LMFDB - Embedded newform 294.6.e.g.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,6,Mod(67,294)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(294, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 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("294.67"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	294.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-4,9,-16,66,-72,0,128,-81,264,60] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$47.1528430250$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.67
Dual form			294.6.e.g.79.1

$q$-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} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(33.0000 + 57.1577i) q^{5} -36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(132.000 - 228.631i) q^{10} +(30.0000 - 51.9615i) q^{11} +(72.0000 + 124.708i) q^{12} -658.000 q^{13} +594.000 q^{15} +(-128.000 - 221.703i) q^{16} +(207.000 - 358.535i) q^{17} +(-162.000 + 280.592i) q^{18} +(-478.000 - 827.920i) q^{19} -1056.00 q^{20} -240.000 q^{22} +(-300.000 - 519.615i) q^{23} +(288.000 - 498.831i) q^{24} +(-615.500 + 1066.08i) q^{25} +(1316.00 + 2279.38i) q^{26} -729.000 q^{27} +5574.00 q^{29} +(-1188.00 - 2057.68i) q^{30} +(1796.00 - 3110.76i) q^{31} +(-512.000 + 886.810i) q^{32} +(-270.000 - 467.654i) q^{33} -1656.00 q^{34} +1296.00 q^{36} +(4229.00 + 7324.84i) q^{37} +(-1912.00 + 3311.68i) q^{38} +(-2961.00 + 5128.60i) q^{39} +(2112.00 + 3658.09i) q^{40} +19194.0 q^{41} +13316.0 q^{43} +(480.000 + 831.384i) q^{44} +(2673.00 - 4629.77i) q^{45} +(-1200.00 + 2078.46i) q^{46} +(9840.00 + 17043.4i) q^{47} -2304.00 q^{48} +4924.00 q^{50} +(-1863.00 - 3226.81i) q^{51} +(5264.00 - 9117.52i) q^{52} +(15633.0 - 27077.2i) q^{53} +(1458.00 + 2525.33i) q^{54} +3960.00 q^{55} -8604.00 q^{57} +(-11148.0 - 19308.9i) q^{58} +(-13170.0 + 22811.1i) q^{59} +(-4752.00 + 8230.71i) q^{60} +(15545.0 + 26924.7i) q^{61} -14368.0 q^{62} +4096.00 q^{64} +(-21714.0 - 37609.8i) q^{65} +(-1080.00 + 1870.61i) q^{66} +(8402.00 - 14552.7i) q^{67} +(3312.00 + 5736.55i) q^{68} -5400.00 q^{69} +6120.00 q^{71} +(-2592.00 - 4489.48i) q^{72} +(12779.0 - 22133.9i) q^{73} +(16916.0 - 29299.4i) q^{74} +(5539.50 + 9594.70i) q^{75} +15296.0 q^{76} +23688.0 q^{78} +(-37204.0 - 64439.2i) q^{79} +(8448.00 - 14632.4i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-38388.0 - 66490.0i) q^{82} -6468.00 q^{83} +27324.0 q^{85} +(-26632.0 - 46128.0i) q^{86} +(25083.0 - 43445.0i) q^{87} +(1920.00 - 3325.54i) q^{88} +(16371.0 + 28355.4i) q^{89} -21384.0 q^{90} +9600.00 q^{92} +(-16164.0 - 27996.9i) q^{93} +(39360.0 - 68173.5i) q^{94} +(31548.0 - 54642.7i) q^{95} +(4608.00 + 7981.29i) q^{96} +166082. q^{97} -4860.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} + 9 q^{3} - 16 q^{4} + 66 q^{5} - 72 q^{6} + 128 q^{8} - 81 q^{9} + 264 q^{10} + 60 q^{11} + 144 q^{12} - 1316 q^{13} + 1188 q^{15} - 256 q^{16} + 414 q^{17} - 324 q^{18} - 956 q^{19} - 2112 q^{20}+ \cdots - 9720 q^{99}+O(q^{100}) $ 2 * q - 4 * q^2 + 9 * q^3 - 16 * q^4 + 66 * q^5 - 72 * q^6 + 128 * q^8 - 81 * q^9 + 264 * q^10 + 60 * q^11 + 144 * q^12 - 1316 * q^13 + 1188 * q^15 - 256 * q^16 + 414 * q^17 - 324 * q^18 - 956 * q^19 - 2112 * q^20 - 480 * q^22 - 600 * q^23 + 576 * q^24 - 1231 * q^25 + 2632 * q^26 - 1458 * q^27 + 11148 * q^29 - 2376 * q^30 + 3592 * q^31 - 1024 * q^32 - 540 * q^33 - 3312 * q^34 + 2592 * q^36 + 8458 * q^37 - 3824 * q^38 - 5922 * q^39 + 4224 * q^40 + 38388 * q^41 + 26632 * q^43 + 960 * q^44 + 5346 * q^45 - 2400 * q^46 + 19680 * q^47 - 4608 * q^48 + 9848 * q^50 - 3726 * q^51 + 10528 * q^52 + 31266 * q^53 + 2916 * q^54 + 7920 * q^55 - 17208 * q^57 - 22296 * q^58 - 26340 * q^59 - 9504 * q^60 + 31090 * q^61 - 28736 * q^62 + 8192 * q^64 - 43428 * q^65 - 2160 * q^66 + 16804 * q^67 + 6624 * q^68 - 10800 * q^69 + 12240 * q^71 - 5184 * q^72 + 25558 * q^73 + 33832 * q^74 + 11079 * q^75 + 30592 * q^76 + 47376 * q^78 - 74408 * q^79 + 16896 * q^80 - 6561 * q^81 - 76776 * q^82 - 12936 * q^83 + 54648 * q^85 - 53264 * q^86 + 50166 * q^87 + 3840 * q^88 + 32742 * q^89 - 42768 * q^90 + 19200 * q^92 - 32328 * q^93 + 78720 * q^94 + 63096 * q^95 + 9216 * q^96 + 332164 * q^97 - 9720 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	4.50000	−	7.79423i	0.288675	−	0.500000i
$3$	4.50000	−	7.79423i	0.288675	−	0.500000i
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	33.0000	+	57.1577i	0.590322	+	1.02247i	0.994189	+	0.107650i	$0.0343325\pi$
$5$	33.0000	+	57.1577i	0.590322	+	1.02247i	−0.403867	+	0.914818i	$0.632334\pi$
$6$	−36.0000			−0.408248
$7$		0			0
$7$		0			0
$8$	64.0000			0.353553
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	132.000	−	228.631i	0.417421	−	0.722994i
$11$	30.0000	−	51.9615i	0.0747549	−	0.129479i	−0.826225	−	0.563341i	$-0.809516\pi$
$11$	30.0000	−	51.9615i	0.0747549	−	0.129479i	0.900980	+	0.433861i	$0.142849\pi$
$12$	72.0000	+	124.708i	0.144338	+	0.250000i
$13$	−658.000			−1.07986			−0.539930	−	0.841710i	$-0.681549\pi$
$13$	−658.000			−1.07986			−0.539930	+	0.841710i	$0.681549\pi$
$14$		0			0
$15$	594.000			0.681645
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	207.000	−	358.535i	0.173719	−	0.300891i	−0.765998	−	0.642843i	$-0.777755\pi$
$17$	207.000	−	358.535i	0.173719	−	0.300891i	0.939717	+	0.341952i	$0.111088\pi$
$18$	−162.000	+	280.592i	−0.117851	+	0.204124i
$19$	−478.000	−	827.920i	−0.303769	−	0.526144i	0.673217	−	0.739445i	$-0.264912\pi$
$19$	−478.000	−	827.920i	−0.303769	−	0.526144i	−0.976987	+	0.213301i	$0.931579\pi$
$20$	−1056.00			−0.590322
$21$		0			0
$22$	−240.000			−0.105719
$23$	−300.000	−	519.615i	−0.118250	−	0.204815i	0.800824	−	0.598900i	$-0.204395\pi$
$23$	−300.000	−	519.615i	−0.118250	−	0.204815i	−0.919074	+	0.394084i	$0.871062\pi$
$24$	288.000	−	498.831i	0.102062	−	0.176777i
$25$	−615.500	+	1066.08i	−0.196960	+	0.341145i
$26$	1316.00	+	2279.38i	0.381788	+	0.661277i
$27$	−729.000			−0.192450
$28$		0			0
$29$	5574.00			1.23076			0.615378	−	0.788232i	$-0.289003\pi$
$29$	5574.00			1.23076			0.615378	+	0.788232i	$0.289003\pi$
$30$	−1188.00	−	2057.68i	−0.240998	−	0.417421i
$31$	1796.00	−	3110.76i	0.335662	−	0.581384i	−0.647950	−	0.761683i	$-0.724373\pi$
$31$	1796.00	−	3110.76i	0.335662	−	0.581384i	0.983612	+	0.180299i	$0.0577067\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$	−270.000	−	467.654i	−0.0431597	−	0.0747549i
$34$	−1656.00			−0.245676
$35$		0			0
$36$	1296.00			0.166667
$37$	4229.00	+	7324.84i	0.507848	+	0.879618i	0.999959	+	0.00908542i	$0.00289202\pi$
$37$	4229.00	+	7324.84i	0.507848	+	0.879618i	−0.492111	+	0.870532i	$0.663775\pi$
$38$	−1912.00	+	3311.68i	−0.214797	+	0.372040i
$39$	−2961.00	+	5128.60i	−0.311729	+	0.539930i
$40$	2112.00	+	3658.09i	0.208710	+	0.361497i
$41$	19194.0			1.78322			0.891612	−	0.452800i	$-0.149575\pi$
$41$	19194.0			1.78322			0.891612	+	0.452800i	$0.149575\pi$
$42$		0			0
$43$	13316.0			1.09825			0.549127	−	0.835739i	$-0.314960\pi$
$43$	13316.0			1.09825			0.549127	+	0.835739i	$0.314960\pi$
$44$	480.000	+	831.384i	0.0373774	+	0.0647396i
$45$	2673.00	−	4629.77i	0.196774	−	0.340823i
$46$	−1200.00	+	2078.46i	−0.0836155	+	0.144826i
$47$	9840.00	+	17043.4i	0.649756	+	1.12541i	0.983181	+	0.182634i	$0.0584624\pi$
$47$	9840.00	+	17043.4i	0.649756	+	1.12541i	−0.333425	+	0.942777i	$0.608204\pi$
$48$	−2304.00			−0.144338
$49$		0			0
$50$	4924.00			0.278544
$51$	−1863.00	−	3226.81i	−0.100297	−	0.173719i
$52$	5264.00	−	9117.52i	0.269965	−	0.467593i
$53$	15633.0	−	27077.2i	0.764456	−	1.32408i	−0.176077	−	0.984376i	$-0.556341\pi$
$53$	15633.0	−	27077.2i	0.764456	−	1.32408i	0.940534	−	0.339701i	$-0.110326\pi$
$54$	1458.00	+	2525.33i	0.0680414	+	0.117851i
$55$	3960.00			0.176518
$56$		0			0
$57$	−8604.00			−0.350763
$58$	−11148.0	−	19308.9i	−0.435138	−	0.753681i
$59$	−13170.0	+	22811.1i	−0.492556	+	0.853132i	−0.999963	−	0.00857419i	$-0.997271\pi$
$59$	−13170.0	+	22811.1i	−0.492556	+	0.853132i	0.507407	+	0.861706i	$0.330604\pi$
$60$	−4752.00	+	8230.71i	−0.170411	+	0.295161i
