LMFDB - Embedded newform 294.6.e.f.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.f.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(12.0000 - 20.7846i) q^{5} -36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

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

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
$5$	12.0000	−	20.7846i	0.214663	−	0.371806i	−0.738506	−	0.674247i	$-0.764468\pi$
$5$	12.0000	−	20.7846i	0.214663	−	0.371806i	0.953168	+	0.302441i	$0.0978015\pi$
$6$	−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	0.821977	−	0.569520i	$-0.192871\pi$
$11$	−33.0000	−	57.1577i	−0.0822304	−	0.142427i	−0.904208	+	0.427093i	$0.859538\pi$
$12$	72.0000	−	124.708i	0.144338	−	0.250000i
$13$	−98.0000			−0.160830			−0.0804151	−	0.996761i	$-0.525625\pi$
$13$	−98.0000			−0.160830			−0.0804151	+	0.996761i	$0.525625\pi$
$14$		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	$-0.195557\pi$
$17$	−108.000	−	187.061i	−0.0906362	−	0.156986i	−0.907779	+	0.419449i	$0.862223\pi$
$18$	−162.000	−	280.592i	−0.117851	−	0.204124i
$19$	−170.000	+	294.449i	−0.108035	+	0.187122i	−0.914974	−	0.403512i	$-0.867789\pi$
$19$	−170.000	+	294.449i	−0.108035	+	0.187122i	0.806939	+	0.590635i	$0.201123\pi$
$20$	−384.000			−0.214663
$21$		0			0
$22$	264.000			0.116291
$23$	519.000	−	898.934i	0.204573	−	0.354330i	−0.745424	−	0.666591i	$-0.767753\pi$
$23$	519.000	−	898.934i	0.204573	−	0.354330i	0.949997	+	0.312260i	$0.101086\pi$
$24$	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	−0.980974	−	0.194137i	$-0.937809\pi$
$31$	−3524.00	−	6103.75i	−0.658615	−	1.14075i	0.322359	−	0.946617i	$-0.395524\pi$
$32$	−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	−0.219994	−	0.975501i	$-0.570604\pi$
$37$	6119.00	−	10598.4i	0.734812	−	1.27273i	0.954806	−	0.297230i	$-0.0960629\pi$
$38$	−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	$-0.597139\pi$
$41$	−6468.00			−0.600911			−0.300456	+	0.953796i	$0.597139\pi$
$42$		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	−0.294637	−	0.955609i	$-0.595199\pi$
$47$	10302.0	−	17843.6i	0.680263	−	1.17825i	0.974900	−	0.222641i	$-0.0714678\pi$
$48$	−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	−0.923230	−	0.384248i	$-0.874461\pi$
$53$	−16245.0	−	28137.2i	−0.794383	−	1.37591i	0.128847	−	0.991664i	$-0.458872\pi$
$54$	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	0.985435	+	0.170051i	$0.0543934\pi$
$59$	17112.0	+	29638.9i	0.639986	+	1.10849i	−0.345449	+	0.938438i	$0.612273\pi$
$60$	−1728.00	−	2992.98i	−0.0619677	−	0.107331i
$61$	17827.0	−	30877.3i	0.613414	−	1.06246i	−0.377247	−	0.926113i	$-0.623129\pi$
$61$	17827.0	−	30877.3i	0.613414	−	1.06246i	0.990661	−	0.136351i	$-0.0435376\pi$
$62$	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	0.766764	−	0.641929i	$-0.221866\pi$
$67$	−6340.00	−	10981.2i	−0.172545	−	0.298857i	−0.939309	+	0.343073i	$0.888532\pi$
$68$	−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	$-0.0458698\pi$
$73$	16867.0	+	29214.5i	0.370451	+	0.641640i	−0.619184	+	0.785246i	$0.712536\pi$
$74$	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	−0.171973	−	0.985102i	$-0.555014\pi$
$79$	42554.0	−	73705.7i	0.767137	−	1.32872i	0.939110	−	0.343618i	$-0.111652\pi$
$80$	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	$-0.176270\pi$
$83$	106764.			1.70110			0.850550	+	0.525895i	$0.176270\pi$
