LMFDB - Embedded newform 2671.2.a.a.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.69051 q^{2} -1.24665 q^{3} +5.23884 q^{4} +2.30924 q^{5} +3.35414 q^{6} -0.0663222 q^{7} -8.71414 q^{8} -1.44585 q^{9} +O(q^{10})$	\(q-2.69051 q^{2} -1.24665 q^{3} +5.23884 q^{4} +2.30924 q^{5} +3.35414 q^{6} -0.0663222 q^{7} -8.71414 q^{8} -1.44585 q^{9} -6.21303 q^{10} -5.57135 q^{11} -6.53103 q^{12} +1.28347 q^{13} +0.178441 q^{14} -2.87883 q^{15} +12.9678 q^{16} -4.04968 q^{17} +3.89008 q^{18} +2.99315 q^{19} +12.0977 q^{20} +0.0826809 q^{21} +14.9898 q^{22} +1.40291 q^{23} +10.8635 q^{24} +0.332590 q^{25} -3.45318 q^{26} +5.54244 q^{27} -0.347452 q^{28} +3.07090 q^{29} +7.74551 q^{30} +8.57649 q^{31} -17.4617 q^{32} +6.94556 q^{33} +10.8957 q^{34} -0.153154 q^{35} -7.57459 q^{36} +10.4625 q^{37} -8.05309 q^{38} -1.60004 q^{39} -20.1230 q^{40} -7.73239 q^{41} -0.222454 q^{42} -6.31963 q^{43} -29.1874 q^{44} -3.33882 q^{45} -3.77453 q^{46} +12.2417 q^{47} -16.1664 q^{48} -6.99560 q^{49} -0.894838 q^{50} +5.04855 q^{51} +6.72388 q^{52} +4.49093 q^{53} -14.9120 q^{54} -12.8656 q^{55} +0.577941 q^{56} -3.73142 q^{57} -8.26230 q^{58} -10.6246 q^{59} -15.0817 q^{60} -7.23912 q^{61} -23.0751 q^{62} +0.0958921 q^{63} +21.0452 q^{64} +2.96383 q^{65} -18.6871 q^{66} +11.8770 q^{67} -21.2156 q^{68} -1.74894 q^{69} +0.412062 q^{70} +9.65523 q^{71} +12.5993 q^{72} +3.66981 q^{73} -28.1494 q^{74} -0.414625 q^{75} +15.6806 q^{76} +0.369505 q^{77} +4.30493 q^{78} -16.9206 q^{79} +29.9457 q^{80} -2.57196 q^{81} +20.8041 q^{82} -2.81842 q^{83} +0.433152 q^{84} -9.35168 q^{85} +17.0030 q^{86} -3.82836 q^{87} +48.5495 q^{88} +4.08266 q^{89} +8.98312 q^{90} -0.0851224 q^{91} +7.34961 q^{92} -10.6919 q^{93} -32.9363 q^{94} +6.91189 q^{95} +21.7687 q^{96} -15.5092 q^{97} +18.8217 q^{98} +8.05535 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.69051	−1.90248	−0.951239	−	0.308455i	$-0.900188\pi$
$2$	−2.69051	−1.90248	−0.951239	+	0.308455i	$0.900188\pi$
$3$	−1.24665	−0.719757	−0.359878	−	0.932999i	$-0.617182\pi$
$3$	−1.24665	−0.719757	−0.359878	+	0.932999i	$0.617182\pi$
$4$	5.23884	2.61942
$5$	2.30924	1.03272	0.516362	−	0.856371i	$-0.327286\pi$
$5$	2.30924	1.03272	0.516362	+	0.856371i	$0.327286\pi$
$6$	3.35414	1.36932
$7$	−0.0663222	−0.0250674	−0.0125337	−	0.999921i	$-0.503990\pi$
$7$	−0.0663222	−0.0250674	−0.0125337	+	0.999921i	$0.503990\pi$
$8$	−8.71414	−3.08091
$9$	−1.44585	−0.481950
$10$	−6.21303	−1.96473
$11$	−5.57135	−1.67983	−0.839913	−	0.542721i	$-0.817394\pi$
$11$	−5.57135	−1.67983	−0.839913	+	0.542721i	$0.817394\pi$
$12$	−6.53103	−1.88535
$13$	1.28347	0.355970	0.177985	−	0.984033i	$-0.443042\pi$
$13$	1.28347	0.355970	0.177985	+	0.984033i	$0.443042\pi$
$14$	0.178441	0.0476902
$15$	−2.87883	−0.743310
$16$	12.9678	3.24195
$17$	−4.04968	−0.982192	−0.491096	−	0.871106i	$-0.663404\pi$
$17$	−4.04968	−0.982192	−0.491096	+	0.871106i	$0.663404\pi$
$18$	3.89008	0.916900
$19$	2.99315	0.686675	0.343337	−	0.939212i	$-0.388443\pi$
$19$	2.99315	0.686675	0.343337	+	0.939212i	$0.388443\pi$
$20$	12.0977	2.70514
$21$	0.0826809	0.0180425
$22$	14.9898	3.19583
$23$	1.40291	0.292526	0.146263	−	0.989246i	$-0.453275\pi$
$23$	1.40291	0.292526	0.146263	+	0.989246i	$0.453275\pi$
$24$	10.8635	2.21751
$25$	0.332590	0.0665181
$26$	−3.45318	−0.677225
$27$	5.54244	1.06664
$28$	−0.347452	−0.0656622
$29$	3.07090	0.570253	0.285126	−	0.958490i	$-0.407964\pi$
$29$	3.07090	0.570253	0.285126	+	0.958490i	$0.407964\pi$
$30$	7.74551	1.41413
$31$	8.57649	1.54038	0.770191	−	0.637813i	$-0.220161\pi$
$31$	8.57649	1.54038	0.770191	+	0.637813i	$0.220161\pi$
$32$	−17.4617	−3.08682
$33$	6.94556	1.20907
$34$	10.8957	1.86860
$35$	−0.153154	−0.0258877
$36$	−7.57459	−1.26243
$37$	10.4625	1.72002	0.860009	−	0.510279i	$-0.170458\pi$
$37$	10.4625	1.72002	0.860009	+	0.510279i	$0.170458\pi$
$38$	−8.05309	−1.30638
$39$	−1.60004	−0.256212
$40$	−20.1230	−3.18173
$41$	−7.73239	−1.20760	−0.603798	−	0.797137i	$-0.706347\pi$
$41$	−7.73239	−1.20760	−0.603798	+	0.797137i	$0.706347\pi$
$42$	−0.222454	−0.0343254
$43$	−6.31963	−0.963734	−0.481867	−	0.876244i	$-0.660041\pi$
$43$	−6.31963	−0.963734	−0.481867	+	0.876244i	$0.660041\pi$
$44$	−29.1874	−4.40017
$45$	−3.33882	−0.497722
$46$	−3.77453	−0.556525
$47$	12.2417	1.78563	0.892815	−	0.450423i	$-0.148727\pi$
$47$	12.2417	1.78563	0.892815	+	0.450423i	$0.148727\pi$
$48$	−16.1664	−2.33341
$49$	−6.99560	−0.999372
$50$	−0.894838	−0.126549
$51$	5.04855	0.706939
$52$	6.72388	0.932435
$53$	4.49093	0.616876	0.308438	−	0.951244i	$-0.400194\pi$
$53$	4.49093	0.616876	0.308438	+	0.951244i	$0.400194\pi$
$54$	−14.9120	−2.02927
$55$	−12.8656	−1.73480
$56$	0.577941	0.0772306
$57$	−3.73142	−0.494239
$58$	−8.26230	−1.08489
$59$	−10.6246	−1.38321	−0.691603	−	0.722278i	$-0.743095\pi$
$59$	−10.6246	−1.38321	−0.691603	+	0.722278i	$0.743095\pi$
$60$	−15.0817	−1.94704
$61$	−7.23912	−0.926875	−0.463437	−	0.886130i	$-0.653384\pi$
$61$	−7.23912	−0.926875	−0.463437	+	0.886130i	$0.653384\pi$
$62$	−23.0751	−2.93054
$63$	0.0958921	0.0120813
$64$	21.0452	2.63066
$65$	2.96383	0.367618
$66$	−18.6871	−2.30022
$67$	11.8770	1.45101	0.725506	−	0.688216i	$-0.241606\pi$
$67$	11.8770	1.45101	0.725506	+	0.688216i	$0.241606\pi$
$68$	−21.2156	−2.57277
$69$	−1.74894	−0.210548
$70$	0.412062	0.0492508
$71$	9.65523	1.14587	0.572933	−	0.819602i	$-0.305806\pi$
$71$	9.65523	1.14587	0.572933	+	0.819602i	$0.305806\pi$
$72$	12.5993	1.48485
$73$	3.66981	0.429519	0.214759	−	0.976667i	$-0.431103\pi$
$73$	3.66981	0.429519	0.214759	+	0.976667i	$0.431103\pi$
