LMFDB - Embedded newform 6037.2.a.a.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$1$
Dimension:	$243$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63978 q^{2} -0.462407 q^{3} +4.96844 q^{4} +1.16438 q^{5} +1.22065 q^{6} +1.07998 q^{7} -7.83603 q^{8} -2.78618 q^{9} +O(q^{10})$	\(q-2.63978 q^{2} -0.462407 q^{3} +4.96844 q^{4} +1.16438 q^{5} +1.22065 q^{6} +1.07998 q^{7} -7.83603 q^{8} -2.78618 q^{9} -3.07372 q^{10} -3.53625 q^{11} -2.29744 q^{12} +2.95313 q^{13} -2.85091 q^{14} -0.538420 q^{15} +10.7485 q^{16} +4.52115 q^{17} +7.35490 q^{18} +3.87504 q^{19} +5.78517 q^{20} -0.499391 q^{21} +9.33491 q^{22} -7.49997 q^{23} +3.62344 q^{24} -3.64421 q^{25} -7.79562 q^{26} +2.67557 q^{27} +5.36582 q^{28} -9.04565 q^{29} +1.42131 q^{30} +1.88259 q^{31} -12.7016 q^{32} +1.63519 q^{33} -11.9349 q^{34} +1.25751 q^{35} -13.8430 q^{36} +1.27588 q^{37} -10.2293 q^{38} -1.36555 q^{39} -9.12415 q^{40} +9.77153 q^{41} +1.31828 q^{42} +11.0369 q^{43} -17.5696 q^{44} -3.24418 q^{45} +19.7983 q^{46} -9.64306 q^{47} -4.97019 q^{48} -5.83364 q^{49} +9.61991 q^{50} -2.09062 q^{51} +14.6725 q^{52} +2.22918 q^{53} -7.06292 q^{54} -4.11755 q^{55} -8.46275 q^{56} -1.79185 q^{57} +23.8785 q^{58} +7.41365 q^{59} -2.67511 q^{60} -7.56489 q^{61} -4.96963 q^{62} -3.00902 q^{63} +12.0325 q^{64} +3.43858 q^{65} -4.31653 q^{66} +4.78204 q^{67} +22.4631 q^{68} +3.46804 q^{69} -3.31956 q^{70} -4.46975 q^{71} +21.8326 q^{72} +9.27180 q^{73} -3.36805 q^{74} +1.68511 q^{75} +19.2529 q^{76} -3.81907 q^{77} +3.60475 q^{78} -1.33702 q^{79} +12.5154 q^{80} +7.12133 q^{81} -25.7947 q^{82} +14.3565 q^{83} -2.48119 q^{84} +5.26436 q^{85} -29.1350 q^{86} +4.18278 q^{87} +27.7101 q^{88} -12.3141 q^{89} +8.56393 q^{90} +3.18932 q^{91} -37.2632 q^{92} -0.870525 q^{93} +25.4556 q^{94} +4.51204 q^{95} +5.87334 q^{96} -11.8504 q^{97} +15.3995 q^{98} +9.85261 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) $ 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * 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 $

$2$	−2.63978	−1.86661	−0.933303	−	0.359089i	$-0.883087\pi$
$2$	−2.63978	−1.86661	−0.933303	+	0.359089i	$0.883087\pi$
$3$	−0.462407	−0.266971	−0.133486	−	0.991051i	$-0.542617\pi$
$3$	−0.462407	−0.266971	−0.133486	+	0.991051i	$0.542617\pi$
$4$	4.96844	2.48422
$5$	1.16438	0.520729	0.260364	−	0.965510i	$-0.416157\pi$
$5$	1.16438	0.520729	0.260364	+	0.965510i	$0.416157\pi$
$6$	1.22065	0.498330
$7$	1.07998	0.408194	0.204097	−	0.978951i	$-0.434574\pi$
$7$	1.07998	0.408194	0.204097	+	0.978951i	$0.434574\pi$
$8$	−7.83603	−2.77045
$9$	−2.78618	−0.928726
$10$	−3.07372	−0.971995
$11$	−3.53625	−1.06622	−0.533109	−	0.846047i	$-0.678976\pi$
$11$	−3.53625	−1.06622	−0.533109	+	0.846047i	$0.678976\pi$
$12$	−2.29744	−0.663215
$13$	2.95313	0.819051	0.409526	−	0.912299i	$-0.365694\pi$
$13$	2.95313	0.819051	0.409526	+	0.912299i	$0.365694\pi$
$14$	−2.85091	−0.761938
$15$	−0.538420	−0.139019
$16$	10.7485	2.68713
$17$	4.52115	1.09654	0.548270	−	0.836301i	$-0.315286\pi$
$17$	4.52115	1.09654	0.548270	+	0.836301i	$0.315286\pi$
$18$	7.35490	1.73357
$19$	3.87504	0.888995	0.444498	−	0.895780i	$-0.353382\pi$
$19$	3.87504	0.888995	0.444498	+	0.895780i	$0.353382\pi$
$20$	5.78517	1.29360
$21$	−0.499391	−0.108976
$22$	9.33491	1.99021
$23$	−7.49997	−1.56385	−0.781926	−	0.623371i	$-0.785763\pi$
$23$	−7.49997	−1.56385	−0.781926	+	0.623371i	$0.785763\pi$
$24$	3.62344	0.739631
$25$	−3.64421	−0.728842
$26$	−7.79562	−1.52885
$27$	2.67557	0.514914
$28$	5.36582	1.01404
$29$	−9.04565	−1.67974	−0.839868	−	0.542791i	$-0.817368\pi$
$29$	−9.04565	−1.67974	−0.839868	+	0.542791i	$0.817368\pi$
$30$	1.42131	0.259495
$31$	1.88259	0.338123	0.169062	−	0.985605i	$-0.445926\pi$
$31$	1.88259	0.338123	0.169062	+	0.985605i	$0.445926\pi$
$32$	−12.7016	−2.24536
$33$	1.63519	0.284649
$34$	−11.9349	−2.04681
$35$	1.25751	0.212558
$36$	−13.8430	−2.30716
$37$	1.27588	0.209754	0.104877	−	0.994485i	$-0.466555\pi$
$37$	1.27588	0.209754	0.104877	+	0.994485i	$0.466555\pi$
$38$	−10.2293	−1.65940
$39$	−1.36555	−0.218663
$40$	−9.12415	−1.44265
$41$	9.77153	1.52606	0.763028	−	0.646365i	$-0.223712\pi$
$41$	9.77153	1.52606	0.763028	+	0.646365i	$0.223712\pi$
$42$	1.31828	0.203415
$43$	11.0369	1.68311	0.841555	−	0.540171i	$-0.181640\pi$
$43$	11.0369	1.68311	0.841555	+	0.540171i	$0.181640\pi$
$44$	−17.5696	−2.64872
$45$	−3.24418	−0.483614
$46$	19.7983	2.91910
$47$	−9.64306	−1.40658	−0.703292	−	0.710901i	$-0.748288\pi$
$47$	−9.64306	−1.40658	−0.703292	+	0.710901i	$0.748288\pi$
$48$	−4.97019	−0.717385
$49$	−5.83364	−0.833378
$50$	9.61991	1.36046
$51$	−2.09062	−0.292745
$52$	14.6725	2.03470
$53$	2.22918	0.306202	0.153101	−	0.988211i	$-0.451074\pi$
$53$	2.22918	0.306202	0.153101	+	0.988211i	$0.451074\pi$
$54$	−7.06292	−0.961142
$55$	−4.11755	−0.555210
$56$	−8.46275	−1.13088
$57$	−1.79185	−0.237336
$58$	23.8785	3.13540
$59$	7.41365	0.965175	0.482588	−	0.875848i	$-0.339697\pi$
$59$	7.41365	0.965175	0.482588	+	0.875848i	$0.339697\pi$
$60$	−2.67511	−0.345355
$61$	−7.56489	−0.968585	−0.484293	−	0.874906i	$-0.660923\pi$
$61$	−7.56489	−0.968585	−0.484293	+	0.874906i	$0.660923\pi$
$62$	−4.96963	−0.631143
$63$	−3.00902	−0.379101
$64$	12.0325	1.50407
$65$	3.43858	0.426503
$66$	−4.31653	−0.531328
$67$	4.78204	0.584219	0.292110	−	0.956385i	$-0.405643\pi$
$67$	4.78204	0.584219	0.292110	+	0.956385i	$0.405643\pi$
$68$	22.4631	2.72405
$69$	3.46804	0.417503
$70$	−3.31956	−0.396763
$71$	−4.46975	−0.530461	−0.265231	−	0.964185i	$-0.585448\pi$
$71$	−4.46975	−0.530461	−0.265231	+	0.964185i	$0.585448\pi$
