LMFDB - Embedded newform 157.2.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [157,2,Mod(1,157)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(157, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("157.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	157.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:	$1.25365131173$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.24217.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 5x^{3} - x^{2} + 3x + 1 $ x^5 - 5x^3 - x^2 + 3x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.96003$ of defining polynomial
Character	$\chi$	$=$	157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.19993 q^{2} -1.48980 q^{3} -0.560160 q^{4} +3.49147 q^{5} +1.78766 q^{6} -4.39354 q^{7} +3.07202 q^{8} -0.780487 q^{9} +O(q^{10})$	\(q-1.19993 q^{2} -1.48980 q^{3} -0.560160 q^{4} +3.49147 q^{5} +1.78766 q^{6} -4.39354 q^{7} +3.07202 q^{8} -0.780487 q^{9} -4.18953 q^{10} -4.85802 q^{11} +0.834528 q^{12} -1.60813 q^{13} +5.27195 q^{14} -5.20160 q^{15} -2.56590 q^{16} -7.57389 q^{17} +0.936533 q^{18} +3.12831 q^{19} -1.95578 q^{20} +6.54551 q^{21} +5.82930 q^{22} -2.67342 q^{23} -4.57671 q^{24} +7.19034 q^{25} +1.92964 q^{26} +5.63218 q^{27} +2.46108 q^{28} +5.35357 q^{29} +6.24157 q^{30} -3.33249 q^{31} -3.06513 q^{32} +7.23749 q^{33} +9.08817 q^{34} -15.3399 q^{35} +0.437198 q^{36} +0.914311 q^{37} -3.75377 q^{38} +2.39579 q^{39} +10.7259 q^{40} +0.714208 q^{41} -7.85417 q^{42} -1.19419 q^{43} +2.72127 q^{44} -2.72505 q^{45} +3.20793 q^{46} -3.35190 q^{47} +3.82269 q^{48} +12.3032 q^{49} -8.62793 q^{50} +11.2836 q^{51} +0.900807 q^{52} -8.76927 q^{53} -6.75824 q^{54} -16.9616 q^{55} -13.4970 q^{56} -4.66057 q^{57} -6.42392 q^{58} +10.4112 q^{59} +2.91373 q^{60} -1.18460 q^{61} +3.99877 q^{62} +3.42910 q^{63} +8.80976 q^{64} -5.61472 q^{65} -8.68451 q^{66} +10.0009 q^{67} +4.24259 q^{68} +3.98287 q^{69} +18.4069 q^{70} +1.93330 q^{71} -2.39767 q^{72} -12.3110 q^{73} -1.09711 q^{74} -10.7122 q^{75} -1.75235 q^{76} +21.3439 q^{77} -2.87479 q^{78} +2.72287 q^{79} -8.95876 q^{80} -6.04938 q^{81} -0.857002 q^{82} -6.56424 q^{83} -3.66653 q^{84} -26.4440 q^{85} +1.43295 q^{86} -7.97576 q^{87} -14.9239 q^{88} -17.1358 q^{89} +3.26987 q^{90} +7.06536 q^{91} +1.49754 q^{92} +4.96476 q^{93} +4.02206 q^{94} +10.9224 q^{95} +4.56644 q^{96} +4.56049 q^{97} -14.7630 q^{98} +3.79162 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} - 7 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} - 3 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 - 7 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 - 3 * q^7 - 12 * q^8 + 4 * q^9	\( 5 q - 5 q^{2} - 7 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} - 3 q^{7} - 12 q^{8} + 4 q^{9} - q^{10} - 14 q^{11} - 10 q^{12} - 7 q^{13} - 2 q^{14} - 5 q^{15} + 13 q^{16} - 9 q^{17} - 9 q^{18} - 3 q^{19} + 6 q^{21} + 16 q^{22} - 13 q^{23} + 29 q^{24} + 8 q^{25} + 17 q^{26} - 7 q^{27} + 9 q^{28} - 2 q^{29} + 20 q^{30} + 3 q^{31} - 9 q^{32} + 23 q^{33} + 19 q^{34} - 19 q^{35} + 31 q^{36} + 3 q^{37} + 7 q^{38} + 8 q^{39} + 17 q^{40} + 5 q^{41} + 16 q^{42} - 23 q^{43} - 8 q^{44} + 15 q^{45} + 12 q^{46} - 8 q^{47} - 37 q^{48} + 4 q^{49} - 8 q^{50} - 10 q^{51} - 19 q^{52} - 25 q^{53} + 35 q^{54} - 3 q^{55} - 22 q^{56} + 14 q^{57} + 4 q^{58} + 7 q^{59} - 22 q^{60} + 4 q^{61} - 9 q^{62} + q^{63} + 18 q^{64} + 3 q^{65} - 43 q^{66} - 12 q^{67} - 4 q^{68} + 29 q^{69} + 15 q^{70} - 18 q^{71} - 64 q^{72} - 3 q^{73} - 12 q^{74} + 12 q^{75} - 33 q^{76} - q^{77} - 36 q^{78} + 22 q^{79} - 10 q^{80} + 13 q^{81} - 8 q^{82} - 27 q^{83} - 39 q^{84} - 6 q^{85} + 36 q^{86} + 6 q^{87} + 23 q^{88} + 25 q^{89} - 29 q^{90} - 14 q^{91} - 26 q^{92} + 2 q^{93} + q^{94} + 5 q^{95} + 53 q^{96} + 20 q^{97} + 12 q^{98} - 10 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 - 7 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 - 3 * q^7 - 12 * q^8 + 4 * q^9 - q^10 - 14 * q^11 - 10 * q^12 - 7 * q^13 - 2 * q^14 - 5 * q^15 + 13 * q^16 - 9 * q^17 - 9 * q^18 - 3 * q^19 + 6 * q^21 + 16 * q^22 - 13 * q^23 + 29 * q^24 + 8 * q^25 + 17 * q^26 - 7 * q^27 + 9 * q^28 - 2 * q^29 + 20 * q^30 + 3 * q^31 - 9 * q^32 + 23 * q^33 + 19 * q^34 - 19 * q^35 + 31 * q^36 + 3 * q^37 + 7 * q^38 + 8 * q^39 + 17 * q^40 + 5 * q^41 + 16 * q^42 - 23 * q^43 - 8 * q^44 + 15 * q^45 + 12 * q^46 - 8 * q^47 - 37 * q^48 + 4 * q^49 - 8 * q^50 - 10 * q^51 - 19 * q^52 - 25 * q^53 + 35 * q^54 - 3 * q^55 - 22 * q^56 + 14 * q^57 + 4 * q^58 + 7 * q^59 - 22 * q^60 + 4 * q^61 - 9 * q^62 + q^63 + 18 * q^64 + 3 * q^65 - 43 * q^66 - 12 * q^67 - 4 * q^68 + 29 * q^69 + 15 * q^70 - 18 * q^71 - 64 * q^72 - 3 * q^73 - 12 * q^74 + 12 * q^75 - 33 * q^76 - q^77 - 36 * q^78 + 22 * q^79 - 10 * q^80 + 13 * q^81 - 8 * q^82 - 27 * q^83 - 39 * q^84 - 6 * q^85 + 36 * q^86 + 6 * q^87 + 23 * q^88 + 25 * q^89 - 29 * q^90 - 14 * q^91 - 26 * q^92 + 2 * q^93 + q^94 + 5 * q^95 + 53 * q^96 + 20 * q^97 + 12 * q^98 - 10 * 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 $

$2$	−1.19993	−0.848481	−0.424241	−	0.905550i	$-0.639459\pi$
$2$	−1.19993	−0.848481	−0.424241	+	0.905550i	$0.639459\pi$
$3$	−1.48980	−0.860138	−0.430069	−	0.902796i	$-0.641511\pi$
$3$	−1.48980	−0.860138	−0.430069	+	0.902796i	$0.641511\pi$
$4$	−0.560160	−0.280080
$5$	3.49147	1.56143	0.780716	−	0.624886i	$-0.214855\pi$
$5$	3.49147	1.56143	0.780716	+	0.624886i	$0.214855\pi$
$6$	1.78766	0.729811
$7$	−4.39354	−1.66060	−0.830301	−	0.557315i	$-0.811831\pi$
$7$	−4.39354	−1.66060	−0.830301	+	0.557315i	$0.811831\pi$
$8$	3.07202	1.08612
$9$	−0.780487	−0.260162
$10$	−4.18953	−1.32485
$11$	−4.85802	−1.46475	−0.732374	−	0.680902i	$-0.761588\pi$
$11$	−4.85802	−1.46475	−0.732374	+	0.680902i	$0.761588\pi$
$12$	0.834528	0.240907
$13$	−1.60813	−0.446014	−0.223007	−	0.974817i	$-0.571587\pi$
$13$	−1.60813	−0.446014	−0.223007	+	0.974817i	$0.571587\pi$
$14$	5.27195	1.40899
$15$	−5.20160	−1.34305
$16$	−2.56590	−0.641475
$17$	−7.57389	−1.83694	−0.918470	−	0.395492i	$-0.870574\pi$
$17$	−7.57389	−1.83694	−0.918470	+	0.395492i	$0.870574\pi$
$18$	0.936533	0.220743
$19$	3.12831	0.717684	0.358842	−	0.933398i	$-0.383172\pi$
$19$	3.12831	0.717684	0.358842	+	0.933398i	$0.383172\pi$
$20$	−1.95578	−0.437326
$21$	6.54551	1.42835
$22$	5.82930	1.24281
