LMFDB - Embedded newform 294.6.e.i.79.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,6,Mod(67,294)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [2,4,-9,-16,-26,-72,0,-128,-81,104,-664] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$47.1528430250$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.6.e.i.67.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00000 - 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-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} + 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}+ \cdots + 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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	−13.0000	+	22.5167i	−0.232551	+	0.402790i	−0.958558	−	0.284897i	$-0.908041\pi$
$5$	−13.0000	+	22.5167i	−0.232551	+	0.402790i	0.726007	+	0.687687i	$0.241374\pi$
$6$	−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	−0.900159	−	0.435562i	$-0.856550\pi$
$11$	−332.000	−	575.041i	−0.827287	−	1.43290i	0.0728713	−	0.997341i	$-0.476784\pi$
$12$	−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	−0.979602	−	0.200946i	$-0.935598\pi$
$17$	−791.000	−	1370.05i	−0.663826	−	1.14978i	0.315776	−	0.948834i	$-0.397735\pi$
$18$	162.000	+	280.592i	0.117851	+	0.204124i
$19$	−118.000	+	204.382i	−0.0749891	+	0.129885i	−0.901082	−	0.433650i	$-0.857226\pi$
$19$	−118.000	+	204.382i	−0.0749891	+	0.129885i	0.826092	+	0.563535i	$0.190559\pi$
$20$	416.000			0.232551
$21$		0			0
$22$	−2656.00			−1.16996
$23$	−1106.00	+	1915.65i	−0.435949	+	0.755086i	−0.997373	−	0.0724429i	$-0.976920\pi$
$23$	−1106.00	+	1915.65i	−0.435949	+	0.755086i	0.561424	+	0.827529i	$0.310254\pi$
$24$	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	0.978988	+	0.203916i	$0.0653670\pi$
$31$	3564.00	+	6173.03i	0.666091	+	1.15370i	−0.312897	+	0.949787i	$0.601300\pi$
$32$	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	−0.966686	−	0.255966i	$-0.917606\pi$
$37$	−2179.00	+	3774.14i	−0.261669	+	0.453225i	0.705016	+	0.709191i	$0.250940\pi$
$38$	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	−0.940749	−	0.339104i	$-0.889876\pi$
$47$	−2676.00	+	4634.97i	−0.176702	+	0.306057i	0.764047	+	0.645161i	$0.223210\pi$
$48$	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	0.908963	+	0.416878i	$0.136876\pi$
$53$	16677.0	+	28885.4i	0.815508	+	1.41250i	−0.0934545	+	0.995624i	$0.529791\pi$
$54$	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	$-0.0734596\pi$
$59$	7718.00	+	13368.0i	0.288652	+	0.499960i	−0.684836	+	0.728697i	$0.740126\pi$
$60$	−1872.00	−	3242.40i	−0.0671317	−	0.116276i
$61$	18381.0	−	31836.8i	0.632477	−	1.09548i	−0.354567	−	0.935031i	$-0.615372\pi$
$61$	18381.0	−	31836.8i	0.632477	−	1.09548i	0.987044	−	0.160451i	$-0.0512949\pi$
$62$	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	−0.997702	−	0.0677597i	$-0.978415\pi$
$67$	−20486.0	−	35482.8i	−0.557532	−	0.965675i	0.440169	−	0.897915i	$-0.354918\pi$
$68$	−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	0.915180	+	0.403045i	$0.132048\pi$
$73$	36727.0	+	63613.0i	0.806637	+	1.39714i	−0.108543	+	0.994092i	$0.534618\pi$
$74$	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	0.109911	+	0.993941i	$0.464944\pi$
$79$	−44700.0	+	77422.7i	−0.805823	+	1.39573i	−0.915734	+	0.401785i	$0.868390\pi$
$80$	−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	−0.0844405	−	0.996429i	$-0.526910\pi$
$89$	61329.0	−	106225.i	0.820712	−	1.42152i	0.905153	−	0.425087i	$-0.139756\pi$
$90$	−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	0.941726	−	0.336382i	$-0.109203\pi$
$101$	18407.0	+	31881.9i	0.179548	+	0.310986i	−0.762178	+	0.647367i	$0.775870\pi$
$102$	28476.0	+	49321.9i	0.271006	+	0.469396i
$103$	−52264.0	+	90523.9i	−0.485411	+	0.840756i	−0.999859	−	0.0167648i	$-0.994663\pi$
$103$	−52264.0	+	90523.9i	−0.485411	+	0.840756i	0.514448	+	0.857521i	$0.327997\pi$
$104$	−20352.0			−0.184512
$105$		0			0
$106$	133416.			1.15330
