LMFDB - Embedded newform 4031.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, 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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$1$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.77273 q^{2} -1.39503 q^{3} +1.14258 q^{4} -2.16266 q^{5} +2.47302 q^{6} +3.73562 q^{7} +1.51997 q^{8} -1.05388 q^{9} +O(q^{10})$	\(q-1.77273 q^{2} -1.39503 q^{3} +1.14258 q^{4} -2.16266 q^{5} +2.47302 q^{6} +3.73562 q^{7} +1.51997 q^{8} -1.05388 q^{9} +3.83382 q^{10} +5.45206 q^{11} -1.59394 q^{12} +3.93093 q^{13} -6.62225 q^{14} +3.01698 q^{15} -4.97967 q^{16} -1.81906 q^{17} +1.86825 q^{18} +1.77289 q^{19} -2.47102 q^{20} -5.21131 q^{21} -9.66504 q^{22} -3.66238 q^{23} -2.12041 q^{24} -0.322895 q^{25} -6.96848 q^{26} +5.65530 q^{27} +4.26825 q^{28} -1.00000 q^{29} -5.34831 q^{30} -8.07220 q^{31} +5.78768 q^{32} -7.60580 q^{33} +3.22470 q^{34} -8.07888 q^{35} -1.20415 q^{36} -7.62182 q^{37} -3.14286 q^{38} -5.48377 q^{39} -3.28719 q^{40} +5.37965 q^{41} +9.23826 q^{42} -7.92755 q^{43} +6.22942 q^{44} +2.27919 q^{45} +6.49242 q^{46} +5.26609 q^{47} +6.94680 q^{48} +6.95483 q^{49} +0.572407 q^{50} +2.53765 q^{51} +4.49140 q^{52} -1.41840 q^{53} -10.0253 q^{54} -11.7910 q^{55} +5.67804 q^{56} -2.47324 q^{57} +1.77273 q^{58} -5.15127 q^{59} +3.44715 q^{60} -12.7156 q^{61} +14.3099 q^{62} -3.93691 q^{63} -0.300666 q^{64} -8.50126 q^{65} +13.4831 q^{66} +6.96779 q^{67} -2.07842 q^{68} +5.10914 q^{69} +14.3217 q^{70} +13.5512 q^{71} -1.60188 q^{72} -11.1071 q^{73} +13.5115 q^{74} +0.450449 q^{75} +2.02567 q^{76} +20.3668 q^{77} +9.72126 q^{78} -3.72137 q^{79} +10.7693 q^{80} -4.72768 q^{81} -9.53669 q^{82} -6.14188 q^{83} -5.95434 q^{84} +3.93401 q^{85} +14.0534 q^{86} +1.39503 q^{87} +8.28699 q^{88} +4.02014 q^{89} -4.04040 q^{90} +14.6844 q^{91} -4.18457 q^{92} +11.2610 q^{93} -9.33537 q^{94} -3.83416 q^{95} -8.07400 q^{96} +10.5701 q^{97} -12.3291 q^{98} -5.74584 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) $ 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * 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 $

$2$	−1.77273	−1.25351	−0.626756	−	0.779216i	$-0.715618\pi$
$2$	−1.77273	−1.25351	−0.626756	+	0.779216i	$0.715618\pi$
$3$	−1.39503	−0.805423	−0.402711	−	0.915327i	$-0.631932\pi$
$3$	−1.39503	−0.805423	−0.402711	+	0.915327i	$0.631932\pi$
$4$	1.14258	0.571291
$5$	−2.16266	−0.967172	−0.483586	−	0.875297i	$-0.660666\pi$
$5$	−2.16266	−0.967172	−0.483586	+	0.875297i	$0.660666\pi$
$6$	2.47302	1.00961
$7$	3.73562	1.41193	0.705965	−	0.708246i	$-0.250513\pi$
$7$	3.73562	1.41193	0.705965	+	0.708246i	$0.250513\pi$
$8$	1.51997	0.537392
$9$	−1.05388	−0.351295
$10$	3.83382	1.21236
$11$	5.45206	1.64386	0.821929	−	0.569590i	$-0.192898\pi$
$11$	5.45206	1.64386	0.821929	+	0.569590i	$0.192898\pi$
$12$	−1.59394	−0.460131
$13$	3.93093	1.09024	0.545121	−	0.838357i	$-0.316484\pi$
$13$	3.93093	1.09024	0.545121	+	0.838357i	$0.316484\pi$
$14$	−6.62225	−1.76987
$15$	3.01698	0.778982
$16$	−4.97967	−1.24492
$17$	−1.81906	−0.441187	−0.220593	−	0.975366i	$-0.570799\pi$
$17$	−1.81906	−0.441187	−0.220593	+	0.975366i	$0.570799\pi$
$18$	1.86825	0.440352
$19$	1.77289	0.406729	0.203364	−	0.979103i	$-0.434812\pi$
$19$	1.77289	0.406729	0.203364	+	0.979103i	$0.434812\pi$
$20$	−2.47102	−0.552536
$21$	−5.21131	−1.13720
$22$	−9.66504	−2.06059
$23$	−3.66238	−0.763659	−0.381830	−	0.924233i	$-0.624706\pi$
$23$	−3.66238	−0.763659	−0.381830	+	0.924233i	$0.624706\pi$
$24$	−2.12041	−0.432828
$25$	−0.322895	−0.0645790
$26$	−6.96848	−1.36663
$27$	5.65530	1.08836
$28$	4.26825	0.806623
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−5.34831	−0.976463
$31$	−8.07220	−1.44981	−0.724905	−	0.688849i	$-0.758117\pi$
$31$	−8.07220	−1.44981	−0.724905	+	0.688849i	$0.758117\pi$
$32$	5.78768	1.02313
$33$	−7.60580	−1.32400
$34$	3.22470	0.553032
$35$	−8.07888	−1.36558
$36$	−1.20415	−0.200691
$37$	−7.62182	−1.25302	−0.626510	−	0.779414i	$-0.715517\pi$
$37$	−7.62182	−1.25302	−0.626510	+	0.779414i	$0.715517\pi$
$38$	−3.14286	−0.509839
$39$	−5.48377	−0.878106
$40$	−3.28719	−0.519750
$41$	5.37965	0.840161	0.420080	−	0.907487i	$-0.362002\pi$
$41$	5.37965	0.840161	0.420080	+	0.907487i	$0.362002\pi$
$42$	9.23826	1.42549
$43$	−7.92755	−1.20894	−0.604470	−	0.796628i	$-0.706615\pi$
$43$	−7.92755	−1.20894	−0.604470	+	0.796628i	$0.706615\pi$
$44$	6.22942	0.939121
$45$	2.27919	0.339762
$46$	6.49242	0.957255
$47$	5.26609	0.768138	0.384069	−	0.923304i	$-0.374522\pi$
$47$	5.26609	0.768138	0.384069	+	0.923304i	$0.374522\pi$
$48$	6.94680	1.00268
$49$	6.95483	0.993548
$50$	0.572407	0.0809505
$51$	2.53765	0.355342
$52$	4.49140	0.622846
$53$	−1.41840	−0.194832	−0.0974162	−	0.995244i	$-0.531058\pi$
$53$	−1.41840	−0.194832	−0.0974162	+	0.995244i	$0.531058\pi$
$54$	−10.0253	−1.36428
$55$	−11.7910	−1.58989
$56$	5.67804	0.758760
$57$	−2.47324	−0.327589
$58$	1.77273	0.232771
$59$	−5.15127	−0.670638	−0.335319	−	0.942105i	$-0.608844\pi$
$59$	−5.15127	−0.670638	−0.335319	+	0.942105i	$0.608844\pi$
$60$	3.44715	0.445025
$61$	−12.7156	−1.62807	−0.814034	−	0.580818i	$-0.802733\pi$
$61$	−12.7156	−1.62807	−0.814034	+	0.580818i	$0.802733\pi$
$62$	14.3099	1.81735
$63$	−3.93691	−0.496003
$64$	−0.300666	−0.0375832
$65$	−8.50126	−1.05445
$66$	13.4831	1.65965
$67$	6.96779	0.851251	0.425626	−	0.904899i	$-0.360054\pi$
$67$	6.96779	0.851251	0.425626	+	0.904899i	$0.360054\pi$
$68$	−2.07842	−0.252046
$69$	5.10914	0.615068
$70$	14.3217	1.71177
$71$	13.5512	1.60824	0.804118	−	0.594470i	$-0.202638\pi$