$23$	−2.67342	−0.557446	−0.278723	−	0.960371i	$-0.589911\pi$
$23$	−2.67342	−0.557446	−0.278723	+	0.960371i	$0.589911\pi$
$24$	−4.57671	−0.934216
$25$	7.19034	1.43807
$26$	1.92964	0.378434
$27$	5.63218	1.08391
$28$	2.46108	0.465101
$29$	5.35357	0.994132	0.497066	−	0.867713i	$-0.334411\pi$
$29$	5.35357	0.994132	0.497066	+	0.867713i	$0.334411\pi$
$30$	6.24157	1.13955
$31$	−3.33249	−0.598533	−0.299267	−	0.954170i	$-0.596742\pi$
$31$	−3.33249	−0.598533	−0.299267	+	0.954170i	$0.596742\pi$
$32$	−3.06513	−0.541844
$33$	7.23749	1.25989
$34$	9.08817	1.55861
$35$	−15.3399	−2.59292
$36$	0.437198	0.0728663
$37$	0.914311	0.150312	0.0751559	−	0.997172i	$-0.476055\pi$
$37$	0.914311	0.150312	0.0751559	+	0.997172i	$0.476055\pi$
$38$	−3.75377	−0.608941
$39$	2.39579	0.383633
$40$	10.7259	1.69591
$41$	0.714208	0.111541	0.0557703	−	0.998444i	$-0.482239\pi$
$41$	0.714208	0.111541	0.0557703	+	0.998444i	$0.482239\pi$
$42$	−7.85417	−1.21193
$43$	−1.19419	−0.182113	−0.0910563	−	0.995846i	$-0.529024\pi$
$43$	−1.19419	−0.182113	−0.0910563	+	0.995846i	$0.529024\pi$
$44$	2.72127	0.410247
$45$	−2.72505	−0.406226
$46$	3.20793	0.472983
$47$	−3.35190	−0.488925	−0.244463	−	0.969659i	$-0.578612\pi$
$47$	−3.35190	−0.488925	−0.244463	+	0.969659i	$0.578612\pi$
$48$	3.82269	0.551757
$49$	12.3032	1.75760
$50$	−8.62793	−1.22017
$51$	11.2836	1.58002
$52$	0.900807	0.124919
$53$	−8.76927	−1.20455	−0.602276	−	0.798288i	$-0.705739\pi$
$53$	−8.76927	−1.20455	−0.602276	+	0.798288i	$0.705739\pi$
$54$	−6.75824	−0.919680
$55$	−16.9616	−2.28710
$56$	−13.4970	−1.80362
$57$	−4.66057	−0.617307
$58$	−6.42392	−0.843502
$59$	10.4112	1.35542	0.677711	−	0.735329i	$-0.262972\pi$
$59$	10.4112	1.35542	0.677711	+	0.735329i	$0.262972\pi$
$60$	2.91373	0.376160
$61$	−1.18460	−0.151673	−0.0758363	−	0.997120i	$-0.524163\pi$
$61$	−1.18460	−0.151673	−0.0758363	+	0.997120i	$0.524163\pi$
$62$	3.99877	0.507844
$63$	3.42910	0.432026
$64$	8.80976	1.10122
$65$	−5.61472	−0.696420
$66$	−8.68451	−1.06899
$67$	10.0009	1.22181	0.610903	−	0.791705i	$-0.290806\pi$
$67$	10.0009	1.22181	0.610903	+	0.791705i	$0.290806\pi$
$68$	4.24259	0.514490
$69$	3.98287	0.479481
$70$	18.4069	2.20004
$71$	1.93330	0.229441	0.114721	−	0.993398i	$-0.463403\pi$
$71$	1.93330	0.229441	0.114721	+	0.993398i	$0.463403\pi$
$72$	−2.39767	−0.282569
$73$	−12.3110	−1.44089	−0.720447	−	0.693510i	$-0.756063\pi$
$73$	−12.3110	−1.44089	−0.720447	+	0.693510i	$0.756063\pi$
$74$	−1.09711	−0.127537
$75$	−10.7122	−1.23694
$76$	−1.75235	−0.201009
$77$	21.3439	2.43236
$78$	−2.87479	−0.325506
$79$	2.72287	0.306346	0.153173	−	0.988199i	$-0.451051\pi$
$79$	2.72287	0.306346	0.153173	+	0.988199i	$0.451051\pi$
$80$	−8.95876	−1.00162
$81$	−6.04938	−0.672153
$82$	−0.857002	−0.0946401
$83$	−6.56424	−0.720519	−0.360259	−	0.932852i	$-0.617312\pi$
$83$	−6.56424	−0.720519	−0.360259	+	0.932852i	$0.617312\pi$
$84$	−3.66653	−0.400051
$85$	−26.4440	−2.86825
$86$	1.43295	0.154519
$87$	−7.97576	−0.855091
$88$	−14.9239	−1.59090
$89$	−17.1358	−1.81639	−0.908197	−	0.418544i	$-0.862541\pi$
$89$	−17.1358	−1.81639	−0.908197	+	0.418544i	$0.862541\pi$
$90$	3.26987	0.344675
$91$	7.06536	0.740651
$92$	1.49754	0.156130
$93$	4.96476	0.514821
$94$	4.02206	0.414844
$95$	10.9224	1.12061
$96$	4.56644	0.466060
$97$	4.56049	0.463048	0.231524	−	0.972829i	$-0.425629\pi$
$97$	4.56049	0.463048	0.231524	+	0.972829i	$0.425629\pi$
$98$	−14.7630	−1.49129
$99$	3.79162	0.381073
$100$	−4.02774	−0.402774
$101$	−5.36057	−0.533397	−0.266698	−	0.963780i	$-0.585933\pi$
$101$	−5.36057	−0.533397	−0.266698	+	0.963780i	$0.585933\pi$
$102$	−13.5396	−1.34062
$103$	−0.276535	−0.0272478	−0.0136239	−	0.999907i	$-0.504337\pi$
$103$	−0.276535	−0.0272478	−0.0136239	+	0.999907i	$0.504337\pi$
$104$	−4.94019	−0.484426
$105$	22.8534	2.23027
$106$	10.5225	1.02204
$107$	−15.0312	−1.45312	−0.726560	−	0.687103i	$-0.758882\pi$
$107$	−15.0312	−1.45312	−0.726560	+	0.687103i	$0.758882\pi$
$108$	−3.15492	−0.303582
$109$	10.3208	0.988550	0.494275	−	0.869305i	$-0.335434\pi$
$109$	10.3208	0.988550	0.494275	+	0.869305i	$0.335434\pi$
$110$	20.3528	1.94056
$111$	−1.36214	−0.129289
$112$	11.2734	1.06524
$113$	16.6913	1.57019	0.785094	−	0.619376i	$-0.212614\pi$
$113$	16.6913	1.57019	0.785094	+	0.619376i	$0.212614\pi$
$114$	5.59237	0.523773
$115$	−9.33416	−0.870415
$116$	−2.99885	−0.278436
$117$	1.25512	0.116036
$118$	−12.4927	−1.15005
$119$	33.2762	3.05042
$120$	−15.9794	−1.45871
$121$	12.6004	1.14549
$122$	1.42144	0.128691
$123$	−1.06403	−0.0959403
$124$	1.86673	0.167637
$125$	7.64751	0.684014
$126$	−4.11469	−0.366566
$127$	−3.72445	−0.330492	−0.165246	−	0.986252i	$-0.552842\pi$
$127$	−3.72445	−0.330492	−0.165246	+	0.986252i	$0.552842\pi$
$128$	−4.44086	−0.392520
$129$	1.77911	0.156642
$130$	6.73729	0.590899
$131$	9.93987	0.868450	0.434225	−	0.900804i	$-0.357022\pi$
$131$	9.93987	0.868450	0.434225	+	0.900804i	$0.357022\pi$
$132$	−4.05415	−0.352869
$133$	−13.7444	−1.19179
$134$	−12.0004	−1.03668
$135$	19.6646	1.69246
$136$	−23.2672	−1.99514
$137$	−1.58905	−0.135762	−0.0678808	−	0.997693i	$-0.521624\pi$
$137$	−1.58905	−0.135762	−0.0678808	+	0.997693i	$0.521624\pi$
$138$	−4.77918	−0.406831
$139$	0.228170	0.0193531	0.00967657	−	0.999953i	$-0.496920\pi$
$139$	0.228170	0.0193531	0.00967657	+	0.999953i	$0.496920\pi$
$140$	8.59279	0.726224
$141$	4.99367	0.420543
$142$	−2.31984	−0.194676
$143$	7.81231	0.653298
$144$	2.00265	0.166888
$145$	18.6918	1.55227
$146$	14.7724	1.22257
$147$	−18.3293	−1.51178
$148$	−0.512160	−0.0420993
$149$	−20.0483	−1.64242	−0.821210	−	0.570626i	$-0.806701\pi$
$149$	−20.0483	−1.64242	−0.821210	+	0.570626i	$0.806701\pi$
$150$	12.8539	1.04952
$151$	−3.04930	−0.248148	−0.124074	−	0.992273i	$-0.539596\pi$
$151$	−3.04930	−0.248148	−0.124074	+	0.992273i	$0.539596\pi$
$152$	9.61024	0.779493
$153$	5.91133	0.477903
$154$	−25.6113	−2.06381
$155$	−11.6353	−0.934569
$156$	−1.34202	−0.107448
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−3.26726	−0.259929
$159$	13.0645	1.03608
$160$	−10.7018	−0.846052
$161$	11.7458	0.925697
$162$	7.25885	0.570309
$163$	1.23328	0.0965980	0.0482990	−	0.998833i	$-0.484620\pi$
$163$	1.23328	0.0965980	0.0482990	+	0.998833i	$0.484620\pi$
$164$	−0.400071	−0.0312403
$165$	25.2695	1.96723
$166$	7.87665	0.611346
$167$	−19.3465	−1.49708	−0.748539	−	0.663090i	$-0.769245\pi$
