LMFDB - Embedded newform 4031.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$1$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.55145 q^{2} +0.350675 q^{3} +0.406987 q^{4} -2.80587 q^{5} -0.544053 q^{6} -3.32540 q^{7} +2.47147 q^{8} -2.87703 q^{9} +O(q^{10})$	\(q-1.55145 q^{2} +0.350675 q^{3} +0.406987 q^{4} -2.80587 q^{5} -0.544053 q^{6} -3.32540 q^{7} +2.47147 q^{8} -2.87703 q^{9} +4.35316 q^{10} -3.82247 q^{11} +0.142720 q^{12} +0.682868 q^{13} +5.15918 q^{14} -0.983948 q^{15} -4.64834 q^{16} +2.91413 q^{17} +4.46355 q^{18} +4.20224 q^{19} -1.14195 q^{20} -1.16613 q^{21} +5.93036 q^{22} +2.71492 q^{23} +0.866683 q^{24} +2.87291 q^{25} -1.05943 q^{26} -2.06092 q^{27} -1.35339 q^{28} -1.00000 q^{29} +1.52654 q^{30} +2.51179 q^{31} +2.26870 q^{32} -1.34044 q^{33} -4.52112 q^{34} +9.33063 q^{35} -1.17091 q^{36} -2.72784 q^{37} -6.51956 q^{38} +0.239465 q^{39} -6.93464 q^{40} +5.25069 q^{41} +1.80919 q^{42} +7.56996 q^{43} -1.55570 q^{44} +8.07257 q^{45} -4.21205 q^{46} +6.67214 q^{47} -1.63005 q^{48} +4.05826 q^{49} -4.45717 q^{50} +1.02191 q^{51} +0.277919 q^{52} -0.715752 q^{53} +3.19741 q^{54} +10.7254 q^{55} -8.21863 q^{56} +1.47362 q^{57} +1.55145 q^{58} -1.54046 q^{59} -0.400454 q^{60} +4.04596 q^{61} -3.89691 q^{62} +9.56726 q^{63} +5.77691 q^{64} -1.91604 q^{65} +2.07963 q^{66} -7.46543 q^{67} +1.18601 q^{68} +0.952053 q^{69} -14.4760 q^{70} +3.18730 q^{71} -7.11050 q^{72} +7.53899 q^{73} +4.23210 q^{74} +1.00746 q^{75} +1.71026 q^{76} +12.7112 q^{77} -0.371516 q^{78} -10.7323 q^{79} +13.0426 q^{80} +7.90837 q^{81} -8.14617 q^{82} +4.35926 q^{83} -0.474601 q^{84} -8.17668 q^{85} -11.7444 q^{86} -0.350675 q^{87} -9.44714 q^{88} +9.22015 q^{89} -12.5242 q^{90} -2.27081 q^{91} +1.10494 q^{92} +0.880820 q^{93} -10.3515 q^{94} -11.7909 q^{95} +0.795574 q^{96} -17.8047 q^{97} -6.29617 q^{98} +10.9974 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) $ 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * 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 $

$2$	−1.55145	−1.09704	−0.548519	−	0.836138i	$-0.684808\pi$
$2$	−1.55145	−1.09704	−0.548519	+	0.836138i	$0.684808\pi$
$3$	0.350675	0.202462	0.101231	−	0.994863i	$-0.467722\pi$
$3$	0.350675	0.202462	0.101231	+	0.994863i	$0.467722\pi$
$4$	0.406987	0.203494
$5$	−2.80587	−1.25482	−0.627412	−	0.778688i	$-0.715886\pi$
$5$	−2.80587	−1.25482	−0.627412	+	0.778688i	$0.715886\pi$
$6$	−0.544053	−0.222109
$7$	−3.32540	−1.25688	−0.628441	−	0.777857i	$-0.716307\pi$
$7$	−3.32540	−1.25688	−0.628441	+	0.777857i	$0.716307\pi$
$8$	2.47147	0.873798
$9$	−2.87703	−0.959009
$10$	4.35316	1.37659
$11$	−3.82247	−1.15252	−0.576259	−	0.817267i	$-0.695488\pi$
$11$	−3.82247	−1.15252	−0.576259	+	0.817267i	$0.695488\pi$
$12$	0.142720	0.0411997
$13$	0.682868	0.189394	0.0946968	−	0.995506i	$-0.469812\pi$
$13$	0.682868	0.189394	0.0946968	+	0.995506i	$0.469812\pi$
$14$	5.15918	1.37885
$15$	−0.983948	−0.254054
$16$	−4.64834	−1.16208
$17$	2.91413	0.706781	0.353390	−	0.935476i	$-0.385029\pi$
$17$	2.91413	0.706781	0.353390	+	0.935476i	$0.385029\pi$
$18$	4.46355	1.05207
$19$	4.20224	0.964060	0.482030	−	0.876155i	$-0.339900\pi$
$19$	4.20224	0.964060	0.482030	+	0.876155i	$0.339900\pi$
$20$	−1.14195	−0.255349
$21$	−1.16613	−0.254471
$22$	5.93036	1.26436
$23$	2.71492	0.566100	0.283050	−	0.959105i	$-0.408654\pi$
$23$	2.71492	0.566100	0.283050	+	0.959105i	$0.408654\pi$
$24$	0.866683	0.176911
$25$	2.87291	0.574582
$26$	−1.05943	−0.207772
$27$	−2.06092	−0.396625
$28$	−1.35339	−0.255767
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	1.52654	0.278707
$31$	2.51179	0.451131	0.225565	−	0.974228i	$-0.427577\pi$
$31$	2.51179	0.451131	0.225565	+	0.974228i	$0.427577\pi$
$32$	2.26870	0.401053
$33$	−1.34044	−0.233341
$34$	−4.52112	−0.775366
$35$	9.33063	1.57716
$36$	−1.17091	−0.195152
$37$	−2.72784	−0.448455	−0.224227	−	0.974537i	$-0.571986\pi$
$37$	−2.72784	−0.448455	−0.224227	+	0.974537i	$0.571986\pi$
$38$	−6.51956	−1.05761
$39$	0.239465	0.0383450
$40$	−6.93464	−1.09646
$41$	5.25069	0.820020	0.410010	−	0.912081i	$-0.365525\pi$
$41$	5.25069	0.820020	0.410010	+	0.912081i	$0.365525\pi$
$42$	1.80919	0.279164
$43$	7.56996	1.15441	0.577204	−	0.816600i	$-0.304144\pi$
$43$	7.56996	1.15441	0.577204	+	0.816600i	$0.304144\pi$
$44$	−1.55570	−0.234530
$45$	8.07257	1.20339
$46$	−4.21205	−0.621033
$47$	6.67214	0.973232	0.486616	−	0.873616i	$-0.338231\pi$
$47$	6.67214	0.973232	0.486616	+	0.873616i	$0.338231\pi$
$48$	−1.63005	−0.235278
$49$	4.05826	0.579751
$50$	−4.45717	−0.630339
$51$	1.02191	0.143096
$52$	0.277919	0.0385404
$53$	−0.715752	−0.0983161	−0.0491581	−	0.998791i	$-0.515654\pi$
$53$	−0.715752	−0.0983161	−0.0491581	+	0.998791i	$0.515654\pi$
$54$	3.19741	0.435113
$55$	10.7254	1.44621
$56$	−8.21863	−1.09826
$57$	1.47362	0.195186
$58$	1.55145	0.203715
$59$	−1.54046	−0.200551	−0.100275	−	0.994960i	$-0.531972\pi$
$59$	−1.54046	−0.200551	−0.100275	+	0.994960i	$0.531972\pi$
$60$	−0.400454	−0.0516984
$61$	4.04596	0.518032	0.259016	−	0.965873i	$-0.416602\pi$
$61$	4.04596	0.518032	0.259016	+	0.965873i	$0.416602\pi$
$62$	−3.89691	−0.494908
$63$	9.56726	1.20536
$64$	5.77691	0.722114
$65$	−1.91604	−0.237656
$66$	2.07963	0.255984
$67$	−7.46543	−0.912048	−0.456024	−	0.889967i	$-0.650727\pi$
$67$	−7.46543	−0.912048	−0.456024	+	0.889967i	$0.650727\pi$
$68$	1.18601	0.143825
$69$	0.952053	0.114614
$70$	−14.4760	−1.73021
$71$	3.18730	0.378263	0.189131	−	0.981952i	$-0.439433\pi$
$71$	3.18730	0.378263	0.189131	+	0.981952i	$0.439433\pi$
$72$	−7.11050	−0.837980
