LMFDB - Embedded newform 126.6.g.h.37.2

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			37.2
Root			$-24.2462 + 41.9956i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.6.g.h.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(11.2462 - 19.4789i) q^{5} +(-96.4847 + 86.5893i) q^{7} -64.0000 q^{8} +O(q^{10})$	\(q+(2.00000 - 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(11.2462 - 19.4789i) q^{5} +(-96.4847 + 86.5893i) q^{7} -64.0000 q^{8} +(-44.9847 - 77.9158i) q^{10} +(170.231 + 294.849i) q^{11} -728.416 q^{13} +(106.985 + 507.411i) q^{14} +(-128.000 + 221.703i) q^{16} +(404.923 + 701.348i) q^{17} +(-513.101 + 888.717i) q^{19} -359.878 q^{20} +1361.85 q^{22} +(711.015 - 1231.51i) q^{23} +(1309.55 + 2268.20i) q^{25} +(-1456.83 + 2523.31i) q^{26} +(1971.69 + 644.217i) q^{28} -5218.03 q^{29} +(3518.87 + 6094.87i) q^{31} +(512.000 + 886.810i) q^{32} +3239.39 q^{34} +(601.584 + 2853.22i) q^{35} +(-6396.05 + 11078.3i) q^{37} +(2052.40 + 3554.87i) q^{38} +(-719.755 + 1246.65i) q^{40} -1173.51 q^{41} +3664.17 q^{43} +(2723.69 - 4717.58i) q^{44} +(-2844.06 - 4926.06i) q^{46} +(4656.60 - 8065.46i) q^{47} +(1811.59 - 16709.1i) q^{49} +10476.4 q^{50} +(5827.33 + 10093.2i) q^{52} +(17821.4 + 30867.6i) q^{53} +7657.78 q^{55} +(6175.02 - 5541.71i) q^{56} +(-10436.1 + 18075.8i) q^{58} +(-15188.1 - 26306.5i) q^{59} +(-16093.1 + 27874.1i) q^{61} +28151.0 q^{62} +4096.00 q^{64} +(-8191.89 + 14188.8i) q^{65} +(-10675.5 - 18490.6i) q^{67} +(6478.78 - 11221.6i) q^{68} +(11087.0 + 3622.49i) q^{70} -61153.7 q^{71} +(-20633.9 - 35739.0i) q^{73} +(25584.2 + 44313.2i) q^{74} +16419.2 q^{76} +(-41955.4 - 13708.2i) q^{77} +(17500.2 - 30311.3i) q^{79} +(2879.02 + 4986.61i) q^{80} +(-2347.01 + 4065.14i) q^{82} -86193.0 q^{83} +18215.4 q^{85} +(7328.33 - 12693.0i) q^{86} +(-10894.8 - 18870.3i) q^{88} +(38996.3 - 67543.6i) q^{89} +(70281.0 - 63073.0i) q^{91} -22752.5 q^{92} +(-18626.4 - 32261.9i) q^{94} +(11540.8 + 19989.3i) q^{95} -161765. q^{97} +(-54258.8 - 39693.7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	11.2462	−	19.4789i	0.201178	−	0.348450i	−0.747730	−	0.664002i	$-0.768856\pi$
$5$	11.2462	−	19.4789i	0.201178	−	0.348450i	0.948908	+	0.315552i	$0.102190\pi$
$6$		0			0
$7$	−96.4847	+	86.5893i	−0.744241	+	0.667912i
$7$	−96.4847	+	86.5893i	−0.744241	+	0.667912i
$8$	−64.0000			−0.353553
$9$		0			0
$10$	−44.9847	−	77.9158i	−0.142254	−	0.246391i
$11$	170.231	+	294.849i	0.424186	+	0.734712i	0.996344	−	0.0854314i	$-0.0272268\pi$
$11$	170.231	+	294.849i	0.424186	+	0.734712i	−0.572158	+	0.820144i	$0.693894\pi$
$12$		0			0
$13$	−728.416			−1.19542			−0.597711	−	0.801712i	$-0.703923\pi$
$13$	−728.416			−1.19542			−0.597711	+	0.801712i	$0.703923\pi$
$14$	106.985	+	507.411i	0.145882	+	0.691895i
$15$		0			0
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	404.923	+	701.348i	0.339821	+	0.588588i	0.984399	−	0.175951i	$-0.0563001\pi$
$17$	404.923	+	701.348i	0.339821	+	0.588588i	−0.644578	+	0.764539i	$0.722967\pi$
$18$		0			0
$19$	−513.101	+	888.717i	−0.326076	+	0.564780i	−0.981730	−	0.190282i	$-0.939060\pi$
$19$	−513.101	+	888.717i	−0.326076	+	0.564780i	0.655654	+	0.755062i	$0.272393\pi$
$20$	−359.878			−0.201178
$21$		0			0
$22$	1361.85			0.599890
$23$	711.015	−	1231.51i	0.280259	−	0.485423i	−0.691190	−	0.722674i	$-0.742913\pi$
$23$	711.015	−	1231.51i	0.280259	−	0.485423i	0.971448	+	0.237251i	$0.0762464\pi$
$24$		0			0
$25$	1309.55	+	2268.20i	0.419055	+	0.725825i
$26$	−1456.83	+	2523.31i	−0.422645	+	0.732043i
$27$		0			0
$28$	1971.69	+	644.217i	0.475274	+	0.155288i
$29$	−5218.03			−1.15216			−0.576079	−	0.817394i	$-0.695418\pi$
$29$	−5218.03			−1.15216			−0.576079	+	0.817394i	$0.695418\pi$
$30$		0			0
$31$	3518.87	+	6094.87i	0.657657	+	1.13909i	0.981221	+	0.192889i	$0.0617856\pi$
$31$	3518.87	+	6094.87i	0.657657	+	1.13909i	−0.323564	+	0.946206i	$0.604881\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$		0			0
$34$	3239.39			0.480580
$35$	601.584	+	2853.22i	0.0830092	+	0.393699i
$36$		0			0
$37$	−6396.05	+	11078.3i	−0.768082	+	1.33036i	0.170519	+	0.985354i	$0.445456\pi$
$37$	−6396.05	+	11078.3i	−0.768082	+	1.33036i	−0.938601	+	0.345004i	$0.887878\pi$
$38$	2052.40	+	3554.87i	0.230570	+	0.399360i
$39$		0			0
$40$	−719.755	+	1246.65i	−0.0711270	+	0.123196i
$41$	−1173.51			−0.109025			−0.0545124	−	0.998513i	$-0.517360\pi$
$41$	−1173.51			−0.109025			−0.0545124	+	0.998513i	$0.517360\pi$
$42$		0			0
$43$	3664.17			0.302207			0.151103	−	0.988518i	$-0.451717\pi$
$43$	3664.17			0.302207			0.151103	+	0.988518i	$0.451717\pi$
$44$	2723.69	−	4717.58i	0.212093	−	0.367356i
$45$		0			0
$46$	−2844.06	−	4926.06i	−0.198173	−	0.343246i
$47$	4656.60	−	8065.46i	0.307485	−	0.532580i	−0.670326	−	0.742066i	$-0.733846\pi$
$47$	4656.60	−	8065.46i	0.307485	−	0.532580i	0.977812	+	0.209487i	$0.0671793\pi$
$48$		0			0
$49$	1811.59	−	16709.1i	0.107788	−	0.994174i
$50$	10476.4			0.592633
$51$		0			0
$52$	5827.33	+	10093.2i	0.298855	+	0.517633i
$53$	17821.4	+	30867.6i	0.871469	+	1.50943i	0.860477	+	0.509489i	$0.170165\pi$
$53$	17821.4	+	30867.6i	0.871469	+	1.50943i	0.0109916	+	0.999940i	$0.496501\pi$
$54$		0			0
$55$	7657.78			0.341347
$56$	6175.02	−	5541.71i	0.263129	−	0.236142i
$57$		0			0
$58$	−10436.1	+	18075.8i	−0.407349	+	0.705549i
$59$	−15188.1	−	26306.5i	−0.568033	−	0.983861i	−0.996760	−	0.0804276i	$-0.974371\pi$
$59$	−15188.1	−	26306.5i	−0.568033	−	0.983861i	0.428728	−	0.903434i	$-0.358962\pi$
$60$		0			0
$61$	−16093.1	+	27874.1i	−0.553753	+	0.959128i	0.444247	+	0.895904i	$0.353471\pi$
$61$	−16093.1	+	27874.1i	−0.553753	+	0.959128i	−0.997999	+	0.0632231i	$0.979862\pi$
$62$	28151.0			0.930067
$63$		0			0
