LMFDB - Embedded newform 2671.2.a.a.1.51

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, 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("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$1$
Dimension:	$100$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.51
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.131029 q^{2} -1.12017 q^{3} -1.98283 q^{4} +1.29847 q^{5} +0.146775 q^{6} +2.28856 q^{7} +0.521867 q^{8} -1.74522 q^{9} +O(q^{10})$	\(q-0.131029 q^{2} -1.12017 q^{3} -1.98283 q^{4} +1.29847 q^{5} +0.146775 q^{6} +2.28856 q^{7} +0.521867 q^{8} -1.74522 q^{9} -0.170138 q^{10} +5.69248 q^{11} +2.22111 q^{12} -0.913752 q^{13} -0.299869 q^{14} -1.45451 q^{15} +3.89728 q^{16} -8.00706 q^{17} +0.228674 q^{18} -5.65323 q^{19} -2.57465 q^{20} -2.56358 q^{21} -0.745881 q^{22} -4.08876 q^{23} -0.584581 q^{24} -3.31397 q^{25} +0.119728 q^{26} +5.31546 q^{27} -4.53784 q^{28} +7.63773 q^{29} +0.190584 q^{30} -1.92098 q^{31} -1.55439 q^{32} -6.37655 q^{33} +1.04916 q^{34} +2.97164 q^{35} +3.46047 q^{36} +7.31330 q^{37} +0.740739 q^{38} +1.02356 q^{39} +0.677631 q^{40} +4.47564 q^{41} +0.335905 q^{42} -8.04904 q^{43} -11.2872 q^{44} -2.26612 q^{45} +0.535747 q^{46} +8.52514 q^{47} -4.36562 q^{48} -1.76247 q^{49} +0.434227 q^{50} +8.96928 q^{51} +1.81182 q^{52} -0.0500696 q^{53} -0.696480 q^{54} +7.39153 q^{55} +1.19433 q^{56} +6.33259 q^{57} -1.00077 q^{58} -8.80212 q^{59} +2.88405 q^{60} +5.56502 q^{61} +0.251705 q^{62} -3.99404 q^{63} -7.59089 q^{64} -1.18648 q^{65} +0.835515 q^{66} -10.6852 q^{67} +15.8766 q^{68} +4.58011 q^{69} -0.389372 q^{70} -0.262230 q^{71} -0.910771 q^{72} +12.0628 q^{73} -0.958256 q^{74} +3.71221 q^{75} +11.2094 q^{76} +13.0276 q^{77} -0.134116 q^{78} -3.23562 q^{79} +5.06052 q^{80} -0.718573 q^{81} -0.586439 q^{82} +4.16373 q^{83} +5.08316 q^{84} -10.3969 q^{85} +1.05466 q^{86} -8.55557 q^{87} +2.97072 q^{88} -11.3034 q^{89} +0.296927 q^{90} -2.09118 q^{91} +8.10732 q^{92} +2.15183 q^{93} -1.11704 q^{94} -7.34057 q^{95} +1.74119 q^{96} +0.149895 q^{97} +0.230935 q^{98} -9.93460 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) $ 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * 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 $

$2$	−0.131029	−0.0926517	−0.0463258	−	0.998926i	$-0.514751\pi$
$2$	−0.131029	−0.0926517	−0.0463258	+	0.998926i	$0.514751\pi$
$3$	−1.12017	−0.646731	−0.323366	−	0.946274i	$-0.604814\pi$
$3$	−1.12017	−0.646731	−0.323366	+	0.946274i	$0.604814\pi$
$4$	−1.98283	−0.991416
$5$	1.29847	0.580695	0.290347	−	0.956921i	$-0.406229\pi$
$5$	1.29847	0.580695	0.290347	+	0.956921i	$0.406229\pi$
$6$	0.146775	0.0599207
$7$	2.28856	0.864996	0.432498	−	0.901635i	$-0.357632\pi$
$7$	2.28856	0.864996	0.432498	+	0.901635i	$0.357632\pi$
$8$	0.521867	0.184508
$9$	−1.74522	−0.581739
$10$	−0.170138	−0.0538023
$11$	5.69248	1.71635	0.858173	−	0.513360i	$-0.171599\pi$
$11$	5.69248	1.71635	0.858173	+	0.513360i	$0.171599\pi$
$12$	2.22111	0.641180
$13$	−0.913752	−0.253429	−0.126715	−	0.991939i	$-0.540443\pi$
$13$	−0.913752	−0.253429	−0.126715	+	0.991939i	$0.540443\pi$
$14$	−0.299869	−0.0801433
$15$	−1.45451	−0.375553
$16$	3.89728	0.974321
$17$	−8.00706	−1.94200	−0.970998	−	0.239086i	$-0.923152\pi$
$17$	−8.00706	−1.94200	−0.970998	+	0.239086i	$0.923152\pi$
$18$	0.228674	0.0538991
$19$	−5.65323	−1.29694	−0.648470	−	0.761240i	$-0.724591\pi$
$19$	−5.65323	−1.29694	−0.648470	+	0.761240i	$0.724591\pi$
$20$	−2.57465	−0.575710
$21$	−2.56358	−0.559420
$22$	−0.745881	−0.159022
$23$	−4.08876	−0.852566	−0.426283	−	0.904590i	$-0.640177\pi$
$23$	−4.08876	−0.852566	−0.426283	+	0.904590i	$0.640177\pi$
$24$	−0.584581	−0.119327
$25$	−3.31397	−0.662794
$26$	0.119728	0.0234806
$27$	5.31546	1.02296
$28$	−4.53784	−0.857571
$29$	7.63773	1.41829	0.709145	−	0.705062i	$-0.249081\pi$
$29$	7.63773	1.41829	0.709145	+	0.705062i	$0.249081\pi$
$30$	0.190584	0.0347957
$31$	−1.92098	−0.345019	−0.172510	−	0.985008i	$-0.555188\pi$
$31$	−1.92098	−0.345019	−0.172510	+	0.985008i	$0.555188\pi$
$32$	−1.55439	−0.274780
$33$	−6.37655	−1.11002
$34$	1.04916	0.179929
$35$	2.97164	0.502299
$36$	3.46047	0.576745
$37$	7.31330	1.20230	0.601150	−	0.799137i	$-0.294710\pi$
$37$	7.31330	1.20230	0.601150	+	0.799137i	$0.294710\pi$
$38$	0.740739	0.120164
$39$	1.02356	0.163901
$40$	0.677631	0.107143
$41$	4.47564	0.698977	0.349489	−	0.936941i	$-0.386355\pi$
$41$	4.47564	0.698977	0.349489	+	0.936941i	$0.386355\pi$
$42$	0.335905	0.0518312
$43$	−8.04904	−1.22747	−0.613733	−	0.789513i	$-0.710333\pi$
$43$	−8.04904	−1.22747	−0.613733	+	0.789513i	$0.710333\pi$
$44$	−11.2872	−1.70161
$45$	−2.26612	−0.337813
$46$	0.535747	0.0789916
$47$	8.52514	1.24352	0.621760	−	0.783208i	$-0.286418\pi$
$47$	8.52514	1.24352	0.621760	+	0.783208i	$0.286418\pi$
$48$	−4.36562	−0.630124
$49$	−1.76247	−0.251782
$50$	0.434227	0.0614089
$51$	8.96928	1.25595
$52$	1.81182	0.251254
$53$	−0.0500696	−0.00687759	−0.00343880	−	0.999994i	$-0.501095\pi$
$53$	−0.0500696	−0.00687759	−0.00343880	+	0.999994i	$0.501095\pi$
$54$	−0.696480	−0.0947789
$55$	7.39153	0.996674
$56$	1.19433	0.159599
$57$	6.33259	0.838772
$58$	−1.00077	−0.131407
$59$	−8.80212	−1.14594	−0.572969	−	0.819577i	$-0.694208\pi$
$59$	−8.80212	−1.14594	−0.572969	+	0.819577i	$0.694208\pi$
$60$	2.88405	0.372330
$61$	5.56502	0.712528	0.356264	−	0.934385i	$-0.384050\pi$
$61$	5.56502	0.712528	0.356264	+	0.934385i	$0.384050\pi$
$62$	0.251705	0.0319666
$63$	−3.99404	−0.503202
$64$	−7.59089	−0.948862
$65$	−1.18648	−0.147165
$66$	0.835515	0.102845
$67$	−10.6852	−1.30541	−0.652705	−	0.757612i	$-0.726366\pi$
$67$	−10.6852	−1.30541	−0.652705	+	0.757612i	$0.726366\pi$