$73$	7.53899	0.882372	0.441186	−	0.897416i	$-0.354558\pi$
$73$	7.53899	0.882372	0.441186	+	0.897416i	$0.354558\pi$
$74$	4.23210	0.491972
$75$	1.00746	0.116331
$76$	1.71026	0.196180
$77$	12.7112	1.44858
$78$	−0.371516	−0.0420660
$79$	−10.7323	−1.20748	−0.603739	−	0.797182i	$-0.706323\pi$
$79$	−10.7323	−1.20748	−0.603739	+	0.797182i	$0.706323\pi$
$80$	13.0426	1.45821
$81$	7.90837	0.878708
$82$	−8.14617	−0.899594
$83$	4.35926	0.478491	0.239246	−	0.970959i	$-0.423100\pi$
$83$	4.35926	0.478491	0.239246	+	0.970959i	$0.423100\pi$
$84$	−0.474601	−0.0517832
$85$	−8.17668	−0.886885
$86$	−11.7444	−1.26643
$87$	−0.350675	−0.0375963
$88$	−9.44714	−1.00707
$89$	9.22015	0.977333	0.488667	−	0.872471i	$-0.337483\pi$
$89$	9.22015	0.977333	0.488667	+	0.872471i	$0.337483\pi$
$90$	−12.5242	−1.32016
$91$	−2.27081	−0.238045
$92$	1.10494	0.115198
$93$	0.880820	0.0913368
$94$	−10.3515	−1.06767
$95$	−11.7909	−1.20973
$96$	0.795574	0.0811979
$97$	−17.8047	−1.80780	−0.903898	−	0.427747i	$-0.859307\pi$
$97$	−17.8047	−1.80780	−0.903898	+	0.427747i	$0.859307\pi$
$98$	−6.29617	−0.636010
$99$	10.9974	1.10528
$100$	1.16924	0.116924
$101$	−2.76335	−0.274964	−0.137482	−	0.990504i	$-0.543901\pi$
$101$	−2.76335	−0.274964	−0.137482	+	0.990504i	$0.543901\pi$
$102$	−1.58544	−0.156982
$103$	−11.6156	−1.14452	−0.572259	−	0.820073i	$-0.693933\pi$
$103$	−11.6156	−1.14452	−0.572259	+	0.820073i	$0.693933\pi$
$104$	1.68769	0.165492
$105$	3.27202	0.319316
$106$	1.11045	0.107857
$107$	−16.1174	−1.55813	−0.779064	−	0.626944i	$-0.784305\pi$
$107$	−16.1174	−1.55813	−0.779064	+	0.626944i	$0.784305\pi$
$108$	−0.838770	−0.0807106
$109$	17.8945	1.71398	0.856990	−	0.515333i	$-0.172332\pi$
$109$	17.8945	1.71398	0.856990	+	0.515333i	$0.172332\pi$
$110$	−16.6398	−1.58655
$111$	−0.956585	−0.0907950
$112$	15.4576	1.46060
$113$	4.06640	0.382535	0.191267	−	0.981538i	$-0.438740\pi$
$113$	4.06640	0.382535	0.191267	+	0.981538i	$0.438740\pi$
$114$	−2.28624	−0.214126
$115$	−7.61771	−0.710355
$116$	−0.406987	−0.0377878
$117$	−1.96463	−0.181630
$118$	2.38994	0.220012
$119$	−9.69064	−0.888340
$120$	−2.43180	−0.221992
$121$	3.61129	0.328299
$122$	−6.27709	−0.568301
$123$	1.84128	0.166023
$124$	1.02227	0.0918022
$125$	5.96833	0.533824
$126$	−14.8431	−1.32233
$127$	14.7589	1.30964	0.654821	−	0.755784i	$-0.272744\pi$
$127$	14.7589	1.30964	0.654821	+	0.755784i	$0.272744\pi$
$128$	−13.5000	−1.19324
$129$	2.65459	0.233724
$130$	2.97263	0.260717
$131$	8.69323	0.759531	0.379765	−	0.925083i	$-0.376005\pi$
$131$	8.69323	0.759531	0.379765	+	0.925083i	$0.376005\pi$
$132$	−0.545543	−0.0474834
$133$	−13.9741	−1.21171
$134$	11.5822	1.00055
$135$	5.78269	0.497694
$136$	7.20220	0.617584
$137$	−15.1191	−1.29171	−0.645854	−	0.763461i	$-0.723499\pi$
$137$	−15.1191	−1.29171	−0.645854	+	0.763461i	$0.723499\pi$
$138$	−1.47706	−0.125736
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	3.79745	0.320943
$141$	2.33975	0.197043
$142$	−4.94492	−0.414969
$143$	−2.61024	−0.218280
$144$	13.3734	1.11445
$145$	2.80587	0.233015
$146$	−11.6963	−0.967996
$147$	1.42313	0.117378
$148$	−1.11020	−0.0912576
$149$	−2.81214	−0.230379	−0.115190	−	0.993344i	$-0.536748\pi$
$149$	−2.81214	−0.230379	−0.115190	+	0.993344i	$0.536748\pi$
$150$	−1.56302	−0.127620
$151$	−4.90219	−0.398934	−0.199467	−	0.979905i	$-0.563921\pi$
$151$	−4.90219	−0.398934	−0.199467	+	0.979905i	$0.563921\pi$
$152$	10.3857	0.842394
$153$	−8.38404	−0.677809
$154$	−19.7208	−1.58915
$155$	−7.04776	−0.566089
$156$	0.0974590	0.00780296
$157$	−11.8804	−0.948162	−0.474081	−	0.880481i	$-0.657220\pi$
$157$	−11.8804	−0.948162	−0.474081	+	0.880481i	$0.657220\pi$
$158$	16.6506	1.32465
$159$	−0.250996	−0.0199053
$160$	−6.36567	−0.503250
$161$	−9.02818	−0.711520
$162$	−12.2694	−0.963976
$163$	−2.69216	−0.210866	−0.105433	−	0.994426i	$-0.533623\pi$
$163$	−2.69216	−0.210866	−0.105433	+	0.994426i	$0.533623\pi$
$164$	2.13696	0.166869
$165$	3.76111	0.292802
$166$	−6.76317	−0.524924
$167$	−4.68479	−0.362520	−0.181260	−	0.983435i	$-0.558018\pi$
$167$	−4.68479	−0.362520	−0.181260	+	0.983435i	$0.558018\pi$
$168$	−2.88207	−0.222356
$169$	−12.5337	−0.964130
$170$	12.6857	0.972947
$171$	−12.0900	−0.924543
$172$	3.08088	0.234915
$173$	2.09648	0.159392	0.0796961	−	0.996819i	$-0.474605\pi$
$173$	2.09648	0.159392	0.0796961	+	0.996819i	$0.474605\pi$
$174$	0.544053	0.0412445
$175$	−9.55357	−0.722182
$176$	17.7681	1.33932
$177$	−0.540200	−0.0406039
$178$	−14.3046	−1.07217
$179$	9.18320	0.686384	0.343192	−	0.939265i	$-0.388492\pi$
$179$	9.18320	0.686384	0.343192	+	0.939265i	$0.388492\pi$
$180$	3.28543	0.244882
$181$	10.5343	0.783006	0.391503	−	0.920177i	$-0.371955\pi$
$181$	10.5343	0.783006	0.391503	+	0.920177i	$0.371955\pi$
$182$	3.52304	0.261145
$183$	1.41882	0.104882
$184$	6.70985	0.494657
$185$	7.65397	0.562731
$186$	−1.36655	−0.100200
$187$	−11.1392	−0.814578
$188$	2.71548	0.198046
$189$	6.85339	0.498511
$190$	18.2930	1.32712
$191$	4.95181	0.358301	0.179150	−	0.983822i	$-0.442665\pi$
$191$	4.95181	0.358301	0.179150	+	0.983822i	$0.442665\pi$
$192$	2.02582	0.146201
$193$	2.74857	0.197846	0.0989231	−	0.995095i	$-0.468460\pi$
$193$	2.74857	0.197846	0.0989231	+	0.995095i	$0.468460\pi$
$194$	27.6231	1.98322
$195$	−0.671907	−0.0481162
$196$	1.65166	0.117976
$197$	7.83508	0.558226	0.279113	−	0.960258i	$-0.409960\pi$
$197$	7.83508	0.558226	0.279113	+	0.960258i	$0.409960\pi$
$198$	−17.0618	−1.21253
$199$	−8.05143	−0.570751	−0.285376	−	0.958416i	$-0.592118\pi$
$199$	−8.05143	−0.570751	−0.285376	+	0.958416i	$0.592118\pi$
$200$	7.10033	0.502069
$201$	−2.61794	−0.184655
