LMFDB - Embedded newform 2671.2.a.a.1.77

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			1.77
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)

$f(q)$	$=$	$q+1.54634 q^{2} -2.06789 q^{3} +0.391158 q^{4} -1.74478 q^{5} -3.19765 q^{6} +1.88754 q^{7} -2.48781 q^{8} +1.27617 q^{9} +O(q^{10})$	\(q+1.54634 q^{2} -2.06789 q^{3} +0.391158 q^{4} -1.74478 q^{5} -3.19765 q^{6} +1.88754 q^{7} -2.48781 q^{8} +1.27617 q^{9} -2.69802 q^{10} -0.306838 q^{11} -0.808872 q^{12} +6.93195 q^{13} +2.91877 q^{14} +3.60801 q^{15} -4.62931 q^{16} +1.31128 q^{17} +1.97338 q^{18} +0.653555 q^{19} -0.682485 q^{20} -3.90322 q^{21} -0.474476 q^{22} -5.94220 q^{23} +5.14452 q^{24} -1.95575 q^{25} +10.7191 q^{26} +3.56470 q^{27} +0.738326 q^{28} -2.01345 q^{29} +5.57920 q^{30} +5.89645 q^{31} -2.18285 q^{32} +0.634508 q^{33} +2.02768 q^{34} -3.29333 q^{35} +0.499183 q^{36} -5.91534 q^{37} +1.01062 q^{38} -14.3345 q^{39} +4.34068 q^{40} +4.28261 q^{41} -6.03569 q^{42} +3.84537 q^{43} -0.120022 q^{44} -2.22663 q^{45} -9.18864 q^{46} -1.38404 q^{47} +9.57290 q^{48} -3.43720 q^{49} -3.02425 q^{50} -2.71158 q^{51} +2.71149 q^{52} -0.851492 q^{53} +5.51222 q^{54} +0.535365 q^{55} -4.69584 q^{56} -1.35148 q^{57} -3.11347 q^{58} -11.8641 q^{59} +1.41130 q^{60} -4.52823 q^{61} +9.11789 q^{62} +2.40881 q^{63} +5.88320 q^{64} -12.0947 q^{65} +0.981163 q^{66} -10.6529 q^{67} +0.512917 q^{68} +12.2878 q^{69} -5.09260 q^{70} -8.42674 q^{71} -3.17486 q^{72} -4.84523 q^{73} -9.14710 q^{74} +4.04427 q^{75} +0.255644 q^{76} -0.579169 q^{77} -22.1660 q^{78} +5.08566 q^{79} +8.07712 q^{80} -11.1999 q^{81} +6.62236 q^{82} -4.28178 q^{83} -1.52678 q^{84} -2.28789 q^{85} +5.94624 q^{86} +4.16359 q^{87} +0.763356 q^{88} +4.34506 q^{89} -3.44312 q^{90} +13.0843 q^{91} -2.32434 q^{92} -12.1932 q^{93} -2.14019 q^{94} -1.14031 q^{95} +4.51390 q^{96} -15.4896 q^{97} -5.31508 q^{98} -0.391577 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.54634	1.09343	0.546713	−	0.837320i	$-0.315879\pi$
$2$	1.54634	1.09343	0.546713	+	0.837320i	$0.315879\pi$
$3$	−2.06789	−1.19390	−0.596948	−	0.802280i	$-0.703620\pi$
$3$	−2.06789	−1.19390	−0.596948	+	0.802280i	$0.703620\pi$
$4$	0.391158	0.195579
$5$	−1.74478	−0.780289	−0.390144	−	0.920754i	$-0.627575\pi$
$5$	−1.74478	−0.780289	−0.390144	+	0.920754i	$0.627575\pi$
$6$	−3.19765	−1.30544
$7$	1.88754	0.713422	0.356711	−	0.934215i	$-0.383898\pi$
$7$	1.88754	0.713422	0.356711	+	0.934215i	$0.383898\pi$
$8$	−2.48781	−0.879574
$9$	1.27617	0.425389
$10$	−2.69802	−0.853187
$11$	−0.306838	−0.0925153	−0.0462576	−	0.998930i	$-0.514730\pi$
$11$	−0.306838	−0.0925153	−0.0462576	+	0.998930i	$0.514730\pi$
$12$	−0.808872	−0.233501
$13$	6.93195	1.92258	0.961289	−	0.275543i	$-0.0888578\pi$
$13$	6.93195	1.92258	0.961289	+	0.275543i	$0.0888578\pi$
$14$	2.91877	0.780074
$15$	3.60801	0.931584
$16$	−4.62931	−1.15733
$17$	1.31128	0.318032	0.159016	−	0.987276i	$-0.449168\pi$
$17$	1.31128	0.318032	0.159016	+	0.987276i	$0.449168\pi$
$18$	1.97338	0.465131
$19$	0.653555	0.149936	0.0749679	−	0.997186i	$-0.476115\pi$
$19$	0.653555	0.149936	0.0749679	+	0.997186i	$0.476115\pi$
$20$	−0.682485	−0.152608
$21$	−3.90322	−0.851752
$22$	−0.474476	−0.101159
$23$	−5.94220	−1.23903	−0.619517	−	0.784983i	$-0.712671\pi$
$23$	−5.94220	−1.23903	−0.619517	+	0.784983i	$0.712671\pi$
$24$	5.14452	1.05012
$25$	−1.95575	−0.391150
$26$	10.7191	2.10219
$27$	3.56470	0.686026
$28$	0.738326	0.139530
$29$	−2.01345	−0.373888	−0.186944	−	0.982371i	$-0.559858\pi$
$29$	−2.01345	−0.373888	−0.186944	+	0.982371i	$0.559858\pi$
$30$	5.57920	1.01862
$31$	5.89645	1.05903	0.529516	−	0.848300i	$-0.322373\pi$
$31$	5.89645	1.05903	0.529516	+	0.848300i	$0.322373\pi$
$32$	−2.18285	−0.385878
$33$	0.634508	0.110454
$34$	2.02768	0.347744
$35$	−3.29333	−0.556675
$36$	0.499183	0.0831972
$37$	−5.91534	−0.972475	−0.486238	−	0.873827i	$-0.661631\pi$
$37$	−5.91534	−0.972475	−0.486238	+	0.873827i	$0.661631\pi$
$38$	1.01062	0.163944
$39$	−14.3345	−2.29536
$40$	4.34068	0.686322
$41$	4.28261	0.668832	0.334416	−	0.942426i	$-0.391461\pi$
$41$	4.28261	0.668832	0.334416	+	0.942426i	$0.391461\pi$
$42$	−6.03569	−0.931327
$43$	3.84537	0.586413	0.293207	−	0.956049i	$-0.405278\pi$
$43$	3.84537	0.586413	0.293207	+	0.956049i	$0.405278\pi$
$44$	−0.120022	−0.0180941
$45$	−2.22663	−0.331926
$46$	−9.18864	−1.35479
$47$	−1.38404	−0.201883	−0.100942	−	0.994892i	$-0.532185\pi$
$47$	−1.38404	−0.201883	−0.100942	+	0.994892i	$0.532185\pi$
$48$	9.57290	1.38173
$49$	−3.43720	−0.491029
$50$	−3.02425	−0.427693
$51$	−2.71158	−0.379697
$52$	2.71149	0.376016
$53$	−0.851492	−0.116961	−0.0584807	−	0.998289i	$-0.518626\pi$
$53$	−0.851492	−0.116961	−0.0584807	+	0.998289i	$0.518626\pi$
$54$	5.51222	0.750119
$55$	0.535365	0.0721886
$56$	−4.69584	−0.627508
$57$	−1.35148	−0.179008
$58$	−3.11347	−0.408819
$59$	−11.8641	−1.54457	−0.772287	−	0.635274i	$-0.780887\pi$
$59$	−11.8641	−1.54457	−0.772287	+	0.635274i	$0.780887\pi$
$60$	1.41130	0.182198
$61$	−4.52823	−0.579780	−0.289890	−	0.957060i	$-0.593619\pi$
$61$	−4.52823	−0.579780	−0.289890	+	0.957060i	$0.593619\pi$
$62$	9.11789	1.15797
$63$	2.40881	0.303482
$64$	5.88320	0.735400
$65$	−12.0947	−1.50017
$66$	0.981163	0.120773
$67$	−10.6529	−1.30146	−0.650731	−	0.759308i	$-0.725537\pi$
$67$	−10.6529	−1.30146	−0.650731	+	0.759308i	$0.725537\pi$
$68$	0.512917	0.0622004
$69$	12.2878	1.47928
$70$	−5.09260	−0.608683
$71$	−8.42674	−1.00007	−0.500035	−	0.866005i	$-0.666680\pi$
$71$	−8.42674	−1.00007	−0.500035	+	0.866005i	$0.666680\pi$
$72$	−3.17486	−0.374161
$73$	−4.84523	−0.567092	−0.283546	−	0.958959i	$-0.591511\pi$
