LMFDB - Embedded newform 2671.2.a.b.1.43

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:	$0$
Dimension:	$122$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.43
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.843748 q^{2} +3.24245 q^{3} -1.28809 q^{4} -0.455443 q^{5} -2.73581 q^{6} +3.76746 q^{7} +2.77432 q^{8} +7.51351 q^{9} +O(q^{10})$	\(q-0.843748 q^{2} +3.24245 q^{3} -1.28809 q^{4} -0.455443 q^{5} -2.73581 q^{6} +3.76746 q^{7} +2.77432 q^{8} +7.51351 q^{9} +0.384279 q^{10} -2.23609 q^{11} -4.17657 q^{12} +0.239946 q^{13} -3.17879 q^{14} -1.47675 q^{15} +0.235355 q^{16} +6.96544 q^{17} -6.33951 q^{18} +4.93167 q^{19} +0.586651 q^{20} +12.2158 q^{21} +1.88669 q^{22} +1.64637 q^{23} +8.99560 q^{24} -4.79257 q^{25} -0.202454 q^{26} +14.6348 q^{27} -4.85283 q^{28} +0.0461060 q^{29} +1.24601 q^{30} -5.52070 q^{31} -5.74722 q^{32} -7.25040 q^{33} -5.87708 q^{34} -1.71586 q^{35} -9.67807 q^{36} -7.08532 q^{37} -4.16108 q^{38} +0.778015 q^{39} -1.26354 q^{40} -7.90719 q^{41} -10.3071 q^{42} +10.1357 q^{43} +2.88028 q^{44} -3.42197 q^{45} -1.38912 q^{46} -0.238142 q^{47} +0.763128 q^{48} +7.19376 q^{49} +4.04372 q^{50} +22.5851 q^{51} -0.309073 q^{52} -8.41295 q^{53} -12.3481 q^{54} +1.01841 q^{55} +10.4521 q^{56} +15.9907 q^{57} -0.0389019 q^{58} +12.6323 q^{59} +1.90219 q^{60} -10.7969 q^{61} +4.65808 q^{62} +28.3069 q^{63} +4.37849 q^{64} -0.109282 q^{65} +6.11751 q^{66} +4.07183 q^{67} -8.97212 q^{68} +5.33828 q^{69} +1.44776 q^{70} -1.30780 q^{71} +20.8449 q^{72} -14.5981 q^{73} +5.97822 q^{74} -15.5397 q^{75} -6.35243 q^{76} -8.42436 q^{77} -0.656449 q^{78} +1.93623 q^{79} -0.107191 q^{80} +24.9123 q^{81} +6.67168 q^{82} +8.60934 q^{83} -15.7351 q^{84} -3.17236 q^{85} -8.55197 q^{86} +0.149497 q^{87} -6.20361 q^{88} +1.96445 q^{89} +2.88728 q^{90} +0.903989 q^{91} -2.12067 q^{92} -17.9006 q^{93} +0.200932 q^{94} -2.24609 q^{95} -18.6351 q^{96} +12.3584 q^{97} -6.06972 q^{98} -16.8008 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) $ 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.843748	−0.596620	−0.298310	−	0.954469i	$-0.596423\pi$
$2$	−0.843748	−0.596620	−0.298310	+	0.954469i	$0.596423\pi$
$3$	3.24245	1.87203	0.936016	−	0.351958i	$-0.114484\pi$
$3$	3.24245	1.87203	0.936016	+	0.351958i	$0.114484\pi$
$4$	−1.28809	−0.644045
$5$	−0.455443	−0.203680	−0.101840	−	0.994801i	$-0.532473\pi$
$5$	−0.455443	−0.203680	−0.101840	+	0.994801i	$0.532473\pi$
$6$	−2.73581	−1.11689
$7$	3.76746	1.42397	0.711983	−	0.702196i	$-0.247797\pi$
$7$	3.76746	1.42397	0.711983	+	0.702196i	$0.247797\pi$
$8$	2.77432	0.980870
$9$	7.51351	2.50450
$10$	0.384279	0.121520
$11$	−2.23609	−0.674205	−0.337103	−	0.941468i	$-0.609447\pi$
$11$	−2.23609	−0.674205	−0.337103	+	0.941468i	$0.609447\pi$
$12$	−4.17657	−1.20567
$13$	0.239946	0.0665492	0.0332746	−	0.999446i	$-0.489406\pi$
$13$	0.239946	0.0665492	0.0332746	+	0.999446i	$0.489406\pi$
$14$	−3.17879	−0.849567
$15$	−1.47675	−0.381296
$16$	0.235355	0.0588387
$17$	6.96544	1.68937	0.844684	−	0.535265i	$-0.179788\pi$
$17$	6.96544	1.68937	0.844684	+	0.535265i	$0.179788\pi$
$18$	−6.33951	−1.49424
$19$	4.93167	1.13140	0.565701	−	0.824610i	$-0.308606\pi$
$19$	4.93167	1.13140	0.565701	+	0.824610i	$0.308606\pi$
$20$	0.586651	0.131179
$21$	12.2158	2.66571
$22$	1.88669	0.402244
$23$	1.64637	0.343292	0.171646	−	0.985159i	$-0.445091\pi$
$23$	1.64637	0.343292	0.171646	+	0.985159i	$0.445091\pi$
$24$	8.99560	1.83622
$25$	−4.79257	−0.958514
$26$	−0.202454	−0.0397046
$27$	14.6348	2.81648
$28$	−4.85283	−0.917098
$29$	0.0461060	0.00856168	0.00428084	−	0.999991i	$-0.498637\pi$
$29$	0.0461060	0.00856168	0.00428084	+	0.999991i	$0.498637\pi$
$30$	1.24601	0.227489
$31$	−5.52070	−0.991548	−0.495774	−	0.868452i	$-0.665116\pi$
$31$	−5.52070	−0.991548	−0.495774	+	0.868452i	$0.665116\pi$
$32$	−5.74722	−1.01597
$33$	−7.25040	−1.26213
$34$	−5.87708	−1.00791
$35$	−1.71586	−0.290034
$36$	−9.67807	−1.61301
$37$	−7.08532	−1.16482	−0.582410	−	0.812895i	$-0.697890\pi$
$37$	−7.08532	−1.16482	−0.582410	+	0.812895i	$0.697890\pi$
$38$	−4.16108	−0.675017
$39$	0.778015	0.124582
$40$	−1.26354	−0.199784
$41$	−7.90719	−1.23490	−0.617448	−	0.786612i	$-0.711833\pi$
$41$	−7.90719	−1.23490	−0.617448	+	0.786612i	$0.711833\pi$
$42$	−10.3071	−1.59042
$43$	10.1357	1.54568	0.772840	−	0.634601i	$-0.218836\pi$
$43$	10.1357	1.54568	0.772840	+	0.634601i	$0.218836\pi$
$44$	2.88028	0.434218
$45$	−3.42197	−0.510118
$46$	−1.38912	−0.204815
$47$	−0.238142	−0.0347366	−0.0173683	−	0.999849i	$-0.505529\pi$
$47$	−0.238142	−0.0347366	−0.0173683	+	0.999849i	$0.505529\pi$
$48$	0.763128	0.110148
$49$	7.19376	1.02768
$50$	4.04372	0.571869
$51$	22.5851	3.16255
$52$	−0.309073	−0.0428607
$53$	−8.41295	−1.15561	−0.577804	−	0.816176i	$-0.696090\pi$
$53$	−8.41295	−1.15561	−0.577804	+	0.816176i	$0.696090\pi$
$54$	−12.3481	−1.68037
$55$	1.01841	0.137322
$56$	10.4521	1.39673
$57$	15.9907	2.11802
$58$	−0.0389019	−0.00510806
$59$	12.6323	1.64458	0.822292	−	0.569066i	$-0.192695\pi$
$59$	12.6323	1.64458	0.822292	+	0.569066i	$0.192695\pi$
$60$	1.90219	0.245572
$61$	−10.7969	−1.38240	−0.691200	−	0.722664i	$-0.742918\pi$
$61$	−10.7969	−1.38240	−0.691200	+	0.722664i	$0.742918\pi$
$62$	4.65808	0.591577
$63$	28.3069	3.56633
$64$	4.37849	0.547311
$65$	−0.109282	−0.0135548
$66$	6.11751	0.753014
$67$	4.07183	0.497453	0.248727	−	0.968574i	$-0.419988\pi$
$67$	4.07183	0.497453	0.248727	+	0.968574i	$0.419988\pi$
$68$	−8.97212	−1.08803
$69$	5.33828	0.642653
$70$	1.44776	0.173040
$71$	−1.30780	−0.155208	−0.0776039	−	0.996984i	$-0.524727\pi$
