LMFDB - Embedded newform 126.6.g.h.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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{9601})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2401x^{2} + 2400x + 5760000 $ x^4 - x^3 + 2401x^2 + 2400x + 5760000
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			$24.7462 - 42.8616i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.6.g.h.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(-37.7462 + 65.3783i) q^{5} +(99.4847 - 83.1252i) q^{7} -64.0000 q^{8} +O(q^{10})$	\(q+(2.00000 - 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(-37.7462 + 65.3783i) q^{5} +(99.4847 - 83.1252i) q^{7} -64.0000 q^{8} +(150.985 + 261.513i) q^{10} +(-74.7309 - 129.438i) q^{11} +349.416 q^{13} +(-88.9847 - 510.875i) q^{14} +(-128.000 + 221.703i) q^{16} +(-574.923 - 995.797i) q^{17} +(1397.60 - 2420.72i) q^{19} +1207.88 q^{20} -597.847 q^{22} +(906.985 - 1570.94i) q^{23} +(-1287.05 - 2229.23i) q^{25} +(698.832 - 1210.41i) q^{26} +(-1947.69 - 713.499i) q^{28} +759.033 q^{29} +(-4515.87 - 7821.72i) q^{31} +(512.000 + 886.810i) q^{32} -4599.39 q^{34} +(1679.42 + 9641.80i) q^{35} +(-3897.45 + 6750.57i) q^{37} +(-5590.40 - 9682.86i) q^{38} +(2415.76 - 4184.21i) q^{40} -7640.49 q^{41} +12188.8 q^{43} +(-1195.69 + 2071.00i) q^{44} +(-3627.94 - 6283.77i) q^{46} +(12299.4 - 21303.2i) q^{47} +(2987.41 - 16539.4i) q^{49} -10296.4 q^{50} +(-2795.33 - 4841.65i) q^{52} +(6798.11 + 11774.7i) q^{53} +11283.2 q^{55} +(-6367.02 + 5320.01i) q^{56} +(1518.07 - 2629.37i) q^{58} +(-13179.4 - 22827.4i) q^{59} +(-17660.9 + 30589.5i) q^{61} -36127.0 q^{62} +4096.00 q^{64} +(-13189.1 + 22844.2i) q^{65} +(-27186.0 - 47087.5i) q^{67} +(-9198.78 + 15932.7i) q^{68} +(36759.0 + 13465.9i) q^{70} +70145.7 q^{71} +(22234.4 + 38511.1i) q^{73} +(15589.8 + 27002.3i) q^{74} -44723.2 q^{76} +(-18194.1 - 6665.05i) q^{77} +(-30806.2 + 53357.9i) q^{79} +(-9663.02 - 16736.8i) q^{80} +(-15281.0 + 26467.5i) q^{82} +87142.0 q^{83} +86804.6 q^{85} +(24377.7 - 42223.4i) q^{86} +(4782.78 + 8284.01i) q^{88} +(49284.7 - 85363.6i) q^{89} +(34761.5 - 29045.3i) q^{91} -29023.5 q^{92} +(-49197.6 - 85212.8i) q^{94} +(105508. + 182745. i) q^{95} +32342.3 q^{97} +(-51319.2 - 43427.4i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} - 32 q^{4} - 53 q^{5} + 6 q^{7} - 256 q^{8}+O(q^{10}) $ 4 * q + 8 * q^2 - 32 * q^4 - 53 * q^5 + 6 * q^7 - 256 * q^8	$ 4 q + 8 q^{2} - 32 q^{4} - 53 q^{5} + 6 q^{7} - 256 q^{8} + 212 q^{10} + 191 q^{11} - 758 q^{13} + 36 q^{14} - 512 q^{16} - 340 q^{17} + 1769 q^{19} + 1696 q^{20} + 1528 q^{22} + 3236 q^{23} + 45 q^{25} - 1516 q^{26} + 48 q^{28} - 8918 q^{29} - 1994 q^{31} + 2048 q^{32} - 2720 q^{34} + 4562 q^{35} - 20587 q^{37} - 7076 q^{38} + 3392 q^{40} - 17628 q^{41} + 31706 q^{43} + 3056 q^{44} - 12944 q^{46} + 33912 q^{47} + 9598 q^{49} + 360 q^{50} + 6064 q^{52} + 49239 q^{53} + 37882 q^{55} - 384 q^{56} - 17836 q^{58} - 56735 q^{59} - 67508 q^{61} - 15952 q^{62} + 16384 q^{64} - 42762 q^{65} - 75723 q^{67} - 5440 q^{68} + 95692 q^{70} + 17984 q^{71} + 3201 q^{73} + 82348 q^{74} - 56608 q^{76} - 120299 q^{77} - 26612 q^{79} - 13568 q^{80} - 35256 q^{82} + 1898 q^{83} + 210040 q^{85} + 63412 q^{86} - 12224 q^{88} + 176562 q^{89} + 210085 q^{91} - 103552 q^{92} - 135648 q^{94} + 234098 q^{95} - 258846 q^{97} - 211156 q^{98}+O(q^{100}) $ 4 * q + 8 * q^2 - 32 * q^4 - 53 * q^5 + 6 * q^7 - 256 * q^8 + 212 * q^10 + 191 * q^11 - 758 * q^13 + 36 * q^14 - 512 * q^16 - 340 * q^17 + 1769 * q^19 + 1696 * q^20 + 1528 * q^22 + 3236 * q^23 + 45 * q^25 - 1516 * q^26 + 48 * q^28 - 8918 * q^29 - 1994 * q^31 + 2048 * q^32 - 2720 * q^34 + 4562 * q^35 - 20587 * q^37 - 7076 * q^38 + 3392 * q^40 - 17628 * q^41 + 31706 * q^43 + 3056 * q^44 - 12944 * q^46 + 33912 * q^47 + 9598 * q^49 + 360 * q^50 + 6064 * q^52 + 49239 * q^53 + 37882 * q^55 - 384 * q^56 - 17836 * q^58 - 56735 * q^59 - 67508 * q^61 - 15952 * q^62 + 16384 * q^64 - 42762 * q^65 - 75723 * q^67 - 5440 * q^68 + 95692 * q^70 + 17984 * q^71 + 3201 * q^73 + 82348 * q^74 - 56608 * q^76 - 120299 * q^77 - 26612 * q^79 - 13568 * q^80 - 35256 * q^82 + 1898 * q^83 + 210040 * q^85 + 63412 * q^86 - 12224 * q^88 + 176562 * q^89 + 210085 * q^91 - 103552 * q^92 - 135648 * q^94 + 234098 * q^95 - 258846 * q^97 - 211156 * 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
$5$	−37.7462	+	65.3783i	−0.675224	+	1.16952i	0.301179	+	0.953568i	$0.402620\pi$
$5$	−37.7462	+	65.3783i	−0.675224	+	1.16952i	−0.976403	+	0.215955i	$0.930714\pi$
$6$		0			0
$7$	99.4847	−	83.1252i	0.767381	−	0.641191i
$7$	99.4847	−	83.1252i	0.767381	−	0.641191i
$8$	−64.0000			−0.353553
$9$		0			0
$10$	150.985	+	261.513i	0.477456	+	0.826977i
$11$	−74.7309	−	129.438i	−0.186217	−	0.322537i	0.757769	−	0.652523i	$-0.226289\pi$
$11$	−74.7309	−	129.438i	−0.186217	−	0.322537i	−0.943986	+	0.329986i	$0.892956\pi$
$12$		0			0
$13$	349.416			0.573435			0.286717	−	0.958015i	$-0.407436\pi$
$13$	349.416			0.573435			0.286717	+	0.958015i	$0.407436\pi$
$14$	−88.9847	−	510.875i	−0.121338	−	0.696618i
$15$		0			0
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	−574.923	−	995.797i	−0.482489	−	0.835696i	0.517309	−	0.855799i	$-0.326934\pi$
$17$	−574.923	−	995.797i	−0.482489	−	0.835696i	−0.999798	+	0.0201029i	$0.993601\pi$
$18$		0			0
$19$	1397.60	−	2420.72i	0.888176	−	1.53837i	0.0461468	−	0.998935i	$-0.485306\pi$
$19$	1397.60	−	2420.72i	0.888176	−	1.53837i	0.842029	−	0.539432i	$-0.181361\pi$
$20$	1207.88			0.675224
$21$		0			0
$22$	−597.847			−0.263350
$23$	906.985	−	1570.94i	0.357504	−	0.619214i	−0.630040	−	0.776563i	$-0.716961\pi$
$23$	906.985	−	1570.94i	0.357504	−	0.619214i	0.987543	+	0.157349i	$0.0502947\pi$
$24$		0			0
$25$	−1287.05	−	2229.23i	−0.411855	−	0.713354i
$26$	698.832	−	1210.41i	0.202740	−	0.351156i
$27$		0			0
$28$	−1947.69	−	713.499i	−0.469489	−	0.171988i
$29$	759.033			0.167597			0.0837984	−	0.996483i	$-0.473295\pi$
$29$	759.033			0.167597			0.0837984	+	0.996483i	$0.473295\pi$
$30$		0			0
$31$	−4515.87	−	7821.72i	−0.843990	−	1.46183i	−0.886495	−	0.462738i	$-0.846867\pi$
$31$	−4515.87	−	7821.72i	−0.843990	−	1.46183i	0.0425050	−	0.999096i	$-0.486466\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$		0			0
