LMFDB - Embedded newform 1638.2.bj.g.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (of order $6$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.1
Root			$0.500000 - 0.399480i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.g.1135.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.38938i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.38938i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(1.69469 + 2.93529i) q^{10} +(-0.712505 + 0.411365i) q^{11} +(-2.74987 + 2.33200i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.29065 + 3.96752i) q^{17} +(-5.11492 - 2.95310i) q^{19} +(-2.93529 - 1.69469i) q^{20} +(0.411365 - 0.712505i) q^{22} +(3.06527 + 5.30921i) q^{23} -6.48787 q^{25} +(1.21546 - 3.39451i) q^{26} +(0.866025 - 0.500000i) q^{28} +(-3.43406 - 5.94797i) q^{29} +4.28683i q^{31} +(0.866025 + 0.500000i) q^{32} -4.58130i q^{34} +(1.69469 - 2.93529i) q^{35} +(-8.39253 + 4.84543i) q^{37} +5.90621 q^{38} +3.38938 q^{40} +(0.0774019 - 0.0446880i) q^{41} +(3.67687 - 6.36853i) q^{43} +0.822730i q^{44} +(-5.30921 - 3.06527i) q^{46} +11.1759i q^{47} +(0.500000 + 0.866025i) q^{49} +(5.61866 - 3.24394i) q^{50} +(0.644638 + 3.54746i) q^{52} +7.01530 q^{53} +(1.39427 + 2.41495i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(5.94797 + 3.43406i) q^{58} +(-1.50790 - 0.870585i) q^{59} +(-1.18972 + 2.06066i) q^{61} +(-2.14342 - 3.71251i) q^{62} -1.00000 q^{64} +(7.90403 + 9.32034i) q^{65} +(0.252636 - 0.145859i) q^{67} +(2.29065 + 3.96752i) q^{68} +3.38938i q^{70} +(-9.48158 - 5.47419i) q^{71} +12.7187i q^{73} +(4.84543 - 8.39253i) q^{74} +(-5.11492 + 2.95310i) q^{76} -0.822730 q^{77} +9.95602 q^{79} +(-2.93529 + 1.69469i) q^{80} +(-0.0446880 + 0.0774019i) q^{82} +3.23553i q^{83} +(13.4474 + 7.76387i) q^{85} +7.35374i q^{86} +(-0.411365 - 0.712505i) q^{88} +(-6.96514 + 4.02133i) q^{89} +(-3.54746 + 0.644638i) q^{91} +6.13055 q^{92} +(-5.58797 - 9.67865i) q^{94} +(-10.0092 + 17.3364i) q^{95} +(12.7945 + 7.38693i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4}+O(q^{10}) $ 12 * q + 6 * q^4	$ 12 q + 6 q^{4} - 2 q^{10} + 18 q^{11} - 8 q^{13} - 12 q^{14} - 6 q^{16} - 4 q^{17} + 12 q^{19} - 2 q^{22} + 6 q^{23} - 24 q^{25} + 14 q^{26} + 10 q^{29} - 2 q^{35} - 6 q^{37} - 8 q^{38} - 4 q^{40} + 24 q^{41} + 26 q^{43} - 6 q^{46} + 6 q^{49} + 12 q^{50} - 4 q^{52} - 36 q^{53} - 6 q^{55} - 6 q^{56} + 24 q^{58} - 6 q^{59} - 28 q^{61} + 2 q^{62} - 12 q^{64} + 34 q^{65} - 42 q^{67} + 4 q^{68} - 48 q^{71} + 12 q^{76} + 4 q^{77} + 44 q^{79} + 6 q^{82} + 54 q^{85} + 2 q^{88} - 12 q^{89} - 16 q^{91} + 12 q^{92} + 8 q^{94} - 32 q^{95} + 60 q^{97}+O(q^{100}) $ 12 * q + 6 * q^4 - 2 * q^10 + 18 * q^11 - 8 * q^13 - 12 * q^14 - 6 * q^16 - 4 * q^17 + 12 * q^19 - 2 * q^22 + 6 * q^23 - 24 * q^25 + 14 * q^26 + 10 * q^29 - 2 * q^35 - 6 * q^37 - 8 * q^38 - 4 * q^40 + 24 * q^41 + 26 * q^43 - 6 * q^46 + 6 * q^49 + 12 * q^50 - 4 * q^52 - 36 * q^53 - 6 * q^55 - 6 * q^56 + 24 * q^58 - 6 * q^59 - 28 * q^61 + 2 * q^62 - 12 * q^64 + 34 * q^65 - 42 * q^67 + 4 * q^68 - 48 * q^71 + 12 * q^76 + 4 * q^77 + 44 * q^79 + 6 * q^82 + 54 * q^85 + 2 * q^88 - 12 * q^89 - 16 * q^91 + 12 * q^92 + 8 * q^94 - 32 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	3.38938i		−	1.51578i	−0.652385	−	0.757888i	$-0.726232\pi$
$5$		−	3.38938i		−	1.51578i	0.652385	−	0.757888i	$-0.273768\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.69469	+	2.93529i	0.535907	+	0.928219i
$11$	−0.712505	+	0.411365i	−0.214828	+	0.124031i	−0.603553	−	0.797323i	$-0.706249\pi$
$11$	−0.712505	+	0.411365i	−0.214828	+	0.124031i	0.388725	+	0.921354i	$0.372916\pi$
$12$		0			0
$13$	−2.74987	+	2.33200i	−0.762676	+	0.646781i
$13$	−2.74987	+	2.33200i	−0.762676	+	0.646781i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.29065	+	3.96752i	−0.555564	+	0.962265i	0.442296	+	0.896869i	$0.354164\pi$
$17$	−2.29065	+	3.96752i	−0.555564	+	0.962265i	−0.997859	+	0.0653954i	$0.979169\pi$
$18$		0			0
$19$	−5.11492	−	2.95310i	−1.17344	−	0.677488i	−0.218955	−	0.975735i	$-0.570265\pi$
$19$	−5.11492	−	2.95310i	−1.17344	−	0.677488i	−0.954489	+	0.298247i	$0.903598\pi$
$20$	−2.93529	−	1.69469i	−0.656350	−	0.378944i
$21$		0			0
$22$	0.411365	−	0.712505i	0.0877033	−	0.151907i
$23$	3.06527	+	5.30921i	0.639154	+	1.10705i	0.985619	+	0.168984i	$0.0540485\pi$
$23$	3.06527	+	5.30921i	0.639154	+	1.10705i	−0.346465	+	0.938063i	$0.612618\pi$
$24$		0			0
$25$	−6.48787			−1.29757
$26$	1.21546	−	3.39451i	0.238370	−	0.665717i
$27$		0			0
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	−3.43406	−	5.94797i	−0.637690	−	1.10451i	−0.985938	−	0.167109i	$-0.946557\pi$
$29$	−3.43406	−	5.94797i	−0.637690	−	1.10451i	0.348249	−	0.937402i	$-0.386776\pi$
$30$		0			0
$31$			4.28683i			0.769938i	0.922930	+	0.384969i	$0.125788\pi$
$31$			4.28683i			0.769938i	−0.922930	+	0.384969i	$0.874212\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	4.58130i		−	0.785686i
$35$	1.69469	−	2.93529i	0.286455	−	0.496154i
$36$		0			0
$37$	−8.39253	+	4.84543i	−1.37972	+	0.796584i	−0.992126	−	0.125245i	$-0.960028\pi$
$37$	−8.39253	+	4.84543i	−1.37972	+	0.796584i	−0.387598	+	0.921829i	$0.626695\pi$
$38$	5.90621			0.958113
$39$		0			0
$40$	3.38938			0.535907
$41$	0.0774019	−	0.0446880i	0.0120881	−	0.00697909i	−0.493944	−	0.869494i	$-0.664445\pi$
$41$	0.0774019	−	0.0446880i	0.0120881	−	0.00697909i	0.506032	+	0.862515i	$0.331112\pi$
$42$		0			0
$43$	3.67687	−	6.36853i	0.560718	−	0.971191i	−0.436716	−	0.899599i	$-0.643859\pi$
$43$	3.67687	−	6.36853i	0.560718	−	0.971191i	0.997434	−	0.0715921i	$-0.0228080\pi$
$44$			0.822730i			0.124031i
$45$		0			0
$46$	−5.30921	−	3.06527i	−0.782800	−	0.451950i
$47$			11.1759i			1.63018i	0.579335	+	0.815089i	$0.303312\pi$
$47$			11.1759i			1.63018i	−0.579335	+	0.815089i	$0.696688\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	5.61866	−	3.24394i	0.794599	−	0.458762i
