LMFDB - Embedded newform 162.6.c.h.55.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,6,Mod(55,162)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("162.55"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,4,0,-16,-66,0,-176] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$25.9821788097$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	162.55
Dual form			162.6.c.h.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00000 - 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(-33.0000 - 57.1577i) q^{5} +(-88.0000 + 152.420i) q^{7} -64.0000 q^{8} -264.000 q^{10} +(-30.0000 + 51.9615i) q^{11} +(329.000 + 569.845i) q^{13} +(352.000 + 609.682i) q^{14} +(-128.000 + 221.703i) q^{16} +414.000 q^{17} +956.000 q^{19} +(-528.000 + 914.523i) q^{20} +(120.000 + 207.846i) q^{22} +(300.000 + 519.615i) q^{23} +(-615.500 + 1066.08i) q^{25} +2632.00 q^{26} +2816.00 q^{28} +(2787.00 - 4827.23i) q^{29} +(1796.00 + 3110.76i) q^{31} +(512.000 + 886.810i) q^{32} +(828.000 - 1434.14i) q^{34} +11616.0 q^{35} -8458.00 q^{37} +(1912.00 - 3311.68i) q^{38} +(2112.00 + 3658.09i) q^{40} +(9597.00 + 16622.5i) q^{41} +(-6658.00 + 11532.0i) q^{43} +960.000 q^{44} +2400.00 q^{46} +(-9840.00 + 17043.4i) q^{47} +(-7084.50 - 12270.7i) q^{49} +(2462.00 + 4264.31i) q^{50} +(5264.00 - 9117.52i) q^{52} +31266.0 q^{53} +3960.00 q^{55} +(5632.00 - 9754.91i) q^{56} +(-11148.0 - 19308.9i) q^{58} +(13170.0 + 22811.1i) q^{59} +(15545.0 - 26924.7i) q^{61} +14368.0 q^{62} +4096.00 q^{64} +(21714.0 - 37609.8i) q^{65} +(8402.00 + 14552.7i) q^{67} +(-3312.00 - 5736.55i) q^{68} +(23232.0 - 40239.0i) q^{70} -6120.00 q^{71} -25558.0 q^{73} +(-16916.0 + 29299.4i) q^{74} +(-7648.00 - 13246.7i) q^{76} +(-5280.00 - 9145.23i) q^{77} +(-37204.0 + 64439.2i) q^{79} +16896.0 q^{80} +76776.0 q^{82} +(-3234.00 + 5601.45i) q^{83} +(-13662.0 - 23663.3i) q^{85} +(26632.0 + 46128.0i) q^{86} +(1920.00 - 3325.54i) q^{88} +32742.0 q^{89} -115808. q^{91} +(4800.00 - 8313.84i) q^{92} +(39360.0 + 68173.5i) q^{94} +(-31548.0 - 54642.7i) q^{95} +(-83041.0 + 143831. i) q^{97} -56676.0 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 16 q^{4} - 66 q^{5} - 176 q^{7} - 128 q^{8} - 528 q^{10} - 60 q^{11} + 658 q^{13} + 704 q^{14} - 256 q^{16} + 828 q^{17} + 1912 q^{19} - 1056 q^{20} + 240 q^{22} + 600 q^{23} - 1231 q^{25}+ \cdots - 113352 q^{98}+O(q^{100}) $ 2 * q + 4 * q^2 - 16 * q^4 - 66 * q^5 - 176 * q^7 - 128 * q^8 - 528 * q^10 - 60 * q^11 + 658 * q^13 + 704 * q^14 - 256 * q^16 + 828 * q^17 + 1912 * q^19 - 1056 * q^20 + 240 * q^22 + 600 * q^23 - 1231 * q^25 + 5264 * q^26 + 5632 * q^28 + 5574 * q^29 + 3592 * q^31 + 1024 * q^32 + 1656 * q^34 + 23232 * q^35 - 16916 * q^37 + 3824 * q^38 + 4224 * q^40 + 19194 * q^41 - 13316 * q^43 + 1920 * q^44 + 4800 * q^46 - 19680 * q^47 - 14169 * q^49 + 4924 * q^50 + 10528 * q^52 + 62532 * q^53 + 7920 * q^55 + 11264 * q^56 - 22296 * q^58 + 26340 * q^59 + 31090 * q^61 + 28736 * q^62 + 8192 * q^64 + 43428 * q^65 + 16804 * q^67 - 6624 * q^68 + 46464 * q^70 - 12240 * q^71 - 51116 * q^73 - 33832 * q^74 - 15296 * q^76 - 10560 * q^77 - 74408 * q^79 + 33792 * q^80 + 153552 * q^82 - 6468 * q^83 - 27324 * q^85 + 53264 * q^86 + 3840 * q^88 + 65484 * q^89 - 231616 * q^91 + 9600 * q^92 + 78720 * q^94 - 63096 * q^95 - 166082 * q^97 - 113352 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	−33.0000	−	57.1577i	−0.590322	−	1.02247i	−0.994189	−	0.107650i	$-0.965667\pi$
$5$	−33.0000	−	57.1577i	−0.590322	−	1.02247i	0.403867	−	0.914818i	$-0.367666\pi$
$6$		0			0
$7$	−88.0000	+	152.420i	−0.678793	+	1.17570i	0.296551	+	0.955017i	$0.404163\pi$
$7$	−88.0000	+	152.420i	−0.678793	+	1.17570i	−0.975345	+	0.220688i	$0.929170\pi$
$8$	−64.0000			−0.353553
$9$		0			0
$10$	−264.000			−0.834841
$11$	−30.0000	+	51.9615i	−0.0747549	+	0.129479i	−0.900980	−	0.433861i	$-0.857151\pi$
$11$	−30.0000	+	51.9615i	−0.0747549	+	0.129479i	0.826225	+	0.563341i	$0.190484\pi$
$12$		0			0
$13$	329.000	+	569.845i	0.539930	+	0.935186i	0.998907	+	0.0467382i	$0.0148827\pi$
$13$	329.000	+	569.845i	0.539930	+	0.935186i	−0.458977	+	0.888448i	$0.651784\pi$
$14$	352.000	+	609.682i	0.479979	+	0.831349i
$15$		0			0
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	414.000			0.347439			0.173719	−	0.984795i	$-0.444421\pi$
$17$	414.000			0.347439			0.173719	+	0.984795i	$0.444421\pi$
$18$		0			0
$19$	956.000			0.607539			0.303769	−	0.952746i	$-0.401755\pi$
$19$	956.000			0.607539			0.303769	+	0.952746i	$0.401755\pi$
$20$	−528.000	+	914.523i	−0.295161	+	0.511234i
$21$		0			0
$22$	120.000	+	207.846i	0.0528597	+	0.0915557i
$23$	300.000	+	519.615i	0.118250	+	0.204815i	0.919074	−	0.394084i	$-0.128938\pi$
$23$	300.000	+	519.615i	0.118250	+	0.204815i	−0.800824	+	0.598900i	$0.795605\pi$
$24$		0			0
$25$	−615.500	+	1066.08i	−0.196960	+	0.341145i
$26$	2632.00			0.763576
$27$		0			0
$28$	2816.00			0.678793
$29$	2787.00	−	4827.23i	0.615378	−	1.06587i	−0.374940	−	0.927049i	$-0.622337\pi$
$29$	2787.00	−	4827.23i	0.615378	−	1.06587i	0.990318	−	0.138817i	$-0.0443300\pi$
$30$		0			0
$31$	1796.00	+	3110.76i	0.335662	+	0.581384i	0.983612	−	0.180299i	$-0.0577067\pi$
$31$	1796.00	+	3110.76i	0.335662	+	0.581384i	−0.647950	+	0.761683i	$0.724373\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$		0			0
$34$	828.000	−	1434.14i	0.122838	−	0.212762i
$35$	11616.0			1.60283
$36$		0			0
$37$	−8458.00			−1.01570			−0.507848	−	0.861447i	$-0.669559\pi$
$37$	−8458.00			−1.01570			−0.507848	+	0.861447i	$0.669559\pi$
$38$	1912.00	−	3311.68i	0.214797	−	0.372040i
$39$		0			0
$40$	2112.00	+	3658.09i	0.208710	+	0.361497i
$41$	9597.00	+	16622.5i	0.891612	+	1.54432i	0.837943	+	0.545758i	$0.183758\pi$
$41$	9597.00	+	16622.5i	0.891612	+	1.54432i	0.0536693	+	0.998559i	$0.482908\pi$
$42$		0			0
$43$	−6658.00	+	11532.0i	−0.549127	+	0.951116i	0.449208	+	0.893427i	$0.351706\pi$
$43$	−6658.00	+	11532.0i	−0.549127	+	0.951116i	−0.998335	+	0.0576883i	$0.981627\pi$
$44$	960.000			0.0747549
$45$		0			0
$46$	2400.00			0.167231
$47$	−9840.00	+	17043.4i	−0.649756	+	1.12541i	0.333425	+	0.942777i	$0.391796\pi$
$47$	−9840.00	+	17043.4i	−0.649756	+	1.12541i	−0.983181	+	0.182634i	$0.941538\pi$
$48$		0			0
$49$	−7084.50	−	12270.7i	−0.421521	−	0.730095i
$50$	2462.00	+	4264.31i	0.139272	+	0.241226i
$51$		0			0
$52$	5264.00	−	9117.52i	0.269965	−	0.467593i
$53$	31266.0			1.52891			0.764456	−	0.644676i	$-0.223008\pi$
$53$	31266.0			1.52891			0.764456	+	0.644676i	$0.223008\pi$
$54$		0			0
$55$	3960.00			0.176518
$56$	5632.00	−	9754.91i	0.239990	−	0.415674i
$57$		0			0
$58$	−11148.0	−	19308.9i	−0.435138	−	0.753681i
$59$	13170.0	+	22811.1i	0.492556	+	0.853132i	0.999963	−	0.00857419i	$-0.00272928\pi$
$59$	13170.0	+	22811.1i	0.492556	+	0.853132i	−0.507407	+	0.861706i	$0.669396\pi$
$60$		0			0
$61$	15545.0	−	26924.7i	0.534892	−	0.926460i	−0.464277	−	0.885690i	$-0.653686\pi$
$61$	15545.0	−	26924.7i	0.534892	−	0.926460i	0.999169	−	0.0407699i	$-0.0129811\pi$
$62$	14368.0			0.474698
$63$		0			0
$64$	4096.00			0.125000
$65$	21714.0	−	37609.8i	0.637465	−	1.10412i
$66$		0			0
$67$	8402.00	+	14552.7i	0.228663	+	0.396056i	0.957412	−	0.288725i	$-0.0932313\pi$
$67$	8402.00	+	14552.7i	0.228663	+	0.396056i	−0.728749	+	0.684781i	$0.759898\pi$
$68$	−3312.00	−	5736.55i	−0.0868596	−	0.150445i
$69$		0			0
$70$	23232.0	−	40239.0i	0.566685	−	0.981527i
$71$	−6120.00			−0.144081			−0.0720403	−	0.997402i	$-0.522951\pi$
$71$	−6120.00			−0.144081			−0.0720403	+	0.997402i	$0.522951\pi$
$72$		0			0
$73$	−25558.0			−0.561332			−0.280666	−	0.959806i	$-0.590555\pi$
