LMFDB - Embedded newform 126.6.g.c.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,6,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, 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:	$20.2083612964$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.6.g.c.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(-3.00000 + 5.19615i) q^{5} +(59.5000 + 115.181i) q^{7} -64.0000 q^{8} +O(q^{10})$	\(q+(2.00000 - 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(-3.00000 + 5.19615i) q^{5} +(59.5000 + 115.181i) q^{7} -64.0000 q^{8} +(12.0000 + 20.7846i) q^{10} +(-333.000 - 576.773i) q^{11} -559.000 q^{13} +(518.000 + 24.2487i) q^{14} +(-128.000 + 221.703i) q^{16} +(-870.000 - 1506.88i) q^{17} +(-578.500 + 1001.99i) q^{19} +96.0000 q^{20} -2664.00 q^{22} +(-1734.00 + 3003.38i) q^{23} +(1544.50 + 2675.15i) q^{25} +(-1118.00 + 1936.43i) q^{26} +(1120.00 - 1745.91i) q^{28} -3372.00 q^{29} +(-3146.50 - 5449.90i) q^{31} +(512.000 + 886.810i) q^{32} -6960.00 q^{34} +(-777.000 - 36.3731i) q^{35} +(-1565.50 + 2711.53i) q^{37} +(2314.00 + 4007.97i) q^{38} +(192.000 - 332.554i) q^{40} +4866.00 q^{41} -11407.0 q^{43} +(-5328.00 + 9228.37i) q^{44} +(6936.00 + 12013.5i) q^{46} +(1155.00 - 2000.52i) q^{47} +(-9726.50 + 13706.6i) q^{49} +12356.0 q^{50} +(4472.00 + 7745.73i) q^{52} +(-14148.0 - 24505.1i) q^{53} +3996.00 q^{55} +(-3808.00 - 7371.61i) q^{56} +(-6744.00 + 11681.0i) q^{58} +(10272.0 + 17791.6i) q^{59} +(2315.00 - 4009.70i) q^{61} -25172.0 q^{62} +4096.00 q^{64} +(1677.00 - 2904.65i) q^{65} +(9372.50 + 16233.6i) q^{67} +(-13920.0 + 24110.1i) q^{68} +(-1680.00 + 2618.86i) q^{70} +38226.0 q^{71} +(-35294.5 - 61131.9i) q^{73} +(6262.00 + 10846.1i) q^{74} +18512.0 q^{76} +(46620.0 - 72673.4i) q^{77} +(31146.5 - 53947.3i) q^{79} +(-768.000 - 1330.22i) q^{80} +(9732.00 - 16856.3i) q^{82} -79818.0 q^{83} +10440.0 q^{85} +(-22814.0 + 39515.0i) q^{86} +(21312.0 + 36913.5i) q^{88} +(-9060.00 + 15692.4i) q^{89} +(-33260.5 - 64386.4i) q^{91} +55488.0 q^{92} +(-4620.00 - 8002.07i) q^{94} +(-3471.00 - 6011.95i) q^{95} +124754. q^{97} +(28028.0 + 61106.8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 16 q^{4} - 6 q^{5} + 119 q^{7} - 128 q^{8}+O(q^{10}) $ 2 * q + 4 * q^2 - 16 * q^4 - 6 * q^5 + 119 * q^7 - 128 * q^8	$ 2 q + 4 q^{2} - 16 q^{4} - 6 q^{5} + 119 q^{7} - 128 q^{8} + 24 q^{10} - 666 q^{11} - 1118 q^{13} + 1036 q^{14} - 256 q^{16} - 1740 q^{17} - 1157 q^{19} + 192 q^{20} - 5328 q^{22} - 3468 q^{23} + 3089 q^{25} - 2236 q^{26} + 2240 q^{28} - 6744 q^{29} - 6293 q^{31} + 1024 q^{32} - 13920 q^{34} - 1554 q^{35} - 3131 q^{37} + 4628 q^{38} + 384 q^{40} + 9732 q^{41} - 22814 q^{43} - 10656 q^{44} + 13872 q^{46} + 2310 q^{47} - 19453 q^{49} + 24712 q^{50} + 8944 q^{52} - 28296 q^{53} + 7992 q^{55} - 7616 q^{56} - 13488 q^{58} + 20544 q^{59} + 4630 q^{61} - 50344 q^{62} + 8192 q^{64} + 3354 q^{65} + 18745 q^{67} - 27840 q^{68} - 3360 q^{70} + 76452 q^{71} - 70589 q^{73} + 12524 q^{74} + 37024 q^{76} + 93240 q^{77} + 62293 q^{79} - 1536 q^{80} + 19464 q^{82} - 159636 q^{83} + 20880 q^{85} - 45628 q^{86} + 42624 q^{88} - 18120 q^{89} - 66521 q^{91} + 110976 q^{92} - 9240 q^{94} - 6942 q^{95} + 249508 q^{97} + 56056 q^{98}+O(q^{100}) $ 2 * q + 4 * q^2 - 16 * q^4 - 6 * q^5 + 119 * q^7 - 128 * q^8 + 24 * q^10 - 666 * q^11 - 1118 * q^13 + 1036 * q^14 - 256 * q^16 - 1740 * q^17 - 1157 * q^19 + 192 * q^20 - 5328 * q^22 - 3468 * q^23 + 3089 * q^25 - 2236 * q^26 + 2240 * q^28 - 6744 * q^29 - 6293 * q^31 + 1024 * q^32 - 13920 * q^34 - 1554 * q^35 - 3131 * q^37 + 4628 * q^38 + 384 * q^40 + 9732 * q^41 - 22814 * q^43 - 10656 * q^44 + 13872 * q^46 + 2310 * q^47 - 19453 * q^49 + 24712 * q^50 + 8944 * q^52 - 28296 * q^53 + 7992 * q^55 - 7616 * q^56 - 13488 * q^58 + 20544 * q^59 + 4630 * q^61 - 50344 * q^62 + 8192 * q^64 + 3354 * q^65 + 18745 * q^67 - 27840 * q^68 - 3360 * q^70 + 76452 * q^71 - 70589 * q^73 + 12524 * q^74 + 37024 * q^76 + 93240 * q^77 + 62293 * q^79 - 1536 * q^80 + 19464 * q^82 - 159636 * q^83 + 20880 * q^85 - 45628 * q^86 + 42624 * q^88 - 18120 * q^89 - 66521 * q^91 + 110976 * q^92 - 9240 * q^94 - 6942 * q^95 + 249508 * q^97 + 56056 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$		0			0
$3$		0			0
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	−3.00000	+	5.19615i	−0.0536656	+	0.0929516i	−0.891610	−	0.452804i	$-0.850424\pi$
$5$	−3.00000	+	5.19615i	−0.0536656	+	0.0929516i	0.837945	+	0.545755i	$0.183757\pi$
$6$		0			0
$7$	59.5000	+	115.181i	0.458957	+	0.888459i
$7$	59.5000	+	115.181i	0.458957	+	0.888459i
$8$	−64.0000			−0.353553
$9$		0			0
$10$	12.0000	+	20.7846i	0.0379473	+	0.0657267i
$11$	−333.000	−	576.773i	−0.829779	−	1.43722i	−0.898211	−	0.439564i	$-0.855133\pi$
$11$	−333.000	−	576.773i	−0.829779	−	1.43722i	0.0684322	−	0.997656i	$-0.478200\pi$
$12$		0			0
$13$	−559.000			−0.917389			−0.458694	−	0.888594i	$-0.651683\pi$
$13$	−559.000			−0.917389			−0.458694	+	0.888594i	$0.651683\pi$
$14$	518.000	+	24.2487i	0.706333	+	0.0330650i
$15$		0			0
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	−870.000	−	1506.88i	−0.730125	−	1.26461i	−0.956830	−	0.290649i	$-0.906129\pi$
$17$	−870.000	−	1506.88i	−0.730125	−	1.26461i	0.226705	−	0.973963i	$-0.427205\pi$
$18$		0			0
$19$	−578.500	+	1001.99i	−0.367637	+	0.636766i	−0.989196	−	0.146602i	$-0.953166\pi$
$19$	−578.500	+	1001.99i	−0.367637	+	0.636766i	0.621558	+	0.783368i	$0.286500\pi$
$20$	96.0000			0.0536656
$21$		0			0
$22$	−2664.00			−1.17348
$23$	−1734.00	+	3003.38i	−0.683486	+	1.18383i	0.290424	+	0.956898i	$0.406204\pi$
$23$	−1734.00	+	3003.38i	−0.683486	+	1.18383i	−0.973910	+	0.226934i	$0.927130\pi$
$24$		0			0
$25$	1544.50	+	2675.15i	0.494240	+	0.856049i
$26$	−1118.00	+	1936.43i	−0.324346	+	0.561784i
$27$		0			0
$28$	1120.00	−	1745.91i	0.269975	−	0.420849i
$29$	−3372.00			−0.744548			−0.372274	−	0.928123i	$-0.621422\pi$
$29$	−3372.00			−0.744548			−0.372274	+	0.928123i	$0.621422\pi$
$30$		0			0
$31$	−3146.50	−	5449.90i	−0.588063	−	1.01855i	−0.994486	−	0.104869i	$-0.966558\pi$
$31$	−3146.50	−	5449.90i	−0.588063	−	1.01855i	0.406423	−	0.913685i	$-0.366776\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$		0			0