$61$	15545.0	+	26924.7i	0.534892	+	0.926460i	0.999169	+	0.0407699i	$0.0129811\pi$
$61$	15545.0	+	26924.7i	0.534892	+	0.926460i	−0.464277	+	0.885690i	$0.653686\pi$
$62$	−14368.0			−0.474698
$63$		0			0
$64$	4096.00			0.125000
$65$	−21714.0	−	37609.8i	−0.637465	−	1.10412i
$66$	−1080.00	+	1870.61i	−0.0305186	+	0.0528597i
$67$	8402.00	−	14552.7i	0.228663	−	0.396056i	−0.728749	−	0.684781i	$-0.759898\pi$
$67$	8402.00	−	14552.7i	0.228663	−	0.396056i	0.957412	+	0.288725i	$0.0932313\pi$
$68$	3312.00	+	5736.55i	0.0868596	+	0.150445i
$69$	−5400.00			−0.136544
$70$		0			0
$71$	6120.00			0.144081			0.0720403	−	0.997402i	$-0.477049\pi$
$71$	6120.00			0.144081			0.0720403	+	0.997402i	$0.477049\pi$
$72$	−2592.00	−	4489.48i	−0.0589256	−	0.102062i
$73$	12779.0	−	22133.9i	0.280666	−	0.486128i	−0.690883	−	0.722967i	$-0.742778\pi$
$73$	12779.0	−	22133.9i	0.280666	−	0.486128i	0.971549	+	0.236839i	$0.0761114\pi$
$74$	16916.0	−	29299.4i	0.359102	−	0.621984i
$75$	5539.50	+	9594.70i	0.113715	+	0.196960i
$76$	15296.0			0.303769
$77$		0			0
$78$	23688.0			0.440851
$79$	−37204.0	−	64439.2i	−0.670690	−	1.16167i	−0.977709	−	0.209966i	$-0.932665\pi$
$79$	−37204.0	−	64439.2i	−0.670690	−	1.16167i	0.307019	−	0.951704i	$-0.400669\pi$
$80$	8448.00	−	14632.4i	0.147580	−	0.255617i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	−38388.0	−	66490.0i	−0.630465	−	1.09200i
$83$	−6468.00			−0.103056			−0.0515282	−	0.998672i	$-0.516409\pi$
$83$	−6468.00			−0.103056			−0.0515282	+	0.998672i	$0.516409\pi$
$84$		0			0
$85$	27324.0			0.410201
$86$	−26632.0	−	46128.0i	−0.388291	−	0.672540i
$87$	25083.0	−	43445.0i	0.355289	−	0.615378i
$88$	1920.00	−	3325.54i	0.0264298	−	0.0457778i
$89$	16371.0	+	28355.4i	0.219079	+	0.379455i	0.954527	−	0.298126i	$-0.0963615\pi$
$89$	16371.0	+	28355.4i	0.219079	+	0.379455i	−0.735448	+	0.677581i	$0.763028\pi$
$90$	−21384.0			−0.278280
$91$		0			0
$92$	9600.00			0.118250
$93$	−16164.0	−	27996.9i	−0.193795	−	0.335662i
$94$	39360.0	−	68173.5i	0.459447	−	0.795786i
$95$	31548.0	−	54642.7i	0.358643	−	0.621189i
$96$	4608.00	+	7981.29i	0.0510310	+	0.0883883i
$97$	166082.			1.79223			0.896114	−	0.443824i	$-0.146378\pi$
$97$	166082.			1.79223			0.896114	+	0.443824i	$0.146378\pi$
$98$		0			0
$99$	−4860.00			−0.0498366
$100$	−9848.00	−	17057.2i	−0.0984800	−	0.170572i
$101$	11001.0	−	19054.3i	0.107307	−	0.185861i	−0.807371	−	0.590044i	$-0.799111\pi$
$101$	11001.0	−	19054.3i	0.107307	−	0.185861i	0.914678	+	0.404182i	$0.132444\pi$
$102$	−7452.00	+	12907.2i	−0.0709206	+	0.122838i
$103$	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	$0.713345\pi$
$104$	−42112.0			−0.381788
$105$		0			0
$106$	−125064.			−1.08110
$107$	−113994.	−	197443.i	−0.962548	−	1.66718i	−0.716062	−	0.698036i	$-0.754057\pi$
$107$	−113994.	−	197443.i	−0.962548	−	1.66718i	−0.246486	−	0.969146i	$-0.579276\pi$
$108$	5832.00	−	10101.3i	0.0481125	−	0.0833333i
$109$	4265.00	−	7387.20i	0.0343837	−	0.0595543i	−0.848321	−	0.529482i	$-0.822386\pi$
$109$	4265.00	−	7387.20i	0.0343837	−	0.0595543i	0.882705	+	0.469927i	$0.155720\pi$
$110$	−7920.00	−	13717.8i	−0.0624085	−	0.108095i
$111$	76122.0			0.586412
$112$		0			0
$113$	−195438.			−1.43984			−0.719918	−	0.694059i	$-0.755821\pi$
$113$	−195438.			−1.43984			−0.719918	+	0.694059i	$0.755821\pi$
$114$	17208.0	+	29805.1i	0.124013	+	0.214797i
$115$	19800.0	−	34294.6i	0.139611	−	0.241814i
$116$	−44592.0	+	77235.6i	−0.307689	+	0.532933i
$117$	26649.0	+	46157.4i	0.179977	+	0.311729i
$118$	105360.			0.696580
$119$		0			0
$120$	38016.0			0.240998
$121$	78725.5	+	136357.i	0.488823	+	0.846667i
$122$	62180.0	−	107699.i	0.378226	−	0.655106i
$123$	86373.0	−	149602.i	0.514772	−	0.891612i
$124$	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
$129$	59922.0	−	103788.i	0.317039	−	0.549127i
$130$	−86856.0	+	150439.i	−0.450756	+	0.780732i
$131$	−75630.0	−	130995.i	−0.385049	−	0.666924i	0.606727	−	0.794910i	$-0.292482\pi$
$131$	−75630.0	−	130995.i	−0.385049	−	0.666924i	−0.991776	+	0.127986i	$0.959149\pi$
$132$	8640.00			0.0431597
$133$		0			0
$134$	−67216.0			−0.323378
$135$	−24057.0	−	41667.9i	−0.113608	−	0.196774i
$136$	13248.0	−	22946.2i	0.0614190	−	0.106381i
$137$	64227.0	−	111244.i	0.292359	−	0.506380i	−0.682008	−	0.731345i	$-0.738893\pi$
$137$	64227.0	−	111244.i	0.292359	−	0.506380i	0.974367	+	0.224964i	$0.0722265\pi$
$138$	10800.0	+	18706.1i	0.0482754	+	0.0836155i
$139$	154196.			0.676918			0.338459	−	0.940981i	$-0.390094\pi$
$139$	154196.			0.676918			0.338459	+	0.940981i	$0.390094\pi$
$140$		0			0
$141$	177120.			0.750274
$142$	−12240.0	−	21200.3i	−0.0509402	−	0.0882310i
$143$	−19740.0	+	34190.7i	−0.0807248	+	0.139819i
$144$	−10368.0	+	17957.9i	−0.0416667	+	0.0721688i
$145$	183942.	+	318597.i	0.726542	+	1.25841i
$146$	−102232.			−0.396922
$147$		0			0
$148$	−135328.			−0.507848
$149$	−14727.0	−	25507.9i	−0.0543436	−	0.0941259i	0.837574	−	0.546324i	$-0.183973\pi$
$149$	−14727.0	−	25507.9i	−0.0543436	−	0.0941259i	−0.891917	+	0.452198i	$0.850640\pi$
$150$	22158.0	−	38378.8i	0.0804086	−	0.139272i
$151$	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	$0.0481394\pi$
$152$	−30592.0	−	52986.9i	−0.107399	−	0.186020i
$153$	−33534.0			−0.115813
$154$		0			0
$155$	237072.			0.792594
$156$	−47376.0	−	82057.6i	−0.155864	−	0.269965i
$157$	−68071.0	+	117902.i	−0.220401	+	0.381745i	−0.954930	−	0.296832i	$-0.904070\pi$
$157$	−68071.0	+	117902.i	−0.220401	+	0.381745i	0.734529	+	0.678577i	$0.237403\pi$
$158$	−148816.	+	257757.i	−0.474250	+	0.821424i
$159$	−140697.	−	243694.i	−0.441359	−	0.764456i
$160$	−67584.0			−0.208710
$161$		0			0
$162$	26244.0			0.0785674
$163$	85562.0	+	148198.i	0.252239	+	0.436890i	0.964142	−	0.265387i	$-0.0854998\pi$
$163$	85562.0	+	148198.i	0.252239	+	0.436890i	−0.711903	+	0.702278i	$0.752166\pi$
$164$	−153552.	+	265960.i	−0.445806	+	0.772159i
$165$	17820.0	−	30865.1i	0.0509563	−	0.0882589i
$166$	12936.0	+	22405.8i	0.0364359	+	0.0631089i
$167$	−676200.			−1.87622			−0.938110	−	0.346336i	$-0.887426\pi$
$167$	−676200.			−1.87622			−0.938110	+	0.346336i	$0.887426\pi$
$168$		0			0
$169$	61671.0			0.166098
$170$	−54648.0	−	94653.1i	−0.145028	−	0.251196i
$171$	−38718.0	+	67061.5i	−0.101256	+	0.175381i
$172$	−106528.	+	184512.i	−0.274563	+	0.475558i
$173$	−66579.0	−	115318.i	−0.169131	−	0.292943i	0.768984	−	0.639268i	$-0.220763\pi$
$173$	−66579.0	−	115318.i	−0.169131	−	0.292943i	−0.938114	+	0.346325i	$0.887429\pi$
$174$	−200664.			−0.502454
$175$		0			0
$176$	−15360.0			−0.0373774
$177$	118530.	+	205300.i	0.284377	+	0.492556i
$178$	65484.0	−	113422.i	0.154912	−	0.268316i
$179$	346698.	−	600499.i	0.808758	−	1.40081i	−0.104966	−	0.994476i	$-0.533473\pi$
$179$	346698.	−	600499.i	0.808758	−	1.40081i	0.913724	−	0.406335i	$-0.133193\pi$
$180$	42768.0	+	74076.3i	0.0983870	+	0.170411i
$181$	377174.			0.855747			0.427873	−	0.903839i	$-0.359263\pi$
$181$	377174.			0.855747			0.427873	+	0.903839i	$0.359263\pi$
$182$		0			0
$183$	279810.			0.617640
$184$	−19200.0	−	33255.4i	−0.0418077	−	0.0724131i
$185$	−279114.	+	483440.i	−0.599587	+	1.03852i
$186$	−64656.0	+	111987.i	−0.137033	+	0.237349i
$187$	−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	$-0.0819068\pi$
$191$	132672.	+	229795.i	0.263145	+	0.455781i	−0.703931	+	0.710269i	$0.748573\pi$
$192$	18432.0	−	31925.2i	0.0360844	−	0.0625000i
$193$	−147649.	+	255736.i	−0.285323	+	0.494194i	−0.972688	−	0.232118i	$-0.925434\pi$
$193$	−147649.	+	255736.i	−0.285323	+	0.494194i	0.687364	+	0.726313i	$0.258768\pi$
$194$	−332164.	−	575325.i	−0.633648	−	1.09751i
$195$	−390852.			−0.736081
$196$		0			0
$197$	201294.			0.369543			0.184772	−	0.982781i	$-0.440845\pi$
$197$	201294.			0.369543			0.184772	+	0.982781i	$0.440845\pi$
$198$	9720.00	+	16835.5i	0.0176199	+	0.0305186i
$199$	−326224.	+	565037.i	−0.583960	+	1.01145i	0.411044	+	0.911615i	$0.365164\pi$
$199$	−326224.	+	565037.i	−0.583960	+	1.01145i	−0.995004	+	0.0998332i	$0.968169\pi$
$200$	−39392.0	+	68228.9i	−0.0696359	+	0.120613i
$201$	−75618.0	−	130974.i	−0.132019	−	0.228663i
