LMFDB - Embedded newform 3481.2.a.q.1.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3481,2,Mod(1,3481)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3481, 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("3481.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3481 = 59^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3481.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:	$27.7959249436$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	no (minimal twist has level 59)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.30
Character	$\chi$	$=$	3481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.611364 q^{2} -3.05270 q^{3} -1.62623 q^{4} +3.28972 q^{5} -1.86631 q^{6} +0.863698 q^{7} -2.21695 q^{8} +6.31896 q^{9} +O(q^{10})$	\(q+0.611364 q^{2} -3.05270 q^{3} -1.62623 q^{4} +3.28972 q^{5} -1.86631 q^{6} +0.863698 q^{7} -2.21695 q^{8} +6.31896 q^{9} +2.01122 q^{10} +3.90068 q^{11} +4.96440 q^{12} +1.64962 q^{13} +0.528034 q^{14} -10.0425 q^{15} +1.89711 q^{16} +3.36707 q^{17} +3.86318 q^{18} +4.36110 q^{19} -5.34986 q^{20} -2.63661 q^{21} +2.38473 q^{22} +2.09334 q^{23} +6.76767 q^{24} +5.82229 q^{25} +1.00852 q^{26} -10.1318 q^{27} -1.40458 q^{28} -4.34024 q^{29} -6.13964 q^{30} +8.10782 q^{31} +5.59372 q^{32} -11.9076 q^{33} +2.05851 q^{34} +2.84133 q^{35} -10.2761 q^{36} +1.24053 q^{37} +2.66622 q^{38} -5.03578 q^{39} -7.29315 q^{40} -3.33261 q^{41} -1.61193 q^{42} -2.91270 q^{43} -6.34342 q^{44} +20.7876 q^{45} +1.27979 q^{46} +6.84105 q^{47} -5.79129 q^{48} -6.25403 q^{49} +3.55954 q^{50} -10.2787 q^{51} -2.68266 q^{52} -2.21291 q^{53} -6.19420 q^{54} +12.8322 q^{55} -1.91477 q^{56} -13.3131 q^{57} -2.65347 q^{58} +16.3315 q^{60} -11.7340 q^{61} +4.95683 q^{62} +5.45767 q^{63} -0.374415 q^{64} +5.42678 q^{65} -7.27987 q^{66} -4.25928 q^{67} -5.47565 q^{68} -6.39034 q^{69} +1.73709 q^{70} +10.6034 q^{71} -14.0088 q^{72} -12.2620 q^{73} +0.758418 q^{74} -17.7737 q^{75} -7.09217 q^{76} +3.36901 q^{77} -3.07869 q^{78} +10.4329 q^{79} +6.24096 q^{80} +11.9724 q^{81} -2.03743 q^{82} +5.75110 q^{83} +4.28774 q^{84} +11.0767 q^{85} -1.78072 q^{86} +13.2494 q^{87} -8.64760 q^{88} -2.47470 q^{89} +12.7088 q^{90} +1.42477 q^{91} -3.40427 q^{92} -24.7507 q^{93} +4.18237 q^{94} +14.3468 q^{95} -17.0759 q^{96} +9.55094 q^{97} -3.82348 q^{98} +24.6482 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 13 q^{2} + 3 q^{3} + 43 q^{4} + 2 q^{5} + 21 q^{6} + 3 q^{7} + 33 q^{8} + 33 q^{9}+O(q^{10}) $ 56 * q + 13 * q^2 + 3 * q^3 + 43 * q^4 + 2 * q^5 + 21 * q^6 + 3 * q^7 + 33 * q^8 + 33 * q^9	\( 56 q + 13 q^{2} + 3 q^{3} + 43 q^{4} + 2 q^{5} + 21 q^{6} + 3 q^{7} + 33 q^{8} + 33 q^{9} + 16 q^{10} + 51 q^{11} + 25 q^{12} + 26 q^{13} + 37 q^{14} - 27 q^{15} + 25 q^{16} - 34 q^{17} + 23 q^{18} + 7 q^{19} + 18 q^{20} - 35 q^{21} + 14 q^{22} + 71 q^{23} + 60 q^{24} + 12 q^{25} + 17 q^{26} - 18 q^{27} + 29 q^{28} + 8 q^{29} + 29 q^{30} + 71 q^{31} + 69 q^{32} + 27 q^{33} + 30 q^{34} - 15 q^{35} + 10 q^{36} + 19 q^{37} + 57 q^{38} + 79 q^{39} + 33 q^{40} + 26 q^{41} + 27 q^{42} + 34 q^{43} + 109 q^{44} - 5 q^{45} + 28 q^{46} + 111 q^{47} + 89 q^{48} - q^{49} + 59 q^{50} + 42 q^{51} + 52 q^{52} + 32 q^{53} + 43 q^{54} + 70 q^{55} + 95 q^{56} - 2 q^{57} - 6 q^{58} - 105 q^{60} + 67 q^{61} + 24 q^{62} - 116 q^{63} + 11 q^{64} + 66 q^{65} + 58 q^{66} + 24 q^{67} - 104 q^{68} + 66 q^{69} - 26 q^{70} - 9 q^{71} + 47 q^{72} + 17 q^{73} - 63 q^{74} - 116 q^{75} - 53 q^{76} + 69 q^{77} + 74 q^{78} + 35 q^{79} - 48 q^{80} + 4 q^{81} - 29 q^{82} + 135 q^{83} - 76 q^{84} + 34 q^{85} - 46 q^{86} + 11 q^{87} + 102 q^{88} + 134 q^{89} + 24 q^{90} + 63 q^{91} + 92 q^{92} - 3 q^{93} - 26 q^{94} - 127 q^{95} + 98 q^{96} - 2 q^{97} + 57 q^{98} + 94 q^{99}+O(q^{100}) \) 56 * q + 13 * q^2 + 3 * q^3 + 43 * q^4 + 2 * q^5 + 21 * q^6 + 3 * q^7 + 33 * q^8 + 33 * q^9 + 16 * q^10 + 51 * q^11 + 25 * q^12 + 26 * q^13 + 37 * q^14 - 27 * q^15 + 25 * q^16 - 34 * q^17 + 23 * q^18 + 7 * q^19 + 18 * q^20 - 35 * q^21 + 14 * q^22 + 71 * q^23 + 60 * q^24 + 12 * q^25 + 17 * q^26 - 18 * q^27 + 29 * q^28 + 8 * q^29 + 29 * q^30 + 71 * q^31 + 69 * q^32 + 27 * q^33 + 30 * q^34 - 15 * q^35 + 10 * q^36 + 19 * q^37 + 57 * q^38 + 79 * q^39 + 33 * q^40 + 26 * q^41 + 27 * q^42 + 34 * q^43 + 109 * q^44 - 5 * q^45 + 28 * q^46 + 111 * q^47 + 89 * q^48 - q^49 + 59 * q^50 + 42 * q^51 + 52 * q^52 + 32 * q^53 + 43 * q^54 + 70 * q^55 + 95 * q^56 - 2 * q^57 - 6 * q^58 - 105 * q^60 + 67 * q^61 + 24 * q^62 - 116 * q^63 + 11 * q^64 + 66 * q^65 + 58 * q^66 + 24 * q^67 - 104 * q^68 + 66 * q^69 - 26 * q^70 - 9 * q^71 + 47 * q^72 + 17 * q^73 - 63 * q^74 - 116 * q^75 - 53 * q^76 + 69 * q^77 + 74 * q^78 + 35 * q^79 - 48 * q^80 + 4 * q^81 - 29 * q^82 + 135 * q^83 - 76 * q^84 + 34 * q^85 - 46 * q^86 + 11 * q^87 + 102 * q^88 + 134 * q^89 + 24 * q^90 + 63 * q^91 + 92 * q^92 - 3 * q^93 - 26 * q^94 - 127 * q^95 + 98 * q^96 - 2 * q^97 + 57 * q^98 + 94 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.611364	0.432300	0.216150	−	0.976360i	$-0.430650\pi$
$2$	0.611364	0.432300	0.216150	+	0.976360i	$0.430650\pi$
$3$	−3.05270	−1.76248	−0.881238	−	0.472673i	$-0.843289\pi$
$3$	−3.05270	−1.76248	−0.881238	+	0.472673i	$0.843289\pi$
$4$	−1.62623	−0.813117
$5$	3.28972	1.47121	0.735605	−	0.677411i	$-0.236898\pi$
$5$	3.28972	1.47121	0.735605	+	0.677411i	$0.236898\pi$
$6$	−1.86631	−0.761917
$7$	0.863698	0.326447	0.163224	−	0.986589i	$-0.447811\pi$
$7$	0.863698	0.326447	0.163224	+	0.986589i	$0.447811\pi$
$8$	−2.21695	−0.783810
$9$	6.31896	2.10632
$10$	2.01122	0.636003
$11$	3.90068	1.17610	0.588049	−	0.808825i	$-0.299896\pi$
$11$	3.90068	1.17610	0.588049	+	0.808825i	$0.299896\pi$
$12$	4.96440	1.43310
$13$	1.64962	0.457521	0.228761	−	0.973483i	$-0.426533\pi$
$13$	1.64962	0.457521	0.228761	+	0.973483i	$0.426533\pi$
$14$	0.528034	0.141123
$15$	−10.0425	−2.59297
$16$	1.89711	0.474277
$17$	3.36707	0.816635	0.408318	−	0.912840i	$-0.366116\pi$
$17$	3.36707	0.816635	0.408318	+	0.912840i	$0.366116\pi$
$18$	3.86318	0.910561
$19$	4.36110	1.00050	0.500252	−	0.865880i	$-0.333241\pi$
$19$	4.36110	1.00050	0.500252	+	0.865880i	$0.333241\pi$
$20$	−5.34986	−1.19627
$21$	−2.63661	−0.575355
$22$	2.38473	0.508427
$23$	2.09334	0.436492	0.218246	−	0.975894i	$-0.429966\pi$
