LMFDB - Embedded newform 1339.2.a.g.1.9

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			1.9
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)

$f(q)$	$=$	$q-1.43550 q^{2} +2.33343 q^{3} +0.0606568 q^{4} +2.88716 q^{5} -3.34964 q^{6} +3.63915 q^{7} +2.78392 q^{8} +2.44491 q^{9} +O(q^{10})$	\(q-1.43550 q^{2} +2.33343 q^{3} +0.0606568 q^{4} +2.88716 q^{5} -3.34964 q^{6} +3.63915 q^{7} +2.78392 q^{8} +2.44491 q^{9} -4.14452 q^{10} +3.33191 q^{11} +0.141539 q^{12} -1.00000 q^{13} -5.22400 q^{14} +6.73700 q^{15} -4.11763 q^{16} -2.35851 q^{17} -3.50967 q^{18} +3.81285 q^{19} +0.175126 q^{20} +8.49172 q^{21} -4.78295 q^{22} +7.05905 q^{23} +6.49610 q^{24} +3.33570 q^{25} +1.43550 q^{26} -1.29526 q^{27} +0.220739 q^{28} -8.67749 q^{29} -9.67096 q^{30} -1.67449 q^{31} +0.343009 q^{32} +7.77479 q^{33} +3.38563 q^{34} +10.5068 q^{35} +0.148301 q^{36} +9.40944 q^{37} -5.47334 q^{38} -2.33343 q^{39} +8.03764 q^{40} -7.40781 q^{41} -12.1898 q^{42} -10.2508 q^{43} +0.202103 q^{44} +7.05886 q^{45} -10.1333 q^{46} -11.0065 q^{47} -9.60823 q^{48} +6.24341 q^{49} -4.78839 q^{50} -5.50342 q^{51} -0.0606568 q^{52} -11.6636 q^{53} +1.85934 q^{54} +9.61976 q^{55} +10.1311 q^{56} +8.89702 q^{57} +12.4565 q^{58} +4.31184 q^{59} +0.408645 q^{60} -13.3225 q^{61} +2.40372 q^{62} +8.89741 q^{63} +7.74288 q^{64} -2.88716 q^{65} -11.1607 q^{66} -3.46302 q^{67} -0.143059 q^{68} +16.4718 q^{69} -15.0825 q^{70} +4.27960 q^{71} +6.80646 q^{72} -7.02456 q^{73} -13.5072 q^{74} +7.78364 q^{75} +0.231275 q^{76} +12.1253 q^{77} +3.34964 q^{78} +7.43314 q^{79} -11.8883 q^{80} -10.3571 q^{81} +10.6339 q^{82} +11.5201 q^{83} +0.515080 q^{84} -6.80939 q^{85} +14.7150 q^{86} -20.2484 q^{87} +9.27578 q^{88} -5.29591 q^{89} -10.1330 q^{90} -3.63915 q^{91} +0.428179 q^{92} -3.90730 q^{93} +15.7999 q^{94} +11.0083 q^{95} +0.800390 q^{96} -9.44406 q^{97} -8.96241 q^{98} +8.14623 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.43550	−1.01505	−0.507525	−	0.861637i	$-0.669440\pi$
$2$	−1.43550	−1.01505	−0.507525	+	0.861637i	$0.669440\pi$
$3$	2.33343	1.34721	0.673604	−	0.739092i	$-0.264745\pi$
$3$	2.33343	1.34721	0.673604	+	0.739092i	$0.264745\pi$
$4$	0.0606568	0.0303284
$5$	2.88716	1.29118	0.645589	−	0.763685i	$-0.276612\pi$
$5$	2.88716	1.29118	0.645589	+	0.763685i	$0.276612\pi$
$6$	−3.34964	−1.36749
$7$	3.63915	1.37547	0.687735	−	0.725962i	$-0.258605\pi$
$7$	3.63915	1.37547	0.687735	+	0.725962i	$0.258605\pi$
$8$	2.78392	0.984266
$9$	2.44491	0.814971
$10$	−4.14452	−1.31061
$11$	3.33191	1.00461	0.502304	−	0.864691i	$-0.332486\pi$
$11$	3.33191	1.00461	0.502304	+	0.864691i	$0.332486\pi$
$12$	0.141539	0.0408587
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−5.22400	−1.39617
$15$	6.73700	1.73949
$16$	−4.11763	−1.02941
$17$	−2.35851	−0.572022	−0.286011	−	0.958226i	$-0.592329\pi$
$17$	−2.35851	−0.572022	−0.286011	+	0.958226i	$0.592329\pi$
$18$	−3.50967	−0.827237
$19$	3.81285	0.874727	0.437363	−	0.899285i	$-0.355912\pi$
$19$	3.81285	0.874727	0.437363	+	0.899285i	$0.355912\pi$
$20$	0.175126	0.0391593
$21$	8.49172	1.85304
$22$	−4.78295	−1.01973
$23$	7.05905	1.47191	0.735957	−	0.677028i	$-0.236732\pi$
$23$	7.05905	1.47191	0.735957	+	0.677028i	$0.236732\pi$
$24$	6.49610	1.32601
$25$	3.33570	0.667140
$26$	1.43550	0.281524
$27$	−1.29526	−0.249272
$28$	0.220739	0.0417158
$29$	−8.67749	−1.61137	−0.805685	−	0.592345i	$-0.798202\pi$
$29$	−8.67749	−1.61137	−0.805685	+	0.592345i	$0.798202\pi$
$30$	−9.67096	−1.76567
$31$	−1.67449	−0.300747	−0.150373	−	0.988629i	$-0.548048\pi$
$31$	−1.67449	−0.300747	−0.150373	+	0.988629i	$0.548048\pi$
$32$	0.343009	0.0606361
$33$	7.77479	1.35342
$34$	3.38563	0.580631
$35$	10.5068	1.77598
$36$	0.148301	0.0247168
$37$	9.40944	1.54690	0.773451	−	0.633856i	$-0.218529\pi$
$37$	9.40944	1.54690	0.773451	+	0.633856i	$0.218529\pi$
$38$	−5.47334	−0.887892
$39$	−2.33343	−0.373648
$40$	8.03764	1.27086
$41$	−7.40781	−1.15691	−0.578453	−	0.815716i	$-0.696343\pi$
$41$	−7.40781	−1.15691	−0.578453	+	0.815716i	$0.696343\pi$
$42$	−12.1898	−1.88093
$43$	−10.2508	−1.56323	−0.781614	−	0.623762i	$-0.785604\pi$
$43$	−10.2508	−1.56323	−0.781614	+	0.623762i	$0.785604\pi$
$44$	0.202103	0.0304681
$45$	7.05886	1.05227
$46$	−10.1333	−1.49407
$47$	−11.0065	−1.60547	−0.802733	−	0.596338i	$-0.796622\pi$
$47$	−11.0065	−1.60547	−0.802733	+	0.596338i	$0.796622\pi$
$48$	−9.60823	−1.38683
$49$	6.24341	0.891916
$50$	−4.78839	−0.677181
$51$	−5.50342	−0.770632
$52$	−0.0606568	−0.00841158
$53$	−11.6636	−1.60212	−0.801059	−	0.598585i	$-0.795730\pi$
$53$	−11.6636	−1.60212	−0.801059	+	0.598585i	$0.795730\pi$
$54$	1.85934	0.253024
$55$	9.61976	1.29713
$56$	10.1311	1.35383
$57$	8.89702	1.17844
$58$	12.4565	1.63562
$59$	4.31184	0.561354	0.280677	−	0.959802i	$-0.409441\pi$
$59$	4.31184	0.561354	0.280677	+	0.959802i	$0.409441\pi$
$60$	0.408645	0.0527558
$61$	−13.3225	−1.70578	−0.852889	−	0.522093i	$-0.825152\pi$
$61$	−13.3225	−1.70578	−0.852889	+	0.522093i	$0.825152\pi$
$62$	2.40372	0.305273
$63$	8.89741	1.12097
$64$	7.74288	0.967860
$65$	−2.88716	−0.358108
$66$	−11.1607	−1.37379
$67$	−3.46302	−0.423076	−0.211538	−	0.977370i	$-0.567847\pi$
$67$	−3.46302	−0.423076	−0.211538	+	0.977370i	$0.567847\pi$
$68$	−0.143059	−0.0173485
$69$	16.4718	1.98298
$70$	−15.0825	−1.80271
$71$	4.27960	0.507895	0.253947	−	0.967218i	$-0.418271\pi$
$71$	4.27960	0.507895	0.253947	+	0.967218i	$0.418271\pi$
$72$	6.80646	0.802149
$73$	−7.02456	−0.822162	−0.411081	−	0.911599i	$-0.634849\pi$
$73$	−7.02456	−0.822162	−0.411081	+	0.911599i	$0.634849\pi$