$34$	−4599.39			−0.682343
$35$	1679.42	+	9641.80i	0.231733	+	1.33042i
$36$		0			0
$37$	−3897.45	+	6750.57i	−0.468032	+	0.810655i	−0.999333	−	0.0365280i	$-0.988370\pi$
$37$	−3897.45	+	6750.57i	−0.468032	+	0.810655i	0.531300	+	0.847183i	$0.321704\pi$
$38$	−5590.40	−	9682.86i	−0.628035	−	1.08779i
$39$		0			0
$40$	2415.76	−	4184.21i	0.238728	−	0.413489i
$41$	−7640.49			−0.709842			−0.354921	−	0.934896i	$-0.615492\pi$
$41$	−7640.49			−0.709842			−0.354921	+	0.934896i	$0.615492\pi$
$42$		0			0
$43$	12188.8			1.00529			0.502645	−	0.864493i	$-0.332360\pi$
$43$	12188.8			1.00529			0.502645	+	0.864493i	$0.332360\pi$
$44$	−1195.69	+	2071.00i	−0.0931083	+	0.161268i
$45$		0			0
$46$	−3627.94	−	6283.77i	−0.252793	−	0.437851i
$47$	12299.4	−	21303.2i	0.812156	−	1.40670i	−0.0991964	−	0.995068i	$-0.531627\pi$
$47$	12299.4	−	21303.2i	0.812156	−	1.40670i	0.911352	−	0.411627i	$-0.135039\pi$
$48$		0			0
$49$	2987.41	−	16539.4i	0.177748	−	0.984076i
$50$	−10296.4			−0.582451
$51$		0			0
$52$	−2795.33	−	4841.65i	−0.143359	−	0.248305i
$53$	6798.11	+	11774.7i	0.332429	+	0.575783i	0.982988	−	0.183672i	$-0.0587986\pi$
$53$	6798.11	+	11774.7i	0.332429	+	0.575783i	−0.650559	+	0.759456i	$0.725465\pi$
$54$		0			0
$55$	11283.2			0.502952
$56$	−6367.02	+	5320.01i	−0.271310	+	0.226695i
$57$		0			0
$58$	1518.07	−	2629.37i	0.0592544	−	0.102632i
$59$	−13179.4	−	22827.4i	−0.492908	−	0.853742i	0.507059	−	0.861912i	$-0.330733\pi$
$59$	−13179.4	−	22827.4i	−0.492908	−	0.853742i	−0.999967	+	0.00816991i	$0.997399\pi$
$60$		0			0
$61$	−17660.9	+	30589.5i	−0.607698	+	1.05256i	0.383921	+	0.923366i	$0.374573\pi$
$61$	−17660.9	+	30589.5i	−0.607698	+	1.05256i	−0.991619	+	0.129198i	$0.958760\pi$
$62$	−36127.0			−1.19358
$63$		0			0
$64$	4096.00			0.125000
$65$	−13189.1	+	22844.2i	−0.387197	+	0.670645i
$66$		0			0
$67$	−27186.0	−	47087.5i	−0.739874	−	1.28150i	−0.952552	−	0.304377i	$-0.901552\pi$
$67$	−27186.0	−	47087.5i	−0.739874	−	1.28150i	0.212678	−	0.977122i	$-0.431781\pi$
$68$	−9198.78	+	15932.7i	−0.241245	+	0.417848i
$69$		0			0
$70$	36759.0	+	13465.9i	0.896641	+	0.328467i
$71$	70145.7			1.65141			0.825706	−	0.564101i	$-0.190777\pi$
$71$	70145.7			1.65141			0.825706	+	0.564101i	$0.190777\pi$
$72$		0			0
$73$	22234.4	+	38511.1i	0.488335	+	0.845822i	0.999910	−	0.0134170i	$-0.00427090\pi$
$73$	22234.4	+	38511.1i	0.488335	+	0.845822i	−0.511574	+	0.859239i	$0.670938\pi$
$74$	15589.8	+	27002.3i	0.330949	+	0.573220i
$75$		0			0
$76$	−44723.2			−0.888176
$77$	−18194.1	−	6665.05i	−0.349707	−	0.128108i
$78$		0			0
$79$	−30806.2	+	53357.9i	−0.555355	+	0.961903i	0.442521	+	0.896758i	$0.354084\pi$
$79$	−30806.2	+	53357.9i	−0.555355	+	0.961903i	−0.997876	+	0.0651450i	$0.979249\pi$
$80$	−9663.02	−	16736.8i	−0.168806	−	0.292381i
$81$		0			0
$82$	−15281.0	+	26467.5i	−0.250967	+	0.434688i
$83$	87142.0			1.38846			0.694228	−	0.719755i	$-0.255746\pi$
$83$	87142.0			1.38846			0.694228	+	0.719755i	$0.255746\pi$
$84$		0			0
$85$	86804.6			1.30315
$86$	24377.7	−	42223.4i	0.355423	−	0.615611i
$87$		0			0
$88$	4782.78	+	8284.01i	0.0658375	+	0.114034i
$89$	49284.7	−	85363.6i	0.659534	−	1.14235i	−0.321203	−	0.947010i	$-0.604087\pi$
$89$	49284.7	−	85363.6i	0.659534	−	1.14235i	0.980736	−	0.195336i	$-0.0625796\pi$
$90$		0			0
$91$	34761.5	−	29045.3i	0.440043	−	0.367681i
$92$	−29023.5			−0.357504
$93$		0			0
$94$	−49197.6	−	85212.8i	−0.574281	−	0.994684i
$95$	105508.	+	182745.i	1.19944	+	2.07748i
$96$		0			0
$97$	32342.3			0.349013			0.174507	−	0.984656i	$-0.444167\pi$
$97$	32342.3			0.349013			0.174507	+	0.984656i	$0.444167\pi$
$98$	−51319.2	−	43427.4i	−0.539778	−	0.456771i
$99$		0			0
$100$	−20592.8	+	35667.7i	−0.205928	+	0.356677i
$101$	15673.2	+	27146.8i	0.152881	+	0.264798i	0.932286	−	0.361723i	$-0.117811\pi$
$101$	15673.2	+	27146.8i	0.152881	+	0.264798i	−0.779404	+	0.626521i	$0.784478\pi$
$102$		0			0
$103$	−49666.5	+	86024.8i	−0.461286	+	0.798970i	−0.999025	−	0.0441406i	$-0.985945\pi$
$103$	−49666.5	+	86024.8i	−0.461286	+	0.798970i	0.537740	+	0.843111i	$0.319278\pi$
$104$	−22362.6			−0.202740
$105$		0			0
$106$	54384.9			0.470125
$107$	−72634.0	+	125806.i	−0.613310	+	1.06228i	0.377368	+	0.926063i	$0.376829\pi$
$107$	−72634.0	+	125806.i	−0.613310	+	1.06228i	−0.990678	+	0.136221i	$0.956504\pi$
$108$		0			0
$109$	90425.4	+	156621.i	0.728994	+	1.26265i	0.957309	+	0.289067i	$0.0933452\pi$
$109$	90425.4	+	156621.i	0.728994	+	1.26265i	−0.228315	+	0.973587i	$0.573321\pi$
$110$	22566.4	−	39086.2i	0.177820	−	0.307994i
$111$		0			0
$112$	5695.02	+	32696.0i	0.0428993	+	0.246292i
$113$	−197832.			−1.45748			−0.728738	−	0.684793i	$-0.759893\pi$
$113$	−197832.			−1.45748			−0.728738	+	0.684793i	$0.759893\pi$
$114$		0			0
$115$	68470.4	+	118594.i	0.482790	+	0.836217i
$116$	−6072.27	−	10517.5i	−0.0418992	−	0.0725715i
$117$		0			0
$118$	−105435.			−0.697077
$119$	−139972.	−	51275.9i	−0.906094	−	0.331930i
$120$		0			0
$121$	69356.1	−	120128.i	0.430647	−	0.745902i
$122$	70643.5	+	122358.i	0.429707	+	0.744275i
$123$		0			0
$124$	−72254.0	+	125148.i	−0.421995	+	0.730917i
$125$	−41589.2			−0.238070
$126$		0			0
$127$	−33517.2			−0.184399			−0.0921996	−	0.995741i	$-0.529390\pi$
$127$	−33517.2			−0.184399			−0.0921996	+	0.995741i	$0.529390\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$		0			0
$130$	52756.4	+	91376.8i	0.273790	+	0.474218i
$131$	−5404.45	+	9360.79i	−0.0275153	+	0.0476578i	−0.879455	−	0.475982i	$-0.842093\pi$
$131$	−5404.45	+	9360.79i	−0.0275153	+	0.0476578i	0.851940	+	0.523640i	$0.175426\pi$
$132$		0			0
$133$	−62182.5	−	357000.i	−0.304817	−	1.75000i
$134$	−217488.			−1.04634
$135$		0			0
$136$	36795.1	+	63731.0i	0.170586	+	0.295463i
$137$	−9466.01	−	16395.6i	−0.0430889	−	0.0746322i	0.843677	−	0.536852i	$-0.180387\pi$
$137$	−9466.01	−	16395.6i	−0.0430889	−	0.0746322i	−0.886766	+	0.462220i	$0.847053\pi$
$138$		0			0
$139$	−168897.			−0.741457			−0.370729	−	0.928741i	$-0.620892\pi$
$139$	−168897.			−0.741457			−0.370729	+	0.928741i	$0.620892\pi$
$140$	120165.	−	100405.i	0.518154	−	0.432948i
$141$		0			0
$142$	140291.	−	242992.i	0.583862	−	1.01128i
$143$	−26112.1	−	45227.6i	−0.106783	−	0.184954i
$144$		0			0
$145$	−28650.6	+	49624.3i	−0.113165	+	0.196008i
