LMFDB - Embedded newform 8007.2.a.i.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$63$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.23503 q^{2} +1.00000 q^{3} -0.474692 q^{4} +0.598945 q^{5} -1.23503 q^{6} -4.57610 q^{7} +3.05633 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.23503 q^{2} +1.00000 q^{3} -0.474692 q^{4} +0.598945 q^{5} -1.23503 q^{6} -4.57610 q^{7} +3.05633 q^{8} +1.00000 q^{9} -0.739717 q^{10} -5.54690 q^{11} -0.474692 q^{12} +6.75283 q^{13} +5.65164 q^{14} +0.598945 q^{15} -2.82528 q^{16} +1.00000 q^{17} -1.23503 q^{18} -2.30367 q^{19} -0.284314 q^{20} -4.57610 q^{21} +6.85061 q^{22} +5.50991 q^{23} +3.05633 q^{24} -4.64127 q^{25} -8.33998 q^{26} +1.00000 q^{27} +2.17224 q^{28} -7.62338 q^{29} -0.739717 q^{30} -6.74640 q^{31} -2.62334 q^{32} -5.54690 q^{33} -1.23503 q^{34} -2.74083 q^{35} -0.474692 q^{36} +0.0201917 q^{37} +2.84510 q^{38} +6.75283 q^{39} +1.83057 q^{40} -5.29980 q^{41} +5.65164 q^{42} -1.28903 q^{43} +2.63307 q^{44} +0.598945 q^{45} -6.80493 q^{46} -4.56404 q^{47} -2.82528 q^{48} +13.9407 q^{49} +5.73212 q^{50} +1.00000 q^{51} -3.20552 q^{52} +9.35478 q^{53} -1.23503 q^{54} -3.32229 q^{55} -13.9861 q^{56} -2.30367 q^{57} +9.41513 q^{58} +7.02044 q^{59} -0.284314 q^{60} +10.9201 q^{61} +8.33202 q^{62} -4.57610 q^{63} +8.89047 q^{64} +4.04458 q^{65} +6.85061 q^{66} -11.8752 q^{67} -0.474692 q^{68} +5.50991 q^{69} +3.38502 q^{70} +14.2185 q^{71} +3.05633 q^{72} +0.419870 q^{73} -0.0249375 q^{74} -4.64127 q^{75} +1.09353 q^{76} +25.3832 q^{77} -8.33998 q^{78} +2.64581 q^{79} -1.69219 q^{80} +1.00000 q^{81} +6.54543 q^{82} -13.9208 q^{83} +2.17224 q^{84} +0.598945 q^{85} +1.59200 q^{86} -7.62338 q^{87} -16.9532 q^{88} +1.44944 q^{89} -0.739717 q^{90} -30.9016 q^{91} -2.61551 q^{92} -6.74640 q^{93} +5.63675 q^{94} -1.37977 q^{95} -2.62334 q^{96} +2.31332 q^{97} -17.2172 q^{98} -5.54690 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) $ 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.23503	−0.873301	−0.436650	−	0.899631i	$-0.643835\pi$
$2$	−1.23503	−0.873301	−0.436650	+	0.899631i	$0.643835\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.474692	−0.237346
$5$	0.598945	0.267856	0.133928	−	0.990991i	$-0.457241\pi$
$5$	0.598945	0.267856	0.133928	+	0.990991i	$0.457241\pi$
$6$	−1.23503	−0.504200
$7$	−4.57610	−1.72960	−0.864802	−	0.502114i	$-0.832556\pi$
$7$	−4.57610	−1.72960	−0.864802	+	0.502114i	$0.832556\pi$
$8$	3.05633	1.08058
$9$	1.00000	0.333333
$10$	−0.739717	−0.233919
$11$	−5.54690	−1.67245	−0.836227	−	0.548383i	$-0.815244\pi$
$11$	−5.54690	−1.67245	−0.836227	+	0.548383i	$0.815244\pi$
$12$	−0.474692	−0.137032
$13$	6.75283	1.87290	0.936450	−	0.350802i	$-0.114091\pi$
$13$	6.75283	1.87290	0.936450	+	0.350802i	$0.114091\pi$
$14$	5.65164	1.51046
$15$	0.598945	0.154647
$16$	−2.82528	−0.706321
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.23503	−0.291100
$19$	−2.30367	−0.528497	−0.264249	−	0.964455i	$-0.585124\pi$
$19$	−2.30367	−0.528497	−0.264249	+	0.964455i	$0.585124\pi$
$20$	−0.284314	−0.0635746
$21$	−4.57610	−0.998587
$22$	6.85061	1.46056
$23$	5.50991	1.14890	0.574448	−	0.818541i	$-0.305217\pi$
$23$	5.50991	1.14890	0.574448	+	0.818541i	$0.305217\pi$
$24$	3.05633	0.623870
$25$	−4.64127	−0.928253
$26$	−8.33998	−1.63560
$27$	1.00000	0.192450
$28$	2.17224	0.410514
$29$	−7.62338	−1.41563	−0.707813	−	0.706400i	$-0.750318\pi$
$29$	−7.62338	−1.41563	−0.707813	+	0.706400i	$0.750318\pi$
$30$	−0.739717	−0.135053
$31$	−6.74640	−1.21169	−0.605844	−	0.795583i	$-0.707165\pi$
$31$	−6.74640	−1.21169	−0.605844	+	0.795583i	$0.707165\pi$
$32$	−2.62334	−0.463745
$33$	−5.54690	−0.965592
$34$	−1.23503	−0.211807
$35$	−2.74083	−0.463285
$36$	−0.474692	−0.0791153
$37$	0.0201917	0.00331950	0.00165975	−	0.999999i	$-0.499472\pi$
$37$	0.0201917	0.00331950	0.00165975	+	0.999999i	$0.499472\pi$
$38$	2.84510	0.461537
$39$	6.75283	1.08132
$40$	1.83057	0.289439
$41$	−5.29980	−0.827689	−0.413845	−	0.910348i	$-0.635814\pi$
$41$	−5.29980	−0.827689	−0.413845	+	0.910348i	$0.635814\pi$
$42$	5.65164	0.872066
$43$	−1.28903	−0.196575	−0.0982877	−	0.995158i	$-0.531337\pi$
$43$	−1.28903	−0.196575	−0.0982877	+	0.995158i	$0.531337\pi$
$44$	2.63307	0.396950
$45$	0.598945	0.0892854
$46$	−6.80493	−1.00333
$47$	−4.56404	−0.665734	−0.332867	−	0.942974i	$-0.608016\pi$
$47$	−4.56404	−0.665734	−0.332867	+	0.942974i	$0.608016\pi$
$48$	−2.82528	−0.407795
$49$	13.9407	1.99153
$50$	5.73212	0.810644
$51$	1.00000	0.140028
$52$	−3.20552	−0.444525
$53$	9.35478	1.28498	0.642489	−	0.766295i	$-0.277902\pi$
$53$	9.35478	1.28498	0.642489	+	0.766295i	$0.277902\pi$
$54$	−1.23503	−0.168067
$55$	−3.32229	−0.447977
$56$	−13.9861	−1.86897
$57$	−2.30367	−0.305128
$58$	9.41513	1.23627
$59$	7.02044	0.913983	0.456992	−	0.889471i	$-0.348927\pi$
$59$	7.02044	0.913983	0.456992	+	0.889471i	$0.348927\pi$
$60$	−0.284314	−0.0367048
$61$	10.9201	1.39818	0.699089	−	0.715035i	$-0.253589\pi$
$61$	10.9201	1.39818	0.699089	+	0.715035i	$0.253589\pi$
$62$	8.33202	1.05817
$63$	−4.57610	−0.576534
$64$	8.89047	1.11131
$65$	4.04458	0.501668
$66$	6.85061	0.843252
$67$	−11.8752	−1.45079	−0.725395	−	0.688333i	$-0.758343\pi$
$67$	−11.8752	−1.45079	−0.725395	+	0.688333i	$0.758343\pi$
$68$	−0.474692	−0.0575649
$69$	5.50991	0.663315
$70$	3.38502	0.404587
$71$	14.2185	1.68743	0.843715	−	0.536792i	$-0.180364\pi$
$71$	14.2185	1.68743	0.843715	+	0.536792i	$0.180364\pi$
$72$	3.05633	0.360192
$73$	0.419870	0.0491421	0.0245710	−	0.999698i	$-0.492178\pi$
$73$	0.419870	0.0491421	0.0245710	+	0.999698i	$0.492178\pi$