$74$	−28.1494	−3.27230
$75$	−0.414625	−0.0478768
$76$	15.6806	1.79869
$77$	0.369505	0.0421089
$78$	4.30493	0.487437
$79$	−16.9206	−1.90371	−0.951855	−	0.306548i	$-0.900826\pi$
$79$	−16.9206	−1.90371	−0.951855	+	0.306548i	$0.900826\pi$
$80$	29.9457	3.34803
$81$	−2.57196	−0.285773
$82$	20.8041	2.29742
$83$	−2.81842	−0.309362	−0.154681	−	0.987965i	$-0.549435\pi$
$83$	−2.81842	−0.309362	−0.154681	+	0.987965i	$0.549435\pi$
$84$	0.433152	0.0472608
$85$	−9.35168	−1.01433
$86$	17.0030	1.83348
$87$	−3.82836	−0.410443
$88$	48.5495	5.17540
$89$	4.08266	0.432761	0.216381	−	0.976309i	$-0.430575\pi$
$89$	4.08266	0.432761	0.216381	+	0.976309i	$0.430575\pi$
$90$	8.98312	0.946904
$91$	−0.0851224	−0.00892325
$92$	7.34961	0.766250
$93$	−10.6919	−1.10870
$94$	−32.9363	−3.39712
$95$	6.91189	0.709145
$96$	21.7687	2.22176
$97$	−15.5092	−1.57472	−0.787358	−	0.616495i	$-0.788552\pi$
$97$	−15.5092	−1.57472	−0.787358	+	0.616495i	$0.788552\pi$
$98$	18.8217	1.90128
$99$	8.05535	0.809593
$100$	1.74239	0.174239
$101$	−16.4224	−1.63409	−0.817043	−	0.576576i	$-0.804388\pi$
$101$	−16.4224	−1.63409	−0.817043	+	0.576576i	$0.804388\pi$
$102$	−13.5832	−1.34494
$103$	2.31223	0.227831	0.113916	−	0.993490i	$-0.463661\pi$
$103$	2.31223	0.227831	0.113916	+	0.993490i	$0.463661\pi$
$104$	−11.1843	−1.09671
$105$	0.190930	0.0186329
$106$	−12.0829	−1.17359
$107$	−11.8315	−1.14379	−0.571896	−	0.820326i	$-0.693792\pi$
$107$	−11.8315	−1.14379	−0.571896	+	0.820326i	$0.693792\pi$
$108$	29.0360	2.79399
$109$	10.0056	0.958364	0.479182	−	0.877716i	$-0.340933\pi$
$109$	10.0056	0.958364	0.479182	+	0.877716i	$0.340933\pi$
$110$	34.6150	3.30041
$111$	−13.0431	−1.23799
$112$	−0.860052	−0.0812673
$113$	−5.22681	−0.491697	−0.245849	−	0.969308i	$-0.579067\pi$
$113$	−5.22681	−0.491697	−0.245849	+	0.969308i	$0.579067\pi$
$114$	10.0394	0.940278
$115$	3.23965	0.302099
$116$	16.0880	1.49373
$117$	−1.85570	−0.171560
$118$	28.5856	2.63152
$119$	0.268584	0.0246210
$120$	25.0865	2.29007
$121$	20.0400	1.82182
$122$	19.4769	1.76336
$123$	9.63962	0.869175
$124$	44.9309	4.03491
$125$	−10.7782	−0.964029
$126$	−0.257999	−0.0229843
$127$	7.10188	0.630190	0.315095	−	0.949060i	$-0.397964\pi$
$127$	7.10188	0.630190	0.315095	+	0.949060i	$0.397964\pi$
$128$	−21.6991	−1.91795
$129$	7.87839	0.693654
$130$	−7.97423	−0.699386
$131$	−4.60239	−0.402113	−0.201057	−	0.979580i	$-0.564437\pi$
$131$	−4.60239	−0.402113	−0.201057	+	0.979580i	$0.564437\pi$
$132$	36.3867	3.16705
$133$	−0.198512	−0.0172132
$134$	−31.9553	−2.76052
$135$	12.7988	1.10155
$136$	35.2895	3.02605
$137$	−16.4235	−1.40316	−0.701578	−	0.712592i	$-0.747521\pi$
$137$	−16.4235	−1.40316	−0.701578	+	0.712592i	$0.747521\pi$
$138$	4.70554	0.400562
$139$	9.49116	0.805030	0.402515	−	0.915413i	$-0.368136\pi$
$139$	9.49116	0.805030	0.402515	+	0.915413i	$0.368136\pi$
$140$	−0.802349	−0.0678109
$141$	−15.2611	−1.28522
$142$	−25.9775	−2.17998
$143$	−7.15065	−0.597967
$144$	−18.7495	−1.56246
$145$	7.09146	0.588913
$146$	−9.87365	−0.817149
$147$	8.72110	0.719304
$148$	54.8112	4.50545
$149$	10.6570	0.873056	0.436528	−	0.899691i	$-0.356208\pi$
$149$	10.6570	0.873056	0.436528	+	0.899691i	$0.356208\pi$
$150$	1.11555	0.0910846
$151$	−6.76603	−0.550611	−0.275306	−	0.961357i	$-0.588779\pi$
$151$	−6.76603	−0.550611	−0.275306	+	0.961357i	$0.588779\pi$
$152$	−26.0827	−2.11558
$153$	5.85523	0.473368
$154$	−0.994156	−0.0801113
$155$	19.8052	1.59079
$156$	−8.38236	−0.671126
$157$	−15.1565	−1.20962	−0.604808	−	0.796371i	$-0.706750\pi$
$157$	−15.1565	−1.20962	−0.604808	+	0.796371i	$0.706750\pi$
$158$	45.5249	3.62177
$159$	−5.59864	−0.444001
$160$	−40.3232	−3.18783
$161$	−0.0930439	−0.00733289
$162$	6.91988	0.543677
$163$	−6.33423	−0.496135	−0.248068	−	0.968743i	$-0.579796\pi$
$163$	−6.33423	−0.496135	−0.248068	+	0.968743i	$0.579796\pi$
$164$	−40.5088	−3.16320
$165$	16.0390	1.24863
$166$	7.58298	0.588553
$167$	16.3044	1.26167	0.630836	−	0.775916i	$-0.282712\pi$
$167$	16.3044	1.26167	0.630836	+	0.775916i	$0.282712\pi$
$168$	−0.720493	−0.0555872
$169$	−11.3527	−0.873285
$170$	25.1608	1.92974
$171$	−4.32764	−0.330943
$172$	−33.1075	−2.52443
$173$	−8.71055	−0.662251	−0.331125	−	0.943587i	$-0.607428\pi$
$173$	−8.71055	−0.662251	−0.331125	+	0.943587i	$0.607428\pi$
$174$	10.3002	0.780859
$175$	−0.0220581	−0.00166744
$176$	−72.2481	−5.44591
$177$	13.2452	0.995571
$178$	−10.9844	−0.823319
$179$	−11.3387	−0.847492	−0.423746	−	0.905781i	$-0.639285\pi$
$179$	−11.3387	−0.847492	−0.423746	+	0.905781i	$0.639285\pi$
$180$	−17.4915	−1.30374
$181$	−18.8202	−1.39889	−0.699447	−	0.714685i	$-0.746570\pi$
$181$	−18.8202	−1.39889	−0.699447	+	0.714685i	$0.746570\pi$
$182$	0.229023	0.0169763
$183$	9.02469	0.667124
$184$	−12.2251	−0.901248
$185$	24.1603	1.77630
$186$	28.7667	2.10928
$187$	22.5622	1.64991
$188$	64.1322	4.67732
$189$	−0.367587	−0.0267380
$190$	−18.5965	−1.34913
$191$	15.0464	1.08872	0.544361	−	0.838851i	$-0.316772\pi$
$191$	15.0464	1.08872	0.544361	+	0.838851i	$0.316772\pi$
$192$	−26.2362	−1.89343
$193$	8.48106	0.610480	0.305240	−	0.952276i	$-0.401263\pi$
$193$	8.48106	0.610480	0.305240	+	0.952276i	$0.401263\pi$
$194$	41.7276	2.99586
$195$	−3.69488	−0.264596
$196$	−36.6489	−2.61778
$197$	2.34029	0.166739	0.0833695	−	0.996519i	$-0.473432\pi$
$197$	2.34029	0.166739	0.0833695	+	0.996519i	$0.473432\pi$
$198$	−21.6730	−1.54023
$199$	−21.3444	−1.51307	−0.756534	−	0.653955i	$-0.773109\pi$
$199$	−21.3444	−1.51307	−0.756534	+	0.653955i	$0.773109\pi$
$200$	−2.89824	−0.204936
$201$	−14.8066	−1.04438
$202$	44.1845	3.10881
