LMFDB - Embedded newform 294.6.e.b.67.1

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-12.0000 - 20.7846i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(-2.00000 - 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-12.0000 - 20.7846i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-48.0000 + 83.1384i) q^{10} +(-33.0000 + 57.1577i) q^{11} +(-72.0000 - 124.708i) q^{12} +98.0000 q^{13} +216.000 q^{15} +(-128.000 - 221.703i) q^{16} +(108.000 - 187.061i) q^{17} +(-162.000 + 280.592i) q^{18} +(170.000 + 294.449i) q^{19} +384.000 q^{20} +264.000 q^{22} +(519.000 + 898.934i) q^{23} +(-288.000 + 498.831i) q^{24} +(1274.50 - 2207.50i) q^{25} +(-196.000 - 339.482i) q^{26} +729.000 q^{27} -2490.00 q^{29} +(-432.000 - 748.246i) q^{30} +(3524.00 - 6103.75i) q^{31} +(-512.000 + 886.810i) q^{32} +(-297.000 - 514.419i) q^{33} -864.000 q^{34} +1296.00 q^{36} +(6119.00 + 10598.4i) q^{37} +(680.000 - 1177.79i) q^{38} +(-441.000 + 763.834i) q^{39} +(-768.000 - 1330.22i) q^{40} +6468.00 q^{41} -15412.0 q^{43} +(-528.000 - 914.523i) q^{44} +(-972.000 + 1683.55i) q^{45} +(2076.00 - 3595.74i) q^{46} +(-10302.0 - 17843.6i) q^{47} +2304.00 q^{48} -10196.0 q^{50} +(972.000 + 1683.55i) q^{51} +(-784.000 + 1357.93i) q^{52} +(-16245.0 + 28137.2i) q^{53} +(-1458.00 - 2525.33i) q^{54} +1584.00 q^{55} -3060.00 q^{57} +(4980.00 + 8625.61i) q^{58} +(-17112.0 + 29638.9i) q^{59} +(-1728.00 + 2992.98i) q^{60} +(-17827.0 - 30877.3i) q^{61} -28192.0 q^{62} +4096.00 q^{64} +(-1176.00 - 2036.89i) q^{65} +(-1188.00 + 2057.68i) q^{66} +(-6340.00 + 10981.2i) q^{67} +(1728.00 + 2992.98i) q^{68} -9342.00 q^{69} -42642.0 q^{71} +(-2592.00 - 4489.48i) q^{72} +(-16867.0 + 29214.5i) q^{73} +(24476.0 - 42393.7i) q^{74} +(11470.5 + 19867.5i) q^{75} -5440.00 q^{76} +3528.00 q^{78} +(42554.0 + 73705.7i) q^{79} +(-3072.00 + 5320.86i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-12936.0 - 22405.8i) q^{82} -106764. q^{83} -5184.00 q^{85} +(30824.0 + 53388.7i) q^{86} +(11205.0 - 19407.6i) q^{87} +(-2112.00 + 3658.09i) q^{88} +(-17442.0 - 30210.4i) q^{89} +7776.00 q^{90} -16608.0 q^{92} +(31716.0 + 54933.7i) q^{93} +(-41208.0 + 71374.3i) q^{94} +(4080.00 - 7066.77i) q^{95} +(-4608.00 - 7981.29i) q^{96} +18662.0 q^{97} +5346.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 9 q^{3} - 16 q^{4} - 24 q^{5} + 72 q^{6} + 128 q^{8} - 81 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 - 9 * q^3 - 16 * q^4 - 24 * q^5 + 72 * q^6 + 128 * q^8 - 81 * q^9	\( 2 q - 4 q^{2} - 9 q^{3} - 16 q^{4} - 24 q^{5} + 72 q^{6} + 128 q^{8} - 81 q^{9} - 96 q^{10} - 66 q^{11} - 144 q^{12} + 196 q^{13} + 432 q^{15} - 256 q^{16} + 216 q^{17} - 324 q^{18} + 340 q^{19} + 768 q^{20} + 528 q^{22} + 1038 q^{23} - 576 q^{24} + 2549 q^{25} - 392 q^{26} + 1458 q^{27} - 4980 q^{29} - 864 q^{30} + 7048 q^{31} - 1024 q^{32} - 594 q^{33} - 1728 q^{34} + 2592 q^{36} + 12238 q^{37} + 1360 q^{38} - 882 q^{39} - 1536 q^{40} + 12936 q^{41} - 30824 q^{43} - 1056 q^{44} - 1944 q^{45} + 4152 q^{46} - 20604 q^{47} + 4608 q^{48} - 20392 q^{50} + 1944 q^{51} - 1568 q^{52} - 32490 q^{53} - 2916 q^{54} + 3168 q^{55} - 6120 q^{57} + 9960 q^{58} - 34224 q^{59} - 3456 q^{60} - 35654 q^{61} - 56384 q^{62} + 8192 q^{64} - 2352 q^{65} - 2376 q^{66} - 12680 q^{67} + 3456 q^{68} - 18684 q^{69} - 85284 q^{71} - 5184 q^{72} - 33734 q^{73} + 48952 q^{74} + 22941 q^{75} - 10880 q^{76} + 7056 q^{78} + 85108 q^{79} - 6144 q^{80} - 6561 q^{81} - 25872 q^{82} - 213528 q^{83} - 10368 q^{85} + 61648 q^{86} + 22410 q^{87} - 4224 q^{88} - 34884 q^{89} + 15552 q^{90} - 33216 q^{92} + 63432 q^{93} - 82416 q^{94} + 8160 q^{95} - 9216 q^{96} + 37324 q^{97} + 10692 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 9 * q^3 - 16 * q^4 - 24 * q^5 + 72 * q^6 + 128 * q^8 - 81 * q^9 - 96 * q^10 - 66 * q^11 - 144 * q^12 + 196 * q^13 + 432 * q^15 - 256 * q^16 + 216 * q^17 - 324 * q^18 + 340 * q^19 + 768 * q^20 + 528 * q^22 + 1038 * q^23 - 576 * q^24 + 2549 * q^25 - 392 * q^26 + 1458 * q^27 - 4980 * q^29 - 864 * q^30 + 7048 * q^31 - 1024 * q^32 - 594 * q^33 - 1728 * q^34 + 2592 * q^36 + 12238 * q^37 + 1360 * q^38 - 882 * q^39 - 1536 * q^40 + 12936 * q^41 - 30824 * q^43 - 1056 * q^44 - 1944 * q^45 + 4152 * q^46 - 20604 * q^47 + 4608 * q^48 - 20392 * q^50 + 1944 * q^51 - 1568 * q^52 - 32490 * q^53 - 2916 * q^54 + 3168 * q^55 - 6120 * q^57 + 9960 * q^58 - 34224 * q^59 - 3456 * q^60 - 35654 * q^61 - 56384 * q^62 + 8192 * q^64 - 2352 * q^65 - 2376 * q^66 - 12680 * q^67 + 3456 * q^68 - 18684 * q^69 - 85284 * q^71 - 5184 * q^72 - 33734 * q^73 + 48952 * q^74 + 22941 * q^75 - 10880 * q^76 + 7056 * q^78 + 85108 * q^79 - 6144 * q^80 - 6561 * q^81 - 25872 * q^82 - 213528 * q^83 - 10368 * q^85 + 61648 * q^86 + 22410 * q^87 - 4224 * q^88 - 34884 * q^89 + 15552 * q^90 - 33216 * q^92 + 63432 * q^93 - 82416 * q^94 + 8160 * q^95 - 9216 * q^96 + 37324 * q^97 + 10692 * q^99

Display 100 coefficients 10 coefficients

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
$5$	−12.0000	−	20.7846i	−0.214663	−	0.371806i	0.738506	−	0.674247i	$-0.235532\pi$
$5$	−12.0000	−	20.7846i	−0.214663	−	0.371806i	−0.953168	+	0.302441i	$0.902198\pi$
$6$	36.0000			0.408248
$7$		0			0
$7$		0			0
$8$	64.0000			0.353553
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	−48.0000	+	83.1384i	−0.151789	+	0.262907i
$11$	−33.0000	+	57.1577i	−0.0822304	+	0.142427i	−0.904208	−	0.427093i	$-0.859538\pi$
$11$	−33.0000	+	57.1577i	−0.0822304	+	0.142427i	0.821977	+	0.569520i	$0.192871\pi$
$12$	−72.0000	−	124.708i	−0.144338	−	0.250000i
$13$	98.0000			0.160830			0.0804151	−	0.996761i	$-0.474375\pi$
$13$	98.0000			0.160830			0.0804151	+	0.996761i	$0.474375\pi$
$14$		0			0
$15$	216.000			0.247871
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	108.000	−	187.061i	0.0906362	−	0.156986i	−0.817143	−	0.576435i	$-0.804443\pi$
$17$	108.000	−	187.061i	0.0906362	−	0.156986i	0.907779	+	0.419449i	$0.137777\pi$
$18$	−162.000	+	280.592i	−0.117851	+	0.204124i
$19$	170.000	+	294.449i	0.108035	+	0.187122i	0.914974	−	0.403512i	$-0.132211\pi$
$19$	170.000	+	294.449i	0.108035	+	0.187122i	−0.806939	+	0.590635i	$0.798877\pi$
$20$	384.000			0.214663
$21$		0			0
$22$	264.000			0.116291
$23$	519.000	+	898.934i	0.204573	+	0.354330i	0.949997	−	0.312260i	$-0.101086\pi$
$23$	519.000	+	898.934i	0.204573	+	0.354330i	−0.745424	+	0.666591i	$0.767753\pi$
$24$	−288.000	+	498.831i	−0.102062	+	0.176777i
$25$	1274.50	−	2207.50i	0.407840	−	0.706400i
$26$	−196.000	−	339.482i	−0.0568621	−	0.0984880i
$27$	729.000			0.192450
$28$		0			0
$29$	−2490.00			−0.549800			−0.274900	−	0.961473i	$-0.588645\pi$
$29$	−2490.00			−0.549800			−0.274900	+	0.961473i	$0.588645\pi$
$30$	−432.000	−	748.246i	−0.0876356	−	0.151789i
$31$	3524.00	−	6103.75i	0.658615	−	1.14075i	−0.322359	−	0.946617i	$-0.604476\pi$
