LMFDB - Embedded newform 54.8.c.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,8,Mod(19,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("54.19");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	54.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:	$16.8687913761$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.14601465675.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 52x^{4} - 99x^{3} + 709x^{2} - 660x + 1872 $ x^6 - 3x^5 + 52x^4 - 99x^3 + 709x^2 - 660*x + 1872
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{9} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			19.1
Root			$0.500000 + 5.21243i$ of defining polynomial
Character	$\chi$	$=$	54.19
Dual form			54.8.c.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-187.789 - 325.261i) q^{5} +(-528.867 + 916.024i) q^{7} -512.000 q^{8} -3004.63 q^{10} +(849.965 - 1472.18i) q^{11} +(6256.75 + 10837.0i) q^{13} +(4230.93 + 7328.19i) q^{14} +(-2048.00 + 3547.24i) q^{16} -16879.9 q^{17} -35281.9 q^{19} +(-12018.5 + 20816.7i) q^{20} +(-6799.72 - 11777.5i) q^{22} +(35482.7 + 61457.8i) q^{23} +(-31467.1 + 54502.6i) q^{25} +100108. q^{26} +67694.9 q^{28} +(-38827.4 + 67251.0i) q^{29} +(63093.8 + 109282. i) q^{31} +(16384.0 + 28377.9i) q^{32} +(-67519.4 + 116947. i) q^{34} +397262. q^{35} -528664. q^{37} +(-141128. + 244440. i) q^{38} +(96148.1 + 166533. i) q^{40} +(-258960. - 448533. i) q^{41} +(135830. - 235264. i) q^{43} -108795. q^{44} +567723. q^{46} +(-211814. + 366873. i) q^{47} +(-147628. - 255699. i) q^{49} +(251737. + 436021. i) q^{50} +(400432. - 693568. i) q^{52} -1.24314e6 q^{53} -638457. q^{55} +(270780. - 469004. i) q^{56} +(310619. + 538008. i) q^{58} +(-1.34086e6 - 2.32244e6i) q^{59} +(377040. - 653052. i) q^{61} +1.00950e6 q^{62} +262144. q^{64} +(2.34990e6 - 4.07014e6i) q^{65} +(131285. + 227392. i) q^{67} +(540156. + 935577. i) q^{68} +(1.58905e6 - 2.75231e6i) q^{70} -990913. q^{71} -1.04389e6 q^{73} +(-2.11466e6 + 3.66269e6i) q^{74} +(1.12902e6 + 1.95552e6i) q^{76} +(899036. + 1.55718e6i) q^{77} +(3.66860e6 - 6.35419e6i) q^{79} +1.53837e6 q^{80} -4.14337e6 q^{82} +(-1.94611e6 + 3.37075e6i) q^{83} +(3.16986e6 + 5.49035e6i) q^{85} +(-1.08664e6 - 1.88211e6i) q^{86} +(-435182. + 753757. i) q^{88} -675681. q^{89} -1.32359e7 q^{91} +(2.27089e6 - 3.93330e6i) q^{92} +(1.69452e6 + 2.93499e6i) q^{94} +(6.62556e6 + 1.14758e7i) q^{95} +(-8.12785e6 + 1.40779e7i) q^{97} -2.36205e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 24 q^{2} - 192 q^{4} - 54 q^{5} + 210 q^{7} - 3072 q^{8} - 864 q^{10} - 6579 q^{11} + 10092 q^{13} - 1680 q^{14} - 12288 q^{16} + 29790 q^{17} - 137490 q^{19} - 3456 q^{20} + 52632 q^{22} + 39654 q^{23}+ \cdots + 7714800 q^{98}+O(q^{100}) $ 6 * q + 24 * q^2 - 192 * q^4 - 54 * q^5 + 210 * q^7 - 3072 * q^8 - 864 * q^10 - 6579 * q^11 + 10092 * q^13 - 1680 * q^14 - 12288 * q^16 + 29790 * q^17 - 137490 * q^19 - 3456 * q^20 + 52632 * q^22 + 39654 * q^23 - 7923 * q^25 + 161472 * q^26 - 26880 * q^28 - 239832 * q^29 + 145704 * q^31 + 98304 * q^32 + 119160 * q^34 + 1087776 * q^35 - 720384 * q^37 - 549960 * q^38 + 27648 * q^40 - 1086993 * q^41 - 299967 * q^43 + 842112 * q^44 + 634464 * q^46 - 131634 * q^47 + 482175 * q^49 + 63384 * q^50 + 645888 * q^52 - 1909152 * q^53 - 5494824 * q^55 - 107520 * q^56 + 1918656 * q^58 - 2504853 * q^59 + 7309038 * q^61 + 2331264 * q^62 + 1572864 * q^64 + 1786698 * q^65 + 3433035 * q^67 - 953280 * q^68 + 4351104 * q^70 - 2269368 * q^71 - 15901746 * q^73 - 2881536 * q^74 + 4399680 * q^76 + 6147432 * q^77 + 7076928 * q^79 + 442368 * q^80 - 17391888 * q^82 + 10914444 * q^83 + 17613396 * q^85 + 2399736 * q^86 + 3368448 * q^88 - 23800356 * q^89 - 37170552 * q^91 + 2537856 * q^92 + 1053072 * q^94 + 17342424 * q^95 + 519357 * q^97 + 7714800 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	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
$5$	−187.789	−	325.261i	−0.671855	−	1.16369i	−0.977377	−	0.211502i	$-0.932164\pi$
$5$	−187.789	−	325.261i	−0.671855	−	1.16369i	0.305522	−	0.952185i	$-0.401169\pi$
$6$		0			0
$7$	−528.867	+	916.024i	−0.582778	+	1.00940i	0.412371	+	0.911016i	$0.364701\pi$
$7$	−528.867	+	916.024i	−0.582778	+	1.00940i	−0.995148	+	0.0983845i	$0.968633\pi$
$8$	−512.000			−0.353553
$9$		0			0
$10$	−3004.63			−0.950147
$11$	849.965	−	1472.18i	0.192542	−	0.333493i	−0.753550	−	0.657391i	$-0.771660\pi$
$11$	849.965	−	1472.18i	0.192542	−	0.333493i	0.946092	+	0.323898i	$0.104993\pi$
$12$		0			0
$13$	6256.75	+	10837.0i	0.789854	+	1.36807i	0.926056	+	0.377386i	$0.123177\pi$
$13$	6256.75	+	10837.0i	0.789854	+	1.36807i	−0.136202	+	0.990681i	$0.543490\pi$
$14$	4230.93	+	7328.19i	0.412086	+	0.713754i
$15$		0			0
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	−16879.9			−0.833293			−0.416646	−	0.909069i	$-0.636795\pi$
$17$	−16879.9			−0.833293			−0.416646	+	0.909069i	$0.636795\pi$
$18$		0			0
$19$	−35281.9			−1.18009			−0.590044	−	0.807371i	$-0.700890\pi$
$19$	−35281.9			−1.18009			−0.590044	+	0.807371i	$0.700890\pi$
$20$	−12018.5	+	20816.7i	−0.335928	+	0.581844i
$21$		0			0
$22$	−6799.72	−	11777.5i	−0.136148	−	0.235815i
$23$	35482.7	+	61457.8i	0.608092	+	1.05325i	0.991555	+	0.129690i	$0.0413981\pi$
$23$	35482.7	+	61457.8i	0.608092	+	1.05325i	−0.383463	+	0.923556i	$0.625269\pi$
$24$		0			0
$25$	−31467.1	+	54502.6i	−0.402779	+	0.697634i
$26$	100108.			1.11702
$27$		0			0
$28$	67694.9			0.582778
$29$	−38827.4	+	67251.0i	−0.295628	+	0.512042i	−0.975131	−	0.221631i	$-0.928862\pi$
$29$	−38827.4	+	67251.0i	−0.295628	+	0.512042i	0.679503	+	0.733673i	$0.262195\pi$
$30$		0			0
$31$	63093.8	+	109282.i	0.380383	+	0.658843i	0.991117	−	0.132993i	$-0.0424588\pi$
$31$	63093.8	+	109282.i	0.380383	+	0.658843i	−0.610734	+	0.791836i	$0.709126\pi$
$32$	16384.0	+	28377.9i	0.0883883	+	0.153093i
$33$		0			0
$34$	−67519.4	+	116947.i	−0.294614	+	0.510286i
$35$	397262.			1.56617
$36$		0			0
$37$	−528664.			−1.71583			−0.857914	−	0.513794i	$-0.828240\pi$
$37$	−528664.			−1.71583			−0.857914	+	0.513794i	$0.828240\pi$
$38$	−141128.	+	244440.i	−0.417224	+	0.722654i
$39$		0			0
$40$	96148.1	+	166533.i	0.237537	+	0.411426i
$41$	−258960.	−	448533.i	−0.586800	−	1.01637i	−0.994648	−	0.103318i	$-0.967054\pi$
$41$	−258960.	−	448533.i	−0.586800	−	1.01637i	0.407849	−	0.913050i	$-0.366279\pi$
$42$		0			0
$43$	135830.	−	235264.i	0.260529	−	0.451249i	−0.705854	−	0.708358i	$-0.749436\pi$
$43$	135830.	−	235264.i	0.260529	−	0.451249i	0.966383	+	0.257109i	$0.0827698\pi$
$44$	−108795.			−0.192542
$45$		0			0
$46$	567723.			0.859972
$47$	−211814.	+	366873.i	−0.297586	+	0.515435i	−0.975583	−	0.219630i	$-0.929515\pi$
$47$	−211814.	+	366873.i	−0.297586	+	0.515435i	0.677997	+	0.735065i	$0.262848\pi$
$48$		0			0
$49$	−147628.	−	255699.i	−0.179260	−	0.310487i
$50$	251737.	+	436021.i	0.284808	+	0.493301i
$51$		0			0
$52$	400432.	−	693568.i	0.394927	−	0.684034i
$53$	−1.24314e6			−1.14698			−0.573490	−	0.819213i	$-0.694411\pi$
$53$	−1.24314e6			−1.14698			−0.573490	+	0.819213i	$0.694411\pi$
$54$		0			0
$55$	−638457.			−0.517443
$56$	270780.	−	469004.i	0.206043	−	0.356877i
$57$		0			0
$58$	310619.	+	538008.i	0.209040	+	0.362068i
$59$	−1.34086e6	−	2.32244e6i	−0.849968	−	1.47219i	−0.881236	−	0.472677i	$-0.843288\pi$
$59$	−1.34086e6	−	2.32244e6i	−0.849968	−	1.47219i	0.0312678	−	0.999511i	$-0.490046\pi$
$60$		0			0
$61$	377040.	−	653052.i	0.212683	−	0.368378i	−0.739870	−	0.672750i	$-0.765113\pi$
$61$	377040.	−	653052.i	0.212683	−	0.368378i	0.952553	+	0.304372i	$0.0984465\pi$
$62$	1.00950e6			0.537943
$63$		0			0
$64$	262144.			0.125000
$65$	2.34990e6	−	4.07014e6i	1.06133	−	1.83829i
