LMFDB - Embedded newform 294.6.e.h.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)

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			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.67
Dual form			294.6.e.h.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} +(-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 $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

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

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
$5$	−27.0000	−	46.7654i	−0.482991	−	0.836564i	0.516819	−	0.856095i	$-0.327116\pi$
$5$	−27.0000	−	46.7654i	−0.482991	−	0.836564i	−0.999809	+	0.0195305i	$0.993783\pi$
$6$	−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	−0.968634	−	0.248491i	$-0.920065\pi$
$11$	−108.000	+	187.061i	−0.269118	+	0.466125i	0.699517	+	0.714616i	$0.253399\pi$
$12$	−72.0000	−	124.708i	−0.144338	−	0.250000i
$13$	−998.000			−1.63784			−0.818921	−	0.573906i	$-0.805428\pi$
$13$	−998.000			−1.63784			−0.818921	+	0.573906i	$0.805428\pi$
$14$		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	−0.452187	−	0.891923i	$-0.649356\pi$
$17$	651.000	−	1127.57i	0.546335	−	0.946279i	0.998522	−	0.0543561i	$-0.0173106\pi$
$18$	162.000	−	280.592i	0.117851	−	0.204124i
$19$	442.000	+	765.566i	0.280891	+	0.486518i	0.971605	−	0.236611i	$-0.0760366\pi$
$19$	442.000	+	765.566i	0.280891	+	0.486518i	−0.690713	+	0.723129i	$0.742703\pi$
$20$	864.000			0.482991
$21$		0			0
$22$	−864.000			−0.380590
$23$	1134.00	+	1964.15i	0.446986	+	0.774202i	0.998188	−	0.0601698i	$-0.0191642\pi$
$23$	1134.00	+	1964.15i	0.446986	+	0.774202i	−0.551203	+	0.834371i	$0.685831\pi$
$24$	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	−0.150015	−	0.988684i	$-0.547932\pi$
$31$	4180.00	−	7239.97i	0.781218	−	1.35311i	0.931233	−	0.364425i	$-0.118734\pi$
$32$	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	0.972133	−	0.234429i	$-0.0753221\pi$
$37$	2357.00	+	4082.44i	0.283045	+	0.490248i	−0.689088	+	0.724677i	$0.741989\pi$
$38$	−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	$-0.349787\pi$
$41$	9786.00			0.909171			0.454585	+	0.890703i	$0.349787\pi$
$42$		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	0.955614	+	0.294622i	$0.0951936\pi$
$47$	11100.0	+	19225.8i	0.732957	+	1.26952i	−0.222657	+	0.974897i	$0.571473\pi$
$48$	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	0.326872	+	0.945069i	$0.394006\pi$
$53$	−13395.0	+	23200.8i	−0.655018	+	1.13452i	−0.981889	+	0.189455i	$0.939328\pi$
$54$	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	−0.474247	−	0.880392i	$-0.657280\pi$
$59$	14046.0	−	24328.4i	0.525318	−	0.909878i	0.999565	−	0.0294862i	$-0.00938712\pi$
$60$	−3888.00	+	6734.21i	−0.139427	+	0.241495i
$61$	−19433.0	−	33658.9i	−0.668675	−	1.15818i	−0.978275	−	0.207312i	$-0.933528\pi$
$61$	−19433.0	−	33658.9i	−0.668675	−	1.15818i	0.309600	−	0.950867i	$-0.399805\pi$
$62$	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	−0.981689	−	0.190489i	$-0.938992\pi$
$67$	−11974.0	+	20739.6i	−0.325876	+	0.564434i	0.655813	+	0.754923i	$0.272326\pi$
$68$	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	$-0.832320\pi$
$73$	145.000	−	251.147i	0.00318464	−	0.00551596i	0.867613	+	0.497239i	$0.165653\pi$