$71$	13.5512	1.60824	0.804118	+	0.594470i	$0.202638\pi$
$72$	−1.60188	−0.188783
$73$	−11.1071	−1.29999	−0.649996	−	0.759938i	$-0.725229\pi$
$73$	−11.1071	−1.29999	−0.649996	+	0.759938i	$0.725229\pi$
$74$	13.5115	1.57067
$75$	0.450449	0.0520134
$76$	2.02567	0.232360
$77$	20.3668	2.32101
$78$	9.72126	1.10072
$79$	−3.72137	−0.418687	−0.209344	−	0.977842i	$-0.567133\pi$
$79$	−3.72137	−0.418687	−0.209344	+	0.977842i	$0.567133\pi$
$80$	10.7693	1.20405
$81$	−4.72768	−0.525298
$82$	−9.53669	−1.05315
$83$	−6.14188	−0.674159	−0.337079	−	0.941476i	$-0.609439\pi$
$83$	−6.14188	−0.674159	−0.337079	+	0.941476i	$0.609439\pi$
$84$	−5.95434	−0.649672
$85$	3.93401	0.426703
$86$	14.0534	1.51542
$87$	1.39503	0.149563
$88$	8.28699	0.883396
$89$	4.02014	0.426134	0.213067	−	0.977038i	$-0.431655\pi$
$89$	4.02014	0.426134	0.213067	+	0.977038i	$0.431655\pi$
$90$	−4.04040	−0.425896
$91$	14.6844	1.53935
$92$	−4.18457	−0.436271
$93$	11.2610	1.16771
$94$	−9.33537	−0.962870
$95$	−3.83416	−0.393377
$96$	−8.07400	−0.824049
$97$	10.5701	1.07323	0.536616	−	0.843827i	$-0.319702\pi$
$97$	10.5701	1.07323	0.536616	+	0.843827i	$0.319702\pi$
$98$	−12.3291	−1.24542
$99$	−5.74584	−0.577478
$100$	−0.368934	−0.0368934
$101$	14.7059	1.46329	0.731644	−	0.681687i	$-0.238754\pi$
$101$	14.7059	1.46329	0.731644	+	0.681687i	$0.238754\pi$
$102$	−4.49857	−0.445425
$103$	−9.88718	−0.974213	−0.487106	−	0.873343i	$-0.661948\pi$
$103$	−9.88718	−0.974213	−0.487106	+	0.873343i	$0.661948\pi$
$104$	5.97490	0.585887
$105$	11.2703	1.09987
$106$	2.51445	0.244225
$107$	−4.44211	−0.429435	−0.214718	−	0.976676i	$-0.568883\pi$
$107$	−4.44211	−0.429435	−0.214718	+	0.976676i	$0.568883\pi$
$108$	6.46164	0.621772
$109$	−15.5199	−1.48654	−0.743268	−	0.668993i	$-0.766725\pi$
$109$	−15.5199	−1.48654	−0.743268	+	0.668993i	$0.766725\pi$
$110$	20.9022	1.99295
$111$	10.6327	1.00921
$112$	−18.6021	−1.75774
$113$	1.29751	0.122059	0.0610296	−	0.998136i	$-0.480562\pi$
$113$	1.29751	0.122059	0.0610296	+	0.998136i	$0.480562\pi$
$114$	4.38439	0.410636
$115$	7.92049	0.738589
$116$	−1.14258	−0.106086
$117$	−4.14274	−0.382996
$118$	9.13183	0.840653
$119$	−6.79531	−0.622925
$120$	4.58574	0.418618
$121$	18.7249	1.70227
$122$	22.5414	2.04080
$123$	−7.50479	−0.676684
$124$	−9.22315	−0.828263
$125$	11.5116	1.02963
$126$	6.97908	0.621746
$127$	−5.71551	−0.507169	−0.253585	−	0.967313i	$-0.581610\pi$
$127$	−5.71551	−0.507169	−0.253585	+	0.967313i	$0.581610\pi$
$128$	−11.0424	−0.976016
$129$	11.0592	0.973707
$130$	15.0705	1.32177
$131$	−20.6216	−1.80172	−0.900859	−	0.434112i	$-0.857062\pi$
$131$	−20.6216	−1.80172	−0.900859	+	0.434112i	$0.857062\pi$
$132$	−8.69025	−0.756389
$133$	6.62284	0.574273
$134$	−12.3520	−1.06705
$135$	−12.2305	−1.05263
$136$	−2.76492	−0.237090
$137$	4.99492	0.426745	0.213373	−	0.976971i	$-0.431555\pi$
$137$	4.99492	0.426745	0.213373	+	0.976971i	$0.431555\pi$
$138$	−9.05714	−0.770995
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	−9.23077	−0.780143
$141$	−7.34637	−0.618676
$142$	−24.0227	−2.01594
$143$	21.4316	1.79220
$144$	5.24799	0.437333
$145$	2.16266	0.179599
$146$	19.6900	1.62955
$147$	−9.70222	−0.800226
$148$	−8.70855	−0.715839
$149$	14.1402	1.15841	0.579205	−	0.815182i	$-0.303363\pi$
$149$	14.1402	1.15841	0.579205	+	0.815182i	$0.303363\pi$
$150$	−0.798526	−0.0651994
$151$	−12.8175	−1.04307	−0.521535	−	0.853230i	$-0.674640\pi$
$151$	−12.8175	−1.04307	−0.521535	+	0.853230i	$0.674640\pi$
$152$	2.69475	0.218573
$153$	1.91708	0.154986
$154$	−36.1049	−2.90942
$155$	17.4574	1.40222
$156$	−6.26565	−0.501654
$157$	−14.6799	−1.17158	−0.585791	−	0.810462i	$-0.699216\pi$
$157$	−14.6799	−1.17158	−0.585791	+	0.810462i	$0.699216\pi$
$158$	6.59700	0.524829
$159$	1.97872	0.156922
$160$	−12.5168	−0.989539
$161$	−13.6812	−1.07823
$162$	8.38091	0.658467
$163$	2.80863	0.219989	0.109994	−	0.993932i	$-0.464917\pi$
$163$	2.80863	0.219989	0.109994	+	0.993932i	$0.464917\pi$
$164$	6.14669	0.479976
$165$	16.4488	1.28054
$166$	10.8879	0.845066
$167$	−17.7861	−1.37633	−0.688165	−	0.725554i	$-0.741583\pi$
$167$	−17.7861	−1.37633	−0.688165	+	0.725554i	$0.741583\pi$
$168$	−7.92105	−0.611122
$169$	2.45217	0.188629
$170$	−6.97395	−0.534877
$171$	−1.86842	−0.142882
$172$	−9.05787	−0.690656
$173$	−14.5083	−1.10304	−0.551522	−	0.834160i	$-0.685953\pi$
$173$	−14.5083	−1.10304	−0.551522	+	0.834160i	$0.685953\pi$
$174$	−2.47302	−0.187479
$175$	−1.20621	−0.0911811
$176$	−27.1495	−2.04647
$177$	7.18619	0.540147
$178$	−7.12664	−0.534164
$179$	−5.34156	−0.399247	−0.199624	−	0.979873i	$-0.563972\pi$
$179$	−5.34156	−0.399247	−0.199624	+	0.979873i	$0.563972\pi$
$180$	2.60416	0.194103
$181$	12.4045	0.922018	0.461009	−	0.887396i	$-0.347488\pi$
$181$	12.4045	0.922018	0.461009	+	0.887396i	$0.347488\pi$
$182$	−26.0316	−1.92959
$183$	17.7387	1.31128
$184$	−5.56672	−0.410384
$185$	16.4834	1.21188
$186$	−19.9627	−1.46374
$187$	−9.91761	−0.725248
$188$	6.01694	0.438830
$189$	21.1260	1.53669
$190$	6.79694	0.493102
$191$	23.2478	1.68216	0.841078	−	0.540914i	$-0.181922\pi$
$191$	23.2478	1.68216	0.841078	+	0.540914i	$0.181922\pi$
$192$	0.419438	0.0302704
$193$	13.0720	0.940943	0.470472	−	0.882415i	$-0.344084\pi$
$193$	13.0720	0.940943	0.470472	+	0.882415i	$0.344084\pi$
$194$	−18.7380	−1.34531
$195$	11.8595	0.849279
$196$	7.94647	0.567605
$197$	5.68340	0.404926	0.202463	−	0.979290i	$-0.435105\pi$
$197$	5.68340	0.404926	0.202463	+	0.979290i	$0.435105\pi$
$198$	10.1858	0.723875
$199$	7.62027	0.540186	0.270093	−	0.962834i	$-0.412945\pi$
$199$	7.62027	0.540186	0.270093	+	0.962834i	$0.412945\pi$
