LMFDB - Embedded newform 8007.2.a.i.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$63$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-2.18826 q^{2} +1.00000 q^{3} +2.78847 q^{4} -0.00677076 q^{5} -2.18826 q^{6} -4.11828 q^{7} -1.72538 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.18826 q^{2} +1.00000 q^{3} +2.78847 q^{4} -0.00677076 q^{5} -2.18826 q^{6} -4.11828 q^{7} -1.72538 q^{8} +1.00000 q^{9} +0.0148162 q^{10} -3.40019 q^{11} +2.78847 q^{12} -2.61954 q^{13} +9.01186 q^{14} -0.00677076 q^{15} -1.80136 q^{16} +1.00000 q^{17} -2.18826 q^{18} +4.90060 q^{19} -0.0188801 q^{20} -4.11828 q^{21} +7.44049 q^{22} -9.01304 q^{23} -1.72538 q^{24} -4.99995 q^{25} +5.73222 q^{26} +1.00000 q^{27} -11.4837 q^{28} -8.89044 q^{29} +0.0148162 q^{30} -5.54123 q^{31} +7.39261 q^{32} -3.40019 q^{33} -2.18826 q^{34} +0.0278839 q^{35} +2.78847 q^{36} -9.25763 q^{37} -10.7238 q^{38} -2.61954 q^{39} +0.0116822 q^{40} +4.27495 q^{41} +9.01186 q^{42} -1.52693 q^{43} -9.48134 q^{44} -0.00677076 q^{45} +19.7228 q^{46} -9.03685 q^{47} -1.80136 q^{48} +9.96024 q^{49} +10.9412 q^{50} +1.00000 q^{51} -7.30451 q^{52} +9.71250 q^{53} -2.18826 q^{54} +0.0230219 q^{55} +7.10562 q^{56} +4.90060 q^{57} +19.4546 q^{58} -1.77734 q^{59} -0.0188801 q^{60} -7.87448 q^{61} +12.1256 q^{62} -4.11828 q^{63} -12.5742 q^{64} +0.0177363 q^{65} +7.44049 q^{66} +13.7451 q^{67} +2.78847 q^{68} -9.01304 q^{69} -0.0610172 q^{70} -4.07741 q^{71} -1.72538 q^{72} +8.69593 q^{73} +20.2581 q^{74} -4.99995 q^{75} +13.6652 q^{76} +14.0029 q^{77} +5.73222 q^{78} -6.17953 q^{79} +0.0121966 q^{80} +1.00000 q^{81} -9.35470 q^{82} +7.91151 q^{83} -11.4837 q^{84} -0.00677076 q^{85} +3.34131 q^{86} -8.89044 q^{87} +5.86663 q^{88} -10.7670 q^{89} +0.0148162 q^{90} +10.7880 q^{91} -25.1326 q^{92} -5.54123 q^{93} +19.7750 q^{94} -0.0331808 q^{95} +7.39261 q^{96} -18.6540 q^{97} -21.7956 q^{98} -3.40019 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) $ 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.18826	−1.54733	−0.773666	−	0.633594i	$-0.781579\pi$
$2$	−2.18826	−1.54733	−0.773666	+	0.633594i	$0.781579\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.78847	1.39424
$5$	−0.00677076	−0.00302798	−0.00151399	−	0.999999i	$-0.500482\pi$
$5$	−0.00677076	−0.00302798	−0.00151399	+	0.999999i	$0.500482\pi$
$6$	−2.18826	−0.893353
$7$	−4.11828	−1.55656	−0.778282	−	0.627915i	$-0.783909\pi$
$7$	−4.11828	−1.55656	−0.778282	+	0.627915i	$0.783909\pi$
$8$	−1.72538	−0.610016
$9$	1.00000	0.333333
$10$	0.0148162	0.00468528
$11$	−3.40019	−1.02520	−0.512598	−	0.858629i	$-0.671317\pi$
$11$	−3.40019	−1.02520	−0.512598	+	0.858629i	$0.671317\pi$
$12$	2.78847	0.804963
$13$	−2.61954	−0.726529	−0.363264	−	0.931686i	$-0.618338\pi$
$13$	−2.61954	−0.726529	−0.363264	+	0.931686i	$0.618338\pi$
$14$	9.01186	2.40852
$15$	−0.00677076	−0.00174820
$16$	−1.80136	−0.450340
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.18826	−0.515777
$19$	4.90060	1.12428	0.562138	−	0.827044i	$-0.309979\pi$
$19$	4.90060	1.12428	0.562138	+	0.827044i	$0.309979\pi$
$20$	−0.0188801	−0.00422172
$21$	−4.11828	−0.898683
$22$	7.44049	1.58632
$23$	−9.01304	−1.87935	−0.939674	−	0.342072i	$-0.888871\pi$
$23$	−9.01304	−1.87935	−0.939674	+	0.342072i	$0.888871\pi$
$24$	−1.72538	−0.352193
$25$	−4.99995	−0.999991
$26$	5.73222	1.12418
$27$	1.00000	0.192450
$28$	−11.4837	−2.17022
$29$	−8.89044	−1.65091	−0.825457	−	0.564465i	$-0.809082\pi$
$29$	−8.89044	−1.65091	−0.825457	+	0.564465i	$0.809082\pi$
$30$	0.0148162	0.00270505
$31$	−5.54123	−0.995234	−0.497617	−	0.867397i	$-0.665791\pi$
$31$	−5.54123	−0.995234	−0.497617	+	0.867397i	$0.665791\pi$
$32$	7.39261	1.30684
$33$	−3.40019	−0.591897
$34$	−2.18826	−0.375283
$35$	0.0278839	0.00471324
$36$	2.78847	0.464746
$37$	−9.25763	−1.52194	−0.760972	−	0.648785i	$-0.775278\pi$
$37$	−9.25763	−1.52194	−0.760972	+	0.648785i	$0.775278\pi$
$38$	−10.7238	−1.73963
$39$	−2.61954	−0.419462
$40$	0.0116822	0.00184711
$41$	4.27495	0.667635	0.333818	−	0.942638i	$-0.391663\pi$
$41$	4.27495	0.667635	0.333818	+	0.942638i	$0.391663\pi$
$42$	9.01186	1.39056
$43$	−1.52693	−0.232854	−0.116427	−	0.993199i	$-0.537144\pi$
$43$	−1.52693	−0.232854	−0.116427	+	0.993199i	$0.537144\pi$
$44$	−9.48134	−1.42937
$45$	−0.00677076	−0.00100933
$46$	19.7228	2.90798
$47$	−9.03685	−1.31816	−0.659080	−	0.752073i	$-0.729054\pi$
$47$	−9.03685	−1.31816	−0.659080	+	0.752073i	$0.729054\pi$
$48$	−1.80136	−0.260004
$49$	9.96024	1.42289
$50$	10.9412	1.54732
$51$	1.00000	0.140028
$52$	−7.30451	−1.01295
$53$	9.71250	1.33411	0.667057	−	0.745007i	$-0.267554\pi$
$53$	9.71250	1.33411	0.667057	+	0.745007i	$0.267554\pi$
$54$	−2.18826	−0.297784
$55$	0.0230219	0.00310427
$56$	7.10562	0.949528
$57$	4.90060	0.649101
$58$	19.4546	2.55451
$59$	−1.77734	−0.231390	−0.115695	−	0.993285i	$-0.536910\pi$
$59$	−1.77734	−0.231390	−0.115695	+	0.993285i	$0.536910\pi$
$60$	−0.0188801	−0.00243741
$61$	−7.87448	−1.00822	−0.504112	−	0.863638i	$-0.668180\pi$
$61$	−7.87448	−1.00822	−0.504112	+	0.863638i	$0.668180\pi$
$62$	12.1256	1.53996
$63$	−4.11828	−0.518855
$64$	−12.5742	−1.57178
$65$	0.0177363	0.00219991
$66$	7.44049	0.915861
$67$	13.7451	1.67923	0.839614	−	0.543184i	$-0.182781\pi$
$67$	13.7451	1.67923	0.839614	+	0.543184i	$0.182781\pi$
$68$	2.78847	0.338152
$69$	−9.01304	−1.08504
$70$	−0.0610172	−0.00729294
$71$	−4.07741	−0.483899	−0.241950	−	0.970289i	$-0.577787\pi$
$71$	−4.07741	−0.483899	−0.241950	+	0.970289i	$0.577787\pi$
$72$	−1.72538	−0.203339
$73$	8.69593	1.01778	0.508891	−	0.860831i	$-0.330056\pi$
$73$	8.69593	1.01778	0.508891	+	0.860831i	$0.330056\pi$