$74$	−13.5072	−1.57018
$75$	7.78364	0.898777
$76$	0.231275	0.0265291
$77$	12.1253	1.38181
$78$	3.34964	0.379272
$79$	7.43314	0.836294	0.418147	−	0.908379i	$-0.362680\pi$
$79$	7.43314	0.836294	0.418147	+	0.908379i	$0.362680\pi$
$80$	−11.8883	−1.32915
$81$	−10.3571	−1.15079
$82$	10.6339	1.17432
$83$	11.5201	1.26449	0.632247	−	0.774767i	$-0.282133\pi$
$83$	11.5201	1.26449	0.632247	+	0.774767i	$0.282133\pi$
$84$	0.515080	0.0561999
$85$	−6.80939	−0.738582
$86$	14.7150	1.58676
$87$	−20.2484	−2.17085
$88$	9.27578	0.988802
$89$	−5.29591	−0.561366	−0.280683	−	0.959801i	$-0.590561\pi$
$89$	−5.29591	−0.561366	−0.280683	+	0.959801i	$0.590561\pi$
$90$	−10.1330	−1.06811
$91$	−3.63915	−0.381487
$92$	0.428179	0.0446408
$93$	−3.90730	−0.405169
$94$	15.7999	1.62963
$95$	11.0083	1.12943
$96$	0.800390	0.0816894
$97$	−9.44406	−0.958899	−0.479450	−	0.877569i	$-0.659164\pi$
$97$	−9.44406	−0.958899	−0.479450	+	0.877569i	$0.659164\pi$
$98$	−8.96241	−0.905341
$99$	8.14623	0.818727
$100$	0.202333	0.0202333
$101$	1.05662	0.105137	0.0525687	−	0.998617i	$-0.483259\pi$
$101$	1.05662	0.105137	0.0525687	+	0.998617i	$0.483259\pi$
$102$	7.90015	0.782231
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−2.78392	−0.272986
$105$	24.5170	2.39261
$106$	16.7431	1.62623
$107$	18.5139	1.78981	0.894904	−	0.446258i	$-0.147244\pi$
$107$	18.5139	1.78981	0.894904	+	0.446258i	$0.147244\pi$
$108$	−0.0785661	−0.00756003
$109$	−15.4533	−1.48016	−0.740078	−	0.672520i	$-0.765212\pi$
$109$	−15.4533	−1.48016	−0.740078	+	0.672520i	$0.765212\pi$
$110$	−13.8091	−1.31665
$111$	21.9563	2.08400
$112$	−14.9847	−1.41592
$113$	4.45788	0.419362	0.209681	−	0.977770i	$-0.432757\pi$
$113$	4.45788	0.419362	0.209681	+	0.977770i	$0.432757\pi$
$114$	−12.7717	−1.19618
$115$	20.3806	1.90050
$116$	−0.526349	−0.0488702
$117$	−2.44491	−0.226032
$118$	−6.18964	−0.569803
$119$	−8.58296	−0.786798
$120$	18.7553	1.71212
$121$	0.101612	0.00923747
$122$	19.1245	1.73145
$123$	−17.2856	−1.55859
$124$	−0.101569	−0.00912116
$125$	−4.80510	−0.429781
$126$	−12.7722	−1.13784
$127$	7.48975	0.664608	0.332304	−	0.943172i	$-0.392174\pi$
$127$	7.48975	0.664608	0.332304	+	0.943172i	$0.392174\pi$
$128$	−11.8009	−1.04306
$129$	−23.9195	−2.10600
$130$	4.14452	0.363498
$131$	−2.67225	−0.233476	−0.116738	−	0.993163i	$-0.537244\pi$
$131$	−2.67225	−0.233476	−0.116738	+	0.993163i	$0.537244\pi$
$132$	0.471594	0.0410470
$133$	13.8755	1.20316
$134$	4.97117	0.429443
$135$	−3.73962	−0.321855
$136$	−6.56590	−0.563021
$137$	15.2229	1.30058	0.650289	−	0.759687i	$-0.274648\pi$
$137$	15.2229	1.30058	0.650289	+	0.759687i	$0.274648\pi$
$138$	−23.6453	−2.01282
$139$	−1.28580	−0.109060	−0.0545299	−	0.998512i	$-0.517366\pi$
$139$	−1.28580	−0.109060	−0.0545299	+	0.998512i	$0.517366\pi$
$140$	0.637310	0.0538625
$141$	−25.6830	−2.16290
$142$	−6.14336	−0.515539
$143$	−3.33191	−0.278628
$144$	−10.0673	−0.838938
$145$	−25.0533	−2.08056
$146$	10.0837	0.834537
$147$	14.5686	1.20160
$148$	0.570746	0.0469150
$149$	16.7970	1.37606	0.688031	−	0.725682i	$-0.258475\pi$
$149$	16.7970	1.37606	0.688031	+	0.725682i	$0.258475\pi$
$150$	−11.1734	−0.912304
$151$	−10.6771	−0.868888	−0.434444	−	0.900699i	$-0.643055\pi$
$151$	−10.6771	−0.868888	−0.434444	+	0.900699i	$0.643055\pi$
$152$	10.6147	0.860964
$153$	−5.76634	−0.466181
$154$	−17.4059	−1.40261
$155$	−4.83451	−0.388317
$156$	−0.141539	−0.0113322
$157$	−14.0648	−1.12250	−0.561248	−	0.827647i	$-0.689679\pi$
$157$	−14.0648	−1.12250	−0.561248	+	0.827647i	$0.689679\pi$
$158$	−10.6703	−0.848881
$159$	−27.2162	−2.15839
$160$	0.990323	0.0782919
$161$	25.6890	2.02457
$162$	14.8677	1.16811
$163$	16.6602	1.30492	0.652462	−	0.757821i	$-0.273736\pi$
$163$	16.6602	1.30492	0.652462	+	0.757821i	$0.273736\pi$
$164$	−0.449334	−0.0350871
$165$	22.4471	1.74750
$166$	−16.5371	−1.28353
$167$	15.0813	1.16703	0.583514	−	0.812103i	$-0.301677\pi$
$167$	15.0813	1.16703	0.583514	+	0.812103i	$0.301677\pi$
$168$	23.6403	1.82389
$169$	1.00000	0.0769231
$170$	9.77487	0.749698
$171$	9.32208	0.712877
$172$	−0.621779	−0.0474102
$173$	23.1659	1.76127	0.880634	−	0.473797i	$-0.157117\pi$
$173$	23.1659	1.76127	0.880634	+	0.473797i	$0.157117\pi$
$174$	29.0665	2.20352
$175$	12.1391	0.917631
$176$	−13.7196	−1.03415
$177$	10.0614	0.756261
$178$	7.60228	0.569815
$179$	16.3787	1.22420	0.612099	−	0.790781i	$-0.290325\pi$
$179$	16.3787	1.22420	0.612099	+	0.790781i	$0.290325\pi$
$180$	0.428168	0.0319137
$181$	3.76683	0.279986	0.139993	−	0.990152i	$-0.455292\pi$
$181$	3.76683	0.279986	0.139993	+	0.990152i	$0.455292\pi$
$182$	5.22400	0.387228
$183$	−31.0873	−2.29804
$184$	19.6519	1.44876
$185$	27.1666	1.99733
$186$	5.60893	0.411267
$187$	−7.85832	−0.574658
$188$	−0.667620	−0.0486912
$189$	−4.71364	−0.342867
$190$	−15.8024	−1.14643
$191$	−11.5515	−0.835837	−0.417918	−	0.908485i	$-0.637240\pi$
$191$	−11.5515	−0.835837	−0.417918	+	0.908485i	$0.637240\pi$
$192$	18.0675	1.30391
$193$	13.6031	0.979170	0.489585	−	0.871956i	$-0.337148\pi$
$193$	13.6031	0.979170	0.489585	+	0.871956i	$0.337148\pi$
$194$	13.5569	0.973331
$195$	−6.73700	−0.482447
$196$	0.378705	0.0270504
$197$	−27.1952	−1.93758	−0.968788	−	0.247889i	$-0.920263\pi$
$197$	−27.1952	−1.93758	−0.968788	+	0.247889i	$0.920263\pi$
$198$	−11.6939	−0.831049
$199$	19.2970	1.36793	0.683965	−	0.729514i	$-0.260254\pi$
$199$	19.2970	1.36793	0.683965	+	0.729514i	$0.260254\pi$
$200$	9.28634	0.656643
$201$	−8.08074	−0.569971
$202$	−1.51677	−0.106720
$203$	−31.5787	−2.21639
$204$	−0.333820	−0.0233720
$205$	−21.3875	−1.49377
$206$	−1.43550	−0.100016
