LMFDB - Embedded newform 147.6.c.d.146.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(146,147)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("147.146");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.c (of order $2$, degree $1$, 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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.9
Character	$\chi$	$=$	147.146
Dual form			147.6.c.d.146.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.81342i q^{2} +(-6.23210 - 14.2885i) q^{3} +17.4578 q^{4} +63.5678 q^{5} +(-54.4880 + 23.7656i) q^{6} -188.603i q^{8} +(-165.322 + 178.095i) q^{9} +O(q^{10})$	\(q-3.81342i q^{2} +(-6.23210 - 14.2885i) q^{3} +17.4578 q^{4} +63.5678 q^{5} +(-54.4880 + 23.7656i) q^{6} -188.603i q^{8} +(-165.322 + 178.095i) q^{9} -242.411i q^{10} -192.638i q^{11} +(-108.799 - 249.446i) q^{12} +82.7575i q^{13} +(-396.161 - 908.287i) q^{15} -160.574 q^{16} +1847.26 q^{17} +(679.150 + 630.442i) q^{18} -2027.69i q^{19} +1109.75 q^{20} -734.608 q^{22} -2754.97i q^{23} +(-2694.86 + 1175.40i) q^{24} +915.859 q^{25} +315.589 q^{26} +(3575.01 + 1252.29i) q^{27} -4548.65i q^{29} +(-3463.68 + 1510.73i) q^{30} +8708.43i q^{31} -5422.97i q^{32} +(-2752.50 + 1200.54i) q^{33} -7044.36i q^{34} +(-2886.16 + 3109.14i) q^{36} -15706.9 q^{37} -7732.44 q^{38} +(1182.48 - 515.754i) q^{39} -11989.1i q^{40} -10556.1 q^{41} -6690.24 q^{43} -3363.03i q^{44} +(-10509.1 + 11321.1i) q^{45} -10505.9 q^{46} +16934.8 q^{47} +(1000.72 + 2294.36i) q^{48} -3492.56i q^{50} +(-11512.3 - 26394.5i) q^{51} +1444.77i q^{52} +29470.9i q^{53} +(4775.52 - 13633.0i) q^{54} -12245.5i q^{55} +(-28972.6 + 12636.8i) q^{57} -17345.9 q^{58} +22654.1 q^{59} +(-6916.10 - 15856.7i) q^{60} -7690.16i q^{61} +33208.9 q^{62} -25818.5 q^{64} +5260.71i q^{65} +(4578.16 + 10496.4i) q^{66} +49920.8 q^{67} +32249.1 q^{68} +(-39364.4 + 17169.3i) q^{69} -16871.4i q^{71} +(33589.3 + 31180.3i) q^{72} -24117.2i q^{73} +59897.1i q^{74} +(-5707.73 - 13086.2i) q^{75} -35399.1i q^{76} +(-1966.79 - 4509.29i) q^{78} -35797.3 q^{79} -10207.4 q^{80} +(-4386.43 - 58885.9i) q^{81} +40254.7i q^{82} -24435.2 q^{83} +117426. q^{85} +25512.7i q^{86} +(-64993.4 + 28347.7i) q^{87} -36332.1 q^{88} -80101.2 q^{89} +(43172.0 + 40075.8i) q^{90} -48095.8i q^{92} +(124430. - 54271.8i) q^{93} -64579.4i q^{94} -128896. i q^{95} +(-77486.1 + 33796.5i) q^{96} -3677.51i q^{97} +(34307.7 + 31847.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 640 q^{4} + 440 q^{9}+O(q^{10}) $ 40 * q - 640 * q^4 + 440 * q^9	$ 40 q - 640 q^{4} + 440 q^{9} - 3176 q^{15} + 3552 q^{16} - 4544 q^{18} + 21088 q^{22} + 30104 q^{25} + 44664 q^{30} - 59320 q^{36} - 26224 q^{37} - 16216 q^{39} + 21584 q^{43} - 27680 q^{46} + 95784 q^{51} - 130304 q^{57} - 131376 q^{58} + 329208 q^{60} + 53968 q^{64} - 187632 q^{67} + 606736 q^{72} + 70312 q^{78} - 597424 q^{79} + 755256 q^{81} + 108112 q^{85} - 1673072 q^{88} + 590480 q^{93} - 258480 q^{99}+O(q^{100}) $ 40 * q - 640 * q^4 + 440 * q^9 - 3176 * q^15 + 3552 * q^16 - 4544 * q^18 + 21088 * q^22 + 30104 * q^25 + 44664 * q^30 - 59320 * q^36 - 26224 * q^37 - 16216 * q^39 + 21584 * q^43 - 27680 * q^46 + 95784 * q^51 - 130304 * q^57 - 131376 * q^58 + 329208 * q^60 + 53968 * q^64 - 187632 * q^67 + 606736 * q^72 + 70312 * q^78 - 597424 * q^79 + 755256 * q^81 + 108112 * q^85 - 1673072 * q^88 + 590480 * q^93 - 258480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	3.81342i		−	0.674124i	−0.941482	−	0.337062i	$-0.890567\pi$
$2$		−	3.81342i		−	0.674124i	0.941482	−	0.337062i	$-0.109433\pi$
$3$	−6.23210	−	14.2885i	−0.399790	−	0.916607i
$3$	−6.23210	−	14.2885i	−0.399790	−	0.916607i
$4$	17.4578			0.545557
$5$	63.5678			1.13713			0.568567	−	0.822637i	$-0.307498\pi$
$5$	63.5678			1.13713			0.568567	+	0.822637i	$0.307498\pi$
$6$	−54.4880	+	23.7656i	−0.617907	+	0.269508i
$7$		0			0
$7$		0			0
$8$		−	188.603i		−	1.04190i
$9$	−165.322	+	178.095i	−0.680336	+	0.732900i
$10$		−	242.411i		−	0.766570i
$11$		−	192.638i		−	0.480020i	−0.970770	−	0.240010i	$-0.922849\pi$
$11$		−	192.638i		−	0.480020i	0.970770	−	0.240010i	$-0.0771507\pi$
$12$	−108.799	−	249.446i	−0.218108	−	0.500061i
$13$			82.7575i			0.135815i	0.997692	+	0.0679077i	$0.0216323\pi$
$13$			82.7575i			0.135815i	−0.997692	+	0.0679077i	$0.978368\pi$
$14$		0			0
$15$	−396.161	−	908.287i	−0.454615	−	1.04231i
$16$	−160.574			−0.156811
$17$	1847.26			1.55026			0.775130	−	0.631801i	$-0.217684\pi$
$17$	1847.26			1.55026			0.775130	+	0.631801i	$0.217684\pi$
$18$	679.150	+	630.442i	0.494065	+	0.458631i
$19$		−	2027.69i		−	1.28860i	−0.764773	−	0.644300i	$-0.777149\pi$
$19$		−	2027.69i		−	1.28860i	0.764773	−	0.644300i	$-0.222851\pi$
$20$	1109.75			0.620372
$21$		0			0
$22$	−734.608			−0.323593
$23$		−	2754.97i		−	1.08592i	−0.839759	−	0.542959i	$-0.817304\pi$
$23$		−	2754.97i		−	1.08592i	0.839759	−	0.542959i	$-0.182696\pi$
$24$	−2694.86	+	1175.40i	−0.955010	+	0.416540i
$25$	915.859			0.293075
$26$	315.589			0.0915565
$27$	3575.01	+	1252.29i	0.943773	+	0.330595i
$28$		0			0
$29$		−	4548.65i		−	1.00436i	−0.864764	−	0.502178i	$-0.832532\pi$
$29$		−	4548.65i		−	1.00436i	0.864764	−	0.502178i	$-0.167468\pi$
$30$	−3463.68	+	1510.73i	−0.702643	+	0.306467i
$31$			8708.43i			1.62755i	0.581177	+	0.813777i	$0.302593\pi$
$31$			8708.43i			1.62755i	−0.581177	+	0.813777i	$0.697407\pi$
$32$		−	5422.97i		−	0.936187i
$33$	−2752.50	+	1200.54i	−0.439990	+	0.191907i
$34$		−	7044.36i		−	1.04507i
$35$		0			0
$36$	−2886.16	+	3109.14i	−0.371162	+	0.399839i
$37$	−15706.9			−1.88619			−0.943097	−	0.332516i	$-0.892102\pi$
$37$	−15706.9			−1.88619			−0.943097	+	0.332516i	$0.892102\pi$
$38$	−7732.44			−0.868676
$39$	1182.48	−	515.754i	0.124489	−	0.0542976i
$40$		−	11989.1i		−	1.18478i
$41$	−10556.1			−0.980713			−0.490356	−	0.871522i	$-0.663133\pi$
$41$	−10556.1			−0.980713			−0.490356	+	0.871522i	$0.663133\pi$
$42$		0			0
$43$	−6690.24			−0.551786			−0.275893	−	0.961188i	$-0.588974\pi$
$43$	−6690.24			−0.551786			−0.275893	+	0.961188i	$0.588974\pi$
$44$		−	3363.03i		−	0.261878i
$45$	−10509.1	+	11321.1i	−0.773634	+	0.833406i
$46$	−10505.9			−0.732044
$47$	16934.8			1.11824			0.559119	−	0.829087i	$-0.311139\pi$
$47$	16934.8			1.11824			0.559119	+	0.829087i	$0.311139\pi$
$48$	1000.72	+	2294.36i	0.0626914	+	0.143734i
$49$		0			0
$50$		−	3492.56i		−	0.197569i
$51$	−11512.3	−	26394.5i	−0.619778	−	1.42098i
$52$			1444.77i			0.0740950i
$53$			29470.9i			1.44113i	0.693388	+	0.720565i	$0.256117\pi$
$53$			29470.9i			1.44113i	−0.693388	+	0.720565i	$0.743883\pi$
$54$	4775.52	−	13633.0i	0.222862	−	0.636220i
$55$		−	12245.5i		−	0.545847i
$56$		0			0
$57$	−28972.6	+	12636.8i	−1.18114	+	0.515169i
$58$	−17345.9			−0.677061
$59$	22654.1			0.847259			0.423630	−	0.905835i	$-0.360756\pi$
$59$	22654.1			0.847259			0.423630	+	0.905835i	$0.360756\pi$
$60$	−6916.10	−	15856.7i	−0.248018	−	0.568637i
$61$		−	7690.16i		−	0.264613i	−0.991209	−	0.132306i	$-0.957762\pi$
$61$		−	7690.16i		−	0.264613i	0.991209	−	0.132306i	$-0.0422383\pi$
$62$	33208.9			1.09717
$63$		0			0
$64$	−25818.5			−0.787917
$65$			5260.71i			0.154440i
$66$	4578.16	+	10496.4i	0.129369	+	0.296608i
