LMFDB - Embedded newform 294.6.e.i.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.i.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-13.0000 - 22.5167i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(2.00000 + 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-13.0000 - 22.5167i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(52.0000 - 90.0666i) q^{10} +(-332.000 + 575.041i) q^{11} +(-72.0000 - 124.708i) q^{12} +318.000 q^{13} +234.000 q^{15} +(-128.000 - 221.703i) q^{16} +(-791.000 + 1370.05i) q^{17} +(162.000 - 280.592i) q^{18} +(-118.000 - 204.382i) q^{19} +416.000 q^{20} -2656.00 q^{22} +(-1106.00 - 1915.65i) q^{23} +(288.000 - 498.831i) q^{24} +(1224.50 - 2120.90i) q^{25} +(636.000 + 1101.58i) q^{26} +729.000 q^{27} -4954.00 q^{29} +(468.000 + 810.600i) q^{30} +(3564.00 - 6173.03i) q^{31} +(512.000 - 886.810i) q^{32} +(-2988.00 - 5175.37i) q^{33} -6328.00 q^{34} +1296.00 q^{36} +(-2179.00 - 3774.14i) q^{37} +(472.000 - 817.528i) q^{38} +(-1431.00 + 2478.56i) q^{39} +(832.000 + 1441.07i) q^{40} +10542.0 q^{41} -8452.00 q^{43} +(-5312.00 - 9200.65i) q^{44} +(-1053.00 + 1823.85i) q^{45} +(4424.00 - 7662.59i) q^{46} +(-2676.00 - 4634.97i) q^{47} +2304.00 q^{48} +9796.00 q^{50} +(-7119.00 - 12330.5i) q^{51} +(-2544.00 + 4406.34i) q^{52} +(16677.0 - 28885.4i) q^{53} +(1458.00 + 2525.33i) q^{54} +17264.0 q^{55} +2124.00 q^{57} +(-9908.00 - 17161.2i) q^{58} +(7718.00 - 13368.0i) q^{59} +(-1872.00 + 3242.40i) q^{60} +(18381.0 + 31836.8i) q^{61} +28512.0 q^{62} +4096.00 q^{64} +(-4134.00 - 7160.30i) q^{65} +(11952.0 - 20701.5i) q^{66} +(-20486.0 + 35482.8i) q^{67} +(-12656.0 - 21920.8i) q^{68} +19908.0 q^{69} -9092.00 q^{71} +(2592.00 + 4489.48i) q^{72} +(36727.0 - 63613.0i) q^{73} +(8716.00 - 15096.6i) q^{74} +(11020.5 + 19088.1i) q^{75} +3776.00 q^{76} -11448.0 q^{78} +(-44700.0 - 77422.7i) q^{79} +(-3328.00 + 5764.27i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(21084.0 + 36518.6i) q^{82} -6428.00 q^{83} +41132.0 q^{85} +(-16904.0 - 29278.6i) q^{86} +(22293.0 - 38612.6i) q^{87} +(21248.0 - 36802.6i) q^{88} +(61329.0 + 106225. i) q^{89} -8424.00 q^{90} +35392.0 q^{92} +(32076.0 + 55557.3i) q^{93} +(10704.0 - 18539.9i) q^{94} +(-3068.00 + 5313.93i) q^{95} +(4608.00 + 7981.29i) q^{96} +21370.0 q^{97} +53784.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 9 q^{3} - 16 q^{4} - 26 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 - 26 * q^5 - 72 * q^6 - 128 * q^8 - 81 * q^9	\( 2 q + 4 q^{2} - 9 q^{3} - 16 q^{4} - 26 q^{5} - 72 q^{6} - 128 q^{8} - 81 q^{9} + 104 q^{10} - 664 q^{11} - 144 q^{12} + 636 q^{13} + 468 q^{15} - 256 q^{16} - 1582 q^{17} + 324 q^{18} - 236 q^{19} + 832 q^{20} - 5312 q^{22} - 2212 q^{23} + 576 q^{24} + 2449 q^{25} + 1272 q^{26} + 1458 q^{27} - 9908 q^{29} + 936 q^{30} + 7128 q^{31} + 1024 q^{32} - 5976 q^{33} - 12656 q^{34} + 2592 q^{36} - 4358 q^{37} + 944 q^{38} - 2862 q^{39} + 1664 q^{40} + 21084 q^{41} - 16904 q^{43} - 10624 q^{44} - 2106 q^{45} + 8848 q^{46} - 5352 q^{47} + 4608 q^{48} + 19592 q^{50} - 14238 q^{51} - 5088 q^{52} + 33354 q^{53} + 2916 q^{54} + 34528 q^{55} + 4248 q^{57} - 19816 q^{58} + 15436 q^{59} - 3744 q^{60} + 36762 q^{61} + 57024 q^{62} + 8192 q^{64} - 8268 q^{65} + 23904 q^{66} - 40972 q^{67} - 25312 q^{68} + 39816 q^{69} - 18184 q^{71} + 5184 q^{72} + 73454 q^{73} + 17432 q^{74} + 22041 q^{75} + 7552 q^{76} - 22896 q^{78} - 89400 q^{79} - 6656 q^{80} - 6561 q^{81} + 42168 q^{82} - 12856 q^{83} + 82264 q^{85} - 33808 q^{86} + 44586 q^{87} + 42496 q^{88} + 122658 q^{89} - 16848 q^{90} + 70784 q^{92} + 64152 q^{93} + 21408 q^{94} - 6136 q^{95} + 9216 q^{96} + 42740 q^{97} + 107568 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 9 * q^3 - 16 * q^4 - 26 * q^5 - 72 * q^6 - 128 * q^8 - 81 * q^9 + 104 * q^10 - 664 * q^11 - 144 * q^12 + 636 * q^13 + 468 * q^15 - 256 * q^16 - 1582 * q^17 + 324 * q^18 - 236 * q^19 + 832 * q^20 - 5312 * q^22 - 2212 * q^23 + 576 * q^24 + 2449 * q^25 + 1272 * q^26 + 1458 * q^27 - 9908 * q^29 + 936 * q^30 + 7128 * q^31 + 1024 * q^32 - 5976 * q^33 - 12656 * q^34 + 2592 * q^36 - 4358 * q^37 + 944 * q^38 - 2862 * q^39 + 1664 * q^40 + 21084 * q^41 - 16904 * q^43 - 10624 * q^44 - 2106 * q^45 + 8848 * q^46 - 5352 * q^47 + 4608 * q^48 + 19592 * q^50 - 14238 * q^51 - 5088 * q^52 + 33354 * q^53 + 2916 * q^54 + 34528 * q^55 + 4248 * q^57 - 19816 * q^58 + 15436 * q^59 - 3744 * q^60 + 36762 * q^61 + 57024 * q^62 + 8192 * q^64 - 8268 * q^65 + 23904 * q^66 - 40972 * q^67 - 25312 * q^68 + 39816 * q^69 - 18184 * q^71 + 5184 * q^72 + 73454 * q^73 + 17432 * q^74 + 22041 * q^75 + 7552 * q^76 - 22896 * q^78 - 89400 * q^79 - 6656 * q^80 - 6561 * q^81 + 42168 * q^82 - 12856 * q^83 + 82264 * q^85 - 33808 * q^86 + 44586 * q^87 + 42496 * q^88 + 122658 * q^89 - 16848 * q^90 + 70784 * q^92 + 64152 * q^93 + 21408 * q^94 - 6136 * q^95 + 9216 * q^96 + 42740 * q^97 + 107568 * 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
$5$	−13.0000	−	22.5167i	−0.232551	−	0.402790i	0.726007	−	0.687687i	$-0.241374\pi$
$5$	−13.0000	−	22.5167i	−0.232551	−	0.402790i	−0.958558	+	0.284897i	$0.908041\pi$
$6$	−36.0000			−0.408248
$7$		0			0
$7$		0			0
$8$	−64.0000			−0.353553
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	52.0000	−	90.0666i	0.164438	−	0.284816i
$11$	−332.000	+	575.041i	−0.827287	+	1.43290i	0.0728713	+	0.997341i	$0.476784\pi$
$11$	−332.000	+	575.041i	−0.827287	+	1.43290i	−0.900159	+	0.435562i	$0.856550\pi$
$12$	−72.0000	−	124.708i	−0.144338	−	0.250000i
$13$	318.000			0.521878			0.260939	−	0.965355i	$-0.415968\pi$
$13$	318.000			0.521878			0.260939	+	0.965355i	$0.415968\pi$
$14$		0			0
$15$	234.000			0.268527
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	−791.000	+	1370.05i	−0.663826	+	1.14978i	0.315776	+	0.948834i	$0.397735\pi$
$17$	−791.000	+	1370.05i	−0.663826	+	1.14978i	−0.979602	+	0.200946i	$0.935598\pi$
$18$	162.000	−	280.592i	0.117851	−	0.204124i
$19$	−118.000	−	204.382i	−0.0749891	−	0.129885i	0.826092	−	0.563535i	$-0.190559\pi$
$19$	−118.000	−	204.382i	−0.0749891	−	0.129885i	−0.901082	+	0.433650i	$0.857226\pi$
$20$	416.000			0.232551
$21$		0			0
$22$	−2656.00			−1.16996
$23$	−1106.00	−	1915.65i	−0.435949	−	0.755086i	0.561424	−	0.827529i	$-0.310254\pi$
$23$	−1106.00	−	1915.65i	−0.435949	−	0.755086i	−0.997373	+	0.0724429i	$0.976920\pi$
$24$	288.000	−	498.831i	0.102062	−	0.176777i
$25$	1224.50	−	2120.90i	0.391840	−	0.678687i
$26$	636.000	+	1101.58i	0.184512	+	0.319584i
$27$	729.000			0.192450
$28$		0			0
$29$	−4954.00			−1.09386			−0.546929	−	0.837179i	$-0.684203\pi$
$29$	−4954.00			−1.09386			−0.546929	+	0.837179i	$0.684203\pi$
$30$	468.000	+	810.600i	0.0949386	+	0.164438i
$31$	3564.00	−	6173.03i	0.666091	−	1.15370i	−0.312897	−	0.949787i	$-0.601300\pi$