$202$	−88008.0			−0.151755
$203$		0			0
$204$	59616.0			0.100297
$205$	633402.	+	1.09708e6i	1.05268	+	1.82329i
$206$	158528.	−	274579.i	0.260278	−	0.450815i
$207$	−24300.0	+	42088.8i	−0.0394167	+	0.0682718i
$208$	84224.0	+	145880.i	0.134983	+	0.233797i
$209$	−57360.0			−0.0908330
$210$		0			0
$211$	−1.14706e6			−1.77370			−0.886850	−	0.462058i	$-0.847111\pi$
$211$	−1.14706e6			−1.77370			−0.886850	+	0.462058i	$0.847111\pi$
$212$	250128.	+	433234.i	0.382228	+	0.662039i
$213$	27540.0	−	47700.7i	0.0415925	−	0.0720403i
$214$	−455976.	+	789774.i	−0.680624	+	1.17888i
$215$	439428.	+	761112.i	0.648323	+	1.12293i
$216$	−46656.0			−0.0680414
$217$		0			0
$218$	−34120.0			−0.0486259
$219$	−115011.	−	199205.i	−0.162043	−	0.280666i
$220$	−31680.0	+	54871.4i	−0.0441294	+	0.0764344i
$221$	−136206.	+	235916.i	−0.187593	+	0.324920i
$222$	−152244.	−	263694.i	−0.207328	−	0.359102i
$223$	701960.			0.945258			0.472629	−	0.881262i	$-0.343305\pi$
$223$	701960.			0.945258			0.472629	+	0.881262i	$0.343305\pi$
$224$		0			0
$225$	99711.0			0.131307
$226$	390876.	+	677017.i	0.509059	+	0.881716i
$227$	−618054.	+	1.07050e6i	−0.796089	+	1.37887i	0.126056	+	0.992023i	$0.459768\pi$
$227$	−618054.	+	1.07050e6i	−0.796089	+	1.37887i	−0.922145	+	0.386844i	$0.873565\pi$
$228$	68832.0	−	119221.i	0.0876906	−	0.151885i
$229$	−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	$0.854574\pi$
$230$	−158400.			−0.197440
$231$		0			0
$232$	356736.			0.435138
$233$	219339.	+	379906.i	0.264683	+	0.458444i	0.967481	−	0.252946i	$-0.0813993\pi$
$233$	219339.	+	379906.i	0.264683	+	0.458444i	−0.702798	+	0.711390i	$0.748066\pi$
$234$	106596.	−	184630.i	0.127263	−	0.220426i
$235$	−649440.	+	1.12486e6i	−0.767131	+	1.32871i
$236$	−210720.	−	364978.i	−0.246278	−	0.426566i
$237$	−669672.			−0.774446
$238$		0			0
$239$	28464.0			0.0322330			0.0161165	−	0.999870i	$-0.494870\pi$
$239$	28464.0			0.0322330			0.0161165	+	0.999870i	$0.494870\pi$
$240$	−76032.0	−	131691.i	−0.0852056	−	0.147580i
$241$	−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	$0.331482\pi$
$242$	314902.	−	545426.i	0.345650	−	0.598684i
$243$	29524.5	+	51137.9i	0.0320750	+	0.0555556i
$244$	−497440.			−0.534892
$245$		0			0
$246$	−690984.			−0.727998
$247$	314524.	+	544772.i	0.328028	+	0.568162i
$248$	114944.	−	199089.i	0.118674	−	0.205550i
$249$	−29106.0	+	50413.1i	−0.0297498	+	0.0515282i
$250$	−250008.	−	433027.i	−0.252990	−	0.438192i
$251$	−110124.			−0.110331			−0.0551655	−	0.998477i	$-0.517569\pi$
$251$	−110124.			−0.110331			−0.0551655	+	0.998477i	$0.517569\pi$
$252$		0			0
$253$	−36000.0			−0.0353591
$254$	−346000.	−	599290.i	−0.336505	−	0.582844i
$255$	122958.	−	212970.i	0.118415	−	0.205101i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−70401.0	−	121938.i	−0.0664884	−	0.115161i	0.830865	−	0.556474i	$-0.187846\pi$
$257$	−70401.0	−	121938.i	−0.0664884	−	0.115161i	−0.897353	+	0.441313i	$0.854513\pi$
$258$	−479376.			−0.448360
$259$		0			0
$260$	694848.			0.637465
$261$	−225747.	−	391005.i	−0.205126	−	0.355289i
$262$	−302520.	+	523980.i	−0.272271	+	0.471587i
$263$	469380.	−	812990.i	0.418442	−	0.724763i	−0.577341	−	0.816503i	$-0.695910\pi$
$263$	469380.	−	812990.i	0.418442	−	0.724763i	0.995783	+	0.0917404i	$0.0292430\pi$
$264$	−17280.0	−	29929.8i	−0.0152593	−	0.0264298i
$265$	2.06356e6			1.80510
$266$		0			0
$267$	294678.			0.252970
$268$	134432.	+	232843.i	0.114331	+	0.198028i
$269$	557253.	−	965191.i	0.469539	−	0.813265i	−0.529854	−	0.848089i	$-0.677753\pi$
$269$	557253.	−	965191.i	0.469539	−	0.813265i	0.999393	+	0.0348231i	$0.0110868\pi$
$270$	−96228.0	+	166672.i	−0.0803326	+	0.139140i
$271$	−283852.	−	491646.i	−0.234784	−	0.406658i	0.724426	−	0.689353i	$-0.242105\pi$
$271$	−283852.	−	491646.i	−0.234784	−	0.406658i	−0.959210	+	0.282695i	$0.908772\pi$
$272$	−105984.			−0.0868596
$273$		0			0
$274$	−513816.			−0.413458
$275$	36930.0	+	63964.6i	0.0294474	+	0.0510045i
$276$	43200.0	−	74824.6i	0.0341359	−	0.0591251i
$277$	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	$0.00910280\pi$
$278$	−308392.	−	534151.i	−0.239327	−	0.414526i
$279$	−290952.			−0.223775
$280$		0			0
$281$	687738.			0.519586			0.259793	−	0.965664i	$-0.416346\pi$
$281$	687738.			0.519586			0.259793	+	0.965664i	$0.416346\pi$
$282$	−354240.	−	613562.i	−0.265262	−	0.459447i
$283$	415454.	−	719587.i	0.308359	−	0.534094i	−0.669644	−	0.742682i	$-0.733553\pi$
$283$	415454.	−	719587.i	0.308359	−	0.534094i	0.978004	+	0.208588i	$0.0668868\pi$
$284$	−48960.0	+	84801.2i	−0.0360202	+	0.0623887i
$285$	−283932.	−	491785.i	−0.207063	−	0.358643i
$286$	157920.			0.114162
$287$		0			0
$288$	82944.0			0.0589256
$289$	624230.	+	1.08120e6i	0.439643	+	0.761484i
$290$	735768.	−	1.27439e6i	0.513743	−	0.889829i
$291$	747369.	−	1.29448e6i	0.517372	−	0.896114i
$292$	204464.	+	354142.i	0.140333	+	0.243064i
$293$	−1.31263e6			−0.893248			−0.446624	−	0.894722i	$-0.647374\pi$
$293$	−1.31263e6			−0.893248			−0.446624	+	0.894722i	$0.647374\pi$
$294$		0			0
$295$	−1.73844e6			−1.16307
$296$	270656.	+	468790.i	0.179551	+	0.310992i
$297$	−21870.0	+	37880.0i	−0.0143866	+	0.0249183i
$298$	−58908.0	+	102032.i	−0.0384267	+	0.0665571i
$299$	197400.	+	341907.i	0.127694	+	0.221172i
$300$	−177264.			−0.113715
$301$		0			0
$302$	−815488.			−0.514518
$303$	−99009.0	−	171489.i	−0.0619538	−	0.107307i
$304$	−122368.	+	211948.i	−0.0759423	+	0.131536i
$305$	−1.02597e6	+	1.77703e6i	−0.631517	+	1.09382i
$306$	67068.0	+	116165.i	0.0409460	+	0.0709206i
$307$	1.69022e6			1.02352			0.511761	−	0.859128i	$-0.328993\pi$
$307$	1.69022e6			1.02352			0.511761	+	0.859128i	$0.328993\pi$
$308$		0			0
$309$	713376.			0.425033
$310$	−474144.	−	821241.i	−0.280224	−	0.485363i
$311$	751020.	−	1.30080e6i	0.440302	−	0.762625i	−0.557410	−	0.830238i	$-0.688205\pi$
$311$	751020.	−	1.30080e6i	0.440302	−	0.762625i	0.997712	+	0.0676123i	$0.0215381\pi$
$312$	−189504.	+	328231.i	−0.110213	+	0.190894i
$313$	−405421.	−	702210.i	−0.233908	−	0.405141i	0.725047	−	0.688700i	$-0.241818\pi$
$313$	−405421.	−	702210.i	−0.233908	−	0.405141i	−0.958955	+	0.283559i	$0.908485\pi$
$314$	544568.			0.311694
$315$		0			0
$316$	1.19053e6			0.670690
$317$	−451779.	−	782504.i	−0.252510	−	0.437359i	0.711707	−	0.702477i	$-0.247923\pi$
$317$	−451779.	−	782504.i	−0.252510	−	0.437359i	−0.964216	+	0.265117i	$0.914589\pi$
$318$	−562788.	+	974777.i	−0.312088	+	0.540552i
$319$	167220.	−	289634.i	0.0920050	−	0.159357i
$320$	135168.	+	234118.i	0.0737902	+	0.127808i
$321$	−2.05189e6			−1.11146
$322$		0			0
$323$	−395784.			−0.211082
$324$	−52488.0	−	90911.9i	−0.0277778	−	0.0481125i
$325$	404999.	−	701479.i	0.212689	−	0.368389i
$326$	342248.	−	592791.i	0.178360	−	0.308928i
$327$	−38385.0	−	66484.8i	−0.0198514	−	0.0343837i
$328$	1.22842e6			0.630465
$329$		0			0
$330$	−142560.			−0.0720631
$331$	−560986.	−	971656.i	−0.281438	−	0.487464i	0.690301	−	0.723522i	$-0.257478\pi$
$331$	−560986.	−	971656.i	−0.281438	−	0.487464i	−0.971739	+	0.236058i	$0.924145\pi$
$332$	51744.0	−	89623.2i	0.0257641	−	0.0446247i
$333$	342549.	−	593312.i	0.169283	−	0.293206i
$334$	1.35240e6	+	2.34243e6i	0.663344	+	1.14895i
$335$	1.10906e6			0.539939
$336$		0			0
$337$	−2.75217e6			−1.32008			−0.660041	−	0.751229i	$-0.729461\pi$
$337$	−2.75217e6			−1.32008			−0.660041	+	0.751229i	$0.729461\pi$
$338$	−123342.	−	213635.i	−0.0587245	−	0.101714i
$339$	−879471.	+	1.52329e6i	−0.415645	+	0.719918i
$340$	−218592.	+	378612.i	−0.102550	+	0.177622i
$341$	−107760.	−	186646.i	−0.0501847	−	0.0869225i
$342$	309744.			0.143198
$343$		0			0
$344$	852224.			0.388291
$345$	−178200.	−	308651.i	−0.0806046	−	0.139611i
$346$	−266316.	+	461273.i	−0.119593	+	0.207142i
$347$	−958746.	+	1.66060e6i	−0.427445	+	0.740356i	−0.996645	−	0.0818428i	$-0.973919\pi$
$347$	−958746.	+	1.66060e6i	−0.427445	+	0.740356i	0.569201	+	0.822199i	$0.307253\pi$
$348$	401328.	+	695120.i	0.177644	+	0.307689i
$349$	1.83659e6			0.807140			0.403570	−	0.914949i	$-0.367769\pi$
$349$	1.83659e6			0.807140			0.403570	+	0.914949i	$0.367769\pi$
$350$		0			0
