LMFDB - Embedded newform 294.6.e.r.79.1

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)

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);

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")

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,-16,54,72,0,-128,-81,-216,-216] 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 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.6.e.r.67.1

$q$-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} +(27.0000 - 46.7654i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-108.000 - 187.061i) q^{10} +(-108.000 - 187.061i) q^{11} +(72.0000 - 124.708i) q^{12} +998.000 q^{13} +486.000 q^{15} +(-128.000 + 221.703i) q^{16} +(-651.000 - 1127.57i) q^{17} +(162.000 + 280.592i) q^{18} +(-442.000 + 765.566i) q^{19} -864.000 q^{20} -864.000 q^{22} +(1134.00 - 1964.15i) q^{23} +(-288.000 - 498.831i) q^{24} +(104.500 + 180.999i) q^{25} +(1996.00 - 3457.17i) q^{26} -729.000 q^{27} -1482.00 q^{29} +(972.000 - 1683.55i) q^{30} +(-4180.00 - 7239.97i) q^{31} +(512.000 + 886.810i) q^{32} +(972.000 - 1683.55i) q^{33} -5208.00 q^{34} +1296.00 q^{36} +(2357.00 - 4082.44i) q^{37} +(1768.00 + 3062.27i) q^{38} +(4491.00 + 7778.64i) q^{39} +(-1728.00 + 2992.98i) q^{40} -9786.00 q^{41} +19436.0 q^{43} +(-1728.00 + 2992.98i) q^{44} +(2187.00 + 3788.00i) q^{45} +(-4536.00 - 7856.58i) q^{46} +(-11100.0 + 19225.8i) q^{47} -2304.00 q^{48} +836.000 q^{50} +(5859.00 - 10148.1i) q^{51} +(-7984.00 - 13828.7i) q^{52} +(-13395.0 - 23200.8i) q^{53} +(-1458.00 + 2525.33i) q^{54} -11664.0 q^{55} -7956.00 q^{57} +(-2964.00 + 5133.80i) q^{58} +(-14046.0 - 24328.4i) q^{59} +(-3888.00 - 6734.21i) q^{60} +(19433.0 - 33658.9i) q^{61} -33440.0 q^{62} +4096.00 q^{64} +(26946.0 - 46671.8i) q^{65} +(-3888.00 - 6734.21i) q^{66} +(-11974.0 - 20739.6i) q^{67} +(-10416.0 + 18041.0i) q^{68} +20412.0 q^{69} -20628.0 q^{71} +(2592.00 - 4489.48i) q^{72} +(-145.000 - 251.147i) q^{73} +(-9428.00 - 16329.8i) q^{74} +(-940.500 + 1628.99i) q^{75} +14144.0 q^{76} +35928.0 q^{78} +(49772.0 - 86207.6i) q^{79} +(6912.00 + 11971.9i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-19572.0 + 33899.7i) q^{82} +19308.0 q^{83} -70308.0 q^{85} +(38872.0 - 67328.3i) q^{86} +(-6669.00 - 11551.0i) q^{87} +(6912.00 + 11971.9i) q^{88} +(-18195.0 + 31514.7i) q^{89} +17496.0 q^{90} -36288.0 q^{92} +(37620.0 - 65159.8i) q^{93} +(44400.0 + 76903.1i) q^{94} +(23868.0 + 41340.6i) q^{95} +(-4608.00 + 7981.29i) q^{96} -79078.0 q^{97} +17496.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} + 9 q^{3} - 16 q^{4} + 54 q^{5} + 72 q^{6} - 128 q^{8} - 81 q^{9} - 216 q^{10} - 216 q^{11} + 144 q^{12} + 1996 q^{13} + 972 q^{15} - 256 q^{16} - 1302 q^{17} + 324 q^{18} - 884 q^{19} - 1728 q^{20}+ \cdots + 34992 q^{99}+O(q^{100}) $ 2 * q + 4 * q^2 + 9 * q^3 - 16 * q^4 + 54 * q^5 + 72 * q^6 - 128 * q^8 - 81 * q^9 - 216 * q^10 - 216 * q^11 + 144 * q^12 + 1996 * q^13 + 972 * q^15 - 256 * q^16 - 1302 * q^17 + 324 * q^18 - 884 * q^19 - 1728 * q^20 - 1728 * q^22 + 2268 * q^23 - 576 * q^24 + 209 * q^25 + 3992 * q^26 - 1458 * q^27 - 2964 * q^29 + 1944 * q^30 - 8360 * q^31 + 1024 * q^32 + 1944 * q^33 - 10416 * q^34 + 2592 * q^36 + 4714 * q^37 + 3536 * q^38 + 8982 * q^39 - 3456 * q^40 - 19572 * q^41 + 38872 * q^43 - 3456 * q^44 + 4374 * q^45 - 9072 * q^46 - 22200 * q^47 - 4608 * q^48 + 1672 * q^50 + 11718 * q^51 - 15968 * q^52 - 26790 * q^53 - 2916 * q^54 - 23328 * q^55 - 15912 * q^57 - 5928 * q^58 - 28092 * q^59 - 7776 * q^60 + 38866 * q^61 - 66880 * q^62 + 8192 * q^64 + 53892 * q^65 - 7776 * q^66 - 23948 * q^67 - 20832 * q^68 + 40824 * q^69 - 41256 * q^71 + 5184 * q^72 - 290 * q^73 - 18856 * q^74 - 1881 * q^75 + 28288 * q^76 + 71856 * q^78 + 99544 * q^79 + 13824 * q^80 - 6561 * q^81 - 39144 * q^82 + 38616 * q^83 - 140616 * q^85 + 77744 * q^86 - 13338 * q^87 + 13824 * q^88 - 36390 * q^89 + 34992 * q^90 - 72576 * q^92 + 75240 * q^93 + 88800 * q^94 + 47736 * q^95 - 9216 * q^96 - 158156 * q^97 + 34992 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	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
$5$	27.0000	−	46.7654i	0.482991	−	0.836564i	−0.516819	−	0.856095i	$-0.672884\pi$
$5$	27.0000	−	46.7654i	0.482991	−	0.836564i	0.999809	+	0.0195305i	$0.00621716\pi$
$6$	36.0000			0.408248
$7$		0			0
$7$		0			0
$8$	−64.0000			−0.353553
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	−108.000	−	187.061i	−0.341526	−	0.591540i
$11$	−108.000	−	187.061i	−0.269118	−	0.466125i	0.699517	−	0.714616i	$-0.253399\pi$
$11$	−108.000	−	187.061i	−0.269118	−	0.466125i	−0.968634	+	0.248491i	$0.920065\pi$
$12$	72.0000	−	124.708i	0.144338	−	0.250000i
$13$	998.000			1.63784			0.818921	−	0.573906i	$-0.194572\pi$
$13$	998.000			1.63784			0.818921	+	0.573906i	$0.194572\pi$
$14$		0			0
$15$	486.000			0.557710
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	−651.000	−	1127.57i	−0.546335	−	0.946279i	−0.998522	−	0.0543561i	$-0.982689\pi$
$17$	−651.000	−	1127.57i	−0.546335	−	0.946279i	0.452187	−	0.891923i	$-0.350644\pi$
$18$	162.000	+	280.592i	0.117851	+	0.204124i
$19$	−442.000	+	765.566i	−0.280891	+	0.486518i	−0.971605	−	0.236611i	$-0.923963\pi$
$19$	−442.000	+	765.566i	−0.280891	+	0.486518i	0.690713	+	0.723129i	$0.257297\pi$
$20$	−864.000			−0.482991
$21$		0			0
$22$	−864.000			−0.380590
$23$	1134.00	−	1964.15i	0.446986	−	0.774202i	−0.551203	−	0.834371i	$-0.685831\pi$
$23$	1134.00	−	1964.15i	0.446986	−	0.774202i	0.998188	+	0.0601698i	$0.0191642\pi$
$24$	−288.000	−	498.831i	−0.102062	−	0.176777i
$25$	104.500	+	180.999i	0.0334400	+	0.0579198i
$26$	1996.00	−	3457.17i	0.579065	−	1.00297i
$27$	−729.000			−0.192450
$28$		0			0
$29$	−1482.00			−0.327230			−0.163615	−	0.986524i	$-0.552315\pi$
$29$	−1482.00			−0.327230			−0.163615	+	0.986524i	$0.552315\pi$
$30$	972.000	−	1683.55i	0.197180	−	0.341526i
$31$	−4180.00	−	7239.97i	−0.781218	−	1.35311i	−0.931233	−	0.364425i	$-0.881266\pi$
$31$	−4180.00	−	7239.97i	−0.781218	−	1.35311i	0.150015	−	0.988684i	$-0.452068\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$	972.000	−	1683.55i	0.155375	−	0.269118i
$34$	−5208.00			−0.772634
$35$		0			0
$36$	1296.00			0.166667
$37$	2357.00	−	4082.44i	0.283045	−	0.490248i	−0.689088	−	0.724677i	$-0.741989\pi$
$37$	2357.00	−	4082.44i	0.283045	−	0.490248i	0.972133	+	0.234429i	$0.0753221\pi$
$38$	1768.00	+	3062.27i	0.198620	+	0.344020i
$39$	4491.00	+	7778.64i	0.472804	+	0.818921i
$40$	−1728.00	+	2992.98i	−0.170763	+	0.295770i
$41$	−9786.00			−0.909171			−0.454585	−	0.890703i	$-0.650213\pi$
$41$	−9786.00			−0.909171			−0.454585	+	0.890703i	$0.650213\pi$
$42$		0			0
$43$	19436.0			1.60301			0.801504	−	0.597989i	$-0.204033\pi$
$43$	19436.0			1.60301			0.801504	+	0.597989i	$0.204033\pi$
$44$	−1728.00	+	2992.98i	−0.134559	+	0.233063i
$45$	2187.00	+	3788.00i	0.160997	+	0.278855i
$46$	−4536.00	−	7856.58i	−0.316066	−	0.547443i
$47$	−11100.0	+	19225.8i	−0.732957	+	1.26952i	0.222657	+	0.974897i	$0.428527\pi$
$47$	−11100.0	+	19225.8i	−0.732957	+	1.26952i	−0.955614	+	0.294622i	$0.904806\pi$
$48$	−2304.00			−0.144338
$49$		0			0
$50$	836.000			0.0472913
$51$	5859.00	−	10148.1i	0.315426	−	0.546335i
$52$	−7984.00	−	13828.7i	−0.409461	−	0.709207i
$53$	−13395.0	−	23200.8i	−0.655018	−	1.13452i	−0.981889	−	0.189455i	$-0.939328\pi$
$53$	−13395.0	−	23200.8i	−0.655018	−	1.13452i	0.326872	−	0.945069i	$-0.394006\pi$
$54$	−1458.00	+	2525.33i	−0.0680414	+	0.117851i
$55$	−11664.0			−0.519925
$56$		0			0
$57$	−7956.00			−0.324345
$58$	−2964.00	+	5133.80i	−0.115693	+	0.200387i
$59$	−14046.0	−	24328.4i	−0.525318	−	0.909878i	−0.999565	−	0.0294862i	$-0.990613\pi$
$59$	−14046.0	−	24328.4i	−0.525318	−	0.909878i	0.474247	−	0.880392i	$-0.342720\pi$
$60$	−3888.00	−	6734.21i	−0.139427	−	0.241495i
$61$	19433.0	−	33658.9i	0.668675	−	1.15818i	−0.309600	−	0.950867i	$-0.600195\pi$
$61$	19433.0	−	33658.9i	0.668675	−	1.15818i	0.978275	−	0.207312i	$-0.0664717\pi$
$62$	−33440.0			−1.10481
$63$		0			0
$64$	4096.00			0.125000
$65$	26946.0	−	46671.8i	0.791063	−	1.37016i
$66$	−3888.00	−	6734.21i	−0.109867	−	0.190295i
$67$	−11974.0	−	20739.6i	−0.325876	−	0.564434i	0.655813	−	0.754923i	$-0.272326\pi$
$67$	−11974.0	−	20739.6i	−0.325876	−	0.564434i	−0.981689	+	0.190489i	$0.938992\pi$
$68$	−10416.0	+	18041.0i	−0.273167	+	0.473140i