$23$	2.09334	0.436492	0.218246	+	0.975894i	$0.429966\pi$
$24$	6.76767	1.38145
$25$	5.82229	1.16446
$26$	1.00852	0.197786
$27$	−10.1318	−1.94986
$28$	−1.40458	−0.265440
$29$	−4.34024	−0.805963	−0.402982	−	0.915208i	$-0.632026\pi$
$29$	−4.34024	−0.805963	−0.402982	+	0.915208i	$0.632026\pi$
$30$	−6.13964	−1.12094
$31$	8.10782	1.45621	0.728104	−	0.685467i	$-0.240402\pi$
$31$	8.10782	1.45621	0.728104	+	0.685467i	$0.240402\pi$
$32$	5.59372	0.988839
$33$	−11.9076	−2.07284
$34$	2.05851	0.353031
$35$	2.84133	0.480272
$36$	−10.2761	−1.71268
$37$	1.24053	0.203943	0.101971	−	0.994787i	$-0.467485\pi$
$37$	1.24053	0.203943	0.101971	+	0.994787i	$0.467485\pi$
$38$	2.66622	0.432518
$39$	−5.03578	−0.806370
$40$	−7.29315	−1.15315
$41$	−3.33261	−0.520466	−0.260233	−	0.965546i	$-0.583799\pi$
$41$	−3.33261	−0.520466	−0.260233	+	0.965546i	$0.583799\pi$
$42$	−1.61193	−0.248726
$43$	−2.91270	−0.444183	−0.222091	−	0.975026i	$-0.571288\pi$
$43$	−2.91270	−0.444183	−0.222091	+	0.975026i	$0.571288\pi$
$44$	−6.34342	−0.956306
$45$	20.7876	3.09884
$46$	1.27979	0.188695
$47$	6.84105	0.997870	0.498935	−	0.866639i	$-0.333725\pi$
$47$	6.84105	0.997870	0.498935	+	0.866639i	$0.333725\pi$
$48$	−5.79129	−0.835901
$49$	−6.25403	−0.893432
$50$	3.55954	0.503394
$51$	−10.2787	−1.43930
$52$	−2.68266	−0.372018
$53$	−2.21291	−0.303966	−0.151983	−	0.988383i	$-0.548566\pi$
$53$	−2.21291	−0.303966	−0.151983	+	0.988383i	$0.548566\pi$
$54$	−6.19420	−0.842924
$55$	12.8322	1.73029
$56$	−1.91477	−0.255873
$57$	−13.3131	−1.76337
$58$	−2.65347	−0.348417
$59$	0	0
$59$	0	0
$60$	16.3315	2.10839
$61$	−11.7340	−1.50239	−0.751195	−	0.660081i	$-0.770522\pi$
$61$	−11.7340	−1.50239	−0.751195	+	0.660081i	$0.770522\pi$
$62$	4.95683	0.629518
$63$	5.45767	0.687602
$64$	−0.374415	−0.0468019
$65$	5.42678	0.673110
$66$	−7.27987	−0.896090
$67$	−4.25928	−0.520354	−0.260177	−	0.965561i	$-0.583781\pi$
$67$	−4.25928	−0.520354	−0.260177	+	0.965561i	$0.583781\pi$
$68$	−5.47565	−0.664020
$69$	−6.39034	−0.769307
$70$	1.73709	0.207622
$71$	10.6034	1.25839	0.629193	−	0.777249i	$-0.283385\pi$
$71$	10.6034	1.25839	0.629193	+	0.777249i	$0.283385\pi$
$72$	−14.0088	−1.65095
$73$	−12.2620	−1.43516	−0.717579	−	0.696477i	$-0.754750\pi$
$73$	−12.2620	−1.43516	−0.717579	+	0.696477i	$0.754750\pi$
$74$	0.758418	0.0881643
$75$	−17.7737	−2.05233
$76$	−7.09217	−0.813528
$77$	3.36901	0.383934
$78$	−3.07869	−0.348593
$79$	10.4329	1.17379	0.586895	−	0.809663i	$-0.300350\pi$
$79$	10.4329	1.17379	0.586895	+	0.809663i	$0.300350\pi$
$80$	6.24096	0.697760
$81$	11.9724	1.33026
$82$	−2.03743	−0.224997
$83$	5.75110	0.631265	0.315633	−	0.948882i	$-0.397783\pi$
$83$	5.75110	0.631265	0.315633	+	0.948882i	$0.397783\pi$
$84$	4.28774	0.467831
$85$	11.0767	1.20144
$86$	−1.78072	−0.192020
$87$	13.2494	1.42049
$88$	−8.64760	−0.921837
$89$	−2.47470	−0.262317	−0.131159	−	0.991361i	$-0.541870\pi$
$89$	−2.47470	−0.262317	−0.131159	+	0.991361i	$0.541870\pi$
$90$	12.7088	1.33963
$91$	1.42477	0.149357
$92$	−3.40427	−0.354919
$93$	−24.7507	−2.56653
$94$	4.18237	0.431379
$95$	14.3468	1.47195
$96$	−17.0759	−1.74280
$97$	9.55094	0.969751	0.484875	−	0.874583i	$-0.338865\pi$
$97$	9.55094	0.969751	0.484875	+	0.874583i	$0.338865\pi$
$98$	−3.82348	−0.386230
$99$	24.6482	2.47724
$100$	−9.46840	−0.946840
$101$	−9.16748	−0.912198	−0.456099	−	0.889929i	$-0.650754\pi$
$101$	−9.16748	−0.912198	−0.456099	+	0.889929i	$0.650754\pi$
$102$	−6.28400	−0.622208
$103$	−0.576469	−0.0568012	−0.0284006	−	0.999597i	$-0.509041\pi$
$103$	−0.576469	−0.0568012	−0.0284006	+	0.999597i	$0.509041\pi$
$104$	−3.65712	−0.358610
$105$	−8.67372	−0.846468
$106$	−1.35289	−0.131405
$107$	−4.68578	−0.452991	−0.226496	−	0.974012i	$-0.572727\pi$
$107$	−4.68578	−0.452991	−0.226496	+	0.974012i	$0.572727\pi$
$108$	16.4766	1.58547
$109$	4.55930	0.436701	0.218351	−	0.975870i	$-0.429932\pi$
$109$	4.55930	0.436701	0.218351	+	0.975870i	$0.429932\pi$
$110$	7.84512	0.748002
$111$	−3.78698	−0.359444
$112$	1.63853	0.154826
$113$	8.15560	0.767215	0.383607	−	0.923496i	$-0.374682\pi$
$113$	8.15560	0.767215	0.383607	+	0.923496i	$0.374682\pi$
$114$	−8.13916	−0.762302
$115$	6.88653	0.642172
$116$	7.05825	0.655342
$117$	10.4239	0.963686
$118$	0	0
$119$	2.90814	0.266588
$120$	22.2638	2.03240
$121$	4.21529	0.383208
$122$	−7.17377	−0.649482
$123$	10.1734	0.917308
$124$	−13.1852	−1.18407
$125$	2.70510	0.241951
$126$	3.33662	0.297250
$127$	−8.04424	−0.713811	−0.356906	−	0.934140i	$-0.616168\pi$
$127$	−8.04424	−0.713811	−0.356906	+	0.934140i	$0.616168\pi$
$128$	−11.4163	−1.00907
$129$	8.89159	0.782861
$130$	3.31774	0.290985
$131$	8.14747	0.711848	0.355924	−	0.934515i	$-0.384166\pi$
$131$	8.14747	0.711848	0.355924	+	0.934515i	$0.384166\pi$
$132$	19.3645	1.68547
$133$	3.76668	0.326612
$134$	−2.60397	−0.224949
$135$	−33.3307	−2.86865
$136$	−7.46463	−0.640087
$137$	8.11900	0.693653	0.346827	−	0.937929i	$-0.387259\pi$
$137$	8.11900	0.693653	0.346827	+	0.937929i	$0.387259\pi$
$138$	−3.90683	−0.332571
$139$	−4.26377	−0.361648	−0.180824	−	0.983515i	$-0.557876\pi$
$139$	−4.26377	−0.361648	−0.180824	+	0.983515i	$0.557876\pi$
$140$	−4.62067	−0.390518
$141$	−20.8837	−1.75872
$142$	6.48251	0.544000
$143$	6.43462	0.538090
$144$	11.9877	0.998978
$145$	−14.2782	−1.18574
$146$	−7.49654	−0.620418
$147$	19.0916	1.57465
$148$	−2.01740	−0.165829
$149$	−9.23562	−0.756611	−0.378306	−	0.925681i	$-0.623493\pi$
$149$	−9.23562	−0.756611	−0.378306	+	0.925681i	$0.623493\pi$
$150$	−10.8662	−0.887220
$151$	22.2323	1.80924	0.904620	−	0.426218i	$-0.140155\pi$
$151$	22.2323	1.80924	0.904620	+	0.426218i	$0.140155\pi$
$152$	−9.66833	−0.784205
$153$	21.2764	1.72009
$154$	2.05969	0.165975
$155$	26.6725	2.14239
$156$	8.18936	0.655673
$157$	8.13867	0.649537	0.324768	−	0.945794i	$-0.394714\pi$
$157$	8.13867	0.649537	0.324768	+	0.945794i	$0.394714\pi$
$158$	6.37829	0.507429
$159$	6.75534	0.535733
$160$	18.4018	1.45479
$161$	1.80802	0.142492
$162$	7.31947	0.575072
$163$	−14.5761	−1.14169	−0.570846	−	0.821057i	$-0.693385\pi$
$163$	−14.5761	−1.14169	−0.570846	+	0.821057i	$0.693385\pi$
$164$	5.41960	0.423200
$165$	−39.1727	−3.04959
$166$	3.51601	0.272896
$167$	−16.9905	−1.31477	−0.657383	−	0.753556i	$-0.728337\pi$
$167$	−16.9905	−1.31477	−0.657383	+	0.753556i	$0.728337\pi$
$168$	5.84523	0.450969
$169$	−10.2788	−0.790674