$107$	−107220.	+	185710.i	−0.905350	+	1.56811i	−0.0849026	+	0.996389i	$0.527058\pi$
$107$	−107220.	+	185710.i	−0.905350	+	1.56811i	−0.820447	+	0.571722i	$0.806275\pi$
$108$	−5832.00	−	10101.3i	−0.0481125	−	0.0833333i
$109$	−14399.0	−	24939.8i	−0.116082	−	0.201060i	0.802130	−	0.597150i	$-0.203700\pi$
$109$	−14399.0	−	24939.8i	−0.116082	−	0.201060i	−0.918212	+	0.396090i	$0.870367\pi$
$110$	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	$-0.885861\pi$
$131$	−32266.0	+	55886.4i	−0.164273	+	0.284530i	0.772124	+	0.635472i	$0.219195\pi$
$132$	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	0.637840	−	0.770169i	$-0.279828\pi$
$137$	−76465.0	−	132441.i	−0.348066	−	0.602868i	−0.985906	+	0.167301i	$0.946495\pi$
$138$	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	−0.658409	−	0.752661i	$-0.728770\pi$
$149$	87429.0	−	151431.i	0.322619	−	0.558792i	0.981028	+	0.193868i	$0.0621034\pi$
$150$	−44082.0	−	76352.3i	−0.159968	−	0.277073i
$151$	226276.	+	391922.i	0.807600	+	1.39880i	0.914522	+	0.404536i	$0.132567\pi$
$151$	226276.	+	391922.i	0.807600	+	1.39880i	−0.106922	+	0.994267i	$0.534100\pi$
$152$	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	0.914289	+	0.405063i	$0.132751\pi$
$157$	249533.	+	432204.i	0.807940	+	1.39939i	−0.106349	+	0.994329i	$0.533916\pi$
$158$	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	−0.267086	−	0.963673i	$-0.586061\pi$
$163$	237794.	−	411871.i	0.701022	−	1.21421i	0.968108	−	0.250534i	$-0.0806060\pi$
$164$	−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	0.337643	+	0.941274i	$0.390370\pi$
$173$	−254437.	+	440698.i	−0.646346	+	1.11950i	−0.983989	+	0.178230i	$0.942963\pi$
$174$	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	−0.996697	−	0.0812080i	$-0.974122\pi$
$179$	−243780.	−	422239.i	−0.568677	−	0.984977i	0.428020	−	0.903769i	$-0.359211\pi$
$180$	−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	−0.990069	−	0.140584i	$-0.955102\pi$
$191$	−188202.	+	325975.i	−0.373285	+	0.646549i	0.616784	+	0.787133i	$0.288435\pi$
$192$	−18432.0	−	31925.2i	−0.0360844	−	0.0625000i
$193$	−422473.	−	731745.i	−0.816405	−	1.41406i	−0.908315	−	0.418288i	$-0.862630\pi$
$193$	−422473.	−	731745.i	−0.816405	−	1.41406i	0.0919095	−	0.995767i	$-0.470703\pi$
$194$	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	0.906603	+	0.421985i	$0.138667\pi$
$199$	457388.	+	792219.i	0.818751	+	1.41812i	−0.0878512	+	0.996134i	$0.528000\pi$
$200$	−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	−0.897890	−	0.440220i	$-0.854900\pi$
$227$	−644526.	−	1.11635e6i	−0.830187	−	1.43793i	0.0677031	−	0.997706i	$-0.478433\pi$
$228$	−16992.0	−	29431.0i	−0.0216475	−	0.0374945i
$229$	−339107.	+	587351.i	−0.427315	+	0.740131i	−0.996633	−	0.0819859i	$-0.973874\pi$
$229$	−339107.	+	587351.i	−0.427315	+	0.740131i	0.569319	+	0.822117i	$0.307207\pi$
$230$	−230048.			−0.286747
$231$		0			0
$232$	317056.			0.386737
$233$	558655.	−	967619.i	0.674146	−	1.16765i	−0.302572	−	0.953127i	$-0.597845\pi$
$233$	558655.	−	967619.i	0.674146	−	1.16765i	0.976718	−	0.214528i	$-0.0688214\pi$
$234$	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	−0.999548	−	0.0300734i	$-0.990426\pi$
$241$	−474109.	−	821181.i	−0.525818	−	0.910744i	0.473730	−	0.880670i	$-0.342907\pi$
$242$	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	−0.509268	−	0.860608i	$-0.670084\pi$
$257$	519549.	−	899885.i	0.490675	−	0.849874i	0.999942	+	0.0107346i	$0.00341700\pi$
$258$	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	−0.992485	−	0.122364i	$-0.960952\pi$
$263$	−675522.	−	1.17004e6i	−0.602213	−	1.04306i	0.390272	−	0.920699i	$-0.372381\pi$
$264$	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	$-0.0105391\pi$
$269$	559055.	+	968312.i	0.471057	+	0.815895i	−0.528395	+	0.848999i	$0.677206\pi$
$270$	37908.0	+	65658.6i	0.0316462	+	0.0548128i
$271$	95052.0	−	164635.i	0.0786209	−	0.136175i	−0.824034	−	0.566540i	$-0.808282\pi$
