LMFDB - Embedded newform 1339.2.a.g.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.18260 q^{2} -0.879021 q^{3} +2.76374 q^{4} +3.84044 q^{5} +1.91855 q^{6} +1.42534 q^{7} -1.66693 q^{8} -2.22732 q^{9} +O(q^{10})$	\(q-2.18260 q^{2} -0.879021 q^{3} +2.76374 q^{4} +3.84044 q^{5} +1.91855 q^{6} +1.42534 q^{7} -1.66693 q^{8} -2.22732 q^{9} -8.38214 q^{10} -0.518032 q^{11} -2.42938 q^{12} -1.00000 q^{13} -3.11094 q^{14} -3.37583 q^{15} -1.88923 q^{16} +8.19891 q^{17} +4.86135 q^{18} +6.55051 q^{19} +10.6140 q^{20} -1.25290 q^{21} +1.13065 q^{22} -9.07323 q^{23} +1.46527 q^{24} +9.74900 q^{25} +2.18260 q^{26} +4.59492 q^{27} +3.93926 q^{28} -2.76664 q^{29} +7.36808 q^{30} +1.84064 q^{31} +7.45730 q^{32} +0.455360 q^{33} -17.8949 q^{34} +5.47393 q^{35} -6.15573 q^{36} +6.12792 q^{37} -14.2971 q^{38} +0.879021 q^{39} -6.40175 q^{40} +11.6764 q^{41} +2.73458 q^{42} -1.71056 q^{43} -1.43170 q^{44} -8.55390 q^{45} +19.8032 q^{46} -0.491754 q^{47} +1.66067 q^{48} -4.96841 q^{49} -21.2781 q^{50} -7.20701 q^{51} -2.76374 q^{52} -5.23985 q^{53} -10.0289 q^{54} -1.98947 q^{55} -2.37594 q^{56} -5.75804 q^{57} +6.03846 q^{58} -7.98902 q^{59} -9.32990 q^{60} -2.46420 q^{61} -4.01737 q^{62} -3.17469 q^{63} -12.4978 q^{64} -3.84044 q^{65} -0.993869 q^{66} -0.907720 q^{67} +22.6596 q^{68} +7.97555 q^{69} -11.9474 q^{70} +2.88561 q^{71} +3.71279 q^{72} -11.7668 q^{73} -13.3748 q^{74} -8.56957 q^{75} +18.1039 q^{76} -0.738371 q^{77} -1.91855 q^{78} -5.21136 q^{79} -7.25549 q^{80} +2.64294 q^{81} -25.4849 q^{82} +14.8827 q^{83} -3.46269 q^{84} +31.4874 q^{85} +3.73348 q^{86} +2.43193 q^{87} +0.863523 q^{88} +15.5203 q^{89} +18.6697 q^{90} -1.42534 q^{91} -25.0760 q^{92} -1.61796 q^{93} +1.07330 q^{94} +25.1569 q^{95} -6.55512 q^{96} -4.87537 q^{97} +10.8440 q^{98} +1.15382 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.18260	−1.54333	−0.771665	−	0.636029i	$-0.780576\pi$
$2$	−2.18260	−1.54333	−0.771665	+	0.636029i	$0.780576\pi$
$3$	−0.879021	−0.507503	−0.253751	−	0.967269i	$-0.581665\pi$
$3$	−0.879021	−0.507503	−0.253751	+	0.967269i	$0.581665\pi$
$4$	2.76374	1.38187
$5$	3.84044	1.71750	0.858749	−	0.512396i	$-0.171242\pi$
$5$	3.84044	1.71750	0.858749	+	0.512396i	$0.171242\pi$
$6$	1.91855	0.783244
$7$	1.42534	0.538728	0.269364	−	0.963038i	$-0.413187\pi$
$7$	1.42534	0.538728	0.269364	+	0.963038i	$0.413187\pi$
$8$	−1.66693	−0.589349
$9$	−2.22732	−0.742441
$10$	−8.38214	−2.65067
$11$	−0.518032	−0.156192	−0.0780962	−	0.996946i	$-0.524884\pi$
$11$	−0.518032	−0.156192	−0.0780962	+	0.996946i	$0.524884\pi$
$12$	−2.42938	−0.701302
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.11094	−0.831435
$15$	−3.37583	−0.871635
$16$	−1.88923	−0.472308
$17$	8.19891	1.98853	0.994264	−	0.106955i	$-0.0341102\pi$
$17$	8.19891	1.98853	0.994264	+	0.106955i	$0.0341102\pi$
$18$	4.86135	1.14583
$19$	6.55051	1.50279	0.751395	−	0.659852i	$-0.229381\pi$
$19$	6.55051	1.50279	0.751395	+	0.659852i	$0.229381\pi$
$20$	10.6140	2.37336
$21$	−1.25290	−0.273406
$22$	1.13065	0.241056
$23$	−9.07323	−1.89190	−0.945949	−	0.324315i	$-0.894866\pi$
$23$	−9.07323	−1.89190	−0.945949	+	0.324315i	$0.894866\pi$
$24$	1.46527	0.299096
$25$	9.74900	1.94980
$26$	2.18260	0.428043
$27$	4.59492	0.884294
$28$	3.93926	0.744451
$29$	−2.76664	−0.513752	−0.256876	−	0.966444i	$-0.582693\pi$
$29$	−2.76664	−0.513752	−0.256876	+	0.966444i	$0.582693\pi$
$30$	7.36808	1.34522
$31$	1.84064	0.330588	0.165294	−	0.986244i	$-0.447143\pi$
$31$	1.84064	0.330588	0.165294	+	0.986244i	$0.447143\pi$
$32$	7.45730	1.31828
$33$	0.455360	0.0792681
$34$	−17.8949	−3.06896
$35$	5.47393	0.925264
$36$	−6.15573	−1.02596
$37$	6.12792	1.00742	0.503712	−	0.863872i	$-0.331967\pi$
$37$	6.12792	1.00742	0.503712	+	0.863872i	$0.331967\pi$
$38$	−14.2971	−2.31930
$39$	0.879021	0.140756
$40$	−6.40175	−1.01221
$41$	11.6764	1.82355	0.911776	−	0.410689i	$-0.134712\pi$
$41$	11.6764	1.82355	0.911776	+	0.410689i	$0.134712\pi$
$42$	2.73458	0.421955
$43$	−1.71056	−0.260859	−0.130429	−	0.991458i	$-0.541636\pi$
$43$	−1.71056	−0.260859	−0.130429	+	0.991458i	$0.541636\pi$
$44$	−1.43170	−0.215837
$45$	−8.55390	−1.27514
$46$	19.8032	2.91982
$47$	−0.491754	−0.0717297	−0.0358649	−	0.999357i	$-0.511419\pi$
$47$	−0.491754	−0.0717297	−0.0358649	+	0.999357i	$0.511419\pi$
$48$	1.66067	0.239698
$49$	−4.96841	−0.709773
$50$	−21.2781	−3.00918
$51$	−7.20701	−1.00918
$52$	−2.76374	−0.383261
$53$	−5.23985	−0.719748	−0.359874	−	0.933001i	$-0.617180\pi$
$53$	−5.23985	−0.719748	−0.359874	+	0.933001i	$0.617180\pi$
$54$	−10.0289	−1.36476
$55$	−1.98947	−0.268260
$56$	−2.37594	−0.317499
$57$	−5.75804	−0.762671
$58$	6.03846	0.792889
$59$	−7.98902	−1.04008	−0.520041	−	0.854141i	$-0.674083\pi$
$59$	−7.98902	−1.04008	−0.520041	+	0.854141i	$0.674083\pi$
$60$	−9.32990	−1.20448
$61$	−2.46420	−0.315509	−0.157754	−	0.987478i	$-0.550425\pi$
$61$	−2.46420	−0.315509	−0.157754	+	0.987478i	$0.550425\pi$
$62$	−4.01737	−0.510206
$63$	−3.17469	−0.399973
$64$	−12.4978	−1.56223
$65$	−3.84044	−0.476348
$66$	−0.993869	−0.122337
$67$	−0.907720	−0.110896	−0.0554478	−	0.998462i	$-0.517659\pi$
$67$	−0.907720	−0.110896	−0.0554478	+	0.998462i	$0.517659\pi$
$68$	22.6596	2.74788
$69$	7.97555	0.960144
$70$	−11.9474	−1.42799
$71$	2.88561	0.342459	0.171229	−	0.985231i	$-0.445226\pi$
$71$	2.88561	0.342459	0.171229	+	0.985231i	$0.445226\pi$
$72$	3.71279	0.437557
$73$	−11.7668	−1.37720	−0.688600	−	0.725142i	$-0.741774\pi$
$73$	−11.7668	−1.37720	−0.688600	+	0.725142i	$0.741774\pi$
$74$	−13.3748	−1.55479