$71$	−1.30780	−0.155208	−0.0776039	+	0.996984i	$0.524727\pi$
$72$	20.8449	2.45659
$73$	−14.5981	−1.70858	−0.854291	−	0.519795i	$-0.826008\pi$
$73$	−14.5981	−1.70858	−0.854291	+	0.519795i	$0.826008\pi$
$74$	5.97822	0.694954
$75$	−15.5397	−1.79437
$76$	−6.35243	−0.728674
$77$	−8.42436	−0.960045
$78$	−0.656449	−0.0743282
$79$	1.93623	0.217843	0.108922	−	0.994050i	$-0.465260\pi$
$79$	1.93623	0.217843	0.108922	+	0.994050i	$0.465260\pi$
$80$	−0.107191	−0.0119843
$81$	24.9123	2.76803
$82$	6.67168	0.736763
$83$	8.60934	0.944997	0.472499	−	0.881331i	$-0.343352\pi$
$83$	8.60934	0.944997	0.472499	+	0.881331i	$0.343352\pi$
$84$	−15.7351	−1.71684
$85$	−3.17236	−0.344091
$86$	−8.55197	−0.922183
$87$	0.149497	0.0160277
$88$	−6.20361	−0.661307
$89$	1.96445	0.208232	0.104116	−	0.994565i	$-0.466799\pi$
$89$	1.96445	0.208232	0.104116	+	0.994565i	$0.466799\pi$
$90$	2.88728	0.304346
$91$	0.903989	0.0947638
$92$	−2.12067	−0.221095
$93$	−17.9006	−1.85621
$94$	0.200932	0.0207245
$95$	−2.24609	−0.230444
$96$	−18.6351	−1.90194
$97$	12.3584	1.25480	0.627402	−	0.778696i	$-0.284118\pi$
$97$	12.3584	1.25480	0.627402	+	0.778696i	$0.284118\pi$
$98$	−6.06972	−0.613135
$99$	−16.8008	−1.68855
$100$	6.17326	0.617326
$101$	14.4952	1.44233	0.721165	−	0.692763i	$-0.243607\pi$
$101$	14.4952	1.44233	0.721165	+	0.692763i	$0.243607\pi$
$102$	−19.0561	−1.88684
$103$	6.66299	0.656524	0.328262	−	0.944587i	$-0.393537\pi$
$103$	6.66299	0.656524	0.328262	+	0.944587i	$0.393537\pi$
$104$	0.665688	0.0652761
$105$	−5.56361	−0.542953
$106$	7.09841	0.689458
$107$	−11.8582	−1.14637	−0.573185	−	0.819426i	$-0.694293\pi$
$107$	−11.8582	−1.14637	−0.573185	+	0.819426i	$0.694293\pi$
$108$	−18.8510	−1.81394
$109$	−4.17572	−0.399962	−0.199981	−	0.979800i	$-0.564088\pi$
$109$	−4.17572	−0.399962	−0.199981	+	0.979800i	$0.564088\pi$
$110$	−0.859280	−0.0819292
$111$	−22.9738	−2.18058
$112$	0.886691	0.0837844
$113$	4.42613	0.416375	0.208187	−	0.978089i	$-0.433244\pi$
$113$	4.42613	0.416375	0.208187	+	0.978089i	$0.433244\pi$
$114$	−13.4921	−1.26365
$115$	−0.749827	−0.0699218
$116$	−0.0593887	−0.00551410
$117$	1.80284	0.166673
$118$	−10.6585	−0.981191
$119$	26.2420	2.40560
$120$	−4.09698	−0.374002
$121$	−5.99992	−0.545448
$122$	9.10985	0.824767
$123$	−25.6387	−2.31177
$124$	7.11116	0.638601
$125$	4.45996	0.398911
$126$	−23.8838	−2.12774
$127$	−14.3052	−1.26939	−0.634693	−	0.772765i	$-0.718873\pi$
$127$	−14.3052	−1.26939	−0.634693	+	0.772765i	$0.718873\pi$
$128$	7.80009	0.689437
$129$	32.8645	2.89356
$130$	0.0922064	0.00808703
$131$	2.88421	0.251994	0.125997	−	0.992031i	$-0.459787\pi$
$131$	2.88421	0.251994	0.125997	+	0.992031i	$0.459787\pi$
$132$	9.33917	0.812871
$133$	18.5799	1.61108
$134$	−3.43560	−0.296791
$135$	−6.66534	−0.573661
$136$	19.3244	1.65705
$137$	9.24370	0.789742	0.394871	−	0.918736i	$-0.370789\pi$
$137$	9.24370	0.789742	0.394871	+	0.918736i	$0.370789\pi$
$138$	−4.50416	−0.383420
$139$	−14.1485	−1.20006	−0.600032	−	0.799976i	$-0.704845\pi$
$139$	−14.1485	−1.20006	−0.600032	+	0.799976i	$0.704845\pi$
$140$	2.21019	0.186795
$141$	−0.772164	−0.0650280
$142$	1.10346	0.0926000
$143$	−0.536541	−0.0448678
$144$	1.76834	0.147362
$145$	−0.0209987	−0.00174384
$146$	12.3171	1.01937
$147$	23.3255	1.92385
$148$	9.12653	0.750196
$149$	2.72622	0.223341	0.111670	−	0.993745i	$-0.464380\pi$
$149$	2.72622	0.223341	0.111670	+	0.993745i	$0.464380\pi$
$150$	13.1116	1.07056
$151$	3.63433	0.295758	0.147879	−	0.989005i	$-0.452755\pi$
$151$	3.63433	0.295758	0.147879	+	0.989005i	$0.452755\pi$
$152$	13.6820	1.10976
$153$	52.3349	4.23103
$154$	7.10804	0.572782
$155$	2.51437	0.201959
$156$	−1.00215	−0.0802365
$157$	−10.4007	−0.830062	−0.415031	−	0.909807i	$-0.636229\pi$
$157$	−10.4007	−0.830062	−0.415031	+	0.909807i	$0.636229\pi$
$158$	−1.63369	−0.129970
$159$	−27.2786	−2.16333
$160$	2.61753	0.206934
$161$	6.20264	0.488836
$162$	−21.0197	−1.65146
$163$	15.4427	1.20956	0.604782	−	0.796391i	$-0.293260\pi$
$163$	15.4427	1.20956	0.604782	+	0.796391i	$0.293260\pi$
$164$	10.1852	0.795329
$165$	3.30214	0.257072
$166$	−7.26411	−0.563804
$167$	4.93620	0.381975	0.190987	−	0.981593i	$-0.438831\pi$
$167$	4.93620	0.381975	0.190987	+	0.981593i	$0.438831\pi$
$168$	33.8906	2.61471
$169$	−12.9424	−0.995571
$170$	2.67667	0.205291
$171$	37.0541	2.83360
$172$	−13.0557	−0.995487
$173$	−22.9394	−1.74405	−0.872024	−	0.489463i	$-0.837193\pi$
$173$	−22.9394	−1.74405	−0.872024	+	0.489463i	$0.837193\pi$
$174$	−0.126138	−0.00956246
$175$	−18.0558	−1.36489
$176$	−0.526274	−0.0396694
$177$	40.9596	3.07871
$178$	−1.65750	−0.124235
$179$	−0.357684	−0.0267345	−0.0133673	−	0.999911i	$-0.504255\pi$
$179$	−0.357684	−0.0267345	−0.0133673	+	0.999911i	$0.504255\pi$
$180$	4.40781	0.328539
$181$	14.3469	1.06639	0.533197	−	0.845991i	$-0.320991\pi$
$181$	14.3469	1.06639	0.533197	+	0.845991i	$0.320991\pi$
$182$	−0.762739	−0.0565380
$183$	−35.0084	−2.58790
$184$	4.56755	0.336725
$185$	3.22696	0.237251
$186$	15.1036	1.10745
$187$	−15.5753	−1.13898
$188$	0.306748	0.0223719
$189$	55.1362	4.01057
$190$	1.89514	0.137488
$191$	1.46789	0.106213	0.0531063	−	0.998589i	$-0.483088\pi$
$191$	1.46789	0.106213	0.0531063	+	0.998589i	$0.483088\pi$
$192$	14.1971	1.02458
$193$	6.19776	0.446125	0.223062	−	0.974804i	$-0.428395\pi$
$193$	6.19776	0.446125	0.223062	+	0.974804i	$0.428395\pi$
$194$	−10.4274	−0.748640
$195$	−0.354342	−0.0253749
$196$	−9.26621	−0.661872
$197$	1.38098	0.0983911	0.0491955	−	0.998789i	$-0.484334\pi$
$197$	1.38098	0.0983911	0.0491955	+	0.998789i	$0.484334\pi$
$198$	14.1757	1.00742
$199$	−3.46092	−0.245338	−0.122669	−	0.992448i	$-0.539145\pi$