$271$	95052.0	−	164635.i	0.0786209	−	0.136175i	0.902655	+	0.430365i	$0.141615\pi$
$272$	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	0.902605	−	0.430469i	$-0.141652\pi$
$277$	100253.	+	173643.i	0.0785051	+	0.135975i	−0.824100	+	0.566444i	$0.808319\pi$
$278$	−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	−0.977145	−	0.212576i	$-0.931815\pi$
$283$	−906290.	−	1.56974e6i	−0.672669	−	1.16510i	0.304476	−	0.952520i	$-0.401519\pi$
$284$	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	0.970658	−	0.240464i	$-0.0772995\pi$
$311$	472616.	+	818595.i	0.277081	+	0.479919i	−0.693577	+	0.720383i	$0.743966\pi$
$312$	91584.0	+	158628.i	0.0532639	+	0.0922558i
$313$	−207677.	+	359707.i	−0.119820	+	0.207533i	−0.919696	−	0.392631i	$-0.871565\pi$
$313$	−207677.	+	359707.i	−0.119820	+	0.207533i	0.799877	+	0.600165i	$0.204898\pi$
$314$	1.99626e6			1.14260
$315$		0			0
$316$	1.43040e6			0.805823
$317$	−592407.	+	1.02608e6i	−0.331110	+	0.573499i	−0.982730	−	0.185047i	$-0.940756\pi$
$317$	−592407.	+	1.02608e6i	−0.331110	+	0.573499i	0.651620	+	0.758546i	$0.274090\pi$
$318$	−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	−0.985179	−	0.171528i	$-0.945129\pi$
$331$	−685774.	+	1.18780e6i	−0.344042	+	0.595898i	0.641138	+	0.767426i	$0.278463\pi$
$332$	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	−0.996092	−	0.0883168i	$-0.971851\pi$
$347$	−1.28866e6	−	2.23202e6i	−0.574531	−	0.995117i	0.421562	−	0.906800i	$-0.361482\pi$
$348$	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	0.979993	+	0.199033i	$0.0637802\pi$
$353$	1.55072e6	+	2.68593e6i	0.662364	+	1.14725i	−0.317628	+	0.948215i	$0.602886\pi$
$354$	−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	−0.830547	−	0.556949i	$-0.811972\pi$
$359$	163754.	−	283630.i	0.0670588	−	0.116149i	0.897605	+	0.440800i	$0.145305\pi$
$360$	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	0.997854	+	0.0654844i	$0.0208593\pi$
$367$	1.43370e6	+	2.48323e6i	0.555638	+	0.962393i	−0.442216	+	0.896909i	$0.645807\pi$
$368$	−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	0.312735	+	0.949840i	$0.398755\pi$
$373$	−1.79015e6	+	3.10063e6i	−0.666218	+	1.15392i	−0.978953	+	0.204084i	$0.934579\pi$
$374$	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	$-0.716702\pi$
$383$	1.02849e6	−	1.78139e6i	0.358263	−	0.620530i	0.987671	+	0.156545i	$0.0500357\pi$
$384$	−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	0.809788	−	0.586723i	$-0.199582\pi$
$389$	−308071.	−	533595.i	−0.103223	−	0.178788i	−0.913011	+	0.407935i	$0.866249\pi$
$390$	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	$-0.946821\pi$
$397$	−1.09606e6	+	1.89843e6i	−0.349026	+	0.604531i	0.637051	+	0.770822i	$0.280154\pi$
$398$	3.65910e6			1.15789
$399$		0			0
$400$	−626944.			−0.195920
$401$	−1.64227e6	+	2.84449e6i	−0.510015	+	0.883373i	0.489917	+	0.871769i	$0.337027\pi$
$401$	−1.64227e6	+	2.84449e6i	−0.510015	+	0.883373i	−0.999933	+	0.0116038i	$0.996306\pi$
$402$	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	0.999217	+	0.0395571i	$0.0125947\pi$
$409$	1.80610e6	+	3.12825e6i	0.533866	+	0.924683i	−0.465351	+	0.885126i	$0.654072\pi$
$410$	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	0.988078	−	0.153957i	$-0.0492018\pi$
$431$	1.39107e6	+	2.40940e6i	0.360708	+	0.624765i	−0.627370	+	0.778722i	$0.715868\pi$
$432$	−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	−0.903011	−	0.429618i	$-0.858648\pi$
$439$	−320796.	+	555635.i	−0.0794452	+	0.137603i	0.823566	+	0.567221i	$0.191982\pi$
$440$	−1.10490e6			−0.272076
$441$		0			0
$442$	−2.01230e6			−0.489934
$443$	−3.02773e6	+	5.24418e6i	−0.733006	+	1.26960i	0.222587	+	0.974913i	$0.428550\pi$
$443$	−3.02773e6	+	5.24418e6i	−0.733006	+	1.26960i	−0.955593	+	0.294691i	$0.904783\pi$
$444$	−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	−0.852988	−	0.521931i	$-0.825212\pi$
$457$	113899.	−	197279.i	0.0255111	−	0.0441865i	0.878499	+	0.477744i	$0.158545\pi$