$51$		0			0
$52$	0.644638	+	3.54746i	0.0893952	+	0.491944i
$53$	7.01530			0.963625			0.481813	−	0.876274i	$-0.339979\pi$
$53$	7.01530			0.963625			0.481813	+	0.876274i	$0.339979\pi$
$54$		0			0
$55$	1.39427	+	2.41495i	0.188003	+	0.325632i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	5.94797	+	3.43406i	0.781007	+	0.450915i
$59$	−1.50790	−	0.870585i	−0.196311	−	0.113340i	0.398622	−	0.917115i	$-0.369488\pi$
$59$	−1.50790	−	0.870585i	−0.196311	−	0.113340i	−0.594934	+	0.803775i	$0.702822\pi$
$60$		0			0
$61$	−1.18972	+	2.06066i	−0.152329	+	0.263841i	−0.932083	−	0.362245i	$-0.882011\pi$
$61$	−1.18972	+	2.06066i	−0.152329	+	0.263841i	0.779754	+	0.626085i	$0.215344\pi$
$62$	−2.14342	−	3.71251i	−0.272214	−	0.471489i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	7.90403	+	9.32034i	0.980374	+	1.15605i
$66$		0			0
$67$	0.252636	−	0.145859i	0.0308644	−	0.0178196i	−0.484488	−	0.874798i	$-0.660994\pi$
$67$	0.252636	−	0.145859i	0.0308644	−	0.0178196i	0.515353	+	0.856978i	$0.327661\pi$
$68$	2.29065	+	3.96752i	0.277782	+	0.481132i
$69$		0			0
$70$			3.38938i			0.405108i
$71$	−9.48158	−	5.47419i	−1.12526	−	0.649667i	−0.182519	−	0.983202i	$-0.558425\pi$
$71$	−9.48158	−	5.47419i	−1.12526	−	0.649667i	−0.942738	+	0.333535i	$0.891758\pi$
$72$		0			0
$73$			12.7187i			1.48861i	0.667841	+	0.744304i	$0.267219\pi$
$73$			12.7187i			1.48861i	−0.667841	+	0.744304i	$0.732781\pi$
$74$	4.84543	−	8.39253i	0.563270	−	0.975612i
$75$		0			0
$76$	−5.11492	+	2.95310i	−0.586722	+	0.338744i
$77$	−0.822730			−0.0937588
$78$		0			0
$79$	9.95602			1.12014			0.560070	−	0.828445i	$-0.310774\pi$
$79$	9.95602			1.12014			0.560070	+	0.828445i	$0.310774\pi$
$80$	−2.93529	+	1.69469i	−0.328175	+	0.189472i
$81$		0			0
$82$	−0.0446880	+	0.0774019i	−0.00493496	+	0.00854761i
$83$			3.23553i			0.355146i	0.984108	+	0.177573i	$0.0568246\pi$
$83$			3.23553i			0.355146i	−0.984108	+	0.177573i	$0.943175\pi$
$84$		0			0
$85$	13.4474	+	7.76387i	1.45858	+	0.842110i
$86$			7.35374i			0.792974i
$87$		0			0
$88$	−0.411365	−	0.712505i	−0.0438517	−	0.0759533i
$89$	−6.96514	+	4.02133i	−0.738303	+	0.426260i	−0.821452	−	0.570277i	$-0.806836\pi$
$89$	−6.96514	+	4.02133i	−0.738303	+	0.426260i	0.0831487	+	0.996537i	$0.473502\pi$
$90$		0			0
$91$	−3.54746	+	0.644638i	−0.371874	+	0.0675764i
$92$	6.13055			0.639154
$93$		0			0
$94$	−5.58797	−	9.67865i	−0.576355	−	0.998277i
$95$	−10.0092	+	17.3364i	−1.02692	+	1.77868i
$96$		0			0
$97$	12.7945	+	7.38693i	1.29909	+	0.750029i	0.980247	−	0.197778i	$-0.0633726\pi$
$97$	12.7945	+	7.38693i	1.29909	+	0.750029i	0.318842	+	0.947808i	$0.396706\pi$
$98$	−0.866025	−	0.500000i	−0.0874818	−	0.0505076i
$99$		0			0
$100$	−3.24394	+	5.61866i	−0.324394	+	0.561866i
$101$	4.11988	+	7.13584i	0.409943	+	0.710043i	0.994883	−	0.101034i	$-0.0322151\pi$
$101$	4.11988	+	7.13584i	0.409943	+	0.710043i	−0.584939	+	0.811077i	$0.698882\pi$
$102$		0			0
$103$	−13.3231			−1.31277			−0.656383	−	0.754428i	$-0.727914\pi$
$103$	−13.3231			−1.31277			−0.656383	+	0.754428i	$0.727914\pi$
$104$	−2.33200	−	2.74987i	−0.228671	−	0.269647i
$105$		0			0
$106$	−6.07543	+	3.50765i	−0.590098	+	0.340693i
$107$	−4.51325	−	7.81717i	−0.436312	−	0.755715i	0.561090	−	0.827755i	$-0.310382\pi$
$107$	−4.51325	−	7.81717i	−0.436312	−	0.755715i	−0.997402	+	0.0720404i	$0.977049\pi$
$108$		0			0
$109$			0.397192i			0.0380441i	0.999819	+	0.0190220i	$0.00605527\pi$
$109$			0.397192i			0.0380441i	−0.999819	+	0.0190220i	$0.993945\pi$
$110$	−2.41495	−	1.39427i	−0.230256	−	0.132939i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	2.23661	−	3.87392i	0.210402	−	0.364428i	−0.741438	−	0.671021i	$-0.765856\pi$
$113$	2.23661	−	3.87392i	0.210402	−	0.364428i	0.951841	+	0.306594i	$0.0991892\pi$
$114$		0			0
$115$	17.9949	−	10.3894i	1.67803	−	0.968813i
$116$	−6.86813			−0.637690
$117$		0			0
$118$	1.74117			0.160288
$119$	−3.96752	+	2.29065i	−0.363702	+	0.209983i
$120$		0			0
$121$	−5.16156	+	8.94008i	−0.469232	+	0.812735i
$122$		−	2.37945i		−	0.215425i
$123$		0			0
$124$	3.71251	+	2.14342i	0.333393	+	0.192484i
$125$			5.04295i			0.451056i
$126$		0			0
$127$	−0.270063	−	0.467763i	−0.0239642	−	0.0415073i	0.853795	−	0.520610i	$-0.174295\pi$
$127$	−0.270063	−	0.467763i	−0.0239642	−	0.0415073i	−0.877759	+	0.479103i	$0.840962\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−11.5053	−	4.11964i	−1.00908	−	0.361316i
$131$	7.72615			0.675037			0.337518	−	0.941319i	$-0.390413\pi$
$131$	7.72615			0.675037			0.337518	+	0.941319i	$0.390413\pi$
$132$		0			0
$133$	−2.95310	−	5.11492i	−0.256067	−	0.443520i
$134$	−0.145859	+	0.252636i	−0.0126003	+	0.0218244i
$135$		0			0
$136$	−3.96752	−	2.29065i	−0.340212	−	0.196421i
$137$	−10.8600	−	6.27005i	−0.927837	−	0.535687i	−0.0417099	−	0.999130i	$-0.513281\pi$
$137$	−10.8600	−	6.27005i	−0.927837	−	0.535687i	−0.886127	+	0.463443i	$0.846614\pi$
$138$		0			0
$139$	−6.04868	+	10.4766i	−0.513042	+	0.888615i	0.486843	+	0.873489i	$0.338148\pi$
$139$	−6.04868	+	10.4766i	−0.513042	+	0.888615i	−0.999886	+	0.0151258i	$0.995185\pi$
$140$	−1.69469	−	2.93529i	−0.143227	−	0.248077i
$141$		0			0
$142$	10.9484			0.918768
$143$	0.999992	−	2.79276i	0.0836235	−	0.233543i
$144$		0			0
$145$	−20.1599	+	11.6393i	−1.67419	+	0.966594i
$146$	−6.35934	−	11.0147i	−0.526303	−	0.911583i
$147$		0			0
$148$			9.69086i			0.796584i
$149$	−14.7292	−	8.50389i	−1.20666	−	0.696666i	−0.244633	−	0.969616i	$-0.578667\pi$
$149$	−14.7292	−	8.50389i	−1.20666	−	0.696666i	−0.962028	+	0.272950i	$0.912001\pi$
$150$		0			0
$151$		−	5.54567i		−	0.451300i	−0.974208	−	0.225650i	$-0.927549\pi$
$151$		−	5.54567i		−	0.451300i	0.974208	−	0.225650i	$-0.0724506\pi$
$152$	2.95310	−	5.11492i	0.239528	−	0.414875i
$153$		0			0
$154$	0.712505	−	0.411365i	0.0574153	−	0.0331487i
$155$	14.5297			1.16705
$156$		0			0