$74$	20.2581	2.35495
$75$	−4.99995	−0.577345
$76$	13.6652	1.56751
$77$	14.0029	1.59578
$78$	5.73222	0.649047
$79$	−6.17953	−0.695251	−0.347626	−	0.937633i	$-0.613012\pi$
$79$	−6.17953	−0.695251	−0.347626	+	0.937633i	$0.613012\pi$
$80$	0.0121966	0.00136362
$81$	1.00000	0.111111
$82$	−9.35470	−1.03305
$83$	7.91151	0.868401	0.434200	−	0.900816i	$-0.357031\pi$
$83$	7.91151	0.868401	0.434200	+	0.900816i	$0.357031\pi$
$84$	−11.4837	−1.25298
$85$	−0.00677076	−0.000734392 0
$86$	3.34131	0.360302
$87$	−8.89044	−0.953155
$88$	5.86663	0.625385
$89$	−10.7670	−1.14130	−0.570651	−	0.821192i	$-0.693309\pi$
$89$	−10.7670	−1.14130	−0.570651	+	0.821192i	$0.693309\pi$
$90$	0.0148162	0.00156176
$91$	10.7880	1.13089
$92$	−25.1326	−2.62026
$93$	−5.54123	−0.574599
$94$	19.7750	2.03963
$95$	−0.0331808	−0.00340428
$96$	7.39261	0.754505
$97$	−18.6540	−1.89403	−0.947014	−	0.321192i	$-0.895916\pi$
$97$	−18.6540	−1.89403	−0.947014	+	0.321192i	$0.895916\pi$
$98$	−21.7956	−2.20169
$99$	−3.40019	−0.341732
$100$	−13.9422	−1.39422
$101$	0.158280	0.0157494	0.00787471	−	0.999969i	$-0.497493\pi$
$101$	0.158280	0.0157494	0.00787471	+	0.999969i	$0.497493\pi$
$102$	−2.18826	−0.216670
$103$	12.8991	1.27098	0.635492	−	0.772107i	$-0.280797\pi$
$103$	12.8991	1.27098	0.635492	+	0.772107i	$0.280797\pi$
$104$	4.51971	0.443194
$105$	0.0278839	0.00272119
$106$	−21.2535	−2.06432
$107$	−14.0490	−1.35817	−0.679085	−	0.734059i	$-0.737623\pi$
$107$	−14.0490	−1.35817	−0.679085	+	0.734059i	$0.737623\pi$
$108$	2.78847	0.268321
$109$	7.92183	0.758774	0.379387	−	0.925238i	$-0.376135\pi$
$109$	7.92183	0.758774	0.379387	+	0.925238i	$0.376135\pi$
$110$	−0.0503778	−0.00480333
$111$	−9.25763	−0.878695
$112$	7.41851	0.700983
$113$	8.50194	0.799795	0.399898	−	0.916560i	$-0.369046\pi$
$113$	8.50194	0.799795	0.399898	+	0.916560i	$0.369046\pi$
$114$	−10.7238	−1.00437
$115$	0.0610251	0.00569062
$116$	−24.7908	−2.30176
$117$	−2.61954	−0.242176
$118$	3.88928	0.358038
$119$	−4.11828	−0.377522
$120$	0.0116822	0.00106643
$121$	0.561289	0.0510263
$122$	17.2314	1.56006
$123$	4.27495	0.385459
$124$	−15.4516	−1.38759
$125$	0.0677073	0.00605592
$126$	9.01186	0.802841
$127$	−8.65015	−0.767577	−0.383788	−	0.923421i	$-0.625381\pi$
$127$	−8.65015	−0.767577	−0.383788	+	0.923421i	$0.625381\pi$
$128$	12.7304	1.12522
$129$	−1.52693	−0.134438
$130$	−0.0388115	−0.00340399
$131$	16.9595	1.48176	0.740878	−	0.671640i	$-0.234410\pi$
$131$	16.9595	1.48176	0.740878	+	0.671640i	$0.234410\pi$
$132$	−9.48134	−0.825245
$133$	−20.1821	−1.75001
$134$	−30.0778	−2.59832
$135$	−0.00677076	−0.000582734 0
$136$	−1.72538	−0.147951
$137$	13.5386	1.15668	0.578338	−	0.815797i	$-0.303701\pi$
$137$	13.5386	1.15668	0.578338	+	0.815797i	$0.303701\pi$
$138$	19.7228	1.67892
$139$	−13.2787	−1.12629	−0.563144	−	0.826358i	$-0.690409\pi$
$139$	−13.2787	−1.12629	−0.563144	+	0.826358i	$0.690409\pi$
$140$	0.0777535	0.00657137
$141$	−9.03685	−0.761040
$142$	8.92242	0.748753
$143$	8.90692	0.744834
$144$	−1.80136	−0.150113
$145$	0.0601950	0.00499893
$146$	−19.0289	−1.57485
$147$	9.96024	0.821507
$148$	−25.8146	−2.12195
$149$	18.1553	1.48734	0.743669	−	0.668548i	$-0.233084\pi$
$149$	18.1553	1.48734	0.743669	+	0.668548i	$0.233084\pi$
$150$	10.9412	0.893344
$151$	−23.3979	−1.90410	−0.952048	−	0.305950i	$-0.901026\pi$
$151$	−23.3979	−1.90410	−0.952048	+	0.305950i	$0.901026\pi$
$152$	−8.45543	−0.685826
$153$	1.00000	0.0808452
$154$	−30.6420	−2.46921
$155$	0.0375183	0.00301354
$156$	−7.30451	−0.584829
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	13.5224	1.07578
$159$	9.71250	0.770251
$160$	−0.0500536	−0.00395708
$161$	37.1182	2.92533
$162$	−2.18826	−0.171926
$163$	−1.95869	−0.153416	−0.0767081	−	0.997054i	$-0.524441\pi$
$163$	−1.95869	−0.153416	−0.0767081	+	0.997054i	$0.524441\pi$
$164$	11.9206	0.930842
$165$	0.0230219	0.00179225
$166$	−17.3124	−1.34370
$167$	−13.4203	−1.03849	−0.519246	−	0.854625i	$-0.673787\pi$
$167$	−13.4203	−1.03849	−0.519246	+	0.854625i	$0.673787\pi$
$168$	7.10562	0.548210
$169$	−6.13802	−0.472156
$170$	0.0148162	0.00113635
$171$	4.90060	0.374759
$172$	−4.25779	−0.324654
$173$	11.2859	0.858051	0.429025	−	0.903292i	$-0.358857\pi$
$173$	11.2859	0.858051	0.429025	+	0.903292i	$0.358857\pi$
$174$	19.4546	1.47485
$175$	20.5912	1.55655
$176$	6.12497	0.461687
$177$	−1.77734	−0.133593
$178$	23.5610	1.76597
$179$	10.1298	0.757137	0.378569	−	0.925573i	$-0.376416\pi$
$179$	10.1298	0.757137	0.378569	+	0.925573i	$0.376416\pi$
$180$	−0.0188801	−0.00140724
$181$	−16.1885	−1.20328	−0.601640	−	0.798767i	$-0.705486\pi$
$181$	−16.1885	−1.20328	−0.601640	+	0.798767i	$0.705486\pi$
$182$	−23.6069	−1.74986
$183$	−7.87448	−0.582098
$184$	15.5510	1.14643
$185$	0.0626812	0.00460841
$186$	12.1256	0.889095
$187$	−3.40019	−0.248646
$188$	−25.1990	−1.83783
$189$	−4.11828	−0.299561
$190$	0.0726082	0.00526755
$191$	−11.3689	−0.822627	−0.411314	−	0.911494i	$-0.634930\pi$
$191$	−11.3689	−0.822627	−0.411314	+	0.911494i	$0.634930\pi$
$192$	−12.5742	−0.907466
$193$	−7.36804	−0.530363	−0.265181	−	0.964199i	$-0.585432\pi$
$193$	−7.36804	−0.530363	−0.265181	+	0.964199i	$0.585432\pi$
$194$	40.8198	2.93069
$195$	0.0177363	0.00127012
$196$	27.7739	1.98385
$197$	27.0058	1.92409	0.962043	−	0.272898i	$-0.0879823\pi$
$197$	27.0058	1.92409	0.962043	+	0.272898i	$0.0879823\pi$
$198$	7.44049	0.528773
$199$	1.94685	0.138009	0.0690044	−	0.997616i	$-0.478018\pi$
$199$	1.94685	0.138009	0.0690044	+	0.997616i	$0.478018\pi$
$200$	8.62684	0.610010
$201$	13.7451	0.969502
$202$	−0.346357	−0.0243696
$203$	36.6133	2.56975
$204$	2.78847	0.195232
$205$	−0.0289447	−0.00202158
$206$	−28.2265	−1.96663
