LMFDB - Embedded newform 731.2.a.e.1.14

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:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 2 x^{18} - 30 x^{17} + 62 x^{16} + 365 x^{15} - 786 x^{14} - 2295 x^{13} + 5233 x^{12} + \cdots + 64 $ x^19 - 2x^18 - 30x^17 + 62x^16 + 365x^15 - 786x^14 - 2295x^13 + 5233x^12 + 7816x^11 - 19517x^10 - 13527x^9 + 40173x^8 + 8942x^7 - 41911x^6 + 1140x^5 + 18520x^4 - 1520x^3 - 2640x^2 - 64x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$1.49769$ 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)

$f(q)$	$=$	$q+1.49769 q^{2} +1.88586 q^{3} +0.243066 q^{4} +2.23917 q^{5} +2.82443 q^{6} +1.15776 q^{7} -2.63134 q^{8} +0.556465 q^{9} +O(q^{10})$	\(q+1.49769 q^{2} +1.88586 q^{3} +0.243066 q^{4} +2.23917 q^{5} +2.82443 q^{6} +1.15776 q^{7} -2.63134 q^{8} +0.556465 q^{9} +3.35357 q^{10} +4.03634 q^{11} +0.458389 q^{12} -5.09762 q^{13} +1.73396 q^{14} +4.22275 q^{15} -4.42705 q^{16} +1.00000 q^{17} +0.833410 q^{18} +8.56419 q^{19} +0.544266 q^{20} +2.18337 q^{21} +6.04517 q^{22} -0.126715 q^{23} -4.96233 q^{24} +0.0138616 q^{25} -7.63464 q^{26} -4.60816 q^{27} +0.281412 q^{28} +0.113675 q^{29} +6.32436 q^{30} -3.73020 q^{31} -1.36766 q^{32} +7.61196 q^{33} +1.49769 q^{34} +2.59241 q^{35} +0.135258 q^{36} -4.36157 q^{37} +12.8265 q^{38} -9.61340 q^{39} -5.89200 q^{40} -10.4498 q^{41} +3.27000 q^{42} -1.00000 q^{43} +0.981098 q^{44} +1.24602 q^{45} -0.189780 q^{46} +4.48146 q^{47} -8.34880 q^{48} -5.65960 q^{49} +0.0207604 q^{50} +1.88586 q^{51} -1.23906 q^{52} +1.84898 q^{53} -6.90159 q^{54} +9.03803 q^{55} -3.04645 q^{56} +16.1509 q^{57} +0.170250 q^{58} +6.83720 q^{59} +1.02641 q^{60} +2.52377 q^{61} -5.58667 q^{62} +0.644251 q^{63} +6.80577 q^{64} -11.4144 q^{65} +11.4003 q^{66} -14.5616 q^{67} +0.243066 q^{68} -0.238967 q^{69} +3.88262 q^{70} +10.5763 q^{71} -1.46425 q^{72} -15.0069 q^{73} -6.53227 q^{74} +0.0261410 q^{75} +2.08167 q^{76} +4.67310 q^{77} -14.3979 q^{78} +14.3561 q^{79} -9.91290 q^{80} -10.3597 q^{81} -15.6506 q^{82} -2.15782 q^{83} +0.530703 q^{84} +2.23917 q^{85} -1.49769 q^{86} +0.214376 q^{87} -10.6210 q^{88} +11.9227 q^{89} +1.86614 q^{90} -5.90181 q^{91} -0.0308003 q^{92} -7.03462 q^{93} +6.71183 q^{94} +19.1766 q^{95} -2.57922 q^{96} +1.85911 q^{97} -8.47631 q^{98} +2.24608 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) $ 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9} - 2 q^{10} + 4 q^{11} + 9 q^{12} + 14 q^{13} + 5 q^{14} - 7 q^{15} + 32 q^{16} + 19 q^{17} + 12 q^{18} + 12 q^{19} + 23 q^{20} + 16 q^{21} + 36 q^{22} - q^{23} - 13 q^{24} + 30 q^{25} - 21 q^{26} + 8 q^{27} + 5 q^{28} + 41 q^{29} - 26 q^{30} - 8 q^{31} - 20 q^{32} - 14 q^{33} + 2 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} - 29 q^{38} + 17 q^{39} - 15 q^{40} + 6 q^{41} - q^{42} - 19 q^{43} + 16 q^{44} + 24 q^{45} + 38 q^{46} - 21 q^{47} - 2 q^{48} + 46 q^{49} - 36 q^{50} + 5 q^{51} + 39 q^{52} - 9 q^{53} + 53 q^{54} + 10 q^{55} - 12 q^{56} - 5 q^{57} - 45 q^{58} - 4 q^{59} - 7 q^{60} + 68 q^{61} - 25 q^{62} + 61 q^{63} - 14 q^{64} + 22 q^{65} - 17 q^{66} + 26 q^{68} - 9 q^{69} - 37 q^{70} + 23 q^{71} - 4 q^{72} - q^{73} - 30 q^{74} - 25 q^{75} + 47 q^{76} - 19 q^{77} + 12 q^{78} + 16 q^{79} + 28 q^{80} - 21 q^{81} - 13 q^{82} - 32 q^{83} - 47 q^{84} + 11 q^{85} - 2 q^{86} - 8 q^{87} + 108 q^{88} + 11 q^{89} + 5 q^{90} + 52 q^{91} - 23 q^{92} - 23 q^{93} + 47 q^{94} - 25 q^{95} - 103 q^{96} + 36 q^{97} - 100 q^{98} - 11 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9 - 2 * q^10 + 4 * q^11 + 9 * q^12 + 14 * q^13 + 5 * q^14 - 7 * q^15 + 32 * q^16 + 19 * q^17 + 12 * q^18 + 12 * q^19 + 23 * q^20 + 16 * q^21 + 36 * q^22 - q^23 - 13 * q^24 + 30 * q^25 - 21 * q^26 + 8 * q^27 + 5 * q^28 + 41 * q^29 - 26 * q^30 - 8 * q^31 - 20 * q^32 - 14 * q^33 + 2 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 - 29 * q^38 + 17 * q^39 - 15 * q^40 + 6 * q^41 - q^42 - 19 * q^43 + 16 * q^44 + 24 * q^45 + 38 * q^46 - 21 * q^47 - 2 * q^48 + 46 * q^49 - 36 * q^50 + 5 * q^51 + 39 * q^52 - 9 * q^53 + 53 * q^54 + 10 * q^55 - 12 * q^56 - 5 * q^57 - 45 * q^58 - 4 * q^59 - 7 * q^60 + 68 * q^61 - 25 * q^62 + 61 * q^63 - 14 * q^64 + 22 * q^65 - 17 * q^66 + 26 * q^68 - 9 * q^69 - 37 * q^70 + 23 * q^71 - 4 * q^72 - q^73 - 30 * q^74 - 25 * q^75 + 47 * q^76 - 19 * q^77 + 12 * q^78 + 16 * q^79 + 28 * q^80 - 21 * q^81 - 13 * q^82 - 32 * q^83 - 47 * q^84 + 11 * q^85 - 2 * q^86 - 8 * q^87 + 108 * q^88 + 11 * q^89 + 5 * q^90 + 52 * q^91 - 23 * q^92 - 23 * q^93 + 47 * q^94 - 25 * q^95 - 103 * q^96 + 36 * q^97 - 100 * q^98 - 11 * 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 $

$2$	1.49769	1.05902	0.529512	−	0.848302i	$-0.322375\pi$
$2$	1.49769	1.05902	0.529512	+	0.848302i	$0.322375\pi$
$3$	1.88586	1.08880	0.544401	−	0.838825i	$-0.316757\pi$
$3$	1.88586	1.08880	0.544401	+	0.838825i	$0.316757\pi$
$4$	0.243066	0.121533
$5$	2.23917	1.00139	0.500693	−	0.865625i	$-0.333079\pi$
$5$	2.23917	1.00139	0.500693	+	0.865625i	$0.333079\pi$
$6$	2.82443	1.15307
$7$	1.15776	0.437591	0.218796	−	0.975771i	$-0.429787\pi$
$7$	1.15776	0.437591	0.218796	+	0.975771i	$0.429787\pi$
$8$	−2.63134	−0.930318
$9$	0.556465	0.185488
$10$	3.35357	1.06049
$11$	4.03634	1.21700	0.608501	−	0.793553i	$-0.291771\pi$
$11$	4.03634	1.21700	0.608501	+	0.793553i	$0.291771\pi$
$12$	0.458389	0.132326
$13$	−5.09762	−1.41383	−0.706913	−	0.707301i	$-0.749913\pi$
$13$	−5.09762	−1.41383	−0.706913	+	0.707301i	$0.749913\pi$
$14$	1.73396	0.463420
$15$	4.22275	1.09031
$16$	−4.42705	−1.10676
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.833410	0.196437
$19$	8.56419	1.96476	0.982380	−	0.186895i	$-0.0598425\pi$
$19$	8.56419	1.96476	0.982380	+	0.186895i	$0.0598425\pi$
$20$	0.544266	0.121702
$21$	2.18337	0.476450
$22$	6.04517	1.28883
$23$	−0.126715	−0.0264220	−0.0132110	−	0.999913i	$-0.504205\pi$
$23$	−0.126715	−0.0264220	−0.0132110	+	0.999913i	$0.504205\pi$
$24$	−4.96233	−1.01293
$25$	0.0138616	0.00277232
$26$	−7.63464	−1.49728
$27$	−4.60816	−0.886841
$28$	0.281412	0.0531819
$29$	0.113675	0.0211090	0.0105545	−	0.999944i	$-0.496640\pi$
$29$	0.113675	0.0211090	0.0105545	+	0.999944i	$0.496640\pi$
$30$	6.32436	1.15466
