229$	−1.55455e10	−	2.69255e10i	−0.373546	−	0.647000i	0.616563	−	0.787306i	$-0.288525\pi$
$229$	−1.55455e10	−	2.69255e10i	−0.373546	−	0.647000i	−0.990108	+	0.140306i	$0.955191\pi$
$230$	1.33078e10	+	2.30497e10i	0.313567	+	0.543114i
$231$		0			0
$232$	−2.71641e10	+	4.70495e10i	−0.615600	+	1.06625i
$233$	−3.41332e10			−0.758710			−0.379355	−	0.925251i	$-0.623854\pi$
$233$	−3.41332e10			−0.758710			−0.379355	+	0.925251i	$0.623854\pi$
$234$		0			0
$235$	−1.53061e10			−0.327385
$236$	−5.00839e8	+	8.67479e8i	−0.0105098	+	0.0182035i
$237$		0			0
$238$	1.44092e9	+	2.49574e9i	0.0291100	+	0.0504200i
$239$	4.51335e10	+	7.81735e10i	0.894764	+	1.54978i	0.834096	+	0.551619i	$0.185990\pi$
$239$	4.51335e10	+	7.81735e10i	0.894764	+	1.54978i	0.0606677	+	0.998158i	$0.480677\pi$
$240$		0			0
$241$	3.86696e10	−	6.69778e10i	0.738403	−	1.27895i	−0.214811	−	0.976656i	$-0.568914\pi$
$241$	3.86696e10	−	6.69778e10i	0.738403	−	1.27895i	0.953214	−	0.302296i	$-0.0977531\pi$
$242$	1.97181e10			0.369570
$243$		0			0
$244$	1.22213e9			0.0220731
$245$	−9.82153e9	+	1.70114e10i	−0.174153	+	0.301642i
$246$		0			0
$247$	−2.18362e10	−	3.78214e10i	−0.373285	−	0.646549i
$248$	−1.06472e10	−	1.84416e10i	−0.178733	−	0.309575i
$249$		0			0
$250$	−2.03039e10	+	3.51673e10i	−0.328737	+	0.569389i
$251$	4.53113e10			0.720568			0.360284	−	0.932843i	$-0.382680\pi$
$251$	4.53113e10			0.720568			0.360284	+	0.932843i	$0.382680\pi$
$252$		0			0
$253$	−1.36554e11			−2.09538
$254$	2.93190e10	−	5.07820e10i	0.441975	−	0.765523i
$255$		0			0
$256$	1.61022e9	+	2.78898e9i	0.0234317	+	0.0405850i
$257$	−6.79435e10	−	1.17682e11i	−0.971514	−	1.68271i	−0.690991	−	0.722864i	$-0.742826\pi$
$257$	−6.79435e10	−	1.17682e11i	−0.971514	−	1.68271i	−0.280523	−	0.959847i	$-0.590508\pi$
$258$		0			0
$259$	5.44483e9	−	9.43073e9i	0.0751858	−	0.130226i
$260$	−2.88496e8			−0.00391525
$261$		0			0
$262$	−7.33858e10			−0.962179
$263$	−2.40866e10	+	4.17191e10i	−0.310437	+	0.537693i	−0.978457	−	0.206450i	$-0.933809\pi$
$263$	−2.40866e10	+	4.17191e10i	−0.310437	+	0.537693i	0.668020	+	0.744143i	$0.267142\pi$
$264$		0			0
$265$	2.44510e9	+	4.23504e9i	0.0304573	+	0.0527535i
$266$	−5.12277e9	−	8.87289e9i	−0.0627390	−	0.108667i
$267$		0			0
$268$	−1.28301e9	+	2.22224e9i	−0.0151923	+	0.0263138i
$269$	−1.33744e11			−1.55736			−0.778682	−	0.627418i	$-0.784112\pi$
$269$	−1.33744e11			−1.55736			−0.778682	+	0.627418i	$0.784112\pi$
$270$		0			0
$271$	−7.03388e10			−0.792197			−0.396098	−	0.918208i	$-0.629636\pi$
$271$	−7.03388e10			−0.792197			−0.396098	+	0.918208i	$0.629636\pi$
$272$	2.17016e10	−	3.75883e10i	0.240398	−	0.416382i
$273$		0			0
$274$	6.36326e8	+	1.10215e9i	0.00682028	+	0.0118131i
$275$	−4.86163e10	−	8.42059e10i	−0.512607	−	0.887862i
$276$		0			0
$277$	6.71636e10	−	1.16331e11i	0.685449	−	1.18723i	−0.287846	−	0.957677i	$-0.592939\pi$
$277$	6.71636e10	−	1.16331e11i	0.685449	−	1.18723i	0.973295	−	0.229556i	$-0.0737274\pi$
$278$	1.52637e11			1.53270
$279$		0			0
$280$	−4.39927e9			−0.0427730
$281$	5.79256e10	−	1.00330e11i	0.554233	−	0.959960i	−0.443730	−	0.896161i	$-0.646345\pi$
$281$	5.79256e10	−	1.00330e11i	0.554233	−	0.959960i	0.997963	−	0.0637992i	$-0.0203217\pi$
$282$		0			0
$283$	−7.01438e10	−	1.21493e11i	−0.650055	−	1.12593i	−0.983109	−	0.183021i	$-0.941412\pi$
$283$	−7.01438e10	−	1.21493e11i	−0.650055	−	1.12593i	0.333054	−	0.942908i	$-0.391921\pi$
$284$	4.36607e8	+	7.56225e8i	0.00398252	+	0.00689793i
$285$		0			0
$286$	−4.66250e10	+	8.07569e10i	−0.412071	+	0.713728i
$287$	−2.27559e10			−0.197982
$288$		0			0
$289$	−9.02832e10			−0.761319
$290$	−2.58006e10	+	4.46879e10i	−0.214209	+	0.371021i
$291$		0			0
$292$	2.65856e8	+	4.60476e8i	0.00214005	+	0.00370667i
$293$	7.99709e10	+	1.38514e11i	0.633910	+	1.09796i	0.986745	+	0.162279i	$0.0518844\pi$
$293$	7.99709e10	+	1.38514e11i	0.633910	+	1.09796i	−0.352835	+	0.935686i	$0.614782\pi$
$294$		0			0
$295$	−3.09205e10	+	5.35558e10i	−0.237710	+	0.411725i
$296$	−1.66613e11			−1.26153
$297$		0			0
$298$	3.27655e10			0.240682
$299$	8.76323e10	−	1.51784e11i	0.634080	−	1.09826i
$300$		0			0
$301$	2.95926e9	+	5.12559e9i	0.0207794	+	0.0359910i
$302$	−5.56671e10	−	9.64182e10i	−0.385094	−	0.667003i
$303$		0			0
$304$	−7.71539e10	+	1.33634e11i	−0.518115	+	0.897402i
$305$	7.54512e10			0.499249
$306$		0			0
$307$	1.98532e11			1.27558			0.637791	−	0.770210i	$-0.279849\pi$
$307$	1.98532e11			1.27558			0.637791	+	0.770210i	$0.279849\pi$
$308$	1.73623e8	−	3.00723e8i	0.00109933	−	0.00190410i
$309$		0			0
$310$	−1.01128e10	−	1.75159e10i	−0.0621934	−	0.107722i
$311$	1.12406e10	+	1.94692e10i	0.0681344	+	0.118012i	0.898080	−	0.439832i	$-0.144962\pi$
$311$	1.12406e10	+	1.94692e10i	0.0681344	+	0.118012i	−0.829946	+	0.557844i	$0.811629\pi$
$312$		0			0
$313$	2.97989e10	−	5.16132e10i	0.175489	−	0.303956i	−0.764841	−	0.644219i	$-0.777183\pi$
$313$	2.97989e10	−	5.16132e10i	0.175489	−	0.303956i	0.940330	+	0.340263i	$0.110516\pi$
$314$	1.27761e11			0.741680
$315$		0			0
$316$	9.22860e8			0.00520647
$317$	−1.51322e11	+	2.62097e11i	−0.841658	+	1.45779i	0.0468350	+	0.998903i	$0.485086\pi$
$317$	−1.51322e11	+	2.62097e11i	−0.841658	+	1.45779i	−0.888493	+	0.458891i	$0.848247\pi$
$318$		0			0
$319$	−1.32373e11	−	2.29276e11i	−0.715715	−	1.23965i
$320$	3.36466e10	+	5.82776e10i	0.179377	+	0.310689i
$321$		0			0
$322$	2.05585e10	−	3.56084e10i	0.106571	−	0.184587i
$323$	−1.00629e11			−0.514414
$324$		0			0
$325$	1.24796e11			0.620479
$326$	−8.85518e10	+	1.53376e11i	−0.434228	+	0.752105i
$327$		0			0
$328$	1.74084e11	+	3.01522e11i	0.830475	+	1.43843i