$203$	−0.203669	−0.0142948
$204$	26.4486	1.85177
$205$	−17.8559	−1.24711
$206$	−6.22109	−0.433444
$207$	−2.02839	−0.140983
$208$	16.6437	1.15404
$209$	−16.6759	−1.15349
$210$	−0.513699	−0.0354486
$211$	−25.9771	−1.78834	−0.894170	−	0.447728i	$-0.852233\pi$
$211$	−25.9771	−1.78834	−0.894170	+	0.447728i	$0.852233\pi$
$212$	23.5273	1.61586
$213$	−12.0367	−0.824744
$214$	31.8327	2.17604
$215$	−14.5935	−0.995271
$216$	−48.2976	−3.28624
$217$	−0.568812	−0.0386134
$218$	−26.9202	−1.82327
$219$	−4.57498	−0.309149
$220$	−67.4008	−4.54416
$221$	−5.19763	−0.349631
$222$	35.0925	2.35526
$223$	−13.7040	−0.917688	−0.458844	−	0.888517i	$-0.651736\pi$
$223$	−13.7040	−0.917688	−0.458844	+	0.888517i	$0.651736\pi$
$224$	1.15810	0.0773786
$225$	−0.480876	−0.0320584
$226$	14.0628	0.935443
$227$	−26.4796	−1.75751	−0.878756	−	0.477271i	$-0.841626\pi$
$227$	−26.4796	−1.75751	−0.878756	+	0.477271i	$0.841626\pi$
$228$	−19.5483	−1.29462
$229$	−4.18429	−0.276506	−0.138253	−	0.990397i	$-0.544149\pi$
$229$	−4.18429	−0.276506	−0.138253	+	0.990397i	$0.544149\pi$
$230$	−8.71631	−0.574736
$231$	−0.460645	−0.0303082
$232$	−26.7603	−1.75690
$233$	−9.76751	−0.639891	−0.319945	−	0.947436i	$-0.603665\pi$
$233$	−9.76751	−0.639891	−0.319945	+	0.947436i	$0.603665\pi$
$234$	4.99279	0.326389
$235$	28.2690	1.84406
$236$	−55.6606	−3.62320
$237$	21.0941	1.37021
$238$	−0.722627	−0.0468410
$239$	−8.53196	−0.551886	−0.275943	−	0.961174i	$-0.588990\pi$
$239$	−8.53196	−0.551886	−0.275943	+	0.961174i	$0.588990\pi$
$240$	−37.3320	−2.40977
$241$	−12.2200	−0.787158	−0.393579	−	0.919291i	$-0.628763\pi$
$241$	−12.2200	−0.787158	−0.393579	+	0.919291i	$0.628763\pi$
$242$	−53.9178	−3.46597
$243$	−13.4210	−0.860956
$244$	−37.9246	−2.42787
$245$	−16.1545	−1.03207
$246$	−25.9355	−1.65359
$247$	3.84160	0.244435
$248$	−74.7367	−4.74578
$249$	3.51359	0.222665
$250$	28.9988	1.83404
$251$	22.0973	1.39477	0.697385	−	0.716696i	$-0.254347\pi$
$251$	22.0973	1.39477	0.697385	+	0.716696i	$0.254347\pi$
$252$	0.502363	0.0316459
$253$	−7.81609	−0.491393
$254$	−19.1077	−1.19892
$255$	11.6583	0.730072
$256$	16.2911	1.01819
$257$	22.5509	1.40668	0.703342	−	0.710852i	$-0.251690\pi$
$257$	22.5509	1.40668	0.703342	+	0.710852i	$0.251690\pi$
$258$	−21.1969	−1.31966
$259$	−0.693894	−0.0431165
$260$	15.5271	0.962948
$261$	−4.44007	−0.274834
$262$	12.3828	0.765011
$263$	9.34783	0.576412	0.288206	−	0.957568i	$-0.406941\pi$
$263$	9.34783	0.576412	0.288206	+	0.957568i	$0.406941\pi$
$264$	−60.5245	−3.72503
$265$	10.3706	0.637063
$266$	0.534099	0.0327477
$267$	−5.08967	−0.311483
$268$	62.2220	3.80081
$269$	−24.2654	−1.47949	−0.739744	−	0.672888i	$-0.765053\pi$
$269$	−24.2654	−1.47949	−0.739744	+	0.672888i	$0.765053\pi$
$270$	−34.4354	−2.09567
$271$	8.64479	0.525134	0.262567	−	0.964914i	$-0.415431\pi$
$271$	8.64479	0.525134	0.262567	+	0.964914i	$0.415431\pi$
$272$	−52.5154	−3.18421
$273$	0.106118	0.00642257
$274$	44.1877	2.66947
$275$	−1.85298	−0.111739
$276$	−9.16243	−0.551513
$277$	0.612340	0.0367919	0.0183960	−	0.999831i	$-0.494144\pi$
$277$	0.612340	0.0367919	0.0183960	+	0.999831i	$0.494144\pi$
$278$	−25.5361	−1.53155
$279$	−12.4003	−0.742388
$280$	1.33460	0.0797579
$281$	0.146286	0.00872672	0.00436336	−	0.999990i	$-0.498611\pi$
$281$	0.146286	0.00872672	0.00436336	+	0.999990i	$0.498611\pi$
$282$	41.0602	2.44510
$283$	24.6165	1.46330	0.731648	−	0.681682i	$-0.238751\pi$
$283$	24.6165	1.46330	0.731648	+	0.681682i	$0.238751\pi$
$284$	50.5823	3.00150
$285$	−8.61674	−0.510412
$286$	19.2389	1.13762
$287$	0.512829	0.0302713
$288$	25.2470	1.48769
$289$	−0.600095	−0.0352997
$290$	−19.0796	−1.12039
$291$	19.3346	1.13341
$292$	19.2255	1.12509
$293$	−30.5734	−1.78611	−0.893057	−	0.449943i	$-0.851444\pi$
$293$	−30.5734	−1.78611	−0.893057	+	0.449943i	$0.851444\pi$
$294$	−23.4642	−1.36846
$295$	−24.5348	−1.42847
$296$	−91.1713	−5.29923
$297$	−30.8789	−1.79178
$298$	−28.6728	−1.66097
$299$	1.80059	0.104131
$300$	−2.17216	−0.125410
$301$	0.419132	0.0241583
$302$	18.2041	1.04753
$303$	20.4730	1.17614
$304$	38.8145	2.22616
$305$	−16.7169	−0.957205
$306$	−15.7536	−0.900571
$307$	5.01261	0.286085	0.143042	−	0.989717i	$-0.454312\pi$
$307$	5.01261	0.286085	0.143042	+	0.989717i	$0.454312\pi$
$308$	1.93578	0.110301
$309$	−2.88256	−0.163983
$310$	−53.2860	−3.02644
$311$	11.3820	0.645415	0.322707	−	0.946499i	$-0.395407\pi$
$311$	11.3820	0.645415	0.322707	+	0.946499i	$0.395407\pi$
$312$	13.9430	0.789366
$313$	27.2274	1.53898	0.769490	−	0.638658i	$-0.220510\pi$
$313$	27.2274	1.53898	0.769490	+	0.638658i	$0.220510\pi$
$314$	40.7786	2.30127
$315$	0.221438	0.0124766
$316$	−88.6441	−4.98662
$317$	−5.03925	−0.283032	−0.141516	−	0.989936i	$-0.545198\pi$
$317$	−5.03925	−0.283032	−0.141516	+	0.989936i	$0.545198\pi$
$318$	15.0632	0.844701
$319$	−17.1091	−0.957925
$320$	48.5985	2.71674
$321$	14.7498	0.823251
$322$	0.250336	0.0139507
$323$	−12.1213	−0.674446
$324$	−13.4741	−0.748561
$325$	0.426869	0.0236784
$326$	17.0423	0.943886
$327$	−12.4735	−0.689789
$328$	67.3811	3.72050
$329$	−0.811895	−0.0447612
$330$	−43.1530	−2.37549
$331$	2.67987	0.147299	0.0736494	−	0.997284i	$-0.476535\pi$
$331$	2.67987	0.147299	0.0736494	+	0.997284i	$0.476535\pi$
$332$	−14.7652	−0.810348
$333$	−15.1272	−0.828963
$334$	−43.8672	−2.40030
$335$	27.4270	1.49849
$336$	1.07219	0.0584927
$337$	−22.4097	−1.22073	−0.610366	−	0.792119i	$-0.708978\pi$
$337$	−22.4097	−1.22073	−0.610366	+	0.792119i	$0.708978\pi$
$338$	30.5446	1.66141
$339$	6.51603	0.353902
$340$	−48.9920	−2.65696
$341$	−47.7826	−2.58757
$342$	11.6436	0.629612