$202$	4.28720	0.301646
$203$	3.32540	0.233397
$204$	0.415905	0.0291192
$205$	−14.7328	−1.02898
$206$	18.0210	1.25558
$207$	−7.81089	−0.542895
$208$	−3.17420	−0.220091
$209$	−16.0629	−1.11110
$210$	−5.07636	−0.350302
$211$	−1.98324	−0.136532	−0.0682659	−	0.997667i	$-0.521747\pi$
$211$	−1.98324	−0.136532	−0.0682659	+	0.997667i	$0.521747\pi$
$212$	−0.291302	−0.0200067
$213$	1.11770	0.0765838
$214$	25.0053	1.70933
$215$	−21.2403	−1.44858
$216$	−5.09352	−0.346570
$217$	−8.35269	−0.567018
$218$	−27.7623	−1.88030
$219$	2.64373	0.178647
$220$	4.36508	0.294294
$221$	1.98997	0.133860
$222$	1.48409	0.0996056
$223$	7.39797	0.495405	0.247702	−	0.968836i	$-0.420325\pi$
$223$	7.39797	0.495405	0.247702	+	0.968836i	$0.420325\pi$
$224$	−7.54431	−0.504076
$225$	−8.26545	−0.551030
$226$	−6.30881	−0.419655
$227$	−13.2342	−0.878386	−0.439193	−	0.898393i	$-0.644736\pi$
$227$	−13.2342	−0.878386	−0.439193	+	0.898393i	$0.644736\pi$
$228$	0.599744	0.0397190
$229$	−0.461974	−0.0305281	−0.0152640	−	0.999883i	$-0.504859\pi$
$229$	−0.461974	−0.0305281	−0.0152640	+	0.999883i	$0.504859\pi$
$230$	11.8185	0.779287
$231$	4.45750	0.293282
$232$	−2.47147	−0.162260
$233$	2.25945	0.148021	0.0740107	−	0.997257i	$-0.476420\pi$
$233$	2.25945	0.148021	0.0740107	+	0.997257i	$0.476420\pi$
$234$	3.04802	0.199255
$235$	−18.7212	−1.22123
$236$	−0.626948	−0.0408108
$237$	−3.76354	−0.244468
$238$	15.0345	0.974543
$239$	30.0187	1.94175	0.970873	−	0.239593i	$-0.0770141\pi$
$239$	30.0187	1.94175	0.970873	+	0.239593i	$0.0770141\pi$
$240$	4.57372	0.295232
$241$	−14.8413	−0.956014	−0.478007	−	0.878356i	$-0.658641\pi$
$241$	−14.8413	−0.956014	−0.478007	+	0.878356i	$0.658641\pi$
$242$	−5.60272	−0.360156
$243$	8.95604	0.574530
$244$	1.64665	0.105416
$245$	−11.3870	−0.727486
$246$	−2.85665	−0.182134
$247$	2.86958	0.182587
$248$	6.20782	0.394197
$249$	1.52868	0.0968763
$250$	−9.25955	−0.585626
$251$	−12.3814	−0.781507	−0.390754	−	0.920495i	$-0.627786\pi$
$251$	−12.3814	−0.781507	−0.390754	+	0.920495i	$0.627786\pi$
$252$	3.89375	0.245283
$253$	−10.3777	−0.652440
$254$	−22.8977	−1.43673
$255$	−2.86735	−0.179561
$256$	9.39065	0.586916
$257$	−17.0022	−1.06057	−0.530284	−	0.847820i	$-0.677915\pi$
$257$	−17.0022	−1.06057	−0.530284	+	0.847820i	$0.677915\pi$
$258$	−4.11846	−0.256404
$259$	9.07116	0.563654
$260$	−0.779804	−0.0483614
$261$	2.87703	0.178084
$262$	−13.4871	−0.833234
$263$	15.3799	0.948363	0.474182	−	0.880427i	$-0.342744\pi$
$263$	15.3799	0.948363	0.474182	+	0.880427i	$0.342744\pi$
$264$	−3.31287	−0.203893
$265$	2.00831	0.123369
$266$	21.6801	1.32929
$267$	3.23327	0.197873
$268$	−3.03834	−0.185596
$269$	−11.1763	−0.681430	−0.340715	−	0.940167i	$-0.610669\pi$
$269$	−11.1763	−0.681430	−0.340715	+	0.940167i	$0.610669\pi$
$270$	−8.97153	−0.545990
$271$	−25.8034	−1.56745	−0.783723	−	0.621111i	$-0.786682\pi$
$271$	−25.8034	−1.56745	−0.783723	+	0.621111i	$0.786682\pi$
$272$	−13.5459	−0.821339
$273$	−0.796314	−0.0481951
$274$	23.4564	1.41705
$275$	−10.9816	−0.662217
$276$	0.387473	0.0233231
$277$	21.8613	1.31352	0.656761	−	0.754099i	$-0.271926\pi$
$277$	21.8613	1.31352	0.656761	+	0.754099i	$0.271926\pi$
$278$	1.55145	0.0930496
$279$	−7.22649	−0.432638
$280$	23.0604	1.37812
$281$	14.7721	0.881232	0.440616	−	0.897696i	$-0.354760\pi$
$281$	14.7721	0.881232	0.440616	+	0.897696i	$0.354760\pi$
$282$	−3.63000	−0.216163
$283$	9.30807	0.553307	0.276654	−	0.960970i	$-0.410775\pi$
$283$	9.30807	0.553307	0.276654	+	0.960970i	$0.410775\pi$
$284$	1.29719	0.0769740
$285$	−4.13479	−0.244924
$286$	4.04966	0.239461
$287$	−17.4606	−1.03067
$288$	−6.52710	−0.384613
$289$	−8.50784	−0.500461
$290$	−4.35316	−0.255626
$291$	−6.24367	−0.366010
$292$	3.06827	0.179557
$293$	−15.9406	−0.931258	−0.465629	−	0.884980i	$-0.654172\pi$
$293$	−15.9406	−0.931258	−0.465629	+	0.884980i	$0.654172\pi$
$294$	−2.20791	−0.128768
$295$	4.32233	0.251656
$296$	−6.74179	−0.391859
$297$	7.87782	0.457118
$298$	4.36288	0.252735
$299$	1.85393	0.107216
$300$	0.410022	0.0236726
$301$	−25.1731	−1.45096
$302$	7.60548	0.437646
$303$	−0.969038	−0.0556698
$304$	−19.5334	−1.12032
$305$	−11.3524	−0.650039
$306$	13.0074	0.743583
$307$	9.76356	0.557236	0.278618	−	0.960402i	$-0.410124\pi$
$307$	9.76356	0.557236	0.278618	+	0.960402i	$0.410124\pi$
$308$	5.17331	0.294777
$309$	−4.07329	−0.231722
$310$	10.9342	0.621022
$311$	−11.9926	−0.680040	−0.340020	−	0.940418i	$-0.610434\pi$
$311$	−11.9926	−0.680040	−0.340020	+	0.940418i	$0.610434\pi$
$312$	0.591831	0.0335058
$313$	9.75494	0.551382	0.275691	−	0.961246i	$-0.411093\pi$
$313$	9.75494	0.551382	0.275691	+	0.961246i	$0.411093\pi$
$314$	18.4319	1.04017
$315$	−26.8445	−1.51252
$316$	−4.36791	−0.245714
$317$	25.8018	1.44917	0.724587	−	0.689184i	$-0.242031\pi$
$317$	25.8018	1.44917	0.724587	+	0.689184i	$0.242031\pi$
$318$	0.389407	0.0218369
$319$	3.82247	0.214017
$320$	−16.2093	−0.906125
$321$	−5.65196	−0.315462
$322$	14.0067	0.780565
$323$	12.2459	0.681379
$324$	3.21860	0.178811
$325$	1.96182	0.108822
$326$	4.17674	0.231328
$327$	6.27514	0.347016
$328$	12.9769	0.716532
$329$	−22.1875	−1.22324
$330$	−5.83516	−0.321215
$331$	−12.7650	−0.701627	−0.350814	−	0.936445i	$-0.614095\pi$
$331$	−12.7650	−0.701627	−0.350814	+	0.936445i	$0.614095\pi$
$332$	1.77416	0.0973699
$333$	7.84808	0.430072
$334$	7.26821	0.397699
$335$	20.9470	1.14446
$336$	5.42057	0.295716
$337$	−19.3249	−1.05270	−0.526348	−	0.850269i	$-0.676439\pi$
$337$	−19.3249	−1.05270	−0.526348	+	0.850269i	$0.676439\pi$
$338$	19.4454	1.05769
$339$	1.42598	0.0774488
$340$	−3.32780	−0.180475
$341$	−9.60124	−0.519936