$64$	4096.00			0.125000
$65$	−8191.89	+	14188.8i	−0.240492	+	0.416544i
$66$		0			0
$67$	−10675.5	−	18490.6i	−0.290538	−	0.503226i	0.683399	−	0.730045i	$-0.260501\pi$
$67$	−10675.5	−	18490.6i	−0.290538	−	0.503226i	−0.973937	+	0.226819i	$0.927168\pi$
$68$	6478.78	−	11221.6i	0.169911	−	0.294294i
$69$		0			0
$70$	11087.0	+	3622.49i	0.270439	+	0.0883612i
$71$	−61153.7			−1.43972			−0.719859	−	0.694121i	$-0.755793\pi$
$71$	−61153.7			−1.43972			−0.719859	+	0.694121i	$0.755793\pi$
$72$		0			0
$73$	−20633.9	−	35739.0i	−0.453184	−	0.784937i	0.545398	−	0.838177i	$-0.316378\pi$
$73$	−20633.9	−	35739.0i	−0.453184	−	0.784937i	−0.998582	+	0.0532401i	$0.983045\pi$
$74$	25584.2	+	44313.2i	0.543116	+	0.940705i
$75$		0			0
$76$	16419.2			0.326076
$77$	−41955.4	−	13708.2i	−0.806419	−	0.263484i
$78$		0			0
$79$	17500.2	−	30311.3i	0.315483	−	0.546433i	−0.664057	−	0.747682i	$-0.731167\pi$
$79$	17500.2	−	30311.3i	0.315483	−	0.546433i	0.979540	+	0.201249i	$0.0645001\pi$
$80$	2879.02	+	4986.61i	0.0502944	+	0.0871125i
$81$		0			0
$82$	−2347.01	+	4065.14i	−0.0385461	+	0.0667638i
$83$	−86193.0			−1.37334			−0.686668	−	0.726972i	$-0.740927\pi$
$83$	−86193.0			−1.37334			−0.686668	+	0.726972i	$0.740927\pi$
$84$		0			0
$85$	18215.4			0.273458
$86$	7328.33	−	12693.0i	0.106846	−	0.185063i
$87$		0			0
$88$	−10894.8	−	18870.3i	−0.149972	−	0.259760i
$89$	38996.3	−	67543.6i	0.521853	−	0.903876i	−0.477824	−	0.878456i	$-0.658574\pi$
$89$	38996.3	−	67543.6i	0.521853	−	0.903876i	0.999677	−	0.0254206i	$-0.00809249\pi$
$90$		0			0
$91$	70281.0	−	63073.0i	0.889681	−	0.798436i
$92$	−22752.5			−0.280259
$93$		0			0
$94$	−18626.4	−	32261.9i	−0.217425	−	0.376591i
$95$	11540.8	+	19989.3i	0.131198	+	0.227242i
$96$		0			0
$97$	−161765.			−1.74565			−0.872823	−	0.488037i	$-0.837713\pi$
$97$	−161765.			−1.74565			−0.872823	+	0.488037i	$0.837713\pi$
$98$	−54258.8	−	39693.7i	−0.570696	−	0.417500i
$99$		0			0
$100$	20952.8	−	36291.2i	0.209528	−	0.362912i
$101$	−32927.2	−	57031.6i	−0.321182	−	0.556304i	0.659550	−	0.751661i	$-0.270747\pi$
$101$	−32927.2	−	57031.6i	−0.321182	−	0.556304i	−0.980732	+	0.195357i	$0.937414\pi$
$102$		0			0
$103$	−65099.0	+	112755.i	−0.604619	+	1.04723i	0.387493	+	0.921873i	$0.373341\pi$
$103$	−65099.0	+	112755.i	−0.604619	+	1.04723i	−0.992112	+	0.125358i	$0.959992\pi$
$104$	46618.6			0.422645
$105$		0			0
$106$	142571.			1.23244
$107$	1295.48	−	2243.83i	0.0109388	−	0.0189466i	−0.860504	−	0.509443i	$-0.829851\pi$
$107$	1295.48	−	2243.83i	0.0109388	−	0.0189466i	0.871443	+	0.490497i	$0.163185\pi$
$108$		0			0
$109$	−55326.9	−	95828.9i	−0.446036	−	0.772557i	0.552088	−	0.833786i	$-0.313831\pi$
$109$	−55326.9	−	95828.9i	−0.446036	−	0.772557i	−0.998124	+	0.0612291i	$0.980498\pi$
$110$	15315.6	−	26527.3i	0.120684	−	0.209032i
$111$		0			0
$112$	−6847.02	−	32474.3i	−0.0515771	−	0.244622i
$113$	193910.			1.42858			0.714291	−	0.699849i	$-0.246749\pi$
$113$	193910.			1.42858			0.714291	+	0.699849i	$0.246749\pi$
$114$		0			0
$115$	−15992.4	−	27699.7i	−0.112764	−	0.195312i
$116$	41744.3	+	72303.2i	0.288039	+	0.498899i
$117$		0			0
$118$	−121505.			−0.803319
$119$	−99798.1	−	32607.3i	−0.646033	−	0.211080i
$120$		0			0
$121$	22568.4	−	39089.6i	0.140132	−	0.242716i
$122$	64372.5	+	111496.i	0.391562	+	0.678206i
$123$		0			0
$124$	56302.0	−	97517.9i	0.328828	−	0.569547i
$125$	129198.			0.739573
$126$		0			0
$127$	27429.2			0.150905			0.0754526	−	0.997149i	$-0.475960\pi$
$127$	27429.2			0.150905			0.0754526	+	0.997149i	$0.475960\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$		0			0
$130$	32767.6	+	56755.1i	0.170054	+	0.294541i
$131$	75188.0	−	130229.i	0.382798	−	0.663026i	−0.608663	−	0.793429i	$-0.708294\pi$
$131$	75188.0	−	130229.i	0.382798	−	0.663026i	0.991461	+	0.130403i	$0.0416271\pi$
$132$		0			0
$133$	−27447.0	−	130177.i	−0.134544	−	0.638122i
$134$	−85404.3			−0.410883
$135$		0			0
$136$	−25915.1	−	44886.3i	−0.120145	−	0.208097i
$137$	48051.0	+	83226.8i	0.218726	+	0.378845i	0.954419	−	0.298471i	$-0.0964765\pi$
$137$	48051.0	+	83226.8i	0.218726	+	0.378845i	−0.735693	+	0.677316i	$0.763143\pi$
$138$		0			0
$139$	100854.			0.442749			0.221375	−	0.975189i	$-0.428946\pi$
$139$	100854.			0.442749			0.221375	+	0.975189i	$0.428946\pi$
$140$	34722.7	−	31161.5i	0.149725	−	0.134369i
$141$		0			0
$142$	−122307.	+	211843.i	−0.509017	+	0.881643i
$143$	−123999.	−	214772.i	−0.507081	−	0.878291i
$144$		0			0
$145$	−58682.9	+	101642.i	−0.231788	+	0.401469i
$146$	−165071.			−0.640898
$147$		0			0
$148$	204674.			0.768082
$149$	−180472.	+	312587.i	−0.665954	+	1.15347i	0.313071	+	0.949730i	$0.398642\pi$
$149$	−180472.	+	312587.i	−0.665954	+	1.15347i	−0.979026	+	0.203737i	$0.934691\pi$
$150$		0			0
$151$	217028.	+	375903.i	0.774592	+	1.34163i	0.935023	+	0.354586i	$0.115378\pi$
$151$	217028.	+	375903.i	0.774592	+	1.34163i	−0.160431	+	0.987047i	$0.551288\pi$
$152$	32838.4	−	56877.9i	0.115285	−	0.199680i
$153$		0			0
$154$	−131397.	+	117921.i	−0.446462	+	0.400674i
$155$	158295.			0.529223
$156$		0			0
$157$	255798.	+	443055.i	0.828225	+	1.43453i	0.899430	+	0.437066i	$0.143982\pi$
$157$	255798.	+	443055.i	0.828225	+	1.43453i	−0.0712046	+	0.997462i	$0.522684\pi$
$158$	−70000.9	−	121245.i	−0.223080	−	0.386386i
$159$		0			0
$160$	23032.2			0.0711270
$161$	38033.9	+	180389.i	0.115639	+	0.548459i
$162$		0			0
$163$	125635.	−	217606.i	0.370374	−	0.641507i	−0.619249	−	0.785195i	$-0.712563\pi$
$163$	125635.	−	217606.i	0.370374	−	0.641507i	0.989623	+	0.143688i	$0.0458962\pi$
$164$	9388.04	+	16260.6i	0.0272562	+	0.0472091i
$165$		0			0
$166$	−172386.	+	298581.i	−0.485547	+	0.840993i
$167$	−419277.			−1.16335			−0.581674	−	0.813422i	$-0.697602\pi$
