LMFDB - Embedded newform 731.2.a.e.1.8

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			1.8
Root			$-0.276381$ 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)

$f(q)$	$=$	$q-0.276381 q^{2} +2.26539 q^{3} -1.92361 q^{4} -3.42185 q^{5} -0.626111 q^{6} +1.42090 q^{7} +1.08441 q^{8} +2.13201 q^{9} +O(q^{10})$	\(q-0.276381 q^{2} +2.26539 q^{3} -1.92361 q^{4} -3.42185 q^{5} -0.626111 q^{6} +1.42090 q^{7} +1.08441 q^{8} +2.13201 q^{9} +0.945732 q^{10} -0.0948639 q^{11} -4.35774 q^{12} +6.11913 q^{13} -0.392710 q^{14} -7.75183 q^{15} +3.54752 q^{16} +1.00000 q^{17} -0.589245 q^{18} +5.35849 q^{19} +6.58231 q^{20} +3.21890 q^{21} +0.0262185 q^{22} -5.70214 q^{23} +2.45662 q^{24} +6.70903 q^{25} -1.69121 q^{26} -1.96635 q^{27} -2.73327 q^{28} +1.52937 q^{29} +2.14245 q^{30} +8.17493 q^{31} -3.14929 q^{32} -0.214904 q^{33} -0.276381 q^{34} -4.86211 q^{35} -4.10116 q^{36} +6.07410 q^{37} -1.48098 q^{38} +13.8622 q^{39} -3.71069 q^{40} +12.1145 q^{41} -0.889643 q^{42} -1.00000 q^{43} +0.182481 q^{44} -7.29540 q^{45} +1.57596 q^{46} +3.39877 q^{47} +8.03652 q^{48} -4.98103 q^{49} -1.85425 q^{50} +2.26539 q^{51} -11.7708 q^{52} +3.28670 q^{53} +0.543460 q^{54} +0.324610 q^{55} +1.54084 q^{56} +12.1391 q^{57} -0.422689 q^{58} -6.46108 q^{59} +14.9115 q^{60} +10.5687 q^{61} -2.25939 q^{62} +3.02937 q^{63} -6.22463 q^{64} -20.9387 q^{65} +0.0593953 q^{66} -12.5290 q^{67} -1.92361 q^{68} -12.9176 q^{69} +1.34379 q^{70} +5.67131 q^{71} +2.31197 q^{72} -16.2559 q^{73} -1.67876 q^{74} +15.1986 q^{75} -10.3077 q^{76} -0.134792 q^{77} -3.83125 q^{78} -8.78371 q^{79} -12.1391 q^{80} -10.8506 q^{81} -3.34822 q^{82} +7.35705 q^{83} -6.19193 q^{84} -3.42185 q^{85} +0.276381 q^{86} +3.46463 q^{87} -0.102871 q^{88} -4.66429 q^{89} +2.01631 q^{90} +8.69469 q^{91} +10.9687 q^{92} +18.5194 q^{93} -0.939355 q^{94} -18.3359 q^{95} -7.13437 q^{96} +18.6360 q^{97} +1.37666 q^{98} -0.202250 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.276381	−0.195431	−0.0977153	−	0.995214i	$-0.531153\pi$
$2$	−0.276381	−0.195431	−0.0977153	+	0.995214i	$0.531153\pi$
$3$	2.26539	1.30793	0.653963	−	0.756527i	$-0.273105\pi$
$3$	2.26539	1.30793	0.653963	+	0.756527i	$0.273105\pi$
$4$	−1.92361	−0.961807
$5$	−3.42185	−1.53030	−0.765148	−	0.643854i	$-0.777334\pi$
$5$	−3.42185	−1.53030	−0.765148	+	0.643854i	$0.777334\pi$
$6$	−0.626111	−0.255609
$7$	1.42090	0.537051	0.268525	−	0.963273i	$-0.413464\pi$
$7$	1.42090	0.537051	0.268525	+	0.963273i	$0.413464\pi$
$8$	1.08441	0.383397
$9$	2.13201	0.710669
$10$	0.945732	0.299067
$11$	−0.0948639	−0.0286025	−0.0143013	−	0.999898i	$-0.504552\pi$
$11$	−0.0948639	−0.0286025	−0.0143013	+	0.999898i	$0.504552\pi$
$12$	−4.35774	−1.25797
$13$	6.11913	1.69714	0.848570	−	0.529083i	$-0.177464\pi$
$13$	6.11913	1.69714	0.848570	+	0.529083i	$0.177464\pi$
$14$	−0.392710	−0.104956
$15$	−7.75183	−2.00151
$16$	3.54752	0.886879
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.589245	−0.138886
$19$	5.35849	1.22932	0.614661	−	0.788792i	$-0.289293\pi$
$19$	5.35849	1.22932	0.614661	+	0.788792i	$0.289293\pi$
$20$	6.58231	1.47185
$21$	3.21890	0.702422
$22$	0.0262185	0.00558981
$23$	−5.70214	−1.18898	−0.594489	−	0.804104i	$-0.702646\pi$
$23$	−5.70214	−1.18898	−0.594489	+	0.804104i	$0.702646\pi$
$24$	2.45662	0.501455
$25$	6.70903	1.34181
$26$	−1.69121	−0.331673
$27$	−1.96635	−0.378424
$28$	−2.73327	−0.516539
$29$	1.52937	0.283997	0.141999	−	0.989867i	$-0.454647\pi$
$29$	1.52937	0.283997	0.141999	+	0.989867i	$0.454647\pi$
$30$	2.14245	0.391157
$31$	8.17493	1.46826	0.734131	−	0.679008i	$-0.237590\pi$
$31$	8.17493	1.46826	0.734131	+	0.679008i	$0.237590\pi$
$32$	−3.14929	−0.556720
$33$	−0.214904	−0.0374100
$34$	−0.276381	−0.0473989
$35$	−4.86211	−0.821847
$36$	−4.10116	−0.683526
$37$	6.07410	0.998576	0.499288	−	0.866436i	$-0.333595\pi$
$37$	6.07410	0.998576	0.499288	+	0.866436i	$0.333595\pi$
$38$	−1.48098	−0.240247
$39$	13.8622	2.21973
$40$	−3.71069	−0.586711
$41$	12.1145	1.89197	0.945985	−	0.324211i	$-0.105099\pi$
$41$	12.1145	1.89197	0.945985	+	0.324211i	$0.105099\pi$
$42$	−0.889643	−0.137275
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0.182481	0.0275101
$45$	−7.29540	−1.08753
$46$	1.57596	0.232363
$47$	3.39877	0.495762	0.247881	−	0.968791i	$-0.420266\pi$
$47$	3.39877	0.495762	0.247881	+	0.968791i	$0.420266\pi$
$48$	8.03652	1.15997
$49$	−4.98103	−0.711576
$50$	−1.85425	−0.262230
$51$	2.26539	0.317218
$52$	−11.7708	−1.63232
$53$	3.28670	0.451463	0.225731	−	0.974190i	$-0.427523\pi$
$53$	3.28670	0.451463	0.225731	+	0.974190i	$0.427523\pi$
$54$	0.543460	0.0739556
$55$	0.324610	0.0437703
$56$	1.54084	0.205904
$57$	12.1391	1.60786
$58$	−0.422689	−0.0555017
$59$	−6.46108	−0.841162	−0.420581	−	0.907255i	$-0.638174\pi$
$59$	−6.46108	−0.841162	−0.420581	+	0.907255i	$0.638174\pi$
$60$	14.9115	1.92507
$61$	10.5687	1.35319	0.676594	−	0.736356i	$-0.263455\pi$
$61$	10.5687	1.35319	0.676594	+	0.736356i	$0.263455\pi$
$62$	−2.25939	−0.286943
$63$	3.02937	0.381665
$64$	−6.22463	−0.778079
$65$	−20.9387	−2.59713
$66$	0.0593953	0.00731105
$67$	−12.5290	−1.53066	−0.765328	−	0.643640i	$-0.777423\pi$
$67$	−12.5290	−1.53066	−0.765328	+	0.643640i	$0.777423\pi$
$68$	−1.92361	−0.233272
$69$	−12.9176	−1.55509
$70$	1.34379	0.160614
$71$	5.67131	0.673060	0.336530	−	0.941673i	$-0.390747\pi$
$71$	5.67131	0.673060	0.336530	+	0.941673i	$0.390747\pi$
$72$	2.31197	0.272468
$73$	−16.2559	−1.90261	−0.951305	−	0.308250i	$-0.900257\pi$
$73$	−16.2559	−1.90261	−0.951305	+	0.308250i	$0.900257\pi$
$74$	−1.67876	−0.195152
$75$	15.1986	1.75498
$76$	−10.3077	−1.18237
