LMFDB - Embedded newform 731.2.a.c.1.4

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			1.4
Root			$-1.30704$ 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)

$f(q)$	$=$	$q+0.291653 q^{2} -0.858197 q^{3} -1.91494 q^{4} +3.99528 q^{5} -0.250296 q^{6} -2.74049 q^{7} -1.14180 q^{8} -2.26350 q^{9} +O(q^{10})$	\(q+0.291653 q^{2} -0.858197 q^{3} -1.91494 q^{4} +3.99528 q^{5} -0.250296 q^{6} -2.74049 q^{7} -1.14180 q^{8} -2.26350 q^{9} +1.16523 q^{10} +3.05674 q^{11} +1.64339 q^{12} -5.80993 q^{13} -0.799273 q^{14} -3.42873 q^{15} +3.49687 q^{16} -1.00000 q^{17} -0.660156 q^{18} -3.69042 q^{19} -7.65071 q^{20} +2.35188 q^{21} +0.891508 q^{22} -2.72155 q^{23} +0.979892 q^{24} +10.9622 q^{25} -1.69448 q^{26} +4.51712 q^{27} +5.24788 q^{28} -10.1277 q^{29} -1.00000 q^{30} +3.83106 q^{31} +3.30348 q^{32} -2.62329 q^{33} -0.291653 q^{34} -10.9490 q^{35} +4.33446 q^{36} -9.47073 q^{37} -1.07632 q^{38} +4.98607 q^{39} -4.56182 q^{40} -10.0824 q^{41} +0.685933 q^{42} -1.00000 q^{43} -5.85347 q^{44} -9.04330 q^{45} -0.793748 q^{46} +7.25723 q^{47} -3.00100 q^{48} +0.510306 q^{49} +3.19717 q^{50} +0.858197 q^{51} +11.1257 q^{52} -0.0256123 q^{53} +1.31743 q^{54} +12.2125 q^{55} +3.12911 q^{56} +3.16711 q^{57} -2.95377 q^{58} -4.19905 q^{59} +6.56581 q^{60} -6.73795 q^{61} +1.11734 q^{62} +6.20310 q^{63} -6.03026 q^{64} -23.2123 q^{65} -0.765089 q^{66} +11.5581 q^{67} +1.91494 q^{68} +2.33563 q^{69} -3.19332 q^{70} -8.72587 q^{71} +2.58447 q^{72} +3.33134 q^{73} -2.76217 q^{74} -9.40775 q^{75} +7.06693 q^{76} -8.37698 q^{77} +1.45420 q^{78} -6.10660 q^{79} +13.9709 q^{80} +2.91392 q^{81} -2.94057 q^{82} -8.98937 q^{83} -4.50371 q^{84} -3.99528 q^{85} -0.291653 q^{86} +8.69156 q^{87} -3.49020 q^{88} -0.838307 q^{89} -2.63751 q^{90} +15.9221 q^{91} +5.21160 q^{92} -3.28780 q^{93} +2.11659 q^{94} -14.7442 q^{95} -2.83503 q^{96} +17.2844 q^{97} +0.148832 q^{98} -6.91893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.291653	0.206230	0.103115	−	0.994669i	$-0.467119\pi$
$2$	0.291653	0.206230	0.103115	+	0.994669i	$0.467119\pi$
$3$	−0.858197	−0.495480	−0.247740	−	0.968827i	$-0.579688\pi$
$3$	−0.858197	−0.495480	−0.247740	+	0.968827i	$0.579688\pi$
$4$	−1.91494	−0.957469
$5$	3.99528	1.78674	0.893371	−	0.449320i	$-0.148334\pi$
$5$	3.99528	1.78674	0.893371	+	0.449320i	$0.148334\pi$
$6$	−0.250296	−0.102183
$7$	−2.74049	−1.03581	−0.517905	−	0.855438i	$-0.673288\pi$
$7$	−2.74049	−1.03581	−0.517905	+	0.855438i	$0.673288\pi$
$8$	−1.14180	−0.403688
$9$	−2.26350	−0.754500
$10$	1.16523	0.368479
$11$	3.05674	0.921642	0.460821	−	0.887493i	$-0.347555\pi$
$11$	3.05674	0.921642	0.460821	+	0.887493i	$0.347555\pi$
$12$	1.64339	0.474407
$13$	−5.80993	−1.61139	−0.805693	−	0.592333i	$-0.798207\pi$
$13$	−5.80993	−1.61139	−0.805693	+	0.592333i	$0.798207\pi$
$14$	−0.799273	−0.213615
$15$	−3.42873	−0.885295
$16$	3.49687	0.874217
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.660156	−0.155600
$19$	−3.69042	−0.846641	−0.423320	−	0.905980i	$-0.639135\pi$
$19$	−3.69042	−0.846641	−0.423320	+	0.905980i	$0.639135\pi$
$20$	−7.65071	−1.71075
$21$	2.35188	0.513223
$22$	0.891508	0.190070
$23$	−2.72155	−0.567482	−0.283741	−	0.958901i	$-0.591576\pi$
$23$	−2.72155	−0.567482	−0.283741	+	0.958901i	$0.591576\pi$
$24$	0.979892	0.200020
$25$	10.9622	2.19245
$26$	−1.69448	−0.332316
$27$	4.51712	0.869320
$28$	5.24788	0.991756
$29$	−10.1277	−1.88067	−0.940334	−	0.340254i	$-0.889487\pi$
$29$	−10.1277	−1.88067	−0.940334	+	0.340254i	$0.889487\pi$
$30$	−1.00000	−0.182574
$31$	3.83106	0.688079	0.344039	−	0.938955i	$-0.388205\pi$
$31$	3.83106	0.688079	0.344039	+	0.938955i	$0.388205\pi$
$32$	3.30348	0.583978
$33$	−2.62329	−0.456655
$34$	−0.291653	−0.0500181
$35$	−10.9490	−1.85072
$36$	4.33446	0.722410
$37$	−9.47073	−1.55698	−0.778489	−	0.627658i	$-0.784014\pi$
$37$	−9.47073	−1.55698	−0.778489	+	0.627658i	$0.784014\pi$
$38$	−1.07632	−0.174602
$39$	4.98607	0.798410
$40$	−4.56182	−0.721287
$41$	−10.0824	−1.57461	−0.787305	−	0.616564i	$-0.788524\pi$
$41$	−10.0824	−1.57461	−0.787305	+	0.616564i	$0.788524\pi$
$42$	0.685933	0.105842
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−5.85347	−0.882444
$45$	−9.04330	−1.34810
$46$	−0.793748	−0.117032
$47$	7.25723	1.05858	0.529288	−	0.848442i	$-0.322459\pi$
$47$	7.25723	1.05858	0.529288	+	0.848442i	$0.322459\pi$
$48$	−3.00100	−0.433157
$49$	0.510306	0.0729009
$50$	3.19717	0.452148
$51$	0.858197	0.120172
$52$	11.1257	1.54285
$53$	−0.0256123	−0.00351813	−0.00175906	−	0.999998i	$-0.500560\pi$
$53$	−0.0256123	−0.00351813	−0.00175906	+	0.999998i	$0.500560\pi$
$54$	1.31743	0.179280
$55$	12.2125	1.64674
$56$	3.12911	0.418144
$57$	3.16711	0.419493
$58$	−2.95377	−0.387850
$59$	−4.19905	−0.546670	−0.273335	−	0.961919i	$-0.588127\pi$
$59$	−4.19905	−0.546670	−0.273335	+	0.961919i	$0.588127\pi$
$60$	6.56581	0.847643
$61$	−6.73795	−0.862706	−0.431353	−	0.902183i	$-0.641964\pi$
$61$	−6.73795	−0.862706	−0.431353	+	0.902183i	$0.641964\pi$
$62$	1.11734	0.141902
$63$	6.20310	0.781518
$64$	−6.03026	−0.753783
$65$	−23.2123	−2.87913
$66$	−0.765089	−0.0941759
$67$	11.5581	1.41205	0.706024	−	0.708188i	$-0.250487\pi$
$67$	11.5581	1.41205	0.706024	+	0.708188i	$0.250487\pi$
$68$	1.91494	0.232220
$69$	2.33563	0.281176
$70$	−3.19332	−0.381674
$71$	−8.72587	−1.03557	−0.517785	−	0.855511i	$-0.673243\pi$
$71$	−8.72587	−1.03557	−0.517785	+	0.855511i	$0.673243\pi$
$72$	2.58447	0.304583
$73$	3.33134	0.389904	0.194952	−	0.980813i	$-0.437545\pi$
$73$	3.33134	0.389904	0.194952	+	0.980813i	$0.437545\pi$
$74$	−2.76217	−0.321095
$75$	−9.40775	−1.08631
