LMFDB - Embedded newform 1339.2.a.g.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1339,2,Mod(1,1339)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, 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("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1339.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:	$10.6919688306$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.508360 q^{2} -0.408426 q^{3} -1.74157 q^{4} +4.07667 q^{5} -0.207627 q^{6} +0.983456 q^{7} -1.90207 q^{8} -2.83319 q^{9} +O(q^{10})$	\(q+0.508360 q^{2} -0.408426 q^{3} -1.74157 q^{4} +4.07667 q^{5} -0.207627 q^{6} +0.983456 q^{7} -1.90207 q^{8} -2.83319 q^{9} +2.07242 q^{10} +6.22328 q^{11} +0.711302 q^{12} -1.00000 q^{13} +0.499950 q^{14} -1.66502 q^{15} +2.51621 q^{16} +0.405594 q^{17} -1.44028 q^{18} -5.40714 q^{19} -7.09981 q^{20} -0.401669 q^{21} +3.16367 q^{22} +5.24918 q^{23} +0.776853 q^{24} +11.6193 q^{25} -0.508360 q^{26} +2.38243 q^{27} -1.71276 q^{28} -1.47940 q^{29} -0.846429 q^{30} +7.38408 q^{31} +5.08327 q^{32} -2.54175 q^{33} +0.206188 q^{34} +4.00923 q^{35} +4.93420 q^{36} +1.40780 q^{37} -2.74878 q^{38} +0.408426 q^{39} -7.75410 q^{40} -2.27708 q^{41} -0.204192 q^{42} -8.17027 q^{43} -10.8383 q^{44} -11.5500 q^{45} +2.66848 q^{46} -7.54879 q^{47} -1.02768 q^{48} -6.03282 q^{49} +5.90677 q^{50} -0.165655 q^{51} +1.74157 q^{52} +6.06153 q^{53} +1.21113 q^{54} +25.3703 q^{55} -1.87060 q^{56} +2.20842 q^{57} -0.752066 q^{58} +8.47699 q^{59} +2.89975 q^{60} +12.8281 q^{61} +3.75377 q^{62} -2.78631 q^{63} -2.44828 q^{64} -4.07667 q^{65} -1.29212 q^{66} +14.9040 q^{67} -0.706371 q^{68} -2.14390 q^{69} +2.03813 q^{70} -5.18862 q^{71} +5.38891 q^{72} +2.21664 q^{73} +0.715670 q^{74} -4.74561 q^{75} +9.41692 q^{76} +6.12032 q^{77} +0.207627 q^{78} -7.96875 q^{79} +10.2577 q^{80} +7.52652 q^{81} -1.15757 q^{82} +10.2675 q^{83} +0.699534 q^{84} +1.65348 q^{85} -4.15344 q^{86} +0.604224 q^{87} -11.8371 q^{88} +9.20675 q^{89} -5.87155 q^{90} -0.983456 q^{91} -9.14182 q^{92} -3.01585 q^{93} -3.83750 q^{94} -22.0432 q^{95} -2.07614 q^{96} +9.79621 q^{97} -3.06684 q^{98} -17.6317 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) $ 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9} + 5 q^{10} + q^{11} + 15 q^{12} - 30 q^{13} + 24 q^{14} + 6 q^{15} + 38 q^{16} + 17 q^{17} + 8 q^{18} + 9 q^{19} + 31 q^{20} + 27 q^{21} + 2 q^{22} + 14 q^{23} + 26 q^{24} + 47 q^{25} + 14 q^{27} - 6 q^{28} + 53 q^{29} + 25 q^{30} + 19 q^{31} - 4 q^{32} + q^{33} - 22 q^{34} + 9 q^{35} + 61 q^{36} + 46 q^{38} - 5 q^{39} - 35 q^{40} + 28 q^{41} - 7 q^{42} + 6 q^{43} - 12 q^{44} + 68 q^{45} + 7 q^{46} + 12 q^{47} + 13 q^{48} + 54 q^{49} - 18 q^{50} + 10 q^{51} - 34 q^{52} + 37 q^{53} + 22 q^{54} + 11 q^{55} + 67 q^{56} - 57 q^{57} - 5 q^{58} + 61 q^{59} - 102 q^{60} + 16 q^{61} - 2 q^{62} - 7 q^{63} + 29 q^{64} - 17 q^{65} - 83 q^{66} - 2 q^{67} + 57 q^{68} + 98 q^{69} - 10 q^{70} + 50 q^{71} - 8 q^{72} - 10 q^{73} - 13 q^{74} + 5 q^{75} - 19 q^{76} + 54 q^{77} - 3 q^{78} + 3 q^{79} + 76 q^{80} + 118 q^{81} + 7 q^{82} + 6 q^{83} + 44 q^{84} + 33 q^{85} - 29 q^{86} - 10 q^{87} - 13 q^{88} + 77 q^{89} + 38 q^{90} - 2 q^{91} - 3 q^{92} + 34 q^{93} - 25 q^{94} + 24 q^{95} - 28 q^{96} + 12 q^{97} - 14 q^{98} - 58 q^{99}+O(q^{100}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9 + 5 * q^10 + q^11 + 15 * q^12 - 30 * q^13 + 24 * q^14 + 6 * q^15 + 38 * q^16 + 17 * q^17 + 8 * q^18 + 9 * q^19 + 31 * q^20 + 27 * q^21 + 2 * q^22 + 14 * q^23 + 26 * q^24 + 47 * q^25 + 14 * q^27 - 6 * q^28 + 53 * q^29 + 25 * q^30 + 19 * q^31 - 4 * q^32 + q^33 - 22 * q^34 + 9 * q^35 + 61 * q^36 + 46 * q^38 - 5 * q^39 - 35 * q^40 + 28 * q^41 - 7 * q^42 + 6 * q^43 - 12 * q^44 + 68 * q^45 + 7 * q^46 + 12 * q^47 + 13 * q^48 + 54 * q^49 - 18 * q^50 + 10 * q^51 - 34 * q^52 + 37 * q^53 + 22 * q^54 + 11 * q^55 + 67 * q^56 - 57 * q^57 - 5 * q^58 + 61 * q^59 - 102 * q^60 + 16 * q^61 - 2 * q^62 - 7 * q^63 + 29 * q^64 - 17 * q^65 - 83 * q^66 - 2 * q^67 + 57 * q^68 + 98 * q^69 - 10 * q^70 + 50 * q^71 - 8 * q^72 - 10 * q^73 - 13 * q^74 + 5 * q^75 - 19 * q^76 + 54 * q^77 - 3 * q^78 + 3 * q^79 + 76 * q^80 + 118 * q^81 + 7 * q^82 + 6 * q^83 + 44 * q^84 + 33 * q^85 - 29 * q^86 - 10 * q^87 - 13 * q^88 + 77 * q^89 + 38 * q^90 - 2 * q^91 - 3 * q^92 + 34 * q^93 - 25 * q^94 + 24 * q^95 - 28 * q^96 + 12 * q^97 - 14 * q^98 - 58 * 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 $

$2$	0.508360	0.359465	0.179732	−	0.983716i	$-0.442477\pi$
$2$	0.508360	0.359465	0.179732	+	0.983716i	$0.442477\pi$
$3$	−0.408426	−0.235805	−0.117902	−	0.993025i	$-0.537617\pi$
$3$	−0.408426	−0.235805	−0.117902	+	0.993025i	$0.537617\pi$
$4$	−1.74157	−0.870785
$5$	4.07667	1.82314	0.911572	−	0.411141i	$-0.134870\pi$
$5$	4.07667	1.82314	0.911572	+	0.411141i	$0.134870\pi$
$6$	−0.207627	−0.0847636
$7$	0.983456	0.371711	0.185856	−	0.982577i	$-0.440494\pi$
$7$	0.983456	0.371711	0.185856	+	0.982577i	$0.440494\pi$
$8$	−1.90207	−0.672482
$9$	−2.83319	−0.944396
$10$	2.07242	0.655356
$11$	6.22328	1.87639	0.938195	−	0.346107i	$-0.112497\pi$
$11$	6.22328	1.87639	0.938195	+	0.346107i	$0.112497\pi$
$12$	0.711302	0.205335
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.499950	0.133617
$15$	−1.66502	−0.429906
$16$	2.51621	0.629051
$17$	0.405594	0.0983711	0.0491855	−	0.998790i	$-0.484337\pi$
$17$	0.405594	0.0983711	0.0491855	+	0.998790i	$0.484337\pi$
$18$	−1.44028	−0.339477
$19$	−5.40714	−1.24048	−0.620242	−	0.784411i	$-0.712966\pi$
$19$	−5.40714	−1.24048	−0.620242	+	0.784411i	$0.712966\pi$
$20$	−7.09981	−1.58757
$21$	−0.401669	−0.0876513
$22$	3.16367	0.674496
$23$	5.24918	1.09453	0.547265	−	0.836959i	$-0.315669\pi$
$23$	5.24918	1.09453	0.547265	+	0.836959i	$0.315669\pi$
$24$	0.776853	0.158574
$25$	11.6193	2.32385
$26$	−0.508360	−0.0996976
$27$	2.38243	0.458498
$28$	−1.71276	−0.323681
$29$	−1.47940	−0.274717	−0.137359	−	0.990521i	$-0.543861\pi$
$29$	−1.47940	−0.274717	−0.137359	+	0.990521i	$0.543861\pi$
$30$	−0.846429	−0.154536
$31$	7.38408	1.32622	0.663110	−	0.748522i	$-0.269236\pi$
$31$	7.38408	1.32622	0.663110	+	0.748522i	$0.269236\pi$
$32$	5.08327	0.898603