$329$	1.18228e10	+	2.04777e10i	0.0556338	+	0.0963606i
$330$		0			0
$331$	−2.25241e10	+	3.90129e10i	−0.103139	+	0.178641i	−0.912976	−	0.408013i	$-0.866222\pi$
$331$	−2.25241e10	+	3.90129e10i	−0.103139	+	0.178641i	0.809838	+	0.586654i	$0.199555\pi$
$332$	4.91711e9			0.0222120
$333$		0			0
$334$	2.07664e11			0.913065
$335$	−7.92095e10	+	1.37195e11i	−0.343618	+	0.595164i
$336$		0			0
$337$	5.12401e10	+	8.87505e10i	0.216409	+	0.374832i	0.953708	−	0.300736i	$-0.0972322\pi$
$337$	5.12401e10	+	8.87505e10i	0.216409	+	0.374832i	−0.737298	+	0.675567i	$0.763899\pi$
$338$	5.91927e10	+	1.02525e11i	0.246685	+	0.427272i
$339$		0			0
$340$	−3.32374e8	+	5.75688e8i	−0.00134888	+	0.00233632i
$341$	1.03770e11			0.415600
$342$		0			0
$343$	6.11354e10			0.238490
$344$	4.52769e10	−	7.84220e10i	0.174327	−	0.301943i
$345$		0			0
$346$	2.08140e11	+	3.60508e11i	0.780750	+	1.35230i
$347$	9.54735e10	+	1.65365e11i	0.353509	+	0.612295i	0.986862	−	0.161568i	$-0.0516551\pi$
$347$	9.54735e10	+	1.65365e11i	0.353509	+	0.612295i	−0.633353	+	0.773863i	$0.718322\pi$
$348$		0			0
$349$	1.08980e11	−	1.88758e11i	0.393216	−	0.681070i	−0.599656	−	0.800258i	$-0.704696\pi$
$349$	1.08980e11	−	1.88758e11i	0.393216	−	0.681070i	0.992872	+	0.119188i	$0.0380292\pi$
$350$	2.92772e10			0.104285
$351$		0			0
$352$	−1.05440e10			−0.0366071
$353$	1.56665e11	−	2.71351e11i	0.537013	−	0.930134i	−0.462050	−	0.886854i	$-0.652886\pi$
$353$	1.56665e11	−	2.71351e11i	0.537013	−	0.930134i	0.999063	−	0.0432798i	$-0.0137807\pi$
$354$		0			0
$355$	2.69550e10	+	4.66873e10i	0.0900764	+	0.156017i
$356$	−1.35119e9	−	2.34033e9i	−0.00445852	−	0.00772238i
$357$		0			0
$358$	2.06462e11	−	3.57603e11i	0.664304	−	1.15061i
$359$	2.37983e11			0.756173			0.378087	−	0.925770i	$-0.376582\pi$
$359$	2.37983e11			0.756173			0.378087	+	0.925770i	$0.376582\pi$
$360$		0			0
$361$	3.50706e10			0.108683
$362$	−1.31348e10	+	2.27502e10i	−0.0402009	+	0.0696301i
$363$		0			0
$364$	2.22842e8	+	3.85973e8i	0.000665335	+	0.00115239i
$365$	1.64132e10	+	2.84286e10i	0.0484035	+	0.0838373i
$366$		0			0
$367$	−1.62673e11	+	2.81757e11i	−0.468077	+	0.810732i	−0.999334	−	0.0364778i	$-0.988386\pi$
$367$	−1.62673e11	+	2.81757e11i	−0.468077	+	0.810732i	0.531258	+	0.847210i	$0.321720\pi$
$368$	−6.19263e11			−1.76019
$369$		0			0
$370$	−1.58250e11			−0.438971
$371$	3.77732e9	−	6.54251e9i	0.0103515	−	0.0179292i
$372$		0			0
$373$	2.56950e11	+	4.45050e11i	0.687319	+	1.19047i	0.972702	+	0.232058i	$0.0745458\pi$
$373$	2.56950e11	+	4.45050e11i	0.687319	+	1.19047i	−0.285383	+	0.958414i	$0.592121\pi$
$374$	1.07433e11	+	1.86079e11i	0.283932	+	0.491784i
$375$		0			0
$376$	1.80890e11	−	3.13311e11i	0.466734	−	0.808407i
$377$	3.39796e11			0.866328
$378$		0			0
$379$	6.49235e11			1.61631			0.808156	−	0.588968i	$-0.200466\pi$
$379$	6.49235e11			1.61631			0.808156	+	0.588968i	$0.200466\pi$
$380$	1.18166e9	−	2.04670e9i	0.00290714	−	0.00503532i
$381$		0			0
$382$	1.16458e11	+	2.01712e11i	0.279824	+	0.484670i
$383$	−2.84096e11	−	4.92069e11i	−0.674638	−	1.16851i	−0.976574	−	0.215180i	$-0.930966\pi$
$383$	−2.84096e11	−	4.92069e11i	−0.674638	−	1.16851i	0.301936	−	0.953328i	$-0.402367\pi$
$384$		0			0
$385$	1.07190e10	−	1.85659e10i	0.0248646	−	0.0430667i
$386$	−2.63552e11			−0.604260
$387$		0			0
$388$	1.88245e9			0.00421679
$389$	9.28790e10	−	1.60871e11i	0.205657	−	0.356209i	−0.744685	−	0.667417i	$-0.767400\pi$
$389$	9.28790e10	−	1.60871e11i	0.205657	−	0.356209i	0.950342	+	0.311207i	$0.100733\pi$
$390$		0			0
$391$	−2.01921e11	−	3.49737e11i	−0.436904	−	0.756740i
$392$	−2.32145e11	−	4.02087e11i	−0.496561	−	0.860069i
$393$		0			0
$394$	−2.93154e11	+	5.07758e11i	−0.612863	+	1.06151i
$395$	5.69749e10			0.117760
$396$		0			0
$397$	−3.00165e11			−0.606461			−0.303230	−	0.952917i	$-0.598065\pi$
$397$	−3.00165e11			−0.606461			−0.303230	+	0.952917i	$0.598065\pi$
$398$	−2.59651e11	+	4.49728e11i	−0.518700	+	0.898414i
$399$		0			0
$400$	−2.20472e11	−	3.81868e11i	−0.430609	−	0.745836i
$401$	−3.06505e11	−	5.30882e11i	−0.591954	−	1.02529i	−0.993969	−	0.109661i	$-0.965023\pi$
$401$	−3.06505e11	−	5.30882e11i	−0.591954	−	1.02529i	0.402015	−	0.915633i	$-0.368310\pi$
$402$		0			0
$403$	−6.65933e10	+	1.15343e11i	−0.125764	+	0.217830i
$404$	7.32936e9			0.0136883
$405$		0			0
$406$	7.97161e10			0.145606
$407$	4.05959e11	−	7.03141e11i	0.733343	−	1.27019i
$408$		0			0
$409$	−8.92235e10	−	1.54540e11i	−0.157661	−	0.273077i	0.776364	−	0.630285i	$-0.217062\pi$
$409$	−8.92235e10	−	1.54540e11i	−0.157661	−	0.273077i	−0.934025	+	0.357208i	$0.883729\pi$
$410$	1.65346e11	+	2.86388e11i	0.288979	+	0.500526i
$411$		0			0
$412$	4.03198e8	−	6.98359e8i	0.000689415	−	0.00119410i
$413$	9.55350e10			0.161580
$414$		0			0
$415$	3.03569e11			0.502391
$416$	6.76655e9	−	1.17200e10i	0.0110776	−	0.0191870i
$417$		0			0
$418$	−3.81946e11	−	6.61550e11i	−0.611940	−	1.05991i
$419$	−5.67027e10	−	9.82119e10i	−0.0898753	−	0.155669i	0.817583	−	0.575811i	$-0.195314\pi$
$419$	−5.67027e10	−	9.82119e10i	−0.0898753	−	0.155669i	−0.907458	+	0.420142i	$0.861980\pi$
$420$		0			0
$421$	−8.52305e10	+	1.47624e11i	−0.132229	+	0.229027i	−0.924535	−	0.381096i	$-0.875547\pi$
$421$	−8.52305e10	+	1.47624e11i	−0.132229	+	0.229027i	0.792307	+	0.610123i	$0.208880\pi$
$422$	5.78999e11			0.888734
$423$		0			0
$424$	−1.15587e11			−0.173685
$425$	1.43777e11	−	2.49029e11i	0.213766	−	0.370254i
$426$		0			0
$427$	−5.82804e10	−	1.00945e11i	−0.0848393	−	0.146946i
$428$	6.03549e9	+	1.04538e10i	0.00869392	+	0.0150583i
$429$		0			0
$430$	4.30043e10	−	7.44856e10i	0.0606602	−	0.105066i
$431$	−6.06017e11			−0.845936			−0.422968	−	0.906145i	$-0.639012\pi$