$75$	−8.56957	−0.989529
$76$	18.1039	2.07666
$77$	−0.738371	−0.0841451
$78$	−1.91855	−0.217233
$79$	−5.21136	−0.586324	−0.293162	−	0.956063i	$-0.594708\pi$
$79$	−5.21136	−0.586324	−0.293162	+	0.956063i	$0.594708\pi$
$80$	−7.25549	−0.811188
$81$	2.64294	0.293659
$82$	−25.4849	−2.81434
$83$	14.8827	1.63358	0.816792	−	0.576933i	$-0.195751\pi$
$83$	14.8827	1.63358	0.816792	+	0.576933i	$0.195751\pi$
$84$	−3.46269	−0.377811
$85$	31.4874	3.41529
$86$	3.73348	0.402591
$87$	2.43193	0.260731
$88$	0.863523	0.0920519
$89$	15.5203	1.64515	0.822577	−	0.568654i	$-0.192536\pi$
$89$	15.5203	1.64515	0.822577	+	0.568654i	$0.192536\pi$
$90$	18.6697	1.96796
$91$	−1.42534	−0.149416
$92$	−25.0760	−2.61435
$93$	−1.61796	−0.167774
$94$	1.07330	0.110703
$95$	25.1569	2.58104
$96$	−6.55512	−0.669029
$97$	−4.87537	−0.495019	−0.247509	−	0.968886i	$-0.579612\pi$
$97$	−4.87537	−0.495019	−0.247509	+	0.968886i	$0.579612\pi$
$98$	10.8440	1.09541
$99$	1.15382	0.115964
$100$	26.9437	2.69437
$101$	15.9935	1.59141	0.795704	−	0.605686i	$-0.207101\pi$
$101$	15.9935	1.59141	0.795704	+	0.605686i	$0.207101\pi$
$102$	15.7300	1.55750
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.66693	0.163456
$105$	−4.81170	−0.469574
$106$	11.4365	1.11081
$107$	−8.23659	−0.796261	−0.398131	−	0.917329i	$-0.630341\pi$
$107$	−8.23659	−0.796261	−0.398131	+	0.917329i	$0.630341\pi$
$108$	12.6992	1.22198
$109$	10.2695	0.983644	0.491822	−	0.870696i	$-0.336331\pi$
$109$	10.2695	0.983644	0.491822	+	0.870696i	$0.336331\pi$
$110$	4.34222	0.414014
$111$	−5.38657	−0.511271
$112$	−2.69280	−0.254445
$113$	7.99875	0.752459	0.376230	−	0.926526i	$-0.377220\pi$
$113$	7.99875	0.752459	0.376230	+	0.926526i	$0.377220\pi$
$114$	12.5675	1.17705
$115$	−34.8452	−3.24933
$116$	−7.64626	−0.709938
$117$	2.22732	0.205916
$118$	17.4368	1.60519
$119$	11.6862	1.07127
$120$	5.62727	0.513697
$121$	−10.7316	−0.975604
$122$	5.37837	0.486934
$123$	−10.2638	−0.925457
$124$	5.08703	0.456829
$125$	18.2383	1.63128
$126$	6.92908	0.617291
$127$	4.30048	0.381606	0.190803	−	0.981628i	$-0.438891\pi$
$127$	4.30048	0.381606	0.190803	+	0.981628i	$0.438891\pi$
$128$	12.3631	1.09276
$129$	1.50362	0.132387
$130$	8.38214	0.735163
$131$	8.15661	0.712646	0.356323	−	0.934363i	$-0.384030\pi$
$131$	8.15661	0.712646	0.356323	+	0.934363i	$0.384030\pi$
$132$	1.25850	0.109538
$133$	9.33670	0.809595
$134$	1.98119	0.171149
$135$	17.6465	1.51877
$136$	−13.6670	−1.17194
$137$	5.80711	0.496134	0.248067	−	0.968743i	$-0.420205\pi$
$137$	5.80711	0.496134	0.248067	+	0.968743i	$0.420205\pi$
$138$	−17.4074	−1.48182
$139$	−2.79057	−0.236693	−0.118346	−	0.992972i	$-0.537759\pi$
$139$	−2.79057	−0.236693	−0.118346	+	0.992972i	$0.537759\pi$
$140$	15.1285	1.27859
$141$	0.432262	0.0364030
$142$	−6.29813	−0.528527
$143$	0.518032	0.0433200
$144$	4.20793	0.350661
$145$	−10.6251	−0.882368
$146$	25.6822	2.12547
$147$	4.36733	0.360212
$148$	16.9360	1.39213
$149$	4.18113	0.342531	0.171266	−	0.985225i	$-0.445214\pi$
$149$	4.18113	0.342531	0.171266	+	0.985225i	$0.445214\pi$
$150$	18.7039	1.52717
$151$	9.30938	0.757587	0.378793	−	0.925481i	$-0.376339\pi$
$151$	9.30938	0.757587	0.378793	+	0.925481i	$0.376339\pi$
$152$	−10.9193	−0.885669
$153$	−18.2616	−1.47636
$154$	1.61157	0.129864
$155$	7.06885	0.567784
$156$	2.42938	0.194506
$157$	6.01811	0.480297	0.240149	−	0.970736i	$-0.422804\pi$
$157$	6.01811	0.480297	0.240149	+	0.970736i	$0.422804\pi$
$158$	11.3743	0.904891
$159$	4.60593	0.365274
$160$	28.6393	2.26414
$161$	−12.9324	−1.01922
$162$	−5.76847	−0.453214
$163$	−20.5685	−1.61105	−0.805523	−	0.592564i	$-0.798116\pi$
$163$	−20.5685	−1.61105	−0.805523	+	0.592564i	$0.798116\pi$
$164$	32.2706	2.51991
$165$	1.74879	0.136143
$166$	−32.4829	−2.52116
$167$	−14.8591	−1.14983	−0.574915	−	0.818213i	$-0.694965\pi$
$167$	−14.8591	−1.14983	−0.574915	+	0.818213i	$0.694965\pi$
$168$	2.08850	0.161131
$169$	1.00000	0.0769231
$170$	−68.7244	−5.27092
$171$	−14.5901	−1.11573
$172$	−4.72755	−0.360472
$173$	−1.05828	−0.0804596	−0.0402298	−	0.999190i	$-0.512809\pi$
$173$	−1.05828	−0.0804596	−0.0402298	+	0.999190i	$0.512809\pi$
$174$	−5.30793	−0.402393
$175$	13.8956	1.05041
$176$	0.978682	0.0737709
$177$	7.02251	0.527844
$178$	−33.8747	−2.53901
$179$	12.5918	0.941156	0.470578	−	0.882358i	$-0.344045\pi$
$179$	12.5918	0.941156	0.470578	+	0.882358i	$0.344045\pi$
$180$	−23.6407	−1.76208
$181$	−12.6250	−0.938407	−0.469203	−	0.883090i	$-0.655459\pi$
$181$	−12.6250	−0.938407	−0.469203	+	0.883090i	$0.655459\pi$
$182$	3.11094	0.230598
$183$	2.16609	0.160122
$184$	15.1244	1.11499
$185$	23.5339	1.73025
$186$	3.53135	0.258931
$187$	−4.24729	−0.310593
$188$	−1.35908	−0.0991210
$189$	6.54933	0.476393
$190$	−54.9074	−3.98340
$191$	24.7235	1.78893	0.894464	−	0.447140i	$-0.147557\pi$
$191$	24.7235	1.78893	0.894464	+	0.447140i	$0.147557\pi$
$192$	10.9858	0.792835
$193$	−10.7913	−0.776777	−0.388389	−	0.921496i	$-0.626968\pi$
$193$	−10.7913	−0.776777	−0.388389	+	0.921496i	$0.626968\pi$
$194$	10.6410	0.763977
$195$	3.37583	0.241748
$196$	−13.7314	−0.980812
$197$	−2.34383	−0.166991	−0.0834954	−	0.996508i	$-0.526608\pi$
$197$	−2.34383	−0.166991	−0.0834954	+	0.996508i	$0.526608\pi$
$198$	−2.51833	−0.178970
$199$	8.00513	0.567469	0.283734	−	0.958903i	$-0.408427\pi$
$199$	8.00513	0.567469	0.283734	+	0.958903i	$0.408427\pi$
$200$	−16.2509	−1.14911
$201$	0.797905	0.0562799
$202$	−34.9073	−2.45607
$203$	−3.94340	−0.276772
$204$	−19.9183	−1.39456
$205$	44.8426	3.13195
$206$	−2.18260	−0.152069
$207$	20.2090	1.40462
$208$	1.88923	0.130995
