LMFDB - Embedded newform 294.6.e.l.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,6,Mod(67,294)]

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

lf = mfeigenbasis(mf)

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")

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

chi := DirichletCharacter("294.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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.l.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} +(36.0000 - 62.3538i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-144.000 - 249.415i) q^{10} +(207.000 + 358.535i) q^{11} +(-72.0000 + 124.708i) q^{12} -1054.00 q^{13} -648.000 q^{15} +(-128.000 + 221.703i) q^{16} +(924.000 + 1600.41i) q^{17} +(162.000 + 280.592i) q^{18} +(-118.000 + 204.382i) q^{19} -1152.00 q^{20} +1656.00 q^{22} +(-1449.00 + 2509.74i) q^{23} +(288.000 + 498.831i) q^{24} +(-1029.50 - 1783.15i) q^{25} +(-2108.00 + 3651.16i) q^{26} +729.000 q^{27} -6522.00 q^{29} +(-1296.00 + 2244.74i) q^{30} +(-3100.00 - 5369.36i) q^{31} +(512.000 + 886.810i) q^{32} +(1863.00 - 3226.81i) q^{33} +7392.00 q^{34} +1296.00 q^{36} +(-4825.00 + 8357.15i) q^{37} +(472.000 + 817.528i) q^{38} +(4743.00 + 8215.12i) q^{39} +(-2304.00 + 3990.65i) q^{40} +8484.00 q^{41} -10804.0 q^{43} +(3312.00 - 5736.55i) q^{44} +(2916.00 + 5050.66i) q^{45} +(5796.00 + 10039.0i) q^{46} +(-30.0000 + 51.9615i) q^{47} +2304.00 q^{48} -8236.00 q^{50} +(8316.00 - 14403.7i) q^{51} +(8432.00 + 14604.7i) q^{52} +(-11253.0 - 19490.8i) q^{53} +(1458.00 - 2525.33i) q^{54} +29808.0 q^{55} +2124.00 q^{57} +(-13044.0 + 22592.9i) q^{58} +(14088.0 + 24401.1i) q^{59} +(5184.00 + 8978.95i) q^{60} +(17597.0 - 30478.9i) q^{61} -24800.0 q^{62} +4096.00 q^{64} +(-37944.0 + 65720.9i) q^{65} +(-7452.00 - 12907.2i) q^{66} +(14108.0 + 24435.8i) q^{67} +(14784.0 - 25606.6i) q^{68} +26082.0 q^{69} -6642.00 q^{71} +(2592.00 - 4489.48i) q^{72} +(26045.0 + 45111.3i) q^{73} +(19300.0 + 33428.6i) q^{74} +(-9265.50 + 16048.3i) q^{75} +3776.00 q^{76} +37944.0 q^{78} +(-21670.0 + 37533.5i) q^{79} +(9216.00 + 15962.6i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(16968.0 - 29389.4i) q^{82} +25716.0 q^{83} +133056. q^{85} +(-21608.0 + 37426.2i) q^{86} +(29349.0 + 50834.0i) q^{87} +(-13248.0 - 22946.2i) q^{88} +(-49362.0 + 85497.5i) q^{89} +23328.0 q^{90} +46368.0 q^{92} +(-27900.0 + 48324.2i) q^{93} +(120.000 + 207.846i) q^{94} +(8496.00 + 14715.5i) q^{95} +(4608.00 - 7981.29i) q^{96} -148954. q^{97} -33534.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 9 q^{3} - 16 q^{4} + 72 q^{5} - 72 q^{6} - 128 q^{8} - 81 q^{9} - 288 q^{10} + 414 q^{11} - 144 q^{12} - 2108 q^{13} - 1296 q^{15} - 256 q^{16} + 1848 q^{17} + 324 q^{18} - 236 q^{19} - 2304 q^{20}+ \cdots - 67068 q^{99}+O(q^{100}) $ 2 * q + 4 * q^2 - 9 * q^3 - 16 * q^4 + 72 * q^5 - 72 * q^6 - 128 * q^8 - 81 * q^9 - 288 * q^10 + 414 * q^11 - 144 * q^12 - 2108 * q^13 - 1296 * q^15 - 256 * q^16 + 1848 * q^17 + 324 * q^18 - 236 * q^19 - 2304 * q^20 + 3312 * q^22 - 2898 * q^23 + 576 * q^24 - 2059 * q^25 - 4216 * q^26 + 1458 * q^27 - 13044 * q^29 - 2592 * q^30 - 6200 * q^31 + 1024 * q^32 + 3726 * q^33 + 14784 * q^34 + 2592 * q^36 - 9650 * q^37 + 944 * q^38 + 9486 * q^39 - 4608 * q^40 + 16968 * q^41 - 21608 * q^43 + 6624 * q^44 + 5832 * q^45 + 11592 * q^46 - 60 * q^47 + 4608 * q^48 - 16472 * q^50 + 16632 * q^51 + 16864 * q^52 - 22506 * q^53 + 2916 * q^54 + 59616 * q^55 + 4248 * q^57 - 26088 * q^58 + 28176 * q^59 + 10368 * q^60 + 35194 * q^61 - 49600 * q^62 + 8192 * q^64 - 75888 * q^65 - 14904 * q^66 + 28216 * q^67 + 29568 * q^68 + 52164 * q^69 - 13284 * q^71 + 5184 * q^72 + 52090 * q^73 + 38600 * q^74 - 18531 * q^75 + 7552 * q^76 + 75888 * q^78 - 43340 * q^79 + 18432 * q^80 - 6561 * q^81 + 33936 * q^82 + 51432 * q^83 + 266112 * q^85 - 43216 * q^86 + 58698 * q^87 - 26496 * q^88 - 98724 * q^89 + 46656 * q^90 + 92736 * q^92 - 55800 * q^93 + 240 * q^94 + 16992 * q^95 + 9216 * q^96 - 297908 * q^97 - 67068 * 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
$5$	36.0000	−	62.3538i	0.643988	−	1.11542i	−0.340547	−	0.940228i	$-0.610612\pi$
$5$	36.0000	−	62.3538i	0.643988	−	1.11542i	0.984534	−	0.175192i	$-0.0560545\pi$
$6$	−36.0000			−0.408248
$7$		0			0
$7$		0			0
$8$	−64.0000			−0.353553
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	−144.000	−	249.415i	−0.455368	−	0.788720i
$11$	207.000	+	358.535i	0.515809	+	0.893407i	0.999832	+	0.0183515i	$0.00584179\pi$
$11$	207.000	+	358.535i	0.515809	+	0.893407i	−0.484023	+	0.875055i	$0.660825\pi$
$12$	−72.0000	+	124.708i	−0.144338	+	0.250000i
$13$	−1054.00			−1.72975			−0.864873	−	0.501991i	$-0.832601\pi$
$13$	−1054.00			−1.72975			−0.864873	+	0.501991i	$0.832601\pi$
$14$		0			0
$15$	−648.000			−0.743613
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	924.000	+	1600.41i	0.775443	+	1.34311i	0.934545	+	0.355844i	$0.115807\pi$
$17$	924.000	+	1600.41i	0.775443	+	1.34311i	−0.159103	+	0.987262i	$0.550860\pi$
$18$	162.000	+	280.592i	0.117851	+	0.204124i
$19$	−118.000	+	204.382i	−0.0749891	+	0.129885i	−0.901082	−	0.433650i	$-0.857226\pi$
$19$	−118.000	+	204.382i	−0.0749891	+	0.129885i	0.826092	+	0.563535i	$0.190559\pi$
$20$	−1152.00			−0.643988
$21$		0			0
$22$	1656.00			0.729464
$23$	−1449.00	+	2509.74i	−0.571148	+	0.989258i	0.425300	+	0.905052i	$0.360169\pi$
$23$	−1449.00	+	2509.74i	−0.571148	+	0.989258i	−0.996448	+	0.0842053i	$0.973165\pi$
$24$	288.000	+	498.831i	0.102062	+	0.176777i
$25$	−1029.50	−	1783.15i	−0.329440	−	0.570607i
$26$	−2108.00	+	3651.16i	−0.611557	+	1.05925i
$27$	729.000			0.192450
$28$		0			0
$29$	−6522.00			−1.44008			−0.720039	−	0.693934i	$-0.755876\pi$
$29$	−6522.00			−1.44008			−0.720039	+	0.693934i	$0.755876\pi$
$30$	−1296.00	+	2244.74i	−0.262907	+	0.455368i
$31$	−3100.00	−	5369.36i	−0.579372	−	1.00350i	−0.995551	−	0.0942192i	$-0.969965\pi$
$31$	−3100.00	−	5369.36i	−0.579372	−	1.00350i	0.416180	−	0.909282i	$-0.363369\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$	1863.00	−	3226.81i	0.297802	−	0.515809i
$34$	7392.00			1.09664
$35$		0			0
$36$	1296.00			0.166667
$37$	−4825.00	+	8357.15i	−0.579419	+	1.00358i	0.416127	+	0.909307i	$0.363387\pi$
$37$	−4825.00	+	8357.15i	−0.579419	+	1.00358i	−0.995546	+	0.0942771i	$0.969946\pi$
$38$	472.000	+	817.528i	0.0530253	+	0.0918425i
$39$	4743.00	+	8215.12i	0.499335	+	0.864873i
$40$	−2304.00	+	3990.65i	−0.227684	+	0.394360i
$41$	8484.00			0.788208			0.394104	−	0.919066i	$-0.371055\pi$
$41$	8484.00			0.788208			0.394104	+	0.919066i	$0.371055\pi$
$42$		0			0
$43$	−10804.0			−0.891073			−0.445537	−	0.895264i	$-0.646987\pi$
$43$	−10804.0			−0.891073			−0.445537	+	0.895264i	$0.646987\pi$
$44$	3312.00	−	5736.55i	0.257904	−	0.446703i
$45$	2916.00	+	5050.66i	0.214663	+	0.371806i
$46$	5796.00	+	10039.0i	0.403863	+	0.699511i
$47$	−30.0000	+	51.9615i	−0.00198096	+	0.00343113i	−0.867014	−	0.498283i	$-0.833964\pi$
$47$	−30.0000	+	51.9615i	−0.00198096	+	0.00343113i	0.865033	+	0.501715i	$0.167297\pi$
$48$	2304.00			0.144338
$49$		0			0
$50$	−8236.00			−0.465899
$51$	8316.00	−	14403.7i	0.447702	−	0.775443i
$52$	8432.00	+	14604.7i	0.432436	+	0.749002i
$53$	−11253.0	−	19490.8i	−0.550274	−	0.953102i	−0.998255	−	0.0590587i	$-0.981190\pi$
$53$	−11253.0	−	19490.8i	−0.550274	−	0.953102i	0.447981	−	0.894043i	$-0.352143\pi$
$54$	1458.00	−	2525.33i	0.0680414	−	0.117851i
$55$	29808.0			1.32870
$56$		0			0
$57$	2124.00			0.0865899
$58$	−13044.0	+	22592.9i	−0.509144	+	0.881864i
$59$	14088.0	+	24401.1i	0.526889	+	0.912599i	0.999509	+	0.0313325i	$0.00997507\pi$
$59$	14088.0	+	24401.1i	0.526889	+	0.912599i	−0.472620	+	0.881266i	$0.656692\pi$
$60$	5184.00	+	8978.95i	0.185903	+	0.321994i
$61$	17597.0	−	30478.9i	0.605500	−	1.04876i	−0.386472	−	0.922301i	$-0.626307\pi$
$61$	17597.0	−	30478.9i	0.605500	−	1.04876i	0.991972	−	0.126456i	$-0.0403601\pi$
$62$	−24800.0			−0.819356
$63$		0			0
$64$	4096.00			0.125000
$65$	−37944.0	+	65720.9i	−1.11393	+	1.92939i
$66$	−7452.00	−	12907.2i	−0.210578	−	0.364732i
$67$	14108.0	+	24435.8i	0.383953	+	0.665027i	0.991623	−	0.129163i	$-0.0412290\pi$
$67$	14108.0	+	24435.8i	0.383953	+	0.665027i	−0.607670	+	0.794190i	$0.707896\pi$
$68$	14784.0	−	25606.6i	0.387721	−	0.671553i