$342$	18.7569	1.01426
$343$	9.78245	0.528203
$344$	18.7090	1.00872
$345$	−2.67134	−0.143820
$346$	−3.25257	−0.174859
$347$	30.1874	1.62054	0.810271	−	0.586055i	$-0.199320\pi$
$347$	30.1874	1.62054	0.810271	+	0.586055i	$0.199320\pi$
$348$	−0.142720	−0.00765060
$349$	−17.2574	−0.923767	−0.461883	−	0.886941i	$-0.652826\pi$
$349$	−17.2574	−0.923767	−0.461883	+	0.886941i	$0.652826\pi$
$350$	14.8219	0.792261
$351$	−1.40734	−0.0751182
$352$	−8.67203	−0.462221
$353$	16.1406	0.859077	0.429538	−	0.903049i	$-0.358676\pi$
$353$	16.1406	0.859077	0.429538	+	0.903049i	$0.358676\pi$
$354$	0.838092	0.0445441
$355$	−8.94315	−0.474653
$356$	3.75248	0.198881
$357$	−3.39826	−0.179855
$358$	−14.2472	−0.752990
$359$	3.96669	0.209354	0.104677	−	0.994506i	$-0.466619\pi$
$359$	3.96669	0.209354	0.104677	+	0.994506i	$0.466619\pi$
$360$	19.9511	1.05152
$361$	−1.34116	−0.0705874
$362$	−16.3434	−0.858988
$363$	1.26639	0.0664680
$364$	−0.924190	−0.0484407
$365$	−21.1534	−1.10722
$366$	−2.20122	−0.115059
$367$	−26.9004	−1.40419	−0.702094	−	0.712085i	$-0.747751\pi$
$367$	−26.9004	−1.40419	−0.702094	+	0.712085i	$0.747751\pi$
$368$	−12.6199	−0.657855
$369$	−15.1064	−0.786407
$370$	−11.8747	−0.617338
$371$	2.38016	0.123572
$372$	0.358483	0.0185865
$373$	26.4384	1.36893	0.684465	−	0.729046i	$-0.260036\pi$
$373$	26.4384	1.36893	0.684465	+	0.729046i	$0.260036\pi$
$374$	17.2819	0.893623
$375$	2.09294	0.108079
$376$	16.4900	0.850408
$377$	−0.682868	−0.0351695
$378$	−10.6327	−0.546885
$379$	5.64307	0.289865	0.144932	−	0.989442i	$-0.453704\pi$
$379$	5.64307	0.289865	0.144932	+	0.989442i	$0.453704\pi$
$380$	−4.79876	−0.246171
$381$	5.17558	0.265153
$382$	−7.68247	−0.393070
$383$	11.4307	0.584079	0.292040	−	0.956406i	$-0.405666\pi$
$383$	11.4307	0.584079	0.292040	+	0.956406i	$0.405666\pi$
$384$	−4.73409	−0.241586
$385$	−35.6661	−1.81771
$386$	−4.26426	−0.217045
$387$	−21.7790	−1.10709
$388$	−7.24630	−0.367875
$389$	−32.7769	−1.66185	−0.830927	−	0.556382i	$-0.812189\pi$
$389$	−32.7769	−1.66185	−0.830927	+	0.556382i	$0.812189\pi$
$390$	1.04243	0.0527854
$391$	7.91163	0.400108
$392$	10.0299	0.506586
$393$	3.04849	0.153776
$394$	−12.1557	−0.612395
$395$	30.1134	1.51517
$396$	4.47578	0.224916
$397$	−10.2491	−0.514390	−0.257195	−	0.966360i	$-0.582798\pi$
$397$	−10.2491	−0.514390	−0.257195	+	0.966360i	$0.582798\pi$
$398$	12.4914	0.626136
$399$	−4.90037	−0.245325
$400$	−13.3543	−0.667713
$401$	−23.7630	−1.18667	−0.593333	−	0.804957i	$-0.702188\pi$
$401$	−23.7630	−1.18667	−0.593333	+	0.804957i	$0.702188\pi$
$402$	4.06159	0.202574
$403$	1.71522	0.0854412
$404$	−1.12465	−0.0559534
$405$	−22.1899	−1.10262
$406$	−5.15918	−0.256046
$407$	10.4271	0.516852
$408$	2.52563	0.125037
$409$	−5.32203	−0.263158	−0.131579	−	0.991306i	$-0.542005\pi$
$409$	−5.32203	−0.263158	−0.131579	+	0.991306i	$0.542005\pi$
$410$	22.8571	1.12883
$411$	−5.30187	−0.261522
$412$	−4.72740	−0.232902
$413$	5.12264	0.252069
$414$	12.1182	0.595576
$415$	−12.2315	−0.600422
$416$	1.54922	0.0759568
$417$	−0.350675	−0.0171726
$418$	24.9208	1.21892
$419$	28.9917	1.41634	0.708168	−	0.706043i	$-0.249522\pi$
$419$	28.9917	1.41634	0.708168	+	0.706043i	$0.249522\pi$
$420$	1.33167	0.0649788
$421$	−13.6625	−0.665871	−0.332936	−	0.942950i	$-0.608039\pi$
$421$	−13.6625	−0.665871	−0.332936	+	0.942950i	$0.608039\pi$
$422$	3.07689	0.149781
$423$	−19.1959	−0.933338
$424$	−1.76896	−0.0859085
$425$	8.37204	0.406104
$426$	−1.73406	−0.0840154
$427$	−13.4544	−0.651105
$428$	−6.55958	−0.317069
$429$	−0.915346	−0.0441933
$430$	32.9533	1.58915
$431$	32.7563	1.57782	0.788908	−	0.614511i	$-0.210647\pi$
$431$	32.7563	1.57782	0.788908	+	0.614511i	$0.210647\pi$
$432$	9.57987	0.460912
$433$	−16.0628	−0.771931	−0.385965	−	0.922513i	$-0.626132\pi$
$433$	−16.0628	−0.771931	−0.385965	+	0.922513i	$0.626132\pi$
$434$	12.9588	0.622040
$435$	0.983948	0.0471767
$436$	7.28282	0.348784
$437$	11.4087	0.545754
$438$	−4.10161	−0.195982
$439$	39.2799	1.87473	0.937365	−	0.348349i	$-0.113258\pi$
$439$	39.2799	1.87473	0.937365	+	0.348349i	$0.113258\pi$
$440$	26.5075	1.26369
$441$	−11.6757	−0.555987
$442$	−3.08733	−0.146849
$443$	−12.2292	−0.581028	−0.290514	−	0.956871i	$-0.593826\pi$
$443$	−12.2292	−0.581028	−0.290514	+	0.956871i	$0.593826\pi$
$444$	−0.389318	−0.0184762
$445$	−25.8705	−1.22638
$446$	−11.4776	−0.543478
$447$	−0.986145	−0.0466430
$448$	−19.2105	−0.907611
$449$	40.8373	1.92723	0.963615	−	0.267294i	$-0.0861296\pi$
$449$	40.8373	1.92723	0.963615	+	0.267294i	$0.0861296\pi$
$450$	12.8234	0.604501
$451$	−20.0706	−0.945088
$452$	1.65497	0.0778434
$453$	−1.71907	−0.0807690
$454$	20.5322	0.963624
$455$	6.37159	0.298705
$456$	3.64201	0.170553
$457$	−24.6290	−1.15210	−0.576049	−	0.817415i	$-0.695406\pi$
$457$	−24.6290	−1.15210	−0.576049	+	0.817415i	$0.695406\pi$
$458$	0.716728	0.0334905
$459$	−6.00580	−0.280327
$460$	−3.10031	−0.144553
$461$	21.4532	0.999177	0.499588	−	0.866263i	$-0.333485\pi$
$461$	21.4532	0.999177	0.499588	+	0.866263i	$0.333485\pi$
$462$	−6.91558	−0.321742
$463$	−24.6768	−1.14683	−0.573415	−	0.819265i	$-0.694382\pi$
$463$	−24.6768	−1.14683	−0.573415	+	0.819265i	$0.694382\pi$
$464$	4.64834	0.215794
$465$	−2.47147	−0.114612
$466$	−3.50541	−0.162385
$467$	−18.5112	−0.856594	−0.428297	−	0.903638i	$-0.640886\pi$
$467$	−18.5112	−0.856594	−0.428297	+	0.903638i	$0.640886\pi$
$468$	−0.799580	−0.0369606
$469$	24.8255	1.14634
$470$	29.0449	1.33974
$471$	−4.16617	−0.191967
$472$	−3.80721	−0.175241
$473$	−28.9360	−1.33048
$474$	5.83893	0.268191
$475$	12.0727	0.553932
$476$	−3.94397	−0.180771