$209$	−3.39337	−0.234725
$210$	10.5020	0.724708
$211$	11.6115	0.799366	0.399683	−	0.916653i	$-0.369120\pi$
$211$	11.6115	0.799366	0.399683	+	0.916653i	$0.369120\pi$
$212$	−14.4816	−0.994598
$213$	−2.53651	−0.173799
$214$	17.9772	1.22889
$215$	−6.56933	−0.448024
$216$	−7.65942	−0.521158
$217$	2.62353	0.178097
$218$	−22.4143	−1.51809
$219$	10.3433	0.698932
$220$	−5.49837	−0.370700
$221$	−8.19891	−0.551518
$222$	11.7567	0.789060
$223$	1.57301	0.105336	0.0526682	−	0.998612i	$-0.483227\pi$
$223$	1.57301	0.105336	0.0526682	+	0.998612i	$0.483227\pi$
$224$	10.6292	0.710192
$225$	−21.7142	−1.44761
$226$	−17.4581	−1.16129
$227$	10.4617	0.694370	0.347185	−	0.937797i	$-0.387138\pi$
$227$	10.4617	0.694370	0.347185	+	0.937797i	$0.387138\pi$
$228$	−15.9137	−1.05391
$229$	4.60003	0.303979	0.151989	−	0.988382i	$-0.451432\pi$
$229$	4.60003	0.303979	0.151989	+	0.988382i	$0.451432\pi$
$230$	76.0531	5.01479
$231$	0.649043	0.0427039
$232$	4.61180	0.302779
$233$	25.4964	1.67032	0.835162	−	0.550004i	$-0.185374\pi$
$233$	25.4964	1.67032	0.835162	+	0.550004i	$0.185374\pi$
$234$	−4.86135	−0.317797
$235$	−1.88855	−0.123196
$236$	−22.0795	−1.43726
$237$	4.58089	0.297561
$238$	−25.5063	−1.65333
$239$	−2.48535	−0.160764	−0.0803821	−	0.996764i	$-0.525614\pi$
$239$	−2.48535	−0.160764	−0.0803821	+	0.996764i	$0.525614\pi$
$240$	6.37772	0.411680
$241$	4.72409	0.304306	0.152153	−	0.988357i	$-0.451379\pi$
$241$	4.72409	0.304306	0.152153	+	0.988357i	$0.451379\pi$
$242$	23.4229	1.50568
$243$	−16.1080	−1.03333
$244$	−6.81041	−0.435992
$245$	−19.0809	−1.21903
$246$	22.4018	1.42829
$247$	−6.55051	−0.416799
$248$	−3.06821	−0.194832
$249$	−13.0822	−0.829048
$250$	−39.8068	−2.51760
$251$	−21.5447	−1.35989	−0.679944	−	0.733264i	$-0.737996\pi$
$251$	−21.5447	−1.35989	−0.679944	+	0.733264i	$0.737996\pi$
$252$	−8.77401	−0.552711
$253$	4.70022	0.295500
$254$	−9.38623	−0.588944
$255$	−27.6781	−1.73327
$256$	−1.98812	−0.124258
$257$	−5.67536	−0.354019	−0.177009	−	0.984209i	$-0.556642\pi$
$257$	−5.67536	−0.354019	−0.177009	+	0.984209i	$0.556642\pi$
$258$	−3.28180	−0.204316
$259$	8.73437	0.542727
$260$	−10.6140	−0.658251
$261$	6.16220	0.381431
$262$	−17.8026	−1.09985
$263$	−26.5707	−1.63842	−0.819211	−	0.573493i	$-0.805588\pi$
$263$	−26.5707	−1.63842	−0.819211	+	0.573493i	$0.805588\pi$
$264$	−0.759054	−0.0467166
$265$	−20.1233	−1.23617
$266$	−20.3783	−1.24947
$267$	−13.6427	−0.834920
$268$	−2.50870	−0.153243
$269$	14.5324	0.886055	0.443027	−	0.896508i	$-0.353904\pi$
$269$	14.5324	0.886055	0.443027	+	0.896508i	$0.353904\pi$
$270$	−38.5153	−2.34397
$271$	15.7654	0.957679	0.478840	−	0.877902i	$-0.341058\pi$
$271$	15.7654	0.957679	0.478840	+	0.877902i	$0.341058\pi$
$272$	−15.4896	−0.939198
$273$	1.25290	0.0758291
$274$	−12.6746	−0.765699
$275$	−5.05029	−0.304544
$276$	22.0423	1.32679
$277$	−4.56859	−0.274500	−0.137250	−	0.990536i	$-0.543826\pi$
$277$	−4.56859	−0.274500	−0.137250	+	0.990536i	$0.543826\pi$
$278$	6.09068	0.365295
$279$	−4.09969	−0.245442
$280$	−9.12467	−0.545303
$281$	−3.82171	−0.227984	−0.113992	−	0.993482i	$-0.536364\pi$
$281$	−3.82171	−0.227984	−0.113992	+	0.993482i	$0.536364\pi$
$282$	−0.943455	−0.0561819
$283$	−17.5501	−1.04324	−0.521622	−	0.853177i	$-0.674673\pi$
$283$	−17.5501	−1.04324	−0.521622	+	0.853177i	$0.674673\pi$
$284$	7.97507	0.473233
$285$	−22.1134	−1.30989
$286$	−1.13065	−0.0668570
$287$	16.6429	0.982397
$288$	−16.6098	−0.978742
$289$	50.2221	2.95424
$290$	23.1904	1.36179
$291$	4.28555	0.251223
$292$	−32.5203	−1.90311
$293$	15.1031	0.882333	0.441167	−	0.897425i	$-0.354565\pi$
$293$	15.1031	0.882333	0.441167	+	0.897425i	$0.354565\pi$
$294$	−9.53214	−0.555925
$295$	−30.6814	−1.78634
$296$	−10.2148	−0.593725
$297$	−2.38032	−0.138120
$298$	−9.12572	−0.528639
$299$	9.07323	0.524718
$300$	−23.6840	−1.36740
$301$	−2.43814	−0.140532
$302$	−20.3186	−1.16921
$303$	−14.0586	−0.807644
$304$	−12.3754	−0.709780
$305$	−9.46363	−0.541886
$306$	39.8578	2.27852
$307$	−3.99431	−0.227967	−0.113984	−	0.993483i	$-0.536361\pi$
$307$	−3.99431	−0.227967	−0.113984	+	0.993483i	$0.536361\pi$
$308$	−2.04066	−0.116278
$309$	−0.879021	−0.0500057
$310$	−15.4285	−0.876278
$311$	15.8908	0.901084	0.450542	−	0.892755i	$-0.351231\pi$
$311$	15.8908	0.901084	0.450542	+	0.892755i	$0.351231\pi$
$312$	−1.46527	−0.0829544
$313$	−23.5921	−1.33350	−0.666752	−	0.745280i	$-0.732316\pi$
$313$	−23.5921	−1.33350	−0.666752	+	0.745280i	$0.732316\pi$
$314$	−13.1351	−0.741257
$315$	−12.1922	−0.686954
$316$	−14.4028	−0.810222
$317$	14.3171	0.804126	0.402063	−	0.915612i	$-0.368293\pi$
$317$	14.3171	0.804126	0.402063	+	0.915612i	$0.368293\pi$
$318$	−10.0529	−0.563739
$319$	1.43321	0.0802442
$320$	−47.9972	−2.68312
$321$	7.24013	0.404105
$322$	28.2263	1.57299
$323$	53.7071	2.98834
$324$	7.30438	0.405799
$325$	−9.74900	−0.540777
$326$	44.8927	2.48638
$327$	−9.02714	−0.499202
$328$	−19.4638	−1.07471
$329$	−0.700917	−0.0386428
$330$	−3.81690	−0.210113
$331$	−32.7965	−1.80266	−0.901330	−	0.433133i	$-0.857408\pi$
$331$	−32.7965	−1.80266	−0.901330	+	0.433133i	$0.857408\pi$
$332$	41.1317	2.25740
$333$	−13.6489	−0.747953
$334$	32.4314	1.77457
$335$	−3.48605	−0.190463
$336$	2.36702	0.129132
$337$	20.1891	1.09977	0.549886	−	0.835240i	$-0.314671\pi$
$337$	20.1891	1.09977	0.549886	+	0.835240i	$0.314671\pi$
$338$	−2.18260	−0.118718
$339$	−7.03107	−0.381875
$340$	87.0230	4.71948
$341$	−0.953507	−0.0516353
$342$	31.8444	1.72195
$343$	−17.0590	−0.921102
$344$	2.85139	0.153737
$345$	30.6296	1.64904
$346$	2.30980	0.124176