$73$	−25558.0			−0.561332			−0.280666	+	0.959806i	$0.590555\pi$
$74$	−16916.0	+	29299.4i	−0.359102	+	0.621984i
$75$		0			0
$76$	−7648.00	−	13246.7i	−0.151885	−	0.263072i
$77$	−5280.00	−	9145.23i	−0.101486	−	0.175779i
$78$		0			0
$79$	−37204.0	+	64439.2i	−0.670690	+	1.16167i	0.307019	+	0.951704i	$0.400669\pi$
$79$	−37204.0	+	64439.2i	−0.670690	+	1.16167i	−0.977709	+	0.209966i	$0.932665\pi$
$80$	16896.0			0.295161
$81$		0			0
$82$	76776.0			1.26093
$83$	−3234.00	+	5601.45i	−0.0515282	+	0.0892494i	−0.890639	−	0.454711i	$-0.849743\pi$
$83$	−3234.00	+	5601.45i	−0.0515282	+	0.0892494i	0.839111	+	0.543960i	$0.183076\pi$
$84$		0			0
$85$	−13662.0	−	23663.3i	−0.205101	−	0.355245i
$86$	26632.0	+	46128.0i	0.388291	+	0.672540i
$87$		0			0
$88$	1920.00	−	3325.54i	0.0264298	−	0.0457778i
$89$	32742.0			0.438157			0.219079	−	0.975707i	$-0.429695\pi$
$89$	32742.0			0.438157			0.219079	+	0.975707i	$0.429695\pi$
$90$		0			0
$91$	−115808.			−1.46600
$92$	4800.00	−	8313.84i	0.0591251	−	0.102408i
$93$		0			0
$94$	39360.0	+	68173.5i	0.459447	+	0.795786i
$95$	−31548.0	−	54642.7i	−0.358643	−	0.621189i
$96$		0			0
$97$	−83041.0	+	143831.i	−0.896114	+	1.55211i	−0.0636941	+	0.997969i	$0.520288\pi$
$97$	−83041.0	+	143831.i	−0.896114	+	1.55211i	−0.832420	+	0.554145i	$0.813045\pi$
$98$	−56676.0			−0.596120
$99$		0			0
$100$	19696.0			0.196960
$101$	−11001.0	+	19054.3i	−0.107307	+	0.185861i	−0.914678	−	0.404182i	$-0.867556\pi$
$101$	−11001.0	+	19054.3i	−0.107307	+	0.185861i	0.807371	+	0.590044i	$0.200889\pi$
$102$		0			0
$103$	39632.0	+	68644.6i	0.368089	+	0.637549i	0.989267	−	0.146121i	$-0.0466788\pi$
$103$	39632.0	+	68644.6i	0.368089	+	0.637549i	−0.621178	+	0.783670i	$0.713345\pi$
$104$	−21056.0	−	36470.1i	−0.190894	−	0.330638i
$105$		0			0
$106$	62532.0	−	108309.i	0.540552	−	0.936264i
$107$	−227988.			−1.92510			−0.962548	−	0.271110i	$-0.912609\pi$
$107$	−227988.			−1.92510			−0.962548	+	0.271110i	$0.912609\pi$
$108$		0			0
$109$	−8530.00			−0.0687674			−0.0343837	−	0.999409i	$-0.510947\pi$
$109$	−8530.00			−0.0687674			−0.0343837	+	0.999409i	$0.510947\pi$
$110$	7920.00	−	13717.8i	0.0624085	−	0.108095i
$111$		0			0
$112$	−22528.0	−	39019.6i	−0.169698	−	0.293926i
$113$	−97719.0	−	169254.i	−0.719918	−	1.24693i	−0.961032	−	0.276437i	$-0.910846\pi$
$113$	−97719.0	−	169254.i	−0.719918	−	1.24693i	0.241114	−	0.970497i	$-0.422487\pi$
$114$		0			0
$115$	19800.0	−	34294.6i	0.139611	−	0.241814i
$116$	−89184.0			−0.615378
$117$		0			0
$118$	105360.			0.696580
$119$	−36432.0	+	63102.1i	−0.235839	+	0.408485i
$120$		0			0
$121$	78725.5	+	136357.i	0.488823	+	0.846667i
$122$	−62180.0	−	107699.i	−0.378226	−	0.655106i
$123$		0			0
$124$	28736.0	−	49772.2i	0.167831	−	0.290692i
$125$	−125004.			−0.715565
$126$		0			0
$127$	173000.			0.951780			0.475890	−	0.879505i	$-0.342126\pi$
$127$	173000.			0.951780			0.475890	+	0.879505i	$0.342126\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−86856.0	−	150439.i	−0.450756	−	0.780732i
$131$	75630.0	+	130995.i	0.385049	+	0.666924i	0.991776	−	0.127986i	$-0.0408513\pi$
$131$	75630.0	+	130995.i	0.385049	+	0.666924i	−0.606727	+	0.794910i	$0.707518\pi$
$132$		0			0
$133$	−84128.0	+	145714.i	−0.412393	+	0.714286i
$134$	67216.0			0.323378
$135$		0			0
$136$	−26496.0			−0.122838
$137$	−64227.0	+	111244.i	−0.292359	+	0.506380i	−0.974367	−	0.224964i	$-0.927773\pi$
$137$	−64227.0	+	111244.i	−0.292359	+	0.506380i	0.682008	+	0.731345i	$0.261107\pi$
$138$		0			0
$139$	−77098.0	−	133538.i	−0.338459	−	0.586228i	0.645684	−	0.763605i	$-0.276572\pi$
$139$	−77098.0	−	133538.i	−0.338459	−	0.586228i	−0.984143	+	0.177376i	$0.943239\pi$
$140$	−92928.0	−	160956.i	−0.400707	−	0.694044i
$141$		0			0
$142$	−12240.0	+	21200.3i	−0.0509402	+	0.0882310i
$143$	−39480.0			−0.161450
$144$		0			0
$145$	−367884.			−1.45308
$146$	−51116.0	+	88535.5i	−0.198461	+	0.343744i
$147$		0			0
$148$	67664.0	+	117197.i	0.253924	+	0.439809i
$149$	14727.0	+	25507.9i	0.0543436	+	0.0941259i	0.891917	−	0.452198i	$-0.149360\pi$
$149$	14727.0	+	25507.9i	0.0543436	+	0.0941259i	−0.837574	+	0.546324i	$0.816027\pi$
$150$		0			0
$151$	101936.	−	176558.i	0.363819	−	0.630153i	−0.624767	−	0.780811i	$-0.714806\pi$
$151$	101936.	−	176558.i	0.363819	−	0.630153i	0.988586	+	0.150658i	$0.0481394\pi$
$152$	−61184.0			−0.214797
$153$		0			0
$154$	−42240.0			−0.143523
$155$	118536.	−	205310.i	0.396297	−	0.686407i
$156$		0			0
$157$	−68071.0	−	117902.i	−0.220401	−	0.381745i	0.734529	−	0.678577i	$-0.237403\pi$
$157$	−68071.0	−	117902.i	−0.220401	−	0.381745i	−0.954930	+	0.296832i	$0.904070\pi$
$158$	148816.	+	257757.i	0.474250	+	0.821424i
$159$		0			0
$160$	33792.0	−	58529.5i	0.104355	−	0.180748i
$161$	−105600.			−0.321070
$162$		0			0
$163$	−171124.			−0.504478			−0.252239	−	0.967665i	$-0.581167\pi$
$163$	−171124.			−0.504478			−0.252239	+	0.967665i	$0.581167\pi$
$164$	153552.	−	265960.i	0.445806	−	0.772159i
$165$		0			0
$166$	12936.0	+	22405.8i	0.0364359	+	0.0631089i
$167$	−338100.	−	585606.i	−0.938110	−	1.62486i	−0.768991	−	0.639259i	$-0.779241\pi$
$167$	−338100.	−	585606.i	−0.938110	−	1.62486i	−0.169119	−	0.985596i	$-0.554092\pi$
$168$		0			0
$169$	−30835.5	+	53408.7i	−0.0830490	+	0.143845i
$170$	−109296.			−0.290056
$171$		0			0
$172$	213056.			0.549127
$173$	66579.0	−	115318.i	0.169131	−	0.292943i	−0.768984	−	0.639268i	$-0.779237\pi$
$173$	66579.0	−	115318.i	0.169131	−	0.292943i	0.938114	+	0.346325i	$0.112571\pi$
$174$		0			0
$175$	−108328.	−	187630.i	−0.267390	−	0.463134i
$176$	−7680.00	−	13302.2i	−0.0186887	−	0.0323698i
$177$		0			0
$178$	65484.0	−	113422.i	0.154912	−	0.268316i
$179$	693396.			1.61752			0.808758	−	0.588141i	$-0.200140\pi$
$179$	693396.			1.61752			0.808758	+	0.588141i	$0.200140\pi$
$180$		0			0
$181$	377174.			0.855747			0.427873	−	0.903839i	$-0.359263\pi$
$181$	377174.			0.855747			0.427873	+	0.903839i	$0.359263\pi$
$182$	−231616.	+	401171.i	−0.518311	+	0.897740i
$183$		0			0
$184$	−19200.0	−	33255.4i	−0.0418077	−	0.0724131i
$185$	279114.	+	483440.i	0.599587	+	1.03852i
$186$		0			0
$187$	−12420.0	+	21512.1i	−0.0259727	+	0.0449861i
$188$	314880.			0.649756
$189$		0			0
$190$	−252384.			−0.507198
$191$	−132672.	+	229795.i	−0.263145	+	0.455781i	−0.967076	−	0.254487i	$-0.918093\pi$
$191$	−132672.	+	229795.i	−0.263145	+	0.455781i	0.703931	+	0.710269i	$0.251427\pi$
$192$		0			0
$193$	−147649.	−	255736.i	−0.285323	−	0.494194i	0.687364	−	0.726313i	$-0.258768\pi$
$193$	−147649.	−	255736.i	−0.285323	−	0.494194i	−0.972688	+	0.232118i	$0.925434\pi$
$194$	332164.	+	575325.i	0.633648	+	1.09751i
$195$		0			0
$196$	−113352.	+	196331.i	−0.210760	+	0.365048i
$197$	−201294.			−0.369543			−0.184772	−	0.982781i	$-0.559155\pi$
$197$	−201294.			−0.369543			−0.184772	+	0.982781i	$0.559155\pi$
$198$		0			0
$199$	652448.			1.16792			0.583960	−	0.811782i	$-0.301502\pi$
$199$	652448.			1.16792			0.583960	+	0.811782i	$0.301502\pi$
$200$	39392.0	−	68228.9i	0.0696359	−	0.120613i
$201$		0			0
$202$	44004.0	+	76217.2i	0.0758776	+	0.131424i
$203$	490512.	+	849592.i	0.835429	+	1.44701i
$204$		0			0
$205$	633402.	−	1.09708e6i	1.05268	−	1.82329i
$206$	317056.			0.520557
$207$		0			0
$208$	−168448.			−0.269965
$209$	−28680.0	+	49675.2i	−0.0454165	+	0.0786636i
$210$		0			0
$211$	573530.	+	993383.i	0.886850	+	1.53607i	0.843579	+	0.537005i	$0.180444\pi$
$211$	573530.	+	993383.i	0.886850	+	1.53607i	0.0432708	+	0.999063i	$0.486222\pi$
$212$	−250128.	−	433234.i	−0.382228	−	0.662039i
$213$		0			0
$214$	−455976.	+	789774.i	−0.680624	+	1.17888i