$200$	−0.490792	−0.0347042
$201$	−9.72030	−0.685617
$202$	−26.0696	−1.83425
$203$	−3.73562	−0.262189
$204$	2.89947	0.203003
$205$	−11.6344	−0.812580
$206$	17.5273	1.22119
$207$	3.85972	0.268269
$208$	−19.5747	−1.35726
$209$	9.66590	0.668604
$210$	−19.9792	−1.37870
$211$	−25.7623	−1.77355	−0.886774	−	0.462203i	$-0.847059\pi$
$211$	−25.7623	−1.77355	−0.886774	+	0.462203i	$0.847059\pi$
$212$	−1.62064	−0.111306
$213$	−18.9044	−1.29531
$214$	7.87467	0.538302
$215$	17.1446	1.16925
$216$	8.59591	0.584877
$217$	−30.1547	−2.04703
$218$	27.5126	1.86339
$219$	15.4948	1.04704
$220$	−13.4721	−0.908291
$221$	−7.15058	−0.481000
$222$	−18.8489	−1.26506
$223$	0.340185	0.0227804	0.0113902	−	0.999935i	$-0.496374\pi$
$223$	0.340185	0.0227804	0.0113902	+	0.999935i	$0.496374\pi$
$224$	21.6205	1.44458
$225$	0.340294	0.0226863
$226$	−2.30013	−0.153002
$227$	2.92280	0.193993	0.0969966	−	0.995285i	$-0.469076\pi$
$227$	2.92280	0.193993	0.0969966	+	0.995285i	$0.469076\pi$
$228$	−2.82588	−0.187148
$229$	17.1639	1.13422	0.567111	−	0.823642i	$-0.308061\pi$
$229$	17.1639	1.13422	0.567111	+	0.823642i	$0.308061\pi$
$230$	−14.0409	−0.925830
$231$	−28.4124	−1.86940
$232$	−1.51997	−0.0997912
$233$	−7.73633	−0.506824	−0.253412	−	0.967358i	$-0.581553\pi$
$233$	−7.73633	−0.506824	−0.253412	+	0.967358i	$0.581553\pi$
$234$	7.34397	0.480090
$235$	−11.3888	−0.742922
$236$	−5.88575	−0.383129
$237$	5.19144	0.337220
$238$	12.0463	0.780843
$239$	11.4269	0.739142	0.369571	−	0.929203i	$-0.379505\pi$
$239$	11.4269	0.739142	0.369571	+	0.929203i	$0.379505\pi$
$240$	−15.0236	−0.969768
$241$	7.36721	0.474564	0.237282	−	0.971441i	$-0.423744\pi$
$241$	7.36721	0.474564	0.237282	+	0.971441i	$0.423744\pi$
$242$	−33.1943	−2.13381
$243$	−10.3706	−0.665277
$244$	−14.5286	−0.930100
$245$	−15.0410	−0.960931
$246$	13.3040	0.848232
$247$	6.96910	0.443433
$248$	−12.2695	−0.779116
$249$	8.56812	0.542983
$250$	−20.4070	−1.29065
$251$	−27.2651	−1.72096	−0.860478	−	0.509487i	$-0.829835\pi$
$251$	−27.2651	−1.72096	−0.860478	+	0.509487i	$0.829835\pi$
$252$	−4.49824	−0.283362
$253$	−19.9675	−1.25535
$254$	10.1321	0.635742
$255$	−5.48807	−0.343676
$256$	20.1765	1.26103
$257$	−20.4871	−1.27795	−0.638975	−	0.769227i	$-0.720641\pi$
$257$	−20.4871	−1.27795	−0.638975	+	0.769227i	$0.720641\pi$
$258$	−19.6050	−1.22055
$259$	−28.4722	−1.76918
$260$	−9.71338	−0.602399
$261$	1.05388	0.0652338
$262$	36.5566	2.25847
$263$	−10.3135	−0.635957	−0.317979	−	0.948098i	$-0.603004\pi$
$263$	−10.3135	−0.635957	−0.317979	+	0.948098i	$0.603004\pi$
$264$	−11.5606	−0.711507
$265$	3.06752	0.188436
$266$	−11.7405	−0.719858
$267$	−5.60823	−0.343218
$268$	7.96127	0.486312
$269$	−16.5722	−1.01042	−0.505211	−	0.862996i	$-0.668585\pi$
$269$	−16.5722	−1.01042	−0.505211	+	0.862996i	$0.668585\pi$
$270$	21.6814	1.31949
$271$	−17.6684	−1.07328	−0.536640	−	0.843811i	$-0.680307\pi$
$271$	−17.6684	−1.07328	−0.536640	+	0.843811i	$0.680307\pi$
$272$	9.05831	0.549241
$273$	−20.4853	−1.23982
$274$	−8.85466	−0.534930
$275$	−1.76044	−0.106159
$276$	5.83761	0.351383
$277$	8.40696	0.505125	0.252563	−	0.967581i	$-0.418727\pi$
$277$	8.40696	0.505125	0.252563	+	0.967581i	$0.418727\pi$
$278$	1.77273	0.106321
$279$	8.50716	0.509311
$280$	−12.2797	−0.733851
$281$	−29.6127	−1.76655	−0.883273	−	0.468858i	$-0.844665\pi$
$281$	−29.6127	−1.76655	−0.883273	+	0.468858i	$0.844665\pi$
$282$	13.0232	0.775517
$283$	0.0946396	0.00562574	0.00281287	−	0.999996i	$-0.499105\pi$
$283$	0.0946396	0.00562574	0.00281287	+	0.999996i	$0.499105\pi$
$284$	15.4834	0.918770
$285$	5.34878	0.316834
$286$	−37.9926	−2.24655
$287$	20.0963	1.18625
$288$	−6.09954	−0.359419
$289$	−13.6910	−0.805354
$290$	−3.83382	−0.225130
$291$	−14.7456	−0.864405
$292$	−12.6908	−0.742673
$293$	18.2997	1.06908	0.534540	−	0.845143i	$-0.320485\pi$
$293$	18.2997	1.06908	0.534540	+	0.845143i	$0.320485\pi$
$294$	17.1994	1.00309
$295$	11.1405	0.648622
$296$	−11.5850	−0.673362
$297$	30.8330	1.78911
$298$	−25.0668	−1.45208
$299$	−14.3965	−0.832574
$300$	0.514675	0.0297148
$301$	−29.6143	−1.70694
$302$	22.7219	1.30750
$303$	−20.5151	−1.17856
$304$	−8.82841	−0.506344
$305$	27.4996	1.57462
$306$	−3.39846	−0.194277
$307$	28.1543	1.60685	0.803427	−	0.595404i	$-0.203008\pi$
$307$	28.1543	1.60685	0.803427	+	0.595404i	$0.203008\pi$
$308$	23.2707	1.32597
$309$	13.7929	0.784653
$310$	−30.9474	−1.75769
$311$	6.28781	0.356549	0.178275	−	0.983981i	$-0.442948\pi$
$311$	6.28781	0.356549	0.178275	+	0.983981i	$0.442948\pi$
$312$	−8.33519	−0.471887
$313$	27.1107	1.53239	0.766195	−	0.642609i	$-0.222148\pi$
$313$	27.1107	1.53239	0.766195	+	0.642609i	$0.222148\pi$
$314$	26.0235	1.46859
$315$	8.51419	0.479720
$316$	−4.25197	−0.239192
$317$	6.71602	0.377209	0.188605	−	0.982053i	$-0.439604\pi$
$317$	6.71602	0.377209	0.188605	+	0.982053i	$0.439604\pi$
$318$	−3.50774	−0.196704
$319$	−5.45206	−0.305257
$320$	0.650238	0.0363494
$321$	6.19689	0.345877
$322$	24.2532	1.35158
$323$	−3.22499	−0.179443
$324$	−5.40176	−0.300098
$325$	−1.26928	−0.0704068
$326$	−4.97895	−0.275759
$327$	21.6508	1.19729
$328$	8.17693	0.451495
$329$	19.6721	1.08456
$330$	−29.1593	−1.60517
$331$	−6.60045	−0.362794	−0.181397	−	0.983410i	$-0.558062\pi$
$331$	−6.60045	−0.362794	−0.181397	+	0.983410i	$0.558062\pi$
$332$	−7.01760	−0.385141
$333$	8.03251	0.440179
$334$	31.5300	1.72525
$335$	−15.0690	−0.823306
$336$	25.9506	1.41572
$337$	4.53428	0.246998	0.123499	−	0.992345i	$-0.460588\pi$
$337$	4.53428	0.246998	0.123499	+	0.992345i	$0.460588\pi$
$338$	−4.34705	−0.236448
$339$	−1.81006	−0.0983092