$33$	−2.54175	−0.442462
$34$	0.206188	0.0353610
$35$	4.00923	0.677683
$36$	4.93420	0.822366
$37$	1.40780	0.231441	0.115720	−	0.993282i	$-0.463082\pi$
$37$	1.40780	0.231441	0.115720	+	0.993282i	$0.463082\pi$
$38$	−2.74878	−0.445910
$39$	0.408426	0.0654005
$40$	−7.75410	−1.22603
$41$	−2.27708	−0.355619	−0.177810	−	0.984065i	$-0.556901\pi$
$41$	−2.27708	−0.355619	−0.177810	+	0.984065i	$0.556901\pi$
$42$	−0.204192	−0.0315076
$43$	−8.17027	−1.24595	−0.622977	−	0.782240i	$-0.714077\pi$
$43$	−8.17027	−1.24595	−0.622977	+	0.782240i	$0.714077\pi$
$44$	−10.8383	−1.63393
$45$	−11.5500	−1.72177
$46$	2.66848	0.393445
$47$	−7.54879	−1.10110	−0.550552	−	0.834801i	$-0.685583\pi$
$47$	−7.54879	−1.10110	−0.550552	+	0.834801i	$0.685583\pi$
$48$	−1.02768	−0.148333
$49$	−6.03282	−0.861831
$50$	5.90677	0.835343
$51$	−0.165655	−0.0231964
$52$	1.74157	0.241512
$53$	6.06153	0.832615	0.416308	−	0.909224i	$-0.363324\pi$
$53$	6.06153	0.832615	0.416308	+	0.909224i	$0.363324\pi$
$54$	1.21113	0.164814
$55$	25.3703	3.42093
$56$	−1.87060	−0.249969
$57$	2.20842	0.292512
$58$	−0.752066	−0.0987512
$59$	8.47699	1.10361	0.551805	−	0.833973i	$-0.313939\pi$
$59$	8.47699	1.10361	0.551805	+	0.833973i	$0.313939\pi$
$60$	2.89975	0.374356
$61$	12.8281	1.64246	0.821232	−	0.570595i	$-0.193287\pi$
$61$	12.8281	1.64246	0.821232	+	0.570595i	$0.193287\pi$
$62$	3.75377	0.476729
$63$	−2.78631	−0.351043
$64$	−2.44828	−0.306035
$65$	−4.07667	−0.505649
$66$	−1.29212	−0.159050
$67$	14.9040	1.82081	0.910405	−	0.413718i	$-0.135770\pi$
$67$	14.9040	1.82081	0.910405	+	0.413718i	$0.135770\pi$
$68$	−0.706371	−0.0856601
$69$	−2.14390	−0.258096
$70$	2.03813	0.243603
$71$	−5.18862	−0.615776	−0.307888	−	0.951423i	$-0.599622\pi$
$71$	−5.18862	−0.615776	−0.307888	+	0.951423i	$0.599622\pi$
$72$	5.38891	0.635089
$73$	2.21664	0.259438	0.129719	−	0.991551i	$-0.458593\pi$
$73$	2.21664	0.259438	0.129719	+	0.991551i	$0.458593\pi$
$74$	0.715670	0.0831949
$75$	−4.74561	−0.547975
$76$	9.41692	1.08019
$77$	6.12032	0.697475
$78$	0.207627	0.0235092
$79$	−7.96875	−0.896554	−0.448277	−	0.893895i	$-0.647962\pi$
$79$	−7.96875	−0.896554	−0.448277	+	0.893895i	$0.647962\pi$
$80$	10.2577	1.14685
$81$	7.52652	0.836280
$82$	−1.15757	−0.127833
$83$	10.2675	1.12701	0.563504	−	0.826113i	$-0.309453\pi$
$83$	10.2675	1.12701	0.563504	+	0.826113i	$0.309453\pi$
$84$	0.699534	0.0763255
$85$	1.65348	0.179345
$86$	−4.15344	−0.447877
$87$	0.604224	0.0647796
$88$	−11.8371	−1.26184
$89$	9.20675	0.975913	0.487957	−	0.872868i	$-0.337742\pi$
$89$	9.20675	0.975913	0.487957	+	0.872868i	$0.337742\pi$
$90$	−5.87155	−0.618916
$91$	−0.983456	−0.103094
$92$	−9.14182	−0.953101
$93$	−3.01585	−0.312729
$94$	−3.83750	−0.395808
$95$	−22.0432	−2.26158
$96$	−2.07614	−0.211895
$97$	9.79621	0.994654	0.497327	−	0.867563i	$-0.334315\pi$
$97$	9.79621	0.994654	0.497327	+	0.867563i	$0.334315\pi$
$98$	−3.06684	−0.309798
$99$	−17.6317	−1.77206
$100$	−20.2357	−2.02357
$101$	−6.35329	−0.632176	−0.316088	−	0.948730i	$-0.602369\pi$
$101$	−6.35329	−0.632176	−0.316088	+	0.948730i	$0.602369\pi$
$102$	−0.0842125	−0.00833828
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.90207	0.186513
$105$	−1.63747	−0.159801
$106$	3.08144	0.299296
$107$	−11.3537	−1.09761	−0.548804	−	0.835951i	$-0.684916\pi$
$107$	−11.3537	−1.09761	−0.548804	+	0.835951i	$0.684916\pi$
$108$	−4.14916	−0.399253
$109$	15.7529	1.50886	0.754428	−	0.656382i	$-0.227914\pi$
$109$	15.7529	1.50886	0.754428	+	0.656382i	$0.227914\pi$
$110$	12.8972	1.22970
$111$	−0.574982	−0.0545749
$112$	2.47458	0.233826
$113$	−3.58582	−0.337326	−0.168663	−	0.985674i	$-0.553945\pi$
$113$	−3.58582	−0.337326	−0.168663	+	0.985674i	$0.553945\pi$
$114$	1.12267	0.105148
$115$	21.3992	1.99549
$116$	2.57647	0.239220
$117$	2.83319	0.261928
$118$	4.30936	0.396709
$119$	0.398884	0.0365656
$120$	3.16697	0.289104
$121$	27.7292	2.52084
$122$	6.52127	0.590408
$123$	0.930017	0.0838568
$124$	−12.8599	−1.15485
$125$	26.9845	2.41357
$126$	−1.41645	−0.126188
$127$	−1.88782	−0.167517	−0.0837583	−	0.996486i	$-0.526692\pi$
$127$	−1.88782	−0.167517	−0.0837583	+	0.996486i	$0.526692\pi$
$128$	−11.4111	−1.00861
$129$	3.33695	0.293802
$130$	−2.07242	−0.181763
$131$	−13.4147	−1.17205	−0.586025	−	0.810293i	$-0.699308\pi$
$131$	−13.4147	−1.17205	−0.586025	+	0.810293i	$0.699308\pi$
$132$	4.42664	0.385289
$133$	−5.31769	−0.461102
$134$	7.57659	0.654517
$135$	9.71237	0.835908
$136$	−0.771467	−0.0661527
$137$	−20.0192	−1.71036	−0.855179	−	0.518334i	$-0.826553\pi$
$137$	−20.0192	−1.71036	−0.855179	+	0.518334i	$0.826553\pi$
$138$	−1.08987	−0.0927763
$139$	−19.0499	−1.61579	−0.807896	−	0.589325i	$-0.799394\pi$
$139$	−19.0499	−1.61579	−0.807896	+	0.589325i	$0.799394\pi$
$140$	−6.98235	−0.590116
$141$	3.08312	0.259646
$142$	−2.63769	−0.221350
$143$	−6.22328	−0.520417
$144$	−7.12888	−0.594074
$145$	−6.03102	−0.500849
$146$	1.12685	0.0932588
$147$	2.46396	0.203224
$148$	−2.45178	−0.201535
$149$	−0.818349	−0.0670418	−0.0335209	−	0.999438i	$-0.510672\pi$
$149$	−0.818349	−0.0670418	−0.0335209	+	0.999438i	$0.510672\pi$
$150$	−2.41248	−0.196978
$151$	−2.69244	−0.219108	−0.109554	−	0.993981i	$-0.534942\pi$
$151$	−2.69244	−0.219108	−0.109554	+	0.993981i	$0.534942\pi$
$152$	10.2847	0.834202
$153$	−1.14913	−0.0929013
$154$	3.11133	0.250718
$155$	30.1025	2.41789
$156$	−0.711302	−0.0569498
$157$	−1.56318	−0.124755	−0.0623775	−	0.998053i	$-0.519868\pi$
$157$	−1.56318	−0.124755	−0.0623775	+	0.998053i	$0.519868\pi$
$158$	−4.05099	−0.322280
$159$	−2.47569	−0.196335
$160$	20.7228	1.63828
$161$	5.16234	0.406849
$162$	3.82618	0.300613
$163$	−1.04853	−0.0821275	−0.0410638	−	0.999157i	$-0.513075\pi$
$163$	−1.04853	−0.0821275	−0.0410638	+	0.999157i	$0.513075\pi$
$164$	3.96569	0.309668
$165$	−10.3619	−0.806671
$166$	5.21960	0.405120
$167$	−7.22541	−0.559119	−0.279559	−	0.960128i	$-0.590188\pi$
$167$	−7.22541	−0.559119	−0.279559	+	0.960128i	$0.590188\pi$
$168$	0.764000	0.0589439
$169$	1.00000	0.0769231
$170$	0.840561	0.0644681
$171$	15.3195	1.17151
$172$	14.2291	1.08496
$173$	−14.9565	−1.13712	−0.568561	−	0.822641i	$-0.692500\pi$
$173$	−14.9565	−1.13712	−0.568561	+	0.822641i	$0.692500\pi$
$174$	0.307164	0.0232860