$170$	6.77192	0.519383
$171$	27.5576	2.10738
$172$	4.73673	0.361172
$173$	−18.9775	−1.44283	−0.721417	−	0.692501i	$-0.756509\pi$
$173$	−18.9775	−1.44283	−0.721417	+	0.692501i	$0.756509\pi$
$174$	8.10023	0.614077
$175$	5.02870	0.380134
$176$	7.40000	0.557796
$177$	0	0
$178$	−1.51294	−0.113400
$179$	17.9578	1.34223	0.671116	−	0.741353i	$-0.265815\pi$
$179$	17.9578	1.34223	0.671116	+	0.741353i	$0.265815\pi$
$180$	−33.8056	−2.51972
$181$	23.7646	1.76641	0.883203	−	0.468991i	$-0.155382\pi$
$181$	23.7646	1.76641	0.883203	+	0.468991i	$0.155382\pi$
$182$	0.871054	0.0645668
$183$	35.8205	2.64792
$184$	−4.64084	−0.342127
$185$	4.08102	0.300042
$186$	−15.1317	−1.10951
$187$	13.1339	0.960444
$188$	−11.1252	−0.811385
$189$	−8.75080	−0.636527
$190$	8.77113	0.636324
$191$	−4.93069	−0.356772	−0.178386	−	0.983961i	$-0.557088\pi$
$191$	−4.93069	−0.356772	−0.178386	+	0.983961i	$0.557088\pi$
$192$	1.14298	0.0824873
$193$	19.1198	1.37627	0.688135	−	0.725583i	$-0.258430\pi$
$193$	19.1198	1.37627	0.688135	+	0.725583i	$0.258430\pi$
$194$	5.83910	0.419223
$195$	−16.5663	−1.18634
$196$	10.1705	0.726465
$197$	9.10388	0.648625	0.324312	−	0.945950i	$-0.394867\pi$
$197$	9.10388	0.648625	0.324312	+	0.945950i	$0.394867\pi$
$198$	15.0690	1.07091
$199$	9.47989	0.672011	0.336006	−	0.941860i	$-0.390924\pi$
$199$	9.47989	0.672011	0.336006	+	0.941860i	$0.390924\pi$
$200$	−12.9077	−0.912713
$201$	13.0023	0.917111
$202$	−5.60466	−0.394343
$203$	−3.74866	−0.263104
$204$	16.7155	1.17032
$205$	−10.9634	−0.765714
$206$	−0.352432	−0.0245551
$207$	13.2278	0.919392
$208$	3.12950	0.216992
$209$	17.0112	1.17669
$210$	−5.30280	−0.365928
$211$	27.8736	1.91890	0.959449	−	0.281883i	$-0.0909591\pi$
$211$	27.8736	1.91890	0.959449	+	0.281883i	$0.0909591\pi$
$212$	3.59871	0.247160
$213$	−32.3688	−2.21787
$214$	−2.86472	−0.195828
$215$	−9.58198	−0.653486
$216$	22.4616	1.52832
$217$	7.00271	0.475375
$218$	2.78739	0.188786
$219$	37.4322	2.52943
$220$	−20.8681	−1.40693
$221$	5.55438	0.373628
$222$	−2.31522	−0.155387
$223$	−2.89535	−0.193887	−0.0969436	−	0.995290i	$-0.530907\pi$
$223$	−2.89535	−0.193887	−0.0969436	+	0.995290i	$0.530907\pi$
$224$	4.83129	0.322804
$225$	36.7908	2.45272
$226$	4.98604	0.331666
$227$	16.8052	1.11540	0.557699	−	0.830043i	$-0.311684\pi$
$227$	16.8052	1.11540	0.557699	+	0.830043i	$0.311684\pi$
$228$	21.6502	1.43382
$229$	16.2710	1.07521	0.537607	−	0.843195i	$-0.319328\pi$
$229$	16.2710	1.07521	0.537607	+	0.843195i	$0.319328\pi$
$230$	4.21017	0.277611
$231$	−10.2846	−0.676675
$232$	9.62210	0.631722
$233$	6.09110	0.399041	0.199521	−	0.979894i	$-0.436062\pi$
$233$	6.09110	0.399041	0.199521	+	0.979894i	$0.436062\pi$
$234$	6.37277	0.416601
$235$	22.5052	1.46808
$236$	0	0
$237$	−31.8484	−2.06878
$238$	1.77793	0.115246
$239$	−4.52017	−0.292386	−0.146193	−	0.989256i	$-0.546702\pi$
$239$	−4.52017	−0.292386	−0.146193	+	0.989256i	$0.546702\pi$
$240$	−19.0518	−1.22979
$241$	−28.1461	−1.81305	−0.906524	−	0.422153i	$-0.861274\pi$
$241$	−28.1461	−1.81305	−0.906524	+	0.422153i	$0.861274\pi$
$242$	2.57707	0.165661
$243$	−6.15266	−0.394694
$244$	19.0823	1.22162
$245$	−20.5740	−1.31443
$246$	6.21967	0.396552
$247$	7.19414	0.457752
$248$	−17.9746	−1.14139
$249$	−17.5564	−1.11259
$250$	1.65380	0.104595
$251$	−5.45943	−0.344596	−0.172298	−	0.985045i	$-0.555119\pi$
$251$	−5.45943	−0.344596	−0.172298	+	0.985045i	$0.555119\pi$
$252$	−8.87546	−0.559101
$253$	8.16546	0.513358
$254$	−4.91796	−0.308580
$255$	−33.8139	−2.11751
$256$	−6.23071	−0.389419
$257$	5.99273	0.373816	0.186908	−	0.982377i	$-0.440153\pi$
$257$	5.99273	0.373816	0.186908	+	0.982377i	$0.440153\pi$
$258$	5.43600	0.338430
$259$	1.07145	0.0665765
$260$	−8.82522	−0.547317
$261$	−27.4258	−1.69762
$262$	4.98107	0.307731
$263$	−7.70348	−0.475017	−0.237509	−	0.971385i	$-0.576331\pi$
$263$	−7.70348	−0.475017	−0.237509	+	0.971385i	$0.576331\pi$
$264$	26.3985	1.62472
$265$	−7.27986	−0.447198
$266$	2.30281	0.141194
$267$	7.55450	0.462328
$268$	6.92659	0.423109
$269$	5.47568	0.333858	0.166929	−	0.985969i	$-0.446615\pi$
$269$	5.47568	0.333858	0.166929	+	0.985969i	$0.446615\pi$
$270$	−20.3772	−1.24012
$271$	9.00580	0.547063	0.273532	−	0.961863i	$-0.411808\pi$
$271$	9.00580	0.547063	0.273532	+	0.961863i	$0.411808\pi$
$272$	6.38770	0.387311
$273$	−4.34939	−0.263237
$274$	4.96367	0.299866
$275$	22.7109	1.36952
$276$	10.3922	0.625537
$277$	10.0015	0.600929	0.300465	−	0.953793i	$-0.402858\pi$
$277$	10.0015	0.600929	0.300465	+	0.953793i	$0.402858\pi$
$278$	−2.60671	−0.156340
$279$	51.2330	3.06724
$280$	−6.29908	−0.376442
$281$	12.6780	0.756303	0.378152	−	0.925744i	$-0.376560\pi$
$281$	12.6780	0.756303	0.378152	+	0.925744i	$0.376560\pi$
$282$	−12.7675	−0.760294
$283$	−31.0109	−1.84340	−0.921702	−	0.387898i	$-0.873201\pi$
$283$	−31.0109	−1.84340	−0.921702	+	0.387898i	$0.873201\pi$
$284$	−17.2435	−1.02322
$285$	−43.7965	−2.59428
$286$	3.93390	0.232616
$287$	−2.87837	−0.169905
$288$	35.3465	2.08281
$289$	−5.66282	−0.333107
$290$	−8.72918	−0.512595
$291$	−29.1561	−1.70916
$292$	19.9409	1.16695
$293$	−5.06402	−0.295843	−0.147922	−	0.988999i	$-0.547258\pi$
$293$	−5.06402	−0.295843	−0.147922	+	0.988999i	$0.547258\pi$
$294$	11.6719	0.680721
$295$	0	0
$296$	−2.75020	−0.159852
$297$	−39.5208	−2.29323
$298$	−5.64632	−0.327083
$299$	3.45322	0.199705
$300$	28.9042	1.66878
$301$	−2.51569	−0.145002
$302$	13.5920	0.782134
$303$	27.9855	1.60773
$304$	8.27347	0.474516
$305$	−38.6017	−2.21033
$306$	13.0076	0.743596
$307$	4.83881	0.276166	0.138083	−	0.990421i	$-0.455906\pi$
$307$	4.83881	0.276166	0.138083	+	0.990421i	$0.455906\pi$
$308$	−5.47880	−0.312184
$309$	1.75978	0.100111
$310$	16.3066	0.926152
$311$	−24.2388	−1.37446	−0.687229	−	0.726441i	$-0.741173\pi$
$311$	−24.2388	−1.37446	−0.687229	+	0.726441i	$0.741173\pi$
$312$	11.1641	0.632041
$313$	33.8953	1.91588	0.957939	−	0.286972i	$-0.0926485\pi$
$313$	33.8953	1.91588	0.957939	+	0.286972i	$0.0926485\pi$
$314$	4.97569	0.280794
$315$	17.9542	1.01161
$316$	−16.9663	−0.954429
$317$	−22.0054	−1.23595	−0.617973	−	0.786200i	$-0.712046\pi$
$317$	−22.0054	−1.23595	−0.617973	+	0.786200i	$0.712046\pi$
$318$	4.12997	0.231597
$319$	−16.9299	−0.947892
$320$	−1.23172	−0.0688554
$321$	14.3043	0.798386
$322$	1.10536	0.0615991
$323$	14.6841	0.817048
$324$	−19.4699	−1.08166