$431$	−6.06017e11			−0.845936			−0.422968	+	0.906145i	$0.639012\pi$
$432$		0			0
$433$	−8.94608e11			−1.22303			−0.611515	−	0.791233i	$-0.709440\pi$
$433$	−8.94608e11			−1.22303			−0.611515	+	0.791233i	$0.709440\pi$
$434$	−1.56228e10	+	2.70595e10i	−0.0211376	+	0.0366113i
$435$		0			0
$436$	−9.06933e9	−	1.57085e10i	−0.0120195	−	0.0208184i
$437$	7.17872e11	+	1.24339e12i	0.941631	+	1.63095i
$438$		0			0
$439$	−4.08082e11	+	7.06819e11i	−0.524393	+	0.908276i	0.475203	+	0.879876i	$0.342375\pi$
$439$	−4.08082e11	+	7.06819e11i	−0.524393	+	0.908276i	−0.999597	+	0.0284000i	$0.990959\pi$
$440$	−3.28003e11			−0.417197
$441$		0			0
$442$	−2.75776e11			−0.343681
$443$	−1.27889e11	+	2.21510e11i	−0.157767	+	0.273260i	−0.934063	−	0.357108i	$-0.883763\pi$
$443$	−1.27889e11	+	2.21510e11i	−0.157767	+	0.273260i	0.776296	+	0.630368i	$0.217096\pi$
$444$		0			0
$445$	−8.34188e10	−	1.44486e11i	−0.100843	−	0.174664i
$446$	1.12628e10	+	1.95077e10i	0.0134784	+	0.0233453i
$447$		0			0
$448$	5.19789e10	−	9.00301e10i	0.0609644	−	0.105593i
$449$	−2.65080e11			−0.307800			−0.153900	−	0.988086i	$-0.549183\pi$
$449$	−2.65080e11			−0.307800			−0.153900	+	0.988086i	$0.549183\pi$
$450$		0			0
$451$	−1.69665e12			−1.93107
$452$	4.63846e9	−	8.03405e9i	0.00522698	−	0.00905340i
$453$		0			0
$454$	−5.92579e11	−	1.02638e12i	−0.654628	−	1.13385i
$455$	1.37577e10	+	2.38290e10i	0.0150485	+	0.0260648i
$456$		0			0
$457$	6.27826e11	−	1.08743e12i	0.673312	−	1.16621i	−0.303647	−	0.952785i	$-0.598204\pi$
$457$	6.27826e11	−	1.08743e12i	0.673312	−	1.16621i	0.976959	−	0.213426i	$-0.0684623\pi$
$458$	6.97989e11			0.741232
$459$		0			0
$460$	9.48441e9			0.00987643
$461$	−7.48601e11	+	1.29662e12i	−0.771963	+	1.33708i	0.164523	+	0.986373i	$0.447392\pi$
$461$	−7.48601e11	+	1.29662e12i	−0.771963	+	1.33708i	−0.936486	+	0.350706i	$0.885942\pi$
$462$		0			0
$463$	9.41238e11	+	1.63027e12i	0.951886	+	1.64871i	0.741339	+	0.671131i	$0.234191\pi$
$463$	9.41238e11	+	1.63027e12i	0.951886	+	1.64871i	0.210547	+	0.977584i	$0.432476\pi$
$464$	−6.00301e11	−	1.03975e12i	−0.601226	−	1.04135i
$465$		0			0
$466$	3.83144e11	−	6.63626e11i	0.376379	−	0.651908i
$467$	1.43018e11			0.139145			0.0695723	−	0.997577i	$-0.477837\pi$
$467$	1.43018e11			0.139145			0.0695723	+	0.997577i	$0.477837\pi$
$468$		0			0
$469$	2.44734e11			0.233570
$470$	1.71810e11	−	2.97584e11i	0.162408	−	0.281300i
$471$		0			0
$472$	−7.30848e11	−	1.26587e12i	−0.677779	−	1.17395i
$473$	2.20638e11	+	3.82156e11i	0.202677	+	0.351047i
$474$		0			0
$475$	−5.11158e11	+	8.85351e11i	−0.460716	+	0.797984i
$476$	1.02694e9			0.000916879
$477$		0			0
$478$	−2.02649e12			−1.77549
$479$	−1.89378e11	+	3.28013e11i	−0.164369	+	0.284696i	−0.936431	−	0.350852i	$-0.885892\pi$
$479$	−1.89378e11	+	3.28013e11i	−0.164369	+	0.284696i	0.772062	+	0.635547i	$0.219225\pi$
$480$		0			0
$481$	5.21041e11	+	9.02470e11i	0.443833	+	0.768741i
$482$	8.68131e11	+	1.50365e12i	0.732612	+	1.26892i
$483$		0			0
$484$	3.51326e9	−	6.08514e9i	0.00291009	−	0.00504042i
$485$	1.16218e11			0.0953750
$486$		0			0
$487$	9.66599e9			0.00778692			0.00389346	−	0.999992i	$-0.498761\pi$
$487$	9.66599e9			0.00778692			0.00389346	+	0.999992i	$0.498761\pi$
$488$	−8.91696e11	+	1.54446e12i	−0.711750	+	1.23279i
$489$		0			0
$490$	−2.20493e11	−	3.81905e11i	−0.172787	−	0.299277i
$491$	3.45410e11	+	5.98267e11i	0.268205	+	0.464545i	0.968398	−	0.249408i	$-0.0802361\pi$
$491$	3.45410e11	+	5.98267e11i	0.268205	+	0.464545i	−0.700193	+	0.713954i	$0.746903\pi$
$492$		0			0
$493$	3.91476e11	−	6.78056e11i	0.298465	−	0.516957i
$494$	9.80443e11			0.740715
$495$		0			0
$496$	4.70589e11			0.349119
$497$	4.16414e10	−	7.21250e10i	0.0306141	−	0.0530252i
$498$		0			0
$499$	−3.98823e11	−	6.90782e11i	−0.287957	−	0.498756i	0.685365	−	0.728200i	$-0.259643\pi$
$499$	−3.98823e11	−	6.90782e11i	−0.287957	−	0.498756i	−0.973322	+	0.229443i	$0.926309\pi$
$500$	7.23525e9	+	1.25318e10i	0.00517712	+	0.00896704i
$501$		0			0
$502$	−5.08618e11	+	8.80952e11i	−0.357458	+	0.619135i
$503$	4.71233e11			0.328231			0.164116	−	0.986441i	$-0.447523\pi$
$503$	4.71233e11			0.328231			0.164116	+	0.986441i	$0.447523\pi$
$504$		0			0
$505$	4.52495e11			0.309601
$506$	1.53281e12	−	2.65491e12i	1.03947	−	1.80042i
$507$		0			0
$508$	−1.04478e10	−	1.80961e10i	−0.00696045	−	0.0120559i
$509$	−1.04994e12	−	1.81855e12i	−0.693320	−	1.20086i	−0.970744	−	0.240117i	$-0.922814\pi$
$509$	−1.04994e12	−	1.81855e12i	−0.693320	−	1.20086i	0.277424	−	0.960748i	$-0.410519\pi$
$510$		0			0
$511$	2.53560e10	−	4.39179e10i	0.0164508	−	0.0284936i
$512$	−1.58981e12			−1.02242
$513$		0			0
$514$	3.05066e12			1.92779
$515$	2.48924e10	−	4.31148e10i	0.0155931	−	0.0270081i
$516$		0			0
$517$	8.81491e11	+	1.52679e12i	0.542638	+	0.939877i
$518$	1.22236e11	+	2.11719e11i	0.0745961	+	0.129204i
$519$		0			0
$520$	2.10493e11	−	3.64585e11i	0.126248	−	0.218667i
$521$	−2.49095e12			−1.48114			−0.740569	−	0.671980i	$-0.765444\pi$
$521$	−2.49095e12			−1.48114			−0.740569	+	0.671980i	$0.765444\pi$
$522$		0			0
$523$	9.27462e11			0.542049			0.271024	−	0.962572i	$-0.412638\pi$
$523$	9.27462e11			0.542049			0.271024	+	0.962572i	$0.412638\pi$
$524$	−1.30754e10	+	2.26473e10i	−0.00757645	+	0.0131228i
$525$		0			0
$526$	−5.40742e11	−	9.36592e11i	−0.308002	−	0.533476i
$527$	1.53443e11	+	2.65771e11i	0.0866562	+	0.150093i
$528$		0			0
$529$	−1.98037e12	+	3.43010e12i	−1.09950	+	1.90439i
$530$	−1.09785e11			−0.0604368
$531$		0			0
$532$	−3.65098e9			−0.00197609
$533$	1.08881e12	−	1.88588e12i	0.584359	−	1.01214i
$534$		0			0
$535$	3.72615e11	+	6.45389e11i	0.196639	+	0.340588i
