LMFDB - Embedded newform 1441.2.a.f.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.187162 q^{2} +3.03513 q^{3} -1.96497 q^{4} +3.17183 q^{5} -0.568060 q^{6} -3.01076 q^{7} +0.742092 q^{8} +6.21199 q^{9} +O(q^{10})$	\(q-0.187162 q^{2} +3.03513 q^{3} -1.96497 q^{4} +3.17183 q^{5} -0.568060 q^{6} -3.01076 q^{7} +0.742092 q^{8} +6.21199 q^{9} -0.593646 q^{10} -1.00000 q^{11} -5.96393 q^{12} -3.91889 q^{13} +0.563499 q^{14} +9.62689 q^{15} +3.79105 q^{16} +5.98035 q^{17} -1.16265 q^{18} +1.02385 q^{19} -6.23255 q^{20} -9.13802 q^{21} +0.187162 q^{22} +3.44495 q^{23} +2.25234 q^{24} +5.06049 q^{25} +0.733467 q^{26} +9.74878 q^{27} +5.91605 q^{28} +6.73231 q^{29} -1.80179 q^{30} +7.30261 q^{31} -2.19372 q^{32} -3.03513 q^{33} -1.11929 q^{34} -9.54960 q^{35} -12.2064 q^{36} +4.80219 q^{37} -0.191626 q^{38} -11.8943 q^{39} +2.35379 q^{40} -4.42133 q^{41} +1.71029 q^{42} +5.88976 q^{43} +1.96497 q^{44} +19.7033 q^{45} -0.644764 q^{46} +8.97593 q^{47} +11.5063 q^{48} +2.06465 q^{49} -0.947131 q^{50} +18.1511 q^{51} +7.70050 q^{52} -9.57979 q^{53} -1.82460 q^{54} -3.17183 q^{55} -2.23426 q^{56} +3.10752 q^{57} -1.26003 q^{58} -6.67741 q^{59} -18.9166 q^{60} -6.28525 q^{61} -1.36677 q^{62} -18.7028 q^{63} -7.17152 q^{64} -12.4300 q^{65} +0.568060 q^{66} -2.79967 q^{67} -11.7512 q^{68} +10.4559 q^{69} +1.78732 q^{70} +4.10552 q^{71} +4.60986 q^{72} +2.85104 q^{73} -0.898787 q^{74} +15.3592 q^{75} -2.01184 q^{76} +3.01076 q^{77} +2.22616 q^{78} -12.0504 q^{79} +12.0246 q^{80} +10.9528 q^{81} +0.827504 q^{82} -8.30768 q^{83} +17.9559 q^{84} +18.9686 q^{85} -1.10234 q^{86} +20.4334 q^{87} -0.742092 q^{88} -17.2507 q^{89} -3.68772 q^{90} +11.7988 q^{91} -6.76923 q^{92} +22.1643 q^{93} -1.67995 q^{94} +3.24748 q^{95} -6.65823 q^{96} +0.194174 q^{97} -0.386425 q^{98} -6.21199 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * 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 $

$2$	−0.187162	−0.132344	−0.0661718	−	0.997808i	$-0.521079\pi$
$2$	−0.187162	−0.132344	−0.0661718	+	0.997808i	$0.521079\pi$
$3$	3.03513	1.75233	0.876165	−	0.482011i	$-0.160093\pi$
$3$	3.03513	1.75233	0.876165	+	0.482011i	$0.160093\pi$
$4$	−1.96497	−0.982485
$5$	3.17183	1.41848	0.709242	−	0.704965i	$-0.249037\pi$
$5$	3.17183	1.41848	0.709242	+	0.704965i	$0.249037\pi$
$6$	−0.568060	−0.231910
$7$	−3.01076	−1.13796	−0.568980	−	0.822352i	$-0.692662\pi$
$7$	−3.01076	−1.13796	−0.568980	+	0.822352i	$0.692662\pi$
$8$	0.742092	0.262369
$9$	6.21199	2.07066
$10$	−0.593646	−0.187727
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−5.96393	−1.72164
$13$	−3.91889	−1.08690	−0.543452	−	0.839440i	$-0.682883\pi$
$13$	−3.91889	−1.08690	−0.543452	+	0.839440i	$0.682883\pi$
$14$	0.563499	0.150601
$15$	9.62689	2.48565
$16$	3.79105	0.947762
$17$	5.98035	1.45045	0.725224	−	0.688513i	$-0.241736\pi$
$17$	5.98035	1.45045	0.725224	+	0.688513i	$0.241736\pi$
$18$	−1.16265	−0.274039
$19$	1.02385	0.234888	0.117444	−	0.993080i	$-0.462530\pi$
$19$	1.02385	0.234888	0.117444	+	0.993080i	$0.462530\pi$
$20$	−6.23255	−1.39364
$21$	−9.13802	−1.99408
$22$	0.187162	0.0399031
$23$	3.44495	0.718322	0.359161	−	0.933276i	$-0.383063\pi$
$23$	3.44495	0.718322	0.359161	+	0.933276i	$0.383063\pi$
$24$	2.25234	0.459757
$25$	5.06049	1.01210
$26$	0.733467	0.143845
$27$	9.74878	1.87615
$28$	5.91605	1.11803
$29$	6.73231	1.25016	0.625080	−	0.780561i	$-0.285067\pi$
$29$	6.73231	1.25016	0.625080	+	0.780561i	$0.285067\pi$
$30$	−1.80179	−0.328960
$31$	7.30261	1.31159	0.655794	−	0.754940i	$-0.272334\pi$
$31$	7.30261	1.31159	0.655794	+	0.754940i	$0.272334\pi$
$32$	−2.19372	−0.387799
$33$	−3.03513	−0.528347
$34$	−1.11929	−0.191957
$35$	−9.54960	−1.61418
$36$	−12.2064	−2.03439
$37$	4.80219	0.789475	0.394737	−	0.918794i	$-0.370836\pi$
$37$	4.80219	0.789475	0.394737	+	0.918794i	$0.370836\pi$
$38$	−0.191626	−0.0310859
$39$	−11.8943	−1.90461
$40$	2.35379	0.372166
$41$	−4.42133	−0.690495	−0.345248	−	0.938512i	$-0.612205\pi$
$41$	−4.42133	−0.690495	−0.345248	+	0.938512i	$0.612205\pi$
$42$	1.71029	0.263904
$43$	5.88976	0.898180	0.449090	−	0.893487i	$-0.351748\pi$
$43$	5.88976	0.898180	0.449090	+	0.893487i	$0.351748\pi$
$44$	1.96497	0.296230
$45$	19.7033	2.93720
$46$	−0.644764	−0.0950653
$47$	8.97593	1.30927	0.654637	−	0.755943i	$-0.272821\pi$
$47$	8.97593	1.30927	0.654637	+	0.755943i	$0.272821\pi$
$48$	11.5063	1.66079
$49$	2.06465	0.294951
$50$	−0.947131	−0.133945
$51$	18.1511	2.54166
$52$	7.70050	1.06787
$53$	−9.57979	−1.31588	−0.657942	−	0.753068i	$-0.728573\pi$
$53$	−9.57979	−1.31588	−0.657942	+	0.753068i	$0.728573\pi$
$54$	−1.82460	−0.248297
$55$	−3.17183	−0.427689
$56$	−2.23426	−0.298565
$57$	3.10752	0.411601
$58$	−1.26003	−0.165450
$59$	−6.67741	−0.869325	−0.434663	−	0.900593i	$-0.643132\pi$
$59$	−6.67741	−0.869325	−0.434663	+	0.900593i	$0.643132\pi$
$60$	−18.9166	−2.44212
$61$	−6.28525	−0.804743	−0.402372	−	0.915476i	$-0.631814\pi$
$61$	−6.28525	−0.804743	−0.402372	+	0.915476i	$0.631814\pi$
$62$	−1.36677	−0.173580
$63$	−18.7028	−2.35633
$64$	−7.17152	−0.896440
$65$	−12.4300	−1.54176
$66$	0.568060	0.0699234
$67$	−2.79967	−0.342034	−0.171017	−	0.985268i	$-0.554705\pi$
$67$	−2.79967	−0.342034	−0.171017	+	0.985268i	$0.554705\pi$
$68$	−11.7512	−1.42504
$69$	10.4559	1.25874
$70$	1.78732	0.213626
$71$	4.10552	0.487235	0.243618	−	0.969871i	$-0.421666\pi$
$71$	4.10552	0.487235	0.243618	+	0.969871i	$0.421666\pi$
$72$	4.60986	0.543278
$73$	2.85104	0.333689	0.166845	−	0.985983i	$-0.446642\pi$
$73$	2.85104	0.333689	0.166845	+	0.985983i	$0.446642\pi$