$146$	177875.			0.690611
$147$		0			0
$148$	124718.			0.468032
$149$	132001.	−	228633.i	0.487093	−	0.843670i	−0.512797	−	0.858510i	$-0.671391\pi$
$149$	132001.	−	228633.i	0.487093	−	0.843670i	0.999890	+	0.0148402i	$0.00472395\pi$
$150$		0			0
$151$	−139587.	−	241772.i	−0.498200	−	0.862908i	0.501798	−	0.864985i	$-0.332672\pi$
$151$	−139587.	−	241772.i	−0.498200	−	0.862908i	−0.999998	+	0.00207707i	$0.999339\pi$
$152$	−89446.4	+	154926.i	−0.314018	+	0.543895i
$153$		0			0
$154$	−59476.6	+	49696.1i	−0.202090	+	0.168858i
$155$	681828.			2.27953
$156$		0			0
$157$	−94301.2	−	163334.i	−0.305329	−	0.528845i	0.672006	−	0.740546i	$-0.265433\pi$
$157$	−94301.2	−	163334.i	−0.305329	−	0.528845i	−0.977334	+	0.211701i	$0.932100\pi$
$158$	123225.	+	213432.i	0.392695	+	0.680168i
$159$		0			0
$160$	−77304.2			−0.238728
$161$	−40353.9	−	231678.i	−0.122693	−	0.704402i
$162$		0			0
$163$	−44858.7	+	77697.5i	−0.132244	+	0.229054i	−0.924541	−	0.381081i	$-0.875552\pi$
$163$	−44858.7	+	77697.5i	−0.132244	+	0.229054i	0.792297	+	0.610136i	$0.208885\pi$
$164$	61124.0	+	105870.i	0.177461	+	0.307371i
$165$		0			0
$166$	174284.	−	301869.i	0.490893	−	0.850252i
$167$	−529411.			−1.46893			−0.734467	−	0.678645i	$-0.762568\pi$
$167$	−529411.			−1.46893			−0.734467	+	0.678645i	$0.762568\pi$
$168$		0			0
$169$	−249202.			−0.671172
$170$	173609.	−	300700.i	0.460734	−	0.798015i
$171$		0			0
$172$	−97510.7	−	168893.i	−0.251322	−	0.435303i
$173$	16919.2	−	29304.8i	0.0429797	−	0.0744430i	−0.843735	−	0.536759i	$-0.819648\pi$
$173$	16919.2	−	29304.8i	0.0429797	−	0.0744430i	0.886715	+	0.462316i	$0.152982\pi$
$174$		0			0
$175$	−313347.	−	114788.i	−0.773446	−	0.283337i
$176$	38262.2			0.0931083
$177$		0			0
$178$	−197139.	−	341454.i	−0.466361	−	0.807761i
$179$	−123872.	−	214552.i	−0.288962	−	0.500496i	0.684601	−	0.728918i	$-0.259977\pi$
$179$	−123872.	−	214552.i	−0.288962	−	0.500496i	−0.973562	+	0.228422i	$0.926643\pi$
$180$		0			0
$181$	369470.			0.838268			0.419134	−	0.907924i	$-0.362334\pi$
$181$	369470.			0.838268			0.419134	+	0.907924i	$0.362334\pi$
$182$	−31092.7	−	178508.i	−0.0695792	−	0.399465i
$183$		0			0
$184$	−58047.0	+	100540.i	−0.126397	+	0.218925i
$185$	−294227.	−	509617.i	−0.632053	−	1.09475i
$186$		0			0
$187$	−85929.1	+	148833.i	−0.179695	+	0.311241i
$188$	−393581.			−0.812156
$189$		0			0
$190$	844065.			1.69626
$191$	−242612.	+	420217.i	−0.481204	+	0.833470i	−0.999767	−	0.0215693i	$-0.993134\pi$
$191$	−242612.	+	420217.i	−0.481204	+	0.833470i	0.518563	+	0.855039i	$0.326467\pi$
$192$		0			0
$193$	165409.	+	286496.i	0.319643	+	0.553637i	0.980413	−	0.196950i	$-0.0631038\pi$
$193$	165409.	+	286496.i	0.319643	+	0.553637i	−0.660771	+	0.750588i	$0.729770\pi$
$194$	64684.7	−	112037.i	0.123395	−	0.213726i
$195$		0			0
$196$	−253075.	+	90920.2i	−0.470554	+	0.169052i
$197$	161963.			0.297337			0.148669	−	0.988887i	$-0.452501\pi$
$197$	161963.			0.297337			0.148669	+	0.988887i	$0.452501\pi$
$198$		0			0
$199$	−27698.1	−	47974.5i	−0.0495813	−	0.0858773i	0.840170	−	0.542324i	$-0.182455\pi$
$199$	−27698.1	−	47974.5i	−0.0495813	−	0.0858773i	−0.889751	+	0.456446i	$0.849122\pi$
$200$	82371.0	+	142671.i	0.145613	+	0.252209i
$201$		0			0
$202$	125386.			0.216207
$203$	75512.2	−	63094.8i	0.128611	−	0.107462i
$204$		0			0
$205$	288399.	−	499522.i	0.479303	−	0.830176i
$206$	198666.	+	344099.i	0.326178	+	0.564957i
$207$		0			0
$208$	−44725.2	+	77466.4i	−0.0716794	+	0.124152i
$209$	−417776.			−0.661572
$210$		0			0
$211$	481748.			0.744926			0.372463	−	0.928047i	$-0.378513\pi$
$211$	481748.			0.744926			0.372463	+	0.928047i	$0.378513\pi$
$212$	108770.	−	188395.i	0.166214	−	0.287892i
$213$		0			0
$214$	290536.	+	503223.i	0.433676	+	0.751149i
$215$	−460082.	+	796885.i	−0.678795	+	1.17571i
$216$		0			0
$217$	−1.09944e6	−	402759.i	−1.58498	−	0.580625i
$218$	723403.			1.03095
$219$		0			0
$220$	−90265.7	−	156345.i	−0.125738	−	0.217784i
$221$	−200887.	−	347947.i	−0.276676	−	0.479217i
$222$		0			0
$223$	638779.			0.860178			0.430089	−	0.902787i	$-0.358482\pi$
$223$	638779.			0.860178			0.430089	+	0.902787i	$0.358482\pi$
$224$	124652.	+	45663.9i	0.165990	+	0.0608070i
$225$		0			0
$226$	−395665.	+	685312.i	−0.515295	+	0.892518i
$227$	−262841.	−	455254.i	−0.338554	−	0.586394i	0.645607	−	0.763670i	$-0.276605\pi$
$227$	−262841.	−	455254.i	−0.338554	−	0.586394i	−0.984161	+	0.177277i	$0.943271\pi$
$228$		0			0
$229$	−466343.	+	807730.i	−0.587647	+	1.01784i	0.406892	+	0.913476i	$0.366612\pi$
$229$	−466343.	+	807730.i	−0.587647	+	1.01784i	−0.994540	+	0.104359i	$0.966721\pi$
$230$	547763.			0.682768
$231$		0			0
$232$	−48578.1			−0.0592544
$233$	−353896.	+	612967.i	−0.427058	+	0.739685i	−0.996610	−	0.0822696i	$-0.973783\pi$
$233$	−353896.	+	612967.i	−0.427058	+	0.739685i	0.569553	+	0.821955i	$0.307116\pi$
$234$		0			0
$235$	928511.	+	1.60823e6i	1.09677	+	1.89967i
$236$	−210871.	+	365238.i	−0.246454	+	0.426871i
$237$		0			0
$238$	−457569.	+	382325.i	−0.523617	+	0.437512i
$239$	500614.			0.566902			0.283451	−	0.958987i	$-0.408521\pi$
$239$	500614.			0.566902			0.283451	+	0.958987i	$0.408521\pi$
$240$		0			0
$241$	−604109.	−	1.04635e6i	−0.669997	−	1.16047i	−0.977904	−	0.209052i	$-0.932962\pi$
$241$	−604109.	−	1.04635e6i	−0.669997	−	1.16047i	0.307907	−	0.951416i	$-0.400371\pi$
$242$	−277424.	−	480513.i	−0.304513	−	0.527432i
$243$		0			0
$244$	565148.			0.607698
$245$	968552.	+	819609.i	1.03088	+	0.872352i
$246$		0			0
$247$	488344.	−	845836.i	0.509311	−	0.882153i
$248$	289016.	+	500590.i	0.298396	+	0.516836i
$249$		0			0
$250$	−83178.3	+	144069.i	−0.0841705	+	0.145788i
$251$	−97826.7			−0.0980106			−0.0490053	−	0.998799i	$-0.515605\pi$
$251$	−97826.7			−0.0980106			−0.0490053	+	0.998799i	$0.515605\pi$
$252$		0			0
$253$	−271119.			−0.266292
$254$	−67034.5	+	116107.i	−0.0651949	+	0.112921i
$255$		0			0
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−553956.	+	959481.i	−0.523170	+	0.906157i	0.476466	+	0.879193i	$0.341917\pi$
$257$	−553956.	+	959481.i	−0.523170	+	0.906157i	−0.999636	+	0.0269643i	$0.991416\pi$
$258$		0			0
$259$	173406.	+	995555.i	0.160626	+	0.922180i
$260$	422052.			0.387197
$261$		0			0
$262$	21617.8	+	37443.2i	0.0194562	+	0.0336992i