$343$	0.928219	0.0501191
$344$	55.0701	2.96918
$345$	−4.03872	−0.217438
$346$	23.4358	1.25992
$347$	25.0487	1.34469	0.672343	−	0.740240i	$-0.265288\pi$
$347$	25.0487	1.34469	0.672343	+	0.740240i	$0.265288\pi$
$348$	−20.0562	−1.07512
$349$	16.3906	0.877368	0.438684	−	0.898642i	$-0.355445\pi$
$349$	16.3906	0.877368	0.438684	+	0.898642i	$0.355445\pi$
$350$	0.0593476	0.00317226
$351$	7.11354	0.379693
$352$	97.2852	5.18532
$353$	9.17918	0.488559	0.244279	−	0.969705i	$-0.421449\pi$
$353$	9.17918	0.488559	0.244279	+	0.969705i	$0.421449\pi$
$354$	−35.6364	−1.89405
$355$	22.2963	1.18336
$356$	21.3884	1.13358
$357$	−0.334831	−0.0177211
$358$	30.5068	1.61234
$359$	−6.13821	−0.323962	−0.161981	−	0.986794i	$-0.551788\pi$
$359$	−6.13821	−0.323962	−0.161981	+	0.986794i	$0.551788\pi$
$360$	29.0949	1.53344
$361$	−10.0411	−0.528478
$362$	50.6359	2.66136
$363$	−24.9829	−1.31126
$364$	−0.445943	−0.0233738
$365$	8.47447	0.443574
$366$	−24.2810	−1.26919
$367$	27.2309	1.42144	0.710720	−	0.703475i	$-0.248369\pi$
$367$	27.2309	1.42144	0.710720	+	0.703475i	$0.248369\pi$
$368$	18.1926	0.948355
$369$	11.1799	0.582002
$370$	−65.0036	−3.37938
$371$	−0.297848	−0.0154635
$372$	−56.0133	−2.90415
$373$	8.67742	0.449300	0.224650	−	0.974440i	$-0.427876\pi$
$373$	8.67742	0.449300	0.224650	+	0.974440i	$0.427876\pi$
$374$	−60.7038	−3.13892
$375$	13.4367	0.693866
$376$	−106.676	−5.50137
$377$	3.94141	0.202993
$378$	0.988997	0.0508685
$379$	14.2574	0.732353	0.366177	−	0.930545i	$-0.380667\pi$
$379$	14.2574	0.732353	0.366177	+	0.930545i	$0.380667\pi$
$380$	36.2103	1.85755
$381$	−8.85360	−0.453584
$382$	−40.4826	−2.07127
$383$	−25.3626	−1.29597	−0.647983	−	0.761655i	$-0.724387\pi$
$383$	−25.3626	−1.29597	−0.647983	+	0.761655i	$0.724387\pi$
$384$	27.0513	1.38045
$385$	0.853275	0.0434869
$386$	−22.8184	−1.16142
$387$	9.13724	0.464472
$388$	−81.2501	−4.12485
$389$	−12.2751	−0.622372	−0.311186	−	0.950349i	$-0.600726\pi$
$389$	−12.2751	−0.622372	−0.311186	+	0.950349i	$0.600726\pi$
$390$	9.94111	0.503388
$391$	−5.68132	−0.287317
$392$	60.9606	3.07898
$393$	5.73760	0.289424
$394$	−6.29658	−0.317217
$395$	−39.0736	−1.96601
$396$	42.2007	2.12067
$397$	22.4815	1.12831	0.564157	−	0.825668i	$-0.309201\pi$
$397$	22.4815	1.12831	0.564157	+	0.825668i	$0.309201\pi$
$398$	57.4274	2.87858
$399$	0.247476	0.0123893
$400$	4.31296	0.215648
$401$	−14.5471	−0.726448	−0.363224	−	0.931702i	$-0.618324\pi$
$401$	−14.5471	−0.726448	−0.363224	+	0.931702i	$0.618324\pi$
$402$	39.8372	1.98690
$403$	11.0076	0.548330
$404$	−86.0342	−4.28036
$405$	−5.93927	−0.295125
$406$	0.547974	0.0271955
$407$	−58.2901	−2.88933
$408$	−43.9938	−2.17802
$409$	−11.7188	−0.579455	−0.289728	−	0.957109i	$-0.593565\pi$
$409$	−11.7188	−0.579455	−0.289728	+	0.957109i	$0.593565\pi$
$410$	48.0416	2.37260
$411$	20.4745	1.00993
$412$	12.1134	0.596786
$413$	0.704647	0.0346734
$414$	5.45742	0.268217
$415$	−6.50840	−0.319485
$416$	−22.4115	−1.09881
$417$	−11.8322	−0.579425
$418$	44.8666	2.19450
$419$	−5.35047	−0.261388	−0.130694	−	0.991423i	$-0.541721\pi$
$419$	−5.35047	−0.261388	−0.130694	+	0.991423i	$0.541721\pi$
$420$	1.00025	0.0488073
$421$	0.0647199	0.00315425	0.00157713	−	0.999999i	$-0.499498\pi$
$421$	0.0647199	0.00315425	0.00157713	+	0.999999i	$0.499498\pi$
$422$	69.8917	3.40228
$423$	−17.6996	−0.860586
$424$	−39.1346	−1.90054
$425$	−1.34688	−0.0653335
$426$	32.3850	1.56906
$427$	0.480115	0.0232344
$428$	−61.9832	−2.99607
$429$	8.91439	0.430391
$430$	39.2640	1.89348
$431$	−4.21605	−0.203080	−0.101540	−	0.994831i	$-0.532377\pi$
$431$	−4.21605	−0.203080	−0.101540	+	0.994831i	$0.532377\pi$
$432$	71.8732	3.45800
$433$	24.5376	1.17920	0.589600	−	0.807696i	$-0.299285\pi$
$433$	24.5376	1.17920	0.589600	+	0.807696i	$0.299285\pi$
$434$	1.53039	0.0734612
$435$	−8.84060	−0.423874
$436$	52.4178	2.51036
$437$	4.19910	0.200870
$438$	12.3090	0.588149
$439$	5.02625	0.239890	0.119945	−	0.992781i	$-0.461728\pi$
$439$	5.02625	0.239890	0.119945	+	0.992781i	$0.461728\pi$
$440$	112.113	5.34476
$441$	10.1146	0.481648
$442$	13.9843	0.665164
$443$	−22.8655	−1.08637	−0.543186	−	0.839612i	$-0.682782\pi$
$443$	−22.8655	−1.08637	−0.543186	+	0.839612i	$0.682782\pi$
$444$	−68.3306	−3.24283
$445$	9.42785	0.446923
$446$	36.8708	1.74588
$447$	−13.2856	−0.628388
$448$	−1.39577	−0.0659438
$449$	−35.6910	−1.68436	−0.842182	−	0.539194i	$-0.818729\pi$
$449$	−35.6910	−1.68436	−0.842182	+	0.539194i	$0.818729\pi$
$450$	1.29380	0.0609904
$451$	43.0799	2.02855
$452$	−27.3825	−1.28796
$453$	8.43490	0.396306
$454$	71.2436	3.34363
$455$	−0.196568	−0.00921525
$456$	32.5161	1.52271
$457$	−39.1476	−1.83125	−0.915624	−	0.402037i	$-0.868302\pi$
$457$	−39.1476	−1.83125	−0.915624	+	0.402037i	$0.868302\pi$
$458$	11.2579	0.526046
$459$	−22.4451	−1.04765
$460$	16.9720	0.791324
$461$	−31.7987	−1.48101	−0.740507	−	0.672049i	$-0.765414\pi$
$461$	−31.7987	−1.48101	−0.740507	+	0.672049i	$0.765414\pi$
$462$	1.23937	0.0576607
$463$	27.2500	1.26641	0.633207	−	0.773982i	$-0.281738\pi$
$463$	27.2500	1.26641	0.633207	+	0.773982i	$0.281738\pi$
$464$	39.8228	1.84873
$465$	−24.6902	−1.14498
$466$	26.2796	1.21738
$467$	−22.4323	−1.03804	−0.519021	−	0.854762i	$-0.673703\pi$
$467$	−22.4323	−1.03804	−0.519021	+	0.854762i	$0.673703\pi$
$468$	−9.72174	−0.449387
$469$	−0.787712	−0.0363732
$470$	−76.0579	−3.50829
$471$	18.8949	0.870630
$472$	92.5842	4.26153
$473$	35.2089	1.61891
$474$	−56.7538	−2.60679
$475$	0.995491	0.0456763
$476$	1.40707	0.0644928
$477$	−6.49321	−0.297304
$478$	22.9553	1.04995
