LMFDB - Embedded newform 1339.2.a.g.1.17

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			1.17
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)

$f(q)$	$=$	$q+0.430342 q^{2} -0.376968 q^{3} -1.81481 q^{4} -3.33541 q^{5} -0.162225 q^{6} -1.83693 q^{7} -1.64167 q^{8} -2.85790 q^{9} +O(q^{10})$	\(q+0.430342 q^{2} -0.376968 q^{3} -1.81481 q^{4} -3.33541 q^{5} -0.162225 q^{6} -1.83693 q^{7} -1.64167 q^{8} -2.85790 q^{9} -1.43537 q^{10} -0.338707 q^{11} +0.684123 q^{12} -1.00000 q^{13} -0.790510 q^{14} +1.25734 q^{15} +2.92313 q^{16} +3.04687 q^{17} -1.22987 q^{18} -4.00087 q^{19} +6.05313 q^{20} +0.692465 q^{21} -0.145760 q^{22} -2.44226 q^{23} +0.618857 q^{24} +6.12498 q^{25} -0.430342 q^{26} +2.20824 q^{27} +3.33368 q^{28} -9.21918 q^{29} +0.541088 q^{30} -3.94611 q^{31} +4.54129 q^{32} +0.127681 q^{33} +1.31120 q^{34} +6.12694 q^{35} +5.18653 q^{36} +4.49648 q^{37} -1.72174 q^{38} +0.376968 q^{39} +5.47565 q^{40} +6.20728 q^{41} +0.297997 q^{42} +6.67514 q^{43} +0.614687 q^{44} +9.53226 q^{45} -1.05101 q^{46} +12.8709 q^{47} -1.10193 q^{48} -3.62567 q^{49} +2.63584 q^{50} -1.14857 q^{51} +1.81481 q^{52} +9.30348 q^{53} +0.950297 q^{54} +1.12973 q^{55} +3.01564 q^{56} +1.50820 q^{57} -3.96740 q^{58} -11.4788 q^{59} -2.28183 q^{60} +2.11289 q^{61} -1.69818 q^{62} +5.24977 q^{63} -3.89196 q^{64} +3.33541 q^{65} +0.0549467 q^{66} +4.63931 q^{67} -5.52949 q^{68} +0.920655 q^{69} +2.63668 q^{70} -13.0428 q^{71} +4.69172 q^{72} -5.12019 q^{73} +1.93502 q^{74} -2.30892 q^{75} +7.26081 q^{76} +0.622182 q^{77} +0.162225 q^{78} +3.29694 q^{79} -9.74985 q^{80} +7.74125 q^{81} +2.67125 q^{82} +6.05709 q^{83} -1.25669 q^{84} -10.1626 q^{85} +2.87259 q^{86} +3.47533 q^{87} +0.556045 q^{88} -4.98751 q^{89} +4.10213 q^{90} +1.83693 q^{91} +4.43223 q^{92} +1.48756 q^{93} +5.53887 q^{94} +13.3446 q^{95} -1.71192 q^{96} -16.2576 q^{97} -1.56028 q^{98} +0.967988 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.430342	0.304298	0.152149	−	0.988358i	$-0.451381\pi$
$2$	0.430342	0.304298	0.152149	+	0.988358i	$0.451381\pi$
$3$	−0.376968	−0.217642	−0.108821	−	0.994061i	$-0.534708\pi$
$3$	−0.376968	−0.217642	−0.108821	+	0.994061i	$0.534708\pi$
$4$	−1.81481	−0.907403
$5$	−3.33541	−1.49164	−0.745821	−	0.666146i	$-0.767943\pi$
$5$	−3.33541	−1.49164	−0.745821	+	0.666146i	$0.767943\pi$
$6$	−0.162225	−0.0662281
$7$	−1.83693	−0.694296	−0.347148	−	0.937810i	$-0.612850\pi$
$7$	−1.83693	−0.694296	−0.347148	+	0.937810i	$0.612850\pi$
$8$	−1.64167	−0.580418
$9$	−2.85790	−0.952632
$10$	−1.43537	−0.453903
$11$	−0.338707	−0.102124	−0.0510619	−	0.998695i	$-0.516261\pi$
$11$	−0.338707	−0.102124	−0.0510619	+	0.998695i	$0.516261\pi$
$12$	0.684123	0.197489
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.790510	−0.211273
$15$	1.25734	0.324645
$16$	2.92313	0.730783
$17$	3.04687	0.738976	0.369488	−	0.929236i	$-0.379533\pi$
$17$	3.04687	0.738976	0.369488	+	0.929236i	$0.379533\pi$
$18$	−1.22987	−0.289884
$19$	−4.00087	−0.917863	−0.458931	−	0.888472i	$-0.651768\pi$
$19$	−4.00087	−0.917863	−0.458931	+	0.888472i	$0.651768\pi$
$20$	6.05313	1.35352
$21$	0.692465	0.151108
$22$	−0.145760	−0.0310761
$23$	−2.44226	−0.509247	−0.254624	−	0.967040i	$-0.581952\pi$
$23$	−2.44226	−0.509247	−0.254624	+	0.967040i	$0.581952\pi$
$24$	0.618857	0.126324
$25$	6.12498	1.22500
$26$	−0.430342	−0.0843970
$27$	2.20824	0.424976
$28$	3.33368	0.630006
$29$	−9.21918	−1.71196	−0.855979	−	0.517011i	$-0.827045\pi$
$29$	−9.21918	−1.71196	−0.855979	+	0.517011i	$0.827045\pi$
$30$	0.541088	0.0987886
$31$	−3.94611	−0.708743	−0.354371	−	0.935105i	$-0.615305\pi$
$31$	−3.94611	−0.708743	−0.354371	+	0.935105i	$0.615305\pi$
$32$	4.54129	0.802794
$33$	0.127681	0.0222265
$34$	1.31120	0.224869
$35$	6.12694	1.03564
$36$	5.18653	0.864421
$37$	4.49648	0.739217	0.369609	−	0.929188i	$-0.379492\pi$
$37$	4.49648	0.739217	0.369609	+	0.929188i	$0.379492\pi$
$38$	−1.72174	−0.279304
$39$	0.376968	0.0603632
$40$	5.47565	0.865776
$41$	6.20728	0.969414	0.484707	−	0.874676i	$-0.338926\pi$
$41$	6.20728	0.969414	0.484707	+	0.874676i	$0.338926\pi$
$42$	0.297997	0.0459819
$43$	6.67514	1.01795	0.508974	−	0.860782i	$-0.330025\pi$
$43$	6.67514	1.01795	0.508974	+	0.860782i	$0.330025\pi$
$44$	0.614687	0.0926675
$45$	9.53226	1.42099
$46$	−1.05101	−0.154963
$47$	12.8709	1.87741	0.938704	−	0.344726i	$-0.112028\pi$
$47$	12.8709	1.87741	0.938704	+	0.344726i	$0.112028\pi$
$48$	−1.10193	−0.159049
$49$	−3.62567	−0.517953
$50$	2.63584	0.372764
$51$	−1.14857	−0.160832
$52$	1.81481	0.251668
$53$	9.30348	1.27793	0.638966	−	0.769235i	$-0.279363\pi$
$53$	9.30348	1.27793	0.638966	+	0.769235i	$0.279363\pi$
$54$	0.950297	0.129319
$55$	1.12973	0.152332
$56$	3.01564	0.402982
$57$	1.50820	0.199766
$58$	−3.96740	−0.520945
$59$	−11.4788	−1.49441	−0.747207	−	0.664592i	$-0.768605\pi$
$59$	−11.4788	−1.49441	−0.747207	+	0.664592i	$0.768605\pi$
$60$	−2.28183	−0.294584
$61$	2.11289	0.270528	0.135264	−	0.990810i	$-0.456812\pi$
$61$	2.11289	0.270528	0.135264	+	0.990810i	$0.456812\pi$
$62$	−1.69818	−0.215669
$63$	5.24977	0.661409
$64$	−3.89196	−0.486495
$65$	3.33541	0.413707
$66$	0.0549467	0.00676347
$67$	4.63931	0.566782	0.283391	−	0.959005i	$-0.408541\pi$
$67$	4.63931	0.566782	0.283391	+	0.959005i	$0.408541\pi$
$68$	−5.52949	−0.670549
$69$	0.920655	0.110834
$70$	2.63668	0.315143
$71$	−13.0428	−1.54789	−0.773945	−	0.633253i	$-0.781719\pi$
$71$	−13.0428	−1.54789	−0.773945	+	0.633253i	$0.781719\pi$
$72$	4.69172	0.552925
$73$	−5.12019	−0.599273	−0.299637	−	0.954053i	$-0.596865\pi$
$73$	−5.12019	−0.599273	−0.299637	+	0.954053i	$0.596865\pi$