$351$	479682.			0.207819
$352$	30720.0	+	53208.6i	0.0132149	+	0.0228889i
$353$	311007.	−	538680.i	0.132841	−	0.230088i	−0.791929	−	0.610613i	$-0.790923\pi$
$353$	311007.	−	538680.i	0.132841	−	0.230088i	0.924771	+	0.380525i	$0.124257\pi$
$354$	474120.	−	821200.i	0.201085	−	0.348290i
$355$	201960.	+	349805.i	0.0850539	+	0.147318i
$356$	−523872.			−0.219079
$357$		0			0
$358$	−2.77358e6			−1.14376
$359$	−1.87031e6	−	3.23947e6i	−0.765909	−	1.32659i	−0.939765	−	0.341822i	$-0.888956\pi$
$359$	−1.87031e6	−	3.23947e6i	−0.765909	−	1.32659i	0.173856	−	0.984771i	$-0.444377\pi$
$360$	171072.	−	296305.i	0.0695701	−	0.120499i
$361$	781082.	−	1.35287e6i	0.315448	−	0.546373i
$362$	−754348.	−	1.30657e6i	−0.302552	−	0.524036i
$363$	1.41706e6			0.564445
$364$		0			0
$365$	1.68683e6			0.662733
$366$	−559620.	−	969290.i	−0.218369	−	0.378226i
$367$	−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	$0.167668\pi$
$368$	−76800.0	+	133022.i	−0.0295625	+	0.0512038i
$369$	−777357.	−	1.34642e6i	−0.297204	−	0.514772i
$370$	2.23291e6			0.847944
$371$		0			0
$372$	517248.			0.193795
$373$	−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
$375$	562518.	−	974310.i	0.206566	−	0.357782i
$376$	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
$381$	778500.	−	1.34840e6i	0.274755	−	0.475890i
$382$	530688.	−	919179.i	0.186072	−	0.322286i
$383$	1.48992e6	+	2.58062e6i	0.518998	+	0.898932i	0.999756	+	0.0220782i	$0.00702828\pi$
$383$	1.48992e6	+	2.58062e6i	0.518998	+	0.898932i	−0.480758	+	0.876853i	$0.659638\pi$
$384$	−147456.			−0.0510310
$385$		0			0
$386$	1.18119e6			0.403508
$387$	−539298.	−	934092.i	−0.183042	−	0.317039i
$388$	−1.32866e6	+	2.30130e6i	−0.448057	+	0.776057i
$389$	−1.72989e6	+	2.99625e6i	−0.579620	+	1.00393i	0.415902	+	0.909409i	$0.363466\pi$
$389$	−1.72989e6	+	2.99625e6i	−0.579620	+	1.00393i	−0.995523	+	0.0945228i	$0.969867\pi$
$390$	781704.	+	1.35395e6i	0.260244	+	0.450756i
$391$	−248400.			−0.0821693
$392$		0			0
$393$	−1.36134e6			−0.444616
$394$	−402588.	−	697303.i	−0.130653	−	0.226298i
$395$	2.45546e6	−	4.25299e6i	0.791846	−	1.37152i
$396$	38880.0	−	67342.1i	0.0124591	−	0.0215799i
$397$	1.95208e6	+	3.38110e6i	0.621615	+	1.07667i	0.989185	+	0.146673i	$0.0468565\pi$
$397$	1.95208e6	+	3.38110e6i	0.621615	+	1.07667i	−0.367570	+	0.929996i	$0.619810\pi$
$398$	2.60979e6			0.825844
$399$		0			0
$400$	315136.			0.0984800
$401$	−2.72058e6	−	4.71218e6i	−0.844890	−	1.46339i	−0.885717	−	0.464226i	$-0.846333\pi$
$401$	−2.72058e6	−	4.71218e6i	−0.844890	−	1.46339i	0.0408270	−	0.999166i	$-0.487001\pi$
$402$	−302472.	+	523897.i	−0.0933512	+	0.161689i
$403$	−1.18177e6	+	2.04688e6i	−0.362468	+	0.627813i
$404$	176016.	+	304869.i	0.0536536	+	0.0929307i
$405$	−433026.			−0.131183
$406$		0			0
$407$	507480.			0.151856
$408$	−119232.	−	206516.i	−0.0354603	−	0.0614190i
$409$	−984973.	+	1.70602e6i	−0.291150	+	0.504286i	−0.974082	−	0.226196i	$-0.927371\pi$
$409$	−984973.	+	1.70602e6i	−0.291150	+	0.504286i	0.682932	+	0.730482i	$0.260704\pi$
$410$	2.53361e6	−	4.38834e6i	0.744354	−	1.28926i
$411$	−578043.	−	1.00120e6i	−0.168793	−	0.292359i
$412$	−1.26822e6			−0.368089
$413$		0			0
$414$	194400.			0.0557437
$415$	−213444.	−	369696.i	−0.0608364	−	0.105372i
$416$	336896.	−	583521.i	0.0954471	−	0.165319i
$417$	693882.	−	1.20184e6i	0.195409	−	0.338459i
$418$	114720.	+	198701.i	0.0321143	+	0.0556236i
$419$	139020.			0.0386850			0.0193425	−	0.999813i	$-0.493843\pi$
$419$	139020.			0.0386850			0.0193425	+	0.999813i	$0.493843\pi$
$420$		0			0
$421$	4.32743e6			1.18994			0.594970	−	0.803748i	$-0.297164\pi$
$421$	4.32743e6			1.18994			0.594970	+	0.803748i	$0.297164\pi$
$422$	2.29412e6	+	3.97353e6i	0.627097	+	1.08616i
$423$	797040.	−	1.38051e6i	0.216585	−	0.375137i
$424$	1.00051e6	−	1.73294e6i	0.270276	−	0.468132i
$425$	254817.	+	441356.i	0.0684315	+	0.118527i
$426$	−220320.			−0.0588207
$427$		0			0
$428$	3.64781e6			0.962548
$429$	177660.	+	307716.i	0.0466065	+	0.0807248i
$430$	1.75771e6	−	3.04445e6i	0.458434	−	0.794031i
$431$	1.39968e6	−	2.42432e6i	0.362941	−	0.628632i	−0.625503	−	0.780222i	$-0.715106\pi$
$431$	1.39968e6	−	2.42432e6i	0.362941	−	0.628632i	0.988443	+	0.151590i	$0.0484394\pi$
$432$	93312.0	+	161621.i	0.0240563	+	0.0416667i
$433$	−5.90241e6			−1.51290			−0.756449	−	0.654052i	$-0.773068\pi$
$433$	−5.90241e6			−1.51290			−0.756449	+	0.654052i	$0.773068\pi$
$434$		0			0
$435$	3.31096e6			0.838939
$436$	68240.0	+	118195.i	0.0171919	+	0.0297772i
$437$	−286800.	+	496752.i	−0.0718415	+	0.124433i
$438$	−460044.	+	796820.i	−0.114581	+	0.198461i
$439$	223256.	+	386691.i	0.0552894	+	0.0957640i	0.892345	−	0.451353i	$-0.149059\pi$
$439$	223256.	+	386691.i	0.0552894	+	0.0957640i	−0.837056	+	0.547117i	$0.815725\pi$
$440$	253440.			0.0624085
$441$		0			0
$442$	1.08965e6			0.265296
$443$	−1.74763e6	−	3.02698e6i	−0.423096	−	0.732824i	0.573144	−	0.819454i	$-0.305723\pi$
$443$	−1.74763e6	−	3.02698e6i	−0.423096	−	0.732824i	−0.996241	+	0.0866303i	$0.972390\pi$
$444$	−608976.	+	1.05478e6i	−0.146603	+	0.253924i
$445$	−1.08049e6	+	1.87146e6i	−0.258654	+	0.448002i
$446$	−1.40392e6	−	2.43166e6i	−0.334199	−	0.578850i
$447$	−265086.			−0.0627506
$448$		0			0
$449$	−1.20613e6			−0.282343			−0.141171	−	0.989985i	$-0.545087\pi$
$449$	−1.20613e6			−0.282343			−0.141171	+	0.989985i	$0.545087\pi$
$450$	−199422.	−	345409.i	−0.0464239	−	0.0804086i
$451$	575820.	−	997349.i	0.133305	−	0.230890i
$452$	1.56350e6	−	2.70807e6i	0.359959	−	0.623467i
$453$	−917424.	−	1.58902e6i	−0.210051	−	0.363819i
$454$	4.94443e6			1.12584
$455$		0			0
$456$	−550656.			−0.124013
$457$	−116773.	−	202257.i	−0.0261548	−	0.0453015i	0.852652	−	0.522480i	$-0.174993\pi$
$457$	−116773.	−	202257.i	−0.0261548	−	0.0453015i	−0.878807	+	0.477178i	$0.841660\pi$
$458$	−211660.	+	366606.i	−0.0471493	+	0.0816650i
$459$	−150903.	+	261372.i	−0.0334323	+	0.0579064i
$460$	316800.	+	548714.i	0.0698057	+	0.120907i
$461$	−1.74489e6			−0.382398			−0.191199	−	0.981551i	$-0.561238\pi$
$461$	−1.74489e6			−0.382398			−0.191199	+	0.981551i	$0.561238\pi$
$462$		0			0
$463$	−2.91786e6			−0.632576			−0.316288	−	0.948663i	$-0.602437\pi$
$463$	−2.91786e6			−0.632576			−0.316288	+	0.948663i	$0.602437\pi$
$464$	−713472.	−	1.23577e6i	−0.153845	−	0.266466i
$465$	1.06682e6	−	1.84779e6i	0.228802	−	0.396297i
$466$	877356.	−	1.51963e6i	0.187159	−	0.324169i
$467$	2.65538e6	+	4.59925e6i	0.563422	+	0.975876i	0.997195	+	0.0748537i	$0.0238490\pi$
$467$	2.65538e6	+	4.59925e6i	0.563422	+	0.975876i	−0.433772	+	0.901023i	$0.642818\pi$
$468$	−852768.			−0.179977
$469$		0			0
$470$	5.19552e6			1.08489
$471$	612639.	+	1.06112e6i	0.127248	+	0.220401i
$472$	−842880.	+	1.45991e6i	−0.174145	+	0.301628i
$473$	399480.	−	691920.i	0.0820998	−	0.142201i
$474$	1.33934e6	+	2.31981e6i	0.273808	+	0.474250i
$475$	1.17684e6			0.239322
$476$		0			0
$477$	−2.53255e6			−0.509638
$478$	−56928.0	−	98602.2i	−0.0113961	−	0.0197386i
$479$	−1.17233e6	+	2.03053e6i	−0.233459	+	0.404363i	−0.958824	−	0.284002i	$-0.908338\pi$
$479$	−1.17233e6	+	2.03053e6i	−0.233459	+	0.404363i	0.725365	+	0.688365i	$0.241671\pi$
$480$	−304128.	+	526765.i	−0.0602495	+	0.104355i
$481$	−2.78268e6	−	4.81975e6i	−0.548404	−	0.949864i
$482$	3.57025e6			0.699972
$483$		0			0
$484$	−2.51922e6			−0.488823
$485$	5.48071e6	+	9.49286e6i	1.05799	+	1.83249i
$486$	118098.	−	204552.i	0.0226805	−	0.0392837i
$487$	−4.90766e6	+	8.50031e6i	−0.937674	+	1.62410i	−0.167878	+	0.985808i	$0.553692\pi$
$487$	−4.90766e6	+	8.50031e6i	−0.937674	+	1.62410i	−0.769795	+	0.638291i	$0.779642\pi$
$488$	994880.	+	1.72318e6i	0.189113	+	0.327553i
$489$	1.54012e6			0.291260
$490$		0			0
$491$	−5.94520e6			−1.11292			−0.556458	−	0.830876i	$-0.687840\pi$
$491$	−5.94520e6			−1.11292			−0.556458	+	0.830876i	$0.687840\pi$
$492$	1.38197e6	+	2.39364e6i	0.257386	+	0.445806i
$493$	1.15382e6	−	1.99847e6i	0.213806	−	0.370323i
$494$	1.25810e6	−	2.17909e6i	0.231951	−	0.401751i
$495$	−160380.	−	277786.i	−0.0294196	−	0.0509563i
$496$	−919552.			−0.167831
$497$		0			0
$498$	232848.			0.0420726