$74$	−0.898787	−0.104482
$75$	15.3592	1.77353
$76$	−2.01184	−0.230774
$77$	3.01076	0.343108
$78$	2.22616	0.252063
$79$	−12.0504	−1.35578	−0.677889	−	0.735164i	$-0.737105\pi$
$79$	−12.0504	−1.35578	−0.677889	+	0.735164i	$0.737105\pi$
$80$	12.0246	1.34439
$81$	10.9528	1.21698
$82$	0.827504	0.0913826
$83$	−8.30768	−0.911886	−0.455943	−	0.890009i	$-0.650698\pi$
$83$	−8.30768	−0.911886	−0.455943	+	0.890009i	$0.650698\pi$
$84$	17.9559	1.95915
$85$	18.9686	2.05744
$86$	−1.10234	−0.118868
$87$	20.4334	2.19069
$88$	−0.742092	−0.0791072
$89$	−17.2507	−1.82858	−0.914288	−	0.405065i	$-0.867249\pi$
$89$	−17.2507	−1.82858	−0.914288	+	0.405065i	$0.867249\pi$
$90$	−3.68772	−0.388720
$91$	11.7988	1.23685
$92$	−6.76923	−0.705741
$93$	22.1643	2.29834
$94$	−1.67995	−0.173274
$95$	3.24748	0.333185
$96$	−6.65823	−0.679552
$97$	0.194174	0.0197154	0.00985771	−	0.999951i	$-0.496862\pi$
$97$	0.194174	0.0197154	0.00985771	+	0.999951i	$0.496862\pi$
$98$	−0.386425	−0.0390348
$99$	−6.21199	−0.624328
$100$	−9.94371	−0.994371
$101$	4.12990	0.410940	0.205470	−	0.978663i	$-0.434128\pi$
$101$	4.12990	0.410940	0.205470	+	0.978663i	$0.434128\pi$
$102$	−3.39720	−0.336373
$103$	11.2823	1.11168	0.555841	−	0.831289i	$-0.312396\pi$
$103$	11.2823	1.11168	0.555841	+	0.831289i	$0.312396\pi$
$104$	−2.90817	−0.285170
$105$	−28.9842	−2.82857
$106$	1.79297	0.174149
$107$	−15.0853	−1.45836	−0.729178	−	0.684324i	$-0.760097\pi$
$107$	−15.0853	−1.45836	−0.729178	+	0.684324i	$0.760097\pi$
$108$	−19.1561	−1.84329
$109$	−0.913571	−0.0875042	−0.0437521	−	0.999042i	$-0.513931\pi$
$109$	−0.913571	−0.0875042	−0.0437521	+	0.999042i	$0.513931\pi$
$110$	0.593646	0.0566019
$111$	14.5752	1.38342
$112$	−11.4139	−1.07851
$113$	−12.1752	−1.14535	−0.572674	−	0.819783i	$-0.694094\pi$
$113$	−12.1752	−1.14535	−0.572674	+	0.819783i	$0.694094\pi$
$114$	−0.581609	−0.0544727
$115$	10.9268	1.01893
$116$	−13.2288	−1.22826
$117$	−24.3441	−2.25061
$118$	1.24976	0.115050
$119$	−18.0054	−1.65055
$120$	7.14404	0.652158
$121$	1.00000	0.0909091
$122$	1.17636	0.106503
$123$	−13.4193	−1.20998
$124$	−14.3494	−1.28862
$125$	0.191857	0.0171602
$126$	3.50045	0.311845
$127$	−2.90646	−0.257907	−0.128953	−	0.991651i	$-0.541162\pi$
$127$	−2.90646	−0.257907	−0.128953	+	0.991651i	$0.541162\pi$
$128$	5.72968	0.506437
$129$	17.8762	1.57391
$130$	2.32643	0.204041
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	5.96393	0.519094
$133$	−3.08257	−0.267293
$134$	0.523992	0.0452660
$135$	30.9214	2.66129
$136$	4.43797	0.380553
$137$	−7.44283	−0.635884	−0.317942	−	0.948110i	$-0.602992\pi$
$137$	−7.44283	−0.635884	−0.317942	+	0.948110i	$0.602992\pi$
$138$	−1.95694	−0.166586
$139$	−9.26433	−0.785790	−0.392895	−	0.919583i	$-0.628526\pi$
$139$	−9.26433	−0.785790	−0.392895	+	0.919583i	$0.628526\pi$
$140$	18.7647	1.58590
$141$	27.2431	2.29428
$142$	−0.768397	−0.0644825
$143$	3.91889	0.327714
$144$	23.5499	1.96250
$145$	21.3537	1.77333
$146$	−0.533607	−0.0441616
$147$	6.26649	0.516851
$148$	−9.43615	−0.775647
$149$	−14.5308	−1.19041	−0.595204	−	0.803575i	$-0.702929\pi$
$149$	−14.5308	−1.19041	−0.595204	+	0.803575i	$0.702929\pi$
$150$	−2.87466	−0.234715
$151$	19.1282	1.55663	0.778316	−	0.627873i	$-0.216074\pi$
$151$	19.1282	1.55663	0.778316	+	0.627873i	$0.216074\pi$
$152$	0.759792	0.0616273
$153$	37.1498	3.00339
$154$	−0.563499	−0.0454081
$155$	23.1626	1.86047
$156$	23.3720	1.87126
$157$	−21.7602	−1.73665	−0.868325	−	0.495996i	$-0.834803\pi$
$157$	−21.7602	−1.73665	−0.868325	+	0.495996i	$0.834803\pi$
$158$	2.25538	0.179428
$159$	−29.0758	−2.30586
$160$	−6.95811	−0.550087
$161$	−10.3719	−0.817422
$162$	−2.04995	−0.161059
$163$	8.63900	0.676659	0.338329	−	0.941028i	$-0.390138\pi$
$163$	8.63900	0.676659	0.338329	+	0.941028i	$0.390138\pi$
$164$	8.68777	0.678401
$165$	−9.62689	−0.749453
$166$	1.55488	0.120682
$167$	−0.0672875	−0.00520686	−0.00260343	−	0.999997i	$-0.500829\pi$
$167$	−0.0672875	−0.00520686	−0.00260343	+	0.999997i	$0.500829\pi$
$168$	−6.78125	−0.523185
$169$	2.35769	0.181360
$170$	−3.55021	−0.272289
$171$	6.36015	0.486373
$172$	−11.5732	−0.882448
$173$	−9.74334	−0.740773	−0.370386	−	0.928878i	$-0.620775\pi$
$173$	−9.74334	−0.740773	−0.370386	+	0.928878i	$0.620775\pi$
$174$	−3.82436	−0.289924
$175$	−15.2359	−1.15173
$176$	−3.79105	−0.285761
$177$	−20.2668	−1.52334
$178$	3.22868	0.242000
$179$	24.7087	1.84682	0.923409	−	0.383818i	$-0.125391\pi$
$179$	24.7087	1.84682	0.923409	+	0.383818i	$0.125391\pi$
$180$	−38.7165	−2.88576
$181$	−15.1136	−1.12339	−0.561694	−	0.827345i	$-0.689850\pi$
$181$	−15.1136	−1.12339	−0.561694	+	0.827345i	$0.689850\pi$
$182$	−2.20829	−0.163689
$183$	−19.0765	−1.41018
$184$	2.55647	0.188466
$185$	15.2317	1.11986
$186$	−4.14832	−0.304170
$187$	−5.98035	−0.437327
$188$	−17.6374	−1.28634
$189$	−29.3512	−2.13499
$190$	−0.607805	−0.0440948
$191$	22.1577	1.60327	0.801637	−	0.597811i	$-0.203963\pi$
$191$	22.1577	1.60327	0.801637	+	0.597811i	$0.203963\pi$
$192$	−21.7665	−1.57086
$193$	8.65604	0.623075	0.311538	−	0.950234i	$-0.399156\pi$
$193$	8.65604	0.623075	0.311538	+	0.950234i	$0.399156\pi$
$194$	−0.0363421	−0.00260921
$195$	−37.7267	−2.70167
$196$	−4.05699	−0.289785
$197$	23.5611	1.67866	0.839329	−	0.543624i	$-0.182948\pi$
$197$	23.5611	1.67866	0.839329	+	0.543624i	$0.182948\pi$
$198$	1.16265	0.0826258
$199$	1.59536	0.113092	0.0565462	−	0.998400i	$-0.481991\pi$
$199$	1.59536	0.113092	0.0565462	+	0.998400i	$0.481991\pi$
$200$	3.75535	0.265543
$201$	−8.49735	−0.599357
$202$	−0.772960	−0.0543853
$203$	−20.2694	−1.42263