$76$	7.06693	0.810632
$77$	−8.37698	−0.954646
$78$	1.45420	0.164656
$79$	−6.10660	−0.687046	−0.343523	−	0.939144i	$-0.611620\pi$
$79$	−6.10660	−0.687046	−0.343523	+	0.939144i	$0.611620\pi$
$80$	13.9709	1.56200
$81$	2.91392	0.323769
$82$	−2.94057	−0.324732
$83$	−8.98937	−0.986712	−0.493356	−	0.869828i	$-0.664230\pi$
$83$	−8.98937	−0.986712	−0.493356	+	0.869828i	$0.664230\pi$
$84$	−4.50371	−0.491395
$85$	−3.99528	−0.433349
$86$	−0.291653	−0.0314497
$87$	8.69156	0.931833
$88$	−3.49020	−0.372056
$89$	−0.838307	−0.0888604	−0.0444302	−	0.999012i	$-0.514147\pi$
$89$	−0.838307	−0.0888604	−0.0444302	+	0.999012i	$0.514147\pi$
$90$	−2.63751	−0.278018
$91$	15.9221	1.66909
$92$	5.21160	0.543347
$93$	−3.28780	−0.340929
$94$	2.11659	0.218310
$95$	−14.7442	−1.51273
$96$	−2.83503	−0.289349
$97$	17.2844	1.75497	0.877483	−	0.479607i	$-0.159221\pi$
$97$	17.2844	1.75497	0.877483	+	0.479607i	$0.159221\pi$
$98$	0.148832	0.0150343
$99$	−6.91893	−0.695379
$100$	−20.9920	−2.09920
$101$	−5.66451	−0.563640	−0.281820	−	0.959467i	$-0.590938\pi$
$101$	−5.66451	−0.563640	−0.281820	+	0.959467i	$0.590938\pi$
$102$	0.250296	0.0247830
$103$	7.12119	0.701672	0.350836	−	0.936437i	$-0.385898\pi$
$103$	7.12119	0.701672	0.350836	+	0.936437i	$0.385898\pi$
$104$	6.63380	0.650498
$105$	9.39642	0.916997
$106$	−0.00746991	−0.000725542 0
$107$	19.2706	1.86296	0.931481	−	0.363790i	$-0.118517\pi$
$107$	19.2706	1.86296	0.931481	+	0.363790i	$0.118517\pi$
$108$	−8.65000	−0.832347
$109$	−3.88034	−0.371669	−0.185835	−	0.982581i	$-0.559499\pi$
$109$	−3.88034	−0.371669	−0.185835	+	0.982581i	$0.559499\pi$
$110$	3.56182	0.339606
$111$	8.12775	0.771452
$112$	−9.58314	−0.905522
$113$	16.4216	1.54481	0.772407	−	0.635128i	$-0.219053\pi$
$113$	16.4216	1.54481	0.772407	+	0.635128i	$0.219053\pi$
$114$	0.923696	0.0865120
$115$	−10.8733	−1.01394
$116$	19.3939	1.80068
$117$	13.1508	1.21579
$118$	−1.22467	−0.112740
$119$	2.74049	0.251221
$120$	3.91494	0.357383
$121$	−1.65633	−0.150575
$122$	−1.96514	−0.177916
$123$	8.65270	0.780188
$124$	−7.33624	−0.658814
$125$	23.8208	2.13059
$126$	1.80915	0.161172
$127$	−9.00730	−0.799268	−0.399634	−	0.916675i	$-0.630863\pi$
$127$	−9.00730	−0.799268	−0.399634	+	0.916675i	$0.630863\pi$
$128$	−8.36570	−0.739430
$129$	0.858197	0.0755600
$130$	−6.76993	−0.593762
$131$	17.6371	1.54096	0.770480	−	0.637464i	$-0.220017\pi$
$131$	17.6371	1.54096	0.770480	+	0.637464i	$0.220017\pi$
$132$	5.02343	0.437234
$133$	10.1136	0.876958
$134$	3.37096	0.291206
$135$	18.0471	1.55325
$136$	1.14180	0.0979088
$137$	−14.7349	−1.25889	−0.629445	−	0.777045i	$-0.716718\pi$
$137$	−14.7349	−1.25889	−0.629445	+	0.777045i	$0.716718\pi$
$138$	0.681192	0.0579869
$139$	9.48346	0.804376	0.402188	−	0.915557i	$-0.368250\pi$
$139$	9.48346	0.804376	0.402188	+	0.915557i	$0.368250\pi$
$140$	20.9667	1.77201
$141$	−6.22813	−0.524503
$142$	−2.54493	−0.213565
$143$	−17.7595	−1.48512
$144$	−7.91515	−0.659596
$145$	−40.4630	−3.36027
$146$	0.971595	0.0804098
$147$	−0.437943	−0.0361210
$148$	18.1359	1.49076
$149$	19.5571	1.60218	0.801091	−	0.598543i	$-0.204253\pi$
$149$	19.5571	1.60218	0.801091	+	0.598543i	$0.204253\pi$
$150$	−2.74380	−0.224030
$151$	2.35499	0.191647	0.0958233	−	0.995398i	$-0.469452\pi$
$151$	2.35499	0.191647	0.0958233	+	0.995398i	$0.469452\pi$
$152$	4.21373	0.341779
$153$	2.26350	0.182993
$154$	−2.44317	−0.196876
$155$	15.3061	1.22942
$156$	−9.54801	−0.764453
$157$	8.30078	0.662475	0.331237	−	0.943547i	$-0.392534\pi$
$157$	8.30078	0.662475	0.331237	+	0.943547i	$0.392534\pi$
$158$	−1.78101	−0.141689
$159$	0.0219804	0.00174316
$160$	13.1983	1.04342
$161$	7.45839	0.587804
$162$	0.849854	0.0667708
$163$	16.9278	1.32588	0.662942	−	0.748670i	$-0.269307\pi$
$163$	16.9278	1.32588	0.662942	+	0.748670i	$0.269307\pi$
$164$	19.3072	1.50764
$165$	−10.4808	−0.815925
$166$	−2.62178	−0.203489
$167$	−3.65977	−0.283202	−0.141601	−	0.989924i	$-0.545225\pi$
$167$	−3.65977	−0.283202	−0.141601	+	0.989924i	$0.545225\pi$
$168$	−2.68539	−0.207182
$169$	20.7553	1.59656
$170$	−1.16523	−0.0893694
$171$	8.35326	0.638790
$172$	1.91494	0.146013
$173$	−8.91665	−0.677920	−0.338960	−	0.940801i	$-0.610075\pi$
$173$	−8.91665	−0.677920	−0.338960	+	0.940801i	$0.610075\pi$
$174$	2.53492	0.192172
$175$	−30.0419	−2.27096
$176$	10.6890	0.805715
$177$	3.60361	0.270864
$178$	−0.244495	−0.0183257
$179$	−1.72001	−0.128559	−0.0642796	−	0.997932i	$-0.520475\pi$
$179$	−1.72001	−0.128559	−0.0642796	+	0.997932i	$0.520475\pi$
$180$	17.3174	1.29076
$181$	−18.1564	−1.34956	−0.674779	−	0.738020i	$-0.735761\pi$
$181$	−18.1564	−1.34956	−0.674779	+	0.738020i	$0.735761\pi$
$182$	4.64372	0.344216
$183$	5.78249	0.427454
$184$	3.10748	0.229086
$185$	−37.8382	−2.78192
$186$	−0.958897	−0.0703098
$187$	−3.05674	−0.223531
$188$	−13.8972	−1.01355
$189$	−12.3791	−0.900449
$190$	−4.30020	−0.311970
$191$	−3.06795	−0.221989	−0.110994	−	0.993821i	$-0.535404\pi$
$191$	−3.06795	−0.221989	−0.110994	+	0.993821i	$0.535404\pi$
$192$	5.17515	0.373484
$193$	11.9306	0.858785	0.429393	−	0.903118i	$-0.358728\pi$
$193$	11.9306	0.858785	0.429393	+	0.903118i	$0.358728\pi$
$194$	5.04105	0.361926
$195$	19.9207	1.42655
$196$	−0.977206	−0.0698004
$197$	−1.46807	−0.104596	−0.0522980	−	0.998632i	$-0.516655\pi$
$197$	−1.46807	−0.104596	−0.0522980	+	0.998632i	$0.516655\pi$
$198$	−2.01793	−0.143408
$199$	−23.7362	−1.68261	−0.841306	−	0.540559i	$-0.818213\pi$
$199$	−23.7362	−1.68261	−0.841306	+	0.540559i	$0.818213\pi$
$200$	−12.5167	−0.885065
$201$	−9.91913	−0.699641
$202$	−1.65207	−0.116239
$203$	27.7549	1.94801
$204$	−1.64339	−0.115061
$205$	−40.2821	−2.81342