$68$	15.8766	1.92533
$69$	4.58011	0.551381
$70$	−0.389372	−0.0465388
$71$	−0.262230	−0.0311210	−0.0155605	−	0.999879i	$-0.504953\pi$
$71$	−0.262230	−0.0311210	−0.0155605	+	0.999879i	$0.504953\pi$
$72$	−0.910771	−0.107335
$73$	12.0628	1.41184	0.705921	−	0.708291i	$-0.250533\pi$
$73$	12.0628	1.41184	0.705921	+	0.708291i	$0.250533\pi$
$74$	−0.958256	−0.111395
$75$	3.71221	0.428649
$76$	11.2094	1.28581
$77$	13.0276	1.48463
$78$	−0.134116	−0.0151857
$79$	−3.23562	−0.364035	−0.182018	−	0.983295i	$-0.558263\pi$
$79$	−3.23562	−0.364035	−0.182018	+	0.983295i	$0.558263\pi$
$80$	5.06052	0.565783
$81$	−0.718573	−0.0798415
$82$	−0.586439	−0.0647614
$83$	4.16373	0.457029	0.228514	−	0.973541i	$-0.426613\pi$
$83$	4.16373	0.457029	0.228514	+	0.973541i	$0.426613\pi$
$84$	5.08316	0.554618
$85$	−10.3969	−1.12771
$86$	1.05466	0.113727
$87$	−8.55557	−0.917253
$88$	2.97072	0.316680
$89$	−11.3034	−1.19816	−0.599081	−	0.800688i	$-0.704467\pi$
$89$	−11.3034	−1.19816	−0.599081	+	0.800688i	$0.704467\pi$
$90$	0.296927	0.0312989
$91$	−2.09118	−0.219215
$92$	8.10732	0.845247
$93$	2.15183	0.223135
$94$	−1.11704	−0.115214
$95$	−7.34057	−0.753127
$96$	1.74119	0.177709
$97$	0.149895	0.0152196	0.00760979	−	0.999971i	$-0.497578\pi$
$97$	0.149895	0.0152196	0.00760979	+	0.999971i	$0.497578\pi$
$98$	0.230935	0.0233280
$99$	−9.93460	−0.998465
$100$	6.57104	0.657104
$101$	−15.7343	−1.56562	−0.782810	−	0.622261i	$-0.786214\pi$
$101$	−15.7343	−1.56562	−0.782810	+	0.622261i	$0.786214\pi$
$102$	−1.17524	−0.116366
$103$	−11.0978	−1.09350	−0.546748	−	0.837297i	$-0.684134\pi$
$103$	−11.0978	−1.09350	−0.546748	+	0.837297i	$0.684134\pi$
$104$	−0.476857	−0.0467597
$105$	−3.32875	−0.324852
$106$	0.00656058	0.000637220 0
$107$	−9.63882	−0.931820	−0.465910	−	0.884832i	$-0.654273\pi$
$107$	−9.63882	−0.931820	−0.465910	+	0.884832i	$0.654273\pi$
$108$	−10.5397	−1.01418
$109$	−18.0189	−1.72589	−0.862947	−	0.505295i	$-0.831384\pi$
$109$	−18.0189	−1.72589	−0.862947	+	0.505295i	$0.831384\pi$
$110$	−0.968507	−0.0923435
$111$	−8.19215	−0.777564
$112$	8.91918	0.842784
$113$	3.59207	0.337913	0.168957	−	0.985623i	$-0.445960\pi$
$113$	3.59207	0.337913	0.168957	+	0.985623i	$0.445960\pi$
$114$	−0.829754	−0.0777136
$115$	−5.30915	−0.495080
$116$	−15.1443	−1.40612
$117$	1.59469	0.147430
$118$	1.15333	0.106173
$119$	−18.3247	−1.67982
$120$	−0.759063	−0.0692926
$121$	21.4043	1.94585
$122$	−0.729181	−0.0660169
$123$	−5.01348	−0.452050
$124$	3.80899	0.342057
$125$	−10.7955	−0.965576
$126$	0.523336	0.0466225
$127$	1.21742	0.108029	0.0540144	−	0.998540i	$-0.482798\pi$
$127$	1.21742	0.108029	0.0540144	+	0.998540i	$0.482798\pi$
$128$	4.10341	0.362694
$129$	9.01630	0.793841
$130$	0.155464	0.0136351
$131$	−5.51349	−0.481716	−0.240858	−	0.970560i	$-0.577429\pi$
$131$	−5.51349	−0.481716	−0.240858	+	0.970560i	$0.577429\pi$
$132$	12.6436	1.10049
$133$	−12.9378	−1.12185
$134$	1.40008	0.120948
$135$	6.90198	0.594027
$136$	−4.17862	−0.358314
$137$	−13.8216	−1.18086	−0.590432	−	0.807088i	$-0.701042\pi$
$137$	−13.8216	−1.18086	−0.590432	+	0.807088i	$0.701042\pi$
$138$	−0.600129	−0.0510863
$139$	−4.52705	−0.383980	−0.191990	−	0.981397i	$-0.561494\pi$
$139$	−4.52705	−0.383980	−0.191990	+	0.981397i	$0.561494\pi$
$140$	−5.89226	−0.497987
$141$	−9.54962	−0.804223
$142$	0.0343598	0.00288341
$143$	−5.20151	−0.434972
$144$	−6.80160	−0.566800
$145$	9.91738	0.823594
$146$	−1.58058	−0.130809
$147$	1.97427	0.162835
$148$	−14.5010	−1.19198
$149$	−2.03871	−0.167018	−0.0835090	−	0.996507i	$-0.526613\pi$
$149$	−2.03871	−0.167018	−0.0835090	+	0.996507i	$0.526613\pi$
$150$	−0.486408	−0.0397151
$151$	−19.0012	−1.54630	−0.773148	−	0.634225i	$-0.781319\pi$
$151$	−19.0012	−1.54630	−0.773148	+	0.634225i	$0.781319\pi$
$152$	−2.95024	−0.239296
$153$	13.9740	1.12973
$154$	−1.70700	−0.137554
$155$	−2.49435	−0.200351
$156$	−2.02954	−0.162494
$157$	−18.4200	−1.47007	−0.735037	−	0.678027i	$-0.762835\pi$
$157$	−18.4200	−1.47007	−0.735037	+	0.678027i	$0.762835\pi$
$158$	0.423960	0.0337285
$159$	0.0560866	0.00444795
$160$	−2.01834	−0.159564
$161$	−9.35739	−0.737466
$162$	0.0941541	0.00739744
$163$	−8.66811	−0.678938	−0.339469	−	0.940617i	$-0.610247\pi$
$163$	−8.66811	−0.678938	−0.339469	+	0.940617i	$0.610247\pi$
$164$	−8.87444	−0.692977
$165$	−8.27978	−0.644580
$166$	−0.545570	−0.0423445
$167$	22.2085	1.71855	0.859274	−	0.511515i	$-0.170916\pi$
$167$	22.2085	1.71855	0.859274	+	0.511515i	$0.170916\pi$
$168$	−1.33785	−0.103217
$169$	−12.1651	−0.935774
$170$	1.36230	0.104484
$171$	9.86611	0.754480
$172$	15.9599	1.21693
$173$	−3.84667	−0.292457	−0.146229	−	0.989251i	$-0.546713\pi$
$173$	−3.84667	−0.292457	−0.146229	+	0.989251i	$0.546713\pi$
$174$	1.12103	0.0849850
$175$	−7.58423	−0.573314
$176$	22.1852	1.67227
$177$	9.85988	0.741114
$178$	1.48108	0.111012
$179$	4.70179	0.351428	0.175714	−	0.984441i	$-0.443777\pi$
$179$	4.70179	0.351428	0.175714	+	0.984441i	$0.443777\pi$
$180$	4.49333	0.334913
$181$	−5.70071	−0.423731	−0.211865	−	0.977299i	$-0.567954\pi$
$181$	−5.70071	−0.423731	−0.211865	+	0.977299i	$0.567954\pi$
$182$	0.274006	0.0203107
$183$	−6.23378	−0.460814
$184$	−2.13379	−0.157305
$185$	9.49612	0.698169
$186$	−0.281953	−0.0206738
$187$	−45.5800	−3.33314
$188$	−16.9039	−1.23284
$189$	12.1648	0.884856
$190$	0.961829	0.0697784
$191$	14.7491	1.06721	0.533603	−	0.845735i	$-0.320838\pi$
$191$	14.7491	1.06721	0.533603	+	0.845735i	$0.320838\pi$
$192$	8.50310	0.613659
$193$	21.0470	1.51500	0.757499	−	0.652836i	$-0.226421\pi$
$193$	21.0470	1.51500	0.757499	+	0.652836i	$0.226421\pi$
$194$	−0.0196407	−0.00141012
$195$	1.32906	0.0951762
$196$	3.49469	0.249620
$197$	8.66773	0.617550	0.308775	−	0.951135i	$-0.400081\pi$