$74$	1.93502	0.224942
$75$	−2.30892	−0.266611
$76$	7.26081	0.832872
$77$	0.622182	0.0709042
$78$	0.162225	0.0183684
$79$	3.29694	0.370935	0.185467	−	0.982650i	$-0.440620\pi$
$79$	3.29694	0.370935	0.185467	+	0.982650i	$0.440620\pi$
$80$	−9.74985	−1.09007
$81$	7.74125	0.860139
$82$	2.67125	0.294991
$83$	6.05709	0.664852	0.332426	−	0.943129i	$-0.392133\pi$
$83$	6.05709	0.664852	0.332426	+	0.943129i	$0.392133\pi$
$84$	−1.25669	−0.137116
$85$	−10.1626	−1.10229
$86$	2.87259	0.309759
$87$	3.47533	0.372595
$88$	0.556045	0.0592746
$89$	−4.98751	−0.528675	−0.264338	−	0.964430i	$-0.585153\pi$
$89$	−4.98751	−0.528675	−0.264338	+	0.964430i	$0.585153\pi$
$90$	4.10213	0.432403
$91$	1.83693	0.192563
$92$	4.43223	0.462092
$93$	1.48756	0.154252
$94$	5.53887	0.571291
$95$	13.3446	1.36912
$96$	−1.71192	−0.174722
$97$	−16.2576	−1.65071	−0.825355	−	0.564615i	$-0.809025\pi$
$97$	−16.2576	−1.65071	−0.825355	+	0.564615i	$0.809025\pi$
$98$	−1.56028	−0.157612
$99$	0.967988	0.0972864
$100$	−11.1157	−1.11157
$101$	10.1885	1.01380	0.506899	−	0.862006i	$-0.330792\pi$
$101$	10.1885	1.01380	0.506899	+	0.862006i	$0.330792\pi$
$102$	−0.494279	−0.0489410
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.64167	0.160979
$105$	−2.30966	−0.225400
$106$	4.00368	0.388872
$107$	−4.25690	−0.411530	−0.205765	−	0.978601i	$-0.565968\pi$
$107$	−4.25690	−0.411530	−0.205765	+	0.978601i	$0.565968\pi$
$108$	−4.00752	−0.385624
$109$	−0.561786	−0.0538093	−0.0269047	−	0.999638i	$-0.508565\pi$
$109$	−0.561786	−0.0538093	−0.0269047	+	0.999638i	$0.508565\pi$
$110$	0.486169	0.0463544
$111$	−1.69503	−0.160885
$112$	−5.36960	−0.507380
$113$	−9.11009	−0.857005	−0.428503	−	0.903541i	$-0.640959\pi$
$113$	−9.11009	−0.857005	−0.428503	+	0.903541i	$0.640959\pi$
$114$	0.649042	0.0607883
$115$	8.14596	0.759614
$116$	16.7310	1.55344
$117$	2.85790	0.264213
$118$	−4.93981	−0.454746
$119$	−5.59691	−0.513068
$120$	−2.06414	−0.188430
$121$	−10.8853	−0.989571
$122$	0.909265	0.0823210
$123$	−2.33995	−0.210986
$124$	7.16143	0.643115
$125$	−3.75229	−0.335615
$126$	2.25919	0.201265
$127$	12.7757	1.13366	0.566829	−	0.823835i	$-0.308170\pi$
$127$	12.7757	1.13366	0.566829	+	0.823835i	$0.308170\pi$
$128$	−10.7574	−0.950833
$129$	−2.51631	−0.221549
$130$	1.43537	0.125890
$131$	−0.157273	−0.0137410	−0.00687051	−	0.999976i	$-0.502187\pi$
$131$	−0.157273	−0.0137410	−0.00687051	+	0.999976i	$0.502187\pi$
$132$	−0.231717	−0.0201684
$133$	7.34934	0.637269
$134$	1.99649	0.172470
$135$	−7.36539	−0.633912
$136$	−5.00196	−0.428915
$137$	−15.0833	−1.28865	−0.644325	−	0.764752i	$-0.722862\pi$
$137$	−15.0833	−1.28865	−0.644325	+	0.764752i	$0.722862\pi$
$138$	0.396196	0.0337265
$139$	−11.2272	−0.952275	−0.476138	−	0.879371i	$-0.657964\pi$
$139$	−11.2272	−0.952275	−0.476138	+	0.879371i	$0.657964\pi$
$140$	−11.1192	−0.939744
$141$	−4.85190	−0.408604
$142$	−5.61284	−0.471019
$143$	0.338707	0.0283241
$144$	−8.35401	−0.696167
$145$	30.7498	2.55363
$146$	−2.20343	−0.182357
$147$	1.36676	0.112729
$148$	−8.16024	−0.670768
$149$	24.1310	1.97688	0.988442	−	0.151598i	$-0.0484418\pi$
$149$	24.1310	1.97688	0.988442	+	0.151598i	$0.0484418\pi$
$150$	−0.993626	−0.0811292
$151$	−2.86654	−0.233276	−0.116638	−	0.993175i	$-0.537212\pi$
$151$	−2.86654	−0.233276	−0.116638	+	0.993175i	$0.537212\pi$
$152$	6.56811	0.532744
$153$	−8.70765	−0.703972
$154$	0.267751	0.0215760
$155$	13.1619	1.05719
$156$	−0.684123	−0.0547737
$157$	−0.0792487	−0.00632474	−0.00316237	−	0.999995i	$-0.501007\pi$
$157$	−0.0792487	−0.00632474	−0.00316237	+	0.999995i	$0.501007\pi$
$158$	1.41881	0.112875
$159$	−3.50711	−0.278132
$160$	−15.1471	−1.19748
$161$	4.48628	0.353568
$162$	3.33138	0.261738
$163$	−5.35419	−0.419372	−0.209686	−	0.977769i	$-0.567244\pi$
$163$	−5.35419	−0.419372	−0.209686	+	0.977769i	$0.567244\pi$
$164$	−11.2650	−0.879649
$165$	−0.425870	−0.0331540
$166$	2.60662	0.202313
$167$	−7.99561	−0.618719	−0.309360	−	0.950945i	$-0.600115\pi$
$167$	−7.99561	−0.618719	−0.309360	+	0.950945i	$0.600115\pi$
$168$	−1.13680	−0.0877060
$169$	1.00000	0.0769231
$170$	−4.37339	−0.335423
$171$	11.4341	0.874385
$172$	−12.1141	−0.923690
$173$	1.10691	0.0841571	0.0420785	−	0.999114i	$-0.486602\pi$
$173$	1.10691	0.0841571	0.0420785	+	0.999114i	$0.486602\pi$
$174$	1.49558	0.113380
$175$	−11.2512	−0.850510
$176$	−0.990084	−0.0746304
$177$	4.32714	0.325248
$178$	−2.14634	−0.160875
$179$	16.6539	1.24477	0.622387	−	0.782710i	$-0.286163\pi$
$179$	16.6539	1.24477	0.622387	+	0.782710i	$0.286163\pi$
$180$	−17.2992	−1.28941
$181$	3.19819	0.237720	0.118860	−	0.992911i	$-0.462076\pi$
$181$	3.19819	0.237720	0.118860	+	0.992911i	$0.462076\pi$
$182$	0.790510	0.0585965
$183$	−0.796492	−0.0588784
$184$	4.00939	0.295576
$185$	−14.9976	−1.10265
$186$	0.640158	0.0469387
$187$	−1.03200	−0.0754670
$188$	−23.3581	−1.70356
$189$	−4.05639	−0.295059
$190$	5.74272	0.416621
$191$	16.5573	1.19804	0.599022	−	0.800733i	$-0.295556\pi$
$191$	16.5573	1.19804	0.599022	+	0.800733i	$0.295556\pi$
$192$	1.46714	0.105882
$193$	−15.7028	−1.13031	−0.565155	−	0.824985i	$-0.691184\pi$
$193$	−15.7028	−1.13031	−0.565155	+	0.824985i	$0.691184\pi$
$194$	−6.99633	−0.502307
$195$	−1.25734	−0.0900402
$196$	6.57989	0.469992
$197$	14.6083	1.04080	0.520398	−	0.853924i	$-0.325783\pi$
$197$	14.6083	1.04080	0.520398	+	0.853924i	$0.325783\pi$
$198$	0.416566	0.0296040
$199$	9.47873	0.671929	0.335965	−	0.941875i	$-0.390938\pi$
$199$	9.47873	0.671929	0.335965	+	0.941875i	$0.390938\pi$
$200$	−10.0552	−0.711010
$201$	−1.74887	−0.123356
$202$	4.38455	0.308496
$203$	16.9350	1.18861
$204$	2.08444	0.145940
