LMFDB - Embedded newform 6047.2.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6047,2,Mod(1,6047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6047, 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("6047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6047 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6047.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:	$48.2855381023$
Analytic rank:	$0$
Dimension:	$287$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65594 q^{2} +2.26002 q^{3} +5.05400 q^{4} -1.82444 q^{5} -6.00248 q^{6} -0.589488 q^{7} -8.11124 q^{8} +2.10770 q^{9} +O(q^{10})$	\(q-2.65594 q^{2} +2.26002 q^{3} +5.05400 q^{4} -1.82444 q^{5} -6.00248 q^{6} -0.589488 q^{7} -8.11124 q^{8} +2.10770 q^{9} +4.84561 q^{10} -4.62899 q^{11} +11.4222 q^{12} -0.721496 q^{13} +1.56564 q^{14} -4.12328 q^{15} +11.4349 q^{16} -7.49473 q^{17} -5.59791 q^{18} -0.271154 q^{19} -9.22075 q^{20} -1.33225 q^{21} +12.2943 q^{22} +0.638132 q^{23} -18.3316 q^{24} -1.67140 q^{25} +1.91625 q^{26} -2.01662 q^{27} -2.97927 q^{28} +1.27091 q^{29} +10.9512 q^{30} +9.96714 q^{31} -14.1480 q^{32} -10.4616 q^{33} +19.9055 q^{34} +1.07549 q^{35} +10.6523 q^{36} -4.57835 q^{37} +0.720167 q^{38} -1.63060 q^{39} +14.7985 q^{40} -7.23211 q^{41} +3.53839 q^{42} -8.91668 q^{43} -23.3949 q^{44} -3.84538 q^{45} -1.69484 q^{46} +9.71348 q^{47} +25.8432 q^{48} -6.65250 q^{49} +4.43914 q^{50} -16.9383 q^{51} -3.64644 q^{52} +8.44971 q^{53} +5.35603 q^{54} +8.44533 q^{55} +4.78148 q^{56} -0.612813 q^{57} -3.37547 q^{58} -5.32056 q^{59} -20.8391 q^{60} +9.74297 q^{61} -26.4721 q^{62} -1.24246 q^{63} +14.7063 q^{64} +1.31633 q^{65} +27.7854 q^{66} +10.8392 q^{67} -37.8784 q^{68} +1.44219 q^{69} -2.85643 q^{70} +7.88187 q^{71} -17.0960 q^{72} +7.15894 q^{73} +12.1598 q^{74} -3.77740 q^{75} -1.37041 q^{76} +2.72873 q^{77} +4.33076 q^{78} -10.2490 q^{79} -20.8624 q^{80} -10.8807 q^{81} +19.2080 q^{82} +0.777160 q^{83} -6.73322 q^{84} +13.6737 q^{85} +23.6821 q^{86} +2.87229 q^{87} +37.5468 q^{88} -1.35050 q^{89} +10.2131 q^{90} +0.425313 q^{91} +3.22512 q^{92} +22.5259 q^{93} -25.7984 q^{94} +0.494705 q^{95} -31.9748 q^{96} +3.63617 q^{97} +17.6686 q^{98} -9.75650 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) $ 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * 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 $

$2$	−2.65594	−1.87803	−0.939016	−	0.343874i	$-0.888261\pi$
$2$	−2.65594	−1.87803	−0.939016	+	0.343874i	$0.888261\pi$
$3$	2.26002	1.30482	0.652412	−	0.757864i	$-0.273757\pi$
$3$	2.26002	1.30482	0.652412	+	0.757864i	$0.273757\pi$
$4$	5.05400	2.52700
$5$	−1.82444	−0.815917	−0.407958	−	0.913001i	$-0.633759\pi$
$5$	−1.82444	−0.815917	−0.407958	+	0.913001i	$0.633759\pi$
$6$	−6.00248	−2.45050
$7$	−0.589488	−0.222805	−0.111403	−	0.993775i	$-0.535534\pi$
$7$	−0.589488	−0.222805	−0.111403	+	0.993775i	$0.535534\pi$
$8$	−8.11124	−2.86776
$9$	2.10770	0.702566
$10$	4.84561	1.53232
$11$	−4.62899	−1.39569	−0.697846	−	0.716248i	$-0.745858\pi$
$11$	−4.62899	−1.39569	−0.697846	+	0.716248i	$0.745858\pi$
$12$	11.4222	3.29729
$13$	−0.721496	−0.200107	−0.100054	−	0.994982i	$-0.531901\pi$
$13$	−0.721496	−0.200107	−0.100054	+	0.994982i	$0.531901\pi$
$14$	1.56564	0.418436
$15$	−4.12328	−1.06463
$16$	11.4349	2.85874
$17$	−7.49473	−1.81774	−0.908870	−	0.417080i	$-0.863054\pi$
$17$	−7.49473	−1.81774	−0.908870	+	0.417080i	$0.863054\pi$
$18$	−5.59791	−1.31944
$19$	−0.271154	−0.0622069	−0.0311035	−	0.999516i	$-0.509902\pi$
$19$	−0.271154	−0.0622069	−0.0311035	+	0.999516i	$0.509902\pi$
$20$	−9.22075	−2.06182
$21$	−1.33225	−0.290722
$22$	12.2943	2.62115
$23$	0.638132	0.133060	0.0665298	−	0.997784i	$-0.478807\pi$
$23$	0.638132	0.133060	0.0665298	+	0.997784i	$0.478807\pi$
$24$	−18.3316	−3.74192
$25$	−1.67140	−0.334280
$26$	1.91625	0.375807
$27$	−2.01662	−0.388099
$28$	−2.97927	−0.563030
$29$	1.27091	0.236003	0.118001	−	0.993013i	$-0.462351\pi$
$29$	1.27091	0.236003	0.118001	+	0.993013i	$0.462351\pi$
$30$	10.9512	1.99940
$31$	9.96714	1.79015	0.895075	−	0.445915i	$-0.147122\pi$
$31$	9.96714	1.79015	0.895075	+	0.445915i	$0.147122\pi$
$32$	−14.1480	−2.50104
$33$	−10.4616	−1.82113
$34$	19.9055	3.41377
$35$	1.07549	0.181791
$36$	10.6523	1.77538
$37$	−4.57835	−0.752676	−0.376338	−	0.926482i	$-0.622817\pi$
$37$	−4.57835	−0.752676	−0.376338	+	0.926482i	$0.622817\pi$
$38$	0.720167	0.116827
$39$	−1.63060	−0.261104
$40$	14.7985	2.33985
$41$	−7.23211	−1.12947	−0.564733	−	0.825274i	$-0.691021\pi$
$41$	−7.23211	−1.12947	−0.564733	+	0.825274i	$0.691021\pi$
$42$	3.53839	0.545985
$43$	−8.91668	−1.35978	−0.679890	−	0.733314i	$-0.737973\pi$
$43$	−8.91668	−1.35978	−0.679890	+	0.733314i	$0.737973\pi$
$44$	−23.3949	−3.52692
$45$	−3.84538	−0.573235
$46$	−1.69484	−0.249890
$47$	9.71348	1.41686	0.708428	−	0.705783i	$-0.249405\pi$
$47$	9.71348	1.41686	0.708428	+	0.705783i	$0.249405\pi$
$48$	25.8432	3.73015
$49$	−6.65250	−0.950358
$50$	4.43914	0.627789
$51$	−16.9383	−2.37183
$52$	−3.64644	−0.505671
$53$	8.44971	1.16066	0.580329	−	0.814382i	$-0.302924\pi$
$53$	8.44971	1.16066	0.580329	+	0.814382i	$0.302924\pi$
$54$	5.35603	0.728863
$55$	8.44533	1.13877
$56$	4.78148	0.638952
$57$	−0.612813	−0.0811691
$58$	−3.37547	−0.443221
$59$	−5.32056	−0.692677	−0.346339	−	0.938110i	$-0.612575\pi$
$59$	−5.32056	−0.692677	−0.346339	+	0.938110i	$0.612575\pi$
$60$	−20.8391	−2.69032
$61$	9.74297	1.24746	0.623730	−	0.781640i	$-0.285617\pi$
$61$	9.74297	1.24746	0.623730	+	0.781640i	$0.285617\pi$
$62$	−26.4721	−3.36196
$63$	−1.24246	−0.156535
$64$	14.7063	1.83829