$67$	49920.8			1.35861			0.679305	−	0.733856i	$-0.262281\pi$
$67$	49920.8			1.35861			0.679305	+	0.733856i	$0.262281\pi$
$68$	32249.1			0.845755
$69$	−39364.4	+	17169.3i	−0.995361	+	0.434139i
$70$		0			0
$71$		−	16871.4i		−	0.397197i	−0.980081	−	0.198599i	$-0.936361\pi$
$71$		−	16871.4i		−	0.397197i	0.980081	−	0.198599i	$-0.0636390\pi$
$72$	33589.3	+	31180.3i	0.763606	+	0.708841i
$73$		−	24117.2i		−	0.529688i	−0.964291	−	0.264844i	$-0.914680\pi$
$73$		−	24117.2i		−	0.529688i	0.964291	−	0.264844i	$-0.0853204\pi$
$74$			59897.1i			1.27153i
$75$	−5707.73	−	13086.2i	−0.117168	−	0.268634i
$76$		−	35399.1i		−	0.703004i
$77$		0			0
$78$	−1966.79	−	4509.29i	−0.0366033	−	0.0839213i
$79$	−35797.3			−0.645331			−0.322666	−	0.946513i	$-0.604579\pi$
$79$	−35797.3			−0.645331			−0.322666	+	0.946513i	$0.604579\pi$
$80$	−10207.4			−0.178315
$81$	−4386.43	−	58885.9i	−0.0742845	−	0.997237i
$82$			40254.7i			0.661122i
$83$	−24435.2			−0.389332			−0.194666	−	0.980870i	$-0.562362\pi$
$83$	−24435.2			−0.389332			−0.194666	+	0.980870i	$0.562362\pi$
$84$		0			0
$85$	117426.			1.76285
$86$			25512.7i			0.371972i
$87$	−64993.4	+	28347.7i	−0.920600	+	0.401531i
$88$	−36332.1			−0.500131
$89$	−80101.2			−1.07192			−0.535962	−	0.844242i	$-0.680051\pi$
$89$	−80101.2			−1.07192			−0.535962	+	0.844242i	$0.680051\pi$
$90$	43172.0	+	40075.8i	0.561819	+	0.521525i
$91$		0			0
$92$		−	48095.8i		−	0.592431i
$93$	124430.	−	54271.8i	1.49183	−	0.650680i
$94$		−	64579.4i		−	0.753832i
$95$		−	128896.i		−	1.46531i
$96$	−77486.1	+	33796.5i	−0.858115	+	0.374278i
$97$		−	3677.51i		−	0.0396849i	−0.999803	−	0.0198424i	$-0.993684\pi$
$97$		−	3677.51i		−	0.0396849i	0.999803	−	0.0198424i	$-0.00631646\pi$
$98$		0			0
$99$	34307.7	+	31847.2i	0.351807	+	0.326575i
$100$	15988.9			0.159889
$101$	112701.			1.09932			0.549661	−	0.835388i	$-0.314757\pi$
$101$	112701.			1.09932			0.549661	+	0.835388i	$0.314757\pi$
$102$	−100653.	+	43901.2i	−0.957916	+	0.417807i
$103$			82676.8i			0.767875i	0.923359	+	0.383937i	$0.125432\pi$
$103$			82676.8i			0.767875i	−0.923359	+	0.383937i	$0.874568\pi$
$104$	15608.4			0.141506
$105$		0			0
$106$	112385.			0.971500
$107$			50961.1i			0.430308i	0.976580	+	0.215154i	$0.0690254\pi$
$107$			50961.1i			0.430308i	−0.976580	+	0.215154i	$0.930975\pi$
$108$	62411.8	+	21862.3i	0.514882	+	0.180359i
$109$	52574.5			0.423847			0.211923	−	0.977286i	$-0.432027\pi$
$109$	52574.5			0.423847			0.211923	+	0.977286i	$0.432027\pi$
$110$	−46697.4			−0.367969
$111$	97887.1	+	224428.i	0.754081	+	1.72890i
$112$		0			0
$113$			152880.i			1.12630i	0.826353	+	0.563152i	$0.190412\pi$
$113$			152880.i			1.12630i	−0.826353	+	0.563152i	$0.809588\pi$
$114$	48189.4	+	110485.i	0.347288	+	0.796234i
$115$		−	175127.i		−	1.23484i
$116$		−	79409.6i		−	0.547934i
$117$	−14738.7	−	13681.6i	−0.0995391	−	0.0924002i
$118$		−	86389.5i		−	0.571158i
$119$		0			0
$120$	−171306.	+	74717.3i	−1.08597	+	0.473662i
$121$	123942.			0.769581
$122$	−29325.8			−0.178382
$123$	65786.4	+	150830.i	0.392079	+	0.898928i
$124$			152030.i			0.887924i
$125$	−140430.			−0.803869
$126$		0			0
$127$	289159.			1.59084			0.795421	−	0.606057i	$-0.207250\pi$
$127$	289159.			1.59084			0.795421	+	0.606057i	$0.207250\pi$
$128$		−	75078.5i		−	0.405033i
$129$	41694.3	+	95593.4i	0.220598	+	0.505771i
$130$	20061.3			0.104112
$131$	232689.			1.18467			0.592335	−	0.805692i	$-0.298206\pi$
$131$	232689.			1.18467			0.592335	+	0.805692i	$0.298206\pi$
$132$	−48052.7	+	20958.8i	−0.240039	+	0.104696i
$133$		0			0
$134$		−	190369.i		−	0.915872i
$135$	227255.	+	79605.5i	1.07320	+	0.375931i
$136$		−	348399.i		−	1.61521i
$137$			151933.i			0.691591i	0.938310	+	0.345796i	$0.112391\pi$
$137$			151933.i			0.691591i	−0.938310	+	0.345796i	$0.887609\pi$
$138$	65473.6	+	150113.i	0.292664	+	0.670997i
$139$		−	325977.i		−	1.43103i	−0.698596	−	0.715516i	$-0.746191\pi$
$139$		−	325977.i		−	1.43103i	0.698596	−	0.715516i	$-0.253809\pi$
$140$		0			0
$141$	−105539.	−	241972.i	−0.447060	−	1.02499i
$142$	−64337.9			−0.267760
$143$	15942.2			0.0651941
$144$	26546.4	−	28597.4i	0.106684	−	0.114927i
$145$		−	289148.i		−	1.14209i
$146$	−91969.1			−0.357075
$147$		0			0
$148$	−274208.			−1.02903
$149$			170153.i			0.627877i	0.949443	+	0.313938i	$0.101649\pi$
$149$			170153.i			0.627877i	−0.949443	+	0.313938i	$0.898351\pi$
$150$	−49903.4	+	21766.0i	−0.181093	+	0.0789860i
$151$	50557.5			0.180444			0.0902222	−	0.995922i	$-0.471242\pi$
$151$	50557.5			0.180444			0.0902222	+	0.995922i	$0.471242\pi$
$152$	−382430.			−1.34259
$153$	−305392.	+	328986.i	−1.05470	+	1.13619i
$154$		0			0
$155$			553575.i			1.85075i
$156$	20643.5	−	9003.93i	0.0679160	−	0.0296224i
$157$			179881.i			0.582420i	0.956659	+	0.291210i	$0.0940578\pi$
$157$			179881.i			0.582420i	−0.956659	+	0.291210i	$0.905942\pi$
$158$			136510.i			0.435033i
$159$	421094.	−	183665.i	1.32095	−	0.576149i
$160$		−	344726.i		−	1.06457i
$161$		0			0
$162$	−224557.	+	16727.3i	−0.672261	+	0.0500770i
$163$	−524639.			−1.54665			−0.773324	−	0.634011i	$-0.781407\pi$
$163$	−524639.			−1.54665			−0.773324	+	0.634011i	$0.781407\pi$
$164$	−184286.			−0.535035
$165$	−174970.	+	76315.5i	−0.500328	+	0.218224i
$166$			93181.7i			0.262458i
$167$	452133.			1.25451			0.627257	−	0.778813i	$-0.284178\pi$
$167$	452133.			1.25451			0.627257	+	0.778813i	$0.284178\pi$
$168$		0			0
$169$	364444.			0.981554
$170$		−	447794.i		−	1.18838i
$171$	361121.	+	335222.i	0.944414	+	0.876681i
$172$	−116797.			−0.301030
$173$	165711.			0.420956			0.210478	−	0.977599i	$-0.432498\pi$
$173$	165711.			0.420956			0.210478	+	0.977599i	$0.432498\pi$
$174$	108102.	+	247847.i	0.270682	+	0.620599i
$175$		0			0
$176$			30932.7i			0.0752724i
$177$	−141183.	−	323692.i	−0.338725	−	0.776604i
$178$			305460.i			0.722610i
$179$		−	318161.i		−	0.742189i	−0.928595	−	0.371094i	$-0.878983\pi$
$179$		−	318161.i		−	0.742189i	0.928595	−	0.371094i	$-0.121017\pi$
$180$	−183467.	+	197641.i	−0.422061	+	0.454670i
$181$			114375.i			0.259498i	0.991547	+	0.129749i	$0.0414171\pi$
$181$			114375.i			0.259498i	−0.991547	+	0.129749i	$0.958583\pi$
$182$		0			0
$183$	−109881.	+	47925.9i	−0.242546	+	0.105789i
$184$	−519597.			−1.13142
$185$	−998453.			−2.14486
$186$	−206961.	−	474505.i	−0.438639	−	1.00568i
$187$		−	355851.i		−	0.744156i
$188$	295644.			0.610063
$189$		0			0
$190$	−491534.			−0.987801
$191$		−	88607.2i		−	0.175746i	−0.996132	−	0.0878730i	$-0.971993\pi$
$191$		−	88607.2i		−	0.175746i	0.996132	−	0.0878730i	$-0.0280070\pi$
$192$	160903.	+	368907.i	0.315001	+	0.722210i
$193$	153238.			0.296124			0.148062	−	0.988978i	$-0.452697\pi$
$193$	153238.			0.296124			0.148062	+	0.988978i	$0.452697\pi$
$194$	−14023.9			−0.0267525
$195$	75167.6	−	32785.3i	0.141561	−	0.0617437i
$196$		0			0
$197$		−	868991.i		−	1.59533i	−0.603103	−	0.797663i	$-0.706069\pi$
$197$		−	868991.i		−	1.59533i	0.603103	−	0.797663i	$-0.293931\pi$
$198$	121447.	−	130830.i	0.220152	−	0.237161i
$199$			173731.i			0.310989i	0.987837	+	0.155495i	$0.0496971\pi$
$199$			173731.i			0.310989i	−0.987837	+	0.155495i	$0.950303\pi$
$200$		−	172734.i		−	0.305354i
$201$	−311112.	−	713293.i	−0.543158	−	1.24531i
$202$		−	429777.i		−	0.741079i
$203$		0			0