$199$	−3.46092	−0.245338	−0.122669	+	0.992448i	$0.539145\pi$
$200$	−13.2961	−0.940178
$201$	13.2027	0.931249
$202$	−12.2303	−0.860523
$203$	0.173703	0.0121915
$204$	−29.0917	−2.03682
$205$	3.60127	0.251524
$206$	−5.62188	−0.391695
$207$	12.3700	0.859776
$208$	0.0564726	0.00391567
$209$	−11.0276	−0.762797
$210$	4.69428	0.323936
$211$	−5.82131	−0.400755	−0.200378	−	0.979719i	$-0.564217\pi$
$211$	−5.82131	−0.400755	−0.200378	+	0.979719i	$0.564217\pi$
$212$	10.8366	0.744263
$213$	−4.24049	−0.290554
$214$	10.0053	0.683947
$215$	−4.61623	−0.314824
$216$	40.6017	2.76260
$217$	−20.7990	−1.41193
$218$	3.52326	0.238625
$219$	−47.3338	−3.19852
$220$	−1.31180	−0.0884417
$221$	1.67133	0.112426
$222$	19.3841	1.30098
$223$	13.8587	0.928046	0.464023	−	0.885823i	$-0.346405\pi$
$223$	13.8587	0.928046	0.464023	+	0.885823i	$0.346405\pi$
$224$	−21.6524	−1.44671
$225$	−36.0090	−2.40060
$226$	−3.73453	−0.248418
$227$	21.0448	1.39679	0.698396	−	0.715712i	$-0.253898\pi$
$227$	21.0448	1.39679	0.698396	+	0.715712i	$0.253898\pi$
$228$	−20.5975	−1.36410
$229$	2.53090	0.167246	0.0836232	−	0.996497i	$-0.473351\pi$
$229$	2.53090	0.167246	0.0836232	+	0.996497i	$0.473351\pi$
$230$	0.632665	0.0417167
$231$	−27.3156	−1.79724
$232$	0.127913	0.00839789
$233$	−23.0198	−1.50807	−0.754037	−	0.656832i	$-0.771896\pi$
$233$	−23.0198	−1.50807	−0.754037	+	0.656832i	$0.771896\pi$
$234$	−1.52114	−0.0994402
$235$	0.108460	0.00707515
$236$	−16.2715	−1.05919
$237$	6.27815	0.407810
$238$	−22.1417	−1.43523
$239$	18.2863	1.18284	0.591420	−	0.806364i	$-0.298568\pi$
$239$	18.2863	1.18284	0.591420	+	0.806364i	$0.298568\pi$
$240$	−0.347561	−0.0224350
$241$	−21.4450	−1.38140	−0.690698	−	0.723144i	$-0.742696\pi$
$241$	−21.4450	−1.38140	−0.690698	+	0.723144i	$0.742696\pi$
$242$	5.06242	0.325425
$243$	36.8724	2.36537
$244$	13.9074	0.890327
$245$	−3.27635	−0.209318
$246$	21.6326	1.37924
$247$	1.18334	0.0752939
$248$	−15.3162	−0.972579
$249$	27.9154	1.76907
$250$	−3.76308	−0.237998
$251$	−16.5116	−1.04220	−0.521101	−	0.853495i	$-0.674479\pi$
$251$	−16.5116	−1.04220	−0.521101	+	0.853495i	$0.674479\pi$
$252$	−36.4618	−2.29688
$253$	−3.68142	−0.231449
$254$	12.0700	0.757340
$255$	−10.2862	−0.644149
$256$	−15.3383	−0.958643
$257$	10.4194	0.649943	0.324972	−	0.945724i	$-0.394645\pi$
$257$	10.4194	0.649943	0.324972	+	0.945724i	$0.394645\pi$
$258$	−27.7294	−1.72636
$259$	−26.6937	−1.65866
$260$	0.140765	0.00872987
$261$	0.346418	0.0214427
$262$	−2.43354	−0.150345
$263$	8.02212	0.494665	0.247332	−	0.968931i	$-0.420446\pi$
$263$	8.02212	0.494665	0.247332	+	0.968931i	$0.420446\pi$
$264$	−20.1149	−1.23799
$265$	3.83162	0.235374
$266$	−15.6767	−0.961201
$267$	6.36965	0.389816
$268$	−5.24488	−0.320382
$269$	−2.84558	−0.173498	−0.0867489	−	0.996230i	$-0.527648\pi$
$269$	−2.84558	−0.173498	−0.0867489	+	0.996230i	$0.527648\pi$
$270$	5.62386	0.342257
$271$	−0.193438	−0.0117505	−0.00587526	−	0.999983i	$-0.501870\pi$
$271$	−0.193438	−0.0117505	−0.00587526	+	0.999983i	$0.501870\pi$
$272$	1.63935	0.0994003
$273$	2.93114	0.177401
$274$	−7.79935	−0.471176
$275$	10.7166	0.646235
$276$	−6.87618	−0.413898
$277$	−15.6758	−0.941868	−0.470934	−	0.882168i	$-0.656083\pi$
$277$	−15.6758	−0.941868	−0.470934	+	0.882168i	$0.656083\pi$
$278$	11.9378	0.715982
$279$	−41.4799	−2.48333
$280$	−4.76035	−0.284485
$281$	−15.3657	−0.916639	−0.458320	−	0.888787i	$-0.651548\pi$
$281$	−15.3657	−0.916639	−0.458320	+	0.888787i	$0.651548\pi$
$282$	0.651512	0.0387970
$283$	8.76468	0.521006	0.260503	−	0.965473i	$-0.416112\pi$
$283$	8.76468	0.521006	0.260503	+	0.965473i	$0.416112\pi$
$284$	1.68457	0.0999608
$285$	−7.28285	−0.431399
$286$	0.452705	0.0267690
$287$	−29.7900	−1.75845
$288$	−43.1818	−2.54451
$289$	31.5174	1.85396
$290$	0.0177176	0.00104041
$291$	40.0715	2.34903
$292$	18.8037	1.10040
$293$	5.84110	0.341241	0.170620	−	0.985337i	$-0.445423\pi$
$293$	5.84110	0.341241	0.170620	+	0.985337i	$0.445423\pi$
$294$	−19.6808	−1.14781
$295$	−5.75328	−0.334969
$296$	−19.6569	−1.14254
$297$	−32.7248	−1.89888
$298$	−2.30024	−0.133250
$299$	0.395041	0.0228458
$300$	20.0165	1.15565
$301$	38.1858	2.20100
$302$	−3.06646	−0.176455
$303$	47.0002	2.70009
$304$	1.16069	0.0665703
$305$	4.91736	0.281567
$306$	−44.1575	−2.52431
$307$	−8.94994	−0.510800	−0.255400	−	0.966836i	$-0.582207\pi$
$307$	−8.94994	−0.510800	−0.255400	+	0.966836i	$0.582207\pi$
$308$	10.8513	0.618312
$309$	21.6044	1.22903
$310$	−2.12149	−0.120493
$311$	26.2704	1.48966	0.744828	−	0.667257i	$-0.232532\pi$
$311$	26.2704	1.48966	0.744828	+	0.667257i	$0.232532\pi$
$312$	2.15846	0.122199
$313$	−34.2157	−1.93399	−0.966994	−	0.254798i	$-0.917991\pi$
$313$	−34.2157	−1.93399	−0.966994	+	0.254798i	$0.917991\pi$
$314$	8.77553	0.495232
$315$	−12.8922	−0.726391
$316$	−2.49404	−0.140301
$317$	10.0629	0.565186	0.282593	−	0.959240i	$-0.408805\pi$
$317$	10.0629	0.565186	0.282593	+	0.959240i	$0.408805\pi$
$318$	23.0163	1.29069
$319$	−0.103097	−0.00577233
$320$	−1.99415	−0.111477
$321$	−38.4495	−2.14604
$322$	−5.23346	−0.291649
$323$	34.3513	1.91135
$324$	−32.0893	−1.78274
$325$	−1.14996	−0.0637883
$326$	−13.0297	−0.721650
$327$	−13.5396	−0.748741
$328$	−21.9371	−1.21127
$329$	−0.897191	−0.0494637
$330$	−2.78618	−0.153374
$331$	23.8012	1.30823	0.654117	−	0.756394i	$-0.273041\pi$
$331$	23.8012	1.30823	0.654117	+	0.756394i	$0.273041\pi$
$332$	−11.0896	−0.608621
$333$	−53.2356	−2.91729
$334$	−4.16491	−0.227894
$335$	−1.85449	−0.101321
$336$	2.87505	0.156847
$337$	19.2597	1.04914	0.524571	−	0.851367i	$-0.324226\pi$
$337$	19.2597	1.04914	0.524571	+	0.851367i	$0.324226\pi$
$338$	10.9201	0.593977