$175$	11.4270	0.863802
$176$	15.6591	1.18035
$177$	−3.46222	−0.260237
$178$	4.68034	0.350807
$179$	−4.86667	−0.363752	−0.181876	−	0.983321i	$-0.558217\pi$
$179$	−4.86667	−0.363752	−0.181876	+	0.983321i	$0.558217\pi$
$180$	20.1151	1.49929
$181$	−20.8775	−1.55181	−0.775907	−	0.630847i	$-0.782708\pi$
$181$	−20.8775	−1.55181	−0.775907	+	0.630847i	$0.782708\pi$
$182$	−0.499950	−0.0370587
$183$	−5.23931	−0.387301
$184$	−9.98429	−0.736052
$185$	5.73914	0.421950
$186$	−1.53314	−0.112415
$187$	2.52413	0.184583
$188$	13.1467	0.958825
$189$	2.34301	0.170429
$190$	−11.2059	−0.812958
$191$	−14.5724	−1.05442	−0.527211	−	0.849734i	$-0.676762\pi$
$191$	−14.5724	−1.05442	−0.527211	+	0.849734i	$0.676762\pi$
$192$	0.999941	0.0721645
$193$	−14.2734	−1.02742	−0.513711	−	0.857963i	$-0.671730\pi$
$193$	−14.2734	−1.02742	−0.513711	+	0.857963i	$0.671730\pi$
$194$	4.98000	0.357543
$195$	1.66502	0.119234
$196$	10.5066	0.750469
$197$	0.155284	0.0110635	0.00553177	−	0.999985i	$-0.498239\pi$
$197$	0.155284	0.0110635	0.00553177	+	0.999985i	$0.498239\pi$
$198$	−8.96327	−0.636992
$199$	19.0316	1.34912	0.674558	−	0.738222i	$-0.264334\pi$
$199$	19.0316	1.34912	0.674558	+	0.738222i	$0.264334\pi$
$200$	−22.1006	−1.56275
$201$	−6.08717	−0.429356
$202$	−3.22976	−0.227245
$203$	−1.45492	−0.102115
$204$	0.288500	0.0201991
$205$	−9.28289	−0.648345
$206$	0.508360	0.0354191
$207$	−14.8719	−1.03367
$208$	−2.51621	−0.174467
$209$	−33.6502	−2.32763
$210$	−0.832426	−0.0574428
$211$	−13.0396	−0.897684	−0.448842	−	0.893611i	$-0.648163\pi$
$211$	−13.0396	−0.897684	−0.448842	+	0.893611i	$0.648163\pi$
$212$	−10.5566	−0.725029
$213$	2.11917	0.145203
$214$	−5.77179	−0.394551
$215$	−33.3075	−2.27155
$216$	−4.53153	−0.308331
$217$	7.26191	0.492971
$218$	8.00816	0.542381
$219$	−0.905332	−0.0611767
$220$	−44.1841	−2.97889
$221$	−0.405594	−0.0272832
$222$	−0.292298	−0.0196178
$223$	21.6134	1.44734	0.723670	−	0.690146i	$-0.242454\pi$
$223$	21.6134	1.44734	0.723670	+	0.690146i	$0.242454\pi$
$224$	4.99917	0.334021
$225$	−32.9195	−2.19464
$226$	−1.82289	−0.121257
$227$	−2.26047	−0.150033	−0.0750163	−	0.997182i	$-0.523901\pi$
$227$	−2.26047	−0.150033	−0.0750163	+	0.997182i	$0.523901\pi$
$228$	−3.84611	−0.254715
$229$	−13.2648	−0.876564	−0.438282	−	0.898838i	$-0.644413\pi$
$229$	−13.2648	−0.876564	−0.438282	+	0.898838i	$0.644413\pi$
$230$	10.8785	0.717307
$231$	−2.49970	−0.164468
$232$	2.81391	0.184742
$233$	26.5989	1.74255	0.871275	−	0.490796i	$-0.163294\pi$
$233$	26.5989	1.74255	0.871275	+	0.490796i	$0.163294\pi$
$234$	1.44028	0.0941540
$235$	−30.7739	−2.00747
$236$	−14.7633	−0.961007
$237$	3.25464	0.211412
$238$	0.202777	0.0131441
$239$	−2.22654	−0.144023	−0.0720114	−	0.997404i	$-0.522942\pi$
$239$	−2.22654	−0.144023	−0.0720114	+	0.997404i	$0.522942\pi$
$240$	−4.18953	−0.270433
$241$	5.22158	0.336352	0.168176	−	0.985757i	$-0.446212\pi$
$241$	5.22158	0.336352	0.168176	+	0.985757i	$0.446212\pi$
$242$	14.0964	0.906153
$243$	−10.2213	−0.655697
$244$	−22.3410	−1.43023
$245$	−24.5938	−1.57124
$246$	0.472783	0.0301436
$247$	5.40714	0.344048
$248$	−14.0450	−0.891858
$249$	−4.19353	−0.265754
$250$	13.7179	0.867594
$251$	−11.3561	−0.716789	−0.358394	−	0.933570i	$-0.616676\pi$
$251$	−11.3561	−0.716789	−0.358394	+	0.933570i	$0.616676\pi$
$252$	4.85256	0.305683
$253$	32.6672	2.05377
$254$	−0.959691	−0.0602163
$255$	−0.675322	−0.0422903
$256$	−0.904411	−0.0565257
$257$	0.576469	0.0359591	0.0179796	−	0.999838i	$-0.494277\pi$
$257$	0.576469	0.0359591	0.0179796	+	0.999838i	$0.494277\pi$
$258$	1.69637	0.105612
$259$	1.38451	0.0860292
$260$	7.09981	0.440311
$261$	4.19141	0.259442
$262$	−6.81951	−0.421311
$263$	−24.6524	−1.52013	−0.760066	−	0.649846i	$-0.774833\pi$
$263$	−24.6524	−1.52013	−0.760066	+	0.649846i	$0.774833\pi$
$264$	4.83457	0.297547
$265$	24.7109	1.51798
$266$	−2.70330	−0.165750
$267$	−3.76027	−0.230125
$268$	−25.9563	−1.58553
$269$	27.9879	1.70645	0.853225	−	0.521543i	$-0.174643\pi$
$269$	27.9879	1.70645	0.853225	+	0.521543i	$0.174643\pi$
$270$	4.93738	0.300479
$271$	3.85470	0.234157	0.117078	−	0.993123i	$-0.462647\pi$
$271$	3.85470	0.234157	0.117078	+	0.993123i	$0.462647\pi$
$272$	1.02056	0.0618805
$273$	0.401669	0.0243101
$274$	−10.1770	−0.614813
$275$	72.3099	4.36045
$276$	3.73376	0.224746
$277$	−11.9423	−0.717546	−0.358773	−	0.933425i	$-0.616805\pi$
$277$	−11.9423	−0.717546	−0.358773	+	0.933425i	$0.616805\pi$
$278$	−9.68422	−0.580821
$279$	−20.9205	−1.25248
$280$	−7.62581	−0.455729
$281$	14.8773	0.887504	0.443752	−	0.896150i	$-0.353647\pi$
$281$	14.8773	0.887504	0.443752	+	0.896150i	$0.353647\pi$
$282$	1.56734	0.0933335
$283$	−29.6655	−1.76343	−0.881714	−	0.471784i	$-0.843610\pi$
$283$	−29.6655	−1.76343	−0.881714	+	0.471784i	$0.843610\pi$
$284$	9.03635	0.536209
$285$	9.00300	0.533291
$286$	−3.16367	−0.187072
$287$	−2.23940	−0.132188
$288$	−14.4019	−0.848638
$289$	−16.8355	−0.990323
$290$	−3.06593	−0.180038
$291$	−4.00103	−0.234544
$292$	−3.86043	−0.225915
$293$	2.53164	0.147900	0.0739500	−	0.997262i	$-0.476439\pi$
$293$	2.53164	0.147900	0.0739500	+	0.997262i	$0.476439\pi$
$294$	1.25258	0.0730519
$295$	34.5579	2.01204
$296$	−2.67773	−0.155640
$297$	14.8265	0.860321
$298$	−0.416016	−0.0240992
$299$	−5.24918	−0.303568
$300$	8.26480	0.477169
$301$	−8.03510	−0.463135
$302$	−1.36873	−0.0787616
$303$	2.59485	0.149070
$304$	−13.6055	−0.780328
$305$	52.2958	2.99445
$306$	−0.584169	−0.0333947
$307$	−31.1206	−1.77615	−0.888073	−	0.459701i	$-0.847956\pi$
$307$	−31.1206	−1.77615	−0.888073	+	0.459701i	$0.847956\pi$
$308$	−10.6590	−0.607351
$309$	−0.408426	−0.0232345
$310$	15.3029	0.869146
$311$	−28.0506	−1.59060	−0.795302	−	0.606213i	$-0.792688\pi$
$311$	−28.0506	−1.59060	−0.795302	+	0.606213i	$0.792688\pi$
$312$	−0.776853	−0.0439806
$313$	−7.85816	−0.444169	−0.222085	−	0.975027i	$-0.571286\pi$
$313$	−7.85816	−0.444169	−0.222085	+	0.975027i	$0.571286\pi$
$314$	−0.794657	−0.0448451
$315$	−11.3589	−0.640001
$316$	13.8781	0.780706
$317$	−7.82874	−0.439706	−0.219853	−	0.975533i	$-0.570558\pi$
$317$	−7.82874	−0.439706	−0.219853	+	0.975533i	$0.570558\pi$
$318$	−1.25854	−0.0705754
$319$	−9.20670	−0.515476
$320$	−9.98084	−0.557946