$204$	−200979.	−	460790.i	−0.338124	−	0.775225i
$205$	−671024.			−1.11520
$206$	315281.			0.517643
$207$	490646.	+	455457.i	0.795870	+	0.738790i
$208$		−	13288.7i		−	0.0212973i
$209$	−390610.			−0.618554
$210$		0			0
$211$	567288.			0.877198			0.438599	−	0.898683i	$-0.355475\pi$
$211$	567288.			0.877198			0.438599	+	0.898683i	$0.355475\pi$
$212$			514497.i			0.786218i
$213$	−241067.	+	105145.i	−0.364074	+	0.158795i
$214$	194336.			0.290081
$215$	−425283.			−0.627455
$216$	236187.	−	674259.i	0.344446	−	0.983314i
$217$		0			0
$218$		−	200489.i		−	0.285725i
$219$	−344598.	+	150301.i	−0.485515	+	0.211764i
$220$		−	213780.i		−	0.297791i
$221$			152874.i			0.210549i
$222$	855839.	−	373285.i	1.16549	−	0.508344i
$223$			346331.i			0.466369i	0.972433	+	0.233184i	$0.0749146\pi$
$223$			346331.i			0.466369i	−0.972433	+	0.233184i	$0.925085\pi$
$224$		0			0
$225$	−151411.	+	163110.i	−0.199390	+	0.214795i
$226$	582998.			0.759269
$227$	159833.			0.205874			0.102937	−	0.994688i	$-0.467176\pi$
$227$	159833.			0.205874			0.102937	+	0.994688i	$0.467176\pi$
$228$	−505799.	+	220611.i	−0.644379	+	0.281054i
$229$		−	296273.i		−	0.373339i	−0.982423	−	0.186670i	$-0.940231\pi$
$229$		−	296273.i		−	0.373339i	0.982423	−	0.186670i	$-0.0597694\pi$
$230$	−667834.			−0.832433
$231$		0			0
$232$	−857892.			−1.04644
$233$		−	151141.i		−	0.182386i	−0.995833	−	0.0911930i	$-0.970932\pi$
$233$		−	151141.i		−	0.182386i	0.995833	−	0.0911930i	$-0.0290680\pi$
$234$	−52173.8	+	56204.8i	−0.0622892	+	0.0671017i
$235$	1.07650e6			1.27159
$236$	395491.			0.462228
$237$	223093.	+	511490.i	0.257997	+	0.591515i
$238$		0			0
$239$			238760.i			0.270375i	0.990820	+	0.135188i	$0.0431637\pi$
$239$			238760.i			0.270375i	−0.990820	+	0.135188i	$0.956836\pi$
$240$	63613.3	+	145848.i	0.0712885	+	0.163445i
$241$			266998.i			0.296119i	0.988978	+	0.148059i	$0.0473027\pi$
$241$			266998.i			0.296119i	−0.988978	+	0.148059i	$0.952697\pi$
$242$		−	472642.i		−	0.518793i
$243$	−814053.	+	429658.i	−0.884376	+	0.466775i
$244$		−	134253.i		−	0.144361i
$245$		0			0
$246$	575178.	−	250871.i	0.605989	−	0.264310i
$247$	167807.			0.175012
$248$	1.64244e6			1.69574
$249$	152283.	+	349142.i	0.155651	+	0.356865i
$250$			535519.i			0.541907i
$251$	945363.			0.947140			0.473570	−	0.880756i	$-0.342965\pi$
$251$	945363.			0.947140			0.473570	+	0.880756i	$0.342965\pi$
$252$		0			0
$253$	−530711.			−0.521263
$254$		−	1.10268e6i		−	1.07243i
$255$	−731810.	−	1.67784e6i	−0.704771	−	1.61584i
$256$	−1.11250e6			−1.06096
$257$	1.53182e6			1.44668			0.723342	−	0.690490i	$-0.242605\pi$
$257$	1.53182e6			1.44668			0.723342	+	0.690490i	$0.242605\pi$
$258$	364538.	−	158998.i	0.340952	−	0.148711i
$259$		0			0
$260$			91840.5i			0.0842560i
$261$	810091.	+	751992.i	0.736093	+	0.683301i
$262$		−	887341.i		−	0.798615i
$263$			1.21470e6i			1.08287i	0.840741	+	0.541437i	$0.182120\pi$
$263$			1.21470e6i			1.08287i	−0.840741	+	0.541437i	$0.817880\pi$
$264$	226426.	+	519131.i	0.199947	+	0.458424i
$265$			1.87340e6i			1.63876i
$266$		0			0
$267$	499199.	+	1.14453e6i	0.428544	+	0.982533i
$268$	871509.			0.741199
$269$	543960.			0.458339			0.229169	−	0.973387i	$-0.426399\pi$
$269$	543960.			0.458339			0.229169	+	0.973387i	$0.426399\pi$
$270$	303569.	−	866619.i	0.253424	−	0.723467i
$271$			837410.i			0.692651i	0.938114	+	0.346326i	$0.112571\pi$
$271$			837410.i			0.692651i	−0.938114	+	0.346326i	$0.887429\pi$
$272$	−296622.			−0.243098
$273$		0			0
$274$	579383.			0.466218
$275$		−	176429.i		−	0.140682i
$276$	−687216.	+	299738.i	−0.543026	+	0.236848i
$277$	−1.86575e6			−1.46102			−0.730508	−	0.682904i	$-0.760717\pi$
$277$	−1.86575e6			−1.46102			−0.730508	+	0.682904i	$0.760717\pi$
$278$	−1.24309e6			−0.964694
$279$	−1.55092e6	−	1.43969e6i	−1.19283	−	1.10728i
$280$		0			0
$281$			2.02315e6i			1.52849i	0.644926	+	0.764245i	$0.276888\pi$
$281$			2.02315e6i			1.52849i	−0.644926	+	0.764245i	$0.723112\pi$
$282$	−922742.	+	402465.i	−0.690967	+	0.301374i
$283$			698218.i			0.518233i	0.965846	+	0.259116i	$0.0834313\pi$
$283$			698218.i			0.518233i	−0.965846	+	0.259116i	$0.916569\pi$
$284$		−	294538.i		−	0.216694i
$285$	−1.84173e6	+	803292.i	−1.34311	+	0.585816i
$286$		−	60794.4i		−	0.0439489i
$287$		0			0
$288$	965803.	+	896536.i	0.686131	+	0.636922i
$289$	1.99250e6			1.40331
$290$	−1.10264e6			−0.769909
$291$	−52546.1	+	22918.6i	−0.0363754	+	0.0158656i
$292$		−	421034.i		−	0.288975i
$293$	−2.04040e6			−1.38850			−0.694251	−	0.719733i	$-0.744264\pi$
$293$	−2.04040e6			−1.38850			−0.694251	+	0.719733i	$0.744264\pi$
$294$		0			0
$295$	1.44007e6			0.963448
$296$			2.96238e6i			1.96522i
$297$	241239.	−	688681.i	0.158692	−	0.453030i
$298$	648866.			0.423267
$299$	227995.			0.147485
$300$	−99644.5	−	228457.i	−0.0639220	−	0.146555i
$301$		0			0
$302$		−	192797.i		−	0.121642i
$303$	−702365.	−	1.61033e6i	−0.439498	−	1.00765i
$304$			325595.i			0.202066i
$305$		−	488846.i		−	0.300900i
$306$	1.25456e6	+	1.16459e6i	0.765930	+	0.710998i
$307$		−	41674.6i		−	0.0252363i	−0.999920	−	0.0126181i	$-0.995983\pi$
$307$		−	41674.6i		−	0.0252363i	0.999920	−	0.0126181i	$-0.00401659\pi$
$308$		0			0
$309$	1.18133e6	−	515250.i	0.703840	−	0.306988i
$310$	2.11102e6			1.24763
$311$	262886.			0.154122			0.0770612	−	0.997026i	$-0.475446\pi$
$311$	262886.			0.154122			0.0770612	+	0.997026i	$0.475446\pi$
$312$	−97272.9	−	223020.i	−0.0565725	−	0.129705i
$313$			2.34426e6i			1.35253i	0.736661	+	0.676263i	$0.236402\pi$
$313$			2.34426e6i			1.35253i	−0.736661	+	0.676263i	$0.763598\pi$
$314$	685962.			0.392623
$315$		0			0
$316$	−624943.			−0.352065
$317$			1.51352e6i			0.845942i	0.906143	+	0.422971i	$0.139013\pi$
$317$			1.51352e6i			0.845942i	−0.906143	+	0.422971i	$0.860987\pi$
$318$	−700394.	−	1.60581e6i	−0.388396	−	0.890484i
$319$	−876242.			−0.482111
$320$	−1.64122e6			−0.895968
$321$	728158.	−	317595.i	0.394424	−	0.172033i
$322$		0			0
$323$		−	3.74566e6i		−	1.99766i
$324$	−76577.4	−	1.02802e6i	−0.0405264	−	0.544050i
$325$			75794.2i			0.0398041i
$326$			2.00067e6i			1.04263i
$327$	−327650.	−	751210.i	−0.169450	−	0.388501i
$328$			1.99091e6i			1.02180i
$329$		0			0
$330$	291023.	+	667235.i	0.147110	+	0.337283i
$331$	2.59783e6			1.30329			0.651645	−	0.758524i	$-0.274079\pi$
$331$	2.59783e6			1.30329			0.651645	+	0.758524i	$0.274079\pi$
$332$	−426585.			−0.212403
$333$	2.59669e6	−	2.79732e6i	1.28325	−	1.38239i
$334$		−	1.72417e6i		−	0.845698i
$335$	3.17336e6			1.54492
$336$		0			0
$337$	−1.26128e6			−0.604974			−0.302487	−	0.953153i	$-0.597817\pi$
$337$	−1.26128e6			−0.604974			−0.302487	+	0.953153i	$0.597817\pi$
$338$		−	1.38978e6i		−	0.661689i
$339$	2.18443e6	−	952767.i	1.03238	−	0.450285i
$340$	2.05000e6			0.961737
$341$	1.67757e6			0.781259
$342$	1.27834e6	−	1.37711e6i	0.590992	−	0.636652i
$343$		0			0
$344$			1.26180e6i			0.574904i
$345$	−2.50230e6	+	1.09141e6i	−1.13186	+	0.493675i
$346$		−	631927.i		−	0.283777i
$347$			603203.i			0.268930i	0.990918	+	0.134465i	$0.0429316\pi$
$347$			603203.i			0.268930i	−0.990918	+	0.134465i	$0.957068\pi$
$348$	−1.13464e6	+	494889.i	−0.502240	+	0.219058i
$349$			1.76256e6i			0.774607i	0.921952	+	0.387303i	$0.126593\pi$