$31$	3524.00	−	6103.75i	0.658615	−	1.14075i	0.980974	−	0.194137i	$-0.0621908\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$	−297.000	−	514.419i	−0.0474757	−	0.0822304i
$34$	−864.000			−0.128179
$35$		0			0
$36$	1296.00			0.166667
$37$	6119.00	+	10598.4i	0.734812	+	1.27273i	0.954806	+	0.297230i	$0.0960629\pi$
$37$	6119.00	+	10598.4i	0.734812	+	1.27273i	−0.219994	+	0.975501i	$0.570604\pi$
$38$	680.000	−	1177.79i	0.0763924	−	0.132315i
$39$	−441.000	+	763.834i	−0.0464277	+	0.0804151i
$40$	−768.000	−	1330.22i	−0.0758947	−	0.131453i
$41$	6468.00			0.600911			0.300456	−	0.953796i	$-0.402861\pi$
$41$	6468.00			0.600911			0.300456	+	0.953796i	$0.402861\pi$
$42$		0			0
$43$	−15412.0			−1.27112			−0.635562	−	0.772050i	$-0.719232\pi$
$43$	−15412.0			−1.27112			−0.635562	+	0.772050i	$0.719232\pi$
$44$	−528.000	−	914.523i	−0.0411152	−	0.0712136i
$45$	−972.000	+	1683.55i	−0.0715542	+	0.123935i
$46$	2076.00	−	3595.74i	0.144655	−	0.250549i
$47$	−10302.0	−	17843.6i	−0.680263	−	1.17825i	−0.974900	−	0.222641i	$-0.928532\pi$
$47$	−10302.0	−	17843.6i	−0.680263	−	1.17825i	0.294637	−	0.955609i	$-0.404801\pi$
$48$	2304.00			0.144338
$49$		0			0
$50$	−10196.0			−0.576773
$51$	972.000	+	1683.55i	0.0523288	+	0.0906362i
$52$	−784.000	+	1357.93i	−0.0402076	+	0.0696415i
$53$	−16245.0	+	28137.2i	−0.794383	+	1.37591i	0.128847	+	0.991664i	$0.458872\pi$
$53$	−16245.0	+	28137.2i	−0.794383	+	1.37591i	−0.923230	+	0.384248i	$0.874461\pi$
$54$	−1458.00	−	2525.33i	−0.0680414	−	0.117851i
$55$	1584.00			0.0706071
$56$		0			0
$57$	−3060.00			−0.124748
$58$	4980.00	+	8625.61i	0.194383	+	0.336682i
$59$	−17112.0	+	29638.9i	−0.639986	+	1.10849i	0.345449	+	0.938438i	$0.387727\pi$
$59$	−17112.0	+	29638.9i	−0.639986	+	1.10849i	−0.985435	+	0.170051i	$0.945607\pi$
$60$	−1728.00	+	2992.98i	−0.0619677	+	0.107331i
$61$	−17827.0	−	30877.3i	−0.613414	−	1.06246i	−0.990661	−	0.136351i	$-0.956462\pi$
$61$	−17827.0	−	30877.3i	−0.613414	−	1.06246i	0.377247	−	0.926113i	$-0.376871\pi$
$62$	−28192.0			−0.931422
$63$		0			0
$64$	4096.00			0.125000
$65$	−1176.00	−	2036.89i	−0.0345242	−	0.0597977i
$66$	−1188.00	+	2057.68i	−0.0335704	+	0.0581456i
$67$	−6340.00	+	10981.2i	−0.172545	+	0.298857i	−0.939309	−	0.343073i	$-0.888532\pi$
$67$	−6340.00	+	10981.2i	−0.172545	+	0.298857i	0.766764	+	0.641929i	$0.221866\pi$
$68$	1728.00	+	2992.98i	0.0453181	+	0.0784932i
$69$	−9342.00			−0.236220
$70$		0			0
$71$	−42642.0			−1.00390			−0.501951	−	0.864896i	$-0.667384\pi$
$71$	−42642.0			−1.00390			−0.501951	+	0.864896i	$0.667384\pi$
$72$	−2592.00	−	4489.48i	−0.0589256	−	0.102062i
$73$	−16867.0	+	29214.5i	−0.370451	+	0.641640i	−0.989635	−	0.143606i	$-0.954130\pi$
$73$	−16867.0	+	29214.5i	−0.370451	+	0.641640i	0.619184	+	0.785246i	$0.287464\pi$
$74$	24476.0	−	42393.7i	0.519590	−	0.899957i
$75$	11470.5	+	19867.5i	0.235467	+	0.407840i
$76$	−5440.00			−0.108035
$77$		0			0
$78$	3528.00			0.0656587
$79$	42554.0	+	73705.7i	0.767137	+	1.32872i	0.939110	+	0.343618i	$0.111652\pi$
$79$	42554.0	+	73705.7i	0.767137	+	1.32872i	−0.171973	+	0.985102i	$0.555014\pi$
$80$	−3072.00	+	5320.86i	−0.0536656	+	0.0929516i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	−12936.0	−	22405.8i	−0.212454	−	0.367982i
$83$	−106764.			−1.70110			−0.850550	−	0.525895i	$-0.823730\pi$
$83$	−106764.			−1.70110			−0.850550	+	0.525895i	$0.823730\pi$
$84$		0			0
$85$	−5184.00			−0.0778247
$86$	30824.0	+	53388.7i	0.449410	+	0.778401i
$87$	11205.0	−	19407.6i	0.158713	−	0.274900i
$88$	−2112.00	+	3658.09i	−0.0290728	+	0.0503556i
$89$	−17442.0	−	30210.4i	−0.233411	−	0.404280i	0.725399	−	0.688329i	$-0.241655\pi$
$89$	−17442.0	−	30210.4i	−0.233411	−	0.404280i	−0.958810	+	0.284049i	$0.908322\pi$
$90$	7776.00			0.101193
$91$		0			0
$92$	−16608.0			−0.204573
$93$	31716.0	+	54933.7i	0.380252	+	0.658615i
$94$	−41208.0	+	71374.3i	−0.481019	+	0.833149i
$95$	4080.00	−	7066.77i	0.0463822	−	0.0803363i
$96$	−4608.00	−	7981.29i	−0.0510310	−	0.0883883i
$97$	18662.0			0.201386			0.100693	−	0.994918i	$-0.467894\pi$
$97$	18662.0			0.201386			0.100693	+	0.994918i	$0.467894\pi$
$98$		0			0
$99$	5346.00			0.0548202
$100$	20392.0	+	35320.0i	0.203920	+	0.353200i
$101$	−76542.0	+	132575.i	−0.746614	+	1.29317i	0.202822	+	0.979216i	$0.434989\pi$
$101$	−76542.0	+	132575.i	−0.746614	+	1.29317i	−0.949437	+	0.313959i	$0.898345\pi$
$102$	3888.00	−	6734.21i	0.0370021	−	0.0640894i
$103$	−17932.0	−	31059.1i	−0.166547	−	0.288467i	0.770657	−	0.637250i	$-0.219928\pi$
$103$	−17932.0	−	31059.1i	−0.166547	−	0.288467i	−0.937203	+	0.348783i	$0.886595\pi$
$104$	6272.00			0.0568621
$105$		0			0
$106$	129960.			1.12343
$107$	47727.0	+	82665.6i	0.403000	+	0.698016i	0.994086	−	0.108592i	$-0.0346342\pi$
$107$	47727.0	+	82665.6i	0.403000	+	0.698016i	−0.591087	+	0.806608i	$0.701301\pi$
$108$	−5832.00	+	10101.3i	−0.0481125	+	0.0833333i
$109$	−106111.	+	183790.i	−0.855449	+	1.48168i	0.0207787	+	0.999784i	$0.493385\pi$
$109$	−106111.	+	183790.i	−0.855449	+	1.48168i	−0.876228	+	0.481897i	$0.839948\pi$
$110$	−3168.00	−	5487.14i	−0.0249634	−	0.0432378i
$111$	−110142.			−0.848488
$112$		0			0
$113$	62106.0			0.457549			0.228774	−	0.973479i	$-0.426528\pi$
$113$	62106.0			0.457549			0.228774	+	0.973479i	$0.426528\pi$
$114$	6120.00	+	10600.2i	0.0441051	+	0.0763924i
$115$	12456.0	−	21574.4i	0.0878282	−	0.152123i
$116$	19920.0	−	34502.5i	0.137450	−	0.238070i
$117$	−3969.00	−	6874.51i	−0.0268050	−	0.0464277i
$118$	136896.			0.905077
$119$		0			0
$120$	13824.0			0.0876356
$121$	78347.5	+	135702.i	0.486476	+	0.842602i
$122$	−71308.0	+	123509.i	−0.433749	+	0.751276i
$123$	−29106.0	+	50413.1i	−0.173468	+	0.300456i
$124$	56384.0	+	97660.0i	0.329308	+	0.570377i
$125$	−136176.			−0.779517
$126$		0			0
$127$	−53044.0			−0.291828			−0.145914	−	0.989297i	$-0.546612\pi$
$127$	−53044.0			−0.291828			−0.145914	+	0.989297i	$0.546612\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$	69354.0	−	120125.i	0.366942	−	0.635562i
$130$	−4704.00	+	8147.57i	−0.0244123	+	0.0422834i
$131$	−34662.0	−	60036.3i	−0.176472	−	0.305658i	0.764198	−	0.644982i	$-0.223135\pi$
$131$	−34662.0	−	60036.3i	−0.176472	−	0.305658i	−0.940670	+	0.339324i	$0.889802\pi$
$132$	9504.00			0.0474757
$133$		0			0
$134$	50720.0			0.244015
$135$	−8748.00	−	15152.0i	−0.0413118	−	0.0715542i
$136$	6912.00	−	11971.9i	0.0320447	−	0.0555031i
$137$	−64923.0	+	112450.i	−0.295527	+	0.511868i	−0.975107	−	0.221733i	$-0.928829\pi$
$137$	−64923.0	+	112450.i	−0.295527	+	0.511868i	0.679580	+	0.733601i	$0.262162\pi$
$138$	18684.0	+	32361.6i	0.0835165	+	0.144655i
$139$	−104356.			−0.458121			−0.229061	−	0.973412i	$-0.573565\pi$
$139$	−104356.			−0.458121			−0.229061	+	0.973412i	$0.573565\pi$
$140$		0			0
$141$	185436.			0.785500
$142$	85284.0	+	147716.i	0.354933	+	0.614762i
$143$	−3234.00	+	5601.45i	−0.0132251	+	0.0229066i