$34$	−6960.00			−1.03255
$35$	−777.000	−	36.3731i	−0.107214	−	0.00501891i
$36$		0			0
$37$	−1565.50	+	2711.53i	−0.187996	+	0.325619i	−0.944582	−	0.328276i	$-0.893533\pi$
$37$	−1565.50	+	2711.53i	−0.187996	+	0.325619i	0.756586	+	0.653894i	$0.226866\pi$
$38$	2314.00	+	4007.97i	0.259959	+	0.450262i
$39$		0			0
$40$	192.000	−	332.554i	0.0189737	−	0.0328634i
$41$	4866.00			0.452077			0.226039	−	0.974118i	$-0.427422\pi$
$41$	4866.00			0.452077			0.226039	+	0.974118i	$0.427422\pi$
$42$		0			0
$43$	−11407.0			−0.940806			−0.470403	−	0.882452i	$-0.655892\pi$
$43$	−11407.0			−0.940806			−0.470403	+	0.882452i	$0.655892\pi$
$44$	−5328.00	+	9228.37i	−0.414890	+	0.718610i
$45$		0			0
$46$	6936.00	+	12013.5i	0.483297	+	0.837096i
$47$	1155.00	−	2000.52i	0.0762671	−	0.132099i	−0.825369	−	0.564593i	$-0.809033\pi$
$47$	1155.00	−	2000.52i	0.0762671	−	0.132099i	0.901637	+	0.432494i	$0.142366\pi$
$48$		0			0
$49$	−9726.50	+	13706.6i	−0.578717	+	0.815528i
$50$	12356.0			0.698961
$51$		0			0
$52$	4472.00	+	7745.73i	0.229347	+	0.397241i
$53$	−14148.0	−	24505.1i	−0.691840	−	1.19830i	−0.971235	−	0.238125i	$-0.923467\pi$
$53$	−14148.0	−	24505.1i	−0.691840	−	1.19830i	0.279395	−	0.960176i	$-0.409866\pi$
$54$		0			0
$55$	3996.00			0.178122
$56$	−3808.00	−	7371.61i	−0.162266	−	0.314118i
$57$		0			0
$58$	−6744.00	+	11681.0i	−0.263237	+	0.455941i
$59$	10272.0	+	17791.6i	0.384171	+	0.665404i	0.991654	−	0.128929i	$-0.0411539\pi$
$59$	10272.0	+	17791.6i	0.384171	+	0.665404i	−0.607483	+	0.794333i	$0.707821\pi$
$60$		0			0
$61$	2315.00	−	4009.70i	0.0796575	−	0.137971i	−0.823445	−	0.567397i	$-0.807951\pi$
$61$	2315.00	−	4009.70i	0.0796575	−	0.137971i	0.903102	+	0.429426i	$0.141284\pi$
$62$	−25172.0			−0.831646
$63$		0			0
$64$	4096.00			0.125000
$65$	1677.00	−	2904.65i	0.0492322	−	0.0852728i
$66$		0			0
$67$	9372.50	+	16233.6i	0.255075	+	0.441803i	0.964916	−	0.262559i	$-0.0845664\pi$
$67$	9372.50	+	16233.6i	0.255075	+	0.441803i	−0.709841	+	0.704362i	$0.751233\pi$
$68$	−13920.0	+	24110.1i	−0.365062	+	0.632306i
$69$		0			0
$70$	−1680.00	+	2618.86i	−0.0409793	+	0.0638804i
$71$	38226.0			0.899939			0.449969	−	0.893044i	$-0.351435\pi$
$71$	38226.0			0.899939			0.449969	+	0.893044i	$0.351435\pi$
$72$		0			0
$73$	−35294.5	−	61131.9i	−0.775175	−	1.34264i	−0.934696	−	0.355448i	$-0.884328\pi$
$73$	−35294.5	−	61131.9i	−0.775175	−	1.34264i	0.159521	−	0.987195i	$-0.449005\pi$
$74$	6262.00	+	10846.1i	0.132933	+	0.230247i
$75$		0			0
$76$	18512.0			0.367637
$77$	46620.0	−	72673.4i	0.896077	−	1.39685i
$78$		0			0
$79$	31146.5	−	53947.3i	0.561489	−	0.972528i	−0.435877	−	0.900006i	$-0.643562\pi$
$79$	31146.5	−	53947.3i	0.561489	−	0.972528i	0.997367	−	0.0725221i	$-0.0231048\pi$
$80$	−768.000	−	1330.22i	−0.0134164	−	0.0232379i
$81$		0			0
$82$	9732.00	−	16856.3i	0.159833	−	0.276840i
$83$	−79818.0			−1.27176			−0.635881	−	0.771787i	$-0.719363\pi$
$83$	−79818.0			−1.27176			−0.635881	+	0.771787i	$0.719363\pi$
$84$		0			0
$85$	10440.0			0.156730
$86$	−22814.0	+	39515.0i	−0.332625	+	0.576124i
$87$		0			0
$88$	21312.0	+	36913.5i	0.293371	+	0.508134i
$89$	−9060.00	+	15692.4i	−0.121242	+	0.209997i	−0.920258	−	0.391313i	$-0.872021\pi$
$89$	−9060.00	+	15692.4i	−0.121242	+	0.209997i	0.799016	+	0.601310i	$0.205354\pi$
$90$		0			0
$91$	−33260.5	−	64386.4i	−0.421042	−	0.815062i
$92$	55488.0			0.683486
$93$		0			0
$94$	−4620.00	−	8002.07i	−0.0539290	−	0.0934078i
$95$	−3471.00	−	6011.95i	−0.0394590	−	0.0683449i
$96$		0			0
$97$	124754.			1.34625			0.673124	−	0.739530i	$-0.264952\pi$
$97$	124754.			1.34625			0.673124	+	0.739530i	$0.264952\pi$
$98$	28028.0	+	61106.8i	0.294800	+	0.642723i
$99$		0			0
$100$	24712.0	−	42802.4i	0.247120	−	0.428024i
$101$	−46695.0	−	80878.1i	−0.455478	−	0.788910i	0.543238	−	0.839579i	$-0.317198\pi$
$101$	−46695.0	−	80878.1i	−0.455478	−	0.788910i	−0.998716	+	0.0506685i	$0.983865\pi$
$102$		0			0
$103$	83865.5	−	145259.i	0.778915	−	1.34912i	−0.153652	−	0.988125i	$-0.549103\pi$
$103$	83865.5	−	145259.i	0.778915	−	1.34912i	0.932567	−	0.360996i	$-0.117563\pi$
$104$	35776.0			0.324346
$105$		0			0
$106$	−113184.			−0.978409
$107$	34590.0	−	59911.6i	0.292073	−	0.505885i	−0.682227	−	0.731141i	$-0.738988\pi$
$107$	34590.0	−	59911.6i	0.292073	−	0.505885i	0.974300	+	0.225256i	$0.0723217\pi$
$108$		0			0
$109$	109779.	+	190144.i	0.885024	+	1.53291i	0.845686	+	0.533680i	$0.179191\pi$
$109$	109779.	+	190144.i	0.885024	+	1.53291i	0.0393377	+	0.999226i	$0.487475\pi$
$110$	7992.00	−	13842.6i	0.0629758	−	0.109077i
$111$		0			0
$112$	−33152.0	−	1551.92i	−0.249727	−	0.0116902i
$113$	39354.0			0.289930			0.144965	−	0.989437i	$-0.453693\pi$
$113$	39354.0			0.289930			0.144965	+	0.989437i	$0.453693\pi$
$114$		0			0
$115$	−10404.0	−	18020.3i	−0.0733594	−	0.127062i
$116$	26976.0	+	46723.8i	0.186137	+	0.322399i
$117$		0			0
$118$	82176.0			0.543300
$119$	121800.	−	189867.i	0.788460	−	1.22909i
$120$		0			0
$121$	−141252.	+	244657.i	−0.877067	+	1.51912i
$122$	−9260.00	−	16038.8i	−0.0563263	−	0.0975601i
$123$		0			0
$124$	−50344.0	+	87198.4i	−0.294031	+	0.509277i
$125$	−37284.0			−0.213426
$126$		0			0
$127$	317093.			1.74453			0.872263	−	0.489037i	$-0.162652\pi$
$127$	317093.			1.74453			0.872263	+	0.489037i	$0.162652\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−6708.00	−	11618.6i	−0.0348125	−	0.0602969i
$131$	−77415.0	+	134087.i	−0.394137	+	0.682665i	−0.992991	−	0.118194i	$-0.962290\pi$
$131$	−77415.0	+	134087.i	−0.394137	+	0.682665i	0.598854	+	0.800858i	$0.295623\pi$
$132$		0			0
$133$	−149832.	−	7013.94i	−0.734470	−	0.0343821i
$134$	74980.0			0.360731
$135$		0			0
$136$	55680.0	+	96440.6i	0.258138	+	0.447108i
$137$	33666.0	+	58311.2i	0.153246	+	0.265430i	0.932419	−	0.361379i	$-0.117694\pi$
$137$	33666.0	+	58311.2i	0.153246	+	0.265430i	−0.779173	+	0.626809i	$0.784361\pi$
$138$		0			0
$139$	−365215.			−1.60329			−0.801644	−	0.597802i	$-0.796041\pi$
$139$	−365215.			−1.60329			−0.801644	+	0.597802i	$0.796041\pi$
$140$	5712.00	+	11057.4i	0.0246302	+	0.0476797i
$141$		0			0
$142$	76452.0	−	132419.i	0.318176	−	0.551098i
$143$	186147.	+	322416.i	0.761230	+	1.31849i
$144$		0			0
$145$	10116.0	−	17521.4i	0.0399566	−	0.0692069i
$146$	−282356.			−1.09626
$147$		0			0
