LMFDB - Embedded newform 731.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.a (trivial)

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:	yes
Analytic conductor:	$5.83706438776$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.2460365.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 6x^{4} + 6x^{3} + 7x^{2} - 7x + 1 $ x^6 - x^5 - 6x^4 + 6x^3 + 7x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.668929$ of defining polynomial
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.55253 q^{2} +0.467968 q^{3} +0.410361 q^{4} -1.37639 q^{5} +0.726536 q^{6} -3.35157 q^{7} -2.46797 q^{8} -2.78101 q^{9} +O(q^{10})$	\(q+1.55253 q^{2} +0.467968 q^{3} +0.410361 q^{4} -1.37639 q^{5} +0.726536 q^{6} -3.35157 q^{7} -2.46797 q^{8} -2.78101 q^{9} -2.13690 q^{10} +2.05761 q^{11} +0.192036 q^{12} -1.60557 q^{13} -5.20343 q^{14} -0.644108 q^{15} -4.65233 q^{16} -1.00000 q^{17} -4.31761 q^{18} +4.43647 q^{19} -0.564818 q^{20} -1.56843 q^{21} +3.19450 q^{22} -2.95501 q^{23} -1.15493 q^{24} -3.10554 q^{25} -2.49271 q^{26} -2.70533 q^{27} -1.37535 q^{28} -3.13539 q^{29} -1.00000 q^{30} -4.72687 q^{31} -2.28696 q^{32} +0.962895 q^{33} -1.55253 q^{34} +4.61308 q^{35} -1.14122 q^{36} +6.73408 q^{37} +6.88777 q^{38} -0.751357 q^{39} +3.39690 q^{40} +9.28079 q^{41} -2.43504 q^{42} -1.00000 q^{43} +0.844362 q^{44} +3.82776 q^{45} -4.58775 q^{46} -8.52365 q^{47} -2.17714 q^{48} +4.23304 q^{49} -4.82146 q^{50} -0.467968 q^{51} -0.658865 q^{52} +9.33387 q^{53} -4.20011 q^{54} -2.83208 q^{55} +8.27157 q^{56} +2.07613 q^{57} -4.86779 q^{58} -9.83672 q^{59} -0.264317 q^{60} +2.75383 q^{61} -7.33862 q^{62} +9.32074 q^{63} +5.75407 q^{64} +2.20990 q^{65} +1.49493 q^{66} +8.84901 q^{67} -0.410361 q^{68} -1.38285 q^{69} +7.16197 q^{70} -1.37235 q^{71} +6.86343 q^{72} -0.237911 q^{73} +10.4549 q^{74} -1.45329 q^{75} +1.82055 q^{76} -6.89622 q^{77} -1.16651 q^{78} -7.25698 q^{79} +6.40343 q^{80} +7.07701 q^{81} +14.4087 q^{82} -2.15336 q^{83} -0.643622 q^{84} +1.37639 q^{85} -1.55253 q^{86} -1.46726 q^{87} -5.07811 q^{88} -13.4194 q^{89} +5.94272 q^{90} +5.38120 q^{91} -1.21262 q^{92} -2.21202 q^{93} -13.2332 q^{94} -6.10633 q^{95} -1.07022 q^{96} -12.3738 q^{97} +6.57194 q^{98} -5.72222 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{5} - 7 q^{6} - 7 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - q^2 - 3 * q^3 + 5 * q^4 + 3 * q^5 - 7 * q^6 - 7 * q^7 - 9 * q^8 - 3 * q^9	\( 6 q - q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{5} - 7 q^{6} - 7 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{10} + 4 q^{11} + 11 q^{12} - 10 q^{13} - 7 q^{14} + q^{15} - q^{16} - 6 q^{17} + q^{18} - 20 q^{19} + q^{20} - 8 q^{21} + 2 q^{22} - 3 q^{23} - 9 q^{24} - 7 q^{25} - 3 q^{26} - 6 q^{27} - 11 q^{28} - 15 q^{29} - 6 q^{30} + 12 q^{31} + q^{32} - 2 q^{33} + q^{34} - 9 q^{35} - 16 q^{36} - 14 q^{37} + 27 q^{38} + 5 q^{39} - 7 q^{40} - 2 q^{41} + 19 q^{42} - 6 q^{43} - 12 q^{44} - 18 q^{45} + 14 q^{46} - 11 q^{47} - 6 q^{48} + 3 q^{49} + 7 q^{50} + 3 q^{51} - 5 q^{52} + 3 q^{53} + 25 q^{54} + 6 q^{55} + 22 q^{56} + 11 q^{57} - 21 q^{58} + 2 q^{59} - q^{60} - 20 q^{61} + 3 q^{62} + 23 q^{63} - 39 q^{64} - 34 q^{65} + 7 q^{66} - 2 q^{67} - 5 q^{68} - 17 q^{69} - q^{70} + q^{71} + 21 q^{72} + 13 q^{73} + 28 q^{74} - 5 q^{75} - 29 q^{76} - 11 q^{77} - 26 q^{79} + 12 q^{80} + 2 q^{81} - 9 q^{82} + 10 q^{83} - 3 q^{84} - 3 q^{85} + q^{86} + 12 q^{87} - 6 q^{88} - 15 q^{89} + 15 q^{90} + 8 q^{91} - 9 q^{92} - 11 q^{93} - 33 q^{94} - 21 q^{95} + 25 q^{96} - 22 q^{97} - 3 q^{98} - 5 q^{99}+O(q^{100}) \) 6 * q - q^2 - 3 * q^3 + 5 * q^4 + 3 * q^5 - 7 * q^6 - 7 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^10 + 4 * q^11 + 11 * q^12 - 10 * q^13 - 7 * q^14 + q^15 - q^16 - 6 * q^17 + q^18 - 20 * q^19 + q^20 - 8 * q^21 + 2 * q^22 - 3 * q^23 - 9 * q^24 - 7 * q^25 - 3 * q^26 - 6 * q^27 - 11 * q^28 - 15 * q^29 - 6 * q^30 + 12 * q^31 + q^32 - 2 * q^33 + q^34 - 9 * q^35 - 16 * q^36 - 14 * q^37 + 27 * q^38 + 5 * q^39 - 7 * q^40 - 2 * q^41 + 19 * q^42 - 6 * q^43 - 12 * q^44 - 18 * q^45 + 14 * q^46 - 11 * q^47 - 6 * q^48 + 3 * q^49 + 7 * q^50 + 3 * q^51 - 5 * q^52 + 3 * q^53 + 25 * q^54 + 6 * q^55 + 22 * q^56 + 11 * q^57 - 21 * q^58 + 2 * q^59 - q^60 - 20 * q^61 + 3 * q^62 + 23 * q^63 - 39 * q^64 - 34 * q^65 + 7 * q^66 - 2 * q^67 - 5 * q^68 - 17 * q^69 - q^70 + q^71 + 21 * q^72 + 13 * q^73 + 28 * q^74 - 5 * q^75 - 29 * q^76 - 11 * q^77 - 26 * q^79 + 12 * q^80 + 2 * q^81 - 9 * q^82 + 10 * q^83 - 3 * q^84 - 3 * q^85 + q^86 + 12 * q^87 - 6 * q^88 - 15 * q^89 + 15 * q^90 + 8 * q^91 - 9 * q^92 - 11 * q^93 - 33 * q^94 - 21 * q^95 + 25 * q^96 - 22 * q^97 - 3 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.55253	1.09781	0.548904	−	0.835886i	$-0.315045\pi$
$2$	1.55253	1.09781	0.548904	+	0.835886i	$0.315045\pi$
$3$	0.467968	0.270182	0.135091	−	0.990833i	$-0.456867\pi$
$3$	0.467968	0.270182	0.135091	+	0.990833i	$0.456867\pi$
$4$	0.410361	0.205180
$5$	−1.37639	−0.615542	−0.307771	−	0.951460i	$-0.599583\pi$
$5$	−1.37639	−0.615542	−0.307771	+	0.951460i	$0.599583\pi$
$6$	0.726536	0.296607
$7$	−3.35157	−1.26678	−0.633388	−	0.773835i	$-0.718336\pi$
$7$	−3.35157	−1.26678	−0.633388	+	0.773835i	$0.718336\pi$
$8$	−2.46797	−0.872559
$9$	−2.78101	−0.927002
$10$	−2.13690	−0.675746
$11$	2.05761	0.620392	0.310196	−	0.950673i	$-0.399605\pi$
$11$	2.05761	0.620392	0.310196	+	0.950673i	$0.399605\pi$
$12$	0.192036	0.0554360
$13$	−1.60557	−0.445306	−0.222653	−	0.974898i	$-0.571472\pi$
$13$	−1.60557	−0.445306	−0.222653	+	0.974898i	$0.571472\pi$
$14$	−5.20343	−1.39068
$15$	−0.644108	−0.166308
$16$	−4.65233	−1.16308
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−4.31761	−1.01767
$19$	4.43647	1.01780	0.508898	−	0.860827i	$-0.330053\pi$
$19$	4.43647	1.01780	0.508898	+	0.860827i	$0.330053\pi$
$20$	−0.564818	−0.126297
$21$	−1.56843	−0.342259
$22$	3.19450	0.681071
$23$	−2.95501	−0.616162	−0.308081	−	0.951360i	$-0.599687\pi$
$23$	−2.95501	−0.616162	−0.308081	+	0.951360i	$0.599687\pi$
$24$	−1.15493	−0.235749
$25$	−3.10554	−0.621108
$26$	−2.49271	−0.488860
$27$	−2.70533	−0.520640
$28$	−1.37535	−0.259918
$29$	−3.13539	−0.582226	−0.291113	−	0.956689i	$-0.594026\pi$