$77$	−0.134792	−0.0153610
$78$	−3.83125	−0.433804
$79$	−8.78371	−0.988245	−0.494123	−	0.869392i	$-0.664511\pi$
$79$	−8.78371	−0.988245	−0.494123	+	0.869392i	$0.664511\pi$
$80$	−12.1391	−1.35719
$81$	−10.8506	−1.20562
$82$	−3.34822	−0.369749
$83$	7.35705	0.807541	0.403771	−	0.914860i	$-0.367699\pi$
$83$	7.35705	0.807541	0.403771	+	0.914860i	$0.367699\pi$
$84$	−6.19193	−0.675595
$85$	−3.42185	−0.371151
$86$	0.276381	0.0298029
$87$	3.46463	0.371447
$88$	−0.102871	−0.0109661
$89$	−4.66429	−0.494414	−0.247207	−	0.968963i	$-0.579513\pi$
$89$	−4.66429	−0.494414	−0.247207	+	0.968963i	$0.579513\pi$
$90$	2.01631	0.212537
$91$	8.69469	0.911451
$92$	10.9687	1.14357
$93$	18.5194	1.92038
$94$	−0.939355	−0.0968870
$95$	−18.3359	−1.88123
$96$	−7.13437	−0.728149
$97$	18.6360	1.89220	0.946099	−	0.323878i	$-0.104987\pi$
$97$	18.6360	1.89220	0.946099	+	0.323878i	$0.104987\pi$
$98$	1.37666	0.139064
$99$	−0.202250	−0.0203269
$100$	−12.9056	−1.29056
$101$	−18.0377	−1.79482	−0.897409	−	0.441200i	$-0.854553\pi$
$101$	−18.0377	−1.79482	−0.897409	+	0.441200i	$0.854553\pi$
$102$	−0.626111	−0.0619942
$103$	14.7351	1.45189	0.725947	−	0.687751i	$-0.241402\pi$
$103$	14.7351	1.45189	0.725947	+	0.687751i	$0.241402\pi$
$104$	6.63565	0.650679
$105$	−11.0146	−1.07491
$106$	−0.908379	−0.0882296
$107$	−12.1191	−1.17160	−0.585800	−	0.810455i	$-0.699220\pi$
$107$	−12.1191	−1.17160	−0.585800	+	0.810455i	$0.699220\pi$
$108$	3.78249	0.363971
$109$	−0.833723	−0.0798562	−0.0399281	−	0.999203i	$-0.512713\pi$
$109$	−0.833723	−0.0798562	−0.0399281	+	0.999203i	$0.512713\pi$
$110$	−0.0897158	−0.00855407
$111$	13.7602	1.30606
$112$	5.04068	0.476299
$113$	7.46642	0.702382	0.351191	−	0.936304i	$-0.385777\pi$
$113$	7.46642	0.702382	0.351191	+	0.936304i	$0.385777\pi$
$114$	−3.35501	−0.314225
$115$	19.5118	1.81949
$116$	−2.94192	−0.273150
$117$	13.0460	1.20610
$118$	1.78572	0.164389
$119$	1.42090	0.130254
$120$	−8.40617	−0.767374
$121$	−10.9910	−0.999182
$122$	−2.92099	−0.264454
$123$	27.4441	2.47456
$124$	−15.7254	−1.41218
$125$	−5.84805	−0.523065
$126$	−0.837260	−0.0745891
$127$	−6.30846	−0.559785	−0.279893	−	0.960031i	$-0.590299\pi$
$127$	−6.30846	−0.559785	−0.279893	+	0.960031i	$0.590299\pi$
$128$	8.01894	0.708781
$129$	−2.26539	−0.199457
$130$	5.78705	0.507558
$131$	14.7505	1.28875	0.644377	−	0.764708i	$-0.277117\pi$
$131$	14.7505	1.28875	0.644377	+	0.764708i	$0.277117\pi$
$132$	0.413392	0.0359812
$133$	7.61389	0.660208
$134$	3.46276	0.299137
$135$	6.72854	0.579101
$136$	1.08441	0.0929875
$137$	−8.24992	−0.704838	−0.352419	−	0.935842i	$-0.614641\pi$
$137$	−8.24992	−0.704838	−0.352419	+	0.935842i	$0.614641\pi$
$138$	3.57017	0.303913
$139$	1.42013	0.120454	0.0602269	−	0.998185i	$-0.480818\pi$
$139$	1.42013	0.120454	0.0602269	+	0.998185i	$0.480818\pi$
$140$	9.35283	0.790458
$141$	7.69955	0.648419
$142$	−1.56744	−0.131537
$143$	−0.580484	−0.0485425
$144$	7.56333	0.630277
$145$	−5.23327	−0.434600
$146$	4.49282	0.371828
$147$	−11.2840	−0.930689
$148$	−11.6842	−0.960437
$149$	−11.0952	−0.908955	−0.454477	−	0.890758i	$-0.650174\pi$
$149$	−11.0952	−0.908955	−0.454477	+	0.890758i	$0.650174\pi$
$150$	−4.20060	−0.342977
$151$	9.19183	0.748020	0.374010	−	0.927425i	$-0.377983\pi$
$151$	9.19183	0.748020	0.374010	+	0.927425i	$0.377983\pi$
$152$	5.81080	0.471318
$153$	2.13201	0.172362
$154$	0.0372540	0.00300201
$155$	−27.9734	−2.24688
$156$	−26.6656	−2.13495
$157$	−5.33297	−0.425618	−0.212809	−	0.977094i	$-0.568261\pi$
$157$	−5.33297	−0.425618	−0.212809	+	0.977094i	$0.568261\pi$
$158$	2.42765	0.193133
$159$	7.44566	0.590479
$160$	10.7764	0.851947
$161$	−8.10219	−0.638542
$162$	2.99889	0.235615
$163$	−18.5850	−1.45569	−0.727846	−	0.685740i	$-0.759479\pi$
$163$	−18.5850	−1.45569	−0.727846	+	0.685740i	$0.759479\pi$
$164$	−23.3037	−1.81971
$165$	0.735368	0.0572483
$166$	−2.03335	−0.157818
$167$	8.48536	0.656617	0.328308	−	0.944571i	$-0.393521\pi$
$167$	8.48536	0.656617	0.328308	+	0.944571i	$0.393521\pi$
$168$	3.49061	0.269307
$169$	24.4437	1.88029
$170$	0.945732	0.0725343
$171$	11.4243	0.873640
$172$	1.92361	0.146674
$173$	20.4526	1.55498	0.777489	−	0.628896i	$-0.216493\pi$
$173$	20.4526	1.55498	0.777489	+	0.628896i	$0.216493\pi$
$174$	−0.957556	−0.0725921
$175$	9.53289	0.720618
$176$	−0.336531	−0.0253670
$177$	−14.6369	−1.10018
$178$	1.28912	0.0966236
$179$	8.40584	0.628282	0.314141	−	0.949376i	$-0.398284\pi$
$179$	8.40584	0.628282	0.314141	+	0.949376i	$0.398284\pi$
$180$	14.0335	1.04600
$181$	−2.78162	−0.206756	−0.103378	−	0.994642i	$-0.532965\pi$
$181$	−2.78162	−0.206756	−0.103378	+	0.994642i	$0.532965\pi$
$182$	−2.40304	−0.178125
$183$	23.9423	1.76987
$184$	−6.18346	−0.455851
$185$	−20.7846	−1.52812
$186$	−5.11841	−0.375300
$187$	−0.0948639	−0.00693713
$188$	−6.53792	−0.476827
$189$	−2.79399	−0.203233
$190$	5.06769	0.367649
$191$	17.3496	1.25537	0.627685	−	0.778467i	$-0.284002\pi$
$191$	17.3496	1.25537	0.627685	+	0.778467i	$0.284002\pi$
$192$	−14.1012	−1.01767
$193$	−11.9951	−0.863426	−0.431713	−	0.902011i	$-0.642091\pi$
$193$	−11.9951	−0.863426	−0.431713	+	0.902011i	$0.642091\pi$
$194$	−5.15063	−0.369793
$195$	−47.4344	−3.39685
$196$	9.58159	0.684399
$197$	−14.1192	−1.00595	−0.502975	−	0.864301i	$-0.667761\pi$
$197$	−14.1192	−1.00595	−0.502975	+	0.864301i	$0.667761\pi$
$198$	0.0558981	0.00397250
$199$	12.5773	0.891580	0.445790	−	0.895138i	$-0.352923\pi$
$199$	12.5773	0.891580	0.445790	+	0.895138i	$0.352923\pi$
$200$	7.27535	0.514445
$201$	−28.3830	−2.00198
$202$	4.98527	0.350762
$203$	2.17309	0.152521
$204$	−4.35774	−0.305103
$205$	−41.4540	−2.89527
