LMFDB - Embedded newform 8007.2.a.h.1.19

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:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-1.18880 q^{2} +1.00000 q^{3} -0.586753 q^{4} -1.07516 q^{5} -1.18880 q^{6} -2.55094 q^{7} +3.07513 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.18880 q^{2} +1.00000 q^{3} -0.586753 q^{4} -1.07516 q^{5} -1.18880 q^{6} -2.55094 q^{7} +3.07513 q^{8} +1.00000 q^{9} +1.27815 q^{10} -3.85818 q^{11} -0.586753 q^{12} -4.45908 q^{13} +3.03256 q^{14} -1.07516 q^{15} -2.48222 q^{16} -1.00000 q^{17} -1.18880 q^{18} -0.0102849 q^{19} +0.630852 q^{20} -2.55094 q^{21} +4.58660 q^{22} +3.24799 q^{23} +3.07513 q^{24} -3.84404 q^{25} +5.30096 q^{26} +1.00000 q^{27} +1.49677 q^{28} +2.31038 q^{29} +1.27815 q^{30} +5.33199 q^{31} -3.19941 q^{32} -3.85818 q^{33} +1.18880 q^{34} +2.74266 q^{35} -0.586753 q^{36} -5.42551 q^{37} +0.0122267 q^{38} -4.45908 q^{39} -3.30625 q^{40} -4.92627 q^{41} +3.03256 q^{42} +13.0891 q^{43} +2.26380 q^{44} -1.07516 q^{45} -3.86121 q^{46} -9.27990 q^{47} -2.48222 q^{48} -0.492703 q^{49} +4.56979 q^{50} -1.00000 q^{51} +2.61638 q^{52} -12.4032 q^{53} -1.18880 q^{54} +4.14815 q^{55} -7.84448 q^{56} -0.0102849 q^{57} -2.74658 q^{58} -4.65978 q^{59} +0.630852 q^{60} -8.79535 q^{61} -6.33867 q^{62} -2.55094 q^{63} +8.76789 q^{64} +4.79421 q^{65} +4.58660 q^{66} -3.67015 q^{67} +0.586753 q^{68} +3.24799 q^{69} -3.26048 q^{70} -7.20801 q^{71} +3.07513 q^{72} -14.4873 q^{73} +6.44984 q^{74} -3.84404 q^{75} +0.00603469 q^{76} +9.84198 q^{77} +5.30096 q^{78} +6.80174 q^{79} +2.66877 q^{80} +1.00000 q^{81} +5.85635 q^{82} -13.5770 q^{83} +1.49677 q^{84} +1.07516 q^{85} -15.5603 q^{86} +2.31038 q^{87} -11.8644 q^{88} -4.63658 q^{89} +1.27815 q^{90} +11.3748 q^{91} -1.90577 q^{92} +5.33199 q^{93} +11.0319 q^{94} +0.0110579 q^{95} -3.19941 q^{96} -2.12363 q^{97} +0.585726 q^{98} -3.85818 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) $ 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * 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 $

$2$	−1.18880	−0.840609	−0.420305	−	0.907383i	$-0.638077\pi$
$2$	−1.18880	−0.840609	−0.420305	+	0.907383i	$0.638077\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.586753	−0.293376
$5$	−1.07516	−0.480825	−0.240413	−	0.970671i	$-0.577283\pi$
$5$	−1.07516	−0.480825	−0.240413	+	0.970671i	$0.577283\pi$
$6$	−1.18880	−0.485326
$7$	−2.55094	−0.964165	−0.482082	−	0.876126i	$-0.660119\pi$
$7$	−2.55094	−0.964165	−0.482082	+	0.876126i	$0.660119\pi$
$8$	3.07513	1.08722
$9$	1.00000	0.333333
$10$	1.27815	0.404186
$11$	−3.85818	−1.16328	−0.581642	−	0.813445i	$-0.697589\pi$
$11$	−3.85818	−1.16328	−0.581642	+	0.813445i	$0.697589\pi$
$12$	−0.586753	−0.169381
$13$	−4.45908	−1.23673	−0.618363	−	0.785892i	$-0.712204\pi$
$13$	−4.45908	−1.23673	−0.618363	+	0.785892i	$0.712204\pi$
$14$	3.03256	0.810486
$15$	−1.07516	−0.277604
$16$	−2.48222	−0.620554
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.18880	−0.280203
$19$	−0.0102849	−0.00235952	−0.00117976	−	0.999999i	$-0.500376\pi$
$19$	−0.0102849	−0.00235952	−0.00117976	+	0.999999i	$0.500376\pi$
$20$	0.630852	0.141063
$21$	−2.55094	−0.556661
$22$	4.58660	0.977867
$23$	3.24799	0.677252	0.338626	−	0.940921i	$-0.390038\pi$
$23$	3.24799	0.677252	0.338626	+	0.940921i	$0.390038\pi$
$24$	3.07513	0.627709
$25$	−3.84404	−0.768807
$26$	5.30096	1.03960
$27$	1.00000	0.192450
$28$	1.49677	0.282863
$29$	2.31038	0.429026	0.214513	−	0.976721i	$-0.431184\pi$
$29$	2.31038	0.429026	0.214513	+	0.976721i	$0.431184\pi$
$30$	1.27815	0.233357
$31$	5.33199	0.957654	0.478827	−	0.877909i	$-0.341062\pi$
$31$	5.33199	0.957654	0.478827	+	0.877909i	$0.341062\pi$
$32$	−3.19941	−0.565581
$33$	−3.85818	−0.671622
$34$	1.18880	0.203878
$35$	2.74266	0.463595
$36$	−0.586753	−0.0977922
$37$	−5.42551	−0.891948	−0.445974	−	0.895046i	$-0.647143\pi$
$37$	−5.42551	−0.891948	−0.445974	+	0.895046i	$0.647143\pi$
$38$	0.0122267	0.00198343
$39$	−4.45908	−0.714024
$40$	−3.30625	−0.522765
$41$	−4.92627	−0.769354	−0.384677	−	0.923051i	$-0.625687\pi$
$41$	−4.92627	−0.769354	−0.384677	+	0.923051i	$0.625687\pi$
$42$	3.03256	0.467934
$43$	13.0891	1.99607	0.998035	−	0.0626515i	$-0.0199557\pi$
$43$	13.0891	1.99607	0.998035	+	0.0626515i	$0.0199557\pi$
$44$	2.26380	0.341280
$45$	−1.07516	−0.160275
$46$	−3.86121	−0.569304
$47$	−9.27990	−1.35361	−0.676806	−	0.736161i	$-0.736636\pi$
$47$	−9.27990	−1.35361	−0.676806	+	0.736161i	$0.736636\pi$
$48$	−2.48222	−0.358277
$49$	−0.492703	−0.0703862
$50$	4.56979	0.646266
$51$	−1.00000	−0.140028
$52$	2.61638	0.362826
$53$	−12.4032	−1.70372	−0.851858	−	0.523772i	$-0.824524\pi$
$53$	−12.4032	−1.70372	−0.851858	+	0.523772i	$0.824524\pi$
$54$	−1.18880	−0.161775
$55$	4.14815	0.559336
$56$	−7.84448	−1.04826
$57$	−0.0102849	−0.00136227
$58$	−2.74658	−0.360643
$59$	−4.65978	−0.606651	−0.303326	−	0.952887i	$-0.598097\pi$
$59$	−4.65978	−0.606651	−0.303326	+	0.952887i	$0.598097\pi$
$60$	0.630852	0.0814426
$61$	−8.79535	−1.12613	−0.563065	−	0.826413i	$-0.690378\pi$
$61$	−8.79535	−1.12613	−0.563065	+	0.826413i	$0.690378\pi$
$62$	−6.33867	−0.805012
$63$	−2.55094	−0.321388
$64$	8.76789	1.09599
$65$	4.79421	0.594649
$66$	4.58660	0.564572
$67$	−3.67015	−0.448380	−0.224190	−	0.974545i	$-0.571974\pi$
$67$	−3.67015	−0.448380	−0.224190	+	0.974545i	$0.571974\pi$
$68$	0.586753	0.0711542
$69$	3.24799	0.391012
$70$	−3.26048	−0.389702
$71$	−7.20801	−0.855433	−0.427717	−	0.903913i	$-0.640682\pi$
$71$	−7.20801	−0.855433	−0.427717	+	0.903913i	$0.640682\pi$
$72$	3.07513	0.362408
$73$	−14.4873	−1.69561	−0.847804	−	0.530309i	$-0.822076\pi$
