LMFDB - Embedded newform 1339.2.a.g.1.14

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			1.14
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)

$f(q)$	$=$	$q-0.496151 q^{2} -2.36213 q^{3} -1.75383 q^{4} +0.249222 q^{5} +1.17197 q^{6} +2.50523 q^{7} +1.86247 q^{8} +2.57965 q^{9} +O(q^{10})$	\(q-0.496151 q^{2} -2.36213 q^{3} -1.75383 q^{4} +0.249222 q^{5} +1.17197 q^{6} +2.50523 q^{7} +1.86247 q^{8} +2.57965 q^{9} -0.123652 q^{10} +2.05797 q^{11} +4.14278 q^{12} -1.00000 q^{13} -1.24297 q^{14} -0.588694 q^{15} +2.58360 q^{16} -2.77299 q^{17} -1.27990 q^{18} -2.77323 q^{19} -0.437094 q^{20} -5.91767 q^{21} -1.02107 q^{22} +2.51192 q^{23} -4.39939 q^{24} -4.93789 q^{25} +0.496151 q^{26} +0.992910 q^{27} -4.39376 q^{28} -7.57153 q^{29} +0.292081 q^{30} -5.75886 q^{31} -5.00679 q^{32} -4.86120 q^{33} +1.37582 q^{34} +0.624357 q^{35} -4.52429 q^{36} +7.93611 q^{37} +1.37594 q^{38} +2.36213 q^{39} +0.464168 q^{40} +6.45627 q^{41} +2.93606 q^{42} +11.2975 q^{43} -3.60935 q^{44} +0.642906 q^{45} -1.24629 q^{46} +1.45058 q^{47} -6.10280 q^{48} -0.723829 q^{49} +2.44994 q^{50} +6.55015 q^{51} +1.75383 q^{52} -5.59954 q^{53} -0.492633 q^{54} +0.512892 q^{55} +4.66591 q^{56} +6.55072 q^{57} +3.75662 q^{58} +0.863531 q^{59} +1.03247 q^{60} +12.5172 q^{61} +2.85726 q^{62} +6.46263 q^{63} -2.68308 q^{64} -0.249222 q^{65} +2.41189 q^{66} -4.58553 q^{67} +4.86336 q^{68} -5.93348 q^{69} -0.309776 q^{70} +13.4190 q^{71} +4.80453 q^{72} +4.17719 q^{73} -3.93751 q^{74} +11.6639 q^{75} +4.86378 q^{76} +5.15570 q^{77} -1.17197 q^{78} -11.4734 q^{79} +0.643890 q^{80} -10.0843 q^{81} -3.20329 q^{82} -8.71013 q^{83} +10.3786 q^{84} -0.691088 q^{85} -5.60526 q^{86} +17.8849 q^{87} +3.83291 q^{88} +15.4599 q^{89} -0.318978 q^{90} -2.50523 q^{91} -4.40549 q^{92} +13.6032 q^{93} -0.719705 q^{94} -0.691149 q^{95} +11.8267 q^{96} +8.40596 q^{97} +0.359129 q^{98} +5.30886 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.496151	−0.350832	−0.175416	−	0.984494i	$-0.556127\pi$
$2$	−0.496151	−0.350832	−0.175416	+	0.984494i	$0.556127\pi$
$3$	−2.36213	−1.36378	−0.681888	−	0.731457i	$-0.738841\pi$
$3$	−2.36213	−1.36378	−0.681888	+	0.731457i	$0.738841\pi$
$4$	−1.75383	−0.876917
$5$	0.249222	0.111455	0.0557277	−	0.998446i	$-0.482252\pi$
$5$	0.249222	0.111455	0.0557277	+	0.998446i	$0.482252\pi$
$6$	1.17197	0.478456
$7$	2.50523	0.946887	0.473444	−	0.880824i	$-0.343011\pi$
$7$	2.50523	0.946887	0.473444	+	0.880824i	$0.343011\pi$
$8$	1.86247	0.658482
$9$	2.57965	0.859885
$10$	−0.123652	−0.0391021
$11$	2.05797	0.620503	0.310251	−	0.950655i	$-0.399587\pi$
$11$	2.05797	0.620503	0.310251	+	0.950655i	$0.399587\pi$
$12$	4.14278	1.19592
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.24297	−0.332198
$15$	−0.588694	−0.152000
$16$	2.58360	0.645901
$17$	−2.77299	−0.672548	−0.336274	−	0.941764i	$-0.609167\pi$
$17$	−2.77299	−0.672548	−0.336274	+	0.941764i	$0.609167\pi$
$18$	−1.27990	−0.301675
$19$	−2.77323	−0.636222	−0.318111	−	0.948053i	$-0.603048\pi$
$19$	−2.77323	−0.636222	−0.318111	+	0.948053i	$0.603048\pi$
$20$	−0.437094	−0.0977371
$21$	−5.91767	−1.29134
$22$	−1.02107	−0.217692
$23$	2.51192	0.523771	0.261886	−	0.965099i	$-0.415656\pi$
$23$	2.51192	0.523771	0.261886	+	0.965099i	$0.415656\pi$
$24$	−4.39939	−0.898022
$25$	−4.93789	−0.987578
$26$	0.496151	0.0973032
$27$	0.992910	0.191086
$28$	−4.39376	−0.830342
$29$	−7.57153	−1.40600	−0.702999	−	0.711191i	$-0.748156\pi$
$29$	−7.57153	−1.40600	−0.702999	+	0.711191i	$0.748156\pi$
$30$	0.292081	0.0533265
$31$	−5.75886	−1.03432	−0.517161	−	0.855888i	$-0.673011\pi$
$31$	−5.75886	−1.03432	−0.517161	+	0.855888i	$0.673011\pi$
$32$	−5.00679	−0.885085
$33$	−4.86120	−0.846226
$34$	1.37582	0.235951
$35$	0.624357	0.105536
$36$	−4.52429	−0.754048
$37$	7.93611	1.30469	0.652344	−	0.757923i	$-0.273786\pi$
$37$	7.93611	1.30469	0.652344	+	0.757923i	$0.273786\pi$
$38$	1.37594	0.223207
$39$	2.36213	0.378243
$40$	0.464168	0.0733913
$41$	6.45627	1.00830	0.504150	−	0.863616i	$-0.331806\pi$
$41$	6.45627	1.00830	0.504150	+	0.863616i	$0.331806\pi$
$42$	2.93606	0.453044
$43$	11.2975	1.72285	0.861426	−	0.507883i	$-0.169572\pi$
$43$	11.2975	1.72285	0.861426	+	0.507883i	$0.169572\pi$
$44$	−3.60935	−0.544129
$45$	0.642906	0.0958388
$46$	−1.24629	−0.183756
$47$	1.45058	0.211588	0.105794	−	0.994388i	$-0.466262\pi$
$47$	1.45058	0.211588	0.105794	+	0.994388i	$0.466262\pi$
$48$	−6.10280	−0.880864
$49$	−0.723829	−0.103404
$50$	2.44994	0.346474
$51$	6.55015	0.917204
$52$	1.75383	0.243213
$53$	−5.59954	−0.769156	−0.384578	−	0.923092i	$-0.625653\pi$
$53$	−5.59954	−0.769156	−0.384578	+	0.923092i	$0.625653\pi$
$54$	−0.492633	−0.0670389
$55$	0.512892	0.0691583
$56$	4.66591	0.623508
$57$	6.55072	0.867664
$58$	3.75662	0.493269
$59$	0.863531	0.112422	0.0562111	−	0.998419i	$-0.482098\pi$
$59$	0.863531	0.112422	0.0562111	+	0.998419i	$0.482098\pi$
$60$	1.03247	0.133291
$61$	12.5172	1.60266	0.801331	−	0.598222i	$-0.204126\pi$
$61$	12.5172	1.60266	0.801331	+	0.598222i	$0.204126\pi$
$62$	2.85726	0.362873
$63$	6.46263	0.814214
$64$	−2.68308	−0.335385
$65$	−0.249222	−0.0309121
$66$	2.41189	0.296883
$67$	−4.58553	−0.560211	−0.280106	−	0.959969i	$-0.590370\pi$
$67$	−4.58553	−0.560211	−0.280106	+	0.959969i	$0.590370\pi$
$68$	4.86336	0.589769
$69$	−5.93348	−0.714307
$70$	−0.309776	−0.0370253
$71$	13.4190	1.59254	0.796269	−	0.604943i	$-0.206804\pi$
$71$	13.4190	1.59254	0.796269	+	0.604943i	$0.206804\pi$
$72$	4.80453	0.566219
$73$	4.17719	0.488903	0.244451	−	0.969662i	$-0.421392\pi$
$73$	4.17719	0.488903	0.244451	+	0.969662i	$0.421392\pi$