$74$	−0.0249375	−0.00289892
$75$	−4.64127	−0.535927
$76$	1.09353	0.125437
$77$	25.3832	2.89268
$78$	−8.33998	−0.944317
$79$	2.64581	0.297676	0.148838	−	0.988862i	$-0.452447\pi$
$79$	2.64581	0.297676	0.148838	+	0.988862i	$0.452447\pi$
$80$	−1.69219	−0.189192
$81$	1.00000	0.111111
$82$	6.54543	0.722821
$83$	−13.9208	−1.52801	−0.764004	−	0.645211i	$-0.776769\pi$
$83$	−13.9208	−1.52801	−0.764004	+	0.645211i	$0.776769\pi$
$84$	2.17224	0.237011
$85$	0.598945	0.0649647
$86$	1.59200	0.171669
$87$	−7.62338	−0.817312
$88$	−16.9532	−1.80721
$89$	1.44944	0.153640	0.0768201	−	0.997045i	$-0.475523\pi$
$89$	1.44944	0.153640	0.0768201	+	0.997045i	$0.475523\pi$
$90$	−0.739717	−0.0779730
$91$	−30.9016	−3.23937
$92$	−2.61551	−0.272686
$93$	−6.74640	−0.699569
$94$	5.63675	0.581386
$95$	−1.37977	−0.141561
$96$	−2.62334	−0.267743
$97$	2.31332	0.234882	0.117441	−	0.993080i	$-0.462531\pi$
$97$	2.31332	0.234882	0.117441	+	0.993080i	$0.462531\pi$
$98$	−17.2172	−1.73920
$99$	−5.54690	−0.557485
$100$	2.20317	0.220317
$101$	−9.06458	−0.901959	−0.450980	−	0.892534i	$-0.648925\pi$
$101$	−9.06458	−0.901959	−0.450980	+	0.892534i	$0.648925\pi$
$102$	−1.23503	−0.122287
$103$	7.61540	0.750368	0.375184	−	0.926950i	$-0.377580\pi$
$103$	7.61540	0.750368	0.375184	+	0.926950i	$0.377580\pi$
$104$	20.6389	2.02381
$105$	−2.74083	−0.267478
$106$	−11.5535	−1.12217
$107$	−13.5864	−1.31344	−0.656722	−	0.754133i	$-0.728057\pi$
$107$	−13.5864	−1.31344	−0.656722	+	0.754133i	$0.728057\pi$
$108$	−0.474692	−0.0456773
$109$	−13.0532	−1.25027	−0.625133	−	0.780518i	$-0.714955\pi$
$109$	−13.0532	−1.25027	−0.625133	+	0.780518i	$0.714955\pi$
$110$	4.10314	0.391219
$111$	0.0201917	0.00191651
$112$	12.9288	1.22165
$113$	17.2836	1.62590	0.812950	−	0.582334i	$-0.197860\pi$
$113$	17.2836	1.62590	0.812950	+	0.582334i	$0.197860\pi$
$114$	2.84510	0.266468
$115$	3.30013	0.307739
$116$	3.61876	0.335993
$117$	6.75283	0.624300
$118$	−8.67048	−0.798182
$119$	−4.57610	−0.419490
$120$	1.83057	0.167108
$121$	19.7682	1.79710
$122$	−13.4867	−1.22103
$123$	−5.29980	−0.477867
$124$	3.20246	0.287589
$125$	−5.77459	−0.516495
$126$	5.65164	0.503488
$127$	15.7929	1.40139	0.700694	−	0.713461i	$-0.252874\pi$
$127$	15.7929	1.40139	0.700694	+	0.713461i	$0.252874\pi$
$128$	−5.73336	−0.506763
$129$	−1.28903	−0.113493
$130$	−4.99519	−0.438107
$131$	−20.9891	−1.83383	−0.916914	−	0.399085i	$-0.869328\pi$
$131$	−20.9891	−1.83383	−0.916914	+	0.399085i	$0.869328\pi$
$132$	2.63307	0.229179
$133$	10.5418	0.914090
$134$	14.6663	1.26698
$135$	0.598945	0.0515490
$136$	3.05633	0.262078
$137$	−17.8800	−1.52759	−0.763797	−	0.645457i	$-0.776667\pi$
$137$	−17.8800	−1.52759	−0.763797	+	0.645457i	$0.776667\pi$
$138$	−6.80493	−0.579274
$139$	−0.968708	−0.0821647	−0.0410824	−	0.999156i	$-0.513081\pi$
$139$	−0.968708	−0.0821647	−0.0410824	+	0.999156i	$0.513081\pi$
$140$	1.30105	0.109959
$141$	−4.56404	−0.384362
$142$	−17.5604	−1.47363
$143$	−37.4573	−3.13234
$144$	−2.82528	−0.235440
$145$	−4.56598	−0.379184
$146$	−0.518554	−0.0429158
$147$	13.9407	1.14981
$148$	−0.00958485	−0.000787870 0
$149$	7.35989	0.602946	0.301473	−	0.953475i	$-0.402522\pi$
$149$	7.35989	0.602946	0.301473	+	0.953475i	$0.402522\pi$
$150$	5.73212	0.468026
$151$	−8.82598	−0.718248	−0.359124	−	0.933290i	$-0.616924\pi$
$151$	−8.82598	−0.718248	−0.359124	+	0.933290i	$0.616924\pi$
$152$	−7.04076	−0.571081
$153$	1.00000	0.0808452
$154$	−31.3491	−2.52618
$155$	−4.04072	−0.324558
$156$	−3.20552	−0.256647
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−3.26766	−0.259961
$159$	9.35478	0.741883
$160$	−1.57123	−0.124217
$161$	−25.2139	−1.98713
$162$	−1.23503	−0.0970334
$163$	−8.56570	−0.670917	−0.335459	−	0.942055i	$-0.608891\pi$
$163$	−8.56570	−0.670917	−0.335459	+	0.942055i	$0.608891\pi$
$164$	2.51577	0.196449
$165$	−3.32229	−0.258640
$166$	17.1927	1.33441
$167$	−5.02938	−0.389185	−0.194593	−	0.980884i	$-0.562338\pi$
$167$	−5.02938	−0.389185	−0.194593	+	0.980884i	$0.562338\pi$
$168$	−13.9861	−1.07905
$169$	32.6008	2.50775
$170$	−0.739717	−0.0567337
$171$	−2.30367	−0.176166
$172$	0.611893	0.0466564
$173$	−19.1087	−1.45281	−0.726404	−	0.687268i	$-0.758810\pi$
$173$	−19.1087	−1.45281	−0.726404	+	0.687268i	$0.758810\pi$
$174$	9.41513	0.713759
$175$	21.2389	1.60551
$176$	15.6716	1.18129
$177$	7.02044	0.527689
$178$	−1.79010	−0.134174
$179$	7.08344	0.529441	0.264720	−	0.964325i	$-0.414720\pi$
$179$	7.08344	0.529441	0.264720	+	0.964325i	$0.414720\pi$
$180$	−0.284314	−0.0211915
$181$	9.44959	0.702383	0.351191	−	0.936304i	$-0.385777\pi$
$181$	9.44959	0.702383	0.351191	+	0.936304i	$0.385777\pi$
$182$	38.1646	2.82895
$183$	10.9201	0.807239
$184$	16.8401	1.24147
$185$	0.0120937	0.000889149 0
$186$	8.33202	0.610934
$187$	−5.54690	−0.405630
$188$	2.16651	0.158009
$189$	−4.57610	−0.332862
$190$	1.70406	0.123626
$191$	18.8115	1.36115	0.680577	−	0.732677i	$-0.261729\pi$
$191$	18.8115	1.36115	0.680577	+	0.732677i	$0.261729\pi$
$192$	8.89047	0.641615
$193$	6.06230	0.436374	0.218187	−	0.975907i	$-0.429986\pi$
$193$	6.06230	0.436374	0.218187	+	0.975907i	$0.429986\pi$
$194$	−2.85703	−0.205122
$195$	4.04458	0.289638
$196$	−6.61753	−0.472681
$197$	−4.65361	−0.331556	−0.165778	−	0.986163i	$-0.553013\pi$
$197$	−4.65361	−0.331556	−0.165778	+	0.986163i	$0.553013\pi$
$198$	6.85061	0.486852
$199$	8.32869	0.590405	0.295203	−	0.955435i	$-0.404613\pi$
$199$	8.32869	0.590405	0.295203	+	0.955435i	$0.404613\pi$
$200$	−14.1852	−1.00305
$201$	−11.8752	−0.837614
$202$	11.1951	0.787682
$203$	34.8853	2.44847
$204$	−0.474692	−0.0332351