$206$	−4.07250	−0.283744
$207$	−12.1570	−0.844969
$208$	21.7077	1.50516
$209$	−0.508327	−0.0351617
$210$	3.04422	0.210071
$211$	−2.32839	−0.160293	−0.0801464	−	0.996783i	$-0.525539\pi$
$211$	−2.32839	−0.160293	−0.0801464	+	0.996783i	$0.525539\pi$
$212$	−6.32234	−0.434220
$213$	12.8477	0.880313
$214$	3.34949	0.228967
$215$	3.42185	0.233368
$216$	−2.13233	−0.145087
$217$	11.6158	0.788531
$218$	0.230425	0.0156063
$219$	−36.8260	−2.48847
$220$	−0.624423	−0.0420986
$221$	6.11913	0.411617
$222$	−3.80306	−0.255245
$223$	−5.20939	−0.348846	−0.174423	−	0.984671i	$-0.555806\pi$
$223$	−5.20939	−0.348846	−0.174423	+	0.984671i	$0.555806\pi$
$224$	−4.47483	−0.298987
$225$	14.3037	0.953580
$226$	−2.06357	−0.137267
$227$	−0.0104994	−0.000696869 0	−0.000348435	−	1.00000i	$-0.500111\pi$
$227$	−0.0104994	−0.000696869 0	−0.000348435		1.00000i	$0.500111\pi$
$228$	−23.3509	−1.54645
$229$	−11.1535	−0.737045	−0.368523	−	0.929619i	$-0.620136\pi$
$229$	−11.1535	−0.737045	−0.368523	+	0.929619i	$0.620136\pi$
$230$	−5.39270	−0.355584
$231$	−0.305358	−0.0200911
$232$	1.65847	0.108884
$233$	1.11502	0.0730476	0.0365238	−	0.999333i	$-0.488372\pi$
$233$	1.11502	0.0730476	0.0365238	+	0.999333i	$0.488372\pi$
$234$	−3.60567	−0.235710
$235$	−11.6301	−0.758662
$236$	12.4286	0.809035
$237$	−19.8986	−1.29255
$238$	−0.392710	−0.0254556
$239$	−3.68538	−0.238387	−0.119194	−	0.992871i	$-0.538031\pi$
$239$	−3.68538	−0.238387	−0.119194	+	0.992871i	$0.538031\pi$
$240$	−27.4997	−1.77510
$241$	−9.61967	−0.619658	−0.309829	−	0.950792i	$-0.600272\pi$
$241$	−9.61967	−0.619658	−0.309829	+	0.950792i	$0.600272\pi$
$242$	3.03770	0.195271
$243$	−18.6818	−1.19844
$244$	−20.3302	−1.30151
$245$	17.0443	1.08892
$246$	−7.58503	−0.483604
$247$	32.7893	2.08633
$248$	8.86499	0.562927
$249$	16.6666	1.05620
$250$	1.61629	0.102223
$251$	−16.7591	−1.05782	−0.528912	−	0.848677i	$-0.677400\pi$
$251$	−16.7591	−1.05782	−0.528912	+	0.848677i	$0.677400\pi$
$252$	−5.82735	−0.367088
$253$	0.540927	0.0340078
$254$	1.74354	0.109399
$255$	−7.75183	−0.485438
$256$	10.2330	0.639562
$257$	−4.26668	−0.266148	−0.133074	−	0.991106i	$-0.542485\pi$
$257$	−4.26668	−0.266148	−0.133074	+	0.991106i	$0.542485\pi$
$258$	0.626111	0.0389800
$259$	8.63071	0.536286
$260$	40.2780	2.49794
$261$	3.26063	0.201828
$262$	−4.07674	−0.251862
$263$	3.26851	0.201545	0.100773	−	0.994909i	$-0.467869\pi$
$263$	3.26851	0.201545	0.100773	+	0.994909i	$0.467869\pi$
$264$	−0.233044	−0.0143429
$265$	−11.2466	−0.690871
$266$	−2.10433	−0.129025
$267$	−10.5665	−0.646657
$268$	24.1009	1.47220
$269$	24.2986	1.48151	0.740756	−	0.671775i	$-0.234468\pi$
$269$	24.2986	1.48151	0.740756	+	0.671775i	$0.234468\pi$
$270$	−1.85964	−0.113174
$271$	−14.0989	−0.856449	−0.428224	−	0.903672i	$-0.640861\pi$
$271$	−14.0989	−0.856449	−0.428224	+	0.903672i	$0.640861\pi$
$272$	3.54752	0.215100
$273$	19.6969	1.19211
$274$	2.28012	0.137747
$275$	−0.636445	−0.0383791
$276$	24.8484	1.49570
$277$	13.6667	0.821155	0.410577	−	0.911826i	$-0.365327\pi$
$277$	13.6667	0.821155	0.410577	+	0.911826i	$0.365327\pi$
$278$	−0.392496	−0.0235404
$279$	17.4290	1.04345
$280$	−5.27253	−0.315094
$281$	−17.8808	−1.06668	−0.533341	−	0.845900i	$-0.679064\pi$
$281$	−17.8808	−1.06668	−0.533341	+	0.845900i	$0.679064\pi$
$282$	−2.12801	−0.126721
$283$	5.60089	0.332939	0.166469	−	0.986047i	$-0.446763\pi$
$283$	5.60089	0.332939	0.166469	+	0.986047i	$0.446763\pi$
$284$	−10.9094	−0.647354
$285$	−41.5381	−2.46050
$286$	0.160435	0.00948669
$287$	17.2136	1.01608
$288$	−6.71430	−0.395644
$289$	1.00000	0.0588235
$290$	1.44638	0.0849341
$291$	42.2178	2.47485
$292$	31.2701	1.82994
$293$	−10.8671	−0.634861	−0.317430	−	0.948282i	$-0.602820\pi$
$293$	−10.8671	−0.634861	−0.317430	+	0.948282i	$0.602820\pi$
$294$	3.11868	0.181885
$295$	22.1088	1.28723
$296$	6.58682	0.382851
$297$	0.186535	0.0108239
$298$	3.06650	0.177638
$299$	−34.8921	−2.01786
$300$	−29.2362	−1.68795
$301$	−1.42090	−0.0818995
$302$	−2.54044	−0.146186
$303$	−40.8625	−2.34749
$304$	19.0093	1.09026
$305$	−36.1646	−2.07078
$306$	−0.589245	−0.0336849
$307$	6.86807	0.391982	0.195991	−	0.980606i	$-0.437208\pi$
$307$	6.86807	0.391982	0.195991	+	0.980606i	$0.437208\pi$
$308$	0.259288	0.0147743
$309$	33.3808	1.89897
$310$	7.73130	0.439108
$311$	−19.1873	−1.08801	−0.544005	−	0.839082i	$-0.683093\pi$
$311$	−19.1873	−1.08801	−0.544005	+	0.839082i	$0.683093\pi$
$312$	15.0324	0.851039
$313$	32.9818	1.86424	0.932120	−	0.362149i	$-0.117957\pi$
$313$	32.9818	1.86424	0.932120	+	0.362149i	$0.117957\pi$
$314$	1.47393	0.0831787
$315$	−10.3661	−0.584061
$316$	16.8965	0.950501
$317$	3.10758	0.174539	0.0872694	−	0.996185i	$-0.472186\pi$
$317$	3.10758	0.174539	0.0872694	+	0.996185i	$0.472186\pi$
$318$	−2.05784	−0.115398
$319$	−0.145082	−0.00812304
$320$	21.2997	1.19069
$321$	−27.4546	−1.53237
$322$	2.23929	0.124791
$323$	5.35849	0.298154
$324$	20.8723	1.15957
$325$	41.0534	2.27723
$326$	5.13655	0.284487
$327$	−1.88871	−0.104446
$328$	13.1371	0.725376
$329$	4.82933	0.266249
$330$	−0.203242	−0.0111881
$331$	−19.2887	−1.06020	−0.530100	−	0.847935i	$-0.677846\pi$
$331$	−19.2887	−1.06020	−0.530100	+	0.847935i	$0.677846\pi$
$332$	−14.1521	−0.776699
$333$	12.9500	0.709657
$334$	−2.34519	−0.128323
$335$	42.8722	2.34236
$336$	11.4191	0.622964
$337$	10.9981	0.599106	0.299553	−	0.954080i	$-0.403162\pi$
$337$	10.9981	0.599106	0.299553	+	0.954080i	$0.403162\pi$
$338$	−6.75577	−0.367465
$339$	16.9144	0.918663
$340$	6.58231	0.356976
$341$	−0.775506	−0.0419960
$342$	−3.15746	−0.170736
$343$	−17.0239	−0.919204
$344$	−1.08441	−0.0584675
$345$	44.2020	2.37976