$167$	−419277.			−1.16335			−0.581674	+	0.813422i	$0.697602\pi$
$168$		0			0
$169$	159297.			0.429032
$170$	36430.7	−	63099.8i	0.0966819	−	0.167458i
$171$		0			0
$172$	−29313.3	−	50772.2i	−0.0755517	−	0.130859i
$173$	−230688.	+	399564.i	−0.586017	+	1.01501i	0.408731	+	0.912655i	$0.365971\pi$
$173$	−230688.	+	399564.i	−0.586017	+	1.01501i	−0.994748	+	0.102356i	$0.967362\pi$
$174$		0			0
$175$	−322753.	−	105454.i	−0.796665	−	0.260296i
$176$	−87158.2			−0.212093
$177$		0			0
$178$	−155985.	−	270174.i	−0.369006	−	0.639137i
$179$	370853.	+	642336.i	0.865105	+	1.49841i	0.866942	+	0.498408i	$0.166082\pi$
$179$	370853.	+	642336.i	0.865105	+	1.49841i	−0.00183697	+	0.999998i	$0.500585\pi$
$180$		0			0
$181$	301371.			0.683762			0.341881	−	0.939743i	$-0.388936\pi$
$181$	301371.			0.683762			0.341881	+	0.939743i	$0.388936\pi$
$182$	−77929.3	−	369606.i	−0.174390	−	0.827106i
$183$		0			0
$184$	−45505.0	+	78816.9i	−0.0990865	+	0.171623i
$185$	143862.	+	249177.i	0.309042	+	0.535277i
$186$		0			0
$187$	−137861.	+	238782.i	−0.288295	+	0.499342i
$188$	−149011.			−0.307485
$189$		0			0
$190$	92326.7			0.185542
$191$	131591.	−	227923.i	0.261002	−	0.452069i	−0.705507	−	0.708703i	$-0.749280\pi$
$191$	131591.	−	227923.i	0.261002	−	0.452069i	0.966508	+	0.256635i	$0.0826138\pi$
$192$		0			0
$193$	415563.	+	719777.i	0.803053	+	1.39093i	0.917598	+	0.397510i	$0.130126\pi$
$193$	415563.	+	719777.i	0.803053	+	1.39093i	−0.114545	+	0.993418i	$0.536541\pi$
$194$	−323531.	+	560372.i	−0.617179	+	1.06899i
$195$		0			0
$196$	−246021.	+	108570.i	−0.457437	+	0.201870i
$197$	1.05421e6			1.93536			0.967681	−	0.252178i	$-0.0811470\pi$
$197$	1.05421e6			1.93536			0.967681	+	0.252178i	$0.0811470\pi$
$198$		0			0
$199$	−349284.	−	604977.i	−0.625239	−	1.08295i	−0.988495	−	0.151256i	$-0.951668\pi$
$199$	−349284.	−	604977.i	−0.625239	−	1.08295i	0.363256	−	0.931689i	$-0.381665\pi$
$200$	−83811.0	−	145165.i	−0.148158	−	0.256618i
$201$		0			0
$202$	−263418.			−0.454220
$203$	503460.	−	451826.i	0.857482	−	0.769539i
$204$		0			0
$205$	−13197.4	+	22858.6i	−0.0219334	+	0.0379897i
$206$	260396.	+	451019.i	0.427530	+	0.740504i
$207$		0			0
$208$	93237.2	−	161492.i	0.149428	−	0.258816i
$209$	−349382.			−0.553268
$210$		0			0
$211$	−99693.6			−0.154156			−0.0770781	−	0.997025i	$-0.524559\pi$
$211$	−99693.6			−0.154156			−0.0770781	+	0.997025i	$0.524559\pi$
$212$	285142.	−	493881.i	0.435734	−	0.754714i
$213$		0			0
$214$	−5181.90	−	8975.32i	−0.00773490	−	0.0133972i
$215$	41207.8	−	71374.1i	0.0607972	−	0.105304i
$216$		0			0
$217$	−867267.	−	283365.i	−1.25027	−	0.408504i
$218$	−442615.			−0.630790
$219$		0			0
$220$	−61262.3	−	106109.i	−0.0853368	−	0.147808i
$221$	−294953.	−	510873.i	−0.406230	−	0.703610i
$222$		0			0
$223$	526194.			0.708572			0.354286	−	0.935137i	$-0.384724\pi$
$223$	526194.			0.708572			0.354286	+	0.935137i	$0.384724\pi$
$224$	−126188.	−	41229.9i	−0.168035	−	0.0549025i
$225$		0			0
$226$	387821.	−	671725.i	0.505080	−	0.874824i
$227$	−490802.	−	850095.i	−0.632182	−	1.09497i	−0.987105	−	0.160076i	$-0.948826\pi$
$227$	−490802.	−	850095.i	−0.632182	−	1.09497i	0.354923	−	0.934896i	$-0.384507\pi$
$228$		0			0
$229$	42540.5	−	73682.3i	0.0536061	−	0.0928484i	−0.837977	−	0.545705i	$-0.816262\pi$
$229$	42540.5	−	73682.3i	0.0536061	−	0.0928484i	0.891583	+	0.452857i	$0.149595\pi$
$230$	−127939.			−0.159472
$231$		0			0
$232$	333954.			0.407349
$233$	56561.4	−	97967.3i	0.0682544	−	0.118220i	−0.829879	−	0.557944i	$-0.811590\pi$
$233$	56561.4	−	97967.3i	0.0682544	−	0.118220i	0.898133	+	0.439724i	$0.144924\pi$
$234$		0			0
$235$	−104738.	−	181411.i	−0.123718	−	0.214286i
$236$	−243009.	+	420905.i	−0.284016	+	0.491931i
$237$		0			0
$238$	−312551.	+	280496.i	−0.357667	+	0.320985i
$239$	895100.			1.01362			0.506812	−	0.862057i	$-0.330824\pi$
$239$	895100.			1.01362			0.506812	+	0.862057i	$0.330824\pi$
$240$		0			0
$241$	−263857.	−	457014.i	−0.292635	−	0.506859i	0.681797	−	0.731542i	$-0.261199\pi$
$241$	−263857.	−	457014.i	−0.292635	−	0.506859i	−0.974432	+	0.224683i	$0.927865\pi$
$242$	−90273.6	−	156358.i	−0.0990883	−	0.171626i
$243$		0			0
$244$	514980.			0.553753
$245$	−305102.	−	223201.i	−0.324735	−	0.237564i
$246$		0			0
$247$	373751.	−	647355.i	0.389798	−	0.675150i
$248$	−225208.	−	390071.i	−0.232517	−	0.402731i
$249$		0			0
$250$	258396.	−	447556.i	0.261479	−	0.452894i
$251$	1.19293e6			1.19517			0.597584	−	0.801806i	$-0.296127\pi$
$251$	1.19293e6			1.19517			0.597584	+	0.801806i	$0.296127\pi$
$252$		0			0
$253$	484147.			0.475528
$254$	54858.5	−	95017.7i	0.0533531	−	0.0924102i
$255$		0			0
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−597462.	+	1.03483e6i	−0.564257	+	0.977322i	0.432861	+	0.901461i	$0.357504\pi$
$257$	−597462.	+	1.03483e6i	−0.564257	+	0.977322i	−0.997118	+	0.0758617i	$0.975829\pi$
$258$		0			0
$259$	−342140.	−	1.62272e6i	−0.316923	−	1.50312i
$260$	262140.			0.240492
$261$		0			0
$262$	−300752.	−	520917.i	−0.270679	−	0.468830i
$263$	−1.06115e6	−	1.83797e6i	−0.945993	−	1.63851i	−0.753750	−	0.657161i	$-0.771757\pi$
$263$	−1.06115e6	−	1.83797e6i	−0.945993	−	1.63851i	−0.192244	−	0.981347i	$-0.561576\pi$
$264$		0			0
$265$	801690.			0.701280
$266$	−505839.	−	165274.i	−0.438337	−	0.143219i
$267$		0			0
$268$	−170809.	+	295849.i	−0.145269	+	0.251613i
$269$	77488.3	+	134214.i	0.0652913	+	0.113088i	0.896823	−	0.442389i	$-0.145869\pi$
$269$	77488.3	+	134214.i	0.0652913	+	0.113088i	−0.831532	+	0.555477i	$0.812536\pi$
$270$		0			0
$271$	−979439.	+	1.69644e6i	−0.810129	+	1.40318i	0.102645	+	0.994718i	$0.467270\pi$
$271$	−979439.	+	1.69644e6i	−0.810129	+	1.40318i	−0.912773	+	0.408466i	$0.866064\pi$
$272$	−207321.			−0.169911
$273$		0			0
$274$	384408.			0.309326