$349$			1.76256e6i			0.774607i	−0.921952	+	0.387303i	$0.873407\pi$
$350$		0			0
$351$	−103637.	+	295859.i	−0.0449000	+	0.128179i
$352$	−1.04467e6			−0.449389
$353$	2.71503e6			1.15968			0.579839	−	0.814731i	$-0.303116\pi$
$353$	2.71503e6			1.15968			0.579839	+	0.814731i	$0.303116\pi$
$354$	−1.23438e6	+	538389.i	−0.523527	+	0.228343i
$355$		−	1.07248e6i		−	0.451667i
$356$	−1.39839e6			−0.584796
$357$		0			0
$358$	−1.21328e6			−0.500327
$359$			132406.i			0.0542216i	0.999632	+	0.0271108i	$0.00863070\pi$
$359$			132406.i			0.0542216i	−0.999632	+	0.0271108i	$0.991369\pi$
$360$	2.13519e6	+	1.98206e6i	0.868323	+	0.806047i
$361$	−1.63544e6			−0.660489
$362$	436159.			0.174934
$363$	−772418.	−	1.77094e6i	−0.307670	−	0.705403i
$364$		0			0
$365$		−	1.53308e6i		−	0.602326i
$366$	182762.	+	419022.i	0.0713152	+	0.163506i
$367$			3.51790e6i			1.36338i	0.731639	+	0.681692i	$0.238756\pi$
$367$			3.51790e6i			1.36338i	−0.731639	+	0.681692i	$0.761244\pi$
$368$			442378.i			0.170284i
$369$	1.74514e6	−	1.87998e6i	0.667215	−	0.718764i
$370$			3.80752e6i			1.44590i
$371$		0			0
$372$	2.17228e6	−	947468.i	0.813877	−	0.354983i
$373$	−2.18553e6			−0.813363			−0.406681	−	0.913570i	$-0.633314\pi$
$373$	−2.18553e6			−0.813363			−0.406681	+	0.913570i	$0.633314\pi$
$374$	−1.35701e6			−0.501654
$375$	875175.	+	2.00653e6i	0.321378	+	0.736832i
$376$		−	3.19396e6i		−	1.16509i
$377$	376435.			0.136407
$378$		0			0
$379$	−3.59224e6			−1.28460			−0.642299	−	0.766454i	$-0.722019\pi$
$379$	−3.59224e6			−1.28460			−0.642299	+	0.766454i	$0.722019\pi$
$380$		−	2.25024e6i		−	0.799410i
$381$	−1.80207e6	−	4.13164e6i	−0.636003	−	1.45818i
$382$	−337897.			−0.118475
$383$	−2.73796e6			−0.953741			−0.476870	−	0.878974i	$-0.658229\pi$
$383$	−2.73796e6			−0.953741			−0.476870	+	0.878974i	$0.658229\pi$
$384$	−1.07276e6	+	467897.i	−0.371256	+	0.161928i
$385$		0			0
$386$		−	584361.i		−	0.199624i
$387$	1.10604e6	−	1.19150e6i	0.375400	−	0.404404i
$388$		−	64201.4i		−	0.0216503i
$389$		−	5.32053e6i		−	1.78271i	−0.453306	−	0.891355i	$-0.649755\pi$
$389$		−	5.32053e6i		−	1.78271i	0.453306	−	0.891355i	$-0.350245\pi$
$390$	−125024.	−	286646.i	−0.0416229	−	0.0954298i
$391$		−	5.08914e6i		−	1.68346i
$392$		0			0
$393$	−1.45014e6	−	3.32477e6i	−0.473619	−	1.08588i
$394$	−3.31383e6			−1.07545
$395$	−2.27555e6			−0.733829
$396$	598938.	+	555983.i	0.191931	+	0.178165i
$397$		−	105023.i		−	0.0334433i	−0.999860	−	0.0167216i	$-0.994677\pi$
$397$		−	105023.i		−	0.0334433i	0.999860	−	0.0167216i	$-0.00532291\pi$
$398$	662510.			0.209645
$399$		0			0
$400$	−147063.			−0.0459573
$401$		−	1.10007e6i		−	0.341634i	−0.985303	−	0.170817i	$-0.945359\pi$
$401$		−	1.10007e6i		−	0.341634i	0.985303	−	0.170817i	$-0.0546407\pi$
$402$	−2.72009e6	+	1.18640e6i	−0.839494	+	0.366156i
$403$	−720688.			−0.221047
$404$	1.96752e6			0.599743
$405$	−278835.	−	3.74324e6i	−0.0844715	−	1.13399i
$406$		0			0
$407$			3.02574e6i			0.905411i
$408$	−4.97809e6	+	2.17126e6i	−1.48051	+	0.645745i
$409$			4.30369e6i			1.27213i	0.771634	+	0.636067i	$0.219440\pi$
$409$			4.30369e6i			1.27213i	−0.771634	+	0.636067i	$0.780560\pi$
$410$			2.55890e6i			0.751785i
$411$	2.17089e6	−	946860.i	0.633917	−	0.276491i
$412$			1.44336e6i			0.418919i
$413$		0			0
$414$	1.73685e6	−	1.87104e6i	0.498036	−	0.536515i
$415$	−1.55329e6			−0.442723
$416$	448792.			0.127149
$417$	−4.65772e6	+	2.03152e6i	−1.31169	+	0.572112i
$418$			1.48956e6i			0.416982i
$419$	−1.85221e6			−0.515413			−0.257707	−	0.966223i	$-0.582967\pi$
$419$	−1.85221e6			−0.515413			−0.257707	+	0.966223i	$0.582967\pi$
$420$		0			0
$421$	−1.78215e6			−0.490047			−0.245024	−	0.969517i	$-0.578796\pi$
$421$	−1.78215e6			−0.490047			−0.245024	+	0.969517i	$0.578796\pi$
$422$		−	2.16331e6i		−	0.591340i
$423$	−2.79969e6	+	3.01599e6i	−0.760779	+	0.819557i
$424$	5.55831e6			1.50151
$425$	1.69183e6			0.454342
$426$	400960.	+	919291.i	0.107048	+	0.245431i
$427$		0			0
$428$			889670.i			0.234758i
$429$	−99353.5	−	227790.i	−0.0260639	−	0.0597574i
$430$			1.62178e6i			0.422982i
$431$		−	5.51881e6i		−	1.43104i	−0.698592	−	0.715520i	$-0.746190\pi$
$431$		−	5.51881e6i		−	1.43104i	0.698592	−	0.715520i	$-0.253810\pi$
$432$	−574054.	−	201086.i	−0.147994	−	0.0518410i
$433$		−	31535.8i		−	0.00808321i	−0.999992	−	0.00404161i	$-0.998714\pi$
$433$		−	31535.8i		−	0.00808321i	0.999992	−	0.00404161i	$-0.00128649\pi$
$434$		0			0
$435$	−4.13148e6	+	1.80200e6i	−1.04685	+	0.456595i
$436$	917836.			0.231232
$437$	−5.58623e6			−1.39931
$438$	573161.	+	1.31410e6i	0.142755	+	0.327298i
$439$			3.40059e6i			0.842158i	0.907024	+	0.421079i	$0.138348\pi$
$439$			3.40059e6i			0.842158i	−0.907024	+	0.421079i	$0.861652\pi$
$440$	−2.30955e6			−0.568717
$441$		0			0
$442$	582974.			0.141936
$443$		−	2.37405e6i		−	0.574751i	−0.957818	−	0.287376i	$-0.907217\pi$
$443$		−	2.37405e6i		−	0.574751i	0.957818	−	0.287376i	$-0.0927828\pi$
$444$	1.70890e6	+	3.91802e6i	0.411394	+	0.943213i
$445$	−5.09185e6			−1.21892
$446$	1.32071e6			0.314390
$447$	2.43123e6	−	1.06041e6i	0.575516	−	0.251019i
$448$		0			0
$449$			8.32130e6i			1.94794i	0.226678	+	0.973970i	$0.427214\pi$
$449$			8.32130e6i			1.94794i	−0.226678	+	0.973970i	$0.572786\pi$
$450$	622006.	+	577396.i	0.144798	+	0.134413i
$451$			2.03349e6i			0.470762i
$452$			2.66896e6i			0.614463i
$453$	−315080.	−	722390.i	−0.0721398	−	0.165397i
$454$		−	609510.i		−	0.138785i
$455$		0			0
$456$	2.38334e6	+	5.46434e6i	0.536753	+	1.23063i
$457$	−3.65827e6			−0.819379			−0.409690	−	0.912225i	$-0.634363\pi$
$457$	−3.65827e6			−0.819379			−0.409690	+	0.912225i	$0.634363\pi$
$458$	−1.12981e6			−0.251677
$459$	6.60395e6	+	2.31331e6i	1.46309	+	0.512509i
$460$		−	3.05734e6i		−	0.673673i
$461$	2.08901e6			0.457813			0.228906	−	0.973448i	$-0.426485\pi$
$461$	2.08901e6			0.457813			0.228906	+	0.973448i	$0.426485\pi$
$462$		0			0
$463$	−2.30721e6			−0.500189			−0.250095	−	0.968221i	$-0.580462\pi$
$463$	−2.30721e6			−0.500189			−0.250095	+	0.968221i	$0.580462\pi$
$464$			730397.i			0.157494i
$465$	7.90975e6	−	3.44994e6i	1.69641	−	0.739910i
$466$	−576363.			−0.122951
$467$	−2.51380e6			−0.533382			−0.266691	−	0.963782i	$-0.585930\pi$
$467$	−2.51380e6			−0.533382			−0.266691	+	0.963782i	$0.585930\pi$
$468$	−257305.	−	238851.i	−0.0543043	−	0.0504096i
$469$		0			0
$470$		−	4.10517e6i		−	0.857208i
$471$	2.57023e6	−	1.12104e6i	0.533850	−	0.232845i
$472$		−	4.27264e6i		−	0.882757i
$473$			1.28879e6i			0.264868i
$474$	1.95052e6	−	850746.i	0.398755	−	0.173922i
$475$		−	1.85708e6i		−	0.377656i
$476$		0			0
$477$	−5.24860e6	−	4.87217e6i	−1.05620	−	0.980453i
$478$	910493.			0.182267
$479$	3.84206e6			0.765112			0.382556	−	0.923932i	$-0.375044\pi$
$479$	3.84206e6			0.765112			0.382556	+	0.923932i	$0.375044\pi$
$480$	−4.92562e6	+	2.14837e6i	−0.975793	+	0.425604i
$481$		−	1.29987e6i		−	0.256174i
$482$	1.01818e6			0.199621
$483$		0			0
$484$	2.16375e6			0.419850
$485$		−	233771.i		−	0.0451270i
$486$	1.63847e6	+	3.10433e6i	0.314664	+	0.596179i
$487$	253644.			0.0484621			0.0242311	−	0.999706i	$-0.492286\pi$
$487$	253644.			0.0484621			0.0242311	+	0.999706i	$0.492286\pi$
$488$	−1.45039e6			−0.275699
$489$	3.26960e6	+	7.49629e6i	0.618334	+	1.41767i