$206$	2.07692	0.144706
$207$	6.16022	0.428165
$208$	−20.3166	−1.40870
$209$	−11.2807	−0.780300
$210$	2.74049	0.189112
$211$	−16.7405	−1.15246	−0.576230	−	0.817287i	$-0.695477\pi$
$211$	−16.7405	−1.15246	−0.576230	+	0.817287i	$0.695477\pi$
$212$	0.0490461	0.00336850
$213$	7.48851	0.513105
$214$	5.62034	0.384198
$215$	−3.99528	−0.272476
$216$	−5.15766	−0.350934
$217$	−10.4990	−0.712718
$218$	−1.13171	−0.0766493
$219$	−2.85895	−0.193190
$220$	−23.3862	−1.57670
$221$	5.80993	0.390818
$222$	2.37048	0.159096
$223$	19.7499	1.32255	0.661275	−	0.750143i	$-0.270016\pi$
$223$	19.7499	1.32255	0.661275	+	0.750143i	$0.270016\pi$
$224$	−9.05316	−0.604890
$225$	−24.8130	−1.65420
$226$	4.78941	0.318587
$227$	−18.2590	−1.21189	−0.605945	−	0.795506i	$-0.707205\pi$
$227$	−18.2590	−1.21189	−0.605945	+	0.795506i	$0.707205\pi$
$228$	−6.06481	−0.401652
$229$	−8.84328	−0.584381	−0.292190	−	0.956360i	$-0.594384\pi$
$229$	−8.84328	−0.584381	−0.292190	+	0.956360i	$0.594384\pi$
$230$	−3.17124	−0.209106
$231$	7.18910	0.473008
$232$	11.5638	0.759204
$233$	0.229827	0.0150565	0.00752823	−	0.999972i	$-0.497604\pi$
$233$	0.229827	0.0150565	0.00752823	+	0.999972i	$0.497604\pi$
$234$	3.83546	0.250732
$235$	28.9946	1.89140
$236$	8.04092	0.523419
$237$	5.24067	0.340418
$238$	0.799273	0.0518092
$239$	−11.0420	−0.714244	−0.357122	−	0.934058i	$-0.616242\pi$
$239$	−11.0420	−0.714244	−0.357122	+	0.934058i	$0.616242\pi$
$240$	−11.9898	−0.773940
$241$	−17.5678	−1.13164	−0.565821	−	0.824528i	$-0.691441\pi$
$241$	−17.5678	−1.13164	−0.565821	+	0.824528i	$0.691441\pi$
$242$	−0.483073	−0.0310531
$243$	−16.0521	−1.02974
$244$	12.9028	0.826015
$245$	2.03882	0.130255
$246$	2.52359	0.160898
$247$	21.4411	1.36426
$248$	−4.37432	−0.277769
$249$	7.71465	0.488896
$250$	6.94740	0.439392
$251$	−6.11065	−0.385701	−0.192851	−	0.981228i	$-0.561773\pi$
$251$	−6.11065	−0.385701	−0.192851	+	0.981228i	$0.561773\pi$
$252$	−11.8786	−0.748279
$253$	−8.31908	−0.523016
$254$	−2.62700	−0.164833
$255$	3.42873	0.214716
$256$	9.62065	0.601290
$257$	−9.41028	−0.586997	−0.293499	−	0.955959i	$-0.594820\pi$
$257$	−9.41028	−0.586997	−0.293499	+	0.955959i	$0.594820\pi$
$258$	0.250296	0.0155827
$259$	25.9545	1.61273
$260$	44.4501	2.75668
$261$	22.9240	1.41896
$262$	5.14391	0.317792
$263$	−10.9976	−0.678143	−0.339072	−	0.940761i	$-0.610113\pi$
$263$	−10.9976	−0.678143	−0.339072	+	0.940761i	$0.610113\pi$
$264$	2.99528	0.184347
$265$	−0.102328	−0.00628598
$266$	2.94965	0.180855
$267$	0.719432	0.0440285
$268$	−22.1331	−1.35199
$269$	22.1408	1.34995	0.674975	−	0.737841i	$-0.264155\pi$
$269$	22.1408	1.34995	0.674975	+	0.737841i	$0.264155\pi$
$270$	5.26350	0.320326
$271$	10.4406	0.634221	0.317110	−	0.948389i	$-0.397287\pi$
$271$	10.4406	0.634221	0.317110	+	0.948389i	$0.397287\pi$
$272$	−3.49687	−0.212029
$273$	−13.6643	−0.827000
$274$	−4.29749	−0.259621
$275$	33.5087	2.02065
$276$	−4.47258	−0.269218
$277$	7.12840	0.428304	0.214152	−	0.976800i	$-0.431301\pi$
$277$	7.12840	0.428304	0.214152	+	0.976800i	$0.431301\pi$
$278$	2.76588	0.165886
$279$	−8.67160	−0.519155
$280$	12.5016	0.747116
$281$	14.8324	0.884827	0.442414	−	0.896811i	$-0.354122\pi$
$281$	14.8324	0.884827	0.442414	+	0.896811i	$0.354122\pi$
$282$	−1.81645	−0.108168
$283$	−6.63105	−0.394175	−0.197088	−	0.980386i	$-0.563148\pi$
$283$	−6.63105	−0.394175	−0.197088	+	0.980386i	$0.563148\pi$
$284$	16.7095	0.991527
$285$	12.6535	0.749527
$286$	−5.17960	−0.306276
$287$	27.6308	1.63100
$288$	−7.47742	−0.440611
$289$	1.00000	0.0588235
$290$	−11.8011	−0.692987
$291$	−14.8334	−0.869551
$292$	−6.37931	−0.373321
$293$	−20.1059	−1.17460	−0.587301	−	0.809369i	$-0.699809\pi$
$293$	−20.1059	−1.17460	−0.587301	+	0.809369i	$0.699809\pi$
$294$	−0.127727	−0.00744922
$295$	−16.7764	−0.976758
$296$	10.8137	0.628534
$297$	13.8077	0.801202
$298$	5.70389	0.330418
$299$	15.8120	0.914433
$300$	18.0153	1.04011
$301$	2.74049	0.157959
$302$	0.686840	0.0395232
$303$	4.86126	0.279272
$304$	−12.9049	−0.740147
$305$	−26.9200	−1.54143
$306$	0.660156	0.0377386
$307$	−8.05642	−0.459804	−0.229902	−	0.973214i	$-0.573841\pi$
$307$	−8.05642	−0.459804	−0.229902	+	0.973214i	$0.573841\pi$
$308$	16.0414	0.914044
$309$	−6.11138	−0.347664
$310$	4.46408	0.253543
$311$	−26.0287	−1.47595	−0.737975	−	0.674828i	$-0.764218\pi$
$311$	−26.0287	−1.47595	−0.737975	+	0.674828i	$0.764218\pi$
$312$	−5.69311	−0.322309
$313$	15.0857	0.852692	0.426346	−	0.904560i	$-0.359801\pi$
$313$	15.0857	0.852692	0.426346	+	0.904560i	$0.359801\pi$
$314$	2.42095	0.136622
$315$	24.7831	1.39637
$316$	11.6938	0.657826
$317$	−15.4286	−0.866559	−0.433279	−	0.901260i	$-0.642644\pi$
$317$	−15.4286	−0.866559	−0.433279	+	0.901260i	$0.642644\pi$
$318$	0.00641066	0.000359492 0
$319$	−30.9578	−1.73330
$320$	−24.0926	−1.34682
$321$	−16.5380	−0.923061
$322$	2.17526	0.121223
$323$	3.69042	0.205340
$324$	−5.57998	−0.309999
$325$	−63.6899	−3.53288
$326$	4.93703	0.273437
$327$	3.33010	0.184155
$328$	11.5121	0.635652
$329$	−19.8884	−1.09648
$330$	−3.05674	−0.168268
$331$	0.688160	0.0378247	0.0189123	−	0.999821i	$-0.493980\pi$
$331$	0.688160	0.0378247	0.0189123	+	0.999821i	$0.493980\pi$
$332$	17.2141	0.944746
$333$	21.4370	1.17474
$334$	−1.06738	−0.0584046
$335$	46.1778	2.52296
$336$	8.22422	0.448668
$337$	−31.6565	−1.72444	−0.862221	−	0.506532i	$-0.830927\pi$
$337$	−31.6565	−1.72444	−0.862221	+	0.506532i	$0.830927\pi$
$338$	6.05335	0.329259
$339$	−14.0930	−0.765424
$340$	7.65071	0.414918
$341$	11.7106	0.634162
$342$	2.43625	0.131737
$343$	17.7850	0.960298
$344$	1.14180	0.0615619
$345$	9.33147	0.502389
$346$	−2.60057	−0.139807
