LMFDB - Embedded newform 2671.2.a.a.1.27

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			1.27
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)

$f(q)$	$=$	$q-1.65282 q^{2} -2.71518 q^{3} +0.731828 q^{4} +1.07828 q^{5} +4.48771 q^{6} +0.230773 q^{7} +2.09607 q^{8} +4.37219 q^{9} +O(q^{10})$	\(q-1.65282 q^{2} -2.71518 q^{3} +0.731828 q^{4} +1.07828 q^{5} +4.48771 q^{6} +0.230773 q^{7} +2.09607 q^{8} +4.37219 q^{9} -1.78220 q^{10} +3.46567 q^{11} -1.98704 q^{12} -3.89594 q^{13} -0.381428 q^{14} -2.92771 q^{15} -4.92808 q^{16} +2.48804 q^{17} -7.22646 q^{18} -3.19208 q^{19} +0.789113 q^{20} -0.626590 q^{21} -5.72815 q^{22} +6.87861 q^{23} -5.69119 q^{24} -3.83732 q^{25} +6.43930 q^{26} -3.72574 q^{27} +0.168886 q^{28} +1.83338 q^{29} +4.83899 q^{30} -10.9078 q^{31} +3.95313 q^{32} -9.40992 q^{33} -4.11230 q^{34} +0.248837 q^{35} +3.19969 q^{36} -1.00794 q^{37} +5.27594 q^{38} +10.5782 q^{39} +2.26014 q^{40} +1.72360 q^{41} +1.03564 q^{42} -5.98734 q^{43} +2.53628 q^{44} +4.71443 q^{45} -11.3691 q^{46} -2.43334 q^{47} +13.3806 q^{48} -6.94674 q^{49} +6.34242 q^{50} -6.75548 q^{51} -2.85116 q^{52} -2.67471 q^{53} +6.15800 q^{54} +3.73695 q^{55} +0.483716 q^{56} +8.66706 q^{57} -3.03025 q^{58} +0.351160 q^{59} -2.14258 q^{60} +4.74355 q^{61} +18.0286 q^{62} +1.00898 q^{63} +3.32234 q^{64} -4.20090 q^{65} +15.5529 q^{66} +14.8935 q^{67} +1.82082 q^{68} -18.6767 q^{69} -0.411284 q^{70} +13.3389 q^{71} +9.16440 q^{72} +3.95972 q^{73} +1.66594 q^{74} +10.4190 q^{75} -2.33605 q^{76} +0.799785 q^{77} -17.4838 q^{78} -5.63832 q^{79} -5.31384 q^{80} -3.00052 q^{81} -2.84880 q^{82} +4.27809 q^{83} -0.458556 q^{84} +2.68280 q^{85} +9.89602 q^{86} -4.97795 q^{87} +7.26428 q^{88} -6.18303 q^{89} -7.79212 q^{90} -0.899078 q^{91} +5.03396 q^{92} +29.6165 q^{93} +4.02188 q^{94} -3.44194 q^{95} -10.7334 q^{96} +9.98300 q^{97} +11.4817 q^{98} +15.1526 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.65282	−1.16872	−0.584362	−	0.811493i	$-0.698655\pi$
$2$	−1.65282	−1.16872	−0.584362	+	0.811493i	$0.698655\pi$
$3$	−2.71518	−1.56761	−0.783804	−	0.621008i	$-0.786723\pi$
$3$	−2.71518	−1.56761	−0.783804	+	0.621008i	$0.786723\pi$
$4$	0.731828	0.365914
$5$	1.07828	0.482220	0.241110	−	0.970498i	$-0.422489\pi$
$5$	1.07828	0.482220	0.241110	+	0.970498i	$0.422489\pi$
$6$	4.48771	1.83210
$7$	0.230773	0.0872241	0.0436120	−	0.999049i	$-0.486113\pi$
$7$	0.230773	0.0872241	0.0436120	+	0.999049i	$0.486113\pi$
$8$	2.09607	0.741071
$9$	4.37219	1.45740
$10$	−1.78220	−0.563581
$11$	3.46567	1.04494	0.522470	−	0.852658i	$-0.325011\pi$
$11$	3.46567	1.04494	0.522470	+	0.852658i	$0.325011\pi$
$12$	−1.98704	−0.573610
$13$	−3.89594	−1.08054	−0.540269	−	0.841492i	$-0.681678\pi$
$13$	−3.89594	−1.08054	−0.540269	+	0.841492i	$0.681678\pi$
$14$	−0.381428	−0.101941
$15$	−2.92771	−0.755932
$16$	−4.92808	−1.23202
$17$	2.48804	0.603439	0.301719	−	0.953397i	$-0.402439\pi$
$17$	2.48804	0.603439	0.301719	+	0.953397i	$0.402439\pi$
$18$	−7.22646	−1.70329
$19$	−3.19208	−0.732313	−0.366156	−	0.930553i	$-0.619326\pi$
$19$	−3.19208	−0.732313	−0.366156	+	0.930553i	$0.619326\pi$
$20$	0.789113	0.176451
$21$	−0.626590	−0.136733
$22$	−5.72815	−1.22125
$23$	6.87861	1.43429	0.717145	−	0.696924i	$-0.245449\pi$
$23$	6.87861	1.43429	0.717145	+	0.696924i	$0.245449\pi$
$24$	−5.69119	−1.16171
$25$	−3.83732	−0.767464
$26$	6.43930	1.26285
$27$	−3.72574	−0.717019
$28$	0.168886	0.0319165
$29$	1.83338	0.340450	0.170225	−	0.985405i	$-0.445551\pi$
$29$	1.83338	0.340450	0.170225	+	0.985405i	$0.445551\pi$
$30$	4.83899	0.883475
$31$	−10.9078	−1.95909	−0.979546	−	0.201219i	$-0.935510\pi$
$31$	−10.9078	−1.95909	−0.979546	+	0.201219i	$0.935510\pi$
$32$	3.95313	0.698821
$33$	−9.40992	−1.63806
$34$	−4.11230	−0.705253
$35$	0.248837	0.0420612
$36$	3.19969	0.533282
$37$	−1.00794	−0.165704	−0.0828518	−	0.996562i	$-0.526403\pi$
$37$	−1.00794	−0.165704	−0.0828518	+	0.996562i	$0.526403\pi$
$38$	5.27594	0.855871
$39$	10.5782	1.69386
$40$	2.26014	0.357359
$41$	1.72360	0.269181	0.134590	−	0.990901i	$-0.457028\pi$
$41$	1.72360	0.269181	0.134590	+	0.990901i	$0.457028\pi$
$42$	1.03564	0.159803
$43$	−5.98734	−0.913061	−0.456530	−	0.889708i	$-0.650908\pi$
$43$	−5.98734	−0.913061	−0.456530	+	0.889708i	$0.650908\pi$
$44$	2.53628	0.382358
$45$	4.71443	0.702786
$46$	−11.3691	−1.67629
$47$	−2.43334	−0.354939	−0.177469	−	0.984126i	$-0.556791\pi$
$47$	−2.43334	−0.354939	−0.177469	+	0.984126i	$0.556791\pi$
$48$	13.3806	1.93133
$49$	−6.94674	−0.992392
$50$	6.34242	0.896953
$51$	−6.75548	−0.945956
$52$	−2.85116	−0.395384
$53$	−2.67471	−0.367399	−0.183700	−	0.982982i	$-0.558807\pi$
$53$	−2.67471	−0.367399	−0.183700	+	0.982982i	$0.558807\pi$
$54$	6.15800	0.837997
$55$	3.73695	0.503891
$56$	0.483716	0.0646392
$57$	8.66706	1.14798
$58$	−3.03025	−0.397892
$59$	0.351160	0.0457171	0.0228586	−	0.999739i	$-0.492723\pi$
$59$	0.351160	0.0457171	0.0228586	+	0.999739i	$0.492723\pi$
$60$	−2.14258	−0.276606
$61$	4.74355	0.607349	0.303674	−	0.952776i	$-0.401786\pi$
$61$	4.74355	0.607349	0.303674	+	0.952776i	$0.401786\pi$
$62$	18.0286	2.28964
$63$	1.00898	0.127120
$64$	3.32234	0.415293
$65$	−4.20090	−0.521057
$66$	15.5529	1.91444
$67$	14.8935	1.81954	0.909768	−	0.415118i	$-0.136260\pi$
$67$	14.8935	1.81954	0.909768	+	0.415118i	$0.136260\pi$
$68$	1.82082	0.220807
$69$	−18.6767	−2.24841
$70$	−0.411284	−0.0491579
$71$	13.3389	1.58303	0.791517	−	0.611148i	$-0.209292\pi$
$71$	13.3389	1.58303	0.791517	+	0.611148i	$0.209292\pi$
$72$	9.16440	1.08003
$73$	3.95972	0.463450	0.231725	−	0.972781i	$-0.425563\pi$