$167$	−19.3465	−1.49708	−0.748539	+	0.663090i	$0.769245\pi$
$168$	20.1079	1.55136
$169$	−10.4139	−0.801072
$170$	31.7310	2.43366
$171$	−2.44161	−0.186714
$172$	0.668938	0.0510060
$173$	−5.45051	−0.414395	−0.207197	−	0.978299i	$-0.566434\pi$
$173$	−5.45051	−0.414395	−0.207197	+	0.978299i	$0.566434\pi$
$174$	9.57038	0.725529
$175$	−31.5911	−2.38806
$176$	12.4652	0.939600
$177$	−15.5106	−1.16585
$178$	20.5618	1.54118
$179$	−5.27777	−0.394479	−0.197239	−	0.980355i	$-0.563198\pi$
$179$	−5.27777	−0.394479	−0.197239	+	0.980355i	$0.563198\pi$
$180$	1.52646	0.113776
$181$	0.630347	0.0468533	0.0234267	−	0.999726i	$-0.492542\pi$
$181$	0.630347	0.0468533	0.0234267	+	0.999726i	$0.492542\pi$
$182$	−8.47796	−0.628428
$183$	1.76482	0.130459
$184$	−8.21280	−0.605456
$185$	3.19229	0.234702
$186$	−5.95738	−0.436816
$187$	36.7941	2.69065
$188$	1.87760	0.136938
$189$	−24.7452	−1.79995
$190$	−13.1061	−0.950820
$191$	−20.7882	−1.50418	−0.752089	−	0.659061i	$-0.770954\pi$
$191$	−20.7882	−1.50418	−0.752089	+	0.659061i	$0.770954\pi$
$192$	−13.1248	−0.947201
$193$	9.35686	0.673522	0.336761	−	0.941590i	$-0.390669\pi$
$193$	9.35686	0.673522	0.336761	+	0.941590i	$0.390669\pi$
$194$	−5.47229	−0.392887
$195$	8.36482	0.599017
$196$	−6.89175	−0.492268
$197$	−19.2688	−1.37285	−0.686423	−	0.727202i	$-0.740820\pi$
$197$	−19.2688	−1.37285	−0.686423	+	0.727202i	$0.740820\pi$
$198$	−4.54970	−0.323333
$199$	12.3993	0.878960	0.439480	−	0.898252i	$-0.355163\pi$
$199$	12.3993	0.878960	0.439480	+	0.898252i	$0.355163\pi$
$200$	22.0889	1.56192
$201$	−14.8994	−1.05092
$202$	6.43233	0.452577
$203$	−23.5211	−1.65086
$204$	−6.32062	−0.442532
$205$	2.49363	0.174163
$206$	0.331823	0.0231192
$207$	2.08657	0.145027
$208$	4.12629	0.286107
$209$	−15.1974	−1.05123
$210$	−27.4226	−1.89234
$211$	−22.9637	−1.58088	−0.790442	−	0.612537i	$-0.790149\pi$
$211$	−22.9637	−1.58088	−0.790442	+	0.612537i	$0.790149\pi$
$212$	4.91219	0.337371
$213$	−2.88024	−0.197351
$214$	18.0364	1.23295
$215$	−4.16948	−0.284356
$216$	17.3022	1.17726
$217$	14.6414	0.993925
$218$	−12.3842	−0.838766
$219$	18.3410	1.23937
$220$	9.50122	0.640572
$221$	12.1798	0.819300
$222$	1.63448	0.109699
$223$	14.1771	0.949371	0.474685	−	0.880156i	$-0.342562\pi$
$223$	14.1771	0.949371	0.474685	+	0.880156i	$0.342562\pi$
$224$	13.4668	0.899787
$225$	−5.61197	−0.374132
$226$	−20.0285	−1.33228
$227$	3.27473	0.217352	0.108676	−	0.994077i	$-0.465339\pi$
$227$	3.27473	0.217352	0.108676	+	0.994077i	$0.465339\pi$
$228$	2.61066	0.172895
$229$	−8.79258	−0.581030	−0.290515	−	0.956870i	$-0.593827\pi$
$229$	−8.79258	−0.581030	−0.290515	+	0.956870i	$0.593827\pi$
$230$	11.2004	0.738530
$231$	−31.7982	−2.09217
$232$	16.4463	1.07975
$233$	15.2646	1.00002	0.500009	−	0.866020i	$-0.333330\pi$
$233$	15.2646	1.00002	0.500009	+	0.866020i	$0.333330\pi$
$234$	−1.50606	−0.0984544
$235$	−11.7031	−0.763423
$236$	−5.83193	−0.379626
$237$	−4.05653	−0.263500
$238$	−39.9292	−2.58823
$239$	−1.19394	−0.0772295	−0.0386147	−	0.999254i	$-0.512295\pi$
$239$	−1.19394	−0.0772295	−0.0386147	+	0.999254i	$0.512295\pi$
$240$	13.3468	0.861531
$241$	−4.19649	−0.270320	−0.135160	−	0.990824i	$-0.543155\pi$
$241$	−4.19649	−0.270320	−0.135160	+	0.990824i	$0.543155\pi$
$242$	−15.1196	−0.971925
$243$	−7.88416	−0.505769
$244$	0.663566	0.0424805
$245$	42.9562	2.74437
$246$	1.27676	0.0814035
$247$	−5.03072	−0.320097
$248$	−10.2375	−0.650081
$249$	9.77942	0.619746
$250$	−9.17651	−0.580373
$251$	−11.1261	−0.702272	−0.351136	−	0.936324i	$-0.614205\pi$
$251$	−11.1261	−0.702272	−0.351136	+	0.936324i	$0.614205\pi$
$252$	−1.92085	−0.121002
$253$	12.9875	0.816519
$254$	4.46909	0.280416
$255$	39.3963	2.46710
$256$	−12.2908	−0.768174
$257$	−5.13276	−0.320173	−0.160086	−	0.987103i	$-0.551177\pi$
$257$	−5.13276	−0.320173	−0.160086	+	0.987103i	$0.551177\pi$
$258$	−2.13481	−0.132908
$259$	−4.01706	−0.249608
$260$	3.14514	0.195053
$261$	−4.17839	−0.258636
$262$	−11.9272	−0.736864
$263$	2.10618	0.129872	0.0649362	−	0.997889i	$-0.479316\pi$
$263$	2.10618	0.129872	0.0649362	+	0.997889i	$0.479316\pi$
$264$	22.2337	1.36839
$265$	−30.6176	−1.88082
$266$	16.4923	1.01121
$267$	25.5290	1.56235
$268$	−5.60211	−0.342203
$269$	22.5264	1.37346	0.686729	−	0.726913i	$-0.259046\pi$
$269$	22.5264	1.37346	0.686729	+	0.726913i	$0.259046\pi$
$270$	−23.5962	−1.43602
$271$	4.16244	0.252850	0.126425	−	0.991976i	$-0.459650\pi$
$271$	4.16244	0.252850	0.126425	+	0.991976i	$0.459650\pi$
$272$	19.4339	1.17835
$273$	−10.5260	−0.637062
$274$	1.90675	0.115191
$275$	−34.9308	−2.10641
$276$	−2.23104	−0.134293
$277$	5.07793	0.305103	0.152552	−	0.988295i	$-0.451251\pi$
$277$	5.07793	0.305103	0.152552	+	0.988295i	$0.451251\pi$
$278$	−0.273789	−0.0164208
$279$	2.60097	0.155716
$280$	−47.1245	−2.81623
$281$	−22.7193	−1.35532	−0.677659	−	0.735376i	$-0.737005\pi$
$281$	−22.7193	−1.35532	−0.677659	+	0.735376i	$0.737005\pi$
$282$	−5.99207	−0.356823
$283$	28.7587	1.70953	0.854764	−	0.519018i	$-0.173702\pi$
$283$	28.7587	1.70953	0.854764	+	0.519018i	$0.173702\pi$
$284$	−1.08296	−0.0642618
$285$	−16.2722	−0.963883
$286$	−9.37425	−0.554311
$287$	−3.13790	−0.185224
$288$	2.39230	0.140967
$289$	40.3639	2.37434
$290$	−22.4289	−1.31707
$291$	−6.79423	−0.398285
$292$	6.89613	0.403566
$293$	15.8247	0.924491	0.462246	−	0.886752i	$-0.347044\pi$
$293$	15.8247	0.924491	0.462246	+	0.886752i	$0.347044\pi$
$294$	21.9940	1.28271
$295$	36.3503	2.11640
$296$	2.80878	0.163257
$297$	−27.3613	−1.58766
$298$	24.0566	1.39356
$299$	4.29919	0.248629
$300$	6.00054	0.346441
$301$	5.24673	0.302416
$302$	3.65895	0.210549
$303$	7.98620	0.458795
$304$	−8.02694	−0.460377
$305$	−4.13600	−0.236827
$306$	−7.09320	−0.405491
$307$	−24.1218	−1.37670	−0.688352	−	0.725377i	$-0.741666\pi$
$307$	−24.1218	−1.37670	−0.688352	+	0.725377i	$0.741666\pi$
$308$	−11.9560	−0.681256
$309$	0.411982	0.0234369
$310$	13.9616	0.792964
$311$	15.3180	0.868605	0.434303	−	0.900767i	$-0.356995\pi$
$311$	15.3180	0.868605	0.434303	+	0.900767i	$0.356995\pi$
$312$	7.35992	0.416673
$313$	0.0990233	0.00559713	0.00279856	−	0.999996i	$-0.499109\pi$
$313$	0.0990233	0.00559713	0.00279856	+	0.999996i	$0.499109\pi$
$314$	1.19993	0.0677162
$315$	11.9726	0.674580
$316$	−1.52524	−0.0858014
$317$	−9.35761	−0.525576	−0.262788	−	0.964854i	$-0.584642\pi$