$536$	−1.87223e12	−	3.24279e12i	−0.979753	−	1.69698i
$537$		0			0
$538$	1.50128e12	−	2.60029e12i	0.772575	−	1.33814i
$539$	2.26252e12			1.15463
$540$		0			0
$541$	1.99506e12			1.00131			0.500655	−	0.865647i	$-0.333093\pi$
$541$	1.99506e12			1.00131			0.500655	+	0.865647i	$0.333093\pi$
$542$	7.89551e11	−	1.36754e12i	0.392992	−	0.680682i
$543$		0			0
$544$	−1.55914e10	−	2.70050e10i	−0.00763289	−	0.0132205i
$545$	−5.59916e11	−	9.69804e11i	−0.271856	−	0.470868i
$546$		0			0
$547$	7.49141e10	−	1.29755e11i	0.0357784	−	0.0619699i	−0.847582	−	0.530665i	$-0.821942\pi$
$547$	7.49141e10	−	1.29755e11i	0.0357784	−	0.0619699i	0.883360	+	0.468695i	$0.155276\pi$
$548$	4.53507e8			0.000214818
$549$		0			0
$550$	2.18287e12			1.01717
$551$	−1.39178e12	+	2.41064e12i	−0.643263	+	1.11416i
$552$		0			0
$553$	−4.40089e10	−	7.62256e10i	−0.0200114	−	0.0346607i
$554$	1.50782e12	+	2.61162e12i	0.680073	+	1.17792i
$555$		0			0
$556$	2.71959e10	−	4.71047e10i	0.0120689	−	0.0209039i
$557$	6.75741e11			0.297462			0.148731	−	0.988878i	$-0.452481\pi$
$557$	6.75741e11			0.297462			0.148731	+	0.988878i	$0.452481\pi$
$558$		0			0
$559$	−5.66370e11			−0.245328
$560$	4.86100e10	−	8.41949e10i	0.0208871	−	0.0361776i
$561$		0			0
$562$	1.30043e12	+	2.25241e12i	0.549886	+	0.952431i
$563$	−6.26828e11	−	1.08570e12i	−0.262943	−	0.455430i	0.704080	−	0.710121i	$-0.251360\pi$
$563$	−6.26828e11	−	1.08570e12i	−0.262943	−	0.455430i	−0.967023	+	0.254691i	$0.918026\pi$
$564$		0			0
$565$	2.86366e11	−	4.96001e11i	0.118224	−	0.204769i
$566$	3.14945e12			1.28991
$567$		0			0
$568$	−1.27423e12			−0.513667
$569$	−1.57582e12	+	2.72940e12i	−0.630233	+	1.09160i	0.357271	+	0.934001i	$0.383707\pi$
$569$	−1.57582e12	+	2.72940e12i	−0.630233	+	1.09160i	−0.987504	+	0.157595i	$0.949626\pi$
$570$		0			0
$571$	2.11655e12	+	3.66597e12i	0.833233	+	1.44320i	0.895461	+	0.445139i	$0.146846\pi$
$571$	2.11655e12	+	3.66597e12i	0.833233	+	1.44320i	−0.0622286	+	0.998062i	$0.519821\pi$
$572$	1.66148e10	+	2.87776e10i	0.00648951	+	0.0112402i
$573$		0			0
$574$	2.55435e11	−	4.42426e11i	0.0982147	−	0.170113i
$575$	−4.10273e12			−1.56519
$576$		0			0
$577$	4.23367e12			1.59011			0.795053	−	0.606540i	$-0.207443\pi$
$577$	4.23367e12			1.59011			0.795053	+	0.606540i	$0.207443\pi$
$578$	1.01343e12	−	1.75531e12i	0.377674	−	0.654150i
$579$		0			0
$580$	9.19399e9	+	1.59245e10i	0.00337348	+	0.00584304i
$581$	−2.34485e11	−	4.06139e11i	−0.0853733	−	0.147871i
$582$		0			0
$583$	2.81631e11	−	4.87800e11i	0.100965	−	0.174877i
$584$	−7.75899e11			−0.276024
$585$		0			0
$586$	−3.59068e12			−1.25788
$587$	6.98767e11	−	1.21030e12i	0.242919	−	0.420747i	−0.718626	−	0.695397i	$-0.755229\pi$
$587$	6.98767e11	−	1.21030e12i	0.242919	−	0.420747i	0.961544	+	0.274650i	$0.0885619\pi$
$588$		0			0
$589$	−5.45524e11	−	9.44875e11i	−0.186765	−	0.323486i
$590$	−6.94163e11	−	1.20233e12i	−0.235845	−	0.408496i
$591$		0			0
$592$	1.84100e12	−	3.18870e12i	0.616035	−	1.06700i
$593$	6.32131e11			0.209923			0.104962	−	0.994476i	$-0.466528\pi$
$593$	6.32131e11			0.209923			0.104962	+	0.994476i	$0.466528\pi$
$594$		0			0
$595$	6.34003e10			0.0207379
$596$	5.83797e9	−	1.01117e10i	0.00189519	−	0.00328257i
$597$		0			0
$598$	1.96734e12	+	3.40754e12i	0.629107	+	1.08964i
$599$	2.57726e12	+	4.46394e12i	0.817970	+	1.41676i	0.907176	+	0.420752i	$0.138234\pi$
$599$	2.57726e12	+	4.46394e12i	0.817970	+	1.41676i	−0.0892062	+	0.996013i	$0.528433\pi$
$600$		0			0
$601$	3.68522e11	−	6.38299e11i	0.115220	−	0.199567i	−0.802648	−	0.596454i	$-0.796576\pi$
$601$	3.68522e11	−	6.38299e11i	0.115220	−	0.199567i	0.917868	+	0.396886i	$0.129909\pi$
$602$	−1.32870e11			−0.0412329
$603$		0			0
$604$	−3.96737e10			−0.0121293
$605$	2.16899e11	−	3.75681e11i	0.0658202	−	0.114004i
$606$		0			0
$607$	−9.36945e11	−	1.62284e12i	−0.280134	−	0.485206i	0.691284	−	0.722583i	$-0.257045\pi$
$607$	−9.36945e11	−	1.62284e12i	−0.280134	−	0.485206i	−0.971417	+	0.237378i	$0.923712\pi$
$608$	5.54306e10	+	9.60087e10i	0.0164507	+	0.0284934i
$609$		0			0
$610$	−8.46937e11	+	1.46694e12i	−0.247666	+	0.428971i
$611$	−2.26276e12			−0.656829
$612$		0			0
$613$	−1.62540e12			−0.464931			−0.232465	−	0.972605i	$-0.574679\pi$
$613$	−1.62540e12			−0.464931			−0.232465	+	0.972605i	$0.574679\pi$
$614$	−2.22852e12	+	3.85991e12i	−0.632788	+	1.09602i
$615$		0			0
$616$	2.53358e11	+	4.38829e11i	0.0708960	+	0.122796i
$617$	2.24278e12	+	3.88460e12i	0.623021	+	1.07910i	0.988920	+	0.148449i	$0.0474282\pi$
$617$	2.24278e12	+	3.88460e12i	0.623021	+	1.07910i	−0.365899	+	0.930654i	$0.619239\pi$
$618$		0			0
$619$	−1.32245e12	+	2.29054e12i	−0.362051	+	0.627091i	−0.988298	−	0.152534i	$-0.951257\pi$
$619$	−1.32245e12	+	2.29054e12i	−0.362051	+	0.627091i	0.626247	+	0.779625i	$0.284590\pi$
$620$	−7.20737e9			−0.00195891
$621$		0			0
$622$	−5.04700e11			−0.135200
$623$	−1.28870e11	+	2.23209e11i	−0.0342732	+	0.0593628i
$624$		0			0
$625$	−1.22244e12	−	2.11734e12i	−0.320457	−	0.555047i
$626$	6.68983e11	+	1.15871e12i	0.174113	+	0.301572i
$627$		0			0
$628$	2.27638e10	−	3.94281e10i	0.00584018	−	0.0101155i
$629$	2.40115e12			0.611633
$630$		0			0
$631$	−2.53561e12			−0.636723			−0.318361	−	0.947969i	$-0.603133\pi$
$631$	−2.53561e12			−0.636723			−0.318361	+	0.947969i	$0.603133\pi$
$632$	−6.73340e11	+	1.16626e12i	−0.167883	+	0.290782i
$633$		0			0
$634$	−3.39717e12	−	5.88407e12i	−0.835056	−	1.44636i
$635$	−6.45018e11	−	1.11720e12i	−0.157431	−	0.272679i
$636$		0			0
$637$	−1.45196e12	+	2.51486e12i	−0.349402	+	0.605183i
$638$	5.94351e12			1.42020
$639$		0			0
$640$	−1.46386e12			−0.344897