$490$		0			0
$491$		−	9.09170e6i		−	1.70193i	−0.525223	−	0.850965i	$-0.676018\pi$
$491$		−	9.09170e6i		−	1.70193i	0.525223	−	0.850965i	$-0.323982\pi$
$492$	1.14849e6	+	2.63316e6i	0.213901	+	0.490416i
$493$		−	8.40253e6i		−	1.55701i
$494$		−	639918.i		−	0.117980i
$495$	2.18087e6	+	2.02445e6i	0.400052	+	0.371360i
$496$		−	1.39835e6i		−	0.255218i
$497$		0			0
$498$	1.33143e6	−	580718.i	0.240571	−	0.104928i
$499$	6.52552e6			1.17318			0.586589	−	0.809885i	$-0.300470\pi$
$499$	6.52552e6			1.17318			0.586589	+	0.809885i	$0.300470\pi$
$500$	−2.45160e6			−0.438556
$501$	−2.81774e6	−	6.46030e6i	−0.501541	−	1.14990i
$502$		−	3.60507e6i		−	0.638490i
$503$	−5.23687e6			−0.922894			−0.461447	−	0.887168i	$-0.652670\pi$
$503$	−5.23687e6			−0.922894			−0.461447	+	0.887168i	$0.652670\pi$
$504$		0			0
$505$	7.16416e6			1.25008
$506$			2.02382e6i			0.351396i
$507$	−2.27125e6	−	5.20736e6i	−0.392415	−	0.899699i
$508$	5.04808e6			0.867895
$509$	−4.98636e6			−0.853079			−0.426539	−	0.904469i	$-0.640267\pi$
$509$	−4.98636e6			−0.853079			−0.426539	+	0.904469i	$0.640267\pi$
$510$	−6.39830e6	+	2.79070e6i	−1.08928	+	0.475103i
$511$		0			0
$512$			1.83991e6i			0.310185i
$513$	2.53927e6	−	7.24901e6i	0.426005	−	1.21614i
$514$		−	5.84146e6i		−	0.975244i
$515$			5.25558e6i			0.873177i
$516$	727891.	+	1.66885e6i	0.120349	+	0.275927i
$517$		−	3.26227e6i		−	0.536777i
$518$		0			0
$519$	−1.03273e6	−	2.36776e6i	−0.168294	−	0.385851i
$520$	992188.			0.160911
$521$	3.66355e6			0.591300			0.295650	−	0.955296i	$-0.404464\pi$
$521$	3.66355e6			0.591300			0.295650	+	0.955296i	$0.404464\pi$
$522$	2.86766e6	−	3.08922e6i	0.460629	−	0.496218i
$523$			1.12666e7i			1.80111i	0.434745	+	0.900553i	$0.356838\pi$
$523$			1.12666e7i			1.80111i	−0.434745	+	0.900553i	$0.643162\pi$
$524$	4.06224e6			0.646305
$525$		0			0
$526$	4.63215e6			0.729992
$527$			1.60867e7i			2.52313i
$528$	441981.	−	192776.i	0.0689952	−	0.0300931i
$529$	−1.15352e6			−0.179220
$530$	7.14405e6			1.10473
$531$	−3.74521e6	+	4.03457e6i	−0.576421	+	0.620956i
$532$		0			0
$533$		−	873593.i		−	0.133196i
$534$	4.36456e6	−	1.90366e6i	0.662349	−	0.288892i
$535$			3.23949e6i			0.489318i
$536$		−	9.41525e6i		−	1.41553i
$537$	−4.54604e6	+	1.98281e6i	−0.680295	+	0.296719i
$538$		−	2.07435e6i		−	0.308977i
$539$		0			0
$540$	3.96738e6	+	1.38974e6i	0.585490	+	0.205092i
$541$	−8.88234e6			−1.30477			−0.652385	−	0.757888i	$-0.726232\pi$
$541$	−8.88234e6			−1.30477			−0.652385	+	0.757888i	$0.726232\pi$
$542$	3.19340e6			0.466933
$543$	1.63424e6	−	712795.i	0.237857	−	0.103744i
$544$		−	1.00176e7i		−	1.45133i
$545$	3.34204e6			0.481971
$546$		0			0
$547$	8.03062e6			1.14757			0.573787	−	0.819004i	$-0.305474\pi$
$547$	8.03062e6			1.14757			0.573787	+	0.819004i	$0.305474\pi$
$548$			2.65241e6i			0.377302i
$549$	1.36958e6	+	1.27135e6i	0.193935	+	0.180026i
$550$	−672798.			−0.0948370
$551$	−9.22327e6			−1.29421
$552$	3.23818e6	+	7.42426e6i	0.452328	+	1.03706i
$553$		0			0
$554$			7.11490e6i			0.984906i
$555$	6.22246e6	+	1.42664e7i	0.857492	+	1.96599i
$556$		−	5.69084e6i		−	0.780710i
$557$			1.30727e7i			1.78536i	0.450690	+	0.892681i	$0.351178\pi$
$557$			1.30727e7i			1.78536i	−0.450690	+	0.892681i	$0.648822\pi$
$558$	−5.49016e6	+	5.91433e6i	−0.746447	+	0.804119i
$559$		−	553668.i		−	0.0749410i
$560$		0			0
$561$	−5.08457e6	+	2.21770e6i	−0.682099	+	0.297506i
$562$	7.71513e6			1.03039
$563$	1.39707e6			0.185757			0.0928786	−	0.995677i	$-0.470393\pi$
$563$	1.39707e6			0.185757			0.0928786	+	0.995677i	$0.470393\pi$
$564$	−1.84248e6	−	4.22431e6i	−0.243897	−	0.559188i
$565$			9.71827e6i			1.28076i
$566$	2.66260e6			0.349353
$567$		0			0
$568$	−3.18201e6			−0.413838
$569$		−	1.33438e7i		−	1.72782i	−0.503644	−	0.863912i	$-0.668007\pi$
$569$		−	1.33438e7i		−	1.72782i	0.503644	−	0.863912i	$-0.331993\pi$
$570$	3.06329e6	+	7.02328e6i	0.394913	+	0.905425i
$571$	437752.			0.0561872			0.0280936	−	0.999605i	$-0.491056\pi$
$571$	437752.			0.0561872			0.0280936	+	0.999605i	$0.491056\pi$
$572$	278316.			0.0355671
$573$	−1.26606e6	+	552209.i	−0.161090	+	0.0702614i
$574$		0			0
$575$		−	2.52317e6i		−	0.318256i
$576$	4.26835e6	−	4.59813e6i	0.536049	−	0.577464i
$577$		−	6.85169e6i		−	0.856757i	−0.903599	−	0.428379i	$-0.859085\pi$
$577$		−	6.85169e6i		−	0.856757i	0.903599	−	0.428379i	$-0.140915\pi$
$578$		−	7.59823e6i		−	0.946003i
$579$	−954996.	−	2.18954e6i	−0.118387	−	0.271429i
$580$		−	5.04789e6i		−	0.623074i
$581$		0			0
$582$	87398.4	+	200380.i	0.0106954	+	0.0245215i
$583$	5.67720e6			0.691771
$584$	−4.54859e6			−0.551880
$585$	−936905.	−	869710.i	−0.113189	−	0.105071i
$586$			7.78091e6i			0.936023i
$587$	1.47999e7			1.77282			0.886410	−	0.462901i	$-0.153192\pi$
$587$	1.47999e7			1.77282			0.886410	+	0.462901i	$0.153192\pi$
$588$		0			0
$589$	1.76580e7			2.09727
$590$		−	5.49159e6i		−	0.649483i
$591$	−1.24166e7	+	5.41564e6i	−1.46229	+	0.637795i
$592$	2.52213e6			0.295776
$593$	109208.			0.0127531			0.00637657	−	0.999980i	$-0.497970\pi$
$593$	109208.			0.0127531			0.00637657	+	0.999980i	$0.497970\pi$
$594$	−2.62623e6	−	919945.i	−0.305398	−	0.106978i
$595$		0			0
$596$			2.97050e6i			0.342543i
$597$	2.48236e6	−	1.08271e6i	0.285055	−	0.124330i
$598$		−	869439.i		−	0.0994229i
$599$		−	2.63088e6i		−	0.299595i	−0.988717	−	0.149798i	$-0.952138\pi$
$599$		−	2.63088e6i		−	0.299595i	0.988717	−	0.149798i	$-0.0478622\pi$
$600$	−2.46811e6	+	1.07650e6i	−0.279889	+	0.122077i
$601$		−	3.21678e6i		−	0.363274i	−0.983366	−	0.181637i	$-0.941860\pi$
$601$		−	3.21678e6i		−	0.363274i	0.983366	−	0.181637i	$-0.0581397\pi$
$602$		0			0
$603$	−8.25300e6	+	8.89064e6i	−0.924312	+	0.995725i
$604$	882624.			0.0984427
$605$	7.87870e6			0.875117
$606$	−6.14086e6	+	2.67841e6i	−0.679278	+	0.296276i
$607$			14387.0i			0.00158489i	1.00000		0.000792446i	$0.000252243\pi$
$607$			14387.0i			0.00158489i	−1.00000		0.000792446i	$0.999748\pi$
$608$	−1.09961e7			−1.20637
$609$		0			0
$610$	−1.86418e6			−0.202844
$611$			1.40148e6i			0.151874i
$612$	−5.33147e6	+	5.74338e6i	−0.575398	+	0.619854i
$613$	−1.05237e7			−1.13114			−0.565570	−	0.824701i	$-0.691344\pi$
$613$	−1.05237e7			−1.13114			−0.565570	+	0.824701i	$0.691344\pi$
$614$	−158923.			−0.0170124
$615$	4.18189e6	+	9.58792e6i	0.445846	+	1.02220i
$616$		0			0
$617$		−	2.62427e6i		−	0.277521i	−0.990326	−	0.138760i	$-0.955688\pi$
$617$		−	2.62427e6i		−	0.277521i	0.990326	−	0.138760i	$-0.0443118\pi$
$618$	−1.96487e6	−	4.50489e6i	−0.206948	−	0.474475i
$619$			6.18138e6i			0.648424i	0.945984	+	0.324212i	$0.105099\pi$
$619$			6.18138e6i			0.648424i	−0.945984	+	0.324212i	$0.894901\pi$
$620$			9.66422e6i			1.00969i
$621$	3.45003e6	−	9.84904e6i	0.359000	−	1.02486i
$622$		−	1.00249e6i		−	0.103898i
$623$		0			0
$624$	−189876.	+	82816.8i	−0.0195213	+	0.00851446i
$625$	−1.17889e7			−1.20718
$626$	8.93966e6			0.911770
$627$	2.43432e6	+	5.58122e6i	0.247291	+	0.566971i
$628$			3.14033e6i			0.317743i
$629$	−2.90147e7			−2.92409
$630$		0			0
$631$	−2.63715e6			−0.263670			−0.131835	−	0.991272i	$-0.542087\pi$
$631$	−2.63715e6			−0.263670			−0.131835	+	0.991272i	$0.542087\pi$
$632$			6.75150e6i			0.672369i
$633$	−3.53540e6	−	8.10569e6i	−0.350695	−	0.804046i