$347$	−14.0369	−0.753543	−0.376771	−	0.926306i	$-0.622966\pi$
$347$	−14.0369	−0.753543	−0.376771	+	0.926306i	$0.622966\pi$
$348$	−16.6438	−0.892202
$349$	−1.09785	−0.0587666	−0.0293833	−	0.999568i	$-0.509354\pi$
$349$	−1.09785	−0.0587666	−0.0293833	+	0.999568i	$0.509354\pi$
$350$	−8.76182	−0.468339
$351$	−26.2441	−1.40081
$352$	10.0979	0.538219
$353$	−4.70964	−0.250669	−0.125334	−	0.992115i	$-0.540000\pi$
$353$	−4.70964	−0.250669	−0.125334	+	0.992115i	$0.540000\pi$
$354$	1.05100	0.0558602
$355$	−34.8623	−1.85030
$356$	1.60531	0.0850811
$357$	−2.35188	−0.124475
$358$	−0.501645	−0.0265128
$359$	12.9863	0.685391	0.342696	−	0.939446i	$-0.388660\pi$
$359$	12.9863	0.685391	0.342696	+	0.939446i	$0.388660\pi$
$360$	10.3257	0.544211
$361$	−5.38080	−0.283200
$362$	−5.29538	−0.278319
$363$	1.42146	0.0746071
$364$	−30.4898	−1.59810
$365$	13.3096	0.696658
$366$	1.68648	0.0881537
$367$	−4.48210	−0.233964	−0.116982	−	0.993134i	$-0.537322\pi$
$367$	−4.48210	−0.233964	−0.116982	+	0.993134i	$0.537322\pi$
$368$	−9.51690	−0.496103
$369$	22.8216	1.18804
$370$	−11.0356	−0.573714
$371$	0.0701905	0.00364411
$372$	6.29594	0.326429
$373$	−7.86900	−0.407441	−0.203721	−	0.979029i	$-0.565303\pi$
$373$	−7.86900	−0.407441	−0.203721	+	0.979029i	$0.565303\pi$
$374$	−0.891508	−0.0460988
$375$	−20.4429	−1.05567
$376$	−8.28633	−0.427335
$377$	58.8413	3.03048
$378$	−3.61041	−0.185699
$379$	17.3002	0.888654	0.444327	−	0.895865i	$-0.353443\pi$
$379$	17.3002	0.888654	0.444327	+	0.895865i	$0.353443\pi$
$380$	28.2343	1.44839
$381$	7.73003	0.396022
$382$	−0.894776	−0.0457807
$383$	−5.67171	−0.289811	−0.144906	−	0.989445i	$-0.546288\pi$
$383$	−5.67171	−0.289811	−0.144906	+	0.989445i	$0.546288\pi$
$384$	7.17942	0.366373
$385$	−33.4684	−1.70571
$386$	3.47960	0.177107
$387$	2.26350	0.115060
$388$	−33.0986	−1.68033
$389$	17.1355	0.868805	0.434402	−	0.900719i	$-0.356960\pi$
$389$	17.1355	0.868805	0.434402	+	0.900719i	$0.356960\pi$
$390$	5.80993	0.294197
$391$	2.72155	0.137635
$392$	−0.582670	−0.0294293
$393$	−15.1361	−0.763515
$394$	−0.428168	−0.0215708
$395$	−24.3976	−1.22757
$396$	13.2493	0.665804
$397$	21.3267	1.07035	0.535177	−	0.844740i	$-0.320245\pi$
$397$	21.3267	1.07035	0.535177	+	0.844740i	$0.320245\pi$
$398$	−6.92272	−0.347005
$399$	−8.67944	−0.434515
$400$	38.3335	1.91667
$401$	−32.6052	−1.62823	−0.814114	−	0.580705i	$-0.802777\pi$
$401$	−32.6052	−1.62823	−0.814114	+	0.580705i	$0.802777\pi$
$402$	−2.89294	−0.144287
$403$	−22.2582	−1.10876
$404$	10.8472	0.539668
$405$	11.6419	0.578492
$406$	8.09480	0.401738
$407$	−28.9496	−1.43498
$408$	−0.979892	−0.0485119
$409$	−10.5782	−0.523056	−0.261528	−	0.965196i	$-0.584226\pi$
$409$	−10.5782	−0.523056	−0.261528	+	0.965196i	$0.584226\pi$
$410$	−11.7484	−0.580211
$411$	12.6455	0.623755
$412$	−13.6366	−0.671829
$413$	11.5075	0.566246
$414$	1.79665	0.0883004
$415$	−35.9150	−1.76300
$416$	−19.1930	−0.941014
$417$	−8.13867	−0.398552
$418$	−3.29004	−0.160921
$419$	−17.3706	−0.848608	−0.424304	−	0.905520i	$-0.639481\pi$
$419$	−17.3706	−0.848608	−0.424304	+	0.905520i	$0.639481\pi$
$420$	−17.9936	−0.877996
$421$	−4.46786	−0.217750	−0.108875	−	0.994055i	$-0.534725\pi$
$421$	−4.46786	−0.217750	−0.108875	+	0.994055i	$0.534725\pi$
$422$	−4.88240	−0.237672
$423$	−16.4267	−0.798695
$424$	0.0292443	0.00142023
$425$	−10.9622	−0.531746
$426$	2.18405	0.105817
$427$	18.4653	0.893599
$428$	−36.9021	−1.78373
$429$	15.2411	0.735848
$430$	−1.16523	−0.0561926
$431$	10.0244	0.482860	0.241430	−	0.970418i	$-0.422384\pi$
$431$	10.0244	0.482860	0.241430	+	0.970418i	$0.422384\pi$
$432$	15.7958	0.759974
$433$	−9.06344	−0.435561	−0.217781	−	0.975998i	$-0.569882\pi$
$433$	−9.06344	−0.435561	−0.217781	+	0.975998i	$0.569882\pi$
$434$	−3.06206	−0.146984
$435$	34.7252	1.66495
$436$	7.43062	0.355862
$437$	10.0437	0.480454
$438$	−0.833820	−0.0398415
$439$	29.4502	1.40558	0.702791	−	0.711397i	$-0.251937\pi$
$439$	29.4502	1.40558	0.702791	+	0.711397i	$0.251937\pi$
$440$	−13.9443	−0.664769
$441$	−1.15508	−0.0550037
$442$	1.69448	0.0805984
$443$	9.04833	0.429899	0.214950	−	0.976625i	$-0.431041\pi$
$443$	9.04833	0.429899	0.214950	+	0.976625i	$0.431041\pi$
$444$	−15.5641	−0.738641
$445$	−3.34927	−0.158771
$446$	5.76011	0.272749
$447$	−16.7839	−0.793849
$448$	16.5259	0.780776
$449$	14.7810	0.697557	0.348779	−	0.937205i	$-0.386597\pi$
$449$	14.7810	0.697557	0.348779	+	0.937205i	$0.386597\pi$
$450$	−7.23678	−0.341145
$451$	−30.8194	−1.45123
$452$	−31.4463	−1.47911
$453$	−2.02105	−0.0949570
$454$	−5.32528	−0.249928
$455$	63.6131	2.98223
$456$	−3.61621	−0.169345
$457$	3.87054	0.181056	0.0905281	−	0.995894i	$-0.471144\pi$
$457$	3.87054	0.181056	0.0905281	+	0.995894i	$0.471144\pi$
$458$	−2.57917	−0.120517
$459$	−4.51712	−0.210841
$460$	20.8218	0.970821
$461$	15.4345	0.718854	0.359427	−	0.933173i	$-0.382972\pi$
$461$	15.4345	0.718854	0.359427	+	0.933173i	$0.382972\pi$
$462$	2.09672	0.0975483
$463$	−17.0689	−0.793260	−0.396630	−	0.917979i	$-0.629820\pi$
$463$	−17.0689	−0.793260	−0.396630	+	0.917979i	$0.629820\pi$
$464$	−35.4152	−1.64411
$465$	−13.1357	−0.609153
$466$	0.0670297	0.00310509
$467$	−34.5188	−1.59734	−0.798670	−	0.601770i	$-0.794462\pi$
$467$	−34.5188	−1.59734	−0.798670	+	0.601770i	$0.794462\pi$
$468$	−25.1829	−1.16408
$469$	−31.6749	−1.46261
$470$	8.45637	0.390063
$471$	−7.12370	−0.328243
$472$	4.79449	0.220684
$473$	−3.05674	−0.140549
$474$	1.52846	0.0702043
$475$	−40.4552	−1.85621
$476$	−5.24788	−0.240536
$477$	0.0579735	0.00265442
$478$	−3.22042	−0.147298
$479$	−6.40545	−0.292673	−0.146336	−	0.989235i	$-0.546748\pi$