$31$	−3.73020	−0.669963	−0.334981	−	0.942225i	$-0.608730\pi$
$31$	−3.73020	−0.669963	−0.334981	+	0.942225i	$0.608730\pi$
$32$	−1.36766	−0.241771
$33$	7.61196	1.32507
$34$	1.49769	0.256851
$35$	2.59241	0.438197
$36$	0.135258	0.0225430
$37$	−4.36157	−0.717038	−0.358519	−	0.933522i	$-0.616718\pi$
$37$	−4.36157	−0.717038	−0.358519	+	0.933522i	$0.616718\pi$
$38$	12.8265	2.08073
$39$	−9.61340	−1.53938
$40$	−5.89200	−0.931607
$41$	−10.4498	−1.63199	−0.815995	−	0.578060i	$-0.803810\pi$
$41$	−10.4498	−1.63199	−0.815995	+	0.578060i	$0.803810\pi$
$42$	3.27000	0.504572
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0.981098	0.147906
$45$	1.24602	0.185745
$46$	−0.189780	−0.0279815
$47$	4.48146	0.653689	0.326844	−	0.945078i	$-0.394015\pi$
$47$	4.48146	0.653689	0.326844	+	0.945078i	$0.394015\pi$
$48$	−8.34880	−1.20504
$49$	−5.65960	−0.808514
$50$	0.0207604	0.00293596
$51$	1.88586	0.264073
$52$	−1.23906	−0.171827
$53$	1.84898	0.253977	0.126989	−	0.991904i	$-0.459469\pi$
$53$	1.84898	0.253977	0.126989	+	0.991904i	$0.459469\pi$
$54$	−6.90159	−0.939187
$55$	9.03803	1.21869
$56$	−3.04645	−0.407099
$57$	16.1509	2.13923
$58$	0.170250	0.0223549
$59$	6.83720	0.890127	0.445064	−	0.895499i	$-0.353181\pi$
$59$	6.83720	0.890127	0.445064	+	0.895499i	$0.353181\pi$
$60$	1.02641	0.132509
$61$	2.52377	0.323136	0.161568	−	0.986862i	$-0.448345\pi$
$61$	2.52377	0.323136	0.161568	+	0.986862i	$0.448345\pi$
$62$	−5.58667	−0.709507
$63$	0.644251	0.0811681
$64$	6.80577	0.850721
$65$	−11.4144	−1.41578
$66$	11.4003	1.40328
$67$	−14.5616	−1.77899	−0.889493	−	0.456948i	$-0.848943\pi$
$67$	−14.5616	−1.77899	−0.889493	+	0.456948i	$0.848943\pi$
$68$	0.243066	0.0294761
$69$	−0.238967	−0.0287683
$70$	3.88262	0.464062
$71$	10.5763	1.25518	0.627590	−	0.778544i	$-0.284041\pi$
$71$	10.5763	1.25518	0.627590	+	0.778544i	$0.284041\pi$
$72$	−1.46425	−0.172563
$73$	−15.0069	−1.75643	−0.878215	−	0.478267i	$-0.841265\pi$
$73$	−15.0069	−1.75643	−0.878215	+	0.478267i	$0.841265\pi$
$74$	−6.53227	−0.759361
$75$	0.0261410	0.00301851
$76$	2.08167	0.238784
$77$	4.67310	0.532549
$78$	−14.3979	−1.63024
$79$	14.3561	1.61519	0.807596	−	0.589736i	$-0.200768\pi$
$79$	14.3561	1.61519	0.807596	+	0.589736i	$0.200768\pi$
$80$	−9.91290	−1.10830
$81$	−10.3597	−1.15108
$82$	−15.6506	−1.72832
$83$	−2.15782	−0.236852	−0.118426	−	0.992963i	$-0.537785\pi$
$83$	−2.15782	−0.236852	−0.118426	+	0.992963i	$0.537785\pi$
$84$	0.530703	0.0579045
$85$	2.23917	0.242872
$86$	−1.49769	−0.161500
$87$	0.214376	0.0229835
$88$	−10.6210	−1.13220
$89$	11.9227	1.26380	0.631902	−	0.775049i	$-0.282275\pi$
$89$	11.9227	1.26380	0.631902	+	0.775049i	$0.282275\pi$
$90$	1.86614	0.196709
$91$	−5.90181	−0.618678
$92$	−0.0308003	−0.00321115
$93$	−7.03462	−0.729456
$94$	6.71183	0.692272
$95$	19.1766	1.96748
$96$	−2.57922	−0.263241
$97$	1.85911	0.188764	0.0943822	−	0.995536i	$-0.469912\pi$
$97$	1.85911	0.188764	0.0943822	+	0.995536i	$0.469912\pi$
$98$	−8.47631	−0.856236
$99$	2.24608	0.225740
$100$	0.00336929	0.000336929 0
$101$	−5.33969	−0.531319	−0.265660	−	0.964067i	$-0.585590\pi$
$101$	−5.33969	−0.531319	−0.265660	+	0.964067i	$0.585590\pi$
$102$	2.82443	0.279660
$103$	9.90878	0.976341	0.488171	−	0.872748i	$-0.337664\pi$
$103$	9.90878	0.976341	0.488171	+	0.872748i	$0.337664\pi$
$104$	13.4136	1.31531
$105$	4.88892	0.477110
$106$	2.76920	0.268968
$107$	−18.0014	−1.74026	−0.870132	−	0.492818i	$-0.835967\pi$
$107$	−18.0014	−1.74026	−0.870132	+	0.492818i	$0.835967\pi$
$108$	−1.12009	−0.107781
$109$	11.3633	1.08841	0.544204	−	0.838953i	$-0.316832\pi$
$109$	11.3633	1.08841	0.544204	+	0.838953i	$0.316832\pi$
$110$	13.5361	1.29062
$111$	−8.22531	−0.780712
$112$	−5.12545	−0.484310
$113$	−10.2086	−0.960349	−0.480174	−	0.877173i	$-0.659427\pi$
$113$	−10.2086	−0.960349	−0.480174	+	0.877173i	$0.659427\pi$
$114$	24.1889	2.26550
$115$	−0.283737	−0.0264586
$116$	0.0276307	0.00256544
$117$	−2.83665	−0.262248
$118$	10.2400	0.942667
$119$	1.15776	0.106131
$120$	−11.1115	−1.01433
$121$	5.29202	0.481093
$122$	3.77982	0.342209
$123$	−19.7069	−1.77691
$124$	−0.906685	−0.0814227
$125$	−11.1648	−0.998609
$126$	0.964887	0.0859590
$127$	−15.3838	−1.36509	−0.682545	−	0.730844i	$-0.739127\pi$
$127$	−15.3838	−1.36509	−0.682545	+	0.730844i	$0.739127\pi$
$128$	12.9282	1.14271
$129$	−1.88586	−0.166041
$130$	−17.0952	−1.49935
$131$	−2.44712	−0.213806	−0.106903	−	0.994269i	$-0.534093\pi$
$131$	−2.44712	−0.213806	−0.106903	+	0.994269i	$0.534093\pi$
$132$	1.85021	0.161040
$133$	9.91525	0.859762
$134$	−21.8088	−1.88399
$135$	−10.3184	−0.888070
$136$	−2.63134	−0.225635
$137$	1.24950	0.106752	0.0533758	−	0.998574i	$-0.483002\pi$
$137$	1.24950	0.106752	0.0533758	+	0.998574i	$0.483002\pi$
$138$	−0.357898	−0.0304663
$139$	−4.46436	−0.378662	−0.189331	−	0.981913i	$-0.560632\pi$
$139$	−4.46436	−0.378662	−0.189331	+	0.981913i	$0.560632\pi$
$140$	0.630128	0.0532555
$141$	8.45141	0.711737
$142$	15.8400	1.32927
$143$	−20.5757	−1.72063
$144$	−2.46350	−0.205292
$145$	0.254538	0.0211382
$146$	−22.4757	−1.86010
$147$	−10.6732	−0.880311
$148$	−1.06015	−0.0871439
$149$	15.9323	1.30523	0.652613	−	0.757692i	$-0.273673\pi$
$149$	15.9323	1.30523	0.652613	+	0.757692i	$0.273673\pi$
$150$	0.0391511	0.00319667
$151$	0.483100	0.0393141	0.0196571	−	0.999807i	$-0.493743\pi$
$151$	0.483100	0.0393141	0.0196571	+	0.999807i	$0.493743\pi$
$152$	−22.5353	−1.82785
$153$	0.556465	0.0449875
$154$	6.99884	0.563983
$155$	−8.35252	−0.670891
$156$	−2.33669	−0.187085
$157$	−17.1968	−1.37246	−0.686229	−	0.727386i	$-0.740735\pi$
$157$	−17.1968	−1.37246	−0.686229	+	0.727386i	$0.740735\pi$
$158$	21.5010	1.71053
$159$	3.48692	0.276531
$160$	−3.06243	−0.242106
$161$	−0.146706	−0.0115620
$162$	−15.5157	−1.21902
$163$	15.2155	1.19177	0.595885	−	0.803070i	$-0.296801\pi$
$163$	15.2155	1.19177	0.595885	+	0.803070i	$0.296801\pi$
$164$	−2.54000	−0.198341
$165$	17.0444	1.32691
$166$	−3.23174	−0.250832
$167$	16.2303	1.25593	0.627967	−	0.778240i	$-0.283887\pi$
$167$	16.2303	1.25593	0.627967	+	0.778240i	$0.283887\pi$
$168$	−5.74517	−0.443250
$169$	12.9857	0.998904
$170$	3.35357	0.257207
$171$	4.76567	0.364440
$172$	−0.243066	−0.0185336
$173$	24.5481	1.86636	0.933179	−	0.359413i	$-0.117023\pi$
