LMFDB - Embedded newform 8007.2.a.e.1.12

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:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-1.58086 q^{2} +1.00000 q^{3} +0.499118 q^{4} -3.53760 q^{5} -1.58086 q^{6} -3.85230 q^{7} +2.37268 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.58086 q^{2} +1.00000 q^{3} +0.499118 q^{4} -3.53760 q^{5} -1.58086 q^{6} -3.85230 q^{7} +2.37268 q^{8} +1.00000 q^{9} +5.59245 q^{10} -4.80037 q^{11} +0.499118 q^{12} +2.42528 q^{13} +6.08995 q^{14} -3.53760 q^{15} -4.74912 q^{16} -1.00000 q^{17} -1.58086 q^{18} +1.75486 q^{19} -1.76568 q^{20} -3.85230 q^{21} +7.58871 q^{22} -7.27500 q^{23} +2.37268 q^{24} +7.51462 q^{25} -3.83402 q^{26} +1.00000 q^{27} -1.92275 q^{28} -1.01319 q^{29} +5.59245 q^{30} -0.736752 q^{31} +2.76232 q^{32} -4.80037 q^{33} +1.58086 q^{34} +13.6279 q^{35} +0.499118 q^{36} +0.762412 q^{37} -2.77418 q^{38} +2.42528 q^{39} -8.39361 q^{40} +4.24448 q^{41} +6.08995 q^{42} +7.99270 q^{43} -2.39595 q^{44} -3.53760 q^{45} +11.5007 q^{46} +11.0591 q^{47} -4.74912 q^{48} +7.84022 q^{49} -11.8796 q^{50} -1.00000 q^{51} +1.21050 q^{52} -7.96423 q^{53} -1.58086 q^{54} +16.9818 q^{55} -9.14029 q^{56} +1.75486 q^{57} +1.60171 q^{58} +0.229221 q^{59} -1.76568 q^{60} +7.63803 q^{61} +1.16470 q^{62} -3.85230 q^{63} +5.13139 q^{64} -8.57966 q^{65} +7.58871 q^{66} +2.68683 q^{67} -0.499118 q^{68} -7.27500 q^{69} -21.5438 q^{70} +5.96838 q^{71} +2.37268 q^{72} -5.15619 q^{73} -1.20527 q^{74} +7.51462 q^{75} +0.875880 q^{76} +18.4925 q^{77} -3.83402 q^{78} +3.52278 q^{79} +16.8005 q^{80} +1.00000 q^{81} -6.70993 q^{82} -3.41706 q^{83} -1.92275 q^{84} +3.53760 q^{85} -12.6353 q^{86} -1.01319 q^{87} -11.3898 q^{88} +5.27093 q^{89} +5.59245 q^{90} -9.34290 q^{91} -3.63108 q^{92} -0.736752 q^{93} -17.4830 q^{94} -6.20798 q^{95} +2.76232 q^{96} -9.65063 q^{97} -12.3943 q^{98} -4.80037 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * 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 $

$2$	−1.58086	−1.11784	−0.558918	−	0.829223i	$-0.688784\pi$
$2$	−1.58086	−1.11784	−0.558918	+	0.829223i	$0.688784\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.499118	0.249559
$5$	−3.53760	−1.58206	−0.791032	−	0.611775i	$-0.790456\pi$
$5$	−3.53760	−1.58206	−0.791032	+	0.611775i	$0.790456\pi$
$6$	−1.58086	−0.645383
$7$	−3.85230	−1.45603	−0.728016	−	0.685560i	$-0.759558\pi$
$7$	−3.85230	−1.45603	−0.728016	+	0.685560i	$0.759558\pi$
$8$	2.37268	0.838870
$9$	1.00000	0.333333
$10$	5.59245	1.76849
$11$	−4.80037	−1.44737	−0.723683	−	0.690133i	$-0.757552\pi$
$11$	−4.80037	−1.44737	−0.723683	+	0.690133i	$0.757552\pi$
$12$	0.499118	0.144083
$13$	2.42528	0.672651	0.336326	−	0.941746i	$-0.390816\pi$
$13$	2.42528	0.672651	0.336326	+	0.941746i	$0.390816\pi$
$14$	6.08995	1.62761
$15$	−3.53760	−0.913405
$16$	−4.74912	−1.18728
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.58086	−0.372612
$19$	1.75486	0.402591	0.201296	−	0.979531i	$-0.435485\pi$
$19$	1.75486	0.402591	0.201296	+	0.979531i	$0.435485\pi$
$20$	−1.76568	−0.394818
$21$	−3.85230	−0.840641
$22$	7.58871	1.61792
$23$	−7.27500	−1.51694	−0.758471	−	0.651707i	$-0.774053\pi$
$23$	−7.27500	−1.51694	−0.758471	+	0.651707i	$0.774053\pi$
$24$	2.37268	0.484322
$25$	7.51462	1.50292
$26$	−3.83402	−0.751914
$27$	1.00000	0.192450
$28$	−1.92275	−0.363366
$29$	−1.01319	−0.188145	−0.0940725	−	0.995565i	$-0.529989\pi$
$29$	−1.01319	−0.188145	−0.0940725	+	0.995565i	$0.529989\pi$
$30$	5.59245	1.02104
$31$	−0.736752	−0.132325	−0.0661623	−	0.997809i	$-0.521076\pi$
$31$	−0.736752	−0.132325	−0.0661623	+	0.997809i	$0.521076\pi$
$32$	2.76232	0.488314
$33$	−4.80037	−0.835637
$34$	1.58086	0.271115
$35$	13.6279	2.30354
$36$	0.499118	0.0831864
$37$	0.762412	0.125340	0.0626699	−	0.998034i	$-0.480038\pi$
$37$	0.762412	0.125340	0.0626699	+	0.998034i	$0.480038\pi$
$38$	−2.77418	−0.450031
$39$	2.42528	0.388355
$40$	−8.39361	−1.32715
$41$	4.24448	0.662876	0.331438	−	0.943477i	$-0.392466\pi$
$41$	4.24448	0.662876	0.331438	+	0.943477i	$0.392466\pi$
$42$	6.08995	0.939699
$43$	7.99270	1.21888	0.609438	−	0.792834i	$-0.291395\pi$
$43$	7.99270	1.21888	0.609438	+	0.792834i	$0.291395\pi$
$44$	−2.39595	−0.361203
$45$	−3.53760	−0.527354
$46$	11.5007	1.69569
$47$	11.0591	1.61314	0.806571	−	0.591137i	$-0.201321\pi$
$47$	11.0591	1.61314	0.806571	+	0.591137i	$0.201321\pi$
$48$	−4.74912	−0.685476
$49$	7.84022	1.12003
$50$	−11.8796	−1.68002
$51$	−1.00000	−0.140028
$52$	1.21050	0.167866
$53$	−7.96423	−1.09397	−0.546985	−	0.837142i	$-0.684225\pi$
$53$	−7.96423	−1.09397	−0.546985	+	0.837142i	$0.684225\pi$
$54$	−1.58086	−0.215128
$55$	16.9818	2.28982
$56$	−9.14029	−1.22142
$57$	1.75486	0.232436
$58$	1.60171	0.210315
$59$	0.229221	0.0298421	0.0149210	−	0.999889i	$-0.495250\pi$
$59$	0.229221	0.0298421	0.0149210	+	0.999889i	$0.495250\pi$
$60$	−1.76568	−0.227948
$61$	7.63803	0.977950	0.488975	−	0.872298i	$-0.337371\pi$
$61$	7.63803	0.977950	0.488975	+	0.872298i	$0.337371\pi$
$62$	1.16470	0.147917
$63$	−3.85230	−0.485344
$64$	5.13139	0.641424
$65$	−8.57966	−1.06418
$66$	7.58871	0.934106
$67$	2.68683	0.328249	0.164124	−	0.986440i	$-0.447520\pi$
$67$	2.68683	0.328249	0.164124	+	0.986440i	$0.447520\pi$
$68$	−0.499118	−0.0605270
$69$	−7.27500	−0.875807
$70$	−21.5438	−2.57498
$71$	5.96838	0.708317	0.354158	−	0.935185i	$-0.384767\pi$
$71$	5.96838	0.708317	0.354158	+	0.935185i	$0.384767\pi$
$72$	2.37268	0.279623
$73$	−5.15619	−0.603487	−0.301743	−	0.953389i	$-0.597569\pi$
$73$	−5.15619	−0.603487	−0.301743	+	0.953389i	$0.597569\pi$