$215$	878856.			1.29665
$216$		0			0
$217$	−632192.			−0.911380
$218$	−17060.0	+	29548.8i	−0.0243130	+	0.0421113i
$219$		0			0
$220$	−31680.0	−	54871.4i	−0.0441294	−	0.0764344i
$221$	136206.	+	235916.i	0.187593	+	0.324920i
$222$		0			0
$223$	−350980.	+	607915.i	−0.472629	+	0.818617i	−0.999509	−	0.0313222i	$-0.990028\pi$
$223$	−350980.	+	607915.i	−0.472629	+	0.818617i	0.526881	+	0.849939i	$0.323362\pi$
$224$	−180224.			−0.239990
$225$		0			0
$226$	−781752.			−1.01812
$227$	618054.	−	1.07050e6i	0.796089	−	1.37887i	−0.126056	−	0.992023i	$-0.540232\pi$
$227$	618054.	−	1.07050e6i	0.796089	−	1.37887i	0.922145	−	0.386844i	$-0.126435\pi$
$228$		0			0
$229$	−52915.0	−	91651.5i	−0.0666792	−	0.115492i	0.830758	−	0.556633i	$-0.187907\pi$
$229$	−52915.0	−	91651.5i	−0.0666792	−	0.115492i	−0.897438	+	0.441141i	$0.854574\pi$
$230$	−79200.0	−	137178.i	−0.0987201	−	0.170988i
$231$		0			0
$232$	−178368.	+	308942.i	−0.217569	+	0.376841i
$233$	438678.			0.529366			0.264683	−	0.964335i	$-0.414733\pi$
$233$	438678.			0.529366			0.264683	+	0.964335i	$0.414733\pi$
$234$		0			0
$235$	1.29888e6			1.53426
$236$	210720.	−	364978.i	0.246278	−	0.426566i
$237$		0			0
$238$	145728.	+	252408.i	0.166763	+	0.288843i
$239$	14232.0	+	24650.5i	0.0161165	+	0.0279146i	0.873971	−	0.485978i	$-0.161536\pi$
$239$	14232.0	+	24650.5i	0.0161165	+	0.0279146i	−0.857855	+	0.513892i	$0.828203\pi$
$240$		0			0
$241$	−446281.	+	772981.i	−0.494955	+	0.857287i	−0.999983	−	0.00581560i	$-0.998149\pi$
$241$	−446281.	+	772981.i	−0.494955	+	0.857287i	0.505028	+	0.863103i	$0.331482\pi$
$242$	629804.			0.691301
$243$		0			0
$244$	−497440.			−0.534892
$245$	−467577.	+	809867.i	−0.497666	+	0.861983i
$246$		0			0
$247$	314524.	+	544772.i	0.328028	+	0.568162i
$248$	−114944.	−	199089.i	−0.118674	−	0.205550i
$249$		0			0
$250$	−250008.	+	433027.i	−0.252990	+	0.438192i
$251$	110124.			0.110331			0.0551655	−	0.998477i	$-0.482431\pi$
$251$	110124.			0.110331			0.0551655	+	0.998477i	$0.482431\pi$
$252$		0			0
$253$	−36000.0			−0.0353591
$254$	346000.	−	599290.i	0.336505	−	0.582844i
$255$		0			0
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	70401.0	+	121938.i	0.0664884	+	0.115161i	0.897353	−	0.441313i	$-0.145487\pi$
$257$	70401.0	+	121938.i	0.0664884	+	0.115161i	−0.830865	+	0.556474i	$0.812154\pi$
$258$		0			0
$259$	744304.	−	1.28917e6i	0.689447	−	1.19416i
$260$	−694848.			−0.637465
$261$		0			0
$262$	605040.			0.544541
$263$	−469380.	+	812990.i	−0.418442	+	0.724763i	−0.995783	−	0.0917404i	$-0.970757\pi$
$263$	−469380.	+	812990.i	−0.418442	+	0.724763i	0.577341	+	0.816503i	$0.304090\pi$
$264$		0			0
$265$	−1.03178e6	−	1.78709e6i	−0.902551	−	1.56326i
$266$	336512.	+	582856.i	0.291606	+	0.505076i
$267$		0			0
$268$	134432.	−	232843.i	0.114331	−	0.198028i
$269$	1.11451e6			0.939078			0.469539	−	0.882912i	$-0.344420\pi$
$269$	1.11451e6			0.939078			0.469539	+	0.882912i	$0.344420\pi$
$270$		0			0
$271$	567704.			0.469568			0.234784	−	0.972048i	$-0.424562\pi$
$271$	567704.			0.469568			0.234784	+	0.972048i	$0.424562\pi$
$272$	−52992.0	+	91784.8i	−0.0434298	+	0.0752227i
$273$		0			0
$274$	256908.	+	444978.i	0.206729	+	0.358065i
$275$	−36930.0	−	63964.6i	−0.0294474	−	0.0510045i
$276$		0			0
$277$	606629.	−	1.05071e6i	0.475033	−	0.822781i	−0.524558	−	0.851375i	$-0.675769\pi$
$277$	606629.	−	1.05071e6i	0.475033	−	0.822781i	0.999591	+	0.0285934i	$0.00910280\pi$
$278$	−616784.			−0.478653
$279$		0			0
$280$	−743424.			−0.566685
$281$	343869.	−	595599.i	0.259793	−	0.449974i	−0.706393	−	0.707819i	$-0.749679\pi$
$281$	343869.	−	595599.i	0.259793	−	0.449974i	0.966186	+	0.257845i	$0.0830124\pi$
$282$		0			0
$283$	415454.	+	719587.i	0.308359	+	0.534094i	0.978004	−	0.208588i	$-0.0668868\pi$
$283$	415454.	+	719587.i	0.308359	+	0.534094i	−0.669644	+	0.742682i	$0.733553\pi$
$284$	48960.0	+	84801.2i	0.0360202	+	0.0623887i
$285$		0			0
$286$	−78960.0	+	136763.i	−0.0570811	+	0.0988673i
$287$	−3.37814e6			−2.42088
$288$		0			0
$289$	−1.24846e6			−0.879286
$290$	−735768.	+	1.27439e6i	−0.513743	+	0.889829i
$291$		0			0
$292$	204464.	+	354142.i	0.140333	+	0.243064i
$293$	−656313.	−	1.13677e6i	−0.446624	−	0.773575i	0.551540	−	0.834149i	$-0.314040\pi$
$293$	−656313.	−	1.13677e6i	−0.446624	−	0.773575i	−0.998164	+	0.0605733i	$0.980707\pi$
$294$		0			0
$295$	869220.	−	1.50553e6i	0.581533	−	1.00725i
$296$	541312.			0.359102
$297$		0			0
$298$	117816.			0.0768535
$299$	−197400.	+	341907.i	−0.127694	+	0.221172i
$300$		0			0
$301$	−1.17181e6	−	2.02963e6i	−0.745487	−	1.29122i
$302$	−407744.	−	706233.i	−0.257259	−	0.445585i
$303$		0			0
$304$	−122368.	+	211948.i	−0.0759423	+	0.131536i
$305$	−2.05194e6			−1.26303
$306$		0			0
$307$	1.69022e6			1.02352			0.511761	−	0.859128i	$-0.328993\pi$
$307$	1.69022e6			1.02352			0.511761	+	0.859128i	$0.328993\pi$
$308$	−84480.0	+	146324.i	−0.0507431	+	0.0878897i
$309$		0			0
$310$	−474144.	−	821241.i	−0.280224	−	0.485363i
$311$	−751020.	−	1.30080e6i	−0.440302	−	0.762625i	0.557410	−	0.830238i	$-0.311795\pi$
$311$	−751020.	−	1.30080e6i	−0.440302	−	0.762625i	−0.997712	+	0.0676123i	$0.978462\pi$
$312$		0			0
$313$	−405421.	+	702210.i	−0.233908	+	0.405141i	−0.958955	−	0.283559i	$-0.908485\pi$
$313$	−405421.	+	702210.i	−0.233908	+	0.405141i	0.725047	+	0.688700i	$0.241818\pi$
$314$	−544568.			−0.311694
$315$		0			0
$316$	1.19053e6			0.670690
$317$	451779.	−	782504.i	0.252510	−	0.437359i	−0.711707	−	0.702477i	$-0.752077\pi$
$317$	451779.	−	782504.i	0.252510	−	0.437359i	0.964216	+	0.265117i	$0.0854107\pi$
$318$		0			0
$319$	167220.	+	289634.i	0.0920050	+	0.159357i
$320$	−135168.	−	234118.i	−0.0737902	−	0.127808i
$321$		0			0
$322$	−211200.	+	365809.i	−0.113515	+	0.196614i
$323$	395784.			0.211082
$324$		0			0
$325$	−809998.			−0.425379
$326$	−342248.	+	592791.i	−0.178360	+	0.308928i
$327$		0			0
$328$	−614208.	−	1.06384e6i	−0.315232	−	0.545999i
$329$	−1.73184e6	−	2.99963e6i	−0.882100	−	1.52784i
$330$		0			0
$331$	−560986.	+	971656.i	−0.281438	+	0.487464i	−0.971739	−	0.236058i	$-0.924145\pi$
$331$	−560986.	+	971656.i	−0.281438	+	0.487464i	0.690301	+	0.723522i	$0.257478\pi$
$332$	103488.			0.0515282
$333$		0			0
$334$	−2.70480e6			−1.32669
$335$	554532.	−	960478.i	0.269969	−	0.467601i
$336$		0			0
$337$	1.37609e6	+	2.38345e6i	0.660041	+	1.14323i	0.980604	+	0.195998i	$0.0627946\pi$
$337$	1.37609e6	+	2.38345e6i	0.660041	+	1.14323i	−0.320563	+	0.947227i	$0.603872\pi$
$338$	123342.	+	213635.i	0.0587245	+	0.101714i
$339$		0			0
$340$	−218592.	+	378612.i	−0.102550	+	0.177622i
$341$	−215520.			−0.100369
$342$		0			0
$343$	−464288.			−0.213085
$344$	426112.	−	738048.i	0.194146	−	0.336270i
$345$		0			0
$346$	−266316.	−	461273.i	−0.119593	−	0.207142i
$347$	958746.	+	1.66060e6i	0.427445	+	0.740356i	0.996645	−	0.0818428i	$-0.0260806\pi$
$347$	958746.	+	1.66060e6i	0.427445	+	0.740356i	−0.569201	+	0.822199i	$0.692747\pi$
$348$		0			0
$349$	−918295.	+	1.59053e6i	−0.403570	+	0.699003i	−0.994154	−	0.107973i	$-0.965564\pi$
$349$	−918295.	+	1.59053e6i	−0.403570	+	0.699003i	0.590584	+	0.806976i	$0.298897\pi$
$350$	−866624.			−0.378147
$351$		0			0
$352$	−61440.0			−0.0264298
$353$	−311007.	+	538680.i	−0.132841	+	0.230088i	−0.924771	−	0.380525i	$-0.875743\pi$
$353$	−311007.	+	538680.i	−0.132841	+	0.230088i	0.791929	+	0.610613i	$0.209077\pi$
$354$		0			0
$355$	201960.	+	349805.i	0.0850539	+	0.147318i
$356$	−261936.	−	453686.i	−0.109539	−	0.189728i
$357$		0			0
$358$	1.38679e6	−	2.40199e6i	0.571878	−	0.990523i
$359$	−3.74062e6			−1.53182			−0.765909	−	0.642949i	$-0.777711\pi$