$325$	9.60454	0.532764
$326$	−8.91133	−0.493553
$327$	−13.9181	−0.769675
$328$	7.38822	0.407946
$329$	5.90861	0.325752
$330$	−23.9488	−1.31834
$331$	−1.90270	−0.104582	−0.0522908	−	0.998632i	$-0.516652\pi$
$331$	−1.90270	−0.104582	−0.0522908	+	0.998632i	$0.516652\pi$
$332$	−9.35263	−0.513292
$333$	7.83889	0.429568
$334$	−10.3874	−0.568373
$335$	−14.0119	−0.765550
$336$	−5.00193	−0.272878
$337$	−21.6467	−1.17917	−0.589587	−	0.807705i	$-0.700709\pi$
$337$	−21.6467	−1.17917	−0.589587	+	0.807705i	$0.700709\pi$
$338$	−6.28406	−0.341808
$339$	−24.8966	−1.35220
$340$	−18.0134	−0.976913
$341$	31.6260	1.71264
$342$	16.8477	0.911021
$343$	−11.4475	−0.618106
$344$	6.45731	0.348155
$345$	−21.0225	−1.13181
$346$	−11.6022	−0.623736
$347$	1.77519	0.0952973	0.0476487	−	0.998864i	$-0.484827\pi$
$347$	1.77519	0.0952973	0.0476487	+	0.998864i	$0.484827\pi$
$348$	−21.5467	−1.15502
$349$	−1.12687	−0.0603200	−0.0301600	−	0.999545i	$-0.509602\pi$
$349$	−1.12687	−0.0603200	−0.0301600	+	0.999545i	$0.509602\pi$
$350$	3.07437	0.164332
$351$	−16.7135	−0.892103
$352$	21.8193	1.16297
$353$	−33.0859	−1.76098	−0.880491	−	0.474062i	$-0.842787\pi$
$353$	−33.0859	−1.76098	−0.880491	+	0.474062i	$0.842787\pi$
$354$	0	0
$355$	34.8821	1.85135
$356$	4.02444	0.213295
$357$	−8.87766	−0.469855
$358$	10.9788	0.580246
$359$	−11.0243	−0.581841	−0.290920	−	0.956747i	$-0.593962\pi$
$359$	−11.0243	−0.581841	−0.290920	+	0.956747i	$0.593962\pi$
$360$	−46.0851	−2.42890
$361$	0.0191926	0.00101014
$362$	14.5288	0.763617
$363$	−12.8680	−0.675395
$364$	−2.31701	−0.121444
$365$	−40.3386	−2.11142
$366$	21.8993	1.14470
$367$	2.29815	0.119963	0.0599813	−	0.998200i	$-0.480896\pi$
$367$	2.29815	0.119963	0.0599813	+	0.998200i	$0.480896\pi$
$368$	3.97130	0.207018
$369$	−21.0586	−1.09627
$370$	2.49499	0.129708
$371$	−1.91129	−0.0992290
$372$	40.2505	2.08689
$373$	−0.996678	−0.0516061	−0.0258030	−	0.999667i	$-0.508214\pi$
$373$	−0.996678	−0.0516061	−0.0258030	+	0.999667i	$0.508214\pi$
$374$	8.02957	0.415199
$375$	−8.25785	−0.426433
$376$	−15.1663	−0.782140
$377$	−7.15974	−0.368745
$378$	−5.34992	−0.275170
$379$	−20.3829	−1.04700	−0.523500	−	0.852026i	$-0.675374\pi$
$379$	−20.3829	−1.04700	−0.523500	+	0.852026i	$0.675374\pi$
$380$	−23.3313	−1.19687
$381$	24.5566	1.25807
$382$	−3.01445	−0.154232
$383$	−25.9964	−1.32835	−0.664176	−	0.747576i	$-0.731217\pi$
$383$	−25.9964	−1.32835	−0.664176	+	0.747576i	$0.731217\pi$
$384$	34.8506	1.77846
$385$	11.0831	0.564848
$386$	11.6891	0.594961
$387$	−18.4052	−0.935590
$388$	−15.5321	−0.788521
$389$	−24.3409	−1.23413	−0.617067	−	0.786911i	$-0.711679\pi$
$389$	−24.3409	−1.23413	−0.617067	+	0.786911i	$0.711679\pi$
$390$	−10.1281	−0.512854
$391$	7.04844	0.356455
$392$	13.8649	0.700281
$393$	−24.8718	−1.25461
$394$	5.56578	0.280400
$395$	34.3213	1.72689
$396$	−40.0838	−2.01429
$397$	−13.1366	−0.659308	−0.329654	−	0.944102i	$-0.606932\pi$
$397$	−13.1366	−0.659308	−0.329654	+	0.944102i	$0.606932\pi$
$398$	5.79566	0.290510
$399$	−11.4985	−0.575646
$400$	11.0455	0.552275
$401$	20.7916	1.03828	0.519141	−	0.854688i	$-0.326252\pi$
$401$	20.7916	1.03828	0.519141	+	0.854688i	$0.326252\pi$
$402$	7.94913	0.396467
$403$	13.3748	0.666246
$404$	14.9085	0.741724
$405$	39.3858	1.95709
$406$	−2.29180	−0.113740
$407$	4.83893	0.239857
$408$	22.7872	1.12814
$409$	35.7072	1.76561	0.882803	−	0.469743i	$-0.155653\pi$
$409$	35.7072	1.76561	0.882803	+	0.469743i	$0.155653\pi$
$410$	−6.70260	−0.331018
$411$	−24.7849	−1.22255
$412$	0.937473	0.0461860
$413$	0	0
$414$	8.08697	0.397453
$415$	18.9195	0.928723
$416$	9.22749	0.452415
$417$	13.0160	0.637396
$418$	10.4001	0.508684
$419$	27.4205	1.33958	0.669788	−	0.742552i	$-0.266385\pi$
$419$	27.4205	1.33958	0.669788	+	0.742552i	$0.266385\pi$
$420$	14.1055	0.688278
$421$	4.80996	0.234423	0.117212	−	0.993107i	$-0.462604\pi$
$421$	4.80996	0.234423	0.117212	+	0.993107i	$0.462604\pi$
$422$	17.0409	0.829538
$423$	43.2283	2.10183
$424$	4.90590	0.238252
$425$	19.6041	0.950937
$426$	−19.7891	−0.958786
$427$	−10.1347	−0.490451
$428$	7.62018	0.368335
$429$	−19.6430	−0.948371
$430$	−5.85808	−0.282502
$431$	−1.74608	−0.0841055	−0.0420528	−	0.999115i	$-0.513390\pi$
$431$	−1.74608	−0.0841055	−0.0420528	+	0.999115i	$0.513390\pi$
$432$	−19.2211	−0.924773
$433$	−22.2246	−1.06804	−0.534022	−	0.845470i	$-0.679320\pi$
$433$	−22.2246	−1.06804	−0.534022	+	0.845470i	$0.679320\pi$
$434$	4.28120	0.205504
$435$	43.5870	2.08984
$436$	−7.41448	−0.355089
$437$	9.12928	0.436713
$438$	22.8847	1.09347
$439$	13.0366	0.622204	0.311102	−	0.950377i	$-0.399302\pi$
$439$	13.0366	0.622204	0.311102	+	0.950377i	$0.399302\pi$
$440$	−28.4482	−1.35622
$441$	−39.5189	−1.88185
$442$	3.39575	0.161519
$443$	−41.4466	−1.96919	−0.984593	−	0.174860i	$-0.944053\pi$
$443$	−41.4466	−1.96919	−0.984593	+	0.174860i	$0.944053\pi$
$444$	6.15851	0.292270
$445$	−8.14107	−0.385924
$446$	−1.77011	−0.0838174
$447$	28.1935	1.33351
$448$	−0.323382	−0.0152784
$449$	6.74263	0.318204	0.159102	−	0.987262i	$-0.449140\pi$
$449$	6.74263	0.318204	0.159102	+	0.987262i	$0.449140\pi$
$450$	22.4926	1.06031
$451$	−12.9994	−0.612119
$452$	−13.2629	−0.623835
$453$	−67.8685	−3.18874
$454$	10.2741	0.482186
$455$	4.68711	0.219735
$456$	29.5145	1.38214
$457$	30.7392	1.43792	0.718959	−	0.695052i	$-0.244619\pi$
$457$	30.7392	1.43792	0.718959	+	0.695052i	$0.244619\pi$
$458$	9.94747	0.464815
$459$	−34.1144	−1.59233
$460$	−11.1991	−0.522161
$461$	32.8050	1.52788	0.763942	−	0.645285i	$-0.223262\pi$
$461$	32.8050	1.52788	0.763942	+	0.645285i	$0.223262\pi$
$462$	−6.28761	−0.292526
$463$	−0.0647647	−0.00300987	−0.00150494	−	0.999999i	$-0.500479\pi$
$463$	−0.0647647	−0.00300987	−0.00150494	+	0.999999i	$0.500479\pi$
$464$	−8.23390	−0.382249
$465$	−81.4230	−3.77590
$466$	3.72388	0.172505
$467$	−26.0890	−1.20725	−0.603627	−	0.797267i	$-0.706278\pi$
$467$	−26.0890	−1.20725	−0.603627	+	0.797267i	$0.706278\pi$
$468$	−16.9516	−0.783590
$469$	−3.67874	−0.169868
$470$	13.7589	0.634649
$471$	−24.8449	−1.14479
$472$	0	0
$473$	−11.3615	−0.522403
$474$	−19.4710	−0.894331
$475$	25.3916	1.16505
$476$	−4.72931	−0.216768
$477$	−13.9833	−0.640250
$478$	−2.76347	−0.126398
$479$	−3.02201	−0.138079	−0.0690395	−	0.997614i	$-0.521993\pi$
$479$	−3.02201	−0.138079	−0.0690395	+	0.997614i	$0.521993\pi$