$275$	−445851.	+	772236.i	−0.355515	+	0.615770i
$276$		0			0
$277$	874763.	+	1.51513e6i	0.685001	+	1.18646i	0.973437	+	0.228957i	$0.0735315\pi$
$277$	874763.	+	1.51513e6i	0.685001	+	1.18646i	−0.288436	+	0.957499i	$0.593135\pi$
$278$	201709.	−	349370.i	0.156536	−	0.271128i
$279$		0			0
$280$	−38501.4	−	182606.i	−0.0293482	−	0.139194i
$281$	−1.40665e6			−1.06272			−0.531361	−	0.847145i	$-0.678319\pi$
$281$	−1.40665e6			−1.06272			−0.531361	+	0.847145i	$0.678319\pi$
$282$		0			0
$283$	−978536.	−	1.69487e6i	−0.726291	−	1.25797i	−0.958441	−	0.285292i	$-0.907909\pi$
$283$	−978536.	−	1.69487e6i	−0.726291	−	1.25797i	0.232150	−	0.972680i	$-0.425424\pi$
$284$	489230.	+	847371.i	0.359929	+	0.623416i
$285$		0			0
$286$	−991991.			−0.717121
$287$	113225.	−	101613.i	0.0811407	−	0.0728189i
$288$		0			0
$289$	382002.	−	661648.i	0.269043	−	0.465996i
$290$	234732.	+	406567.i	0.163899	+	0.283882i
$291$		0			0
$292$	−330142.	+	571823.i	−0.226592	+	0.392469i
$293$	1.26998e6			0.864229			0.432114	−	0.901819i	$-0.357768\pi$
$293$	1.26998e6			0.864229			0.432114	+	0.901819i	$0.357768\pi$
$294$		0			0
$295$	−683232.			−0.457102
$296$	409348.	−	709011.i	0.271558	−	0.470353i
$297$		0			0
$298$	721888.	+	1.25035e6i	0.470901	+	0.815624i
$299$	−517915.	+	897055.i	−0.335027	+	0.580285i
$300$		0			0
$301$	−353536.	+	317277.i	−0.224914	+	0.201847i
$302$	1.73622e6			1.09544
$303$		0			0
$304$	−131354.	−	227511.i	−0.0815190	−	0.141195i
$305$	361972.	+	626954.i	0.222805	+	0.385910i
$306$		0			0
$307$	−41854.4			−0.0253451			−0.0126726	−	0.999920i	$-0.504034\pi$
$307$	−41854.4			−0.0253451			−0.0126726	+	0.999920i	$0.504034\pi$
$308$	145697.	+	691017.i	0.0875131	+	0.415061i
$309$		0			0
$310$	316591.	−	548351.i	0.187109	−	0.324082i
$311$	−1.14595e6	−	1.98484e6i	−0.671837	−	1.16366i	−0.977383	−	0.211478i	$-0.932172\pi$
$311$	−1.14595e6	−	1.98484e6i	−0.671837	−	1.16366i	0.305546	−	0.952177i	$-0.401161\pi$
$312$		0			0
$313$	−1.13575e6	+	1.96717e6i	−0.655271	+	1.13496i	0.326555	+	0.945178i	$0.394112\pi$
$313$	−1.13575e6	+	1.96717e6i	−0.655271	+	1.13496i	−0.981826	+	0.189785i	$0.939221\pi$
$314$	2.04639e6			1.17129
$315$		0			0
$316$	−560007.			−0.315483
$317$	−992372.	+	1.71884e6i	−0.554659	+	0.960698i	0.443271	+	0.896388i	$0.353818\pi$
$317$	−992372.	+	1.71884e6i	−0.554659	+	0.960698i	−0.997930	+	0.0643100i	$0.979515\pi$
$318$		0			0
$319$	−888270.	−	1.53853e6i	−0.488729	−	0.846504i
$320$	46064.3	−	79785.8i	0.0251472	−	0.0435562i
$321$		0			0
$322$	700952.	+	229024.i	0.376746	+	0.123095i
$323$	−831066.			−0.443230
$324$		0			0
$325$	−953895.	−	1.65219e6i	−0.500947	−	0.867666i
$326$	−502539.	−	870423.i	−0.261894	−	0.453614i
$327$		0			0
$328$	75104.3			0.0385461
$329$	249092.	+	1.18141e6i	0.126873	+	0.601740i
$330$		0			0
$331$	−319230.	+	552923.i	−0.160153	+	0.277393i	−0.934923	−	0.354850i	$-0.884532\pi$
$331$	−319230.	+	552923.i	−0.160153	+	0.277393i	0.774771	+	0.632242i	$0.217865\pi$
$332$	689544.	+	1.19432e6i	0.343334	+	0.594672i
$333$		0			0
$334$	−838553.	+	1.45242e6i	−0.411305	+	0.712402i
$335$	−480236.			−0.233799
$336$		0			0
$337$	2.72026e6			1.30478			0.652388	−	0.757886i	$-0.273767\pi$
$337$	2.72026e6			1.30478			0.652388	+	0.757886i	$0.273767\pi$
$338$	318593.	−	551820.i	0.151686	−	0.262727i
$339$		0			0
$340$	−145723.	−	252399.i	−0.0683645	−	0.118411i
$341$	−1.19804e6	+	2.07507e6i	−0.557938	+	0.966377i
$342$		0			0
$343$	1.27204e6	+	1.76903e6i	0.583800	+	0.811897i
$344$	−234507.			−0.106846
$345$		0			0
$346$	922753.	+	1.59825e6i	0.414376	+	0.717721i
$347$	1.31038e6	+	2.26965e6i	0.584217	+	1.01189i	0.994973	+	0.100148i	$0.0319317\pi$
$347$	1.31038e6	+	2.26965e6i	0.584217	+	1.01189i	−0.410755	+	0.911746i	$0.634735\pi$
$348$		0			0
$349$	575592.			0.252960			0.126480	−	0.991969i	$-0.459632\pi$
$349$	575592.			0.252960			0.126480	+	0.991969i	$0.459632\pi$
$350$	−1.01081e6	+	907142.i	−0.441062	+	0.395827i
$351$		0			0
$352$	−174316.	+	301925.i	−0.0749862	+	0.129880i
$353$	−1.29486e6	−	2.24276e6i	−0.553077	−	0.957957i	−0.998050	−	0.0624135i	$-0.980120\pi$
$353$	−1.29486e6	−	2.24276e6i	−0.553077	−	0.957957i	0.444974	−	0.895544i	$-0.353213\pi$
$354$		0			0
$355$	−687746.	+	1.19121e6i	−0.289639	+	0.501669i
$356$	−1.24788e6			−0.521853
$357$		0			0
$358$	2.96682e6			1.22344
$359$	1.43389e6	−	2.48358e6i	0.587193	−	1.01705i	−0.407405	−	0.913248i	$-0.633566\pi$
$359$	1.43389e6	−	2.48358e6i	0.587193	−	1.01705i	0.994598	−	0.103801i	$-0.0331005\pi$
$360$		0			0
$361$	711505.	+	1.23236e6i	0.287349	+	0.497703i
$362$	602742.	−	1.04398e6i	0.241746	−	0.418717i
$363$		0			0
$364$	−1.43621e6	−	469258.i	−0.568153	−	0.185634i
$365$	−928210.			−0.364682
$366$		0			0
$367$	977255.	+	1.69265e6i	0.378741	+	0.655999i	0.990879	−	0.134752i	$-0.0430237\pi$
$367$	977255.	+	1.69265e6i	0.378741	+	0.655999i	−0.612138	+	0.790751i	$0.709690\pi$
$368$	182020.	+	315268.i	0.0700647	+	0.121356i
$369$		0			0
$370$	1.15090e6			0.437052
$371$	−4.39229e6	−	1.43510e6i	−1.65675	−	0.541314i
$372$		0			0
$373$	−1.10555e6	+	1.91486e6i	−0.411439	+	0.712633i	−0.995047	−	0.0994020i	$-0.968307\pi$
$373$	−1.10555e6	+	1.91486e6i	−0.411439	+	0.712633i	0.583608	+	0.812035i	$0.301640\pi$
$374$	551444.	+	955129.i	0.203855	+	0.353088i
$375$		0			0
$376$	−298022.	+	516190.i	−0.108712	+	0.188295i
$377$	3.80090e6			1.37731
$378$		0			0
$379$	3.81232e6			1.36330			0.681649	−	0.731679i	$-0.261263\pi$
$379$	3.81232e6			1.36330			0.681649	+	0.731679i	$0.261263\pi$
$380$	184653.	−	319829.i	0.0655992	−	0.113621i
$381$		0			0
$382$	−526365.	−	911691.i	−0.184556	−	0.319661i
$383$	1.90303e6	−	3.29614e6i	0.662901	−	1.14818i	−0.316949	−	0.948442i	$-0.602658\pi$