$74$	−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	0.830985	+	0.556295i	$0.187778\pi$
$79$	49772.0	+	86207.6i	0.897258	+	1.55410i	0.0662732	+	0.997802i	$0.478889\pi$
$80$	−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	$-0.549158\pi$
$83$	−19308.0			−0.307639			−0.153820	+	0.988099i	$0.549158\pi$
$84$		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	$-0.0883751\pi$
$89$	18195.0	+	31514.7i	0.243488	+	0.421733i	−0.718218	+	0.695819i	$0.755042\pi$
$90$	−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	$-0.359685\pi$
$97$	79078.0			0.853348			0.426674	+	0.904405i	$0.359685\pi$
$98$		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	0.0735382	−	0.997292i	$-0.476571\pi$
$101$	92313.0	−	159891.i	0.900450	−	1.55962i	0.826911	−	0.562332i	$-0.190096\pi$
$102$	−23436.0	+	40592.3i	−0.223040	+	0.386317i
$103$	32296.0	+	55938.3i	0.299955	+	0.519537i	0.976125	−	0.217208i	$-0.0696951\pi$
$103$	32296.0	+	55938.3i	0.299955	+	0.519537i	−0.676171	+	0.736745i	$0.736362\pi$
$104$	63872.0			0.579065
$105$		0			0
$106$	−107160.			−0.926335
$107$	−74796.0	−	129550.i	−0.631566	−	1.09390i	−0.987232	−	0.159291i	$-0.949079\pi$
$107$	−74796.0	−	129550.i	−0.631566	−	1.09390i	0.355665	−	0.934613i	$-0.384254\pi$
$108$	−5832.00	+	10101.3i	−0.0481125	+	0.0833333i
$109$	31913.0	−	55274.9i	0.257277	−	0.445617i	−0.708234	−	0.705977i	$-0.750508\pi$
$109$	31913.0	−	55274.9i	0.257277	−	0.445617i	0.965512	+	0.260360i	$0.0838413\pi$
$110$	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	$-0.100410\pi$
$131$	40590.0	+	70303.9i	0.206653	+	0.357933i	−0.744005	+	0.668174i	$0.767076\pi$
$132$	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	−0.399885	−	0.916565i	$-0.630950\pi$
$137$	130455.	−	225955.i	0.593826	−	1.02854i	0.993711	−	0.111972i	$-0.0357166\pi$
$138$	−40824.0	−	70709.2i	−0.182481	−	0.316066i
$139$	297964.			1.30806			0.654029	−	0.756470i	$-0.273078\pi$
$139$	297964.			1.30806			0.654029	+	0.756470i	$0.273078\pi$
$140$		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	0.954233	+	0.299063i	$0.0966742\pi$
$149$	199485.	+	345518.i	0.736113	+	1.27499i	−0.218120	+	0.975922i	$0.569992\pi$
$150$	−3762.00	+	6515.98i	−0.0136518	+	0.0236457i
$151$	112484.	−	194828.i	0.401466	−	0.695359i	−0.592437	−	0.805616i	$-0.701834\pi$
$151$	112484.	−	194828.i	0.401466	−	0.695359i	0.993903	+	0.110258i	$0.0351676\pi$
$152$	−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	$-0.956569\pi$
$157$	−116609.	+	201973.i	−0.377557	+	0.653949i	0.613149	+	0.789967i	$0.289903\pi$
$158$	−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	−0.972736	−	0.231917i	$-0.925500\pi$
$163$	−233110.	−	403758.i	−0.687214	−	1.19029i	0.285522	−	0.958372i	$-0.407833\pi$
$164$	−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	$-0.455319\pi$
$167$	100848.			0.279818			0.139909	+	0.990164i	$0.455319\pi$
$168$		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	−0.881634	−	0.471934i	$-0.843556\pi$
$173$	−334419.	−	579231.i	−0.849524	−	1.47142i	0.0321096	−	0.999484i	$-0.489777\pi$
$174$	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	−0.244972	−	0.969530i	$-0.578779\pi$
$179$	307428.	−	532481.i	0.717151	−	1.24214i	0.962124	−	0.272613i	$-0.0878877\pi$
$180$	−34992.0	−	60607.9i	−0.0804984	−	0.139427i