$204$	−35.6664	−2.49715
$205$	−14.0237	−0.979456
$206$	−2.11162	−0.147124
$207$	21.4000	1.48740
$208$	−14.8567	−1.03013
$209$	−1.02385	−0.0708213
$210$	5.42475	0.374343
$211$	6.40580	0.440994	0.220497	−	0.975388i	$-0.429232\pi$
$211$	6.40580	0.440994	0.220497	+	0.975388i	$0.429232\pi$
$212$	18.8240	1.29284
$213$	12.4608	0.853798
$214$	2.82340	0.193004
$215$	18.6813	1.27405
$216$	7.23449	0.492244
$217$	−21.9864	−1.49253
$218$	0.170986	0.0115806
$219$	8.65327	0.584734
$220$	6.23255	0.420198
$221$	−23.4363	−1.57650
$222$	−2.72793	−0.183087
$223$	27.2568	1.82525	0.912627	−	0.408794i	$-0.134051\pi$
$223$	27.2568	1.82525	0.912627	+	0.408794i	$0.134051\pi$
$224$	6.60477	0.441300
$225$	31.4357	2.09571
$226$	2.27874	0.151579
$227$	−18.3486	−1.21784	−0.608919	−	0.793233i	$-0.708396\pi$
$227$	−18.3486	−1.21784	−0.608919	+	0.793233i	$0.708396\pi$
$228$	−6.10618	−0.404392
$229$	9.62813	0.636244	0.318122	−	0.948050i	$-0.396948\pi$
$229$	9.62813	0.636244	0.318122	+	0.948050i	$0.396948\pi$
$230$	−2.04508	−0.134849
$231$	9.13802	0.601238
$232$	4.99599	0.328003
$233$	−23.3154	−1.52744	−0.763721	−	0.645547i	$-0.776630\pi$
$233$	−23.3154	−1.52744	−0.763721	+	0.645547i	$0.776630\pi$
$234$	4.55629	0.297854
$235$	28.4701	1.85719
$236$	13.1209	0.854099
$237$	−36.5745	−2.37577
$238$	3.36992	0.218440
$239$	23.3651	1.51136	0.755680	−	0.654941i	$-0.227306\pi$
$239$	23.3651	1.51136	0.755680	+	0.654941i	$0.227306\pi$
$240$	36.4960	2.35581
$241$	−14.2540	−0.918183	−0.459091	−	0.888389i	$-0.651825\pi$
$241$	−14.2540	−0.918183	−0.459091	+	0.888389i	$0.651825\pi$
$242$	−0.187162	−0.0120312
$243$	3.99680	0.256395
$244$	12.3503	0.790648
$245$	6.54873	0.418383
$246$	2.51158	0.160132
$247$	−4.01236	−0.255300
$248$	5.41921	0.344120
$249$	−25.2149	−1.59793
$250$	−0.0359084	−0.00227104
$251$	−23.7925	−1.50177	−0.750884	−	0.660434i	$-0.770372\pi$
$251$	−23.7925	−1.50177	−0.750884	+	0.660434i	$0.770372\pi$
$252$	36.7504	2.31506
$253$	−3.44495	−0.216582
$254$	0.543979	0.0341323
$255$	57.5722	3.60531
$256$	13.2707	0.829416
$257$	10.9278	0.681654	0.340827	−	0.940126i	$-0.389293\pi$
$257$	10.9278	0.681654	0.340827	+	0.940126i	$0.389293\pi$
$258$	−3.34574	−0.208296
$259$	−14.4582	−0.898390
$260$	24.4247	1.51475
$261$	41.8210	2.58866
$262$	−0.187162	−0.0115629
$263$	11.8780	0.732430	0.366215	−	0.930530i	$-0.380653\pi$
$263$	11.8780	0.732430	0.366215	+	0.930530i	$0.380653\pi$
$264$	−2.25234	−0.138622
$265$	−30.3854	−1.86656
$266$	0.576940	0.0353744
$267$	−52.3582	−3.20427
$268$	5.50127	0.336044
$269$	−6.12856	−0.373665	−0.186832	−	0.982392i	$-0.559822\pi$
$269$	−6.12856	−0.373665	−0.186832	+	0.982392i	$0.559822\pi$
$270$	−5.78732	−0.352205
$271$	15.1214	0.918560	0.459280	−	0.888292i	$-0.348108\pi$
$271$	15.1214	0.918560	0.459280	+	0.888292i	$0.348108\pi$
$272$	22.6718	1.37468
$273$	35.8109	2.16737
$274$	1.39301	0.0841551
$275$	−5.06049	−0.305159
$276$	−20.5455	−1.23669
$277$	−1.74853	−0.105059	−0.0525295	−	0.998619i	$-0.516728\pi$
$277$	−1.74853	−0.105059	−0.0525295	+	0.998619i	$0.516728\pi$
$278$	1.73393	0.103994
$279$	45.3637	2.71586
$280$	−7.08668	−0.423510
$281$	26.0702	1.55522	0.777609	−	0.628748i	$-0.216432\pi$
$281$	26.0702	1.55522	0.777609	+	0.628748i	$0.216432\pi$
$282$	−5.09887	−0.303633
$283$	−30.8117	−1.83156	−0.915782	−	0.401676i	$-0.868428\pi$
$283$	−30.8117	−1.83156	−0.915782	+	0.401676i	$0.868428\pi$
$284$	−8.06722	−0.478702
$285$	9.85651	0.583849
$286$	−0.733467	−0.0433708
$287$	13.3115	0.785755
$288$	−13.6274	−0.803001
$289$	18.7646	1.10380
$290$	−3.99661	−0.234689
$291$	0.589344	0.0345479
$292$	−5.60221	−0.327845
$293$	26.9867	1.57658	0.788289	−	0.615305i	$-0.210967\pi$
$293$	26.9867	1.57658	0.788289	+	0.615305i	$0.210967\pi$
$294$	−1.17285	−0.0684019
$295$	−21.1796	−1.23312
$296$	3.56366	0.207134
$297$	−9.74878	−0.565681
$298$	2.71961	0.157543
$299$	−13.5004	−0.780748
$300$	−30.1804	−1.74247
$301$	−17.7326	−1.02209
$302$	−3.58007	−0.206010
$303$	12.5348	0.720103
$304$	3.88147	0.222618
$305$	−19.9357	−1.14152
$306$	−6.95304	−0.397479
$307$	8.99365	0.513295	0.256647	−	0.966505i	$-0.417382\pi$
$307$	8.99365	0.513295	0.256647	+	0.966505i	$0.417382\pi$
$308$	−5.91605	−0.337098
$309$	34.2433	1.94803
$310$	−4.33516	−0.246221
$311$	−7.25999	−0.411676	−0.205838	−	0.978586i	$-0.565992\pi$
$311$	−7.25999	−0.411676	−0.205838	+	0.978586i	$0.565992\pi$
$312$	−8.82667	−0.499712
$313$	−6.42686	−0.363268	−0.181634	−	0.983366i	$-0.558139\pi$
$313$	−6.42686	−0.363268	−0.181634	+	0.983366i	$0.558139\pi$
$314$	4.07268	0.229834
$315$	−59.3220	−3.34241
$316$	23.6787	1.33203
$317$	−23.6561	−1.32866	−0.664329	−	0.747440i	$-0.731283\pi$
$317$	−23.6561	−1.32866	−0.664329	+	0.747440i	$0.731283\pi$
$318$	5.44189	0.305166
$319$	−6.73231	−0.376937
$320$	−22.7468	−1.27159
$321$	−45.7859	−2.55552
$322$	1.94123	0.108180
$323$	6.12299	0.340692
$324$	−21.5219	−1.19566
$325$	−19.8315	−1.10005
$326$	−1.61689	−0.0895514
$327$	−2.77280	−0.153336
$328$	−3.28103	−0.181165
$329$	−27.0243	−1.48990
$330$	1.80179	0.0991852
$331$	−2.42263	−0.133160	−0.0665799	−	0.997781i	$-0.521209\pi$
$331$	−2.42263	−0.133160	−0.0665799	+	0.997781i	$0.521209\pi$
$332$	16.3243	0.895915
$333$	29.8311	1.63473
$334$	0.0125937	0.000689094 0
$335$	−8.88007	−0.485170
$336$	−34.6427	−1.88991
$337$	−11.0048	−0.599469	−0.299734	−	0.954023i	$-0.596898\pi$
$337$	−11.0048	−0.599469	−0.299734	+	0.954023i	$0.596898\pi$
$338$	−0.441269	−0.0240019
$339$	−36.9533	−2.00703
$340$	−37.2728	−2.02140
$341$	−7.30261	−0.395459
$342$	−1.19038	−0.0643683
$343$	14.8591	0.802317