$29$	−3.13539	−0.582226	−0.291113	+	0.956689i	$0.594026\pi$
$30$	−1.00000	−0.182574
$31$	−4.72687	−0.848970	−0.424485	−	0.905435i	$-0.639545\pi$
$31$	−4.72687	−0.848970	−0.424485	+	0.905435i	$0.639545\pi$
$32$	−2.28696	−0.404281
$33$	0.962895	0.167618
$34$	−1.55253	−0.266257
$35$	4.61308	0.779753
$36$	−1.14122	−0.190203
$37$	6.73408	1.10708	0.553538	−	0.832824i	$-0.313277\pi$
$37$	6.73408	1.10708	0.553538	+	0.832824i	$0.313277\pi$
$38$	6.88777	1.11734
$39$	−0.751357	−0.120313
$40$	3.39690	0.537096
$41$	9.28079	1.44942	0.724708	−	0.689056i	$-0.241975\pi$
$41$	9.28079	1.44942	0.724708	+	0.689056i	$0.241975\pi$
$42$	−2.43504	−0.375735
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0.844362	0.127292
$45$	3.82776	0.570609
$46$	−4.58775	−0.676427
$47$	−8.52365	−1.24330	−0.621651	−	0.783295i	$-0.713538\pi$
$47$	−8.52365	−1.24330	−0.621651	+	0.783295i	$0.713538\pi$
$48$	−2.17714	−0.314243
$49$	4.23304	0.604720
$50$	−4.82146	−0.681857
$51$	−0.467968	−0.0655287
$52$	−0.658865	−0.0913681
$53$	9.33387	1.28211	0.641053	−	0.767497i	$-0.278498\pi$
$53$	9.33387	1.28211	0.641053	+	0.767497i	$0.278498\pi$
$54$	−4.20011	−0.571563
$55$	−2.83208	−0.381877
$56$	8.27157	1.10534
$57$	2.07613	0.274990
$58$	−4.86779	−0.639172
$59$	−9.83672	−1.28063	−0.640316	−	0.768111i	$-0.721197\pi$
$59$	−9.83672	−1.28063	−0.640316	+	0.768111i	$0.721197\pi$
$60$	−0.264317	−0.0341232
$61$	2.75383	0.352591	0.176296	−	0.984337i	$-0.443589\pi$
$61$	2.75383	0.352591	0.176296	+	0.984337i	$0.443589\pi$
$62$	−7.33862	−0.932006
$63$	9.32074	1.17430
$64$	5.75407	0.719259
$65$	2.20990	0.274104
$66$	1.49493	0.184013
$67$	8.84901	1.08108	0.540539	−	0.841319i	$-0.318220\pi$
$67$	8.84901	1.08108	0.540539	+	0.841319i	$0.318220\pi$
$68$	−0.410361	−0.0497636
$69$	−1.38285	−0.166476
$70$	7.16197	0.856019
$71$	−1.37235	−0.162868	−0.0814342	−	0.996679i	$-0.525950\pi$
$71$	−1.37235	−0.162868	−0.0814342	+	0.996679i	$0.525950\pi$
$72$	6.86343	0.808863
$73$	−0.237911	−0.0278454	−0.0139227	−	0.999903i	$-0.504432\pi$
$73$	−0.237911	−0.0278454	−0.0139227	+	0.999903i	$0.504432\pi$
$74$	10.4549	1.21536
$75$	−1.45329	−0.167812
$76$	1.82055	0.208832
$77$	−6.89622	−0.785897
$78$	−1.16651	−0.132081
$79$	−7.25698	−0.816474	−0.408237	−	0.912876i	$-0.633856\pi$
$79$	−7.25698	−0.816474	−0.408237	+	0.912876i	$0.633856\pi$
$80$	6.40343	0.715925
$81$	7.07701	0.786334
$82$	14.4087	1.59118
$83$	−2.15336	−0.236362	−0.118181	−	0.992992i	$-0.537706\pi$
$83$	−2.15336	−0.236362	−0.118181	+	0.992992i	$0.537706\pi$
$84$	−0.643622	−0.0702249
$85$	1.37639	0.149291
$86$	−1.55253	−0.167414
$87$	−1.46726	−0.157307
$88$	−5.07811	−0.541328
$89$	−13.4194	−1.42246	−0.711229	−	0.702961i	$-0.751861\pi$
$89$	−13.4194	−1.42246	−0.711229	+	0.702961i	$0.751861\pi$
$90$	5.94272	0.626418
$91$	5.38120	0.564103
$92$	−1.21262	−0.126424
$93$	−2.21202	−0.229376
$94$	−13.2332	−1.36491
$95$	−6.10633	−0.626496
$96$	−1.07022	−0.109229
$97$	−12.3738	−1.25636	−0.628182	−	0.778066i	$-0.716201\pi$
$97$	−12.3738	−1.25636	−0.628182	+	0.778066i	$0.716201\pi$
$98$	6.57194	0.663866
$99$	−5.72222	−0.575104
$100$	−1.27439	−0.127439
$101$	−16.9693	−1.68850	−0.844252	−	0.535946i	$-0.819955\pi$
$101$	−16.9693	−1.68850	−0.844252	+	0.535946i	$0.819955\pi$
$102$	−0.726536	−0.0719378
$103$	1.00189	0.0987190	0.0493595	−	0.998781i	$-0.484282\pi$
$103$	1.00189	0.0987190	0.0493595	+	0.998781i	$0.484282\pi$
$104$	3.96250	0.388555
$105$	2.15878	0.210675
$106$	14.4911	1.40750
$107$	17.2371	1.66637	0.833185	−	0.552994i	$-0.186515\pi$
$107$	17.2371	1.66637	0.833185	+	0.552994i	$0.186515\pi$
$108$	−1.11016	−0.106825
$109$	−9.48121	−0.908135	−0.454068	−	0.890967i	$-0.650028\pi$
$109$	−9.48121	−0.908135	−0.454068	+	0.890967i	$0.650028\pi$
$110$	−4.39690	−0.419228
$111$	3.15134	0.299112
$112$	15.5926	1.47336
$113$	−5.69643	−0.535875	−0.267937	−	0.963436i	$-0.586342\pi$
$113$	−5.69643	−0.535875	−0.267937	+	0.963436i	$0.586342\pi$
$114$	3.22326	0.301886
$115$	4.06725	0.379273
$116$	−1.28664	−0.119462
$117$	4.46511	0.412799
$118$	−15.2718	−1.40589
$119$	3.35157	0.307238
$120$	1.58964	0.145114
$121$	−6.76625	−0.615114
$122$	4.27541	0.387077
$123$	4.34312	0.391606
$124$	−1.93972	−0.174192
$125$	11.1564	0.997860
$126$	14.4708	1.28916
$127$	−9.03729	−0.801930	−0.400965	−	0.916093i	$-0.631325\pi$
$127$	−9.03729	−0.801930	−0.400965	+	0.916093i	$0.631325\pi$
$128$	13.5073	1.19389
$129$	−0.467968	−0.0412023
$130$	3.43095	0.300914
$131$	13.2079	1.15398	0.576990	−	0.816751i	$-0.304227\pi$
$131$	13.2079	1.15398	0.576990	+	0.816751i	$0.304227\pi$
$132$	0.395134	0.0343920
$133$	−14.8691	−1.28932
$134$	13.7384	1.18682
$135$	3.72359	0.320476
$136$	2.46797	0.211627
$137$	0.498421	0.0425830	0.0212915	−	0.999773i	$-0.493222\pi$
$137$	0.498421	0.0425830	0.0212915	+	0.999773i	$0.493222\pi$
$138$	−2.14692	−0.182758
$139$	13.0119	1.10366	0.551829	−	0.833957i	$-0.313930\pi$
$139$	13.0119	1.10366	0.551829	+	0.833957i	$0.313930\pi$
$140$	1.89303	0.159990
$141$	−3.98880	−0.335917
$142$	−2.13062	−0.178798
$143$	−3.30364	−0.276264
$144$	12.9381	1.07818
$145$	4.31552	0.358385
$146$	−0.369365	−0.0305689
$147$	1.98093	0.163384
$148$	2.76341	0.227151
$149$	−18.6715	−1.52963	−0.764813	−	0.644253i	$-0.777168\pi$
$149$	−18.6715	−1.52963	−0.764813	+	0.644253i	$0.777168\pi$
$150$	−2.25629	−0.184225
$151$	−14.9169	−1.21392	−0.606960	−	0.794733i	$-0.707611\pi$
$151$	−14.9169	−1.21392	−0.606960	+	0.794733i	$0.707611\pi$
$152$	−10.9491	−0.888086
$153$	2.78101	0.224831
$154$	−10.7066	−0.862764
$155$	6.50603	0.522577
$156$	−0.308328	−0.0246860
$157$	19.2406	1.53556	0.767782	−	0.640711i	$-0.221360\pi$
$157$	19.2406	1.53556	0.767782	+	0.640711i	$0.221360\pi$
$158$	−11.2667	−0.896331
$159$	4.36795	0.346401
$160$	3.14775	0.248852
$161$	9.90393	0.780539
$162$	10.9873	0.863244
$163$	6.92729	0.542587	0.271294	−	0.962497i	$-0.412549\pi$
$163$	6.92729	0.542587	0.271294	+	0.962497i	$0.412549\pi$
$164$	3.80848	0.297392
$165$	−1.32532	−0.103176
$166$	−3.34316	−0.259480
$167$	11.3060	0.874881	0.437441	−	0.899247i	$-0.355885\pi$
$167$	11.3060	0.874881	0.437441	+	0.899247i	$0.355885\pi$
$168$	3.87083	0.298641
$169$	−10.4221	−0.801703
$170$	2.13690	0.163893
$171$	−12.3378	−0.943499
$172$	−0.410361	−0.0312897