$69$	20412.0			0.516134
$70$		0			0
$71$	−20628.0			−0.485636			−0.242818	−	0.970072i	$-0.578072\pi$
$71$	−20628.0			−0.485636			−0.242818	+	0.970072i	$0.578072\pi$
$72$	2592.00	−	4489.48i	0.0589256	−	0.102062i
$73$	−145.000	−	251.147i	−0.00318464	−	0.00551596i	0.864429	−	0.502755i	$-0.167680\pi$
$73$	−145.000	−	251.147i	−0.00318464	−	0.00551596i	−0.867613	+	0.497239i	$0.834347\pi$
$74$	−9428.00	−	16329.8i	−0.200143	−	0.346658i
$75$	−940.500	+	1628.99i	−0.0193066	+	0.0334400i
$76$	14144.0			0.280891
$77$		0			0
$78$	35928.0			0.668646
$79$	49772.0	−	86207.6i	0.897258	−	1.55410i	0.0662732	−	0.997802i	$-0.478889\pi$
$79$	49772.0	−	86207.6i	0.897258	−	1.55410i	0.830985	−	0.556295i	$-0.187778\pi$
$80$	6912.00	+	11971.9i	0.120748	+	0.209141i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	−19572.0	+	33899.7i	−0.321440	+	0.556751i
$83$	19308.0			0.307639			0.153820	−	0.988099i	$-0.450842\pi$
$83$	19308.0			0.307639			0.153820	+	0.988099i	$0.450842\pi$
$84$		0			0
$85$	−70308.0			−1.05550
$86$	38872.0	−	67328.3i	0.566749	−	0.981638i
$87$	−6669.00	−	11551.0i	−0.0944632	−	0.163615i
$88$	6912.00	+	11971.9i	0.0951474	+	0.164800i
$89$	−18195.0	+	31514.7i	−0.243488	+	0.421733i	−0.961705	−	0.274085i	$-0.911625\pi$
$89$	−18195.0	+	31514.7i	−0.243488	+	0.421733i	0.718218	+	0.695819i	$0.244958\pi$
$90$	17496.0			0.227684
$91$		0			0
$92$	−36288.0			−0.446986
$93$	37620.0	−	65159.8i	0.451036	−	0.781218i
$94$	44400.0	+	76903.1i	0.518279	+	0.897685i
$95$	23868.0	+	41340.6i	0.271336	+	0.469967i
$96$	−4608.00	+	7981.29i	−0.0510310	+	0.0883883i
$97$	−79078.0			−0.853348			−0.426674	−	0.904405i	$-0.640315\pi$
$97$	−79078.0			−0.853348			−0.426674	+	0.904405i	$0.640315\pi$
$98$		0			0
$99$	17496.0			0.179412
$100$	1672.00	−	2895.99i	0.0167200	−	0.0289599i
$101$	−92313.0	−	159891.i	−0.900450	−	1.55962i	−0.826911	−	0.562332i	$-0.809904\pi$
$101$	−92313.0	−	159891.i	−0.900450	−	1.55962i	−0.0735382	−	0.997292i	$-0.523429\pi$
$102$	−23436.0	−	40592.3i	−0.223040	−	0.386317i
$103$	−32296.0	+	55938.3i	−0.299955	+	0.519537i	−0.976125	−	0.217208i	$-0.930305\pi$
$103$	−32296.0	+	55938.3i	−0.299955	+	0.519537i	0.676171	+	0.736745i	$0.263638\pi$
$104$	−63872.0			−0.579065
$105$		0			0
$106$	−107160.			−0.926335
$107$	−74796.0	+	129550.i	−0.631566	+	1.09390i	0.355665	+	0.934613i	$0.384254\pi$
$107$	−74796.0	+	129550.i	−0.631566	+	1.09390i	−0.987232	+	0.159291i	$0.949079\pi$
$108$	5832.00	+	10101.3i	0.0481125	+	0.0833333i
$109$	31913.0	+	55274.9i	0.257277	+	0.445617i	0.965512	−	0.260360i	$-0.0838413\pi$
$109$	31913.0	+	55274.9i	0.257277	+	0.445617i	−0.708234	+	0.705977i	$0.750508\pi$
$110$	−23328.0	+	40405.3i	−0.183821	+	0.318388i
$111$	42426.0			0.326832
$112$		0			0
$113$	−71022.0			−0.523235			−0.261618	−	0.965172i	$-0.584256\pi$
$113$	−71022.0			−0.523235			−0.261618	+	0.965172i	$0.584256\pi$
$114$	−15912.0	+	27560.4i	−0.114673	+	0.198620i
$115$	−61236.0	−	106064.i	−0.431780	−	0.747864i
$116$	11856.0	+	20535.2i	0.0818075	+	0.141695i
$117$	−40419.0	+	70007.8i	−0.272974	+	0.472804i
$118$	−112368.			−0.742912
$119$		0			0
$120$	−31104.0			−0.197180
$121$	57197.5	−	99069.0i	0.355151	−	0.615140i
$122$	−77732.0	−	134636.i	−0.472825	−	0.818957i
$123$	−44037.0	−	76274.3i	−0.262455	−	0.454585i
$124$	−66880.0	+	115840.i	−0.390609	+	0.676554i
$125$	180036.			1.03059
$126$		0			0
$127$	269624.			1.48337			0.741685	−	0.670749i	$-0.234027\pi$
$127$	269624.			1.48337			0.741685	+	0.670749i	$0.234027\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$	87462.0	+	151489.i	0.462749	+	0.801504i
$130$	−107784.	−	186687.i	−0.559366	−	0.968850i
$131$	−40590.0	+	70303.9i	−0.206653	+	0.357933i	−0.950658	−	0.310241i	$-0.899590\pi$
$131$	−40590.0	+	70303.9i	−0.206653	+	0.357933i	0.744005	+	0.668174i	$0.232924\pi$
$132$	−31104.0			−0.155375
$133$		0			0
$134$	−95792.0			−0.460858
$135$	−19683.0	+	34092.0i	−0.0929516	+	0.160997i
$136$	41664.0	+	72164.2i	0.193158	+	0.334560i
$137$	130455.	+	225955.i	0.593826	+	1.02854i	0.993711	+	0.111972i	$0.0357166\pi$
$137$	130455.	+	225955.i	0.593826	+	1.02854i	−0.399885	+	0.916565i	$0.630950\pi$
$138$	40824.0	−	70709.2i	0.182481	−	0.316066i
$139$	−297964.			−1.30806			−0.654029	−	0.756470i	$-0.726922\pi$
$139$	−297964.			−1.30806			−0.654029	+	0.756470i	$0.726922\pi$
$140$		0			0
$141$	−199800.			−0.846346
$142$	−41256.0	+	71457.5i	−0.171698	+	0.297390i
$143$	−107784.	−	186687.i	−0.440772	−	0.763440i
$144$	−10368.0	−	17957.9i	−0.0416667	−	0.0721688i
$145$	−40014.0	+	69306.3i	−0.158049	+	0.273749i
$146$	−1160.00			−0.00450377
$147$		0			0
$148$	−75424.0			−0.283045
$149$	199485.	−	345518.i	0.736113	−	1.27499i	−0.218120	−	0.975922i	$-0.569992\pi$
$149$	199485.	−	345518.i	0.736113	−	1.27499i	0.954233	−	0.299063i	$-0.0966742\pi$
$150$	3762.00	+	6515.98i	0.0136518	+	0.0236457i
$151$	112484.	+	194828.i	0.401466	+	0.695359i	0.993903	−	0.110258i	$-0.0351676\pi$
$151$	112484.	+	194828.i	0.401466	+	0.695359i	−0.592437	+	0.805616i	$0.701834\pi$
$152$	28288.0	−	48996.3i	0.0993101	−	0.172010i
$153$	105462.			0.364223
$154$		0			0
$155$	−451440.			−1.50928
$156$	71856.0	−	124458.i	0.236402	−	0.409461i
$157$	116609.	+	201973.i	0.377557	+	0.653949i	0.990706	−	0.136019i	$-0.0434308\pi$
$157$	116609.	+	201973.i	0.377557	+	0.653949i	−0.613149	+	0.789967i	$0.710097\pi$
$158$	−199088.	−	344831.i	−0.634457	−	1.09891i
$159$	120555.	−	208807.i	0.378175	−	0.655018i
$160$	55296.0			0.170763
$161$		0			0
$162$	−26244.0			−0.0785674
$163$	−233110.	+	403758.i	−0.687214	+	1.19029i	0.285522	+	0.958372i	$0.407833\pi$
$163$	−233110.	+	403758.i	−0.687214	+	1.19029i	−0.972736	+	0.231917i	$0.925500\pi$
$164$	78288.0	+	135599.i	0.227293	+	0.393683i
$165$	−52488.0	−	90911.9i	−0.150089	−	0.259963i
$166$	38616.0	−	66884.9i	0.108767	−	0.188390i
$167$	−100848.			−0.279818			−0.139909	−	0.990164i	$-0.544681\pi$
$167$	−100848.			−0.279818			−0.139909	+	0.990164i	$0.544681\pi$
$168$		0			0
$169$	624711.			1.68253
$170$	−140616.	+	243554.i	−0.373175	+	0.646358i
$171$	−35802.0	−	62010.9i	−0.0936304	−	0.162173i
$172$	−155488.	−	269313.i	−0.400752	−	0.694123i
$173$	334419.	−	579231.i	0.849524	−	1.47142i	−0.0321096	−	0.999484i	$-0.510223\pi$
$173$	334419.	−	579231.i	0.849524	−	1.47142i	0.881634	−	0.471934i	$-0.156444\pi$
$174$	−53352.0			−0.133591
$175$		0			0
$176$	55296.0			0.134559
$177$	126414.	−	218955.i	0.303293	−	0.525318i
$178$	72780.0	+	126059.i	0.172172	+	0.298210i
$179$	307428.	+	532481.i	0.717151	+	1.24214i	0.962124	+	0.272613i	$0.0878877\pi$
$179$	307428.	+	532481.i	0.717151	+	1.24214i	−0.244972	+	0.969530i	$0.578779\pi$
$180$	34992.0	−	60607.9i	0.0804984	−	0.139427i
$181$	540686.			1.22673			0.613365	−	0.789800i	$-0.289816\pi$
$181$	540686.			1.22673			0.613365	+	0.789800i	$0.289816\pi$
$182$		0			0
$183$	349794.			0.772120
$184$	−72576.0	+	125705.i	−0.158033	+	0.273722i
$185$	−127278.	−	220452.i	−0.273416	−	0.473571i
$186$	−150480.	−	260639.i	−0.318931	−	0.552404i
$187$	−140616.	+	243554.i	−0.294056	+	0.509321i
$188$	355200.			0.732957
$189$		0			0
$190$	190944.			0.383727
$191$	20958.0	−	36300.3i	0.0415687	−	0.0719991i	−0.844493	−	0.535567i	$-0.820098\pi$
$191$	20958.0	−	36300.3i	0.0415687	−	0.0719991i	0.886061	+	0.463568i	$0.153431\pi$
$192$	18432.0	+	31925.2i	0.0360844	+	0.0625000i
$193$	266999.	+	462456.i	0.515960	+	0.893670i	0.999828	+	0.0185286i	$0.00589817\pi$
$193$	266999.	+	462456.i	0.515960	+	0.893670i	−0.483868	+	0.875141i	$0.660768\pi$
$194$	−158156.	+	273934.i	−0.301704	+	0.522567i
$195$	485028.			0.913441
$196$		0			0
$197$	824886.			1.51436			0.757179	−	0.653208i	$-0.226577\pi$
$197$	824886.			1.51436			0.757179	+	0.653208i	$0.226577\pi$
$198$	34992.0	−	60607.9i	0.0634316	−	0.109867i
$199$	199772.	+	346015.i	0.357604	+	0.619388i	0.987560	−	0.157243i	$-0.0502606\pi$
$199$	199772.	+	346015.i	0.357604	+	0.619388i	−0.629956	+	0.776631i	$0.716927\pi$
$200$	−6688.00	−	11584.0i	−0.0118228	−	0.0204777i
$201$	107766.	−	186656.i	0.188145	−	0.325876i
$202$	−738504.			−1.27343
$203$		0			0
$204$	−187488.			−0.315426
$205$	−264222.	+	457646.i	−0.439121	+	0.760580i
$206$	129184.	+	223753.i	0.212100	+	0.367368i
$207$	91854.0	+	159096.i	0.148995	+	0.258067i
$208$	−127744.	+	221259.i	−0.204730	+	0.354603i
$209$	190944.			0.302371
$210$		0			0