$344$	4.37074	0.235655
$345$	33.1642	1.78550
$346$	1.82358	0.0980365
$347$	7.84505	0.421144	0.210572	−	0.977578i	$-0.432467\pi$
$347$	7.84505	0.421144	0.210572	+	0.977578i	$0.432467\pi$
$348$	−40.1511	−2.15232
$349$	11.3048	0.605134	0.302567	−	0.953128i	$-0.402156\pi$
$349$	11.3048	0.605134	0.302567	+	0.953128i	$0.402156\pi$
$350$	2.85158	0.152423
$351$	−38.2044	−2.03920
$352$	2.19372	0.116926
$353$	4.93085	0.262442	0.131221	−	0.991353i	$-0.458110\pi$
$353$	4.93085	0.262442	0.131221	+	0.991353i	$0.458110\pi$
$354$	3.79317	0.201605
$355$	13.0220	0.691136
$356$	33.8972	1.79655
$357$	−54.6486	−2.89231
$358$	−4.62454	−0.244414
$359$	−17.2444	−0.910126	−0.455063	−	0.890459i	$-0.650383\pi$
$359$	−17.2444	−0.910126	−0.455063	+	0.890459i	$0.650383\pi$
$360$	14.6217	0.770631
$361$	−17.9517	−0.944828
$362$	2.82870	0.148673
$363$	3.03513	0.159303
$364$	−23.1843	−1.21519
$365$	9.04301	0.473333
$366$	3.57040	0.186628
$367$	20.7804	1.08473	0.542363	−	0.840144i	$-0.317530\pi$
$367$	20.7804	1.08473	0.542363	+	0.840144i	$0.317530\pi$
$368$	13.0600	0.680799
$369$	−27.4652	−1.42978
$370$	−2.85080	−0.148206
$371$	28.8424	1.49742
$372$	−43.5523	−2.25808
$373$	−37.3020	−1.93143	−0.965713	−	0.259613i	$-0.916405\pi$
$373$	−37.3020	−1.93143	−0.965713	+	0.259613i	$0.916405\pi$
$374$	1.11929	0.0578773
$375$	0.582310	0.0300704
$376$	6.66097	0.343513
$377$	−26.3832	−1.35880
$378$	5.49343	0.282551
$379$	0.941260	0.0483493	0.0241746	−	0.999708i	$-0.492304\pi$
$379$	0.941260	0.0483493	0.0241746	+	0.999708i	$0.492304\pi$
$380$	−6.38120	−0.327349
$381$	−8.82148	−0.451938
$382$	−4.14708	−0.212183
$383$	−14.2968	−0.730534	−0.365267	−	0.930903i	$-0.619022\pi$
$383$	−14.2968	−0.730534	−0.365267	+	0.930903i	$0.619022\pi$
$384$	17.3903	0.887445
$385$	9.54960	0.486693
$386$	−1.62008	−0.0824600
$387$	36.5871	1.85983
$388$	−0.381547	−0.0193701
$389$	13.0790	0.663134	0.331567	−	0.943432i	$-0.392423\pi$
$389$	13.0790	0.663134	0.331567	+	0.943432i	$0.392423\pi$
$390$	7.06101	0.357548
$391$	20.6020	1.04189
$392$	1.53216	0.0773859
$393$	3.03513	0.153102
$394$	−4.40974	−0.222160
$395$	−38.2219	−1.92315
$396$	12.2064	0.613393
$397$	−29.8671	−1.49899	−0.749494	−	0.662011i	$-0.769703\pi$
$397$	−29.8671	−1.49899	−0.749494	+	0.662011i	$0.769703\pi$
$398$	−0.298592	−0.0149670
$399$	−9.35598	−0.468385
$400$	19.1846	0.959228
$401$	31.4078	1.56843	0.784216	−	0.620487i	$-0.213065\pi$
$401$	31.4078	1.56843	0.784216	+	0.620487i	$0.213065\pi$
$402$	1.59038	0.0793210
$403$	−28.6181	−1.42557
$404$	−8.11513	−0.403743
$405$	34.7404	1.72626
$406$	3.79365	0.188276
$407$	−4.80219	−0.238036
$408$	13.4698	0.666854
$409$	−11.1925	−0.553432	−0.276716	−	0.960952i	$-0.589246\pi$
$409$	−11.1925	−0.553432	−0.276716	+	0.960952i	$0.589246\pi$
$410$	2.62470	0.129625
$411$	−22.5899	−1.11428
$412$	−22.1695	−1.09221
$413$	20.1041	0.989256
$414$	−4.00527	−0.196848
$415$	−26.3505	−1.29350
$416$	8.59696	0.421501
$417$	−28.1184	−1.37696
$418$	0.191626	0.00937274
$419$	−31.4655	−1.53719	−0.768594	−	0.639737i	$-0.779043\pi$
$419$	−31.4655	−1.53719	−0.768594	+	0.639737i	$0.779043\pi$
$420$	56.9532	2.77903
$421$	−28.7222	−1.39983	−0.699917	−	0.714224i	$-0.746780\pi$
$421$	−28.7222	−1.39983	−0.699917	+	0.714224i	$0.746780\pi$
$422$	−1.19892	−0.0583627
$423$	55.7584	2.71106
$424$	−7.10908	−0.345247
$425$	30.2635	1.46799
$426$	−2.33218	−0.112995
$427$	18.9233	0.915765
$428$	29.6423	1.43281
$429$	11.8943	0.574263
$430$	−3.49643	−0.168613
$431$	22.3749	1.07776	0.538880	−	0.842383i	$-0.318848\pi$
$431$	22.3749	1.07776	0.538880	+	0.842383i	$0.318848\pi$
$432$	36.9581	1.77815
$433$	20.0812	0.965040	0.482520	−	0.875885i	$-0.339722\pi$
$433$	20.0812	0.965040	0.482520	+	0.875885i	$0.339722\pi$
$434$	4.11502	0.197527
$435$	64.8113	3.10746
$436$	1.79514	0.0859716
$437$	3.52712	0.168725
$438$	−1.61956	−0.0773857
$439$	−8.45029	−0.403310	−0.201655	−	0.979457i	$-0.564632\pi$
$439$	−8.45029	−0.403310	−0.201655	+	0.979457i	$0.564632\pi$
$440$	−2.35379	−0.112212
$441$	12.8256	0.610743
$442$	4.38639	0.208639
$443$	−4.83048	−0.229503	−0.114752	−	0.993394i	$-0.536607\pi$
$443$	−4.83048	−0.229503	−0.114752	+	0.993394i	$0.536607\pi$
$444$	−28.6399	−1.35919
$445$	−54.7164	−2.59381
$446$	−5.10144	−0.241560
$447$	−44.1028	−2.08599
$448$	21.5917	1.02011
$449$	−36.6146	−1.72795	−0.863974	−	0.503536i	$-0.832032\pi$
$449$	−36.6146	−1.72795	−0.863974	+	0.503536i	$0.832032\pi$
$450$	−5.88356	−0.277354
$451$	4.42133	0.208192
$452$	23.9239	1.12529
$453$	58.0565	2.72773
$454$	3.43416	0.161173
$455$	37.4238	1.75446
$456$	2.30606	0.107991
$457$	13.5850	0.635479	0.317739	−	0.948178i	$-0.397076\pi$
$457$	13.5850	0.635479	0.317739	+	0.948178i	$0.397076\pi$
$458$	−1.80202	−0.0842028
$459$	58.3011	2.72126
$460$	−21.4708	−1.00108
$461$	15.6582	0.729273	0.364636	−	0.931150i	$-0.381193\pi$
$461$	15.6582	0.729273	0.364636	+	0.931150i	$0.381193\pi$
$462$	−1.71029	−0.0795699
$463$	−4.82036	−0.224021	−0.112011	−	0.993707i	$-0.535729\pi$
$463$	−4.82036	−0.224021	−0.112011	+	0.993707i	$0.535729\pi$
$464$	25.5225	1.18485
$465$	70.3015	3.26015
$466$	4.36375	0.202147
$467$	−41.1068	−1.90219	−0.951097	−	0.308892i	$-0.900042\pi$
$467$	−41.1068	−1.90219	−0.951097	+	0.308892i	$0.900042\pi$
$468$	47.8354	2.21119
$469$	8.42913	0.389221
$470$	−5.32852	−0.245786
$471$	−66.0448	−3.04318
$472$	−4.95525	−0.228084
$473$	−5.88976	−0.270811
$474$	6.84536	0.314418
$475$	5.18119	0.237729
$476$	35.3800	1.62164
$477$	−59.5095	−2.72475
$478$	−4.37305	−0.200019
$479$	−10.1525	−0.463877	−0.231939	−	0.972730i	$-0.574507\pi$