$205$	−20.7038	−1.44602
$206$	0.430342	0.0299833
$207$	6.97973	0.485125
$208$	−2.92313	−0.202683
$209$	1.35512	0.0937357
$210$	−0.993943	−0.0685886
$211$	−23.6724	−1.62968	−0.814838	−	0.579688i	$-0.803174\pi$
$211$	−23.6724	−1.62968	−0.814838	+	0.579688i	$0.803174\pi$
$212$	−16.8840	−1.15960
$213$	4.91670	0.336887
$214$	−1.83192	−0.125228
$215$	−22.2643	−1.51842
$216$	−3.62520	−0.246664
$217$	7.24875	0.492077
$218$	−0.241760	−0.0163740
$219$	1.93015	0.130427
$220$	−2.05023	−0.138227
$221$	−3.04687	−0.204955
$222$	−0.729442	−0.0489570
$223$	13.5806	0.909424	0.454712	−	0.890639i	$-0.349742\pi$
$223$	13.5806	0.909424	0.454712	+	0.890639i	$0.349742\pi$
$224$	−8.34205	−0.557377
$225$	−17.5046	−1.16697
$226$	−3.92045	−0.260785
$227$	4.69759	0.311790	0.155895	−	0.987774i	$-0.450174\pi$
$227$	4.69759	0.311790	0.155895	+	0.987774i	$0.450174\pi$
$228$	−2.73709	−0.181268
$229$	13.6972	0.905140	0.452570	−	0.891729i	$-0.350507\pi$
$229$	13.6972	0.905140	0.452570	+	0.891729i	$0.350507\pi$
$230$	3.50555	0.231149
$231$	−0.234543	−0.0154318
$232$	15.1349	0.993652
$233$	12.8714	0.843236	0.421618	−	0.906774i	$-0.361462\pi$
$233$	12.8714	0.843236	0.421618	+	0.906774i	$0.361462\pi$
$234$	1.22987	0.0803993
$235$	−42.9296	−2.80042
$236$	20.8318	1.35603
$237$	−1.24284	−0.0807311
$238$	−2.40858	−0.156125
$239$	−12.1082	−0.783216	−0.391608	−	0.920132i	$-0.628081\pi$
$239$	−12.1082	−0.783216	−0.391608	+	0.920132i	$0.628081\pi$
$240$	3.67538	0.237245
$241$	4.40334	0.283644	0.141822	−	0.989892i	$-0.454704\pi$
$241$	4.40334	0.283644	0.141822	+	0.989892i	$0.454704\pi$
$242$	−4.68439	−0.301124
$243$	−9.54292	−0.612178
$244$	−3.83449	−0.245478
$245$	12.0931	0.772600
$246$	−1.00698	−0.0642025
$247$	4.00087	0.254569
$248$	6.47822	0.411367
$249$	−2.28333	−0.144700
$250$	−1.61477	−0.102127
$251$	−1.47109	−0.0928544	−0.0464272	−	0.998922i	$-0.514784\pi$
$251$	−1.47109	−0.0928544	−0.0464272	+	0.998922i	$0.514784\pi$
$252$	−9.52731	−0.600164
$253$	0.827210	0.0520063
$254$	5.49791	0.344969
$255$	3.83097	0.239905
$256$	3.15454	0.197158
$257$	15.7051	0.979656	0.489828	−	0.871819i	$-0.337060\pi$
$257$	15.7051	0.979656	0.489828	+	0.871819i	$0.337060\pi$
$258$	−1.08287	−0.0674168
$259$	−8.25975	−0.513236
$260$	−6.05313	−0.375399
$261$	26.3474	1.63087
$262$	−0.0676812	−0.00418136
$263$	27.9769	1.72513	0.862564	−	0.505948i	$-0.168857\pi$
$263$	27.9769	1.72513	0.862564	+	0.505948i	$0.168857\pi$
$264$	−0.209611	−0.0129007
$265$	−31.0310	−1.90622
$266$	3.16273	0.193919
$267$	1.88013	0.115062
$268$	−8.41944	−0.514299
$269$	15.9077	0.969909	0.484954	−	0.874539i	$-0.338836\pi$
$269$	15.9077	0.969909	0.484954	+	0.874539i	$0.338836\pi$
$270$	−3.16963	−0.192898
$271$	−23.3153	−1.41630	−0.708152	−	0.706060i	$-0.750471\pi$
$271$	−23.3153	−1.41630	−0.708152	+	0.706060i	$0.750471\pi$
$272$	8.90642	0.540031
$273$	−0.692465	−0.0419099
$274$	−6.49096	−0.392133
$275$	−2.07457	−0.125101
$276$	−1.67081	−0.100571
$277$	13.5362	0.813312	0.406656	−	0.913581i	$-0.366695\pi$
$277$	13.5362	0.813312	0.406656	+	0.913581i	$0.366695\pi$
$278$	−4.83152	−0.289775
$279$	11.2776	0.675171
$280$	−10.0584	−0.601105
$281$	−3.18095	−0.189759	−0.0948797	−	0.995489i	$-0.530247\pi$
$281$	−3.18095	−0.189759	−0.0948797	+	0.995489i	$0.530247\pi$
$282$	−2.08797	−0.124337
$283$	18.3042	1.08807	0.544036	−	0.839062i	$-0.316895\pi$
$283$	18.3042	1.08807	0.544036	+	0.839062i	$0.316895\pi$
$284$	23.6701	1.40456
$285$	−5.03047	−0.297979
$286$	0.145760	0.00861895
$287$	−11.4024	−0.673061
$288$	−12.9785	−0.764767
$289$	−7.71656	−0.453915
$290$	13.2329	0.777063
$291$	6.12859	0.359264
$292$	9.29215	0.543782
$293$	−16.9690	−0.991340	−0.495670	−	0.868511i	$-0.665077\pi$
$293$	−16.9690	−0.991340	−0.495670	+	0.868511i	$0.665077\pi$
$294$	0.588175	0.0343030
$295$	38.2866	2.22913
$296$	−7.38174	−0.429055
$297$	−0.747945	−0.0434001
$298$	10.3846	0.601561
$299$	2.44226	0.141240
$300$	4.19024	0.241924
$301$	−12.2618	−0.706758
$302$	−1.23359	−0.0709852
$303$	−3.84075	−0.220645
$304$	−11.6951	−0.670759
$305$	−7.04736	−0.403531
$306$	−3.74727	−0.214217
$307$	1.62986	0.0930209	0.0465105	−	0.998918i	$-0.485190\pi$
$307$	1.62986	0.0930209	0.0465105	+	0.998918i	$0.485190\pi$
$308$	−1.12914	−0.0643387
$309$	−0.376968	−0.0214450
$310$	5.66412	0.321701
$311$	31.9967	1.81436	0.907182	−	0.420738i	$-0.138229\pi$
$311$	31.9967	1.81436	0.907182	+	0.420738i	$0.138229\pi$
$312$	−0.618857	−0.0350359
$313$	−16.8441	−0.952086	−0.476043	−	0.879422i	$-0.657929\pi$
$313$	−16.8441	−0.952086	−0.476043	+	0.879422i	$0.657929\pi$
$314$	−0.0341040	−0.00192460
$315$	−17.5101	−0.986585
$316$	−5.98331	−0.336587
$317$	−14.0692	−0.790205	−0.395103	−	0.918637i	$-0.629291\pi$
$317$	−14.0692	−0.790205	−0.395103	+	0.918637i	$0.629291\pi$
$318$	−1.50926	−0.0846350
$319$	3.12260	0.174832
$320$	12.9813	0.725676
$321$	1.60471	0.0895664
$322$	1.93063	0.107590
$323$	−12.1902	−0.678278
$324$	−14.0489	−0.780493
$325$	−6.12498	−0.339753
$326$	−2.30413	−0.127614
$327$	0.211775	0.0117112
$328$	−10.1903	−0.562666
$329$	−23.6429	−1.30348
$330$	−0.183270	−0.0100887
$331$	20.2189	1.11133	0.555665	−	0.831406i	$-0.312464\pi$
$331$	20.2189	1.11133	0.555665	+	0.831406i	$0.312464\pi$
$332$	−10.9924	−0.603289
$333$	−12.8505	−0.704202
$334$	−3.44085	−0.188275
$335$	−15.4740	−0.845435
$336$	2.02417	0.110427
$337$	20.8866	1.13776	0.568882	−	0.822419i	$-0.307376\pi$
$337$	20.8866	1.13776	0.568882	+	0.822419i	$0.307376\pi$
$338$	0.430342	0.0234075
$339$	3.43421	0.186521
$340$	18.4431	1.00022
$341$	1.33657	0.0723795
$342$	4.92056	0.266073
$343$	19.5187	1.05391
$344$	−10.9584	−0.590836