$74$	−1.20527	−0.140109
$75$	7.51462	0.867713
$76$	0.875880	0.100470
$77$	18.4925	2.10741
$78$	−3.83402	−0.434118
$79$	3.52278	0.396343	0.198172	−	0.980167i	$-0.436500\pi$
$79$	3.52278	0.396343	0.198172	+	0.980167i	$0.436500\pi$
$80$	16.8005	1.87835
$81$	1.00000	0.111111
$82$	−6.70993	−0.740988
$83$	−3.41706	−0.375071	−0.187535	−	0.982258i	$-0.560050\pi$
$83$	−3.41706	−0.375071	−0.187535	+	0.982258i	$0.560050\pi$
$84$	−1.92275	−0.209790
$85$	3.53760	0.383707
$86$	−12.6353	−1.36250
$87$	−1.01319	−0.108626
$88$	−11.3898	−1.21415
$89$	5.27093	0.558717	0.279359	−	0.960187i	$-0.409878\pi$
$89$	5.27093	0.558717	0.279359	+	0.960187i	$0.409878\pi$
$90$	5.59245	0.589496
$91$	−9.34290	−0.979402
$92$	−3.63108	−0.378567
$93$	−0.736752	−0.0763976
$94$	−17.4830	−1.80323
$95$	−6.20798	−0.636925
$96$	2.76232	0.281928
$97$	−9.65063	−0.979873	−0.489937	−	0.871758i	$-0.662980\pi$
$97$	−9.65063	−0.979873	−0.489937	+	0.871758i	$0.662980\pi$
$98$	−12.3943	−1.25201
$99$	−4.80037	−0.482455
$100$	3.75068	0.375068
$101$	15.7385	1.56604	0.783021	−	0.621995i	$-0.213678\pi$
$101$	15.7385	1.56604	0.783021	+	0.621995i	$0.213678\pi$
$102$	1.58086	0.156528
$103$	−9.19924	−0.906428	−0.453214	−	0.891402i	$-0.649723\pi$
$103$	−9.19924	−0.906428	−0.453214	+	0.891402i	$0.649723\pi$
$104$	5.75442	0.564267
$105$	13.6279	1.32995
$106$	12.5903	1.22288
$107$	−5.65567	−0.546754	−0.273377	−	0.961907i	$-0.588141\pi$
$107$	−5.65567	−0.546754	−0.273377	+	0.961907i	$0.588141\pi$
$108$	0.499118	0.0480277
$109$	0.761443	0.0729330	0.0364665	−	0.999335i	$-0.488390\pi$
$109$	0.761443	0.0729330	0.0364665	+	0.999335i	$0.488390\pi$
$110$	−26.8458	−2.55965
$111$	0.762412	0.0723650
$112$	18.2950	1.72872
$113$	−5.95512	−0.560210	−0.280105	−	0.959969i	$-0.590369\pi$
$113$	−5.95512	−0.560210	−0.280105	+	0.959969i	$0.590369\pi$
$114$	−2.77418	−0.259826
$115$	25.7360	2.39990
$116$	−0.505703	−0.0469533
$117$	2.42528	0.224217
$118$	−0.362367	−0.0333586
$119$	3.85230	0.353140
$120$	−8.39361	−0.766228
$121$	12.0435	1.09487
$122$	−12.0747	−1.09319
$123$	4.24448	0.382712
$124$	−0.367726	−0.0330228
$125$	−8.89571	−0.795657
$126$	6.08995	0.542536
$127$	10.5579	0.936862	0.468431	−	0.883500i	$-0.344819\pi$
$127$	10.5579	0.936862	0.468431	+	0.883500i	$0.344819\pi$
$128$	−13.6367	−1.20532
$129$	7.99270	0.703718
$130$	13.5632	1.18958
$131$	−13.8248	−1.20788	−0.603941	−	0.797029i	$-0.706404\pi$
$131$	−13.8248	−1.20788	−0.603941	+	0.797029i	$0.706404\pi$
$132$	−2.39595	−0.208541
$133$	−6.76023	−0.586186
$134$	−4.24750	−0.366928
$135$	−3.53760	−0.304468
$136$	−2.37268	−0.203456
$137$	15.3289	1.30964	0.654819	−	0.755786i	$-0.272745\pi$
$137$	15.3289	1.30964	0.654819	+	0.755786i	$0.272745\pi$
$138$	11.5007	0.979009
$139$	−8.01914	−0.680175	−0.340087	−	0.940394i	$-0.610457\pi$
$139$	−8.01914	−0.680175	−0.340087	+	0.940394i	$0.610457\pi$
$140$	6.80194	0.574869
$141$	11.0591	0.931348
$142$	−9.43518	−0.791782
$143$	−11.6422	−0.973572
$144$	−4.74912	−0.395760
$145$	3.58427	0.297657
$146$	8.15122	0.674600
$147$	7.84022	0.646651
$148$	0.380534	0.0312797
$149$	−4.63856	−0.380006	−0.190003	−	0.981784i	$-0.560850\pi$
$149$	−4.63856	−0.380006	−0.190003	+	0.981784i	$0.560850\pi$
$150$	−11.8796	−0.969962
$151$	11.1849	0.910216	0.455108	−	0.890436i	$-0.349601\pi$
$151$	11.1849	0.910216	0.455108	+	0.890436i	$0.349601\pi$
$152$	4.16372	0.337722
$153$	−1.00000	−0.0808452
$154$	−29.2340	−2.35574
$155$	2.60633	0.209346
$156$	1.21050	0.0969176
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−5.56902	−0.443047
$159$	−7.96423	−0.631604
$160$	−9.77199	−0.772544
$161$	28.0255	2.20872
$162$	−1.58086	−0.124204
$163$	12.6969	0.994499	0.497249	−	0.867608i	$-0.334343\pi$
$163$	12.6969	0.994499	0.497249	+	0.867608i	$0.334343\pi$
$164$	2.11850	0.165427
$165$	16.9818	1.32203
$166$	5.40189	0.419268
$167$	12.7587	0.987299	0.493649	−	0.869661i	$-0.335663\pi$
$167$	12.7587	0.987299	0.493649	+	0.869661i	$0.335663\pi$
$168$	−9.14029	−0.705189
$169$	−7.11803	−0.547541
$170$	−5.59245	−0.428921
$171$	1.75486	0.134197
$172$	3.98930	0.304182
$173$	−18.0809	−1.37467	−0.687333	−	0.726342i	$-0.741219\pi$
$173$	−18.0809	−1.37467	−0.687333	+	0.726342i	$0.741219\pi$
$174$	1.60171	0.121426
$175$	−28.9486	−2.18831
$176$	22.7975	1.71843
$177$	0.229221	0.0172293
$178$	−8.33260	−0.624555
$179$	−8.85007	−0.661485	−0.330743	−	0.943721i	$-0.607299\pi$
$179$	−8.85007	−0.661485	−0.330743	+	0.943721i	$0.607299\pi$
$180$	−1.76568	−0.131606
$181$	20.5968	1.53095	0.765473	−	0.643468i	$-0.222505\pi$
$181$	20.5968	1.53095	0.765473	+	0.643468i	$0.222505\pi$
$182$	14.7698	1.09481
$183$	7.63803	0.564620
$184$	−17.2613	−1.27252
$185$	−2.69711	−0.198295
$186$	1.16470	0.0854001
$187$	4.80037	0.351038
$188$	5.51982	0.402574
$189$	−3.85230	−0.280214
$190$	9.81394	0.711978
$191$	−14.1872	−1.02655	−0.513275	−	0.858224i	$-0.671568\pi$
$191$	−14.1872	−1.02655	−0.513275	+	0.858224i	$0.671568\pi$
$192$	5.13139	0.370326
$193$	1.19405	0.0859493	0.0429747	−	0.999076i	$-0.486317\pi$
$193$	1.19405	0.0859493	0.0429747	+	0.999076i	$0.486317\pi$
$194$	15.2563	1.09534
$195$	−8.57966	−0.614402
$196$	3.91320	0.279514
$197$	11.6432	0.829542	0.414771	−	0.909926i	$-0.363862\pi$
$197$	11.6432	0.829542	0.414771	+	0.909926i	$0.363862\pi$
$198$	7.58871	0.539306
$199$	12.0052	0.851028	0.425514	−	0.904952i	$-0.360093\pi$
$199$	12.0052	0.851028	0.425514	+	0.904952i	$0.360093\pi$
$200$	17.8298	1.26076
$201$	2.68683	0.189514
$202$	−24.8804	−1.75058
$203$	3.90312	0.273945
$204$	−0.499118	−0.0349453
$205$	−15.0153	−1.04871