$479$	−10.1525	−0.463877	−0.231939	+	0.972730i	$0.574507\pi$
$480$	−21.1187	−0.963934
$481$	−18.8192	−0.858083
$482$	2.66781	0.121516
$483$	−31.4801	−1.43239
$484$	−1.96497	−0.0893168
$485$	0.615888	0.0279660
$486$	−0.748049	−0.0339322
$487$	36.3225	1.64593	0.822966	−	0.568091i	$-0.192318\pi$
$487$	36.3225	1.64593	0.822966	+	0.568091i	$0.192318\pi$
$488$	−4.66423	−0.211140
$489$	26.2204	1.18573
$490$	−1.22567	−0.0553703
$491$	−16.4201	−0.741030	−0.370515	−	0.928826i	$-0.620819\pi$
$491$	−16.4201	−0.741030	−0.370515	+	0.928826i	$0.620819\pi$
$492$	26.3685	1.18878
$493$	40.2616	1.81329
$494$	0.750961	0.0337874
$495$	−19.7033	−0.885599
$496$	27.6846	1.24307
$497$	−12.3607	−0.554454
$498$	4.71926	0.211475
$499$	−17.6137	−0.788499	−0.394249	−	0.919003i	$-0.628995\pi$
$499$	−17.6137	−0.788499	−0.394249	+	0.919003i	$0.628995\pi$
$500$	−0.376994	−0.0168597
$501$	−0.204226	−0.00912414
$502$	4.45305	0.198749
$503$	−20.2195	−0.901544	−0.450772	−	0.892639i	$-0.648851\pi$
$503$	−20.2195	−0.901544	−0.450772	+	0.892639i	$0.648851\pi$
$504$	−13.8792	−0.618228
$505$	13.0993	0.582913
$506$	0.644764	0.0286633
$507$	7.15587	0.317803
$508$	5.71111	0.253390
$509$	−34.7629	−1.54084	−0.770419	−	0.637538i	$-0.779953\pi$
$509$	−34.7629	−1.54084	−0.770419	+	0.637538i	$0.779953\pi$
$510$	−10.7753	−0.477139
$511$	−8.58379	−0.379725
$512$	−13.9431	−0.616205
$513$	9.98130	0.440685
$514$	−2.04526	−0.0902125
$515$	35.7856	1.57690
$516$	−35.1261	−1.54634
$517$	−8.97593	−0.394761
$518$	2.70603	0.118896
$519$	−29.5723	−1.29808
$520$	−9.22423	−0.404509
$521$	3.67382	0.160953	0.0804765	−	0.996757i	$-0.474356\pi$
$521$	3.67382	0.160953	0.0804765	+	0.996757i	$0.474356\pi$
$522$	−7.82731	−0.342592
$523$	−26.8036	−1.17204	−0.586020	−	0.810296i	$-0.699306\pi$
$523$	−26.8036	−1.17204	−0.586020	+	0.810296i	$0.699306\pi$
$524$	−1.96497	−0.0858401
$525$	−46.2429	−2.01820
$526$	−2.22311	−0.0969324
$527$	43.6722	1.90239
$528$	−11.5063	−0.500748
$529$	−11.1323	−0.484013
$530$	5.68700	0.247027
$531$	−41.4800	−1.80008
$532$	6.05716	0.262611
$533$	17.3267	0.750502
$534$	9.79946	0.424064
$535$	−47.8481	−2.06865
$536$	−2.07761	−0.0897392
$537$	74.9941	3.23623
$538$	1.14703	0.0494521
$539$	−2.06465	−0.0889310
$540$	−60.7597	−2.61468
$541$	1.18495	0.0509452	0.0254726	−	0.999676i	$-0.491891\pi$
$541$	1.18495	0.0509452	0.0254726	+	0.999676i	$0.491891\pi$
$542$	−2.83015	−0.121565
$543$	−45.8718	−1.96855
$544$	−13.1192	−0.562483
$545$	−2.89769	−0.124123
$546$	−6.70244	−0.286838
$547$	32.8531	1.40470	0.702349	−	0.711833i	$-0.252135\pi$
$547$	32.8531	1.40470	0.702349	+	0.711833i	$0.252135\pi$
$548$	14.6249	0.624746
$549$	−39.0439	−1.66635
$550$	0.947131	0.0403858
$551$	6.89289	0.293647
$552$	7.75921	0.330254
$553$	36.2809	1.54282
$554$	0.327258	0.0139039
$555$	46.2301	1.96236
$556$	18.2041	0.772027
$557$	9.07679	0.384596	0.192298	−	0.981337i	$-0.438406\pi$
$557$	9.07679	0.384596	0.192298	+	0.981337i	$0.438406\pi$
$558$	−8.49037	−0.359426
$559$	−23.0813	−0.976235
$560$	−36.2030	−1.52986
$561$	−18.1511	−0.766341
$562$	−4.87935	−0.205823
$563$	9.09703	0.383394	0.191697	−	0.981454i	$-0.438601\pi$
$563$	9.09703	0.383394	0.191697	+	0.981454i	$0.438601\pi$
$564$	−53.5318	−2.25410
$565$	−38.6177	−1.62466
$566$	5.76677	0.242396
$567$	−32.9762	−1.38487
$568$	3.04667	0.127836
$569$	38.9523	1.63296	0.816482	−	0.577370i	$-0.195921\pi$
$569$	38.9523	1.63296	0.816482	+	0.577370i	$0.195921\pi$
$570$	−1.84476	−0.0772687
$571$	−13.2984	−0.556522	−0.278261	−	0.960506i	$-0.589758\pi$
$571$	−13.2984	−0.556522	−0.278261	+	0.960506i	$0.589758\pi$
$572$	−7.70050	−0.321974
$573$	67.2513	2.80946
$574$	−2.49141	−0.103990
$575$	17.4331	0.727012
$576$	−44.5494	−1.85622
$577$	17.3401	0.721877	0.360938	−	0.932590i	$-0.382456\pi$
$577$	17.3401	0.721877	0.360938	+	0.932590i	$0.382456\pi$
$578$	−3.51202	−0.146081
$579$	26.2722	1.09183
$580$	−41.9595	−1.74227
$581$	25.0124	1.03769
$582$	−0.110303	−0.00457220
$583$	9.57979	0.396754
$584$	2.11573	0.0875497
$585$	−77.2152	−3.19246
$586$	−5.05088	−0.208650
$587$	11.6031	0.478909	0.239455	−	0.970908i	$-0.423031\pi$
$587$	11.6031	0.478909	0.239455	+	0.970908i	$0.423031\pi$
$588$	−12.3135	−0.507799
$589$	7.47679	0.308076
$590$	3.96402	0.163196
$591$	71.5109	2.94156
$592$	18.2053	0.748234
$593$	17.9004	0.735081	0.367540	−	0.930008i	$-0.380200\pi$
$593$	17.9004	0.735081	0.367540	+	0.930008i	$0.380200\pi$
$594$	1.82460	0.0748643
$595$	−57.1099	−2.34128
$596$	28.5526	1.16956
$597$	4.84213	0.198175
$598$	2.52676	0.103327
$599$	1.75837	0.0718450	0.0359225	−	0.999355i	$-0.488563\pi$
$599$	1.75837	0.0718450	0.0359225	+	0.999355i	$0.488563\pi$
$600$	11.3979	0.465319
$601$	−23.9162	−0.975564	−0.487782	−	0.872966i	$-0.662194\pi$
$601$	−23.9162	−0.975564	−0.487782	+	0.872966i	$0.662194\pi$
$602$	3.31887	0.135267
$603$	−17.3915	−0.708237
$604$	−37.5864	−1.52937
$605$	3.17183	0.128953
$606$	−2.34603	−0.0953010
$607$	−46.7431	−1.89724	−0.948621	−	0.316414i	$-0.897521\pi$
$607$	−46.7431	−1.89724	−0.948621	+	0.316414i	$0.897521\pi$
$608$	−2.24605	−0.0910893
$609$	−61.5200	−2.49292
$610$	3.73121	0.151072
$611$	−35.1757	−1.42306
$612$	−72.9983	−2.95078
$613$	39.7838	1.60685	0.803426	−	0.595404i	$-0.203008\pi$
$613$	39.7838	1.60685	0.803426	+	0.595404i	$0.203008\pi$
$614$	−1.68327	−0.0679312
$615$	−42.5636	−1.71633
$616$	2.23426	0.0900208
$617$	17.1482	0.690362	0.345181	−	0.938536i	$-0.387818\pi$
$617$	17.1482	0.690362	0.345181	+	0.938536i	$0.387818\pi$
$618$	−6.40905	−0.257810