$173$	18.8950	1.43656	0.718281	−	0.695754i	$-0.244929\pi$
$173$	18.8950	1.43656	0.718281	+	0.695754i	$0.244929\pi$
$174$	−2.27797	−0.172693
$175$	10.4084	0.786805
$176$	−9.57266	−0.721566
$177$	−4.60327	−0.346003
$178$	−20.8341	−1.56158
$179$	−16.1432	−1.20660	−0.603300	−	0.797515i	$-0.706148\pi$
$179$	−16.1432	−1.20660	−0.603300	+	0.797515i	$0.706148\pi$
$180$	1.57076	0.117078
$181$	−17.6672	−1.31319	−0.656596	−	0.754242i	$-0.728004\pi$
$181$	−17.6672	−1.31319	−0.656596	+	0.754242i	$0.728004\pi$
$182$	8.35449	0.619276
$183$	1.28870	0.0952637
$184$	7.29287	0.537637
$185$	−9.26875	−0.681452
$186$	−3.43424	−0.251811
$187$	−2.05761	−0.150467
$188$	−3.49777	−0.255101
$189$	9.06710	0.659534
$190$	−9.48028	−0.687772
$191$	−5.21087	−0.377045	−0.188523	−	0.982069i	$-0.560370\pi$
$191$	−5.21087	−0.377045	−0.188523	+	0.982069i	$0.560370\pi$
$192$	2.69272	0.194331
$193$	−10.0275	−0.721797	−0.360898	−	0.932605i	$-0.617530\pi$
$193$	−10.0275	−0.721797	−0.360898	+	0.932605i	$0.617530\pi$
$194$	−19.2107	−1.37925
$195$	1.03416	0.0740580
$196$	1.73707	0.124077
$197$	−8.23341	−0.586606	−0.293303	−	0.956020i	$-0.594754\pi$
$197$	−8.23341	−0.586606	−0.293303	+	0.956020i	$0.594754\pi$
$198$	−8.88394	−0.631354
$199$	−0.596092	−0.0422559	−0.0211279	−	0.999777i	$-0.506726\pi$
$199$	−0.596092	−0.0422559	−0.0211279	+	0.999777i	$0.506726\pi$
$200$	7.66438	0.541953
$201$	4.14105	0.292087
$202$	−26.3454	−1.85365
$203$	10.5085	0.737550
$204$	−0.192036	−0.0134452
$205$	−12.7740	−0.892176
$206$	1.55547	0.108374
$207$	8.21790	0.571183
$208$	7.46965	0.517927
$209$	9.12851	0.631432
$210$	3.35157	0.231280
$211$	−2.11726	−0.145758	−0.0728790	−	0.997341i	$-0.523219\pi$
$211$	−2.11726	−0.145758	−0.0728790	+	0.997341i	$0.523219\pi$
$212$	3.83026	0.263063
$213$	−0.642217	−0.0440040
$214$	26.7611	1.82935
$215$	1.37639	0.0938693
$216$	6.67666	0.454289
$217$	15.8424	1.07545
$218$	−14.7199	−0.996958
$219$	−0.111335	−0.00752332
$220$	−1.16217	−0.0783538
$221$	1.60557	0.108003
$222$	4.89256	0.328367
$223$	−21.3509	−1.42976	−0.714881	−	0.699247i	$-0.753519\pi$
$223$	−21.3509	−1.42976	−0.714881	+	0.699247i	$0.753519\pi$
$224$	7.66490	0.512133
$225$	8.63653	0.575768
$226$	−8.84389	−0.588287
$227$	17.2277	1.14344	0.571720	−	0.820449i	$-0.306276\pi$
$227$	17.2277	1.14344	0.571720	+	0.820449i	$0.306276\pi$
$228$	0.851961	0.0564225
$229$	−0.830329	−0.0548697	−0.0274348	−	0.999624i	$-0.508734\pi$
$229$	−0.830329	−0.0548697	−0.0274348	+	0.999624i	$0.508734\pi$
$230$	6.31455	0.416369
$231$	−3.22721	−0.212335
$232$	7.73803	0.508027
$233$	−17.7159	−1.16061	−0.580303	−	0.814401i	$-0.697066\pi$
$233$	−17.7159	−1.16061	−0.580303	+	0.814401i	$0.697066\pi$
$234$	6.93223	0.453174
$235$	11.7319	0.765304
$236$	−4.03661	−0.262761
$237$	−3.39604	−0.220596
$238$	5.20343	0.337288
$239$	−20.7223	−1.34041	−0.670207	−	0.742174i	$-0.733795\pi$
$239$	−20.7223	−1.34041	−0.670207	+	0.742174i	$0.733795\pi$
$240$	2.99660	0.193430
$241$	8.01971	0.516595	0.258297	−	0.966065i	$-0.416839\pi$
$241$	8.01971	0.516595	0.258297	+	0.966065i	$0.416839\pi$
$242$	−10.5048	−0.675276
$243$	11.4278	0.733093
$244$	1.13006	0.0723449
$245$	−5.82633	−0.372230
$246$	6.74283	0.429907
$247$	−7.12308	−0.453231
$248$	11.6658	0.740776
$249$	−1.00770	−0.0638606
$250$	17.3207	1.09546
$251$	12.0601	0.761228	0.380614	−	0.924734i	$-0.375713\pi$
$251$	12.0601	0.761228	0.380614	+	0.924734i	$0.375713\pi$
$252$	3.82487	0.240944
$253$	−6.08025	−0.382262
$254$	−14.0307	−0.880365
$255$	0.644108	0.0403356
$256$	9.46240	0.591400
$257$	−0.113536	−0.00708217	−0.00354108	−	0.999994i	$-0.501127\pi$
$257$	−0.113536	−0.00708217	−0.00354108	+	0.999994i	$0.501127\pi$
$258$	−0.726536	−0.0452322
$259$	−22.5698	−1.40242
$260$	0.906857	0.0562409
$261$	8.71952	0.539725
$262$	20.5057	1.26685
$263$	−1.04330	−0.0643325	−0.0321663	−	0.999483i	$-0.510241\pi$
$263$	−1.04330	−0.0643325	−0.0321663	+	0.999483i	$0.510241\pi$
$264$	−2.37639	−0.146257
$265$	−12.8471	−0.789190
$266$	−23.0849	−1.41542
$267$	−6.27987	−0.384322
$268$	3.63129	0.221816
$269$	−3.25815	−0.198653	−0.0993265	−	0.995055i	$-0.531669\pi$
$269$	−3.25815	−0.198653	−0.0993265	+	0.995055i	$0.531669\pi$
$270$	5.78101	0.351821
$271$	2.16125	0.131286	0.0656432	−	0.997843i	$-0.479090\pi$
$271$	2.16125	0.131286	0.0656432	+	0.997843i	$0.479090\pi$
$272$	4.65233	0.282089
$273$	2.51823	0.152410
$274$	0.773816	0.0467479
$275$	−6.38998	−0.385330
$276$	−0.567468	−0.0341575
$277$	−2.06077	−0.123820	−0.0619098	−	0.998082i	$-0.519719\pi$
$277$	−2.06077	−0.123820	−0.0619098	+	0.998082i	$0.519719\pi$
$278$	20.2015	1.21160
$279$	13.1454	0.786997
$280$	−11.3849	−0.680380
$281$	19.6254	1.17075	0.585375	−	0.810763i	$-0.300947\pi$
$281$	19.6254	1.17075	0.585375	+	0.810763i	$0.300947\pi$
$282$	−6.19274	−0.368772
$283$	29.8412	1.77388	0.886939	−	0.461888i	$-0.152828\pi$
$283$	29.8412	1.77388	0.886939	+	0.461888i	$0.152828\pi$
$284$	−0.563160	−0.0334174
$285$	−2.85757	−0.169268
$286$	−5.12901	−0.303285
$287$	−31.1053	−1.83608
$288$	6.36004	0.374769
$289$	1.00000	0.0588235
$290$	6.70000	0.393437
$291$	−5.79052	−0.339447
$292$	−0.0976295	−0.00571334
$293$	9.76035	0.570206	0.285103	−	0.958497i	$-0.407972\pi$
$293$	9.76035	0.570206	0.285103	+	0.958497i	$0.407972\pi$
$294$	3.07546	0.179364
$295$	13.5392	0.788283
$296$	−16.6195	−0.965989
$297$	−5.56650	−0.323001
$298$	−28.9881	−1.67923
$299$	4.74448	0.274381
$300$	−0.596375	−0.0344317
$301$	3.35157	0.193181
$302$	−23.1590	−1.33265
$303$	−7.94108	−0.456203
$304$	−20.6399	−1.18378
$305$	−3.79035	−0.217035
$306$	4.31761	0.246821
$307$	5.45230	0.311179	0.155590	−	0.987822i	$-0.450272\pi$
$307$	5.45230	0.311179	0.155590	+	0.987822i	$0.450272\pi$
$308$	−2.82994	−0.161251
$309$	0.468852	0.0266721
$310$	10.1008	0.573689
$311$	6.91146	0.391913	0.195956	−	0.980613i	$-0.437219\pi$
$311$	6.91146	0.391913	0.195956	+	0.980613i	$0.437219\pi$
$312$	1.85433	0.104981
$313$	−30.2823	−1.71166	−0.855830	−	0.517258i	$-0.826953\pi$
$313$	−30.2823	−1.71166	−0.855830	+	0.517258i	$0.826953\pi$
$314$	29.8716	1.68575
$315$	−12.8290	−0.722833
$316$	−2.97798	−0.167525
$317$	−1.05835	−0.0594431	−0.0297215	−	0.999558i	$-0.509462\pi$
$317$	−1.05835	−0.0594431	−0.0297215	+	0.999558i	$0.509462\pi$