$69$	26082.0			0.659505
$70$		0			0
$71$	−6642.00			−0.156370			−0.0781849	−	0.996939i	$-0.524912\pi$
$71$	−6642.00			−0.156370			−0.0781849	+	0.996939i	$0.524912\pi$
$72$	2592.00	−	4489.48i	0.0589256	−	0.102062i
$73$	26045.0	+	45111.3i	0.572028	+	0.990781i	0.996358	+	0.0852736i	$0.0271764\pi$
$73$	26045.0	+	45111.3i	0.572028	+	0.990781i	−0.424330	+	0.905508i	$0.639490\pi$
$74$	19300.0	+	33428.6i	0.409711	+	0.709641i
$75$	−9265.50	+	16048.3i	−0.190202	+	0.329440i
$76$	3776.00			0.0749891
$77$		0			0
$78$	37944.0			0.706166
$79$	−21670.0	+	37533.5i	−0.390653	+	0.676631i	−0.992536	−	0.121954i	$-0.961084\pi$
$79$	−21670.0	+	37533.5i	−0.390653	+	0.676631i	0.601883	+	0.798584i	$0.294417\pi$
$80$	9216.00	+	15962.6i	0.160997	+	0.278855i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	16968.0	−	29389.4i	0.278674	−	0.482677i
$83$	25716.0			0.409740			0.204870	−	0.978789i	$-0.434323\pi$
$83$	25716.0			0.409740			0.204870	+	0.978789i	$0.434323\pi$
$84$		0			0
$85$	133056.			1.99750
$86$	−21608.0	+	37426.2i	−0.315042	+	0.545669i
$87$	29349.0	+	50834.0i	0.415715	+	0.720039i
$88$	−13248.0	−	22946.2i	−0.182366	−	0.315867i
$89$	−49362.0	+	85497.5i	−0.660568	+	1.14414i	0.319898	+	0.947452i	$0.396351\pi$
$89$	−49362.0	+	85497.5i	−0.660568	+	1.14414i	−0.980467	+	0.196686i	$0.936982\pi$
$90$	23328.0			0.303579
$91$		0			0
$92$	46368.0			0.571148
$93$	−27900.0	+	48324.2i	−0.334501	+	0.579372i
$94$	120.000	+	207.846i	0.00140075	+	0.00242618i
$95$	8496.00	+	14715.5i	0.0965841	+	0.167289i
$96$	4608.00	−	7981.29i	0.0510310	−	0.0883883i
$97$	−148954.			−1.60740			−0.803698	−	0.595038i	$-0.797137\pi$
$97$	−148954.			−1.60740			−0.803698	+	0.595038i	$0.797137\pi$
$98$		0			0
$99$	−33534.0			−0.343872
$100$	−16472.0	+	28530.3i	−0.164720	+	0.285303i
$101$	−24174.0	−	41870.6i	−0.235801	−	0.408419i	0.723704	−	0.690110i	$-0.242438\pi$
$101$	−24174.0	−	41870.6i	−0.235801	−	0.408419i	−0.959505	+	0.281691i	$0.909105\pi$
$102$	−33264.0	−	57614.9i	−0.316573	−	0.548321i
$103$	91796.0	−	158995.i	0.852571	−	1.47670i	−0.0263087	−	0.999654i	$-0.508375\pi$
$103$	91796.0	−	158995.i	0.852571	−	1.47670i	0.878880	−	0.477043i	$-0.158291\pi$
$104$	67456.0			0.611557
$105$		0			0
$106$	−90024.0			−0.778204
$107$	1119.00	−	1938.16i	0.00944867	−	0.0163656i	−0.861262	−	0.508160i	$-0.830326\pi$
$107$	1119.00	−	1938.16i	0.00944867	−	0.0163656i	0.870711	+	0.491795i	$0.163659\pi$
$108$	−5832.00	−	10101.3i	−0.0481125	−	0.0833333i
$109$	−30079.0	−	52098.4i	−0.242492	−	0.420008i	0.718932	−	0.695081i	$-0.244631\pi$
$109$	−30079.0	−	52098.4i	−0.242492	−	0.420008i	−0.961423	+	0.275073i	$0.911298\pi$
$110$	59616.0	−	103258.i	0.469766	−	0.813658i
$111$	86850.0			0.669056
$112$		0			0
$113$	−7014.00			−0.0516737			−0.0258369	−	0.999666i	$-0.508225\pi$
$113$	−7014.00			−0.0516737			−0.0258369	+	0.999666i	$0.508225\pi$
$114$	4248.00	−	7357.75i	0.0306142	−	0.0530253i
$115$	104328.	+	180701.i	0.735625	+	1.27414i
$116$	52176.0	+	90371.5i	0.360019	+	0.623572i
$117$	42687.0	−	73936.1i	0.288291	−	0.499335i
$118$	112704.			0.745134
$119$		0			0
$120$	41472.0			0.262907
$121$	−5172.50	+	8959.03i	−0.0321172	+	0.0556285i
$122$	−70388.0	−	121916.i	−0.428153	−	0.741583i
$123$	−38178.0	−	66126.2i	−0.227536	−	0.394104i
$124$	−49600.0	+	85909.7i	−0.289686	+	0.501751i
$125$	76752.0			0.439354
$126$		0			0
$127$	−1780.00			−0.00979289			−0.00489644	−	0.999988i	$-0.501559\pi$
$127$	−1780.00			−0.00979289			−0.00489644	+	0.999988i	$0.501559\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$	48618.0	+	84208.8i	0.257231	+	0.445537i
$130$	151776.	+	262884.i	0.787671	+	1.36429i
$131$	132570.	−	229618.i	0.674943	−	1.16904i	−0.301543	−	0.953453i	$-0.597502\pi$
$131$	132570.	−	229618.i	0.674943	−	1.16904i	0.976486	−	0.215583i	$-0.0691651\pi$
$132$	−59616.0			−0.297802
$133$		0			0
$134$	112864.			0.542992
$135$	26244.0	−	45455.9i	0.123935	−	0.214663i
$136$	−59136.0	−	102427.i	−0.274160	−	0.474860i
$137$	103365.	+	179033.i	0.470514	+	0.814953i	0.999431	−	0.0337198i	$-0.0107354\pi$
$137$	103365.	+	179033.i	0.470514	+	0.814953i	−0.528918	+	0.848673i	$0.677402\pi$
$138$	52164.0	−	90350.7i	0.233170	−	0.403863i
$139$	−236836.			−1.03971			−0.519853	−	0.854256i	$-0.674013\pi$
$139$	−236836.			−1.03971			−0.519853	+	0.854256i	$0.674013\pi$
$140$		0			0
$141$	540.000			0.00228742
$142$	−13284.0	+	23008.6i	−0.0552851	+	0.0957566i
$143$	−218178.	−	377895.i	−0.892218	−	1.54537i
$144$	−10368.0	−	17957.9i	−0.0416667	−	0.0721688i
$145$	−234792.	+	406672.i	−0.927392	+	1.60629i
$146$	208360.			0.808970
$147$		0			0
$148$	154400.			0.579419
$149$	−236853.	+	410241.i	−0.874004	+	1.51382i	−0.0161832	+	0.999869i	$0.505151\pi$
$149$	−236853.	+	410241.i	−0.874004	+	1.51382i	−0.857820	+	0.513950i	$0.828182\pi$
$150$	37062.0	+	64193.3i	0.134493	+	0.232949i
$151$	−197476.	−	342038.i	−0.704810	−	1.22077i	−0.966760	−	0.255685i	$-0.917699\pi$
$151$	−197476.	−	342038.i	−0.704810	−	1.22077i	0.261950	−	0.965081i	$-0.415634\pi$
$152$	7552.00	−	13080.4i	0.0265126	−	0.0459212i
$153$	−149688.			−0.516962
$154$		0			0
$155$	−446400.			−1.49243
$156$	75888.0	−	131442.i	0.249667	−	0.432436i
$157$	72545.0	+	125652.i	0.234887	+	0.406836i	0.959240	−	0.282594i	$-0.0911948\pi$
$157$	72545.0	+	125652.i	0.234887	+	0.406836i	−0.724353	+	0.689429i	$0.757861\pi$
$158$	86680.0	+	150134.i	0.276233	+	0.478450i
$159$	−101277.	+	175417.i	−0.317701	+	0.550274i
$160$	73728.0			0.227684
$161$		0			0
$162$	−26244.0			−0.0785674
$163$	−265240.	+	459409.i	−0.781934	+	1.35435i	0.148880	+	0.988855i	$0.452433\pi$
$163$	−265240.	+	459409.i	−0.781934	+	1.35435i	−0.930814	+	0.365494i	$0.880900\pi$
$164$	−67872.0	−	117558.i	−0.197052	−	0.341304i
$165$	−134136.	−	232330.i	−0.383562	−	0.664349i
$166$	51432.0	−	89082.8i	0.144865	−	0.250913i
$167$	−312348.			−0.866658			−0.433329	−	0.901236i	$-0.642661\pi$
$167$	−312348.			−0.866658			−0.433329	+	0.901236i	$0.642661\pi$
$168$		0			0
$169$	739623.			1.99202
$170$	266112.	−	460920.i	0.706223	−	1.22321i
$171$	−9558.00	−	16554.9i	−0.0249964	−	0.0432950i
$172$	86432.0	+	149705.i	0.222768	+	0.385846i
$173$	37554.0	−	65045.4i	0.0953984	−	0.165235i	−0.814376	−	0.580337i	$-0.802921\pi$
$173$	37554.0	−	65045.4i	0.0953984	−	0.165235i	0.909775	+	0.415102i	$0.136254\pi$
$174$	234792.			0.587909
$175$		0			0
$176$	−105984.			−0.257904
$177$	126792.	−	219610.i	0.304200	−	0.526889i
$178$	197448.	+	341990.i	0.467092	+	0.809028i
$179$	−193359.	−	334908.i	−0.451057	−	0.781254i	0.547395	−	0.836875i	$-0.315620\pi$
$179$	−193359.	−	334908.i	−0.451057	−	0.781254i	−0.998452	+	0.0556203i	$0.982286\pi$
$180$	46656.0	−	80810.6i	0.107331	−	0.185903i
$181$	−417598.			−0.947462			−0.473731	−	0.880669i	$-0.657093\pi$
$181$	−417598.			−0.947462			−0.473731	+	0.880669i	$0.657093\pi$
$182$		0			0
$183$	−316746.			−0.699171
$184$	92736.0	−	160623.i	0.201931	−	0.349755i
$185$	347400.	+	601714.i	0.746278	+	1.29259i
$186$	111600.	+	193297.i	0.236528	+	0.409678i
$187$	−382536.	+	662572.i	−0.799960	+	1.38557i
$188$	960.000			0.00198096
$189$		0			0
$190$	67968.0			0.136590
$191$	494025.	−	855676.i	0.979863	−	1.69717i	0.317013	−	0.948421i	$-0.397320\pi$
$191$	494025.	−	855676.i	0.979863	−	1.69717i	0.662850	−	0.748752i	$-0.269347\pi$
$192$	−18432.0	−	31925.2i	−0.0360844	−	0.0625000i
$193$	204629.	+	354428.i	0.395434	+	0.684912i	0.993156	−	0.116791i	$-0.0372609\pi$
$193$	204629.	+	354428.i	0.395434	+	0.684912i	−0.597723	+	0.801703i	$0.703928\pi$
$194$	−297908.	+	515992.i	−0.568300	+	0.984325i
$195$	682992.			1.28626
$196$		0			0
$197$	−922230.			−1.69307			−0.846533	−	0.532337i	$-0.821314\pi$
$197$	−922230.			−1.69307			−0.846533	+	0.532337i	$0.821314\pi$
$198$	−67068.0	+	116165.i	−0.121577	+	0.210578i
$199$	−94744.0	−	164101.i	−0.169597	−	0.293751i	0.768681	−	0.639632i	$-0.220913\pi$
$199$	−94744.0	−	164101.i	−0.169597	−	0.293751i	−0.938278	+	0.345881i	$0.887580\pi$
$200$	65888.0	+	114121.i	0.116475	+	0.201740i
$201$	126972.	−	219922.i	0.221676	−	0.383953i
$202$	−193392.			−0.333473
$203$		0			0
$204$	−266112.			−0.447702
$205$	305424.	−	529010.i	0.507596	−	0.879183i
$206$	−367184.	−	635981.i	−0.602859	−	1.04418i
$207$	−117369.	−	203289.i	−0.190383	−	0.329753i