$346$	−5.65269	−0.303890
$347$	−30.2249	−1.62256	−0.811279	−	0.584660i	$-0.801228\pi$
$347$	−30.2249	−1.62256	−0.811279	+	0.584660i	$0.801228\pi$
$348$	−6.66460	−0.357260
$349$	16.9245	0.905948	0.452974	−	0.891524i	$-0.350363\pi$
$349$	16.9245	0.905948	0.452974	+	0.891524i	$0.350363\pi$
$350$	−2.63471	−0.140831
$351$	−12.0323	−0.642238
$352$	0.298753	0.0159236
$353$	−9.93117	−0.528583	−0.264291	−	0.964443i	$-0.585138\pi$
$353$	−9.93117	−0.528583	−0.264291	+	0.964443i	$0.585138\pi$
$354$	4.04535	0.215008
$355$	−19.4063	−1.02998
$356$	8.97230	0.475531
$357$	3.21890	0.170362
$358$	−2.32321	−0.122785
$359$	−21.0256	−1.10969	−0.554844	−	0.831954i	$-0.687222\pi$
$359$	−21.0256	−1.10969	−0.554844	+	0.831954i	$0.687222\pi$
$360$	−7.91121	−0.416957
$361$	9.71338	0.511231
$362$	0.768786	0.0404065
$363$	−24.8989	−1.30686
$364$	−16.7252	−0.876640
$365$	55.6252	2.91156
$366$	−6.61720	−0.345887
$367$	−0.186335	−0.00972663	−0.00486331	−	0.999988i	$-0.501548\pi$
$367$	−0.186335	−0.00972663	−0.00486331	+	0.999988i	$0.501548\pi$
$368$	−20.2284	−1.05448
$369$	25.8282	1.34456
$370$	5.74447	0.298641
$371$	4.67008	0.242458
$372$	−35.6242	−1.84703
$373$	29.2207	1.51299	0.756496	−	0.653998i	$-0.226910\pi$
$373$	29.2207	1.51299	0.756496	+	0.653998i	$0.226910\pi$
$374$	0.0262185	0.00135573
$375$	−13.2481	−0.684130
$376$	3.68566	0.190074
$377$	9.35842	0.481983
$378$	0.772205	0.0397179
$379$	19.4398	0.998556	0.499278	−	0.866442i	$-0.333599\pi$
$379$	19.4398	0.998556	0.499278	+	0.866442i	$0.333599\pi$
$380$	35.2712	1.80938
$381$	−14.2911	−0.732157
$382$	−4.79508	−0.245338
$383$	−8.77224	−0.448240	−0.224120	−	0.974562i	$-0.571951\pi$
$383$	−8.77224	−0.448240	−0.224120	+	0.974562i	$0.571951\pi$
$384$	18.1661	0.927033
$385$	0.461239	0.0235069
$386$	3.31521	0.168740
$387$	−2.13201	−0.108376
$388$	−35.8484	−1.81993
$389$	−1.54350	−0.0782586	−0.0391293	−	0.999234i	$-0.512458\pi$
$389$	−1.54350	−0.0782586	−0.0391293	+	0.999234i	$0.512458\pi$
$390$	13.1100	0.663848
$391$	−5.70214	−0.288370
$392$	−5.40149	−0.272816
$393$	33.4156	1.68559
$394$	3.90227	0.196593
$395$	30.0565	1.51231
$396$	0.389051	0.0195506
$397$	−32.5670	−1.63449	−0.817246	−	0.576290i	$-0.804500\pi$
$397$	−32.5670	−1.63449	−0.817246	+	0.576290i	$0.804500\pi$
$398$	−3.47612	−0.174242
$399$	17.2485	0.863503
$400$	23.8004	1.19002
$401$	20.9485	1.04612	0.523060	−	0.852296i	$-0.324790\pi$
$401$	20.9485	1.04612	0.523060	+	0.852296i	$0.324790\pi$
$402$	7.84452	0.391249
$403$	50.0235	2.49185
$404$	34.6976	1.72627
$405$	37.1290	1.84495
$406$	−0.600600	−0.0298073
$407$	−0.576213	−0.0285618
$408$	2.45662	0.121621
$409$	−7.77288	−0.384344	−0.192172	−	0.981361i	$-0.561553\pi$
$409$	−7.77288	−0.384344	−0.192172	+	0.981361i	$0.561553\pi$
$410$	11.4571	0.565825
$411$	−18.6893	−0.921876
$412$	−28.3447	−1.39644
$413$	−9.18057	−0.451747
$414$	3.35996	0.165133
$415$	−25.1747	−1.23578
$416$	−19.2709	−0.944833
$417$	3.21715	0.157545
$418$	0.140492	0.00687167
$419$	16.2387	0.793313	0.396657	−	0.917967i	$-0.370170\pi$
$419$	16.2387	0.793313	0.396657	+	0.917967i	$0.370170\pi$
$420$	21.1878	1.03386
$421$	6.96350	0.339380	0.169690	−	0.985497i	$-0.445723\pi$
$421$	6.96350	0.339380	0.169690	+	0.985497i	$0.445723\pi$
$422$	0.643521	0.0313261
$423$	7.24620	0.352322
$424$	3.56413	0.173089
$425$	6.70903	0.325436
$426$	−3.55087	−0.172040
$427$	15.0172	0.726731
$428$	23.3125	1.12685
$429$	−1.31502	−0.0634900
$430$	−0.945732	−0.0456073
$431$	−1.85918	−0.0895535	−0.0447768	−	0.998997i	$-0.514258\pi$
$431$	−1.85918	−0.0895535	−0.0447768	+	0.998997i	$0.514258\pi$
$432$	−6.97565	−0.335616
$433$	3.61511	0.173731	0.0868655	−	0.996220i	$-0.472315\pi$
$433$	3.61511	0.173731	0.0868655	+	0.996220i	$0.472315\pi$
$434$	−3.21038	−0.154103
$435$	−11.8554	−0.568424
$436$	1.60376	0.0768062
$437$	−30.5548	−1.46164
$438$	10.1780	0.486324
$439$	−13.4441	−0.641652	−0.320826	−	0.947138i	$-0.603960\pi$
$439$	−13.4441	−0.641652	−0.320826	+	0.947138i	$0.603960\pi$
$440$	0.352010	0.0167814
$441$	−10.6196	−0.505695
$442$	−1.69121	−0.0804426
$443$	32.0177	1.52121	0.760605	−	0.649216i	$-0.224903\pi$
$443$	32.0177	1.52121	0.760605	+	0.649216i	$0.224903\pi$
$444$	−26.4694	−1.25618
$445$	15.9605	0.756600
$446$	1.43977	0.0681753
$447$	−25.1350	−1.18885
$448$	−8.84460	−0.417868
$449$	−35.6387	−1.68190	−0.840948	−	0.541117i	$-0.818002\pi$
$449$	−35.6387	−1.68190	−0.840948	+	0.541117i	$0.818002\pi$
$450$	−3.95327	−0.186359
$451$	−1.14923	−0.0541151
$452$	−14.3625	−0.675555
$453$	20.8231	0.978354
$454$	0.00290183	0.000136190 0
$455$	−29.7519	−1.39479
$456$	13.1637	0.616449
$457$	−20.7438	−0.970353	−0.485176	−	0.874416i	$-0.661245\pi$
$457$	−20.7438	−0.970353	−0.485176	+	0.874416i	$0.661245\pi$
$458$	3.08262	0.144041
$459$	−1.96635	−0.0917813
$460$	−37.5332	−1.75000
$461$	20.7127	0.964684	0.482342	−	0.875983i	$-0.339786\pi$
$461$	20.7127	0.964684	0.482342	+	0.875983i	$0.339786\pi$
$462$	0.0843949	0.00392641
$463$	−16.0902	−0.747775	−0.373888	−	0.927474i	$-0.621975\pi$
$463$	−16.0902	−0.747775	−0.373888	+	0.927474i	$0.621975\pi$
$464$	5.42547	0.251871
$465$	−63.3707	−2.93874
$466$	−0.308171	−0.0142757
$467$	16.5892	0.767657	0.383829	−	0.923404i	$-0.374605\pi$
$467$	16.5892	0.767657	0.383829	+	0.923404i	$0.374605\pi$
$468$	−25.0955	−1.16004
$469$	−17.8024	−0.822041
$470$	3.21433	0.148266
$471$	−12.0813	−0.556676
$472$	−7.00647	−0.322499
$473$	0.0948639	0.00436184
$474$	5.49958	0.252604
$475$	35.9503	1.64951
$476$	−2.73327	−0.125279
$477$	7.00726	0.320840
$478$	1.01857	0.0465882
$479$	7.76731	0.354898	0.177449	−	0.984130i	$-0.443216\pi$