$73$	−14.4873	−1.69561	−0.847804	+	0.530309i	$0.822076\pi$
$74$	6.44984	0.749779
$75$	−3.84404	−0.443871
$76$	0.00603469	0.000692226 0
$77$	9.84198	1.12160
$78$	5.30096	0.600215
$79$	6.80174	0.765255	0.382628	−	0.923903i	$-0.375019\pi$
$79$	6.80174	0.765255	0.382628	+	0.923903i	$0.375019\pi$
$80$	2.66877	0.298378
$81$	1.00000	0.111111
$82$	5.85635	0.646726
$83$	−13.5770	−1.49027	−0.745134	−	0.666915i	$-0.767614\pi$
$83$	−13.5770	−1.49027	−0.745134	+	0.666915i	$0.767614\pi$
$84$	1.49677	0.163311
$85$	1.07516	0.116617
$86$	−15.5603	−1.67792
$87$	2.31038	0.247698
$88$	−11.8644	−1.26475
$89$	−4.63658	−0.491477	−0.245738	−	0.969336i	$-0.579030\pi$
$89$	−4.63658	−0.491477	−0.245738	+	0.969336i	$0.579030\pi$
$90$	1.27815	0.134729
$91$	11.3748	1.19241
$92$	−1.90577	−0.198690
$93$	5.33199	0.552902
$94$	11.0319	1.13786
$95$	0.0110579	0.00113451
$96$	−3.19941	−0.326538
$97$	−2.12363	−0.215622	−0.107811	−	0.994171i	$-0.534384\pi$
$97$	−2.12363	−0.215622	−0.107811	+	0.994171i	$0.534384\pi$
$98$	0.585726	0.0591673
$99$	−3.85818	−0.387761
$100$	2.25550	0.225550
$101$	−12.6330	−1.25703	−0.628516	−	0.777796i	$-0.716337\pi$
$101$	−12.6330	−1.25703	−0.628516	+	0.777796i	$0.716337\pi$
$102$	1.18880	0.117709
$103$	18.4927	1.82214	0.911072	−	0.412247i	$-0.135256\pi$
$103$	18.4927	1.82214	0.911072	+	0.412247i	$0.135256\pi$
$104$	−13.7123	−1.34460
$105$	2.74266	0.267656
$106$	14.7450	1.43216
$107$	9.67866	0.935672	0.467836	−	0.883815i	$-0.345034\pi$
$107$	9.67866	0.935672	0.467836	+	0.883815i	$0.345034\pi$
$108$	−0.586753	−0.0564603
$109$	−16.3620	−1.56719	−0.783595	−	0.621272i	$-0.786616\pi$
$109$	−16.3620	−1.56719	−0.783595	+	0.621272i	$0.786616\pi$
$110$	−4.93132	−0.470183
$111$	−5.42551	−0.514966
$112$	6.33198	0.598316
$113$	12.5308	1.17880	0.589401	−	0.807840i	$-0.299364\pi$
$113$	12.5308	1.17880	0.589401	+	0.807840i	$0.299364\pi$
$114$	0.0122267	0.00114513
$115$	−3.49210	−0.325640
$116$	−1.35562	−0.125866
$117$	−4.45908	−0.412242
$118$	5.53955	0.509957
$119$	2.55094	0.233844
$120$	−3.30625	−0.301818
$121$	3.88552	0.353229
$122$	10.4559	0.946634
$123$	−4.92627	−0.444187
$124$	−3.12856	−0.280953
$125$	9.50873	0.850487
$126$	3.03256	0.270162
$127$	−9.56500	−0.848756	−0.424378	−	0.905485i	$-0.639507\pi$
$127$	−9.56500	−0.848756	−0.424378	+	0.905485i	$0.639507\pi$
$128$	−4.02446	−0.355715
$129$	13.0891	1.15243
$130$	−5.69937	−0.499867
$131$	7.24596	0.633082	0.316541	−	0.948579i	$-0.397478\pi$
$131$	7.24596	0.633082	0.316541	+	0.948579i	$0.397478\pi$
$132$	2.26380	0.197038
$133$	0.0262361	0.00227496
$134$	4.36308	0.376913
$135$	−1.07516	−0.0925348
$136$	−3.07513	−0.263691
$137$	16.6238	1.42027	0.710135	−	0.704065i	$-0.248634\pi$
$137$	16.6238	1.42027	0.710135	+	0.704065i	$0.248634\pi$
$138$	−3.86121	−0.328688
$139$	9.68611	0.821565	0.410783	−	0.911733i	$-0.365256\pi$
$139$	9.68611	0.821565	0.410783	+	0.911733i	$0.365256\pi$
$140$	−1.60927	−0.136008
$141$	−9.27990	−0.781508
$142$	8.56888	0.719085
$143$	17.2039	1.43866
$144$	−2.48222	−0.206851
$145$	−2.48402	−0.206286
$146$	17.2225	1.42534
$147$	−0.492703	−0.0406375
$148$	3.18343	0.261676
$149$	16.3593	1.34020	0.670101	−	0.742270i	$-0.266251\pi$
$149$	16.3593	1.34020	0.670101	+	0.742270i	$0.266251\pi$
$150$	4.56979	0.373122
$151$	−2.19887	−0.178942	−0.0894709	−	0.995989i	$-0.528518\pi$
$151$	−2.19887	−0.178942	−0.0894709	+	0.995989i	$0.528518\pi$
$152$	−0.0316274	−0.00256532
$153$	−1.00000	−0.0808452
$154$	−11.7001	−0.942825
$155$	−5.73273	−0.460464
$156$	2.61638	0.209478
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−8.08591	−0.643281
$159$	−12.4032	−0.983641
$160$	3.43987	0.271945
$161$	−8.28542	−0.652983
$162$	−1.18880	−0.0934010
$163$	−14.5539	−1.13995	−0.569973	−	0.821663i	$-0.693046\pi$
$163$	−14.5539	−1.13995	−0.569973	+	0.821663i	$0.693046\pi$
$164$	2.89050	0.225710
$165$	4.14815	0.322933
$166$	16.1403	1.25273
$167$	18.3086	1.41676	0.708382	−	0.705829i	$-0.249425\pi$
$167$	18.3086	1.41676	0.708382	+	0.705829i	$0.249425\pi$
$168$	−7.84448	−0.605215
$169$	6.88340	0.529492
$170$	−1.27815	−0.0980295
$171$	−0.0102849	−0.000786505 0
$172$	−7.68007	−0.585600
$173$	14.6260	1.11199	0.555996	−	0.831185i	$-0.312337\pi$
$173$	14.6260	1.11199	0.555996	+	0.831185i	$0.312337\pi$
$174$	−2.74658	−0.208217
$175$	9.80591	0.741257
$176$	9.57682	0.721880
$177$	−4.65978	−0.350250
$178$	5.51197	0.413140
$179$	23.2584	1.73842	0.869208	−	0.494446i	$-0.164629\pi$
$179$	23.2584	1.73842	0.869208	+	0.494446i	$0.164629\pi$
$180$	0.630852	0.0470209
$181$	−1.87403	−0.139296	−0.0696479	−	0.997572i	$-0.522188\pi$
$181$	−1.87403	−0.139296	−0.0696479	+	0.997572i	$0.522188\pi$
$182$	−13.5224	−1.00235
$183$	−8.79535	−0.650171
$184$	9.98800	0.736325
$185$	5.83327	0.428871
$186$	−6.33867	−0.464774
$187$	3.85818	0.282138
$188$	5.44501	0.397118
$189$	−2.55094	−0.185554
$190$	−0.0131456	−0.000953683 0
$191$	17.0068	1.23057	0.615283	−	0.788306i	$-0.289042\pi$
$191$	17.0068	1.23057	0.615283	+	0.788306i	$0.289042\pi$
$192$	8.76789	0.632768
$193$	−16.8727	−1.21452	−0.607262	−	0.794502i	$-0.707732\pi$
$193$	−16.8727	−1.21452	−0.607262	+	0.794502i	$0.707732\pi$
$194$	2.52458	0.181254
$195$	4.79421	0.343321
$196$	0.289095	0.0206496
$197$	−25.3474	−1.80592	−0.902962	−	0.429720i	$-0.858612\pi$
$197$	−25.3474	−1.80592	−0.902962	+	0.429720i	$0.858612\pi$
$198$	4.58660	0.325956
$199$	8.94770	0.634285	0.317143	−	0.948378i	$-0.397277\pi$
$199$	8.94770	0.634285	0.317143	+	0.948378i	$0.397277\pi$
$200$	−11.8209	−0.835866
$201$	−3.67015	−0.258873
$202$	15.0181	1.05667
$203$	−5.89363	−0.413652