$321$	4.63716	0.258821
$322$	2.62433	0.146248
$323$	−2.19311	−0.122028
$324$	−13.1080	−0.728220
$325$	−11.6193	−0.644520
$326$	−0.533033	−0.0295220
$327$	−6.43391	−0.355796
$328$	4.33115	0.239147
$329$	−7.42390	−0.409293
$330$	−5.26757	−0.289970
$331$	21.7913	1.19776	0.598878	−	0.800840i	$-0.295613\pi$
$331$	21.7913	1.19776	0.598878	+	0.800840i	$0.295613\pi$
$332$	−17.8816	−0.981382
$333$	−3.98856	−0.218572
$334$	−3.67311	−0.200984
$335$	60.7586	3.31960
$336$	−1.01068	−0.0551372
$337$	−17.3679	−0.946087	−0.473044	−	0.881039i	$-0.656845\pi$
$337$	−17.3679	−0.946087	−0.473044	+	0.881039i	$0.656845\pi$
$338$	0.508360	0.0276511
$339$	1.46454	0.0795430
$340$	−2.87964	−0.156171
$341$	45.9532	2.48851
$342$	7.78780	0.421116
$343$	−12.8172	−0.692063
$344$	15.5404	0.837882
$345$	−8.73999	−0.470545
$346$	−7.60329	−0.408755
$347$	−8.78018	−0.471345	−0.235672	−	0.971833i	$-0.575729\pi$
$347$	−8.78018	−0.471345	−0.235672	+	0.971833i	$0.575729\pi$
$348$	−1.05230	−0.0564091
$349$	5.98741	0.320499	0.160249	−	0.987077i	$-0.448770\pi$
$349$	5.98741	0.320499	0.160249	+	0.987077i	$0.448770\pi$
$350$	5.80904	0.310506
$351$	−2.38243	−0.127164
$352$	31.6346	1.68613
$353$	16.1240	0.858195	0.429098	−	0.903258i	$-0.358832\pi$
$353$	16.1240	0.858195	0.429098	+	0.903258i	$0.358832\pi$
$354$	−1.76006	−0.0935459
$355$	−21.1523	−1.12265
$356$	−16.0342	−0.849810
$357$	−0.162915	−0.00862236
$358$	−2.47402	−0.130756
$359$	−15.5971	−0.823182	−0.411591	−	0.911369i	$-0.635027\pi$
$359$	−15.5971	−0.823182	−0.411591	+	0.911369i	$0.635027\pi$
$360$	21.9688	1.15786
$361$	10.2372	0.538800
$362$	−10.6133	−0.557823
$363$	−11.3253	−0.594426
$364$	1.71276	0.0897728
$365$	9.03651	0.472992
$366$	−2.66346	−0.139221
$367$	1.37920	0.0719938	0.0359969	−	0.999352i	$-0.488539\pi$
$367$	1.37920	0.0719938	0.0359969	+	0.999352i	$0.488539\pi$
$368$	13.2080	0.688516
$369$	6.45138	0.335846
$370$	2.91755	0.151676
$371$	5.96125	0.309492
$372$	5.25231	0.272320
$373$	−0.825430	−0.0427391	−0.0213696	−	0.999772i	$-0.506803\pi$
$373$	−0.825430	−0.0427391	−0.0213696	+	0.999772i	$0.506803\pi$
$374$	1.28317	0.0663509
$375$	−11.0212	−0.569132
$376$	14.3583	0.740472
$377$	1.47940	0.0761928
$378$	1.19109	0.0612632
$379$	12.8269	0.658872	0.329436	−	0.944178i	$-0.393141\pi$
$379$	12.8269	0.658872	0.329436	+	0.944178i	$0.393141\pi$
$380$	38.3897	1.96935
$381$	0.771033	0.0395012
$382$	−7.40803	−0.379028
$383$	−23.0748	−1.17907	−0.589534	−	0.807743i	$-0.700689\pi$
$383$	−23.0748	−1.17907	−0.589534	+	0.807743i	$0.700689\pi$
$384$	4.66061	0.237836
$385$	24.9505	1.27160
$386$	−7.25603	−0.369322
$387$	23.1479	1.17667
$388$	−17.0608	−0.866130
$389$	−3.44740	−0.174790	−0.0873952	−	0.996174i	$-0.527854\pi$
$389$	−3.44740	−0.174790	−0.0873952	+	0.996174i	$0.527854\pi$
$390$	0.846429	0.0428606
$391$	2.12904	0.107670
$392$	11.4748	0.579565
$393$	5.47892	0.276375
$394$	0.0789403	0.00397695
$395$	−32.4860	−1.63455
$396$	30.7069	1.54308
$397$	1.59462	0.0800317	0.0400159	−	0.999199i	$-0.487259\pi$
$397$	1.59462	0.0800317	0.0400159	+	0.999199i	$0.487259\pi$
$398$	9.67491	0.484960
$399$	2.17188	0.108730
$400$	29.2364	1.46182
$401$	−15.8287	−0.790448	−0.395224	−	0.918585i	$-0.629333\pi$
$401$	−15.8287	−0.790448	−0.395224	+	0.918585i	$0.629333\pi$
$402$	−3.09447	−0.154338
$403$	−7.38408	−0.367827
$404$	11.0647	0.550489
$405$	30.6832	1.52466
$406$	−0.739624	−0.0367069
$407$	8.76114	0.434273
$408$	0.315087	0.0155991
$409$	10.7295	0.530540	0.265270	−	0.964174i	$-0.414539\pi$
$409$	10.7295	0.530540	0.265270	+	0.964174i	$0.414539\pi$
$410$	−4.71905	−0.233057
$411$	8.17637	0.403310
$412$	−1.74157	−0.0858010
$413$	8.33674	0.410224
$414$	−7.56029	−0.371568
$415$	41.8574	2.05470
$416$	−5.08327	−0.249228
$417$	7.78048	0.381012
$418$	−17.1064	−0.836702
$419$	−24.0946	−1.17710	−0.588549	−	0.808462i	$-0.700300\pi$
$419$	−24.0946	−1.17710	−0.588549	+	0.808462i	$0.700300\pi$
$420$	2.85177	0.139152
$421$	−19.4988	−0.950315	−0.475157	−	0.879901i	$-0.657609\pi$
$421$	−19.4988	−0.950315	−0.475157	+	0.879901i	$0.657609\pi$
$422$	−6.62882	−0.322686
$423$	21.3871	1.03988
$424$	−11.5294	−0.559918
$425$	4.71270	0.228600
$426$	1.07730	0.0521954
$427$	12.6158	0.610522
$428$	19.7733	0.955780
$429$	2.54175	0.122717
$430$	−16.9322	−0.816544
$431$	−22.2895	−1.07365	−0.536823	−	0.843695i	$-0.680376\pi$
$431$	−22.2895	−1.07365	−0.536823	+	0.843695i	$0.680376\pi$
$432$	5.99467	0.288419
$433$	30.5354	1.46744	0.733720	−	0.679452i	$-0.237783\pi$
$433$	30.5354	1.46744	0.733720	+	0.679452i	$0.237783\pi$
$434$	3.69167	0.177206
$435$	2.46322	0.118103
$436$	−27.4348	−1.31389
$437$	−28.3831	−1.35775
$438$	−0.460235	−0.0219909
$439$	−11.8630	−0.566188	−0.283094	−	0.959092i	$-0.591361\pi$
$439$	−11.8630	−0.566188	−0.283094	+	0.959092i	$0.591361\pi$
$440$	−48.2559	−2.30051
$441$	17.0921	0.813910
$442$	−0.206188	−0.00980736
$443$	14.9257	0.709142	0.354571	−	0.935029i	$-0.384627\pi$
$443$	14.9257	0.709142	0.354571	+	0.935029i	$0.384627\pi$
$444$	1.00137	0.0475230
$445$	37.5329	1.77923
$446$	10.9874	0.520268
$447$	0.334235	0.0158088
$448$	−2.40777	−0.113757
$449$	22.4532	1.05963	0.529816	−	0.848113i	$-0.322261\pi$
$449$	22.4532	1.05963	0.529816	+	0.848113i	$0.322261\pi$
$450$	−16.7350	−0.788895
$451$	−14.1709	−0.667281
$452$	6.24496	0.293738
$453$	1.09966	0.0516667
$454$	−1.14913	−0.0539315
$455$	−4.00923	−0.187955
$456$	−4.20055	−0.196709
$457$	42.6120	1.99331	0.996653	−	0.0817496i	$-0.0260508\pi$
$457$	42.6120	1.99331	0.996653	+	0.0817496i	$0.0260508\pi$
$458$	−6.74331	−0.315094
$459$	0.966298	0.0451029
$460$	−37.2682	−1.73764
$461$	−10.4297	−0.485759	−0.242880	−	0.970056i	$-0.578092\pi$
$461$	−10.4297	−0.485759	−0.242880	+	0.970056i	$0.578092\pi$
$462$	−1.27075	−0.0591205
$463$	17.8134	0.827861	0.413930	−	0.910309i	$-0.364156\pi$
$463$	17.8134	0.827861	0.413930	+	0.910309i	$0.364156\pi$
$464$	−3.72247	−0.172811
$465$	−12.2946	−0.570150
$466$	13.5218	0.626385
$467$	−14.4354	−0.667993	−0.333996	−	0.942574i	$-0.608397\pi$
$467$	−14.4354	−0.667993	−0.333996	+	0.942574i	$0.608397\pi$
$468$	−4.93420	−0.228083
$469$	14.6574	0.676816
$470$	−15.6442	−0.721615
$471$	0.638442	0.0294178