$383$	1.90303e6	−	3.29614e6i	0.662901	−	1.14818i	0.979850	−	0.199735i	$-0.0640082\pi$
$384$		0			0
$385$	−738859.	+	663082.i	−0.254044	+	0.227990i
$386$	3.32451e6			1.13569
$387$		0			0
$388$	1.29412e6	+	2.24149e6i	0.436411	+	0.755887i
$389$	1.53762e6	+	2.66324e6i	0.515200	+	0.892352i	0.999844	+	0.0176410i	$0.00561558\pi$
$389$	1.53762e6	+	2.66324e6i	0.515200	+	0.892352i	−0.484645	+	0.874711i	$0.661051\pi$
$390$		0			0
$391$	1.15163e6			0.380952
$392$	−115942.	+	1.06938e6i	−0.0381088	+	0.351494i
$393$		0			0
$394$	2.10842e6	−	3.65190e6i	0.684254	−	1.18516i
$395$	−393621.	−	681772.i	−0.126936	−	0.219860i
$396$		0			0
$397$	−1.09566e6	+	1.89774e6i	−0.348900	+	0.604312i	−0.986054	−	0.166424i	$-0.946778\pi$
$397$	−1.09566e6	+	1.89774e6i	−0.348900	+	0.604312i	0.637154	+	0.770736i	$0.280111\pi$
$398$	−2.79427e6			−0.884221
$399$		0			0
$400$	−670488.			−0.209528
$401$	888340.	−	1.53865e6i	0.275879	−	0.477836i	−0.694478	−	0.719514i	$-0.744365\pi$
$401$	888340.	−	1.53865e6i	0.275879	−	0.477836i	0.970356	+	0.241678i	$0.0776978\pi$
$402$		0			0
$403$	−2.56320e6	−	4.43960e6i	−0.786177	−	1.36170i
$404$	−526835.	+	912505.i	−0.160591	+	0.278152i
$405$		0			0
$406$	−558250.	−	2.64769e6i	−0.168079	−	0.797172i
$407$	−4.35522e6			−1.30324
$408$		0			0
$409$	−1.18059e6	−	2.04484e6i	−0.348973	−	0.604438i	0.637095	−	0.770786i	$-0.280136\pi$
$409$	−1.18059e6	−	2.04484e6i	−0.348973	−	0.604438i	−0.986067	+	0.166347i	$0.946803\pi$
$410$	52789.8	+	91434.6i	0.0155092	+	0.0268628i
$411$		0			0
$412$	2.08317e6			0.604619
$413$	3.74328e6	+	1.22305e6i	1.07989	+	0.352834i
$414$		0			0
$415$	−969341.	+	1.67895e6i	−0.276284	+	0.478539i
$416$	−372949.	−	645966.i	−0.105661	−	0.183011i
$417$		0			0
$418$	−698765.	+	1.21030e6i	−0.195610	+	0.338806i
$419$	3.23493e6			0.900181			0.450090	−	0.892983i	$-0.351392\pi$
$419$	3.23493e6			0.900181			0.450090	+	0.892983i	$0.351392\pi$
$420$		0			0
$421$	−2.85759e6			−0.785769			−0.392884	−	0.919588i	$-0.628523\pi$
$421$	−2.85759e6			−0.785769			−0.392884	+	0.919588i	$0.628523\pi$
$422$	−199387.	+	345349.i	−0.0545025	+	0.0944010i
$423$		0			0
$424$	−1.14057e6	−	1.97552e6i	−0.308111	−	0.533664i
$425$	−1.06053e6	+	1.83690e6i	−0.284808	+	0.493301i
$426$		0			0
$427$	−860859.	−	4.08292e6i	−0.228487	−	1.08368i
$428$	−41455.2			−0.0109388
$429$		0			0
$430$	−164831.	−	285496.i	−0.0429901	−	0.0744611i
$431$	−44193.1	−	76544.7i	−0.0114594	−	0.0198482i	0.860239	−	0.509891i	$-0.170314\pi$
$431$	−44193.1	−	76544.7i	−0.0114594	−	0.0198482i	−0.871698	+	0.490043i	$0.836981\pi$
$432$		0			0
$433$	−3.09418e6			−0.793097			−0.396549	−	0.918014i	$-0.629792\pi$
$433$	−3.09418e6			−0.793097			−0.396549	+	0.918014i	$0.629792\pi$
$434$	−2.71614e6	+	2.43757e6i	−0.692194	+	0.621203i
$435$		0			0
$436$	−885230.	+	1.53326e6i	−0.223018	+	0.386278i
$437$	729645.	+	1.26378e6i	0.182771	+	0.316569i
$438$		0			0
$439$	−242589.	+	420177.i	−0.0600773	+	0.104057i	−0.894500	−	0.447068i	$-0.852468\pi$
$439$	−242589.	+	420177.i	−0.0600773	+	0.104057i	0.834422	+	0.551125i	$0.185801\pi$
$440$	−490098.			−0.120684
$441$		0			0
$442$	−2.35962e6			−0.574495
$443$	637598.	−	1.10435e6i	0.154361	−	0.267361i	−0.778465	−	0.627688i	$-0.784001\pi$
$443$	637598.	−	1.10435e6i	0.154361	−	0.267361i	0.932826	+	0.360327i	$0.117335\pi$
$444$		0			0
$445$	−877118.	−	1.51921e6i	−0.209970	−	0.363679i
$446$	1.05239e6	−	1.82279e6i	0.250518	−	0.433910i
$447$		0			0
$448$	−395201.	+	354670.i	−0.0930301	+	0.0834890i
$449$	3.79144e6			0.887541			0.443770	−	0.896141i	$-0.353641\pi$
$449$	3.79144e6			0.887541			0.443770	+	0.896141i	$0.353641\pi$
$450$		0			0
$451$	−199767.	−	346006.i	−0.0462468	−	0.0801019i
$452$	−1.55128e6	−	2.68690e6i	−0.357145	−	0.618594i
$453$		0			0
$454$	−3.92642e6			−0.894040
$455$	−438203.	−	2.07833e6i	−0.0992310	−	0.470637i
$456$		0			0
$457$	−851404.	+	1.47467e6i	−0.190698	+	0.330298i	−0.945482	−	0.325675i	$-0.894408\pi$
$457$	−851404.	+	1.47467e6i	−0.190698	+	0.330298i	0.754784	+	0.655973i	$0.227742\pi$
$458$	−170162.	−	294729.i	−0.0379052	−	0.0656537i
$459$		0			0
$460$	−255878.	+	443194.i	−0.0563818	+	0.0976562i
$461$	−4.55537e6			−0.998323			−0.499161	−	0.866509i	$-0.666358\pi$
$461$	−4.55537e6			−0.998323			−0.499161	+	0.866509i	$0.666358\pi$
$462$		0			0
$463$	5.82647e6			1.26314			0.631572	−	0.775317i	$-0.282410\pi$
$463$	5.82647e6			1.26314			0.631572	+	0.775317i	$0.282410\pi$
$464$	667908.	−	1.15685e6i	0.144020	−	0.249449i
$465$		0			0
$466$	−226246.	−	391869.i	−0.0482631	−	0.0835942i
$467$	−1.77131e6	+	3.06799e6i	−0.375839	+	0.650972i	−0.990452	−	0.137857i	$-0.955979\pi$
$467$	−1.77131e6	+	3.06799e6i	−0.375839	+	0.650972i	0.614614	+	0.788828i	$0.289312\pi$
$468$		0			0
$469$	2.63111e6	+	859670.i	0.552341	+	0.180468i
$470$	−837902.			−0.174964
$471$		0			0
$472$	972038.	+	1.68362e6i	0.200830	+	0.347847i
$473$	623754.	+	1.08037e6i	0.128192	+	0.222035i
$474$		0			0
$475$	−2.68772e6			−0.546575
$476$	346565.	+	1.64370e6i	0.0701079	+	0.332511i
$477$		0			0
$478$	1.79020e6	−	3.10072e6i	0.358370	−	0.620715i
$479$	−2.11771e6	−	3.66798e6i	−0.421723	−	0.730446i	0.574385	−	0.818585i	$-0.305241\pi$
$479$	−2.11771e6	−	3.66798e6i	−0.421723	−	0.730446i	−0.996108	+	0.0881390i	$0.971908\pi$
$480$		0			0
$481$	4.65899e6	−	8.06960e6i	0.918182	−	1.59034i
$482$	−2.11086e6			−0.413849
$483$		0			0
$484$	−722189.			−0.140132
$485$	−1.81924e6	+	3.15102e6i	−0.351185	+	0.608270i
$486$		0			0
$487$	2.82740e6	+	4.89719e6i	0.540212	+	0.935675i	0.998891	+	0.0470729i	$0.0149893\pi$
$487$	2.82740e6	+	4.89719e6i	0.540212	+	0.935675i	−0.458679	+	0.888602i	$0.651677\pi$
$488$	1.02996e6	−	1.78394e6i	0.195781	−	0.339103i
$489$		0			0
$490$	−1.38339e6	+	610501.i	−0.260289	+	0.114867i