$211$	868868.			1.34353			0.671765	−	0.740764i	$-0.265536\pi$
$211$	868868.			1.34353			0.671765	+	0.740764i	$0.265536\pi$
$212$	−214320.	+	371213.i	−0.327509	+	0.567262i
$213$	−92826.0	−	160779.i	−0.140191	−	0.242818i
$214$	299184.	+	518202.i	0.446585	+	0.773508i
$215$	524772.	−	908932.i	0.774238	−	1.34102i
$216$	46656.0			0.0680414
$217$		0			0
$218$	255304.			0.363845
$219$	1305.00	−	2260.33i	0.00183865	−	0.00318464i
$220$	93312.0	+	161621.i	0.129981	+	0.225134i
$221$	−649698.	−	1.12531e6i	−0.894810	−	1.54986i
$222$	84852.0	−	146968.i	0.115553	−	0.200143i
$223$	−626656.			−0.843853			−0.421927	−	0.906630i	$-0.638646\pi$
$223$	−626656.			−0.843853			−0.421927	+	0.906630i	$0.638646\pi$
$224$		0			0
$225$	−16929.0			−0.0222933
$226$	−142044.	+	246027.i	−0.184992	+	0.320415i
$227$	225198.	+	390054.i	0.290068	+	0.502413i	0.973826	−	0.227297i	$-0.0729887\pi$
$227$	225198.	+	390054.i	0.290068	+	0.502413i	−0.683758	+	0.729709i	$0.739655\pi$
$228$	63648.0	+	110242.i	0.0810863	+	0.140446i
$229$	532265.	−	921910.i	0.670717	−	1.16172i	−0.306984	−	0.951715i	$-0.599320\pi$
$229$	532265.	−	921910.i	0.670717	−	1.16172i	0.977701	−	0.210001i	$-0.0673467\pi$
$230$	−489888.			−0.610629
$231$		0			0
$232$	94848.0			0.115693
$233$	−718089.	+	1.24377e6i	−0.866540	+	1.50089i	−0.00102954	+	0.999999i	$0.500328\pi$
$233$	−718089.	+	1.24377e6i	−0.866540	+	1.50089i	−0.865510	+	0.500891i	$0.833006\pi$
$234$	161676.	+	280031.i	0.193022	+	0.334323i
$235$	599400.	+	1.03819e6i	0.708023	+	1.22633i
$236$	−224736.	+	389254.i	−0.262659	+	0.454939i
$237$	895896.			1.03606
$238$		0			0
$239$	−997860.			−1.12999			−0.564995	−	0.825094i	$-0.691122\pi$
$239$	−997860.			−1.12999			−0.564995	+	0.825094i	$0.691122\pi$
$240$	−62208.0	+	107747.i	−0.0697137	+	0.120748i
$241$	113987.	+	197431.i	0.126419	+	0.218964i	0.922287	−	0.386506i	$-0.126318\pi$
$241$	113987.	+	197431.i	0.126419	+	0.218964i	−0.795868	+	0.605471i	$0.792985\pi$
$242$	−228790.	−	396276.i	−0.251130	−	0.434970i
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$	−621856.			−0.668675
$245$		0			0
$246$	−352296.			−0.371168
$247$	−441116.	+	764035.i	−0.460056	+	0.796840i
$248$	267520.	+	463358.i	0.276202	+	0.478396i
$249$	86886.0	+	150491.i	0.0888079	+	0.153820i
$250$	360072.	−	623663.i	0.364367	−	0.631103i
$251$	1.51657e6			1.51942			0.759712	−	0.650260i	$-0.225340\pi$
$251$	1.51657e6			1.51942			0.759712	+	0.650260i	$0.225340\pi$
$252$		0			0
$253$	−489888.			−0.481167
$254$	539248.	−	934005.i	0.524450	−	0.908374i
$255$	−316386.	−	547997.i	−0.304696	−	0.527749i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−227943.	+	394809.i	−0.215275	+	0.372867i	−0.953358	−	0.301843i	$-0.902398\pi$
$257$	−227943.	+	394809.i	−0.215275	+	0.372867i	0.738083	+	0.674710i	$0.235731\pi$
$258$	699696.			0.654425
$259$		0			0
$260$	−862272.			−0.791063
$261$	60021.0	−	103959.i	0.0545383	−	0.0944632i
$262$	162360.	+	281216.i	0.146125	+	0.253097i
$263$	376326.	+	651816.i	0.335486	+	0.581079i	0.983578	−	0.180483i	$-0.0577660\pi$
$263$	376326.	+	651816.i	0.335486	+	0.581079i	−0.648092	+	0.761562i	$0.724433\pi$
$264$	−62208.0	+	107747.i	−0.0549334	+	0.0951474i
$265$	−1.44666e6			−1.26547
$266$		0			0
$267$	−327510.			−0.281155
$268$	−191584.	+	331833.i	−0.162938	+	0.282217i
$269$	−71841.0	−	124432.i	−0.0605329	−	0.104846i	0.834171	−	0.551506i	$-0.185947\pi$
$269$	−71841.0	−	124432.i	−0.0605329	−	0.104846i	−0.894704	+	0.446660i	$0.852613\pi$
$270$	78732.0	+	136368.i	0.0657267	+	0.113842i
$271$	−378748.	+	656011.i	−0.313276	+	0.542610i	−0.979070	−	0.203526i	$-0.934760\pi$
$271$	−378748.	+	656011.i	−0.313276	+	0.542610i	0.665794	+	0.746136i	$0.268093\pi$
$272$	333312.			0.273167
$273$		0			0
$274$	1.04364e6			0.839797
$275$	22572.0	−	39095.9i	0.0179986	−	0.0311745i
$276$	−163296.	−	282837.i	−0.129034	−	0.223493i
$277$	581069.	+	1.00644e6i	0.455018	+	0.788114i	0.998689	−	0.0511843i	$-0.0162996\pi$
$277$	581069.	+	1.00644e6i	0.455018	+	0.788114i	−0.543672	+	0.839298i	$0.682966\pi$
$278$	−595928.	+	1.03218e6i	−0.462468	+	0.801018i
$279$	677160.			0.520812
$280$		0			0
$281$	−414366.			−0.313053			−0.156527	−	0.987674i	$-0.550030\pi$
$281$	−414366.			−0.313053			−0.156527	+	0.987674i	$0.550030\pi$
$282$	−399600.	+	692128.i	−0.299228	+	0.518279i
$283$	−60214.0	−	104294.i	−0.0446922	−	0.0774091i	0.842814	−	0.538205i	$-0.180897\pi$
$283$	−60214.0	−	104294.i	−0.0446922	−	0.0774091i	−0.887506	+	0.460796i	$0.847564\pi$
$284$	165024.	+	285830.i	0.121409	+	0.210287i
$285$	−214812.	+	372065.i	−0.156656	+	0.271336i
$286$	−862272.			−0.623346
$287$		0			0
$288$	−82944.0			−0.0589256
$289$	−137674.	+	238457.i	−0.0969629	+	0.167945i
$290$	160056.	+	277225.i	0.111758	+	0.193570i
$291$	−355851.	−	616352.i	−0.246340	−	0.426674i
$292$	−2320.00	+	4018.36i	−0.00159232	+	0.00275798i
$293$	2.20159e6			1.49819			0.749094	−	0.662463i	$-0.230489\pi$
$293$	2.20159e6			1.49819			0.749094	+	0.662463i	$0.230489\pi$
$294$		0			0
$295$	−1.51697e6			−1.01490
$296$	−150848.	+	261276.i	−0.100071	+	0.173329i
$297$	78732.0	+	136368.i	0.0517917	+	0.0897059i
$298$	−797940.	−	1.38207e6i	−0.520511	−	0.901551i
$299$	1.13173e6	−	1.96022e6i	0.732092	−	1.26802i
$300$	30096.0			0.0193066
$301$		0			0
$302$	899872.			0.567758
$303$	830817.	−	1.43902e6i	0.519875	−	0.900450i
$304$	−113152.	−	195985.i	−0.0702228	−	0.121629i
$305$	−1.04938e6	−	1.81758e6i	−0.645928	−	1.11878i
$306$	210924.	−	365331.i	0.128772	−	0.223040i
$307$	110900.			0.0671561			0.0335781	−	0.999436i	$-0.489310\pi$
$307$	110900.			0.0671561			0.0335781	+	0.999436i	$0.489310\pi$
$308$		0			0
$309$	−581328.			−0.346358
$310$	−902880.	+	1.56383e6i	−0.533612	+	0.924244i
$311$	455304.	+	788610.i	0.266932	+	0.462340i	0.968068	−	0.250688i	$-0.0806568\pi$
$311$	455304.	+	788610.i	0.266932	+	0.462340i	−0.701136	+	0.713028i	$0.747323\pi$
$312$	−287424.	−	497833.i	−0.167162	−	0.289532i
$313$	−1.56124e6	+	2.70414e6i	−0.900758	+	1.56016i	−0.0742450	+	0.997240i	$0.523655\pi$
$313$	−1.56124e6	+	2.70414e6i	−0.900758	+	1.56016i	−0.826513	+	0.562918i	$0.809679\pi$
$314$	932872.			0.533947
$315$		0			0
$316$	−1.59270e6			−0.897258
$317$	1.38344e6	−	2.39619e6i	0.773237	−	1.33929i	−0.162543	−	0.986701i	$-0.551970\pi$
$317$	1.38344e6	−	2.39619e6i	0.773237	−	1.33929i	0.935780	−	0.352584i	$-0.114697\pi$
$318$	−482220.	−	835230.i	−0.267410	−	0.463167i
$319$	160056.	+	277225.i	0.0880634	+	0.152530i
$320$	110592.	−	191551.i	0.0603738	−	0.104571i
$321$	−1.34633e6			−0.729270
$322$		0			0
$323$	1.15097e6			0.613842
$324$	−52488.0	+	90911.9i	−0.0277778	+	0.0481125i
$325$	104291.	+	180637.i	0.0547695	+	0.0948635i
$326$	932440.	+	1.61503e6i	0.485934	+	0.841662i
$327$	−287217.	+	497474.i	−0.148539	+	0.257277i
$328$	626304.			0.321440
$329$		0			0
$330$	−419904.			−0.212259
$331$	−1.61129e6	+	2.79083e6i	−0.808356	+	1.40011i	0.105646	+	0.994404i	$0.466309\pi$
$331$	−1.61129e6	+	2.79083e6i	−0.808356	+	1.40011i	−0.914002	+	0.405710i	$0.867024\pi$
$332$	−154464.	−	267539.i	−0.0769099	−	0.133212i
$333$	190917.	+	330678.i	0.0943483	+	0.163416i
$334$	−201696.	+	349348.i	−0.0989307	+	0.171353i
$335$	−1.29319e6			−0.629580
$336$		0			0
$337$	1.63306e6			0.783298			0.391649	−	0.920115i	$-0.371905\pi$
$337$	1.63306e6			0.783298			0.391649	+	0.920115i	$0.371905\pi$
$338$	1.24942e6	−	2.16406e6i	0.594864	−	1.03033i
$339$	−319599.	−	553562.i	−0.151045	−	0.261618i
$340$	562464.	+	974216.i	0.263875	+	0.457044i
$341$	−902880.	+	1.56383e6i	−0.420479	+	0.728291i
$342$	−286416.			−0.132413
$343$		0			0
$344$	−1.24390e6			−0.566749
$345$	551124.	−	954575.i	0.249288	−	0.431780i
$346$	−1.33768e6	−	2.31692e6i	−0.600704	−	1.04045i
$347$	−518208.	−	897563.i	−0.231036	−	0.400167i	0.727077	−	0.686556i	$-0.240878\pi$
$347$	−518208.	−	897563.i	−0.231036	−	0.400167i	−0.958113	+	0.286389i	$0.907545\pi$
$348$	−106704.	+	184817.i	−0.0472316	+	0.0818075i
$349$	−4.22999e6			−1.85898			−0.929491	−	0.368844i	$-0.879754\pi$
$349$	−4.22999e6			−1.85898			−0.929491	+	0.368844i	$0.879754\pi$
$350$		0			0
$351$	−727542.			−0.315203
$352$	110592.	−	191551.i	0.0475737	−	0.0824001i
$353$	−119403.	−	206812.i	−0.0510010	−	0.0883363i	0.839398	−	0.543517i	$-0.182908\pi$
$353$	−119403.	−	206812.i	−0.0510010	−	0.0883363i	−0.890399	+	0.455181i	$0.849574\pi$