$84$		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	$-0.758345\pi$
$89$	17442.0	−	30210.4i	0.233411	−	0.404280i	0.958810	+	0.284049i	$0.0916779\pi$
$90$	−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	$-0.532106\pi$
$97$	−18662.0			−0.201386			−0.100693	+	0.994918i	$0.532106\pi$
$98$		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	0.949437	+	0.313959i	$0.101655\pi$
$101$	76542.0	+	132575.i	0.746614	+	1.29317i	−0.202822	+	0.979216i	$0.565011\pi$
$102$	3888.00	+	6734.21i	0.0370021	+	0.0640894i
$103$	17932.0	−	31059.1i	0.166547	−	0.288467i	−0.770657	−	0.637250i	$-0.780072\pi$
$103$	17932.0	−	31059.1i	0.166547	−	0.288467i	0.937203	+	0.348783i	$0.113405\pi$
$104$	−6272.00			−0.0568621
$105$		0			0
$106$	129960.			1.12343
$107$	47727.0	−	82665.6i	0.403000	−	0.698016i	−0.591087	−	0.806608i	$-0.701301\pi$
$107$	47727.0	−	82665.6i	0.403000	−	0.698016i	0.994086	+	0.108592i	$0.0346342\pi$
$108$	5832.00	+	10101.3i	0.0481125	+	0.0833333i
$109$	−106111.	−	183790.i	−0.855449	−	1.48168i	−0.876228	−	0.481897i	$-0.839948\pi$
$109$	−106111.	−	183790.i	−0.855449	−	1.48168i	0.0207787	−	0.999784i	$-0.493385\pi$
$110$	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	$-0.776865\pi$
$131$	34662.0	−	60036.3i	0.176472	−	0.305658i	0.940670	+	0.339324i	$0.110198\pi$
$132$	−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	0.679580	−	0.733601i	$-0.262162\pi$
$137$	−64923.0	−	112450.i	−0.295527	−	0.511868i	−0.975107	+	0.221733i	$0.928829\pi$
$138$	−18684.0	+	32361.6i	−0.0835165	+	0.144655i
$139$	104356.			0.458121			0.229061	−	0.973412i	$-0.426435\pi$
$139$	104356.			0.458121			0.229061	+	0.973412i	$0.426435\pi$
$140$		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	−0.993814	−	0.111055i	$-0.964577\pi$
$149$	−108597.	+	188096.i	−0.400730	+	0.694085i	0.593084	+	0.805141i	$0.297910\pi$
$150$	−45882.0	−	79470.0i	−0.166500	−	0.288386i
$151$	−110500.	−	191392.i	−0.394385	−	0.683094i	0.598638	−	0.801020i	$-0.295709\pi$
$151$	−110500.	−	191392.i	−0.394385	−	0.683094i	−0.993022	+	0.117926i	$0.962376\pi$
$152$	−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	−0.990810	−	0.135261i	$-0.956813\pi$
$157$	−189185.	−	327678.i	−0.612544	−	1.06096i	0.378266	−	0.925697i	$-0.376521\pi$
$158$	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	−0.932877	−	0.360195i	$-0.882710\pi$
$163$	−52408.0	+	90773.3i	−0.154500	+	0.267602i	0.778377	+	0.627797i	$0.216043\pi$
$164$	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	$-0.298200\pi$
$167$	426972.			1.18470			0.592350	+	0.805681i	$0.298200\pi$
$168$		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	$-0.695186\pi$
$173$	165534.	−	286713.i	0.420506	−	0.728337i	0.995989	+	0.0894763i	$0.0285193\pi$
$174$	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	0.999280	−	0.0379485i	$-0.0120823\pi$
$179$	200097.	+	346578.i	0.466775	+	0.808479i	−0.532504	+	0.846427i	$0.678749\pi$
$180$	15552.0	−	26936.9i	0.0357771	−	0.0619677i
$181$	−588098.			−1.33430			−0.667150	−	0.744924i	$-0.732486\pi$
$181$	−588098.			−1.33430			−0.667150	+	0.744924i	$0.732486\pi$
$182$		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	−0.150901	+	0.988549i	$0.548217\pi$
$191$	−469671.	+	813494.i	−0.931559	+	1.61351i	−0.780658	+	0.624958i	$0.785116\pi$
$192$	18432.0	+	31925.2i	0.0360844	+	0.0625000i
$193$	−169195.	−	293054.i	−0.326960	−	0.566311i	0.654947	−	0.755675i	$-0.272691\pi$