$458$	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	−0.901518	−	0.432742i	$-0.857546\pi$
$467$	−358150.	+	620334.i	−0.0759929	+	0.131623i	0.825525	+	0.564366i	$0.190879\pi$
$468$	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	−0.999677	−	0.0254070i	$-0.991912\pi$
$479$	−2.62046e6	−	4.53877e6i	−0.521842	−	0.903856i	0.477836	−	0.878449i	$-0.341421\pi$
$480$	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	0.807725	−	0.589559i	$-0.200698\pi$
$487$	−558508.	−	967364.i	−0.106710	−	0.184828i	−0.914436	+	0.404731i	$0.867365\pi$
$488$	−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	−0.405960	−	0.913891i	$-0.633063\pi$
$499$	3.27324e6	−	5.66941e6i	0.588473	−	1.01926i	0.994433	−	0.105374i	$-0.0336038\pi$
$500$	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	−0.560315	−	0.828280i	$-0.689320\pi$
$509$	2.55522e6	−	4.42578e6i	0.437154	−	0.757173i	0.997469	+	0.0711070i	$0.0226532\pi$
$510$	−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	−0.930309	−	0.366778i	$-0.880461\pi$
$521$	−4.85000e6	−	8.40044e6i	−0.782793	−	1.35584i	0.147516	−	0.989060i	$-0.452872\pi$
$522$	−802548.	−	1.39005e6i	−0.128912	−	0.223283i
$523$	1.58647e6	−	2.74785e6i	0.253617	−	0.439278i	−0.710902	−	0.703291i	$-0.751713\pi$
$523$	1.58647e6	−	2.74785e6i	0.253617	−	0.439278i	0.964519	+	0.264013i	$0.0850463\pi$
$524$	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	−0.513238	−	0.858246i	$-0.671554\pi$
$541$	3.31287e6	−	5.73806e6i	0.486644	−	0.842893i	0.999882	+	0.0153538i	$0.00488746\pi$
$542$	−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	0.643171	−	0.765723i	$-0.277619\pi$
$557$	−2.50088e6	−	4.33165e6i	−0.341550	−	0.591583i	−0.984721	+	0.174140i	$0.944285\pi$
$558$	−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	$-0.215053\pi$
$563$	−1.13886e6	−	1.97257e6i	−0.151426	−	0.262277i	−0.931752	+	0.363096i	$0.881720\pi$
$564$	−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	0.421870	+	0.906656i	$0.361374\pi$
$569$	−4.43490e6	+	7.68147e6i	−0.574252	+	0.994634i	−0.996122	+	0.0879781i	$0.971959\pi$
$570$	110448.	+	191302.i	0.0142387	+	0.0246622i
$571$	−7.00509e6	−	1.21332e7i	−0.899132	−	1.55734i	−0.828606	−	0.559832i	$-0.810866\pi$
$571$	−7.00509e6	−	1.21332e7i	−0.899132	−	1.55734i	−0.0705261	−	0.997510i	$-0.522468\pi$
$572$	−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	−0.998460	−	0.0554701i	$-0.982334\pi$
$577$	−4.37663e6	−	7.58055e6i	−0.547269	−	0.947897i	0.451192	−	0.892427i	$-0.350999\pi$
$578$	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	−0.915808	−	0.401616i	$-0.868449\pi$
$593$	−942759.	+	1.63291e6i	−0.110094	+	0.190689i	0.805714	+	0.592305i	$0.201782\pi$
$594$	−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	−0.959150	−	0.282900i	$-0.908704\pi$
$599$	−6.36281e6	−	1.10207e7i	−0.724573	−	1.25500i	0.234576	−	0.972098i	$-0.424630\pi$
$600$	−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	0.395582	+	0.918431i	$0.370543\pi$
$607$	−5.42472e6	+	9.39589e6i	−0.597593	+	1.03506i	−0.993175	+	0.116631i	$0.962790\pi$
$608$	−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	0.967199	−	0.254018i	$-0.0817523\pi$
$613$	2.45256e6	+	4.24795e6i	0.263614	+	0.456592i	−0.703586	+	0.710610i	$0.748419\pi$
$614$	−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	$-0.0823174\pi$
$619$	2.49668e6	+	4.32438e6i	0.261901	+	0.453625i	−0.704846	+	0.709360i	$0.748984\pi$
$620$	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	0.967016	−	0.254717i	$-0.0819823\pi$
$641$	2.73503e6	+	4.73722e6i	0.262916	+	0.455385i	−0.704099	+	0.710102i	$0.748649\pi$
$642$	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	0.859079	−	0.511843i	$-0.171037\pi$
$647$	−146184.	−	253198.i	−0.0137290	−	0.0237793i	−0.872808	+	0.488063i	$0.837704\pi$
$648$	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	−0.980173	−	0.198142i	$-0.936509\pi$