$472$	−16.1238	−0.742157
$473$	−50.8459	−2.33790
$474$	1.65453	0.0759951
$475$	−62.8270	−2.88270
$476$	−0.694684	−0.0318408
$477$	−17.1735	−0.786319
$478$	−1.13188	−0.0517711
$479$	24.3233	1.11136	0.555680	−	0.831396i	$-0.312458\pi$
$479$	24.3233	1.11136	0.555680	+	0.831396i	$0.312458\pi$
$480$	−8.46374	−0.386315
$481$	−1.40780	−0.0641902
$482$	2.65444	0.120907
$483$	−2.10843	−0.0959371
$484$	−48.2924	−2.19511
$485$	39.9359	1.81340
$486$	−5.19610	−0.235700
$487$	1.13205	0.0512982	0.0256491	−	0.999671i	$-0.491835\pi$
$487$	1.13205	0.0512982	0.0256491	+	0.999671i	$0.491835\pi$
$488$	−24.3998	−1.10453
$489$	0.428248	0.0193661
$490$	−12.5025	−0.564806
$491$	15.3496	0.692718	0.346359	−	0.938102i	$-0.387418\pi$
$491$	15.3496	0.692718	0.346359	+	0.938102i	$0.387418\pi$
$492$	−1.61969	−0.0730212
$493$	−0.600035	−0.0270242
$494$	2.74878	0.123673
$495$	−71.8788	−3.23071
$496$	18.5799	0.834260
$497$	−5.10278	−0.228891
$498$	−2.13182	−0.0955292
$499$	19.4334	0.869959	0.434979	−	0.900440i	$-0.356756\pi$
$499$	19.4334	0.869959	0.434979	+	0.900440i	$0.356756\pi$
$500$	−46.9955	−2.10170
$501$	2.95104	0.131843
$502$	−5.77297	−0.257660
$503$	−15.7524	−0.702363	−0.351182	−	0.936307i	$-0.614220\pi$
$503$	−15.7524	−0.702363	−0.351182	+	0.936307i	$0.614220\pi$
$504$	5.29975	0.236070
$505$	−25.9003	−1.15255
$506$	16.6067	0.738257
$507$	−0.408426	−0.0181388
$508$	3.28776	0.145871
$509$	12.6284	0.559744	0.279872	−	0.960037i	$-0.409708\pi$
$509$	12.6284	0.559744	0.279872	+	0.960037i	$0.409708\pi$
$510$	−0.343307	−0.0152019
$511$	2.17996	0.0964360
$512$	22.3625	0.988293
$513$	−12.8821	−0.568759
$514$	0.293054	0.0129260
$515$	4.07667	0.179640
$516$	−5.81153	−0.255839
$517$	−46.9782	−2.06610
$518$	0.703829	0.0309245
$519$	6.10862	0.268139
$520$	7.75410	0.340040
$521$	35.4699	1.55397	0.776983	−	0.629522i	$-0.216749\pi$
$521$	35.4699	1.55397	0.776983	+	0.629522i	$0.216749\pi$
$522$	2.13075	0.0932602
$523$	−15.2595	−0.667253	−0.333626	−	0.942705i	$-0.608272\pi$
$523$	−15.2595	−0.667253	−0.333626	+	0.942705i	$0.608272\pi$
$524$	23.3627	1.02060
$525$	−4.66709	−0.203689
$526$	−12.5323	−0.546434
$527$	2.99494	0.130462
$528$	−6.39557	−0.278331
$529$	4.55393	0.197997
$530$	12.5620	0.545659
$531$	−24.0169	−1.04224
$532$	9.26112	0.401521
$533$	2.27708	0.0986311
$534$	−1.91157	−0.0827219
$535$	−46.2855	−2.00109
$536$	−28.3483	−1.22446
$537$	1.98767	0.0857745
$538$	14.2279	0.613409
$539$	−37.5439	−1.61713
$540$	−16.9148	−0.727896
$541$	−21.5708	−0.927402	−0.463701	−	0.885992i	$-0.653479\pi$
$541$	−21.5708	−0.927402	−0.463701	+	0.885992i	$0.653479\pi$
$542$	1.95958	0.0841711
$543$	8.52692	0.365925
$544$	2.06175	0.0883966
$545$	64.2195	2.75086
$546$	0.204192	0.00873863
$547$	0.154373	0.00660053	0.00330027	−	0.999995i	$-0.498949\pi$
$547$	0.154373	0.00660053	0.00330027	+	0.999995i	$0.498949\pi$
$548$	34.8649	1.48935
$549$	−36.3443	−1.55114
$550$	36.7595	1.56743
$551$	7.99931	0.340782
$552$	4.07784	0.173565
$553$	−7.83691	−0.333259
$554$	−6.07101	−0.257933
$555$	−2.34401	−0.0994978
$556$	33.1768	1.40701
$557$	−4.67393	−0.198041	−0.0990204	−	0.995085i	$-0.531571\pi$
$557$	−4.67393	−0.198041	−0.0990204	+	0.995085i	$0.531571\pi$
$558$	−10.6351	−0.450221
$559$	8.17027	0.345566
$560$	10.0880	0.426297
$561$	−1.03092	−0.0435255
$562$	7.56302	0.319027
$563$	6.06180	0.255475	0.127737	−	0.991808i	$-0.459229\pi$
$563$	6.06180	0.255475	0.127737	+	0.991808i	$0.459229\pi$
$564$	−5.36947	−0.226096
$565$	−14.6182	−0.614993
$566$	−15.0807	−0.633891
$567$	7.40200	0.310855
$568$	9.86910	0.414098
$569$	6.84878	0.287116	0.143558	−	0.989642i	$-0.454146\pi$
$569$	6.84878	0.287116	0.143558	+	0.989642i	$0.454146\pi$
$570$	4.57676	0.191700
$571$	16.7375	0.700443	0.350222	−	0.936667i	$-0.386106\pi$
$571$	16.7375	0.700443	0.350222	+	0.936667i	$0.386106\pi$
$572$	10.8383	0.453171
$573$	5.95175	0.248638
$574$	−1.13842	−0.0475169
$575$	60.9916	2.54353
$576$	6.93644	0.289018
$577$	−15.5044	−0.645457	−0.322728	−	0.946492i	$-0.604600\pi$
$577$	−15.5044	−0.645457	−0.322728	+	0.946492i	$0.604600\pi$
$578$	−8.55849	−0.355986
$579$	5.82963	0.242271
$580$	10.5034	0.436131
$581$	10.0977	0.418922
$582$	−2.03396	−0.0843105
$583$	37.7226	1.56231
$584$	−4.21619	−0.174467
$585$	11.5500	0.477533
$586$	1.28698	0.0531648
$587$	−22.6073	−0.933105	−0.466552	−	0.884494i	$-0.654504\pi$
$587$	−22.6073	−0.933105	−0.466552	+	0.884494i	$0.654504\pi$
$588$	−4.29116	−0.176964
$589$	−39.9268	−1.64515
$590$	17.5679	0.723257
$591$	−0.0634221	−0.00260884
$592$	3.54232	0.145588
$593$	45.8877	1.88438	0.942191	−	0.335075i	$-0.108762\pi$
$593$	45.8877	1.88438	0.942191	+	0.335075i	$0.108762\pi$
$594$	7.53720	0.309255
$595$	1.62612	0.0666644
$596$	1.42521	0.0583790
$597$	−7.77301	−0.318128
$598$	−2.66848	−0.109122
$599$	17.2550	0.705021	0.352510	−	0.935808i	$-0.385328\pi$
$599$	17.2550	0.705021	0.352510	+	0.935808i	$0.385328\pi$
$600$	9.02645	0.368503
$601$	−20.6780	−0.843474	−0.421737	−	0.906718i	$-0.638580\pi$
$601$	−20.6780	−0.843474	−0.421737	+	0.906718i	$0.638580\pi$
$602$	−4.08472	−0.166481
$603$	−42.2258	−1.71957
$604$	4.68908	0.190796
$605$	113.043	4.59585
$606$	1.31912	0.0535855
$607$	−10.6974	−0.434194	−0.217097	−	0.976150i	$-0.569659\pi$
$607$	−10.6974	−0.434194	−0.217097	+	0.976150i	$0.569659\pi$
$608$	−27.4860	−1.11470
$609$	0.594228	0.0240793
$610$	26.5851	1.07640
$611$	7.54879	0.305391
$612$	2.00128	0.0808970
$613$	38.0508	1.53686	0.768429	−	0.639935i	$-0.221039\pi$
$613$	38.0508	1.53686	0.768429	+	0.639935i	$0.221039\pi$
$614$	−15.8205	−0.638463
$615$	3.79137	0.152883
$616$	−11.6412	−0.469039
$617$	11.8551	0.477267	0.238634	−	0.971110i	$-0.423300\pi$
$617$	11.8551	0.477267	0.238634	+	0.971110i	$0.423300\pi$
$618$	−0.207627	−0.00835200
$619$	−19.5172	−0.784464	−0.392232	−	0.919866i	$-0.628297\pi$
$619$	−19.5172	−0.784464	−0.392232	+	0.919866i	$0.628297\pi$
$620$	−52.4255	−2.10546
$621$	12.5058	0.501840
$622$	−14.2598	−0.571766
$623$	9.05443	0.362758
$624$	1.02768	0.0411403
$625$	51.9108	2.07643
$626$	−3.99478	−0.159663
$627$	13.7436	0.548867
$628$	2.72238	0.108635
$629$	0.570996	0.0227671
$630$	−5.77441	−0.230058
$631$	−26.5386	−1.05649	−0.528243	−	0.849093i	$-0.677149\pi$