$347$	−7.83421	−0.420563	−0.210281	−	0.977641i	$-0.567438\pi$
$347$	−7.83421	−0.420563	−0.210281	+	0.977641i	$0.567438\pi$
$348$	6.72122	0.360295
$349$	−12.5390	−0.671197	−0.335599	−	0.942005i	$-0.608939\pi$
$349$	−12.5390	−0.671197	−0.335599	+	0.942005i	$0.608939\pi$
$350$	−30.3286	−1.62113
$351$	−4.59492	−0.245259
$352$	−3.86312	−0.205905
$353$	−9.76602	−0.519793	−0.259896	−	0.965637i	$-0.583688\pi$
$353$	−9.76602	−0.519793	−0.259896	+	0.965637i	$0.583688\pi$
$354$	−15.3273	−0.814638
$355$	11.0820	0.588173
$356$	42.8941	2.27339
$357$	−10.2724	−0.543675
$358$	−27.4829	−1.45251
$359$	12.6143	0.665759	0.332880	−	0.942969i	$-0.391980\pi$
$359$	12.6143	0.665759	0.332880	+	0.942969i	$0.391980\pi$
$360$	14.2588	0.751503
$361$	23.9092	1.25838
$362$	27.5553	1.44827
$363$	9.43334	0.495122
$364$	−3.93926	−0.206473
$365$	−45.1897	−2.36534
$366$	−4.72769	−0.247121
$367$	−10.9121	−0.569609	−0.284805	−	0.958586i	$-0.591929\pi$
$367$	−10.9121	−0.569609	−0.284805	+	0.958586i	$0.591929\pi$
$368$	17.1414	0.893559
$369$	−26.0072	−1.35388
$370$	−51.3651	−2.67035
$371$	−7.46856	−0.387748
$372$	−4.47161	−0.231842
$373$	13.0141	0.673845	0.336923	−	0.941532i	$-0.390614\pi$
$373$	13.0141	0.673845	0.336923	+	0.941532i	$0.390614\pi$
$374$	9.27014	0.479347
$375$	−16.0318	−0.827879
$376$	0.819720	0.0422739
$377$	2.76664	0.142489
$378$	−14.2945	−0.735232
$379$	1.74676	0.0897249	0.0448624	−	0.998993i	$-0.485715\pi$
$379$	1.74676	0.0897249	0.0448624	+	0.998993i	$0.485715\pi$
$380$	69.5270	3.56666
$381$	−3.78021	−0.193666
$382$	−53.9614	−2.76091
$383$	11.9189	0.609026	0.304513	−	0.952508i	$-0.401506\pi$
$383$	11.9189	0.609026	0.304513	+	0.952508i	$0.401506\pi$
$384$	−10.8675	−0.554577
$385$	−2.83567	−0.144519
$386$	23.5531	1.19882
$387$	3.80998	0.193672
$388$	−13.4742	−0.684051
$389$	25.2449	1.27997	0.639984	−	0.768388i	$-0.278941\pi$
$389$	25.2449	1.27997	0.639984	+	0.768388i	$0.278941\pi$
$390$	−7.36808	−0.373097
$391$	−74.3906	−3.76209
$392$	8.28199	0.418304
$393$	−7.16983	−0.361670
$394$	5.11563	0.257722
$395$	−20.0139	−1.00701
$396$	3.18886	0.160246
$397$	15.4573	0.775782	0.387891	−	0.921705i	$-0.373204\pi$
$397$	15.4573	0.775782	0.387891	+	0.921705i	$0.373204\pi$
$398$	−17.4720	−0.875792
$399$	−8.20716	−0.410872
$400$	−18.4181	−0.920906
$401$	18.1039	0.904065	0.452033	−	0.892001i	$-0.350699\pi$
$401$	18.1039	0.904065	0.452033	+	0.892001i	$0.350699\pi$
$402$	−1.74151	−0.0868584
$403$	−1.84064	−0.0916886
$404$	44.2017	2.19912
$405$	10.1500	0.504360
$406$	8.60686	0.427151
$407$	−3.17446	−0.157352
$408$	12.0136	0.594761
$409$	2.10859	0.104263	0.0521315	−	0.998640i	$-0.483398\pi$
$409$	2.10859	0.104263	0.0521315	+	0.998640i	$0.483398\pi$
$410$	−97.8735	−4.83363
$411$	−5.10457	−0.251790
$412$	2.76374	0.136160
$413$	−11.3871	−0.560321
$414$	−44.1081	−2.16780
$415$	57.1560	2.80568
$416$	−7.45730	−0.365624
$417$	2.45296	0.120122
$418$	7.40637	0.362257
$419$	11.9569	0.584135	0.292067	−	0.956398i	$-0.405657\pi$
$419$	11.9569	0.584135	0.292067	+	0.956398i	$0.405657\pi$
$420$	−13.2983	−0.648889
$421$	23.3864	1.13978	0.569891	−	0.821720i	$-0.306985\pi$
$421$	23.3864	1.13978	0.569891	+	0.821720i	$0.306985\pi$
$422$	−25.3432	−1.23369
$423$	1.09530	0.0532551
$424$	8.73447	0.424183
$425$	79.9312	3.87723
$426$	5.53619	0.268229
$427$	−3.51232	−0.169973
$428$	−22.7638	−1.10033
$429$	−0.455360	−0.0219850
$430$	14.3382	0.691449
$431$	−1.31322	−0.0632554	−0.0316277	−	0.999500i	$-0.510069\pi$
$431$	−1.31322	−0.0632554	−0.0316277	+	0.999500i	$0.510069\pi$
$432$	−8.68088	−0.417659
$433$	18.6100	0.894340	0.447170	−	0.894449i	$-0.352432\pi$
$433$	18.6100	0.894340	0.447170	+	0.894449i	$0.352432\pi$
$434$	−5.72611	−0.274862
$435$	9.33970	0.447804
$436$	28.3823	1.35927
$437$	−59.4343	−2.84313
$438$	−22.5752	−1.07868
$439$	13.9715	0.666824	0.333412	−	0.942781i	$-0.391800\pi$
$439$	13.9715	0.666824	0.333412	+	0.942781i	$0.391800\pi$
$440$	3.31631	0.158099
$441$	11.0662	0.526964
$442$	17.8949	0.851175
$443$	−35.4197	−1.68284	−0.841421	−	0.540381i	$-0.818280\pi$
$443$	−35.4197	−1.68284	−0.841421	+	0.540381i	$0.818280\pi$
$444$	−14.8871	−0.706509
$445$	59.6050	2.82555
$446$	−3.43324	−0.162569
$447$	−3.67530	−0.173836
$448$	−17.8136	−0.841615
$449$	−30.9328	−1.45981	−0.729905	−	0.683548i	$-0.760436\pi$
$449$	−30.9328	−1.45981	−0.729905	+	0.683548i	$0.760436\pi$
$450$	47.3933	2.23414
$451$	−6.04876	−0.284825
$452$	22.1064	1.03980
$453$	−8.18314	−0.384477
$454$	−22.8338	−1.07164
$455$	−5.47393	−0.256622
$456$	9.59825	0.449479
$457$	−28.8335	−1.34877	−0.674387	−	0.738378i	$-0.735592\pi$
$457$	−28.8335	−1.34877	−0.674387	+	0.738378i	$0.735592\pi$
$458$	−10.0400	−0.469139
$459$	37.6734	1.75844
$460$	−96.3030	−4.49015
$461$	−32.5908	−1.51790	−0.758951	−	0.651147i	$-0.774288\pi$
$461$	−32.5908	−1.51790	−0.758951	+	0.651147i	$0.774288\pi$
$462$	−1.41660	−0.0659062
$463$	−1.85955	−0.0864204	−0.0432102	−	0.999066i	$-0.513759\pi$
$463$	−1.85955	−0.0864204	−0.0432102	+	0.999066i	$0.513759\pi$
$464$	5.22682	0.242649
$465$	−6.21367	−0.288152
$466$	−55.6484	−2.57786
$467$	−29.4607	−1.36328	−0.681639	−	0.731688i	$-0.738733\pi$
$467$	−29.4607	−1.36328	−0.681639	+	0.731688i	$0.738733\pi$
$468$	6.15573	0.284549
$469$	−1.29381	−0.0597426
$470$	4.12195	0.190132
$471$	−5.29004	−0.243752
$472$	13.3171	0.612971
$473$	0.886127	0.0407441
$474$	−9.99825	−0.459235
$475$	63.8609	2.93014
$476$	32.2977	1.48036
$477$	11.6708	0.534371
$478$	5.42453	0.248112
$479$	−36.5385	−1.66949	−0.834744	−	0.550638i	$-0.814385\pi$