$354$	−505656.	−	875822.i	−0.214460	−	0.371456i
$355$	−556956.	+	964676.i	−0.234558	+	0.406266i
$356$	582240.			0.243488
$357$		0			0
$358$	2.45942e6			1.01421
$359$	1.33214e6	−	2.30733e6i	0.545523	−	0.944874i	−0.453051	−	0.891485i	$-0.649664\pi$
$359$	1.33214e6	−	2.30733e6i	0.545523	−	0.944874i	0.998574	−	0.0533889i	$-0.0170023\pi$
$360$	−139968.	−	242432.i	−0.0569210	−	0.0985901i
$361$	847322.	+	1.46760e6i	0.342200	+	0.592708i
$362$	1.08137e6	−	1.87299e6i	0.433714	−	0.751215i
$363$	1.02956e6			0.410094
$364$		0			0
$365$	−15660.0			−0.00615261
$366$	699588.	−	1.21172e6i	0.272986	−	0.472825i
$367$	855416.	+	1.48162e6i	0.331522	+	0.574213i	0.982810	−	0.184617i	$-0.0591046\pi$
$367$	855416.	+	1.48162e6i	0.331522	+	0.574213i	−0.651289	+	0.758830i	$0.725771\pi$
$368$	290304.	+	502821.i	0.111746	+	0.193550i
$369$	396333.	−	686469.i	0.151528	−	0.262455i
$370$	−1.01822e6			−0.386669
$371$		0			0
$372$	−1.20384e6			−0.451036
$373$	1.98324e6	−	3.43508e6i	0.738081	−	1.27839i	−0.215277	−	0.976553i	$-0.569065\pi$
$373$	1.98324e6	−	3.43508e6i	0.738081	−	1.27839i	0.953358	−	0.301841i	$-0.0976013\pi$
$374$	562464.	+	974216.i	0.207929	+	0.360144i
$375$	810162.	+	1.40324e6i	0.297505	+	0.515293i
$376$	710400.	−	1.23045e6i	0.259139	−	0.448842i
$377$	−1.47904e6			−0.535951
$378$		0			0
$379$	828668.			0.296335			0.148167	−	0.988962i	$-0.452663\pi$
$379$	828668.			0.296335			0.148167	+	0.988962i	$0.452663\pi$
$380$	381888.	−	661449.i	0.135668	−	0.234984i
$381$	1.21331e6	+	2.10151e6i	0.428212	+	0.741685i
$382$	−83832.0	−	145201.i	−0.0293935	−	0.0509110i
$383$	1.27843e6	−	2.21431e6i	0.445329	−	0.771332i	−0.552746	−	0.833350i	$-0.686420\pi$
$383$	1.27843e6	−	2.21431e6i	0.445329	−	0.771332i	0.998075	+	0.0620176i	$0.0197535\pi$
$384$	147456.			0.0510310
$385$		0			0
$386$	2.13599e6			0.729678
$387$	−787158.	+	1.36340e6i	−0.267168	+	0.462749i
$388$	632624.	+	1.09574e6i	0.213337	+	0.369511i
$389$	−1.45893e6	−	2.52694e6i	−0.488832	−	0.846682i	0.511086	−	0.859530i	$-0.329244\pi$
$389$	−1.45893e6	−	2.52694e6i	−0.488832	−	0.846682i	−0.999917	+	0.0128481i	$0.995910\pi$
$390$	970056.	−	1.68019e6i	0.322950	−	0.559366i
$391$	−2.95294e6			−0.976815
$392$		0			0
$393$	−730620.			−0.238622
$394$	1.64977e6	−	2.85749e6i	0.535406	−	0.927351i
$395$	−2.68769e6	−	4.65521e6i	−0.866735	−	1.50123i
$396$	−139968.	−	242432.i	−0.0448529	−	0.0776875i
$397$	−1.25357e6	+	2.17126e6i	−0.399185	+	0.691408i	−0.993626	−	0.112731i	$-0.964040\pi$
$397$	−1.25357e6	+	2.17126e6i	−0.399185	+	0.691408i	0.594441	+	0.804139i	$0.297373\pi$
$398$	1.59818e6			0.505728
$399$		0			0
$400$	−53504.0			−0.0167200
$401$	−495333.	+	857942.i	−0.153828	+	0.266438i	−0.932632	−	0.360830i	$-0.882494\pi$
$401$	−495333.	+	857942.i	−0.153828	+	0.266438i	0.778803	+	0.627268i	$0.215827\pi$
$402$	−431064.	−	746625.i	−0.133038	−	0.230429i
$403$	−4.17164e6	−	7.22549e6i	−1.27951	−	2.21618i
$404$	−1.47701e6	+	2.55825e6i	−0.450225	+	0.779812i
$405$	−354294.			−0.107331
$406$		0			0
$407$	−1.01822e6			−0.304689
$408$	−374976.	+	649477.i	−0.111520	+	0.193158i
$409$	−2.25912e6	−	3.91291e6i	−0.667777	−	1.15662i	−0.978524	−	0.206131i	$-0.933913\pi$
$409$	−2.25912e6	−	3.91291e6i	−0.667777	−	1.15662i	0.310748	−	0.950492i	$-0.399421\pi$
$410$	1.05689e6	+	1.83058e6i	0.310506	+	0.537811i
$411$	−1.17409e6	+	2.03359e6i	−0.342846	+	0.593826i
$412$	1.03347e6			0.299955
$413$		0			0
$414$	734832.			0.210711
$415$	521316.	−	902946.i	0.148587	−	0.257360i
$416$	510976.	+	885036.i	0.144766	+	0.250742i
$417$	−1.34084e6	−	2.32240e6i	−0.377604	−	0.654029i
$418$	381888.	−	661449.i	0.106904	−	0.185164i
$419$	605220.			0.168414			0.0842070	−	0.996448i	$-0.473164\pi$
$419$	605220.			0.168414			0.0842070	+	0.996448i	$0.473164\pi$
$420$		0			0
$421$	4.49893e6			1.23710			0.618549	−	0.785746i	$-0.287721\pi$
$421$	4.49893e6			1.23710			0.618549	+	0.785746i	$0.287721\pi$
$422$	1.73774e6	−	3.00985e6i	0.475010	−	0.822741i
$423$	−899100.	−	1.55729e6i	−0.244319	−	0.423173i
$424$	857280.	+	1.48485e6i	0.231584	+	0.401115i
$425$	136059.	−	235661.i	0.0365389	−	0.0632872i
$426$	−742608.			−0.198260
$427$		0			0
$428$	2.39347e6			0.631566
$429$	970056.	−	1.68019e6i	0.254480	−	0.440772i
$430$	−2.09909e6	−	3.63573e6i	−0.547469	−	0.948244i
$431$	−2.68797e6	−	4.65570e6i	−0.696998	−	1.20724i	−0.969503	−	0.245081i	$-0.921186\pi$
$431$	−2.68797e6	−	4.65570e6i	−0.696998	−	1.20724i	0.272505	−	0.962154i	$-0.412148\pi$
$432$	93312.0	−	161621.i	0.0240563	−	0.0416667i
$433$	−1.98561e6			−0.508950			−0.254475	−	0.967079i	$-0.581903\pi$
$433$	−1.98561e6			−0.508950			−0.254475	+	0.967079i	$0.581903\pi$
$434$		0			0
$435$	−720252.			−0.182499
$436$	510608.	−	884399.i	0.128639	−	0.222809i
$437$	1.00246e6	+	1.73630e6i	0.251109	+	0.434933i
$438$	−5220.00	−	9041.31i	−0.00130013	−	0.00225188i
$439$	−1.69364e6	+	2.93346e6i	−0.419429	+	0.726473i	−0.995882	−	0.0906576i	$-0.971103\pi$
$439$	−1.69364e6	+	2.93346e6i	−0.419429	+	0.726473i	0.576453	+	0.817130i	$0.304436\pi$
$440$	746496.			0.183821
$441$		0			0
$442$	−5.19758e6			−1.26545
$443$	−1.07047e6	+	1.85411e6i	−0.259159	+	0.448876i	−0.966017	−	0.258479i	$-0.916779\pi$
$443$	−1.07047e6	+	1.85411e6i	−0.259159	+	0.448876i	0.706858	+	0.707355i	$0.250112\pi$
$444$	−339408.	−	587872.i	−0.0817080	−	0.141522i
$445$	982530.	+	1.70179e6i	0.235205	+	0.407386i
$446$	−1.25331e6	+	2.17080e6i	−0.298347	+	0.516753i
$447$	3.59073e6			0.849990
$448$		0			0
$449$	−6.97808e6			−1.63350			−0.816752	−	0.576990i	$-0.804227\pi$
$449$	−6.97808e6			−1.63350			−0.816752	+	0.576990i	$0.804227\pi$
$450$	−33858.0	+	58643.8i	−0.00788188	+	0.0136518i
$451$	1.05689e6	+	1.83058e6i	0.244674	+	0.423788i
$452$	568176.	+	984110.i	0.130809	+	0.226567i
$453$	−1.01236e6	+	1.75345e6i	−0.231786	+	0.401466i
$454$	1.80158e6			0.410218
$455$		0			0
$456$	509184.			0.114673
$457$	2.59000e6	−	4.48600e6i	0.580107	−	1.00478i	−0.415359	−	0.909658i	$-0.636344\pi$
$457$	2.59000e6	−	4.48600e6i	0.580107	−	1.00478i	0.995466	−	0.0951178i	$-0.0303228\pi$
$458$	−2.12906e6	−	3.68764e6i	−0.474268	−	0.821457i
$459$	474579.	+	821995.i	0.105142	+	0.182112i
$460$	−979776.	+	1.69702e6i	−0.215890	+	0.373932i
$461$	−7.83001e6			−1.71597			−0.857985	−	0.513674i	$-0.828284\pi$
$461$	−7.83001e6			−1.71597			−0.857985	+	0.513674i	$0.828284\pi$
$462$		0			0
$463$	165320.			0.0358404			0.0179202	−	0.999839i	$-0.494296\pi$
$463$	165320.			0.0358404			0.0179202	+	0.999839i	$0.494296\pi$
$464$	189696.	−	328563.i	0.0409038	−	0.0708474i
$465$	−2.03148e6	−	3.51863e6i	−0.435693	−	0.754642i
$466$	2.87236e6	+	4.97507e6i	0.612736	+	1.06129i
$467$	896646.	−	1.55304e6i	0.190252	−	0.329526i	−0.755082	−	0.655631i	$-0.772403\pi$
$467$	896646.	−	1.55304e6i	0.190252	−	0.329526i	0.945334	+	0.326105i	$0.105736\pi$
$468$	1.29341e6			0.272974
$469$		0			0
$470$	4.79520e6			1.00130
$471$	−1.04948e6	+	1.81775e6i	−0.217983	+	0.377557i
$472$	898944.	+	1.55702e6i	0.185728	+	0.321691i
$473$	−2.09909e6	−	3.63573e6i	−0.431398	−	0.747203i
$474$	1.79179e6	−	3.10347e6i	0.366304	−	0.634457i
$475$	−184756.			−0.0375720
$476$		0			0
$477$	2.16999e6			0.436678
$478$	−1.99572e6	+	3.45669e6i	−0.399512	+	0.691975i
$479$	3.29828e6	+	5.71280e6i	0.656824	+	1.13765i	0.981433	+	0.191805i	$0.0614341\pi$
$479$	3.29828e6	+	5.71280e6i	0.656824	+	1.13765i	−0.324609	+	0.945848i	$0.605233\pi$
$480$	248832.	+	430990.i	0.0492950	+	0.0853815i
$481$	2.35229e6	−	4.07428e6i	0.463583	−	0.802949i
$482$	911896.			0.178784
$483$		0			0
$484$	−1.83032e6			−0.355151
$485$	−2.13511e6	+	3.69811e6i	−0.412159	+	0.713881i
$486$	−118098.	−	204552.i	−0.0226805	−	0.0392837i
$487$	2.98696e6	+	5.17357e6i	0.570700	+	0.988481i	0.996494	+	0.0836609i	$0.0266613\pi$
$487$	2.98696e6	+	5.17357e6i	0.570700	+	0.988481i	−0.425795	+	0.904820i	$0.640005\pi$
$488$	−1.24371e6	+	2.15417e6i	−0.236412	+	0.409478i
$489$	−4.19598e6			−0.793526
$490$		0			0
$491$	381264.			0.0713710			0.0356855	−	0.999363i	$-0.488639\pi$
$491$	381264.			0.0713710			0.0356855	+	0.999363i	$0.488639\pi$
$492$	−704592.	+	1.22039e6i	−0.131228	+	0.227293i
$493$	964782.	+	1.67105e6i	0.178777	+	0.309651i
$494$	1.76446e6	+	3.05614e6i	0.325309	+	0.563451i
$495$	472392.	−	818207.i	0.0866542	−	0.150089i
$496$	2.14016e6			0.390609
$497$		0			0
$498$	695088.			0.125593