$66$		0			0
$67$	131285.	+	227392.i	0.0533278	+	0.0923664i	0.891457	−	0.453105i	$-0.149684\pi$
$67$	131285.	+	227392.i	0.0533278	+	0.0923664i	−0.838129	+	0.545472i	$0.816351\pi$
$68$	540156.	+	935577.i	0.208323	+	0.360826i
$69$		0			0
$70$	1.58905e6	−	2.75231e6i	0.553724	−	0.959079i
$71$	−990913.			−0.328573			−0.164286	−	0.986413i	$-0.552532\pi$
$71$	−990913.			−0.328573			−0.164286	+	0.986413i	$0.552532\pi$
$72$		0			0
$73$	−1.04389e6			−0.314068			−0.157034	−	0.987593i	$-0.550193\pi$
$73$	−1.04389e6			−0.314068			−0.157034	+	0.987593i	$0.550193\pi$
$74$	−2.11466e6	+	3.66269e6i	−0.606637	+	1.05073i
$75$		0			0
$76$	1.12902e6	+	1.95552e6i	0.295022	+	0.510993i
$77$	899036.	+	1.55718e6i	0.224419	+	0.388705i
$78$		0			0
$79$	3.66860e6	−	6.35419e6i	0.837153	−	1.44999i	−0.0551117	−	0.998480i	$-0.517551\pi$
$79$	3.66860e6	−	6.35419e6i	0.837153	−	1.44999i	0.892265	−	0.451512i	$-0.149115\pi$
$80$	1.53837e6			0.335928
$81$		0			0
$82$	−4.14337e6			−0.829860
$83$	−1.94611e6	+	3.37075e6i	−0.373588	+	0.647074i	−0.990115	−	0.140260i	$-0.955206\pi$
$83$	−1.94611e6	+	3.37075e6i	−0.373588	+	0.647074i	0.616526	+	0.787334i	$0.288539\pi$
$84$		0			0
$85$	3.16986e6	+	5.49035e6i	0.559852	+	0.969692i
$86$	−1.08664e6	−	1.88211e6i	−0.184222	−	0.319081i
$87$		0			0
$88$	−435182.	+	753757.i	−0.0680740	+	0.117908i
$89$	−675681.			−0.101596			−0.0507980	−	0.998709i	$-0.516176\pi$
$89$	−675681.			−0.101596			−0.0507980	+	0.998709i	$0.516176\pi$
$90$		0			0
$91$	−1.32359e7			−1.84124
$92$	2.27089e6	−	3.93330e6i	0.304046	−	0.526623i
$93$		0			0
$94$	1.69452e6	+	2.93499e6i	0.210425	+	0.364467i
$95$	6.62556e6	+	1.14758e7i	0.792849	+	1.37325i
$96$		0			0
$97$	−8.12785e6	+	1.40779e7i	−0.904221	+	1.56616i	−0.0822619	+	0.996611i	$0.526214\pi$
$97$	−8.12785e6	+	1.40779e7i	−0.904221	+	1.56616i	−0.821959	+	0.569546i	$0.807119\pi$
$98$	−2.36205e6			−0.253512
$99$		0			0
$100$	4.02779e6			0.402779
$101$	−212270.	+	367662.i	−0.0205005	+	0.0355079i	−0.876094	−	0.482141i	$-0.839859\pi$
$101$	−212270.	+	367662.i	−0.0205005	+	0.0355079i	0.855593	+	0.517649i	$0.173193\pi$
$102$		0			0
$103$	2.43167e6	+	4.21178e6i	0.219268	+	0.379783i	0.954584	−	0.297941i	$-0.0962999\pi$
$103$	2.43167e6	+	4.21178e6i	0.219268	+	0.379783i	−0.735317	+	0.677724i	$0.762967\pi$
$104$	−3.20345e6	−	5.54854e6i	−0.279256	−	0.483685i
$105$		0			0
$106$	−4.97257e6	+	8.61275e6i	−0.405519	+	0.702379i
$107$	−2.83648e6			−0.223839			−0.111920	−	0.993717i	$-0.535700\pi$
$107$	−2.83648e6			−0.223839			−0.111920	+	0.993717i	$0.535700\pi$
$108$		0			0
$109$	6.31389e6			0.466987			0.233493	−	0.972358i	$-0.424984\pi$
$109$	6.31389e6			0.466987			0.233493	+	0.972358i	$0.424984\pi$
$110$	−2.55383e6	+	4.42336e6i	−0.182944	+	0.316868i
$111$		0			0
$112$	−2.16624e6	−	3.75203e6i	−0.145694	−	0.252350i
$113$	1.07218e7	+	1.85708e7i	0.699029	+	1.21075i	0.968804	+	0.247830i	$0.0797174\pi$
$113$	1.07218e7	+	1.85708e7i	0.699029	+	1.21075i	−0.269775	+	0.962923i	$0.586949\pi$
$114$		0			0
$115$	1.33265e7	−	2.30822e7i	0.817100	−	1.41526i
$116$	4.96990e6			0.295628
$117$		0			0
$118$	−2.14538e7			−1.20204
$119$	8.92719e6	−	1.54624e7i	0.485624	−	0.841126i
$120$		0			0
$121$	8.29871e6	+	1.43738e7i	0.425855	+	0.737602i
$122$	−3.01632e6	−	5.22442e6i	−0.150390	−	0.260483i
$123$		0			0
$124$	4.03801e6	−	6.99403e6i	0.190191	−	0.329421i
$125$	−5.70534e6			−0.261274
$126$		0			0
$127$	1.35681e7			0.587768			0.293884	−	0.955841i	$-0.405052\pi$
$127$	1.35681e7			0.587768			0.293884	+	0.955841i	$0.405052\pi$
$128$	1.04858e6	−	1.81619e6i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.87992e7	−	3.25612e7i	−0.750477	−	1.29986i
$131$	−1.17657e7	−	2.03788e7i	−0.457265	−	0.792005i	0.541551	−	0.840668i	$-0.317837\pi$
$131$	−1.17657e7	−	2.03788e7i	−0.457265	−	0.792005i	−0.998815	+	0.0486627i	$0.984504\pi$
$132$		0			0
$133$	1.86594e7	−	3.23191e7i	0.687729	−	1.19118i
$134$	2.10056e6			0.0754169
$135$		0			0
$136$	8.64249e6			0.294614
$137$	−1.39952e7	+	2.42405e7i	−0.465006	+	0.805414i	−0.999202	−	0.0399467i	$-0.987281\pi$
$137$	−1.39952e7	+	2.42405e7i	−0.465006	+	0.805414i	0.534196	+	0.845361i	$0.320615\pi$
$138$		0			0
$139$	4.00094e6	+	6.92982e6i	0.126360	+	0.218862i	0.922264	−	0.386561i	$-0.126337\pi$
$139$	4.00094e6	+	6.92982e6i	0.126360	+	0.218862i	−0.795904	+	0.605423i	$0.793004\pi$
$140$	−1.27124e7	−	2.20185e7i	−0.391542	−	0.678171i
$141$		0			0
$142$	−3.96365e6	+	6.86525e6i	−0.116168	+	0.201209i
$143$	2.12721e7			0.608322
$144$		0			0
$145$	2.91655e7			0.794476
$146$	−4.17555e6	+	7.23226e6i	−0.111040	+	0.192327i
$147$		0			0
$148$	1.69172e7	+	2.93015e7i	0.428957	+	0.742975i
$149$	−1.35829e7	−	2.35262e7i	−0.336387	−	0.582639i	0.647363	−	0.762182i	$-0.275872\pi$
$149$	−1.35829e7	−	2.35262e7i	−0.336387	−	0.582639i	−0.983750	+	0.179542i	$0.942538\pi$
$150$		0			0
$151$	−2.09932e7	+	3.63612e7i	−0.496202	+	0.859447i	−0.999990	−	0.00438023i	$-0.998606\pi$
$151$	−2.09932e7	+	3.63612e7i	−0.496202	+	0.859447i	0.503789	+	0.863827i	$0.331939\pi$
$152$	1.80643e7			0.417224
$153$		0			0
$154$	1.43846e7			0.317376
$155$	2.36967e7	−	4.10439e7i	0.511125	−	0.885294i
$156$		0			0
$157$	−4.10239e7	−	7.10556e7i	−0.846036	−	1.46538i	−0.884719	−	0.466125i	$-0.845650\pi$
$157$	−4.10239e7	−	7.10556e7i	−0.846036	−	1.46538i	0.0386831	−	0.999252i	$-0.487684\pi$
$158$	−2.93488e7	−	5.08336e7i	−0.591957	−	1.02530i
$159$		0			0
$160$	6.15348e6	−	1.06581e7i	0.118768	−	0.205713i
$161$	−7.50625e7			−1.41753
$162$		0			0
$163$	−2.89286e7			−0.523203			−0.261602	−	0.965176i	$-0.584251\pi$
$163$	−2.89286e7			−0.523203			−0.261602	+	0.965176i	$0.584251\pi$
$164$	−1.65735e7	+	2.87061e7i	−0.293400	+	0.508184i
$165$		0			0
$166$	1.55688e7	+	2.69660e7i	0.264167	+	0.457550i
$167$	1.33585e7	+	2.31376e7i	0.221947	+	0.384424i	0.955399	−	0.295318i	$-0.0954254\pi$
$167$	1.33585e7	+	2.31376e7i	0.221947	+	0.384424i	−0.733452	+	0.679741i	$0.762092\pi$
$168$		0			0
$169$	−4.69195e7	+	8.12669e7i	−0.747738	+	1.29512i
$170$	5.07177e7			0.791751
$171$		0			0
$172$	−1.73862e7			−0.260529
$173$	−1.31561e7	+	2.27871e7i	−0.193182	+	0.334601i	−0.946303	−	0.323281i	$-0.895214\pi$
$173$	−1.31561e7	+	2.27871e7i	−0.193182	+	0.334601i	0.753121	+	0.657882i	$0.228547\pi$
$174$		0			0
$175$	−3.32838e7	−	5.76492e7i	−0.469461	−	0.813131i
$176$	3.48146e6	+	6.03006e6i	0.0481356	+	0.0833733i
$177$		0			0
$178$	−2.70272e6	+	4.68125e6i	−0.0359196	+	0.0622146i
$179$	2.19724e7			0.286347			0.143174	−	0.989698i	$-0.454269\pi$
$179$	2.19724e7			0.286347			0.143174	+	0.989698i	$0.454269\pi$
$180$		0			0
$181$	1.26202e8			1.58195			0.790975	−	0.611849i	$-0.209574\pi$
$181$	1.26202e8			1.58195			0.790975	+	0.611849i	$0.209574\pi$
$182$	−5.29437e7	+	9.17012e7i	−0.650976	+	1.12752i
$183$		0			0
$184$	−1.81671e7	−	3.14664e7i	−0.214993	−	0.372379i
$185$	9.92774e7	+	1.71954e8i	1.15279	+	1.99669i
$186$		0			0
$187$	−1.43473e7	+	2.48502e7i	−0.160444	+	0.277898i
$188$	2.71122e7			0.297586
$189$		0			0
$190$	1.06009e8			1.12126
$191$	8.97257e7	−	1.55409e8i	0.931752	−	1.61384i	0.151425	−	0.988469i	$-0.451614\pi$
$191$	8.97257e7	−	1.55409e8i	0.931752	−	1.61384i	0.780326	−	0.625372i	$-0.215053\pi$
$192$		0			0
$193$	1.49157e7	+	2.58348e7i	0.149346	+	0.258675i	0.930986	−	0.365055i	$-0.118950\pi$
$193$	1.49157e7	+	2.58348e7i	0.149346	+	0.258675i	−0.781640	+	0.623730i	$0.785617\pi$
$194$	6.50228e7	+	1.12623e8i	0.639381	+	1.10744i
$195$		0			0
$196$	−9.44820e6	+	1.63648e7i	−0.0896299	+	0.155243i
$197$	−6.70863e7			−0.625176			−0.312588	−	0.949889i	$-0.601196\pi$
$197$	−6.70863e7			−0.625176			−0.312588	+	0.949889i	$0.601196\pi$