$345$	−3.07076	−0.165324
$346$	0.476351	0.0256088
$347$	−12.3065	−0.660646	−0.330323	−	0.943868i	$-0.607158\pi$
$347$	−12.3065	−0.660646	−0.330323	+	0.943868i	$0.607158\pi$
$348$	−6.30705	−0.338094
$349$	15.8632	0.849135	0.424568	−	0.905396i	$-0.360426\pi$
$349$	15.8632	0.849135	0.424568	+	0.905396i	$0.360426\pi$
$350$	−4.84186	−0.258808
$351$	−2.20824	−0.117867
$352$	−1.53816	−0.0819844
$353$	−4.46568	−0.237684	−0.118842	−	0.992913i	$-0.537918\pi$
$353$	−4.46568	−0.237684	−0.118842	+	0.992913i	$0.537918\pi$
$354$	1.86215	0.0989721
$355$	43.5030	2.30890
$356$	9.05137	0.479722
$357$	2.10986	0.111665
$358$	7.16688	0.378782
$359$	−25.4896	−1.34529	−0.672646	−	0.739964i	$-0.734842\pi$
$359$	−25.4896	−1.34529	−0.672646	+	0.739964i	$0.734842\pi$
$360$	−15.6488	−0.824766
$361$	−2.99302	−0.157528
$362$	1.37632	0.0723375
$363$	4.10340	0.215373
$364$	−3.33368	−0.174732
$365$	17.0780	0.893901
$366$	−0.342764	−0.0179165
$367$	−1.21460	−0.0634015	−0.0317008	−	0.999497i	$-0.510092\pi$
$367$	−1.21460	−0.0634015	−0.0317008	+	0.999497i	$0.510092\pi$
$368$	−7.13906	−0.372149
$369$	−17.7398	−0.923495
$370$	−6.45411	−0.335533
$371$	−17.0899	−0.887263
$372$	−2.69963	−0.139969
$373$	−5.24265	−0.271454	−0.135727	−	0.990746i	$-0.543337\pi$
$373$	−5.24265	−0.271454	−0.135727	+	0.990746i	$0.543337\pi$
$374$	−0.444111	−0.0229644
$375$	1.41449	0.0730440
$376$	−21.1297	−1.08968
$377$	9.21918	0.474812
$378$	−1.74563	−0.0897857
$379$	13.1558	0.675766	0.337883	−	0.941188i	$-0.390289\pi$
$379$	13.1558	0.675766	0.337883	+	0.941188i	$0.390289\pi$
$380$	−24.2178	−1.24235
$381$	−4.81602	−0.246732
$382$	7.12529	0.364562
$383$	24.6095	1.25749	0.628744	−	0.777612i	$-0.283569\pi$
$383$	24.6095	1.25749	0.628744	+	0.777612i	$0.283569\pi$
$384$	4.05521	0.206942
$385$	−2.07523	−0.105764
$386$	−6.75756	−0.343951
$387$	−19.0768	−0.969730
$388$	29.5044	1.49786
$389$	26.0989	1.32327	0.661633	−	0.749827i	$-0.269864\pi$
$389$	26.0989	1.32327	0.661633	+	0.749827i	$0.269864\pi$
$390$	−0.541088	−0.0273990
$391$	−7.44127	−0.376321
$392$	5.95216	0.300629
$393$	0.0592869	0.00299063
$394$	6.28655	0.316712
$395$	−10.9967	−0.553302
$396$	−1.75671	−0.0882780
$397$	21.8541	1.09683	0.548413	−	0.836207i	$-0.315232\pi$
$397$	21.8541	1.09683	0.548413	+	0.836207i	$0.315232\pi$
$398$	4.07910	0.204467
$399$	−2.77047	−0.138697
$400$	17.9041	0.895207
$401$	23.1474	1.15592	0.577962	−	0.816063i	$-0.303848\pi$
$401$	23.1474	1.15592	0.577962	+	0.816063i	$0.303848\pi$
$402$	−0.752612	−0.0375369
$403$	3.94611	0.196570
$404$	−18.4902	−0.919922
$405$	−25.8203	−1.28302
$406$	7.28785	0.361690
$407$	−1.52299	−0.0754917
$408$	1.88558	0.0933501
$409$	24.9925	1.23580	0.617899	−	0.786257i	$-0.287984\pi$
$409$	24.9925	1.23580	0.617899	+	0.786257i	$0.287984\pi$
$410$	−8.90973	−0.440020
$411$	5.68590	0.280465
$412$	−1.81481	−0.0894091
$413$	21.0858	1.03757
$414$	3.00367	0.147622
$415$	−20.2029	−0.991722
$416$	−4.54129	−0.222655
$417$	4.23228	0.207256
$418$	0.583166	0.0285236
$419$	−5.36939	−0.262312	−0.131156	−	0.991362i	$-0.541869\pi$
$419$	−5.36939	−0.262312	−0.131156	+	0.991362i	$0.541869\pi$
$420$	4.19158	0.204528
$421$	−26.1277	−1.27339	−0.636694	−	0.771117i	$-0.719699\pi$
$421$	−26.1277	−1.27339	−0.636694	+	0.771117i	$0.719699\pi$
$422$	−10.1872	−0.495907
$423$	−36.7836	−1.78848
$424$	−15.2733	−0.741735
$425$	18.6621	0.905243
$426$	2.11586	0.102514
$427$	−3.88124	−0.187826
$428$	7.72544	0.373423
$429$	−0.127681	−0.00616452
$430$	−9.58128	−0.462050
$431$	−20.0121	−0.963950	−0.481975	−	0.876185i	$-0.660080\pi$
$431$	−20.0121	−0.963950	−0.481975	+	0.876185i	$0.660080\pi$
$432$	6.45497	0.310565
$433$	−26.7853	−1.28722	−0.643610	−	0.765354i	$-0.722564\pi$
$433$	−26.7853	−1.28722	−0.643610	+	0.765354i	$0.722564\pi$
$434$	3.11944	0.149738
$435$	−11.5917	−0.555778
$436$	1.01953	0.0488267
$437$	9.77118	0.467419
$438$	0.830623	0.0396887
$439$	−5.09440	−0.243143	−0.121571	−	0.992583i	$-0.538793\pi$
$439$	−5.09440	−0.243143	−0.121571	+	0.992583i	$0.538793\pi$
$440$	−1.85464	−0.0884164
$441$	10.3618	0.493418
$442$	−1.31120	−0.0623673
$443$	−23.8040	−1.13096	−0.565481	−	0.824762i	$-0.691309\pi$
$443$	−23.8040	−1.13096	−0.565481	+	0.824762i	$0.691309\pi$
$444$	3.07615	0.145988
$445$	16.6354	0.788595
$446$	5.84430	0.276736
$447$	−9.09659	−0.430254
$448$	7.14927	0.337771
$449$	23.0899	1.08968	0.544841	−	0.838540i	$-0.316590\pi$
$449$	23.0899	1.08968	0.544841	+	0.838540i	$0.316590\pi$
$450$	−7.53295	−0.355106
$451$	−2.10245	−0.0990003
$452$	16.5330	0.777649
$453$	1.08059	0.0507707
$454$	2.02157	0.0948770
$455$	−6.12694	−0.287235
$456$	−2.47597	−0.115948
$457$	10.2211	0.478123	0.239062	−	0.971004i	$-0.423160\pi$
$457$	10.2211	0.478123	0.239062	+	0.971004i	$0.423160\pi$
$458$	5.89450	0.275432
$459$	6.72822	0.314047
$460$	−14.7833	−0.689276
$461$	8.49927	0.395850	0.197925	−	0.980217i	$-0.436580\pi$
$461$	8.49927	0.395850	0.197925	+	0.980217i	$0.436580\pi$
$462$	−0.100933	−0.00469585
$463$	−15.9838	−0.742832	−0.371416	−	0.928466i	$-0.621128\pi$
$463$	−15.9838	−0.742832	−0.371416	+	0.928466i	$0.621128\pi$
$464$	−26.9489	−1.25107
$465$	−4.96162	−0.230090
$466$	5.53912	0.256595
$467$	14.8431	0.686859	0.343429	−	0.939179i	$-0.388411\pi$
$467$	14.8431	0.686859	0.343429	+	0.939179i	$0.388411\pi$
$468$	−5.18653	−0.239747
$469$	−8.52210	−0.393514
$470$	−18.4744	−0.852161
$471$	0.0298742	0.00137653
$472$	18.8444	0.867385
$473$	−2.26091	−0.103957
$474$	−0.534846	−0.0245663
$475$	−24.5053	−1.12438
$476$	10.1573	0.465559
$477$	−26.5884	−1.21740
$478$	−5.21068	−0.238331
$479$	−10.3122	−0.471178	−0.235589	−	0.971853i	$-0.575702\pi$