$73$	−4.84523	−0.567092	−0.283546	+	0.958959i	$0.591511\pi$
$74$	−9.14710	−1.06333
$75$	4.04427	0.466992
$76$	0.255644	0.0293243
$77$	−0.579169	−0.0660024
$78$	−22.1660	−2.50980
$79$	5.08566	0.572182	0.286091	−	0.958202i	$-0.407644\pi$
$79$	5.08566	0.572182	0.286091	+	0.958202i	$0.407644\pi$
$80$	8.07712	0.903050
$81$	−11.1999	−1.24443
$82$	6.62236	0.731317
$83$	−4.28178	−0.469987	−0.234993	−	0.971997i	$-0.575507\pi$
$83$	−4.28178	−0.469987	−0.234993	+	0.971997i	$0.575507\pi$
$84$	−1.52678	−0.166585
$85$	−2.28789	−0.248157
$86$	5.94624	0.641199
$87$	4.16359	0.446384
$88$	0.763356	0.0813740
$89$	4.34506	0.460575	0.230288	−	0.973123i	$-0.426033\pi$
$89$	4.34506	0.460575	0.230288	+	0.973123i	$0.426033\pi$
$90$	−3.44312	−0.362936
$91$	13.0843	1.37161
$92$	−2.32434	−0.242329
$93$	−12.1932	−1.26438
$94$	−2.14019	−0.220744
$95$	−1.14031	−0.116993
$96$	4.51390	0.460698
$97$	−15.4896	−1.57273	−0.786367	−	0.617760i	$-0.788040\pi$
$97$	−15.4896	−1.57273	−0.786367	+	0.617760i	$0.788040\pi$
$98$	−5.31508	−0.536904
$99$	−0.391577	−0.0393550
$100$	−0.765007	−0.0765007
$101$	−3.21397	−0.319801	−0.159901	−	0.987133i	$-0.551117\pi$
$101$	−3.21397	−0.319801	−0.159901	+	0.987133i	$0.551117\pi$
$102$	−4.19301	−0.415170
$103$	5.02961	0.495582	0.247791	−	0.968814i	$-0.420295\pi$
$103$	5.02961	0.495582	0.247791	+	0.968814i	$0.420295\pi$
$104$	−17.2454	−1.69105
$105$	6.81025	0.664612
$106$	−1.31669	−0.127889
$107$	−6.65900	−0.643750	−0.321875	−	0.946782i	$-0.604313\pi$
$107$	−6.65900	−0.643750	−0.321875	+	0.946782i	$0.604313\pi$
$108$	1.39436	0.134172
$109$	−13.9433	−1.33553	−0.667763	−	0.744374i	$-0.732748\pi$
$109$	−13.9433	−1.33553	−0.667763	+	0.744374i	$0.732748\pi$
$110$	0.827855	0.0789329
$111$	12.2323	1.16103
$112$	−8.73800	−0.825663
$113$	−2.25942	−0.212549	−0.106274	−	0.994337i	$-0.533892\pi$
$113$	−2.25942	−0.212549	−0.106274	+	0.994337i	$0.533892\pi$
$114$	−2.08984	−0.195732
$115$	10.3678	0.966804
$116$	−0.787578	−0.0731248
$117$	8.84632	0.817843
$118$	−18.3459	−1.68888
$119$	2.47509	0.226891
$120$	−8.97604	−0.819397
$121$	−10.9059	−0.991441
$122$	−7.00216	−0.633946
$123$	−8.85597	−0.798516
$124$	2.30644	0.207125
$125$	12.1362	1.08550
$126$	3.72483	0.331835
$127$	7.24772	0.643131	0.321566	−	0.946887i	$-0.395791\pi$
$127$	7.24772	0.643131	0.321566	+	0.946887i	$0.395791\pi$
$128$	13.4631	1.18998
$129$	−7.95180	−0.700117
$130$	−18.7025	−1.64032
$131$	−8.93833	−0.780946	−0.390473	−	0.920614i	$-0.627688\pi$
$131$	−8.93833	−0.780946	−0.390473	+	0.920614i	$0.627688\pi$
$132$	0.248193	0.0216024
$133$	1.23361	0.106968
$134$	−16.4730	−1.42305
$135$	−6.21961	−0.535298
$136$	−3.26221	−0.279732
$137$	−8.00027	−0.683509	−0.341755	−	0.939789i	$-0.611021\pi$
$137$	−8.00027	−0.683509	−0.341755	+	0.939789i	$0.611021\pi$
$138$	19.0011	1.61748
$139$	11.2435	0.953665	0.476832	−	0.878994i	$-0.341785\pi$
$139$	11.2435	0.953665	0.476832	+	0.878994i	$0.341785\pi$
$140$	−1.28821	−0.108874
$141$	2.86204	0.241027
$142$	−13.0306	−1.09350
$143$	−2.12699	−0.177868
$144$	−5.90777	−0.492314
$145$	3.51303	0.291741
$146$	−7.49237	−0.620073
$147$	7.10776	0.586238
$148$	−2.31383	−0.190196
$149$	−7.78725	−0.637956	−0.318978	−	0.947762i	$-0.603340\pi$
$149$	−7.78725	−0.637956	−0.318978	+	0.947762i	$0.603340\pi$
$150$	6.25381	0.510621
$151$	−14.0095	−1.14008	−0.570038	−	0.821618i	$-0.693072\pi$
$151$	−14.0095	−1.14008	−0.570038	+	0.821618i	$0.693072\pi$
$152$	−1.62592	−0.131880
$153$	1.67341	0.135287
$154$	−0.895590	−0.0721687
$155$	−10.2880	−0.826351
$156$	−5.60706	−0.448924
$157$	−18.5373	−1.47943	−0.739717	−	0.672918i	$-0.765041\pi$
$157$	−18.5373	−1.47943	−0.739717	+	0.672918i	$0.765041\pi$
$158$	7.86415	0.625638
$159$	1.76079	0.139640
$160$	3.80860	0.301096
$161$	−11.2161	−0.883954
$162$	−17.3188	−1.36069
$163$	18.1687	1.42308	0.711541	−	0.702645i	$-0.247998\pi$
$163$	18.1687	1.42308	0.711541	+	0.702645i	$0.247998\pi$
$164$	1.67518	0.130810
$165$	−1.10708	−0.0861857
$166$	−6.62108	−0.513895
$167$	−21.0059	−1.62548	−0.812741	−	0.582625i	$-0.802026\pi$
$167$	−21.0059	−1.62548	−0.812741	+	0.582625i	$0.802026\pi$
$168$	9.71047	0.749179
$169$	35.0519	2.69630
$170$	−3.53785	−0.271341
$171$	0.834045	0.0637810
$172$	1.50415	0.114690
$173$	−11.5862	−0.880881	−0.440441	−	0.897782i	$-0.645178\pi$
$173$	−11.5862	−0.880881	−0.440441	+	0.897782i	$0.645178\pi$
$174$	6.43832	0.488088
$175$	−3.69155	−0.279055
$176$	1.42045	0.107071
$177$	24.5336	1.84406
$178$	6.71892	0.503605
$179$	17.0024	1.27082	0.635410	−	0.772175i	$-0.280831\pi$
$179$	17.0024	1.27082	0.635410	+	0.772175i	$0.280831\pi$
$180$	−0.870964	−0.0649178
$181$	18.7169	1.39122	0.695609	−	0.718421i	$-0.255135\pi$
$181$	18.7169	1.39122	0.695609	+	0.718421i	$0.255135\pi$
$182$	20.2328	1.49975
$183$	9.36387	0.692197
$184$	14.7831	1.08982
$185$	10.3210	0.758811
$186$	−18.8548	−1.38250
$187$	−0.402351	−0.0294228
$188$	−0.541379	−0.0394841
$189$	6.72850	0.489426
$190$	−1.76330	−0.127923
$191$	5.60366	0.405467	0.202733	−	0.979234i	$-0.435018\pi$
$191$	5.60366	0.405467	0.202733	+	0.979234i	$0.435018\pi$
$192$	−12.1658	−0.877991
$193$	27.0590	1.94775	0.973874	−	0.227090i	$-0.0729212\pi$
$193$	27.0590	1.94775	0.973874	+	0.227090i	$0.0729212\pi$
$194$	−23.9522	−1.71967
$195$	25.0105	1.79104
$196$	−1.34449	−0.0960351
$197$	−1.26863	−0.0903864	−0.0451932	−	0.998978i	$-0.514390\pi$
$197$	−1.26863	−0.0903864	−0.0451932	+	0.998978i	$0.514390\pi$
$198$	−0.605510	−0.0430317
$199$	−10.0839	−0.714830	−0.357415	−	0.933946i	$-0.616342\pi$
$199$	−10.0839	−0.714830	−0.357415	+	0.933946i	$0.616342\pi$