$74$	−3.93751	−0.457726
$75$	11.6639	1.34683
$76$	4.86378	0.557914
$77$	5.15570	0.587546
$78$	−1.17197	−0.132700
$79$	−11.4734	−1.29086	−0.645432	−	0.763818i	$-0.723322\pi$
$79$	−11.4734	−1.29086	−0.645432	+	0.763818i	$0.723322\pi$
$80$	0.643890	0.0719891
$81$	−10.0843	−1.12048
$82$	−3.20329	−0.353744
$83$	−8.71013	−0.956061	−0.478030	−	0.878343i	$-0.658649\pi$
$83$	−8.71013	−0.956061	−0.478030	+	0.878343i	$0.658649\pi$
$84$	10.3786	1.13240
$85$	−0.691088	−0.0749590
$86$	−5.60526	−0.604431
$87$	17.8849	1.91747
$88$	3.83291	0.408590
$89$	15.4599	1.63874	0.819372	−	0.573263i	$-0.194323\pi$
$89$	15.4599	1.63874	0.819372	+	0.573263i	$0.194323\pi$
$90$	−0.318978	−0.0336233
$91$	−2.50523	−0.262619
$92$	−4.40549	−0.459304
$93$	13.6032	1.41058
$94$	−0.719705	−0.0742319
$95$	−0.691149	−0.0709103
$96$	11.8267	1.20706
$97$	8.40596	0.853496	0.426748	−	0.904371i	$-0.359659\pi$
$97$	8.40596	0.853496	0.426748	+	0.904371i	$0.359659\pi$
$98$	0.359129	0.0362775
$99$	5.30886	0.533561
$100$	8.66024	0.866024
$101$	18.2083	1.81179	0.905895	−	0.423503i	$-0.139200\pi$
$101$	18.2083	1.81179	0.905895	+	0.423503i	$0.139200\pi$
$102$	−3.24986	−0.321784
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.86247	−0.182630
$105$	−1.47481	−0.143927
$106$	2.77822	0.269844
$107$	−13.8491	−1.33884	−0.669420	−	0.742884i	$-0.733457\pi$
$107$	−13.8491	−1.33884	−0.669420	+	0.742884i	$0.733457\pi$
$108$	−1.74140	−0.167566
$109$	14.9546	1.43239	0.716193	−	0.697902i	$-0.245883\pi$
$109$	14.9546	1.43239	0.716193	+	0.697902i	$0.245883\pi$
$110$	−0.254472	−0.0242629
$111$	−18.7461	−1.77930
$112$	6.47251	0.611595
$113$	12.8152	1.20556	0.602778	−	0.797909i	$-0.294060\pi$
$113$	12.8152	1.20556	0.602778	+	0.797909i	$0.294060\pi$
$114$	−3.25015	−0.304404
$115$	0.626025	0.0583771
$116$	13.2792	1.23294
$117$	−2.57965	−0.238489
$118$	−0.428442	−0.0394413
$119$	−6.94696	−0.636827
$120$	−1.09642	−0.100089
$121$	−6.76474	−0.614977
$122$	−6.21041	−0.562264
$123$	−15.2506	−1.37510
$124$	10.1001	0.907014
$125$	−2.47674	−0.221526
$126$	−3.20644	−0.285652
$127$	−19.6394	−1.74272	−0.871358	−	0.490648i	$-0.836760\pi$
$127$	−19.6394	−1.74272	−0.871358	+	0.490648i	$0.836760\pi$
$128$	11.3448	1.00275
$129$	−26.6861	−2.34958
$130$	0.123652	0.0108450
$131$	−3.03509	−0.265177	−0.132588	−	0.991171i	$-0.542329\pi$
$131$	−3.03509	−0.265177	−0.132588	+	0.991171i	$0.542329\pi$
$132$	8.52574	0.742070
$133$	−6.94757	−0.602431
$134$	2.27511	0.196540
$135$	0.247455	0.0212975
$136$	−5.16460	−0.442861
$137$	11.5797	0.989318	0.494659	−	0.869087i	$-0.335293\pi$
$137$	11.5797	0.989318	0.494659	+	0.869087i	$0.335293\pi$
$138$	2.94390	0.250601
$139$	15.4114	1.30717	0.653587	−	0.756851i	$-0.273263\pi$
$139$	15.4114	1.30717	0.653587	+	0.756851i	$0.273263\pi$
$140$	−1.09502	−0.0925460
$141$	−3.42645	−0.288559
$142$	−6.65783	−0.558713
$143$	−2.05797	−0.172096
$144$	6.66480	0.555400
$145$	−1.88699	−0.156706
$146$	−2.07252	−0.171523
$147$	1.70978	0.141020
$148$	−13.9186	−1.14410
$149$	11.6917	0.957817	0.478909	−	0.877865i	$-0.341033\pi$
$149$	11.6917	0.957817	0.478909	+	0.877865i	$0.341033\pi$
$150$	−5.78707	−0.472512
$151$	8.10716	0.659751	0.329875	−	0.944024i	$-0.392993\pi$
$151$	8.10716	0.659751	0.329875	+	0.944024i	$0.392993\pi$
$152$	−5.16505	−0.418941
$153$	−7.15335	−0.578314
$154$	−2.55800	−0.206130
$155$	−1.43523	−0.115281
$156$	−4.14278	−0.331688
$157$	−17.5512	−1.40074	−0.700369	−	0.713781i	$-0.746981\pi$
$157$	−17.5512	−1.40074	−0.700369	+	0.713781i	$0.746981\pi$
$158$	5.69256	0.452876
$159$	13.2268	1.04896
$160$	−1.24780	−0.0986474
$161$	6.29293	0.495952
$162$	5.00336	0.393101
$163$	19.9625	1.56358	0.781791	−	0.623540i	$-0.214306\pi$
$163$	19.9625	1.56358	0.781791	+	0.623540i	$0.214306\pi$
$164$	−11.3232	−0.884196
$165$	−1.21152	−0.0943165
$166$	4.32154	0.335417
$167$	14.0319	1.08582	0.542911	−	0.839790i	$-0.317322\pi$
$167$	14.0319	1.08582	0.542911	+	0.839790i	$0.317322\pi$
$168$	−11.0215	−0.850326
$169$	1.00000	0.0769231
$170$	0.342884	0.0262980
$171$	−7.15397	−0.547078
$172$	−19.8139	−1.51080
$173$	24.1022	1.83246	0.916230	−	0.400653i	$-0.131217\pi$
$173$	24.1022	1.83246	0.916230	+	0.400653i	$0.131217\pi$
$174$	−8.87363	−0.672708
$175$	−12.3705	−0.935125
$176$	5.31699	0.400783
$177$	−2.03977	−0.153319
$178$	−7.67043	−0.574923
$179$	−6.28854	−0.470028	−0.235014	−	0.971992i	$-0.575514\pi$
$179$	−6.28854	−0.470028	−0.235014	+	0.971992i	$0.575514\pi$
$180$	−1.12755	−0.0840426
$181$	25.7950	1.91732	0.958662	−	0.284548i	$-0.0918434\pi$
$181$	25.7950	1.91732	0.958662	+	0.284548i	$0.0918434\pi$
$182$	1.24297	0.0921352
$183$	−29.5672	−2.18567
$184$	4.67837	0.344894
$185$	1.97785	0.145414
$186$	−6.74922	−0.494877
$187$	−5.70673	−0.417318
$188$	−2.54407	−0.185545
$189$	2.48747	0.180936
$190$	0.342914	0.0248776
$191$	−15.3284	−1.10912	−0.554561	−	0.832143i	$-0.687114\pi$
$191$	−15.3284	−1.10912	−0.554561	+	0.832143i	$0.687114\pi$
$192$	6.33778	0.457390
$193$	−4.35195	−0.313260	−0.156630	−	0.987657i	$-0.550063\pi$
$193$	−4.35195	−0.313260	−0.156630	+	0.987657i	$0.550063\pi$
$194$	−4.17063	−0.299434
$195$	0.588694	0.0421572
$196$	1.26948	0.0906769
$197$	−1.27643	−0.0909420	−0.0454710	−	0.998966i	$-0.514479\pi$
$197$	−1.27643	−0.0909420	−0.0454710	+	0.998966i	$0.514479\pi$
$198$	−2.63400	−0.187190
$199$	−22.2922	−1.58025	−0.790126	−	0.612944i	$-0.789985\pi$
$199$	−22.2922	−1.58025	−0.790126	+	0.612944i	$0.789985\pi$
$200$	−9.19666	−0.650302
$201$	10.8316	0.764003
$202$	−9.03404	−0.635633
$203$	−18.9684	−1.33132
$204$	−11.4879	−0.804312
$205$	1.60904	0.112380
$206$	−0.496151	−0.0345685
