LMFDB - Embedded newform 1638.2.bj.f.127.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.195105024.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 $ x^8 - 4x^7 + 5x^6 + 4x^5 - 20x^4 + 12x^3 + 45x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.2
Root			$-1.58726 + 0.693255i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.f.1135.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.78801i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.78801i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.894007 - 1.54846i) q^{10} +(-2.74922 + 1.58726i) q^{11} +(1.47952 + 3.28801i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.78052 + 4.81599i) q^{17} +(-5.36028 - 3.09476i) q^{19} +(1.54846 + 0.894007i) q^{20} +(1.58726 - 2.74922i) q^{22} +(-3.06678 - 5.31181i) q^{23} +1.80301 q^{25} +(-2.92531 - 2.10774i) q^{26} +(0.866025 - 0.500000i) q^{28} +(1.03880 + 1.79925i) q^{29} -5.63862i q^{31} +(0.866025 + 0.500000i) q^{32} -5.56103i q^{34} +(-0.894007 + 1.54846i) q^{35} +(-2.68202 + 1.54846i) q^{37} +6.18952 q^{38} -1.78801 q^{40} +(1.29768 - 0.749217i) q^{41} +(-4.81931 + 8.34729i) q^{43} +3.17452i q^{44} +(5.31181 + 3.06678i) q^{46} -10.5086i q^{47} +(0.500000 + 0.866025i) q^{49} +(-1.56145 + 0.901504i) q^{50} +(3.58726 + 0.362708i) q^{52} -3.60200 q^{53} +(-2.83804 - 4.91564i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-1.79925 - 1.03880i) q^{58} +(2.40874 + 1.39069i) q^{59} +(-0.844395 + 1.46254i) q^{61} +(2.81931 + 4.88319i) q^{62} -1.00000 q^{64} +(-5.87901 + 2.64539i) q^{65} +(-10.0064 + 5.77720i) q^{67} +(2.78052 + 4.81599i) q^{68} -1.78801i q^{70} +(0.518313 + 0.299248i) q^{71} -0.423973i q^{73} +(1.54846 - 2.68202i) q^{74} +(-5.36028 + 3.09476i) q^{76} -3.17452 q^{77} +6.96254 q^{79} +(1.54846 - 0.894007i) q^{80} +(-0.749217 + 1.29768i) q^{82} -4.30228i q^{83} +(-8.61106 - 4.97160i) q^{85} -9.63862i q^{86} +(-1.58726 - 2.74922i) q^{88} +(14.1102 - 8.14654i) q^{89} +(-0.362708 + 3.58726i) q^{91} -6.13356 q^{92} +(5.25429 + 9.10069i) q^{94} +(5.53347 - 9.58425i) q^{95} +(-15.1461 - 8.74462i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 + 6 * q^10 - 6 * q^11 + 12 * q^13 - 8 * q^14 - 4 * q^16 - 2 * q^17 - 12 * q^19 + 6 * q^20 - 4 * q^22 - 8 * q^23 - 24 * q^25 - 6 * q^26 - 2 * q^29 + 6 * q^35 + 18 * q^37 + 4 * q^38 + 12 * q^40 - 12 * q^41 - 8 * q^43 + 18 * q^46 + 4 * q^49 - 12 * q^50 + 12 * q^52 + 12 * q^53 - 22 * q^55 - 4 * q^56 - 24 * q^58 - 18 * q^59 - 8 * q^61 - 8 * q^62 - 8 * q^64 - 46 * q^65 + 18 * q^67 + 2 * q^68 - 6 * q^71 + 6 * q^74 - 12 * q^76 + 8 * q^77 - 4 * q^79 + 6 * q^80 + 10 * q^82 - 54 * q^85 + 4 * q^88 + 18 * q^89 + 6 * q^91 - 16 * q^92 - 2 * q^94 + 50 * q^95 - 54 * 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
$5$			1.78801i			0.799624i	0.916597	+	0.399812i	$0.130925\pi$
$5$			1.78801i			0.799624i	−0.916597	+	0.399812i	$0.869075\pi$
$6$		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
$10$	−0.894007	−	1.54846i	−0.282710	−	0.489668i
$11$	−2.74922	+	1.58726i	−0.828920	+	0.478577i	−0.853483	−	0.521121i	$-0.825514\pi$
$11$	−2.74922	+	1.58726i	−0.828920	+	0.478577i	0.0245627	+	0.999698i	$0.492181\pi$
$12$		0			0
$13$	1.47952	+	3.28801i	0.410344	+	0.911931i
$13$	1.47952	+	3.28801i	0.410344	+	0.911931i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.78052	+	4.81599i	−0.674374	+	1.16805i	0.302277	+	0.953220i	$0.402253\pi$
$17$	−2.78052	+	4.81599i	−0.674374	+	1.16805i	−0.976651	+	0.214830i	$0.931080\pi$
$18$		0			0
$19$	−5.36028	−	3.09476i	−1.22973	−	0.709986i	−0.262758	−	0.964862i	$-0.584632\pi$
$19$	−5.36028	−	3.09476i	−1.22973	−	0.709986i	−0.966974	+	0.254875i	$0.917966\pi$
$20$	1.54846	+	0.894007i	0.346247	+	0.199906i
$21$		0			0
$22$	1.58726	−	2.74922i	0.338405	−	0.586135i
$23$	−3.06678	−	5.31181i	−0.639467	−	1.10759i	−0.985550	−	0.169386i	$-0.945822\pi$
$23$	−3.06678	−	5.31181i	−0.639467	−	1.10759i	0.346083	−	0.938204i	$-0.387512\pi$
$24$		0			0
$25$	1.80301			0.360602
$26$	−2.92531	−	2.10774i	−0.573700	−	0.413363i
$27$		0			0
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	1.03880	+	1.79925i	0.192900	+	0.334112i	0.946210	−	0.323553i	$-0.104877\pi$
$29$	1.03880	+	1.79925i	0.192900	+	0.334112i	−0.753310	+	0.657665i	$0.771544\pi$
$30$		0			0
$31$		−	5.63862i		−	1.01273i	−0.862320	−	0.506363i	$-0.830989\pi$
$31$		−	5.63862i		−	1.01273i	0.862320	−	0.506363i	$-0.169011\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	5.56103i		−	0.953709i
$35$	−0.894007	+	1.54846i	−0.151115	+	0.261738i
$36$		0			0
$37$	−2.68202	+	1.54846i	−0.440921	+	0.254566i	−0.703988	−	0.710211i	$-0.748599\pi$
$37$	−2.68202	+	1.54846i	−0.440921	+	0.254566i	0.263067	+	0.964778i	$0.415266\pi$
$38$	6.18952			1.00407
$39$		0			0
$40$	−1.78801			−0.282710
$41$	1.29768	−	0.749217i	0.202664	−	0.117008i	−0.395234	−	0.918581i	$-0.629336\pi$
$41$	1.29768	−	0.749217i	0.202664	−	0.117008i	0.597897	+	0.801573i	$0.296003\pi$
$42$		0			0
$43$	−4.81931	+	8.34729i	−0.734938	+	1.27295i	0.219812	+	0.975542i	$0.429456\pi$
$43$	−4.81931	+	8.34729i	−0.734938	+	1.27295i	−0.954750	+	0.297408i	$0.903878\pi$
$44$			3.17452i			0.478577i
$45$		0			0
$46$	5.31181	+	3.06678i	0.783184	+	0.452172i
$47$		−	10.5086i		−	1.53283i	−0.642344	−	0.766416i	$-0.722038\pi$
$47$		−	10.5086i		−	1.53283i	0.642344	−	0.766416i	$-0.277962\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−1.56145	+	0.901504i	−0.220823	+	0.127492i
$51$		0			0
$52$	3.58726	+	0.362708i	0.497464	+	0.0502985i
$53$	−3.60200			−0.494773			−0.247386	−	0.968917i	$-0.579572\pi$
$53$	−3.60200			−0.494773			−0.247386	+	0.968917i	$0.579572\pi$
$54$		0			0
$55$	−2.83804	−	4.91564i	−0.382682	−	0.662824i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	−1.79925	−	1.03880i	−0.236253	−	0.136401i