$479$	7.76731	0.354898	0.177449	+	0.984130i	$0.443216\pi$
$480$	24.4127	1.11428
$481$	37.1682	1.69472
$482$	2.65869	0.121100
$483$	−18.3546	−0.835165
$484$	21.1424	0.961020
$485$	−63.7695	−2.89562
$486$	5.16328	0.234211
$487$	−17.9714	−0.814364	−0.407182	−	0.913347i	$-0.633489\pi$
$487$	−17.9714	−0.814364	−0.407182	+	0.913347i	$0.633489\pi$
$488$	11.4609	0.518808
$489$	−42.1024	−1.90394
$490$	−4.71072	−0.212809
$491$	−15.5813	−0.703173	−0.351586	−	0.936155i	$-0.614358\pi$
$491$	−15.5813	−0.703173	−0.351586	+	0.936155i	$0.614358\pi$
$492$	−52.7919	−2.38004
$493$	1.52937	0.0688794
$494$	−9.06232	−0.407733
$495$	0.692070	0.0311062
$496$	29.0007	1.30217
$497$	8.05838	0.361468
$498$	−4.60633	−0.206414
$499$	−37.0119	−1.65688	−0.828439	−	0.560079i	$-0.810771\pi$
$499$	−37.0119	−1.65688	−0.828439	+	0.560079i	$0.810771\pi$
$500$	11.2494	0.503088
$501$	19.2227	0.858806
$502$	4.63188	0.206731
$503$	−22.7932	−1.01630	−0.508148	−	0.861270i	$-0.669670\pi$
$503$	−22.7932	−1.01630	−0.508148	+	0.861270i	$0.669670\pi$
$504$	3.28509	0.146329
$505$	61.7222	2.74660
$506$	−0.149502	−0.00664616
$507$	55.3746	2.45927
$508$	12.1350	0.538405
$509$	30.3931	1.34715	0.673575	−	0.739119i	$-0.264758\pi$
$509$	30.3931	1.34715	0.673575	+	0.739119i	$0.264758\pi$
$510$	2.14245	0.0948695
$511$	−23.0981	−1.02180
$512$	−18.8661	−0.833771
$513$	−10.5366	−0.465204
$514$	1.17923	0.0520135
$515$	−50.4213	−2.22183
$516$	4.35774	0.191839
$517$	−0.322421	−0.0141800
$518$	−2.38536	−0.104807
$519$	46.3331	2.03380
$520$	−22.7062	−0.995731
$521$	−29.5286	−1.29367	−0.646837	−	0.762629i	$-0.723908\pi$
$521$	−29.5286	−1.29367	−0.646837	+	0.762629i	$0.723908\pi$
$522$	−0.901175	−0.0394433
$523$	−35.7803	−1.56456	−0.782281	−	0.622926i	$-0.785944\pi$
$523$	−35.7803	−1.56456	−0.782281	+	0.622926i	$0.785944\pi$
$524$	−28.3742	−1.23953
$525$	21.5957	0.942515
$526$	−0.903353	−0.0393881
$527$	8.17493	0.356106
$528$	−0.762375	−0.0331781
$529$	9.51438	0.413669
$530$	3.10833	0.135017
$531$	−13.7751	−0.597787
$532$	−14.6462	−0.634993
$533$	74.1303	3.21094
$534$	2.92036	0.126377
$535$	41.4698	1.79290
$536$	−13.5865	−0.586849
$537$	19.0425	0.821746
$538$	−6.71566	−0.289533
$539$	0.472520	0.0203529
$540$	−12.9431	−0.556983
$541$	21.8254	0.938348	0.469174	−	0.883106i	$-0.344552\pi$
$541$	21.8254	0.938348	0.469174	+	0.883106i	$0.344552\pi$
$542$	3.89667	0.167376
$543$	−6.30146	−0.270422
$544$	−3.14929	−0.135025
$545$	2.85287	0.122204
$546$	−5.44384	−0.232975
$547$	−23.4493	−1.00262	−0.501309	−	0.865268i	$-0.667148\pi$
$547$	−23.4493	−1.00262	−0.501309	+	0.865268i	$0.667148\pi$
$548$	15.8697	0.677918
$549$	22.5326	0.961668
$550$	0.175901	0.00750044
$551$	8.19512	0.349124
$552$	−14.0080	−0.596219
$553$	−12.4808	−0.530738
$554$	−3.77722	−0.160479
$555$	−47.0854	−1.99866
$556$	−2.73178	−0.115853
$557$	−29.1062	−1.23327	−0.616634	−	0.787250i	$-0.711504\pi$
$557$	−29.1062	−1.23327	−0.616634	+	0.787250i	$0.711504\pi$
$558$	−4.81704	−0.203922
$559$	−6.11913	−0.258812
$560$	−17.2484	−0.728879
$561$	−0.214904	−0.00907325
$562$	4.94192	0.208462
$563$	−7.99581	−0.336983	−0.168492	−	0.985703i	$-0.553890\pi$
$563$	−7.99581	−0.336983	−0.168492	+	0.985703i	$0.553890\pi$
$564$	−14.8110	−0.623654
$565$	−25.5489	−1.07485
$566$	−1.54798	−0.0650664
$567$	−15.4176	−0.647479
$568$	6.15003	0.258049
$569$	−6.55381	−0.274750	−0.137375	−	0.990519i	$-0.543867\pi$
$569$	−6.55381	−0.274750	−0.137375	+	0.990519i	$0.543867\pi$
$570$	11.4803	0.480858
$571$	19.4351	0.813335	0.406668	−	0.913576i	$-0.366691\pi$
$571$	19.4351	0.813335	0.406668	+	0.913576i	$0.366691\pi$
$572$	1.11663	0.0466885
$573$	39.3036	1.64193
$574$	−4.75749	−0.198574
$575$	−38.2558	−1.59538
$576$	−13.2710	−0.552956
$577$	19.0474	0.792955	0.396477	−	0.918044i	$-0.370232\pi$
$577$	19.0474	0.792955	0.396477	+	0.918044i	$0.370232\pi$
$578$	−0.276381	−0.0114959
$579$	−27.1736	−1.12930
$580$	10.0668	0.418001
$581$	10.4537	0.433691
$582$	−11.6682	−0.483662
$583$	−0.311789	−0.0129130
$584$	−17.6281	−0.729455
$585$	−44.6415	−1.84570
$586$	3.00345	0.124071
$587$	21.9106	0.904345	0.452173	−	0.891930i	$-0.350649\pi$
$587$	21.9106	0.904345	0.452173	+	0.891930i	$0.350649\pi$
$588$	21.7061	0.895143
$589$	43.8053	1.80497
$590$	−6.11045	−0.251563
$591$	−31.9855	−1.31571
$592$	21.5480	0.885616
$593$	−27.0749	−1.11183	−0.555916	−	0.831238i	$-0.687633\pi$
$593$	−27.0749	−1.11183	−0.555916	+	0.831238i	$0.687633\pi$
$594$	−0.0515548	−0.00211532
$595$	−4.86211	−0.199327
$596$	21.3429	0.874239
$597$	28.4925	1.16612
$598$	9.64350	0.394352
$599$	−17.1644	−0.701320	−0.350660	−	0.936503i	$-0.614043\pi$
$599$	−17.1644	−0.701320	−0.350660	+	0.936503i	$0.614043\pi$
$600$	16.4815	0.672855
$601$	17.5985	0.717857	0.358929	−	0.933365i	$-0.383142\pi$
$601$	17.5985	0.717857	0.358929	+	0.933365i	$0.383142\pi$
$602$	0.392710	0.0160057
$603$	−26.7118	−1.08779
$604$	−17.6815	−0.719451
$605$	37.6095	1.52904
$606$	11.2936	0.458771
$607$	5.37034	0.217975	0.108988	−	0.994043i	$-0.465239\pi$
$607$	5.37034	0.217975	0.108988	+	0.994043i	$0.465239\pi$
$608$	−16.8754	−0.684388
$609$	4.92290	0.199486
$610$	9.99519	0.404694
$611$	20.7975	0.841377
$612$	−4.10116	−0.165779
$613$	22.5211	0.909620	0.454810	−	0.890589i	$-0.349707\pi$
$613$	22.5211	0.909620	0.454810	+	0.890589i	$0.349707\pi$
$614$	−1.89820	−0.0766052
$615$	−93.9097	−3.78680
$616$	−0.146170	−0.00588937
$617$	−9.03905	−0.363898	−0.181949	−	0.983308i	$-0.558241\pi$
$617$	−9.03905	−0.363898	−0.181949	+	0.983308i	$0.558241\pi$
$618$	−9.22581	−0.371117
$619$	−18.2287	−0.732675	−0.366337	−	0.930482i	$-0.619388\pi$