$157$	2.29353			0.183044			0.0915218	−	0.995803i	$-0.470827\pi$
$157$	2.29353			0.183044			0.0915218	+	0.995803i	$0.470827\pi$
$158$	−8.62217	+	4.97801i	−0.685943	+	0.396029i
$159$		0			0
$160$	1.69469	−	2.93529i	0.133977	−	0.232055i
$161$			6.13055i			0.483155i
$162$		0			0
$163$	−20.2269	−	11.6780i	−1.58429	−	0.914691i	−0.994223	−	0.107337i	$-0.965768\pi$
$163$	−20.2269	−	11.6780i	−1.58429	−	0.914691i	−0.590068	−	0.807354i	$-0.700899\pi$
$164$		−	0.0893760i		−	0.00697909i
$165$		0			0
$166$	−1.61777	−	2.80205i	−0.125563	−	0.217482i
$167$	18.8603	−	10.8890i	1.45945	−	0.842614i	0.460467	−	0.887677i	$-0.347682\pi$
$167$	18.8603	−	10.8890i	1.45945	−	0.842614i	0.998984	+	0.0450626i	$0.0143487\pi$
$168$		0			0
$169$	2.12355	−	12.8254i	0.163350	−	0.986568i
$170$	−15.5277			−1.19092
$171$		0			0
$172$	−3.67687	−	6.36853i	−0.280359	−	0.485596i
$173$	−4.04866	+	7.01249i	−0.307814	+	0.533150i	−0.977884	−	0.209148i	$-0.932931\pi$
$173$	−4.04866	+	7.01249i	−0.307814	+	0.533150i	0.670070	+	0.742298i	$0.266264\pi$
$174$		0			0
$175$	−5.61866	−	3.24394i	−0.424731	−	0.245218i
$176$	0.712505	+	0.411365i	0.0537071	+	0.0310078i
$177$		0			0
$178$	4.02133	−	6.96514i	0.301411	−	0.522059i
$179$	−4.95442	−	8.58130i	−0.370310	−	0.641397i	0.619303	−	0.785152i	$-0.287415\pi$
$179$	−4.95442	−	8.58130i	−0.370310	−	0.641397i	−0.989613	+	0.143756i	$0.954082\pi$
$180$		0			0
$181$	1.27902			0.0950685			0.0475343	−	0.998870i	$-0.484864\pi$
$181$	1.27902			0.0950685			0.0475343	+	0.998870i	$0.484864\pi$
$182$	2.74987	−	2.33200i	0.203834	−	0.172859i
$183$		0			0
$184$	−5.30921	+	3.06527i	−0.391400	+	0.225975i
$185$	16.4230	+	28.4454i	1.20744	+	2.09135i
$186$		0			0
$187$		−	3.76917i		−	0.275629i
$188$	9.67865	+	5.58797i	0.705888	+	0.407545i
$189$		0			0
$190$		−	20.0184i		−	1.45228i
$191$	−5.01710	+	8.68988i	−0.363025	+	0.628777i	−0.988457	−	0.151501i	$-0.951589\pi$
$191$	−5.01710	+	8.68988i	−0.363025	+	0.628777i	0.625432	+	0.780278i	$0.284923\pi$
$192$		0			0
$193$	−13.7336	+	7.92911i	−0.988567	+	0.570750i	−0.904846	−	0.425740i	$-0.860014\pi$
$193$	−13.7336	+	7.92911i	−0.988567	+	0.570750i	−0.0837217	+	0.996489i	$0.526681\pi$
$194$	−14.7739			−1.06070
$195$		0			0
$196$	1.00000			0.0714286
$197$	−12.8242	+	7.40403i	−0.913683	+	0.527515i	−0.881614	−	0.471971i	$-0.843543\pi$
$197$	−12.8242	+	7.40403i	−0.913683	+	0.527515i	−0.0320686	+	0.999486i	$0.510210\pi$
$198$		0			0
$199$	−1.27771	+	2.21306i	−0.0905747	+	0.156880i	−0.907753	−	0.419505i	$-0.862204\pi$
$199$	−1.27771	+	2.21306i	−0.0905747	+	0.156880i	0.817178	+	0.576385i	$0.195537\pi$
$200$		−	6.48787i		−	0.458762i
$201$		0			0
$202$	−7.13584	−	4.11988i	−0.502076	−	0.289874i
$203$		−	6.86813i		−	0.482048i
$204$		0			0
$205$	−0.151464	−	0.262344i	−0.0105787	−	0.0183229i
$206$	11.5382	−	6.66156i	0.803901	−	0.464133i
$207$		0			0
$208$	3.39451	+	1.21546i	0.235367	+	0.0842767i
$209$	4.85921			0.336119
$210$		0			0
$211$	4.31824	+	7.47942i	0.297280	+	0.514904i	0.975513	−	0.219943i	$-0.0705872\pi$
$211$	4.31824	+	7.47942i	0.297280	+	0.514904i	−0.678233	+	0.734847i	$0.737254\pi$
$212$	3.50765	−	6.07543i	0.240906	−	0.417262i
$213$		0			0
$214$	7.81717	+	4.51325i	0.534371	+	0.308519i
$215$	−21.5853	−	12.4623i	−1.47211	−	0.849922i
$216$		0			0
$217$	−2.14342	+	3.71251i	−0.145505	+	0.252021i
$218$	−0.198596	−	0.343978i	−0.0134506	−	0.0232971i
$219$		0			0
$220$	2.78854			0.188003
$221$	−2.95328	−	16.2519i	−0.198659	−	1.09322i
$222$		0			0
$223$	−17.2579	+	9.96384i	−1.15567	+	0.667228i	−0.950263	−	0.311448i	$-0.899186\pi$
$223$	−17.2579	+	9.96384i	−1.15567	+	0.667228i	−0.205410	+	0.978676i	$0.565853\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$			4.47322i			0.297554i
$227$	−0.305381	−	0.176312i	−0.0202689	−	0.0117022i	0.489831	−	0.871817i	$-0.337058\pi$
$227$	−0.305381	−	0.176312i	−0.0202689	−	0.0117022i	−0.510100	+	0.860115i	$0.670392\pi$
$228$		0			0
$229$			8.31317i			0.549350i	0.961537	+	0.274675i	$0.0885702\pi$
$229$			8.31317i			0.549350i	−0.961537	+	0.274675i	$0.911430\pi$
$230$	−10.3894	+	17.9949i	−0.685054	+	1.18655i
$231$		0			0
$232$	5.94797	−	3.43406i	0.390504	−	0.225457i
$233$	15.3798			1.00756			0.503781	−	0.863831i	$-0.331942\pi$
$233$	15.3798			1.00756			0.503781	+	0.863831i	$0.331942\pi$
$234$		0			0
$235$	37.8795			2.47098
$236$	−1.50790	+	0.870585i	−0.0981557	+	0.0566702i
$237$		0			0
$238$	2.29065	−	3.96752i	0.148481	−	0.257176i
$239$			2.88606i			0.186684i	0.995634	+	0.0933418i	$0.0297549\pi$
$239$			2.88606i			0.186684i	−0.995634	+	0.0933418i	$0.970245\pi$
$240$		0			0
$241$	−5.42777	−	3.13372i	−0.349633	−	0.201861i	0.314891	−	0.949128i	$-0.398032\pi$
$241$	−5.42777	−	3.13372i	−0.349633	−	0.201861i	−0.664524	+	0.747267i	$0.731366\pi$
$242$		−	10.3231i		−	0.663595i
$243$		0			0
$244$	1.18972	+	2.06066i	0.0761643	+	0.131920i
$245$	2.93529	−	1.69469i	0.187529	−	0.108270i
$246$		0			0
$247$	20.9520	−	3.80736i	1.33314	−	0.242257i
$248$	−4.28683			−0.272214
$249$		0			0
$250$	−2.52148	−	4.36733i	−0.159472	−	0.276214i
$251$	−8.63325	+	14.9532i	−0.544926	+	0.943839i	0.453686	+	0.891162i	$0.350109\pi$
$251$	−8.63325	+	14.9532i	−0.544926	+	0.943839i	−0.998612	+	0.0526775i	$0.983224\pi$
$252$		0			0
$253$	−4.36805	−	2.52189i	−0.274617	−	0.158550i
$254$	0.467763	+	0.270063i	0.0293501	+	0.0169453i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.59655	+	9.69351i	0.349103	+	0.604664i	0.986090	−	0.166210i	$-0.0531530\pi$
$257$	5.59655	+	9.69351i	0.349103	+	0.604664i	−0.636987	+	0.770874i	$0.719820\pi$
$258$		0			0
$259$	−9.69086			−0.602161
$260$	12.0237	−	2.18492i	0.745676	−	0.135503i
$261$		0			0
$262$	−6.69104	+	3.86307i	−0.413374	+	0.238661i
$263$	−14.2913	−	24.7533i	−0.881240	−	1.52635i	−0.849963	−	0.526842i	$-0.823376\pi$
$263$	−14.2913	−	24.7533i	−0.881240	−	1.52635i	−0.0312773	−	0.999511i	$-0.509957\pi$