$181$	−540686.			−1.22673			−0.613365	−	0.789800i	$-0.710184\pi$
$181$	−540686.			−1.22673			−0.613365	+	0.789800i	$0.710184\pi$
$182$		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	0.886061	−	0.463568i	$-0.153431\pi$
$191$	20958.0	+	36300.3i	0.0415687	+	0.0719991i	−0.844493	+	0.535567i	$0.820098\pi$
$192$	−18432.0	+	31925.2i	−0.0360844	+	0.0625000i
$193$	266999.	−	462456.i	0.515960	−	0.893670i	−0.483868	−	0.875141i	$-0.660768\pi$
$193$	266999.	−	462456.i	0.515960	−	0.893670i	0.999828	−	0.0185286i	$-0.00589817\pi$
$194$	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	$-0.949739\pi$
$199$	−199772.	+	346015.i	−0.357604	+	0.619388i	0.629956	+	0.776631i	$0.283073\pi$
$200$	−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	$-0.361354\pi$
$223$	626656.			0.843853			0.421927	+	0.906630i	$0.361354\pi$
$224$		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	$-0.927011\pi$
$227$	−225198.	+	390054.i	−0.290068	+	0.502413i	0.683758	+	0.729709i	$0.260345\pi$
$228$	63648.0	−	110242.i	0.0810863	−	0.140446i
$229$	−532265.	−	921910.i	−0.670717	−	1.16172i	−0.977701	−	0.210001i	$-0.932653\pi$
$229$	−532265.	−	921910.i	−0.670717	−	1.16172i	0.306984	−	0.951715i	$-0.400680\pi$
$230$	489888.			0.610629
$231$		0			0
$232$	94848.0			0.115693
$233$	−718089.	−	1.24377e6i	−0.866540	−	1.50089i	−0.865510	−	0.500891i	$-0.833006\pi$
$233$	−718089.	−	1.24377e6i	−0.866540	−	1.50089i	−0.00102954	−	0.999999i	$-0.500328\pi$
$234$	−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	$-0.873682\pi$
$241$	−113987.	+	197431.i	−0.126419	+	0.218964i	0.795868	+	0.605471i	$0.207015\pi$
$242$	−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	$-0.774660\pi$
$251$	−1.51657e6			−1.51942			−0.759712	+	0.650260i	$0.774660\pi$
$252$		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	$-0.0976019\pi$
$257$	227943.	+	394809.i	0.215275	+	0.372867i	−0.738083	+	0.674710i	$0.764269\pi$
$258$	−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	−0.648092	−	0.761562i	$-0.724433\pi$
$263$	376326.	−	651816.i	0.335486	−	0.581079i	0.983578	+	0.180483i	$0.0577660\pi$
$264$	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	$-0.814053\pi$
$269$	71841.0	−	124432.i	0.0605329	−	0.104846i	0.894704	+	0.446660i	$0.147387\pi$
$270$	78732.0	−	136368.i	0.0657267	−	0.113842i
$271$	378748.	+	656011.i	0.313276	+	0.542610i	0.979070	−	0.203526i	$-0.0652402\pi$
$271$	378748.	+	656011.i	0.313276	+	0.542610i	−0.665794	+	0.746136i	$0.731907\pi$
$272$	−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	−0.543672	−	0.839298i	$-0.682966\pi$
$277$	581069.	−	1.00644e6i	0.455018	−	0.788114i	0.998689	+	0.0511843i	$0.0162996\pi$
$278$	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	$-0.819103\pi$
$283$	60214.0	−	104294.i	0.0446922	−	0.0774091i	0.887506	+	0.460796i	$0.152436\pi$
$284$	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	$-0.769511\pi$
$293$	−2.20159e6			−1.49819			−0.749094	+	0.662463i	$0.769511\pi$
$294$		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	$-0.510690\pi$
$307$	−110900.			−0.0671561			−0.0335781	+	0.999436i	$0.510690\pi$
$308$		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	$-0.919343\pi$
$311$	−455304.	+	788610.i	−0.266932	+	0.462340i	0.701136	+	0.713028i	$0.252677\pi$