$207$	6.47988	0.450383
$208$	−2.58360	−0.179141
$209$	−5.70723	−0.394777
$210$	0.731730	0.0504942
$211$	3.01105	0.207289	0.103645	−	0.994614i	$-0.466950\pi$
$211$	3.01105	0.207289	0.103645	+	0.994614i	$0.466950\pi$
$212$	9.82067	0.674486
$213$	−31.6973	−2.17186
$214$	6.87123	0.469708
$215$	2.81558	0.192021
$216$	1.84926	0.125826
$217$	−14.4273	−0.979386
$218$	−7.41972	−0.502527
$219$	−9.86706	−0.666754
$220$	−0.899527	−0.0606461
$221$	2.77299	0.186531
$222$	9.30090	0.624236
$223$	26.4658	1.77228	0.886141	−	0.463416i	$-0.153376\pi$
$223$	26.4658	1.77228	0.886141	+	0.463416i	$0.153376\pi$
$224$	−12.5432	−0.838076
$225$	−12.7380	−0.849203
$226$	−6.35830	−0.422947
$227$	10.8002	0.716835	0.358417	−	0.933561i	$-0.383316\pi$
$227$	10.8002	0.716835	0.358417	+	0.933561i	$0.383316\pi$
$228$	−11.4889	−0.760870
$229$	−16.2805	−1.07584	−0.537922	−	0.842995i	$-0.680790\pi$
$229$	−16.2805	−1.07584	−0.537922	+	0.842995i	$0.680790\pi$
$230$	−0.310603	−0.0204805
$231$	−12.1784	−0.801281
$232$	−14.1017	−0.925825
$233$	−18.7628	−1.22919	−0.614595	−	0.788843i	$-0.710681\pi$
$233$	−18.7628	−1.22919	−0.614595	+	0.788843i	$0.710681\pi$
$234$	1.27990	0.0836696
$235$	0.361515	0.0235826
$236$	−1.51449	−0.0985849
$237$	27.1018	1.76045
$238$	3.44674	0.223419
$239$	−11.1647	−0.722186	−0.361093	−	0.932530i	$-0.617596\pi$
$239$	−11.1647	−0.722186	−0.361093	+	0.932530i	$0.617596\pi$
$240$	−1.52095	−0.0981770
$241$	20.1745	1.29955	0.649776	−	0.760126i	$-0.274863\pi$
$241$	20.1745	1.29955	0.649776	+	0.760126i	$0.274863\pi$
$242$	3.35633	0.215753
$243$	20.8418	1.33700
$244$	−21.9531	−1.40540
$245$	−0.180394	−0.0115249
$246$	7.56658	0.482427
$247$	2.77323	0.176456
$248$	−10.7257	−0.681082
$249$	20.5745	1.30385
$250$	1.22884	0.0777184
$251$	−6.01252	−0.379507	−0.189754	−	0.981832i	$-0.560769\pi$
$251$	−6.01252	−0.379507	−0.189754	+	0.981832i	$0.560769\pi$
$252$	−11.3344	−0.713998
$253$	5.16946	0.325001
$254$	9.74412	0.611400
$255$	1.63244	0.102227
$256$	−0.262578	−0.0164112
$257$	12.6369	0.788268	0.394134	−	0.919053i	$-0.371045\pi$
$257$	12.6369	0.788268	0.394134	+	0.919053i	$0.371045\pi$
$258$	13.2404	0.824309
$259$	19.8818	1.23539
$260$	0.437094	0.0271074
$261$	−19.5319	−1.20900
$262$	1.50586	0.0930325
$263$	−5.84259	−0.360270	−0.180135	−	0.983642i	$-0.557653\pi$
$263$	−5.84259	−0.360270	−0.180135	+	0.983642i	$0.557653\pi$
$264$	−9.05384	−0.557225
$265$	−1.39553	−0.0857265
$266$	3.44704	0.211352
$267$	−36.5182	−2.23488
$268$	8.04226	0.491259
$269$	29.4559	1.79596	0.897978	−	0.440040i	$-0.145036\pi$
$269$	29.4559	1.79596	0.897978	+	0.440040i	$0.145036\pi$
$270$	−0.122775	−0.00747184
$271$	27.7675	1.68675	0.843377	−	0.537322i	$-0.180564\pi$
$271$	27.7675	1.68675	0.843377	+	0.537322i	$0.180564\pi$
$272$	−7.16429	−0.434399
$273$	5.91767	0.358154
$274$	−5.74527	−0.347084
$275$	−10.1620	−0.612794
$276$	10.4063	0.626388
$277$	−11.3225	−0.680303	−0.340151	−	0.940371i	$-0.610478\pi$
$277$	−11.3225	−0.680303	−0.340151	+	0.940371i	$0.610478\pi$
$278$	−7.64636	−0.458598
$279$	−14.8559	−0.889397
$280$	1.16285	0.0694933
$281$	−0.538638	−0.0321324	−0.0160662	−	0.999871i	$-0.505114\pi$
$281$	−0.538638	−0.0321324	−0.0160662	+	0.999871i	$0.505114\pi$
$282$	1.70004	0.101236
$283$	−22.1049	−1.31400	−0.656999	−	0.753892i	$-0.728174\pi$
$283$	−22.1049	−1.31400	−0.656999	+	0.753892i	$0.728174\pi$
$284$	−23.5346	−1.39652
$285$	1.63258	0.0967058
$286$	1.02107	0.0603769
$287$	16.1744	0.954747
$288$	−12.9158	−0.761071
$289$	−9.31055	−0.547680
$290$	0.936232	0.0549774
$291$	−19.8560	−1.16398
$292$	−7.32609	−0.428727
$293$	−0.636535	−0.0371868	−0.0185934	−	0.999827i	$-0.505919\pi$
$293$	−0.636535	−0.0371868	−0.0185934	+	0.999827i	$0.505919\pi$
$294$	−0.848308	−0.0494743
$295$	0.215211	0.0125300
$296$	14.7808	0.859114
$297$	2.04338	0.118569
$298$	−5.80082	−0.336033
$299$	−2.51192	−0.145268
$300$	−20.4566	−1.18106
$301$	28.3028	1.63135
$302$	−4.02237	−0.231462
$303$	−43.0103	−2.47087
$304$	−7.16492	−0.410936
$305$	3.11955	0.178625
$306$	3.54914	0.202891
$307$	0.00698656	0.000398744 0	0.000199372	−	1.00000i	$-0.499937\pi$
$307$	0.00698656	0.000398744 0	0.000199372		1.00000i	$0.499937\pi$
$308$	−9.04224	−0.515229
$309$	−2.36213	−0.134377
$310$	0.712092	0.0404441
$311$	26.3668	1.49512	0.747562	−	0.664192i	$-0.231224\pi$
$311$	26.3668	1.49512	0.747562	+	0.664192i	$0.231224\pi$
$312$	4.39939	0.249067
$313$	−0.820111	−0.0463554	−0.0231777	−	0.999731i	$-0.507378\pi$
$313$	−0.820111	−0.0463554	−0.0231777	+	0.999731i	$0.507378\pi$
$314$	8.70805	0.491424
$315$	1.61063	0.0907485
$316$	20.1225	1.13198
$317$	32.3382	1.81630	0.908148	−	0.418650i	$-0.137497\pi$
$317$	32.3382	1.81630	0.908148	+	0.418650i	$0.137497\pi$
$318$	−6.56251	−0.368007
$319$	−15.5820	−0.872425
$320$	−0.668681	−0.0373804
$321$	32.7133	1.82588
$322$	−3.12224	−0.173996
$323$	7.69012	0.427890
$324$	17.6863	0.982571
$325$	4.93789	0.273905
$326$	−9.90441	−0.548555
$327$	−35.3246	−1.95345
$328$	12.0246	0.663948
$329$	3.63402	0.200350
$330$	0.601095	0.0330892
$331$	8.00063	0.439754	0.219877	−	0.975528i	$-0.429434\pi$
$331$	8.00063	0.439754	0.219877	+	0.975528i	$0.429434\pi$
$332$	15.2761	0.838386
$333$	20.4724	1.12188
$334$	−6.96195	−0.380941
$335$	−1.14281	−0.0624385
$336$	−15.2889	−0.834079
$337$	3.15984	0.172128	0.0860638	−	0.996290i	$-0.472571\pi$
$337$	3.15984	0.172128	0.0860638	+	0.996290i	$0.472571\pi$
$338$	−0.496151	−0.0269871
$339$	−30.2713	−1.64411
$340$	1.21205	0.0657329
$341$	−11.8516	−0.641799
$342$	3.54945	0.191932
$343$	−19.3500	−1.04480
$344$	21.0412	1.13447
$345$	−1.47875	−0.0796133