$204$	0.586753	0.0410809
$205$	5.29652	0.369925
$206$	−21.9842	−1.53171
$207$	3.24799	0.225751
$208$	11.0684	0.767455
$209$	0.0396809	0.00274479
$210$	−3.26048	−0.224994
$211$	−9.12151	−0.627951	−0.313975	−	0.949431i	$-0.601661\pi$
$211$	−9.12151	−0.627951	−0.313975	+	0.949431i	$0.601661\pi$
$212$	7.27764	0.499830
$213$	−7.20801	−0.493884
$214$	−11.5060	−0.786534
$215$	−14.0729	−0.959761
$216$	3.07513	0.209236
$217$	−13.6016	−0.923336
$218$	19.4511	1.31739
$219$	−14.4873	−0.978960
$220$	−2.43394	−0.164096
$221$	4.45908	0.299950
$222$	6.44984	0.432885
$223$	25.1141	1.68176	0.840881	−	0.541221i	$-0.182038\pi$
$223$	25.1141	1.68176	0.840881	+	0.541221i	$0.182038\pi$
$224$	8.16150	0.545313
$225$	−3.84404	−0.256269
$226$	−14.8967	−0.990912
$227$	−12.2578	−0.813581	−0.406791	−	0.913521i	$-0.633352\pi$
$227$	−12.2578	−0.813581	−0.406791	+	0.913521i	$0.633352\pi$
$228$	0.00603469	0.000399657 0
$229$	−18.9959	−1.25529	−0.627643	−	0.778502i	$-0.715980\pi$
$229$	−18.9959	−1.25529	−0.627643	+	0.778502i	$0.715980\pi$
$230$	4.15141	0.273736
$231$	9.84198	0.647554
$232$	7.10471	0.466447
$233$	10.2791	0.673406	0.336703	−	0.941611i	$-0.390688\pi$
$233$	10.2791	0.673406	0.336703	+	0.941611i	$0.390688\pi$
$234$	5.30096	0.346534
$235$	9.97735	0.650851
$236$	2.73414	0.177977
$237$	6.80174	0.441820
$238$	−3.03256	−0.196572
$239$	−13.8362	−0.894989	−0.447495	−	0.894287i	$-0.647684\pi$
$239$	−13.8362	−0.894989	−0.447495	+	0.894287i	$0.647684\pi$
$240$	2.66877	0.172269
$241$	−18.7965	−1.21079	−0.605396	−	0.795925i	$-0.706985\pi$
$241$	−18.7965	−1.21079	−0.605396	+	0.795925i	$0.706985\pi$
$242$	−4.61911	−0.296927
$243$	1.00000	0.0641500
$244$	5.16070	0.330380
$245$	0.529734	0.0338434
$246$	5.85635	0.373387
$247$	0.0458611	0.00291807
$248$	16.3966	1.04118
$249$	−13.5770	−0.860406
$250$	−11.3040	−0.714927
$251$	−3.53016	−0.222821	−0.111411	−	0.993774i	$-0.535537\pi$
$251$	−3.53016	−0.222821	−0.111411	+	0.993774i	$0.535537\pi$
$252$	1.49677	0.0942878
$253$	−12.5313	−0.787836
$254$	11.3709	0.713472
$255$	1.07516	0.0673290
$256$	−12.7515	−0.796969
$257$	−15.6001	−0.973107	−0.486554	−	0.873651i	$-0.661746\pi$
$257$	−15.6001	−0.973107	−0.486554	+	0.873651i	$0.661746\pi$
$258$	−15.5603	−0.968745
$259$	13.8401	0.859984
$260$	−2.81302	−0.174456
$261$	2.31038	0.143009
$262$	−8.61400	−0.532175
$263$	2.96505	0.182833	0.0914164	−	0.995813i	$-0.470861\pi$
$263$	2.96505	0.182833	0.0914164	+	0.995813i	$0.470861\pi$
$264$	−11.8644	−0.730204
$265$	13.3354	0.819190
$266$	−0.0311895	−0.00191235
$267$	−4.63658	−0.283754
$268$	2.15347	0.131544
$269$	16.2436	0.990390	0.495195	−	0.868782i	$-0.335097\pi$
$269$	16.2436	0.990390	0.495195	+	0.868782i	$0.335097\pi$
$270$	1.27815	0.0777856
$271$	−0.0591187	−0.00359121	−0.00179560	−	0.999998i	$-0.500572\pi$
$271$	−0.0591187	−0.00359121	−0.00179560	+	0.999998i	$0.500572\pi$
$272$	2.48222	0.150506
$273$	11.3748	0.688437
$274$	−19.7624	−1.19389
$275$	14.8310	0.894341
$276$	−1.90577	−0.114714
$277$	26.0713	1.56647	0.783236	−	0.621724i	$-0.213568\pi$
$277$	26.0713	1.56647	0.783236	+	0.621724i	$0.213568\pi$
$278$	−11.5149	−0.690615
$279$	5.33199	0.319218
$280$	8.43406	0.504031
$281$	3.89105	0.232121	0.116060	−	0.993242i	$-0.462973\pi$
$281$	3.89105	0.232121	0.116060	+	0.993242i	$0.462973\pi$
$282$	11.0319	0.656943
$283$	−16.5345	−0.982873	−0.491437	−	0.870913i	$-0.663528\pi$
$283$	−16.5345	−0.982873	−0.491437	+	0.870913i	$0.663528\pi$
$284$	4.22932	0.250964
$285$	0.0110579	0.000655012 0
$286$	−20.4520	−1.20935
$287$	12.5666	0.741784
$288$	−3.19941	−0.188527
$289$	1.00000	0.0588235
$290$	2.95300	0.173406
$291$	−2.12363	−0.124490
$292$	8.50046	0.497452
$293$	−13.5121	−0.789383	−0.394692	−	0.918814i	$-0.629149\pi$
$293$	−13.5121	−0.789383	−0.394692	+	0.918814i	$0.629149\pi$
$294$	0.585726	0.0341602
$295$	5.01000	0.291693
$296$	−16.6842	−0.969747
$297$	−3.85818	−0.223874
$298$	−19.4479	−1.12659
$299$	−14.4830	−0.837576
$300$	2.25550	0.130221
$301$	−33.3895	−1.92454
$302$	2.61402	0.150420
$303$	−12.6330	−0.725748
$304$	0.0255293	0.00146421
$305$	9.45639	0.541471
$306$	1.18880	0.0679592
$307$	32.4962	1.85466	0.927328	−	0.374250i	$-0.122100\pi$
$307$	32.4962	1.85466	0.927328	+	0.374250i	$0.122100\pi$
$308$	−5.77481	−0.329050
$309$	18.4927	1.05202
$310$	6.81507	0.387070
$311$	−8.20269	−0.465132	−0.232566	−	0.972581i	$-0.574712\pi$
$311$	−8.20269	−0.465132	−0.232566	+	0.972581i	$0.574712\pi$
$312$	−13.7123	−0.776304
$313$	6.79575	0.384119	0.192059	−	0.981383i	$-0.438483\pi$
$313$	6.79575	0.384119	0.192059	+	0.981383i	$0.438483\pi$
$314$	1.18880	0.0670879
$315$	2.74266	0.154532
$316$	−3.99094	−0.224508
$317$	4.40837	0.247599	0.123799	−	0.992307i	$-0.460492\pi$
$317$	4.40837	0.247599	0.123799	+	0.992307i	$0.460492\pi$
$318$	14.7450	0.826858
$319$	−8.91383	−0.499079
$320$	−9.42686	−0.526978
$321$	9.67866	0.540210
$322$	9.84972	0.548903
$323$	0.0102849	0.000572266 0
$324$	−0.586753	−0.0325974
$325$	17.1409	0.950804
$326$	17.3016	0.958249
$327$	−16.3620	−0.904818
$328$	−15.1489	−0.836460
$329$	23.6725	1.30511
$330$	−4.93132	−0.271460
$331$	17.9204	0.984992	0.492496	−	0.870315i	$-0.336085\pi$
$331$	17.9204	0.984992	0.492496	+	0.870315i	$0.336085\pi$
$332$	7.96633	0.437209
$333$	−5.42551	−0.297316
$334$	−21.7653	−1.19095
$335$	3.94599	0.215593
$336$	6.33198	0.345438
$337$	22.6597	1.23435	0.617176	−	0.786825i	$-0.288277\pi$
$337$	22.6597	1.23435	0.617176	+	0.786825i	$0.288277\pi$
$338$	−8.18299	−0.445096
$339$	12.5308	0.680582
$340$	−0.630852	−0.0342127
$341$	−20.5718	−1.11402
$342$	0.0122267	0.000661143 0
$343$	19.1134	1.03203
$344$	40.2508	2.17018