$359$	−3.74062e6			−1.53182			−0.765909	+	0.642949i	$0.777711\pi$
$360$		0			0
$361$	−1.56216e6			−0.630897
$362$	754348.	−	1.30657e6i	0.302552	−	0.524036i
$363$		0			0
$364$	926464.	+	1.60468e6i	0.366501	+	0.634798i
$365$	843414.	+	1.46084e6i	0.331367	+	0.573944i
$366$		0			0
$367$	−8116.00	+	14057.3i	−0.00314541	+	0.00544801i	−0.867594	−	0.497274i	$-0.834335\pi$
$367$	−8116.00	+	14057.3i	−0.00314541	+	0.00544801i	0.864448	+	0.502722i	$0.167668\pi$
$368$	−153600.			−0.0591251
$369$		0			0
$370$	2.23291e6			0.847944
$371$	−2.75141e6	+	4.76558e6i	−1.03782	+	1.79755i
$372$		0			0
$373$	−146803.	−	254270.i	−0.0546340	−	0.0946288i	0.837415	−	0.546568i	$-0.184066\pi$
$373$	−146803.	−	254270.i	−0.0546340	−	0.0946288i	−0.892049	+	0.451939i	$0.850733\pi$
$374$	49680.0	+	86048.3i	0.0183655	+	0.0318100i
$375$		0			0
$376$	629760.	−	1.09078e6i	0.229724	−	0.397893i
$377$	3.66769e6			1.32904
$378$		0			0
$379$	3.18012e6			1.13722			0.568611	−	0.822607i	$-0.307481\pi$
$379$	3.18012e6			1.13722			0.568611	+	0.822607i	$0.307481\pi$
$380$	−504768.	+	874284.i	−0.179322	+	0.310594i
$381$		0			0
$382$	530688.	+	919179.i	0.186072	+	0.322286i
$383$	−1.48992e6	−	2.58062e6i	−0.518998	−	0.898932i	−0.999756	−	0.0220782i	$-0.992972\pi$
$383$	−1.48992e6	−	2.58062e6i	−0.518998	−	0.898932i	0.480758	−	0.876853i	$-0.340362\pi$
$384$		0			0
$385$	−348480.	+	603585.i	−0.119819	+	0.207533i
$386$	−1.18119e6			−0.403508
$387$		0			0
$388$	2.65731e6			0.896114
$389$	1.72989e6	−	2.99625e6i	0.579620	−	1.00393i	−0.415902	−	0.909409i	$-0.636534\pi$
$389$	1.72989e6	−	2.99625e6i	0.579620	−	1.00393i	0.995523	−	0.0945228i	$-0.0301325\pi$
$390$		0			0
$391$	124200.	+	215121.i	0.0410847	+	0.0711607i
$392$	453408.	+	785326.i	0.149030	+	0.258128i
$393$		0			0
$394$	−402588.	+	697303.i	−0.130653	+	0.226298i
$395$	4.91093e6			1.58369
$396$		0			0
$397$	−3.90416e6			−1.24323			−0.621615	−	0.783323i	$-0.713523\pi$
$397$	−3.90416e6			−1.24323			−0.621615	+	0.783323i	$0.713523\pi$
$398$	1.30490e6	−	2.26015e6i	0.412922	−	0.715202i
$399$		0			0
$400$	−157568.	−	272916.i	−0.0492400	−	0.0852862i
$401$	2.72058e6	+	4.71218e6i	0.844890	+	1.46339i	0.885717	+	0.464226i	$0.153667\pi$
$401$	2.72058e6	+	4.71218e6i	0.844890	+	1.46339i	−0.0408270	+	0.999166i	$0.512999\pi$
$402$		0			0
$403$	−1.18177e6	+	2.04688e6i	−0.362468	+	0.627813i
$404$	352032.			0.107307
$405$		0			0
$406$	3.92410e6			1.18148
$407$	253740.	−	439491.i	0.0759282	−	0.131511i
$408$		0			0
$409$	−984973.	−	1.70602e6i	−0.291150	−	0.504286i	0.682932	−	0.730482i	$-0.260704\pi$
$409$	−984973.	−	1.70602e6i	−0.291150	−	0.504286i	−0.974082	+	0.226196i	$0.927371\pi$
$410$	−2.53361e6	−	4.38834e6i	−0.744354	−	1.28926i
$411$		0			0
$412$	634112.	−	1.09831e6i	0.184045	−	0.318774i
$413$	−4.63584e6			−1.33738
$414$		0			0
$415$	426888.			0.121673
$416$	−336896.	+	583521.i	−0.0954471	+	0.165319i
$417$		0			0
$418$	114720.	+	198701.i	0.0321143	+	0.0556236i
$419$	69510.0	+	120395.i	0.0193425	+	0.0335022i	0.875535	−	0.483155i	$-0.160509\pi$
$419$	69510.0	+	120395.i	0.0193425	+	0.0335022i	−0.856192	+	0.516658i	$0.827176\pi$
$420$		0			0
$421$	−2.16372e6	+	3.74766e6i	−0.594970	+	1.03052i	0.398581	+	0.917133i	$0.369503\pi$
$421$	−2.16372e6	+	3.74766e6i	−0.594970	+	1.03052i	−0.993551	+	0.113385i	$0.963831\pi$
$422$	4.58824e6			1.25419
$423$		0			0
$424$	−2.00102e6			−0.540552
$425$	−254817.	+	441356.i	−0.0684315	+	0.118527i
$426$		0			0
$427$	2.73592e6	+	4.73875e6i	0.726162	+	1.25775i
$428$	1.82390e6	+	3.15909e6i	0.481274	+	0.833591i
$429$		0			0
$430$	1.75771e6	−	3.04445e6i	0.458434	−	0.794031i
$431$	2.79936e6			0.725881			0.362941	−	0.931812i	$-0.381773\pi$
$431$	2.79936e6			0.725881			0.362941	+	0.931812i	$0.381773\pi$
$432$		0			0
$433$	−5.90241e6			−1.51290			−0.756449	−	0.654052i	$-0.773068\pi$
$433$	−5.90241e6			−1.51290			−0.756449	+	0.654052i	$0.773068\pi$
$434$	−1.26438e6	+	2.18998e6i	−0.322222	+	0.558104i
$435$		0			0
$436$	68240.0	+	118195.i	0.0171919	+	0.0297772i
$437$	286800.	+	496752.i	0.0718415	+	0.124433i
$438$		0			0
$439$	223256.	−	386691.i	0.0552894	−	0.0957640i	−0.837056	−	0.547117i	$-0.815725\pi$
$439$	223256.	−	386691.i	0.0552894	−	0.0957640i	0.892345	+	0.451353i	$0.149059\pi$
$440$	−253440.			−0.0624085
$441$		0			0
$442$	1.08965e6			0.265296
$443$	1.74763e6	−	3.02698e6i	0.423096	−	0.732824i	−0.573144	−	0.819454i	$-0.694277\pi$
$443$	1.74763e6	−	3.02698e6i	0.423096	−	0.732824i	0.996241	+	0.0866303i	$0.0276099\pi$
$444$		0			0
$445$	−1.08049e6	−	1.87146e6i	−0.258654	−	0.448002i
$446$	1.40392e6	+	2.43166e6i	0.334199	+	0.578850i
$447$		0			0
$448$	−360448.	+	624314.i	−0.0848492	+	0.146963i
$449$	1.20613e6			0.282343			0.141171	−	0.989985i	$-0.454913\pi$
$449$	1.20613e6			0.282343			0.141171	+	0.989985i	$0.454913\pi$
$450$		0			0
$451$	−1.15164e6			−0.266609
$452$	−1.56350e6	+	2.70807e6i	−0.359959	+	0.623467i
$453$		0			0
$454$	−2.47222e6	−	4.28200e6i	−0.562920	−	0.975006i
$455$	3.82166e6	+	6.61932e6i	0.865414	+	1.49894i
$456$		0			0
$457$	−116773.	+	202257.i	−0.0261548	+	0.0453015i	−0.878807	−	0.477178i	$-0.841660\pi$
$457$	−116773.	+	202257.i	−0.0261548	+	0.0453015i	0.852652	+	0.522480i	$0.174993\pi$
$458$	−423320.			−0.0942986
$459$		0			0
$460$	−633600.			−0.139611
$461$	−872445.	+	1.51112e6i	−0.191199	+	0.331166i	−0.945648	−	0.325192i	$-0.894571\pi$
$461$	−872445.	+	1.51112e6i	−0.191199	+	0.331166i	0.754449	+	0.656359i	$0.227904\pi$
$462$		0			0
$463$	1.45893e6	+	2.52694e6i	0.316288	+	0.547827i	0.979710	−	0.200418i	$-0.0642301\pi$
$463$	1.45893e6	+	2.52694e6i	0.316288	+	0.547827i	−0.663423	+	0.748245i	$0.730897\pi$
$464$	713472.	+	1.23577e6i	0.153845	+	0.266466i
$465$		0			0
$466$	877356.	−	1.51963e6i	0.187159	−	0.324169i
$467$	5.31076e6			1.12684			0.563422	−	0.826169i	$-0.309484\pi$
$467$	5.31076e6			1.12684			0.563422	+	0.826169i	$0.309484\pi$
$468$		0			0
$469$	−2.95750e6			−0.620859
$470$	2.59776e6	−	4.49945e6i	0.542443	−	0.939539i
$471$		0			0
$472$	−842880.	−	1.45991e6i	−0.174145	−	0.301628i
$473$	−399480.	−	691920.i	−0.0820998	−	0.142201i
$474$		0			0
$475$	−588418.	+	1.01917e6i	−0.119661	+	0.207259i
$476$	1.16582e6			0.235839
$477$		0			0
$478$	113856.			0.0227922
$479$	1.17233e6	−	2.03053e6i	0.233459	−	0.404363i	−0.725365	−	0.688365i	$-0.758329\pi$
$479$	1.17233e6	−	2.03053e6i	0.233459	−	0.404363i	0.958824	+	0.284002i	$0.0916622\pi$
$480$		0			0
$481$	−2.78268e6	−	4.81975e6i	−0.548404	−	0.949864i
$482$	1.78512e6	+	3.09193e6i	0.349986	+	0.606194i
$483$		0			0
$484$	1.25961e6	−	2.18171e6i	0.244412	−	0.423333i
$485$	1.09614e7			2.11598
$486$		0			0
$487$	9.81531e6			1.87535			0.937674	−	0.347517i	$-0.112975\pi$
$487$	9.81531e6			1.87535			0.937674	+	0.347517i	$0.112975\pi$
$488$	−994880.	+	1.72318e6i	−0.189113	+	0.327553i
$489$		0			0
$490$	1.87031e6	+	3.23947e6i	0.351903	+	0.609514i
$491$	−2.97260e6	−	5.14869e6i	−0.556458	−	0.963814i	−0.997788	−	0.0664690i	$-0.978827\pi$
$491$	−2.97260e6	−	5.14869e6i	−0.556458	−	0.963814i	0.441330	−	0.897345i	$-0.354507\pi$
$492$		0			0
$493$	1.15382e6	−	1.99847e6i	0.213806	−	0.370323i
$494$	2.51619e6			0.463902
$495$		0			0
$496$	−919552.			−0.167831
$497$	538560.	−	932813.i	0.0978010	−	0.169396i
$498$		0			0
$499$	−3.23916e6	−	5.61039e6i	−0.582346	−	1.00865i	−0.995201	−	0.0978554i	$-0.968802\pi$
$499$	−3.23916e6	−	5.61039e6i	−0.582346	−	1.00865i	0.412855	−	0.910797i	$-0.364532\pi$
$500$	1.00003e6	+	1.73211e6i	0.178891	+	0.309849i
$501$		0			0
$502$	220248.	−	381481.i	0.0390079	−	0.0675637i