$197$	8.66773	0.617550	0.308775	+	0.951135i	$0.400081\pi$
$198$	1.30172	0.0925095
$199$	4.73929	0.335960	0.167980	−	0.985790i	$-0.446276\pi$
$199$	4.73929	0.335960	0.167980	+	0.985790i	$0.446276\pi$
$200$	−1.72945	−0.122291
$201$	11.9693	0.844249
$202$	2.06165	0.145057
$203$	17.4794	1.22682
$204$	−17.7846	−1.24517
$205$	5.81150	0.405892
$206$	1.45413	0.101314
$207$	7.13577	0.495970
$208$	−3.56115	−0.246921
$209$	−32.1809	−2.22600
$210$	0.436163	0.0300981
$211$	15.9020	1.09474	0.547370	−	0.836891i	$-0.315629\pi$
$211$	15.9020	1.09474	0.547370	+	0.836891i	$0.315629\pi$
$212$	0.0992796	0.00681855
$213$	0.293742	0.0201269
$214$	1.26297	0.0863347
$215$	−10.4515	−0.712784
$216$	2.77396	0.188744
$217$	−4.39630	−0.298440
$218$	2.36100	0.159907
$219$	−13.5124	−0.913082
$220$	−14.6562	−0.988118
$221$	7.31646	0.492158
$222$	1.07341	0.0720426
$223$	−9.02988	−0.604685	−0.302343	−	0.953199i	$-0.597769\pi$
$223$	−9.02988	−0.604685	−0.302343	+	0.953199i	$0.597769\pi$
$224$	−3.55733	−0.237684
$225$	5.78359	0.385573
$226$	−0.470666	−0.0313082
$227$	21.0511	1.39721	0.698605	−	0.715508i	$-0.253805\pi$
$227$	21.0511	1.39721	0.698605	+	0.715508i	$0.253805\pi$
$228$	−12.5565	−0.831572
$229$	−9.46831	−0.625683	−0.312842	−	0.949805i	$-0.601281\pi$
$229$	−9.46831	−0.625683	−0.312842	+	0.949805i	$0.601281\pi$
$230$	0.695653	0.0458700
$231$	−14.5931	−0.960159
$232$	3.98588	0.261686
$233$	13.4016	0.877966	0.438983	−	0.898495i	$-0.355339\pi$
$233$	13.4016	0.877966	0.438983	+	0.898495i	$0.355339\pi$
$234$	−0.208952	−0.0136596
$235$	11.0697	0.722105
$236$	17.4531	1.13610
$237$	3.62445	0.235433
$238$	2.40107	0.155638
$239$	−4.64408	−0.300401	−0.150200	−	0.988656i	$-0.547992\pi$
$239$	−4.64408	−0.300401	−0.150200	+	0.988656i	$0.547992\pi$
$240$	−5.66865	−0.365910
$241$	−0.0176571	−0.00113740	−0.000568698	−	1.00000i	$-0.500181\pi$
$241$	−0.0176571	−0.00113740	−0.000568698		1.00000i	$0.500181\pi$
$242$	−2.80459	−0.180286
$243$	−15.1414	−0.971324
$244$	−11.0345	−0.706412
$245$	−2.28852	−0.146208
$246$	0.656913	0.0418832
$247$	5.16565	0.328682
$248$	−1.00250	−0.0636588
$249$	−4.66409	−0.295575
$250$	1.41452	0.0894622
$251$	−20.5922	−1.29977	−0.649883	−	0.760034i	$-0.725182\pi$
$251$	−20.5922	−1.29977	−0.649883	+	0.760034i	$0.725182\pi$
$252$	7.91951	0.498882
$253$	−23.2752	−1.46330
$254$	−0.159518	−0.0100091
$255$	11.6464	0.729324
$256$	14.6441	0.915258
$257$	−11.4177	−0.712218	−0.356109	−	0.934445i	$-0.615897\pi$
$257$	−11.4177	−0.712218	−0.356109	+	0.934445i	$0.615897\pi$
$258$	−1.18140	−0.0735507
$259$	16.7370	1.03998
$260$	2.35259	0.145902
$261$	−13.3295	−0.825074
$262$	0.722428	0.0446318
$263$	4.27765	0.263771	0.131886	−	0.991265i	$-0.457897\pi$
$263$	4.27765	0.263771	0.131886	+	0.991265i	$0.457897\pi$
$264$	−3.32771	−0.204807
$265$	−0.0650141	−0.00399378
$266$	1.69523	0.103941
$267$	12.6618	0.774889
$268$	21.1870	1.29420
$269$	−0.287648	−0.0175382	−0.00876911	−	0.999962i	$-0.502791\pi$
$269$	−0.287648	−0.0175382	−0.00876911	+	0.999962i	$0.502791\pi$
$270$	−0.904361	−0.0550376
$271$	−17.7271	−1.07685	−0.538423	−	0.842675i	$-0.680980\pi$
$271$	−17.7271	−1.07685	−0.538423	+	0.842675i	$0.680980\pi$
$272$	−31.2058	−1.89213
$273$	2.34248	0.141773
$274$	1.81104	0.109409
$275$	−18.8647	−1.13758
$276$	−9.08159	−0.546648
$277$	−8.56106	−0.514384	−0.257192	−	0.966360i	$-0.582797\pi$
$277$	−8.56106	−0.514384	−0.257192	+	0.966360i	$0.582797\pi$
$278$	0.593176	0.0355764
$279$	3.35253	0.200711
$280$	1.55080	0.0926781
$281$	−28.7555	−1.71541	−0.857704	−	0.514143i	$-0.828110\pi$
$281$	−28.7555	−1.71541	−0.857704	+	0.514143i	$0.828110\pi$
$282$	1.25128	0.0745126
$283$	25.3925	1.50943	0.754715	−	0.656053i	$-0.227775\pi$
$283$	25.3925	1.50943	0.754715	+	0.656053i	$0.227775\pi$
$284$	0.519957	0.0308538
$285$	8.22270	0.487071
$286$	0.681550	0.0403009
$287$	10.2428	0.604613
$288$	2.71275	0.159850
$289$	47.1130	2.77135
$290$	−1.29947	−0.0763073
$291$	−0.167909	−0.00984297
$292$	−23.9185	−1.39972
$293$	−5.73868	−0.335257	−0.167629	−	0.985850i	$-0.553611\pi$
$293$	−5.73868	−0.335257	−0.167629	+	0.985850i	$0.553611\pi$
$294$	−0.258687	−0.0150870
$295$	−11.4293	−0.665440
$296$	3.81657	0.221834
$297$	30.2581	1.75575
$298$	0.267131	0.0154745
$299$	3.73611	0.216065
$300$	−7.36069	−0.424970
$301$	−18.4207	−1.06175
$302$	2.48971	0.143267
$303$	17.6251	1.01254
$304$	−22.0322	−1.26364
$305$	7.22603	0.413761
$306$	−1.83101	−0.104672
$307$	−14.0325	−0.800878	−0.400439	−	0.916323i	$-0.631142\pi$
$307$	−14.0325	−0.800878	−0.400439	+	0.916323i	$0.631142\pi$
$308$	−25.8315	−1.47189
$309$	12.4314	0.707198
$310$	0.326832	0.0185628
$311$	0.487688	0.0276543	0.0138271	−	0.999904i	$-0.495599\pi$
$311$	0.487688	0.0276543	0.0138271	+	0.999904i	$0.495599\pi$
$312$	0.534162	0.0302410
$313$	−7.14971	−0.404125	−0.202063	−	0.979373i	$-0.564764\pi$
$313$	−7.14971	−0.404125	−0.202063	+	0.979373i	$0.564764\pi$
$314$	2.41355	0.136205
$315$	−5.18615	−0.292207
$316$	6.41568	0.360910
$317$	−9.17075	−0.515081	−0.257540	−	0.966268i	$-0.582912\pi$
$317$	−9.17075	−0.515081	−0.257540	+	0.966268i	$0.582912\pi$
$318$	−0.00734898	−0.000412110 0
$319$	43.4776	2.43428
$320$	−9.85657	−0.550999
$321$	10.7971	0.602637
$322$	1.22609	0.0683274
$323$	45.2658	2.51865
$324$	1.42481	0.0791561
$325$	3.02814	0.167971
$326$	1.13578	0.0629048
$327$	20.1842	1.11619
$328$	2.33569	0.128967
$329$	19.5103	1.07564
$330$	1.08489	0.0597214
$331$	−2.11123	−0.116044	−0.0580218	−	0.998315i	$-0.518479\pi$
$331$	−2.11123	−0.116044	−0.0580218	+	0.998315i	$0.518479\pi$
$332$	−8.25598	−0.453106
$333$	−12.7633	−0.699424
$334$	−2.90997	−0.159226
$335$	−13.8745	−0.758045
$336$	−9.99101	−0.545054