$200$	4.86553	0.344045
$201$	22.0291	1.55381
$202$	−4.96987	−0.349679
$203$	−3.80046	−0.266740
$204$	−1.06066	−0.0742608
$205$	−7.47221	−0.521882
$206$	7.77747	0.541882
$207$	−7.58323	−0.527071
$208$	−32.0902	−2.22505
$209$	−0.200536	−0.0138714
$210$	10.5309	0.726704
$211$	10.1374	0.697889	0.348944	−	0.937143i	$-0.386540\pi$
$211$	10.1374	0.697889	0.348944	+	0.937143i	$0.386540\pi$
$212$	−0.333068	−0.0228752
$213$	17.4256	1.19398
$214$	−10.2971	−0.703893
$215$	−6.70932	−0.457572
$216$	−8.86829	−0.603411
$217$	11.1298	0.755537
$218$	−21.5611	−1.46030
$219$	10.0194	0.677049
$220$	0.209412	0.0141186
$221$	9.08972	0.611441
$222$	18.9152	1.26951
$223$	0.403780	0.0270391	0.0135195	−	0.999909i	$-0.495696\pi$
$223$	0.403780	0.0270391	0.0135195	+	0.999909i	$0.495696\pi$
$224$	−4.12022	−0.275294
$225$	−2.49586	−0.166391
$226$	−3.49383	−0.232406
$227$	5.43465	0.360711	0.180355	−	0.983602i	$-0.442275\pi$
$227$	5.43465	0.360711	0.180355	+	0.983602i	$0.442275\pi$
$228$	−0.528643	−0.0350102
$229$	9.48203	0.626590	0.313295	−	0.949656i	$-0.398567\pi$
$229$	9.48203	0.626590	0.313295	+	0.949656i	$0.398567\pi$
$230$	16.0321	1.05713
$231$	1.19766	0.0788001
$232$	5.00909	0.328863
$233$	12.2180	0.800429	0.400215	−	0.916421i	$-0.368936\pi$
$233$	12.2180	0.800429	0.400215	+	0.916421i	$0.368936\pi$
$234$	13.6794	0.894250
$235$	2.41484	0.157527
$236$	−4.64074	−0.302087
$237$	−10.5166	−0.683126
$238$	3.82732	0.248088
$239$	5.41421	0.350216	0.175108	−	0.984549i	$-0.443973\pi$
$239$	5.41421	0.350216	0.175108	+	0.984549i	$0.443973\pi$
$240$	−16.7026	−1.07815
$241$	−20.4055	−1.31443	−0.657216	−	0.753703i	$-0.728266\pi$
$241$	−20.4055	−1.31443	−0.657216	+	0.753703i	$0.728266\pi$
$242$	−16.8641	−1.08407
$243$	12.4661	0.799698
$244$	−1.77125	−0.113393
$245$	5.99716	0.383144
$246$	−13.6943	−0.873117
$247$	4.53041	0.288263
$248$	−14.6692	−0.931498
$249$	8.85425	0.561115
$250$	18.7667	1.18691
$251$	−13.7351	−0.866951	−0.433476	−	0.901165i	$-0.642713\pi$
$251$	−13.7351	−0.866951	−0.433476	+	0.901165i	$0.642713\pi$
$252$	0.942227	0.0593547
$253$	1.82329	0.114630
$254$	11.2074	0.703216
$255$	4.73110	0.296273
$256$	9.05212	0.565757
$257$	−31.3823	−1.95758	−0.978788	−	0.204877i	$-0.934321\pi$
$257$	−31.3823	−1.95758	−0.978788	+	0.204877i	$0.934321\pi$
$258$	−12.2962	−0.765525
$259$	−11.1654	−0.693785
$260$	−4.73095	−0.293401
$261$	−2.56950	−0.159048
$262$	−13.8217	−0.853906
$263$	−3.95361	−0.243790	−0.121895	−	0.992543i	$-0.538897\pi$
$263$	−3.95361	−0.243790	−0.121895	+	0.992543i	$0.538897\pi$
$264$	−1.57854	−0.0971522
$265$	1.48567	0.0912637
$266$	1.90758	0.116961
$267$	−8.98510	−0.549879
$268$	−4.16698	−0.254539
$269$	17.6431	1.07572	0.537858	−	0.843035i	$-0.319234\pi$
$269$	17.6431	1.07572	0.537858	+	0.843035i	$0.319234\pi$
$270$	−9.61761	−0.585309
$271$	11.4826	0.697520	0.348760	−	0.937212i	$-0.386603\pi$
$271$	11.4826	0.697520	0.348760	+	0.937212i	$0.386603\pi$
$272$	−6.07032	−0.368067
$273$	−27.0569	−1.63756
$274$	−12.3711	−0.747367
$275$	0.600099	0.0361873
$276$	4.80648	0.289316
$277$	2.30131	0.138272	0.0691361	−	0.997607i	$-0.477976\pi$
$277$	2.30131	0.138272	0.0691361	+	0.997607i	$0.477976\pi$
$278$	17.3863	1.04276
$279$	7.52485	0.450501
$280$	8.19319	0.489637
$281$	−21.7173	−1.29554	−0.647771	−	0.761835i	$-0.724299\pi$
$281$	−21.7173	−1.29554	−0.647771	+	0.761835i	$0.724299\pi$
$282$	4.42568	0.263546
$283$	3.51888	0.209176	0.104588	−	0.994516i	$-0.466648\pi$
$283$	3.51888	0.209176	0.104588	+	0.994516i	$0.466648\pi$
$284$	−3.29619	−0.195593
$285$	2.35803	0.139678
$286$	−3.28904	−0.194485
$287$	8.08359	0.477159
$288$	−2.78568	−0.164148
$289$	−15.2805	−0.898856
$290$	5.43232	0.318997
$291$	32.0308	1.87768
$292$	−1.89525	−0.110911
$293$	16.2308	0.948213	0.474106	−	0.880468i	$-0.342771\pi$
$293$	16.2308	0.948213	0.474106	+	0.880468i	$0.342771\pi$
$294$	10.9910	0.641007
$295$	20.7002	1.20521
$296$	14.7162	0.855364
$297$	−1.09379	−0.0634679
$298$	−12.0417	−0.697558
$299$	−41.1910	−2.38214
$300$	1.58195	0.0913340
$301$	7.25828	0.418360
$302$	−21.6634	−1.24659
$303$	6.64612	0.381810
$304$	−3.02551	−0.173525
$305$	7.90075	0.452396
$306$	2.58765	0.147926
$307$	−32.0036	−1.82654	−0.913270	−	0.407355i	$-0.866451\pi$
$307$	−32.0036	−1.82654	−0.913270	+	0.407355i	$0.866451\pi$
$308$	−0.226547	−0.0129087
$309$	−10.4007	−0.591674
$310$	−15.9087	−0.903554
$311$	−13.6399	−0.773446	−0.386723	−	0.922196i	$-0.626393\pi$
$311$	−13.6399	−0.773446	−0.386723	+	0.922196i	$0.626393\pi$
$312$	35.6616	2.01894
$313$	19.6809	1.11243	0.556216	−	0.831037i	$-0.312253\pi$
$313$	19.6809	1.11243	0.556216	+	0.831037i	$0.312253\pi$
$314$	−28.6649	−1.61765
$315$	−4.20284	−0.236803
$316$	1.98930	0.111907
$317$	−6.89761	−0.387408	−0.193704	−	0.981060i	$-0.562050\pi$
$317$	−6.89761	−0.387408	−0.193704	+	0.981060i	$0.562050\pi$
$318$	2.72278	0.152686
$319$	0.617804	0.0345904
$320$	−10.2649	−0.573824
$321$	13.7701	0.768571
$322$	−17.3439	−0.966538
$323$	0.856993	0.0476844
$324$	−4.38093	−0.243385
$325$	−13.5572	−0.752016
$326$	28.0949	1.55603
$327$	28.8332	1.59448
$328$	−10.6543	−0.588287
$329$	−2.61243	−0.144028
$330$	−1.71191	−0.0942377
$331$	27.0144	1.48485	0.742423	−	0.669932i	$-0.233677\pi$
$331$	27.0144	1.48485	0.742423	+	0.669932i	$0.233677\pi$
$332$	−1.67485	−0.0919196
$333$	−7.54895	−0.413680
$334$	−32.4821	−1.77734
$335$	18.5870	1.01552
$336$	18.0692	0.985756
$337$	6.25499	0.340731	0.170366	−	0.985381i	$-0.445505\pi$
$337$	6.25499	0.340731	0.170366	+	0.985381i	$0.445505\pi$
$338$	54.2021	2.94821
$339$	4.67224	0.253761
$340$	−0.894927	−0.0485342