$312$	−287424.	+	497833.i	−0.167162	+	0.289532i
$313$	1.56124e6	+	2.70414e6i	0.900758	+	1.56016i	0.826513	+	0.562918i	$0.190321\pi$
$313$	1.56124e6	+	2.70414e6i	0.900758	+	1.56016i	0.0742450	+	0.997240i	$0.476345\pi$
$314$	−932872.			−0.533947
$315$		0			0
$316$	−1.59270e6			−0.897258
$317$	1.38344e6	+	2.39619e6i	0.773237	+	1.33929i	0.935780	+	0.352584i	$0.114697\pi$
$317$	1.38344e6	+	2.39619e6i	0.773237	+	1.33929i	−0.162543	+	0.986701i	$0.551970\pi$
$318$	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	−0.914002	−	0.405710i	$-0.867024\pi$
$331$	−1.61129e6	−	2.79083e6i	−0.808356	−	1.40011i	0.105646	−	0.994404i	$-0.466309\pi$
$332$	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	−0.958113	−	0.286389i	$-0.907545\pi$
$347$	−518208.	+	897563.i	−0.231036	+	0.400167i	0.727077	+	0.686556i	$0.240878\pi$
$348$	106704.	+	184817.i	0.0472316	+	0.0818075i
$349$	4.22999e6			1.85898			0.929491	−	0.368844i	$-0.120246\pi$
$349$	4.22999e6			1.85898			0.929491	+	0.368844i	$0.120246\pi$
$350$		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	$-0.817092\pi$
$353$	119403.	−	206812.i	0.0510010	−	0.0883363i	0.890399	+	0.455181i	$0.150426\pi$
$354$	−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	0.998574	+	0.0533889i	$0.0170023\pi$
$359$	1.33214e6	+	2.30733e6i	0.545523	+	0.944874i	−0.453051	+	0.891485i	$0.649664\pi$
$360$	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	$-0.940895\pi$
$367$	−855416.	+	1.48162e6i	−0.331522	+	0.574213i	0.651289	+	0.758830i	$0.274229\pi$
$368$	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	0.953358	+	0.301841i	$0.0976013\pi$
$373$	1.98324e6	+	3.43508e6i	0.738081	+	1.27839i	−0.215277	+	0.976553i	$0.569065\pi$
$374$	−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	$-0.313580\pi$
$383$	−1.27843e6	−	2.21431e6i	−0.445329	−	0.771332i	−0.998075	+	0.0620176i	$0.980247\pi$
$384$	−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	−0.999917	−	0.0128481i	$-0.995910\pi$
$389$	−1.45893e6	+	2.52694e6i	−0.488832	+	0.846682i	0.511086	+	0.859530i	$0.329244\pi$
$390$	−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	$-0.0359598\pi$
$397$	1.25357e6	+	2.17126e6i	0.399185	+	0.691408i	−0.594441	+	0.804139i	$0.702627\pi$
$398$	−1.59818e6			−0.505728
$399$		0			0
$400$	−53504.0			−0.0167200
$401$	−495333.	−	857942.i	−0.153828	−	0.266438i	0.778803	−	0.627268i	$-0.215827\pi$
$401$	−495333.	−	857942.i	−0.153828	−	0.266438i	−0.932632	+	0.360830i	$0.882494\pi$
$402$	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	−0.310748	−	0.950492i	$-0.600579\pi$
$409$	2.25912e6	−	3.91291e6i	0.667777	−	1.15662i	0.978524	−	0.206131i	$-0.0660872\pi$
$410$	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	$-0.526836\pi$
$419$	−605220.			−0.168414			−0.0842070	+	0.996448i	$0.526836\pi$
$420$		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	0.272505	+	0.962154i	$0.412148\pi$
$431$	−2.68797e6	+	4.65570e6i	−0.696998	+	1.20724i	−0.969503	+	0.245081i	$0.921186\pi$
$432$	−93312.0	−	161621.i	−0.0240563	−	0.0416667i
$433$	1.98561e6			0.508950			0.254475	−	0.967079i	$-0.418097\pi$
$433$	1.98561e6			0.508950			0.254475	+	0.967079i	$0.418097\pi$
$434$		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	$-0.0288969\pi$