$31$	3564.00	−	6173.03i	0.666091	−	1.15370i	0.978988	−	0.203916i	$-0.0653670\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$	−2988.00	−	5175.37i	−0.477635	−	0.827287i
$34$	−6328.00			−0.938792
$35$		0			0
$36$	1296.00			0.166667
$37$	−2179.00	−	3774.14i	−0.261669	−	0.453225i	0.705016	−	0.709191i	$-0.250940\pi$
$37$	−2179.00	−	3774.14i	−0.261669	−	0.453225i	−0.966686	+	0.255966i	$0.917606\pi$
$38$	472.000	−	817.528i	0.0530253	−	0.0918425i
$39$	−1431.00	+	2478.56i	−0.150653	+	0.260939i
$40$	832.000	+	1441.07i	0.0822192	+	0.142408i
$41$	10542.0			0.979407			0.489704	−	0.871889i	$-0.337105\pi$
$41$	10542.0			0.979407			0.489704	+	0.871889i	$0.337105\pi$
$42$		0			0
$43$	−8452.00			−0.697089			−0.348545	−	0.937292i	$-0.613324\pi$
$43$	−8452.00			−0.697089			−0.348545	+	0.937292i	$0.613324\pi$
$44$	−5312.00	−	9200.65i	−0.413644	−	0.716452i
$45$	−1053.00	+	1823.85i	−0.0775170	+	0.134263i
$46$	4424.00	−	7662.59i	0.308262	−	0.533926i
$47$	−2676.00	−	4634.97i	−0.176702	−	0.306057i	0.764047	−	0.645161i	$-0.223210\pi$
$47$	−2676.00	−	4634.97i	−0.176702	−	0.306057i	−0.940749	+	0.339104i	$0.889876\pi$
$48$	2304.00			0.144338
$49$		0			0
$50$	9796.00			0.554145
$51$	−7119.00	−	12330.5i	−0.383260	−	0.663826i
$52$	−2544.00	+	4406.34i	−0.130469	+	0.225980i
$53$	16677.0	−	28885.4i	0.815508	−	1.41250i	−0.0934545	−	0.995624i	$-0.529791\pi$
$53$	16677.0	−	28885.4i	0.815508	−	1.41250i	0.908963	−	0.416878i	$-0.136876\pi$
$54$	1458.00	+	2525.33i	0.0680414	+	0.117851i
$55$	17264.0			0.769546
$56$		0			0
$57$	2124.00			0.0865899
$58$	−9908.00	−	17161.2i	−0.386737	−	0.669849i
$59$	7718.00	−	13368.0i	0.288652	−	0.499960i	−0.684836	−	0.728697i	$-0.740126\pi$
$59$	7718.00	−	13368.0i	0.288652	−	0.499960i	0.973488	+	0.228737i	$0.0734596\pi$
$60$	−1872.00	+	3242.40i	−0.0671317	+	0.116276i
$61$	18381.0	+	31836.8i	0.632477	+	1.09548i	0.987044	+	0.160451i	$0.0512949\pi$
$61$	18381.0	+	31836.8i	0.632477	+	1.09548i	−0.354567	+	0.935031i	$0.615372\pi$
$62$	28512.0			0.941995
$63$		0			0
$64$	4096.00			0.125000
$65$	−4134.00	−	7160.30i	−0.121363	−	0.210207i
$66$	11952.0	−	20701.5i	0.337739	−	0.584980i
$67$	−20486.0	+	35482.8i	−0.557532	+	0.965675i	0.440169	+	0.897915i	$0.354918\pi$
$67$	−20486.0	+	35482.8i	−0.557532	+	0.965675i	−0.997702	+	0.0677597i	$0.978415\pi$
$68$	−12656.0	−	21920.8i	−0.331913	−	0.574890i
$69$	19908.0			0.503390
$70$		0			0
$71$	−9092.00			−0.214049			−0.107025	−	0.994256i	$-0.534132\pi$
$71$	−9092.00			−0.214049			−0.107025	+	0.994256i	$0.534132\pi$
$72$	2592.00	+	4489.48i	0.0589256	+	0.102062i
$73$	36727.0	−	63613.0i	0.806637	−	1.39714i	−0.108543	−	0.994092i	$-0.534618\pi$
$73$	36727.0	−	63613.0i	0.806637	−	1.39714i	0.915180	−	0.403045i	$-0.132048\pi$
$74$	8716.00	−	15096.6i	0.185028	−	0.320478i
$75$	11020.5	+	19088.1i	0.226229	+	0.391840i
$76$	3776.00			0.0749891
$77$		0			0
$78$	−11448.0			−0.213056
$79$	−44700.0	−	77422.7i	−0.805823	−	1.39573i	−0.915734	−	0.401785i	$-0.868390\pi$
$79$	−44700.0	−	77422.7i	−0.805823	−	1.39573i	0.109911	−	0.993941i	$-0.464944\pi$
$80$	−3328.00	+	5764.27i	−0.0581378	+	0.100698i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	21084.0	+	36518.6i	0.346273	+	0.599762i
$83$	−6428.00			−0.102419			−0.0512095	−	0.998688i	$-0.516308\pi$
$83$	−6428.00			−0.102419			−0.0512095	+	0.998688i	$0.516308\pi$
$84$		0			0
$85$	41132.0			0.617494
$86$	−16904.0	−	29278.6i	−0.246458	−	0.426878i
$87$	22293.0	−	38612.6i	0.315770	−	0.546929i
$88$	21248.0	−	36802.6i	0.292490	−	0.506608i
$89$	61329.0	+	106225.i	0.820712	+	1.42152i	0.905153	+	0.425087i	$0.139756\pi$
$89$	61329.0	+	106225.i	0.820712	+	1.42152i	−0.0844405	+	0.996429i	$0.526910\pi$
$90$	−8424.00			−0.109626
$91$		0			0
$92$	35392.0			0.435949
$93$	32076.0	+	55557.3i	0.384568	+	0.666091i
$94$	10704.0	−	18539.9i	0.124947	−	0.216415i
$95$	−3068.00	+	5313.93i	−0.0348776	+	0.0604097i
$96$	4608.00	+	7981.29i	0.0510310	+	0.0883883i
$97$	21370.0			0.230608			0.115304	−	0.993330i	$-0.463216\pi$
$97$	21370.0			0.230608			0.115304	+	0.993330i	$0.463216\pi$
$98$		0			0
$99$	53784.0			0.551525
$100$	19592.0	+	33934.3i	0.195920	+	0.339343i
$101$	18407.0	−	31881.9i	0.179548	−	0.310986i	−0.762178	−	0.647367i	$-0.775870\pi$
$101$	18407.0	−	31881.9i	0.179548	−	0.310986i	0.941726	+	0.336382i	$0.109203\pi$
$102$	28476.0	−	49321.9i	0.271006	−	0.469396i
$103$	−52264.0	−	90523.9i	−0.485411	−	0.840756i	0.514448	−	0.857521i	$-0.327997\pi$
$103$	−52264.0	−	90523.9i	−0.485411	−	0.840756i	−0.999859	+	0.0167648i	$0.994663\pi$
$104$	−20352.0			−0.184512
$105$		0			0
$106$	133416.			1.15330
$107$	−107220.	−	185710.i	−0.905350	−	1.56811i	−0.820447	−	0.571722i	$-0.806275\pi$
$107$	−107220.	−	185710.i	−0.905350	−	1.56811i	−0.0849026	−	0.996389i	$-0.527058\pi$
$108$	−5832.00	+	10101.3i	−0.0481125	+	0.0833333i
$109$	−14399.0	+	24939.8i	−0.116082	+	0.201060i	−0.918212	−	0.396090i	$-0.870367\pi$
$109$	−14399.0	+	24939.8i	−0.116082	+	0.201060i	0.802130	+	0.597150i	$0.203700\pi$
$110$	34528.0	+	59804.3i	0.272076	+	0.471249i
$111$	39222.0			0.302150
$112$		0			0
$113$	−56014.0			−0.412668			−0.206334	−	0.978482i	$-0.566153\pi$
$113$	−56014.0			−0.412668			−0.206334	+	0.978482i	$0.566153\pi$
$114$	4248.00	+	7357.75i	0.0306142	+	0.0530253i
$115$	−28756.0	+	49806.9i	−0.202761	+	0.351192i
$116$	39632.0	−	68644.6i	0.273465	−	0.473654i
$117$	−12879.0	−	22307.1i	−0.0869796	−	0.150653i
$118$	61744.0			0.408216
$119$		0			0
$120$	−14976.0			−0.0949386
$121$	−139922.	−	242353.i	−0.868809	−	1.50482i
$122$	−73524.0	+	127347.i	−0.447229	+	0.774623i
$123$	−47439.0	+	82166.8i	−0.282731	+	0.489704i
$124$	57024.0	+	98768.5i	0.333045	+	0.576852i
$125$	−144924.			−0.829593
$126$		0			0
$127$	185400.			1.02000			0.510000	−	0.860174i	$-0.329645\pi$
$127$	185400.			1.02000			0.510000	+	0.860174i	$0.329645\pi$
$128$	8192.00	+	14189.0i	0.0441942	+	0.0765466i
$129$	38034.0	−	65876.8i	0.201232	−	0.348545i
$130$	16536.0	−	28641.2i	0.0858168	−	0.148639i
$131$	−32266.0	−	55886.4i	−0.164273	−	0.284530i	0.772124	−	0.635472i	$-0.219195\pi$
$131$	−32266.0	−	55886.4i	−0.164273	−	0.284530i	−0.936397	+	0.350943i	$0.885861\pi$
$132$	95616.0			0.477635
$133$		0			0
$134$	−163888.			−0.788470
$135$	−9477.00	−	16414.6i	−0.0447545	−	0.0775170i
$136$	50624.0	−	87683.3i	0.234698	−	0.406509i
$137$	−76465.0	+	132441.i	−0.348066	+	0.602868i	−0.985906	−	0.167301i	$-0.946495\pi$
$137$	−76465.0	+	132441.i	−0.348066	+	0.602868i	0.637840	+	0.770169i	$0.279828\pi$
$138$	39816.0	+	68963.3i	0.177975	+	0.308262i
$139$	−343460.			−1.50778			−0.753892	−	0.656998i	$-0.771826\pi$
$139$	−343460.			−1.50778			−0.753892	+	0.656998i	$0.771826\pi$
$140$		0			0
$141$	48168.0			0.204038
$142$	−18184.0	−	31495.6i	−0.0756778	−	0.131078i
$143$	−105576.	+	182863.i	−0.431743	+	0.747800i
$144$	−10368.0	+	17957.9i	−0.0416667	+	0.0721688i