$263$	753427.	+	1.30497e6i	0.671663	+	1.16336i	0.977432	+	0.211249i	$0.0677532\pi$
$263$	753427.	+	1.30497e6i	0.671663	+	1.16336i	−0.305769	+	0.952106i	$0.598913\pi$
$264$		0			0
$265$	−1.02641e6			−0.897856
$266$	−1.36105e6	−	498593.i	−1.17942	−	0.432058i
$267$		0			0
$268$	−434975.	+	753399.i	−0.369937	+	0.640750i
$269$	−1.06751e6	−	1.84898e6i	−0.899481	−	1.55795i	−0.828159	−	0.560493i	$-0.810612\pi$
$269$	−1.06751e6	−	1.84898e6i	−0.899481	−	1.55795i	−0.0713221	−	0.997453i	$-0.522722\pi$
$270$		0			0
$271$	−614299.	+	1.06400e6i	−0.508108	+	0.880070i	0.491847	+	0.870681i	$0.336322\pi$
$271$	−614299.	+	1.06400e6i	−0.508108	+	0.880070i	−0.999956	+	0.00938828i	$0.997012\pi$
$272$	294361.			0.241245
$273$		0			0
$274$	−75728.1			−0.0609369
$275$	−192364.	+	333185.i	−0.153388	+	0.265677i
$276$		0			0
$277$	923412.	+	1.59940e6i	0.723097	+	1.25244i	0.959753	+	0.280847i	$0.0906152\pi$
$277$	923412.	+	1.59940e6i	0.723097	+	1.25244i	−0.236656	+	0.971593i	$0.576051\pi$
$278$	−337795.	+	585078.i	−0.262145	+	0.454048i
$279$		0			0
$280$	−107483.	−	617075.i	−0.0819300	−	0.470374i
$281$	2.28326e6			1.72500			0.862500	−	0.506056i	$-0.168897\pi$
$281$	2.28326e6			1.72500			0.862500	+	0.506056i	$0.168897\pi$
$282$		0			0
$283$	−668463.	−	1.15781e6i	−0.496148	−	0.859354i	0.503842	−	0.863796i	$-0.331919\pi$
$283$	−668463.	−	1.15781e6i	−0.496148	−	0.859354i	−0.999990	+	0.00444218i	$0.998586\pi$
$284$	−561166.	−	971968.i	−0.412853	−	0.715082i
$285$		0			0
$286$	−208897.			−0.151014
$287$	−760112.	+	635118.i	−0.544720	+	0.455145i
$288$		0			0
$289$	48854.5	−	84618.5i	0.0344081	−	0.0595965i
$290$	114602.	+	198497.i	0.0800200	+	0.138599i
$291$		0			0
$292$	355750.	−	616178.i	0.244168	−	0.422911i
$293$	2.23033e6			1.51775			0.758875	−	0.651236i	$-0.225749\pi$
$293$	2.23033e6			1.51775			0.758875	+	0.651236i	$0.225749\pi$
$294$		0			0
$295$	1.98989e6			1.33129
$296$	249436.	−	432037.i	0.165474	−	0.286610i
$297$		0			0
$298$	−528004.	−	914530.i	−0.344427	−	0.596565i
$299$	316915.	−	548913.i	0.205005	−	0.355079i
$300$		0			0
$301$	1.21260e6	−	1.01320e6i	0.771440	−	0.644583i
$302$	−1.11670e6			−0.704561
$303$		0			0
$304$	357786.	+	619703.i	0.222044	+	0.384592i
$305$	−1.33326e6	−	2.30928e6i	−0.820664	−	1.42143i
$306$		0			0
$307$	1.77782e6			1.07657			0.538284	−	0.842763i	$-0.319073\pi$
$307$	1.77782e6			1.07657			0.538284	+	0.842763i	$0.319073\pi$
$308$	53199.2	+	305425.i	0.0319542	+	0.183454i
$309$		0			0
$310$	1.36366e6	−	2.36192e6i	0.805936	−	1.39592i
$311$	701358.	+	1.21479e6i	0.411187	+	0.712196i	0.995020	−	0.0996776i	$-0.0317811\pi$
$311$	701358.	+	1.21479e6i	0.411187	+	0.712196i	−0.583833	+	0.811874i	$0.698448\pi$
$312$		0			0
$313$	−609472.	+	1.05564e6i	−0.351636	+	0.609051i	−0.986536	−	0.163543i	$-0.947708\pi$
$313$	−609472.	+	1.05564e6i	−0.351636	+	0.609051i	0.634900	+	0.772594i	$0.281041\pi$
$314$	−754409.			−0.431800
$315$		0			0
$316$	985799.			0.555355
$317$	1.34001e6	−	2.32096e6i	0.748961	−	1.29724i	−0.199361	−	0.979926i	$-0.563887\pi$
$317$	1.34001e6	−	2.32096e6i	0.748961	−	1.29724i	0.948321	−	0.317312i	$-0.102780\pi$
$318$		0			0
$319$	−56723.2	−	98247.5i	−0.0312093	−	0.0540561i
$320$	−154608.	+	267789.i	−0.0844030	+	0.146190i
$321$		0			0
$322$	−883264.	−	323566.i	−0.474735	−	0.173910i
$323$	−3.21405e6			−1.71414
$324$		0			0
$325$	−449715.	−	778929.i	−0.236172	−	0.409062i
$326$	179435.	+	310790.i	0.0935110	+	0.161966i
$327$		0			0
$328$	488992.			0.250967
$329$	−547229.	−	3.14173e6i	−0.278727	−	1.60022i
$330$		0			0
$331$	−71280.1	+	123461.i	−0.0357601	+	0.0619383i	−0.883352	−	0.468711i	$-0.844719\pi$
$331$	−71280.1	+	123461.i	−0.0357601	+	0.0619383i	0.847591	+	0.530649i	$0.178052\pi$
$332$	−697136.	−	1.20747e6i	−0.347114	−	0.601219i
$333$		0			0
$334$	−1.05882e6	+	1.83393e6i	−0.519346	+	0.899534i
$335$	4.10466e6			1.99832
$336$		0			0
$337$	−1.21206e6			−0.581367			−0.290683	−	0.956819i	$-0.593883\pi$
$337$	−1.21206e6			−0.581367			−0.290683	+	0.956819i	$0.593883\pi$
$338$	−498403.	+	863260.i	−0.237295	+	0.411007i
$339$		0			0
$340$	−694437.	−	1.20280e6i	−0.325788	−	0.564282i
$341$	−674950.	+	1.16905e6i	−0.314330	+	0.544435i
$342$		0			0
$343$	−1.07764e6	−	1.89374e6i	−0.494580	−	0.869132i
$344$	−780085.			−0.355423
$345$		0			0
$346$	−67676.6	−	117219.i	−0.0303912	−	0.0526392i
$347$	1.73426e6	+	3.00383e6i	0.773199	+	1.33922i	0.935801	+	0.352529i	$0.114678\pi$
$347$	1.73426e6	+	3.00383e6i	0.773199	+	1.33922i	−0.162602	+	0.986692i	$0.551989\pi$
$348$		0			0
$349$	1.01692e6			0.446911			0.223456	−	0.974714i	$-0.428266\pi$
$349$	1.01692e6			0.446911			0.223456	+	0.974714i	$0.428266\pi$
$350$	−1.02433e6	+	855888.i	−0.446962	+	0.373462i
$351$		0			0
$352$	76524.4	−	132544.i	0.0329187	−	0.0570169i
$353$	781927.	+	1.35434e6i	0.333987	+	0.578483i	0.983290	−	0.182048i	$-0.0582725\pi$
$353$	781927.	+	1.35434e6i	0.333987	+	0.578483i	−0.649303	+	0.760530i	$0.724939\pi$
$354$		0			0
$355$	−2.64773e6	+	4.58601e6i	−1.11507	+	1.93136i
$356$	−1.57711e6			−0.659534
$357$		0			0
$358$	−990975.			−0.408653
$359$	24776.6	−	42914.3i	0.0101462	−	0.0175738i	−0.860908	−	0.508761i	$-0.830104\pi$
$359$	24776.6	−	42914.3i	0.0101462	−	0.0175738i	0.871054	+	0.491187i	$0.163437\pi$
$360$		0			0
$361$	−2.66853e6	−	4.62202e6i	−1.07771	−	1.86666i
$362$	738940.	−	1.27988e6i	0.296373	−	0.513332i
$363$		0			0
$364$	−680555.	−	249308.i	−0.269222	−	0.0986239i
$365$	−3.35705e6			−1.31894
$366$		0			0
$367$	−1.77416e6	−	3.07293e6i	−0.687585	−	1.19093i	−0.972617	−	0.232414i	$-0.925337\pi$
$367$	−1.77416e6	−	3.07293e6i	−0.687585	−	1.19093i	0.285032	−	0.958518i	$-0.407996\pi$
$368$	232188.	+	402162.i	0.0893759	+	0.154804i
$369$		0			0
$370$	−2.35382e6			−0.893858
$371$	1.65508e6	+	606306.i	0.624287	+	0.228695i
$372$		0			0
$373$	1.12787e6	−	1.95352e6i	0.419745	−	0.727020i	−0.576169	−	0.817331i	$-0.695453\pi$
$373$	1.12787e6	−	1.95352e6i	0.419745	−	0.727020i	0.995914	+	0.0903112i	$0.0287862\pi$
$374$	343716.	+	595334.i	0.127064	+	0.220081i
$375$		0			0
$376$	−787162.	+	1.36340e6i	−0.287140	+	0.497342i
$377$	265218.			0.0961059
$378$		0			0
$379$	4.39503e6			1.57168			0.785840	−	0.618430i	$-0.212231\pi$
$379$	4.39503e6			1.57168			0.785840	+	0.618430i	$0.212231\pi$