$206$	14.5427	1.01324
$207$	−7.27500	−0.505647
$208$	−11.5179	−0.798625
$209$	−8.42395	−0.582697
$210$	−21.5438	−1.48666
$211$	−13.8510	−0.953544	−0.476772	−	0.879027i	$-0.658193\pi$
$211$	−13.8510	−0.953544	−0.476772	+	0.879027i	$0.658193\pi$
$212$	−3.97509	−0.273010
$213$	5.96838	0.408947
$214$	8.94082	0.611182
$215$	−28.2750	−1.92834
$216$	2.37268	0.161441
$217$	2.83819	0.192669
$218$	−1.20373	−0.0815272
$219$	−5.15619	−0.348423
$220$	8.47592	0.571446
$221$	−2.42528	−0.163142
$222$	−1.20527	−0.0808922
$223$	21.5425	1.44259	0.721297	−	0.692626i	$-0.243546\pi$
$223$	21.5425	1.44259	0.721297	+	0.692626i	$0.243546\pi$
$224$	−10.6413	−0.711002
$225$	7.51462	0.500975
$226$	9.41421	0.626224
$227$	−3.89994	−0.258848	−0.129424	−	0.991589i	$-0.541313\pi$
$227$	−3.89994	−0.258848	−0.129424	+	0.991589i	$0.541313\pi$
$228$	0.875880	0.0580066
$229$	28.8788	1.90837	0.954183	−	0.299224i	$-0.0967278\pi$
$229$	28.8788	1.90837	0.954183	+	0.299224i	$0.0967278\pi$
$230$	−40.6851	−2.68269
$231$	18.4925	1.21671
$232$	−2.40398	−0.157829
$233$	3.82664	0.250691	0.125346	−	0.992113i	$-0.459996\pi$
$233$	3.82664	0.250691	0.125346	+	0.992113i	$0.459996\pi$
$234$	−3.83402	−0.250638
$235$	−39.1228	−2.55209
$236$	0.114409	0.00744736
$237$	3.52278	0.228829
$238$	−6.08995	−0.394753
$239$	16.4165	1.06190	0.530949	−	0.847404i	$-0.321836\pi$
$239$	16.4165	1.06190	0.530949	+	0.847404i	$0.321836\pi$
$240$	16.8005	1.08447
$241$	−27.8172	−1.79186	−0.895932	−	0.444190i	$-0.853491\pi$
$241$	−27.8172	−1.79186	−0.895932	+	0.444190i	$0.853491\pi$
$242$	−19.0391	−1.22388
$243$	1.00000	0.0641500
$244$	3.81228	0.244056
$245$	−27.7356	−1.77196
$246$	−6.70993	−0.427809
$247$	4.25601	0.270804
$248$	−1.74808	−0.111003
$249$	−3.41706	−0.216547
$250$	14.0629	0.889414
$251$	24.7440	1.56183	0.780913	−	0.624640i	$-0.214754\pi$
$251$	24.7440	1.56183	0.780913	+	0.624640i	$0.214754\pi$
$252$	−1.92275	−0.121122
$253$	34.9227	2.19557
$254$	−16.6906	−1.04726
$255$	3.53760	0.221533
$256$	11.2949	0.705929
$257$	−18.2528	−1.13858	−0.569289	−	0.822137i	$-0.692781\pi$
$257$	−18.2528	−1.13858	−0.569289	+	0.822137i	$0.692781\pi$
$258$	−12.6353	−0.786642
$259$	−2.93704	−0.182499
$260$	−4.28227	−0.265575
$261$	−1.01319	−0.0627150
$262$	21.8551	1.35021
$263$	29.8867	1.84289	0.921445	−	0.388508i	$-0.127010\pi$
$263$	29.8867	1.84289	0.921445	+	0.388508i	$0.127010\pi$
$264$	−11.3898	−0.700991
$265$	28.1743	1.73073
$266$	10.6870	0.655261
$267$	5.27093	0.322576
$268$	1.34105	0.0819175
$269$	−6.43186	−0.392157	−0.196079	−	0.980588i	$-0.562821\pi$
$269$	−6.43186	−0.392157	−0.196079	+	0.980588i	$0.562821\pi$
$270$	5.59245	0.340346
$271$	10.0760	0.612076	0.306038	−	0.952019i	$-0.400997\pi$
$271$	10.0760	0.612076	0.306038	+	0.952019i	$0.400997\pi$
$272$	4.74912	0.287958
$273$	−9.34290	−0.565458
$274$	−24.2329	−1.46396
$275$	−36.0729	−2.17528
$276$	−3.63108	−0.218566
$277$	14.1352	0.849301	0.424650	−	0.905357i	$-0.360397\pi$
$277$	14.1352	0.849301	0.424650	+	0.905357i	$0.360397\pi$
$278$	12.6771	0.760324
$279$	−0.736752	−0.0441082
$280$	32.3347	1.93237
$281$	−30.2938	−1.80718	−0.903589	−	0.428401i	$-0.859077\pi$
$281$	−30.2938	−1.80718	−0.903589	+	0.428401i	$0.859077\pi$
$282$	−17.4830	−1.04110
$283$	22.8584	1.35879	0.679395	−	0.733773i	$-0.262242\pi$
$283$	22.8584	1.35879	0.679395	+	0.733773i	$0.262242\pi$
$284$	2.97893	0.176767
$285$	−6.20798	−0.367729
$286$	18.4047	1.08829
$287$	−16.3510	−0.965170
$288$	2.76232	0.162771
$289$	1.00000	0.0588235
$290$	−5.66623	−0.332732
$291$	−9.65063	−0.565730
$292$	−2.57355	−0.150606
$293$	−18.5166	−1.08175	−0.540877	−	0.841102i	$-0.681908\pi$
$293$	−18.5166	−1.08175	−0.540877	+	0.841102i	$0.681908\pi$
$294$	−12.3943	−0.722850
$295$	−0.810893	−0.0472120
$296$	1.80896	0.105144
$297$	−4.80037	−0.278546
$298$	7.33292	0.424785
$299$	−17.6439	−1.02037
$300$	3.75068	0.216546
$301$	−30.7903	−1.77472
$302$	−17.6818	−1.01747
$303$	15.7385	0.904155
$304$	−8.33401	−0.477988
$305$	−27.0203	−1.54718
$306$	1.58086	0.0903718
$307$	−7.26341	−0.414545	−0.207272	−	0.978283i	$-0.566459\pi$
$307$	−7.26341	−0.414545	−0.207272	+	0.978283i	$0.566459\pi$
$308$	9.22993	0.525924
$309$	−9.19924	−0.523327
$310$	−4.12025	−0.234014
$311$	−25.0635	−1.42122	−0.710611	−	0.703585i	$-0.751581\pi$
$311$	−25.0635	−1.42122	−0.710611	+	0.703585i	$0.751581\pi$
$312$	5.75442	0.325780
$313$	−11.8317	−0.668767	−0.334384	−	0.942437i	$-0.608528\pi$
$313$	−11.8317	−0.668767	−0.334384	+	0.942437i	$0.608528\pi$
$314$	−1.58086	−0.0892131
$315$	13.6279	0.767845
$316$	1.75828	0.0989111
$317$	3.63674	0.204260	0.102130	−	0.994771i	$-0.467434\pi$
$317$	3.63674	0.204260	0.102130	+	0.994771i	$0.467434\pi$
$318$	12.5903	0.706031
$319$	4.86369	0.272315
$320$	−18.1528	−1.01477
$321$	−5.65567	−0.315669
$322$	−44.3043	−2.46898
$323$	−1.75486	−0.0976428
$324$	0.499118	0.0277288
$325$	18.2250	1.01094
$326$	−20.0720	−1.11169
$327$	0.761443	0.0421079
$328$	10.0708	0.556067
$329$	−42.6032	−2.34879
$330$	−26.8458	−1.47781
$331$	−17.6453	−0.969874	−0.484937	−	0.874549i	$-0.661157\pi$
$331$	−17.6453	−0.969874	−0.484937	+	0.874549i	$0.661157\pi$
$332$	−1.70552	−0.0936023
$333$	0.762412	0.0417799
$334$	−20.1697	−1.10364
$335$	−9.50493	−0.519310
$336$	18.2950	0.998076
$337$	−17.4892	−0.952695	−0.476348	−	0.879257i	$-0.658040\pi$
$337$	−17.4892	−0.952695	−0.476348	+	0.879257i	$0.658040\pi$
$338$	11.2526	0.612061
$339$	−5.95512	−0.323438
$340$	1.76568	0.0957575
$341$	3.53668	0.191522
$342$	−2.77418	−0.150010
$343$	−3.23679	−0.174770
$344$	18.9642	1.02248