$631$	−26.5386	−1.05649	−0.528243	+	0.849093i	$0.677149\pi$
$632$	15.1571	0.602916
$633$	5.32572	0.211678
$634$	−3.97982	−0.158059
$635$	−7.69601	−0.305407
$636$	4.31158	0.170965
$637$	6.03282	0.239029
$638$	−4.68032	−0.185296
$639$	14.7003	0.581537
$640$	−46.5195	−1.83884
$641$	12.8216	0.506424	0.253212	−	0.967411i	$-0.418513\pi$
$641$	12.8216	0.506424	0.253212	+	0.967411i	$0.418513\pi$
$642$	2.35735	0.0930371
$643$	48.4857	1.91209	0.956044	−	0.293223i	$-0.0947278\pi$
$643$	48.4857	1.91209	0.956044	+	0.293223i	$0.0947278\pi$
$644$	−8.99058	−0.354278
$645$	13.6037	0.535643
$646$	−1.11489	−0.0438647
$647$	24.4414	0.960892	0.480446	−	0.877024i	$-0.340475\pi$
$647$	24.4414	0.960892	0.480446	+	0.877024i	$0.340475\pi$
$648$	−14.3159	−0.562383
$649$	52.7547	2.07080
$650$	−5.90677	−0.231682
$651$	−2.96595	−0.116245
$652$	1.82610	0.0715154
$653$	12.9766	0.507814	0.253907	−	0.967229i	$-0.418284\pi$
$653$	12.9766	0.507814	0.253907	+	0.967229i	$0.418284\pi$
$654$	−3.27074	−0.127896
$655$	−54.6875	−2.13682
$656$	−5.72959	−0.223703
$657$	−6.28015	−0.245012
$658$	−3.77401	−0.147126
$659$	−6.89549	−0.268610	−0.134305	−	0.990940i	$-0.542880\pi$
$659$	−6.89549	−0.268610	−0.134305	+	0.990940i	$0.542880\pi$
$660$	18.0459	0.702437
$661$	−15.8822	−0.617745	−0.308873	−	0.951103i	$-0.599952\pi$
$661$	−15.8822	−0.617745	−0.308873	+	0.951103i	$0.599952\pi$
$662$	11.0778	0.430552
$663$	0.165655	0.00643352
$664$	−19.5295	−0.757892
$665$	−21.6785	−0.840655
$666$	−2.02763	−0.0785689
$667$	−7.76563	−0.300686
$668$	12.5835	0.486872
$669$	−8.82748	−0.341290
$670$	30.8873	1.19328
$671$	79.8326	3.08190
$672$	−2.04179	−0.0787638
$673$	−40.9827	−1.57977	−0.789884	−	0.613256i	$-0.789859\pi$
$673$	−40.9827	−1.57977	−0.789884	+	0.613256i	$0.789859\pi$
$674$	−8.82912	−0.340085
$675$	27.6820	1.06548
$676$	−1.74157	−0.0669835
$677$	2.82867	0.108715	0.0543573	−	0.998522i	$-0.482689\pi$
$677$	2.82867	0.108715	0.0543573	+	0.998522i	$0.482689\pi$
$678$	0.744515	0.0285929
$679$	9.63414	0.369724
$680$	−3.14502	−0.120606
$681$	0.923235	0.0353784
$682$	23.3608	0.894530
$683$	15.5454	0.594829	0.297414	−	0.954748i	$-0.403876\pi$
$683$	15.5454	0.594829	0.297414	+	0.954748i	$0.403876\pi$
$684$	−26.6799	−1.02013
$685$	−81.6118	−3.11823
$686$	−6.51575	−0.248773
$687$	5.41770	0.206698
$688$	−20.5581	−0.783770
$689$	−6.06153	−0.230926
$690$	−4.44306	−0.169145
$691$	32.0769	1.22026	0.610132	−	0.792300i	$-0.291116\pi$
$691$	32.0769	1.22026	0.610132	+	0.792300i	$0.291116\pi$
$692$	26.0478	0.990188
$693$	−17.3400	−0.658693
$694$	−4.46349	−0.169432
$695$	−77.6602	−2.94582
$696$	−1.14927	−0.0435631
$697$	−0.923569	−0.0349827
$698$	3.04376	0.115208
$699$	−10.8637	−0.410902
$700$	−19.9010	−0.752185
$701$	−25.0378	−0.945665	−0.472832	−	0.881152i	$-0.656768\pi$
$701$	−25.0378	−0.945665	−0.472832	+	0.881152i	$0.656768\pi$
$702$	−1.21113	−0.0457112
$703$	−7.61218	−0.287099
$704$	−15.2363	−0.574241
$705$	12.5689	0.473371
$706$	8.19681	0.308491
$707$	−6.24818	−0.234987
$708$	6.02970	0.226610
$709$	22.2455	0.835448	0.417724	−	0.908574i	$-0.362828\pi$
$709$	22.2455	0.835448	0.417724	+	0.908574i	$0.362828\pi$
$710$	−10.7530	−0.403553
$711$	22.5770	0.846702
$712$	−17.5118	−0.656284
$713$	38.7604	1.45159
$714$	−0.0828193	−0.00309943
$715$	−25.3703	−0.948795
$716$	8.47564	0.316750
$717$	0.909376	0.0339613
$718$	−7.92893	−0.295905
$719$	25.7092	0.958791	0.479395	−	0.877599i	$-0.340856\pi$
$719$	25.7092	0.958791	0.479395	+	0.877599i	$0.340856\pi$
$720$	−29.0621	−1.08308
$721$	0.983456	0.0366258
$722$	5.20418	0.193680
$723$	−2.13263	−0.0793134
$724$	36.3597	1.35130
$725$	−17.1895	−0.638402
$726$	−5.75735	−0.213675
$727$	−4.27041	−0.158381	−0.0791903	−	0.996860i	$-0.525233\pi$
$727$	−4.27041	−0.158381	−0.0791903	+	0.996860i	$0.525233\pi$
$728$	1.87060	0.0693289
$729$	−18.4049	−0.681663
$730$	4.59380	0.170024
$731$	−3.31382	−0.122566
$732$	9.12463	0.337256
$733$	35.8012	1.32235	0.661174	−	0.750232i	$-0.270058\pi$
$733$	35.8012	1.32235	0.661174	+	0.750232i	$0.270058\pi$
$734$	0.701131	0.0258792
$735$	10.0448	0.370506
$736$	26.6830	0.983549
$737$	92.7516	3.41655
$738$	3.27963	0.120725
$739$	−20.4348	−0.751707	−0.375853	−	0.926679i	$-0.622650\pi$
$739$	−20.4348	−0.751707	−0.375853	+	0.926679i	$0.622650\pi$
$740$	−9.99511	−0.367428
$741$	−2.20842	−0.0811283
$742$	3.03046	0.111252
$743$	14.1832	0.520332	0.260166	−	0.965564i	$-0.416223\pi$
$743$	14.1832	0.520332	0.260166	+	0.965564i	$0.416223\pi$
$744$	5.73634	0.210304
$745$	−3.33614	−0.122227
$746$	−0.419616	−0.0153632
$747$	−29.0898	−1.06434
$748$	−4.39595	−0.160732
$749$	−11.1659	−0.407993
$750$	−5.60273	−0.204583
$751$	−46.7133	−1.70459	−0.852296	−	0.523059i	$-0.824791\pi$
$751$	−46.7133	−1.70459	−0.852296	+	0.523059i	$0.824791\pi$
$752$	−18.9943	−0.692651
$753$	4.63811	0.169022
$754$	0.752066	0.0273886
$755$	−10.9762	−0.399465
$756$	−4.08052	−0.148407
$757$	−26.9817	−0.980668	−0.490334	−	0.871535i	$-0.663125\pi$
$757$	−26.9817	−0.980668	−0.490334	+	0.871535i	$0.663125\pi$
$758$	6.52066	0.236841
$759$	−13.3421	−0.484288
$760$	41.9275	1.52087
$761$	−21.3385	−0.773519	−0.386760	−	0.922181i	$-0.626406\pi$
$761$	−21.3385	−0.773519	−0.386760	+	0.922181i	$0.626406\pi$
$762$	0.391963	0.0141993
$763$	15.4923	0.560859
$764$	25.3789	0.918175
$765$	−4.68461	−0.169372
$766$	−11.7303	−0.423834
$767$	−8.47699	−0.306086
$768$	0.369385	0.0133290
$769$	36.7598	1.32559	0.662796	−	0.748800i	$-0.269370\pi$
$769$	36.7598	1.32559	0.662796	+	0.748800i	$0.269370\pi$
$770$	12.6839	0.457095
$771$	−0.235445	−0.00847934
$772$	24.8581	0.894664
$773$	18.9981	0.683316	0.341658	−	0.939824i	$-0.389012\pi$
$773$	18.9981	0.683316	0.341658	+	0.939824i	$0.389012\pi$
$774$	11.7675	0.422973
$775$	85.7975	3.08194
$776$	−18.6330	−0.668887
$777$	−0.565469	−0.0202861
$778$	−1.75252	−0.0628310
$779$	12.3125	0.441140
$780$	−2.89975	−0.103828
$781$	−32.2903	−1.15544
$782$	1.08232	0.0387036
$783$	−3.52455	−0.125957
$784$	−15.1798	−0.542136
$785$	−6.37256	−0.227446
$786$	2.78527	0.0993472
$787$	−0.995691	−0.0354925	−0.0177463	−	0.999843i	$-0.505649\pi$
$787$	−0.995691	−0.0354925	−0.0177463	+	0.999843i	$0.505649\pi$