$479$	−6.40545	−0.292673	−0.146336	+	0.989235i	$0.546748\pi$
$480$	−11.3267	−0.516993
$481$	55.0243	2.50889
$482$	−5.12371	−0.233378
$483$	−6.40077	−0.291245
$484$	3.17177	0.144171
$485$	69.0560	3.13567
$486$	−4.68163	−0.212363
$487$	−28.4585	−1.28958	−0.644788	−	0.764361i	$-0.723054\pi$
$487$	−28.4585	−1.28958	−0.644788	+	0.764361i	$0.723054\pi$
$488$	7.69342	0.348265
$489$	−14.5273	−0.656949
$490$	0.594627	0.0268625
$491$	25.9394	1.17063	0.585314	−	0.810807i	$-0.300971\pi$
$491$	25.9394	1.17063	0.585314	+	0.810807i	$0.300971\pi$
$492$	−16.5694	−0.747006
$493$	10.1277	0.456129
$494$	6.25336	0.281352
$495$	−27.6430	−1.24246
$496$	13.3967	0.601530
$497$	23.9132	1.07265
$498$	2.25000	0.100825
$499$	−36.4020	−1.62958	−0.814790	−	0.579757i	$-0.803148\pi$
$499$	−36.4020	−1.62958	−0.814790	+	0.579757i	$0.803148\pi$
$500$	−45.6153	−2.03998
$501$	3.14080	0.140321
$502$	−1.78219	−0.0795430
$503$	38.9182	1.73528	0.867638	−	0.497197i	$-0.165637\pi$
$503$	38.9182	1.73528	0.867638	+	0.497197i	$0.165637\pi$
$504$	−7.08272	−0.315490
$505$	−22.6313	−1.00708
$506$	−2.42628	−0.107861
$507$	−17.8122	−0.791066
$508$	17.2484	0.765275
$509$	−22.3222	−0.989415	−0.494708	−	0.869060i	$-0.664725\pi$
$509$	−22.3222	−0.989415	−0.494708	+	0.869060i	$0.664725\pi$
$510$	1.00000	0.0442807
$511$	−9.12952	−0.403866
$512$	19.5373	0.863434
$513$	−16.6701	−0.736001
$514$	−2.74454	−0.121056
$515$	28.4511	1.25371
$516$	−1.64339	−0.0723464
$517$	22.1835	0.975629
$518$	7.56970	0.332593
$519$	7.65224	0.335896
$520$	26.5039	1.16227
$521$	−9.08470	−0.398008	−0.199004	−	0.979999i	$-0.563771\pi$
$521$	−9.08470	−0.398008	−0.199004	+	0.979999i	$0.563771\pi$
$522$	6.68586	0.292632
$523$	−10.0141	−0.437888	−0.218944	−	0.975737i	$-0.570261\pi$
$523$	−10.0141	−0.437888	−0.218944	+	0.975737i	$0.570261\pi$
$524$	−33.7740	−1.47542
$525$	25.7819	1.12521
$526$	−3.20749	−0.139853
$527$	−3.83106	−0.166884
$528$	−9.17328	−0.399216
$529$	−15.5932	−0.677964
$530$	−0.0298444	−0.00129636
$531$	9.50454	0.412462
$532$	−19.3669	−0.839660
$533$	58.5782	2.53730
$534$	0.209825	0.00908000
$535$	76.9915	3.32863
$536$	−13.1971	−0.570027
$537$	1.47610	0.0636986
$538$	6.45743	0.278400
$539$	1.55988	0.0671886
$540$	−34.5591	−1.48719
$541$	17.4916	0.752024	0.376012	−	0.926615i	$-0.377295\pi$
$541$	17.4916	0.752024	0.376012	+	0.926615i	$0.377295\pi$
$542$	3.04503	0.130795
$543$	15.5818	0.668679
$544$	−3.30348	−0.141635
$545$	−15.5030	−0.664077
$546$	−3.98523	−0.170552
$547$	9.21314	0.393926	0.196963	−	0.980411i	$-0.436892\pi$
$547$	9.21314	0.393926	0.196963	+	0.980411i	$0.436892\pi$
$548$	28.2165	1.20535
$549$	15.2513	0.650912
$550$	9.77292	0.416719
$551$	37.3755	1.59225
$552$	−2.66682	−0.113508
$553$	16.7351	0.711649
$554$	2.07902	0.0883290
$555$	32.4726	1.37839
$556$	−18.1602	−0.770166
$557$	−8.45542	−0.358268	−0.179134	−	0.983825i	$-0.557329\pi$
$557$	−8.45542	−0.358268	−0.179134	+	0.983825i	$0.557329\pi$
$558$	−2.52910	−0.107065
$559$	5.80993	0.245734
$560$	−38.2873	−1.61793
$561$	2.62329	0.110755
$562$	4.32592	0.182478
$563$	−29.1351	−1.22790	−0.613949	−	0.789346i	$-0.710420\pi$
$563$	−29.1351	−1.22790	−0.613949	+	0.789346i	$0.710420\pi$
$564$	11.9265	0.502196
$565$	65.6088	2.76018
$566$	−1.93397	−0.0812907
$567$	−7.98558	−0.335363
$568$	9.96323	0.418048
$569$	−13.0424	−0.546767	−0.273383	−	0.961905i	$-0.588143\pi$
$569$	−13.0424	−0.546767	−0.273383	+	0.961905i	$0.588143\pi$
$570$	3.69042	0.154575
$571$	1.70766	0.0714633	0.0357317	−	0.999361i	$-0.488624\pi$
$571$	1.70766	0.0714633	0.0357317	+	0.999361i	$0.488624\pi$
$572$	34.0083	1.42196
$573$	2.63290	0.109991
$574$	8.05861	0.336360
$575$	−29.8343	−1.24417
$576$	13.6495	0.568729
$577$	34.3329	1.42930	0.714648	−	0.699484i	$-0.246587\pi$
$577$	34.3329	1.42930	0.714648	+	0.699484i	$0.246587\pi$
$578$	0.291653	0.0121312
$579$	−10.2388	−0.425511
$580$	77.4841	3.21735
$581$	24.6353	1.02205
$582$	−4.32621	−0.179327
$583$	−0.0782903	−0.00324245
$584$	−3.80374	−0.157400
$585$	52.5410	2.17230
$586$	−5.86396	−0.242238
$587$	9.88207	0.407877	0.203938	−	0.978984i	$-0.434626\pi$
$587$	9.88207	0.407877	0.203938	+	0.978984i	$0.434626\pi$
$588$	0.838634	0.0345847
$589$	−14.1382	−0.582555
$590$	−4.89288	−0.201437
$591$	1.25990	0.0518252
$592$	−33.1179	−1.36114
$593$	10.8310	0.444774	0.222387	−	0.974958i	$-0.428615\pi$
$593$	10.8310	0.444774	0.222387	+	0.974958i	$0.428615\pi$
$594$	4.02704	0.165232
$595$	10.9490	0.448866
$596$	−37.4507	−1.53404
$597$	20.3703	0.833701
$598$	4.61162	0.188583
$599$	14.7511	0.602715	0.301358	−	0.953511i	$-0.402560\pi$
$599$	14.7511	0.602715	0.301358	+	0.953511i	$0.402560\pi$
$600$	10.7418	0.438532
$601$	11.1801	0.456047	0.228023	−	0.973656i	$-0.426774\pi$
$601$	11.1801	0.456047	0.228023	+	0.973656i	$0.426774\pi$
$602$	0.799273	0.0325759
$603$	−26.1618	−1.06539
$604$	−4.50966	−0.183496
$605$	−6.61749	−0.269039
$606$	1.41780	0.0575943
$607$	−44.3193	−1.79887	−0.899433	−	0.437059i	$-0.856020\pi$
$607$	−44.3193	−1.79887	−0.899433	+	0.437059i	$0.856020\pi$
$608$	−12.1912	−0.494419
$609$	−23.8192	−0.965201
$610$	−7.85129	−0.317889
$611$	−42.1640	−1.70577
$612$	−4.33446	−0.175210
$613$	−11.9423	−0.482344	−0.241172	−	0.970482i	$-0.577532\pi$
$613$	−11.9423	−0.482344	−0.241172	+	0.970482i	$0.577532\pi$
$614$	−2.34968	−0.0948253
$615$	34.5699	1.39399
$616$	9.56487	0.385379
$617$	20.8460	0.839230	0.419615	−	0.907702i	$-0.362165\pi$
$617$	20.8460	0.839230	0.419615	+	0.907702i	$0.362165\pi$
$618$	−1.78240	−0.0716987
$619$	−44.3104	−1.78098	−0.890492	−	0.454999i	$-0.849640\pi$
$619$	−44.3104	−1.78098	−0.890492	+	0.454999i	$0.849640\pi$