$491$	−8.33183e6			−1.55968			−0.779842	−	0.625976i	$-0.784701\pi$
$491$	−8.33183e6			−1.55968			−0.779842	+	0.625976i	$0.784701\pi$
$492$		0			0
$493$	−2.11290e6	−	3.65966e6i	−0.391528	−	0.678146i
$494$	−1.49500e6	−	2.58942e6i	−0.275629	−	0.477403i
$495$		0			0
$496$	−1.80166e6			−0.328828
$497$	5.90040e6	−	5.29526e6i	1.07150	−	0.961604i
$498$		0			0
$499$	3.61884e6	−	6.26802e6i	0.650607	−	1.12688i	−0.332369	−	0.943149i	$-0.607848\pi$
$499$	3.61884e6	−	6.26802e6i	0.650607	−	1.12688i	0.982976	−	0.183734i	$-0.0588187\pi$
$500$	−1.03359e6	−	1.79022e6i	−0.184893	−	0.320245i
$501$		0			0
$502$	2.38585e6	−	4.13242e6i	0.422556	−	0.731888i
$503$	6.16761e6			1.08692			0.543459	−	0.839436i	$-0.317114\pi$
$503$	6.16761e6			1.08692			0.543459	+	0.839436i	$0.317114\pi$
$504$		0			0
$505$	−1.48122e6			−0.258459
$506$	968294.	−	1.67713e6i	0.168124	−	0.291200i
$507$		0			0
$508$	−219434.	−	380071.i	−0.0377263	−	0.0653439i
$509$	917439.	−	1.58905e6i	0.156958	−	0.271859i	−0.776812	−	0.629732i	$-0.783165\pi$
$509$	917439.	−	1.58905e6i	0.156958	−	0.271859i	0.933770	+	0.357873i	$0.116498\pi$
$510$		0			0
$511$	5.08547e6	+	1.66159e6i	0.861546	+	0.281495i
$512$	−262144.			−0.0441942
$513$		0			0
$514$	2.38985e6	+	4.13934e6i	0.398990	+	0.691071i
$515$	1.46423e6	+	2.53612e6i	0.243272	+	0.421359i
$516$		0			0
$517$	3.17079e6			0.521724
$518$	−6.30553e6	−	2.06022e6i	−1.03252	−	0.337357i
$519$		0			0
$520$	524281.	−	908081.i	0.0850268	−	0.147271i
$521$	2.65520e6	+	4.59894e6i	0.428551	+	0.742273i	0.996745	−	0.0806224i	$-0.0256908\pi$
$521$	2.65520e6	+	4.59894e6i	0.428551	+	0.742273i	−0.568193	+	0.822895i	$0.692357\pi$
$522$		0			0
$523$	1.49418e6	−	2.58799e6i	0.238862	−	0.413722i	−0.721526	−	0.692388i	$-0.756559\pi$
$523$	1.49418e6	−	2.58799e6i	0.238862	−	0.413722i	0.960388	+	0.278666i	$0.0898922\pi$
$524$	−2.40601e6			−0.382798
$525$		0			0
$526$	−8.48921e6			−1.33784
$527$	−2.84975e6	+	4.93591e6i	−0.446972	+	0.774178i
$528$		0			0
$529$	2.20709e6	+	3.82279e6i	0.342910	+	0.593937i
$530$	1.60338e6	−	2.77713e6i	0.247940	−	0.429445i
$531$		0			0
$532$	−1.58420e6	+	1.42173e6i	−0.242679	+	0.217790i
$533$	854800.			0.130331
$534$		0			0
$535$	−29138.3	−	50469.0i	−0.00440128	−	0.00762325i
$536$	683235.	+	1.18340e6i	0.102721	+	0.177917i
$537$		0			0
$538$	619907.			0.0923359
$539$	5.23504e6	−	2.31026e6i	0.776154	−	0.342522i
$540$		0			0
$541$	−1.08416e6	+	1.87782e6i	−0.159258	+	0.275843i	−0.934601	−	0.355697i	$-0.884243\pi$
$541$	−1.08416e6	+	1.87782e6i	−0.159258	+	0.275843i	0.775343	+	0.631540i	$0.217577\pi$
$542$	3.91775e6	+	6.78575e6i	0.572848	+	0.992201i
$543$		0			0
$544$	−414642.	+	718180.i	−0.0600725	+	0.104049i
$545$	−2.48886e6			−0.358930
$546$		0			0
$547$	−9.13272e6			−1.30506			−0.652532	−	0.757761i	$-0.726293\pi$
$547$	−9.13272e6			−1.30506			−0.652532	+	0.757761i	$0.726293\pi$
$548$	768816.	−	1.33163e6i	0.109363	−	0.189423i
$549$		0			0
$550$	1.78340e6	+	3.08894e6i	0.251387	+	0.435415i
$551$	2.67738e6	−	4.63735e6i	0.375691	−	0.650715i
$552$		0			0
$553$	936128.	+	4.43991e6i	0.130173	+	0.617392i
$554$	6.99810e6			0.968737
$555$		0			0
$556$	−806835.	−	1.39748e6i	−0.110687	−	0.191716i
$557$	−4.61014e6	−	7.98500e6i	−0.629617	−	1.09053i	−0.987629	−	0.156811i	$-0.949879\pi$
$557$	−4.61014e6	−	7.98500e6i	−0.629617	−	1.09053i	0.358012	−	0.933717i	$-0.383455\pi$
$558$		0			0
$559$	−2.66904e6			−0.361264
$560$	−709568.	−	231839.i	−0.0956146	−	0.0312404i
$561$		0			0
$562$	−2.81330e6	+	4.87277e6i	−0.375729	+	0.650782i
$563$	4.24638e6	+	7.35495e6i	0.564610	+	0.977933i	0.997086	+	0.0762872i	$0.0243066\pi$
$563$	4.24638e6	+	7.35495e6i	0.564610	+	0.977933i	−0.432476	+	0.901645i	$0.642360\pi$
$564$		0			0
$565$	2.18075e6	−	3.77717e6i	0.287399	−	0.497789i
$566$	−7.82828e6			−1.02713
$567$		0			0
$568$	3.91384e6			0.509017
$569$	−2.35456e6	+	4.07822e6i	−0.304880	+	0.528068i	−0.977235	−	0.212162i	$-0.931950\pi$
$569$	−2.35456e6	+	4.07822e6i	−0.304880	+	0.528068i	0.672355	+	0.740229i	$0.265283\pi$
$570$		0			0
$571$	864035.	+	1.49655e6i	0.110902	+	0.192089i	0.916134	−	0.400871i	$-0.131293\pi$
$571$	864035.	+	1.49655e6i	0.110902	+	0.192089i	−0.805232	+	0.592960i	$0.797959\pi$
$572$	−1.98398e6	+	3.43636e6i	−0.253541	+	0.439145i
$573$		0			0
$574$	−125547.	−	595450.i	−0.0159048	−	0.0754337i
$575$	3.72443e6			0.469776
$576$		0			0
$577$	−1.19249e6	−	2.06546e6i	−0.149113	−	0.258272i	0.781787	−	0.623546i	$-0.214309\pi$
$577$	−1.19249e6	−	2.06546e6i	−0.149113	−	0.258272i	−0.930900	+	0.365274i	$0.880975\pi$
$578$	−1.52801e6	−	2.64659e6i	−0.190242	−	0.329509i
$579$		0			0
$580$	1.87785e6			0.231788
$581$	8.31630e6	−	7.46339e6i	1.02209	−	0.917267i
$582$		0			0
$583$	−6.06750e6	+	1.05092e7i	−0.739330	+	1.28056i
$584$	1.32057e6	+	2.28729e6i	0.160225	+	0.277517i
$585$		0			0
$586$	2.53997e6	−	4.39935e6i	0.305551	−	0.529230i
$587$	3.44904e6			0.413145			0.206573	−	0.978431i	$-0.433769\pi$
$587$	3.44904e6			0.413145			0.206573	+	0.978431i	$0.433769\pi$
$588$		0			0
$589$	−7.22214e6			−0.857784
$590$	−1.36646e6	+	2.36678e6i	−0.161610	+	0.279917i
$591$		0			0
$592$	−1.63739e6	−	2.83604e6i	−0.192021	−	0.332589i
$593$	567341.	−	982664.i	0.0662533	−	0.114754i	−0.830996	−	0.556278i	$-0.812229\pi$
$593$	567341.	−	982664.i	0.0662533	−	0.114754i	0.897249	+	0.441524i	$0.145562\pi$
$594$		0			0
$595$	−1.75750e6	+	1.57725e6i	−0.203518	+	0.182646i
$596$	5.77511e6			0.665954
$597$		0			0
$598$	2.07166e6	+	3.58822e6i	0.236900	+	0.410323i
$599$	3.80933e6	+	6.59795e6i	0.433792	+	0.751349i	0.997196	−	0.0748320i	$-0.0238420\pi$
$599$	3.80933e6	+	6.59795e6i	0.433792	+	0.751349i	−0.563404	+	0.826181i	$0.690509\pi$
$600$		0			0