$318$	6.78140	0.380282
$319$	−6.45139	−0.361209
$320$	−7.91987	−0.442734
$321$	8.06640	0.450223
$322$	15.3762	0.856881
$323$	−4.43647	−0.246852
$324$	2.90413	0.161340
$325$	4.98617	0.276583
$326$	10.7549	0.595656
$327$	−4.43691	−0.245361
$328$	−22.9047	−1.26470
$329$	28.5676	1.57498
$330$	−2.05761	−0.113268
$331$	6.60561	0.363077	0.181539	−	0.983384i	$-0.441892\pi$
$331$	6.60561	0.363077	0.181539	+	0.983384i	$0.441892\pi$
$332$	−0.883654	−0.0484968
$333$	−18.7275	−1.02626
$334$	17.5529	0.960451
$335$	−12.1797	−0.665449
$336$	7.29684	0.398076
$337$	−7.79916	−0.424847	−0.212424	−	0.977178i	$-0.568136\pi$
$337$	−7.79916	−0.424847	−0.212424	+	0.977178i	$0.568136\pi$
$338$	−16.1807	−0.880115
$339$	−2.66575	−0.144783
$340$	0.564818	0.0306316
$341$	−9.72604	−0.526694
$342$	−19.1549	−1.03578
$343$	9.27367	0.500731
$344$	2.46797	0.133064
$345$	1.90335	0.102473
$346$	29.3351	1.57707
$347$	−9.84344	−0.528424	−0.264212	−	0.964465i	$-0.585112\pi$
$347$	−9.84344	−0.528424	−0.264212	+	0.964465i	$0.585112\pi$
$348$	−0.602106	−0.0322763
$349$	−30.2937	−1.62158	−0.810791	−	0.585335i	$-0.800963\pi$
$349$	−30.2937	−1.62158	−0.810791	+	0.585335i	$0.800963\pi$
$350$	16.1595	0.863760
$351$	4.34360	0.231844
$352$	−4.70566	−0.250812
$353$	−3.33858	−0.177695	−0.0888473	−	0.996045i	$-0.528318\pi$
$353$	−3.33858	−0.177695	−0.0888473	+	0.996045i	$0.528318\pi$
$354$	−7.14674	−0.379845
$355$	1.88890	0.100252
$356$	−5.50681	−0.291861
$357$	1.56843	0.0830101
$358$	−25.0629	−1.32461
$359$	32.9629	1.73972	0.869858	−	0.493301i	$-0.164210\pi$
$359$	32.9629	1.73972	0.869858	+	0.493301i	$0.164210\pi$
$360$	−9.44679	−0.497889
$361$	0.682261	0.0359085
$362$	−27.4289	−1.44163
$363$	−3.16639	−0.166192
$364$	2.20823	0.115743
$365$	0.327460	0.0171400
$366$	2.00075	0.104581
$367$	19.8773	1.03759	0.518793	−	0.854900i	$-0.326382\pi$
$367$	19.8773	1.03759	0.518793	+	0.854900i	$0.326382\pi$
$368$	13.7477	0.716646
$369$	−25.8099	−1.34361
$370$	−14.3900	−0.748103
$371$	−31.2831	−1.62414
$372$	−0.907728	−0.0470635
$373$	31.8286	1.64802	0.824011	−	0.566574i	$-0.191732\pi$
$373$	31.8286	1.64802	0.824011	+	0.566574i	$0.191732\pi$
$374$	−3.19450	−0.165184
$375$	5.22085	0.269603
$376$	21.0361	1.08485
$377$	5.03409	0.259269
$378$	14.0770	0.724042
$379$	−18.3892	−0.944590	−0.472295	−	0.881440i	$-0.656574\pi$
$379$	−18.3892	−0.944590	−0.472295	+	0.881440i	$0.656574\pi$
$380$	−2.50580	−0.128545
$381$	−4.22917	−0.216667
$382$	−8.09005	−0.413923
$383$	31.4493	1.60699	0.803493	−	0.595314i	$-0.202972\pi$
$383$	31.4493	1.60699	0.803493	+	0.595314i	$0.202972\pi$
$384$	6.32099	0.322567
$385$	9.49191	0.483753
$386$	−15.5681	−0.792394
$387$	2.78101	0.141366
$388$	−5.07771	−0.257782
$389$	−36.1960	−1.83521	−0.917604	−	0.397496i	$-0.869879\pi$
$389$	−36.1960	−1.83521	−0.917604	+	0.397496i	$0.869879\pi$
$390$	1.60557	0.0813014
$391$	2.95501	0.149441
$392$	−10.4470	−0.527654
$393$	6.18088	0.311784
$394$	−12.7826	−0.643980
$395$	9.98846	0.502574
$396$	−2.34817	−0.118000
$397$	−16.0708	−0.806569	−0.403284	−	0.915075i	$-0.632131\pi$
$397$	−16.0708	−0.806569	−0.403284	+	0.915075i	$0.632131\pi$
$398$	−0.925454	−0.0463888
$399$	−6.95829	−0.348350
$400$	14.4480	0.722399
$401$	18.3382	0.915766	0.457883	−	0.889013i	$-0.348608\pi$
$401$	18.3382	0.915766	0.457883	+	0.889013i	$0.348608\pi$
$402$	6.42913	0.320656
$403$	7.58933	0.378052
$404$	−6.96352	−0.346448
$405$	−9.74075	−0.484022
$406$	16.3148	0.809688
$407$	13.8561	0.686821
$408$	1.15493	0.0571776
$409$	−21.6593	−1.07098	−0.535491	−	0.844541i	$-0.679874\pi$
$409$	−21.6593	−1.07098	−0.535491	+	0.844541i	$0.679874\pi$
$410$	−19.8321	−0.979438
$411$	0.233245	0.0115051
$412$	0.411136	0.0202552
$413$	32.9685	1.62227
$414$	12.7586	0.627049
$415$	2.96387	0.145491
$416$	3.67188	0.180029
$417$	6.08918	0.298188
$418$	14.1723	0.693191
$419$	−0.799500	−0.0390581	−0.0195291	−	0.999809i	$-0.506217\pi$
$419$	−0.799500	−0.0390581	−0.0195291	+	0.999809i	$0.506217\pi$
$420$	0.885877	0.0432264
$421$	−21.4459	−1.04521	−0.522604	−	0.852576i	$-0.675039\pi$
$421$	−21.4459	−1.04521	−0.522604	+	0.852576i	$0.675039\pi$
$422$	−3.28711	−0.160014
$423$	23.7043	1.15254
$424$	−23.0357	−1.11871
$425$	3.10554	0.150641
$426$	−0.997064	−0.0483079
$427$	−9.22965	−0.446654
$428$	7.07342	0.341907
$429$	−1.54600	−0.0746415
$430$	2.13690	0.103050
$431$	−12.5374	−0.603905	−0.301953	−	0.953323i	$-0.597638\pi$
$431$	−12.5374	−0.603905	−0.301953	+	0.953323i	$0.597638\pi$
$432$	12.5861	0.605547
$433$	0.316199	0.0151956	0.00759778	−	0.999971i	$-0.497582\pi$
$433$	0.316199	0.0151956	0.00759778	+	0.999971i	$0.497582\pi$
$434$	24.5959	1.18064
$435$	2.01953	0.0968290
$436$	−3.89072	−0.186332
$437$	−13.1098	−0.627127
$438$	−0.172851	−0.00825915
$439$	−39.0690	−1.86466	−0.932331	−	0.361607i	$-0.882228\pi$
$439$	−39.0690	−1.86466	−0.932331	+	0.361607i	$0.882228\pi$
$440$	6.98948	0.333210
$441$	−11.7721	−0.560577
$442$	2.49271	0.118566
$443$	2.92193	0.138825	0.0694125	−	0.997588i	$-0.477888\pi$
$443$	2.92193	0.138825	0.0694125	+	0.997588i	$0.477888\pi$
$444$	1.29319	0.0613719
$445$	18.4704	0.875582
$446$	−33.1480	−1.56960
$447$	−8.73765	−0.413277
$448$	−19.2852	−0.911140
$449$	3.14960	0.148639	0.0743195	−	0.997234i	$-0.476322\pi$
$449$	3.14960	0.148639	0.0743195	+	0.997234i	$0.476322\pi$
$450$	13.4085	0.632083
$451$	19.0962	0.899206
$452$	−2.33759	−0.109951
$453$	−6.98063	−0.327979
$454$	26.7465	1.25528
$455$	−7.40664	−0.347229
$456$	−5.12381	−0.239945
$457$	−31.7688	−1.48608	−0.743040	−	0.669247i	$-0.766617\pi$
$457$	−31.7688	−1.48608	−0.743040	+	0.669247i	$0.766617\pi$
$458$	−1.28911	−0.0602363
$459$	2.70533	0.126274
$460$	1.66904	0.0778195
$461$	27.5045	1.28101	0.640505	−	0.767954i	$-0.278725\pi$
$461$	27.5045	1.28101	0.640505	+	0.767954i	$0.278725\pi$
$462$	−5.01035	−0.233103
$463$	−6.28353	−0.292020	−0.146010	−	0.989283i	$-0.546643\pi$
$463$	−6.28353	−0.292020	−0.146010	+	0.989283i	$0.546643\pi$
$464$	14.5868	0.677177
$465$	3.04462	0.141191
$466$	−27.5045	−1.27412
$467$	−15.1305	−0.700158	−0.350079	−	0.936720i	$-0.613845\pi$
$467$	−15.1305	−0.700158	−0.350079	+	0.936720i	$0.613845\pi$
$468$	1.83231	0.0846984
$469$	−29.6581	−1.36948
$470$	18.2142	0.840156
$471$	9.00397	0.414881
$472$	24.2767	1.11743