$205$	−3.17429	−0.221702
$206$	−9.40528	−0.655297
$207$	5.50991	0.382965
$208$	−19.0787	−1.32287
$209$	12.7782	0.883887
$210$	3.38502	0.233588
$211$	11.5124	0.792549	0.396274	−	0.918132i	$-0.370303\pi$
$211$	11.5124	0.792549	0.396274	+	0.918132i	$0.370303\pi$
$212$	−4.44064	−0.304985
$213$	14.2185	0.974238
$214$	16.7796	1.14703
$215$	−0.772059	−0.0526540
$216$	3.05633	0.207957
$217$	30.8722	2.09574
$218$	16.1211	1.09186
$219$	0.419870	0.0283722
$220$	1.57706	0.106326
$221$	6.75283	0.454245
$222$	−0.0249375	−0.00167369
$223$	4.53140	0.303445	0.151723	−	0.988423i	$-0.451518\pi$
$223$	4.53140	0.303445	0.151723	+	0.988423i	$0.451518\pi$
$224$	12.0046	0.802094
$225$	−4.64127	−0.309418
$226$	−21.3458	−1.41990
$227$	16.2024	1.07539	0.537696	−	0.843139i	$-0.319295\pi$
$227$	16.2024	1.07539	0.537696	+	0.843139i	$0.319295\pi$
$228$	1.09353	0.0724209
$229$	−9.79534	−0.647294	−0.323647	−	0.946178i	$-0.604909\pi$
$229$	−9.79534	−0.647294	−0.323647	+	0.946178i	$0.604909\pi$
$230$	−4.07577	−0.268749
$231$	25.3832	1.67009
$232$	−23.2995	−1.52969
$233$	21.2002	1.38887	0.694435	−	0.719556i	$-0.255654\pi$
$233$	21.2002	1.38887	0.694435	+	0.719556i	$0.255654\pi$
$234$	−8.33998	−0.545201
$235$	−2.73361	−0.178321
$236$	−3.33255	−0.216930
$237$	2.64581	0.171864
$238$	5.65164	0.366341
$239$	1.22894	0.0794936	0.0397468	−	0.999210i	$-0.487345\pi$
$239$	1.22894	0.0794936	0.0397468	+	0.999210i	$0.487345\pi$
$240$	−1.69219	−0.109230
$241$	−15.3261	−0.987240	−0.493620	−	0.869678i	$-0.664327\pi$
$241$	−15.3261	−0.987240	−0.493620	+	0.869678i	$0.664327\pi$
$242$	−24.4143	−1.56941
$243$	1.00000	0.0641500
$244$	−5.18369	−0.331852
$245$	8.34970	0.533443
$246$	6.54543	0.417321
$247$	−15.5563	−0.989822
$248$	−20.6192	−1.30932
$249$	−13.9208	−0.882196
$250$	7.13181	0.451055
$251$	5.22169	0.329590	0.164795	−	0.986328i	$-0.447304\pi$
$251$	5.22169	0.329590	0.164795	+	0.986328i	$0.447304\pi$
$252$	2.17224	0.136838
$253$	−30.5630	−1.92148
$254$	−19.5047	−1.22383
$255$	0.598945	0.0375074
$256$	−10.7001	−0.668753
$257$	−4.79243	−0.298944	−0.149472	−	0.988766i	$-0.547757\pi$
$257$	−4.79243	−0.298944	−0.149472	+	0.988766i	$0.547757\pi$
$258$	1.59200	0.0991134
$259$	−0.0923994	−0.00574142
$260$	−1.91993	−0.119069
$261$	−7.62338	−0.471875
$262$	25.9223	1.60148
$263$	1.13653	0.0700812	0.0350406	−	0.999386i	$-0.488844\pi$
$263$	1.13653	0.0700812	0.0350406	+	0.999386i	$0.488844\pi$
$264$	−16.9532	−1.04339
$265$	5.60300	0.344190
$266$	−13.0195	−0.798275
$267$	1.44944	0.0887042
$268$	5.63708	0.344339
$269$	19.9697	1.21757	0.608786	−	0.793334i	$-0.291657\pi$
$269$	19.9697	1.21757	0.608786	+	0.793334i	$0.291657\pi$
$270$	−0.739717	−0.0450177
$271$	0.326765	0.0198496	0.00992478	−	0.999951i	$-0.496841\pi$
$271$	0.326765	0.0198496	0.00992478	+	0.999951i	$0.496841\pi$
$272$	−2.82528	−0.171308
$273$	−30.9016	−1.87025
$274$	22.0824	1.33405
$275$	25.7447	1.55246
$276$	−2.61551	−0.157435
$277$	−13.4619	−0.808845	−0.404422	−	0.914572i	$-0.632527\pi$
$277$	−13.4619	−0.808845	−0.404422	+	0.914572i	$0.632527\pi$
$278$	1.19639	0.0717545
$279$	−6.74640	−0.403896
$280$	−8.37688	−0.500614
$281$	10.6834	0.637319	0.318660	−	0.947869i	$-0.396767\pi$
$281$	10.6834	0.637319	0.318660	+	0.947869i	$0.396767\pi$
$282$	5.63675	0.335663
$283$	−11.2352	−0.667863	−0.333931	−	0.942597i	$-0.608375\pi$
$283$	−11.2352	−0.667863	−0.333931	+	0.942597i	$0.608375\pi$
$284$	−6.74942	−0.400505
$285$	−1.37977	−0.0817304
$286$	46.2611	2.73547
$287$	24.2524	1.43157
$288$	−2.62334	−0.154582
$289$	1.00000	0.0588235
$290$	5.63914	0.331142
$291$	2.31332	0.135609
$292$	−0.199309	−0.0116637
$293$	16.6668	0.973688	0.486844	−	0.873489i	$-0.338148\pi$
$293$	16.6668	0.973688	0.486844	+	0.873489i	$0.338148\pi$
$294$	−17.2172	−1.00413
$295$	4.20486	0.244816
$296$	0.0617126	0.00358697
$297$	−5.54690	−0.321864
$298$	−9.08972	−0.526553
$299$	37.2075	2.15177
$300$	2.20317	0.127200
$301$	5.89874	0.339997
$302$	10.9004	0.627246
$303$	−9.06458	−0.520746
$304$	6.50851	0.373288
$305$	6.54055	0.374511
$306$	−1.23503	−0.0706022
$307$	−25.9226	−1.47948	−0.739740	−	0.672892i	$-0.765052\pi$
$307$	−25.9226	−1.47948	−0.739740	+	0.672892i	$0.765052\pi$
$308$	−12.0492	−0.686567
$309$	7.61540	0.433225
$310$	4.99042	0.283437
$311$	12.7070	0.720545	0.360273	−	0.932847i	$-0.382684\pi$
$311$	12.7070	0.720545	0.360273	+	0.932847i	$0.382684\pi$
$312$	20.6389	1.16845
$313$	11.7327	0.663170	0.331585	−	0.943425i	$-0.392417\pi$
$313$	11.7327	0.663170	0.331585	+	0.943425i	$0.392417\pi$
$314$	−1.23503	−0.0696970
$315$	−2.74083	−0.154428
$316$	−1.25594	−0.0706523
$317$	22.2583	1.25015	0.625075	−	0.780565i	$-0.285068\pi$
$317$	22.2583	1.25015	0.625075	+	0.780565i	$0.285068\pi$
$318$	−11.5535	−0.647887
$319$	42.2861	2.36757
$320$	5.32490	0.297671
$321$	−13.5864	−0.758317
$322$	31.1400	1.73537
$323$	−2.30367	−0.128179
$324$	−0.474692	−0.0263718
$325$	−31.3417	−1.73852
$326$	10.5789	0.585913
$327$	−13.0532	−0.721841
$328$	−16.1979	−0.894380
$329$	20.8855	1.15146
$330$	4.10314	0.225870
$331$	−25.0686	−1.37789	−0.688947	−	0.724812i	$-0.741927\pi$
$331$	−25.0686	−1.37789	−0.688947	+	0.724812i	$0.741927\pi$
$332$	6.60810	0.362667
$333$	0.0201917	0.00110650
$334$	6.21145	0.339876
$335$	−7.11261	−0.388603
$336$	12.9288	0.705323
$337$	18.6626	1.01661	0.508307	−	0.861176i	$-0.330271\pi$
$337$	18.6626	1.01661	0.508307	+	0.861176i	$0.330271\pi$
$338$	−40.2631	−2.19002
$339$	17.2836	0.938714
$340$	−0.284314	−0.0154191
$341$	37.4216	2.02649
$342$	2.84510	0.153846
$343$	−31.7613	−1.71495
$344$	−3.93970	−0.212415
$345$	3.30013	0.177673