$479$	17.8549	0.815811	0.407906	−	0.913024i	$-0.366259\pi$
$479$	17.8549	0.815811	0.407906	+	0.913024i	$0.366259\pi$
$480$	50.2691	2.29446
$481$	13.4282	0.612275
$482$	32.8780	1.49755
$483$	0.115994	0.00527789
$484$	104.986	4.77210
$485$	−35.8144	−1.62625
$486$	36.1093	1.63795
$487$	−16.4244	−0.744260	−0.372130	−	0.928181i	$-0.621372\pi$
$487$	−16.4244	−0.744260	−0.372130	+	0.928181i	$0.621372\pi$
$488$	63.0827	2.85562
$489$	7.89660	0.357097
$490$	43.4639	1.96350
$491$	−21.9769	−0.991804	−0.495902	−	0.868379i	$-0.665162\pi$
$491$	−21.9769	−0.991804	−0.495902	+	0.868379i	$0.665162\pi$
$492$	50.5005	2.27674
$493$	−12.4362	−0.560097
$494$	−10.3359	−0.465033
$495$	18.6017	0.836086
$496$	111.218	4.99384
$497$	−0.640357	−0.0287239
$498$	−9.45336	−0.423615
$499$	2.34398	0.104931	0.0524655	−	0.998623i	$-0.483292\pi$
$499$	2.34398	0.104931	0.0524655	+	0.998623i	$0.483292\pi$
$500$	−56.4651	−2.52520
$501$	−20.3260	−0.908097
$502$	−59.4531	−2.65352
$503$	−1.52092	−0.0678145	−0.0339072	−	0.999425i	$-0.510795\pi$
$503$	−1.52092	−0.0678145	−0.0339072	+	0.999425i	$0.510795\pi$
$504$	−0.835617	−0.0372213
$505$	−37.9232	−1.68756
$506$	21.0293	0.934865
$507$	14.1529	0.628553
$508$	37.2057	1.65073
$509$	1.75363	0.0777284	0.0388642	−	0.999245i	$-0.487626\pi$
$509$	1.75363	0.0777284	0.0388642	+	0.999245i	$0.487626\pi$
$510$	−31.3668	−1.38895
$511$	−0.243390	−0.0107669
$512$	−0.433171	−0.0191436
$513$	16.5893	0.732437
$514$	−60.6733	−2.67618
$515$	5.33951	0.235287
$516$	41.2737	1.81697
$517$	−68.2027	−2.99955
$518$	1.86693	0.0820281
$519$	10.8590	0.476659
$520$	−25.8273	−1.13260
$521$	24.9660	1.09378	0.546890	−	0.837205i	$-0.315812\pi$
$521$	24.9660	1.09378	0.546890	+	0.837205i	$0.315812\pi$
$522$	11.9461	0.522865
$523$	16.5074	0.721820	0.360910	−	0.932601i	$-0.382466\pi$
$523$	16.5074	0.721820	0.360910	+	0.932601i	$0.382466\pi$
$524$	−24.1112	−1.05330
$525$	0.0274989	0.00120015
$526$	−25.1504	−1.09661
$527$	−34.7320	−1.51295
$528$	90.0685	3.91973
$529$	−21.0319	−0.914428
$530$	−27.9023	−1.21200
$531$	15.3616	0.666636
$532$	−1.03997	−0.0450886
$533$	−9.92427	−0.429868
$534$	13.6938	0.592589
$535$	−27.3217	−1.18122
$536$	−103.498	−4.47044
$537$	14.1354	0.609988
$538$	65.2863	2.81469
$539$	38.9750	1.67877
$540$	67.0511	2.88542
$541$	−4.33014	−0.186167	−0.0930836	−	0.995658i	$-0.529672\pi$
$541$	−4.33014	−0.186167	−0.0930836	+	0.995658i	$0.529672\pi$
$542$	−23.2589	−0.999055
$543$	23.4623	1.00686
$544$	70.7142	3.03185
$545$	23.1054	0.989725
$546$	−0.285512	−0.0122188
$547$	−4.12676	−0.176448	−0.0882238	−	0.996101i	$-0.528119\pi$
$547$	−4.12676	−0.176448	−0.0882238	+	0.996101i	$0.528119\pi$
$548$	−86.0403	−3.67546
$549$	10.4667	0.446708
$550$	4.98546	0.212581
$551$	9.19166	0.391578
$552$	15.2405	0.648679
$553$	1.12221	0.0477212
$554$	−1.64751	−0.0699958
$555$	−30.1196	−1.27851
$556$	49.7227	2.10871
$557$	20.7943	0.881083	0.440542	−	0.897732i	$-0.354786\pi$
$557$	20.7943	0.881083	0.440542	+	0.897732i	$0.354786\pi$
$558$	33.3632	1.41238
$559$	−8.11103	−0.343060
$560$	−1.98607	−0.0839267
$561$	−28.1273	−1.18753
$562$	−0.393585	−0.0166024
$563$	5.54832	0.233834	0.116917	−	0.993142i	$-0.462699\pi$
$563$	5.54832	0.233834	0.116917	+	0.993142i	$0.462699\pi$
$564$	−79.9507	−3.36653
$565$	−12.0700	−0.507787
$566$	−66.2308	−2.78389
$567$	0.170578	0.00716361
$568$	−84.1370	−3.53031
$569$	−18.4069	−0.771659	−0.385829	−	0.922570i	$-0.626085\pi$
$569$	−18.4069	−0.771659	−0.385829	+	0.922570i	$0.626085\pi$
$570$	23.1834	0.971047
$571$	14.1792	0.593380	0.296690	−	0.954974i	$-0.404117\pi$
$571$	14.1792	0.593380	0.296690	+	0.954974i	$0.404117\pi$
$572$	−37.4611	−1.56633
$573$	−18.7577	−0.783615
$574$	−1.37977	−0.0575906
$575$	0.466593	0.0194583
$576$	−30.4283	−1.26785
$577$	−40.5835	−1.68951	−0.844756	−	0.535152i	$-0.820254\pi$
$577$	−40.5835	−1.68951	−0.844756	+	0.535152i	$0.820254\pi$
$578$	1.61456	0.0671569
$579$	−10.5729	−0.439397
$580$	37.1510	1.54261
$581$	0.186924	0.00775490
$582$	−52.0199	−2.15629
$583$	−25.0205	−1.03624
$584$	−31.9792	−1.32331
$585$	−4.28526	−0.177174
$586$	82.2579	3.39804
$587$	−11.6163	−0.479457	−0.239728	−	0.970840i	$-0.577058\pi$
$587$	−11.6163	−0.479457	−0.239728	+	0.970840i	$0.577058\pi$
$588$	45.6885	1.88416
$589$	25.6707	1.05774
$590$	66.0110	2.71763
$591$	−2.91754	−0.120012
$592$	135.675	5.57621
$593$	−6.40003	−0.262818	−0.131409	−	0.991328i	$-0.541950\pi$
$593$	−6.40003	−0.262818	−0.131409	+	0.991328i	$0.541950\pi$
$594$	83.0800	3.40881
$595$	0.620224	0.0254267
$596$	55.8304	2.28690
$597$	26.6091	1.08904
$598$	−4.84449	−0.198106
$599$	40.3846	1.65007	0.825035	−	0.565081i	$-0.191155\pi$
$599$	40.3846	1.65007	0.825035	+	0.565081i	$0.191155\pi$
$600$	3.61310	0.147504
$601$	28.9563	1.18115	0.590576	−	0.806982i	$-0.298900\pi$
$601$	28.9563	1.18115	0.590576	+	0.806982i	$0.298900\pi$
$602$	−1.12768	−0.0459607
$603$	−17.1724	−0.699316
$604$	−35.4461	−1.44228
$605$	46.2771	1.88143
$606$	−55.0829	−2.23759
$607$	−39.3176	−1.59585	−0.797927	−	0.602754i	$-0.794070\pi$
$607$	−39.3176	−1.59585	−0.797927	+	0.602754i	$0.794070\pi$
$608$	−52.2653	−2.11964
$609$	0.253905	0.0102888
$610$	44.9769	1.82106
$611$	15.7118	0.635631
$612$	30.6747	1.23995
$613$	−26.6907	−1.07803	−0.539014	−	0.842297i	$-0.681203\pi$
$613$	−26.6907	−1.07803	−0.539014	+	0.842297i	$0.681203\pi$
$614$	−13.4865	−0.544269
$615$	22.2602	0.897618
$616$	−3.21991	−0.129734
$617$	−31.6579	−1.27450	−0.637250	−	0.770657i	$-0.719928\pi$
$617$	−31.6579	−1.27450	−0.637250	+	0.770657i	$0.719928\pi$
$618$	7.75555	0.311974
$619$	17.2945	0.695123	0.347561	−	0.937657i	$-0.387010\pi$