$198$		0			0
$199$	−1.18177e8			−1.06304			−0.531519	−	0.847046i	$-0.678379\pi$
$199$	−1.18177e8			−1.06304			−0.531519	+	0.847046i	$0.678379\pi$
$200$	1.61112e7	−	2.79053e7i	0.142404	−	0.246651i
$201$		0			0
$202$	1.69816e6	+	2.94130e6i	0.0144960	+	0.0251078i
$203$	−4.10690e7	−	7.11336e7i	−0.344570	−	0.596813i
$204$		0			0
$205$	−9.72600e7	+	1.68459e8i	−0.788489	+	1.36570i
$206$	3.89067e7			0.310091
$207$		0			0
$208$	−5.12553e7			−0.394927
$209$	−2.99884e7	+	5.19414e7i	−0.227217	+	0.393552i
$210$		0			0
$211$	−5.19927e7	−	9.00540e7i	−0.381025	−	0.659955i	0.610184	−	0.792260i	$-0.291096\pi$
$211$	−5.19927e7	−	9.00540e7i	−0.381025	−	0.659955i	−0.991209	+	0.132305i	$0.957762\pi$
$212$	3.97806e7	+	6.89020e7i	0.286745	+	0.496657i
$213$		0			0
$214$	−1.13459e7	+	1.96517e7i	−0.0791392	+	0.137073i
$215$	−1.02030e8			−0.700150
$216$		0			0
$217$	−1.33473e8			−0.886715
$218$	2.52556e7	−	4.37439e7i	0.165105	−	0.285970i
$219$		0			0
$220$	2.04306e7	+	3.53869e7i	0.129361	+	0.224059i
$221$	−1.05613e8	−	1.82927e8i	−0.658180	−	1.14000i
$222$		0			0
$223$	8.07648e7	−	1.39889e8i	0.487703	−	0.844726i	−0.512197	−	0.858868i	$-0.671168\pi$
$223$	8.07648e7	−	1.39889e8i	0.487703	−	0.844726i	0.999900	+	0.0141421i	$0.00450171\pi$
$224$	−3.46598e7			−0.206043
$225$		0			0
$226$	1.71550e8			0.988576
$227$	1.90267e7	−	3.29553e7i	0.107963	−	0.186997i	−0.806982	−	0.590576i	$-0.798901\pi$
$227$	1.90267e7	−	3.29553e7i	0.107963	−	0.186997i	0.914945	+	0.403579i	$0.132234\pi$
$228$		0			0
$229$	1.44858e8	+	2.50901e8i	0.797110	+	1.38064i	0.921491	+	0.388401i	$0.126972\pi$
$229$	1.44858e8	+	2.50901e8i	0.797110	+	1.38064i	−0.124381	+	0.992235i	$0.539694\pi$
$230$	−1.06612e8	−	1.84658e8i	−0.577777	−	1.00074i
$231$		0			0
$232$	1.98796e7	−	3.44325e7i	0.104520	−	0.181034i
$233$	7.45094e7			0.385892			0.192946	−	0.981209i	$-0.438196\pi$
$233$	7.45094e7			0.385892			0.192946	+	0.981209i	$0.438196\pi$
$234$		0			0
$235$	1.59106e8			0.799740
$236$	−8.58153e7	+	1.48636e8i	−0.424984	+	0.736094i
$237$		0			0
$238$	−7.14175e7	−	1.23699e8i	−0.343388	−	0.594766i
$239$	8.98328e7	+	1.55595e8i	0.425640	+	0.737230i	0.996480	−	0.0838313i	$-0.0267157\pi$
$239$	8.98328e7	+	1.55595e8i	0.425640	+	0.737230i	−0.570840	+	0.821061i	$0.693382\pi$
$240$		0			0
$241$	3.04341e7	−	5.27134e7i	0.140056	−	0.242583i	−0.787462	−	0.616364i	$-0.788605\pi$
$241$	3.04341e7	−	5.27134e7i	0.140056	−	0.242583i	0.927517	+	0.373780i	$0.121939\pi$
$242$	1.32779e8			0.602250
$243$		0			0
$244$	−4.82611e7			−0.212683
$245$	−5.54459e7	+	9.60352e7i	−0.240873	+	0.417205i
$246$		0			0
$247$	−2.20750e8	−	3.82350e8i	−0.932098	−	1.61444i
$248$	−3.23041e7	−	5.59523e7i	−0.134486	−	0.232936i
$249$		0			0
$250$	−2.28213e7	+	3.95277e7i	−0.0923743	+	0.159997i
$251$	−2.14309e8			−0.855426			−0.427713	−	0.903915i	$-0.640681\pi$
$251$	−2.14309e8			−0.855426			−0.427713	+	0.903915i	$0.640681\pi$
$252$		0			0
$253$	1.20636e8			0.468334
$254$	5.42724e7	−	9.40025e7i	0.207807	−	0.359933i
$255$		0			0
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	−2.63538e7	−	4.56461e7i	−0.0968450	−	0.167740i	0.813532	−	0.581520i	$-0.197542\pi$
$257$	−2.63538e7	−	4.56461e7i	−0.0968450	−	0.167740i	−0.910377	+	0.413779i	$0.864208\pi$
$258$		0			0
$259$	2.79593e8	−	4.84269e8i	0.999946	−	1.73196i
$260$	−3.00787e8			−1.06133
$261$		0			0
$262$	−1.88251e8			−0.646670
$263$	2.44289e8	−	4.23121e8i	0.828055	−	1.43423i	−0.0715077	−	0.997440i	$-0.522781\pi$
$263$	2.44289e8	−	4.23121e8i	0.828055	−	1.43423i	0.899562	−	0.436793i	$-0.143886\pi$
$264$		0			0
$265$	2.33449e8	+	4.04346e8i	0.770604	+	1.33473i
$266$	−1.49275e8	−	2.58553e8i	−0.486298	−	0.842293i
$267$		0			0
$268$	8.40224e6	−	1.45531e7i	0.0266639	−	0.0461832i
$269$	1.69083e8			0.529622			0.264811	−	0.964300i	$-0.414690\pi$
$269$	1.69083e8			0.529622			0.264811	+	0.964300i	$0.414690\pi$
$270$		0			0
$271$	−1.99531e8			−0.609001			−0.304501	−	0.952512i	$-0.598490\pi$
$271$	−1.99531e8			−0.609001			−0.304501	+	0.952512i	$0.598490\pi$
$272$	3.45700e7	−	5.98769e7i	0.104162	−	0.180413i
$273$		0			0
$274$	1.11962e8	+	1.93924e8i	0.328809	+	0.569514i
$275$	5.34919e7	+	9.26506e7i	0.155104	+	0.268648i
$276$		0			0
$277$	1.77438e8	−	3.07331e8i	0.501611	−	0.868816i	−0.498387	−	0.866955i	$-0.666074\pi$
$277$	1.77438e8	−	3.07331e8i	0.501611	−	0.868816i	0.999998	−	0.00186126i	$-0.000592457\pi$
$278$	6.40150e7			0.178700
$279$		0			0
$280$	−2.03398e8			−0.553724
$281$	−1.40245e8	+	2.42912e8i	−0.377065	+	0.653096i	−0.990634	−	0.136545i	$-0.956400\pi$
$281$	−1.40245e8	+	2.42912e8i	−0.377065	+	0.653096i	0.613569	+	0.789641i	$0.289733\pi$
$282$		0			0
$283$	7.95244e7	+	1.37740e8i	0.208568	+	0.361251i	0.951264	−	0.308379i	$-0.0997863\pi$
$283$	7.95244e7	+	1.37740e8i	0.208568	+	0.361251i	−0.742696	+	0.669629i	$0.766453\pi$
$284$	3.17092e7	+	5.49220e7i	0.0821431	+	0.142276i
$285$		0			0
$286$	8.50882e7	−	1.47377e8i	0.215074	−	0.372519i
$287$	5.47822e8			1.36790
$288$		0			0
$289$	−1.25409e8			−0.305623
$290$	1.16662e8	−	2.02064e8i	0.280890	−	0.486515i
$291$		0			0
$292$	3.34044e7	+	5.78581e7i	0.0785170	+	0.135995i
$293$	1.72190e8	+	2.98242e8i	0.399918	+	0.692679i	0.993715	−	0.111936i	$-0.0357051\pi$
$293$	1.72190e8	+	2.98242e8i	0.399918	+	0.692679i	−0.593797	+	0.804615i	$0.702372\pi$
$294$		0			0
$295$	−5.03600e8	+	8.72260e8i	−1.14211	+	1.97819i
$296$	2.70676e8			0.606637
$297$		0			0
$298$	−2.17326e8			−0.475723
$299$	−4.44013e8	+	7.69052e8i	−0.960608	+	1.66382i
$300$		0			0
$301$	1.43672e8	+	2.48847e8i	0.303661	+	0.525956i
$302$	1.67945e8	+	2.90890e8i	0.350868	+	0.607721i
$303$		0			0
$304$	7.22574e7	−	1.25153e8i	0.147511	−	0.255497i
$305$	−2.83216e8			−0.571569
$306$		0			0
$307$	5.28744e8			1.04294			0.521472	−	0.853269i	$-0.325383\pi$
$307$	5.28744e8			1.04294			0.521472	+	0.853269i	$0.325383\pi$
$308$	5.75383e7	−	9.96592e7i	0.112209	−	0.194352i
$309$		0			0
$310$	−1.89574e8	−	3.28351e8i	−0.361420	−	0.625997i
$311$	−1.43382e8	−	2.48345e8i	−0.270292	−	0.468159i	0.698645	−	0.715469i	$-0.253787\pi$
$311$	−1.43382e8	−	2.48345e8i	−0.270292	−	0.468159i	−0.968937	+	0.247310i	$0.920454\pi$
$312$		0			0
$313$	−1.25124e7	+	2.16722e7i	−0.0230641	+	0.0399482i	−0.877327	−	0.479893i	$-0.840676\pi$
$313$	−1.25124e7	+	2.16722e7i	−0.0230641	+	0.0399482i	0.854263	+	0.519841i	$0.174009\pi$
$314$	−6.56383e8			−1.19648
$315$		0			0
$316$	−4.69580e8			−0.837153
$317$	−2.60137e8	+	4.50570e8i	−0.458663	+	0.794428i	−0.998891	−	0.0470910i	$-0.985005\pi$
$317$	−2.60137e8	+	4.50570e8i	−0.458663	+	0.794428i	0.540227	+	0.841519i	$0.318338\pi$
$318$		0			0
$319$	6.60038e7	+	1.14322e8i	0.113842	+	0.197180i
$320$	−4.92278e7	−	8.52651e7i	−0.0839819	−	0.145461i
$321$		0			0
$322$	−3.00250e8	+	5.20048e8i	−0.501172	+	0.868056i
$323$	5.95554e8			0.983359
$324$		0			0
$325$	−7.87527e8			−1.27255
$326$	−1.15714e8	+	2.00423e8i	−0.184980	+	0.320395i
$327$		0			0
$328$	1.32588e8	+	2.29649e8i	0.207465	+	0.359340i
$329$	−2.24043e8	−	3.88054e8i	−0.346853	−	0.600768i
$330$		0			0
$331$	2.52520e8	−	4.37377e8i	0.382734	−	0.662915i	−0.608718	−	0.793387i	$-0.708316\pi$
$331$	2.52520e8	−	4.37377e8i	0.382734	−	0.662915i	0.991452	+	0.130472i	$0.0416492\pi$
$332$	2.49102e8			0.373588
$333$		0			0
$334$	2.13736e8			0.313881
$335$	4.93078e7	−	8.54037e7i	0.0716571	−	0.124114i
$336$		0			0
$337$	9.18750e7	+	1.59132e8i	0.130765	+	0.226492i	0.923972	−	0.382461i	$-0.124923\pi$
$337$	9.18750e7	+	1.59132e8i	0.130765	+	0.226492i	−0.793206	+	0.608953i	$0.791590\pi$
$338$	3.75356e8	+	6.50135e8i	0.528731	+	0.915789i
$339$		0			0
$340$	2.02871e8	−	3.51383e8i	0.279926	−	0.484846i
$341$	2.14510e8			0.292960