$479$	−36.5385	−1.66949	−0.834744	+	0.550638i	$0.814385\pi$
$480$	−25.1746	−1.14906
$481$	−6.12792	−0.279409
$482$	−10.3108	−0.469644
$483$	11.3679	0.517256
$484$	−29.6594	−1.34816
$485$	−18.7236	−0.850194
$486$	35.1572	1.59476
$487$	31.3201	1.41925	0.709624	−	0.704581i	$-0.248865\pi$
$487$	31.3201	1.41925	0.709624	+	0.704581i	$0.248865\pi$
$488$	4.10766	0.185945
$489$	18.0801	0.817610
$490$	41.6459	1.88137
$491$	21.7086	0.979693	0.489847	−	0.871809i	$-0.337053\pi$
$491$	21.7086	0.979693	0.489847	+	0.871809i	$0.337053\pi$
$492$	−28.3665	−1.27886
$493$	−22.6834	−1.02161
$494$	14.2971	0.643259
$495$	4.43119	0.199167
$496$	−3.47739	−0.156139
$497$	4.11297	0.184492
$498$	28.5531	1.27950
$499$	−31.0557	−1.39024	−0.695122	−	0.718892i	$-0.744649\pi$
$499$	−31.0557	−1.39024	−0.695122	+	0.718892i	$0.744649\pi$
$500$	50.4057	2.25421
$501$	13.0614	0.583542
$502$	47.0234	2.09876
$503$	−7.03172	−0.313529	−0.156764	−	0.987636i	$-0.550106\pi$
$503$	−7.03172	−0.313529	−0.156764	+	0.987636i	$0.550106\pi$
$504$	5.29199	0.235724
$505$	61.4219	2.73324
$506$	−10.2587	−0.456054
$507$	−0.879021	−0.0390387
$508$	11.8854	0.527329
$509$	−44.1018	−1.95478	−0.977389	−	0.211447i	$-0.932182\pi$
$509$	−44.1018	−1.95478	−0.977389	+	0.211447i	$0.932182\pi$
$510$	60.4102	2.67501
$511$	−16.7717	−0.741935
$512$	−20.3870	−0.900987
$513$	30.0991	1.32891
$514$	12.3870	0.546368
$515$	3.84044	0.169230
$516$	4.15562	0.182941
$517$	0.254744	0.0112036
$518$	−19.0636	−0.837608
$519$	0.930251	0.0408335
$520$	6.40175	0.280735
$521$	−14.3214	−0.627433	−0.313716	−	0.949517i	$-0.601574\pi$
$521$	−14.3214	−0.627433	−0.313716	+	0.949517i	$0.601574\pi$
$522$	−13.4496	−0.588673
$523$	−22.5235	−0.984886	−0.492443	−	0.870345i	$-0.663896\pi$
$523$	−22.5235	−0.984886	−0.492443	+	0.870345i	$0.663896\pi$
$524$	22.5427	0.984784
$525$	−12.2145	−0.533086
$526$	57.9932	2.52863
$527$	15.0912	0.657383
$528$	−0.860281	−0.0374389
$529$	59.3234	2.57928
$530$	43.9212	1.90781
$531$	17.7941	0.772199
$532$	25.8042	1.11875
$533$	−11.6764	−0.505762
$534$	29.7765	1.28856
$535$	−31.6321	−1.36758
$536$	1.51311	0.0653563
$537$	−11.0685	−0.477639
$538$	−31.7184	−1.36748
$539$	2.57379	0.110861
$540$	48.7704	2.09874
$541$	32.4653	1.39579	0.697896	−	0.716200i	$-0.254120\pi$
$541$	32.4653	1.39579	0.697896	+	0.716200i	$0.254120\pi$
$542$	−34.4095	−1.47802
$543$	11.0976	0.476244
$544$	61.1417	2.62143
$545$	39.4396	1.68941
$546$	−2.73458	−0.117029
$547$	−41.2391	−1.76326	−0.881628	−	0.471945i	$-0.843552\pi$
$547$	−41.2391	−1.76326	−0.881628	+	0.471945i	$0.843552\pi$
$548$	16.0493	0.685593
$549$	5.48858	0.234247
$550$	11.0228	0.470012
$551$	−18.1229	−0.772062
$552$	−13.2947	−0.565860
$553$	−7.42796	−0.315869
$554$	9.97141	0.423644
$555$	−20.6868	−0.878106
$556$	−7.71239	−0.327078
$557$	22.1264	0.937527	0.468764	−	0.883324i	$-0.344700\pi$
$557$	22.1264	0.937527	0.468764	+	0.883324i	$0.344700\pi$
$558$	8.94797	0.378798
$559$	1.71056	0.0723492
$560$	−10.3415	−0.437009
$561$	3.73346	0.157627
$562$	8.34127	0.351855
$563$	23.5913	0.994254	0.497127	−	0.867678i	$-0.334388\pi$
$563$	23.5913	0.994254	0.497127	+	0.867678i	$0.334388\pi$
$564$	1.19466	0.0503042
$565$	30.7187	1.29235
$566$	38.3048	1.61007
$567$	3.76708	0.158202
$568$	−4.81011	−0.201828
$569$	−2.16499	−0.0907612	−0.0453806	−	0.998970i	$-0.514450\pi$
$569$	−2.16499	−0.0907612	−0.0453806	+	0.998970i	$0.514450\pi$
$570$	48.2647	2.02159
$571$	−38.5074	−1.61149	−0.805743	−	0.592266i	$-0.798234\pi$
$571$	−38.5074	−1.61149	−0.805743	+	0.592266i	$0.798234\pi$
$572$	1.43170	0.0598625
$573$	−21.7324	−0.907886
$574$	−36.3247	−1.51616
$575$	−88.4549	−3.68882
$576$	27.8367	1.15986
$577$	18.3054	0.762062	0.381031	−	0.924562i	$-0.375569\pi$
$577$	18.3054	0.762062	0.381031	+	0.924562i	$0.375569\pi$
$578$	−109.615	−4.55937
$579$	9.48580	0.394217
$580$	−29.3650	−1.21932
$581$	21.2128	0.880056
$582$	−9.35363	−0.387721
$583$	2.71441	0.112419
$584$	19.6144	0.811651
$585$	8.55390	0.353660
$586$	−32.9640	−1.36173
$587$	−6.61439	−0.273005	−0.136502	−	0.990640i	$-0.543586\pi$
$587$	−6.61439	−0.273005	−0.136502	+	0.990640i	$0.543586\pi$
$588$	12.0702	0.497765
$589$	12.0571	0.496804
$590$	66.9651	2.75691
$591$	2.06027	0.0847482
$592$	−11.5771	−0.475815
$593$	−16.1055	−0.661374	−0.330687	−	0.943740i	$-0.607280\pi$
$593$	−16.1055	−0.661374	−0.330687	+	0.943740i	$0.607280\pi$
$594$	5.19527	0.213165
$595$	44.8803	1.83991
$596$	11.5555	0.473333
$597$	−7.03667	−0.287992
$598$	−19.8032	−0.809813
$599$	29.0944	1.18877	0.594383	−	0.804182i	$-0.297396\pi$
$599$	29.0944	1.18877	0.594383	+	0.804182i	$0.297396\pi$
$600$	14.2849	0.583178
$601$	−22.1442	−0.903282	−0.451641	−	0.892200i	$-0.649161\pi$
$601$	−22.1442	−0.903282	−0.451641	+	0.892200i	$0.649161\pi$
$602$	5.32147	0.216887
$603$	2.02179	0.0823335
$604$	25.7287	1.04689
$605$	−41.2143	−1.67560
$606$	30.6842	1.24646
$607$	−31.4501	−1.27652	−0.638260	−	0.769821i	$-0.720346\pi$
$607$	−31.4501	−1.27652	−0.638260	+	0.769821i	$0.720346\pi$
$608$	48.8491	1.98109
$609$	3.46633	0.140463
$610$	20.6553	0.836309
$611$	0.491754	0.0198942
$612$	−50.4703	−2.04014
$613$	−28.1711	−1.13782	−0.568910	−	0.822400i	$-0.692635\pi$
$613$	−28.1711	−1.13782	−0.568910	+	0.822400i	$0.692635\pi$
$614$	8.71797	0.351829
$615$	−39.4176	−1.58947
$616$	1.23081	0.0495909
$617$	−37.9165	−1.52646	−0.763231	−	0.646125i	$-0.776388\pi$
$617$	−37.9165	−1.52646	−0.763231	+	0.646125i	$0.776388\pi$
$618$	1.91855	0.0771754
$619$	17.7675	0.714134	0.357067	−	0.934079i	$-0.383777\pi$