$208$	134912.	−	233674.i	0.216218	−	0.374501i
$209$	−97704.0			−0.154720
$210$		0			0
$211$	−611380.			−0.945377			−0.472689	−	0.881230i	$-0.656716\pi$
$211$	−611380.			−0.945377			−0.472689	+	0.881230i	$0.656716\pi$
$212$	−180048.	+	311852.i	−0.275137	+	0.476551i
$213$	29889.0	+	51769.3i	0.0451401	+	0.0781849i
$214$	−4476.00	−	7752.66i	−0.00668122	−	0.0115722i
$215$	−388944.	+	673671.i	−0.573840	+	0.993920i
$216$	−46656.0			−0.0680414
$217$		0			0
$218$	−240632.			−0.342935
$219$	234405.	−	406001.i	0.330260	−	0.572028i
$220$	−238464.	−	413032.i	−0.332174	−	0.575343i
$221$	−973896.	−	1.68684e6i	−1.34132	−	2.32323i
$222$	173700.	−	300857.i	0.236547	−	0.409711i
$223$	−783256.			−1.05473			−0.527365	−	0.849639i	$-0.676820\pi$
$223$	−783256.			−1.05473			−0.527365	+	0.849639i	$0.676820\pi$
$224$		0			0
$225$	166779.			0.219627
$226$	−14028.0	+	24297.2i	−0.0182694	+	0.0316436i
$227$	−40356.0	−	69898.6i	−0.0519809	−	0.0900335i	0.838864	−	0.544341i	$-0.183220\pi$
$227$	−40356.0	−	69898.6i	−0.0519809	−	0.0900335i	−0.890845	+	0.454307i	$0.849887\pi$
$228$	−16992.0	−	29431.0i	−0.0216475	−	0.0374945i
$229$	−76369.0	+	132275.i	−0.0962340	+	0.166682i	−0.910123	−	0.414338i	$-0.864013\pi$
$229$	−76369.0	+	132275.i	−0.0962340	+	0.166682i	0.813889	+	0.581020i	$0.197346\pi$
$230$	834624.			1.04033
$231$		0			0
$232$	417408.			0.509144
$233$	177141.	−	306817.i	0.213761	−	0.370246i	−0.739127	−	0.673566i	$-0.764762\pi$
$233$	177141.	−	306817.i	0.213761	−	0.370246i	0.952889	+	0.303320i	$0.0980952\pi$
$234$	−170748.	−	295744.i	−0.203852	−	0.353083i
$235$	2160.00	+	3741.23i	0.00255143	+	0.00441921i
$236$	225408.	−	390418.i	0.263445	−	0.456299i
$237$	390060.			0.451087
$238$		0			0
$239$	275370.			0.311833			0.155916	−	0.987770i	$-0.450167\pi$
$239$	275370.			0.311833			0.155916	+	0.987770i	$0.450167\pi$
$240$	82944.0	−	143663.i	0.0929516	−	0.160997i
$241$	292349.	+	506363.i	0.324234	+	0.561590i	0.981357	−	0.192193i	$-0.0615600\pi$
$241$	292349.	+	506363.i	0.324234	+	0.561590i	−0.657123	+	0.753784i	$0.728227\pi$
$242$	20690.0	+	35836.1i	0.0227103	+	0.0393353i
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$	−563104.			−0.605500
$245$		0			0
$246$	−305424.			−0.321785
$247$	124372.	−	215419.i	0.129712	−	0.224668i
$248$	198400.	+	343639.i	0.204839	+	0.354791i
$249$	−115722.	−	200436.i	−0.118282	−	0.204870i
$250$	153504.	−	265877.i	0.155335	−	0.269048i
$251$	−184752.			−0.185099			−0.0925497	−	0.995708i	$-0.529502\pi$
$251$	−184752.			−0.185099			−0.0925497	+	0.995708i	$0.529502\pi$
$252$		0			0
$253$	−1.19977e6			−1.17841
$254$	−3560.00	+	6166.10i	−0.00346231	+	0.00599689i
$255$	−598752.	−	1.03707e6i	−0.576629	−	0.998751i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−117990.	+	204365.i	−0.111433	+	0.193007i	−0.916348	−	0.400383i	$-0.868877\pi$
$257$	−117990.	+	204365.i	−0.111433	+	0.193007i	0.804915	+	0.593389i	$0.202211\pi$
$258$	388944.			0.363779
$259$		0			0
$260$	1.21421e6			1.11393
$261$	264141.	−	457506.i	0.240013	−	0.415715i
$262$	−530280.	−	918472.i	−0.477257	−	0.826633i
$263$	122247.	+	211738.i	0.108981	+	0.188760i	0.915358	−	0.402642i	$-0.131908\pi$
$263$	122247.	+	211738.i	0.108981	+	0.188760i	−0.806377	+	0.591402i	$0.798575\pi$
$264$	−119232.	+	206516.i	−0.105289	+	0.182366i
$265$	−1.62043e6			−1.41748
$266$		0			0
$267$	888516.			0.762759
$268$	225728.	−	390972.i	0.191977	−	0.332513i
$269$	−763896.	−	1.32311e6i	−0.643656	−	1.11484i	−0.984610	−	0.174764i	$-0.944084\pi$
$269$	−763896.	−	1.32311e6i	−0.643656	−	1.11484i	0.340955	−	0.940080i	$-0.389250\pi$
$270$	−104976.	−	181824.i	−0.0876356	−	0.151789i
$271$	−1.03528e6	+	1.79316e6i	−0.856317	+	1.48318i	0.0191007	+	0.999818i	$0.493920\pi$
$271$	−1.03528e6	+	1.79316e6i	−0.856317	+	1.48318i	−0.875418	+	0.483367i	$0.839414\pi$
$272$	−473088.			−0.387721
$273$		0			0
$274$	826920.			0.665407
$275$	426213.	−	738223.i	0.339856	−	0.588648i
$276$	−208656.	−	361403.i	−0.164876	−	0.285574i
$277$	1.20364e6	+	2.08476e6i	0.942530	+	1.63251i	0.760622	+	0.649195i	$0.224894\pi$
$277$	1.20364e6	+	2.08476e6i	0.942530	+	1.63251i	0.181909	+	0.983315i	$0.441773\pi$
$278$	−473672.	+	820424.i	−0.367592	+	0.636688i
$279$	502200.			0.386248
$280$		0			0
$281$	341886.			0.258295			0.129147	−	0.991625i	$-0.458776\pi$
$281$	341886.			0.258295			0.129147	+	0.991625i	$0.458776\pi$
$282$	1080.00	−	1870.61i	0.000808725	−	0.00140075i
$283$	−289282.	−	501051.i	−0.214712	−	0.371891i	0.738472	−	0.674284i	$-0.235548\pi$
$283$	−289282.	−	501051.i	−0.214712	−	0.371891i	−0.953183	+	0.302393i	$0.902214\pi$
$284$	53136.0	+	92034.3i	0.0390925	+	0.0677101i
$285$	76464.0	−	132440.i	0.0557628	−	0.0965841i
$286$	−1.74542e6			−1.26179
$287$		0			0
$288$	−82944.0			−0.0589256
$289$	−997624.	+	1.72793e6i	−0.702623	+	1.21698i
$290$	939168.	+	1.62669e6i	0.655765	+	1.13582i
$291$	670293.	+	1.16098e6i	0.464015	+	0.803698i
$292$	416720.	−	721780.i	0.286014	−	0.495391i
$293$	780540.			0.531161			0.265580	−	0.964089i	$-0.414436\pi$
$293$	780540.			0.531161			0.265580	+	0.964089i	$0.414436\pi$
$294$		0			0
$295$	2.02867e6			1.35724
$296$	308800.	−	534857.i	0.204856	−	0.354820i
$297$	150903.	+	261372.i	0.0992674	+	0.171936i
$298$	947412.	+	1.64097e6i	0.618014	+	1.07043i
$299$	1.52725e6	−	2.64527e6i	0.987941	−	1.71116i
$300$	296496.			0.190202
$301$		0			0
$302$	−1.57981e6			−0.996752
$303$	−217566.	+	376835.i	−0.136140	+	0.235801i
$304$	−30208.0	−	52321.8i	−0.0187473	−	0.0324712i
$305$	−1.26698e6	−	2.19448e6i	−0.779869	−	1.35077i
$306$	−299376.	+	518534.i	−0.182774	+	0.316573i
$307$	−2.24825e6			−1.36144			−0.680721	−	0.732543i	$-0.738333\pi$
$307$	−2.24825e6			−1.36144			−0.680721	+	0.732543i	$0.738333\pi$
$308$		0			0
$309$	−1.65233e6			−0.984465
$310$	−892800.	+	1.54637e6i	−0.527655	+	0.913925i
$311$	−290706.	−	503518.i	−0.170433	−	0.295198i	0.768138	−	0.640284i	$-0.221183\pi$
$311$	−290706.	−	503518.i	−0.170433	−	0.295198i	−0.938571	+	0.345086i	$0.887850\pi$
$312$	−303552.	−	525767.i	−0.176541	−	0.305779i
$313$	1.00204e6	−	1.73558e6i	0.578125	−	1.00134i	−0.417569	−	0.908645i	$-0.637118\pi$
$313$	1.00204e6	−	1.73558e6i	0.578125	−	1.00134i	0.995694	−	0.0926973i	$-0.0295489\pi$
$314$	580360.			0.332180
$315$		0			0
$316$	693440.			0.390653
$317$	639159.	−	1.10706e6i	0.357241	−	0.618759i	−0.630258	−	0.776386i	$-0.717051\pi$
$317$	639159.	−	1.10706e6i	0.357241	−	0.618759i	0.987499	+	0.157627i	$0.0503843\pi$
$318$	405108.	+	701668.i	0.224648	+	0.389102i
$319$	−1.35005e6	−	2.33836e6i	−0.742804	−	1.28657i
$320$	147456.	−	255401.i	0.0804984	−	0.139427i
$321$	−20142.0			−0.0109104
$322$		0			0
$323$	−436128.			−0.232599
$324$	−52488.0	+	90911.9i	−0.0277778	+	0.0481125i
$325$	1.08509e6	+	1.87944e6i	0.569847	+	0.987005i
$326$	1.06096e6	+	1.83764e6i	0.552911	+	0.957669i
$327$	−270711.	+	468885.i	−0.140003	+	0.242492i
$328$	−542976.			−0.278674
$329$		0			0
$330$	−1.07309e6			−0.542438
$331$	−1.29906e6	+	2.25003e6i	−0.651716	+	1.12881i	0.330990	+	0.943634i	$0.392617\pi$
$331$	−1.29906e6	+	2.25003e6i	−0.651716	+	1.12881i	−0.982706	+	0.185171i	$0.940716\pi$
$332$	−205728.	−	356331.i	−0.102435	−	0.177423i
$333$	−390825.	−	676929.i	−0.193140	−	0.334528i
$334$	−624696.	+	1.08201e6i	−0.306410	+	0.530717i
$335$	2.03155e6			0.989045
$336$		0			0
$337$	3.06190e6			1.46864			0.734321	−	0.678802i	$-0.237501\pi$
$337$	3.06190e6			1.46864			0.734321	+	0.678802i	$0.237501\pi$
$338$	1.47925e6	−	2.56213e6i	0.704285	−	1.21986i
$339$	31563.0	+	54668.7i	0.0149169	+	0.0258369i
$340$	−1.06445e6	−	1.84368e6i	−0.499375	−	0.864944i
$341$	1.28340e6	−	2.22291e6i	0.597690	−	1.03523i
$342$	−76464.0			−0.0353502
$343$		0			0
$344$	691456.			0.315042
$345$	938952.	−	1.62631e6i	0.424713	−	0.735625i
$346$	−150216.	−	260182.i	−0.0674568	−	0.116839i
$347$	712749.	+	1.23452e6i	0.317770	+	0.550394i	0.980022	−	0.198887i	$-0.0637327\pi$
$347$	712749.	+	1.23452e6i	0.317770	+	0.550394i	−0.662252	+	0.749281i	$0.730399\pi$
$348$	469584.	−	813343.i	0.207857	−	0.360019i
$349$	2.93322e6			1.28908			0.644542	−	0.764569i	$-0.277048\pi$
$349$	2.93322e6			1.28908			0.644542	+	0.764569i	$0.277048\pi$
$350$		0			0
$351$	−768366.			−0.332890
$352$	−211968.	+	367139.i	−0.0911830	+	0.157934i