$346$	−11.9584	−0.642885
$347$	12.4952	0.670779	0.335390	−	0.942080i	$-0.391132\pi$
$347$	12.4952	0.670779	0.335390	+	0.942080i	$0.391132\pi$
$348$	−31.3672	−1.68146
$349$	−18.8441	−1.00870	−0.504351	−	0.863499i	$-0.668268\pi$
$349$	−18.8441	−1.00870	−0.504351	+	0.863499i	$0.668268\pi$
$350$	6.13766	0.328072
$351$	−0.992910	−0.0529976
$352$	−10.3039	−0.549197
$353$	11.7883	0.627429	0.313714	−	0.949517i	$-0.398427\pi$
$353$	11.7883	0.627429	0.313714	+	0.949517i	$0.398427\pi$
$354$	1.01203	0.0537890
$355$	3.34430	0.177497
$356$	−27.1141	−1.43704
$357$	16.4096	0.868489
$358$	3.12007	0.164901
$359$	33.7733	1.78249	0.891243	−	0.453526i	$-0.149834\pi$
$359$	33.7733	1.78249	0.891243	+	0.453526i	$0.149834\pi$
$360$	1.19739	0.0631081
$361$	−11.3092	−0.595221
$362$	−12.7982	−0.672658
$363$	15.9792	0.838690
$364$	4.39376	0.230295
$365$	1.04105	0.0544908
$366$	14.6698	0.766803
$367$	−18.1376	−0.946776	−0.473388	−	0.880854i	$-0.656969\pi$
$367$	−18.1376	−0.946776	−0.473388	+	0.880854i	$0.656969\pi$
$368$	6.48980	0.338304
$369$	16.6550	0.867022
$370$	−0.981312	−0.0510160
$371$	−14.0281	−0.728304
$372$	−23.8577	−1.23696
$373$	−9.46560	−0.490110	−0.245055	−	0.969509i	$-0.578806\pi$
$373$	−9.46560	−0.490110	−0.245055	+	0.969509i	$0.578806\pi$
$374$	2.83140	0.146408
$375$	5.85037	0.302112
$376$	2.70165	0.139327
$377$	7.57153	0.389954
$378$	−1.23416	−0.0634783
$379$	29.2580	1.50288	0.751442	−	0.659799i	$-0.229358\pi$
$379$	29.2580	1.50288	0.751442	+	0.659799i	$0.229358\pi$
$380$	1.21216	0.0621825
$381$	46.3908	2.37667
$382$	7.60519	0.389115
$383$	−20.8058	−1.06313	−0.531564	−	0.847018i	$-0.678395\pi$
$383$	−20.8058	−1.06313	−0.531564	+	0.847018i	$0.678395\pi$
$384$	−26.7979	−1.36752
$385$	1.28491	0.0654851
$386$	2.15922	0.109902
$387$	29.1436	1.48145
$388$	−14.7427	−0.748445
$389$	−4.84936	−0.245872	−0.122936	−	0.992415i	$-0.539231\pi$
$389$	−4.84936	−0.245872	−0.122936	+	0.992415i	$0.539231\pi$
$390$	−0.292081	−0.0147901
$391$	−6.96551	−0.352261
$392$	−1.34811	−0.0680898
$393$	7.16927	0.361642
$394$	0.633303	0.0319054
$395$	−2.85943	−0.143874
$396$	−9.31087	−0.467889
$397$	−14.5294	−0.729209	−0.364605	−	0.931162i	$-0.618796\pi$
$397$	−14.5294	−0.729209	−0.364605	+	0.931162i	$0.618796\pi$
$398$	11.0603	0.554403
$399$	16.4111	0.821581
$400$	−12.7575	−0.637877
$401$	16.0736	0.802677	0.401339	−	0.915930i	$-0.368545\pi$
$401$	16.0736	0.802677	0.401339	+	0.915930i	$0.368545\pi$
$402$	−5.37412	−0.268036
$403$	5.75886	0.286869
$404$	−31.9343	−1.58879
$405$	−2.51324	−0.124884
$406$	9.41120	0.467070
$407$	16.3323	0.809562
$408$	12.1995	0.603963
$409$	3.54583	0.175330	0.0876650	−	0.996150i	$-0.472059\pi$
$409$	3.54583	0.175330	0.0876650	+	0.996150i	$0.472059\pi$
$410$	−0.798328	−0.0394266
$411$	−27.3527	−1.34921
$412$	−1.75383	−0.0864052
$413$	2.16334	0.106451
$414$	−3.21500	−0.158009
$415$	−2.17075	−0.106558
$416$	5.00679	0.245478
$417$	−36.4036	−1.78269
$418$	2.83165	0.138500
$419$	32.6588	1.59549	0.797743	−	0.602998i	$-0.206027\pi$
$419$	32.6588	1.59549	0.797743	+	0.602998i	$0.206027\pi$
$420$	2.58658	0.126212
$421$	−6.68298	−0.325708	−0.162854	−	0.986650i	$-0.552070\pi$
$421$	−6.68298	−0.325708	−0.162854	+	0.986650i	$0.552070\pi$
$422$	−1.49394	−0.0727237
$423$	3.74199	0.181942
$424$	−10.4290	−0.506476
$425$	13.6927	0.664193
$426$	15.7267	0.761959
$427$	31.3584	1.51754
$428$	24.2890	1.17405
$429$	4.86120	0.234701
$430$	−1.39695	−0.0673671
$431$	−17.8707	−0.860801	−0.430401	−	0.902638i	$-0.641628\pi$
$431$	−17.8707	−0.860801	−0.430401	+	0.902638i	$0.641628\pi$
$432$	2.56528	0.123422
$433$	−32.8284	−1.57763	−0.788815	−	0.614631i	$-0.789305\pi$
$433$	−32.8284	−1.57763	−0.788815	+	0.614631i	$0.789305\pi$
$434$	7.15810	0.343600
$435$	4.45731	0.213712
$436$	−26.2278	−1.25608
$437$	−6.96612	−0.333235
$438$	4.89555	0.233918
$439$	−1.50152	−0.0716637	−0.0358318	−	0.999358i	$-0.511408\pi$
$439$	−1.50152	−0.0716637	−0.0358318	+	0.999358i	$0.511408\pi$
$440$	0.955245	0.0455395
$441$	−1.86723	−0.0889157
$442$	−1.37582	−0.0654411
$443$	22.4896	1.06851	0.534256	−	0.845323i	$-0.320592\pi$
$443$	22.4896	1.06851	0.534256	+	0.845323i	$0.320592\pi$
$444$	32.8776	1.56030
$445$	3.85294	0.182647
$446$	−13.1310	−0.621773
$447$	−27.6172	−1.30625
$448$	−6.72172	−0.317572
$449$	−21.2052	−1.00074	−0.500368	−	0.865813i	$-0.666802\pi$
$449$	−21.2052	−1.00074	−0.500368	+	0.865813i	$0.666802\pi$
$450$	6.32000	0.297927
$451$	13.2868	0.625653
$452$	−22.4758	−1.05717
$453$	−19.1501	−0.899753
$454$	−5.35853	−0.251488
$455$	−0.624357	−0.0292703
$456$	12.2005	0.571342
$457$	−24.2890	−1.13619	−0.568095	−	0.822963i	$-0.692320\pi$
$457$	−24.2890	−1.13619	−0.568095	+	0.822963i	$0.692320\pi$
$458$	8.07757	0.377440
$459$	−2.75332	−0.128514
$460$	−1.09794	−0.0511919
$461$	−6.52736	−0.304010	−0.152005	−	0.988380i	$-0.548573\pi$
$461$	−6.52736	−0.304010	−0.152005	+	0.988380i	$0.548573\pi$
$462$	6.04234	0.281115
$463$	−18.4993	−0.859737	−0.429869	−	0.902891i	$-0.641440\pi$
$463$	−18.4993	−0.859737	−0.429869	+	0.902891i	$0.641440\pi$
$464$	−19.5618	−0.908135
$465$	3.39020	0.157217
$466$	9.30917	0.431239
$467$	2.45856	0.113769	0.0568843	−	0.998381i	$-0.481883\pi$
$467$	2.45856	0.113769	0.0568843	+	0.998381i	$0.481883\pi$
$468$	4.52429	0.209135
$469$	−11.4878	−0.530457
$470$	−0.179366	−0.00827354
$471$	41.4582	1.91029
$472$	1.60830	0.0740280
$473$	23.2500	1.06903
$474$	−13.4466	−0.617621
$475$	13.6939	0.628319
$476$	12.1838	0.558444
$477$	−14.4449	−0.661386
$478$	5.53939	0.253366
$479$	−22.4925	−1.02771	−0.513854	−	0.857878i	$-0.671783\pi$