$503$	−4.71794e6			−0.831444			−0.415722	−	0.909492i	$-0.636471\pi$
$503$	−4.71794e6			−0.831444			−0.415722	+	0.909492i	$0.636471\pi$
$504$		0			0
$505$	1.45213e6			0.253383
$506$	−72000.0	+	124708.i	−0.0125013	+	0.0216529i
$507$		0			0
$508$	−1.38400e6	−	2.39716e6i	−0.237945	−	0.412133i
$509$	−953853.	−	1.65212e6i	−0.163188	−	0.282649i	0.772823	−	0.634622i	$-0.218844\pi$
$509$	−953853.	−	1.65212e6i	−0.163188	−	0.282649i	−0.936010	+	0.351973i	$0.885511\pi$
$510$		0			0
$511$	2.24910e6	−	3.89556e6i	0.381028	−	0.659960i
$512$	−262144.			−0.0441942
$513$		0			0
$514$	563208.			0.0940288
$515$	2.61571e6	−	4.53055e6i	0.434582	−	0.752718i
$516$		0			0
$517$	−590400.	−	1.02260e6i	−0.0971449	−	0.168260i
$518$	−2.97722e6	−	5.15669e6i	−0.487513	−	0.844397i
$519$		0			0
$520$	−1.38970e6	+	2.40702e6i	−0.225378	+	0.390366i
$521$	−8.01974e6			−1.29439			−0.647196	−	0.762324i	$-0.724059\pi$
$521$	−8.01974e6			−1.29439			−0.647196	+	0.762324i	$0.724059\pi$
$522$		0			0
$523$	1.91162e6			0.305596			0.152798	−	0.988257i	$-0.451172\pi$
$523$	1.91162e6			0.305596			0.152798	+	0.988257i	$0.451172\pi$
$524$	1.21008e6	−	2.09592e6i	0.192524	−	0.333462i
$525$		0			0
$526$	1.87752e6	+	3.25196e6i	0.295883	+	0.512485i
$527$	743544.	+	1.28786e6i	0.116622	+	0.201995i
$528$		0			0
$529$	3.03817e6	−	5.26227e6i	0.472034	−	0.817587i
$530$	−8.25422e6			−1.27640
$531$		0			0
$532$	2.69210e6			0.412393
$533$	−6.31483e6	+	1.09376e7i	−0.962816	+	1.66765i
$534$		0			0
$535$	7.52360e6	+	1.30313e7i	1.13643	+	1.96835i
$536$	−537728.	−	931372.i	−0.0808445	−	0.140027i
$537$		0			0
$538$	2.22901e6	−	3.86076e6i	0.332014	−	0.575066i
$539$	850140.			0.126043
$540$		0			0
$541$	−1.19900e7			−1.76128			−0.880639	−	0.473788i	$-0.842886\pi$
$541$	−1.19900e7			−1.76128			−0.880639	+	0.473788i	$0.842886\pi$
$542$	1.13541e6	−	1.96658e6i	0.166017	−	0.287551i
$543$		0			0
$544$	211968.	+	367139.i	0.0307095	+	0.0531905i
$545$	281490.	+	487555.i	0.0405949	+	0.0703125i
$546$		0			0
$547$	−2.22905e6	+	3.86082e6i	−0.318530	+	0.551711i	−0.980182	−	0.198101i	$-0.936523\pi$
$547$	−2.22905e6	+	3.86082e6i	−0.318530	+	0.551711i	0.661651	+	0.749812i	$0.269856\pi$
$548$	2.05526e6			0.292359
$549$		0			0
$550$	−295440.			−0.0416450
$551$	2.66437e6	−	4.61483e6i	0.373866	−	0.647555i
$552$		0			0
$553$	−6.54790e6	−	1.13413e7i	−0.910520	−	1.57707i
$554$	−2.42652e6	−	4.20285e6i	−0.335899	−	0.581794i
$555$		0			0
$556$	−1.23357e6	+	2.13660e6i	−0.169230	+	0.293114i
$557$	−9.02612e6			−1.23272			−0.616358	−	0.787466i	$-0.711393\pi$
$557$	−9.02612e6			−1.23272			−0.616358	+	0.787466i	$0.711393\pi$
$558$		0			0
$559$	−8.76193e6			−1.18596
$560$	−1.48685e6	+	2.57530e6i	−0.200353	+	0.347022i
$561$		0			0
$562$	−1.37548e6	−	2.38239e6i	−0.183701	−	0.318180i
$563$	3.42449e6	+	5.93140e6i	0.455329	+	0.788653i	0.998707	−	0.0508350i	$-0.0161883\pi$
$563$	3.42449e6	+	5.93140e6i	0.455329	+	0.788653i	−0.543378	+	0.839488i	$0.682855\pi$
$564$		0			0
$565$	−6.44945e6	+	1.11708e7i	−0.849967	+	1.47219i
$566$	3.32363e6			0.436086
$567$		0			0
$568$	391680.			0.0509402
$569$	−2.73161e6	+	4.73129e6i	−0.353703	+	0.612631i	−0.986895	−	0.161364i	$-0.948411\pi$
$569$	−2.73161e6	+	4.73129e6i	−0.353703	+	0.612631i	0.633192	+	0.773994i	$0.281744\pi$
$570$		0			0
$571$	5.11619e6	+	8.86150e6i	0.656684	+	1.13741i	0.981469	+	0.191622i	$0.0613748\pi$
$571$	5.11619e6	+	8.86150e6i	0.656684	+	1.13741i	−0.324785	+	0.945788i	$0.605292\pi$
$572$	315840.	+	547051.i	0.0403624	+	0.0699097i
$573$		0			0
$574$	−6.75629e6	+	1.17022e7i	−0.855911	+	1.48248i
$575$	−738600.			−0.0931622
$576$		0			0
$577$	1.59437e7			1.99365			0.996825	−	0.0796186i	$-0.0253702\pi$
$577$	1.59437e7			1.99365			0.996825	+	0.0796186i	$0.0253702\pi$
$578$	−2.49692e6	+	4.32480e6i	−0.310875	+	0.538451i
$579$		0			0
$580$	2.94307e6	+	5.09755e6i	0.363271	+	0.629204i
$581$	−569184.	−	985856.i	−0.0699540	−	0.121164i
$582$		0			0
$583$	−937980.	+	1.62463e6i	−0.114294	+	0.197962i
$584$	1.63571e6			0.198461
$585$		0			0
$586$	−5.25050e6			−0.631622
$587$	−4.73857e6	+	8.20744e6i	−0.567612	+	0.983133i	0.429189	+	0.903215i	$0.358799\pi$
$587$	−4.73857e6	+	8.20744e6i	−0.567612	+	0.983133i	−0.996801	+	0.0799185i	$0.974534\pi$
$588$		0			0
$589$	1.71698e6	+	2.97389e6i	0.203928	+	0.353213i
$590$	−3.47688e6	−	6.02213e6i	−0.411206	−	0.712230i
$591$		0			0
$592$	1.08262e6	−	1.87516e6i	0.126962	−	0.219904i
$593$	−2.45349e6			−0.286515			−0.143258	−	0.989685i	$-0.545758\pi$
$593$	−2.45349e6			−0.286515			−0.143258	+	0.989685i	$0.545758\pi$
$594$		0			0
$595$	4.80902e6			0.556884
$596$	235632.	−	408127.i	0.0271718	−	0.0470630i
$597$		0			0
$598$	789600.	+	1.36763e6i	0.0902930	+	0.156392i
$599$	−4.64989e6	−	8.05385e6i	−0.529512	−	0.917142i	−0.999407	−	0.0344196i	$-0.989042\pi$
$599$	−4.64989e6	−	8.05385e6i	−0.529512	−	0.917142i	0.469895	−	0.882722i	$-0.344292\pi$
$600$		0			0
$601$	5.73085e6	−	9.92613e6i	0.647192	−	1.12097i	−0.336599	−	0.941648i	$-0.609277\pi$
$601$	5.73085e6	−	9.92613e6i	0.647192	−	1.12097i	0.983791	−	0.179321i	$-0.0573900\pi$
$602$	−9.37446e6			−1.05428
$603$		0			0
$604$	−3.26195e6			−0.363819
$605$	5.19588e6	−	8.99953e6i	0.577126	−	0.999612i
$606$		0			0
$607$	−5.63919e6	−	9.76736e6i	−0.621219	−	1.07598i	−0.989259	−	0.146173i	$-0.953304\pi$
$607$	−5.63919e6	−	9.76736e6i	−0.621219	−	1.07598i	0.368040	−	0.929810i	$-0.380029\pi$
$608$	489472.	+	847790.i	0.0536993	+	0.0930100i
$609$		0			0
$610$	−4.10388e6	+	7.10813e6i	−0.446550	+	0.773447i
$611$	−1.29494e7			−1.40329
$612$		0			0
$613$	93782.0			0.0100802			0.00504009	−	0.999987i	$-0.498396\pi$
$613$	93782.0			0.0100802			0.00504009	+	0.999987i	$0.498396\pi$
$614$	3.38044e6	−	5.85509e6i	0.361870	−	0.626777i
$615$		0			0
$616$	337920.	+	585295.i	0.0358808	+	0.0621474i
$617$	−7.48208e6	−	1.29593e7i	−0.791242	−	1.37047i	−0.925198	−	0.379484i	$-0.876102\pi$
$617$	−7.48208e6	−	1.29593e7i	−0.791242	−	1.37047i	0.133957	−	0.990987i	$-0.457232\pi$
$618$		0			0
$619$	2.53444e6	−	4.38978e6i	0.265861	−	0.460485i	−0.701928	−	0.712248i	$-0.747677\pi$
$619$	2.53444e6	−	4.38978e6i	0.265861	−	0.460485i	0.967789	+	0.251763i	$0.0810104\pi$
$620$	−3.79315e6			−0.396297
$621$		0			0
$622$	−6.00816e6			−0.622681
$623$	−2.88130e6	+	4.99055e6i	−0.297418	+	0.515144i
$624$		0			0
$625$	6.04857e6	+	1.04764e7i	0.619374	+	1.07279i
$626$	1.62168e6	+	2.80884e6i	0.165398	+	0.286478i
$627$		0			0
$628$	−1.08914e6	+	1.88644e6i	−0.110200	+	0.190873i
$629$	−3.50161e6			−0.352892
$630$		0			0
$631$	1.55919e7			1.55892			0.779462	−	0.626450i	$-0.215493\pi$
$631$	1.55919e7			1.55892			0.779462	+	0.626450i	$0.215493\pi$
$632$	2.38106e6	−	4.12411e6i	0.237125	−	0.410712i
$633$		0			0
$634$	−1.80712e6	−	3.13002e6i	−0.178551	−	0.309260i
$635$	−5.70900e6	−	9.88828e6i	−0.561857	−	0.973165i
$636$		0			0
$637$	4.66160e6	−	8.07413e6i	0.455184	−	0.788401i
$638$	1.33776e6			0.130115
$639$		0			0
$640$	−1.08134e6			−0.104355
$641$	5.48506e6	−	9.50041e6i	0.527274	−	0.913266i	−0.472220	−	0.881481i	$-0.656547\pi$
$641$	5.48506e6	−	9.50041e6i	0.527274	−	0.913266i	0.999495	−	0.0317855i	$-0.0101193\pi$
$642$		0			0
$643$	1.41852e6	+	2.45695e6i	0.135303	+	0.234352i	0.925713	−	0.378226i	$-0.123466\pi$
$643$	1.41852e6	+	2.45695e6i	0.135303	+	0.234352i	−0.790410	+	0.612578i	$0.790132\pi$
$644$	844800.	+	1.46324e6i	0.0802674	+	0.139027i
$645$		0			0
$646$	791568.	−	1.37104e6i	0.0746289	−	0.129261i
$647$	6.05686e6			0.568835			0.284418	−	0.958700i	$-0.408200\pi$
$647$	6.05686e6			0.568835			0.284418	+	0.958700i	$0.408200\pi$
$648$		0			0