$173$	24.5481	1.86636	0.933179	+	0.359413i	$0.117023\pi$
$174$	0.321068	0.0243401
$175$	0.0160484	0.00121314
$176$	−17.8691	−1.34693
$177$	12.8940	0.969172
$178$	17.8565	1.33840
$179$	0.0621516	0.00464543	0.00232272	−	0.999997i	$-0.499261\pi$
$179$	0.0621516	0.00464543	0.00232272	+	0.999997i	$0.499261\pi$
$180$	0.302865	0.0225742
$181$	17.6068	1.30870	0.654351	−	0.756191i	$-0.272942\pi$
$181$	17.6068	1.30870	0.654351	+	0.756191i	$0.272942\pi$
$182$	−8.83906	−0.655195
$183$	4.75948	0.351831
$184$	0.333431	0.0245808
$185$	−9.76628	−0.718031
$186$	−10.5357	−0.772512
$187$	4.03634	0.295166
$188$	1.08929	0.0794449
$189$	−5.33514	−0.388074
$190$	28.7206	2.08361
$191$	2.92087	0.211346	0.105673	−	0.994401i	$-0.466300\pi$
$191$	2.92087	0.211346	0.105673	+	0.994401i	$0.466300\pi$
$192$	12.8347	0.926266
$193$	−14.1805	−1.02073	−0.510367	−	0.859957i	$-0.670490\pi$
$193$	−14.1805	−1.02073	−0.510367	+	0.859957i	$0.670490\pi$
$194$	2.78437	0.199906
$195$	−21.5260	−1.54151
$196$	−1.37566	−0.0982613
$197$	−0.377891	−0.0269237	−0.0134618	−	0.999909i	$-0.504285\pi$
$197$	−0.377891	−0.0269237	−0.0134618	+	0.999909i	$0.504285\pi$
$198$	3.36393	0.239064
$199$	−1.41451	−0.100272	−0.0501359	−	0.998742i	$-0.515965\pi$
$199$	−1.41451	−0.100272	−0.0501359	+	0.998742i	$0.515965\pi$
$200$	−0.0364746	−0.00257914
$201$	−27.4612	−1.93696
$202$	−7.99719	−0.562680
$203$	0.131609	0.00923711
$204$	0.458389	0.0320937
$205$	−23.3989	−1.63425
$206$	14.8403	1.03397
$207$	−0.0705127	−0.00490097
$208$	22.5674	1.56477
$209$	34.5680	2.39112
$210$	7.32207	0.505271
$211$	−8.02903	−0.552741	−0.276371	−	0.961051i	$-0.589132\pi$
$211$	−8.02903	−0.552741	−0.276371	+	0.961051i	$0.589132\pi$
$212$	0.449426	0.0308667
$213$	19.9455	1.36664
$214$	−26.9605	−1.84298
$215$	−2.23917	−0.152710
$216$	12.1256	0.825044
$217$	−4.31866	−0.293170
$218$	17.0187	1.15265
$219$	−28.3010	−1.91240
$220$	2.19684	0.148111
$221$	−5.09762	−0.342903
$222$	−12.3189	−0.826793
$223$	15.7196	1.05267	0.526333	−	0.850279i	$-0.323567\pi$
$223$	15.7196	1.05267	0.526333	+	0.850279i	$0.323567\pi$
$224$	−1.58342	−0.105797
$225$	0.00771350	0.000514233 0
$226$	−15.2894	−1.01703
$227$	5.80707	0.385429	0.192714	−	0.981255i	$-0.438271\pi$
$227$	5.80707	0.385429	0.192714	+	0.981255i	$0.438271\pi$
$228$	3.92573	0.259988
$229$	−3.86004	−0.255079	−0.127539	−	0.991834i	$-0.540708\pi$
$229$	−3.86004	−0.255079	−0.127539	+	0.991834i	$0.540708\pi$
$230$	−0.424949	−0.0280203
$231$	8.81281	0.579840
$232$	−0.299118	−0.0196381
$233$	26.1887	1.71568	0.857838	−	0.513920i	$-0.171807\pi$
$233$	26.1887	1.71568	0.857838	+	0.513920i	$0.171807\pi$
$234$	−4.24841	−0.277727
$235$	10.0347	0.654594
$236$	1.66189	0.108180
$237$	27.0737	1.75862
$238$	1.73396	0.112396
$239$	−10.7266	−0.693844	−0.346922	−	0.937894i	$-0.612773\pi$
$239$	−10.7266	−0.693844	−0.346922	+	0.937894i	$0.612773\pi$
$240$	−18.6943	−1.20671
$241$	3.53722	0.227852	0.113926	−	0.993489i	$-0.463657\pi$
$241$	3.53722	0.227852	0.113926	+	0.993489i	$0.463657\pi$
$242$	7.92579	0.509489
$243$	−5.71252	−0.366459
$244$	0.613445	0.0392718
$245$	−12.6728	−0.809634
$246$	−29.5148	−1.88179
$247$	−43.6570	−2.77783
$248$	9.81540	0.623278
$249$	−4.06935	−0.257884
$250$	−16.7214	−1.05755
$251$	11.0524	0.697619	0.348810	−	0.937194i	$-0.386586\pi$
$251$	11.0524	0.697619	0.348810	+	0.937194i	$0.386586\pi$
$252$	0.156596	0.00986462
$253$	−0.511466	−0.0321556
$254$	−23.0401	−1.44566
$255$	4.22275	0.264439
$256$	5.75092	0.359433
$257$	30.2656	1.88792	0.943958	−	0.330065i	$-0.107071\pi$
$257$	30.2656	1.88792	0.943958	+	0.330065i	$0.107071\pi$
$258$	−2.82443	−0.175841
$259$	−5.04964	−0.313769
$260$	−2.77446	−0.172065
$261$	0.0632564	0.00391547
$262$	−3.66502	−0.226426
$263$	−23.3799	−1.44167	−0.720834	−	0.693107i	$-0.756241\pi$
$263$	−23.3799	−1.44167	−0.720834	+	0.693107i	$0.756241\pi$
$264$	−20.0296	−1.23274
$265$	4.14018	0.254329
$266$	14.8499	0.910509
$267$	22.4845	1.37603
$268$	−3.53945	−0.216206
$269$	−13.3754	−0.815514	−0.407757	−	0.913090i	$-0.633689\pi$
$269$	−13.3754	−0.815514	−0.407757	+	0.913090i	$0.633689\pi$
$270$	−15.4538	−0.940488
$271$	22.3443	1.35732	0.678661	−	0.734451i	$-0.262560\pi$
$271$	22.3443	1.35732	0.678661	+	0.734451i	$0.262560\pi$
$272$	−4.42705	−0.268429
$273$	−11.1300	−0.673617
$274$	1.87135	0.113053
$275$	0.0559501	0.00337392
$276$	−0.0580849	−0.00349630
$277$	−7.05997	−0.424192	−0.212096	−	0.977249i	$-0.568029\pi$
$277$	−7.05997	−0.424192	−0.212096	+	0.977249i	$0.568029\pi$
$278$	−6.68621	−0.401012
$279$	−2.07572	−0.124270
$280$	−6.82150	−0.407663
$281$	−4.74187	−0.282876	−0.141438	−	0.989947i	$-0.545173\pi$
$281$	−4.74187	−0.282876	−0.141438	+	0.989947i	$0.545173\pi$
$282$	12.6576	0.753747
$283$	−0.893108	−0.0530897	−0.0265449	−	0.999648i	$-0.508450\pi$
$283$	−0.893108	−0.0530897	−0.0265449	+	0.999648i	$0.508450\pi$
$284$	2.57075	0.152546
$285$	36.1644	2.14220
$286$	−30.8160	−1.82219
$287$	−12.0984	−0.714144
$288$	−0.761057	−0.0448457
$289$	1.00000	0.0588235
$290$	0.381218	0.0223859
$291$	3.50603	0.205527
$292$	−3.64768	−0.213465
$293$	−1.18224	−0.0690673	−0.0345336	−	0.999404i	$-0.510995\pi$
$293$	−1.18224	−0.0690673	−0.0345336	+	0.999404i	$0.510995\pi$
$294$	−15.9851	−0.932271
$295$	15.3096	0.891360
$296$	11.4768	0.667073
$297$	−18.6001	−1.07929
$298$	23.8616	1.38227
$299$	0.645947	0.0373561
$300$	0.00635401	0.000366849 0
$301$	−1.15776	−0.0667320
$302$	0.723533	0.0416346
$303$	−10.0699	−0.578501
$304$	−37.9141	−2.17452
$305$	5.65115	0.323584
$306$	0.833410	0.0476429
$307$	15.3776	0.877648	0.438824	−	0.898573i	$-0.355395\pi$
$307$	15.3776	0.877648	0.438824	+	0.898573i	$0.355395\pi$
$308$	1.13587	0.0647224
$309$	18.6866	1.06304
$310$	−12.5095	−0.710490
$311$	−22.2267	−1.26036	−0.630179	−	0.776450i	$-0.717018\pi$
$311$	−22.2267	−1.26036	−0.630179	+	0.776450i	$0.717018\pi$
$312$	25.2961	1.43211
$313$	−21.6072	−1.22131	−0.610655	−	0.791897i	$-0.709094\pi$
$313$	−21.6072	−1.22131	−0.610655	+	0.791897i	$0.709094\pi$
$314$	−25.7555	−1.45347
$315$	1.44259	0.0812805
$316$	3.48950	0.196300
$317$	−19.8589	−1.11539	−0.557694	−	0.830046i	$-0.688314\pi$
$317$	−19.8589	−1.11539	−0.557694	+	0.830046i	$0.688314\pi$
$318$	5.22232	0.292853
$319$	0.458832	0.0256897