$59$	2.40874	+	1.39069i	0.313592	+	0.181052i	0.648533	−	0.761187i	$-0.275383\pi$
$59$	2.40874	+	1.39069i	0.313592	+	0.181052i	−0.334941	+	0.942239i	$0.608716\pi$
$60$		0			0
$61$	−0.844395	+	1.46254i	−0.108114	+	0.187259i	−0.915006	−	0.403440i	$-0.867814\pi$
$61$	−0.844395	+	1.46254i	−0.108114	+	0.187259i	0.806892	+	0.590699i	$0.201148\pi$
$62$	2.81931	+	4.88319i	0.358053	+	0.620166i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−5.87901	+	2.64539i	−0.729202	+	0.328121i
$66$		0			0
$67$	−10.0064	+	5.77720i	−1.22248	+	0.705797i	−0.965445	−	0.260606i	$-0.916078\pi$
$67$	−10.0064	+	5.77720i	−1.22248	+	0.705797i	−0.257031	+	0.966403i	$0.582744\pi$
$68$	2.78052	+	4.81599i	0.337187	+	0.584025i
$69$		0			0
$70$		−	1.78801i		−	0.213708i
$71$	0.518313	+	0.299248i	0.0615124	+	0.0355142i	0.530441	−	0.847722i	$-0.322026\pi$
$71$	0.518313	+	0.299248i	0.0615124	+	0.0355142i	−0.468928	+	0.883236i	$0.655360\pi$
$72$		0			0
$73$		−	0.423973i		−	0.0496223i	−0.999692	−	0.0248112i	$-0.992102\pi$
$73$		−	0.423973i		−	0.0496223i	0.999692	−	0.0248112i	$-0.00789845\pi$
$74$	1.54846	−	2.68202i	0.180005	−	0.311778i
$75$		0			0
$76$	−5.36028	+	3.09476i	−0.614866	+	0.354993i
$77$	−3.17452			−0.361770
$78$		0			0
$79$	6.96254			0.783346			0.391673	−	0.920104i	$-0.371896\pi$
$79$	6.96254			0.783346			0.391673	+	0.920104i	$0.371896\pi$
$80$	1.54846	−	0.894007i	0.173124	−	0.0999530i
$81$		0			0
$82$	−0.749217	+	1.29768i	−0.0827372	+	0.143305i
$83$		−	4.30228i		−	0.472237i	−0.971724	−	0.236118i	$-0.924125\pi$
$83$		−	4.30228i		−	0.472237i	0.971724	−	0.236118i	$-0.0758753\pi$
$84$		0			0
$85$	−8.61106	−	4.97160i	−0.934001	−	0.539246i
$86$		−	9.63862i		−	1.03936i
$87$		0			0
$88$	−1.58726	−	2.74922i	−0.169203	−	0.293068i
$89$	14.1102	−	8.14654i	1.49568	−	0.863532i	0.495693	−	0.868498i	$-0.334914\pi$
$89$	14.1102	−	8.14654i	1.49568	−	0.863532i	0.999988	+	0.00496618i	$0.00158079\pi$
$90$		0			0
$91$	−0.362708	+	3.58726i	−0.0380221	+	0.376047i
$92$	−6.13356			−0.639467
$93$		0			0
$94$	5.25429	+	9.10069i	0.541938	+	0.938665i
$95$	5.53347	−	9.58425i	0.567722	−	0.983323i
$96$		0			0
$97$	−15.1461	−	8.74462i	−1.53786	−	0.887881i	−0.998964	−	0.0455062i	$-0.985510\pi$
$97$	−15.1461	−	8.74462i	−1.53786	−	0.887881i	−0.538892	−	0.842375i	$-0.681157\pi$
$98$	−0.866025	−	0.500000i	−0.0874818	−	0.0505076i
$99$		0			0
$100$	0.901504	−	1.56145i	0.0901504	−	0.156145i
$101$	2.03433	+	3.52357i	0.202424	+	0.350608i	0.949309	−	0.314345i	$-0.101785\pi$
$101$	2.03433	+	3.52357i	0.202424	+	0.350608i	−0.746885	+	0.664953i	$0.768452\pi$
$102$		0			0
$103$	−18.0768			−1.78116			−0.890578	−	0.454831i	$-0.849700\pi$
$103$	−18.0768			−1.78116			−0.890578	+	0.454831i	$0.849700\pi$
$104$	−3.28801	+	1.47952i	−0.322416	+	0.145079i
$105$		0			0
$106$	3.11942	−	1.80100i	0.302985	−	0.174929i
$107$	−0.770847	−	1.33515i	−0.0745206	−	0.129073i	0.826357	−	0.563146i	$-0.190409\pi$
$107$	−0.770847	−	1.33515i	−0.0745206	−	0.129073i	−0.900878	+	0.434073i	$0.857076\pi$
$108$		0			0
$109$		−	7.37731i		−	0.706618i	−0.935507	−	0.353309i	$-0.885056\pi$
$109$		−	7.37731i		−	0.706618i	0.935507	−	0.353309i	$-0.114944\pi$
$110$	4.91564	+	2.83804i	0.468688	+	0.270597i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	−4.95660	+	8.58509i	−0.466278	+	0.807617i	−0.999258	−	0.0385104i	$-0.987739\pi$
$113$	−4.95660	+	8.58509i	−0.466278	+	0.807617i	0.532980	+	0.846128i	$0.321072\pi$
$114$		0			0
$115$	9.49759	−	5.48344i	0.885655	−	0.511333i
$116$	2.07759			0.192900
$117$		0			0
$118$	−2.78138			−0.256047
$119$	−4.81599	+	2.78052i	−0.441481	+	0.254889i
$120$		0			0
$121$	−0.461204	+	0.798828i	−0.0419276	+	0.0726208i
$122$		−	1.68879i		−	0.152896i
$123$		0			0
$124$	−4.88319	−	2.81931i	−0.438524	−	0.253182i
$125$			12.1639i			1.08797i
$126$		0			0
$127$	9.17452	+	15.8907i	0.814107	+	1.41008i	0.909967	+	0.414680i	$0.136107\pi$
$127$	9.17452	+	15.8907i	0.814107	+	1.41008i	−0.0958600	+	0.995395i	$0.530560\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	3.76868	−	5.23048i	0.330535	−	0.458744i
$131$	−5.91928			−0.517170			−0.258585	−	0.965989i	$-0.583256\pi$
$131$	−5.91928			−0.517170			−0.258585	+	0.965989i	$0.583256\pi$
$132$		0			0
$133$	−3.09476	−	5.36028i	−0.268350	−	0.464795i
$134$	5.77720	−	10.0064i	0.499074	−	0.864421i
$135$		0			0
$136$	−4.81599	−	2.78052i	−0.412968	−	0.238427i
$137$	−7.62363	−	4.40150i	−0.651331	−	0.376046i	0.137635	−	0.990483i	$-0.456050\pi$
$137$	−7.62363	−	4.40150i	−0.651331	−	0.376046i	−0.788966	+	0.614437i	$0.789383\pi$
$138$		0			0
$139$	−9.48720	+	16.4323i	−0.804694	+	1.39377i	0.111804	+	0.993730i	$0.464337\pi$
$139$	−9.48720	+	16.4323i	−0.804694	+	1.39377i	−0.916498	+	0.400040i	$0.868996\pi$
$140$	0.894007	+	1.54846i	0.0755574	+	0.130869i
$141$		0			0
$142$	−0.598496			−0.0502247
$143$	−9.28645	−	6.69108i	−0.776572	−	0.559537i
$144$		0			0
$145$	−3.21708	+	1.85738i	−0.267164	+	0.154247i
$146$	0.211987	+	0.367172i	0.0175441	+	0.0303873i
$147$		0			0
$148$			3.09693i			0.254566i
$149$	−12.0919	−	6.98127i	−0.990608	−	0.571928i	−0.0851520	−	0.996368i	$-0.527138\pi$
$149$	−12.0919	−	6.98127i	−0.990608	−	0.571928i	−0.905456	+	0.424440i	$0.860471\pi$
$150$		0			0
$151$		−	17.8426i		−	1.45201i	−0.687688	−	0.726006i	$-0.741374\pi$
$151$		−	17.8426i		−	1.45201i	0.687688	−	0.726006i	$-0.258626\pi$
$152$	3.09476	−	5.36028i	0.251018	−	0.434776i
$153$		0			0
$154$	2.74922	−	1.58726i	0.221538	−	0.127905i
$155$	10.0819			0.809800
$156$		0			0
$157$	4.57916			0.365457			0.182728	−	0.983163i	$-0.441507\pi$
$157$	4.57916			0.365457			0.182728	+	0.983163i	$0.441507\pi$
$158$	−6.02973	+	3.48127i	−0.479700	+	0.276955i
