LMFDB - Embedded newform 8021.2.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52538 q^{2} +0.561190 q^{3} +4.37756 q^{4} +2.21627 q^{5} -1.41722 q^{6} -4.18126 q^{7} -6.00425 q^{8} -2.68507 q^{9} +O(q^{10})$	\(q-2.52538 q^{2} +0.561190 q^{3} +4.37756 q^{4} +2.21627 q^{5} -1.41722 q^{6} -4.18126 q^{7} -6.00425 q^{8} -2.68507 q^{9} -5.59693 q^{10} -0.438957 q^{11} +2.45664 q^{12} -1.00000 q^{13} +10.5593 q^{14} +1.24375 q^{15} +6.40791 q^{16} -4.31308 q^{17} +6.78082 q^{18} -7.53294 q^{19} +9.70185 q^{20} -2.34648 q^{21} +1.10853 q^{22} +3.11748 q^{23} -3.36952 q^{24} -0.0881546 q^{25} +2.52538 q^{26} -3.19040 q^{27} -18.3037 q^{28} +5.50046 q^{29} -3.14094 q^{30} -1.31263 q^{31} -4.17393 q^{32} -0.246338 q^{33} +10.8922 q^{34} -9.26680 q^{35} -11.7540 q^{36} -3.88134 q^{37} +19.0236 q^{38} -0.561190 q^{39} -13.3070 q^{40} +4.96565 q^{41} +5.92577 q^{42} -9.13582 q^{43} -1.92156 q^{44} -5.95083 q^{45} -7.87284 q^{46} +9.01762 q^{47} +3.59605 q^{48} +10.4830 q^{49} +0.222624 q^{50} -2.42046 q^{51} -4.37756 q^{52} -4.30197 q^{53} +8.05698 q^{54} -0.972847 q^{55} +25.1054 q^{56} -4.22741 q^{57} -13.8908 q^{58} +13.3601 q^{59} +5.44458 q^{60} -15.2474 q^{61} +3.31490 q^{62} +11.2270 q^{63} -2.27505 q^{64} -2.21627 q^{65} +0.622098 q^{66} -0.147191 q^{67} -18.8808 q^{68} +1.74950 q^{69} +23.4022 q^{70} -1.73322 q^{71} +16.1218 q^{72} +12.0797 q^{73} +9.80187 q^{74} -0.0494715 q^{75} -32.9759 q^{76} +1.83540 q^{77} +1.41722 q^{78} -0.742504 q^{79} +14.2017 q^{80} +6.26478 q^{81} -12.5402 q^{82} -18.0524 q^{83} -10.2719 q^{84} -9.55894 q^{85} +23.0715 q^{86} +3.08680 q^{87} +2.63561 q^{88} -11.3749 q^{89} +15.0281 q^{90} +4.18126 q^{91} +13.6470 q^{92} -0.736635 q^{93} -22.7729 q^{94} -16.6950 q^{95} -2.34237 q^{96} -6.23376 q^{97} -26.4735 q^{98} +1.17863 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) $ 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * 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 $

$2$	−2.52538	−1.78572	−0.892858	−	0.450339i	$-0.851303\pi$
$2$	−2.52538	−1.78572	−0.892858	+	0.450339i	$0.851303\pi$
$3$	0.561190	0.324003	0.162002	−	0.986791i	$-0.448205\pi$
$3$	0.561190	0.324003	0.162002	+	0.986791i	$0.448205\pi$
$4$	4.37756	2.18878
$5$	2.21627	0.991145	0.495573	−	0.868566i	$-0.334958\pi$
$5$	2.21627	0.991145	0.495573	+	0.868566i	$0.334958\pi$
$6$	−1.41722	−0.578577
$7$	−4.18126	−1.58037	−0.790185	−	0.612869i	$-0.790015\pi$
$7$	−4.18126	−1.58037	−0.790185	+	0.612869i	$0.790015\pi$
$8$	−6.00425	−2.12282
$9$	−2.68507	−0.895022
$10$	−5.59693	−1.76990
$11$	−0.438957	−0.132351	−0.0661753	−	0.997808i	$-0.521080\pi$
$11$	−0.438957	−0.132351	−0.0661753	+	0.997808i	$0.521080\pi$
$12$	2.45664	0.709171
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	10.5593	2.82209
$15$	1.24375	0.321134
$16$	6.40791	1.60198
$17$	−4.31308	−1.04608	−0.523038	−	0.852309i	$-0.675201\pi$
$17$	−4.31308	−1.04608	−0.523038	+	0.852309i	$0.675201\pi$
$18$	6.78082	1.59825
$19$	−7.53294	−1.72818	−0.864088	−	0.503341i	$-0.832104\pi$
$19$	−7.53294	−1.72818	−0.864088	+	0.503341i	$0.832104\pi$
$20$	9.70185	2.16940
$21$	−2.34648	−0.512044
$22$	1.10853	0.236340
$23$	3.11748	0.650040	0.325020	−	0.945707i	$-0.394629\pi$
$23$	3.11748	0.650040	0.325020	+	0.945707i	$0.394629\pi$
$24$	−3.36952	−0.687801
$25$	−0.0881546	−0.0176309
$26$	2.52538	0.495268
$27$	−3.19040	−0.613993
$28$	−18.3037	−3.45908
$29$	5.50046	1.02141	0.510705	−	0.859756i	$-0.329384\pi$
$29$	5.50046	1.02141	0.510705	+	0.859756i	$0.329384\pi$
$30$	−3.14094	−0.573454
$31$	−1.31263	−0.235755	−0.117878	−	0.993028i	$-0.537609\pi$
$31$	−1.31263	−0.235755	−0.117878	+	0.993028i	$0.537609\pi$
$32$	−4.17393	−0.737854
$33$	−0.246338	−0.0428820
$34$	10.8922	1.86799
$35$	−9.26680	−1.56638
$36$	−11.7540	−1.95901
$37$	−3.88134	−0.638088	−0.319044	−	0.947740i	$-0.603362\pi$
$37$	−3.88134	−0.638088	−0.319044	+	0.947740i	$0.603362\pi$
$38$	19.0236	3.08603
$39$	−0.561190	−0.0898623
$40$	−13.3070	−2.10403
$41$	4.96565	0.775504	0.387752	−	0.921764i	$-0.373252\pi$
$41$	4.96565	0.775504	0.387752	+	0.921764i	$0.373252\pi$
$42$	5.92577	0.914366
$43$	−9.13582	−1.39320	−0.696600	−	0.717460i	$-0.745305\pi$
$43$	−9.13582	−1.39320	−0.696600	+	0.717460i	$0.745305\pi$
$44$	−1.92156	−0.289686
$45$	−5.95083	−0.887097
$46$	−7.87284	−1.16079
$47$	9.01762	1.31535	0.657677	−	0.753300i	$-0.271539\pi$
$47$	9.01762	1.31535	0.657677	+	0.753300i	$0.271539\pi$
$48$	3.59605	0.519046
$49$	10.4830	1.49757
$50$	0.222624	0.0314838
$51$	−2.42046	−0.338932
$52$	−4.37756	−0.607058
$53$	−4.30197	−0.590921	−0.295460	−	0.955355i	$-0.595473\pi$
$53$	−4.30197	−0.590921	−0.295460	+	0.955355i	$0.595473\pi$
$54$	8.05698	1.09642
$55$	−0.972847	−0.131179
$56$	25.1054	3.35484
$57$	−4.22741	−0.559934
$58$	−13.8908	−1.82395
$59$	13.3601	1.73934	0.869668	−	0.493638i	$-0.164333\pi$
$59$	13.3601	1.73934	0.869668	+	0.493638i	$0.164333\pi$
$60$	5.44458	0.702892
$61$	−15.2474	−1.95223	−0.976116	−	0.217249i	$-0.930292\pi$
$61$	−15.2474	−1.95223	−0.976116	+	0.217249i	$0.930292\pi$
$62$	3.31490	0.420992
$63$	11.2270	1.41447
$64$	−2.27505	−0.284381
$65$	−2.21627	−0.274894
$66$	0.622098	0.0765750
$67$	−0.147191	−0.0179822	−0.00899112	−	0.999960i	$-0.502862\pi$
$67$	−0.147191	−0.0179822	−0.00899112	+	0.999960i	$0.502862\pi$
$68$	−18.8808	−2.28963
$69$	1.74950	0.210615
$70$	23.4022	2.79710
$71$	−1.73322	−0.205695	−0.102847	−	0.994697i	$-0.532795\pi$
$71$	−1.73322	−0.205695	−0.102847	+	0.994697i	$0.532795\pi$
$72$	16.1218	1.89997
$73$	12.0797	1.41382	0.706911	−	0.707303i	$-0.250088\pi$