$620$	−29.3103	−1.17713
$621$	−12.2936	−0.493324
$622$	−7.59134	−0.304385
$623$	2.29738	0.0920424
$624$	17.4356	0.697983
$625$	40.3594	1.61438
$626$	4.39978	0.175851
$627$	9.68103	0.386623
$628$	−15.8955	−0.634299
$629$	9.47073	0.377623
$630$	7.22807	0.287973
$631$	11.4916	0.457473	0.228736	−	0.973488i	$-0.426541\pi$
$631$	11.4916	0.457473	0.228736	+	0.973488i	$0.426541\pi$
$632$	6.97254	0.277353
$633$	14.3666	0.571021
$634$	−4.49981	−0.178710
$635$	−35.9866	−1.42809
$636$	−0.0420912	−0.00166902
$637$	−2.96485	−0.117472
$638$	−9.02893	−0.357459
$639$	19.7510	0.781337
$640$	−33.4233	−1.32117
$641$	−11.5475	−0.456100	−0.228050	−	0.973649i	$-0.573235\pi$
$641$	−11.5475	−0.456100	−0.228050	+	0.973649i	$0.573235\pi$
$642$	−4.82335	−0.190363
$643$	26.3988	1.04107	0.520533	−	0.853842i	$-0.325733\pi$
$643$	26.3988	1.04107	0.520533	+	0.853842i	$0.325733\pi$
$644$	−14.2824	−0.562804
$645$	3.42873	0.135006
$646$	1.07632	0.0423473
$647$	33.2667	1.30785	0.653924	−	0.756561i	$-0.273122\pi$
$647$	33.2667	1.30785	0.653924	+	0.756561i	$0.273122\pi$
$648$	−3.32713	−0.130702
$649$	−12.8354	−0.503834
$650$	−18.5753	−0.728585
$651$	9.01020	0.353138
$652$	−32.4156	−1.26949
$653$	−11.1145	−0.434945	−0.217472	−	0.976067i	$-0.569781\pi$
$653$	−11.1145	−0.434945	−0.217472	+	0.976067i	$0.569781\pi$
$654$	0.971232	0.0379782
$655$	70.4651	2.75330
$656$	−35.2569	−1.37655
$657$	−7.54049	−0.294182
$658$	−5.80051	−0.226127
$659$	−32.1156	−1.25104	−0.625522	−	0.780206i	$-0.715114\pi$
$659$	−32.1156	−1.25104	−0.625522	+	0.780206i	$0.715114\pi$
$660$	20.0700	0.781223
$661$	−7.71808	−0.300199	−0.150099	−	0.988671i	$-0.547959\pi$
$661$	−7.71808	−0.300199	−0.150099	+	0.988671i	$0.547959\pi$
$662$	0.200704	0.00780057
$663$	−4.98607	−0.193643
$664$	10.2641	0.398324
$665$	40.4065	1.56690
$666$	6.25216	0.242266
$667$	27.5631	1.06725
$668$	7.00824	0.271157
$669$	−16.9493	−0.655297
$670$	13.4679	0.520310
$671$	−20.5962	−0.795107
$672$	7.76939	0.299711
$673$	23.9188	0.922003	0.461002	−	0.887399i	$-0.347490\pi$
$673$	23.9188	0.922003	0.461002	+	0.887399i	$0.347490\pi$
$674$	−9.23272	−0.355631
$675$	49.5177	1.90594
$676$	−39.7452	−1.52866
$677$	13.7725	0.529321	0.264661	−	0.964342i	$-0.414740\pi$
$677$	13.7725	0.529321	0.264661	+	0.964342i	$0.414740\pi$
$678$	−4.11025	−0.157853
$679$	−47.3678	−1.81781
$680$	4.56182	0.174938
$681$	15.6698	0.600467
$682$	3.41542	0.130783
$683$	10.7891	0.412835	0.206418	−	0.978464i	$-0.433819\pi$
$683$	10.7891	0.412835	0.206418	+	0.978464i	$0.433819\pi$
$684$	−15.9960	−0.611622
$685$	−58.8701	−2.24931
$686$	5.18704	0.198042
$687$	7.58928	0.289549
$688$	−3.49687	−0.133317
$689$	0.148806	0.00566906
$690$	2.72155	0.103608
$691$	4.14875	0.157826	0.0789130	−	0.996882i	$-0.474855\pi$
$691$	4.14875	0.157826	0.0789130	+	0.996882i	$0.474855\pi$
$692$	17.0748	0.649088
$693$	18.9613	0.720280
$694$	−4.09392	−0.155403
$695$	37.8890	1.43721
$696$	−9.92405	−0.376170
$697$	10.0824	0.381899
$698$	−0.320192	−0.0121194
$699$	−0.197237	−0.00746018
$700$	57.5285	2.17437
$701$	9.71741	0.367021	0.183511	−	0.983018i	$-0.441254\pi$
$701$	9.71741	0.367021	0.183511	+	0.983018i	$0.441254\pi$
$702$	−7.65418	−0.288889
$703$	34.9510	1.31820
$704$	−18.4330	−0.694718
$705$	−24.8831	−0.937152
$706$	−1.37358	−0.0516954
$707$	15.5236	0.583824
$708$	−6.90069	−0.259344
$709$	−35.0387	−1.31591	−0.657953	−	0.753059i	$-0.728578\pi$
$709$	−35.0387	−1.31591	−0.657953	+	0.753059i	$0.728578\pi$
$710$	−10.1677	−0.381586
$711$	13.8223	0.518376
$712$	0.957182	0.0358719
$713$	−10.4264	−0.390472
$714$	−0.685933	−0.0256704
$715$	−70.9540	−2.65353
$716$	3.29371	0.123092
$717$	9.47617	0.353894
$718$	3.78750	0.141348
$719$	27.6154	1.02988	0.514940	−	0.857226i	$-0.327814\pi$
$719$	27.6154	1.02988	0.514940	+	0.857226i	$0.327814\pi$
$720$	−31.6232	−1.17853
$721$	−19.5156	−0.726798
$722$	−1.56933	−0.0584042
$723$	15.0766	0.560706
$724$	34.7685	1.29216
$725$	−111.022	−4.12326
$726$	0.414572	0.0153862
$727$	14.5140	0.538293	0.269146	−	0.963099i	$-0.413258\pi$
$727$	14.5140	0.538293	0.269146	+	0.963099i	$0.413258\pi$
$728$	−18.1799	−0.673792
$729$	5.03407	0.186447
$730$	3.88179	0.143672
$731$	1.00000	0.0369863
$732$	−11.0731	−0.409274
$733$	−37.2894	−1.37732	−0.688659	−	0.725086i	$-0.741800\pi$
$733$	−37.2894	−1.37732	−0.688659	+	0.725086i	$0.741800\pi$
$734$	−1.30722	−0.0482503
$735$	−1.74970	−0.0645388
$736$	−8.99058	−0.331397
$737$	35.3301	1.30140
$738$	6.65597	0.245010
$739$	−19.9962	−0.735571	−0.367785	−	0.929911i	$-0.619884\pi$
$739$	−19.9962	−0.735571	−0.367785	+	0.929911i	$0.619884\pi$
$740$	72.4578	2.66360
$741$	−18.4007	−0.675966
$742$	0.0204713	0.000751523 0
$743$	−18.9825	−0.696399	−0.348199	−	0.937420i	$-0.613207\pi$
$743$	−18.9825	−0.696399	−0.348199	+	0.937420i	$0.613207\pi$
$744$	3.75402	0.137629
$745$	78.1361	2.86269
$746$	−2.29502	−0.0840265
$747$	20.3474	0.744473
$748$	5.85347	0.214024
$749$	−52.8110	−1.92967
$750$	−5.96223	−0.217710
$751$	−40.6916	−1.48486	−0.742429	−	0.669925i	$-0.766326\pi$
$751$	−40.6916	−1.48486	−0.742429	+	0.669925i	$0.766326\pi$
$752$	25.3776	0.925425
$753$	5.24414	0.191107
$754$	17.1612	0.624975
$755$	9.40884	0.342423
$756$	23.7053	0.862152
$757$	−25.2060	−0.916128	−0.458064	−	0.888919i	$-0.651457\pi$
$757$	−25.2060	−0.916128	−0.458064	+	0.888919i	$0.651457\pi$
$758$	5.04567	0.183267
$759$	7.13940	0.259144
$760$	16.8350	0.610671
$761$	−26.2909	−0.953043	−0.476521	−	0.879163i	$-0.658103\pi$
$761$	−26.2909	−0.953043	−0.476521	+	0.879163i	$0.658103\pi$
$762$	2.25449	0.0816714
$763$	10.6341	0.384979
$764$	5.87493	0.212547