$159$		0			0
$160$	−0.894007	+	1.54846i	−0.0706774	+	0.122417i
$161$		−	6.13356i		−	0.483392i
$162$		0			0
$163$	10.6267	+	6.13531i	0.832344	+	0.480554i	0.854655	−	0.519197i	$-0.173769\pi$
$163$	10.6267	+	6.13531i	0.832344	+	0.480554i	−0.0223103	+	0.999751i	$0.507102\pi$
$164$		−	1.49843i		−	0.117008i
$165$		0			0
$166$	2.15114	+	3.72589i	0.166961	+	0.289185i
$167$	−14.4610	+	8.34904i	−1.11902	+	0.646068i	−0.941151	−	0.337985i	$-0.890255\pi$
$167$	−14.4610	+	8.34904i	−1.11902	+	0.646068i	−0.177872	+	0.984054i	$0.556921\pi$
$168$		0			0
$169$	−8.62206	+	9.72934i	−0.663236	+	0.748411i
$170$	9.94320			0.762609
$171$		0			0
$172$	4.81931	+	8.34729i	0.367469	+	0.636475i
$173$	−3.68865	+	6.38894i	−0.280443	+	0.485742i	−0.971494	−	0.237064i	$-0.923815\pi$
$173$	−3.68865	+	6.38894i	−0.280443	+	0.485742i	0.691051	+	0.722806i	$0.257148\pi$
$174$		0			0
$175$	1.56145	+	0.901504i	0.118035	+	0.0681473i
$176$	2.74922	+	1.58726i	0.207230	+	0.119644i
$177$		0			0
$178$	−8.14654	+	14.1102i	−0.610609	+	1.05761i
$179$	−9.91008	−	17.1648i	−0.740714	−	1.28295i	−0.952171	−	0.305567i	$-0.901154\pi$
$179$	−9.91008	−	17.1648i	−0.740714	−	1.28295i	0.211457	−	0.977387i	$-0.432179\pi$
$180$		0			0
$181$	−18.3266			−1.36220			−0.681102	−	0.732189i	$-0.738499\pi$
$181$	−18.3266			−1.36220			−0.681102	+	0.732189i	$0.738499\pi$
$182$	−1.47952	−	3.28801i	−0.109669	−	0.243724i
$183$		0			0
$184$	5.31181	−	3.06678i	0.391592	−	0.226086i
$185$	−2.76868	−	4.79549i	−0.203557	−	0.352571i
$186$		0			0
$187$		−	17.6536i		−	1.29096i
$188$	−9.10069	−	5.25429i	−0.663736	−	0.383208i
$189$		0			0
$190$			11.0669i			0.802880i
$191$	−7.51518	+	13.0167i	−0.543779	+	0.941854i	0.454903	+	0.890541i	$0.349674\pi$
$191$	−7.51518	+	13.0167i	−0.543779	+	0.941854i	−0.998683	+	0.0513127i	$0.983659\pi$
$192$		0			0
$193$	−4.72408	+	2.72745i	−0.340047	+	0.196326i	−0.660293	−	0.751008i	$-0.729568\pi$
$193$	−4.72408	+	2.72745i	−0.340047	+	0.196326i	0.320246	+	0.947334i	$0.396234\pi$
$194$	17.4892			1.25565
$195$		0			0
$196$	1.00000			0.0714286
$197$	6.60751	−	3.81485i	0.470766	−	0.271797i	−0.245795	−	0.969322i	$-0.579049\pi$
$197$	6.60751	−	3.81485i	0.470766	−	0.271797i	0.716560	+	0.697525i	$0.245716\pi$
$198$		0			0
$199$	2.99512	−	5.18769i	0.212318	−	0.367746i	−0.740121	−	0.672473i	$-0.765232\pi$
$199$	2.99512	−	5.18769i	0.212318	−	0.367746i	0.952440	+	0.304727i	$0.0985653\pi$
$200$			1.80301i			0.127492i
$201$		0			0
$202$	−3.52357	−	2.03433i	−0.247917	−	0.143135i
$203$			2.07759i			0.145818i
$204$		0			0
$205$	1.33961	+	2.32027i	0.0935624	+	0.162055i
$206$	15.6549	−	9.03838i	1.09073	−	0.629734i
$207$		0			0
$208$	2.10774	−	2.92531i	0.146146	−	0.202833i
$209$	19.6488			1.35913
$210$		0			0
$211$	1.38651	+	2.40150i	0.0954512	+	0.165326i	0.909797	−	0.415054i	$-0.136237\pi$
$211$	1.38651	+	2.40150i	0.0954512	+	0.165326i	−0.814346	+	0.580380i	$0.802904\pi$
$212$	−1.80100	+	3.11942i	−0.123693	+	0.214243i
$213$		0			0
$214$	1.33515	+	0.770847i	0.0912687	+	0.0526940i
$215$	−14.9251	−	8.61699i	−1.01788	−	0.587674i
$216$		0			0
$217$	2.81931	−	4.88319i	0.191387	−	0.331493i
$218$	3.68865	+	6.38894i	0.249827	+	0.432713i
$219$		0			0
$220$	−5.67609			−0.382682
$221$	−19.9489	−	2.01703i	−1.34191	−	0.135680i
$222$		0			0
$223$	19.5163	−	11.2677i	1.30691	−	0.754542i	0.325327	−	0.945602i	$-0.394526\pi$
$223$	19.5163	−	11.2677i	1.30691	−	0.754542i	0.981578	+	0.191060i	$0.0611924\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$		−	9.91321i		−	0.659417i
$227$	1.58616	+	0.915773i	0.105277	+	0.0607820i	0.551714	−	0.834033i	$-0.313974\pi$
$227$	1.58616	+	0.915773i	0.105277	+	0.0607820i	−0.446437	+	0.894815i	$0.647307\pi$
$228$		0			0
$229$		−	22.6060i		−	1.49385i	−0.664910	−	0.746924i	$-0.731530\pi$
$229$		−	22.6060i		−	1.49385i	0.664910	−	0.746924i	$-0.268470\pi$
$230$	−5.48344	+	9.49759i	−0.361567	+	0.626253i
$231$		0			0
$232$	−1.79925	+	1.03880i	−0.118126	+	0.0682003i
$233$	9.43897			0.618367			0.309184	−	0.951002i	$-0.399944\pi$
$233$	9.43897			0.618367			0.309184	+	0.951002i	$0.399944\pi$
$234$		0			0
$235$	18.7895			1.22569
$236$	2.40874	−	1.39069i	0.156796	−	0.0905262i
$237$		0			0
$238$	2.78052	−	4.81599i	0.180234	−	0.312175i
$239$			15.8757i			1.02692i	0.858115	+	0.513458i	$0.171636\pi$
$239$			15.8757i			1.02692i	−0.858115	+	0.513458i	$0.828364\pi$
$240$		0			0
$241$	20.7197	+	11.9625i	1.33467	+	0.770575i	0.986012	−	0.166674i	$-0.0533027\pi$
$241$	20.7197	+	11.9625i	1.33467	+	0.770575i	0.348662	+	0.937248i	$0.386636\pi$
$242$		−	0.922407i		−	0.0592946i
$243$		0			0
$244$	0.844395	+	1.46254i	0.0540569	+	0.0936293i
$245$	−1.54846	+	0.894007i	−0.0989278	+	0.0571160i
$246$		0			0
$247$	2.24499	−	22.2034i	0.142845	−	1.41277i
$248$	5.63862			0.358053
$249$		0			0
$250$	−6.08193	−	10.5342i	−0.384655	−	0.666243i
$251$	10.2618	−	17.7739i	0.647718	−	1.12188i	−0.335949	−	0.941880i	$-0.609057\pi$
$251$	10.2618	−	17.7739i	0.647718	−	1.12188i	0.983667	−	0.180000i	$-0.0576098\pi$
$252$		0			0
$253$	16.8625	+	9.73555i	1.06013	+	0.612069i
$254$	−15.8907	−	9.17452i	−0.997074	−	0.575661i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.413344	+	0.715933i	0.0257837	+	0.0446587i	0.878629	−	0.477504i	$-0.158459\pi$
$257$	0.413344	+	0.715933i	0.0257837	+	0.0446587i	−0.852846	+	0.522163i	$0.825125\pi$
$258$		0			0
$259$	−3.09693			−0.192434
$260$	−0.648527	+	6.41407i	−0.0402199	+	0.397784i
$261$		0			0
$262$	5.12624	−	2.95964i	0.316700	−	0.182847i
$263$	10.1805	+	17.6331i	0.627754	+	1.08730i	0.988001	+	0.154445i	$0.0493588\pi$
$263$	10.1805	+	17.6331i	0.627754	+	1.08730i	−0.360248	+	0.932857i	$0.617308\pi$
$264$		0			0
$265$		−	6.44042i		−	0.395632i
$266$	5.36028	+	3.09476i	0.328660	+	0.189752i