$73$	12.0797	1.41382	0.706911	+	0.707303i	$0.250088\pi$
$74$	9.80187	1.13944
$75$	−0.0494715	−0.00571247
$76$	−32.9759	−3.78260
$77$	1.83540	0.209163
$78$	1.41722	0.160468
$79$	−0.742504	−0.0835382	−0.0417691	−	0.999127i	$-0.513299\pi$
$79$	−0.742504	−0.0835382	−0.0417691	+	0.999127i	$0.513299\pi$
$80$	14.2017	1.58779
$81$	6.26478	0.696087
$82$	−12.5402	−1.38483
$83$	−18.0524	−1.98151	−0.990753	−	0.135676i	$-0.956679\pi$
$83$	−18.0524	−1.98151	−0.990753	+	0.135676i	$0.956679\pi$
$84$	−10.2719	−1.12075
$85$	−9.55894	−1.03681
$86$	23.0715	2.48786
$87$	3.08680	0.330940
$88$	2.63561	0.280957
$89$	−11.3749	−1.20574	−0.602868	−	0.797841i	$-0.705975\pi$
$89$	−11.3749	−1.20574	−0.602868	+	0.797841i	$0.705975\pi$
$90$	15.0281	1.58410
$91$	4.18126	0.438316
$92$	13.6470	1.42279
$93$	−0.736635	−0.0763855
$94$	−22.7729	−2.34885
$95$	−16.6950	−1.71287
$96$	−2.34237	−0.239067
$97$	−6.23376	−0.632942	−0.316471	−	0.948602i	$-0.602498\pi$
$97$	−6.23376	−0.632942	−0.316471	+	0.948602i	$0.602498\pi$
$98$	−26.4735	−2.67423
$99$	1.17863	0.118457
$100$	−0.385902	−0.0385902
$101$	−14.7501	−1.46769	−0.733845	−	0.679317i	$-0.762276\pi$
$101$	−14.7501	−1.46769	−0.733845	+	0.679317i	$0.762276\pi$
$102$	6.11258	0.605236
$103$	1.00145	0.0986761	0.0493380	−	0.998782i	$-0.484289\pi$
$103$	1.00145	0.0986761	0.0493380	+	0.998782i	$0.484289\pi$
$104$	6.00425	0.588765
$105$	−5.20043	−0.507510
$106$	10.8641	1.05522
$107$	−7.05796	−0.682319	−0.341160	−	0.940005i	$-0.610820\pi$
$107$	−7.05796	−0.682319	−0.341160	+	0.940005i	$0.610820\pi$
$108$	−13.9662	−1.34390
$109$	13.2454	1.26868	0.634342	−	0.773053i	$-0.281271\pi$
$109$	13.2454	1.26868	0.634342	+	0.773053i	$0.281271\pi$
$110$	2.45681	0.234248
$111$	−2.17817	−0.206743
$112$	−26.7932	−2.53172
$113$	−13.2034	−1.24207	−0.621035	−	0.783783i	$-0.713287\pi$
$113$	−13.2034	−1.24207	−0.621035	+	0.783783i	$0.713287\pi$
$114$	10.6758	0.999883
$115$	6.90918	0.644284
$116$	24.0786	2.23564
$117$	2.68507	0.248234
$118$	−33.7393	−3.10596
$119$	18.0341	1.65319
$120$	−7.46777	−0.681711
$121$	−10.8073	−0.982483
$122$	38.5056	3.48613
$123$	2.78667	0.251266
$124$	−5.74612	−0.516017
$125$	−11.2767	−1.00862
$126$	−28.3524	−2.52583
$127$	2.45024	0.217424	0.108712	−	0.994073i	$-0.465327\pi$
$127$	2.45024	0.217424	0.108712	+	0.994073i	$0.465327\pi$
$128$	14.0932	1.24568
$129$	−5.12693	−0.451401
$130$	5.59693	0.490883
$131$	−11.1396	−0.973273	−0.486637	−	0.873605i	$-0.661776\pi$
$131$	−11.1396	−0.973273	−0.486637	+	0.873605i	$0.661776\pi$
$132$	−1.07836	−0.0938592
$133$	31.4972	2.73116
$134$	0.371714	0.0321112
$135$	−7.07078	−0.608556
$136$	25.8968	2.22063
$137$	3.78953	0.323761	0.161881	−	0.986810i	$-0.448244\pi$
$137$	3.78953	0.323761	0.161881	+	0.986810i	$0.448244\pi$
$138$	−4.41816	−0.376098
$139$	−4.12176	−0.349603	−0.174801	−	0.984604i	$-0.555928\pi$
$139$	−4.12176	−0.349603	−0.174801	+	0.984604i	$0.555928\pi$
$140$	−40.5660	−3.42845
$141$	5.06059	0.426179
$142$	4.37704	0.367313
$143$	0.438957	0.0367074
$144$	−17.2057	−1.43381
$145$	12.1905	1.01237
$146$	−30.5059	−2.52468
$147$	5.88293	0.485216
$148$	−16.9908	−1.39664
$149$	−6.10482	−0.500126	−0.250063	−	0.968230i	$-0.580451\pi$
$149$	−6.10482	−0.500126	−0.250063	+	0.968230i	$0.580451\pi$
$150$	0.124934	0.0102009
$151$	19.7281	1.60545	0.802725	−	0.596349i	$-0.203382\pi$
$151$	19.7281	1.60545	0.802725	+	0.596349i	$0.203382\pi$
$152$	45.2297	3.66861
$153$	11.5809	0.936261
$154$	−4.63508	−0.373505
$155$	−2.90914	−0.233668
$156$	−2.45664	−0.196689
$157$	−11.8840	−0.948448	−0.474224	−	0.880404i	$-0.657271\pi$
$157$	−11.8840	−0.948448	−0.474224	+	0.880404i	$0.657271\pi$
$158$	1.87511	0.149175
$159$	−2.41422	−0.191460
$160$	−9.25055	−0.731320
$161$	−13.0350	−1.02730
$162$	−15.8210	−1.24301
$163$	−18.4785	−1.44735	−0.723675	−	0.690141i	$-0.757548\pi$
$163$	−18.4785	−1.44735	−0.723675	+	0.690141i	$0.757548\pi$
$164$	21.7374	1.69741
$165$	−0.545952	−0.0425023
$166$	45.5892	3.53841
$167$	−3.33040	−0.257714	−0.128857	−	0.991663i	$-0.541131\pi$
$167$	−3.33040	−0.257714	−0.128857	+	0.991663i	$0.541131\pi$
$168$	14.0889	1.08698
$169$	1.00000	0.0769231
$170$	24.1400	1.85145
$171$	20.2264	1.54676
$172$	−39.9926	−3.04941
$173$	17.4845	1.32932	0.664660	−	0.747146i	$-0.268577\pi$
$173$	17.4845	1.32932	0.664660	+	0.747146i	$0.268577\pi$
$174$	−7.79536	−0.590965
$175$	0.368598	0.0278634
$176$	−2.81280	−0.212023
$177$	7.49754	0.563550
$178$	28.7260	2.15310
$179$	13.2690	0.991770	0.495885	−	0.868388i	$-0.334844\pi$
$179$	13.2690	0.991770	0.495885	+	0.868388i	$0.334844\pi$
$180$	−26.0501	−1.94166
$181$	−12.0245	−0.893771	−0.446885	−	0.894591i	$-0.647467\pi$
$181$	−12.0245	−0.893771	−0.446885	+	0.894591i	$0.647467\pi$
$182$	−10.5593	−0.782707
$183$	−8.55670	−0.632529
$184$	−18.7181	−1.37992
$185$	−8.60209	−0.632438
$186$	1.86028	0.136403
$187$	1.89326	0.138449
$188$	39.4752	2.87902
$189$	13.3399	0.970335
$190$	42.1613	3.05870
$191$	24.2925	1.75774	0.878872	−	0.477058i	$-0.158297\pi$
$191$	24.2925	1.75774	0.878872	+	0.477058i	$0.158297\pi$
$192$	−1.27673	−0.0921403
$193$	−6.85591	−0.493499	−0.246750	−	0.969079i	$-0.579362\pi$
$193$	−6.85591	−0.493499	−0.246750	+	0.969079i	$0.579362\pi$
$194$	15.7426	1.13025
$195$	−1.24375	−0.0890666
$196$	45.8898	3.27784
$197$	20.2539	1.44303	0.721514	−	0.692400i	$-0.243446\pi$
$197$	20.2539	1.44303	0.721514	+	0.692400i	$0.243446\pi$
$198$	−2.97649	−0.211530
$199$	10.2406	0.725939	0.362970	−	0.931801i	$-0.381763\pi$
$199$	10.2406	0.725939	0.362970	+	0.931801i	$0.381763\pi$