$480$	−56.1751	−2.56403
$481$	2.04641	0.0933081
$482$	−17.2075	−0.783780
$483$	−5.51933	−0.251138
$484$	−6.85504	−0.311593
$485$	31.4200	1.42671
$486$	−3.76152	−0.170626
$487$	−17.3046	−0.784145	−0.392072	−	0.919934i	$-0.628242\pi$
$487$	−17.3046	−0.784145	−0.392072	+	0.919934i	$0.628242\pi$
$488$	26.0138	1.17759
$489$	44.4966	2.01220
$490$	−12.5782	−0.568226
$491$	16.1489	0.728790	0.364395	−	0.931245i	$-0.381276\pi$
$491$	16.1489	0.728790	0.364395	+	0.931245i	$0.381276\pi$
$492$	−16.5444	−0.745879
$493$	−14.6139	−0.658178
$494$	4.39824	0.197886
$495$	81.0859	3.64454
$496$	15.3814	0.690645
$497$	9.15810	0.410797
$498$	−10.7333	−0.480972
$499$	−3.72962	−0.166961	−0.0834804	−	0.996509i	$-0.526604\pi$
$499$	−3.72962	−0.166961	−0.0834804	+	0.996509i	$0.526604\pi$
$500$	−4.39913	−0.196735
$501$	51.8669	2.31724
$502$	−3.33770	−0.148969
$503$	−17.8789	−0.797182	−0.398591	−	0.917129i	$-0.630501\pi$
$503$	−17.8789	−0.797182	−0.398591	+	0.917129i	$0.630501\pi$
$504$	−12.0994	−0.538949
$505$	−30.1585	−1.34203
$506$	4.99207	0.221924
$507$	31.3780	1.39354
$508$	13.0818	0.580412
$509$	33.0995	1.46711	0.733554	−	0.679631i	$-0.237860\pi$
$509$	33.0995	1.46711	0.733554	+	0.679631i	$0.237860\pi$
$510$	−20.6726	−0.915399
$511$	−10.5907	−0.468504
$512$	19.0235	0.840726
$513$	−44.1857	−1.95085
$514$	3.66374	0.161600
$515$	−1.89642	−0.0835664
$516$	−14.4598	−0.636558
$517$	26.6847	1.17359
$518$	0.655045	0.0287810
$519$	57.9326	2.54296
$520$	−12.0309	−0.527590
$521$	17.6086	0.771448	0.385724	−	0.922614i	$-0.373952\pi$
$521$	17.6086	0.771448	0.385724	+	0.922614i	$0.373952\pi$
$522$	−16.7672	−0.733878
$523$	−10.0215	−0.438210	−0.219105	−	0.975701i	$-0.570314\pi$
$523$	−10.0215	−0.438210	−0.219105	+	0.975701i	$0.570314\pi$
$524$	−13.2497	−0.578816
$525$	−15.3511	−0.669977
$526$	−4.70963	−0.205350
$527$	27.2996	1.18919
$528$	−22.5900	−0.983102
$529$	−18.6179	−0.809474
$530$	−4.45064	−0.193324
$531$	0	0
$532$	−6.12550	−0.265574
$533$	−5.49752	−0.238124
$534$	4.61855	0.199864
$535$	−15.4149	−0.666445
$536$	9.44261	0.407859
$537$	−54.8198	−2.36565
$538$	3.34763	0.144327
$539$	−24.3949	−1.05076
$540$	54.2036	2.33255
$541$	−1.04939	−0.0451168	−0.0225584	−	0.999746i	$-0.507181\pi$
$541$	−1.04939	−0.0451168	−0.0225584	+	0.999746i	$0.507181\pi$
$542$	5.50582	0.236495
$543$	−72.5460	−3.11325
$544$	18.8345	0.807521
$545$	14.9988	0.642479
$546$	−2.65906	−0.113797
$547$	32.5295	1.39086	0.695432	−	0.718592i	$-0.255213\pi$
$547$	32.5295	1.39086	0.695432	+	0.718592i	$0.255213\pi$
$548$	−13.2034	−0.564021
$549$	−74.1469	−3.16451
$550$	13.8846	0.592041
$551$	−18.9282	−0.806370
$552$	14.1671	0.602990
$553$	9.01086	0.383181
$554$	6.11453	0.259781
$555$	−12.4581	−0.528817
$556$	6.93389	0.294062
$557$	−20.1377	−0.853261	−0.426630	−	0.904426i	$-0.640300\pi$
$557$	−20.1377	−0.853261	−0.426630	+	0.904426i	$0.640300\pi$
$558$	31.3220	1.32597
$559$	−4.80484	−0.203223
$560$	5.39031	0.227782
$561$	−40.0937	−1.69276
$562$	7.75084	0.326950
$563$	22.5113	0.948738	0.474369	−	0.880326i	$-0.342676\pi$
$563$	22.5113	0.948738	0.474369	+	0.880326i	$0.342676\pi$
$564$	33.9617	1.43005
$565$	26.8297	1.12873
$566$	−18.9589	−0.796903
$567$	10.3405	0.434261
$568$	−23.5071	−0.986335
$569$	26.1716	1.09717	0.548586	−	0.836094i	$-0.315166\pi$
$569$	26.1716	1.09717	0.548586	+	0.836094i	$0.315166\pi$
$570$	−26.7756	−1.12151
$571$	4.08016	0.170749	0.0853747	−	0.996349i	$-0.472791\pi$
$571$	4.08016	0.170749	0.0853747	+	0.996349i	$0.472791\pi$
$572$	−10.4642	−0.437530
$573$	15.0519	0.628802
$574$	−1.75973	−0.0734497
$575$	12.1881	0.508277
$576$	−2.36592	−0.0985798
$577$	37.4482	1.55899	0.779494	−	0.626410i	$-0.215476\pi$
$577$	37.4482	1.55899	0.779494	+	0.626410i	$0.215476\pi$
$578$	−3.46204	−0.144002
$579$	−58.3668	−2.42564
$580$	23.2197	0.964146
$581$	4.96721	0.206075
$582$	−17.8250	−0.738870
$583$	−8.63184	−0.357494
$584$	27.1842	1.12489
$585$	34.2916	1.41778
$586$	−3.09596	−0.127893
$587$	−1.01004	−0.0416890	−0.0208445	−	0.999783i	$-0.506635\pi$
$587$	−1.01004	−0.0416890	−0.0208445	+	0.999783i	$0.506635\pi$
$588$	−31.0475	−1.28038
$589$	35.3590	1.45694
$590$	0	0
$591$	−27.7914	−1.14318
$592$	2.35343	0.0967252
$593$	−0.124298	−0.00510429	−0.00255214	−	0.999997i	$-0.500812\pi$
$593$	−0.124298	−0.00510429	−0.00255214	+	0.999997i	$0.500812\pi$
$594$	−24.1616	−0.991362
$595$	9.56697	0.392207
$596$	15.0193	0.615213
$597$	−28.9392	−1.18440
$598$	2.11117	0.0863322
$599$	35.4094	1.44679	0.723395	−	0.690434i	$-0.242580\pi$
$599$	35.4094	1.44679	0.723395	+	0.690434i	$0.242580\pi$
$600$	39.4033	1.60863
$601$	−11.2507	−0.458926	−0.229463	−	0.973317i	$-0.573697\pi$
$601$	−11.2507	−0.458926	−0.229463	+	0.973317i	$0.573697\pi$
$602$	−1.53800	−0.0626844
$603$	−26.9142	−1.09603
$604$	−36.1550	−1.47112
$605$	13.8671	0.563779
$606$	17.1093	0.695019
$607$	36.1182	1.46599	0.732996	−	0.680233i	$-0.238121\pi$
$607$	36.1182	1.46599	0.732996	+	0.680233i	$0.238121\pi$
$608$	24.3948	0.989338
$609$	11.4435	0.463715
$610$	−23.5997	−0.955524
$611$	11.2851	0.456547
$612$	−34.6004	−1.39864
$613$	−21.3800	−0.863532	−0.431766	−	0.901986i	$-0.642109\pi$
$613$	−21.3800	−0.863532	−0.431766	+	0.901986i	$0.642109\pi$
$614$	2.95828	0.119386
$615$	33.4678	1.34955
$616$	−7.46892	−0.300931
$617$	−39.9629	−1.60885	−0.804423	−	0.594057i	$-0.797525\pi$
$617$	−39.9629	−1.60885	−0.804423	+	0.594057i	$0.797525\pi$
$618$	1.07587	0.0432778
$619$	5.76117	0.231561	0.115781	−	0.993275i	$-0.463063\pi$
$619$	5.76117	0.231561	0.115781	+	0.993275i	$0.463063\pi$
$620$	−43.3757	−1.74201
$621$	−21.2093	−0.851099
$622$	−14.8187	−0.594177
$623$	−2.13739	−0.0856328
$624$	−9.55341	−0.382442
$625$	−20.2124	−0.808496
$626$	20.7224	0.828233
$627$	−51.9302	−2.07389
$628$	−13.2354	−0.528149
$629$	4.17697	0.166547
$630$	10.9766	0.437317
$631$	−18.2099	−0.724923	−0.362462	−	0.931999i	$-0.618064\pi$
$631$	−18.2099	−0.724923	−0.362462	+	0.931999i	$0.618064\pi$
$632$	−23.1292	−0.920028
$633$	−85.0896	−3.38201
$634$	−13.4533	−0.534299
$635$	−26.4633	−1.05017
$636$	−10.9858	−0.435614
$637$	−10.3167	−0.408764
$638$	−10.3503	−0.409773
$639$	67.0021	2.65056
$640$	−37.5566	−1.48456
$641$	−27.4019	−1.08231	−0.541156	−	0.840922i	$-0.682013\pi$
$641$	−27.4019	−1.08231	−0.541156	+	0.840922i	$0.682013\pi$
$642$	8.74511	0.345142