$345$	−3.49210	−0.188008
$346$	−17.3874	−0.934751
$347$	22.6658	1.21677	0.608383	−	0.793644i	$-0.291819\pi$
$347$	22.6658	1.21677	0.608383	+	0.793644i	$0.291819\pi$
$348$	−1.35562	−0.0726688
$349$	−20.6345	−1.10454	−0.552271	−	0.833665i	$-0.686238\pi$
$349$	−20.6345	−1.10454	−0.552271	+	0.833665i	$0.686238\pi$
$350$	−11.6573	−0.623107
$351$	−4.45908	−0.238008
$352$	12.3439	0.657931
$353$	28.5938	1.52189	0.760946	−	0.648815i	$-0.224735\pi$
$353$	28.5938	1.52189	0.760946	+	0.648815i	$0.224735\pi$
$354$	5.53955	0.294424
$355$	7.74974	0.411314
$356$	2.72053	0.144188
$357$	2.55094	0.135010
$358$	−27.6496	−1.46133
$359$	10.7442	0.567057	0.283529	−	0.958964i	$-0.408495\pi$
$359$	10.7442	0.567057	0.283529	+	0.958964i	$0.408495\pi$
$360$	−3.30625	−0.174255
$361$	−18.9999	−0.999994
$362$	2.22785	0.117093
$363$	3.88552	0.203937
$364$	−6.67423	−0.349824
$365$	15.5761	0.815291
$366$	10.4559	0.546540
$367$	−26.2415	−1.36980	−0.684899	−	0.728638i	$-0.740154\pi$
$367$	−26.2415	−1.36980	−0.684899	+	0.728638i	$0.740154\pi$
$368$	−8.06220	−0.420271
$369$	−4.92627	−0.256451
$370$	−6.93460	−0.360513
$371$	31.6399	1.64266
$372$	−3.12856	−0.162208
$373$	−8.53000	−0.441666	−0.220833	−	0.975312i	$-0.570878\pi$
$373$	−8.53000	−0.441666	−0.220833	+	0.975312i	$0.570878\pi$
$374$	−4.58660	−0.237168
$375$	9.50873	0.491029
$376$	−28.5369	−1.47168
$377$	−10.3022	−0.530588
$378$	3.03256	0.155978
$379$	−33.7375	−1.73298	−0.866489	−	0.499196i	$-0.833629\pi$
$379$	−33.7375	−1.73298	−0.866489	+	0.499196i	$0.833629\pi$
$380$	−0.00648824	−0.000332840 0
$381$	−9.56500	−0.490030
$382$	−20.2176	−1.03442
$383$	−19.3118	−0.986789	−0.493394	−	0.869806i	$-0.664244\pi$
$383$	−19.3118	−0.986789	−0.493394	+	0.869806i	$0.664244\pi$
$384$	−4.02446	−0.205372
$385$	−10.5817	−0.539292
$386$	20.0583	1.02094
$387$	13.0891	0.665357
$388$	1.24605	0.0632585
$389$	11.8785	0.602263	0.301132	−	0.953583i	$-0.402636\pi$
$389$	11.8785	0.602263	0.301132	+	0.953583i	$0.402636\pi$
$390$	−5.69937	−0.288599
$391$	−3.24799	−0.164258
$392$	−1.51513	−0.0765255
$393$	7.24596	0.365510
$394$	30.1330	1.51808
$395$	−7.31294	−0.367954
$396$	2.26380	0.113760
$397$	−8.56305	−0.429767	−0.214884	−	0.976640i	$-0.568937\pi$
$397$	−8.56305	−0.429767	−0.214884	+	0.976640i	$0.568937\pi$
$398$	−10.6370	−0.533186
$399$	0.0262361	0.00131345
$400$	9.54172	0.477086
$401$	18.7135	0.934506	0.467253	−	0.884124i	$-0.345244\pi$
$401$	18.7135	0.934506	0.467253	+	0.884124i	$0.345244\pi$
$402$	4.36308	0.217611
$403$	−23.7758	−1.18436
$404$	7.41246	0.368784
$405$	−1.07516	−0.0534250
$406$	7.00635	0.347719
$407$	20.9325	1.03759
$408$	−3.07513	−0.152242
$409$	23.0626	1.14037	0.570185	−	0.821516i	$-0.306872\pi$
$409$	23.0626	1.14037	0.570185	+	0.821516i	$0.306872\pi$
$410$	−6.29650	−0.310962
$411$	16.6238	0.819994
$412$	−10.8507	−0.534574
$413$	11.8868	0.584912
$414$	−3.86121	−0.189768
$415$	14.5974	0.716558
$416$	14.2664	0.699469
$417$	9.68611	0.474331
$418$	−0.0471727	−0.00230729
$419$	−16.5282	−0.807454	−0.403727	−	0.914879i	$-0.632285\pi$
$419$	−16.5282	−0.807454	−0.403727	+	0.914879i	$0.632285\pi$
$420$	−1.60927	−0.0785241
$421$	7.26571	0.354109	0.177055	−	0.984201i	$-0.443343\pi$
$421$	7.26571	0.354109	0.177055	+	0.984201i	$0.443343\pi$
$422$	10.8437	0.527861
$423$	−9.27990	−0.451204
$424$	−38.1416	−1.85232
$425$	3.84404	0.186463
$426$	8.56888	0.415164
$427$	22.4364	1.08577
$428$	−5.67898	−0.274504
$429$	17.2039	0.830613
$430$	16.7298	0.806784
$431$	−8.75514	−0.421720	−0.210860	−	0.977516i	$-0.567626\pi$
$431$	−8.75514	−0.421720	−0.210860	+	0.977516i	$0.567626\pi$
$432$	−2.48222	−0.119426
$433$	13.2935	0.638847	0.319423	−	0.947612i	$-0.396511\pi$
$433$	13.2935	0.638847	0.319423	+	0.947612i	$0.396511\pi$
$434$	16.1696	0.776165
$435$	−2.48402	−0.119100
$436$	9.60042	0.459777
$437$	−0.0334052	−0.00159799
$438$	17.2225	0.822923
$439$	16.9154	0.807326	0.403663	−	0.914908i	$-0.367737\pi$
$439$	16.9154	0.807326	0.403663	+	0.914908i	$0.367737\pi$
$440$	12.7561	0.608123
$441$	−0.492703	−0.0234621
$442$	−5.30096	−0.252141
$443$	22.8659	1.08639	0.543195	−	0.839607i	$-0.317215\pi$
$443$	22.8659	1.08639	0.543195	+	0.839607i	$0.317215\pi$
$444$	3.18343	0.151079
$445$	4.98505	0.236314
$446$	−29.8556	−1.41370
$447$	16.3593	0.773766
$448$	−22.3664	−1.05671
$449$	2.84920	0.134462	0.0672310	−	0.997737i	$-0.478584\pi$
$449$	2.84920	0.134462	0.0672310	+	0.997737i	$0.478584\pi$
$450$	4.56979	0.215422
$451$	19.0064	0.894977
$452$	−7.35251	−0.345833
$453$	−2.19887	−0.103312
$454$	14.5721	0.683904
$455$	−12.2298	−0.573340
$456$	−0.0316274	−0.00148109
$457$	24.5855	1.15006	0.575030	−	0.818132i	$-0.304990\pi$
$457$	24.5855	1.15006	0.575030	+	0.818132i	$0.304990\pi$
$458$	22.5824	1.05520
$459$	−1.00000	−0.0466760
$460$	2.04900	0.0955351
$461$	9.55695	0.445111	0.222556	−	0.974920i	$-0.428560\pi$
$461$	9.55695	0.445111	0.222556	+	0.974920i	$0.428560\pi$
$462$	−11.7001	−0.544340
$463$	29.9919	1.39384	0.696920	−	0.717148i	$-0.254553\pi$
$463$	29.9919	1.39384	0.696920	+	0.717148i	$0.254553\pi$
$464$	−5.73485	−0.266234
$465$	−5.73273	−0.265849
$466$	−12.2198	−0.566072
$467$	−38.2325	−1.76919	−0.884594	−	0.466363i	$-0.845564\pi$
$467$	−38.2325	−1.76919	−0.884594	+	0.466363i	$0.845564\pi$
$468$	2.61638	0.120942
$469$	9.36234	0.432313
$470$	−11.8611	−0.547111
$471$	−1.00000	−0.0460776
$472$	−14.3294	−0.659566
$473$	−50.5001	−2.32200
$474$	−8.08591	−0.371398
$475$	0.0395355	0.00181401
$476$	−1.49677	−0.0686044
$477$	−12.4032	−0.567906
$478$	16.4485	0.752336
$479$	−3.86119	−0.176422	−0.0882111	−	0.996102i	$-0.528115\pi$