$207$	−9.01304	−0.626449
$208$	4.71873	0.327185
$209$	−16.6630	−1.15260
$210$	−0.0610172	−0.00421058
$211$	−2.26287	−0.155783	−0.0778913	−	0.996962i	$-0.524819\pi$
$211$	−2.26287	−0.155783	−0.0778913	+	0.996962i	$0.524819\pi$
$212$	27.0830	1.86007
$213$	−4.07741	−0.279379
$214$	30.7429	2.10154
$215$	0.0103384	0.000705076 0
$216$	−1.72538	−0.117398
$217$	22.8203	1.54915
$218$	−17.3350	−1.17408
$219$	8.69593	0.587617
$220$	0.0641959	0.00432808
$221$	−2.61954	−0.176209
$222$	20.2581	1.35963
$223$	16.8270	1.12682	0.563410	−	0.826178i	$-0.309489\pi$
$223$	16.8270	1.12682	0.563410	+	0.826178i	$0.309489\pi$
$224$	−30.4449	−2.03418
$225$	−4.99995	−0.333330
$226$	−18.6044	−1.23755
$227$	−0.158511	−0.0105208	−0.00526039	−	0.999986i	$-0.501674\pi$
$227$	−0.158511	−0.0105208	−0.00526039	+	0.999986i	$0.501674\pi$
$228$	13.6652	0.905000
$229$	−5.38835	−0.356072	−0.178036	−	0.984024i	$-0.556974\pi$
$229$	−5.38835	−0.356072	−0.178036	+	0.984024i	$0.556974\pi$
$230$	−0.133539	−0.00880528
$231$	14.0029	0.921326
$232$	15.3394	1.00708
$233$	3.25217	0.213057	0.106528	−	0.994310i	$-0.466026\pi$
$233$	3.25217	0.213057	0.106528	+	0.994310i	$0.466026\pi$
$234$	5.73222	0.374727
$235$	0.0611864	0.00399136
$236$	−4.95607	−0.322613
$237$	−6.17953	−0.401404
$238$	9.01186	0.584152
$239$	−18.4847	−1.19568	−0.597838	−	0.801617i	$-0.703973\pi$
$239$	−18.4847	−1.19568	−0.597838	+	0.801617i	$0.703973\pi$
$240$	0.0121966	0.000787286 0
$241$	−4.56669	−0.294166	−0.147083	−	0.989124i	$-0.546988\pi$
$241$	−4.56669	−0.294166	−0.147083	+	0.989124i	$0.546988\pi$
$242$	−1.22825	−0.0789546
$243$	1.00000	0.0641500
$244$	−21.9578	−1.40570
$245$	−0.0674384	−0.00430848
$246$	−9.35470	−0.596434
$247$	−12.8373	−0.816819
$248$	9.56075	0.607108
$249$	7.91151	0.501371
$250$	−0.148161	−0.00937053
$251$	25.8178	1.62960	0.814801	−	0.579740i	$-0.196846\pi$
$251$	25.8178	1.62960	0.814801	+	0.579740i	$0.196846\pi$
$252$	−11.4837	−0.723406
$253$	30.6460	1.92670
$254$	18.9288	1.18770
$255$	−0.00677076	−0.000424001 0
$256$	−2.70900	−0.169313
$257$	−24.9026	−1.55338	−0.776691	−	0.629882i	$-0.783103\pi$
$257$	−24.9026	−1.55338	−0.776691	+	0.629882i	$0.783103\pi$
$258$	3.34131	0.208021
$259$	38.1255	2.36900
$260$	0.0494571	0.00306720
$261$	−8.89044	−0.550304
$262$	−37.1117	−2.29277
$263$	2.07967	0.128238	0.0641190	−	0.997942i	$-0.479576\pi$
$263$	2.07967	0.128238	0.0641190	+	0.997942i	$0.479576\pi$
$264$	5.86663	0.361066
$265$	−0.0657610	−0.00403967
$266$	44.1636	2.70784
$267$	−10.7670	−0.658931
$268$	38.3278	2.34124
$269$	−18.3952	−1.12157	−0.560787	−	0.827960i	$-0.689501\pi$
$269$	−18.3952	−1.12157	−0.560787	+	0.827960i	$0.689501\pi$
$270$	0.0148162	0.000901683 0
$271$	−7.84327	−0.476445	−0.238222	−	0.971211i	$-0.576565\pi$
$271$	−7.84327	−0.476445	−0.238222	+	0.971211i	$0.576565\pi$
$272$	−1.80136	−0.109224
$273$	10.7880	0.652919
$274$	−29.6259	−1.78976
$275$	17.0008	1.02519
$276$	−25.1326	−1.51281
$277$	29.4697	1.77066	0.885330	−	0.464963i	$-0.153933\pi$
$277$	29.4697	1.77066	0.885330	+	0.464963i	$0.153933\pi$
$278$	29.0573	1.74274
$279$	−5.54123	−0.331745
$280$	−0.0481104	−0.00287515
$281$	1.35705	0.0809551	0.0404775	−	0.999180i	$-0.487112\pi$
$281$	1.35705	0.0809551	0.0404775	+	0.999180i	$0.487112\pi$
$282$	19.7750	1.17758
$283$	−13.9974	−0.832058	−0.416029	−	0.909351i	$-0.636579\pi$
$283$	−13.9974	−0.832058	−0.416029	+	0.909351i	$0.636579\pi$
$284$	−11.3697	−0.674670
$285$	−0.0331808	−0.00196546
$286$	−19.4906	−1.15251
$287$	−17.6055	−1.03922
$288$	7.39261	0.435614
$289$	1.00000	0.0588235
$290$	−0.131722	−0.00773500
$291$	−18.6540	−1.09352
$292$	24.2484	1.41903
$293$	20.2352	1.18215	0.591077	−	0.806615i	$-0.298703\pi$
$293$	20.2352	1.18215	0.591077	+	0.806615i	$0.298703\pi$
$294$	−21.7956	−1.27114
$295$	0.0120340	0.000700644 0
$296$	15.9730	0.928410
$297$	−3.40019	−0.197299
$298$	−39.7284	−2.30141
$299$	23.6100	1.36540
$300$	−13.9422	−0.804956
$301$	6.28831	0.362452
$302$	51.2007	2.94627
$303$	0.158280	0.00909294
$304$	−8.82776	−0.506307
$305$	0.0533162	0.00305288
$306$	−2.18826	−0.125094
$307$	20.4841	1.16909	0.584544	−	0.811362i	$-0.301273\pi$
$307$	20.4841	1.16909	0.584544	+	0.811362i	$0.301273\pi$
$308$	39.0468	2.22490
$309$	12.8991	0.733803
$310$	−0.0820998	−0.00466295
$311$	15.4882	0.878253	0.439127	−	0.898425i	$-0.355288\pi$
$311$	15.4882	0.878253	0.439127	+	0.898425i	$0.355288\pi$
$312$	4.51971	0.255878
$313$	6.65533	0.376181	0.188091	−	0.982152i	$-0.439770\pi$
$313$	6.65533	0.376181	0.188091	+	0.982152i	$0.439770\pi$
$314$	−2.18826	−0.123491
$315$	0.0278839	0.00157108
$316$	−17.2315	−0.969345
$317$	−0.922570	−0.0518167	−0.0259084	−	0.999664i	$-0.508248\pi$
$317$	−0.922570	−0.0518167	−0.0259084	+	0.999664i	$0.508248\pi$
$318$	−21.2535	−1.19183
$319$	30.2292	1.69251
$320$	0.0851370	0.00475930
$321$	−14.0490	−0.784140
$322$	−81.2242	−4.52645
$323$	4.90060	0.272677
$324$	2.78847	0.154915
$325$	13.0976	0.726522
$326$	4.28611	0.237386
$327$	7.92183	0.438078
$328$	−7.37593	−0.407268
$329$	37.2163	2.05180
$330$	−0.0503778	−0.00277321
$331$	4.00374	0.220065	0.110033	−	0.993928i	$-0.464904\pi$
$331$	4.00374	0.220065	0.110033	+	0.993928i	$0.464904\pi$
$332$	22.0610	1.21076
$333$	−9.25763	−0.507315
$334$	29.3670	1.60689
$335$	−0.0930646	−0.00508466
$336$	7.41851	0.404713
$337$	−28.1280	−1.53223	−0.766114	−	0.642704i	$-0.777812\pi$
$337$	−28.1280	−1.53223	−0.766114	+	0.642704i	$0.777812\pi$
$338$	13.4316	0.730582
$339$	8.50194	0.461762
$340$	−0.0188801	−0.00102392
$341$	18.8412	1.02031
$342$	−10.7238	−0.579876
$343$	−12.1911	−0.658258
$344$	2.63453	0.142045
$345$	0.0610251	0.00328548