$144$	−10368.0	+	17957.9i	−0.0416667	+	0.0721688i
$145$	29880.0	+	51753.7i	0.118021	+	0.204419i
$146$	134936.			0.523897
$147$		0			0
$148$	−195808.			−0.734812
$149$	−108597.	−	188096.i	−0.400730	−	0.694085i	0.593084	−	0.805141i	$-0.297910\pi$
$149$	−108597.	−	188096.i	−0.400730	−	0.694085i	−0.993814	+	0.111055i	$0.964577\pi$
$150$	45882.0	−	79470.0i	0.166500	−	0.288386i
$151$	−110500.	+	191392.i	−0.394385	+	0.683094i	−0.993022	−	0.117926i	$-0.962376\pi$
$151$	−110500.	+	191392.i	−0.394385	+	0.683094i	0.598638	+	0.801020i	$0.295709\pi$
$152$	10880.0	+	18844.7i	0.0381962	+	0.0661577i
$153$	−17496.0			−0.0604241
$154$		0			0
$155$	−169152.			−0.565520
$156$	−7056.00	−	12221.4i	−0.0232138	−	0.0402076i
$157$	189185.	−	327678.i	0.612544	−	1.06096i	−0.378266	−	0.925697i	$-0.623479\pi$
$157$	189185.	−	327678.i	0.612544	−	1.06096i	0.990810	−	0.135261i	$-0.0431873\pi$
$158$	170216.	−	294823.i	0.542447	−	0.939547i
$159$	−146205.	−	253234.i	−0.458637	−	0.794383i
$160$	24576.0			0.0758947
$161$		0			0
$162$	26244.0			0.0785674
$163$	−52408.0	−	90773.3i	−0.154500	−	0.267602i	0.778377	−	0.627797i	$-0.216043\pi$
$163$	−52408.0	−	90773.3i	−0.154500	−	0.267602i	−0.932877	+	0.360195i	$0.882710\pi$
$164$	−51744.0	+	89623.2i	−0.150228	+	0.260202i
$165$	−7128.00	+	12346.1i	−0.0203825	+	0.0353036i
$166$	213528.	+	369841.i	0.601429	+	1.04171i
$167$	−426972.			−1.18470			−0.592350	−	0.805681i	$-0.701800\pi$
$167$	−426972.			−1.18470			−0.592350	+	0.805681i	$0.701800\pi$
$168$		0			0
$169$	−361689.			−0.974134
$170$	10368.0	+	17957.9i	0.0275152	+	0.0476577i
$171$	13770.0	−	23850.3i	0.0360117	−	0.0623741i
$172$	123296.	−	213555.i	0.317781	−	0.550413i
$173$	−165534.	−	286713.i	−0.420506	−	0.728337i	0.575483	−	0.817814i	$-0.304814\pi$
$173$	−165534.	−	286713.i	−0.420506	−	0.728337i	−0.995989	+	0.0894763i	$0.971481\pi$
$174$	−89640.0			−0.224455
$175$		0			0
$176$	16896.0			0.0411152
$177$	−154008.	−	266750.i	−0.369496	−	0.639986i
$178$	−69768.0	+	120842.i	−0.165046	+	0.285869i
$179$	200097.	−	346578.i	0.466775	−	0.808479i	−0.532504	−	0.846427i	$-0.678749\pi$
$179$	200097.	−	346578.i	0.466775	−	0.808479i	0.999280	+	0.0379485i	$0.0120823\pi$
$180$	−15552.0	−	26936.9i	−0.0357771	−	0.0619677i
$181$	588098.			1.33430			0.667150	−	0.744924i	$-0.267514\pi$
$181$	588098.			1.33430			0.667150	+	0.744924i	$0.267514\pi$
$182$		0			0
$183$	320886.			0.708309
$184$	33216.0	+	57531.8i	0.0723274	+	0.125275i
$185$	146856.	−	254362.i	0.315473	−	0.546415i
$186$	126864.	−	219735.i	0.268878	−	0.465711i
$187$	7128.00	+	12346.1i	0.0149061	+	0.0258181i
$188$	329664.			0.680263
$189$		0			0
$190$	−32640.0			−0.0655943
$191$	−469671.	−	813494.i	−0.931559	−	1.61351i	−0.780658	−	0.624958i	$-0.785116\pi$
$191$	−469671.	−	813494.i	−0.931559	−	1.61351i	−0.150901	−	0.988549i	$-0.548217\pi$
$192$	−18432.0	+	31925.2i	−0.0360844	+	0.0625000i
$193$	−169195.	+	293054.i	−0.326960	+	0.566311i	−0.981907	−	0.189364i	$-0.939357\pi$
$193$	−169195.	+	293054.i	−0.326960	+	0.566311i	0.654947	+	0.755675i	$0.272691\pi$
$194$	−37324.0	−	64647.1i	−0.0712006	−	0.123323i
$195$	21168.0			0.0398651
$196$		0			0
$197$	−237942.			−0.436823			−0.218412	−	0.975857i	$-0.570088\pi$
$197$	−237942.			−0.436823			−0.218412	+	0.975857i	$0.570088\pi$
$198$	−10692.0	−	18519.1i	−0.0193819	−	0.0335704i
$199$	−102232.	+	177071.i	−0.183001	+	0.316968i	−0.942901	−	0.333073i	$-0.891915\pi$
$199$	−102232.	+	177071.i	−0.183001	+	0.316968i	0.759900	+	0.650040i	$0.225248\pi$
$200$	81568.0	−	141280.i	0.144193	−	0.249750i
$201$	−57060.0	−	98830.8i	−0.0996189	−	0.172545i
$202$	612336.			1.05587
$203$		0			0
$204$	−31104.0			−0.0523288
$205$	−77616.0	−	134435.i	−0.128993	−	0.223423i
$206$	−71728.0	+	124237.i	−0.117766	+	0.203977i
$207$	42039.0	−	72813.7i	0.0681909	−	0.118110i
$208$	−12544.0	−	21726.8i	−0.0201038	−	0.0348208i
$209$	−22440.0			−0.0355351
$210$		0			0
$211$	−348724.			−0.539232			−0.269616	−	0.962968i	$-0.586897\pi$
$211$	−348724.			−0.539232			−0.269616	+	0.962968i	$0.586897\pi$
$212$	−259920.	−	450195.i	−0.397192	−	0.687956i
$213$	191889.	−	332361.i	0.289802	−	0.501951i
$214$	190908.	−	330662.i	0.284964	−	0.493572i
$215$	184944.	+	320332.i	0.272863	+	0.472612i
$216$	46656.0			0.0680414
$217$		0			0
$218$	848888.			1.20979
$219$	−151803.	−	262931.i	−0.213880	−	0.370451i
$220$	−12672.0	+	21948.5i	−0.0176518	+	0.0305738i
$221$	10584.0	−	18332.0i	0.0145770	−	0.0252482i
$222$	220284.	+	381543.i	0.299986	+	0.519590i
$223$	1.47006e6			1.97957			0.989787	−	0.142554i	$-0.0455316\pi$
$223$	1.47006e6			1.97957			0.989787	+	0.142554i	$0.0455316\pi$
$224$		0			0
$225$	−206469.			−0.271893
$226$	−124212.	−	215141.i	−0.161768	−	0.280190i
$227$	294780.	−	510574.i	0.379694	−	0.657649i	−0.611324	−	0.791381i	$-0.709363\pi$
$227$	294780.	−	510574.i	0.379694	−	0.657649i	0.991018	+	0.133732i	$0.0426961\pi$
$228$	24480.0	−	42400.6i	0.0311870	−	0.0540176i
$229$	522671.	+	905293.i	0.658627	+	1.14078i	0.980971	+	0.194153i	$0.0621959\pi$
$229$	522671.	+	905293.i	0.658627	+	1.14078i	−0.322344	+	0.946623i	$0.604471\pi$
$230$	−99648.0			−0.124208
$231$		0			0
$232$	−159360.			−0.194383
$233$	−325611.	−	563975.i	−0.392925	−	0.680565i	0.599909	−	0.800068i	$-0.295203\pi$
$233$	−325611.	−	563975.i	−0.392925	−	0.680565i	−0.992834	+	0.119503i	$0.961870\pi$
$234$	−15876.0	+	27498.0i	−0.0189540	+	0.0328293i
$235$	−247248.	+	428246.i	−0.292054	+	0.505852i
$236$	−273792.	−	474222.i	−0.319993	−	0.554244i
$237$	−765972.			−0.885813
$238$		0			0
$239$	−513462.			−0.581452			−0.290726	−	0.956806i	$-0.593897\pi$
$239$	−513462.			−0.581452			−0.290726	+	0.956806i	$0.593897\pi$
$240$	−27648.0	−	47887.7i	−0.0309839	−	0.0536656i
$241$	347357.	−	601640.i	0.385242	−	0.667258i	−0.606561	−	0.795037i	$-0.707451\pi$
$241$	347357.	−	601640.i	0.385242	−	0.667258i	0.991803	+	0.127779i	$0.0407847\pi$
$242$	313390.	−	542807.i	0.343991	−	0.595809i
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$	570464.			0.613414
$245$		0			0
$246$	232848.			0.245321
$247$	16660.0	+	28856.0i	0.0173753	+	0.0300949i
$248$	225536.	−	390640.i	0.232856	−	0.403318i
$249$	480438.	−	832143.i	0.491065	−	0.850550i
$250$	272352.	+	471728.i	0.275601	+	0.477355i
$251$	−1.39608e6			−1.39870			−0.699352	−	0.714777i	$-0.746528\pi$
$251$	−1.39608e6			−1.39870			−0.699352	+	0.714777i	$0.746528\pi$
$252$		0			0
$253$	−68508.0			−0.0672884
$254$	106088.	+	183750.i	0.103177	+	0.178707i
$255$	23328.0	−	40405.3i	0.0224661	−	0.0389124i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	502602.	+	870532.i	0.474670	+	0.822152i	0.999579	−	0.0290061i	$-0.00923423\pi$
$257$	502602.	+	870532.i	0.474670	+	0.822152i	−0.524910	+	0.851158i	$0.675901\pi$
$258$	−554832.			−0.518934
$259$		0			0
$260$	37632.0			0.0345242
