LMFDB - Embedded newform 294.6.e.p.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:	$1$
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.p.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	0.958558	−	0.284897i	$-0.0919594\pi$
$5$	13.0000	+	22.5167i	0.232551	+	0.402790i	−0.726007	+	0.687687i	$0.758626\pi$
$6$	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	$-0.584032\pi$
$13$	−318.000			−0.521878			−0.260939	+	0.965355i	$0.584032\pi$
$14$		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	$-0.602265\pi$
$17$	791.000	−	1370.05i	0.663826	−	1.14978i	0.979602	−	0.200946i	$-0.0644017\pi$
$18$	162.000	−	280.592i	0.117851	−	0.204124i
$19$	118.000	+	204.382i	0.0749891	+	0.129885i	0.901082	−	0.433650i	$-0.142774\pi$
$19$	118.000	+	204.382i	0.0749891	+	0.129885i	−0.826092	+	0.563535i	$0.809441\pi$
$20$	−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	$0.398700\pi$
$31$	−3564.00	+	6173.03i	−0.666091	+	1.15370i	−0.978988	+	0.203916i	$0.934633\pi$
$32$	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	$-0.662895\pi$
$41$	−10542.0			−0.979407			−0.489704	+	0.871889i	$0.662895\pi$
$42$		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	0.940749	−	0.339104i	$-0.110124\pi$
$47$	2676.00	+	4634.97i	0.176702	+	0.306057i	−0.764047	+	0.645161i	$0.776790\pi$
$48$	−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	−0.973488	−	0.228737i	$-0.926540\pi$
$59$	−7718.00	+	13368.0i	−0.288652	+	0.499960i	0.684836	+	0.728697i	$0.259874\pi$
$60$	−1872.00	+	3242.40i	−0.0671317	+	0.116276i
$61$	−18381.0	−	31836.8i	−0.632477	−	1.09548i	−0.987044	−	0.160451i	$-0.948705\pi$
$61$	−18381.0	−	31836.8i	−0.632477	−	1.09548i	0.354567	−	0.935031i	$-0.384628\pi$
$62$	−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	$0.465382\pi$
$73$	−36727.0	+	63613.0i	−0.806637	+	1.39714i	−0.915180	+	0.403045i	$0.867952\pi$
$74$	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	$-0.483692\pi$
$83$	6428.00			0.102419			0.0512095	+	0.998688i	$0.483692\pi$
$84$		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	$-0.860244\pi$
$89$	−61329.0	−	106225.i	−0.820712	−	1.42152i	0.0844405	−	0.996429i	$-0.473090\pi$
$90$	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	$-0.536784\pi$
$97$	−21370.0			−0.230608			−0.115304	+	0.993330i	$0.536784\pi$
$98$		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	−0.941726	−	0.336382i	$-0.890797\pi$
$101$	−18407.0	+	31881.9i	−0.179548	+	0.310986i	0.762178	+	0.647367i	$0.224130\pi$
$102$	28476.0	−	49321.9i	0.271006	−	0.469396i
$103$	52264.0	+	90523.9i	0.485411	+	0.840756i	0.999859	−	0.0167648i	$-0.00533666\pi$
$103$	52264.0	+	90523.9i	0.485411	+	0.840756i	−0.514448	+	0.857521i	$0.672003\pi$
$104$	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	0.936397	−	0.350943i	$-0.114139\pi$
$131$	32266.0	+	55886.4i	0.164273	+	0.284530i	−0.772124	+	0.635472i	$0.780805\pi$
$132$	−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	$-0.228174\pi$
$139$	343460.			1.50778			0.753892	+	0.656998i	$0.228174\pi$
$140$		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	$0.466084\pi$
$157$	−249533.	+	432204.i	−0.807940	+	1.39939i	−0.914289	+	0.405063i	$0.867249\pi$
$158$	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	$-0.553340\pi$
$167$	−120224.			−0.333580			−0.166790	+	0.985992i	$0.553340\pi$
$168$		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	$0.0570370\pi$
$173$	254437.	+	440698.i	0.646346	+	1.11950i	−0.337643	+	0.941274i	$0.609630\pi$
$174$	−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	$-0.288109\pi$
$181$	544410.			1.23518			0.617589	+	0.786501i	$0.288109\pi$
$182$		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	$0.472000\pi$
$199$	−457388.	+	792219.i	−0.818751	+	1.41812i	−0.906603	+	0.421985i	$0.861333\pi$
$200$	−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	$-0.166015\pi$
$223$	1.28776e6			1.73409			0.867047	+	0.498226i	$0.166015\pi$