$479$	−22.4925	−1.02771	−0.513854	+	0.857878i	$0.671783\pi$
$480$	2.94747	0.134533
$481$	−7.93611	−0.361855
$482$	−10.0096	−0.455924
$483$	−14.8647	−0.676368
$484$	11.8642	0.539283
$485$	2.09495	0.0951267
$486$	−10.3407	−0.469063
$487$	0.679158	0.0307756	0.0153878	−	0.999882i	$-0.495102\pi$
$487$	0.679158	0.0307756	0.0153878	+	0.999882i	$0.495102\pi$
$488$	23.3129	1.05532
$489$	−47.1540	−2.13238
$490$	0.0895026	0.00404332
$491$	20.1596	0.909790	0.454895	−	0.890545i	$-0.349677\pi$
$491$	20.1596	0.909790	0.454895	+	0.890545i	$0.349677\pi$
$492$	26.7469	1.20585
$493$	20.9957	0.945601
$494$	−1.37594	−0.0619065
$495$	1.32308	0.0594682
$496$	−14.8786	−0.668069
$497$	33.6176	1.50795
$498$	−10.2080	−0.457433
$499$	5.55766	0.248795	0.124398	−	0.992232i	$-0.460300\pi$
$499$	5.55766	0.248795	0.124398	+	0.992232i	$0.460300\pi$
$500$	4.34379	0.194260
$501$	−33.1452	−1.48082
$502$	2.98312	0.133143
$503$	−1.44322	−0.0643499	−0.0321749	−	0.999482i	$-0.510243\pi$
$503$	−1.44322	−0.0643499	−0.0321749	+	0.999482i	$0.510243\pi$
$504$	12.0364	0.536146
$505$	4.53789	0.201934
$506$	−2.56483	−0.114021
$507$	−2.36213	−0.104906
$508$	34.4443	1.52822
$509$	37.8505	1.67769	0.838847	−	0.544367i	$-0.183230\pi$
$509$	37.8505	1.67769	0.838847	+	0.544367i	$0.183230\pi$
$510$	−0.809937	−0.0358646
$511$	10.4648	0.462936
$512$	−22.5593	−0.996991
$513$	−2.75356	−0.121573
$514$	−6.26981	−0.276549
$515$	0.249222	0.0109820
$516$	46.8031	2.06039
$517$	2.98525	0.131291
$518$	−9.86436	−0.433415
$519$	−56.9326	−2.49907
$520$	−0.464168	−0.0203551
$521$	16.6897	0.731187	0.365594	−	0.930775i	$-0.380866\pi$
$521$	16.6897	0.731187	0.365594	+	0.930775i	$0.380866\pi$
$522$	9.69079	0.424154
$523$	−29.5828	−1.29357	−0.646783	−	0.762674i	$-0.723886\pi$
$523$	−29.5828	−1.29357	−0.646783	+	0.762674i	$0.723886\pi$
$524$	5.32304	0.232538
$525$	29.2208	1.27530
$526$	2.89881	0.126394
$527$	15.9692	0.695630
$528$	−12.5594	−0.546578
$529$	−16.6903	−0.725664
$530$	0.692392	0.0300756
$531$	2.22761	0.0966701
$532$	12.1849	0.528282
$533$	−6.45627	−0.279652
$534$	18.1186	0.784066
$535$	−3.45149	−0.149221
$536$	−8.54040	−0.368889
$537$	14.8544	0.641013
$538$	−14.6146	−0.630079
$539$	−1.48962	−0.0641625
$540$	−0.433994	−0.0186761
$541$	12.2220	0.525464	0.262732	−	0.964869i	$-0.415376\pi$
$541$	12.2220	0.525464	0.262732	+	0.964869i	$0.415376\pi$
$542$	−13.7769	−0.591767
$543$	−60.9310	−2.61480
$544$	13.8838	0.595262
$545$	3.72700	0.159647
$546$	−2.93606	−0.125652
$547$	−10.0174	−0.428314	−0.214157	−	0.976799i	$-0.568700\pi$
$547$	−10.0174	−0.428314	−0.214157	+	0.976799i	$0.568700\pi$
$548$	−20.3088	−0.867550
$549$	32.2900	1.37810
$550$	5.04191	0.214988
$551$	20.9976	0.894527
$552$	−11.0509	−0.470358
$553$	−28.7436	−1.22230
$554$	5.61767	0.238672
$555$	−4.67194	−0.198313
$556$	−27.0290	−1.14628
$557$	−19.8708	−0.841952	−0.420976	−	0.907072i	$-0.638312\pi$
$557$	−19.8708	−0.841952	−0.420976	+	0.907072i	$0.638312\pi$
$558$	7.37075	0.312029
$559$	−11.2975	−0.477833
$560$	1.61309	0.0681655
$561$	13.4800	0.569128
$562$	0.267246	0.0112731
$563$	11.2529	0.474253	0.237127	−	0.971479i	$-0.423794\pi$
$563$	11.2529	0.474253	0.237127	+	0.971479i	$0.423794\pi$
$564$	6.00942	0.253042
$565$	3.19384	0.134366
$566$	10.9673	0.460992
$567$	−25.2636	−1.06097
$568$	24.9924	1.04866
$569$	43.0630	1.80530	0.902648	−	0.430380i	$-0.141621\pi$
$569$	43.0630	1.80530	0.902648	+	0.430380i	$0.141621\pi$
$570$	−0.810007	−0.0339275
$571$	−3.79277	−0.158723	−0.0793613	−	0.996846i	$-0.525288\pi$
$571$	−3.79277	−0.158723	−0.0793613	+	0.996846i	$0.525288\pi$
$572$	3.60935	0.150914
$573$	36.2076	1.51259
$574$	−8.02497	−0.334956
$575$	−12.4036	−0.517265
$576$	−6.92142	−0.288392
$577$	6.17698	0.257151	0.128576	−	0.991700i	$-0.458960\pi$
$577$	6.17698	0.257151	0.128576	+	0.991700i	$0.458960\pi$
$578$	4.61944	0.192143
$579$	10.2799	0.427217
$580$	3.30947	0.137418
$581$	−21.8209	−0.905282
$582$	9.85156	0.408360
$583$	−11.5237	−0.477263
$584$	7.77988	0.321934
$585$	−0.642906	−0.0265809
$586$	0.315818	0.0130463
$587$	42.8292	1.76775	0.883876	−	0.467722i	$-0.154925\pi$
$587$	42.8292	1.76775	0.883876	+	0.467722i	$0.154925\pi$
$588$	−2.99867	−0.123663
$589$	15.9706	0.658058
$590$	−0.106777	−0.00439594
$591$	3.01510	0.124025
$592$	20.5037	0.842699
$593$	7.78912	0.319861	0.159930	−	0.987128i	$-0.448873\pi$
$593$	7.78912	0.319861	0.159930	+	0.987128i	$0.448873\pi$
$594$	−1.01383	−0.0415978
$595$	−1.73133	−0.0709778
$596$	−20.5052	−0.839926
$597$	52.6571	2.15511
$598$	1.24629	0.0509646
$599$	−10.1867	−0.416219	−0.208109	−	0.978106i	$-0.566731\pi$
$599$	−10.1867	−0.416219	−0.208109	+	0.978106i	$0.566731\pi$
$600$	21.7237	0.886867
$601$	−5.82676	−0.237679	−0.118839	−	0.992913i	$-0.537917\pi$
$601$	−5.82676	−0.237679	−0.118839	+	0.992913i	$0.537917\pi$
$602$	−14.0425	−0.572328
$603$	−11.8291	−0.481717
$604$	−14.2186	−0.578547
$605$	−1.68592	−0.0685424
$606$	21.3396	0.866861
$607$	−38.2376	−1.55202	−0.776009	−	0.630722i	$-0.782759\pi$
$607$	−38.2376	−1.55202	−0.776009	+	0.630722i	$0.782759\pi$
$608$	13.8850	0.563110
$609$	44.8059	1.81562
$610$	−1.54777	−0.0626674
$611$	−1.45058	−0.0586840
$612$	12.5458	0.507133
$613$	13.5694	0.548064	0.274032	−	0.961721i	$-0.411642\pi$
$613$	13.5694	0.548064	0.274032	+	0.961721i	$0.411642\pi$
$614$	−0.00346639	−0.000139892 0
$615$	−3.80077	−0.153262
$616$	9.60232	0.386889
$617$	−23.2970	−0.937901	−0.468950	−	0.883224i	$-0.655368\pi$
$617$	−23.2970	−0.937901	−0.468950	+	0.883224i	$0.655368\pi$
$618$	1.17197	0.0471437
$619$	−7.77474	−0.312493	−0.156247	−	0.987718i	$-0.549939\pi$