$317$	−9.35761	−0.525576	−0.262788	+	0.964854i	$0.584642\pi$
$318$	−15.6765	−0.879095
$319$	−26.0077	−1.45615
$320$	30.7590	1.71948
$321$	22.3935	1.24988
$322$	−14.0941	−0.785436
$323$	−23.6935	−1.31834
$324$	3.38862	0.188257
$325$	−11.5630	−0.641398
$326$	−1.47985	−0.0819616
$327$	−15.3759	−0.850290
$328$	2.19406	0.121147
$329$	14.7267	0.811910
$330$	−30.3217	−1.66915
$331$	−19.7599	−1.08610	−0.543052	−	0.839699i	$-0.682731\pi$
$331$	−19.7599	−1.08610	−0.543052	+	0.839699i	$0.682731\pi$
$332$	3.67702	0.201803
$333$	−0.713609	−0.0391055
$334$	23.2145	1.27024
$335$	34.9179	1.90777
$336$	−16.7951	−0.916249
$337$	−1.99683	−0.108774	−0.0543872	−	0.998520i	$-0.517321\pi$
$337$	−1.99683	−0.108774	−0.0543872	+	0.998520i	$0.517321\pi$
$338$	12.4960	0.679694
$339$	−24.8668	−1.35058
$340$	14.8129	0.803340
$341$	16.1893	0.876701
$342$	2.92977	0.158424
$343$	−23.2998	−1.25807
$344$	−3.66858	−0.197797
$345$	13.9061	0.748677
$346$	6.54025	0.351606
$347$	−26.3061	−1.41219	−0.706093	−	0.708119i	$-0.749544\pi$
$347$	−26.3061	−1.41219	−0.706093	+	0.708119i	$0.749544\pi$
$348$	4.46770	0.239494
$349$	−3.89923	−0.208721	−0.104360	−	0.994540i	$-0.533280\pi$
$349$	−3.89923	−0.208721	−0.104360	+	0.994540i	$0.533280\pi$
$350$	37.9072	2.02622
$351$	−9.05725	−0.483440
$352$	14.8905	0.793665
$353$	13.9238	0.741090	0.370545	−	0.928815i	$-0.379171\pi$
$353$	13.9238	0.741090	0.370545	+	0.928815i	$0.379171\pi$
$354$	18.6117	0.989201
$355$	6.75007	0.358257
$356$	9.59880	0.508735
$357$	−49.5750	−2.62379
$358$	6.33297	0.334708
$359$	7.05080	0.372127	0.186064	−	0.982538i	$-0.440427\pi$
$359$	7.05080	0.372127	0.186064	+	0.982538i	$0.440427\pi$
$360$	−8.37140	−0.441212
$361$	−9.21367	−0.484930
$362$	−0.756374	−0.0397541
$363$	−18.7721	−0.985278
$364$	−3.95773	−0.207441
$365$	−42.9835	−2.24986
$366$	−2.11767	−0.110692
$367$	30.0490	1.56855	0.784273	−	0.620416i	$-0.213036\pi$
$367$	30.0490	1.56855	0.784273	+	0.620416i	$0.213036\pi$
$368$	6.85973	0.357588
$369$	−0.557430	−0.0290187
$370$	−3.83053	−0.199140
$371$	38.5281	2.00028
$372$	−2.78106	−0.144191
$373$	23.7124	1.22778	0.613890	−	0.789392i	$-0.289604\pi$
$373$	23.7124	1.22778	0.613890	+	0.789392i	$0.289604\pi$
$374$	−44.1505	−2.28297
$375$	−11.3933	−0.588347
$376$	−10.2971	−0.531033
$377$	−8.60920	−0.443397
$378$	29.6926	1.52722
$379$	14.0205	0.720186	0.360093	−	0.932916i	$-0.382745\pi$
$379$	14.0205	0.720186	0.360093	+	0.932916i	$0.382745\pi$
$380$	−6.11829	−0.313861
$381$	5.54870	0.284268
$382$	24.9444	1.27627
$383$	20.7044	1.05795	0.528973	−	0.848639i	$-0.322577\pi$
$383$	20.7044	1.05795	0.528973	+	0.848639i	$0.322577\pi$
$384$	6.61600	0.337622
$385$	74.5216	3.79797
$386$	−11.2276	−0.571470
$387$	0.932052	0.0473788
$388$	−2.55460	−0.129690
$389$	1.12757	0.0571698	0.0285849	−	0.999591i	$-0.490900\pi$
$389$	1.12757	0.0571698	0.0285849	+	0.999591i	$0.490900\pi$
$390$	−10.0372	−0.508255
$391$	20.2482	1.02400
$392$	37.7957	1.90897
$393$	−14.8084	−0.746987
$394$	23.1213	1.16483
$395$	9.50680	0.478339
$396$	−2.12392	−0.106731
$397$	−11.3913	−0.571712	−0.285856	−	0.958273i	$-0.592278\pi$
$397$	−11.3913	−0.571712	−0.285856	+	0.958273i	$0.592278\pi$
$398$	−14.8783	−0.745781
$399$	20.4764	1.02510
$400$	−18.4497	−0.922486
$401$	23.6158	1.17932	0.589658	−	0.807653i	$-0.299263\pi$
$401$	23.6158	1.17932	0.589658	+	0.807653i	$0.299263\pi$
$402$	17.8783	0.891688
$403$	5.35906	0.266954
$404$	3.00278	0.149394
$405$	−21.1212	−1.04952
$406$	28.2238	1.40072
$407$	−4.44174	−0.220169
$408$	34.6635	1.71610
$409$	3.24341	0.160376	0.0801880	−	0.996780i	$-0.474448\pi$
$409$	3.24341	0.160376	0.0801880	+	0.996780i	$0.474448\pi$
$410$	−2.99220	−0.147774
$411$	2.36737	0.116774
$412$	0.154904	0.00763155
$413$	−45.7420	−2.25081
$414$	−2.50375	−0.123052
$415$	−22.9188	−1.12504
$416$	4.92911	0.241670
$417$	−0.339928	−0.0166464
$418$	18.2359	0.891946
$419$	26.9228	1.31527	0.657633	−	0.753338i	$-0.271558\pi$
$419$	26.9228	1.31527	0.657633	+	0.753338i	$0.271558\pi$
$420$	−12.8016	−0.624653
$421$	−5.26481	−0.256591	−0.128296	−	0.991736i	$-0.540951\pi$
$421$	−5.26481	−0.256591	−0.128296	+	0.991736i	$0.540951\pi$
$422$	27.5549	1.34135
$423$	2.61612	0.127200
$424$	−26.9394	−1.30829
$425$	−54.4589	−2.64164
$426$	3.45610	0.167449
$427$	5.20459	0.251868
$428$	8.41987	0.406990
$429$	−11.6388	−0.561926
$430$	5.00310	0.241271
$431$	8.49664	0.409269	0.204634	−	0.978838i	$-0.434399\pi$
$431$	8.49664	0.409269	0.204634	+	0.978838i	$0.434399\pi$
$432$	−14.4516	−0.695304
$433$	−8.03435	−0.386106	−0.193053	−	0.981188i	$-0.561839\pi$
$433$	−8.03435	−0.386106	−0.193053	+	0.981188i	$0.561839\pi$
$434$	−17.5687	−0.843327
$435$	−27.8471	−1.33517
$436$	−5.78128	−0.276873
$437$	−8.36329	−0.400070
$438$	−22.0080	−1.05158
$439$	−16.3867	−0.782097	−0.391048	−	0.920370i	$-0.627887\pi$
$439$	−16.3867	−0.782097	−0.391048	+	0.920370i	$0.627887\pi$
$440$	−52.1065	−2.48408
$441$	−9.60248	−0.457261
$442$	−14.6149	−0.695160
$443$	−26.5101	−1.25953	−0.629766	−	0.776785i	$-0.716849\pi$
$443$	−26.5101	−1.25953	−0.629766	+	0.776785i	$0.716849\pi$
$444$	0.763018	0.0362112
$445$	−59.8291	−2.83617
$446$	−17.0116	−0.805523
$447$	29.8680	1.41271
$448$	−38.7060	−1.82869
$449$	−21.2585	−1.00325	−0.501625	−	0.865085i	$-0.667264\pi$
$449$	−21.2585	−1.00325	−0.501625	+	0.865085i	$0.667264\pi$
$450$	6.73399	0.317444
$451$	−3.46964	−0.163379
$452$	−9.34981	−0.439778
$453$	4.54285	0.213442
$454$	−3.92946	−0.184419
$455$	24.6685	1.15648
$456$	−14.3174	−0.670472
$457$	0.823900	0.0385404	0.0192702	−	0.999814i	$-0.493866\pi$
$457$	0.823900	0.0385404	0.0192702	+	0.999814i	$0.493866\pi$
$458$	10.5505	0.492993
$459$	−42.6575	−1.99108
$460$	5.22862	0.243786
$461$	32.0960	1.49486	0.747430	−	0.664341i	$-0.231288\pi$
$461$	32.0960	1.49486	0.747430	+	0.664341i	$0.231288\pi$
$462$	38.1557	1.77517
$463$	−1.12165	−0.0521275	−0.0260638	−	0.999660i	$-0.508297\pi$
$463$	−1.12165	−0.0521275	−0.0260638	+	0.999660i	$0.508297\pi$
$464$	−13.7367	−0.637711
$465$	17.3343	0.803858
$466$	−18.3165	−0.848496
$467$	23.0403	1.06618	0.533090	−	0.846059i	$-0.321031\pi$
$467$	23.0403	1.06618	0.533090	+	0.846059i	$0.321031\pi$
$468$	−0.703069	−0.0324994
$469$	−43.9394	−2.02893
$470$	14.0429	0.647750
$471$	1.48980	0.0686465
$472$	31.9834	1.47215
$473$	5.80141	0.266749