$473$	−2.05761	−0.0946089
$474$	−5.27246	−0.242172
$475$	−13.7776	−0.632161
$476$	1.37535	0.0630393
$477$	−25.9575	−1.18851
$478$	−32.1721	−1.47152
$479$	18.3840	0.839984	0.419992	−	0.907528i	$-0.362033\pi$
$479$	18.3840	0.839984	0.419992	+	0.907528i	$0.362033\pi$
$480$	1.47305	0.0672351
$481$	−10.8121	−0.492988
$482$	12.4509	0.567121
$483$	4.63472	0.210887
$484$	−2.77661	−0.126209
$485$	17.0312	0.773345
$486$	17.7420	0.804795
$487$	−25.0292	−1.13418	−0.567091	−	0.823655i	$-0.691931\pi$
$487$	−25.0292	−1.13418	−0.567091	+	0.823655i	$0.691931\pi$
$488$	−6.79635	−0.307657
$489$	3.24175	0.146597
$490$	−9.04557	−0.408637
$491$	8.38193	0.378271	0.189136	−	0.981951i	$-0.439431\pi$
$491$	8.38193	0.378271	0.189136	+	0.981951i	$0.439431\pi$
$492$	1.78225	0.0803498
$493$	3.13539	0.141211
$494$	−11.0588	−0.497560
$495$	7.87602	0.354001
$496$	21.9909	0.987422
$497$	4.59954	0.206318
$498$	−1.56449	−0.0701066
$499$	12.4436	0.557050	0.278525	−	0.960429i	$-0.410154\pi$
$499$	12.4436	0.557050	0.278525	+	0.960429i	$0.410154\pi$
$500$	4.57816	0.204741
$501$	5.29083	0.236377
$502$	18.7238	0.835682
$503$	−16.3260	−0.727942	−0.363971	−	0.931410i	$-0.618579\pi$
$503$	−16.3260	−0.727942	−0.363971	+	0.931410i	$0.618579\pi$
$504$	−23.0033	−1.02465
$505$	23.3564	1.03935
$506$	−9.43979	−0.419650
$507$	−4.87723	−0.216605
$508$	−3.70855	−0.164540
$509$	18.4749	0.818887	0.409443	−	0.912336i	$-0.365723\pi$
$509$	18.4749	0.818887	0.409443	+	0.912336i	$0.365723\pi$
$510$	1.00000	0.0442807
$511$	0.797377	0.0352739
$512$	−12.3239	−0.544645
$513$	−12.0021	−0.529906
$514$	−0.176268	−0.00777485
$515$	−1.37899	−0.0607657
$516$	−0.192036	−0.00845391
$517$	−17.5383	−0.771334
$518$	−35.0403	−1.53958
$519$	8.84226	0.388132
$520$	−5.45396	−0.239172
$521$	16.3339	0.715600	0.357800	−	0.933798i	$-0.383527\pi$
$521$	16.3339	0.715600	0.357800	+	0.933798i	$0.383527\pi$
$522$	13.5374	0.592514
$523$	−10.8949	−0.476399	−0.238200	−	0.971216i	$-0.576557\pi$
$523$	−10.8949	−0.476399	−0.238200	+	0.971216i	$0.576557\pi$
$524$	5.42001	0.236774
$525$	4.87082	0.212580
$526$	−1.61976	−0.0706247
$527$	4.72687	0.205906
$528$	−4.47970	−0.194954
$529$	−14.2679	−0.620345
$530$	−19.9455	−0.866378
$531$	27.3560	1.18715
$532$	−6.10172	−0.264543
$533$	−14.9010	−0.645434
$534$	−9.74971	−0.421911
$535$	−23.7250	−1.02572
$536$	−21.8391	−0.943304
$537$	−7.55450	−0.326001
$538$	−5.05839	−0.218083
$539$	8.70993	0.375163
$540$	1.52802	0.0657554
$541$	14.6315	0.629055	0.314528	−	0.949248i	$-0.398154\pi$
$541$	14.6315	0.629055	0.314528	+	0.949248i	$0.398154\pi$
$542$	3.35541	0.144127
$543$	−8.26769	−0.354800
$544$	2.28696	0.0980524
$545$	13.0499	0.558995
$546$	3.90963	0.167317
$547$	38.8321	1.66034	0.830170	−	0.557510i	$-0.188243\pi$
$547$	38.8321	1.66034	0.830170	+	0.557510i	$0.188243\pi$
$548$	0.204533	0.00873720
$549$	−7.65841	−0.326853
$550$	−9.92066	−0.423019
$551$	−13.9100	−0.592588
$552$	3.41283	0.145260
$553$	24.3223	1.03429
$554$	−3.19941	−0.135930
$555$	−4.33748	−0.184116
$556$	5.33960	0.226449
$557$	−15.0377	−0.637167	−0.318583	−	0.947895i	$-0.603207\pi$
$557$	−15.0377	−0.637167	−0.318583	+	0.947895i	$0.603207\pi$
$558$	20.4087	0.863971
$559$	1.60557	0.0679085
$560$	−21.4616	−0.906917
$561$	−0.962895	−0.0406534
$562$	30.4690	1.28526
$563$	25.9281	1.09274	0.546370	−	0.837544i	$-0.316009\pi$
$563$	25.9281	1.09274	0.546370	+	0.837544i	$0.316009\pi$
$564$	−1.63685	−0.0689236
$565$	7.84052	0.329853
$566$	46.3295	1.94737
$567$	−23.7191	−0.996109
$568$	3.38692	0.142112
$569$	33.5425	1.40617	0.703086	−	0.711104i	$-0.251805\pi$
$569$	33.5425	1.40617	0.703086	+	0.711104i	$0.251805\pi$
$570$	−4.43647	−0.185823
$571$	−1.78040	−0.0745073	−0.0372536	−	0.999306i	$-0.511861\pi$
$571$	−1.78040	−0.0745073	−0.0372536	+	0.999306i	$0.511861\pi$
$572$	−1.35568	−0.0566840
$573$	−2.43852	−0.101871
$574$	−48.2920	−2.01567
$575$	9.17690	0.382703
$576$	−16.0021	−0.666755
$577$	−5.31057	−0.221082	−0.110541	−	0.993872i	$-0.535258\pi$
$577$	−5.31057	−0.221082	−0.110541	+	0.993872i	$0.535258\pi$
$578$	1.55253	0.0645769
$579$	−4.69256	−0.195016
$580$	1.77092	0.0735336
$581$	7.21714	0.299417
$582$	−8.98998	−0.372647
$583$	19.2054	0.795408
$584$	0.587158	0.0242968
$585$	−6.14575	−0.254095
$586$	15.1533	0.625976
$587$	−13.6765	−0.564488	−0.282244	−	0.959343i	$-0.591079\pi$
$587$	−13.6765	−0.564488	−0.282244	+	0.959343i	$0.591079\pi$
$588$	0.812896	0.0335232
$589$	−20.9706	−0.864079
$590$	21.0201	0.865383
$591$	−3.85297	−0.158490
$592$	−31.3292	−1.28762
$593$	−23.1903	−0.952312	−0.476156	−	0.879361i	$-0.657970\pi$
$593$	−23.1903	−0.952312	−0.476156	+	0.879361i	$0.657970\pi$
$594$	−8.64218	−0.354593
$595$	−4.61308	−0.189118
$596$	−7.66204	−0.313849
$597$	−0.278952	−0.0114168
$598$	7.36597	0.301217
$599$	3.62388	0.148068	0.0740339	−	0.997256i	$-0.476413\pi$
$599$	3.62388	0.148068	0.0740339	+	0.997256i	$0.476413\pi$
$600$	3.58668	0.146426
$601$	10.7756	0.439548	0.219774	−	0.975551i	$-0.429468\pi$
$601$	10.7756	0.439548	0.219774	+	0.975551i	$0.429468\pi$
$602$	5.20343	0.212076
$603$	−24.6091	−1.00216
$604$	−6.12131	−0.249073
$605$	9.31303	0.378628
$606$	−12.3288	−0.500823
$607$	11.1257	0.451578	0.225789	−	0.974176i	$-0.427504\pi$
$607$	11.1257	0.451578	0.225789	+	0.974176i	$0.427504\pi$
$608$	−10.1460	−0.411475
$609$	4.91763	0.199272
$610$	−5.88464	−0.238262
$611$	13.6853	0.553650
$612$	1.14122	0.0461309
$613$	−33.5257	−1.35409	−0.677046	−	0.735941i	$-0.736740\pi$
$613$	−33.5257	−1.35409	−0.677046	+	0.735941i	$0.736740\pi$
$614$	8.46488	0.341615
$615$	−5.97784	−0.241050
$616$	17.0197	0.685741
$617$	40.9696	1.64937	0.824686	−	0.565591i	$-0.191352\pi$
$617$	40.9696	1.64937	0.824686	+	0.565591i	$0.191352\pi$
$618$	0.727909	0.0292808
$619$	−18.3291	−0.736709	−0.368355	−	0.929685i	$-0.620079\pi$
$619$	−18.3291	−0.736709	−0.368355	+	0.929685i	$0.620079\pi$
$620$	2.66982	0.107223
$621$	7.99426	0.320799
$622$	10.7303	0.430245
$623$	44.9762	1.80193
$624$	3.49556	0.139934
$625$	0.172088	0.00688353
$626$	−47.0144	−1.87907
$627$	4.27185	0.170601
$628$	7.89558	0.315068
$629$	−6.73408	−0.268506
$630$	−19.9175	−0.793531
$631$	4.31547	0.171796	0.0858981	−	0.996304i	$-0.472624\pi$
$631$	4.31547	0.171796	0.0858981	+	0.996304i	$0.472624\pi$