$73$	3.95972	0.463450	0.231725	+	0.972781i	$0.425563\pi$
$74$	1.66594	0.193662
$75$	10.4190	1.20308
$76$	−2.33605	−0.267964
$77$	0.799785	0.0911439
$78$	−17.4838	−1.97966
$79$	−5.63832	−0.634360	−0.317180	−	0.948365i	$-0.602736\pi$
$79$	−5.63832	−0.634360	−0.317180	+	0.948365i	$0.602736\pi$
$80$	−5.31384	−0.594105
$81$	−3.00052	−0.333391
$82$	−2.84880	−0.314598
$83$	4.27809	0.469581	0.234791	−	0.972046i	$-0.424560\pi$
$83$	4.27809	0.469581	0.234791	+	0.972046i	$0.424560\pi$
$84$	−0.458556	−0.0500326
$85$	2.68280	0.290990
$86$	9.89602	1.06712
$87$	−4.97795	−0.533692
$88$	7.26428	0.774375
$89$	−6.18303	−0.655399	−0.327700	−	0.944782i	$-0.606273\pi$
$89$	−6.18303	−0.655399	−0.327700	+	0.944782i	$0.606273\pi$
$90$	−7.79212	−0.821362
$91$	−0.899078	−0.0942490
$92$	5.03396	0.524827
$93$	29.6165	3.07109
$94$	4.02188	0.414825
$95$	−3.44194	−0.353136
$96$	−10.7334	−1.09548
$97$	9.98300	1.01362	0.506810	−	0.862058i	$-0.330825\pi$
$97$	9.98300	1.01362	0.506810	+	0.862058i	$0.330825\pi$
$98$	11.4817	1.15983
$99$	15.1526	1.52289
$100$	−2.80826	−0.280826
$101$	10.0055	0.995580	0.497790	−	0.867298i	$-0.334145\pi$
$101$	10.0055	0.995580	0.497790	+	0.867298i	$0.334145\pi$
$102$	11.1656	1.10556
$103$	14.9716	1.47520	0.737600	−	0.675238i	$-0.235959\pi$
$103$	14.9716	1.47520	0.737600	+	0.675238i	$0.235959\pi$
$104$	−8.16614	−0.800756
$105$	−0.675637	−0.0659354
$106$	4.42082	0.429388
$107$	−11.8398	−1.14460	−0.572299	−	0.820045i	$-0.693948\pi$
$107$	−11.8398	−1.14460	−0.572299	+	0.820045i	$0.693948\pi$
$108$	−2.72660	−0.262367
$109$	1.77144	0.169674	0.0848368	−	0.996395i	$-0.472963\pi$
$109$	1.77144	0.169674	0.0848368	+	0.996395i	$0.472963\pi$
$110$	−6.17653	−0.588909
$111$	2.73672	0.259758
$112$	−1.13727	−0.107462
$113$	−16.7140	−1.57232	−0.786159	−	0.618025i	$-0.787933\pi$
$113$	−16.7140	−1.57232	−0.786159	+	0.618025i	$0.787933\pi$
$114$	−14.3251	−1.34167
$115$	7.41704	0.691643
$116$	1.34172	0.124575
$117$	−17.0338	−1.57477
$118$	−0.580405	−0.0534306
$119$	0.574173	0.0526344
$120$	−6.13667	−0.560199
$121$	1.01090	0.0918998
$122$	−7.84025	−0.709823
$123$	−4.67987	−0.421970
$124$	−7.98261	−0.716860
$125$	−9.52907	−0.852306
$126$	−1.66767	−0.148568
$127$	−2.98081	−0.264504	−0.132252	−	0.991216i	$-0.542221\pi$
$127$	−2.98081	−0.264504	−0.132252	+	0.991216i	$0.542221\pi$
$128$	−13.3975	−1.18418
$129$	16.2567	1.43132
$130$	6.94334	0.608971
$131$	−3.08658	−0.269675	−0.134838	−	0.990868i	$-0.543051\pi$
$131$	−3.08658	−0.269675	−0.134838	+	0.990868i	$0.543051\pi$
$132$	−6.88645	−0.599388
$133$	−0.736646	−0.0638753
$134$	−24.6164	−2.12653
$135$	−4.01738	−0.345761
$136$	5.21510	0.447191
$137$	−0.792611	−0.0677173	−0.0338587	−	0.999427i	$-0.510780\pi$
$137$	−0.792611	−0.0677173	−0.0338587	+	0.999427i	$0.510780\pi$
$138$	30.8692	2.62776
$139$	−1.15471	−0.0979410	−0.0489705	−	0.998800i	$-0.515594\pi$
$139$	−1.15471	−0.0979410	−0.0489705	+	0.998800i	$0.515594\pi$
$140$	0.182106	0.0153908
$141$	6.60694	0.556405
$142$	−22.0468	−1.85013
$143$	−13.5020	−1.12910
$144$	−21.5465	−1.79554
$145$	1.97689	0.164172
$146$	−6.54472	−0.541645
$147$	18.8616	1.55568
$148$	−0.737636	−0.0606333
$149$	−11.2582	−0.922308	−0.461154	−	0.887320i	$-0.652564\pi$
$149$	−11.2582	−0.922308	−0.461154	+	0.887320i	$0.652564\pi$
$150$	−17.2208	−1.40607
$151$	−11.5120	−0.936829	−0.468415	−	0.883509i	$-0.655175\pi$
$151$	−11.5120	−0.936829	−0.468415	+	0.883509i	$0.655175\pi$
$152$	−6.69080	−0.542696
$153$	10.8782	0.879450
$154$	−1.32190	−0.106522
$155$	−11.7616	−0.944713
$156$	7.74140	0.619808
$157$	−22.1262	−1.76586	−0.882932	−	0.469501i	$-0.844434\pi$
$157$	−22.1262	−1.76586	−0.882932	+	0.469501i	$0.844434\pi$
$158$	9.31915	0.741392
$159$	7.26231	0.575938
$160$	4.26256	0.336985
$161$	1.58740	0.125105
$162$	4.95934	0.389642
$163$	20.9306	1.63941	0.819704	−	0.572787i	$-0.194138\pi$
$163$	20.9306	1.63941	0.819704	+	0.572787i	$0.194138\pi$
$164$	1.26138	0.0984970
$165$	−10.1465	−0.789904
$166$	−7.07093	−0.548811
$167$	3.01980	0.233679	0.116840	−	0.993151i	$-0.462724\pi$
$167$	3.01980	0.233679	0.116840	+	0.993151i	$0.462724\pi$
$168$	−1.31337	−0.101329
$169$	2.17833	0.167564
$170$	−4.43419	−0.340087
$171$	−13.9564	−1.06727
$172$	−4.38170	−0.334102
$173$	−1.36027	−0.103420	−0.0517098	−	0.998662i	$-0.516467\pi$
$173$	−1.36027	−0.103420	−0.0517098	+	0.998662i	$0.516467\pi$
$174$	8.22768	0.623738
$175$	−0.885551	−0.0669413
$176$	−17.0791	−1.28739
$177$	−0.953461	−0.0716665
$178$	10.2195	0.765981
$179$	−0.727852	−0.0544022	−0.0272011	−	0.999630i	$-0.508659\pi$
$179$	−0.727852	−0.0544022	−0.0272011	+	0.999630i	$0.508659\pi$
$180$	3.45015	0.257159
$181$	−16.7815	−1.24736	−0.623679	−	0.781681i	$-0.714363\pi$
$181$	−16.7815	−1.24736	−0.623679	+	0.781681i	$0.714363\pi$
$182$	1.48602	0.110151
$183$	−12.8796	−0.952085
$184$	14.4180	1.06291
$185$	−1.08683	−0.0799056
$186$	−48.9509	−3.58926
$187$	8.62274	0.630558
$188$	−1.78078	−0.129877
$189$	−0.859801	−0.0625413
$190$	5.68892	0.412718
$191$	12.9753	0.938862	0.469431	−	0.882969i	$-0.344459\pi$
$191$	12.9753	0.938862	0.469431	+	0.882969i	$0.344459\pi$
$192$	−9.02076	−0.651017
$193$	−23.4759	−1.68983	−0.844917	−	0.534897i	$-0.820350\pi$
$193$	−23.4759	−1.68983	−0.844917	+	0.534897i	$0.820350\pi$
$194$	−16.5001	−1.18464
$195$	11.4062	0.816814
$196$	−5.08382	−0.363130
$197$	6.86925	0.489414	0.244707	−	0.969597i	$-0.421308\pi$
$197$	6.86925	0.489414	0.244707	+	0.969597i	$0.421308\pi$
$198$	−25.0446	−1.77984
$199$	−18.3386	−1.29999	−0.649996	−	0.759938i	$-0.725229\pi$
$199$	−18.3386	−1.29999	−0.649996	+	0.759938i	$0.725229\pi$
$200$	−8.04327	−0.568745