$619$	−7.77474	−0.312493	−0.156247	+	0.987718i	$0.549939\pi$
$620$	2.51716	0.101092
$621$	2.49411	0.100085
$622$	−13.0819	−0.524537
$623$	38.7305	1.55171
$624$	6.10280	0.244308
$625$	24.0722	0.962887
$626$	0.406899	0.0162630
$627$	13.4812	0.538388
$628$	30.7819	1.22833
$629$	−22.0067	−0.877465
$630$	−0.799114	−0.0318375
$631$	−40.3646	−1.60689	−0.803445	−	0.595379i	$-0.797002\pi$
$631$	−40.3646	−1.60689	−0.803445	+	0.595379i	$0.797002\pi$
$632$	−21.3689	−0.850010
$633$	−7.11249	−0.282696
$634$	−16.0446	−0.637214
$635$	−4.89457	−0.194235
$636$	−23.1977	−0.919848
$637$	0.723829	0.0286792
$638$	7.73103	0.306075
$639$	34.6163	1.36940
$640$	2.82737	0.111762
$641$	−4.31719	−0.170519	−0.0852594	−	0.996359i	$-0.527172\pi$
$641$	−4.31719	−0.170519	−0.0852594	+	0.996359i	$0.527172\pi$
$642$	−16.2307	−0.640576
$643$	−37.5573	−1.48112	−0.740558	−	0.671992i	$-0.765439\pi$
$643$	−37.5573	−1.48112	−0.740558	+	0.671992i	$0.765439\pi$
$644$	−11.0368	−0.434909
$645$	−6.65077	−0.261874
$646$	−3.81546	−0.150117
$647$	−25.0767	−0.985866	−0.492933	−	0.870067i	$-0.664075\pi$
$647$	−25.0767	−0.985866	−0.492933	+	0.870067i	$0.664075\pi$
$648$	−18.7818	−0.737818
$649$	1.77712	0.0697582
$650$	−2.44994	−0.0960945
$651$	34.0790	1.33566
$652$	−35.0109	−1.37113
$653$	−11.3984	−0.446053	−0.223027	−	0.974812i	$-0.571594\pi$
$653$	−11.3984	−0.446053	−0.223027	+	0.974812i	$0.571594\pi$
$654$	17.5263	0.685334
$655$	−0.756410	−0.0295554
$656$	16.6804	0.651262
$657$	10.7757	0.420400
$658$	−1.80303	−0.0702892
$659$	−15.2415	−0.593726	−0.296863	−	0.954920i	$-0.595941\pi$
$659$	−15.2415	−0.593726	−0.296863	+	0.954920i	$0.595941\pi$
$660$	2.12480	0.0827077
$661$	44.7783	1.74167	0.870837	−	0.491571i	$-0.163577\pi$
$661$	44.7783	1.74167	0.870837	+	0.491571i	$0.163577\pi$
$662$	−3.96952	−0.154280
$663$	−6.55015	−0.254387
$664$	−16.2223	−0.629549
$665$	−1.73149	−0.0671441
$666$	−10.1574	−0.393592
$667$	−19.0191	−0.736421
$668$	−24.6097	−0.952176
$669$	−62.5157	−2.41700
$670$	0.567008	0.0219054
$671$	25.7600	0.994455
$672$	29.6286	1.14295
$673$	0.493649	0.0190288	0.00951439	−	0.999955i	$-0.496971\pi$
$673$	0.493649	0.0190288	0.00951439	+	0.999955i	$0.496971\pi$
$674$	−1.56776	−0.0603878
$675$	−4.90288	−0.188712
$676$	−1.75383	−0.0674552
$677$	0.266371	0.0102375	0.00511873	−	0.999987i	$-0.498371\pi$
$677$	0.266371	0.0102375	0.00511873	+	0.999987i	$0.498371\pi$
$678$	15.0191	0.576806
$679$	21.0589	0.808165
$680$	−1.28713	−0.0493592
$681$	−25.5115	−0.977602
$682$	5.88017	0.225163
$683$	26.9119	1.02976	0.514878	−	0.857264i	$-0.327837\pi$
$683$	26.9119	1.02976	0.514878	+	0.857264i	$0.327837\pi$
$684$	12.5469	0.479742
$685$	2.88591	0.110265
$686$	9.60050	0.366549
$687$	38.4566	1.46721
$688$	29.1882	1.11279
$689$	5.59954	0.213326
$690$	0.733684	0.0279309
$691$	−0.409525	−0.0155790	−0.00778952	−	0.999970i	$-0.502480\pi$
$691$	−0.409525	−0.0155790	−0.00778952	+	0.999970i	$0.502480\pi$
$692$	−42.2713	−1.60692
$693$	13.2999	0.505222
$694$	−6.19952	−0.235331
$695$	3.84085	0.145692
$696$	33.3101	1.26262
$697$	−17.9032	−0.678130
$698$	9.34953	0.353885
$699$	44.3201	1.67634
$700$	21.6959	0.820027
$701$	−24.8098	−0.937053	−0.468526	−	0.883450i	$-0.655215\pi$
$701$	−24.8098	−0.937053	−0.468526	+	0.883450i	$0.655215\pi$
$702$	0.492633	0.0185932
$703$	−22.0086	−0.830071
$704$	−5.52171	−0.208107
$705$	−0.853945	−0.0321614
$706$	−5.84878	−0.220122
$707$	45.6158	1.71556
$708$	3.57742	0.134448
$709$	43.1530	1.62064	0.810322	−	0.585985i	$-0.199292\pi$
$709$	43.1530	1.62064	0.810322	+	0.585985i	$0.199292\pi$
$710$	−1.65928	−0.0622715
$711$	−29.5975	−1.10999
$712$	28.7935	1.07908
$713$	−14.4658	−0.541748
$714$	−8.14165	−0.304694
$715$	−0.512892	−0.0191811
$716$	11.0291	0.412175
$717$	26.3725	0.984900
$718$	−16.7567	−0.625353
$719$	2.63182	0.0981504	0.0490752	−	0.998795i	$-0.484373\pi$
$719$	2.63182	0.0981504	0.0490752	+	0.998795i	$0.484373\pi$
$720$	1.66101	0.0619023
$721$	2.50523	0.0932996
$722$	5.61107	0.208823
$723$	−47.6547	−1.77230
$724$	−45.2401	−1.68133
$725$	37.3874	1.38853
$726$	−7.92810	−0.294239
$727$	34.7996	1.29065	0.645324	−	0.763909i	$-0.276722\pi$
$727$	34.7996	1.29065	0.645324	+	0.763909i	$0.276722\pi$
$728$	−4.66591	−0.172930
$729$	−18.9780	−0.702888
$730$	−0.516516	−0.0191171
$731$	−31.3278	−1.15870
$732$	51.8560	1.91665
$733$	−44.3810	−1.63925	−0.819624	−	0.572902i	$-0.805818\pi$
$733$	−44.3810	−1.63925	−0.819624	+	0.572902i	$0.805818\pi$
$734$	8.99900	0.332159
$735$	0.426114	0.0157174
$736$	−12.5767	−0.463582
$737$	−9.43690	−0.347613
$738$	−8.26337	−0.304179
$739$	−7.16625	−0.263615	−0.131807	−	0.991275i	$-0.542078\pi$
$739$	−7.16625	−0.263615	−0.131807	+	0.991275i	$0.542078\pi$
$740$	−3.46882	−0.127516
$741$	−6.55072	−0.240647
$742$	6.96007	0.255512
$743$	−23.5550	−0.864151	−0.432075	−	0.901838i	$-0.642219\pi$
$743$	−23.5550	−0.864151	−0.432075	+	0.901838i	$0.642219\pi$
$744$	25.3355	0.928843
$745$	2.91381	0.106754
$746$	4.69637	0.171946
$747$	−22.4691	−0.822102
$748$	10.0087	0.365953
$749$	−34.6951	−1.26773
$750$	−2.90267	−0.105990
$751$	−0.629480	−0.0229700	−0.0114850	−	0.999934i	$-0.503656\pi$
$751$	−0.629480	−0.0229700	−0.0114850	+	0.999934i	$0.503656\pi$
$752$	3.74771	0.136665
$753$	14.2024	0.517563
$754$	−3.75662	−0.136808
$755$	2.02048	0.0735328
$756$	−4.36260	−0.158666
$757$	36.9213	1.34193	0.670964	−	0.741490i	$-0.265880\pi$
$757$	36.9213	1.34193	0.670964	+	0.741490i	$0.265880\pi$
$758$	−14.5164	−0.527260
$759$	−12.2109	−0.443229
$760$	−1.28724	−0.0466932
$761$	−25.2272	−0.914485	−0.457243	−	0.889342i	$-0.651163\pi$
$761$	−25.2272	−0.914485	−0.457243	+	0.889342i	$0.651163\pi$