$632$	17.9100	0.712422
$633$	−0.990809	−0.0393811
$634$	−1.64313	−0.0652570
$635$	12.4389	0.493622
$636$	1.79244	0.0710748
$637$	−6.79646	−0.269285
$638$	−10.0160	−0.396537
$639$	3.81652	0.150979
$640$	−18.5914	−0.734888
$641$	39.4483	1.55811	0.779057	−	0.626953i	$-0.215698\pi$
$641$	39.4483	1.55811	0.779057	+	0.626953i	$0.215698\pi$
$642$	12.5234	0.494258
$643$	44.4275	1.75205	0.876024	−	0.482267i	$-0.160186\pi$
$643$	44.4275	1.75205	0.876024	+	0.482267i	$0.160186\pi$
$644$	4.06418	0.160151
$645$	0.644108	0.0253617
$646$	−6.88777	−0.270996
$647$	−14.5542	−0.572183	−0.286091	−	0.958202i	$-0.592356\pi$
$647$	−14.5542	−0.572183	−0.286091	+	0.958202i	$0.592356\pi$
$648$	−17.4658	−0.686123
$649$	−20.2401	−0.794494
$650$	7.74120	0.303635
$651$	7.41376	0.290568
$652$	2.84269	0.111328
$653$	−5.75768	−0.225315	−0.112658	−	0.993634i	$-0.535936\pi$
$653$	−5.75768	−0.225315	−0.112658	+	0.993634i	$0.535936\pi$
$654$	−6.88845	−0.269360
$655$	−18.1793	−0.710323
$656$	−43.1773	−1.68579
$657$	0.661633	0.0258128
$658$	44.3522	1.72903
$659$	34.6474	1.34967	0.674835	−	0.737969i	$-0.264215\pi$
$659$	34.6474	1.34967	0.674835	+	0.737969i	$0.264215\pi$
$660$	−0.543860	−0.0211697
$661$	−2.04505	−0.0795432	−0.0397716	−	0.999209i	$-0.512663\pi$
$661$	−2.04505	−0.0795432	−0.0397716	+	0.999209i	$0.512663\pi$
$662$	10.2554	0.398589
$663$	0.751357	0.0291803
$664$	5.31442	0.206240
$665$	20.4658	0.793630
$666$	−29.0751	−1.12664
$667$	9.26509	0.358746
$668$	4.63952	0.179509
$669$	−9.99154	−0.386295
$670$	−18.9094	−0.730535
$671$	5.66629	0.218745
$672$	3.58693	0.138369
$673$	−37.3113	−1.43825	−0.719123	−	0.694883i	$-0.755456\pi$
$673$	−37.3113	−1.43825	−0.719123	+	0.694883i	$0.755456\pi$
$674$	−12.1085	−0.466400
$675$	8.40150	0.323374
$676$	−4.27684	−0.164494
$677$	0.572224	0.0219924	0.0109962	−	0.999940i	$-0.496500\pi$
$677$	0.572224	0.0219924	0.0109962	+	0.999940i	$0.496500\pi$
$678$	−4.13866	−0.158944
$679$	41.4715	1.59153
$680$	−3.39690	−0.130265
$681$	8.06199	0.308936
$682$	−15.1000	−0.578209
$683$	−40.0033	−1.53069	−0.765343	−	0.643623i	$-0.777430\pi$
$683$	−40.0033	−1.53069	−0.765343	+	0.643623i	$0.777430\pi$
$684$	−5.06297	−0.193588
$685$	−0.686024	−0.0262116
$686$	14.3977	0.549706
$687$	−0.388568	−0.0148248
$688$	4.65233	0.177368
$689$	−14.9862	−0.570929
$690$	2.95501	0.112495
$691$	19.8850	0.756461	0.378231	−	0.925711i	$-0.376533\pi$
$691$	19.8850	0.756461	0.378231	+	0.925711i	$0.376533\pi$
$692$	7.75378	0.294754
$693$	19.1784	0.728528
$694$	−15.2823	−0.580107
$695$	−17.9096	−0.679348
$696$	3.62115	0.137259
$697$	−9.28079	−0.351535
$698$	−47.0319	−1.78019
$699$	−8.29046	−0.313574
$700$	4.27122	0.161437
$701$	19.6778	0.743222	0.371611	−	0.928389i	$-0.378806\pi$
$701$	19.6778	0.743222	0.371611	+	0.928389i	$0.378806\pi$
$702$	6.74359	0.254520
$703$	29.8756	1.12678
$704$	11.8396	0.446223
$705$	5.49015	0.206771
$706$	−5.18325	−0.195074
$707$	56.8737	2.13896
$708$	−1.88900	−0.0709931
$709$	19.6415	0.737653	0.368827	−	0.929498i	$-0.379760\pi$
$709$	19.6415	0.737653	0.368827	+	0.929498i	$0.379760\pi$
$710$	2.93258	0.110058
$711$	20.1817	0.756873
$712$	33.1187	1.24118
$713$	13.9679	0.523103
$714$	2.43504	0.0911291
$715$	4.54711	0.170052
$716$	−6.62454	−0.247571
$717$	−9.69738	−0.362155
$718$	51.1761	1.90987
$719$	37.4428	1.39638	0.698191	−	0.715912i	$-0.253989\pi$
$719$	37.4428	1.39638	0.698191	+	0.715912i	$0.253989\pi$
$720$	−17.8080	−0.663664
$721$	−3.35790	−0.125055
$722$	1.05923	0.0394206
$723$	3.75297	0.139574
$724$	−7.24993	−0.269442
$725$	9.73707	0.361626
$726$	−4.91593	−0.182447
$727$	37.6367	1.39587	0.697933	−	0.716163i	$-0.254103\pi$
$727$	37.6367	1.39587	0.697933	+	0.716163i	$0.254103\pi$
$728$	−13.2806	−0.492213
$729$	−15.8832	−0.588266
$730$	0.508392	0.0188164
$731$	1.00000	0.0369863
$732$	0.528833	0.0195462
$733$	2.42520	0.0895766	0.0447883	−	0.998996i	$-0.485739\pi$
$733$	2.42520	0.0895766	0.0447883	+	0.998996i	$0.485739\pi$
$734$	30.8602	1.13907
$735$	−2.72654	−0.100570
$736$	6.75798	0.249102
$737$	18.2078	0.670692
$738$	−40.0708	−1.47503
$739$	−9.87099	−0.363110	−0.181555	−	0.983381i	$-0.558113\pi$
$739$	−9.87099	−0.363110	−0.181555	+	0.983381i	$0.558113\pi$
$740$	−3.80353	−0.139821
$741$	−3.33337	−0.122455
$742$	−48.5681	−1.78299
$743$	25.0556	0.919202	0.459601	−	0.888125i	$-0.347992\pi$
$743$	25.0556	0.919202	0.459601	+	0.888125i	$0.347992\pi$
$744$	5.45920	0.200144
$745$	25.6993	0.941548
$746$	49.4149	1.80921
$747$	5.98850	0.219108
$748$	−0.844362	−0.0308729
$749$	−57.7713	−2.11092
$750$	8.10554	0.295973
$751$	−17.8673	−0.651987	−0.325993	−	0.945372i	$-0.605699\pi$
$751$	−17.8673	−0.651987	−0.325993	+	0.945372i	$0.605699\pi$
$752$	39.6548	1.44606
$753$	5.64375	0.205670
$754$	7.81560	0.284627
$755$	20.5315	0.747218
$756$	3.72078	0.135324
$757$	−29.2824	−1.06429	−0.532144	−	0.846654i	$-0.678614\pi$
$757$	−29.2824	−1.06429	−0.532144	+	0.846654i	$0.678614\pi$
$758$	−28.5499	−1.03698
$759$	−2.84536	−0.103280
$760$	15.0702	0.546654
$761$	29.8059	1.08046	0.540231	−	0.841517i	$-0.318337\pi$
$761$	29.8059	1.08046	0.540231	+	0.841517i	$0.318337\pi$
$762$	−6.56592	−0.237858
$763$	31.7770	1.15040
$764$	−2.13834	−0.0773623
$765$	−3.82776	−0.138393
$766$	48.8262	1.76416
$767$	15.7936	0.570273
$768$	4.42810	0.159785
$769$	−6.62324	−0.238840	−0.119420	−	0.992844i	$-0.538104\pi$
$769$	−6.62324	−0.238840	−0.119420	+	0.992844i	$0.538104\pi$
$770$	14.7365	0.531067
$771$	−0.0531311	−0.00191347
$772$	−4.11490	−0.148099
$773$	42.7240	1.53667	0.768337	−	0.640045i	$-0.221084\pi$
$773$	42.7240	1.53667	0.768337	+	0.640045i	$0.221084\pi$
$774$	4.31761	0.155193
$775$	14.6795	0.527302
$776$	30.5380	1.09625
$777$	−10.5619	−0.378907
$778$	−56.1954	−2.01470
$779$	41.1740	1.47521
$780$	0.424380	0.0151952
$781$	−2.82376	−0.101042
$782$	4.58775	0.164058
$783$	8.48224	0.303131
$784$	−19.6935	−0.703339
$785$	−26.4826	−0.945204
$786$	9.59602	0.342279
$787$	−54.3543	−1.93752	−0.968760	−	0.247999i	$-0.920227\pi$
$787$	−54.3543	−1.93752	−0.968760	+	0.247999i	$0.920227\pi$
$788$	−3.37867	−0.120360
$789$	−0.488231	−0.0173815
$790$	15.5074	0.551730
$791$	19.0920	0.678833
$792$	14.1223	0.501812
$793$	−4.42147	−0.157011
$794$	−24.9504	−0.885457