$346$	23.5999	1.26874
$347$	35.7627	1.91984	0.959922	−	0.280267i	$-0.0904229\pi$
$347$	35.7627	1.91984	0.959922	+	0.280267i	$0.0904229\pi$
$348$	3.61876	0.193986
$349$	25.0848	1.34276	0.671380	−	0.741114i	$-0.265702\pi$
$349$	25.0848	1.34276	0.671380	+	0.741114i	$0.265702\pi$
$350$	−26.2307	−1.40209
$351$	6.75283	0.360440
$352$	14.5514	0.775592
$353$	14.6944	0.782103	0.391051	−	0.920369i	$-0.372111\pi$
$353$	14.6944	0.782103	0.391051	+	0.920369i	$0.372111\pi$
$354$	−8.67048	−0.460831
$355$	8.51612	0.451988
$356$	−0.688037	−0.0364659
$357$	−4.57610	−0.242193
$358$	−8.74828	−0.462361
$359$	28.1206	1.48415	0.742074	−	0.670318i	$-0.233842\pi$
$359$	28.1206	1.48415	0.742074	+	0.670318i	$0.233842\pi$
$360$	1.83057	0.0964796
$361$	−13.6931	−0.720691
$362$	−11.6706	−0.613391
$363$	19.7682	1.03756
$364$	14.6688	0.768852
$365$	0.251479	0.0131630
$366$	−13.4867	−0.704962
$367$	32.4882	1.69587	0.847934	−	0.530102i	$-0.177846\pi$
$367$	32.4882	1.69587	0.847934	+	0.530102i	$0.177846\pi$
$368$	−15.5671	−0.811489
$369$	−5.29980	−0.275896
$370$	−0.0149362	−0.000776494 0
$371$	−42.8084	−2.22250
$372$	3.20246	0.166040
$373$	−16.8996	−0.875027	−0.437514	−	0.899212i	$-0.644141\pi$
$373$	−16.8996	−0.875027	−0.437514	+	0.899212i	$0.644141\pi$
$374$	6.85061	0.354237
$375$	−5.77459	−0.298198
$376$	−13.9492	−0.719376
$377$	−51.4794	−2.65132
$378$	5.65164	0.290689
$379$	6.83321	0.350999	0.175499	−	0.984480i	$-0.443846\pi$
$379$	6.83321	0.350999	0.175499	+	0.984480i	$0.443846\pi$
$380$	0.654965	0.0335990
$381$	15.7929	0.809092
$382$	−23.2328	−1.18870
$383$	−10.8899	−0.556446	−0.278223	−	0.960517i	$-0.589745\pi$
$383$	−10.8899	−0.556446	−0.278223	+	0.960517i	$0.589745\pi$
$384$	−5.73336	−0.292579
$385$	15.2031	0.774823
$386$	−7.48714	−0.381086
$387$	−1.28903	−0.0655251
$388$	−1.09811	−0.0557483
$389$	7.74941	0.392911	0.196455	−	0.980513i	$-0.437057\pi$
$389$	7.74941	0.392911	0.196455	+	0.980513i	$0.437057\pi$
$390$	−4.99519	−0.252941
$391$	5.50991	0.278648
$392$	42.6073	2.15199
$393$	−20.9891	−1.05876
$394$	5.74736	0.289548
$395$	1.58469	0.0797345
$396$	2.63307	0.132317
$397$	−12.3342	−0.619037	−0.309519	−	0.950893i	$-0.600168\pi$
$397$	−12.3342	−0.619037	−0.309519	+	0.950893i	$0.600168\pi$
$398$	−10.2862	−0.515601
$399$	10.5418	0.527750
$400$	13.1129	0.655644
$401$	33.3317	1.66451	0.832254	−	0.554395i	$-0.187050\pi$
$401$	33.3317	1.66451	0.832254	+	0.554395i	$0.187050\pi$
$402$	14.6663	0.731489
$403$	−45.5573	−2.26937
$404$	4.30288	0.214076
$405$	0.598945	0.0297618
$406$	−43.0845	−2.13825
$407$	−0.112002	−0.00555171
$408$	3.05633	0.151311
$409$	−11.4802	−0.567659	−0.283830	−	0.958875i	$-0.591605\pi$
$409$	−11.4802	−0.567659	−0.283830	+	0.958875i	$0.591605\pi$
$410$	3.92035	0.193612
$411$	−17.8800	−0.881957
$412$	−3.61497	−0.178097
$413$	−32.1262	−1.58083
$414$	−6.80493	−0.334444
$415$	−8.33780	−0.409287
$416$	−17.7150	−0.868547
$417$	−0.968708	−0.0474378
$418$	−15.7815	−0.771899
$419$	−19.2787	−0.941824	−0.470912	−	0.882180i	$-0.656075\pi$
$419$	−19.2787	−0.941824	−0.470912	+	0.882180i	$0.656075\pi$
$420$	1.30105	0.0634848
$421$	31.0639	1.51396	0.756982	−	0.653436i	$-0.226673\pi$
$421$	31.0639	1.51396	0.756982	+	0.653436i	$0.226673\pi$
$422$	−14.2182	−0.692133
$423$	−4.56404	−0.221911
$424$	28.5913	1.38852
$425$	−4.64127	−0.225134
$426$	−17.5604	−0.850802
$427$	−49.9716	−2.41829
$428$	6.44934	0.311740
$429$	−37.4573	−1.80846
$430$	0.953518	0.0459827
$431$	37.7979	1.82066	0.910331	−	0.413880i	$-0.135827\pi$
$431$	37.7979	1.82066	0.910331	+	0.413880i	$0.135827\pi$
$432$	−2.82528	−0.135932
$433$	0.195177	0.00937960	0.00468980	−	0.999989i	$-0.498507\pi$
$433$	0.195177	0.00937960	0.00468980	+	0.999989i	$0.498507\pi$
$434$	−38.1282	−1.83021
$435$	−4.56598	−0.218922
$436$	6.19623	0.296746
$437$	−12.6930	−0.607188
$438$	−0.518554	−0.0247774
$439$	−7.88753	−0.376451	−0.188226	−	0.982126i	$-0.560274\pi$
$439$	−7.88753	−0.376451	−0.188226	+	0.982126i	$0.560274\pi$
$440$	−10.1540	−0.484073
$441$	13.9407	0.663842
$442$	−8.33998	−0.396692
$443$	32.7872	1.55777	0.778884	−	0.627168i	$-0.215786\pi$
$443$	32.7872	1.55777	0.778884	+	0.627168i	$0.215786\pi$
$444$	−0.00958485	−0.000454877 0
$445$	0.868133	0.0411535
$446$	−5.59644	−0.264999
$447$	7.35989	0.348111
$448$	−40.6837	−1.92212
$449$	−8.35943	−0.394506	−0.197253	−	0.980353i	$-0.563202\pi$
$449$	−8.35943	−0.394506	−0.197253	+	0.980353i	$0.563202\pi$
$450$	5.73212	0.270215
$451$	29.3975	1.38427
$452$	−8.20436	−0.385901
$453$	−8.82598	−0.414681
$454$	−20.0105	−0.939140
$455$	−18.5084	−0.867686
$456$	−7.04076	−0.329714
$457$	28.5859	1.33719	0.668595	−	0.743627i	$-0.266896\pi$
$457$	28.5859	1.33719	0.668595	+	0.743627i	$0.266896\pi$
$458$	12.0976	0.565282
$459$	1.00000	0.0466760
$460$	−1.56655	−0.0730406
$461$	11.6018	0.540348	0.270174	−	0.962812i	$-0.412919\pi$
$461$	11.6018	0.540348	0.270174	+	0.962812i	$0.412919\pi$
$462$	−31.3491	−1.45849
$463$	−9.13245	−0.424421	−0.212210	−	0.977224i	$-0.568066\pi$
$463$	−9.13245	−0.424421	−0.212210	+	0.977224i	$0.568066\pi$
$464$	21.5382	0.999886
$465$	−4.04072	−0.187384
$466$	−26.1829	−1.21290
$467$	4.93120	0.228189	0.114094	−	0.993470i	$-0.463603\pi$
$467$	4.93120	0.228189	0.114094	+	0.993470i	$0.463603\pi$
$468$	−3.20552	−0.148175
$469$	54.3422	2.50929
$470$	3.37610	0.155728
$471$	1.00000	0.0460776
$472$	21.4568	0.987628
$473$	7.15013	0.328764
$474$	−3.26766	−0.150089
$475$	10.6919	0.490579
$476$	2.17224	0.0995644
$477$	9.35478	0.428326
$478$	−1.51778	−0.0694218
$479$	20.2283	0.924257	0.462128	−	0.886813i	$-0.347086\pi$