$479$	−10.3122	−0.471178	−0.235589	+	0.971853i	$0.575702\pi$
$480$	5.70996	0.260623
$481$	−4.49648	−0.205022
$482$	1.89494	0.0863123
$483$	−1.69118	−0.0769515
$484$	19.7547	0.897939
$485$	54.2258	2.46227
$486$	−4.10672	−0.186284
$487$	−30.4294	−1.37889	−0.689443	−	0.724340i	$-0.742145\pi$
$487$	−30.4294	−1.37889	−0.689443	+	0.724340i	$0.742145\pi$
$488$	−3.46867	−0.157019
$489$	2.01836	0.0912733
$490$	5.20417	0.235101
$491$	−26.3491	−1.18912	−0.594559	−	0.804052i	$-0.702673\pi$
$491$	−26.3491	−1.18912	−0.594559	+	0.804052i	$0.702673\pi$
$492$	4.24655	0.191449
$493$	−28.0897	−1.26510
$494$	1.72174	0.0774649
$495$	−3.22864	−0.145117
$496$	−11.5350	−0.517937
$497$	23.9587	1.07469
$498$	−0.982612	−0.0440319
$499$	−25.5607	−1.14426	−0.572128	−	0.820165i	$-0.693882\pi$
$499$	−25.5607	−1.14426	−0.572128	+	0.820165i	$0.693882\pi$
$500$	6.80967	0.304538
$501$	3.01409	0.134660
$502$	−0.633072	−0.0282554
$503$	−9.45615	−0.421629	−0.210814	−	0.977526i	$-0.567612\pi$
$503$	−9.45615	−0.421629	−0.210814	+	0.977526i	$0.567612\pi$
$504$	−8.61839	−0.383894
$505$	−33.9830	−1.51222
$506$	0.355983	0.0158254
$507$	−0.376968	−0.0167417
$508$	−23.1854	−1.02868
$509$	15.0583	0.667446	0.333723	−	0.942671i	$-0.391695\pi$
$509$	15.0583	0.667446	0.333723	+	0.942671i	$0.391695\pi$
$510$	1.64863	0.0730024
$511$	9.40546	0.416073
$512$	22.8724	1.01083
$513$	−8.83488	−0.390069
$514$	6.75856	0.298107
$515$	−3.33541	−0.146976
$516$	4.56662	0.201034
$517$	−4.35944	−0.191728
$518$	−3.55451	−0.156176
$519$	−0.417271	−0.0183162
$520$	−5.47565	−0.240123
$521$	23.7854	1.04206	0.521028	−	0.853540i	$-0.325549\pi$
$521$	23.7854	1.04206	0.521028	+	0.853540i	$0.325549\pi$
$522$	11.3384	0.496269
$523$	44.6303	1.95155	0.975774	−	0.218780i	$-0.0702076\pi$
$523$	44.6303	1.95155	0.975774	+	0.218780i	$0.0702076\pi$
$524$	0.285420	0.0124686
$525$	4.24134	0.185107
$526$	12.0396	0.524953
$527$	−12.0233	−0.523743
$528$	0.373230	0.0162427
$529$	−17.0354	−0.740667
$530$	−13.3539	−0.580057
$531$	32.8052	1.42363
$532$	−13.3376	−0.578259
$533$	−6.20728	−0.268867
$534$	0.809100	0.0350132
$535$	14.1985	0.613855
$536$	−7.61621	−0.328970
$537$	−6.27800	−0.270916
$538$	6.84574	0.295141
$539$	1.22804	0.0528954
$540$	13.3667	0.575213
$541$	40.0173	1.72048	0.860238	−	0.509892i	$-0.170315\pi$
$541$	40.0173	1.72048	0.860238	+	0.509892i	$0.170315\pi$
$542$	−10.0335	−0.430978
$543$	−1.20562	−0.0517379
$544$	13.8367	0.593245
$545$	1.87379	0.0802642
$546$	−0.297997	−0.0127531
$547$	1.98079	0.0846927	0.0423463	−	0.999103i	$-0.486517\pi$
$547$	1.98079	0.0846927	0.0423463	+	0.999103i	$0.486517\pi$
$548$	27.3732	1.16932
$549$	−6.03842	−0.257713
$550$	−0.892775	−0.0380681
$551$	36.8847	1.57134
$552$	−1.51141	−0.0643300
$553$	−6.05626	−0.257538
$554$	5.82520	0.247489
$555$	5.65362	0.239983
$556$	20.3751	0.864097
$557$	−16.7428	−0.709417	−0.354709	−	0.934977i	$-0.615420\pi$
$557$	−16.7428	−0.709417	−0.354709	+	0.934977i	$0.615420\pi$
$558$	4.85321	0.205453
$559$	−6.67514	−0.282328
$560$	17.9098	0.756829
$561$	0.389029	0.0164248
$562$	−1.36889	−0.0577433
$563$	−3.64413	−0.153582	−0.0767908	−	0.997047i	$-0.524467\pi$
$563$	−3.64413	−0.153582	−0.0767908	+	0.997047i	$0.524467\pi$
$564$	8.80525	0.370768
$565$	30.3859	1.27835
$566$	7.87707	0.331098
$567$	−14.2202	−0.597191
$568$	21.4119	0.898424
$569$	44.8872	1.88177	0.940885	−	0.338726i	$-0.109996\pi$
$569$	44.8872	1.88177	0.940885	+	0.338726i	$0.109996\pi$
$570$	−2.16482	−0.0906744
$571$	−12.6632	−0.529937	−0.264968	−	0.964257i	$-0.585361\pi$
$571$	−12.6632	−0.529937	−0.264968	+	0.964257i	$0.585361\pi$
$572$	−0.614687	−0.0257013
$573$	−6.24156	−0.260745
$574$	−4.90692	−0.204811
$575$	−14.9588	−0.623826
$576$	11.1228	0.463450
$577$	−15.9147	−0.662538	−0.331269	−	0.943536i	$-0.607477\pi$
$577$	−15.9147	−0.662538	−0.331269	+	0.943536i	$0.607477\pi$
$578$	−3.32076	−0.138125
$579$	5.91944	0.246004
$580$	−55.8049	−2.31717
$581$	−11.1265	−0.461604
$582$	2.63739	0.109323
$583$	−3.15115	−0.130507
$584$	8.40567	0.347829
$585$	−9.53226	−0.394111
$586$	−7.30247	−0.301662
$587$	36.3926	1.50209	0.751043	−	0.660254i	$-0.229551\pi$
$587$	36.3926	1.50209	0.751043	+	0.660254i	$0.229551\pi$
$588$	−2.48041	−0.102290
$589$	15.7879	0.650529
$590$	16.4763	0.678319
$591$	−5.50685	−0.226522
$592$	13.1438	0.540207
$593$	31.2761	1.28435	0.642177	−	0.766556i	$-0.278031\pi$
$593$	31.2761	1.28435	0.642177	+	0.766556i	$0.278031\pi$
$594$	−0.321872	−0.0132066
$595$	18.6680	0.765314
$596$	−43.7930	−1.79383
$597$	−3.57318	−0.146240
$598$	1.05101	0.0429789
$599$	−29.8080	−1.21792	−0.608960	−	0.793201i	$-0.708413\pi$
$599$	−29.8080	−1.21792	−0.608960	+	0.793201i	$0.708413\pi$
$600$	3.79049	0.154746
$601$	13.3222	0.543424	0.271712	−	0.962379i	$-0.412410\pi$
$601$	13.3222	0.543424	0.271712	+	0.962379i	$0.412410\pi$
$602$	−5.27676	−0.215065
$603$	−13.2587	−0.539934
$604$	5.20221	0.211675
$605$	36.3069	1.47609
$606$	−1.65284	−0.0671419
$607$	−17.8860	−0.725971	−0.362985	−	0.931795i	$-0.618242\pi$
$607$	−17.8860	−0.725971	−0.362985	+	0.931795i	$0.618242\pi$
$608$	−18.1691	−0.736855
$609$	−6.38396	−0.258691
$610$	−3.03278	−0.122794
$611$	−12.8709	−0.520699
$612$	15.8027	0.638786
$613$	−25.1852	−1.01722	−0.508610	−	0.860997i	$-0.669840\pi$
$613$	−25.1852	−1.01722	−0.508610	+	0.860997i	$0.669840\pi$
$614$	0.701396	0.0283060
$615$	7.80469	0.314715
$616$	−1.02142	−0.0411541
$617$	28.2744	1.13829	0.569143	−	0.822238i	$-0.307275\pi$
$617$	28.2744	1.13829	0.569143	+	0.822238i	$0.307275\pi$
$618$	−0.162225	−0.00652565
$619$	5.21213	0.209493	0.104746	−	0.994499i	$-0.466597\pi$