$148$	50096.0			0.187996
$149$	−84030.0	+	145544.i	−0.310076	+	0.537068i	−0.978379	−	0.206822i	$-0.933688\pi$
$149$	−84030.0	+	145544.i	−0.310076	+	0.537068i	0.668302	+	0.743890i	$0.267021\pi$
$150$		0			0
$151$	−76768.0	−	132966.i	−0.273992	−	0.474568i	0.695888	−	0.718150i	$-0.255011\pi$
$151$	−76768.0	−	132966.i	−0.273992	−	0.474568i	−0.969880	+	0.243582i	$0.921678\pi$
$152$	37024.0	−	64127.4i	0.129979	−	0.225131i
$153$		0			0
$154$	−158508.	−	306843.i	−0.538579	−	1.04259i
$155$	37758.0			0.126235
$156$		0			0
$157$	−101209.	−	175299.i	−0.327695	−	0.567585i	0.654359	−	0.756184i	$-0.272939\pi$
$157$	−101209.	−	175299.i	−0.327695	−	0.567585i	−0.982054	+	0.188599i	$0.939605\pi$
$158$	−124586.	−	215789.i	−0.397033	−	0.687681i
$159$		0			0
$160$	−6144.00			−0.0189737
$161$	−449106.	−	21023.6i	−1.36548	−	0.0639209i
$162$		0			0
$163$	89882.0	−	155680.i	0.264974	−	0.458949i	−0.702583	−	0.711602i	$-0.747970\pi$
$163$	89882.0	−	155680.i	0.264974	−	0.458949i	0.967557	+	0.252653i	$0.0813032\pi$
$164$	−38928.0	−	67425.3i	−0.113019	−	0.195755i
$165$		0			0
$166$	−159636.	+	276498.i	−0.449636	+	0.778792i
$167$	−217302.			−0.602938			−0.301469	−	0.953476i	$-0.597477\pi$
$167$	−217302.			−0.602938			−0.301469	+	0.953476i	$0.597477\pi$
$168$		0			0
$169$	−58812.0			−0.158398
$170$	20880.0	−	36165.2i	0.0554126	−	0.0959774i
$171$		0			0
$172$	91256.0	+	158060.i	0.235202	+	0.407381i
$173$	−36990.0	+	64068.6i	−0.0939656	+	0.162753i	−0.909176	−	0.416411i	$-0.863288\pi$
$173$	−36990.0	+	64068.6i	−0.0939656	+	0.162753i	0.815211	+	0.579164i	$0.196621\pi$
$174$		0			0
$175$	−216230.	+	337069.i	−0.533729	+	0.832001i
$176$	170496.			0.414890
$177$		0			0
$178$	36240.0	+	62769.5i	0.0857311	+	0.148491i
$179$	394683.	+	683611.i	0.920695	+	1.59469i	0.798342	+	0.602204i	$0.205711\pi$
$179$	394683.	+	683611.i	0.920695	+	1.59469i	0.122353	+	0.992487i	$0.460956\pi$
$180$		0			0
$181$	−477739.			−1.08391			−0.541956	−	0.840407i	$-0.682316\pi$
$181$	−477739.			−1.08391			−0.541956	+	0.840407i	$0.682316\pi$
$182$	−289562.	−	13555.0i	−0.647982	−	0.0303335i
$183$		0			0
$184$	110976.	−	192216.i	0.241649	−	0.418548i
$185$	−9393.00	−	16269.2i	−0.0201779	−	0.0349491i
$186$		0			0
$187$	−579420.	+	1.00358e6i	−1.21168	+	2.09870i
$188$	−36960.0			−0.0762671
$189$		0			0
$190$	−27768.0			−0.0558034
$191$	179487.	−	310881.i	0.356000	−	0.616609i	−0.631289	−	0.775548i	$-0.717474\pi$
$191$	179487.	−	310881.i	0.356000	−	0.616609i	0.987289	+	0.158938i	$0.0508071\pi$
$192$		0			0
$193$	90966.5	+	157559.i	0.175788	+	0.304473i	0.940434	−	0.339978i	$-0.110419\pi$
$193$	90966.5	+	157559.i	0.175788	+	0.304473i	−0.764646	+	0.644451i	$0.777086\pi$
$194$	249508.	−	432161.i	0.475971	−	0.824405i
$195$		0			0
$196$	267736.	+	25121.7i	0.497813	+	0.0467098i
$197$	−717924.			−1.31799			−0.658996	−	0.752146i	$-0.729019\pi$
$197$	−717924.			−1.31799			−0.658996	+	0.752146i	$0.729019\pi$
$198$		0			0
$199$	−101548.	−	175886.i	−0.181777	−	0.314847i	0.760709	−	0.649093i	$-0.224852\pi$
$199$	−101548.	−	175886.i	−0.181777	−	0.314847i	−0.942486	+	0.334246i	$0.891518\pi$
$200$	−98848.0	−	171210.i	−0.174740	−	0.302659i
$201$		0			0
$202$	−373560.			−0.644142
$203$	−200634.	−	388392.i	−0.341715	−	0.661500i
$204$		0			0
$205$	−14598.0	+	25284.5i	−0.0242610	+	0.0420213i
$206$	−335462.	−	581037.i	−0.550776	−	0.953973i
$207$		0			0
$208$	71552.0	−	123932.i	0.114674	−	0.198620i
$209$	770562.			1.22023
$210$		0			0
$211$	1.17098e6			1.81069			0.905343	−	0.424680i	$-0.139613\pi$
$211$	1.17098e6			1.81069			0.905343	+	0.424680i	$0.139613\pi$
$212$	−226368.	+	392081.i	−0.345920	+	0.599151i
$213$		0			0
$214$	−138360.	−	239647.i	−0.206527	−	0.357715i
$215$	34221.0	−	59272.5i	0.0504890	−	0.0874495i
$216$		0			0
$217$	440510.	−	686687.i	0.635048	−	0.989942i
$218$	878236.			1.25161
$219$		0			0
$220$	−31968.0	−	55370.2i	−0.0445306	−	0.0771293i
$221$	486330.	+	842348.i	0.669808	+	1.16014i
$222$		0			0
$223$	1.24635e6			1.67833			0.839167	−	0.543873i	$-0.183043\pi$
$223$	1.24635e6			1.67833			0.839167	+	0.543873i	$0.183043\pi$
$224$	−71680.0	+	111738.i	−0.0954504	+	0.148793i
$225$		0			0
$226$	78708.0	−	136326.i	0.102506	−	0.177545i
$227$	−459471.	−	795827.i	−0.591825	−	1.02507i	−0.993987	−	0.109503i	$-0.965074\pi$
$227$	−459471.	−	795827.i	−0.591825	−	1.02507i	0.402161	−	0.915569i	$-0.368259\pi$
$228$		0			0
$229$	−601874.	+	1.04248e6i	−0.758433	+	1.31364i	0.185216	+	0.982698i	$0.440701\pi$
$229$	−601874.	+	1.04248e6i	−0.758433	+	1.31364i	−0.943649	+	0.330947i	$0.892632\pi$
$230$	−83232.0			−0.103746
$231$		0			0
$232$	215808.			0.263237
$233$	−459531.	+	795931.i	−0.554530	+	0.960474i	0.443410	+	0.896319i	$0.353769\pi$
$233$	−459531.	+	795931.i	−0.554530	+	0.960474i	−0.997940	+	0.0641551i	$0.979565\pi$
$234$		0			0
$235$	6930.00	+	12003.1i	0.00818585	+	0.0141783i
$236$	164352.	−	284666.i	0.192086	−	0.332702i
$237$		0			0
$238$	−414120.	−	801662.i	−0.473897	−	0.917380i
$239$	625338.			0.708142			0.354071	−	0.935219i	$-0.384797\pi$
$239$	625338.			0.708142			0.354071	+	0.935219i	$0.384797\pi$
$240$		0			0
$241$	−626911.	−	1.08584e6i	−0.695286	−	1.20427i	−0.970084	−	0.242768i	$-0.921945\pi$
$241$	−626911.	−	1.08584e6i	−0.695286	−	1.20427i	0.274799	−	0.961502i	$-0.411389\pi$
$242$	565010.	+	978626.i	0.620180	+	1.07418i
$243$		0			0
$244$	−74080.0			−0.0796575
$245$	−42042.0	−	91660.1i	−0.0447474	−	0.0975585i
$246$		0			0
$247$	323382.	−	560113.i	0.337266	−	0.584162i
$248$	201376.	+	348793.i	0.207911	+	0.360113i
$249$		0			0
$250$	−74568.0	+	129156.i	−0.0754575	+	0.130696i
$251$	1.51333e6			1.51618			0.758089	−	0.652152i	$-0.226133\pi$
$251$	1.51333e6			1.51618			0.758089	+	0.652152i	$0.226133\pi$
$252$		0			0
$253$	2.30969e6			2.26857
$254$	634186.	−	1.09844e6i	0.616783	−	1.06830i
$255$		0			0
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−777465.	+	1.34661e6i	−0.734257	+	1.27177i	0.220792	+	0.975321i	$0.429136\pi$
$257$	−777465.	+	1.34661e6i	−0.734257	+	1.27177i	−0.955049	+	0.296449i	$0.904197\pi$
$258$		0			0
$259$	−405464.	−	18980.7i	−0.375581	−	0.0175818i
$260$	−53664.0			−0.0492322
$261$		0			0
$262$	309660.	+	536347.i	0.278697	+	0.482717i