$346$	−24.6965	−1.32769
$347$	−35.4809	−1.90472	−0.952358	−	0.304982i	$-0.901350\pi$
$347$	−35.4809	−1.90472	−0.952358	+	0.304982i	$0.901350\pi$
$348$	−24.7908	−1.32892
$349$	−12.4110	−0.664345	−0.332173	−	0.943219i	$-0.607782\pi$
$349$	−12.4110	−0.664345	−0.332173	+	0.943219i	$0.607782\pi$
$350$	−45.0589	−2.40850
$351$	−2.61954	−0.139821
$352$	−25.1363	−1.33977
$353$	33.4563	1.78070	0.890349	−	0.455278i	$-0.150460\pi$
$353$	33.4563	1.78070	0.890349	+	0.455278i	$0.150460\pi$
$354$	3.88928	0.206713
$355$	0.0276072	0.00146524
$356$	−30.0236	−1.59125
$357$	−4.11828	−0.217963
$358$	−22.1666	−1.17154
$359$	−17.5564	−0.926591	−0.463296	−	0.886204i	$-0.653333\pi$
$359$	−17.5564	−0.926591	−0.463296	+	0.886204i	$0.653333\pi$
$360$	0.0116822	0.000615704 0
$361$	5.01591	0.263995
$362$	35.4246	1.86188
$363$	0.561289	0.0294601
$364$	30.0820	1.57673
$365$	−0.0588781	−0.00308182
$366$	17.2314	0.900700
$367$	12.9134	0.674075	0.337037	−	0.941491i	$-0.390575\pi$
$367$	12.9134	0.674075	0.337037	+	0.941491i	$0.390575\pi$
$368$	16.2357	0.846346
$369$	4.27495	0.222545
$370$	−0.137163	−0.00713074
$371$	−39.9988	−2.07663
$372$	−15.4516	−0.801127
$373$	−23.1860	−1.20053	−0.600263	−	0.799803i	$-0.704937\pi$
$373$	−23.1860	−1.20053	−0.600263	+	0.799803i	$0.704937\pi$
$374$	7.44049	0.384739
$375$	0.0677073	0.00349639
$376$	15.5920	0.804099
$377$	23.2888	1.19944
$378$	9.01186	0.463520
$379$	−3.75920	−0.193097	−0.0965486	−	0.995328i	$-0.530780\pi$
$379$	−3.75920	−0.193097	−0.0965486	+	0.995328i	$0.530780\pi$
$380$	−0.0925238	−0.00474637
$381$	−8.65015	−0.443161
$382$	24.8782	1.27288
$383$	15.6183	0.798056	0.399028	−	0.916939i	$-0.369348\pi$
$383$	15.6183	0.798056	0.399028	+	0.916939i	$0.369348\pi$
$384$	12.7304	0.649647
$385$	−0.0948105	−0.00483199
$386$	16.1232	0.820648
$387$	−1.52693	−0.0776180
$388$	−52.0162	−2.64072
$389$	18.0901	0.917202	0.458601	−	0.888642i	$-0.348351\pi$
$389$	18.0901	0.917202	0.458601	+	0.888642i	$0.348351\pi$
$390$	−0.0388115	−0.00196530
$391$	−9.01304	−0.455809
$392$	−17.1852	−0.867986
$393$	16.9595	0.855492
$394$	−59.0957	−2.97720
$395$	0.0418401	0.00210520
$396$	−9.48134	−0.476455
$397$	−17.5913	−0.882881	−0.441440	−	0.897291i	$-0.645532\pi$
$397$	−17.5913	−0.882881	−0.441440	+	0.897291i	$0.645532\pi$
$398$	−4.26022	−0.213546
$399$	−20.1821	−1.01037
$400$	9.00672	0.450336
$401$	−30.3047	−1.51335	−0.756673	−	0.653794i	$-0.773176\pi$
$401$	−30.3047	−1.51335	−0.756673	+	0.653794i	$0.773176\pi$
$402$	−30.0778	−1.50014
$403$	14.5155	0.723066
$404$	0.441359	0.0219584
$405$	−0.00677076	−0.000336442 0
$406$	−80.1194	−3.97626
$407$	31.4777	1.56029
$408$	−1.72538	−0.0854193
$409$	−23.1937	−1.14685	−0.573427	−	0.819257i	$-0.694386\pi$
$409$	−23.1937	−1.14685	−0.573427	+	0.819257i	$0.694386\pi$
$410$	0.0633384	0.00312806
$411$	13.5386	0.667808
$412$	35.9687	1.77205
$413$	7.31960	0.360174
$414$	19.7228	0.969325
$415$	−0.0535669	−0.00262950
$416$	−19.3652	−0.949458
$417$	−13.2787	−0.650263
$418$	36.4629	1.78346
$419$	17.1658	0.838604	0.419302	−	0.907847i	$-0.362275\pi$
$419$	17.1658	0.838604	0.419302	+	0.907847i	$0.362275\pi$
$420$	0.0777535	0.00379398
$421$	−33.5763	−1.63641	−0.818204	−	0.574929i	$-0.805030\pi$
$421$	−33.5763	−1.63641	−0.818204	+	0.574929i	$0.805030\pi$
$422$	4.95175	0.241048
$423$	−9.03685	−0.439387
$424$	−16.7578	−0.813830
$425$	−4.99995	−0.242533
$426$	8.92242	0.432293
$427$	32.4293	1.56937
$428$	−39.1753	−1.89361
$429$	8.90692	0.430030
$430$	−0.0226232	−0.00109099
$431$	−38.3797	−1.84868	−0.924342	−	0.381566i	$-0.875385\pi$
$431$	−38.3797	−1.84868	−0.924342	+	0.381566i	$0.875385\pi$
$432$	−1.80136	−0.0866680
$433$	33.5301	1.61135	0.805676	−	0.592356i	$-0.201802\pi$
$433$	33.5301	1.61135	0.805676	+	0.592356i	$0.201802\pi$
$434$	−49.9368	−2.39704
$435$	0.0601950	0.00288613
$436$	22.0898	1.05791
$437$	−44.1693	−2.11290
$438$	−19.0289	−0.909238
$439$	4.71747	0.225152	0.112576	−	0.993643i	$-0.464090\pi$
$439$	4.71747	0.225152	0.112576	+	0.993643i	$0.464090\pi$
$440$	−0.0397216	−0.00189365
$441$	9.96024	0.474297
$442$	5.73222	0.272654
$443$	21.6354	1.02793	0.513965	−	0.857811i	$-0.328176\pi$
$443$	21.6354	1.02793	0.513965	+	0.857811i	$0.328176\pi$
$444$	−25.8146	−1.22511
$445$	0.0729010	0.00345584
$446$	−36.8218	−1.74356
$447$	18.1553	0.858715
$448$	51.7842	2.44657
$449$	34.7089	1.63801	0.819006	−	0.573785i	$-0.194525\pi$
$449$	34.7089	1.63801	0.819006	+	0.573785i	$0.194525\pi$
$450$	10.9412	0.515773
$451$	−14.5356	−0.684457
$452$	23.7074	1.11510
$453$	−23.3979	−1.09933
$454$	0.346864	0.0162791
$455$	−0.0730429	−0.00342430
$456$	−8.45543	−0.395962
$457$	−3.99829	−0.187032	−0.0935161	−	0.995618i	$-0.529811\pi$
$457$	−3.99829	−0.187032	−0.0935161	+	0.995618i	$0.529811\pi$
$458$	11.7911	0.550962
$459$	1.00000	0.0466760
$460$	0.170167	0.00793407
$461$	27.6018	1.28554	0.642772	−	0.766058i	$-0.277784\pi$
$461$	27.6018	1.28554	0.642772	+	0.766058i	$0.277784\pi$
$462$	−30.6420	−1.42560
$463$	−5.41919	−0.251851	−0.125926	−	0.992040i	$-0.540190\pi$
$463$	−5.41919	−0.251851	−0.125926	+	0.992040i	$0.540190\pi$
$464$	16.0149	0.743473
$465$	0.0375183	0.00173987
$466$	−7.11660	−0.329670
$467$	14.7193	0.681130	0.340565	−	0.940221i	$-0.389382\pi$
$467$	14.7193	0.681130	0.340565	+	0.940221i	$0.389382\pi$
$468$	−7.30451	−0.337651
$469$	−56.6061	−2.61383
$470$	−0.133892	−0.00617596
$471$	1.00000	0.0460776
$472$	3.06660	0.141152
$473$	5.19184	0.238721
$474$	13.5224	0.621105
$475$	−24.5028	−1.12427
$476$	−11.4837	−0.526355
$477$	9.71250	0.444705
$478$	40.4493	1.85011
$479$	−28.9658	−1.32348	−0.661741	−	0.749732i	$-0.730182\pi$