$499$	−771754.	+	1.33672e6i	−0.138748	+	0.240319i	−0.927023	−	0.375004i	$-0.877641\pi$
$499$	−771754.	+	1.33672e6i	−0.138748	+	0.240319i	0.788275	+	0.615323i	$0.210975\pi$
$500$	−1.44029e6	−	2.49465e6i	−0.257647	−	0.446257i
$501$	−453816.	−	786032.i	−0.0807766	−	0.139909i
$502$	3.03314e6	−	5.25356e6i	0.537197	−	0.930453i
$503$	−4.02300e6			−0.708974			−0.354487	−	0.935061i	$-0.615344\pi$
$503$	−4.02300e6			−0.708974			−0.354487	+	0.935061i	$0.615344\pi$
$504$		0			0
$505$	−9.96980e6			−1.73964
$506$	−979776.	+	1.69702e6i	−0.170118	+	0.294653i
$507$	2.81120e6	+	4.86914e6i	0.485704	+	0.841264i
$508$	−2.15699e6	−	3.73602e6i	−0.370842	−	0.642318i
$509$	973575.	−	1.68628e6i	0.166562	−	0.288493i	−0.770647	−	0.637262i	$-0.780067\pi$
$509$	973575.	−	1.68628e6i	0.166562	−	0.288493i	0.937209	+	0.348769i	$0.113400\pi$
$510$	−2.53109e6			−0.430905
$511$		0			0
$512$	−262144.			−0.0441942
$513$	322218.	−	558098.i	0.0540576	−	0.0936304i
$514$	911772.	+	1.57924e6i	0.152222	+	0.263657i
$515$	1.74398e6	+	3.02067e6i	0.289751	+	0.501863i
$516$	1.39939e6	−	2.42382e6i	0.231374	−	0.400752i
$517$	4.79520e6			0.789006
$518$		0			0
$519$	6.01954e6			0.980946
$520$	−1.72454e6	+	2.98700e6i	−0.279683	+	0.484425i
$521$	−3.69285e6	−	6.39620e6i	−0.596028	−	1.03235i	−0.993401	−	0.114694i	$-0.963411\pi$
$521$	−3.69285e6	−	6.39620e6i	−0.596028	−	1.03235i	0.397372	−	0.917657i	$-0.369922\pi$
$522$	−240084.	−	415838.i	−0.0385644	−	0.0667956i
$523$	164870.	−	285563.i	0.0263565	−	0.0456508i	−0.852546	−	0.522652i	$-0.824943\pi$
$523$	164870.	−	285563.i	0.0263565	−	0.0456508i	0.878903	+	0.477001i	$0.158276\pi$
$524$	1.29888e6			0.206653
$525$		0			0
$526$	3.01061e6			0.474449
$527$	−5.44236e6	+	9.42644e6i	−0.853612	+	1.47850i
$528$	248832.	+	430990.i	0.0388438	+	0.0672794i
$529$	646260.	+	1.11935e6i	0.100408	+	0.173912i
$530$	−2.89332e6	+	5.01138e6i	−0.447411	+	0.774939i
$531$	2.27545e6			0.350212
$532$		0			0
$533$	−9.76643e6			−1.48908
$534$	−655020.	+	1.13453e6i	−0.0994034	+	0.172172i
$535$	4.03898e6	+	6.99573e6i	0.610081	+	1.05669i
$536$	766336.	+	1.32733e6i	0.115215	+	0.199557i
$537$	−2.76685e6	+	4.79233e6i	−0.414048	+	0.717151i
$538$	−574728.			−0.0856065
$539$		0			0
$540$	629856.			0.0929516
$541$	−43543.0	+	75418.7i	−0.00639625	+	0.0110786i	−0.869206	−	0.494450i	$-0.835369\pi$
$541$	−43543.0	+	75418.7i	−0.00639625	+	0.0110786i	0.862810	+	0.505529i	$0.168703\pi$
$542$	1.51499e6	+	2.62404e6i	0.221520	+	0.383683i
$543$	2.43309e6	+	4.21423e6i	0.354126	+	0.613365i
$544$	666624.	−	1.15463e6i	0.0965792	−	0.167280i
$545$	3.44660e6			0.497050
$546$		0			0
$547$	6.91531e6			0.988196			0.494098	−	0.869406i	$-0.335498\pi$
$547$	6.91531e6			0.988196			0.494098	+	0.869406i	$0.335498\pi$
$548$	2.08728e6	−	3.61528e6i	0.296913	−	0.514269i
$549$	1.57407e6	+	2.72637e6i	0.222892	+	0.386060i
$550$	−90288.0	−	156383.i	−0.0127269	−	0.0220437i
$551$	655044.	−	1.13457e6i	0.0919161	−	0.159203i
$552$	−1.30637e6			−0.182481
$553$		0			0
$554$	4.64855e6			0.643492
$555$	1.14550e6	−	1.98407e6i	0.157857	−	0.273416i
$556$	2.38371e6	+	4.12871e6i	0.327014	+	0.566405i
$557$	761289.	+	1.31859e6i	0.103971	+	0.180083i	0.913317	−	0.407249i	$-0.133512\pi$
$557$	761289.	+	1.31859e6i	0.103971	+	0.180083i	−0.809346	+	0.587332i	$0.800178\pi$
$558$	1.35432e6	−	2.34575e6i	0.184135	−	0.318931i
$559$	1.93971e7			2.62548
$560$		0			0
$561$	−2.53109e6			−0.339547
$562$	−828732.	+	1.43541e6i	−0.110681	+	0.191705i
$563$	3.93231e6	+	6.81096e6i	0.522850	+	0.905602i	0.999646	+	0.0265885i	$0.00846439\pi$
$563$	3.93231e6	+	6.81096e6i	0.522850	+	0.905602i	−0.476797	+	0.879013i	$0.658202\pi$
$564$	1.59840e6	+	2.76851e6i	0.211586	+	0.366478i
$565$	−1.91759e6	+	3.32137e6i	−0.252718	+	0.437720i
$566$	−481712.			−0.0632043
$567$		0			0
$568$	1.32019e6			0.171698
$569$	731607.	−	1.26718e6i	0.0947321	−	0.164081i	−0.814765	−	0.579792i	$-0.803134\pi$
$569$	731607.	−	1.26718e6i	0.0947321	−	0.164081i	0.909497	+	0.415711i	$0.136467\pi$
$570$	859248.	+	1.48826e6i	0.110772	+	0.191863i
$571$	−4.59927e6	−	7.96618e6i	−0.590336	−	1.02249i	−0.994187	−	0.107667i	$-0.965662\pi$
$571$	−4.59927e6	−	7.96618e6i	−0.590336	−	1.02249i	0.403851	−	0.914825i	$-0.367671\pi$
$572$	−1.72454e6	+	2.98700e6i	−0.220386	+	0.381720i
$573$	377244.			0.0479994
$574$		0			0
$575$	474012.			0.0597888
$576$	−165888.	+	287326.i	−0.0208333	+	0.0360844i
$577$	−1.64470e6	−	2.84870e6i	−0.205658	−	0.356211i	0.744684	−	0.667417i	$-0.232600\pi$
$577$	−1.64470e6	−	2.84870e6i	−0.205658	−	0.356211i	−0.950342	+	0.311207i	$0.899267\pi$
$578$	550694.	+	953830.i	0.0685631	+	0.118755i
$579$	−2.40299e6	+	4.16210e6i	−0.297890	+	0.515960i
$580$	1.28045e6			0.158049
$581$		0			0
$582$	−2.84681e6			−0.348378
$583$	−2.89332e6	+	5.01138e6i	−0.352554	+	0.610641i
$584$	9280.00	+	16073.4i	0.00112594	+	0.00195019i
$585$	2.18263e6	+	3.78042e6i	0.263688	+	0.456720i
$586$	4.40317e6	−	7.62652e6i	0.529690	−	0.917450i
$587$	5.12929e6			0.614416			0.307208	−	0.951642i	$-0.400605\pi$
$587$	5.12929e6			0.614416			0.307208	+	0.951642i	$0.400605\pi$
$588$		0			0
$589$	7.39024e6			0.877749
$590$	−3.03394e6	+	5.25493e6i	−0.358820	+	0.621494i
$591$	3.71199e6	+	6.42935e6i	0.437157	+	0.757179i
$592$	603392.	+	1.04511e6i	0.0707612	+	0.122562i
$593$	1.37716e6	−	2.38532e6i	0.160823	−	0.278554i	−0.774341	−	0.632769i	$-0.781918\pi$
$593$	1.37716e6	−	2.38532e6i	0.160823	−	0.278554i	0.935164	+	0.354214i	$0.115252\pi$
$594$	629856.			0.0732445
$595$		0			0
$596$	−6.38352e6			−0.736113
$597$	−1.79795e6	+	3.11414e6i	−0.206463	+	0.357604i
$598$	−4.52693e6	−	7.84087e6i	−0.517667	−	0.896626i
$599$	4.94308e6	+	8.56167e6i	0.562899	+	0.974970i	0.997242	+	0.0742224i	$0.0236475\pi$
$599$	4.94308e6	+	8.56167e6i	0.562899	+	0.974970i	−0.434342	+	0.900748i	$0.643019\pi$
$600$	60192.0	−	104256.i	0.00682591	−	0.0118228i
$601$	1.37039e7			1.54760			0.773798	−	0.633433i	$-0.218355\pi$
$601$	1.37039e7			1.54760			0.773798	+	0.633433i	$0.218355\pi$
$602$		0			0
$603$	1.93979e6			0.217251
$604$	1.79974e6	−	3.11725e6i	0.200733	−	0.347679i
$605$	−3.08866e6	−	5.34972e6i	−0.343070	−	0.594214i
$606$	−3.32327e6	−	5.75607e6i	−0.367607	−	0.636714i
$607$	3.92655e6	−	6.80099e6i	0.432553	−	0.749204i	−0.564539	−	0.825406i	$-0.690946\pi$
$607$	3.92655e6	−	6.80099e6i	0.432553	−	0.749204i	0.997092	+	0.0762020i	$0.0242794\pi$
$608$	−905216.			−0.0993101
$609$		0			0
$610$	−8.39506e6			−0.913480
$611$	−1.10778e7	+	1.91873e7i	−1.20047	+	2.07927i
$612$	−843696.	−	1.46132e6i	−0.0910558	−	0.157713i
$613$	−7.34884e6	−	1.27286e7i	−0.789892	−	1.36813i	−0.926033	−	0.377444i	$-0.876803\pi$
$613$	−7.34884e6	−	1.27286e7i	−0.789892	−	1.36813i	0.136140	−	0.990690i	$-0.456530\pi$
$614$	221800.	−	384169.i	0.0237433	−	0.0411246i
$615$	−4.75600e6			−0.507053
$616$		0			0
$617$	6.28370e6			0.664511			0.332256	−	0.943189i	$-0.392190\pi$
$617$	6.28370e6			0.664511			0.332256	+	0.943189i	$0.392190\pi$
$618$	−1.16266e6	+	2.01378e6i	−0.122456	+	0.212100i
$619$	1.13346e6	+	1.96321e6i	0.118900	+	0.205940i	0.919332	−	0.393483i	$-0.128730\pi$
$619$	1.13346e6	+	1.96321e6i	0.118900	+	0.205940i	−0.800432	+	0.599423i	$0.795397\pi$
$620$	3.61152e6	+	6.25534e6i	0.377321	+	0.653539i
$621$	−826686.	+	1.43186e6i	−0.0860224	+	0.148995i
$622$	3.64243e6			0.377499
$623$		0			0
$624$	−2.29939e6			−0.236402
$625$	4.53441e6	−	7.85383e6i	0.464324	−	0.804232i
$626$	6.24495e6	+	1.08166e7i	0.636932	+	1.10320i
$627$	859248.	+	1.48826e6i	0.0872870	+	0.151186i
$628$	1.86574e6	−	3.23156e6i	0.188779	−	0.326974i
$629$	−6.13763e6			−0.618549
$630$		0			0
$631$	−1.17477e7			−1.17457			−0.587285	−	0.809380i	$-0.699803\pi$
$631$	−1.17477e7			−1.17457			−0.587285	+	0.809380i	$0.699803\pi$
$632$	−3.18541e6	+	5.51729e6i	−0.317229	+	0.549456i
$633$	3.90991e6	+	6.77216e6i	0.387844	+	0.671765i
$634$	−5.53376e6	−	9.58476e6i	−0.546761	−	0.947018i
$635$	7.27985e6	−	1.26091e7i	0.716453	−	1.24093i
$636$	−3.85776e6			−0.378175
$637$		0			0
$638$	1.28045e6			0.124540
$639$	835434.	−	1.44701e6i	0.0809394	−	0.140191i
$640$	−442368.	−	766204.i	−0.0426907	−	0.0739425i
$641$	−2.96616e6	−	5.13753e6i	−0.285134	−	0.493867i	0.687508	−	0.726177i	$-0.258705\pi$
$641$	−2.96616e6	−	5.13753e6i	−0.285134	−	0.493867i	−0.972642	+	0.232311i	$0.925371\pi$
$642$	−2.69266e6	+	4.66382e6i	−0.257836	+	0.446585i