$267$		0			0
$268$			11.5544i			0.705797i
$269$	−10.2587	+	17.7687i	−0.625487	+	1.08338i	0.362959	+	0.931805i	$0.381766\pi$
$269$	−10.2587	+	17.7687i	−0.625487	+	1.08338i	−0.988446	+	0.151570i	$0.951567\pi$
$270$		0			0
$271$	−10.5495	+	6.09076i	−0.640837	+	0.369988i	−0.784937	−	0.619576i	$-0.787305\pi$
$271$	−10.5495	+	6.09076i	−0.640837	+	0.369988i	0.144100	+	0.989563i	$0.453971\pi$
$272$	5.56103			0.337187
$273$		0			0
$274$	8.80301			0.531809
$275$	−4.95686	+	2.86185i	−0.298910	+	0.172576i
$276$		0			0
$277$	4.31242	−	7.46933i	0.259108	−	0.448789i	−0.706895	−	0.707318i	$-0.749905\pi$
$277$	4.31242	−	7.46933i	0.259108	−	0.448789i	0.966003	+	0.258530i	$0.0832380\pi$
$278$		−	18.9744i		−	1.13801i
$279$		0			0
$280$	−1.54846	−	0.894007i	−0.0925385	−	0.0534271i
$281$			24.2922i			1.44915i	0.689194	+	0.724577i	$0.257965\pi$
$281$			24.2922i			1.44915i	−0.689194	+	0.724577i	$0.742035\pi$
$282$		0			0
$283$	5.36054	+	9.28472i	0.318651	+	0.551919i	0.980207	−	0.197976i	$-0.0634369\pi$
$283$	5.36054	+	9.28472i	0.318651	+	0.551919i	−0.661556	+	0.749896i	$0.730104\pi$
$284$	0.518313	−	0.299248i	0.0307562	−	0.0177571i
$285$		0			0
$286$	11.3878	+	1.15142i	0.673377	+	0.0680852i
$287$	1.49843			0.0884498
$288$		0			0
$289$	−6.96254	−	12.0595i	−0.409561	−	0.709380i
$290$	1.85738	−	3.21708i	0.109069	−	0.188913i
$291$		0			0
$292$	−0.367172	−	0.211987i	−0.0214871	−	0.0124056i
$293$	18.5571	+	10.7139i	1.08412	+	0.625914i	0.932004	−	0.362449i	$-0.118059\pi$
$293$	18.5571	+	10.7139i	1.08412	+	0.625914i	0.152112	+	0.988363i	$0.451393\pi$
$294$		0			0
$295$	−2.48657	+	4.30687i	−0.144774	+	0.250755i
$296$	−1.54846	−	2.68202i	−0.0900027	−	0.155889i
$297$		0			0
$298$	13.9625			0.808828
$299$	12.9280	−	17.9425i	0.747644	−	1.03764i
$300$		0			0
$301$	−8.34729	+	4.81931i	−0.481130	+	0.277781i
$302$	8.92131	+	15.4522i	0.513364	+	0.889172i
$303$		0			0
$304$			6.18952i			0.354993i
$305$	−2.61503	−	1.50979i	−0.149736	−	0.0864503i
$306$		0			0
$307$			7.59364i			0.433392i	0.976239	+	0.216696i	$0.0695280\pi$
$307$			7.59364i			0.433392i	−0.976239	+	0.216696i	$0.930472\pi$
$308$	−1.58726	+	2.74922i	−0.0904426	+	0.156651i
$309$		0			0
$310$	−8.73121	+	5.04097i	−0.495899	+	0.286308i
$311$	−25.6355			−1.45366			−0.726828	−	0.686820i	$-0.759006\pi$
$311$	−25.6355			−1.45366			−0.726828	+	0.686820i	$0.759006\pi$
$312$		0			0
$313$	−1.71308			−0.0968293			−0.0484146	−	0.998827i	$-0.515417\pi$
$313$	−1.71308			−0.0968293			−0.0484146	+	0.998827i	$0.515417\pi$
$314$	−3.96567	+	2.28958i	−0.223796	+	0.129208i
$315$		0			0
$316$	3.48127	−	6.02973i	0.195837	−	0.339199i
$317$			33.2098i			1.86525i	0.360850	+	0.932624i	$0.382487\pi$
$317$			33.2098i			1.86525i	−0.360850	+	0.932624i	$0.617513\pi$
$318$		0			0
$319$	−5.71175	−	3.29768i	−0.319797	−	0.184635i
$320$		−	1.78801i		−	0.0999530i
$321$		0			0
$322$	3.06678	+	5.31181i	0.170905	+	0.296016i
$323$	29.8087	−	17.2101i	1.65860	−	0.957593i
$324$		0			0
$325$	2.66758	+	5.92832i	0.147971	+	0.328844i
$326$	−12.2706			−0.679606
$327$		0			0
$328$	0.749217	+	1.29768i	0.0413686	+	0.0716525i
$329$	5.25429	−	9.10069i	0.289678	−	0.501737i
$330$		0			0
$331$	4.29537	+	2.47994i	0.236095	+	0.136310i	0.613381	−	0.789787i	$-0.289809\pi$
$331$	4.29537	+	2.47994i	0.236095	+	0.136310i	−0.377286	+	0.926097i	$0.623142\pi$
$332$	−3.72589	−	2.15114i	−0.204485	−	0.118059i
$333$		0			0
$334$	8.34904	−	14.4610i	0.456839	−	0.791269i
$335$	−10.3297	−	17.8916i	−0.564372	−	0.977521i
$336$		0			0
$337$	23.6174			1.28652			0.643260	−	0.765648i	$-0.277581\pi$
$337$	23.6174			1.28652			0.643260	+	0.765648i	$0.277581\pi$
$338$	2.60226	−	12.7369i	0.141544	−	0.692795i
$339$		0			0
$340$	−8.61106	+	4.97160i	−0.467000	+	0.269623i
$341$	8.94997	+	15.5018i	0.484668	+	0.839470i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−8.34729	−	4.81931i	−0.450056	−	0.259840i
$345$		0			0
$346$		−	7.37731i		−	0.396607i
$347$	−3.58483	+	6.20911i	−0.192444	+	0.333323i	−0.946060	−	0.323993i	$-0.894975\pi$
$347$	−3.58483	+	6.20911i	−0.192444	+	0.333323i	0.753616	+	0.657315i	$0.228308\pi$
$348$		0			0
$349$	10.7155	−	6.18662i	0.573590	−	0.331162i	−0.184992	−	0.982740i	$-0.559226\pi$
$349$	10.7155	−	6.18662i	0.573590	−	0.331162i	0.758582	+	0.651578i	$0.225893\pi$
$350$	−1.80301			−0.0963749
$351$		0			0
$352$	−3.17452			−0.169203
$353$	−22.7018	+	13.1069i	−1.20830	+	0.697610i	−0.962387	−	0.271683i	$-0.912420\pi$
$353$	−22.7018	+	13.1069i	−1.20830	+	0.697610i	−0.245909	+	0.969293i	$0.579087\pi$
$354$		0			0
$355$	−0.535059	+	0.926750i	−0.0283980	+	0.0491868i
$356$		−	16.2931i		−	0.863532i
$357$		0			0
$358$	17.1648	+	9.91008i	0.907186	+	0.523764i
$359$		−	3.61956i		−	0.191033i	−0.995428	−	0.0955165i	$-0.969550\pi$
$359$		−	3.61956i		−	0.191033i	0.995428	−	0.0955165i	$-0.0304503\pi$
$360$		0			0
$361$	9.65506	+	16.7231i	0.508161	+	0.880161i
$362$	15.8713	−	9.16329i	0.834176	−	0.481612i
$363$		0			0
$364$	2.92531	+	2.10774i	0.153328	+	0.110476i
$365$	0.758070			0.0396792
$366$		0			0
$367$	4.03245	+	6.98440i	0.210492	+	0.364583i	0.951869	−	0.306506i	$-0.0991601\pi$
$367$	4.03245	+	6.98440i	0.210492	+	0.364583i	−0.741377	+	0.671089i	$0.765827\pi$
$368$	−3.06678	+	5.31181i	−0.159867	+	0.276897i
$369$		0			0
$370$	4.79549	+	2.76868i	0.249306	+	0.143937i
$371$	−3.11942	−	1.80100i	−0.161952	−	0.0935032i
$372$		0			0
$373$	−14.5851	+	25.2621i	−0.755187	+	1.30802i	0.190094	+	0.981766i	$0.439121\pi$
$373$	−14.5851	+	25.2621i	−0.755187	+	1.30802i	−0.945281	+	0.326257i	$0.894213\pi$
$374$	8.82681	+	15.2885i	0.456423	+	0.790549i
$375$		0			0
$376$	10.5086			0.541938
$377$	−4.37904	+	6.07759i	−0.225532	+	0.313012i
$378$		0			0
$379$	−23.3797	+	13.4983i	−1.20094	+	0.693361i	−0.960763	−	0.277369i	$-0.910538\pi$