$201$	−40.4386	−2.85232
$202$	−16.5373	−1.16356
$203$	0.423095	0.0296954
$204$	−4.94385	−0.346139
$205$	1.85851	0.129804
$206$	−24.7455	−1.72410
$207$	30.0746	2.09033
$208$	19.1995	1.33125
$209$	−11.0627	−0.765223
$210$	1.11671	0.0770603
$211$	−12.8154	−0.882248	−0.441124	−	0.897446i	$-0.645420\pi$
$211$	−12.8154	−0.882248	−0.441124	+	0.897446i	$0.645420\pi$
$212$	−1.95743	−0.134437
$213$	−36.2174	−2.48158
$214$	19.5691	1.33772
$215$	−6.45600	−0.440296
$216$	−7.80940	−0.531362
$217$	−2.51722	−0.170880
$218$	−2.92788	−0.198301
$219$	−10.7513	−0.726509
$220$	2.73481	0.184381
$221$	−9.69326	−0.652039
$222$	−4.52333	−0.303586
$223$	−6.24976	−0.418515	−0.209257	−	0.977861i	$-0.567105\pi$
$223$	−6.24976	−0.418515	−0.209257	+	0.977861i	$0.567105\pi$
$224$	0.912276	0.0609540
$225$	−16.7775	−1.11850
$226$	27.6252	1.83760
$227$	16.4366	1.09093	0.545466	−	0.838133i	$-0.316353\pi$
$227$	16.4366	1.09093	0.545466	+	0.838133i	$0.316353\pi$
$228$	6.34280	0.420062
$229$	2.10096	0.138836	0.0694178	−	0.997588i	$-0.477886\pi$
$229$	2.10096	0.138836	0.0694178	+	0.997588i	$0.477886\pi$
$230$	−12.2591	−0.808339
$231$	−2.17156	−0.142878
$232$	3.84288	0.252298
$233$	20.7805	1.36138	0.680688	−	0.732573i	$-0.261681\pi$
$233$	20.7805	1.36138	0.680688	+	0.732573i	$0.261681\pi$
$234$	28.1538	1.84047
$235$	−2.62381	−0.171158
$236$	0.256989	0.0167285
$237$	15.3090	0.994429
$238$	−0.949008	−0.0615150
$239$	−3.74561	−0.242283	−0.121142	−	0.992635i	$-0.538656\pi$
$239$	−3.74561	−0.242283	−0.121142	+	0.992635i	$0.538656\pi$
$240$	14.4280	0.931324
$241$	−12.6713	−0.816229	−0.408114	−	0.912931i	$-0.633814\pi$
$241$	−12.6713	−0.816229	−0.408114	+	0.912931i	$0.633814\pi$
$242$	−1.67084	−0.107405
$243$	19.3242	1.23965
$244$	3.47146	0.222238
$245$	−7.49051	−0.478551
$246$	7.73501	0.493166
$247$	12.4361	0.791292
$248$	−22.8634	−1.45183
$249$	−11.6158	−0.736120
$250$	15.7499	0.996110
$251$	22.3466	1.41051	0.705254	−	0.708955i	$-0.250833\pi$
$251$	22.3466	1.41051	0.705254	+	0.708955i	$0.250833\pi$
$252$	0.738403	0.0465150
$253$	23.8390	1.49875
$254$	4.92676	0.309132
$255$	−7.28427	−0.456159
$256$	15.4990	0.968690
$257$	2.28663	0.142636	0.0713179	−	0.997454i	$-0.477280\pi$
$257$	2.28663	0.142636	0.0713179	+	0.997454i	$0.477280\pi$
$258$	−26.8694	−1.67282
$259$	−0.232605	−0.0144533
$260$	−3.07433	−0.190662
$261$	8.01588	0.496171
$262$	5.10157	0.315176
$263$	19.0099	1.17220	0.586102	−	0.810238i	$-0.300662\pi$
$263$	19.0099	1.17220	0.586102	+	0.810238i	$0.300662\pi$
$264$	−19.7238	−1.21392
$265$	−2.88407	−0.177167
$266$	1.21755	0.0746526
$267$	16.7880	1.02741
$268$	10.8995	0.665794
$269$	−30.6675	−1.86983	−0.934917	−	0.354867i	$-0.884526\pi$
$269$	−30.6675	−1.86983	−0.934917	+	0.354867i	$0.884526\pi$
$270$	6.64002	0.404099
$271$	−26.7592	−1.62550	−0.812752	−	0.582609i	$-0.802032\pi$
$271$	−26.7592	−1.62550	−0.812752	+	0.582609i	$0.802032\pi$
$272$	−12.2613	−0.743449
$273$	2.44116	0.147745
$274$	1.31005	0.0791428
$275$	−13.2989	−0.801954
$276$	−13.6681	−0.822723
$277$	28.9216	1.73773	0.868865	−	0.495049i	$-0.164850\pi$
$277$	28.9216	1.73773	0.868865	+	0.495049i	$0.164850\pi$
$278$	1.90853	0.114466
$279$	−47.6908	−2.85518
$280$	0.521579	0.0311703
$281$	7.48756	0.446671	0.223335	−	0.974742i	$-0.428306\pi$
$281$	7.48756	0.446671	0.223335	+	0.974742i	$0.428306\pi$
$282$	−10.9201	−0.650284
$283$	7.48108	0.444704	0.222352	−	0.974966i	$-0.428627\pi$
$283$	7.48108	0.444704	0.222352	+	0.974966i	$0.428627\pi$
$284$	9.76176	0.579254
$285$	9.34548	0.553579
$286$	22.3165	1.31960
$287$	0.397760	0.0234790
$288$	17.2838	1.01846
$289$	−10.8096	−0.635861
$290$	−3.26745	−0.191871
$291$	−27.1056	−1.58896
$292$	2.89783	0.169583
$293$	−8.91087	−0.520579	−0.260289	−	0.965531i	$-0.583818\pi$
$293$	−8.91087	−0.520579	−0.260289	+	0.965531i	$0.583818\pi$
$294$	−31.1750	−1.81816
$295$	0.378647	0.0220457
$296$	−2.11270	−0.122798
$297$	−12.9122	−0.749242
$298$	18.6078	1.07792
$299$	−26.7986	−1.54981
$300$	7.62492	0.440225
$301$	−1.38172	−0.0796408
$302$	19.0272	1.09489
$303$	−27.1666	−1.56068
$304$	15.7308	0.902225
$305$	5.11485	0.292876
$306$	−17.9797	−1.02783
$307$	3.47677	0.198430	0.0992148	−	0.995066i	$-0.468367\pi$
$307$	3.47677	0.198430	0.0992148	+	0.995066i	$0.468367\pi$
$308$	0.585305	0.0333508
$309$	−40.6507	−2.31254
$310$	19.4398	1.10411
$311$	−25.9010	−1.46871	−0.734356	−	0.678765i	$-0.762516\pi$
$311$	−25.9010	−1.46871	−0.734356	+	0.678765i	$0.762516\pi$
$312$	22.1725	1.25527
$313$	−14.4999	−0.819580	−0.409790	−	0.912180i	$-0.634398\pi$
$313$	−14.4999	−0.819580	−0.409790	+	0.912180i	$0.634398\pi$
$314$	36.5707	2.06381
$315$	1.08796	0.0612998
$316$	−4.12628	−0.232121
$317$	27.0521	1.51940	0.759699	−	0.650275i	$-0.225346\pi$
$317$	27.0521	1.51940	0.759699	+	0.650275i	$0.225346\pi$
$318$	−12.0033	−0.673113
$319$	6.35389	0.355750
$320$	3.58240	0.200263
$321$	32.1472	1.79428
$322$	−2.62369	−0.146213
$323$	−7.94203	−0.441906
$324$	−2.19587	−0.121993
$325$	14.9500	0.829275
$326$	−34.5946	−1.91601
$327$	−4.80978	−0.265982
$328$	3.61277	0.199482
$329$	−0.561549	−0.0309592
$330$	16.7704	0.923179
$331$	−18.4581	−1.01455	−0.507274	−	0.861785i	$-0.669347\pi$
$331$	−18.4581	−1.01455	−0.507274	+	0.861785i	$0.669347\pi$
$332$	3.13083	0.171826
$333$	−4.40689	−0.241496
$334$	−4.99120	−0.273106
$335$	16.0593	0.877416
$336$	3.08789	0.168458
$337$	27.9148	1.52061	0.760307	−	0.649564i	$-0.225049\pi$
$337$	27.9148	1.52061	0.760307	+	0.649564i	$0.225049\pi$
$338$	−3.60039	−0.195835
$339$	45.3814	2.46478
$340$	1.96335	0.106477
$341$	−37.8028	−2.04713
$342$	23.0674	1.24734