$634$	5.77170e6			0.570270
$635$	1.83812e7			1.80900
$636$	7.35138e6	−	3.20640e6i	0.720653	−	0.314322i
$637$		0			0
$638$			3.34148e6i			0.325003i
$639$	3.00471e6	+	2.78922e6i	0.291106	+	0.270228i
$640$		−	4.77257e6i		−	0.460577i
$641$			1.69974e6i			0.163395i	0.996657	+	0.0816974i	$0.0260341\pi$
$641$			1.69974e6i			0.163395i	−0.996657	+	0.0816974i	$0.973966\pi$
$642$	−1.21112e6	−	2.77677e6i	−0.115971	−	0.265890i
$643$		−	1.34352e7i		−	1.28149i	−0.767752	−	0.640747i	$-0.778625\pi$
$643$		−	1.34352e7i		−	1.28149i	0.767752	−	0.640747i	$-0.221375\pi$
$644$		0			0
$645$	2.65041e6	+	6.07666e6i	0.250850	+	0.575129i
$646$	−1.42838e7			−1.34667
$647$	−8.38468e6			−0.787455			−0.393728	−	0.919227i	$-0.628815\pi$
$647$	−8.38468e6			−0.787455			−0.393728	+	0.919227i	$0.628815\pi$
$648$	−1.11061e7	+	827295.i	−1.03902	+	0.0773968i
$649$		−	4.36403e6i		−	0.406701i
$650$	289035.			0.0268329
$651$		0			0
$652$	−9.15905e6			−0.843784
$653$			2.57521e6i			0.236336i	0.992994	+	0.118168i	$0.0377021\pi$
$653$			2.57521e6i			0.236336i	−0.992994	+	0.118168i	$0.962298\pi$
$654$	−2.86468e6	+	1.24947e6i	−0.261898	+	0.114230i
$655$	1.47915e7			1.34713
$656$	1.69503e6			0.153786
$657$	4.29515e6	+	3.98710e6i	0.388208	+	0.360366i
$658$		0			0
$659$		−	2.05040e6i		−	0.183919i	−0.995763	−	0.0919594i	$-0.970687\pi$
$659$		−	2.05040e6i		−	0.183919i	0.995763	−	0.0919594i	$-0.0293130\pi$
$660$	−3.05460e6	+	1.33230e6i	−0.272957	+	0.119054i
$661$		−	8.33117e6i		−	0.741655i	−0.928702	−	0.370828i	$-0.879074\pi$
$661$		−	8.33117e6i		−	0.741655i	0.928702	−	0.370828i	$-0.120926\pi$
$662$		−	9.90663e6i		−	0.878579i
$663$	2.18434e6	−	952729.i	0.192991	−	0.0841754i
$664$			4.60856e6i			0.405644i
$665$		0			0
$666$	−1.06674e7	−	9.90229e6i	−0.931904	−	0.865068i
$667$	−1.25314e7			−1.09065
$668$	7.89326e6			0.684408
$669$	4.94855e6	−	2.15837e6i	0.427477	−	0.186449i
$670$		−	1.21013e7i		−	1.04147i
$671$	−1.48141e6			−0.127019
$672$		0			0
$673$	−1.55463e7			−1.32309			−0.661546	−	0.749905i	$-0.730099\pi$
$673$	−1.55463e7			−1.32309			−0.661546	+	0.749905i	$0.730099\pi$
$674$			4.80979e6i			0.407828i
$675$	3.27420e6	+	1.14692e6i	0.276596	+	0.0968892i
$676$	6.36240e6			0.535494
$677$	2.77723e6			0.232885			0.116442	−	0.993197i	$-0.462851\pi$
$677$	2.77723e6			0.232885			0.116442	+	0.993197i	$0.462851\pi$
$678$	−3.63330e6	−	8.33016e6i	−0.303548	−	0.695951i
$679$		0			0
$680$		−	2.21469e7i		−	1.83671i
$681$	−996095.	−	2.28377e6i	−0.0823063	−	0.188705i
$682$		−	6.39729e6i		−	0.526665i
$683$			3.92979e6i			0.322342i	0.986926	+	0.161171i	$0.0515271\pi$
$683$			3.92979e6i			0.322342i	−0.986926	+	0.161171i	$0.948473\pi$
$684$	6.30439e6	+	5.85224e6i	0.515232	+	0.478279i
$685$			9.65801e6i			0.786432i
$686$		0			0
$687$	−4.23330e6	+	1.84641e6i	−0.342205	+	0.149257i
$688$	1.07428e6			0.0865260
$689$	−2.43894e6			−0.195728
$690$	4.16201e6	+	9.54234e6i	0.332798	+	0.763013i
$691$		−	1.15551e7i		−	0.920620i	−0.887758	−	0.460310i	$-0.847738\pi$
$691$		−	1.15551e7i		−	0.920620i	0.887758	−	0.460310i	$-0.152262\pi$
$692$	2.89296e6			0.229655
$693$		0			0
$694$	2.30027e6			0.181292
$695$		−	2.07216e7i		−	1.62728i
$696$	5.34647e6	+	1.22580e7i	0.418354	+	0.959171i
$697$	−1.94997e7			−1.52036
$698$	6.72140e6			0.522181
$699$	−2.15957e6	+	941925.i	−0.167176	+	0.0729161i
$700$		0			0
$701$			700700.i			0.0538564i	0.999637	+	0.0269282i	$0.00857255\pi$
$701$			700700.i			0.0538564i	−0.999637	+	0.0269282i	$0.991427\pi$
$702$	1.12823e6	+	395211.i	0.0864085	+	0.0302681i
$703$			3.18488e7i			2.43055i
$704$			4.97361e6i			0.378216i
$705$	−6.70889e6	−	1.53816e7i	−0.508368	−	1.16555i
$706$		−	1.03535e7i		−	0.781766i
$707$		0			0
$708$	−2.46474e6	−	5.65096e6i	−0.184794	−	0.423681i
$709$	−1.16966e7			−0.873862			−0.436931	−	0.899495i	$-0.643935\pi$
$709$	−1.16966e7			−0.873862			−0.436931	+	0.899495i	$0.643935\pi$
$710$	−4.08981e6			−0.304479
$711$	5.91808e6	−	6.37531e6i	0.439042	−	0.472963i
$712$			1.51074e7i			1.11683i
$713$	2.39915e7			1.76739
$714$		0			0
$715$	1.01341e6			0.0741345
$716$		−	5.55440e6i		−	0.404906i
$717$	3.41152e6	−	1.48798e6i	0.247828	−	0.108093i
$718$	504921.			0.0365521
$719$	4.09661e6			0.295531			0.147765	−	0.989022i	$-0.452792\pi$
$719$	4.09661e6			0.295531			0.147765	+	0.989022i	$0.452792\pi$
$720$	1.68750e6	−	1.81787e6i	0.121314	−	0.130687i
$721$		0			0
$722$			6.23660e6i			0.445251i
$723$	3.81500e6	−	1.66396e6i	0.271424	−	0.118385i
$724$			1.99673e6i			0.141571i
$725$		−	4.16593e6i		−	0.294352i
$726$	−6.75334e6	+	2.94555e6i	−0.475529	+	0.207408i
$727$			91957.7i			0.00645285i	0.999995	+	0.00322643i	$0.00102701\pi$
$727$			91957.7i			0.00645285i	−0.999995	+	0.00322643i	$0.998973\pi$
$728$		0			0
$729$	1.12124e7	+	8.95391e6i	0.781413	+	0.624014i
$730$	−5.84627e6			−0.406043
$731$	−1.23586e7			−0.855412
$732$	−1.91828e6	+	836681.i	−0.132323	+	0.0577142i
$733$		−	2.26633e7i		−	1.55798i	−0.627035	−	0.778991i	$-0.715732\pi$
$733$		−	2.26633e7i		−	1.55798i	0.627035	−	0.778991i	$-0.284268\pi$
$734$	1.34152e7			0.919090
$735$		0			0
$736$	−1.49401e7			−1.01662
$737$		−	9.61663e6i		−	0.652160i
$738$	−7.16914e6	−	6.65497e6i	−0.484536	−	0.449785i
$739$	2.86778e7			1.93168			0.965839	−	0.259142i	$-0.0834396\pi$
$739$	2.86778e7			1.93168			0.965839	+	0.259142i	$0.0834396\pi$
$740$	−1.74308e7			−1.17014
$741$	−1.04579e6	−	2.39771e6i	−0.0699679	−	0.160417i
$742$		0			0
$743$			3.69650e6i			0.245651i	0.992428	+	0.122826i	$0.0391956\pi$
$743$			3.69650e6i			0.245651i	−0.992428	+	0.122826i	$0.960804\pi$
$744$	−1.02359e7	−	2.34680e7i	−0.677941	−	1.55433i
$745$			1.08163e7i			0.713981i
$746$			8.33434e6i			0.548307i
$747$	4.03967e6	−	4.35178e6i	0.264877	−	0.285342i
$748$		−	6.21238e6i		−	0.405979i
$749$		0			0
$750$	7.65176e6	−	3.33741e6i	0.496716	−	0.216649i
$751$	2.20198e7			1.42467			0.712334	−	0.701840i	$-0.247638\pi$
$751$	2.20198e7			1.42467			0.712334	+	0.701840i	$0.247638\pi$
$752$	−2.71929e6			−0.175352
$753$	−5.89160e6	−	1.35078e7i	−0.378657	−	0.868155i
$754$		−	1.43551e6i		−	0.0919553i
$755$	3.21383e6			0.205190
$756$		0			0
$757$	1.92307e7			1.21971			0.609853	−	0.792514i	$-0.291228\pi$
$757$	1.92307e7			1.21971			0.609853	+	0.792514i	$0.291228\pi$
$758$			1.36987e7i			0.865979i
$759$	3.30745e6	+	7.58306e6i	0.208396	+	0.477793i
$760$	−2.43102e7			−1.52670
$761$	−1.48971e7			−0.932479			−0.466239	−	0.884659i	$-0.654391\pi$
$761$	−1.48971e7			−0.932479			−0.466239	+	0.884659i	$0.654391\pi$
$762$	−1.57557e7	+	6.87205e6i	−0.982993	+	0.428745i
$763$		0			0
$764$		−	1.54689e6i		−	0.0958795i
$765$	−1.94131e7	+	2.09129e7i	−1.19933	+	1.29200i
$766$			1.04410e7i			0.642940i
$767$			1.87480e6i			0.115071i
$768$	6.93320e6	+	1.58959e7i	0.424161	+	0.972483i
$769$			1.64954e7i			1.00588i	0.864322	+	0.502939i	$0.167748\pi$
$769$			1.64954e7i			1.00588i	−0.864322	+	0.502939i	$0.832252\pi$
$770$		0			0
$771$	−9.54643e6	−	2.18873e7i	−0.578369	−	1.32604i
$772$	2.67520e6			0.161552
$773$	1.48795e6			0.0895654			0.0447827	−	0.998997i	$-0.485740\pi$
$773$	1.48795e6			0.0895654			0.0447827	+	0.998997i	$0.485740\pi$
$774$	−4.54368e6	−	4.21780e6i	−0.272618	−	0.253066i
$775$			7.97569e6i			0.476995i