$795$	−6.01202	−0.213225
$796$	−0.244613	−0.00867008
$797$	39.0251	1.38234	0.691171	−	0.722692i	$-0.257095\pi$
$797$	39.0251	1.38234	0.691171	+	0.722692i	$0.257095\pi$
$798$	−10.8030	−0.382421
$799$	8.52365	0.301545
$800$	7.10224	0.251102
$801$	37.3195	1.31862
$802$	28.4707	1.00533
$803$	−0.489528	−0.0172751
$804$	1.69933	0.0599307
$805$	−13.6317	−0.480454
$806$	11.7827	0.415028
$807$	−1.52471	−0.0536724
$808$	41.8796	1.47332
$809$	1.18490	0.0416590	0.0208295	−	0.999783i	$-0.493369\pi$
$809$	1.18490	0.0416590	0.0208295	+	0.999783i	$0.493369\pi$
$810$	−15.1228	−0.531363
$811$	10.4542	0.367098	0.183549	−	0.983011i	$-0.441241\pi$
$811$	10.4542	0.367098	0.183549	+	0.983011i	$0.441241\pi$
$812$	4.31227	0.151331
$813$	1.01139	0.0354712
$814$	21.5121	0.753997
$815$	−9.53468	−0.333985
$816$	2.17714	0.0762152
$817$	−4.43647	−0.155212
$818$	−33.6268	−1.17573
$819$	−14.9651	−0.522924
$820$	−5.24196	−0.183057
$821$	13.1726	0.459727	0.229863	−	0.973223i	$-0.426172\pi$
$821$	13.1726	0.459727	0.229863	+	0.973223i	$0.426172\pi$
$822$	0.362121	0.0126304
$823$	−31.6599	−1.10360	−0.551798	−	0.833978i	$-0.686058\pi$
$823$	−31.6599	−1.10360	−0.551798	+	0.833978i	$0.686058\pi$
$824$	−2.47263	−0.0861381
$825$	−2.99031	−0.104109
$826$	51.1847	1.78094
$827$	3.05427	0.106208	0.0531038	−	0.998589i	$-0.483089\pi$
$827$	3.05427	0.106208	0.0531038	+	0.998589i	$0.483089\pi$
$828$	3.37230	0.117196
$829$	−1.45481	−0.0505276	−0.0252638	−	0.999681i	$-0.508043\pi$
$829$	−1.45481	−0.0505276	−0.0252638	+	0.999681i	$0.508043\pi$
$830$	4.60151	0.159721
$831$	−0.964374	−0.0334538
$832$	−9.23859	−0.320290
$833$	−4.23304	−0.146666
$834$	9.45365	0.327353
$835$	−15.5614	−0.538526
$836$	3.74598	0.129558
$837$	12.7877	0.442008
$838$	−1.24125	−0.0428783
$839$	−6.85018	−0.236494	−0.118247	−	0.992984i	$-0.537728\pi$
$839$	−6.85018	−0.236494	−0.118247	+	0.992984i	$0.537728\pi$
$840$	−5.32779	−0.183826
$841$	−19.1694	−0.661012
$842$	−33.2954	−1.14744
$843$	9.18404	0.316315
$844$	−0.868840	−0.0299067
$845$	14.3450	0.493482
$846$	36.8017	1.26527
$847$	22.6776	0.779211
$848$	−43.4242	−1.49119
$849$	13.9647	0.479269
$850$	4.82146	0.165375
$851$	−19.8993	−0.682138
$852$	−0.263541	−0.00902877
$853$	−17.5620	−0.601310	−0.300655	−	0.953733i	$-0.597205\pi$
$853$	−17.5620	−0.601310	−0.300655	+	0.953733i	$0.597205\pi$
$854$	−14.3293	−0.490340
$855$	16.9817	0.580763
$856$	−42.5406	−1.45401
$857$	−6.67420	−0.227986	−0.113993	−	0.993482i	$-0.536364\pi$
$857$	−6.67420	−0.227986	−0.113993	+	0.993482i	$0.536364\pi$
$858$	−2.40021	−0.0819420
$859$	−19.3448	−0.660036	−0.330018	−	0.943975i	$-0.607055\pi$
$859$	−19.3448	−0.660036	−0.330018	+	0.943975i	$0.607055\pi$
$860$	0.564818	0.0192601
$861$	−14.5563	−0.496076
$862$	−19.4647	−0.662971
$863$	−30.8248	−1.04929	−0.524645	−	0.851321i	$-0.675802\pi$
$863$	−30.8248	−1.04929	−0.524645	+	0.851321i	$0.675802\pi$
$864$	6.18696	0.210485
$865$	−26.0070	−0.884264
$866$	0.490910	0.0166818
$867$	0.467968	0.0158930
$868$	6.50112	0.220662
$869$	−14.9320	−0.506534
$870$	3.13539	0.106300
$871$	−14.2077	−0.481411
$872$	23.3993	0.792401
$873$	34.4115	1.16465
$874$	−20.3534	−0.688464
$875$	−37.3915	−1.26406
$876$	−0.0456875	−0.00154364
$877$	−9.29617	−0.313909	−0.156955	−	0.987606i	$-0.550168\pi$
$877$	−9.29617	−0.313909	−0.156955	+	0.987606i	$0.550168\pi$
$878$	−60.6559	−2.04704
$879$	4.56753	0.154059
$880$	13.1757	0.444154
$881$	10.8604	0.365896	0.182948	−	0.983123i	$-0.441436\pi$
$881$	10.8604	0.365896	0.182948	+	0.983123i	$0.441436\pi$
$882$	−18.2766	−0.615405
$883$	5.78586	0.194710	0.0973549	−	0.995250i	$-0.468962\pi$
$883$	5.78586	0.194710	0.0973549	+	0.995250i	$0.468962\pi$
$884$	0.658865	0.0221600
$885$	6.33592	0.212980
$886$	4.53639	0.152403
$887$	23.4572	0.787615	0.393807	−	0.919193i	$-0.371158\pi$
$887$	23.4572	0.787615	0.393807	+	0.919193i	$0.371158\pi$
$888$	−7.77740	−0.260992
$889$	30.2891	1.01587
$890$	28.6760	0.961220
$891$	14.5617	0.487836
$892$	−8.76157	−0.293359
$893$	−37.8149	−1.26543
$894$	−13.5655	−0.453698
$895$	22.2194	0.742713
$896$	−45.2707	−1.51239
$897$	2.22027	0.0741326
$898$	4.88986	0.163177
$899$	14.8206	0.494293
$900$	3.54409	0.118136
$901$	−9.33387	−0.310956
$902$	29.6475	0.987155
$903$	1.56843	0.0521941
$904$	14.0586	0.467582
$905$	24.3170	0.808325
$906$	−10.8377	−0.360057
$907$	−24.4247	−0.811009	−0.405504	−	0.914093i	$-0.632904\pi$
$907$	−24.4247	−0.811009	−0.405504	+	0.914093i	$0.632904\pi$
$908$	7.06956	0.234611
$909$	47.1916	1.56525
$910$	−11.4991	−0.381190
$911$	−29.5612	−0.979406	−0.489703	−	0.871889i	$-0.662895\pi$
$911$	−29.5612	−0.979406	−0.489703	+	0.871889i	$0.662895\pi$
$912$	−9.65882	−0.319835
$913$	−4.43077	−0.146637
$914$	−49.3221	−1.63143
$915$	−1.77376	−0.0586388
$916$	−0.340735	−0.0112582
$917$	−44.2672	−1.46183
$918$	4.20011	0.138624
$919$	−8.03175	−0.264943	−0.132471	−	0.991187i	$-0.542291\pi$
$919$	−8.03175	−0.264943	−0.132471	+	0.991187i	$0.542291\pi$
$920$	−10.0379	−0.330938
$921$	2.55150	0.0840749
$922$	42.7016	1.40630
$923$	2.20341	0.0725262
$924$	−1.32432	−0.0435670
$925$	−20.9130	−0.687614
$926$	−9.75539	−0.320582
$927$	−2.78626	−0.0915127
$928$	7.17049	0.235383
$929$	34.6810	1.13785	0.568924	−	0.822390i	$-0.307360\pi$
$929$	34.6810	1.13785	0.568924	+	0.822390i	$0.307360\pi$
$930$	4.72687	0.155000
$931$	18.7798	0.615481
$932$	−7.26990	−0.238134
$933$	3.23434	0.105888
$934$	−23.4907	−0.768638
$935$	2.83208	0.0926188
$936$	−11.0197	−0.360192
$937$	35.9363	1.17399	0.586994	−	0.809591i	$-0.300311\pi$
$937$	35.9363	1.17399	0.586994	+	0.809591i	$0.300311\pi$
$938$	−46.0452	−1.50343
$939$	−14.1712	−0.462459
$940$	4.81431	0.157025
$941$	−48.1664	−1.57018	−0.785090	−	0.619382i	$-0.787383\pi$
$941$	−48.1664	−1.57018	−0.785090	+	0.619382i	$0.787383\pi$
$942$	13.9790	0.455460
$943$	−27.4248	−0.893075
$944$	45.7636	1.48948
$945$	−12.4799	−0.405971
$946$	−3.19450	−0.103862
$947$	50.0891	1.62768	0.813839	−	0.581091i	$-0.197374\pi$
$947$	50.0891	1.62768	0.813839	+	0.581091i	$0.197374\pi$
$948$	−1.39360	−0.0452621
$949$	0.381984	0.0123997
$950$	−21.3902	−0.693991
$951$	−0.495276	−0.0160604
$952$	−8.27157	−0.268083
$953$	−47.1986	−1.52891	−0.764457	−	0.644675i	$-0.776993\pi$
$953$	−47.1986	−1.52891	−0.764457	+	0.644675i	$0.776993\pi$