$479$	−28.9658	−1.32348	−0.661741	+	0.749732i	$0.730182\pi$
$480$	−0.0500536	−0.00228462
$481$	24.2507	1.10574
$482$	9.99309	0.455173
$483$	37.1182	1.68894
$484$	1.56514	0.0711428
$485$	0.126302	0.00573507
$486$	−2.18826	−0.0992614
$487$	−5.47421	−0.248060	−0.124030	−	0.992278i	$-0.539582\pi$
$487$	−5.47421	−0.248060	−0.124030	+	0.992278i	$0.539582\pi$
$488$	13.5865	0.615032
$489$	−1.95869	−0.0885749
$490$	0.147573	0.00666665
$491$	0.428986	0.0193599	0.00967993	−	0.999953i	$-0.496919\pi$
$491$	0.428986	0.0193599	0.00967993	+	0.999953i	$0.496919\pi$
$492$	11.9206	0.537422
$493$	−8.89044	−0.400405
$494$	28.0914	1.26389
$495$	0.0230219	0.00103476
$496$	9.98175	0.448194
$497$	16.7919	0.753220
$498$	−17.3124	−0.775788
$499$	−4.29347	−0.192202	−0.0961011	−	0.995372i	$-0.530637\pi$
$499$	−4.29347	−0.192202	−0.0961011	+	0.995372i	$0.530637\pi$
$500$	0.188800	0.00844339
$501$	−13.4203	−0.599573
$502$	−56.4959	−2.52154
$503$	36.3175	1.61932	0.809658	−	0.586903i	$-0.199653\pi$
$503$	36.3175	1.61932	0.809658	+	0.586903i	$0.199653\pi$
$504$	7.10562	0.316509
$505$	−0.00107167	−4.76889e−5 0
$506$	−67.0614	−2.98124
$507$	−6.13802	−0.272599
$508$	−24.1207	−1.07018
$509$	15.9501	0.706977	0.353489	−	0.935439i	$-0.384995\pi$
$509$	15.9501	0.706977	0.353489	+	0.935439i	$0.384995\pi$
$510$	0.0148162	0.000656071 0
$511$	−35.8123	−1.58424
$512$	−19.5328	−0.863238
$513$	4.90060	0.216367
$514$	54.4933	2.40360
$515$	−0.0873366	−0.00384851
$516$	−4.25779	−0.187439
$517$	30.7270	1.35137
$518$	−83.4285	−3.66564
$519$	11.2859	0.495396
$520$	−0.0306019	−0.00134198
$521$	37.3215	1.63508	0.817542	−	0.575868i	$-0.195336\pi$
$521$	37.3215	1.63508	0.817542	+	0.575868i	$0.195336\pi$
$522$	19.4546	0.851504
$523$	−14.0074	−0.612499	−0.306250	−	0.951951i	$-0.599074\pi$
$523$	−14.0074	−0.612499	−0.306250	+	0.951951i	$0.599074\pi$
$524$	47.2910	2.06592
$525$	20.5912	0.898674
$526$	−4.55086	−0.198427
$527$	−5.54123	−0.241380
$528$	6.12497	0.266555
$529$	58.2348	2.53195
$530$	0.143902	0.00625070
$531$	−1.77734	−0.0771301
$532$	−56.2772	−2.43992
$533$	−11.1984	−0.485056
$534$	23.5610	1.01959
$535$	0.0951226	0.00411251
$536$	−23.7155	−1.02435
$537$	10.1298	0.437133
$538$	40.2534	1.73545
$539$	−33.8667	−1.45874
$540$	−0.0188801	−0.000812470 0
$541$	−1.18105	−0.0507774	−0.0253887	−	0.999678i	$-0.508082\pi$
$541$	−1.18105	−0.0507774	−0.0253887	+	0.999678i	$0.508082\pi$
$542$	17.1631	0.737218
$543$	−16.1885	−0.694715
$544$	7.39261	0.316956
$545$	−0.0536368	−0.00229755
$546$	−23.6069	−1.01028
$547$	28.4918	1.21822	0.609110	−	0.793086i	$-0.291527\pi$
$547$	28.4918	1.21822	0.609110	+	0.793086i	$0.291527\pi$
$548$	37.7519	1.61268
$549$	−7.87448	−0.336075
$550$	−37.2021	−1.58630
$551$	−43.5685	−1.85608
$552$	15.5510	0.661892
$553$	25.4490	1.08220
$554$	−64.4872	−2.73980
$555$	0.0626812	0.00266067
$556$	−37.0274	−1.57031
$557$	−16.7111	−0.708070	−0.354035	−	0.935232i	$-0.615191\pi$
$557$	−16.7111	−0.708070	−0.354035	+	0.935232i	$0.615191\pi$
$558$	12.1256	0.513319
$559$	3.99984	0.169175
$560$	−0.0502290	−0.00212256
$561$	−3.40019	−0.143556
$562$	−2.96958	−0.125264
$563$	−2.85075	−0.120145	−0.0600724	−	0.998194i	$-0.519133\pi$
$563$	−2.85075	−0.120145	−0.0600724	+	0.998194i	$0.519133\pi$
$564$	−25.1990	−1.06107
$565$	−0.0575646	−0.00242176
$566$	30.6299	1.28747
$567$	−4.11828	−0.172952
$568$	7.03510	0.295186
$569$	30.6845	1.28636	0.643180	−	0.765715i	$-0.277615\pi$
$569$	30.6845	1.28636	0.643180	+	0.765715i	$0.277615\pi$
$570$	0.0726082	0.00304122
$571$	−2.91571	−0.122019	−0.0610094	−	0.998137i	$-0.519432\pi$
$571$	−2.91571	−0.122019	−0.0610094	+	0.998137i	$0.519432\pi$
$572$	24.8367	1.03848
$573$	−11.3689	−0.474944
$574$	38.5253	1.60801
$575$	45.0648	1.87933
$576$	−12.5742	−0.523926
$577$	−29.6958	−1.23625	−0.618126	−	0.786079i	$-0.712108\pi$
$577$	−29.6958	−1.23625	−0.618126	+	0.786079i	$0.712108\pi$
$578$	−2.18826	−0.0910195
$579$	−7.36804	−0.306205
$580$	0.167852	0.00696969
$581$	−32.5818	−1.35172
$582$	40.8198	1.69204
$583$	−33.0243	−1.36773
$584$	−15.0038	−0.620863
$585$	0.0177363	0.000733304 0
$586$	−44.2799	−1.82919
$587$	5.87887	0.242647	0.121323	−	0.992613i	$-0.461286\pi$
$587$	5.87887	0.242647	0.121323	+	0.992613i	$0.461286\pi$
$588$	27.7739	1.14538
$589$	−27.1554	−1.11892
$590$	−0.0263334	−0.00108413
$591$	27.0058	1.11087
$592$	16.6763	0.685393
$593$	−20.1280	−0.826560	−0.413280	−	0.910604i	$-0.635617\pi$
$593$	−20.1280	−0.826560	−0.413280	+	0.910604i	$0.635617\pi$
$594$	7.44049	0.305287
$595$	0.0278839	0.00114313
$596$	50.6255	2.07370
$597$	1.94685	0.0796794
$598$	−51.6647	−2.11273
$599$	−29.5588	−1.20774	−0.603869	−	0.797083i	$-0.706375\pi$
$599$	−29.5588	−1.20774	−0.603869	+	0.797083i	$0.706375\pi$
$600$	8.62684	0.352189
$601$	−41.8419	−1.70677	−0.853383	−	0.521285i	$-0.825453\pi$
$601$	−41.8419	−1.70677	−0.853383	+	0.521285i	$0.825453\pi$
$602$	−13.7604	−0.560834
$603$	13.7451	0.559743
$604$	−65.2445	−2.65476
$605$	−0.00380036	−0.000154506 0
$606$	−0.346357	−0.0140698
$607$	4.49171	0.182313	0.0911564	−	0.995837i	$-0.470944\pi$
$607$	4.49171	0.182313	0.0911564	+	0.995837i	$0.470944\pi$
$608$	36.2283	1.46925
$609$	36.6133	1.48365
$610$	−0.116670	−0.00472382
$611$	23.6724	0.957682
$612$	2.78847	0.112717
$613$	−14.3208	−0.578413	−0.289207	−	0.957267i	$-0.593391\pi$
$613$	−14.3208	−0.578413	−0.289207	+	0.957267i	$0.593391\pi$
$614$	−44.8245	−1.80897
$615$	−0.0289447	−0.00116716
$616$	−24.1605	−0.973452
$617$	−20.0005	−0.805189	−0.402595	−	0.915378i	$-0.631892\pi$
$617$	−20.0005	−0.805189	−0.402595	+	0.915378i	$0.631892\pi$
$618$	−28.2265	−1.13544
$619$	27.1505	1.09127	0.545635	−	0.838023i	$-0.316289\pi$