$776$	−693592.			−0.0413475
$777$		0			0
$778$	−2.02894e7			−1.20177
$779$			2.14044e7i			1.26375i
$780$	1.31226e6	−	572360.i	0.0772297	−	0.0336847i
$781$	−3.25007e6			−0.190663
$782$	−1.94070e7			−1.13486
$783$	5.69625e6	−	1.62615e7i	0.332036	−	0.947884i
$784$		0			0
$785$			1.14346e7i			0.662290i
$786$	−1.26788e7	+	5.53000e6i	−0.732016	+	0.319278i
$787$			3.58878e6i			0.206543i	0.994653	+	0.103271i	$0.0329310\pi$
$787$			3.58878e6i			0.206543i	−0.994653	+	0.103271i	$0.967069\pi$
$788$		−	1.51707e7i		−	0.870342i
$789$	1.73562e7	−	7.57011e6i	0.992571	−	0.432922i
$790$			8.67765e6i			0.494691i
$791$		0			0
$792$	6.00649e6	−	6.47056e6i	0.340258	−	0.366546i
$793$	636419.			0.0359385
$794$	−400498.			−0.0225449
$795$	2.67680e7	−	1.16752e7i	1.50210	−	0.655159i
$796$			3.03297e6i			0.169662i
$797$	−1.32728e7			−0.740146			−0.370073	−	0.929003i	$-0.620667\pi$
$797$	−1.32728e7			−0.740146			−0.370073	+	0.929003i	$0.620667\pi$
$798$		0			0
$799$	3.12828e7			1.73356
$800$		−	4.96668e6i		−	0.274373i
$801$	1.32425e7	−	1.42656e7i	0.729269	−	0.785613i
$802$	−4.19505e6			−0.230304
$803$	−4.64588e6			−0.254261
$804$	−5.43133e6	−	1.24525e7i	−0.296324	−	0.679388i
$805$		0			0
$806$			2.74829e6i			0.149013i
$807$	−3.39002e6	−	7.77237e6i	−0.183239	−	0.420116i
$808$		−	2.12558e7i		−	1.14538i
$809$		−	2.49729e7i		−	1.34152i	−0.741674	−	0.670761i	$-0.765968\pi$
$809$		−	2.49729e7i		−	1.34152i	0.741674	−	0.670761i	$-0.234032\pi$
$810$	−1.42746e7	+	1.06332e6i	−0.764452	+	0.0569443i
$811$			9.04873e6i			0.483099i	0.970389	+	0.241549i	$0.0776555\pi$
$811$			9.04873e6i			0.483099i	−0.970389	+	0.241549i	$0.922344\pi$
$812$		0			0
$813$	1.19653e7	−	5.21882e6i	0.634889	−	0.276915i
$814$	1.15384e7			0.610360
$815$	−3.33501e7			−1.75875
$816$	1.84858e6	+	4.23828e6i	0.0971880	+	0.222825i
$817$			1.35657e7i			0.711031i
$818$	1.64118e7			0.857576
$819$		0			0
$820$	−1.17146e7			−0.608406
$821$		−	1.49381e7i		−	0.773460i	−0.922193	−	0.386730i	$-0.873605\pi$
$821$		−	1.49381e7i		−	0.773460i	0.922193	−	0.386730i	$-0.126395\pi$
$822$	−3.61077e6	−	8.27851e6i	−0.186389	−	0.427339i
$823$	−2.63768e7			−1.35745			−0.678723	−	0.734395i	$-0.737466\pi$
$823$	−2.63768e7			−1.35745			−0.678723	+	0.734395i	$0.737466\pi$
$824$	1.55931e7			0.800047
$825$	−2.52090e6	+	1.09952e6i	−0.128950	+	0.0562431i
$826$		0			0
$827$		−	1.07002e6i		−	0.0544036i	−0.999630	−	0.0272018i	$-0.991340\pi$
$827$		−	1.07002e6i		−	0.0544036i	0.999630	−	0.0272018i	$-0.00865967\pi$
$828$	8.56560e6	+	7.95128e6i	0.434192	+	0.403052i
$829$		−	7.72434e6i		−	0.390369i	−0.980767	−	0.195184i	$-0.937469\pi$
$829$		−	7.72434e6i		−	0.390369i	0.980767	−	0.195184i	$-0.0625305\pi$
$830$			5.92335e6i			0.298450i
$831$	1.16276e7	+	2.66588e7i	0.584099	+	1.33918i
$832$		−	2.13667e6i		−	0.107011i
$833$		0			0
$834$	7.74705e6	+	1.77618e7i	0.385675	+	0.884245i
$835$	2.87411e7			1.42655
$836$	−6.81919e6			−0.337456
$837$	−1.09055e7	+	3.11327e7i	−0.538062	+	1.53604i
$838$			7.06326e6i			0.347452i
$839$	−2.77221e7			−1.35963			−0.679815	−	0.733383i	$-0.737940\pi$
$839$	−2.77221e7			−1.35963			−0.679815	+	0.733383i	$0.737940\pi$
$840$		0			0
$841$	−179112.			−0.00873241
$842$			6.79607e6i			0.330353i
$843$	2.89078e7	−	1.26085e7i	1.40103	−	0.611075i
$844$	9.90362e6			0.478562
$845$	2.31669e7			1.11616
$846$	1.15012e7	+	1.06764e7i	0.552483	+	0.512859i
$847$		0			0
$848$		−	4.73226e6i		−	0.225985i
$849$	9.97648e6	−	4.35137e6i	0.475016	−	0.207184i
$850$		−	6.45164e6i		−	0.306283i
$851$			4.32721e7i			2.04825i
$852$	−4.20851e6	+	1.83559e6i	−0.198623	+	0.0866319i
$853$			3.01558e7i			1.41905i	0.704680	+	0.709525i	$0.251091\pi$
$853$			3.01558e7i			1.41905i	−0.704680	+	0.709525i	$0.748909\pi$
$854$		0			0
$855$	2.29557e7	+	2.13093e7i	1.07393	+	0.996905i
$856$	9.61145e6			0.448337
$857$	3.43656e7			1.59835			0.799174	−	0.601099i	$-0.205270\pi$
$857$	3.43656e7			1.59835			0.799174	+	0.601099i	$0.205270\pi$
$858$	−868660.	+	378877.i	−0.0402839	+	0.0175703i
$859$		−	3.41443e7i		−	1.57883i	−0.613859	−	0.789416i	$-0.710384\pi$
$859$		−	3.41443e7i		−	1.57883i	0.613859	−	0.789416i	$-0.289616\pi$
$860$	−7.42452e6			−0.342312
$861$		0			0
$862$	−2.10455e7			−0.964699
$863$			4.30318e6i			0.196681i	0.995153	+	0.0983406i	$0.0313535\pi$
$863$			4.30318e6i			0.196681i	−0.995153	+	0.0983406i	$0.968647\pi$
$864$	6.79116e6	−	1.93872e7i	0.309499	−	0.883548i
$865$	1.05339e7			0.478684
$866$	−120259.			−0.00544909
$867$	−1.24174e7	−	2.84698e7i	−0.561028	−	1.28628i
$868$		0			0
$869$			6.89591e6i			0.309772i
$870$	6.87178e6	+	1.57551e7i	0.307802	+	0.705704i
$871$			4.13133e6i			0.184520i
$872$		−	9.91573e6i		−	0.441605i
$873$	654946.	+	607973.i	0.0290850	+	0.0269991i
$874$			2.13027e7i			0.943312i
$875$		0			0
$876$	−6.01594e6	+	2.62393e6i	−0.264876	+	0.115529i
$877$	2.73346e7			1.20009			0.600046	−	0.799966i	$-0.295149\pi$
$877$	2.73346e7			1.20009			0.600046	+	0.799966i	$0.295149\pi$
$878$	1.29679e7			0.567719
$879$	1.27160e7	+	2.91542e7i	0.555109	+	1.27271i
$880$			1.96632e6i			0.0855948i
$881$	−1.72146e7			−0.747234			−0.373617	−	0.927583i	$-0.621883\pi$
$881$	−1.72146e7			−0.747234			−0.373617	+	0.927583i	$0.621883\pi$
$882$		0			0
$883$	−2.66941e7			−1.15216			−0.576081	−	0.817393i	$-0.695419\pi$
$883$	−2.66941e7			−1.15216			−0.576081	+	0.817393i	$0.695419\pi$
$884$			2.66885e6i			0.114867i
$885$	−8.97466e6	−	2.05764e7i	−0.385176	−	0.883103i
$886$	−9.05324e6			−0.387454
$887$	−2.93197e7			−1.25127			−0.625633	−	0.780117i	$-0.715159\pi$
$887$	−2.93197e7			−1.25127			−0.625633	+	0.780117i	$0.715159\pi$
$888$	4.23279e7	−	1.84619e7i	1.80133	−	0.785675i
$889$		0			0
$890$			1.94174e7i			0.821705i
$891$	−1.13436e7	+	844991.i	−0.478694	+	0.0356581i
$892$			6.04619e6i			0.254431i
$893$		−	3.43385e7i		−	1.44096i
$894$	−4.04380e6	−	9.27131e6i	−0.169218	−	0.387969i
$895$		−	2.02248e7i		−	0.843968i
$896$		0			0
$897$	−1.42089e6	−	3.25770e6i	−0.0589628	−	0.135185i
$898$	3.17326e7			1.31315
$899$	3.96116e7			1.63465
$900$	−2.64331e6	+	2.84754e6i	−0.108778	+	0.117183i
$901$			5.44402e7i			2.23413i
$902$	7.75456e6			0.317352
$903$		0			0
$904$	2.88338e7			1.17349
$905$			7.27054e6i			0.295084i
$906$	−2.75478e6	+	1.20153e6i	−0.111498	+	0.0486312i
$907$	2.24470e7			0.906024			0.453012	−	0.891504i	$-0.350350\pi$
$907$	2.24470e7			0.906024			0.453012	+	0.891504i	$0.350350\pi$
$908$	2.79033e6			0.112316
$909$	−1.86320e7	+	2.00715e7i	−0.747909	+	0.805693i
$910$		0			0
$911$			3.46785e7i			1.38441i	0.721701	+	0.692205i	$0.243361\pi$
$911$			3.46785e7i			1.38441i	−0.721701	+	0.692205i	$0.756639\pi$
$912$	4.65226e6	−	2.02914e6i	0.185216	−	0.0807841i
$913$			4.70714e6i			0.186887i
$914$			1.39505e7i			0.552363i
$915$	−6.98487e6	+	3.04654e6i	−0.275807	+	0.120297i
$916$		−	5.17229e6i		−	0.203678i
$917$		0			0
$918$	8.82161e6	−	2.51836e7i	0.345495	−	0.986306i
$919$	−889356.			−0.0347366			−0.0173683	−	0.999849i	$-0.505529\pi$
$919$	−889356.			−0.0347366			−0.0173683	+	0.999849i	$0.505529\pi$
$920$	−3.30296e7			−1.28657
$921$	−595467.	+	259720.i	−0.0231318	+	0.0100892i
$922$		−	7.96627e6i		−	0.308623i
$923$	1.39624e6			0.0539455
$924$		0			0
$925$	−1.43853e7			−0.552796