$207$	17.2588	1.19957
$208$	4.11763	0.285507
$209$	12.7041	0.878758
$210$	−35.1941	−2.42862
$211$	12.2925	0.846253	0.423127	−	0.906071i	$-0.360933\pi$
$211$	12.2925	0.846253	0.423127	+	0.906071i	$0.360933\pi$
$212$	−0.707477	−0.0485897
$213$	9.98616	0.684240
$214$	−26.5767	−1.81675
$215$	−29.5956	−2.01841
$216$	−3.60590	−0.245350
$217$	−6.09371	−0.413668
$218$	22.1832	1.50243
$219$	−16.3913	−1.10762
$220$	0.583503	0.0393398
$221$	2.35851	0.158650
$222$	−31.5182	−2.11537
$223$	19.4946	1.30546	0.652728	−	0.757592i	$-0.273624\pi$
$223$	19.4946	1.30546	0.652728	+	0.757592i	$0.273624\pi$
$224$	1.24826	0.0834031
$225$	8.15550	0.543700
$226$	−6.39928	−0.425673
$227$	12.6334	0.838507	0.419253	−	0.907869i	$-0.362292\pi$
$227$	12.6334	0.838507	0.419253	+	0.907869i	$0.362292\pi$
$228$	0.539665	0.0357402
$229$	13.8918	0.917995	0.458997	−	0.888438i	$-0.348209\pi$
$229$	13.8918	0.917995	0.458997	+	0.888438i	$0.348209\pi$
$230$	−29.2564	−1.92911
$231$	28.2936	1.86158
$232$	−24.1575	−1.58602
$233$	−3.67248	−0.240592	−0.120296	−	0.992738i	$-0.538384\pi$
$233$	−3.67248	−0.240592	−0.120296	+	0.992738i	$0.538384\pi$
$234$	3.50967	0.229434
$235$	−31.7776	−2.07294
$236$	0.261542	0.0170250
$237$	17.3447	1.12666
$238$	12.3208	0.798640
$239$	5.03602	0.325753	0.162877	−	0.986646i	$-0.447923\pi$
$239$	5.03602	0.325753	0.162877	+	0.986646i	$0.447923\pi$
$240$	−27.7405	−1.79064
$241$	−25.8803	−1.66710	−0.833549	−	0.552445i	$-0.813695\pi$
$241$	−25.8803	−1.66710	−0.833549	+	0.552445i	$0.813695\pi$
$242$	−0.145864	−0.00937651
$243$	−20.2819	−1.30109
$244$	−0.808103	−0.0517335
$245$	18.0257	1.15162
$246$	24.8135	1.58205
$247$	−3.81285	−0.242606
$248$	−4.66165	−0.296015
$249$	26.8814	1.70354
$250$	6.89772	0.436250
$251$	−17.9785	−1.13479	−0.567397	−	0.823444i	$-0.692050\pi$
$251$	−17.9785	−1.13479	−0.567397	+	0.823444i	$0.692050\pi$
$252$	0.539688	0.0339972
$253$	23.5201	1.47870
$254$	−10.7515	−0.674611
$255$	−15.8893	−0.995024
$256$	1.45444	0.0909023
$257$	10.2395	0.638721	0.319360	−	0.947633i	$-0.396532\pi$
$257$	10.2395	0.638721	0.319360	+	0.947633i	$0.396532\pi$
$258$	34.3364	2.13769
$259$	34.2424	2.12772
$260$	−0.175126	−0.0108608
$261$	−21.2157	−1.31322
$262$	3.83602	0.236990
$263$	−10.0615	−0.620419	−0.310210	−	0.950668i	$-0.600399\pi$
$263$	−10.0615	−0.620419	−0.310210	+	0.950668i	$0.600399\pi$
$264$	21.6444	1.33212
$265$	−33.6747	−2.06862
$266$	−19.9183	−1.22127
$267$	−12.3577	−0.756277
$268$	−0.210056	−0.0128312
$269$	7.96518	0.485646	0.242823	−	0.970071i	$-0.421927\pi$
$269$	7.96518	0.485646	0.242823	+	0.970071i	$0.421927\pi$
$270$	5.36821	0.326699
$271$	−6.89507	−0.418846	−0.209423	−	0.977825i	$-0.567159\pi$
$271$	−6.89507	−0.418846	−0.209423	+	0.977825i	$0.567159\pi$
$272$	9.71146	0.588844
$273$	−8.49172	−0.513942
$274$	−21.8524	−1.32015
$275$	11.1142	0.670214
$276$	0.999129	0.0601405
$277$	−19.0054	−1.14192	−0.570962	−	0.820976i	$-0.693430\pi$
$277$	−19.0054	−1.14192	−0.570962	+	0.820976i	$0.693430\pi$
$278$	1.84576	0.110701
$279$	−4.09398	−0.245100
$280$	29.2502	1.74803
$281$	−3.35856	−0.200355	−0.100177	−	0.994970i	$-0.531941\pi$
$281$	−3.35856	−0.200355	−0.100177	+	0.994970i	$0.531941\pi$
$282$	36.8679	2.19545
$283$	16.9341	1.00663	0.503314	−	0.864104i	$-0.332114\pi$
$283$	16.9341	1.00663	0.503314	+	0.864104i	$0.332114\pi$
$284$	0.259587	0.0154036
$285$	25.6871	1.52158
$286$	4.78295	0.282822
$287$	−26.9581	−1.59129
$288$	0.838628	0.0494167
$289$	−11.4375	−0.672791
$290$	35.9640	2.11188
$291$	−22.0371	−1.29184
$292$	−0.426087	−0.0249349
$293$	9.43686	0.551307	0.275654	−	0.961257i	$-0.411106\pi$
$293$	9.43686	0.551307	0.275654	+	0.961257i	$0.411106\pi$
$294$	−20.9132	−1.21968
$295$	12.4490	0.724808
$296$	26.1952	1.52256
$297$	−4.31568	−0.250421
$298$	−24.1120	−1.39677
$299$	−7.05905	−0.408236
$300$	0.472130	0.0272585
$301$	−37.3041	−2.15017
$302$	15.3269	0.881965
$303$	2.46555	0.141642
$304$	−15.6999	−0.900451
$305$	−38.4643	−2.20246
$306$	8.27758	0.473198
$307$	−18.3451	−1.04701	−0.523505	−	0.852022i	$-0.675376\pi$
$307$	−18.3451	−1.04701	−0.523505	+	0.852022i	$0.675376\pi$
$308$	0.735483	0.0419080
$309$	2.33343	0.132744
$310$	6.93994	0.394162
$311$	−20.2243	−1.14681	−0.573406	−	0.819271i	$-0.694378\pi$
$311$	−20.2243	−1.14681	−0.573406	+	0.819271i	$0.694378\pi$
$312$	−6.49610	−0.367770
$313$	16.0279	0.905950	0.452975	−	0.891523i	$-0.350363\pi$
$313$	16.0279	0.905950	0.452975	+	0.891523i	$0.350363\pi$
$314$	20.1901	1.13939
$315$	25.6883	1.44737
$316$	0.450870	0.0253634
$317$	11.4571	0.643494	0.321747	−	0.946826i	$-0.395730\pi$
$317$	11.4571	0.643494	0.321747	+	0.946826i	$0.395730\pi$
$318$	39.0689	2.19087
$319$	−28.9126	−1.61879
$320$	22.3549	1.24968
$321$	43.2010	2.41125
$322$	−36.8765	−2.05505
$323$	−8.99262	−0.500363
$324$	−0.628231	−0.0349017
$325$	−3.33570	−0.185031
$326$	−23.9156	−1.32457
$327$	−36.0592	−1.99408
$328$	−20.6228	−1.13870
$329$	−40.0544	−2.20827
$330$	−32.2227	−1.77380
$331$	−26.1727	−1.43858	−0.719291	−	0.694709i	$-0.755533\pi$
$331$	−26.1727	−1.43858	−0.719291	+	0.694709i	$0.755533\pi$
$332$	0.698772	0.0383501
$333$	23.0053	1.26068
$334$	−21.6492	−1.18459
$335$	−9.99831	−0.546266
$336$	−34.9658	−1.90754
$337$	−31.3026	−1.70516	−0.852581	−	0.522594i	$-0.824964\pi$
$337$	−31.3026	−1.70516	−0.852581	+	0.522594i	$0.824964\pi$
$338$	−1.43550	−0.0780808
$339$	10.4022	0.564968
$340$	−0.413035	−0.0224000
$341$	−5.57924	−0.302133
$342$	−13.3818	−0.723607
$343$	−2.75333	−0.148666
$344$	−28.5374	−1.53863
$345$	47.5568	2.56037
$346$	−33.2546	−1.78778