$343$	−3.21853	−0.173785
$344$	−12.5499	−0.676643
$345$	−20.1386	−1.08423
$346$	2.24829	0.120869
$347$	−30.7699	−1.65181	−0.825907	−	0.563807i	$-0.809336\pi$
$347$	−30.7699	−1.65181	−0.825907	+	0.563807i	$0.809336\pi$
$348$	−3.64300	−0.195285
$349$	−15.6322	−0.836773	−0.418386	−	0.908269i	$-0.637404\pi$
$349$	−15.6322	−0.836773	−0.418386	+	0.908269i	$0.637404\pi$
$350$	1.46366	0.0782359
$351$	14.5153	0.774767
$352$	13.7002	0.730226
$353$	−23.5301	−1.25238	−0.626190	−	0.779671i	$-0.715386\pi$
$353$	−23.5301	−1.25238	−0.626190	+	0.779671i	$0.715386\pi$
$354$	1.57590	0.0837583
$355$	14.3830	0.763370
$356$	−4.52491	−0.239820
$357$	−1.55898	−0.0825101
$358$	1.20301	0.0635812
$359$	26.0489	1.37481	0.687403	−	0.726276i	$-0.258751\pi$
$359$	26.0489	1.37481	0.687403	+	0.726276i	$0.258751\pi$
$360$	9.88175	0.520814
$361$	−8.81064	−0.463718
$362$	27.7368	1.45782
$363$	−2.74477	−0.144063
$364$	−0.657970	−0.0344870
$365$	4.26967	0.223485
$366$	21.2877	1.11272
$367$	−24.1554	−1.26090	−0.630450	−	0.776230i	$-0.717130\pi$
$367$	−24.1554	−1.26090	−0.630450	+	0.776230i	$0.717130\pi$
$368$	−33.8984	−1.76708
$369$	7.53590	0.392303
$370$	1.79634	0.0933875
$371$	−0.617251	−0.0320461
$372$	21.6742	1.12376
$373$	−25.3064	−1.31032	−0.655158	−	0.755492i	$-0.727398\pi$
$373$	−25.3064	−1.31032	−0.655158	+	0.755492i	$0.727398\pi$
$374$	−14.2519	−0.736947
$375$	25.8731	1.33608
$376$	−5.10043	−0.263035
$377$	−7.14273	−0.367869
$378$	1.42110	0.0730935
$379$	−15.1788	−0.779681	−0.389841	−	0.920882i	$-0.627470\pi$
$379$	−15.1788	−0.779681	−0.389841	+	0.920882i	$0.627470\pi$
$380$	−2.51891	−0.129217
$381$	8.09344	0.414639
$382$	−21.4460	−1.09727
$383$	−7.63958	−0.390364	−0.195182	−	0.980767i	$-0.562530\pi$
$383$	−7.63958	−0.390364	−0.195182	+	0.980767i	$0.562530\pi$
$384$	36.3766	1.85634
$385$	0.862389	0.0439514
$386$	38.8016	1.97495
$387$	−26.1778	−1.33069
$388$	7.30584	0.370898
$389$	−11.9759	−0.607205	−0.303602	−	0.952799i	$-0.598189\pi$
$389$	−11.9759	−0.607205	−0.303602	+	0.952799i	$0.598189\pi$
$390$	−18.8524	−0.954629
$391$	17.1143	0.865506
$392$	−14.5608	−0.735433
$393$	8.38060	0.422745
$394$	−11.3537	−0.571989
$395$	−6.07966	−0.305901
$396$	11.0891	0.557248
$397$	18.5553	0.931263	0.465631	−	0.884979i	$-0.345827\pi$
$397$	18.5553	0.931263	0.465631	+	0.884979i	$0.345827\pi$
$398$	30.3106	1.51933
$399$	2.00012	0.100131
$400$	18.9106	0.945532
$401$	11.9067	0.594594	0.297297	−	0.954785i	$-0.403915\pi$
$401$	11.9067	0.594594	0.297297	+	0.954785i	$0.403915\pi$
$402$	66.8379	3.33357
$403$	42.4960	2.11688
$404$	7.32227	0.364297
$405$	−3.23539	−0.160768
$406$	−0.699301	−0.0347057
$407$	−3.49318	−0.173150
$408$	−14.1599	−0.701021
$409$	−24.4739	−1.21016	−0.605078	−	0.796167i	$-0.706858\pi$
$409$	−24.4739	−1.21016	−0.605078	+	0.796167i	$0.706858\pi$
$410$	−3.07180	−0.151705
$411$	2.15208	0.106154
$412$	10.9567	0.539796
$413$	0.0810382	0.00398763
$414$	−49.7080	−2.44302
$415$	4.61296	0.226441
$416$	−15.4011	−0.755103
$417$	3.13523	0.153533
$418$	18.2847	0.894334
$419$	19.6993	0.962376	0.481188	−	0.876618i	$-0.340206\pi$
$419$	19.6993	0.962376	0.481188	+	0.876618i	$0.340206\pi$
$420$	−0.494450	−0.0241267
$421$	−2.35033	−0.114548	−0.0572740	−	0.998358i	$-0.518241\pi$
$421$	−2.35033	−0.114548	−0.0572740	+	0.998358i	$0.518241\pi$
$422$	21.1816	1.03110
$423$	−10.6390	−0.517287
$424$	−5.60636	−0.272269
$425$	−9.54742	−0.463118
$426$	59.8610	2.90028
$427$	1.09468	0.0529754
$428$	−8.66471	−0.418825
$429$	36.6605	1.76998
$430$	10.6706	0.514584
$431$	13.4185	0.646349	0.323174	−	0.946339i	$-0.395250\pi$
$431$	13.4185	0.646349	0.323174	+	0.946339i	$0.395250\pi$
$432$	18.3608	0.883383
$433$	−13.5046	−0.648988	−0.324494	−	0.945888i	$-0.605194\pi$
$433$	−13.5046	−0.648988	−0.324494	+	0.945888i	$0.605194\pi$
$434$	4.16052	0.199711
$435$	−5.36760	−0.257357
$436$	1.29639	0.0620859
$437$	−21.9571	−1.05035
$438$	17.7701	0.849087
$439$	−21.4099	−1.02184	−0.510920	−	0.859628i	$-0.670695\pi$
$439$	−21.4099	−1.02184	−0.510920	+	0.859628i	$0.670695\pi$
$440$	7.83290	0.373419
$441$	−30.3725	−1.44631
$442$	16.0213	0.762053
$443$	−1.37461	−0.0653098	−0.0326549	−	0.999467i	$-0.510396\pi$
$443$	−1.37461	−0.0653098	−0.0326549	+	0.999467i	$0.510396\pi$
$444$	2.00281	0.0950493
$445$	−6.66701	−0.316047
$446$	10.3298	0.489128
$447$	30.5680	1.44582
$448$	0.766708	0.0362235
$449$	−39.2179	−1.85081	−0.925404	−	0.378982i	$-0.876274\pi$
$449$	−39.2179	−1.85081	−0.925404	+	0.378982i	$0.876274\pi$
$450$	27.7303	1.30722
$451$	5.97343	0.281278
$452$	−12.2318	−0.575333
$453$	31.2570	1.46858
$454$	−27.1668	−1.27500
$455$	−0.969454	−0.0454487
$456$	18.1667	0.850735
$457$	−1.38237	−0.0646645	−0.0323323	−	0.999477i	$-0.510293\pi$
$457$	−1.38237	−0.0646645	−0.0323323	+	0.999477i	$0.510293\pi$
$458$	−3.47253	−0.162260
$459$	−9.26980	−0.432677
$460$	5.42800	0.253082
$461$	−18.4702	−0.860244	−0.430122	−	0.902771i	$-0.641530\pi$
$461$	−18.4702	−0.860244	−0.430122	+	0.902771i	$0.641530\pi$
$462$	3.58920	0.166985
$463$	15.5326	0.721860	0.360930	−	0.932593i	$-0.382459\pi$
$463$	15.5326	0.721860	0.360930	+	0.932593i	$0.382459\pi$
$464$	−9.03504	−0.419441
$465$	31.9348	1.48094
$466$	−34.3465	−1.59107
$467$	24.2082	1.12022	0.560110	−	0.828418i	$-0.310759\pi$
$467$	24.2082	1.12022	0.560110	+	0.828418i	$0.310759\pi$
$468$	−12.4658	−0.576232
$469$	3.43703	0.158707
$470$	4.33670	0.200037
$471$	60.0766	2.76818
$472$	0.736054	0.0338796
$473$	−20.7502	−0.954094
$474$	−25.3031	−1.16221
$475$	12.2490	0.562024
$476$	0.420196	0.0192597
$477$	−11.6943	−0.535447
$478$	6.19083	0.283162