$353$	1.00638e6	+	1.74310e6i	0.429858	+	0.744536i	0.996860	−	0.0791801i	$-0.0252302\pi$
$353$	1.00638e6	+	1.74310e6i	0.429858	+	0.744536i	−0.567002	+	0.823716i	$0.691897\pi$
$354$	−507168.	−	878441.i	−0.215102	−	0.372567i
$355$	−239112.	+	414154.i	−0.100700	+	0.174418i
$356$	1.57958e6			0.660568
$357$		0			0
$358$	−1.54687e6			−0.637891
$359$	−2.03855e6	+	3.53087e6i	−0.834806	+	1.44593i	0.0593826	+	0.998235i	$0.481087\pi$
$359$	−2.03855e6	+	3.53087e6i	−0.834806	+	1.44593i	−0.894188	+	0.447691i	$0.852247\pi$
$360$	−186624.	−	323242.i	−0.0758947	−	0.131453i
$361$	1.21020e6	+	2.09613e6i	0.488753	+	0.846546i
$362$	−835196.	+	1.44660e6i	−0.334979	+	0.580200i
$363$	93105.0			0.0370857
$364$		0			0
$365$	3.75048e6			1.47352
$366$	−633492.	+	1.09724e6i	−0.247194	+	0.428153i
$367$	−297376.	−	515070.i	−0.115250	−	0.199619i	0.802630	−	0.596478i	$-0.203434\pi$
$367$	−297376.	−	515070.i	−0.115250	−	0.199619i	−0.917880	+	0.396859i	$0.870100\pi$
$368$	−370944.	−	642494.i	−0.142787	−	0.247314i
$369$	−343602.	+	595136.i	−0.131368	+	0.227536i
$370$	2.77920e6			1.05540
$371$		0			0
$372$	892800.			0.334501
$373$	−1.02261e6	+	1.77121e6i	−0.380573	+	0.659172i	−0.991144	−	0.132789i	$-0.957607\pi$
$373$	−1.02261e6	+	1.77121e6i	−0.380573	+	0.659172i	0.610571	+	0.791962i	$0.290940\pi$
$374$	1.53014e6	+	2.65029e6i	0.565657	+	0.979747i
$375$	−345384.	−	598223.i	−0.126831	−	0.219677i
$376$	1920.00	−	3325.54i	0.000700377	−	0.00121309i
$377$	6.87419e6			2.49097
$378$		0			0
$379$	−3.22198e6			−1.15219			−0.576096	−	0.817382i	$-0.695425\pi$
$379$	−3.22198e6			−1.15219			−0.576096	+	0.817382i	$0.695425\pi$
$380$	135936.	−	235448.i	0.0482920	−	0.0836443i
$381$	8010.00	+	13873.7i	0.00282696	+	0.00489644i
$382$	−1.97610e6	−	3.42271e6i	−0.692868	−	1.20008i
$383$	864828.	−	1.49793e6i	0.301254	−	0.521787i	−0.675166	−	0.737666i	$-0.735928\pi$
$383$	864828.	−	1.49793e6i	0.301254	−	0.521787i	0.976420	+	0.215878i	$0.0692615\pi$
$384$	−147456.			−0.0510310
$385$		0			0
$386$	1.63703e6			0.559228
$387$	437562.	−	757880.i	0.148512	−	0.257231i
$388$	1.19163e6	+	2.06397e6i	0.401849	+	0.696023i
$389$	874593.	+	1.51484e6i	0.293043	+	0.507566i	0.974528	−	0.224267i	$-0.0719986\pi$
$389$	874593.	+	1.51484e6i	0.293043	+	0.507566i	−0.681484	+	0.731833i	$0.738665\pi$
$390$	1.36598e6	−	2.36595e6i	0.454762	−	0.787671i
$391$	−5.35550e6			−1.77157
$392$		0			0
$393$	−2.38626e6			−0.779357
$394$	−1.84446e6	+	3.19470e6i	−0.598589	+	1.03679i
$395$	1.56024e6	+	2.70241e6i	0.503151	+	0.871484i
$396$	268272.	+	464661.i	0.0859681	+	0.148901i
$397$	−941023.	+	1.62990e6i	−0.299657	+	0.519021i	−0.976057	−	0.217513i	$-0.930205\pi$
$397$	−941023.	+	1.62990e6i	−0.299657	+	0.519021i	0.676401	+	0.736534i	$0.263539\pi$
$398$	−757952.			−0.239847
$399$		0			0
$400$	527104.			0.164720
$401$	−2.09062e6	+	3.62106e6i	−0.649253	+	1.12454i	0.334049	+	0.942556i	$0.391585\pi$
$401$	−2.09062e6	+	3.62106e6i	−0.649253	+	1.12454i	−0.983302	+	0.181983i	$0.941748\pi$
$402$	−507888.	−	879688.i	−0.156748	−	0.271496i
$403$	3.26740e6	+	5.65930e6i	1.00217	+	1.73580i
$404$	−386784.	+	669930.i	−0.117900	+	0.204209i
$405$	−472392.			−0.143108
$406$		0			0
$407$	−3.99510e6			−1.19548
$408$	−532224.	+	921839.i	−0.158287	+	0.274160i
$409$	235841.	+	408489.i	0.0697126	+	0.120746i	0.898775	−	0.438411i	$-0.144458\pi$
$409$	235841.	+	408489.i	0.0697126	+	0.120746i	−0.829062	+	0.559156i	$0.811125\pi$
$410$	−1.22170e6	−	2.11604e6i	−0.358925	−	0.621676i
$411$	930285.	−	1.61130e6i	0.271651	−	0.470514i
$412$	−2.93747e6			−0.852571
$413$		0			0
$414$	−938952.			−0.269242
$415$	925776.	−	1.60349e6i	0.263867	−	0.457032i
$416$	−539648.	−	934698.i	−0.152889	−	0.264812i
$417$	1.06576e6	+	1.84595e6i	0.300137	+	0.519853i
$418$	−195408.	+	338457.i	−0.0547018	+	0.0947463i
$419$	−3.54094e6			−0.985333			−0.492666	−	0.870218i	$-0.663978\pi$
$419$	−3.54094e6			−0.985333			−0.492666	+	0.870218i	$0.663978\pi$
$420$		0			0
$421$	2.72763e6			0.750032			0.375016	−	0.927018i	$-0.377637\pi$
$421$	2.72763e6			0.750032			0.375016	+	0.927018i	$0.377637\pi$
$422$	−1.22276e6	+	2.11788e6i	−0.334241	+	0.578923i
$423$	−2430.00	−	4208.88i	−0.000660321	−	0.00114371i
$424$	720192.	+	1.24741e6i	0.194551	+	0.336972i
$425$	1.90252e6	−	3.29525e6i	0.510924	−	0.884946i
$426$	239112.			0.0638377
$427$		0			0
$428$	−35808.0			−0.00944867
$429$	−1.96360e6	+	3.40106e6i	−0.515122	+	0.892218i
$430$	1.55578e6	+	2.69468e6i	0.405766	+	0.702808i
$431$	2.38258e6	+	4.12676e6i	0.617810	+	1.07008i	0.989884	+	0.141876i	$0.0453134\pi$
$431$	2.38258e6	+	4.12676e6i	0.617810	+	1.07008i	−0.372074	+	0.928203i	$0.621353\pi$
$432$	−93312.0	+	161621.i	−0.0240563	+	0.0416667i
$433$	6.90300e6			1.76937			0.884684	−	0.466191i	$-0.154374\pi$
$433$	6.90300e6			1.76937			0.884684	+	0.466191i	$0.154374\pi$
$434$		0			0
$435$	4.22626e6			1.07086
$436$	−481264.	+	833574.i	−0.121246	+	0.210004i
$437$	−341964.	−	592299.i	−0.0856597	−	0.148367i
$438$	−937620.	−	1.62401e6i	−0.233529	−	0.404485i
$439$	−2.70063e6	+	4.67762e6i	−0.668811	+	1.15841i	0.309426	+	0.950924i	$0.399863\pi$
$439$	−2.70063e6	+	4.67762e6i	−0.668811	+	1.15841i	−0.978237	+	0.207491i	$0.933470\pi$
$440$	−1.90771e6			−0.469766
$441$		0			0
$442$	−7.79117e6			−1.89691
$443$	2.02932e6	−	3.51488e6i	0.491293	−	0.850944i	−0.508657	−	0.860969i	$-0.669858\pi$
$443$	2.02932e6	−	3.51488e6i	0.491293	−	0.850944i	0.999950	+	0.0100250i	$0.00319110\pi$
$444$	−694800.	−	1.20343e6i	−0.167264	−	0.289710i
$445$	3.55406e6	+	6.15582e6i	0.850796	+	1.47362i
$446$	−1.56651e6	+	2.71328e6i	−0.372904	+	0.645888i
$447$	4.26335e6			1.00921
$448$		0			0
$449$	212994.			0.0498599			0.0249300	−	0.999689i	$-0.492064\pi$
$449$	212994.			0.0498599			0.0249300	+	0.999689i	$0.492064\pi$
$450$	333558.	−	577739.i	0.0776498	−	0.134493i
$451$	1.75619e6	+	3.04181e6i	0.406565	+	0.704191i
$452$	56112.0	+	97188.8i	0.0129184	+	0.0223754i
$453$	−1.77728e6	+	3.07835e6i	−0.406922	+	0.704810i
$454$	−322848.			−0.0735120
$455$		0			0
$456$	−135936.			−0.0306142
$457$	458075.	−	793409.i	0.102600	−	0.177708i	−0.810155	−	0.586215i	$-0.800617\pi$
$457$	458075.	−	793409.i	0.102600	−	0.177708i	0.912755	+	0.408507i	$0.133951\pi$
$458$	305476.	+	529100.i	0.0680477	+	0.117862i
$459$	673596.	+	1.16670e6i	0.149234	+	0.258481i
$460$	1.66925e6	−	2.89122e6i	0.367812	−	0.637070i
$461$	−4.15835e6			−0.911315			−0.455657	−	0.890155i	$-0.650596\pi$
$461$	−4.15835e6			−0.911315			−0.455657	+	0.890155i	$0.650596\pi$
$462$		0			0
$463$	8.40799e6			1.82280			0.911401	−	0.411519i	$-0.135002\pi$
$463$	8.40799e6			1.82280			0.911401	+	0.411519i	$0.135002\pi$
$464$	834816.	−	1.44594e6i	0.180010	−	0.311786i
$465$	2.00880e6	+	3.47934e6i	0.430828	+	0.746217i
$466$	−708564.	−	1.22727e6i	−0.151152	−	0.261803i
$467$	−36024.0	+	62395.4i	−0.00764363	+	0.0132392i	−0.869822	−	0.493366i	$-0.835766\pi$
$467$	−36024.0	+	62395.4i	−0.00764363	+	0.0132392i	0.862178	+	0.506605i	$0.169100\pi$
$468$	−1.36598e6			−0.288291
$469$		0			0
$470$	17280.0			0.00360827
$471$	652905.	−	1.13086e6i	0.135612	−	0.234887i
$472$	−901632.	−	1.56167e6i	−0.186283	−	0.322652i
$473$	−2.23643e6	−	3.87361e6i	−0.459623	−	0.796091i
$474$	780120.	−	1.35121e6i	0.159483	−	0.276233i
$475$	485924.			0.0988176
$476$		0			0
$477$	1.82299e6			0.366849
$478$	550740.	−	953910.i	0.110250	−	0.190958i
$479$	−2.40280e6	−	4.16178e6i	−0.478497	−	0.828781i	0.521199	−	0.853435i	$-0.325485\pi$
$479$	−2.40280e6	−	4.16178e6i	−0.478497	−	0.828781i	−0.999696	+	0.0246541i	$0.992152\pi$
$480$	−331776.	−	574653.i	−0.0657267	−	0.113842i
$481$	5.08555e6	−	8.80843e6i	1.00225	−	1.73594i
$482$	2.33879e6			0.458537
$483$		0			0
$484$	165520.			0.0321172
$485$	−5.36234e6	+	9.28785e6i	−1.03514	+	1.79292i
$486$	118098.	+	204552.i	0.0226805	+	0.0392837i
$487$	−2.20902e6	−	3.82614e6i	−0.422064	−	0.731036i	0.574077	−	0.818801i	$-0.305361\pi$
$487$	−2.20902e6	−	3.82614e6i	−0.422064	−	0.731036i	−0.996141	+	0.0877652i	$0.972027\pi$
$488$	−1.12621e6	+	1.95065e6i	−0.214077	+	0.370791i
$489$	4.77432e6			0.902899
$490$		0			0
$491$	−5.64998e6			−1.05765			−0.528826	−	0.848730i	$-0.677368\pi$
$491$	−5.64998e6			−1.05765			−0.528826	+	0.848730i	$0.677368\pi$
$492$	−610848.	+	1.05802e6i	−0.113768	+	0.197052i
$493$	−6.02633e6	−	1.04379e7i	−1.11670	−	1.93418i