$320$	15.2392	0.851900
$321$	−33.9482	−1.89480
$322$	−0.219719	−0.0122445
$323$	8.56419	0.476524
$324$	−2.51811	−0.139895
$325$	−0.0706612	−0.00391958
$326$	22.7881	1.26211
$327$	21.4296	1.18506
$328$	27.4970	1.51827
$329$	5.18845	0.286048
$330$	25.5272	1.40523
$331$	33.8142	1.85860	0.929299	−	0.369328i	$-0.120412\pi$
$331$	33.8142	1.85860	0.929299	+	0.369328i	$0.120412\pi$
$332$	−0.524494	−0.0287853
$333$	−2.42706	−0.133002
$334$	24.3078	1.33007
$335$	−32.6059	−1.78145
$336$	−9.66588	−0.527317
$337$	−8.46942	−0.461359	−0.230679	−	0.973030i	$-0.574095\pi$
$337$	−8.46942	−0.461359	−0.230679	+	0.973030i	$0.574095\pi$
$338$	19.4486	1.05786
$339$	−19.2521	−1.04563
$340$	0.544266	0.0295170
$341$	−15.0563	−0.815346
$342$	7.13748	0.385951
$343$	−14.6567	−0.791390
$344$	2.63134	0.141872
$345$	−0.535087	−0.0288081
$346$	36.7654	1.97652
$347$	−22.2020	−1.19186	−0.595932	−	0.803035i	$-0.703217\pi$
$347$	−22.2020	−1.19186	−0.595932	+	0.803035i	$0.703217\pi$
$348$	0.0521076	0.00279326
$349$	15.3410	0.821183	0.410592	−	0.911819i	$-0.365322\pi$
$349$	15.3410	0.821183	0.410592	+	0.911819i	$0.365322\pi$
$350$	0.0240355	0.00128475
$351$	23.4907	1.25384
$352$	−5.52036	−0.294236
$353$	18.6450	0.992373	0.496186	−	0.868216i	$-0.334733\pi$
$353$	18.6450	0.992373	0.496186	+	0.868216i	$0.334733\pi$
$354$	19.3112	1.02638
$355$	23.6822	1.25692
$356$	2.89801	0.153594
$357$	2.18337	0.115556
$358$	0.0930837	0.00491963
$359$	20.2294	1.06767	0.533833	−	0.845590i	$-0.320751\pi$
$359$	20.2294	1.06767	0.533833	+	0.845590i	$0.320751\pi$
$360$	−3.27869	−0.172802
$361$	54.3453	2.86028
$362$	26.3695	1.38595
$363$	9.98000	0.523814
$364$	−1.43453	−0.0751899
$365$	−33.6030	−1.75886
$366$	7.12821	0.372598
$367$	25.4540	1.32869	0.664344	−	0.747427i	$-0.268711\pi$
$367$	25.4540	1.32869	0.664344	+	0.747427i	$0.268711\pi$
$368$	0.560975	0.0292429
$369$	−5.81496	−0.302715
$370$	−14.6268	−0.760412
$371$	2.14067	0.111138
$372$	−1.70988	−0.0886532
$373$	31.9826	1.65600	0.827999	−	0.560729i	$-0.189479\pi$
$373$	31.9826	1.65600	0.827999	+	0.560729i	$0.189479\pi$
$374$	6.04517	0.312588
$375$	−21.0552	−1.08729
$376$	−11.7922	−0.608138
$377$	−0.579474	−0.0298444
$378$	−7.99036	−0.410980
$379$	12.1703	0.625147	0.312574	−	0.949894i	$-0.398809\pi$
$379$	12.1703	0.625147	0.312574	+	0.949894i	$0.398809\pi$
$380$	4.66120	0.239114
$381$	−29.0116	−1.48631
$382$	4.37454	0.223821
$383$	2.92897	0.149663	0.0748317	−	0.997196i	$-0.476158\pi$
$383$	2.92897	0.149663	0.0748317	+	0.997196i	$0.476158\pi$
$384$	24.3808	1.24418
$385$	10.4638	0.533287
$386$	−21.2379	−1.08098
$387$	−0.556465	−0.0282867
$388$	0.451888	0.0229411
$389$	−7.73302	−0.392080	−0.196040	−	0.980596i	$-0.562808\pi$
$389$	−7.73302	−0.392080	−0.196040	+	0.980596i	$0.562808\pi$
$390$	−32.2392	−1.63249
$391$	−0.126715	−0.00640827
$392$	14.8923	0.752175
$393$	−4.61493	−0.232792
$394$	−0.565963	−0.0285128
$395$	32.1458	1.61743
$396$	0.545947	0.0274349
$397$	12.2982	0.617231	0.308615	−	0.951187i	$-0.400134\pi$
$397$	12.2982	0.617231	0.308615	+	0.951187i	$0.400134\pi$
$398$	−2.11849	−0.106190
$399$	18.6988	0.936109
$400$	−0.0613661	−0.00306830
$401$	−1.78276	−0.0890266	−0.0445133	−	0.999009i	$-0.514174\pi$
$401$	−1.78276	−0.0890266	−0.0445133	+	0.999009i	$0.514174\pi$
$402$	−41.1283	−2.05129
$403$	19.0151	0.947211
$404$	−1.29790	−0.0645730
$405$	−23.1972	−1.15268
$406$	0.197108	0.00978233
$407$	−17.6048	−0.872636
$408$	−4.96233	−0.245672
$409$	−7.76235	−0.383823	−0.191912	−	0.981412i	$-0.561469\pi$
$409$	−7.76235	−0.383823	−0.191912	+	0.981412i	$0.561469\pi$
$410$	−35.0442	−1.73071
$411$	2.35637	0.116231
$412$	2.40849	0.118658
$413$	7.91582	0.389512
$414$	−0.105606	−0.00519025
$415$	−4.83172	−0.237180
$416$	6.97184	0.341822
$417$	−8.41915	−0.412288
$418$	51.7720	2.53225
$419$	−10.4270	−0.509393	−0.254697	−	0.967021i	$-0.581976\pi$
$419$	−10.4270	−0.509393	−0.254697	+	0.967021i	$0.581976\pi$
$420$	1.18833	0.0579847
$421$	−17.7188	−0.863564	−0.431782	−	0.901978i	$-0.642115\pi$
$421$	−17.7188	−0.863564	−0.431782	+	0.901978i	$0.642115\pi$
$422$	−12.0250	−0.585366
$423$	2.49378	0.121252
$424$	−4.86530	−0.236280
$425$	0.0138616	0.000672387 0
$426$	29.8721	1.44731
$427$	2.92192	0.141402
$428$	−4.37554	−0.211500
$429$	−38.8029	−1.87342
$430$	−3.35357	−0.161723
$431$	23.0088	1.10830	0.554148	−	0.832418i	$-0.313044\pi$
$431$	23.0088	1.10830	0.554148	+	0.832418i	$0.313044\pi$
$432$	20.4006	0.981523
$433$	21.9303	1.05390	0.526952	−	0.849895i	$-0.323335\pi$
$433$	21.9303	1.05390	0.526952	+	0.849895i	$0.323335\pi$
$434$	−6.46800	−0.310474
$435$	0.480023	0.0230153
$436$	2.76204	0.132278
$437$	−1.08521	−0.0519128
$438$	−42.3860	−2.02528
$439$	18.1367	0.865616	0.432808	−	0.901486i	$-0.357523\pi$
$439$	18.1367	0.865616	0.432808	+	0.901486i	$0.357523\pi$
$440$	−23.7821	−1.13377
$441$	−3.14937	−0.149970
$442$	−7.63464	−0.363143
$443$	−31.5975	−1.50124	−0.750622	−	0.660732i	$-0.770246\pi$
$443$	−31.5975	−1.50124	−0.750622	+	0.660732i	$0.770246\pi$
$444$	−1.99930	−0.0948824
$445$	26.6969	1.26555
$446$	23.5431	1.11480
$447$	30.0461	1.42113
$448$	7.87943	0.372268
$449$	13.7784	0.650242	0.325121	−	0.945672i	$-0.394595\pi$
$449$	13.7784	0.650242	0.325121	+	0.945672i	$0.394595\pi$
$450$	0.0115524	0.000544586 0
$451$	−42.1790	−1.98613
$452$	−2.48138	−0.116714
$453$	0.911059	0.0428053
$454$	8.69717	0.408179
$455$	−13.2151	−0.619535
$456$	−42.4983	−1.99017
$457$	19.7141	0.922187	0.461093	−	0.887352i	$-0.347457\pi$
$457$	19.7141	0.922187	0.461093	+	0.887352i	$0.347457\pi$
$458$	−5.78113	−0.270135
$459$	−4.60816	−0.215091
$460$	−0.0689669	−0.00321560
$461$	−29.3919	−1.36892	−0.684458	−	0.729052i	$-0.739961\pi$
$461$	−29.3919	−1.36892	−0.684458	+	0.729052i	$0.739961\pi$
$462$	13.1988	0.614065
$463$	34.5035	1.60351	0.801757	−	0.597650i	$-0.203899\pi$
$463$	34.5035	1.60351	0.801757	+	0.597650i	$0.203899\pi$
$464$	−0.503247	−0.0233627
$465$	−15.7517	−0.730467
$466$	39.2224	1.81694
$467$	−21.7581	−1.00684	−0.503422	−	0.864041i	$-0.667926\pi$
$467$	−21.7581	−1.00684	−0.503422	+	0.864041i	$0.667926\pi$
$468$	−0.689494	−0.0318719
$469$	−16.8588	−0.778469
$470$	15.0289	0.693231
$471$	−32.4308	−1.49433
$472$	−17.9910	−0.828102
$473$	−4.03634	−0.185591