$653$	−3.47040e6	+	6.01091e6i	−0.318491	+	0.551642i	0.661683	+	0.749784i	$0.269843\pi$
$654$	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	$-0.195783\pi$
$661$	−1.02609e6	−	1.77725e6i	−0.0913448	−	0.158214i	−0.908077	+	0.418803i	$0.862450\pi$
$662$	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	$-0.820390\pi$
$677$	484767.	−	839641.i	0.0406501	−	0.0704080i	0.885635	+	0.464383i	$0.153724\pi$
$678$	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	0.990417	+	0.138106i	$0.0441016\pi$
$683$	7.49539e6	+	1.29824e7i	0.614812	+	1.06489i	−0.375605	+	0.926780i	$0.622565\pi$
$684$	−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	$-0.741260\pi$
$691$	3.58019e6	−	6.20107e6i	0.285240	−	0.494051i	0.972667	+	0.232203i	$0.0745932\pi$
$692$	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	0.0760603	+	0.997103i	$0.475766\pi$
$709$	−1.10491e7	+	1.91375e7i	−0.825487	+	1.42978i	−0.901547	+	0.432681i	$0.857567\pi$
$710$	−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	0.425124	+	0.905135i	$0.360230\pi$
$719$	−7.91940e6	+	1.37168e7i	−0.571308	+	0.989534i	−0.996432	+	0.0843990i	$0.973103\pi$
$720$	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	−0.960198	−	0.279319i	$-0.909891\pi$
$733$	−3.46502e6	+	6.00158e6i	−0.238202	+	0.412578i	0.721996	+	0.691897i	$0.243225\pi$
$734$	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	0.520363	−	0.853945i	$-0.325797\pi$
$739$	−7.11656e6	−	1.23262e7i	−0.479357	−	0.830270i	−0.999720	+	0.0236749i	$0.992463\pi$
$740$	−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	−0.854771	−	0.519006i	$-0.826302\pi$
$751$	341376.	−	591281.i	0.0220868	−	0.0382555i	0.876858	+	0.480750i	$0.159636\pi$
$752$	−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	$-0.714676\pi$
$761$	5.81837e6	−	1.00777e7i	0.364200	−	0.630812i	0.988647	+	0.150254i	$0.0480092\pi$
$762$	−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	$-0.301568\pi$
$769$	1.91472e7			1.16759			0.583793	+	0.811902i	$0.301568\pi$
$770$		0			0
$771$	−9.35188e6			−0.566582
$772$	−6.75957e6	+	1.17079e7i	−0.408203	+	0.707028i
$773$	2.69630e6	+	4.67013e6i	0.162301	+	0.281113i	0.935693	−	0.352814i	$-0.114775\pi$
$773$	2.69630e6	+	4.67013e6i	0.162301	+	0.281113i	−0.773393	+	0.633927i	$0.781442\pi$
$774$	−1.36922e6	−	2.37157e6i	−0.0821527	−	0.142293i
$775$	−8.72824e6	+	1.51177e7i	−0.522002	+	0.904134i
$776$	−1.36768e6			−0.0815324
$777$		0			0
$778$	−2.46457e6			−0.145979
$779$	−1.24396e6	+	2.15459e6i	−0.0734449	+	0.127210i
$780$	−595296.	−	1.03108e6i	−0.0350345	−	0.0606816i
$781$	3.01854e6	+	5.22827e6i	0.177080	+	0.306712i
$782$	6.99877e6	−	1.21222e7i	0.409265	−	0.708868i
$783$	−3.61147e6			−0.210513
$784$		0			0
$785$	−1.29757e7			−0.751549
$786$	1.16158e6	−	2.01191e6i	0.0670643	−	0.116159i
$787$	−1.52174e6	−	2.63573e6i	−0.0875796	−	0.151692i	0.818908	−	0.573925i	$-0.194580\pi$
$787$	−1.52174e6	−	2.63573e6i	−0.0875796	−	0.151692i	−0.906488	+	0.422233i	$0.861247\pi$
$788$	3.94235e6	+	6.82835e6i	0.226173	+	0.391742i
$789$	−6.07970e6	+	1.05303e7i	−0.347688	+	0.602213i
$790$	−9.29760e6			−0.530033
$791$		0			0
$792$	−3.44218e6			−0.194993
$793$	5.84516e6	−	1.01241e7i	0.330075	−	0.571708i
$794$	4.38424e6	+	7.59372e6i	0.246799	+	0.427468i
$795$	3.90242e6	+	6.75919e6i	0.218986	+	0.379295i
$796$	7.31821e6	−	1.26755e7i	0.409376	−	0.709060i
$797$	2.29652e7			1.28063			0.640316	−	0.768111i	$-0.278803\pi$
$797$	2.29652e7			1.28063			0.640316	+	0.768111i	$0.278803\pi$
$798$		0			0
$799$	8.46686e6			0.469197
$800$	−1.25389e6	+	2.17180e6i	−0.0692682	+	0.119976i
$801$	4.96765e6	+	8.60422e6i	0.273571	+	0.473838i
$802$	6.56908e6	+	1.13780e7i	0.360635	+	0.624639i
$803$	2.43867e7	−	4.22391e7i	1.33464	−	2.31167i
$804$	5.89997e6			0.321892
$805$		0			0
$806$	9.06682e6			0.491606
$807$	5.03150e6	−	8.71480e6i	0.271965	−	0.471057i
$808$	−1.17805e6	−	2.04044e6i	−0.0634797	−	0.109950i
$809$	−9.53934e6	−	1.65226e7i	−0.512445	−	0.887580i	−0.999896	−	0.0144301i	$-0.995407\pi$