$347$	7.44250	0.399534	0.199767	−	0.979843i	$-0.435981\pi$
$347$	7.44250	0.399534	0.199767	+	0.979843i	$0.435981\pi$
$348$	−1.22820	−0.0658384
$349$	10.9745	0.587452	0.293726	−	0.955890i	$-0.405105\pi$
$349$	10.9745	0.587452	0.293726	+	0.955890i	$0.405105\pi$
$350$	−17.4257	−0.931442
$351$	1.29526	0.0691357
$352$	1.14288	0.0609155
$353$	21.1970	1.12820	0.564100	−	0.825706i	$-0.309223\pi$
$353$	21.1970	1.12820	0.564100	+	0.825706i	$0.309223\pi$
$354$	−14.4431	−0.767643
$355$	12.3559	0.655783
$356$	−0.321233	−0.0170253
$357$	−20.0278	−1.05998
$358$	−23.5116	−1.24262
$359$	29.5203	1.55802	0.779011	−	0.627010i	$-0.215721\pi$
$359$	29.5203	1.55802	0.779011	+	0.627010i	$0.215721\pi$
$360$	19.6513	1.03572
$361$	−4.46220	−0.234853
$362$	−5.40728	−0.284200
$363$	0.237105	0.0124448
$364$	−0.220739	−0.0115699
$365$	−20.2810	−1.06156
$366$	44.6258	2.33263
$367$	24.1304	1.25959	0.629797	−	0.776759i	$-0.283138\pi$
$367$	24.1304	1.25959	0.629797	+	0.776759i	$0.283138\pi$
$368$	−29.0666	−1.51520
$369$	−18.1115	−0.942845
$370$	−38.9976	−2.02739
$371$	−42.4456	−2.20367
$372$	−0.237005	−0.0122881
$373$	−15.4486	−0.799900	−0.399950	−	0.916537i	$-0.630973\pi$
$373$	−15.4486	−0.799900	−0.399950	+	0.916537i	$0.630973\pi$
$374$	11.2806	0.583307
$375$	−11.2124	−0.579005
$376$	−30.6413	−1.58021
$377$	8.67749	0.446914
$378$	6.76642	0.348027
$379$	−29.0750	−1.49348	−0.746742	−	0.665114i	$-0.768383\pi$
$379$	−29.0750	−1.49348	−0.746742	+	0.665114i	$0.768383\pi$
$380$	0.667728	0.0342537
$381$	17.4768	0.895365
$382$	16.5822	0.848417
$383$	−0.741066	−0.0378667	−0.0189334	−	0.999821i	$-0.506027\pi$
$383$	−0.741066	−0.0378667	−0.0189334	+	0.999821i	$0.506027\pi$
$384$	−27.5366	−1.40522
$385$	35.0077	1.78416
$386$	−19.5272	−0.993907
$387$	−25.0623	−1.27399
$388$	−0.572846	−0.0290819
$389$	−17.5260	−0.888604	−0.444302	−	0.895877i	$-0.646548\pi$
$389$	−17.5260	−0.888604	−0.444302	+	0.895877i	$0.646548\pi$
$390$	9.67096	0.489708
$391$	−16.6488	−0.841967
$392$	17.3812	0.877883
$393$	−6.23553	−0.314541
$394$	39.0387	1.96674
$395$	21.4607	1.07980
$396$	0.494124	0.0248307
$397$	7.00107	0.351374	0.175687	−	0.984446i	$-0.443785\pi$
$397$	7.00107	0.351374	0.175687	+	0.984446i	$0.443785\pi$
$398$	−27.7009	−1.38852
$399$	32.3776	1.62091
$400$	−13.7352	−0.686760
$401$	24.3095	1.21396	0.606980	−	0.794717i	$-0.292381\pi$
$401$	24.3095	1.21396	0.606980	+	0.794717i	$0.292381\pi$
$402$	11.5999	0.578550
$403$	1.67449	0.0834121
$404$	0.0640910	0.00318865
$405$	−29.9027	−1.48588
$406$	45.3312	2.24975
$407$	31.3514	1.55403
$408$	−15.3211	−0.758507
$409$	−26.2674	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$409$	−26.2674	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$410$	30.7018	1.51625
$411$	35.5216	1.75215
$412$	0.0606568	0.00298835
$413$	15.6914	0.772125
$414$	−24.7750	−1.21762
$415$	33.2604	1.63269
$416$	−0.343009	−0.0168174
$417$	−3.00032	−0.146926
$418$	−18.2367	−0.891984
$419$	13.2552	0.647558	0.323779	−	0.946133i	$-0.395046\pi$
$419$	13.2552	0.647558	0.323779	+	0.946133i	$0.395046\pi$
$420$	1.48712	0.0725640
$421$	17.7332	0.864263	0.432131	−	0.901811i	$-0.357762\pi$
$421$	17.7332	0.864263	0.432131	+	0.901811i	$0.357762\pi$
$422$	−17.6459	−0.858990
$423$	−26.9100	−1.30841
$424$	−32.4706	−1.57691
$425$	−7.86727	−0.381618
$426$	−14.3351	−0.694539
$427$	−48.4828	−2.34625
$428$	1.12299	0.0542820
$429$	−7.77479	−0.375370
$430$	42.4845	2.04879
$431$	3.12464	0.150508	0.0752542	−	0.997164i	$-0.476023\pi$
$431$	3.12464	0.150508	0.0752542	+	0.997164i	$0.476023\pi$
$432$	5.33339	0.256603
$433$	11.3748	0.546637	0.273318	−	0.961924i	$-0.411879\pi$
$433$	11.3748	0.546637	0.273318	+	0.961924i	$0.411879\pi$
$434$	8.74751	0.419894
$435$	−58.4603	−2.80295
$436$	−0.937347	−0.0448908
$437$	26.9151	1.28752
$438$	23.5297	1.12429
$439$	−0.209566	−0.0100020	−0.00500102	−	0.999987i	$-0.501592\pi$
$439$	−0.209566	−0.0100020	−0.00500102	+	0.999987i	$0.501592\pi$
$440$	26.7807	1.27672
$441$	15.2646	0.726886
$442$	−3.38563	−0.161038
$443$	13.5580	0.644159	0.322080	−	0.946713i	$-0.395618\pi$
$443$	13.5580	0.644159	0.322080	+	0.946713i	$0.395618\pi$
$444$	1.33180	0.0632044
$445$	−15.2902	−0.724823
$446$	−27.9845	−1.32511
$447$	39.1946	1.85384
$448$	28.1775	1.33126
$449$	31.8804	1.50453	0.752266	−	0.658860i	$-0.228961\pi$
$449$	31.8804	1.50453	0.752266	+	0.658860i	$0.228961\pi$
$450$	−11.7072	−0.551883
$451$	−24.6821	−1.16224
$452$	0.270400	0.0127186
$453$	−24.9142	−1.17057
$454$	−18.1352	−0.851127
$455$	−10.5068	−0.492567
$456$	24.7686	1.15990
$457$	−23.4645	−1.09762	−0.548812	−	0.835946i	$-0.684920\pi$
$457$	−23.4645	−1.09762	−0.548812	+	0.835946i	$0.684920\pi$
$458$	−19.9416	−0.931811
$459$	3.05487	0.142589
$460$	1.23622	0.0576392
$461$	−14.2661	−0.664438	−0.332219	−	0.943202i	$-0.607797\pi$
$461$	−14.2661	−0.664438	−0.332219	+	0.943202i	$0.607797\pi$
$462$	−40.6155	−1.88960
$463$	−31.0802	−1.44442	−0.722209	−	0.691675i	$-0.756873\pi$
$463$	−31.0802	−1.44442	−0.722209	+	0.691675i	$0.756873\pi$
$464$	35.7307	1.65876
$465$	−11.2810	−0.523145
$466$	5.27184	0.244213
$467$	−6.22789	−0.288192	−0.144096	−	0.989564i	$-0.546027\pi$
$467$	−6.22789	−0.288192	−0.144096	+	0.989564i	$0.546027\pi$
$468$	−0.148301	−0.00685520
$469$	−12.6025	−0.581928
$470$	45.6167	2.10414
$471$	−32.8194	−1.51224
$472$	12.0038	0.552522
$473$	−34.1547	−1.57043
$474$	−24.8984	−1.14362
$475$	12.7185	0.583565
$476$	−0.520615	−0.0238623
$477$	−28.5165	−1.30568
$478$	−7.22920	−0.330656
$479$	16.1583	0.738294	0.369147	−	0.929371i	$-0.379650\pi$