$340$	4.49493	0.243772
$341$	−44.0101	−2.38328
$342$	3.31221	0.179104
$343$	−0.168724	−0.00911022
$344$	−12.0497	−0.649674
$345$	−11.0493	−0.594877
$346$	25.7193	1.38268
$347$	28.0089	1.50360	0.751798	−	0.659394i	$-0.229187\pi$
$347$	28.0089	1.50360	0.751798	+	0.659394i	$0.229187\pi$
$348$	1.59394	0.0854441
$349$	−8.55451	−0.457913	−0.228956	−	0.973437i	$-0.573531\pi$
$349$	−8.55451	−0.457913	−0.228956	+	0.973437i	$0.573531\pi$
$350$	2.13829	0.114297
$351$	22.2306	1.18658
$352$	31.5548	1.68187
$353$	−7.09717	−0.377744	−0.188872	−	0.982002i	$-0.560483\pi$
$353$	−7.09717	−0.377744	−0.188872	+	0.982002i	$0.560483\pi$
$354$	−12.7392	−0.677081
$355$	−29.3067	−1.55544
$356$	4.59334	0.243447
$357$	9.47968	0.501718
$358$	9.46917	0.500461
$359$	−15.3399	−0.809610	−0.404805	−	0.914403i	$-0.632661\pi$
$359$	−15.3399	−0.809610	−0.404805	+	0.914403i	$0.632661\pi$
$360$	3.46431	0.182585
$361$	−15.8569	−0.834572
$362$	−21.9898	−1.15576
$363$	−26.1219	−1.37104
$364$	16.7782	0.879415
$365$	24.0210	1.25732
$366$	−31.4460	−1.64371
$367$	34.3142	1.79119	0.895594	−	0.444872i	$-0.146751\pi$
$367$	34.3142	1.79119	0.895594	+	0.444872i	$0.146751\pi$
$368$	18.2374	0.950693
$369$	−5.66953	−0.295144
$370$	−29.2207	−1.51911
$371$	−5.29860	−0.275090
$372$	12.8666	0.667102
$373$	25.8444	1.33817	0.669086	−	0.743185i	$-0.266686\pi$
$373$	25.8444	1.33817	0.669086	+	0.743185i	$0.266686\pi$
$374$	17.5813	0.909106
$375$	−16.0591	−0.829288
$376$	8.00432	0.412791
$377$	−3.93093	−0.202453
$378$	−37.4508	−1.92626
$379$	4.07128	0.209127	0.104564	−	0.994518i	$-0.466655\pi$
$379$	4.07128	0.209127	0.104564	+	0.994518i	$0.466655\pi$
$380$	−4.38084	−0.224732
$381$	7.97332	0.408486
$382$	−41.2122	−2.10860
$383$	13.9396	0.712279	0.356139	−	0.934433i	$-0.384093\pi$
$383$	13.9396	0.712279	0.356139	+	0.934433i	$0.384093\pi$
$384$	15.4044	0.786105
$385$	−44.0465	−2.24482
$386$	−23.1732	−1.17948
$387$	8.35471	0.424694
$388$	12.0772	0.613128
$389$	−21.1005	−1.06984	−0.534920	−	0.844903i	$-0.679658\pi$
$389$	−21.1005	−1.06984	−0.534920	+	0.844903i	$0.679658\pi$
$390$	−21.0238	−1.06458
$391$	6.66208	0.336916
$392$	10.5712	0.533924
$393$	28.7678	1.45114
$394$	−10.0752	−0.507579
$395$	8.04807	0.404942
$396$	−6.56509	−0.329908
$397$	−25.4364	−1.27662	−0.638309	−	0.769780i	$-0.720366\pi$
$397$	−25.4364	−1.27662	−0.638309	+	0.769780i	$0.720366\pi$
$398$	−13.5087	−0.677130
$399$	−9.23908	−0.462532
$400$	1.60791	0.0803956
$401$	−2.51858	−0.125772	−0.0628859	−	0.998021i	$-0.520030\pi$
$401$	−2.51858	−0.125772	−0.0628859	+	0.998021i	$0.520030\pi$
$402$	17.2315	0.859429
$403$	−31.7312	−1.58065
$404$	16.8026	0.835963
$405$	10.2244	0.508053
$406$	6.62225	0.328657
$407$	−41.5546	−2.05979
$408$	3.85716	0.190958
$409$	−7.24837	−0.358409	−0.179204	−	0.983812i	$-0.557352\pi$
$409$	−7.24837	−0.358409	−0.179204	+	0.983812i	$0.557352\pi$
$410$	20.6246	1.01858
$411$	−6.96808	−0.343710
$412$	−11.2969	−0.556559
$413$	−19.2432	−0.946895
$414$	−6.84226	−0.336279
$415$	13.2828	0.652027
$416$	22.7509	1.11546
$417$	1.39503	0.0683150
$418$	−17.1351	−0.838103
$419$	25.1094	1.22667	0.613337	−	0.789821i	$-0.289827\pi$
$419$	25.1094	1.22667	0.613337	+	0.789821i	$0.289827\pi$
$420$	12.8772	0.628345
$421$	11.6449	0.567538	0.283769	−	0.958893i	$-0.408415\pi$
$421$	11.6449	0.567538	0.283769	+	0.958893i	$0.408415\pi$
$422$	45.6696	2.22316
$423$	−5.54985	−0.269843
$424$	−2.15593	−0.104701
$425$	0.587365	0.0284914
$426$	33.5125	1.62369
$427$	−47.5007	−2.29872
$428$	−5.07547	−0.245332
$429$	−29.8978	−1.44348
$430$	−30.3928	−1.46567
$431$	−28.8899	−1.39158	−0.695789	−	0.718246i	$-0.744945\pi$
$431$	−28.8899	−1.39158	−0.695789	+	0.718246i	$0.744945\pi$
$432$	−28.1615	−1.35492
$433$	10.1554	0.488035	0.244018	−	0.969771i	$-0.421535\pi$
$433$	10.1554	0.488035	0.244018	+	0.969771i	$0.421535\pi$
$434$	53.4562	2.56598
$435$	−3.01698	−0.144653
$436$	−17.7328	−0.849245
$437$	−6.49300	−0.310602
$438$	−27.4682	−1.31248
$439$	−20.0788	−0.958310	−0.479155	−	0.877730i	$-0.659057\pi$
$439$	−20.0788	−0.958310	−0.479155	+	0.877730i	$0.659057\pi$
$440$	−17.9219	−0.854395
$441$	−7.32958	−0.349028
$442$	12.6761	0.602939
$443$	−14.2968	−0.679263	−0.339631	−	0.940559i	$-0.610302\pi$
$443$	−14.2968	−0.679263	−0.339631	+	0.940559i	$0.610302\pi$
$444$	12.1487	0.576553
$445$	−8.69421	−0.412145
$446$	−0.603056	−0.0285555
$447$	−19.7260	−0.933009
$448$	−1.12317	−0.0530649
$449$	21.7782	1.02778	0.513888	−	0.857857i	$-0.328205\pi$
$449$	21.7782	1.02778	0.513888	+	0.857857i	$0.328205\pi$
$450$	−0.603250	−0.0284375
$451$	29.3302	1.38110
$452$	1.48251	0.0697313
$453$	17.8808	0.840112
$454$	−5.18135	−0.243173
$455$	−31.7575	−1.48881
$456$	−3.75926	−0.176043
$457$	−6.89700	−0.322628	−0.161314	−	0.986903i	$-0.551573\pi$
$457$	−6.89700	−0.322628	−0.161314	+	0.986903i	$0.551573\pi$
$458$	−30.4270	−1.42176
$459$	−10.2873	−0.480171
$460$	9.04981	0.421949
$461$	−0.316932	−0.0147610	−0.00738049	−	0.999973i	$-0.502349\pi$
$461$	−0.316932	−0.0147610	−0.00738049	+	0.999973i	$0.502349\pi$
$462$	50.3675	2.34331
$463$	−31.4197	−1.46020	−0.730098	−	0.683342i	$-0.760526\pi$
$463$	−31.4197	−1.46020	−0.730098	+	0.683342i	$0.760526\pi$
$464$	4.97967	0.231175
$465$	−24.3537	−1.12938
$466$	13.7144	0.635309
$467$	15.0087	0.694519	0.347260	−	0.937769i	$-0.387112\pi$
$467$	15.0087	0.694519	0.347260	+	0.937769i	$0.387112\pi$
$468$	−4.73342	−0.218802
$469$	26.0290	1.20191
$470$	20.1893	0.931261
$471$	20.4789	0.943618
$472$	−7.82980	−0.360396
$473$	−43.2215	−1.98733
$474$	−9.20303	−0.422709
$475$	−0.572457	−0.0262661