$641$	3.55984e11	−	6.16583e11i	0.0832856	−	0.144255i	−0.821374	−	0.570390i	$-0.806792\pi$
$641$	3.55984e11	−	6.16583e11i	0.0832856	−	0.144255i	0.904659	+	0.426135i	$0.140125\pi$
$642$		0			0
$643$	2.98845e11	+	5.17615e11i	0.0689441	+	0.119415i	0.898437	−	0.439103i	$-0.144704\pi$
$643$	2.98845e11	+	5.17615e11i	0.0689441	+	0.119415i	−0.829493	+	0.558518i	$0.811370\pi$
$644$	−7.32600e9	−	1.26890e10i	−0.00167834	−	0.00290697i
$645$		0			0
$646$	1.12956e12	−	1.95645e12i	0.255189	−	0.442001i
$647$	3.90064e12			0.875119			0.437559	−	0.899189i	$-0.355843\pi$
$647$	3.90064e12			0.875119			0.437559	+	0.899189i	$0.355843\pi$
$648$		0			0
$649$	7.12295e12			1.57601
$650$	−1.40084e12	+	2.42632e12i	−0.307806	+	0.533136i
$651$		0			0
$652$	3.15553e10	+	5.46553e10i	0.00683845	+	0.0118445i
$653$	−1.36814e11	−	2.36968e11i	−0.0294456	−	0.0510013i	0.850927	−	0.525284i	$-0.176041\pi$
$653$	−1.36814e11	−	2.36968e11i	−0.0294456	−	0.0510013i	−0.880373	+	0.474283i	$0.842708\pi$
$654$		0			0
$655$	−8.07244e11	+	1.39819e12i	−0.171364	+	0.296811i
$656$	−7.69419e12			−1.62217
$657$		0			0
$658$	−5.30843e11			−0.110395
$659$	9.66194e11	−	1.67350e12i	0.199563	−	0.345653i	−0.748824	−	0.662769i	$-0.769381\pi$
$659$	9.66194e11	−	1.67350e12i	0.199563	−	0.345653i	0.948387	+	0.317116i	$0.102714\pi$
$660$		0			0
$661$	−4.49910e12	−	7.79266e12i	−0.916682	−	1.58774i	−0.804420	−	0.594061i	$-0.797524\pi$
$661$	−4.49910e12	−	7.79266e12i	−0.916682	−	1.58774i	−0.112262	−	0.993679i	$-0.535810\pi$
$662$	−5.05665e11	−	8.75838e11i	−0.102330	−	0.177240i
$663$		0			0
$664$	−3.58764e12	+	6.21397e12i	−0.716230	+	1.24055i
$665$	−2.25402e11			−0.0446951
$666$		0			0
$667$	−1.11709e13			−2.18536
$668$	3.70003e10	−	6.40865e10i	0.00718971	−	0.0124529i
$669$		0			0
$670$	−1.77825e12	−	3.08002e12i	−0.340923	−	0.590496i
$671$	−4.34530e12	−	7.52628e12i	−0.827501	−	1.43327i
$672$		0			0
$673$	1.90075e12	−	3.29219e12i	0.357155	−	0.618610i	−0.630330	−	0.776328i	$-0.717080\pi$
$673$	1.90075e12	−	3.29219e12i	0.357155	−	0.618610i	0.987484	+	0.157718i	$0.0504136\pi$
$674$	−2.30068e12			−0.429424
$675$		0			0
$676$	4.21865e10			0.00776986
$677$	1.25508e12	−	2.17385e12i	0.229626	−	0.397724i	−0.728071	−	0.685501i	$-0.759583\pi$
$677$	1.25508e12	−	2.17385e12i	0.229626	−	0.397724i	0.957697	+	0.287778i	$0.0929164\pi$
$678$		0			0
$679$	−8.97696e10	−	1.55485e11i	−0.0162075	−	0.0280722i
$680$	−4.85015e11	−	8.40071e11i	−0.0869892	−	0.150670i
$681$		0			0
$682$	−1.16481e12	+	2.01751e12i	−0.206170	+	0.357097i
$683$	−1.00278e12			−0.176325			−0.0881623	−	0.996106i	$-0.528099\pi$
$683$	−1.00278e12			−0.176325			−0.0881623	+	0.996106i	$0.528099\pi$
$684$		0			0
$685$	2.79983e10			0.00485875
$686$	−6.86243e11	+	1.18861e12i	−0.118309	+	0.204918i
$687$		0			0
$688$	1.00058e12	+	1.73305e12i	0.170256	+	0.294893i
$689$	3.61469e11	+	6.26083e11i	0.0611061	+	0.105839i
$690$		0			0
$691$	−5.71239e11	+	9.89415e11i	−0.0953161	+	0.165092i	−0.909741	−	0.415177i	$-0.863720\pi$
$691$	−5.71239e11	+	9.89415e11i	−0.0953161	+	0.165092i	0.814424	+	0.580270i	$0.197053\pi$
$692$	1.48340e11			0.0245913
$693$		0			0
$694$	−4.28675e12			−0.701472
$695$	1.67900e12	−	2.90812e12i	0.272973	−	0.472803i
$696$		0			0
$697$	−2.50882e12	−	4.34540e12i	−0.402644	−	0.697401i
$698$	2.44659e12	+	4.23761e12i	0.390132	+	0.675728i
$699$		0			0
$700$	5.21644e9	−	9.03515e9i	0.000821171	−	0.00142231i
$701$	−5.29555e12			−0.828285			−0.414143	−	0.910212i	$-0.635919\pi$
$701$	−5.29555e12			−0.828285			−0.414143	+	0.910212i	$0.635919\pi$
$702$		0			0
$703$	−8.53660e12			−1.31821
$704$	3.87547e12	−	6.71252e12i	0.594631	−	1.02993i
$705$		0			0
$706$	3.51711e12	+	6.09182e12i	0.532801	+	0.922838i
$707$	−3.49519e11	−	6.05384e11i	−0.0526118	−	0.0911263i
$708$		0			0
$709$	5.07483e12	−	8.78986e12i	0.754246	−	1.30639i	−0.191502	−	0.981492i	$-0.561336\pi$
$709$	5.07483e12	−	8.78986e12i	0.754246	−	1.30639i	0.945748	−	0.324901i	$-0.105331\pi$
$710$	−1.21027e12			−0.178740
$711$		0			0
$712$	3.94343e12			0.575062
$713$	2.18928e12	−	3.79194e12i	0.317247	−	0.549489i
$714$		0			0
$715$	1.02575e12	+	1.77665e12i	0.146779	+	0.254229i
$716$	−7.35724e10	−	1.27431e11i	−0.0104618	−	0.0181204i
$717$		0			0
$718$	−2.67136e12	+	4.62692e12i	−0.375121	+	0.649729i
$719$	5.75277e12			0.802780			0.401390	−	0.915907i	$-0.368527\pi$
$719$	5.75277e12			0.802780			0.401390	+	0.915907i	$0.368527\pi$
$720$		0			0
$721$	−7.69100e10			−0.0105992
$722$	−3.93667e11	+	6.81850e11i	−0.0539152	+	0.0933838i
$723$		0			0
$724$	4.68058e9	+	8.10700e9i	0.000633105	+	0.00109657i
$725$	−3.97710e12	−	6.88854e12i	−0.534620	−	0.925989i
$726$		0			0
$727$	5.50847e12	−	9.54095e12i	0.731351	−	1.26674i	−0.224954	−	0.974369i	$-0.572223\pi$
$727$	5.50847e12	−	9.54095e12i	0.731351	−	1.26674i	0.956306	−	0.292368i	$-0.0944434\pi$
$728$	−6.50362e11			−0.0858152
$729$		0			0
$730$	−7.36953e11			−0.0960476
$731$	−6.52510e11	+	1.13018e12i	−0.0845199	+	0.146393i
$732$		0			0
$733$	8.78360e11	+	1.52136e12i	0.112384	+	0.194655i	0.916731	−	0.399505i	$-0.130818\pi$
$733$	8.78360e11	+	1.52136e12i	0.112384	+	0.194655i	−0.804347	+	0.594160i	$0.797485\pi$
$734$	−3.65199e12	−	6.32543e12i	−0.464405	−	0.804374i
$735$		0			0
$736$	−2.22453e11	+	3.85299e11i	−0.0279439	+	0.0484003i
$737$	1.82470e13			2.27818
$738$		0			0
$739$	−4.52901e12			−0.558603			−0.279301	−	0.960204i	$-0.590103\pi$
$739$	−4.52901e12			−0.558603			−0.279301	+	0.960204i	$0.590103\pi$
$740$	−2.81960e10	+	4.88370e10i	−0.00345657	+	0.00598695i
$741$		0			0
$742$	8.48006e10	+	1.46879e11i	0.0102703	+	0.0177886i