$765$	9.04330	0.326961
$766$	−1.65417	−0.0597677
$767$	24.3962	0.880896
$768$	−8.25641	−0.297927
$769$	17.5206	0.631809	0.315905	−	0.948791i	$-0.397692\pi$
$769$	17.5206	0.631809	0.315905	+	0.948791i	$0.397692\pi$
$770$	−9.76115	−0.351767
$771$	8.07587	0.290845
$772$	−22.8464	−0.822261
$773$	−47.6695	−1.71455	−0.857277	−	0.514855i	$-0.827846\pi$
$773$	−47.6695	−1.71455	−0.857277	+	0.514855i	$0.827846\pi$
$774$	0.660156	0.0237288
$775$	41.9970	1.50858
$776$	−19.7354	−0.708460
$777$	−22.2740	−0.799077
$778$	4.99762	0.179173
$779$	37.2084	1.33313
$780$	−38.1469	−1.36588
$781$	−26.6727	−0.954426
$782$	0.793748	0.0283844
$783$	−45.7480	−1.63490
$784$	1.78447	0.0637312
$785$	33.1639	1.18367
$786$	−4.41449	−0.157460
$787$	41.4827	1.47870	0.739349	−	0.673322i	$-0.235133\pi$
$787$	41.4827	1.47870	0.739349	+	0.673322i	$0.235133\pi$
$788$	2.81127	0.100147
$789$	9.43813	0.336006
$790$	−7.11562	−0.253162
$791$	−45.0033	−1.60013
$792$	7.90006	0.280716
$793$	39.1471	1.39015
$794$	6.21999	0.220739
$795$	0.0878179	0.00311458
$796$	45.4533	1.61105
$797$	−29.7609	−1.05419	−0.527093	−	0.849808i	$-0.676718\pi$
$797$	−29.7609	−1.05419	−0.527093	+	0.849808i	$0.676718\pi$
$798$	−2.53138	−0.0896100
$799$	−7.25723	−0.256742
$800$	36.2135	1.28034
$801$	1.89751	0.0670451
$802$	−9.50941	−0.335789
$803$	10.1831	0.359352
$804$	18.9945	0.669885
$805$	29.7983	1.05025
$806$	−6.49167	−0.228659
$807$	−19.0012	−0.668873
$808$	6.46776	0.227535
$809$	−45.4805	−1.59901	−0.799504	−	0.600661i	$-0.794904\pi$
$809$	−45.4805	−1.59901	−0.799504	+	0.600661i	$0.794904\pi$
$810$	3.39540	0.119302
$811$	20.1527	0.707659	0.353829	−	0.935310i	$-0.384879\pi$
$811$	20.1527	0.707659	0.353829	+	0.935310i	$0.384879\pi$
$812$	−53.1489	−1.86516
$813$	−8.96008	−0.314244
$814$	−8.44323	−0.295935
$815$	67.6311	2.36901
$816$	3.00100	0.105056
$817$	3.69042	0.129111
$818$	−3.08515	−0.107870
$819$	−36.0396	−1.25933
$820$	77.1377	2.69377
$821$	12.2357	0.427029	0.213515	−	0.976940i	$-0.431509\pi$
$821$	12.2357	0.427029	0.213515	+	0.976940i	$0.431509\pi$
$822$	3.68809	0.128637
$823$	31.1224	1.08486	0.542430	−	0.840101i	$-0.317505\pi$
$823$	31.1224	1.08486	0.542430	+	0.840101i	$0.317505\pi$
$824$	−8.13100	−0.283257
$825$	−28.7571	−1.00119
$826$	3.35619	0.116777
$827$	45.4529	1.58055	0.790276	−	0.612750i	$-0.209937\pi$
$827$	45.4529	1.58055	0.790276	+	0.612750i	$0.209937\pi$
$828$	−11.7965	−0.409955
$829$	0.205090	0.00712306	0.00356153	−	0.999994i	$-0.498866\pi$
$829$	0.205090	0.00712306	0.00356153	+	0.999994i	$0.498866\pi$
$830$	−10.4747	−0.363583
$831$	−6.11757	−0.212216
$832$	35.0354	1.21464
$833$	−0.510306	−0.0176811
$834$	−2.37367	−0.0821934
$835$	−14.6218	−0.506008
$836$	21.6018	0.747113
$837$	17.3053	0.598160
$838$	−5.06618	−0.175008
$839$	−15.1516	−0.523093	−0.261546	−	0.965191i	$-0.584232\pi$
$839$	−15.1516	−0.523093	−0.261546	+	0.965191i	$0.584232\pi$
$840$	−10.7289	−0.370181
$841$	73.5704	2.53691
$842$	−1.30307	−0.0449066
$843$	−12.7291	−0.438414
$844$	32.0570	1.10345
$845$	82.9233	2.85265
$846$	−4.79091	−0.164715
$847$	4.53916	0.155967
$848$	−0.0895629	−0.00307560
$849$	5.69075	0.195306
$850$	−3.19717	−0.109662
$851$	25.7751	0.883558
$852$	−14.3400	−0.491282
$853$	11.5839	0.396624	0.198312	−	0.980139i	$-0.436454\pi$
$853$	11.5839	0.396624	0.198312	+	0.980139i	$0.436454\pi$
$854$	5.38546	0.184287
$855$	33.3736	1.14135
$856$	−22.0033	−0.752056
$857$	−13.1807	−0.450246	−0.225123	−	0.974330i	$-0.572278\pi$
$857$	−13.1807	−0.450246	−0.225123	+	0.974330i	$0.572278\pi$
$858$	4.44512	0.151754
$859$	6.31531	0.215476	0.107738	−	0.994179i	$-0.465639\pi$
$859$	6.31531	0.215476	0.107738	+	0.994179i	$0.465639\pi$
$860$	7.65071	0.260887
$861$	−23.7127	−0.808126
$862$	2.92366	0.0995801
$863$	−54.1093	−1.84190	−0.920950	−	0.389680i	$-0.872586\pi$
$863$	−54.1093	−1.84190	−0.920950	+	0.389680i	$0.872586\pi$
$864$	14.9222	0.507663
$865$	−35.6245	−1.21127
$866$	−2.64338	−0.0898257
$867$	−0.858197	−0.0291459
$868$	20.1049	0.682406
$869$	−18.6663	−0.633211
$870$	10.1277	0.343361
$871$	−67.1518	−2.27535
$872$	4.43059	0.150039
$873$	−39.1233	−1.32412
$874$	2.92926	0.0990838
$875$	−65.2807	−2.20689
$876$	5.47471	0.184973
$877$	−10.1191	−0.341699	−0.170849	−	0.985297i	$-0.554651\pi$
$877$	−10.1191	−0.341699	−0.170849	+	0.985297i	$0.554651\pi$
$878$	8.58924	0.289873
$879$	17.2548	0.581992
$880$	42.7056	1.43961
$881$	35.1813	1.18529	0.592643	−	0.805465i	$-0.298084\pi$
$881$	35.1813	1.18529	0.592643	+	0.805465i	$0.298084\pi$
$882$	−0.336882	−0.0113434
$883$	41.6661	1.40218	0.701088	−	0.713075i	$-0.252698\pi$
$883$	41.6661	1.40218	0.701088	+	0.713075i	$0.252698\pi$
$884$	−11.1257	−0.374197
$885$	14.3974	0.483964
$886$	2.63897	0.0886580
$887$	5.82622	0.195625	0.0978126	−	0.995205i	$-0.468815\pi$
$887$	5.82622	0.195625	0.0978126	+	0.995205i	$0.468815\pi$
$888$	−9.28029	−0.311426
$889$	24.6844	0.827890
$890$	−0.976824	−0.0327432
$891$	8.90711	0.298399
$892$	−37.8198	−1.26630
$893$	−26.7822	−0.896233
$894$	−4.89506	−0.163715
$895$	−6.87190	−0.229702
$896$	22.9262	0.765909
$897$	−13.5698	−0.453083
$898$	4.31091	0.143857
$899$	−38.7998	−1.29405
$900$	47.5154	1.58385
$901$	0.0256123	0.000853271 0
$902$	−8.98856	−0.299286
$903$	−2.35188	−0.0782658
$904$	−18.7502	−0.623623
$905$	−72.5400	−2.41131
$906$	−0.589444	−0.0195830
$907$	10.9136	0.362381	0.181191	−	0.983448i	$-0.442005\pi$
$907$	10.9136	0.362381	0.181191	+	0.983448i	$0.442005\pi$
$908$	34.9648	1.16035
$909$	12.8216	0.425266
$910$	18.5530	0.615025
$911$	−13.1513	−0.435723	−0.217861	−	0.975980i	$-0.569908\pi$
$911$	−13.1513	−0.435723	−0.217861	+	0.975980i	$0.569908\pi$