$494$	−497488.	−	861674.i	−0.0917203	−	0.158864i
$495$	−1.20722e6	+	2.09097e6i	−0.221450	+	0.383562i
$496$	1.58720e6			0.289686
$497$		0			0
$498$	−925776.			−0.167276
$499$	4.61172e6	−	7.98774e6i	0.829109	−	1.43606i	−0.0696286	−	0.997573i	$-0.522181\pi$
$499$	4.61172e6	−	7.98774e6i	0.829109	−	1.43606i	0.898738	−	0.438486i	$-0.144485\pi$
$500$	−614016.	−	1.06351e6i	−0.109839	−	0.190246i
$501$	1.40557e6	+	2.43451e6i	0.250183	+	0.433329i
$502$	−369504.	+	640000.i	−0.0654425	+	0.113350i
$503$	1.45562e6			0.256525			0.128262	−	0.991740i	$-0.459060\pi$
$503$	1.45562e6			0.256525			0.128262	+	0.991740i	$0.459060\pi$
$504$		0			0
$505$	−3.48106e6			−0.607411
$506$	−2.39954e6	+	4.15613e6i	−0.416632	+	0.721627i
$507$	−3.32830e6	−	5.76479e6i	−0.575047	−	0.996010i
$508$	14240.0	+	24664.4i	0.00244822	+	0.00424044i
$509$	183672.	−	318129.i	0.0314231	−	0.0544263i	−0.849886	−	0.526966i	$-0.823329\pi$
$509$	183672.	−	318129.i	0.0314231	−	0.0544263i	0.881309	+	0.472540i	$0.156663\pi$
$510$	−4.79002e6			−0.815477
$511$		0			0
$512$	−262144.			−0.0441942
$513$	−86022.0	+	148994.i	−0.0144317	+	0.0249964i
$514$	471960.	+	817459.i	0.0787948	+	0.136477i
$515$	−6.60931e6	−	1.14477e7i	−1.09809	−	1.90195i
$516$	777888.	−	1.34734e6i	0.128615	−	0.222768i
$517$	−24840.0			−0.00408719
$518$		0			0
$519$	−675972.			−0.110157
$520$	2.42842e6	−	4.20614e6i	0.393835	−	0.682143i
$521$	−2.88181e6	−	4.99144e6i	−0.465127	−	0.805623i	0.534080	−	0.845434i	$-0.320658\pi$
$521$	−2.88181e6	−	4.99144e6i	−0.465127	−	0.805623i	−0.999207	+	0.0398104i	$0.987325\pi$
$522$	−1.05656e6	−	1.83002e6i	−0.169715	−	0.293955i
$523$	−117550.	+	203603.i	−0.0187918	+	0.0325484i	−0.875268	−	0.483638i	$-0.839315\pi$
$523$	−117550.	+	203603.i	−0.0187918	+	0.0325484i	0.856477	+	0.516186i	$0.172649\pi$
$524$	−4.24224e6			−0.674943
$525$		0			0
$526$	977976.			0.154122
$527$	5.72880e6	−	9.92257e6i	0.898539	−	1.55632i
$528$	476928.	+	826064.i	0.0744506	+	0.128952i
$529$	−981030.	−	1.69919e6i	−0.152420	−	0.264000i
$530$	−3.24086e6	+	5.61334e6i	−0.501154	+	0.868024i
$531$	−2.28226e6			−0.351259
$532$		0			0
$533$	−8.94214e6			−1.36340
$534$	1.77703e6	−	3.07791e6i	0.269676	−	0.467092i
$535$	−80568.0	−	139548.i	−0.0121697	−	0.0210785i
$536$	−902912.	−	1.56389e6i	−0.135748	−	0.235122i
$537$	−1.74023e6	+	3.01417e6i	−0.260418	+	0.451057i
$538$	−6.11117e6			−0.910266
$539$		0			0
$540$	−839808.			−0.123935
$541$	−54505.0	+	94405.4i	−0.00800651	+	0.0138677i	−0.870001	−	0.493050i	$-0.835882\pi$
$541$	−54505.0	+	94405.4i	−0.00800651	+	0.0138677i	0.861994	+	0.506918i	$0.169215\pi$
$542$	4.14112e6	+	7.17263e6i	0.605508	+	1.04877i
$543$	1.87919e6	+	3.25485e6i	0.273509	+	0.473731i
$544$	−946176.	+	1.63882e6i	−0.137080	+	0.237430i
$545$	−4.33138e6			−0.624647
$546$		0			0
$547$	1.61953e6			0.231430			0.115715	−	0.993282i	$-0.463084\pi$
$547$	1.61953e6			0.231430			0.115715	+	0.993282i	$0.463084\pi$
$548$	1.65384e6	−	2.86453e6i	0.235257	−	0.407477i
$549$	1.42536e6	+	2.46879e6i	0.201833	+	0.349586i
$550$	−1.70485e6	−	2.95289e6i	−0.240314	−	0.416237i
$551$	769596.	−	1.33298e6i	0.107990	−	0.187044i
$552$	−1.66925e6			−0.233170
$553$		0			0
$554$	9.62908e6			1.33294
$555$	3.12660e6	−	5.41543e6i	0.430864	−	0.746278i
$556$	1.89469e6	+	3.28170e6i	0.259927	+	0.450206i
$557$	3.31493e6	+	5.74163e6i	0.452727	+	0.784146i	0.998554	−	0.0537514i	$-0.0171178\pi$
$557$	3.31493e6	+	5.74163e6i	0.452727	+	0.784146i	−0.545827	+	0.837898i	$0.683785\pi$
$558$	1.00440e6	−	1.73967e6i	0.136559	−	0.236528i
$559$	1.13874e7			1.54133
$560$		0			0
$561$	6.88565e6			0.923714
$562$	683772.	−	1.18433e6i	0.0913210	−	0.158173i
$563$	−3.92647e6	−	6.80085e6i	−0.522073	−	0.904258i	−0.999670	−	0.0256785i	$-0.991825\pi$
$563$	−3.92647e6	−	6.80085e6i	−0.522073	−	0.904258i	0.477597	−	0.878579i	$-0.341508\pi$
$564$	−4320.00	−	7482.46i	−0.000571855	−	0.000990482i
$565$	−252504.	+	437350.i	−0.0332772	+	0.0576378i
$566$	−2.31426e6			−0.303648
$567$		0			0
$568$	425088.			0.0552851
$569$	1.24077e6	−	2.14908e6i	0.160661	−	0.278274i	−0.774445	−	0.632642i	$-0.781971\pi$
$569$	1.24077e6	−	2.14908e6i	0.160661	−	0.278274i	0.935106	+	0.354368i	$0.115304\pi$
$570$	−305856.	−	529758.i	−0.0394303	−	0.0682952i
$571$	−5.68376e6	−	9.84455e6i	−0.729533	−	1.26359i	−0.957081	−	0.289822i	$-0.906404\pi$
$571$	−5.68376e6	−	9.84455e6i	−0.729533	−	1.26359i	0.227547	−	0.973767i	$-0.426929\pi$
$572$	−3.49085e6	+	6.04633e6i	−0.446109	+	0.772683i
$573$	−8.89245e6			−1.13145
$574$		0			0
$575$	5.96698e6			0.752636
$576$	−165888.	+	287326.i	−0.0208333	+	0.0360844i
$577$	4.10252e6	+	7.10578e6i	0.512993	+	0.888530i	0.999886	+	0.0150686i	$0.00479668\pi$
$577$	4.10252e6	+	7.10578e6i	0.512993	+	0.888530i	−0.486893	+	0.873461i	$0.661870\pi$
$578$	3.99049e6	+	6.91174e6i	0.496829	+	0.860533i
$579$	1.84166e6	−	3.18985e6i	0.228304	−	0.395434i
$580$	7.51334e6			0.927392
$581$		0			0
$582$	5.36234e6			0.656217
$583$	4.65874e6	−	8.06918e6i	0.567672	−	0.983236i
$584$	−1.66688e6	−	2.88712e6i	−0.202242	−	0.350294i
$585$	−3.07346e6	−	5.32340e6i	−0.371312	−	0.643130i
$586$	1.56108e6	−	2.70387e6i	0.187794	−	0.325268i
$587$	−1.38400e7			−1.65783			−0.828917	−	0.559371i	$-0.811043\pi$
$587$	−1.38400e7			−1.65783			−0.828917	+	0.559371i	$0.811043\pi$
$588$		0			0
$589$	1.46320e6			0.173786
$590$	4.05734e6	−	7.02753e6i	0.479857	−	0.831137i
$591$	4.15004e6	+	7.18807e6i	0.488746	+	0.846533i
$592$	−1.23520e6	−	2.13943e6i	−0.144855	−	0.250896i
$593$	2.69476e6	−	4.66745e6i	0.314690	−	0.545059i	−0.664682	−	0.747127i	$-0.731433\pi$
$593$	2.69476e6	−	4.66745e6i	0.314690	−	0.545059i	0.979372	+	0.202068i	$0.0647662\pi$
$594$	1.20722e6			0.140385
$595$		0			0
$596$	7.57930e6			0.874004
$597$	−852696.	+	1.47691e6i	−0.0979171	+	0.169597i
$598$	−6.10898e6	−	1.05811e7i	−0.698580	−	1.20998i
$599$	5.74425e6	+	9.94934e6i	0.654134	+	1.13299i	0.982110	+	0.188307i	$0.0603000\pi$
$599$	5.74425e6	+	9.94934e6i	0.654134	+	1.13299i	−0.327977	+	0.944686i	$0.606367\pi$
$600$	592992.	−	1.02709e6i	0.0672467	−	0.116475i
$601$	−2.79225e6			−0.315333			−0.157666	−	0.987492i	$-0.550397\pi$
$601$	−2.79225e6			−0.315333			−0.157666	+	0.987492i	$0.550397\pi$
$602$		0			0
$603$	−2.28550e6			−0.255969
$604$	−3.15962e6	+	5.47262e6i	−0.352405	+	0.610383i
$605$	372420.	+	645050.i	0.0413661	+	0.0716482i
$606$	870264.	+	1.50734e6i	0.0962652	+	0.166736i
$607$	−356944.	+	618245.i	−0.0393213	+	0.0681066i	−0.885016	−	0.465560i	$-0.845853\pi$
$607$	−356944.	+	618245.i	−0.0393213	+	0.0681066i	0.845695	+	0.533667i	$0.179186\pi$
$608$	−241664.			−0.0265126
$609$		0			0
$610$	−1.01359e7			−1.10290
$611$	31620.0	−	54767.4i	0.00342656	−	0.00593498i
$612$	1.19750e6	+	2.07414e6i	0.129240	+	0.223851i
$613$	−1.55486e6	−	2.69309e6i	−0.167124	−	0.289468i	0.770283	−	0.637702i	$-0.220115\pi$
$613$	−1.55486e6	−	2.69309e6i	−0.167124	−	0.289468i	−0.937408	+	0.348234i	$0.886781\pi$
$614$	−4.49650e6	+	7.78817e6i	−0.481342	+	0.833709i
$615$	−5.49763e6			−0.586122
$616$		0			0
$617$	3.62384e6			0.383227			0.191613	−	0.981470i	$-0.438628\pi$
$617$	3.62384e6			0.383227			0.191613	+	0.981470i	$0.438628\pi$
$618$	−3.30466e6	+	5.72383e6i	−0.348061	+	0.602859i
$619$	−2.12598e6	−	3.68230e6i	−0.223014	−	0.386272i	0.732708	−	0.680543i	$-0.238256\pi$
$619$	−2.12598e6	−	3.68230e6i	−0.223014	−	0.386272i	−0.955722	+	0.294272i	$0.904923\pi$
$620$	3.57120e6	+	6.18550e6i	0.373108	+	0.646243i
$621$	−1.05632e6	+	1.82960e6i	−0.109918	+	0.190383i
$622$	−2.32565e6			−0.241028
$623$		0			0
$624$	−2.42842e6			−0.249667
$625$	5.98026e6	−	1.03581e7i	0.612379	−	1.06067i
$626$	−4.00814e6	−	6.94230e6i	−0.408796	−	0.708056i
$627$	439668.	+	761527.i	0.0446638	+	0.0773600i
$628$	1.16072e6	−	2.01043e6i	0.117443	−	0.203418i
$629$	−1.78332e7			−1.79723
$630$		0			0
$631$	−1.70299e7			−1.70270			−0.851349	−	0.524600i	$-0.824215\pi$
$631$	−1.70299e7			−1.70270			−0.851349	+	0.524600i	$0.824215\pi$
$632$	1.38688e6	−	2.40215e6i	0.138117	−	0.239225i
$633$	2.75121e6	+	4.76524e6i	0.272907	+	0.472689i
$634$	−2.55664e6	−	4.42822e6i	−0.252607	−	0.437529i
$635$	−64080.0	+	110990.i	−0.00630650	+	0.0109232i
$636$	3.24086e6			0.317701
$637$		0			0
$638$	−1.08004e7			−1.05048
$639$	269001.	−	465923.i	0.0260616	−	0.0451401i