$619$	17.7675	0.714134	0.357067	+	0.934079i	$0.383777\pi$
$620$	19.5364	0.784603
$621$	−41.6908	−1.67299
$622$	−34.6832	−1.39067
$623$	22.1218	0.886289
$624$	−1.66067	−0.0664802
$625$	21.2980	0.851919
$626$	51.4920	2.05804
$627$	2.98284	0.119123
$628$	16.6325	0.663707
$629$	50.2423	2.00329
$630$	26.6107	1.06020
$631$	−40.2609	−1.60276	−0.801381	−	0.598155i	$-0.795901\pi$
$631$	−40.2609	−1.60276	−0.801381	+	0.598155i	$0.795901\pi$
$632$	8.68698	0.345550
$633$	−10.2067	−0.405681
$634$	−31.2484	−1.24103
$635$	16.5158	0.655408
$636$	12.7296	0.504761
$637$	4.96841	0.196856
$638$	−3.12811	−0.123843
$639$	−6.42719	−0.254256
$640$	47.4799	1.87681
$641$	−5.12482	−0.202418	−0.101209	−	0.994865i	$-0.532271\pi$
$641$	−5.12482	−0.202418	−0.101209	+	0.994865i	$0.532271\pi$
$642$	−15.8023	−0.623667
$643$	−36.2780	−1.43066	−0.715331	−	0.698785i	$-0.753724\pi$
$643$	−36.2780	−1.43066	−0.715331	+	0.698785i	$0.753724\pi$
$644$	−35.7418	−1.40842
$645$	5.77457	0.227374
$646$	−117.221	−4.61200
$647$	8.44834	0.332139	0.166069	−	0.986114i	$-0.446892\pi$
$647$	8.44834	0.332139	0.166069	+	0.986114i	$0.446892\pi$
$648$	−4.40559	−0.173068
$649$	4.13856	0.162453
$650$	21.2781	0.834598
$651$	−2.30614	−0.0903846
$652$	−56.8458	−2.22625
$653$	−25.7369	−1.00716	−0.503581	−	0.863948i	$-0.667985\pi$
$653$	−25.7369	−1.00716	−0.503581	+	0.863948i	$0.667985\pi$
$654$	19.7026	0.770433
$655$	31.3250	1.22397
$656$	−22.0595	−0.861278
$657$	26.2085	1.02249
$658$	1.52982	0.0596386
$659$	−21.2735	−0.828700	−0.414350	−	0.910118i	$-0.635991\pi$
$659$	−21.2735	−0.828700	−0.414350	+	0.910118i	$0.635991\pi$
$660$	4.83318	0.188131
$661$	6.83751	0.265948	0.132974	−	0.991120i	$-0.457547\pi$
$661$	6.83751	0.265948	0.132974	+	0.991120i	$0.457547\pi$
$662$	71.5817	2.78210
$663$	7.20701	0.279897
$664$	−24.8084	−0.962751
$665$	35.8571	1.39048
$666$	29.7900	1.15434
$667$	25.1023	0.971967
$668$	−41.0666	−1.58891
$669$	−1.38271	−0.0534585
$670$	7.60864	0.293947
$671$	1.27653	0.0492801
$672$	−9.34327	−0.360424
$673$	−34.9838	−1.34852	−0.674262	−	0.738492i	$-0.735538\pi$
$673$	−34.9838	−1.34852	−0.674262	+	0.738492i	$0.735538\pi$
$674$	−44.0647	−1.69731
$675$	44.7959	1.72420
$676$	2.76374	0.106298
$677$	−5.86870	−0.225552	−0.112776	−	0.993620i	$-0.535974\pi$
$677$	−5.86870	−0.225552	−0.112776	+	0.993620i	$0.535974\pi$
$678$	15.3460	0.589359
$679$	−6.94905	−0.266680
$680$	−52.4874	−2.01280
$681$	−9.19609	−0.352395
$682$	2.08112	0.0796903
$683$	−11.8355	−0.452871	−0.226436	−	0.974026i	$-0.572707\pi$
$683$	−11.8355	−0.452871	−0.226436	+	0.974026i	$0.572707\pi$
$684$	−40.3232	−1.54180
$685$	22.3019	0.852110
$686$	37.2330	1.42156
$687$	−4.04352	−0.154270
$688$	3.23165	0.123206
$689$	5.23985	0.199622
$690$	−66.8522	−2.54502
$691$	−12.4626	−0.474098	−0.237049	−	0.971498i	$-0.576180\pi$
$691$	−12.4626	−0.474098	−0.237049	+	0.971498i	$0.576180\pi$
$692$	−2.92481	−0.111185
$693$	1.64459	0.0624728
$694$	17.0989	0.649067
$695$	−10.7170	−0.406519
$696$	−4.05386	−0.153661
$697$	95.7340	3.62618
$698$	27.3676	1.03588
$699$	−22.4119	−0.847694
$700$	38.4039	1.45153
$701$	−7.42664	−0.280500	−0.140250	−	0.990116i	$-0.544791\pi$
$701$	−7.42664	−0.280500	−0.140250	+	0.990116i	$0.544791\pi$
$702$	10.0289	0.378516
$703$	40.1410	1.51395
$704$	6.47427	0.244008
$705$	1.66008	0.0625221
$706$	21.3153	0.802212
$707$	22.7961	0.857335
$708$	19.4084	0.729411
$709$	−16.5599	−0.621919	−0.310960	−	0.950423i	$-0.600650\pi$
$709$	−16.5599	−0.621919	−0.310960	+	0.950423i	$0.600650\pi$
$710$	−24.1876	−0.907745
$711$	11.6074	0.435311
$712$	−25.8713	−0.969570
$713$	−16.7005	−0.625439
$714$	22.4206	0.839070
$715$	1.98947	0.0744020
$716$	34.8004	1.30055
$717$	2.18468	0.0815883
$718$	−27.5320	−1.02749
$719$	−34.2126	−1.27592	−0.637958	−	0.770071i	$-0.720221\pi$
$719$	−34.2126	−1.27592	−0.637958	+	0.770071i	$0.720221\pi$
$720$	16.1603	0.602259
$721$	1.42534	0.0530824
$722$	−52.1843	−1.94210
$723$	−4.15258	−0.154436
$724$	−34.8921	−1.29676
$725$	−26.9720	−1.00171
$726$	−20.5892	−0.764136
$727$	−42.6528	−1.58191	−0.790953	−	0.611877i	$-0.790415\pi$
$727$	−42.6528	−1.58191	−0.790953	+	0.611877i	$0.790415\pi$
$728$	2.37594	0.0880583
$729$	6.23043	0.230757
$730$	98.6310	3.65050
$731$	−14.0248	−0.518725
$732$	5.98649	0.221267
$733$	−11.0262	−0.407262	−0.203631	−	0.979048i	$-0.565274\pi$
$733$	−11.0262	−0.407262	−0.203631	+	0.979048i	$0.565274\pi$
$734$	23.8168	0.879095
$735$	16.7725	0.618663
$736$	−67.6617	−2.49404
$737$	0.470228	0.0173211
$738$	56.7632	2.08948
$739$	17.4709	0.642676	0.321338	−	0.946965i	$-0.395867\pi$
$739$	17.4709	0.642676	0.321338	+	0.946965i	$0.395867\pi$
$740$	65.0416	2.39098
$741$	5.75804	0.211527
$742$	16.3009	0.598424
$743$	33.7676	1.23881	0.619406	−	0.785071i	$-0.287373\pi$
$743$	33.7676	1.23881	0.619406	+	0.785071i	$0.287373\pi$
$744$	2.69702	0.0988776
$745$	16.0574	0.588297
$746$	−28.4046	−1.03997
$747$	−33.1485	−1.21284
$748$	−11.7384	−0.429199
$749$	−11.7399	−0.428968
$750$	34.9910	1.27769
$751$	−26.3853	−0.962814	−0.481407	−	0.876497i	$-0.659874\pi$
$751$	−26.3853	−0.962814	−0.481407	+	0.876497i	$0.659874\pi$
$752$	0.929038	0.0338785
$753$	18.9382	0.690147
$754$	−6.03846	−0.219908
$755$	35.7521	1.30115
$756$	18.1006	0.658313
$757$	−23.1246	−0.840477	−0.420239	−	0.907414i	$-0.638054\pi$
$757$	−23.1246	−0.840477	−0.420239	+	0.907414i	$0.638054\pi$
$758$	−3.81247	−0.138475
$759$	−4.13159	−0.149967
$760$	−41.9348	−1.52113
$761$	27.1834	0.985399	0.492699	−	0.870200i	$-0.336010\pi$
$761$	27.1834	0.985399	0.492699	+	0.870200i	$0.336010\pi$