$643$	−6.94443e6			−0.662383			−0.331191	−	0.943564i	$-0.607451\pi$
$643$	−6.94443e6			−0.662383			−0.331191	+	0.943564i	$0.607451\pi$
$644$		0			0
$645$	9.44590e6			0.894013
$646$	2.30194e6	−	3.98707e6i	0.217026	−	0.375900i
$647$	2.48525e6	+	4.30458e6i	0.233404	+	0.404268i	0.958808	−	0.284056i	$-0.0916801\pi$
$647$	2.48525e6	+	4.30458e6i	0.233404	+	0.404268i	−0.725403	+	0.688324i	$0.758347\pi$
$648$	209952.	+	363648.i	0.0196419	+	0.0340207i
$649$	−3.03394e6	+	5.25493e6i	−0.282745	+	0.489728i
$650$	834328.			0.0774557
$651$		0			0
$652$	7.45952e6			0.687214
$653$	9.16773e6	−	1.58790e7i	0.841354	−	1.45727i	−0.0473954	−	0.998876i	$-0.515092\pi$
$653$	9.16773e6	−	1.58790e7i	0.841354	−	1.45727i	0.888750	−	0.458392i	$-0.151575\pi$
$654$	1.14887e6	+	1.98990e6i	0.105033	+	0.181922i
$655$	2.19186e6	+	3.79641e6i	0.199623	+	0.345756i
$656$	1.25261e6	−	2.16958e6i	0.113646	−	0.196841i
$657$	23490.0			0.00212310
$658$		0			0
$659$	9.01402e6			0.808546			0.404273	−	0.914638i	$-0.367525\pi$
$659$	9.01402e6			0.808546			0.404273	+	0.914638i	$0.367525\pi$
$660$	−839808.	+	1.45459e6i	−0.0750447	+	0.129981i
$661$	−349699.	−	605696.i	−0.0311308	−	0.0539202i	0.850040	−	0.526718i	$-0.176578\pi$
$661$	−349699.	−	605696.i	−0.0311308	−	0.0539202i	−0.881171	+	0.472798i	$0.843244\pi$
$662$	6.44514e6	+	1.11633e7i	0.571594	+	0.990030i
$663$	5.84728e6	−	1.01278e7i	0.516619	−	0.894810i
$664$	−1.23571e6			−0.108767
$665$		0			0
$666$	1.52734e6			0.133429
$667$	−1.68059e6	+	2.91086e6i	−0.146267	+	0.253342i
$668$	806784.	+	1.39739e6i	0.0699546	+	0.121165i
$669$	−2.81995e6	−	4.88430e6i	−0.243600	−	0.421927i
$670$	−2.58638e6	+	4.47975e6i	−0.222590	+	0.385537i
$671$	−8.39506e6			−0.719809
$672$		0			0
$673$	−5.80603e6			−0.494130			−0.247065	−	0.968999i	$-0.579466\pi$
$673$	−5.80603e6			−0.494130			−0.247065	+	0.968999i	$0.579466\pi$
$674$	3.26612e6	−	5.65708e6i	0.276938	−	0.479670i
$675$	−76180.5	−	131948.i	−0.00643553	−	0.0111467i
$676$	−4.99769e6	−	8.65625e6i	−0.420632	−	0.728556i
$677$	−492537.	+	853099.i	−0.0413016	+	0.0715365i	−0.885937	−	0.463805i	$-0.846484\pi$
$677$	−492537.	+	853099.i	−0.0413016	+	0.0715365i	0.844636	+	0.535342i	$0.179817\pi$
$678$	−2.55679e6			−0.213610
$679$		0			0
$680$	4.49971e6			0.373175
$681$	−2.02678e6	+	3.51049e6i	−0.167471	+	0.290068i
$682$	3.61152e6	+	6.25534e6i	0.297323	+	0.514979i
$683$	9.41042e6	+	1.62993e7i	0.771894	+	1.33696i	0.936524	+	0.350604i	$0.114024\pi$
$683$	9.41042e6	+	1.62993e7i	0.771894	+	1.33696i	−0.164630	+	0.986355i	$0.552643\pi$
$684$	−572832.	+	992174.i	−0.0468152	+	0.0810863i
$685$	1.40891e7			1.14725
$686$		0			0
$687$	9.58077e6			0.774477
$688$	−2.48781e6	+	4.30901e6i	−0.200376	+	0.347061i
$689$	−1.33682e7	−	2.31544e7i	−1.07282	−	1.85817i
$690$	−2.20450e6	−	3.81830e6i	−0.176273	−	0.305314i
$691$	9.66924e6	−	1.67476e7i	0.770366	−	1.33431i	−0.166996	−	0.985958i	$-0.553407\pi$
$691$	9.66924e6	−	1.67476e7i	0.770366	−	1.33431i	0.937362	−	0.348356i	$-0.113260\pi$
$692$	−1.07014e7			−0.849524
$693$		0			0
$694$	−4.14566e6			−0.326735
$695$	−8.04503e6	+	1.39344e7i	−0.631780	+	1.09427i
$696$	426816.	+	739267.i	0.0333978	+	0.0578467i
$697$	6.37069e6	+	1.10344e7i	0.496712	+	0.860330i
$698$	−8.45997e6	+	1.46531e7i	−0.657250	+	1.13839i
$699$	−1.29256e7			−1.00059
$700$		0			0
$701$	−1.41489e6			−0.108750			−0.0543748	−	0.998521i	$-0.517317\pi$
$701$	−1.41489e6			−0.108750			−0.0543748	+	0.998521i	$0.517317\pi$
$702$	−1.45508e6	+	2.52028e6i	−0.111441	+	0.193022i
$703$	2.08359e6	+	3.60888e6i	0.159010	+	0.275413i
$704$	−442368.	−	766204.i	−0.0336397	−	0.0582657i
$705$	−5.39460e6	+	9.34372e6i	−0.408777	+	0.708023i
$706$	−955224.			−0.0721263
$707$		0			0
$708$	−4.04525e6			−0.303293
$709$	377453.	−	653768.i	0.0281999	−	0.0488436i	−0.851581	−	0.524223i	$-0.824356\pi$
$709$	377453.	−	653768.i	0.0281999	−	0.0488436i	0.879781	+	0.475379i	$0.157689\pi$
$710$	2.22782e6	+	3.85870e6i	0.165857	+	0.287274i
$711$	4.03153e6	+	6.98282e6i	0.299086	+	0.518032i
$712$	1.16448e6	−	2.01694e6i	0.0860859	−	0.149105i
$713$	−1.89605e7			−1.39677
$714$		0			0
$715$	−1.16407e7			−0.851555
$716$	4.91885e6	−	8.51969e6i	0.358576	−	0.621071i
$717$	−4.49037e6	−	7.77755e6i	−0.326200	−	0.564995i
$718$	−5.32855e6	−	9.22932e6i	−0.385743	−	0.668127i
$719$	−544272.	+	942707.i	−0.0392639	+	0.0680071i	−0.884990	−	0.465611i	$-0.845835\pi$
$719$	−544272.	+	942707.i	−0.0392639	+	0.0680071i	0.845726	+	0.533618i	$0.179168\pi$
$720$	−1.11974e6			−0.0804984
$721$		0			0
$722$	6.77857e6			0.483944
$723$	−1.02588e6	+	1.77688e6i	−0.0729881	+	0.126419i
$724$	−4.32549e6	−	7.49196e6i	−0.306682	−	0.531189i
$725$	−154869.	−	268241.i	−0.0109426	−	0.0189531i
$726$	2.05911e6	−	3.56648e6i	0.144990	−	0.251130i
$727$	−755392.			−0.0530074			−0.0265037	−	0.999649i	$-0.508437\pi$
$727$	−755392.			−0.0530074			−0.0265037	+	0.999649i	$0.508437\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−31320.0	+	54247.8i	−0.00217528	+	0.00376769i
$731$	−1.26528e7	−	2.19154e7i	−0.875779	−	1.51689i
$732$	−2.79835e6	−	4.84689e6i	−0.193030	−	0.334338i
$733$	−781843.	+	1.35419e6i	−0.0537477	+	0.0930937i	−0.891647	−	0.452730i	$-0.850450\pi$
$733$	−781843.	+	1.35419e6i	−0.0537477	+	0.0930937i	0.837900	+	0.545824i	$0.183783\pi$
$734$	6.84333e6			0.468843
$735$		0			0
$736$	2.32243e6			0.158033
$737$	−2.58638e6	+	4.47975e6i	−0.175398	+	0.303798i
$738$	−1.58533e6	−	2.74588e6i	−0.107147	−	0.185584i
$739$	5.27719e6	+	9.14037e6i	0.355461	+	0.615677i	0.987197	−	0.159507i	$-0.0509906\pi$
$739$	5.27719e6	+	9.14037e6i	0.355461	+	0.615677i	−0.631736	+	0.775184i	$0.717657\pi$
$740$	−2.03645e6	+	3.52723e6i	−0.136708	+	0.236785i
$741$	−7.94009e6			−0.531227
$742$		0			0
$743$	1.73678e7			1.15418			0.577088	−	0.816682i	$-0.304189\pi$
$743$	1.73678e7			1.15418			0.577088	+	0.816682i	$0.304189\pi$
$744$	−2.40768e6	+	4.17022e6i	−0.159465	+	0.276202i
$745$	−1.07722e7	−	1.86580e7i	−0.711072	−	1.23161i
$746$	−7.93298e6	−	1.37403e7i	−0.521902	−	0.903961i
$747$	−781974.	+	1.35442e6i	−0.0512732	+	0.0888079i
$748$	4.49971e6			0.294056
$749$		0			0
$750$	6.48130e6			0.420735
$751$	1.40091e7	−	2.42644e7i	0.906378	−	1.56989i	0.0873221	−	0.996180i	$-0.472169\pi$
$751$	1.40091e7	−	2.42644e7i	0.906378	−	1.56989i	0.819056	−	0.573713i	$-0.194498\pi$
$752$	−2.84160e6	−	4.92180e6i	−0.183239	−	0.317380i
$753$	6.82457e6	+	1.18205e7i	0.438620	+	0.759712i
$754$	−2.95807e6	+	5.12353e6i	−0.189487	+	0.328202i
$755$	1.21483e7			0.775617
$756$		0			0
$757$	−1.01979e7			−0.646801			−0.323401	−	0.946262i	$-0.604826\pi$
$757$	−1.01979e7			−0.646801			−0.323401	+	0.946262i	$0.604826\pi$
$758$	1.65734e6	−	2.87059e6i	0.104770	−	0.181467i
$759$	−2.20450e6	−	3.81830e6i	−0.138901	−	0.240583i
$760$	−1.52755e6	−	2.64580e6i	−0.0959317	−	0.166159i
$761$	−1.28768e6	+	2.23032e6i	−0.0806018	+	0.139606i	−0.903509	−	0.428570i	$-0.859018\pi$
$761$	−1.28768e6	+	2.23032e6i	−0.0806018	+	0.139606i	0.822907	+	0.568176i	$0.192351\pi$
$762$	9.70646e6			0.605583
$763$		0			0
$764$	−670656.			−0.0415687
$765$	2.84747e6	−	4.93197e6i	0.175916	−	0.304696i
$766$	−5.11373e6	−	8.85724e6i	−0.314895	−	0.545414i
$767$	−1.40179e7	−	2.42797e7i	−0.860389	−	1.49024i
$768$	294912.	−	510803.i	0.0180422	−	0.0312500i
$769$	971234.			0.0592254			0.0296127	−	0.999561i	$-0.490573\pi$
$769$	971234.			0.0592254			0.0296127	+	0.999561i	$0.490573\pi$
$770$		0			0
$771$	−4.10297e6			−0.248578
$772$	4.27198e6	−	7.39929e6i	0.257980	−	0.446835i
$773$	8.64606e6	+	1.49754e7i	0.520439	+	0.901426i	0.999718	+	0.0237637i	$0.00756494\pi$
$773$	8.64606e6	+	1.49754e7i	0.520439	+	0.901426i	−0.479279	+	0.877663i	$0.659102\pi$
$774$	3.14863e6	+	5.45359e6i	0.188916	+	0.327213i
$775$	873620.	−	1.51315e6i	0.0522478	−	0.0904959i
$776$	5.06099e6			0.301704
$777$		0			0
$778$	−1.16714e7			−0.691313
$779$	4.32541e6	−	7.49183e6i	0.255378	−	0.442328i
$780$	−3.88022e6	−	6.72075e6i	−0.228360	−	0.395531i
$781$	2.22782e6	+	3.85870e6i	0.130693	+	0.226367i
$782$	−5.90587e6	+	1.02293e7i	−0.345356	+	0.598174i
$783$	1.08038e6			0.0629755
$784$		0			0
$785$	1.25938e7			0.729427
$786$	−1.46124e6	+	2.53094e6i	−0.0843656	+	0.146125i
$787$	8.27573e6	+	1.43340e7i	0.476288	+	0.824955i	0.999631	−	0.0271674i	$-0.00864870\pi$
$787$	8.27573e6	+	1.43340e7i	0.476288	+	0.824955i	−0.523343	+	0.852122i	$0.675315\pi$