$72$	21.8326	2.57299
$73$	9.27180	1.08518	0.542591	−	0.839997i	$-0.317443\pi$
$73$	9.27180	1.08518	0.542591	+	0.839997i	$0.317443\pi$
$74$	−3.36805	−0.391528
$75$	1.68511	0.194580
$76$	19.2529	2.20846
$77$	−3.81907	−0.435224
$78$	3.60475	0.408158
$79$	−1.33702	−0.150426	−0.0752132	−	0.997167i	$-0.523964\pi$
$79$	−1.33702	−0.150426	−0.0752132	+	0.997167i	$0.523964\pi$
$80$	12.5154	1.39926
$81$	7.12133	0.791259
$82$	−25.7947	−2.84855
$83$	14.3565	1.57584	0.787918	−	0.615781i	$-0.211159\pi$
$83$	14.3565	1.57584	0.787918	+	0.615781i	$0.211159\pi$
$84$	−2.48119	−0.270720
$85$	5.26436	0.571000
$86$	−29.1350	−3.14171
$87$	4.18278	0.448441
$88$	27.7101	2.95391
$89$	−12.3141	−1.30529	−0.652645	−	0.757664i	$-0.726341\pi$
$89$	−12.3141	−1.30529	−0.652645	+	0.757664i	$0.726341\pi$
$90$	8.56393	0.902718
$91$	3.18932	0.334332
$92$	−37.2632	−3.88495
$93$	−0.870525	−0.0902692
$94$	25.4556	2.62554
$95$	4.51204	0.462925
$96$	5.87334	0.599445
$97$	−11.8504	−1.20323	−0.601613	−	0.798787i	$-0.705475\pi$
$97$	−11.8504	−1.20323	−0.601613	+	0.798787i	$0.705475\pi$
$98$	15.3995	1.55559
$99$	9.85261	0.990225
$100$	−18.1060	−1.81060
$101$	10.7574	1.07040	0.535202	−	0.844724i	$-0.320236\pi$
$101$	10.7574	1.07040	0.535202	+	0.844724i	$0.320236\pi$
$102$	5.51876	0.546439
$103$	4.83337	0.476246	0.238123	−	0.971235i	$-0.423468\pi$
$103$	4.83337	0.476246	0.238123	+	0.971235i	$0.423468\pi$
$104$	−23.1408	−2.26914
$105$	−0.581483	−0.0567469
$106$	−5.88456	−0.571559
$107$	−17.4142	−1.68349	−0.841745	−	0.539875i	$-0.818471\pi$
$107$	−17.4142	−1.68349	−0.841745	+	0.539875i	$0.818471\pi$
$108$	13.2934	1.27916
$109$	11.3211	1.08436	0.542182	−	0.840261i	$-0.317598\pi$
$109$	11.3211	1.08436	0.542182	+	0.840261i	$0.317598\pi$
$110$	10.8694	1.03636
$111$	−0.589978	−0.0559983
$112$	11.6082	1.09687
$113$	−17.1996	−1.61800	−0.809002	−	0.587805i	$-0.799992\pi$
$113$	−17.1996	−1.61800	−0.809002	+	0.587805i	$0.799992\pi$
$114$	4.73008	0.443013
$115$	−8.73285	−0.814343
$116$	−44.9428	−4.17283
$117$	−8.22795	−0.760674
$118$	−19.5704	−1.80160
$119$	4.88276	0.447602
$120$	4.21907	0.385147
$121$	1.50503	0.136821
$122$	19.9697	1.80797
$123$	−4.51843	−0.407413
$124$	9.35354	0.839973
$125$	−10.0652	−0.900257
$126$	7.94315	0.707632
$127$	−21.8838	−1.94187	−0.970935	−	0.239343i	$-0.923068\pi$
$127$	−21.8838	−1.94187	−0.970935	+	0.239343i	$0.923068\pi$
$128$	−6.35996	−0.562146
$129$	−5.10354	−0.449342
$130$	−9.07710	−0.796114
$131$	11.5111	1.00573	0.502865	−	0.864365i	$-0.332279\pi$
$131$	11.5111	1.00573	0.502865	+	0.864365i	$0.332279\pi$
$132$	8.12432	0.707132
$133$	4.18497	0.362883
$134$	−12.6235	−1.09051
$135$	3.11540	0.268131
$136$	−35.4279	−3.03792
$137$	0.629591	0.0537896	0.0268948	−	0.999638i	$-0.491438\pi$
$137$	0.629591	0.0537896	0.0268948	+	0.999638i	$0.491438\pi$
$138$	−9.15487	−0.779315
$139$	16.0683	1.36289	0.681446	−	0.731869i	$-0.261351\pi$
$139$	16.0683	1.36289	0.681446	+	0.731869i	$0.261351\pi$
$140$	6.24787	0.528042
$141$	4.45902	0.375517
$142$	11.7991	0.990162
$143$	−10.4430	−0.873287
$144$	−29.9473	−2.49561
$145$	−10.5326	−0.874686
$146$	−24.4755	−2.02561
$147$	2.69752	0.222488
$148$	6.33915	0.521075
$149$	−8.64172	−0.707958	−0.353979	−	0.935253i	$-0.615171\pi$
$149$	−8.64172	−0.707958	−0.353979	+	0.935253i	$0.615171\pi$
$150$	−4.44832	−0.363204
$151$	−22.6347	−1.84198	−0.920991	−	0.389584i	$-0.872619\pi$
$151$	−22.6347	−1.84198	−0.920991	+	0.389584i	$0.872619\pi$
$152$	−30.3649	−2.46292
$153$	−12.5967	−1.01839
$154$	10.0815	0.812392
$155$	2.19206	0.176071
$156$	−6.78465	−0.543207
$157$	−5.79446	−0.462449	−0.231224	−	0.972900i	$-0.574273\pi$
$157$	−5.79446	−0.462449	−0.231224	+	0.972900i	$0.574273\pi$
$158$	3.52944	0.280787
$159$	−1.03079	−0.0817471
$160$	−14.7896	−1.16922
$161$	−8.09982	−0.638355
$162$	−18.7988	−1.47697
$163$	−15.3616	−1.20321	−0.601605	−	0.798793i	$-0.705472\pi$
$163$	−15.3616	−1.20321	−0.601605	+	0.798793i	$0.705472\pi$
$164$	48.5493	3.79106
$165$	1.90399	0.148225
$166$	−37.8981	−2.94146
$167$	6.86062	0.530891	0.265446	−	0.964126i	$-0.414481\pi$
$167$	6.86062	0.530891	0.265446	+	0.964126i	$0.414481\pi$
$168$	3.91324	0.301913
$169$	−4.27902	−0.329155
$170$	−13.8968	−1.06583
$171$	−10.7966	−0.825633
$172$	54.8361	4.18122
$173$	14.4710	1.10021	0.550104	−	0.835096i	$-0.314588\pi$
$173$	14.4710	1.10021	0.550104	+	0.835096i	$0.314588\pi$
$174$	−11.0416	−0.837062
$175$	−3.93567	−0.297509
$176$	−38.0094	−2.86506
$177$	−3.42813	−0.257674
$178$	32.5065	2.43646
$179$	−21.6027	−1.61466	−0.807332	−	0.590097i	$-0.799089\pi$
$179$	−21.6027	−1.61466	−0.807332	+	0.590097i	$0.799089\pi$
$180$	−16.1185	−1.20140
$181$	12.2298	0.909030	0.454515	−	0.890739i	$-0.349813\pi$
$181$	12.2298	0.909030	0.454515	+	0.890739i	$0.349813\pi$
$182$	−8.41911	−0.624066
$183$	3.49806	0.258584
$184$	58.7700	4.33258
$185$	1.48562	0.109225
$186$	2.29799	0.168497
$187$	−15.9879	−1.16915
$188$	−47.9110	−3.49427
$189$	2.88957	0.210185
$190$	−11.9108	−0.864099
$191$	−16.4226	−1.18830	−0.594150	−	0.804354i	$-0.702511\pi$
$191$	−16.4226	−1.18830	−0.594150	+	0.804354i	$0.702511\pi$
$192$	−5.56394	−0.401542
$193$	−0.910777	−0.0655592	−0.0327796	−	0.999463i	$-0.510436\pi$
$193$	−0.910777	−0.0655592	−0.0327796	+	0.999463i	$0.510436\pi$
$194$	31.2825	2.24595
$195$	−1.59003	−0.113864
$196$	−28.9841	−2.07029
$197$	26.8361	1.91199	0.955995	−	0.293382i	$-0.0947809\pi$
$197$	26.8361	1.91199	0.955995	+	0.293382i	$0.0947809\pi$
$198$	−26.0087	−1.84836
$199$	18.6149	1.31957	0.659787	−	0.751453i	$-0.270646\pi$