$200$	0.529302	0.0374273
$201$	−0.0826021	−0.00582630
$202$	37.2497	2.62088
$203$	−22.9989	−1.61420
$204$	−10.5957	−0.741847
$205$	11.0052	0.768637
$206$	−2.52905	−0.176207
$207$	−8.37065	−0.581800
$208$	−6.40791	−0.444309
$209$	3.30664	0.228725
$210$	13.1331	0.906269
$211$	23.1463	1.59346	0.796730	−	0.604335i	$-0.206561\pi$
$211$	23.1463	1.59346	0.796730	+	0.604335i	$0.206561\pi$
$212$	−18.8321	−1.29340
$213$	−0.972663	−0.0666458
$214$	17.8241	1.21843
$215$	−20.2474	−1.38086
$216$	19.1560	1.30340
$217$	5.48845	0.372581
$218$	−33.4498	−2.26551
$219$	6.77900	0.458083
$220$	−4.25870	−0.287121
$221$	4.31308	0.290129
$222$	5.50071	0.369183
$223$	8.76939	0.587242	0.293621	−	0.955922i	$-0.405140\pi$
$223$	8.76939	0.587242	0.293621	+	0.955922i	$0.405140\pi$
$224$	17.4523	1.16608
$225$	0.236701	0.0157801
$226$	33.3436	2.21798
$227$	19.1557	1.27141	0.635703	−	0.771934i	$-0.280710\pi$
$227$	19.1557	1.27141	0.635703	+	0.771934i	$0.280710\pi$
$228$	−18.5057	−1.22557
$229$	11.6150	0.767540	0.383770	−	0.923429i	$-0.374626\pi$
$229$	11.6150	0.767540	0.383770	+	0.923429i	$0.374626\pi$
$230$	−17.4483	−1.15051
$231$	1.03001	0.0677694
$232$	−33.0261	−2.16827
$233$	−27.6645	−1.81236	−0.906179	−	0.422893i	$-0.861014\pi$
$233$	−27.6645	−1.81236	−0.906179	+	0.422893i	$0.861014\pi$
$234$	−6.78082	−0.443276
$235$	19.9855	1.30371
$236$	58.4846	3.80702
$237$	−0.416685	−0.0270666
$238$	−45.5431	−2.95212
$239$	13.1346	0.849604	0.424802	−	0.905286i	$-0.360344\pi$
$239$	13.1346	0.849604	0.424802	+	0.905286i	$0.360344\pi$
$240$	7.96982	0.514450
$241$	−3.98986	−0.257009	−0.128505	−	0.991709i	$-0.541018\pi$
$241$	−3.98986	−0.257009	−0.128505	+	0.991709i	$0.541018\pi$
$242$	27.2926	1.75444
$243$	13.0869	0.839527
$244$	−66.7465	−4.27301
$245$	23.2331	1.48431
$246$	−7.03741	−0.448689
$247$	7.53294	0.479310
$248$	7.88136	0.500467
$249$	−10.1308	−0.642014
$250$	28.4780	1.80111
$251$	3.08307	0.194602	0.0973009	−	0.995255i	$-0.468979\pi$
$251$	3.08307	0.194602	0.0973009	+	0.995255i	$0.468979\pi$
$252$	49.1467	3.09595
$253$	−1.36844	−0.0860332
$254$	−6.18780	−0.388257
$255$	−5.36438	−0.335931
$256$	−31.0407	−1.94004
$257$	5.02328	0.313343	0.156672	−	0.987651i	$-0.449924\pi$
$257$	5.02328	0.313343	0.156672	+	0.987651i	$0.449924\pi$
$258$	12.9475	0.806074
$259$	16.2289	1.00842
$260$	−9.70185	−0.601683
$261$	−14.7691	−0.914185
$262$	28.1318	1.73799
$263$	1.21042	0.0746376	0.0373188	−	0.999303i	$-0.488118\pi$
$263$	1.21042	0.0746376	0.0373188	+	0.999303i	$0.488118\pi$
$264$	1.47908	0.0910308
$265$	−9.53431	−0.585688
$266$	−79.5425	−4.87707
$267$	−6.38347	−0.390662
$268$	−0.644337	−0.0393592
$269$	28.9809	1.76700	0.883499	−	0.468433i	$-0.155181\pi$
$269$	28.9809	1.76700	0.883499	+	0.468433i	$0.155181\pi$
$270$	17.8564	1.08671
$271$	−1.55814	−0.0946503	−0.0473251	−	0.998880i	$-0.515070\pi$
$271$	−1.55814	−0.0946503	−0.0473251	+	0.998880i	$0.515070\pi$
$272$	−27.6378	−1.67579
$273$	2.34648	0.142016
$274$	−9.57000	−0.578145
$275$	0.0386961	0.00233346
$276$	7.65854	0.460990
$277$	7.95436	0.477931	0.238965	−	0.971028i	$-0.423192\pi$
$277$	7.95436	0.477931	0.238965	+	0.971028i	$0.423192\pi$
$278$	10.4090	0.624291
$279$	3.52450	0.211006
$280$	55.6402	3.32514
$281$	16.1371	0.962658	0.481329	−	0.876540i	$-0.340154\pi$
$281$	16.1371	0.962658	0.481329	+	0.876540i	$0.340154\pi$
$282$	−12.7799	−0.761034
$283$	0.761708	0.0452789	0.0226394	−	0.999744i	$-0.492793\pi$
$283$	0.761708	0.0452789	0.0226394	+	0.999744i	$0.492793\pi$
$284$	−7.58726	−0.450221
$285$	−9.36907	−0.554976
$286$	−1.10853	−0.0655490
$287$	−20.7627	−1.22558
$288$	11.2073	0.660395
$289$	1.60267	0.0942744
$290$	−30.7857	−1.80780
$291$	−3.49832	−0.205075
$292$	52.8796	3.09455
$293$	0.323100	0.0188757	0.00943786	−	0.999955i	$-0.496996\pi$
$293$	0.323100	0.0188757	0.00943786	+	0.999955i	$0.496996\pi$
$294$	−14.8567	−0.866458
$295$	29.6095	1.72393
$296$	23.3045	1.35455
$297$	1.40045	0.0812623
$298$	15.4170	0.893083
$299$	−3.11748	−0.180289
$300$	−0.216564	−0.0125033
$301$	38.1993	2.20177
$302$	−49.8210	−2.86688
$303$	−8.27761	−0.475536
$304$	−48.2704	−2.76850
$305$	−33.7924	−1.93495
$306$	−29.2462	−1.67190
$307$	22.1054	1.26162	0.630810	−	0.775938i	$-0.282723\pi$
$307$	22.1054	1.26162	0.630810	+	0.775938i	$0.282723\pi$
$308$	8.03455	0.457811
$309$	0.562005	0.0319713
$310$	7.34670	0.417264
$311$	19.9134	1.12919	0.564593	−	0.825370i	$-0.309033\pi$
$311$	19.9134	1.12919	0.564593	+	0.825370i	$0.309033\pi$
$312$	3.36952	0.190762
$313$	−21.7020	−1.22667	−0.613335	−	0.789823i	$-0.710172\pi$
$313$	−21.7020	−1.22667	−0.613335	+	0.789823i	$0.710172\pi$
$314$	30.0117	1.69366
$315$	24.8820	1.40194
$316$	−3.25035	−0.182847
$317$	17.4840	0.981998	0.490999	−	0.871160i	$-0.336632\pi$
$317$	17.4840	0.981998	0.490999	+	0.871160i	$0.336632\pi$
$318$	6.09683	0.341893
$319$	−2.41447	−0.135184
$320$	−5.04211	−0.281863
$321$	−3.96086	−0.221073
$322$	32.9184	1.83447
$323$	32.4902	1.80780
$324$	27.4244	1.52358
$325$	0.0881546	0.00488994
$326$	46.6653	2.58455
$327$	7.43321	0.411057
$328$	−29.8150	−1.64626
$329$	−37.7050	−2.07875
$330$	1.37874	0.0758970
$331$	13.6414	0.749798	0.374899	−	0.927066i	$-0.377677\pi$
$331$	13.6414	0.749798	0.374899	+	0.927066i	$0.377677\pi$
$332$	−79.0254	−4.33708
$333$	10.4217	0.571103
$334$	8.41055	0.460205
$335$	−0.326215	−0.0178230
$336$	−15.0360	−0.820284
$337$	14.9833	0.816193	0.408096	−	0.912939i	$-0.366193\pi$
$337$	14.9833	0.816193	0.408096	+	0.912939i	$0.366193\pi$
$338$	−2.52538	−0.137363
$339$	−7.40960	−0.402434