$342$		0			0
$343$	−5.58786e8			−0.747681
$344$	−6.95449e7	+	1.20455e8i	−0.0921108	+	0.159541i
$345$		0			0
$346$	1.05249e8	+	1.82296e8i	0.136600	+	0.236598i
$347$	−1.43066e8	−	2.47797e8i	−0.183816	−	0.318378i	0.759361	−	0.650670i	$-0.225512\pi$
$347$	−1.43066e8	−	2.47797e8i	−0.183816	−	0.318378i	−0.943177	+	0.332291i	$0.892178\pi$
$348$		0			0
$349$	1.83182e7	−	3.17281e7i	0.0230672	−	0.0399535i	−0.854261	−	0.519844i	$-0.825990\pi$
$349$	1.83182e7	−	3.17281e7i	0.0230672	−	0.0399535i	0.877329	+	0.479890i	$0.159324\pi$
$350$	−5.32541e8			−0.663918
$351$		0			0
$352$	5.57033e7			0.0680740
$353$	2.38469e8	−	4.13040e8i	0.288549	−	0.499782i	−0.684914	−	0.728624i	$-0.740160\pi$
$353$	2.38469e8	−	4.13040e8i	0.288549	−	0.499782i	0.973464	+	0.228841i	$0.0734937\pi$
$354$		0			0
$355$	1.86083e8	+	3.22305e8i	0.220753	+	0.382356i
$356$	2.16218e7	+	3.74500e7i	0.0253990	+	0.0439923i
$357$		0			0
$358$	8.78898e7	−	1.52230e8i	0.101239	−	0.175351i
$359$	3.73983e8			0.426600			0.213300	−	0.976987i	$-0.431579\pi$
$359$	3.73983e8			0.426600			0.213300	+	0.976987i	$0.431579\pi$
$360$		0			0
$361$	3.50942e8			0.392609
$362$	5.04809e8	−	8.74356e8i	0.559303	−	0.968742i
$363$		0			0
$364$	4.23550e8	+	7.33610e8i	0.460309	+	0.797279i
$365$	1.96031e8	+	3.39535e8i	0.211008	+	0.365477i
$366$		0			0
$367$	2.91624e8	−	5.05107e8i	0.307958	−	0.533399i	−0.669957	−	0.742400i	$-0.733688\pi$
$367$	2.91624e8	−	5.05107e8i	0.307958	−	0.533399i	0.977916	+	0.209000i	$0.0670209\pi$
$368$	−2.90674e8			−0.304046
$369$		0			0
$370$	1.58844e9			1.63029
$371$	6.57457e8	−	1.13875e9i	0.668434	−	1.15776i
$372$		0			0
$373$	−7.38605e8	−	1.27930e9i	−0.736939	−	1.27642i	−0.953867	−	0.300228i	$-0.902937\pi$
$373$	−7.38605e8	−	1.27930e9i	−0.736939	−	1.27642i	0.216928	−	0.976188i	$-0.430396\pi$
$374$	1.14778e8	+	1.98802e8i	0.113451	+	0.196503i
$375$		0			0
$376$	1.08449e8	−	1.87839e8i	0.105213	−	0.182234i
$377$	−9.71732e8			−0.934011
$378$		0			0
$379$	−6.08958e8			−0.574580			−0.287290	−	0.957844i	$-0.592754\pi$
$379$	−6.08958e8			−0.574580			−0.287290	+	0.957844i	$0.592754\pi$
$380$	4.24036e8	−	7.34452e8i	0.396424	−	0.686627i
$381$		0			0
$382$	−7.17806e8	−	1.24328e9i	−0.658848	−	1.14116i
$383$	−4.24357e8	−	7.35008e8i	−0.385954	−	0.668492i	0.605947	−	0.795505i	$-0.292794\pi$
$383$	−4.24357e8	−	7.35008e8i	−0.385954	−	0.668492i	−0.991901	+	0.127013i	$0.959461\pi$
$384$		0			0
$385$	3.37659e8	−	5.84842e8i	0.301554	−	0.522307i
$386$	2.38651e8			0.211207
$387$		0			0
$388$	1.04036e9			0.904221
$389$	−1.26651e8	+	2.19367e8i	−0.109090	+	0.188950i	−0.915402	−	0.402541i	$-0.868127\pi$
$389$	−1.26651e8	+	2.19367e8i	−0.109090	+	0.188950i	0.806312	+	0.591491i	$0.201460\pi$
$390$		0			0
$391$	−5.98943e8	−	1.03740e9i	−0.506719	−	0.877662i
$392$	7.55856e7	+	1.30918e8i	0.0633779	+	0.109774i
$393$		0			0
$394$	−2.68345e8	+	4.64788e8i	−0.221033	+	0.382841i
$395$	−2.75569e9			−2.24978
$396$		0			0
$397$	9.92215e8			0.795865			0.397932	−	0.917415i	$-0.369728\pi$
$397$	9.92215e8			0.795865			0.397932	+	0.917415i	$0.369728\pi$
$398$	−4.72710e8	+	8.18758e8i	−0.375841	+	0.650975i
$399$		0			0
$400$	−1.28889e8	−	2.23243e8i	−0.100695	−	0.174408i
$401$	−4.74376e8	−	8.21644e8i	−0.367382	−	0.636324i	0.621774	−	0.783197i	$-0.286412\pi$
$401$	−4.74376e8	−	8.21644e8i	−0.367382	−	0.636324i	−0.989155	+	0.146873i	$0.953079\pi$
$402$		0			0
$403$	−7.89524e8	+	1.36750e9i	−0.600894	+	1.04078i
$404$	2.71706e7			0.0205005
$405$		0			0
$406$	−6.57104e8			−0.487296
$407$	−4.49346e8	+	7.78290e8i	−0.330370	+	0.572217i
$408$		0			0
$409$	−3.88383e8	−	6.72699e8i	−0.280691	−	0.486171i	0.690864	−	0.722985i	$-0.257230\pi$
$409$	−3.88383e8	−	6.72699e8i	−0.280691	−	0.486171i	−0.971555	+	0.236813i	$0.923897\pi$
$410$	7.78080e8	+	1.34767e9i	0.557546	+	0.965698i
$411$		0			0
$412$	1.55627e8	−	2.69554e8i	0.109634	−	0.189891i
$413$	2.83655e9			1.98137
$414$		0			0
$415$	1.46183e9			1.00399
$416$	−2.05021e8	+	3.55107e8i	−0.139628	+	0.241842i
$417$		0			0
$418$	2.39907e8	+	4.15531e8i	0.160667	+	0.278283i
$419$	−3.14943e8	−	5.45498e8i	−0.209162	−	0.362280i	0.742289	−	0.670080i	$-0.233740\pi$
$419$	−3.14943e8	−	5.45498e8i	−0.209162	−	0.362280i	−0.951451	+	0.307801i	$0.900407\pi$
$420$		0			0
$421$	−5.52425e8	+	9.56829e8i	−0.360816	+	0.624952i	−0.988095	−	0.153842i	$-0.950835\pi$
$421$	−5.52425e8	+	9.56829e8i	−0.360816	+	0.624952i	0.627279	+	0.778795i	$0.284169\pi$
$422$	−8.31883e8			−0.538851
$423$		0			0
$424$	6.36490e8			0.405519
$425$	5.31160e8	−	9.19997e8i	0.335633	−	0.581333i
$426$		0			0
$427$	3.98808e8	+	6.90755e8i	0.247894	+	0.429365i
$428$	9.07674e7	+	1.57214e8i	0.0559599	+	0.0969253i
$429$		0			0
$430$	−4.08118e8	+	7.06881e8i	−0.247541	+	0.428753i
$431$	2.85661e8			0.171863			0.0859313	−	0.996301i	$-0.472613\pi$
$431$	2.85661e8			0.171863			0.0859313	+	0.996301i	$0.472613\pi$
$432$		0			0
$433$	4.76788e8			0.282239			0.141120	−	0.989993i	$-0.454930\pi$
$433$	4.76788e8			0.282239			0.141120	+	0.989993i	$0.454930\pi$
$434$	−5.33892e8	+	9.24727e8i	−0.313501	+	0.543000i
$435$		0			0
$436$	−2.02045e8	−	3.49952e8i	−0.116747	−	0.202211i
$437$	−1.25190e9	−	2.16835e9i	−0.717602	−	1.24292i
$438$		0			0
$439$	−1.25879e9	+	2.18029e9i	−0.710112	+	1.22995i	0.254703	+	0.967019i	$0.418022\pi$
$439$	−1.25879e9	+	2.18029e9i	−0.710112	+	1.22995i	−0.964815	+	0.262931i	$0.915311\pi$
$440$	3.26890e8			0.182944
$441$		0			0
$442$	−1.68981e9			−0.930807
$443$	−2.29324e8	+	3.97201e8i	−0.125325	+	0.217069i	−0.921860	−	0.387523i	$-0.873331\pi$
$443$	−2.29324e8	+	3.97201e8i	−0.125325	+	0.217069i	0.796535	+	0.604592i	$0.206664\pi$
$444$		0			0
$445$	1.26886e8	+	2.19772e8i	0.0682578	+	0.118226i
$446$	−6.46118e8	−	1.11911e9i	−0.344858	−	0.597311i
$447$		0			0
$448$	−1.38639e8	+	2.40130e8i	−0.0728472	+	0.126175i
$449$	1.46433e9			0.763444			0.381722	−	0.924277i	$-0.375331\pi$
$449$	1.46433e9			0.763444			0.381722	+	0.924277i	$0.375331\pi$
$450$		0			0
$451$	−8.80429e8			−0.451936
$452$	6.86198e8	−	1.18853e9i	0.349514	−	0.605377i
$453$		0			0
$454$	−1.52214e8	−	2.63642e8i	−0.0763411	−	0.132227i
$455$	2.48557e9	+	4.30513e9i	1.23704	+	2.14262i
$456$		0			0
$457$	−6.98299e8	+	1.20949e9i	−0.342243	+	0.592783i	−0.984849	−	0.173414i	$-0.944520\pi$
$457$	−6.98299e8	+	1.20949e9i	−0.342243	+	0.592783i	0.642606	+	0.766197i	$0.277853\pi$
$458$	2.31773e9			1.12728
$459$		0			0
$460$	−1.70580e9			−0.817100
$461$	−1.98110e9	+	3.43137e9i	−0.941789	+	1.63123i	−0.179733	+	0.983715i	$0.557524\pi$
$461$	−1.98110e9	+	3.43137e9i	−0.941789	+	1.63123i	−0.762056	+	0.647511i	$0.775810\pi$
$462$		0			0
$463$	9.40813e8	+	1.62954e9i	0.440524	+	0.763010i	0.997728	−	0.0673653i	$-0.0214593\pi$
$463$	9.40813e8	+	1.62954e9i	0.440524	+	0.763010i	−0.557204	+	0.830375i	$0.688126\pi$
$464$	−1.59037e8	−	2.75460e8i	−0.0739069	−	0.128011i
$465$		0			0
$466$	2.98038e8	−	5.16217e8i	0.136433	−	0.236310i
$467$	−9.69518e8			−0.440501			−0.220250	−	0.975443i	$-0.570687\pi$
$467$	−9.69518e8			−0.440501			−0.220250	+	0.975443i	$0.570687\pi$
$468$		0			0
$469$	−2.77729e8			−0.124313
$470$	6.36424e8	−	1.10232e9i	0.282751	−	0.489739i
$471$		0			0
$472$	6.86522e8	+	1.18909e9i	0.300509	+	0.520497i
$473$	−2.30901e8	−	3.99933e8i	−0.100326	−	0.173769i
$474$		0			0
$475$	1.11022e9	−	1.92296e9i	0.475315	−	0.823269i
$476$	−1.14268e9			−0.485624
$477$		0			0
$478$	1.43733e9			0.601946
$479$	−1.00435e9	+	1.73959e9i	−0.417552	+	0.723222i	−0.995693	−	0.0927156i	$-0.970445\pi$
$479$	−1.00435e9	+	1.73959e9i	−0.417552	+	0.723222i	0.578140	+	0.815937i	$0.303779\pi$
$480$		0			0
$481$	−3.30772e9	−	5.72913e9i	−1.35525	−	2.34737i