$339$	14.3515	0.779467
$340$	4.08629	0.221610
$341$	12.3448	0.668507
$342$	−31.2643	−1.69058
$343$	0.730000	0.0394163
$344$	28.1196	1.51611
$345$	−2.43128	−0.130896
$346$	19.3550	1.04053
$347$	15.1443	0.812990	0.406495	−	0.913653i	$-0.366751\pi$
$347$	15.1443	0.812990	0.406495	+	0.913653i	$0.366751\pi$
$348$	−0.192565	−0.0103226
$349$	−7.37392	−0.394717	−0.197358	−	0.980331i	$-0.563236\pi$
$349$	−7.37392	−0.394717	−0.197358	+	0.980331i	$0.563236\pi$
$350$	15.2346	0.814322
$351$	3.51158	0.187434
$352$	12.8513	0.684975
$353$	−0.452116	−0.0240637	−0.0120319	−	0.999928i	$-0.503830\pi$
$353$	−0.452116	−0.0240637	−0.0120319	+	0.999928i	$0.503830\pi$
$354$	−34.5596	−1.83682
$355$	0.595630	0.0316128
$356$	−2.53039	−0.134110
$357$	85.0886	4.50337
$358$	0.301795	0.0159503
$359$	−31.7387	−1.67511	−0.837553	−	0.546356i	$-0.816014\pi$
$359$	−31.7387	−1.67511	−0.837553	+	0.546356i	$0.816014\pi$
$360$	−9.49364	−0.500359
$361$	5.32135	0.280071
$362$	−12.1051	−0.636231
$363$	−19.4545	−1.02110
$364$	−1.16442	−0.0610321
$365$	6.64861	0.348004
$366$	29.5383	1.54399
$367$	−26.8435	−1.40122	−0.700610	−	0.713544i	$-0.747089\pi$
$367$	−26.8435	−1.40122	−0.700610	+	0.713544i	$0.747089\pi$
$368$	0.387481	0.0201989
$369$	−59.4108	−3.09280
$370$	−2.72274	−0.141548
$371$	−31.6955	−1.64555
$372$	23.0576	1.19548
$373$	−32.0923	−1.66168	−0.830839	−	0.556512i	$-0.812139\pi$
$373$	−32.0923	−1.66168	−0.830839	+	0.556512i	$0.812139\pi$
$374$	13.1416	0.679538
$375$	14.4612	0.746773
$376$	−0.660682	−0.0340721
$377$	0.0110630	0.000569772 0
$378$	−46.5211	−2.39279
$379$	−17.9196	−0.920468	−0.460234	−	0.887798i	$-0.652235\pi$
$379$	−17.9196	−0.920468	−0.460234	+	0.887798i	$0.652235\pi$
$380$	2.89317	0.148416
$381$	−46.3841	−2.37633
$382$	−1.23853	−0.0633685
$383$	19.1081	0.976377	0.488189	−	0.872738i	$-0.337658\pi$
$383$	19.1081	0.976377	0.488189	+	0.872738i	$0.337658\pi$
$384$	25.2914	1.29065
$385$	3.83682	0.195542
$386$	−5.22935	−0.266167
$387$	76.1547	3.87116
$388$	−15.9187	−0.808150
$389$	−27.3435	−1.38637	−0.693185	−	0.720760i	$-0.743793\pi$
$389$	−27.3435	−1.38637	−0.693185	+	0.720760i	$0.743793\pi$
$390$	0.298975	0.0151392
$391$	11.4677	0.579946
$392$	19.9578	1.00802
$393$	9.35191	0.471741
$394$	−1.16520	−0.0587020
$395$	−0.881844	−0.0443704
$396$	21.6410	1.08750
$397$	12.8211	0.643473	0.321737	−	0.946829i	$-0.395733\pi$
$397$	12.8211	0.643473	0.321737	+	0.946829i	$0.395733\pi$
$398$	2.92014	0.146374
$399$	60.2444	3.01599
$400$	−1.12796	−0.0563978
$401$	4.64682	0.232051	0.116026	−	0.993246i	$-0.462985\pi$
$401$	4.64682	0.232051	0.116026	+	0.993246i	$0.462985\pi$
$402$	−11.1398	−0.555601
$403$	−1.32467	−0.0659867
$404$	−18.6712	−0.928926
$405$	−11.3461	−0.563794
$406$	−0.146561	−0.00727371
$407$	15.8434	0.785327
$408$	62.6583	3.10205
$409$	15.1362	0.748438	0.374219	−	0.927340i	$-0.377911\pi$
$409$	15.1362	0.748438	0.374219	+	0.927340i	$0.377911\pi$
$410$	−3.03857	−0.150064
$411$	29.9723	1.47842
$412$	−8.58253	−0.422831
$413$	47.5916	2.34183
$414$	−10.4372	−0.512959
$415$	−3.92106	−0.192477
$416$	−1.37902	−0.0676122
$417$	−45.8760	−2.24656
$418$	9.30454	0.455100
$419$	−4.67916	−0.228592	−0.114296	−	0.993447i	$-0.536461\pi$
$419$	−4.67916	−0.228592	−0.114296	+	0.993447i	$0.536461\pi$
$420$	7.16643	0.349686
$421$	6.37642	0.310768	0.155384	−	0.987854i	$-0.450339\pi$
$421$	6.37642	0.310768	0.155384	+	0.987854i	$0.450339\pi$
$422$	4.91172	0.239099
$423$	−1.78928	−0.0869979
$424$	−23.3402	−1.13350
$425$	−33.3824	−1.61928
$426$	3.57791	0.173350
$427$	−40.6769	−1.96849
$428$	15.2744	0.738314
$429$	−1.73971	−0.0839939
$430$	3.89493	0.187830
$431$	−28.8708	−1.39066	−0.695328	−	0.718693i	$-0.744741\pi$
$431$	−28.8708	−1.39066	−0.695328	+	0.718693i	$0.744741\pi$
$432$	3.44438	0.165718
$433$	−39.1564	−1.88173	−0.940867	−	0.338776i	$-0.889987\pi$
$433$	−39.1564	−1.88173	−0.940867	+	0.338776i	$0.889987\pi$
$434$	17.5491	0.842386
$435$	−0.0680872	−0.00326453
$436$	5.37871	0.257593
$437$	8.11935	0.388401
$438$	39.9378	1.90830
$439$	−7.74997	−0.369886	−0.184943	−	0.982749i	$-0.559210\pi$
$439$	−7.74997	−0.369886	−0.184943	+	0.982749i	$0.559210\pi$
$440$	2.82539	0.134695
$441$	54.0504	2.57383
$442$	−1.41018	−0.0670756
$443$	24.9663	1.18619	0.593093	−	0.805134i	$-0.297907\pi$
$443$	24.9663	1.18619	0.593093	+	0.805134i	$0.297907\pi$
$444$	29.5924	1.40439
$445$	−0.894696	−0.0424127
$446$	−11.6932	−0.553691
$447$	8.83965	0.418101
$448$	16.4958	0.779353
$449$	−24.8347	−1.17202	−0.586011	−	0.810303i	$-0.699303\pi$
$449$	−24.8347	−1.17202	−0.586011	+	0.810303i	$0.699303\pi$
$450$	30.3825	1.43225
$451$	17.6812	0.832573
$452$	−5.70125	−0.268164
$453$	11.7842	0.553668
$454$	−17.7565	−0.833353
$455$	−0.411715	−0.0193015
$456$	44.3633	2.07750
$457$	38.1394	1.78409	0.892043	−	0.451951i	$-0.149272\pi$
$457$	38.1394	1.78409	0.892043	+	0.451951i	$0.149272\pi$
$458$	−2.13544	−0.0997825
$459$	101.938	4.75807
$460$	0.965845	0.0450328
$461$	−15.6859	−0.730563	−0.365282	−	0.930897i	$-0.619027\pi$
$461$	−15.6859	−0.730563	−0.365282	+	0.930897i	$0.619027\pi$
$462$	23.0475	1.07227
$463$	23.5997	1.09677	0.548386	−	0.836225i	$-0.315242\pi$
$463$	23.5997	1.09677	0.548386	+	0.836225i	$0.315242\pi$
$464$	0.0108513	0.000503758 0
$465$	8.15271	0.378073
$466$	19.4229	0.899747
$467$	−39.7070	−1.83742	−0.918711	−	0.394931i	$-0.870769\pi$
$467$	−39.7070	−1.83742	−0.918711	+	0.394931i	$0.870769\pi$
$468$	−2.32222	−0.107345
$469$	15.3405	0.708357
$470$	−0.0915129	−0.00422118
$471$	−33.7236	−1.55390
$472$	35.0460	1.61312
$473$	−22.6643	−1.04210
$474$	−5.29718	−0.243307
$475$	−23.6354	−1.08447