$479$	20.2283	0.924257	0.462128	+	0.886813i	$0.347086\pi$
$480$	−1.57123	−0.0717167
$481$	0.136351	0.00621709
$482$	18.9282	0.862158
$483$	−25.2139	−1.14727
$484$	−9.38378	−0.426536
$485$	1.38555	0.0629146
$486$	−1.23503	−0.0560223
$487$	3.91646	0.177472	0.0887359	−	0.996055i	$-0.471717\pi$
$487$	3.91646	0.177472	0.0887359	+	0.996055i	$0.471717\pi$
$488$	33.3755	1.51084
$489$	−8.56570	−0.387354
$490$	−10.3122	−0.465856
$491$	33.6252	1.51748	0.758742	−	0.651391i	$-0.225814\pi$
$491$	33.6252	1.51748	0.758742	+	0.651391i	$0.225814\pi$
$492$	2.51577	0.113420
$493$	−7.62338	−0.343340
$494$	19.2125	0.864412
$495$	−3.32229	−0.149326
$496$	19.0605	0.855841
$497$	−65.0654	−2.91858
$498$	17.1927	0.770422
$499$	−19.5915	−0.877035	−0.438518	−	0.898723i	$-0.644496\pi$
$499$	−19.5915	−0.877035	−0.438518	+	0.898723i	$0.644496\pi$
$500$	2.74115	0.122588
$501$	−5.02938	−0.224696
$502$	−6.44897	−0.287832
$503$	31.6293	1.41028	0.705141	−	0.709068i	$-0.250884\pi$
$503$	31.6293	1.41028	0.705141	+	0.709068i	$0.250884\pi$
$504$	−13.9861	−0.622989
$505$	−5.42918	−0.241595
$506$	37.7463	1.67803
$507$	32.6008	1.44785
$508$	−7.49674	−0.332614
$509$	22.2314	0.985391	0.492695	−	0.870202i	$-0.336012\pi$
$509$	22.2314	0.985391	0.492695	+	0.870202i	$0.336012\pi$
$510$	−0.739717	−0.0327552
$511$	−1.92137	−0.0849963
$512$	24.6817	1.09079
$513$	−2.30367	−0.101709
$514$	5.91882	0.261068
$515$	4.56121	0.200991
$516$	0.611893	0.0269371
$517$	25.3163	1.11341
$518$	0.114116	0.00501398
$519$	−19.1087	−0.838779
$520$	12.3615	0.542090
$521$	2.00626	0.0878959	0.0439479	−	0.999034i	$-0.486006\pi$
$521$	2.00626	0.0878959	0.0439479	+	0.999034i	$0.486006\pi$
$522$	9.41513	0.412089
$523$	0.727731	0.0318215	0.0159107	−	0.999873i	$-0.494935\pi$
$523$	0.727731	0.0318215	0.0159107	+	0.999873i	$0.494935\pi$
$524$	9.96337	0.435252
$525$	21.2389	0.926941
$526$	−1.40365	−0.0612019
$527$	−6.74640	−0.293878
$528$	15.6716	0.682018
$529$	7.35912	0.319962
$530$	−6.91989	−0.300581
$531$	7.02044	0.304661
$532$	−5.00411	−0.216956
$533$	−35.7886	−1.55018
$534$	−1.79010	−0.0774654
$535$	−8.13748	−0.351814
$536$	−36.2946	−1.56769
$537$	7.08344	0.305673
$538$	−24.6632	−1.06331
$539$	−77.3277	−3.33074
$540$	−0.284314	−0.0122349
$541$	30.5303	1.31260	0.656299	−	0.754501i	$-0.272121\pi$
$541$	30.5303	1.31260	0.656299	+	0.754501i	$0.272121\pi$
$542$	−0.403566	−0.0173346
$543$	9.44959	0.405521
$544$	−2.62334	−0.112475
$545$	−7.81812	−0.334892
$546$	38.1646	1.63329
$547$	5.06260	0.216461	0.108231	−	0.994126i	$-0.465482\pi$
$547$	5.06260	0.216461	0.108231	+	0.994126i	$0.465482\pi$
$548$	8.48751	0.362568
$549$	10.9201	0.466059
$550$	−31.7955	−1.35577
$551$	17.5617	0.748154
$552$	16.8401	0.716762
$553$	−12.1075	−0.514862
$554$	16.6259	0.706365
$555$	0.0120937	0.000513350 0
$556$	0.459838	0.0195015
$557$	1.00960	0.0427779	0.0213890	−	0.999771i	$-0.493191\pi$
$557$	1.00960	0.0427779	0.0213890	+	0.999771i	$0.493191\pi$
$558$	8.33202	0.352723
$559$	−8.70462	−0.368166
$560$	7.74362	0.327228
$561$	−5.54690	−0.234191
$562$	−13.1944	−0.556571
$563$	−14.3276	−0.603837	−0.301919	−	0.953334i	$-0.597627\pi$
$563$	−14.3276	−0.603837	−0.301919	+	0.953334i	$0.597627\pi$
$564$	2.16651	0.0912267
$565$	10.3519	0.435507
$566$	13.8758	0.583245
$567$	−4.57610	−0.192178
$568$	43.4565	1.82339
$569$	41.3031	1.73152	0.865758	−	0.500464i	$-0.166837\pi$
$569$	41.3031	1.73152	0.865758	+	0.500464i	$0.166837\pi$
$570$	1.70406	0.0713752
$571$	−40.8376	−1.70900	−0.854500	−	0.519451i	$-0.826136\pi$
$571$	−40.8376	−1.70900	−0.854500	+	0.519451i	$0.826136\pi$
$572$	17.7807	0.743448
$573$	18.8115	0.785862
$574$	−29.9525	−1.25019
$575$	−25.5730	−1.06647
$576$	8.89047	0.370436
$577$	−2.51227	−0.104587	−0.0522935	−	0.998632i	$-0.516653\pi$
$577$	−2.51227	−0.104587	−0.0522935	+	0.998632i	$0.516653\pi$
$578$	−1.23503	−0.0513706
$579$	6.06230	0.251941
$580$	2.16743	0.0899978
$581$	63.7031	2.64285
$582$	−2.85703	−0.118428
$583$	−51.8901	−2.14907
$584$	1.28326	0.0531017
$585$	4.04458	0.167223
$586$	−20.5841	−0.850322
$587$	−26.8825	−1.10956	−0.554780	−	0.831997i	$-0.687198\pi$
$587$	−26.8825	−1.10956	−0.554780	+	0.831997i	$0.687198\pi$
$588$	−6.61753	−0.272902
$589$	15.5414	0.640374
$590$	−5.19314	−0.213798
$591$	−4.65361	−0.191424
$592$	−0.0570474	−0.00234463
$593$	−22.0313	−0.904715	−0.452358	−	0.891837i	$-0.649417\pi$
$593$	−22.0313	−0.904715	−0.452358	+	0.891837i	$0.649417\pi$
$594$	6.85061	0.281084
$595$	−2.74083	−0.112363
$596$	−3.49368	−0.143107
$597$	8.32869	0.340871
$598$	−45.9525	−1.87914
$599$	4.82816	0.197273	0.0986367	−	0.995124i	$-0.468552\pi$
$599$	4.82816	0.197273	0.0986367	+	0.995124i	$0.468552\pi$
$600$	−14.1852	−0.579109
$601$	−21.3476	−0.870786	−0.435393	−	0.900240i	$-0.643391\pi$
$601$	−21.3476	−0.870786	−0.435393	+	0.900240i	$0.643391\pi$
$602$	−7.28514	−0.296920
$603$	−11.8752	−0.483597
$604$	4.18962	0.170473
$605$	11.8400	0.481366
$606$	11.1951	0.454768
$607$	1.82100	0.0739123	0.0369561	−	0.999317i	$-0.488234\pi$
$607$	1.82100	0.0739123	0.0369561	+	0.999317i	$0.488234\pi$
$608$	6.04329	0.245088
$609$	34.8853	1.41362
$610$	−8.07780	−0.327061
$611$	−30.8202	−1.24685
$612$	−0.474692	−0.0191883
$613$	3.72964	0.150639	0.0753195	−	0.997159i	$-0.476002\pi$
$613$	3.72964	0.150639	0.0753195	+	0.997159i	$0.476002\pi$
$614$	32.0153	1.29203
$615$	−3.17429	−0.128000
$616$	77.5793	3.12576
$617$	−6.58661	−0.265167	−0.132583	−	0.991172i	$-0.542327\pi$
$617$	−6.58661	−0.265167	−0.132583	+	0.991172i	$0.542327\pi$
$618$	−9.40528	−0.378336