$199$	18.6149	1.31957	0.659787	+	0.751453i	$0.270646\pi$
$200$	28.5561	2.01922
$201$	−2.21125	−0.155970
$202$	−28.3972	−1.99802
$203$	−9.76912	−0.685658
$204$	−10.3871	−0.727242
$205$	11.3778	0.794661
$206$	−12.7590	−0.888964
$207$	20.8963	1.45239
$208$	31.7418	2.20089
$209$	−13.7031	−0.947863
$210$	1.53499	0.105924
$211$	−2.42474	−0.166926	−0.0834630	−	0.996511i	$-0.526598\pi$
$211$	−2.42474	−0.166926	−0.0834630	+	0.996511i	$0.526598\pi$
$212$	11.0756	0.760673
$213$	2.06684	0.141618
$214$	45.9695	3.14241
$215$	12.8512	0.876444
$216$	−20.9659	−1.42655
$217$	2.03316	0.138020
$218$	−29.8852	−2.02408
$219$	−4.28735	−0.289712
$220$	−20.4578	−1.37926
$221$	13.3516	0.898123
$222$	1.55741	0.104527
$223$	−22.4339	−1.50229	−0.751143	−	0.660140i	$-0.770497\pi$
$223$	−22.4339	−1.50229	−0.751143	+	0.660140i	$0.770497\pi$
$224$	−13.7175	−0.916541
$225$	10.1534	0.676895
$226$	45.4032	3.02018
$227$	−9.98575	−0.662777	−0.331389	−	0.943494i	$-0.607517\pi$
$227$	−9.98575	−0.662777	−0.331389	+	0.943494i	$0.607517\pi$
$228$	−8.90269	−0.589595
$229$	−12.9300	−0.854441	−0.427221	−	0.904147i	$-0.640507\pi$
$229$	−12.9300	−0.854441	−0.427221	+	0.904147i	$0.640507\pi$
$230$	23.0528	1.52006
$231$	1.76597	0.116192
$232$	70.8820	4.65363
$233$	−15.8900	−1.04099	−0.520494	−	0.853865i	$-0.674252\pi$
$233$	−15.8900	−1.04099	−0.520494	+	0.853865i	$0.674252\pi$
$234$	21.7200	1.41988
$235$	−11.2282	−0.732449
$236$	36.8343	2.39771
$237$	0.618248	0.0401595
$238$	−12.8894	−0.835496
$239$	1.77725	0.114961	0.0574805	−	0.998347i	$-0.481693\pi$
$239$	1.77725	0.114961	0.0574805	+	0.998347i	$0.481693\pi$
$240$	−5.78721	−0.373563
$241$	1.79660	0.115729	0.0578646	−	0.998324i	$-0.481571\pi$
$241$	1.79660	0.115729	0.0578646	+	0.998324i	$0.481571\pi$
$242$	−3.97295	−0.255391
$243$	−11.3197	−0.726158
$244$	−37.5857	−2.40618
$245$	−6.79260	−0.433964
$246$	11.9277	0.760480
$247$	11.4435	0.728133
$248$	−14.7520	−0.936755
$249$	−6.63857	−0.420702
$250$	26.5699	1.68043
$251$	11.4939	0.725488	0.362744	−	0.931889i	$-0.381840\pi$
$251$	11.4939	0.725488	0.362744	+	0.931889i	$0.381840\pi$
$252$	−14.9501	−0.941769
$253$	26.5217	1.66741
$254$	57.7683	3.62471
$255$	−2.43428	−0.152441
$256$	−7.27618	−0.454761
$257$	6.38212	0.398106	0.199053	−	0.979989i	$-0.436213\pi$
$257$	6.38212	0.398106	0.199053	+	0.979989i	$0.436213\pi$
$258$	13.4722	0.838744
$259$	1.37793	0.0856204
$260$	17.0844	1.05953
$261$	25.2028	1.56001
$262$	−30.3868	−1.87730
$263$	−9.89083	−0.609895	−0.304947	−	0.952369i	$-0.598639\pi$
$263$	−9.89083	−0.609895	−0.304947	+	0.952369i	$0.598639\pi$
$264$	−12.8134	−0.788608
$265$	2.59563	0.159448
$266$	−11.0474	−0.677359
$267$	5.69412	0.348475
$268$	23.7593	1.45133
$269$	11.7750	0.717935	0.358967	−	0.933350i	$-0.383129\pi$
$269$	11.7750	0.717935	0.358967	+	0.933350i	$0.383129\pi$
$270$	−8.22396	−0.500494
$271$	6.38218	0.387690	0.193845	−	0.981032i	$-0.437904\pi$
$271$	6.38218	0.387690	0.193845	+	0.981032i	$0.437904\pi$
$272$	48.5957	2.94654
$273$	−1.47477	−0.0892569
$274$	−1.66198	−0.100404
$275$	12.8868	0.777104
$276$	17.2308	1.03717
$277$	14.0837	0.846206	0.423103	−	0.906081i	$-0.360941\pi$
$277$	14.0837	0.846206	0.423103	+	0.906081i	$0.360941\pi$
$278$	−42.4167	−2.54398
$279$	−5.24524	−0.314024
$280$	−9.85390	−0.588883
$281$	12.4161	0.740681	0.370340	−	0.928896i	$-0.379241\pi$
$281$	12.4161	0.740681	0.370340	+	0.928896i	$0.379241\pi$
$282$	−11.7708	−0.700943
$283$	−5.63857	−0.335178	−0.167589	−	0.985857i	$-0.553598\pi$
$283$	−5.63857	−0.335178	−0.167589	+	0.985857i	$0.553598\pi$
$284$	−22.2077	−1.31778
$285$	−2.08640	−0.123588
$286$	27.5672	1.63008
$287$	10.5531	0.622927
$288$	35.3891	2.08532
$289$	3.44083	0.202402
$290$	27.8038	1.63270
$291$	5.47972	0.321227
$292$	46.0664	2.69583
$293$	−0.606540	−0.0354344	−0.0177172	−	0.999843i	$-0.505640\pi$
$293$	−0.606540	−0.0354344	−0.0177172	+	0.999843i	$0.505640\pi$
$294$	−7.12086	−0.415297
$295$	8.63234	0.502594
$296$	−9.99786	−0.581114
$297$	−9.46148	−0.549011
$298$	22.8122	1.32148
$299$	−22.1484	−1.28088
$300$	8.37236	0.483379
$301$	11.9196	0.687036
$302$	59.7505	3.43826
$303$	−4.97431	−0.285767
$304$	41.6509	2.38884
$305$	−8.80844	−0.504370
$306$	33.2526	1.90093
$307$	−2.64808	−0.151134	−0.0755670	−	0.997141i	$-0.524077\pi$
$307$	−2.64808	−0.151134	−0.0755670	+	0.997141i	$0.524077\pi$
$308$	−18.9748	−1.08119
$309$	−2.23499	−0.127144
$310$	−5.78656	−0.328654
$311$	−20.7036	−1.17399	−0.586997	−	0.809589i	$-0.699690\pi$
$311$	−20.7036	−1.17399	−0.586997	+	0.809589i	$0.699690\pi$
$312$	10.7005	0.605796
$313$	2.10843	0.119176	0.0595878	−	0.998223i	$-0.481021\pi$
$313$	2.10843	0.119176	0.0595878	+	0.998223i	$0.481021\pi$
$314$	15.2961	0.863209
$315$	−3.50365	−0.197409
$316$	−6.64290	−0.373692
$317$	8.20867	0.461045	0.230522	−	0.973067i	$-0.425957\pi$
$317$	8.20867	0.461045	0.230522	+	0.973067i	$0.425957\pi$
$318$	2.72106	0.152590
$319$	31.9876	1.79096
$320$	14.0105	0.783211
$321$	8.05244	0.449443
$322$	21.3818	1.19156
$323$	17.5197	0.974820
$324$	35.3819	1.96566
$325$	−10.7618	−0.596959
$326$	40.5512	2.24592
$327$	−5.23496	−0.289494
$328$	−76.5700	−4.22787
$329$	−10.4143	−0.574160
$330$	−5.02610	−0.276678
$331$	3.87340	0.212901	0.106451	−	0.994318i	$-0.466051\pi$
$331$	3.87340	0.212901	0.106451	+	0.994318i	$0.466051\pi$
$332$	71.3296	3.91472
$333$	−3.55484	−0.194804
$334$	−18.1105	−0.990965
$335$	5.56813	0.304220
$336$	−5.36771	−0.292832
$337$	−10.2185	−0.556638	−0.278319	−	0.960489i	$-0.589777\pi$
$337$	−10.2185	−0.556638	−0.278319	+	0.960489i	$0.589777\pi$
$338$	11.2957	0.614403