$193$	−169195.	−	293054.i	−0.326960	−	0.566311i	−0.981907	+	0.189364i	$0.939357\pi$
$194$	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	$-0.108085\pi$
$199$	102232.	+	177071.i	0.183001	+	0.316968i	−0.759900	+	0.650040i	$0.774752\pi$
$200$	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	$-0.954468\pi$
$223$	−1.47006e6			−1.97957			−0.989787	+	0.142554i	$0.954468\pi$
$224$		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	$-0.290637\pi$
$227$	−294780.	−	510574.i	−0.379694	−	0.657649i	−0.991018	+	0.133732i	$0.957304\pi$
$228$	24480.0	+	42400.6i	0.0311870	+	0.0540176i
$229$	−522671.	+	905293.i	−0.658627	+	1.14078i	0.322344	+	0.946623i	$0.395529\pi$
$229$	−522671.	+	905293.i	−0.658627	+	1.14078i	−0.980971	+	0.194153i	$0.937804\pi$
$230$	99648.0			0.124208
$231$		0			0
$232$	−159360.			−0.194383
$233$	−325611.	+	563975.i	−0.392925	+	0.680565i	−0.992834	−	0.119503i	$-0.961870\pi$
$233$	−325611.	+	563975.i	−0.392925	+	0.680565i	0.599909	+	0.800068i	$0.295203\pi$
$234$	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	$-0.292549\pi$
$241$	−347357.	−	601640.i	−0.385242	−	0.667258i	−0.991803	+	0.127779i	$0.959215\pi$
$242$	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	$-0.253472\pi$
$251$	1.39608e6			1.39870			0.699352	+	0.714777i	$0.253472\pi$
$252$		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	$-0.990766\pi$
$257$	−502602.	+	870532.i	−0.474670	+	0.822152i	0.524910	+	0.851158i	$0.324099\pi$
$258$	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	−0.997621	−	0.0689415i	$-0.978038\pi$
$263$	−626505.	−	1.08514e6i	−0.558515	−	0.967377i	0.439105	−	0.898436i	$-0.355296\pi$
$264$	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	−0.951687	−	0.307070i	$-0.900651\pi$
$269$	−880344.	−	1.52480e6i	−0.741774	−	1.28479i	0.209913	−	0.977720i	$-0.432682\pi$
$270$	−34992.0	−	60607.9i	−0.0292119	−	0.0505964i
$271$	385264.	−	667297.i	0.318666	−	0.551945i	−0.661544	−	0.749906i	$-0.730099\pi$
$271$	385264.	−	667297.i	0.318666	−	0.551945i	0.980210	+	0.197961i	$0.0634320\pi$
$272$	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	0.693560	−	0.720399i	$-0.256041\pi$
$277$	−353869.	−	612919.i	−0.277104	−	0.479959i	−0.970664	+	0.240441i	$0.922708\pi$
$278$	−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	0.993243	+	0.116055i	$0.0370249\pi$
$283$	804514.	+	1.39346e6i	0.597128	+	1.03426i	−0.396115	+	0.918201i	$0.629642\pi$
$284$	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	$-0.556289\pi$
$293$	−517020.			−0.351834			−0.175917	+	0.984405i	$0.556289\pi$
$294$		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	$-0.634037\pi$
$307$	−1.35002e6			−0.817512			−0.408756	+	0.912644i	$0.634037\pi$
$308$		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	$-0.0376263\pi$
$311$	672690.	+	1.16513e6i	0.394379	+	0.683085i	−0.598643	+	0.801016i	$0.704293\pi$
$312$	−28224.0	−	48885.4i	−0.0164147	−	0.0284310i
$313$	128077.	−	221836.i	0.0738942	−	0.127988i	−0.826711	−	0.562627i	$-0.809791\pi$
$313$	128077.	−	221836.i	0.0738942	−	0.127988i	0.900605	+	0.434639i	$0.143124\pi$
$314$	1.51348e6			0.866269
$315$		0			0
$316$	−1.36173e6			−0.767137
$317$	−923145.	+	1.59893e6i	−0.515967	+	0.893681i	0.483861	+	0.875145i	$0.339234\pi$
$317$	−923145.	+	1.59893e6i	−0.515967	+	0.893681i	−0.999828	+	0.0185361i	$0.994099\pi$