$482$	−2.43473e8	−	4.21707e8i	−0.0990343	−	0.171532i
$483$		0			0
$484$	5.31117e8	−	9.19922e8i	0.212927	−	0.368801i
$485$	6.10529e9			2.43002
$486$		0			0
$487$	3.02884e9			1.18830			0.594148	−	0.804356i	$-0.297490\pi$
$487$	3.02884e9			1.18830			0.594148	+	0.804356i	$0.297490\pi$
$488$	−1.93044e8	+	3.34363e8i	−0.0751948	+	0.130241i
$489$		0			0
$490$	4.43567e8	+	7.68281e8i	0.170323	+	0.295008i
$491$	2.25862e9	+	3.91204e9i	0.861107	+	1.49148i	0.870861	+	0.491529i	$0.163562\pi$
$491$	2.25862e9	+	3.91204e9i	0.861107	+	1.49148i	−0.00975413	+	0.999952i	$0.503105\pi$
$492$		0			0
$493$	6.55401e8	−	1.13519e9i	0.246344	−	0.426681i
$494$	−3.53200e9			−1.31819
$495$		0			0
$496$	−5.16865e8			−0.190191
$497$	5.24061e8	−	9.07700e8i	0.191485	−	0.331661i
$498$		0			0
$499$	2.32832e9	+	4.03277e9i	0.838862	+	1.45295i	0.890846	+	0.454305i	$0.150112\pi$
$499$	2.32832e9	+	4.03277e9i	0.838862	+	1.45295i	−0.0519839	+	0.998648i	$0.516554\pi$
$500$	1.82571e8	+	3.16222e8i	0.0653185	+	0.113135i
$501$		0			0
$502$	−8.57236e8	+	1.48478e9i	−0.302439	+	0.523840i
$503$	−2.88413e9			−1.01048			−0.505239	−	0.862980i	$-0.668596\pi$
$503$	−2.88413e9			−1.01048			−0.505239	+	0.862980i	$0.668596\pi$
$504$		0			0
$505$	1.59448e8			0.0550934
$506$	4.82545e8	−	8.35792e8i	0.165581	−	0.286795i
$507$		0			0
$508$	−4.34179e8	−	7.52020e8i	−0.146942	−	0.254511i
$509$	−6.60362e8	−	1.14378e9i	−0.221957	−	0.384442i	0.733445	−	0.679749i	$-0.237911\pi$
$509$	−6.60362e8	−	1.14378e9i	−0.221957	−	0.384442i	−0.955402	+	0.295307i	$0.904578\pi$
$510$		0			0
$511$	5.52077e8	−	9.56225e8i	0.183032	−	0.317020i
$512$	−1.34218e8			−0.0441942
$513$		0			0
$514$	−4.21661e8			−0.136960
$515$	9.13283e8	−	1.58185e9i	0.294632	−	0.510318i
$516$		0			0
$517$	3.60070e8	+	6.23659e8i	0.114596	+	0.198486i
$518$	−2.23674e9	−	3.87415e9i	−0.707069	−	1.22468i
$519$		0			0
$520$	−1.20315e9	+	2.08391e9i	−0.375239	+	0.649932i
$521$	−5.14654e9			−1.59435			−0.797175	−	0.603749i	$-0.793673\pi$
$521$	−5.14654e9			−1.59435			−0.797175	+	0.603749i	$0.793673\pi$
$522$		0			0
$523$	−2.17050e9			−0.663444			−0.331722	−	0.943377i	$-0.607630\pi$
$523$	−2.17050e9			−0.663444			−0.331722	+	0.943377i	$0.607630\pi$
$524$	−7.53004e8	+	1.30424e9i	−0.228632	+	0.396003i
$525$		0			0
$526$	−1.95431e9	−	3.38497e9i	−0.585523	−	1.01416i
$527$	−1.06502e9	−	1.84466e9i	−0.316970	−	0.549009i
$528$		0			0
$529$	−8.15632e8	+	1.41272e9i	−0.239552	+	0.414916i
$530$	3.73518e9			1.08980
$531$		0			0
$532$	−2.38841e9			−0.687729
$533$	3.24050e9	−	5.61271e9i	0.926972	−	1.60556i
$534$		0			0
$535$	5.32661e8	+	9.22595e8i	0.150388	+	0.260479i
$536$	−6.72180e7	−	1.16425e8i	−0.0188542	−	0.0326565i
$537$		0			0
$538$	6.76330e8	−	1.17144e9i	0.187250	−	0.324326i
$539$	−5.01915e8			−0.138060
$540$		0			0
$541$	−9.27955e7			−0.0251963			−0.0125981	−	0.999921i	$-0.504010\pi$
$541$	−9.27955e7			−0.0251963			−0.0125981	+	0.999921i	$0.504010\pi$
$542$	−7.98125e8	+	1.38239e9i	−0.215314	+	0.372936i
$543$		0			0
$544$	−2.76560e8	−	4.79015e8i	−0.0736534	−	0.127571i
$545$	−1.18568e9	−	2.05366e9i	−0.313747	−	0.543427i
$546$		0			0
$547$	2.73518e9	−	4.73747e9i	0.714547	−	1.23763i	−0.248588	−	0.968609i	$-0.579966\pi$
$547$	2.73518e9	−	4.73747e9i	0.714547	−	1.23763i	0.963134	−	0.269022i	$-0.0867003\pi$
$548$	1.79139e9			0.465006
$549$		0			0
$550$	8.55870e8			0.219350
$551$	1.36990e9	−	2.37274e9i	0.348867	−	0.604255i
$552$		0			0
$553$	3.88039e9	+	6.72104e9i	0.975749	+	1.69005i
$554$	−1.41950e9	−	2.45865e9i	−0.354693	−	0.614346i
$555$		0			0
$556$	2.56060e8	−	4.43509e8i	0.0631800	−	0.109431i
$557$	−4.50060e9			−1.10351			−0.551756	−	0.834006i	$-0.686042\pi$
$557$	−4.50060e9			−1.10351			−0.551756	+	0.834006i	$0.686042\pi$
$558$		0			0
$559$	3.39941e9			0.823119
$560$	−8.13592e8	+	1.40918e9i	−0.195771	+	0.339086i
$561$		0			0
$562$	1.12196e9	+	1.94330e9i	0.266625	+	0.461809i
$563$	3.06529e9	+	5.30923e9i	0.723922	+	1.25387i	0.959416	+	0.281994i	$0.0909957\pi$
$563$	3.06529e9	+	5.30923e9i	0.723922	+	1.25387i	−0.235494	+	0.971876i	$0.575671\pi$
$564$		0			0
$565$	4.02690e9	−	6.97479e9i	0.939292	−	1.62690i
$566$	1.27239e9			0.294960
$567$		0			0
$568$	5.07347e8			0.116168
$569$	−1.71059e9	+	2.96282e9i	−0.389271	+	0.674238i	−0.992352	−	0.123443i	$-0.960606\pi$
$569$	−1.71059e9	+	2.96282e9i	−0.389271	+	0.674238i	0.603080	+	0.797680i	$0.293940\pi$
$570$		0			0
$571$	−1.14292e9	−	1.97960e9i	−0.256916	−	0.444991i	0.708498	−	0.705712i	$-0.249373\pi$
$571$	−1.14292e9	−	1.97960e9i	−0.256916	−	0.444991i	−0.965414	+	0.260721i	$0.916040\pi$
$572$	−6.80706e8	−	1.17902e9i	−0.152080	−	0.263411i
$573$		0			0
$574$	2.19129e9	−	3.79542e9i	0.483624	−	0.837661i
$575$	−4.46615e9			−0.979706
$576$		0			0
$577$	−7.03121e9			−1.52375			−0.761877	−	0.647722i	$-0.775722\pi$
$577$	−7.03121e9			−1.52375			−0.761877	+	0.647722i	$0.775722\pi$
$578$	−5.01636e8	+	8.68859e8i	−0.108054	+	0.187155i
$579$		0			0
$580$	−9.33295e8	−	1.61651e9i	−0.198619	−	0.344018i
$581$	−2.05846e9	−	3.56536e9i	−0.435438	−	0.754200i
$582$		0			0
$583$	−1.05663e9	+	1.83013e9i	−0.220842	+	0.382510i
$584$	5.34470e8			0.111040
$585$		0			0
$586$	2.75504e9			0.565570
$587$	−4.47158e8	+	7.74500e8i	−0.0912488	+	0.158048i	−0.908037	−	0.418890i	$-0.862419\pi$
$587$	−4.47158e8	+	7.74500e8i	−0.0912488	+	0.158048i	0.816788	+	0.576938i	$0.195753\pi$
$588$		0			0
$589$	−2.22607e9	−	3.85567e9i	−0.448886	−	0.777493i
$590$	4.02880e9	+	6.97808e9i	0.807594	+	1.39879i
$591$		0			0
$592$	1.08270e9	−	1.87530e9i	0.214478	−	0.371488i
$593$	8.80907e9			1.73476			0.867379	−	0.497649i	$-0.165803\pi$
$593$	8.80907e9			1.73476			0.867379	+	0.497649i	$0.165803\pi$
$594$		0			0
$595$	−6.70572e9			−1.30508
$596$	−8.69302e8	+	1.50568e9i	−0.168193	+	0.291320i
$597$		0			0
$598$	3.55210e9	+	6.15242e9i	0.679252	+	1.17650i
$599$	4.91595e8	+	8.51468e8i	0.0934574	+	0.161873i	0.908964	−	0.416875i	$-0.136875\pi$
$599$	4.91595e8	+	8.51468e8i	0.0934574	+	0.161873i	−0.815506	+	0.578748i	$0.803541\pi$
$600$		0			0
$601$	−1.02236e9	+	1.77078e9i	−0.192107	+	0.332739i	−0.945948	−	0.324317i	$-0.894865\pi$
$601$	−1.02236e9	+	1.77078e9i	−0.192107	+	0.332739i	0.753841	+	0.657056i	$0.228199\pi$
$602$	2.29875e9			0.429441
$603$		0			0
$604$	2.68712e9			0.496202
$605$	3.11682e9	−	5.39848e9i	0.572226	−	0.991124i
$606$		0			0
$607$	−1.78806e9	−	3.09701e9i	−0.324505	−	0.562059i	0.656907	−	0.753971i	$-0.271864\pi$
$607$	−1.78806e9	−	3.09701e9i	−0.324505	−	0.562059i	−0.981412	+	0.191913i	$0.938531\pi$
$608$	−5.78059e8	−	1.00123e9i	−0.104306	−	0.180663i
$609$		0			0
$610$	−1.13286e9	+	1.96218e9i	−0.202080	+	0.350013i
$611$	−5.30108e9			−0.940199
$612$		0			0
$613$	1.22567e9			0.214913			0.107457	−	0.994210i	$-0.465729\pi$
$613$	1.22567e9			0.214913			0.107457	+	0.994210i	$0.465729\pi$
$614$	2.11497e9	−	3.66324e9i	0.368736	−	0.638670i
$615$		0			0
$616$	−4.60306e8	−	7.97274e8i	−0.0793441	−	0.137428i
$617$	3.80166e9	+	6.58468e9i	0.651592	+	1.12859i	0.982737	+	0.185010i	$0.0592319\pi$
$617$	3.80166e9	+	6.58468e9i	0.651592	+	1.12859i	−0.331145	+	0.943580i	$0.607435\pi$
$618$		0			0
$619$	−2.87850e9	+	4.98571e9i	−0.487808	+	0.844908i	−0.999902	−	0.0140213i	$-0.995537\pi$
$619$	−2.87850e9	+	4.98571e9i	−0.487808	+	0.844908i	0.512094	+	0.858930i	$0.328870\pi$
$620$	−3.03318e9			−0.511125
$621$		0			0
$622$	−2.29411e9			−0.382250
$623$	3.57345e8	−	6.18940e8i	0.0592079	−	0.102551i
$624$		0			0
$625$	3.52977e9	+	6.11374e9i	0.578317	+	1.00167i
$626$	1.00099e8	+	1.73377e8i	0.0163088	+	0.0282476i
$627$		0			0
$628$	−2.62553e9	+	4.54756e9i	−0.423018	+	0.732688i
$629$	8.92377e9			1.42979
$630$		0			0