$477$	2.05924	0.0942861
$478$	−46.5724	−2.13017
$479$	−33.9491	−1.55117	−0.775587	−	0.631241i	$-0.782546\pi$
$479$	−33.9491	−1.55117	−0.775587	+	0.631241i	$0.782546\pi$
$480$	−2.23228	−0.101889
$481$	−1.86276	−0.0849344
$482$	23.0255	1.04878
$483$	−3.16595	−0.144056
$484$	1.46975	0.0668067
$485$	49.9578	2.26847
$486$	−13.8948	−0.630281
$487$	−19.2546	−0.872509	−0.436254	−	0.899823i	$-0.643695\pi$
$487$	−19.2546	−0.872509	−0.436254	+	0.899823i	$0.643695\pi$
$488$	9.99949	0.452656
$489$	−0.944070	−0.0426923
$490$	17.6662	0.798080
$491$	5.25042	0.236948	0.118474	−	0.992957i	$-0.462200\pi$
$491$	5.25042	0.236948	0.118474	+	0.992957i	$0.462200\pi$
$492$	0.749379	0.0337846
$493$	−2.91413	−0.131246
$494$	−4.45200	−0.200305
$495$	−30.8572	−1.38693
$496$	−11.6756	−0.524252
$497$	−10.5990	−0.475431
$498$	−2.37167	−0.106277
$499$	−20.5863	−0.921570	−0.460785	−	0.887512i	$-0.652432\pi$
$499$	−20.5863	−0.921570	−0.460785	+	0.887512i	$0.652432\pi$
$500$	2.42904	0.108630
$501$	−1.64284	−0.0733966
$502$	19.2091	0.857344
$503$	−19.8253	−0.883965	−0.441982	−	0.897024i	$-0.645725\pi$
$503$	−19.8253	−0.883965	−0.441982	+	0.897024i	$0.645725\pi$
$504$	23.6452	1.05324
$505$	7.75361	0.345031
$506$	16.1004	0.715752
$507$	−4.39525	−0.195200
$508$	6.00669	0.266504
$509$	6.68879	0.296475	0.148238	−	0.988952i	$-0.452640\pi$
$509$	6.68879	0.296475	0.148238	+	0.988952i	$0.452640\pi$
$510$	4.44855	0.196985
$511$	−25.0701	−1.10904
$512$	12.4308	0.549370
$513$	−8.66050	−0.382370
$514$	26.3780	1.16348
$515$	32.5919	1.43617
$516$	1.08039	0.0475613
$517$	−25.5041	−1.12167
$518$	−14.0734	−0.618350
$519$	0.735181	0.0322709
$520$	−4.73545	−0.207663
$521$	−32.2542	−1.41308	−0.706540	−	0.707673i	$-0.749745\pi$
$521$	−32.2542	−1.41308	−0.706540	+	0.707673i	$0.749745\pi$
$522$	−4.46355	−0.195364
$523$	−28.2310	−1.23445	−0.617227	−	0.786785i	$-0.711744\pi$
$523$	−28.2310	−1.23445	−0.617227	+	0.786785i	$0.711744\pi$
$524$	3.53803	0.154560
$525$	−3.35019	−0.146214
$526$	−23.8610	−1.04039
$527$	7.31968	0.318850
$528$	6.23083	0.271162
$529$	−15.6292	−0.679531
$530$	−3.11578	−0.135341
$531$	4.43195	0.192330
$532$	−5.68729	−0.246575
$533$	3.58553	0.155307
$534$	−5.01625	−0.217074
$535$	45.2234	1.95518
$536$	−18.4506	−0.796946
$537$	3.22031	0.138967
$538$	17.3394	0.747554
$539$	−15.5126	−0.668174
$540$	2.35348	0.101278
$541$	8.83992	0.380058	0.190029	−	0.981778i	$-0.439142\pi$
$541$	8.83992	0.380058	0.190029	+	0.981778i	$0.439142\pi$
$542$	40.0326	1.71955
$543$	3.69410	0.158529
$544$	6.61128	0.283456
$545$	−50.2096	−2.15074
$546$	1.23544	0.0528719
$547$	25.5225	1.09127	0.545633	−	0.838024i	$-0.316289\pi$
$547$	25.5225	1.09127	0.545633	+	0.838024i	$0.316289\pi$
$548$	−6.15326	−0.262854
$549$	−11.6403	−0.496798
$550$	17.0374	0.726477
$551$	−4.20224	−0.179022
$552$	2.35297	0.100149
$553$	35.6891	1.51766
$554$	−33.9167	−1.44098
$555$	2.68405	0.113932
$556$	−0.406987	−0.0172601
$557$	4.84318	0.205212	0.102606	−	0.994722i	$-0.467282\pi$
$557$	4.84318	0.205212	0.102606	+	0.994722i	$0.467282\pi$
$558$	11.2115	0.474621
$559$	5.16929	0.218638
$560$	−43.3719	−1.83280
$561$	−3.90623	−0.164921
$562$	−22.9182	−0.966746
$563$	−18.8352	−0.793809	−0.396904	−	0.917860i	$-0.629916\pi$
$563$	−18.8352	−0.793809	−0.396904	+	0.917860i	$0.629916\pi$
$564$	0.952248	0.0400969
$565$	−11.4098	−0.480014
$566$	−14.4410	−0.606999
$567$	−26.2985	−1.10443
$568$	7.87732	0.330525
$569$	−2.33201	−0.0977631	−0.0488816	−	0.998805i	$-0.515566\pi$
$569$	−2.33201	−0.0977631	−0.0488816	+	0.998805i	$0.515566\pi$
$570$	6.41490	0.268691
$571$	−37.3353	−1.56243	−0.781216	−	0.624260i	$-0.785400\pi$
$571$	−37.3353	−1.56243	−0.781216	+	0.624260i	$0.785400\pi$
$572$	−1.06234	−0.0444185
$573$	1.73647	0.0725423
$574$	27.0892	1.13068
$575$	7.79972	0.325271
$576$	−16.6203	−0.692514
$577$	−20.9917	−0.873897	−0.436949	−	0.899486i	$-0.643941\pi$
$577$	−20.9917	−0.873897	−0.436949	+	0.899486i	$0.643941\pi$
$578$	13.1995	0.549025
$579$	0.963853	0.0400564
$580$	1.14195	0.0474170
$581$	−14.4963	−0.601407
$582$	9.68672	0.401527
$583$	2.73594	0.113311
$584$	18.6324	0.771015
$585$	5.51250	0.227914
$586$	24.7309	1.02163
$587$	−13.3654	−0.551650	−0.275825	−	0.961208i	$-0.588951\pi$
$587$	−13.3654	−0.551650	−0.275825	+	0.961208i	$0.588951\pi$
$588$	0.579195	0.0238856
$589$	10.5551	0.434917
$590$	−6.70587	−0.276076
$591$	2.74756	0.113020
$592$	12.6799	0.521142
$593$	9.02449	0.370592	0.185296	−	0.982683i	$-0.440676\pi$
$593$	9.02449	0.370592	0.185296	+	0.982683i	$0.440676\pi$
$594$	−12.2220	−0.501476
$595$	27.1907	1.11471
$596$	−1.14450	−0.0468807
$597$	−2.82343	−0.115555
$598$	−2.87628	−0.117620
$599$	11.5226	0.470802	0.235401	−	0.971898i	$-0.424360\pi$
$599$	11.5226	0.470802	0.235401	+	0.971898i	$0.424360\pi$
$600$	2.48990	0.101650
$601$	−21.9151	−0.893935	−0.446967	−	0.894550i	$-0.647496\pi$
$601$	−21.9151	−0.893935	−0.446967	+	0.894550i	$0.647496\pi$
$602$	39.0548	1.59175
$603$	21.4783	0.874662
$604$	−1.99513	−0.0811805
$605$	−10.1328	−0.411957
$606$	1.50341	0.0610719
$607$	−22.5695	−0.916068	−0.458034	−	0.888935i	$-0.651446\pi$
$607$	−22.5695	−0.916068	−0.458034	+	0.888935i	$0.651446\pi$
$608$	9.53361	0.386639
$609$	1.16613	0.0472540
$610$	17.6127	0.713118
$611$	4.55619	0.184324
$612$	−3.41220	−0.137930
$613$	33.9013	1.36926	0.684630	−	0.728890i	$-0.259964\pi$
$613$	33.9013	1.36926	0.684630	+	0.728890i	$0.259964\pi$
$614$	−15.1476	−0.611309
$615$	−5.16640	−0.208329
$616$	31.4155	1.26577
$617$	20.3914	0.820926	0.410463	−	0.911877i	$-0.365367\pi$
$617$	20.3914	0.820926	0.410463	+	0.911877i	$0.365367\pi$