$809$	−9.53934e6	−	1.65226e7i	−0.512445	−	0.887580i	0.487451	−	0.873150i	$-0.337927\pi$
$810$	341172.	−	590927.i	0.0182709	−	0.0316462i
$811$	1.09414e7			0.584147			0.292074	−	0.956396i	$-0.405655\pi$
$811$	1.09414e7			0.584147			0.292074	+	0.956396i	$0.405655\pi$
$812$		0			0
$813$	−1.71094e6			−0.0907836
$814$	5.78742e6	−	1.00241e7i	0.306143	−	0.530255i
$815$	6.18264e6	+	1.07087e7i	0.326047	+	0.564730i
$816$	−1.82246e6	−	3.15660e6i	−0.0958150	−	0.165956i
$817$	997336.	−	1.72744e6i	0.0522741	−	0.0905414i
$818$	1.44488e7			0.755001
$819$		0			0
$820$	4.38547e6			0.227762
$821$	−1.06297e7	+	1.84112e7i	−0.550380	+	0.953286i	0.447867	+	0.894100i	$0.352184\pi$
$821$	−1.06297e7	+	1.84112e7i	−0.550380	+	0.953286i	−0.998247	+	0.0591856i	$0.981150\pi$
$822$	2.75274e6	+	4.76789e6i	0.142097	+	0.246120i
$823$	7.11282e6	+	1.23198e7i	0.366052	+	0.634020i	0.988944	−	0.148287i	$-0.0473760\pi$
$823$	7.11282e6	+	1.23198e7i	0.366052	+	0.634020i	−0.622893	+	0.782307i	$0.714043\pi$
$824$	3.34490e6	−	5.79353e6i	0.171619	−	0.297252i
$825$	−1.46352e7			−0.748625
$826$		0			0
$827$	2.76103e6			0.140381			0.0701904	−	0.997534i	$-0.477639\pi$
$827$	2.76103e6			0.140381			0.0701904	+	0.997534i	$0.477639\pi$
$828$	−1.43338e6	+	2.48268e6i	−0.0726581	+	0.125848i
$829$	1.91073e7	+	3.30949e7i	0.965637	+	1.67253i	0.707894	+	0.706319i	$0.249645\pi$
$829$	1.91073e7	+	3.30949e7i	0.965637	+	1.67253i	0.257743	+	0.966214i	$0.417021\pi$
$830$	−334256.	−	578948.i	−0.0168416	−	0.0291705i
$831$	902277.	−	1.56279e6i	0.0453249	−	0.0785051i
$832$	1.30253e6			0.0652347
$833$		0			0
$834$	1.23646e7			0.615550
$835$	−1.56291e6	+	2.70704e6i	−0.0775744	+	0.134363i
$836$	−1.25363e6	−	2.17135e6i	−0.0620375	−	0.107452i
$837$	2.59816e6	+	4.50014e6i	0.128189	+	0.222030i
$838$	1.08298e7	−	1.87577e7i	0.532733	−	0.922721i
$839$	1.06044e7			0.520094			0.260047	−	0.965596i	$-0.416262\pi$
$839$	1.06044e7			0.520094			0.260047	+	0.965596i	$0.416262\pi$
$840$		0			0
$841$	4.03097e6			0.196526
$842$	7.21259e6	−	1.24926e7i	0.350599	−	0.607256i
$843$	−4.91566e6	−	8.51418e6i	−0.238239	−	0.412643i
$844$	−2.49424e6	−	4.32015e6i	−0.120526	−	0.208758i
$845$	3.51220e6	−	6.08330e6i	0.169214	−	0.293088i
$846$	−1.73405e6			−0.0832981
$847$		0			0
$848$	−8.53862e6			−0.407754
$849$	−8.15661e6	+	1.41277e7i	−0.388365	+	0.672669i
$850$	−7.74864e6	−	1.34210e7i	−0.367856	−	0.637145i
$851$	−4.81995e6	−	8.34839e6i	−0.228149	−	0.395166i
$852$	654624.	−	1.13384e6i	0.0308953	−	0.0535123i
$853$	−4.07009e7			−1.91527			−0.957637	−	0.287977i	$-0.907017\pi$
$853$	−4.07009e7			−1.91527			−0.957637	+	0.287977i	$0.907017\pi$
$854$		0			0
$855$	497016.			0.0232517
$856$	6.86208e6	−	1.18855e7i	0.320089	−	0.554411i
$857$	1.55060e7	+	2.68572e7i	0.721187	+	1.24913i	0.960524	+	0.278196i	$0.0897364\pi$
$857$	1.55060e7	+	2.68572e7i	0.721187	+	1.24913i	−0.239338	+	0.970936i	$0.576930\pi$
$858$	3.80074e6	+	6.58307e6i	0.176258	+	0.305288i
$859$	−5.45519e6	+	9.44866e6i	−0.252247	+	0.436905i	−0.964144	−	0.265379i	$-0.914503\pi$
$859$	−5.45519e6	+	9.44866e6i	−0.252247	+	0.436905i	0.711897	+	0.702284i	$0.247836\pi$
$860$	−3.51603e6			−0.162109
$861$		0			0
$862$	1.11286e7			0.510118
$863$	−5.20447e6	+	9.01441e6i	−0.237875	+	0.412012i	−0.960104	−	0.279642i	$-0.909784\pi$
$863$	−5.20447e6	+	9.01441e6i	−0.237875	+	0.412012i	0.722229	+	0.691654i	$0.243118\pi$
$864$	373248.	+	646484.i	0.0170103	+	0.0294628i
$865$	−6.61536e6	−	1.14581e7i	−0.300617	−	0.520684i
$866$	1.25524e7	−	2.17414e7i	0.568763	−	0.985127i
$867$	9.74580e6			0.440321
$868$		0			0
$869$	5.93616e7			2.66659
$870$	−2.31847e6	+	4.01571e6i	−0.103849	+	0.179872i
$871$	−6.51455e6	−	1.12835e7i	−0.290964	−	0.503964i
$872$	921536.	+	1.59615e6i	0.0410413	+	0.0710856i
$873$	−865485.	+	1.49906e6i	−0.0384347	+	0.0665709i
$874$	−2.08813e6			−0.0924652
$875$		0			0
$876$	−1.05774e7			−0.465712
$877$	−8.20318e6	+	1.42083e7i	−0.360150	+	0.623797i	−0.987985	−	0.154549i	$-0.950608\pi$