$339$	7.95324	0.431960
$340$	26.1557	1.41849
$341$	−6.65731	−0.360513
$342$	28.5005	1.54113
$343$	−13.8601	−0.748374
$344$	−86.4854	−4.66298
$345$	4.03814	0.217406
$346$	−38.2002	−2.05366
$347$	−34.2363	−1.83790	−0.918951	−	0.394371i	$-0.870962\pi$
$347$	−34.2363	−1.83790	−0.918951	+	0.394371i	$0.870962\pi$
$348$	20.7819	1.11403
$349$	16.2482	0.869744	0.434872	−	0.900492i	$-0.356794\pi$
$349$	16.2482	0.869744	0.434872	+	0.900492i	$0.356794\pi$
$350$	10.3893	0.555332
$351$	7.90132	0.421741
$352$	44.9161	2.39404
$353$	12.3749	0.658649	0.329324	−	0.944217i	$-0.393179\pi$
$353$	12.3749	0.658649	0.329324	+	0.944217i	$0.393179\pi$
$354$	9.04950	0.480976
$355$	−5.20450	−0.276226
$356$	−61.1818	−3.24263
$357$	−2.25782	−0.119497
$358$	57.0265	3.01394
$359$	9.75994	0.515110	0.257555	−	0.966264i	$-0.417083\pi$
$359$	9.75994	0.515110	0.257555	+	0.966264i	$0.417083\pi$
$360$	25.4215	1.33983
$361$	−3.98406	−0.209687
$362$	−32.2839	−1.69680
$363$	−0.695938	−0.0365273
$364$	15.8460	0.830554
$365$	10.7959	0.565085
$366$	−9.23412	−0.482675
$367$	−3.29747	−0.172127	−0.0860633	−	0.996290i	$-0.527429\pi$
$367$	−3.29747	−0.172127	−0.0860633	+	0.996290i	$0.527429\pi$
$368$	−80.6135	−4.20227
$369$	−27.2252	−1.41729
$370$	−3.92171	−0.203880
$371$	2.40747	0.124990
$372$	−4.32515	−0.224248
$373$	13.2919	0.688231	0.344115	−	0.938927i	$-0.388179\pi$
$373$	13.2919	0.688231	0.344115	+	0.938927i	$0.388179\pi$
$374$	42.2046	2.18235
$375$	4.65422	0.240343
$376$	75.5633	3.89688
$377$	−26.7130	−1.37579
$378$	−7.62782	−0.392333
$379$	14.9494	0.767898	0.383949	−	0.923354i	$-0.374564\pi$
$379$	14.9494	0.767898	0.383949	+	0.923354i	$0.374564\pi$
$380$	22.4178	1.15001
$381$	10.1192	0.518423
$382$	43.3521	2.21809
$383$	−4.40403	−0.225036	−0.112518	−	0.993650i	$-0.535892\pi$
$383$	−4.40403	−0.225036	−0.112518	+	0.993650i	$0.535892\pi$
$384$	2.94089	0.150077
$385$	−4.44687	−0.226634
$386$	2.40425	0.122373
$387$	−30.7508	−1.56315
$388$	−58.8780	−2.98908
$389$	−25.1230	−1.27379	−0.636894	−	0.770952i	$-0.719781\pi$
$389$	−25.1230	−1.27379	−0.636894	+	0.770952i	$0.719781\pi$
$390$	4.19732	0.212539
$391$	−33.9085	−1.71483
$392$	45.7126	2.30883
$393$	−5.32282	−0.268501
$394$	−70.8413	−3.56893
$395$	−1.55680	−0.0783313
$396$	48.9521	2.45994
$397$	−27.6842	−1.38943	−0.694716	−	0.719284i	$-0.744470\pi$
$397$	−27.6842	−1.38943	−0.694716	+	0.719284i	$0.744470\pi$
$398$	−49.1392	−2.46313
$399$	−1.93516	−0.0968792
$400$	−39.1698	−1.95849
$401$	27.8624	1.39138	0.695690	−	0.718342i	$-0.255099\pi$
$401$	27.8624	1.39138	0.695690	+	0.718342i	$0.255099\pi$
$402$	5.83722	0.291134
$403$	5.55954	0.276940
$404$	53.4476	2.65912
$405$	8.29197	0.412031
$406$	25.7883	1.27985
$407$	−4.51184	−0.223644
$408$	16.3821	0.811036
$409$	−4.10333	−0.202897	−0.101448	−	0.994841i	$-0.532348\pi$
$409$	−4.10333	−0.202897	−0.101448	+	0.994841i	$0.532348\pi$
$410$	−30.0349	−1.48332
$411$	−0.291128	−0.0143603
$412$	24.0143	1.18310
$413$	8.00660	0.393979
$414$	−55.1616	−2.71104
$415$	16.7165	0.820583
$416$	−37.5096	−1.83906
$417$	−7.43008	−0.363853
$418$	36.1732	1.76929
$419$	1.44486	0.0705859	0.0352929	−	0.999377i	$-0.488764\pi$
$419$	1.44486	0.0705859	0.0352929	+	0.999377i	$0.488764\pi$
$420$	−2.88906	−0.140972
$421$	13.3159	0.648979	0.324490	−	0.945889i	$-0.394807\pi$
$421$	13.3159	0.648979	0.324490	+	0.945889i	$0.394807\pi$
$422$	6.40078	0.311585
$423$	26.8673	1.30633
$424$	−17.4679	−0.848318
$425$	−16.4760	−0.799205
$426$	−5.45601	−0.264345
$427$	−8.16993	−0.395371
$428$	−86.5212	−4.18216
$429$	4.82892	0.233142
$430$	−33.9243	−1.63598
$431$	−8.45869	−0.407441	−0.203720	−	0.979029i	$-0.565303\pi$
$431$	−8.45869	−0.407441	−0.203720	+	0.979029i	$0.565303\pi$
$432$	28.7584	1.38364
$433$	−7.54957	−0.362809	−0.181405	−	0.983409i	$-0.558064\pi$
$433$	−7.54957	−0.362809	−0.181405	+	0.983409i	$0.558064\pi$
$434$	−5.36710	−0.257629
$435$	4.87036	0.233516
$436$	56.2482	2.69380
$437$	−29.0627	−1.39026
$438$	11.3177	0.540779
$439$	−4.51849	−0.215656	−0.107828	−	0.994170i	$-0.534390\pi$
$439$	−4.51849	−0.215656	−0.107828	+	0.994170i	$0.534390\pi$
$440$	32.2652	1.53818
$441$	16.2536	0.773980
$442$	−35.2452	−1.67644
$443$	−21.0732	−1.00122	−0.500609	−	0.865674i	$-0.666890\pi$
$443$	−21.0732	−1.00122	−0.500609	+	0.865674i	$0.666890\pi$
$444$	−2.93127	−0.139112
$445$	−14.3383	−0.679702
$446$	59.2206	2.80418
$447$	3.99600	0.189004
$448$	12.9949	0.613951
$449$	−41.1367	−1.94136	−0.970682	−	0.240369i	$-0.922732\pi$
$449$	−41.1367	−1.94136	−0.970682	+	0.240369i	$0.922732\pi$
$450$	−26.8028	−1.26350
$451$	−34.5545	−1.62711
$452$	−85.4553	−4.01948
$453$	10.4664	0.491756
$454$	26.3602	1.23714
$455$	3.71360	0.174096
$456$	14.0410	0.657528
$457$	−29.7467	−1.39149	−0.695746	−	0.718288i	$-0.744926\pi$
$457$	−29.7467	−1.39149	−0.695746	+	0.718288i	$0.744926\pi$
$458$	34.1325	1.59491
$459$	12.0967	0.564624
$460$	−43.3887	−2.02301
$461$	−8.00612	−0.372882	−0.186441	−	0.982466i	$-0.559695\pi$
$461$	−8.00612	−0.372882	−0.186441	+	0.982466i	$0.559695\pi$
$462$	−4.66177	−0.216885
$463$	0.0708474	0.00329256	0.00164628	−	0.999999i	$-0.499476\pi$
$463$	0.0708474	0.00329256	0.00164628	+	0.999999i	$0.499476\pi$
$464$	−97.2273	−4.51366
$465$	−1.01363	−0.0470058
$466$	41.9461	1.94311
$467$	−42.1628	−1.95106	−0.975530	−	0.219865i	$-0.929438\pi$
$467$	−42.1628	−1.95106	−0.975530	+	0.219865i	$0.929438\pi$
$468$	−40.8801	−1.88968
$469$	5.16451	0.238475
$470$	29.6401	1.36719
$471$	2.67940	0.123460
$472$	−58.0936	−2.67397
$473$	−39.0292	−1.79456
$474$	−1.63204	−0.0749620
$475$	−14.1215	−0.647937