$65$	1.31633	0.163271
$66$	27.7854	3.42014
$67$	10.8392	1.32422	0.662111	−	0.749406i	$-0.269661\pi$
$67$	10.8392	1.32422	0.662111	+	0.749406i	$0.269661\pi$
$68$	−37.8784	−4.59343
$69$	1.44219	0.173619
$70$	−2.85643	−0.341408
$71$	7.88187	0.935405	0.467703	−	0.883886i	$-0.345082\pi$
$71$	7.88187	0.935405	0.467703	+	0.883886i	$0.345082\pi$
$72$	−17.0960	−2.01479
$73$	7.15894	0.837891	0.418945	−	0.908011i	$-0.362400\pi$
$73$	7.15894	0.837891	0.418945	+	0.908011i	$0.362400\pi$
$74$	12.1598	1.41355
$75$	−3.77740	−0.436177
$76$	−1.37041	−0.157197
$77$	2.72873	0.310968
$78$	4.33076	0.490362
$79$	−10.2490	−1.15310	−0.576552	−	0.817060i	$-0.695602\pi$
$79$	−10.2490	−1.15310	−0.576552	+	0.817060i	$0.695602\pi$
$80$	−20.8624	−2.33249
$81$	−10.8807	−1.20897
$82$	19.2080	2.12117
$83$	0.777160	0.0853044	0.0426522	−	0.999090i	$-0.486419\pi$
$83$	0.777160	0.0853044	0.0426522	+	0.999090i	$0.486419\pi$
$84$	−6.73322	−0.734655
$85$	13.6737	1.48312
$86$	23.6821	2.55371
$87$	2.87229	0.307942
$88$	37.5468	4.00251
$89$	−1.35050	−0.143153	−0.0715763	−	0.997435i	$-0.522803\pi$
$89$	−1.35050	−0.143153	−0.0715763	+	0.997435i	$0.522803\pi$
$90$	10.2131	1.07655
$91$	0.425313	0.0445849
$92$	3.22512	0.336242
$93$	22.5259	2.33583
$94$	−25.7984	−2.66090
$95$	0.494705	0.0507557
$96$	−31.9748	−3.26342
$97$	3.63617	0.369197	0.184598	−	0.982814i	$-0.440902\pi$
$97$	3.63617	0.369197	0.184598	+	0.982814i	$0.440902\pi$
$98$	17.6686	1.78480
$99$	−9.75650	−0.980566
$100$	−8.44727	−0.844727
$101$	−15.8065	−1.57280	−0.786402	−	0.617715i	$-0.788059\pi$
$101$	−15.8065	−1.57280	−0.786402	+	0.617715i	$0.788059\pi$
$102$	44.9870	4.45437
$103$	14.9911	1.47712	0.738561	−	0.674187i	$-0.235506\pi$
$103$	14.9911	1.47712	0.738561	+	0.674187i	$0.235506\pi$
$104$	5.85223	0.573858
$105$	2.43063	0.237205
$106$	−22.4419	−2.17975
$107$	−5.24808	−0.507351	−0.253676	−	0.967289i	$-0.581640\pi$
$107$	−5.24808	−0.507351	−0.253676	+	0.967289i	$0.581640\pi$
$108$	−10.1920	−0.980728
$109$	−13.8047	−1.32225	−0.661125	−	0.750276i	$-0.729921\pi$
$109$	−13.8047	−1.32225	−0.661125	+	0.750276i	$0.729921\pi$
$110$	−22.4303	−2.13864
$111$	−10.3472	−0.982110
$112$	−6.74076	−0.636942
$113$	−19.4092	−1.82586	−0.912931	−	0.408113i	$-0.866187\pi$
$113$	−19.4092	−1.82586	−0.912931	+	0.408113i	$0.866187\pi$
$114$	1.62759	0.152438
$115$	−1.16424	−0.108566
$116$	6.42320	0.596380
$117$	−1.52070	−0.140588
$118$	14.1311	1.30087
$119$	4.41805	0.405002
$120$	33.4450	3.05309
$121$	10.4275	0.947957
$122$	−25.8767	−2.34277
$123$	−16.3447	−1.47375
$124$	50.3739	4.52371
$125$	12.1716	1.08866
$126$	3.29990	0.293978
$127$	12.6809	1.12525	0.562624	−	0.826713i	$-0.309792\pi$
$127$	12.6809	1.12525	0.562624	+	0.826713i	$0.309792\pi$
$128$	−10.7631	−0.951334
$129$	−20.1519	−1.77427
$130$	−3.49609	−0.306627
$131$	−9.17532	−0.801652	−0.400826	−	0.916154i	$-0.631277\pi$
$131$	−9.17532	−0.801652	−0.400826	+	0.916154i	$0.631277\pi$
$132$	−52.8730	−4.60201
$133$	0.159842	0.0138600
$134$	−28.7883	−2.48693
$135$	3.67922	0.316657
$136$	60.7916	5.21284
$137$	9.48332	0.810215	0.405107	−	0.914269i	$-0.367234\pi$
$137$	9.48332	0.810215	0.405107	+	0.914269i	$0.367234\pi$
$138$	−3.83037	−0.326063
$139$	10.4387	0.885403	0.442701	−	0.896669i	$-0.354020\pi$
$139$	10.4387	0.885403	0.442701	+	0.896669i	$0.354020\pi$
$140$	5.43552	0.459385
$141$	21.9527	1.84875
$142$	−20.9337	−1.75672
$143$	3.33980	0.279288
$144$	24.1014	2.00845
$145$	−2.31871	−0.192559
$146$	−19.0137	−1.57359
$147$	−15.0348	−1.24005
$148$	−23.1390	−1.90201
$149$	−2.78749	−0.228360	−0.114180	−	0.993460i	$-0.536424\pi$
$149$	−2.78749	−0.228360	−0.114180	+	0.993460i	$0.536424\pi$
$150$	10.0325	0.819154
$151$	15.0662	1.22607	0.613034	−	0.790056i	$-0.289949\pi$
$151$	15.0662	1.22607	0.613034	+	0.790056i	$0.289949\pi$
$152$	2.19939	0.178394
$153$	−15.7966	−1.27708
$154$	−7.24734	−0.584007
$155$	−18.1845	−1.46061
$156$	−8.24104	−0.659812
$157$	−16.2377	−1.29591	−0.647956	−	0.761678i	$-0.724376\pi$
$157$	−16.2377	−1.29591	−0.647956	+	0.761678i	$0.724376\pi$
$158$	27.2207	2.16557
$159$	19.0965	1.51445
$160$	25.8123	2.04064
$161$	−0.376171	−0.0296464
$162$	28.8985	2.27048
$163$	7.06394	0.553291	0.276645	−	0.960972i	$-0.410777\pi$
$163$	7.06394	0.553291	0.276645	+	0.960972i	$0.410777\pi$
$164$	−36.5511	−2.85416
$165$	19.0866	1.48589
$166$	−2.06409	−0.160204
$167$	19.6220	1.51840	0.759198	−	0.650860i	$-0.225591\pi$
$167$	19.6220	1.51840	0.759198	+	0.650860i	$0.225591\pi$
$168$	10.8062	0.833720
$169$	−12.4794	−0.959957
$170$	−36.3166	−2.78535
$171$	−0.571510	−0.0437044
$172$	−45.0649	−3.43617
$173$	−8.65185	−0.657788	−0.328894	−	0.944367i	$-0.606676\pi$
$173$	−8.65185	−0.657788	−0.328894	+	0.944367i	$0.606676\pi$
$174$	−7.62863	−0.578325
$175$	0.985270	0.0744794
$176$	−52.9322	−3.98992
$177$	−12.0246	−0.903822
$178$	3.58684	0.268845
$179$	7.96950	0.595668	0.297834	−	0.954618i	$-0.403736\pi$
$179$	7.96950	0.595668	0.297834	+	0.954618i	$0.403736\pi$
$180$	−19.4345	−1.44857
$181$	24.3714	1.81152	0.905758	−	0.423796i	$-0.139303\pi$
$181$	24.3714	1.81152	0.905758	+	0.423796i	$0.139303\pi$
$182$	−1.12961	−0.0837319
$183$	22.0193	1.62772
$184$	−5.17604	−0.381583
$185$	8.35295	0.614121
$186$	−59.8275	−4.38676
$187$	34.6930	2.53701
$188$	49.0919	3.58040
$189$	1.18878	0.0864707
$190$	−1.31391	−0.0953207
$191$	19.5039	1.41125	0.705626	−	0.708584i	$-0.250666\pi$
$191$	19.5039	1.41125	0.705626	+	0.708584i	$0.250666\pi$
$192$	33.2367	2.39865
$193$	3.62177	0.260701	0.130350	−	0.991468i	$-0.458390\pi$
$193$	3.62177	0.260701	0.130350	+	0.991468i	$0.458390\pi$
$194$	−9.65743	−0.693363