$631$	−2.41912e9			−0.383313			−0.191657	−	0.981462i	$-0.561386\pi$
$631$	−2.41912e9			−0.383313			−0.191657	+	0.981462i	$0.561386\pi$
$632$	−1.87832e9	+	3.25335e9i	−0.295978	+	0.512650i
$633$		0			0
$634$	2.08109e9	+	3.60456e9i	0.324324	+	0.561746i
$635$	−2.54794e9	−	4.41316e9i	−0.394895	−	0.683978i
$636$		0			0
$637$	1.84734e9	−	3.19969e9i	0.283178	−	0.490479i
$638$	1.05606e9			0.160997
$639$		0			0
$640$	−7.87645e8			−0.118768
$641$	−3.95891e9	+	6.85703e9i	−0.593707	+	1.02833i	0.400021	+	0.916506i	$0.369003\pi$
$641$	−3.95891e9	+	6.85703e9i	−0.593707	+	1.02833i	−0.993728	+	0.111825i	$0.964330\pi$
$642$		0			0
$643$	5.35854e9	+	9.28126e9i	0.794891	+	1.37679i	0.922908	+	0.385020i	$0.125805\pi$
$643$	5.35854e9	+	9.28126e9i	0.794891	+	1.37679i	−0.128017	+	0.991772i	$0.540861\pi$
$644$	2.40200e9	+	4.16038e9i	0.354382	+	0.613808i
$645$		0			0
$646$	2.38222e9	−	4.12612e9i	0.347670	−	0.602182i
$647$	−8.06643e9			−1.17089			−0.585446	−	0.810712i	$-0.699080\pi$
$647$	−8.06643e9			−1.17089			−0.585446	+	0.810712i	$0.699080\pi$
$648$		0			0
$649$	−4.55875e9			−0.654620
$650$	−3.15011e9	+	5.45614e9i	−0.449913	+	0.779272i
$651$		0			0
$652$	9.25715e8	+	1.60338e9i	0.130801	+	0.226554i
$653$	5.00680e9	+	8.67202e9i	0.703661	+	1.21878i	0.967172	+	0.254121i	$0.0817861\pi$
$653$	5.00680e9	+	8.67202e9i	0.703661	+	1.21878i	−0.263511	+	0.964656i	$0.584881\pi$
$654$		0			0
$655$	−4.41894e9	+	7.65382e9i	−0.614431	+	1.06423i
$656$	2.12140e9			0.293400
$657$		0			0
$658$	−3.58469e9			−0.490525
$659$	7.05570e9	−	1.22208e10i	0.960376	−	1.66342i	0.238821	−	0.971064i	$-0.423239\pi$
$659$	7.05570e9	−	1.22208e10i	0.960376	−	1.66342i	0.721555	−	0.692357i	$-0.243428\pi$
$660$		0			0
$661$	−4.81075e9	−	8.33246e9i	−0.647899	−	1.12219i	−0.983624	−	0.180234i	$-0.942315\pi$
$661$	−4.81075e9	−	8.33246e9i	−0.647899	−	1.12219i	0.335725	−	0.941960i	$-0.391019\pi$
$662$	−2.02016e9	−	3.49902e9i	−0.270634	−	0.468752i
$663$		0			0
$664$	9.96406e8	−	1.72583e9i	0.132083	−	0.228775i
$665$	−1.40162e10			−1.84822
$666$		0			0
$667$	−5.51080e9			−0.719075
$668$	8.54943e8	−	1.48080e9i	0.110974	−	0.192212i
$669$		0			0
$670$	−3.94463e8	−	6.83230e8i	−0.0506692	−	0.0877617i
$671$	−6.40941e8	−	1.11014e9i	−0.0819011	−	0.141857i
$672$		0			0
$673$	−5.84290e9	+	1.01202e10i	−0.738884	+	1.27978i	0.214115	+	0.976808i	$0.431313\pi$
$673$	−5.84290e9	+	1.01202e10i	−0.738884	+	1.27978i	−0.952998	+	0.302975i	$0.902020\pi$
$674$	1.47000e9			0.184930
$675$		0			0
$676$	6.00569e9			0.747738
$677$	−5.55719e9	+	9.62534e9i	−0.688327	+	1.19222i	0.284051	+	0.958809i	$0.408321\pi$
$677$	−5.55719e9	+	9.62534e9i	−0.688327	+	1.19222i	−0.972379	+	0.233409i	$0.925012\pi$
$678$		0			0
$679$	−8.59710e9	−	1.48906e10i	−1.05392	−	1.82544i
$680$	−1.62297e9	−	2.81106e9i	−0.197938	−	0.342838i
$681$		0			0
$682$	8.58041e8	−	1.48617e9i	0.103577	−	0.179400i
$683$	1.61450e10			1.93894			0.969472	−	0.245201i	$-0.0788539\pi$
$683$	1.61450e10			1.93894			0.969472	+	0.245201i	$0.0788539\pi$
$684$		0			0
$685$	1.05126e10			1.24967
$686$	−2.23515e9	+	3.87139e9i	−0.264345	+	0.457859i
$687$		0			0
$688$	5.56359e8	+	9.63642e8i	0.0651322	+	0.112812i
$689$	−7.77803e9	−	1.34719e10i	−0.905946	−	1.56915i
$690$		0			0
$691$	6.98902e8	−	1.21053e9i	0.0805829	−	0.139574i	−0.822918	−	0.568161i	$-0.807655\pi$
$691$	6.98902e8	−	1.21053e9i	0.0805829	−	0.139574i	0.903500	+	0.428587i	$0.140988\pi$
$692$	1.68398e9			0.193182
$693$		0			0
$694$	−2.28905e9			−0.259955
$695$	1.50267e9	−	2.60269e9i	0.169791	−	0.294087i
$696$		0			0
$697$	4.37122e9	+	7.57117e9i	0.488976	+	0.846931i
$698$	−1.46546e8	−	2.53825e8i	−0.0163110	−	0.0282514i
$699$		0			0
$700$	−2.13016e9	+	3.68955e9i	−0.234731	+	0.406565i
$701$	1.34244e9			0.147191			0.0735956	−	0.997288i	$-0.476553\pi$
$701$	1.34244e9			0.147191			0.0735956	+	0.997288i	$0.476553\pi$
$702$		0			0
$703$	1.86523e10			2.02483
$704$	2.22813e8	−	3.85924e8i	0.0240678	−	0.0416867i
$705$		0			0
$706$	−1.90775e9	−	3.30432e9i	−0.204035	−	0.353399i
$707$	−2.24525e8	−	3.88889e8i	−0.0238944	−	0.0413864i
$708$		0			0
$709$	7.93153e9	−	1.37378e10i	0.835786	−	1.44762i	−0.0576025	−	0.998340i	$-0.518346\pi$
$709$	7.93153e9	−	1.37378e10i	0.835786	−	1.44762i	0.893389	−	0.449285i	$-0.148321\pi$
$710$	2.97732e9			0.312192
$711$		0			0
$712$	3.45949e8			0.0359196
$713$	−4.47748e9	+	7.75522e9i	−0.462616	+	0.801274i
$714$		0			0
$715$	−3.99466e9	−	6.91896e9i	−0.408704	−	0.707896i
$716$	−7.03118e8	−	1.21784e9i	−0.0715868	−	0.123992i
$717$		0			0
$718$	1.49593e9	−	2.59103e9i	0.150826	−	0.261238i
$719$	−2.14766e9			−0.215483			−0.107742	−	0.994179i	$-0.534362\pi$
$719$	−2.14766e9			−0.215483			−0.107742	+	0.994179i	$0.534362\pi$
$720$		0			0
$721$	−5.14412e9			−0.511137
$722$	1.40377e9	−	2.43140e9i	0.138808	−	0.240423i
$723$		0			0
$724$	−4.03848e9	−	6.99485e9i	−0.395487	−	0.685004i
$725$	−2.44357e9	−	4.23239e9i	−0.238145	−	0.412480i
$726$		0			0
$727$	5.14336e9	−	8.90856e9i	0.496451	−	0.859879i	−0.503540	−	0.863972i	$-0.667969\pi$
$727$	5.14336e9	−	8.90856e9i	0.496451	−	0.859879i	0.999992	+	0.00409288i	$0.00130281\pi$
$728$	6.77680e9			0.650976
$729$		0			0
$730$	3.13649e9			0.298411
$731$	−2.29279e9	+	3.97123e9i	−0.217097	+	0.376023i
$732$		0			0
$733$	1.60210e9	+	2.77493e9i	0.150254	+	0.260248i	0.931321	−	0.364200i	$-0.118657\pi$
$733$	1.60210e9	+	2.77493e9i	0.150254	+	0.260248i	−0.781067	+	0.624448i	$0.785324\pi$
$734$	−2.33299e9	−	4.04086e9i	−0.217759	−	0.377170i
$735$		0			0
$736$	−1.16270e9	+	2.01385e9i	−0.107496	+	0.186189i
$737$	4.46351e8			0.0410715
$738$		0			0
$739$	1.29766e10			1.18279			0.591394	−	0.806383i	$-0.298578\pi$
$739$	1.29766e10			1.18279			0.591394	+	0.806383i	$0.298578\pi$
$740$	6.35375e9	−	1.10050e10i	0.576394	−	0.998343i
$741$		0			0
$742$	−5.25966e9	−	9.10999e9i	−0.472654	−	0.818661i
$743$	3.62353e9	+	6.27614e9i	0.324094	+	0.561348i	0.981329	−	0.192339i	$-0.0616072\pi$
$743$	3.62353e9	+	6.27614e9i	0.324094	+	0.561348i	−0.657234	+	0.753686i	$0.728274\pi$
$744$		0			0
$745$	−5.10143e9	+	8.83593e9i	−0.452007	+	0.782898i
$746$	−1.18177e10			−1.04219
$747$		0			0
$748$	1.83645e9			0.160444
$749$	1.50012e9	−	2.59828e9i	0.130449	−	0.225944i
$750$		0			0
$751$	4.47123e9	+	7.74440e9i	0.385201	+	0.667188i	0.991797	−	0.127822i	$-0.0407988\pi$
$751$	4.47123e9	+	7.74440e9i	0.385201	+	0.667188i	−0.606596	+	0.795010i	$0.707465\pi$
$752$	−8.67592e8	−	1.50271e9i	−0.0743966	−	0.128859i
$753$		0			0
$754$	−3.88693e9	+	6.73236e9i	−0.330223	+	0.571962i
$755$	1.57692e10			1.33350
$756$		0			0
$757$	1.36108e10			1.14037			0.570187	−	0.821515i	$-0.306871\pi$
$757$	1.36108e10			1.14037			0.570187	+	0.821515i	$0.306871\pi$
$758$	−2.43583e9	+	4.21899e9i	−0.203145	+	0.351857i
$759$		0			0
$760$	−3.39229e9	−	5.87562e9i	−0.280314	−	0.485519i
$761$	−1.10122e10	−	1.90738e10i	−0.905794	−	1.56888i	−0.819848	−	0.572582i	$-0.805942\pi$
$761$	−1.10122e10	−	1.90738e10i	−0.905794	−	1.56888i	−0.0859464	−	0.996300i	$-0.527391\pi$
$762$		0			0
$763$	−3.33921e9	+	5.78368e9i	−0.272149	+	0.471377i
$764$	−1.14849e10			−0.931752
$765$		0			0
$766$	−6.78971e9			−0.545821
$767$	1.67789e10	−	2.90619e10i	1.34270	−	2.32563i
$768$		0			0
$769$	−5.17112e9	−	8.95663e9i	−0.410055	−	0.710236i	0.584840	−	0.811148i	$-0.301157\pi$
$769$	−5.17112e9	−	8.95663e9i	−0.410055	−	0.710236i	−0.994895	+	0.100912i	$0.967824\pi$
$770$	−2.70127e9	−	4.67873e9i	−0.213231	−	0.369327i
$771$		0			0
$772$	9.54605e8	−	1.65342e9i	0.0746729	−	0.129337i
$773$	−3.65169e9			−0.284358			−0.142179	−	0.989841i	$-0.545411\pi$
$773$	−3.65169e9			−0.284358			−0.142179	+	0.989841i	$0.545411\pi$
$774$		0			0
$775$	−7.94152e9			−0.612841