$476$	24.2597	1.11194
$477$	−6.21091	−0.284378
$478$	−4.69156	−0.214587
$479$	37.0366	1.69225	0.846124	−	0.532986i	$-0.178930\pi$
$479$	37.0366	1.69225	0.846124	+	0.532986i	$0.178930\pi$
$480$	6.83882	0.312148
$481$	3.76785	0.171799
$482$	−4.74263	−0.216021
$483$	3.74542	0.170422
$484$	7.47766	0.339894
$485$	−13.7984	−0.626555
$486$	29.8815	1.35545
$487$	39.7471	1.80111	0.900556	−	0.434740i	$-0.143160\pi$
$487$	39.7471	1.80111	0.900556	+	0.434740i	$0.143160\pi$
$488$	59.2787	2.68342
$489$	7.10330	0.321222
$490$	17.9310	0.810039
$491$	7.27081	0.328127	0.164063	−	0.986450i	$-0.447540\pi$
$491$	7.27081	0.328127	0.164063	+	0.986450i	$0.447540\pi$
$492$	−22.4495	−1.01210
$493$	−40.8968	−1.84190
$494$	−30.2083	−1.35914
$495$	11.4722	0.515638
$496$	20.2351	0.908581
$497$	−4.82724	−0.216531
$498$	17.5244	0.785286
$499$	−15.4179	−0.690201	−0.345100	−	0.938566i	$-0.612155\pi$
$499$	−15.4179	−0.690201	−0.345100	+	0.938566i	$0.612155\pi$
$500$	−50.0082	−2.23644
$501$	−3.17240	−0.141733
$502$	−30.3414	−1.35420
$503$	−38.4858	−1.71600	−0.857999	−	0.513651i	$-0.828293\pi$
$503$	−38.4858	−1.71600	−0.857999	+	0.513651i	$0.828293\pi$
$504$	23.5787	1.05028
$505$	12.5258	0.557390
$506$	−70.0116	−3.11239
$507$	1.97865	0.0878749
$508$	−108.728	−4.82403
$509$	21.6998	0.961825	0.480912	−	0.876769i	$-0.340306\pi$
$509$	21.6998	0.961825	0.480912	+	0.876769i	$0.340306\pi$
$510$	6.42596	0.284546
$511$	10.0134	0.442965
$512$	31.9274	1.41101
$513$	10.3680	0.457756
$514$	−16.8474	−0.743107
$515$	5.62790	0.247995
$516$	−25.3566	−1.11626
$517$	34.1002	1.49973
$518$	−3.63743	−0.159820
$519$	−6.69149	−0.293724
$520$	−26.9448	−1.18161
$521$	22.3051	0.977206	0.488603	−	0.872506i	$-0.337507\pi$
$521$	22.3051	0.977206	0.488603	+	0.872506i	$0.337507\pi$
$522$	−66.5299	−2.91193
$523$	−6.23761	−0.272752	−0.136376	−	0.990657i	$-0.543546\pi$
$523$	−6.23761	−0.272752	−0.136376	+	0.990657i	$0.543546\pi$
$524$	57.1922	2.49845
$525$	1.81988	0.0794263
$526$	26.1096	1.13843
$527$	8.51149	0.370766
$528$	17.5758	0.764889
$529$	33.2496	1.44563
$530$	−6.85189	−0.297627
$531$	−20.6558	−0.896384
$532$	20.7928	0.901480
$533$	28.8566	1.24992
$534$	−15.0312	−0.650465
$535$	−20.2768	−0.876641
$536$	−37.4722	−1.61855
$537$	9.98927	0.431069
$538$	−31.0834	−1.34010
$539$	20.6292	0.888562
$540$	15.4787	0.666095
$541$	6.77028	0.291077	0.145539	−	0.989353i	$-0.453509\pi$
$541$	6.77028	0.291077	0.145539	+	0.989353i	$0.453509\pi$
$542$	−16.8476	−0.723665
$543$	−5.65513	−0.242685
$544$	−57.4261	−2.46212
$545$	13.1821	0.564660
$546$	3.89306	0.166608
$547$	−38.7051	−1.65491	−0.827456	−	0.561531i	$-0.810213\pi$
$547$	−38.7051	−1.65491	−0.827456	+	0.561531i	$0.810213\pi$
$548$	3.12809	0.133625
$549$	21.0771	0.899551
$550$	−34.0184	−1.45055
$551$	−35.0523	−1.49328
$552$	−27.1757	−1.15667
$553$	−1.44395	−0.0614032
$554$	−37.1778	−1.57953
$555$	−0.686962	−0.0291599
$556$	79.8342	3.38572
$557$	9.18226	0.389065	0.194532	−	0.980896i	$-0.437681\pi$
$557$	9.18226	0.389065	0.194532	+	0.980896i	$0.437681\pi$
$558$	13.8463	0.586160
$559$	32.5934	1.37855
$560$	13.5164	0.571171
$561$	7.39293	0.312130
$562$	−32.7757	−1.38256
$563$	−7.79835	−0.328661	−0.164331	−	0.986405i	$-0.552546\pi$
$563$	−7.79835	−0.328661	−0.164331	+	0.986405i	$0.552546\pi$
$564$	22.1544	0.932868
$565$	−20.0270	−0.842541
$566$	14.8846	0.625645
$567$	7.69090	0.322987
$568$	35.0250	1.46962
$569$	25.4702	1.06777	0.533884	−	0.845558i	$-0.320732\pi$
$569$	25.4702	1.06777	0.533884	+	0.845558i	$0.320732\pi$
$570$	5.50764	0.230690
$571$	−21.6681	−0.906780	−0.453390	−	0.891312i	$-0.649786\pi$
$571$	−21.6681	−0.906780	−0.453390	+	0.891312i	$0.649786\pi$
$572$	−51.8854	−2.16944
$573$	7.59395	0.317242
$574$	−27.8578	−1.16276
$575$	27.3315	1.13980
$576$	−33.5248	−1.39687
$577$	−33.3083	−1.38664	−0.693321	−	0.720629i	$-0.743853\pi$
$577$	−33.3083	−1.38664	−0.693321	+	0.720629i	$0.743853\pi$
$578$	−9.08303	−0.377804
$579$	0.421150	0.0175024
$580$	−52.3307	−2.17291
$581$	15.5048	0.643247
$582$	−14.4653	−0.599604
$583$	−7.88294	−0.326478
$584$	−72.6541	−3.00645
$585$	−9.58050	−0.396105
$586$	1.60113	0.0661421
$587$	39.3040	1.62225	0.811125	−	0.584873i	$-0.198856\pi$
$587$	39.3040	1.62225	0.811125	+	0.584873i	$0.198856\pi$
$588$	13.4025	0.552708
$589$	7.29512	0.300590
$590$	−22.7875	−0.938146
$591$	−12.4092	−0.510446
$592$	13.7139	0.563636
$593$	−1.56017	−0.0640684	−0.0320342	−	0.999487i	$-0.510199\pi$
$593$	−1.56017	−0.0640684	−0.0320342	+	0.999487i	$0.510199\pi$
$594$	24.9762	1.02479
$595$	5.68541	0.233079
$596$	−42.9359	−1.75872
$597$	−8.60766	−0.352288
$598$	58.4669	2.39089
$599$	−43.3818	−1.77253	−0.886266	−	0.463177i	$-0.846710\pi$
$599$	−43.3818	−1.77253	−0.886266	+	0.463177i	$0.846710\pi$
$600$	−13.2046	−0.539074
$601$	9.74341	0.397442	0.198721	−	0.980056i	$-0.436321\pi$
$601$	9.74341	0.397442	0.198721	+	0.980056i	$0.436321\pi$
$602$	−31.4652	−1.28243
$603$	−13.3236	−0.542580
$604$	−112.459	−4.57589
$605$	1.75244	0.0712467
$606$	13.1311	0.533414
$607$	43.3375	1.75902	0.879508	−	0.475884i	$-0.157872\pi$
$607$	43.3375	1.75902	0.879508	+	0.475884i	$0.157872\pi$
$608$	−49.2194	−1.99611
$609$	4.51732	0.183051
$610$	23.2524	0.941460
$611$	−28.4772	−1.15206
$612$	−62.5862	−2.52990
$613$	−21.0719	−0.851086	−0.425543	−	0.904938i	$-0.639917\pi$
$613$	−21.0719	−0.851086	−0.425543	+	0.904938i	$0.639917\pi$
$614$	6.99035	0.282108
$615$	−5.26119	−0.212152
$616$	29.9264	1.20577
$617$	26.1486	1.05270	0.526352	−	0.850267i	$-0.323560\pi$
$617$	26.1486	1.05270	0.526352	+	0.850267i	$0.323560\pi$
$618$	5.89988	0.237328