$476$	−7.76419	−0.355871
$477$	1.49483	0.0684436
$478$	−20.2568	−0.926523
$479$	−23.9979	−1.09649	−0.548247	−	0.836317i	$-0.684704\pi$
$479$	−23.9979	−1.09649	−0.548247	+	0.836317i	$0.684704\pi$
$480$	17.4613	0.796997
$481$	−29.9608	−1.36610
$482$	−13.0601	−0.594871
$483$	19.0858	0.868434
$484$	21.3948	0.972490
$485$	−22.8596	−1.03800
$486$	18.3844	0.833932
$487$	−22.5092	−1.01999	−0.509995	−	0.860177i	$-0.670353\pi$
$487$	−22.5092	−1.01999	−0.509995	+	0.860177i	$0.670353\pi$
$488$	−19.3274	−0.874910
$489$	−3.91813	−0.177184
$490$	26.6636	1.20454
$491$	8.62984	0.389459	0.194730	−	0.980857i	$-0.437617\pi$
$491$	8.62984	0.389459	0.194730	+	0.980857i	$0.437617\pi$
$492$	−8.57484	−0.386584
$493$	1.81906	0.0819263
$494$	−12.3543	−0.555848
$495$	12.4263	0.558520
$496$	40.1969	1.80489
$497$	50.6222	2.27072
$498$	−15.1890	−0.680635
$499$	−11.5217	−0.515780	−0.257890	−	0.966174i	$-0.583027\pi$
$499$	−11.5217	−0.515780	−0.257890	+	0.966174i	$0.583027\pi$
$500$	13.1530	0.588219
$501$	24.8122	1.10853
$502$	48.3337	2.15724
$503$	−27.8681	−1.24258	−0.621288	−	0.783582i	$-0.713390\pi$
$503$	−27.8681	−1.24258	−0.621288	+	0.783582i	$0.713390\pi$
$504$	−5.98399	−0.266548
$505$	−31.8038	−1.41525
$506$	35.3971	1.57359
$507$	−3.42086	−0.151926
$508$	−6.53043	−0.289741
$509$	33.1858	1.47093	0.735466	−	0.677561i	$-0.236963\pi$
$509$	33.1858	1.47093	0.735466	+	0.677561i	$0.236963\pi$
$510$	9.72888	0.430802
$511$	−41.4920	−1.83550
$512$	−13.6828	−0.604700
$513$	10.0262	0.442669
$514$	36.3182	1.60193
$515$	21.3826	0.942231
$516$	12.6360	0.556270
$517$	28.7110	1.26271
$518$	50.4736	2.21768
$519$	20.2395	0.888417
$520$	−12.9217	−0.566654
$521$	6.50743	0.285096	0.142548	−	0.989788i	$-0.454471\pi$
$521$	6.50743	0.285096	0.142548	+	0.989788i	$0.454471\pi$
$522$	−1.86825	−0.0817713
$523$	−43.0607	−1.88291	−0.941455	−	0.337137i	$-0.890541\pi$
$523$	−43.0607	−1.88291	−0.941455	+	0.337137i	$0.890541\pi$
$524$	−23.5619	−1.02931
$525$	1.68271	0.0734393
$526$	18.2831	0.797180
$527$	14.6838	0.639637
$528$	37.8744	1.64827
$529$	−9.58697	−0.416825
$530$	−5.43790	−0.236207
$531$	5.42884	0.235592
$532$	7.56713	0.328077
$533$	21.1470	0.915979
$534$	9.94189	0.430228
$535$	9.60678	0.415337
$536$	10.5909	0.457456
$537$	7.45166	0.321563
$538$	29.3780	1.26658
$539$	37.9182	1.63325
$540$	−13.9743	−0.601360
$541$	16.9080	0.726932	0.363466	−	0.931607i	$-0.381593\pi$
$541$	16.9080	0.726932	0.363466	+	0.931607i	$0.381593\pi$
$542$	31.3214	1.34537
$543$	−17.3047	−0.742614
$544$	−10.5281	−0.451390
$545$	33.5643	1.43774
$546$	36.3149	1.55413
$547$	−6.58138	−0.281400	−0.140700	−	0.990052i	$-0.544935\pi$
$547$	−6.58138	−0.281400	−0.140700	+	0.990052i	$0.544935\pi$
$548$	5.70711	0.243796
$549$	13.4008	0.571931
$550$	3.12079	0.133071
$551$	−1.77289	−0.0755277
$552$	7.76576	0.330533
$553$	−13.9016	−0.591157
$554$	−14.9033	−0.633180
$555$	−22.9949	−0.976079
$556$	−1.14258	−0.0484563
$557$	−27.4639	−1.16368	−0.581841	−	0.813302i	$-0.697667\pi$
$557$	−27.4639	−1.16368	−0.581841	+	0.813302i	$0.697667\pi$
$558$	−15.0809	−0.638427
$559$	−31.1626	−1.31804
$560$	40.2301	1.70003
$561$	13.8354	0.584131
$562$	52.4954	2.21439
$563$	12.2906	0.517987	0.258993	−	0.965879i	$-0.416609\pi$
$563$	12.2906	0.517987	0.258993	+	0.965879i	$0.416609\pi$
$564$	−8.39383	−0.353444
$565$	−2.80607	−0.118052
$566$	−0.167771	−0.00705193
$567$	−17.6608	−0.741684
$568$	20.5975	0.864253
$569$	−41.3392	−1.73303	−0.866514	−	0.499152i	$-0.833645\pi$
$569$	−41.3392	−1.73303	−0.866514	+	0.499152i	$0.833645\pi$
$570$	−9.48196	−0.397156
$571$	−18.0905	−0.757064	−0.378532	−	0.925588i	$-0.623571\pi$
$571$	−18.0905	−0.757064	−0.378532	+	0.925588i	$0.623571\pi$
$572$	24.4874	1.02387
$573$	−32.4315	−1.35485
$574$	−35.6254	−1.48698
$575$	1.18256	0.0493164
$576$	0.316867	0.0132028
$577$	−27.2262	−1.13344	−0.566721	−	0.823910i	$-0.691788\pi$
$577$	−27.2262	−1.13344	−0.566721	+	0.823910i	$0.691788\pi$
$578$	24.2705	1.00952
$579$	−18.2359	−0.757857
$580$	2.47102	0.102603
$581$	−22.9437	−0.951865
$582$	26.1401	1.08354
$583$	−7.73321	−0.320277
$584$	−16.8825	−0.698605
$585$	8.95934	0.370423
$586$	−32.4405	−1.34010
$587$	−34.0089	−1.40370	−0.701849	−	0.712326i	$-0.747642\pi$
$587$	−34.0089	−1.40370	−0.701849	+	0.712326i	$0.747642\pi$
$588$	−11.0856	−0.457162
$589$	−14.3111	−0.589680
$590$	−19.7490	−0.813055
$591$	−7.92853	−0.326136
$592$	37.9542	1.55991
$593$	8.73057	0.358522	0.179261	−	0.983802i	$-0.442629\pi$
$593$	8.73057	0.358522	0.179261	+	0.983802i	$0.442629\pi$
$594$	−54.6587	−2.24267
$595$	14.6959	0.602475
$596$	16.1563	0.661789
$597$	−10.6305	−0.435078
$598$	25.5212	1.04364
$599$	31.3108	1.27933	0.639663	−	0.768655i	$-0.279074\pi$
$599$	31.3108	1.27933	0.639663	+	0.768655i	$0.279074\pi$
$600$	0.684671	0.0279516
$601$	−14.9545	−0.610007	−0.305004	−	0.952351i	$-0.598658\pi$
$601$	−14.9545	−0.610007	−0.305004	+	0.952351i	$0.598658\pi$
$602$	52.4982	2.13967
$603$	−7.34324	−0.299040
$604$	−14.6450	−0.595896
$605$	−40.4957	−1.64639
$606$	36.3679	1.47734
$607$	−8.82904	−0.358360	−0.179180	−	0.983816i	$-0.557344\pi$
$607$	−8.82904	−0.358360	−0.179180	+	0.983816i	$0.557344\pi$
$608$	10.2609	0.416135
$609$	5.21131	0.211173
$610$	−48.7494	−1.97380
$611$	20.7006	0.837457
$612$	2.19042	0.0885423
$613$	25.3203	1.02268	0.511339	−	0.859379i	$-0.329150\pi$
$613$	25.3203	1.02268	0.511339	+	0.859379i	$0.329150\pi$
$614$	−49.9101	−2.01421
$615$	16.2303	0.654470
$616$	30.9570	1.24729
$617$	16.2437	0.653946	0.326973	−	0.945034i	$-0.393971\pi$
$617$	16.2437	0.653946	0.326973	+	0.945034i	$0.393971\pi$