$762$	8.25069	0.298891
$763$	14.6376	0.529916
$764$	68.3292	2.47206
$765$	−70.1327	−2.53565
$766$	−26.0141	−0.939928
$767$	7.98902	0.288467
$768$	1.74760	0.0630611
$769$	−37.9882	−1.36989	−0.684945	−	0.728595i	$-0.740174\pi$
$769$	−37.9882	−1.36989	−0.684945	+	0.728595i	$0.740174\pi$
$770$	6.18913	0.223041
$771$	4.98875	0.179666
$772$	−29.8244	−1.07340
$773$	46.5021	1.67256	0.836282	−	0.548300i	$-0.184725\pi$
$773$	46.5021	1.67256	0.836282	+	0.548300i	$0.184725\pi$
$774$	−8.31566	−0.298900
$775$	17.9443	0.644580
$776$	8.12690	0.291739
$777$	−7.67769	−0.275436
$778$	−55.0995	−1.97541
$779$	76.4866	2.74042
$780$	9.32990	0.334064
$781$	−1.49484	−0.0534895
$782$	162.365	5.80615
$783$	−12.7125	−0.454308
$784$	9.38648	0.335231
$785$	23.1122	0.824909
$786$	15.6489	0.558176
$787$	−15.0323	−0.535844	−0.267922	−	0.963441i	$-0.586337\pi$
$787$	−15.0323	−0.535844	−0.267922	+	0.963441i	$0.586337\pi$
$788$	−6.47772	−0.230759
$789$	23.3562	0.831503
$790$	43.6824	1.55415
$791$	11.4009	0.405370
$792$	−1.92334	−0.0683431
$793$	2.46420	0.0875064
$794$	−33.7372	−1.19729
$795$	17.6888	0.627358
$796$	22.1241	0.784167
$797$	43.6655	1.54671	0.773356	−	0.633972i	$-0.218576\pi$
$797$	43.6655	1.54671	0.773356	+	0.633972i	$0.218576\pi$
$798$	17.9129	0.634111
$799$	−4.03185	−0.142637
$800$	72.7012	2.57037
$801$	−34.5688	−1.22143
$802$	−39.5135	−1.39527
$803$	6.09557	0.215108
$804$	2.20520	0.0777714
$805$	−49.6662	−1.75050
$806$	4.01737	0.141506
$807$	−12.7743	−0.449675
$808$	−26.6600	−0.937895
$809$	−46.8227	−1.64620	−0.823100	−	0.567897i	$-0.807757\pi$
$809$	−46.8227	−1.64620	−0.823100	+	0.567897i	$0.807757\pi$
$810$	−22.1535	−0.778393
$811$	31.1185	1.09272	0.546359	−	0.837551i	$-0.316013\pi$
$811$	31.1185	1.09272	0.546359	+	0.837551i	$0.316013\pi$
$812$	−10.8985	−0.382463
$813$	−13.8581	−0.486025
$814$	6.92857	0.242846
$815$	−78.9920	−2.76697
$816$	13.6157	0.476645
$817$	−11.2051	−0.392016
$818$	−4.60220	−0.160912
$819$	3.17469	0.110933
$820$	123.933	4.32794
$821$	−29.7714	−1.03903	−0.519515	−	0.854461i	$-0.673887\pi$
$821$	−29.7714	−1.03903	−0.519515	+	0.854461i	$0.673887\pi$
$822$	11.1412	0.388595
$823$	−22.9598	−0.800328	−0.400164	−	0.916444i	$-0.631047\pi$
$823$	−22.9598	−0.800328	−0.400164	+	0.916444i	$0.631047\pi$
$824$	−1.66693	−0.0580703
$825$	4.43931	0.154557
$826$	24.8534	0.864760
$827$	−28.3618	−0.986237	−0.493118	−	0.869962i	$-0.664143\pi$
$827$	−28.3618	−0.986237	−0.493118	+	0.869962i	$0.664143\pi$
$828$	55.8524	1.94100
$829$	44.1481	1.53333	0.766664	−	0.642048i	$-0.221915\pi$
$829$	44.1481	1.53333	0.766664	+	0.642048i	$0.221915\pi$
$830$	−124.749	−4.33009
$831$	4.01589	0.139310
$832$	12.4978	0.433284
$833$	−40.7355	−1.41140
$834$	−5.35384	−0.185388
$835$	−57.0654	−1.97483
$836$	−9.37839	−0.324358
$837$	8.45758	0.292337
$838$	−26.0972	−0.901513
$839$	7.80973	0.269622	0.134811	−	0.990871i	$-0.456957\pi$
$839$	7.80973	0.269622	0.134811	+	0.990871i	$0.456957\pi$
$840$	8.02077	0.276743
$841$	−21.3457	−0.736059
$842$	−51.0431	−1.75906
$843$	3.35936	0.115703
$844$	32.0910	1.10462
$845$	3.84044	0.132115
$846$	−2.39059	−0.0821902
$847$	−15.2962	−0.525585
$848$	9.89929	0.339943
$849$	15.4269	0.529449
$850$	−174.458	−5.98385
$851$	−55.6000	−1.90594
$852$	−7.01025	−0.240167
$853$	35.8717	1.22822	0.614111	−	0.789220i	$-0.289515\pi$
$853$	35.8717	1.22822	0.614111	+	0.789220i	$0.289515\pi$
$854$	7.66600	0.262325
$855$	−56.0325	−1.91627
$856$	13.7298	0.469276
$857$	43.2846	1.47857	0.739286	−	0.673391i	$-0.235163\pi$
$857$	43.2846	1.47857	0.739286	+	0.673391i	$0.235163\pi$
$858$	0.993869	0.0339301
$859$	51.2443	1.74843	0.874217	−	0.485536i	$-0.161375\pi$
$859$	51.2443	1.74843	0.874217	+	0.485536i	$0.161375\pi$
$860$	−18.1559	−0.619111
$861$	−14.6294	−0.498569
$862$	2.86623	0.0976240
$863$	40.6408	1.38343	0.691715	−	0.722171i	$-0.256856\pi$
$863$	40.6408	1.38343	0.691715	+	0.722171i	$0.256856\pi$
$864$	34.2657	1.16574
$865$	−4.06427	−0.138189
$866$	−40.6182	−1.38026
$867$	−44.1463	−1.49929
$868$	7.25074	0.246106
$869$	2.69965	0.0915793
$870$	−20.3848	−0.691110
$871$	0.907720	0.0307569
$872$	−17.1186	−0.579710
$873$	10.8590	0.367522
$874$	129.721	4.38789
$875$	25.9957	0.878815
$876$	28.5860	0.965833
$877$	−6.73356	−0.227376	−0.113688	−	0.993516i	$-0.536266\pi$
$877$	−6.73356	−0.227376	−0.113688	+	0.993516i	$0.536266\pi$
$878$	−30.4942	−1.02913
$879$	−13.2759	−0.447787
$880$	3.75857	0.126701
$881$	29.1477	0.982013	0.491006	−	0.871156i	$-0.336629\pi$
$881$	29.1477	0.982013	0.491006	+	0.871156i	$0.336629\pi$
$882$	−24.1532	−0.813280
$883$	47.6242	1.60268	0.801342	−	0.598207i	$-0.204120\pi$
$883$	47.6242	1.60268	0.801342	+	0.598207i	$0.204120\pi$
$884$	−22.6596	−0.762126
$885$	26.9695	0.906571
$886$	77.3070	2.59718
$887$	−13.3650	−0.448752	−0.224376	−	0.974503i	$-0.572034\pi$
$887$	−13.3650	−0.448752	−0.224376	+	0.974503i	$0.572034\pi$
$888$	8.97904	0.301317
$889$	6.12965	0.205582
$890$	−130.094	−4.36075
$891$	−1.36912	−0.0458674
$892$	4.34738	0.145561
$893$	−3.22124	−0.107795
$894$	8.02170	0.268286
$895$	48.3581	1.61643
$896$	17.6217	0.588699
$897$	−7.97555	−0.266296
$898$	67.5140	2.25297
$899$	−5.09237	−0.169840
$900$	−60.0122	−2.00041
$901$	−42.9610	−1.43124
$902$	13.2020	0.439579
$903$	2.14317	0.0713203
$904$	−13.3334	−0.443461
$905$	−48.4855	−1.61171
$906$	17.8605	0.593376
$907$	−33.8493	−1.12395	−0.561975	−	0.827154i	$-0.689958\pi$
$907$	−33.8493	−1.12395	−0.561975	+	0.827154i	$0.689958\pi$
$908$	28.9135	0.959528
$909$	−35.6226	−1.18153