$474$	40.5479	1.86243
$475$	0.118713	0.00544695
$476$	0.281412	0.0128985
$477$	1.02889	0.0471098
$478$	−16.0650	−0.734798
$479$	36.8878	1.68545	0.842724	−	0.538347i	$-0.180951\pi$
$479$	36.8878	1.68545	0.842724	+	0.538347i	$0.180951\pi$
$480$	−5.77531	−0.263605
$481$	22.2336	1.01377
$482$	5.29765	0.241301
$483$	−0.276666	−0.0125887
$484$	1.28631	0.0584687
$485$	4.16286	0.189026
$486$	−8.55557	−0.388089
$487$	14.3674	0.651049	0.325525	−	0.945534i	$-0.394459\pi$
$487$	14.3674	0.651049	0.325525	+	0.945534i	$0.394459\pi$
$488$	−6.64090	−0.300619
$489$	28.6943	1.29760
$490$	−18.9799	−0.857422
$491$	−14.7599	−0.666107	−0.333053	−	0.942908i	$-0.608079\pi$
$491$	−14.7599	−0.666107	−0.333053	+	0.942908i	$0.608079\pi$
$492$	−4.79009	−0.215954
$493$	0.113675	0.00511968
$494$	−65.3845	−2.94179
$495$	5.02935	0.226052
$496$	16.5138	0.741490
$497$	12.2448	0.549256
$498$	−6.09461	−0.273106
$499$	−3.91513	−0.175265	−0.0876327	−	0.996153i	$-0.527930\pi$
$499$	−3.91513	−0.175265	−0.0876327	+	0.996153i	$0.527930\pi$
$500$	−2.71379	−0.121364
$501$	30.6080	1.36746
$502$	16.5530	0.738796
$503$	−26.6889	−1.19000	−0.594999	−	0.803726i	$-0.702848\pi$
$503$	−26.6889	−1.19000	−0.594999	+	0.803726i	$0.702848\pi$
$504$	−1.69524	−0.0755121
$505$	−11.9565	−0.532055
$506$	−0.766016	−0.0340536
$507$	24.4893	1.08761
$508$	−3.73928	−0.165904
$509$	−19.1127	−0.847156	−0.423578	−	0.905860i	$-0.639226\pi$
$509$	−19.1127	−0.847156	−0.423578	+	0.905860i	$0.639226\pi$
$510$	6.32436	0.280047
$511$	−17.3744	−0.768598
$512$	−17.2434	−0.762058
$513$	−39.4652	−1.74243
$514$	45.3284	1.99935
$515$	22.1874	0.977693
$516$	−0.458389	−0.0201795
$517$	18.0887	0.795540
$518$	−7.56278	−0.332289
$519$	46.2943	2.03209
$520$	30.0352	1.31713
$521$	−15.9884	−0.700465	−0.350233	−	0.936663i	$-0.613897\pi$
$521$	−15.9884	−0.700465	−0.350233	+	0.936663i	$0.613897\pi$
$522$	0.0947383	0.00414658
$523$	19.0333	0.832270	0.416135	−	0.909303i	$-0.363384\pi$
$523$	19.0333	0.832270	0.416135	+	0.909303i	$0.363384\pi$
$524$	−0.594813	−0.0259845
$525$	0.0302650	0.00132087
$526$	−35.0158	−1.52676
$527$	−3.73020	−0.162490
$528$	−33.6986	−1.46654
$529$	−22.9839	−0.999302
$530$	6.20069	0.269341
$531$	3.80466	0.165108
$532$	2.41007	0.104490
$533$	53.2693	2.30735
$534$	33.6748	1.45725
$535$	−40.3082	−1.74267
$536$	38.3166	1.65502
$537$	0.117209	0.00505795
$538$	−20.0322	−0.863649
$539$	−22.8440	−0.983963
$540$	−2.50807	−0.107930
$541$	19.0592	0.819419	0.409710	−	0.912216i	$-0.365630\pi$
$541$	19.0592	0.819419	0.409710	+	0.912216i	$0.365630\pi$
$542$	33.4648	1.43744
$543$	33.2039	1.42492
$544$	−1.36766	−0.0586381
$545$	25.4443	1.08992
$546$	−16.6692	−0.713377
$547$	−1.07936	−0.0461501	−0.0230750	−	0.999734i	$-0.507346\pi$
$547$	−1.07936	−0.0461501	−0.0230750	+	0.999734i	$0.507346\pi$
$548$	0.303710	0.0129739
$549$	1.40439	0.0599380
$550$	0.0837958	0.00357306
$551$	0.973538	0.0414741
$552$	0.628803	0.0267637
$553$	16.6209	0.706794
$554$	−10.5736	−0.449230
$555$	−18.4178	−0.781793
$556$	−1.08514	−0.0460200
$557$	29.3345	1.24294	0.621471	−	0.783437i	$-0.286536\pi$
$557$	29.3345	1.24294	0.621471	+	0.783437i	$0.286536\pi$
$558$	−3.10878	−0.131605
$559$	5.09762	0.215606
$560$	−11.4767	−0.484981
$561$	7.61196	0.321377
$562$	−7.10183	−0.299573
$563$	−19.9267	−0.839809	−0.419904	−	0.907568i	$-0.637936\pi$
$563$	−19.9267	−0.839809	−0.419904	+	0.907568i	$0.637936\pi$
$564$	2.05425	0.0864997
$565$	−22.8589	−0.961679
$566$	−1.33760	−0.0562233
$567$	−11.9941	−0.503704
$568$	−27.8299	−1.16772
$569$	15.5672	0.652610	0.326305	−	0.945265i	$-0.394196\pi$
$569$	15.5672	0.652610	0.326305	+	0.945265i	$0.394196\pi$
$570$	54.1630	2.26864
$571$	−19.2776	−0.806743	−0.403372	−	0.915036i	$-0.632162\pi$
$571$	−19.2776	−0.806743	−0.403372	+	0.915036i	$0.632162\pi$
$572$	−5.00127	−0.209113
$573$	5.50834	0.230114
$574$	−18.1196	−0.756296
$575$	−0.00175648	−7.32502e−5 0
$576$	3.78717	0.157799
$577$	14.3301	0.596569	0.298285	−	0.954477i	$-0.403586\pi$
$577$	14.3301	0.596569	0.298285	+	0.954477i	$0.403586\pi$
$578$	1.49769	0.0622956
$579$	−26.7424	−1.11138
$580$	0.0618697	0.00256900
$581$	−2.49823	−0.103644
$582$	5.25093	0.217658
$583$	7.46312	0.309091
$584$	39.4883	1.63404
$585$	−6.35172	−0.262611
$586$	−1.77063	−0.0731439
$587$	−47.5614	−1.96307	−0.981535	−	0.191282i	$-0.938736\pi$
$587$	−47.5614	−1.96307	−0.981535	+	0.191282i	$0.938736\pi$
$588$	−2.59430	−0.106987
$589$	−31.9461	−1.31632
$590$	22.9290	0.943973
$591$	−0.712650	−0.0293145
$592$	19.3089	0.793591
$593$	−46.5030	−1.90965	−0.954824	−	0.297171i	$-0.903957\pi$
$593$	−46.5030	−1.90965	−0.954824	+	0.297171i	$0.903957\pi$
$594$	−27.8571	−1.14299
$595$	2.59241	0.106278
$596$	3.87261	0.158628
$597$	−2.66756	−0.109176
$598$	0.967426	0.0395610
$599$	−36.9475	−1.50963	−0.754817	−	0.655935i	$-0.772275\pi$
$599$	−36.9475	−1.50963	−0.754817	+	0.655935i	$0.772275\pi$
$600$	−0.0687859	−0.00280817
$601$	−27.0336	−1.10272	−0.551362	−	0.834266i	$-0.685892\pi$
$601$	−27.0336	−1.10272	−0.551362	+	0.834266i	$0.685892\pi$
$602$	−1.73396	−0.0706709
$603$	−8.10304	−0.329981
$604$	0.117425	0.00477797
$605$	11.8497	0.481759
$606$	−15.0816	−0.612647
$607$	16.4571	0.667972	0.333986	−	0.942578i	$-0.391606\pi$
$607$	16.4571	0.667972	0.333986	+	0.942578i	$0.391606\pi$
$608$	−11.7129	−0.475022
$609$	0.248195	0.0100574
$610$	8.46365	0.342683
$611$	−22.8448	−0.924202
$612$	0.135258	0.00546748
$613$	14.8338	0.599130	0.299565	−	0.954076i	$-0.403158\pi$
$613$	14.8338	0.599130	0.299565	+	0.954076i	$0.403158\pi$
$614$	23.0309	0.929451
$615$	−44.1270	−1.77937
$616$	−12.2965	−0.495440
$617$	7.83450	0.315405	0.157703	−	0.987487i	$-0.449591\pi$
$617$	7.83450	0.315405	0.157703	+	0.987487i	$0.449591\pi$
$618$	27.9866	1.12579
$619$	−42.3827	−1.70350	−0.851752	−	0.523946i	$-0.824459\pi$
$619$	−42.3827	−1.70350	−0.851752	+	0.523946i	$0.824459\pi$
$620$	−2.03022	−0.0815355
$621$	0.583925	0.0234321
$622$	−33.2886	−1.33475
$623$	13.8036	0.553029
$624$	42.5590	1.70372
$625$	−25.0691	−1.00276
$626$	−32.3608	−1.29340
$627$	65.1903	2.60345
$628$	−4.17998	−0.166799
$629$	−4.36157	−0.173907
$630$	2.16054	0.0860780
$631$	−6.34000	−0.252392	−0.126196	−	0.992005i	$-0.540277\pi$