$618$	−24.4512	−0.983571
$619$	−1.01566	−0.0408230	−0.0204115	−	0.999792i	$-0.506498\pi$
$619$	−1.01566	−0.0408230	−0.0204115	+	0.999792i	$0.506498\pi$
$620$	19.9466	0.801073
$621$	−20.7119	−0.831138
$622$	−11.1466	−0.446939
$623$	15.0177	0.601672
$624$	27.3074	1.09317
$625$	−23.2813	−0.931251
$626$	−48.0601	−1.92087
$627$	−13.4842	−0.538509
$628$	−16.7730	−0.669314
$629$	13.8645	0.552815
$630$	−15.0934	−0.601335
$631$	38.4311	1.52992	0.764959	−	0.644079i	$-0.222759\pi$
$631$	38.4311	1.52992	0.764959	+	0.644079i	$0.222759\pi$
$632$	−5.65639	−0.224999
$633$	35.9392	1.42846
$634$	−11.9057	−0.472836
$635$	12.3607	0.490520
$636$	2.26084	0.0896483
$637$	27.3389	1.08321
$638$	9.66504	0.382643
$639$	−14.2814	−0.564964
$640$	23.8809	0.943975
$641$	−43.4914	−1.71781	−0.858903	−	0.512138i	$-0.828854\pi$
$641$	−43.4914	−1.71781	−0.858903	+	0.512138i	$0.828854\pi$
$642$	−10.9854	−0.433560
$643$	45.0616	1.77706	0.888529	−	0.458821i	$-0.151728\pi$
$643$	45.0616	1.77706	0.888529	+	0.458821i	$0.151728\pi$
$644$	−15.6319	−0.615985
$645$	−23.9173	−0.941742
$646$	5.71705	0.224934
$647$	−2.12450	−0.0835227	−0.0417613	−	0.999128i	$-0.513297\pi$
$647$	−2.12450	−0.0835227	−0.0417613	+	0.999128i	$0.513297\pi$
$648$	−7.18595	−0.282291
$649$	−28.0850	−1.10243
$650$	2.25009	0.0882557
$651$	42.0667	1.64873
$652$	3.20909	0.125678
$653$	15.6984	0.614327	0.307164	−	0.951657i	$-0.400620\pi$
$653$	15.6984	0.614327	0.307164	+	0.951657i	$0.400620\pi$
$654$	−38.3810	−1.50082
$655$	44.5976	1.74257
$656$	−26.7889	−1.04593
$657$	11.7056	0.456680
$658$	−34.8734	−1.35951
$659$	14.5096	0.565214	0.282607	−	0.959236i	$-0.408801\pi$
$659$	14.5096	0.565214	0.282607	+	0.959236i	$0.408801\pi$
$660$	18.7941	0.731558
$661$	−48.8269	−1.89914	−0.949572	−	0.313548i	$-0.898482\pi$
$661$	−48.8269	−1.89914	−0.949572	+	0.313548i	$0.898482\pi$
$662$	11.7008	0.454766
$663$	9.97530	0.387408
$664$	−9.33549	−0.362287
$665$	−14.3230	−0.555420
$666$	−14.2395	−0.551769
$667$	3.66238	0.141808
$668$	−20.3221	−0.786285
$669$	−0.474569	−0.0183479
$670$	26.7133	1.03202
$671$	−69.3263	−2.67631
$672$	−30.1614	−1.16350
$673$	−38.2960	−1.47620	−0.738101	−	0.674691i	$-0.764277\pi$
$673$	−38.2960	−1.47620	−0.738101	+	0.674691i	$0.764277\pi$
$674$	−8.03806	−0.309615
$675$	−1.82607	−0.0702854
$676$	2.80181	0.107762
$677$	40.6909	1.56388	0.781939	−	0.623356i	$-0.214231\pi$
$677$	40.6909	1.56388	0.781939	+	0.623356i	$0.214231\pi$
$678$	3.20876	0.123232
$679$	39.4859	1.51533
$680$	5.97959	0.229307
$681$	−4.07740	−0.156246
$682$	78.0182	2.98747
$683$	7.05178	0.269829	0.134914	−	0.990857i	$-0.456924\pi$
$683$	7.05178	0.269829	0.134914	+	0.990857i	$0.456924\pi$
$684$	−2.13482	−0.0816270
$685$	−10.8023	−0.412736
$686$	0.299102	0.0114198
$687$	−23.9442	−0.913528
$688$	39.4766	1.50503
$689$	−5.57563	−0.212415
$690$	19.5875	0.745685
$691$	−43.1729	−1.64237	−0.821187	−	0.570659i	$-0.806688\pi$
$691$	−43.1729	−1.64237	−0.821187	+	0.570659i	$0.806688\pi$
$692$	−16.5769	−0.630159
$693$	−21.4642	−0.815359
$694$	−49.6523	−1.88477
$695$	2.16266	0.0820344
$696$	2.12041	0.0803741
$697$	−9.78590	−0.370668
$698$	15.1649	0.573999
$699$	10.7924	0.408207
$700$	−1.37820	−0.0520909
$701$	−19.3060	−0.729178	−0.364589	−	0.931169i	$-0.618791\pi$
$701$	−19.3060	−0.729178	−0.364589	+	0.931169i	$0.618791\pi$
$702$	−39.4088	−1.48739
$703$	−13.5126	−0.509639
$704$	−1.63925	−0.0617814
$705$	15.8877	0.598366
$706$	12.5814	0.473507
$707$	54.9354	2.06606
$708$	8.21081	0.308581
$709$	−5.60958	−0.210672	−0.105336	−	0.994437i	$-0.533592\pi$
$709$	−5.60958	−0.210672	−0.105336	+	0.994437i	$0.533592\pi$
$710$	51.9530	1.94976
$711$	3.92189	0.147082
$712$	6.11051	0.229001
$713$	29.5635	1.10716
$714$	−16.8049	−0.628909
$715$	−46.3494	−1.73337
$716$	−6.10317	−0.228086
$717$	−15.9408	−0.595322
$718$	27.1936	1.01486
$719$	40.7256	1.51881	0.759404	−	0.650619i	$-0.225490\pi$
$719$	40.7256	1.51881	0.759404	+	0.650619i	$0.225490\pi$
$720$	−11.3496	−0.422976
$721$	−36.9347	−1.37552
$722$	28.1100	1.04615
$723$	−10.2775	−0.382224
$724$	14.1731	0.526740
$725$	0.322895	0.0119920
$726$	46.3072	1.71862
$727$	41.6231	1.54372	0.771858	−	0.635795i	$-0.219328\pi$
$727$	41.6231	1.54372	0.771858	+	0.635795i	$0.219328\pi$
$728$	22.3199	0.827232
$729$	28.6504	1.06113
$730$	−42.5828	−1.57606
$731$	14.4207	0.533368
$732$	20.2679	0.749123
$733$	17.1924	0.635017	0.317509	−	0.948255i	$-0.397154\pi$
$733$	17.1924	0.635017	0.317509	+	0.948255i	$0.397154\pi$
$734$	−60.8300	−2.24528
$735$	20.9826	0.773956
$736$	−21.1967	−0.781320
$737$	37.9888	1.39934
$738$	10.0506	0.369966
$739$	−4.14398	−0.152439	−0.0762195	−	0.997091i	$-0.524285\pi$
$739$	−4.14398	−0.152439	−0.0762195	+	0.997091i	$0.524285\pi$
$740$	18.8336	0.692339
$741$	−9.72212	−0.357151
$742$	9.39301	0.344828
$743$	−32.3530	−1.18692	−0.593458	−	0.804865i	$-0.702238\pi$
$743$	−32.3530	−1.18692	−0.593458	+	0.804865i	$0.702238\pi$
$744$	17.1164	0.627518
$745$	−30.5804	−1.12038
$746$	−45.8152	−1.67741
$747$	6.47282	0.236828
$748$	−11.3317	−0.414327
$749$	−16.5940	−0.606332
$750$	28.4685	1.03952
$751$	47.3663	1.72842	0.864211	−	0.503129i	$-0.167818\pi$
$751$	47.3663	1.72842	0.864211	+	0.503129i	$0.167818\pi$
$752$	−26.2234	−0.956269
$753$	38.0357	1.38610
$754$	6.96848	0.253777
$755$	27.7198	1.00883
$756$	24.1382	0.877899
$757$	20.4474	0.743175	0.371587	−	0.928398i	$-0.378814\pi$
$757$	20.4474	0.743175	0.371587	+	0.928398i	$0.378814\pi$
$758$	−7.21728	−0.262144
$759$	27.8553	1.01108
$760$	−5.82782	−0.211397