$337$	6.94622	0.378385	0.189192	−	0.981940i	$-0.439413\pi$
$337$	6.94622	0.378385	0.189192	+	0.981940i	$0.439413\pi$
$338$	1.59398	0.0867010
$339$	−4.02373	−0.218539
$340$	20.6154	1.11803
$341$	−10.9352	−0.592172
$342$	−1.29275	−0.0699039
$343$	−20.0535	−1.08279
$344$	−4.20053	−0.226477
$345$	5.94715	0.320184
$346$	0.504027	0.0270966
$347$	7.96200	0.427423	0.213711	−	0.976897i	$-0.431445\pi$
$347$	7.96200	0.427423	0.213711	+	0.976897i	$0.431445\pi$
$348$	16.9642	0.909379
$349$	−18.2951	−0.979316	−0.489658	−	0.871915i	$-0.662878\pi$
$349$	−18.2951	−0.979316	−0.489658	+	0.871915i	$0.662878\pi$
$350$	0.993756	0.0531185
$351$	−4.85701	−0.259248
$352$	−8.84835	−0.471618
$353$	−35.8330	−1.90720	−0.953598	−	0.301083i	$-0.902652\pi$
$353$	−35.8330	−1.90720	−0.953598	+	0.301083i	$0.902652\pi$
$354$	−1.29193	−0.0686654
$355$	−0.340498	−0.0180718
$356$	22.4128	1.18788
$357$	20.5268	1.08639
$358$	−0.616072	−0.0325604
$359$	2.51957	0.132978	0.0664890	−	0.997787i	$-0.478820\pi$
$359$	2.51957	0.132978	0.0664890	+	0.997787i	$0.478820\pi$
$360$	−1.18261	−0.0623291
$361$	12.9590	0.682055
$362$	0.746960	0.0392594
$363$	−23.9765	−1.25844
$364$	4.14646	0.217333
$365$	15.6632	0.819849
$366$	0.816808	0.0426952
$367$	−21.2291	−1.10815	−0.554075	−	0.832467i	$-0.686928\pi$
$367$	−21.2291	−1.10815	−0.554075	+	0.832467i	$0.686928\pi$
$368$	−15.9351	−0.830672
$369$	−7.81096	−0.406622
$370$	−1.24427	−0.0646865
$371$	−0.114588	−0.00594909
$372$	−4.26672	−0.221219
$373$	−34.6438	−1.79379	−0.896895	−	0.442243i	$-0.854183\pi$
$373$	−34.6438	−1.79379	−0.896895	+	0.442243i	$0.854183\pi$
$374$	5.97231	0.308821
$375$	12.0928	0.624468
$376$	4.44899	0.229439
$377$	−6.97899	−0.359436
$378$	−1.59394	−0.0819834
$379$	−12.9445	−0.664914	−0.332457	−	0.943118i	$-0.607878\pi$
$379$	−12.9445	−0.664914	−0.332457	+	0.943118i	$0.607878\pi$
$380$	14.5551	0.746662
$381$	−1.36372	−0.0698656
$382$	−1.93256	−0.0988784
$383$	−11.0244	−0.563319	−0.281659	−	0.959514i	$-0.590885\pi$
$383$	−11.0244	−0.563319	−0.281659	+	0.959514i	$0.590885\pi$
$384$	−4.59653	−0.234566
$385$	16.9160	0.862119
$386$	−2.75778	−0.140367
$387$	14.0473	0.714065
$388$	−0.297217	−0.0150889
$389$	19.3253	0.979833	0.489916	−	0.871769i	$-0.337027\pi$
$389$	19.3253	0.979833	0.489916	+	0.871769i	$0.337027\pi$
$390$	−0.174146	−0.00881823
$391$	32.7389	1.65568
$392$	−0.919777	−0.0464558
$393$	6.17605	0.311541
$394$	−1.13573	−0.0572170
$395$	−4.20136	−0.211393
$396$	19.6986	0.989894
$397$	−27.1383	−1.36203	−0.681016	−	0.732269i	$-0.738462\pi$
$397$	−27.1383	−1.36203	−0.681016	+	0.732269i	$0.738462\pi$
$398$	−0.620986	−0.0311272
$399$	14.4925	0.725534
$400$	−12.9155	−0.645773
$401$	−0.254658	−0.0127170	−0.00635851	−	0.999980i	$-0.502024\pi$
$401$	−0.254658	−0.0127170	−0.00635851	+	0.999980i	$0.502024\pi$
$402$	−1.56833	−0.0782211
$403$	1.75530	0.0874379
$404$	31.1984	1.55218
$405$	−0.933048	−0.0463635
$406$	−2.29032	−0.113667
$407$	41.6308	2.06356
$408$	4.68077	0.231733
$409$	11.5382	0.570529	0.285265	−	0.958449i	$-0.407918\pi$
$409$	11.5382	0.570529	0.285265	+	0.958449i	$0.407918\pi$
$410$	−0.761476	−0.0376066
$411$	15.4826	0.763701
$412$	22.0050	1.08411
$413$	−20.1442	−0.991232
$414$	−0.934995	−0.0459525
$415$	5.40649	0.265394
$416$	1.42033	0.0696374
$417$	5.07108	0.248332
$418$	4.21664	0.206243
$419$	27.6686	1.35170	0.675849	−	0.737040i	$-0.263777\pi$
$419$	27.6686	1.35170	0.675849	+	0.737040i	$0.263777\pi$
$420$	6.60034	0.322064
$421$	−10.6285	−0.518002	−0.259001	−	0.965877i	$-0.583393\pi$
$421$	−10.6285	−0.518002	−0.259001	+	0.965877i	$0.583393\pi$
$422$	−2.08363	−0.101429
$423$	−14.8782	−0.723403
$424$	−0.0261297	−0.00126897
$425$	26.5351	1.28714
$426$	−0.0384888	−0.00186479
$427$	12.7359	0.616334
$428$	19.1122	0.923821
$429$	5.82658	0.281310
$430$	1.36945	0.0660406
$431$	−23.5430	−1.13402	−0.567012	−	0.823709i	$-0.691901\pi$
$431$	−23.5430	−1.13402	−0.567012	+	0.823709i	$0.691901\pi$
$432$	20.7158	0.996691
$433$	24.3121	1.16836	0.584182	−	0.811623i	$-0.301415\pi$
$433$	24.3121	1.16836	0.584182	+	0.811623i	$0.301415\pi$
$434$	0.576043	0.0276510
$435$	−11.1092	−0.532644
$436$	35.7284	1.71108
$437$	23.1147	1.10573
$438$	1.77052	0.0845986
$439$	−1.24205	−0.0592798	−0.0296399	−	0.999561i	$-0.509436\pi$
$439$	−1.24205	−0.0592798	−0.0296399	+	0.999561i	$0.509436\pi$
$440$	3.85740	0.183894
$441$	3.07590	0.146471
$442$	−0.958670	−0.0455993
$443$	−26.4085	−1.25471	−0.627353	−	0.778735i	$-0.715862\pi$
$443$	−26.4085	−1.25471	−0.627353	+	0.778735i	$0.715862\pi$
$444$	16.2437	0.770890
$445$	−14.6772	−0.695767
$446$	1.18318	0.0560251
$447$	2.28371	0.108016
$448$	−17.3723	−0.820762
$449$	36.3003	1.71312	0.856558	−	0.516051i	$-0.172598\pi$
$449$	36.3003	1.71312	0.856558	+	0.516051i	$0.172598\pi$
$450$	−0.757819	−0.0357239
$451$	25.4775	1.19969
$452$	−7.12246	−0.335013
$453$	21.2846	1.00004
$454$	−2.75831	−0.129454
$455$	−2.71534	−0.127297
$456$	3.30477	0.154760
$457$	30.2093	1.41313	0.706566	−	0.707647i	$-0.250243\pi$
$457$	30.2093	1.41313	0.706566	+	0.707647i	$0.250243\pi$
$458$	1.24063	0.0579706
$459$	−42.5612	−1.98658
$460$	10.5271	0.490830
$461$	16.6353	0.774782	0.387391	−	0.921915i	$-0.373376\pi$
$461$	16.6353	0.774782	0.387391	+	0.921915i	$0.373376\pi$
$462$	1.91213	0.0889603
$463$	26.3733	1.22567	0.612835	−	0.790211i	$-0.290029\pi$
$463$	26.3733	1.22567	0.612835	+	0.790211i	$0.290029\pi$
$464$	29.7664	1.38187
$465$	2.79410	0.129573
$466$	−1.75600	−0.0813450
$467$	19.6968	0.911459	0.455730	−	0.890118i	$-0.349378\pi$
$467$	19.6968	0.911459	0.455730	+	0.890118i	$0.349378\pi$
$468$	−3.16201	−0.146164
$469$	−24.4539	−1.12917
$470$	−1.45045	−0.0669043
$471$	20.6335	0.950742