$631$	−6.34000	−0.252392	−0.126196	+	0.992005i	$0.540277\pi$
$632$	−37.7758	−1.50264
$633$	−15.1416	−0.601825
$634$	−29.7425	−1.18122
$635$	−34.4468	−1.36698
$636$	0.847553	0.0336077
$637$	28.8505	1.14310
$638$	0.687187	0.0272060
$639$	5.88536	0.232821
$640$	28.9485	1.14429
$641$	−2.77819	−0.109732	−0.0548660	−	0.998494i	$-0.517473\pi$
$641$	−2.77819	−0.109732	−0.0548660	+	0.998494i	$0.517473\pi$
$642$	−50.8437	−2.00664
$643$	21.5523	0.849939	0.424969	−	0.905208i	$-0.360285\pi$
$643$	21.5523	0.849939	0.424969	+	0.905208i	$0.360285\pi$
$644$	−0.0356592	−0.00140517
$645$	−4.22275	−0.166271
$646$	12.8265	0.504651
$647$	−32.3670	−1.27248	−0.636239	−	0.771492i	$-0.719511\pi$
$647$	−32.3670	−1.27248	−0.636239	+	0.771492i	$0.719511\pi$
$648$	27.2600	1.07087
$649$	27.5972	1.08329
$650$	−0.105828	−0.00415093
$651$	−8.14439	−0.319204
$652$	3.69838	0.144840
$653$	−23.9822	−0.938495	−0.469248	−	0.883067i	$-0.655475\pi$
$653$	−23.9822	−0.938495	−0.469248	+	0.883067i	$0.655475\pi$
$654$	32.0948	1.25501
$655$	−5.47951	−0.214102
$656$	46.2619	1.80623
$657$	−8.35084	−0.325797
$658$	7.77067	0.302932
$659$	−18.3081	−0.713184	−0.356592	−	0.934260i	$-0.616061\pi$
$659$	−18.3081	−0.713184	−0.356592	+	0.934260i	$0.616061\pi$
$660$	4.14293	0.161263
$661$	18.1951	0.707708	0.353854	−	0.935301i	$-0.384871\pi$
$661$	18.1951	0.707708	0.353854	+	0.935301i	$0.384871\pi$
$662$	50.6431	1.96830
$663$	−9.61340	−0.373353
$664$	5.67795	0.220347
$665$	22.2019	0.860952
$666$	−3.63498	−0.140853
$667$	−0.0144044	−0.000557741 0
$668$	3.94503	0.152638
$669$	29.6450	1.14614
$670$	−48.8334	−1.88660
$671$	10.1868	0.393257
$672$	−2.98611	−0.115192
$673$	−34.9203	−1.34608	−0.673039	−	0.739607i	$-0.735011\pi$
$673$	−34.9203	−1.34608	−0.673039	+	0.739607i	$0.735011\pi$
$674$	−12.6845	−0.488590
$675$	−0.0638765	−0.00245861
$676$	3.15640	0.121400
$677$	21.8279	0.838916	0.419458	−	0.907775i	$-0.362220\pi$
$677$	21.8279	0.838916	0.419458	+	0.907775i	$0.362220\pi$
$678$	−28.8336	−1.10735
$679$	2.15240	0.0826016
$680$	−5.89200	−0.225948
$681$	10.9513	0.419655
$682$	−22.5497	−0.863471
$683$	7.97467	0.305142	0.152571	−	0.988292i	$-0.451245\pi$
$683$	7.97467	0.305142	0.152571	+	0.988292i	$0.451245\pi$
$684$	1.15837	0.0442916
$685$	2.79783	0.106899
$686$	−21.9512	−0.838101
$687$	−7.27949	−0.277730
$688$	4.42705	0.168780
$689$	−9.42541	−0.359080
$690$	−0.801393	−0.0305085
$691$	−49.7943	−1.89426	−0.947132	−	0.320846i	$-0.896033\pi$
$691$	−49.7943	−1.89426	−0.947132	+	0.320846i	$0.896033\pi$
$692$	5.96682	0.226824
$693$	2.60042	0.0987816
$694$	−33.2516	−1.26221
$695$	−9.99644	−0.379187
$696$	−0.564095	−0.0213820
$697$	−10.4498	−0.395816
$698$	22.9760	0.869653
$699$	49.3881	1.86803
$700$	0.00390082	0.000147437 0
$701$	−12.6308	−0.477059	−0.238530	−	0.971135i	$-0.576665\pi$
$701$	−12.6308	−0.477059	−0.238530	+	0.971135i	$0.576665\pi$
$702$	35.1817	1.32785
$703$	−37.3533	−1.40881
$704$	27.4704	1.03533
$705$	18.9241	0.712723
$706$	27.9244	1.05095
$707$	−6.18207	−0.232501
$708$	3.13410	0.117787
$709$	44.0366	1.65383	0.826915	−	0.562327i	$-0.190094\pi$
$709$	44.0366	1.65383	0.826915	+	0.562327i	$0.190094\pi$
$710$	35.4685	1.33111
$711$	7.98869	0.299599
$712$	−31.3726	−1.17574
$713$	0.472673	0.0177017
$714$	3.27000	0.122377
$715$	−46.0724	−1.72301
$716$	0.0151070	0.000564574 0
$717$	−20.2288	−0.755458
$718$	30.2973	1.13069
$719$	16.0040	0.596848	0.298424	−	0.954433i	$-0.403539\pi$
$719$	16.0040	0.596848	0.298424	+	0.954433i	$0.403539\pi$
$720$	−5.51618	−0.205576
$721$	11.4720	0.427238
$722$	81.3923	3.02911
$723$	6.67070	0.248086
$724$	4.27962	0.159051
$725$	0.00157572	5.85209e−5 0
$726$	14.9469	0.554732
$727$	−31.3216	−1.16165	−0.580827	−	0.814027i	$-0.697271\pi$
$727$	−31.3216	−1.16165	−0.580827	+	0.814027i	$0.697271\pi$
$728$	15.5296	0.575567
$729$	20.3062	0.752082
$730$	−50.3268	−1.86268
$731$	−1.00000	−0.0369863
$732$	1.15687	0.0427592
$733$	−15.2399	−0.562897	−0.281449	−	0.959576i	$-0.590815\pi$
$733$	−15.2399	−0.562897	−0.281449	+	0.959576i	$0.590815\pi$
$734$	38.1221	1.40711
$735$	−23.8991	−0.881530
$736$	0.173304	0.00638807
$737$	−58.7757	−2.16503
$738$	−8.70900	−0.320583
$739$	7.64718	0.281306	0.140653	−	0.990059i	$-0.455080\pi$
$739$	7.64718	0.281306	0.140653	+	0.990059i	$0.455080\pi$
$740$	−2.37385	−0.0872646
$741$	−82.3310	−3.02450
$742$	3.20606	0.117698
$743$	32.1928	1.18104	0.590520	−	0.807023i	$-0.298923\pi$
$743$	32.1928	1.18104	0.590520	+	0.807023i	$0.298923\pi$
$744$	18.5105	0.678626
$745$	35.6751	1.30703
$746$	47.9000	1.75374
$747$	−1.20075	−0.0439332
$748$	0.981098	0.0358725
$749$	−20.8413	−0.761524
$750$	−31.5341	−1.15146
$751$	−35.0142	−1.27768	−0.638842	−	0.769338i	$-0.720586\pi$
$751$	−35.0142	−1.27768	−0.638842	+	0.769338i	$0.720586\pi$
$752$	−19.8397	−0.723478
$753$	20.8432	0.759569
$754$	−0.867871	−0.0316060
$755$	1.08174	0.0393686
$756$	−1.29679	−0.0471639
$757$	−24.2054	−0.879760	−0.439880	−	0.898057i	$-0.644979\pi$
$757$	−24.2054	−0.879760	−0.439880	+	0.898057i	$0.644979\pi$
$758$	18.2273	0.662046
$759$	−0.964553	−0.0350110
$760$	−50.4602	−1.83038
$761$	21.6639	0.785314	0.392657	−	0.919685i	$-0.371556\pi$
$761$	21.6639	0.785314	0.392657	+	0.919685i	$0.371556\pi$
$762$	−43.4503	−1.57404
$763$	13.1560	0.476278
$764$	0.709965	0.0256856
$765$	1.24602	0.0450498
$766$	4.38668	0.158497
$767$	−34.8535	−1.25849
$768$	10.8454	0.391351
$769$	−3.95225	−0.142522	−0.0712609	−	0.997458i	$-0.522702\pi$
$769$	−3.95225	−0.142522	−0.0712609	+	0.997458i	$0.522702\pi$
$770$	15.6716	0.564764
$771$	57.0767	2.05557
$772$	−3.44680	−0.124053
$773$	−42.1523	−1.51611	−0.758057	−	0.652188i	$-0.773851\pi$
$773$	−42.1523	−1.51611	−0.758057	+	0.652188i	$0.773851\pi$
$774$	−0.833410	−0.0299563
$775$	−0.0517065	−0.00185735
$776$	−4.89195	−0.175611
$777$	−9.52291	−0.341633
$778$	−11.5816	−0.415222
$779$	−89.4943	−3.20647
$780$	−5.23225	−0.187344
$781$	42.6897	1.52756
$782$	−0.189780	−0.00678652
$783$	−0.523835	−0.0187203
$784$	25.0553	0.894833
$785$	−38.5066	−1.37436
$786$	−6.91171	−0.246533
$787$	3.93447	0.140249	0.0701243	−	0.997538i	$-0.477660\pi$
$787$	3.93447	0.140249	0.0701243	+	0.997538i	$0.477660\pi$
$788$	−0.0918527	−0.00327212
$789$	−44.0913	−1.56969
$790$	48.1443	1.71290