$743$	1.12798e12	+	1.95371e12i	0.135784	+	0.235186i	0.925897	−	0.377776i	$-0.123311\pi$
$743$	1.12798e12	+	1.95371e12i	0.135784	+	0.235186i	−0.790112	+	0.612962i	$0.789978\pi$
$744$		0			0
$745$	3.60421e11	−	6.24267e11i	0.0428654	−	0.0742450i
$746$	−1.15370e13			−1.36386
$747$		0			0
$748$	7.65669e10			0.00894301
$749$	5.75635e11	−	9.97029e11i	0.0668312	−	0.115755i
$750$		0			0
$751$	4.64621e12	+	8.04747e12i	0.532990	+	0.923165i	0.999258	+	0.0385219i	$0.0122649\pi$
$751$	4.64621e12	+	8.04747e12i	0.532990	+	0.923165i	−0.466268	+	0.884644i	$0.654402\pi$
$752$	3.99750e12	+	6.92388e12i	0.455836	+	0.789531i
$753$		0			0
$754$	−3.81420e12	+	6.60639e12i	−0.429766	+	0.744377i
$755$	−2.44935e12			−0.274340
$756$		0			0
$757$	7.28505e12			0.806308			0.403154	−	0.915132i	$-0.367914\pi$
$757$	7.28505e12			0.806308			0.403154	+	0.915132i	$0.367914\pi$
$758$	−7.28764e12	+	1.26226e13i	−0.801818	+	1.38879i
$759$		0			0
$760$	1.72433e12	+	2.98663e12i	0.187482	+	0.324729i
$761$	−1.39337e12	−	2.41339e12i	−0.150604	−	0.260853i	0.780846	−	0.624724i	$-0.214788\pi$
$761$	−1.39337e12	−	2.41339e12i	−0.150604	−	0.260853i	−0.931449	+	0.363871i	$0.881455\pi$
$762$		0			0
$763$	−8.64988e11	+	1.49820e12i	−0.0923952	+	0.160033i
$764$	8.29995e10			0.00881364
$765$		0			0
$766$	1.27559e13			1.33869
$767$	−4.57110e12	+	7.91737e12i	−0.476915	+	0.826041i
$768$		0			0
$769$	−2.31500e12	−	4.00969e12i	−0.238716	−	0.413469i	0.721630	−	0.692279i	$-0.243393\pi$
$769$	−2.31500e12	−	4.00969e12i	−0.238716	−	0.413469i	−0.960346	+	0.278810i	$0.910060\pi$
$770$	2.40641e11	+	4.16802e11i	0.0246696	+	0.0427289i
$771$		0			0
$772$	−4.69582e10	+	8.13340e10i	−0.00475810	+	0.00824127i
$773$	−8.49811e12			−0.856080			−0.428040	−	0.903760i	$-0.640796\pi$
$773$	−8.49811e12			−0.856080			−0.428040	+	0.903760i	$0.640796\pi$
$774$		0			0
$775$	3.11773e12			0.310442
$776$	−1.37348e12	+	2.37894e12i	−0.135971	+	0.235508i
$777$		0			0
$778$	2.08513e12	+	3.61155e12i	0.204044	+	0.353415i
$779$	8.91939e12	+	1.54488e13i	0.867794	+	1.50306i
$780$		0			0
$781$	3.10472e12	−	5.37753e12i	0.298602	−	0.517194i
$782$	9.06623e12			0.866954
$783$		0			0
$784$	1.02604e13			0.969933
$785$	1.40538e12	−	2.43418e12i	0.132093	−	0.228791i
$786$		0			0
$787$	−1.78539e12	−	3.09239e12i	−0.165900	−	0.287348i	0.771074	−	0.636745i	$-0.219720\pi$
$787$	−1.78539e12	−	3.09239e12i	−0.165900	−	0.287348i	−0.936975	+	0.349397i	$0.886386\pi$
$788$	1.04465e11	+	1.80939e11i	0.00965168	+	0.0167172i
$789$		0			0
$790$	−6.39542e11	+	1.10772e12i	−0.0584180	+	0.101183i
$791$	−8.84787e11			−0.0803608
$792$		0			0
$793$	1.11542e13			1.00164
$794$	3.36934e12	−	5.83587e12i	0.300852	−	0.521091i
$795$		0			0
$796$	9.25262e10	+	1.60260e11i	0.00816875	+	0.0141487i
$797$	4.53442e12	+	7.85384e12i	0.398070	+	0.689477i	0.993488	−	0.113939i	$-0.0363469\pi$
$797$	4.53442e12	+	7.85384e12i	0.398070	+	0.689477i	−0.595418	+	0.803416i	$0.703014\pi$
$798$		0			0
$799$	−2.60690e12	+	4.51529e12i	−0.226289	+	0.391945i
$800$	−3.16793e11			−0.0273445
$801$		0			0
$802$	1.37620e13			1.17462
$803$	1.89051e12	−	3.27445e12i	0.160457	−	0.277919i
$804$		0			0
$805$	−4.52288e11	−	7.83385e11i	−0.0379606	−	0.0657497i
$806$	−1.49502e12	−	2.58944e12i	−0.124778	−	0.216122i
$807$		0			0
$808$	−5.34767e12	+	9.26243e12i	−0.441381	+	0.764494i
$809$	−1.10403e13			−0.906173			−0.453087	−	0.891467i	$-0.649677\pi$
$809$	−1.10403e13			−0.906173			−0.453087	+	0.891467i	$0.649677\pi$
$810$		0			0
$811$	−1.04507e12			−0.0848302			−0.0424151	−	0.999100i	$-0.513505\pi$
$811$	−1.04507e12			−0.0848302			−0.0424151	+	0.999100i	$0.513505\pi$
$812$	1.42033e10	−	2.46009e10i	0.00114654	−	0.00198586i
$813$		0			0
$814$	9.11375e12	+	1.57855e13i	0.727591	+	1.26023i
$815$	1.94814e12	+	3.37428e12i	0.154672	+	0.267899i
$816$		0			0
$817$	2.31981e12	−	4.01804e12i	0.182160	−	0.315511i
$818$	4.00612e12			0.312849
$819$		0			0
$820$	1.17841e11			0.00910198
$821$	−5.21592e12	+	9.03424e12i	−0.400670	+	0.693981i	−0.993807	−	0.111121i	$-0.964556\pi$
$821$	−5.21592e12	+	9.03424e12i	−0.400670	+	0.693981i	0.593137	+	0.805102i	$0.297889\pi$
$822$		0			0
$823$	−3.51649e12	−	6.09074e12i	−0.267184	−	0.462776i	0.700950	−	0.713211i	$-0.252760\pi$
$823$	−3.51649e12	−	6.09074e12i	−0.267184	−	0.462776i	−0.968133	+	0.250435i	$0.919426\pi$
$824$	5.88365e11	+	1.01908e12i	0.0444605	+	0.0770078i
$825$		0			0
$826$	−1.07238e12	+	1.85741e12i	−0.0801563	+	0.138835i
$827$	1.69223e13			1.25801			0.629006	−	0.777400i	$-0.283462\pi$
$827$	1.69223e13			1.25801			0.629006	+	0.777400i	$0.283462\pi$
$828$		0			0
$829$	2.27155e12			0.167042			0.0835212	−	0.996506i	$-0.473383\pi$
$829$	2.27155e12			0.167042			0.0835212	+	0.996506i	$0.473383\pi$
$830$	−3.40756e12	+	5.90206e12i	−0.249225	+	0.431671i
$831$		0			0
$832$	4.97410e12	+	8.61540e12i	0.359882	+	0.623334i
$833$	3.34557e12	+	5.79470e12i	0.240751	+	0.416993i
$834$		0			0
$835$	2.28430e12	−	3.95653e12i	0.162616	−	0.281660i
$836$	−2.72212e11			−0.0192743
$837$		0			0
$838$	2.54594e12			0.178341
$839$	8.97286e12	−	1.55414e13i	0.625175	−	1.08284i	−0.363332	−	0.931660i	$-0.618361\pi$
$839$	8.97286e12	−	1.55414e13i	0.625175	−	1.08284i	0.988507	−	0.151176i	$-0.0483059\pi$
$840$		0			0
$841$	−3.57528e12	−	6.19256e12i	−0.246449	−	0.426863i
$842$	−1.91342e12	−	3.31414e12i	−0.131192	−	0.227230i
$843$		0			0
$844$	1.03163e11	−	1.78683e11i	0.00699812	−	0.0121211i
$845$	2.60448e12			0.175738
$846$		0			0
$847$	−6.70154e11			−0.0447404
$848$	1.27718e12	−	2.21214e12i	0.0848146	−	0.146903i
$849$		0			0
$850$	3.22778e12	+	5.59068e12i	0.212089	+	0.367350i