$318$	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	−0.0573948	−	0.998352i	$-0.518279\pi$
$331$	1.66619e6	−	2.88593e6i	0.835900	−	1.44782i	0.893295	−	0.449470i	$-0.148387\pi$
$332$	−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	0.944447	−	0.328663i	$-0.106598\pi$
$347$	420765.	+	728786.i	0.187593	+	0.324920i	−0.756854	+	0.653583i	$0.773265\pi$
$348$	−179280.	+	310522.i	−0.0793567	+	0.137450i
$349$	977242.			0.429476			0.214738	−	0.976672i	$-0.431110\pi$
$349$	977242.			0.429476			0.214738	+	0.976672i	$0.431110\pi$
$350$		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	0.953110	+	0.302623i	$0.0978623\pi$
$353$	1.72928e6	+	2.99521e6i	0.738634	+	1.27935i	−0.214476	+	0.976729i	$0.568804\pi$
$354$	−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	−0.253324	−	0.967382i	$-0.581524\pi$
$359$	1.73651e6	−	3.00771e6i	0.711115	−	1.23169i	0.964439	−	0.264306i	$-0.0851429\pi$
$360$	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	0.992118	+	0.125304i	$0.0399906\pi$
$367$	1.55997e6	+	2.70194e6i	0.604575	+	1.04716i	−0.387543	+	0.921852i	$0.626676\pi$
$368$	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	−0.615096	−	0.788452i	$-0.710883\pi$
$373$	1.00836e6	−	1.74654e6i	0.375272	−	0.649989i	0.990368	+	0.138463i	$0.0442161\pi$
$374$	−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	$-0.788420\pi$
$383$	403716.	−	699257.i	0.140630	−	0.243579i	0.927734	+	0.373242i	$0.121754\pi$
$384$	−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	0.781646	−	0.623722i	$-0.214380\pi$
$389$	−445695.	−	771966.i	−0.149336	−	0.258657i	−0.930982	+	0.365065i	$0.881047\pi$
$390$	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	$-0.776088\pi$
$397$	561727.	−	972940.i	0.178875	−	0.309820i	0.941495	+	0.337026i	$0.109421\pi$
$398$	−817856.			−0.258803
$399$		0			0
$400$	−652544.			−0.203920
$401$	−860187.	+	1.48989e6i	−0.267136	+	0.462693i	−0.968121	−	0.250483i	$-0.919411\pi$
$401$	−860187.	+	1.48989e6i	−0.267136	+	0.462693i	0.700985	+	0.713176i	$0.252744\pi$
$402$	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	$-0.163033\pi$
$409$	38623.0	+	66897.0i	0.0114166	+	0.0197742i	−0.860261	+	0.509855i	$0.829699\pi$
$410$	−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	$-0.242137\pi$
$419$	5.20615e6			1.44871			0.724356	+	0.689427i	$0.242137\pi$
$420$		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	0.901208	−	0.433388i	$-0.142682\pi$
$431$	290313.	+	502837.i	0.0752789	+	0.130387i	−0.825929	+	0.563775i	$0.809349\pi$
$432$	93312.0	−	161621.i	0.0240563	−	0.0416667i
$433$	−4.15087e6			−1.06395			−0.531973	−	0.846761i	$-0.678549\pi$
$433$	−4.15087e6			−1.06395			−0.531973	+	0.846761i	$0.678549\pi$
$434$		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	$-0.673627\pi$
$439$	1.94204e6	−	3.36371e6i	0.480946	−	0.833022i	0.999761	+	0.0218641i	$0.00696011\pi$
$440$	−101376.			−0.0249634
$441$		0			0
$442$	−84672.0			−0.0206150
$443$	1.15749e6	−	2.00484e6i	0.280226	−	0.485366i	−0.691214	−	0.722650i	$-0.742924\pi$
$443$	1.15749e6	−	2.00484e6i	0.280226	−	0.485366i	0.971440	+	0.237284i	$0.0762571\pi$
$444$	−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	0.169887	+	0.985464i	$0.445660\pi$
$457$	−3.43108e6	+	5.94280e6i	−0.768493	+	1.33107i	−0.938380	+	0.345605i	$0.887674\pi$
$458$	−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	$-0.605575\pi$
$461$	−2.97167e6			−0.651250			−0.325625	+	0.945499i	$0.605575\pi$