$618$	6.31950	0.254207
$619$	−8.65709	−0.347958	−0.173979	−	0.984749i	$-0.555662\pi$
$619$	−8.65709	−0.347958	−0.173979	+	0.984749i	$0.555662\pi$
$620$	−2.86835	−0.115196
$621$	−5.59524	−0.224529
$622$	18.6059	0.746031
$623$	−30.6606	−1.22839
$624$	−1.11311	−0.0445601
$625$	−31.1109	−1.24444
$626$	−15.1343	−0.604887
$627$	−5.63287	−0.224955
$628$	−4.83518	−0.192945
$629$	−7.94929	−0.316959
$630$	41.6478	1.65929
$631$	−25.1540	−1.00136	−0.500682	−	0.865631i	$-0.666917\pi$
$631$	−25.1540	−1.00136	−0.500682	+	0.865631i	$0.666917\pi$
$632$	−26.5246	−1.05509
$633$	−0.695471	−0.0276425
$634$	−40.0301	−1.58980
$635$	−41.4116	−1.64337
$636$	−0.102152	−0.00405060
$637$	2.77126	0.109801
$638$	−5.93036	−0.234785
$639$	−9.16994	−0.362757
$640$	37.8791	1.49730
$641$	16.3829	0.647087	0.323543	−	0.946213i	$-0.395126\pi$
$641$	16.3829	0.647087	0.323543	+	0.946213i	$0.395126\pi$
$642$	8.76872	0.346074
$643$	22.0943	0.871313	0.435657	−	0.900113i	$-0.356516\pi$
$643$	22.0943	0.871313	0.435657	+	0.900113i	$0.356516\pi$
$644$	−3.67435	−0.144790
$645$	−7.44845	−0.293282
$646$	−18.9988	−0.747500
$647$	13.7729	0.541468	0.270734	−	0.962654i	$-0.412734\pi$
$647$	13.7729	0.541468	0.270734	+	0.962654i	$0.412734\pi$
$648$	19.5453	0.767813
$649$	5.88837	0.231139
$650$	−3.04366	−0.119382
$651$	−2.92908	−0.114800
$652$	−1.09567	−0.0429099
$653$	−10.3941	−0.406754	−0.203377	−	0.979101i	$-0.565192\pi$
$653$	−10.3941	−0.406754	−0.203377	+	0.979101i	$0.565192\pi$
$654$	−9.73554	−0.380690
$655$	−24.3921	−0.953077
$656$	−24.4070	−0.952932
$657$	−21.6899	−0.846203
$658$	34.4228	1.34194
$659$	−12.1426	−0.473009	−0.236504	−	0.971630i	$-0.576002\pi$
$659$	−12.1426	−0.473009	−0.236504	+	0.971630i	$0.576002\pi$
$660$	1.53072	0.0595833
$661$	−30.1150	−1.17134	−0.585669	−	0.810551i	$-0.699168\pi$
$661$	−30.1150	−1.17134	−0.585669	+	0.810551i	$0.699168\pi$
$662$	19.8042	0.769712
$663$	0.697831	0.0271015
$664$	10.7738	0.418105
$665$	39.2096	1.52048
$666$	−12.1759	−0.471806
$667$	−2.71492	−0.105122
$668$	−1.90665	−0.0737705
$669$	2.59428	0.100301
$670$	−32.4982	−1.25552
$671$	−15.4656	−0.597042
$672$	−2.64560	−0.102056
$673$	14.1911	0.547025	0.273513	−	0.961868i	$-0.411814\pi$
$673$	14.1911	0.547025	0.273513	+	0.961868i	$0.411814\pi$
$674$	29.9816	1.15485
$675$	−5.92085	−0.227894
$676$	−5.10105	−0.196194
$677$	7.71599	0.296550	0.148275	−	0.988946i	$-0.452628\pi$
$677$	7.71599	0.296550	0.148275	+	0.988946i	$0.452628\pi$
$678$	−2.21234	−0.0849643
$679$	59.2078	2.27219
$680$	−20.2085	−0.774959
$681$	−4.64091	−0.177840
$682$	14.8958	0.570390
$683$	−46.6393	−1.78460	−0.892302	−	0.451439i	$-0.850911\pi$
$683$	−46.6393	−1.78460	−0.892302	+	0.451439i	$0.850911\pi$
$684$	−4.92046	−0.188139
$685$	42.4221	1.62087
$686$	−15.1770	−0.579459
$687$	−0.162002	−0.00618078
$688$	−35.1877	−1.34152
$689$	−0.488765	−0.0186204
$690$	4.14444	0.157776
$691$	7.64777	0.290935	0.145467	−	0.989363i	$-0.453531\pi$
$691$	7.64777	0.290935	0.145467	+	0.989363i	$0.453531\pi$
$692$	0.853239	0.0324353
$693$	−36.5706	−1.38920
$694$	−46.8341	−1.77780
$695$	2.80587	0.106433
$696$	−0.866683	−0.0328515
$697$	15.3012	0.579574
$698$	26.7739	1.01341
$699$	0.792331	0.0299687
$700$	−3.88818	−0.146959
$701$	−31.8255	−1.20203	−0.601017	−	0.799236i	$-0.705238\pi$
$701$	−31.8255	−1.20203	−0.601017	+	0.799236i	$0.705238\pi$
$702$	2.18341	0.0824076
$703$	−11.4631	−0.432337
$704$	−22.0821	−0.832249
$705$	−6.56504	−0.247254
$706$	−25.0413	−0.942440
$707$	9.18924	0.345597
$708$	−0.219855	−0.00826264
$709$	−36.6723	−1.37726	−0.688628	−	0.725115i	$-0.741787\pi$
$709$	−36.6723	−1.37726	−0.688628	+	0.725115i	$0.741787\pi$
$710$	13.8748	0.520712
$711$	30.8771	1.15798
$712$	22.7874	0.853992
$713$	6.81930	0.255385
$714$	5.27222	0.197308
$715$	7.32401	0.273902
$716$	3.73744	0.139675
$717$	10.5268	0.393130
$718$	−6.15411	−0.229669
$719$	25.2100	0.940175	0.470088	−	0.882620i	$-0.344222\pi$
$719$	25.2100	0.940175	0.470088	+	0.882620i	$0.344222\pi$
$720$	−37.5240	−1.39844
$721$	38.6264	1.43852
$722$	2.08074	0.0774371
$723$	−5.20447	−0.193556
$724$	4.28731	0.159337
$725$	−2.87291	−0.106697
$726$	−1.96473	−0.0729180
$727$	12.4930	0.463341	0.231670	−	0.972794i	$-0.425581\pi$
$727$	12.4930	0.463341	0.231670	+	0.972794i	$0.425581\pi$
$728$	−5.61224	−0.208004
$729$	−20.5845	−0.762387
$730$	32.8184	1.21466
$731$	22.0599	0.815914
$732$	0.577440	0.0213428
$733$	21.3731	0.789434	0.394717	−	0.918803i	$-0.370843\pi$
$733$	21.3731	0.789434	0.394717	+	0.918803i	$0.370843\pi$
$734$	41.7345	1.54045
$735$	−3.99311	−0.147288
$736$	6.15932	0.227036
$737$	28.5364	1.05115
$738$	23.4367	0.862718
$739$	−2.40609	−0.0885093	−0.0442547	−	0.999020i	$-0.514091\pi$
$739$	−2.40609	−0.0885093	−0.0442547	+	0.999020i	$0.514091\pi$
$740$	3.11507	0.114512
$741$	1.00629	0.0369669
$742$	−3.69269	−0.135563
$743$	22.5879	0.828669	0.414334	−	0.910125i	$-0.364014\pi$
$743$	22.5879	0.828669	0.414334	+	0.910125i	$0.364014\pi$
$744$	2.17693	0.0798100
$745$	7.89049	0.289085
$746$	−41.0178	−1.50177
$747$	−12.5417	−0.458878
$748$	−4.53351	−0.165761
$749$	53.5968	1.95838
$750$	−3.24709	−0.118567
$751$	−37.0373	−1.35151	−0.675755	−	0.737126i	$-0.736182\pi$
$751$	−37.0373	−1.35151	−0.675755	+	0.737126i	$0.736182\pi$
$752$	−31.0144	−1.13098
$753$	−4.34184	−0.158226
$754$	1.05943	0.0385823
$755$	13.7549	0.500592
$756$	2.78924	0.101444
$757$	36.6217	1.33104	0.665520	−	0.746380i	$-0.268210\pi$
$757$	36.6217	1.33104	0.665520	+	0.746380i	$0.268210\pi$
$758$	−8.75492	−0.317993
$759$	−3.63919	−0.132094
$760$	−29.1410	−1.05706