$380$	1.68813e6	−	2.92393e6i	0.599718	−	1.03874i
$381$		0			0
$382$	970449.	+	1.68087e6i	0.340263	+	0.589352i
$383$	−613904.	+	1.06331e6i	−0.213847	+	0.370394i	−0.952915	−	0.303237i	$-0.901933\pi$
$383$	−613904.	+	1.06331e6i	−0.213847	+	0.370394i	0.739068	+	0.673631i	$0.235266\pi$
$384$		0			0
$385$	1.12251e6	−	937919.i	0.385956	−	0.322488i
$386$	1.32327e6			0.452043
$387$		0			0
$388$	−258739.	−	448149.i	−0.0872533	−	0.151127i
$389$	1.02712e6	+	1.77903e6i	0.344150	+	0.596086i	0.985199	−	0.171415i	$-0.0548337\pi$
$389$	1.02712e6	+	1.77903e6i	0.344150	+	0.596086i	−0.641049	+	0.767500i	$0.721500\pi$
$390$		0			0
$391$	−2.08579e6			−0.689967
$392$	−191194.	+	1.05852e6i	−0.0628434	+	0.347923i
$393$		0			0
$394$	323925.	−	561055.i	0.105125	−	0.182081i
$395$	−2.32563e6	−	4.02812e6i	−0.749978	−	1.29900i
$396$		0			0
$397$	1.90184e6	−	3.29408e6i	0.605615	−	1.04896i	−0.386339	−	0.922357i	$-0.626260\pi$
$397$	1.90184e6	−	3.29408e6i	0.605615	−	1.04896i	0.991954	−	0.126599i	$-0.0404062\pi$
$398$	−221585.			−0.0701185
$399$		0			0
$400$	658968.			0.205928
$401$	592622.	−	1.02645e6i	0.184042	−	0.318770i	−0.759211	−	0.650844i	$-0.774415\pi$
$401$	592622.	−	1.02645e6i	0.184042	−	0.318770i	0.943253	+	0.332074i	$0.107748\pi$
$402$		0			0
$403$	−1.57792e6	−	2.73303e6i	−0.483974	−	0.838267i
$404$	250771.	−	434349.i	0.0764406	−	0.132399i
$405$		0			0
$406$	−67542.3	−	387771.i	−0.0203358	−	0.116751i
$407$	1.16504e6			0.348621
$408$		0			0
$409$	2.15197e6	+	3.72731e6i	0.636102	+	1.10176i	0.986280	+	0.165079i	$0.0527878\pi$
$409$	2.15197e6	+	3.72731e6i	0.636102	+	1.10176i	−0.350178	+	0.936683i	$0.613879\pi$
$410$	−1.15360e6	−	1.99809e6i	−0.338918	−	0.587023i
$411$		0			0
$412$	1.58933e6			0.461286
$413$	−3.20868e6	−	1.17544e6i	−0.925660	−	0.339097i
$414$		0			0
$415$	−3.28928e6	+	5.69719e6i	−0.937519	+	1.62383i
$416$	178901.	+	309865.i	0.0506850	+	0.0877889i
$417$		0			0
$418$	−835551.	+	1.44722e6i	−0.233901	+	0.405129i
$419$	113725.			0.0316461			0.0158230	−	0.999875i	$-0.494963\pi$
$419$	113725.			0.0316461			0.0158230	+	0.999875i	$0.494963\pi$
$420$		0			0
$421$	443417.			0.121929			0.0609645	−	0.998140i	$-0.480582\pi$
$421$	443417.			0.121929			0.0609645	+	0.998140i	$0.480582\pi$
$422$	963495.	−	1.66882e6i	0.263371	−	0.456172i
$423$		0			0
$424$	−435079.	−	753579.i	−0.117531	−	0.203570i
$425$	−1.47991e6	+	2.56327e6i	−0.397431	+	0.688371i
$426$		0			0
$427$	785774.	+	4.51125e6i	0.208559	+	1.19737i
$428$	2.32429e6			0.613310
$429$		0			0
$430$	1.84033e6	+	3.18754e6i	0.479981	+	0.831351i
$431$	2.31655e6	+	4.01239e6i	0.600688	+	1.04042i	0.992717	+	0.120469i	$0.0384399\pi$
$431$	2.31655e6	+	4.01239e6i	0.600688	+	1.04042i	−0.392029	+	0.919953i	$0.628227\pi$
$432$		0			0
$433$	6.57955e6			1.68646			0.843231	−	0.537552i	$-0.180651\pi$
$433$	6.57955e6			1.68646			0.843231	+	0.537552i	$0.180651\pi$
$434$	−3.59408e6	+	3.00306e6i	−0.915933	+	0.765314i
$435$		0			0
$436$	1.44681e6	−	2.50594e6i	0.364497	−	0.631327i
$437$	−2.53520e6	−	4.39110e6i	−0.635052	−	1.09994i
$438$		0			0
$439$	910348.	−	1.57677e6i	0.225448	−	0.390487i	−0.731006	−	0.682371i	$-0.760949\pi$
$439$	910348.	−	1.57677e6i	0.225448	−	0.390487i	0.956454	+	0.291884i	$0.0942822\pi$
$440$	−722126.			−0.177820
$441$		0			0
$442$	−1.60710e6			−0.391279
$443$	−1.03495e6	+	1.79259e6i	−0.250559	+	0.433982i	−0.963680	−	0.267060i	$-0.913948\pi$
$443$	−1.03495e6	+	1.79259e6i	−0.250559	+	0.433982i	0.713121	+	0.701041i	$0.247281\pi$
$444$		0			0
$445$	3.72062e6	+	6.44430e6i	0.890666	+	1.54268i
$446$	1.27756e6	−	2.21279e6i	0.304119	−	0.526749i
$447$		0			0
$448$	407489.	−	340481.i	0.0959227	−	0.0801489i
$449$	−5.72581e6			−1.34036			−0.670180	−	0.742199i	$-0.733783\pi$
$449$	−5.72581e6			−1.34036			−0.670180	+	0.742199i	$0.733783\pi$
$450$		0			0
$451$	570981.	+	988968.i	0.132184	+	0.228950i
$452$	1.58266e6	+	2.74125e6i	0.364369	+	0.631105i
$453$		0			0
$454$	−2.10273e6			−0.478788
$455$	586814.	+	3.36900e6i	0.132884	+	0.762908i
$456$		0			0
$457$	−159338.	+	275982.i	−0.0356886	+	0.0618144i	−0.883318	−	0.468774i	$-0.844696\pi$
$457$	−159338.	+	275982.i	−0.0356886	+	0.0618144i	0.847629	+	0.530589i	$0.178029\pi$
$458$	1.86537e6	+	3.23092e6i	0.415529	+	0.719718i
$459$		0			0
$460$	1.09553e6	−	1.89751e6i	0.241395	−	0.418108i
$461$	3.42470e6			0.750535			0.375267	−	0.926917i	$-0.377551\pi$
$461$	3.42470e6			0.750535			0.375267	+	0.926917i	$0.377551\pi$
$462$		0			0
$463$	3.82945e6			0.830201			0.415101	−	0.909775i	$-0.363746\pi$
$463$	3.82945e6			0.830201			0.415101	+	0.909775i	$0.363746\pi$
$464$	−97156.2	+	168280.i	−0.0209496	+	0.0362858i
$465$		0			0
$466$	1.41559e6	+	2.45187e6i	0.301975	+	0.523037i
$467$	1.42231e6	−	2.46351e6i	0.301788	−	0.522712i	−0.674753	−	0.738044i	$-0.735750\pi$
$467$	1.42231e6	−	2.46351e6i	0.301788	−	0.522712i	0.976541	+	0.215332i	$0.0690832\pi$
$468$		0			0
$469$	−6.61874e6	−	2.42464e6i	−1.38945	−	0.508998i
$470$	7.42809e6			1.55107
$471$		0			0
$472$	843482.	+	1.46095e6i	0.174269	+	0.301843i
$473$	−910882.	−	1.57769e6i	−0.187202	−	0.324243i
$474$		0			0
$475$	−7.19511e6			−1.46320
$476$	409275.	+	2.34971e6i	0.0827938	+	0.475333i
$477$		0			0
$478$	1.00123e6	−	1.73418e6i	0.200430	−	0.347155i
$479$	651827.	+	1.12900e6i	0.129806	+	0.224830i	0.923601	−	0.383355i	$-0.125231\pi$
$479$	651827.	+	1.12900e6i	0.129806	+	0.224830i	−0.793796	+	0.608185i	$0.791898\pi$
$480$		0			0
$481$	−1.36183e6	+	2.35876e6i	−0.268386	+	0.464858i
$482$	−4.83287e6			−0.947519
$483$		0			0
$484$	−2.21940e6			−0.430647
$485$	−1.22080e6	+	2.11449e6i	−0.235662	+	0.408179i
$486$		0			0
$487$	−3.11812e6	−	5.40074e6i	−0.595759	−	1.03188i	−0.993439	−	0.114360i	$-0.963518\pi$
$487$	−3.11812e6	−	5.40074e6i	−0.595759	−	1.03188i	0.397681	−	0.917524i	$-0.369815\pi$
$488$	1.13030e6	−	1.95773e6i	0.214854	−	0.372137i
$489$		0			0
$490$	4.77631e6	−	1.71594e6i	0.898675	−	0.322859i
$491$	3.93928e6			0.737417			0.368709	−	0.929545i	$-0.379800\pi$
$491$	3.93928e6			0.737417			0.368709	+	0.929545i	$0.379800\pi$
$492$		0			0
$493$	−436386.	−	755843.i	−0.0808637	−	0.140060i
$494$	−1.95338e6	−	3.38335e6i	−0.360137	−	0.623776i
$495$		0			0
$496$	2.31213e6			0.421995
$497$	6.97843e6	−	5.83088e6i	1.26726	−	1.05887i