$912$	11.0749	0.366728
$913$	−27.4782	−0.909395
$914$	1.12885	0.0373392
$915$	23.1026	0.763750
$916$	16.9343	0.559526
$917$	−48.3344	−1.59614
$918$	−1.31743	−0.0434817
$919$	48.1109	1.58703	0.793517	−	0.608548i	$-0.208248\pi$
$919$	48.1109	1.58703	0.793517	+	0.608548i	$0.208248\pi$
$920$	12.4152	0.409318
$921$	6.91399	0.227824
$922$	4.50151	0.148249
$923$	50.6967	1.66870
$924$	−13.7667	−0.452891
$925$	−103.820	−3.41359
$926$	−4.97820	−0.163594
$927$	−16.1188	−0.529411
$928$	−33.4567	−1.09827
$929$	−25.2216	−0.827495	−0.413748	−	0.910392i	$-0.635780\pi$
$929$	−25.2216	−0.827495	−0.413748	+	0.910392i	$0.635780\pi$
$930$	−3.83106	−0.125625
$931$	−1.88325	−0.0617209
$932$	−0.440104	−0.0144161
$933$	22.3377	0.731304
$934$	−10.0675	−0.329419
$935$	−12.2125	−0.399392
$936$	−15.0156	−0.490800
$937$	21.8619	0.714197	0.357098	−	0.934067i	$-0.383766\pi$
$937$	21.8619	0.714197	0.357098	+	0.934067i	$0.383766\pi$
$938$	−9.23808	−0.301634
$939$	−12.9465	−0.422492
$940$	−55.5230	−1.81096
$941$	55.9850	1.82506	0.912530	−	0.409010i	$-0.134126\pi$
$941$	55.9850	1.82506	0.912530	+	0.409010i	$0.134126\pi$
$942$	−2.07765	−0.0676935
$943$	27.4398	0.893564
$944$	−14.6835	−0.477908
$945$	−49.4580	−1.60887
$946$	−0.891508	−0.0289854
$947$	9.19797	0.298894	0.149447	−	0.988770i	$-0.452251\pi$
$947$	9.19797	0.298894	0.149447	+	0.988770i	$0.452251\pi$
$948$	−10.0356	−0.325940
$949$	−19.3549	−0.628286
$950$	−11.7989	−0.382807
$951$	13.2408	0.429363
$952$	−3.12911	−0.101415
$953$	26.3104	0.852276	0.426138	−	0.904658i	$-0.359874\pi$
$953$	26.3104	0.852276	0.426138	+	0.904658i	$0.359874\pi$
$954$	0.0169081	0.000547421 0
$955$	−12.2573	−0.396637
$956$	21.1447	0.683867
$957$	26.5679	0.858817
$958$	−1.86817	−0.0603578
$959$	40.3810	1.30397
$960$	20.6762	0.667320
$961$	−16.3230	−0.526548
$962$	16.0480	0.517408
$963$	−43.6190	−1.40560
$964$	33.6413	1.08351
$965$	47.6662	1.53443
$966$	−1.86680	−0.0600634
$967$	−23.2676	−0.748237	−0.374118	−	0.927381i	$-0.622055\pi$
$967$	−23.2676	−0.748237	−0.374118	+	0.927381i	$0.622055\pi$
$968$	1.89120	0.0607855
$969$	−3.16711	−0.101742
$970$	20.1404	0.646669
$971$	−22.6891	−0.728128	−0.364064	−	0.931374i	$-0.618611\pi$
$971$	−22.6891	−0.728128	−0.364064	+	0.931374i	$0.618611\pi$
$972$	30.7387	0.985945
$973$	−25.9894	−0.833181
$974$	−8.30000	−0.265949
$975$	54.6584	1.75047
$976$	−23.5617	−0.754192
$977$	−33.2179	−1.06273	−0.531367	−	0.847142i	$-0.678321\pi$
$977$	−33.2179	−1.06273	−0.531367	+	0.847142i	$0.678321\pi$
$978$	−4.23694	−0.135483
$979$	−2.56249	−0.0818975
$980$	−3.90421	−0.124715
$981$	8.78315	0.280424
$982$	7.56530	0.241418
$983$	4.77329	0.152244	0.0761222	−	0.997098i	$-0.475746\pi$
$983$	4.77329	0.152244	0.0761222	+	0.997098i	$0.475746\pi$
$984$	−9.87969	−0.314953
$985$	−5.86536	−0.186886
$986$	2.95377	0.0940674
$987$	17.0682	0.543285
$988$	−41.0584	−1.30624
$989$	2.72155	0.0865403
$990$	−8.06217	−0.256233
$991$	−18.2124	−0.578537	−0.289268	−	0.957248i	$-0.593412\pi$
$991$	−18.2124	−0.578537	−0.289268	+	0.957248i	$0.593412\pi$
$992$	12.6558	0.401823
$993$	−0.590576	−0.0187414
$994$	6.97435	0.221213
$995$	−94.8325	−3.00639
$996$	−14.7731	−0.468103
$997$	19.0963	0.604785	0.302393	−	0.953183i	$-0.402215\pi$
$997$	19.0963	0.604785	0.302393	+	0.953183i	$0.402215\pi$
$998$	−10.6168	−0.336068
$999$	−42.7804	−1.35351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.c.1.4	✓	6
3.2	odd	2		6579.2.a.j.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.c.1.4	✓	6	1.1	even	1	trivial
6579.2.a.j.1.3		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)

\(f(q)\)	\(=\)	\(q+0.291653 q^{2} -0.858197 q^{3} -1.91494 q^{4} +3.99528 q^{5} -0.250296 q^{6} -2.74049 q^{7} -1.14180 q^{8} -2.26350 q^{9} +O(q^{10})\)	\(q+0.291653 q^{2} -0.858197 q^{3} -1.91494 q^{4} +3.99528 q^{5} -0.250296 q^{6} -2.74049 q^{7} -1.14180 q^{8} -2.26350 q^{9} +1.16523 q^{10} +3.05674 q^{11} +1.64339 q^{12} -5.80993 q^{13} -0.799273 q^{14} -3.42873 q^{15} +3.49687 q^{16} -1.00000 q^{17} -0.660156 q^{18} -3.69042 q^{19} -7.65071 q^{20} +2.35188 q^{21} +0.891508 q^{22} -2.72155 q^{23} +0.979892 q^{24} +10.9622 q^{25} -1.69448 q^{26} +4.51712 q^{27} +5.24788 q^{28} -10.1277 q^{29} -1.00000 q^{30} +3.83106 q^{31} +3.30348 q^{32} -2.62329 q^{33} -0.291653 q^{34} -10.9490 q^{35} +4.33446 q^{36} -9.47073 q^{37} -1.07632 q^{38} +4.98607 q^{39} -4.56182 q^{40} -10.0824 q^{41} +0.685933 q^{42} -1.00000 q^{43} -5.85347 q^{44} -9.04330 q^{45} -0.793748 q^{46} +7.25723 q^{47} -3.00100 q^{48} +0.510306 q^{49} +3.19717 q^{50} +0.858197 q^{51} +11.1257 q^{52} -0.0256123 q^{53} +1.31743 q^{54} +12.2125 q^{55} +3.12911 q^{56} +3.16711 q^{57} -2.95377 q^{58} -4.19905 q^{59} +6.56581 q^{60} -6.73795 q^{61} +1.11734 q^{62} +6.20310 q^{63} -6.03026 q^{64} -23.2123 q^{65} -0.765089 q^{66} +11.5581 q^{67} +1.91494 q^{68} +2.33563 q^{69} -3.19332 q^{70} -8.72587 q^{71} +2.58447 q^{72} +3.33134 q^{73} -2.76217 q^{74} -9.40775 q^{75} +7.06693 q^{76} -8.37698 q^{77} +1.45420 q^{78} -6.10660 q^{79} +13.9709 q^{80} +2.91392 q^{81} -2.94057 q^{82} -8.98937 q^{83} -4.50371 q^{84} -3.99528 q^{85} -0.291653 q^{86} +8.69156 q^{87} -3.49020 q^{88} -0.838307 q^{89} -2.63751 q^{90} +15.9221 q^{91} +5.21160 q^{92} -3.28780 q^{93} +2.11659 q^{94} -14.7442 q^{95} -2.83503 q^{96} +17.2844 q^{97} +0.148832 q^{98} -6.91893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{5} - 7 q^{6} - 7 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 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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