$788$	−0.270438	−0.00963396
$789$	10.0687	0.358454
$790$	−16.5146	−0.587562
$791$	−3.52650	−0.125388
$792$	33.5367	1.19167
$793$	−12.8281	−0.455538
$794$	0.810642	0.0287686
$795$	−10.0926	−0.357946
$796$	−33.1449	−1.17479
$797$	−2.63432	−0.0933123	−0.0466562	−	0.998911i	$-0.514857\pi$
$797$	−2.63432	−0.0933123	−0.0466562	+	0.998911i	$0.514857\pi$
$798$	1.10410	0.0390846
$799$	−3.06175	−0.108317
$800$	59.0638	2.08822
$801$	−26.0844	−0.921648
$802$	−8.04669	−0.284138
$803$	13.7948	0.486807
$804$	10.6012	0.373877
$805$	21.0452	0.741745
$806$	−3.75377	−0.132221
$807$	−11.4310	−0.402389
$808$	12.0844	0.425127
$809$	26.5410	0.933131	0.466566	−	0.884487i	$-0.345491\pi$
$809$	26.5410	0.933131	0.466566	+	0.884487i	$0.345491\pi$
$810$	15.5981	0.548061
$811$	−19.9944	−0.702098	−0.351049	−	0.936357i	$-0.614175\pi$
$811$	−19.9944	−0.702098	−0.351049	+	0.936357i	$0.614175\pi$
$812$	2.53385	0.0889206
$813$	−1.57436	−0.0552153
$814$	4.45381	0.156106
$815$	−4.27453	−0.149730
$816$	−0.416823	−0.0145917
$817$	44.1778	1.54559
$818$	5.45445	0.190710
$819$	2.78631	0.0973617
$820$	16.1668	0.564569
$821$	15.8369	0.552711	0.276355	−	0.961056i	$-0.410873\pi$
$821$	15.8369	0.552711	0.276355	+	0.961056i	$0.410873\pi$
$822$	4.15654	0.144976
$823$	−52.2815	−1.82242	−0.911210	−	0.411943i	$-0.864850\pi$
$823$	−52.2815	−1.82242	−0.911210	+	0.411943i	$0.864850\pi$
$824$	−1.90207	−0.0662616
$825$	−29.5332	−1.02822
$826$	4.23807	0.147461
$827$	19.8959	0.691847	0.345923	−	0.938263i	$-0.387566\pi$
$827$	19.8959	0.691847	0.345923	+	0.938263i	$0.387566\pi$
$828$	25.9005	0.900105
$829$	−46.7170	−1.62255	−0.811275	−	0.584665i	$-0.801226\pi$
$829$	−46.7170	−1.62255	−0.811275	+	0.584665i	$0.801226\pi$
$830$	21.2786	0.738591
$831$	4.87756	0.169201
$832$	2.44828	0.0848788
$833$	−2.44688	−0.0847792
$834$	3.95529	0.136960
$835$	−29.4556	−1.01935
$836$	58.6041	2.02687
$837$	17.5920	0.608069
$838$	−12.2487	−0.423125
$839$	−32.9589	−1.13787	−0.568934	−	0.822383i	$-0.692644\pi$
$839$	−32.9589	−1.13787	−0.568934	+	0.822383i	$0.692644\pi$
$840$	3.11458	0.107463
$841$	−26.8114	−0.924530
$842$	−9.91243	−0.341605
$843$	−6.07627	−0.209278
$844$	22.7094	0.781690
$845$	4.07667	0.140242
$846$	10.8724	0.373800
$847$	27.2705	0.937024
$848$	15.2521	0.523758
$849$	12.1161	0.415825
$850$	2.39575	0.0821736
$851$	7.38980	0.253319
$852$	−3.69068	−0.126441
$853$	−32.1611	−1.10118	−0.550588	−	0.834777i	$-0.685596\pi$
$853$	−32.1611	−1.10118	−0.550588	+	0.834777i	$0.685596\pi$
$854$	6.41338	0.219461
$855$	62.4524	2.13583
$856$	21.5955	0.738120
$857$	45.6656	1.55991	0.779953	−	0.625838i	$-0.215243\pi$
$857$	45.6656	1.55991	0.779953	+	0.625838i	$0.215243\pi$
$858$	1.29212	0.0441124
$859$	51.2233	1.74772	0.873859	−	0.486180i	$-0.161610\pi$
$859$	51.2233	1.74772	0.873859	+	0.486180i	$0.161610\pi$
$860$	58.0074	1.97803
$861$	0.914630	0.0311705
$862$	−11.3311	−0.385938
$863$	10.8324	0.368739	0.184369	−	0.982857i	$-0.440976\pi$
$863$	10.8324	0.368739	0.184369	+	0.982857i	$0.440976\pi$
$864$	12.1105	0.412008
$865$	−60.9727	−2.07314
$866$	15.5230	0.527493
$867$	6.87605	0.233523
$868$	−12.6471	−0.429272
$869$	−49.5918	−1.68229
$870$	1.25220	0.0424537
$871$	−14.9040	−0.505002
$872$	−29.9631	−1.01468
$873$	−27.7545	−0.939348
$874$	−14.4288	−0.488063
$875$	26.5381	0.897151
$876$	1.57670	0.0532718
$877$	−49.0437	−1.65609	−0.828043	−	0.560664i	$-0.810546\pi$
$877$	−49.0437	−1.65609	−0.828043	+	0.560664i	$0.810546\pi$
$878$	−6.03065	−0.203525
$879$	−1.03399	−0.0348755
$880$	63.8368	2.15194
$881$	−4.67034	−0.157348	−0.0786739	−	0.996900i	$-0.525069\pi$
$881$	−4.67034	−0.157348	−0.0786739	+	0.996900i	$0.525069\pi$
$882$	8.68894	0.292572
$883$	−37.5100	−1.26231	−0.631155	−	0.775656i	$-0.717419\pi$
$883$	−37.5100	−1.26231	−0.631155	+	0.775656i	$0.717419\pi$
$884$	0.706371	0.0237578
$885$	−14.1143	−0.474449
$886$	7.58764	0.254912
$887$	−31.3449	−1.05246	−0.526229	−	0.850343i	$-0.676395\pi$
$887$	−31.3449	−1.05246	−0.526229	+	0.850343i	$0.676395\pi$
$888$	1.09365	0.0367006
$889$	−1.85658	−0.0622678
$890$	19.0802	0.639570
$891$	46.8397	1.56919
$892$	−37.6413	−1.26032
$893$	40.8174	1.36590
$894$	0.169912	0.00568270
$895$	−19.8398	−0.663172
$896$	−11.2224	−0.374913
$897$	2.14390	0.0715828
$898$	11.4143	0.380901
$899$	−10.9240	−0.364335
$900$	57.3317	1.91106
$901$	2.45852	0.0819053
$902$	−7.20391	−0.239864
$903$	3.28174	0.109210
$904$	6.82047	0.226845
$905$	−85.1108	−2.82918
$906$	0.559025	0.0185724
$907$	−48.2460	−1.60198	−0.800991	−	0.598676i	$-0.795694\pi$
$907$	−48.2460	−1.60198	−0.800991	+	0.598676i	$0.795694\pi$
$908$	3.93677	0.130646
$909$	18.0001	0.597024
$910$	−2.03813	−0.0675634
$911$	10.3233	0.342025	0.171013	−	0.985269i	$-0.445296\pi$
$911$	10.3233	0.342025	0.171013	+	0.985269i	$0.445296\pi$
$912$	5.55683	0.184005
$913$	63.8977	2.11471
$914$	21.6622	0.716523
$915$	−21.3589	−0.706105
$916$	23.1016	0.763299
$917$	−13.1928	−0.435664
$918$	0.491228	0.0162129
$919$	29.7681	0.981958	0.490979	−	0.871171i	$-0.336639\pi$
$919$	29.7681	0.981958	0.490979	+	0.871171i	$0.336639\pi$
$920$	−40.7027	−1.34193
$921$	12.7105	0.418824
$922$	−5.30204	−0.174613
$923$	5.18862	0.170786
$924$	4.35340	0.143216
$925$	16.3576	0.537834
$926$	9.05564	0.297587
$927$	−2.83319	−0.0930541
$928$	−7.52017	−0.246862
$929$	−15.5478	−0.510108	−0.255054	−	0.966927i	$-0.582093\pi$
$929$	−15.5478	−0.510108	−0.255054	+	0.966927i	$0.582093\pi$
$930$	−6.25010	−0.204949
$931$	32.6203	1.06909
$932$	−46.3238	−1.51739
$933$	11.4566	0.375072
$934$	−7.33841	−0.240120
$935$	10.2900	0.336520
$936$	−5.38891	−0.176142
$937$	−42.5489	−1.39001	−0.695006	−	0.719004i	$-0.744598\pi$
$937$	−42.5489	−1.39001	−0.695006	+	0.719004i	$0.744598\pi$
$938$	7.45124	0.243291
$939$	3.20948	0.104737
$940$	53.5950	1.74808
$941$	21.8609	0.712643	0.356322	−	0.934363i	$-0.384031\pi$
$941$	21.8609	0.712643	0.356322	+	0.934363i	$0.384031\pi$
$942$	0.324558	0.0105747
$943$	−11.9528	−0.389236
$944$	21.3298	0.694227
$945$	9.55168	0.310716
$946$	−25.8480	−0.840392
$947$	45.4759	1.47777	0.738884	−	0.673833i	$-0.235353\pi$
$947$	45.4759	1.47777	0.738884	+	0.673833i	$0.235353\pi$
$948$	−5.66819	−0.184094
$949$	−2.21664	−0.0719551