$379$	−23.3797	+	13.4983i	−1.20094	+	0.693361i	−0.240173	+	0.970730i	$0.577204\pi$
$380$	−5.53347	−	9.58425i	−0.283861	−	0.491662i
$381$		0			0
$382$		−	15.0304i		−	0.769020i
$383$	−22.6159	−	13.0573i	−1.15562	−	0.667197i	−0.205368	−	0.978685i	$-0.565839\pi$
$383$	−22.6159	−	13.0573i	−1.15562	−	0.667197i	−0.950250	+	0.311488i	$0.899173\pi$
$384$		0			0
$385$		−	5.67609i		−	0.289280i
$386$	2.72745	−	4.72408i	0.138824	−	0.240450i
$387$		0			0
$388$	−15.1461	+	8.74462i	−0.768928	+	0.443941i
$389$	32.7110			1.65852			0.829258	−	0.558866i	$-0.188764\pi$
$389$	32.7110			1.65852			0.829258	+	0.558866i	$0.188764\pi$
$390$		0			0
$391$	34.1089			1.72496
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$		0			0
$394$	−3.81485	+	6.60751i	−0.192189	+	0.332882i
$395$			12.4491i			0.626383i
$396$		0			0
$397$	−0.524826	−	0.303008i	−0.0263403	−	0.0152076i	0.486772	−	0.873529i	$-0.338174\pi$
$397$	−0.524826	−	0.303008i	−0.0263403	−	0.0152076i	−0.513112	+	0.858321i	$0.671508\pi$
$398$			5.99023i			0.300263i
$399$		0			0
$400$	−0.901504	−	1.56145i	−0.0450752	−	0.0780726i
$401$	−8.83963	+	5.10356i	−0.441430	+	0.254860i	−0.704204	−	0.709998i	$-0.748696\pi$
$401$	−8.83963	+	5.10356i	−0.441430	+	0.254860i	0.262774	+	0.964857i	$0.415363\pi$
$402$		0			0
$403$	18.5399	−	8.34244i	0.923537	−	0.415566i
$404$	4.06866			0.202424
$405$		0			0
$406$	−1.03880	−	1.79925i	−0.0515546	−	0.0892952i
$407$	4.91564	−	8.51413i	0.243659	−	0.422030i
$408$		0			0
$409$	8.01863	+	4.62956i	0.396496	+	0.228917i	0.684971	−	0.728570i	$-0.259815\pi$
$409$	8.01863	+	4.62956i	0.396496	+	0.228917i	−0.288475	+	0.957487i	$0.593148\pi$
$410$	−2.32027	−	1.33961i	−0.114590	−	0.0661586i
$411$		0			0
$412$	−9.03838	+	15.6549i	−0.445289	+	0.771263i
$413$	1.39069	+	2.40874i	0.0684313	+	0.118527i
$414$		0			0
$415$	7.69254			0.377612
$416$	−0.362708	+	3.58726i	−0.0177832	+	0.175880i
$417$		0			0
$418$	−17.0163	+	9.82438i	−0.832296	+	0.480526i
$419$	6.42444	+	11.1275i	0.313855	+	0.543612i	0.979193	−	0.202930i	$-0.0650462\pi$
$419$	6.42444	+	11.1275i	0.313855	+	0.543612i	−0.665339	+	0.746542i	$0.731713\pi$
$420$		0			0
$421$			7.21371i			0.351575i	0.984428	+	0.175787i	$0.0562471\pi$
$421$			7.21371i			0.351575i	−0.984428	+	0.175787i	$0.943753\pi$
$422$	−2.40150	−	1.38651i	−0.116903	−	0.0674942i
$423$		0			0
$424$		−	3.60200i		−	0.174929i
$425$	−5.01329	+	8.68328i	−0.243180	+	0.421201i
$426$		0			0
$427$	−1.46254	+	0.844395i	−0.0707771	+	0.0408632i
$428$	−1.54169			−0.0745206
$429$		0			0
$430$	17.2340			0.831097
$431$	5.17941	−	2.99033i	0.249483	−	0.144039i	−0.370044	−	0.929014i	$-0.620658\pi$
$431$	5.17941	−	2.99033i	0.249483	−	0.144039i	0.619528	+	0.784975i	$0.287324\pi$
$432$		0			0
$433$	6.30144	−	10.9144i	0.302828	−	0.524513i	−0.673947	−	0.738779i	$-0.735403\pi$
$433$	6.30144	−	10.9144i	0.302828	−	0.524513i	0.976775	+	0.214266i	$0.0687359\pi$
$434$			5.63862i			0.270663i
$435$		0			0
$436$	−6.38894	−	3.68865i	−0.305975	−	0.176655i
$437$			37.9637i			1.81605i
$438$		0			0
$439$	9.77965	+	16.9389i	0.466757	+	0.808447i	0.999279	−	0.0379690i	$-0.0120888\pi$
$439$	9.77965	+	16.9389i	0.466757	+	0.808447i	−0.532522	+	0.846416i	$0.678755\pi$
$440$	4.91564	−	2.83804i	0.234344	−	0.135298i
$441$		0			0
$442$	18.2847	−	8.22764i	0.869717	−	0.391349i
$443$	40.2601			1.91281			0.956407	−	0.292038i	$-0.0943335\pi$
$443$	40.2601			1.91281			0.956407	+	0.292038i	$0.0943335\pi$
$444$		0			0
$445$	14.5661	+	25.2293i	0.690500	+	1.19598i
$446$	−11.2677	+	19.5163i	−0.533542	+	0.924121i
$447$		0			0
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	24.7821	+	14.3079i	1.16954	+	0.675234i	0.953571	−	0.301167i	$-0.0973762\pi$
$449$	24.7821	+	14.3079i	1.16954	+	0.675234i	0.215967	+	0.976401i	$0.430710\pi$
$450$		0			0
$451$	−2.37841	+	4.11952i	−0.111995	+	0.193981i
$452$	4.95660	+	8.58509i	0.233139	+	0.403809i
$453$		0			0
$454$	−1.83155			−0.0859587
$455$	−6.41407	−	0.648527i	−0.300696	−	0.0304034i
$456$		0			0
$457$	5.49961	−	3.17520i	0.257261	−	0.148530i	−0.365824	−	0.930684i	$-0.619213\pi$
$457$	5.49961	−	3.17520i	0.257261	−	0.148530i	0.623084	+	0.782155i	$0.285879\pi$
$458$	11.3030	+	19.5774i	0.528155	+	0.914791i
$459$		0			0
$460$		−	10.9669i		−	0.511333i
$461$	−20.9785	−	12.1119i	−0.977065	−	0.564109i	−0.0756821	−	0.997132i	$-0.524113\pi$
$461$	−20.9785	−	12.1119i	−0.977065	−	0.564109i	−0.901383	+	0.433023i	$0.857447\pi$
$462$		0			0
$463$			17.3851i			0.807954i	0.914769	+	0.403977i	$0.132372\pi$
$463$			17.3851i			0.807954i	−0.914769	+	0.403977i	$0.867628\pi$
$464$	1.03880	−	1.79925i	0.0482249	−	0.0835280i
$465$		0			0
$466$	−8.17439	+	4.71948i	−0.378671	+	0.218626i
$467$	14.8537			0.687349			0.343675	−	0.939089i	$-0.388328\pi$
$467$	14.8537			0.687349			0.343675	+	0.939089i	$0.388328\pi$
$468$		0			0
$469$	−11.5544			−0.533532
$470$	−16.2722	+	9.39473i	−0.750579	+	0.433347i
$471$		0			0
$472$	−1.39069	+	2.40874i	−0.0640117	+	0.110871i
$473$		−	30.5980i		−	1.40690i
$474$		0			0
$475$	−9.66463	−	5.57988i	−0.443444	−	0.256022i
$476$			5.56103i			0.254889i
$477$		0			0
$478$	−7.93787	−	13.7488i	−0.363070	−	0.628855i
$479$	33.5014	−	19.3420i	1.53072	−	0.883759i	0.531387	−	0.847129i	$-0.321671\pi$
$479$	33.5014	−	19.3420i	1.53072	−	0.883759i	0.999329	−	0.0366302i	$-0.0116624\pi$
$480$		0			0
$481$	−9.05947	−	6.52754i	−0.413076	−	0.297630i
$482$	−23.9251			−1.08976
$483$		0			0
$484$	0.461204	+	0.798828i	0.0209638	+	0.0363104i
$485$	15.6355	−	27.0815i	0.709971	−	1.22971i
$486$		0			0
$487$	22.2780	+	12.8622i	1.00951	+	0.582843i	0.911049	−	0.412298i	$-0.135274\pi$
$487$	22.2780	+	12.8622i	1.00951	+	0.582843i	0.0984640	+	0.995141i	$0.468607\pi$