$439$	1.69364e6	+	2.93346e6i	0.419429	+	0.726473i	−0.576453	+	0.817130i	$0.695564\pi$
$440$	−746496.			−0.183821
$441$		0			0
$442$	−5.19758e6			−1.26545
$443$	−1.07047e6	−	1.85411e6i	−0.259159	−	0.448876i	0.706858	−	0.707355i	$-0.250112\pi$
$443$	−1.07047e6	−	1.85411e6i	−0.259159	−	0.448876i	−0.966017	+	0.258479i	$0.916779\pi$
$444$	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	0.995466	+	0.0951178i	$0.0303228\pi$
$457$	2.59000e6	+	4.48600e6i	0.580107	+	1.00478i	−0.415359	+	0.909658i	$0.636344\pi$
$458$	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	$-0.171716\pi$
$461$	7.83001e6			1.71597			0.857985	+	0.513674i	$0.171716\pi$
$462$		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	$-0.227597\pi$
$467$	−896646.	−	1.55304e6i	−0.190252	−	0.329526i	−0.945334	+	0.326105i	$0.894264\pi$
$468$	−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	0.324609	+	0.945848i	$0.394767\pi$
$479$	−3.29828e6	+	5.71280e6i	−0.656824	+	1.13765i	−0.981433	+	0.191805i	$0.938566\pi$
$480$	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	−0.425795	−	0.904820i	$-0.640005\pi$
$487$	2.98696e6	−	5.17357e6i	0.570700	−	0.988481i	0.996494	−	0.0836609i	$-0.0266613\pi$
$488$	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	0.788275	−	0.615323i	$-0.210975\pi$
$499$	−771754.	−	1.33672e6i	−0.138748	−	0.240319i	−0.927023	+	0.375004i	$0.877641\pi$
$500$	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	$-0.384656\pi$
$503$	4.02300e6			0.708974			0.354487	+	0.935061i	$0.384656\pi$
$504$		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	$-0.219933\pi$
$509$	−973575.	−	1.68628e6i	−0.166562	−	0.288493i	−0.937209	+	0.348769i	$0.886600\pi$
$510$	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	−0.397372	−	0.917657i	$-0.630078\pi$
$521$	3.69285e6	−	6.39620e6i	0.596028	−	1.03235i	0.993401	−	0.114694i	$-0.0365888\pi$
$522$	−240084.	+	415838.i	−0.0385644	+	0.0667956i
$523$	−164870.	−	285563.i	−0.0263565	−	0.0456508i	0.852546	−	0.522652i	$-0.175057\pi$
$523$	−164870.	−	285563.i	−0.0263565	−	0.0456508i	−0.878903	+	0.477001i	$0.841724\pi$
$524$	−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	0.862810	−	0.505529i	$-0.168703\pi$
$541$	−43543.0	−	75418.7i	−0.00639625	−	0.0110786i	−0.869206	+	0.494450i	$0.835369\pi$
$542$	−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	−0.809346	−	0.587332i	$-0.800178\pi$
$557$	761289.	−	1.31859e6i	0.103971	−	0.180083i	0.913317	+	0.407249i	$0.133512\pi$
$558$	−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	0.476797	+	0.879013i	$0.341798\pi$
$563$	−3.93231e6	+	6.81096e6i	−0.522850	+	0.905602i	−0.999646	+	0.0265885i	$0.991536\pi$
$564$	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	0.909497	−	0.415711i	$-0.136467\pi$
$569$	731607.	+	1.26718e6i	0.0947321	+	0.164081i	−0.814765	+	0.579792i	$0.803134\pi$
$570$	−859248.	+	1.48826e6i	−0.110772	+	0.191863i
$571$	−4.59927e6	+	7.96618e6i	−0.590336	+	1.02249i	0.403851	+	0.914825i	$0.367671\pi$
$571$	−4.59927e6	+	7.96618e6i	−0.590336	+	1.02249i	−0.994187	+	0.107667i	$0.965662\pi$
$572$	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	$-0.767400\pi$
$577$	1.64470e6	−	2.84870e6i	0.205658	−	0.356211i	0.950342	+	0.311207i	$0.100733\pi$