$472$	−4.59354	−0.211435
$473$	−45.8190	−2.10676
$474$	−0.474908	−0.0218133
$475$	18.7346	0.859604
$476$	36.3347	1.66540
$477$	0.0873823	0.00400096
$478$	0.608510	0.0278326
$479$	−17.0313	−0.778181	−0.389090	−	0.921200i	$-0.627211\pi$
$479$	−17.0313	−0.778181	−0.389090	+	0.921200i	$0.627211\pi$
$480$	2.26088	0.103195
$481$	−6.68254	−0.304698
$482$	0.00231360	0.000105382 0
$483$	10.4819	0.476942
$484$	−42.4411	−1.92914
$485$	0.194635	0.00883793
$486$	1.98397	0.0899948
$487$	25.6486	1.16225	0.581124	−	0.813815i	$-0.302613\pi$
$487$	25.6486	1.16225	0.581124	+	0.813815i	$0.302613\pi$
$488$	2.90420	0.131467
$489$	9.70977	0.439091
$490$	0.299863	0.0135465
$491$	−25.3860	−1.14565	−0.572827	−	0.819676i	$-0.694153\pi$
$491$	−25.3860	−1.14565	−0.572827	+	0.819676i	$0.694153\pi$
$492$	9.94089	0.448170
$493$	−61.1557	−2.75432
$494$	−0.676851	−0.0304530
$495$	−12.8998	−0.579804
$496$	−7.48662	−0.336159
$497$	−0.600130	−0.0269195
$498$	0.611132	0.0273855
$499$	−29.3432	−1.31358	−0.656791	−	0.754073i	$-0.728087\pi$
$499$	−29.3432	−1.31358	−0.656791	+	0.754073i	$0.728087\pi$
$500$	21.4056	0.957287
$501$	−24.8774	−1.11144
$502$	2.69818	0.120425
$503$	−2.07546	−0.0925400	−0.0462700	−	0.998929i	$-0.514733\pi$
$503$	−2.07546	−0.0925400	−0.0462700	+	0.998929i	$0.514733\pi$
$504$	−2.08436	−0.0928447
$505$	−20.4305	−0.909147
$506$	3.04973	0.135577
$507$	13.6270	0.605194
$508$	−2.41395	−0.107101
$509$	2.58735	0.114682	0.0573411	−	0.998355i	$-0.481738\pi$
$509$	2.58735	0.114682	0.0573411	+	0.998355i	$0.481738\pi$
$510$	−1.52601	−0.0675730
$511$	27.6065	1.22124
$512$	−10.1256	−0.447494
$513$	−30.0495	−1.32672
$514$	1.49605	0.0659881
$515$	−14.4102	−0.634987
$516$	−17.8778	−0.787027
$517$	48.5292	2.13431
$518$	−2.19303	−0.0963562
$519$	4.30893	0.189141
$520$	−0.619186	−0.0271531
$521$	−31.1005	−1.36254	−0.681268	−	0.732034i	$-0.738571\pi$
$521$	−31.1005	−1.36254	−0.681268	+	0.732034i	$0.738571\pi$
$522$	1.74655	0.0764445
$523$	−0.181014	−0.00791518	−0.00395759	−	0.999992i	$-0.501260\pi$
$523$	−0.181014	−0.00791518	−0.00395759	+	0.999992i	$0.501260\pi$
$524$	10.9323	0.477581
$525$	8.49564	0.370780
$526$	−0.560497	−0.0244388
$527$	15.3814	0.670026
$528$	−24.8512	−1.08151
$529$	−6.28204	−0.273132
$530$	0.00851874	0.000370030 0
$531$	15.3616	0.666636
$532$	25.6535	1.11222
$533$	−4.08962	−0.177141
$534$	−1.65906	−0.0717948
$535$	−12.5157	−0.541103
$536$	−5.57628	−0.240859
$537$	−5.26681	−0.227280
$538$	0.0376903	0.00162495
$539$	−10.0328	−0.432145
$540$	−13.6855	−0.588928
$541$	16.3553	0.703168	0.351584	−	0.936156i	$-0.385643\pi$
$541$	16.3553	0.703168	0.351584	+	0.936156i	$0.385643\pi$
$542$	2.32277	0.0997716
$543$	6.38578	0.274040
$544$	12.4461	0.533623
$545$	−23.3970	−1.00222
$546$	−0.306933	−0.0131355
$547$	23.9569	1.02432	0.512161	−	0.858890i	$-0.328845\pi$
$547$	23.9569	1.02432	0.512161	+	0.858890i	$0.328845\pi$
$548$	27.4060	1.17073
$549$	−9.71217	−0.414505
$550$	2.47183	0.105399
$551$	−43.1779	−1.83944
$552$	2.39021	0.101734
$553$	−7.40492	−0.314889
$554$	1.12175	0.0476585
$555$	−10.6373	−0.451528
$556$	8.97638	0.380683
$557$	−26.2109	−1.11059	−0.555297	−	0.831652i	$-0.687395\pi$
$557$	−26.2109	−1.11059	−0.555297	+	0.831652i	$0.687395\pi$
$558$	−0.439280	−0.0185962
$559$	7.35482	0.311076
$560$	11.5813	0.489400
$561$	51.0574	2.15565
$562$	3.76781	0.158935
$563$	37.2626	1.57043	0.785215	−	0.619223i	$-0.212552\pi$
$563$	37.2626	1.57043	0.785215	+	0.619223i	$0.212552\pi$
$564$	18.9353	0.797319
$565$	4.66420	0.196224
$566$	−3.32717	−0.139851
$567$	−1.64450	−0.0690625
$568$	−0.136849	−0.00574206
$569$	7.76367	0.325470	0.162735	−	0.986670i	$-0.447968\pi$
$569$	7.76367	0.325470	0.162735	+	0.986670i	$0.447968\pi$
$570$	−1.07741	−0.0451279
$571$	38.3555	1.60513	0.802565	−	0.596565i	$-0.203468\pi$
$571$	38.3555	1.60513	0.802565	+	0.596565i	$0.203468\pi$
$572$	10.3137	0.431238
$573$	−16.5215	−0.690195
$574$	−1.34210	−0.0560184
$575$	13.5500	0.565075
$576$	13.2478	0.551990
$577$	17.9289	0.746389	0.373194	−	0.927753i	$-0.378262\pi$
$577$	17.9289	0.746389	0.373194	+	0.927753i	$0.378262\pi$
$578$	−6.17318	−0.256770
$579$	−23.5763	−0.979797
$580$	−19.6645	−0.816524
$581$	9.52897	0.395328
$582$	0.0220009	0.000911968 0
$583$	−0.285020	−0.0118043
$584$	6.29517	0.260496
$585$	2.07067	0.0856115
$586$	0.751935	0.0310621
$587$	−29.8627	−1.23257	−0.616284	−	0.787524i	$-0.711363\pi$
$587$	−29.8627	−1.23257	−0.616284	+	0.787524i	$0.711363\pi$
$588$	−3.91465	−0.161437
$589$	10.8598	0.447469
$590$	1.49757	0.0616541
$591$	−9.70934	−0.399389
$592$	28.5020	1.17142
$593$	−24.6524	−1.01235	−0.506176	−	0.862430i	$-0.668941\pi$
$593$	−24.6524	−1.01235	−0.506176	+	0.862430i	$0.668941\pi$
$594$	−3.96470	−0.162674
$595$	−23.7941	−0.975462
$596$	4.04243	0.165584
$597$	−5.30882	−0.217276
$598$	−0.489540	−0.0200188
$599$	−24.4881	−1.00056	−0.500278	−	0.865865i	$-0.666769\pi$
$599$	−24.4881	−1.00056	−0.500278	+	0.865865i	$0.666769\pi$
$600$	1.93728	0.0790892
$601$	−21.3106	−0.869279	−0.434640	−	0.900604i	$-0.643124\pi$
$601$	−21.3106	−0.869279	−0.434640	+	0.900604i	$0.643124\pi$
$602$	2.41366	0.0983733
$603$	18.6481	0.759407
$604$	37.6762	1.53302
$605$	27.7929	1.12994
$606$	−2.30940	−0.0938131
$607$	9.69519	0.393515	0.196758	−	0.980452i	$-0.436959\pi$
$607$	9.69519	0.393515	0.196758	+	0.980452i	$0.436959\pi$
$608$	8.78734	0.356374
$609$	−19.5800	−0.793420
$610$	−0.946822	−0.0383357
$611$	−7.78986	−0.315144
$612$	−27.7082	−1.12004
$613$	22.4512	0.906796	0.453398	−	0.891308i	$-0.350212\pi$
$613$	22.4512	0.906796	0.453398	+	0.891308i	$0.350212\pi$
$614$	1.83867	0.0742027
$615$	−6.50987	−0.262503
$616$	6.79868	0.273927