$649$	−1.58040e6			−0.147284
$650$	−1.62000e6	+	2.80592e6i	−0.150394	+	0.260490i
$651$		0			0
$652$	1.36899e6	+	2.37116e6i	0.126119	+	0.218445i
$653$	−544461.	−	943034.i	−0.0499671	−	0.0865455i	0.839960	−	0.542648i	$-0.182578\pi$
$653$	−544461.	−	943034.i	−0.0499671	−	0.0865455i	−0.889927	+	0.456103i	$0.849245\pi$
$654$		0			0
$655$	4.99158e6	−	8.64567e6i	0.454606	−	0.787400i
$656$	−4.91366e6			−0.445806
$657$		0			0
$658$	−1.38547e7			−1.24748
$659$	3.70901e6	−	6.42420e6i	0.332694	−	0.576243i	−0.650345	−	0.759639i	$-0.725376\pi$
$659$	3.70901e6	−	6.42420e6i	0.332694	−	0.576243i	0.983039	+	0.183396i	$0.0587091\pi$
$660$		0			0
$661$	−383827.	−	664808.i	−0.0341690	−	0.0591824i	0.848435	−	0.529299i	$-0.177545\pi$
$661$	−383827.	−	664808.i	−0.0341690	−	0.0591824i	−0.882604	+	0.470117i	$0.844212\pi$
$662$	2.24394e6	+	3.88663e6i	0.199006	+	0.344689i
$663$		0			0
$664$	206976.	−	358493.i	0.0182180	−	0.0315544i
$665$	1.11049e7			0.973779
$666$		0			0
$667$	3.34440e6			0.291074
$668$	−5.40960e6	+	9.36970e6i	−0.469055	+	0.812428i
$669$		0			0
$670$	−2.21813e6	−	3.84191e6i	−0.190897	−	0.330644i
$671$	932700.	+	1.61548e6i	0.0799716	+	0.138515i
$672$		0			0
$673$	−711313.	+	1.23203e6i	−0.0605373	+	0.104854i	−0.894706	−	0.446656i	$-0.852615\pi$
$673$	−711313.	+	1.23203e6i	−0.0605373	+	0.104854i	0.834168	+	0.551510i	$0.185948\pi$
$674$	1.10087e7			0.933439
$675$		0			0
$676$	986736.			0.0830490
$677$	−3.08115e6	+	5.33671e6i	−0.258370	+	0.447509i	−0.965805	−	0.259268i	$-0.916519\pi$
$677$	−3.08115e6	+	5.33671e6i	−0.258370	+	0.447509i	0.707436	+	0.706778i	$0.249852\pi$
$678$		0			0
$679$	−1.46152e7	−	2.53143e7i	−1.21655	−	2.10713i
$680$	874368.	+	1.51445e6i	0.0725140	+	0.125598i
$681$		0			0
$682$	−431040.	+	746583.i	−0.0354860	+	0.0614635i
$683$	−1.50621e7			−1.23548			−0.617739	−	0.786383i	$-0.711951\pi$
$683$	−1.50621e7			−1.23548			−0.617739	+	0.786383i	$0.711951\pi$
$684$		0			0
$685$	8.47796e6			0.690343
$686$	−928576.	+	1.60834e6i	−0.0753368	+	0.130487i
$687$		0			0
$688$	−1.70445e6	−	2.95219e6i	−0.137282	−	0.237779i
$689$	1.02865e7	+	1.78168e7i	0.825506	+	1.42982i
$690$		0			0
$691$	2.93818e6	−	5.08907e6i	0.234090	−	0.405456i	−0.724918	−	0.688835i	$-0.758122\pi$
$691$	2.93818e6	−	5.08907e6i	0.234090	−	0.405456i	0.959008	+	0.283380i	$0.0914556\pi$
$692$	−2.13053e6			−0.169131
$693$		0			0
$694$	7.66997e6			0.604498
$695$	−5.08847e6	+	8.81349e6i	−0.399600	+	0.692127i
$696$		0			0
$697$	3.97316e6	+	6.88171e6i	0.309780	+	0.536555i
$698$	3.67318e6	+	6.36213e6i	0.285367	+	0.494270i
$699$		0			0
$700$	−1.73325e6	+	3.00207e6i	−0.133695	+	0.231567i
$701$	−3.60077e6			−0.276758			−0.138379	−	0.990379i	$-0.544189\pi$
$701$	−3.60077e6			−0.276758			−0.138379	+	0.990379i	$0.544189\pi$
$702$		0			0
$703$	−8.08585e6			−0.617074
$704$	−122880.	+	212834.i	−0.00934436	+	0.0161849i
$705$		0			0
$706$	1.24403e6	+	2.15472e6i	0.0939330	+	0.162697i
$707$	−1.93618e6	−	3.35356e6i	−0.145679	−	0.252323i
$708$		0			0
$709$	−4.61258e6	+	7.98922e6i	−0.344610	+	0.596883i	−0.985283	−	0.170932i	$-0.945322\pi$
$709$	−4.61258e6	+	7.98922e6i	−0.344610	+	0.596883i	0.640673	+	0.767814i	$0.278656\pi$
$710$	1.61568e6			0.120284
$711$		0			0
$712$	−2.09549e6			−0.154912
$713$	−1.07760e6	+	1.86646e6i	−0.0793841	+	0.137497i
$714$		0			0
$715$	1.30284e6	+	2.25659e6i	0.0953073	+	0.165077i
$716$	−5.54717e6	−	9.60798e6i	−0.404379	−	0.700405i
$717$		0			0
$718$	−7.48123e6	+	1.29579e7i	−0.541579	+	0.938043i
$719$	2.63923e7			1.90395			0.951975	−	0.306177i	$-0.0990500\pi$
$719$	2.63923e7			1.90395			0.951975	+	0.306177i	$0.0990500\pi$
$720$		0			0
$721$	−1.39505e7			−0.999426
$722$	−3.12433e6	+	5.41149e6i	−0.223056	+	0.386344i
$723$		0			0
$724$	−3.01739e6	−	5.22628e6i	−0.213937	−	0.370549i
$725$	3.43080e6	+	5.94231e6i	0.242410	+	0.419866i
$726$		0			0
$727$	4.89742e6	−	8.48259e6i	0.343662	−	0.595240i	−0.641448	−	0.767167i	$-0.721666\pi$
$727$	4.89742e6	−	8.48259e6i	0.343662	−	0.595240i	0.985110	+	0.171927i	$0.0549992\pi$
$728$	7.41171e6			0.518311
$729$		0			0
$730$	6.74731e6			0.468623
$731$	−2.75641e6	+	4.77425e6i	−0.190788	+	0.330454i
$732$		0			0
$733$	−2.03792e6	−	3.52978e6i	−0.140096	−	0.242654i	0.787436	−	0.616396i	$-0.211408\pi$
$733$	−2.03792e6	−	3.52978e6i	−0.140096	−	0.242654i	−0.927533	+	0.373742i	$0.878075\pi$
$734$	32464.0	+	56229.3i	0.00222414	+	0.00385232i
$735$		0			0
$736$	−307200.	+	532086.i	−0.0209039	+	0.0362066i
$737$	−1.00824e6			−0.0683747
$738$		0			0
$739$	−1.65709e7			−1.11618			−0.558089	−	0.829781i	$-0.688465\pi$
$739$	−1.65709e7			−1.11618			−0.558089	+	0.829781i	$0.688465\pi$
$740$	4.46582e6	−	7.73503e6i	0.299794	−	0.519258i
$741$		0			0
$742$	1.10056e7	+	1.90623e7i	0.733846	+	1.27106i
$743$	7.20707e6	+	1.24830e7i	0.478946	+	0.829559i	0.999709	−	0.0241427i	$-0.00768562\pi$
$743$	7.20707e6	+	1.24830e7i	0.478946	+	0.829559i	−0.520762	+	0.853702i	$0.674352\pi$
$744$		0			0
$745$	971982.	−	1.68352e6i	0.0641605	−	0.111129i
$746$	−1.17442e6			−0.0772641
$747$		0			0
$748$	397440.			0.0259727
$749$	2.00629e7	−	3.47500e7i	1.30674	−	2.26334i
$750$		0			0
$751$	−8.39722e6	−	1.45444e7i	−0.543295	−	0.941015i	−0.998712	−	0.0507363i	$-0.983843\pi$
$751$	−8.39722e6	−	1.45444e7i	−0.543295	−	0.941015i	0.455417	−	0.890278i	$-0.349490\pi$
$752$	−2.51904e6	−	4.36311e6i	−0.162439	−	0.281353i
$753$		0			0
$754$	7.33538e6	−	1.27053e7i	0.469888	−	0.813870i
$755$	−1.34556e7			−0.859081
$756$		0			0
$757$	1.32943e7			0.843188			0.421594	−	0.906785i	$-0.361471\pi$
$757$	1.32943e7			0.843188			0.421594	+	0.906785i	$0.361471\pi$
$758$	6.36023e6	−	1.10162e7i	0.402068	−	0.696403i
$759$		0			0
$760$	2.01907e6	+	3.49714e6i	0.126800	+	0.219623i
$761$	−1.07393e6	−	1.86010e6i	−0.0672225	−	0.116433i	0.830455	−	0.557085i	$-0.188080\pi$
$761$	−1.07393e6	−	1.86010e6i	−0.0672225	−	0.116433i	−0.897678	+	0.440653i	$0.854747\pi$
$762$		0			0
$763$	750640.	−	1.30015e6i	0.0466789	−	0.0808502i
$764$	4.24550e6			0.263145
$765$		0			0
$766$	−1.19194e7			−0.733975
$767$	−8.66586e6	+	1.50097e7i	−0.531892	+	0.921264i
$768$		0			0
$769$	6.55296e6	+	1.13501e7i	0.399596	+	0.692121i	0.993676	−	0.112285i	$-0.0358169\pi$
$769$	6.55296e6	+	1.13501e7i	0.399596	+	0.692121i	−0.594080	+	0.804406i	$0.702484\pi$
$770$	1.39392e6	+	2.41434e6i	0.0847249	+	0.146748i
$771$		0			0
$772$	−2.36238e6	+	4.09177e6i	−0.142662	+	0.247097i
$773$	2.37154e7			1.42752			0.713759	−	0.700392i	$-0.246991\pi$
$773$	2.37154e7			1.42752			0.713759	+	0.700392i	$0.246991\pi$
$774$		0			0
$775$	−4.42175e6			−0.264448
$776$	5.31462e6	−	9.20520e6i	0.316824	−	0.548755i
$777$		0			0
$778$	−6.91955e6	−	1.19850e7i	−0.409854	−	0.709887i
$779$	9.17473e6	+	1.58911e7i	0.541689	+	0.938232i
$780$		0			0
$781$	183600.	−	318005.i	0.0107707	−	0.0186554i
$782$	993600.			0.0581025
$783$		0			0
$784$	3.62726e6			0.210760
$785$	−4.49269e6	+	7.78156e6i	−0.260215	+	0.450705i
$786$		0			0
$787$	4.20024e6	+	7.27503e6i	0.241734	+	0.418695i	0.961208	−	0.275824i	$-0.0889506\pi$
$787$	4.20024e6	+	7.27503e6i	0.241734	+	0.418695i	−0.719474	+	0.694519i	$0.755617\pi$
$788$	1.61035e6	+	2.78921e6i	0.0923858	+	0.160017i
$789$		0			0
$790$	9.82186e6	−	1.70120e7i	0.559920	−	0.969810i
$791$	3.43971e7			1.95470
$792$		0			0
$793$	2.04572e7			1.15522
$794$	−7.80832e6	+	1.35244e7i	−0.439548	+	0.761320i
$795$		0			0
$796$	−5.21958e6	−	9.04058e6i	−0.291980	−	0.505724i
$797$	2.70512e6	+	4.68540e6i	0.150848	+	0.261277i	0.931539	−	0.363640i	$-0.118466\pi$
$797$	2.70512e6	+	4.68540e6i	0.150848	+	0.261277i	−0.780691	+	0.624917i	$0.785133\pi$