$145$	64402.0	+	111548.i	0.254378	+	0.440595i
$146$	293816.			1.14076
$147$		0			0
$148$	69728.0			0.261669
$149$	87429.0	+	151431.i	0.322619	+	0.558792i	0.981028	−	0.193868i	$-0.0621034\pi$
$149$	87429.0	+	151431.i	0.322619	+	0.558792i	−0.658409	+	0.752661i	$0.728770\pi$
$150$	−44082.0	+	76352.3i	−0.159968	+	0.277073i
$151$	226276.	−	391922.i	0.807600	−	1.39880i	−0.106922	−	0.994267i	$-0.534100\pi$
$151$	226276.	−	391922.i	0.807600	−	1.39880i	0.914522	−	0.404536i	$-0.132567\pi$
$152$	7552.00	+	13080.4i	0.0265126	+	0.0459212i
$153$	128142.			0.442551
$154$		0			0
$155$	−185328.			−0.619601
$156$	−22896.0	−	39657.0i	−0.0753266	−	0.130469i
$157$	249533.	−	432204.i	0.807940	−	1.39939i	−0.106349	−	0.994329i	$-0.533916\pi$
$157$	249533.	−	432204.i	0.807940	−	1.39939i	0.914289	−	0.405063i	$-0.132751\pi$
$158$	178800.	−	309691.i	0.569803	−	0.986928i
$159$	150093.	+	259969.i	0.470834	+	0.815508i
$160$	−26624.0			−0.0822192
$161$		0			0
$162$	−26244.0			−0.0785674
$163$	237794.	+	411871.i	0.701022	+	1.21421i	0.968108	+	0.250534i	$0.0806060\pi$
$163$	237794.	+	411871.i	0.701022	+	1.21421i	−0.267086	+	0.963673i	$0.586061\pi$
$164$	−84336.0	+	146074.i	−0.244852	+	0.424096i
$165$	−77688.0	+	134560.i	−0.222149	+	0.384773i
$166$	−12856.0	−	22267.2i	−0.0362106	−	0.0627186i
$167$	120224.			0.333580			0.166790	−	0.985992i	$-0.446660\pi$
$167$	120224.			0.333580			0.166790	+	0.985992i	$0.446660\pi$
$168$		0			0
$169$	−270169.			−0.727644
$170$	82264.0	+	142485.i	0.218317	+	0.378136i
$171$	−9558.00	+	16554.9i	−0.0249964	+	0.0432950i
$172$	67616.0	−	117114.i	0.174272	−	0.301848i
$173$	−254437.	−	440698.i	−0.646346	−	1.11950i	−0.983989	−	0.178230i	$-0.942963\pi$
$173$	−254437.	−	440698.i	−0.646346	−	1.11950i	0.337643	−	0.941274i	$-0.390370\pi$
$174$	178344.			0.446566
$175$		0			0
$176$	169984.			0.413644
$177$	69462.0	+	120312.i	0.166653	+	0.288652i
$178$	−245316.	+	424900.i	−0.580331	+	1.00516i
$179$	−243780.	+	422239.i	−0.568677	+	0.984977i	0.428020	+	0.903769i	$0.359211\pi$
$179$	−243780.	+	422239.i	−0.568677	+	0.984977i	−0.996697	+	0.0812080i	$0.974122\pi$
$180$	−16848.0	−	29181.6i	−0.0387585	−	0.0671317i
$181$	−544410.			−1.23518			−0.617589	−	0.786501i	$-0.711891\pi$
$181$	−544410.			−1.23518			−0.617589	+	0.786501i	$0.711891\pi$
$182$		0			0
$183$	−330858.			−0.730321
$184$	70784.0	+	122601.i	0.154131	+	0.266963i
$185$	−56654.0	+	98127.6i	−0.121703	+	0.210796i
$186$	−128304.	+	222229.i	−0.271930	+	0.470997i
$187$	−525224.	−	909715.i	−1.09835	−	1.90240i
$188$	85632.0			0.176702
$189$		0			0
$190$	−24544.0			−0.0493243
$191$	−188202.	−	325975.i	−0.373285	−	0.646549i	0.616784	−	0.787133i	$-0.288435\pi$
$191$	−188202.	−	325975.i	−0.373285	−	0.646549i	−0.990069	+	0.140584i	$0.955102\pi$
$192$	−18432.0	+	31925.2i	−0.0360844	+	0.0625000i
$193$	−422473.	+	731745.i	−0.816405	+	1.41406i	0.0919095	+	0.995767i	$0.470703\pi$
$193$	−422473.	+	731745.i	−0.816405	+	1.41406i	−0.908315	+	0.418288i	$0.862630\pi$
$194$	42740.0	+	74027.9i	0.0815324	+	0.141218i
$195$	74412.0			0.140138
$196$		0			0
$197$	−492794.			−0.904690			−0.452345	−	0.891843i	$-0.649412\pi$
$197$	−492794.			−0.904690			−0.452345	+	0.891843i	$0.649412\pi$
$198$	107568.	+	186313.i	0.194993	+	0.337739i
$199$	457388.	−	792219.i	0.818751	−	1.41812i	−0.0878512	−	0.996134i	$-0.528000\pi$
$199$	457388.	−	792219.i	0.818751	−	1.41812i	0.906603	−	0.421985i	$-0.138667\pi$
$200$	−78368.0	+	135737.i	−0.138536	+	0.239952i
$201$	−184374.	−	319345.i	−0.321892	−	0.557532i
$202$	147256.			0.253919
$203$		0			0
$204$	227808.			0.383260
$205$	−137046.	−	237371.i	−0.227762	−	0.394496i
$206$	209056.	−	362096.i	0.343237	−	0.594505i
$207$	−89586.0	+	155168.i	−0.145316	+	0.251695i
$208$	−40704.0	−	70501.4i	−0.0652347	−	0.112990i
$209$	156704.			0.248150
$210$		0			0
$211$	311780.			0.482106			0.241053	−	0.970512i	$-0.422507\pi$
$211$	311780.			0.482106			0.241053	+	0.970512i	$0.422507\pi$
$212$	266832.	+	462167.i	0.407754	+	0.706251i
$213$	40914.0	−	70865.1i	0.0617907	−	0.107025i
$214$	428880.	−	742842.i	0.640179	−	1.10882i
$215$	109876.	+	190311.i	0.162109	+	0.280781i
$216$	−46656.0			−0.0680414
$217$		0			0
$218$	−115192.			−0.164165
$219$	330543.	+	572517.i	0.465712	+	0.806637i
$220$	−138112.	+	239217.i	−0.192387	+	0.333223i
$221$	−251538.	+	435677.i	−0.346436	+	0.600045i
$222$	78444.0	+	135869.i	0.106826	+	0.185028i
$223$	−1.28776e6			−1.73409			−0.867047	−	0.498226i	$-0.833985\pi$
$223$	−1.28776e6			−1.73409			−0.867047	+	0.498226i	$0.833985\pi$
$224$		0			0
$225$	−198369.			−0.261227
$226$	−112028.	−	194038.i	−0.145900	−	0.252706i
$227$	−644526.	+	1.11635e6i	−0.830187	+	1.43793i	0.0677031	+	0.997706i	$0.478433\pi$
$227$	−644526.	+	1.11635e6i	−0.830187	+	1.43793i	−0.897890	+	0.440220i	$0.854900\pi$
$228$	−16992.0	+	29431.0i	−0.0216475	+	0.0374945i
$229$	−339107.	−	587351.i	−0.427315	−	0.740131i	0.569319	−	0.822117i	$-0.307207\pi$
$229$	−339107.	−	587351.i	−0.427315	−	0.740131i	−0.996633	+	0.0819859i	$0.973874\pi$
$230$	−230048.			−0.286747
$231$		0			0
$232$	317056.			0.386737
$233$	558655.	+	967619.i	0.674146	+	1.16765i	0.976718	+	0.214528i	$0.0688214\pi$
$233$	558655.	+	967619.i	0.674146	+	1.16765i	−0.302572	+	0.953127i	$0.597845\pi$
$234$	51516.0	−	89228.3i	0.0615039	−	0.106528i
$235$	−69576.0	+	120509.i	−0.0821845	+	0.142348i
$236$	123488.	+	213887.i	0.144326	+	0.249980i
$237$	804600.			0.930485
$238$		0			0
$239$	−1.26196e6			−1.42906			−0.714528	−	0.699606i	$-0.753359\pi$
$239$	−1.26196e6			−1.42906			−0.714528	+	0.699606i	$0.753359\pi$
$240$	−29952.0	−	51878.4i	−0.0335659	−	0.0581378i
$241$	−474109.	+	821181.i	−0.525818	+	0.910744i	0.473730	+	0.880670i	$0.342907\pi$
$241$	−474109.	+	821181.i	−0.525818	+	0.910744i	−0.999548	+	0.0300734i	$0.990426\pi$
$242$	559690.	−	969412.i	0.614340	−	1.06407i
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$	−588192.			−0.632477
$245$		0			0
$246$	−379512.			−0.399841
$247$	−37524.0	−	64993.5i	−0.0391351	−	0.0677840i
$248$	−228096.	+	395074.i	−0.235499	+	0.407896i
$249$	28926.0	−	50101.3i	0.0295658	−	0.0512095i
$250$	−289848.	−	502031.i	−0.293306	−	0.508020i
$251$	−486396.			−0.487310			−0.243655	−	0.969862i	$-0.578347\pi$
$251$	−486396.			−0.487310			−0.243655	+	0.969862i	$0.578347\pi$
$252$		0			0
$253$	1.46877e6			1.44262
$254$	370800.	+	642244.i	0.360625	+	0.624620i
$255$	−185094.	+	320592.i	−0.178255	+	0.308747i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	519549.	+	899885.i	0.490675	+	0.849874i	0.999942	−	0.0107346i	$-0.00341700\pi$
$257$	519549.	+	899885.i	0.490675	+	0.849874i	−0.509268	+	0.860608i	$0.670084\pi$
$258$	304272.			0.284585
$259$		0			0
$260$	132288.			0.121363
$261$	200637.	+	347513.i	0.182310	+	0.315770i
$262$	129064.	−	223545.i	0.116159	−	0.201193i