$578$	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	$-0.599395\pi$
$587$	−5.12929e6			−0.614416			−0.307208	+	0.951642i	$0.599395\pi$
$588$		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	$-0.218082\pi$
$593$	−1.37716e6	−	2.38532e6i	−0.160823	−	0.278554i	−0.935164	+	0.354214i	$0.884748\pi$
$594$	−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	−0.434342	−	0.900748i	$-0.643019\pi$
$599$	4.94308e6	−	8.56167e6i	0.562899	−	0.974970i	0.997242	−	0.0742224i	$-0.0236475\pi$
$600$	−60192.0	−	104256.i	−0.00682591	−	0.0118228i
$601$	−1.37039e7			−1.54760			−0.773798	−	0.633433i	$-0.781645\pi$
$601$	−1.37039e7			−1.54760			−0.773798	+	0.633433i	$0.781645\pi$
$602$		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	$-0.309054\pi$
$607$	−3.92655e6	−	6.80099e6i	−0.432553	−	0.749204i	−0.997092	+	0.0762020i	$0.975721\pi$
$608$	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	0.136140	+	0.990690i	$0.456530\pi$
$613$	−7.34884e6	+	1.27286e7i	−0.789892	+	1.36813i	−0.926033	+	0.377444i	$0.876803\pi$
$614$	−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	$-0.871270\pi$
$619$	−1.13346e6	+	1.96321e6i	−0.118900	+	0.205940i	0.800432	+	0.599423i	$0.204603\pi$
$620$	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	−0.972642	−	0.232311i	$-0.925371\pi$
$641$	−2.96616e6	+	5.13753e6i	−0.285134	+	0.493867i	0.687508	+	0.726177i	$0.258705\pi$
$642$	2.69266e6	+	4.66382e6i	0.257836	+	0.446585i
$643$	6.94443e6			0.662383			0.331191	−	0.943564i	$-0.392549\pi$
$643$	6.94443e6			0.662383			0.331191	+	0.943564i	$0.392549\pi$
$644$		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	$-0.908320\pi$
$647$	−2.48525e6	+	4.30458e6i	−0.233404	+	0.404268i	0.725403	+	0.688324i	$0.241653\pi$
$648$	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	0.888750	+	0.458392i	$0.151575\pi$
$653$	9.16773e6	+	1.58790e7i	0.841354	+	1.45727i	−0.0473954	+	0.998876i	$0.515092\pi$
$654$	−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	$-0.823422\pi$
$661$	349699.	−	605696.i	0.0311308	−	0.0539202i	0.881171	+	0.472798i	$0.156756\pi$
$662$	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	$-0.153516\pi$
$677$	492537.	+	853099.i	0.0413016	+	0.0715365i	−0.844636	+	0.535342i	$0.820183\pi$
$678$	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	−0.164630	−	0.986355i	$-0.552643\pi$
$683$	9.41042e6	−	1.62993e7i	0.771894	−	1.33696i	0.936524	−	0.350604i	$-0.114024\pi$
$684$	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	−0.937362	−	0.348356i	$-0.886740\pi$
$691$	−9.66924e6	−	1.67476e7i	−0.770366	−	1.33431i	0.166996	−	0.985958i	$-0.446593\pi$
$692$	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	0.879781	−	0.475379i	$-0.157689\pi$
$709$	377453.	+	653768.i	0.0281999	+	0.0488436i	−0.851581	+	0.524223i	$0.824356\pi$
$710$	−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	$-0.154165\pi$
$719$	544272.	+	942707.i	0.0392639	+	0.0680071i	−0.845726	+	0.533618i	$0.820832\pi$
$720$	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	$-0.491563\pi$
$727$	755392.			0.0530074			0.0265037	+	0.999649i	$0.491563\pi$
$728$		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	$-0.149550\pi$
$733$	781843.	+	1.35419e6i	0.0537477	+	0.0930937i	−0.837900	+	0.545824i	$0.816217\pi$