$340$	−41.8449	−2.26936
$341$	0.576189	0.0312024
$342$	−51.0795	−2.76206
$343$	−14.5632	−0.786339
$344$	54.8538	2.95752
$345$	3.87736	0.208750
$346$	−44.1550	−2.37379
$347$	−34.0746	−1.82922	−0.914611	−	0.404336i	$-0.867503\pi$
$347$	−34.0746	−1.82922	−0.914611	+	0.404336i	$0.867503\pi$
$348$	13.5127	0.724355
$349$	−7.41981	−0.397173	−0.198587	−	0.980083i	$-0.563635\pi$
$349$	−7.41981	−0.397173	−0.198587	+	0.980083i	$0.563635\pi$
$350$	−0.930850	−0.0497560
$351$	3.19040	0.170291
$352$	1.83218	0.0976554
$353$	−9.19721	−0.489518	−0.244759	−	0.969584i	$-0.578709\pi$
$353$	−9.19721	−0.489518	−0.244759	+	0.969584i	$0.578709\pi$
$354$	−18.9342	−1.00634
$355$	−3.84127	−0.203874
$356$	−49.7943	−2.63909
$357$	10.1206	0.535637
$358$	−33.5092	−1.77102
$359$	−17.0852	−0.901724	−0.450862	−	0.892594i	$-0.648883\pi$
$359$	−17.0852	−0.901724	−0.450862	+	0.892594i	$0.648883\pi$
$360$	35.7303	1.88315
$361$	37.7452	1.98659
$362$	30.3664	1.59602
$363$	−6.06495	−0.318328
$364$	18.3037	0.959376
$365$	26.7719	1.40130
$366$	21.6089	1.12952
$367$	1.14307	0.0596675	0.0298338	−	0.999555i	$-0.490502\pi$
$367$	1.14307	0.0596675	0.0298338	+	0.999555i	$0.490502\pi$
$368$	19.9766	1.04135
$369$	−13.3331	−0.694093
$370$	21.7236	1.12935
$371$	17.9877	0.933873
$372$	−3.22466	−0.167191
$373$	−3.51071	−0.181778	−0.0908889	−	0.995861i	$-0.528971\pi$
$373$	−3.51071	−0.181778	−0.0908889	+	0.995861i	$0.528971\pi$
$374$	−4.78120	−0.247230
$375$	−6.32838	−0.326796
$376$	−54.1440	−2.79227
$377$	−5.50046	−0.283288
$378$	−33.6884	−1.73274
$379$	11.2074	0.575686	0.287843	−	0.957678i	$-0.407062\pi$
$379$	11.2074	0.575686	0.287843	+	0.957678i	$0.407062\pi$
$380$	−73.0835	−3.74910
$381$	1.37505	0.0704459
$382$	−61.3479	−3.13883
$383$	25.3543	1.29554	0.647771	−	0.761835i	$-0.275701\pi$
$383$	25.3543	1.29554	0.647771	+	0.761835i	$0.275701\pi$
$384$	7.90897	0.403603
$385$	4.06773	0.207311
$386$	17.3138	0.881249
$387$	24.5303	1.24694
$388$	−27.2886	−1.38537
$389$	33.0211	1.67424	0.837119	−	0.547021i	$-0.184238\pi$
$389$	33.0211	1.67424	0.837119	+	0.547021i	$0.184238\pi$
$390$	3.14094	0.159048
$391$	−13.4460	−0.679991
$392$	−62.9423	−3.17907
$393$	−6.25144	−0.315343
$394$	−51.1488	−2.57684
$395$	−1.64559	−0.0827985
$396$	5.15952	0.259276
$397$	6.58574	0.330529	0.165265	−	0.986249i	$-0.447152\pi$
$397$	6.58574	0.330529	0.165265	+	0.986249i	$0.447152\pi$
$398$	−25.8615	−1.29632
$399$	17.6759	0.884902
$400$	−0.564887	−0.0282443
$401$	−35.3250	−1.76404	−0.882022	−	0.471208i	$-0.843818\pi$
$401$	−35.3250	−1.76404	−0.882022	+	0.471208i	$0.843818\pi$
$402$	0.208602	0.0104041
$403$	1.31263	0.0653868
$404$	−64.5695	−3.21245
$405$	13.8844	0.689923
$406$	58.0810	2.88251
$407$	1.70374	0.0844513
$408$	14.5330	0.719492
$409$	18.6883	0.924076	0.462038	−	0.886860i	$-0.347118\pi$
$409$	18.6883	0.924076	0.462038	+	0.886860i	$0.347118\pi$
$410$	−27.7924	−1.37257
$411$	2.12664	0.104900
$412$	4.38392	0.215980
$413$	−55.8620	−2.74879
$414$	21.1391	1.03893
$415$	−40.0089	−1.96396
$416$	4.17393	0.204644
$417$	−2.31309	−0.113272
$418$	−8.35053	−0.408438
$419$	9.56354	0.467210	0.233605	−	0.972332i	$-0.424948\pi$
$419$	9.56354	0.467210	0.233605	+	0.972332i	$0.424948\pi$
$420$	−22.7652	−1.11083
$421$	4.60471	0.224420	0.112210	−	0.993685i	$-0.464207\pi$
$421$	4.60471	0.224420	0.112210	+	0.993685i	$0.464207\pi$
$422$	−58.4534	−2.84547
$423$	−24.2129	−1.17727
$424$	25.8301	1.25442
$425$	0.380218	0.0184433
$426$	2.45635	0.119010
$427$	63.7535	3.08525
$428$	−30.8967	−1.49345
$429$	0.246338	0.0118933
$430$	51.1325	2.46583
$431$	−25.5726	−1.23179	−0.615895	−	0.787829i	$-0.711205\pi$
$431$	−25.5726	−1.23179	−0.615895	+	0.787829i	$0.711205\pi$
$432$	−20.4438	−0.983603
$433$	−8.55446	−0.411101	−0.205551	−	0.978646i	$-0.565899\pi$
$433$	−8.55446	−0.411101	−0.205551	+	0.978646i	$0.565899\pi$
$434$	−13.8605	−0.665323
$435$	6.84118	0.328010
$436$	57.9827	2.77687
$437$	−23.4838	−1.12338
$438$	−17.1196	−0.818005
$439$	−21.2231	−1.01293	−0.506463	−	0.862262i	$-0.669047\pi$
$439$	−21.2231	−1.01293	−0.506463	+	0.862262i	$0.669047\pi$
$440$	5.84122	0.278469
$441$	−28.1475	−1.34036
$442$	−10.8922	−0.518088
$443$	12.8341	0.609766	0.304883	−	0.952390i	$-0.401383\pi$
$443$	12.8341	0.609766	0.304883	+	0.952390i	$0.401383\pi$
$444$	−9.53506	−0.452514
$445$	−25.2098	−1.19506
$446$	−22.1461	−1.04865
$447$	−3.42596	−0.162042
$448$	9.51257	0.449427
$449$	8.77417	0.414079	0.207039	−	0.978333i	$-0.433617\pi$
$449$	8.77417	0.414079	0.207039	+	0.978333i	$0.433617\pi$
$450$	−0.597761	−0.0281787
$451$	−2.17971	−0.102638
$452$	−57.7986	−2.71862
$453$	11.0712	0.520171
$454$	−48.3754	−2.27037
$455$	9.26680	0.434434
$456$	25.3824	1.18864
$457$	−37.5430	−1.75619	−0.878093	−	0.478490i	$-0.841184\pi$
$457$	−37.5430	−1.75619	−0.878093	+	0.478490i	$0.841184\pi$
$458$	−29.3323	−1.37061
$459$	13.7605	0.642283
$460$	30.2453	1.41020
$461$	6.76373	0.315018	0.157509	−	0.987518i	$-0.449654\pi$
$461$	6.76373	0.315018	0.157509	+	0.987518i	$0.449654\pi$
$462$	−2.60116	−0.121017
$463$	17.6068	0.818258	0.409129	−	0.912477i	$-0.365833\pi$
$463$	17.6068	0.818258	0.409129	+	0.912477i	$0.365833\pi$
$464$	35.2465	1.63628
$465$	−1.63258	−0.0757091
$466$	69.8634	3.23636
$467$	−0.945753	−0.0437642	−0.0218821	−	0.999761i	$-0.506966\pi$
$467$	−0.945753	−0.0437642	−0.0218821	+	0.999761i	$0.506966\pi$
$468$	11.7540	0.543331
$469$	0.615444	0.0284186
$470$	−50.4709	−2.32805
$471$	−6.66919	−0.307300
$472$	−80.2173	−3.69230
$473$	4.01024	0.184391
$474$	1.05229	0.0483333
$475$	0.664064	0.0304693