$619$	17.2945	0.695123	0.347561	+	0.937657i	$0.387010\pi$
$620$	103.756	4.16695
$621$	7.77553	0.312021
$622$	−30.6234	−1.22789
$623$	−0.270771	−0.0108482
$624$	−20.7490	−0.830624
$625$	−26.5523	−1.06209
$626$	−73.2555	−2.92788
$627$	20.7891	0.830235
$628$	−79.4023	−3.16850
$629$	−42.3696	−1.68939
$630$	−0.595781	−0.0237365
$631$	−36.4277	−1.45016	−0.725082	−	0.688663i	$-0.758198\pi$
$631$	−36.4277	−1.45016	−0.725082	+	0.688663i	$0.758198\pi$
$632$	147.448	5.86517
$633$	32.3845	1.28717
$634$	13.5581	0.538463
$635$	16.4000	0.650812
$636$	−29.3304	−1.16302
$637$	−8.97863	−0.355746
$638$	46.0322	1.82243
$639$	−13.9600	−0.552250
$640$	−50.1084	−1.98071
$641$	−21.3914	−0.844909	−0.422454	−	0.906384i	$-0.638831\pi$
$641$	−21.3914	−0.844909	−0.422454	+	0.906384i	$0.638831\pi$
$642$	−39.6844	−1.56622
$643$	19.6220	0.773818	0.386909	−	0.922118i	$-0.373543\pi$
$643$	19.6220	0.773818	0.386909	+	0.922118i	$0.373543\pi$
$644$	−0.487442	−0.0192079
$645$	18.1931	0.716353
$646$	32.6124	1.28312
$647$	24.2369	0.952851	0.476425	−	0.879215i	$-0.341932\pi$
$647$	24.2369	0.952851	0.476425	+	0.879215i	$0.341932\pi$
$648$	22.4124	0.880443
$649$	59.1934	2.32354
$650$	−1.14849	−0.0450477
$651$	0.709112	0.0277923
$652$	−33.1840	−1.29959
$653$	10.8056	0.422855	0.211427	−	0.977394i	$-0.432189\pi$
$653$	10.8056	0.422855	0.211427	+	0.977394i	$0.432189\pi$
$654$	33.5602	1.31231
$655$	−10.6280	−0.415272
$656$	−100.272	−3.91496
$657$	−5.30600	−0.207007
$658$	2.18441	0.0851572
$659$	−11.9401	−0.465119	−0.232560	−	0.972582i	$-0.574710\pi$
$659$	−11.9401	−0.465119	−0.232560	+	0.972582i	$0.574710\pi$
$660$	84.0256	3.27069
$661$	8.89140	0.345835	0.172918	−	0.984936i	$-0.444681\pi$
$661$	8.89140	0.345835	0.172918	+	0.984936i	$0.444681\pi$
$662$	−7.21021	−0.280233
$663$	6.47965	0.251649
$664$	24.5601	0.953116
$665$	−0.458412	−0.0177765
$666$	40.6998	1.57708
$667$	4.30819	0.166814
$668$	85.4162	3.30485
$669$	17.0842	0.660512
$670$	−73.7925	−2.85085
$671$	40.3317	1.55699
$672$	−1.44375	−0.0556938
$673$	34.9804	1.34840	0.674198	−	0.738550i	$-0.264489\pi$
$673$	34.9804	1.34840	0.674198	+	0.738550i	$0.264489\pi$
$674$	60.2934	2.32242
$675$	1.84336	0.0709511
$676$	−59.4751	−2.28750
$677$	5.43092	0.208727	0.104364	−	0.994539i	$-0.466719\pi$
$677$	5.43092	0.208727	0.104364	+	0.994539i	$0.466719\pi$
$678$	−17.5315	−0.673291
$679$	1.02860	0.0394741
$680$	81.4918	3.12507
$681$	33.0109	1.26498
$682$	128.560	4.92280
$683$	−5.70041	−0.218120	−0.109060	−	0.994035i	$-0.534784\pi$
$683$	−5.70041	−0.218120	−0.109060	+	0.994035i	$0.534784\pi$
$684$	−22.6718	−0.866879
$685$	−37.9259	−1.44907
$686$	−2.49738	−0.0953505
$687$	5.21637	0.199017
$688$	−81.9516	−3.12437
$689$	5.76396	0.219589
$690$	10.8662	0.413670
$691$	−15.0683	−0.573225	−0.286613	−	0.958047i	$-0.592529\pi$
$691$	−15.0683	−0.573225	−0.286613	+	0.958047i	$0.592529\pi$
$692$	−45.6332	−1.73471
$693$	−0.534249	−0.0202944
$694$	−67.3938	−2.55823
$695$	21.9174	0.831373
$696$	33.3608	1.26454
$697$	31.3137	1.18609
$698$	−44.0990	−1.66917
$699$	12.1767	0.460565
$700$	−0.115559	−0.00436772
$701$	29.7599	1.12402	0.562009	−	0.827131i	$-0.310029\pi$
$701$	29.7599	1.12402	0.562009	+	0.827131i	$0.310029\pi$
$702$	−19.1391	−0.722357
$703$	31.3157	1.18109
$704$	−117.250	−4.41904
$705$	−35.2416	−1.32728
$706$	−24.6967	−0.929472
$707$	1.08917	0.0409624
$708$	69.3896	2.60782
$709$	23.4738	0.881578	0.440789	−	0.897611i	$-0.354699\pi$
$709$	23.4738	0.881578	0.440789	+	0.897611i	$0.354699\pi$
$710$	−59.9883	−2.25132
$711$	24.4646	0.917494
$712$	−35.5769	−1.33330
$713$	12.0320	0.450602
$714$	0.900867	0.0337141
$715$	−16.5126	−0.617535
$716$	−59.4015	−2.21994
$717$	10.6364	0.397224
$718$	16.5149	0.616331
$719$	17.1540	0.639736	0.319868	−	0.947462i	$-0.396361\pi$
$719$	17.1540	0.639736	0.319868	+	0.947462i	$0.396361\pi$
$720$	−43.2971	−1.61359
$721$	−0.153353	−0.00571115
$722$	27.0156	1.00542
$723$	15.2341	0.566562
$724$	−98.5960	−3.66429
$725$	1.02135	0.0379321
$726$	67.2168	2.49465
$727$	−14.8196	−0.549630	−0.274815	−	0.961497i	$-0.588617\pi$
$727$	−14.8196	−0.549630	−0.274815	+	0.961497i	$0.588617\pi$
$728$	0.741768	0.0274918
$729$	24.4472	0.905452
$730$	−22.8006	−0.843890
$731$	25.5925	0.946571
$732$	47.2789	1.74748
$733$	7.16613	0.264687	0.132343	−	0.991204i	$-0.457750\pi$
$733$	7.16613	0.264687	0.132343	+	0.991204i	$0.457750\pi$
$734$	−73.2649	−2.70426
$735$	20.1391	0.742843
$736$	−24.4971	−0.902975
$737$	−66.1712	−2.43745
$738$	−30.0796	−1.10724
$739$	−44.5692	−1.63951	−0.819753	−	0.572717i	$-0.805889\pi$
$739$	−44.5692	−1.63951	−0.819753	+	0.572717i	$0.805889\pi$
$740$	126.572	4.65289
$741$	−4.78916	−0.175934
$742$	0.801364	0.0294190
$743$	−31.5578	−1.15774	−0.578872	−	0.815418i	$-0.696507\pi$
$743$	−31.5578	−1.15774	−0.578872	+	0.815418i	$0.696507\pi$
$744$	93.1709	3.41581
$745$	24.6096	0.901626
$746$	−23.3467	−0.854783
$747$	4.07501	0.149097
$748$	118.200	4.32181
$749$	0.784689	0.0286719
$750$	−36.1515	−1.32006
$751$	−36.0530	−1.31559	−0.657797	−	0.753195i	$-0.728512\pi$
$751$	−36.0530	−1.31559	−0.657797	+	0.753195i	$0.728512\pi$
$752$	158.747	5.78892
$753$	−27.5477	−1.00390
$754$	−10.6044	−0.386189
$755$	−15.6244	−0.568629
$756$	−1.92573	−0.0700382
$757$	−48.7057	−1.77024	−0.885119	−	0.465365i	$-0.845923\pi$
$757$	−48.7057	−1.77024	−0.885119	+	0.465365i	$0.845923\pi$
$758$	−38.3597	−1.39329
$759$	9.74397	0.353684
$760$	−60.2312	−2.18481
$761$	−12.0373	−0.436351	−0.218175	−	0.975910i	$-0.570010\pi$
$761$	−12.0373	−0.436351	−0.218175	+	0.975910i	$0.570010\pi$