$195$	2.97493	0.213039
$196$	−33.6218	−2.40156
$197$	25.9458	1.84856	0.924279	−	0.381717i	$-0.124667\pi$
$197$	25.9458	1.84856	0.924279	+	0.381717i	$0.124667\pi$
$198$	25.9127	1.84153
$199$	10.7473	0.761858	0.380929	−	0.924604i	$-0.375604\pi$
$199$	10.7473	0.761858	0.380929	+	0.924604i	$0.375604\pi$
$200$	13.5571	0.958635
$201$	24.4969	1.72788
$202$	41.9811	2.95378
$203$	−0.749188	−0.0525827
$204$	−85.6060	−5.99362
$205$	13.1946	0.921550
$206$	−39.8155	−2.77408
$207$	1.34499	0.0934832
$208$	−8.25027	−0.572053
$209$	1.25517	0.0868217
$210$	−6.45559	−0.445478
$211$	9.54261	0.656940	0.328470	−	0.944514i	$-0.393467\pi$
$211$	9.54261	0.656940	0.328470	+	0.944514i	$0.393467\pi$
$212$	42.7049	2.93298
$213$	17.8132	1.22054
$214$	13.9386	0.952822
$215$	16.2680	1.10947
$216$	16.3573	1.11298
$217$	−5.87550	−0.398855
$218$	36.6644	2.48323
$219$	16.1794	1.09330
$220$	42.6827	2.87767
$221$	5.40742	0.363743
$222$	27.4814	1.84443
$223$	8.68707	0.581729	0.290865	−	0.956764i	$-0.406057\pi$
$223$	8.68707	0.581729	0.290865	+	0.956764i	$0.406057\pi$
$224$	8.34008	0.557245
$225$	−3.52281	−0.234854
$226$	51.5496	3.42903
$227$	−4.90652	−0.325657	−0.162828	−	0.986654i	$-0.552062\pi$
$227$	−4.90652	−0.325657	−0.162828	+	0.986654i	$0.552062\pi$
$228$	−3.09716	−0.205114
$229$	7.92607	0.523769	0.261885	−	0.965099i	$-0.415656\pi$
$229$	7.92607	0.523769	0.261885	+	0.965099i	$0.415656\pi$
$230$	3.09214	0.203890
$231$	6.16699	0.405758
$232$	−10.3087	−0.676799
$233$	21.1242	1.38389	0.691947	−	0.721949i	$-0.256753\pi$
$233$	21.1242	1.38389	0.691947	+	0.721949i	$0.256753\pi$
$234$	4.03887	0.264029
$235$	−17.7217	−1.15604
$236$	−26.8901	−1.75040
$237$	−23.1630	−1.50460
$238$	−11.7341	−0.760607
$239$	−1.65155	−0.106830	−0.0534150	−	0.998572i	$-0.517011\pi$
$239$	−1.65155	−0.106830	−0.0534150	+	0.998572i	$0.517011\pi$
$240$	−47.1495	−3.04349
$241$	−22.6241	−1.45735	−0.728674	−	0.684861i	$-0.759863\pi$
$241$	−22.6241	−1.45735	−0.728674	+	0.684861i	$0.759863\pi$
$242$	−27.6949	−1.78029
$243$	−18.5408	−1.18939
$244$	49.2410	3.15233
$245$	12.1371	0.775413
$246$	43.4106	2.76776
$247$	0.195636	0.0124480
$248$	−80.8458	−5.13372
$249$	1.75640	0.111307
$250$	−32.3270	−2.04454
$251$	−15.9685	−1.00793	−0.503963	−	0.863725i	$-0.668125\pi$
$251$	−15.9685	−1.00793	−0.503963	+	0.863725i	$0.668125\pi$
$252$	−6.27940	−0.395565
$253$	−2.95390	−0.185710
$254$	−33.6797	−2.11325
$255$	30.9029	1.93522
$256$	−0.826543	−0.0516589
$257$	−3.34957	−0.208940	−0.104470	−	0.994528i	$-0.533315\pi$
$257$	−3.34957	−0.208940	−0.104470	+	0.994528i	$0.533315\pi$
$258$	53.5221	3.33214
$259$	2.69888	0.167700
$260$	6.65274	0.412585
$261$	2.67870	0.165807
$262$	24.3691	1.50553
$263$	−3.54667	−0.218697	−0.109348	−	0.994003i	$-0.534876\pi$
$263$	−3.54667	−0.218697	−0.109348	+	0.994003i	$0.534876\pi$
$264$	84.8567	5.22257
$265$	−15.4160	−0.946999
$266$	−0.424530	−0.0260296
$267$	−3.05216	−0.186789
$268$	54.7815	3.34631
$269$	−14.1367	−0.861929	−0.430965	−	0.902369i	$-0.641827\pi$
$269$	−14.1367	−0.861929	−0.430965	+	0.902369i	$0.641827\pi$
$270$	−9.77178	−0.594691
$271$	−32.3487	−1.96505	−0.982523	−	0.186143i	$-0.940401\pi$
$271$	−32.3487	−1.96505	−0.982523	+	0.186143i	$0.940401\pi$
$272$	−85.7019	−5.19644
$273$	0.961217	0.0581755
$274$	−25.1871	−1.52161
$275$	7.73690	0.466552
$276$	7.28884	0.438737
$277$	−2.63165	−0.158121	−0.0790603	−	0.996870i	$-0.525192\pi$
$277$	−2.63165	−0.158121	−0.0790603	+	0.996870i	$0.525192\pi$
$278$	−27.7246	−1.66281
$279$	21.0077	1.25770
$280$	−8.72354	−0.521331
$281$	0.350848	0.0209299	0.0104649	−	0.999945i	$-0.496669\pi$
$281$	0.350848	0.0209299	0.0104649	+	0.999945i	$0.496669\pi$
$282$	−58.3049	−3.47201
$283$	28.9597	1.72147	0.860737	−	0.509050i	$-0.170003\pi$
$283$	28.9597	1.72147	0.860737	+	0.509050i	$0.170003\pi$
$284$	39.8350	2.36377
$285$	1.11804	0.0662272
$286$	−8.87029	−0.524511
$287$	4.26324	0.251651
$288$	−29.8197	−1.75714
$289$	39.1710	2.30418
$290$	6.15836	0.361631
$291$	8.21781	0.481737
$292$	36.1813	2.11735
$293$	5.13804	0.300168	0.150084	−	0.988673i	$-0.452046\pi$
$293$	5.13804	0.300168	0.150084	+	0.988673i	$0.452046\pi$
$294$	39.9315	2.32885
$295$	9.70706	0.565167
$296$	37.1361	2.15849
$297$	9.33493	0.541667
$298$	7.40340	0.428867
$299$	−0.460410	−0.0266262
$300$	−19.0910	−1.10222
$301$	5.25627	0.302966
$302$	−40.0148	−2.30259
$303$	−35.7230	−2.05223
$304$	−3.10063	−0.177833
$305$	−17.7755	−1.01782
$306$	41.9549	2.39840
$307$	21.3992	1.22132	0.610658	−	0.791894i	$-0.290905\pi$
$307$	21.3992	1.22132	0.610658	+	0.791894i	$0.290905\pi$
$308$	13.7910	0.785816
$309$	33.8803	1.92738
$310$	48.2969	2.74308
$311$	33.5392	1.90183	0.950917	−	0.309446i	$-0.100144\pi$
$311$	33.5392	1.90183	0.950917	+	0.309446i	$0.100144\pi$
$312$	13.2262	0.748784
$313$	−15.4582	−0.873752	−0.436876	−	0.899522i	$-0.643915\pi$
$313$	−15.4582	−0.873752	−0.436876	+	0.899522i	$0.643915\pi$
$314$	43.1264	2.43376
$315$	2.26680	0.127720
$316$	−51.7986	−2.91390
$317$	14.5331	0.816260	0.408130	−	0.912924i	$-0.366181\pi$
$317$	14.5331	0.816260	0.408130	+	0.912924i	$0.366181\pi$
$318$	−50.7192	−2.84419
$319$	−5.88305	−0.329387
$320$	−26.8309	−1.49989
$321$	−11.8608	−0.662004
$322$	0.999086	0.0556769
$323$	2.03222	0.113076
$324$	−54.9911	−3.05506
$325$	1.20591	0.0668918
$326$	−18.7614	−1.03910
$327$	−31.1989	−1.72530
$328$	58.6614	3.23903
$329$	−5.72598	−0.315683
$330$	−50.6929	−2.79055
$331$	−19.7967	−1.08813	−0.544063	−	0.839044i	$-0.683115\pi$
$331$	−19.7967	−1.08813	−0.544063	+	0.839044i	$0.683115\pi$
$332$	3.92777	0.215564
$333$	−9.64977	−0.528804
$334$	−52.1148	−2.85160