$643$	−32.6666	−1.28824	−0.644122	−	0.764923i	$-0.722777\pi$
$643$	−32.6666	−1.28824	−0.644122	+	0.764923i	$0.722777\pi$
$644$	−2.94026	−0.115862
$645$	29.2509	1.15175
$646$	8.97735	0.353209
$647$	13.1440	0.516743	0.258372	−	0.966046i	$-0.416814\pi$
$647$	13.1440	0.516743	0.258372	+	0.966046i	$0.416814\pi$
$648$	−26.5421	−1.04267
$649$	0	0
$650$	5.87187	0.230314
$651$	−21.3771	−0.837837
$652$	23.7042	0.928329
$653$	−28.4561	−1.11357	−0.556786	−	0.830656i	$-0.687966\pi$
$653$	−28.4561	−1.11357	−0.556786	+	0.830656i	$0.687966\pi$
$654$	−8.50905	−0.332730
$655$	26.8029	1.04728
$656$	−6.32231	−0.246845
$657$	−77.4830	−3.02290
$658$	3.61231	0.140822
$659$	−2.37460	−0.0925013	−0.0462506	−	0.998930i	$-0.514727\pi$
$659$	−2.37460	−0.0925013	−0.0462506	+	0.998930i	$0.514727\pi$
$660$	63.7040	2.47967
$661$	3.26370	0.126943	0.0634716	−	0.997984i	$-0.479783\pi$
$661$	3.26370	0.126943	0.0634716	+	0.997984i	$0.479783\pi$
$662$	−1.16324	−0.0452106
$663$	−16.9558	−0.658510
$664$	−12.7499	−0.494792
$665$	12.3913	0.480515
$666$	4.79241	0.185702
$667$	−9.08562	−0.351797
$668$	27.6306	1.06906
$669$	8.83864	0.341722
$670$	−8.56635	−0.330947
$671$	−45.7707	−1.76696
$672$	−14.7485	−0.568934
$673$	−2.12969	−0.0820935	−0.0410468	−	0.999157i	$-0.513069\pi$
$673$	−2.12969	−0.0820935	−0.0410468	+	0.999157i	$0.513069\pi$
$674$	−13.2340	−0.509756
$675$	−58.9901	−2.27053
$676$	16.7157	0.642911
$677$	−31.4939	−1.21041	−0.605204	−	0.796071i	$-0.706908\pi$
$677$	−31.4939	−1.21041	−0.605204	+	0.796071i	$0.706908\pi$
$678$	−15.2209	−0.584554
$679$	8.24913	0.316573
$680$	−24.5566	−0.941701
$681$	−51.3010	−1.96586
$682$	19.3350	0.740375
$683$	11.8642	0.453972	0.226986	−	0.973898i	$-0.427113\pi$
$683$	11.8642	0.453972	0.226986	+	0.973898i	$0.427113\pi$
$684$	−44.8151	−1.71355
$685$	26.7093	1.02051
$686$	−6.99858	−0.267207
$687$	−49.6703	−1.89504
$688$	−5.52570	−0.210665
$689$	−3.65045	−0.139071
$690$	−12.8524	−0.489282
$691$	−28.5403	−1.08572	−0.542862	−	0.839822i	$-0.682659\pi$
$691$	−28.5403	−1.08572	−0.542862	+	0.839822i	$0.682659\pi$
$692$	30.8619	1.17319
$693$	21.2886	0.808688
$694$	1.08529	0.0411970
$695$	−14.0266	−0.532060
$696$	−29.3733	−1.11339
$697$	−11.2211	−0.425031
$698$	−0.688928	−0.0260763
$699$	−18.5943	−0.703300
$700$	−8.17784	−0.309093
$701$	2.53507	0.0957483	0.0478741	−	0.998853i	$-0.484755\pi$
$701$	2.53507	0.0957483	0.0478741	+	0.998853i	$0.484755\pi$
$702$	−10.2181	−0.385656
$703$	5.41010	0.204046
$704$	−1.46047	−0.0550437
$705$	−68.7015	−2.58745
$706$	−20.2275	−0.761272
$707$	−7.91794	−0.297785
$708$	0	0
$709$	−8.23468	−0.309260	−0.154630	−	0.987972i	$-0.549419\pi$
$709$	−8.23468	−0.309260	−0.154630	+	0.987972i	$0.549419\pi$
$710$	21.3257	0.800338
$711$	65.9249	2.47238
$712$	5.48627	0.205607
$713$	16.9725	0.635623
$714$	−5.42748	−0.203118
$715$	21.1681	0.791643
$716$	−29.2036	−1.09139
$717$	13.7987	0.515322
$718$	−6.73987	−0.251530
$719$	12.2132	0.455476	0.227738	−	0.973722i	$-0.426867\pi$
$719$	12.2132	0.455476	0.227738	+	0.973722i	$0.426867\pi$
$720$	39.4364	1.46971
$721$	−0.497895	−0.0185426
$722$	0.0117337	0.000436681 0
$723$	85.9215	3.19545
$724$	−38.6468	−1.43630
$725$	−25.2701	−0.938510
$726$	−7.86703	−0.291973
$727$	2.02018	0.0749242	0.0374621	−	0.999298i	$-0.488073\pi$
$727$	2.02018	0.0749242	0.0374621	+	0.999298i	$0.488073\pi$
$728$	−3.15864	−0.117067
$729$	−17.1349	−0.634625
$730$	−24.6616	−0.912765
$731$	−9.80727	−0.362735
$732$	−58.2525	−2.15307
$733$	45.7120	1.68841	0.844205	−	0.536020i	$-0.180073\pi$
$733$	45.7120	1.68841	0.844205	+	0.536020i	$0.180073\pi$
$734$	1.40501	0.0518598
$735$	62.8062	2.31664
$736$	11.7096	0.431621
$737$	−16.6141	−0.611988
$738$	−12.8745	−0.473916
$739$	21.8045	0.802093	0.401047	−	0.916058i	$-0.368647\pi$
$739$	21.8045	0.802093	0.401047	+	0.916058i	$0.368647\pi$
$740$	−6.63669	−0.243970
$741$	−21.9615	−0.806777
$742$	−1.16849	−0.0428967
$743$	18.2820	0.670702	0.335351	−	0.942093i	$-0.391145\pi$
$743$	18.2820	0.670702	0.335351	+	0.942093i	$0.391145\pi$
$744$	54.8710	2.01167
$745$	−30.3826	−1.11313
$746$	−0.609333	−0.0223093
$747$	36.3409	1.32965
$748$	−21.3587	−0.780953
$749$	−4.04710	−0.147878
$750$	−5.04855	−0.184347
$751$	−19.3200	−0.704999	−0.352499	−	0.935812i	$-0.614668\pi$
$751$	−19.3200	−0.704999	−0.352499	+	0.935812i	$0.614668\pi$
$752$	12.9782	0.473266
$753$	16.6660	0.607343
$754$	−4.37721	−0.159408
$755$	73.1382	2.66177
$756$	14.2308	0.517571
$757$	−25.3533	−0.921482	−0.460741	−	0.887535i	$-0.652416\pi$
$757$	−25.3533	−0.921482	−0.460741	+	0.887535i	$0.652416\pi$
$758$	−12.4614	−0.452618
$759$	−24.9267	−0.904781
$760$	−31.8062	−1.15373
$761$	−29.0427	−1.05280	−0.526399	−	0.850238i	$-0.676458\pi$
$761$	−29.0427	−1.05280	−0.526399	+	0.850238i	$0.676458\pi$
$762$	15.0130	0.543865
$763$	3.93786	0.142560
$764$	8.01846	0.290098
$765$	69.9935	2.53062
$766$	−15.8932	−0.574246
$767$	0	0
$768$	19.0205	0.686342
$769$	26.2013	0.944844	0.472422	−	0.881373i	$-0.343380\pi$
$769$	26.2013	0.944844	0.472422	+	0.881373i	$0.343380\pi$
$770$	6.77581	0.244183
$771$	−18.2940	−0.658842
$772$	−31.0932	−1.11907
$773$	−11.2636	−0.405123	−0.202562	−	0.979270i	$-0.564927\pi$
$773$	−11.2636	−0.405123	−0.202562	+	0.979270i	$0.564927\pi$
$774$	−11.2523	−0.404455
$775$	47.2060	1.69569
$776$	−21.1739	−0.760100
$777$	−3.27081	−0.117340
$778$	−14.8812	−0.533515
$779$	−14.5338	−0.520728
$780$	26.9407	0.964633
$781$	41.3603	1.47999
$782$	4.30916	0.154095
$783$	43.9744	1.57152
$784$	−11.8646	−0.423734
$785$	26.7740	0.955605
$786$	−15.2057	−0.542369
$787$	−2.67750	−0.0954424	−0.0477212	−	0.998861i	$-0.515196\pi$
$787$	−2.67750	−0.0954424	−0.0477212	+	0.998861i	$0.515196\pi$
$788$	−14.8050	−0.527408
$789$	23.5164	0.837206
$790$	20.9828	0.746535
$791$	7.04398	0.250455
$792$	−54.6438	−1.94168
$793$	−19.3567	−0.687375
$794$	−8.03126	−0.285019
$795$	22.2232	0.788176
$796$	−15.4165	−0.546424
$797$	49.4553	1.75180	0.875899	−	0.482495i	$-0.160269\pi$
$797$	49.4553	1.75180	0.875899	+	0.482495i	$0.160269\pi$
$798$	−7.02978	−0.248851
$799$	23.0343	0.814896
$800$	32.5682	1.15146
$801$	−15.6375	−0.552524
$802$	12.7112	0.448849
$803$	−47.8301	−1.68789
$804$	−21.1448	−0.745719
$805$	5.94788	0.209635
$806$	8.17686	0.288018
$807$	−16.7156	−0.588417
$808$	20.3238	0.714990
$809$	50.9880	1.79264	0.896322	−	0.443404i	$-0.146229\pi$