$263$	−675522.	+	1.17004e6i	−0.602213	+	1.04306i	0.390272	+	0.920699i	$0.372381\pi$
$263$	−675522.	+	1.17004e6i	−0.602213	+	1.04306i	−0.992485	+	0.122364i	$0.960952\pi$
$264$	191232.	+	331224.i	0.168869	+	0.292490i
$265$	−867204.			−0.758589
$266$		0			0
$267$	−1.10392e6			−0.947677
$268$	−327776.	−	567725.i	−0.278766	−	0.482837i
$269$	559055.	−	968312.i	0.471057	−	0.815895i	−0.528395	−	0.848999i	$-0.677206\pi$
$269$	559055.	−	968312.i	0.471057	−	0.815895i	0.999452	+	0.0331036i	$0.0105391\pi$
$270$	37908.0	−	65658.6i	0.0316462	−	0.0548128i
$271$	95052.0	+	164635.i	0.0786209	+	0.136175i	0.902655	−	0.430365i	$-0.141615\pi$
$271$	95052.0	+	164635.i	0.0786209	+	0.136175i	−0.824034	+	0.566540i	$0.808282\pi$
$272$	404992.			0.331913
$273$		0			0
$274$	−611720.			−0.492239
$275$	813068.	+	1.40828e6i	0.648329	+	1.12294i
$276$	−159264.	+	275853.i	−0.125848	+	0.217974i
$277$	100253.	−	173643.i	0.0785051	−	0.135975i	−0.824100	−	0.566444i	$-0.808319\pi$
$277$	100253.	−	173643.i	0.0785051	−	0.135975i	0.902605	+	0.430469i	$0.141652\pi$
$278$	−686920.	−	1.18978e6i	−0.533082	−	0.923325i
$279$	−577368.			−0.444061
$280$		0			0
$281$	1.09237e6			0.825285			0.412643	−	0.910893i	$-0.364606\pi$
$281$	1.09237e6			0.825285			0.412643	+	0.910893i	$0.364606\pi$
$282$	96336.0	+	166859.i	0.0721383	+	0.124947i
$283$	−906290.	+	1.56974e6i	−0.672669	+	1.16510i	0.304476	+	0.952520i	$0.401519\pi$
$283$	−906290.	+	1.56974e6i	−0.672669	+	1.16510i	−0.977145	+	0.212576i	$0.931815\pi$
$284$	72736.0	−	125982.i	0.0535123	−	0.0926860i
$285$	−27612.0	−	47825.4i	−0.0201366	−	0.0348776i
$286$	−844608.			−0.610577
$287$		0			0
$288$	−82944.0			−0.0589256
$289$	−541434.	−	937790.i	−0.381330	−	0.660482i
$290$	−257608.	+	446190.i	−0.179872	+	0.311548i
$291$	−96165.0	+	166563.i	−0.0665709	+	0.115304i
$292$	587632.	+	1.01781e6i	0.403319	+	0.698568i
$293$	2.10031e6			1.42927			0.714634	−	0.699499i	$-0.246593\pi$
$293$	2.10031e6			1.42927			0.714634	+	0.699499i	$0.246593\pi$
$294$		0			0
$295$	−401336.			−0.268505
$296$	139456.	+	241545.i	0.0925141	+	0.160239i
$297$	−242028.	+	419205.i	−0.159212	+	0.275762i
$298$	−349716.	+	605726.i	−0.228126	+	0.395126i
$299$	−351708.	−	609176.i	−0.227512	−	0.394062i
$300$	−352656.			−0.226229
$301$		0			0
$302$	1.81021e6			1.14212
$303$	165663.	+	286937.i	0.103662	+	0.179548i
$304$	−30208.0	+	52321.8i	−0.0187473	+	0.0324712i
$305$	477906.	−	827757.i	0.294166	−	0.509511i
$306$	256284.	+	443897.i	0.156465	+	0.271006i
$307$	−1.64104e6			−0.993743			−0.496872	−	0.867824i	$-0.665518\pi$
$307$	−1.64104e6			−0.993743			−0.496872	+	0.867824i	$0.665518\pi$
$308$		0			0
$309$	940752.			0.560504
$310$	−370656.	−	641995.i	−0.219062	−	0.379426i
$311$	472616.	−	818595.i	0.277081	−	0.479919i	−0.693577	−	0.720383i	$-0.743966\pi$
$311$	472616.	−	818595.i	0.277081	−	0.479919i	0.970658	+	0.240464i	$0.0772995\pi$
$312$	91584.0	−	158628.i	0.0532639	−	0.0922558i
$313$	−207677.	−	359707.i	−0.119820	−	0.207533i	0.799877	−	0.600165i	$-0.204898\pi$
$313$	−207677.	−	359707.i	−0.119820	−	0.207533i	−0.919696	+	0.392631i	$0.871565\pi$
$314$	1.99626e6			1.14260
$315$		0			0
$316$	1.43040e6			0.805823
$317$	−592407.	−	1.02608e6i	−0.331110	−	0.573499i	0.651620	−	0.758546i	$-0.274090\pi$
$317$	−592407.	−	1.02608e6i	−0.331110	−	0.573499i	−0.982730	+	0.185047i	$0.940756\pi$
$318$	−600372.	+	1.03987e6i	−0.332930	+	0.576651i
$319$	1.64473e6	−	2.84875e6i	0.904935	−	1.56739i
$320$	−53248.0	−	92228.2i	−0.0290689	−	0.0503488i
$321$	1.92996e6			1.04541
$322$		0			0
$323$	373352.			0.199119
$324$	−52488.0	−	90911.9i	−0.0277778	−	0.0481125i
$325$	389391.	−	674445.i	0.204493	−	0.354191i
$326$	−951176.	+	1.64749e6i	−0.495698	+	0.858574i
$327$	−129591.	−	224458.i	−0.0670202	−	0.116082i
$328$	−674688.			−0.346273
$329$		0			0
$330$	−621504.			−0.314166
$331$	−685774.	−	1.18780e6i	−0.344042	−	0.595898i	0.641138	−	0.767426i	$-0.278463\pi$
$331$	−685774.	−	1.18780e6i	−0.344042	−	0.595898i	−0.985179	+	0.171528i	$0.945129\pi$
$332$	51424.0	−	89069.0i	0.0256048	−	0.0443487i
$333$	−176499.	+	305705.i	−0.0872231	+	0.151075i
$334$	240448.	+	416468.i	0.117938	+	0.204275i
$335$	1.06527e6			0.518619
$336$		0			0
$337$	963522.			0.462154			0.231077	−	0.972935i	$-0.425775\pi$
$337$	963522.			0.462154			0.231077	+	0.972935i	$0.425775\pi$
$338$	−540338.	−	935893.i	−0.257261	−	0.445589i
$339$	252063.	−	436586.i	0.119127	−	0.206334i
$340$	−329056.	+	569942.i	−0.154373	+	0.267383i
$341$	2.36650e6	+	4.09889e6i	1.10210	+	1.90889i
$342$	−76464.0			−0.0353502
$343$		0			0
$344$	540928.			0.246458
$345$	−258804.	−	448262.i	−0.117064	−	0.202761i
$346$	1.01775e6	−	1.76279e6i	0.457036	−	0.791609i
$347$	−1.28866e6	+	2.23202e6i	−0.574531	+	0.995117i	0.421562	+	0.906800i	$0.361482\pi$
$347$	−1.28866e6	+	2.23202e6i	−0.574531	+	0.995117i	−0.996092	+	0.0883168i	$0.971851\pi$
$348$	356688.	+	617802.i	0.157885	+	0.273465i
$349$	−3.06751e6			−1.34810			−0.674051	−	0.738684i	$-0.735447\pi$
$349$	−3.06751e6			−1.34810			−0.674051	+	0.738684i	$0.735447\pi$
$350$		0			0
$351$	231822.			0.100435
$352$	339968.	+	588842.i	0.146245	+	0.253304i
$353$	1.55072e6	−	2.68593e6i	0.662364	−	1.14725i	−0.317628	−	0.948215i	$-0.602886\pi$
$353$	1.55072e6	−	2.68593e6i	0.662364	−	1.14725i	0.979993	−	0.199033i	$-0.0637802\pi$
$354$	−277848.	+	481247.i	−0.117842	+	0.204108i
$355$	118196.	+	204721.i	0.0497774	+	0.0862169i
$356$	−1.96253e6			−0.820712
$357$		0			0
$358$	−1.95024e6			−0.804230
$359$	163754.	+	283630.i	0.0670588	+	0.116149i	0.897605	−	0.440800i	$-0.145305\pi$
$359$	163754.	+	283630.i	0.0670588	+	0.116149i	−0.830547	+	0.556949i	$0.811972\pi$
$360$	67392.0	−	116726.i	0.0274064	−	0.0474693i
$361$	1.21020e6	−	2.09613e6i	0.488753	−	0.846546i
$362$	−1.08882e6	−	1.88589e6i	−0.436701	−	0.756389i
$363$	2.51860e6			1.00321
$364$		0			0
$365$	−1.90980e6			−0.750337
$366$	−661716.	−	1.14613e6i	−0.258208	−	0.447229i
$367$	1.43370e6	−	2.48323e6i	0.555638	−	0.962393i	−0.442216	−	0.896909i	$-0.645807\pi$
$367$	1.43370e6	−	2.48323e6i	0.555638	−	0.962393i	0.997854	−	0.0654844i	$-0.0208593\pi$
$368$	−283136.	+	490406.i	−0.108987	+	0.188771i
$369$	−426951.	−	739501.i	−0.163235	−	0.282731i
$370$	−453232.			−0.172114
$371$		0			0
$372$	−1.02643e6			−0.384568
$373$	−1.79015e6	−	3.10063e6i	−0.666218	−	1.15392i	−0.978953	−	0.204084i	$-0.934579\pi$
$373$	−1.79015e6	−	3.10063e6i	−0.666218	−	1.15392i	0.312735	−	0.949840i	$-0.398755\pi$
$374$	2.10090e6	−	3.63886e6i	0.776650	−	1.34520i
$375$	652158.	−	1.12957e6i	0.239483	−	0.414797i
$376$	171264.	+	296638.i	0.0624736	+	0.108207i
$377$	−1.57537e6			−0.570860
$378$		0			0
$379$	1.64235e6			0.587310			0.293655	−	0.955912i	$-0.405128\pi$
$379$	1.64235e6			0.587310			0.293655	+	0.955912i	$0.405128\pi$
$380$	−49088.0	−	85022.9i	−0.0174388	−	0.0302049i
$381$	−834300.	+	1.44505e6i	−0.294449	+	0.510000i