$479$	−3.86119	−0.176422	−0.0882111	+	0.996102i	$0.528115\pi$
$480$	3.43987	0.157008
$481$	24.1928	1.10310
$482$	22.3453	1.01780
$483$	−8.28542	−0.377000
$484$	−2.27984	−0.103629
$485$	2.28324	0.103677
$486$	−1.18880	−0.0539251
$487$	−18.2202	−0.825638	−0.412819	−	0.910813i	$-0.635456\pi$
$487$	−18.2202	−0.825638	−0.412819	+	0.910813i	$0.635456\pi$
$488$	−27.0469	−1.22435
$489$	−14.5539	−0.658148
$490$	−0.629748	−0.0284491
$491$	12.5545	0.566577	0.283288	−	0.959035i	$-0.408575\pi$
$491$	12.5545	0.566577	0.283288	+	0.959035i	$0.408575\pi$
$492$	2.89050	0.130314
$493$	−2.31038	−0.104054
$494$	−0.0545198	−0.00245296
$495$	4.14815	0.186445
$496$	−13.2351	−0.594276
$497$	18.3872	0.824778
$498$	16.1403	0.723265
$499$	30.1059	1.34773	0.673863	−	0.738856i	$-0.264634\pi$
$499$	30.1059	1.34773	0.673863	+	0.738856i	$0.264634\pi$
$500$	−5.57928	−0.249513
$501$	18.3086	0.817969
$502$	4.19665	0.187306
$503$	5.51171	0.245755	0.122877	−	0.992422i	$-0.460788\pi$
$503$	5.51171	0.245755	0.122877	+	0.992422i	$0.460788\pi$
$504$	−7.84448	−0.349421
$505$	13.5825	0.604413
$506$	14.8972	0.662262
$507$	6.88340	0.305703
$508$	5.61229	0.249005
$509$	32.7058	1.44966	0.724830	−	0.688927i	$-0.241918\pi$
$509$	32.7058	1.44966	0.724830	+	0.688927i	$0.241918\pi$
$510$	−1.27815	−0.0565973
$511$	36.9562	1.63485
$512$	23.2079	1.02565
$513$	−0.0102849	−0.000454089 0
$514$	18.5454	0.818003
$515$	−19.8826	−0.876133
$516$	−7.68007	−0.338096
$517$	35.8035	1.57463
$518$	−16.4532	−0.722911
$519$	14.6260	0.642009
$520$	14.7429	0.646517
$521$	10.9060	0.477800	0.238900	−	0.971044i	$-0.423213\pi$
$521$	10.9060	0.477800	0.238900	+	0.971044i	$0.423213\pi$
$522$	−2.74658	−0.120214
$523$	−16.4587	−0.719687	−0.359843	−	0.933013i	$-0.617170\pi$
$523$	−16.4587	−0.719687	−0.359843	+	0.933013i	$0.617170\pi$
$524$	−4.25159	−0.185731
$525$	9.80591	0.427965
$526$	−3.52485	−0.153691
$527$	−5.33199	−0.232265
$528$	9.57682	0.416778
$529$	−12.4506	−0.541329
$530$	−15.8532	−0.688618
$531$	−4.65978	−0.202217
$532$	−0.0153941	−0.000667420 0
$533$	21.9666	0.951481
$534$	5.51197	0.238526
$535$	−10.4061	−0.449894
$536$	−11.2862	−0.487490
$537$	23.2584	1.00368
$538$	−19.3104	−0.832530
$539$	1.90094	0.0818791
$540$	0.630852	0.0271475
$541$	−10.9245	−0.469683	−0.234841	−	0.972034i	$-0.575457\pi$
$541$	−10.9245	−0.469683	−0.234841	+	0.972034i	$0.575457\pi$
$542$	0.0702804	0.00301880
$543$	−1.87403	−0.0804224
$544$	3.19941	0.137173
$545$	17.5917	0.753545
$546$	−13.5224	−0.578707
$547$	45.5178	1.94620	0.973100	−	0.230384i	$-0.0739982\pi$
$547$	45.5178	1.94620	0.973100	+	0.230384i	$0.0739982\pi$
$548$	−9.75409	−0.416674
$549$	−8.79535	−0.375376
$550$	−17.6311	−0.751791
$551$	−0.0237620	−0.00101229
$552$	9.98800	0.425117
$553$	−17.3508	−0.737832
$554$	−30.9936	−1.31679
$555$	5.83327	0.247609
$556$	−5.68335	−0.241028
$557$	22.3483	0.946928	0.473464	−	0.880813i	$-0.343003\pi$
$557$	22.3483	0.946928	0.473464	+	0.880813i	$0.343003\pi$
$558$	−6.33867	−0.268337
$559$	−58.3654	−2.46859
$560$	−6.80788	−0.287685
$561$	3.85818	0.162892
$562$	−4.62568	−0.195123
$563$	31.0882	1.31021	0.655107	−	0.755536i	$-0.272624\pi$
$563$	31.0882	1.31021	0.655107	+	0.755536i	$0.272624\pi$
$564$	5.44501	0.229276
$565$	−13.4726	−0.566798
$566$	19.6562	0.826212
$567$	−2.55094	−0.107129
$568$	−22.1656	−0.930047
$569$	13.2317	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$569$	13.2317	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$570$	−0.0131456	−0.000550609 0
$571$	−18.4678	−0.772854	−0.386427	−	0.922320i	$-0.626291\pi$
$571$	−18.4678	−0.772854	−0.386427	+	0.922320i	$0.626291\pi$
$572$	−10.0944	−0.422070
$573$	17.0068	0.710467
$574$	−14.9392	−0.623551
$575$	−12.4854	−0.520676
$576$	8.76789	0.365329
$577$	−7.02919	−0.292629	−0.146315	−	0.989238i	$-0.546741\pi$
$577$	−7.02919	−0.292629	−0.146315	+	0.989238i	$0.546741\pi$
$578$	−1.18880	−0.0494476
$579$	−16.8727	−0.701205
$580$	1.45750	0.0605196
$581$	34.6341	1.43686
$582$	2.52458	0.104647
$583$	47.8539	1.98191
$584$	−44.5503	−1.84351
$585$	4.79421	0.198216
$586$	16.0632	0.663563
$587$	9.96063	0.411119	0.205560	−	0.978645i	$-0.434099\pi$
$587$	9.96063	0.411119	0.205560	+	0.978645i	$0.434099\pi$
$588$	0.289095	0.0119221
$589$	−0.0548389	−0.00225960
$590$	−5.95589	−0.245200
$591$	−25.3474	−1.04265
$592$	13.4673	0.553501
$593$	15.7294	0.645929	0.322965	−	0.946411i	$-0.395321\pi$
$593$	15.7294	0.645929	0.322965	+	0.946411i	$0.395321\pi$
$594$	4.58660	0.188191
$595$	−2.74266	−0.112438
$596$	−9.59884	−0.393184
$597$	8.94770	0.366205
$598$	17.2174	0.704074
$599$	24.6980	1.00913	0.504566	−	0.863373i	$-0.331653\pi$
$599$	24.6980	1.00913	0.504566	+	0.863373i	$0.331653\pi$
$600$	−11.8209	−0.482587
$601$	10.8527	0.442691	0.221345	−	0.975195i	$-0.428955\pi$
$601$	10.8527	0.442691	0.221345	+	0.975195i	$0.428955\pi$
$602$	39.6935	1.61779
$603$	−3.67015	−0.149460
$604$	1.29020	0.0524973
$605$	−4.17754	−0.169841
$606$	15.0181	0.610071
$607$	−44.8256	−1.81942	−0.909708	−	0.415249i	$-0.863695\pi$
$607$	−44.8256	−1.81942	−0.909708	+	0.415249i	$0.863695\pi$
$608$	0.0329056	0.00133450
$609$	−5.89363	−0.238822
$610$	−11.2418	−0.455166
$611$	41.3798	1.67405
$612$	0.586753	0.0237181
$613$	19.2451	0.777301	0.388651	−	0.921385i	$-0.372941\pi$
$613$	19.2451	0.777301	0.388651	+	0.921385i	$0.372941\pi$
$614$	−38.6315	−1.55904
$615$	5.29652	0.213576
$616$	30.2654	1.21943
$617$	14.9326	0.601163	0.300581	−	0.953756i	$-0.402819\pi$
$617$	14.9326	0.601163	0.300581	+	0.953756i	$0.402819\pi$
$618$	−21.9842	−0.884334
$619$	−9.75985	−0.392282	−0.196141	−	0.980576i	$-0.562841\pi$