$499$	−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
$501$	−3.04290e6	+	5.27046e6i	−0.541618	+	0.938110i
$502$	220248.	+	381481.i	0.0390079	+	0.0675637i
$503$	4.71794e6			0.831444			0.415722	−	0.909492i	$-0.363529\pi$
$503$	4.71794e6			0.831444			0.415722	+	0.909492i	$0.363529\pi$
$504$		0			0
$505$	1.45213e6			0.253383
$506$	72000.0	+	124708.i	0.0125013	+	0.0216529i
$507$	277520.	−	480678.i	0.0479483	−	0.0830490i
$508$	−1.38400e6	+	2.39716e6i	−0.237945	+	0.412133i
$509$	953853.	+	1.65212e6i	0.163188	+	0.282649i	0.936010	−	0.351973i	$-0.114489\pi$
$509$	953853.	+	1.65212e6i	0.163188	+	0.282649i	−0.772823	+	0.634622i	$0.781156\pi$
$510$	−983664.			−0.167464
$511$		0			0
$512$	262144.			0.0441942
$513$	348462.	+	603554.i	0.0584604	+	0.101256i
$514$	−281604.	+	487752.i	−0.0470144	+	0.0814314i
$515$	−2.61571e6	+	4.53055e6i	−0.434582	+	0.752718i
$516$	958752.	+	1.66061e6i	0.158519	+	0.274563i
$517$	1.18080e6			0.194290
$518$		0			0
$519$	−1.19842e6			−0.195295
$520$	−1.38970e6	−	2.40702e6i	−0.225378	−	0.390366i
$521$	−4.00987e6	+	6.94530e6i	−0.647196	+	1.12098i	0.336594	+	0.941650i	$0.390725\pi$
$521$	−4.00987e6	+	6.94530e6i	−0.647196	+	1.12098i	−0.983790	+	0.179326i	$0.942608\pi$
$522$	−902988.	+	1.56402e6i	−0.145046	+	0.251227i
$523$	−955810.	−	1.65551e6i	−0.152798	−	0.264654i	0.779457	−	0.626456i	$-0.215495\pi$
$523$	−955810.	−	1.65551e6i	−0.152798	−	0.264654i	−0.932255	+	0.361802i	$0.882162\pi$
$524$	2.42016e6			0.385049
$525$		0			0
$526$	−3.75504e6			−0.591766
$527$	−743544.	−	1.28786e6i	−0.116622	−	0.201995i
$528$	−69120.0	+	119719.i	−0.0107899	+	0.0186887i
$529$	3.03817e6	−	5.26227e6i	0.472034	−	0.817587i
$530$	−4.12711e6	−	7.14837e6i	−0.638200	−	1.10539i
$531$	2.13354e6			0.328371
$532$		0			0
$533$	−1.26297e7			−1.92563
$534$	−589356.	−	1.02079e6i	−0.0894385	−	0.154912i
$535$	7.52360e6	−	1.30313e7i	1.13643	−	1.96835i
$536$	537728.	−	931372.i	0.0808445	−	0.140027i
$537$	−3.12028e6	−	5.40449e6i	−0.466937	−	0.808758i
$538$	−4.45802e6			−0.664028
$539$		0			0
$540$	769824.			0.113608
$541$	5.99502e6	+	1.03837e7i	0.880639	+	1.52531i	0.850632	+	0.525762i	$0.176220\pi$
$541$	5.99502e6	+	1.03837e7i	0.880639	+	1.52531i	0.0300068	+	0.999550i	$0.490447\pi$
$542$	−1.13541e6	+	1.96658e6i	−0.166017	+	0.287551i
$543$	1.69728e6	−	2.93978e6i	0.247033	−	0.427873i
$544$	211968.	+	367139.i	0.0307095	+	0.0531905i
$545$	562980.			0.0811898
$546$		0			0
$547$	4.45809e6			0.637061			0.318530	−	0.947913i	$-0.396811\pi$
$547$	4.45809e6			0.637061			0.318530	+	0.947913i	$0.396811\pi$
$548$	1.02763e6	+	1.77991e6i	0.146179	+	0.253190i
$549$	1.25914e6	−	2.18090e6i	0.178297	−	0.308820i
$550$	147720.	−	255859.i	0.0208225	−	0.0360656i
$551$	−2.66437e6	−	4.61483e6i	−0.373866	−	0.647555i
$552$	−345600.			−0.0482754
$553$		0			0
$554$	−4.85303e6			−0.671798
$555$	2.51203e6	+	4.35096e6i	0.346172	+	0.599587i
$556$	−1.23357e6	+	2.13660e6i	−0.169230	+	0.293114i
$557$	−4.51306e6	+	7.81685e6i	−0.616358	+	1.06756i	0.373787	+	0.927515i	$0.378059\pi$
$557$	−4.51306e6	+	7.81685e6i	−0.616358	+	1.06756i	−0.990145	+	0.140049i	$0.955274\pi$
$558$	581904.	+	1.00789e6i	0.0791163	+	0.137033i
$559$	−8.76193e6			−1.18596
$560$		0			0
$561$	−223560.			−0.0299907
$562$	−1.37548e6	−	2.38239e6i	−0.183701	−	0.318180i
$563$	−3.42449e6	+	5.93140e6i	−0.455329	+	0.788653i	−0.998707	−	0.0508350i	$-0.983812\pi$
$563$	−3.42449e6	+	5.93140e6i	−0.455329	+	0.788653i	0.543378	+	0.839488i	$0.317145\pi$
$564$	−1.41696e6	+	2.45425e6i	−0.187568	+	0.324878i
$565$	−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	$-0.0515892\pi$
$569$	2.73161e6	+	4.73129e6i	0.353703	+	0.612631i	−0.633192	+	0.773994i	$0.718256\pi$
$570$	−1.13573e6	+	1.96714e6i	−0.146416	+	0.253599i
$571$	5.11619e6	−	8.86150e6i	0.656684	−	1.13741i	−0.324785	−	0.945788i	$-0.605292\pi$
$571$	5.11619e6	−	8.86150e6i	0.656684	−	1.13741i	0.981469	−	0.191622i	$-0.0613748\pi$
$572$	−315840.	−	547051.i	−0.0403624	−	0.0699097i
$573$	2.38810e6			0.303854
$574$		0			0
$575$	738600.			0.0931622
$576$	−165888.	−	287326.i	−0.0208333	−	0.0360844i
$577$	−7.97184e6	+	1.38076e7i	−0.996825	+	1.72655i	−0.429461	+	0.903085i	$0.641296\pi$
$577$	−7.97184e6	+	1.38076e7i	−0.996825	+	1.72655i	−0.567364	+	0.823467i	$0.692037\pi$
$578$	2.49692e6	−	4.32480e6i	0.310875	−	0.538451i
$579$	1.32884e6	+	2.30162e6i	0.164731	+	0.285323i
$580$	−5.88614e6			−0.726542
$581$		0			0
$582$	−5.97895e6			−0.731674
$583$	−937980.	−	1.62463e6i	−0.114294	−	0.197962i
$584$	817856.	−	1.41657e6i	0.0992304	−	0.171872i
$585$	−1.75883e6	+	3.04639e6i	−0.212488	+	0.368041i
$586$	2.62525e6	+	4.54707e6i	0.315811	+	0.547000i
$587$	−9.47713e6			−1.13522			−0.567612	−	0.823296i	$-0.692133\pi$
$587$	−9.47713e6			−1.13522			−0.567612	+	0.823296i	$0.692133\pi$
$588$		0			0
$589$	−3.43395e6			−0.407855
$590$	3.47688e6	+	6.02213e6i	0.411206	+	0.712230i
$591$	905823.	−	1.56893e6i	0.106678	−	0.184772i
$592$	1.08262e6	−	1.87516e6i	0.126962	−	0.219904i
$593$	−1.22674e6	−	2.12478e6i	−0.143258	−	0.248129i	0.785464	−	0.618907i	$-0.212424\pi$
$593$	−1.22674e6	−	2.12478e6i	−0.143258	−	0.248129i	−0.928722	+	0.370778i	$0.879091\pi$
$594$	174960.			0.0203457
$595$		0			0
$596$	471264.			0.0543436
$597$	2.93602e6	+	5.08533e6i	0.337150	+	0.583960i
$598$	789600.	−	1.36763e6i	0.0902930	−	0.156392i
$599$	4.64989e6	−	8.05385e6i	0.529512	−	0.917142i	−0.469895	−	0.882722i	$-0.655708\pi$
$599$	4.64989e6	−	8.05385e6i	0.529512	−	0.917142i	0.999407	−	0.0344196i	$-0.0109583\pi$
$600$	354528.	+	614061.i	0.0402043	+	0.0696359i
$601$	−1.14617e7			−1.29438			−0.647192	−	0.762327i	$-0.724057\pi$
$601$	−1.14617e7			−1.29438			−0.647192	+	0.762327i	$0.724057\pi$
$602$		0			0
$603$	−1.36112e6			−0.152442
$604$	1.63098e6	+	2.82493e6i	0.181909	+	0.315076i
$605$	−5.19588e6	+	8.99953e6i	−0.577126	+	0.999612i
$606$	−396036.	+	685954.i	−0.0438080	+	0.0758776i
$607$	−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	$-0.380029\pi$
$608$	978944.			0.107399
$609$		0			0
$610$	8.20776e6			0.893100
$611$	−6.47472e6	−	1.12145e7i	−0.701646	−	1.21529i
$612$	268272.	−	464661.i	0.0289532	−	0.0501484i
$613$	−46891.0	+	81217.6i	−0.00504009	+	0.00872969i	−0.868534	−	0.495629i	$-0.834938\pi$
$613$	−46891.0	+	81217.6i	−0.00504009	+	0.00872969i	0.863494	+	0.504358i	$0.168271\pi$
$614$	−3.38044e6	−	5.85509e6i	−0.361870	−	0.626777i
$615$	1.14012e7			1.21553
$616$		0			0
$617$	−1.49642e7			−1.58248			−0.791242	−	0.611504i	$-0.790565\pi$
$617$	−1.49642e7			−1.58248			−0.791242	+	0.611504i	$0.790565\pi$
$618$	−1.42675e6	−	2.47121e6i	−0.150272	−	0.260278i
$619$	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	$0.0810104\pi$
$620$	−1.89658e6	+	3.28497e6i	−0.198149	+	0.343203i
$621$	218700.	+	378800.i	0.0227573	+	0.0394167i
$622$	−6.00816e6			−0.622681
$623$		0			0
$624$	1.51603e6			0.155864
$625$	6.04857e6	+	1.04764e7i	0.619374	+	1.07279i
$626$	−1.62168e6	+	2.80884e6i	−0.165398	+	0.286478i
$627$	−258120.	+	447077.i	−0.0262212	+	0.0454165i
$628$	−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
$633$	−5.16177e6	+	8.94045e6i	−0.512023	+	0.886850i
$634$	−1.80712e6	+	3.13002e6i	−0.178551	+	0.309260i
$635$	5.70900e6	+	9.88828e6i	0.561857	+	0.973165i
$636$	4.50230e6			0.441359
$637$		0			0
$638$	−1.33776e6			−0.130115
$639$	−247860.	−	429306.i	−0.0240134	−	0.0415925i
$640$	540672.	−	936471.i	0.0521776	−	0.0903742i
$641$	−5.48506e6	+	9.50041e6i	−0.527274	+	0.913266i	0.472220	+	0.881481i	$0.343453\pi$
$641$	−5.48506e6	+	9.50041e6i	−0.527274	+	0.913266i	−0.999495	+	0.0317855i	$0.989881\pi$
$642$	4.10378e6	+	7.10796e6i	0.392959	+	0.680624i
$643$	−2.83704e6			−0.270607			−0.135303	−	0.990804i	$-0.543201\pi$
$643$	−2.83704e6			−0.270607			−0.135303	+	0.990804i	$0.543201\pi$
$644$		0			0
$645$	7.90970e6			0.748619
$646$	791568.	+	1.37104e6i	0.0746289	+	0.129261i
$647$	3.02843e6	−	5.24539e6i	0.284418	−	0.492626i	−0.688050	−	0.725663i	$-0.741533\pi$
$647$	3.02843e6	−	5.24539e6i	0.284418	−	0.492626i	0.972468	+	0.233037i	$0.0748664\pi$
$648$	−209952.	+	363648.i	−0.0196419	+	0.0340207i