$264$		0			0
$265$		−	23.7775i		−	1.46064i
$266$	5.11492	+	2.95310i	0.313616	+	0.181066i
$267$		0			0
$268$		−	0.291719i		−	0.0178196i
$269$	−9.18769	+	15.9135i	−0.560183	+	0.970266i	0.437297	+	0.899317i	$0.355936\pi$
$269$	−9.18769	+	15.9135i	−0.560183	+	0.970266i	−0.997480	+	0.0709485i	$0.977397\pi$
$270$		0			0
$271$	17.6518	−	10.1913i	1.07227	−	0.619075i	0.143468	−	0.989655i	$-0.454174\pi$
$271$	17.6518	−	10.1913i	1.07227	−	0.619075i	0.928801	+	0.370580i	$0.120841\pi$
$272$	4.58130			0.277782
$273$		0			0
$274$	12.5401			0.757575
$275$	4.62264	−	2.66888i	0.278756	−	0.160940i
$276$		0			0
$277$	3.61609	−	6.26326i	0.217270	−	0.376323i	−0.736702	−	0.676217i	$-0.763618\pi$
$277$	3.61609	−	6.26326i	0.217270	−	0.376323i	0.953972	+	0.299894i	$0.0969514\pi$
$278$		−	12.0974i		−	0.725551i
$279$		0			0
$280$	2.93529	+	1.69469i	0.175417	+	0.101277i
$281$			12.4585i			0.743215i	0.928390	+	0.371607i	$0.121193\pi$
$281$			12.4585i			0.743215i	−0.928390	+	0.371607i	$0.878807\pi$
$282$		0			0
$283$	6.53035	+	11.3109i	0.388189	+	0.672363i	0.992206	−	0.124608i	$-0.0397674\pi$
$283$	6.53035	+	11.3109i	0.388189	+	0.672363i	−0.604017	+	0.796972i	$0.706434\pi$
$284$	−9.48158	+	5.47419i	−0.562628	+	0.324834i
$285$		0			0
$286$	0.530363	+	2.91860i	0.0313610	+	0.172580i
$287$	0.0893760			0.00527570
$288$		0			0
$289$	−1.99414	−	3.45395i	−0.117302	−	0.203174i
$290$	11.6393	−	20.1599i	0.683485	−	1.18383i
$291$		0			0
$292$	11.0147	+	6.35934i	0.644586	+	0.372152i
$293$	12.6078	+	7.27909i	0.736553	+	0.425249i	0.820815	−	0.571195i	$-0.193520\pi$
$293$	12.6078	+	7.27909i	0.736553	+	0.425249i	−0.0842617	+	0.996444i	$0.526853\pi$
$294$		0			0
$295$	−2.95074	+	5.11083i	−0.171799	+	0.297564i
$296$	−4.84543	−	8.39253i	−0.281635	−	0.487806i
$297$		0			0
$298$	17.0078			0.985235
$299$	−20.8102	−	7.45140i	−1.20348	−	0.430926i
$300$		0			0
$301$	6.36853	−	3.67687i	0.367076	−	0.211931i
$302$	2.77283	+	4.80269i	0.159559	+	0.276364i
$303$		0			0
$304$			5.90621i			0.338744i
$305$	6.98436	+	4.03242i	0.399923	+	0.230896i
$306$		0			0
$307$			3.24267i			0.185069i	0.995709	+	0.0925345i	$0.0294968\pi$
$307$			3.24267i			0.185069i	−0.995709	+	0.0925345i	$0.970503\pi$
$308$	−0.411365	+	0.712505i	−0.0234397	+	0.0405988i
$309$		0			0
$310$	−12.5831	+	7.26484i	−0.714671	+	0.412615i
$311$	10.2709			0.582408			0.291204	−	0.956661i	$-0.405944\pi$
$311$	10.2709			0.582408			0.291204	+	0.956661i	$0.405944\pi$
$312$		0			0
$313$	−6.13382			−0.346704			−0.173352	−	0.984860i	$-0.555460\pi$
$313$	−6.13382			−0.346704			−0.173352	+	0.984860i	$0.555460\pi$
$314$	−1.98625	+	1.14676i	−0.112091	+	0.0647157i
$315$		0			0
$316$	4.97801	−	8.62217i	0.280035	−	0.485035i
$317$			5.04487i			0.283348i	0.989913	+	0.141674i	$0.0452485\pi$
$317$			5.04487i			0.283348i	−0.989913	+	0.141674i	$0.954752\pi$
$318$		0			0
$319$	4.89358	+	2.82531i	0.273988	+	0.158187i
$320$			3.38938i			0.189472i
$321$		0			0
$322$	−3.06527	−	5.30921i	−0.170821	−	0.295871i
$323$	23.4330	−	13.5290i	1.30385	−	0.752776i
$324$		0			0
$325$	17.8408	−	15.1297i	0.989629	−	0.839246i
$326$	23.3560			1.29357
$327$		0			0
$328$	0.0446880	+	0.0774019i	0.00246748	+	0.00427380i
$329$	−5.58797	+	9.67865i	−0.308075	+	0.533601i
$330$		0			0
$331$	−19.9943	−	11.5437i	−1.09898	−	0.634499i	−0.163030	−	0.986621i	$-0.552127\pi$
$331$	−19.9943	−	11.5437i	−1.09898	−	0.634499i	−0.935954	+	0.352122i	$0.885460\pi$
$332$	2.80205	+	1.61777i	0.153783	+	0.0887865i
$333$		0			0
$334$	−10.8890	+	18.8603i	−0.595818	+	1.03199i
$335$	−0.494372	−	0.856278i	−0.0270104	−	0.0467834i
$336$		0			0
$337$	29.1429			1.58751			0.793757	−	0.608235i	$-0.208122\pi$
$337$	29.1429			1.58751			0.793757	+	0.608235i	$0.208122\pi$
$338$	4.57365	+	12.1689i	0.248774	+	0.661900i
$339$		0			0
$340$	13.4474	−	7.76387i	0.729288	−	0.421055i
$341$	−1.76345	−	3.05439i	−0.0954963	−	0.165405i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	6.36853	+	3.67687i	0.343368	+	0.198244i
$345$		0			0
$346$		−	8.09733i		−	0.435315i
$347$	−14.5541	+	25.2085i	−0.781306	+	1.35326i	0.149875	+	0.988705i	$0.452113\pi$
$347$	−14.5541	+	25.2085i	−0.781306	+	1.35326i	−0.931181	+	0.364557i	$0.881221\pi$
$348$		0			0
$349$	22.3263	−	12.8901i	1.19510	−	0.689992i	0.235642	−	0.971840i	$-0.424281\pi$
$349$	22.3263	−	12.8901i	1.19510	−	0.689992i	0.959459	+	0.281848i	$0.0909475\pi$
$350$	6.48787			0.346791
$351$		0			0
$352$	−0.822730			−0.0438517
$353$	8.58906	−	4.95890i	0.457149	−	0.263935i	−0.253695	−	0.967284i	$-0.581646\pi$
$353$	8.58906	−	4.95890i	0.457149	−	0.263935i	0.710845	+	0.703349i	$0.248313\pi$
$354$		0			0
$355$	−18.5541	+	32.1367i	−0.984750	+	1.70564i
$356$			8.04265i			0.426260i
$357$		0			0
$358$	8.58130	+	4.95442i	0.453536	+	0.261849i
$359$		−	25.2683i		−	1.33361i	−0.745233	−	0.666804i	$-0.767662\pi$
$359$		−	25.2683i		−	1.33361i	0.745233	−	0.666804i	$-0.232338\pi$
$360$		0			0
$361$	7.94164	+	13.7553i	0.417981	+	0.723964i
$362$	−1.10766	+	0.639508i	−0.0582174	+	0.0336118i
$363$		0			0
$364$	−1.21546	+	3.39451i	−0.0637072	+	0.177920i
$365$	43.1084			2.25640
$366$		0			0
$367$	−17.8919	−	30.9897i	−0.933950	−	1.61765i	−0.776496	−	0.630122i	$-0.783005\pi$
$367$	−17.8919	−	30.9897i	−0.933950	−	1.61765i	−0.157454	−	0.987526i	$-0.550329\pi$
$368$	3.06527	−	5.30921i	0.159788	−	0.276762i
$369$		0			0
$370$	−28.4454	−	16.4230i	−1.47881	−	0.853790i
$371$	6.07543	+	3.50765i	0.315420	+	0.182108i
$372$		0			0
$373$	11.6652	−	20.2047i	0.604000	−	1.04616i	−0.388209	−	0.921572i	$-0.626906\pi$
$373$	11.6652	−	20.2047i	0.604000	−	1.04616i	0.992209	−	0.124587i	$-0.0397607\pi$
$374$	1.88459	+	3.26420i	0.0974496	+	0.168788i
$375$		0			0
$376$	−11.1759			−0.576355
$377$	23.3139	+	8.34790i	1.20073	+	0.429939i
$378$		0			0
$379$	21.0502	−	12.1533i	1.08127	−	0.624274i	0.150034	−	0.988681i	$-0.452062\pi$