$498$		0			0
$499$	−3.98785e6	+	6.90717e6i	−0.716948	+	1.24179i	0.245255	+	0.969459i	$0.421128\pi$
$499$	−3.98785e6	+	6.90717e6i	−0.716948	+	1.24179i	−0.962203	+	0.272333i	$0.912205\pi$
$500$	332713.	+	576276.i	0.0595176	+	0.103087i
$501$		0			0
$502$	−195653.	+	338882.i	−0.0346520	+	0.0600190i
$503$	2.70777e6			0.477190			0.238595	−	0.971119i	$-0.423313\pi$
$503$	2.70777e6			0.477190			0.238595	+	0.971119i	$0.423313\pi$
$504$		0			0
$505$	−2.36641e6			−0.412917
$506$	−542238.	+	939184.i	−0.0941486	+	0.163070i
$507$		0			0
$508$	268138.	+	464428.i	0.0460998	+	0.0798472i
$509$	1.95025e6	−	3.37793e6i	0.333653	−	0.577904i	−0.649572	−	0.760300i	$-0.725052\pi$
$509$	1.95025e6	−	3.37793e6i	0.333653	−	0.577904i	0.983225	+	0.182396i	$0.0583852\pi$
$510$		0			0
$511$	5.41323e6	+	1.98303e6i	0.917073	+	0.335951i
$512$	−262144.			−0.0441942
$513$		0			0
$514$	2.21583e6	+	3.83792e6i	0.369937	+	0.640750i
$515$	−3.74944e6	−	6.49422e6i	−0.622943	−	1.07897i
$516$		0			0
$517$	−3.67658e6			−0.604947
$518$	3.79551e6	+	1.39041e6i	0.621507	+	0.227677i
$519$		0			0
$520$	844103.	−	1.46203e6i	0.136895	−	0.237109i
$521$	3.50032e6	+	6.06273e6i	0.564954	+	0.978529i	0.997054	+	0.0767034i	$0.0244394\pi$
$521$	3.50032e6	+	6.06273e6i	0.564954	+	0.978529i	−0.432100	+	0.901826i	$0.642227\pi$
$522$		0			0
$523$	1.05604e6	−	1.82911e6i	0.168821	−	0.292406i	−0.769185	−	0.639026i	$-0.779337\pi$
$523$	1.05604e6	−	1.82911e6i	0.168821	−	0.292406i	0.938005	+	0.346620i	$0.112671\pi$
$524$	172943.			0.0275153
$525$		0			0
$526$	6.02741e6			0.949875
$527$	−5.19256e6	+	8.99378e6i	−0.814433	+	1.41064i
$528$		0			0
$529$	1.57293e6	+	2.72439e6i	0.244382	+	0.423283i
$530$	−2.05282e6	+	3.55559e6i	−0.317440	+	0.549822i
$531$		0			0
$532$	−4.44928e6	+	3.71763e6i	−0.681570	+	0.569491i
$533$	−2.66971e6			−0.407048
$534$		0			0
$535$	−5.48331e6	−	9.49737e6i	−0.828244	−	1.43456i
$536$	1.73990e6	+	3.01360e6i	0.261585	+	0.453078i
$537$		0			0
$538$	−8.54009e6			−1.27206
$539$	−2.36407e6	+	849318.i	−0.350500	+	0.125921i
$540$		0			0
$541$	−2.85283e6	+	4.94125e6i	−0.419067	+	0.725845i	−0.995846	−	0.0910551i	$-0.970976\pi$
$541$	−2.85283e6	+	4.94125e6i	−0.419067	+	0.725845i	0.576779	+	0.816900i	$0.304309\pi$
$542$	2.45720e6	+	4.25599e6i	0.359287	+	0.622303i
$543$		0			0
$544$	588722.	−	1.01970e6i	0.0852929	−	0.147732i
$545$	−1.36528e7			−1.96894
$546$		0			0
$547$	2.28054e6			0.325888			0.162944	−	0.986635i	$-0.447901\pi$
$547$	2.28054e6			0.325888			0.162944	+	0.986635i	$0.447901\pi$
$548$	−151456.	+	262330.i	−0.0215445	+	0.0373161i
$549$		0			0
$550$	769457.	+	1.33274e6i	0.108462	+	0.187862i
$551$	1.06083e6	−	1.83740e6i	0.148855	−	0.257825i
$552$		0			0
$553$	1.37064e6	+	7.86907e6i	0.190595	+	1.09424i
$554$	7.38730e6			1.02261
$555$		0			0
$556$	1.35118e6	+	2.34031e6i	0.185364	+	0.321060i
$557$	−3.36970e6	−	5.83650e6i	−0.460208	−	0.797103i	0.538763	−	0.842457i	$-0.318892\pi$
$557$	−3.36970e6	−	5.83650e6i	−0.460208	−	0.797103i	−0.998971	+	0.0453541i	$0.985558\pi$
$558$		0			0
$559$	4.25897e6			0.576468
$560$	−2.35258e6	−	861819.i	−0.317010	−	0.116130i
$561$		0			0
$562$	4.56652e6	−	7.90944e6i	0.609880	−	1.05634i
$563$	−4.83410e6	−	8.37291e6i	−0.642754	−	1.11328i	−0.984815	−	0.173605i	$-0.944458\pi$
$563$	−4.83410e6	−	8.37291e6i	−0.642754	−	1.11328i	0.342061	−	0.939678i	$-0.388875\pi$
$564$		0			0
$565$	7.46742e6	−	1.29339e7i	0.984123	−	1.70455i
$566$	−5.34770e6			−0.701659
$567$		0			0
$568$	−4.48933e6			−0.583862
$569$	−6.97934e6	+	1.20886e7i	−0.903719	+	1.56529i	−0.0810922	+	0.996707i	$0.525841\pi$
$569$	−6.97934e6	+	1.20886e7i	−0.903719	+	1.56529i	−0.822627	+	0.568581i	$0.807493\pi$
$570$		0			0
$571$	1.17920e6	+	2.04244e6i	0.151355	+	0.262155i	0.931726	−	0.363162i	$-0.118303\pi$
$571$	1.17920e6	+	2.04244e6i	0.151355	+	0.262155i	−0.780371	+	0.625317i	$0.784970\pi$
$572$	−417794.	+	723641.i	−0.0533915	+	0.0924769i
$573$		0			0
$574$	679887.	+	3.90334e6i	0.0861305	+	0.494489i
$575$	−4.66933e6			−0.588959
$576$		0			0
$577$	−2.50549e6	−	4.33963e6i	−0.313295	−	0.542642i	0.665779	−	0.746149i	$-0.268099\pi$
$577$	−2.50549e6	−	4.33963e6i	−0.313295	−	0.542642i	−0.979074	+	0.203507i	$0.934766\pi$
$578$	−195418.	−	338474.i	−0.0243302	−	0.0421411i
$579$		0			0
$580$	916819.			0.113165
$581$	8.66929e6	−	7.24369e6i	1.06547	−	0.890266i
$582$		0			0
$583$	1.01606e6	−	1.75986e6i	0.123807	−	0.214441i
$584$	−1.42300e6	−	2.46471e6i	−0.172653	−	0.299043i
$585$		0			0
$586$	4.46066e6	−	7.72609e6i	0.536606	−	0.929428i
$587$	−3.95106e6			−0.473280			−0.236640	−	0.971597i	$-0.576046\pi$
$587$	−3.95106e6			−0.473280			−0.236640	+	0.971597i	$0.576046\pi$
$588$		0			0
$589$	−2.52455e7			−2.99845
$590$	3.97978e6	−	6.89318e6i	0.470683	−	0.815247i
$591$		0			0
$592$	−997746.	−	1.72815e6i	−0.117008	−	0.202664i
$593$	−1.26840e6	+	2.19694e6i	−0.148122	+	0.256555i	−0.930533	−	0.366207i	$-0.880656\pi$
$593$	−1.26840e6	+	2.19694e6i	−0.148122	+	0.256555i	0.782411	+	0.622762i	$0.213990\pi$
$594$		0			0
$595$	8.63573e6	−	7.21565e6i	1.00002	−	0.835571i
$596$	−4.22403e6			−0.487093
$597$		0			0
$598$	−1.26766e6	−	2.19565e6i	−0.144960	−	0.251079i
$599$	3.58857e6	+	6.21558e6i	0.408652	+	0.707807i	0.994739	−	0.102442i	$-0.0326655\pi$
$599$	3.58857e6	+	6.21558e6i	0.408652	+	0.707807i	−0.586087	+	0.810248i	$0.699332\pi$
$600$		0			0
$601$	1.12527e7			1.27078			0.635392	−	0.772190i	$-0.280838\pi$
$601$	1.12527e7			1.27078			0.635392	+	0.772190i	$0.280838\pi$
$602$	−1.08462e6	−	6.22698e6i	−0.121979	−	0.700303i
$603$		0			0
$604$	−2.23340e6	+	3.86836e6i	−0.249100	+	0.431454i
$605$	5.23585e6	+	9.06877e6i	0.581566	+	1.00730i
$606$		0			0
$607$	7.01851e6	−	1.21564e7i	0.773167	−	1.33916i	−0.162652	−	0.986684i	$-0.552005\pi$
$607$	7.01851e6	−	1.21564e7i	0.773167	−	1.33916i	0.935819	−	0.352481i	$-0.114662\pi$
$608$	2.86229e6			0.314018
$609$		0			0
$610$	−1.06661e7			−1.16059
$611$	4.29761e6	−	7.44367e6i	0.465719	−	0.806648i
$612$		0			0
$613$	3.81436e6	+	6.60667e6i	0.409988	+	0.710119i	0.994888	−	0.100986i	$-0.0321997\pi$
$613$	3.81436e6	+	6.60667e6i	0.409988	+	0.710119i	−0.584900	+	0.811105i	$0.698866\pi$
$614$	3.55564e6	−	6.15855e6i	0.380624	−	0.659261i
$615$		0			0
$616$	1.16442e6	+	426563.i	0.123640	+	0.0452930i