$462$		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	−0.00211530	+	0.999998i	$0.500673\pi$
$467$	−4.08650e6	+	7.07803e6i	−0.867081	+	1.50183i	−0.864966	+	0.501831i	$0.832660\pi$
$468$	−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	$-0.0916845\pi$
$479$	1.17199e6	+	2.02994e6i	0.233391	+	0.404245i	−0.725413	+	0.688314i	$0.758351\pi$
$480$	−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	0.850490	−	0.525991i	$-0.176306\pi$
$487$	−158464.	−	274468.i	−0.0302767	−	0.0524407i	−0.880767	+	0.473550i	$0.842972\pi$
$488$	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	−0.559934	−	0.828538i	$-0.689173\pi$
$499$	2.43387e6	−	4.21558e6i	0.437568	−	0.757890i	0.997501	+	0.0706479i	$0.0225067\pi$
$500$	−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	$-0.511976\pi$
$503$	−426888.			−0.0752305			−0.0376153	+	0.999292i	$0.511976\pi$
$504$		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	0.110496	+	0.993877i	$0.464756\pi$
$509$	−4.70810e6	+	8.15468e6i	−0.805474	+	1.39512i	−0.915971	+	0.401246i	$0.868577\pi$
$510$	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	$-0.119216\pi$
$521$	920196.	+	1.59383e6i	0.148520	+	0.257245i	−0.782160	+	0.623077i	$0.785882\pi$
$522$	403380.	+	698675.i	0.0647945	+	0.112227i
$523$	−489554.	+	847932.i	−0.0782612	+	0.135552i	−0.902500	−	0.430690i	$-0.858270\pi$
$523$	−489554.	+	847932.i	−0.0782612	+	0.135552i	0.824239	+	0.566243i	$0.191603\pi$
$524$	−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	−0.997522	−	0.0703538i	$-0.977587\pi$
$541$	−2.98058e6	+	5.16252e6i	−0.437833	+	0.758349i	0.559689	+	0.828703i	$0.310921\pi$
$542$	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	0.950319	−	0.311277i	$-0.100757\pi$
$557$	1.50533e6	+	2.60731e6i	0.205586	+	0.356086i	−0.744733	+	0.667362i	$0.767423\pi$
$558$	−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	0.930987	+	0.365051i	$0.118949\pi$
$563$	5.87863e6	+	1.01821e7i	0.781637	+	1.35384i	−0.149350	+	0.988784i	$0.547718\pi$
$564$	−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	0.0276496	+	0.999618i	$0.491198\pi$
$569$	−6.57891e6	+	1.13950e7i	−0.851870	+	1.47548i	−0.879519	+	0.475864i	$0.842136\pi$
$570$	−146880.	−	254404.i	−0.0189354	−	0.0327972i
$571$	5.16722e6	+	8.94989e6i	0.663234	+	1.14875i	0.979761	+	0.200171i	$0.0641499\pi$
$571$	5.16722e6	+	8.94989e6i	0.663234	+	1.14875i	−0.316527	+	0.948583i	$0.602517\pi$
$572$	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	$-0.330676\pi$
$577$	−3.94067e6	−	6.82544e6i	−0.492754	−	0.853475i	−0.999965	+	0.00834679i	$0.997343\pi$
$578$	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	$-0.489426\pi$
$587$	554568.			0.0664293			0.0332146	+	0.999448i	$0.489426\pi$
$588$		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	0.461646	+	0.887064i	$0.347259\pi$
$593$	−4.60184e6	+	7.97063e6i	−0.537397	+	0.930799i	−0.999043	+	0.0437346i	$0.986074\pi$
$594$	−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	0.513459	−	0.858114i	$-0.328364\pi$
$599$	−4.27148e6	−	7.39841e6i	−0.486419	−	0.842503i	−0.999878	+	0.0156113i	$0.995031\pi$
$600$	−734112.	+	1.27152e6i	−0.0832500	+	0.144193i
$601$	9.61555e6			1.08590			0.542948	−	0.839767i	$-0.317308\pi$
$601$	9.61555e6			1.08590			0.542948	+	0.839767i	$0.317308\pi$
$602$		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	$-0.794443\pi$