$261$	100845.	+	174669.i	0.0916333	+	0.158713i
$262$	−138648.	+	240145.i	−0.124784	+	0.216133i
$263$	−626505.	+	1.08514e6i	−0.558515	+	0.967377i	0.439105	+	0.898436i	$0.355296\pi$
$263$	−626505.	+	1.08514e6i	−0.558515	+	0.967377i	−0.997621	+	0.0689415i	$0.978038\pi$
$264$	−19008.0	−	32922.8i	−0.0167852	−	0.0290728i
$265$	779760.			0.682097
$266$		0			0
$267$	313956.			0.269520
$268$	−101440.	−	175699.i	−0.0862725	−	0.149428i
$269$	880344.	−	1.52480e6i	0.741774	−	1.28479i	−0.209913	−	0.977720i	$-0.567318\pi$
$269$	880344.	−	1.52480e6i	0.741774	−	1.28479i	0.951687	−	0.307070i	$-0.0993487\pi$
$270$	−34992.0	+	60607.9i	−0.0292119	+	0.0505964i
$271$	−385264.	−	667297.i	−0.318666	−	0.551945i	0.661544	−	0.749906i	$-0.269901\pi$
$271$	−385264.	−	667297.i	−0.318666	−	0.551945i	−0.980210	+	0.197961i	$0.936568\pi$
$272$	−55296.0			−0.0453181
$273$		0			0
$274$	519384.			0.417938
$275$	84117.0	+	145695.i	0.0670737	+	0.116175i
$276$	74736.0	−	129447.i	0.0590551	−	0.102286i
$277$	−353869.	+	612919.i	−0.277104	+	0.479959i	−0.970664	−	0.240441i	$-0.922708\pi$
$277$	−353869.	+	612919.i	−0.277104	+	0.479959i	0.693560	+	0.720399i	$0.256041\pi$
$278$	208712.	+	361500.i	0.161970	+	0.280541i
$279$	−570888.			−0.439077
$280$		0			0
$281$	2.30432e6			1.74091			0.870456	−	0.492247i	$-0.163824\pi$
$281$	2.30432e6			1.74091			0.870456	+	0.492247i	$0.163824\pi$
$282$	−370872.	−	642369.i	−0.277716	−	0.481019i
$283$	−804514.	+	1.39346e6i	−0.597128	+	1.03426i	0.396115	+	0.918201i	$0.370358\pi$
$283$	−804514.	+	1.39346e6i	−0.597128	+	1.03426i	−0.993243	+	0.116055i	$0.962975\pi$
$284$	341136.	−	590865.i	0.250976	−	0.434703i
$285$	36720.0	+	63600.9i	0.0267788	+	0.0463822i
$286$	25872.0			0.0187032
$287$		0			0
$288$	82944.0			0.0589256
$289$	686600.	+	1.18923e6i	0.483570	+	0.837568i
$290$	119520.	−	207015.i	0.0834537	−	0.144546i
$291$	−83979.0	+	145456.i	−0.0581351	+	0.100693i
$292$	−269872.	−	467432.i	−0.185225	−	0.320820i
$293$	517020.			0.351834			0.175917	−	0.984405i	$-0.443711\pi$
$293$	517020.			0.351834			0.175917	+	0.984405i	$0.443711\pi$
$294$		0			0
$295$	821376.			0.549524
$296$	391616.	+	678299.i	0.259795	+	0.449979i
$297$	−24057.0	+	41667.9i	−0.0158252	+	0.0274101i
$298$	−434388.	+	752382.i	−0.283359	+	0.490792i
$299$	50862.0	+	88095.6i	0.0329015	+	0.0569870i
$300$	−367056.			−0.235467
$301$		0			0
$302$	884000.			0.557744
$303$	−688878.	−	1.19317e6i	−0.431058	−	0.746614i
$304$	43520.0	−	75378.9i	0.0270088	−	0.0467806i
$305$	−427848.	+	741054.i	−0.263354	+	0.456142i
$306$	34992.0	+	60607.9i	0.0213631	+	0.0370021i
$307$	1.35002e6			0.817512			0.408756	−	0.912644i	$-0.365963\pi$
$307$	1.35002e6			0.817512			0.408756	+	0.912644i	$0.365963\pi$
$308$		0			0
$309$	322776.			0.192311
$310$	338304.	+	585960.i	0.199941	+	0.346309i
$311$	−672690.	+	1.16513e6i	−0.394379	+	0.683085i	−0.993022	−	0.117931i	$-0.962374\pi$
$311$	−672690.	+	1.16513e6i	−0.394379	+	0.683085i	0.598643	+	0.801016i	$0.295707\pi$
$312$	−28224.0	+	48885.4i	−0.0164147	+	0.0284310i
$313$	−128077.	−	221836.i	−0.0738942	−	0.127988i	0.826711	−	0.562627i	$-0.190209\pi$
$313$	−128077.	−	221836.i	−0.0738942	−	0.127988i	−0.900605	+	0.434639i	$0.856876\pi$
$314$	−1.51348e6			−0.866269
$315$		0			0
$316$	−1.36173e6			−0.767137
$317$	−923145.	−	1.59893e6i	−0.515967	−	0.893681i	−0.999828	−	0.0185361i	$-0.994099\pi$
$317$	−923145.	−	1.59893e6i	−0.515967	−	0.893681i	0.483861	−	0.875145i	$-0.339234\pi$
$318$	−584820.	+	1.01294e6i	−0.324306	+	0.561714i
$319$	82170.0	−	142323.i	0.0452102	−	0.0783064i
$320$	−49152.0	−	85133.8i	−0.0268328	−	0.0464758i
$321$	−859086.			−0.465344
$322$		0			0
$323$	73440.0			0.0391675
$324$	−52488.0	−	90911.9i	−0.0277778	−	0.0481125i
$325$	124901.	−	216335.i	0.0655930	−	0.113610i
$326$	−209632.	+	363093.i	−0.109248	+	0.189223i
$327$	−954999.	−	1.65411e6i	−0.493894	−	0.855449i
$328$	413952.			0.212454
$329$		0			0
$330$	57024.0			0.0288252
$331$	1.66619e6	+	2.88593e6i	0.835900	+	1.44782i	0.893295	+	0.449470i	$0.148387\pi$
$331$	1.66619e6	+	2.88593e6i	0.835900	+	1.44782i	−0.0573948	+	0.998352i	$0.518279\pi$
$332$	854112.	−	1.47937e6i	0.425275	−	0.736598i
$333$	495639.	−	858472.i	0.244937	−	0.424244i
$334$	853944.	+	1.47907e6i	0.418855	+	0.725477i
$335$	304320.			0.148156
$336$		0			0
$337$	−1.63481e6			−0.784136			−0.392068	−	0.919936i	$-0.628240\pi$
$337$	−1.63481e6			−0.784136			−0.392068	+	0.919936i	$0.628240\pi$
$338$	723378.	+	1.25293e6i	0.344408	+	0.596533i
$339$	−279477.	+	484068.i	−0.132083	+	0.228774i
$340$	41472.0	−	71831.6i	0.0194562	−	0.0336991i
$341$	232584.	+	402847.i	0.108316	+	0.187609i
$342$	−110160.			−0.0509282
$343$		0			0
$344$	−986368.			−0.449410
$345$	112104.	+	194170.i	0.0507076	+	0.0878282i
$346$	−662136.	+	1.14685e6i	−0.297342	+	0.515012i
$347$	420765.	−	728786.i	0.187593	−	0.324920i	−0.756854	−	0.653583i	$-0.773265\pi$
$347$	420765.	−	728786.i	0.187593	−	0.324920i	0.944447	+	0.328663i	$0.106598\pi$
$348$	179280.	+	310522.i	0.0793567	+	0.137450i
$349$	−977242.			−0.429476			−0.214738	−	0.976672i	$-0.568890\pi$
$349$	−977242.			−0.429476			−0.214738	+	0.976672i	$0.568890\pi$
$350$		0			0
$351$	71442.0			0.0309518
$352$	−33792.0	−	58529.5i	−0.0145364	−	0.0251778i
$353$	−1.72928e6	+	2.99521e6i	−0.738634	+	1.27935i	0.214476	+	0.976729i	$0.431196\pi$
$353$	−1.72928e6	+	2.99521e6i	−0.738634	+	1.27935i	−0.953110	+	0.302623i	$0.902138\pi$
$354$	−616032.	+	1.06700e6i	−0.261273	+	0.452539i
$355$	511704.	+	886297.i	0.215500	+	0.373258i
$356$	558144.			0.233411
$357$		0			0
$358$	−1.60078e6			−0.660120
$359$	1.73651e6	+	3.00771e6i	0.711115	+	1.23169i	0.964439	+	0.264306i	$0.0851429\pi$
$359$	1.73651e6	+	3.00771e6i	0.711115	+	1.23169i	−0.253324	+	0.967382i	$0.581524\pi$
$360$	−62208.0	+	107747.i	−0.0252982	+	0.0438178i
$361$	1.18025e6	−	2.04425e6i	0.476657	−	0.825594i
$362$	−1.17620e6	−	2.03723e6i	−0.471746	−	0.817088i
$363$	−1.41026e6			−0.561734
$364$		0			0
$365$	809616.			0.318088
$366$	−641772.	−	1.11158e6i	−0.250425	−	0.433749i
$367$	−1.55997e6	+	2.70194e6i	−0.604575	+	1.04716i	0.387543	+	0.921852i	$0.373324\pi$
$367$	−1.55997e6	+	2.70194e6i	−0.604575	+	1.04716i	−0.992118	+	0.125304i	$0.960009\pi$
$368$	132864.	−	230127.i	0.0511432	−	0.0885826i
$369$	−261954.	−	453718.i	−0.100152	−	0.173468i
$370$	−1.17485e6			−0.446146
$371$		0			0
$372$	−1.01491e6			−0.380252
$373$	1.00836e6	+	1.74654e6i	0.375272	+	0.649989i	0.990368	−	0.138463i	$-0.0442161\pi$
$373$	1.00836e6	+	1.74654e6i	0.375272	+	0.649989i	−0.615096	+	0.788452i	$0.710883\pi$
$374$	28512.0	−	49384.2i	0.0105402	−	0.0182562i
$375$	612792.	−	1.06139e6i	0.225027	−	0.389758i
$376$	−659328.	−	1.14199e6i	−0.240509	−	0.416574i
$377$	−244020.			−0.0884244
$378$		0			0
$379$	−5.38083e6			−1.92420			−0.962102	−	0.272690i	$-0.912087\pi$
$379$	−5.38083e6			−1.92420			−0.962102	+	0.272690i	$0.912087\pi$