$379$	21.0502	−	12.1533i	1.08127	−	0.624274i	0.931240	+	0.364407i	$0.118728\pi$
$380$	10.0092	+	17.3364i	0.513460	+	0.889339i
$381$		0			0
$382$		−	10.0342i		−	0.513395i
$383$	−4.25348	−	2.45575i	−0.217343	−	0.125483i	0.387376	−	0.921922i	$-0.373381\pi$
$383$	−4.25348	−	2.45575i	−0.217343	−	0.125483i	−0.604719	+	0.796439i	$0.706715\pi$
$384$		0			0
$385$			2.78854i			0.142117i
$386$	7.92911	−	13.7336i	0.403581	−	0.699023i
$387$		0			0
$388$	12.7945	−	7.38693i	0.649545	−	0.375015i
$389$	5.14522			0.260873			0.130437	−	0.991457i	$-0.458362\pi$
$389$	5.14522			0.260873			0.130437	+	0.991457i	$0.458362\pi$
$390$		0			0
$391$	−28.0858			−1.42036
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$		0			0
$394$	7.40403	−	12.8242i	0.373009	−	0.646071i
$395$		−	33.7447i		−	1.69788i
$396$		0			0
$397$	−10.6954	−	6.17498i	−0.536786	−	0.309913i	0.206990	−	0.978343i	$-0.433633\pi$
$397$	−10.6954	−	6.17498i	−0.536786	−	0.309913i	−0.743775	+	0.668430i	$0.766967\pi$
$398$		−	2.55543i		−	0.128092i
$399$		0			0
$400$	3.24394	+	5.61866i	0.162197	+	0.280933i
$401$	−28.1366	+	16.2447i	−1.40508	+	0.811221i	−0.994908	−	0.100788i	$-0.967864\pi$
$401$	−28.1366	+	16.2447i	−1.40508	+	0.811221i	−0.410169	+	0.912010i	$0.634530\pi$
$402$		0			0
$403$	−9.99689	−	11.7882i	−0.497981	−	0.587213i
$404$	8.23976			0.409943
$405$		0			0
$406$	3.43406	+	5.94797i	0.170430	+	0.295193i
$407$	3.98648	−	6.90479i	0.197603	−	0.342258i
$408$		0			0
$409$	3.26348	+	1.88417i	0.161369	+	0.0931662i	0.578510	−	0.815676i	$-0.303635\pi$
$409$	3.26348	+	1.88417i	0.161369	+	0.0931662i	−0.417141	+	0.908842i	$0.636968\pi$
$410$	0.262344	+	0.151464i	0.0129563	+	0.00748029i
$411$		0			0
$412$	−6.66156	+	11.5382i	−0.328191	+	0.568444i
$413$	−0.870585	−	1.50790i	−0.0428387	−	0.0741988i
$414$		0			0
$415$	10.9664			0.538321
$416$	−3.54746	+	0.644638i	−0.173928	+	0.0316060i
$417$		0			0
$418$	−4.20820	+	2.42961i	−0.205830	+	0.118836i
$419$	−5.26504	−	9.11931i	−0.257214	−	0.445508i	0.708281	−	0.705931i	$-0.249471\pi$
$419$	−5.26504	−	9.11931i	−0.257214	−	0.445508i	−0.965495	+	0.260423i	$0.916138\pi$
$420$		0			0
$421$		−	24.9973i		−	1.21830i	−0.793057	−	0.609148i	$-0.791512\pi$
$421$		−	24.9973i		−	1.21830i	0.793057	−	0.609148i	$-0.208488\pi$
$422$	−7.47942	−	4.31824i	−0.364092	−	0.210209i
$423$		0			0
$424$			7.01530i			0.340693i
$425$	14.8614	−	25.7408i	0.720885	−	1.24861i
$426$		0			0
$427$	−2.06066	+	1.18972i	−0.0997225	+	0.0575748i
$428$	−9.02649			−0.436312
$429$		0			0
$430$	24.9246			1.20197
$431$	−10.3736	+	5.98919i	−0.499678	+	0.288489i	−0.728581	−	0.684960i	$-0.759820\pi$
$431$	−10.3736	+	5.98919i	−0.499678	+	0.288489i	0.228902	+	0.973449i	$0.426486\pi$
$432$		0			0
$433$	3.98475	−	6.90179i	0.191495	−	0.331679i	−0.754251	−	0.656586i	$-0.772000\pi$
$433$	3.98475	−	6.90179i	0.191495	−	0.331679i	0.945746	+	0.324907i	$0.105333\pi$
$434$		−	4.28683i		−	0.205775i
$435$		0			0
$436$	0.343978	+	0.198596i	0.0164736	+	0.00951101i
$437$		−	36.2083i		−	1.73208i
$438$		0			0
$439$	2.17827	+	3.77288i	0.103963	+	0.180070i	0.913314	−	0.407256i	$-0.133514\pi$
$439$	2.17827	+	3.77288i	0.103963	+	0.180070i	−0.809351	+	0.587325i	$0.800181\pi$
$440$	−2.41495	+	1.39427i	−0.115128	+	0.0664693i
$441$		0			0
$442$	10.6836	+	12.5980i	0.508166	+	0.599224i
$443$	11.4823			0.545542			0.272771	−	0.962079i	$-0.412060\pi$
$443$	11.4823			0.545542			0.272771	+	0.962079i	$0.412060\pi$
$444$		0			0
$445$	13.6298	+	23.6075i	0.646114	+	1.11910i
$446$	9.96384	−	17.2579i	0.471801	−	0.817184i
$447$		0			0
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	25.5692	+	14.7624i	1.20669	+	0.696680i	0.962034	−	0.272931i	$-0.0879930\pi$
$449$	25.5692	+	14.7624i	1.20669	+	0.696680i	0.244652	+	0.969611i	$0.421326\pi$
$450$		0			0
$451$	−0.0367662	+	0.0636809i	−0.00173125	+	0.00299861i
$452$	−2.23661	−	3.87392i	−0.105201	−	0.182214i
$453$		0			0
$454$	0.352624			0.0165495
$455$	2.18492	+	12.0237i	0.102431	+	0.563678i
$456$		0			0
$457$	−14.3744	+	8.29907i	−0.672407	+	0.388214i	−0.796988	−	0.603995i	$-0.793575\pi$
$457$	−14.3744	+	8.29907i	−0.672407	+	0.388214i	0.124581	+	0.992209i	$0.460241\pi$
$458$	−4.15659	−	7.19942i	−0.194224	−	0.336407i
$459$		0			0
$460$		−	20.7787i		−	0.968813i
$461$	−22.8996	−	13.2211i	−1.06654	−	0.615769i	−0.139308	−	0.990249i	$-0.544488\pi$
$461$	−22.8996	−	13.2211i	−1.06654	−	0.615769i	−0.927235	+	0.374481i	$0.877821\pi$
$462$		0			0
$463$		−	10.4717i		−	0.486663i	−0.969943	−	0.243331i	$-0.921760\pi$
$463$		−	10.4717i		−	0.486663i	0.969943	−	0.243331i	$-0.0782403\pi$
$464$	−3.43406	+	5.94797i	−0.159422	+	0.276128i
$465$		0			0
$466$	−13.3193	+	7.68988i	−0.617003	+	0.356227i
$467$	−27.9010			−1.29110			−0.645551	−	0.763717i	$-0.723372\pi$
$467$	−27.9010			−1.29110			−0.645551	+	0.763717i	$0.723372\pi$
$468$		0			0
$469$	0.291719			0.0134703
$470$	−32.8046	+	18.9397i	−1.51316	+	0.873625i
$471$		0			0
$472$	0.870585	−	1.50790i	0.0400719	−	0.0694066i
$473$			6.05015i			0.278186i
$474$		0			0
$475$	33.1850	+	19.1594i	1.52263	+	0.879091i
$476$			4.58130i			0.209983i
$477$		0			0
$478$	−1.44303	−	2.49940i	−0.0660026	−	0.114320i
$479$	5.95941	−	3.44067i	0.272292	−	0.157208i	−0.357637	−	0.933861i	$-0.616417\pi$
$479$	5.95941	−	3.44067i	0.272292	−	0.157208i	0.629929	+	0.776653i	$0.283084\pi$
$480$		0			0
$481$	11.7788	−	32.8957i	0.537067	−	1.49991i
$482$	6.26744			0.285474
$483$		0			0
$484$	5.16156	+	8.94008i	0.234616	+	0.406367i
$485$	25.0371	−	43.3655i	1.13688	−	1.96913i
$486$		0			0
$487$	−35.3392	−	20.4031i	−1.60137	−	0.924553i	−0.991213	−	0.132275i	$-0.957772\pi$
$487$	−35.3392	−	20.4031i	−1.60137	−	0.924553i	−0.610160	−	0.792278i	$-0.708895\pi$
$488$	−2.06066	−	1.18972i	−0.0932818	−	0.0538563i
$489$		0			0
$490$	−1.69469	+	2.93529i	−0.0765582	+	0.132603i
$491$	−3.36353	−	5.82581i	−0.151794	−	0.262915i	0.780093	−	0.625664i	$-0.215172\pi$