$335$	−19.7756	−1.08045
$336$	−15.2343	−0.831097
$337$	27.4458	1.49507	0.747534	−	0.664224i	$-0.231238\pi$
$337$	27.4458	1.49507	0.747534	+	0.664224i	$0.231238\pi$
$338$	33.1446	1.80283
$339$	−43.8652	−2.38243
$340$	69.1071	3.74786
$341$	−46.1377	−2.49850
$342$	1.51789	0.0820783
$343$	8.04798	0.434550
$344$	72.3253	3.89952
$345$	−2.63120	−0.141659
$346$	22.9788	1.23535
$347$	−0.795804	−0.0427210	−0.0213605	−	0.999772i	$-0.506800\pi$
$347$	−0.795804	−0.0427210	−0.0213605	+	0.999772i	$0.506800\pi$
$348$	14.5166	0.778170
$349$	−34.1195	−1.82637	−0.913187	−	0.407541i	$-0.866386\pi$
$349$	−34.1195	−1.82637	−0.913187	+	0.407541i	$0.866386\pi$
$350$	−2.61682	−0.139875
$351$	1.45499	0.0776614
$352$	65.4910	3.49068
$353$	−6.61691	−0.352182	−0.176091	−	0.984374i	$-0.556345\pi$
$353$	−6.61691	−0.352182	−0.176091	+	0.984374i	$0.556345\pi$
$354$	31.9365	1.69741
$355$	−14.3800	−0.763213
$356$	−6.82543	−0.361747
$357$	9.98490	0.528457
$358$	−21.1665	−1.11868
$359$	16.4727	0.869395	0.434697	−	0.900577i	$-0.356855\pi$
$359$	16.4727	0.869395	0.434697	+	0.900577i	$0.356855\pi$
$360$	31.1908	1.64390
$361$	−18.9265	−0.996130
$362$	−64.7290	−3.40208
$363$	23.5664	1.23692
$364$	2.14953	0.112666
$365$	−13.0611	−0.683649
$366$	−58.4819	−3.05690
$367$	−25.1764	−1.31420	−0.657099	−	0.753805i	$-0.728216\pi$
$367$	−25.1764	−1.31420	−0.657099	+	0.753805i	$0.728216\pi$
$368$	7.29700	0.380382
$369$	−15.2431	−0.793524
$370$	−22.1849	−1.15334
$371$	−4.98100	−0.258601
$372$	113.846	5.90265
$373$	−16.5531	−0.857086	−0.428543	−	0.903521i	$-0.640973\pi$
$373$	−16.5531	−0.857086	−0.428543	+	0.903521i	$0.640973\pi$
$374$	−92.1425	−4.76458
$375$	27.5081	1.42051
$376$	−78.7884	−4.06320
$377$	−0.916960	−0.0472258
$378$	−3.15731	−0.162395
$379$	23.4720	1.20567	0.602837	−	0.797864i	$-0.294037\pi$
$379$	23.4720	1.20567	0.602837	+	0.797864i	$0.294037\pi$
$380$	2.50024	0.128260
$381$	28.6591	1.46825
$382$	−51.8011	−2.65038
$383$	20.8144	1.06357	0.531784	−	0.846880i	$-0.321522\pi$
$383$	20.8144	1.06357	0.531784	+	0.846880i	$0.321522\pi$
$384$	−24.3249	−1.24132
$385$	−4.97842	−0.253724
$386$	−9.61920	−0.489604
$387$	−18.7937	−0.955335
$388$	18.3772	0.932961
$389$	−9.09389	−0.461079	−0.230539	−	0.973063i	$-0.574049\pi$
$389$	−9.09389	−0.461079	−0.230539	+	0.973063i	$0.574049\pi$
$390$	−7.90124	−0.400095
$391$	−4.78263	−0.241868
$392$	53.9601	2.72540
$393$	−20.7364	−1.04601
$394$	−68.9103	−3.47165
$395$	18.6988	0.940837
$396$	−49.3094	−2.47789
$397$	−22.5748	−1.13300	−0.566498	−	0.824063i	$-0.691702\pi$
$397$	−22.5748	−1.13300	−0.566498	+	0.824063i	$0.691702\pi$
$398$	−28.5442	−1.43079
$399$	0.361246	0.0180849
$400$	−19.1124	−0.955619
$401$	9.53359	0.476085	0.238042	−	0.971255i	$-0.423494\pi$
$401$	9.53359	0.476085	0.238042	+	0.971255i	$0.423494\pi$
$402$	−65.0622	−3.24501
$403$	−7.19125	−0.358222
$404$	−79.8861	−3.97448
$405$	19.8512	0.986416
$406$	1.98980	0.0987520
$407$	21.1931	1.05050
$408$	137.390	6.80183
$409$	19.0366	0.941301	0.470651	−	0.882320i	$-0.344019\pi$
$409$	19.0366	0.941301	0.470651	+	0.882320i	$0.344019\pi$
$410$	−35.0440	−1.73070
$411$	21.4325	1.05719
$412$	75.7653	3.73269
$413$	3.13640	0.154332
$414$	−3.57220	−0.175564
$415$	−1.41789	−0.0696013
$416$	10.2077	0.500476
$417$	23.5918	1.15529
$418$	−3.33365	−0.163054
$419$	−12.6992	−0.620395	−0.310198	−	0.950672i	$-0.600395\pi$
$419$	−12.6992	−0.620395	−0.310198	+	0.950672i	$0.600395\pi$
$420$	12.2844	0.599417
$421$	−11.2827	−0.549886	−0.274943	−	0.961461i	$-0.588659\pi$
$421$	−11.2827	−0.549886	−0.274943	+	0.961461i	$0.588659\pi$
$422$	−25.3446	−1.23375
$423$	20.4731	0.995435
$424$	−68.5377	−3.32848
$425$	12.5267	0.607635
$426$	−47.3107	−2.29221
$427$	−5.74336	−0.277941
$428$	−26.5238	−1.28208
$429$	7.54801	0.364422
$430$	−43.2067	−2.08361
$431$	−11.5919	−0.558362	−0.279181	−	0.960238i	$-0.590063\pi$
$431$	−11.5919	−0.558362	−0.279181	+	0.960238i	$0.590063\pi$
$432$	−23.0600	−1.10947
$433$	14.7703	0.709813	0.354906	−	0.934902i	$-0.384513\pi$
$433$	14.7703	0.709813	0.354906	+	0.934902i	$0.384513\pi$
$434$	15.6050	0.749063
$435$	−5.24034	−0.251255
$436$	−69.7690	−3.34133
$437$	−0.173032	−0.00827723
$438$	−42.9714	−2.05325
$439$	−0.581366	−0.0277471	−0.0138735	−	0.999904i	$-0.504416\pi$
$439$	−0.581366	−0.0277471	−0.0138735	+	0.999904i	$0.504416\pi$
$440$	−68.5021	−3.26571
$441$	−14.0215	−0.667689
$442$	−14.3618	−0.683120
$443$	−11.8361	−0.562349	−0.281175	−	0.959657i	$-0.590724\pi$
$443$	−11.8361	−0.562349	−0.281175	+	0.959657i	$0.590724\pi$
$444$	−52.2946	−2.48179
$445$	2.46391	0.116801
$446$	−23.0723	−1.09251
$447$	−6.29979	−0.297970
$448$	−8.66921	−0.409582
$449$	1.12969	0.0533132	0.0266566	−	0.999645i	$-0.491514\pi$
$449$	1.12969	0.0533132	0.0266566	+	0.999645i	$0.491514\pi$
$450$	9.35636	0.441063
$451$	33.4773	1.57639
$452$	−98.0941	−4.61396
$453$	34.0499	1.59980
$454$	13.0314	0.611594
$455$	−0.775960	−0.0363776
$456$	4.97068	0.232773
$457$	−29.2876	−1.37002	−0.685008	−	0.728536i	$-0.740201\pi$
$457$	−29.2876	−1.37002	−0.685008	+	0.728536i	$0.740201\pi$
$458$	−21.0511	−0.983655
$459$	15.1141	0.705464
$460$	−5.88405	−0.274345
$461$	18.1993	0.847626	0.423813	−	0.905750i	$-0.360691\pi$
$461$	18.1993	0.847626	0.423813	+	0.905750i	$0.360691\pi$
$462$	−16.3791	−0.762027
$463$	−27.7171	−1.28812	−0.644062	−	0.764973i	$-0.722752\pi$
$463$	−27.7171	−1.28812	−0.644062	+	0.764973i	$0.722752\pi$
$464$	14.5328	0.674670
$465$	−41.0973	−1.90584
$466$	−56.1046	−2.59899
$467$	21.4376	0.992015	0.496008	−	0.868318i	$-0.334799\pi$
$467$	21.4376	0.992015	0.496008	+	0.868318i	$0.334799\pi$