$761$	−29.4092	−1.06608	−0.533041	−	0.846090i	$-0.678951\pi$
$761$	−29.4092	−1.06608	−0.533041	+	0.846090i	$0.678951\pi$
$762$	−14.1346	−0.512041
$763$	−57.9764	−2.09889
$764$	26.5626	0.961000
$765$	−4.14599	−0.149898
$766$	−24.7111	−0.892849
$767$	−20.2493	−0.731158
$768$	−28.1468	−1.01566
$769$	−32.0952	−1.15738	−0.578691	−	0.815547i	$-0.696436\pi$
$769$	−32.0952	−1.15738	−0.578691	+	0.815547i	$0.696436\pi$
$770$	78.0827	2.81390
$771$	28.5802	1.02929
$772$	14.9358	0.537552
$773$	−28.7423	−1.03379	−0.516893	−	0.856050i	$-0.672912\pi$
$773$	−28.7423	−1.03379	−0.516893	+	0.856050i	$0.672912\pi$
$774$	−14.8107	−0.532359
$775$	2.60647	0.0936273
$776$	16.0663	0.576746
$777$	39.7197	1.42493
$778$	37.4056	1.34106
$779$	9.53753	0.341718
$780$	13.5505	0.485185
$781$	73.8821	2.64371
$782$	−11.8101	−0.422328
$783$	−5.65530	−0.202104
$784$	−34.6328	−1.23689
$785$	31.7476	1.13312
$786$	−50.9977	−1.81903
$787$	−15.8626	−0.565441	−0.282720	−	0.959202i	$-0.591237\pi$
$787$	−15.8626	−0.565441	−0.282720	+	0.959202i	$0.591237\pi$
$788$	6.49375	0.231330
$789$	14.3877	0.512214
$790$	−14.2671	−0.507600
$791$	4.84699	0.172339
$792$	−8.73352	−0.310332
$793$	−49.9841	−1.77499
$794$	45.0920	1.60026
$795$	−4.27929	−0.151771
$796$	8.70678	0.308604
$797$	22.7866	0.807142	0.403571	−	0.914948i	$-0.367769\pi$
$797$	22.7866	0.807142	0.403571	+	0.914948i	$0.367769\pi$
$798$	16.3784	0.579790
$799$	−9.57933	−0.338892
$800$	−1.86881	−0.0660725
$801$	−4.23676	−0.149699
$802$	4.46477	0.157656
$803$	−60.5567	−2.13700
$804$	−11.1062	−0.391687
$805$	29.5879	1.04284
$806$	56.2510	1.98136
$807$	23.1187	0.813817
$808$	22.3525	0.786359
$809$	14.1227	0.496529	0.248265	−	0.968692i	$-0.420140\pi$
$809$	14.1227	0.496529	0.248265	+	0.968692i	$0.420140\pi$
$810$	−18.1251	−0.636850
$811$	−17.8637	−0.627281	−0.313641	−	0.949542i	$-0.601549\pi$
$811$	−17.8637	−0.627281	−0.313641	+	0.949542i	$0.601549\pi$
$812$	−4.26825	−0.149786
$813$	24.6480	0.864444
$814$	73.6652	2.58196
$815$	−6.07412	−0.212767
$816$	−12.6366	−0.442371
$817$	−14.0547	−0.491711
$818$	12.8494	0.449270
$819$	−15.4757	−0.540764
$820$	−13.2932	−0.464219
$821$	−8.90320	−0.310724	−0.155362	−	0.987858i	$-0.549654\pi$
$821$	−8.90320	−0.310724	−0.155362	+	0.987858i	$0.549654\pi$
$822$	12.3525	0.430845
$823$	7.92475	0.276239	0.138120	−	0.990416i	$-0.455894\pi$
$823$	7.92475	0.276239	0.138120	+	0.990416i	$0.455894\pi$
$824$	−15.0283	−0.523534
$825$	2.45588	0.0855026
$826$	34.1130	1.18694
$827$	39.2178	1.36374	0.681869	−	0.731475i	$-0.261168\pi$
$827$	39.2178	1.36374	0.681869	+	0.731475i	$0.261168\pi$
$828$	4.41005	0.153260
$829$	−40.4664	−1.40545	−0.702727	−	0.711459i	$-0.748035\pi$
$829$	−40.4664	−1.40545	−0.702727	+	0.711459i	$0.748035\pi$
$830$	−23.5469	−0.817323
$831$	−11.7280	−0.406839
$832$	−1.18189	−0.0409748
$833$	−12.6513	−0.438340
$834$	−2.47302	−0.0856337
$835$	38.4653	1.33115
$836$	11.0441	0.381968
$837$	−45.6507	−1.57792
$838$	−44.5123	−1.53765
$839$	−22.7643	−0.785912	−0.392956	−	0.919557i	$-0.628548\pi$
$839$	−22.7643	−0.785912	−0.392956	+	0.919557i	$0.628548\pi$
$840$	17.1306	0.591060
$841$	1.00000	0.0344828
$842$	−20.6433	−0.711416
$843$	41.3107	1.42282
$844$	−29.4355	−1.01321
$845$	−5.30322	−0.182436
$846$	9.83840	0.338251
$847$	69.9492	2.40348
$848$	7.06317	0.242550
$849$	−0.132025	−0.00453110
$850$	−1.04124	−0.0357143
$851$	27.9140	0.956880
$852$	−21.5998	−0.739998
$853$	−3.83624	−0.131350	−0.0656751	−	0.997841i	$-0.520920\pi$
$853$	−3.83624	−0.131350	−0.0656751	+	0.997841i	$0.520920\pi$
$854$	84.2060	2.88147
$855$	4.04076	0.138191
$856$	−6.75189	−0.230775
$857$	−39.8323	−1.36064	−0.680322	−	0.732913i	$-0.738160\pi$
$857$	−39.8323	−1.36064	−0.680322	+	0.732913i	$0.738160\pi$
$858$	53.0009	1.80942
$859$	14.0912	0.480787	0.240393	−	0.970676i	$-0.422724\pi$
$859$	14.0912	0.480787	0.240393	+	0.970676i	$0.422724\pi$
$860$	19.5891	0.667983
$861$	−28.0350	−0.955431
$862$	51.2141	1.74436
$863$	−40.5117	−1.37903	−0.689517	−	0.724269i	$-0.742177\pi$
$863$	−40.5117	−1.37903	−0.689517	+	0.724269i	$0.742177\pi$
$864$	32.7311	1.11353
$865$	31.3765	1.06683
$866$	−18.0027	−0.611758
$867$	19.0994	0.648651
$868$	−34.4542	−1.16945
$869$	−20.2891	−0.688262
$870$	5.34831	0.181325
$871$	27.3899	0.928070
$872$	−23.5898	−0.798853
$873$	−11.1397	−0.377020
$874$	11.5103	0.389343
$875$	43.0030	1.45377
$876$	17.7041	0.598166
$877$	5.64130	0.190493	0.0952466	−	0.995454i	$-0.469636\pi$
$877$	5.64130	0.190493	0.0952466	+	0.995454i	$0.469636\pi$
$878$	35.5944	1.20125
$879$	−25.5287	−0.861060
$880$	58.7151	1.97929
$881$	−23.0396	−0.776222	−0.388111	−	0.921613i	$-0.626872\pi$
$881$	−23.0396	−0.776222	−0.388111	+	0.921613i	$0.626872\pi$
$882$	12.9934	0.437510
$883$	−8.33649	−0.280545	−0.140273	−	0.990113i	$-0.544798\pi$
$883$	−8.33649	−0.280545	−0.140273	+	0.990113i	$0.544798\pi$
$884$	−8.17013	−0.274791
$885$	−15.5413	−0.522415
$886$	25.3445	0.851464
$887$	33.6630	1.13029	0.565146	−	0.824991i	$-0.308820\pi$
$887$	33.6630	1.13029	0.565146	+	0.824991i	$0.308820\pi$
$888$	16.1614	0.542341
$889$	−21.3509	−0.716088
$890$	15.4125	0.516628
$891$	−25.7756	−0.863515
$892$	0.388689	0.0130143
$893$	9.33620	0.312424
$894$	34.9690	1.16954
$895$	11.5520	0.386141
$896$	−41.2500	−1.37807
$897$	20.0836	0.670574
$898$	−38.6069	−1.28833
$899$	8.07220	0.269223
$900$	0.388813	0.0129604
$901$	2.58016	0.0859574
$902$	−51.9946	−1.73123
$903$	41.3129	1.37481
$904$	1.97218	0.0655936
$905$	−26.8267	−0.891749
$906$	−31.6978	−1.05309
$907$	51.6497	1.71500	0.857501	−	0.514483i	$-0.172016\pi$
$907$	51.6497	1.71500	0.857501	+	0.514483i	$0.172016\pi$