$877$	−8.20318e6	+	1.42083e7i	−0.360150	+	0.623797i	0.627836	+	0.778346i	$0.283941\pi$
$878$	1.28318e6	+	2.22254e6i	0.0561762	+	0.0973001i
$879$	−9.45138e6	−	1.63703e7i	−0.412594	−	0.714634i
$880$	−2.20979e6	+	3.82747e6i	−0.0961933	+	0.166612i
$881$	1.48577e7			0.644927			0.322464	−	0.946582i	$-0.395489\pi$
$881$	1.48577e7			0.644927			0.322464	+	0.946582i	$0.395489\pi$
$882$		0			0
$883$	−2.72018e7			−1.17407			−0.587037	−	0.809560i	$-0.699706\pi$
$883$	−2.72018e7			−1.17407			−0.587037	+	0.809560i	$0.699706\pi$
$884$	−4.02461e6	+	6.97083e6i	−0.173218	+	0.300022i
$885$	1.80601e6	+	3.12810e6i	0.0775108	+	0.134253i
$886$	1.21109e7	+	2.09767e7i	0.518314	+	0.897745i
$887$	−1.35621e7	+	2.34902e7i	−0.578785	+	1.00249i	0.416834	+	0.908983i	$0.363140\pi$
$887$	−1.35621e7	+	2.34902e7i	−0.578785	+	1.00249i	−0.995619	+	0.0935028i	$0.970194\pi$
$888$	−2.51021e6			−0.106826
$889$		0			0
$890$	1.27564e7			0.539827
$891$	−2.17825e6	+	3.77284e6i	−0.0919208	+	0.159212i
$892$	1.03021e7	+	1.78437e7i	0.433524	+	0.750885i
$893$	−631536.	−	1.09385e6i	−0.0265014	−	0.0459018i
$894$	−3.14744e6	+	5.45153e6i	−0.131709	+	0.228126i
$895$	1.26766e7			0.528986
$896$		0			0
$897$	6.33074e6			0.262708
$898$	−1.03336e7	+	1.78984e7i	−0.427624	+	0.740666i
$899$	−1.76561e7	−	3.05812e7i	−0.728609	−	1.26199i
$900$	1.58695e6	+	2.74868e6i	0.0653067	+	0.113114i
$901$	2.63830e7	−	4.56967e7i	1.08271	−	1.87531i
$902$	−2.79996e7			−1.14587
$903$		0			0
$904$	3.58490e6			0.145900
$905$	7.07733e6	−	1.22583e7i	0.287242	−	0.497518i
$906$	−8.14594e6	−	1.41092e7i	−0.329701	−	0.571059i
$907$	4.21135e6	+	7.29427e6i	0.169982	+	0.294417i	0.938413	−	0.345515i	$-0.112296\pi$
$907$	4.21135e6	+	7.29427e6i	0.169982	+	0.294417i	−0.768431	+	0.639932i	$0.778962\pi$
$908$	−1.03124e7	+	1.78616e7i	−0.415093	+	0.718963i
$909$	−2.98193e6			−0.119698
$910$		0			0
$911$	3.08637e7			1.23212			0.616060	−	0.787700i	$-0.288728\pi$
$911$	3.08637e7			1.23212			0.616060	+	0.787700i	$0.288728\pi$
$912$	−271872.	+	470896.i	−0.0108237	+	0.0187473i
$913$	2.13410e6	+	3.69636e6i	0.0847300	+	0.146757i
$914$	−455596.	−	789115.i	−0.0180391	−	0.0312446i
$915$	4.30115e6	−	7.44982e6i	0.169837	−	0.294166i
$916$	1.08514e7			0.427315
$917$		0			0
$918$	−4.61311e6			−0.180671
$919$	−2.46948e6	+	4.27726e6i	−0.0964531	+	0.167062i	−0.910214	−	0.414138i	$-0.864083\pi$
$919$	−2.46948e6	+	4.27726e6i	−0.0964531	+	0.167062i	0.813761	+	0.581200i	$0.197416\pi$
$920$	1.84038e6	+	3.18764e6i	0.0716867	+	0.124165i
$921$	7.38470e6	+	1.27907e7i	0.286869	+	0.496872i
$922$	1.17029e6	−	2.02701e6i	0.0453385	−	0.0785285i
$923$	−2.89126e6			−0.111707
$924$		0			0
$925$	−1.06727e7			−0.410130
$926$	−6.82907e6	+	1.18283e7i	−0.261718	+	0.453310i
$927$	−4.23338e6	−	7.33244e6i	−0.161804	−	0.280252i
$928$	−2.53645e6	−	4.39326e6i	−0.0966843	−	0.167462i
$929$	−2.81288e6	+	4.87204e6i	−0.106933	+	0.185213i	−0.914526	−	0.404527i	$-0.867436\pi$
$929$	−2.81288e6	+	4.87204e6i	−0.106933	+	0.185213i	0.807593	+	0.589740i	$0.200770\pi$
$930$	6.67181e6			0.252951
$931$		0			0
$932$	−1.78770e7			−0.674146
$933$	4.25354e6	−	7.36735e6i	0.159973	−	0.277081i
$934$	1.43260e6	+	2.48134e6i	0.0537351	+	0.0930719i
$935$	−1.36558e7	−	2.36526e7i	−0.510845	−	0.884809i
$936$	824256.	−	1.42765e6i	0.0307519	−	0.0532639i
$937$	2.60073e7			0.967714			0.483857	−	0.875147i	$-0.339236\pi$
$937$	2.60073e7			0.967714			0.483857	+	0.875147i	$0.339236\pi$
$938$		0			0
$939$	3.73819e6			0.138356
$940$	−1.11322e6	+	1.92815e6i	−0.0410922	+	0.0711738i
$941$	−1.51080e6	−	2.61678e6i	−0.0556203	−	0.0963372i	0.836875	−	0.547395i	$-0.184380\pi$
$941$	−1.51080e6	−	2.61678e6i	−0.0556203	−	0.0963372i	−0.892495	+	0.451057i	$0.851047\pi$
$942$	−8.98319e6	−	1.55593e7i	−0.329840	−	0.571300i
$943$	−1.16595e7	+	2.01948e7i	−0.426972	+	0.739536i
$944$	−3.95162e6			−0.144326
$945$		0			0
$946$	2.24485e7			0.815567