$263$	−557658.	−	965892.i	−0.497140	−	0.861071i	0.502855	−	0.864371i	$-0.332283\pi$
$263$	−557658.	−	965892.i	−0.497140	−	0.861071i	−0.999995	+	0.00329949i	$0.998950\pi$
$264$		0			0
$265$	169776.			0.148512
$266$	−323960.	+	505004.i	−0.280729	+	0.437613i
$267$		0			0
$268$	149960.	−	259738.i	0.127538	−	0.220902i
$269$	17835.0	+	30891.1i	0.0150277	+	0.0260287i	0.873441	−	0.486929i	$-0.161883\pi$
$269$	17835.0	+	30891.1i	0.0150277	+	0.0260287i	−0.858414	+	0.512958i	$0.828550\pi$
$270$		0			0
$271$	146384.	−	253545.i	0.121079	−	0.209716i	−0.799114	−	0.601179i	$-0.794698\pi$
$271$	146384.	−	253545.i	0.121079	−	0.209716i	0.920194	+	0.391464i	$0.128031\pi$
$272$	445440.			0.365062
$273$		0			0
$274$	269328.			0.216723
$275$	1.02864e6	−	1.78165e6i	0.820220	−	1.42066i
$276$		0			0
$277$	−431607.	−	747564.i	−0.337978	−	0.585395i	0.646074	−	0.763275i	$-0.276410\pi$
$277$	−431607.	−	747564.i	−0.337978	−	0.585395i	−0.984052	+	0.177879i	$0.943076\pi$
$278$	−730430.	+	1.26514e6i	−0.566848	+	0.981810i
$279$		0			0
$280$	49728.0	+	2327.88i	0.0379058	+	0.00177445i
$281$	−1.47110e6			−1.11142			−0.555709	−	0.831377i	$-0.687553\pi$
$281$	−1.47110e6			−1.11142			−0.555709	+	0.831377i	$0.687553\pi$
$282$		0			0
$283$	−344420.	−	596554.i	−0.255637	−	0.442775i	0.709432	−	0.704774i	$-0.248952\pi$
$283$	−344420.	−	596554.i	−0.255637	−	0.442775i	−0.965068	+	0.261999i	$0.915618\pi$
$284$	−305808.	−	529675.i	−0.224985	−	0.389685i
$285$		0			0
$286$	1.48918e6			1.07654
$287$	289527.	+	560473.i	0.207484	+	0.401652i
$288$		0			0
$289$	−803872.	+	1.39235e6i	−0.566164	+	0.980624i
$290$	−40464.0	−	70085.7i	−0.0282536	−	0.0489367i
$291$		0			0
$292$	−564712.	+	978110.i	−0.387588	+	0.671321i
$293$	−722832.			−0.491890			−0.245945	−	0.969284i	$-0.579098\pi$
$293$	−722832.			−0.491890			−0.245945	+	0.969284i	$0.579098\pi$
$294$		0			0
$295$	−123264.			−0.0824672
$296$	100192.	−	173538.i	0.0664666	−	0.115124i
$297$		0			0
$298$	336120.	+	582177.i	0.219257	+	0.379764i
$299$	969306.	−	1.67889e6i	0.627022	−	1.08603i
$300$		0			0
$301$	−678716.	−	1.31387e6i	−0.431790	−	0.835868i
$302$	−614144.			−0.387483
$303$		0			0
$304$	−148096.	−	256510.i	−0.0919093	−	0.159192i
$305$	13890.0	+	24058.2i	0.00854973	+	0.0148086i
$306$		0			0
$307$	−20125.0			−0.0121868			−0.00609340	−	0.999981i	$-0.501940\pi$
$307$	−20125.0			−0.0121868			−0.00609340	+	0.999981i	$0.501940\pi$
$308$	−1.37995e6	−	64598.6i	−0.828871	−	0.0388013i
$309$		0			0
$310$	75516.0	−	130798.i	0.0446308	−	0.0773028i
$311$	−871779.	−	1.50997e6i	−0.511099	−	0.885250i	−0.999917	−	0.0128643i	$-0.995905\pi$
$311$	−871779.	−	1.50997e6i	−0.511099	−	0.885250i	0.488818	−	0.872386i	$-0.337428\pi$
$312$		0			0
$313$	−904272.	+	1.56624e6i	−0.521721	+	0.903647i	0.477960	+	0.878382i	$0.341376\pi$
$313$	−904272.	+	1.56624e6i	−0.521721	+	0.903647i	−0.999681	+	0.0252651i	$0.991957\pi$
$314$	−809672.			−0.463431
$315$		0			0
$316$	−996688.			−0.561489
$317$	511776.	−	886422.i	0.286043	−	0.495442i	−0.686818	−	0.726829i	$-0.740993\pi$
$317$	511776.	−	886422.i	0.286043	−	0.495442i	0.972862	+	0.231388i	$0.0743266\pi$
$318$		0			0
$319$	1.12288e6	+	1.94488e6i	0.617810	+	1.07008i
$320$	−12288.0	+	21283.4i	−0.00670820	+	0.0116190i
$321$		0			0
$322$	−971040.	+	1.51370e6i	−0.521912	+	0.813581i
$323$	2.01318e6			1.07368
$324$		0			0
$325$	−863376.	−	1.49541e6i	−0.453410	−	0.785330i
$326$	−359528.	−	622721.i	−0.187365	−	0.324526i
$327$		0			0
$328$	−311424.			−0.159833
$329$	299145.	+	14003.6i	0.152367	+	0.00713265i
$330$		0			0
$331$	503766.	−	872549.i	0.252731	−	0.437744i	−0.711545	−	0.702640i	$-0.752004\pi$
$331$	503766.	−	872549.i	0.252731	−	0.437744i	0.964277	+	0.264896i	$0.0853378\pi$
$332$	638544.	+	1.10599e6i	0.317940	+	0.550689i
$333$		0			0
$334$	−434604.	+	752756.i	−0.213171	+	0.369223i
$335$	−112470.			−0.0547551
$336$		0			0
$337$	−1.56571e6			−0.750993			−0.375496	−	0.926824i	$-0.622528\pi$
$337$	−1.56571e6			−0.750993			−0.375496	+	0.926824i	$0.622528\pi$
$338$	−117624.	+	203731.i	−0.0560021	+	0.0969985i
$339$		0			0
$340$	−83520.0	−	144661.i	−0.0391826	−	0.0678662i
$341$	−2.09557e6	+	3.62963e6i	−0.975924	+	1.69035i
$342$		0			0
$343$	−2.15747e6	−	304770.i	−0.990169	−	0.139874i
$344$	730048.			0.332625
$345$		0			0
$346$	147960.	+	256274.i	0.0664437	+	0.115084i
$347$	378642.	+	655827.i	0.168813	+	0.292392i	0.938003	−	0.346628i	$-0.112673\pi$
$347$	378642.	+	655827.i	0.168813	+	0.292392i	−0.769190	+	0.639020i	$0.779340\pi$
$348$		0			0
$349$	−455638.			−0.200243			−0.100121	−	0.994975i	$-0.531923\pi$
$349$	−455638.			−0.200243			−0.100121	+	0.994975i	$0.531923\pi$
$350$	735182.	+	1.42318e6i	0.320793	+	0.620998i
$351$		0			0
$352$	340992.	−	590615.i	0.146686	−	0.254067i
$353$	−1.81569e6	−	3.14487e6i	−0.775543	−	1.34328i	−0.934489	−	0.355992i	$-0.884143\pi$
$353$	−1.81569e6	−	3.14487e6i	−0.775543	−	1.34328i	0.158946	−	0.987287i	$-0.449190\pi$
$354$		0			0
$355$	−114678.	+	198628.i	−0.0482958	+	0.0836508i
$356$	289920.			0.121242
$357$		0			0
$358$	3.15746e6			1.30206
$359$	−2.01242e6	+	3.48561e6i	−0.824104	+	1.42739i	0.0784980	+	0.996914i	$0.474988\pi$
$359$	−2.01242e6	+	3.48561e6i	−0.824104	+	1.42739i	−0.902602	+	0.430476i	$0.858346\pi$
$360$		0			0
$361$	568725.	+	985061.i	0.229686	+	0.397828i
$362$	−955478.	+	1.65494e6i	−0.383221	+	0.663758i
$363$		0			0
$364$	−626080.	+	975962.i	−0.247672	+	0.386082i
$365$	423534.			0.166401
$366$		0			0
$367$	−1.28894e6	−	2.23251e6i	−0.499536	−	0.865222i	0.500464	−	0.865757i	$-0.333163\pi$
$367$	−1.28894e6	−	2.23251e6i	−0.499536	−	0.865222i	−1.00000		0.000535822i	$0.999829\pi$
$368$	−443904.	−	768864.i	−0.170871	−	0.295958i
$369$		0			0
$370$	−75144.0			−0.0285358
$371$	1.98072e6	−	3.08764e6i	0.747116	−	1.16464i
$372$		0			0
$373$	1.26566e6	−	2.19220e6i	0.471028	−	0.815844i	−0.528423	−	0.848981i	$-0.677216\pi$
$373$	1.26566e6	−	2.19220e6i	0.471028	−	0.815844i	0.999451	+	0.0331372i	$0.0105498\pi$
$374$	2.31768e6	+	4.01434e6i	0.856790	+	1.48400i
$375$		0			0
$376$	−73920.0	+	128033.i	−0.0269645	+	0.0467039i
$377$	1.88495e6			0.683040
$378$		0			0
$379$	−3.06677e6			−1.09669			−0.548344	−	0.836253i	$-0.684742\pi$
$379$	−3.06677e6			−1.09669			−0.548344	+	0.836253i	$0.684742\pi$