$619$	27.1505	1.09127	0.545635	+	0.838023i	$0.316289\pi$
$620$	0.104619	0.00420159
$621$	−9.01304	−0.361681
$622$	−33.8921	−1.35895
$623$	44.3416	1.77651
$624$	4.71873	0.188900
$625$	24.9993	0.999972
$626$	−14.5636	−0.582077
$627$	−16.6630	−0.665455
$628$	2.78847	0.111272
$629$	−9.25763	−0.369126
$630$	−0.0610172	−0.00243098
$631$	−34.6345	−1.37878	−0.689388	−	0.724392i	$-0.742120\pi$
$631$	−34.6345	−1.37878	−0.689388	+	0.724392i	$0.742120\pi$
$632$	10.6621	0.424114
$633$	−2.26287	−0.0899412
$634$	2.01882	0.0801777
$635$	0.0585681	0.00232420
$636$	27.0830	1.07391
$637$	−26.0912	−1.03377
$638$	−66.1493	−2.61887
$639$	−4.07741	−0.161300
$640$	−0.0861946	−0.00340714
$641$	21.4302	0.846443	0.423222	−	0.906026i	$-0.360899\pi$
$641$	21.4302	0.846443	0.423222	+	0.906026i	$0.360899\pi$
$642$	30.7429	1.21333
$643$	−42.2512	−1.66623	−0.833113	−	0.553102i	$-0.813444\pi$
$643$	−42.2512	−1.66623	−0.833113	+	0.553102i	$0.813444\pi$
$644$	103.503	4.07860
$645$	0.0103384	0.000407076 0
$646$	−10.7238	−0.421922
$647$	−30.4667	−1.19777	−0.598884	−	0.800836i	$-0.704389\pi$
$647$	−30.4667	−1.19777	−0.598884	+	0.800836i	$0.704389\pi$
$648$	−1.72538	−0.0677795
$649$	6.04330	0.237220
$650$	−28.6609	−1.12417
$651$	22.8203	0.894399
$652$	−5.46175	−0.213899
$653$	16.2693	0.636665	0.318333	−	0.947979i	$-0.396877\pi$
$653$	16.2693	0.636665	0.318333	+	0.947979i	$0.396877\pi$
$654$	−17.3350	−0.677853
$655$	−0.114828	−0.00448672
$656$	−7.70073	−0.300663
$657$	8.69593	0.339261
$658$	−81.4389	−3.17482
$659$	−1.58163	−0.0616116	−0.0308058	−	0.999525i	$-0.509807\pi$
$659$	−1.58163	−0.0616116	−0.0308058	+	0.999525i	$0.509807\pi$
$660$	0.0641959	0.00249882
$661$	0.787657	0.0306363	0.0153182	−	0.999883i	$-0.495124\pi$
$661$	0.787657	0.0306363	0.0153182	+	0.999883i	$0.495124\pi$
$662$	−8.76122	−0.340514
$663$	−2.61954	−0.101734
$664$	−13.6504	−0.529738
$665$	0.136648	0.00529898
$666$	20.2581	0.784984
$667$	80.1299	3.10264
$668$	−37.4221	−1.44790
$669$	16.8270	0.650570
$670$	0.203649	0.00786766
$671$	26.7747	1.03363
$672$	−30.4449	−1.17444
$673$	40.2724	1.55239	0.776194	−	0.630495i	$-0.217148\pi$
$673$	40.2724	1.55239	0.776194	+	0.630495i	$0.217148\pi$
$674$	61.5513	2.37087
$675$	−4.99995	−0.192448
$676$	−17.1157	−0.658297
$677$	−36.7023	−1.41058	−0.705292	−	0.708917i	$-0.749184\pi$
$677$	−36.7023	−1.41058	−0.705292	+	0.708917i	$0.749184\pi$
$678$	−18.6044	−0.714499
$679$	76.8225	2.94818
$680$	0.0116822	0.000447991 0
$681$	−0.158511	−0.00607417
$682$	−41.2295	−1.57876
$683$	18.2323	0.697638	0.348819	−	0.937190i	$-0.386583\pi$
$683$	18.2323	0.697638	0.348819	+	0.937190i	$0.386583\pi$
$684$	13.6652	0.522502
$685$	−0.0916663	−0.00350239
$686$	26.6773	1.01854
$687$	−5.38835	−0.205578
$688$	2.75054	0.104864
$689$	−25.4423	−0.969273
$690$	−0.133539	−0.00508373
$691$	−31.4261	−1.19550	−0.597752	−	0.801681i	$-0.703939\pi$
$691$	−31.4261	−1.19550	−0.597752	+	0.801681i	$0.703939\pi$
$692$	31.4704	1.19633
$693$	14.0029	0.531928
$694$	77.6415	2.94723
$695$	0.0899072	0.00341038
$696$	15.3394	0.581440
$697$	4.27495	0.161925
$698$	27.1584	1.02796
$699$	3.25217	0.123009
$700$	57.4181	2.17020
$701$	21.2610	0.803019	0.401509	−	0.915855i	$-0.368486\pi$
$701$	21.2610	0.803019	0.401509	+	0.915855i	$0.368486\pi$
$702$	5.73222	0.216349
$703$	−45.3680	−1.71108
$704$	42.7547	1.61138
$705$	0.0611864	0.00230441
$706$	−73.2110	−2.75533
$707$	−0.651841	−0.0245150
$708$	−4.95607	−0.186261
$709$	19.5053	0.732537	0.366268	−	0.930509i	$-0.380635\pi$
$709$	19.5053	0.732537	0.366268	+	0.930509i	$0.380635\pi$
$710$	−0.0604116	−0.00226721
$711$	−6.17953	−0.231750
$712$	18.5773	0.696212
$713$	49.9433	1.87039
$714$	9.01186	0.337260
$715$	−0.0603066	−0.00225534
$716$	28.2467	1.05563
$717$	−18.4847	−0.690323
$718$	38.4179	1.43374
$719$	27.2140	1.01491	0.507455	−	0.861678i	$-0.330586\pi$
$719$	27.2140	1.01491	0.507455	+	0.861678i	$0.330586\pi$
$720$	0.0121966	0.000454540 0
$721$	−53.1220	−1.97837
$722$	−10.9761	−0.408489
$723$	−4.56669	−0.169837
$724$	−45.1412	−1.67766
$725$	44.4518	1.65090
$726$	−1.22825	−0.0455845
$727$	−14.0347	−0.520517	−0.260258	−	0.965539i	$-0.583808\pi$
$727$	−14.0347	−0.520517	−0.260258	+	0.965539i	$0.583808\pi$
$728$	−18.6134	−0.689860
$729$	1.00000	0.0370370
$730$	0.128840	0.00476860
$731$	−1.52693	−0.0564754
$732$	−21.9578	−0.811583
$733$	33.3333	1.23119	0.615597	−	0.788061i	$-0.288915\pi$
$733$	33.3333	1.23119	0.615597	+	0.788061i	$0.288915\pi$
$734$	−28.2579	−1.04302
$735$	−0.0674384	−0.00248750
$736$	−66.6299	−2.45601
$737$	−46.7358	−1.72154
$738$	−9.35470	−0.344351
$739$	−15.5962	−0.573714	−0.286857	−	0.957973i	$-0.592611\pi$
$739$	−15.5962	−0.573714	−0.286857	+	0.957973i	$0.592611\pi$
$740$	0.174785	0.00642522
$741$	−12.8373	−0.471591
$742$	87.5277	3.21324
$743$	−39.2056	−1.43832	−0.719158	−	0.694847i	$-0.755472\pi$
$743$	−39.2056	−1.43832	−0.719158	+	0.694847i	$0.755472\pi$
$744$	9.56075	0.350514
$745$	−0.122925	−0.00450362
$746$	50.7369	1.85761
$747$	7.91151	0.289467
$748$	−9.48134	−0.346672
$749$	57.8578	2.11408
$750$	−0.148161	−0.00541008
$751$	23.0271	0.840270	0.420135	−	0.907462i	$-0.361983\pi$
$751$	23.0271	0.840270	0.420135	+	0.907462i	$0.361983\pi$
$752$	16.2786	0.593621
$753$	25.8178	0.940852
$754$	−50.9620	−1.85593
$755$	0.158422	0.00576555
$756$	−11.4837	−0.417659
$757$	1.84282	0.0669786	0.0334893	−	0.999439i	$-0.489338\pi$
$757$	1.84282	0.0669786	0.0334893	+	0.999439i	$0.489338\pi$
$758$	8.22611	0.298786
$759$	30.6460	1.11238
$760$	0.0572496	0.00207666
$761$	−14.0314	−0.508639	−0.254320	−	0.967120i	$-0.581852\pi$
$761$	−14.0314	−0.508639	−0.254320	+	0.967120i	$0.581852\pi$