$619$	−20.4074	−0.820241	−0.410121	−	0.912031i	$-0.634513\pi$
$619$	−20.4074	−0.820241	−0.410121	+	0.912031i	$0.634513\pi$
$620$	10.8911	0.437398
$621$	−20.0667	−0.805250
$622$	54.6529	2.19138
$623$	−13.2990	−0.532812
$624$	−14.6776	−0.587575
$625$	6.50130	0.260052
$626$	−5.56579	−0.222454
$627$	6.33641	0.253052
$628$	−28.7894	−1.14882
$629$	5.76847	0.230004
$630$	9.24888	0.368484
$631$	−35.3703	−1.40807	−0.704034	−	0.710166i	$-0.748620\pi$
$631$	−35.3703	−1.40807	−0.704034	+	0.710166i	$0.748620\pi$
$632$	10.4769	0.416749
$633$	1.12122	0.0445644
$634$	−21.6691	−0.860589
$635$	−25.4811	−1.01119
$636$	−5.12142	−0.203078
$637$	−17.2275	−0.682579
$638$	−84.4404	−3.34303
$639$	12.4535	0.492653
$640$	−7.40544	−0.292726
$641$	−17.3748	−0.686262	−0.343131	−	0.939288i	$-0.611488\pi$
$641$	−17.3748	−0.686262	−0.343131	+	0.939288i	$0.611488\pi$
$642$	−21.2567	−0.838933
$643$	2.72941	0.107638	0.0538188	−	0.998551i	$-0.482861\pi$
$643$	2.72941	0.107638	0.0538188	+	0.998551i	$0.482861\pi$
$644$	−40.2435	−1.58582
$645$	−5.94249	−0.233985
$646$	−46.2480	−1.81960
$647$	−28.5610	−1.12285	−0.561424	−	0.827528i	$-0.689746\pi$
$647$	−28.5610	−1.12285	−0.561424	+	0.827528i	$0.689746\pi$
$648$	−55.8030	−2.19215
$649$	−26.2165	−1.02909
$650$	28.4089	1.11429
$651$	−0.940149	−0.0368474
$652$	−76.3230	−2.98904
$653$	−18.6627	−0.730327	−0.365164	−	0.930943i	$-0.618987\pi$
$653$	−18.6627	−0.730327	−0.365164	+	0.930943i	$0.618987\pi$
$654$	13.8191	0.540372
$655$	13.4033	0.523712
$656$	105.029	4.10071
$657$	−25.8329	−1.00784
$658$	27.4915	1.07173
$659$	10.4449	0.406876	0.203438	−	0.979088i	$-0.434788\pi$
$659$	10.4449	0.406876	0.203438	+	0.979088i	$0.434788\pi$
$660$	9.45984	0.368224
$661$	12.2965	0.478280	0.239140	−	0.970985i	$-0.423134\pi$
$661$	12.2965	0.478280	0.239140	+	0.970985i	$0.423134\pi$
$662$	−10.2249	−0.397403
$663$	−6.17386	−0.239773
$664$	−112.498	−4.36578
$665$	4.87291	0.188963
$666$	9.38400	0.363623
$667$	67.8421	2.62686
$668$	34.0866	1.31885
$669$	10.3736	0.401067
$670$	−14.6987	−0.567858
$671$	26.7513	1.03272
$672$	6.34309	0.244690
$673$	−48.6705	−1.87611	−0.938054	−	0.346488i	$-0.887374\pi$
$673$	−48.6705	−1.87611	−0.938054	+	0.346488i	$0.887374\pi$
$674$	26.9746	1.03902
$675$	−9.75034	−0.375291
$676$	−21.2600	−0.817694
$677$	−45.6083	−1.75287	−0.876435	−	0.481520i	$-0.840085\pi$
$677$	−45.6083	−1.75287	−0.876435	+	0.481520i	$0.840085\pi$
$678$	−20.9948	−0.806300
$679$	−12.7982	−0.491150
$680$	−41.2517	−1.58193
$681$	4.61748	0.176942
$682$	17.5738	0.672937
$683$	1.55575	0.0595292	0.0297646	−	0.999557i	$-0.490524\pi$
$683$	1.55575	0.0595292	0.0297646	+	0.999557i	$0.490524\pi$
$684$	−53.6420	−2.05105
$685$	0.733086	0.0280098
$686$	36.5876	1.39692
$687$	5.97895	0.228111
$688$	118.630	4.52273
$689$	6.58307	0.250795
$690$	−10.6598	−0.405811
$691$	−1.71243	−0.0651438	−0.0325719	−	0.999469i	$-0.510370\pi$
$691$	−1.71243	−0.0651438	−0.0325719	+	0.999469i	$0.510370\pi$
$692$	71.8982	2.73316
$693$	10.6406	0.404204
$694$	90.3764	3.43064
$695$	18.7096	0.709697
$696$	−32.7764	−1.24238
$697$	44.1786	1.67338
$698$	−42.8915	−1.62347
$699$	7.34765	0.277914
$700$	−19.5542	−0.739077
$701$	21.1727	0.799680	0.399840	−	0.916585i	$-0.369066\pi$
$701$	21.1727	0.799680	0.399840	+	0.916585i	$0.369066\pi$
$702$	−20.8577	−0.787225
$703$	4.94410	0.186470
$704$	−42.5500	−1.60366
$705$	5.19202	0.195543
$706$	−32.6670	−1.22944
$707$	11.6178	0.436932
$708$	−17.0324	−0.640118
$709$	44.6595	1.67722	0.838612	−	0.544729i	$-0.183368\pi$
$709$	44.6595	1.67722	0.838612	+	0.544729i	$0.183368\pi$
$710$	13.7387	0.515606
$711$	3.72517	0.139705
$712$	96.4935	3.61625
$713$	−14.1194	−0.528775
$714$	5.96016	0.223053
$715$	−12.1597	−0.454746
$716$	−107.332	−4.01118
$717$	−0.821815	−0.0306913
$718$	−25.7641	−0.961507
$719$	27.7906	1.03642	0.518208	−	0.855255i	$-0.326599\pi$
$719$	27.7906	1.03642	0.518208	+	0.855255i	$0.326599\pi$
$720$	−34.8701	−1.29953
$721$	5.21995	0.194401
$722$	10.5170	0.391404
$723$	−0.830761	−0.0308963
$724$	60.7628	2.25823
$725$	32.9642	1.22426
$726$	1.83712	0.0681820
$727$	−0.165154	−0.00612521	−0.00306261	−	0.999995i	$-0.500975\pi$
$727$	−0.165154	−0.00612521	−0.00306261	+	0.999995i	$0.500975\pi$
$728$	−24.9916	−0.926251
$729$	−16.1297	−0.597396
$730$	−28.4989	−1.05479
$731$	49.8995	1.84560
$732$	17.3799	0.642380
$733$	16.9700	0.626802	0.313401	−	0.949621i	$-0.398532\pi$
$733$	16.9700	0.626802	0.313401	+	0.949621i	$0.398532\pi$
$734$	8.70460	0.321293
$735$	3.14095	0.115856
$736$	95.2620	3.51140
$737$	−16.9105	−0.622905
$738$	71.8686	2.64552
$739$	14.3134	0.526528	0.263264	−	0.964724i	$-0.415201\pi$
$739$	14.3134	0.526528	0.263264	+	0.964724i	$0.415201\pi$
$740$	7.38121	0.271339
$741$	−5.29156	−0.194390
$742$	−6.35520	−0.233307
$743$	−19.0905	−0.700364	−0.350182	−	0.936682i	$-0.613880\pi$
$743$	−19.0905	−0.700364	−0.350182	+	0.936682i	$0.613880\pi$
$744$	6.82145	0.250087
$745$	−10.0623	−0.368654
$746$	−35.0878	−1.28466
$747$	−39.9999	−1.46352
$748$	−79.4350	−2.90443
$749$	−18.8069	−0.687191
$750$	−12.2861	−0.448625
$751$	−25.1746	−0.918634	−0.459317	−	0.888272i	$-0.651906\pi$
$751$	−25.1746	−0.918634	−0.459317	+	0.888272i	$0.651906\pi$
$752$	−103.649	−3.77967
$753$	−5.31486	−0.193684
$754$	70.5164	2.56806
$755$	−26.3554	−0.959173
$756$	14.3566	0.522146
$757$	39.1000	1.42111	0.710557	−	0.703639i	$-0.248443\pi$
$757$	39.1000	1.42111	0.710557	+	0.703639i	$0.248443\pi$
$758$	−39.4631	−1.43336
$759$	−12.2639	−0.445150
$760$	−35.3564	−1.28251
$761$	−6.07121	−0.220081	−0.110041	−	0.993927i	$-0.535098\pi$