$380$	65280.0	+	113068.i	0.0231911	+	0.0401681i
$381$	238698.	−	413437.i	0.0842435	−	0.145914i
$382$	−1.87868e6	+	3.25398e6i	−0.658712	+	1.14092i
$383$	−403716.	−	699257.i	−0.140630	−	0.243579i	0.787104	−	0.616821i	$-0.211580\pi$
$383$	−403716.	−	699257.i	−0.140630	−	0.243579i	−0.927734	+	0.373242i	$0.878246\pi$
$384$	147456.			0.0510310
$385$		0			0
$386$	1.35356e6			0.462391
$387$	624186.	+	1.08112e6i	0.211854	+	0.366942i
$388$	−149296.	+	258588.i	−0.0503465	+	0.0872026i
$389$	−445695.	+	771966.i	−0.149336	+	0.258657i	−0.930982	−	0.365065i	$-0.881047\pi$
$389$	−445695.	+	771966.i	−0.149336	+	0.258657i	0.781646	+	0.623722i	$0.214380\pi$
$390$	−42336.0	−	73328.1i	−0.0140945	−	0.0244123i
$391$	224208.			0.0741667
$392$		0			0
$393$	623916.			0.203772
$394$	475884.	+	824255.i	0.154440	+	0.267498i
$395$	1.02130e6	−	1.76894e6i	0.329351	−	0.570453i
$396$	−42768.0	+	74076.3i	−0.0137051	+	0.0237379i
$397$	−561727.	−	972940.i	−0.178875	−	0.309820i	0.762621	−	0.646846i	$-0.223912\pi$
$397$	−561727.	−	972940.i	−0.178875	−	0.309820i	−0.941495	+	0.337026i	$0.890579\pi$
$398$	817856.			0.258803
$399$		0			0
$400$	−652544.			−0.203920
$401$	−860187.	−	1.48989e6i	−0.267136	−	0.462693i	0.700985	−	0.713176i	$-0.252744\pi$
$401$	−860187.	−	1.48989e6i	−0.267136	−	0.462693i	−0.968121	+	0.250483i	$0.919411\pi$
$402$	−228240.	+	395323.i	−0.0704412	+	0.122008i
$403$	345352.	−	598167.i	0.105925	−	0.183468i
$404$	−1.22467e6	−	2.12119e6i	−0.373307	−	0.646587i
$405$	157464.			0.0477028
$406$		0			0
$407$	−807708.			−0.241695
$408$	62208.0	+	107747.i	0.0185010	+	0.0320447i
$409$	−38623.0	+	66897.0i	−0.0114166	+	0.0197742i	−0.871677	−	0.490080i	$-0.836967\pi$
$409$	−38623.0	+	66897.0i	−0.0114166	+	0.0197742i	0.860261	+	0.509855i	$0.170301\pi$
$410$	−310464.	+	537739.i	−0.0912119	+	0.157984i
$411$	−584307.	−	1.01205e6i	−0.170623	−	0.295527i
$412$	573824.			0.166547
$413$		0			0
$414$	−336312.			−0.0964365
$415$	1.28117e6	+	2.21905e6i	0.365162	+	0.632480i
$416$	−50176.0	+	86907.4i	−0.0142155	+	0.0246220i
$417$	469602.	−	813375.i	0.132248	−	0.229061i
$418$	44880.0	+	77734.4i	0.0125635	+	0.0217607i
$419$	−5.20615e6			−1.44871			−0.724356	−	0.689427i	$-0.757863\pi$
$419$	−5.20615e6			−1.44871			−0.724356	+	0.689427i	$0.757863\pi$
$420$		0			0
$421$	1.71847e6			0.472539			0.236270	−	0.971688i	$-0.424075\pi$
$421$	1.71847e6			0.472539			0.236270	+	0.971688i	$0.424075\pi$
$422$	697448.	+	1.20802e6i	0.190647	+	0.330211i
$423$	−834462.	+	1.44533e6i	−0.226754	+	0.392750i
$424$	−1.03968e6	+	1.80078e6i	−0.280857	+	0.486458i
$425$	−275292.	−	476820.i	−0.0739301	−	0.128051i
$426$	−1.53511e6			−0.409842
$427$		0			0
$428$	−1.52726e6			−0.403000
$429$	−29106.0	−	50413.1i	−0.00763553	−	0.0132251i
$430$	739776.	−	1.28133e6i	0.192943	−	0.334187i
$431$	290313.	−	502837.i	0.0752789	−	0.130387i	−0.825929	−	0.563775i	$-0.809349\pi$
$431$	290313.	−	502837.i	0.0752789	−	0.130387i	0.901208	+	0.433388i	$0.142682\pi$
$432$	−93312.0	−	161621.i	−0.0240563	−	0.0416667i
$433$	4.15087e6			1.06395			0.531973	−	0.846761i	$-0.321451\pi$
$433$	4.15087e6			1.06395			0.531973	+	0.846761i	$0.321451\pi$
$434$		0			0
$435$	−537840.			−0.136279
$436$	−1.69778e6	−	2.94063e6i	−0.427725	−	0.740841i
$437$	−176460.	+	305638.i	−0.0442021	+	0.0765602i
$438$	−607212.	+	1.05172e6i	−0.151236	+	0.261948i
$439$	−1.94204e6	−	3.36371e6i	−0.480946	−	0.833022i	0.518815	−	0.854886i	$-0.326373\pi$
$439$	−1.94204e6	−	3.36371e6i	−0.480946	−	0.833022i	−0.999761	+	0.0218641i	$0.993040\pi$
$440$	101376.			0.0249634
$441$		0			0
$442$	−84672.0			−0.0206150
$443$	1.15749e6	+	2.00484e6i	0.280226	+	0.485366i	0.971440	−	0.237284i	$-0.0762571\pi$
$443$	1.15749e6	+	2.00484e6i	0.280226	+	0.485366i	−0.691214	+	0.722650i	$0.742924\pi$
$444$	881136.	−	1.52617e6i	0.212122	−	0.367406i
$445$	−418608.	+	725050.i	−0.100209	+	0.173567i
$446$	−2.94011e6	−	5.09242e6i	−0.699885	−	1.21224i
$447$	1.95475e6			0.462723
$448$		0			0
$449$	−1.92281e6			−0.450113			−0.225056	−	0.974346i	$-0.572257\pi$
$449$	−1.92281e6			−0.450113			−0.225056	+	0.974346i	$0.572257\pi$
$450$	412938.	+	715230.i	0.0961288	+	0.166500i
$451$	−213444.	+	369696.i	−0.0494132	+	0.0855861i
$452$	−496848.	+	860566.i	−0.114387	+	0.198124i
$453$	−994500.	−	1.72252e6i	−0.227698	−	0.394385i
$454$	−2.35824e6			−0.536968
$455$		0			0
$456$	−195840.			−0.0441051
$457$	−3.43108e6	−	5.94280e6i	−0.768493	−	1.33107i	−0.938380	−	0.345605i	$-0.887674\pi$
$457$	−3.43108e6	−	5.94280e6i	−0.768493	−	1.33107i	0.169887	−	0.985464i	$-0.445660\pi$
$458$	2.09068e6	−	3.62117e6i	0.465720	−	0.806650i
$459$	78732.0	−	136368.i	0.0174429	−	0.0302121i
$460$	199296.	+	345191.i	0.0439141	+	0.0760615i
$461$	2.97167e6			0.651250			0.325625	−	0.945499i	$-0.394425\pi$
$461$	2.97167e6			0.651250			0.325625	+	0.945499i	$0.394425\pi$
$462$		0			0
$463$	4.87423e6			1.05670			0.528352	−	0.849025i	$-0.322810\pi$
$463$	4.87423e6			1.05670			0.528352	+	0.849025i	$0.322810\pi$
$464$	318720.	+	552039.i	0.0687249	+	0.119035i
$465$	761184.	−	1.31841e6i	0.163252	−	0.282760i
$466$	−1.30244e6	+	2.25590e6i	−0.277840	+	0.481232i
$467$	4.08650e6	+	7.07803e6i	0.867081	+	1.50183i	0.864966	+	0.501831i	$0.167340\pi$
$467$	4.08650e6	+	7.07803e6i	0.867081	+	1.50183i	0.00211530	+	0.999998i	$0.499327\pi$
$468$	127008.			0.0268050
$469$		0			0
$470$	1.97798e6			0.413027
$471$	1.70266e6	+	2.94910e6i	0.353653	+	0.612544i
$472$	−1.09517e6	+	1.89689e6i	−0.226269	+	0.391910i
$473$	508596.	−	880914.i	0.104525	−	0.181043i
$474$	1.53194e6	+	2.65340e6i	0.313182	+	0.542447i
$475$	866660.			0.176244
$476$		0			0
$477$	2.63169e6			0.529589
$478$	1.02692e6	+	1.77868e6i	0.205574	+	0.356065i
$479$	−1.17199e6	+	2.02994e6i	−0.233391	+	0.404245i	−0.958804	−	0.284069i	$-0.908315\pi$
$479$	−1.17199e6	+	2.02994e6i	−0.233391	+	0.404245i	0.725413	+	0.688314i	$0.241649\pi$
$480$	−110592.	+	191551.i	−0.0219089	+	0.0379473i
$481$	599662.	+	1.03865e6i	0.118180	+	0.204694i
$482$	−2.77886e6			−0.544814
$483$		0			0
$484$	−2.50712e6			−0.486476
$485$	−223944.	−	387882.i	−0.0432300	−	0.0748765i
$486$	−118098.	+	204552.i	−0.0226805	+	0.0392837i
$487$	−158464.	+	274468.i	−0.0302767	+	0.0524407i	−0.880767	−	0.473550i	$-0.842972\pi$
$487$	−158464.	+	274468.i	−0.0302767	+	0.0524407i	0.850490	+	0.525991i	$0.176306\pi$
$488$	−1.14093e6	−	1.97615e6i	−0.216875	−	0.375638i
$489$	943344.			0.178401
$490$		0			0
$491$	−5.20041e6			−0.973495			−0.486748	−	0.873543i	$-0.661817\pi$
$491$	−5.20041e6			−0.973495			−0.486748	+	0.873543i	$0.661817\pi$
$492$	−465696.	−	806609.i	−0.0867341	−	0.150228i
$493$	−268920.	+	465783.i	−0.0498317	+	0.0863111i
$494$	66640.0	−	115424.i	0.0122862	−	0.0212803i
$495$	−64152.0	−	111115.i	−0.0117679	−	0.0203825i
$496$	−1.80429e6			−0.329308
$497$		0			0
$498$	−3.84350e6			−0.694471