$619$	5.21213	0.209493	0.104746	+	0.994499i	$0.466597\pi$
$620$	−23.8863	−0.959298
$621$	−5.39310	−0.216418
$622$	13.7695	0.552107
$623$	9.16174	0.367057
$624$	1.10193	0.0441124
$625$	−18.1095	−0.724380
$626$	−7.24873	−0.289718
$627$	−0.510837	−0.0204009
$628$	0.143821	0.00573908
$629$	13.7002	0.546264
$630$	−7.53535	−0.300215
$631$	−1.98097	−0.0788613	−0.0394306	−	0.999222i	$-0.512554\pi$
$631$	−1.98097	−0.0788613	−0.0394306	+	0.999222i	$0.512554\pi$
$632$	−5.41249	−0.215297
$633$	8.92374	0.354687
$634$	−6.05457	−0.240458
$635$	−42.6122	−1.69101
$636$	6.36473	0.252378
$637$	3.62567	0.143654
$638$	1.34378	0.0532009
$639$	37.2748	1.47457
$640$	35.8805	1.41830
$641$	36.1857	1.42925	0.714625	−	0.699508i	$-0.246598\pi$
$641$	36.1857	1.42925	0.714625	+	0.699508i	$0.246598\pi$
$642$	0.690575	0.0272548
$643$	−12.9173	−0.509410	−0.254705	−	0.967019i	$-0.581978\pi$
$643$	−12.9173	−0.509410	−0.254705	+	0.967019i	$0.581978\pi$
$644$	−8.14172	−0.320829
$645$	8.39294	0.330472
$646$	−5.24593	−0.206399
$647$	−17.5538	−0.690112	−0.345056	−	0.938582i	$-0.612140\pi$
$647$	−17.5538	−0.690112	−0.345056	+	0.938582i	$0.612140\pi$
$648$	−12.7086	−0.499240
$649$	3.88795	0.152615
$650$	−2.63584	−0.103386
$651$	−2.73255	−0.107097
$652$	9.71681	0.380540
$653$	36.0454	1.41057	0.705283	−	0.708926i	$-0.250820\pi$
$653$	36.0454	1.41057	0.705283	+	0.708926i	$0.250820\pi$
$654$	0.0911357	0.00356369
$655$	0.524571	0.0204967
$656$	18.1447	0.708432
$657$	14.6330	0.570887
$658$	−10.1745	−0.396645
$659$	0.698256	0.0272002	0.0136001	−	0.999908i	$-0.495671\pi$
$659$	0.698256	0.0272002	0.0136001	+	0.999908i	$0.495671\pi$
$660$	0.772872	0.0300840
$661$	2.62668	0.102166	0.0510830	−	0.998694i	$-0.483733\pi$
$661$	2.62668	0.102166	0.0510830	+	0.998694i	$0.483733\pi$
$662$	8.70104	0.338175
$663$	1.14857	0.0446069
$664$	−9.94375	−0.385892
$665$	−24.5131	−0.950577
$666$	−5.53010	−0.214287
$667$	22.5157	0.871810
$668$	14.5105	0.561428
$669$	−5.11945	−0.197929
$670$	−6.65911	−0.257264
$671$	−0.715650	−0.0276274
$672$	3.14468	0.121309
$673$	20.7971	0.801669	0.400835	−	0.916150i	$-0.368720\pi$
$673$	20.7971	0.801669	0.400835	+	0.916150i	$0.368720\pi$
$674$	8.98837	0.346219
$675$	13.5254	0.520594
$676$	−1.81481	−0.0698002
$677$	26.5035	1.01861	0.509307	−	0.860585i	$-0.329902\pi$
$677$	26.5035	1.01861	0.509307	+	0.860585i	$0.329902\pi$
$678$	1.47789	0.0567578
$679$	29.8642	1.14608
$680$	16.6836	0.639788
$681$	−1.77084	−0.0678588
$682$	0.575184	0.0220249
$683$	6.33721	0.242487	0.121243	−	0.992623i	$-0.461312\pi$
$683$	6.33721	0.242487	0.121243	+	0.992623i	$0.461312\pi$
$684$	−20.7506	−0.793420
$685$	50.3089	1.92220
$686$	8.39970	0.320702
$687$	−5.16342	−0.196997
$688$	19.5123	0.743900
$689$	−9.30348	−0.354434
$690$	−1.32148	−0.0503078
$691$	−34.0834	−1.29659	−0.648296	−	0.761388i	$-0.724518\pi$
$691$	−34.0834	−1.29659	−0.648296	+	0.761388i	$0.724518\pi$
$692$	−2.00883	−0.0763644
$693$	−1.77813	−0.0675456
$694$	−5.29599	−0.201033
$695$	37.4472	1.42045
$696$	−5.70535	−0.216261
$697$	18.9128	0.716374
$698$	6.82658	0.258390
$699$	−4.85212	−0.183524
$700$	20.4187	0.771756
$701$	42.8818	1.61962	0.809811	−	0.586691i	$-0.199570\pi$
$701$	42.8818	1.61962	0.809811	+	0.586691i	$0.199570\pi$
$702$	−0.950297	−0.0358667
$703$	−17.9899	−0.678500
$704$	1.31823	0.0496827
$705$	16.1831	0.609490
$706$	−1.92177	−0.0723267
$707$	−18.7157	−0.703875
$708$	−7.85292	−0.295131
$709$	−45.0314	−1.69119	−0.845594	−	0.533827i	$-0.820753\pi$
$709$	−45.0314	−1.69119	−0.845594	+	0.533827i	$0.820753\pi$
$710$	18.7212	0.702592
$711$	−9.42231	−0.353364
$712$	8.18786	0.306853
$713$	9.63744	0.360925
$714$	0.907959	0.0339795
$715$	−1.12973	−0.0422494
$716$	−30.2237	−1.12951
$717$	4.56441	0.170461
$718$	−10.9693	−0.409369
$719$	0.351667	0.0131150	0.00655749	−	0.999978i	$-0.497913\pi$
$719$	0.351667	0.0131150	0.00655749	+	0.999978i	$0.497913\pi$
$720$	27.8641	1.03843
$721$	−1.83693	−0.0684110
$722$	−1.28802	−0.0479353
$723$	−1.65992	−0.0617330
$724$	−5.80410	−0.215708
$725$	−56.4673	−2.09714
$726$	1.76586	0.0655374
$727$	−43.4921	−1.61303	−0.806516	−	0.591212i	$-0.798650\pi$
$727$	−43.4921	−1.61303	−0.806516	+	0.591212i	$0.798650\pi$
$728$	−3.01564	−0.111767
$729$	−19.6264	−0.726903
$730$	7.34936	0.272012
$731$	20.3383	0.752239
$732$	1.44548	0.0534264
$733$	11.1718	0.412641	0.206321	−	0.978484i	$-0.433851\pi$
$733$	11.1718	0.412641	0.206321	+	0.978484i	$0.433851\pi$
$734$	−0.522693	−0.0192929
$735$	−4.55871	−0.168151
$736$	−11.0910	−0.408820
$737$	−1.57136	−0.0578819
$738$	−7.63416	−0.281017
$739$	−19.8848	−0.731474	−0.365737	−	0.930718i	$-0.619183\pi$
$739$	−19.8848	−0.731474	−0.365737	+	0.930718i	$0.619183\pi$
$740$	27.2178	1.00055
$741$	−1.50820	−0.0554051
$742$	−7.35449	−0.269992
$743$	−11.0157	−0.404126	−0.202063	−	0.979373i	$-0.564765\pi$
$743$	−11.0157	−0.404126	−0.202063	+	0.979373i	$0.564765\pi$
$744$	−2.44208	−0.0895310
$745$	−80.4867	−2.94880
$746$	−2.25613	−0.0826028
$747$	−17.3105	−0.633359
$748$	1.87287	0.0684790
$749$	7.81964	0.285724
$750$	0.608715	0.0222271
$751$	29.1396	1.06332	0.531660	−	0.846958i	$-0.321568\pi$
$751$	29.1396	1.06332	0.531660	+	0.846958i	$0.321568\pi$
$752$	37.6232	1.37198
$753$	0.554554	0.0202091
$754$	3.96740	0.144484
$755$	9.56109	0.347964
$756$	7.36156	0.267737
$757$	−8.23965	−0.299475	−0.149738	−	0.988726i	$-0.547843\pi$
$757$	−8.23965	−0.299475	−0.149738	+	0.988726i	$0.547843\pi$
$758$	5.66148	0.205634
$759$	−0.311832	−0.0113188
$760$	−21.9074	−0.794664
$761$	−35.2992	−1.27960	−0.639798	−	0.768543i	$-0.720982\pi$
$761$	−35.2992	−1.27960	−0.639798	+	0.768543i	$0.720982\pi$