$619$	−9.75985	−0.392282	−0.196141	+	0.980576i	$0.562841\pi$
$620$	3.36370	0.135089
$621$	3.24799	0.130337
$622$	9.75136	0.390994
$623$	11.8276	0.473864
$624$	11.0684	0.443091
$625$	8.99679	0.359872
$626$	−8.07880	−0.322894
$627$	0.0396809	0.00158470
$628$	0.586753	0.0234140
$629$	5.42551	0.216329
$630$	−3.26048	−0.129901
$631$	−15.9626	−0.635460	−0.317730	−	0.948181i	$-0.602921\pi$
$631$	−15.9626	−0.635460	−0.317730	+	0.948181i	$0.602921\pi$
$632$	20.9163	0.832004
$633$	−9.12151	−0.362548
$634$	−5.24067	−0.208134
$635$	10.2839	0.408103
$636$	7.27764	0.288577
$637$	2.19700	0.0870485
$638$	10.5968	0.419530
$639$	−7.20801	−0.285144
$640$	4.32692	0.171037
$641$	4.81291	0.190099	0.0950493	−	0.995473i	$-0.469699\pi$
$641$	4.81291	0.190099	0.0950493	+	0.995473i	$0.469699\pi$
$642$	−11.5060	−0.454106
$643$	−38.7929	−1.52984	−0.764921	−	0.644124i	$-0.777222\pi$
$643$	−38.7929	−1.52984	−0.764921	+	0.644124i	$0.777222\pi$
$644$	4.86150	0.191570
$645$	−14.0729	−0.554118
$646$	−0.0122267	−0.000481052 0
$647$	−30.0381	−1.18092	−0.590460	−	0.807067i	$-0.701054\pi$
$647$	−30.0381	−1.18092	−0.590460	+	0.807067i	$0.701054\pi$
$648$	3.07513	0.120803
$649$	17.9782	0.705708
$650$	−20.3771	−0.799255
$651$	−13.6016	−0.533088
$652$	8.53952	0.334433
$653$	−3.81936	−0.149463	−0.0747315	−	0.997204i	$-0.523810\pi$
$653$	−3.81936	−0.149463	−0.0747315	+	0.997204i	$0.523810\pi$
$654$	19.4511	0.760598
$655$	−7.79055	−0.304402
$656$	12.2281	0.477426
$657$	−14.4873	−0.565203
$658$	−28.1418	−1.09708
$659$	−4.12756	−0.160787	−0.0803935	−	0.996763i	$-0.525618\pi$
$659$	−4.12756	−0.160787	−0.0803935	+	0.996763i	$0.525618\pi$
$660$	−2.43394	−0.0947409
$661$	−19.1931	−0.746524	−0.373262	−	0.927726i	$-0.621761\pi$
$661$	−19.1931	−0.746524	−0.373262	+	0.927726i	$0.621761\pi$
$662$	−21.3037	−0.827993
$663$	4.45908	0.173176
$664$	−41.7510	−1.62025
$665$	−0.0282080	−0.00109386
$666$	6.44984	0.249926
$667$	7.50407	0.290559
$668$	−10.7426	−0.415645
$669$	25.1141	0.970965
$670$	−4.69100	−0.181229
$671$	33.9340	1.31001
$672$	8.16150	0.314837
$673$	−22.0728	−0.850842	−0.425421	−	0.904995i	$-0.639874\pi$
$673$	−22.0728	−0.850842	−0.425421	+	0.904995i	$0.639874\pi$
$674$	−26.9379	−1.03761
$675$	−3.84404	−0.147957
$676$	−4.03886	−0.155341
$677$	−13.8555	−0.532512	−0.266256	−	0.963902i	$-0.585787\pi$
$677$	−13.8555	−0.532512	−0.266256	+	0.963902i	$0.585787\pi$
$678$	−14.8967	−0.572103
$679$	5.41726	0.207895
$680$	3.30625	0.126789
$681$	−12.2578	−0.469721
$682$	24.4557	0.936458
$683$	−27.9739	−1.07039	−0.535196	−	0.844728i	$-0.679762\pi$
$683$	−27.9739	−1.07039	−0.535196	+	0.844728i	$0.679762\pi$
$684$	0.00603469	0.000230742 0
$685$	−17.8732	−0.682902
$686$	−22.7221	−0.867533
$687$	−18.9959	−0.724739
$688$	−32.4900	−1.23867
$689$	55.3071	2.10703
$690$	4.15141	0.158041
$691$	16.4976	0.627599	0.313800	−	0.949489i	$-0.398398\pi$
$691$	16.4976	0.627599	0.313800	+	0.949489i	$0.398398\pi$
$692$	−8.58183	−0.326232
$693$	9.84198	0.373866
$694$	−26.9451	−1.02282
$695$	−10.4141	−0.395029
$696$	7.10471	0.269303
$697$	4.92627	0.186596
$698$	24.5303	0.928487
$699$	10.2791	0.388791
$700$	−5.75364	−0.217467
$701$	3.57145	0.134892	0.0674459	−	0.997723i	$-0.478515\pi$
$701$	3.57145	0.134892	0.0674459	+	0.997723i	$0.478515\pi$
$702$	5.30096	0.200072
$703$	0.0558007	0.00210456
$704$	−33.8281	−1.27494
$705$	9.97735	0.375769
$706$	−33.9923	−1.27932
$707$	32.2261	1.21199
$708$	2.73414	0.102755
$709$	−23.2360	−0.872646	−0.436323	−	0.899790i	$-0.643719\pi$
$709$	−23.2360	−0.872646	−0.436323	+	0.899790i	$0.643719\pi$
$710$	−9.21290	−0.345754
$711$	6.80174	0.255085
$712$	−14.2581	−0.534345
$713$	17.3182	0.648573
$714$	−3.03256	−0.113491
$715$	−18.4969	−0.691746
$716$	−13.6469	−0.510010
$717$	−13.8362	−0.516722
$718$	−12.7727	−0.476673
$719$	−9.69583	−0.361594	−0.180797	−	0.983520i	$-0.557868\pi$
$719$	−9.69583	−0.361594	−0.180797	+	0.983520i	$0.557868\pi$
$720$	2.66877	0.0994593
$721$	−47.1739	−1.75685
$722$	22.5871	0.840604
$723$	−18.7965	−0.699051
$724$	1.09959	0.0408661
$725$	−8.88117	−0.329838
$726$	−4.61911	−0.171431
$727$	−25.3941	−0.941816	−0.470908	−	0.882182i	$-0.656074\pi$
$727$	−25.3941	−0.941816	−0.470908	+	0.882182i	$0.656074\pi$
$728$	34.9792	1.29641
$729$	1.00000	0.0370370
$730$	−18.5169	−0.685341
$731$	−13.0891	−0.484118
$732$	5.16070	0.190745
$733$	19.7452	0.729305	0.364652	−	0.931144i	$-0.381188\pi$
$733$	19.7452	0.729305	0.364652	+	0.931144i	$0.381188\pi$
$734$	31.1960	1.15146
$735$	0.529734	0.0195395
$736$	−10.3916	−0.383041
$737$	14.1601	0.521594
$738$	5.85635	0.215575
$739$	−48.4255	−1.78136	−0.890680	−	0.454631i	$-0.849771\pi$
$739$	−48.4255	−1.78136	−0.890680	+	0.454631i	$0.849771\pi$
$740$	−3.42269	−0.125821
$741$	0.0458611	0.00168475
$742$	−37.6136	−1.38084
$743$	−34.9284	−1.28140	−0.640700	−	0.767791i	$-0.721356\pi$
$743$	−34.9284	−1.28140	−0.640700	+	0.767791i	$0.721356\pi$
$744$	16.3966	0.601128
$745$	−17.5888	−0.644403
$746$	10.1405	0.371269
$747$	−13.5770	−0.496756
$748$	−2.26380	−0.0827726
$749$	−24.6897	−0.902142
$750$	−11.3040	−0.412763
$751$	0.502320	0.0183299	0.00916495	−	0.999958i	$-0.497083\pi$
$751$	0.502320	0.0183299	0.00916495	+	0.999958i	$0.497083\pi$
$752$	23.0347	0.839989
$753$	−3.53016	−0.128646
$754$	12.2472	0.446017
$755$	2.36414	0.0860397
$756$	1.49677	0.0544371
$757$	26.4469	0.961228	0.480614	−	0.876932i	$-0.340414\pi$
$757$	26.4469	0.961228	0.480614	+	0.876932i	$0.340414\pi$
$758$	40.1072	1.45676
$759$	−12.5313	−0.454858
$760$	0.0340044	0.00123347
$761$	−14.0911	−0.510802	−0.255401	−	0.966835i	$-0.582207\pi$
$761$	−14.0911	−0.510802	−0.255401	+	0.966835i	$0.582207\pi$