$809$	50.9880	1.79264	0.896322	+	0.443404i	$0.146229\pi$
$810$	24.0790	0.846051
$811$	−30.3047	−1.06414	−0.532071	−	0.846700i	$-0.678586\pi$
$811$	−30.3047	−1.06414	−0.532071	+	0.846700i	$0.678586\pi$
$812$	6.09620	0.213935
$813$	−27.4920	−0.964185
$814$	2.95834	0.103690
$815$	−47.9515	−1.67967
$816$	−19.4997	−0.682626
$817$	−12.7026	−0.444407
$818$	21.8301	0.763271
$819$	9.00307	0.314593
$820$	17.8290	0.622615
$821$	32.8598	1.14681	0.573407	−	0.819271i	$-0.305621\pi$
$821$	32.8598	1.14681	0.573407	+	0.819271i	$0.305621\pi$
$822$	−15.1526	−0.528506
$823$	−0.0903793	−0.00315042	−0.00157521	−	0.999999i	$-0.500501\pi$
$823$	−0.0903793	−0.00315042	−0.00157521	+	0.999999i	$0.500501\pi$
$824$	1.27800	0.0445213
$825$	−69.3294	−2.41374
$826$	0	0
$827$	22.6616	0.788021	0.394011	−	0.919106i	$-0.371087\pi$
$827$	22.6616	0.788021	0.394011	+	0.919106i	$0.371087\pi$
$828$	−21.5114	−0.747574
$829$	−2.32193	−0.0806439	−0.0403220	−	0.999187i	$-0.512838\pi$
$829$	−2.32193	−0.0806439	−0.0403220	+	0.999187i	$0.512838\pi$
$830$	11.5667	0.401487
$831$	−30.5314	−1.05912
$832$	−0.617642	−0.0214129
$833$	−21.0578	−0.729608
$834$	7.95751	0.275546
$835$	−55.8942	−1.93430
$836$	−27.6643	−0.956789
$837$	−82.1466	−2.83940
$838$	16.7639	0.579098
$839$	4.08898	0.141167	0.0705836	−	0.997506i	$-0.477514\pi$
$839$	4.08898	0.141167	0.0705836	+	0.997506i	$0.477514\pi$
$840$	19.2292	0.663470
$841$	−10.1623	−0.350424
$842$	2.94064	0.101341
$843$	−38.7019	−1.33297
$844$	−45.3290	−1.56029
$845$	−33.8143	−1.16325
$846$	26.4282	0.908622
$847$	3.64074	0.125097
$848$	−4.19812	−0.144164
$849$	94.6668	3.24895
$850$	11.9852	0.411090
$851$	2.59687	0.0890194
$852$	52.6393	1.80339
$853$	25.7176	0.880553	0.440276	−	0.897862i	$-0.354880\pi$
$853$	25.7176	0.880553	0.440276	+	0.897862i	$0.354880\pi$
$854$	−6.19597	−0.212022
$855$	90.6569	3.10040
$856$	10.3881	0.355059
$857$	−13.0273	−0.445003	−0.222502	−	0.974932i	$-0.571422\pi$
$857$	−13.0273	−0.445003	−0.222502	+	0.974932i	$0.571422\pi$
$858$	−12.0090	−0.409980
$859$	−33.8615	−1.15534	−0.577670	−	0.816270i	$-0.696038\pi$
$859$	−33.8615	−1.15534	−0.577670	+	0.816270i	$0.696038\pi$
$860$	15.5825	0.531360
$861$	8.78678	0.299453
$862$	−1.06749	−0.0363588
$863$	35.1800	1.19754	0.598770	−	0.800921i	$-0.295656\pi$
$863$	35.1800	1.19754	0.598770	+	0.800921i	$0.295656\pi$
$864$	−56.6743	−1.92810
$865$	−62.4308	−2.12271
$866$	−13.5873	−0.461715
$867$	17.2869	0.587093
$868$	−11.3880	−0.386535
$869$	40.6953	1.38049
$870$	26.6475	0.903436
$871$	−7.02618	−0.238073
$872$	−10.1077	−0.342291
$873$	60.3520	2.04261
$874$	5.58131	0.188791
$875$	2.33639	0.0789844
$876$	−60.8735	−2.05672
$877$	36.0231	1.21641	0.608207	−	0.793779i	$-0.291889\pi$
$877$	36.0231	1.21641	0.608207	+	0.793779i	$0.291889\pi$
$878$	7.97012	0.268978
$879$	15.4589	0.521417
$880$	24.3440	0.820635
$881$	20.8472	0.702359	0.351180	−	0.936308i	$-0.385781\pi$
$881$	20.8472	0.702359	0.351180	+	0.936308i	$0.385781\pi$
$882$	−24.1604	−0.813524
$883$	−1.69417	−0.0570133	−0.0285067	−	0.999594i	$-0.509075\pi$
$883$	−1.69417	−0.0570133	−0.0285067	+	0.999594i	$0.509075\pi$
$884$	−9.03272	−0.303803
$885$	0	0
$886$	−25.3389	−0.851278
$887$	−36.8546	−1.23746	−0.618728	−	0.785605i	$-0.712352\pi$
$887$	−36.8546	−1.23746	−0.618728	+	0.785605i	$0.712352\pi$
$888$	8.39553	0.281736
$889$	−6.94780	−0.233022
$890$	−4.97716	−0.166835
$891$	46.7003	1.56452
$892$	4.70852	0.157653
$893$	29.8345	0.998374
$894$	17.2365	0.576475
$895$	59.0763	1.97470
$896$	−9.86028	−0.329409
$897$	−10.5416	−0.351974
$898$	4.12220	0.137560
$899$	−35.1899	−1.17365
$900$	−59.8304	−1.99435
$901$	−7.45103	−0.248230
$902$	−7.94738	−0.264619
$903$	7.67965	0.255563
$904$	−18.0806	−0.601350
$905$	78.1789	2.59875
$906$	−41.4924	−1.37849
$907$	11.8363	0.393020	0.196510	−	0.980502i	$-0.437039\pi$
$907$	11.8363	0.393020	0.196510	+	0.980502i	$0.437039\pi$
$908$	−27.3291	−0.906949
$909$	−57.9289	−1.92138
$910$	2.86553	0.0949913
$911$	−45.3563	−1.50272	−0.751361	−	0.659891i	$-0.770602\pi$
$911$	−45.3563	−1.50272	−0.751361	+	0.659891i	$0.770602\pi$
$912$	−25.2564	−0.836323
$913$	22.4332	0.742430
$914$	18.7928	0.621611
$915$	117.839	3.89565
$916$	−26.4604	−0.874276
$917$	7.03696	0.232381
$918$	−20.8563	−0.688361
$919$	57.9084	1.91022	0.955111	−	0.296249i	$-0.0957358\pi$
$919$	57.9084	1.91022	0.955111	+	0.296249i	$0.0957358\pi$
$920$	−15.2671	−0.503340
$921$	−14.7714	−0.486735
$922$	20.0558	0.660503
$923$	17.4915	0.575739
$924$	16.7251	0.550216
$925$	7.22275	0.237483
$926$	−0.0395948	−0.00130117
$927$	−3.64268	−0.119641
$928$	−24.2781	−0.796968
$929$	−4.86504	−0.159617	−0.0798084	−	0.996810i	$-0.525431\pi$
$929$	−4.86504	−0.159617	−0.0798084	+	0.996810i	$0.525431\pi$
$930$	−49.7791	−1.63232
$931$	−27.2744	−0.893883
$932$	−9.90555	−0.324467
$933$	73.9938	2.42245
$934$	−15.9498	−0.521895
$935$	43.2068	1.41301
$936$	−23.1092	−0.755346
$937$	36.6568	1.19752	0.598762	−	0.800927i	$-0.295660\pi$
$937$	36.6568	1.19752	0.598762	+	0.800927i	$0.295660\pi$
$938$	−2.24905	−0.0734339
$939$	−103.472	−3.37669
$940$	−36.5987	−1.19372
$941$	37.8551	1.23404	0.617020	−	0.786947i	$-0.288340\pi$
$941$	37.8551	1.23404	0.617020	+	0.786947i	$0.288340\pi$
$942$	−15.1893	−0.494893
$943$	−6.97629	−0.227179
$944$	0	0
$945$	−28.7877	−0.936464
$946$	−6.94601	−0.225834
$947$	31.2248	1.01467	0.507335	−	0.861749i	$-0.330630\pi$
$947$	31.2248	1.01467	0.507335	+	0.861749i	$0.330630\pi$
$948$	51.7930	1.68216
$949$	−20.2276	−0.656615
$950$	15.5235	0.503649
$951$	67.1758	2.17832
$952$	−6.44719	−0.208955
$953$	19.7214	0.638837	0.319419	−	0.947614i	$-0.396512\pi$
$953$	19.7214	0.638837	0.319419	+	0.947614i	$0.396512\pi$
$954$	−8.54887	−0.276780
$955$	−16.2206	−0.524887
$956$	7.35086	0.237744
$957$	51.6818	1.67064
$958$	−1.84755	−0.0596915
$959$	7.01237	0.226441
$960$	3.76008	0.121356
$961$	34.7367	1.12054
$962$	1.25110	0.0403371
$963$	−29.6092	−0.954145
$964$	45.7721	1.47422
$965$	62.8987	2.02478
$966$	−3.37432	−0.108567
$967$	−22.1308	−0.711678	−0.355839	−	0.934547i	$-0.615805\pi$
$967$	−22.1308	−0.711678	−0.355839	+	0.934547i	$0.615805\pi$
$968$	−9.34507	−0.300362
$969$	−44.8262	−1.44003
$970$	19.2090	0.616765
$971$	5.27379	0.169244	0.0846220	−	0.996413i	$-0.473032\pi$
$971$	5.27379	0.169244	0.0846220	+	0.996413i	$0.473032\pi$