$617$	−43.7764	−1.76237	−0.881187	−	0.472769i	$-0.843255\pi$
$617$	−43.7764	−1.76237	−0.881187	+	0.472769i	$0.843255\pi$
$618$	−1.62888	−0.0655230
$619$	16.0449	0.644900	0.322450	−	0.946587i	$-0.395494\pi$
$619$	16.0449	0.644900	0.322450	+	0.946587i	$0.395494\pi$
$620$	4.94587	0.198631
$621$	−21.7336	−0.872140
$622$	−0.0639014	−0.00256221
$623$	−25.8687	−1.03641
$624$	3.98910	0.159692
$625$	2.55222	0.102089
$626$	0.936820	0.0374429
$627$	36.0481	1.43962
$628$	36.5237	1.45745
$629$	−58.5580	−2.33486
$630$	0.679538	0.0270734
$631$	41.1356	1.63758	0.818790	−	0.574093i	$-0.194645\pi$
$631$	41.1356	1.63758	0.818790	+	0.574093i	$0.194645\pi$
$632$	−1.68856	−0.0671674
$633$	−17.8130	−0.708002
$634$	1.20164	0.0477231
$635$	1.58079	0.0627318
$636$	−0.111210	−0.00440977
$637$	1.61046	0.0638088
$638$	−5.69684	−0.225540
$639$	0.457648	0.0181043
$640$	5.32817	0.210615
$641$	−5.46992	−0.216049	−0.108024	−	0.994148i	$-0.534452\pi$
$641$	−5.46992	−0.216049	−0.108024	+	0.994148i	$0.534452\pi$
$642$	−1.41474	−0.0558353
$643$	21.2394	0.837602	0.418801	−	0.908078i	$-0.362451\pi$
$643$	21.2394	0.837602	0.418801	+	0.908078i	$0.362451\pi$
$644$	18.5541	0.731135
$645$	11.7074	0.460979
$646$	−5.93114	−0.233358
$647$	−26.4205	−1.03870	−0.519349	−	0.854562i	$-0.673825\pi$
$647$	−26.4205	−1.03870	−0.519349	+	0.854562i	$0.673825\pi$
$648$	−0.375000	−0.0147314
$649$	−50.1059	−1.96683
$650$	−0.396775	−0.0155628
$651$	4.92461	0.193011
$652$	17.1874	0.673110
$653$	41.6287	1.62906	0.814529	−	0.580123i	$-0.196996\pi$
$653$	41.6287	1.62906	0.814529	+	0.580123i	$0.196996\pi$
$654$	−2.64472	−0.103417
$655$	−7.15912	−0.279730
$656$	17.4428	0.681028
$657$	−21.0522	−0.821323
$658$	−2.55642	−0.0996598
$659$	42.9891	1.67462	0.837308	−	0.546732i	$-0.184128\pi$
$659$	42.9891	1.67462	0.837308	+	0.546732i	$0.184128\pi$
$660$	16.4174	0.639047
$661$	13.3828	0.520531	0.260265	−	0.965537i	$-0.416190\pi$
$661$	13.3828	0.520531	0.260265	+	0.965537i	$0.416190\pi$
$662$	0.276633	0.0107516
$663$	−8.19569	−0.318294
$664$	2.17292	0.0843255
$665$	−16.7994	−0.651452
$666$	1.67236	0.0648028
$667$	−31.2288	−1.20919
$668$	−44.0358	−1.70380
$669$	10.1150	0.391069
$670$	1.81796	0.0702341
$671$	31.6788	1.22295
$672$	3.98482	0.153718
$673$	51.2892	1.97705	0.988526	−	0.151048i	$-0.0482648\pi$
$673$	51.2892	1.97705	0.988526	+	0.151048i	$0.0482648\pi$
$674$	−0.910158	−0.0350580
$675$	−17.6152	−0.678011
$676$	24.1213	0.927741
$677$	−10.5157	−0.404149	−0.202075	−	0.979370i	$-0.564768\pi$
$677$	−10.5157	−0.404149	−0.202075	+	0.979370i	$0.564768\pi$
$678$	0.527226	0.0202480
$679$	0.343045	0.0131649
$680$	−5.42583	−0.208071
$681$	−23.5808	−0.903619
$682$	1.43283	0.0548657
$683$	2.66511	0.101978	0.0509889	−	0.998699i	$-0.483763\pi$
$683$	2.66511	0.101978	0.0509889	+	0.998699i	$0.483763\pi$
$684$	−19.5628	−0.748004
$685$	−17.9470	−0.685721
$686$	2.62759	0.100322
$687$	10.6061	0.404649
$688$	−31.3694	−1.19595
$689$	0.0457512	0.00174298
$690$	−0.779251	−0.0296656
$691$	−28.2638	−1.07521	−0.537603	−	0.843198i	$-0.680670\pi$
$691$	−28.2638	−1.07521	−0.537603	+	0.843198i	$0.680670\pi$
$692$	7.62730	0.289947
$693$	−22.7360	−0.863669
$694$	−1.04325	−0.0396014
$695$	−5.87826	−0.222975
$696$	−4.46487	−0.169240
$697$	−35.8367	−1.35741
$698$	2.39720	0.0907353
$699$	−15.0121	−0.567808
$700$	15.0382	0.568392
$701$	−39.3880	−1.48766	−0.743832	−	0.668366i	$-0.766994\pi$
$701$	−39.3880	−1.48766	−0.743832	+	0.668366i	$0.766994\pi$
$702$	0.636410	0.0240197
$703$	−41.3438	−1.55931
$704$	−43.2110	−1.62858
$705$	−12.3999	−0.467008
$706$	4.69516	0.176705
$707$	−36.0089	−1.35426
$708$	−19.5505	−0.734752
$709$	30.9139	1.16099	0.580497	−	0.814262i	$-0.302858\pi$
$709$	30.9139	1.16099	0.580497	+	0.814262i	$0.302858\pi$
$710$	0.0446152	0.00167438
$711$	5.64685	0.211773
$712$	−5.89890	−0.221071
$713$	7.85445	0.294151
$714$	−2.68961	−0.100656
$715$	−6.75402	−0.252586
$716$	−9.32286	−0.348412
$717$	5.20217	0.194278
$718$	−0.330138	−0.0123206
$719$	43.3181	1.61549	0.807746	−	0.589530i	$-0.200687\pi$
$719$	43.3181	1.61549	0.807746	+	0.589530i	$0.200687\pi$
$720$	−8.83169	−0.329138
$721$	−25.3980	−0.945869
$722$	−1.69801	−0.0631935
$723$	0.0197790	0.000735590 0
$724$	11.3036	0.420093
$725$	−25.3112	−0.940034
$726$	3.14162	0.116597
$727$	28.6425	1.06229	0.531147	−	0.847280i	$-0.321761\pi$
$727$	28.6425	1.06229	0.531147	+	0.847280i	$0.321761\pi$
$728$	−1.09132	−0.0404469
$729$	19.1167	0.708027
$730$	−2.05234	−0.0759604
$731$	64.4491	2.38374
$732$	12.3605	0.456859
$733$	41.8686	1.54645	0.773225	−	0.634131i	$-0.218642\pi$
$733$	41.8686	1.54645	0.773225	+	0.634131i	$0.218642\pi$
$734$	2.78163	0.102672
$735$	2.56354	0.0945575
$736$	6.35554	0.234268
$737$	−60.8255	−2.24054
$738$	1.02346	0.0376742
$739$	−18.2688	−0.672028	−0.336014	−	0.941857i	$-0.609079\pi$
$739$	−18.2688	−0.672028	−0.336014	+	0.941857i	$0.609079\pi$
$740$	−18.8292	−0.692175
$741$	−5.78641	−0.212569
$742$	0.0150143	0.000551193 0
$743$	−9.78498	−0.358976	−0.179488	−	0.983760i	$-0.557444\pi$
$743$	−9.78498	−0.358976	−0.179488	+	0.983760i	$0.557444\pi$
$744$	1.12297	0.0411701
$745$	−2.64721	−0.0969864
$746$	4.53936	0.166198
$747$	−7.26661	−0.265871
$748$	90.3775	3.30453
$749$	−22.0591	−0.806021
$750$	−1.58451	−0.0578580
$751$	32.3855	1.18176	0.590881	−	0.806759i	$-0.298780\pi$
$751$	32.3855	1.18176	0.590881	+	0.806759i	$0.298780\pi$
$752$	33.2249	1.21159
$753$	23.0668	0.840599
$754$	0.914451	0.0333024
$755$	−24.6726	−0.897926
$756$	−24.1207	−0.877260
$757$	17.5830	0.639066	0.319533	−	0.947575i	$-0.396474\pi$
$757$	17.5830	0.639066	0.319533	+	0.947575i	$0.396474\pi$
$758$	1.69611	0.0616054
$759$	26.0722	0.946361
$760$	−3.83080	−0.138958