$476$	78.9455	3.61846
$477$	11.5511	0.528887
$478$	−33.1698	−1.51715
$479$	−4.51068	−0.206098	−0.103049	−	0.994676i	$-0.532860\pi$
$479$	−4.51068	−0.206098	−0.103049	+	0.994676i	$0.532860\pi$
$480$	−5.19131	−0.236950
$481$	3.88134	0.176974
$482$	10.0759	0.458945
$483$	−7.31512	−0.332849
$484$	−47.3097	−2.15044
$485$	−13.8157	−0.627338
$486$	−33.0495	−1.49916
$487$	9.73957	0.441342	0.220671	−	0.975348i	$-0.429175\pi$
$487$	9.73957	0.441342	0.220671	+	0.975348i	$0.429175\pi$
$488$	91.5493	4.14424
$489$	−10.3700	−0.468946
$490$	−58.6724	−2.65055
$491$	−5.30297	−0.239320	−0.119660	−	0.992815i	$-0.538180\pi$
$491$	−5.30297	−0.239320	−0.119660	+	0.992815i	$0.538180\pi$
$492$	12.1988	0.549965
$493$	−23.7239	−1.06847
$494$	−19.0236	−0.855911
$495$	2.61216	0.117408
$496$	−8.41122	−0.377675
$497$	7.24703	0.325074
$498$	25.5842	1.14645
$499$	15.9601	0.714471	0.357236	−	0.934014i	$-0.383719\pi$
$499$	15.9601	0.714471	0.357236	+	0.934014i	$0.383719\pi$
$500$	−49.3645	−2.20765
$501$	−1.86899	−0.0835003
$502$	−7.78594	−0.347504
$503$	9.76299	0.435310	0.217655	−	0.976026i	$-0.430159\pi$
$503$	9.76299	0.435310	0.217655	+	0.976026i	$0.430159\pi$
$504$	−67.4095	−3.00266
$505$	−32.6902	−1.45469
$506$	3.45584	0.153631
$507$	0.561190	0.0249233
$508$	10.7261	0.475893
$509$	−11.1798	−0.495536	−0.247768	−	0.968819i	$-0.579697\pi$
$509$	−11.1798	−0.495536	−0.247768	+	0.968819i	$0.579697\pi$
$510$	13.5471	0.599876
$511$	−50.5084	−2.23436
$512$	50.2032	2.21869
$513$	24.0331	1.06109
$514$	−12.6857	−0.559542
$515$	2.21949	0.0978023
$516$	−22.4434	−0.988018
$517$	−3.95835	−0.174088
$518$	−40.9842	−1.80074
$519$	9.81210	0.430703
$520$	13.3070	0.583552
$521$	−2.25067	−0.0986038	−0.0493019	−	0.998784i	$-0.515700\pi$
$521$	−2.25067	−0.0986038	−0.0493019	+	0.998784i	$0.515700\pi$
$522$	37.2976	1.63247
$523$	22.0680	0.964965	0.482482	−	0.875906i	$-0.339735\pi$
$523$	22.0680	0.964965	0.482482	+	0.875906i	$0.339735\pi$
$524$	−48.7643	−2.13028
$525$	0.206853	0.00902782
$526$	−3.05677	−0.133282
$527$	5.66148	0.246618
$528$	−1.57851	−0.0686960
$529$	−13.2813	−0.577448
$530$	24.0778	1.04587
$531$	−35.8727	−1.55674
$532$	137.881	5.97790
$533$	−4.96565	−0.215086
$534$	16.1207	0.697611
$535$	−15.6423	−0.676277
$536$	0.883771	0.0381731
$537$	7.44641	0.321336
$538$	−73.1879	−3.15536
$539$	−4.60157	−0.198204
$540$	−30.9528	−1.33200
$541$	−8.12464	−0.349305	−0.174653	−	0.984630i	$-0.555880\pi$
$541$	−8.12464	−0.349305	−0.174653	+	0.984630i	$0.555880\pi$
$542$	3.93490	0.169019
$543$	−6.74800	−0.289584
$544$	18.0025	0.771851
$545$	29.3555	1.25745
$546$	−5.92577	−0.253599
$547$	12.7529	0.545274	0.272637	−	0.962117i	$-0.412104\pi$
$547$	12.7529	0.545274	0.272637	+	0.962117i	$0.412104\pi$
$548$	16.5889	0.708642
$549$	40.9403	1.74729
$550$	−0.0977225	−0.00416690
$551$	−41.4347	−1.76518
$552$	−10.5044	−0.447098
$553$	3.10460	0.132021
$554$	−20.0878	−0.853449
$555$	−4.82740	−0.204912
$556$	−18.0432	−0.765204
$557$	−38.2412	−1.62033	−0.810167	−	0.586200i	$-0.800623\pi$
$557$	−38.2412	−1.62033	−0.810167	+	0.586200i	$0.800623\pi$
$558$	−8.90071	−0.376797
$559$	9.13582	0.386404
$560$	−59.3808	−2.50930
$561$	1.06248	0.0448578
$562$	−40.7523	−1.71903
$563$	−34.8140	−1.46724	−0.733618	−	0.679562i	$-0.762170\pi$
$563$	−34.8140	−1.46724	−0.733618	+	0.679562i	$0.762170\pi$
$564$	22.1531	0.932812
$565$	−29.2622	−1.23107
$566$	−1.92361	−0.0808552
$567$	−26.1947	−1.10007
$568$	10.4067	0.436654
$569$	45.6370	1.91320	0.956601	−	0.291401i	$-0.0941214\pi$
$569$	45.6370	1.91320	0.956601	+	0.291401i	$0.0941214\pi$
$570$	23.6605	0.991029
$571$	−5.92399	−0.247911	−0.123956	−	0.992288i	$-0.539558\pi$
$571$	−5.92399	−0.247911	−0.123956	+	0.992288i	$0.539558\pi$
$572$	1.92156	0.0803445
$573$	13.6327	0.569514
$574$	52.4337	2.18854
$575$	−0.274821	−0.0114608
$576$	6.10865	0.254527
$577$	−42.1894	−1.75637	−0.878184	−	0.478323i	$-0.841245\pi$
$577$	−42.1894	−1.75637	−0.878184	+	0.478323i	$0.841245\pi$
$578$	−4.04734	−0.168347
$579$	−3.84746	−0.159895
$580$	53.3646	2.21585
$581$	75.4818	3.13151
$582$	8.83460	0.366206
$583$	1.88838	0.0782087
$584$	−72.5295	−3.00129
$585$	5.95083	0.246036
$586$	−0.815952	−0.0337067
$587$	−20.5794	−0.849401	−0.424701	−	0.905334i	$-0.639621\pi$
$587$	−20.5794	−0.849401	−0.424701	+	0.905334i	$0.639621\pi$
$588$	25.7529	1.06203
$589$	9.88797	0.407427
$590$	−74.7754	−3.07846
$591$	11.3663	0.467546
$592$	−24.8713	−1.02220
$593$	27.6760	1.13652	0.568258	−	0.822850i	$-0.307618\pi$
$593$	27.6760	1.13652	0.568258	+	0.822850i	$0.307618\pi$
$594$	−3.53667	−0.145111
$595$	39.9685	1.63855
$596$	−26.7242	−1.09467
$597$	5.74694	0.235206
$598$	7.87284	0.321944
$599$	1.56490	0.0639399	0.0319699	−	0.999489i	$-0.489822\pi$
$599$	1.56490	0.0639399	0.0319699	+	0.999489i	$0.489822\pi$
$600$	0.297039	0.0121266
$601$	29.3003	1.19519	0.597593	−	0.801800i	$-0.296124\pi$
$601$	29.3003	1.19519	0.597593	+	0.801800i	$0.296124\pi$
$602$	−96.4678	−3.93174
$603$	0.395217	0.0160945
$604$	86.3610	3.51398
$605$	−23.9519	−0.973784
$606$	20.9041	0.849172
$607$	42.8791	1.74041	0.870204	−	0.492692i	$-0.163987\pi$
$607$	42.8791	1.74041	0.870204	+	0.492692i	$0.163987\pi$
$608$	31.4420	1.27514
$609$	−12.9067	−0.523007
$610$	85.3387	3.45526
$611$	−9.01762	−0.364814
$612$	50.6961	2.04927
$613$	−2.77022	−0.111888	−0.0559442	−	0.998434i	$-0.517817\pi$
$613$	−2.77022	−0.111888	−0.0559442	+	0.998434i	$0.517817\pi$
$614$	−55.8245	−2.25289
$615$	6.17601	0.249041
$616$	−11.0202	−0.444015
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	−1.41928	−0.0570917