$640$	−589824.	−	1.02161e6i	−0.0569210	−	0.0985901i
$641$	904689.	+	1.56697e6i	0.0869669	+	0.150631i	0.906228	−	0.422790i	$-0.138949\pi$
$641$	904689.	+	1.56697e6i	0.0869669	+	0.150631i	−0.819261	+	0.573421i	$0.805616\pi$
$642$	−40284.0	+	69773.9i	−0.00385740	+	0.00668122i
$643$	1.53012e7			1.45948			0.729740	−	0.683725i	$-0.239641\pi$
$643$	1.53012e7			1.45948			0.729740	+	0.683725i	$0.239641\pi$
$644$		0			0
$645$	7.00099e6			0.662614
$646$	−872256.	+	1.51079e6i	−0.0822361	+	0.142437i
$647$	−8.37730e6	−	1.45099e7i	−0.786762	−	1.36271i	−0.927941	−	0.372728i	$-0.878422\pi$
$647$	−8.37730e6	−	1.45099e7i	−0.786762	−	1.36271i	0.141179	−	0.989984i	$-0.454911\pi$
$648$	209952.	+	363648.i	0.0196419	+	0.0340207i
$649$	−5.83243e6	+	1.01021e7i	−0.543548	+	0.941453i
$650$	8.68074e6			0.805886
$651$		0			0
$652$	8.48768e6			0.781934
$653$	−7.39295e6	+	1.28050e7i	−0.678477	+	1.17516i	0.296963	+	0.954889i	$0.404026\pi$
$653$	−7.39295e6	+	1.28050e7i	−0.678477	+	1.17516i	−0.975440	+	0.220267i	$0.929307\pi$
$654$	1.08284e6	+	1.87554e6i	0.0989969	+	0.171468i
$655$	−9.54504e6	−	1.65325e7i	−0.869310	−	1.50569i
$656$	−1.08595e6	+	1.88092e6i	−0.0985260	+	0.170652i
$657$	−4.21929e6			−0.381352
$658$		0			0
$659$	933762.			0.0837573			0.0418786	−	0.999123i	$-0.486666\pi$
$659$	933762.			0.0837573			0.0418786	+	0.999123i	$0.486666\pi$
$660$	−2.14618e6	+	3.71729e6i	−0.191781	+	0.332174i
$661$	−3.04862e6	−	5.28036e6i	−0.271394	−	0.470067i	0.697825	−	0.716268i	$-0.254151\pi$
$661$	−3.04862e6	−	5.28036e6i	−0.271394	−	0.470067i	−0.969219	+	0.246201i	$0.920818\pi$
$662$	5.19623e6	+	9.00014e6i	0.460833	+	0.798186i
$663$	−8.76506e6	+	1.51815e7i	−0.774411	+	1.34132i
$664$	−1.64582e6			−0.144865
$665$		0			0
$666$	−3.12660e6			−0.273141
$667$	9.45038e6	−	1.63685e7i	0.822498	−	1.42461i
$668$	2.49878e6	+	4.32802e6i	0.216664	+	0.375274i
$669$	3.52465e6	+	6.10488e6i	0.304475	+	0.527365i
$670$	4.06310e6	−	7.03750e6i	0.349680	−	0.605664i
$671$	1.45703e7			1.24929
$672$		0			0
$673$	2.09190e6			0.178034			0.0890171	−	0.996030i	$-0.471627\pi$
$673$	2.09190e6			0.178034			0.0890171	+	0.996030i	$0.471627\pi$
$674$	6.12380e6	−	1.06067e7i	0.519243	−	0.899356i
$675$	−750506.	−	1.29991e6i	−0.0634008	−	0.109813i
$676$	−5.91698e6	−	1.02485e7i	−0.498005	−	0.862570i
$677$	−682266.	+	1.18172e6i	−0.0572113	+	0.0990929i	−0.893213	−	0.449635i	$-0.851554\pi$
$677$	−682266.	+	1.18172e6i	−0.0572113	+	0.0990929i	0.836001	+	0.548728i	$0.184888\pi$
$678$	252504.			0.0210957
$679$		0			0
$680$	−8.51558e6			−0.706223
$681$	−363204.	+	629088.i	−0.0300112	+	0.0519809i
$682$	−5.13360e6	−	8.89166e6i	−0.422631	−	0.732018i
$683$	−5.77415e6	−	1.00011e7i	−0.473627	−	0.820346i	0.525917	−	0.850536i	$-0.323722\pi$
$683$	−5.77415e6	−	1.00011e7i	−0.473627	−	0.820346i	−0.999544	+	0.0301898i	$0.990389\pi$
$684$	−152928.	+	264879.i	−0.0124982	+	0.0216475i
$685$	1.48846e7			1.21202
$686$		0			0
$687$	1.37464e6			0.111121
$688$	1.38291e6	−	2.39527e6i	0.111384	−	0.192923i
$689$	1.18607e7	+	2.05433e7i	0.951833	+	1.64862i
$690$	−3.75581e6	−	6.50525e6i	−0.300318	−	0.520165i
$691$	−2.08872e6	+	3.61777e6i	−0.166412	+	0.288234i	−0.937156	−	0.348911i	$-0.886552\pi$
$691$	−2.08872e6	+	3.61777e6i	−0.166412	+	0.288234i	0.770744	+	0.637145i	$0.219885\pi$
$692$	−1.20173e6			−0.0953984
$693$		0			0
$694$	5.70199e6			0.449395
$695$	−8.52610e6	+	1.47676e7i	−0.669558	+	1.15971i
$696$	−1.87834e6	−	3.25337e6i	−0.146977	−	0.254572i
$697$	7.83922e6	+	1.35779e7i	0.611210	+	1.05865i
$698$	5.86644e6	−	1.01610e7i	0.455760	−	0.789400i
$699$	−3.18854e6			−0.246830
$700$		0			0
$701$	−1.70278e7			−1.30877			−0.654385	−	0.756161i	$-0.727073\pi$
$701$	−1.70278e7			−1.30877			−0.654385	+	0.756161i	$0.727073\pi$
$702$	−1.53673e6	+	2.66170e6i	−0.117694	+	0.203852i
$703$	−1.13870e6	−	1.97229e6i	−0.0869002	−	0.150516i
$704$	847872.	+	1.46856e6i	0.0644761	+	0.111676i
$705$	19440.0	−	33671.1i	0.00147307	−	0.00255143i
$706$	8.05104e6			0.607911
$707$		0			0
$708$	−4.05734e6			−0.304200
$709$	−1.13466e7	+	1.96529e7i	−0.847715	+	1.46829i	0.0355270	+	0.999369i	$0.488689\pi$
$709$	−1.13466e7	+	1.96529e7i	−0.847715	+	1.46829i	−0.883242	+	0.468917i	$0.844644\pi$
$710$	956448.	+	1.65662e6i	0.0712058	+	0.123332i
$711$	−1.75527e6	−	3.04022e6i	−0.130218	−	0.225544i
$712$	3.15917e6	−	5.47184e6i	0.233546	−	0.404514i
$713$	1.79676e7			1.32363
$714$		0			0
$715$	−3.14176e7			−2.29831
$716$	−3.09374e6	+	5.35852e6i	−0.225529	+	0.390627i
$717$	−1.23916e6	−	2.14630e6i	−0.0900184	−	0.155916i
$718$	8.15420e6	+	1.41235e7i	0.590297	+	1.02242i
$719$	−2.56272e6	+	4.43876e6i	−0.184875	+	0.320213i	−0.943535	−	0.331274i	$-0.892521\pi$
$719$	−2.56272e6	+	4.43876e6i	−0.184875	+	0.320213i	0.758659	+	0.651488i	$0.225855\pi$
$720$	−1.49299e6			−0.107331
$721$		0			0
$722$	9.68161e6			0.691202
$723$	2.63114e6	−	4.55727e6i	0.187197	−	0.324234i
$724$	3.34078e6	+	5.78641e6i	0.236866	+	0.410263i
$725$	6.71440e6	+	1.16297e7i	0.474419	+	0.821718i
$726$	186210.	−	322525.i	0.0131118	−	0.0227103i
$727$	−1.54328e7			−1.08295			−0.541476	−	0.840716i	$-0.682134\pi$
$727$	−1.54328e7			−1.08295			−0.541476	+	0.840716i	$0.682134\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	7.50096e6	−	1.29920e7i	0.520966	−	0.902340i
$731$	−9.98290e6	−	1.72909e7i	−0.690976	−	1.19681i
$732$	2.53397e6	+	4.38896e6i	0.174793	+	0.302750i
$733$	3.42233e6	−	5.92764e6i	0.235267	−	0.407495i	−0.724083	−	0.689713i	$-0.757737\pi$
$733$	3.42233e6	−	5.92764e6i	0.235267	−	0.407495i	0.959350	+	0.282218i	$0.0910701\pi$
$734$	−2.37901e6			−0.162988
$735$		0			0
$736$	−2.96755e6			−0.201931
$737$	−5.84071e6	+	1.01164e7i	−0.396093	+	0.686053i
$738$	1.37441e6	+	2.38054e6i	0.0928912	+	0.160892i
$739$	−1.49694e6	−	2.59278e6i	−0.100831	−	0.174645i	0.811196	−	0.584774i	$-0.198817\pi$
$739$	−1.49694e6	−	2.59278e6i	−0.100831	−	0.174645i	−0.912027	+	0.410129i	$0.865484\pi$
$740$	5.55840e6	−	9.62743e6i	0.373139	−	0.646295i
$741$	−2.23870e6			−0.149779
$742$		0			0
$743$	2.23250e7			1.48361			0.741804	−	0.670617i	$-0.233971\pi$
$743$	2.23250e7			1.48361			0.741804	+	0.670617i	$0.233971\pi$
$744$	1.78560e6	−	3.09275e6i	0.118264	−	0.204839i
$745$	1.70534e7	+	2.95374e7i	1.12569	+	1.94976i
$746$	4.09044e6	+	7.08486e6i	0.269106	+	0.466105i
$747$	−1.04150e6	+	1.80393e6i	−0.0682900	+	0.118282i
$748$	1.22412e7			0.799960
$749$		0			0
$750$	−2.76307e6			−0.179366
$751$	7.07202e6	−	1.22491e7i	0.457555	−	0.792509i	−0.541276	−	0.840845i	$-0.682059\pi$
$751$	7.07202e6	−	1.22491e7i	0.457555	−	0.792509i	0.998831	+	0.0483363i	$0.0153919\pi$
$752$	−7680.00	−	13302.2i	−0.000495241	−	0.000857783i
$753$	831384.	+	1.44000e6i	0.0534336	+	0.0925497i
$754$	1.37484e7	−	2.38129e7i	0.880690	−	1.52540i
$755$	−2.84365e7			−1.81556
$756$		0			0
$757$	−8.15367e6			−0.517147			−0.258573	−	0.965992i	$-0.583252\pi$
$757$	−8.15367e6			−0.517147			−0.258573	+	0.965992i	$0.583252\pi$
$758$	−6.44396e6	+	1.11613e7i	−0.407361	+	0.705571i
$759$	5.39897e6	+	9.35130e6i	0.340178	+	0.589206i
$760$	−543744.	−	941792.i	−0.0341476	−	0.0591454i
$761$	1.12873e6	−	1.95501e6i	0.0706524	−	0.122374i	−0.828535	−	0.559937i	$-0.810825\pi$
$761$	1.12873e6	−	1.95501e6i	0.0706524	−	0.122374i	0.899187	+	0.437564i	$0.144159\pi$
$762$	64080.0			0.00399793
$763$		0			0
$764$	−1.58088e7			−0.979863
$765$	−5.38877e6	+	9.33362e6i	−0.332917	+	0.576629i
$766$	−3.45931e6	−	5.99170e6i	−0.213019	−	0.368959i
$767$	−1.48488e7	−	2.57188e7i	−0.911384	−	1.57856i
$768$	−294912.	+	510803.i	−0.0180422	+	0.0312500i
$769$	−748774.			−0.0456599			−0.0228299	−	0.999739i	$-0.507268\pi$
$769$	−748774.			−0.0456599			−0.0228299	+	0.999739i	$0.507268\pi$
$770$		0			0
$771$	2.12382e6			0.128671
$772$	3.27406e6	−	5.67085e6i	0.197717	−	0.342456i
$773$	4.73113e6	+	8.19455e6i	0.284784	+	0.493261i	0.972557	−	0.232666i	$-0.0747447\pi$
$773$	4.73113e6	+	8.19455e6i	0.284784	+	0.493261i	−0.687773	+	0.725926i	$0.741411\pi$
$774$	−1.75025e6	−	3.03152e6i	−0.105014	−	0.181890i
$775$	−6.38290e6	+	1.10555e7i	−0.381737	+	0.661187i
$776$	9.53306e6			0.568300
$777$		0			0
$778$	6.99674e6			0.414426
$779$	−1.00111e6	+	1.73398e6i	−0.0591070	+	0.102376i
$780$	−5.46394e6	−	9.46381e6i	−0.321565	−	0.556967i
$781$	−1.37489e6	−	2.38139e6i	−0.0806569	−	0.139702i