$468$	−7.68560	−0.355267
$469$	−6.38959	−0.295044
$470$	47.0677	2.17107
$471$	−36.6976	−1.69094
$472$	43.1563	1.98643
$473$	41.2752	1.89784
$474$	61.5195	2.82568
$475$	0.453207	0.0207945
$476$	22.3289	1.02344
$477$	17.8094	0.815438
$478$	4.38642	0.200630
$479$	15.1840	0.693773	0.346886	−	0.937907i	$-0.387239\pi$
$479$	15.1840	0.693773	0.346886	+	0.937907i	$0.387239\pi$
$480$	58.3363	2.66267
$481$	3.30326	0.150616
$482$	60.0882	2.73694
$483$	−0.850154	−0.0386834
$484$	52.7008	2.39549
$485$	−6.63398	−0.301234
$486$	49.2431	2.23371
$487$	−42.3597	−1.91950	−0.959750	−	0.280857i	$-0.909381\pi$
$487$	−42.3597	−1.91950	−0.959750	+	0.280857i	$0.909381\pi$
$488$	−79.0276	−3.57741
$489$	15.9647	0.721947
$490$	−32.2354	−1.45625
$491$	−20.0479	−0.904751	−0.452375	−	0.891828i	$-0.649423\pi$
$491$	−20.0479	−0.904751	−0.452375	+	0.891828i	$0.649423\pi$
$492$	−82.6063	−3.72418
$493$	−9.52516	−0.428992
$494$	−0.519598	−0.0233778
$495$	17.8002	0.800060
$496$	113.974	5.11757
$497$	−4.64626	−0.208413
$498$	−4.66489	−0.209039
$499$	0.497568	0.0222742	0.0111371	−	0.999938i	$-0.496455\pi$
$499$	0.497568	0.0222742	0.0111371	+	0.999938i	$0.496455\pi$
$500$	61.5153	2.75105
$501$	44.3461	1.98124
$502$	42.4115	1.89292
$503$	6.38032	0.284484	0.142242	−	0.989832i	$-0.454569\pi$
$503$	6.38032	0.284484	0.142242	+	0.989832i	$0.454569\pi$
$504$	10.0779	0.448906
$505$	28.8381	1.28328
$506$	7.84538	0.348770
$507$	−28.2038	−1.25258
$508$	64.0893	2.84350
$509$	−5.10669	−0.226350	−0.113175	−	0.993575i	$-0.536102\pi$
$509$	−5.10669	−0.226350	−0.113175	+	0.993575i	$0.536102\pi$
$510$	−82.0762	−3.63440
$511$	−4.22011	−0.186687
$512$	23.7215	1.04835
$513$	0.546815	0.0241425
$514$	8.89625	0.392397
$515$	−27.3505	−1.20521
$516$	−101.848	−4.48359
$517$	−44.9636	−1.97750
$518$	−7.16806	−0.314946
$519$	−19.5534	−0.858297
$520$	−10.6771	−0.468221
$521$	4.80462	0.210494	0.105247	−	0.994446i	$-0.466437\pi$
$521$	4.80462	0.210494	0.105247	+	0.994446i	$0.466437\pi$
$522$	−7.11446	−0.311392
$523$	5.53309	0.241945	0.120973	−	0.992656i	$-0.461399\pi$
$523$	5.53309	0.241945	0.120973	+	0.992656i	$0.461399\pi$
$524$	−46.3721	−2.02577
$525$	2.22673	0.0971826
$526$	9.41972	0.410719
$527$	−74.7010	−3.25403
$528$	−119.628	−5.20614
$529$	−22.5928	−0.982295
$530$	40.9440	1.77849
$531$	−11.2141	−0.486651
$532$	0.807841	0.0350243
$533$	5.21794	0.226014
$534$	8.10634	0.350795
$535$	9.57484	0.413956
$536$	−87.9196	−3.79755
$537$	18.0112	0.777242
$538$	37.5462	1.61873
$539$	30.7944	1.32641
$540$	18.5948	0.800192
$541$	36.1495	1.55419	0.777093	−	0.629385i	$-0.216693\pi$
$541$	36.1495	1.55419	0.777093	+	0.629385i	$0.216693\pi$
$542$	85.9162	3.69042
$543$	55.0800	2.36371
$544$	106.036	4.54624
$545$	25.1859	1.07885
$546$	−2.55293	−0.109255
$547$	−26.4982	−1.13298	−0.566490	−	0.824069i	$-0.691699\pi$
$547$	−26.4982	−1.13298	−0.566490	+	0.824069i	$0.691699\pi$
$548$	47.9287	2.04741
$549$	20.5352	0.876422
$550$	−20.5487	−0.876200
$551$	−0.344613	−0.0146810
$552$	−11.6980	−0.497898
$553$	6.04167	0.256918
$554$	6.98950	0.296956
$555$	18.8778	0.801320
$556$	52.7574	2.23741
$557$	−29.7278	−1.25961	−0.629805	−	0.776754i	$-0.716865\pi$
$557$	−29.7278	−1.25961	−0.629805	+	0.776754i	$0.716865\pi$
$558$	−55.7951	−2.36200
$559$	6.43335	0.272102
$560$	12.2981	0.519691
$561$	78.4070	3.31035
$562$	−0.931832	−0.0393069
$563$	−3.43710	−0.144856	−0.0724282	−	0.997374i	$-0.523075\pi$
$563$	−3.43710	−0.144856	−0.0724282	+	0.997374i	$0.523075\pi$
$564$	110.949	4.67179
$565$	35.4110	1.48975
$566$	−76.9151	−3.23298
$567$	6.41404	0.269364
$568$	−63.9317	−2.68252
$569$	38.6378	1.61978	0.809891	−	0.586581i	$-0.199526\pi$
$569$	38.6378	1.61978	0.809891	+	0.586581i	$0.199526\pi$
$570$	−2.96945	−0.124377
$571$	17.9548	0.751384	0.375692	−	0.926745i	$-0.377405\pi$
$571$	17.9548	0.751384	0.375692	+	0.926745i	$0.377405\pi$
$572$	16.8793	0.705761
$573$	44.0792	1.84144
$574$	−11.3229	−0.472609
$575$	−1.06657	−0.0444792
$576$	30.9965	1.29152
$577$	33.3648	1.38900	0.694498	−	0.719494i	$-0.255626\pi$
$577$	33.3648	1.38900	0.694498	+	0.719494i	$0.255626\pi$
$578$	−104.036	−4.32732
$579$	8.18528	0.340169
$580$	−11.7188	−0.486596
$581$	−0.458126	−0.0190063
$582$	−21.8260	−0.904717
$583$	−39.1136	−1.61992
$584$	−58.0679	−2.40287
$585$	2.77442	0.114708
$586$	−13.6463	−0.563724
$587$	−14.3670	−0.592989	−0.296495	−	0.955035i	$-0.595818\pi$
$587$	−14.3670	−0.592989	−0.296495	+	0.955035i	$0.595818\pi$
$588$	−75.9859	−3.13361
$589$	−2.70263	−0.111360
$590$	−25.7813	−1.06140
$591$	58.6380	2.41204
$592$	−52.3532	−2.15170
$593$	26.9654	1.10734	0.553668	−	0.832737i	$-0.313228\pi$
$593$	26.9654	1.10734	0.553668	+	0.832737i	$0.313228\pi$
$594$	−24.7930	−1.01727
$595$	−8.06049	−0.330448
$596$	−14.0880	−0.577066
$597$	24.2892	0.994090
$598$	1.22282	0.0500048
$599$	34.8993	1.42595	0.712974	−	0.701190i	$-0.247348\pi$
$599$	34.8993	1.42595	0.712974	+	0.701190i	$0.247348\pi$
$600$	30.6394	1.25085
$601$	−28.9550	−1.18110	−0.590550	−	0.807001i	$-0.701089\pi$
$601$	−28.9550	−1.18110	−0.590550	+	0.807001i	$0.701089\pi$
$602$	−13.9603	−0.568980
$603$	22.8458	0.930353
$604$	76.1445	3.09828
$605$	−19.0245	−0.773454
$606$	94.8781	3.85416
$607$	−6.52006	−0.264641	−0.132320	−	0.991207i	$-0.542243\pi$
$607$	−6.52006	−0.264641	−0.132320	+	0.991207i	$0.542243\pi$
$608$	3.83629	0.155582
$609$	−1.69318	−0.0686112
$610$	47.2106	1.91150
$611$	−7.00824	−0.283523
$612$	−79.8362	−3.22719
$613$	36.6332	1.47960	0.739800	−	0.672827i	$-0.234920\pi$
$613$	36.6332	1.47960	0.739800	+	0.672827i	$0.234920\pi$
$614$	−56.8349	−2.29367
$615$	29.8200	1.20246