$734$	−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	−0.631736	−	0.775184i	$-0.717657\pi$
$739$	5.27719e6	−	9.14037e6i	0.355461	−	0.615677i	0.987197	+	0.159507i	$0.0509906\pi$
$740$	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	0.819056	+	0.573713i	$0.194498\pi$
$751$	1.40091e7	+	2.42644e7i	0.906378	+	1.56989i	0.0873221	+	0.996180i	$0.472169\pi$
$752$	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	$-0.140982\pi$
$761$	1.28768e6	+	2.23032e6i	0.0806018	+	0.139606i	−0.822907	+	0.568176i	$0.807649\pi$
$762$	−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	$-0.509427\pi$
$769$	−971234.			−0.0592254			−0.0296127	+	0.999561i	$0.509427\pi$
$770$		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	0.479279	+	0.877663i	$0.340898\pi$
$773$	−8.64606e6	+	1.49754e7i	−0.520439	+	0.901426i	−0.999718	+	0.0237637i	$0.992435\pi$
$774$	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	$-0.991351\pi$
$787$	−8.27573e6	+	1.43340e7i	−0.476288	+	0.824955i	0.523343	+	0.852122i	$0.324685\pi$
$788$	−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	$-0.525860\pi$
$797$	−2.91057e6			−0.162305			−0.0811526	+	0.996702i	$0.525860\pi$
$798$		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	−0.666601	−	0.745415i	$-0.732251\pi$
$809$	5.81261e6	−	1.00677e7i	0.312248	−	0.540830i	0.978849	+	0.204585i	$0.0655846\pi$
$810$	708588.	+	1.22731e6i	0.0379473	+	0.0657267i
$811$	−3.09020e7			−1.64981			−0.824906	−	0.565270i	$-0.808772\pi$
$811$	−3.09020e7			−1.64981			−0.824906	+	0.565270i	$0.808772\pi$
$812$		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	0.995823	+	0.0913056i	$0.0291040\pi$
$821$	1.11435e7	+	1.93011e7i	0.576984	+	0.999366i	−0.418839	+	0.908061i	$0.637563\pi$
$822$	−4.69638e6	+	8.13437e6i	−0.242429	+	0.419898i
$823$	8.24475e6	−	1.42803e7i	0.424305	−	0.734918i	−0.572050	−	0.820218i	$-0.693852\pi$
$823$	8.24475e6	−	1.42803e7i	0.424305	−	0.734918i	0.996355	+	0.0853009i	$0.0271852\pi$
$824$	−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	−0.321657	−	0.946856i	$-0.604240\pi$
$829$	1.30433e7	−	2.25916e7i	0.659173	−	1.14172i	0.980830	−	0.194865i	$-0.0624269\pi$
$830$	−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	$-0.579565\pi$
$839$	−1.00872e7			−0.494729			−0.247365	+	0.968922i	$0.579565\pi$
$840$		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	$-0.305691\pi$
$853$	2.43630e7			1.14646			0.573229	+	0.819395i	$0.305691\pi$
$854$		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	$-0.815142\pi$
$857$	1.22806e6	−	2.12706e6i	0.0571172	−	0.0989300i	0.893170	+	0.449719i	$0.148476\pi$
$858$	−3.88022e6	+	6.72075e6i	−0.179945	+	0.311673i
$859$	4.31491e6	+	7.47364e6i	0.199521	+	0.345581i	0.948373	−	0.317156i	$-0.102728\pi$
$859$	4.31491e6	+	7.47364e6i	0.199521	+	0.345581i	−0.748852	+	0.662737i	$0.769395\pi$
$860$	1.67927e7			0.774238
$861$		0			0
$862$	−2.15038e7			−0.985703
$863$	−5.25997e6	−	9.11053e6i	−0.240412	−	0.416406i	0.720420	−	0.693538i	$-0.243949\pi$
$863$	−5.25997e6	−	9.11053e6i	−0.240412	−	0.416406i	−0.960832	+	0.277133i	$0.910616\pi$
$864$	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	0.963921	−	0.266187i	$-0.0857638\pi$
$877$	5.72699e6	+	9.91944e6i	0.251436	+	0.435500i	−0.712485	+	0.701687i	$0.752430\pi$