$479$	16.1583	0.738294	0.369147	+	0.929371i	$0.379650\pi$
$480$	2.31085	0.105476
$481$	−9.40944	−0.429033
$482$	37.1512	1.69219
$483$	59.9435	2.72752
$484$	0.00616347	0.000280158 0
$485$	−27.2665	−1.23811
$486$	29.1147	1.32067
$487$	4.63890	0.210209	0.105104	−	0.994461i	$-0.466482\pi$
$487$	4.63890	0.210209	0.105104	+	0.994461i	$0.466482\pi$
$488$	−37.0890	−1.67894
$489$	38.8754	1.75801
$490$	−25.8759	−1.16896
$491$	4.27337	0.192855	0.0964273	−	0.995340i	$-0.469258\pi$
$491$	4.27337	0.192855	0.0964273	+	0.995340i	$0.469258\pi$
$492$	−1.04849	−0.0472696
$493$	20.4659	0.921738
$494$	5.47334	0.246257
$495$	23.5195	1.05712
$496$	6.89492	0.309591
$497$	15.5741	0.698594
$498$	−38.5882	−1.72918
$499$	−20.6797	−0.925751	−0.462876	−	0.886423i	$-0.653182\pi$
$499$	−20.6797	−0.925751	−0.462876	+	0.886423i	$0.653182\pi$
$500$	−0.291462	−0.0130346
$501$	35.1913	1.57223
$502$	25.8081	1.15187
$503$	−13.7316	−0.612263	−0.306132	−	0.951989i	$-0.599035\pi$
$503$	−13.7316	−0.612263	−0.306132	+	0.951989i	$0.599035\pi$
$504$	24.7697	1.10333
$505$	3.05063	0.135751
$506$	−33.7631	−1.50095
$507$	2.33343	0.103631
$508$	0.454304	0.0201565
$509$	36.7130	1.62728	0.813638	−	0.581372i	$-0.197484\pi$
$509$	36.7130	1.62728	0.813638	+	0.581372i	$0.197484\pi$
$510$	22.8090	1.01000
$511$	−25.5634	−1.13086
$512$	21.5140	0.950793
$513$	−4.93862	−0.218045
$514$	−14.6988	−0.648334
$515$	2.88716	0.127224
$516$	−1.45088	−0.0638715
$517$	−36.6727	−1.61286
$518$	−49.1549	−2.15974
$519$	54.0560	2.37280
$520$	−8.03764	−0.352474
$521$	5.32979	0.233503	0.116751	−	0.993161i	$-0.462752\pi$
$521$	5.32979	0.233503	0.116751	+	0.993161i	$0.462752\pi$
$522$	30.4551	1.33299
$523$	28.9002	1.26372	0.631859	−	0.775083i	$-0.282292\pi$
$523$	28.9002	1.26372	0.631859	+	0.775083i	$0.282292\pi$
$524$	−0.162090	−0.00708095
$525$	28.3258	1.23624
$526$	14.4433	0.629757
$527$	3.94929	0.172034
$528$	−32.0137	−1.39322
$529$	26.8302	1.16653
$530$	48.3400	2.09975
$531$	10.5421	0.457487
$532$	0.841644	0.0364899
$533$	7.40781	0.320868
$534$	17.7394	0.767660
$535$	53.4527	2.31096
$536$	−9.64080	−0.416419
$537$	38.2185	1.64925
$538$	−11.4340	−0.492955
$539$	20.8025	0.896026
$540$	−0.226833	−0.00976134
$541$	1.90946	0.0820943	0.0410471	−	0.999157i	$-0.486931\pi$
$541$	1.90946	0.0820943	0.0410471	+	0.999157i	$0.486931\pi$
$542$	9.89787	0.425150
$543$	8.78964	0.377200
$544$	−0.808990	−0.0346851
$545$	−44.6161	−1.91115
$546$	12.1898	0.521677
$547$	−3.28850	−0.140606	−0.0703031	−	0.997526i	$-0.522397\pi$
$547$	−3.28850	−0.140606	−0.0703031	+	0.997526i	$0.522397\pi$
$548$	0.923370	0.0394444
$549$	−32.5725	−1.39016
$550$	−15.9545	−0.680302
$551$	−33.0859	−1.40951
$552$	45.8563	1.95178
$553$	27.0503	1.15030
$554$	27.2822	1.15911
$555$	63.3914	2.69081
$556$	−0.0779923	−0.00330761
$557$	−23.1431	−0.980603	−0.490302	−	0.871553i	$-0.663113\pi$
$557$	−23.1431	−0.980603	−0.490302	+	0.871553i	$0.663113\pi$
$558$	5.87690	0.248789
$559$	10.2508	0.433562
$560$	−43.2632	−1.82820
$561$	−18.3369	−0.774184
$562$	4.82120	0.203370
$563$	6.13403	0.258518	0.129259	−	0.991611i	$-0.458740\pi$
$563$	6.13403	0.258518	0.129259	+	0.991611i	$0.458740\pi$
$564$	−1.55785	−0.0655972
$565$	12.8706	0.541471
$566$	−24.3089	−1.02178
$567$	−37.6912	−1.58288
$568$	11.9141	0.499904
$569$	−10.0606	−0.421763	−0.210882	−	0.977512i	$-0.567633\pi$
$569$	−10.0606	−0.421763	−0.210882	+	0.977512i	$0.567633\pi$
$570$	−36.8739	−1.54448
$571$	−14.7588	−0.617635	−0.308817	−	0.951121i	$-0.599933\pi$
$571$	−14.7588	−0.617635	−0.308817	+	0.951121i	$0.599933\pi$
$572$	−0.202103	−0.00845034
$573$	−26.9546	−1.12605
$574$	38.6984	1.61524
$575$	23.5469	0.981973
$576$	18.9307	0.788778
$577$	30.1860	1.25666	0.628330	−	0.777947i	$-0.283739\pi$
$577$	30.1860	1.25666	0.628330	+	0.777947i	$0.283739\pi$
$578$	16.4184	0.682917
$579$	31.7418	1.31915
$580$	−1.51965	−0.0631002
$581$	41.9234	1.73927
$582$	31.6342	1.31128
$583$	−38.8621	−1.60950
$584$	−19.5558	−0.809226
$585$	−7.05886	−0.291848
$586$	−13.5466	−0.559605
$587$	−0.200566	−0.00827825	−0.00413913	−	0.999991i	$-0.501318\pi$
$587$	−0.200566	−0.00827825	−0.00413913	+	0.999991i	$0.501318\pi$
$588$	0.883684	0.0364425
$589$	−6.38456	−0.263071
$590$	−17.8705	−0.735717
$591$	−63.4582	−2.61032
$592$	−38.7446	−1.59239
$593$	−2.05489	−0.0843842	−0.0421921	−	0.999110i	$-0.513434\pi$
$593$	−2.05489	−0.0843842	−0.0421921	+	0.999110i	$0.513434\pi$
$594$	6.19515	0.254190
$595$	−24.7804	−1.01590
$596$	1.01885	0.0417337
$597$	45.0284	1.84289
$598$	10.1333	0.414380
$599$	−5.11074	−0.208819	−0.104410	−	0.994534i	$-0.533295\pi$
$599$	−5.11074	−0.208819	−0.104410	+	0.994534i	$0.533295\pi$
$600$	21.6691	0.884636
$601$	10.9293	0.445815	0.222907	−	0.974840i	$-0.428445\pi$
$601$	10.9293	0.445815	0.222907	+	0.974840i	$0.428445\pi$
$602$	53.5500	2.18254
$603$	−8.46679	−0.344795
$604$	−0.647637	−0.0263520
$605$	0.293371	0.0119272
$606$	−3.53929	−0.143774
$607$	−8.16430	−0.331379	−0.165689	−	0.986178i	$-0.552985\pi$
$607$	−8.16430	−0.331379	−0.165689	+	0.986178i	$0.552985\pi$
$608$	1.30784	0.0530400
$609$	−73.6868	−2.98594
$610$	55.2155	2.23561
$611$	11.0065	0.445276
$612$	−0.349768	−0.0141385
$613$	−16.9636	−0.685154	−0.342577	−	0.939490i	$-0.611300\pi$
$613$	−16.9636	−0.685154	−0.342577	+	0.939490i	$0.611300\pi$
$614$	26.3344	1.06277
$615$	−49.9064	−2.01242
$616$	33.7560	1.36007
$617$	−15.8485	−0.638037	−0.319019	−	0.947748i	$-0.603353\pi$
$617$	−15.8485	−0.638037	−0.319019	+	0.947748i	$0.603353\pi$
$618$	−3.34964	−0.134742
$619$	9.72200	0.390760	0.195380	−	0.980728i	$-0.437406\pi$