$345$	25.7360	1.38558
$346$	28.5834	1.53665
$347$	−11.4729	−0.615898	−0.307949	−	0.951403i	$-0.599643\pi$
$347$	−11.4729	−0.615898	−0.307949	+	0.951403i	$0.599643\pi$
$348$	−0.505703	−0.0271085
$349$	−28.9256	−1.54835	−0.774176	−	0.632971i	$-0.781835\pi$
$349$	−28.9256	−1.54835	−0.774176	+	0.632971i	$0.781835\pi$
$350$	45.7636	2.44617
$351$	2.42528	0.129452
$352$	−13.2602	−0.706769
$353$	−24.9696	−1.32900	−0.664499	−	0.747289i	$-0.731355\pi$
$353$	−24.9696	−1.32900	−0.664499	+	0.747289i	$0.731355\pi$
$354$	−0.362367	−0.0192596
$355$	−21.1137	−1.12060
$356$	2.63082	0.139433
$357$	3.85230	0.203885
$358$	13.9907	0.739432
$359$	10.3710	0.547358	0.273679	−	0.961821i	$-0.411759\pi$
$359$	10.3710	0.547358	0.273679	+	0.961821i	$0.411759\pi$
$360$	−8.39361	−0.442382
$361$	−15.9205	−0.837920
$362$	−32.5606	−1.71135
$363$	12.0435	0.632122
$364$	−4.66321	−0.244419
$365$	18.2406	0.954754
$366$	−12.0747	−0.631153
$367$	−24.3395	−1.27051	−0.635255	−	0.772303i	$-0.719105\pi$
$367$	−24.3395	−1.27051	−0.635255	+	0.772303i	$0.719105\pi$
$368$	34.5498	1.80103
$369$	4.24448	0.220959
$370$	4.26375	0.221662
$371$	30.6806	1.59286
$372$	−0.367726	−0.0190657
$373$	4.47354	0.231631	0.115816	−	0.993271i	$-0.463052\pi$
$373$	4.47354	0.231631	0.115816	+	0.993271i	$0.463052\pi$
$374$	−7.58871	−0.392403
$375$	−8.89571	−0.459373
$376$	26.2399	1.35322
$377$	−2.45727	−0.126556
$378$	6.08995	0.313233
$379$	0.986729	0.0506849	0.0253424	−	0.999679i	$-0.491932\pi$
$379$	0.986729	0.0506849	0.0253424	+	0.999679i	$0.491932\pi$
$380$	−3.09852	−0.158950
$381$	10.5579	0.540898
$382$	22.4280	1.14751
$383$	16.1312	0.824266	0.412133	−	0.911124i	$-0.364784\pi$
$383$	16.1312	0.824266	0.412133	+	0.911124i	$0.364784\pi$
$384$	−13.6367	−0.695893
$385$	−65.4189	−3.33406
$386$	−1.88762	−0.0960773
$387$	7.99270	0.406292
$388$	−4.81681	−0.244536
$389$	−26.5216	−1.34470	−0.672348	−	0.740235i	$-0.734714\pi$
$389$	−26.5216	−1.34470	−0.672348	+	0.740235i	$0.734714\pi$
$390$	13.5632	0.686802
$391$	7.27500	0.367912
$392$	18.6024	0.939561
$393$	−13.8248	−0.697371
$394$	−18.4062	−0.927292
$395$	−12.4622	−0.627040
$396$	−2.39595	−0.120401
$397$	−1.06167	−0.0532835	−0.0266417	−	0.999645i	$-0.508481\pi$
$397$	−1.06167	−0.0532835	−0.0266417	+	0.999645i	$0.508481\pi$
$398$	−18.9786	−0.951310
$399$	−6.76023	−0.338435
$400$	−35.6878	−1.78439
$401$	−12.6139	−0.629907	−0.314953	−	0.949107i	$-0.601989\pi$
$401$	−12.6139	−0.629907	−0.314953	+	0.949107i	$0.601989\pi$
$402$	−4.24750	−0.211846
$403$	−1.78683	−0.0890083
$404$	7.85539	0.390820
$405$	−3.53760	−0.175785
$406$	−6.17029	−0.306226
$407$	−3.65986	−0.181412
$408$	−2.37268	−0.117465
$409$	−10.4223	−0.515351	−0.257675	−	0.966232i	$-0.582957\pi$
$409$	−10.4223	−0.515351	−0.257675	+	0.966232i	$0.582957\pi$
$410$	23.7370	1.17229
$411$	15.3289	0.756120
$412$	−4.59151	−0.226208
$413$	−0.883029	−0.0434510
$414$	11.5007	0.565231
$415$	12.0882	0.593385
$416$	6.69940	0.328465
$417$	−8.01914	−0.392699
$418$	13.3171	0.651360
$419$	2.42233	0.118338	0.0591692	−	0.998248i	$-0.481155\pi$
$419$	2.42233	0.118338	0.0591692	+	0.998248i	$0.481155\pi$
$420$	6.80194	0.331900
$421$	4.98654	0.243029	0.121515	−	0.992590i	$-0.461225\pi$
$421$	4.98654	0.243029	0.121515	+	0.992590i	$0.461225\pi$
$422$	21.8965	1.06591
$423$	11.0591	0.537714
$424$	−18.8966	−0.917700
$425$	−7.51462	−0.364513
$426$	−9.43518	−0.457136
$427$	−29.4240	−1.42393
$428$	−2.82285	−0.136448
$429$	−11.6422	−0.562092
$430$	44.6988	2.15557
$431$	−8.26742	−0.398228	−0.199114	−	0.979976i	$-0.563806\pi$
$431$	−8.26742	−0.398228	−0.199114	+	0.979976i	$0.563806\pi$
$432$	−4.74912	−0.228492
$433$	2.46995	0.118698	0.0593490	−	0.998237i	$-0.481098\pi$
$433$	2.46995	0.118698	0.0593490	+	0.998237i	$0.481098\pi$
$434$	−4.48678	−0.215372
$435$	3.58427	0.171853
$436$	0.380050	0.0182011
$437$	−12.7666	−0.610708
$438$	8.15122	0.389480
$439$	15.7951	0.753861	0.376930	−	0.926242i	$-0.376980\pi$
$439$	15.7951	0.753861	0.376930	+	0.926242i	$0.376980\pi$
$440$	40.2924	1.92087
$441$	7.84022	0.373344
$442$	3.83402	0.182366
$443$	10.3206	0.490347	0.245174	−	0.969479i	$-0.421155\pi$
$443$	10.3206	0.490347	0.245174	+	0.969479i	$0.421155\pi$
$444$	0.380534	0.0180593
$445$	−18.6464	−0.883926
$446$	−34.0557	−1.61259
$447$	−4.63856	−0.219396
$448$	−19.7677	−0.933934
$449$	25.0616	1.18273	0.591364	−	0.806405i	$-0.298590\pi$
$449$	25.0616	1.18273	0.591364	+	0.806405i	$0.298590\pi$
$450$	−11.8796	−0.560008
$451$	−20.3751	−0.959424
$452$	−2.97231	−0.139806
$453$	11.1849	0.525514
$454$	6.16527	0.289350
$455$	33.0514	1.54948
$456$	4.16372	0.194984
$457$	−23.3835	−1.09383	−0.546916	−	0.837187i	$-0.684198\pi$
$457$	−23.3835	−1.09383	−0.546916	+	0.837187i	$0.684198\pi$
$458$	−45.6534	−2.13324
$459$	−1.00000	−0.0466760
$460$	12.8453	0.598916
$461$	−17.9057	−0.833952	−0.416976	−	0.908917i	$-0.636910\pi$
$461$	−17.9057	−0.833952	−0.416976	+	0.908917i	$0.636910\pi$
$462$	−29.2340	−1.36009
$463$	21.4086	0.994943	0.497471	−	0.867480i	$-0.334262\pi$
$463$	21.4086	0.994943	0.497471	+	0.867480i	$0.334262\pi$
$464$	4.81177	0.223381
$465$	2.60633	0.120866
$466$	−6.04937	−0.280232
$467$	−32.4640	−1.50225	−0.751127	−	0.660158i	$-0.770489\pi$
$467$	−32.4640	−1.50225	−0.751127	+	0.660158i	$0.770489\pi$
$468$	1.21050	0.0559554
$469$	−10.3505	−0.477941
$470$	61.8477	2.85282
$471$	1.00000	0.0460776
$472$	0.543870	0.0250336
$473$	−38.3679	−1.76416
$474$	−5.56902	−0.255793
$475$	13.1871	0.605064
$476$	1.92275	0.0881293
$477$	−7.96423	−0.364657
$478$	−25.9522	−1.18703
$479$	−23.7640	−1.08580	−0.542901	−	0.839796i	$-0.682674\pi$