$224$		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	$-0.521567\pi$
$227$	644526.	−	1.11635e6i	0.830187	−	1.43793i	0.897890	−	0.440220i	$-0.145100\pi$
$228$	−16992.0	+	29431.0i	−0.0216475	+	0.0374945i
$229$	339107.	+	587351.i	0.427315	+	0.740131i	0.996633	−	0.0819859i	$-0.0261262\pi$
$229$	339107.	+	587351.i	0.427315	+	0.740131i	−0.569319	+	0.822117i	$0.692793\pi$
$230$	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	$-0.657093\pi$
$241$	474109.	−	821181.i	0.525818	−	0.910744i	0.999548	−	0.0300734i	$-0.00957410\pi$
$242$	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	$-0.421653\pi$
$251$	486396.			0.487310			0.243655	+	0.969862i	$0.421653\pi$
$252$		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	0.509268	−	0.860608i	$-0.329916\pi$
$257$	−519549.	−	899885.i	−0.490675	−	0.849874i	−0.999942	+	0.0107346i	$0.996583\pi$
$258$	−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	−0.999452	−	0.0331036i	$-0.989461\pi$
$269$	−559055.	+	968312.i	−0.471057	+	0.815895i	0.528395	+	0.848999i	$0.322794\pi$
$270$	37908.0	−	65658.6i	0.0316462	−	0.0548128i
$271$	−95052.0	−	164635.i	−0.0786209	−	0.136175i	0.824034	−	0.566540i	$-0.191718\pi$
$271$	−95052.0	−	164635.i	−0.0786209	−	0.136175i	−0.902655	+	0.430365i	$0.858385\pi$
$272$	−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	$-0.598481\pi$
$283$	906290.	−	1.56974e6i	0.672669	−	1.16510i	0.977145	−	0.212576i	$-0.0681853\pi$
$284$	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	$-0.753407\pi$
$293$	−2.10031e6			−1.42927			−0.714634	+	0.699499i	$0.753407\pi$
$294$		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	$-0.334482\pi$
$307$	1.64104e6			0.993743			0.496872	+	0.867824i	$0.334482\pi$
$308$		0			0
$309$	940752.			0.560504
$310$	−370656.	−	641995.i	−0.219062	−	0.379426i
$311$	−472616.	+	818595.i	−0.277081	+	0.479919i	−0.970658	−	0.240464i	$-0.922701\pi$
$311$	−472616.	+	818595.i	−0.277081	+	0.479919i	0.693577	+	0.720383i	$0.256034\pi$
$312$	91584.0	−	158628.i	0.0532639	−	0.0922558i
$313$	207677.	+	359707.i	0.119820	+	0.207533i	0.919696	−	0.392631i	$-0.128435\pi$
$313$	207677.	+	359707.i	0.119820	+	0.207533i	−0.799877	+	0.600165i	$0.795102\pi$
$314$	−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	$-0.264553\pi$
$349$	3.06751e6			1.34810			0.674051	+	0.738684i	$0.264553\pi$
$350$		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	$0.397114\pi$
$353$	−1.55072e6	+	2.68593e6i	−0.662364	+	1.14725i	−0.979993	+	0.199033i	$0.936220\pi$
$354$	−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	$0.354193\pi$
$367$	−1.43370e6	+	2.48323e6i	−0.555638	+	0.962393i	−0.997854	+	0.0654844i	$0.979141\pi$
$368$	−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	0.629408	−	0.777075i	$-0.283298\pi$
$383$	−1.02849e6	−	1.78139e6i	−0.358263	−	0.620530i	−0.987671	+	0.156545i	$0.949964\pi$
$384$	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	0.986077	−	0.166291i	$-0.0531792\pi$
$397$	1.09606e6	+	1.89843e6i	0.349026	+	0.604531i	−0.637051	+	0.770822i	$0.719846\pi$
$398$	−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	$0.345928\pi$
$409$	−1.80610e6	+	3.12825e6i	−0.533866	+	0.924683i	−0.999217	+	0.0395571i	$0.987405\pi$
$410$	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	$-0.771587\pi$
$419$	−5.41489e6			−1.50680			−0.753398	+	0.657564i	$0.771587\pi$
$420$		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	$-0.797488\pi$
$433$	−6.27619e6			−1.60871			−0.804353	+	0.594152i	$0.797488\pi$
$434$		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	0.903011	−	0.429618i	$-0.141352\pi$
$439$	320796.	+	555635.i	0.0794452	+	0.137603i	−0.823566	+	0.567221i	$0.808018\pi$
$440$	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	$-0.520423\pi$
$461$	−585146.			−0.128237			−0.0641183	+	0.997942i	$0.520423\pi$
$462$		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	0.901518	−	0.432742i	$-0.142454\pi$
$467$	358150.	+	620334.i	0.0759929	+	0.131623i	−0.825525	+	0.564366i	$0.809121\pi$