$762$	−23.0169	−0.833813
$763$	37.4646	1.35631
$764$	26.8834	0.972608
$765$	−1.78277	−0.0644561
$766$	10.3228	0.372979
$767$	−0.863531	−0.0311803
$768$	0.620244	0.0223811
$769$	−39.0179	−1.40702	−0.703510	−	0.710685i	$-0.748385\pi$
$769$	−39.0179	−1.40702	−0.703510	+	0.710685i	$0.748385\pi$
$770$	−0.637510	−0.0229743
$771$	−29.8500	−1.07502
$772$	7.63260	0.274703
$773$	−14.8463	−0.533986	−0.266993	−	0.963698i	$-0.586030\pi$
$773$	−14.8463	−0.533986	−0.266993	+	0.963698i	$0.586030\pi$
$774$	−14.4596	−0.519741
$775$	28.4366	1.02147
$776$	15.6558	0.562012
$777$	−46.9633	−1.68480
$778$	2.40601	0.0862598
$779$	−17.9047	−0.641503
$780$	−1.03247	−0.0369684
$781$	27.6159	0.988173
$782$	3.45595	0.123584
$783$	−7.51785	−0.268666
$784$	−1.87009	−0.0667888
$785$	−4.37414	−0.156120
$786$	−3.55704	−0.126875
$787$	32.3858	1.15443	0.577215	−	0.816592i	$-0.304140\pi$
$787$	32.3858	1.15443	0.577215	+	0.816592i	$0.304140\pi$
$788$	2.23865	0.0797486
$789$	13.8010	0.491327
$790$	1.41871	0.0504754
$791$	32.1051	1.14153
$792$	9.88759	0.351340
$793$	−12.5172	−0.444498
$794$	7.20877	0.255830
$795$	3.29642	0.116912
$796$	39.0968	1.38575
$797$	18.7411	0.663844	0.331922	−	0.943307i	$-0.392303\pi$
$797$	18.7411	0.663844	0.331922	+	0.943307i	$0.392303\pi$
$798$	−8.14236	−0.288237
$799$	−4.02243	−0.142303
$800$	24.7230	0.874090
$801$	39.8811	1.40913
$802$	−7.97493	−0.281605
$803$	8.59654	0.303365
$804$	−18.9968	−0.669967
$805$	1.56833	0.0552765
$806$	−2.85726	−0.100643
$807$	−69.5786	−2.44928
$808$	33.9123	1.19303
$809$	47.8987	1.68403	0.842014	−	0.539455i	$-0.181370\pi$
$809$	47.8987	1.68403	0.842014	+	0.539455i	$0.181370\pi$
$810$	1.24695	0.0438132
$811$	−2.37085	−0.0832518	−0.0416259	−	0.999133i	$-0.513254\pi$
$811$	−2.37085	−0.0832518	−0.0416259	+	0.999133i	$0.513254\pi$
$812$	33.2675	1.16746
$813$	−65.5904	−2.30035
$814$	−8.10329	−0.284020
$815$	4.97509	0.174270
$816$	16.9230	0.592423
$817$	−31.3305	−1.09612
$818$	−1.75927	−0.0615113
$819$	−6.46263	−0.225822
$820$	−2.82199	−0.0985483
$821$	49.4295	1.72510	0.862550	−	0.505971i	$-0.168866\pi$
$821$	49.4295	1.72510	0.862550	+	0.505971i	$0.168866\pi$
$822$	13.5711	0.473345
$823$	−9.55877	−0.333198	−0.166599	−	0.986025i	$-0.553278\pi$
$823$	−9.55877	−0.333198	−0.166599	+	0.986025i	$0.553278\pi$
$824$	1.86247	0.0648822
$825$	24.0041	0.835714
$826$	−1.07334	−0.0373464
$827$	−17.5546	−0.610433	−0.305216	−	0.952283i	$-0.598729\pi$
$827$	−17.5546	−0.610433	−0.305216	+	0.952283i	$0.598729\pi$
$828$	−11.3646	−0.394949
$829$	30.5898	1.06243	0.531214	−	0.847238i	$-0.321736\pi$
$829$	30.5898	1.06243	0.531214	+	0.847238i	$0.321736\pi$
$830$	1.07702	0.0373840
$831$	26.7452	0.927781
$832$	2.68308	0.0930190
$833$	2.00717	0.0695442
$834$	18.0617	0.625426
$835$	3.49706	0.121021
$836$	10.0095	0.346187
$837$	−5.71802	−0.197644
$838$	−16.2037	−0.559747
$839$	−7.10678	−0.245353	−0.122677	−	0.992447i	$-0.539148\pi$
$839$	−7.10678	−0.245353	−0.122677	+	0.992447i	$0.539148\pi$
$840$	−2.74679	−0.0947734
$841$	28.3281	0.976831
$842$	3.31577	0.114269
$843$	1.27233	0.0438214
$844$	−5.28089	−0.181776
$845$	0.249222	0.00857349
$846$	−1.85659	−0.0638309
$847$	−16.9472	−0.582314
$848$	−14.4670	−0.496798
$849$	52.2145	1.79200
$850$	−6.79364	−0.233020
$851$	19.9349	0.683358
$852$	55.5918	1.90454
$853$	−9.75959	−0.334162	−0.167081	−	0.985943i	$-0.553434\pi$
$853$	−9.75959	−0.334162	−0.167081	+	0.985943i	$0.553434\pi$
$854$	−15.5585	−0.532401
$855$	−1.78292	−0.0609747
$856$	−25.7935	−0.881603
$857$	16.9821	0.580098	0.290049	−	0.957012i	$-0.406328\pi$
$857$	16.9821	0.580098	0.290049	+	0.957012i	$0.406328\pi$
$858$	−2.41189	−0.0823406
$859$	−29.0885	−0.992486	−0.496243	−	0.868184i	$-0.665287\pi$
$859$	−29.0885	−0.992486	−0.496243	+	0.868184i	$0.665287\pi$
$860$	−4.93806	−0.168386
$861$	−38.2061	−1.30206
$862$	8.86657	0.301997
$863$	−19.7880	−0.673591	−0.336796	−	0.941578i	$-0.609343\pi$
$863$	−19.7880	−0.673591	−0.336796	+	0.941578i	$0.609343\pi$
$864$	−4.97129	−0.169127
$865$	6.00680	0.204237
$866$	16.2878	0.553483
$867$	21.9927	0.746912
$868$	25.3030	0.858840
$869$	−23.6121	−0.800984
$870$	−2.21150	−0.0749769
$871$	4.58553	0.155375
$872$	27.8524	0.943201
$873$	21.6845	0.733908
$874$	3.45625	0.116909
$875$	−6.20479	−0.209760
$876$	17.3052	0.584688
$877$	50.6888	1.71164	0.855820	−	0.517274i	$-0.173053\pi$
$877$	50.6888	1.71164	0.855820	+	0.517274i	$0.173053\pi$
$878$	0.744981	0.0251419
$879$	1.50358	0.0507145
$880$	1.32511	0.0446694
$881$	38.3742	1.29286	0.646430	−	0.762974i	$-0.276261\pi$
$881$	38.3742	1.29286	0.646430	+	0.762974i	$0.276261\pi$
$882$	0.926428	0.0311944
$883$	−17.0338	−0.573234	−0.286617	−	0.958045i	$-0.592531\pi$
$883$	−17.0338	−0.573234	−0.286617	+	0.958045i	$0.592531\pi$
$884$	−4.86336	−0.163572
$885$	−0.508355	−0.0170882
$886$	−11.1582	−0.374868
$887$	−16.8404	−0.565446	−0.282723	−	0.959202i	$-0.591238\pi$
$887$	−16.8404	−0.565446	−0.282723	+	0.959202i	$0.591238\pi$
$888$	−34.9140	−1.17164
$889$	−49.2012	−1.65016
$890$	−1.91164	−0.0640782
$891$	−20.7533	−0.695262
$892$	−46.4166	−1.55414
$893$	−4.02278	−0.134617
$894$	13.7023	0.458273
$895$	−1.56724	−0.0523871
$896$	28.4213	0.949490
$897$	5.93348	0.198113
$898$	10.5210	0.351090
$899$	43.6034	1.45425
$900$	22.3404	0.744681
$901$	15.5274	0.517294
$902$	−6.59228	−0.219499
$903$	−66.8549	−2.22479
$904$	23.8680	0.793837
$905$	6.42866	0.213696
$906$	9.50137	0.315662
$907$	5.62641	0.186822	0.0934110	−	0.995628i	$-0.470223\pi$
$907$	5.62641	0.186822	0.0934110	+	0.995628i	$0.470223\pi$
$908$	−18.9418	−0.628605
$909$	46.9710	1.55793