$762$	11.3709	0.411923
$763$	41.7384	1.51103
$764$	−9.97876	−0.361019
$765$	1.07516	0.0388724
$766$	22.9579	0.829504
$767$	20.7783	0.750262
$768$	−12.7515	−0.460130
$769$	42.7454	1.54144	0.770720	−	0.637174i	$-0.219897\pi$
$769$	42.7454	1.54144	0.770720	+	0.637174i	$0.219897\pi$
$770$	12.5795	0.453334
$771$	−15.6001	−0.561824
$772$	9.90011	0.356313
$773$	−29.8357	−1.07311	−0.536557	−	0.843864i	$-0.680275\pi$
$773$	−29.8357	−1.07311	−0.536557	+	0.843864i	$0.680275\pi$
$774$	−15.5603	−0.559305
$775$	−20.4964	−0.736251
$776$	−6.53045	−0.234430
$777$	13.8401	0.496512
$778$	−14.1212	−0.506268
$779$	0.0506661	0.00181530
$780$	−2.81302	−0.100722
$781$	27.8098	0.995111
$782$	3.86121	0.138077
$783$	2.31038	0.0825661
$784$	1.22300	0.0436784
$785$	1.07516	0.0383740
$786$	−8.61400	−0.307251
$787$	36.1878	1.28995	0.644977	−	0.764202i	$-0.276867\pi$
$787$	36.1878	1.28995	0.644977	+	0.764202i	$0.276867\pi$
$788$	14.8726	0.529816
$789$	2.96505	0.105559
$790$	8.69363	0.309305
$791$	−31.9654	−1.13656
$792$	−11.8644	−0.421583
$793$	39.2192	1.39271
$794$	10.1798	0.361266
$795$	13.3354	0.472959
$796$	−5.25009	−0.186084
$797$	16.2453	0.575440	0.287720	−	0.957715i	$-0.407103\pi$
$797$	16.2453	0.575440	0.287720	+	0.957715i	$0.407103\pi$
$798$	−0.0311895	−0.00110410
$799$	9.27990	0.328299
$800$	12.2986	0.434823
$801$	−4.63658	−0.163826
$802$	−22.2466	−0.785554
$803$	55.8945	1.97247
$804$	2.15347	0.0759471
$805$	8.90814	0.313971
$806$	28.2647	0.995580
$807$	16.2436	0.571802
$808$	−38.8482	−1.36668
$809$	38.3586	1.34862	0.674308	−	0.738450i	$-0.264442\pi$
$809$	38.3586	1.34862	0.674308	+	0.738450i	$0.264442\pi$
$810$	1.27815	0.0449095
$811$	−0.423069	−0.0148559	−0.00742797	−	0.999972i	$-0.502364\pi$
$811$	−0.423069	−0.0148559	−0.00742797	+	0.999972i	$0.502364\pi$
$812$	3.45810	0.121356
$813$	−0.0591187	−0.00207338
$814$	−24.8846	−0.872206
$815$	15.6477	0.548115
$816$	2.48222	0.0868949
$817$	−0.134620	−0.00470976
$818$	−27.4168	−0.958605
$819$	11.3748	0.397469
$820$	−3.10775	−0.108527
$821$	−6.35721	−0.221868	−0.110934	−	0.993828i	$-0.535384\pi$
$821$	−6.35721	−0.221868	−0.110934	+	0.993828i	$0.535384\pi$
$822$	−19.7624	−0.689294
$823$	−5.52957	−0.192749	−0.0963743	−	0.995345i	$-0.530725\pi$
$823$	−5.52957	−0.192749	−0.0963743	+	0.995345i	$0.530725\pi$
$824$	56.8677	1.98108
$825$	14.8310	0.516348
$826$	−14.1311	−0.491682
$827$	−3.80165	−0.132196	−0.0660981	−	0.997813i	$-0.521055\pi$
$827$	−3.80165	−0.132196	−0.0660981	+	0.997813i	$0.521055\pi$
$828$	−1.90577	−0.0662300
$829$	−21.3952	−0.743086	−0.371543	−	0.928416i	$-0.621171\pi$
$829$	−21.3952	−0.743086	−0.371543	+	0.928416i	$0.621171\pi$
$830$	−17.3534	−0.602345
$831$	26.0713	0.904403
$832$	−39.0967	−1.35544
$833$	0.492703	0.0170712
$834$	−11.5149	−0.398727
$835$	−19.6847	−0.681216
$836$	−0.0232829	−0.000805255 0
$837$	5.33199	0.184301
$838$	19.6487	0.678753
$839$	45.6866	1.57728	0.788638	−	0.614858i	$-0.210787\pi$
$839$	45.6866	1.57728	0.788638	+	0.614858i	$0.210787\pi$
$840$	8.43406	0.291003
$841$	−23.6622	−0.815937
$842$	−8.63748	−0.297667
$843$	3.89105	0.134015
$844$	5.35207	0.184226
$845$	−7.40074	−0.254593
$846$	11.0319	0.379286
$847$	−9.91172	−0.340571
$848$	30.7875	1.05725
$849$	−16.5345	−0.567462
$850$	−4.56979	−0.156743
$851$	−17.6220	−0.604073
$852$	4.22932	0.144894
$853$	−42.4406	−1.45314	−0.726569	−	0.687093i	$-0.758886\pi$
$853$	−42.4406	−1.45314	−0.726569	+	0.687093i	$0.758886\pi$
$854$	−26.6724	−0.912712
$855$	0.0110579	0.000378171 0
$856$	29.7632	1.01728
$857$	−9.91452	−0.338674	−0.169337	−	0.985558i	$-0.554163\pi$
$857$	−9.91452	−0.338674	−0.169337	+	0.985558i	$0.554163\pi$
$858$	−20.4520	−0.698221
$859$	1.88719	0.0643899	0.0321950	−	0.999482i	$-0.489750\pi$
$859$	1.88719	0.0643899	0.0321950	+	0.999482i	$0.489750\pi$
$860$	8.25729	0.281571
$861$	12.5666	0.428269
$862$	10.4081	0.354502
$863$	12.1518	0.413654	0.206827	−	0.978378i	$-0.433686\pi$
$863$	12.1518	0.413654	0.206827	+	0.978378i	$0.433686\pi$
$864$	−3.19941	−0.108846
$865$	−15.7252	−0.534674
$866$	−15.8034	−0.537020
$867$	1.00000	0.0339618
$868$	7.98077	0.270885
$869$	−26.2423	−0.890209
$870$	2.95300	0.100116
$871$	16.3655	0.554524
$872$	−50.3152	−1.70389
$873$	−2.12363	−0.0718741
$874$	0.0397121	0.00134328
$875$	−24.2562	−0.820010
$876$	8.50046	0.287204
$877$	2.40395	0.0811758	0.0405879	−	0.999176i	$-0.487077\pi$
$877$	2.40395	0.0811758	0.0405879	+	0.999176i	$0.487077\pi$
$878$	−20.1090	−0.678645
$879$	−13.5121	−0.455751
$880$	−10.2966	−0.347098
$881$	43.5241	1.46636	0.733182	−	0.680032i	$-0.238034\pi$
$881$	43.5241	1.46636	0.733182	+	0.680032i	$0.238034\pi$
$882$	0.585726	0.0197224
$883$	−17.5132	−0.589367	−0.294684	−	0.955595i	$-0.595214\pi$
$883$	−17.5132	−0.589367	−0.294684	+	0.955595i	$0.595214\pi$
$884$	−2.61638	−0.0879983
$885$	5.01000	0.168409
$886$	−27.1829	−0.913229
$887$	30.1727	1.01310	0.506550	−	0.862210i	$-0.330920\pi$
$887$	30.1727	1.01310	0.506550	+	0.862210i	$0.330920\pi$
$888$	−16.6842	−0.559884
$889$	24.3997	0.818341
$890$	−5.92624	−0.198648
$891$	−3.85818	−0.129254
$892$	−14.7357	−0.493389
$893$	0.0954427	0.00319387
$894$	−19.4479	−0.650435
$895$	−25.0065	−0.835874
$896$	10.2661	0.342968
$897$	−14.4830	−0.483575
$898$	−3.38713	−0.113030
$899$	12.3189	0.410858
$900$	2.25550	0.0751833
$901$	12.4032	0.413212
$902$	−22.5948	−0.752326
$903$	−33.3895	−1.11113
$904$	38.5340	1.28162
$905$	2.01488	0.0669769
$906$	2.61402	0.0868451
$907$	51.1709	1.69910	0.849551	−	0.527506i	$-0.176873\pi$
$907$	51.1709	1.69910	0.849551	+	0.527506i	$0.176873\pi$
$908$	7.19232	0.238686