$476$	−33.8021	−1.54932
$477$	−63.2108	−2.89422
$478$	−15.4290	−0.705705
$479$	−9.32086	−0.425881	−0.212941	−	0.977065i	$-0.568304\pi$
$479$	−9.32086	−0.425881	−0.212941	+	0.977065i	$0.568304\pi$
$480$	8.48722	0.387387
$481$	−1.70010	−0.0775178
$482$	18.0942	0.824168
$483$	20.1118	0.915117
$484$	7.72844	0.351293
$485$	−5.62853	−0.255579
$486$	−31.1110	−1.41123
$487$	4.82629	0.218700	0.109350	−	0.994003i	$-0.465123\pi$
$487$	4.82629	0.218700	0.109350	+	0.994003i	$0.465123\pi$
$488$	−29.9540	−1.35595
$489$	50.0722	2.26434
$490$	2.76441	0.124883
$491$	25.6282	1.15658	0.578292	−	0.815830i	$-0.303719\pi$
$491$	25.6282	1.15658	0.578292	+	0.815830i	$0.303719\pi$
$492$	33.0250	1.48888
$493$	0.321149	0.0144638
$494$	−0.998437	−0.0449218
$495$	7.65182	0.343924
$496$	−1.29933	−0.0583414
$497$	−4.92710	−0.221011
$498$	−23.5535	−1.05546
$499$	19.7470	0.883996	0.441998	−	0.897016i	$-0.354270\pi$
$499$	19.7470	0.883996	0.441998	+	0.897016i	$0.354270\pi$
$500$	−5.74482	−0.256916
$501$	16.0054	0.715069
$502$	13.9316	0.621799
$503$	43.1323	1.92317	0.961586	−	0.274503i	$-0.0885133\pi$
$503$	43.1323	1.92317	0.961586	+	0.274503i	$0.0885133\pi$
$504$	78.5322	3.49810
$505$	−6.60176	−0.293774
$506$	3.10619	0.138087
$507$	−41.9652	−1.86374
$508$	18.4264	0.817541
$509$	−27.1601	−1.20385	−0.601925	−	0.798552i	$-0.705600\pi$
$509$	−27.1601	−1.20385	−0.601925	+	0.798552i	$0.705600\pi$
$510$	8.67899	0.384312
$511$	−54.9979	−2.43296
$512$	−2.65853	−0.117492
$513$	72.1742	3.18657
$514$	−8.79133	−0.387769
$515$	−3.03461	−0.133721
$516$	−42.3325	−1.86358
$517$	0.532506	0.0234196
$518$	22.5227	0.989592
$519$	−74.3799	−3.26491
$520$	−0.303183	−0.0132954
$521$	4.98809	0.218532	0.109266	−	0.994013i	$-0.465150\pi$
$521$	4.98809	0.218532	0.109266	+	0.994013i	$0.465150\pi$
$522$	−0.292290	−0.0127932
$523$	−12.7994	−0.559680	−0.279840	−	0.960047i	$-0.590281\pi$
$523$	−12.7994	−0.559680	−0.279840	+	0.960047i	$0.590281\pi$
$524$	−3.71512	−0.162296
$525$	−58.5452	−2.55512
$526$	−6.76864	−0.295127
$527$	−38.4541	−1.67509
$528$	−1.70642	−0.0742623
$529$	−20.2895	−0.882151
$530$	−3.23292	−0.140429
$531$	94.9128	4.11886
$532$	−23.9325	−1.03761
$533$	−1.89730	−0.0821813
$534$	−5.37438	−0.232572
$535$	5.40071	0.233493
$536$	11.2966	0.487937
$537$	−1.15977	−0.0500479
$538$	2.40095	0.103512
$539$	−16.0859	−0.692867
$540$	8.58555	0.369463
$541$	−24.0544	−1.03418	−0.517091	−	0.855931i	$-0.672985\pi$
$541$	−24.0544	−1.03418	−0.517091	+	0.855931i	$0.672985\pi$
$542$	0.163213	0.00701059
$543$	46.5190	1.99632
$544$	−40.0319	−1.71635
$545$	1.90180	0.0814643
$546$	−2.47315	−0.105841
$547$	18.6609	0.797883	0.398941	−	0.916976i	$-0.369378\pi$
$547$	18.6609	0.797883	0.398941	+	0.916976i	$0.369378\pi$
$548$	−11.9067	−0.508630
$549$	−81.1225	−3.46222
$550$	−9.04211	−0.385557
$551$	0.227380	0.00968670
$552$	14.8101	0.630359
$553$	7.29469	0.310202
$554$	13.2264	0.561937
$555$	10.4633	0.444141
$556$	18.2246	0.772895
$557$	−9.86689	−0.418073	−0.209037	−	0.977908i	$-0.567033\pi$
$557$	−9.86689	−0.418073	−0.209037	+	0.977908i	$0.567033\pi$
$558$	34.9985	1.48161
$559$	2.43202	0.102864
$560$	−0.403837	−0.0170652
$561$	−50.5023	−2.13221
$562$	12.9648	0.546885
$563$	14.2871	0.602127	0.301064	−	0.953604i	$-0.402658\pi$
$563$	14.2871	0.602127	0.301064	+	0.953604i	$0.402658\pi$
$564$	0.994617	0.0418809
$565$	−2.01585	−0.0848073
$566$	−7.39518	−0.310842
$567$	93.8561	3.94159
$568$	−3.62826	−0.152239
$569$	−5.01063	−0.210056	−0.105028	−	0.994469i	$-0.533493\pi$
$569$	−5.01063	−0.210056	−0.105028	+	0.994469i	$0.533493\pi$
$570$	6.14489	0.257381
$571$	−2.08278	−0.0871618	−0.0435809	−	0.999050i	$-0.513877\pi$
$571$	−2.08278	−0.0871618	−0.0435809	+	0.999050i	$0.513877\pi$
$572$	0.691113	0.0288969
$573$	4.75955	0.198833
$574$	25.1353	1.04913
$575$	−7.89035	−0.329050
$576$	32.8978	1.37074
$577$	20.9371	0.871623	0.435811	−	0.900038i	$-0.356461\pi$
$577$	20.9371	0.871623	0.435811	+	0.900038i	$0.356461\pi$
$578$	−26.5927	−1.10611
$579$	20.0960	0.835159
$580$	0.0270482	0.00112311
$581$	32.4353	1.34564
$582$	−33.8102	−1.40148
$583$	18.8121	0.779116
$584$	−40.4999	−1.67590
$585$	−0.821091	−0.0339479
$586$	−4.92842	−0.203591
$587$	32.7983	1.35373	0.676866	−	0.736107i	$-0.263338\pi$
$587$	32.7983	1.35373	0.676866	+	0.736107i	$0.263338\pi$
$588$	−30.0453	−1.23905
$589$	−27.2263	−1.12184
$590$	4.85432	0.199849
$591$	4.47778	0.184191
$592$	−1.66757	−0.0685365
$593$	15.2504	0.626261	0.313130	−	0.949710i	$-0.398622\pi$
$593$	15.2504	0.626261	0.313130	+	0.949710i	$0.398622\pi$
$594$	27.6114	1.13291
$595$	−11.9517	−0.489974
$596$	−3.51162	−0.143842
$597$	−11.2219	−0.459281
$598$	−0.333315	−0.0136303
$599$	−41.0613	−1.67772	−0.838859	−	0.544348i	$-0.816777\pi$
$599$	−41.0613	−1.67772	−0.838859	+	0.544348i	$0.816777\pi$
$600$	−43.1121	−1.76004
$601$	34.7653	1.41811	0.709053	−	0.705155i	$-0.249123\pi$
$601$	34.7653	1.41811	0.709053	+	0.705155i	$0.249123\pi$
$602$	−32.2192	−1.31316
$603$	30.5937	1.24587
$604$	−4.68135	−0.190481
$605$	2.73262	0.111097
$606$	−39.6563	−1.61093
$607$	−2.73333	−0.110943	−0.0554713	−	0.998460i	$-0.517666\pi$
$607$	−2.73333	−0.110943	−0.0554713	+	0.998460i	$0.517666\pi$
$608$	−28.3434	−1.14948
$609$	0.563223	0.0228230
$610$	−4.14902	−0.167989
$611$	−0.0571413	−0.00231169
$612$	−67.4121	−2.72497
$613$	31.9333	1.28977	0.644887	−	0.764278i	$-0.276904\pi$
$613$	31.9333	1.28977	0.644887	+	0.764278i	$0.276904\pi$
$614$	7.55149	0.304753
$615$	11.6770	0.470861
$616$	−23.3719	−0.941679
$617$	−15.6131	−0.628559	−0.314280	−	0.949330i	$-0.601763\pi$
$617$	−15.6131	−0.628559	−0.314280	+	0.949330i	$0.601763\pi$