$341$	−1.80926	−0.0979767
$342$	1.28971	0.0697398
$343$	−19.7006	−1.06373
$344$	−9.56655	−0.515794
$345$	−21.4395	−1.15426
$346$	−17.9161	−0.963178
$347$	4.78370	0.256803	0.128401	−	0.991722i	$-0.459015\pi$
$347$	4.78370	0.256803	0.128401	+	0.991722i	$0.459015\pi$
$348$	1.62862	0.0873034
$349$	2.56423	0.137260	0.0686301	−	0.997642i	$-0.478137\pi$
$349$	2.56423	0.137260	0.0686301	+	0.997642i	$0.478137\pi$
$350$	−5.70838	−0.305126
$351$	24.7103	1.31894
$352$	0.669783	0.0356996
$353$	−6.02872	−0.320876	−0.160438	−	0.987046i	$-0.551291\pi$
$353$	−6.02872	−0.320876	−0.160438	+	0.987046i	$0.551291\pi$
$354$	37.9373	2.01634
$355$	14.7028	0.780343
$356$	1.69961	0.0900789
$357$	−5.11821	−0.270884
$358$	26.2914	1.38955
$359$	−2.93649	−0.154982	−0.0774909	−	0.996993i	$-0.524691\pi$
$359$	−2.93649	−0.154982	−0.0774909	+	0.996993i	$0.524691\pi$
$360$	5.53943	0.291954
$361$	−18.5729	−0.977519
$362$	28.9427	1.52119
$363$	22.5521	1.18368
$364$	5.11804	0.268258
$365$	8.45386	0.442495
$366$	14.4797	0.756866
$367$	20.4948	1.06982	0.534911	−	0.844908i	$-0.320345\pi$
$367$	20.4948	1.06982	0.534911	+	0.844908i	$0.320345\pi$
$368$	27.5083	1.43397
$369$	5.46532	0.284513
$370$	15.9597	0.829704
$371$	−1.60722	−0.0834429
$372$	−4.76947	−0.247286
$373$	22.8550	1.18339	0.591693	−	0.806163i	$-0.298460\pi$
$373$	22.8550	1.18339	0.591693	+	0.806163i	$0.298460\pi$
$374$	−0.622170	−0.0321716
$375$	−25.0964	−1.29597
$376$	3.44323	0.177571
$377$	−13.9571	−0.718830
$378$	10.4045	0.535151
$379$	19.5355	1.00347	0.501735	−	0.865021i	$-0.332695\pi$
$379$	19.5355	1.00347	0.501735	+	0.865021i	$0.332695\pi$
$380$	−0.446041	−0.0228814
$381$	−14.9875	−0.767832
$382$	8.66515	0.443348
$383$	−16.8779	−0.862419	−0.431209	−	0.902252i	$-0.641913\pi$
$383$	−16.8779	−0.862419	−0.431209	+	0.902252i	$0.641913\pi$
$384$	−27.8402	−1.42072
$385$	1.01052	0.0515009
$386$	41.8423	2.12972
$387$	4.90733	0.249454
$388$	−6.05890	−0.307594
$389$	−2.87767	−0.145904	−0.0729519	−	0.997335i	$-0.523242\pi$
$389$	−2.87767	−0.145904	−0.0729519	+	0.997335i	$0.523242\pi$
$390$	38.6747	1.95837
$391$	−7.79187	−0.394052
$392$	8.55111	0.431896
$393$	18.4835	0.932368
$394$	−1.96173	−0.0988308
$395$	−8.87335	−0.446467
$396$	−0.153169	−0.00769701
$397$	−36.9782	−1.85588	−0.927941	−	0.372728i	$-0.878422\pi$
$397$	−36.9782	−1.85588	−0.927941	+	0.372728i	$0.878422\pi$
$398$	−15.5931	−0.781613
$399$	−2.55097	−0.127708
$400$	9.05377	0.452689
$401$	−7.19062	−0.359082	−0.179541	−	0.983750i	$-0.557461\pi$
$401$	−7.19062	−0.359082	−0.179541	+	0.983750i	$0.557461\pi$
$402$	34.0644	1.69898
$403$	40.8739	2.03607
$404$	−1.25717	−0.0625465
$405$	19.5413	0.971017
$406$	−5.87680	−0.291661
$407$	1.81505	0.0899688
$408$	6.74590	0.333972
$409$	−8.54008	−0.422280	−0.211140	−	0.977456i	$-0.567718\pi$
$409$	−8.54008	−0.422280	−0.211140	+	0.977456i	$0.567718\pi$
$410$	−11.5546	−0.570639
$411$	16.5437	0.816040
$412$	1.96737	0.0969255
$413$	−22.3939	−1.10193
$414$	−11.7262	−0.576313
$415$	7.47076	0.366725
$416$	−15.1314	−0.741880
$417$	−23.2504	−1.13858
$418$	−0.310096	−0.0151673
$419$	−28.2122	−1.37826	−0.689129	−	0.724638i	$-0.742007\pi$
$419$	−28.2122	−1.37826	−0.689129	+	0.724638i	$0.742007\pi$
$420$	2.66389	0.129984
$421$	−15.5860	−0.759614	−0.379807	−	0.925066i	$-0.624010\pi$
$421$	−15.5860	−0.759614	−0.379807	+	0.925066i	$0.624010\pi$
$422$	15.6759	0.763089
$423$	−1.76627	−0.0858788
$424$	2.11835	0.102876
$425$	−2.56453	−0.124398
$426$	26.9458	1.30553
$427$	−8.54720	−0.413628
$428$	−2.60472	−0.125904
$429$	4.39838	0.212356
$430$	−10.3749	−0.500320
$431$	−28.6596	−1.38048	−0.690242	−	0.723579i	$-0.742496\pi$
$431$	−28.6596	−1.38048	−0.690242	+	0.723579i	$0.742496\pi$
$432$	−16.5021	−0.793957
$433$	19.0016	0.913160	0.456580	−	0.889682i	$-0.349074\pi$
$433$	19.0016	0.913160	0.456580	+	0.889682i	$0.349074\pi$
$434$	17.2104	0.826124
$435$	−7.26455	−0.348308
$436$	−5.45404	−0.261201
$437$	−3.88355	−0.185776
$438$	15.4934	0.740302
$439$	36.4304	1.73873	0.869363	−	0.494174i	$-0.164529\pi$
$439$	36.4304	1.73873	0.869363	+	0.494174i	$0.164529\pi$
$440$	−1.33189	−0.0634952
$441$	−4.38644	−0.208878
$442$	14.0558	0.668565
$443$	−12.8194	−0.609066	−0.304533	−	0.952502i	$-0.598500\pi$
$443$	−12.8194	−0.609066	−0.304533	+	0.952502i	$0.598500\pi$
$444$	4.78475	0.227074
$445$	−7.58116	−0.359382
$446$	0.624380	0.0295652
$447$	16.1032	0.761654
$448$	11.1048	0.524650
$449$	−23.0578	−1.08816	−0.544082	−	0.839032i	$-0.683122\pi$
$449$	−23.0578	−1.08816	−0.544082	+	0.839032i	$0.683122\pi$
$450$	−3.85944	−0.181936
$451$	−1.31407	−0.0618771
$452$	−0.883792	−0.0415701
$453$	28.9701	1.36113
$454$	8.40381	0.394410
$455$	−22.8292	−1.07025
$456$	3.36223	0.157451
$457$	−37.3515	−1.74723	−0.873616	−	0.486616i	$-0.838231\pi$
$457$	−37.3515	−1.74723	−0.873616	+	0.486616i	$0.838231\pi$
$458$	14.6624	0.685130
$459$	4.67431	0.218178
$460$	4.05546	0.189087
$461$	17.1255	0.797614	0.398807	−	0.917035i	$-0.369424\pi$
$461$	17.1255	0.797614	0.398807	+	0.917035i	$0.369424\pi$
$462$	1.85198	0.0861620
$463$	−17.6626	−0.820853	−0.410426	−	0.911894i	$-0.634620\pi$
$463$	−17.6626	−0.820853	−0.410426	+	0.911894i	$0.634620\pi$
$464$	9.32089	0.432712
$465$	21.2744	0.986578
$466$	18.8932	0.875209
$467$	−20.0938	−0.929829	−0.464914	−	0.885356i	$-0.653915\pi$
$467$	−20.0938	−0.929829	−0.464914	+	0.885356i	$0.653915\pi$
$468$	3.46031	0.159953
$469$	−20.1078	−0.928492
$470$	3.73416	0.172244
$471$	38.3330	1.76629
$472$	29.5156	1.35857
$473$	−1.17991	−0.0542522
$474$	−16.2622	−0.746947
$475$	−1.27819	−0.0586474
$476$	0.968151	0.0443751
$477$	−1.08665	−0.0497541