$601$	9.78414e6			1.10493			0.552467	−	0.833535i	$-0.313686\pi$
$601$	9.78414e6			1.10493			0.552467	+	0.833535i	$0.313686\pi$
$602$	392010.	+	1.85924e6i	0.0440865	+	0.209095i
$603$		0			0
$604$	3.47245e6	−	6.01445e6i	0.387296	−	0.670817i
$605$	−507616.	−	879217.i	−0.0563829	−	0.0976580i
$606$		0			0
$607$	−926673.	+	1.60504e6i	−0.102083	+	0.176813i	−0.912543	−	0.408981i	$-0.865884\pi$
$607$	−926673.	+	1.60504e6i	−0.102083	+	0.176813i	0.810460	+	0.585795i	$0.199217\pi$
$608$	−1.05083e6			−0.115285
$609$		0			0
$610$	2.89578e6			0.315094
$611$	−3.39194e6	+	5.87501e6i	−0.367574	+	0.636657i
$612$		0			0
$613$	3.56048e6	+	6.16694e6i	0.382699	+	0.662855i	0.991447	−	0.130509i	$-0.0416612\pi$
$613$	3.56048e6	+	6.16694e6i	0.382699	+	0.662855i	−0.608748	+	0.793364i	$0.708328\pi$
$614$	−83708.7	+	144988.i	−0.00896086	+	0.0155207i
$615$		0			0
$616$	2.68515e6	+	877325.i	0.285112	+	0.0931555i
$617$	2.75212e6			0.291041			0.145521	−	0.989355i	$-0.453514\pi$
$617$	2.75212e6			0.291041			0.145521	+	0.989355i	$0.453514\pi$
$618$		0			0
$619$	6.51660e6	+	1.12871e7i	0.683588	+	1.18401i	0.973878	+	0.227070i	$0.0729147\pi$
$619$	6.51660e6	+	1.12871e7i	0.683588	+	1.18401i	−0.290291	+	0.956939i	$0.593752\pi$
$620$	−1.26636e6	−	2.19341e6i	−0.132306	−	0.229160i
$621$		0			0
$622$	−9.16758e6			−0.950120
$623$	2.08600e6	+	9.89358e6i	0.215325	+	1.02125i
$624$		0			0
$625$	−2.63935e6	+	4.57149e6i	−0.270269	+	0.468120i
$626$	4.54299e6	+	7.86869e6i	0.463347	+	0.802540i
$627$		0			0
$628$	4.09277e6	−	7.08889e6i	0.414112	−	0.717264i
$629$	−1.03597e7			−1.04404
$630$		0			0
$631$	−4.40820e6			−0.440745			−0.220373	−	0.975416i	$-0.570727\pi$
$631$	−4.40820e6			−0.440745			−0.220373	+	0.975416i	$0.570727\pi$
$632$	−1.12001e6	+	1.93992e6i	−0.111540	+	0.193193i
$633$		0			0
$634$	3.96949e6	+	6.87535e6i	0.392203	+	0.679316i
$635$	308474.	−	534293.i	0.0303588	−	0.0525829i
$636$		0			0
$637$	−1.31959e6	+	1.21712e7i	−0.128852	+	1.18846i
$638$	−7.10616e6			−0.691168
$639$		0			0
$640$	−184257.	−	319143.i	−0.0177818	−	0.0307989i
$641$	−3.99195e6	−	6.91426e6i	−0.383742	−	0.664661i	0.607851	−	0.794051i	$-0.292032\pi$
$641$	−3.99195e6	−	6.91426e6i	−0.383742	−	0.664661i	−0.991594	+	0.129389i	$0.958698\pi$
$642$		0			0
$643$	1.52102e6			0.145080			0.0725398	−	0.997366i	$-0.476890\pi$
$643$	1.52102e6			0.145080			0.0725398	+	0.997366i	$0.476890\pi$
$644$	2.19527e6	−	1.97012e6i	0.208580	−	0.187188i
$645$		0			0
$646$	−1.66213e6	+	2.87890e6i	−0.156706	+	0.271422i
$647$	−6.26247e6	−	1.08469e7i	−0.588146	−	1.01870i	−0.994475	−	0.104972i	$-0.966525\pi$
$647$	−6.26247e6	−	1.08469e7i	−0.588146	−	1.01870i	0.406329	−	0.913727i	$-0.366809\pi$
$648$		0			0
$649$	5.17096e6	−	8.95637e6i	0.481903	−	0.834681i
$650$	−7.63116e6			−0.708447
$651$		0			0
$652$	−4.02031e6			−0.370374
$653$	−8.53702e6	+	1.47865e7i	−0.783471	+	1.35701i	0.146436	+	0.989220i	$0.453220\pi$
$653$	−8.53702e6	+	1.47865e7i	−0.783471	+	1.35701i	−0.929908	+	0.367792i	$0.880114\pi$
$654$		0			0
$655$	−1.69115e6	−	2.92916e6i	−0.154021	−	0.266772i
$656$	150209.	−	260169.i	0.0136281	−	0.0236046i
$657$		0			0
$658$	4.59069e6	+	1.49993e6i	0.413346	+	0.135054i
$659$	2.12585e6			0.190686			0.0953432	−	0.995444i	$-0.469605\pi$
$659$	2.12585e6			0.190686			0.0953432	+	0.995444i	$0.469605\pi$
$660$		0			0
$661$	1.30005e6	+	2.25176e6i	0.115733	+	0.200456i	0.918073	−	0.396412i	$-0.129745\pi$
$661$	1.30005e6	+	2.25176e6i	0.115733	+	0.200456i	−0.802339	+	0.596868i	$0.796412\pi$
$662$	1.27692e6	+	2.21169e6i	0.113245	+	0.196146i
$663$		0			0
$664$	5.51635e6			0.485547
$665$	−2.84438e6	−	929350.i	−0.249421	−	0.0814940i
$666$		0			0
$667$	−3.71010e6	+	6.42608e6i	−0.322902	+	0.559283i
$668$	3.35421e6	+	5.80967e6i	0.290837	+	0.503744i
$669$		0			0
$670$	−960472.	+	1.66359e6i	−0.0826604	+	0.143172i
$671$	−1.09582e7			−0.939577
$672$		0			0
$673$	−1.44746e7			−1.23188			−0.615942	−	0.787792i	$-0.711224\pi$
$673$	−1.44746e7			−1.23188			−0.615942	+	0.787792i	$0.711224\pi$
$674$	5.44052e6	−	9.42326e6i	0.461308	−	0.799008i
$675$		0			0
$676$	−1.27437e6	−	2.20728e6i	−0.107258	−	0.185776i
$677$	−1.64423e6	+	2.84788e6i	−0.137876	+	0.238809i	−0.926693	−	0.375820i	$-0.877361\pi$
$677$	−1.64423e6	+	2.84788e6i	−0.137876	+	0.238809i	0.788816	+	0.614629i	$0.210694\pi$
$678$		0			0
$679$	1.56079e7	−	1.40071e7i	1.29918	−	1.16594i
$680$	−1.16578e6			−0.0966819
$681$		0			0
$682$	4.79217e6	+	8.30027e6i	0.394522	+	0.683332i
$683$	4.40943e6	+	7.63736e6i	0.361685	+	0.626458i	0.988238	−	0.152921i	$-0.0488681\pi$
$683$	4.40943e6	+	7.63736e6i	0.361685	+	0.626458i	−0.626553	+	0.779379i	$0.715535\pi$
$684$		0			0
$685$	2.16156e6			0.176011
$686$	8.67219e6	−	868394.i	0.703588	−	0.0704541i
$687$		0			0
$688$	−469013.	+	812355.i	−0.0377758	+	0.0654297i
$689$	−1.29814e7	−	2.24844e7i	−1.04177	−	1.80440i
$690$		0			0
$691$	4.29808e6	−	7.44450e6i	0.342436	−	0.593117i	−0.642448	−	0.766329i	$-0.722081\pi$
$691$	4.29808e6	−	7.44450e6i	0.342436	−	0.593117i	0.984885	+	0.173212i	$0.0554146\pi$
$692$	7.38202e6			0.586017
$693$		0			0
$694$	1.04831e7			0.826208
$695$	1.13423e6	−	1.96454e6i	0.0890713	−	0.154276i
$696$		0			0
$697$	−475180.	−	823035.i	−0.0370490	−	0.0641707i
$698$	1.15118e6	−	1.99391e6i	0.0894348	−	0.154906i
$699$		0			0
$700$	1.12081e6	+	5.31583e6i	0.0864545	+	0.410040i
$701$	−2.06437e7			−1.58669			−0.793347	−	0.608770i	$-0.791663\pi$
$701$	−2.06437e7			−1.58669			−0.793347	+	0.608770i	$0.791663\pi$
$702$		0			0
$703$	−6.56364e6	−	1.13686e7i	−0.500906	−	0.867595i
$704$	697266.	+	1.20770e6i	0.0530233	+	0.0918390i
$705$		0			0
$706$	−1.03589e7			−0.782169
$707$	8.11530e6	+	2.65153e6i	0.610599	+	0.199503i
$708$		0			0