$479$	−23.7640	−1.08580	−0.542901	+	0.839796i	$0.682674\pi$
$480$	−9.77199	−0.446028
$481$	1.84906	0.0843099
$482$	43.9751	2.00301
$483$	28.0255	1.27520
$484$	6.01115	0.273234
$485$	34.1401	1.55022
$486$	−1.58086	−0.0717093
$487$	14.2473	0.645608	0.322804	−	0.946466i	$-0.395375\pi$
$487$	14.2473	0.645608	0.322804	+	0.946466i	$0.395375\pi$
$488$	18.1226	0.820373
$489$	12.6969	0.574174
$490$	43.8461	1.98076
$491$	−13.8647	−0.625704	−0.312852	−	0.949802i	$-0.601284\pi$
$491$	−13.8647	−0.625704	−0.312852	+	0.949802i	$0.601284\pi$
$492$	2.11850	0.0955092
$493$	1.01319	0.0456319
$494$	−6.72816	−0.302714
$495$	16.9818	0.763275
$496$	3.49892	0.157106
$497$	−22.9920	−1.03133
$498$	5.40189	0.242064
$499$	−28.3173	−1.26766	−0.633829	−	0.773473i	$-0.718518\pi$
$499$	−28.3173	−1.26766	−0.633829	+	0.773473i	$0.718518\pi$
$500$	−4.44001	−0.198563
$501$	12.7587	0.570017
$502$	−39.1167	−1.74587
$503$	−22.3818	−0.997953	−0.498977	−	0.866615i	$-0.666291\pi$
$503$	−22.3818	−0.997953	−0.498977	+	0.866615i	$0.666291\pi$
$504$	−9.14029	−0.407141
$505$	−55.6766	−2.47758
$506$	−55.2078	−2.45429
$507$	−7.11803	−0.316123
$508$	5.26964	0.233803
$509$	−23.7814	−1.05409	−0.527047	−	0.849836i	$-0.676701\pi$
$509$	−23.7814	−1.05409	−0.527047	+	0.849836i	$0.676701\pi$
$510$	−5.59245	−0.247638
$511$	19.8632	0.878697
$512$	9.41771	0.416208
$513$	1.75486	0.0774788
$514$	28.8551	1.27274
$515$	32.5433	1.43403
$516$	3.98930	0.175619
$517$	−53.0880	−2.33481
$518$	4.64305	0.204004
$519$	−18.0809	−0.793664
$520$	−20.3568	−0.892706
$521$	30.9013	1.35381	0.676906	−	0.736070i	$-0.263321\pi$
$521$	30.9013	1.35381	0.676906	+	0.736070i	$0.263321\pi$
$522$	1.60171	0.0701051
$523$	21.0092	0.918668	0.459334	−	0.888264i	$-0.348088\pi$
$523$	21.0092	0.918668	0.459334	+	0.888264i	$0.348088\pi$
$524$	−6.90023	−0.301438
$525$	−28.9486	−1.26342
$526$	−47.2466	−2.06005
$527$	0.736752	0.0320934
$528$	22.7975	0.992134
$529$	29.9256	1.30111
$530$	−44.5396	−1.93467
$531$	0.229221	0.00994736
$532$	−3.37416	−0.146288
$533$	10.2940	0.445884
$534$	−8.33260	−0.360587
$535$	20.0075	0.865000
$536$	6.37500	0.275358
$537$	−8.85007	−0.381909
$538$	10.1679	0.438368
$539$	−37.6360	−1.62110
$540$	−1.76568	−0.0759828
$541$	12.6476	0.543762	0.271881	−	0.962331i	$-0.412354\pi$
$541$	12.6476	0.543762	0.271881	+	0.962331i	$0.412354\pi$
$542$	−15.9288	−0.684201
$543$	20.5968	0.883892
$544$	−2.76232	−0.118434
$545$	−2.69368	−0.115385
$546$	14.7698	0.632090
$547$	27.0303	1.15573	0.577867	−	0.816131i	$-0.303885\pi$
$547$	27.0303	1.15573	0.577867	+	0.816131i	$0.303885\pi$
$548$	7.65095	0.326832
$549$	7.63803	0.325983
$550$	57.0263	2.43161
$551$	−1.77801	−0.0757456
$552$	−17.2613	−0.734688
$553$	−13.5708	−0.577089
$554$	−22.3457	−0.949379
$555$	−2.69711	−0.114486
$556$	−4.00250	−0.169744
$557$	30.6429	1.29838	0.649191	−	0.760626i	$-0.275108\pi$
$557$	30.6429	1.29838	0.649191	+	0.760626i	$0.275108\pi$
$558$	1.16470	0.0493058
$559$	19.3845	0.819878
$560$	−64.7205	−2.73494
$561$	4.80037	0.202672
$562$	47.8903	2.02013
$563$	−34.0002	−1.43294	−0.716469	−	0.697619i	$-0.754243\pi$
$563$	−34.0002	−1.43294	−0.716469	+	0.697619i	$0.754243\pi$
$564$	5.51982	0.232426
$565$	21.0668	0.886288
$566$	−36.1359	−1.51891
$567$	−3.85230	−0.161781
$568$	14.1611	0.594186
$569$	−31.7725	−1.33197	−0.665986	−	0.745964i	$-0.731989\pi$
$569$	−31.7725	−1.33197	−0.665986	+	0.745964i	$0.731989\pi$
$570$	9.81394	0.411061
$571$	26.3491	1.10267	0.551337	−	0.834283i	$-0.314118\pi$
$571$	26.3491	1.10267	0.551337	+	0.834283i	$0.314118\pi$
$572$	−5.81085	−0.242964
$573$	−14.1872	−0.592678
$574$	25.8487	1.07890
$575$	−54.6688	−2.27985
$576$	5.13139	0.213808
$577$	6.91871	0.288030	0.144015	−	0.989576i	$-0.453999\pi$
$577$	6.91871	0.288030	0.144015	+	0.989576i	$0.453999\pi$
$578$	−1.58086	−0.0657551
$579$	1.19405	0.0496229
$580$	1.78897	0.0742831
$581$	13.1635	0.546115
$582$	15.2563	0.632394
$583$	38.2312	1.58338
$584$	−12.2340	−0.506247
$585$	−8.57966	−0.354725
$586$	29.2722	1.20922
$587$	7.67877	0.316937	0.158468	−	0.987364i	$-0.449344\pi$
$587$	7.67877	0.316937	0.158468	+	0.987364i	$0.449344\pi$
$588$	3.91320	0.161378
$589$	−1.29289	−0.0532727
$590$	1.28191	0.0527753
$591$	11.6432	0.478936
$592$	−3.62078	−0.148813
$593$	−17.8218	−0.731855	−0.365927	−	0.930643i	$-0.619248\pi$
$593$	−17.8218	−0.731855	−0.365927	+	0.930643i	$0.619248\pi$
$594$	7.58871	0.311369
$595$	−13.6279	−0.558690
$596$	−2.31519	−0.0948340
$597$	12.0052	0.491341
$598$	27.8925	1.14061
$599$	−9.41239	−0.384580	−0.192290	−	0.981338i	$-0.561591\pi$
$599$	−9.41239	−0.384580	−0.192290	+	0.981338i	$0.561591\pi$
$600$	17.8298	0.727899
$601$	26.7330	1.09046	0.545231	−	0.838286i	$-0.316442\pi$
$601$	26.7330	1.09046	0.545231	+	0.838286i	$0.316442\pi$
$602$	48.6751	1.98385
$603$	2.68683	0.109416
$604$	5.58260	0.227153
$605$	−42.6052	−1.73215
$606$	−24.8804	−1.01070
$607$	−41.0397	−1.66575	−0.832875	−	0.553461i	$-0.813307\pi$
$607$	−41.0397	−1.66575	−0.832875	+	0.553461i	$0.813307\pi$
$608$	4.84748	0.196591
$609$	3.90312	0.158162
$610$	42.7153	1.72949
$611$	26.8215	1.08508
$612$	−0.499118	−0.0201757
$613$	−45.4730	−1.83664	−0.918319	−	0.395841i	$-0.870453\pi$
$613$	−45.4730	−1.83664	−0.918319	+	0.395841i	$0.870453\pi$
$614$	11.4824	0.463394
$615$	−15.0153	−0.605474
$616$	43.8768	1.76785
$617$	2.09276	0.0842514	0.0421257	−	0.999112i	$-0.486587\pi$
$617$	2.09276	0.0842514	0.0421257	+	0.999112i	$0.486587\pi$
$618$	14.5427	0.584994
$619$	17.4035	0.699505	0.349752	−	0.936842i	$-0.386266\pi$