$478$	8.37219	0.382935
$479$	−25.6946	−1.17402	−0.587009	−	0.809580i	$-0.699695\pi$
$479$	−25.6946	−1.17402	−0.587009	+	0.809580i	$0.699695\pi$
$480$	−7.87575	−0.359477
$481$	−41.0048	−1.86966
$482$	−31.5537	−1.43723
$483$	23.1937	1.05535
$484$	−4.26591	−0.193905
$485$	27.0260	1.22719
$486$	19.2767	0.874410
$487$	−16.6057	−0.752476	−0.376238	−	0.926523i	$-0.622782\pi$
$487$	−16.6057	−0.752476	−0.376238	+	0.926523i	$0.622782\pi$
$488$	11.2654	0.509960
$489$	−37.5708	−1.69901
$490$	9.27363	0.418940
$491$	40.1429	1.81162	0.905811	−	0.423682i	$-0.139262\pi$
$491$	40.1429	1.81162	0.905811	+	0.423682i	$0.139262\pi$
$492$	−3.46409	−0.156173
$493$	−2.64019	−0.118908
$494$	7.00554	0.315194
$495$	0.683215	0.0307082
$496$	−27.2965	−1.22565
$497$	−15.9058	−0.713472
$498$	13.6917	0.613538
$499$	29.3810	1.31527	0.657637	−	0.753335i	$-0.271556\pi$
$499$	29.3810	1.31527	0.657637	+	0.753335i	$0.271556\pi$
$500$	4.74719	0.212301
$501$	43.4378	1.94066
$502$	−21.2391	−0.947946
$503$	14.7931	0.659593	0.329797	−	0.944052i	$-0.393020\pi$
$503$	14.7931	0.659593	0.329797	+	0.944052i	$0.393020\pi$
$504$	−5.99267	−0.266935
$505$	5.60766	0.249537
$506$	2.81943	0.125339
$507$	−72.4835	−3.21911
$508$	2.83501	0.125783
$509$	19.3280	0.856697	0.428348	−	0.903614i	$-0.359096\pi$
$509$	19.3280	0.856697	0.428348	+	0.903614i	$0.359096\pi$
$510$	7.31588	0.323953
$511$	−9.14556	−0.404576
$512$	−12.9286	−0.571369
$513$	2.32973	0.102860
$514$	−48.5276	−2.14046
$515$	−8.77555	−0.386697
$516$	−3.11041	−0.136928
$517$	0.424677	0.0186773
$518$	−17.2655	−0.758602
$519$	23.9589	1.05168
$520$	30.0894	1.31951
$521$	30.1875	1.32254	0.661269	−	0.750148i	$-0.270018\pi$
$521$	30.1875	1.32254	0.661269	+	0.750148i	$0.270018\pi$
$522$	−3.97331	−0.173907
$523$	0.668091	0.0292136	0.0146068	−	0.999893i	$-0.495350\pi$
$523$	0.668091	0.0292136	0.0146068	+	0.999893i	$0.495350\pi$
$524$	−3.49630	−0.152737
$525$	7.63371	0.333163
$526$	−6.11362	−0.266567
$527$	7.73188	0.336806
$528$	−2.93734	−0.127831
$529$	12.3097	0.535204
$530$	2.29734	0.0997900
$531$	−15.1406	−0.657045
$532$	0.482537	0.0209206
$533$	29.6869	1.28588
$534$	−13.8940	−0.601252
$535$	11.6185	0.502311
$536$	26.5025	1.14473
$537$	−35.1591	−1.51723
$538$	27.2821	1.17622
$539$	1.05467	0.0454277
$540$	−2.43285	−0.104693
$541$	−24.4499	−1.05118	−0.525592	−	0.850737i	$-0.676156\pi$
$541$	−24.4499	−1.05118	−0.525592	+	0.850737i	$0.676156\pi$
$542$	17.7560	0.762686
$543$	−38.7045	−1.66097
$544$	−2.86233	−0.122721
$545$	24.3280	1.04210
$546$	−41.8391	−1.79055
$547$	−23.5462	−1.00676	−0.503381	−	0.864065i	$-0.667911\pi$
$547$	−23.5462	−1.00676	−0.503381	+	0.864065i	$0.667911\pi$
$548$	−3.12937	−0.133680
$549$	−5.77877	−0.246632
$550$	0.927955	0.0395681
$551$	−1.31590	−0.0560593
$552$	−30.5697	−1.30113
$553$	9.59938	0.408207
$554$	3.55860	0.151190
$555$	−21.3426	−0.905942
$556$	4.39801	0.186517
$557$	−30.5579	−1.29478	−0.647389	−	0.762160i	$-0.724139\pi$
$557$	−30.5579	−1.29478	−0.647389	+	0.762160i	$0.724139\pi$
$558$	11.6359	0.492589
$559$	26.6559	1.12742
$560$	15.2459	0.644256
$561$	0.832017	0.0351278
$562$	−33.5822	−1.41658
$563$	18.1586	0.765292	0.382646	−	0.923895i	$-0.375013\pi$
$563$	18.1586	0.765292	0.382646	+	0.923895i	$0.375013\pi$
$564$	1.11951	0.0471399
$565$	3.94219	0.165849
$566$	5.44137	0.228718
$567$	−21.1402	−0.887806
$568$	20.9641	0.879636
$569$	6.02685	0.252659	0.126329	−	0.991988i	$-0.459680\pi$
$569$	6.02685	0.252659	0.126329	+	0.991988i	$0.459680\pi$
$570$	3.64631	0.152727
$571$	−4.70262	−0.196798	−0.0983992	−	0.995147i	$-0.531372\pi$
$571$	−4.70262	−0.196798	−0.0983992	+	0.995147i	$0.531372\pi$
$572$	−0.831989	−0.0347872
$573$	−11.5878	−0.484085
$574$	12.5000	0.521738
$575$	11.6214	0.484648
$576$	7.50794	0.312831
$577$	2.08344	0.0867347	0.0433674	−	0.999059i	$-0.486191\pi$
$577$	2.08344	0.0867347	0.0433674	+	0.999059i	$0.486191\pi$
$578$	−23.6289	−0.982832
$579$	−55.9550	−2.32541
$580$	1.37415	0.0570584
$581$	−8.08202	−0.335299
$582$	49.5305	2.05310
$583$	0.261271	0.0108207
$584$	12.0540	0.498799
$585$	−15.4349	−0.638153
$586$	25.0983	1.03680
$587$	30.4920	1.25854	0.629269	−	0.777187i	$-0.283354\pi$
$587$	30.4920	1.25854	0.629269	+	0.777187i	$0.283354\pi$
$588$	2.78026	0.114656
$589$	3.85365	0.158787
$590$	32.0095	1.31781
$591$	2.62339	0.107912
$592$	27.3839	1.12547
$593$	−36.3521	−1.49280	−0.746401	−	0.665497i	$-0.768220\pi$
$593$	−36.3521	−1.49280	−0.746401	+	0.665497i	$0.768220\pi$
$594$	−1.69136	−0.0693974
$595$	−4.31848	−0.177040
$596$	−3.04605	−0.124771
$597$	20.8524	0.853433
$598$	−63.6952	−2.60469
$599$	28.1285	1.14930	0.574650	−	0.818399i	$-0.305138\pi$
$599$	28.1285	1.14930	0.574650	+	0.818399i	$0.305138\pi$
$600$	−10.0614	−0.410754
$601$	4.46493	0.182128	0.0910641	−	0.995845i	$-0.470973\pi$
$601$	4.46493	0.182128	0.0910641	+	0.995845i	$0.470973\pi$
$602$	11.2237	0.457446
$603$	−13.5949	−0.553627
$604$	−5.47993	−0.222975
$605$	19.0283	0.773610
$606$	10.2771	0.417481
$607$	4.19870	0.170420	0.0852101	−	0.996363i	$-0.472844\pi$
$607$	4.19870	0.170420	0.0852101	+	0.996363i	$0.472844\pi$
$608$	−1.42662	−0.0578569
$609$	7.85894	0.318460
$610$	12.2172	0.494661
$611$	−9.59410	−0.388136
$612$	0.654568	0.0264593
$613$	13.8745	0.560385	0.280192	−	0.959944i	$-0.409602\pi$
$613$	13.8745	0.560385	0.280192	+	0.959944i	$0.409602\pi$
$614$	−49.4883	−1.99719
$615$	15.4517	0.623073
$616$	1.44086	0.0580540
$617$	−22.7532	−0.916009	−0.458004	−	0.888950i	$-0.651436\pi$
$617$	−22.7532	−0.916009	−0.458004	+	0.888950i	$0.651436\pi$
$618$	−16.0829	−0.646951