$761$	−6.07121	−0.220081	−0.110041	+	0.993927i	$0.535098\pi$
$762$	−26.7125	−0.967692
$763$	12.2266	0.442631
$764$	−81.5948	−2.95200
$765$	−14.6675	−0.530303
$766$	11.6257	0.420053
$767$	21.8935	0.790528
$768$	3.36456	0.121408
$769$	24.2809	0.875592	0.437796	−	0.899074i	$-0.355759\pi$
$769$	24.2809	0.875592	0.437796	+	0.899074i	$0.355759\pi$
$770$	11.7388	0.423036
$771$	−2.95114	−0.106283
$772$	−4.52514	−0.162863
$773$	4.63953	0.166872	0.0834362	−	0.996513i	$-0.473411\pi$
$773$	4.63953	0.166872	0.0834362	+	0.996513i	$0.473411\pi$
$774$	81.1753	2.91778
$775$	−6.86056	−0.246438
$776$	92.8601	3.33348
$777$	−0.637165	−0.0228582
$778$	66.3192	2.37766
$779$	37.8651	1.35666
$780$	−7.89994	−0.282863
$781$	15.8061	0.565587
$782$	89.5111	3.20091
$783$	−24.2023	−0.864920
$784$	−62.7030	−2.23939
$785$	−6.74698	−0.240810
$786$	14.0511	0.501185
$787$	−19.5358	−0.696375	−0.348187	−	0.937425i	$-0.613203\pi$
$787$	−19.5358	−0.696375	−0.348187	+	0.937425i	$0.613203\pi$
$788$	133.333	4.74980
$789$	4.57359	0.162824
$790$	4.10962	0.146214
$791$	−18.5753	−0.660460
$792$	−77.2053	−2.74337
$793$	−22.3401	−0.793321
$794$	73.0803	2.59352
$795$	−1.20024	−0.0425680
$796$	92.4869	3.27811
$797$	−46.8619	−1.65993	−0.829967	−	0.557812i	$-0.811641\pi$
$797$	−46.8619	−1.65993	−0.829967	+	0.557812i	$0.811641\pi$
$798$	5.10840	0.180835
$799$	−43.5978	−1.54238
$800$	46.2875	1.63651
$801$	34.3092	1.21226
$802$	−73.5505	−2.59716
$803$	−32.7874	−1.15704
$804$	−10.9865	−0.387463
$805$	−9.43131	−0.332410
$806$	−14.6760	−0.516939
$807$	−5.44485	−0.191668
$808$	−84.2954	−2.96550
$809$	−4.81301	−0.169216	−0.0846082	−	0.996414i	$-0.526964\pi$
$809$	−4.81301	−0.169216	−0.0846082	+	0.996414i	$0.526964\pi$
$810$	−21.8890	−0.769100
$811$	−52.7359	−1.85181	−0.925904	−	0.377758i	$-0.876695\pi$
$811$	−52.7359	−1.85181	−0.925904	+	0.377758i	$0.876695\pi$
$812$	−48.5373	−1.70333
$813$	−2.95117	−0.103502
$814$	11.9103	0.417455
$815$	−17.8868	−0.626546
$816$	−22.4710	−0.786642
$817$	42.7684	1.49628
$818$	10.8319	0.378728
$819$	−8.88603	−0.310503
$820$	56.5300	1.97411
$821$	−37.2125	−1.29872	−0.649362	−	0.760479i	$-0.724964\pi$
$821$	−37.2125	−1.29872	−0.649362	+	0.760479i	$0.724964\pi$
$822$	0.768513	0.0268050
$823$	−0.962568	−0.0335530	−0.0167765	−	0.999859i	$-0.505340\pi$
$823$	−0.962568	−0.0335530	−0.0167765	+	0.999859i	$0.505340\pi$
$824$	−37.8744	−1.31942
$825$	−5.95896	−0.207464
$826$	−21.1357	−0.735404
$827$	−13.5180	−0.470068	−0.235034	−	0.971987i	$-0.575520\pi$
$827$	−13.5180	−0.470068	−0.235034	+	0.971987i	$0.575520\pi$
$828$	103.822	3.60806
$829$	49.4659	1.71802	0.859011	−	0.511957i	$-0.171079\pi$
$829$	49.4659	1.71802	0.859011	+	0.511957i	$0.171079\pi$
$830$	−44.1280	−1.53170
$831$	−6.51240	−0.225913
$832$	35.5337	1.23191
$833$	−26.3748	−0.913832
$834$	19.6138	0.679170
$835$	7.98840	0.276450
$836$	−68.0830	−2.35470
$837$	5.03701	0.174105
$838$	−3.81410	−0.131756
$839$	−23.5857	−0.814270	−0.407135	−	0.913368i	$-0.633472\pi$
$839$	−23.5857	−0.814270	−0.407135	+	0.913368i	$0.633472\pi$
$840$	4.55652	0.157215
$841$	52.8238	1.82151
$842$	−35.1511	−1.21139
$843$	−5.74128	−0.197740
$844$	−12.0472	−0.414681
$845$	−4.98242	−0.171401
$846$	−70.9237	−2.43841
$847$	1.62540	0.0558496
$848$	23.9604	0.822804
$849$	2.60732	0.0894828
$850$	43.4931	1.49180
$851$	−9.56910	−0.328024
$852$	10.2690	0.351810
$853$	13.5585	0.464233	0.232117	−	0.972688i	$-0.425435\pi$
$853$	13.5585	0.464233	0.232117	+	0.972688i	$0.425435\pi$
$854$	21.5668	0.738002
$855$	−12.5713	−0.429931
$856$	136.458	4.66403
$857$	−33.8041	−1.15473	−0.577363	−	0.816488i	$-0.695918\pi$
$857$	−33.8041	−1.15473	−0.577363	+	0.816488i	$0.695918\pi$
$858$	−12.7473	−0.435185
$859$	−3.89713	−0.132968	−0.0664842	−	0.997787i	$-0.521178\pi$
$859$	−3.89713	−0.132968	−0.0664842	+	0.997787i	$0.521178\pi$
$860$	63.8504	2.17728
$861$	−4.87981	−0.166304
$862$	22.3291	0.760532
$863$	−21.6699	−0.737651	−0.368826	−	0.929499i	$-0.620240\pi$
$863$	−21.6699	−0.737651	−0.368826	+	0.929499i	$0.620240\pi$
$864$	−33.9842	−1.15617
$865$	16.8498	0.572910
$866$	19.9292	0.677222
$867$	−1.59107	−0.0540354
$868$	10.1016	0.342872
$869$	4.72803	0.160387
$870$	−12.8567	−0.435882
$871$	14.1220	0.478505
$872$	−88.7125	−3.00418
$873$	33.0174	1.11747
$874$	76.7191	2.59506
$875$	−10.8702	−0.367480
$876$	−21.3014	−0.719709
$877$	−41.7030	−1.40821	−0.704105	−	0.710096i	$-0.748652\pi$
$877$	−41.7030	−1.40821	−0.704105	+	0.710096i	$0.748652\pi$
$878$	11.9278	0.402545
$879$	0.280468	0.00945997
$880$	−44.2575	−1.49192
$881$	−41.7981	−1.40821	−0.704106	−	0.710095i	$-0.748652\pi$
$881$	−41.7981	−1.40821	−0.704106	+	0.710095i	$0.748652\pi$
$882$	−42.9059	−1.44472
$883$	−45.2072	−1.52134	−0.760672	−	0.649137i	$-0.775130\pi$
$883$	−45.2072	−1.52134	−0.760672	+	0.649137i	$0.775130\pi$
$884$	66.3364	2.23113
$885$	−3.99166	−0.134178
$886$	55.6286	1.86888
$887$	43.3555	1.45573	0.727867	−	0.685718i	$-0.240512\pi$
$887$	43.3555	1.45573	0.727867	+	0.685718i	$0.240512\pi$
$888$	4.62309	0.155141
$889$	−23.6340	−0.792660
$890$	37.8500	1.26874
$891$	−25.1828	−0.843655
$892$	−111.462	−3.73201
$893$	−37.3672	−1.25045
$894$	−10.5486	−0.352796
$895$	−25.1539	−0.840802
$896$	−6.86863	−0.229465
$897$	10.2416	0.341957
$898$	108.592	3.62376
$899$	−17.0293	−0.567958
$900$	50.4466	1.68155
$901$	10.0785	0.335763
$902$	91.2164	3.03717
$903$	−5.51172	−0.183419
$904$	134.777	4.48261
$905$	14.2401	0.473358
$906$	−27.6291	−0.917915
$907$	−20.8084	−0.690931	−0.345465	−	0.938431i	$-0.612279\pi$
$907$	−20.8084	−0.690931	−0.345465	+	0.938431i	$0.612279\pi$