$762$	−2.07253	−0.0750800
$763$	1.03196	0.0373596
$764$	−30.0483	−1.08711
$765$	29.0436	1.05007
$766$	10.5905	0.382651
$767$	11.4788	0.414476
$768$	−1.18916	−0.0429101
$769$	7.03928	0.253843	0.126921	−	0.991913i	$-0.459490\pi$
$769$	7.03928	0.253843	0.126921	+	0.991913i	$0.459490\pi$
$770$	−0.893060	−0.0321836
$771$	−5.92031	−0.213215
$772$	28.4975	1.02565
$773$	28.6926	1.03200	0.516000	−	0.856588i	$-0.327420\pi$
$773$	28.6926	1.03200	0.516000	+	0.856588i	$0.327420\pi$
$774$	−8.20956	−0.295087
$775$	−24.1699	−0.868207
$776$	26.6896	0.958102
$777$	3.11366	0.111702
$778$	11.2315	0.402667
$779$	−24.8345	−0.889790
$780$	2.28183	0.0817028
$781$	4.41767	0.158077
$782$	−3.20229	−0.114514
$783$	−20.3581	−0.727540
$784$	−10.5983	−0.378511
$785$	0.264327	0.00943424
$786$	0.0255136	0.000910041 0
$787$	41.9818	1.49649	0.748244	−	0.663423i	$-0.230897\pi$
$787$	41.9818	1.49649	0.748244	+	0.663423i	$0.230897\pi$
$788$	−26.5112	−0.944422
$789$	−10.5464	−0.375461
$790$	−4.73232	−0.168368
$791$	16.7346	0.595016
$792$	−1.58912	−0.0564668
$793$	−2.11289	−0.0750309
$794$	9.40474	0.333762
$795$	11.6977	0.414874
$796$	−17.2021	−0.609711
$797$	−44.5287	−1.57729	−0.788644	−	0.614850i	$-0.789216\pi$
$797$	−44.5287	−1.57729	−0.788644	+	0.614850i	$0.789216\pi$
$798$	−1.19225	−0.0422051
$799$	39.2159	1.38736
$800$	27.8153	0.983420
$801$	14.2538	0.503633
$802$	9.96129	0.351745
$803$	1.73424	0.0612001
$804$	3.17386	0.111933
$805$	−14.9636	−0.527397
$806$	1.69818	0.0598157
$807$	−5.99669	−0.211093
$808$	−16.7262	−0.588426
$809$	−3.61943	−0.127252	−0.0636261	−	0.997974i	$-0.520267\pi$
$809$	−3.61943	−0.127252	−0.0636261	+	0.997974i	$0.520267\pi$
$810$	−11.1115	−0.390420
$811$	−37.8646	−1.32961	−0.664803	−	0.747018i	$-0.731485\pi$
$811$	−37.8646	−1.32961	−0.664803	+	0.747018i	$0.731485\pi$
$812$	−30.7338	−1.07854
$813$	8.78912	0.308248
$814$	−0.655406	−0.0229720
$815$	17.8584	0.625554
$816$	−3.35743	−0.117534
$817$	−26.7064	−0.934337
$818$	10.7553	0.376050
$819$	−5.24977	−0.183442
$820$	37.5735	1.31212
$821$	31.6502	1.10460	0.552301	−	0.833645i	$-0.313750\pi$
$821$	31.6502	1.10460	0.552301	+	0.833645i	$0.313750\pi$
$822$	2.44688	0.0853448
$823$	2.10927	0.0735244	0.0367622	−	0.999324i	$-0.488296\pi$
$823$	2.10927	0.0735244	0.0367622	+	0.999324i	$0.488296\pi$
$824$	−1.64167	−0.0571903
$825$	0.782047	0.0272274
$826$	9.07411	0.315729
$827$	−48.0575	−1.67112	−0.835562	−	0.549397i	$-0.814858\pi$
$827$	−48.0575	−1.67112	−0.835562	+	0.549397i	$0.814858\pi$
$828$	−12.6669	−0.440204
$829$	−36.6568	−1.27314	−0.636572	−	0.771217i	$-0.719648\pi$
$829$	−36.6568	−1.27314	−0.636572	+	0.771217i	$0.719648\pi$
$830$	−8.69416	−0.301779
$831$	−5.10272	−0.177011
$832$	3.89196	0.134929
$833$	−11.0470	−0.382755
$834$	1.82133	0.0630674
$835$	26.6687	0.922908
$836$	−2.45928	−0.0850561
$837$	−8.71395	−0.301198
$838$	−2.31067	−0.0798209
$839$	−17.2006	−0.593832	−0.296916	−	0.954904i	$-0.595958\pi$
$839$	−17.2006	−0.593832	−0.296916	+	0.954904i	$0.595958\pi$
$840$	3.79170	0.130826
$841$	55.9932	1.93080
$842$	−11.2439	−0.387489
$843$	1.19911	0.0412997
$844$	42.9608	1.47877
$845$	−3.33541	−0.114742
$846$	−15.8295	−0.544230
$847$	19.9955	0.687055
$848$	27.1953	0.933891
$849$	−6.90010	−0.236811
$850$	8.03106	0.275463
$851$	−10.9816	−0.376444
$852$	−8.92285	−0.305692
$853$	−24.6734	−0.844800	−0.422400	−	0.906410i	$-0.638812\pi$
$853$	−24.6734	−0.844800	−0.422400	+	0.906410i	$0.638812\pi$
$854$	−1.67026	−0.0571552
$855$	−38.1374	−1.30427
$856$	6.98842	0.238859
$857$	43.6041	1.48949	0.744743	−	0.667351i	$-0.232572\pi$
$857$	43.6041	1.48949	0.744743	+	0.667351i	$0.232572\pi$
$858$	−0.0549467	−0.00187585
$859$	20.8660	0.711939	0.355970	−	0.934498i	$-0.384151\pi$
$859$	20.8660	0.711939	0.355970	+	0.934498i	$0.384151\pi$
$860$	40.4054	1.37781
$861$	4.29833	0.146487
$862$	−8.61206	−0.293328
$863$	17.0774	0.581322	0.290661	−	0.956826i	$-0.406125\pi$
$863$	17.0774	0.581322	0.290661	+	0.956826i	$0.406125\pi$
$864$	10.0282	0.341168
$865$	−3.69201	−0.125532
$866$	−11.5268	−0.391698
$867$	2.90889	0.0987912
$868$	−13.1551	−0.446512
$869$	−1.11669	−0.0378813
$870$	−4.98838	−0.169122
$871$	−4.63931	−0.157197
$872$	0.922267	0.0312319
$873$	46.4625	1.57252
$874$	4.20495	0.142235
$875$	6.89270	0.233016
$876$	−3.50284	−0.118350
$877$	27.8466	0.940313	0.470157	−	0.882583i	$-0.344197\pi$
$877$	27.8466	0.940313	0.470157	+	0.882583i	$0.344197\pi$
$878$	−2.19233	−0.0739877
$879$	6.39677	0.215758
$880$	3.30234	0.111322
$881$	24.7370	0.833412	0.416706	−	0.909041i	$-0.363185\pi$
$881$	24.7370	0.833412	0.416706	+	0.909041i	$0.363185\pi$
$882$	4.45911	0.150146
$883$	−40.1010	−1.34951	−0.674754	−	0.738043i	$-0.735750\pi$
$883$	−40.1010	−1.34951	−0.674754	+	0.738043i	$0.735750\pi$
$884$	5.52949	0.185977
$885$	−14.4328	−0.485153
$886$	−10.2438	−0.344149
$887$	27.0214	0.907289	0.453644	−	0.891183i	$-0.350124\pi$
$887$	27.0214	0.907289	0.453644	+	0.891183i	$0.350124\pi$
$888$	2.78268	0.0933806
$889$	−23.4681	−0.787094
$890$	7.15892	0.239967
$891$	−2.62201	−0.0878407
$892$	−24.6461	−0.825214
$893$	−51.4946	−1.72320
$894$	−3.91464	−0.130925
$895$	−55.5478	−1.85676
$896$	19.7607	0.660160
$897$	−0.920655	−0.0307398
$898$	9.93656	0.331587
$899$	36.3799	1.21334
$900$	31.7674	1.05891
$901$	28.3465	0.944360
$902$	−0.904771	−0.0301256
$903$	4.62230	0.153821
$904$	14.9558	0.497422
$905$	−10.6673	−0.354593
$906$	0.465024	0.0154494
$907$	59.4928	1.97542	0.987712	−	0.156283i	$-0.0499512\pi$
$907$	59.4928	1.97542	0.987712	+	0.156283i	$0.0499512\pi$
$908$	−8.52522	−0.282919
$909$	−29.1178	−0.965775