$788$	−6.59909e6	−	1.14300e7i	−0.378589	−	0.655736i
$789$	−3.38693e6	+	5.86634e6i	−0.193693	+	0.335486i
$790$	−2.15015e7			−1.22575
$791$		0			0
$792$	−1.11974e6			−0.0634316
$793$	1.93941e7	−	3.35916e7i	1.09518	−	1.89692i
$794$	5.01430e6	+	8.68502e6i	0.282266	+	0.488900i
$795$	−6.50997e6	−	1.12756e7i	−0.365310	−	0.632735i
$796$	3.19635e6	−	5.53624e6i	0.178802	−	0.309694i
$797$	2.91057e6			0.162305			0.0811526	−	0.996702i	$-0.474140\pi$
$797$	2.91057e6			0.162305			0.0811526	+	0.996702i	$0.474140\pi$
$798$		0			0
$799$	2.89044e7			1.60176
$800$	−107008.	+	185343.i	−0.00591141	+	0.0102389i
$801$	−1.47380e6	−	2.55269e6i	−0.0811626	−	0.140578i
$802$	1.98133e6	+	3.43177e6i	0.108773	+	0.188400i
$803$	−31320.0	+	54247.8i	−0.00171409	+	0.00296889i
$804$	−3.44851e6			−0.188145
$805$		0			0
$806$	−3.33731e7			−1.80950
$807$	646569.	−	1.11989e6i	0.0349487	−	0.0605329i
$808$	5.90803e6	+	1.02330e7i	0.318357	+	0.551411i
$809$	5.81261e6	+	1.00677e7i	0.312248	+	0.540830i	0.978849	−	0.204585i	$-0.0655846\pi$
$809$	5.81261e6	+	1.00677e7i	0.312248	+	0.540830i	−0.666601	+	0.745415i	$0.732251\pi$
$810$	−708588.	+	1.22731e6i	−0.0379473	+	0.0657267i
$811$	3.09020e7			1.64981			0.824906	−	0.565270i	$-0.191228\pi$
$811$	3.09020e7			1.64981			0.824906	+	0.565270i	$0.191228\pi$
$812$		0			0
$813$	−6.81746e6			−0.361740
$814$	−2.03645e6	+	3.52723e6i	−0.107724	+	0.186583i
$815$	1.25879e7	+	2.18030e7i	0.663836	+	1.14980i
$816$	1.49990e6	+	2.59791e6i	0.0788566	+	0.136584i
$817$	−8.59071e6	+	1.48795e7i	−0.450271	+	0.779892i
$818$	−1.80730e7			−0.944379
$819$		0			0
$820$	8.45510e6			0.439121
$821$	1.11435e7	−	1.93011e7i	0.576984	−	0.999366i	−0.418839	−	0.908061i	$-0.637563\pi$
$821$	1.11435e7	−	1.93011e7i	0.576984	−	0.999366i	0.995823	−	0.0913056i	$-0.0291040\pi$
$822$	4.69638e6	+	8.13437e6i	0.242429	+	0.419898i
$823$	8.24475e6	+	1.42803e7i	0.424305	+	0.734918i	0.996355	−	0.0853009i	$-0.0271852\pi$
$823$	8.24475e6	+	1.42803e7i	0.424305	+	0.734918i	−0.572050	+	0.820218i	$0.693852\pi$
$824$	2.06694e6	−	3.58005e6i	0.106050	−	0.183684i
$825$	406296.			0.0207830
$826$		0			0
$827$	−2.37457e7			−1.20732			−0.603658	−	0.797244i	$-0.706291\pi$
$827$	−2.37457e7			−1.20732			−0.603658	+	0.797244i	$0.706291\pi$
$828$	1.46966e6	−	2.54553e6i	0.0744976	−	0.129034i
$829$	−1.30433e7	−	2.25916e7i	−0.659173	−	1.14172i	−0.980830	−	0.194865i	$-0.937573\pi$
$829$	−1.30433e7	−	2.25916e7i	−0.659173	−	1.14172i	0.321657	−	0.946856i	$-0.395760\pi$
$830$	−2.08526e6	−	3.61178e6i	−0.105067	−	0.181981i
$831$	−5.22962e6	+	9.05797e6i	−0.262705	+	0.455018i
$832$	4.08781e6			0.204730
$833$		0			0
$834$	−1.07267e7			−0.534012
$835$	−2.72290e6	+	4.71619e6i	−0.135150	+	0.234086i
$836$	−1.52755e6	−	2.64580e6i	−0.0755928	−	0.130931i
$837$	3.04722e6	+	5.27794e6i	0.150345	+	0.260406i
$838$	1.21044e6	−	2.09654e6i	0.0595433	−	0.103132i
$839$	1.00872e7			0.494729			0.247365	−	0.968922i	$-0.420435\pi$
$839$	1.00872e7			0.494729			0.247365	+	0.968922i	$0.420435\pi$
$840$		0			0
$841$	−1.83148e7			−0.892920
$842$	8.99787e6	−	1.55848e7i	0.437380	−	0.757565i
$843$	−1.86465e6	−	3.22966e6i	−0.0903707	−	0.156527i
$844$	−6.95094e6	−	1.20394e7i	−0.335883	−	0.581766i
$845$	1.68672e7	−	2.92148e7i	0.812646	−	1.40754i
$846$	−7.19280e6			−0.345519
$847$		0			0
$848$	6.85824e6			0.327509
$849$	541926.	−	938643.i	0.0258030	−	0.0446922i
$850$	−544236.	−	942644.i	−0.0258369	−	0.0447508i
$851$	−5.34568e6	−	9.25898e6i	−0.253034	−	0.438268i
$852$	−1.48522e6	+	2.57247e6i	−0.0700956	+	0.121409i
$853$	−2.43630e7			−1.14646			−0.573229	−	0.819395i	$-0.694309\pi$
$853$	−2.43630e7			−1.14646			−0.573229	+	0.819395i	$0.694309\pi$
$854$		0			0
$855$	−3.86662e6			−0.180890
$856$	4.78694e6	−	8.29123e6i	0.223292	−	0.386754i
$857$	−1.22806e6	−	2.12706e6i	−0.0571172	−	0.0989300i	0.836053	−	0.548649i	$-0.184858\pi$
$857$	−1.22806e6	−	2.12706e6i	−0.0571172	−	0.0989300i	−0.893170	+	0.449719i	$0.851524\pi$
$858$	−3.88022e6	−	6.72075e6i	−0.179945	−	0.311673i
$859$	−4.31491e6	+	7.47364e6i	−0.199521	+	0.345581i	−0.948373	−	0.317156i	$-0.897272\pi$
$859$	−4.31491e6	+	7.47364e6i	−0.199521	+	0.345581i	0.748852	+	0.662737i	$0.230605\pi$
$860$	−1.67927e7			−0.774238
$861$		0			0
$862$	−2.15038e7			−0.985703
$863$	−5.25997e6	+	9.11053e6i	−0.240412	+	0.416406i	−0.960832	−	0.277133i	$-0.910616\pi$
$863$	−5.25997e6	+	9.11053e6i	−0.240412	+	0.416406i	0.720420	+	0.693538i	$0.243949\pi$
$864$	−373248.	−	646484.i	−0.0170103	−	0.0294628i
$865$	−1.80586e7	−	3.12785e7i	−0.820624	−	1.42136i
$866$	−3.97123e6	+	6.87837e6i	−0.179941	+	0.311667i
$867$	−2.47812e6			−0.111963
$868$		0			0
$869$	−2.15015e7			−0.965872
$870$	−1.44050e6	+	2.49503e6i	−0.0645233	+	0.111758i
$871$	−1.19501e7	−	2.06981e7i	−0.533733	−	0.924453i
$872$	−2.04243e6	−	3.53760e6i	−0.0909612	−	0.157549i
$873$	3.20266e6	−	5.54717e6i	0.142225	−	0.246340i
$874$	8.01965e6			0.355121
$875$		0			0
$876$	−41760.0			−0.00183865
$877$	5.72699e6	−	9.91944e6i	0.251436	−	0.435500i	−0.712485	−	0.701687i	$-0.752430\pi$
$877$	5.72699e6	−	9.91944e6i	0.251436	−	0.435500i	0.963921	+	0.266187i	$0.0857638\pi$
$878$	6.77454e6	+	1.17339e7i	0.296581	+	0.513694i
$879$	9.90714e6	+	1.71597e7i	0.432490	+	0.749094i
$880$	1.49299e6	−	2.58594e6i	0.0649906	−	0.112567i
$881$	−1.18134e7			−0.512786			−0.256393	−	0.966573i	$-0.582534\pi$
$881$	−1.18134e7			−0.512786			−0.256393	+	0.966573i	$0.582534\pi$
$882$		0			0
$883$	4.63221e6			0.199934			0.0999670	−	0.994991i	$-0.468126\pi$
$883$	4.63221e6			0.199934			0.0999670	+	0.994991i	$0.468126\pi$
$884$	−1.03952e7	+	1.80050e7i	−0.447405	+	0.774928i
$885$	−6.82636e6	−	1.18236e7i	−0.292975	−	0.507448i
$886$	4.28189e6	+	7.41645e6i	0.183253	+	0.317403i
$887$	−2.23864e7	+	3.87744e7i	−0.955377	+	1.65476i	−0.221875	+	0.975075i	$0.571218\pi$
$887$	−2.23864e7	+	3.87744e7i	−0.955377	+	1.65476i	−0.733502	+	0.679687i	$0.762116\pi$
$888$	−2.71526e6			−0.115553
$889$		0			0
$890$	7.86024e6			0.332630
$891$	−708588.	+	1.22731e6i	−0.0299020	+	0.0517917i
$892$	5.01325e6	+	8.68320e6i	0.210963	+	0.365399i
$893$	−9.81240e6	−	1.69956e7i	−0.411762	−	0.713193i
$894$	7.18146e6	−	1.24387e7i	0.300517	−	0.520511i
$895$	3.32022e7			1.38551
$896$		0			0
$897$	2.03712e7			0.845347
$898$	−1.39562e7	+	2.41728e7i	−0.577531	+	1.00031i
$899$	6.19476e6	+	1.07296e7i	0.255638	+	0.442778i
$900$	135432.	+	234575.i	0.00557333	+	0.00965330i
$901$	−1.74403e7	+	3.02075e7i	−0.715718	+	1.23966i
$902$	8.45510e6			0.346021
$903$		0			0
$904$	4.54541e6			0.184992
$905$	1.45985e7	−	2.52854e7i	0.592499	−	1.02624i
$906$	4.04942e6	+	7.01381e6i	0.163898	+	0.283879i
$907$	1.04178e7	+	1.80442e7i	0.420493	+	0.728315i	0.995988	−	0.0894902i	$-0.0285238\pi$
$907$	1.04178e7	+	1.80442e7i	0.420493	+	0.728315i	−0.575495	+	0.817806i	$0.695190\pi$
$908$	3.60317e6	−	6.24087e6i	0.145034	−	0.251206i
$909$	1.49547e7			0.600300
$910$		0			0
$911$	5.27869e6			0.210732			0.105366	−	0.994434i	$-0.466399\pi$
$911$	5.27869e6			0.210732			0.105366	+	0.994434i	$0.466399\pi$
$912$	1.01837e6	−	1.76387e6i	0.0405432	−	0.0702228i
$913$	−2.08526e6	−	3.61178e6i	−0.0827912	−	0.143399i
$914$	−1.03600e7	−	1.79440e7i	−0.410198	−	0.710484i
$915$	9.44444e6	−	1.63582e7i	0.372927	−	0.645928i
$916$	−1.70325e7			−0.670717
$917$		0			0
$918$	3.79663e6			0.148693
$919$	−1.25643e7	+	2.17620e7i	−0.490738	+	0.849984i	−0.999943	−	0.0106615i	$-0.996606\pi$
$919$	−1.25643e7	+	2.17620e7i	−0.490738	+	0.849984i	0.509205	+	0.860645i	$0.329940\pi$
$920$	3.91910e6	+	6.78809e6i	0.152657	+	0.264410i
$921$	499050.	+	864380.i	0.0193863	+	0.0335781i
$922$	−1.56600e7	+	2.71239e7i	−0.606687	+	1.05081i
$923$	−2.05867e7			−0.795396
$924$		0			0
$925$	985226.			0.0378601
$926$	330640.	−	572685.i	0.0126715	−	0.0219477i
$927$	−2.61598e6	−	4.53100e6i	−0.0999849	−	0.173179i
$928$	−758784.	−	1.31425e6i	−0.0289233	−	0.0500967i
$929$	−6.90210e6	+	1.19548e7i	−0.262387	+	0.454467i	−0.966876	−	0.255248i	$-0.917843\pi$
$929$	−6.90210e6	+	1.19548e7i	−0.262387	+	0.454467i	0.704489	+	0.709715i	$0.251176\pi$
$930$	−1.62518e7			−0.616162
$931$		0			0
$932$	2.29788e7			0.866540
$933$	−4.09774e6	+	7.09749e6i	−0.154113	+	0.266932i
$934$	−3.58658e6	−	6.21215e6i	−0.134528	−	0.233010i
$935$	7.59326e6	+	1.31519e7i	0.284053	+	0.491994i
$936$	2.58682e6	−	4.48050e6i	0.0965108	−	0.167162i