$619$	17.4035	0.699505	0.349752	+	0.936842i	$0.386266\pi$
$620$	1.30087	0.0522442
$621$	−7.27500	−0.291936
$622$	39.6219	1.58869
$623$	−20.3052	−0.813511
$624$	−11.5179	−0.461086
$625$	−6.10361	−0.244144
$626$	18.7043	0.747573
$627$	−8.42395	−0.336420
$628$	0.499118	0.0199170
$629$	−0.762412	−0.0303994
$630$	−21.5438	−0.858326
$631$	34.0744	1.35648	0.678240	−	0.734840i	$-0.262743\pi$
$631$	34.0744	1.35648	0.678240	+	0.734840i	$0.262743\pi$
$632$	8.35843	0.332481
$633$	−13.8510	−0.550529
$634$	−5.74918	−0.228329
$635$	−37.3496	−1.48218
$636$	−3.97509	−0.157623
$637$	19.0147	0.753390
$638$	−7.68882	−0.304403
$639$	5.96838	0.236106
$640$	48.2410	1.90689
$641$	25.3528	1.00137	0.500687	−	0.865628i	$-0.333081\pi$
$641$	25.3528	1.00137	0.500687	+	0.865628i	$0.333081\pi$
$642$	8.94082	0.352866
$643$	28.8439	1.13749	0.568747	−	0.822513i	$-0.307428\pi$
$643$	28.8439	1.13749	0.568747	+	0.822513i	$0.307428\pi$
$644$	13.9880	0.551205
$645$	−28.2750	−1.11333
$646$	2.77418	0.109149
$647$	−30.0805	−1.18259	−0.591294	−	0.806456i	$-0.701383\pi$
$647$	−30.0805	−1.18259	−0.591294	+	0.806456i	$0.701383\pi$
$648$	2.37268	0.0932078
$649$	−1.10035	−0.0431924
$650$	−28.8112	−1.13007
$651$	2.83819	0.111237
$652$	6.33726	0.248186
$653$	−5.84435	−0.228707	−0.114354	−	0.993440i	$-0.536480\pi$
$653$	−5.84435	−0.228707	−0.114354	+	0.993440i	$0.536480\pi$
$654$	−1.20373	−0.0470697
$655$	48.9068	1.91095
$656$	−20.1575	−0.787019
$657$	−5.15619	−0.201162
$658$	67.3496	2.62556
$659$	−5.79259	−0.225647	−0.112824	−	0.993615i	$-0.535990\pi$
$659$	−5.79259	−0.225647	−0.112824	+	0.993615i	$0.535990\pi$
$660$	8.47592	0.329925
$661$	10.1149	0.393424	0.196712	−	0.980461i	$-0.436974\pi$
$661$	10.1149	0.393424	0.196712	+	0.980461i	$0.436974\pi$
$662$	27.8948	1.08416
$663$	−2.42528	−0.0941900
$664$	−8.10759	−0.314636
$665$	23.9150	0.927384
$666$	−1.20527	−0.0467031
$667$	7.37097	0.285405
$668$	6.36811	0.246389
$669$	21.5425	0.832882
$670$	15.0260	0.580504
$671$	−36.6654	−1.41545
$672$	−10.6413	−0.410497
$673$	−41.0567	−1.58262	−0.791309	−	0.611416i	$-0.790600\pi$
$673$	−41.0567	−1.58262	−0.791309	+	0.611416i	$0.790600\pi$
$674$	27.6479	1.06496
$675$	7.51462	0.289238
$676$	−3.55274	−0.136644
$677$	−0.224724	−0.00863685	−0.00431843	−	0.999991i	$-0.501375\pi$
$677$	−0.224724	−0.00863685	−0.00431843	+	0.999991i	$0.501375\pi$
$678$	9.41421	0.361550
$679$	37.1771	1.42673
$680$	8.39361	0.321880
$681$	−3.89994	−0.149446
$682$	−5.59100	−0.214090
$683$	26.8739	1.02830	0.514151	−	0.857699i	$-0.328107\pi$
$683$	26.8739	1.02830	0.514151	+	0.857699i	$0.328107\pi$
$684$	0.875880	0.0334901
$685$	−54.2276	−2.07193
$686$	5.11691	0.195364
$687$	28.8788	1.10180
$688$	−37.9583	−1.44715
$689$	−19.3155	−0.735861
$690$	−40.6851	−1.54885
$691$	37.4828	1.42591	0.712956	−	0.701209i	$-0.247356\pi$
$691$	37.4828	1.42591	0.712956	+	0.701209i	$0.247356\pi$
$692$	−9.02451	−0.343061
$693$	18.4925	0.702471
$694$	18.1371	0.688473
$695$	28.3685	1.07608
$696$	−2.40398	−0.0911228
$697$	−4.24448	−0.160771
$698$	45.7273	1.73080
$699$	3.82664	0.144737
$700$	−14.4488	−0.546112
$701$	−25.0402	−0.945756	−0.472878	−	0.881128i	$-0.656785\pi$
$701$	−25.0402	−0.945756	−0.472878	+	0.881128i	$0.656785\pi$
$702$	−3.83402	−0.144706
$703$	1.33792	0.0504607
$704$	−24.6326	−0.928375
$705$	−39.1228	−1.47345
$706$	39.4735	1.48560
$707$	−60.6295	−2.28021
$708$	0.114409	0.00429974
$709$	−8.84718	−0.332263	−0.166131	−	0.986104i	$-0.553128\pi$
$709$	−8.84718	−0.332263	−0.166131	+	0.986104i	$0.553128\pi$
$710$	33.3779	1.25265
$711$	3.52278	0.132114
$712$	12.5062	0.468691
$713$	5.35987	0.200729
$714$	−6.08995	−0.227911
$715$	41.1855	1.54025
$716$	−4.41723	−0.165080
$717$	16.4165	0.613087
$718$	−16.3950	−0.611857
$719$	15.6770	0.584655	0.292327	−	0.956318i	$-0.405570\pi$
$719$	15.6770	0.584655	0.292327	+	0.956318i	$0.405570\pi$
$720$	16.8005	0.626117
$721$	35.4383	1.31979
$722$	25.1681	0.936658
$723$	−27.8172	−1.03453
$724$	10.2802	0.382061
$725$	−7.61375	−0.282768
$726$	−19.0391	−0.706609
$727$	26.7565	0.992343	0.496172	−	0.868225i	$-0.334739\pi$
$727$	26.7565	0.992343	0.496172	+	0.868225i	$0.334739\pi$
$728$	−22.1677	−0.821591
$729$	1.00000	0.0370370
$730$	−28.8358	−1.06726
$731$	−7.99270	−0.295621
$732$	3.81228	0.140906
$733$	4.26635	0.157581	0.0787906	−	0.996891i	$-0.474894\pi$
$733$	4.26635	0.157581	0.0787906	+	0.996891i	$0.474894\pi$
$734$	38.4773	1.42022
$735$	−27.7356	−1.02304
$736$	−20.0959	−0.740744
$737$	−12.8978	−0.475096
$738$	−6.70993	−0.246996
$739$	−30.5678	−1.12445	−0.562227	−	0.826983i	$-0.690055\pi$
$739$	−30.5678	−1.12445	−0.562227	+	0.826983i	$0.690055\pi$
$740$	−1.34618	−0.0494864
$741$	4.25601	0.156348
$742$	−48.5017	−1.78055
$743$	7.08018	0.259747	0.129873	−	0.991531i	$-0.458543\pi$
$743$	7.08018	0.259747	0.129873	+	0.991531i	$0.458543\pi$
$744$	−1.74808	−0.0640877
$745$	16.4094	0.601193
$746$	−7.07204	−0.258926
$747$	−3.41706	−0.125024
$748$	2.39595	0.0876047
$749$	21.7873	0.796092
$750$	14.0629	0.513504
$751$	−16.6583	−0.607869	−0.303934	−	0.952693i	$-0.598300\pi$
$751$	−16.6583	−0.607869	−0.303934	+	0.952693i	$0.598300\pi$
$752$	−52.5212	−1.91525
$753$	24.7440	0.901720
$754$	3.88460	0.141469
$755$	−39.5678	−1.44002
$756$	−1.92275	−0.0699299
$757$	−18.1079	−0.658142	−0.329071	−	0.944305i	$-0.606736\pi$
$757$	−18.1079	−0.658142	−0.329071	+	0.944305i	$0.606736\pi$
$758$	−1.55988	−0.0566574
$759$	34.9227	1.26761
$760$	−14.7296	−0.534298
$761$	−16.4803	−0.597411	−0.298706	−	0.954345i	$-0.596555\pi$
$761$	−16.4803	−0.597411	−0.298706	+	0.954345i	$0.596555\pi$