$499$	2.43387e6	+	4.21558e6i	0.437568	+	0.757890i	0.997501	−	0.0706479i	$-0.0225067\pi$
$499$	2.43387e6	+	4.21558e6i	0.437568	+	0.757890i	−0.559934	+	0.828538i	$0.689173\pi$
$500$	1.08941e6	−	1.88691e6i	0.194879	−	0.337541i
$501$	1.92137e6	−	3.32792e6i	0.341993	−	0.592350i
$502$	2.79216e6	+	4.83616e6i	0.494517	+	0.856528i
$503$	426888.			0.0752305			0.0376153	−	0.999292i	$-0.488024\pi$
$503$	426888.			0.0752305			0.0376153	+	0.999292i	$0.488024\pi$
$504$		0			0
$505$	3.67402e6			0.641081
$506$	137016.	+	237319.i	0.0237900	+	0.0412055i
$507$	1.62760e6	−	2.81909e6i	0.281208	−	0.487067i
$508$	424352.	−	734999.i	0.0729570	−	0.126365i
$509$	4.70810e6	+	8.15468e6i	0.805474	+	1.39512i	0.915971	+	0.401246i	$0.131423\pi$
$509$	4.70810e6	+	8.15468e6i	0.805474	+	1.39512i	−0.110496	+	0.993877i	$0.535244\pi$
$510$	−186624.			−0.0317718
$511$		0			0
$512$	262144.			0.0441942
$513$	123930.	+	214653.i	0.0207914	+	0.0360117i
$514$	2.01041e6	−	3.48213e6i	0.335642	−	0.581349i
$515$	−430368.	+	745419.i	−0.0715026	+	0.123846i
$516$	1.10966e6	+	1.92199e6i	0.183471	+	0.317781i
$517$	1.35986e6			0.223753
$518$		0			0
$519$	2.97961e6			0.485558
$520$	−75264.0	−	130361.i	−0.0122062	−	0.0211417i
$521$	−920196.	+	1.59383e6i	−0.148520	+	0.257245i	−0.930681	−	0.365832i	$-0.880784\pi$
$521$	−920196.	+	1.59383e6i	−0.148520	+	0.257245i	0.782160	+	0.623077i	$0.214118\pi$
$522$	403380.	−	698675.i	0.0647945	−	0.112227i
$523$	489554.	+	847932.i	0.0782612	+	0.135552i	0.902500	−	0.430690i	$-0.141730\pi$
$523$	489554.	+	847932.i	0.0782612	+	0.135552i	−0.824239	+	0.566243i	$0.808397\pi$
$524$	1.10918e6			0.176472
$525$		0			0
$526$	5.01204e6			0.789860
$527$	−761184.	−	1.31841e6i	−0.119389	−	0.206787i
$528$	−76032.0	+	131691.i	−0.0118689	+	0.0205576i
$529$	2.67945e6	−	4.64094e6i	0.416300	−	0.721053i
$530$	−1.55952e6	−	2.70117e6i	−0.241158	−	0.417698i
$531$	2.77214e6			0.426658
$532$		0			0
$533$	633864.			0.0966447
$534$	−627912.	−	1.08758e6i	−0.0952896	−	0.165046i
$535$	1.14545e6	−	1.98397e6i	0.173018	−	0.299676i
$536$	−405760.	+	702797.i	−0.0610039	+	0.105662i
$537$	1.80087e6	+	3.11920e6i	0.269493	+	0.466775i
$538$	−7.04275e6			−1.04903
$539$		0			0
$540$	279936.			0.0413118
$541$	−2.98058e6	−	5.16252e6i	−0.437833	−	0.758349i	0.559689	−	0.828703i	$-0.310921\pi$
$541$	−2.98058e6	−	5.16252e6i	−0.437833	−	0.758349i	−0.997522	+	0.0703538i	$0.977587\pi$
$542$	−1.54106e6	+	2.66919e6i	−0.225331	+	0.390284i
$543$	−2.64644e6	+	4.58377e6i	−0.385179	+	0.667150i
$544$	110592.	+	191551.i	0.0160224	+	0.0277515i
$545$	5.09333e6			0.734531
$546$		0			0
$547$	8.73025e6			1.24755			0.623775	−	0.781604i	$-0.285598\pi$
$547$	8.73025e6			1.24755			0.623775	+	0.781604i	$0.285598\pi$
$548$	−1.03877e6	−	1.79920e6i	−0.147763	−	0.255934i
$549$	−1.44399e6	+	2.50106e6i	−0.204471	+	0.354155i
$550$	336468.	−	582780.i	0.0474282	−	0.0821481i
$551$	−423300.	−	733177.i	−0.0593977	−	0.102880i
$552$	−597888.			−0.0835165
$553$		0			0
$554$	2.83095e6			0.391885
$555$	1.32170e6	+	2.28926e6i	0.182138	+	0.315473i
$556$	834848.	−	1.44600e6i	0.114530	−	0.198372i
$557$	1.50533e6	−	2.60731e6i	0.205586	−	0.356086i	−0.744733	−	0.667362i	$-0.767423\pi$
$557$	1.50533e6	−	2.60731e6i	0.205586	−	0.356086i	0.950319	+	0.311277i	$0.100757\pi$
$558$	1.14178e6	+	1.97761e6i	0.155237	+	0.268878i
$559$	−1.51038e6			−0.204435
$560$		0			0
$561$	−128304.			−0.0172121
$562$	−4.60864e6	−	7.98239e6i	−0.615505	−	1.06609i
$563$	−5.87863e6	+	1.01821e7i	−0.781637	+	1.35384i	0.149350	+	0.988784i	$0.452282\pi$
$563$	−5.87863e6	+	1.01821e7i	−0.781637	+	1.35384i	−0.930987	+	0.365051i	$0.881051\pi$
$564$	−1.48349e6	+	2.56948e6i	−0.196375	+	0.340132i
$565$	−745272.	−	1.29085e6i	−0.0982186	−	0.170120i
$566$	6.43611e6			0.844467
$567$		0			0
$568$	−2.72909e6			−0.354933
$569$	−6.57891e6	−	1.13950e7i	−0.851870	−	1.47548i	−0.879519	−	0.475864i	$-0.842136\pi$
$569$	−6.57891e6	−	1.13950e7i	−0.851870	−	1.47548i	0.0276496	−	0.999618i	$-0.491198\pi$
$570$	146880.	−	254404.i	0.0189354	−	0.0327972i
$571$	5.16722e6	−	8.94989e6i	0.663234	−	1.14875i	−0.316527	−	0.948583i	$-0.602517\pi$
$571$	5.16722e6	−	8.94989e6i	0.663234	−	1.14875i	0.979761	−	0.200171i	$-0.0641499\pi$
$572$	−51744.0	−	89623.2i	−0.00661256	−	0.0114533i
$573$	8.45408e6			1.07567
$574$		0			0
$575$	2.64586e6			0.333732
$576$	−165888.	−	287326.i	−0.0208333	−	0.0360844i
$577$	3.94067e6	−	6.82544e6i	0.492754	−	0.853475i	−0.507211	−	0.861822i	$-0.669324\pi$
$577$	3.94067e6	−	6.82544e6i	0.492754	−	0.853475i	0.999965	+	0.00834679i	$0.00265690\pi$
$578$	2.74640e6	−	4.75691e6i	0.341936	−	0.592250i
$579$	−1.52276e6	−	2.63749e6i	−0.188770	−	0.326960i
$580$	−956160.			−0.118021
$581$		0			0
$582$	671832.			0.0822154
$583$	−1.07217e6	−	1.85705e6i	−0.130645	−	0.226284i
$584$	−1.07949e6	+	1.86973e6i	−0.130974	+	0.226854i
$585$	−95256.0	+	164988.i	−0.0115081	+	0.0199326i
$586$	−1.03404e6	−	1.79101e6i	−0.124392	−	0.215454i
$587$	−554568.			−0.0664293			−0.0332146	−	0.999448i	$-0.510574\pi$
$587$	−554568.			−0.0664293			−0.0332146	+	0.999448i	$0.510574\pi$
$588$		0			0
$589$	2.39632e6			0.284614
$590$	−1.64275e6	−	2.84533e6i	−0.194286	−	0.336514i
$591$	1.07074e6	−	1.85457e6i	0.126100	−	0.218412i
$592$	1.56646e6	−	2.71320e6i	0.183703	−	0.318183i
$593$	4.60184e6	+	7.97063e6i	0.537397	+	0.930799i	0.999043	+	0.0437346i	$0.0139256\pi$
$593$	4.60184e6	+	7.97063e6i	0.537397	+	0.930799i	−0.461646	+	0.887064i	$0.652741\pi$
$594$	192456.			0.0223803
$595$		0			0
$596$	3.47510e6			0.400730
$597$	−920088.	−	1.59364e6i	−0.105656	−	0.183001i
$598$	203448.	−	352382.i	0.0232649	−	0.0402959i
$599$	−4.27148e6	+	7.39841e6i	−0.486419	+	0.842503i	−0.999878	−	0.0156113i	$-0.995031\pi$
$599$	−4.27148e6	+	7.39841e6i	−0.486419	+	0.842503i	0.513459	+	0.858114i	$0.328364\pi$
$600$	734112.	+	1.27152e6i	0.0832500	+	0.144193i
$601$	−9.61555e6			−1.08590			−0.542948	−	0.839767i	$-0.682692\pi$
$601$	−9.61555e6			−1.08590			−0.542948	+	0.839767i	$0.682692\pi$
$602$		0			0
$603$	1.02708e6			0.115030
$604$	−1.76800e6	−	3.06227e6i	−0.197192	−	0.341547i
$605$	1.88034e6	−	3.25684e6i	0.208856	−	0.361750i
$606$	−2.75551e6	+	4.77269e6i	−0.304804	+	0.527936i
$607$	−1.10632e6	−	1.91620e6i	−0.121873	−	0.211091i	0.798633	−	0.601818i	$-0.205557\pi$
$607$	−1.10632e6	−	1.91620e6i	−0.121873	−	0.211091i	−0.920506	+	0.390727i	$0.872224\pi$
$608$	−348160.			−0.0381962
$609$		0			0
$610$	3.42278e6			0.372439
$611$	−1.00960e6	−	1.74867e6i	−0.109407	−	0.189498i
$612$	139968.	−	242432.i	0.0151060	−	0.0261644i
$613$	3.98108e6	−	6.89543e6i	0.427907	−	0.741157i	−0.568780	−	0.822490i	$-0.692584\pi$
$613$	3.98108e6	−	6.89543e6i	0.427907	−	0.741157i	0.996687	+	0.0813331i	$0.0259177\pi$
$614$	−2.70004e6	−	4.67661e6i	−0.289034	−	0.500622i
$615$	1.39709e6			0.148948
$616$		0			0