$382$	752808.	−	1.30390e6i	0.263953	−	0.457179i
$383$	1.02849e6	+	1.78139e6i	0.358263	+	0.620530i	0.987671	−	0.156545i	$-0.0500357\pi$
$383$	1.02849e6	+	1.78139e6i	0.358263	+	0.620530i	−0.629408	+	0.777075i	$0.716702\pi$
$384$	−147456.			−0.0510310
$385$		0			0
$386$	−3.37978e6			−1.15457
$387$	342306.	+	592891.i	0.116182	+	0.201232i
$388$	−170960.	+	296111.i	−0.0576521	+	0.0998564i
$389$	−308071.	+	533595.i	−0.103223	+	0.178788i	−0.913011	−	0.407935i	$-0.866249\pi$
$389$	−308071.	+	533595.i	−0.103223	+	0.178788i	0.809788	+	0.586723i	$0.199582\pi$
$390$	148824.	+	257771.i	0.0495463	+	0.0858168i
$391$	3.49938e6			1.15758
$392$		0			0
$393$	580788.			0.189686
$394$	−985588.	−	1.70709e6i	−0.319856	−	0.554007i
$395$	−1.16220e6	+	2.01299e6i	−0.374790	+	0.649156i
$396$	−430272.	+	745253.i	−0.137881	+	0.238817i
$397$	−1.09606e6	−	1.89843e6i	−0.349026	−	0.604531i	0.637051	−	0.770822i	$-0.280154\pi$
$397$	−1.09606e6	−	1.89843e6i	−0.349026	−	0.604531i	−0.986077	+	0.166291i	$0.946821\pi$
$398$	3.65910e6			1.15789
$399$		0			0
$400$	−626944.			−0.195920
$401$	−1.64227e6	−	2.84449e6i	−0.510015	−	0.883373i	−0.999933	−	0.0116038i	$-0.996306\pi$
$401$	−1.64227e6	−	2.84449e6i	−0.510015	−	0.883373i	0.489917	−	0.871769i	$-0.337027\pi$
$402$	737496.	−	1.27738e6i	0.227612	−	0.394235i
$403$	1.13335e6	−	1.96302e6i	0.347618	−	0.602092i
$404$	294512.	+	510110.i	0.0897738	+	0.155493i
$405$	170586.			0.0516780
$406$		0			0
$407$	2.89371e6			0.865903
$408$	455616.	+	789150.i	0.135503	+	0.234698i
$409$	1.80610e6	−	3.12825e6i	0.533866	−	0.924683i	−0.465351	−	0.885126i	$-0.654072\pi$
$409$	1.80610e6	−	3.12825e6i	0.533866	−	0.924683i	0.999217	−	0.0395571i	$-0.0125947\pi$
$410$	548184.	−	949483.i	0.161052	−	0.278951i
$411$	−688185.	−	1.19197e6i	−0.200956	−	0.348066i
$412$	1.67245e6			0.485411
$413$		0			0
$414$	−716688.			−0.205508
$415$	83564.0	+	144737.i	0.0238177	+	0.0412534i
$416$	162816.	−	282006.i	0.0461279	−	0.0798959i
$417$	1.54557e6	−	2.67701e6i	0.435260	−	0.753892i
$418$	313408.	+	542839.i	0.0877343	+	0.151960i
$419$	5.41489e6			1.50680			0.753398	−	0.657564i	$-0.228413\pi$
$419$	5.41489e6			1.50680			0.753398	+	0.657564i	$0.228413\pi$
$420$		0			0
$421$	3.60629e6			0.991644			0.495822	−	0.868424i	$-0.334867\pi$
$421$	3.60629e6			0.991644			0.495822	+	0.868424i	$0.334867\pi$
$422$	623560.	+	1.08004e6i	0.170450	+	0.295228i
$423$	−216756.	+	375432.i	−0.0589007	+	0.102019i
$424$	−1.06733e6	+	1.84867e6i	−0.288326	+	0.499395i
$425$	1.93716e6	+	3.35526e6i	0.520227	+	0.901060i
$426$	327312.			0.0873852
$427$		0			0
$428$	3.43104e6			0.905350
$429$	−950184.	−	1.64577e6i	−0.249267	−	0.431743i
$430$	−439504.	+	761243.i	−0.114628	+	0.198542i
$431$	1.39107e6	−	2.40940e6i	0.360708	−	0.624765i	−0.627370	−	0.778722i	$-0.715868\pi$
$431$	1.39107e6	−	2.40940e6i	0.360708	−	0.624765i	0.988078	+	0.153957i	$0.0492018\pi$
$432$	−93312.0	−	161621.i	−0.0240563	−	0.0416667i
$433$	6.27619e6			1.60871			0.804353	−	0.594152i	$-0.202512\pi$
$433$	6.27619e6			1.60871			0.804353	+	0.594152i	$0.202512\pi$
$434$		0			0
$435$	−1.15924e6			−0.293730
$436$	−230384.	−	399037.i	−0.0580412	−	0.100530i
$437$	−261016.	+	452093.i	−0.0653828	+	0.113246i
$438$	−1.32217e6	+	2.29007e6i	−0.329308	+	0.570379i
$439$	−320796.	−	555635.i	−0.0794452	−	0.137603i	0.823566	−	0.567221i	$-0.191982\pi$
$439$	−320796.	−	555635.i	−0.0794452	−	0.137603i	−0.903011	+	0.429618i	$0.858648\pi$
$440$	−1.10490e6			−0.272076
$441$		0			0
$442$	−2.01230e6			−0.489934
$443$	−3.02773e6	−	5.24418e6i	−0.733006	−	1.26960i	−0.955593	−	0.294691i	$-0.904783\pi$
$443$	−3.02773e6	−	5.24418e6i	−0.733006	−	1.26960i	0.222587	−	0.974913i	$-0.428550\pi$
$444$	−313776.	+	543476.i	−0.0755374	+	0.130835i
$445$	1.59455e6	−	2.76185e6i	0.381715	−	0.661150i
$446$	−2.57552e6	−	4.46093e6i	−0.613095	−	1.06191i
$447$	−1.57372e6			−0.372528
$448$		0			0
$449$	−5.16681e6			−1.20950			−0.604752	−	0.796414i	$-0.706728\pi$
$449$	−5.16681e6			−1.20950			−0.604752	+	0.796414i	$0.706728\pi$
$450$	−396738.	−	687170.i	−0.0923576	−	0.159968i
$451$	−3.49994e6	+	6.06208e6i	−0.810251	+	1.40340i
$452$	448112.	−	776153.i	0.103167	−	0.178690i
$453$	2.03648e6	+	3.52729e6i	0.466268	+	0.807600i
$454$	−5.15621e6			−1.17406
$455$		0			0
$456$	−135936.			−0.0306142
$457$	113899.	+	197279.i	0.0255111	+	0.0441865i	0.878499	−	0.477744i	$-0.158545\pi$
$457$	113899.	+	197279.i	0.0255111	+	0.0441865i	−0.852988	+	0.521931i	$0.825212\pi$
$458$	1.35643e6	−	2.34940e6i	0.302157	−	0.523352i
$459$	−576639.	+	998768.i	−0.127753	+	0.221275i
$460$	−460096.	−	796910.i	−0.101380	−	0.175596i
$461$	585146.			0.128237			0.0641183	−	0.997942i	$-0.479577\pi$
$461$	585146.			0.128237			0.0641183	+	0.997942i	$0.479577\pi$
$462$		0			0
$463$	−3.41454e6			−0.740251			−0.370126	−	0.928982i	$-0.620685\pi$
$463$	−3.41454e6			−0.740251			−0.370126	+	0.928982i	$0.620685\pi$
$464$	634112.	+	1.09831e6i	0.136732	+	0.236827i
$465$	833976.	−	1.44449e6i	0.178863	−	0.309800i
$466$	−2.23462e6	+	3.87048e6i	−0.476693	+	0.825657i
$467$	−358150.	−	620334.i	−0.0759929	−	0.131623i	0.825525	−	0.564366i	$-0.190879\pi$
$467$	−358150.	−	620334.i	−0.0759929	−	0.131623i	−0.901518	+	0.432742i	$0.857546\pi$
$468$	412128.			0.0869796
$469$		0			0
$470$	−556608.			−0.116226
$471$	2.24580e6	+	3.88983e6i	0.466464	+	0.807940i
$472$	−493952.	+	855550.i	−0.102054	+	0.176763i
$473$	2.80606e6	−	4.86025e6i	0.576693	−	0.998862i
$474$	1.60920e6	+	2.78722e6i	0.328976	+	0.569803i
$475$	−577964.			−0.117535
$476$		0			0
$477$	−2.70167e6			−0.543672
$478$	−2.52391e6	−	4.37154e6i	−0.505248	−	0.875115i
$479$	−2.62046e6	+	4.53877e6i	−0.521842	+	0.903856i	0.477836	+	0.878449i	$0.341421\pi$
$479$	−2.62046e6	+	4.53877e6i	−0.521842	+	0.903856i	−0.999677	+	0.0254070i	$0.991912\pi$
$480$	119808.	−	207514.i	0.0237346	−	0.0411096i
$481$	−692922.	−	1.20018e6i	−0.136559	−	0.236528i
$482$	−3.79287e6			−0.743619
$483$		0			0
$484$	4.47752e6			0.868809
$485$	−277810.	−	481181.i	−0.0536282	−	0.0928868i
$486$	118098.	−	204552.i	0.0226805	−	0.0392837i
$487$	−558508.	+	967364.i	−0.106710	+	0.184828i	−0.914436	−	0.404731i	$-0.867365\pi$
$487$	−558508.	+	967364.i	−0.106710	+	0.184828i	0.807725	+	0.589559i	$0.200698\pi$
$488$	−1.17638e6	−	2.03756e6i	−0.223614	−	0.387311i
$489$	−4.28029e6			−0.809471
$490$		0			0
$491$	1.34458e6			0.251699			0.125850	−	0.992049i	$-0.459834\pi$
$491$	1.34458e6			0.251699			0.125850	+	0.992049i	$0.459834\pi$
$492$	−759024.	−	1.31467e6i	−0.141365	−	0.244852i
$493$	3.91861e6	−	6.78724e6i	0.726131	−	1.25770i
$494$	150096.	−	259974.i	0.0276727	−	0.0479305i
$495$	−699192.	−	1.21104e6i	−0.128258	−	0.222149i
$496$	−1.82477e6			−0.333045
$497$		0			0
$498$	231408.			0.0418124
$499$	3.27324e6	+	5.66941e6i	0.588473	+	1.01926i	0.994433	+	0.105374i	$0.0336038\pi$