$619$	36.6726	1.47400	0.736998	−	0.675895i	$-0.236243\pi$
$619$	36.6726	1.47400	0.736998	+	0.675895i	$0.236243\pi$
$620$	−4.02423	−0.161617
$621$	−21.1821	−0.850010
$622$	−21.0918	−0.845706
$623$	8.20146	0.328585
$624$	66.3589	2.65648
$625$	−11.3963	−0.455852
$626$	30.4334	1.21636
$627$	0.414686	0.0165610
$628$	−7.25100	−0.289347
$629$	−7.75665	−0.309278
$630$	−6.49901	−0.258927
$631$	−13.3893	−0.533019	−0.266510	−	0.963832i	$-0.585870\pi$
$631$	−13.3893	−0.533019	−0.266510	+	0.963832i	$0.585870\pi$
$632$	−12.6522	−0.503276
$633$	−20.9631	−0.833207
$634$	−10.6660	−0.423602
$635$	−12.6457	−0.501828
$636$	0.688748	0.0273106
$637$	−23.8265	−0.944041
$638$	0.955334	0.0378220
$639$	−10.7539	−0.425419
$640$	−23.4901	−0.928529
$641$	33.4324	1.32050	0.660249	−	0.751046i	$-0.270451\pi$
$641$	33.4324	1.32050	0.660249	+	0.751046i	$0.270451\pi$
$642$	21.2932	0.840375
$643$	−15.1303	−0.596679	−0.298340	−	0.954460i	$-0.596433\pi$
$643$	−15.1303	−0.596679	−0.298340	+	0.954460i	$0.596433\pi$
$644$	−4.38728	−0.172883
$645$	13.8741	0.546293
$646$	1.32520	0.0521393
$647$	46.7258	1.83698	0.918491	−	0.395441i	$-0.129408\pi$
$647$	46.7258	1.83698	0.918491	+	0.395441i	$0.129408\pi$
$648$	27.8632	1.09457
$649$	3.64036	0.142897
$650$	−20.9639	−0.822273
$651$	−23.0151	−0.902033
$652$	7.10684	0.278325
$653$	−5.52883	−0.216360	−0.108180	−	0.994131i	$-0.534502\pi$
$653$	−5.52883	−0.216360	−0.108180	+	0.994131i	$0.534502\pi$
$654$	44.5859	1.74345
$655$	15.5954	0.609363
$656$	−19.8255	−0.774057
$657$	−6.18332	−0.241234
$658$	−4.03969	−0.157484
$659$	8.62487	0.335977	0.167989	−	0.985789i	$-0.446273\pi$
$659$	8.62487	0.335977	0.167989	+	0.985789i	$0.446273\pi$
$660$	−0.433042	−0.0168561
$661$	10.8481	0.421942	0.210971	−	0.977492i	$-0.432337\pi$
$661$	10.8481	0.421942	0.210971	+	0.977492i	$0.432337\pi$
$662$	41.7734	1.62357
$663$	−18.7965	−0.729997
$664$	10.6523	0.413388
$665$	−2.15238	−0.0834655
$666$	−11.6732	−0.452328
$667$	11.9643	0.463260
$668$	−8.21661	−0.317910
$669$	−0.834972	−0.0322819
$670$	28.7418	1.11039
$671$	1.38943	0.0536385
$672$	8.52015	0.328672
$673$	−21.1870	−0.816701	−0.408350	−	0.912825i	$-0.633896\pi$
$673$	−21.1870	−0.816701	−0.408350	+	0.912825i	$0.633896\pi$
$674$	9.67232	0.372564
$675$	−6.97165	−0.268339
$676$	13.7109	0.527341
$677$	−14.3655	−0.552112	−0.276056	−	0.961142i	$-0.589028\pi$
$677$	−14.3655	−0.552112	−0.276056	+	0.961142i	$0.589028\pi$
$678$	7.22485	0.277469
$679$	−29.2373	−1.12202
$680$	5.69184	0.218272
$681$	−11.2383	−0.430651
$682$	−2.79772	−0.107130
$683$	28.5575	1.09272	0.546360	−	0.837550i	$-0.316013\pi$
$683$	28.5575	1.09272	0.546360	+	0.837550i	$0.316013\pi$
$684$	0.326244	0.0124742
$685$	13.9587	0.533335
$686$	−30.4638	−1.16311
$687$	−19.6078	−0.748084
$688$	−17.8014	−0.678672
$689$	−5.90250	−0.224867
$690$	−33.1527	−1.26210
$691$	−40.7068	−1.54856	−0.774280	−	0.632843i	$-0.781888\pi$
$691$	−40.7068	−1.54856	−0.774280	+	0.632843i	$0.781888\pi$
$692$	−4.53203	−0.172282
$693$	−0.739116	−0.0280767
$694$	7.39722	0.280795
$695$	−19.6175	−0.744134
$696$	−10.3582	−0.392628
$697$	5.61570	0.212710
$698$	3.96517	0.150084
$699$	−25.2655	−0.955629
$700$	−1.44398	−0.0545773
$701$	−37.2962	−1.40866	−0.704330	−	0.709873i	$-0.748752\pi$
$701$	−37.2962	−1.40866	−0.704330	+	0.709873i	$0.748752\pi$
$702$	38.2105	1.44216
$703$	−3.86600	−0.145809
$704$	−1.80519	−0.0680357
$705$	−4.99363	−0.188071
$706$	−9.32243	−0.350854
$707$	−6.06648	−0.228153
$708$	9.59654	0.360660
$709$	25.6987	0.965134	0.482567	−	0.875859i	$-0.339705\pi$
$709$	25.6987	0.965134	0.482567	+	0.875859i	$0.339705\pi$
$710$	22.7355	0.853247
$711$	6.49015	0.243400
$712$	−10.8097	−0.405110
$713$	−35.0378	−1.31218
$714$	−7.91447	−0.296192
$715$	3.71112	0.138788
$716$	6.65063	0.248546
$717$	−11.1960	−0.418122
$718$	−4.54080	−0.169461
$719$	18.3021	0.682552	0.341276	−	0.939963i	$-0.389141\pi$
$719$	18.3021	0.682552	0.341276	+	0.939963i	$0.389141\pi$
$720$	10.3078	0.384147
$721$	9.49357	0.353559
$722$	−28.7199	−1.06884
$723$	42.1962	1.56930
$724$	7.32128	0.272093
$725$	3.93780	0.146246
$726$	34.8731	1.29426
$727$	−4.21238	−0.156229	−0.0781143	−	0.996944i	$-0.524890\pi$
$727$	−4.21238	−0.156229	−0.0781143	+	0.996944i	$0.524890\pi$
$728$	−32.5513	−1.20643
$729$	7.82126	0.289676
$730$	13.0725	0.483836
$731$	5.04235	0.186498
$732$	3.66276	0.135379
$733$	37.1529	1.37227	0.686137	−	0.727472i	$-0.259305\pi$
$733$	37.1529	1.37227	0.686137	+	0.727472i	$0.259305\pi$
$734$	31.6919	1.16977
$735$	−12.4015	−0.457435
$736$	12.9709	0.478115
$737$	3.26873	0.120405
$738$	8.45123	0.311094
$739$	−18.4168	−0.677474	−0.338737	−	0.940881i	$-0.610000\pi$
$739$	−18.4168	−0.677474	−0.338737	+	0.940881i	$0.610000\pi$
$740$	4.03713	0.148408
$741$	−9.36839	−0.344156
$742$	−2.48531	−0.0912386
$743$	−0.209791	−0.00769647	−0.00384823	−	0.999993i	$-0.501225\pi$
$743$	−0.209791	−0.00769647	−0.00384823	+	0.999993i	$0.501225\pi$
$744$	30.3344	1.11211
$745$	13.5870	0.497790
$746$	35.3415	1.29394
$747$	−5.46427	−0.199927
$748$	−0.157383	−0.00575448
$749$	−12.5691	−0.459266
$750$	−38.8075	−1.41705
$751$	−37.9456	−1.38465	−0.692327	−	0.721584i	$-0.743414\pi$
$751$	−37.9456	−1.38465	−0.692327	+	0.721584i	$0.743414\pi$
$752$	6.40715	0.233645
$753$	28.4026	1.03505
$754$	−21.5825	−0.785986
$755$	24.4435	0.889588
$756$	2.63191	0.0957216
$757$	9.17266	0.333386	0.166693	−	0.986009i	$-0.446691\pi$
$757$	9.17266	0.333386	0.166693	+	0.986009i	$0.446691\pi$
$758$	30.2084	1.09722
$759$	−3.77037	−0.136856
$760$	2.83687	0.102904
$761$	20.9849	0.760703	0.380351	−	0.924842i	$-0.375803\pi$
$761$	20.9849	0.760703	0.380351	+	0.924842i	$0.375803\pi$