$619$	9.72200	0.390760	0.195380	+	0.980728i	$0.437406\pi$
$620$	−0.293246	−0.0117770
$621$	−9.14329	−0.366908
$622$	29.0319	1.16407
$623$	−19.2726	−0.772142
$624$	9.60823	0.384637
$625$	−30.5516	−1.22206
$626$	−23.0080	−0.919585
$627$	29.6441	1.18387
$628$	−0.853128	−0.0340435
$629$	−22.1922	−0.884861
$630$	−36.8755	−1.46915
$631$	25.0643	0.997793	0.498896	−	0.866662i	$-0.333739\pi$
$631$	25.0643	0.997793	0.498896	+	0.866662i	$0.333739\pi$
$632$	20.6933	0.823136
$633$	28.6838	1.14008
$634$	−16.4466	−0.653179
$635$	21.6241	0.858126
$636$	−1.65085	−0.0654605
$637$	−6.24341	−0.247373
$638$	41.5040	1.64316
$639$	10.4632	0.413920
$640$	−34.0711	−1.34678
$641$	26.4189	1.04349	0.521743	−	0.853103i	$-0.325282\pi$
$641$	26.4189	1.04349	0.521743	+	0.853103i	$0.325282\pi$
$642$	−62.0150	−2.44754
$643$	19.0726	0.752148	0.376074	−	0.926590i	$-0.377274\pi$
$643$	19.0726	0.752148	0.376074	+	0.926590i	$0.377274\pi$
$644$	1.55821	0.0614021
$645$	−69.0595	−2.71921
$646$	12.9089	0.507894
$647$	10.2073	0.401292	0.200646	−	0.979664i	$-0.435696\pi$
$647$	10.2073	0.401292	0.200646	+	0.979664i	$0.435696\pi$
$648$	−28.8335	−1.13269
$649$	14.3667	0.563941
$650$	4.78839	0.187816
$651$	−14.2193	−0.557297
$652$	1.01055	0.0395763
$653$	2.42575	0.0949270	0.0474635	−	0.998873i	$-0.484886\pi$
$653$	2.42575	0.0949270	0.0474635	+	0.998873i	$0.484886\pi$
$654$	51.7630	2.02409
$655$	−7.71523	−0.301459
$656$	30.5027	1.19093
$657$	−17.1744	−0.670039
$658$	57.4980	2.24151
$659$	−24.6842	−0.961561	−0.480781	−	0.876841i	$-0.659647\pi$
$659$	−24.6842	−0.961561	−0.480781	+	0.876841i	$0.659647\pi$
$660$	1.36157	0.0529989
$661$	35.8122	1.39293	0.696467	−	0.717589i	$-0.254754\pi$
$661$	35.8122	1.39293	0.696467	+	0.717589i	$0.254754\pi$
$662$	37.5709	1.46023
$663$	5.50342	0.213735
$664$	32.0711	1.24460
$665$	40.0609	1.55349
$666$	−33.0240	−1.27965
$667$	−61.2549	−2.37180
$668$	0.914785	0.0353941
$669$	45.4894	1.75872
$670$	14.3526	0.554488
$671$	−44.3895	−1.71364
$672$	2.91274	0.112361
$673$	−5.50846	−0.212336	−0.106168	−	0.994348i	$-0.533858\pi$
$673$	−5.50846	−0.212336	−0.106168	+	0.994348i	$0.533858\pi$
$674$	44.9349	1.73083
$675$	−4.32059	−0.166300
$676$	0.0606568	0.00233295
$677$	27.1616	1.04391	0.521953	−	0.852974i	$-0.325204\pi$
$677$	27.1616	1.04391	0.521953	+	0.852974i	$0.325204\pi$
$678$	−14.9323	−0.573471
$679$	−34.3684	−1.31894
$680$	−18.9568	−0.726961
$681$	29.4792	1.12964
$682$	8.00899	0.306680
$683$	37.9273	1.45125	0.725623	−	0.688092i	$-0.241552\pi$
$683$	37.9273	1.45125	0.725623	+	0.688092i	$0.241552\pi$
$684$	0.565447	0.0216204
$685$	43.9509	1.67928
$686$	3.95240	0.150903
$687$	32.4155	1.23673
$688$	42.2090	1.60920
$689$	11.6636	0.444348
$690$	−68.2678	−2.59891
$691$	−33.2515	−1.26495	−0.632473	−	0.774583i	$-0.717960\pi$
$691$	−33.2515	−1.26495	−0.632473	+	0.774583i	$0.717960\pi$
$692$	1.40517	0.0534164
$693$	29.6453	1.12613
$694$	−10.6837	−0.405548
$695$	−3.71230	−0.140816
$696$	−56.3699	−2.13670
$697$	17.4714	0.661775
$698$	−15.7539	−0.596294
$699$	−8.56949	−0.324128
$700$	0.736320	0.0278303
$701$	32.9912	1.24606	0.623030	−	0.782198i	$-0.285901\pi$
$701$	32.9912	1.24606	0.623030	+	0.782198i	$0.285901\pi$
$702$	−1.85934	−0.0701763
$703$	35.8767	1.35312
$704$	25.7986	0.972320
$705$	−74.1510	−2.79269
$706$	−30.4282	−1.14518
$707$	3.84519	0.144613
$708$	0.610292	0.0229362
$709$	12.1450	0.456115	0.228058	−	0.973648i	$-0.426763\pi$
$709$	12.1450	0.456115	0.228058	+	0.973648i	$0.426763\pi$
$710$	−17.7369	−0.665653
$711$	18.1734	0.681555
$712$	−14.7434	−0.552533
$713$	−11.8203	−0.442673
$714$	28.7498	1.07594
$715$	−9.61976	−0.359758
$716$	0.993477	0.0371280
$717$	11.7512	0.438857
$718$	−42.3764	−1.58147
$719$	8.03858	0.299788	0.149894	−	0.988702i	$-0.452107\pi$
$719$	8.03858	0.299788	0.149894	+	0.988702i	$0.452107\pi$
$720$	−29.0658	−1.08322
$721$	3.63915	0.135529
$722$	6.40549	0.238388
$723$	−60.3900	−2.24593
$724$	0.228484	0.00849153
$725$	−28.9455	−1.07501
$726$	−0.340364	−0.0126321
$727$	33.0873	1.22714	0.613570	−	0.789640i	$-0.289733\pi$
$727$	33.0873	1.22714	0.613570	+	0.789640i	$0.289733\pi$
$728$	−10.1311	−0.375484
$729$	−16.2551	−0.602041
$730$	29.1134	1.07753
$731$	24.1765	0.894201
$732$	−1.88565	−0.0696958
$733$	−43.5101	−1.60708	−0.803541	−	0.595249i	$-0.797053\pi$
$733$	−43.5101	−1.60708	−0.803541	+	0.595249i	$0.797053\pi$
$734$	−34.6391	−1.27855
$735$	42.0619	1.55148
$736$	2.42132	0.0892511
$737$	−11.5385	−0.425025
$738$	25.9990	0.957036
$739$	42.6617	1.56934	0.784668	−	0.619917i	$-0.212834\pi$
$739$	42.6617	1.56934	0.784668	+	0.619917i	$0.212834\pi$
$740$	1.64784	0.0605757
$741$	−8.89702	−0.326840
$742$	60.9306	2.23683
$743$	1.57867	0.0579159	0.0289579	−	0.999581i	$-0.490781\pi$
$743$	1.57867	0.0579159	0.0289579	+	0.999581i	$0.490781\pi$
$744$	−10.8776	−0.398794
$745$	48.4956	1.77674
$746$	22.1765	0.811939
$747$	28.1656	1.03053
$748$	−0.476661	−0.0174284
$749$	67.3749	2.46183
$750$	16.0954	0.587720
$751$	−5.21748	−0.190389	−0.0951943	−	0.995459i	$-0.530347\pi$
$751$	−5.21748	−0.190389	−0.0951943	+	0.995459i	$0.530347\pi$
$752$	45.3208	1.65268
$753$	−41.9517	−1.52880
$754$	−12.4565	−0.453640
$755$	−30.8264	−1.12189
$756$	−0.285914	−0.0103986
$757$	−24.7737	−0.900415	−0.450208	−	0.892924i	$-0.648650\pi$
$757$	−24.7737	−0.900415	−0.450208	+	0.892924i	$0.648650\pi$
$758$	41.7372	1.51596
$759$	54.8826	1.99211
$760$	30.6463	1.11166
$761$	5.18315	0.187889	0.0939445	−	0.995577i	$-0.470052\pi$
$761$	5.18315	0.187889	0.0939445	+	0.995577i	$0.470052\pi$
$762$	−25.0880	−0.908841