$762$	−16.6906	−0.604635
$763$	−2.93331	−0.106193
$764$	−7.08109	−0.256185
$765$	3.53760	0.127902
$766$	−25.5012	−0.921395
$767$	0.555925	0.0200733
$768$	11.2949	0.407568
$769$	33.7503	1.21707	0.608534	−	0.793528i	$-0.291758\pi$
$769$	33.7503	1.21707	0.608534	+	0.793528i	$0.291758\pi$
$770$	103.418	3.72693
$771$	−18.2528	−0.657358
$772$	0.595970	0.0214494
$773$	22.7886	0.819649	0.409824	−	0.912164i	$-0.365590\pi$
$773$	22.7886	0.819649	0.409824	+	0.912164i	$0.365590\pi$
$774$	−12.6353	−0.454168
$775$	−5.53641	−0.198874
$776$	−22.8979	−0.821987
$777$	−2.93704	−0.105366
$778$	41.9269	1.50315
$779$	7.44845	0.266868
$780$	−4.28227	−0.153330
$781$	−28.6504	−1.02519
$782$	−11.5007	−0.411266
$783$	−1.01319	−0.0362085
$784$	−37.2341	−1.32979
$785$	−3.53760	−0.126262
$786$	21.8551	0.779547
$787$	−39.8451	−1.42032	−0.710162	−	0.704039i	$-0.751378\pi$
$787$	−39.8451	−1.42032	−0.710162	+	0.704039i	$0.751378\pi$
$788$	5.81132	0.207020
$789$	29.8867	1.06399
$790$	19.7010	0.700929
$791$	22.9409	0.815685
$792$	−11.3898	−0.404717
$793$	18.5243	0.657819
$794$	1.67834	0.0595622
$795$	28.1743	0.999238
$796$	5.99203	0.212382
$797$	−54.9131	−1.94512	−0.972561	−	0.232648i	$-0.925261\pi$
$797$	−54.9131	−1.94512	−0.972561	+	0.232648i	$0.925261\pi$
$798$	10.6870	0.378315
$799$	−11.0591	−0.391244
$800$	20.7578	0.733899
$801$	5.27093	0.186239
$802$	19.9408	0.704133
$803$	24.7516	0.873466
$804$	1.34105	0.0472951
$805$	−99.1429	−3.49433
$806$	2.82473	0.0994967
$807$	−6.43186	−0.226412
$808$	37.3425	1.31371
$809$	48.0642	1.68985	0.844923	−	0.534887i	$-0.179646\pi$
$809$	48.0642	1.68985	0.844923	+	0.534887i	$0.179646\pi$
$810$	5.59245	0.196499
$811$	52.4064	1.84024	0.920119	−	0.391638i	$-0.128092\pi$
$811$	52.4064	1.84024	0.920119	+	0.391638i	$0.128092\pi$
$812$	1.94812	0.0683656
$813$	10.0760	0.353382
$814$	5.78572	0.202790
$815$	−44.9166	−1.57336
$816$	4.74912	0.166252
$817$	14.0260	0.490709
$818$	16.4762	0.576078
$819$	−9.34290	−0.326467
$820$	−7.49440	−0.261716
$821$	27.0103	0.942666	0.471333	−	0.881955i	$-0.343773\pi$
$821$	27.0103	0.942666	0.471333	+	0.881955i	$0.343773\pi$
$822$	−24.2329	−0.845219
$823$	21.4070	0.746202	0.373101	−	0.927791i	$-0.378294\pi$
$823$	21.4070	0.746202	0.373101	+	0.927791i	$0.378294\pi$
$824$	−21.8269	−0.760376
$825$	−36.0729	−1.25590
$826$	1.39595	0.0485712
$827$	2.54490	0.0884948	0.0442474	−	0.999021i	$-0.485911\pi$
$827$	2.54490	0.0884948	0.0442474	+	0.999021i	$0.485911\pi$
$828$	−3.63108	−0.126189
$829$	−4.45015	−0.154560	−0.0772800	−	0.997009i	$-0.524624\pi$
$829$	−4.45015	−0.154560	−0.0772800	+	0.997009i	$0.524624\pi$
$830$	−19.1097	−0.663308
$831$	14.1352	0.490344
$832$	12.4450	0.431454
$833$	−7.84022	−0.271648
$834$	12.6771	0.438973
$835$	−45.1352	−1.56197
$836$	−4.20455	−0.145417
$837$	−0.736752	−0.0254659
$838$	−3.82936	−0.132283
$839$	−3.53469	−0.122031	−0.0610156	−	0.998137i	$-0.519434\pi$
$839$	−3.53469	−0.122031	−0.0610156	+	0.998137i	$0.519434\pi$
$840$	32.3347	1.11565
$841$	−27.9734	−0.964601
$842$	−7.88303	−0.271667
$843$	−30.2938	−1.04337
$844$	−6.91330	−0.237966
$845$	25.1807	0.866244
$846$	−17.4830	−0.601077
$847$	−46.3953	−1.59416
$848$	37.8231	1.29885
$849$	22.8584	0.784498
$850$	11.8796	0.407466
$851$	−5.54654	−0.190133
$852$	2.97893	0.102056
$853$	−10.1369	−0.347082	−0.173541	−	0.984827i	$-0.555521\pi$
$853$	−10.1369	−0.347082	−0.173541	+	0.984827i	$0.555521\pi$
$854$	46.5152	1.59172
$855$	−6.20798	−0.212308
$856$	−13.4191	−0.458656
$857$	12.2463	0.418325	0.209162	−	0.977881i	$-0.432926\pi$
$857$	12.2463	0.418325	0.209162	+	0.977881i	$0.432926\pi$
$858$	18.4047	0.628327
$859$	−24.7164	−0.843314	−0.421657	−	0.906755i	$-0.638551\pi$
$859$	−24.7164	−0.843314	−0.421657	+	0.906755i	$0.638551\pi$
$860$	−14.1126	−0.481234
$861$	−16.3510	−0.557241
$862$	13.0696	0.445153
$863$	45.0279	1.53277	0.766385	−	0.642382i	$-0.222054\pi$
$863$	45.0279	1.53277	0.766385	+	0.642382i	$0.222054\pi$
$864$	2.76232	0.0939761
$865$	63.9630	2.17481
$866$	−3.90464	−0.132685
$867$	1.00000	0.0339618
$868$	1.41659	0.0480823
$869$	−16.9106	−0.573654
$870$	−5.66623	−0.192103
$871$	6.51631	0.220797
$872$	1.80666	0.0611813
$873$	−9.65063	−0.326624
$874$	20.1822	0.682671
$875$	34.2690	1.15850
$876$	−2.57355	−0.0869522
$877$	−21.4479	−0.724244	−0.362122	−	0.932131i	$-0.617948\pi$
$877$	−21.4479	−0.724244	−0.362122	+	0.932131i	$0.617948\pi$
$878$	−24.9699	−0.842693
$879$	−18.5166	−0.624551
$880$	−80.6485	−2.71866
$881$	3.83436	0.129183	0.0645915	−	0.997912i	$-0.479426\pi$
$881$	3.83436	0.129183	0.0645915	+	0.997912i	$0.479426\pi$
$882$	−12.3943	−0.417338
$883$	33.3115	1.12102	0.560510	−	0.828147i	$-0.310605\pi$
$883$	33.3115	1.12102	0.560510	+	0.828147i	$0.310605\pi$
$884$	−1.21050	−0.0407135
$885$	−0.810893	−0.0272579
$886$	−16.3154	−0.548128
$887$	53.4388	1.79430	0.897150	−	0.441727i	$-0.145634\pi$
$887$	53.4388	1.79430	0.897150	+	0.441727i	$0.145634\pi$
$888$	1.80896	0.0607048
$889$	−40.6722	−1.36410
$890$	29.4774	0.988085
$891$	−4.80037	−0.160818
$892$	10.7523	0.360013
$893$	19.4072	0.649437
$894$	7.33292	0.245249
$895$	31.3080	1.04651
$896$	52.5325	1.75499
$897$	−17.6439	−0.589112
$898$	−39.6188	−1.32210
$899$	0.746471	0.0248962
$900$	3.75068	0.125023
$901$	7.96423	0.265327
$902$	32.2101	1.07248
$903$	−30.7903	−1.02464
$904$	−14.1296	−0.469944
$905$	−72.8631	−2.42205
$906$	−17.6818	−0.587439
$907$	26.7813	0.889258	0.444629	−	0.895715i	$-0.353336\pi$
$907$	26.7813	0.889258	0.444629	+	0.895715i	$0.353336\pi$
$908$	−1.94653	−0.0645980