$380$	−55536.0	+	96191.2i	−0.0197295	+	0.0341725i
$381$		0			0
$382$	−717948.	−	1.24352e6i	−0.251730	−	0.436009i
$383$	−1.96260e6	+	3.39932e6i	−0.683652	+	1.18412i	0.290207	+	0.956964i	$0.406276\pi$
$383$	−1.96260e6	+	3.39932e6i	−0.683652	+	1.18412i	−0.973859	+	0.227155i	$0.927057\pi$
$384$		0			0
$385$	237762.	+	460265.i	0.0817505	+	0.158254i
$386$	727732.			0.248601
$387$		0			0
$388$	−998032.	−	1.72864e6i	−0.336562	−	0.582943i
$389$	−2.01334e6	−	3.48722e6i	−0.674597	−	1.16844i	−0.976587	−	0.215125i	$-0.930984\pi$
$389$	−2.01334e6	−	3.48722e6i	−0.674597	−	1.16844i	0.301990	−	0.953311i	$-0.402349\pi$
$390$		0			0
$391$	6.03432e6			1.99612
$392$	622496.	−	877221.i	0.204607	−	0.288333i
$393$		0			0
$394$	−1.43585e6	+	2.48696e6i	−0.465981	+	0.807102i
$395$	186879.	+	323684.i	0.0602654	+	0.104383i
$396$		0			0
$397$	−2.28720e6	+	3.96155e6i	−0.728329	+	1.26150i	0.229260	+	0.973365i	$0.426370\pi$
$397$	−2.28720e6	+	3.96155e6i	−0.728329	+	1.26150i	−0.957589	+	0.288138i	$0.906964\pi$
$398$	−812384.			−0.257071
$399$		0			0
$400$	−790784.			−0.247120
$401$	−1.13472e6	+	1.96539e6i	−0.352393	+	0.610363i	−0.986668	−	0.162744i	$-0.947965\pi$
$401$	−1.13472e6	+	1.96539e6i	−0.352393	+	0.610363i	0.634275	+	0.773108i	$0.281299\pi$
$402$		0			0
$403$	1.75889e6	+	3.04649e6i	0.539482	+	0.934410i
$404$	−747120.	+	1.29405e6i	−0.227739	+	0.394455i
$405$		0			0
$406$	−1.74670e6	−	81766.7i	−0.525899	−	0.0246185i
$407$	2.08525e6			0.623981
$408$		0			0
$409$	2.02298e6	+	3.50391e6i	0.597976	+	1.03572i	0.993120	+	0.117105i	$0.0373615\pi$
$409$	2.02298e6	+	3.50391e6i	0.597976	+	1.03572i	−0.395144	+	0.918619i	$0.629305\pi$
$410$	58392.0	+	101138.i	0.0171551	+	0.0297135i
$411$		0			0
$412$	−2.68370e6			−0.778915
$413$	−1.43808e6	+	2.24174e6i	−0.414866	+	0.646712i
$414$		0			0
$415$	239454.	−	414746.i	0.0682499	−	0.118212i
$416$	−286208.	−	495727.i	−0.0810865	−	0.140446i
$417$		0			0
$418$	1.54112e6	−	2.66931e6i	0.431417	−	0.747236i
$419$	3.91281e6			1.08881			0.544407	−	0.838821i	$-0.316755\pi$
$419$	3.91281e6			1.08881			0.544407	+	0.838821i	$0.316755\pi$
$420$		0			0
$421$	−2.78086e6			−0.764671			−0.382335	−	0.924024i	$-0.624880\pi$
$421$	−2.78086e6			−0.764671			−0.382335	+	0.924024i	$0.624880\pi$
$422$	2.34196e6	−	4.05639e6i	0.640174	−	1.10881i
$423$		0			0
$424$	905472.	+	1.56832e6i	0.244602	+	0.423663i
$425$	2.68743e6	−	4.65477e6i	0.721714	−	1.25004i
$426$		0			0
$427$	599585.	+	28067.9i	0.159141	+	0.00744972i
$428$	−1.10688e6			−0.292073
$429$		0			0
$430$	−136884.	−	237090.i	−0.0357011	−	0.0618361i
$431$	−2.19104e6	−	3.79498e6i	−0.568141	−	0.984049i	−0.996750	−	0.0805589i	$-0.974329\pi$
$431$	−2.19104e6	−	3.79498e6i	−0.568141	−	0.984049i	0.428609	−	0.903490i	$-0.359004\pi$
$432$		0			0
$433$	1.24946e6			0.320261			0.160130	−	0.987096i	$-0.448809\pi$
$433$	1.24946e6			0.320261			0.160130	+	0.987096i	$0.448809\pi$
$434$	−1.49773e6	−	2.89935e6i	−0.381690	−	0.738883i
$435$		0			0
$436$	1.75647e6	−	3.04230e6i	0.442512	−	0.766453i
$437$	−2.00624e6	−	3.47491e6i	−0.502550	−	0.870441i
$438$		0			0
$439$	3.37210e6	−	5.84066e6i	0.835102	−	1.44644i	−0.0588449	−	0.998267i	$-0.518742\pi$
$439$	3.37210e6	−	5.84066e6i	0.835102	−	1.44644i	0.893947	−	0.448172i	$-0.147925\pi$
$440$	−255744.			−0.0629758
$441$		0			0
$442$	3.89064e6			0.947252
$443$	239448.	−	414736.i	0.0579698	−	0.100407i	−0.835584	−	0.549362i	$-0.814871\pi$
$443$	239448.	−	414736.i	0.0579698	−	0.100407i	0.893554	+	0.448956i	$0.148204\pi$
$444$		0			0
$445$	−54360.0	−	94154.3i	−0.0130131	−	0.0225393i
$446$	2.49270e6	−	4.31749e6i	0.593381	−	1.02777i
$447$		0			0
$448$	243712.	+	471783.i	0.0573696	+	0.111057i
$449$	−724506.			−0.169600			−0.0848001	−	0.996398i	$-0.527025\pi$
$449$	−724506.			−0.169600			−0.0848001	+	0.996398i	$0.527025\pi$
$450$		0			0
$451$	−1.62038e6	−	2.80658e6i	−0.375124	−	0.649734i
$452$	−314832.	−	545305.i	−0.0724824	−	0.125543i
$453$		0			0
$454$	−3.67577e6			−0.836967
$455$	434343.	+	20332.5i	0.0983568	+	0.00460430i
$456$		0			0
$457$	1.16978e6	−	2.02612e6i	0.262008	−	0.453811i	−0.704768	−	0.709438i	$-0.748949\pi$
$457$	1.16978e6	−	2.02612e6i	0.262008	−	0.453811i	0.966775	+	0.255627i	$0.0822820\pi$
$458$	2.40750e6	+	4.16991e6i	0.536293	+	0.928887i
$459$		0			0
$460$	−166464.	+	288324.i	−0.0366797	+	0.0635311i
$461$	−2.98247e6			−0.653617			−0.326809	−	0.945091i	$-0.605973\pi$
$461$	−2.98247e6			−0.653617			−0.326809	+	0.945091i	$0.605973\pi$
$462$		0			0
$463$	4.28423e6			0.928795			0.464398	−	0.885627i	$-0.346271\pi$
$463$	4.28423e6			0.928795			0.464398	+	0.885627i	$0.346271\pi$
$464$	431616.	−	747581.i	0.0930685	−	0.161199i
$465$		0			0
$466$	1.83812e6	+	3.18372e6i	0.392112	+	0.679158i
$467$	−2.87018e6	+	4.97129e6i	−0.608998	+	1.05482i	0.382407	+	0.923994i	$0.375095\pi$
$467$	−2.87018e6	+	4.97129e6i	−0.608998	+	1.05482i	−0.991406	+	0.130822i	$0.958238\pi$
$468$		0			0
$469$	−1.31215e6	+	2.04544e6i	−0.275455	+	0.429393i
$470$	55440.0			0.0115765
$471$		0			0
$472$	−657408.	−	1.13866e6i	−0.135825	−	0.235256i
$473$	3.79853e6	+	6.57925e6i	0.780662	+	1.35215i
$474$		0			0
$475$	−3.57397e6			−0.726804
$476$	−3.60528e6	−	168771.i	−0.729326	−	0.0341413i
$477$		0			0
$478$	1.25068e6	−	2.16623e6i	0.250366	−	0.433646i
$479$	1.32526e6	+	2.29541e6i	0.263913	+	0.457111i	0.967278	−	0.253718i	$-0.0816534\pi$
$479$	1.32526e6	+	2.29541e6i	0.263913	+	0.457111i	−0.703365	+	0.710829i	$0.748320\pi$
$480$		0			0
$481$	875114.	−	1.51574e6i	0.172465	−	0.298719i
$482$	−5.01529e6			−0.983282
$483$		0			0
$484$	4.52008e6			0.877067
$485$	−374262.	+	648241.i	−0.0722473	+	0.125136i
$486$		0			0
$487$	−1.40277e6	−	2.42967e6i	−0.268018	−	0.464221i	0.700332	−	0.713817i	$-0.253035\pi$
$487$	−1.40277e6	−	2.42967e6i	−0.268018	−	0.464221i	−0.968350	+	0.249597i	$0.919702\pi$
$488$	−148160.	+	256621.i	−0.0281632	+	0.0487800i
$489$		0			0
$490$	−401604.	−	37682.5i	−0.0755628	−	0.00709005i
$491$	4.68450e6			0.876919			0.438460	−	0.898751i	$-0.355524\pi$
$491$	4.68450e6			0.876919			0.438460	+	0.898751i	$0.355524\pi$
$492$		0			0
$493$	2.93364e6	+	5.08121e6i	0.543613	+	0.941565i
$494$	−1.29353e6	−	2.24045e6i	−0.238483	−	0.413065i
$495$		0			0
$496$	1.61101e6			0.294031