$763$	−56.2369	−2.03591
$764$	−0.700676	−0.0253496
$765$	−16.6484	−0.601923
$766$	1.06380	0.0384366
$767$	−4.31184	−0.155692
$768$	3.39383	0.122464
$769$	21.8295	0.787192	0.393596	−	0.919284i	$-0.371231\pi$
$769$	21.8295	0.787192	0.393596	+	0.919284i	$0.371231\pi$
$770$	−50.2536	−1.81101
$771$	23.8931	0.860490
$772$	0.825118	0.0296966
$773$	−4.41972	−0.158966	−0.0794831	−	0.996836i	$-0.525327\pi$
$773$	−4.41972	−0.158966	−0.0794831	+	0.996836i	$0.525327\pi$
$774$	35.9769	1.29316
$775$	−5.58559	−0.200640
$776$	−26.2916	−0.943812
$777$	79.9023	2.86648
$778$	25.1586	0.901978
$779$	−28.2448	−1.01198
$780$	−0.408645	−0.0146318
$781$	14.2592	0.510235
$782$	23.8994	0.854639
$783$	11.2396	0.401670
$784$	−25.7081	−0.918146
$785$	−40.6075	−1.44934
$786$	8.95109	0.319275
$787$	40.0571	1.42788	0.713940	−	0.700207i	$-0.246909\pi$
$787$	40.0571	1.42788	0.713940	+	0.700207i	$0.246909\pi$
$788$	−1.64957	−0.0587636
$789$	−23.4779	−0.835835
$790$	−30.8068	−1.09606
$791$	16.2229	0.576819
$792$	22.6785	0.805845
$793$	13.3225	0.473098
$794$	−10.0500	−0.356662
$795$	−78.5777	−2.78686
$796$	1.17050	0.0414871
$797$	−6.35764	−0.225199	−0.112600	−	0.993640i	$-0.535918\pi$
$797$	−6.35764	−0.225199	−0.112600	+	0.993640i	$0.535918\pi$
$798$	−46.4780	−1.64530
$799$	25.9589	0.918362
$800$	1.14418	0.0404527
$801$	−12.9481	−0.457497
$802$	−34.8963	−1.23223
$803$	−23.4052	−0.825951
$804$	−0.490152	−0.0172863
$805$	74.1682	2.61408
$806$	−2.40372	−0.0846676
$807$	18.5862	0.654266
$808$	2.94155	0.103483
$809$	−50.2866	−1.76798	−0.883991	−	0.467505i	$-0.845153\pi$
$809$	−50.2866	−1.76798	−0.883991	+	0.467505i	$0.845153\pi$
$810$	42.9253	1.50824
$811$	16.7245	0.587276	0.293638	−	0.955917i	$-0.405134\pi$
$811$	16.7245	0.587276	0.293638	+	0.955917i	$0.405134\pi$
$812$	−1.91546	−0.0672195
$813$	−16.0892	−0.564273
$814$	−45.0049	−1.57742
$815$	48.1006	1.68489
$816$	22.6611	0.793296
$817$	−39.0846	−1.36740
$818$	37.7068	1.31839
$819$	−8.89741	−0.310901
$820$	−1.29730	−0.0453037
$821$	12.4532	0.434620	0.217310	−	0.976103i	$-0.430272\pi$
$821$	12.4532	0.434620	0.217310	+	0.976103i	$0.430272\pi$
$822$	−50.9912	−1.77852
$823$	−48.2627	−1.68233	−0.841166	−	0.540777i	$-0.818130\pi$
$823$	−48.2627	−1.68233	−0.841166	+	0.540777i	$0.818130\pi$
$824$	2.78392	0.0969826
$825$	25.9344	0.902918
$826$	−22.5250	−0.783746
$827$	−26.5695	−0.923913	−0.461957	−	0.886903i	$-0.652852\pi$
$827$	−26.5695	−0.923913	−0.461957	+	0.886903i	$0.652852\pi$
$828$	1.04686	0.0363810
$829$	−11.1657	−0.387802	−0.193901	−	0.981021i	$-0.562114\pi$
$829$	−11.1657	−0.387802	−0.193901	+	0.981021i	$0.562114\pi$
$830$	−47.7452	−1.65726
$831$	−44.3479	−1.53841
$832$	−7.74288	−0.268436
$833$	−14.7251	−0.510195
$834$	4.30696	0.149138
$835$	43.5422	1.50684
$836$	0.770587	0.0266513
$837$	2.16889	0.0749678
$838$	−19.0278	−0.657305
$839$	14.4739	0.499695	0.249848	−	0.968285i	$-0.419619\pi$
$839$	14.4739	0.499695	0.249848	+	0.968285i	$0.419619\pi$
$840$	68.2534	2.35496
$841$	46.2988	1.59651
$842$	−25.4560	−0.877270
$843$	−7.83697	−0.269920
$844$	0.745626	0.0256655
$845$	2.88716	0.0993214
$846$	38.6293	1.32810
$847$	0.369782	0.0127059
$848$	48.0264	1.64923
$849$	39.5146	1.35614
$850$	11.2935	0.387362
$851$	66.4217	2.27691
$852$	0.605728	0.0207519
$853$	−26.2794	−0.899789	−0.449895	−	0.893082i	$-0.648538\pi$
$853$	−26.2794	−0.899789	−0.449895	+	0.893082i	$0.648538\pi$
$854$	69.5969	2.38156
$855$	26.9143	0.920451
$856$	51.5414	1.76165
$857$	−20.1505	−0.688329	−0.344164	−	0.938909i	$-0.611838\pi$
$857$	−20.1505	−0.688329	−0.344164	+	0.938909i	$0.611838\pi$
$858$	11.1607	0.381020
$859$	0.612317	0.0208920	0.0104460	−	0.999945i	$-0.496675\pi$
$859$	0.612317	0.0208920	0.0104460	+	0.999945i	$0.496675\pi$
$860$	−1.79518	−0.0612150
$861$	−62.9050	−2.14380
$862$	−4.48541	−0.152774
$863$	−58.1821	−1.98054	−0.990271	−	0.139154i	$-0.955562\pi$
$863$	−58.1821	−1.98054	−0.990271	+	0.139154i	$0.955562\pi$
$864$	−0.444285	−0.0151149
$865$	66.8836	2.27411
$866$	−16.3285	−0.554864
$867$	−26.6885	−0.906390
$868$	−0.369625	−0.0125459
$869$	24.7665	0.840148
$870$	83.9196	2.84514
$871$	3.46302	0.117340
$872$	−43.0208	−1.45687
$873$	−23.0899	−0.781475
$874$	−38.6366	−1.30690
$875$	−17.4865	−0.591151
$876$	−0.994246	−0.0335925
$877$	27.6305	0.933016	0.466508	−	0.884517i	$-0.345512\pi$
$877$	27.6305	0.933016	0.466508	+	0.884517i	$0.345512\pi$
$878$	0.300832	0.0101526
$879$	22.0203	0.742726
$880$	−39.6106	−1.33527
$881$	0.0733470	0.00247112	0.00123556	−	0.999999i	$-0.499607\pi$
$881$	0.0733470	0.00247112	0.00123556	+	0.999999i	$0.499607\pi$
$882$	−21.9123	−0.737827
$883$	−9.02907	−0.303852	−0.151926	−	0.988392i	$-0.548548\pi$
$883$	−9.02907	−0.303852	−0.151926	+	0.988392i	$0.548548\pi$
$884$	0.143059	0.00481161
$885$	29.0489	0.976467
$886$	−19.4625	−0.653855
$887$	−1.42730	−0.0479240	−0.0239620	−	0.999713i	$-0.507628\pi$
$887$	−1.42730	−0.0479240	−0.0239620	+	0.999713i	$0.507628\pi$
$888$	61.1247	2.05121
$889$	27.2563	0.914147
$890$	21.9490	0.735732
$891$	−34.5090	−1.15610
$892$	1.18248	0.0395924
$893$	−41.9662	−1.40434
$894$	−56.2638	−1.88174
$895$	47.2878	1.58066
$896$	−42.9453	−1.43470
$897$	−16.4718	−0.549979
$898$	−45.7643	−1.52718
$899$	14.5303	0.484614
$900$	0.494686	0.0164895
$901$	27.5087	0.916447
$902$	35.4312	1.17973
$903$	−87.0467	−2.89673
$904$	12.4104	0.412763
$905$	10.8754	0.361512
$906$	35.7644	1.18819
$907$	24.0158	0.797430	0.398715	−	0.917075i	$-0.369456\pi$
$907$	24.0158	0.797430	0.398715	+	0.917075i	$0.369456\pi$
$908$	0.766300	0.0254306