$878$	−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	$-0.417466\pi$
$881$	1.18134e7			0.512786			0.256393	+	0.966573i	$0.417466\pi$
$882$		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	0.733502	+	0.679687i	$0.237884\pi$
$887$	2.23864e7	+	3.87744e7i	0.955377	+	1.65476i	0.221875	+	0.975075i	$0.428782\pi$
$888$	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	−0.575495	−	0.817806i	$-0.695190\pi$
$907$	1.04178e7	−	1.80442e7i	0.420493	−	0.728315i	0.995988	+	0.0894902i	$0.0285238\pi$
$908$	−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	0.509205	−	0.860645i	$-0.329940\pi$
$919$	−1.25643e7	−	2.17620e7i	−0.490738	−	0.849984i	−0.999943	+	0.0106615i	$0.996606\pi$
$920$	−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	$-0.0821570\pi$
$929$	6.90210e6	+	1.19548e7i	0.262387	+	0.454467i	−0.704489	+	0.709715i	$0.748824\pi$
$930$	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	$-0.157160\pi$
$937$	4.73307e7			1.76114			0.880570	+	0.473915i	$0.157160\pi$
$938$		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	0.393630	+	0.919269i	$0.371219\pi$
$941$	−1.62785e7	+	2.81952e7i	−0.599295	+	1.03801i	−0.992925	+	0.118741i	$0.962114\pi$
$942$	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	0.909817	−	0.415010i	$-0.136222\pi$
$947$	2.63558e6	+	4.56497e6i	0.0954997	+	0.165410i	−0.814317	+	0.580420i	$0.802888\pi$
$948$	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	−0.988391	−	0.151934i	$-0.951450\pi$
$971$	−1.83851e7	−	3.18439e7i	−0.625774	−	1.08387i	0.362617	−	0.931938i	$-0.381883\pi$
$972$	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	−0.668098	−	0.744073i	$-0.732891\pi$
$977$	9.25913e6	−	1.60373e7i	0.310337	−	0.537520i	0.978435	+	0.206553i	$0.0662247\pi$
$978$	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	$-0.685048\pi$
$983$	1.36085e7	−	2.35706e7i	0.449185	−	0.778012i	0.998333	+	0.0577135i	$0.0183810\pi$
$984$	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	−0.967370	−	0.253369i	$-0.918461\pi$
$991$	−8.16990e6	+	1.41507e7i	−0.264261	+	0.457713i	0.703109	+	0.711082i	$0.251795\pi$
$992$	−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	$-0.993133\pi$
$997$	−1.51031e7	+	2.61594e7i	−0.481203	+	0.833468i	0.518564	+	0.855039i	$0.326467\pi$
$998$	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.h.67.1		2
7.2	even	3	inner	294.6.e.h.79.1		2
7.3	odd	6		42.6.a.a.1.1	✓	1
7.4	even	3		294.6.a.h.1.1		1
7.5	odd	6		294.6.e.r.79.1		2
7.6	odd	2		294.6.e.r.67.1		2
21.11	odd	6		882.6.a.o.1.1		1
21.17	even	6		126.6.a.k.1.1		1
28.3	even	6		336.6.a.j.1.1		1
35.3	even	12		1050.6.g.o.799.2		2
35.17	even	12		1050.6.g.o.799.1		2
35.24	odd	6		1050.6.a.n.1.1		1
84.59	odd	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	7.3	odd	6
126.6.a.k.1.1		1	21.17	even	6
294.6.a.h.1.1		1	7.4	even	3
294.6.e.h.67.1		2	1.1	even	1	trivial
294.6.e.h.79.1		2	7.2	even	3	inner
294.6.e.r.67.1		2	7.6	odd	2
294.6.e.r.79.1		2	7.5	odd	6
336.6.a.j.1.1		1	28.3	even	6
882.6.a.o.1.1		1	21.11	odd	6
1008.6.a.x.1.1		1	84.59	odd	6
1050.6.a.n.1.1		1	35.24	odd	6
1050.6.g.o.799.1		2	35.17	even	12
1050.6.g.o.799.2		2	35.3	even	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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