$762$	−23.1757	−0.839567
$763$	−26.3185	−0.952794
$764$	2.19192	0.0793008
$765$	−2.91973	−0.105563
$766$	−26.0989	−0.942991
$767$	−82.2414	−2.96956
$768$	−18.7188	−0.675456
$769$	−7.69384	−0.277447	−0.138724	−	0.990331i	$-0.544300\pi$
$769$	−7.69384	−0.277447	−0.138724	+	0.990331i	$0.544300\pi$
$770$	1.56261	0.0563124
$771$	64.8952	2.33714
$772$	10.5843	0.380939
$773$	−35.0644	−1.26118	−0.630589	−	0.776117i	$-0.717186\pi$
$773$	−35.0644	−1.26118	−0.630589	+	0.776117i	$0.717186\pi$
$774$	7.58839	0.272759
$775$	−11.5320	−0.414241
$776$	38.5353	1.38334
$777$	23.0888	0.828308
$778$	−4.44985	−0.159535
$779$	2.79892	0.100282
$780$	9.78308	0.350290
$781$	2.58565	0.0925218
$782$	−12.0489	−0.430866
$783$	−7.17734	−0.256497
$784$	15.9119	0.568282
$785$	32.3434	1.15439
$786$	28.5817	1.01948
$787$	12.8284	0.457283	0.228642	−	0.973511i	$-0.426572\pi$
$787$	12.8284	0.457283	0.228642	+	0.973511i	$0.426572\pi$
$788$	−0.496237	−0.0176777
$789$	8.17564	0.291060
$790$	−13.7212	−0.488178
$791$	−4.26475	−0.151637
$792$	0.974170	0.0346156
$793$	−31.3894	−1.11467
$794$	−57.1807	−2.02927
$795$	−3.07219	−0.108959
$796$	−3.94441	−0.139806
$797$	12.7537	0.451759	0.225880	−	0.974155i	$-0.427474\pi$
$797$	12.7537	0.451759	0.225880	+	0.974155i	$0.427474\pi$
$798$	−3.94466	−0.139639
$799$	−1.81486	−0.0642052
$800$	4.26911	0.150936
$801$	5.54502	0.195924
$802$	−11.1191	−0.392630
$803$	1.48670	0.0524646
$804$	8.61686	0.303893
$805$	19.5696	0.689739
$806$	63.2048	2.22629
$807$	−36.4839	−1.28429
$808$	7.99574	0.281289
$809$	−39.2859	−1.38122	−0.690610	−	0.723227i	$-0.742658\pi$
$809$	−39.2859	−1.38122	−0.690610	+	0.723227i	$0.742658\pi$
$810$	30.2175	1.06173
$811$	48.6285	1.70758	0.853789	−	0.520618i	$-0.174299\pi$
$811$	48.6285	1.70758	0.853789	+	0.520618i	$0.174299\pi$
$812$	−1.48658	−0.0521688
$813$	−23.7448	−0.832767
$814$	2.80668	0.0983742
$815$	−31.7003	−1.11041
$816$	12.5527	0.439434
$817$	2.51316	0.0879244
$818$	−13.2058	−0.461731
$819$	16.6978	0.583467
$820$	−2.92282	−0.102069
$821$	−18.6143	−0.649643	−0.324821	−	0.945775i	$-0.605304\pi$
$821$	−18.6143	−0.649643	−0.324821	+	0.945775i	$0.605304\pi$
$822$	25.5821	0.892278
$823$	27.0436	0.942681	0.471340	−	0.881951i	$-0.343770\pi$
$823$	27.0436	0.942681	0.471340	+	0.881951i	$0.343770\pi$
$824$	−12.5127	−0.435901
$825$	−1.24094	−0.0432039
$826$	−34.6286	−1.20488
$827$	33.6184	1.16903	0.584514	−	0.811384i	$-0.301285\pi$
$827$	33.6184	1.16903	0.584514	+	0.811384i	$0.301285\pi$
$828$	−2.96624	−0.103084
$829$	−37.1031	−1.28864	−0.644322	−	0.764754i	$-0.722860\pi$
$829$	−37.1031	−1.28864	−0.644322	+	0.764754i	$0.722860\pi$
$830$	11.5523	0.400987
$831$	−4.75885	−0.165083
$832$	40.7820	1.41386
$833$	−4.50713	−0.156163
$834$	−35.9530	−1.24495
$835$	36.6506	1.26834
$836$	−0.0784413	−0.00271295
$837$	21.0190	0.726524
$838$	−43.6256	−1.50702
$839$	36.0101	1.24321	0.621603	−	0.783333i	$-0.286482\pi$
$839$	36.0101	1.24321	0.621603	+	0.783333i	$0.286482\pi$
$840$	−16.9426	−0.584576
$841$	−24.9460	−0.860207
$842$	−24.1012	−0.830581
$843$	44.9089	1.54674
$844$	3.96534	0.136493
$845$	−61.1579	−2.10389
$846$	−2.73124	−0.0939020
$847$	−20.5852	−0.707316
$848$	3.94182	0.135363
$849$	−7.27665	−0.249734
$850$	−3.96563	−0.136020
$851$	35.1501	1.20493
$852$	6.81616	0.233518
$853$	45.0443	1.54229	0.771144	−	0.636660i	$-0.219685\pi$
$853$	45.0443	1.54229	0.771144	+	0.636660i	$0.219685\pi$
$854$	−13.2168	−0.452271
$855$	−1.45522	−0.0497676
$856$	16.5663	0.566226
$857$	7.27558	0.248529	0.124265	−	0.992249i	$-0.460343\pi$
$857$	7.27558	0.248529	0.124265	+	0.992249i	$0.460343\pi$
$858$	6.80137	0.232195
$859$	−31.0024	−1.05779	−0.528894	−	0.848688i	$-0.677393\pi$
$859$	−31.0024	−1.05779	−0.528894	+	0.848688i	$0.677393\pi$
$860$	−2.62440	−0.0894915
$861$	−16.7160	−0.569679
$862$	−44.3174	−1.50946
$863$	−20.9094	−0.711763	−0.355881	−	0.934531i	$-0.615819\pi$
$863$	−20.9094	−0.711763	−0.355881	+	0.934531i	$0.615819\pi$
$864$	−7.78121	−0.264722
$865$	20.2153	0.687342
$866$	29.3829	0.998472
$867$	31.5985	1.07314
$868$	4.35350	0.147767
$869$	−1.56048	−0.0529355
$870$	−11.2334	−0.380849
$871$	−73.8456	−2.50216
$872$	34.6883	1.17469
$873$	−19.7673	−0.669023
$874$	−6.00528	−0.203132
$875$	22.9076	0.774418
$876$	3.91917	0.132417
$877$	−2.86032	−0.0965861	−0.0482930	−	0.998833i	$-0.515378\pi$
$877$	−2.86032	−0.0965861	−0.0482930	+	0.998833i	$0.515378\pi$
$878$	56.3336	1.90117
$879$	−33.5635	−1.13207
$880$	−2.47837	−0.0835459
$881$	7.88294	0.265583	0.132792	−	0.991144i	$-0.457606\pi$
$881$	7.88294	0.265583	0.132792	+	0.991144i	$0.457606\pi$
$882$	−6.78292	−0.228393
$883$	−1.30936	−0.0440634	−0.0220317	−	0.999757i	$-0.507013\pi$
$883$	−1.30936	−0.0440634	−0.0220317	+	0.999757i	$0.507013\pi$
$884$	3.55552	0.119585
$885$	−42.8058	−1.43890
$886$	−19.8231	−0.665969
$887$	19.3898	0.651047	0.325523	−	0.945534i	$-0.394460\pi$
$887$	19.3898	0.651047	0.325523	+	0.945534i	$0.394460\pi$
$888$	−30.4316	−1.02122
$889$	13.6803	0.458824
$890$	−11.7230	−0.392957
$891$	3.43656	0.115129
$892$	0.157942	0.00528828
$893$	−0.904547	−0.0302695
$894$	24.9009	0.832812
$895$	−29.6654	−0.991606
$896$	25.4121	0.848959
$897$	85.1785	2.84403
$898$	−35.6551	−1.18983
$899$	−11.8722	−0.395960
$900$	−0.976277	−0.0325426
$901$	−1.11654	−0.0371975
$902$	−2.03199	−0.0676580
$903$	−15.0093	−0.499479
$904$	5.62102	0.186952
$905$	−32.6569	−1.08555
$906$	44.7975	1.48830
$907$	19.5213	0.648196	0.324098	−	0.946024i	$-0.394939\pi$
$907$	19.5213	0.648196	0.324098	+	0.946024i	$0.394939\pi$
$908$	2.12581	0.0705475
$909$	−4.10155	−0.136040