$791$	−11.8191	−0.420240
$792$	−5.91019	−0.210010
$793$	−12.8652	−0.456858
$794$	18.4189	0.653663
$795$	7.80779	0.276914
$796$	−0.343820	−0.0121864
$797$	−51.3597	−1.81925	−0.909627	−	0.415425i	$-0.863633\pi$
$797$	−51.3597	−1.81925	−0.909627	+	0.415425i	$0.863633\pi$
$798$	28.0049	0.991363
$799$	4.48146	0.158543
$800$	−0.0189580	−0.000670268 0
$801$	6.63456	0.234421
$802$	−2.67001	−0.0942814
$803$	−60.5731	−2.13758
$804$	−6.67489	−0.235405
$805$	−0.328498	−0.0115780
$806$	28.4787	1.00312
$807$	−25.2242	−0.887933
$808$	14.0505	0.494296
$809$	0.690452	0.0242750	0.0121375	−	0.999926i	$-0.496136\pi$
$809$	0.690452	0.0242750	0.0121375	+	0.999926i	$0.496136\pi$
$810$	−34.7421	−1.22071
$811$	−19.8280	−0.696254	−0.348127	−	0.937447i	$-0.613182\pi$
$811$	−19.8280	−0.696254	−0.348127	+	0.937447i	$0.613182\pi$
$812$	0.0319896	0.00112262
$813$	42.1383	1.47785
$814$	−26.3664	−0.924143
$815$	34.0700	1.19342
$816$	−8.34880	−0.292266
$817$	−8.56419	−0.299623
$818$	−11.6256	−0.406478
$819$	−3.28415	−0.114757
$820$	−5.68749	−0.198616
$821$	26.1186	0.911546	0.455773	−	0.890096i	$-0.349363\pi$
$821$	26.1186	0.911546	0.455773	+	0.890096i	$0.349363\pi$
$822$	3.52911	0.123092
$823$	1.38986	0.0484476	0.0242238	−	0.999707i	$-0.492289\pi$
$823$	1.38986	0.0484476	0.0242238	+	0.999707i	$0.492289\pi$
$824$	−26.0733	−0.908308
$825$	0.105514	0.00367353
$826$	11.8554	0.412503
$827$	52.0980	1.81162	0.905812	−	0.423680i	$-0.139262\pi$
$827$	52.0980	1.81162	0.905812	+	0.423680i	$0.139262\pi$
$828$	−0.0171393	−0.000595630 0
$829$	−24.2937	−0.843756	−0.421878	−	0.906653i	$-0.638629\pi$
$829$	−24.2937	−0.843756	−0.421878	+	0.906653i	$0.638629\pi$
$830$	−7.23640	−0.251179
$831$	−13.3141	−0.461861
$832$	−34.6932	−1.20277
$833$	−5.65960	−0.196093
$834$	−12.6093	−0.436623
$835$	36.3422	1.25767
$836$	8.40231	0.290600
$837$	17.1893	0.594151
$838$	−15.6164	−0.539460
$839$	−40.2531	−1.38969	−0.694846	−	0.719158i	$-0.744528\pi$
$839$	−40.2531	−1.38969	−0.694846	+	0.719158i	$0.744528\pi$
$840$	−12.8644	−0.443864
$841$	−28.9871	−0.999554
$842$	−26.5373	−0.914535
$843$	−8.94249	−0.307996
$844$	−1.95159	−0.0671764
$845$	29.0772	1.00029
$846$	3.73490	0.128408
$847$	6.12687	0.210522
$848$	−8.18554	−0.281093
$849$	−1.68428	−0.0578042
$850$	0.0207604	0.000712074 0
$851$	0.552678	0.0189456
$852$	4.84808	0.166092
$853$	28.7041	0.982809	0.491405	−	0.870931i	$-0.336484\pi$
$853$	28.7041	0.982809	0.491405	+	0.870931i	$0.336484\pi$
$854$	4.37612	0.149748
$855$	10.6711	0.364945
$856$	47.3678	1.61900
$857$	14.0983	0.481588	0.240794	−	0.970576i	$-0.422592\pi$
$857$	14.0983	0.481588	0.240794	+	0.970576i	$0.422592\pi$
$858$	−58.1146	−1.98400
$859$	−4.48460	−0.153013	−0.0765063	−	0.997069i	$-0.524377\pi$
$859$	−4.48460	−0.153013	−0.0765063	+	0.997069i	$0.524377\pi$
$860$	−0.544266	−0.0185593
$861$	−22.8158	−0.777561
$862$	34.4600	1.17371
$863$	−21.0440	−0.716345	−0.358172	−	0.933655i	$-0.616600\pi$
$863$	−21.0440	−0.716345	−0.358172	+	0.933655i	$0.616600\pi$
$864$	6.30242	0.214413
$865$	54.9673	1.86894
$866$	32.8448	1.11611
$867$	1.88586	0.0640471
$868$	−1.04972	−0.0356299
$869$	57.9462	1.96569
$870$	0.718924	0.0243738
$871$	74.2297	2.51518
$872$	−29.9007	−1.01257
$873$	1.03453	0.0350136
$874$	−1.62531	−0.0549770
$875$	−12.9261	−0.436983
$876$	−6.87902	−0.232420
$877$	−10.4566	−0.353094	−0.176547	−	0.984292i	$-0.556493\pi$
$877$	−10.4566	−0.353094	−0.176547	+	0.984292i	$0.556493\pi$
$878$	27.1631	0.916709
$879$	−2.22954	−0.0752005
$880$	−40.0118	−1.34880
$881$	−2.26323	−0.0762501	−0.0381251	−	0.999273i	$-0.512139\pi$
$881$	−2.26323	−0.0762501	−0.0381251	+	0.999273i	$0.512139\pi$
$882$	−4.71677	−0.158822
$883$	−21.2221	−0.714180	−0.357090	−	0.934070i	$-0.616231\pi$
$883$	−21.2221	−0.714180	−0.357090	+	0.934070i	$0.616231\pi$
$884$	−1.23906	−0.0416741
$885$	28.8718	0.970514
$886$	−47.3232	−1.58985
$887$	6.17564	0.207358	0.103679	−	0.994611i	$-0.466939\pi$
$887$	6.17564	0.207358	0.103679	+	0.994611i	$0.466939\pi$
$888$	21.6436	0.726310
$889$	−17.8107	−0.597351
$890$	39.9836	1.34025
$891$	−41.8154	−1.40087
$892$	3.82092	0.127934
$893$	38.3801	1.28434
$894$	44.9996	1.50501
$895$	0.139168	0.00465187
$896$	14.9678	0.500038
$897$	1.21817	0.0406733
$898$	20.6357	0.688622
$899$	−0.424032	−0.0141422
$900$	0.00187489	6.24964e−5 0
$901$	1.84898	0.0615985
$902$	−63.1710	−2.10336
$903$	−2.18337	−0.0726579
$904$	26.8624	0.893430
$905$	39.4245	1.31051
$906$	1.36448	0.0453319
$907$	8.42749	0.279830	0.139915	−	0.990163i	$-0.455317\pi$
$907$	8.42749	0.279830	0.139915	+	0.990163i	$0.455317\pi$
$908$	1.41150	0.0468424
$909$	−2.97135	−0.0985536
$910$	−19.7921	−0.656103
$911$	−1.23788	−0.0410127	−0.0205064	−	0.999790i	$-0.506528\pi$
$911$	−1.23788	−0.0410127	−0.0205064	+	0.999790i	$0.506528\pi$
$912$	−71.5007	−2.36762
$913$	−8.70969	−0.288249
$914$	29.5256	0.976619
$915$	10.6573	0.352318
$916$	−0.938246	−0.0310005
$917$	−2.83317	−0.0935596
$918$	−6.90159	−0.227786
$919$	28.4172	0.937396	0.468698	−	0.883358i	$-0.344723\pi$
$919$	28.4172	0.937396	0.468698	+	0.883358i	$0.344723\pi$
$920$	0.746607	0.0246149
$921$	29.0001	0.955584
$922$	−44.0198	−1.44972
$923$	−53.9142	−1.77461
$924$	2.14210	0.0704698
$925$	−0.0604584	−0.00198786
$926$	51.6755	1.69816
$927$	5.51389	0.181100
$928$	−0.155470	−0.00510355
$929$	−13.1892	−0.432725	−0.216363	−	0.976313i	$-0.569419\pi$
$929$	−13.1892	−0.432725	−0.216363	+	0.976313i	$0.569419\pi$
$930$	−23.5911	−0.773582
$931$	−48.4699	−1.58854
$932$	6.36559	0.208512
$933$	−41.9163	−1.37228
$934$	−32.5868	−1.06627
$935$	9.03803	0.295575
$936$	7.46418	0.243974
$937$	2.82819	0.0923929	0.0461964	−	0.998932i	$-0.485290\pi$
$937$	2.82819	0.0923929	0.0461964	+	0.998932i	$0.485290\pi$
$938$	−25.2493	−0.824418
$939$	−40.7481	−1.32976
$940$	2.43911	0.0795549
$941$	−7.72965	−0.251979	−0.125990	−	0.992032i	$-0.540211\pi$
$941$	−7.72965	−0.251979	−0.125990	+	0.992032i	$0.540211\pi$
$942$	−48.5712	−1.58254
$943$	1.32415	0.0431204
$944$	−30.2686	−0.985160
$945$	−11.9462	−0.388612
$946$	−6.04517	−0.196545
$947$	48.2619	1.56830	0.784151	−	0.620571i	$-0.213099\pi$
$947$	48.2619	1.56830	0.784151	+	0.620571i	$0.213099\pi$
$948$	6.58070	0.213731
$949$	76.4997	2.48329
$950$	0.177796	0.00576845