$762$	23.8207	0.862933
$763$	−0.663594	−0.0240237
$764$	78.8259	2.85182
$765$	13.5211	0.488858
$766$	68.2382	2.46555
$767$	−13.6363	−0.492379
$768$	−20.3094	−0.732851
$769$	−21.9873	−0.792881	−0.396441	−	0.918060i	$-0.629755\pi$
$769$	−21.9873	−0.792881	−0.396441	+	0.918060i	$0.629755\pi$
$770$	−2.29574	−0.0827329
$771$	−28.1131	−1.01247
$772$	44.4309	1.59910
$773$	−33.2817	−1.19706	−0.598529	−	0.801101i	$-0.704248\pi$
$773$	−33.2817	−1.19706	−0.598529	+	0.801101i	$0.704248\pi$
$774$	−24.5838	−0.883648
$775$	2.85246	0.102463
$776$	135.149	4.85157
$777$	0.865046	0.0310334
$778$	33.0263	1.18405
$779$	−23.1442	−0.829226
$780$	−19.3569	−0.693088
$781$	−53.7927	−1.92486
$782$	15.2857	0.546614
$783$	17.0203	0.608256
$784$	−90.7175	−3.23991
$785$	−34.9999	−1.24920
$786$	−15.4371	−0.550622
$787$	−22.8040	−0.812876	−0.406438	−	0.913678i	$-0.633229\pi$
$787$	−22.8040	−0.812876	−0.406438	+	0.913678i	$0.633229\pi$
$788$	12.2604	0.436760
$789$	−11.6535	−0.414876
$790$	105.128	3.74028
$791$	0.346654	0.0123256
$792$	−70.1954	−2.49429
$793$	−9.29118	−0.329939
$794$	−60.4867	−2.14659
$795$	−12.9286	−0.458530
$796$	−111.820	−3.96336
$797$	40.7116	1.44208	0.721040	−	0.692894i	$-0.243665\pi$
$797$	40.7116	1.44208	0.721040	+	0.692894i	$0.243665\pi$
$798$	−0.665837	−0.0235704
$799$	−49.5748	−1.75383
$800$	−5.80759	−0.205329
$801$	−5.90292	−0.208570
$802$	39.1392	1.38205
$803$	−20.4458	−0.721517
$804$	−77.5693	−2.73566
$805$	−0.214861	−0.00757285
$806$	−29.6162	−1.04318
$807$	30.2506	1.06487
$808$	143.107	5.03448
$809$	52.9821	1.86275	0.931376	−	0.364060i	$-0.118610\pi$
$809$	52.9821	1.86275	0.931376	+	0.364060i	$0.118610\pi$
$810$	15.9797	0.561468
$811$	42.3366	1.48664	0.743319	−	0.668937i	$-0.233251\pi$
$811$	42.3366	1.48664	0.743319	+	0.668937i	$0.233251\pi$
$812$	−1.06699	−0.0374440
$813$	−10.7771	−0.377968
$814$	156.830	5.49689
$815$	−14.6273	−0.512370
$816$	65.4686	2.29186
$817$	−18.9156	−0.661772
$818$	31.5294	1.10240
$819$	0.123074	0.00430057
$820$	−93.5445	−3.26671
$821$	19.1905	0.669752	0.334876	−	0.942262i	$-0.391306\pi$
$821$	19.1905	0.669752	0.334876	+	0.942262i	$0.391306\pi$
$822$	−55.0868	−1.92137
$823$	21.5219	0.750205	0.375102	−	0.926983i	$-0.377608\pi$
$823$	21.5219	0.750205	0.375102	+	0.926983i	$0.377608\pi$
$824$	−20.1491	−0.701928
$825$	2.31002	0.0804247
$826$	−1.89586	−0.0659654
$827$	37.5722	1.30651	0.653257	−	0.757137i	$-0.273402\pi$
$827$	37.5722	1.30651	0.653257	+	0.757137i	$0.273402\pi$
$828$	−10.6264	−0.369294
$829$	−17.5865	−0.610806	−0.305403	−	0.952223i	$-0.598791\pi$
$829$	−17.5865	−0.610806	−0.305403	+	0.952223i	$0.598791\pi$
$830$	17.5109	0.607813
$831$	−0.763377	−0.0264812
$832$	27.0109	0.936434
$833$	28.3299	0.981574
$834$	31.8347	1.10234
$835$	37.6508	1.30296
$836$	−87.3623	−3.02149
$837$	47.5347	1.64304
$838$	14.3955	0.497284
$839$	−10.4066	−0.359276	−0.179638	−	0.983733i	$-0.557493\pi$
$839$	−10.4066	−0.359276	−0.179638	+	0.983733i	$0.557493\pi$
$840$	−1.66379	−0.0574062
$841$	−19.5695	−0.674812
$842$	−0.174129	−0.00600090
$843$	−0.182369	−0.00628111
$844$	−136.090	−4.68442
$845$	−26.2161	−0.901863
$846$	47.6210	1.63724
$847$	−1.32910	−0.0456683
$848$	58.2374	1.99988
$849$	−30.6882	−1.05322
$850$	3.62381	0.124296
$851$	14.6779	0.503151
$852$	−63.0586	−2.16035
$853$	−45.8358	−1.56939	−0.784694	−	0.619883i	$-0.787180\pi$
$853$	−45.8358	−1.56939	−0.784694	+	0.619883i	$0.787180\pi$
$854$	−1.29175	−0.0442029
$855$	−9.99357	−0.341773
$856$	103.101	3.52392
$857$	21.2252	0.725039	0.362519	−	0.931976i	$-0.381917\pi$
$857$	21.2252	0.725039	0.362519	+	0.931976i	$0.381917\pi$
$858$	−23.9843	−0.818809
$859$	−20.8462	−0.711264	−0.355632	−	0.934626i	$-0.615734\pi$
$859$	−20.8462	−0.711264	−0.355632	+	0.934626i	$0.615734\pi$
$860$	−76.4532	−2.60703
$861$	−0.639321	−0.0217880
$862$	11.3433	0.386356
$863$	−27.8608	−0.948394	−0.474197	−	0.880419i	$-0.657262\pi$
$863$	−27.8608	−0.948394	−0.474197	+	0.880419i	$0.657262\pi$
$864$	−96.7803	−3.29253
$865$	−20.1148	−0.683922
$866$	−66.0185	−2.24340
$867$	0.748111	0.0254072
$868$	−2.97991	−0.101145
$869$	94.2704	3.19790
$870$	23.7857	0.806411
$871$	15.2438	0.516517
$872$	−87.1903	−2.95264
$873$	22.4239	0.758936
$874$	−11.2977	−0.382151
$875$	0.714832	0.0241657
$876$	−23.9676	−0.809791
$877$	44.1428	1.49060	0.745298	−	0.666732i	$-0.232307\pi$
$877$	44.1428	1.49060	0.745298	+	0.666732i	$0.232307\pi$
$878$	−13.5232	−0.456385
$879$	38.1144	1.28557
$880$	−166.838	−5.62412
$881$	−7.15316	−0.240996	−0.120498	−	0.992714i	$-0.538449\pi$
$881$	−7.15316	−0.240996	−0.120498	+	0.992714i	$0.538449\pi$
$882$	−27.2134	−0.916324
$883$	25.9027	0.871694	0.435847	−	0.900021i	$-0.356449\pi$
$883$	25.9027	0.871694	0.435847	+	0.900021i	$0.356449\pi$
$884$	−27.2296	−0.915830
$885$	30.5864	1.02815
$886$	61.5199	2.06680
$887$	−19.3694	−0.650359	−0.325180	−	0.945652i	$-0.605425\pi$
$887$	−19.3694	−0.650359	−0.325180	+	0.945652i	$0.605425\pi$
$888$	113.659	3.81415
$889$	−0.471013	−0.0157973
$890$	−25.3657	−0.850261
$891$	14.3293	0.480050
$892$	−71.7931	−2.40381
$893$	36.6411	1.22615
$894$	35.7451	1.19549
$895$	−26.1837	−0.875225
$896$	1.43913	0.0480780
$897$	−2.24471	−0.0749486
$898$	96.0270	3.20446
$899$	26.3376	0.878407
$900$	−2.51923	−0.0839745
$901$	−18.1868	−0.605891
$902$	−115.907	−3.85927
$903$	−0.522513	−0.0173881
$904$	45.5472	1.51488
$905$	−43.4603	−1.44467
$906$	−22.6942	−0.753964
$907$	−50.1281	−1.66448	−0.832238	−	0.554419i	$-0.812941\pi$
$907$	−50.1281	−1.66448	−0.832238	+	0.554419i	$0.812941\pi$
$908$	−138.722	−4.60366