$619$	−26.5985	−1.06909	−0.534543	−	0.845142i	$-0.679516\pi$
$619$	−26.5985	−1.06909	−0.534543	+	0.845142i	$0.679516\pi$
$620$	−45.5139	−1.82788
$621$	33.5841	1.34768
$622$	1.35879	0.0544827
$623$	51.9378	2.08084
$624$	−45.0919	−1.80512
$625$	−24.6939	−0.987756
$626$	1.20286	0.0480761
$627$	−3.10752	−0.124102
$628$	42.7581	1.70623
$629$	28.7188	1.14509
$630$	11.1028	0.442347
$631$	17.1655	0.683347	0.341674	−	0.939819i	$-0.389006\pi$
$631$	17.1655	0.683347	0.341674	+	0.939819i	$0.389006\pi$
$632$	−8.94252	−0.355714
$633$	19.4424	0.772767
$634$	4.42752	0.175839
$635$	−9.21880	−0.365837
$636$	57.1332	2.26548
$637$	−8.09115	−0.320583
$638$	1.26003	0.0498852
$639$	25.5034	1.00890
$640$	18.1736	0.718373
$641$	35.1364	1.38781	0.693903	−	0.720069i	$-0.255890\pi$
$641$	35.1364	1.38781	0.693903	+	0.720069i	$0.255890\pi$
$642$	8.56938	0.338207
$643$	33.8622	1.33539	0.667697	−	0.744433i	$-0.267280\pi$
$643$	33.8622	1.33539	0.667697	+	0.744433i	$0.267280\pi$
$644$	20.3805	0.803105
$645$	56.7001	2.23256
$646$	−1.14599	−0.0450884
$647$	−29.3747	−1.15484	−0.577419	−	0.816448i	$-0.695940\pi$
$647$	−29.3747	−1.15484	−0.577419	+	0.816448i	$0.695940\pi$
$648$	8.12798	0.319297
$649$	6.67741	0.262111
$650$	3.71170	0.145585
$651$	−66.7315	−2.61541
$652$	−16.9754	−0.664807
$653$	−27.2906	−1.06796	−0.533982	−	0.845496i	$-0.679305\pi$
$653$	−27.2906	−1.06796	−0.533982	+	0.845496i	$0.679305\pi$
$654$	0.518963	0.0202931
$655$	3.17183	0.123934
$656$	−16.7615	−0.654425
$657$	17.7106	0.690957
$658$	5.05793	0.197179
$659$	42.4630	1.65412	0.827061	−	0.562112i	$-0.190011\pi$
$659$	42.4630	1.65412	0.827061	+	0.562112i	$0.190011\pi$
$660$	18.9166	0.736326
$661$	14.2222	0.553180	0.276590	−	0.960988i	$-0.410796\pi$
$661$	14.2222	0.553180	0.276590	+	0.960988i	$0.410796\pi$
$662$	0.453424	0.0176228
$663$	−71.1322	−2.76254
$664$	−6.16506	−0.239251
$665$	−9.77737	−0.379150
$666$	−5.58325	−0.216347
$667$	23.1925	0.898017
$668$	0.132218	0.00511566
$669$	82.7279	3.19845
$670$	1.66201	0.0642091
$671$	6.28525	0.242639
$672$	20.0463	0.773303
$673$	40.7582	1.57111	0.785556	−	0.618790i	$-0.212377\pi$
$673$	40.7582	1.57111	0.785556	+	0.618790i	$0.212377\pi$
$674$	2.05968	0.0793358
$675$	49.3336	1.89885
$676$	−4.63278	−0.178184
$677$	26.5768	1.02143	0.510714	−	0.859751i	$-0.329381\pi$
$677$	26.5768	1.02143	0.510714	+	0.859751i	$0.329381\pi$
$678$	6.91625	0.265617
$679$	−0.584612	−0.0224353
$680$	14.0765	0.539808
$681$	−55.6902	−2.13405
$682$	1.36677	0.0523364
$683$	−1.65949	−0.0634987	−0.0317494	−	0.999496i	$-0.510108\pi$
$683$	−1.65949	−0.0634987	−0.0317494	+	0.999496i	$0.510108\pi$
$684$	−12.4975	−0.477854
$685$	−23.6074	−0.901991
$686$	−2.78106	−0.106181
$687$	29.2226	1.11491
$688$	22.3284	0.851261
$689$	37.5421	1.43024
$690$	−6.20708	−0.236299
$691$	42.5763	1.61968	0.809839	−	0.586652i	$-0.199554\pi$
$691$	42.5763	1.61968	0.809839	+	0.586652i	$0.199554\pi$
$692$	19.1454	0.727798
$693$	18.7028	0.710460
$694$	−1.46829	−0.0557357
$695$	−29.3849	−1.11463
$696$	15.1635	0.574770
$697$	−26.4411	−1.00153
$698$	−2.11584	−0.0800856
$699$	−70.7651	−2.67658
$700$	29.9381	1.13155
$701$	−3.97408	−0.150099	−0.0750495	−	0.997180i	$-0.523911\pi$
$701$	−3.97408	−0.150099	−0.0750495	+	0.997180i	$0.523911\pi$
$702$	7.15041	0.269875
$703$	4.91673	0.185438
$704$	7.17152	0.270287
$705$	86.4103	3.25440
$706$	−0.922867	−0.0347326
$707$	−12.4341	−0.467633
$708$	39.8236	1.49666
$709$	12.9411	0.486015	0.243007	−	0.970024i	$-0.421866\pi$
$709$	12.9411	0.486015	0.243007	+	0.970024i	$0.421866\pi$
$710$	−2.43722	−0.0914674
$711$	−74.8570	−2.80736
$712$	−12.8016	−0.479762
$713$	25.1572	0.942143
$714$	10.2281	0.382778
$715$	12.4300	0.464857
$716$	−48.5519	−1.81447
$717$	70.9159	2.64840
$718$	3.22750	0.120449
$719$	8.10475	0.302256	0.151128	−	0.988514i	$-0.451709\pi$
$719$	8.10475	0.302256	0.151128	+	0.988514i	$0.451709\pi$
$720$	74.6963	2.78377
$721$	−33.9684	−1.26505
$722$	3.35988	0.125042
$723$	−43.2628	−1.60896
$724$	29.6979	1.10371
$725$	34.0688	1.26528
$726$	−0.568060	−0.0210827
$727$	−27.1626	−1.00741	−0.503703	−	0.863877i	$-0.668029\pi$
$727$	−27.1626	−1.00741	−0.503703	+	0.863877i	$0.668029\pi$
$728$	8.75581	0.324512
$729$	−20.7276	−0.767690
$730$	−1.69251	−0.0626425
$731$	35.2228	1.30276
$732$	37.4848	1.38548
$733$	−23.7691	−0.877933	−0.438966	−	0.898503i	$-0.644655\pi$
$733$	−23.7691	−0.877933	−0.438966	+	0.898503i	$0.644655\pi$
$734$	−3.88929	−0.143556
$735$	19.8762	0.733145
$736$	−7.55728	−0.278565
$737$	2.79967	0.103127
$738$	5.14044	0.189222
$739$	−22.8501	−0.840556	−0.420278	−	0.907395i	$-0.638067\pi$
$739$	−22.8501	−0.840556	−0.420278	+	0.907395i	$0.638067\pi$
$740$	−29.9299	−1.10024
$741$	−12.1780	−0.447371
$742$	−5.39820	−0.198174
$743$	−10.5119	−0.385645	−0.192823	−	0.981234i	$-0.561764\pi$
$743$	−10.5119	−0.385645	−0.192823	+	0.981234i	$0.561764\pi$
$744$	16.4480	0.603012
$745$	−46.0891	−1.68858
$746$	6.98152	0.255612
$747$	−51.6072	−1.88821
$748$	11.7512	0.429667
$749$	45.4183	1.65955
$750$	−0.108986	−0.00397962
$751$	19.2455	0.702278	0.351139	−	0.936323i	$-0.385794\pi$
$751$	19.2455	0.702278	0.351139	+	0.936323i	$0.385794\pi$
$752$	34.0282	1.24088
$753$	−72.2132	−2.63160
$754$	4.93793	0.179829
$755$	60.6714	2.20806
$756$	57.6742	2.09759
$757$	−29.7340	−1.08070	−0.540350	−	0.841440i	$-0.681708\pi$
$757$	−29.7340	−1.08070	−0.540350	+	0.841440i	$0.681708\pi$
$758$	−0.176168	−0.00639871
$759$	−10.4559	−0.379524
$760$	2.40993	0.0874173
$761$	32.1043	1.16378	0.581889	−	0.813268i	$-0.302314\pi$
$761$	32.1043	1.16378	0.581889	+	0.813268i	$0.302314\pi$