$619$	−42.5150	−1.70882	−0.854411	−	0.519597i	$-0.826082\pi$
$619$	−42.5150	−1.70882	−0.854411	+	0.519597i	$0.826082\pi$
$620$	1.91810	0.0770326
$621$	5.50991	0.221105
$622$	−15.6935	−0.629253
$623$	−6.63277	−0.265736
$624$	−19.0787	−0.763758
$625$	19.7477	0.789907
$626$	−14.4903	−0.579147
$627$	12.7782	0.510313
$628$	−0.474692	−0.0189423
$629$	0.0201917	0.000805097 0
$630$	3.38502	0.134862
$631$	43.7022	1.73976	0.869878	−	0.493267i	$-0.164198\pi$
$631$	43.7022	1.73976	0.869878	+	0.493267i	$0.164198\pi$
$632$	8.08645	0.321662
$633$	11.5124	0.457578
$634$	−27.4897	−1.09176
$635$	9.45905	0.375371
$636$	−4.44064	−0.176083
$637$	94.1391	3.72993
$638$	−52.2248	−2.06760
$639$	14.2185	0.562476
$640$	−3.43397	−0.135740
$641$	9.58978	0.378773	0.189387	−	0.981903i	$-0.439350\pi$
$641$	9.58978	0.378773	0.189387	+	0.981903i	$0.439350\pi$
$642$	16.7796	0.662238
$643$	−46.7295	−1.84283	−0.921416	−	0.388577i	$-0.872967\pi$
$643$	−46.7295	−1.84283	−0.921416	+	0.388577i	$0.872967\pi$
$644$	11.9688	0.471638
$645$	−0.772059	−0.0303998
$646$	2.84510	0.111939
$647$	14.9230	0.586683	0.293341	−	0.956008i	$-0.405233\pi$
$647$	14.9230	0.586683	0.293341	+	0.956008i	$0.405233\pi$
$648$	3.05633	0.120064
$649$	−38.9417	−1.52860
$650$	38.7080	1.51825
$651$	30.8722	1.20998
$652$	4.06607	0.159240
$653$	23.9899	0.938798	0.469399	−	0.882986i	$-0.344471\pi$
$653$	23.9899	0.938798	0.469399	+	0.882986i	$0.344471\pi$
$654$	16.1211	0.630384
$655$	−12.5713	−0.491202
$656$	14.9734	0.584614
$657$	0.419870	0.0163807
$658$	−25.7943	−1.00557
$659$	20.2257	0.787880	0.393940	−	0.919136i	$-0.371112\pi$
$659$	20.2257	0.787880	0.393940	+	0.919136i	$0.371112\pi$
$660$	1.57706	0.0613872
$661$	15.8888	0.618003	0.309001	−	0.951062i	$-0.400005\pi$
$661$	15.8888	0.618003	0.309001	+	0.951062i	$0.400005\pi$
$662$	30.9605	1.20332
$663$	6.75283	0.262258
$664$	−42.5466	−1.65113
$665$	6.31396	0.244845
$666$	−0.0249375	−0.000966307 0
$667$	−42.0041	−1.62641
$668$	2.38741	0.0923715
$669$	4.53140	0.175194
$670$	8.78431	0.339367
$671$	−60.5729	−2.33839
$672$	12.0046	0.463089
$673$	−13.7702	−0.530802	−0.265401	−	0.964138i	$-0.585504\pi$
$673$	−13.7702	−0.530802	−0.265401	+	0.964138i	$0.585504\pi$
$674$	−23.0489	−0.887810
$675$	−4.64127	−0.178642
$676$	−15.4753	−0.595205
$677$	−27.6924	−1.06431	−0.532154	−	0.846648i	$-0.678617\pi$
$677$	−27.6924	−1.06431	−0.532154	+	0.846648i	$0.678617\pi$
$678$	−21.3458	−0.819779
$679$	−10.5860	−0.406252
$680$	1.83057	0.0701992
$681$	16.2024	0.620878
$682$	−46.2169	−1.76974
$683$	−43.6385	−1.66978	−0.834890	−	0.550417i	$-0.814469\pi$
$683$	−43.6385	−1.66978	−0.834890	+	0.550417i	$0.814469\pi$
$684$	1.09353	0.0418122
$685$	−10.7091	−0.409176
$686$	39.2262	1.49766
$687$	−9.79534	−0.373715
$688$	3.64188	0.138845
$689$	63.1713	2.40664
$690$	−4.07577	−0.155162
$691$	33.6937	1.28177	0.640885	−	0.767637i	$-0.278568\pi$
$691$	33.6937	1.28177	0.640885	+	0.767637i	$0.278568\pi$
$692$	9.07075	0.344818
$693$	25.3832	0.964228
$694$	−44.1682	−1.67660
$695$	−0.580203	−0.0220083
$696$	−23.2995	−0.883167
$697$	−5.29980	−0.200744
$698$	−30.9806	−1.17263
$699$	21.2002	0.801864
$700$	−10.0819	−0.381061
$701$	−5.11513	−0.193196	−0.0965979	−	0.995323i	$-0.530796\pi$
$701$	−5.11513	−0.193196	−0.0965979	+	0.995323i	$0.530796\pi$
$702$	−8.33998	−0.314772
$703$	−0.0465150	−0.00175435
$704$	−49.3146	−1.85861
$705$	−2.73361	−0.102954
$706$	−18.1480	−0.683011
$707$	41.4804	1.56003
$708$	−3.33255	−0.125245
$709$	5.69343	0.213821	0.106911	−	0.994269i	$-0.465904\pi$
$709$	5.69343	0.213821	0.106911	+	0.994269i	$0.465904\pi$
$710$	−10.5177	−0.394722
$711$	2.64581	0.0992255
$712$	4.42996	0.166020
$713$	−37.1720	−1.39210
$714$	5.65164	0.211507
$715$	−22.4349	−0.839017
$716$	−3.36245	−0.125661
$717$	1.22894	0.0458957
$718$	−34.7299	−1.29611
$719$	20.5790	0.767467	0.383733	−	0.923444i	$-0.374638\pi$
$719$	20.5790	0.767467	0.383733	+	0.923444i	$0.374638\pi$
$720$	−1.69219	−0.0630642
$721$	−34.8488	−1.29784
$722$	16.9115	0.629380
$723$	−15.3261	−0.569984
$724$	−4.48565	−0.166708
$725$	35.3821	1.31406
$726$	−24.4143	−0.906101
$727$	8.77484	0.325441	0.162720	−	0.986672i	$-0.447973\pi$
$727$	8.77484	0.325441	0.162720	+	0.986672i	$0.447973\pi$
$728$	−94.4456	−3.50039
$729$	1.00000	0.0370370
$730$	−0.310585	−0.0114953
$731$	−1.28903	−0.0476765
$732$	−5.18369	−0.191595
$733$	13.6133	0.502819	0.251409	−	0.967881i	$-0.419106\pi$
$733$	13.6133	0.502819	0.251409	+	0.967881i	$0.419106\pi$
$734$	−40.1240	−1.48100
$735$	8.34970	0.307983
$736$	−14.4543	−0.532794
$737$	65.8708	2.42638
$738$	6.54543	0.240940
$739$	20.3745	0.749488	0.374744	−	0.927128i	$-0.377731\pi$
$739$	20.3745	0.749488	0.374744	+	0.927128i	$0.377731\pi$
$740$	−0.00574080	−0.000211036 0
$741$	−15.5563	−0.571474
$742$	52.8698	1.94091
$743$	22.9217	0.840917	0.420459	−	0.907312i	$-0.361869\pi$
$743$	22.9217	0.840917	0.420459	+	0.907312i	$0.361869\pi$
$744$	−20.6192	−0.755936
$745$	4.40817	0.161503
$746$	20.8715	0.764162
$747$	−13.9208	−0.509336
$748$	2.63307	0.0962746
$749$	62.1725	2.27173
$750$	7.13181	0.260417
$751$	−27.0498	−0.987061	−0.493530	−	0.869729i	$-0.664294\pi$
$751$	−27.0498	−0.987061	−0.493530	+	0.869729i	$0.664294\pi$
$752$	12.8947	0.470222
$753$	5.22169	0.190289
$754$	63.5788	2.31540
$755$	−5.28627	−0.192387
$756$	2.17224	0.0790035
$757$	−19.9010	−0.723313	−0.361657	−	0.932311i	$-0.617789\pi$
$757$	−19.9010	−0.723313	−0.361657	+	0.932311i	$0.617789\pi$
$758$	−8.43925	−0.306527
$759$	−30.5630	−1.10936
$760$	−4.21702	−0.152968
$761$	12.0365	0.436323	0.218162	−	0.975913i	$-0.429994\pi$