$937$	−4.73307e7			−1.76114			−0.880570	−	0.473915i	$-0.842840\pi$
$937$	−4.73307e7			−1.76114			−0.880570	+	0.473915i	$0.842840\pi$
$938$		0			0
$939$	−2.81023e7			−1.04011
$940$	9.59040e6	−	1.66111e7i	0.354011	−	0.613166i
$941$	1.62785e7	+	2.81952e7i	0.599295	+	1.03801i	0.992925	+	0.118741i	$0.0378858\pi$
$941$	1.62785e7	+	2.81952e7i	0.599295	+	1.03801i	−0.393630	+	0.919269i	$0.628781\pi$
$942$	4.19792e6	+	7.27102e6i	0.154137	+	0.266973i
$943$	−1.10973e7	+	1.92211e7i	−0.406386	+	0.703882i
$944$	7.19155e6			0.262659
$945$		0			0
$946$	−1.67927e7			−0.610088
$947$	2.63558e6	−	4.56497e6i	0.0954997	−	0.165410i	−0.814317	−	0.580420i	$-0.802888\pi$
$947$	2.63558e6	−	4.56497e6i	0.0954997	−	0.165410i	0.909817	+	0.415010i	$0.136222\pi$
$948$	−7.16717e6	−	1.24139e7i	−0.259016	−	0.448629i
$949$	−144710.	−	250645.i	−0.00521595	−	0.00903428i
$950$	−369512.	+	640014.i	−0.0132837	+	0.0230081i
$951$	2.49019e7			0.892857
$952$		0			0
$953$	8.20579e6			0.292677			0.146338	−	0.989235i	$-0.453251\pi$
$953$	8.20579e6			0.292677			0.146338	+	0.989235i	$0.453251\pi$
$954$	4.33998e6	−	7.51707e6i	0.154389	−	0.267410i
$955$	−1.13173e6	−	1.96022e6i	−0.0401546	−	0.0695498i
$956$	7.98288e6	+	1.38268e7i	0.282498	+	0.489300i
$957$	−1.44050e6	+	2.49503e6i	−0.0508434	+	0.0880634i
$958$	2.63863e7			0.928890
$959$		0			0
$960$	1.99066e6			0.0697137
$961$	−2.06302e7	+	3.57326e7i	−0.720602	+	1.24812i
$962$	−9.40914e6	−	1.62971e7i	−0.327803	−	0.567771i
$963$	−6.05848e6	−	1.04936e7i	−0.210522	−	0.364635i
$964$	1.82379e6	−	3.15890e6i	0.0632096	−	0.109482i
$965$	2.88359e7			0.996816
$966$		0			0
$967$	−1.18118e7			−0.406210			−0.203105	−	0.979157i	$-0.565103\pi$
$967$	−1.18118e7			−0.406210			−0.203105	+	0.979157i	$0.565103\pi$
$968$	−3.66064e6	+	6.34041e6i	−0.125565	+	0.217485i
$969$	5.17936e6	+	8.97091e6i	0.177201	+	0.306921i
$970$	8.54042e6	+	1.47924e7i	0.291441	+	0.504790i
$971$	1.83851e7	−	3.18439e7i	0.625774	−	1.08387i	−0.362617	−	0.931938i	$-0.618117\pi$
$971$	1.83851e7	−	3.18439e7i	0.625774	−	1.08387i	0.988391	−	0.151934i	$-0.0485502\pi$
$972$	−944784.			−0.0320750
$973$		0			0
$974$	2.38957e7			0.807091
$975$	−938619.	+	1.62574e6i	−0.0316212	+	0.0547695i
$976$	4.97485e6	+	8.61669e6i	0.167169	+	0.289545i
$977$	9.25913e6	+	1.60373e7i	0.310337	+	0.537520i	0.978435	−	0.206553i	$-0.0662247\pi$
$977$	9.25913e6	+	1.60373e7i	0.310337	+	0.537520i	−0.668098	+	0.744073i	$0.732891\pi$
$978$	−8.39196e6	+	1.45353e7i	−0.280554	+	0.485934i
$979$	7.86024e6			0.262107
$980$		0			0
$981$	−5.16991e6			−0.171518
$982$	762528.	−	1.32074e6i	0.0252335	−	0.0437057i
$983$	−1.36085e7	−	2.35706e7i	−0.449185	−	0.778012i	0.549148	−	0.835725i	$-0.314952\pi$
$983$	−1.36085e7	−	2.35706e7i	−0.449185	−	0.778012i	−0.998333	+	0.0577135i	$0.981619\pi$
$984$	2.81837e6	+	4.88156e6i	0.0927919	+	0.160720i
$985$	2.22719e7	−	3.85761e7i	0.731420	−	1.26686i
$986$	7.71826e6			0.252829
$987$		0			0
$988$	1.41157e7			0.460056
$989$	2.20404e7	−	3.81751e7i	0.716521	−	1.24105i
$990$	−1.88957e6	−	3.27283e6i	−0.0612738	−	0.106129i
$991$	−8.16990e6	−	1.41507e7i	−0.264261	−	0.457713i	0.703109	−	0.711082i	$-0.251795\pi$
$991$	−8.16990e6	−	1.41507e7i	−0.264261	−	0.457713i	−0.967370	+	0.253369i	$0.918461\pi$
$992$	4.28032e6	−	7.41373e6i	0.138101	−	0.239198i
$993$	−2.90031e7			−0.933409
$994$		0			0
$995$	2.15754e7			0.690877
$996$	1.39018e6	−	2.40786e6i	0.0444039	−	0.0769099i
$997$	1.51031e7	+	2.61594e7i	0.481203	+	0.833468i	0.999767	−	0.0215704i	$-0.00686660\pi$
$997$	1.51031e7	+	2.61594e7i	0.481203	+	0.833468i	−0.518564	+	0.855039i	$0.673533\pi$
$998$	3.08702e6	+	5.34687e6i	0.0981098	+	0.169931i
$999$	−1.71825e6	+	2.97610e6i	−0.0544720	+	0.0943483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.6.e.r.79.1		2
7.2	even	3		42.6.a.a.1.1	✓	1
7.3	odd	6		294.6.e.h.67.1		2
7.4	even	3	inner	294.6.e.r.67.1		2
7.5	odd	6		294.6.a.h.1.1		1
7.6	odd	2		294.6.e.h.79.1		2
21.2	odd	6		126.6.a.k.1.1		1
21.5	even	6		882.6.a.o.1.1		1
28.23	odd	6		336.6.a.j.1.1		1
35.2	odd	12		1050.6.g.o.799.1		2
35.9	even	6		1050.6.a.n.1.1		1
35.23	odd	12		1050.6.g.o.799.2		2
84.23	even	6		1008.6.a.x.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.6.a.a.1.1	✓	1	7.2	even	3
126.6.a.k.1.1		1	21.2	odd	6
294.6.a.h.1.1		1	7.5	odd	6
294.6.e.h.67.1		2	7.3	odd	6
294.6.e.h.79.1		2	7.6	odd	2
294.6.e.r.67.1		2	7.4	even	3	inner
294.6.e.r.79.1		2	1.1	even	1	trivial
336.6.a.j.1.1		1	28.23	odd	6
882.6.a.o.1.1		1	21.5	even	6
1008.6.a.x.1.1		1	84.23	even	6
1050.6.a.n.1.1		1	35.9	even	6
1050.6.g.o.799.1		2	35.2	odd	12
1050.6.g.o.799.2		2	35.23	odd	12

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} +(27.0000 - 46.7654i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-108.000 - 187.061i) q^{10} +(-108.000 - 187.061i) q^{11} +(72.0000 - 124.708i) q^{12} +998.000 q^{13} +486.000 q^{15} +(-128.000 + 221.703i) q^{16} +(-651.000 - 1127.57i) q^{17} +(162.000 + 280.592i) q^{18} +(-442.000 + 765.566i) q^{19} -864.000 q^{20} -864.000 q^{22} +(1134.00 - 1964.15i) q^{23} +(-288.000 - 498.831i) q^{24} +(104.500 + 180.999i) q^{25} +(1996.00 - 3457.17i) q^{26} -729.000 q^{27} -1482.00 q^{29} +(972.000 - 1683.55i) q^{30} +(-4180.00 - 7239.97i) q^{31} +(512.000 + 886.810i) q^{32} +(972.000 - 1683.55i) q^{33} -5208.00 q^{34} +1296.00 q^{36} +(2357.00 - 4082.44i) q^{37} +(1768.00 + 3062.27i) q^{38} +(4491.00 + 7778.64i) q^{39} +(-1728.00 + 2992.98i) q^{40} -9786.00 q^{41} +19436.0 q^{43} +(-1728.00 + 2992.98i) q^{44} +(2187.00 + 3788.00i) q^{45} +(-4536.00 - 7856.58i) q^{46} +(-11100.0 + 19225.8i) q^{47} -2304.00 q^{48} +836.000 q^{50} +(5859.00 - 10148.1i) q^{51} +(-7984.00 - 13828.7i) q^{52} +(-13395.0 - 23200.8i) q^{53} +(-1458.00 + 2525.33i) q^{54} -11664.0 q^{55} -7956.00 q^{57} +(-2964.00 + 5133.80i) q^{58} +(-14046.0 - 24328.4i) q^{59} +(-3888.00 - 6734.21i) q^{60} +(19433.0 - 33658.9i) q^{61} -33440.0 q^{62} +4096.00 q^{64} +(26946.0 - 46671.8i) q^{65} +(-3888.00 - 6734.21i) q^{66} +(-11974.0 - 20739.6i) q^{67} +(-10416.0 + 18041.0i) q^{68} +20412.0 q^{69} -20628.0 q^{71} +(2592.00 - 4489.48i) q^{72} +(-145.000 - 251.147i) q^{73} +(-9428.00 - 16329.8i) q^{74} +(-940.500 + 1628.99i) q^{75} +14144.0 q^{76} +35928.0 q^{78} +(49772.0 - 86207.6i) q^{79} +(6912.00 + 11971.9i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-19572.0 + 33899.7i) q^{82} +19308.0 q^{83} -70308.0 q^{85} +(38872.0 - 67328.3i) q^{86} +(-6669.00 - 11551.0i) q^{87} +(6912.00 + 11971.9i) q^{88} +(-18195.0 + 31514.7i) q^{89} +17496.0 q^{90} -36288.0 q^{92} +(37620.0 - 65159.8i) q^{93} +(44400.0 + 76903.1i) q^{94} +(23868.0 + 41340.6i) q^{95} +(-4608.00 + 7981.29i) q^{96} -79078.0 q^{97} +17496.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} + 9 q^{3} - 16 q^{4} + 54 q^{5} + 72 q^{6} - 128 q^{8} - 81 q^{9} - 216 q^{10} - 216 q^{11} + 144 q^{12} + 1996 q^{13} + 972 q^{15} - 256 q^{16} - 1302 q^{17} + 324 q^{18} - 884 q^{19} - 1728 q^{20}+ \cdots + 34992 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 + 9 * q^3 - 16 * q^4 + 54 * q^5 + 72 * q^6 - 128 * q^8 - 81 * q^9 - 216 * q^10 - 216 * q^11 + 144 * q^12 + 1996 * q^13 + 972 * q^15 - 256 * q^16 - 1302 * q^17 + 324 * q^18 - 884 * q^19 - 1728 * q^20 - 1728 * q^22 + 2268 * q^23 - 576 * q^24 + 209 * q^25 + 3992 * q^26 - 1458 * q^27 - 2964 * q^29 + 1944 * q^30 - 8360 * q^31 + 1024 * q^32 + 1944 * q^33 - 10416 * q^34 + 2592 * q^36 + 4714 * q^37 + 3536 * q^38 + 8982 * q^39 - 3456 * q^40 - 19572 * q^41 + 38872 * q^43 - 3456 * q^44 + 4374 * q^45 - 9072 * q^46 - 22200 * q^47 - 4608 * q^48 + 1672 * q^50 + 11718 * q^51 - 15968 * q^52 - 26790 * q^53 - 2916 * q^54 - 23328 * q^55 - 15912 * q^57 - 5928 * q^58 - 28092 * q^59 - 7776 * q^60 + 38866 * q^61 - 66880 * q^62 + 8192 * q^64 + 53892 * q^65 - 7776 * q^66 - 23948 * q^67 - 20832 * q^68 + 40824 * q^69 - 41256 * q^71 + 5184 * q^72 - 290 * q^73 - 18856 * q^74 - 1881 * q^75 + 28288 * q^76 + 71856 * q^78 + 99544 * q^79 + 13824 * q^80 - 6561 * q^81 - 39144 * q^82 + 38616 * q^83 - 140616 * q^85 + 77744 * q^86 - 13338 * q^87 + 13824 * q^88 - 36390 * q^89 + 34992 * q^90 - 72576 * q^92 + 75240 * q^93 + 88800 * q^94 + 47736 * q^95 - 9216 * q^96 - 158156 * q^97 + 34992 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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