$649$	790200.	+	1.36867e6i	0.0736420	+	0.127552i
$650$	−3.23999e6			−0.300788
$651$		0			0
$652$	−2.73798e6			−0.252239
$653$	544461.	+	943034.i	0.0499671	+	0.0865455i	0.889927	−	0.456103i	$-0.150755\pi$
$653$	544461.	+	943034.i	0.0499671	+	0.0865455i	−0.839960	+	0.542648i	$0.817422\pi$
$654$	−153540.	+	265939.i	−0.0140371	+	0.0243130i
$655$	4.99158e6	−	8.64567e6i	0.454606	−	0.787400i
$656$	−2.45683e6	−	4.25536e6i	−0.222903	−	0.386079i
$657$	−2.07020e6			−0.187111
$658$		0			0
$659$	7.41803e6			0.665388			0.332694	−	0.943035i	$-0.392042\pi$
$659$	7.41803e6			0.665388			0.332694	+	0.943035i	$0.392042\pi$
$660$	285120.	+	493842.i	0.0254781	+	0.0441294i
$661$	−383827.	+	664808.i	−0.0341690	+	0.0591824i	−0.882604	−	0.470117i	$-0.844212\pi$
$661$	−383827.	+	664808.i	−0.0341690	+	0.0591824i	0.848435	+	0.529299i	$0.177545\pi$
$662$	−2.24394e6	+	3.88663e6i	−0.199006	+	0.344689i
$663$	1.22585e6	+	2.12324e6i	0.108307	+	0.187593i
$664$	−413952.			−0.0364359
$665$		0			0
$666$	−2.74039e6			−0.239402
$667$	−1.67220e6	−	2.89634e6i	−0.145537	−	0.252078i
$668$	5.40960e6	−	9.36970e6i	0.469055	−	0.812428i
$669$	3.15882e6	−	5.47124e6i	0.272872	−	0.472629i
$670$	−2.21813e6	−	3.84191e6i	−0.190897	−	0.330644i
$671$	1.86540e6			0.159943
$672$		0			0
$673$	1.42263e6			0.121075			0.0605373	−	0.998166i	$-0.480719\pi$
$673$	1.42263e6			0.121075			0.0605373	+	0.998166i	$0.480719\pi$
$674$	5.50435e6	+	9.53381e6i	0.466720	+	0.808382i
$675$	448700.	−	777170.i	0.0379050	−	0.0656533i
$676$	−493368.	+	854538.i	−0.0415245	+	0.0719225i
$677$	3.08115e6	+	5.33671e6i	0.258370	+	0.447509i	0.965805	−	0.259268i	$-0.0834814\pi$
$677$	3.08115e6	+	5.33671e6i	0.258370	+	0.447509i	−0.707436	+	0.706778i	$0.750148\pi$
$678$	7.03577e6			0.587810
$679$		0			0
$680$	1.74874e6			0.145028
$681$	5.56249e6	+	9.63451e6i	0.459622	+	0.796089i
$682$	−431040.	+	746583.i	−0.0354860	+	0.0614635i
$683$	−7.53107e6	+	1.30442e7i	−0.617739	+	1.06996i	0.372158	+	0.928169i	$0.378618\pi$
$683$	−7.53107e6	+	1.30442e7i	−0.617739	+	1.06996i	−0.989897	+	0.141786i	$0.954715\pi$
$684$	−619488.	−	1.07298e6i	−0.0506282	−	0.0876906i
$685$	8.47796e6			0.690343
$686$		0			0
$687$	−952470.			−0.0769945
$688$	−1.70445e6	−	2.95219e6i	−0.137282	−	0.237779i
$689$	−1.02865e7	+	1.78168e7i	−0.825506	+	1.42982i
$690$	−712800.	+	1.23461e6i	−0.0569961	+	0.0987201i
$691$	2.93818e6	+	5.08907e6i	0.234090	+	0.405456i	0.959008	−	0.283380i	$-0.0914556\pi$
$691$	2.93818e6	+	5.08907e6i	0.234090	+	0.405456i	−0.724918	+	0.688835i	$0.758122\pi$
$692$	2.13053e6			0.169131
$693$		0			0
$694$	7.66997e6			0.604498
$695$	5.08847e6	+	8.81349e6i	0.399600	+	0.692127i
$696$	1.60531e6	−	2.78048e6i	0.125614	−	0.217569i
$697$	3.97316e6	−	6.88171e6i	0.309780	−	0.536555i
$698$	−3.67318e6	−	6.36213e6i	−0.285367	−	0.494270i
$699$	3.94810e6			0.305630
$700$		0			0
$701$	3.60077e6			0.276758			0.138379	−	0.990379i	$-0.455811\pi$
$701$	3.60077e6			0.276758			0.138379	+	0.990379i	$0.455811\pi$
$702$	−959364.	−	1.66167e6i	−0.0734752	−	0.127263i
$703$	4.04292e6	−	7.00255e6i	0.308537	−	0.534402i
$704$	122880.	−	212834.i	0.00934436	−	0.0161849i
$705$	5.84496e6	+	1.01238e7i	0.442903	+	0.767131i
$706$	−2.48806e6			−0.187866
$707$		0			0
$708$	−3.79296e6			−0.284377
$709$	−4.61258e6	−	7.98922e6i	−0.344610	−	0.596883i	0.640673	−	0.767814i	$-0.278656\pi$
$709$	−4.61258e6	−	7.98922e6i	−0.344610	−	0.596883i	−0.985283	+	0.170932i	$0.945322\pi$
$710$	807840.	−	1.39922e6i	0.0601422	−	0.104169i
$711$	−3.01352e6	+	5.21958e6i	−0.223563	+	0.387223i
$712$	1.04774e6	+	1.81475e6i	0.0774560	+	0.134158i
$713$	−2.15520e6			−0.158768
$714$		0			0
$715$	−2.60568e6			−0.190615
$716$	5.54717e6	+	9.60798e6i	0.404379	+	0.700405i
$717$	128088.	−	221855.i	0.00930488	−	0.0161165i
$718$	−7.48123e6	+	1.29579e7i	−0.541579	+	0.938043i
$719$	1.31962e7	+	2.28564e7i	0.951975	+	1.64887i	0.741144	+	0.671346i	$0.234283\pi$
$719$	1.31962e7	+	2.28564e7i	0.951975	+	1.64887i	0.210830	+	0.977523i	$0.432383\pi$
$720$	−1.36858e6			−0.0983870
$721$		0			0
$722$	−6.24865e6			−0.446111
$723$	4.01653e6	+	6.95683e6i	0.285762	+	0.494955i
$724$	−3.01739e6	+	5.22628e6i	−0.213937	+	0.370549i
$725$	−3.43080e6	+	5.94231e6i	−0.242410	+	0.419866i
$726$	−2.83412e6	−	4.90884e6i	−0.199561	−	0.345650i
$727$	−9.79485e6			−0.687324			−0.343662	−	0.939093i	$-0.611667\pi$
$727$	−9.79485e6			−0.687324			−0.343662	+	0.939093i	$0.611667\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−3.37366e6	−	5.84334e6i	−0.234312	−	0.405839i
$731$	2.75641e6	−	4.77425e6i	0.190788	−	0.330454i
$732$	−2.23848e6	+	3.87716e6i	−0.154410	+	0.267446i
$733$	−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	$0.878075\pi$
$734$	64928.0			0.00444828
$735$		0			0
$736$	614400.			0.0418077
$737$	−504120.	−	873161.i	−0.0341873	−	0.0592142i
$738$	−3.10943e6	+	5.38569e6i	−0.210155	+	0.363999i
$739$	8.28543e6	−	1.43508e7i	0.558089	−	0.966639i	−0.439567	−	0.898210i	$-0.644868\pi$
$739$	8.28543e6	−	1.43508e7i	0.558089	−	0.966639i	0.997656	−	0.0684291i	$-0.0217987\pi$
$740$	−4.46582e6	−	7.73503e6i	−0.299794	−	0.519258i
$741$	5.66143e6			0.378775
$742$		0			0
$743$	1.44141e7			0.957892			0.478946	−	0.877844i	$-0.341019\pi$
$743$	1.44141e7			0.957892			0.478946	+	0.877844i	$0.341019\pi$
$744$	−1.03450e6	−	1.79180e6i	−0.0685167	−	0.118674i
$745$	971982.	−	1.68352e6i	0.0641605	−	0.111129i
$746$	−587212.	+	1.01708e6i	−0.0386321	+	0.0669127i
$747$	261954.	+	453718.i	0.0171761	+	0.0297498i
$748$	397440.			0.0259727
$749$		0			0
$750$	−4.50014e6			−0.292128
$751$	−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
$753$	−495558.	+	858332.i	−0.0318498	+	0.0551655i
$754$	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
$759$	−162000.	+	280592.i	−0.0102073	+	0.0176795i
$760$	2.01907e6	−	3.49714e6i	0.126800	−	0.219623i
$761$	1.07393e6	+	1.86010e6i	0.0672225	+	0.116433i	0.897678	−	0.440653i	$-0.145253\pi$
$761$	1.07393e6	+	1.86010e6i	0.0672225	+	0.116433i	−0.830455	+	0.557085i	$0.811920\pi$
$762$	−6.22800e6			−0.388563
$763$		0			0
$764$	−4.24550e6			−0.263145
$765$	−1.10662e6	−	1.91673e6i	−0.0683669	−	0.118415i
$766$	5.95968e6	−	1.03225e7i	0.366987	−	0.635641i
$767$	8.66586e6	−	1.50097e7i	0.531892	−	0.921264i
$768$	294912.	+	510803.i	0.0180422	+	0.0312500i
$769$	−1.31059e7			−0.799193			−0.399596	−	0.916691i	$-0.630850\pi$
$769$	−1.31059e7			−0.799193			−0.399596	+	0.916691i	$0.630850\pi$
$770$		0			0
$771$	−1.26722e6			−0.0767742
$772$	−2.36238e6	−	4.09177e6i	−0.142662	−	0.247097i
$773$	1.18577e7	−	2.05381e7i	0.713759	−	1.23627i	−0.249678	−	0.968329i	$-0.580325\pi$
$773$	1.18577e7	−	2.05381e7i	0.713759	−	1.23627i	0.963436	−	0.267937i	$-0.0863419\pi$
$774$	−2.15719e6	+	3.73637e6i	−0.129430	+	0.224180i
$775$	2.21088e6	+	3.82935e6i	0.132224	+	0.229019i
$776$	1.06292e7			0.633648
$777$		0			0
$778$	1.38391e7			0.819707
$779$	−9.17473e6	−	1.58911e7i	−0.541689	−	0.938232i
$780$	3.12682e6	−	5.41580e6i	0.184020	−	0.318733i
$781$	183600.	−	318005.i	0.0107707	−	0.0186554i
$782$	496800.	+	860483.i	0.0290512	+	0.0503182i
$783$	−4.06345e6			−0.236859
$784$		0			0
$785$	−8.98537e6			−0.520430
$786$	2.72268e6	+	4.71582e6i	0.157196	+	0.272271i
$787$	4.20024e6	−	7.27503e6i	0.241734	−	0.418695i	−0.719474	−	0.694519i	$-0.755617\pi$
$787$	4.20024e6	−	7.27503e6i	0.241734	−	0.418695i	0.961208	+	0.275824i	$0.0889506\pi$
$788$	−1.61035e6	+	2.78921e6i	−0.0923858	+	0.160017i
$789$	−4.22442e6	−	7.31691e6i	−0.241588	−	0.418442i
$790$	−1.96437e7			−1.11984
$791$		0			0
$792$	−311040.			−0.0176199
$793$	−1.02286e7	−	1.77165e7i	−0.577609	−	1.00045i
$794$	7.80832e6	−	1.35244e7i	0.439548	−	0.761320i
$795$	9.28600e6	−	1.60838e7i	0.521088	−	0.902551i
$796$	−5.21958e6	−	9.04058e6i	−0.291980	−	0.505724i
$797$	5.41023e6			0.301696			0.150848	−	0.988557i	$-0.451800\pi$
$797$	5.41023e6			0.301696			0.150848	+	0.988557i	$0.451800\pi$
$798$		0			0
$799$	8.14752e6			0.451501
$800$	−630272.	−	1.09166e6i	−0.0348179	−	0.0603064i
$801$	1.32605e6	−	2.29679e6i	0.0730262	−	0.126485i
$802$	−1.08823e7	+	1.88487e7i	−0.597427	+	1.03477i