$908$	3.33954	0.110827
$909$	−15.4983	−0.514045
$910$	56.2975	1.86624
$911$	14.8868	0.493221	0.246610	−	0.969115i	$-0.420683\pi$
$911$	14.8868	0.493221	0.246610	+	0.969115i	$0.420683\pi$
$912$	12.3159	0.407821
$913$	−33.4859	−1.10822
$914$	12.2265	0.404418
$915$	−38.3628	−1.26823
$916$	19.6111	0.647970
$917$	−77.0344	−2.54390
$918$	18.2367	0.601900
$919$	−28.3293	−0.934498	−0.467249	−	0.884126i	$-0.654755\pi$
$919$	−28.3293	−0.934498	−0.467249	+	0.884126i	$0.654755\pi$
$920$	12.0389	0.396912
$921$	−39.2762	−1.29420
$922$	0.561835	0.0185031
$923$	53.2689	1.75337
$924$	−32.4634	−1.06797
$925$	2.46105	0.0809188
$926$	55.6987	1.83037
$927$	10.4199	0.342236
$928$	−5.78768	−0.189990
$929$	−4.84591	−0.158989	−0.0794947	−	0.996835i	$-0.525331\pi$
$929$	−4.84591	−0.158989	−0.0794947	+	0.996835i	$0.525331\pi$
$930$	43.1726	1.41569
$931$	12.3302	0.404105
$932$	−8.83939	−0.289544
$933$	−8.77171	−0.287173
$934$	−26.6064	−0.870588
$935$	21.4484	0.701439
$936$	−6.29685	−0.205819
$937$	0.553136	0.0180702	0.00903509	−	0.999959i	$-0.497124\pi$
$937$	0.553136	0.0180702	0.00903509	+	0.999959i	$0.497124\pi$
$938$	−46.1425	−1.50661
$939$	−37.8204	−1.23422
$940$	−13.0126	−0.424424
$941$	49.5592	1.61558	0.807792	−	0.589468i	$-0.200663\pi$
$941$	49.5592	1.61558	0.807792	+	0.589468i	$0.200663\pi$
$942$	−36.3036	−1.18284
$943$	−19.7023	−0.641596
$944$	25.6516	0.834889
$945$	−45.6885	−1.48625
$946$	76.6201	2.49113
$947$	−5.00757	−0.162724	−0.0813621	−	0.996685i	$-0.525927\pi$
$947$	−5.00757	−0.162724	−0.0813621	+	0.996685i	$0.525927\pi$
$948$	5.93164	0.192651
$949$	−43.6613	−1.41731
$950$	1.01481	0.0329249
$951$	−9.36907	−0.303813
$952$	−10.3287	−0.334755
$953$	−25.2521	−0.817997	−0.408999	−	0.912535i	$-0.634122\pi$
$953$	−25.2521	−0.817997	−0.408999	+	0.912535i	$0.634122\pi$
$954$	−2.64993	−0.0857948
$955$	−50.2772	−1.62693
$956$	13.0561	0.422265
$957$	7.60580	0.245861
$958$	42.5419	1.37447
$959$	18.6591	0.602534
$960$	−0.907103	−0.0292766
$961$	34.1605	1.10195
$962$	53.1125	1.71242
$963$	4.68147	0.150858
$964$	8.41764	0.271114
$965$	−28.2703	−0.910054
$966$	−33.8340	−1.08859
$967$	−23.2433	−0.747454	−0.373727	−	0.927539i	$-0.621920\pi$
$967$	−23.2433	−0.747454	−0.373727	+	0.927539i	$0.621920\pi$
$968$	28.4614	0.914785
$969$	4.49897	0.144528
$970$	40.5239	1.30114
$971$	−5.37637	−0.172536	−0.0862680	−	0.996272i	$-0.527494\pi$
$971$	−5.37637	−0.172536	−0.0862680	+	0.996272i	$0.527494\pi$
$972$	−11.8493	−0.380066
$973$	−3.73562	−0.119758
$974$	39.9029	1.27857
$975$	1.77068	0.0567072
$976$	63.3196	2.02681
$977$	45.4013	1.45252	0.726259	−	0.687421i	$-0.241257\pi$
$977$	45.4013	1.45252	0.726259	+	0.687421i	$0.241257\pi$
$978$	6.94580	0.222102
$979$	21.9181	0.700504
$980$	−17.1855	−0.548971
$981$	16.3562	0.522212
$982$	−15.2984	−0.488192
$983$	−23.4219	−0.747043	−0.373522	−	0.927621i	$-0.621850\pi$
$983$	−23.4219	−0.747043	−0.373522	+	0.927621i	$0.621850\pi$
$984$	−11.4071	−0.363645
$985$	−12.2913	−0.391632
$986$	−3.22470	−0.102696
$987$	−27.4432	−0.873527
$988$	7.96276	0.253329
$989$	29.0337	0.923218
$990$	−22.0285	−0.700112
$991$	−17.4885	−0.555542	−0.277771	−	0.960647i	$-0.589596\pi$
$991$	−17.4885	−0.555542	−0.277771	+	0.960647i	$0.589596\pi$
$992$	−46.7193	−1.48334
$993$	9.20784	0.292202
$994$	−89.7397	−2.84637
$995$	−16.4801	−0.522453
$996$	9.78978	0.310201
$997$	12.1176	0.383769	0.191884	−	0.981418i	$-0.438540\pi$
$997$	12.1176	0.383769	0.191884	+	0.981418i	$0.438540\pi$
$998$	20.4248	0.646537
$999$	−43.1037	−1.36374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.13	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.13	✓	61	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-1.77273 q^{2} -1.39503 q^{3} +1.14258 q^{4} -2.16266 q^{5} +2.47302 q^{6} +3.73562 q^{7} +1.51997 q^{8} -1.05388 q^{9} +O(q^{10})\)	\(q-1.77273 q^{2} -1.39503 q^{3} +1.14258 q^{4} -2.16266 q^{5} +2.47302 q^{6} +3.73562 q^{7} +1.51997 q^{8} -1.05388 q^{9} +3.83382 q^{10} +5.45206 q^{11} -1.59394 q^{12} +3.93093 q^{13} -6.62225 q^{14} +3.01698 q^{15} -4.97967 q^{16} -1.81906 q^{17} +1.86825 q^{18} +1.77289 q^{19} -2.47102 q^{20} -5.21131 q^{21} -9.66504 q^{22} -3.66238 q^{23} -2.12041 q^{24} -0.322895 q^{25} -6.96848 q^{26} +5.65530 q^{27} +4.26825 q^{28} -1.00000 q^{29} -5.34831 q^{30} -8.07220 q^{31} +5.78768 q^{32} -7.60580 q^{33} +3.22470 q^{34} -8.07888 q^{35} -1.20415 q^{36} -7.62182 q^{37} -3.14286 q^{38} -5.48377 q^{39} -3.28719 q^{40} +5.37965 q^{41} +9.23826 q^{42} -7.92755 q^{43} +6.22942 q^{44} +2.27919 q^{45} +6.49242 q^{46} +5.26609 q^{47} +6.94680 q^{48} +6.95483 q^{49} +0.572407 q^{50} +2.53765 q^{51} +4.49140 q^{52} -1.41840 q^{53} -10.0253 q^{54} -11.7910 q^{55} +5.67804 q^{56} -2.47324 q^{57} +1.77273 q^{58} -5.15127 q^{59} +3.44715 q^{60} -12.7156 q^{61} +14.3099 q^{62} -3.93691 q^{63} -0.300666 q^{64} -8.50126 q^{65} +13.4831 q^{66} +6.96779 q^{67} -2.07842 q^{68} +5.10914 q^{69} +14.3217 q^{70} +13.5512 q^{71} -1.60188 q^{72} -11.1071 q^{73} +13.5115 q^{74} +0.450449 q^{75} +2.02567 q^{76} +20.3668 q^{77} +9.72126 q^{78} -3.72137 q^{79} +10.7693 q^{80} -4.72768 q^{81} -9.53669 q^{82} -6.14188 q^{83} -5.95434 q^{84} +3.93401 q^{85} +14.0534 q^{86} +1.39503 q^{87} +8.28699 q^{88} +4.02014 q^{89} -4.04040 q^{90} +14.6844 q^{91} -4.18457 q^{92} +11.2610 q^{93} -9.33537 q^{94} -3.83416 q^{95} -8.07400 q^{96} +10.5701 q^{97} -12.3291 q^{98} -5.74584 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * q^99

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