$617$	−1.37397e7			−1.45299			−0.726497	−	0.687170i	$-0.758853\pi$
$617$	−1.37397e7			−1.45299			−0.726497	+	0.687170i	$0.758853\pi$
$618$	−645552.	−	1.11813e6i	−0.0679923	−	0.117766i
$619$	4.35057e6	−	7.53540e6i	0.456372	−	0.790460i	−0.542394	−	0.840124i	$-0.682482\pi$
$619$	4.35057e6	−	7.53540e6i	0.456372	−	0.790460i	0.998766	+	0.0496646i	$0.0158152\pi$
$620$	1.35322e6	−	2.34384e6i	0.141380	−	0.244877i
$621$	378351.	+	655323.i	0.0393700	+	0.0681909i
$622$	5.38152e6			0.557736
$623$		0			0
$624$	225792.			0.0232138
$625$	−2.34870e6	−	4.06807e6i	−0.240507	−	0.416570i
$626$	−512308.	+	887343.i	−0.0522511	+	0.0905015i
$627$	100980.	−	174902.i	0.0102581	−	0.0177675i
$628$	3.02696e6	+	5.24285e6i	0.306272	+	0.530479i
$629$	2.64341e6			0.266402
$630$		0			0
$631$	445412.			0.0445337			0.0222668	−	0.999752i	$-0.492912\pi$
$631$	445412.			0.0445337			0.0222668	+	0.999752i	$0.492912\pi$
$632$	2.72346e6	+	4.71716e6i	0.271224	+	0.469773i
$633$	1.56926e6	−	2.71803e6i	0.155663	−	0.269616i
$634$	−3.69258e6	+	6.39574e6i	−0.364844	+	0.631928i
$635$	636528.	+	1.10250e6i	0.0626445	+	0.108504i
$636$	4.67856e6			0.458637
$637$		0			0
$638$	−657360.			−0.0639369
$639$	1.72700e6	+	2.99125e6i	0.167317	+	0.289802i
$640$	−196608.	+	340535.i	−0.0189737	+	0.0328634i
$641$	4.00059e6	−	6.92923e6i	0.384573	−	0.666101i	−0.607136	−	0.794598i	$-0.707682\pi$
$641$	4.00059e6	−	6.92923e6i	0.384573	−	0.666101i	0.991710	+	0.128497i	$0.0410152\pi$
$642$	1.71817e6	+	2.97596e6i	0.164524	+	0.284964i
$643$	−1.58402e7			−1.51090			−0.755448	−	0.655209i	$-0.772581\pi$
$643$	−1.58402e7			−1.51090			−0.755448	+	0.655209i	$0.772581\pi$
$644$		0			0
$645$	−3.32899e6			−0.315075
$646$	−146880.	−	254404.i	−0.0138478	−	0.0239851i
$647$	−650934.	+	1.12745e6i	−0.0611331	+	0.105886i	−0.894972	−	0.446122i	$-0.852805\pi$
$647$	−650934.	+	1.12745e6i	−0.0611331	+	0.105886i	0.833839	+	0.552008i	$0.186138\pi$
$648$	−209952.	+	363648.i	−0.0196419	+	0.0340207i
$649$	−1.12939e6	−	1.95616e6i	−0.105253	−	0.182303i
$650$	−999208.			−0.0927625
$651$		0			0
$652$	1.67706e6			0.154500
$653$	−3.67074e6	−	6.35791e6i	−0.336877	−	0.583488i	0.646967	−	0.762518i	$-0.276037\pi$
$653$	−3.67074e6	−	6.35791e6i	−0.336877	−	0.583488i	−0.983844	+	0.179031i	$0.942704\pi$
$654$	−3.82000e6	+	6.61643e6i	−0.349236	+	0.604894i
$655$	−831888.	+	1.44087e6i	−0.0757638	+	0.131227i
$656$	−827904.	−	1.43397e6i	−0.0751139	−	0.130101i
$657$	2.73245e6			0.246967
$658$		0			0
$659$	−6.18934e6			−0.555176			−0.277588	−	0.960700i	$-0.589535\pi$
$659$	−6.18934e6			−0.555176			−0.277588	+	0.960700i	$0.589535\pi$
$660$	−114048.	−	197537.i	−0.0101913	−	0.0176518i
$661$	9.83448e6	−	1.70338e7i	0.875484	−	1.51638i	0.0192367	−	0.999815i	$-0.493876\pi$
$661$	9.83448e6	−	1.70338e7i	0.875484	−	1.51638i	0.856247	−	0.516567i	$-0.172790\pi$
$662$	6.66476e6	−	1.15437e7i	0.591071	−	1.02376i
$663$	95256.0	+	164988.i	0.00841605	+	0.0145770i
$664$	−6.83290e6			−0.601429
$665$		0			0
$666$	−3.96511e6			−0.346394
$667$	−1.29231e6	−	2.23835e6i	−0.112474	−	0.194811i
$668$	3.41578e6	−	5.91630e6i	0.296175	−	0.512990i
$669$	−6.61525e6	+	1.14580e7i	−0.571454	+	0.989787i
$670$	−608640.	−	1.05420e6i	−0.0523810	−	0.0907265i
$671$	2.35316e6			0.201765
$672$		0			0
$673$	7.18259e6			0.611285			0.305642	−	0.952146i	$-0.401129\pi$
$673$	7.18259e6			0.611285			0.305642	+	0.952146i	$0.401129\pi$
$674$	3.26961e6	+	5.66313e6i	0.277234	+	0.480183i
$675$	929111.	−	1.60927e6i	0.0784888	−	0.135947i
$676$	2.89351e6	−	5.01171e6i	0.243533	−	0.421812i
$677$	9.45961e6	+	1.63845e7i	0.793234	+	1.37392i	0.923954	+	0.382502i	$0.124938\pi$
$677$	9.45961e6	+	1.63845e7i	0.793234	+	1.37392i	−0.130720	+	0.991419i	$0.541729\pi$
$678$	2.23582e6			0.186794
$679$		0			0
$680$	−331776.			−0.0275152
$681$	2.65302e6	+	4.59517e6i	0.219216	+	0.379694i
$682$	930336.	−	1.61139e6i	0.0765912	−	0.132660i
$683$	−1.06102e7	+	1.83774e7i	−0.870306	+	1.50741i	−0.00862478	+	0.999963i	$0.502745\pi$
$683$	−1.06102e7	+	1.83774e7i	−0.870306	+	1.50741i	−0.861681	+	0.507451i	$0.830588\pi$
$684$	220320.	+	381605.i	0.0180059	+	0.0311870i
$685$	3.11630e6			0.253754
$686$		0			0
$687$	−9.40808e6			−0.760517
$688$	1.97274e6	+	3.41688e6i	0.158890	+	0.275206i
$689$	−1.59201e6	+	2.75744e6i	−0.127761	+	0.221288i
$690$	448416.	−	776679.i	0.0358557	−	0.0621039i
$691$	−8.16379e6	−	1.41401e7i	−0.650424	−	1.12657i	−0.983020	−	0.183498i	$-0.941258\pi$
$691$	−8.16379e6	−	1.41401e7i	−0.650424	−	1.12657i	0.332596	−	0.943069i	$-0.392076\pi$
$692$	5.29709e6			0.420506
$693$		0			0
$694$	−3.36612e6			−0.265296
$695$	1.25227e6	+	2.16900e6i	0.0983415	+	0.170332i
$696$	717120.	−	1.24209e6i	0.0561137	−	0.0971917i
$697$	698544.	−	1.20991e6i	0.0544643	−	0.0943349i
$698$	1.95448e6	+	3.38527e6i	0.151843	+	0.262999i
$699$	5.86100e6			0.453710
$700$		0			0
$701$	−5.40470e6			−0.415409			−0.207705	−	0.978192i	$-0.566599\pi$
$701$	−5.40470e6			−0.415409			−0.207705	+	0.978192i	$0.566599\pi$
$702$	−142884.	−	247482.i	−0.0109431	−	0.0189540i
$703$	−2.08046e6	+	3.60346e6i	−0.158771	+	0.274999i
$704$	−135168.	+	234118.i	−0.0102788	+	0.0178034i
$705$	−2.22523e6	−	3.85421e6i	−0.168617	−	0.292054i
$706$	1.38343e7			1.04459
$707$		0			0
$708$	4.92826e6			0.369496
$709$	−1.10597e7	−	1.91560e7i	−0.826284	−	1.43117i	−0.900934	−	0.433957i	$-0.857117\pi$
$709$	−1.10597e7	−	1.91560e7i	−0.826284	−	1.43117i	0.0746491	−	0.997210i	$-0.476216\pi$
$710$	2.04682e6	−	3.54519e6i	0.152382	−	0.263933i
$711$	3.44687e6	−	5.97016e6i	0.255712	−	0.442906i
$712$	−1.11629e6	−	1.93347e6i	−0.0825232	−	0.142934i
$713$	7.31582e6			0.538939
$714$		0			0
$715$	155232.			0.0113558
$716$	3.20155e6	+	5.54525e6i	0.233388	+	0.404239i
$717$	2.31058e6	−	4.00204e6i	0.167851	−	0.290726i
$718$	6.94602e6	−	1.20309e7i	0.502834	−	0.870935i
$719$	−1.27909e7	−	2.21546e7i	−0.922742	−	1.59824i	−0.795153	−	0.606409i	$-0.792609\pi$
$719$	−1.27909e7	−	2.21546e7i	−0.922742	−	1.59824i	−0.127589	−	0.991827i	$-0.540724\pi$
$720$	497664.			0.0357771
$721$		0			0
$722$	−9.44200e6			−0.674095
$723$	3.12621e6	+	5.41476e6i	0.222419	+	0.385242i
$724$	−4.70478e6	+	8.14892e6i	−0.333575	+	0.577769i
$725$	−3.17350e6	+	5.49667e6i	−0.224230	+	0.388378i
$726$	2.82051e6	+	4.88527e6i	0.198603	+	0.343991i
$727$	−9.29438e6			−0.652205			−0.326103	−	0.945334i	$-0.605735\pi$
$727$	−9.29438e6			−0.652205			−0.326103	+	0.945334i	$0.605735\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−1.61923e6	−	2.80459e6i	−0.112461	−	0.194788i
$731$	−1.66450e6	+	2.88299e6i	−0.115210	+	0.199549i
$732$	−2.56709e6	+	4.44633e6i	−0.177077	+	0.306707i
$733$	−1.70350e6	−	2.95054e6i	−0.117107	−	0.202835i	0.801513	−	0.597977i	$-0.204029\pi$
$733$	−1.70350e6	−	2.95054e6i	−0.117107	−	0.202835i	−0.918620	+	0.395142i	$0.870695\pi$
$734$	1.24797e7			0.854999
$735$		0			0
$736$	−1.06291e6			−0.0723274