$497$	2.27445e6	+	4.40292e6i	0.413033	+	0.799558i
$498$		0			0
$499$	−737876.	+	1.27804e6i	−0.132658	+	0.229770i	−0.924700	−	0.380696i	$-0.875684\pi$
$499$	−737876.	+	1.27804e6i	−0.132658	+	0.229770i	0.792043	+	0.610466i	$0.209018\pi$
$500$	298272.	+	516622.i	0.0533565	+	0.0924162i
$501$		0			0
$502$	3.02666e6	−	5.24234e6i	0.536050	−	0.928465i
$503$	−63606.0			−0.0112093			−0.00560465	−	0.999984i	$-0.501784\pi$
$503$	−63606.0			−0.0112093			−0.00560465	+	0.999984i	$0.501784\pi$
$504$		0			0
$505$	560340.			0.0977740
$506$	4.61938e6	−	8.00099e6i	0.802060	−	1.38921i
$507$		0			0
$508$	−2.53674e6	−	4.39377e6i	−0.436131	−	0.755402i
$509$	3.10578e6	−	5.37937e6i	0.531345	−	0.920317i	−0.467986	−	0.883736i	$-0.655020\pi$
$509$	3.10578e6	−	5.37937e6i	0.531345	−	0.920317i	0.999331	−	0.0365806i	$-0.0116466\pi$
$510$		0			0
$511$	4.94123e6	−	7.70262e6i	0.837111	−	1.30493i
$512$	−262144.			−0.0441942
$513$		0			0
$514$	3.10986e6	+	5.38644e6i	0.519198	+	0.899277i
$515$	503193.	+	871556.i	0.0836020	+	0.144803i
$516$		0			0
$517$	−1.53846e6			−0.253139
$518$	−876680.	+	1.36661e6i	−0.143554	+	0.223779i
$519$		0			0
$520$	−107328.	+	185898.i	−0.0174062	+	0.0301485i
$521$	706026.	+	1.22287e6i	0.113953	+	0.197373i	0.917361	−	0.398057i	$-0.130315\pi$
$521$	706026.	+	1.22287e6i	0.113953	+	0.197373i	−0.803408	+	0.595429i	$0.796982\pi$
$522$		0			0
$523$	−2.61467e6	+	4.52875e6i	−0.417987	+	0.723976i	−0.995737	−	0.0922386i	$-0.970598\pi$
$523$	−2.61467e6	+	4.52875e6i	−0.417987	+	0.723976i	0.577749	+	0.816214i	$0.303931\pi$
$524$	2.47728e6			0.394137
$525$		0			0
$526$	−4.46126e6			−0.703062
$527$	−5.47491e6	+	9.48282e6i	−0.858718	+	1.48734i
$528$		0			0
$529$	−2.79534e6	−	4.84167e6i	−0.434306	−	0.752240i
$530$	339552.	−	588121.i	0.0525069	−	0.0909447i
$531$		0			0
$532$	1.10146e6	+	2.13224e6i	0.168730	+	0.326630i
$533$	−2.72009e6			−0.414730
$534$		0			0
$535$	207540.	+	359470.i	0.0313485	+	0.0542973i
$536$	−599840.	−	1.03895e6i	−0.0901827	−	0.156201i
$537$		0			0
$538$	142680.			0.0212524
$539$	1.11445e7	+	1.04569e6i	1.65230	+	0.155035i
$540$		0			0
$541$	−2.20686e6	+	3.82240e6i	−0.324177	+	0.561491i	−0.981345	−	0.192253i	$-0.938421\pi$
$541$	−2.20686e6	+	3.82240e6i	−0.324177	+	0.561491i	0.657169	+	0.753744i	$0.271754\pi$
$542$	−585536.	−	1.01418e6i	−0.0856161	−	0.148291i
$543$		0			0
$544$	890880.	−	1.54305e6i	0.129069	−	0.223554i
$545$	−1.31735e6			−0.189981
$546$		0			0
$547$	−1.19038e7			−1.70105			−0.850523	−	0.525938i	$-0.823714\pi$
$547$	−1.19038e7			−1.70105			−0.850523	+	0.525938i	$0.823714\pi$
$548$	538656.	−	932980.i	0.0766232	−	0.132715i
$549$		0			0
$550$	−4.11455e6	−	7.12661e6i	−0.579983	−	1.00456i
$551$	1.95070e6	−	3.37871e6i	0.273723	−	0.474103i
$552$		0			0
$553$	8.06694e6	+	377631.i	1.12175	+	0.0525116i
$554$	−3.45285e6			−0.477973
$555$		0			0
$556$	2.92172e6	+	5.06057e6i	0.400822	+	0.694244i
$557$	6.45665e6	+	1.11832e7i	0.881798	+	1.52732i	0.849340	+	0.527847i	$0.177000\pi$
$557$	6.45665e6	+	1.11832e7i	0.881798	+	1.52732i	0.0324587	+	0.999473i	$0.489666\pi$
$558$		0			0
$559$	6.37651e6			0.863085
$560$	107520.	−	167607.i	0.0144884	−	0.0225851i
$561$		0			0
$562$	−2.94221e6	+	5.09605e6i	−0.392946	+	0.680602i
$563$	−5.68492e6	−	9.84657e6i	−0.755881	−	1.30922i	−0.944935	−	0.327257i	$-0.893876\pi$
$563$	−5.68492e6	−	9.84657e6i	−0.755881	−	1.30922i	0.189055	−	0.981967i	$-0.439458\pi$
$564$		0			0
$565$	−118062.	+	204489.i	−0.0155593	+	0.0269494i
$566$	−2.75536e6			−0.361525
$567$		0			0
$568$	−2.44646e6			−0.318176
$569$	−2.84898e6	+	4.93457e6i	−0.368900	+	0.638953i	−0.989394	−	0.145258i	$-0.953599\pi$
$569$	−2.84898e6	+	4.93457e6i	−0.368900	+	0.638953i	0.620494	+	0.784211i	$0.286932\pi$
$570$		0			0
$571$	3.52110e6	+	6.09873e6i	0.451948	+	0.782797i	0.998507	−	0.0546236i	$-0.0173959\pi$
$571$	3.52110e6	+	6.09873e6i	0.451948	+	0.782797i	−0.546559	+	0.837421i	$0.684063\pi$
$572$	2.97835e6	−	5.15866e6i	0.380615	−	0.659245i
$573$		0			0
$574$	2.52059e6	+	117994.i	0.319317	+	0.0149479i
$575$	−1.07127e7			−1.35122
$576$		0			0
$577$	1.29098e6	+	2.23605e6i	0.161429	+	0.279603i	0.935381	−	0.353641i	$-0.115056\pi$
$577$	1.29098e6	+	2.23605e6i	0.161429	+	0.279603i	−0.773952	+	0.633244i	$0.781723\pi$
$578$	3.21549e6	+	5.56939e6i	0.400338	+	0.693406i
$579$		0			0
$580$	−323712.			−0.0399566
$581$	−4.74917e6	−	9.19355e6i	−0.583684	−	1.12991i
$582$		0			0
$583$	−9.42257e6	+	1.63204e7i	−1.14815	+	1.98865i
$584$	2.25885e6	+	3.91244e6i	0.274066	+	0.474696i
$585$		0			0
$586$	−1.44566e6	+	2.50396e6i	−0.173910	+	0.301220i
$587$	−4.69459e6			−0.562345			−0.281172	−	0.959657i	$-0.590723\pi$
$587$	−4.69459e6			−0.562345			−0.281172	+	0.959657i	$0.590723\pi$
$588$		0			0
$589$	7.28100e6			0.864774
$590$	−246528.	+	426999.i	−0.0291566	+	0.0505006i
$591$		0			0
$592$	−400768.	−	694151.i	−0.0469990	−	0.0814047i
$593$	6.71175e6	−	1.16251e7i	0.783789	−	1.35756i	−0.145931	−	0.989295i	$-0.546618\pi$
$593$	6.71175e6	−	1.16251e7i	0.783789	−	1.35756i	0.929720	−	0.368268i	$-0.120049\pi$
$594$		0			0
$595$	621180.	+	1.20249e6i	0.0719325	+	0.139248i
$596$	2.68896e6			0.310076
$597$		0			0
$598$	−3.87722e6	−	6.71555e6i	−0.443372	−	0.767942i
$599$	2.52301e6	+	4.36997e6i	0.287310	+	0.497636i	0.973167	−	0.230101i	$-0.0739056\pi$
$599$	2.52301e6	+	4.36997e6i	0.287310	+	0.497636i	−0.685856	+	0.727737i	$0.740572\pi$
$600$		0			0
$601$	−1.06391e7			−1.20148			−0.600742	−	0.799443i	$-0.705128\pi$
$601$	−1.06391e7			−1.20148			−0.600742	+	0.799443i	$0.705128\pi$
$602$	−5.90883e6	−	276605.i	−0.664523	−	0.0311078i
$603$		0			0
$604$	−1.22829e6	+	2.12746e6i	−0.136996	+	0.237284i
$605$	−847515.	−	1.46794e6i	−0.0941367	−	0.163050i
$606$		0			0
$607$	−708041.	+	1.22636e6i	−0.0779986	+	0.135098i	−0.902386	−	0.430928i	$-0.858186\pi$
$607$	−708041.	+	1.22636e6i	−0.0779986	+	0.135098i	0.824388	+	0.566026i	$0.191520\pi$
$608$	−1.18477e6			−0.129979
$609$		0			0
$610$	111120.			0.0120912
$611$	−645645.	+	1.11829e6i	−0.0699666	+	0.121186i
$612$		0			0
$613$	−4.73152e6	−	8.19523e6i	−0.508568	−	0.880866i	−0.999951	−	0.00992215i	$-0.996842\pi$
$613$	−4.73152e6	−	8.19523e6i	−0.508568	−	0.880866i	0.491383	−	0.870944i	$-0.336492\pi$