$491$	−3.36353	−	5.82581i	−0.151794	−	0.262915i	−0.931887	+	0.362749i	$0.881838\pi$
$492$		0			0
$493$	31.4649			1.41711
$494$	−16.2413	+	13.7733i	−0.730730	+	0.619689i
$495$		0			0
$496$	3.71251	−	2.14342i	0.166696	−	0.0962422i
$497$	−5.47419	−	9.48158i	−0.245551	−	0.425307i
$498$		0			0
$499$		−	1.16200i		−	0.0520184i	−0.999662	−	0.0260092i	$-0.991720\pi$
$499$		−	1.16200i		−	0.0520184i	0.999662	−	0.0260092i	$-0.00827993\pi$
$500$	4.36733	+	2.52148i	0.195313	+	0.112764i
$501$		0			0
$502$		−	17.2665i		−	0.770641i
$503$	4.97527	−	8.61741i	0.221836	−	0.384231i	−0.733529	−	0.679658i	$-0.762128\pi$
$503$	4.97527	−	8.61741i	0.221836	−	0.384231i	0.955366	+	0.295426i	$0.0954617\pi$
$504$		0			0
$505$	24.1861	−	13.9638i	1.07627	−	0.621382i
$506$	5.04379			0.224224
$507$		0			0
$508$	−0.540127			−0.0239642
$509$	0.0452068	−	0.0261002i	0.00200376	−	0.00115687i	−0.498998	−	0.866603i	$-0.666298\pi$
$509$	0.0452068	−	0.0261002i	0.00200376	−	0.00115687i	0.501002	+	0.865446i	$0.332965\pi$
$510$		0			0
$511$	−6.35934	+	11.0147i	−0.281321	+	0.487262i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−9.69351	−	5.59655i	−0.427562	−	0.246853i
$515$			45.1570i			1.98986i
$516$		0			0
$517$	−4.59739	−	7.96292i	−0.202193	−	0.350209i
$518$	8.39253	−	4.84543i	0.368747	−	0.212896i
$519$		0			0
$520$	−9.32034	+	7.90403i	−0.408724	+	0.346615i
$521$	−26.0984			−1.14339			−0.571695	−	0.820466i	$-0.693714\pi$
$521$	−26.0984			−1.14339			−0.571695	+	0.820466i	$0.693714\pi$
$522$		0			0
$523$	9.76606	+	16.9153i	0.427040	+	0.739655i	0.996609	−	0.0822887i	$-0.0262229\pi$
$523$	9.76606	+	16.9153i	0.427040	+	0.739655i	−0.569568	+	0.821944i	$0.692890\pi$
$524$	3.86307	−	6.69104i	0.168759	−	0.292299i
$525$		0			0
$526$	24.7533	+	14.2913i	1.07929	+	0.623131i
$527$	−17.0081	−	9.81962i	−0.740884	−	0.427750i
$528$		0			0
$529$	−7.29180	+	12.6298i	−0.317035	+	0.549120i
$530$	11.8887	+	20.5919i	0.516414	+	0.894455i
$531$		0			0
$532$	−5.90621			−0.256067
$533$	−0.108633	+	0.303387i	−0.00470540	+	0.0131412i
$534$		0			0
$535$	−26.4953	+	15.2971i	−1.14549	+	0.661351i
$536$	0.145859	+	0.252636i	0.00630016	+	0.0109122i
$537$		0			0
$538$		−	18.3754i		−	0.792219i
$539$	−0.712505	−	0.411365i	−0.0306898	−	0.0177188i
$540$		0			0
$541$			32.8802i			1.41363i	0.707399	+	0.706814i	$0.249868\pi$
$541$			32.8802i			1.41363i	−0.707399	+	0.706814i	$0.750132\pi$
$542$	−10.1913	+	17.6518i	−0.437752	+	0.758209i
$543$		0			0
$544$	−3.96752	+	2.29065i	−0.170106	+	0.0982107i
$545$	1.34623			0.0576662
$546$		0			0
$547$	−39.0180			−1.66829			−0.834144	−	0.551546i	$-0.814038\pi$
$547$	−39.0180			−1.66829			−0.834144	+	0.551546i	$0.814038\pi$
$548$	−10.8600	+	6.27005i	−0.463918	+	0.267843i
$549$		0			0
$550$	−2.66888	+	4.62264i	−0.113802	+	0.197110i
$551$			40.5646i			1.72811i
$552$		0			0
$553$	8.62217	+	4.97801i	0.366652	+	0.211687i
$554$			7.23219i			0.307266i
$555$		0			0
$556$	6.04868	+	10.4766i	0.256521	+	0.444308i
$557$	25.5903	−	14.7746i	1.08430	−	0.626020i	0.152245	−	0.988343i	$-0.451350\pi$
$557$	25.5903	−	14.7746i	1.08430	−	0.626020i	0.932053	+	0.362323i	$0.118016\pi$
$558$		0			0
$559$	4.74050	+	26.0871i	0.200502	+	1.10337i
$560$	−3.38938			−0.143227
$561$		0			0
$562$	−6.22927	−	10.7894i	−0.262766	−	0.455124i
$563$	13.5662	−	23.4973i	0.571745	−	0.990292i	−0.424642	−	0.905362i	$-0.639600\pi$
$563$	13.5662	−	23.4973i	0.571745	−	0.990292i	0.996387	−	0.0849304i	$-0.0270668\pi$
$564$		0			0
$565$	−13.1302	−	7.58071i	−0.552390	−	0.318923i
$566$	−11.3109	−	6.53035i	−0.475433	−	0.274491i
$567$		0			0
$568$	5.47419	−	9.48158i	0.229692	−	0.397838i
$569$	−21.2297	−	36.7709i	−0.889996	−	1.54152i	−0.839879	−	0.542774i	$-0.817374\pi$
$569$	−21.2297	−	36.7709i	−0.889996	−	1.54152i	−0.0501168	−	0.998743i	$-0.515959\pi$
$570$		0			0
$571$	−11.2678			−0.471543			−0.235771	−	0.971809i	$-0.575762\pi$
$571$	−11.2678			−0.471543			−0.235771	+	0.971809i	$0.575762\pi$
$572$	−1.91861	−	2.26240i	−0.0802210	−	0.0945957i
$573$		0			0
$574$	−0.0774019	+	0.0446880i	−0.00323069	+	0.00186524i
$575$	−19.8871	−	34.4455i	−0.829349	−	1.43647i
$576$		0			0
$577$		−	22.8987i		−	0.953286i	−0.879097	−	0.476643i	$-0.841853\pi$
$577$		−	22.8987i		−	0.953286i	0.879097	−	0.476643i	$-0.158147\pi$
$578$	3.45395	+	1.99414i	0.143665	+	0.0829452i
$579$		0			0
$580$			23.2787i			0.966594i
$581$	−1.61777	+	2.80205i	−0.0671163	+	0.116249i
$582$		0			0
$583$	−4.99844	+	2.88585i	−0.207014	+	0.119520i
$584$	−12.7187			−0.526303
$585$		0			0
$586$	−14.5582			−0.601393
$587$	−31.0054	+	17.9010i	−1.27973	+	0.738852i	−0.976798	−	0.214161i	$-0.931298\pi$
$587$	−31.0054	+	17.9010i	−1.27973	+	0.738852i	−0.302931	+	0.953013i	$0.597965\pi$
$588$		0			0
$589$	12.6595	−	21.9268i	0.521624	−	0.903479i
$590$		−	5.90148i		−	0.242960i
$591$		0			0
$592$	8.39253	+	4.84543i	0.344931	+	0.199146i
$593$			14.6093i			0.599931i	0.953950	+	0.299965i	$0.0969752\pi$
$593$			14.6093i			0.599931i	−0.953950	+	0.299965i	$0.903025\pi$
$594$		0			0
$595$	7.76387	+	13.4474i	0.318288	+	0.551290i
$596$	−14.7292	+	8.50389i	−0.603331	+	0.348333i
$597$		0			0
$598$	21.7478	−	3.95198i	0.889335	−	0.161609i
$599$	37.5729			1.53519			0.767594	−	0.640936i	$-0.221454\pi$
$599$	37.5729			1.53519			0.767594	+	0.640936i	$0.221454\pi$
$600$		0			0
$601$	2.72579	+	4.72121i	0.111187	+	0.192582i	0.916249	−	0.400609i	$-0.131201\pi$
$601$	2.72579	+	4.72121i	0.111187	+	0.192582i	−0.805062	+	0.593191i	$0.797868\pi$
$602$	−3.67687	+	6.36853i	−0.149858	+	0.259562i
$603$		0			0
$604$	−4.80269	−	2.77283i	−0.195419	−	0.112825i
$605$	30.3013	+	17.4945i	1.23192	+	0.711251i
$606$		0			0
$607$	19.9693	−	34.5879i	0.810531	−	1.40388i	−0.101962	−	0.994788i	$-0.532512\pi$
$607$	19.9693	−	34.5879i	0.810531	−	1.40388i	0.912493	−	0.409092i	$-0.134155\pi$
$608$	−2.95310	−	5.11492i	−0.119764	−	0.207438i