$761$	12.0365	0.436323	0.218162	+	0.975913i	$0.429994\pi$
$762$	−19.5047	−0.706581
$763$	59.7325	2.16246
$764$	−8.92967	−0.323064
$765$	0.598945	0.0216549
$766$	13.4493	0.485944
$767$	47.4079	1.71180
$768$	−10.7001	−0.386105
$769$	49.5297	1.78609	0.893044	−	0.449969i	$-0.148565\pi$
$769$	49.5297	1.78609	0.893044	+	0.449969i	$0.148565\pi$
$770$	−18.7764	−0.676654
$771$	−4.79243	−0.172595
$772$	−2.87773	−0.103572
$773$	−43.5215	−1.56536	−0.782680	−	0.622425i	$-0.786148\pi$
$773$	−43.5215	−1.56536	−0.782680	+	0.622425i	$0.786148\pi$
$774$	1.59200	0.0572232
$775$	31.3118	1.12475
$776$	7.07026	0.253807
$777$	−0.0923994	−0.00331481
$778$	−9.57078	−0.343129
$779$	12.2090	0.437431
$780$	−1.91993	−0.0687444
$781$	−78.8688	−2.82215
$782$	−6.80493	−0.243344
$783$	−7.62338	−0.272437
$784$	−39.3864	−1.40666
$785$	0.598945	0.0213773
$786$	25.9223	0.924617
$787$	16.6780	0.594506	0.297253	−	0.954799i	$-0.403929\pi$
$787$	16.6780	0.594506	0.297253	+	0.954799i	$0.403929\pi$
$788$	2.20903	0.0786934
$789$	1.13653	0.0404614
$790$	−1.95715	−0.0696322
$791$	−79.0913	−2.81216
$792$	−16.9532	−0.602404
$793$	73.7418	2.61865
$794$	15.2332	0.540606
$795$	5.60300	0.198718
$796$	−3.95356	−0.140130
$797$	21.3888	0.757630	0.378815	−	0.925472i	$-0.376332\pi$
$797$	21.3888	0.757630	0.378815	+	0.925472i	$0.376332\pi$
$798$	−13.0195	−0.460885
$799$	−4.56404	−0.161464
$800$	12.1756	0.430472
$801$	1.44944	0.0512134
$802$	−41.1658	−1.45362
$803$	−2.32898	−0.0821879
$804$	5.63708	0.198804
$805$	−15.1017	−0.532266
$806$	56.2648	1.98184
$807$	19.9697	0.702966
$808$	−27.7043	−0.974635
$809$	22.7369	0.799386	0.399693	−	0.916649i	$-0.369117\pi$
$809$	22.7369	0.799386	0.399693	+	0.916649i	$0.369117\pi$
$810$	−0.739717	−0.0259910
$811$	8.30863	0.291755	0.145878	−	0.989303i	$-0.453399\pi$
$811$	8.30863	0.291755	0.145878	+	0.989303i	$0.453399\pi$
$812$	−16.5598	−0.581135
$813$	0.326765	0.0114602
$814$	0.138326	0.00484832
$815$	−5.13038	−0.179709
$816$	−2.82528	−0.0989047
$817$	2.96950	0.103890
$818$	14.1784	0.495737
$819$	−30.9016	−1.07979
$820$	1.50681	0.0526200
$821$	−41.0245	−1.43176	−0.715882	−	0.698221i	$-0.753975\pi$
$821$	−41.0245	−1.43176	−0.715882	+	0.698221i	$0.753975\pi$
$822$	22.0824	0.770213
$823$	56.1410	1.95695	0.978477	−	0.206357i	$-0.0661607\pi$
$823$	56.1410	1.95695	0.978477	+	0.206357i	$0.0661607\pi$
$824$	23.2752	0.810829
$825$	25.7447	0.896314
$826$	39.6770	1.38054
$827$	38.9008	1.35271	0.676357	−	0.736574i	$-0.263558\pi$
$827$	38.9008	1.35271	0.676357	+	0.736574i	$0.263558\pi$
$828$	−2.61551	−0.0908953
$829$	18.3040	0.635724	0.317862	−	0.948137i	$-0.397035\pi$
$829$	18.3040	0.635724	0.317862	+	0.948137i	$0.397035\pi$
$830$	10.2975	0.357430
$831$	−13.4619	−0.466987
$832$	60.0359	2.08137
$833$	13.9407	0.483016
$834$	1.19639	0.0414275
$835$	−3.01232	−0.104246
$836$	−6.06571	−0.209787
$837$	−6.74640	−0.233190
$838$	23.8098	0.822496
$839$	−19.4878	−0.672794	−0.336397	−	0.941720i	$-0.609208\pi$
$839$	−19.4878	−0.672794	−0.336397	+	0.941720i	$0.609208\pi$
$840$	−8.37688	−0.289030
$841$	29.1159	1.00400
$842$	−38.3650	−1.32215
$843$	10.6834	0.367956
$844$	−5.46486	−0.188108
$845$	19.5261	0.671717
$846$	5.63675	0.193795
$847$	−90.4610	−3.10828
$848$	−26.4299	−0.907607
$849$	−11.2352	−0.385591
$850$	5.73212	0.196610
$851$	0.111255	0.00381376
$852$	−6.74942	−0.231231
$853$	19.2016	0.657449	0.328724	−	0.944426i	$-0.393381\pi$
$853$	19.2016	0.657449	0.328724	+	0.944426i	$0.393381\pi$
$854$	61.7166	2.11190
$855$	−1.37977	−0.0471871
$856$	−41.5244	−1.41927
$857$	−47.3684	−1.61807	−0.809037	−	0.587758i	$-0.800011\pi$
$857$	−47.3684	−1.61807	−0.809037	+	0.587758i	$0.800011\pi$
$858$	46.2611	1.57933
$859$	−40.3443	−1.37653	−0.688265	−	0.725459i	$-0.741627\pi$
$859$	−40.3443	−1.37653	−0.688265	+	0.725459i	$0.741627\pi$
$860$	0.366490	0.0124972
$861$	24.2524	0.826519
$862$	−46.6817	−1.58999
$863$	37.8354	1.28793	0.643965	−	0.765055i	$-0.277288\pi$
$863$	37.8354	1.28793	0.643965	+	0.765055i	$0.277288\pi$
$864$	−2.62334	−0.0892477
$865$	−11.4451	−0.389144
$866$	−0.241050	−0.00819121
$867$	1.00000	0.0339618
$868$	−14.6548	−0.497415
$869$	−14.6760	−0.497850
$870$	5.63914	0.191185
$871$	−80.1915	−2.71718
$872$	−39.8947	−1.35101
$873$	2.31332	0.0782939
$874$	15.6763	0.530258
$875$	26.4251	0.893331
$876$	−0.199309	−0.00673402
$877$	−18.2399	−0.615917	−0.307958	−	0.951400i	$-0.599646\pi$
$877$	−18.2399	−0.615917	−0.307958	+	0.951400i	$0.599646\pi$
$878$	9.74136	0.328755
$879$	16.6668	0.562159
$880$	9.38641	0.316416
$881$	−26.3523	−0.887833	−0.443916	−	0.896068i	$-0.646411\pi$
$881$	−26.3523	−0.887833	−0.443916	+	0.896068i	$0.646411\pi$
$882$	−17.2172	−0.579734
$883$	40.0490	1.34776	0.673878	−	0.738842i	$-0.264627\pi$
$883$	40.0490	1.34776	0.673878	+	0.738842i	$0.264627\pi$
$884$	−3.20552	−0.107813
$885$	4.20486	0.141345
$886$	−40.4933	−1.36040
$887$	−8.86739	−0.297738	−0.148869	−	0.988857i	$-0.547563\pi$
$887$	−8.86739	−0.297738	−0.148869	+	0.988857i	$0.547563\pi$
$888$	0.0617126	0.00207094
$889$	−72.2697	−2.42385
$890$	−1.07217	−0.0359394
$891$	−5.54690	−0.185828
$892$	−2.15102	−0.0720215
$893$	10.5140	0.351838
$894$	−9.08972	−0.304006
$895$	4.24259	0.141814
$896$	26.2364	0.876498
$897$	37.2075	1.24232
$898$	10.3242	0.344522
$899$	51.4303	1.71530
$900$	2.20317	0.0734390
$901$	9.35478	0.311653
$902$	−36.3069	−1.20889
$903$	5.89874	0.196298
$904$	52.8242	1.75691
$905$	5.65978	0.188138
$906$	10.9004	0.362141
$907$	−35.3036	−1.17224	−0.586119	−	0.810225i	$-0.699345\pi$
$907$	−35.3036	−1.17224	−0.586119	+	0.810225i	$0.699345\pi$