$798$		0			0
$799$	−4.07376e6	+	7.05596e6i	−0.225750	+	0.391011i
$800$	−1.26054e6			−0.0696359
$801$		0			0
$802$	2.17646e7			1.19485
$803$	766740.	−	1.32803e6i	0.0419623	−	0.0726808i
$804$		0			0
$805$	3.48480e6	+	6.03585e6i	0.189534	+	0.328283i
$806$	4.72707e6	+	8.18753e6i	0.256304	+	0.443931i
$807$		0			0
$808$	704064.	−	1.21947e6i	0.0379388	−	0.0657120i
$809$	2.60777e7			1.40087			0.700436	−	0.713715i	$-0.252989\pi$
$809$	2.60777e7			1.40087			0.700436	+	0.713715i	$0.252989\pi$
$810$		0			0
$811$	1.90021e7			1.01449			0.507247	−	0.861800i	$-0.330663\pi$
$811$	1.90021e7			1.01449			0.507247	+	0.861800i	$0.330663\pi$
$812$	7.84819e6	−	1.35935e7i	0.417714	−	0.723503i
$813$		0			0
$814$	−1.01496e6	−	1.75796e6i	−0.0536893	−	0.0929926i
$815$	5.64709e6	+	9.78105e6i	0.297804	+	0.515812i
$816$		0			0
$817$	−6.36505e6	+	1.10246e7i	−0.333616	+	0.577839i
$818$	−7.87978e6			−0.411748
$819$		0			0
$820$	−2.02689e7			−1.05268
$821$	−1.55086e7	+	2.68618e7i	−0.803001	+	1.39084i	0.114632	+	0.993408i	$0.463431\pi$
$821$	−1.55086e7	+	2.68618e7i	−0.803001	+	1.39084i	−0.917633	+	0.397430i	$0.869902\pi$
$822$		0			0
$823$	7.81448e6	+	1.35351e7i	0.402162	+	0.696564i	0.993987	−	0.109502i	$-0.0349257\pi$
$823$	7.81448e6	+	1.35351e7i	0.402162	+	0.696564i	−0.591825	+	0.806066i	$0.701592\pi$
$824$	−2.53645e6	−	4.39326e6i	−0.130139	−	0.225408i
$825$		0			0
$826$	−9.27168e6	+	1.60590e7i	−0.472834	+	0.818972i
$827$	−1.58421e7			−0.805467			−0.402733	−	0.915317i	$-0.631940\pi$
$827$	−1.58421e7			−0.805467			−0.402733	+	0.915317i	$0.631940\pi$
$828$		0			0
$829$	2.06176e6			0.104196			0.0520980	−	0.998642i	$-0.483409\pi$
$829$	2.06176e6			0.104196			0.0520980	+	0.998642i	$0.483409\pi$
$830$	853776.	−	1.47878e6i	0.0430179	−	0.0745091i
$831$		0			0
$832$	1.34758e6	+	2.33408e6i	0.0674913	+	0.116898i
$833$	−2.93298e6	−	5.08008e6i	−0.146453	−	0.253663i
$834$		0			0
$835$	−2.23146e7	+	3.86500e7i	−1.10757	+	1.91838i
$836$	917760.			0.0454165
$837$		0			0
$838$	556080.			0.0273544
$839$	1.51950e7	−	2.63185e7i	0.745240	−	1.29079i	−0.204843	−	0.978795i	$-0.565668\pi$
$839$	1.51950e7	−	2.63185e7i	0.745240	−	1.29079i	0.950083	−	0.311999i	$-0.100998\pi$
$840$		0			0
$841$	−5.27916e6	−	9.14378e6i	−0.257380	−	0.445796i
$842$	8.65486e6	+	1.49907e7i	0.420707	+	0.728686i
$843$		0			0
$844$	9.17648e6	−	1.58941e7i	0.443425	−	0.768034i
$845$	4.07029e6			0.196103
$846$		0			0
$847$	−2.77114e7			−1.32724
$848$	−4.00205e6	+	6.93175e6i	−0.191114	+	0.331019i
$849$		0			0
$850$	1.01927e6	+	1.76542e6i	0.0483884	+	0.0838111i
$851$	−2.53740e6	−	4.39491e6i	−0.120106	−	0.208030i
$852$		0			0
$853$	1.48869e7	−	2.57849e7i	0.700538	−	1.21337i	−0.267740	−	0.963491i	$-0.586277\pi$
$853$	1.48869e7	−	2.57849e7i	0.700538	−	1.21337i	0.968278	−	0.249876i	$-0.0803898\pi$
$854$	2.18874e7			1.02695
$855$		0			0
$856$	1.45912e7			0.680624
$857$	4.32050e6	−	7.48333e6i	0.200947	−	0.348051i	−0.747887	−	0.663826i	$-0.768931\pi$
$857$	4.32050e6	−	7.48333e6i	0.200947	−	0.348051i	0.948834	+	0.315776i	$0.102265\pi$
$858$		0			0
$859$	1.67831e7	+	2.90693e7i	0.776051	+	1.34416i	0.934202	+	0.356745i	$0.116114\pi$
$859$	1.67831e7	+	2.90693e7i	0.776051	+	1.34416i	−0.158151	+	0.987415i	$0.550553\pi$
$860$	−7.03085e6	−	1.21778e7i	−0.324162	−	0.561464i
$861$		0			0
$862$	5.59872e6	−	9.69727e6i	0.256638	−	0.444510i
$863$	−3.90191e7			−1.78341			−0.891703	−	0.452621i	$-0.850489\pi$
$863$	−3.90191e7			−1.78341			−0.891703	+	0.452621i	$0.850489\pi$
$864$		0			0
$865$	−8.78843e6			−0.399366
$866$	−1.18048e7	+	2.04466e7i	−0.534891	+	0.926458i
$867$		0			0
$868$	5.05754e6	+	8.75991e6i	0.227845	+	0.394639i
$869$	−2.23224e6	−	3.86635e6i	−0.100275	−	0.173681i
$870$		0			0
$871$	−5.52852e6	+	9.57567e6i	−0.246924	+	0.427685i
$872$	545920.			0.0243130
$873$		0			0
$874$	2.29440e6			0.101599
$875$	1.10004e7	−	1.90532e7i	0.485721	−	0.841293i
$876$		0			0
$877$	9.06909e6	+	1.57081e7i	0.398166	+	0.689645i	0.993500	−	0.113834i	$-0.0363133\pi$
$877$	9.06909e6	+	1.57081e7i	0.398166	+	0.689645i	−0.595333	+	0.803479i	$0.702980\pi$
$878$	−893024.	−	1.54676e6i	−0.0390955	−	0.0677154i
$879$		0			0
$880$	−506880.	+	877942.i	−0.0220647	+	0.0382172i
$881$	−3.05312e7			−1.32527			−0.662634	−	0.748943i	$-0.730562\pi$
$881$	−3.05312e7			−1.32527			−0.662634	+	0.748943i	$0.730562\pi$
$882$		0			0
$883$	−4.35533e7			−1.87983			−0.939916	−	0.341405i	$-0.889097\pi$
$883$	−4.35533e7			−1.87983			−0.939916	+	0.341405i	$0.889097\pi$
$884$	2.17930e6	−	3.77465e6i	0.0937963	−	0.162460i
$885$		0			0
$886$	−6.99050e6	−	1.21079e7i	−0.299174	−	0.518185i
$887$	−6.70758e6	−	1.16179e7i	−0.286257	−	0.495812i	0.686656	−	0.726983i	$-0.259078\pi$
$887$	−6.70758e6	−	1.16179e7i	−0.286257	−	0.495812i	−0.972913	+	0.231170i	$0.925745\pi$
$888$		0			0
$889$	−1.52240e7	+	2.63687e7i	−0.646062	+	1.11901i
$890$	−8.64389e6			−0.365792
$891$		0			0
$892$	1.12314e7			0.472629
$893$	−9.40704e6	+	1.62935e7i	−0.394752	+	0.683731i
$894$		0			0
$895$	−2.28821e7	−	3.96329e7i	−0.954856	−	1.65386i
$896$	1.44179e6	+	2.49726e6i	0.0599974	+	0.103919i
$897$		0			0
$898$	2.41225e6	−	4.17814e6i	0.0998233	−	0.172899i
$899$	2.00218e7			0.826236
$900$		0			0
$901$	1.29441e7			0.531203
$902$	−2.30328e6	+	3.98940e6i	−0.0942606	+	0.163264i
$903$		0			0
$904$	6.25402e6	+	1.08323e7i	0.254529	+	0.440858i
$905$	−1.24467e7	−	2.15584e7i	−0.505166	−	0.874973i
$906$		0			0
$907$	−1.55408e6	+	2.69175e6i	−0.0627272	+	0.108647i	−0.895684	−	0.444692i	$-0.853313\pi$
$907$	−1.55408e6	+	2.69175e6i	−0.0627272	+	0.108647i	0.832956	+	0.553339i	$0.186646\pi$
$908$	−1.97777e7			−0.796089
$909$		0			0
$910$	3.05733e7			1.22388
$911$	595176.	−	1.03088e6i	0.0237602	−	0.0411538i	−0.853901	−	0.520436i	$-0.825770\pi$
$911$	595176.	−	1.03088e6i	0.0237602	−	0.0411538i	0.877661	+	0.479282i	$0.159103\pi$
$912$		0			0
$913$	−194040.	−	336087.i	−0.00770397	−	0.0133437i
$914$	467092.	+	809027.i	0.0184943	+	0.0320330i
$915$		0			0
$916$	−846640.	+	1.46642e6i	−0.0333396	+	0.0577458i
$917$	−2.66218e7			−1.04547
$918$		0			0
$919$	−4.71996e7			−1.84353			−0.921764	−	0.387752i	$-0.873252\pi$
$919$	−4.71996e7			−1.84353			−0.921764	+	0.387752i	$0.873252\pi$
$920$	−1.26720e6	+	2.19485e6i	−0.0493601	+	0.0854941i
$921$		0			0
$922$	3.48978e6	+	6.04448e6i	0.135198	+	0.234170i
$923$	−2.01348e6	−	3.48745e6i	−0.0777935	−	0.134742i
$924$		0			0
$925$	5.20590e6	−	9.01688e6i	0.200051	−	0.346499i
$926$	1.16715e7			0.447299
$927$		0			0
$928$	5.70778e6			0.217569
$929$	667977.	−	1.15697e6i	0.0253935	−	0.0439828i	−0.853049	−	0.521830i	$-0.825249\pi$
$929$	667977.	−	1.15697e6i	0.0253935	−	0.0439828i	0.878443	+	0.477847i	$0.158583\pi$
$930$		0			0
$931$	−6.77278e6	−	1.17308e7i	−0.256090	−	0.443561i
$932$	−3.50942e6	−	6.07850e6i	−0.132342	−	0.229222i
$933$		0			0
$934$	1.06215e7	−	1.83970e7i	0.398400	−	0.690049i
$935$	1.63944e6			0.0613291
$936$		0			0
$937$	1.47238e7			0.547861			0.273931	−	0.961749i	$-0.411676\pi$
$937$	1.47238e7			0.547861			0.273931	+	0.961749i	$0.411676\pi$
$938$	−5.91501e6	+	1.02451e7i	−0.219507	+	0.380197i
$939$		0			0
$940$	−1.03910e7	−	1.79978e7i	−0.383565	−	0.664355i
$941$	−1.34598e7	−	2.33131e7i	−0.495525	−	0.858274i	0.504462	−	0.863434i	$-0.331691\pi$
$941$	−1.34598e7	−	2.33131e7i	−0.495525	−	0.858274i	−0.999987	+	0.00516005i	$0.998357\pi$
$942$		0			0
$943$	−5.75820e6	+	9.97349e6i	−0.210866	+	0.365231i
$944$	−6.74304e6			−0.246278
$945$		0			0
$946$	−3.19584e6			−0.116107
$947$	−1.86580e6	+	3.23166e6i	−0.0676068	+	0.117098i	−0.897847	−	0.440307i	$-0.854870\pi$