$488$	−1.46254	−	0.844395i	−0.0662059	−	0.0382240i
$489$		0			0
$490$	0.894007	−	1.54846i	0.0403871	−	0.0699525i
$491$	9.17452	+	15.8907i	0.414040	+	0.717139i	0.995327	−	0.0965597i	$-0.0307839\pi$
$491$	9.17452	+	15.8907i	0.414040	+	0.717139i	−0.581287	+	0.813699i	$0.697451\pi$
$492$		0			0
$493$	−11.5536			−0.520346
$494$	9.15749	+	20.3512i	0.412015	+	0.915644i
$495$		0			0
$496$	−4.88319	+	2.81931i	−0.219262	+	0.126591i
$497$	0.299248	+	0.518313i	0.0134231	+	0.0232495i
$498$		0			0
$499$		−	17.8096i		−	0.797269i	−0.917110	−	0.398635i	$-0.869484\pi$
$499$		−	17.8096i		−	0.797269i	0.917110	−	0.398635i	$-0.130516\pi$
$500$	10.5342	+	6.08193i	0.471105	+	0.271992i
$501$		0			0
$502$			20.5236i			0.916012i
$503$	15.4711	−	26.7967i	0.689823	−	1.19481i	−0.282072	−	0.959393i	$-0.591022\pi$
$503$	15.4711	−	26.7967i	0.689823	−	1.19481i	0.971895	−	0.235415i	$-0.0756448\pi$
$504$		0			0
$505$	−6.30019	+	3.63741i	−0.280355	+	0.161863i
$506$	−19.4711			−0.865596
$507$		0			0
$508$	18.3490			0.814107
$509$	−11.9583	+	6.90414i	−0.530044	+	0.306021i	−0.741034	−	0.671467i	$-0.765664\pi$
$509$	−11.9583	+	6.90414i	−0.530044	+	0.306021i	0.210991	+	0.977488i	$0.432331\pi$
$510$		0			0
$511$	0.211987	−	0.367172i	0.00937774	−	0.0162427i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−0.715933	−	0.413344i	−0.0315784	−	0.0182318i
$515$		−	32.3215i		−	1.42425i
$516$		0			0
$517$	16.6798	+	28.8903i	0.733579	+	1.27060i
$518$	2.68202	−	1.54846i	0.117841	−	0.0680356i
$519$		0			0
$520$	−2.64539	−	5.87901i	−0.116008	−	0.257812i
$521$	11.4549			0.501848			0.250924	−	0.968007i	$-0.419266\pi$
$521$	11.4549			0.501848			0.250924	+	0.968007i	$0.419266\pi$
$522$		0			0
$523$	−0.465198	−	0.805747i	−0.0203417	−	0.0352329i	0.855675	−	0.517513i	$-0.173142\pi$
$523$	−0.465198	−	0.805747i	−0.0203417	−	0.0352329i	−0.876017	+	0.482280i	$0.839809\pi$
$524$	−2.95964	+	5.12624i	−0.129292	+	0.223941i
$525$		0			0
$526$	−17.6331	−	10.1805i	−0.768838	−	0.443889i
$527$	27.1556	+	15.6783i	1.18292	+	0.682957i
$528$		0			0
$529$	−7.31025	+	12.6617i	−0.317837	+	0.550510i
$530$	3.22021	+	5.57757i	0.139877	+	0.242274i
$531$		0			0
$532$	−6.18952			−0.268350
$533$	4.38338	+	3.15832i	0.189865	+	0.136802i
$534$		0			0
$535$	2.38726	−	1.37828i	0.103210	−	0.0595884i
$536$	−5.77720	−	10.0064i	−0.249537	−	0.432211i
$537$		0			0
$538$		−	20.5175i		−	0.884572i
$539$	−2.74922	−	1.58726i	−0.118417	−	0.0683682i
$540$		0			0
$541$		−	22.7965i		−	0.980097i	−0.871695	−	0.490048i	$-0.836979\pi$
$541$		−	22.7965i		−	0.980097i	0.871695	−	0.490048i	$-0.163021\pi$
$542$	6.09076	−	10.5495i	0.261621	−	0.453140i
$543$		0			0
$544$	−4.81599	+	2.78052i	−0.206484	+	0.119214i
$545$	13.1907			0.565029
$546$		0			0
$547$	31.6698			1.35410			0.677052	−	0.735935i	$-0.263257\pi$
$547$	31.6698			1.35410			0.677052	+	0.735935i	$0.263257\pi$
$548$	−7.62363	+	4.40150i	−0.325665	+	0.188023i
$549$		0			0
$550$	2.86185	−	4.95686i	0.122029	−	0.211361i
$551$		−	12.8593i		−	0.547824i
$552$		0			0
$553$	6.02973	+	3.48127i	0.256410	+	0.148039i
$554$			8.62484i			0.366434i
$555$		0			0
$556$	9.48720	+	16.4323i	0.402347	+	0.696885i
$557$	9.38623	−	5.41914i	0.397707	−	0.229616i	−0.287787	−	0.957694i	$-0.592920\pi$
$557$	9.38623	−	5.41914i	0.397707	−	0.229616i	0.685494	+	0.728078i	$0.259586\pi$
$558$		0			0
$559$	−34.5763	−	3.49601i	−1.46242	−	0.147865i
$560$	1.78801			0.0755574
$561$		0			0
$562$	−12.1461	−	21.0377i	−0.512353	−	0.887422i
$563$	−7.73626	+	13.3996i	−0.326044	+	0.564725i	−0.981723	−	0.190315i	$-0.939049\pi$
$563$	−7.73626	+	13.3996i	−0.326044	+	0.564725i	0.655679	+	0.755040i	$0.272383\pi$
$564$		0			0
$565$	−15.3503	−	8.86247i	−0.645790	−	0.372847i
$566$	−9.28472	−	5.36054i	−0.390266	−	0.225320i
$567$		0			0
$568$	−0.299248	+	0.518313i	−0.0125562	+	0.0217479i
$569$	−16.8667	−	29.2139i	−0.707088	−	1.22471i	−0.965933	−	0.258793i	$-0.916675\pi$
$569$	−16.8667	−	29.2139i	−0.707088	−	1.22471i	0.258845	−	0.965919i	$-0.416658\pi$
$570$		0			0
$571$	−43.6140			−1.82519			−0.912594	−	0.408868i	$-0.865924\pi$
$571$	−43.6140			−1.82519			−0.912594	+	0.408868i	$0.865924\pi$
$572$	−10.4379	+	4.69676i	−0.436429	+	0.196381i
$573$		0			0
$574$	−1.29768	+	0.749217i	−0.0541642	+	0.0312717i
$575$	−5.52943	−	9.57725i	−0.230593	−	0.399399i
$576$		0			0
$577$			10.8368i			0.451143i	0.974227	+	0.225571i	$0.0724249\pi$
$577$			10.8368i			0.451143i	−0.974227	+	0.225571i	$0.927575\pi$
$578$	12.0595	+	6.96254i	0.501608	+	0.289603i
$579$		0			0
$580$			3.71476i			0.154247i
$581$	2.15114	−	3.72589i	0.0892444	−	0.154576i
$582$		0			0
$583$	9.90268	−	5.71731i	0.410127	−	0.236787i
$584$	0.423973			0.0175441
$585$		0			0
$586$	−21.4278			−0.885176
$587$	−22.5632	+	13.0269i	−0.931284	+	0.537677i	−0.887217	−	0.461352i	$-0.847365\pi$
$587$	−22.5632	+	13.0269i	−0.931284	+	0.537677i	−0.0440666	+	0.999029i	$0.514031\pi$
$588$		0			0
$589$	−17.4502	+	30.2246i	−0.719022	+	1.24538i
$590$		−	4.97314i		−	0.204741i
$591$		0			0
$592$	2.68202	+	1.54846i	0.110230	+	0.0636415i
$593$			1.68393i			0.0691509i	0.999402	+	0.0345754i	$0.0110079\pi$
$593$			1.68393i			0.0691509i	−0.999402	+	0.0345754i	$0.988992\pi$
$594$		0			0
$595$	−4.97160	−	8.61106i	−0.203816	−	0.353019i
$596$	−12.0919	+	6.98127i	−0.495304	+	0.285964i
$597$		0			0
$598$	−2.22469	+	22.0027i	−0.0909743	+	0.899756i
$599$	6.54081			0.267250			0.133625	−	0.991032i	$-0.457338\pi$
$599$	6.54081			0.267250			0.133625	+	0.991032i	$0.457338\pi$
$600$		0			0
$601$	−19.2387	−	33.3224i	−0.784763	−	1.35925i	−0.929140	−	0.369727i	$-0.879451\pi$
$601$	−19.2387	−	33.3224i	−0.784763	−	1.35925i	0.144377	−	0.989523i	$-0.453882\pi$
$602$	4.81931	−	8.34729i	0.196420	−	0.340210i
$603$		0			0