$762$	1.65105	0.0598111
$763$	2.75054	0.0995762
$764$	−43.5392	−1.57519
$765$	117.833	4.26026
$766$	2.67582	0.0966815
$767$	26.1680	0.944873
$768$	40.2781	1.45341
$769$	35.9873	1.29773	0.648867	−	0.760902i	$-0.275243\pi$
$769$	35.9873	1.29773	0.648867	+	0.760902i	$0.275243\pi$
$770$	−1.78732	−0.0644106
$771$	33.1671	1.19448
$772$	−17.0089	−0.612162
$773$	3.11976	0.112210	0.0561050	−	0.998425i	$-0.482132\pi$
$773$	3.11976	0.112210	0.0561050	+	0.998425i	$0.482132\pi$
$774$	−6.84771	−0.246136
$775$	36.9548	1.32746
$776$	0.144095	0.00517272
$777$	−43.8825	−1.57428
$778$	−2.44790	−0.0877614
$779$	−4.52678	−0.162189
$780$	74.1319	2.65435
$781$	−4.10552	−0.146907
$782$	−3.85592	−0.137887
$783$	65.6318	2.34549
$784$	7.82721	0.279543
$785$	−69.0195	−2.46341
$786$	−0.568060	−0.0202620
$787$	25.1859	0.897782	0.448891	−	0.893587i	$-0.351819\pi$
$787$	25.1859	0.897782	0.448891	+	0.893587i	$0.351819\pi$
$788$	−46.2968	−1.64926
$789$	36.0513	1.28346
$790$	7.15368	0.254516
$791$	36.6566	1.30336
$792$	−4.60986	−0.163804
$793$	24.6312	0.874679
$794$	5.58999	0.198381
$795$	−92.2236	−3.27083
$796$	−3.13484	−0.111112
$797$	41.6145	1.47406	0.737031	−	0.675859i	$-0.236227\pi$
$797$	41.6145	1.47406	0.737031	+	0.675859i	$0.236227\pi$
$798$	1.75108	0.0619877
$799$	53.6792	1.89903
$800$	−11.1013	−0.392491
$801$	−107.161	−3.78636
$802$	−5.87836	−0.207572
$803$	−2.85104	−0.100611
$804$	16.6970	0.588859
$805$	−32.8979	−1.15950
$806$	5.35623	0.188665
$807$	−18.6010	−0.654784
$808$	3.06476	0.107818
$809$	−28.8611	−1.01470	−0.507351	−	0.861740i	$-0.669375\pi$
$809$	−28.8611	−1.01470	−0.507351	+	0.861740i	$0.669375\pi$
$810$	−6.50208	−0.228460
$811$	−17.2041	−0.604118	−0.302059	−	0.953289i	$-0.597674\pi$
$811$	−17.2041	−0.604118	−0.302059	+	0.953289i	$0.597674\pi$
$812$	39.8287	1.39771
$813$	45.8953	1.60962
$814$	0.898787	0.0315025
$815$	27.4014	0.959830
$816$	68.8118	2.40889
$817$	6.03024	0.210971
$818$	2.09480	0.0732431
$819$	73.2941	2.56110
$820$	27.5561	0.962301
$821$	−19.1585	−0.668637	−0.334318	−	0.942460i	$-0.608506\pi$
$821$	−19.1585	−0.668637	−0.334318	+	0.942460i	$0.608506\pi$
$822$	4.22797	0.147467
$823$	−18.9824	−0.661685	−0.330843	−	0.943686i	$-0.607333\pi$
$823$	−18.9824	−0.661685	−0.330843	+	0.943686i	$0.607333\pi$
$824$	8.37253	0.291671
$825$	−15.3592	−0.534739
$826$	−3.76272	−0.130922
$827$	−36.4096	−1.26609	−0.633043	−	0.774117i	$-0.718194\pi$
$827$	−36.4096	−1.26609	−0.633043	+	0.774117i	$0.718194\pi$
$828$	−42.0504	−1.46135
$829$	−7.60906	−0.264274	−0.132137	−	0.991231i	$-0.542184\pi$
$829$	−7.60906	−0.264274	−0.132137	+	0.991231i	$0.542184\pi$
$830$	4.93182	0.171186
$831$	−5.30701	−0.184098
$832$	28.1044	0.974344
$833$	12.3474	0.427811
$834$	5.26270	0.182232
$835$	−0.213424	−0.00738585
$836$	2.01184	0.0695809
$837$	71.1916	2.46074
$838$	5.88914	0.203437
$839$	−5.18259	−0.178923	−0.0894615	−	0.995990i	$-0.528515\pi$
$839$	−5.18259	−0.178923	−0.0894615	+	0.995990i	$0.528515\pi$
$840$	−21.5090	−0.742130
$841$	16.3240	0.562898
$842$	5.37570	0.185259
$843$	79.1264	2.72526
$844$	−12.5872	−0.433270
$845$	7.47817	0.257257
$846$	−10.4358	−0.358792
$847$	−3.01076	−0.103451
$848$	−36.3174	−1.24715
$849$	−93.5173	−3.20950
$850$	−5.66417	−0.194280
$851$	16.5433	0.567097
$852$	−24.4850	−0.838843
$853$	19.8194	0.678603	0.339301	−	0.940678i	$-0.389809\pi$
$853$	19.8194	0.678603	0.339301	+	0.940678i	$0.389809\pi$
$854$	−3.54173	−0.121196
$855$	20.1733	0.689912
$856$	−11.1947	−0.382627
$857$	34.5684	1.18083	0.590416	−	0.807099i	$-0.298964\pi$
$857$	34.5684	1.18083	0.590416	+	0.807099i	$0.298964\pi$
$858$	−2.22616	−0.0760000
$859$	12.4209	0.423794	0.211897	−	0.977292i	$-0.432036\pi$
$859$	12.4209	0.423794	0.211897	+	0.977292i	$0.432036\pi$
$860$	−36.7082	−1.25174
$861$	40.4022	1.37690
$862$	−4.18773	−0.142635
$863$	−34.8692	−1.18696	−0.593481	−	0.804848i	$-0.702247\pi$
$863$	−34.8692	−1.18696	−0.593481	+	0.804848i	$0.702247\pi$
$864$	−21.3861	−0.727571
$865$	−30.9042	−1.05077
$866$	−3.75843	−0.127717
$867$	56.9529	1.93422
$868$	43.2026	1.46639
$869$	12.0504	0.408783
$870$	−12.1302	−0.411252
$871$	10.9716	0.371758
$872$	−0.677954	−0.0229584
$873$	1.20621	0.0408240
$874$	−0.660143	−0.0223297
$875$	−0.577635	−0.0195276
$876$	−17.0034	−0.574492
$877$	13.1681	0.444656	0.222328	−	0.974972i	$-0.428634\pi$
$877$	13.1681	0.444656	0.222328	+	0.974972i	$0.428634\pi$
$878$	1.58157	0.0533755
$879$	81.9079	2.76269
$880$	−12.0246	−0.405348
$881$	27.8269	0.937510	0.468755	−	0.883328i	$-0.344703\pi$
$881$	27.8269	0.937510	0.468755	+	0.883328i	$0.344703\pi$
$882$	−2.40047	−0.0808279
$883$	30.7428	1.03458	0.517289	−	0.855811i	$-0.326941\pi$
$883$	30.7428	1.03458	0.517289	+	0.855811i	$0.326941\pi$
$884$	46.0517	1.54889
$885$	−64.2827	−2.16084
$886$	0.904082	0.0303732
$887$	−15.4667	−0.519321	−0.259660	−	0.965700i	$-0.583611\pi$
$887$	−15.4667	−0.519321	−0.259660	+	0.965700i	$0.583611\pi$
$888$	10.8162	0.362967
$889$	8.75065	0.293487
$890$	10.2408	0.343273
$891$	−10.9528	−0.366933
$892$	−53.5589	−1.79328
$893$	9.19003	0.307532
$894$	8.25436	0.276067
$895$	78.3718	2.61968
$896$	−17.2507	−0.576305
$897$	−40.9754	−1.36813
$898$	6.85286	0.228683
$899$	49.1635	1.63969
$900$	−61.7702	−2.05901
$901$	−57.2905	−1.90862
$902$	−0.827504	−0.0275529
$903$	−53.8207	−1.79104
$904$	−9.03513	−0.300504
$905$	−47.9379	−1.59351
$906$	−10.8660	−0.360998
$907$	10.9136	0.362380	0.181190	−	0.983448i	$-0.442005\pi$
$907$	10.9136	0.362380	0.181190	+	0.983448i	$0.442005\pi$
$908$	36.0544	1.19651