$616$	−22.1334	−0.891780
$617$	−39.7467	−1.60014	−0.800070	−	0.599906i	$-0.795205\pi$
$617$	−39.7467	−1.60014	−0.800070	+	0.599906i	$0.795205\pi$
$618$	−89.9840	−3.61969
$619$	15.7473	0.632936	0.316468	−	0.948603i	$-0.397503\pi$
$619$	15.7473	0.632936	0.316468	+	0.948603i	$0.397503\pi$
$620$	−91.9045	−3.69097
$621$	−1.28687	−0.0516404
$622$	−89.0780	−3.57170
$623$	0.796102	0.0318952
$624$	−18.6458	−0.746429
$625$	−13.8494	−0.553976
$626$	41.0561	1.64093
$627$	2.83670	0.113287
$628$	−82.0656	−3.27477
$629$	34.3135	1.36817
$630$	−6.02049	−0.239862
$631$	−28.8552	−1.14871	−0.574354	−	0.818607i	$-0.694747\pi$
$631$	−28.8552	−1.14871	−0.574354	+	0.818607i	$0.694747\pi$
$632$	83.1322	3.30682
$633$	21.5665	0.857192
$634$	−38.5990	−1.53296
$635$	−23.1356	−0.918109
$636$	96.5139	3.82703
$637$	4.79976	0.190173
$638$	15.6250	0.618600
$639$	16.6126	0.657184
$640$	19.6367	0.776209
$641$	41.0628	1.62188	0.810941	−	0.585128i	$-0.198956\pi$
$641$	41.0628	1.62188	0.810941	+	0.585128i	$0.198956\pi$
$642$	31.5015	1.24326
$643$	28.3667	1.11867	0.559337	−	0.828940i	$-0.311056\pi$
$643$	28.3667	1.11867	0.559337	+	0.828940i	$0.311056\pi$
$644$	−1.90117	−0.0749165
$645$	36.7660	1.44766
$646$	−5.39746	−0.212360
$647$	−23.1022	−0.908239	−0.454120	−	0.890941i	$-0.650046\pi$
$647$	−23.1022	−0.908239	−0.454120	+	0.890941i	$0.650046\pi$
$648$	88.2560	3.46702
$649$	24.6288	0.966764
$650$	−3.20282	−0.125625
$651$	−13.2788	−0.520436
$652$	35.7012	1.39817
$653$	2.86487	0.112111	0.0560556	−	0.998428i	$-0.482148\pi$
$653$	2.86487	0.112111	0.0560556	+	0.998428i	$0.482148\pi$
$654$	82.8623	3.24017
$655$	16.7399	0.654081
$656$	−82.6988	−3.22884
$657$	15.0889	0.588673
$658$	15.2078	0.592863
$659$	18.1761	0.708040	0.354020	−	0.935238i	$-0.384814\pi$
$659$	18.1761	0.708040	0.354020	+	0.935238i	$0.384814\pi$
$660$	96.4639	3.75485
$661$	−16.4297	−0.639041	−0.319520	−	0.947579i	$-0.603522\pi$
$661$	−16.4297	−0.639041	−0.319520	+	0.947579i	$0.603522\pi$
$662$	52.5788	2.04353
$663$	12.2209	0.474620
$664$	−6.30373	−0.244632
$665$	−0.291622	−0.0113086
$666$	25.6292	0.993111
$667$	0.811011	0.0314025
$668$	99.1697	3.83699
$669$	19.6330	0.759054
$670$	52.5227	2.02913
$671$	−45.1001	−1.74107
$672$	18.8488	0.727107
$673$	−2.64608	−0.101999	−0.0509994	−	0.998699i	$-0.516241\pi$
$673$	−2.64608	−0.101999	−0.0509994	+	0.998699i	$0.516241\pi$
$674$	−72.8943	−2.80778
$675$	3.37059	0.129734
$676$	−63.0711	−2.42581
$677$	−23.4947	−0.902976	−0.451488	−	0.892277i	$-0.649107\pi$
$677$	−23.4947	−0.902976	−0.451488	+	0.892277i	$0.649107\pi$
$678$	116.503	4.47428
$679$	−2.14347	−0.0822590
$680$	−110.911	−4.25324
$681$	−11.0888	−0.424925
$682$	122.539	4.69226
$683$	21.2647	0.813670	0.406835	−	0.913502i	$-0.366632\pi$
$683$	21.2647	0.813670	0.406835	+	0.913502i	$0.366632\pi$
$684$	−2.88841	−0.110441
$685$	−17.3018	−0.661068
$686$	−21.3749	−0.816099
$687$	17.9131	0.683427
$688$	−101.962	−3.88725
$689$	−6.09644	−0.232256
$690$	6.98830	0.266040
$691$	−23.0255	−0.875933	−0.437966	−	0.898991i	$-0.644301\pi$
$691$	−23.0255	−0.875933	−0.437966	+	0.898991i	$0.644301\pi$
$692$	−43.7265	−1.66223
$693$	5.75134	0.218475
$694$	2.11361	0.0802314
$695$	−19.0449	−0.722415
$696$	−23.2979	−0.883103
$697$	54.2027	2.05307
$698$	90.6192	3.42999
$699$	47.7412	1.80574
$700$	4.97956	0.188210
$701$	−44.3258	−1.67416	−0.837081	−	0.547079i	$-0.815740\pi$
$701$	−44.3258	−1.67416	−0.837081	+	0.547079i	$0.815740\pi$
$702$	−3.86435	−0.145851
$703$	1.24144	0.0468217
$704$	−68.0755	−2.56569
$705$	−40.0514	−1.50842
$706$	17.5741	0.661410
$707$	9.31773	0.350429
$708$	−60.7722	−2.28396
$709$	−24.5317	−0.921306	−0.460653	−	0.887580i	$-0.652385\pi$
$709$	−24.5317	−0.921306	−0.460653	+	0.887580i	$0.652385\pi$
$710$	38.1925	1.43334
$711$	−21.6018	−0.810132
$712$	10.9542	0.410527
$713$	6.36035	0.238197
$714$	−26.5193	−0.992458
$715$	−6.09328	−0.227876
$716$	40.2779	1.50525
$717$	−3.73255	−0.139394
$718$	−43.7504	−1.63275
$719$	27.7979	1.03669	0.518344	−	0.855172i	$-0.326549\pi$
$719$	27.7979	1.03669	0.518344	+	0.855172i	$0.326549\pi$
$720$	−43.9717	−1.63873
$721$	−8.83710	−0.329111
$722$	50.2675	1.87076
$723$	−51.1310	−1.90158
$724$	123.173	4.57770
$725$	−2.12421	−0.0788911
$726$	−62.5910	−2.32297
$727$	47.0499	1.74498	0.872492	−	0.488628i	$-0.162503\pi$
$727$	47.0499	1.74498	0.872492	+	0.488628i	$0.162503\pi$
$728$	−3.44982	−0.127859
$729$	−9.26039	−0.342977
$730$	34.6895	1.28391
$731$	66.8281	2.47173
$732$	111.286	4.11324
$733$	12.6285	0.466445	0.233222	−	0.972423i	$-0.425073\pi$
$733$	12.6285	0.466445	0.233222	+	0.972423i	$0.425073\pi$
$734$	66.8669	2.46810
$735$	27.4302	1.01178
$736$	−9.02830	−0.332787
$737$	−50.1747	−1.84821
$738$	40.4847	1.49026
$739$	45.6504	1.67928	0.839639	−	0.543144i	$-0.182766\pi$
$739$	45.6504	1.67928	0.839639	+	0.543144i	$0.182766\pi$
$740$	42.2158	1.55188
$741$	0.442142	0.0162425
$742$	13.2292	0.485660
$743$	27.2374	0.999244	0.499622	−	0.866244i	$-0.333472\pi$
$743$	27.2374	0.999244	0.499622	+	0.866244i	$0.333472\pi$
$744$	−182.713	−6.69860
$745$	5.08562	0.186323
$746$	43.9640	1.60963
$747$	1.63802	0.0599320
$748$	175.339	6.41102
$749$	3.09368	0.113041
$750$	−73.0597	−2.66776
$751$	−46.7958	−1.70760	−0.853802	−	0.520598i	$-0.825709\pi$
$751$	−46.7958	−1.70760	−0.853802	+	0.520598i	$0.825709\pi$
$752$	111.073	4.05042
$753$	−36.0893	−1.31517
$754$	2.43539	0.0886916
$755$	−27.4874	−1.00037
$756$	6.00807	0.218512
$757$	8.75111	0.318065	0.159032	−	0.987273i	$-0.449163\pi$
$757$	8.75111	0.318065	0.159032	+	0.987273i	$0.449163\pi$
$758$	−62.3401	−2.26429
$759$	−6.67589	−0.242319