$474$	4.86757	0.223575
$475$	22.4936	1.03208
$476$	−18.6400	−0.854362
$477$	6.84430	0.313379
$478$	1.43265	0.0655277
$479$	11.0126	0.503176	0.251588	−	0.967834i	$-0.419047\pi$
$479$	11.0126	0.503176	0.251588	+	0.967834i	$0.419047\pi$
$480$	15.9436	0.727722
$481$	−1.47033	−0.0670411
$482$	5.03551	0.229361
$483$	−17.4989	−0.796227
$484$	−7.05822	−0.320828
$485$	15.9228	0.723018
$486$	9.46047	0.429136
$487$	9.92653	0.449814	0.224907	−	0.974380i	$-0.427792\pi$
$487$	9.92653	0.449814	0.224907	+	0.974380i	$0.427792\pi$
$488$	−3.63912	−0.164735
$489$	−1.83734	−0.0830876
$490$	−51.5446	−2.32855
$491$	−36.2658	−1.63665	−0.818327	−	0.574754i	$-0.805098\pi$
$491$	−36.2658	−1.63665	−0.818327	+	0.574754i	$0.805098\pi$
$492$	0.596026	0.0268709
$493$	−40.5473	−1.82616
$494$	6.03652	0.271596
$495$	13.2383	0.595019
$496$	8.55085	0.383944
$497$	−8.49405	−0.381010
$498$	−11.7347	−0.525842
$499$	−24.8563	−1.11272	−0.556361	−	0.830941i	$-0.687803\pi$
$499$	−24.8563	−1.11272	−0.556361	+	0.830941i	$0.687803\pi$
$500$	−4.28383	−0.191579
$501$	28.8225	1.28769
$502$	13.3506	0.595865
$503$	17.3216	0.772333	0.386166	−	0.922429i	$-0.373799\pi$
$503$	17.3216	0.772333	0.386166	+	0.922429i	$0.373799\pi$
$504$	10.5343	0.469234
$505$	−18.7163	−0.832863
$506$	−15.5842	−0.692801
$507$	15.5147	0.689032
$508$	2.08629	0.0925640
$509$	2.30382	0.102115	0.0510575	−	0.998696i	$-0.483741\pi$
$509$	2.30382	0.102115	0.0510575	+	0.998696i	$0.483741\pi$
$510$	−47.2730	−2.09328
$511$	54.0889	2.39275
$512$	23.6298	1.04430
$513$	17.6192	0.777907
$514$	6.15897	0.271660
$515$	−0.965512	−0.0425455
$516$	−0.996586	−0.0438722
$517$	16.2836	0.716152
$518$	4.82021	0.211788
$519$	8.12018	0.356437
$520$	−17.2485	−0.756398
$521$	−6.47817	−0.283814	−0.141907	−	0.989880i	$-0.545323\pi$
$521$	−6.47817	−0.283814	−0.141907	+	0.989880i	$0.545323\pi$
$522$	5.01379	0.219448
$523$	8.34387	0.364852	0.182426	−	0.983220i	$-0.441605\pi$
$523$	8.34387	0.364852	0.182426	+	0.983220i	$0.441605\pi$
$524$	−5.56791	−0.243235
$525$	47.0644	2.05406
$526$	−2.52727	−0.110194
$527$	25.2399	1.09947
$528$	−18.5707	−0.808186
$529$	−15.8528	−0.689253
$530$	36.7391	1.59584
$531$	−8.12580	−0.352630
$532$	7.69904	0.333796
$533$	−1.14854	−0.0497486
$534$	−30.6331	−1.32562
$535$	−52.4809	−2.26895
$536$	30.7230	1.32703
$537$	7.86283	0.339306
$538$	−27.0302	−1.16535
$539$	−59.7691	−2.57444
$540$	−11.0153	−0.474023
$541$	0.0868394	0.00373352	0.00186676	−	0.999998i	$-0.499406\pi$
$541$	0.0868394	0.00373352	0.00186676	+	0.999998i	$0.499406\pi$
$542$	−4.99465	−0.214539
$543$	−0.939092	−0.0403003
$544$	23.2150	0.995334
$545$	36.0346	1.54355
$546$	12.6305	0.540535
$547$	−3.01441	−0.128887	−0.0644434	−	0.997921i	$-0.520527\pi$
$547$	−3.01441	−0.128887	−0.0644434	+	0.997921i	$0.520527\pi$
$548$	0.890121	0.0380241
$549$	0.924567	0.0394595
$550$	41.9147	1.78725
$551$	16.7476	0.713473
$552$	12.2355	0.520776
$553$	−11.9630	−0.508719
$554$	−6.09318	−0.258874
$555$	−4.75588	−0.201876
$556$	−0.127812	−0.00542042
$557$	32.8726	1.39286	0.696429	−	0.717625i	$-0.254771\pi$
$557$	32.8726	1.39286	0.696429	+	0.717625i	$0.254771\pi$
$558$	−3.12099	−0.132122
$559$	1.92041	0.0812247
$560$	39.3607	1.66329
$561$	−54.8160	−2.31433
$562$	27.2616	1.14996
$563$	−44.4066	−1.87151	−0.935757	−	0.352645i	$-0.885282\pi$
$563$	−44.4066	−1.87151	−0.935757	+	0.352645i	$0.885282\pi$
$564$	−2.79725	−0.117786
$565$	58.2772	2.45174
$566$	−34.5085	−1.45050
$567$	26.5782	1.11618
$568$	5.93915	0.249201
$569$	2.31686	0.0971279	0.0485639	−	0.998820i	$-0.484536\pi$
$569$	2.31686	0.0971279	0.0485639	+	0.998820i	$0.484536\pi$
$570$	19.5256	0.817837
$571$	−7.09620	−0.296967	−0.148483	−	0.988915i	$-0.547439\pi$
$571$	−7.09620	−0.296967	−0.148483	+	0.988915i	$0.547439\pi$
$572$	−4.37614	−0.182976
$573$	30.9703	1.29380
$574$	3.76527	0.157159
$575$	−19.2228	−0.801646
$576$	−6.87590	−0.286496
$577$	−42.4904	−1.76890	−0.884449	−	0.466636i	$-0.845466\pi$
$577$	−42.4904	−1.76890	−0.884449	+	0.466636i	$0.845466\pi$
$578$	−48.4340	−2.01459
$579$	−13.9399	−0.579322
$580$	−10.4704	−0.434759
$581$	28.8402	1.19649
$582$	8.15263	0.337937
$583$	42.6013	1.76436
$584$	−37.8197	−1.56499
$585$	4.38222	0.181182
$586$	−18.9886	−0.784413
$587$	−28.9392	−1.19445	−0.597224	−	0.802074i	$-0.703730\pi$
$587$	−28.9392	−1.19445	−0.597224	+	0.802074i	$0.703730\pi$
$588$	10.2673	0.423418
$589$	−10.4251	−0.429558
$590$	−43.6180	−1.79572
$591$	28.7067	1.18084
$592$	−2.34603	−0.0964214
$593$	21.3909	0.878420	0.439210	−	0.898384i	$-0.355258\pi$
$593$	21.3909	0.878420	0.439210	+	0.898384i	$0.355258\pi$
$594$	32.8317	1.34710
$595$	116.183	4.76303
$596$	11.2302	0.460009
$597$	−18.4724	−0.756027
$598$	−5.15875	−0.210957
$599$	−32.5801	−1.33118	−0.665592	−	0.746315i	$-0.731821\pi$
$599$	−32.5801	−1.33118	−0.665592	+	0.746315i	$0.731821\pi$
$600$	−32.9081	−1.34347
$601$	−23.1465	−0.944167	−0.472084	−	0.881554i	$-0.656498\pi$
$601$	−23.1465	−0.944167	−0.472084	+	0.881554i	$0.656498\pi$
$602$	−6.29572	−0.256595
$603$	−7.80559	−0.317868
$604$	1.70809	0.0695013
$605$	43.9938	1.78860
$606$	−9.58290	−0.389279
$607$	−18.3485	−0.744744	−0.372372	−	0.928083i	$-0.621456\pi$
$607$	−18.3485	−0.744744	−0.372372	+	0.928083i	$0.621456\pi$
$608$	−9.58869	−0.388873
$609$	35.0418	1.41997
$610$	4.96292	0.200943
$611$	5.39028	0.218067
$612$	−3.31129	−0.133851
$613$	48.5324	1.96021	0.980103	−	0.198490i	$-0.0636038\pi$
$613$	48.5324	1.96021	0.980103	+	0.198490i	$0.0636038\pi$
$614$	28.9446	1.16811
$615$	−3.71502	−0.149804
$616$	65.5689	2.64185
$617$	24.9898	1.00605	0.503025	−	0.864272i	$-0.332220\pi$
$617$	24.9898	1.00605	0.503025	+	0.864272i	$0.332220\pi$
$618$	−0.494351	−0.0198857
$619$	7.12617	0.286425	0.143213	−	0.989692i	$-0.454257\pi$
$619$	7.12617	0.286425	0.143213	+	0.989692i	$0.454257\pi$
$620$	6.51762	0.261754
$621$	−15.0572	−0.604224
$622$	−18.3806	−0.736995
$623$	75.2869	3.01631
$624$	−6.14736	−0.246091
$625$	−9.25068	−0.370027
$626$	−0.118821	−0.00474906
$627$	22.6411	0.904200
$628$	0.560160	0.0223528
$629$	−6.92490	−0.276114
$630$	−14.3663	−0.572368
$631$	19.4131	0.772823	0.386411	−	0.922327i	$-0.373714\pi$
$631$	19.4131	0.772823	0.386411	+	0.922327i	$0.373714\pi$
$632$	8.36470	0.332730
$633$	34.2113	1.35978
$634$	11.2285	0.445941
$635$	−13.0038	−0.516040
$636$	−7.31820	−0.290185