$499$	3.27324e6	+	5.66941e6i	0.588473	+	1.01926i	−0.405960	+	0.913891i	$0.633063\pi$
$500$	1.15939e6	−	2.00813e6i	0.207398	−	0.359224i
$501$	−541008.	+	937053.i	−0.0962962	+	0.166790i
$502$	−972792.	−	1.68493e6i	−0.172290	−	0.298415i
$503$	−8.22050e6			−1.44870			−0.724350	−	0.689432i	$-0.757860\pi$
$503$	−8.22050e6			−1.44870			−0.724350	+	0.689432i	$0.757860\pi$
$504$		0			0
$505$	−957164.			−0.167016
$506$	2.93754e6	+	5.08796e6i	0.510043	+	0.883421i
$507$	1.21576e6	−	2.10576e6i	0.210053	−	0.363822i
$508$	−1.48320e6	+	2.56898e6i	−0.255000	+	0.441673i
$509$	2.55522e6	+	4.42578e6i	0.437154	+	0.757173i	0.997469	−	0.0711070i	$-0.0226532\pi$
$509$	2.55522e6	+	4.42578e6i	0.437154	+	0.757173i	−0.560315	+	0.828280i	$0.689320\pi$
$510$	−1.48075e6			−0.252091
$511$		0			0
$512$	−262144.			−0.0441942
$513$	−86022.0	−	148994.i	−0.0144317	−	0.0249964i
$514$	−2.07820e6	+	3.59954e6i	−0.346959	+	0.600951i
$515$	−1.35886e6	+	2.35362e6i	−0.225766	+	0.391038i
$516$	608544.	+	1.05403e6i	0.100616	+	0.174272i
$517$	3.55373e6			0.584733
$518$		0			0
$519$	4.57987e6			0.746336
$520$	264576.	+	458259.i	0.0429084	+	0.0743195i
$521$	−4.85000e6	+	8.40044e6i	−0.782793	+	1.35584i	0.147516	+	0.989060i	$0.452872\pi$
$521$	−4.85000e6	+	8.40044e6i	−0.782793	+	1.35584i	−0.930309	+	0.366778i	$0.880461\pi$
$522$	−802548.	+	1.39005e6i	−0.128912	+	0.223283i
$523$	1.58647e6	+	2.74785e6i	0.253617	+	0.439278i	0.964519	−	0.264013i	$-0.0850463\pi$
$523$	1.58647e6	+	2.74785e6i	0.253617	+	0.439278i	−0.710902	+	0.703291i	$0.751713\pi$
$524$	1.03251e6			0.164273
$525$		0			0
$526$	−5.40418e6			−0.851658
$527$	5.63825e6	+	9.76573e6i	0.884337	+	1.53172i
$528$	−764928.	+	1.32489e6i	−0.119409	+	0.206822i
$529$	771700.	−	1.33662e6i	0.119897	−	0.207668i
$530$	−1.73441e6	−	3.00408e6i	−0.268202	−	0.464539i
$531$	−1.25032e6			−0.192435
$532$		0			0
$533$	3.35236e6			0.511131
$534$	−2.20784e6	−	3.82410e6i	−0.335054	−	0.580331i
$535$	−2.78772e6	+	4.82847e6i	−0.421080	+	0.729332i
$536$	1.31110e6	−	2.27090e6i	0.197117	−	0.341418i
$537$	−2.19402e6	−	3.80015e6i	−0.328326	−	0.568677i
$538$	4.47244e6			0.666176
$539$		0			0
$540$	303264.			0.0447545
$541$	3.31287e6	+	5.73806e6i	0.486644	+	0.842893i	0.999882	−	0.0153538i	$-0.00488746\pi$
$541$	3.31287e6	+	5.73806e6i	0.486644	+	0.842893i	−0.513238	+	0.858246i	$0.671554\pi$
$542$	−380208.	+	658540.i	−0.0555934	+	0.0962905i
$543$	2.44984e6	−	4.24326e6i	0.356565	−	0.617589i
$544$	809984.	+	1.40293e6i	0.117349	+	0.203254i
$545$	748748.			0.107980
$546$		0			0
$547$	3.84707e6			0.549745			0.274873	−	0.961481i	$-0.411364\pi$
$547$	3.84707e6			0.549745			0.274873	+	0.961481i	$0.411364\pi$
$548$	−1.22344e6	−	2.11906e6i	−0.174033	−	0.301434i
$549$	1.48886e6	−	2.57878e6i	0.210826	−	0.365161i
$550$	−3.25227e6	+	5.63310e6i	−0.458438	+	0.794037i
$551$	584572.	+	1.01251e6i	0.0820274	+	0.142076i
$552$	−1.27411e6			−0.177975
$553$		0			0
$554$	802024.			0.111023
$555$	−509886.	−	883148.i	−0.0702653	−	0.121703i
$556$	2.74768e6	−	4.75912e6i	0.376946	−	0.652890i
$557$	−2.50088e6	+	4.33165e6i	−0.341550	+	0.591583i	−0.984721	−	0.174140i	$-0.944285\pi$
$557$	−2.50088e6	+	4.33165e6i	−0.341550	+	0.591583i	0.643171	+	0.765723i	$0.277619\pi$
$558$	−1.15474e6	−	2.00006e6i	−0.156999	−	0.271930i
$559$	−2.68774e6			−0.363795
$560$		0			0
$561$	9.45403e6			1.26826
$562$	2.18474e6	+	3.78408e6i	0.291782	+	0.505382i
$563$	−1.13886e6	+	1.97257e6i	−0.151426	+	0.262277i	−0.931752	−	0.363096i	$-0.881720\pi$
$563$	−1.13886e6	+	1.97257e6i	−0.151426	+	0.262277i	0.780326	+	0.625373i	$0.215053\pi$
$564$	−385344.	+	667435.i	−0.0510095	+	0.0883510i
$565$	728182.	+	1.26125e6i	0.0959663	+	0.166219i
$566$	−7.25032e6			−0.951297
$567$		0			0
$568$	581888.			0.0756778
$569$	−4.43490e6	−	7.68147e6i	−0.574252	−	0.994634i	−0.996122	−	0.0879781i	$-0.971959\pi$
$569$	−4.43490e6	−	7.68147e6i	−0.574252	−	0.994634i	0.421870	−	0.906656i	$-0.361374\pi$
$570$	110448.	−	191302.i	0.0142387	−	0.0246622i
$571$	−7.00509e6	+	1.21332e7i	−0.899132	+	1.55734i	−0.0705261	+	0.997510i	$0.522468\pi$
$571$	−7.00509e6	+	1.21332e7i	−0.899132	+	1.55734i	−0.828606	+	0.559832i	$0.810866\pi$
$572$	−1.68922e6	−	2.92581e6i	−0.215871	−	0.373900i
$573$	3.38764e6			0.431033
$574$		0			0
$575$	−5.41719e6			−0.683289
$576$	−165888.	−	287326.i	−0.0208333	−	0.0360844i
$577$	−4.37663e6	+	7.58055e6i	−0.547269	+	0.947897i	0.451192	+	0.892427i	$0.350999\pi$
$577$	−4.37663e6	+	7.58055e6i	−0.547269	+	0.947897i	−0.998460	+	0.0554701i	$0.982334\pi$
$578$	2.16573e6	−	3.75116e6i	0.269641	−	0.467031i
$579$	−3.80226e6	−	6.58570e6i	−0.471352	−	0.816405i
$580$	−2.06086e6			−0.254378
$581$		0			0
$582$	−769320.			−0.0941455
$583$	1.10735e7	+	1.91799e7i	1.34932	+	2.33709i
$584$	−2.35053e6	+	4.07123e6i	−0.285189	+	0.493962i
$585$	−334854.	+	579984.i	−0.0404544	+	0.0700691i
$586$	4.20061e6	+	7.27567e6i	0.505322	+	0.875244i
$587$	−1.06117e7			−1.27113			−0.635564	−	0.772048i	$-0.719232\pi$
$587$	−1.06117e7			−1.27113			−0.635564	+	0.772048i	$0.719232\pi$
$588$		0			0
$589$	−1.68221e6			−0.199798
$590$	−802672.	−	1.39027e6i	−0.0949310	−	0.164425i
$591$	2.21757e6	−	3.84095e6i	0.261162	−	0.452345i
$592$	−557824.	+	966180.i	−0.0654173	+	0.113306i
$593$	−942759.	−	1.63291e6i	−0.110094	−	0.190689i	0.805714	−	0.592305i	$-0.201782\pi$
$593$	−942759.	−	1.63291e6i	−0.110094	−	0.190689i	−0.915808	+	0.401616i	$0.868449\pi$
$594$	−1.93622e6			−0.225159
$595$		0			0
$596$	−2.79773e6			−0.322619
$597$	4.11649e6	+	7.12997e6i	0.472706	+	0.818751i
$598$	1.40683e6	−	2.43670e6i	0.160875	−	0.278644i
$599$	−6.36281e6	+	1.10207e7i	−0.724573	+	1.25500i	0.234576	+	0.972098i	$0.424630\pi$
$599$	−6.36281e6	+	1.10207e7i	−0.724573	+	1.25500i	−0.959150	+	0.282900i	$0.908704\pi$
$600$	−705312.	−	1.22164e6i	−0.0799840	−	0.138536i
$601$	7.18846e6			0.811801			0.405900	−	0.913917i	$-0.366958\pi$
$601$	7.18846e6			0.811801			0.405900	+	0.913917i	$0.366958\pi$
$602$		0			0
$603$	3.31873e6			0.371688
$604$	3.62042e6	+	6.27074e6i	0.403800	+	0.699402i
$605$	−3.63798e6	+	6.30117e6i	−0.404085	+	0.699895i
$606$	−662652.	+	1.14775e6i	−0.0733000	+	0.126959i
$607$	−5.42472e6	−	9.39589e6i	−0.597593	−	1.03506i	−0.993175	−	0.116631i	$-0.962790\pi$
$607$	−5.42472e6	−	9.39589e6i	−0.597593	−	1.03506i	0.395582	−	0.918431i	$-0.370543\pi$
$608$	−241664.			−0.0265126
$609$		0			0
$610$	3.82325e6			0.416014
$611$	−850968.	−	1.47392e6i	−0.0922168	−	0.159724i
$612$	−1.02514e6	+	1.77559e6i	−0.110638	+	0.191630i
$613$	2.45256e6	−	4.24795e6i	0.263614	−	0.456592i	−0.703586	−	0.710610i	$-0.748419\pi$
$613$	2.45256e6	−	4.24795e6i	0.263614	−	0.456592i	0.967199	+	0.254018i	$0.0817523\pi$
$614$	−3.28209e6	−	5.68474e6i	−0.351341	−	0.608541i
$615$	2.46683e6			0.262997
$616$		0			0
$617$	2.58445e6			0.273310			0.136655	−	0.990619i	$-0.456365\pi$
$617$	2.58445e6			0.273310			0.136655	+	0.990619i	$0.456365\pi$