$908$	−7.69115	−0.255240
$909$	−9.06458	−0.300653
$910$	22.8585	0.757751
$911$	−49.1679	−1.62901	−0.814503	−	0.580159i	$-0.802990\pi$
$911$	−49.1679	−1.62901	−0.814503	+	0.580159i	$0.802990\pi$
$912$	6.50851	0.215518
$913$	77.2175	2.55552
$914$	−35.3045	−1.16777
$915$	6.54055	0.216224
$916$	4.64977	0.153633
$917$	96.0483	3.17179
$918$	−1.23503	−0.0407622
$919$	−35.9326	−1.18531	−0.592654	−	0.805457i	$-0.701920\pi$
$919$	−35.9326	−1.18531	−0.592654	+	0.805457i	$0.701920\pi$
$920$	10.0863	0.332535
$921$	−25.9226	−0.854179
$922$	−14.3286	−0.471886
$923$	96.0154	3.16038
$924$	−12.0492	−0.396389
$925$	−0.0937152	−0.00308134
$926$	11.2789	0.370647
$927$	7.61540	0.250123
$928$	19.9987	0.656489
$929$	−10.3365	−0.339129	−0.169564	−	0.985519i	$-0.554236\pi$
$929$	−10.3365	−0.339129	−0.169564	+	0.985519i	$0.554236\pi$
$930$	4.99042	0.163642
$931$	−32.1147	−1.05252
$932$	−10.0636	−0.329643
$933$	12.7070	0.416007
$934$	−6.09019	−0.199277
$935$	−3.32229	−0.108651
$936$	20.6389	0.674603
$937$	33.2119	1.08499	0.542493	−	0.840060i	$-0.317480\pi$
$937$	33.2119	1.08499	0.542493	+	0.840060i	$0.317480\pi$
$938$	−67.1145	−2.19137
$939$	11.7327	0.382882
$940$	1.29762	0.0423238
$941$	−15.0842	−0.491731	−0.245866	−	0.969304i	$-0.579072\pi$
$941$	−15.0842	−0.491731	−0.245866	+	0.969304i	$0.579072\pi$
$942$	−1.23503	−0.0402396
$943$	−29.2014	−0.950929
$944$	−19.8347	−0.645566
$945$	−2.74083	−0.0891592
$946$	−8.83066	−0.287109
$947$	−33.7147	−1.09558	−0.547791	−	0.836615i	$-0.684531\pi$
$947$	−33.7147	−1.09558	−0.547791	+	0.836615i	$0.684531\pi$
$948$	−1.25594	−0.0407911
$949$	2.83531	0.0920381
$950$	−13.2049	−0.428423
$951$	22.2583	0.721775
$952$	−13.9861	−0.453291
$953$	51.1351	1.65643	0.828215	−	0.560411i	$-0.189357\pi$
$953$	51.1351	1.65643	0.828215	+	0.560411i	$0.189357\pi$
$954$	−11.5535	−0.374058
$955$	11.2671	0.364593
$956$	−0.583369	−0.0188675
$957$	42.2861	1.36692
$958$	−24.9827	−0.807154
$959$	81.8208	2.64213
$960$	5.32490	0.171861
$961$	14.5138	0.468189
$962$	−0.168399	−0.00542939
$963$	−13.5864	−0.437814
$964$	7.27517	0.234318
$965$	3.63098	0.116885
$966$	31.1400	1.00191
$967$	16.9298	0.544425	0.272213	−	0.962237i	$-0.412245\pi$
$967$	16.9298	0.544425	0.272213	+	0.962237i	$0.412245\pi$
$968$	60.4180	1.94191
$969$	−2.30367	−0.0740044
$970$	−1.71120	−0.0549433
$971$	30.4446	0.977014	0.488507	−	0.872560i	$-0.337542\pi$
$971$	30.4446	0.977014	0.488507	+	0.872560i	$0.337542\pi$
$972$	−0.474692	−0.0152258
$973$	4.43290	0.142112
$974$	−4.83696	−0.154986
$975$	−31.3417	−1.00374
$976$	−30.8524	−0.987562
$977$	−18.2934	−0.585259	−0.292629	−	0.956226i	$-0.594530\pi$
$977$	−18.2934	−0.585259	−0.292629	+	0.956226i	$0.594530\pi$
$978$	10.5789	0.338277
$979$	−8.03990	−0.256956
$980$	−3.96354	−0.126611
$981$	−13.0532	−0.416755
$982$	−41.5283	−1.32522
$983$	−52.4589	−1.67318	−0.836590	−	0.547830i	$-0.815454\pi$
$983$	−52.4589	−1.67318	−0.836590	+	0.547830i	$0.815454\pi$
$984$	−16.1979	−0.516371
$985$	−2.78725	−0.0888093
$986$	9.41513	0.299839
$987$	20.8855	0.664793
$988$	7.38444	0.234930
$989$	−7.10245	−0.225845
$990$	4.10314	0.130406
$991$	−44.9283	−1.42720	−0.713598	−	0.700556i	$-0.752935\pi$
$991$	−44.9283	−1.42720	−0.713598	+	0.700556i	$0.752935\pi$
$992$	17.6981	0.561914
$993$	−25.0686	−0.795527
$994$	80.3580	2.54880
$995$	4.98843	0.158144
$996$	6.60810	0.209386
$997$	30.3456	0.961056	0.480528	−	0.876979i	$-0.340445\pi$
$997$	30.3456	0.961056	0.480528	+	0.876979i	$0.340445\pi$
$998$	24.1961	0.765915
$999$	0.0201917	0.000638838 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.i.1.17	✓	63

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.i.1.17	✓	63	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.23503 q^{2} +1.00000 q^{3} -0.474692 q^{4} +0.598945 q^{5} -1.23503 q^{6} -4.57610 q^{7} +3.05633 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.23503 q^{2} +1.00000 q^{3} -0.474692 q^{4} +0.598945 q^{5} -1.23503 q^{6} -4.57610 q^{7} +3.05633 q^{8} +1.00000 q^{9} -0.739717 q^{10} -5.54690 q^{11} -0.474692 q^{12} +6.75283 q^{13} +5.65164 q^{14} +0.598945 q^{15} -2.82528 q^{16} +1.00000 q^{17} -1.23503 q^{18} -2.30367 q^{19} -0.284314 q^{20} -4.57610 q^{21} +6.85061 q^{22} +5.50991 q^{23} +3.05633 q^{24} -4.64127 q^{25} -8.33998 q^{26} +1.00000 q^{27} +2.17224 q^{28} -7.62338 q^{29} -0.739717 q^{30} -6.74640 q^{31} -2.62334 q^{32} -5.54690 q^{33} -1.23503 q^{34} -2.74083 q^{35} -0.474692 q^{36} +0.0201917 q^{37} +2.84510 q^{38} +6.75283 q^{39} +1.83057 q^{40} -5.29980 q^{41} +5.65164 q^{42} -1.28903 q^{43} +2.63307 q^{44} +0.598945 q^{45} -6.80493 q^{46} -4.56404 q^{47} -2.82528 q^{48} +13.9407 q^{49} +5.73212 q^{50} +1.00000 q^{51} -3.20552 q^{52} +9.35478 q^{53} -1.23503 q^{54} -3.32229 q^{55} -13.9861 q^{56} -2.30367 q^{57} +9.41513 q^{58} +7.02044 q^{59} -0.284314 q^{60} +10.9201 q^{61} +8.33202 q^{62} -4.57610 q^{63} +8.89047 q^{64} +4.04458 q^{65} +6.85061 q^{66} -11.8752 q^{67} -0.474692 q^{68} +5.50991 q^{69} +3.38502 q^{70} +14.2185 q^{71} +3.05633 q^{72} +0.419870 q^{73} -0.0249375 q^{74} -4.64127 q^{75} +1.09353 q^{76} +25.3832 q^{77} -8.33998 q^{78} +2.64581 q^{79} -1.69219 q^{80} +1.00000 q^{81} +6.54543 q^{82} -13.9208 q^{83} +2.17224 q^{84} +0.598945 q^{85} +1.59200 q^{86} -7.62338 q^{87} -16.9532 q^{88} +1.44944 q^{89} -0.739717 q^{90} -30.9016 q^{91} -2.61551 q^{92} -6.74640 q^{93} +5.63675 q^{94} -1.37977 q^{95} -2.62334 q^{96} +2.31332 q^{97} -17.2172 q^{98} -5.54690 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

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