$910$	11.9474	0.396052
$911$	−41.1372	−1.36294	−0.681468	−	0.731848i	$-0.738658\pi$
$911$	−41.1372	−1.36294	−0.681468	+	0.731848i	$0.738658\pi$
$912$	10.8783	0.360215
$913$	−7.70968	−0.255153
$914$	62.9319	2.08160
$915$	8.31872	0.275009
$916$	12.7133	0.420058
$917$	11.6259	0.383922
$918$	−82.2258	−2.71386
$919$	−5.21229	−0.171938	−0.0859688	−	0.996298i	$-0.527399\pi$
$919$	−5.21229	−0.171938	−0.0859688	+	0.996298i	$0.527399\pi$
$920$	58.0846	1.91499
$921$	3.51108	0.115694
$922$	71.1325	2.34263
$923$	−2.88561	−0.0949810
$924$	1.79378	0.0590112
$925$	59.7411	1.96428
$926$	4.05864	0.133375
$927$	−2.22732	−0.0731549
$928$	−20.6317	−0.677267
$929$	19.6876	0.645928	0.322964	−	0.946411i	$-0.395321\pi$
$929$	19.6876	0.645928	0.322964	+	0.946411i	$0.395321\pi$
$930$	13.5619	0.444714
$931$	−32.5456	−1.06664
$932$	70.4653	2.30817
$933$	−13.9683	−0.457303
$934$	64.3009	2.10399
$935$	−16.3115	−0.533443
$936$	−3.71279	−0.121356
$937$	6.83765	0.223376	0.111688	−	0.993743i	$-0.464374\pi$
$937$	6.83765	0.223376	0.111688	+	0.993743i	$0.464374\pi$
$938$	2.82387	0.0922025
$939$	20.7379	0.676757
$940$	−5.21947	−0.170240
$941$	−18.2563	−0.595139	−0.297569	−	0.954700i	$-0.596176\pi$
$941$	−18.2563	−0.595139	−0.297569	+	0.954700i	$0.596176\pi$
$942$	11.5460	0.376190
$943$	−105.943	−3.44997
$944$	15.0931	0.491239
$945$	25.1523	0.818205
$946$	−1.93406	−0.0628817
$947$	15.5875	0.506525	0.253263	−	0.967398i	$-0.418496\pi$
$947$	15.5875	0.506525	0.253263	+	0.967398i	$0.418496\pi$
$948$	12.6604	0.411190
$949$	11.7668	0.381966
$950$	−139.383	−4.52218
$951$	−12.5850	−0.408096
$952$	−19.4801	−0.631355
$953$	5.27848	0.170987	0.0854934	−	0.996339i	$-0.472753\pi$
$953$	5.27848	0.170987	0.0854934	+	0.996339i	$0.472753\pi$
$954$	−25.4727	−0.824710
$955$	94.9491	3.07248
$956$	−6.86887	−0.222155
$957$	−1.25982	−0.0407241
$958$	79.7490	2.57657
$959$	8.27709	0.267281
$960$	42.1905	1.36169
$961$	−27.6121	−0.890712
$962$	13.3748	0.431221
$963$	18.3455	0.591177
$964$	13.0562	0.420510
$965$	−41.4435	−1.33411
$966$	−24.8115	−0.798297
$967$	−22.1726	−0.713023	−0.356512	−	0.934291i	$-0.616034\pi$
$967$	−22.1726	−0.713023	−0.356512	+	0.934291i	$0.616034\pi$
$968$	17.8889	0.574971
$969$	−47.2096	−1.51659
$970$	40.8660	1.31213
$971$	−0.889020	−0.0285300	−0.0142650	−	0.999898i	$-0.504541\pi$
$971$	−0.889020	−0.0285300	−0.0142650	+	0.999898i	$0.504541\pi$
$972$	−44.5182	−1.42792
$973$	−3.97750	−0.127513
$974$	−68.3591	−2.19037
$975$	8.56957	0.274446
$976$	4.65545	0.149017
$977$	−5.39755	−0.172683	−0.0863415	−	0.996266i	$-0.527518\pi$
$977$	−5.39755	−0.172683	−0.0863415	+	0.996266i	$0.527518\pi$
$978$	−39.4616	−1.26184
$979$	−8.04003	−0.256960
$980$	−52.7345	−1.68454
$981$	−22.8736	−0.730297
$982$	−47.3811	−1.51199
$983$	3.39171	0.108179	0.0540894	−	0.998536i	$-0.482774\pi$
$983$	3.39171	0.108179	0.0540894	+	0.998536i	$0.482774\pi$
$984$	17.1091	0.545418
$985$	−9.00133	−0.286806
$986$	49.5088	1.57668
$987$	0.616120	0.0196113
$988$	−18.1039	−0.575962
$989$	15.5203	0.493518
$990$	−9.67151	−0.307381
$991$	15.1747	0.482039	0.241020	−	0.970520i	$-0.422518\pi$
$991$	15.1747	0.482039	0.241020	+	0.970520i	$0.422518\pi$
$992$	13.7262	0.435806
$993$	28.8288	0.914855
$994$	−8.97697	−0.284732
$995$	30.7432	0.974626
$996$	−36.1556	−1.14564
$997$	−30.5683	−0.968109	−0.484054	−	0.875038i	$-0.660836\pi$
$997$	−30.5683	−0.968109	−0.484054	+	0.875038i	$0.660836\pi$
$998$	67.7821	2.14560
$999$	28.1573	0.890859

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.g.1.5	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.g.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.18260 q^{2} -0.879021 q^{3} +2.76374 q^{4} +3.84044 q^{5} +1.91855 q^{6} +1.42534 q^{7} -1.66693 q^{8} -2.22732 q^{9} +O(q^{10})\)	\(q-2.18260 q^{2} -0.879021 q^{3} +2.76374 q^{4} +3.84044 q^{5} +1.91855 q^{6} +1.42534 q^{7} -1.66693 q^{8} -2.22732 q^{9} -8.38214 q^{10} -0.518032 q^{11} -2.42938 q^{12} -1.00000 q^{13} -3.11094 q^{14} -3.37583 q^{15} -1.88923 q^{16} +8.19891 q^{17} +4.86135 q^{18} +6.55051 q^{19} +10.6140 q^{20} -1.25290 q^{21} +1.13065 q^{22} -9.07323 q^{23} +1.46527 q^{24} +9.74900 q^{25} +2.18260 q^{26} +4.59492 q^{27} +3.93926 q^{28} -2.76664 q^{29} +7.36808 q^{30} +1.84064 q^{31} +7.45730 q^{32} +0.455360 q^{33} -17.8949 q^{34} +5.47393 q^{35} -6.15573 q^{36} +6.12792 q^{37} -14.2971 q^{38} +0.879021 q^{39} -6.40175 q^{40} +11.6764 q^{41} +2.73458 q^{42} -1.71056 q^{43} -1.43170 q^{44} -8.55390 q^{45} +19.8032 q^{46} -0.491754 q^{47} +1.66067 q^{48} -4.96841 q^{49} -21.2781 q^{50} -7.20701 q^{51} -2.76374 q^{52} -5.23985 q^{53} -10.0289 q^{54} -1.98947 q^{55} -2.37594 q^{56} -5.75804 q^{57} +6.03846 q^{58} -7.98902 q^{59} -9.32990 q^{60} -2.46420 q^{61} -4.01737 q^{62} -3.17469 q^{63} -12.4978 q^{64} -3.84044 q^{65} -0.993869 q^{66} -0.907720 q^{67} +22.6596 q^{68} +7.97555 q^{69} -11.9474 q^{70} +2.88561 q^{71} +3.71279 q^{72} -11.7668 q^{73} -13.3748 q^{74} -8.56957 q^{75} +18.1039 q^{76} -0.738371 q^{77} -1.91855 q^{78} -5.21136 q^{79} -7.25549 q^{80} +2.64294 q^{81} -25.4849 q^{82} +14.8827 q^{83} -3.46269 q^{84} +31.4874 q^{85} +3.73348 q^{86} +2.43193 q^{87} +0.863523 q^{88} +15.5203 q^{89} +18.6697 q^{90} -1.42534 q^{91} -25.0760 q^{92} -1.61796 q^{93} +1.07330 q^{94} +25.1569 q^{95} -6.55512 q^{96} -4.87537 q^{97} +10.8440 q^{98} +1.15382 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) \) 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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