$614$	−40250.0	+	69715.0i	−0.00430869	+	0.00746286i
$615$		0			0
$616$	−2.98368e6	+	4.65110e6i	−0.316811	+	0.493860i
$617$	−1.29388e7			−1.36830			−0.684148	−	0.729343i	$-0.739826\pi$
$617$	−1.29388e7			−1.36830			−0.684148	+	0.729343i	$0.739826\pi$
$618$		0			0
$619$	1.90188e6	+	3.29415e6i	0.199506	+	0.345555i	0.948368	−	0.317171i	$-0.102733\pi$
$619$	1.90188e6	+	3.29415e6i	0.199506	+	0.345555i	−0.748862	+	0.662726i	$0.769400\pi$
$620$	−302064.	−	523190.i	−0.0315587	−	0.0546614i
$621$		0			0
$622$	−6.97423e6			−0.722804
$623$	−2.34654e6	−	109847.i	−0.242219	−	0.0113388i
$624$		0			0
$625$	−4.71471e6	+	8.16612e6i	−0.482786	+	0.836210i
$626$	3.61709e6	+	6.26498e6i	0.368912	+	0.638975i
$627$		0			0
$628$	−1.61934e6	+	2.80479e6i	−0.163848	+	0.283792i
$629$	5.44794e6			0.549042
$630$		0			0
$631$	−9.17498e6			−0.917343			−0.458671	−	0.888606i	$-0.651674\pi$
$631$	−9.17498e6			−0.917343			−0.458671	+	0.888606i	$0.651674\pi$
$632$	−1.99338e6	+	3.45263e6i	−0.198516	+	0.343841i
$633$		0			0
$634$	−2.04710e6	−	3.54569e6i	−0.202263	−	0.350330i
$635$	−951279.	+	1.64766e6i	−0.0936211	+	0.162156i
$636$		0			0
$637$	5.43711e6	−	7.66198e6i	0.530909	−	0.748157i
$638$	8.98301e6			0.873716
$639$		0			0
$640$	49152.0	+	85133.8i	0.00474342	+	0.00821584i
$641$	5.12269e6	+	8.87275e6i	0.492439	+	0.852930i	0.999962	−	0.00870851i	$-0.00277204\pi$
$641$	5.12269e6	+	8.87275e6i	0.492439	+	0.852930i	−0.507523	+	0.861638i	$0.669439\pi$
$642$		0			0
$643$	−5.72346e6			−0.545922			−0.272961	−	0.962025i	$-0.588003\pi$
$643$	−5.72346e6			−0.545922			−0.272961	+	0.962025i	$0.588003\pi$
$644$	3.30154e6	+	6.39118e6i	0.313691	+	0.607249i
$645$		0			0
$646$	4.02636e6	−	6.97386e6i	0.379604	−	0.657494i
$647$	−4.99397e6	−	8.64981e6i	−0.469013	−	0.812355i	0.530359	−	0.847773i	$-0.322057\pi$
$647$	−4.99397e6	−	8.64981e6i	−0.469013	−	0.812355i	−0.999373	+	0.0354179i	$0.988724\pi$
$648$		0			0
$649$	6.84115e6	−	1.18492e7i	0.637555	−	1.10428i
$650$	−6.90700e6			−0.641219
$651$		0			0
$652$	−2.87622e6			−0.264974
$653$	−599439.	+	1.03826e6i	−0.0550126	+	0.0952846i	−0.892220	−	0.451601i	$-0.850853\pi$
$653$	−599439.	+	1.03826e6i	−0.0550126	+	0.0952846i	0.837208	+	0.546885i	$0.184187\pi$
$654$		0			0
$655$	−464490.	−	804520.i	−0.0423032	−	0.0732713i
$656$	−622848.	+	1.07880e6i	−0.0565096	+	0.0978776i
$657$		0			0
$658$	646800.	−	1.00826e6i	0.0582378	−	0.0907838i
$659$	−1.18065e7			−1.05903			−0.529516	−	0.848300i	$-0.677626\pi$
$659$	−1.18065e7			−1.05903			−0.529516	+	0.848300i	$0.677626\pi$
$660$		0			0
$661$	−2.36020e6	−	4.08798e6i	−0.210109	−	0.363919i	0.741640	−	0.670799i	$-0.234049\pi$
$661$	−2.36020e6	−	4.08798e6i	−0.210109	−	0.363919i	−0.951748	+	0.306879i	$0.900715\pi$
$662$	−2.01507e6	−	3.49020e6i	−0.178708	−	0.309532i
$663$		0			0
$664$	5.10835e6			0.449636
$665$	485940.	−	757505.i	0.0426117	−	0.0664250i
$666$		0			0
$667$	5.84705e6	−	1.01274e7i	0.508888	−	0.881420i
$668$	1.73842e6	+	3.01102e6i	0.150734	+	0.261080i
$669$		0			0
$670$	−224940.	+	389608.i	−0.0193589	+	0.0335305i
$671$	−3.08358e6			−0.264392
$672$		0			0
$673$	−8.70826e6			−0.741129			−0.370564	−	0.928807i	$-0.620836\pi$
$673$	−8.70826e6			−0.741129			−0.370564	+	0.928807i	$0.620836\pi$
$674$	−3.13141e6	+	5.42377e6i	−0.265516	+	0.459887i
$675$		0			0
$676$	470496.	+	814923.i	0.0395995	+	0.0685883i
$677$	2.55553e6	−	4.42630e6i	0.214293	−	0.371167i	−0.738760	−	0.673968i	$-0.764588\pi$
$677$	2.55553e6	−	4.42630e6i	0.214293	−	0.371167i	0.953054	+	0.302801i	$0.0979218\pi$
$678$		0			0
$679$	7.42286e6	+	1.43693e7i	0.617870	+	1.19609i
$680$	−668160.			−0.0554126
$681$		0			0
$682$	8.38228e6	+	1.45185e7i	0.690083	+	1.19526i
$683$	−8.85989e6	−	1.53458e7i	−0.726736	−	1.25874i	−0.958256	−	0.285913i	$-0.907703\pi$
$683$	−8.85989e6	−	1.53458e7i	−0.726736	−	1.25874i	0.231520	−	0.972830i	$-0.425630\pi$
$684$		0			0
$685$	−403992.			−0.0328962
$686$	−5.37069e6	+	6.86416e6i	−0.435733	+	0.556899i
$687$		0			0
$688$	1.46010e6	−	2.52896e6i	0.117601	−	0.203691i
$689$	7.90873e6	+	1.36983e7i	0.634686	+	1.09931i
$690$		0			0
$691$	1.12997e7	−	1.95716e7i	0.900265	−	1.55931i	0.0731160	−	0.997323i	$-0.476706\pi$
$691$	1.12997e7	−	1.95716e7i	0.900265	−	1.55931i	0.827149	−	0.561982i	$-0.189961\pi$
$692$	1.18368e6			0.0939656
$693$		0			0
$694$	3.02914e6			0.238737
$695$	1.09564e6	−	1.89771e6i	0.0860415	−	0.149028i
$696$		0			0
$697$	−4.23342e6	−	7.33250e6i	−0.330073	−	0.571702i
$698$	−911276.	+	1.57838e6i	−0.0707964	+	0.122623i
$699$		0			0
$700$	6.40041e6	+	299617.i	0.493699	+	0.0231111i
$701$	818148.			0.0628835			0.0314418	−	0.999506i	$-0.489990\pi$
$701$	818148.			0.0628835			0.0314418	+	0.999506i	$0.489990\pi$
$702$		0			0
$703$	−1.81128e6	−	3.13724e6i	−0.138229	−	0.239419i
$704$	−1.36397e6	−	2.36246e6i	−0.103722	−	0.179652i
$705$		0			0
$706$	−1.45255e7			−1.09678
$707$	6.53730e6	−	1.01906e7i	0.491869	−	0.766749i
$708$		0			0
$709$	2.54591e6	−	4.40965e6i	0.190208	−	0.329449i	−0.755111	−	0.655597i	$-0.772417\pi$
$709$	2.54591e6	−	4.40965e6i	0.190208	−	0.329449i	0.945319	+	0.326147i	$0.105751\pi$
$710$	458712.	+	794512.i	0.0341503	+	0.0591500i
$711$		0			0
$712$	579840.	−	1.00431e6i	0.0428655	−	0.0742453i
$713$	2.18241e7			1.60773
$714$		0			0
$715$	−2.23376e6			−0.163408
$716$	6.31493e6	−	1.09378e7i	0.460348	−	0.797345i
$717$		0			0
$718$	8.04967e6	+	1.39424e7i	0.582730	+	1.00932i
$719$	−240429.	+	416435.i	−0.0173446	+	0.0300418i	−0.874567	−	0.484904i	$-0.838855\pi$
$719$	−240429.	+	416435.i	−0.0173446	+	0.0300418i	0.857223	+	0.514946i	$0.172188\pi$
$720$		0			0
$721$	2.17212e7	+	1.01682e6i	1.55613	+	0.0728457i
$722$	4.54980e6			0.324825
$723$		0			0
$724$	3.82191e6	+	6.61975e6i	0.270978	+	0.469348i
$725$	−5.20805e6	−	9.02061e6i	−0.367985	−	0.637369i
$726$		0			0
$727$	−1.40783e7			−0.987905			−0.493952	−	0.869489i	$-0.664448\pi$
$727$	−1.40783e7			−0.987905			−0.493952	+	0.869489i	$0.664448\pi$
$728$	2.12867e6	+	4.12073e6i	0.148861	+	0.288168i
$729$		0			0
$730$	847068.	−	1.46716e6i	0.0588317	−	0.101899i
$731$	9.92409e6	+	1.71890e7i	0.686906	+	1.18976i
$732$		0			0
$733$	−1.01966e6	+	1.76610e6i	−0.0700964	+	0.121411i	−0.898943	−	0.438065i	$-0.855664\pi$
$733$	−1.01966e6	+	1.76610e6i	−0.0700964	+	0.121411i	0.828847	+	0.559475i	$0.188997\pi$