$617$	4.41080e6			0.466450			0.233225	−	0.972423i	$-0.425072\pi$
$617$	4.41080e6			0.466450			0.233225	+	0.972423i	$0.425072\pi$
$618$		0			0
$619$	4.52178e6	+	7.83195e6i	0.474332	+	0.821567i	0.999568	−	0.0293895i	$-0.00935632\pi$
$619$	4.52178e6	+	7.83195e6i	0.474332	+	0.821567i	−0.525236	+	0.850957i	$0.676023\pi$
$620$	−5.45462e6	−	9.44768e6i	−0.569883	−	0.987065i
$621$		0			0
$622$	5.61087e6			0.581506
$623$	−2.19279e6	−	1.25892e7i	−0.226348	−	1.29950i
$624$		0			0
$625$	5.59185e6	−	9.68538e6i	0.572606	−	0.991782i
$626$	2.43789e6	+	4.22255e6i	0.248644	+	0.430664i
$627$		0			0
$628$	−1.50882e6	+	2.61335e6i	−0.152664	+	0.264423i
$629$	8.96293e6			0.903282
$630$		0			0
$631$	−7.33039e6			−0.732916			−0.366458	−	0.930435i	$-0.619430\pi$
$631$	−7.33039e6			−0.732916			−0.366458	+	0.930435i	$0.619430\pi$
$632$	1.97160e6	−	3.41491e6i	0.196348	−	0.340084i
$633$		0			0
$634$	−5.36003e6	−	9.28384e6i	−0.529595	−	0.917286i
$635$	1.26515e6	−	2.19130e6i	0.124511	−	0.215659i
$636$		0			0
$637$	1.04385e6	−	5.77912e6i	0.101927	−	0.564304i
$638$	−453786.			−0.0441366
$639$		0			0
$640$	618433.	+	1.07116e6i	0.0596819	+	0.103372i
$641$	1.84412e6	+	3.19411e6i	0.177273	+	0.307047i	0.940946	−	0.338558i	$-0.109939\pi$
$641$	1.84412e6	+	3.19411e6i	0.177273	+	0.307047i	−0.763672	+	0.645604i	$0.776606\pi$
$642$		0			0
$643$	−1.17584e7			−1.12155			−0.560776	−	0.827968i	$-0.689497\pi$
$643$	−1.17584e7			−1.12155			−0.560776	+	0.827968i	$0.689497\pi$
$644$	−2.88739e6	+	2.41258e6i	−0.274342	+	0.229228i
$645$		0			0
$646$	−6.42811e6	+	1.11338e7i	−0.606041	+	1.04969i
$647$	−4.97025e6	−	8.60873e6i	−0.466786	−	0.808497i	0.532494	−	0.846434i	$-0.321255\pi$
$647$	−4.97025e6	−	8.60873e6i	−0.466786	−	0.808497i	−0.999280	+	0.0379368i	$0.987921\pi$
$648$		0			0
$649$	−1.96982e6	+	3.41182e6i	−0.183575	+	0.317962i
$650$	−3.59772e6			−0.333998
$651$		0			0
$652$	1.43548e6			0.132244
$653$	−513100.	+	888714.i	−0.0470889	+	0.0815604i	−0.888609	−	0.458665i	$-0.848328\pi$
$653$	−513100.	+	888714.i	−0.0470889	+	0.0815604i	0.841520	+	0.540226i	$0.181661\pi$
$654$		0			0
$655$	−407995.	−	706668.i	−0.0371579	−	0.0643594i
$656$	977983.	−	1.69392e6i	0.0887303	−	0.153685i
$657$		0			0
$658$	−1.19777e7	−	4.38781e6i	−1.07847	−	0.395078i
$659$	−1.00207e7			−0.898846			−0.449423	−	0.893319i	$-0.648370\pi$
$659$	−1.00207e7			−0.898846			−0.449423	+	0.893319i	$0.648370\pi$
$660$		0			0
$661$	−1.31413e6	−	2.27614e6i	−0.116986	−	0.202626i	0.801586	−	0.597880i	$-0.203990\pi$
$661$	−1.31413e6	−	2.27614e6i	−0.116986	−	0.202626i	−0.918572	+	0.395254i	$0.870657\pi$
$662$	285120.	+	493843.i	0.0252862	+	0.0437970i
$663$		0			0
$664$	−5.57709e6			−0.490893
$665$	2.56872e7	+	9.40999e6i	2.25249	+	0.825154i
$666$		0			0
$667$	688431.	−	1.19240e6i	0.0599165	−	0.103778i
$668$	4.23529e6	+	7.33574e6i	0.367233	+	0.636067i
$669$		0			0
$670$	8.20933e6	−	1.42190e7i	0.706514	−	1.22372i
$671$	5.27925e6			0.452654
$672$		0			0
$673$	−1.50220e7			−1.27847			−0.639233	−	0.769013i	$-0.720748\pi$
$673$	−1.50220e7			−1.27847			−0.639233	+	0.769013i	$0.720748\pi$
$674$	−2.42412e6	+	4.19871e6i	−0.205544	+	0.356013i
$675$		0			0
$676$	1.99361e6	+	3.45304e6i	0.167793	+	0.290626i
$677$	−3.01655e6	+	5.22482e6i	−0.252953	+	0.438127i	−0.964337	−	0.264676i	$-0.914735\pi$
$677$	−3.01655e6	+	5.22482e6i	−0.252953	+	0.438127i	0.711385	+	0.702803i	$0.248068\pi$
$678$		0			0
$679$	3.21757e6	−	2.68846e6i	0.267826	−	0.223784i
$680$	−5.55550e6			−0.460734
$681$		0			0
$682$	2.69980e6	+	4.67619e6i	0.222265	+	0.384974i
$683$	5.53601e6	+	9.58865e6i	0.454093	+	0.786513i	0.998636	−	0.0522205i	$-0.0166299\pi$
$683$	5.53601e6	+	9.58865e6i	0.454093	+	0.786513i	−0.544542	+	0.838734i	$0.683297\pi$
$684$		0			0
$685$	1.42922e6			0.116379
$686$	−8.71539e6	−	54443.0i	−0.707093	−	0.00441705i
$687$		0			0
$688$	−1.56017e6	+	2.70230e6i	−0.125661	+	0.217652i
$689$	2.37537e6	+	4.11426e6i	0.190626	+	0.330174i
$690$		0			0
$691$	5.27739e6	−	9.14071e6i	0.420460	−	0.728257i	−0.575525	−	0.817784i	$-0.695202\pi$
$691$	5.27739e6	−	9.14071e6i	0.420460	−	0.728257i	0.995984	+	0.0895269i	$0.0285355\pi$
$692$	−541413.			−0.0429797
$693$		0			0
$694$	1.38741e7			1.09347
$695$	6.37523e6	−	1.10422e7i	0.500650	−	0.867151i
$696$		0			0
$697$	4.39270e6	+	7.60838e6i	0.342491	+	0.593212i
$698$	2.03383e6	−	3.52270e6i	0.158007	−	0.273676i
$699$		0			0
$700$	916220.	+	5.26017e6i	0.0706732	+	0.405746i
$701$	7.20675e6			0.553917			0.276958	−	0.960882i	$-0.410674\pi$
$701$	7.20675e6			0.553917			0.276958	+	0.960882i	$0.410674\pi$
$702$		0			0
$703$	1.08941e7	+	1.88692e7i	0.831390	+	1.44001i
$704$	−306098.	−	530177.i	−0.0232771	−	0.0403171i
$705$		0			0
$706$	6.25542e6			0.472329
$707$	3.81583e6	+	1.39785e6i	0.287104	+	0.105175i
$708$		0			0
$709$	−1.34687e6	+	2.33284e6i	−0.100626	+	0.174289i	−0.911943	−	0.410318i	$-0.865418\pi$
$709$	−1.34687e6	+	2.33284e6i	−0.100626	+	0.174289i	0.811317	+	0.584607i	$0.198751\pi$
$710$	1.05909e7	+	1.83440e7i	0.788476	+	1.36568i
$711$		0			0
$712$	−3.15422e6	+	5.46327e6i	−0.233180	+	0.403880i
$713$	−1.63833e7			−1.20692
$714$		0			0
$715$	3.94253e6			0.288410
$716$	−1.98195e6	+	3.43284e6i	−0.144481	+	0.250248i
$717$		0			0
$718$	−99106.3	−	171657.i	−0.00717447	−	0.0124266i
$719$	3.46275e6	−	5.99766e6i	0.249804	−	0.432673i	−0.713667	−	0.700485i	$-0.752967\pi$
$719$	3.46275e6	−	5.99766e6i	0.249804	−	0.432673i	0.963471	+	0.267812i	$0.0863005\pi$
$720$		0			0
$721$	2.20978e6	+	1.26867e7i	0.158311	+	0.908887i
$722$	−2.13482e7			−1.52412
$723$		0			0
$724$	−2.95576e6	−	5.11953e6i	−0.209567	−	0.362981i
$725$	−976911.	−	1.69206e6i	−0.0690256	−	0.119556i
$726$		0			0
$727$	4.11366e6			0.288664			0.144332	−	0.989529i	$-0.453897\pi$
$727$	4.11366e6			0.288664			0.144332	+	0.989529i	$0.453897\pi$
$728$	−2.22474e6	+	1.85890e6i	−0.155579	+	0.129995i
$729$		0			0
$730$	−6.71411e6	+	1.16292e7i	−0.466317	+	0.807685i
$731$	−7.00765e6	−	1.21376e7i	−0.485041	−	0.840116i
$732$		0			0
$733$	−3.96019e6	+	6.85925e6i	−0.272243	+	0.471538i	−0.969436	−	0.245345i	$-0.921099\pi$
$733$	−3.96019e6	+	6.85925e6i	−0.272243	+	0.471538i	0.697193	+	0.716883i	$0.254432\pi$
$734$	−1.41932e7			−0.972392
$735$		0			0