$468$	−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	$-0.658579\pi$
$479$	2.62046e6	−	4.53877e6i	0.521842	−	0.903856i	0.999677	−	0.0254070i	$-0.00808816\pi$
$480$	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	$-0.242140\pi$
$503$	8.22050e6			1.44870			0.724350	+	0.689432i	$0.242140\pi$
$504$		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	0.560315	−	0.828280i	$-0.310680\pi$
$509$	−2.55522e6	−	4.42578e6i	−0.437154	−	0.757173i	−0.997469	+	0.0711070i	$0.977347\pi$
$510$	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	$-0.547128\pi$
$521$	4.85000e6	−	8.40044e6i	0.782793	−	1.35584i	0.930309	−	0.366778i	$-0.119539\pi$
$522$	−802548.	+	1.39005e6i	−0.128912	+	0.223283i
$523$	−1.58647e6	−	2.74785e6i	−0.253617	−	0.439278i	0.710902	−	0.703291i	$-0.248287\pi$
$523$	−1.58647e6	−	2.74785e6i	−0.253617	−	0.439278i	−0.964519	+	0.264013i	$0.914954\pi$
$524$	−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	−0.780326	−	0.625373i	$-0.784947\pi$
$563$	1.13886e6	−	1.97257e6i	0.151426	−	0.262277i	0.931752	+	0.363096i	$0.118280\pi$
$564$	−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	$-0.649001\pi$
$577$	4.37663e6	−	7.58055e6i	0.547269	−	0.947897i	0.998460	−	0.0554701i	$-0.0176657\pi$
$578$	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	$-0.280768\pi$
$587$	1.06117e7			1.27113			0.635564	+	0.772048i	$0.280768\pi$
$588$		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	0.915808	−	0.401616i	$-0.131551\pi$
$593$	942759.	+	1.63291e6i	0.110094	+	0.190689i	−0.805714	+	0.592305i	$0.798218\pi$
$594$	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	$-0.633042\pi$
$601$	−7.18846e6			−0.811801			−0.405900	+	0.913917i	$0.633042\pi$
$602$		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	$0.0372095\pi$
$607$	5.42472e6	+	9.39589e6i	0.597593	+	1.03506i	−0.395582	+	0.918431i	$0.629457\pi$
$608$	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	−0.966747	−	0.255735i	$-0.917683\pi$
$619$	−2.49668e6	+	4.32438e6i	−0.261901	+	0.453625i	0.704846	+	0.709360i	$0.251016\pi$
$620$	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	$-0.652220\pi$
$643$	−9.64934e6			−0.920386			−0.460193	+	0.887819i	$0.652220\pi$
$644$		0			0
$645$	−1.97777e6			−0.187187
$646$	746704.	+	1.29333e6i	0.0703991	+	0.121935i
$647$	146184.	−	253198.i	0.0137290	−	0.0237793i	−0.859079	−	0.511843i	$-0.828963\pi$
$647$	146184.	−	253198.i	0.0137290	−	0.0237793i	0.872808	+	0.488063i	$0.162296\pi$
$648$	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	−0.816732	−	0.577017i	$-0.804217\pi$
$661$	1.02609e6	−	1.77725e6i	0.0913448	−	0.158214i	0.908077	+	0.418803i	$0.137550\pi$
$662$	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	0.844985	−	0.534791i	$-0.179610\pi$
$677$	−484767.	−	839641.i	−0.0406501	−	0.0704080i	−0.885635	+	0.464383i	$0.846276\pi$
$678$	−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	0.687427	−	0.726253i	$-0.258740\pi$
$691$	−3.58019e6	−	6.20107e6i	−0.285240	−	0.494051i	−0.972667	+	0.232203i	$0.925407\pi$
$692$	−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	$0.0268970\pi$
$719$	7.91940e6	+	1.37168e7i	0.571308	+	0.989534i	−0.425124	+	0.905135i	$0.639770\pi$
$720$	−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	$-0.571108\pi$
$727$	−6.31418e6			−0.443078			−0.221539	+	0.975151i	$0.571108\pi$
$728$		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	0.960198	−	0.279319i	$-0.0901087\pi$
$733$	3.46502e6	+	6.00158e6i	0.238202	+	0.412578i	−0.721996	+	0.691897i	$0.756775\pi$
$734$	−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	0.624448	−	0.781067i	$-0.285324\pi$
$761$	−5.81837e6	−	1.00777e7i	−0.364200	−	0.630812i	−0.988647	+	0.150254i	$0.951991\pi$
$762$	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
$769$	−1.91472e7			−1.16759			−0.583793	−	0.811902i	$-0.698432\pi$

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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