$737$	−418440.	−	724759.i	−0.0283769	−	0.0491502i
$738$	−1.04782e6	+	1.81487e6i	−0.0708181	+	0.122661i
$739$	−1.09068e7	+	1.88911e7i	−0.734658	+	1.27246i	0.220216	+	0.975451i	$0.429324\pi$
$739$	−1.09068e7	+	1.88911e7i	−0.734658	+	1.27246i	−0.954873	+	0.297013i	$0.904009\pi$
$740$	2.34970e6	+	4.06979e6i	0.157737	+	0.273208i
$741$	−299880.			−0.0200633
$742$		0			0
$743$	3.79246e6			0.252028			0.126014	−	0.992028i	$-0.459782\pi$
$743$	3.79246e6			0.252028			0.126014	+	0.992028i	$0.459782\pi$
$744$	2.02982e6	+	3.51576e6i	0.134439	+	0.232856i
$745$	−2.60633e6	+	4.51429e6i	−0.172044	+	0.297988i
$746$	4.03346e6	−	6.98616e6i	0.265357	−	0.459612i
$747$	4.32394e6	+	7.48929e6i	0.283517	+	0.491065i
$748$	−228096.			−0.0149061
$749$		0			0
$750$	−4.90234e6			−0.318236
$751$	1.00741e7	+	1.74489e7i	0.651790	+	1.12893i	0.982688	+	0.185267i	$0.0593149\pi$
$751$	1.00741e7	+	1.74489e7i	0.651790	+	1.12893i	−0.330898	+	0.943666i	$0.607352\pi$
$752$	−2.63731e6	+	4.56796e6i	−0.170066	+	0.294563i
$753$	6.28236e6	−	1.08814e7i	0.403771	−	0.699352i
$754$	488040.	+	845310.i	0.0312627	+	0.0541487i
$755$	5.30400e6			0.338638
$756$		0			0
$757$	1.18427e7			0.751126			0.375563	−	0.926797i	$-0.377449\pi$
$757$	1.18427e7			0.751126			0.375563	+	0.926797i	$0.377449\pi$
$758$	1.07617e7	+	1.86397e7i	0.680309	+	1.17833i
$759$	308286.	−	533967.i	0.0194245	−	0.0336442i
$760$	261120.	−	452273.i	0.0163986	−	0.0284032i
$761$	−1.48895e6	−	2.57894e6i	−0.0932008	−	0.161429i	0.815655	−	0.578538i	$-0.196377\pi$
$761$	−1.48895e6	−	2.57894e6i	−0.0932008	−	0.161429i	−0.908856	+	0.417109i	$0.863043\pi$
$762$	−1.90958e6			−0.119138
$763$		0			0
$764$	1.50295e7			0.931559
$765$	209952.	+	363648.i	0.0129708	+	0.0224661i
$766$	−1.61486e6	+	2.79703e6i	−0.0994407	+	0.172236i
$767$	−1.67698e6	+	2.90461e6i	−0.102929	+	0.178279i
$768$	−294912.	−	510803.i	−0.0180422	−	0.0312500i
$769$	−2.02441e7

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)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-12.0000 - 20.7846i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-12.0000 - 20.7846i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-48.0000 + 83.1384i) q^{10} +(-33.0000 + 57.1577i) q^{11} +(-72.0000 - 124.708i) q^{12} +98.0000 q^{13} +216.000 q^{15} +(-128.000 - 221.703i) q^{16} +(108.000 - 187.061i) q^{17} +(-162.000 + 280.592i) q^{18} +(170.000 + 294.449i) q^{19} +384.000 q^{20} +264.000 q^{22} +(519.000 + 898.934i) q^{23} +(-288.000 + 498.831i) q^{24} +(1274.50 - 2207.50i) q^{25} +(-196.000 - 339.482i) q^{26} +729.000 q^{27} -2490.00 q^{29} +(-432.000 - 748.246i) q^{30} +(3524.00 - 6103.75i) q^{31} +(-512.000 + 886.810i) q^{32} +(-297.000 - 514.419i) q^{33} -864.000 q^{34} +1296.00 q^{36} +(6119.00 + 10598.4i) q^{37} +(680.000 - 1177.79i) q^{38} +(-441.000 + 763.834i) q^{39} +(-768.000 - 1330.22i) q^{40} +6468.00 q^{41} -15412.0 q^{43} +(-528.000 - 914.523i) q^{44} +(-972.000 + 1683.55i) q^{45} +(2076.00 - 3595.74i) q^{46} +(-10302.0 - 17843.6i) q^{47} +2304.00 q^{48} -10196.0 q^{50} +(972.000 + 1683.55i) q^{51} +(-784.000 + 1357.93i) q^{52} +(-16245.0 + 28137.2i) q^{53} +(-1458.00 - 2525.33i) q^{54} +1584.00 q^{55} -3060.00 q^{57} +(4980.00 + 8625.61i) q^{58} +(-17112.0 + 29638.9i) q^{59} +(-1728.00 + 2992.98i) q^{60} +(-17827.0 - 30877.3i) q^{61} -28192.0 q^{62} +4096.00 q^{64} +(-1176.00 - 2036.89i) q^{65} +(-1188.00 + 2057.68i) q^{66} +(-6340.00 + 10981.2i) q^{67} +(1728.00 + 2992.98i) q^{68} -9342.00 q^{69} -42642.0 q^{71} +(-2592.00 - 4489.48i) q^{72} +(-16867.0 + 29214.5i) q^{73} +(24476.0 - 42393.7i) q^{74} +(11470.5 + 19867.5i) q^{75} -5440.00 q^{76} +3528.00 q^{78} +(42554.0 + 73705.7i) q^{79} +(-3072.00 + 5320.86i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-12936.0 - 22405.8i) q^{82} -106764. q^{83} -5184.00 q^{85} +(30824.0 + 53388.7i) q^{86} +(11205.0 - 19407.6i) q^{87} +(-2112.00 + 3658.09i) q^{88} +(-17442.0 - 30210.4i) q^{89} +7776.00 q^{90} -16608.0 q^{92} +(31716.0 + 54933.7i) q^{93} +(-41208.0 + 71374.3i) q^{94} +(4080.00 - 7066.77i) q^{95} +(-4608.00 - 7981.29i) q^{96} +18662.0 q^{97} +5346.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 9 q^{3} - 16 q^{4} - 24 q^{5} + 72 q^{6} + 128 q^{8} - 81 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 - 9 * q^3 - 16 * q^4 - 24 * q^5 + 72 * q^6 + 128 * q^8 - 81 * q^9	\( 2 q - 4 q^{2} - 9 q^{3} - 16 q^{4} - 24 q^{5} + 72 q^{6} + 128 q^{8} - 81 q^{9} - 96 q^{10} - 66 q^{11} - 144 q^{12} + 196 q^{13} + 432 q^{15} - 256 q^{16} + 216 q^{17} - 324 q^{18} + 340 q^{19} + 768 q^{20} + 528 q^{22} + 1038 q^{23} - 576 q^{24} + 2549 q^{25} - 392 q^{26} + 1458 q^{27} - 4980 q^{29} - 864 q^{30} + 7048 q^{31} - 1024 q^{32} - 594 q^{33} - 1728 q^{34} + 2592 q^{36} + 12238 q^{37} + 1360 q^{38} - 882 q^{39} - 1536 q^{40} + 12936 q^{41} - 30824 q^{43} - 1056 q^{44} - 1944 q^{45} + 4152 q^{46} - 20604 q^{47} + 4608 q^{48} - 20392 q^{50} + 1944 q^{51} - 1568 q^{52} - 32490 q^{53} - 2916 q^{54} + 3168 q^{55} - 6120 q^{57} + 9960 q^{58} - 34224 q^{59} - 3456 q^{60} - 35654 q^{61} - 56384 q^{62} + 8192 q^{64} - 2352 q^{65} - 2376 q^{66} - 12680 q^{67} + 3456 q^{68} - 18684 q^{69} - 85284 q^{71} - 5184 q^{72} - 33734 q^{73} + 48952 q^{74} + 22941 q^{75} - 10880 q^{76} + 7056 q^{78} + 85108 q^{79} - 6144 q^{80} - 6561 q^{81} - 25872 q^{82} - 213528 q^{83} - 10368 q^{85} + 61648 q^{86} + 22410 q^{87} - 4224 q^{88} - 34884 q^{89} + 15552 q^{90} - 33216 q^{92} + 63432 q^{93} - 82416 q^{94} + 8160 q^{95} - 9216 q^{96} + 37324 q^{97} + 10692 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 9 * q^3 - 16 * q^4 - 24 * q^5 + 72 * q^6 + 128 * q^8 - 81 * q^9 - 96 * q^10 - 66 * q^11 - 144 * q^12 + 196 * q^13 + 432 * q^15 - 256 * q^16 + 216 * q^17 - 324 * q^18 + 340 * q^19 + 768 * q^20 + 528 * q^22 + 1038 * q^23 - 576 * q^24 + 2549 * q^25 - 392 * q^26 + 1458 * q^27 - 4980 * q^29 - 864 * q^30 + 7048 * q^31 - 1024 * q^32 - 594 * q^33 - 1728 * q^34 + 2592 * q^36 + 12238 * q^37 + 1360 * q^38 - 882 * q^39 - 1536 * q^40 + 12936 * q^41 - 30824 * q^43 - 1056 * q^44 - 1944 * q^45 + 4152 * q^46 - 20604 * q^47 + 4608 * q^48 - 20392 * q^50 + 1944 * q^51 - 1568 * q^52 - 32490 * q^53 - 2916 * q^54 + 3168 * q^55 - 6120 * q^57 + 9960 * q^58 - 34224 * q^59 - 3456 * q^60 - 35654 * q^61 - 56384 * q^62 + 8192 * q^64 - 2352 * q^65 - 2376 * q^66 - 12680 * q^67 + 3456 * q^68 - 18684 * q^69 - 85284 * q^71 - 5184 * q^72 - 33734 * q^73 + 48952 * q^74 + 22941 * q^75 - 10880 * q^76 + 7056 * q^78 + 85108 * q^79 - 6144 * q^80 - 6561 * q^81 - 25872 * q^82 - 213528 * q^83 - 10368 * q^85 + 61648 * q^86 + 22410 * q^87 - 4224 * q^88 - 34884 * q^89 + 15552 * q^90 - 33216 * q^92 + 63432 * q^93 - 82416 * q^94 + 8160 * q^95 - 9216 * q^96 + 37324 * q^97 + 10692 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more