$618$	−18.2287	−0.733266
$619$	−36.4824	−1.46635	−0.733175	−	0.680040i	$-0.761962\pi$
$619$	−36.4824	−1.46635	−0.733175	+	0.680040i	$0.761962\pi$
$620$	−3.23873	−0.130070
$621$	24.0944	0.966874
$622$	−22.1656	−0.888758
$623$	7.40100	0.296515
$624$	0.183110	0.00733026
$625$	21.9316	0.877264
$626$	28.8695	1.15386
$627$	−35.7566	−1.42798
$628$	13.3970	0.534597
$629$	−49.3524	−1.96781
$630$	10.8777	0.433379
$631$	−42.2229	−1.68087	−0.840434	−	0.541913i	$-0.817700\pi$
$631$	−42.2229	−1.68087	−0.840434	+	0.541913i	$0.817700\pi$
$632$	5.37173	0.213676
$633$	−18.8753	−0.750227
$634$	−8.49051	−0.337201
$635$	6.51522	0.258549
$636$	35.1373	1.39328
$637$	1.72612	0.0683913
$638$	0.0869879	0.00344388
$639$	−9.82620	−0.388718
$640$	−3.55250	−0.140425
$641$	−33.2400	−1.31290	−0.656451	−	0.754369i	$-0.727943\pi$
$641$	−33.2400	−1.31290	−0.656451	+	0.754369i	$0.727943\pi$
$642$	32.4417	1.28037
$643$	−38.3561	−1.51262	−0.756309	−	0.654214i	$-0.772999\pi$
$643$	−38.3561	−1.51262	−0.756309	+	0.654214i	$0.772999\pi$
$644$	−7.98955	−0.314832
$645$	−14.9679	−0.589361
$646$	−28.9838	−1.14035
$647$	6.16864	0.242514	0.121257	−	0.992621i	$-0.461307\pi$
$647$	6.16864	0.242514	0.121257	+	0.992621i	$0.461307\pi$
$648$	69.1146	2.71508
$649$	−28.2469	−1.10879
$650$	0.970277	0.0380574
$651$	−67.4399	−2.64318
$652$	−19.8916	−0.779014
$653$	45.2695	1.77153	0.885767	−	0.464131i	$-0.153633\pi$
$653$	45.2695	1.77153	0.885767	+	0.464131i	$0.153633\pi$
$654$	11.4240	0.446714
$655$	−1.31359	−0.0513263
$656$	−1.86100	−0.0726597
$657$	−109.683	−4.27915
$658$	0.757003	0.0295110
$659$	−42.6336	−1.66077	−0.830385	−	0.557190i	$-0.811880\pi$
$659$	−42.6336	−1.66077	−0.830385	+	0.557190i	$0.811880\pi$
$660$	−4.25346	−0.165566
$661$	−20.3166	−0.790225	−0.395113	−	0.918633i	$-0.629294\pi$
$661$	−20.3166	−0.790225	−0.395113	+	0.918633i	$0.629294\pi$
$662$	−20.0822	−0.780518
$663$	5.41922	0.210465
$664$	23.8850	0.926919
$665$	−8.46207	−0.328145
$666$	44.9174	1.74052
$667$	0.0759076	0.00293915
$668$	−6.35827	−0.246009
$669$	44.9361	1.73733
$670$	1.56472	0.0604504
$671$	24.1428	0.932021
$672$	−70.2070	−2.70829
$673$	25.5001	0.982955	0.491477	−	0.870890i	$-0.336457\pi$
$673$	25.5001	0.982955	0.491477	+	0.870890i	$0.336457\pi$
$674$	−16.2503	−0.625939
$675$	−70.1386	−2.69963
$676$	16.6710	0.641193
$677$	−8.43362	−0.324130	−0.162065	−	0.986780i	$-0.551815\pi$
$677$	−8.43362	−0.324130	−0.162065	+	0.986780i	$0.551815\pi$
$678$	−12.1091	−0.465045
$679$	46.5597	1.78680
$680$	−8.80114	−0.337508
$681$	68.2368	2.61484
$682$	−10.4159	−0.398844
$683$	28.2535	1.08109	0.540544	−	0.841316i	$-0.318218\pi$
$683$	28.2535	1.08109	0.540544	+	0.841316i	$0.318218\pi$
$684$	−47.7291	−1.82497
$685$	−4.20998	−0.160855
$686$	−0.615936	−0.0235165
$687$	8.20632	0.313091
$688$	2.38549	0.0909458
$689$	−2.01866	−0.0769047
$690$	2.05139	0.0780950
$691$	−29.9619	−1.13981	−0.569903	−	0.821712i	$-0.693019\pi$
$691$	−29.9619	−1.13981	−0.569903	+	0.821712i	$0.693019\pi$
$692$	29.5480	1.12325
$693$	−63.2965	−2.40444
$694$	−12.7780	−0.485046
$695$	6.44385	0.244429
$696$	0.414751	0.0157211
$697$	−55.0771	−2.08619
$698$	6.22172	0.235496
$699$	−74.6405	−2.82316
$700$	23.2575	0.879052
$701$	35.3794	1.33626	0.668130	−	0.744045i	$-0.267095\pi$
$701$	35.3794	1.33626	0.668130	+	0.744045i	$0.267095\pi$
$702$	−2.96289	−0.111827
$703$	−34.9425	−1.31788
$704$	−9.79068	−0.369000
$705$	0.351677	0.0132449
$706$	0.381472	0.0143569
$707$	54.6103	2.05383
$708$	−52.7596	−1.98283
$709$	−40.2450	−1.51143	−0.755716	−	0.654900i	$-0.772711\pi$
$709$	−40.2450	−1.51143	−0.755716	+	0.654900i	$0.772711\pi$
$710$	−0.502561	−0.0188608
$711$	14.5479	0.545589
$712$	5.45002	0.204248
$713$	−9.08912	−0.340390
$714$	−71.7933	−2.68680
$715$	0.244364	0.00913868
$716$	0.460729	0.0172182
$717$	59.2923	2.21431
$718$	26.7795	0.999401
$719$	−33.6935	−1.25655	−0.628277	−	0.777990i	$-0.716240\pi$
$719$	−33.6935	−1.25655	−0.628277	+	0.777990i	$0.716240\pi$
$720$	−0.805378	−0.0300147
$721$	25.1025	0.934868
$722$	−4.48988	−0.167096
$723$	−69.5345	−2.58602
$724$	−18.4800	−0.686805
$725$	−0.220966	−0.00820649
$726$	16.4147	0.609206
$727$	5.82622	0.216083	0.108041	−	0.994146i	$-0.465542\pi$
$727$	5.82622	0.216083	0.108041	+	0.994146i	$0.465542\pi$
$728$	2.50795	0.0929509
$729$	44.8203	1.66001
$730$	−5.60975	−0.207626
$731$	70.5996	2.61122
$732$	45.0940	1.66672
$733$	−48.4035	−1.78782	−0.893911	−	0.448244i	$-0.852050\pi$
$733$	−48.4035	−1.78782	−0.893911	+	0.448244i	$0.852050\pi$
$734$	22.6492	0.835996
$735$	−10.6234	−0.391850
$736$	−9.46205	−0.348776
$737$	−9.10496	−0.335386
$738$	50.1277	1.84523
$739$	6.23074	0.229201	0.114601	−	0.993412i	$-0.463441\pi$
$739$	6.23074	0.229201	0.114601	+	0.993412i	$0.463441\pi$
$740$	−4.15661	−0.152800
$741$	3.83691	0.140953
$742$	26.7430	0.981765
$743$	29.3752	1.07767	0.538836	−	0.842411i	$-0.318864\pi$
$743$	29.3752	1.07767	0.538836	+	0.842411i	$0.318864\pi$
$744$	−49.6620	−1.82070
$745$	−1.24164	−0.0454901
$746$	27.0778	0.991390
$747$	64.6863	2.36675
$748$	20.0624	0.733554
$749$	−44.6751	−1.63239
$750$	−12.2016	−0.445540
$751$	−6.13271	−0.223786	−0.111893	−	0.993720i	$-0.535691\pi$
$751$	−6.13271	−0.223786	−0.111893	+	0.993720i	$0.535691\pi$
$752$	−0.0560479	−0.00204386
$753$	−53.5381	−1.95104
$754$	−0.00933436	−0.000339938 0
$755$	−1.65523	−0.0602400
$756$	−71.0204	−2.58299
$757$	4.63356	0.168410	0.0842048	−	0.996448i	$-0.473165\pi$
$757$	4.63356	0.168410	0.0842048	+	0.996448i	$0.473165\pi$
$758$	15.1196	0.549169
$759$	−11.9368	−0.433280
$760$	−6.23138	−0.226036