$619$	4.36063	0.175268	0.0876342	−	0.996153i	$-0.472069\pi$
$619$	4.36063	0.175268	0.0876342	+	0.996153i	$0.472069\pi$
$620$	−12.7349	−0.511448
$621$	−9.94602	−0.399120
$622$	−50.2890	−2.01640
$623$	47.5614	1.90551
$624$	−3.59605	−0.143957
$625$	−24.5515	−0.982058
$626$	54.8059	2.19048
$627$	1.85565	0.0741076
$628$	−52.0230	−2.07594
$629$	16.7405	0.667489
$630$	−62.8365	−2.50347
$631$	44.7521	1.78155	0.890777	−	0.454442i	$-0.150161\pi$
$631$	44.7521	1.78155	0.890777	+	0.454442i	$0.150161\pi$
$632$	4.45818	0.177337
$633$	12.9895	0.516286
$634$	−44.1538	−1.75357
$635$	5.43039	0.215498
$636$	−10.5684	−0.419064
$637$	−10.4830	−0.415350
$638$	6.09745	0.241400
$639$	4.65380	0.184102
$640$	31.2344	1.23465
$641$	38.4861	1.52011	0.760055	−	0.649859i	$-0.225172\pi$
$641$	38.4861	1.52011	0.760055	+	0.649859i	$0.225172\pi$
$642$	10.0027	0.394774
$643$	43.7842	1.72668	0.863339	−	0.504624i	$-0.168369\pi$
$643$	43.7842	1.72668	0.863339	+	0.504624i	$0.168369\pi$
$644$	−57.0616	−2.24854
$645$	−11.3627	−0.447404
$646$	−82.0502	−3.22822
$647$	−23.7058	−0.931973	−0.465986	−	0.884792i	$-0.654300\pi$
$647$	−23.7058	−0.931973	−0.465986	+	0.884792i	$0.654300\pi$
$648$	−37.6153	−1.47767
$649$	−5.86451	−0.230202
$650$	−0.222624	−0.00873204
$651$	3.08006	0.120717
$652$	−80.8908	−3.16793
$653$	11.8624	0.464213	0.232107	−	0.972690i	$-0.425438\pi$
$653$	11.8624	0.464213	0.232107	+	0.972690i	$0.425438\pi$
$654$	−18.7717	−0.734031
$655$	−24.6884	−0.964655
$656$	31.8194	1.24234
$657$	−32.4348	−1.26540
$658$	95.2197	3.71205
$659$	−27.1403	−1.05724	−0.528618	−	0.848860i	$-0.677290\pi$
$659$	−27.1403	−1.05724	−0.528618	+	0.848860i	$0.677290\pi$
$660$	−2.38994	−0.0930281
$661$	−26.5612	−1.03311	−0.516556	−	0.856254i	$-0.672786\pi$
$661$	−26.5612	−1.03311	−0.516556	+	0.856254i	$0.672786\pi$
$662$	−34.4497	−1.33893
$663$	2.42046	0.0940027
$664$	108.391	4.20639
$665$	69.8063	2.70697
$666$	−26.3187	−1.01983
$667$	17.1476	0.663958
$668$	−14.5790	−0.564080
$669$	4.92129	0.190268
$670$	0.823817	0.0318268
$671$	6.69296	0.258379
$672$	9.79405	0.377814
$673$	−43.4610	−1.67530	−0.837650	−	0.546207i	$-0.816071\pi$
$673$	−43.4610	−1.67530	−0.837650	+	0.546207i	$0.816071\pi$
$674$	−37.8386	−1.45749
$675$	0.281249	0.0108253
$676$	4.37756	0.168368
$677$	−8.12178	−0.312145	−0.156073	−	0.987746i	$-0.549883\pi$
$677$	−8.12178	−0.312145	−0.156073	+	0.987746i	$0.549883\pi$
$678$	18.7121	0.718633
$679$	26.0650	1.00028
$680$	57.3943	2.20097
$681$	10.7500	0.411939
$682$	−1.45510	−0.0557185
$683$	4.77954	0.182884	0.0914421	−	0.995810i	$-0.470852\pi$
$683$	4.77954	0.182884	0.0914421	+	0.995810i	$0.470852\pi$
$684$	88.5425	3.38551
$685$	8.39861	0.320894
$686$	36.7777	1.40418
$687$	6.51821	0.248685
$688$	−58.5415	−2.23188
$689$	4.30197	0.163892
$690$	−9.79182	−0.372768
$691$	44.2608	1.68376	0.841879	−	0.539666i	$-0.181449\pi$
$691$	44.2608	1.68376	0.841879	+	0.539666i	$0.181449\pi$
$692$	76.5393	2.90959
$693$	−4.92816	−0.187205
$694$	86.0515	3.26647
$695$	−9.13492	−0.346507
$696$	−18.5339	−0.702527
$697$	−21.4172	−0.811236
$698$	18.7379	0.709239
$699$	−15.5250	−0.587210
$700$	1.61356	0.0609868
$701$	6.85444	0.258889	0.129444	−	0.991587i	$-0.458681\pi$
$701$	6.85444	0.258889	0.129444	+	0.991587i	$0.458681\pi$
$702$	−8.05698	−0.304091
$703$	29.2379	1.10273
$704$	0.998648	0.0376380
$705$	11.2156	0.422405
$706$	23.2265	0.874140
$707$	61.6741	2.31949
$708$	32.8209	1.23349
$709$	44.3731	1.66647	0.833233	−	0.552921i	$-0.186487\pi$
$709$	44.3731	1.66647	0.833233	+	0.552921i	$0.186487\pi$
$710$	9.70069	0.364060
$711$	1.99367	0.0747685
$712$	68.2977	2.55956
$713$	−4.09210	−0.153250
$714$	−25.5583	−0.956496
$715$	0.972847	0.0363824
$716$	58.0857	2.17077
$717$	7.37098	0.275274
$718$	43.1467	1.61022
$719$	13.2075	0.492558	0.246279	−	0.969199i	$-0.420792\pi$
$719$	13.2075	0.492558	0.246279	+	0.969199i	$0.420792\pi$
$720$	−38.1324	−1.42111
$721$	−4.18734	−0.155945
$722$	−95.3211	−3.54748
$723$	−2.23907	−0.0832718
$724$	−52.6378	−1.95627
$725$	−0.484891	−0.0180084
$726$	15.3163	0.568442
$727$	−23.0042	−0.853179	−0.426589	−	0.904445i	$-0.640285\pi$
$727$	−23.0042	−0.853179	−0.426589	+	0.904445i	$0.640285\pi$
$728$	−25.1054	−0.930466
$729$	−11.4501	−0.424077
$730$	−67.6092	−2.50233
$731$	39.4035	1.45739
$732$	−37.4575	−1.38447
$733$	22.4029	0.827469	0.413735	−	0.910397i	$-0.364224\pi$
$733$	22.4029	0.827469	0.413735	+	0.910397i	$0.364224\pi$
$734$	−2.88668	−0.106549
$735$	13.0382	0.480920
$736$	−13.0122	−0.479635
$737$	0.0646105	0.00237996
$738$	33.6712	1.23945
$739$	−10.5386	−0.387670	−0.193835	−	0.981034i	$-0.562093\pi$
$739$	−10.5386	−0.387670	−0.193835	+	0.981034i	$0.562093\pi$
$740$	−37.6562	−1.38427
$741$	4.22741	0.155298
$742$	−45.4257	−1.66763
$743$	8.93787	0.327899	0.163949	−	0.986469i	$-0.447577\pi$
$743$	8.93787	0.327899	0.163949	+	0.986469i	$0.447577\pi$
$744$	4.42294	0.162153
$745$	−13.5299	−0.495698
$746$	8.86589	0.324603
$747$	48.4718	1.77349
$748$	8.28785	0.303034
$749$	29.5112	1.07832
$750$	15.9816	0.583565
$751$	10.3634	0.378168	0.189084	−	0.981961i	$-0.439448\pi$
$751$	10.3634	0.378168	0.189084	+	0.981961i	$0.439448\pi$
$752$	57.7841	2.10717
$753$	1.73019	0.0630516
$754$	13.8908	0.505872
$755$	43.7228	1.59124
$756$	58.3962	2.12385
$757$	15.5587	0.565490	0.282745	−	0.959195i	$-0.408755\pi$
$757$	15.5587	0.565490	0.282745	+	0.959195i	$0.408755\pi$
$758$	−28.3030	−1.02801
$759$	−0.767955	−0.0278750
$760$	100.241	3.63613
$761$	−30.6364	−1.11057	−0.555284	−	0.831661i	$-0.687390\pi$