$951$	−37.4512	−1.21444
$952$	−3.04645	−0.0987360
$953$	21.1553	0.685289	0.342644	−	0.939465i	$-0.388677\pi$
$953$	21.1553	0.685289	0.342644	+	0.939465i	$0.388677\pi$
$954$	1.54096	0.0498905
$955$	6.54030	0.211639
$956$	−2.60727	−0.0843251
$957$	0.865293	0.0279710
$958$	55.2464	1.78493
$959$	1.44661	0.0467136
$960$	28.7391	0.927549
$961$	−17.0856	−0.551150
$962$	33.2990	1.07360
$963$	−10.0172	−0.322799
$964$	0.859779	0.0276916
$965$	−31.7524	−1.02215
$966$	−0.414359	−0.0133318
$967$	18.8295	0.605515	0.302758	−	0.953068i	$-0.402093\pi$
$967$	18.8295	0.605515	0.302758	+	0.953068i	$0.402093\pi$
$968$	−13.9251	−0.447569
$969$	16.1509	0.518840
$970$	6.23466	0.200183
$971$	−19.7447	−0.633638	−0.316819	−	0.948486i	$-0.602615\pi$
$971$	−19.7447	−0.633638	−0.316819	+	0.948486i	$0.602615\pi$
$972$	−1.38852	−0.0445369
$973$	−5.16865	−0.165699
$974$	21.5179	0.689477
$975$	−0.133257	−0.00426764
$976$	−11.1729	−0.357635
$977$	−18.1841	−0.581762	−0.290881	−	0.956759i	$-0.593948\pi$
$977$	−18.1841	−0.581762	−0.290881	+	0.956759i	$0.593948\pi$
$978$	42.9751	1.37419
$979$	48.1240	1.53805
$980$	−3.08033	−0.0983974
$981$	6.32329	0.201887
$982$	−22.1058	−0.705423
$983$	−31.5638	−1.00673	−0.503364	−	0.864074i	$-0.667905\pi$
$983$	−31.5638	−1.00673	−0.503364	+	0.864074i	$0.667905\pi$
$984$	51.8555	1.65309
$985$	−0.846162	−0.0269609
$986$	0.170250	0.00542187
$987$	9.78468	0.311450
$988$	−10.6116	−0.337598
$989$	0.126715	0.00402931
$990$	7.53238	0.239395
$991$	−52.4203	−1.66519	−0.832593	−	0.553886i	$-0.813144\pi$
$991$	−52.4203	−1.66519	−0.832593	+	0.553886i	$0.813144\pi$
$992$	5.10166	0.161978
$993$	63.7689	2.02364
$994$	18.3389	0.581675
$995$	−3.16732	−0.100411
$996$	−0.989122	−0.0313415
$997$	28.4004	0.899450	0.449725	−	0.893167i	$-0.351522\pi$
$997$	28.4004	0.899450	0.449725	+	0.893167i	$0.351522\pi$
$998$	−5.86364	−0.185610
$999$	20.0988	0.635899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.e.1.14	✓	19
3.2	odd	2		6579.2.a.t.1.6		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.e.1.14	✓	19	1.1	even	1	trivial
6579.2.a.t.1.6		19	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)

\(f(q)\)	\(=\)	\(q+1.49769 q^{2} +1.88586 q^{3} +0.243066 q^{4} +2.23917 q^{5} +2.82443 q^{6} +1.15776 q^{7} -2.63134 q^{8} +0.556465 q^{9} +O(q^{10})\)	\(q+1.49769 q^{2} +1.88586 q^{3} +0.243066 q^{4} +2.23917 q^{5} +2.82443 q^{6} +1.15776 q^{7} -2.63134 q^{8} +0.556465 q^{9} +3.35357 q^{10} +4.03634 q^{11} +0.458389 q^{12} -5.09762 q^{13} +1.73396 q^{14} +4.22275 q^{15} -4.42705 q^{16} +1.00000 q^{17} +0.833410 q^{18} +8.56419 q^{19} +0.544266 q^{20} +2.18337 q^{21} +6.04517 q^{22} -0.126715 q^{23} -4.96233 q^{24} +0.0138616 q^{25} -7.63464 q^{26} -4.60816 q^{27} +0.281412 q^{28} +0.113675 q^{29} +6.32436 q^{30} -3.73020 q^{31} -1.36766 q^{32} +7.61196 q^{33} +1.49769 q^{34} +2.59241 q^{35} +0.135258 q^{36} -4.36157 q^{37} +12.8265 q^{38} -9.61340 q^{39} -5.89200 q^{40} -10.4498 q^{41} +3.27000 q^{42} -1.00000 q^{43} +0.981098 q^{44} +1.24602 q^{45} -0.189780 q^{46} +4.48146 q^{47} -8.34880 q^{48} -5.65960 q^{49} +0.0207604 q^{50} +1.88586 q^{51} -1.23906 q^{52} +1.84898 q^{53} -6.90159 q^{54} +9.03803 q^{55} -3.04645 q^{56} +16.1509 q^{57} +0.170250 q^{58} +6.83720 q^{59} +1.02641 q^{60} +2.52377 q^{61} -5.58667 q^{62} +0.644251 q^{63} +6.80577 q^{64} -11.4144 q^{65} +11.4003 q^{66} -14.5616 q^{67} +0.243066 q^{68} -0.238967 q^{69} +3.88262 q^{70} +10.5763 q^{71} -1.46425 q^{72} -15.0069 q^{73} -6.53227 q^{74} +0.0261410 q^{75} +2.08167 q^{76} +4.67310 q^{77} -14.3979 q^{78} +14.3561 q^{79} -9.91290 q^{80} -10.3597 q^{81} -15.6506 q^{82} -2.15782 q^{83} +0.530703 q^{84} +2.23917 q^{85} -1.49769 q^{86} +0.214376 q^{87} -10.6210 q^{88} +11.9227 q^{89} +1.86614 q^{90} -5.90181 q^{91} -0.0308003 q^{92} -7.03462 q^{93} +6.71183 q^{94} +19.1766 q^{95} -2.57922 q^{96} +1.85911 q^{97} -8.47631 q^{98} +2.24608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9} - 2 q^{10} + 4 q^{11} + 9 q^{12} + 14 q^{13} + 5 q^{14} - 7 q^{15} + 32 q^{16} + 19 q^{17} + 12 q^{18} + 12 q^{19} + 23 q^{20} + 16 q^{21} + 36 q^{22} - q^{23} - 13 q^{24} + 30 q^{25} - 21 q^{26} + 8 q^{27} + 5 q^{28} + 41 q^{29} - 26 q^{30} - 8 q^{31} - 20 q^{32} - 14 q^{33} + 2 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} - 29 q^{38} + 17 q^{39} - 15 q^{40} + 6 q^{41} - q^{42} - 19 q^{43} + 16 q^{44} + 24 q^{45} + 38 q^{46} - 21 q^{47} - 2 q^{48} + 46 q^{49} - 36 q^{50} + 5 q^{51} + 39 q^{52} - 9 q^{53} + 53 q^{54} + 10 q^{55} - 12 q^{56} - 5 q^{57} - 45 q^{58} - 4 q^{59} - 7 q^{60} + 68 q^{61} - 25 q^{62} + 61 q^{63} - 14 q^{64} + 22 q^{65} - 17 q^{66} + 26 q^{68} - 9 q^{69} - 37 q^{70} + 23 q^{71} - 4 q^{72} - q^{73} - 30 q^{74} - 25 q^{75} + 47 q^{76} - 19 q^{77} + 12 q^{78} + 16 q^{79} + 28 q^{80} - 21 q^{81} - 13 q^{82} - 32 q^{83} - 47 q^{84} + 11 q^{85} - 2 q^{86} - 8 q^{87} + 108 q^{88} + 11 q^{89} + 5 q^{90} + 52 q^{91} - 23 q^{92} - 23 q^{93} + 47 q^{94} - 25 q^{95} - 103 q^{96} + 36 q^{97} - 100 q^{98} - 11 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9 - 2 * q^10 + 4 * q^11 + 9 * q^12 + 14 * q^13 + 5 * q^14 - 7 * q^15 + 32 * q^16 + 19 * q^17 + 12 * q^18 + 12 * q^19 + 23 * q^20 + 16 * q^21 + 36 * q^22 - q^23 - 13 * q^24 + 30 * q^25 - 21 * q^26 + 8 * q^27 + 5 * q^28 + 41 * q^29 - 26 * q^30 - 8 * q^31 - 20 * q^32 - 14 * q^33 + 2 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 - 29 * q^38 + 17 * q^39 - 15 * q^40 + 6 * q^41 - q^42 - 19 * q^43 + 16 * q^44 + 24 * q^45 + 38 * q^46 - 21 * q^47 - 2 * q^48 + 46 * q^49 - 36 * q^50 + 5 * q^51 + 39 * q^52 - 9 * q^53 + 53 * q^54 + 10 * q^55 - 12 * q^56 - 5 * q^57 - 45 * q^58 - 4 * q^59 - 7 * q^60 + 68 * q^61 - 25 * q^62 + 61 * q^63 - 14 * q^64 + 22 * q^65 - 17 * q^66 + 26 * q^68 - 9 * q^69 - 37 * q^70 + 23 * q^71 - 4 * q^72 - q^73 - 30 * q^74 - 25 * q^75 + 47 * q^76 - 19 * q^77 + 12 * q^78 + 16 * q^79 + 28 * q^80 - 21 * q^81 - 13 * q^82 - 32 * q^83 - 47 * q^84 + 11 * q^85 - 2 * q^86 - 8 * q^87 + 108 * q^88 + 11 * q^89 + 5 * q^90 + 52 * q^91 - 23 * q^92 - 23 * q^93 + 47 * q^94 - 25 * q^95 - 103 * q^96 + 36 * q^97 - 100 * q^98 - 11 * q^99

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