$909$	2.58334	0.0856840
$910$	15.0825	0.499981
$911$	9.18970	0.304468	0.152234	−	0.988344i	$-0.451353\pi$
$911$	9.18970	0.304468	0.152234	+	0.988344i	$0.451353\pi$
$912$	−36.6347	−1.21310
$913$	38.3839	1.27032
$914$	33.6833	1.11414
$915$	−89.7540	−2.96718
$916$	0.842631	0.0278413
$917$	−9.72473	−0.321139
$918$	−4.38526	−0.144735
$919$	3.54818	0.117044	0.0585219	−	0.998286i	$-0.481361\pi$
$919$	3.54818	0.117044	0.0585219	+	0.998286i	$0.481361\pi$
$920$	56.7381	1.87060
$921$	−42.8071	−1.41054
$922$	20.4789	0.674438
$923$	−4.27960	−0.140865
$924$	1.71620	0.0564588
$925$	31.3871	1.03200
$926$	44.6155	1.46616
$927$	2.44491	0.0803015
$928$	−2.97646	−0.0977071
$929$	−24.4727	−0.802922	−0.401461	−	0.915876i	$-0.631497\pi$
$929$	−24.4727	−0.802922	−0.401461	+	0.915876i	$0.631497\pi$
$930$	16.1939	0.531019
$931$	23.8052	0.780183
$932$	−0.222761	−0.00729678
$933$	−47.1920	−1.54500
$934$	8.94013	0.292530
$935$	−22.6882	−0.741985
$936$	−6.80646	−0.222476
$937$	−10.1436	−0.331377	−0.165688	−	0.986178i	$-0.552985\pi$
$937$	−10.1436	−0.331377	−0.165688	+	0.986178i	$0.552985\pi$
$938$	18.0908	0.590686
$939$	37.4000	1.22050
$940$	−1.92753	−0.0628690
$941$	36.2636	1.18216	0.591079	−	0.806614i	$-0.298702\pi$
$941$	36.2636	1.18216	0.591079	+	0.806614i	$0.298702\pi$
$942$	47.1122	1.53500
$943$	−52.2921	−1.70287
$944$	−17.7546	−0.577862
$945$	−13.6090	−0.442702
$946$	49.0290	1.59407
$947$	−49.3714	−1.60436	−0.802178	−	0.597085i	$-0.796325\pi$
$947$	−49.3714	−1.60436	−0.802178	+	0.597085i	$0.796325\pi$
$948$	1.05208	0.0341699
$949$	7.02456	0.228027
$950$	−18.2574	−0.592349
$951$	26.7343	0.866920
$952$	−23.8943	−0.774419
$953$	15.0175	0.486464	0.243232	−	0.969968i	$-0.421792\pi$
$953$	15.0175	0.486464	0.243232	+	0.969968i	$0.421792\pi$
$954$	40.9354	1.32533
$955$	−33.3510	−1.07921
$956$	0.305469	0.00987957
$957$	−67.4656	−2.18085
$958$	−23.1953	−0.749406
$959$	55.3983	1.78890
$960$	52.1638	1.68358
$961$	−28.1961	−0.909551
$962$	13.5072	0.435491
$963$	45.2649	1.45864
$964$	−1.56982	−0.0505604
$965$	39.2742	1.26428
$966$	−86.0488	−2.76857
$967$	8.98939	0.289079	0.144540	−	0.989499i	$-0.453830\pi$
$967$	8.98939	0.289079	0.144540	+	0.989499i	$0.453830\pi$
$968$	0.282881	0.00909213
$969$	−20.9837	−0.674093
$970$	39.1411	1.25674
$971$	17.9738	0.576806	0.288403	−	0.957509i	$-0.406876\pi$
$971$	17.9738	0.576806	0.288403	+	0.957509i	$0.406876\pi$
$972$	−1.23024	−0.0394599
$973$	−4.67921	−0.150008
$974$	−6.65914	−0.213372
$975$	−7.78364	−0.249276
$976$	54.8574	1.75594
$977$	24.2953	0.777277	0.388638	−	0.921390i	$-0.372946\pi$
$977$	24.2953	0.777277	0.388638	+	0.921390i	$0.372946\pi$
$978$	−55.8056	−1.78447
$979$	−17.6455	−0.563953
$980$	1.09338	0.0349269
$981$	−37.7820	−1.20629
$982$	−6.13442	−0.195757
$983$	−29.3667	−0.936652	−0.468326	−	0.883556i	$-0.655143\pi$
$983$	−29.3667	−0.936652	−0.468326	+	0.883556i	$0.655143\pi$
$984$	−48.1219	−1.53407
$985$	−78.5169	−2.50176
$986$	−29.3788	−0.935611
$987$	−93.4643	−2.97500
$988$	−0.231275	−0.00735784
$989$	−72.3608	−2.30094
$990$	−33.7622	−1.07303
$991$	57.1943	1.81684	0.908418	−	0.418063i	$-0.137291\pi$
$991$	57.1943	1.81684	0.908418	+	0.418063i	$0.137291\pi$
$992$	−0.574365	−0.0182361
$993$	−61.0723	−1.93807
$994$	−22.3566	−0.709108
$995$	55.7137	1.76624
$996$	1.63054	0.0516656
$997$	−30.8971	−0.978520	−0.489260	−	0.872138i	$-0.662733\pi$
$997$	−30.8971	−0.978520	−0.489260	+	0.872138i	$0.662733\pi$
$998$	29.6857	0.939684
$999$	−12.1876	−0.385600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.g.1.9	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.g.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-1.43550 q^{2} +2.33343 q^{3} +0.0606568 q^{4} +2.88716 q^{5} -3.34964 q^{6} +3.63915 q^{7} +2.78392 q^{8} +2.44491 q^{9} +O(q^{10})\)	\(q-1.43550 q^{2} +2.33343 q^{3} +0.0606568 q^{4} +2.88716 q^{5} -3.34964 q^{6} +3.63915 q^{7} +2.78392 q^{8} +2.44491 q^{9} -4.14452 q^{10} +3.33191 q^{11} +0.141539 q^{12} -1.00000 q^{13} -5.22400 q^{14} +6.73700 q^{15} -4.11763 q^{16} -2.35851 q^{17} -3.50967 q^{18} +3.81285 q^{19} +0.175126 q^{20} +8.49172 q^{21} -4.78295 q^{22} +7.05905 q^{23} +6.49610 q^{24} +3.33570 q^{25} +1.43550 q^{26} -1.29526 q^{27} +0.220739 q^{28} -8.67749 q^{29} -9.67096 q^{30} -1.67449 q^{31} +0.343009 q^{32} +7.77479 q^{33} +3.38563 q^{34} +10.5068 q^{35} +0.148301 q^{36} +9.40944 q^{37} -5.47334 q^{38} -2.33343 q^{39} +8.03764 q^{40} -7.40781 q^{41} -12.1898 q^{42} -10.2508 q^{43} +0.202103 q^{44} +7.05886 q^{45} -10.1333 q^{46} -11.0065 q^{47} -9.60823 q^{48} +6.24341 q^{49} -4.78839 q^{50} -5.50342 q^{51} -0.0606568 q^{52} -11.6636 q^{53} +1.85934 q^{54} +9.61976 q^{55} +10.1311 q^{56} +8.89702 q^{57} +12.4565 q^{58} +4.31184 q^{59} +0.408645 q^{60} -13.3225 q^{61} +2.40372 q^{62} +8.89741 q^{63} +7.74288 q^{64} -2.88716 q^{65} -11.1607 q^{66} -3.46302 q^{67} -0.143059 q^{68} +16.4718 q^{69} -15.0825 q^{70} +4.27960 q^{71} +6.80646 q^{72} -7.02456 q^{73} -13.5072 q^{74} +7.78364 q^{75} +0.231275 q^{76} +12.1253 q^{77} +3.34964 q^{78} +7.43314 q^{79} -11.8883 q^{80} -10.3571 q^{81} +10.6339 q^{82} +11.5201 q^{83} +0.515080 q^{84} -6.80939 q^{85} +14.7150 q^{86} -20.2484 q^{87} +9.27578 q^{88} -5.29591 q^{89} -10.1330 q^{90} -3.63915 q^{91} +0.428179 q^{92} -3.90730 q^{93} +15.7999 q^{94} +11.0083 q^{95} +0.800390 q^{96} -9.44406 q^{97} -8.96241 q^{98} +8.14623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) \) 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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