$910$	−35.3017	−1.17024
$911$	−10.1115	−0.335007	−0.167504	−	0.985871i	$-0.553571\pi$
$911$	−10.1115	−0.335007	−0.167504	+	0.985871i	$0.553571\pi$
$912$	6.25642	0.207171
$913$	1.31382	0.0434809
$914$	−57.7581	−1.91047
$915$	−16.3379	−0.540114
$916$	3.70898	0.122548
$917$	−16.8714	−0.557144
$918$	7.22806	0.238562
$919$	−28.3079	−0.933793	−0.466896	−	0.884312i	$-0.654628\pi$
$919$	−28.3079	−0.933793	−0.466896	+	0.884312i	$0.654628\pi$
$920$	−25.7932	−0.850376
$921$	66.1798	2.18070
$922$	26.4818	0.872131
$923$	−58.4138	−1.92271
$924$	0.468474	0.0154117
$925$	11.5689	0.380384
$926$	−27.3124	−0.897541
$927$	6.41862	0.210815
$928$	4.39507	0.144275
$929$	5.56234	0.182494	0.0912472	−	0.995828i	$-0.470915\pi$
$929$	5.56234	0.182494	0.0912472	+	0.995828i	$0.470915\pi$
$930$	32.8974	1.07875
$931$	−2.24640	−0.0736229
$932$	4.77918	0.156547
$933$	28.2058	0.923415
$934$	−31.0717	−1.01670
$935$	0.702013	0.0229583
$936$	−22.0080	−0.719353
$937$	−4.15505	−0.135740	−0.0678698	−	0.997694i	$-0.521620\pi$
$937$	−4.15505	−0.135740	−0.0678698	+	0.997694i	$0.521620\pi$
$938$	−31.0934	−1.01524
$939$	−40.6980	−1.32813
$940$	0.944586	0.0308090
$941$	−40.8626	−1.33208	−0.666042	−	0.745914i	$-0.732013\pi$
$941$	−40.8626	−1.33208	−0.666042	+	0.745914i	$0.732013\pi$
$942$	59.2758	1.93131
$943$	−25.4481	−0.828705
$944$	54.9226	1.78758
$945$	−11.7397	−0.381894
$946$	−1.82453	−0.0593207
$947$	48.1825	1.56572	0.782860	−	0.622198i	$-0.213760\pi$
$947$	48.1825	1.56572	0.782860	+	0.622198i	$0.213760\pi$
$948$	−4.11365	−0.133605
$949$	−33.5869	−1.09028
$950$	−1.97651	−0.0641265
$951$	14.2635	0.462525
$952$	−6.15755	−0.199567
$953$	9.31898	0.301871	0.150936	−	0.988544i	$-0.451771\pi$
$953$	9.31898	0.301871	0.150936	+	0.988544i	$0.451771\pi$
$954$	−1.68032	−0.0544024
$955$	−9.77715	−0.316381
$956$	2.11781	0.0684950
$957$	−1.27755	−0.0412974
$958$	−39.7326	−1.28370
$959$	−15.1008	−0.487631
$960$	21.2266	0.685086
$961$	3.76808	0.121551
$962$	−63.4073	−2.04433
$963$	−8.49800	−0.273844
$964$	−7.98177	−0.257075
$965$	−47.2119	−1.51981
$966$	35.8653	1.15395
$967$	−6.11776	−0.196734	−0.0983670	−	0.995150i	$-0.531362\pi$
$967$	−6.11776	−0.196734	−0.0983670	+	0.995150i	$0.531362\pi$
$968$	27.1317	0.872046
$969$	−1.77217	−0.0569302
$970$	41.7913	1.34184
$971$	23.7273	0.761445	0.380722	−	0.924689i	$-0.375675\pi$
$971$	23.7273	0.761445	0.380722	+	0.924689i	$0.375675\pi$
$972$	4.87620	0.156404
$973$	21.2226	0.680366
$974$	−25.6780	−0.822776
$975$	28.0347	0.897829
$976$	20.9626	0.670996
$977$	−20.1535	−0.644767	−0.322383	−	0.946609i	$-0.604484\pi$
$977$	−20.1535	−0.644767	−0.322383	+	0.946609i	$0.604484\pi$
$978$	−58.0972	−1.85774
$979$	−1.33323	−0.0426102
$980$	2.34584	0.0749351
$981$	−17.7940	−0.568118
$982$	62.0744	1.98087
$983$	−40.2884	−1.28500	−0.642500	−	0.766286i	$-0.722103\pi$
$983$	−40.2884	−1.28500	−0.642500	+	0.766286i	$0.722103\pi$
$984$	22.0320	0.702354
$985$	2.21348	0.0705275
$986$	−4.08263	−0.130017
$987$	5.40221	0.171954
$988$	1.77211	0.0563783
$989$	−22.8499	−0.726586
$990$	1.05648	0.0335772
$991$	−9.05772	−0.287728	−0.143864	−	0.989597i	$-0.545953\pi$
$991$	−9.05772	−0.287728	−0.143864	+	0.989597i	$0.545953\pi$
$992$	−12.8711	−0.408657
$993$	−55.8628	−1.77275
$994$	−24.5957	−0.780128
$995$	17.5942	0.557774
$996$	3.46341	0.109742
$997$	−17.5484	−0.555764	−0.277882	−	0.960615i	$-0.589632\pi$
$997$	−17.5484	−0.555764	−0.277882	+	0.960615i	$0.589632\pi$
$998$	45.4329	1.43815
$999$	−21.0864	−0.667144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.a.1.77	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.a.1.77	✓	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)

\(f(q)\)	\(=\)	\(q+1.54634 q^{2} -2.06789 q^{3} +0.391158 q^{4} -1.74478 q^{5} -3.19765 q^{6} +1.88754 q^{7} -2.48781 q^{8} +1.27617 q^{9} +O(q^{10})\)	\(q+1.54634 q^{2} -2.06789 q^{3} +0.391158 q^{4} -1.74478 q^{5} -3.19765 q^{6} +1.88754 q^{7} -2.48781 q^{8} +1.27617 q^{9} -2.69802 q^{10} -0.306838 q^{11} -0.808872 q^{12} +6.93195 q^{13} +2.91877 q^{14} +3.60801 q^{15} -4.62931 q^{16} +1.31128 q^{17} +1.97338 q^{18} +0.653555 q^{19} -0.682485 q^{20} -3.90322 q^{21} -0.474476 q^{22} -5.94220 q^{23} +5.14452 q^{24} -1.95575 q^{25} +10.7191 q^{26} +3.56470 q^{27} +0.738326 q^{28} -2.01345 q^{29} +5.57920 q^{30} +5.89645 q^{31} -2.18285 q^{32} +0.634508 q^{33} +2.02768 q^{34} -3.29333 q^{35} +0.499183 q^{36} -5.91534 q^{37} +1.01062 q^{38} -14.3345 q^{39} +4.34068 q^{40} +4.28261 q^{41} -6.03569 q^{42} +3.84537 q^{43} -0.120022 q^{44} -2.22663 q^{45} -9.18864 q^{46} -1.38404 q^{47} +9.57290 q^{48} -3.43720 q^{49} -3.02425 q^{50} -2.71158 q^{51} +2.71149 q^{52} -0.851492 q^{53} +5.51222 q^{54} +0.535365 q^{55} -4.69584 q^{56} -1.35148 q^{57} -3.11347 q^{58} -11.8641 q^{59} +1.41130 q^{60} -4.52823 q^{61} +9.11789 q^{62} +2.40881 q^{63} +5.88320 q^{64} -12.0947 q^{65} +0.981163 q^{66} -10.6529 q^{67} +0.512917 q^{68} +12.2878 q^{69} -5.09260 q^{70} -8.42674 q^{71} -3.17486 q^{72} -4.84523 q^{73} -9.14710 q^{74} +4.04427 q^{75} +0.255644 q^{76} -0.579169 q^{77} -22.1660 q^{78} +5.08566 q^{79} +8.07712 q^{80} -11.1999 q^{81} +6.62236 q^{82} -4.28178 q^{83} -1.52678 q^{84} -2.28789 q^{85} +5.94624 q^{86} +4.16359 q^{87} +0.763356 q^{88} +4.34506 q^{89} -3.44312 q^{90} +13.0843 q^{91} -2.32434 q^{92} -12.1932 q^{93} -2.14019 q^{94} -1.14031 q^{95} +4.51390 q^{96} -15.4896 q^{97} -5.31508 q^{98} -0.391577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) \) 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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