$909$	23.7443	0.787549
$910$	0.528868	0.0175318
$911$	32.5322	1.07784	0.538920	−	0.842357i	$-0.318832\pi$
$911$	32.5322	1.07784	0.538920	+	0.842357i	$0.318832\pi$
$912$	−48.3882	−1.60229
$913$	15.7024	0.519674
$914$	105.327	3.48391
$915$	20.8402	0.688955
$916$	−21.9208	−0.724285
$917$	0.305241	0.0100799
$918$	60.3888	1.99313
$919$	−6.65838	−0.219640	−0.109820	−	0.993952i	$-0.535027\pi$
$919$	−6.65838	−0.219640	−0.109820	+	0.993952i	$0.535027\pi$
$920$	−28.2307	−0.930740
$921$	−6.24899	−0.205911
$922$	85.5547	2.81760
$923$	12.3922	0.407894
$924$	−2.41324	−0.0793899
$925$	3.47971	0.114412
$926$	−73.3164	−2.40932
$927$	−3.34315	−0.109803
$928$	−53.6231	−1.76027
$929$	−23.2593	−0.763114	−0.381557	−	0.924345i	$-0.624612\pi$
$929$	−23.2593	−0.763114	−0.381557	+	0.924345i	$0.624612\pi$
$930$	66.4293	2.17830
$931$	−20.9389	−0.686243
$932$	−51.1704	−1.67614
$933$	−14.1894	−0.464542
$934$	60.3542	1.97485
$935$	52.1015	1.70390
$936$	16.1709	0.528561
$937$	54.5043	1.78058	0.890289	−	0.455397i	$-0.150503\pi$
$937$	54.5043	1.78058	0.890289	+	0.455397i	$0.150503\pi$
$938$	2.11935	0.0691991
$939$	−33.9431	−1.10769
$940$	148.097	4.83038
$941$	−24.6339	−0.803041	−0.401521	−	0.915850i	$-0.631518\pi$
$941$	−24.6339	−0.803041	−0.401521	+	0.915850i	$0.631518\pi$
$942$	−50.8368	−1.65635
$943$	−10.8478	−0.353254
$944$	−137.778	−4.48428
$945$	−0.848847	−0.0276130
$946$	−94.7298	−3.07993
$947$	47.8711	1.55560	0.777801	−	0.628511i	$-0.216335\pi$
$947$	47.8711	1.55560	0.777801	+	0.628511i	$0.216335\pi$
$948$	110.509	3.58915
$949$	4.71008	0.152896
$950$	−2.67838	−0.0868981
$951$	6.28220	0.203714
$952$	−2.34048	−0.0758552
$953$	−23.8993	−0.774175	−0.387088	−	0.922043i	$-0.626519\pi$
$953$	−23.8993	−0.774175	−0.387088	+	0.922043i	$0.626519\pi$
$954$	17.4701	0.565614
$955$	34.7458	1.12435
$956$	−44.6976	−1.44562
$957$	21.3291	0.689473
$958$	−48.0388	−1.55206
$959$	1.08924	0.0351736
$960$	−60.5856	−1.95539
$961$	42.5561	1.37278
$962$	−36.1288	−1.16484
$963$	17.1065	0.551251
$964$	−64.0185	−2.06190
$965$	19.5848	0.630457
$966$	−0.312082	−0.0100411
$967$	17.3477	0.557866	0.278933	−	0.960311i	$-0.410019\pi$
$967$	17.3477	0.557866	0.278933	+	0.960311i	$0.410019\pi$
$968$	−174.631	−5.61286
$969$	15.1111	0.485437
$970$	96.3589	3.09390
$971$	−36.1140	−1.15895	−0.579477	−	0.814989i	$-0.696743\pi$
$971$	−36.1140	−1.15895	−0.579477	+	0.814989i	$0.696743\pi$
$972$	−70.3104	−2.25521
$973$	−0.629475	−0.0201800
$974$	44.1899	1.41594
$975$	−0.532158	−0.0170427
$976$	−93.8754	−3.00488
$977$	36.6400	1.17222	0.586109	−	0.810232i	$-0.300659\pi$
$977$	36.6400	1.17222	0.586109	+	0.810232i	$0.300659\pi$
$978$	−21.2459	−0.679368
$979$	−22.7460	−0.726964
$980$	−84.6310	−2.70344
$981$	−14.4666	−0.461884
$982$	59.1291	1.88688
$983$	−29.3310	−0.935513	−0.467757	−	0.883857i	$-0.654938\pi$
$983$	−29.3310	−0.935513	−0.467757	+	0.883857i	$0.654938\pi$
$984$	−84.0010	−2.67785
$985$	5.40430	0.172195
$986$	33.4597	1.06557
$987$	1.01215	0.0322172
$988$	20.1256	0.640279
$989$	−8.86585	−0.281918
$990$	−50.0482	−1.59063
$991$	4.39683	0.139670	0.0698350	−	0.997559i	$-0.477753\pi$
$991$	4.39683	0.139670	0.0698350	+	0.997559i	$0.477753\pi$
$992$	−149.760	−4.75488
$993$	−3.34087	−0.106019
$994$	1.72289	0.0546466
$995$	−49.2894	−1.56258
$996$	18.4072	0.583253
$997$	35.2756	1.11719	0.558595	−	0.829440i	$-0.311341\pi$
$997$	35.2756	1.11719	0.558595	+	0.829440i	$0.311341\pi$
$998$	−6.30651	−0.199629
$999$	57.9876	1.83465

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.a.1.3	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.a.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.69051 q^{2} -1.24665 q^{3} +5.23884 q^{4} +2.30924 q^{5} +3.35414 q^{6} -0.0663222 q^{7} -8.71414 q^{8} -1.44585 q^{9} +O(q^{10})\)	\(q-2.69051 q^{2} -1.24665 q^{3} +5.23884 q^{4} +2.30924 q^{5} +3.35414 q^{6} -0.0663222 q^{7} -8.71414 q^{8} -1.44585 q^{9} -6.21303 q^{10} -5.57135 q^{11} -6.53103 q^{12} +1.28347 q^{13} +0.178441 q^{14} -2.87883 q^{15} +12.9678 q^{16} -4.04968 q^{17} +3.89008 q^{18} +2.99315 q^{19} +12.0977 q^{20} +0.0826809 q^{21} +14.9898 q^{22} +1.40291 q^{23} +10.8635 q^{24} +0.332590 q^{25} -3.45318 q^{26} +5.54244 q^{27} -0.347452 q^{28} +3.07090 q^{29} +7.74551 q^{30} +8.57649 q^{31} -17.4617 q^{32} +6.94556 q^{33} +10.8957 q^{34} -0.153154 q^{35} -7.57459 q^{36} +10.4625 q^{37} -8.05309 q^{38} -1.60004 q^{39} -20.1230 q^{40} -7.73239 q^{41} -0.222454 q^{42} -6.31963 q^{43} -29.1874 q^{44} -3.33882 q^{45} -3.77453 q^{46} +12.2417 q^{47} -16.1664 q^{48} -6.99560 q^{49} -0.894838 q^{50} +5.04855 q^{51} +6.72388 q^{52} +4.49093 q^{53} -14.9120 q^{54} -12.8656 q^{55} +0.577941 q^{56} -3.73142 q^{57} -8.26230 q^{58} -10.6246 q^{59} -15.0817 q^{60} -7.23912 q^{61} -23.0751 q^{62} +0.0958921 q^{63} +21.0452 q^{64} +2.96383 q^{65} -18.6871 q^{66} +11.8770 q^{67} -21.2156 q^{68} -1.74894 q^{69} +0.412062 q^{70} +9.65523 q^{71} +12.5993 q^{72} +3.66981 q^{73} -28.1494 q^{74} -0.414625 q^{75} +15.6806 q^{76} +0.369505 q^{77} +4.30493 q^{78} -16.9206 q^{79} +29.9457 q^{80} -2.57196 q^{81} +20.8041 q^{82} -2.81842 q^{83} +0.433152 q^{84} -9.35168 q^{85} +17.0030 q^{86} -3.82836 q^{87} +48.5495 q^{88} +4.08266 q^{89} +8.98312 q^{90} -0.0851224 q^{91} +7.34961 q^{92} -10.6919 q^{93} -32.9363 q^{94} +6.91189 q^{95} +21.7687 q^{96} -15.5092 q^{97} +18.8217 q^{98} +8.05535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) \) 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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