$604$	−15.4522	−	8.92131i	−0.628740	−	0.363003i
$605$	−1.42832	−	0.824638i	−0.0580693	−	0.0335263i
$606$		0			0
$607$	4.71797	−	8.17176i	0.191496	−	0.331682i	−0.754250	−	0.656587i	$-0.771999\pi$
$607$	4.71797	−	8.17176i	0.191496	−	0.331682i	0.945746	+	0.324906i	$0.105333\pi$
$608$	−3.09476	−	5.36028i	−0.125509	−	0.217388i
$609$		0			0
$610$	3.01958			0.122259
$611$	34.5523	−	15.5476i	1.39784	−	0.628989i
$612$		0			0
$613$	−22.0191	+	12.7127i	−0.889342	+	0.513462i	−0.873727	−	0.486416i	$-0.838304\pi$
$613$	−22.0191	+	12.7127i	−0.889342	+	0.513462i	−0.0156146	+	0.999878i	$0.504970\pi$
$614$	−3.79682	−	6.57628i	−0.153227	−	0.265397i
$615$		0			0
$616$		−	3.17452i		−	0.127905i
$617$	−24.8545	−	14.3497i	−1.00060	−	0.577699i	−0.0921772	−	0.995743i	$-0.529383\pi$
$617$	−24.8545	−	14.3497i	−1.00060	−	0.577699i	−0.908427	+	0.418044i	$0.862716\pi$
$618$		0			0
$619$		−	9.61494i		−	0.386457i	−0.981154	−	0.193229i	$-0.938104\pi$
$619$		−	9.61494i		−	0.386457i	0.981154	−	0.193229i	$-0.0618959\pi$
$620$	5.04097	−	8.73121i	0.202450	−	0.350654i
$621$		0			0
$622$	22.2010	−	12.8177i	0.890178	−	0.513945i
$623$	16.2931			0.652769
$624$		0			0
$625$	−12.7341			−0.509365
$626$	1.48357	−	0.856542i	0.0592956	−	0.0342343i
$627$		0			0
$628$	2.28958	−	3.96567i	0.0913642	−	0.158247i
$629$		−	17.2221i		−	0.686691i
$630$		0			0
$631$	29.9445	+	17.2885i	1.19207	+	0.688244i	0.958776	−	0.284162i	$-0.0917153\pi$
$631$	29.9445	+	17.2885i	1.19207	+	0.688244i	0.233297	+	0.972406i	$0.425049\pi$
$632$			6.96254i			0.276955i
$633$		0			0
$634$	−16.6049	−	28.7605i	−0.659465	−	1.14223i
$635$	−28.4129	+	16.4042i	−1.12753	+	0.650980i
$636$		0			0
$637$	−2.10774	+	2.92531i	−0.0835119	+	0.115905i
$638$	6.59536			0.261113
$639$		0			0
$640$	0.894007	+	1.54846i	0.0353387	+	0.0612085i
$641$	−3.25646	+	5.64035i	−0.128622	+	0.222780i	−0.923143	−	0.384457i	$-0.874389\pi$
$641$	−3.25646	+	5.64035i	−0.128622	+	0.222780i	0.794521	+	0.607237i	$0.207722\pi$
$642$		0			0
$643$	−21.8991	−	12.6435i	−0.863617	−	0.498609i	0.00160504	−	0.999999i	$-0.499489\pi$
$643$	−21.8991	−	12.6435i	−0.863617	−	0.498609i	−0.865222	+	0.501389i	$0.832822\pi$
$644$	−5.31181	−	3.06678i	−0.209315	−	0.120848i
$645$		0			0
$646$	−17.2101	+	29.8087i	−0.677120	+	1.17281i
$647$	−5.95794	−	10.3194i	−0.234231	−	0.405699i	0.724818	−	0.688940i	$-0.241924\pi$
$647$	−5.95794	−	10.3194i	−0.234231	−	0.405699i	−0.959049	+	0.283241i	$0.908590\pi$
$648$		0			0
$649$	−8.82955			−0.346590
$650$	−5.27435	−	3.80028i	−0.206877	−	0.149059i
$651$		0			0
$652$	10.6267	−	6.13531i	0.416172	−	0.240277i
$653$	20.7508	+	35.9415i	0.812043	+	1.40650i	0.911432	+	0.411451i	$0.134978\pi$
$653$	20.7508	+	35.9415i	0.812043	+	1.40650i	−0.0993891	+	0.995049i	$0.531689\pi$
$654$		0			0
$655$		−	10.5837i		−	0.413541i
$656$	−1.29768	−	0.749217i	−0.0506660	−	0.0292520i
$657$		0			0
$658$			10.5086i			0.409667i
$659$	7.86778	−	13.6274i	0.306485	−	0.530848i	−0.671106	−	0.741362i	$-0.734180\pi$
$659$	7.86778	−	13.6274i	0.306485	−	0.530848i	0.977591	+	0.210514i	$0.0675137\pi$
$660$		0			0
$661$	−22.6071	+	13.0522i	−0.879315	+	0.507673i	−0.870432	−	0.492288i	$-0.836161\pi$
$661$	−22.6071	+	13.0522i	−0.879315	+	0.507673i	−0.00888248	+	0.999961i	$0.502827\pi$
$662$	−4.95987			−0.192771
$663$		0			0
$664$	4.30228			0.166961
$665$	9.58425	−	5.53347i	0.371661	−	0.214579i
$666$		0			0
$667$	6.37151	−	11.0358i	0.246706	−	0.427307i
$668$			16.6981i			0.646068i
$669$		0			0
$670$	17.8916	+	10.3297i	0.691212	+	0.399071i
$671$		−	5.36110i		−	0.206963i
$672$		0			0
$673$	0.620853	+	1.07535i	0.0239321	+	0.0414516i	0.877743	−	0.479131i	$-0.159048\pi$
$673$	0.620853	+	1.07535i	0.0239321	+	0.0414516i	−0.853811	+	0.520583i	$0.825715\pi$
$674$	−20.4532	+	11.8087i	−0.787829	+	0.454853i
$675$		0			0
$676$	4.11482	+	12.3316i	0.158262	+	0.474292i
$677$	−29.2845			−1.12550			−0.562748	−	0.826629i	$-0.690256\pi$
$677$	−29.2845			−1.12550			−0.562748	+	0.826629i	$0.690256\pi$
$678$		0			0
$679$	−8.74462	−	15.1461i	−0.335588	−	0.581255i
$680$	4.97160	−	8.61106i	0.190652	−	0.330219i
$681$		0			0
$682$	−15.5018	−	8.94997i	−0.593595	−	0.342712i
$683$	37.0486	+	21.3900i	1.41762	+	0.818466i	0.996090	−	0.0883461i	$-0.0281581\pi$
$683$	37.0486	+	21.3900i	1.41762	+	0.818466i	0.421535	+	0.906812i	$0.361491\pi$
$684$		0			0
$685$	7.86995	−	13.6311i	0.300695	−	0.520819i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	9.63862			0.367469
$689$	−5.32922	−	11.8434i	−0.203027	−	0.451198i
$690$		0			0
$691$	−16.3649	+	9.44827i	−0.622549	+	0.359429i	−0.777861	−	0.628437i	$-0.783695\pi$
$691$	−16.3649	+	9.44827i	−0.622549	+	0.359429i	0.155312	+	0.987866i	$0.450362\pi$
$692$	3.68865	+	6.38894i	0.140222	+	0.242871i
$693$		0			0
$694$		−	7.16967i		−	0.272157i
$695$	−29.3812	−	16.9632i	−1.11449	−	0.643452i
$696$		0			0
$697$			8.33284i			0.315629i
$698$	−6.18662	+	10.7155i	−0.234167	+	0.405589i
$699$		0			0
$700$	1.56145	−	0.901504i	0.0590173	−	0.0340737i
$701$	3.35161			0.126589			0.0632943	−	0.997995i	$-0.479839\pi$
$701$	3.35161			0.126589			0.0632943	+	0.997995i	$0.479839\pi$
$702$		0			0
$703$	19.1685			0.722954
$704$	2.74922	−	1.58726i	0.103615	−	0.0598222i
$705$		0			0
$706$	13.1069	−	22.7018i	0.493285	−	0.854395i
$707$			4.06866i			0.153018i
$708$		0			0
$709$	31.8468	+	18.3867i	1.19603	+	0.690529i	0.959668	−	0.281136i	$-0.0907113\pi$
$709$	31.8468	+	18.3867i	1.19603	+	0.690529i	0.236363	+	0.971665i	$0.424045\pi$
$710$		−	1.07012i		−	0.0401608i
$711$		0			0
$712$	8.14654	+	14.1102i	0.305305	+	0.528803i
$713$	−29.9513	+	17.2924i	−1.12169	+	0.647606i
$714$		0			0
$715$	11.9637	−	16.6043i	0.447419	−	0.620965i
$716$	−19.8202			−0.740714
$717$		0			0
$718$	1.80978	+	3.13463i	0.0675404	+	0.116983i