$909$	25.6549	0.850919
$910$	−7.00432	−0.232191
$911$	2.88743	0.0956648	0.0478324	−	0.998855i	$-0.484769\pi$
$911$	2.88743	0.0956648	0.0478324	+	0.998855i	$0.484769\pi$
$912$	11.7808	0.390100
$913$	8.30768	0.274944
$914$	−2.54259	−0.0841015
$915$	−60.5074	−2.00031
$916$	−18.9190	−0.625101
$917$	−3.01076	−0.0994239
$918$	−10.9117	−0.360141
$919$	26.7524	0.882479	0.441240	−	0.897389i	$-0.354539\pi$
$919$	26.7524	0.882479	0.441240	+	0.897389i	$0.354539\pi$
$920$	8.10869	0.267335
$921$	27.2969	0.899462
$922$	−2.93061	−0.0965145
$923$	−16.0891	−0.529578
$924$	−17.9559	−0.590707
$925$	24.3014	0.799025
$926$	0.902189	0.0296478
$927$	70.0857	2.30192
$928$	−14.7688	−0.484811
$929$	13.5243	0.443719	0.221860	−	0.975079i	$-0.428787\pi$
$929$	13.5243	0.443719	0.221860	+	0.975079i	$0.428787\pi$
$930$	−13.1578	−0.431460
$931$	2.11390	0.0692803
$932$	45.8140	1.50069
$933$	−22.0350	−0.721393
$934$	7.69362	0.251743
$935$	−18.9686	−0.620341
$936$	−18.0655	−0.590491
$937$	−23.4937	−0.767506	−0.383753	−	0.923436i	$-0.625369\pi$
$937$	−23.4937	−0.767506	−0.383753	+	0.923436i	$0.625369\pi$
$938$	−1.57761	−0.0515109
$939$	−19.5063	−0.636565
$940$	−55.9429	−1.82466
$941$	−16.3110	−0.531722	−0.265861	−	0.964011i	$-0.585656\pi$
$941$	−16.3110	−0.531722	−0.265861	+	0.964011i	$0.585656\pi$
$942$	12.3611	0.402746
$943$	−15.2313	−0.495998
$944$	−25.3144	−0.823914
$945$	−93.0969	−3.02844
$946$	1.10234	0.0358401
$947$	−2.63427	−0.0856024	−0.0428012	−	0.999084i	$-0.513628\pi$
$947$	−2.63427	−0.0856024	−0.0428012	+	0.999084i	$0.513628\pi$
$948$	71.8679	2.33416
$949$	−11.1729	−0.362688
$950$	−0.969722	−0.0314619
$951$	−71.7992	−2.32825
$952$	−13.3616	−0.433053
$953$	−14.3963	−0.466341	−0.233171	−	0.972436i	$-0.574910\pi$
$953$	−14.3963	−0.466341	−0.233171	+	0.972436i	$0.574910\pi$
$954$	11.1379	0.360603
$955$	70.2803	2.27422
$956$	−45.9117	−1.48489
$957$	−20.4334	−0.660518
$958$	1.90015	0.0613912
$959$	22.4085	0.723609
$960$	−69.0394	−2.22824
$961$	22.3282	0.720264
$962$	3.52225	0.113562
$963$	−93.7100	−3.01976
$964$	28.0087	0.902101
$965$	27.4555	0.883822
$966$	5.89187	0.189568
$967$	−5.77981	−0.185866	−0.0929331	−	0.995672i	$-0.529624\pi$
$967$	−5.77981	−0.185866	−0.0929331	+	0.995672i	$0.529624\pi$
$968$	0.742092	0.0238517
$969$	18.5840	0.597006
$970$	−0.115271	−0.00370112
$971$	33.6759	1.08071	0.540356	−	0.841437i	$-0.318290\pi$
$971$	33.6759	1.08071	0.540356	+	0.841437i	$0.318290\pi$
$972$	−7.85359	−0.251904
$973$	27.8926	0.894197
$974$	−6.79820	−0.217828
$975$	−60.1910	−1.92766
$976$	−23.8277	−0.762705
$977$	−30.1471	−0.964493	−0.482246	−	0.876036i	$-0.660179\pi$
$977$	−30.1471	−0.964493	−0.482246	+	0.876036i	$0.660179\pi$
$978$	−4.90747	−0.156924
$979$	17.2507	0.551336
$980$	−12.8681	−0.411055
$981$	−5.67509	−0.181192
$982$	3.07322	0.0980705
$983$	35.8584	1.14370	0.571852	−	0.820357i	$-0.306225\pi$
$983$	35.8584	1.14370	0.571852	+	0.820357i	$0.306225\pi$
$984$	−9.95834	−0.317460
$985$	74.7317	2.38115
$986$	−7.53544	−0.239977
$987$	−82.0223	−2.61080
$988$	7.88417	0.250829
$989$	20.2899	0.645183
$990$	3.68772	0.117203
$991$	−5.02397	−0.159592	−0.0797959	−	0.996811i	$-0.525427\pi$
$991$	−5.02397	−0.159592	−0.0797959	+	0.996811i	$0.525427\pi$
$992$	−16.0199	−0.508633
$993$	−7.35298	−0.233340
$994$	2.31346	0.0733784
$995$	5.06022	0.160420
$996$	49.5464	1.56994
$997$	−27.2799	−0.863963	−0.431981	−	0.901882i	$-0.642185\pi$
$997$	−27.2799	−0.863963	−0.431981	+	0.901882i	$0.642185\pi$
$998$	3.29662	0.104353
$999$	46.8154	1.48118

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.f.1.14	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.f.1.14	✓	31	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-0.187162 q^{2} +3.03513 q^{3} -1.96497 q^{4} +3.17183 q^{5} -0.568060 q^{6} -3.01076 q^{7} +0.742092 q^{8} +6.21199 q^{9} +O(q^{10})\)	\(q-0.187162 q^{2} +3.03513 q^{3} -1.96497 q^{4} +3.17183 q^{5} -0.568060 q^{6} -3.01076 q^{7} +0.742092 q^{8} +6.21199 q^{9} -0.593646 q^{10} -1.00000 q^{11} -5.96393 q^{12} -3.91889 q^{13} +0.563499 q^{14} +9.62689 q^{15} +3.79105 q^{16} +5.98035 q^{17} -1.16265 q^{18} +1.02385 q^{19} -6.23255 q^{20} -9.13802 q^{21} +0.187162 q^{22} +3.44495 q^{23} +2.25234 q^{24} +5.06049 q^{25} +0.733467 q^{26} +9.74878 q^{27} +5.91605 q^{28} +6.73231 q^{29} -1.80179 q^{30} +7.30261 q^{31} -2.19372 q^{32} -3.03513 q^{33} -1.11929 q^{34} -9.54960 q^{35} -12.2064 q^{36} +4.80219 q^{37} -0.191626 q^{38} -11.8943 q^{39} +2.35379 q^{40} -4.42133 q^{41} +1.71029 q^{42} +5.88976 q^{43} +1.96497 q^{44} +19.7033 q^{45} -0.644764 q^{46} +8.97593 q^{47} +11.5063 q^{48} +2.06465 q^{49} -0.947131 q^{50} +18.1511 q^{51} +7.70050 q^{52} -9.57979 q^{53} -1.82460 q^{54} -3.17183 q^{55} -2.23426 q^{56} +3.10752 q^{57} -1.26003 q^{58} -6.67741 q^{59} -18.9166 q^{60} -6.28525 q^{61} -1.36677 q^{62} -18.7028 q^{63} -7.17152 q^{64} -12.4300 q^{65} +0.568060 q^{66} -2.79967 q^{67} -11.7512 q^{68} +10.4559 q^{69} +1.78732 q^{70} +4.10552 q^{71} +4.60986 q^{72} +2.85104 q^{73} -0.898787 q^{74} +15.3592 q^{75} -2.01184 q^{76} +3.01076 q^{77} +2.22616 q^{78} -12.0504 q^{79} +12.0246 q^{80} +10.9528 q^{81} +0.827504 q^{82} -8.30768 q^{83} +17.9559 q^{84} +18.9686 q^{85} -1.10234 q^{86} +20.4334 q^{87} -0.742092 q^{88} -17.2507 q^{89} -3.68772 q^{90} +11.7988 q^{91} -6.76923 q^{92} +22.1643 q^{93} -1.67995 q^{94} +3.24748 q^{95} -6.65823 q^{96} +0.194174 q^{97} -0.386425 q^{98} -6.21199 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

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