$479$	1.62179	0.0741013	0.0370506	−	0.999313i	$-0.488204\pi$
$479$	1.62179	0.0741013	0.0370506	+	0.999313i	$0.488204\pi$
$480$	−11.5736	−0.528261
$481$	3.92685	0.179049
$482$	20.9434	0.953946
$483$	−4.31007	−0.196115
$484$	0.739803	0.0336274
$485$	10.7644	0.488787
$486$	−31.9395	−1.44880
$487$	0.912339	0.0413420	0.0206710	−	0.999786i	$-0.493420\pi$
$487$	0.912339	0.0413420	0.0206710	+	0.999786i	$0.493420\pi$
$488$	9.94278	0.450089
$489$	−56.8302	−2.56995
$490$	12.3805	0.559294
$491$	36.3672	1.64123	0.820613	−	0.571484i	$-0.193632\pi$
$491$	36.3672	1.64123	0.820613	+	0.571484i	$0.193632\pi$
$492$	−3.42486	−0.154405
$493$	4.56152	0.205441
$494$	−20.5547	−0.924802
$495$	16.3387	0.734369
$496$	53.7544	2.41364
$497$	3.07825	0.138079
$498$	19.1988	0.860320
$499$	20.1984	0.904205	0.452103	−	0.891966i	$-0.350674\pi$
$499$	20.1984	0.904205	0.452103	+	0.891966i	$0.350674\pi$
$500$	−6.97364	−0.311871
$501$	−8.19930	−0.366318
$502$	−36.9351	−1.64849
$503$	−16.3398	−0.728555	−0.364278	−	0.931290i	$-0.618684\pi$
$503$	−16.3398	−0.728555	−0.364278	+	0.931290i	$0.618684\pi$
$504$	2.11490	0.0942050
$505$	10.7886	0.480088
$506$	−39.4017	−1.75162
$507$	−5.91454	−0.262674
$508$	−2.18144	−0.0967859
$509$	34.5946	1.53338	0.766689	−	0.642019i	$-0.221903\pi$
$509$	34.5946	1.53338	0.766689	+	0.642019i	$0.221903\pi$
$510$	12.0396	0.533123
$511$	0.913797	0.0404240
$512$	1.17783	0.0520533
$513$	11.8929	0.525082
$514$	−3.77939	−0.166702
$515$	16.1436	0.711370
$516$	11.8971	0.523741
$517$	−8.43315	−0.370890
$518$	0.384454	0.0168920
$519$	3.69338	0.162121
$520$	−8.80535	−0.386140
$521$	−15.9455	−0.698587	−0.349293	−	0.937013i	$-0.613578\pi$
$521$	−15.9455	−0.698587	−0.349293	+	0.937013i	$0.613578\pi$
$522$	−13.2488	−0.579886
$523$	0.678239	0.0296573	0.0148287	−	0.999890i	$-0.495280\pi$
$523$	0.678239	0.0296573	0.0148287	+	0.999890i	$0.495280\pi$
$524$	−2.25884	−0.0986780
$525$	2.40443	0.104938
$526$	−31.4201	−1.36998
$527$	−27.1390	−1.18219
$528$	46.3729	2.01812
$529$	24.3153	1.05719
$530$	4.76687	0.207059
$531$	1.53534	0.0666280
$532$	−0.539098	−0.0233729
$533$	−6.71503	−0.290860
$534$	−27.7476	−1.20076
$535$	−12.7666	−0.551948
$536$	31.2178	1.34840
$537$	1.97625	0.0852814
$538$	50.6881	2.18532
$539$	−24.0752	−1.03699
$540$	−2.94003	−0.126519
$541$	9.37786	0.403186	0.201593	−	0.979469i	$-0.435388\pi$
$541$	9.37786	0.403186	0.201593	+	0.979469i	$0.435388\pi$
$542$	44.2282	1.89977
$543$	45.5647	1.95537
$544$	9.83555	0.421696
$545$	1.91011	0.0818199
$546$	−4.03480	−0.172674
$547$	−37.6034	−1.60781	−0.803903	−	0.594761i	$-0.797247\pi$
$547$	−37.6034	−1.60781	−0.803903	+	0.594761i	$0.797247\pi$
$548$	−0.580055	−0.0247787
$549$	20.7397	0.885148
$550$	21.9807	0.937262
$551$	−5.85229	−0.249316
$552$	−39.1475	−1.66623
$553$	−1.30117	−0.0553315
$554$	−47.8023	−2.03093
$555$	2.95095	0.125261
$556$	−0.845047	−0.0358380
$557$	4.73722	0.200722	0.100361	−	0.994951i	$-0.468000\pi$
$557$	4.73722	0.200722	0.100361	+	0.994951i	$0.468000\pi$
$558$	78.8246	3.33691
$559$	23.3263	0.986597
$560$	−1.22629	−0.0518202
$561$	−23.4123	−0.988467
$562$	−12.3756	−0.522034
$563$	−35.3949	−1.49172	−0.745858	−	0.666105i	$-0.767960\pi$
$563$	−35.3949	−1.49172	−0.745858	+	0.666105i	$0.767960\pi$
$564$	4.83515	0.203596
$565$	−18.0223	−0.758203
$566$	−12.3649	−0.519736
$567$	−0.692440	−0.0290797
$568$	27.9591	1.17314
$569$	16.3832	0.686819	0.343410	−	0.939186i	$-0.388418\pi$
$569$	16.3832	0.686819	0.343410	+	0.939186i	$0.388418\pi$
$570$	−15.4464	−0.646980
$571$	35.4800	1.48479	0.742396	−	0.669961i	$-0.233689\pi$
$571$	35.4800	1.48479	0.742396	+	0.669961i	$0.233689\pi$
$572$	−9.88118	−0.413153
$573$	−35.2303	−1.47177
$574$	−0.657427	−0.0274405
$575$	−26.3954	−1.10077
$576$	14.5259	0.605247
$577$	8.12635	0.338304	0.169152	−	0.985590i	$-0.445897\pi$
$577$	8.12635	0.338304	0.169152	+	0.985590i	$0.445897\pi$
$578$	17.8664	0.743146
$579$	63.7413	2.64900
$580$	1.44674	0.0600727
$581$	0.987268	0.0409588
$582$	44.8008	1.85705
$583$	−9.26966	−0.383910
$584$	8.29983	0.343449
$585$	−18.3671	−0.759387
$586$	14.7281	0.608412
$587$	2.80630	0.115829	0.0579143	−	0.998322i	$-0.481555\pi$
$587$	2.80630	0.115829	0.0579143	+	0.998322i	$0.481555\pi$
$588$	13.8035	0.569246
$589$	34.8184	1.43467
$590$	−0.625837	−0.0257653
$591$	−18.6512	−0.767209
$592$	4.96719	0.204150
$593$	−30.4457	−1.25025	−0.625127	−	0.780523i	$-0.714953\pi$
$593$	−30.4457	−1.25025	−0.625127	+	0.780523i	$0.714953\pi$
$594$	21.3416	0.875657
$595$	0.619118	0.0253813
$596$	−8.23907	−0.337486
$597$	49.7927	2.03788
$598$	44.2934	1.81129
$599$	1.85156	0.0756525	0.0378263	−	0.999284i	$-0.487957\pi$
$599$	1.85156	0.0756525	0.0378263	+	0.999284i	$0.487957\pi$
$600$	21.8389	0.891570
$601$	−30.0376	−1.22526	−0.612630	−	0.790369i	$-0.709889\pi$
$601$	−30.0376	−1.22526	−0.612630	+	0.790369i	$0.709889\pi$
$602$	2.28374	0.0930781
$603$	65.1174	2.65178
$604$	−8.42477	−0.342799
$605$	1.09003	0.0443159
$606$	44.9016	1.82400
$607$	−24.4436	−0.992136	−0.496068	−	0.868284i	$-0.665223\pi$
$607$	−24.4436	−0.992136	−0.496068	+	0.868284i	$0.665223\pi$
$608$	−12.6187	−0.511755
$609$	−1.14878	−0.0465508
$610$	−8.45395	−0.342291
$611$	9.48013	0.383525
$612$	7.96097	0.321803
$613$	−31.9215	−1.28930	−0.644649	−	0.764479i	$-0.722996\pi$
$613$	−31.9215	−1.28930	−0.644649	+	0.764479i	$0.722996\pi$
$614$	−5.74649	−0.231909
$615$	−5.04620	−0.203482
$616$	1.67640	0.0675441
$617$	−29.1791	−1.17471	−0.587353	−	0.809331i	$-0.699830\pi$
$617$	−29.1791	−1.17471	−0.587353	+	0.809331i	$0.699830\pi$
$618$	67.1884	2.70271
$619$	−9.40537	−0.378034	−0.189017	−	0.981974i	$-0.560530\pi$