$803$	−766740.	−	1.32803e6i	−0.0419623	−	0.0726808i
$804$	2.41978e6			0.132019
$805$		0			0
$806$	9.45414e6			0.512607
$807$	−5.01528e6	−	8.68671e6i	−0.271088	−	0.469539i
$808$	704064.	−	1.21947e6i	0.0379388	−	0.0657120i
$809$	1.30389e7	−	2.25840e7i	0.700436	−	1.21319i	−0.267877	−	0.963453i	$-0.586322\pi$
$809$	1.30389e7	−	2.25840e7i	0.700436	−	1.21319i	0.968313	−	0.249738i	$-0.0803445\pi$
$810$	866052.	+	1.50005e6i	0.0463801	+	0.0803326i
$811$	1.90021e7			1.01449			0.507247	−	0.861800i	$-0.330663\pi$
$811$	1.90021e7			1.01449			0.507247	+	0.861800i	$0.330663\pi$
$812$		0			0
$813$	−5.10934e6			−0.271105
$814$	−1.01496e6	−	1.75796e6i	−0.0536893	−	0.0929926i
$815$	−5.64709e6	+	9.78105e6i	−0.297804	+	0.515812i
$816$	−476928.	+	826064.i	−0.0250742	+	0.0434298i
$817$	−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	0.917633	+	0.397430i	$0.130098\pi$
$821$	1.55086e7	+	2.68618e7i	0.803001	+	1.39084i	−0.114632	+	0.993408i	$0.536569\pi$
$822$	−2.31217e6	+	4.00480e6i	−0.119355	+	0.206729i
$823$	7.81448e6	−	1.35351e7i	0.402162	−	0.696564i	−0.591825	−	0.806066i	$-0.701592\pi$
$823$	7.81448e6	−	1.35351e7i	0.402162	−	0.696564i	0.993987	+	0.109502i	$0.0349257\pi$
$824$	2.53645e6	+	4.39326e6i	0.130139	+	0.225408i
$825$	664740.			0.0340030
$826$		0			0
$827$	1.58421e7			0.805467			0.402733	−	0.915317i	$-0.368060\pi$
$827$	1.58421e7			0.805467			0.402733	+	0.915317i	$0.368060\pi$
$828$	−388800.	−	673421.i	−0.0197084	−	0.0341359i
$829$	−1.03088e6	+	1.78553e6i	−0.0520980	+	0.0902364i	−0.890898	−	0.454203i	$-0.849924\pi$
$829$	−1.03088e6	+	1.78553e6i	−0.0520980	+	0.0902364i	0.838800	+	0.544439i	$0.183257\pi$
$830$	−853776.	+	1.47878e6i	−0.0430179	+	0.0745091i
$831$	−5.45966e6	−	9.45641e6i	−0.274260	−	0.475033i
$832$	−2.69517e6			−0.134983
$833$		0			0
$834$	−5.55106e6			−0.276351
$835$	−2.23146e7	−	3.86500e7i	−1.10757	−	1.91838i
$836$	458880.	−	794803.i	0.0227082	−	0.0393318i
$837$	−1.30928e6	+	2.26775e6i	−0.0645982	+	0.111887i
$838$	−278040.	−	481579.i	−0.0136772	−	0.0236896i
$839$	3.03900e7			1.49048			0.745240	−	0.666796i	$-0.232335\pi$
$839$	3.03900e7			1.49048			0.745240	+	0.666796i	$0.232335\pi$
$840$		0			0
$841$	1.05583e7			0.514760
$842$	−8.65486e6	−	1.49907e7i	−0.420707	−	0.728686i
$843$	3.09482e6	−	5.36039e6i	0.149991	−	0.259793i
$844$	9.17648e6	−	1.58941e7i	0.443425	−	0.768034i
$845$	2.03514e6	+	3.52497e6i	0.0980513	+	0.169830i
$846$	−6.37632e6			−0.306298
$847$		0			0
$848$	−8.00410e6			−0.382228
$849$	−3.73909e6	−	6.47629e6i	−0.178031	−	0.308359i
$850$	1.01927e6	−	1.76542e6i	0.0483884	−	0.0838111i
$851$	2.53740e6	−	4.39491e6i	0.120106	−	0.208030i
$852$	440640.	+	763211.i	0.0207962	+	0.0360202i
$853$	−2.97738e7			−1.40108			−0.700538	−	0.713615i	$-0.747056\pi$
$853$	−2.97738e7			−1.40108			−0.700538	+	0.713615i	$0.747056\pi$
$854$		0			0
$855$	−5.11078e6			−0.239096
$856$	−7.29562e6	−	1.26364e7i	−0.340312	−	0.589438i
$857$	−4.32050e6	+	7.48333e6i	−0.200947	+	0.348051i	−0.948834	−	0.315776i	$-0.897735\pi$
$857$	−4.32050e6	+	7.48333e6i	−0.200947	+	0.348051i	0.747887	+	0.663826i	$0.231069\pi$
$858$	710640.	−	1.23086e6i	0.0329558	−	0.0570811i
$859$	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	$0.550553\pi$
$860$	−1.40617e7			−0.648323
$861$		0			0
$862$	−1.11974e7			−0.513276
$863$	−1.95096e7	−	3.37915e7i	−0.891703	−	1.54448i	−0.837833	−	0.545927i	$-0.816177\pi$
$863$	−1.95096e7	−	3.37915e7i	−0.891703	−	1.54448i	−0.0538706	−	0.998548i	$-0.517156\pi$
$864$	373248.	−	646484.i	0.0170103	−	0.0294628i
$865$	4.39421e6	−	7.61100e6i	0.199683	−	0.345861i
$866$	1.18048e7	+	2.04466e7i	0.534891	+	0.926458i
$867$	1.12361e7			0.507656
$868$		0			0
$869$	−4.46448e6			−0.200549
$870$	−6.62191e6	−	1.14695e7i	−0.296610	−	0.513743i
$871$	−5.52852e6	+	9.57567e6i	−0.246924	+	0.427685i
$872$	272960.	−	472781.i	0.0121565	−	0.0210556i
$873$	−6.72632e6	−	1.16503e7i	−0.298705	−	0.517372i
$874$	2.29440e6			0.101599
$875$		0			0
$876$	3.68035e6			0.162043
$877$	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
$879$	−5.90682e6	+	1.02309e7i	−0.257858	+	0.446624i
$880$	−506880.	−	877942.i	−0.0220647	−	0.0382172i
$881$	3.05312e7			1.32527			0.662634	−	0.748943i	$-0.269438\pi$
$881$	3.05312e7			1.32527			0.662634	+	0.748943i	$0.269438\pi$
$882$		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
$885$	−7.82298e6	+	1.35498e7i	−0.335748	+	0.581533i
$886$	−6.99050e6	+	1.21079e7i	−0.299174	+	0.518185i
$887$	6.70758e6	+	1.16179e7i	0.286257	+	0.495812i	0.972913	−	0.231170i	$-0.0742554\pi$
$887$	6.70758e6	+	1.16179e7i	0.286257	+	0.495812i	−0.686656	+	0.726983i	$0.740922\pi$
$888$	4.87181e6			0.207328
$889$		0			0
$890$	8.64389e6			0.365792
$891$	196830.	+	340920.i	0.00830610	+	0.0143866i
$892$	−5.61568e6	+	9.72664e6i	−0.236314	+	0.409309i
$893$	9.40704e6	−	1.62935e7i	0.394752	−	0.683731i
$894$	530172.	+	918285.i	0.0221857	+	0.0384267i
$895$	4.57641e7			1.90971
$896$		0			0
$897$	3.55320e6			0.147448
$898$	2.41225e6	+	4.17814e6i	0.0998233	+	0.172899i
$899$	1.00109e7	−	1.73394e7i	0.413118	−	0.715541i
$900$	−797688.	+	1.38164e6i	−0.0328267	+	0.0568575i
$901$	−6.47206e6	−	1.12099e7i	−0.265602	−	0.460035i
$902$	−4.60656e6			−0.188521
$903$		0			0
$904$	−1.25080e7			−0.509059
$905$	1.24467e7	+	2.15584e7i	0.505166	+	0.874973i
$906$	−3.66970e6	+	6.35610e6i	−0.148528	+	0.257259i
$907$	−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	$0.186646\pi$
$908$	−9.88886e6	−	1.71280e7i	−0.398045	−	0.689434i
$909$	−1.78216e6			−0.0715381
$910$		0			0
$911$	1.19035e6			0.0475203			0.0237602	−	0.999718i	$-0.492436\pi$
$911$	1.19035e6			0.0475203			0.0237602	+	0.999718i	$0.492436\pi$
$912$	1.10131e6	+	1.90753e6i	0.0438453	+	0.0759423i
$913$	−194040.	+	336087.i	−0.00770397	+	0.0133437i
$914$	−467092.	+	809027.i	−0.0184943	+	0.0320330i
$915$	9.23373e6	+	1.59933e7i	0.364607	+	0.631517i
$916$	1.69328e6			0.0666792
$917$		0			0
$918$	1.20722e6			0.0472804
$919$	2.35998e7	+	4.08761e7i	0.921764	+	1.59654i	0.796685	+	0.604395i	$0.206585\pi$
$919$	2.35998e7	+	4.08761e7i	0.921764	+	1.59654i	0.125079	+	0.992147i	$0.460082\pi$
$920$	1.26720e6	−	2.19485e6i	0.0493601	−	0.0854941i
$921$	7.60599e6	−	1.31740e7i	0.295465	−	0.511761i
$922$	3.48978e6	+	6.04448e6i	0.135198	+	0.234170i
$923$	−4.02696e6			−0.155587
$924$		0			0
$925$	−1.04118e7			−0.400103
$926$	5.83573e6	+	1.01078e7i	0.223649	+	0.387372i
$927$	3.21019e6	−	5.56022e6i	0.122696	−	0.212516i
$928$	−2.85389e6	+	4.94308e6i	−0.108784	+	0.188420i
$929$	−667977.	−	1.15697e6i	−0.0253935	−	0.0439828i	0.853049	−	0.521830i	$-0.174751\pi$
$929$	−667977.	−	1.15697e6i	−0.0253935	−	0.0439828i	−0.878443	+	0.477847i	$0.841417\pi$
$930$	−8.53459e6			−0.323575
$931$		0			0
$932$	−7.01885e6			−0.264683
$933$	−6.75918e6	−	1.17072e7i	−0.254208	−	0.440302i
$934$	1.06215e7	−	1.83970e7i	0.398400	−	0.690049i
$935$	819720.	−	1.41980e6i	0.0306645	−	0.0531125i
$936$	1.70554e6	+	2.95408e6i	0.0636314	+	0.110213i
$937$	1.47238e7			0.547861			0.273931	−	0.961749i	$-0.411676\pi$
$937$	1.47238e7			0.547861			0.273931	+	0.961749i	$0.411676\pi$
$938$		0			0
$939$	−7.29758e6			−0.270094
$940$	−1.03910e7	−	1.79978e7i	−0.383565	−	0.664355i
$941$	1.34598e7	−	2.33131e7i	0.495525	−	0.858274i	−0.504462	−	0.863434i	$-0.668309\pi$
$941$	1.34598e7	−	2.33131e7i	0.495525	−	0.858274i	0.999987	+	0.00516005i	$0.00164250\pi$
$942$	2.45056e6	−	4.24449e6i	0.0899782	−	0.155847i
$943$	−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	$-0.145130\pi$
$947$	1.86580e6	+	3.23166e6i	0.0676068	+	0.117098i	−0.830241	+	0.557405i	$0.811797\pi$
$948$	5.35738e6	−	9.27925e6i	0.193612	−	0.335345i
$949$	−8.40858e6	+	1.45641e7i	−0.303080	+	0.524950i
$950$	−2.35367e6	−	4.07668e6i	−0.0846130	−	0.146554i
$951$	−8.13202e6			−0.291573
$952$		0			0
$953$	2.18735e7			0.780166			0.390083	−	0.920780i	$-0.372446\pi$
$953$	2.18735e7			0.780166			0.390083	+	0.920780i	$0.372446\pi$
$954$	5.06509e6	+	8.77300e6i	0.180184	+	0.312088i
$955$	−8.75635e6	+	1.51664e7i	−0.310681	+	0.538115i