$947$	−1.86580e6	+	3.23166e6i	−0.0676068	+	0.117098i	0.830241	+	0.557405i	$0.188203\pi$
$948$		0			0
$949$	−8.40858e6	−	1.45641e7i	−0.303080	−	0.524950i
$950$	2.35367e6	+	4.07668e6i	0.0846130	+	0.146554i
$951$		0			0
$952$	2.33165e6	−	4.03853e6i	0.0833817	−	0.144421i
$953$	−2.18735e7			−0.780166			−0.390083	−	0.920780i	$-0.627554\pi$
$953$	−2.18735e7			−0.780166			−0.390083	+	0.920780i	$0.627554\pi$
$954$		0			0
$955$	1.75127e7			0.621362
$956$	227712.	−	394409.i	0.00805826	−	0.0139573i
$957$		0			0
$958$	−4.68931e6	−	8.12213e6i	−0.165080	−	0.285928i
$959$	−1.13040e7	−	1.95790e7i	−0.396902	−	0.687455i
$960$		0			0
$961$	7.86334e6	−	1.36197e7i	0.274662	−	0.475729i
$962$	−2.22615e7			−0.775561
$963$		0			0
$964$	1.42810e7			0.494955
$965$	−9.74483e6	+	1.68785e7i	−0.336865	+	0.583468i
$966$		0			0
$967$	−8.80125e6	−	1.52442e7i	−0.302676	−	0.524250i	0.674065	−	0.738672i	$-0.264547\pi$
$967$	−8.80125e6	−	1.52442e7i	−0.302676	−	0.524250i	−0.976741	+	0.214422i	$0.931213\pi$
$968$	−5.03843e6	−	8.72682e6i	−0.172825	−	0.299342i
$969$		0			0
$970$	2.19228e7	−	3.79714e7i	0.748113	−	1.29577i
$971$	−1.67317e7			−0.569497			−0.284749	−	0.958602i	$-0.591910\pi$
$971$	−1.67317e7			−0.569497			−0.284749	+	0.958602i	$0.591910\pi$
$972$		0			0
$973$	2.71385e7			0.918975
$974$	1.96306e7	−	3.40012e7i	0.663035	−	1.14841i
$975$		0			0
$976$	3.97952e6	+	6.89273e6i	0.133723	+	0.231615i
$977$	2.77691e7	+	4.80975e7i	0.930733	+	1.61208i	0.782071	+	0.623189i	$0.214163\pi$
$977$	2.77691e7	+	4.80975e7i	0.930733	+	1.61208i	0.148662	+	0.988888i	$0.452503\pi$
$978$		0			0
$979$	−982260.	+	1.70132e6i	−0.0327544	+	0.0567323i
$980$	1.49625e7			0.497666
$981$		0			0
$982$	−2.37808e7			−0.786951
$983$	−1.93392e7	+	3.34965e7i	−0.638344	+	1.10564i	0.347452	+	0.937698i	$0.387047\pi$
$983$	−1.93392e7	+	3.34965e7i	−0.638344	+	1.10564i	−0.985796	+	0.167947i	$0.946286\pi$
$984$		0			0
$985$	6.64270e6	+	1.15055e7i	0.218149	+	0.377846i
$986$	−4.61527e6	−	7.99389e6i	−0.151184	−	0.261858i
$987$		0			0
$988$	5.03238e6	−	8.71634e6i	0.164014	−	0.284081i
$989$	−7.98960e6			−0.259737
$990$		0			0
$991$	9.58498e6			0.310033			0.155016	−	0.987912i	$-0.450457\pi$
$991$	9.58498e6			0.310033			0.155016	+	0.987912i	$0.450457\pi$
$992$	−1.83910e6	+	3.18542e6i	−0.0593372	+	0.102775i
$993$		0			0
$994$	−2.15424e6	−	3.73125e6i	−0.0691557	−	0.119781i
$995$	−2.15308e7	−	3.72924e7i	−0.689449	−	1.19416i
$996$		0			0
$997$	5.18252e6	−	8.97638e6i	0.165121	−	0.285998i	−0.771577	−	0.636136i	$-0.780532\pi$
$997$	5.18252e6	−	8.97638e6i	0.165121	−	0.285998i	0.936698	+	0.350137i	$0.113865\pi$
$998$	−2.59133e7			−0.823561
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.6.c.h.55.1		2
3.2	odd	2		162.6.c.e.55.1		2
9.2	odd	6		6.6.a.a.1.1	✓	1
9.4	even	3	inner	162.6.c.h.109.1		2
9.5	odd	6		162.6.c.e.109.1		2
9.7	even	3		18.6.a.b.1.1		1
36.7	odd	6		144.6.a.j.1.1		1
36.11	even	6		48.6.a.c.1.1		1
45.2	even	12		150.6.c.b.49.2		2
45.7	odd	12		450.6.c.j.199.1		2
45.29	odd	6		150.6.a.d.1.1		1
45.34	even	6		450.6.a.m.1.1		1
45.38	even	12		150.6.c.b.49.1		2
45.43	odd	12		450.6.c.j.199.2		2
63.2	odd	6		294.6.e.g.67.1		2
63.11	odd	6		294.6.e.g.79.1		2
63.20	even	6		294.6.a.m.1.1		1
63.34	odd	6		882.6.a.a.1.1		1
63.38	even	6		294.6.e.a.79.1		2
63.47	even	6		294.6.e.a.67.1		2
72.11	even	6		192.6.a.g.1.1		1
72.29	odd	6		192.6.a.o.1.1		1
72.43	odd	6		576.6.a.i.1.1		1
72.61	even	6		576.6.a.j.1.1		1
99.65	even	6		726.6.a.a.1.1		1
117.38	odd	6		1014.6.a.c.1.1		1
144.11	even	12		768.6.d.p.385.1		2
144.29	odd	12		768.6.d.c.385.1		2
144.83	even	12		768.6.d.p.385.2		2
144.101	odd	12		768.6.d.c.385.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.6.a.a.1.1	✓	1	9.2	odd	6
18.6.a.b.1.1		1	9.7	even	3
48.6.a.c.1.1		1	36.11	even	6
144.6.a.j.1.1		1	36.7	odd	6
150.6.a.d.1.1		1	45.29	odd	6
150.6.c.b.49.1		2	45.38	even	12
150.6.c.b.49.2		2	45.2	even	12
162.6.c.e.55.1		2	3.2	odd	2
162.6.c.e.109.1		2	9.5	odd	6
162.6.c.h.55.1		2	1.1	even	1	trivial
162.6.c.h.109.1		2	9.4	even	3	inner
192.6.a.g.1.1		1	72.11	even	6
192.6.a.o.1.1		1	72.29	odd	6
294.6.a.m.1.1		1	63.20	even	6
294.6.e.a.67.1		2	63.47	even	6
294.6.e.a.79.1		2	63.38	even	6
294.6.e.g.67.1		2	63.2	odd	6
294.6.e.g.79.1		2	63.11	odd	6
450.6.a.m.1.1		1	45.34	even	6
450.6.c.j.199.1		2	45.7	odd	12
450.6.c.j.199.2		2	45.43	odd	12
576.6.a.i.1.1		1	72.43	odd	6
576.6.a.j.1.1		1	72.61	even	6
726.6.a.a.1.1		1	99.65	even	6
768.6.d.c.385.1		2	144.29	odd	12
768.6.d.c.385.2		2	144.101	odd	12
768.6.d.p.385.1		2	144.11	even	12
768.6.d.p.385.2		2	144.83	even	12
882.6.a.a.1.1		1	63.34	odd	6
1014.6.a.c.1.1		1	117.38	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(-33.0000 - 57.1577i) q^{5} +(-88.0000 + 152.420i) q^{7} -64.0000 q^{8} -264.000 q^{10} +(-30.0000 + 51.9615i) q^{11} +(329.000 + 569.845i) q^{13} +(352.000 + 609.682i) q^{14} +(-128.000 + 221.703i) q^{16} +414.000 q^{17} +956.000 q^{19} +(-528.000 + 914.523i) q^{20} +(120.000 + 207.846i) q^{22} +(300.000 + 519.615i) q^{23} +(-615.500 + 1066.08i) q^{25} +2632.00 q^{26} +2816.00 q^{28} +(2787.00 - 4827.23i) q^{29} +(1796.00 + 3110.76i) q^{31} +(512.000 + 886.810i) q^{32} +(828.000 - 1434.14i) q^{34} +11616.0 q^{35} -8458.00 q^{37} +(1912.00 - 3311.68i) q^{38} +(2112.00 + 3658.09i) q^{40} +(9597.00 + 16622.5i) q^{41} +(-6658.00 + 11532.0i) q^{43} +960.000 q^{44} +2400.00 q^{46} +(-9840.00 + 17043.4i) q^{47} +(-7084.50 - 12270.7i) q^{49} +(2462.00 + 4264.31i) q^{50} +(5264.00 - 9117.52i) q^{52} +31266.0 q^{53} +3960.00 q^{55} +(5632.00 - 9754.91i) q^{56} +(-11148.0 - 19308.9i) q^{58} +(13170.0 + 22811.1i) q^{59} +(15545.0 - 26924.7i) q^{61} +14368.0 q^{62} +4096.00 q^{64} +(21714.0 - 37609.8i) q^{65} +(8402.00 + 14552.7i) q^{67} +(-3312.00 - 5736.55i) q^{68} +(23232.0 - 40239.0i) q^{70} -6120.00 q^{71} -25558.0 q^{73} +(-16916.0 + 29299.4i) q^{74} +(-7648.00 - 13246.7i) q^{76} +(-5280.00 - 9145.23i) q^{77} +(-37204.0 + 64439.2i) q^{79} +16896.0 q^{80} +76776.0 q^{82} +(-3234.00 + 5601.45i) q^{83} +(-13662.0 - 23663.3i) q^{85} +(26632.0 + 46128.0i) q^{86} +(1920.00 - 3325.54i) q^{88} +32742.0 q^{89} -115808. q^{91} +(4800.00 - 8313.84i) q^{92} +(39360.0 + 68173.5i) q^{94} +(-31548.0 - 54642.7i) q^{95} +(-83041.0 + 143831. i) q^{97} -56676.0 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 16 q^{4} - 66 q^{5} - 176 q^{7} - 128 q^{8} - 528 q^{10} - 60 q^{11} + 658 q^{13} + 704 q^{14} - 256 q^{16} + 828 q^{17} + 1912 q^{19} - 1056 q^{20} + 240 q^{22} + 600 q^{23} - 1231 q^{25}+ \cdots - 113352 q^{98}+O(q^{100}) \) 2 * q + 4 * q^2 - 16 * q^4 - 66 * q^5 - 176 * q^7 - 128 * q^8 - 528 * q^10 - 60 * q^11 + 658 * q^13 + 704 * q^14 - 256 * q^16 + 828 * q^17 + 1912 * q^19 - 1056 * q^20 + 240 * q^22 + 600 * q^23 - 1231 * q^25 + 5264 * q^26 + 5632 * q^28 + 5574 * q^29 + 3592 * q^31 + 1024 * q^32 + 1656 * q^34 + 23232 * q^35 - 16916 * q^37 + 3824 * q^38 + 4224 * q^40 + 19194 * q^41 - 13316 * q^43 + 1920 * q^44 + 4800 * q^46 - 19680 * q^47 - 14169 * q^49 + 4924 * q^50 + 10528 * q^52 + 62532 * q^53 + 7920 * q^55 + 11264 * q^56 - 22296 * q^58 + 26340 * q^59 + 31090 * q^61 + 28736 * q^62 + 8192 * q^64 + 43428 * q^65 + 16804 * q^67 - 6624 * q^68 + 46464 * q^70 - 12240 * q^71 - 51116 * q^73 - 33832 * q^74 - 15296 * q^76 - 10560 * q^77 - 74408 * q^79 + 33792 * q^80 + 153552 * q^82 - 6468 * q^83 - 27324 * q^85 + 53264 * q^86 + 3840 * q^88 + 65484 * q^89 - 231616 * q^91 + 9600 * q^92 + 78720 * q^94 - 63096 * q^95 - 166082 * q^97 - 113352 * q^98

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