$910$	0.309776	0.0102690
$911$	−48.0036	−1.59043	−0.795215	−	0.606327i	$-0.792642\pi$
$911$	−48.0036	−1.59043	−0.795215	+	0.606327i	$0.792642\pi$
$912$	16.9245	0.560425
$913$	−17.9252	−0.593238
$914$	12.0510	0.398612
$915$	−7.36879	−0.243605
$916$	28.5532	0.943426
$917$	−7.60359	−0.251093
$918$	1.36606	0.0450868
$919$	17.1177	0.564659	0.282330	−	0.959317i	$-0.408893\pi$
$919$	17.1177	0.564659	0.282330	+	0.959317i	$0.408893\pi$
$920$	1.16595	0.0384403
$921$	−0.0165032	−0.000543797 0
$922$	3.23856	0.106656
$923$	−13.4190	−0.441690
$924$	21.3589	0.702657
$925$	−39.1876	−1.28848
$926$	9.17847	0.301623
$927$	2.57965	0.0847270
$928$	37.9091	1.24443
$929$	39.0511	1.28122	0.640612	−	0.767865i	$-0.278681\pi$
$929$	39.0511	1.28122	0.640612	+	0.767865i	$0.278681\pi$
$930$	−1.68205	−0.0551567
$931$	2.00734	0.0657880
$932$	32.9068	1.07790
$933$	−62.2818	−2.03901
$934$	−1.21982	−0.0399137
$935$	−1.42224	−0.0465123
$936$	−4.80453	−0.157041
$937$	−10.0130	−0.327110	−0.163555	−	0.986534i	$-0.552296\pi$
$937$	−10.0130	−0.327110	−0.163555	+	0.986534i	$0.552296\pi$
$938$	5.69968	0.186101
$939$	1.93721	0.0632184
$940$	−0.634037	−0.0206800
$941$	13.6890	0.446247	0.223124	−	0.974790i	$-0.428375\pi$
$941$	13.6890	0.446247	0.223124	+	0.974790i	$0.428375\pi$
$942$	−20.5695	−0.670192
$943$	16.2176	0.528119
$944$	2.23102	0.0726135
$945$	0.619930	0.0201663
$946$	−11.5355	−0.375051
$947$	−19.4106	−0.630761	−0.315380	−	0.948965i	$-0.602132\pi$
$947$	−19.4106	−0.630761	−0.315380	+	0.948965i	$0.602132\pi$
$948$	−47.5320	−1.54377
$949$	−4.17719	−0.135597
$950$	−6.79424	−0.220434
$951$	−76.3871	−2.47702
$952$	−12.9385	−0.419339
$953$	−52.0732	−1.68682	−0.843409	−	0.537272i	$-0.819455\pi$
$953$	−52.0732	−1.68682	−0.843409	+	0.537272i	$0.819455\pi$
$954$	7.16684	0.232035
$955$	−3.82016	−0.123618
$956$	19.5811	0.633297
$957$	36.8067	1.18979
$958$	11.1597	0.360552
$959$	29.0097	0.936773
$960$	1.57951	0.0509785
$961$	2.16444	0.0698205
$962$	3.93751	0.126950
$963$	−35.7258	−1.15125
$964$	−35.3827	−1.13960
$965$	−1.08460	−0.0349145
$966$	7.37514	0.237291
$967$	−6.08948	−0.195824	−0.0979122	−	0.995195i	$-0.531216\pi$
$967$	−6.08948	−0.195824	−0.0979122	+	0.995195i	$0.531216\pi$
$968$	−12.5991	−0.404951
$969$	−18.1651	−0.583546
$970$	−1.03941	−0.0333735
$971$	−61.4838	−1.97311	−0.986554	−	0.163433i	$-0.947743\pi$
$971$	−61.4838	−1.97311	−0.986554	+	0.163433i	$0.947743\pi$
$972$	−36.5531	−1.17244
$973$	38.6090	1.23775
$974$	−0.336965	−0.0107970
$975$	−11.6639	−0.373545
$976$	32.3394	1.03516
$977$	−31.9702	−1.02282	−0.511409	−	0.859337i	$-0.670876\pi$
$977$	−31.9702	−1.02282	−0.511409	+	0.859337i	$0.670876\pi$
$978$	23.3955	0.748106
$979$	31.8160	1.01684
$980$	0.316381	0.0101064
$981$	38.5776	1.23169
$982$	−10.0022	−0.319183
$983$	42.9374	1.36949	0.684745	−	0.728783i	$-0.259914\pi$
$983$	42.9374	1.36949	0.684745	+	0.728783i	$0.259914\pi$
$984$	−28.4037	−0.905476
$985$	−0.318115	−0.0101360
$986$	−10.4171	−0.331747
$987$	−8.58404	−0.273233
$988$	−4.86378	−0.154738
$989$	28.3784	0.902380
$990$	−0.656449	−0.0208633
$991$	−34.8770	−1.10790	−0.553952	−	0.832549i	$-0.686881\pi$
$991$	−34.8770	−1.10790	−0.553952	+	0.832549i	$0.686881\pi$
$992$	28.8334	0.915462
$993$	−18.8985	−0.599727
$994$	−16.6794	−0.529038
$995$	−5.55570	−0.176128
$996$	−36.0842	−1.14337
$997$	−25.7037	−0.814044	−0.407022	−	0.913418i	$-0.633433\pi$
$997$	−25.7037	−0.814044	−0.407022	+	0.913418i	$0.633433\pi$
$998$	−2.75744	−0.0872852
$999$	7.87984	0.249307

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.g.1.14	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.g.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-0.496151 q^{2} -2.36213 q^{3} -1.75383 q^{4} +0.249222 q^{5} +1.17197 q^{6} +2.50523 q^{7} +1.86247 q^{8} +2.57965 q^{9} +O(q^{10})\)	\(q-0.496151 q^{2} -2.36213 q^{3} -1.75383 q^{4} +0.249222 q^{5} +1.17197 q^{6} +2.50523 q^{7} +1.86247 q^{8} +2.57965 q^{9} -0.123652 q^{10} +2.05797 q^{11} +4.14278 q^{12} -1.00000 q^{13} -1.24297 q^{14} -0.588694 q^{15} +2.58360 q^{16} -2.77299 q^{17} -1.27990 q^{18} -2.77323 q^{19} -0.437094 q^{20} -5.91767 q^{21} -1.02107 q^{22} +2.51192 q^{23} -4.39939 q^{24} -4.93789 q^{25} +0.496151 q^{26} +0.992910 q^{27} -4.39376 q^{28} -7.57153 q^{29} +0.292081 q^{30} -5.75886 q^{31} -5.00679 q^{32} -4.86120 q^{33} +1.37582 q^{34} +0.624357 q^{35} -4.52429 q^{36} +7.93611 q^{37} +1.37594 q^{38} +2.36213 q^{39} +0.464168 q^{40} +6.45627 q^{41} +2.93606 q^{42} +11.2975 q^{43} -3.60935 q^{44} +0.642906 q^{45} -1.24629 q^{46} +1.45058 q^{47} -6.10280 q^{48} -0.723829 q^{49} +2.44994 q^{50} +6.55015 q^{51} +1.75383 q^{52} -5.59954 q^{53} -0.492633 q^{54} +0.512892 q^{55} +4.66591 q^{56} +6.55072 q^{57} +3.75662 q^{58} +0.863531 q^{59} +1.03247 q^{60} +12.5172 q^{61} +2.85726 q^{62} +6.46263 q^{63} -2.68308 q^{64} -0.249222 q^{65} +2.41189 q^{66} -4.58553 q^{67} +4.86336 q^{68} -5.93348 q^{69} -0.309776 q^{70} +13.4190 q^{71} +4.80453 q^{72} +4.17719 q^{73} -3.93751 q^{74} +11.6639 q^{75} +4.86378 q^{76} +5.15570 q^{77} -1.17197 q^{78} -11.4734 q^{79} +0.643890 q^{80} -10.0843 q^{81} -3.20329 q^{82} -8.71013 q^{83} +10.3786 q^{84} -0.691088 q^{85} -5.60526 q^{86} +17.8849 q^{87} +3.83291 q^{88} +15.4599 q^{89} -0.318978 q^{90} -2.50523 q^{91} -4.40549 q^{92} +13.6032 q^{93} -0.719705 q^{94} -0.691149 q^{95} +11.8267 q^{96} +8.40596 q^{97} +0.359129 q^{98} +5.30886 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) \) 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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