$637$	−19.7851	−0.783913
$638$	31.2076	1.23552
$639$	−1.50892	−0.0596920
$640$	−15.5051	−0.612893
$641$	−40.8061	−1.61174	−0.805872	−	0.592090i	$-0.798303\pi$
$641$	−40.8061	−1.61174	−0.805872	+	0.592090i	$0.798303\pi$
$642$	−26.8707	−1.06050
$643$	26.9396	1.06239	0.531197	−	0.847249i	$-0.321743\pi$
$643$	26.9396	1.06239	0.531197	+	0.847249i	$0.321743\pi$
$644$	−6.57951	−0.259269
$645$	6.21170	0.244586
$646$	28.4306	1.11859
$647$	−44.5203	−1.75027	−0.875137	−	0.483876i	$-0.839229\pi$
$647$	−44.5203	−1.75027	−0.875137	+	0.483876i	$0.839229\pi$
$648$	−18.5838	−0.730041
$649$	−50.5778	−1.98535
$650$	13.8748	0.544214
$651$	−21.8129	−0.854913
$652$	−0.690834	−0.0270551
$653$	−38.7740	−1.51734	−0.758671	−	0.651474i	$-0.774151\pi$
$653$	−38.7740	−1.51734	−0.758671	+	0.651474i	$0.774151\pi$
$654$	18.4501	0.721455
$655$	34.7047	1.35603
$656$	−1.83259	−0.0715505
$657$	9.60859	0.374867
$658$	−17.6711	−0.688890
$659$	6.71581	0.261611	0.130805	−	0.991408i	$-0.458244\pi$
$659$	6.71581	0.261611	0.130805	+	0.991408i	$0.458244\pi$
$660$	−14.1549	−0.550980
$661$	8.15588	0.317227	0.158614	−	0.987341i	$-0.449298\pi$
$661$	8.15588	0.317227	0.158614	+	0.987341i	$0.449298\pi$
$662$	23.7106	0.921539
$663$	−18.1455	−0.704711
$664$	−20.1655	−0.782572
$665$	−47.9880	−1.86089
$666$	0.856283	0.0331803
$667$	−14.3123	−0.554176
$668$	10.8371	0.419302
$669$	−21.1211	−0.816590
$670$	−41.8991	−1.61870
$671$	5.75482	0.222162
$672$	−20.0628	−0.773941
$673$	36.1078	1.39185	0.695926	−	0.718113i	$-0.254994\pi$
$673$	36.1078	1.39185	0.695926	+	0.718113i	$0.254994\pi$
$674$	2.39606	0.0922930
$675$	40.4973	1.55874
$676$	5.83347	0.224364
$677$	−35.0162	−1.34578	−0.672891	−	0.739742i	$-0.734947\pi$
$677$	−35.0162	−1.34578	−0.672891	+	0.739742i	$0.734947\pi$
$678$	29.8385	1.14594
$679$	−20.0367	−0.768938
$680$	−81.2365	−3.11528
$681$	−4.87871	−0.186953
$682$	−19.4261	−0.743864
$683$	11.8352	0.452862	0.226431	−	0.974027i	$-0.427294\pi$
$683$	11.8352	0.452862	0.226431	+	0.974027i	$0.427294\pi$
$684$	1.36769	0.0522950
$685$	−5.54811	−0.211982
$686$	27.9582	1.06745
$687$	13.0992	0.499766
$688$	3.06418	0.116821
$689$	14.1021	0.537246
$690$	−16.6863	−0.635238
$691$	−4.39774	−0.167298	−0.0836490	−	0.996495i	$-0.526657\pi$
$691$	−4.39774	−0.167298	−0.0836490	+	0.996495i	$0.526657\pi$
$692$	3.05316	0.116064
$693$	−16.6587	−0.632810
$694$	31.5656	1.19821
$695$	0.796648	0.0302186
$696$	−24.5017	−0.928734
$697$	−5.40934	−0.204893
$698$	4.67881	0.177096
$699$	−22.7412	−0.860153
$700$	17.6960	0.668847
$701$	−5.54262	−0.209342	−0.104671	−	0.994507i	$-0.533379\pi$
$701$	−5.54262	−0.209342	−0.104671	+	0.994507i	$0.533379\pi$
$702$	10.8681	0.410190
$703$	2.86025	0.107876
$704$	−42.7980	−1.61301
$705$	17.4352	0.656649
$706$	−16.7076	−0.628800
$707$	23.5519	0.885760
$708$	8.68842	0.326531
$709$	−34.9575	−1.31286	−0.656428	−	0.754389i	$-0.727933\pi$
$709$	−34.9575	−1.31286	−0.656428	+	0.754389i	$0.727933\pi$
$710$	−8.09963	−0.303974
$711$	−2.12516	−0.0796998
$712$	−52.6416	−1.97283
$713$	8.90915	0.333650
$714$	59.4867	2.22623
$715$	27.2764	1.02008
$716$	2.95639	0.110486
$717$	1.77873	0.0664280
$718$	−8.46050	−0.315743
$719$	6.99149	0.260739	0.130369	−	0.991466i	$-0.458384\pi$
$719$	6.99149	0.260739	0.130369	+	0.991466i	$0.458384\pi$
$720$	6.99220	0.260584
$721$	1.21497	0.0452477
$722$	11.0558	0.411454
$723$	6.25194	0.232512
$724$	−0.353095	−0.0131227
$725$	38.4940	1.42963
$726$	22.5252	0.835990
$727$	51.0634	1.89383	0.946917	−	0.321477i	$-0.104179\pi$
$727$	51.0634	1.89383	0.946917	+	0.321477i	$0.104179\pi$
$728$	21.7049	0.804439
$729$	29.8940	1.10718
$730$	51.5773	1.90896
$731$	9.04468	0.334530
$732$	−0.988583	−0.0365391
$733$	−48.7051	−1.79896	−0.899481	−	0.436959i	$-0.856055\pi$
$733$	−48.7051	−1.79896	−0.899481	+	0.436959i	$0.856055\pi$
$734$	−36.0568	−1.33088
$735$	−63.9962	−2.36054
$736$	8.19438	0.302049
$737$	−48.5847	−1.78964
$738$	0.668879	0.0246218
$739$	−29.7088	−1.09286	−0.546429	−	0.837506i	$-0.684013\pi$
$739$	−29.7088	−1.09286	−0.546429	+	0.837506i	$0.684013\pi$
$740$	−1.78819	−0.0657352
$741$	7.49478	0.275327
$742$	−46.2312	−1.69720
$743$	−29.7684	−1.09210	−0.546048	−	0.837754i	$-0.683868\pi$
$743$	−29.7684	−1.09210	−0.546048	+	0.837754i	$0.683868\pi$
$744$	15.2518	0.559159
$745$	−69.9980	−2.56453
$746$	−28.4533	−1.04175
$747$	5.12330	0.187452
$748$	−20.6106	−0.753598
$749$	66.0402	2.41306
$750$	13.6712	0.499201
$751$	41.4823	1.51371	0.756855	−	0.653583i	$-0.226735\pi$
$751$	41.4823	1.51371	0.756855	+	0.653583i	$0.226735\pi$
$752$	8.60065	0.313633
$753$	16.5757	0.604051
$754$	10.3305	0.376214
$755$	−10.6465	−0.387467
$756$	13.8613	0.504129
$757$	44.0050	1.59939	0.799694	−	0.600408i	$-0.204995\pi$
$757$	44.0050	1.59939	0.799694	+	0.600408i	$0.204995\pi$
$758$	−16.8237	−0.611064
$759$	−19.3489	−0.702319
$760$	33.5538	1.21713
$761$	−3.63351	−0.131715	−0.0658574	−	0.997829i	$-0.520978\pi$
$761$	−3.63351	−0.131715	−0.0658574	+	0.997829i	$0.520978\pi$
$762$	−6.65807	−0.241196
$763$	−45.3447	−1.64159
$764$	11.6447	0.421290
$765$	20.6392	0.746212
$766$	−24.8439	−0.897647
$767$	−16.7425	−0.604536
$768$	18.3108	0.660735
$769$	−7.76779	−0.280114	−0.140057	−	0.990143i	$-0.544729\pi$
$769$	−7.76779	−0.280114	−0.140057	+	0.990143i	$0.544729\pi$
$770$	−89.4209	−3.22251
$771$	7.64679	0.275393
$772$	−5.24134	−0.188640
$773$	49.8305	1.79228	0.896139	−	0.443774i	$-0.146361\pi$
$773$	49.8305	1.79228	0.896139	+	0.443774i	$0.146361\pi$
$774$	−1.11840	−0.0402001
$775$	−23.9618	−0.860732
$776$	14.0099	0.502927
$777$	5.98463	0.214697
$778$	−1.35300	−0.0485075
$779$	2.23427	0.0800509
$780$	−4.68564	−0.167773
$781$	−9.39204	−0.336073
$782$	−24.2965	−0.868841
$783$	30.1523	1.07755
$784$	−31.5688	−1.12746
$785$	−3.49147	−0.124616
$786$	17.7691	0.633805
$787$	45.4061	1.61855	0.809277	−	0.587427i	$-0.199859\pi$
$787$	45.4061	1.61855	0.809277	+	0.587427i	$0.199859\pi$
$788$	10.7936	0.384507
$789$	−3.13779	−0.111708
$790$	−11.4075	−0.405861
$791$	−73.3340	−2.60746
$792$	11.6480	0.413892
$793$	1.90499	0.0676481
$794$	13.6688	0.485087
$795$	45.6142	1.61777
$796$	−6.94556	−0.246179
$797$	−23.0070	−0.814948	−0.407474	−	0.913217i	$-0.633590\pi$
$797$	−23.0070	−0.814948	−0.407474	+	0.913217i	$0.633590\pi$
$798$	−24.5703	−0.869779
$799$	25.3869	0.898126