$761$	0.761719	0.0276123	0.0138061	−	0.999905i	$-0.495605\pi$
$761$	0.761719	0.0276123	0.0138061	+	0.999905i	$0.495605\pi$
$762$	0.178688	0.00647317
$763$	−41.2373	−1.49289
$764$	−29.2449	−1.05804
$765$	18.1449	0.656031
$766$	1.44451	0.0521924
$767$	8.04295	0.290414
$768$	−16.4039	−0.591926
$769$	−49.7564	−1.79426	−0.897132	−	0.441763i	$-0.854353\pi$
$769$	−49.7564	−1.79426	−0.897132	+	0.441763i	$0.854353\pi$
$770$	−2.21649	−0.0798767
$771$	12.7898	0.460613
$772$	−41.7327	−1.50199
$773$	−28.1190	−1.01137	−0.505685	−	0.862718i	$-0.668760\pi$
$773$	−28.1190	−1.01137	−0.505685	+	0.862718i	$0.668760\pi$
$774$	−1.84061	−0.0661593
$775$	6.36608	0.228676
$776$	0.0782255	0.00280813
$777$	−18.7483	−0.672590
$778$	−2.53218	−0.0907831
$779$	−25.3018	−0.906532
$780$	−2.63531	−0.0943592
$781$	−1.49274	−0.0534143
$782$	−4.28976	−0.153401
$783$	40.5980	1.45085
$784$	−6.86886	−0.245316
$785$	−23.9178	−0.853664
$786$	−0.809243	−0.0288648
$787$	−13.8763	−0.494636	−0.247318	−	0.968934i	$-0.579549\pi$
$787$	−13.8763	−0.494636	−0.247318	+	0.968934i	$0.579549\pi$
$788$	−17.1866	−0.612249
$789$	−4.79170	−0.170589
$790$	0.550501	0.0195860
$791$	8.22068	0.292294
$792$	−5.18455	−0.184225
$793$	−5.08505	−0.180575
$794$	3.55591	0.126195
$795$	0.0728269	0.00258290
$796$	−9.39722	−0.333076
$797$	10.1859	0.360804	0.180402	−	0.983593i	$-0.442260\pi$
$797$	10.1859	0.360804	0.180402	+	0.983593i	$0.442260\pi$
$798$	−1.89895	−0.0672220
$799$	−68.2613	−2.41491
$800$	5.15121	0.182123
$801$	19.7269	0.697017
$802$	0.0333676	0.00117825
$803$	68.6671	2.42321
$804$	−23.7331	−0.837002
$805$	−12.1503	−0.428243
$806$	−0.229996	−0.00810126
$807$	0.322215	0.0113425
$808$	−8.21121	−0.288869
$809$	45.8873	1.61331	0.806656	−	0.591021i	$-0.201275\pi$
$809$	45.8873	1.61331	0.806656	+	0.591021i	$0.201275\pi$
$810$	0.122257	0.00429566
$811$	39.2045	1.37666	0.688328	−	0.725400i	$-0.258345\pi$
$811$	39.2045	1.37666	0.688328	+	0.725400i	$0.258345\pi$
$812$	−34.6588	−1.21628
$813$	19.8574	0.696430
$814$	−5.45485	−0.191192
$815$	−11.2553	−0.394256
$816$	34.9558	1.22370
$817$	45.5031	1.59195
$818$	−1.51185	−0.0528605
$819$	3.64956	0.127526
$820$	−11.5232	−0.402408
$821$	−23.5362	−0.821419	−0.410709	−	0.911766i	$-0.634719\pi$
$821$	−23.5362	−0.821419	−0.410709	+	0.911766i	$0.634719\pi$
$822$	−2.02868	−0.0707582
$823$	−12.8739	−0.448756	−0.224378	−	0.974502i	$-0.572035\pi$
$823$	−12.8739	−0.448756	−0.224378	+	0.974502i	$0.572035\pi$
$824$	−5.79156	−0.201759
$825$	21.1317	0.735711
$826$	2.63948	0.0918393
$827$	34.6062	1.20338	0.601688	−	0.798731i	$-0.294495\pi$
$827$	34.6062	1.20338	0.601688	+	0.798731i	$0.294495\pi$
$828$	−14.1490	−0.491713
$829$	45.2922	1.57306	0.786532	−	0.617549i	$-0.211874\pi$
$829$	45.2922	1.57306	0.786532	+	0.617549i	$0.211874\pi$
$830$	−0.708409	−0.0245892
$831$	9.58985	0.332668
$832$	6.93619	0.240469
$833$	14.1122	0.488960
$834$	−0.664459	−0.0230083
$835$	28.8372	0.997952
$836$	63.8093	2.20689
$837$	−10.2109	−0.352941
$838$	−3.62539	−0.125237
$839$	23.0845	0.796965	0.398482	−	0.917176i	$-0.369537\pi$
$839$	23.0845	0.796965	0.398482	+	0.917176i	$0.369537\pi$
$840$	−1.73716	−0.0599378
$841$	29.3349	1.01155
$842$	1.39264	0.0479937
$843$	32.2111	1.10941
$844$	−31.5310	−1.08534
$845$	−15.7960	−0.543399
$846$	1.94948	0.0670245
$847$	48.9851	1.68315
$848$	−0.195135	−0.00670098
$849$	−28.4440	−0.976195
$850$	−3.47688	−0.119256
$851$	−29.9023	−1.02504
$852$	−0.582442	−0.0199541
$853$	20.4560	0.700401	0.350201	−	0.936675i	$-0.386113\pi$
$853$	20.4560	0.700401	0.350201	+	0.936675i	$0.386113\pi$
$854$	−1.66878	−0.0571044
$855$	12.8109	0.438123
$856$	−5.03019	−0.171928
$857$	0.341338	0.0116599	0.00582994	−	0.999983i	$-0.498144\pi$
$857$	0.341338	0.0116599	0.00582994	+	0.999983i	$0.498144\pi$
$858$	−0.763453	−0.0260639
$859$	37.9445	1.29465	0.647326	−	0.762214i	$-0.275887\pi$
$859$	37.9445	1.29465	0.647326	+	0.762214i	$0.275887\pi$
$860$	20.7235	0.706665
$861$	−11.4737	−0.391022
$862$	3.08482	0.105069
$863$	40.6572	1.38399	0.691993	−	0.721904i	$-0.256733\pi$
$863$	40.6572	1.38399	0.691993	+	0.721904i	$0.256733\pi$
$864$	−8.26231	−0.281089
$865$	−4.99480	−0.169828
$866$	−3.18559	−0.108251
$867$	−52.7746	−1.79232
$868$	8.71712	0.295878
$869$	−18.4187	−0.624811
$870$	1.45563	0.0493503
$871$	9.76366	0.330829
$872$	−9.40346	−0.318441
$873$	−0.261600	−0.00885381
$874$	−3.02870	−0.102447
$875$	−24.7061	−0.835219
$876$	26.7928	0.905244
$877$	36.1016	1.21907	0.609533	−	0.792761i	$-0.291357\pi$
$877$	36.1016	1.21907	0.609533	+	0.792761i	$0.291357\pi$
$878$	0.162745	0.00549238
$879$	6.42831	0.216821
$880$	28.8069	0.971080
$881$	5.06452	0.170628	0.0853141	−	0.996354i	$-0.472811\pi$
$881$	5.06452	0.170628	0.0853141	+	0.996354i	$0.472811\pi$
$882$	−0.403032	−0.0135708
$883$	−2.04011	−0.0686551	−0.0343276	−	0.999411i	$-0.510929\pi$
$883$	−2.04011	−0.0686551	−0.0343276	+	0.999411i	$0.510929\pi$
$884$	−14.5073	−0.487934
$885$	12.8028	0.430361
$886$	3.46029	0.116251
$887$	12.0732	0.405380	0.202690	−	0.979243i	$-0.435032\pi$
$887$	12.0732	0.405380	0.202690	+	0.979243i	$0.435032\pi$
$888$	−4.27522	−0.143467
$889$	2.78615	0.0934445
$890$	1.92314	0.0644639
$891$	−4.09046	−0.137036
$892$	17.9047	0.599495
$893$	−48.1946	−1.61277
$894$	−0.299233	−0.0100078
$895$	6.10515	0.204073
$896$	9.39093	0.313729
$897$	−4.18509	−0.139736
$898$	−4.75640	−0.158723
$899$	−14.6720	−0.489337
$900$	−11.4679	−0.382263
$901$	0.400910	0.0133563
$902$	−3.33829	−0.111153
$903$	20.6344	0.686669
$904$	1.87458	0.0623477
$905$	−7.40222	−0.246058
$906$	−2.78891	−0.0926552
$907$	22.0338	0.731621	0.365810	−	0.930689i	$-0.380792\pi$
$907$	22.0338	0.731621	0.365810	+	0.930689i	$0.380792\pi$