$909$	15.7385	0.522014
$910$	−52.2497	−1.73206
$911$	53.1814	1.76198	0.880989	−	0.473138i	$-0.156879\pi$
$911$	53.1814	1.76198	0.880989	+	0.473138i	$0.156879\pi$
$912$	−8.33401	−0.275967
$913$	16.4031	0.542864
$914$	36.9660	1.22273
$915$	−27.0203	−0.893264
$916$	14.4139	0.476250
$917$	53.2574	1.75872
$918$	1.58086	0.0521762
$919$	−24.2882	−0.801194	−0.400597	−	0.916254i	$-0.631197\pi$
$919$	−24.2882	−0.801194	−0.400597	+	0.916254i	$0.631197\pi$
$920$	61.0635	2.01320
$921$	−7.26341	−0.239338
$922$	28.3064	0.932222
$923$	14.4750	0.476450
$924$	9.22993	0.303642
$925$	5.72924	0.188376
$926$	−33.8440	−1.11218
$927$	−9.19924	−0.302143
$928$	−2.79876	−0.0918739
$929$	−21.3849	−0.701615	−0.350807	−	0.936448i	$-0.614093\pi$
$929$	−21.3849	−0.701615	−0.350807	+	0.936448i	$0.614093\pi$
$930$	−4.12025	−0.135108
$931$	13.7585	0.450915
$932$	1.90994	0.0625623
$933$	−25.0635	−0.820543
$934$	51.3210	1.67927
$935$	−16.9818	−0.555364
$936$	5.75442	0.188089
$937$	−40.6432	−1.32776	−0.663878	−	0.747841i	$-0.731090\pi$
$937$	−40.6432	−1.32776	−0.663878	+	0.747841i	$0.731090\pi$
$938$	16.3627	0.534260
$939$	−11.8317	−0.386113
$940$	−19.5269	−0.636898
$941$	44.7569	1.45903	0.729517	−	0.683963i	$-0.239745\pi$
$941$	44.7569	1.45903	0.729517	+	0.683963i	$0.239745\pi$
$942$	−1.58086	−0.0515072
$943$	−30.8786	−1.00554
$944$	−1.08860	−0.0354309
$945$	13.6279	0.443316
$946$	60.6543	1.97204
$947$	−19.5829	−0.636359	−0.318180	−	0.948030i	$-0.603072\pi$
$947$	−19.5829	−0.636359	−0.318180	+	0.948030i	$0.603072\pi$
$948$	1.75828	0.0571064
$949$	−12.5052	−0.405936
$950$	−20.8469	−0.676363
$951$	3.63674	0.117929
$952$	9.14029	0.296239
$953$	−16.1190	−0.522146	−0.261073	−	0.965319i	$-0.584076\pi$
$953$	−16.1190	−0.522146	−0.261073	+	0.965319i	$0.584076\pi$
$954$	12.5903	0.407627
$955$	50.1886	1.62407
$956$	8.19379	0.265006
$957$	4.86369	0.157221
$958$	37.5675	1.21375
$959$	−59.0516	−1.90688
$960$	−18.1528	−0.585879
$961$	−30.4572	−0.982490
$962$	−2.92311	−0.0942447
$963$	−5.65567	−0.182251
$964$	−13.8841	−0.447176
$965$	−4.22406	−0.135977
$966$	−44.3043	−1.42547
$967$	12.3387	0.396786	0.198393	−	0.980123i	$-0.436428\pi$
$967$	12.3387	0.396786	0.198393	+	0.980123i	$0.436428\pi$
$968$	28.5755	0.918451
$969$	−1.75486	−0.0563741
$970$	−53.9707	−1.73289
$971$	−24.6652	−0.791545	−0.395772	−	0.918349i	$-0.629523\pi$
$971$	−24.6652	−0.791545	−0.395772	+	0.918349i	$0.629523\pi$
$972$	0.499118	0.0160092
$973$	30.8921	0.990357
$974$	−22.5230	−0.721684
$975$	18.2250	0.583668
$976$	−36.2739	−1.16110
$977$	−48.4016	−1.54850	−0.774252	−	0.632878i	$-0.781873\pi$
$977$	−48.4016	−1.54850	−0.774252	+	0.632878i	$0.781873\pi$
$978$	−20.0720	−0.641833
$979$	−25.3024	−0.808668
$980$	−13.8433	−0.442209
$981$	0.761443	0.0243110
$982$	21.9181	0.699435
$983$	−38.7403	−1.23562	−0.617812	−	0.786326i	$-0.711981\pi$
$983$	−38.7403	−1.23562	−0.617812	+	0.786326i	$0.711981\pi$
$984$	10.0708	0.321046
$985$	−41.1889	−1.31239
$986$	−1.60171	−0.0510090
$987$	−42.6032	−1.35607
$988$	2.12425	0.0675815
$989$	−58.1469	−1.84896
$990$	−26.8458	−0.853216
$991$	−30.7620	−0.977187	−0.488594	−	0.872512i	$-0.662490\pi$
$991$	−30.7620	−0.977187	−0.488594	+	0.872512i	$0.662490\pi$
$992$	−2.03515	−0.0646160
$993$	−17.6453	−0.559957
$994$	36.3471	1.15286
$995$	−42.4697	−1.34638
$996$	−1.70552	−0.0540413
$997$	−26.0982	−0.826537	−0.413269	−	0.910609i	$-0.635613\pi$
$997$	−26.0982	−0.826537	−0.413269	+	0.910609i	$0.635613\pi$
$998$	44.7658	1.41704
$999$	0.762412	0.0241217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.12	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.12	✓	46	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)

\(f(q)\)	\(=\)	\(q-1.58086 q^{2} +1.00000 q^{3} +0.499118 q^{4} -3.53760 q^{5} -1.58086 q^{6} -3.85230 q^{7} +2.37268 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.58086 q^{2} +1.00000 q^{3} +0.499118 q^{4} -3.53760 q^{5} -1.58086 q^{6} -3.85230 q^{7} +2.37268 q^{8} +1.00000 q^{9} +5.59245 q^{10} -4.80037 q^{11} +0.499118 q^{12} +2.42528 q^{13} +6.08995 q^{14} -3.53760 q^{15} -4.74912 q^{16} -1.00000 q^{17} -1.58086 q^{18} +1.75486 q^{19} -1.76568 q^{20} -3.85230 q^{21} +7.58871 q^{22} -7.27500 q^{23} +2.37268 q^{24} +7.51462 q^{25} -3.83402 q^{26} +1.00000 q^{27} -1.92275 q^{28} -1.01319 q^{29} +5.59245 q^{30} -0.736752 q^{31} +2.76232 q^{32} -4.80037 q^{33} +1.58086 q^{34} +13.6279 q^{35} +0.499118 q^{36} +0.762412 q^{37} -2.77418 q^{38} +2.42528 q^{39} -8.39361 q^{40} +4.24448 q^{41} +6.08995 q^{42} +7.99270 q^{43} -2.39595 q^{44} -3.53760 q^{45} +11.5007 q^{46} +11.0591 q^{47} -4.74912 q^{48} +7.84022 q^{49} -11.8796 q^{50} -1.00000 q^{51} +1.21050 q^{52} -7.96423 q^{53} -1.58086 q^{54} +16.9818 q^{55} -9.14029 q^{56} +1.75486 q^{57} +1.60171 q^{58} +0.229221 q^{59} -1.76568 q^{60} +7.63803 q^{61} +1.16470 q^{62} -3.85230 q^{63} +5.13139 q^{64} -8.57966 q^{65} +7.58871 q^{66} +2.68683 q^{67} -0.499118 q^{68} -7.27500 q^{69} -21.5438 q^{70} +5.96838 q^{71} +2.37268 q^{72} -5.15619 q^{73} -1.20527 q^{74} +7.51462 q^{75} +0.875880 q^{76} +18.4925 q^{77} -3.83402 q^{78} +3.52278 q^{79} +16.8005 q^{80} +1.00000 q^{81} -6.70993 q^{82} -3.41706 q^{83} -1.92275 q^{84} +3.53760 q^{85} -12.6353 q^{86} -1.01319 q^{87} -11.3898 q^{88} +5.27093 q^{89} +5.59245 q^{90} -9.34290 q^{91} -3.63108 q^{92} -0.736752 q^{93} -17.4830 q^{94} -6.20798 q^{95} +2.76232 q^{96} -9.65063 q^{97} -12.3943 q^{98} -4.80037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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