$619$	−9.40537	−0.378034	−0.189017	+	0.981974i	$0.560530\pi$
$620$	−8.60746	−0.345684
$621$	−25.6279	−1.02841
$622$	42.8098	1.71652
$623$	−1.42688	−0.0571666
$624$	−52.1301	−2.08687
$625$	8.91163	0.356465
$626$	23.9657	0.957862
$627$	30.0372	1.19957
$628$	−16.1926	−0.646154
$629$	−2.50779	−0.0999920
$630$	−1.79821	−0.0716425
$631$	−29.9573	−1.19258	−0.596290	−	0.802769i	$-0.703359\pi$
$631$	−29.9573	−1.19258	−0.596290	+	0.802769i	$0.703359\pi$
$632$	−11.8183	−0.470106
$633$	34.7961	1.38302
$634$	−44.7124	−1.77576
$635$	−3.21414	−0.127549
$636$	5.31476	0.210744
$637$	27.0641	1.07232
$638$	−10.5019	−0.415773
$639$	58.3201	2.30711
$640$	−14.4462	−0.571037
$641$	6.00044	0.237003	0.118502	−	0.992954i	$-0.462191\pi$
$641$	6.00044	0.237003	0.118502	+	0.992954i	$0.462191\pi$
$642$	−53.1337	−2.09702
$643$	−29.5166	−1.16402	−0.582010	−	0.813182i	$-0.697734\pi$
$643$	−29.5166	−1.16402	−0.582010	+	0.813182i	$0.697734\pi$
$644$	1.16170	0.0457775
$645$	17.5292	0.690212
$646$	13.1268	0.516466
$647$	0.960568	0.0377638	0.0188819	−	0.999822i	$-0.493989\pi$
$647$	0.960568	0.0377638	0.0188819	+	0.999822i	$0.493989\pi$
$648$	−6.28929	−0.247067
$649$	1.21701	0.0477716
$650$	−24.7097	−0.969192
$651$	6.83470	0.267873
$652$	15.3176	0.599883
$653$	−9.92050	−0.388219	−0.194110	−	0.980980i	$-0.562182\pi$
$653$	−9.92050	−0.388219	−0.194110	+	0.980980i	$0.562182\pi$
$654$	7.94973	0.310859
$655$	−3.32818	−0.130043
$656$	−8.49403	−0.331636
$657$	17.3127	0.675431
$658$	0.928142	0.0361827
$659$	5.89650	0.229695	0.114848	−	0.993383i	$-0.463362\pi$
$659$	5.89650	0.229695	0.114848	+	0.993383i	$0.463362\pi$
$660$	−7.42549	−0.289037
$661$	7.20094	0.280084	0.140042	−	0.990146i	$-0.455276\pi$
$661$	7.20094	0.280084	0.140042	+	0.990146i	$0.455276\pi$
$662$	30.5079	1.18572
$663$	26.3189	1.02214
$664$	8.96715	0.347993
$665$	−0.794308	−0.0308019
$666$	7.28381	0.282242
$667$	12.6111	0.488304
$668$	2.20998	0.0855065
$669$	16.9692	0.656068
$670$	−26.5433	−1.02546
$671$	16.4396	0.634643
$672$	−2.47699	−0.0955520
$673$	−4.10097	−0.158081	−0.0790405	−	0.996871i	$-0.525186\pi$
$673$	−4.10097	−0.158081	−0.0790405	+	0.996871i	$0.525186\pi$
$674$	−46.1382	−1.77718
$675$	14.2969	0.550287
$676$	1.59416	0.0613139
$677$	−37.0413	−1.42361	−0.711807	−	0.702375i	$-0.752123\pi$
$677$	−37.0413	−1.42361	−0.711807	+	0.702375i	$0.752123\pi$
$678$	−75.0075	−2.88064
$679$	2.30381	0.0884120
$680$	5.62332	0.215644
$681$	−44.6282	−1.71016
$682$	62.4813	2.39253
$683$	−16.3550	−0.625806	−0.312903	−	0.949785i	$-0.601301\pi$
$683$	−16.3550	−0.625806	−0.312903	+	0.949785i	$0.601301\pi$
$684$	−10.2137	−0.390529
$685$	−0.854653	−0.0326546
$686$	5.31967	0.203106
$687$	−5.70449	−0.217640
$688$	29.5061	1.12491
$689$	10.4205	0.396989
$690$	33.2856	1.26716
$691$	−19.2278	−0.731461	−0.365731	−	0.930721i	$-0.619181\pi$
$691$	−19.2278	−0.731461	−0.365731	+	0.930721i	$0.619181\pi$
$692$	−0.995485	−0.0378427
$693$	3.49681	0.132833
$694$	50.8572	1.93051
$695$	−1.24509	−0.0472291
$696$	−10.4341	−0.395504
$697$	4.28838	0.162434
$698$	25.8373	0.977956
$699$	−56.4228	−2.13411
$700$	−0.648071	−0.0244948
$701$	12.9588	0.489445	0.244723	−	0.969593i	$-0.421303\pi$
$701$	12.9588	0.489445	0.244723	+	0.969593i	$0.421303\pi$
$702$	−23.9912	−0.905488
$703$	3.21741	0.121347
$704$	11.5142	0.433956
$705$	7.12411	0.268310
$706$	38.8911	1.46368
$707$	2.30899	0.0868385
$708$	−0.697770	−0.0262238
$709$	−27.8653	−1.04650	−0.523252	−	0.852178i	$-0.675281\pi$
$709$	−27.8653	−1.04650	−0.523252	+	0.852178i	$0.675281\pi$
$710$	−23.7726	−0.892168
$711$	−24.6518	−0.924515
$712$	−12.9600	−0.485698
$713$	−75.0303	−2.80991
$714$	2.57673	0.0964315
$715$	−14.5589	−0.544473
$716$	−0.532663	−0.0199065
$717$	10.1700	0.379805
$718$	−43.0542	−1.60677
$719$	15.1659	0.565593	0.282796	−	0.959180i	$-0.408738\pi$
$719$	15.1659	0.565593	0.282796	+	0.959180i	$0.408738\pi$
$720$	−23.2331	−0.865847
$721$	3.45505	0.128673
$722$	14.5624	0.541958
$723$	34.4048	1.27953
$724$	−12.2812	−0.456426
$725$	−7.03526	−0.261283
$726$	4.53662	0.168370
$727$	31.2156	1.15772	0.578862	−	0.815426i	$-0.303497\pi$
$727$	31.2156	1.15772	0.578862	+	0.815426i	$0.303497\pi$
$728$	−1.88453	−0.0698452
$729$	−43.4670	−1.60989
$730$	−7.05702	−0.261192
$731$	−14.8968	−0.550976
$732$	−9.42563	−0.348381
$733$	−21.9080	−0.809190	−0.404595	−	0.914496i	$-0.632588\pi$
$733$	−21.9080	−0.809190	−0.404595	+	0.914496i	$0.632588\pi$
$734$	39.9246	1.47364
$735$	20.3381	0.750181
$736$	27.1920	1.00231
$737$	51.6161	1.90131
$738$	−12.4555	−0.458494
$739$	−28.8906	−1.06276	−0.531379	−	0.847134i	$-0.678326\pi$
$739$	−28.8906	−1.06276	−0.531379	+	0.847134i	$0.678326\pi$
$740$	−0.795375	−0.0292386
$741$	−33.7663	−1.24044
$742$	1.02021	0.0374530
$743$	−4.44252	−0.162980	−0.0814900	−	0.996674i	$-0.525968\pi$
$743$	−4.44252	−0.162980	−0.0814900	+	0.996674i	$0.525968\pi$
$744$	62.0782	2.27590
$745$	−12.1395	−0.444755
$746$	41.8271	1.53140
$747$	18.7046	0.684366
$748$	6.31037	0.230730
$749$	−2.73231	−0.0998365
$750$	−42.7637	−1.56151
$751$	−47.3139	−1.72651	−0.863253	−	0.504771i	$-0.831577\pi$
$751$	−47.3139	−1.72651	−0.863253	+	0.504771i	$0.831577\pi$
$752$	11.9917	0.437292
$753$	−60.6751	−2.21112
$754$	11.8057	0.429937
$755$	−12.4131	−0.451758
$756$	−0.629227	−0.0228848
$757$	34.7378	1.26257	0.631284	−	0.775552i	$-0.282528\pi$
$757$	34.7378	1.26257	0.631284	+	0.775552i	$0.282528\pi$
$758$	25.0878	0.911231
$759$	−64.7272	−2.34945
$760$	−7.21453	−0.261699
$761$	−36.7778	−1.33319	−0.666597	−	0.745418i	$-0.732250\pi$
$761$	−36.7778	−1.33319	−0.666597	+	0.745418i	$0.732250\pi$