$719$	−8.08486	+	14.0034i	−0.301514	+	0.522238i	−0.976479	−	0.215612i	$-0.930825\pi$
$719$	−8.08486	+	14.0034i	−0.301514	+	0.522238i	0.674965	+	0.737850i	$0.264159\pi$
$720$		0			0
$721$	−15.6549	−	9.03838i	−0.583020	−	0.336607i
$722$	−16.7231	−	9.65506i	−0.622368	−	0.359324i
$723$		0			0
$724$	−9.16329	+	15.8713i	−0.340551	+	0.589851i
$725$	1.87296	+	3.24406i	0.0695599	+	0.120481i
$726$		0			0
$727$	27.2522			1.01073			0.505363	−	0.862907i	$-0.331358\pi$
$727$	27.2522			1.01073			0.505363	+	0.862907i	$0.331358\pi$
$728$	−3.58726	−	0.362708i	−0.132953	−	0.0134429i
$729$		0			0
$730$	−0.656508	+	0.379035i	−0.0242984	+	0.0140287i
$731$	−26.8003	−	46.4196i	−0.991247	−	1.71689i
$732$		0			0
$733$		−	39.6734i		−	1.46537i	−0.680567	−	0.732686i	$-0.738267\pi$
$733$		−	39.6734i		−	1.46537i	0.680567	−	0.732686i	$-0.261733\pi$
$734$	−6.98440	−	4.03245i	−0.257799	−	0.148840i
$735$		0			0
$736$		−	6.13356i		−	0.226086i
$737$	18.3398	−	31.7655i	0.675557	−	1.17010i
$738$		0			0
$739$	−22.0125	+	12.7089i	−0.809742	+	0.467505i	−0.846866	−	0.531806i	$-0.821514\pi$
$739$	−22.0125	+	12.7089i	−0.809742	+	0.467505i	0.0371244	+	0.999311i	$0.488180\pi$
$740$	−5.53735			−0.203557
$741$		0			0
$742$	3.60200			0.132234
$743$	21.5143	−	12.4213i	0.789285	−	0.455694i	−0.0504260	−	0.998728i	$-0.516058\pi$
$743$	21.5143	−	12.4213i	0.789285	−	0.455694i	0.839711	+	0.543034i	$0.182725\pi$
$744$		0			0
$745$	12.4826	−	21.6205i	0.457327	−	0.792114i
$746$		−	29.1702i		−	1.06800i
$747$		0			0
$748$	−15.2885	−	8.82681i	−0.559002	−	0.322740i
$749$		−	1.54169i		−	0.0563323i
$750$		0			0
$751$	−22.7211	−	39.3540i	−0.829103	−	1.43605i	−0.898743	−	0.438476i	$-0.855518\pi$
$751$	−22.7211	−	39.3540i	−0.829103	−	1.43605i	0.0696398	−	0.997572i	$-0.477815\pi$
$752$	−9.10069	+	5.25429i	−0.331868	+	0.191604i
$753$		0			0
$754$	0.753559	−	7.45287i	0.0274430	−	0.271417i
$755$	31.9028			1.16106
$756$		0			0
$757$	−3.20643	−	5.55369i	−0.116540	−	0.201852i	0.801855	−	0.597519i	$-0.203847\pi$
$757$	−3.20643	−	5.55369i	−0.116540	−	0.201852i	−0.918394	+	0.395667i	$0.870514\pi$
$758$	13.4983	−	23.3797i	0.490280	−	0.849190i
$759$		0			0
$760$	9.58425	+	5.53347i	0.347657	+	0.200720i
$761$	−27.8313	−	16.0684i	−1.00888	−	0.582479i	−0.0980185	−	0.995185i	$-0.531250\pi$
$761$	−27.8313	−	16.0684i	−1.00888	−	0.582479i	−0.910864	+	0.412706i	$0.864584\pi$
$762$		0			0
$763$	3.68865	−	6.38894i	0.133538	−	0.231295i
$764$	7.51518	+	13.0167i	0.271890	+	0.470927i
$765$		0			0
$766$	26.1146			0.943558
$767$	−1.00883	+	9.97753i	−0.0364267	+	0.360268i
$768$		0			0
$769$	−33.7551	+	19.4885i	−1.21724	+	0.702774i	−0.964327	−	0.264714i	$-0.914722\pi$
$769$	−33.7551	+	19.4885i	−1.21724	+	0.702774i	−0.252914	+	0.967489i	$0.581389\pi$
$770$	2.83804	+	4.91564i	0.102276	+	0.177147i
$771$		0			0
$772$			5.45490i			0.196326i
$773$	−2.09922	−	1.21199i	−0.0755038	−	0.0435921i	0.461773	−	0.886998i	$-0.347214\pi$
$773$	−2.09922	−	1.21199i	−0.0755038	−	0.0435921i	−0.537277	+	0.843406i	$0.680547\pi$
$774$		0			0
$775$		−	10.1665i		−	0.365191i
$776$	8.74462	−	15.1461i	0.313913	−	0.543714i
$777$		0			0
$778$	−28.3286	+	16.3555i	−1.01563	+	0.586374i
$779$	−9.27458			−0.332296
$780$		0			0
$781$	−1.89994			−0.0679851
$782$	−29.5392	+	17.0544i	−1.05632	+	0.609866i

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.78801i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.78801i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.894007 - 1.54846i) q^{10} +(-2.74922 + 1.58726i) q^{11} +(1.47952 + 3.28801i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.78052 + 4.81599i) q^{17} +(-5.36028 - 3.09476i) q^{19} +(1.54846 + 0.894007i) q^{20} +(1.58726 - 2.74922i) q^{22} +(-3.06678 - 5.31181i) q^{23} +1.80301 q^{25} +(-2.92531 - 2.10774i) q^{26} +(0.866025 - 0.500000i) q^{28} +(1.03880 + 1.79925i) q^{29} -5.63862i q^{31} +(0.866025 + 0.500000i) q^{32} -5.56103i q^{34} +(-0.894007 + 1.54846i) q^{35} +(-2.68202 + 1.54846i) q^{37} +6.18952 q^{38} -1.78801 q^{40} +(1.29768 - 0.749217i) q^{41} +(-4.81931 + 8.34729i) q^{43} +3.17452i q^{44} +(5.31181 + 3.06678i) q^{46} -10.5086i q^{47} +(0.500000 + 0.866025i) q^{49} +(-1.56145 + 0.901504i) q^{50} +(3.58726 + 0.362708i) q^{52} -3.60200 q^{53} +(-2.83804 - 4.91564i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-1.79925 - 1.03880i) q^{58} +(2.40874 + 1.39069i) q^{59} +(-0.844395 + 1.46254i) q^{61} +(2.81931 + 4.88319i) q^{62} -1.00000 q^{64} +(-5.87901 + 2.64539i) q^{65} +(-10.0064 + 5.77720i) q^{67} +(2.78052 + 4.81599i) q^{68} -1.78801i q^{70} +(0.518313 + 0.299248i) q^{71} -0.423973i q^{73} +(1.54846 - 2.68202i) q^{74} +(-5.36028 + 3.09476i) q^{76} -3.17452 q^{77} +6.96254 q^{79} +(1.54846 - 0.894007i) q^{80} +(-0.749217 + 1.29768i) q^{82} -4.30228i q^{83} +(-8.61106 - 4.97160i) q^{85} -9.63862i q^{86} +(-1.58726 - 2.74922i) q^{88} +(14.1102 - 8.14654i) q^{89} +(-0.362708 + 3.58726i) q^{91} -6.13356 q^{92} +(5.25429 + 9.10069i) q^{94} +(5.53347 - 9.58425i) q^{95} +(-15.1461 - 8.74462i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 + 6 * q^10 - 6 * q^11 + 12 * q^13 - 8 * q^14 - 4 * q^16 - 2 * q^17 - 12 * q^19 + 6 * q^20 - 4 * q^22 - 8 * q^23 - 24 * q^25 - 6 * q^26 - 2 * q^29 + 6 * q^35 + 18 * q^37 + 4 * q^38 + 12 * q^40 - 12 * q^41 - 8 * q^43 + 18 * q^46 + 4 * q^49 - 12 * q^50 + 12 * q^52 + 12 * q^53 - 22 * q^55 - 4 * q^56 - 24 * q^58 - 18 * q^59 - 8 * q^61 - 8 * q^62 - 8 * q^64 - 46 * q^65 + 18 * q^67 + 2 * q^68 - 6 * q^71 + 6 * q^74 - 12 * q^76 + 8 * q^77 - 4 * q^79 + 6 * q^80 + 10 * q^82 - 54 * q^85 + 4 * q^88 + 18 * q^89 + 6 * q^91 - 16 * q^92 - 2 * q^94 + 50 * q^95 - 54 * q^97

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