$619$	−18.2287	−0.732675	−0.366337	+	0.930482i	$0.619388\pi$
$620$	53.8100	2.16106
$621$	11.2124	0.449938
$622$	5.30299	0.212631
$623$	−6.62751	−0.265525
$624$	49.1765	1.96864
$625$	−13.5340	−0.541362
$626$	−9.11553	−0.364330
$627$	−1.15156	−0.0459889
$628$	10.2586	0.409362
$629$	6.07410	0.242190
$630$	2.86498	0.114143
$631$	−37.3994	−1.48885	−0.744423	−	0.667709i	$-0.767275\pi$
$631$	−37.3994	−1.48885	−0.744423	+	0.667709i	$0.767275\pi$
$632$	−9.52515	−0.378890
$633$	−5.27471	−0.209651
$634$	−0.858874	−0.0341102
$635$	21.5866	0.856637
$636$	−14.3226	−0.567927
$637$	−30.4796	−1.20765
$638$	0.0400979	0.00158749
$639$	12.0913	0.478323
$640$	−27.4396	−1.08464
$641$	2.90454	0.114722	0.0573612	−	0.998353i	$-0.481731\pi$
$641$	2.90454	0.114722	0.0573612	+	0.998353i	$0.481731\pi$
$642$	7.58792	0.299471
$643$	17.8710	0.704763	0.352381	−	0.935857i	$-0.385372\pi$
$643$	17.8710	0.704763	0.352381	+	0.935857i	$0.385372\pi$
$644$	15.5855	0.614154
$645$	7.75183	0.305228
$646$	−1.48098	−0.0582685
$647$	−12.6722	−0.498196	−0.249098	−	0.968478i	$-0.580134\pi$
$647$	−12.6722	−0.498196	−0.249098	+	0.968478i	$0.580134\pi$
$648$	−11.7665	−0.462231
$649$	0.612923	0.0240593
$650$	−11.3464	−0.445041
$651$	26.3143	1.03134
$652$	35.7504	1.40010
$653$	−8.27103	−0.323670	−0.161835	−	0.986818i	$-0.551741\pi$
$653$	−8.27103	−0.323670	−0.161835	+	0.986818i	$0.551741\pi$
$654$	0.522003	0.0204119
$655$	−50.4738	−1.97218
$656$	42.9765	1.67795
$657$	−34.6577	−1.35213
$658$	−1.33473	−0.0520333
$659$	5.22192	0.203417	0.101709	−	0.994814i	$-0.467569\pi$
$659$	5.22192	0.203417	0.101709	+	0.994814i	$0.467569\pi$
$660$	−1.41456	−0.0550618
$661$	23.7274	0.922890	0.461445	−	0.887169i	$-0.347331\pi$
$661$	23.7274	0.922890	0.461445	+	0.887169i	$0.347331\pi$
$662$	5.33101	0.207196
$663$	13.8622	0.538364
$664$	7.97806	0.309609
$665$	−26.0536	−1.01031
$666$	−3.57913	−0.138689
$667$	−8.72069	−0.337666
$668$	−16.3226	−0.631539
$669$	−11.8013	−0.456265
$670$	−11.8490	−0.457769
$671$	−1.00259	−0.0387046
$672$	−10.1373	−0.391053
$673$	4.24874	0.163777	0.0818884	−	0.996642i	$-0.473905\pi$
$673$	4.24874	0.163777	0.0818884	+	0.996642i	$0.473905\pi$
$674$	−3.03967	−0.117084
$675$	−13.1923	−0.507772
$676$	−47.0203	−1.80847
$677$	−14.2128	−0.546244	−0.273122	−	0.961979i	$-0.588056\pi$
$677$	−14.2128	−0.546244	−0.273122	+	0.961979i	$0.588056\pi$
$678$	−4.67480	−0.179535
$679$	26.4799	1.01621
$680$	−3.71069	−0.142298
$681$	−0.0237852	−0.000911453 0
$682$	0.214335	0.00820730
$683$	39.2335	1.50123	0.750614	−	0.660740i	$-0.229758\pi$
$683$	39.2335	1.50123	0.750614	+	0.660740i	$0.229758\pi$
$684$	−21.9760	−0.840273
$685$	28.2300	1.07861
$686$	4.70507	0.179641
$687$	−25.2671	−0.964000
$688$	−3.54752	−0.135248
$689$	20.1117	0.766195
$690$	−12.2166	−0.465077
$691$	19.9576	0.759221	0.379611	−	0.925146i	$-0.376058\pi$
$691$	19.9576	0.759221	0.379611	+	0.925146i	$0.376058\pi$
$692$	−39.3428	−1.49559
$693$	−0.287378	−0.0109166
$694$	8.35357	0.317097
$695$	−4.85946	−0.184330
$696$	3.75708	0.142412
$697$	12.1145	0.458870
$698$	−4.67761	−0.177050
$699$	2.52597	0.0955408
$700$	−18.3376	−0.693096
$701$	29.5778	1.11714	0.558569	−	0.829458i	$-0.311351\pi$
$701$	29.5778	1.11714	0.558569	+	0.829458i	$0.311351\pi$
$702$	3.32550	0.125513
$703$	32.5480	1.22757
$704$	0.590493	0.0222550
$705$	−26.3467	−0.992274
$706$	2.74478	0.103301
$707$	−25.6298	−0.963908
$708$	28.1557	1.05816
$709$	−16.5593	−0.621899	−0.310949	−	0.950426i	$-0.600647\pi$
$709$	−16.5593	−0.621899	−0.310949	+	0.950426i	$0.600647\pi$
$710$	5.36354	0.201290
$711$	−18.7269	−0.702315
$712$	−5.05801	−0.189557
$713$	−46.6146	−1.74573
$714$	−0.889643	−0.0332940
$715$	1.98633	0.0742844
$716$	−16.1696	−0.604286
$717$	−8.34883	−0.311793
$718$	5.81107	0.216867
$719$	−16.1128	−0.600906	−0.300453	−	0.953797i	$-0.597138\pi$
$719$	−16.1128	−0.600906	−0.300453	+	0.953797i	$0.597138\pi$
$720$	−25.8805	−0.964511
$721$	20.9372	0.779741
$722$	−2.68459	−0.0999101
$723$	−21.7923	−0.810466
$724$	5.35076	0.198859
$725$	10.2606	0.381069
$726$	6.88158	0.255400
$727$	−7.18835	−0.266601	−0.133301	−	0.991076i	$-0.542558\pi$
$727$	−7.18835	−0.266601	−0.133301	+	0.991076i	$0.542558\pi$
$728$	9.42861	0.349448
$729$	−9.76982	−0.361845
$730$	−15.3737	−0.569008
$731$	−1.00000	−0.0369863
$732$	−46.0558	−1.70227
$733$	−29.2238	−1.07940	−0.539702	−	0.841856i	$-0.681463\pi$
$733$	−29.2238	−1.07940	−0.539702	+	0.841856i	$0.681463\pi$
$734$	0.0514995	0.00190088
$735$	38.6121	1.42423
$736$	17.9577	0.661928
$737$	1.18855	0.0437807
$738$	−7.13842	−0.262769
$739$	−26.3633	−0.969788	−0.484894	−	0.874573i	$-0.661142\pi$
$739$	−26.3633	−0.969788	−0.484894	+	0.874573i	$0.661142\pi$
$740$	39.9816	1.46975
$741$	74.2806	2.72877
$742$	−1.29072	−0.0473838
$743$	32.6723	1.19863	0.599316	−	0.800513i	$-0.295439\pi$
$743$	32.6723	1.19863	0.599316	+	0.800513i	$0.295439\pi$
$744$	20.0827	0.736267
$745$	37.9661	1.39097
$746$	−8.07604	−0.295685
$747$	15.6853	0.573894
$748$	0.182481	0.00667218
$749$	−17.2201	−0.629209
$750$	3.66153	0.133700
$751$	6.16586	0.224995	0.112498	−	0.993652i	$-0.464115\pi$
$751$	6.16586	0.224995	0.112498	+	0.993652i	$0.464115\pi$
$752$	12.0572	0.439681
$753$	−37.9659	−1.38355
$754$	−2.58649	−0.0941942
$755$	−31.4530	−1.14469
$756$	5.37456	0.195471
$757$	11.7457	0.426904	0.213452	−	0.976954i	$-0.431529\pi$
$757$	11.7457	0.426904	0.213452	+	0.976954i	$0.431529\pi$
$758$	−5.37279	−0.195148
$759$	1.22541	0.0444796
$760$	−19.8837	−0.721257
$761$	10.0769	0.365288	0.182644	−	0.983179i	$-0.441534\pi$
$761$	10.0769	0.365288	0.182644	+	0.983179i	$0.441534\pi$
$762$	3.94979	0.143086