$609$		0			0
$610$	−8.06485			−0.326536
$611$	−26.0623	−	30.7324i	−1.05437	−	1.24330i
$612$		0			0
$613$	14.4238	−	8.32758i	0.582572	−	0.336348i	−0.179583	−	0.983743i	$-0.557475\pi$
$613$	14.4238	−	8.32758i	0.582572	−	0.336348i	0.762155	+	0.647395i	$0.224142\pi$
$614$	−1.62134	−	2.80824i	−0.0654318	−	0.113331i
$615$		0			0
$616$		−	0.822730i		−	0.0331487i
$617$	23.3525	+	13.4826i	0.940137	+	0.542788i	0.890003	−	0.455954i	$-0.150702\pi$
$617$	23.3525	+	13.4826i	0.940137	+	0.542788i	0.0501339	+	0.998743i	$0.484035\pi$
$618$		0			0
$619$		−	12.7533i		−	0.512597i	−0.966598	−	0.256298i	$-0.917497\pi$
$619$		−	12.7533i		−	0.512597i	0.966598	−	0.256298i	$-0.0825029\pi$
$620$	7.26484	−	12.5831i	0.291763	−	0.505349i
$621$		0			0
$622$	−8.89484	+	5.13544i	−0.356651	+	0.205912i
$623$	−8.04265			−0.322222
$624$		0			0
$625$	−15.3469			−0.613875
$626$	5.31204	−	3.06691i	0.212312	−	0.122578i
$627$		0			0
$628$	1.14676	−	1.98625i	0.0457609	−	0.0792602i
$629$		−	44.3967i		−	1.77021i
$630$		0			0
$631$	32.5218	+	18.7764i	1.29467	+	0.747479i	0.979478	−	0.201549i	$-0.0645976\pi$
$631$	32.5218	+	18.7764i	1.29467	+	0.747479i	0.315193	+	0.949028i	$0.397931\pi$
$632$			9.95602i			0.396029i
$633$		0			0
$634$	−2.52244	−	4.36899i	−0.100179	−	0.173515i
$635$	−1.58543	+	0.915346i	−0.0629157	+	0.0363244i
$636$		0			0
$637$	−3.39451	−	1.21546i	−0.134495	−	0.0481581i
$638$	−5.65062			−0.223710
$639$		0			0
$640$	−1.69469	−	2.93529i	−0.0669884	−	0.116027i
$641$	−0.988115	+	1.71147i	−0.0390282	+	0.0675988i	−0.884880	−	0.465820i	$-0.845760\pi$
$641$	−0.988115	+	1.71147i	−0.0390282	+	0.0675988i	0.845851	+	0.533418i	$0.179093\pi$
$642$		0			0
$643$	−33.8360	−	19.5352i	−1.33436	−	0.770394i	−0.348397	−	0.937347i	$-0.613274\pi$
$643$	−33.8360	−	19.5352i	−1.33436	−	0.770394i	−0.985965	+	0.166953i	$0.946607\pi$
$644$	5.30921	+	3.06527i	0.209212	+	0.120789i
$645$		0			0
$646$	−13.5290	+	23.4330i	−0.532293	+	0.921959i
$647$	−6.05254	−	10.4833i	−0.237950	−	0.412141i	0.722176	−	0.691709i	$-0.243142\pi$
$647$	−6.05254	−	10.4833i	−0.237950	−	0.412141i	−0.960126	+	0.279568i	$0.909809\pi$
$648$		0			0
$649$	1.43251			0.0562311
$650$	−7.88572	+	22.0231i	−0.309303	+	0.863818i
$651$		0			0
$652$	−20.2269	+	11.6780i	−0.792145	+	0.457345i
$653$	20.1232	+	34.8544i	0.787481	+	1.36396i	0.927505	+	0.373810i	$0.121949\pi$
$653$	20.1232	+	34.8544i	0.787481	+	1.36396i	−0.140024	+	0.990148i	$0.544718\pi$
$654$		0			0
$655$		−	26.1868i		−	1.02320i
$656$	−0.0774019	−	0.0446880i	−0.00302204	−	0.00174477i
$657$		0			0
$658$		−	11.1759i		−	0.435684i
$659$	−1.81164	+	3.13785i	−0.0705714	+	0.122233i	−0.899152	−	0.437637i	$-0.855816\pi$
$659$	−1.81164	+	3.13785i	−0.0705714	+	0.122233i	0.828580	+	0.559870i	$0.189149\pi$
$660$		0			0
$661$	−20.4698	+	11.8182i	−0.796182	+	0.459676i	−0.842135	−	0.539268i	$-0.818701\pi$
$661$	−20.4698	+	11.8182i	−0.796182	+	0.459676i	0.0459521	+	0.998944i	$0.485368\pi$
$662$	23.0874			0.897317
$663$		0			0
$664$	−3.23553			−0.125563
$665$	−17.3364	+	10.0092i	−0.672277	+	0.388139i
$666$		0			0
$667$	21.0527	−	36.4643i	0.815163	−	1.41190i
$668$		−	21.7780i		−	0.842614i
$669$		0			0
$670$	0.856278	+	0.494372i	0.0330809	+	0.0190993i
$671$		−	1.95764i		−	0.0755740i
$672$		0			0
$673$	23.4355	+	40.5914i	0.903372	+	1.56469i	0.823088	+	0.567913i	$0.192249\pi$
$673$	23.4355	+	40.5914i	0.903372	+	1.56469i	0.0802832	+	0.996772i	$0.474418\pi$
$674$	−25.2385	+	14.5714i	−0.972150	+	0.561271i
$675$		0			0
$676$	−10.0453	−	8.25174i	−0.386359	−	0.317375i
$677$	13.7304			0.527704			0.263852	−	0.964563i	$-0.415007\pi$
$677$	13.7304			0.527704			0.263852	+	0.964563i	$0.415007\pi$
$678$		0			0
$679$	7.38693	+	12.7945i	0.283484	+	0.491009i
$680$	−7.76387	+	13.4474i	−0.297731	+	0.515685i
$681$		0			0
$682$	3.05439	+	1.76345i	0.116959	+	0.0675261i
$683$	−3.03610	−	1.75289i	−0.116173	−	0.0670725i	0.440788	−	0.897611i	$-0.354699\pi$
$683$	−3.03610	−	1.75289i	−0.116173	−	0.0670725i	−0.556961	+	0.830539i	$0.688033\pi$
$684$		0			0
$685$	−21.2516	+	36.8088i	−0.811981	+	1.40639i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	−7.35374			−0.280359
$689$	−19.2911	+	16.3597i	−0.734934	+	0.623254i
$690$		0			0
$691$	−27.5196	+	15.8885i	−1.04690	+	0.604426i	−0.921779	−	0.387716i	$-0.873264\pi$
$691$	−27.5196	+	15.8885i	−1.04690	+	0.604426i	−0.125117	+	0.992142i	$0.539931\pi$
$692$	4.04866	+	7.01249i	0.153907	+	0.266575i
$693$		0			0
$694$		−	29.1082i		−	1.10493i
$695$	35.5092	+	20.5012i	1.34694	+	0.777656i
$696$		0			0
$697$			0.409458i			0.0155093i
$698$	−12.8901	+	22.3263i	−0.487898	+	0.845064i
$699$		0			0
$700$	−5.61866	+	3.24394i	−0.212365	+	0.122609i
$701$	31.6828			1.19664			0.598322	−	0.801256i	$-0.295834\pi$
$701$	31.6828			1.19664			0.598322	+	0.801256i	$0.295834\pi$
$702$		0			0
$703$	57.2362			2.15870
$704$	0.712505	−	0.411365i	0.0268536	−	0.0155039i
$705$		0			0
$706$	−4.95890	+	8.58906i	−0.186630	+	0.323253i
$707$			8.23976i			0.309888i
$708$		0			0
$709$	−30.5835	−	17.6574i	−1.14859	−	0.663137i	−0.200044	−	0.979787i	$-0.564108\pi$
$709$	−30.5835	−	17.6574i	−1.14859	−	0.663137i	−0.948542	+	0.316650i	$0.897442\pi$
$710$		−	37.1082i		−	1.39265i
$711$		0			0
$712$	−4.02133	−	6.96514i	−0.150706	−	0.261030i
$713$	−22.7597	+	13.1403i	−0.852357	+	0.492108i
$714$		0			0
$715$	−9.46572	−	3.38935i	−0.353998	−	0.126754i
$716$	−9.90883			−0.370310
$717$		0			0
$718$	12.6341	+	21.8829i	0.471501	+	0.816664i
$719$	0.609778	−	1.05617i	0.0227409	−	0.0393884i	−0.854431	−	0.519565i	$-0.826094\pi$
$719$	0.609778	−	1.05617i	0.0227409	−	0.0393884i	0.877172	+	0.480177i	$0.159427\pi$
$720$		0			0
$721$	−11.5382	−	6.66156i	−0.429703	−	0.248089i
$722$	−13.7553	−	7.94164i	−0.511920	−	0.295557i
$723$		0			0
$724$	0.639508	−	1.10766i	0.0237671	−	0.0411659i
$725$	22.2798	+	38.5897i	0.827450	+	1.43318i
$726$		0			0