$910$	−2.63668	−0.0874050
$911$	2.73622	0.0906550	0.0453275	−	0.998972i	$-0.485567\pi$
$911$	2.73622	0.0906550	0.0453275	+	0.998972i	$0.485567\pi$
$912$	4.40867	0.145986
$913$	−2.05158	−0.0678973
$914$	4.39857	0.145492
$915$	2.65663	0.0878255
$916$	−24.8578	−0.821326
$917$	0.288900	0.00954033
$918$	2.89544	0.0955637
$919$	−17.2079	−0.567636	−0.283818	−	0.958878i	$-0.591601\pi$
$919$	−17.2079	−0.567636	−0.283818	+	0.958878i	$0.591601\pi$
$920$	−13.3730	−0.440894
$921$	−0.614404	−0.0202453
$922$	3.65759	0.120456
$923$	13.0428	0.429308
$924$	0.425649	0.0140028
$925$	27.5409	0.905539
$926$	−6.87852	−0.226042
$927$	−2.85790	−0.0938656
$928$	−41.8669	−1.37435
$929$	30.3143	0.994581	0.497290	−	0.867584i	$-0.334328\pi$
$929$	30.3143	0.994581	0.497290	+	0.867584i	$0.334328\pi$
$930$	−2.13519	−0.0700157
$931$	14.5058	0.475410
$932$	−23.3592	−0.765155
$933$	−12.0617	−0.394883
$934$	6.38762	0.209009
$935$	3.44213	0.112570
$936$	−4.69172	−0.153354
$937$	−0.119654	−0.00390892	−0.00195446	−	0.999998i	$-0.500622\pi$
$937$	−0.119654	−0.00390892	−0.00195446	+	0.999998i	$0.500622\pi$
$938$	−3.66742	−0.119745
$939$	6.34969	0.207214
$940$	77.9089	2.54111
$941$	17.6288	0.574683	0.287342	−	0.957828i	$-0.407228\pi$
$941$	17.6288	0.574683	0.287342	+	0.957828i	$0.407228\pi$
$942$	0.0128561	0.000418875 0
$943$	−15.1598	−0.493671
$944$	−33.5541	−1.09209
$945$	13.5297	0.440122
$946$	−0.972965	−0.0316338
$947$	−46.4814	−1.51044	−0.755222	−	0.655469i	$-0.772471\pi$
$947$	−46.4814	−1.51044	−0.755222	+	0.655469i	$0.772471\pi$
$948$	2.25551	0.0732557
$949$	5.12019	0.166208
$950$	−10.5456	−0.342146
$951$	5.30364	0.171982
$952$	9.18828	0.297794
$953$	3.35495	0.108678	0.0543388	−	0.998523i	$-0.482695\pi$
$953$	3.35495	0.108678	0.0543388	+	0.998523i	$0.482695\pi$
$954$	−11.4421	−0.370451
$955$	−55.2254	−1.78705
$956$	21.9741	0.710692
$957$	−1.17712	−0.0380508
$958$	−4.43778	−0.143378
$959$	27.7070	0.894705
$960$	−4.89353	−0.157938
$961$	−15.4282	−0.497684
$962$	−1.93502	−0.0623877
$963$	12.1658	0.392036
$964$	−7.99121	−0.257380
$965$	52.3753	1.68602
$966$	−0.727787	−0.0234162
$967$	−26.2329	−0.843592	−0.421796	−	0.906691i	$-0.638600\pi$
$967$	−26.2329	−0.843592	−0.421796	+	0.906691i	$0.638600\pi$
$968$	17.8700	0.574365
$969$	4.59530	0.147622
$970$	23.3356	0.749262
$971$	48.7629	1.56488	0.782439	−	0.622728i	$-0.213976\pi$
$971$	48.7629	1.56488	0.782439	+	0.622728i	$0.213976\pi$
$972$	17.3185	0.555492
$973$	20.6236	0.661161
$974$	−13.0950	−0.419592
$975$	2.30892	0.0739447
$976$	6.17626	0.197697
$977$	27.5047	0.879953	0.439976	−	0.898009i	$-0.354987\pi$
$977$	27.5047	0.879953	0.439976	+	0.898009i	$0.354987\pi$
$978$	0.868584	0.0277742
$979$	1.68930	0.0539904
$980$	−21.9466	−0.701060
$981$	1.60552	0.0512605
$982$	−11.3391	−0.361846
$983$	−0.590646	−0.0188387	−0.00941935	−	0.999956i	$-0.502998\pi$
$983$	−0.590646	−0.0188387	−0.00941935	+	0.999956i	$0.502998\pi$
$984$	3.84142	0.122460
$985$	−48.7246	−1.55250
$986$	−12.0882	−0.384966
$987$	8.91262	0.283692
$988$	−7.26081	−0.230997
$989$	−16.3024	−0.518387
$990$	−1.38942	−0.0441586
$991$	−9.59168	−0.304690	−0.152345	−	0.988327i	$-0.548682\pi$
$991$	−9.59168	−0.304690	−0.152345	+	0.988327i	$0.548682\pi$
$992$	−17.9204	−0.568974
$993$	−7.62187	−0.241873
$994$	10.3104	0.327027
$995$	−31.6155	−1.00228
$996$	4.14380	0.131301
$997$	18.6827	0.591687	0.295843	−	0.955236i	$-0.404399\pi$
$997$	18.6827	0.591687	0.295843	+	0.955236i	$0.404399\pi$
$998$	−10.9999	−0.348194
$999$	9.92930	0.314149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.g.1.17	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.g.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+0.430342 q^{2} -0.376968 q^{3} -1.81481 q^{4} -3.33541 q^{5} -0.162225 q^{6} -1.83693 q^{7} -1.64167 q^{8} -2.85790 q^{9} +O(q^{10})\)	\(q+0.430342 q^{2} -0.376968 q^{3} -1.81481 q^{4} -3.33541 q^{5} -0.162225 q^{6} -1.83693 q^{7} -1.64167 q^{8} -2.85790 q^{9} -1.43537 q^{10} -0.338707 q^{11} +0.684123 q^{12} -1.00000 q^{13} -0.790510 q^{14} +1.25734 q^{15} +2.92313 q^{16} +3.04687 q^{17} -1.22987 q^{18} -4.00087 q^{19} +6.05313 q^{20} +0.692465 q^{21} -0.145760 q^{22} -2.44226 q^{23} +0.618857 q^{24} +6.12498 q^{25} -0.430342 q^{26} +2.20824 q^{27} +3.33368 q^{28} -9.21918 q^{29} +0.541088 q^{30} -3.94611 q^{31} +4.54129 q^{32} +0.127681 q^{33} +1.31120 q^{34} +6.12694 q^{35} +5.18653 q^{36} +4.49648 q^{37} -1.72174 q^{38} +0.376968 q^{39} +5.47565 q^{40} +6.20728 q^{41} +0.297997 q^{42} +6.67514 q^{43} +0.614687 q^{44} +9.53226 q^{45} -1.05101 q^{46} +12.8709 q^{47} -1.10193 q^{48} -3.62567 q^{49} +2.63584 q^{50} -1.14857 q^{51} +1.81481 q^{52} +9.30348 q^{53} +0.950297 q^{54} +1.12973 q^{55} +3.01564 q^{56} +1.50820 q^{57} -3.96740 q^{58} -11.4788 q^{59} -2.28183 q^{60} +2.11289 q^{61} -1.69818 q^{62} +5.24977 q^{63} -3.89196 q^{64} +3.33541 q^{65} +0.0549467 q^{66} +4.63931 q^{67} -5.52949 q^{68} +0.920655 q^{69} +2.63668 q^{70} -13.0428 q^{71} +4.69172 q^{72} -5.12019 q^{73} +1.93502 q^{74} -2.30892 q^{75} +7.26081 q^{76} +0.622182 q^{77} +0.162225 q^{78} +3.29694 q^{79} -9.74985 q^{80} +7.74125 q^{81} +2.67125 q^{82} +6.05709 q^{83} -1.25669 q^{84} -10.1626 q^{85} +2.87259 q^{86} +3.47533 q^{87} +0.556045 q^{88} -4.98751 q^{89} +4.10213 q^{90} +1.83693 q^{91} +4.43223 q^{92} +1.48756 q^{93} +5.53887 q^{94} +13.3446 q^{95} -1.71192 q^{96} -16.2576 q^{97} -1.56028 q^{98} +0.967988 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) \) 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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