$776$	4.16146e9	−	7.20786e9i	0.319690	−	0.553720i
$777$		0			0
$778$	1.01321e9	+	1.75493e9i	0.0771385	+	0.133608i
$779$	9.13662e9	+	1.58251e10i	0.692476	+	1.19940i
$780$		0			0
$781$	−8.42241e8	+	1.45880e9i	−0.0632642	+	0.109577i
$782$	−9.58309e9			−0.716608
$783$		0			0
$784$	1.20937e9			0.0896299
$785$	−1.54077e10	+	2.66869e10i	−1.13683	+	1.96904i
$786$		0			0
$787$	−1.19537e10	−	2.07044e10i	−0.874158	−	1.51409i	−0.857657	−	0.514222i	$-0.828081\pi$
$787$	−1.19537e10	−	2.07044e10i	−0.874158	−	1.51409i	−0.0165008	−	0.999864i	$-0.505253\pi$
$788$	2.14676e9	+	3.71830e9i	0.156294	+	0.270709i
$789$		0			0
$790$	−1.10228e10	+	1.90920e10i	−0.795419	+	1.37771i
$791$	−2.26817e10			−1.62951
$792$		0			0
$793$	9.43617e9			0.671954
$794$	3.96886e9	−	6.87427e9i	0.281381	−	0.487366i
$795$		0			0
$796$	3.78168e9	+	6.55006e9i	0.265760	+	0.460309i
$797$	1.36082e10	+	2.35700e10i	0.952128	+	1.64913i	0.740807	+	0.671718i	$0.234443\pi$
$797$	1.36082e10	+	2.35700e10i	0.952128	+	1.64913i	0.211321	+	0.977417i	$0.432223\pi$
$798$		0			0
$799$	3.57540e9	−	6.19277e9i	0.247977	−	0.429508i
$800$	−2.06223e9			−0.142404
$801$		0			0
$802$	−7.59002e9			−0.519556
$803$	−8.87267e8	+	1.53679e9i	−0.0604714	+	0.104740i
$804$		0			0
$805$	1.40959e10	+	2.44149e10i	0.952375	+	1.64956i
$806$	6.31619e9	+	1.09400e10i	0.424896	+	0.735942i
$807$		0			0
$808$	1.08682e8	−	1.88243e8i	0.00724801	−	0.0125539i
$809$	2.09999e10			1.39443			0.697216	−	0.716861i	$-0.254422\pi$
$809$	2.09999e10			1.39443			0.697216	+	0.716861i	$0.254422\pi$
$810$		0			0
$811$	−1.21414e10			−0.799276			−0.399638	−	0.916673i	$-0.630864\pi$
$811$	−1.21414e10			−0.799276			−0.399638	+	0.916673i	$0.630864\pi$
$812$	−2.62842e9	+	4.55255e9i	−0.172285	+	0.298407i
$813$		0			0
$814$	3.59477e9	+	6.22632e9i	0.233607	+	0.404619i
$815$	5.43248e9	+	9.40933e9i	0.351517	+	0.608845i
$816$		0			0
$817$	−4.79234e9	+	8.30057e9i	−0.307447	+	0.532514i
$818$	−6.21413e9			−0.396957
$819$		0			0
$820$	1.24493e10			0.788489
$821$	−5.66101e9	+	9.80516e9i	−0.357020	+	0.618377i	−0.987462	−	0.157860i	$-0.949541\pi$
$821$	−5.66101e9	+	9.80516e9i	−0.357020	+	0.618377i	0.630441	+	0.776237i	$0.282874\pi$
$822$		0			0
$823$	2.91399e9	+	5.04718e9i	0.182217	+	0.315609i	0.942635	−	0.333825i	$-0.108339\pi$
$823$	2.91399e9	+	5.04718e9i	0.182217	+	0.315609i	−0.760418	+	0.649434i	$0.775006\pi$
$824$	−1.24502e9	−	2.15643e9i	−0.0775228	−	0.134273i
$825$		0			0
$826$	1.13462e10	−	1.96522e10i	0.700520	−	1.21334i
$827$	−2.11794e10			−1.30210			−0.651050	−	0.759034i	$-0.725671\pi$
$827$	−2.11794e10			−1.30210			−0.651050	+	0.759034i	$0.725671\pi$
$828$		0			0
$829$	−1.77492e10			−1.08203			−0.541013	−	0.841014i	$-0.681959\pi$
$829$	−1.77492e10			−1.08203			−0.541013	+	0.841014i	$0.681959\pi$
$830$	5.84733e9	−	1.01279e10i	0.354964	−	0.614815i
$831$		0			0
$832$	1.64017e9	+	2.84085e9i	0.0987317	+	0.171008i
$833$	2.49194e9	+	4.31617e9i	0.149376	+	0.258727i
$834$		0			0
$835$	5.01716e9	−	8.68997e9i	0.298233	−	0.516554i
$836$	3.83851e9			0.227217
$837$		0			0
$838$	−5.03909e9			−0.295800
$839$	−1.31911e10	+	2.28476e10i	−0.771104	+	1.33559i	0.165855	+	0.986150i	$0.446962\pi$
$839$	−1.31911e10	+	2.28476e10i	−0.771104	+	1.33559i	−0.936959	+	0.349441i	$0.886372\pi$
$840$		0			0
$841$	5.60981e9	+	9.71647e9i	0.325209	+	0.563278i
$842$	4.41940e9	+	7.65463e9i	0.255136	+	0.441908i
$843$		0			0
$844$	−3.32753e9	+	5.76345e9i	−0.190513	+	0.329977i
$845$	3.52439e10			2.00949
$846$		0			0
$847$	−1.75556e10			−0.992715
$848$	2.54596e9	−	4.40973e9i	0.143372	−	0.248328i
$849$		0			0
$850$	−4.24928e9	−	7.35997e9i	−0.237328	−	0.411065i
$851$	−1.87584e10	−	3.24905e10i	−1.04338	−	1.80719i
$852$		0			0
$853$	−1.33903e10	+	2.31927e10i	−0.738701	+	1.27947i	0.214379	+	0.976750i	$0.431227\pi$
$853$	−1.33903e10	+	2.31927e10i	−0.738701	+	1.27947i	−0.953080	+	0.302717i	$0.902106\pi$
$854$	6.38092e9			0.350575
$855$		0			0
$856$	1.45228e9			0.0791392
$857$	6.44399e9	−	1.11613e10i	0.349721	−	0.605735i	−0.636479	−	0.771294i	$-0.719610\pi$
$857$	6.44399e9	−	1.11613e10i	0.349721	−	0.605735i	0.986200	+	0.165560i	$0.0529430\pi$
$858$		0			0
$859$	−2.13794e9	−	3.70302e9i	−0.115085	−	0.199333i	0.802729	−	0.596344i	$-0.203381\pi$
$859$	−2.13794e9	−	3.70302e9i	−0.115085	−	0.199333i	−0.917814	+	0.397011i	$0.870047\pi$
$860$	3.26495e9	+	5.65505e9i	0.175038	+	0.303174i
$861$		0			0
$862$	1.14265e9	−	1.97912e9i	0.0607626	−	0.105244i
$863$	2.63998e10			1.39818			0.699089	−	0.715035i	$-0.253589\pi$
$863$	2.63998e10			1.39818			0.699089	+	0.715035i	$0.253589\pi$
$864$		0			0
$865$	9.88231e9			0.519161
$866$	1.90715e9	−	3.30328e9i	0.0997867	−	0.172836i
$867$		0			0
$868$	4.27113e9	+	7.39782e9i	0.221679	+	0.383959i
$869$	−6.23635e9	−	1.08017e10i	−0.322375	−	0.558370i
$870$		0			0
$871$	−1.64283e9	+	2.84547e9i	−0.0842423	+	0.145912i
$872$	−3.23271e9			−0.165105
$873$		0			0
$874$	−2.00304e10			−1.01484
$875$	3.01736e9	−	5.22622e9i	0.152265	−	0.263730i
$876$		0			0
$877$	−7.19624e9	−	1.24642e10i	−0.360252	−	0.623975i	0.627750	−	0.778415i	$-0.283976\pi$
$877$	−7.19624e9	−	1.24642e10i	−0.360252	−	0.623975i	−0.988002	+	0.154440i	$0.950643\pi$
$878$	1.00703e10	+	1.74423e10i	0.502125	+	0.869706i
$879$		0			0
$880$	1.30756e9	−	2.26476e9i	0.0646803	−	0.112030i
$881$	−2.86878e10			−1.41345			−0.706727	−	0.707487i	$-0.749829\pi$
$881$	−2.86878e10			−1.41345			−0.706727	+	0.707487i	$0.749829\pi$
$882$		0			0
$883$	1.10176e10			0.538550			0.269275	−	0.963063i	$-0.413216\pi$
$883$	1.10176e10			0.538550			0.269275	+	0.963063i	$0.413216\pi$
$884$	−6.75923e9	+	1.17073e10i	−0.329090	+	0.570000i
$885$		0			0
$886$	1.83459e9	+	3.17761e9i	0.0886180	+	0.153491i
$887$	8.77534e9	+	1.51993e10i	0.422213	+	0.731294i	0.996156	−	0.0876014i	$-0.0279202\pi$
$887$	8.77534e9	+	1.51993e10i	0.422213	+	0.731294i	−0.573943	+	0.818895i	$0.694587\pi$
$888$		0			0
$889$	−7.17571e9	+	1.24287e10i	−0.342538	+	0.593293i
$890$	2.03017e9			0.0965311
$891$		0			0
$892$	−1.03379e10			−0.487703
$893$	7.47322e9	−	1.29440e10i	0.351178	−	0.608259i
$894$		0			0
$895$	−4.12619e9	−	7.14677e9i	−0.192384	−	0.333218i
$896$	1.10911e9	+	1.92104e9i	0.0515108	+	0.0892193i
$897$		0			0
$898$	5.85733e9	−	1.01452e10i	0.269918	−	0.467512i
$899$	−9.79907e9			−0.449807
$900$		0			0
$901$	2.09841e10			0.955770
$902$	−3.52172e9	+	6.09979e9i	−0.159783	+	0.276753i
$903$		0			0
$904$	−5.48959e9	−	9.50824e9i	−0.247144	−	0.428066i
$905$	−2.36994e10	−	4.10486e10i	−1.06284	−	1.84089i
$906$		0			0
$907$	8.42225e9	−	1.45878e10i	0.374803	−	0.649177i	−0.615495	−	0.788141i	$-0.711044\pi$
$907$	8.42225e9	−	1.45878e10i	0.374803	−	0.649177i	0.990297	+	0.138964i	$0.0443771\pi$
$908$	−2.43542e9			−0.107963
$909$		0			0
$910$	3.97691e10			1.74945
$911$	7.36357e9	−	1.27541e10i	0.322682	−	0.558901i	−0.658359	−	0.752704i	$-0.728749\pi$
$911$	7.36357e9	−	1.27541e10i	0.322682	−	0.558901i	0.981040	+	0.193803i	$0.0620823\pi$
$912$		0			0
$913$	3.30824e9	+	5.73005e9i	0.143863	+	0.249178i
$914$	5.58639e9	+	9.67592e9i	0.242003	+	0.419161i
$915$		0			0
$916$	9.27091e9	−	1.60577e10i	0.398555	−	0.690318i
$917$	2.48899e10			1.06593
$918$		0			0
$919$	7.11506e9			0.302395			0.151197	−	0.988504i	$-0.451687\pi$
$919$	7.11506e9			0.302395			0.151197	+	0.988504i	$0.451687\pi$
$920$	−6.82319e9	+	1.18181e10i	−0.288888	+	0.500369i
$921$		0			0
$922$	1.58488e10	+	2.74510e10i	0.665946	+	1.15345i
$923$	−6.19989e9	−	1.07385e10i	−0.259524	−	0.449509i
$924$		0			0
$925$	1.66355e10	−	2.88136e10i	0.691099	−	1.19702i
$926$	1.50530e10			0.622995
$927$		0			0
$928$	−2.54459e9			−0.104520