$761$	29.8065	1.08048	0.540242	−	0.841510i	$-0.318333\pi$
$761$	29.8065	1.08048	0.540242	+	0.841510i	$0.318333\pi$
$762$	39.1365	1.41777
$763$	−15.7319	−0.569532
$764$	−1.89077	−0.0684056
$765$	−23.8356	−0.861777
$766$	−16.1224	−0.582526
$767$	3.03107	0.109446
$768$	−49.7337	−1.79461
$769$	−48.5233	−1.74979	−0.874897	−	0.484308i	$-0.839071\pi$
$769$	−48.5233	−1.74979	−0.874897	+	0.484308i	$0.839071\pi$
$770$	−3.23730	−0.116664
$771$	33.7844	1.21671
$772$	−7.98327	−0.287324
$773$	−29.1497	−1.04844	−0.524221	−	0.851582i	$-0.675644\pi$
$773$	−29.1497	−1.04844	−0.524221	+	0.851582i	$0.675644\pi$
$774$	−64.2553	−2.30961
$775$	26.4584	0.950413
$776$	34.2861	1.23080
$777$	−86.5530	−3.10507
$778$	23.0710	0.827136
$779$	−38.9957	−1.39716
$780$	0.456424	0.0163426
$781$	2.92436	0.104642
$782$	−9.67584	−0.346007
$783$	0.674755	0.0241138
$784$	1.69309	0.0604674
$785$	4.73690	0.169067
$786$	−7.89065	−0.281450
$787$	−14.1697	−0.505094	−0.252547	−	0.967585i	$-0.581268\pi$
$787$	−14.1697	−0.505094	−0.252547	+	0.967585i	$0.581268\pi$
$788$	−1.77883	−0.0633683
$789$	26.0113	0.926028
$790$	0.744054	0.0264722
$791$	16.6753	0.592904
$792$	−46.6109	−1.65625
$793$	−2.59067	−0.0919976
$794$	−10.8178	−0.383909
$795$	12.4238	0.440628
$796$	4.45798	0.158009
$797$	3.04716	0.107936	0.0539680	−	0.998543i	$-0.482813\pi$
$797$	3.04716	0.107936	0.0539680	+	0.998543i	$0.482813\pi$
$798$	−50.8311	−1.79940
$799$	−1.65876	−0.0586829
$800$	27.5439	0.973826
$801$	14.7599	0.521517
$802$	−3.92075	−0.138446
$803$	32.6427	1.15193
$804$	−17.0063	−0.599766
$805$	−2.82495	−0.0995663
$806$	1.11769	0.0393690
$807$	−9.22665	−0.324793
$808$	40.2144	1.41474
$809$	−21.1128	−0.742286	−0.371143	−	0.928576i	$-0.621034\pi$
$809$	−21.1128	−0.742286	−0.371143	+	0.928576i	$0.621034\pi$
$810$	9.57327	0.336370
$811$	−23.3714	−0.820680	−0.410340	−	0.911933i	$-0.634590\pi$
$811$	−23.3714	−0.820680	−0.410340	+	0.911933i	$0.634590\pi$
$812$	−0.223745	−0.00785190
$813$	−0.627213	−0.0219973
$814$	−13.3678	−0.468542
$815$	−7.03326	−0.246364
$816$	5.31552	0.186080
$817$	49.9859	1.74879
$818$	−12.7712	−0.446533
$819$	6.79213	0.237336
$820$	−4.63877	−0.161993
$821$	30.6215	1.06870	0.534350	−	0.845263i	$-0.320557\pi$
$821$	30.6215	1.06870	0.534350	+	0.845263i	$0.320557\pi$
$822$	−25.2890	−0.882056
$823$	36.3101	1.26569	0.632846	−	0.774278i	$-0.281887\pi$
$823$	36.3101	1.26569	0.632846	+	0.774278i	$0.281887\pi$
$824$	18.4852	0.643964
$825$	34.7481	1.20977
$826$	−40.1553	−1.39718
$827$	−17.2567	−0.600074	−0.300037	−	0.953928i	$-0.596999\pi$
$827$	−17.2567	−0.600074	−0.300037	+	0.953928i	$0.596999\pi$
$828$	−15.9337	−0.553734
$829$	−19.5336	−0.678431	−0.339215	−	0.940709i	$-0.610162\pi$
$829$	−19.5336	−0.678431	−0.339215	+	0.940709i	$0.610162\pi$
$830$	3.30839	0.114836
$831$	−50.8281	−1.76321
$832$	1.05060	0.0364231
$833$	50.1078	1.73613
$834$	38.7078	1.34034
$835$	−2.24816	−0.0778007
$836$	14.2046	0.491276
$837$	−80.7947	−2.79267
$838$	3.94803	0.136382
$839$	21.7991	0.752590	0.376295	−	0.926500i	$-0.377198\pi$
$839$	21.7991	0.752590	0.376295	+	0.926500i	$0.377198\pi$
$840$	−15.4352	−0.532566
$841$	−28.9979	−0.999927
$842$	−5.38009	−0.185410
$843$	−49.8225	−1.71598
$844$	7.49837	0.258104
$845$	5.89453	0.202778
$846$	1.50970	0.0519046
$847$	−22.6045	−0.776699
$848$	−1.98003	−0.0679945
$849$	28.4191	0.975340
$850$	28.1663	0.966096
$851$	−11.6651	−0.399873
$852$	5.46214	0.187130
$853$	38.7327	1.32618	0.663091	−	0.748539i	$-0.269244\pi$
$853$	38.7327	1.32618	0.663091	+	0.748539i	$0.269244\pi$
$854$	34.3210	1.17444
$855$	−16.8760	−0.577148
$856$	−32.8983	−1.12444
$857$	0.554351	0.0189363	0.00946813	−	0.999955i	$-0.496986\pi$
$857$	0.554351	0.0189363	0.00946813	+	0.999955i	$0.496986\pi$
$858$	1.46788	0.0501124
$859$	−37.6669	−1.28518	−0.642589	−	0.766211i	$-0.722140\pi$
$859$	−37.6669	−1.28518	−0.642589	+	0.766211i	$0.722140\pi$
$860$	5.94612	0.202761
$861$	−96.5929	−3.29188
$862$	24.3596	0.829692
$863$	14.0519	0.478334	0.239167	−	0.970978i	$-0.423126\pi$
$863$	14.0519	0.478334	0.239167	+	0.970978i	$0.423126\pi$
$864$	−84.1096	−2.86147
$865$	10.4476	0.355228
$866$	33.0381	1.12268
$867$	102.194	3.47068
$868$	26.7910	0.909347
$869$	−4.32958	−0.146871
$870$	0.0574484	0.00194768
$871$	0.977022	0.0331051
$872$	−11.5848	−0.392310
$873$	92.8548	3.14266
$874$	−6.85068	−0.231728
$875$	16.8027	0.568035
$876$	60.9701	2.05999
$877$	−53.3506	−1.80152	−0.900761	−	0.434316i	$-0.856990\pi$
$877$	−53.3506	−1.80152	−0.900761	+	0.434316i	$0.856990\pi$
$878$	6.53902	0.220681
$879$	18.9395	0.638814
$880$	0.239688	0.00807987
$881$	−8.11603	−0.273436	−0.136718	−	0.990610i	$-0.543655\pi$
$881$	−8.11603	−0.273436	−0.136718	+	0.990610i	$0.543655\pi$
$882$	−45.6049	−1.53560
$883$	−54.2198	−1.82464	−0.912321	−	0.409477i	$-0.865711\pi$
$883$	−54.2198	−1.82464	−0.912321	+	0.409477i	$0.865711\pi$
$884$	−2.15283	−0.0724074
$885$	−18.6548	−0.627073
$886$	−21.0653	−0.707702
$887$	53.3558	1.79151	0.895756	−	0.444546i	$-0.146635\pi$
$887$	53.3558	1.79151	0.895756	+	0.444546i	$0.146635\pi$
$888$	−63.7367	−2.13886
$889$	−53.8945	−1.80756
$890$	0.754898	0.0253042
$891$	−55.7060	−1.86622
$892$	−17.8512	−0.597703
$893$	−1.17444	−0.0393010
$894$	−7.45843	−0.249447
$895$	0.162904	0.00544529
$896$	29.3865	0.981735
$897$	1.28090	0.0427681
$898$	20.9542	0.699252
$899$	−0.254538	−0.00848931
$900$	46.3829	1.54610
$901$	−58.5999	−1.95225
$902$	−14.9184	−0.496730
$903$	123.816	4.12033
$904$	12.2795	0.408410
$905$	−6.53417	−0.217203
$906$	−9.94285	−0.330329
$907$	26.1423	0.868041	0.434020	−	0.900903i	$-0.357095\pi$
$907$	26.1423	0.868041	0.434020	+	0.900903i	$0.357095\pi$