$761$	22.7761	0.825634	0.412817	−	0.910814i	$-0.364545\pi$
$761$	22.7761	0.825634	0.412817	+	0.910814i	$0.364545\pi$
$762$	−8.02963	−0.290883
$763$	−59.5062	−2.15427
$764$	2.01532	0.0729119
$765$	23.5245	0.850531
$766$	−17.7341	−0.640758
$767$	−1.05193	−0.0379831
$768$	3.29306	0.118828
$769$	9.60357	0.346313	0.173157	−	0.984894i	$-0.444603\pi$
$769$	9.60357	0.346313	0.173157	+	0.984894i	$0.444603\pi$
$770$	55.3340	1.99410
$771$	−5.96223	−0.214725
$772$	1.11863	0.0402604
$773$	−25.8298	−0.929032	−0.464516	−	0.885565i	$-0.653772\pi$
$773$	−25.8298	−0.929032	−0.464516	+	0.885565i	$0.653772\pi$
$774$	33.7890	1.21452
$775$	7.21615	0.259212
$776$	−44.0039	−1.57965
$777$	3.18102	0.114119
$778$	50.8516	1.82312
$779$	22.0647	0.790549
$780$	−0.273457	−0.00979134
$781$	−12.1834	−0.435955
$782$	−12.2745	−0.438934
$783$	2.06092	0.0736514
$784$	−18.8642	−0.673720
$785$	33.3350	1.18978
$786$	−4.72957	−0.168698
$787$	52.1260	1.85809	0.929046	−	0.369963i	$-0.120630\pi$
$787$	52.1260	1.85809	0.929046	+	0.369963i	$0.120630\pi$
$788$	3.18877	0.113595
$789$	5.39333	0.192008
$790$	−46.7194	−1.66220
$791$	−13.5224	−0.480801
$792$	27.1797	0.965788
$793$	2.76286	0.0981120
$794$	15.9010	0.564306
$795$	0.704263	0.0249776
$796$	−3.27683	−0.116144
$797$	6.38007	0.225994	0.112997	−	0.993595i	$-0.463955\pi$
$797$	6.38007	0.225994	0.112997	+	0.993595i	$0.463955\pi$
$798$	7.60266	0.269131
$799$	19.4435	0.687862
$800$	6.51776	0.230438
$801$	−26.5266	−0.937272
$802$	36.8670	1.30182
$803$	−28.8176	−1.01695
$804$	−1.06547	−0.0375761
$805$	25.3319	0.892832
$806$	−2.66107	−0.0937323
$807$	−3.91924	−0.137964
$808$	−6.82956	−0.240263
$809$	30.2008	1.06180	0.530902	−	0.847433i	$-0.321853\pi$
$809$	30.2008	1.06180	0.530902	+	0.847433i	$0.321853\pi$
$810$	34.4264	1.20962
$811$	34.1849	1.20039	0.600197	−	0.799852i	$-0.295089\pi$
$811$	34.1849	1.20039	0.600197	+	0.799852i	$0.295089\pi$
$812$	1.35339	0.0474948
$813$	−9.04860	−0.317348
$814$	−16.1771	−0.567007
$815$	7.55384	0.264600
$816$	−4.75019	−0.166290
$817$	31.8108	1.11292
$818$	8.25685	0.288694
$819$	6.53318	0.228288
$820$	−5.99604	−0.209391
$821$	31.6474	1.10450	0.552251	−	0.833678i	$-0.313769\pi$
$821$	31.6474	1.10450	0.552251	+	0.833678i	$0.313769\pi$
$822$	8.22557	0.286900
$823$	−10.2327	−0.356690	−0.178345	−	0.983968i	$-0.557074\pi$
$823$	−10.2327	−0.356690	−0.178345	+	0.983968i	$0.557074\pi$
$824$	−28.7076	−1.00008
$825$	−3.85098	−0.134074
$826$	−7.94751	−0.276529
$827$	−13.5749	−0.472044	−0.236022	−	0.971748i	$-0.575844\pi$
$827$	−13.5749	−0.472044	−0.236022	+	0.971748i	$0.575844\pi$
$828$	−3.17893	−0.110476
$829$	1.92847	0.0669784	0.0334892	−	0.999439i	$-0.489338\pi$
$829$	1.92847	0.0669784	0.0334892	+	0.999439i	$0.489338\pi$
$830$	18.9766	0.658686
$831$	7.66622	0.265938
$832$	3.94487	0.136764
$833$	11.8263	0.409757
$834$	0.544053	0.0188390
$835$	13.1449	0.454899
$836$	−6.53741	−0.226101
$837$	−5.17661	−0.178930
$838$	−44.9791	−1.55378
$839$	26.7842	0.924694	0.462347	−	0.886699i	$-0.347007\pi$
$839$	26.7842	0.924694	0.462347	+	0.886699i	$0.347007\pi$
$840$	8.08670	0.279018
$841$	1.00000	0.0344828
$842$	21.1967	0.730487
$843$	5.18021	0.178416
$844$	−0.807152	−0.0277833
$845$	35.1679	1.20981
$846$	29.7815	1.02391
$847$	−12.0090	−0.412633
$848$	3.32706	0.114252
$849$	3.26410	0.112024
$850$	−12.9888	−0.445512
$851$	−7.40587	−0.253870
$852$	0.454891	0.0155843
$853$	−49.7999	−1.70511	−0.852557	−	0.522634i	$-0.824950\pi$
$853$	−49.7999	−1.70511	−0.852557	+	0.522634i	$0.824950\pi$
$854$	20.8738	0.714288
$855$	33.9229	1.16014
$856$	−39.8338	−1.36149
$857$	43.8420	1.49761	0.748806	−	0.662789i	$-0.230627\pi$
$857$	43.8420	1.49761	0.748806	+	0.662789i	$0.230627\pi$
$858$	1.42011	0.0484818
$859$	−44.7687	−1.52749	−0.763744	−	0.645519i	$-0.776641\pi$
$859$	−44.7687	−1.52749	−0.763744	+	0.645519i	$0.776641\pi$
$860$	−8.64455	−0.294777
$861$	−6.12300	−0.208671
$862$	−50.8197	−1.73093
$863$	2.95384	0.100550	0.0502749	−	0.998735i	$-0.483990\pi$
$863$	2.95384	0.100550	0.0502749	+	0.998735i	$0.483990\pi$
$864$	−4.67561	−0.159067
$865$	−5.88244	−0.200009
$866$	24.9206	0.846838
$867$	−2.98348	−0.101324
$868$	−3.39944	−0.115384
$869$	41.0239	1.39164
$870$	−1.52654	−0.0517546
$871$	−5.09791	−0.172736
$872$	44.2257	1.49767
$873$	51.2247	1.73369
$874$	−17.7001	−0.598713
$875$	−19.8471	−0.670954
$876$	1.07596	0.0363535
$877$	−15.3677	−0.518931	−0.259466	−	0.965752i	$-0.583546\pi$
$877$	−15.3677	−0.518931	−0.259466	+	0.965752i	$0.583546\pi$
$878$	−60.9407	−2.05665
$879$	−5.58995	−0.188544
$880$	−49.8551	−1.68061
$881$	49.4609	1.66638	0.833190	−	0.552987i	$-0.186512\pi$
$881$	49.4609	1.66638	0.833190	+	0.552987i	$0.186512\pi$
$882$	18.1143	0.609939
$883$	14.2953	0.481074	0.240537	−	0.970640i	$-0.422677\pi$
$883$	14.2953	0.481074	0.240537	+	0.970640i	$0.422677\pi$
$884$	0.809892	0.0272396
$885$	1.51573	0.0509508
$886$	18.9730	0.637410
$887$	−3.34807	−0.112417	−0.0562087	−	0.998419i	$-0.517901\pi$
$887$	−3.34807	−0.112417	−0.0562087	+	0.998419i	$0.517901\pi$
$888$	−2.36418	−0.0793365
$889$	−49.0793	−1.64607
$890$	40.1368	1.34539
$891$	−30.2295	−1.01273
$892$	3.01088	0.100812
$893$	28.0380	0.938255
$894$	1.52995	0.0511692
$895$	−25.7669	−0.861291
$896$	44.8927	1.49976
$897$	0.650127	0.0217071
$898$	−63.3569	−2.11425
$899$	−2.51179	−0.0837729
$900$	−3.36393	−0.112131
$901$	−2.08580	−0.0694880
$902$	31.1385	1.03680
$903$	−8.82758	−0.293763
$904$	10.0500	0.334258
$905$	−29.5578	−0.982534
$906$	2.66705	0.0886067
$907$	6.53410	0.216961	0.108481	−	0.994099i	$-0.465401\pi$