$851$	−1.71294e13	−	2.96690e13i	−1.11959	−	1.93919i
$852$		0			0
$853$	1.10051e13	−	1.90614e13i	0.711744	−	1.23278i	−0.252458	−	0.967608i	$-0.581239\pi$
$853$	1.10051e13	−	1.90614e13i	0.711744	−	1.23278i	0.964202	−	0.265169i	$-0.0854279\pi$
$854$	2.61678e12			0.168348
$855$		0			0
$856$	−1.76145e13			−1.12135
$857$	−1.17024e13	+	2.02692e13i	−0.741074	+	1.28358i	0.210933	+	0.977500i	$0.432350\pi$
$857$	−1.17024e13	+	2.02692e13i	−0.741074	+	1.28358i	−0.952007	+	0.306077i	$0.900984\pi$
$858$		0			0
$859$	−2.13404e10	−	3.69627e10i	−0.00133732	−	0.00231630i	0.865356	−	0.501158i	$-0.167092\pi$
$859$	−2.13404e10	−	3.69627e10i	−0.00133732	−	0.00231630i	−0.866693	+	0.498841i	$0.833759\pi$
$860$	−1.53245e10	−	2.65428e10i	−0.000955308	−	0.00165464i
$861$		0			0
$862$	6.80253e12	−	1.17823e13i	0.419650	−	0.726856i
$863$	−3.10119e13			−1.90318			−0.951590	−	0.307370i	$-0.900551\pi$
$863$	−3.10119e13			−1.90318			−0.951590	+	0.307370i	$0.900551\pi$
$864$		0			0
$865$	9.15814e12			0.556205
$866$	1.00419e13	−	1.73932e13i	0.606719	−	1.05087i
$867$		0			0
$868$	5.56715e9	+	9.64259e9i	0.000332885	+	0.000576574i
$869$	−3.28124e12	−	5.68327e12i	−0.195186	−	0.338072i
$870$		0			0
$871$	−1.17099e13	+	2.02821e13i	−0.689398	+	1.19407i
$872$	2.64688e13			1.55028
$873$		0			0
$874$	−3.22324e13			−1.86849
$875$	6.90062e11	−	1.19522e12i	0.0397971	−	0.0689307i
$876$		0			0
$877$	8.20232e12	+	1.42068e13i	0.468208	+	0.810960i	0.999340	−	0.0363292i	$-0.0115665\pi$
$877$	8.20232e12	+	1.42068e13i	0.468208	+	0.810960i	−0.531132	+	0.847289i	$0.678233\pi$
$878$	−9.16142e12	−	1.58680e13i	−0.520280	−	0.901152i
$879$		0			0
$880$	3.62429e12	−	6.27745e12i	0.203728	−	0.352867i
$881$	−2.25741e13			−1.26246			−0.631231	−	0.775595i	$-0.717450\pi$
$881$	−2.25741e13			−1.26246			−0.631231	+	0.775595i	$0.717450\pi$
$882$		0			0
$883$	−7.75871e12			−0.429503			−0.214752	−	0.976669i	$-0.568894\pi$
$883$	−7.75871e12			−0.429503			−0.214752	+	0.976669i	$0.568894\pi$
$884$	−4.91361e10	+	8.51063e10i	−0.00270624	+	0.00468734i
$885$		0			0
$886$	−2.87109e12	−	4.97288e12i	−0.156529	−	0.271117i
$887$	2.22018e12	+	3.84546e12i	0.120429	+	0.208589i	0.919937	−	0.392066i	$-0.128240\pi$
$887$	2.22018e12	+	3.84546e12i	0.120429	+	0.208589i	−0.799508	+	0.600656i	$0.794906\pi$
$888$		0			0
$889$	−9.96457e11	+	1.72591e12i	−0.0535058	+	0.0926747i
$890$	3.74549e12			0.200103
$891$		0			0
$892$	8.02694e9			0.000424530
$893$	9.26810e12	−	1.60528e13i	0.487707	−	0.844734i
$894$		0			0
$895$	−4.54217e12	−	7.86726e12i	−0.236624	−	0.409845i
$896$	1.13072e12	+	1.95847e12i	0.0586097	+	0.101515i
$897$		0			0
$898$	2.97552e12	−	5.15375e12i	0.152693	−	0.264472i
$899$	8.48897e12			0.433447
$900$		0			0
$901$	1.66578e12			0.0842087
$902$	1.90448e13	−	3.29866e13i	0.957961	−	1.65924i
$903$		0			0
$904$	6.76866e12	+	1.17237e13i	0.337089	+	0.583856i
$905$	2.88966e11	+	5.00505e11i	0.0143195	+	0.0248022i
$906$		0			0
$907$	−8.55346e12	+	1.48150e13i	−0.419671	+	0.726891i	−0.995906	−	0.0903925i	$-0.971188\pi$
$907$	−8.55346e12	+	1.48150e13i	−0.419671	+	0.726891i	0.576235	+	0.817284i	$0.304521\pi$
$908$	−4.22329e11			−0.0206189
$909$		0			0
$910$	−6.17717e11			−0.0298609
$911$	−9.41178e12	+	1.63017e13i	−0.452730	+	0.784151i	−0.998555	−	0.0537482i	$-0.982883\pi$
$911$	−9.41178e12	+	1.63017e13i	−0.452730	+	0.784151i	0.545825	+	0.837899i	$0.316216\pi$
$912$		0			0
$913$	−1.74828e13	−	3.02812e13i	−0.832709	−	1.44229i
$914$	1.40947e13	+	2.44127e13i	0.668031	+	1.15706i
$915$		0			0
$916$	1.24364e11	−	2.15404e11i	0.00583665	−	0.0101094i
$917$	2.49414e12			0.116482
$918$		0			0
$919$	−4.20992e13			−1.94695			−0.973473	−	0.228800i	$-0.926520\pi$
$919$	−4.20992e13			−1.94695			−0.973473	+	0.228800i	$0.926520\pi$
$920$	−6.92004e12	+	1.19859e13i	−0.318466	+	0.551600i
$921$		0			0
$922$	−1.68061e13	−	2.91090e13i	−0.765908	−	1.32659i
$923$	3.98486e12	+	6.90197e12i	0.180720	+	0.313015i
$924$		0			0
$925$	1.21969e13	−	2.11257e13i	0.547788	−	0.948797i
$926$	−4.22615e13			−1.88884
$927$		0			0
$928$	−8.62564e11			−0.0381791
$929$	−6.18447e12	+	1.07118e13i	−0.272415	+	0.471837i	−0.969480	−	0.245171i	$-0.921156\pi$
$929$	−6.18447e12	+	1.07118e13i	−0.272415	+	0.471837i	0.697064	+	0.717009i	$0.254489\pi$
$930$		0			0
$931$	−1.18942e13	−	2.06014e13i	−0.518875	−	0.898718i
$932$	−1.36533e11	−	2.36482e11i	−0.00592742	−	0.0102666i
$933$		0			0
$934$	−1.60538e12	+	2.78060e12i	−0.0690266	+	0.119558i
$935$	4.72703e12			0.202272
$936$		0			0
$937$	2.10110e13			0.890467			0.445234	−	0.895414i	$-0.353121\pi$
$937$	2.10110e13			0.890467			0.445234	+	0.895414i	$0.353121\pi$
$938$	−2.74713e12	+	4.75817e12i	−0.115869	+	0.200691i
$939$		0			0
$940$	−6.12243e10	−	1.06044e11i	−0.00255769	−	0.00443005i
$941$	−7.49876e12	−	1.29882e13i	−0.311771	−	0.540004i	0.666975	−	0.745080i	$-0.267589\pi$
$941$	−7.49876e12	−	1.29882e13i	−0.311771	−	0.540004i	−0.978746	+	0.205077i	$0.934256\pi$
$942$		0			0
$943$	−3.57950e13	+	6.19988e13i	−1.47408	+	2.55318i
$944$	3.23021e13			1.32391
$945$		0			0
$946$	−9.90662e12			−0.402175
$947$	−6.54160e11	+	1.13304e12i	−0.0264307	+	0.0457794i	−0.878938	−	0.476936i	$-0.841747\pi$
$947$	−6.54160e11	+	1.13304e12i	−0.0264307	+	0.0457794i	0.852507	+	0.522715i	$0.175081\pi$
$948$		0			0
$949$	2.42643e12	+	4.20271e12i	0.0971115	+	0.168202i
$950$	−1.14755e13	−	1.98761e13i	−0.457103	−	0.791725i
$951$		0			0
$952$	−7.49276e11	+	1.29778e12i	−0.0295649	+	0.0512078i
$953$	4.18691e13			1.64428			0.822140	−	0.569285i	$-0.192780\pi$
$953$	4.18691e13			1.64428			0.822140	+	0.569285i	$0.192780\pi$
$954$		0			0
$955$	5.12417e12			0.199346