$956$	−227712.	+	394409.i	−0.00805826	+	0.0139573i
$957$	−1.50498e6	−	2.60670e6i	−0.0531191	−	0.0920050i
$958$	9.37862e6			0.330161
$959$		0			0
$960$	2.43302e6			0.0852056
$961$	7.86334e6	+	1.36197e7i	0.274662	+	0.475729i
$962$	−1.11307e7	+	1.92790e7i	−0.387780	+	0.671655i
$963$	−9.23351e6	+	1.59929e7i	−0.320849	+	0.555728i
$964$	−7.14050e6	−	1.23677e7i	−0.247478	−	0.428644i
$965$	−1.94897e7			−0.673730
$966$		0			0
$967$	1.76025e7			0.605352			0.302676	−	0.953093i	$-0.402120\pi$
$967$	1.76025e7			0.605352			0.302676	+	0.953093i	$0.402120\pi$
$968$	5.03843e6	+	8.72682e6i	0.172825	+	0.299342i
$969$	−1.78103e6	+	3.08483e6i	−0.0609342	+	0.105541i
$970$	2.19228e7	−	3.79714e7i	0.748113	−	1.29577i
$971$	−8.36584e6	−	1.44901e7i	−0.284749	−	0.493199i	0.687800	−	0.725901i	$-0.258577\pi$
$971$	−8.36584e6	−	1.44901e7i	−0.284749	−	0.493199i	−0.972548	+	0.232702i	$0.925243\pi$
$972$	−944784.			−0.0320750
$973$		0			0
$974$	3.92612e7			1.32607
$975$	−3.64499e6	−	6.31331e6i	−0.122796	−	0.212689i
$976$	3.97952e6	−	6.89273e6i	0.133723	−	0.231615i
$977$	−2.77691e7	+	4.80975e7i	−0.930733	+	1.61208i	−0.148662	+	0.988888i	$0.547497\pi$
$977$	−2.77691e7	+	4.80975e7i	−0.930733	+	1.61208i	−0.782071	+	0.623189i	$0.785837\pi$
$978$	−3.08023e6	−	5.33512e6i	−0.102976	−	0.178360i
$979$	1.96452e6			0.0655088
$980$		0			0
$981$	−690930.			−0.0229225
$982$	1.18904e7	+	2.05948e7i	0.393475	+	0.681519i
$983$	1.93392e7	−	3.34965e7i	0.638344	−	1.10564i	−0.347452	−	0.937698i	$-0.612953\pi$
$983$	1.93392e7	−	3.34965e7i	0.638344	−	1.10564i	0.985796	−	0.167947i	$-0.0537137\pi$
$984$	5.52787e6	−	9.57456e6i	0.182000	−	0.315232i
$985$	6.64270e6	+	1.15055e7i	0.218149	+	0.377846i
$986$	−9.23054e6			−0.302367
$987$		0			0
$988$	−1.00648e7			−0.328028
$989$	−3.99480e6	−	6.91920e6i	−0.129869	−	0.224939i
$990$	−641520.	+	1.11115e6i	−0.0208028	+	0.0360315i
$991$	−4.79249e6	+	8.30084e6i	−0.155016	+	0.268496i	−0.933065	−	0.359708i	$-0.882876\pi$
$991$	−4.79249e6	+	8.30084e6i	−0.155016	+	0.268496i	0.778049	+	0.628204i	$0.216210\pi$
$992$	1.83910e6	+	3.18542e6i	0.0593372	+	0.102775i
$993$	−1.00977e7			−0.324976
$994$		0			0
$995$	−4.30616e7			−1.37890
$996$	−465696.	−	806609.i	−0.0148749	−	0.0257641i
$997$	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	$0.113865\pi$
$998$	−1.29566e7	+	2.24415e7i	−0.411780	+	0.713225i
$999$	−3.08294e6	−	5.33981e6i	−0.0977353	−	0.169283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.6.e.g.67.1		2
7.2	even	3	inner	294.6.e.g.79.1		2
7.3	odd	6		294.6.a.m.1.1		1
7.4	even	3		6.6.a.a.1.1	✓	1
7.5	odd	6		294.6.e.a.79.1		2
7.6	odd	2		294.6.e.a.67.1		2
21.11	odd	6		18.6.a.b.1.1		1
21.17	even	6		882.6.a.a.1.1		1
28.11	odd	6		48.6.a.c.1.1		1
35.4	even	6		150.6.a.d.1.1		1
35.18	odd	12		150.6.c.b.49.1		2
35.32	odd	12		150.6.c.b.49.2		2
56.11	odd	6		192.6.a.g.1.1		1
56.53	even	6		192.6.a.o.1.1		1
63.4	even	3		162.6.c.e.55.1		2
63.11	odd	6		162.6.c.h.109.1		2
63.25	even	3		162.6.c.e.109.1		2
63.32	odd	6		162.6.c.h.55.1		2
77.32	odd	6		726.6.a.a.1.1		1
84.11	even	6		144.6.a.j.1.1		1
91.25	even	6		1014.6.a.c.1.1		1
105.32	even	12		450.6.c.j.199.1		2
105.53	even	12		450.6.c.j.199.2		2
105.74	odd	6		450.6.a.m.1.1		1
112.11	odd	12		768.6.d.p.385.1		2
112.53	even	12		768.6.d.c.385.2		2
112.67	odd	12		768.6.d.p.385.2		2
112.109	even	12		768.6.d.c.385.1		2
168.11	even	6		576.6.a.i.1.1		1
168.53	odd	6		576.6.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.6.a.a.1.1	✓	1	7.4	even	3
18.6.a.b.1.1		1	21.11	odd	6
48.6.a.c.1.1		1	28.11	odd	6
144.6.a.j.1.1		1	84.11	even	6
150.6.a.d.1.1		1	35.4	even	6
150.6.c.b.49.1		2	35.18	odd	12
150.6.c.b.49.2		2	35.32	odd	12
162.6.c.e.55.1		2	63.4	even	3
162.6.c.e.109.1		2	63.25	even	3
162.6.c.h.55.1		2	63.32	odd	6
162.6.c.h.109.1		2	63.11	odd	6
192.6.a.g.1.1		1	56.11	odd	6
192.6.a.o.1.1		1	56.53	even	6
294.6.a.m.1.1		1	7.3	odd	6
294.6.e.a.67.1		2	7.6	odd	2
294.6.e.a.79.1		2	7.5	odd	6
294.6.e.g.67.1		2	1.1	even	1	trivial
294.6.e.g.79.1		2	7.2	even	3	inner
450.6.a.m.1.1		1	105.74	odd	6
450.6.c.j.199.1		2	105.32	even	12
450.6.c.j.199.2		2	105.53	even	12
576.6.a.i.1.1		1	168.11	even	6
576.6.a.j.1.1		1	168.53	odd	6
726.6.a.a.1.1		1	77.32	odd	6
768.6.d.c.385.1		2	112.109	even	12
768.6.d.c.385.2		2	112.53	even	12
768.6.d.p.385.1		2	112.11	odd	12
768.6.d.p.385.2		2	112.67	odd	12
882.6.a.a.1.1		1	21.17	even	6
1014.6.a.c.1.1		1	91.25	even	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(33.0000 + 57.1577i) q^{5} -36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(132.000 - 228.631i) q^{10} +(30.0000 - 51.9615i) q^{11} +(72.0000 + 124.708i) q^{12} -658.000 q^{13} +594.000 q^{15} +(-128.000 - 221.703i) q^{16} +(207.000 - 358.535i) q^{17} +(-162.000 + 280.592i) q^{18} +(-478.000 - 827.920i) q^{19} -1056.00 q^{20} -240.000 q^{22} +(-300.000 - 519.615i) q^{23} +(288.000 - 498.831i) q^{24} +(-615.500 + 1066.08i) q^{25} +(1316.00 + 2279.38i) q^{26} -729.000 q^{27} +5574.00 q^{29} +(-1188.00 - 2057.68i) q^{30} +(1796.00 - 3110.76i) q^{31} +(-512.000 + 886.810i) q^{32} +(-270.000 - 467.654i) q^{33} -1656.00 q^{34} +1296.00 q^{36} +(4229.00 + 7324.84i) q^{37} +(-1912.00 + 3311.68i) q^{38} +(-2961.00 + 5128.60i) q^{39} +(2112.00 + 3658.09i) q^{40} +19194.0 q^{41} +13316.0 q^{43} +(480.000 + 831.384i) q^{44} +(2673.00 - 4629.77i) q^{45} +(-1200.00 + 2078.46i) q^{46} +(9840.00 + 17043.4i) q^{47} -2304.00 q^{48} +4924.00 q^{50} +(-1863.00 - 3226.81i) q^{51} +(5264.00 - 9117.52i) q^{52} +(15633.0 - 27077.2i) q^{53} +(1458.00 + 2525.33i) q^{54} +3960.00 q^{55} -8604.00 q^{57} +(-11148.0 - 19308.9i) q^{58} +(-13170.0 + 22811.1i) q^{59} +(-4752.00 + 8230.71i) q^{60} +(15545.0 + 26924.7i) q^{61} -14368.0 q^{62} +4096.00 q^{64} +(-21714.0 - 37609.8i) q^{65} +(-1080.00 + 1870.61i) q^{66} +(8402.00 - 14552.7i) q^{67} +(3312.00 + 5736.55i) q^{68} -5400.00 q^{69} +6120.00 q^{71} +(-2592.00 - 4489.48i) q^{72} +(12779.0 - 22133.9i) q^{73} +(16916.0 - 29299.4i) q^{74} +(5539.50 + 9594.70i) q^{75} +15296.0 q^{76} +23688.0 q^{78} +(-37204.0 - 64439.2i) q^{79} +(8448.00 - 14632.4i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-38388.0 - 66490.0i) q^{82} -6468.00 q^{83} +27324.0 q^{85} +(-26632.0 - 46128.0i) q^{86} +(25083.0 - 43445.0i) q^{87} +(1920.00 - 3325.54i) q^{88} +(16371.0 + 28355.4i) q^{89} -21384.0 q^{90} +9600.00 q^{92} +(-16164.0 - 27996.9i) q^{93} +(39360.0 - 68173.5i) q^{94} +(31548.0 - 54642.7i) q^{95} +(4608.00 + 7981.29i) q^{96} +166082. q^{97} -4860.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} + 9 q^{3} - 16 q^{4} + 66 q^{5} - 72 q^{6} + 128 q^{8} - 81 q^{9} + 264 q^{10} + 60 q^{11} + 144 q^{12} - 1316 q^{13} + 1188 q^{15} - 256 q^{16} + 414 q^{17} - 324 q^{18} - 956 q^{19} - 2112 q^{20}+ \cdots - 9720 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 + 9 * q^3 - 16 * q^4 + 66 * q^5 - 72 * q^6 + 128 * q^8 - 81 * q^9 + 264 * q^10 + 60 * q^11 + 144 * q^12 - 1316 * q^13 + 1188 * q^15 - 256 * q^16 + 414 * q^17 - 324 * q^18 - 956 * q^19 - 2112 * q^20 - 480 * q^22 - 600 * q^23 + 576 * q^24 - 1231 * q^25 + 2632 * q^26 - 1458 * q^27 + 11148 * q^29 - 2376 * q^30 + 3592 * q^31 - 1024 * q^32 - 540 * q^33 - 3312 * q^34 + 2592 * q^36 + 8458 * q^37 - 3824 * q^38 - 5922 * q^39 + 4224 * q^40 + 38388 * q^41 + 26632 * q^43 + 960 * q^44 + 5346 * q^45 - 2400 * q^46 + 19680 * q^47 - 4608 * q^48 + 9848 * q^50 - 3726 * q^51 + 10528 * q^52 + 31266 * q^53 + 2916 * q^54 + 7920 * q^55 - 17208 * q^57 - 22296 * q^58 - 26340 * q^59 - 9504 * q^60 + 31090 * q^61 - 28736 * q^62 + 8192 * q^64 - 43428 * q^65 - 2160 * q^66 + 16804 * q^67 + 6624 * q^68 - 10800 * q^69 + 12240 * q^71 - 5184 * q^72 + 25558 * q^73 + 33832 * q^74 + 11079 * q^75 + 30592 * q^76 + 47376 * q^78 - 74408 * q^79 + 16896 * q^80 - 6561 * q^81 - 76776 * q^82 - 12936 * q^83 + 54648 * q^85 - 53264 * q^86 + 50166 * q^87 + 3840 * q^88 + 32742 * q^89 - 42768 * q^90 + 19200 * q^92 - 32328 * q^93 + 78720 * q^94 + 63096 * q^95 + 9216 * q^96 + 332164 * q^97 - 9720 * q^99

Introduction

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