$736$	1.85750e6			0.126397
$737$	−4.06326e6	+	7.03777e6i	−0.275554	+	0.477273i
$738$		0			0
$739$	−8.02050e6	−	1.38919e7i	−0.540245	−	0.935731i	−0.998890	−	0.0471115i	$-0.984998\pi$
$739$	−8.02050e6	−	1.38919e7i	−0.540245	−	0.935731i	0.458645	−	0.888620i	$-0.348335\pi$
$740$	−4.70764e6	+	8.15387e6i	−0.316027	+	0.547374i
$741$		0			0
$742$	5.41046e6	−	4.52075e6i	0.360765	−	0.301440i
$743$	−1.53453e7			−1.01977			−0.509887	−	0.860241i	$-0.670313\pi$
$743$	−1.53453e7			−1.01977			−0.509887	+	0.860241i	$0.670313\pi$
$744$		0			0
$745$	9.96507e6	+	1.72600e7i	0.657794	+	1.13933i
$746$	−4.51147e6	−	7.81409e6i	−0.296805	−	0.514081i
$747$		0			0
$748$	2.74973e6			0.179695
$749$	3.23166e6	+	1.85535e7i	0.210485	+	1.20843i
$750$		0			0
$751$	−1.12488e7	+	1.94835e7i	−0.727790	+	1.26057i	0.230025	+	0.973185i	$0.426119\pi$
$751$	−1.12488e7	+	1.94835e7i	−0.727790	+	1.26057i	−0.957815	+	0.287385i	$0.907214\pi$
$752$	3.14865e6	+	5.45362e6i	0.203039	+	0.351674i
$753$		0			0
$754$	530436.	−	918743.i	0.0339786	−	0.0588526i
$755$	2.10756e7			1.34559
$756$		0			0
$757$	2.30349e7			1.46099			0.730494	−	0.682919i	$-0.239290\pi$
$757$	2.30349e7			1.46099			0.730494	+	0.682919i	$0.239290\pi$
$758$	8.79006e6	−	1.52248e7i	0.555673	−	0.962453i
$759$		0			0
$760$	−6.75252e6	−	1.16957e7i	−0.424065	−	0.734501i
$761$	2.70368e6	−	4.68290e6i	0.169236	−	0.293126i	−0.768915	−	0.639351i	$-0.779203\pi$
$761$	2.70368e6	−	4.68290e6i	0.169236	−	0.293126i	0.938152	+	0.346225i	$0.112537\pi$
$762$		0			0
$763$	2.20151e7	+	8.06480e6i	1.36902	+	0.501513i
$764$	7.76359e6			0.481204
$765$		0			0
$766$	2.45562e6	+	4.25325e6i	0.151213	+	0.261908i
$767$	−4.60509e6	−	7.97626e6i	−0.282651	−	0.489565i
$768$		0			0
$769$	−7.93100e6			−0.483629			−0.241814	−	0.970323i	$-0.577742\pi$
$769$	−7.93100e6			−0.483629			−0.241814	+	0.970323i	$0.577742\pi$
$770$	−1.00403e6	−	5.76432e6i	−0.0610269	−	0.350365i
$771$		0			0
$772$	2.64654e6	−	4.58394e6i	0.159821	−	0.276819i
$773$	134790.	+	233462.i	0.00811349	+	0.0140530i	0.870054	−	0.492957i	$-0.164084\pi$
$773$	134790.	+	233462.i	0.00811349	+	0.0140530i	−0.861940	+	0.507010i	$0.830751\pi$
$774$		0			0
$775$	−1.16243e7	+	2.01338e7i	−0.695203

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)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(-37.7462 + 65.3783i) q^{5} +(99.4847 - 83.1252i) q^{7} -64.0000 q^{8} +O(q^{10})\)	\(q+(2.00000 - 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(-37.7462 + 65.3783i) q^{5} +(99.4847 - 83.1252i) q^{7} -64.0000 q^{8} +(150.985 + 261.513i) q^{10} +(-74.7309 - 129.438i) q^{11} +349.416 q^{13} +(-88.9847 - 510.875i) q^{14} +(-128.000 + 221.703i) q^{16} +(-574.923 - 995.797i) q^{17} +(1397.60 - 2420.72i) q^{19} +1207.88 q^{20} -597.847 q^{22} +(906.985 - 1570.94i) q^{23} +(-1287.05 - 2229.23i) q^{25} +(698.832 - 1210.41i) q^{26} +(-1947.69 - 713.499i) q^{28} +759.033 q^{29} +(-4515.87 - 7821.72i) q^{31} +(512.000 + 886.810i) q^{32} -4599.39 q^{34} +(1679.42 + 9641.80i) q^{35} +(-3897.45 + 6750.57i) q^{37} +(-5590.40 - 9682.86i) q^{38} +(2415.76 - 4184.21i) q^{40} -7640.49 q^{41} +12188.8 q^{43} +(-1195.69 + 2071.00i) q^{44} +(-3627.94 - 6283.77i) q^{46} +(12299.4 - 21303.2i) q^{47} +(2987.41 - 16539.4i) q^{49} -10296.4 q^{50} +(-2795.33 - 4841.65i) q^{52} +(6798.11 + 11774.7i) q^{53} +11283.2 q^{55} +(-6367.02 + 5320.01i) q^{56} +(1518.07 - 2629.37i) q^{58} +(-13179.4 - 22827.4i) q^{59} +(-17660.9 + 30589.5i) q^{61} -36127.0 q^{62} +4096.00 q^{64} +(-13189.1 + 22844.2i) q^{65} +(-27186.0 - 47087.5i) q^{67} +(-9198.78 + 15932.7i) q^{68} +(36759.0 + 13465.9i) q^{70} +70145.7 q^{71} +(22234.4 + 38511.1i) q^{73} +(15589.8 + 27002.3i) q^{74} -44723.2 q^{76} +(-18194.1 - 6665.05i) q^{77} +(-30806.2 + 53357.9i) q^{79} +(-9663.02 - 16736.8i) q^{80} +(-15281.0 + 26467.5i) q^{82} +87142.0 q^{83} +86804.6 q^{85} +(24377.7 - 42223.4i) q^{86} +(4782.78 + 8284.01i) q^{88} +(49284.7 - 85363.6i) q^{89} +(34761.5 - 29045.3i) q^{91} -29023.5 q^{92} +(-49197.6 - 85212.8i) q^{94} +(105508. + 182745. i) q^{95} +32342.3 q^{97} +(-51319.2 - 43427.4i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 32 q^{4} - 53 q^{5} + 6 q^{7} - 256 q^{8}+O(q^{10}) \) 4 * q + 8 * q^2 - 32 * q^4 - 53 * q^5 + 6 * q^7 - 256 * q^8	\( 4 q + 8 q^{2} - 32 q^{4} - 53 q^{5} + 6 q^{7} - 256 q^{8} + 212 q^{10} + 191 q^{11} - 758 q^{13} + 36 q^{14} - 512 q^{16} - 340 q^{17} + 1769 q^{19} + 1696 q^{20} + 1528 q^{22} + 3236 q^{23} + 45 q^{25} - 1516 q^{26} + 48 q^{28} - 8918 q^{29} - 1994 q^{31} + 2048 q^{32} - 2720 q^{34} + 4562 q^{35} - 20587 q^{37} - 7076 q^{38} + 3392 q^{40} - 17628 q^{41} + 31706 q^{43} + 3056 q^{44} - 12944 q^{46} + 33912 q^{47} + 9598 q^{49} + 360 q^{50} + 6064 q^{52} + 49239 q^{53} + 37882 q^{55} - 384 q^{56} - 17836 q^{58} - 56735 q^{59} - 67508 q^{61} - 15952 q^{62} + 16384 q^{64} - 42762 q^{65} - 75723 q^{67} - 5440 q^{68} + 95692 q^{70} + 17984 q^{71} + 3201 q^{73} + 82348 q^{74} - 56608 q^{76} - 120299 q^{77} - 26612 q^{79} - 13568 q^{80} - 35256 q^{82} + 1898 q^{83} + 210040 q^{85} + 63412 q^{86} - 12224 q^{88} + 176562 q^{89} + 210085 q^{91} - 103552 q^{92} - 135648 q^{94} + 234098 q^{95} - 258846 q^{97} - 211156 q^{98}+O(q^{100}) \) 4 * q + 8 * q^2 - 32 * q^4 - 53 * q^5 + 6 * q^7 - 256 * q^8 + 212 * q^10 + 191 * q^11 - 758 * q^13 + 36 * q^14 - 512 * q^16 - 340 * q^17 + 1769 * q^19 + 1696 * q^20 + 1528 * q^22 + 3236 * q^23 + 45 * q^25 - 1516 * q^26 + 48 * q^28 - 8918 * q^29 - 1994 * q^31 + 2048 * q^32 - 2720 * q^34 + 4562 * q^35 - 20587 * q^37 - 7076 * q^38 + 3392 * q^40 - 17628 * q^41 + 31706 * q^43 + 3056 * q^44 - 12944 * q^46 + 33912 * q^47 + 9598 * q^49 + 360 * q^50 + 6064 * q^52 + 49239 * q^53 + 37882 * q^55 - 384 * q^56 - 17836 * q^58 - 56735 * q^59 - 67508 * q^61 - 15952 * q^62 + 16384 * q^64 - 42762 * q^65 - 75723 * q^67 - 5440 * q^68 + 95692 * q^70 + 17984 * q^71 + 3201 * q^73 + 82348 * q^74 - 56608 * q^76 - 120299 * q^77 - 26612 * q^79 - 13568 * q^80 - 35256 * q^82 + 1898 * q^83 + 210040 * q^85 + 63412 * q^86 - 12224 * q^88 + 176562 * q^89 + 210085 * q^91 - 103552 * q^92 - 135648 * q^94 + 234098 * q^95 - 258846 * q^97 - 211156 * q^98

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