$956$	−3.61068e11	+	6.25388e11i	−0.0139807	+	0.0242153i
$957$		0			0
$958$	−4.25153e12	−	7.36386e12i	−0.163080	−	0.282463i
$959$	−2.16266e10	−	3.74584e10i	−0.000825667	−	0.00143010i
$960$		0			0
$961$	1.15561e13	−	2.00158e13i	0.437077	−	0.757039i
$962$	−2.33947e13			−0.880703
$963$		0			0
$964$	6.18714e11			0.0230751
$965$	−2.89907e12	+	5.02134e12i	−0.107618	+	0.186401i
$966$		0			0
$967$	5.53530e11	+	9.58742e11i	0.0203574	+	0.0352600i	0.876025	−	0.482266i	$-0.160186\pi$
$967$	5.53530e11	+	9.58742e11i	0.0203574	+	0.0352600i	−0.855667	+	0.517526i	$0.826853\pi$
$968$	5.12671e12	+	8.87972e12i	0.187672	+	0.325058i
$969$		0			0
$970$	−1.30454e12	+	2.25953e12i	−0.0473135	+	0.0819494i
$971$	−2.21624e13			−0.800075			−0.400038	−	0.916499i	$-0.631003\pi$
$971$	−2.21624e13			−0.800075			−0.400038	+	0.916499i	$0.631003\pi$
$972$		0			0
$973$	−5.18762e12			−0.185550
$974$	−1.08500e11	+	1.87928e11i	−0.00386292	+	0.00669078i
$975$		0			0
$976$	−1.97057e13	−	3.41312e13i	−0.695131	−	1.20400i
$977$	1.09841e13	+	1.90251e13i	0.385692	+	0.668038i	0.991865	−	0.127295i	$-0.0406293\pi$
$977$	1.09841e13	+	1.90251e13i	0.385692	+	0.668038i	−0.606173	+	0.795333i	$0.707296\pi$
$978$		0			0
$979$	−9.60832e12	+	1.66421e13i	−0.334292	+	0.579010i
$980$	−1.57145e11			−0.00544229
$981$		0			0
$982$	−1.55088e13			−0.532204
$983$	−2.03615e13	+	3.52671e13i	−0.695533	+	1.20470i	0.274467	+	0.961596i	$0.411499\pi$
$983$	−2.03615e13	+	3.52671e13i	−0.695533	+	1.20470i	−0.970001	+	0.243103i	$0.921835\pi$
$984$		0			0
$985$	6.44939e12	+	1.11707e13i	0.218301	+	0.378109i
$986$	8.78861e12	+	1.52223e13i	0.296124	+	0.512903i
$987$		0			0
$988$	1.74690e11	−	3.02571e11i	0.00583258	−	0.0101023i
$989$	1.86196e13			0.618853
$990$		0			0
$991$	1.69138e13			0.557070			0.278535	−	0.960426i	$-0.410151\pi$
$991$	1.69138e13			0.557070			0.278535	+	0.960426i	$0.410151\pi$
$992$	1.69045e11	−	2.92795e11i	0.00554244	−	0.00959979i
$993$		0			0
$994$	9.34847e11	+	1.61920e12i	0.0303740	+	0.0526093i
$995$	5.71232e12	+	9.89403e12i	0.184760	+	0.320014i
$996$		0			0
$997$	2.00331e13	−	3.46983e13i	0.642125	−	1.11219i	−0.342833	−	0.939396i	$-0.611386\pi$
$997$	2.00331e13	−	3.46983e13i	0.642125	−	1.11219i	0.984958	−	0.172796i	$-0.0552802\pi$
$998$	1.79071e13			0.571397
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.c.f.55.1		4
3.2	odd	2	inner	81.10.c.f.55.2		4
9.2	odd	6		27.10.a.a.1.1	✓	2
9.4	even	3	inner	81.10.c.f.28.1		4
9.5	odd	6	inner	81.10.c.f.28.2		4
9.7	even	3		27.10.a.a.1.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.a.a.1.1	✓	2	9.2	odd	6
27.10.a.a.1.2	yes	2	9.7	even	3
81.10.c.f.28.1		4	9.4	even	3	inner
81.10.c.f.28.2		4	9.5	odd	6	inner
81.10.c.f.55.1		4	1.1	even	1	trivial
81.10.c.f.55.2		4	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	81.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-11.2250 + 19.4422i) q^{2} +(4.00000 + 6.92820i) q^{4} +(246.949 + 427.729i) q^{5} +(381.500 - 660.777i) q^{7} -11674.0 q^{8} -11088.0 q^{10} +(28444.1 - 49266.6i) q^{11} +(36507.5 + 63232.8i) q^{13} +(8564.65 + 14834.4i) q^{14} +(128992. - 223421. i) q^{16} +168240. q^{17} -598129. q^{19} +(-1975.60 + 3421.83i) q^{20} +(638568. + 1.10603e6i) q^{22} +(-1.20020e6 - 2.07880e6i) q^{23} +(854594. - 1.48020e6i) q^{25} -1.63918e6 q^{26} +6104.00 q^{28} +(2.32689e6 - 4.03029e6i) q^{29} +(912050. + 1.57972e6i) q^{31} +(-92673.4 - 160515. i) q^{32} +(-1.88849e6 + 3.27096e6i) q^{34} +376845. q^{35} +1.42722e7 q^{37} +(6.71398e6 - 1.16290e7i) q^{38} +(-2.88288e6 - 4.99329e6i) q^{40} +(-1.49122e7 - 2.58286e7i) q^{41} +(-3.87845e6 + 6.71768e6i) q^{43} +455105. q^{44} +5.38887e7 q^{46} +(-1.54952e7 + 2.68384e7i) q^{47} +(1.98857e7 + 3.44431e7i) q^{49} +(1.91856e7 + 3.32304e7i) q^{50} +(-292060. + 505863. i) q^{52} +9.90123e6 q^{53} +2.80970e7 q^{55} +(-4.45362e6 + 7.71390e6i) q^{56} +(5.22386e7 + 9.04799e7i) q^{58} +(6.26049e7 + 1.08435e8i) q^{59} +(7.63832e7 - 1.32300e8i) q^{61} -4.09509e7 q^{62} +1.36249e8 q^{64} +(-1.80310e7 + 3.12306e7i) q^{65} +(1.60376e8 + 2.77779e8i) q^{67} +(672960. + 1.16560e6i) q^{68} +(-4.23007e6 + 7.32670e6i) q^{70} +1.09152e8 q^{71} +6.64640e7 q^{73} +(-1.60205e8 + 2.77483e8i) q^{74} +(-2.39252e6 - 4.14396e6i) q^{76} +(-2.17028e7 - 3.75904e7i) q^{77} +(5.76787e7 - 9.99025e7i) q^{79} +1.27418e8 q^{80} +6.69554e8 q^{82} +(3.07319e8 - 5.32293e8i) q^{83} +(4.15467e7 + 7.19611e7i) q^{85} +(-8.70710e7 - 1.50811e8i) q^{86} +(-3.32055e8 + 5.75137e8i) q^{88} -3.37797e8 q^{89} +5.57104e7 q^{91} +(9.60157e6 - 1.66304e7i) q^{92} +(-3.47865e8 - 6.02520e8i) q^{94} +(-1.47708e8 - 2.55837e8i) q^{95} +(1.17653e8 - 2.03782e8i) q^{97} -8.92867e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{4} + 1526 q^{7} - 44352 q^{10} + 146030 q^{13} + 515968 q^{16} - 2392516 q^{19} + 2554272 q^{22} + 3418378 q^{25} + 24416 q^{28} + 3648200 q^{31} - 7553952 q^{34} + 57088700 q^{37} - 11531520 q^{40}+ \cdots + 470613686 q^{97}+O(q^{100}) \) 4 * q + 16 * q^4 + 1526 * q^7 - 44352 * q^10 + 146030 * q^13 + 515968 * q^16 - 2392516 * q^19 + 2554272 * q^22 + 3418378 * q^25 + 24416 * q^28 + 3648200 * q^31 - 7553952 * q^34 + 57088700 * q^37 - 11531520 * q^40 - 15513808 * q^43 + 215554752 * q^46 + 79542876 * q^49 - 1168240 * q^52 + 112387968 * q^55 + 208954368 * q^58 + 305532986 * q^61 + 544995328 * q^64 + 641504138 * q^67 - 16920288 * q^70 + 265855940 * q^73 - 9570064 * q^76 + 230714906 * q^79 + 2678215680 * q^82 + 166186944 * q^85 - 1328221440 * q^88 + 222841780 * q^91 - 1391461344 * q^94 + 470613686 * q^97

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