$908$	−41.7408	−1.38522
$909$	27.4597	0.910782
$910$	0.355789	0.0117943
$911$	36.5880	1.21221	0.606106	−	0.795384i	$-0.292731\pi$
$911$	36.5880	1.21221	0.606106	+	0.795384i	$0.292731\pi$
$912$	24.6799	0.817233
$913$	23.7019	0.784420
$914$	−3.95830	−0.130929
$915$	−8.09440	−0.267592
$916$	18.7741	0.620312
$917$	−12.6180	−0.416682
$918$	5.57676	0.184060
$919$	−30.6652	−1.01155	−0.505776	−	0.862665i	$-0.668794\pi$
$919$	−30.6652	−1.01155	−0.505776	+	0.862665i	$0.668794\pi$
$920$	−2.77067	−0.0913463
$921$	15.7188	0.517953
$922$	−2.17971	−0.0717849
$923$	0.239613	0.00788696
$924$	28.9358	0.951916
$925$	−24.2360	−0.796876
$926$	−3.45567	−0.113560
$927$	19.3680	0.636129
$928$	−11.8720	−0.389718
$929$	−21.1696	−0.694551	−0.347276	−	0.937763i	$-0.612893\pi$
$929$	−21.1696	−0.694551	−0.347276	+	0.937763i	$0.612893\pi$
$930$	−0.366108	−0.0120052
$931$	9.96367	0.326546
$932$	−26.5730	−0.870429
$933$	−0.546294	−0.0178849
$934$	−2.58086	−0.0844482
$935$	−59.1844	−1.93554
$936$	0.832219	0.0272019
$937$	−38.8374	−1.26876	−0.634381	−	0.773020i	$-0.718745\pi$
$937$	−38.8374	−1.26876	−0.634381	+	0.773020i	$0.718745\pi$
$938$	3.20417	0.104620
$939$	8.00890	0.261360
$940$	−21.9493	−0.715906
$941$	13.4221	0.437548	0.218774	−	0.975776i	$-0.429794\pi$
$941$	13.4221	0.437548	0.218774	+	0.975776i	$0.429794\pi$
$942$	−2.70359	−0.0880879
$943$	−18.2998	−0.595924
$944$	−34.3043	−1.11651
$945$	15.7956	0.513831
$946$	6.00363	0.195195
$947$	59.8867	1.94606	0.973028	−	0.230688i	$-0.0740975\pi$
$947$	59.8867	1.94606	0.973028	+	0.230688i	$0.0740975\pi$
$948$	−7.18667	−0.233412
$949$	−11.0224	−0.357802
$950$	−2.45478	−0.0796437
$951$	10.2728	0.333119
$952$	−9.56305	−0.309940
$953$	−36.4019	−1.17917	−0.589587	−	0.807705i	$-0.700710\pi$
$953$	−36.4019	−1.17917	−0.589587	+	0.807705i	$0.700710\pi$
$954$	−0.0114496	−0.000370696 0
$955$	19.1513	0.619721
$956$	9.20843	0.297822
$957$	−48.7024	−1.57432
$958$	2.23160	0.0720997
$959$	−31.6317	−1.02144
$960$	11.0411	0.356348
$961$	−27.3098	−0.880962
$962$	0.875608	0.0282307
$963$	16.8218	0.542076
$964$	0.0350111	0.00112763
$965$	27.3290	0.879752
$966$	−1.37343	−0.0441895
$967$	−5.36420	−0.172501	−0.0862505	−	0.996273i	$-0.527489\pi$
$967$	−5.36420	−0.172501	−0.0862505	+	0.996273i	$0.527489\pi$
$968$	11.1702	0.359024
$969$	−50.7054	−1.62889
$970$	−0.0255029	−0.000818848 0
$971$	−4.64544	−0.149079	−0.0745397	−	0.997218i	$-0.523749\pi$
$971$	−4.64544	−0.149079	−0.0745397	+	0.997218i	$0.523749\pi$
$972$	30.0229	0.962986
$973$	−10.3605	−0.332141
$974$	−3.36071	−0.107684
$975$	−3.39204	−0.108632
$976$	21.6885	0.694231
$977$	−6.62437	−0.211932	−0.105966	−	0.994370i	$-0.533794\pi$
$977$	−6.62437	−0.211932	−0.105966	+	0.994370i	$0.533794\pi$
$978$	−1.27226	−0.0406825
$979$	−64.3446	−2.05646
$980$	4.53776	0.144953
$981$	31.4468	1.00402
$982$	3.32631	0.106147
$983$	26.1818	0.835069	0.417534	−	0.908661i	$-0.362894\pi$
$983$	26.1818	0.835069	0.417534	+	0.908661i	$0.362894\pi$
$984$	−2.61637	−0.0834069
$985$	11.2548	0.358608
$986$	8.01319	0.255192
$987$	−21.8549	−0.695650
$988$	−10.2426	−0.325861
$989$	32.9106	1.04650
$990$	1.69025	0.0537198
$991$	32.0501	1.01810	0.509052	−	0.860736i	$-0.329996\pi$
$991$	32.0501	1.01810	0.509052	+	0.860736i	$0.329996\pi$
$992$	2.98596	0.0948045
$993$	2.36494	0.0750491
$994$	0.0786346	0.00249414
$995$	6.15385	0.195090
$996$	9.24811	0.293038
$997$	−34.2230	−1.08385	−0.541927	−	0.840426i	$-0.682305\pi$
$997$	−34.2230	−1.08385	−0.541927	+	0.840426i	$0.682305\pi$
$998$	3.84482	0.121706
$999$	38.8735	1.22990

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.a.1.51	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.a.1.51	✓	100	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:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q-0.131029 q^{2} -1.12017 q^{3} -1.98283 q^{4} +1.29847 q^{5} +0.146775 q^{6} +2.28856 q^{7} +0.521867 q^{8} -1.74522 q^{9} +O(q^{10})\)	\(q-0.131029 q^{2} -1.12017 q^{3} -1.98283 q^{4} +1.29847 q^{5} +0.146775 q^{6} +2.28856 q^{7} +0.521867 q^{8} -1.74522 q^{9} -0.170138 q^{10} +5.69248 q^{11} +2.22111 q^{12} -0.913752 q^{13} -0.299869 q^{14} -1.45451 q^{15} +3.89728 q^{16} -8.00706 q^{17} +0.228674 q^{18} -5.65323 q^{19} -2.57465 q^{20} -2.56358 q^{21} -0.745881 q^{22} -4.08876 q^{23} -0.584581 q^{24} -3.31397 q^{25} +0.119728 q^{26} +5.31546 q^{27} -4.53784 q^{28} +7.63773 q^{29} +0.190584 q^{30} -1.92098 q^{31} -1.55439 q^{32} -6.37655 q^{33} +1.04916 q^{34} +2.97164 q^{35} +3.46047 q^{36} +7.31330 q^{37} +0.740739 q^{38} +1.02356 q^{39} +0.677631 q^{40} +4.47564 q^{41} +0.335905 q^{42} -8.04904 q^{43} -11.2872 q^{44} -2.26612 q^{45} +0.535747 q^{46} +8.52514 q^{47} -4.36562 q^{48} -1.76247 q^{49} +0.434227 q^{50} +8.96928 q^{51} +1.81182 q^{52} -0.0500696 q^{53} -0.696480 q^{54} +7.39153 q^{55} +1.19433 q^{56} +6.33259 q^{57} -1.00077 q^{58} -8.80212 q^{59} +2.88405 q^{60} +5.56502 q^{61} +0.251705 q^{62} -3.99404 q^{63} -7.59089 q^{64} -1.18648 q^{65} +0.835515 q^{66} -10.6852 q^{67} +15.8766 q^{68} +4.58011 q^{69} -0.389372 q^{70} -0.262230 q^{71} -0.910771 q^{72} +12.0628 q^{73} -0.958256 q^{74} +3.71221 q^{75} +11.2094 q^{76} +13.0276 q^{77} -0.134116 q^{78} -3.23562 q^{79} +5.06052 q^{80} -0.718573 q^{81} -0.586439 q^{82} +4.16373 q^{83} +5.08316 q^{84} -10.3969 q^{85} +1.05466 q^{86} -8.55557 q^{87} +2.97072 q^{88} -11.3034 q^{89} +0.296927 q^{90} -2.09118 q^{91} +8.10732 q^{92} +2.15183 q^{93} -1.11704 q^{94} -7.34057 q^{95} +1.74119 q^{96} +0.149895 q^{97} +0.230935 q^{98} -9.93460 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * q^99

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