$763$	−1.18464	−0.0428868
$764$	−33.3739	−1.20742
$765$	−7.29540	−0.263766
$766$	2.42448	0.0875999
$767$	−39.5362	−1.42757
$768$	23.1817	0.836499
$769$	−50.0718	−1.80564	−0.902818	−	0.430022i	$-0.858506\pi$
$769$	−50.0718	−1.80564	−0.902818	+	0.430022i	$0.858506\pi$
$770$	−0.127477	−0.00459397
$771$	−9.66570	−0.348102
$772$	23.0739	0.830449
$773$	−26.0981	−0.938683	−0.469341	−	0.883017i	$-0.655509\pi$
$773$	−26.0981	−0.938683	−0.469341	+	0.883017i	$0.655509\pi$
$774$	0.589245	0.0211800
$775$	54.8459	1.97012
$776$	20.2091	0.725463
$777$	19.5519	0.701422
$778$	0.426594	0.0152941
$779$	64.9155	2.32584
$780$	91.2455	3.26711
$781$	−0.538002	−0.0192512
$782$	1.57596	0.0563562
$783$	−3.00728	−0.107471
$784$	−17.6703	−0.631082
$785$	18.2486	0.651321
$786$	−9.23543	−0.329417
$787$	23.1253	0.824328	0.412164	−	0.911110i	$-0.364773\pi$
$787$	23.1253	0.824328	0.412164	+	0.911110i	$0.364773\pi$
$788$	27.1598	0.967529
$789$	7.40446	0.263606
$790$	−8.30704	−0.295551
$791$	10.6091	0.377215
$792$	−0.219322	−0.00779328
$793$	64.6714	2.29655
$794$	9.00089	0.319430
$795$	−25.4779	−0.903608
$796$	−24.1938	−0.857528
$797$	−16.9643	−0.600905	−0.300453	−	0.953797i	$-0.597138\pi$
$797$	−16.9643	−0.600905	−0.300453	+	0.953797i	$0.597138\pi$
$798$	−4.76714	−0.168755
$799$	3.39877	0.120240
$800$	−21.1287	−0.747011
$801$	−9.94430	−0.351365
$802$	−5.78977	−0.204444
$803$	1.54210	0.0544195
$804$	54.5980	1.92552
$805$	27.7244	0.977158
$806$	−13.8255	−0.486983
$807$	55.0459	1.93771
$808$	−19.5603	−0.688128
$809$	−12.3272	−0.433402	−0.216701	−	0.976238i	$-0.569530\pi$
$809$	−12.3272	−0.433402	−0.216701	+	0.976238i	$0.569530\pi$
$810$	−10.2617	−0.360560
$811$	6.15505	0.216133	0.108066	−	0.994144i	$-0.465534\pi$
$811$	6.15505	0.216133	0.108066	+	0.994144i	$0.465534\pi$
$812$	−4.18018	−0.146696
$813$	−31.9396	−1.12017
$814$	0.159254	0.00558185
$815$	63.5952	2.22764
$816$	8.03652	0.281335
$817$	−5.35849	−0.187470
$818$	2.14827	0.0751127
$819$	18.5371	0.647740
$820$	79.7415	2.78469
$821$	−23.3288	−0.814181	−0.407090	−	0.913388i	$-0.633457\pi$
$821$	−23.3288	−0.814181	−0.407090	+	0.913388i	$0.633457\pi$
$822$	5.16536	0.180163
$823$	−50.7351	−1.76851	−0.884257	−	0.467001i	$-0.845334\pi$
$823$	−50.7351	−1.76851	−0.884257	+	0.467001i	$0.845334\pi$
$824$	15.9789	0.556652
$825$	−1.44180	−0.0501970
$826$	2.53733	0.0882851
$827$	12.3124	0.428143	0.214072	−	0.976818i	$-0.431327\pi$
$827$	12.3124	0.428143	0.214072	+	0.976818i	$0.431327\pi$
$828$	23.3854	0.812697
$829$	18.1633	0.630839	0.315419	−	0.948952i	$-0.397855\pi$
$829$	18.1633	0.630839	0.315419	+	0.948952i	$0.397855\pi$
$830$	6.95780	0.241509
$831$	30.9605	1.07401
$832$	−38.0893	−1.32051
$833$	−4.98103	−0.172583
$834$	−0.889158	−0.0307890
$835$	−29.0356	−1.00482
$836$	0.977824	0.0338188
$837$	−16.0748	−0.555625
$838$	−4.48807	−0.155038
$839$	14.8283	0.511931	0.255966	−	0.966686i	$-0.417607\pi$
$839$	14.8283	0.511931	0.255966	+	0.966686i	$0.417607\pi$
$840$	−11.9443	−0.412119
$841$	−26.6610	−0.919346
$842$	−1.92458	−0.0663252
$843$	−40.5071	−1.39514
$844$	4.47892	0.154171
$845$	−83.6427	−2.87739
$846$	−2.00271	−0.0688546
$847$	−15.6171	−0.536612
$848$	11.6596	0.400393
$849$	12.6882	0.435459
$850$	−1.85425	−0.0636001
$851$	−34.6354	−1.18728
$852$	−24.7141	−0.846691
$853$	25.3882	0.869275	0.434637	−	0.900606i	$-0.356877\pi$
$853$	25.3882	0.869275	0.434637	+	0.900606i	$0.356877\pi$
$854$	−4.15045	−0.142025
$855$	−39.0923	−1.33693
$856$	−13.1421	−0.449188
$857$	−41.5143	−1.41810	−0.709051	−	0.705157i	$-0.750876\pi$
$857$	−41.5143	−1.41810	−0.709051	+	0.705157i	$0.750876\pi$
$858$	0.363447	0.0124079
$859$	−1.40718	−0.0480125	−0.0240062	−	0.999712i	$-0.507642\pi$
$859$	−1.40718	−0.0480125	−0.0240062	+	0.999712i	$0.507642\pi$
$860$	−6.58231	−0.224455
$861$	38.9955	1.32896
$862$	0.513841	0.0175015
$863$	−42.4205	−1.44401	−0.722004	−	0.691888i	$-0.756779\pi$
$863$	−42.4205	−1.44401	−0.722004	+	0.691888i	$0.756779\pi$
$864$	6.19259	0.210676
$865$	−69.9855	−2.37958
$866$	−0.999146	−0.0339524
$867$	2.26539	0.0769368
$868$	−22.3443	−0.758415
$869$	0.833257	0.0282663
$870$	3.27661	0.111087
$871$	−76.6663	−2.59774
$872$	−0.904098	−0.0306166
$873$	39.7320	1.34473
$874$	8.44476	0.285648
$875$	−8.30951	−0.280913
$876$	70.8391	2.39343
$877$	−43.8141	−1.47950	−0.739748	−	0.672884i	$-0.765055\pi$
$877$	−43.8141	−1.47950	−0.739748	+	0.672884i	$0.765055\pi$
$878$	3.71569	0.125398
$879$	−24.6182	−0.830351
$880$	1.15156	0.0388190
$881$	−53.3283	−1.79668	−0.898338	−	0.439305i	$-0.855225\pi$
$881$	−53.3283	−1.79668	−0.898338	+	0.439305i	$0.855225\pi$
$882$	2.93505	0.0988283
$883$	−28.4937	−0.958888	−0.479444	−	0.877573i	$-0.659162\pi$
$883$	−28.4937	−0.958888	−0.479444	+	0.877573i	$0.659162\pi$
$884$	−11.7708	−0.395896
$885$	50.0852	1.68360
$886$	−8.84908	−0.297291
$887$	16.7193	0.561380	0.280690	−	0.959798i	$-0.409437\pi$
$887$	16.7193	0.561380	0.280690	+	0.959798i	$0.409437\pi$
$888$	14.9217	0.500741
$889$	−8.96371	−0.300633
$890$	−4.41117	−0.147863
$891$	1.02933	0.0344837
$892$	10.0209	0.335523
$893$	18.2123	0.609451
$894$	6.94683	0.232337
$895$	−28.7635	−0.961457
$896$	11.3941	0.380651
$897$	−79.0443	−2.63921
$898$	9.84985	0.328694
$899$	12.5025	0.416982
$900$	−27.5148	−0.917160
$901$	3.28670	0.109496
$902$	0.317625	0.0105758
$903$	−3.21890	−0.107118
$904$	8.09666	0.269291
$905$	9.51827	0.316398
$906$	−5.75510	−0.191200
$907$	29.8986	0.992766	0.496383	−	0.868104i	$-0.334661\pi$
$907$	29.8986	0.992766	0.496383	+	0.868104i	$0.334661\pi$
$908$	0.0201968	0.000670253 0
$909$	−38.4565	−1.27552
$910$	8.22284	0.272585