$800$	−22.0393	−0.779209
$801$	13.3743	0.472557
$802$	−28.3373	−1.00063
$803$	59.8071	2.11055
$804$	8.34604	0.294342
$805$	41.0100	1.44541
$806$	−6.43052	−0.226505
$807$	−33.5599	−1.18136
$808$	−16.4678	−0.579335
$809$	−51.1932	−1.79986	−0.899929	−	0.436037i	$-0.856382\pi$
$809$	−51.1932	−1.79986	−0.899929	+	0.436037i	$0.856382\pi$
$810$	25.3440	0.890499
$811$	−1.46056	−0.0512872	−0.0256436	−	0.999671i	$-0.508164\pi$
$811$	−1.46056	−0.0512872	−0.0256436	+	0.999671i	$0.508164\pi$
$812$	13.1756	0.462372
$813$	−6.20122	−0.217486
$814$	5.32980	0.186809
$815$	4.30596	0.150831
$816$	−28.9526	−1.01354
$817$	−3.73580	−0.130699
$818$	−3.89187	−0.136076
$819$	−5.51443	−0.192690
$820$	−1.39683	−0.0487795
$821$	0.919919	0.0321054	0.0160527	−	0.999871i	$-0.494890\pi$
$821$	0.919919	0.0321054	0.0160527	+	0.999871i	$0.494890\pi$
$822$	−2.84069	−0.0990803
$823$	−17.2562	−0.601513	−0.300757	−	0.953701i	$-0.597239\pi$
$823$	−17.2562	−0.601513	−0.300757	+	0.953701i	$0.597239\pi$
$824$	−0.849521	−0.0295945
$825$	52.0401	1.81180
$826$	54.8873	1.90977
$827$	35.4247	1.23184	0.615919	−	0.787809i	$-0.288785\pi$
$827$	35.4247	1.23184	0.615919	+	0.787809i	$0.288785\pi$
$828$	−1.16881	−0.0406190
$829$	45.4229	1.57760	0.788801	−	0.614648i	$-0.210702\pi$
$829$	45.4229	1.57760	0.788801	+	0.614648i	$0.210702\pi$
$830$	27.5011	0.954576
$831$	−7.56512	−0.262431
$832$	−14.1672	−0.491159
$833$	−93.1830	−3.22860
$834$	0.407891	0.0141241
$835$	−67.5478	−2.33759
$836$	8.51297	0.294427
$837$	−18.7692	−0.648758
$838$	−32.3056	−1.11598
$839$	32.5284	1.12301	0.561503	−	0.827475i	$-0.310223\pi$
$839$	32.5284	1.12301	0.561503	+	0.827475i	$0.310223\pi$
$840$	70.2062	2.42234
$841$	−0.339332	−0.0117011
$842$	6.31742	0.217713
$843$	33.8472	1.16576
$844$	12.8633	0.442774
$845$	−36.3599	−1.25082
$846$	−3.13917	−0.107927
$847$	−55.3602	−1.90220
$848$	22.5011	0.772690
$849$	−42.8448	−1.47043
$850$	65.3471	2.24139
$851$	−2.44434	−0.0837908
$852$	1.61340	0.0552740
$853$	−49.8216	−1.70586	−0.852929	−	0.522026i	$-0.825176\pi$
$853$	−49.8216	−1.70586	−0.852929	+	0.522026i	$0.825176\pi$
$854$	−6.24517	−0.213705
$855$	−8.52479	−0.291542
$856$	−46.1762	−1.57827
$857$	−19.6666	−0.671799	−0.335900	−	0.941898i	$-0.609040\pi$
$857$	−19.6666	−0.671799	−0.335900	+	0.941898i	$0.609040\pi$
$858$	13.9658	0.476784
$859$	5.30714	0.181077	0.0905386	−	0.995893i	$-0.471141\pi$
$859$	5.30714	0.181077	0.0905386	+	0.995893i	$0.471141\pi$
$860$	2.33558	0.0796425
$861$	4.67485	0.159319
$862$	−10.1954	−0.347257
$863$	19.0715	0.649200	0.324600	−	0.945851i	$-0.394770\pi$
$863$	19.0715	0.649200	0.324600	+	0.945851i	$0.394770\pi$
$864$	−17.2634	−0.587312
$865$	−19.0303	−0.647049
$866$	9.64069	0.327604
$867$	−60.1342	−2.04226
$868$	−8.20154	−0.278378
$869$	−13.2277	−0.448720
$870$	33.4147	1.13286
$871$	−16.0827	−0.544942
$872$	31.7056	1.07369
$873$	−3.55941	−0.120468
$874$	10.0354	0.339452
$875$	−33.5996	−1.13588
$876$	−10.2739	−0.347122
$877$	24.2698	0.819533	0.409767	−	0.912190i	$-0.365610\pi$
$877$	24.2698	0.819533	0.409767	+	0.912190i	$0.365610\pi$
$878$	19.6630	0.663594
$879$	−23.5757	−0.795190
$880$	43.5219	1.46712
$881$	25.0063	0.842482	0.421241	−	0.906949i	$-0.361595\pi$
$881$	25.0063	0.842482	0.421241	+	0.906949i	$0.361595\pi$
$882$	11.5223	0.387977
$883$	24.0465	0.809228	0.404614	−	0.914488i	$-0.367406\pi$
$883$	24.0465	0.809228	0.404614	+	0.914488i	$0.367406\pi$
$884$	−6.82262	−0.229469
$885$	−54.1548	−1.82039
$886$	31.8104	1.06869
$887$	−43.8617	−1.47273	−0.736365	−	0.676584i	$-0.763459\pi$
$887$	−43.8617	−1.47273	−0.736365	+	0.676584i	$0.763459\pi$
$888$	−4.18453	−0.140424
$889$	16.3635	0.548815
$890$	71.7910	2.40644
$891$	29.3880	0.984535
$892$	−7.94146	−0.265900
$893$	−10.4858	−0.350894
$894$	−35.8396	−1.19866
$895$	−18.4271	−0.615952
$896$	19.5111	0.651820
$897$	−6.40495	−0.213855
$898$	25.5088	0.851239
$899$	−17.8407	−0.595021
$900$	3.14360	0.104787
$901$	66.4175	2.21269
$902$	4.16333	0.138624
$903$	−7.81659	−0.260120
$904$	51.2761	1.70542
$905$	2.20084	0.0731582
$906$	−5.45112	−0.181101
$907$	12.8633	0.427118	0.213559	−	0.976930i	$-0.431494\pi$
$907$	12.8633	0.427118	0.213559	+	0.976930i	$0.431494\pi$
$908$	−1.83437	−0.0608759
$909$	4.18386	0.138770
$910$	−29.6005	−0.981248
$911$	−42.1385	−1.39611	−0.698056	−	0.716044i	$-0.745951\pi$
$911$	−42.1385	−1.39611	−0.698056	+	0.716044i	$0.745951\pi$
$912$	11.9586	0.395987
$913$	31.8892	1.05538
$914$	−0.988625	−0.0327008
$915$	6.16182	0.203704
$916$	4.92525	0.162735
$917$	−43.6712	−1.44215
$918$	51.1862	1.68940
$919$	10.9725	0.361949	0.180975	−	0.983488i	$-0.442075\pi$
$919$	10.9725	0.361949	0.180975	+	0.983488i	$0.442075\pi$
$920$	−28.6747	−0.945378
$921$	35.9367	1.18416
$922$	−38.5131	−1.26836
$923$	−3.10900	−0.102334
$924$	17.8121	0.585974
$925$	6.57421	0.216159
$926$	1.34591	0.0442292
$927$	0.215832	0.00708885
$928$	−16.4094	−0.538664
$929$	−12.2815	−0.402944	−0.201472	−	0.979494i	$-0.564572\pi$
$929$	−12.2815	−0.402944	−0.201472	+	0.979494i	$0.564572\pi$
$930$	−20.8000	−0.682058
$931$	38.4882	1.26140
$932$	−8.55061	−0.280085
$933$	−22.8208	−0.747121
$934$	−27.6469	−0.904633
$935$	128.466	4.20127
$936$	3.85576	0.126029
$937$	12.2715	0.400892	0.200446	−	0.979705i	$-0.435761\pi$
$937$	12.2715	0.400892	0.200446	+	0.979705i	$0.435761\pi$
$938$	52.7244	1.72151
$939$	−0.147525	−0.00481430
$940$	6.55558	0.213819
$941$	35.5475	1.15882	0.579408	−	0.815038i	$-0.303284\pi$
$941$	35.5475	1.15882	0.579408	+	0.815038i	$0.303284\pi$
$942$	−1.78766	−0.0582452
$943$	−1.90938	−0.0621779
$944$	−26.7141	−0.869469
$945$	−86.3971	−2.81050
$946$	−6.96130	−0.226331
$947$	−26.8115	−0.871256	−0.435628	−	0.900127i	$-0.643474\pi$
$947$	−26.8115	−0.871256	−0.435628	+	0.900127i	$0.643474\pi$
$948$	2.27231	0.0738011
$949$	19.7976	0.642659
$950$	−26.9909	−0.875699
$951$	13.9410	0.452068
$952$	102.225	3.31314
$953$	−43.1937	−1.39918	−0.699591	−	0.714544i	$-0.746634\pi$
$953$	−43.1937	−1.39918	−0.699591	+	0.714544i	$0.746634\pi$
$954$	−8.21271	−0.265896
$955$	−72.5812	−2.34867
$956$	0.668796	0.0216304
$957$	38.7464	1.25249
$958$	−13.2143	−0.426936
$959$	6.98155	0.225446
$960$	−45.8248	−1.47899
$961$	−19.8945	−0.641758
$962$	1.76429	0.0568831
$963$	11.7317	0.378048
$964$	2.35070	0.0757111
$965$	32.6692	1.05166
$966$	20.9975	0.675583