$950$	−31.9387	−1.03623
$951$	3.19746	0.103685
$952$	−0.758703	−0.0245897
$953$	−36.9828	−1.19799	−0.598995	−	0.800753i	$-0.704433\pi$
$953$	−36.9828	−1.19799	−0.598995	+	0.800753i	$0.704433\pi$
$954$	−8.73030	−0.282654
$955$	−59.4069	−1.92236
$956$	3.87767	0.125413
$957$	3.76026	0.121552
$958$	12.3650	0.399495
$959$	−19.6880	−0.635759
$960$	4.07643	0.131566
$961$	23.5246	0.758858
$962$	−0.715670	−0.0230741
$963$	32.1673	1.03658
$964$	−9.09375	−0.292890
$965$	−58.1880	−1.87314
$966$	−1.07184	−0.0344860
$967$	30.7842	0.989954	0.494977	−	0.868906i	$-0.335176\pi$
$967$	30.7842	0.989954	0.494977	+	0.868906i	$0.335176\pi$
$968$	−52.7428	−1.69522
$969$	0.895722	0.0287747
$970$	20.3018	0.651853
$971$	−39.0731	−1.25392	−0.626958	−	0.779053i	$-0.715700\pi$
$971$	−39.0731	−1.25392	−0.626958	+	0.779053i	$0.715700\pi$
$972$	17.8011	0.570971
$973$	−18.7347	−0.600608
$974$	0.575490	0.0184399
$975$	4.74561	0.151981
$976$	32.2780	1.03319
$977$	55.2217	1.76670	0.883349	−	0.468716i	$-0.155283\pi$
$977$	55.2217	1.76670	0.883349	+	0.468716i	$0.155283\pi$
$978$	0.217704	0.00696142
$979$	57.2962	1.83119
$980$	42.8318	1.36821
$981$	−44.6310	−1.42496
$982$	7.80313	0.249008
$983$	−15.4744	−0.493558	−0.246779	−	0.969072i	$-0.579372\pi$
$983$	−15.4744	−0.493558	−0.246779	+	0.969072i	$0.579372\pi$
$984$	−1.76895	−0.0563921
$985$	0.633042	0.0201704
$986$	−0.305034	−0.00971426
$987$	3.03211	0.0965132
$988$	−9.41692	−0.299592
$989$	−42.8873	−1.36374
$990$	−36.5403	−1.16133
$991$	−36.0388	−1.14481	−0.572405	−	0.819971i	$-0.693989\pi$
$991$	−36.0388	−1.14481	−0.572405	+	0.819971i	$0.693989\pi$
$992$	37.5353	1.19175
$993$	−8.90012	−0.282437
$994$	−2.59405	−0.0822783
$995$	77.5856	2.45963
$996$	7.30332	0.231415
$997$	−3.47336	−0.110002	−0.0550012	−	0.998486i	$-0.517516\pi$
$997$	−3.47336	−0.110002	−0.0550012	+	0.998486i	$0.517516\pi$
$998$	9.87917	0.312720
$999$	3.35398	0.106115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.g.1.18	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.g.1.18	✓	30	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:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q+0.508360 q^{2} -0.408426 q^{3} -1.74157 q^{4} +4.07667 q^{5} -0.207627 q^{6} +0.983456 q^{7} -1.90207 q^{8} -2.83319 q^{9} +O(q^{10})\)	\(q+0.508360 q^{2} -0.408426 q^{3} -1.74157 q^{4} +4.07667 q^{5} -0.207627 q^{6} +0.983456 q^{7} -1.90207 q^{8} -2.83319 q^{9} +2.07242 q^{10} +6.22328 q^{11} +0.711302 q^{12} -1.00000 q^{13} +0.499950 q^{14} -1.66502 q^{15} +2.51621 q^{16} +0.405594 q^{17} -1.44028 q^{18} -5.40714 q^{19} -7.09981 q^{20} -0.401669 q^{21} +3.16367 q^{22} +5.24918 q^{23} +0.776853 q^{24} +11.6193 q^{25} -0.508360 q^{26} +2.38243 q^{27} -1.71276 q^{28} -1.47940 q^{29} -0.846429 q^{30} +7.38408 q^{31} +5.08327 q^{32} -2.54175 q^{33} +0.206188 q^{34} +4.00923 q^{35} +4.93420 q^{36} +1.40780 q^{37} -2.74878 q^{38} +0.408426 q^{39} -7.75410 q^{40} -2.27708 q^{41} -0.204192 q^{42} -8.17027 q^{43} -10.8383 q^{44} -11.5500 q^{45} +2.66848 q^{46} -7.54879 q^{47} -1.02768 q^{48} -6.03282 q^{49} +5.90677 q^{50} -0.165655 q^{51} +1.74157 q^{52} +6.06153 q^{53} +1.21113 q^{54} +25.3703 q^{55} -1.87060 q^{56} +2.20842 q^{57} -0.752066 q^{58} +8.47699 q^{59} +2.89975 q^{60} +12.8281 q^{61} +3.75377 q^{62} -2.78631 q^{63} -2.44828 q^{64} -4.07667 q^{65} -1.29212 q^{66} +14.9040 q^{67} -0.706371 q^{68} -2.14390 q^{69} +2.03813 q^{70} -5.18862 q^{71} +5.38891 q^{72} +2.21664 q^{73} +0.715670 q^{74} -4.74561 q^{75} +9.41692 q^{76} +6.12032 q^{77} +0.207627 q^{78} -7.96875 q^{79} +10.2577 q^{80} +7.52652 q^{81} -1.15757 q^{82} +10.2675 q^{83} +0.699534 q^{84} +1.65348 q^{85} -4.15344 q^{86} +0.604224 q^{87} -11.8371 q^{88} +9.20675 q^{89} -5.87155 q^{90} -0.983456 q^{91} -9.14182 q^{92} -3.01585 q^{93} -3.83750 q^{94} -22.0432 q^{95} -2.07614 q^{96} +9.79621 q^{97} -3.06684 q^{98} -17.6317 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9} + 5 q^{10} + q^{11} + 15 q^{12} - 30 q^{13} + 24 q^{14} + 6 q^{15} + 38 q^{16} + 17 q^{17} + 8 q^{18} + 9 q^{19} + 31 q^{20} + 27 q^{21} + 2 q^{22} + 14 q^{23} + 26 q^{24} + 47 q^{25} + 14 q^{27} - 6 q^{28} + 53 q^{29} + 25 q^{30} + 19 q^{31} - 4 q^{32} + q^{33} - 22 q^{34} + 9 q^{35} + 61 q^{36} + 46 q^{38} - 5 q^{39} - 35 q^{40} + 28 q^{41} - 7 q^{42} + 6 q^{43} - 12 q^{44} + 68 q^{45} + 7 q^{46} + 12 q^{47} + 13 q^{48} + 54 q^{49} - 18 q^{50} + 10 q^{51} - 34 q^{52} + 37 q^{53} + 22 q^{54} + 11 q^{55} + 67 q^{56} - 57 q^{57} - 5 q^{58} + 61 q^{59} - 102 q^{60} + 16 q^{61} - 2 q^{62} - 7 q^{63} + 29 q^{64} - 17 q^{65} - 83 q^{66} - 2 q^{67} + 57 q^{68} + 98 q^{69} - 10 q^{70} + 50 q^{71} - 8 q^{72} - 10 q^{73} - 13 q^{74} + 5 q^{75} - 19 q^{76} + 54 q^{77} - 3 q^{78} + 3 q^{79} + 76 q^{80} + 118 q^{81} + 7 q^{82} + 6 q^{83} + 44 q^{84} + 33 q^{85} - 29 q^{86} - 10 q^{87} - 13 q^{88} + 77 q^{89} + 38 q^{90} - 2 q^{91} - 3 q^{92} + 34 q^{93} - 25 q^{94} + 24 q^{95} - 28 q^{96} + 12 q^{97} - 14 q^{98} - 58 q^{99}+O(q^{100}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9 + 5 * q^10 + q^11 + 15 * q^12 - 30 * q^13 + 24 * q^14 + 6 * q^15 + 38 * q^16 + 17 * q^17 + 8 * q^18 + 9 * q^19 + 31 * q^20 + 27 * q^21 + 2 * q^22 + 14 * q^23 + 26 * q^24 + 47 * q^25 + 14 * q^27 - 6 * q^28 + 53 * q^29 + 25 * q^30 + 19 * q^31 - 4 * q^32 + q^33 - 22 * q^34 + 9 * q^35 + 61 * q^36 + 46 * q^38 - 5 * q^39 - 35 * q^40 + 28 * q^41 - 7 * q^42 + 6 * q^43 - 12 * q^44 + 68 * q^45 + 7 * q^46 + 12 * q^47 + 13 * q^48 + 54 * q^49 - 18 * q^50 + 10 * q^51 - 34 * q^52 + 37 * q^53 + 22 * q^54 + 11 * q^55 + 67 * q^56 - 57 * q^57 - 5 * q^58 + 61 * q^59 - 102 * q^60 + 16 * q^61 - 2 * q^62 - 7 * q^63 + 29 * q^64 - 17 * q^65 - 83 * q^66 - 2 * q^67 + 57 * q^68 + 98 * q^69 - 10 * q^70 + 50 * q^71 - 8 * q^72 - 10 * q^73 - 13 * q^74 + 5 * q^75 - 19 * q^76 + 54 * q^77 - 3 * q^78 + 3 * q^79 + 76 * q^80 + 118 * q^81 + 7 * q^82 + 6 * q^83 + 44 * q^84 + 33 * q^85 - 29 * q^86 - 10 * q^87 - 13 * q^88 + 77 * q^89 + 38 * q^90 - 2 * q^91 - 3 * q^92 + 34 * q^93 - 25 * q^94 + 24 * q^95 - 28 * q^96 + 12 * q^97 - 14 * q^98 - 58 * q^99

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