$782$	−1.07110e7	+	1.85520e7i	−0.626345	+	1.08486i
$783$	−4.75454e6			−0.277143
$784$		0			0
$785$	1.04465e7			0.605056
$786$	−4.77252e6	+	8.26625e6i	−0.275544	+	0.477257i
$787$	9.98170e6	+	1.72888e7i	0.574470	+	0.995012i	0.996099	+	0.0882432i	$0.0281253\pi$
$787$	9.98170e6	+	1.72888e7i	0.574470	+	0.995012i	−0.421629	+	0.906769i	$0.638541\pi$
$788$	7.37784e6	+	1.27788e7i	0.423266	+	0.733119i
$789$	1.10022e6	−	1.90564e6i	0.0629199	−	0.108981i
$790$	1.24819e7			0.711564
$791$		0			0
$792$	2.14618e6			0.121577
$793$	−1.85472e7	+	3.21248e7i	−1.04736	+	1.81408i
$794$	3.76409e6	+	6.51960e6i	0.211889	+	0.367003i
$795$	7.29194e6	+	1.26300e7i	0.409190	+	0.708739i
$796$	−1.51590e6	+	2.62562e6i	−0.0847987	+	0.146876i
$797$	−4.05368e6			−0.226050			−0.113025	−	0.993592i	$-0.536054\pi$
$797$	−4.05368e6			−0.226050			−0.113025	+	0.993592i	$0.536054\pi$
$798$		0			0
$799$	−110880.			−0.00614450
$800$	1.05421e6	−	1.82594e6i	0.0582373	−	0.100870i
$801$	−3.99832e6	−	6.92530e6i	−0.220189	−	0.381379i
$802$	8.36248e6	+	1.44842e7i	0.459091	+	0.795169i
$803$	−1.07826e7	+	1.86761e7i	−0.590114	+	1.02211i
$804$	−4.06310e6			−0.221676
$805$		0			0
$806$	2.61392e7			1.41728
$807$	−6.87506e6	+	1.19080e7i	−0.371615	+	0.643656i
$808$	1.54714e6	+	2.67972e6i	0.0833681	+	0.144398i
$809$	−9.27160e6	−	1.60589e7i	−0.498062	−	0.862669i	0.501935	−	0.864905i	$-0.332622\pi$
$809$	−9.27160e6	−	1.60589e7i	−0.498062	−	0.862669i	−0.999997	+	0.00223609i	$0.999288\pi$
$810$	−944784.	+	1.63641e6i	−0.0505964	+	0.0876356i
$811$	1.63648e7			0.873690			0.436845	−	0.899537i	$-0.356096\pi$
$811$	1.63648e7			0.873690			0.436845	+	0.899537i	$0.356096\pi$
$812$		0			0
$813$	1.86350e7			0.988790
$814$	−7.99020e6	+	1.38394e7i	−0.422665	+	0.732078i
$815$	1.90973e7	+	3.30775e7i	1.00711	+	1.74437i
$816$	2.12890e6	+	3.68736e6i	0.111926	+	0.193861i
$817$	1.27487e6	−	2.20814e6i	0.0668208	−	0.115737i
$818$	1.88673e6			0.0985884
$819$		0			0
$820$	−9.77357e6			−0.507596
$821$	2.72507e6	−	4.71996e6i	0.141098	−	0.244388i	−0.786813	−	0.617192i	$-0.788270\pi$
$821$	2.72507e6	−	4.71996e6i	0.141098	−	0.244388i	0.927910	+	0.372804i	$0.121603\pi$
$822$	−3.72114e6	−	6.44520e6i	−0.192086	−	0.332703i
$823$	1.09577e7	+	1.89792e7i	0.563921	+	0.976740i	0.997149	+	0.0754554i	$0.0240410\pi$
$823$	1.09577e7	+	1.89792e7i	0.563921	+	0.976740i	−0.433228	+	0.901284i	$0.642626\pi$
$824$	−5.87494e6	+	1.01757e7i	−0.301429	+	0.522091i
$825$	−7.67183e6			−0.392432
$826$		0			0
$827$	8.11859e6			0.412778			0.206389	−	0.978470i	$-0.433829\pi$
$827$	8.11859e6			0.412778			0.206389	+	0.978470i	$0.433829\pi$
$828$	−1.87790e6	+	3.25263e6i	−0.0951914	+	0.164876i
$829$	−8.03308e6	−	1.39137e7i	−0.405972	−	0.703163i	0.588462	−	0.808525i	$-0.299733\pi$
$829$	−8.03308e6	−	1.39137e7i	−0.405972	−	0.703163i	−0.994434	+	0.105361i	$0.966400\pi$
$830$	−3.70310e6	−	6.41396e6i	−0.186582	−	0.323170i
$831$	1.08327e7	−	1.87628e7i	0.544170	−	0.942530i
$832$	−4.31718e6			−0.216218
$833$		0			0
$834$	8.52610e6			0.424458
$835$	−1.12445e7	+	1.94761e7i	−0.558117	+	0.966687i
$836$	781632.	+	1.35383e6i	0.0386800	+	0.0669958i
$837$	−2.25990e6	−	3.91426e6i	−0.111500	−	0.193124i
$838$	−7.08187e6	+	1.22662e7i	−0.348368	+	0.603391i
$839$	−2.63504e7			−1.29236			−0.646178	−	0.763186i	$-0.723634\pi$
$839$	−2.63504e7			−1.29236			−0.646178	+	0.763186i	$0.723634\pi$
$840$		0			0
$841$	2.20253e7			1.07382
$842$	5.45525e6	−	9.44877e6i	0.265176	−	0.459299i
$843$	−1.53849e6	−	2.66474e6i	−0.0745633	−	0.129147i
$844$	4.89104e6	+	8.47153e6i	0.236344	+	0.409360i
$845$	2.66264e7	−	4.61183e7i	1.28284	−	2.22194i
$846$	−19440.0			−0.000933835
$847$		0			0
$848$	5.76154e6			0.275137
$849$	−2.60354e6	+	4.50946e6i	−0.123964	+	0.214712i
$850$	−7.61006e6	−	1.31810e7i	−0.361278	−	0.625751i
$851$	−1.39829e7	−	2.42190e7i	−0.661869	−	1.14639i
$852$	478224.	−	828308.i	0.0225700	−	0.0390925i
$853$	2.78129e7			1.30880			0.654400	−	0.756148i	$-0.272921\pi$
$853$	2.78129e7			1.30880			0.654400	+	0.756148i	$0.272921\pi$
$854$		0			0
$855$	−1.37635e6			−0.0643894
$856$	−71616.0	+	124043.i	−0.00334061	+	0.00578610i
$857$	1.34681e6	+	2.33275e6i	0.0626406	+	0.108497i	0.895645	−	0.444770i	$-0.146714\pi$
$857$	1.34681e6	+	2.33275e6i	0.0626406	+	0.108497i	−0.833004	+	0.553266i	$0.813381\pi$
$858$	7.85441e6	+	1.36042e7i	0.364246	+	0.630893i
$859$	9.41945e6	−	1.63150e7i	0.435555	−	0.754403i	−0.561786	−	0.827283i	$-0.689886\pi$
$859$	9.41945e6	−	1.63150e7i	0.435555	−	0.754403i	0.997341	+	0.0728798i	$0.0232189\pi$
$860$	1.24462e7			0.573840
$861$		0			0
$862$	1.90607e7			0.873716
$863$	6.43151e6	−	1.11397e7i	0.293959	−	0.509151i	−0.680784	−	0.732485i	$-0.738361\pi$
$863$	6.43151e6	−	1.11397e7i	0.293959	−	0.509151i	0.974742	+	0.223334i	$0.0716939\pi$
$864$	373248.	+	646484.i	0.0170103	+	0.0294628i
$865$	−2.70389e6	−	4.68327e6i	−0.122871	−	0.212818i
$866$	1.38060e7	−	2.39127e7i	0.625566	−	1.08351i
$867$	1.79572e7			0.811319
$868$		0			0
$869$	−1.79428e7			−0.806009
$870$	8.45251e6	−	1.46402e7i	0.378606	−	0.655765i
$871$	−1.48698e7	−	2.57553e7i	−0.664142	−	1.15033i
$872$	1.92506e6	+	3.33429e6i	0.0857338	+	0.148495i
$873$	6.03264e6	−	1.04488e7i	0.267899	−	0.464015i
$874$	−2.73571e6			−0.121141
$875$		0			0
$876$	−7.50096e6			−0.330260
$877$	7.94056e6	−	1.37535e7i	0.348620	−	0.603827i	−0.637385	−	0.770546i	$-0.719984\pi$
$877$	7.94056e6	−	1.37535e7i	0.348620	−	0.603827i	0.986005	+	0.166718i	$0.0533171\pi$
$878$	1.08025e7	+	1.87105e7i	0.472921	+	0.819123i
$879$	−3.51243e6	−	6.08371e6i	−0.153333	−	0.265580i
$880$	−3.81542e6	+	6.60851e6i	−0.166087	+	0.287671i
$881$	1.73681e7			0.753899			0.376950	−	0.926234i	$-0.376973\pi$
$881$	1.73681e7			0.753899			0.376950	+	0.926234i	$0.376973\pi$
$882$		0			0
$883$	2.23513e7			0.964721			0.482361	−	0.875973i	$-0.339780\pi$
$883$	2.23513e7			0.964721			0.482361	+	0.875973i	$0.339780\pi$
$884$	−1.55823e7	+	2.69894e7i	−0.670659	+	1.16162i
$885$	−9.12902e6	−	1.58119e7i	−0.391802	−	0.678620i
$886$	−8.11727e6	−	1.40595e7i	−0.347397	−	0.601709i
$887$	4.45570e6	−	7.71750e6i	0.190155	−	0.329358i	−0.755147	−	0.655556i	$-0.772434\pi$
$887$	4.45570e6	−	7.71750e6i	0.190155	−	0.329358i	0.945301	+	0.326198i	$0.105768\pi$
$888$	−5.55840e6			−0.236547
$889$		0			0
$890$	2.84325e7			1.20321
$891$	1.35813e6	−	2.35234e6i	0.0573121	−	0.0992674i
$892$	6.26605e6	+	1.08531e7i	0.263683	+	0.456712i
$893$	−7080.00	−	12262.9i	−0.000297101	−	0.000514595i
$894$	8.52671e6	−	1.47687e7i	0.356810	−	0.618014i
$895$	−2.78437e7			−1.16190
$896$		0			0
$897$	−2.74904e7			−1.14078
$898$	425988.	−	737833.i	0.0176281	−	0.0305328i
$899$	2.02182e7	+	3.50189e7i	0.834340	+	1.44512i
$900$	−1.33423e6	−	2.31096e6i	−0.0549067	−	0.0951011i
$901$	2.07955e7	−	3.60189e7i	0.853411	−	1.47815i
$902$	1.40495e7			0.574969
$903$		0			0
$904$	448896.			0.0182694
$905$	−1.50335e7	+	2.60388e7i	−0.610154	+	1.05682i
$906$	7.10914e6	+	1.23134e7i	0.287737	+	0.498376i
$907$	2.26663e6	+	3.92593e6i	0.0914878	+	0.158462i	0.908137	−	0.418672i	$-0.137504\pi$
$907$	2.26663e6	+	3.92593e6i	0.0914878	+	0.158462i	−0.816650	+	0.577134i	$0.804171\pi$
$908$	−645696.	+	1.11838e6i	−0.0259904	+	0.0450167i
$909$	3.91619e6			0.157200
$910$		0			0
$911$	−9.83085e6			−0.392460			−0.196230	−	0.980558i	$-0.562870\pi$
$911$	−9.83085e6			−0.392460			−0.196230	+	0.980558i	$0.562870\pi$
$912$	−271872.	+	470896.i	−0.0108237	+	0.0187473i
$913$	5.32321e6	+	9.22007e6i	0.211347	+	0.366064i
$914$	−1.83230e6	−	3.17364e6i	−0.0725489	−	0.125658i
$915$	−1.14029e7	+	1.97503e7i	−0.450257	+	0.779869i
$916$	2.44381e6			0.0962340
$917$		0			0
$918$	5.38877e6			0.211049
$919$	2.41024e7	−	4.17467e7i	0.941396	−	1.63055i	0.178584	−	0.983925i	$-0.442848\pi$
$919$	2.41024e7	−	4.17467e7i	0.941396	−	1.63055i	0.762812	−	0.646621i	$-0.223818\pi$
$920$	−6.67699e6	−	1.15649e7i	−0.260083	−	0.450476i
$921$	1.01171e7	+	1.75234e7i	0.393014	+	0.680721i
$922$	−8.31670e6	+	1.44049e7i	−0.322199	+	0.558064i
$923$	7.00067e6			0.270480
$924$		0			0
$925$	1.98694e7			0.763536
$926$	1.68160e7	−	2.91261e7i	0.644458	−	1.11623i
$927$	7.43548e6	+	1.28786e7i	0.284190	+	0.492232i
$928$	−3.33926e6	−	5.78377e6i	−0.127286	−	0.220466i
$929$	3.38509e6	−	5.86314e6i	0.128686	−	0.222890i	−0.794482	−	0.607288i	$-0.792257\pi$