$967$	57.8674	1.86089	0.930445	−	0.366430i	$-0.119420\pi$
$967$	57.8674	1.86089	0.930445	+	0.366430i	$0.119420\pi$
$968$	38.7086	1.24414
$969$	35.2986	1.13396
$970$	−19.1063	−0.613467
$971$	−16.3981	−0.526239	−0.263120	−	0.964763i	$-0.584751\pi$
$971$	−16.3981	−0.526239	−0.263120	+	0.964763i	$0.584751\pi$
$972$	4.41639	0.141656
$973$	−1.00247	−0.0321378
$974$	−11.9112	−0.381658
$975$	17.2265	0.551691
$976$	3.03957	0.0972943
$977$	4.03774	0.129179	0.0645894	−	0.997912i	$-0.479426\pi$
$977$	4.03774	0.129179	0.0645894	+	0.997912i	$0.479426\pi$
$978$	2.20469	0.0704983
$979$	83.2462	2.66056
$980$	−24.0623	−0.768643
$981$	−8.05523	−0.257184
$982$	43.5166	1.38867
$983$	16.4489	0.524637	0.262319	−	0.964981i	$-0.415513\pi$
$983$	16.4489	0.524637	0.262319	+	0.964981i	$0.415513\pi$
$984$	−3.26872	−0.104203
$985$	−67.2765	−2.14361
$986$	48.6541	1.54946
$987$	−21.9399	−0.698355
$988$	2.81800	0.0896527
$989$	3.19257	0.101518
$990$	−15.8851	−0.504862
$991$	−41.6247	−1.32225	−0.661125	−	0.750275i	$-0.729921\pi$
$991$	−41.6247	−1.32225	−0.661125	+	0.750275i	$0.729921\pi$
$992$	10.2145	0.324312
$993$	29.4384	0.934200
$994$	10.1923	0.323280
$995$	43.2916	1.37244
$996$	−5.47804	−0.173578
$997$	−6.19399	−0.196166	−0.0980828	−	0.995178i	$-0.531271\pi$
$997$	−6.19399	−0.196166	−0.0980828	+	0.995178i	$0.531271\pi$
$998$	29.8259	0.944123
$999$	5.14957	0.162925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	157.2.a.a.1.3	✓	5
3.2	odd	2		1413.2.a.d.1.3		5
4.3	odd	2		2512.2.a.f.1.3		5
5.4	even	2		3925.2.a.f.1.3		5
7.6	odd	2		7693.2.a.b.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
157.2.a.a.1.3	✓	5	1.1	even	1	trivial
1413.2.a.d.1.3		5	3.2	odd	2
2512.2.a.f.1.3		5	4.3	odd	2
3925.2.a.f.1.3		5	5.4	even	2
7693.2.a.b.1.3		5	7.6	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:	\( N \)	\(=\)	\( 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	157.a (trivial)

\(f(q)\)	\(=\)	\(q-1.19993 q^{2} -1.48980 q^{3} -0.560160 q^{4} +3.49147 q^{5} +1.78766 q^{6} -4.39354 q^{7} +3.07202 q^{8} -0.780487 q^{9} +O(q^{10})\)	\(q-1.19993 q^{2} -1.48980 q^{3} -0.560160 q^{4} +3.49147 q^{5} +1.78766 q^{6} -4.39354 q^{7} +3.07202 q^{8} -0.780487 q^{9} -4.18953 q^{10} -4.85802 q^{11} +0.834528 q^{12} -1.60813 q^{13} +5.27195 q^{14} -5.20160 q^{15} -2.56590 q^{16} -7.57389 q^{17} +0.936533 q^{18} +3.12831 q^{19} -1.95578 q^{20} +6.54551 q^{21} +5.82930 q^{22} -2.67342 q^{23} -4.57671 q^{24} +7.19034 q^{25} +1.92964 q^{26} +5.63218 q^{27} +2.46108 q^{28} +5.35357 q^{29} +6.24157 q^{30} -3.33249 q^{31} -3.06513 q^{32} +7.23749 q^{33} +9.08817 q^{34} -15.3399 q^{35} +0.437198 q^{36} +0.914311 q^{37} -3.75377 q^{38} +2.39579 q^{39} +10.7259 q^{40} +0.714208 q^{41} -7.85417 q^{42} -1.19419 q^{43} +2.72127 q^{44} -2.72505 q^{45} +3.20793 q^{46} -3.35190 q^{47} +3.82269 q^{48} +12.3032 q^{49} -8.62793 q^{50} +11.2836 q^{51} +0.900807 q^{52} -8.76927 q^{53} -6.75824 q^{54} -16.9616 q^{55} -13.4970 q^{56} -4.66057 q^{57} -6.42392 q^{58} +10.4112 q^{59} +2.91373 q^{60} -1.18460 q^{61} +3.99877 q^{62} +3.42910 q^{63} +8.80976 q^{64} -5.61472 q^{65} -8.68451 q^{66} +10.0009 q^{67} +4.24259 q^{68} +3.98287 q^{69} +18.4069 q^{70} +1.93330 q^{71} -2.39767 q^{72} -12.3110 q^{73} -1.09711 q^{74} -10.7122 q^{75} -1.75235 q^{76} +21.3439 q^{77} -2.87479 q^{78} +2.72287 q^{79} -8.95876 q^{80} -6.04938 q^{81} -0.857002 q^{82} -6.56424 q^{83} -3.66653 q^{84} -26.4440 q^{85} +1.43295 q^{86} -7.97576 q^{87} -14.9239 q^{88} -17.1358 q^{89} +3.26987 q^{90} +7.06536 q^{91} +1.49754 q^{92} +4.96476 q^{93} +4.02206 q^{94} +10.9224 q^{95} +4.56644 q^{96} +4.56049 q^{97} -14.7630 q^{98} +3.79162 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} - 7 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} - 3 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 - 7 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 - 3 * q^7 - 12 * q^8 + 4 * q^9	\( 5 q - 5 q^{2} - 7 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} - 3 q^{7} - 12 q^{8} + 4 q^{9} - q^{10} - 14 q^{11} - 10 q^{12} - 7 q^{13} - 2 q^{14} - 5 q^{15} + 13 q^{16} - 9 q^{17} - 9 q^{18} - 3 q^{19} + 6 q^{21} + 16 q^{22} - 13 q^{23} + 29 q^{24} + 8 q^{25} + 17 q^{26} - 7 q^{27} + 9 q^{28} - 2 q^{29} + 20 q^{30} + 3 q^{31} - 9 q^{32} + 23 q^{33} + 19 q^{34} - 19 q^{35} + 31 q^{36} + 3 q^{37} + 7 q^{38} + 8 q^{39} + 17 q^{40} + 5 q^{41} + 16 q^{42} - 23 q^{43} - 8 q^{44} + 15 q^{45} + 12 q^{46} - 8 q^{47} - 37 q^{48} + 4 q^{49} - 8 q^{50} - 10 q^{51} - 19 q^{52} - 25 q^{53} + 35 q^{54} - 3 q^{55} - 22 q^{56} + 14 q^{57} + 4 q^{58} + 7 q^{59} - 22 q^{60} + 4 q^{61} - 9 q^{62} + q^{63} + 18 q^{64} + 3 q^{65} - 43 q^{66} - 12 q^{67} - 4 q^{68} + 29 q^{69} + 15 q^{70} - 18 q^{71} - 64 q^{72} - 3 q^{73} - 12 q^{74} + 12 q^{75} - 33 q^{76} - q^{77} - 36 q^{78} + 22 q^{79} - 10 q^{80} + 13 q^{81} - 8 q^{82} - 27 q^{83} - 39 q^{84} - 6 q^{85} + 36 q^{86} + 6 q^{87} + 23 q^{88} + 25 q^{89} - 29 q^{90} - 14 q^{91} - 26 q^{92} + 2 q^{93} + q^{94} + 5 q^{95} + 53 q^{96} + 20 q^{97} + 12 q^{98} - 10 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 - 7 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 - 3 * q^7 - 12 * q^8 + 4 * q^9 - q^10 - 14 * q^11 - 10 * q^12 - 7 * q^13 - 2 * q^14 - 5 * q^15 + 13 * q^16 - 9 * q^17 - 9 * q^18 - 3 * q^19 + 6 * q^21 + 16 * q^22 - 13 * q^23 + 29 * q^24 + 8 * q^25 + 17 * q^26 - 7 * q^27 + 9 * q^28 - 2 * q^29 + 20 * q^30 + 3 * q^31 - 9 * q^32 + 23 * q^33 + 19 * q^34 - 19 * q^35 + 31 * q^36 + 3 * q^37 + 7 * q^38 + 8 * q^39 + 17 * q^40 + 5 * q^41 + 16 * q^42 - 23 * q^43 - 8 * q^44 + 15 * q^45 + 12 * q^46 - 8 * q^47 - 37 * q^48 + 4 * q^49 - 8 * q^50 - 10 * q^51 - 19 * q^52 - 25 * q^53 + 35 * q^54 - 3 * q^55 - 22 * q^56 + 14 * q^57 + 4 * q^58 + 7 * q^59 - 22 * q^60 + 4 * q^61 - 9 * q^62 + q^63 + 18 * q^64 + 3 * q^65 - 43 * q^66 - 12 * q^67 - 4 * q^68 + 29 * q^69 + 15 * q^70 - 18 * q^71 - 64 * q^72 - 3 * q^73 - 12 * q^74 + 12 * q^75 - 33 * q^76 - q^77 - 36 * q^78 + 22 * q^79 - 10 * q^80 + 13 * q^81 - 8 * q^82 - 27 * q^83 - 39 * q^84 - 6 * q^85 + 36 * q^86 + 6 * q^87 + 23 * q^88 + 25 * q^89 - 29 * q^90 - 14 * q^91 - 26 * q^92 + 2 * q^93 + q^94 + 5 * q^95 + 53 * q^96 + 20 * q^97 + 12 * q^98 - 10 * q^99

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