$762$	18.9288	0.685717
$763$	−32.6243	−1.18108
$764$	−31.7020	−1.14694
$765$	−0.00677076	−0.000244797 0
$766$	−34.1768	−1.23486
$767$	4.65582	0.168112
$768$	−2.70900	−0.0977527
$769$	−14.2372	−0.513406	−0.256703	−	0.966490i	$-0.582636\pi$
$769$	−14.2372	−0.513406	−0.256703	+	0.966490i	$0.582636\pi$
$770$	0.207470	0.00747670
$771$	−24.9026	−0.896846
$772$	−20.5456	−0.739452
$773$	−16.1833	−0.582071	−0.291036	−	0.956712i	$-0.594000\pi$
$773$	−16.1833	−0.582071	−0.291036	+	0.956712i	$0.594000\pi$
$774$	3.34131	0.120101
$775$	27.7059	0.995225
$776$	32.1853	1.15539
$777$	38.1255	1.36774
$778$	−39.5857	−1.41922
$779$	20.9498	0.750606
$780$	0.0494571	0.00177085
$781$	13.8640	0.496092
$782$	19.7228	0.705288
$783$	−8.89044	−0.317718
$784$	−17.9420	−0.640785
$785$	−0.00677076	−0.000241659 0
$786$	−37.1117	−1.32373
$787$	16.6164	0.592312	0.296156	−	0.955140i	$-0.404295\pi$
$787$	16.6164	0.592312	0.296156	+	0.955140i	$0.404295\pi$
$788$	75.3051	2.68263
$789$	2.07967	0.0740382
$790$	−0.0915570	−0.00325745
$791$	−35.0134	−1.24493
$792$	5.86663	0.208462
$793$	20.6275	0.732504
$794$	38.4943	1.36611
$795$	−0.0657610	−0.00233230
$796$	5.42875	0.192417
$797$	21.2121	0.751372	0.375686	−	0.926747i	$-0.377407\pi$
$797$	21.2121	0.751372	0.375686	+	0.926747i	$0.377407\pi$
$798$	44.1636	1.56337
$799$	−9.03685	−0.319701
$800$	−36.9627	−1.30683
$801$	−10.7670	−0.380434
$802$	66.3145	2.34165
$803$	−29.5678	−1.04343
$804$	38.3278	1.35172
$805$	−0.251319	−0.00885781
$806$	−31.7636	−1.11882
$807$	−18.3952	−0.647541
$808$	−0.273094	−0.00960740
$809$	6.59006	0.231694	0.115847	−	0.993267i	$-0.463042\pi$
$809$	6.59006	0.231694	0.115847	+	0.993267i	$0.463042\pi$
$810$	0.0148162	0.000520587 0
$811$	−2.53302	−0.0889465	−0.0444733	−	0.999011i	$-0.514161\pi$
$811$	−2.53302	−0.0889465	−0.0444733	+	0.999011i	$0.514161\pi$
$812$	102.095	3.58284
$813$	−7.84327	−0.275076
$814$	−68.8813	−2.41429
$815$	0.0132618	0.000464541 0
$816$	−1.80136	−0.0630602
$817$	−7.48286	−0.261792
$818$	50.7537	1.77456
$819$	10.7880	0.376963
$820$	−0.0807114	−0.00281857
$821$	−12.5413	−0.437696	−0.218848	−	0.975759i	$-0.570230\pi$
$821$	−12.5413	−0.437696	−0.218848	+	0.975759i	$0.570230\pi$
$822$	−29.6259	−1.03332
$823$	37.3286	1.30119	0.650597	−	0.759423i	$-0.274519\pi$
$823$	37.3286	1.30119	0.650597	+	0.759423i	$0.274519\pi$
$824$	−22.2559	−0.775320
$825$	17.0008	0.591892
$826$	−16.0172	−0.557309
$827$	20.3301	0.706946	0.353473	−	0.935445i	$-0.385001\pi$
$827$	20.3301	0.706946	0.353473	+	0.935445i	$0.385001\pi$
$828$	−25.1326	−0.873419
$829$	38.8687	1.34997	0.674983	−	0.737833i	$-0.264151\pi$
$829$	38.8687	1.34997	0.674983	+	0.737833i	$0.264151\pi$
$830$	0.117218	0.00406870
$831$	29.4697	1.02229
$832$	32.9386	1.14194
$833$	9.96024	0.345102
$834$	29.0573	1.00617
$835$	0.0908654	0.00314453
$836$	−46.4643	−1.60700
$837$	−5.54123	−0.191533
$838$	−37.5632	−1.29760
$839$	2.22290	0.0767429	0.0383715	−	0.999264i	$-0.487783\pi$
$839$	2.22290	0.0767429	0.0383715	+	0.999264i	$0.487783\pi$
$840$	−0.0481104	−0.00165997
$841$	50.0399	1.72552
$842$	73.4735	2.53207
$843$	1.35705	0.0467394
$844$	−6.30996	−0.217198
$845$	0.0415591	0.00142968
$846$	19.7750	0.679877
$847$	−2.31155	−0.0794257
$848$	−17.4957	−0.600805
$849$	−13.9974	−0.480389
$850$	10.9412	0.375280
$851$	83.4393	2.86026
$852$	−11.3697	−0.389521
$853$	49.2036	1.68470	0.842350	−	0.538930i	$-0.181171\pi$
$853$	49.2036	1.68470	0.842350	+	0.538930i	$0.181171\pi$
$854$	−70.9637	−2.42833
$855$	−0.0331808	−0.00113476
$856$	24.2400	0.828505
$857$	41.9470	1.43288	0.716442	−	0.697647i	$-0.245770\pi$
$857$	41.9470	1.43288	0.716442	+	0.697647i	$0.245770\pi$
$858$	−19.4906	−0.665400
$859$	−53.3376	−1.81985	−0.909927	−	0.414768i	$-0.863863\pi$
$859$	−53.3376	−1.81985	−0.909927	+	0.414768i	$0.863863\pi$
$860$	0.0288285	0.000983043 0
$861$	−17.6055	−0.599992
$862$	83.9846	2.86053
$863$	−10.6620	−0.362938	−0.181469	−	0.983397i	$-0.558085\pi$
$863$	−10.6620	−0.362938	−0.181469	+	0.983397i	$0.558085\pi$
$864$	7.39261	0.251502
$865$	−0.0764141	−0.00259816
$866$	−73.3725	−2.49330
$867$	1.00000	0.0339618
$868$	63.6339	2.15988
$869$	21.0116	0.712769
$870$	−0.131722	−0.00446580
$871$	−36.0057	−1.22001
$872$	−13.6682	−0.462864
$873$	−18.6540	−0.631343
$874$	96.6539	3.26937
$875$	−0.278838	−0.00942643
$876$	24.2484	0.819277
$877$	−26.4530	−0.893255	−0.446628	−	0.894720i	$-0.647375\pi$
$877$	−26.4530	−0.893255	−0.446628	+	0.894720i	$0.647375\pi$
$878$	−10.3230	−0.348386
$879$	20.2352	0.682517
$880$	−0.0414707	−0.00139798
$881$	−12.2198	−0.411694	−0.205847	−	0.978584i	$-0.565995\pi$
$881$	−12.2198	−0.411694	−0.205847	+	0.978584i	$0.565995\pi$
$882$	−21.7956	−0.733895
$883$	39.6338	1.33378	0.666892	−	0.745155i	$-0.267624\pi$
$883$	39.6338	1.33378	0.666892	+	0.745155i	$0.267624\pi$
$884$	−7.30451	−0.245677
$885$	0.0120340	0.000404517 0
$886$	−47.3439	−1.59055
$887$	−24.5432	−0.824081	−0.412040	−	0.911166i	$-0.635184\pi$
$887$	−24.5432	−0.824081	−0.412040	+	0.911166i	$0.635184\pi$
$888$	15.9730	0.536018
$889$	35.6238	1.19478
$890$	−0.159526	−0.00534733
$891$	−3.40019	−0.113911
$892$	46.9217	1.57105
$893$	−44.2860	−1.48198
$894$	−39.7284	−1.32872
$895$	−0.0685865	−0.00229259
$896$	−52.4275	−1.75148
$897$	23.6100	0.788314
$898$	−75.9519	−2.53455
$899$	49.2640	1.64305
$900$	−13.9422	−0.464741
$901$	9.71250	0.323570
$902$	31.8077	1.05908
$903$	6.28831	0.209262
$904$	−14.6691	−0.487887
$905$	0.109608	0.00364351
$906$	51.2007	1.70103
$907$	−19.2437	−0.638976	−0.319488	−	0.947590i	$-0.603511\pi$
$907$	−19.2437	−0.638976	−0.319488	+	0.947590i	$0.603511\pi$