$954$	−40.3000	−1.30476
$955$	7.17221	0.232087
$956$	−8.50363	−0.275027
$957$	−3.01905	−0.0975919
$958$	28.5417	0.922141
$959$	−1.67050	−0.0539431
$960$	−3.70625	−0.119619
$961$	−8.65672	−0.279249
$962$	−16.7861	−0.541206
$963$	−47.9364	−1.54473
$964$	3.29097	0.105995
$965$	13.8018	0.444296
$966$	7.19556	0.231513
$967$	50.7117	1.63078	0.815390	−	0.578912i	$-0.196523\pi$
$967$	50.7117	1.63078	0.815390	+	0.578912i	$0.196523\pi$
$968$	16.6989	0.536723
$969$	−2.07613	−0.0666948
$970$	26.4414	0.848984
$971$	14.3657	0.461017	0.230508	−	0.973070i	$-0.425961\pi$
$971$	14.3657	0.461017	0.230508	+	0.973070i	$0.425961\pi$
$972$	4.68952	0.150416
$973$	−43.6105	−1.39809
$974$	−38.8587	−1.24511
$975$	2.33337	0.0747277
$976$	−12.8117	−0.410092
$977$	3.90889	0.125056	0.0625282	−	0.998043i	$-0.480084\pi$
$977$	3.90889	0.125056	0.0625282	+	0.998043i	$0.480084\pi$
$978$	5.03293	0.160935
$979$	−27.6119	−0.882481
$980$	−2.39090	−0.0763744
$981$	26.3673	0.841843
$982$	13.0132	0.415269
$983$	46.8969	1.49578	0.747889	−	0.663824i	$-0.231067\pi$
$983$	46.8969	1.49578	0.747889	+	0.663824i	$0.231067\pi$
$984$	−10.7187	−0.341699
$985$	11.3324	0.361081
$986$	4.86779	0.155022
$987$	13.3687	0.425532
$988$	−2.92303	−0.0929941
$989$	2.95501	0.0939638
$990$	12.2278	0.388625
$991$	−31.8168	−1.01069	−0.505347	−	0.862916i	$-0.668635\pi$
$991$	−31.8168	−1.01069	−0.505347	+	0.862916i	$0.668635\pi$
$992$	10.8101	0.343222
$993$	3.09121	0.0980967
$994$	7.14094	0.226497
$995$	0.820458	0.0260103
$996$	−0.413522	−0.0131029
$997$	−19.3075	−0.611473	−0.305737	−	0.952116i	$-0.598903\pi$
$997$	−19.3075	−0.611473	−0.305737	+	0.952116i	$0.598903\pi$
$998$	19.3191	0.611534
$999$	−18.2179	−0.576389

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.c.1.5	✓	6
3.2	odd	2		6579.2.a.j.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.c.1.5	✓	6	1.1	even	1	trivial
6579.2.a.j.1.2		6	3.2	odd	2

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q+1.55253 q^{2} +0.467968 q^{3} +0.410361 q^{4} -1.37639 q^{5} +0.726536 q^{6} -3.35157 q^{7} -2.46797 q^{8} -2.78101 q^{9} +O(q^{10})\)	\(q+1.55253 q^{2} +0.467968 q^{3} +0.410361 q^{4} -1.37639 q^{5} +0.726536 q^{6} -3.35157 q^{7} -2.46797 q^{8} -2.78101 q^{9} -2.13690 q^{10} +2.05761 q^{11} +0.192036 q^{12} -1.60557 q^{13} -5.20343 q^{14} -0.644108 q^{15} -4.65233 q^{16} -1.00000 q^{17} -4.31761 q^{18} +4.43647 q^{19} -0.564818 q^{20} -1.56843 q^{21} +3.19450 q^{22} -2.95501 q^{23} -1.15493 q^{24} -3.10554 q^{25} -2.49271 q^{26} -2.70533 q^{27} -1.37535 q^{28} -3.13539 q^{29} -1.00000 q^{30} -4.72687 q^{31} -2.28696 q^{32} +0.962895 q^{33} -1.55253 q^{34} +4.61308 q^{35} -1.14122 q^{36} +6.73408 q^{37} +6.88777 q^{38} -0.751357 q^{39} +3.39690 q^{40} +9.28079 q^{41} -2.43504 q^{42} -1.00000 q^{43} +0.844362 q^{44} +3.82776 q^{45} -4.58775 q^{46} -8.52365 q^{47} -2.17714 q^{48} +4.23304 q^{49} -4.82146 q^{50} -0.467968 q^{51} -0.658865 q^{52} +9.33387 q^{53} -4.20011 q^{54} -2.83208 q^{55} +8.27157 q^{56} +2.07613 q^{57} -4.86779 q^{58} -9.83672 q^{59} -0.264317 q^{60} +2.75383 q^{61} -7.33862 q^{62} +9.32074 q^{63} +5.75407 q^{64} +2.20990 q^{65} +1.49493 q^{66} +8.84901 q^{67} -0.410361 q^{68} -1.38285 q^{69} +7.16197 q^{70} -1.37235 q^{71} +6.86343 q^{72} -0.237911 q^{73} +10.4549 q^{74} -1.45329 q^{75} +1.82055 q^{76} -6.89622 q^{77} -1.16651 q^{78} -7.25698 q^{79} +6.40343 q^{80} +7.07701 q^{81} +14.4087 q^{82} -2.15336 q^{83} -0.643622 q^{84} +1.37639 q^{85} -1.55253 q^{86} -1.46726 q^{87} -5.07811 q^{88} -13.4194 q^{89} +5.94272 q^{90} +5.38120 q^{91} -1.21262 q^{92} -2.21202 q^{93} -13.2332 q^{94} -6.10633 q^{95} -1.07022 q^{96} -12.3738 q^{97} +6.57194 q^{98} -5.72222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{5} - 7 q^{6} - 7 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - q^2 - 3 * q^3 + 5 * q^4 + 3 * q^5 - 7 * q^6 - 7 * q^7 - 9 * q^8 - 3 * q^9	\( 6 q - q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{5} - 7 q^{6} - 7 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{10} + 4 q^{11} + 11 q^{12} - 10 q^{13} - 7 q^{14} + q^{15} - q^{16} - 6 q^{17} + q^{18} - 20 q^{19} + q^{20} - 8 q^{21} + 2 q^{22} - 3 q^{23} - 9 q^{24} - 7 q^{25} - 3 q^{26} - 6 q^{27} - 11 q^{28} - 15 q^{29} - 6 q^{30} + 12 q^{31} + q^{32} - 2 q^{33} + q^{34} - 9 q^{35} - 16 q^{36} - 14 q^{37} + 27 q^{38} + 5 q^{39} - 7 q^{40} - 2 q^{41} + 19 q^{42} - 6 q^{43} - 12 q^{44} - 18 q^{45} + 14 q^{46} - 11 q^{47} - 6 q^{48} + 3 q^{49} + 7 q^{50} + 3 q^{51} - 5 q^{52} + 3 q^{53} + 25 q^{54} + 6 q^{55} + 22 q^{56} + 11 q^{57} - 21 q^{58} + 2 q^{59} - q^{60} - 20 q^{61} + 3 q^{62} + 23 q^{63} - 39 q^{64} - 34 q^{65} + 7 q^{66} - 2 q^{67} - 5 q^{68} - 17 q^{69} - q^{70} + q^{71} + 21 q^{72} + 13 q^{73} + 28 q^{74} - 5 q^{75} - 29 q^{76} - 11 q^{77} - 26 q^{79} + 12 q^{80} + 2 q^{81} - 9 q^{82} + 10 q^{83} - 3 q^{84} - 3 q^{85} + q^{86} + 12 q^{87} - 6 q^{88} - 15 q^{89} + 15 q^{90} + 8 q^{91} - 9 q^{92} - 11 q^{93} - 33 q^{94} - 21 q^{95} + 25 q^{96} - 22 q^{97} - 3 q^{98} - 5 q^{99}+O(q^{100}) \) 6 * q - q^2 - 3 * q^3 + 5 * q^4 + 3 * q^5 - 7 * q^6 - 7 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^10 + 4 * q^11 + 11 * q^12 - 10 * q^13 - 7 * q^14 + q^15 - q^16 - 6 * q^17 + q^18 - 20 * q^19 + q^20 - 8 * q^21 + 2 * q^22 - 3 * q^23 - 9 * q^24 - 7 * q^25 - 3 * q^26 - 6 * q^27 - 11 * q^28 - 15 * q^29 - 6 * q^30 + 12 * q^31 + q^32 - 2 * q^33 + q^34 - 9 * q^35 - 16 * q^36 - 14 * q^37 + 27 * q^38 + 5 * q^39 - 7 * q^40 - 2 * q^41 + 19 * q^42 - 6 * q^43 - 12 * q^44 - 18 * q^45 + 14 * q^46 - 11 * q^47 - 6 * q^48 + 3 * q^49 + 7 * q^50 + 3 * q^51 - 5 * q^52 + 3 * q^53 + 25 * q^54 + 6 * q^55 + 22 * q^56 + 11 * q^57 - 21 * q^58 + 2 * q^59 - q^60 - 20 * q^61 + 3 * q^62 + 23 * q^63 - 39 * q^64 - 34 * q^65 + 7 * q^66 - 2 * q^67 - 5 * q^68 - 17 * q^69 - q^70 + q^71 + 21 * q^72 + 13 * q^73 + 28 * q^74 - 5 * q^75 - 29 * q^76 - 11 * q^77 - 26 * q^79 + 12 * q^80 + 2 * q^81 - 9 * q^82 + 10 * q^83 - 3 * q^84 - 3 * q^85 + q^86 + 12 * q^87 - 6 * q^88 - 15 * q^89 + 15 * q^90 + 8 * q^91 - 9 * q^92 - 11 * q^93 - 33 * q^94 - 21 * q^95 + 25 * q^96 - 22 * q^97 - 3 * q^98 - 5 * q^99

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