$926$			8.79835e6i			0.337189i
$927$	−1.47243e7	−	1.36683e7i	−0.562775	−	0.522413i
$928$	−2.46672e7			−0.940266
$929$	2.47988e7			0.942737			0.471369	−	0.881936i	$-0.343760\pi$
$929$	2.47988e7			0.942737			0.471369	+	0.881936i	$0.343760\pi$
$930$	−1.31561e7	−	3.01632e7i	−0.498791	−	1.14359i
$931$		0			0
$932$		−	2.63859e6i		−	0.0995020i
$933$	−1.63833e6	−	3.75624e6i	−0.0616166	−	0.141270i
$934$			9.58617e6i			0.359565i
$935$		−	2.26206e7i		−	0.846206i
$936$	−2.58040e6	+	2.77977e6i	−0.0962715	+	0.103710i
$937$			5.18147e7i			1.92799i	0.265928	+	0.963993i	$0.414322\pi$
$937$			5.18147e7i			1.92799i	−0.265928	+	0.963993i	$0.585678\pi$
$938$		0			0
$939$	3.34960e7	−	1.46097e7i	1.23973	−	0.540726i
$940$	1.87934e7			0.693723
$941$	−1.13634e7			−0.418346			−0.209173	−	0.977879i	$-0.567077\pi$
$941$	−1.13634e7			−0.418346			−0.209173	+	0.977879i	$0.567077\pi$
$942$	−4.27499e6	−	9.80136e6i	−0.156967	−	0.359881i
$943$			2.90816e7i			1.06497i
$944$	−3.63766e6			−0.132859
$945$		0			0
$946$	4.91471e6			0.178554
$947$		−	5.98134e6i		−	0.216732i	−0.994111	−	0.108366i	$-0.965438\pi$
$947$		−	5.98134e6i		−	0.216732i	0.994111	−	0.108366i	$-0.0345619\pi$
$948$	3.89471e6	+	8.92949e6i	0.140752	+	0.322705i
$949$	1.99588e6			0.0719398
$950$	−7.08183e6			−0.254587
$951$	2.16259e7	−	9.43242e6i	0.775396	−	0.338199i
$952$		0			0
$953$		−	4.05570e7i		−	1.44655i	−0.690559	−	0.723276i	$-0.742636\pi$
$953$		−	4.05570e7i		−	1.44655i	0.690559	−	0.723276i	$-0.257364\pi$
$954$	−1.85796e7	+	2.00151e7i	−0.660947	+	0.712012i
$955$		−	5.63256e6i		−	0.199847i
$956$			4.16823e6i			0.147505i
$957$	5.46083e6	+	1.25202e7i	0.192743	+	0.441907i
$958$		−	1.46514e7i		−	0.515780i
$959$		0			0
$960$	1.02283e7	+	2.34506e7i	0.358199	+	0.821250i
$961$	−4.72076e7			−1.64893
$962$	−4.95693e6			−0.172693
$963$	−9.07591e6	−	8.42499e6i	−0.315373	−	0.292754i
$964$			4.66121e6i			0.161550i
$965$	9.74100e6			0.336733
$966$		0			0
$967$	1.60320e7			0.551343			0.275672	−	0.961252i	$-0.411100\pi$
$967$	1.60320e7			0.551343			0.275672	+	0.961252i	$0.411100\pi$
$968$		−	2.33758e7i		−	0.801824i
$969$	−5.35199e7	+	2.33434e7i	−1.83107	+	0.798646i
$970$	−891468.			−0.0304212
$971$	−3.81288e7			−1.29779			−0.648896	−	0.760877i	$-0.724769\pi$
$971$	−3.81288e7			−1.29779			−0.648896	+	0.760877i	$0.724769\pi$
$972$	−1.42116e7	+	7.50089e6i	−0.482478	+	0.254652i
$973$		0			0
$974$		−	967252.i		−	0.0326695i
$975$	1.08299e6	−	472358.i	0.0364847	−	0.0159133i
$976$			1.23484e6i			0.0414942i
$977$			3.12818e6i			0.104847i	0.998625	+	0.0524235i	$0.0166946\pi$
$977$			3.12818e6i			0.104847i	−0.998625	+	0.0524235i	$0.983305\pi$
$978$	2.85865e7	−	1.24684e7i	0.955684	−	0.416833i
$979$			1.54305e7i			0.514545i
$980$		0			0
$981$	−8.69171e6	+	9.36324e6i	−0.288358	+	0.310637i
$982$	−3.46705e7			−1.14731
$983$	−29166.0			−0.000962704			−0.000481352	−	1.00000i	$-0.500153\pi$
$983$	−29166.0			−0.000962704			−0.000481352		1.00000i	$0.500153\pi$
$984$	2.84471e7	−	1.24075e7i	0.936590	−	0.408506i
$985$		−	5.52398e7i		−	1.81410i
$986$	−3.20424e7			−1.04962
$987$		0			0
$988$	2.92954e6			0.0954788
$989$			1.84314e7i			0.599195i
$990$	7.72010e6	−	8.31656e6i	0.250343	−	0.269684i
$991$	2.82226e6			0.0912878			0.0456439	−	0.998958i	$-0.485466\pi$
$991$	2.82226e6			0.0912878			0.0456439	+	0.998958i	$0.485466\pi$
$992$	4.72256e7			1.52370
$993$	−1.61900e7	−	3.71191e7i	−0.521042	−	1.19461i
$994$		0			0
$995$			1.10437e7i			0.353636i
$996$	2.65852e6	+	6.09526e6i	0.0849165	+	0.194690i
$997$			7.02821e6i			0.223927i	0.993712	+	0.111964i	$0.0357140\pi$
$997$			7.02821e6i			0.223927i	−0.993712	+	0.111964i	$0.964286\pi$
$998$		−	2.48846e7i		−	0.790867i
$999$	−5.61523e7	−	1.96697e7i	−1.78014	−	0.623567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.c.d.146.9	✓	40
3.2	odd	2	inner	147.6.c.d.146.32	yes	40
7.6	odd	2	inner	147.6.c.d.146.31	yes	40
21.20	even	2	inner	147.6.c.d.146.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.c.d.146.9	✓	40	1.1	even	1	trivial
147.6.c.d.146.10	yes	40	21.20	even	2	inner
147.6.c.d.146.31	yes	40	7.6	odd	2	inner
147.6.c.d.146.32	yes	40	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.81342i q^{2} +(-6.23210 - 14.2885i) q^{3} +17.4578 q^{4} +63.5678 q^{5} +(-54.4880 + 23.7656i) q^{6} -188.603i q^{8} +(-165.322 + 178.095i) q^{9} +O(q^{10})\)	\(q-3.81342i q^{2} +(-6.23210 - 14.2885i) q^{3} +17.4578 q^{4} +63.5678 q^{5} +(-54.4880 + 23.7656i) q^{6} -188.603i q^{8} +(-165.322 + 178.095i) q^{9} -242.411i q^{10} -192.638i q^{11} +(-108.799 - 249.446i) q^{12} +82.7575i q^{13} +(-396.161 - 908.287i) q^{15} -160.574 q^{16} +1847.26 q^{17} +(679.150 + 630.442i) q^{18} -2027.69i q^{19} +1109.75 q^{20} -734.608 q^{22} -2754.97i q^{23} +(-2694.86 + 1175.40i) q^{24} +915.859 q^{25} +315.589 q^{26} +(3575.01 + 1252.29i) q^{27} -4548.65i q^{29} +(-3463.68 + 1510.73i) q^{30} +8708.43i q^{31} -5422.97i q^{32} +(-2752.50 + 1200.54i) q^{33} -7044.36i q^{34} +(-2886.16 + 3109.14i) q^{36} -15706.9 q^{37} -7732.44 q^{38} +(1182.48 - 515.754i) q^{39} -11989.1i q^{40} -10556.1 q^{41} -6690.24 q^{43} -3363.03i q^{44} +(-10509.1 + 11321.1i) q^{45} -10505.9 q^{46} +16934.8 q^{47} +(1000.72 + 2294.36i) q^{48} -3492.56i q^{50} +(-11512.3 - 26394.5i) q^{51} +1444.77i q^{52} +29470.9i q^{53} +(4775.52 - 13633.0i) q^{54} -12245.5i q^{55} +(-28972.6 + 12636.8i) q^{57} -17345.9 q^{58} +22654.1 q^{59} +(-6916.10 - 15856.7i) q^{60} -7690.16i q^{61} +33208.9 q^{62} -25818.5 q^{64} +5260.71i q^{65} +(4578.16 + 10496.4i) q^{66} +49920.8 q^{67} +32249.1 q^{68} +(-39364.4 + 17169.3i) q^{69} -16871.4i q^{71} +(33589.3 + 31180.3i) q^{72} -24117.2i q^{73} +59897.1i q^{74} +(-5707.73 - 13086.2i) q^{75} -35399.1i q^{76} +(-1966.79 - 4509.29i) q^{78} -35797.3 q^{79} -10207.4 q^{80} +(-4386.43 - 58885.9i) q^{81} +40254.7i q^{82} -24435.2 q^{83} +117426. q^{85} +25512.7i q^{86} +(-64993.4 + 28347.7i) q^{87} -36332.1 q^{88} -80101.2 q^{89} +(43172.0 + 40075.8i) q^{90} -48095.8i q^{92} +(124430. - 54271.8i) q^{93} -64579.4i q^{94} -128896. i q^{95} +(-77486.1 + 33796.5i) q^{96} -3677.51i q^{97} +(34307.7 + 31847.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 640 q^{4} + 440 q^{9}+O(q^{10}) \) 40 * q - 640 * q^4 + 440 * q^9	\( 40 q - 640 q^{4} + 440 q^{9} - 3176 q^{15} + 3552 q^{16} - 4544 q^{18} + 21088 q^{22} + 30104 q^{25} + 44664 q^{30} - 59320 q^{36} - 26224 q^{37} - 16216 q^{39} + 21584 q^{43} - 27680 q^{46} + 95784 q^{51} - 130304 q^{57} - 131376 q^{58} + 329208 q^{60} + 53968 q^{64} - 187632 q^{67} + 606736 q^{72} + 70312 q^{78} - 597424 q^{79} + 755256 q^{81} + 108112 q^{85} - 1673072 q^{88} + 590480 q^{93} - 258480 q^{99}+O(q^{100}) \) 40 * q - 640 * q^4 + 440 * q^9 - 3176 * q^15 + 3552 * q^16 - 4544 * q^18 + 21088 * q^22 + 30104 * q^25 + 44664 * q^30 - 59320 * q^36 - 26224 * q^37 - 16216 * q^39 + 21584 * q^43 - 27680 * q^46 + 95784 * q^51 - 130304 * q^57 - 131376 * q^58 + 329208 * q^60 + 53968 * q^64 - 187632 * q^67 + 606736 * q^72 + 70312 * q^78 - 597424 * q^79 + 755256 * q^81 + 108112 * q^85 - 1673072 * q^88 + 590480 * q^93 - 258480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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