$947$	1.74141e7	−	3.01621e7i	0.630995	−	1.09292i	−0.356354	−	0.934351i	$-0.615980\pi$
$947$	1.74141e7	−	3.01621e7i	0.630995	−	1.09292i	0.987349	−	0.158564i	$-0.0506865\pi$
$948$	−6.43680e6	−	1.11489e7i	−0.232621	−	0.402912i
$949$	1.16792e7	+	2.02289e7i	0.420966	+	0.729135i
$950$	−1.15593e6	+	2.00213e6i	−0.0415549	+	0.0719751i
$951$	1.06633e7			0.382333
$952$		0			0
$953$	−9.39009e6			−0.334917			−0.167459	−	0.985879i	$-0.553556\pi$
$953$	−9.39009e6			−0.334917			−0.167459	+	0.985879i	$0.553556\pi$
$954$	−5.40335e6	+	9.35887e6i	−0.192217	+	0.332930i
$955$	−4.89325e6	−	8.47536e6i	−0.173616	−	0.300711i
$956$	1.00956e7	+	1.74862e7i	0.357264	+	0.618800i
$957$	1.48026e7	−	2.56388e7i	0.522464	−	0.904935i
$958$	−2.09637e7			−0.737996
$959$		0			0
$960$	958464.			0.0335659
$961$	−1.10896e7	+	1.92078e7i	−0.387354	+	0.670917i
$962$	2.77169e6	+	4.80070e6i	0.0965621	+	0.167250i
$963$	−8.68482e6	−	1.50425e7i	−0.301783	−	0.522704i
$964$	−7.58574e6	+	1.31389e7i	−0.262909	+	0.455372i
$965$	2.19686e7			0.759423
$966$		0			0
$967$	1.44768e7			0.497860			0.248930	−	0.968521i	$-0.419921\pi$
$967$	1.44768e7			0.497860			0.248930	+	0.968521i	$0.419921\pi$
$968$	8.95504e6	−	1.55106e7i	0.307170	−	0.532034i
$969$	−1.68008e6	−	2.90999e6i	−0.0574806	−	0.0995594i
$970$	1.11124e6	+	1.92472e6i	0.0379209	+	0.0656809i
$971$	−4.62488e6	+	8.01052e6i	−0.157417	+	0.272655i	−0.933937	−	0.357439i	$-0.883650\pi$
$971$	−4.62488e6	+	8.01052e6i	−0.157417	+	0.272655i	0.776519	+	0.630093i	$0.216983\pi$
$972$	944784.			0.0320750
$973$		0			0
$974$	−4.46806e6			−0.150911
$975$	3.50452e6	−	6.07000e6i	0.118064	−	0.204493i
$976$	4.70554e6	+	8.15023e6i	0.158119	+	0.273870i
$977$	2.48890e7	+	4.31090e7i	0.834202	+	1.44488i	0.894678	+	0.446711i	$0.147405\pi$
$977$	2.48890e7	+	4.31090e7i	0.834202	+	1.44488i	−0.0604765	+	0.998170i	$0.519262\pi$
$978$	−8.56058e6	+	1.48274e7i	−0.286191	+	0.495698i
$979$	−8.14449e7			−2.71586
$980$		0			0
$981$	2.33264e6			0.0773882
$982$	2.68915e6	−	4.65775e6i	0.0889891	−	0.154134i
$983$	4.47800e6	+	7.75613e6i	0.147809	+	0.256013i	0.930417	−	0.366502i	$-0.119445\pi$
$983$	4.47800e6	+	7.75613e6i	0.147809	+	0.256013i	−0.782608	+	0.622514i	$0.786111\pi$
$984$	3.03610e6	+	5.25867e6i	0.0999603	+	0.173136i
$985$	6.40632e6	−	1.10961e7i	0.210387	−	0.364400i
$986$	3.13489e7			1.02690
$987$		0			0
$988$	1.20077e6			0.0391351
$989$	9.34791e6	−	1.61911e7i	0.303895	−	0.526362i
$990$	2.79677e6	+	4.84414e6i	0.0906919	+	0.157083i
$991$	−1.31200e7	−	2.27245e7i	−0.424376	−	0.735040i	0.571986	−	0.820263i	$-0.306173\pi$
$991$	−1.31200e7	−	2.27245e7i	−0.424376	−	0.735040i	−0.996362	+	0.0852230i	$0.972840\pi$
$992$	−3.64954e6	+	6.32118e6i	−0.117749	+	0.203948i
$993$	1.23439e7			0.397265
$994$		0			0
$995$	−2.37842e7			−0.761606
$996$	462816.	−	801621.i	0.0147829	−	0.0256048i
$997$	−1.40253e7	−	2.42926e7i	−0.446863	−	0.773990i	0.551316	−	0.834296i	$-0.314126\pi$
$997$	−1.40253e7	−	2.42926e7i	−0.446863	−	0.773990i	−0.998180	+	0.0603060i	$0.980792\pi$
$998$	−1.30930e7	−	2.26777e7i	−0.416113	−	0.720729i
$999$	−1.58849e6	+	2.75135e6i	−0.0503583	+	0.0872231i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.6.a.d.1.1	✓	1	7.2	even	3
126.6.a.i.1.1		1	21.2	odd	6
294.6.a.b.1.1		1	7.5	odd	6
294.6.e.i.67.1		2	7.4	even	3	inner
294.6.e.i.79.1		2	1.1	even	1	trivial
294.6.e.p.67.1		2	7.3	odd	6
294.6.e.p.79.1		2	7.6	odd	2
336.6.a.h.1.1		1	28.23	odd	6
882.6.a.s.1.1		1	21.5	even	6
1008.6.a.j.1.1		1	84.23	even	6
1050.6.a.k.1.1		1	35.9	even	6
1050.6.g.i.799.1		2	35.2	odd	12
1050.6.g.i.799.2		2	35.23	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 9 q^{3} - 16 q^{4} - 26 q^{5} - 72 q^{6} - 128 q^{8} - 81 q^{9} + 104 q^{10} - 664 q^{11} - 144 q^{12} + 636 q^{13} + 468 q^{15} - 256 q^{16} - 1582 q^{17} + 324 q^{18} - 236 q^{19} + 832 q^{20}+ \cdots + 107568 q^{99}+O(q^{100}) \) 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

Introduction

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