$972$	10.0057	0.320932
$973$	−3.68261	−0.118059
$974$	−10.5794	−0.338985
$975$	−29.3198	−0.938984
$976$	−22.2607	−0.712548
$977$	−5.81265	−0.185963	−0.0929816	−	0.995668i	$-0.529640\pi$
$977$	−5.81265	−0.185963	−0.0929816	+	0.995668i	$0.529640\pi$
$978$	27.2036	0.869875
$979$	−9.65299	−0.308511
$980$	33.4582	1.06878
$981$	28.8100	0.919833
$982$	9.87285	0.315055
$983$	48.9133	1.56009	0.780046	−	0.625722i	$-0.215196\pi$
$983$	48.9133	1.56009	0.780046	+	0.625722i	$0.215196\pi$
$984$	−22.5540	−0.718995
$985$	29.9493	0.954263
$986$	−8.93442	−0.284530
$987$	−18.0372	−0.574130
$988$	−11.6994	−0.372206
$989$	−6.09728	−0.193882
$990$	49.5730	1.57553
$991$	9.71855	0.308720	0.154360	−	0.988015i	$-0.450668\pi$
$991$	9.71855	0.308720	0.154360	+	0.988015i	$0.450668\pi$
$992$	45.3529	1.43995
$993$	5.80836	0.184323
$994$	5.59893	0.177587
$995$	31.1862	0.988670
$996$	28.5508	0.904665
$997$	2.20539	0.0698454	0.0349227	−	0.999390i	$-0.488882\pi$
$997$	2.20539	0.0698454	0.0349227	+	0.999390i	$0.488882\pi$
$998$	−2.28016	−0.0721771
$999$	−12.5688	−0.397660

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3481.2.a.q.1.30		56
59.11	odd	58		59.2.c.a.3.3	✓	112
59.43	odd	58		59.2.c.a.20.3	yes	112
59.58	odd	2		3481.2.a.p.1.27		56
177.11	even	58		531.2.i.a.298.2		112
177.161	even	58		531.2.i.a.433.2		112
236.11	even	58		944.2.m.c.593.1		112
236.43	even	58		944.2.m.c.433.1		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.2.c.a.3.3	✓	112	59.11	odd	58
59.2.c.a.20.3	yes	112	59.43	odd	58
531.2.i.a.298.2		112	177.11	even	58
531.2.i.a.433.2		112	177.161	even	58
944.2.m.c.433.1		112	236.43	even	58
944.2.m.c.593.1		112	236.11	even	58
3481.2.a.p.1.27		56	59.58	odd	2
3481.2.a.q.1.30		56	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:	\( N \)	\(=\)	\( 3481 = 59^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3481.a (trivial)

\(f(q)\)	\(=\)	\(q+0.611364 q^{2} -3.05270 q^{3} -1.62623 q^{4} +3.28972 q^{5} -1.86631 q^{6} +0.863698 q^{7} -2.21695 q^{8} +6.31896 q^{9} +O(q^{10})\)	\(q+0.611364 q^{2} -3.05270 q^{3} -1.62623 q^{4} +3.28972 q^{5} -1.86631 q^{6} +0.863698 q^{7} -2.21695 q^{8} +6.31896 q^{9} +2.01122 q^{10} +3.90068 q^{11} +4.96440 q^{12} +1.64962 q^{13} +0.528034 q^{14} -10.0425 q^{15} +1.89711 q^{16} +3.36707 q^{17} +3.86318 q^{18} +4.36110 q^{19} -5.34986 q^{20} -2.63661 q^{21} +2.38473 q^{22} +2.09334 q^{23} +6.76767 q^{24} +5.82229 q^{25} +1.00852 q^{26} -10.1318 q^{27} -1.40458 q^{28} -4.34024 q^{29} -6.13964 q^{30} +8.10782 q^{31} +5.59372 q^{32} -11.9076 q^{33} +2.05851 q^{34} +2.84133 q^{35} -10.2761 q^{36} +1.24053 q^{37} +2.66622 q^{38} -5.03578 q^{39} -7.29315 q^{40} -3.33261 q^{41} -1.61193 q^{42} -2.91270 q^{43} -6.34342 q^{44} +20.7876 q^{45} +1.27979 q^{46} +6.84105 q^{47} -5.79129 q^{48} -6.25403 q^{49} +3.55954 q^{50} -10.2787 q^{51} -2.68266 q^{52} -2.21291 q^{53} -6.19420 q^{54} +12.8322 q^{55} -1.91477 q^{56} -13.3131 q^{57} -2.65347 q^{58} +16.3315 q^{60} -11.7340 q^{61} +4.95683 q^{62} +5.45767 q^{63} -0.374415 q^{64} +5.42678 q^{65} -7.27987 q^{66} -4.25928 q^{67} -5.47565 q^{68} -6.39034 q^{69} +1.73709 q^{70} +10.6034 q^{71} -14.0088 q^{72} -12.2620 q^{73} +0.758418 q^{74} -17.7737 q^{75} -7.09217 q^{76} +3.36901 q^{77} -3.07869 q^{78} +10.4329 q^{79} +6.24096 q^{80} +11.9724 q^{81} -2.03743 q^{82} +5.75110 q^{83} +4.28774 q^{84} +11.0767 q^{85} -1.78072 q^{86} +13.2494 q^{87} -8.64760 q^{88} -2.47470 q^{89} +12.7088 q^{90} +1.42477 q^{91} -3.40427 q^{92} -24.7507 q^{93} +4.18237 q^{94} +14.3468 q^{95} -17.0759 q^{96} +9.55094 q^{97} -3.82348 q^{98} +24.6482 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 13 q^{2} + 3 q^{3} + 43 q^{4} + 2 q^{5} + 21 q^{6} + 3 q^{7} + 33 q^{8} + 33 q^{9}+O(q^{10}) \) 56 * q + 13 * q^2 + 3 * q^3 + 43 * q^4 + 2 * q^5 + 21 * q^6 + 3 * q^7 + 33 * q^8 + 33 * q^9	\( 56 q + 13 q^{2} + 3 q^{3} + 43 q^{4} + 2 q^{5} + 21 q^{6} + 3 q^{7} + 33 q^{8} + 33 q^{9} + 16 q^{10} + 51 q^{11} + 25 q^{12} + 26 q^{13} + 37 q^{14} - 27 q^{15} + 25 q^{16} - 34 q^{17} + 23 q^{18} + 7 q^{19} + 18 q^{20} - 35 q^{21} + 14 q^{22} + 71 q^{23} + 60 q^{24} + 12 q^{25} + 17 q^{26} - 18 q^{27} + 29 q^{28} + 8 q^{29} + 29 q^{30} + 71 q^{31} + 69 q^{32} + 27 q^{33} + 30 q^{34} - 15 q^{35} + 10 q^{36} + 19 q^{37} + 57 q^{38} + 79 q^{39} + 33 q^{40} + 26 q^{41} + 27 q^{42} + 34 q^{43} + 109 q^{44} - 5 q^{45} + 28 q^{46} + 111 q^{47} + 89 q^{48} - q^{49} + 59 q^{50} + 42 q^{51} + 52 q^{52} + 32 q^{53} + 43 q^{54} + 70 q^{55} + 95 q^{56} - 2 q^{57} - 6 q^{58} - 105 q^{60} + 67 q^{61} + 24 q^{62} - 116 q^{63} + 11 q^{64} + 66 q^{65} + 58 q^{66} + 24 q^{67} - 104 q^{68} + 66 q^{69} - 26 q^{70} - 9 q^{71} + 47 q^{72} + 17 q^{73} - 63 q^{74} - 116 q^{75} - 53 q^{76} + 69 q^{77} + 74 q^{78} + 35 q^{79} - 48 q^{80} + 4 q^{81} - 29 q^{82} + 135 q^{83} - 76 q^{84} + 34 q^{85} - 46 q^{86} + 11 q^{87} + 102 q^{88} + 134 q^{89} + 24 q^{90} + 63 q^{91} + 92 q^{92} - 3 q^{93} - 26 q^{94} - 127 q^{95} + 98 q^{96} - 2 q^{97} + 57 q^{98} + 94 q^{99}+O(q^{100}) \) 56 * q + 13 * q^2 + 3 * q^3 + 43 * q^4 + 2 * q^5 + 21 * q^6 + 3 * q^7 + 33 * q^8 + 33 * q^9 + 16 * q^10 + 51 * q^11 + 25 * q^12 + 26 * q^13 + 37 * q^14 - 27 * q^15 + 25 * q^16 - 34 * q^17 + 23 * q^18 + 7 * q^19 + 18 * q^20 - 35 * q^21 + 14 * q^22 + 71 * q^23 + 60 * q^24 + 12 * q^25 + 17 * q^26 - 18 * q^27 + 29 * q^28 + 8 * q^29 + 29 * q^30 + 71 * q^31 + 69 * q^32 + 27 * q^33 + 30 * q^34 - 15 * q^35 + 10 * q^36 + 19 * q^37 + 57 * q^38 + 79 * q^39 + 33 * q^40 + 26 * q^41 + 27 * q^42 + 34 * q^43 + 109 * q^44 - 5 * q^45 + 28 * q^46 + 111 * q^47 + 89 * q^48 - q^49 + 59 * q^50 + 42 * q^51 + 52 * q^52 + 32 * q^53 + 43 * q^54 + 70 * q^55 + 95 * q^56 - 2 * q^57 - 6 * q^58 - 105 * q^60 + 67 * q^61 + 24 * q^62 - 116 * q^63 + 11 * q^64 + 66 * q^65 + 58 * q^66 + 24 * q^67 - 104 * q^68 + 66 * q^69 - 26 * q^70 - 9 * q^71 + 47 * q^72 + 17 * q^73 - 63 * q^74 - 116 * q^75 - 53 * q^76 + 69 * q^77 + 74 * q^78 + 35 * q^79 - 48 * q^80 + 4 * q^81 - 29 * q^82 + 135 * q^83 - 76 * q^84 + 34 * q^85 - 46 * q^86 + 11 * q^87 + 102 * q^88 + 134 * q^89 + 24 * q^90 + 63 * q^91 + 92 * q^92 - 3 * q^93 - 26 * q^94 - 127 * q^95 + 98 * q^96 - 2 * q^97 + 57 * q^98 + 94 * q^99

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