$618$	1.88150e6	+	3.25886e6i	0.198168	+	0.343237i
$619$	2.49668e6	−	4.32438e6i	0.261901	−	0.453625i	−0.704846	−	0.709360i	$-0.748984\pi$
$619$	2.49668e6	−	4.32438e6i	0.261901	−	0.453625i	0.966747	+	0.255735i	$0.0823174\pi$
$620$	1.48262e6	−	2.56798e6i	0.154900	−	0.268295i
$621$	−806274.	−	1.39651e6i	−0.0838984	−	0.145316i
$622$	3.78093e6			0.391852
$623$		0			0
$624$	732672.			0.0753266
$625$	−1.94255e6	−	3.36460e6i	−0.198917	−	0.344535i
$626$	830708.	−	1.43883e6i	0.0847252	−	0.146748i
$627$	−705168.	+	1.22139e6i	−0.0716347	+	0.124075i
$628$	3.99253e6	+	6.91526e6i	0.403970	+	0.699696i
$629$	6.89436e6			0.694812
$630$		0			0
$631$	−1.18219e7			−1.18199			−0.590997	−	0.806674i	$-0.701265\pi$
$631$	−1.18219e7			−1.18199			−0.590997	+	0.806674i	$0.701265\pi$
$632$	2.86080e6	+	4.95505e6i	0.284902	+	0.493464i
$633$	−1.40301e6	+	2.43008e6i	−0.139172	+	0.241053i
$634$	2.36963e6	−	4.10432e6i	0.234130	−	0.405525i
$635$	−2.41020e6	−	4.17459e6i	−0.237202	−	0.410846i
$636$	−4.80298e6			−0.470834
$637$		0			0
$638$	1.31578e7			1.27977
$639$	368226.	+	637786.i	0.0356749	+	0.0617907i
$640$	212992.	−	368913.i	0.0205548	−	0.0356020i
$641$	2.73503e6	−	4.73722e6i	0.262916	−	0.455385i	−0.704099	−	0.710102i	$-0.748649\pi$
$641$	2.73503e6	−	4.73722e6i	0.262916	−	0.455385i	0.967016	+	0.254717i	$0.0819823\pi$
$642$	3.85992e6	+	6.68558e6i	0.369607	+	0.640179i
$643$	9.64934e6			0.920386			0.460193	−	0.887819i	$-0.347780\pi$
$643$	9.64934e6			0.920386			0.460193	+	0.887819i	$0.347780\pi$
$644$		0			0
$645$	−1.97777e6			−0.187187
$646$	746704.	+	1.29333e6i	0.0703991	+	0.121935i
$647$	−146184.	+	253198.i	−0.0137290	+	0.0237793i	−0.872808	−	0.488063i	$-0.837704\pi$
$647$	−146184.	+	253198.i	−0.0137290	+	0.0237793i	0.859079	+	0.511843i	$0.171037\pi$
$648$	209952.	−	363648.i	0.0196419	−	0.0340207i
$649$	5.12475e6	+	8.87633e6i	0.477596	+	0.827221i
$650$	3.11513e6			0.289196
$651$		0			0
$652$	−7.60941e6			−0.701022
$653$	−3.47040e6	−	6.01091e6i	−0.318491	−	0.551642i	0.661683	−	0.749784i	$-0.269843\pi$
$653$	−3.47040e6	−	6.01091e6i	−0.318491	−	0.551642i	−0.980173	+	0.198142i	$0.936509\pi$
$654$	518364.	−	897833.i	0.0473904	−	0.0820826i
$655$	−838916.	+	1.45305e6i	−0.0764038	+	0.132335i
$656$	−1.34938e6	−	2.33719e6i	−0.122426	−	0.212048i
$657$	−5.94977e6			−0.537758
$658$		0			0
$659$	−1.32912e7			−1.19221			−0.596104	−	0.802908i	$-0.703285\pi$
$659$	−1.32912e7			−1.19221			−0.596104	+	0.802908i	$0.703285\pi$
$660$	−1.24301e6	−	2.15295e6i	−0.111074	−	0.192387i
$661$	−1.02609e6	+	1.77725e6i	−0.0913448	+	0.158214i	−0.908077	−	0.418803i	$-0.862450\pi$
$661$	−1.02609e6	+	1.77725e6i	−0.0913448	+	0.158214i	0.816732	+	0.577017i	$0.195783\pi$
$662$	2.74310e6	−	4.75118e6i	0.243274	−	0.421363i
$663$	−2.26384e6	−	3.92109e6i	−0.200015	−	0.346436i
$664$	411392.			0.0362106
$665$		0			0
$666$	−1.41199e6			−0.123352
$667$	5.47912e6	+	9.49012e6i	0.476866	+	0.825956i
$668$	−961792.	+	1.66587e6i	−0.0833950	+	0.144444i
$669$	5.79492e6	−	1.00371e7i	0.500590	−	0.867047i
$670$	2.13054e6	+	3.69021e6i	0.183360	+	0.317588i
$671$	−2.44100e7			−2.09296
$672$		0			0
$673$	−1.57039e7			−1.33650			−0.668252	−	0.743935i	$-0.732957\pi$
$673$	−1.57039e7			−1.33650			−0.668252	+	0.743935i	$0.732957\pi$
$674$	1.92704e6	+	3.33774e6i	0.163396	+	0.283010i
$675$	892660.	−	1.54613e6i	0.0754096	−	0.130613i
$676$	2.16135e6	−	3.74357e6i	0.181911	−	0.315079i
$677$	484767.	+	839641.i	0.0406501	+	0.0704080i	0.885635	−	0.464383i	$-0.153724\pi$
$677$	484767.	+	839641.i	0.0406501	+	0.0704080i	−0.844985	+	0.534791i	$0.820390\pi$
$678$	2.01650e6			0.168471
$679$		0			0
$680$	−2.63245e6			−0.218317
$681$	−5.80073e6	−	1.00472e7i	−0.479309	−	0.830187i
$682$	−9.46598e6	+	1.63956e7i	−0.779300	+	1.34979i
$683$	7.49539e6	−	1.29824e7i	0.614812	−	1.06489i	−0.375605	−	0.926780i	$-0.622565\pi$
$683$	7.49539e6	−	1.29824e7i	0.614812	−	1.06489i	0.990417	−	0.138106i	$-0.0441016\pi$
$684$	−152928.	−	264879.i	−0.0124982	−	0.0216475i
$685$	3.97618e6			0.323772
$686$		0			0
$687$	6.10393e6			0.493421
$688$	1.08186e6	+	1.87383e6i	0.0871361	+	0.150924i
$689$	5.30329e6	−	9.18556e6i	0.425595	−	0.737153i
$690$	1.03522e6	−	1.79305e6i	0.0827767	−	0.143373i
$691$	3.58019e6	+	6.20107e6i	0.285240	+	0.494051i	0.972667	−	0.232203i	$-0.0745932\pi$
$691$	3.58019e6	+	6.20107e6i	0.285240	+	0.494051i	−0.687427	+	0.726253i	$0.741260\pi$
$692$	8.14198e6			0.646346
$693$		0			0
$694$	−1.03092e7			−0.812509
$695$	4.46498e6	+	7.73357e6i	0.350637	+	0.607321i
$696$	−1.42675e6	+	2.47121e6i	−0.111641	+	0.193369i
$697$	−8.33872e6	+	1.44431e7i	−0.650156	+	1.12610i
$698$	−6.13503e6	−	1.06262e7i	−0.476626	−	0.825541i
$699$	−1.00558e7			−0.778437
$700$		0			0
$701$	−91834.0			−0.00705844			−0.00352922	−	0.999994i	$-0.501123\pi$
$701$	−91834.0			−0.00705844			−0.00352922	+	0.999994i	$0.501123\pi$
$702$	463644.	+	803055.i	0.0355093	+	0.0615039i
$703$	−514244.	+	890697.i	−0.0392447	+	0.0679738i
$704$	−1.35987e6	+	2.35537e6i	−0.103411	+	0.179113i
$705$	−626184.	−	1.08458e6i	−0.0474492	−	0.0821845i
$706$	1.24058e7			0.936725
$707$		0			0
$708$	−2.22278e6			−0.166653
$709$	−1.10491e7	−	1.91375e7i	−0.825487	−	1.42978i	−0.901547	−	0.432681i	$-0.857567\pi$
$709$	−1.10491e7	−	1.91375e7i	−0.825487	−	1.42978i	0.0760603	−	0.997103i	$-0.475766\pi$
$710$	−472784.	+	818886.i	−0.0351979	+	0.0609646i
$711$	−3.62070e6	+	6.27124e6i	−0.268608	+	0.465242i
$712$	−3.92506e6	−	6.79840e6i	−0.290166	−	0.502582i
$713$	−1.57671e7			−1.16153
$714$		0			0
$715$	5.48995e6			0.401609
$716$	−3.90048e6	−	6.75583e6i	−0.284338	−	0.492489i
$717$	5.67880e6	−	9.83597e6i	0.412533	−	0.714528i
$718$	−655016.	+	1.13452e6i	−0.0474177	+	0.0821299i
$719$	−7.91940e6	−	1.37168e7i	−0.571308	−	0.989534i	−0.996432	−	0.0843990i	$-0.973103\pi$
$719$	−7.91940e6	−	1.37168e7i	−0.571308	−	0.989534i	0.425124	−	0.905135i	$-0.360230\pi$
$720$	539136.			0.0387585
$721$		0			0
$722$	9.68161e6			0.691202
$723$	−4.26698e6	−	7.39063e6i	−0.303581	−	0.525818i
$724$	4.35528e6	−	7.54357e6i	0.308795	−	0.534848i
$725$	−6.06617e6	+	1.05069e7i	−0.428617	+	0.742387i
$726$	5.03721e6	+	8.72470e6i	0.354690	+	0.614340i
$727$	6.31418e6			0.443078			0.221539	−	0.975151i	$-0.428892\pi$
$727$	6.31418e6			0.443078			0.221539	+	0.975151i	$0.428892\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−3.81961e6	−	6.61576e6i	−0.265284	−	0.459486i
$731$	6.68553e6	−	1.15797e7i	0.462746	−	0.801499i
$732$	2.64686e6	−	4.58450e6i	0.182580	−	0.316238i
$733$	−3.46502e6	−	6.00158e6i	−0.238202	−	0.412578i	0.721996	−	0.691897i	$-0.243225\pi$
$733$	−3.46502e6	−	6.00158e6i	−0.238202	−	0.412578i	−0.960198	+	0.279319i	$0.909891\pi$
$734$	1.14696e7			0.785791
$735$		0			0
$736$	−2.26509e6			−0.154131
$737$	−1.36027e7	−	2.35606e7i	−0.922479	−	1.59778i
$738$	1.70780e6	−	2.95800e6i	0.115424	−	0.199921i