$908$	−49.6136	−1.64648
$909$	−29.9721	−0.994112
$910$	−9.80308	−0.324969
$911$	−0.724916	−0.0240175	−0.0120088	−	0.999928i	$-0.503823\pi$
$911$	−0.724916	−0.0240175	−0.0120088	+	0.999928i	$0.503823\pi$
$912$	−19.2597	−0.637752
$913$	−50.7683	−1.68018
$914$	78.5248	2.59737
$915$	4.07309	0.134652
$916$	−64.2421	−2.12262
$917$	12.4318	0.410533
$918$	−31.9326	−1.05393
$919$	−49.5530	−1.63460	−0.817301	−	0.576210i	$-0.804531\pi$
$919$	−49.5530	−1.63460	−0.817301	+	0.576210i	$0.804531\pi$
$920$	68.4309	2.25610
$921$	1.22449	0.0403484
$922$	21.1344	0.696024
$923$	−13.1997	−0.434475
$924$	8.77411	0.288647
$925$	−4.64959	−0.152878
$926$	−0.187022	−0.00614591
$927$	−13.4666	−0.442303
$928$	114.895	3.77160
$929$	13.1961	0.432951	0.216475	−	0.976288i	$-0.430544\pi$
$929$	13.1961	0.432951	0.216475	+	0.976288i	$0.430544\pi$
$930$	2.67575	0.0877412
$931$	−22.6056	−0.740869
$932$	−78.9484	−2.58604
$933$	9.57350	0.313422
$934$	111.300	3.64186
$935$	−18.6161	−0.608811
$936$	64.4745	2.10741
$937$	−21.5504	−0.704021	−0.352010	−	0.935996i	$-0.614502\pi$
$937$	−21.5504	−0.704021	−0.352010	+	0.935996i	$0.614502\pi$
$938$	−13.6332	−0.445139
$939$	−0.974954	−0.0318164
$940$	−55.7868	−1.81956
$941$	−44.5187	−1.45127	−0.725634	−	0.688081i	$-0.758453\pi$
$941$	−44.5187	−1.45127	−0.725634	+	0.688081i	$0.758453\pi$
$942$	−7.07304	−0.230452
$943$	−73.2862	−2.38653
$944$	79.6857	2.59355
$945$	3.36457	0.109449
$946$	103.028	3.34974
$947$	−31.6413	−1.02820	−0.514102	−	0.857729i	$-0.671875\pi$
$947$	−31.6413	−1.02820	−0.514102	+	0.857729i	$0.671875\pi$
$948$	3.07173	0.0997650
$949$	27.3808	0.888820
$950$	37.2775	1.20944
$951$	−3.79575	−0.123086
$952$	−38.2614	−1.24006
$953$	32.3703	1.04858	0.524288	−	0.851541i	$-0.324332\pi$
$953$	32.3703	1.04858	0.524288	+	0.851541i	$0.324332\pi$
$954$	16.3954	0.530822
$955$	−19.1223	−0.618782
$956$	8.83018	0.285588
$957$	−14.7913	−0.478136
$958$	−97.7686	−3.15876
$959$	0.679946	0.0219566
$960$	−6.47856	−0.209095
$961$	−27.4558	−0.885673
$962$	−9.94631	−0.320682
$963$	48.5190	1.56350
$964$	8.92629	0.287497
$965$	−1.06049	−0.0341385
$966$	−9.88708	−0.318112
$967$	18.6120	0.598521	0.299260	−	0.954172i	$-0.403260\pi$
$967$	18.6120	0.598521	0.299260	+	0.954172i	$0.403260\pi$
$968$	−11.7935	−0.379056
$969$	−8.10122	−0.260249
$970$	36.4248	1.16953
$971$	17.7037	0.568138	0.284069	−	0.958804i	$-0.408316\pi$
$971$	17.7037	0.568138	0.284069	+	0.958804i	$0.408316\pi$
$972$	−56.2411	−1.80393
$973$	17.3534	0.556324
$974$	−104.924	−3.36197
$975$	4.97635	0.159371
$976$	−81.3113	−2.60271
$977$	−14.8217	−0.474187	−0.237094	−	0.971487i	$-0.576195\pi$
$977$	−14.8217	−0.474187	−0.237094	+	0.971487i	$0.576195\pi$
$978$	−18.7512	−0.599596
$979$	43.5456	1.39172
$980$	−33.7486	−1.07806
$981$	−31.5426	−1.00708
$982$	−19.1933	−0.612484
$983$	−14.9774	−0.477705	−0.238853	−	0.971056i	$-0.576771\pi$
$983$	−14.9774	−0.477705	−0.238853	+	0.971056i	$0.576771\pi$
$984$	35.4065	1.12872
$985$	31.2475	0.995628
$986$	107.959	3.43810
$987$	4.81566	0.153284
$988$	56.8563	1.80884
$989$	−82.7764	−2.63214
$990$	−30.2842	−0.962494
$991$	−42.2434	−1.34191	−0.670953	−	0.741500i	$-0.734115\pi$
$991$	−42.2434	−1.34191	−0.670953	+	0.741500i	$0.734115\pi$
$992$	−23.9120	−0.759207
$993$	−1.79109	−0.0568385
$994$	12.7428	0.404178
$995$	21.6749	0.687140
$996$	−32.9833	−1.04512
$997$	−19.2581	−0.609909	−0.304954	−	0.952367i	$-0.598641\pi$
$997$	−19.2581	−0.609909	−0.304954	+	0.952367i	$0.598641\pi$
$998$	40.6999	1.28833
$999$	3.41372	0.108005

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.a.1.14	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.a.1.14	✓	243	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63978 q^{2} -0.462407 q^{3} +4.96844 q^{4} +1.16438 q^{5} +1.22065 q^{6} +1.07998 q^{7} -7.83603 q^{8} -2.78618 q^{9} +O(q^{10})\)	\(q-2.63978 q^{2} -0.462407 q^{3} +4.96844 q^{4} +1.16438 q^{5} +1.22065 q^{6} +1.07998 q^{7} -7.83603 q^{8} -2.78618 q^{9} -3.07372 q^{10} -3.53625 q^{11} -2.29744 q^{12} +2.95313 q^{13} -2.85091 q^{14} -0.538420 q^{15} +10.7485 q^{16} +4.52115 q^{17} +7.35490 q^{18} +3.87504 q^{19} +5.78517 q^{20} -0.499391 q^{21} +9.33491 q^{22} -7.49997 q^{23} +3.62344 q^{24} -3.64421 q^{25} -7.79562 q^{26} +2.67557 q^{27} +5.36582 q^{28} -9.04565 q^{29} +1.42131 q^{30} +1.88259 q^{31} -12.7016 q^{32} +1.63519 q^{33} -11.9349 q^{34} +1.25751 q^{35} -13.8430 q^{36} +1.27588 q^{37} -10.2293 q^{38} -1.36555 q^{39} -9.12415 q^{40} +9.77153 q^{41} +1.31828 q^{42} +11.0369 q^{43} -17.5696 q^{44} -3.24418 q^{45} +19.7983 q^{46} -9.64306 q^{47} -4.97019 q^{48} -5.83364 q^{49} +9.61991 q^{50} -2.09062 q^{51} +14.6725 q^{52} +2.22918 q^{53} -7.06292 q^{54} -4.11755 q^{55} -8.46275 q^{56} -1.79185 q^{57} +23.8785 q^{58} +7.41365 q^{59} -2.67511 q^{60} -7.56489 q^{61} -4.96963 q^{62} -3.00902 q^{63} +12.0325 q^{64} +3.43858 q^{65} -4.31653 q^{66} +4.78204 q^{67} +22.4631 q^{68} +3.46804 q^{69} -3.31956 q^{70} -4.46975 q^{71} +21.8326 q^{72} +9.27180 q^{73} -3.36805 q^{74} +1.68511 q^{75} +19.2529 q^{76} -3.81907 q^{77} +3.60475 q^{78} -1.33702 q^{79} +12.5154 q^{80} +7.12133 q^{81} -25.7947 q^{82} +14.3565 q^{83} -2.48119 q^{84} +5.26436 q^{85} -29.1350 q^{86} +4.18278 q^{87} +27.7101 q^{88} -12.3141 q^{89} +8.56393 q^{90} +3.18932 q^{91} -37.2632 q^{92} -0.870525 q^{93} +25.4556 q^{94} +4.51204 q^{95} +5.87334 q^{96} -11.8504 q^{97} +15.3995 q^{98} +9.85261 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * q^99

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