$761$	−30.6364	−1.11057	−0.555284	+	0.831661i	$0.687390\pi$
$762$	−3.47253	−0.125796
$763$	−55.3827	−2.00499
$764$	106.342	3.84731
$765$	25.6664	0.927971
$766$	−64.0292	−2.31347
$767$	−13.3601	−0.482405
$768$	−17.4197	−0.628580
$769$	48.4643	1.74767	0.873835	−	0.486223i	$-0.161626\pi$
$769$	48.4643	1.74767	0.873835	+	0.486223i	$0.161626\pi$
$770$	−10.2726	−0.370198
$771$	2.81901	0.101524
$772$	−30.0121	−1.08016
$773$	47.3866	1.70438	0.852189	−	0.523235i	$-0.175275\pi$
$773$	47.3866	1.70438	0.852189	+	0.523235i	$0.175275\pi$
$774$	−61.9484	−2.22669
$775$	0.115714	0.00415659
$776$	37.4290	1.34362
$777$	9.10749	0.326730
$778$	−83.3910	−2.98971
$779$	−37.4059	−1.34021
$780$	−5.44458	−0.194947
$781$	0.760808	0.0272238
$782$	33.9562	1.21427
$783$	−17.5487	−0.627138
$784$	67.1739	2.39907
$785$	−26.3382	−0.940050
$786$	15.7873	0.563114
$787$	−33.4205	−1.19131	−0.595656	−	0.803240i	$-0.703108\pi$
$787$	−33.4205	−1.19131	−0.595656	+	0.803240i	$0.703108\pi$
$788$	88.6625	3.15847
$789$	0.679275	0.0241828
$790$	4.15574	0.147855
$791$	55.2068	1.96293
$792$	−7.07678	−0.251463
$793$	15.2474	0.541452
$794$	−16.6315	−0.590231
$795$	−5.35056	−0.189765
$796$	44.8290	1.58892
$797$	8.08967	0.286551	0.143275	−	0.989683i	$-0.454237\pi$
$797$	8.08967	0.286551	0.143275	+	0.989683i	$0.454237\pi$
$798$	−44.6385	−1.58018
$799$	−38.8937	−1.37596
$800$	0.367951	0.0130090
$801$	30.5423	1.07916
$802$	89.2091	3.15008
$803$	−5.30247	−0.187120
$804$	−0.361595	−0.0127525
$805$	−28.8891	−1.01821
$806$	−3.31490	−0.116762
$807$	16.2638	0.572513
$808$	88.5633	3.11565
$809$	30.0262	1.05566	0.527832	−	0.849349i	$-0.323005\pi$
$809$	30.0262	1.05566	0.527832	+	0.849349i	$0.323005\pi$
$810$	−35.0635	−1.23201
$811$	−37.4815	−1.31615	−0.658077	−	0.752951i	$-0.728630\pi$
$811$	−37.4815	−1.31615	−0.658077	+	0.752951i	$0.728630\pi$
$812$	−100.679	−3.53314
$813$	−0.874412	−0.0306670
$814$	−4.30260	−0.150806
$815$	−40.9534	−1.43453
$816$	−15.5101	−0.542961
$817$	68.8196	2.40769
$818$	−47.1951	−1.65014
$819$	−11.2270	−0.392302
$820$	48.1759	1.68238
$821$	−21.7060	−0.757543	−0.378772	−	0.925490i	$-0.623653\pi$
$821$	−21.7060	−0.757543	−0.378772	+	0.925490i	$0.623653\pi$
$822$	−5.37059	−0.187321
$823$	−52.5909	−1.83320	−0.916602	−	0.399801i	$-0.869079\pi$
$823$	−52.5909	−1.83320	−0.916602	+	0.399801i	$0.869079\pi$
$824$	−6.01297	−0.209472
$825$	0.0217159	0.000756049 0
$826$	141.073	4.90856
$827$	−22.5466	−0.784022	−0.392011	−	0.919961i	$-0.628220\pi$
$827$	−22.5466	−0.784022	−0.392011	+	0.919961i	$0.628220\pi$
$828$	−36.6430	−1.27343
$829$	−1.30593	−0.0453570	−0.0226785	−	0.999743i	$-0.507219\pi$
$829$	−1.30593	−0.0453570	−0.0226785	+	0.999743i	$0.507219\pi$
$830$	101.038	3.50708
$831$	4.46390	0.154851
$832$	2.27505	0.0788731
$833$	−45.2139	−1.56657
$834$	5.84143	0.202272
$835$	−7.38107	−0.255432
$836$	14.4750	0.500629
$837$	4.18782	0.144752
$838$	−24.1516	−0.834304
$839$	9.55597	0.329909	0.164954	−	0.986301i	$-0.447252\pi$
$839$	9.55597	0.329909	0.164954	+	0.986301i	$0.447252\pi$
$840$	31.2247	1.07735
$841$	1.25508	0.0432785
$842$	−11.6286	−0.400750
$843$	9.05597	0.311904
$844$	101.325	3.48773
$845$	2.21627	0.0762419
$846$	61.1468	2.10227
$847$	45.1882	1.55269
$848$	−27.5666	−0.946642
$849$	0.427463	0.0146705
$850$	−0.960196	−0.0329345
$851$	−12.1000	−0.414783
$852$	−4.25789	−0.145873
$853$	−23.7695	−0.813851	−0.406925	−	0.913461i	$-0.633399\pi$
$853$	−23.7695	−0.813851	−0.406925	+	0.913461i	$0.633399\pi$
$854$	−161.002	−5.50938
$855$	44.8272	1.53306
$856$	42.3778	1.44844
$857$	−33.9005	−1.15802	−0.579009	−	0.815321i	$-0.696560\pi$
$857$	−33.9005	−1.15802	−0.579009	+	0.815321i	$0.696560\pi$
$858$	−0.622098	−0.0212381
$859$	−33.2872	−1.13575	−0.567873	−	0.823117i	$-0.692233\pi$
$859$	−33.2872	−1.13575	−0.567873	+	0.823117i	$0.692233\pi$
$860$	−88.6344	−3.02241
$861$	−11.6518	−0.397092
$862$	64.5806	2.19962
$863$	21.3942	0.728266	0.364133	−	0.931347i	$-0.381365\pi$
$863$	21.3942	0.728266	0.364133	+	0.931347i	$0.381365\pi$
$864$	13.3165	0.453037
$865$	38.7503	1.31755
$866$	21.6033	0.734110
$867$	0.899399	0.0305452
$868$	24.0260	0.815497
$869$	0.325927	0.0110563
$870$	−17.2766	−0.585732
$871$	0.147191	0.00498738
$872$	−79.5290	−2.69319
$873$	16.7380	0.566497
$874$	59.3056	2.00604
$875$	47.1509	1.59399
$876$	29.6755	1.00264
$877$	23.6044	0.797063	0.398531	−	0.917155i	$-0.369520\pi$
$877$	23.6044	0.797063	0.398531	+	0.917155i	$0.369520\pi$
$878$	53.5966	1.80880
$879$	0.181321	0.00611579
$880$	−6.23392	−0.210145
$881$	20.8872	0.703709	0.351854	−	0.936055i	$-0.385551\pi$
$881$	20.8872	0.703709	0.351854	+	0.936055i	$0.385551\pi$
$882$	71.0831	2.39349
$883$	20.8508	0.701687	0.350843	−	0.936434i	$-0.385895\pi$
$883$	20.8508	0.701687	0.350843	+	0.936434i	$0.385895\pi$
$884$	18.8808	0.635029
$885$	16.6166	0.558560
$886$	−32.4110	−1.08887
$887$	−26.9697	−0.905554	−0.452777	−	0.891624i	$-0.649567\pi$
$887$	−26.9697	−0.905554	−0.452777	+	0.891624i	$0.649567\pi$
$888$	13.0783	0.438878
$889$	−10.2451	−0.343610
$890$	63.6644	2.13404
$891$	−2.74997	−0.0921274
$892$	38.3885	1.28534
$893$	−67.9292	−2.27316
$894$	8.65186	0.289362
$895$	29.4076	0.982988
$896$	−58.9275	−1.96863
$897$	−1.74950	−0.0584141
$898$	−22.1581	−0.739427
$899$	−7.22007	−0.240803
$900$	1.03617	0.0345391
$901$	18.5547	0.618148
$902$	5.50459	0.183283
$903$	21.4370	0.713380
$904$	79.2764	2.63669
$905$	−26.6494	−0.885857
$906$	−27.9591	−0.928877
$907$	44.2095	1.46795	0.733976	−	0.679176i	$-0.237663\pi$
$907$	44.2095	1.46795	0.733976	+	0.679176i	$0.237663\pi$