$911$	21.0607	0.697771	0.348885	−	0.937165i	$-0.386560\pi$
$911$	21.0607	0.697771	0.348885	+	0.937165i	$0.386560\pi$
$912$	43.0636	1.42598
$913$	−0.697918	−0.0230977
$914$	5.73318	0.189637
$915$	−81.9270	−2.70842
$916$	21.4551	0.708895
$917$	20.9590	0.692127
$918$	0.543460	0.0179369
$919$	−19.4695	−0.642240	−0.321120	−	0.947039i	$-0.604059\pi$
$919$	−19.4695	−0.642240	−0.321120	+	0.947039i	$0.604059\pi$
$920$	21.1589	0.697587
$921$	15.5589	0.512683
$922$	−5.72458	−0.188529
$923$	34.7035	1.14228
$924$	0.587390	0.0193237
$925$	40.7513	1.33990
$926$	4.44702	0.146138
$927$	31.4153	1.03182
$928$	−4.81643	−0.158107
$929$	12.9462	0.424752	0.212376	−	0.977188i	$-0.431880\pi$
$929$	12.9462	0.424752	0.212376	+	0.977188i	$0.431880\pi$
$930$	17.5144	0.574321
$931$	−26.6908	−0.874756
$932$	−2.14487	−0.0702577
$933$	−43.4667	−1.42304
$934$	−4.58494	−0.150024
$935$	0.324610	0.0106159
$936$	14.1472	0.462417
$937$	−17.3787	−0.567736	−0.283868	−	0.958863i	$-0.591618\pi$
$937$	−17.3787	−0.567736	−0.283868	+	0.958863i	$0.591618\pi$
$938$	4.92025	0.160652
$939$	74.7167	2.43829
$940$	22.3718	0.729687
$941$	−25.8279	−0.841965	−0.420983	−	0.907069i	$-0.638315\pi$
$941$	−25.8279	−0.841965	−0.420983	+	0.907069i	$0.638315\pi$
$942$	3.33903	0.108792
$943$	−69.0787	−2.24951
$944$	−22.9208	−0.746009
$945$	9.56060	0.311006
$946$	−0.0262185	−0.000852438 0
$947$	−45.0452	−1.46377	−0.731886	−	0.681428i	$-0.761359\pi$
$947$	−45.0452	−1.46377	−0.731886	+	0.681428i	$0.761359\pi$
$948$	38.2772	1.24318
$949$	−99.4720	−3.22900
$950$	−9.93596	−0.322365
$951$	7.03988	0.228284
$952$	1.54084	0.0499390
$953$	43.5333	1.41018	0.705091	−	0.709117i	$-0.250906\pi$
$953$	43.5333	1.41018	0.705091	+	0.709117i	$0.250906\pi$
$954$	−1.93667	−0.0627020
$955$	−59.3676	−1.92109
$956$	7.08924	0.229282
$957$	−0.328668	−0.0106243
$958$	−2.14674	−0.0693579
$959$	−11.7223	−0.378534
$960$	48.2523	1.55734
$961$	35.8295	1.15579
$962$	−10.2726	−0.331201
$963$	−25.8381	−0.832620
$964$	18.5045	0.595991
$965$	41.0454	1.32130
$966$	5.07287	0.163217
$967$	−45.7631	−1.47164	−0.735821	−	0.677176i	$-0.763203\pi$
$967$	−45.7631	−1.47164	−0.735821	+	0.677176i	$0.763203\pi$
$968$	−11.9188	−0.383083
$969$	12.1391	0.389963
$970$	17.6247	0.565893
$971$	19.6852	0.631729	0.315865	−	0.948804i	$-0.397705\pi$
$971$	19.6852	0.631729	0.315865	+	0.948804i	$0.397705\pi$
$972$	35.9365	1.15266
$973$	2.01787	0.0646898
$974$	4.96696	0.159152
$975$	93.0022	2.97845
$976$	37.4928	1.20011
$977$	4.20295	0.134464	0.0672321	−	0.997737i	$-0.478583\pi$
$977$	4.20295	0.134464	0.0672321	+	0.997737i	$0.478583\pi$
$978$	11.6363	0.372088
$979$	0.442473	0.0141415
$980$	−32.7867	−1.04733
$981$	−1.77750	−0.0567513
$982$	4.30636	0.137422
$983$	59.0687	1.88400	0.941999	−	0.335616i	$-0.108944\pi$
$983$	59.0687	1.88400	0.941999	+	0.335616i	$0.108944\pi$
$984$	29.7607	0.948737
$985$	48.3137	1.53940
$986$	−0.422689	−0.0134611
$987$	10.9403	0.348234
$988$	−63.0739	−2.00665
$989$	5.70214	0.181317
$990$	−0.191275	−0.00607911
$991$	23.3442	0.741553	0.370776	−	0.928722i	$-0.379092\pi$
$991$	23.3442	0.741553	0.370776	+	0.928722i	$0.379092\pi$
$992$	−25.7452	−0.817411
$993$	−43.6964	−1.38666
$994$	−2.22718	−0.0706419
$995$	−43.0375	−1.36438
$996$	−32.0601	−1.01586
$997$	31.5167	0.998143	0.499071	−	0.866561i	$-0.333675\pi$
$997$	31.5167	0.998143	0.499071	+	0.866561i	$0.333675\pi$
$998$	10.2294	0.323805
$999$	−11.9438	−0.377885

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.e.1.8	✓	19
3.2	odd	2		6579.2.a.t.1.12		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.e.1.8	✓	19	1.1	even	1	trivial
6579.2.a.t.1.12		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)

\(f(q)\)	\(=\)	\(q-0.276381 q^{2} +2.26539 q^{3} -1.92361 q^{4} -3.42185 q^{5} -0.626111 q^{6} +1.42090 q^{7} +1.08441 q^{8} +2.13201 q^{9} +O(q^{10})\)	\(q-0.276381 q^{2} +2.26539 q^{3} -1.92361 q^{4} -3.42185 q^{5} -0.626111 q^{6} +1.42090 q^{7} +1.08441 q^{8} +2.13201 q^{9} +0.945732 q^{10} -0.0948639 q^{11} -4.35774 q^{12} +6.11913 q^{13} -0.392710 q^{14} -7.75183 q^{15} +3.54752 q^{16} +1.00000 q^{17} -0.589245 q^{18} +5.35849 q^{19} +6.58231 q^{20} +3.21890 q^{21} +0.0262185 q^{22} -5.70214 q^{23} +2.45662 q^{24} +6.70903 q^{25} -1.69121 q^{26} -1.96635 q^{27} -2.73327 q^{28} +1.52937 q^{29} +2.14245 q^{30} +8.17493 q^{31} -3.14929 q^{32} -0.214904 q^{33} -0.276381 q^{34} -4.86211 q^{35} -4.10116 q^{36} +6.07410 q^{37} -1.48098 q^{38} +13.8622 q^{39} -3.71069 q^{40} +12.1145 q^{41} -0.889643 q^{42} -1.00000 q^{43} +0.182481 q^{44} -7.29540 q^{45} +1.57596 q^{46} +3.39877 q^{47} +8.03652 q^{48} -4.98103 q^{49} -1.85425 q^{50} +2.26539 q^{51} -11.7708 q^{52} +3.28670 q^{53} +0.543460 q^{54} +0.324610 q^{55} +1.54084 q^{56} +12.1391 q^{57} -0.422689 q^{58} -6.46108 q^{59} +14.9115 q^{60} +10.5687 q^{61} -2.25939 q^{62} +3.02937 q^{63} -6.22463 q^{64} -20.9387 q^{65} +0.0593953 q^{66} -12.5290 q^{67} -1.92361 q^{68} -12.9176 q^{69} +1.34379 q^{70} +5.67131 q^{71} +2.31197 q^{72} -16.2559 q^{73} -1.67876 q^{74} +15.1986 q^{75} -10.3077 q^{76} -0.134792 q^{77} -3.83125 q^{78} -8.78371 q^{79} -12.1391 q^{80} -10.8506 q^{81} -3.34822 q^{82} +7.35705 q^{83} -6.19193 q^{84} -3.42185 q^{85} +0.276381 q^{86} +3.46463 q^{87} -0.102871 q^{88} -4.66429 q^{89} +2.01631 q^{90} +8.69469 q^{91} +10.9687 q^{92} +18.5194 q^{93} -0.939355 q^{94} -18.3359 q^{95} -7.13437 q^{96} +18.6360 q^{97} +1.37666 q^{98} -0.202250 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) \) 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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