$760$	−4.01267	−0.145555
$761$	10.4006	0.377023	0.188511	−	0.982071i	$-0.439634\pi$
$761$	10.4006	0.377023	0.188511	+	0.982071i	$0.439634\pi$
$762$	−76.1168	−2.75742
$763$	8.13770	0.294604
$764$	98.5728	3.56624
$765$	28.8201	1.04199
$766$	−55.2818	−1.99741
$767$	3.83876	0.138610
$768$	−1.86800	−0.0674058
$769$	24.7691	0.893196	0.446598	−	0.894735i	$-0.352635\pi$
$769$	24.7691	0.893196	0.446598	+	0.894735i	$0.352635\pi$
$770$	13.2224	0.476501
$771$	−7.57010	−0.272630
$772$	18.3044	0.658791
$773$	−13.0453	−0.469208	−0.234604	−	0.972091i	$-0.575379\pi$
$773$	−13.0453	−0.469208	−0.234604	+	0.972091i	$0.575379\pi$
$774$	49.9148	1.79415
$775$	−16.6591	−0.598412
$776$	−29.4938	−1.05877
$777$	6.09953	0.218819
$778$	24.1528	0.865920
$779$	1.96101	0.0702606
$780$	15.0353	0.538351
$781$	−36.4851	−1.30554
$782$	12.7024	0.454235
$783$	−2.56296	−0.0915926
$784$	−76.0710	−2.71682
$785$	29.6248	1.05736
$786$	55.0746	1.96445
$787$	−19.1588	−0.682938	−0.341469	−	0.939893i	$-0.610924\pi$
$787$	−19.1588	−0.682938	−0.341469	+	0.939893i	$0.610924\pi$
$788$	131.130	4.67131
$789$	−8.01554	−0.285361
$790$	−49.6627	−1.76692
$791$	11.4415	0.406812
$792$	79.1374	2.81202
$793$	−7.02952	−0.249625
$794$	59.9572	2.12780
$795$	−34.8406	−1.23567
$796$	54.3170	1.92522
$797$	17.3845	0.615791	0.307895	−	0.951420i	$-0.400375\pi$
$797$	17.3845	0.615791	0.307895	+	0.951420i	$0.400375\pi$
$798$	−0.959446	−0.0339640
$799$	−72.7999	−2.57548
$800$	23.6470	0.836048
$801$	−2.84644	−0.100574
$802$	−25.3206	−0.894103
$803$	−33.1387	−1.16944
$804$	123.807	4.36635
$805$	0.686303	0.0241890
$806$	19.0995	0.672752
$807$	−31.9492	−1.12467
$808$	128.210	4.51042
$809$	−45.8232	−1.61106	−0.805529	−	0.592556i	$-0.798119\pi$
$809$	−45.8232	−1.61106	−0.805529	+	0.592556i	$0.798119\pi$
$810$	−52.7237	−1.85252
$811$	−15.2785	−0.536499	−0.268250	−	0.963349i	$-0.586445\pi$
$811$	−15.2785	−0.536499	−0.268250	+	0.963349i	$0.586445\pi$
$812$	−3.78640	−0.132877
$813$	−73.1088	−2.56404
$814$	−56.2876	−1.97288
$815$	−12.8878	−0.451439
$816$	−193.688	−6.78044
$817$	2.41779	0.0845878
$818$	−50.5601	−1.76779
$819$	0.896431	0.0313238
$820$	66.6855	2.32876
$821$	−36.1535	−1.26176	−0.630882	−	0.775878i	$-0.717307\pi$
$821$	−36.1535	−1.26176	−0.630882	+	0.775878i	$0.717307\pi$
$822$	−56.9234	−1.98543
$823$	38.5113	1.34242	0.671210	−	0.741268i	$-0.265775\pi$
$823$	38.5113	1.34242	0.671210	+	0.741268i	$0.265775\pi$
$824$	−121.597	−4.23603
$825$	17.4856	0.608769
$826$	−8.33009	−0.289841
$827$	2.33940	0.0813490	0.0406745	−	0.999172i	$-0.487049\pi$
$827$	2.33940	0.0813490	0.0406745	+	0.999172i	$0.487049\pi$
$828$	6.79758	0.236232
$829$	41.6185	1.44547	0.722736	−	0.691124i	$-0.242884\pi$
$829$	41.6185	1.44547	0.722736	+	0.691124i	$0.242884\pi$
$830$	3.76582	0.130713
$831$	−5.94759	−0.206320
$832$	−10.6106	−0.367855
$833$	49.8587	1.72750
$834$	−62.6583	−2.16968
$835$	−35.7993	−1.23888
$836$	6.34362	0.219399
$837$	−20.1000	−0.694756
$838$	33.7282	1.16512
$839$	42.4787	1.46653	0.733264	−	0.679944i	$-0.237996\pi$
$839$	42.4787	1.46653	0.733264	+	0.679944i	$0.237996\pi$
$840$	−19.7154	−0.680246
$841$	−27.3848	−0.944303
$842$	29.9662	1.03270
$843$	0.792925	0.0273098
$844$	48.2284	1.66009
$845$	22.7681	0.783245
$846$	−54.3752	−1.86946
$847$	−6.14690	−0.211210
$848$	96.6220	3.31801
$849$	65.4495	2.24622
$850$	−33.2701	−1.14116
$851$	−2.92159	−0.100151
$852$	90.0279	3.08431
$853$	31.6750	1.08453	0.542265	−	0.840207i	$-0.317567\pi$
$853$	31.6750	1.08453	0.542265	+	0.840207i	$0.317567\pi$
$854$	15.2540	0.521981
$855$	1.04269	0.0356592
$856$	42.5685	1.45496
$857$	2.17240	0.0742078	0.0371039	−	0.999311i	$-0.488187\pi$
$857$	2.17240	0.0742078	0.0371039	+	0.999311i	$0.488187\pi$
$858$	−20.0471	−0.684395
$859$	21.2968	0.726636	0.363318	−	0.931665i	$-0.381644\pi$
$859$	21.2968	0.726636	0.363318	+	0.931665i	$0.381644\pi$
$860$	82.2184	2.80363
$861$	9.63501	0.328360
$862$	30.7874	1.04862
$863$	−37.6701	−1.28231	−0.641153	−	0.767413i	$-0.721544\pi$
$863$	−37.6701	−1.28231	−0.641153	+	0.767413i	$0.721544\pi$
$864$	28.5312	0.970652
$865$	15.7848	0.536700
$866$	−39.2289	−1.33305
$867$	88.5274	3.00655
$868$	−29.6948	−1.00791
$869$	47.4426	1.60938
$870$	13.9180	0.471865
$871$	−7.82046	−0.264986
$872$	111.973	3.79189
$873$	7.66393	0.259385
$874$	0.459562	0.0155449
$875$	−7.17501	−0.242560
$876$	81.7706	2.76277
$877$	29.0469	0.980844	0.490422	−	0.871485i	$-0.336843\pi$
$877$	29.0469	0.980844	0.490422	+	0.871485i	$0.336843\pi$
$878$	1.54407	0.0521099
$879$	11.6121	0.391666
$880$	96.5719	3.25544
$881$	−44.6213	−1.50333	−0.751664	−	0.659546i	$-0.770749\pi$
$881$	−44.6213	−1.50333	−0.751664	+	0.659546i	$0.770749\pi$
$882$	37.2401	1.25394
$883$	−29.7745	−1.00199	−0.500996	−	0.865450i	$-0.667033\pi$
$883$	−29.7745	−1.00199	−0.500996	+	0.865450i	$0.667033\pi$
$884$	27.3291	0.919178
$885$	21.9382	0.737443
$886$	31.4359	1.05611
$887$	17.6227	0.591711	0.295856	−	0.955233i	$-0.404395\pi$
$887$	17.6227	0.591711	0.295856	+	0.955233i	$0.404395\pi$
$888$	83.9284	2.81645
$889$	−7.47524	−0.250711
$890$	−6.54399	−0.219355
$891$	50.3666	1.68735
$892$	43.9045	1.47003
$893$	−2.63385	−0.0881383
$894$	16.7318	0.559596
$895$	−14.5399	−0.486015
$896$	6.34472	0.211962
$897$	−1.04054	−0.0347425
$898$	−3.00038	−0.100124
$899$	12.6674	0.422481
$900$	−17.8043	−0.593476
$901$	−63.3283	−2.10977
$902$	−88.9137	−2.96050
$903$	11.8793	0.395318
$904$	157.433	5.23613
$905$	−44.4644	−1.47805
$906$	−90.4344	−3.00448
$907$	9.67583	0.321281	0.160640	−	0.987013i	$-0.448644\pi$
$907$	9.67583	0.321281	0.160640	+	0.987013i	$0.448644\pi$