$929$	3.38509e6	−	5.86314e6i	0.128686	−	0.222890i	0.923168	+	0.384398i	$0.125591\pi$
$930$	1.60704e7			0.609283
$931$		0			0
$932$	−5.66851e6			−0.213761
$933$	−2.61635e6	+	4.53166e6i	−0.0983994	+	0.170433i
$934$	144096.	+	249582.i	0.00540486	+	0.00936150i
$935$	2.75426e7	+	4.77052e7i	1.03033	+	1.78458i
$936$	−2.73197e6	+	4.73191e6i	−0.101926	+	0.176541i
$937$	1.25127e7			0.465590			0.232795	−	0.972526i	$-0.425213\pi$
$937$	1.25127e7			0.465590			0.232795	+	0.972526i	$0.425213\pi$
$938$		0			0
$939$	−1.80366e7			−0.667562
$940$	34560.0	−	59859.7i	0.00127572	−	0.00220961i
$941$	6.93293e6	+	1.20082e7i	0.255236	+	0.442082i	0.964960	−	0.262398i	$-0.0845134\pi$
$941$	6.93293e6	+	1.20082e7i	0.255236	+	0.442082i	−0.709723	+	0.704481i	$0.751180\pi$
$942$	−2.61162e6	−	4.52346e6i	−0.0958921	−	0.166090i
$943$	−1.22933e7	+	2.12926e7i	−0.450184	+	0.779741i
$944$	−7.21306e6			−0.263445
$945$		0			0
$946$	−1.78914e7			−0.650006
$947$	−2.44644e6	+	4.23735e6i	−0.0886460	+	0.153539i	−0.906939	−	0.421262i	$-0.861587\pi$
$947$	−2.44644e6	+	4.23735e6i	−0.0886460	+	0.153539i	0.818293	+	0.574801i	$0.194921\pi$
$948$	−3.12048e6	−	5.40483e6i	−0.112772	−	0.195327i
$949$	−2.74514e7	−	4.75473e7i	−0.989463	−	1.71380i
$950$	971848.	−	1.68329e6i	0.0349373	−	0.0605132i
$951$	−1.15049e7			−0.412506
$952$		0			0
$953$	−1.40055e7			−0.499535			−0.249768	−	0.968306i	$-0.580354\pi$
$953$	−1.40055e7			−0.499535			−0.249768	+	0.968306i	$0.580354\pi$
$954$	3.64597e6	−	6.31501e6i	0.129701	−	0.224648i
$955$	−3.55698e7	−	6.16087e7i	−1.26204	−	2.18592i
$956$	−2.20296e6	−	3.81564e6i	−0.0779582	−	0.135028i
$957$	−1.21505e7	+	2.10453e7i	−0.428858	+	0.742804i
$958$	−1.92224e7			−0.676697
$959$		0			0
$960$	−2.65421e6			−0.0929516
$961$	−4.90542e6	+	8.49644e6i	−0.171344	+	0.296776i
$962$	−2.03422e7	−	3.52337e7i	−0.708696	−	1.22750i
$963$	90639.0	+	156991.i	0.00314956	+	0.00545519i
$964$	4.67758e6	−	8.10181e6i	0.162117	−	0.280795i
$965$	2.94666e7			1.01862
$966$		0			0
$967$	−1.02386e7			−0.352106			−0.176053	−	0.984381i	$-0.556333\pi$
$967$	−1.02386e7			−0.352106			−0.176053	+	0.984381i	$0.556333\pi$
$968$	331040.	−	573378.i	0.0113551	−	0.0196677i
$969$	1.96258e6	+	3.39928e6i	0.0671455	+	0.116299i
$970$	2.14494e7	+	3.71514e7i	0.731957	+	1.26779i
$971$	−5.87261e6	+	1.01717e7i	−0.199886	+	0.346214i	−0.948491	−	0.316803i	$-0.897391\pi$
$971$	−5.87261e6	+	1.01717e7i	−0.199886	+	0.346214i	0.748605	+	0.663016i	$0.230724\pi$
$972$	944784.			0.0320750
$973$		0			0
$974$	−1.76722e7			−0.596888
$975$	9.76584e6	−	1.69149e7i	0.329002	−	0.569847i
$976$	4.50483e6	+	7.80260e6i	0.151375	+	0.262189i
$977$	−1.13097e7	−	1.95890e7i	−0.379067	−	0.656564i	0.611860	−	0.790966i	$-0.290422\pi$
$977$	−1.13097e7	−	1.95890e7i	−0.379067	−	0.656564i	−0.990927	+	0.134403i	$0.957088\pi$
$978$	9.54864e6	−	1.65387e7i	0.319223	−	0.552911i
$979$	−4.08717e7			−1.36291
$980$		0			0
$981$	4.87280e6			0.161661
$982$	−1.13000e7	+	1.95721e7i	−0.373937	+	0.647677i
$983$	−1.39787e7	−	2.42119e7i	−0.461407	−	0.799180i	0.537625	−	0.843184i	$-0.319322\pi$
$983$	−1.39787e7	−	2.42119e7i	−0.461407	−	0.799180i	−0.999031	+	0.0440045i	$0.985988\pi$
$984$	2.44339e6	+	4.23208e6i	0.0804462	+	0.139337i
$985$	−3.32003e7	+	5.75046e7i	−1.09031	+	1.88848i
$986$	−4.82106e7			−1.57925
$987$		0			0
$988$	−3.97990e6			−0.129712
$989$	1.56550e7	−	2.71152e7i	0.508935	−	0.881501i
$990$	4.82890e6	+	8.36389e6i	0.156589	+	0.271219i
$991$	8.32375e6	+	1.44172e7i	0.269237	+	0.466332i	0.968665	−	0.248371i	$-0.0798952\pi$
$991$	8.32375e6	+	1.44172e7i	0.269237	+	0.466332i	−0.699428	+	0.714703i	$0.746562\pi$
$992$	3.17440e6	−	5.49822e6i	0.102419	−	0.177396i
$993$	2.33830e7			0.752537
$994$		0			0
$995$	−1.36431e7			−0.436874
$996$	−1.85155e6	+	3.20698e6i	−0.0591409	+	0.102435i
$997$	2.58640e7	+	4.47978e7i	0.824058	+	1.42731i	0.902637	+	0.430403i	$0.141629\pi$
$997$	2.58640e7	+	4.47978e7i	0.824058	+	1.42731i	−0.0785783	+	0.996908i	$0.525038\pi$
$998$	−1.84469e7	−	3.19509e7i	−0.586269	−	1.01545i
$999$	−3.51742e6	+	6.09236e6i	−0.111509	+	0.193140i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.6.a.c.1.1	✓	1	7.2	even	3
126.6.a.l.1.1		1	21.2	odd	6
294.6.a.c.1.1		1	7.5	odd	6
294.6.e.l.67.1		2	7.4	even	3	inner
294.6.e.l.79.1		2	1.1	even	1	trivial
294.6.e.n.67.1		2	7.3	odd	6
294.6.e.n.79.1		2	7.6	odd	2
336.6.a.b.1.1		1	28.23	odd	6
882.6.a.n.1.1		1	21.5	even	6
1008.6.a.ba.1.1		1	84.23	even	6
1050.6.a.g.1.1		1	35.9	even	6
1050.6.g.b.799.1		2	35.2	odd	12
1050.6.g.b.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 $\F_{q}$

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} +(36.0000 - 62.3538i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-144.000 - 249.415i) q^{10} +(207.000 + 358.535i) q^{11} +(-72.0000 + 124.708i) q^{12} -1054.00 q^{13} -648.000 q^{15} +(-128.000 + 221.703i) q^{16} +(924.000 + 1600.41i) q^{17} +(162.000 + 280.592i) q^{18} +(-118.000 + 204.382i) q^{19} -1152.00 q^{20} +1656.00 q^{22} +(-1449.00 + 2509.74i) q^{23} +(288.000 + 498.831i) q^{24} +(-1029.50 - 1783.15i) q^{25} +(-2108.00 + 3651.16i) q^{26} +729.000 q^{27} -6522.00 q^{29} +(-1296.00 + 2244.74i) q^{30} +(-3100.00 - 5369.36i) q^{31} +(512.000 + 886.810i) q^{32} +(1863.00 - 3226.81i) q^{33} +7392.00 q^{34} +1296.00 q^{36} +(-4825.00 + 8357.15i) q^{37} +(472.000 + 817.528i) q^{38} +(4743.00 + 8215.12i) q^{39} +(-2304.00 + 3990.65i) q^{40} +8484.00 q^{41} -10804.0 q^{43} +(3312.00 - 5736.55i) q^{44} +(2916.00 + 5050.66i) q^{45} +(5796.00 + 10039.0i) q^{46} +(-30.0000 + 51.9615i) q^{47} +2304.00 q^{48} -8236.00 q^{50} +(8316.00 - 14403.7i) q^{51} +(8432.00 + 14604.7i) q^{52} +(-11253.0 - 19490.8i) q^{53} +(1458.00 - 2525.33i) q^{54} +29808.0 q^{55} +2124.00 q^{57} +(-13044.0 + 22592.9i) q^{58} +(14088.0 + 24401.1i) q^{59} +(5184.00 + 8978.95i) q^{60} +(17597.0 - 30478.9i) q^{61} -24800.0 q^{62} +4096.00 q^{64} +(-37944.0 + 65720.9i) q^{65} +(-7452.00 - 12907.2i) q^{66} +(14108.0 + 24435.8i) q^{67} +(14784.0 - 25606.6i) q^{68} +26082.0 q^{69} -6642.00 q^{71} +(2592.00 - 4489.48i) q^{72} +(26045.0 + 45111.3i) q^{73} +(19300.0 + 33428.6i) q^{74} +(-9265.50 + 16048.3i) q^{75} +3776.00 q^{76} +37944.0 q^{78} +(-21670.0 + 37533.5i) q^{79} +(9216.00 + 15962.6i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(16968.0 - 29389.4i) q^{82} +25716.0 q^{83} +133056. q^{85} +(-21608.0 + 37426.2i) q^{86} +(29349.0 + 50834.0i) q^{87} +(-13248.0 - 22946.2i) q^{88} +(-49362.0 + 85497.5i) q^{89} +23328.0 q^{90} +46368.0 q^{92} +(-27900.0 + 48324.2i) q^{93} +(120.000 + 207.846i) q^{94} +(8496.00 + 14715.5i) q^{95} +(4608.00 - 7981.29i) q^{96} -148954. q^{97} -33534.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 9 q^{3} - 16 q^{4} + 72 q^{5} - 72 q^{6} - 128 q^{8} - 81 q^{9} - 288 q^{10} + 414 q^{11} - 144 q^{12} - 2108 q^{13} - 1296 q^{15} - 256 q^{16} + 1848 q^{17} + 324 q^{18} - 236 q^{19} - 2304 q^{20}+ \cdots - 67068 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 9 * q^3 - 16 * q^4 + 72 * q^5 - 72 * q^6 - 128 * q^8 - 81 * q^9 - 288 * q^10 + 414 * q^11 - 144 * q^12 - 2108 * q^13 - 1296 * q^15 - 256 * q^16 + 1848 * q^17 + 324 * q^18 - 236 * q^19 - 2304 * q^20 + 3312 * q^22 - 2898 * q^23 + 576 * q^24 - 2059 * q^25 - 4216 * q^26 + 1458 * q^27 - 13044 * q^29 - 2592 * q^30 - 6200 * q^31 + 1024 * q^32 + 3726 * q^33 + 14784 * q^34 + 2592 * q^36 - 9650 * q^37 + 944 * q^38 + 9486 * q^39 - 4608 * q^40 + 16968 * q^41 - 21608 * q^43 + 6624 * q^44 + 5832 * q^45 + 11592 * q^46 - 60 * q^47 + 4608 * q^48 - 16472 * q^50 + 16632 * q^51 + 16864 * q^52 - 22506 * q^53 + 2916 * q^54 + 59616 * q^55 + 4248 * q^57 - 26088 * q^58 + 28176 * q^59 + 10368 * q^60 + 35194 * q^61 - 49600 * q^62 + 8192 * q^64 - 75888 * q^65 - 14904 * q^66 + 28216 * q^67 + 29568 * q^68 + 52164 * q^69 - 13284 * q^71 + 5184 * q^72 + 52090 * q^73 + 38600 * q^74 - 18531 * q^75 + 7552 * q^76 + 75888 * q^78 - 43340 * q^79 + 18432 * q^80 - 6561 * q^81 + 33936 * q^82 + 51432 * q^83 + 266112 * q^85 - 43216 * q^86 + 58698 * q^87 - 26496 * q^88 - 98724 * q^89 + 46656 * q^90 + 92736 * q^92 - 55800 * q^93 + 240 * q^94 + 16992 * q^95 + 9216 * q^96 - 297908 * q^97 - 67068 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more