$908$	−27.1076	−0.899597
$909$	108.910	3.61232
$910$	0.347384	0.0115157
$911$	52.0996	1.72614	0.863068	−	0.505087i	$-0.168540\pi$
$911$	52.0996	1.72614	0.863068	+	0.505087i	$0.168540\pi$
$912$	3.76349	0.124622
$913$	−19.2512	−0.637122
$914$	−32.1800	−1.06442
$915$	15.9443	0.527103
$916$	−3.26002	−0.107714
$917$	10.8661	0.358832
$918$	−86.0101	−2.83876
$919$	29.3400	0.967838	0.483919	−	0.875113i	$-0.339213\pi$
$919$	29.3400	0.967838	0.483919	+	0.875113i	$0.339213\pi$
$920$	−2.08026	−0.0685841
$921$	−29.0198	−0.956233
$922$	13.2349	0.435868
$923$	−0.313803	−0.0103290
$924$	35.1850	1.15750
$925$	33.9569	1.11650
$926$	−19.9122	−0.654356
$927$	50.0624	1.64427
$928$	−0.264981	−0.00869844
$929$	22.0412	0.723148	0.361574	−	0.932343i	$-0.382240\pi$
$929$	22.0412	0.723148	0.361574	+	0.932343i	$0.382240\pi$
$930$	−6.87883	−0.225566
$931$	35.4773	1.16272
$932$	29.6515	0.971268
$933$	85.1804	2.78868
$934$	33.5027	1.09624
$935$	7.09367	0.231988
$936$	5.00165	0.163484
$937$	15.1011	0.493330	0.246665	−	0.969101i	$-0.420665\pi$
$937$	15.1011	0.493330	0.246665	+	0.969101i	$0.420665\pi$
$938$	−12.9435	−0.422620
$939$	−110.943	−3.62049
$940$	−0.139706	−0.00455672
$941$	25.8072	0.841292	0.420646	−	0.907225i	$-0.361803\pi$
$941$	25.8072	0.841292	0.420646	+	0.907225i	$0.361803\pi$
$942$	28.4542	0.927089
$943$	−13.0182	−0.423930
$944$	2.97307	0.0967652
$945$	−25.1114	−0.816874
$946$	19.1229	0.621740
$947$	−34.0160	−1.10537	−0.552686	−	0.833390i	$-0.686397\pi$
$947$	−34.0160	−1.10537	−0.552686	+	0.833390i	$0.686397\pi$
$948$	−8.08682	−0.262648
$949$	−3.50277	−0.113705
$950$	19.9423	0.647013
$951$	32.6283	1.05805
$952$	72.8038	2.35958
$953$	21.3156	0.690481	0.345240	−	0.938514i	$-0.387797\pi$
$953$	21.3156	0.690481	0.345240	+	0.938514i	$0.387797\pi$
$954$	53.3339	1.72675
$955$	−0.668538	−0.0216334
$956$	−23.5543	−0.761802
$957$	−0.334287	−0.0108060
$958$	7.86446	0.254089
$959$	34.8253	1.12457
$960$	−6.46595	−0.208688
$961$	−0.521821	−0.0168329
$962$	1.43445	0.0462486
$963$	−89.0963	−2.87109
$964$	27.6231	0.889681
$965$	−2.82273	−0.0908667
$966$	−16.9693	−0.545977
$967$	−31.2199	−1.00396	−0.501982	−	0.864878i	$-0.667396\pi$
$967$	−31.2199	−1.00396	−0.501982	+	0.864878i	$0.667396\pi$
$968$	−16.6457	−0.535013
$969$	111.382	3.57812
$970$	4.74906	0.152483
$971$	22.0529	0.707711	0.353855	−	0.935300i	$-0.384870\pi$
$971$	22.0529	0.707711	0.353855	+	0.935300i	$0.384870\pi$
$972$	−47.4950	−1.52340
$973$	−53.3041	−1.70885
$974$	−4.07217	−0.130481
$975$	−3.72869	−0.119414
$976$	−2.54110	−0.0813386
$977$	−6.52628	−0.208794	−0.104397	−	0.994536i	$-0.533291\pi$
$977$	−6.52628	−0.208794	−0.104397	+	0.994536i	$0.533291\pi$
$978$	−42.2483	−1.35095
$979$	−4.39268	−0.140391
$980$	4.22023	0.134810
$981$	−31.3743	−1.00171
$982$	−21.6237	−0.690041
$983$	−2.33451	−0.0744593	−0.0372296	−	0.999307i	$-0.511853\pi$
$983$	−2.33451	−0.0744593	−0.0372296	+	0.999307i	$0.511853\pi$
$984$	−71.1300	−2.26754
$985$	−0.628959	−0.0200403
$986$	−0.270969	−0.00862940
$987$	−2.90910	−0.0925977
$988$	−1.52424	−0.0484926
$989$	16.6871	0.530619
$990$	−6.45621	−0.205192
$991$	6.99763	0.222287	0.111143	−	0.993804i	$-0.464549\pi$
$991$	6.99763	0.222287	0.111143	+	0.993804i	$0.464549\pi$
$992$	31.7287	1.00739
$993$	77.1744	2.44905
$994$	4.15723	0.131859
$995$	1.57625	0.0499705
$996$	−35.9575	−1.13936
$997$	−61.4735	−1.94689	−0.973443	−	0.228929i	$-0.926478\pi$
$997$	−61.4735	−1.94689	−0.973443	+	0.228929i	$0.926478\pi$
$998$	−16.6615	−0.527409
$999$	−103.693	−3.28069

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.b.1.43	✓	122

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.b.1.43	✓	122	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q-0.843748 q^{2} +3.24245 q^{3} -1.28809 q^{4} -0.455443 q^{5} -2.73581 q^{6} +3.76746 q^{7} +2.77432 q^{8} +7.51351 q^{9} +O(q^{10})\)	\(q-0.843748 q^{2} +3.24245 q^{3} -1.28809 q^{4} -0.455443 q^{5} -2.73581 q^{6} +3.76746 q^{7} +2.77432 q^{8} +7.51351 q^{9} +0.384279 q^{10} -2.23609 q^{11} -4.17657 q^{12} +0.239946 q^{13} -3.17879 q^{14} -1.47675 q^{15} +0.235355 q^{16} +6.96544 q^{17} -6.33951 q^{18} +4.93167 q^{19} +0.586651 q^{20} +12.2158 q^{21} +1.88669 q^{22} +1.64637 q^{23} +8.99560 q^{24} -4.79257 q^{25} -0.202454 q^{26} +14.6348 q^{27} -4.85283 q^{28} +0.0461060 q^{29} +1.24601 q^{30} -5.52070 q^{31} -5.74722 q^{32} -7.25040 q^{33} -5.87708 q^{34} -1.71586 q^{35} -9.67807 q^{36} -7.08532 q^{37} -4.16108 q^{38} +0.778015 q^{39} -1.26354 q^{40} -7.90719 q^{41} -10.3071 q^{42} +10.1357 q^{43} +2.88028 q^{44} -3.42197 q^{45} -1.38912 q^{46} -0.238142 q^{47} +0.763128 q^{48} +7.19376 q^{49} +4.04372 q^{50} +22.5851 q^{51} -0.309073 q^{52} -8.41295 q^{53} -12.3481 q^{54} +1.01841 q^{55} +10.4521 q^{56} +15.9907 q^{57} -0.0389019 q^{58} +12.6323 q^{59} +1.90219 q^{60} -10.7969 q^{61} +4.65808 q^{62} +28.3069 q^{63} +4.37849 q^{64} -0.109282 q^{65} +6.11751 q^{66} +4.07183 q^{67} -8.97212 q^{68} +5.33828 q^{69} +1.44776 q^{70} -1.30780 q^{71} +20.8449 q^{72} -14.5981 q^{73} +5.97822 q^{74} -15.5397 q^{75} -6.35243 q^{76} -8.42436 q^{77} -0.656449 q^{78} +1.93623 q^{79} -0.107191 q^{80} +24.9123 q^{81} +6.67168 q^{82} +8.60934 q^{83} -15.7351 q^{84} -3.17236 q^{85} -8.55197 q^{86} +0.149497 q^{87} -6.20361 q^{88} +1.96445 q^{89} +2.88728 q^{90} +0.903989 q^{91} -2.12067 q^{92} -17.9006 q^{93} +0.200932 q^{94} -2.24609 q^{95} -18.6351 q^{96} +12.3584 q^{97} -6.06972 q^{98} -16.8008 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * q^99

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