$908$	−0.442005	−0.0146685
$909$	0.158280	0.00524981
$910$	0.159837	0.00529854
$911$	−48.2374	−1.59818	−0.799088	−	0.601213i	$-0.794684\pi$
$911$	−48.2374	−1.59818	−0.799088	+	0.601213i	$0.794684\pi$
$912$	−8.82776	−0.292316
$913$	−26.9006	−0.890281
$914$	8.74929	0.289401
$915$	0.0533162	0.00176258
$916$	−15.0253	−0.496449
$917$	−69.8438	−2.30645
$918$	−2.18826	−0.0722233
$919$	12.1360	0.400328	0.200164	−	0.979762i	$-0.435852\pi$
$919$	12.1360	0.400328	0.200164	+	0.979762i	$0.435852\pi$
$920$	−0.105292	−0.00347137
$921$	20.4841	0.674974
$922$	−60.3998	−1.98916
$923$	10.6809	0.351567
$924$	39.0468	1.28455
$925$	46.2877	1.52193
$926$	11.8586	0.389698
$927$	12.8991	0.423661
$928$	−65.7236	−2.15748
$929$	−20.3579	−0.667919	−0.333960	−	0.942587i	$-0.608385\pi$
$929$	−20.3579	−0.667919	−0.333960	+	0.942587i	$0.608385\pi$
$930$	−0.0820998	−0.00269216
$931$	48.8112	1.59972
$932$	9.06860	0.297052
$933$	15.4882	0.507060
$934$	−32.2097	−1.05393
$935$	0.0230219	0.000752895 0
$936$	4.51971	0.147731
$937$	−33.6437	−1.09909	−0.549545	−	0.835464i	$-0.685199\pi$
$937$	−33.6437	−1.09909	−0.549545	+	0.835464i	$0.685199\pi$
$938$	123.869	4.04446
$939$	6.65533	0.217188
$940$	0.170617	0.00556490
$941$	30.7852	1.00357	0.501784	−	0.864993i	$-0.332677\pi$
$941$	30.7852	1.00357	0.501784	+	0.864993i	$0.332677\pi$
$942$	−2.18826	−0.0712973
$943$	−38.5303	−1.25472
$944$	3.20164	0.104204
$945$	0.0278839	0.000907063 0
$946$	−11.3611	−0.369381
$947$	29.9570	0.973471	0.486736	−	0.873549i	$-0.338188\pi$
$947$	29.9570	0.973471	0.486736	+	0.873549i	$0.338188\pi$
$948$	−17.2315	−0.559652
$949$	−22.7793	−0.739448
$950$	53.6184	1.73961
$951$	−0.922570	−0.0299164
$952$	7.10562	0.230294
$953$	−41.2472	−1.33613	−0.668064	−	0.744104i	$-0.732877\pi$
$953$	−41.2472	−1.33613	−0.668064	+	0.744104i	$0.732877\pi$
$954$	−21.2535	−0.688106
$955$	0.0769763	0.00249090
$956$	−51.5441	−1.66705
$957$	30.2292	0.977171
$958$	63.3847	2.04787
$959$	−55.7556	−1.80044
$960$	0.0851370	0.00274779
$961$	−0.294793	−0.00950945
$962$	−53.0668	−1.71094
$963$	−14.0490	−0.452723
$964$	−12.7341	−0.410137
$965$	0.0498872	0.00160593
$966$	−81.2242	−2.61335
$967$	11.8756	0.381893	0.190947	−	0.981600i	$-0.438844\pi$
$967$	11.8756	0.381893	0.190947	+	0.981600i	$0.438844\pi$
$968$	−0.968440	−0.0311268
$969$	4.90060	0.157430
$970$	−0.276381	−0.00887406
$971$	21.9741	0.705182	0.352591	−	0.935777i	$-0.385301\pi$
$971$	21.9741	0.705182	0.352591	+	0.935777i	$0.385301\pi$
$972$	2.78847	0.0894403
$973$	54.6856	1.75314
$974$	11.9790	0.383832
$975$	13.0976	0.419458
$976$	14.1848	0.454044
$977$	−30.9125	−0.988978	−0.494489	−	0.869184i	$-0.664645\pi$
$977$	−30.9125	−0.988978	−0.494489	+	0.869184i	$0.664645\pi$
$978$	4.28611	0.137055
$979$	36.6099	1.17006
$980$	−0.188050	−0.00600704
$981$	7.92183	0.252925
$982$	−0.938732	−0.0299561
$983$	−0.979002	−0.0312253	−0.0156127	−	0.999878i	$-0.504970\pi$
$983$	−0.979002	−0.0312253	−0.0156127	+	0.999878i	$0.504970\pi$
$984$	−7.37593	−0.235136
$985$	−0.182850	−0.00582608
$986$	19.4546	0.619560
$987$	37.2163	1.18461
$988$	−35.7965	−1.13884
$989$	13.7622	0.437614
$990$	−0.0503778	−0.00160111
$991$	45.6413	1.44984	0.724921	−	0.688832i	$-0.241876\pi$
$991$	45.6413	1.44984	0.724921	+	0.688832i	$0.241876\pi$
$992$	−40.9641	−1.30061
$993$	4.00374	0.127055
$994$	−36.7450	−1.16548
$995$	−0.0131817	−0.000417887 0
$996$	22.0610	0.699031
$997$	44.9585	1.42385	0.711925	−	0.702255i	$-0.247824\pi$
$997$	44.9585	1.42385	0.711925	+	0.702255i	$0.247824\pi$
$998$	9.39522	0.297401
$999$	−9.25763	−0.292898

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.i.1.8	✓	63

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.i.1.8	✓	63	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.18826 q^{2} +1.00000 q^{3} +2.78847 q^{4} -0.00677076 q^{5} -2.18826 q^{6} -4.11828 q^{7} -1.72538 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.18826 q^{2} +1.00000 q^{3} +2.78847 q^{4} -0.00677076 q^{5} -2.18826 q^{6} -4.11828 q^{7} -1.72538 q^{8} +1.00000 q^{9} +0.0148162 q^{10} -3.40019 q^{11} +2.78847 q^{12} -2.61954 q^{13} +9.01186 q^{14} -0.00677076 q^{15} -1.80136 q^{16} +1.00000 q^{17} -2.18826 q^{18} +4.90060 q^{19} -0.0188801 q^{20} -4.11828 q^{21} +7.44049 q^{22} -9.01304 q^{23} -1.72538 q^{24} -4.99995 q^{25} +5.73222 q^{26} +1.00000 q^{27} -11.4837 q^{28} -8.89044 q^{29} +0.0148162 q^{30} -5.54123 q^{31} +7.39261 q^{32} -3.40019 q^{33} -2.18826 q^{34} +0.0278839 q^{35} +2.78847 q^{36} -9.25763 q^{37} -10.7238 q^{38} -2.61954 q^{39} +0.0116822 q^{40} +4.27495 q^{41} +9.01186 q^{42} -1.52693 q^{43} -9.48134 q^{44} -0.00677076 q^{45} +19.7228 q^{46} -9.03685 q^{47} -1.80136 q^{48} +9.96024 q^{49} +10.9412 q^{50} +1.00000 q^{51} -7.30451 q^{52} +9.71250 q^{53} -2.18826 q^{54} +0.0230219 q^{55} +7.10562 q^{56} +4.90060 q^{57} +19.4546 q^{58} -1.77734 q^{59} -0.0188801 q^{60} -7.87448 q^{61} +12.1256 q^{62} -4.11828 q^{63} -12.5742 q^{64} +0.0177363 q^{65} +7.44049 q^{66} +13.7451 q^{67} +2.78847 q^{68} -9.01304 q^{69} -0.0610172 q^{70} -4.07741 q^{71} -1.72538 q^{72} +8.69593 q^{73} +20.2581 q^{74} -4.99995 q^{75} +13.6652 q^{76} +14.0029 q^{77} +5.73222 q^{78} -6.17953 q^{79} +0.0121966 q^{80} +1.00000 q^{81} -9.35470 q^{82} +7.91151 q^{83} -11.4837 q^{84} -0.00677076 q^{85} +3.34131 q^{86} -8.89044 q^{87} +5.86663 q^{88} -10.7670 q^{89} +0.0148162 q^{90} +10.7880 q^{91} -25.1326 q^{92} -5.54123 q^{93} +19.7750 q^{94} -0.0331808 q^{95} +7.39261 q^{96} -18.6540 q^{97} -21.7956 q^{98} -3.40019 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

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