$762$	−13.3770	−0.484599
$763$	0.408802	0.0147996
$764$	9.49572	0.343543
$765$	11.7297	0.424088
$766$	12.6269	0.456228
$767$	−1.36810	−0.0493991
$768$	−42.0826	−1.51853
$769$	−37.3302	−1.34616	−0.673080	−	0.739570i	$-0.735029\pi$
$769$	−37.3302	−1.34616	−0.673080	+	0.739570i	$0.735029\pi$
$770$	−1.42538	−0.0513670
$771$	−6.20860	−0.223597
$772$	−17.1803	−0.618334
$773$	16.9332	0.609043	0.304522	−	0.952505i	$-0.401503\pi$
$773$	16.9332	0.609043	0.304522	+	0.952505i	$0.401503\pi$
$774$	43.2673	1.55521
$775$	41.8566	1.50353
$776$	20.9250	0.751164
$777$	0.631563	0.0226572
$778$	19.7941	0.709654
$779$	−5.50186	−0.197124
$780$	8.34736	0.298884
$781$	46.2282	1.65417
$782$	−28.2869	−1.01154
$783$	−6.83069	−0.244109
$784$	34.2341	1.22265
$785$	−23.8582	−0.851534
$786$	−13.8517	−0.494072
$787$	16.4355	0.585864	0.292932	−	0.956133i	$-0.405369\pi$
$787$	16.4355	0.585864	0.292932	+	0.956133i	$0.405369\pi$
$788$	5.02711	0.179083
$789$	−51.6154	−1.83756
$790$	10.0486	0.357514
$791$	−3.85713	−0.137144
$792$	31.7608	1.12857
$793$	−18.4806	−0.656264
$794$	−30.6686	−1.08839
$795$	7.83077	0.277729
$796$	−13.4207	−0.475685
$797$	−5.75893	−0.203992	−0.101996	−	0.994785i	$-0.532523\pi$
$797$	−5.75893	−0.203992	−0.101996	+	0.994785i	$0.532523\pi$
$798$	−3.30585	−0.117026
$799$	−6.05425	−0.214184
$800$	−15.1694	−0.536320
$801$	−27.0334	−0.955177
$802$	−19.6797	−0.694915
$803$	13.7231	0.484278
$804$	−29.5941	−1.04370
$805$	1.71165	0.0603279
$806$	−70.2384	−2.47404
$807$	83.2678	2.93117
$808$	20.9721	0.737795
$809$	−8.20173	−0.288358	−0.144179	−	0.989552i	$-0.546054\pi$
$809$	−8.20173	−0.288358	−0.144179	+	0.989552i	$0.546054\pi$
$810$	5.34753	0.187893
$811$	27.5021	0.965730	0.482865	−	0.875695i	$-0.339596\pi$
$811$	27.5021	0.965730	0.482865	+	0.875695i	$0.339596\pi$
$812$	0.309633	0.0108660
$813$	72.6559	2.54816
$814$	5.77361	0.202365
$815$	22.5689	0.790555
$816$	33.2916	1.16544
$817$	19.1121	0.668646
$818$	40.4510	1.41434
$819$	−3.93094	−0.137358
$820$	1.36011	0.0474972
$821$	18.7614	0.654777	0.327388	−	0.944890i	$-0.393831\pi$
$821$	18.7614	0.654777	0.327388	+	0.944890i	$0.393831\pi$
$822$	−3.55701	−0.124065
$823$	39.0680	1.36183	0.680913	−	0.732364i	$-0.261583\pi$
$823$	39.0680	1.36183	0.680913	+	0.732364i	$0.261583\pi$
$824$	31.3815	1.09323
$825$	36.1089	1.25715
$826$	−0.133942	−0.00466044
$827$	−9.29966	−0.323381	−0.161690	−	0.986842i	$-0.551695\pi$
$827$	−9.29966	−0.323381	−0.161690	+	0.986842i	$0.551695\pi$
$828$	22.0094	0.764881
$829$	−37.4416	−1.30040	−0.650201	−	0.759762i	$-0.725315\pi$
$829$	−37.4416	−1.30040	−0.650201	+	0.759762i	$0.725315\pi$
$830$	−7.62441	−0.264647
$831$	−78.5273	−2.72408
$832$	−12.9436	−0.448740
$833$	−17.2838	−0.598848
$834$	−5.18199	−0.179438
$835$	3.25618	0.112685
$836$	−8.09600	−0.280006
$837$	40.6395	1.40471
$838$	−32.5595	−1.12475
$839$	44.5924	1.53950	0.769750	−	0.638346i	$-0.220381\pi$
$839$	44.5924	1.53950	0.769750	+	0.638346i	$0.220381\pi$
$840$	−1.41618	−0.0488628
$841$	−25.6387	−0.884094
$842$	3.88468	0.133875
$843$	−20.3301	−0.700205
$844$	−9.37866	−0.322827
$845$	2.34884	0.0808024
$846$	17.5844	0.604565
$847$	0.233288	0.00801587
$848$	13.1812	0.452644
$849$	−20.3125	−0.697122
$850$	15.7802	0.541256
$851$	−6.93320	−0.237667
$852$	−26.5049	−0.908044
$853$	−23.6512	−0.809802	−0.404901	−	0.914360i	$-0.632694\pi$
$853$	−23.6512	−0.809802	−0.404901	+	0.914360i	$0.632694\pi$
$854$	−1.80932	−0.0619136
$855$	−15.0488	−0.514659
$856$	−24.8170	−0.848228
$857$	−30.2409	−1.03301	−0.516506	−	0.856284i	$-0.672767\pi$
$857$	−30.2409	−1.03301	−0.516506	+	0.856284i	$0.672767\pi$
$858$	−60.5933	−2.06862
$859$	30.4384	1.03855	0.519273	−	0.854609i	$-0.326203\pi$
$859$	30.4384	1.03855	0.519273	+	0.854609i	$0.326203\pi$
$860$	−4.72469	−0.161110
$861$	−1.07999	−0.0368059
$862$	−22.1785	−0.755403
$863$	−5.57790	−0.189874	−0.0949369	−	0.995483i	$-0.530265\pi$
$863$	−5.57790	−0.189874	−0.0949369	+	0.995483i	$0.530265\pi$
$864$	−14.7283	−0.501068
$865$	−1.46675	−0.0498710
$866$	22.3207	0.758487
$867$	29.3501	0.996782
$868$	−1.84217	−0.0625274
$869$	−19.5406	−0.662869
$870$	8.87171	0.300779
$871$	−58.0243	−1.96608
$872$	3.71306	0.125740
$873$	43.6476	1.47725
$874$	36.2912	1.22757
$875$	−2.19905	−0.0743416
$876$	−7.86814	−0.265840
$877$	−24.2704	−0.819552	−0.409776	−	0.912186i	$-0.634393\pi$
$877$	−24.2704	−0.819552	−0.409776	+	0.912186i	$0.634393\pi$
$878$	35.3869	1.19425
$879$	24.1946	0.816064
$880$	−18.4160	−0.620804
$881$	−33.8372	−1.14000	−0.570001	−	0.821644i	$-0.693057\pi$
$881$	−33.8372	−1.14000	−0.570001	+	0.821644i	$0.693057\pi$
$882$	50.2004	1.69033
$883$	−29.6330	−0.997229	−0.498615	−	0.866824i	$-0.666158\pi$
$883$	−29.6330	−0.997229	−0.498615	+	0.866824i	$0.666158\pi$
$884$	−7.09380	−0.238590
$885$	−1.02809	−0.0345590
$886$	2.27199	0.0763290
$887$	−18.1856	−0.610613	−0.305307	−	0.952254i	$-0.598759\pi$
$887$	−18.1856	−0.610613	−0.305307	+	0.952254i	$0.598759\pi$
$888$	5.73635	0.192499
$889$	−0.687892	−0.0230711
$890$	11.0194	0.369371
$891$	−10.3988	−0.348374
$892$	−4.57375	−0.153141
$893$	7.76740	0.259926
$894$	−50.5236	−1.68976
$895$	−0.784826	−0.0262338
$896$	−3.09178	−0.103289
$897$	72.7631	2.42949
$898$	64.8203	2.16308
$899$	−19.9981	−0.666973
$900$	−12.2782	−0.409275
$901$	−6.65479	−0.221703
$902$	−9.87303	−0.328736
$903$	3.75161	0.124846
$904$	−35.0336	−1.16520
$905$	−18.0951	−0.601500
$906$	−51.6623	−1.71637
$907$	−13.3125	−0.442036	−0.221018	−	0.975270i	$-0.570938\pi$
$907$	−13.3125	−0.442036	−0.221018	+	0.975270i	$0.570938\pi$
$908$	12.0287	0.399188
$909$	43.7458	1.45096