$909$	−12.6330	−0.419011
$910$	14.5387	0.481955
$911$	−8.17506	−0.270852	−0.135426	−	0.990787i	$-0.543240\pi$
$911$	−8.17506	−0.270852	−0.135426	+	0.990787i	$0.543240\pi$
$912$	0.0255293	0.000845360 0
$913$	52.3824	1.73360
$914$	−29.2272	−0.966750
$915$	9.45639	0.312619
$916$	11.1459	0.368271
$917$	−18.4840	−0.610396
$918$	1.18880	0.0392363
$919$	−39.5865	−1.30584	−0.652919	−	0.757428i	$-0.726456\pi$
$919$	−39.5865	−1.30584	−0.652919	+	0.757428i	$0.726456\pi$
$920$	−10.7387	−0.354043
$921$	32.4962	1.07079
$922$	−11.3613	−0.374165
$923$	32.1411	1.05794
$924$	−5.77481	−0.189977
$925$	20.8558	0.685736
$926$	−35.6544	−1.17168
$927$	18.4927	0.607382
$928$	−7.39183	−0.242649
$929$	−0.285902	−0.00938014	−0.00469007	−	0.999989i	$-0.501493\pi$
$929$	−0.285902	−0.00938014	−0.00469007	+	0.999989i	$0.501493\pi$
$930$	6.81507	0.223475
$931$	0.00506740	0.000166077 0
$932$	−6.03129	−0.197562
$933$	−8.20269	−0.268544
$934$	45.4508	1.48719
$935$	−4.14815	−0.135659
$936$	−13.7123	−0.448200
$937$	−22.1169	−0.722526	−0.361263	−	0.932464i	$-0.617654\pi$
$937$	−22.1169	−0.722526	−0.361263	+	0.932464i	$0.617654\pi$
$938$	−11.1300	−0.363406
$939$	6.79575	0.221771
$940$	−5.85424	−0.190944
$941$	−19.9193	−0.649351	−0.324675	−	0.945825i	$-0.605255\pi$
$941$	−19.9193	−0.649351	−0.324675	+	0.945825i	$0.605255\pi$
$942$	1.18880	0.0387332
$943$	−16.0005	−0.521047
$944$	11.5666	0.376460
$945$	2.74266	0.0892188
$946$	60.0345	1.95189
$947$	18.1683	0.590389	0.295195	−	0.955437i	$-0.404616\pi$
$947$	18.1683	0.590389	0.295195	+	0.955437i	$0.404616\pi$
$948$	−3.99094	−0.129620
$949$	64.6000	2.09700
$950$	−0.0469998	−0.00152488
$951$	4.40837	0.142951
$952$	7.84448	0.254241
$953$	−38.1394	−1.23546	−0.617728	−	0.786392i	$-0.711947\pi$
$953$	−38.1394	−1.23546	−0.617728	+	0.786392i	$0.711947\pi$
$954$	14.7450	0.477386
$955$	−18.2849	−0.591687
$956$	8.11843	0.262569
$957$	−8.91383	−0.288143
$958$	4.59018	0.148302
$959$	−42.4064	−1.36938
$960$	−9.42686	−0.304251
$961$	−2.56988	−0.0828992
$962$	−28.7604	−0.927272
$963$	9.67866	0.311891
$964$	11.0289	0.355218
$965$	18.1408	0.583973
$966$	9.84972	0.316909
$967$	−47.4433	−1.52567	−0.762837	−	0.646590i	$-0.776194\pi$
$967$	−47.4433	−1.52567	−0.762837	+	0.646590i	$0.776194\pi$
$968$	11.9485	0.384039
$969$	0.0102849	0.000330398 0
$970$	−2.71432	−0.0871515
$971$	−22.6996	−0.728466	−0.364233	−	0.931308i	$-0.618669\pi$
$971$	−22.6996	−0.728466	−0.364233	+	0.931308i	$0.618669\pi$
$972$	−0.586753	−0.0188201
$973$	−24.7087	−0.792124
$974$	21.6602	0.694038
$975$	17.1409	0.548947
$976$	21.8320	0.698824
$977$	44.4419	1.42182	0.710912	−	0.703281i	$-0.248282\pi$
$977$	44.4419	1.42182	0.710912	+	0.703281i	$0.248282\pi$
$978$	17.3016	0.553245
$979$	17.8887	0.571727
$980$	−0.310823	−0.00992887
$981$	−16.3620	−0.522397
$982$	−14.9248	−0.476270
$983$	27.2058	0.867729	0.433865	−	0.900978i	$-0.357150\pi$
$983$	27.2058	0.867729	0.433865	+	0.900978i	$0.357150\pi$
$984$	−15.1489	−0.482931
$985$	27.2524	0.868334
$986$	2.74658	0.0874688
$987$	23.6725	0.753503
$988$	−0.0269092	−0.000856094 0
$989$	42.5133	1.35184
$990$	−4.93132	−0.156728
$991$	−16.3958	−0.520831	−0.260416	−	0.965497i	$-0.583860\pi$
$991$	−16.3958	−0.520831	−0.260416	+	0.965497i	$0.583860\pi$
$992$	−17.0592	−0.541631
$993$	17.9204	0.568685
$994$	−21.8587	−0.693316
$995$	−9.62019	−0.304980
$996$	7.96633	0.252423
$997$	−41.8309	−1.32480	−0.662399	−	0.749151i	$-0.730462\pi$
$997$	−41.8309	−1.32480	−0.662399	+	0.749151i	$0.730462\pi$
$998$	−35.7899	−1.13291
$999$	−5.42551	−0.171655

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.h.1.19	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.h.1.19	✓	56	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)

\(f(q)\)	\(=\)	\(q-1.18880 q^{2} +1.00000 q^{3} -0.586753 q^{4} -1.07516 q^{5} -1.18880 q^{6} -2.55094 q^{7} +3.07513 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.18880 q^{2} +1.00000 q^{3} -0.586753 q^{4} -1.07516 q^{5} -1.18880 q^{6} -2.55094 q^{7} +3.07513 q^{8} +1.00000 q^{9} +1.27815 q^{10} -3.85818 q^{11} -0.586753 q^{12} -4.45908 q^{13} +3.03256 q^{14} -1.07516 q^{15} -2.48222 q^{16} -1.00000 q^{17} -1.18880 q^{18} -0.0102849 q^{19} +0.630852 q^{20} -2.55094 q^{21} +4.58660 q^{22} +3.24799 q^{23} +3.07513 q^{24} -3.84404 q^{25} +5.30096 q^{26} +1.00000 q^{27} +1.49677 q^{28} +2.31038 q^{29} +1.27815 q^{30} +5.33199 q^{31} -3.19941 q^{32} -3.85818 q^{33} +1.18880 q^{34} +2.74266 q^{35} -0.586753 q^{36} -5.42551 q^{37} +0.0122267 q^{38} -4.45908 q^{39} -3.30625 q^{40} -4.92627 q^{41} +3.03256 q^{42} +13.0891 q^{43} +2.26380 q^{44} -1.07516 q^{45} -3.86121 q^{46} -9.27990 q^{47} -2.48222 q^{48} -0.492703 q^{49} +4.56979 q^{50} -1.00000 q^{51} +2.61638 q^{52} -12.4032 q^{53} -1.18880 q^{54} +4.14815 q^{55} -7.84448 q^{56} -0.0102849 q^{57} -2.74658 q^{58} -4.65978 q^{59} +0.630852 q^{60} -8.79535 q^{61} -6.33867 q^{62} -2.55094 q^{63} +8.76789 q^{64} +4.79421 q^{65} +4.58660 q^{66} -3.67015 q^{67} +0.586753 q^{68} +3.24799 q^{69} -3.26048 q^{70} -7.20801 q^{71} +3.07513 q^{72} -14.4873 q^{73} +6.44984 q^{74} -3.84404 q^{75} +0.00603469 q^{76} +9.84198 q^{77} +5.30096 q^{78} +6.80174 q^{79} +2.66877 q^{80} +1.00000 q^{81} +5.85635 q^{82} -13.5770 q^{83} +1.49677 q^{84} +1.07516 q^{85} -15.5603 q^{86} +2.31038 q^{87} -11.8644 q^{88} -4.63658 q^{89} +1.27815 q^{90} +11.3748 q^{91} -1.90577 q^{92} +5.33199 q^{93} +11.0319 q^{94} +0.0110579 q^{95} -3.19941 q^{96} -2.12363 q^{97} +0.585726 q^{98} -3.85818 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

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