$908$	−24.7975	−0.822936
$909$	−33.3153	−1.10500
$910$	2.06090	0.0683182
$911$	−1.43889	−0.0476724	−0.0238362	−	0.999716i	$-0.507588\pi$
$911$	−1.43889	−0.0476724	−0.0238362	+	0.999716i	$0.507588\pi$
$912$	−7.00748	−0.232041
$913$	−3.59747	−0.119059
$914$	77.7860	2.57293
$915$	−40.1730	−1.32808
$916$	40.0584	1.32357
$917$	5.40874	0.178612
$918$	−40.1420	−1.32488
$919$	13.1244	0.432933	0.216467	−	0.976290i	$-0.430547\pi$
$919$	13.1244	0.432933	0.216467	+	0.976290i	$0.430547\pi$
$920$	9.44340	0.311340
$921$	48.3626	1.59360
$922$	−48.3362	−1.59187
$923$	−5.68674	−0.187181
$924$	31.1680	1.02535
$925$	7.65226	0.251605
$926$	73.6150	2.41914
$927$	31.5968	1.03777
$928$	−17.9809	−0.590252
$929$	25.8207	0.847149	0.423575	−	0.905861i	$-0.360775\pi$
$929$	25.8207	0.847149	0.423575	+	0.905861i	$0.360775\pi$
$930$	109.152	3.57923
$931$	1.80385	0.0591188
$932$	106.762	3.49710
$933$	75.7993	2.48156
$934$	−56.9370	−1.86304
$935$	−63.2955	−2.06998
$936$	12.3347	0.403173
$937$	45.8209	1.49690	0.748452	−	0.663189i	$-0.230798\pi$
$937$	45.8209	1.49690	0.748452	+	0.663189i	$0.230798\pi$
$938$	16.9704	0.554102
$939$	−34.9360	−1.14009
$940$	−89.5655	−2.92131
$941$	1.46473	0.0477489	0.0238744	−	0.999715i	$-0.492400\pi$
$941$	1.46473	0.0477489	0.0238744	+	0.999715i	$0.492400\pi$
$942$	97.4666	3.17563
$943$	−4.61504	−0.150286
$944$	−60.8403	−1.98018
$945$	−2.16885	−0.0705528
$946$	−109.624	−3.56419
$947$	15.7000	0.510183	0.255091	−	0.966917i	$-0.417894\pi$
$947$	15.7000	0.510183	0.255091	+	0.966917i	$0.417894\pi$
$948$	−117.066	−3.80212
$949$	−5.16515	−0.167668
$950$	−1.20369	−0.0390528
$951$	32.8451	1.06508
$952$	−35.8359	−1.16145
$953$	−36.1360	−1.17056	−0.585279	−	0.810832i	$-0.699015\pi$
$953$	−36.1360	−1.17056	−0.585279	+	0.810832i	$0.699015\pi$
$954$	−47.3007	−1.53142
$955$	−35.5838	−1.15146
$956$	−8.34695	−0.269960
$957$	−13.2958	−0.429792
$958$	−40.3277	−1.30293
$959$	−5.59030	−0.180520
$960$	−60.6385	−1.95710
$961$	68.3438	2.20464
$962$	−8.77326	−0.282861
$963$	−11.0614	−0.356448
$964$	−114.342	−3.68272
$965$	−6.60772	−0.212710
$966$	2.25796	0.0726485
$967$	42.2522	1.35874	0.679369	−	0.733797i	$-0.262254\pi$
$967$	42.2522	1.35874	0.679369	+	0.733797i	$0.262254\pi$
$968$	−84.5802	−2.71851
$969$	4.59287	0.147544
$970$	17.6194	0.565726
$971$	−31.7947	−1.02034	−0.510170	−	0.860074i	$-0.670418\pi$
$971$	−31.7947	−1.02034	−0.510170	+	0.860074i	$0.670418\pi$
$972$	−93.7050	−3.00559
$973$	−6.15351	−0.197272
$974$	112.505	3.60488
$975$	2.72538	0.0872821
$976$	111.410	3.56616
$977$	−11.7077	−0.374562	−0.187281	−	0.982306i	$-0.559968\pi$
$977$	−11.7077	−0.374562	−0.187281	+	0.982306i	$0.559968\pi$
$978$	−42.4011	−1.35584
$979$	6.25144	0.199797
$980$	61.3411	1.95947
$981$	−29.0961	−0.928967
$982$	53.2461	1.69915
$983$	34.0822	1.08705	0.543527	−	0.839392i	$-0.317088\pi$
$983$	34.0822	1.08705	0.543527	+	0.839392i	$0.317088\pi$
$984$	132.576	4.22637
$985$	−47.3366	−1.50827
$986$	25.2982	0.805660
$987$	−12.9408	−0.411911
$988$	0.988747	0.0314562
$989$	−5.69001	−0.180932
$990$	−47.2762	−1.50254
$991$	−37.8780	−1.20324	−0.601618	−	0.798784i	$-0.705477\pi$
$991$	−37.8780	−1.20324	−0.601618	+	0.798784i	$0.705477\pi$
$992$	−141.015	−4.47724
$993$	−44.7410	−1.41981
$994$	12.3402	0.391407
$995$	−19.6079	−0.621612
$996$	8.87685	0.281274
$997$	−23.6320	−0.748433	−0.374217	−	0.927341i	$-0.622088\pi$
$997$	−23.6320	−0.748433	−0.374217	+	0.927341i	$0.622088\pi$
$998$	−1.32151	−0.0418317
$999$	9.23281	0.292113

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.b.1.9	✓	287

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.b.1.9	✓	287	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:	\( N \)	\(=\)	\( 6047 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65594 q^{2} +2.26002 q^{3} +5.05400 q^{4} -1.82444 q^{5} -6.00248 q^{6} -0.589488 q^{7} -8.11124 q^{8} +2.10770 q^{9} +O(q^{10})\)	\(q-2.65594 q^{2} +2.26002 q^{3} +5.05400 q^{4} -1.82444 q^{5} -6.00248 q^{6} -0.589488 q^{7} -8.11124 q^{8} +2.10770 q^{9} +4.84561 q^{10} -4.62899 q^{11} +11.4222 q^{12} -0.721496 q^{13} +1.56564 q^{14} -4.12328 q^{15} +11.4349 q^{16} -7.49473 q^{17} -5.59791 q^{18} -0.271154 q^{19} -9.22075 q^{20} -1.33225 q^{21} +12.2943 q^{22} +0.638132 q^{23} -18.3316 q^{24} -1.67140 q^{25} +1.91625 q^{26} -2.01662 q^{27} -2.97927 q^{28} +1.27091 q^{29} +10.9512 q^{30} +9.96714 q^{31} -14.1480 q^{32} -10.4616 q^{33} +19.9055 q^{34} +1.07549 q^{35} +10.6523 q^{36} -4.57835 q^{37} +0.720167 q^{38} -1.63060 q^{39} +14.7985 q^{40} -7.23211 q^{41} +3.53839 q^{42} -8.91668 q^{43} -23.3949 q^{44} -3.84538 q^{45} -1.69484 q^{46} +9.71348 q^{47} +25.8432 q^{48} -6.65250 q^{49} +4.43914 q^{50} -16.9383 q^{51} -3.64644 q^{52} +8.44971 q^{53} +5.35603 q^{54} +8.44533 q^{55} +4.78148 q^{56} -0.612813 q^{57} -3.37547 q^{58} -5.32056 q^{59} -20.8391 q^{60} +9.74297 q^{61} -26.4721 q^{62} -1.24246 q^{63} +14.7063 q^{64} +1.31633 q^{65} +27.7854 q^{66} +10.8392 q^{67} -37.8784 q^{68} +1.44219 q^{69} -2.85643 q^{70} +7.88187 q^{71} -17.0960 q^{72} +7.15894 q^{73} +12.1598 q^{74} -3.77740 q^{75} -1.37041 q^{76} +2.72873 q^{77} +4.33076 q^{78} -10.2490 q^{79} -20.8624 q^{80} -10.8807 q^{81} +19.2080 q^{82} +0.777160 q^{83} -6.73322 q^{84} +13.6737 q^{85} +23.6821 q^{86} +2.87229 q^{87} +37.5468 q^{88} -1.35050 q^{89} +10.2131 q^{90} +0.425313 q^{91} +3.22512 q^{92} +22.5259 q^{93} -25.7984 q^{94} +0.494705 q^{95} -31.9748 q^{96} +3.63617 q^{97} +17.6686 q^{98} -9.75650 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * q^99

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