$910$	1.60234	0.0531170
$911$	−9.25251	−0.306549	−0.153275	−	0.988184i	$-0.548982\pi$
$911$	−9.25251	−0.306549	−0.153275	+	0.988184i	$0.548982\pi$
$912$	−42.7120	−1.41434
$913$	14.8265	0.490684
$914$	2.28481	0.0755749
$915$	−13.8877	−0.459114
$916$	1.53755	0.0508019
$917$	−0.712299	−0.0235222
$918$	15.3214	0.505680
$919$	32.3666	1.06768	0.533838	−	0.845587i	$-0.320749\pi$
$919$	32.3666	1.06768	0.533838	+	0.845587i	$0.320749\pi$
$920$	15.5466	0.512556
$921$	−9.44004	−0.311060
$922$	30.5280	1.00539
$923$	−51.9674	−1.71053
$924$	−1.58921	−0.0522811
$925$	3.86777	0.127172
$926$	−25.6726	−0.843654
$927$	65.4589	2.14995
$928$	7.24758	0.237913
$929$	58.3837	1.91551	0.957753	−	0.287590i	$-0.0928542\pi$
$929$	58.3837	1.91551	0.957753	+	0.287590i	$0.0928542\pi$
$930$	−52.7826	−1.73081
$931$	22.1745	0.726741
$932$	15.2078	0.498147
$933$	70.3258	2.30236
$934$	−40.0119	−1.30923
$935$	9.29770	0.304067
$936$	−35.7039	−1.16702
$937$	−2.84918	−0.0930786	−0.0465393	−	0.998916i	$-0.514819\pi$
$937$	−2.84918	−0.0930786	−0.0465393	+	0.998916i	$0.514819\pi$
$938$	−5.68081	−0.185485
$939$	39.3697	1.28478
$940$	−1.92018	−0.0626293
$941$	1.63537	0.0533116	0.0266558	−	0.999645i	$-0.491514\pi$
$941$	1.63537	0.0533116	0.0266558	+	0.999645i	$0.491514\pi$
$942$	−99.2960	−3.23524
$943$	11.8560	0.386083
$944$	−1.73054	−0.0563244
$945$	−0.927103	−0.0301587
$946$	34.2964	1.11507
$947$	−2.80811	−0.0912513	−0.0456257	−	0.998959i	$-0.514528\pi$
$947$	−2.80811	−0.0912513	−0.0456257	+	0.998959i	$0.514528\pi$
$948$	11.2036	0.363875
$949$	−15.4268	−0.500776
$950$	−20.2455	−0.656850
$951$	−73.4513	−2.38182
$952$	1.20351	0.0390058
$953$	−16.5227	−0.535221	−0.267611	−	0.963527i	$-0.586234\pi$
$953$	−16.5227	−0.535221	−0.267611	+	0.963527i	$0.586234\pi$
$954$	19.3287	0.625789
$955$	13.9910	0.452738
$956$	−2.74114	−0.0886549
$957$	−17.2519	−0.557676
$958$	−2.68053	−0.0866039
$959$	−0.182913	−0.00590658
$960$	−9.72687	−0.313933
$961$	87.9794	2.83804
$962$	−6.49040	−0.209259
$963$	−51.7659	−1.66813
$964$	−9.27320	−0.298670
$965$	−25.3135	−0.814871
$966$	7.12379	0.229204
$967$	12.7996	0.411607	0.205804	−	0.978593i	$-0.434019\pi$
$967$	12.7996	0.411607	0.205804	+	0.978593i	$0.434019\pi$
$968$	2.11891	0.0681043
$969$	21.5640	0.692736
$970$	−17.7917	−0.571257
$971$	−4.23233	−0.135822	−0.0679110	−	0.997691i	$-0.521633\pi$
$971$	−4.23233	−0.135822	−0.0679110	+	0.997691i	$0.521633\pi$
$972$	14.1420	0.453604
$973$	−0.266475	−0.00854281
$974$	−1.50794	−0.0483174
$975$	−40.5918	−1.29998
$976$	−23.3766	−0.748267
$977$	−45.2491	−1.44765	−0.723823	−	0.689986i	$-0.757617\pi$
$977$	−45.2491	−1.44765	−0.723823	+	0.689986i	$0.757617\pi$
$978$	93.9304	3.00356
$979$	−21.4284	−0.684853
$980$	−5.48177	−0.175109
$981$	7.74509	0.247282
$982$	−60.1085	−1.91814
$983$	34.7682	1.10893	0.554467	−	0.832206i	$-0.312922\pi$
$983$	34.7682	1.10893	0.554467	+	0.832206i	$0.312922\pi$
$984$	−9.80932	−0.312710
$985$	7.40695	0.236005
$986$	−7.53940	−0.240103
$987$	1.52471	0.0485319
$988$	9.10111	0.289545
$989$	−41.1846	−1.30959
$990$	−27.0050	−0.858274
$991$	−36.8806	−1.17155	−0.585775	−	0.810474i	$-0.699210\pi$
$991$	−36.8806	−1.17155	−0.585775	+	0.810474i	$0.699210\pi$
$992$	−43.1198	−1.36905
$993$	50.1169	1.59041
$994$	−5.08781	−0.161376
$995$	−19.7741	−0.626882
$996$	−8.50075	−0.269357
$997$	15.5948	0.493891	0.246945	−	0.969029i	$-0.420573\pi$
$997$	15.5948	0.493891	0.246945	+	0.969029i	$0.420573\pi$
$998$	−33.3844	−1.05677
$999$	3.75531	0.118813

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.a.1.27	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.a.1.27	✓	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)

\(f(q)\)	\(=\)	\(q-1.65282 q^{2} -2.71518 q^{3} +0.731828 q^{4} +1.07828 q^{5} +4.48771 q^{6} +0.230773 q^{7} +2.09607 q^{8} +4.37219 q^{9} +O(q^{10})\)	\(q-1.65282 q^{2} -2.71518 q^{3} +0.731828 q^{4} +1.07828 q^{5} +4.48771 q^{6} +0.230773 q^{7} +2.09607 q^{8} +4.37219 q^{9} -1.78220 q^{10} +3.46567 q^{11} -1.98704 q^{12} -3.89594 q^{13} -0.381428 q^{14} -2.92771 q^{15} -4.92808 q^{16} +2.48804 q^{17} -7.22646 q^{18} -3.19208 q^{19} +0.789113 q^{20} -0.626590 q^{21} -5.72815 q^{22} +6.87861 q^{23} -5.69119 q^{24} -3.83732 q^{25} +6.43930 q^{26} -3.72574 q^{27} +0.168886 q^{28} +1.83338 q^{29} +4.83899 q^{30} -10.9078 q^{31} +3.95313 q^{32} -9.40992 q^{33} -4.11230 q^{34} +0.248837 q^{35} +3.19969 q^{36} -1.00794 q^{37} +5.27594 q^{38} +10.5782 q^{39} +2.26014 q^{40} +1.72360 q^{41} +1.03564 q^{42} -5.98734 q^{43} +2.53628 q^{44} +4.71443 q^{45} -11.3691 q^{46} -2.43334 q^{47} +13.3806 q^{48} -6.94674 q^{49} +6.34242 q^{50} -6.75548 q^{51} -2.85116 q^{52} -2.67471 q^{53} +6.15800 q^{54} +3.73695 q^{55} +0.483716 q^{56} +8.66706 q^{57} -3.03025 q^{58} +0.351160 q^{59} -2.14258 q^{60} +4.74355 q^{61} +18.0286 q^{62} +1.00898 q^{63} +3.32234 q^{64} -4.20090 q^{65} +15.5529 q^{66} +14.8935 q^{67} +1.82082 q^{68} -18.6767 q^{69} -0.411284 q^{70} +13.3389 q^{71} +9.16440 q^{72} +3.95972 q^{73} +1.66594 q^{74} +10.4190 q^{75} -2.33605 q^{76} +0.799785 q^{77} -17.4838 q^{78} -5.63832 q^{79} -5.31384 q^{80} -3.00052 q^{81} -2.84880 q^{82} +4.27809 q^{83} -0.458556 q^{84} +2.68280 q^{85} +9.89602 q^{86} -4.97795 q^{87} +7.26428 q^{88} -6.18303 q^{89} -7.79212 q^{90} -0.899078 q^{91} +5.03396 q^{92} +29.6165 q^{93} +4.02188 q^{94} -3.44194 q^{95} -10.7334 q^{96} +9.98300 q^{97} +11.4817 q^{98} +15.1526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) \) 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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