$727$	5.75380			0.213397			0.106698	−	0.994291i	$-0.465972\pi$
$727$	5.75380			0.213397			0.106698	+	0.994291i	$0.465972\pi$
$728$	−0.644638	−	3.54746i	−0.0238919	−	0.131477i
$729$		0			0
$730$	−37.3330	+	21.5542i	−1.38175	+	0.797756i
$731$	16.8448	+	29.1761i	0.623029	+	1.07912i
$732$		0			0
$733$			35.2258i			1.30110i	0.759466	+	0.650548i	$0.225461\pi$
$733$			35.2258i			1.30110i	−0.759466	+	0.650548i	$0.774539\pi$
$734$	30.9897	+	17.8919i	1.14385	+	0.660402i
$735$		0			0
$736$			6.13055i			0.225975i
$737$	−0.120003	+	0.207851i	−0.00442036	+	0.00765629i
$738$		0			0
$739$	−25.4199	+	14.6762i	−0.935088	+	0.539873i	−0.888417	−	0.459037i	$-0.848194\pi$
$739$	−25.4199	+	14.6762i	−0.935088	+	0.539873i	−0.0466705	+	0.998910i	$0.514861\pi$
$740$	32.8460			1.20744
$741$		0			0
$742$	−7.01530			−0.257540
$743$	12.9763	−	7.49190i	0.476056	−	0.274851i	−0.242715	−	0.970098i	$-0.578038\pi$
$743$	12.9763	−	7.49190i	0.476056	−	0.274851i	0.718771	+	0.695246i	$0.244705\pi$
$744$		0			0
$745$	−28.8229	+	49.9227i	−1.05599	+	1.82903i
$746$			23.3304i			0.854185i
$747$		0			0
$748$	−3.26420	−	1.88459i	−0.119351	−	0.0689073i
$749$		−	9.02649i		−	0.329821i
$750$		0			0
$751$	21.9195	+	37.9657i	0.799855	+	1.38539i	0.919710	+	0.392598i	$0.128424\pi$
$751$	21.9195	+	37.9657i	0.799855	+	1.38539i	−0.119856	+	0.992791i	$0.538243\pi$
$752$	9.67865	−	5.58797i	0.352944	−	0.203772i
$753$		0			0
$754$	−24.3644	+	4.42745i	−0.887298	+	0.161238i
$755$	−18.7963			−0.684069
$756$		0			0
$757$	18.1798	+	31.4884i	0.660758	+	1.14447i	0.980417	+	0.196933i	$0.0630983\pi$
$757$	18.1798	+	31.4884i	0.660758	+	1.14447i	−0.319659	+	0.947533i	$0.603568\pi$
$758$	−12.1533	+	21.0502i	−0.441428	+	0.764576i
$759$		0			0
$760$	−17.3364	−	10.0092i	−0.628857	−	0.363071i
$761$	15.7906	+	9.11673i	0.572410	+	0.330481i	0.758111	−	0.652125i	$-0.226122\pi$
$761$	15.7906	+	9.11673i	0.572410	+	0.330481i	−0.185701	+	0.982606i	$0.559456\pi$
$762$		0			0
$763$	−0.198596	+	0.343978i	−0.00718965	+	0.0124528i
$764$	5.01710	+	8.68988i	0.181512	+	0.314389i
$765$		0			0
$766$	4.91150			0.177460
$767$	6.17672	−	1.12242i	0.223029	−	0.0405284i
$768$		0			0
$769$	−5.66870	+	3.27283i	−0.204419	+	0.118021i	−0.598715	−	0.800962i	$-0.704322\pi$
$769$	−5.66870	+	3.27283i	−0.204419	+	0.118021i	0.394296	+	0.918983i	$0.370988\pi$
$770$	−1.39427	−	2.41495i	−0.0502460	−	0.0870287i
$771$		0			0
$772$			15.8582i			0.570750i
$773$	−38.6651	−	22.3233i	−1.39069	−	0.802913i	−0.397295	−	0.917691i	$-0.630051\pi$
$773$	−38.6651	−	22.3233i	−1.39069	−	0.802913i	−0.993391	+	0.114778i	$0.963384\pi$
$774$		0			0
$775$		−	27.8124i		−	0.999051i
$776$	−7.38693	+	12.7945i	−0.265175	+	0.459297i
$777$		0			0
$778$	−4.45589	+	2.57261i	−0.159752	+	0.0922326i
$779$	−0.527873			−0.0189130
$780$		0			0
$781$	9.00757			0.322316
$782$	24.3231	−

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.38938i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.38938i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(1.69469 + 2.93529i) q^{10} +(-0.712505 + 0.411365i) q^{11} +(-2.74987 + 2.33200i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.29065 + 3.96752i) q^{17} +(-5.11492 - 2.95310i) q^{19} +(-2.93529 - 1.69469i) q^{20} +(0.411365 - 0.712505i) q^{22} +(3.06527 + 5.30921i) q^{23} -6.48787 q^{25} +(1.21546 - 3.39451i) q^{26} +(0.866025 - 0.500000i) q^{28} +(-3.43406 - 5.94797i) q^{29} +4.28683i q^{31} +(0.866025 + 0.500000i) q^{32} -4.58130i q^{34} +(1.69469 - 2.93529i) q^{35} +(-8.39253 + 4.84543i) q^{37} +5.90621 q^{38} +3.38938 q^{40} +(0.0774019 - 0.0446880i) q^{41} +(3.67687 - 6.36853i) q^{43} +0.822730i q^{44} +(-5.30921 - 3.06527i) q^{46} +11.1759i q^{47} +(0.500000 + 0.866025i) q^{49} +(5.61866 - 3.24394i) q^{50} +(0.644638 + 3.54746i) q^{52} +7.01530 q^{53} +(1.39427 + 2.41495i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(5.94797 + 3.43406i) q^{58} +(-1.50790 - 0.870585i) q^{59} +(-1.18972 + 2.06066i) q^{61} +(-2.14342 - 3.71251i) q^{62} -1.00000 q^{64} +(7.90403 + 9.32034i) q^{65} +(0.252636 - 0.145859i) q^{67} +(2.29065 + 3.96752i) q^{68} +3.38938i q^{70} +(-9.48158 - 5.47419i) q^{71} +12.7187i q^{73} +(4.84543 - 8.39253i) q^{74} +(-5.11492 + 2.95310i) q^{76} -0.822730 q^{77} +9.95602 q^{79} +(-2.93529 + 1.69469i) q^{80} +(-0.0446880 + 0.0774019i) q^{82} +3.23553i q^{83} +(13.4474 + 7.76387i) q^{85} +7.35374i q^{86} +(-0.411365 - 0.712505i) q^{88} +(-6.96514 + 4.02133i) q^{89} +(-3.54746 + 0.644638i) q^{91} +6.13055 q^{92} +(-5.58797 - 9.67865i) q^{94} +(-10.0092 + 17.3364i) q^{95} +(12.7945 + 7.38693i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4}+O(q^{10}) \) 12 * q + 6 * q^4	\( 12 q + 6 q^{4} - 2 q^{10} + 18 q^{11} - 8 q^{13} - 12 q^{14} - 6 q^{16} - 4 q^{17} + 12 q^{19} - 2 q^{22} + 6 q^{23} - 24 q^{25} + 14 q^{26} + 10 q^{29} - 2 q^{35} - 6 q^{37} - 8 q^{38} - 4 q^{40} + 24 q^{41} + 26 q^{43} - 6 q^{46} + 6 q^{49} + 12 q^{50} - 4 q^{52} - 36 q^{53} - 6 q^{55} - 6 q^{56} + 24 q^{58} - 6 q^{59} - 28 q^{61} + 2 q^{62} - 12 q^{64} + 34 q^{65} - 42 q^{67} + 4 q^{68} - 48 q^{71} + 12 q^{76} + 4 q^{77} + 44 q^{79} + 6 q^{82} + 54 q^{85} + 2 q^{88} - 12 q^{89} - 16 q^{91} + 12 q^{92} + 8 q^{94} - 32 q^{95} + 60 q^{97}+O(q^{100}) \) 12 * q + 6 * q^4 - 2 * q^10 + 18 * q^11 - 8 * q^13 - 12 * q^14 - 6 * q^16 - 4 * q^17 + 12 * q^19 - 2 * q^22 + 6 * q^23 - 24 * q^25 + 14 * q^26 + 10 * q^29 - 2 * q^35 - 6 * q^37 - 8 * q^38 - 4 * q^40 + 24 * q^41 + 26 * q^43 - 6 * q^46 + 6 * q^49 + 12 * q^50 - 4 * q^52 - 36 * q^53 - 6 * q^55 - 6 * q^56 + 24 * q^58 - 6 * q^59 - 28 * q^61 + 2 * q^62 - 12 * q^64 + 34 * q^65 - 42 * q^67 + 4 * q^68 - 48 * q^71 + 12 * q^76 + 4 * q^77 + 44 * q^79 + 6 * q^82 + 54 * q^85 + 2 * q^88 - 12 * q^89 - 16 * q^91 + 12 * q^92 + 8 * q^94 - 32 * q^95 + 60 * q^97

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