$929$	−1.69702e10	+	2.93933e10i	−0.694437	+	1.20280i	0.275933	+	0.961177i	$0.411013\pi$
$929$	−1.69702e10	+	2.93933e10i	−0.694437	+	1.20280i	−0.970370	+	0.241624i	$0.922320\pi$
$930$		0			0
$931$	5.20860e9	+	9.02156e9i	0.211542	+	0.366402i
$932$	−2.38430e9	−	4.12973e9i	−0.0964730	−	0.167096i
$933$		0			0
$934$	−3.87807e9	+	6.71702e9i	−0.155741	+	0.269751i
$935$	1.07771e10			0.431181
$936$		0			0
$937$	−3.78364e10			−1.50252			−0.751261	−	0.660005i	$-0.770554\pi$
$937$	−3.78364e10			−1.50252			−0.751261	+	0.660005i	$0.770554\pi$
$938$	−1.11092e9	+	1.92416e9i	−0.0439513	+	0.0761258i
$939$		0			0
$940$	−5.09139e9	−	8.81854e9i	−0.199935	−	0.346298i
$941$	8.44461e9	+	1.46265e10i	0.330382	+	0.572238i	0.982587	−	0.185805i	$-0.0594892\pi$
$941$	8.44461e9	+	1.46265e10i	0.330382	+	0.572238i	−0.652205	+	0.758043i	$0.726156\pi$
$942$		0			0
$943$	1.83772e10	−	3.18303e10i	0.713657	−	1.23609i
$944$	1.09844e10			0.424984
$945$		0			0
$946$	−3.69442e9			−0.141882
$947$	5.84561e9	−	1.01249e10i	0.223668	−	0.387405i	−0.732251	−	0.681035i	$-0.761530\pi$
$947$	5.84561e9	−	1.01249e10i	0.223668	−	0.387405i	0.955919	+	0.293630i	$0.0948634\pi$
$948$		0			0
$949$	−6.53134e9	−	1.13126e10i	−0.248068	−	0.429666i
$950$	−8.88176e9	−	1.53837e10i	−0.336098	−	0.582139i
$951$		0			0
$952$	−4.57072e9	+	7.91672e9i	−0.171694	+	0.297383i
$953$	−5.10551e10			−1.91079			−0.955397	−	0.295323i	$-0.904573\pi$
$953$	−5.10551e10			−1.91079			−0.955397	+	0.295323i	$0.904573\pi$
$954$		0			0
$955$	−6.73981e10			−2.50401
$956$	5.74930e9	−	9.95808e9i	0.212820	−	0.368615i
$957$		0			0
$958$	8.03480e9	+	1.39167e10i	0.295254	+	0.511395i
$959$	−1.48032e10	−	2.56400e10i	−0.541990	−	0.938755i
$960$		0			0
$961$	5.79464e9	−	1.00366e10i	0.210618	−	0.364800i
$962$	−5.29235e10			−1.91662
$963$		0			0
$964$	−3.89556e9			−0.140056
$965$	5.60202e9	−	9.70298e9i	0.200678	−	0.347584i
$966$		0			0
$967$	4.34365e9	+	7.52343e9i	0.154476	+	0.267561i	0.932868	−	0.360218i	$-0.117298\pi$
$967$	4.34365e9	+	7.52343e9i	0.154476	+	0.267561i	−0.778392	+	0.627779i	$0.783964\pi$
$968$	−4.24894e9	−	7.35937e9i	−0.150562	−	0.260782i
$969$		0			0
$970$	2.44212e10	−	4.22987e10i	0.859143	−	1.48808i
$971$	−3.91347e10			−1.37181			−0.685906	−	0.727690i	$-0.740594\pi$
$971$	−3.91347e10			−1.37181			−0.685906	+	0.727690i	$0.740594\pi$
$972$		0			0
$973$	−8.46384e9			−0.294559
$974$	1.21153e10	−	2.09844e10i	0.420126	−	0.727679i
$975$		0			0
$976$	1.54436e9	+	2.67490e9i	0.0531708	+	0.0920945i
$977$	−1.36255e10	−	2.36001e10i	−0.467437	−	0.809624i	0.531871	−	0.846825i	$-0.321489\pi$
$977$	−1.36255e10	−	2.36001e10i	−0.467437	−	0.809624i	−0.999308	+	0.0372010i	$0.988156\pi$
$978$		0			0
$979$	−5.74305e8	+	9.94725e8i	−0.0195615	+	0.0338816i
$980$	7.09708e9			0.240873
$981$		0			0
$982$	3.61379e10			1.21779
$983$	3.56677e9	−	6.17782e9i	0.119767	−	0.207443i	−0.799908	−	0.600122i	$-0.795119\pi$
$983$	3.56677e9	−	6.17782e9i	0.119767	−	0.207443i	0.919675	+	0.392680i	$0.128452\pi$
$984$		0			0
$985$	1.25981e10	+	2.18205e10i	0.420028	+	0.727509i
$986$	−5.24321e9	−	9.08150e9i	−0.174192	−	0.301709i
$987$		0			0
$988$	−1.41280e10	+	2.44704e10i	−0.466049	+	0.807220i
$989$	1.92784e10			0.633702
$990$		0			0
$991$	−1.99378e10			−0.650760			−0.325380	−	0.945583i	$-0.605492\pi$
$991$	−1.99378e10			−0.650760			−0.325380	+	0.945583i	$0.605492\pi$
$992$	−2.06746e9	+	3.58094e9i	−0.0672428	+	0.116468i
$993$		0			0
$994$	−4.19249e9	−	7.26160e9i	−0.135400	−	0.234520i
$995$	2.21925e10	+	3.84385e10i	0.714208	+	1.23704i
$996$		0			0
$997$	6.37020e9	−	1.10335e10i	0.203573	−	0.352598i	−0.746104	−	0.665829i	$-0.768078\pi$
$997$	6.37020e9	−	1.10335e10i	0.203573	−	0.352598i	0.949677	+	0.313231i	$0.101411\pi$
$998$	3.72531e10			1.18633
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.8.c.a.19.1		6
3.2	odd	2		18.8.c.a.7.2	✓	6
4.3	odd	2		432.8.i.a.289.1		6
9.2	odd	6		162.8.a.f.1.1		3
9.4	even	3	inner	54.8.c.a.37.1		6
9.5	odd	6		18.8.c.a.13.2	yes	6
9.7	even	3		162.8.a.e.1.3		3
12.11	even	2		144.8.i.a.97.2		6
36.23	even	6		144.8.i.a.49.2		6
36.31	odd	6		432.8.i.a.145.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.8.c.a.7.2	✓	6	3.2	odd	2
18.8.c.a.13.2	yes	6	9.5	odd	6
54.8.c.a.19.1		6	1.1	even	1	trivial
54.8.c.a.37.1		6	9.4	even	3	inner
144.8.i.a.49.2		6	36.23	even	6
144.8.i.a.97.2		6	12.11	even	2
162.8.a.e.1.3		3	9.7	even	3
162.8.a.f.1.1		3	9.2	odd	6
432.8.i.a.145.1		6	36.31	odd	6
432.8.i.a.289.1		6	4.3	odd	2

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	54.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-187.789 - 325.261i) q^{5} +(-528.867 + 916.024i) q^{7} -512.000 q^{8} -3004.63 q^{10} +(849.965 - 1472.18i) q^{11} +(6256.75 + 10837.0i) q^{13} +(4230.93 + 7328.19i) q^{14} +(-2048.00 + 3547.24i) q^{16} -16879.9 q^{17} -35281.9 q^{19} +(-12018.5 + 20816.7i) q^{20} +(-6799.72 - 11777.5i) q^{22} +(35482.7 + 61457.8i) q^{23} +(-31467.1 + 54502.6i) q^{25} +100108. q^{26} +67694.9 q^{28} +(-38827.4 + 67251.0i) q^{29} +(63093.8 + 109282. i) q^{31} +(16384.0 + 28377.9i) q^{32} +(-67519.4 + 116947. i) q^{34} +397262. q^{35} -528664. q^{37} +(-141128. + 244440. i) q^{38} +(96148.1 + 166533. i) q^{40} +(-258960. - 448533. i) q^{41} +(135830. - 235264. i) q^{43} -108795. q^{44} +567723. q^{46} +(-211814. + 366873. i) q^{47} +(-147628. - 255699. i) q^{49} +(251737. + 436021. i) q^{50} +(400432. - 693568. i) q^{52} -1.24314e6 q^{53} -638457. q^{55} +(270780. - 469004. i) q^{56} +(310619. + 538008. i) q^{58} +(-1.34086e6 - 2.32244e6i) q^{59} +(377040. - 653052. i) q^{61} +1.00950e6 q^{62} +262144. q^{64} +(2.34990e6 - 4.07014e6i) q^{65} +(131285. + 227392. i) q^{67} +(540156. + 935577. i) q^{68} +(1.58905e6 - 2.75231e6i) q^{70} -990913. q^{71} -1.04389e6 q^{73} +(-2.11466e6 + 3.66269e6i) q^{74} +(1.12902e6 + 1.95552e6i) q^{76} +(899036. + 1.55718e6i) q^{77} +(3.66860e6 - 6.35419e6i) q^{79} +1.53837e6 q^{80} -4.14337e6 q^{82} +(-1.94611e6 + 3.37075e6i) q^{83} +(3.16986e6 + 5.49035e6i) q^{85} +(-1.08664e6 - 1.88211e6i) q^{86} +(-435182. + 753757. i) q^{88} -675681. q^{89} -1.32359e7 q^{91} +(2.27089e6 - 3.93330e6i) q^{92} +(1.69452e6 + 2.93499e6i) q^{94} +(6.62556e6 + 1.14758e7i) q^{95} +(-8.12785e6 + 1.40779e7i) q^{97} -2.36205e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 24 q^{2} - 192 q^{4} - 54 q^{5} + 210 q^{7} - 3072 q^{8} - 864 q^{10} - 6579 q^{11} + 10092 q^{13} - 1680 q^{14} - 12288 q^{16} + 29790 q^{17} - 137490 q^{19} - 3456 q^{20} + 52632 q^{22} + 39654 q^{23}+ \cdots + 7714800 q^{98}+O(q^{100}) \) 6 * q + 24 * q^2 - 192 * q^4 - 54 * q^5 + 210 * q^7 - 3072 * q^8 - 864 * q^10 - 6579 * q^11 + 10092 * q^13 - 1680 * q^14 - 12288 * q^16 + 29790 * q^17 - 137490 * q^19 - 3456 * q^20 + 52632 * q^22 + 39654 * q^23 - 7923 * q^25 + 161472 * q^26 - 26880 * q^28 - 239832 * q^29 + 145704 * q^31 + 98304 * q^32 + 119160 * q^34 + 1087776 * q^35 - 720384 * q^37 - 549960 * q^38 + 27648 * q^40 - 1086993 * q^41 - 299967 * q^43 + 842112 * q^44 + 634464 * q^46 - 131634 * q^47 + 482175 * q^49 + 63384 * q^50 + 645888 * q^52 - 1909152 * q^53 - 5494824 * q^55 - 107520 * q^56 + 1918656 * q^58 - 2504853 * q^59 + 7309038 * q^61 + 2331264 * q^62 + 1572864 * q^64 + 1786698 * q^65 + 3433035 * q^67 - 953280 * q^68 + 4351104 * q^70 - 2269368 * q^71 - 15901746 * q^73 - 2881536 * q^74 + 4399680 * q^76 + 6147432 * q^77 + 7076928 * q^79 + 442368 * q^80 - 17391888 * q^82 + 10914444 * q^83 + 17613396 * q^85 + 2399736 * q^86 + 3368448 * q^88 - 23800356 * q^89 - 37170552 * q^91 + 2537856 * q^92 + 1053072 * q^94 + 17342424 * q^95 + 519357 * q^97 + 7714800 * q^98

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