$709$	213441.	−	369691.i	0.0159464	−	0.0276200i	−0.857942	−	0.513746i	$-0.828257\pi$
$709$	213441.	−	369691.i	0.0159464	−	0.0276200i	0.873888	+	0.486126i	$0.161591\pi$
$710$	2.75098e6	+	4.76484e6i	0.204806	+	0.354734i
$711$		0			0
$712$	−2.49576e6	+	4.32279e6i	−0.184503	+	0.319569i
$713$	1.00079e7			0.737257
$714$		0			0
$715$	−5.57805e6			−0.408054
$716$	5.93365e6	−	1.02774e7i	0.432553	−	0.749203i
$717$		0			0
$718$	−5.73558e6	−	9.93431e6i	−0.415208	−	0.719162i
$719$	1.90362e6	−	3.29716e6i	0.137328	−	0.237858i	−0.789157	−	0.614192i	$-0.789482\pi$
$719$	1.90362e6	−	3.29716e6i	0.137328	−	0.237858i	0.926484	+	0.376334i	$0.122815\pi$
$720$		0			0
$721$	−3.48230e6	−	1.65160e7i	−0.249476	−	1.18322i
$722$	5.69204e6			0.406373
$723$		0			0
$724$	−2.41097e6	−	4.17592e6i	−0.170940	−	0.296077i
$725$	−6.83326e6	−	1.18356e7i	−0.482817	−	0.836264i
$726$		0			0
$727$	−2.22044e7			−1.55813			−0.779065	−	0.626943i	$-0.784306\pi$
$727$	−2.22044e7			−1.55813			−0.779065	+	0.626943i	$0.784306\pi$
$728$	−4.49798e6	+	4.03667e6i	−0.314550	+	0.282290i
$729$		0			0
$730$	−1.85642e6	+	3.21541e6i	−0.128934	+	0.223321i
$731$	1.48371e6	+	2.56986e6i	0.102696	+	0.177875i
$732$		0			0
$733$	1.45286e7	−	2.51643e7i	0.998766	−	1.72991i	0.456365	−	0.889793i	$-0.349151\pi$
$733$	1.45286e7	−	2.51643e7i	0.998766	−	1.72991i	0.542401	−	0.840120i	$-0.317515\pi$
$734$	7.81804e6			0.535621
$735$		0			0
$736$	1.45616e6			0.0990865
$737$	3.63461e6	−	6.29533e6i	0.246484	−	0.426923i
$738$		0			0
$739$	−1.06761e7	−	1.84916e7i	−0.719122	−	1.24556i	−0.961348	−	0.275337i	$-0.911211\pi$
$739$	−1.06761e7	−	1.84916e7i	−0.719122	−	1.24556i	0.242226	−	0.970220i	$-0.422123\pi$
$740$	2.30180e6	−	3.98683e6i	0.154521	−	0.267638i
$741$		0			0
$742$	−1.37559e7	+	1.23451e7i	−0.917234	+	0.823163i
$743$	−3.91874e6			−0.260420			−0.130210	−	0.991486i	$-0.541565\pi$
$743$	−3.91874e6			−0.260420			−0.130210	+	0.991486i	$0.541565\pi$
$744$		0			0
$745$	4.05924e6	+	7.03081e6i	0.267950	+	0.464103i
$746$	4.42219e6	+	7.65946e6i	0.290931	+	0.503908i
$747$		0			0
$748$	4.41155e6			0.288295
$749$	69298.0	+	328669.i	0.00451353	+	0.0214069i
$750$		0			0
$751$	−2.83456e6	+	4.90960e6i	−0.183394	+	0.317648i	−0.943034	−	0.332696i	$-0.892042\pi$
$751$	−2.83456e6	+	4.90960e6i	−0.183394	+	0.317648i	0.759640	+	0.650344i	$0.225375\pi$
$752$	1.19209e6	+	2.06476e6i	0.0768713	+	0.133145i
$753$		0			0
$754$	7.60180e6	−	1.31667e7i	0.486954	−	0.843429i
$755$	9.76293e6			0.623323
$756$		0			0
$757$	−1.91706e7			−1.21590			−0.607949	−	0.793976i	$-0.708007\pi$
$757$	−1.91706e7			−1.21590			−0.607949	+	0.793976i	$0.708007\pi$
$758$	7.62463e6	−	1.32063e7i	0.481999	−	0.834846i
$759$		0			0
$760$	−738614.	−	1.27932e6i	−0.0463856	−	0.0803423i
$761$	7.31680e6	−	1.26731e7i	0.457993	−	0.793268i	−0.540861	−	0.841112i	$-0.681902\pi$
$761$	7.31680e6	−	1.26731e7i	0.457993	−	0.793268i	0.998855	+	0.0478438i	$0.0152350\pi$
$762$		0			0
$763$	1.36360e7	+	4.45531e6i	0.847958	+	0.277056i
$764$	−4.21092e6			−0.261002
$765$		0			0
$766$	−7.61212e6	−	1.31846e7i	−0.468742	−	0.811884i
$767$	1.10632e7	+	1.91621e7i	0.679038	+	1.17613i
$768$		0			0
$769$	1.57337e7			0.959432			0.479716	−	0.877424i	$-0.340740\pi$
$769$	1.57337e7			0.959432			0.479716	+	0.877424i	$0.340740\pi$
$770$	819266.	+	3.88565e6i	0.0497964	+	0.236176i
$771$		0			0
$772$	6.64902e6	−	1.15164e7i	0.401526	−	0.695464i
$773$	2.02452e6	+	3.50658e6i	0.121864	+	0.211074i	0.920503	−	0.390736i	$-0.127780\pi$
$773$	2.02452e6	+	3.50658e6i	0.121864	+	0.211074i	−0.798639	+	0.601810i	$0.794446\pi$
$774$		0			0
$775$	−9.21626e6	+	1.59630e7i

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)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(11.2462 - 19.4789i) q^{5} +(-96.4847 + 86.5893i) q^{7} -64.0000 q^{8} +O(q^{10})\)	\(q+(2.00000 - 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(11.2462 - 19.4789i) q^{5} +(-96.4847 + 86.5893i) q^{7} -64.0000 q^{8} +(-44.9847 - 77.9158i) q^{10} +(170.231 + 294.849i) q^{11} -728.416 q^{13} +(106.985 + 507.411i) q^{14} +(-128.000 + 221.703i) q^{16} +(404.923 + 701.348i) q^{17} +(-513.101 + 888.717i) q^{19} -359.878 q^{20} +1361.85 q^{22} +(711.015 - 1231.51i) q^{23} +(1309.55 + 2268.20i) q^{25} +(-1456.83 + 2523.31i) q^{26} +(1971.69 + 644.217i) q^{28} -5218.03 q^{29} +(3518.87 + 6094.87i) q^{31} +(512.000 + 886.810i) q^{32} +3239.39 q^{34} +(601.584 + 2853.22i) q^{35} +(-6396.05 + 11078.3i) q^{37} +(2052.40 + 3554.87i) q^{38} +(-719.755 + 1246.65i) q^{40} -1173.51 q^{41} +3664.17 q^{43} +(2723.69 - 4717.58i) q^{44} +(-2844.06 - 4926.06i) q^{46} +(4656.60 - 8065.46i) q^{47} +(1811.59 - 16709.1i) q^{49} +10476.4 q^{50} +(5827.33 + 10093.2i) q^{52} +(17821.4 + 30867.6i) q^{53} +7657.78 q^{55} +(6175.02 - 5541.71i) q^{56} +(-10436.1 + 18075.8i) q^{58} +(-15188.1 - 26306.5i) q^{59} +(-16093.1 + 27874.1i) q^{61} +28151.0 q^{62} +4096.00 q^{64} +(-8191.89 + 14188.8i) q^{65} +(-10675.5 - 18490.6i) q^{67} +(6478.78 - 11221.6i) q^{68} +(11087.0 + 3622.49i) q^{70} -61153.7 q^{71} +(-20633.9 - 35739.0i) q^{73} +(25584.2 + 44313.2i) q^{74} +16419.2 q^{76} +(-41955.4 - 13708.2i) q^{77} +(17500.2 - 30311.3i) q^{79} +(2879.02 + 4986.61i) q^{80} +(-2347.01 + 4065.14i) q^{82} -86193.0 q^{83} +18215.4 q^{85} +(7328.33 - 12693.0i) q^{86} +(-10894.8 - 18870.3i) q^{88} +(38996.3 - 67543.6i) q^{89} +(70281.0 - 63073.0i) q^{91} -22752.5 q^{92} +(-18626.4 - 32261.9i) q^{94} +(11540.8 + 19989.3i) q^{95} -161765. q^{97} +(-54258.8 - 39693.7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 32 q^{4} - 53 q^{5} + 6 q^{7} - 256 q^{8}+O(q^{10}) \) 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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