$734$	−1.03115e7			−0.706450
$735$		0			0
$736$	−3.55123e6			−0.241649
$737$	6.24209e6	−	1.08116e7i	0.423312	−	0.733199i
$738$		0			0
$739$	8.24785e6	+	1.42857e7i	0.555558	+	0.962255i	0.997860	+	0.0653888i	$0.0208288\pi$
$739$	8.24785e6	+	1.42857e7i	0.555558	+	0.962255i	−0.442302	+	0.896866i	$0.645838\pi$
$740$	−150288.	+	260306.i	−0.0100889	+	0.0174745i
$741$		0			0
$742$	−6.73445e6	−	1.30367e7i	−0.449047	−	0.869276i
$743$	2.38121e7			1.58243			0.791217	−	0.611536i	$-0.209448\pi$
$743$	2.38121e7			1.58243			0.791217	+	0.611536i	$0.209448\pi$
$744$		0			0
$745$	−504180.	−	873265.i	−0.0332809	−	0.0576442i
$746$	−5.06266e6	−	8.76878e6i	−0.333067	−	0.576889i
$747$		0			0
$748$	1.85414e7			1.21168
$749$	8.95881e6	+	419381.i	0.583507	+	0.0273152i
$750$		0			0
$751$	−962480.	+	1.66707e6i	−0.0622719	+	0.107858i	−0.895481	−	0.445101i	$-0.853168\pi$
$751$	−962480.	+	1.66707e6i	−0.0622719	+	0.107858i	0.833209	+	0.552959i	$0.186501\pi$
$752$	295680.	+	512133.i	0.0190668	+	0.0330246i
$753$		0			0
$754$	3.76990e6	−	6.52965e6i	0.241491	−	0.418275i
$755$	921216.			0.0588158
$756$		0			0
$757$	8.98092e6			0.569615			0.284807	−	0.958585i	$-0.408070\pi$
$757$	8.98092e6			0.569615			0.284807	+	0.958585i	$0.408070\pi$
$758$	−6.13354e6	+	1.06236e7i	−0.387738	+	0.671581i
$759$		0			0
$760$	222144.	+	384765.i	0.0139508	+	0.0241636i
$761$	7.29955e6	−	1.26432e7i	0.456914	−	0.791398i	−0.541882	−	0.840454i	$-0.682288\pi$
$761$	7.29955e6	−	1.26432e7i	0.456914	−	0.791398i	0.998796	+	0.0490566i	$0.0156215\pi$
$762$		0			0
$763$	−1.53691e7	+	2.39581e7i	−0.955736	+	1.48984i
$764$	−5.74358e6			−0.356000
$765$		0			0
$766$	7.85040e6	+	1.35973e7i	0.483415	+	0.837299i
$767$	−5.74205e6	−	9.94552e6i	−0.352434	−	0.610434i
$768$		0			0
$769$	2.78381e7			1.69755			0.848776	−	0.528753i	$-0.177340\pi$
$769$	2.78381e7			1.69755			0.848776	+	0.528753i	$0.177340\pi$
$770$	2.06993e6	+	96897.9i	0.125814	+	0.00588962i
$771$		0			0
$772$	1.45546e6	−	2.52094e6i	0.0878938	−	0.152237i
$773$	−1.41429e7	−	2.44962e7i	−0.851312	−	1.47451i	−0.880025	−	0.474927i	$-0.842474\pi$
$773$	−1.41429e7	−	2.44962e7i	−0.851312	−	1.47451i	0.0287135	−	0.999588i	$-0.490859\pi$
$774$		0			0

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(-3.00000 + 5.19615i) q^{5} +(59.5000 + 115.181i) q^{7} -64.0000 q^{8} +O(q^{10})\)	\(q+(2.00000 - 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(-3.00000 + 5.19615i) q^{5} +(59.5000 + 115.181i) q^{7} -64.0000 q^{8} +(12.0000 + 20.7846i) q^{10} +(-333.000 - 576.773i) q^{11} -559.000 q^{13} +(518.000 + 24.2487i) q^{14} +(-128.000 + 221.703i) q^{16} +(-870.000 - 1506.88i) q^{17} +(-578.500 + 1001.99i) q^{19} +96.0000 q^{20} -2664.00 q^{22} +(-1734.00 + 3003.38i) q^{23} +(1544.50 + 2675.15i) q^{25} +(-1118.00 + 1936.43i) q^{26} +(1120.00 - 1745.91i) q^{28} -3372.00 q^{29} +(-3146.50 - 5449.90i) q^{31} +(512.000 + 886.810i) q^{32} -6960.00 q^{34} +(-777.000 - 36.3731i) q^{35} +(-1565.50 + 2711.53i) q^{37} +(2314.00 + 4007.97i) q^{38} +(192.000 - 332.554i) q^{40} +4866.00 q^{41} -11407.0 q^{43} +(-5328.00 + 9228.37i) q^{44} +(6936.00 + 12013.5i) q^{46} +(1155.00 - 2000.52i) q^{47} +(-9726.50 + 13706.6i) q^{49} +12356.0 q^{50} +(4472.00 + 7745.73i) q^{52} +(-14148.0 - 24505.1i) q^{53} +3996.00 q^{55} +(-3808.00 - 7371.61i) q^{56} +(-6744.00 + 11681.0i) q^{58} +(10272.0 + 17791.6i) q^{59} +(2315.00 - 4009.70i) q^{61} -25172.0 q^{62} +4096.00 q^{64} +(1677.00 - 2904.65i) q^{65} +(9372.50 + 16233.6i) q^{67} +(-13920.0 + 24110.1i) q^{68} +(-1680.00 + 2618.86i) q^{70} +38226.0 q^{71} +(-35294.5 - 61131.9i) q^{73} +(6262.00 + 10846.1i) q^{74} +18512.0 q^{76} +(46620.0 - 72673.4i) q^{77} +(31146.5 - 53947.3i) q^{79} +(-768.000 - 1330.22i) q^{80} +(9732.00 - 16856.3i) q^{82} -79818.0 q^{83} +10440.0 q^{85} +(-22814.0 + 39515.0i) q^{86} +(21312.0 + 36913.5i) q^{88} +(-9060.00 + 15692.4i) q^{89} +(-33260.5 - 64386.4i) q^{91} +55488.0 q^{92} +(-4620.00 - 8002.07i) q^{94} +(-3471.00 - 6011.95i) q^{95} +124754. q^{97} +(28028.0 + 61106.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 16 q^{4} - 6 q^{5} + 119 q^{7} - 128 q^{8}+O(q^{10}) \) 2 * q + 4 * q^2 - 16 * q^4 - 6 * q^5 + 119 * q^7 - 128 * q^8	\( 2 q + 4 q^{2} - 16 q^{4} - 6 q^{5} + 119 q^{7} - 128 q^{8} + 24 q^{10} - 666 q^{11} - 1118 q^{13} + 1036 q^{14} - 256 q^{16} - 1740 q^{17} - 1157 q^{19} + 192 q^{20} - 5328 q^{22} - 3468 q^{23} + 3089 q^{25} - 2236 q^{26} + 2240 q^{28} - 6744 q^{29} - 6293 q^{31} + 1024 q^{32} - 13920 q^{34} - 1554 q^{35} - 3131 q^{37} + 4628 q^{38} + 384 q^{40} + 9732 q^{41} - 22814 q^{43} - 10656 q^{44} + 13872 q^{46} + 2310 q^{47} - 19453 q^{49} + 24712 q^{50} + 8944 q^{52} - 28296 q^{53} + 7992 q^{55} - 7616 q^{56} - 13488 q^{58} + 20544 q^{59} + 4630 q^{61} - 50344 q^{62} + 8192 q^{64} + 3354 q^{65} + 18745 q^{67} - 27840 q^{68} - 3360 q^{70} + 76452 q^{71} - 70589 q^{73} + 12524 q^{74} + 37024 q^{76} + 93240 q^{77} + 62293 q^{79} - 1536 q^{80} + 19464 q^{82} - 159636 q^{83} + 20880 q^{85} - 45628 q^{86} + 42624 q^{88} - 18120 q^{89} - 66521 q^{91} + 110976 q^{92} - 9240 q^{94} - 6942 q^{95} + 249508 q^{97} + 56056 q^{98}+O(q^{100}) \) 2 * q + 4 * q^2 - 16 * q^4 - 6 * q^5 + 119 * q^7 - 128 * q^8 + 24 * q^10 - 666 * q^11 - 1118 * q^13 + 1036 * q^14 - 256 * q^16 - 1740 * q^17 - 1157 * q^19 + 192 * q^20 - 5328 * q^22 - 3468 * q^23 + 3089 * q^25 - 2236 * q^26 + 2240 * q^28 - 6744 * q^29 - 6293 * q^31 + 1024 * q^32 - 13920 * q^34 - 1554 * q^35 - 3131 * q^37 + 4628 * q^38 + 384 * q^40 + 9732 * q^41 - 22814 * q^43 - 10656 * q^44 + 13872 * q^46 + 2310 * q^47 - 19453 * q^49 + 24712 * q^50 + 8944 * q^52 - 28296 * q^53 + 7992 * q^55 - 7616 * q^56 - 13488 * q^58 + 20544 * q^59 + 4630 * q^61 - 50344 * q^62 + 8192 * q^64 + 3354 * q^65 + 18745 * q^67 - 27840 * q^68 - 3360 * q^70 + 76452 * q^71 - 70589 * q^73 + 12524 * q^74 + 37024 * q^76 + 93240 * q^77 + 62293 * q^79 - 1536 * q^80 + 19464 * q^82 - 159636 * q^83 + 20880 * q^85 - 45628 * q^86 + 42624 * q^88 - 18120 * q^89 - 66521 * q^91 + 110976 * q^92 - 9240 * q^94 - 6942 * q^95 + 249508 * q^97 + 56056 * q^98

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