$739$	−7.11656e6	+	1.23262e7i	−0.479357	+	0.830270i	−0.999720	−	0.0236749i	$-0.992463\pi$
$739$	−7.11656e6	+	1.23262e7i	−0.479357	+	0.830270i	0.520363	+	0.853945i	$0.325797\pi$
$740$	−906464.	−	1.57004e6i	−0.0608515	−	0.105398i
$741$	675432.			0.0451894
$742$		0			0
$743$	−5.94460e6			−0.395048			−0.197524	−	0.980298i	$-0.563290\pi$
$743$	−5.94460e6			−0.395048			−0.197524	+	0.980298i	$0.563290\pi$
$744$	−2.05286e6	−	3.55566e6i	−0.135965	−	0.235499i
$745$	2.27315e6	−	3.93722e6i	0.150051	−	0.259896i
$746$	7.16059e6	−	1.24025e7i	0.471088	−	0.815948i
$747$	260334.	+	450912.i	0.0170698	+	0.0295658i
$748$	1.68072e7			1.09835
$749$		0			0
$750$	5.21726e6			0.338680
$751$	341376.	+	591281.i	0.0220868	+	0.0382555i	0.876858	−	0.480750i	$-0.159636\pi$
$751$	341376.	+	591281.i	0.0220868	+	0.0382555i	−0.854771	+	0.519006i	$0.826302\pi$
$752$	−685056.	+	1.18655e6i	−0.0441755	+	0.0765142i
$753$	2.18878e6	−	3.79108e6i	0.140674	−	0.243655i
$754$	−3.15074e6	−	5.45725e6i	−0.201830	−	0.349579i
$755$	−1.17664e7			−0.751233
$756$		0			0
$757$	1.46333e7			0.928116			0.464058	−	0.885805i	$-0.346393\pi$
$757$	1.46333e7			0.928116			0.464058	+	0.885805i	$0.346393\pi$
$758$	3.28470e6	+	5.68926e6i	0.207645	+	0.359652i
$759$	−6.60946e6	+	1.14479e7i	−0.416448	+	0.721310i
$760$	196352.	−	340092.i	0.0123311	−	0.0213581i
$761$	5.81837e6	+	1.00777e7i	0.364200	+	0.630812i	0.988647	−	0.150254i	$-0.0480092\pi$
$761$	5.81837e6	+	1.00777e7i	0.364200	+	0.630812i	−0.624448	+	0.781067i	$0.714676\pi$
$762$	−6.67440e6			−0.416414
$763$		0			0
$764$	6.02246e6			0.373285
$765$	−1.66585e6	−	2.88533e6i	−0.102916	−	0.178255i
$766$	−4.11395e6	+	7.12557e6i	−0.253330	+	0.438781i
$767$	2.45432e6	−	4.25101e6i	0.150641	−	0.260918i
$768$	−294912.	−	510803.i	−0.0180422	−	0.0312500i
$769$

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)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-13.0000 - 22.5167i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(2.00000 + 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-13.0000 - 22.5167i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(52.0000 - 90.0666i) q^{10} +(-332.000 + 575.041i) q^{11} +(-72.0000 - 124.708i) q^{12} +318.000 q^{13} +234.000 q^{15} +(-128.000 - 221.703i) q^{16} +(-791.000 + 1370.05i) q^{17} +(162.000 - 280.592i) q^{18} +(-118.000 - 204.382i) q^{19} +416.000 q^{20} -2656.00 q^{22} +(-1106.00 - 1915.65i) q^{23} +(288.000 - 498.831i) q^{24} +(1224.50 - 2120.90i) q^{25} +(636.000 + 1101.58i) q^{26} +729.000 q^{27} -4954.00 q^{29} +(468.000 + 810.600i) q^{30} +(3564.00 - 6173.03i) q^{31} +(512.000 - 886.810i) q^{32} +(-2988.00 - 5175.37i) q^{33} -6328.00 q^{34} +1296.00 q^{36} +(-2179.00 - 3774.14i) q^{37} +(472.000 - 817.528i) q^{38} +(-1431.00 + 2478.56i) q^{39} +(832.000 + 1441.07i) q^{40} +10542.0 q^{41} -8452.00 q^{43} +(-5312.00 - 9200.65i) q^{44} +(-1053.00 + 1823.85i) q^{45} +(4424.00 - 7662.59i) q^{46} +(-2676.00 - 4634.97i) q^{47} +2304.00 q^{48} +9796.00 q^{50} +(-7119.00 - 12330.5i) q^{51} +(-2544.00 + 4406.34i) q^{52} +(16677.0 - 28885.4i) q^{53} +(1458.00 + 2525.33i) q^{54} +17264.0 q^{55} +2124.00 q^{57} +(-9908.00 - 17161.2i) q^{58} +(7718.00 - 13368.0i) q^{59} +(-1872.00 + 3242.40i) q^{60} +(18381.0 + 31836.8i) q^{61} +28512.0 q^{62} +4096.00 q^{64} +(-4134.00 - 7160.30i) q^{65} +(11952.0 - 20701.5i) q^{66} +(-20486.0 + 35482.8i) q^{67} +(-12656.0 - 21920.8i) q^{68} +19908.0 q^{69} -9092.00 q^{71} +(2592.00 + 4489.48i) q^{72} +(36727.0 - 63613.0i) q^{73} +(8716.00 - 15096.6i) q^{74} +(11020.5 + 19088.1i) q^{75} +3776.00 q^{76} -11448.0 q^{78} +(-44700.0 - 77422.7i) q^{79} +(-3328.00 + 5764.27i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(21084.0 + 36518.6i) q^{82} -6428.00 q^{83} +41132.0 q^{85} +(-16904.0 - 29278.6i) q^{86} +(22293.0 - 38612.6i) q^{87} +(21248.0 - 36802.6i) q^{88} +(61329.0 + 106225. i) q^{89} -8424.00 q^{90} +35392.0 q^{92} +(32076.0 + 55557.3i) q^{93} +(10704.0 - 18539.9i) q^{94} +(-3068.00 + 5313.93i) q^{95} +(4608.00 + 7981.29i) q^{96} +21370.0 q^{97} +53784.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 9 q^{3} - 16 q^{4} - 26 q^{5} - 72 q^{6} - 128 q^{8} - 81 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 - 9 * q^3 - 16 * q^4 - 26 * q^5 - 72 * q^6 - 128 * q^8 - 81 * q^9	\( 2 q + 4 q^{2} - 9 q^{3} - 16 q^{4} - 26 q^{5} - 72 q^{6} - 128 q^{8} - 81 q^{9} + 104 q^{10} - 664 q^{11} - 144 q^{12} + 636 q^{13} + 468 q^{15} - 256 q^{16} - 1582 q^{17} + 324 q^{18} - 236 q^{19} + 832 q^{20} - 5312 q^{22} - 2212 q^{23} + 576 q^{24} + 2449 q^{25} + 1272 q^{26} + 1458 q^{27} - 9908 q^{29} + 936 q^{30} + 7128 q^{31} + 1024 q^{32} - 5976 q^{33} - 12656 q^{34} + 2592 q^{36} - 4358 q^{37} + 944 q^{38} - 2862 q^{39} + 1664 q^{40} + 21084 q^{41} - 16904 q^{43} - 10624 q^{44} - 2106 q^{45} + 8848 q^{46} - 5352 q^{47} + 4608 q^{48} + 19592 q^{50} - 14238 q^{51} - 5088 q^{52} + 33354 q^{53} + 2916 q^{54} + 34528 q^{55} + 4248 q^{57} - 19816 q^{58} + 15436 q^{59} - 3744 q^{60} + 36762 q^{61} + 57024 q^{62} + 8192 q^{64} - 8268 q^{65} + 23904 q^{66} - 40972 q^{67} - 25312 q^{68} + 39816 q^{69} - 18184 q^{71} + 5184 q^{72} + 73454 q^{73} + 17432 q^{74} + 22041 q^{75} + 7552 q^{76} - 22896 q^{78} - 89400 q^{79} - 6656 q^{80} - 6561 q^{81} + 42168 q^{82} - 12856 q^{83} + 82264 q^{85} - 33808 q^{86} + 44586 q^{87} + 42496 q^{88} + 122658 q^{89} - 16848 q^{90} + 70784 q^{92} + 64152 q^{93} + 21408 q^{94} - 6136 q^{95} + 9216 q^{96} + 42740 q^{97} + 107568 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 9 * q^3 - 16 * q^4 - 26 * q^5 - 72 * q^6 - 128 * q^8 - 81 * q^9 + 104 * q^10 - 664 * q^11 - 144 * q^12 + 636 * q^13 + 468 * q^15 - 256 * q^16 - 1582 * q^17 + 324 * q^18 - 236 * q^19 + 832 * q^20 - 5312 * q^22 - 2212 * q^23 + 576 * q^24 + 2449 * q^25 + 1272 * q^26 + 1458 * q^27 - 9908 * q^29 + 936 * q^30 + 7128 * q^31 + 1024 * q^32 - 5976 * q^33 - 12656 * q^34 + 2592 * q^36 - 4358 * q^37 + 944 * q^38 - 2862 * q^39 + 1664 * q^40 + 21084 * q^41 - 16904 * q^43 - 10624 * q^44 - 2106 * q^45 + 8848 * q^46 - 5352 * q^47 + 4608 * q^48 + 19592 * q^50 - 14238 * q^51 - 5088 * q^52 + 33354 * q^53 + 2916 * q^54 + 34528 * q^55 + 4248 * q^57 - 19816 * q^58 + 15436 * q^59 - 3744 * q^60 + 36762 * q^61 + 57024 * q^62 + 8192 * q^64 - 8268 * q^65 + 23904 * q^66 - 40972 * q^67 - 25312 * q^68 + 39816 * q^69 - 18184 * q^71 + 5184 * q^72 + 73454 * q^73 + 17432 * q^74 + 22041 * q^75 + 7552 * q^76 - 22896 * q^78 - 89400 * q^79 - 6656 * q^80 - 6561 * q^81 + 42168 * q^82 - 12856 * q^83 + 82264 * q^85 - 33808 * q^86 + 44586 * q^87 + 42496 * q^88 + 122658 * q^89 - 16848 * q^90 + 70784 * q^92 + 64152 * q^93 + 21408 * q^94 - 6136 * q^95 + 9216 * q^96 + 42740 * q^97 + 107568 * q^99

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