$607$	1.10632e6	−	1.91620e6i	0.121873	−	0.211091i	0.920506	+	0.390727i	$0.127776\pi$
$608$	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	0.996687	−	0.0813331i	$-0.0259177\pi$
$613$	3.98108e6	+	6.89543e6i	0.427907	+	0.741157i	−0.568780	+	0.822490i	$0.692584\pi$
$614$	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	$-0.317518\pi$
$619$	−4.35057e6	−	7.53540e6i	−0.456372	−	0.790460i	−0.998766	+	0.0496646i	$0.984185\pi$
$620$	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	0.991710	−	0.128497i	$-0.0410152\pi$
$641$	4.00059e6	+	6.92923e6i	0.384573	+	0.666101i	−0.607136	+	0.794598i	$0.707682\pi$
$642$	−1.71817e6	+	2.97596e6i	−0.164524	+	0.284964i
$643$	1.58402e7			1.51090			0.755448	−	0.655209i	$-0.227419\pi$
$643$	1.58402e7			1.51090			0.755448	+	0.655209i	$0.227419\pi$
$644$		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	$-0.147195\pi$
$647$	650934.	+	1.12745e6i	0.0611331	+	0.105886i	−0.833839	+	0.552008i	$0.813862\pi$
$648$	−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	−0.983844	−	0.179031i	$-0.942704\pi$
$653$	−3.67074e6	+	6.35791e6i	−0.336877	+	0.583488i	0.646967	+	0.762518i	$0.276037\pi$
$654$	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	−0.856247	−	0.516567i	$-0.827210\pi$
$661$	−9.83448e6	−	1.70338e7i	−0.875484	−	1.51638i	−0.0192367	−	0.999815i	$-0.506124\pi$
$662$	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	0.130720	+	0.991419i	$0.458271\pi$
$677$	−9.45961e6	+	1.63845e7i	−0.793234	+	1.37392i	−0.923954	+	0.382502i	$0.875062\pi$
$678$	−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	−0.861681	−	0.507451i	$-0.830588\pi$
$683$	−1.06102e7	−	1.83774e7i	−0.870306	−	1.50741i	−0.00862478	−	0.999963i	$-0.502745\pi$
$684$	−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	−0.332596	−	0.943069i	$-0.607924\pi$
$691$	8.16379e6	−	1.41401e7i	0.650424	−	1.12657i	0.983020	−	0.183498i	$-0.0587422\pi$
$692$	−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	0.0746491	+	0.997210i	$0.476216\pi$
$709$	−1.10597e7	+	1.91560e7i	−0.826284	+	1.43117i	−0.900934	+	0.433957i	$0.857117\pi$
$710$	−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	0.127589	−	0.991827i	$-0.459276\pi$
$719$	1.27909e7	−	2.21546e7i	0.922742	−	1.59824i	0.795153	−	0.606409i	$-0.207391\pi$
$720$	−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	$-0.394265\pi$
$727$	9.29438e6			0.652205			0.326103	+	0.945334i	$0.394265\pi$
$728$		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	$-0.795971\pi$
$733$	1.70350e6	−	2.95054e6i	0.117107	−	0.202835i	0.918620	+	0.395142i	$0.129305\pi$
$734$	−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	−0.954873	−	0.297013i	$-0.904009\pi$
$739$	−1.09068e7	−	1.88911e7i	−0.734658	−	1.27246i	0.220216	−	0.975451i	$-0.429324\pi$
$740$	−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	−0.330898	−	0.943666i	$-0.607352\pi$
$751$	1.00741e7	−	1.74489e7i	0.651790	−	1.12893i	0.982688	−	0.185267i	$-0.0593149\pi$
$752$	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	$-0.803623\pi$
$761$	1.48895e6	−	2.57894e6i	0.0932008	−	0.161429i	0.908856	+	0.417109i	$0.136957\pi$
$762$	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			1.23447			0.617237	−	0.786777i	$-0.288252\pi$
$769$	2.02441e7			1.23447			0.617237	+	0.786777i	$0.288252\pi$
$770$

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

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