$907$	6.53410	0.216961	0.108481	+	0.994099i	$0.465401\pi$
$908$	−5.38616	−0.178746
$909$	7.95024	0.263693
$910$	−9.88519	−0.327691
$911$	−20.3177	−0.673154	−0.336577	−	0.941656i	$-0.609269\pi$
$911$	−20.3177	−0.673154	−0.336577	+	0.941656i	$0.609269\pi$
$912$	−6.84988	−0.226822
$913$	−16.6632	−0.551470
$914$	38.2106	1.26390
$915$	−3.98101	−0.131608
$916$	−0.188017	−0.00621227
$917$	−28.9084	−0.954640
$918$	9.31769	0.307529
$919$	10.9398	0.360870	0.180435	−	0.983587i	$-0.442250\pi$
$919$	10.9398	0.360870	0.180435	+	0.983587i	$0.442250\pi$
$920$	−18.8270	−0.620707
$921$	3.42383	0.112819
$922$	−33.2836	−1.09614
$923$	2.17650	0.0716405
$924$	1.81415	0.0596811
$925$	−7.83685	−0.257674
$926$	38.2848	1.25812
$927$	33.4184	1.09760
$928$	−2.26870	−0.0744736
$929$	−19.3792	−0.635810	−0.317905	−	0.948123i	$-0.602979\pi$
$929$	−19.3792	−0.635810	−0.317905	+	0.948123i	$0.602979\pi$
$930$	3.83435	0.125733
$931$	17.0538	0.558915
$932$	0.919566	0.0301214
$933$	−4.20551	−0.137682
$934$	28.7191	0.939717
$935$	31.2551	1.02215
$936$	−4.85554	−0.158708
$937$	−6.13718	−0.200493	−0.100247	−	0.994963i	$-0.531963\pi$
$937$	−6.13718	−0.200493	−0.100247	+	0.994963i	$0.531963\pi$
$938$	−38.5155	−1.25758
$939$	3.42081	0.111634
$940$	−7.61928	−0.248513
$941$	11.5877	0.377749	0.188874	−	0.982001i	$-0.439516\pi$
$941$	11.5877	0.377749	0.188874	+	0.982001i	$0.439516\pi$
$942$	6.46358	0.210595
$943$	14.2552	0.464213
$944$	7.16058	0.233057
$945$	−19.2297	−0.625543
$946$	44.8926	1.45958
$947$	−20.3808	−0.662286	−0.331143	−	0.943581i	$-0.607434\pi$
$947$	−20.3808	−0.662286	−0.331143	+	0.943581i	$0.607434\pi$
$948$	−1.53171	−0.0497477
$949$	5.14814	0.167116
$950$	−18.7301	−0.607685
$951$	9.04803	0.293403
$952$	−23.9502	−0.776230
$953$	−42.9792	−1.39223	−0.696117	−	0.717928i	$-0.745091\pi$
$953$	−42.9792	−1.39223	−0.696117	+	0.717928i	$0.745091\pi$
$954$	−3.19480	−0.103435
$955$	−13.8941	−0.449604
$956$	12.2172	0.395133
$957$	1.34044	0.0433304
$958$	52.6702	1.70170
$959$	50.2769	1.62352
$960$	−5.68418	−0.183456
$961$	−24.6909	−0.796481
$962$	2.88997	0.0931763
$963$	46.3702	1.49426
$964$	−6.04023	−0.194543
$965$	−7.71213	−0.248262
$966$	4.91181	0.158035
$967$	40.5274	1.30327	0.651636	−	0.758531i	$-0.274083\pi$
$967$	40.5274	1.30327	0.651636	+	0.758531i	$0.274083\pi$
$968$	8.92520	0.286867
$969$	4.29432	0.137953
$970$	−77.5068	−2.48859
$971$	21.7713	0.698674	0.349337	−	0.936997i	$-0.386407\pi$
$971$	21.7713	0.698674	0.349337	+	0.936997i	$0.386407\pi$
$972$	3.64499	0.116913
$973$	3.32540	0.106607
$974$	29.8725	0.957176
$975$	0.687960	0.0220324
$976$	−18.8070	−0.601997
$977$	4.53355	0.145041	0.0725205	−	0.997367i	$-0.476896\pi$
$977$	4.53355	0.145041	0.0725205	+	0.997367i	$0.476896\pi$
$978$	1.46468	0.0468351
$979$	−35.2437	−1.12639
$980$	−4.63434	−0.148039
$981$	−51.4829	−1.64372
$982$	−8.14574	−0.259941
$983$	27.9410	0.891179	0.445590	−	0.895237i	$-0.352994\pi$
$983$	27.9410	0.891179	0.445590	+	0.895237i	$0.352994\pi$
$984$	4.55068	0.145071
$985$	−21.9842	−0.700475
$986$	4.52112	0.143982
$987$	−7.78060	−0.247659
$988$	1.16788	0.0371553
$989$	20.5518	0.653510
$990$	47.8732	1.52151
$991$	−34.5666	−1.09805	−0.549023	−	0.835807i	$-0.685000\pi$
$991$	−34.5666	−1.09805	−0.549023	+	0.835807i	$0.685000\pi$
$992$	5.69849	0.180927
$993$	−4.47636	−0.142053
$994$	16.4438	0.521566
$995$	22.5913	0.716192
$996$	0.622154	0.0197137
$997$	21.2031	0.671509	0.335754	−	0.941950i	$-0.391009\pi$
$997$	21.2031	0.671509	0.335754	+	0.941950i	$0.391009\pi$
$998$	31.9386	1.01100
$999$	5.62188	0.177868

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.15	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.15	✓	61	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-1.55145 q^{2} +0.350675 q^{3} +0.406987 q^{4} -2.80587 q^{5} -0.544053 q^{6} -3.32540 q^{7} +2.47147 q^{8} -2.87703 q^{9} +O(q^{10})\)	\(q-1.55145 q^{2} +0.350675 q^{3} +0.406987 q^{4} -2.80587 q^{5} -0.544053 q^{6} -3.32540 q^{7} +2.47147 q^{8} -2.87703 q^{9} +4.35316 q^{10} -3.82247 q^{11} +0.142720 q^{12} +0.682868 q^{13} +5.15918 q^{14} -0.983948 q^{15} -4.64834 q^{16} +2.91413 q^{17} +4.46355 q^{18} +4.20224 q^{19} -1.14195 q^{20} -1.16613 q^{21} +5.93036 q^{22} +2.71492 q^{23} +0.866683 q^{24} +2.87291 q^{25} -1.05943 q^{26} -2.06092 q^{27} -1.35339 q^{28} -1.00000 q^{29} +1.52654 q^{30} +2.51179 q^{31} +2.26870 q^{32} -1.34044 q^{33} -4.52112 q^{34} +9.33063 q^{35} -1.17091 q^{36} -2.72784 q^{37} -6.51956 q^{38} +0.239465 q^{39} -6.93464 q^{40} +5.25069 q^{41} +1.80919 q^{42} +7.56996 q^{43} -1.55570 q^{44} +8.07257 q^{45} -4.21205 q^{46} +6.67214 q^{47} -1.63005 q^{48} +4.05826 q^{49} -4.45717 q^{50} +1.02191 q^{51} +0.277919 q^{52} -0.715752 q^{53} +3.19741 q^{54} +10.7254 q^{55} -8.21863 q^{56} +1.47362 q^{57} +1.55145 q^{58} -1.54046 q^{59} -0.400454 q^{60} +4.04596 q^{61} -3.89691 q^{62} +9.56726 q^{63} +5.77691 q^{64} -1.91604 q^{65} +2.07963 q^{66} -7.46543 q^{67} +1.18601 q^{68} +0.952053 q^{69} -14.4760 q^{70} +3.18730 q^{71} -7.11050 q^{72} +7.53899 q^{73} +4.23210 q^{74} +1.00746 q^{75} +1.71026 q^{76} +12.7112 q^{77} -0.371516 q^{78} -10.7323 q^{79} +13.0426 q^{80} +7.90837 q^{81} -8.14617 q^{82} +4.35926 q^{83} -0.474601 q^{84} -8.17668 q^{85} -11.7444 q^{86} -0.350675 q^{87} -9.44714 q^{88} +9.22015 q^{89} -12.5242 q^{90} -2.27081 q^{91} +1.10494 q^{92} +0.880820 q^{93} -10.3515 q^{94} -11.7909 q^{95} +0.795574 q^{96} -17.8047 q^{97} -6.29617 q^{98} +10.9974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * q^99

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