$908$	83.8551	2.78283
$909$	39.6050	1.31362
$910$	−23.4022	−0.775776
$911$	57.4625	1.90382	0.951909	−	0.306380i	$-0.0991177\pi$
$911$	57.4625	1.90382	0.951909	+	0.306380i	$0.0991177\pi$
$912$	−27.0889	−0.897002
$913$	7.92422	0.262253
$914$	94.8104	3.13605
$915$	−18.9639	−0.626928
$916$	50.8453	1.67998
$917$	46.5777	1.53813
$918$	−34.7504	−1.14693
$919$	−14.6121	−0.482007	−0.241004	−	0.970524i	$-0.577477\pi$
$919$	−14.6121	−0.482007	−0.241004	+	0.970524i	$0.577477\pi$
$920$	−41.4844	−1.36770
$921$	12.4053	0.408768
$922$	−17.0810	−0.562533
$923$	1.73322	0.0570495
$924$	4.50891	0.148332
$925$	0.342158	0.0112501
$926$	−44.4639	−1.46118
$927$	−2.68897	−0.0883173
$928$	−22.9585	−0.753651
$929$	9.26055	0.303829	0.151914	−	0.988394i	$-0.451456\pi$
$929$	9.26055	0.303829	0.151914	+	0.988394i	$0.451456\pi$
$930$	4.12289	0.135195
$931$	−78.9676	−2.58806
$932$	−121.103	−3.96685
$933$	11.1752	0.365859
$934$	2.38839	0.0781505
$935$	4.19597	0.137223
$936$	−16.1218	−0.526958
$937$	−6.05904	−0.197940	−0.0989702	−	0.995090i	$-0.531555\pi$
$937$	−6.05904	−0.197940	−0.0989702	+	0.995090i	$0.531555\pi$
$938$	−1.55423	−0.0507475
$939$	−12.1789	−0.397445
$940$	87.4876	2.85353
$941$	26.0666	0.849746	0.424873	−	0.905253i	$-0.360319\pi$
$941$	26.0666	0.849746	0.424873	+	0.905253i	$0.360319\pi$
$942$	16.8423	0.548750
$943$	15.4803	0.504109
$944$	85.6102	2.78638
$945$	29.5648	0.961743
$946$	−10.1274	−0.329270
$947$	−22.3528	−0.726368	−0.363184	−	0.931717i	$-0.618310\pi$
$947$	−22.3528	−0.726368	−0.363184	+	0.931717i	$0.618310\pi$
$948$	−1.82407	−0.0592429
$949$	−12.0797	−0.392124
$950$	−1.67702	−0.0544096
$951$	9.81183	0.318170
$952$	−108.281	−3.50942
$953$	−40.9303	−1.32586	−0.662931	−	0.748681i	$-0.730688\pi$
$953$	−40.9303	−1.32586	−0.662931	+	0.748681i	$0.730688\pi$
$954$	−29.1709	−0.944442
$955$	53.8387	1.74218
$956$	57.4973	1.85960
$957$	−1.35497	−0.0438001
$958$	11.3912	0.368033
$959$	−15.8450	−0.511662
$960$	−2.82958	−0.0913244
$961$	−29.2770	−0.944419
$962$	−9.80187	−0.316025
$963$	18.9511	0.610691
$964$	−17.4658	−0.562537
$965$	−15.1945	−0.489129
$966$	18.4735	0.594374
$967$	14.3077	0.460106	0.230053	−	0.973178i	$-0.426110\pi$
$967$	14.3077	0.460106	0.230053	+	0.973178i	$0.426110\pi$
$968$	64.8898	2.08564
$969$	18.2332	0.585733
$970$	34.8899	1.12025
$971$	−32.9530	−1.05751	−0.528757	−	0.848773i	$-0.677342\pi$
$971$	−32.9530	−1.05751	−0.528757	+	0.848773i	$0.677342\pi$
$972$	57.2888	1.83754
$973$	17.2342	0.552502
$974$	−24.5961	−0.788111
$975$	0.0494715	0.00158435
$976$	−97.7041	−3.12743
$977$	−18.1260	−0.579901	−0.289950	−	0.957042i	$-0.593639\pi$
$977$	−18.1260	−0.579901	−0.289950	+	0.957042i	$0.593639\pi$
$978$	26.1881	0.837403
$979$	4.99309	0.159580
$980$	101.704	3.24882
$981$	−35.5649	−1.13550
$982$	13.3920	0.427357
$983$	38.8967	1.24061	0.620305	−	0.784360i	$-0.287009\pi$
$983$	38.8967	1.24061	0.620305	+	0.784360i	$0.287009\pi$
$984$	−16.7319	−0.533392
$985$	44.8880	1.43025
$986$	59.9120	1.90799
$987$	−21.1597	−0.673520
$988$	32.9759	1.04910
$989$	−28.4808	−0.905636
$990$	−6.59670	−0.209657
$991$	24.2060	0.768930	0.384465	−	0.923139i	$-0.374386\pi$
$991$	24.2060	0.768930	0.384465	+	0.923139i	$0.374386\pi$
$992$	5.47883	0.173953
$993$	7.65540	0.242937
$994$	−18.3015	−0.580490
$995$	22.6960	0.719511
$996$	−44.3482	−1.40523
$997$	10.9061	0.345399	0.172699	−	0.984975i	$-0.444751\pi$
$997$	10.9061	0.345399	0.172699	+	0.984975i	$0.444751\pi$
$998$	−40.3053	−1.27584
$999$	12.3830	0.391782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.c.1.10	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.c.1.10	✓	169	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.52538 q^{2} +0.561190 q^{3} +4.37756 q^{4} +2.21627 q^{5} -1.41722 q^{6} -4.18126 q^{7} -6.00425 q^{8} -2.68507 q^{9} +O(q^{10})\)	\(q-2.52538 q^{2} +0.561190 q^{3} +4.37756 q^{4} +2.21627 q^{5} -1.41722 q^{6} -4.18126 q^{7} -6.00425 q^{8} -2.68507 q^{9} -5.59693 q^{10} -0.438957 q^{11} +2.45664 q^{12} -1.00000 q^{13} +10.5593 q^{14} +1.24375 q^{15} +6.40791 q^{16} -4.31308 q^{17} +6.78082 q^{18} -7.53294 q^{19} +9.70185 q^{20} -2.34648 q^{21} +1.10853 q^{22} +3.11748 q^{23} -3.36952 q^{24} -0.0881546 q^{25} +2.52538 q^{26} -3.19040 q^{27} -18.3037 q^{28} +5.50046 q^{29} -3.14094 q^{30} -1.31263 q^{31} -4.17393 q^{32} -0.246338 q^{33} +10.8922 q^{34} -9.26680 q^{35} -11.7540 q^{36} -3.88134 q^{37} +19.0236 q^{38} -0.561190 q^{39} -13.3070 q^{40} +4.96565 q^{41} +5.92577 q^{42} -9.13582 q^{43} -1.92156 q^{44} -5.95083 q^{45} -7.87284 q^{46} +9.01762 q^{47} +3.59605 q^{48} +10.4830 q^{49} +0.222624 q^{50} -2.42046 q^{51} -4.37756 q^{52} -4.30197 q^{53} +8.05698 q^{54} -0.972847 q^{55} +25.1054 q^{56} -4.22741 q^{57} -13.8908 q^{58} +13.3601 q^{59} +5.44458 q^{60} -15.2474 q^{61} +3.31490 q^{62} +11.2270 q^{63} -2.27505 q^{64} -2.21627 q^{65} +0.622098 q^{66} -0.147191 q^{67} -18.8808 q^{68} +1.74950 q^{69} +23.4022 q^{70} -1.73322 q^{71} +16.1218 q^{72} +12.0797 q^{73} +9.80187 q^{74} -0.0494715 q^{75} -32.9759 q^{76} +1.83540 q^{77} +1.41722 q^{78} -0.742504 q^{79} +14.2017 q^{80} +6.26478 q^{81} -12.5402 q^{82} -18.0524 q^{83} -10.2719 q^{84} -9.55894 q^{85} +23.0715 q^{86} +3.08680 q^{87} +2.63561 q^{88} -11.3749 q^{89} +15.0281 q^{90} +4.18126 q^{91} +13.6470 q^{92} -0.736635 q^{93} -22.7729 q^{94} -16.6950 q^{95} -2.34237 q^{96} -6.23376 q^{97} -26.4735 q^{98} +1.17863 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * q^99

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