LMFDB - Embedded newform 8015.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65622 q^{2} -1.51381 q^{3} +5.05553 q^{4} -1.00000 q^{5} +4.02102 q^{6} -1.00000 q^{7} -8.11618 q^{8} -0.708384 q^{9} +O(q^{10})$	\(q-2.65622 q^{2} -1.51381 q^{3} +5.05553 q^{4} -1.00000 q^{5} +4.02102 q^{6} -1.00000 q^{7} -8.11618 q^{8} -0.708384 q^{9} +2.65622 q^{10} -5.61743 q^{11} -7.65310 q^{12} +6.70734 q^{13} +2.65622 q^{14} +1.51381 q^{15} +11.4473 q^{16} -3.50154 q^{17} +1.88163 q^{18} +2.65152 q^{19} -5.05553 q^{20} +1.51381 q^{21} +14.9212 q^{22} +2.95131 q^{23} +12.2863 q^{24} +1.00000 q^{25} -17.8162 q^{26} +5.61378 q^{27} -5.05553 q^{28} +5.39028 q^{29} -4.02102 q^{30} -0.273942 q^{31} -14.1743 q^{32} +8.50372 q^{33} +9.30089 q^{34} +1.00000 q^{35} -3.58126 q^{36} +12.0812 q^{37} -7.04304 q^{38} -10.1536 q^{39} +8.11618 q^{40} +11.6828 q^{41} -4.02102 q^{42} -2.58198 q^{43} -28.3991 q^{44} +0.708384 q^{45} -7.83933 q^{46} -1.30017 q^{47} -17.3291 q^{48} +1.00000 q^{49} -2.65622 q^{50} +5.30067 q^{51} +33.9092 q^{52} +7.69853 q^{53} -14.9115 q^{54} +5.61743 q^{55} +8.11618 q^{56} -4.01390 q^{57} -14.3178 q^{58} -6.89816 q^{59} +7.65310 q^{60} +2.54520 q^{61} +0.727653 q^{62} +0.708384 q^{63} +14.7555 q^{64} -6.70734 q^{65} -22.5878 q^{66} +11.2045 q^{67} -17.7022 q^{68} -4.46771 q^{69} -2.65622 q^{70} -15.2309 q^{71} +5.74937 q^{72} +2.48419 q^{73} -32.0904 q^{74} -1.51381 q^{75} +13.4048 q^{76} +5.61743 q^{77} +26.9703 q^{78} -14.8242 q^{79} -11.4473 q^{80} -6.37304 q^{81} -31.0322 q^{82} -2.64228 q^{83} +7.65310 q^{84} +3.50154 q^{85} +6.85832 q^{86} -8.15985 q^{87} +45.5921 q^{88} -8.52428 q^{89} -1.88163 q^{90} -6.70734 q^{91} +14.9204 q^{92} +0.414696 q^{93} +3.45355 q^{94} -2.65152 q^{95} +21.4572 q^{96} -9.89389 q^{97} -2.65622 q^{98} +3.97930 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	−2.65622	−1.87823	−0.939117	−	0.343597i	$-0.888355\pi$
$2$	−2.65622	−1.87823	−0.939117	+	0.343597i	$0.888355\pi$
$3$	−1.51381	−0.873998	−0.436999	−	0.899462i	$-0.643959\pi$
$3$	−1.51381	−0.873998	−0.436999	+	0.899462i	$0.643959\pi$
$4$	5.05553	2.52777
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	4.02102	1.64157
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−8.11618	−2.86950
$9$	−0.708384	−0.236128
$10$	2.65622	0.839972
$11$	−5.61743	−1.69372	−0.846860	−	0.531816i	$-0.821510\pi$
$11$	−5.61743	−1.69372	−0.846860	+	0.531816i	$0.821510\pi$
$12$	−7.65310	−2.20926
$13$	6.70734	1.86028	0.930141	−	0.367202i	$-0.119684\pi$
$13$	6.70734	1.86028	0.930141	+	0.367202i	$0.119684\pi$
$14$	2.65622	0.709906
$15$	1.51381	0.390864
$16$	11.4473	2.86183
$17$	−3.50154	−0.849249	−0.424625	−	0.905370i	$-0.639594\pi$
$17$	−3.50154	−0.849249	−0.424625	+	0.905370i	$0.639594\pi$
$18$	1.88163	0.443504
$19$	2.65152	0.608301	0.304150	−	0.952624i	$-0.401627\pi$
$19$	2.65152	0.608301	0.304150	+	0.952624i	$0.401627\pi$
$20$	−5.05553	−1.13045
$21$	1.51381	0.330340
$22$	14.9212	3.18120
$23$	2.95131	0.615390	0.307695	−	0.951485i	$-0.400442\pi$
$23$	2.95131	0.615390	0.307695	+	0.951485i	$0.400442\pi$
$24$	12.2863	2.50794
$25$	1.00000	0.200000
$26$	−17.8162	−3.49405
$27$	5.61378	1.08037
$28$	−5.05553	−0.955405
$29$	5.39028	1.00095	0.500475	−	0.865751i	$-0.333159\pi$
$29$	5.39028	1.00095	0.500475	+	0.865751i	$0.333159\pi$
$30$	−4.02102	−0.734134
$31$	−0.273942	−0.0492015	−0.0246008	−	0.999697i	$-0.507831\pi$
$31$	−0.273942	−0.0492015	−0.0246008	+	0.999697i	$0.507831\pi$
$32$	−14.1743	−2.50569
$33$	8.50372	1.48031
$34$	9.30089	1.59509
$35$	1.00000	0.169031
$36$	−3.58126	−0.596876
$37$	12.0812	1.98614	0.993069	−	0.117537i	$-0.0374999\pi$
$37$	12.0812	1.98614	0.993069	+	0.117537i	$0.0374999\pi$
$38$	−7.04304	−1.14253
$39$	−10.1536	−1.62588
$40$	8.11618	1.28328
$41$	11.6828	1.82455	0.912275	−	0.409577i	$-0.134324\pi$
$41$	11.6828	1.82455	0.912275	+	0.409577i	$0.134324\pi$
$42$	−4.02102	−0.620456
$43$	−2.58198	−0.393748	−0.196874	−	0.980429i	$-0.563079\pi$
$43$	−2.58198	−0.393748	−0.196874	+	0.980429i	$0.563079\pi$
$44$	−28.3991	−4.28133
$45$	0.708384	0.105600
$46$	−7.83933	−1.15585
$47$	−1.30017	−0.189650	−0.0948249	−	0.995494i	$-0.530229\pi$
$47$	−1.30017	−0.189650	−0.0948249	+	0.995494i	$0.530229\pi$
$48$	−17.3291	−2.50123
$49$	1.00000	0.142857
$50$	−2.65622	−0.375647
$51$	5.30067	0.742242
$52$	33.9092	4.70236
$53$	7.69853	1.05747	0.528737	−	0.848786i	$-0.322666\pi$
$53$	7.69853	1.05747	0.528737	+	0.848786i	$0.322666\pi$
$54$	−14.9115	−2.02919
$55$	5.61743	0.757454
$56$	8.11618	1.08457
$57$	−4.01390	−0.531654
$58$	−14.3178	−1.88002
$59$	−6.89816	−0.898063	−0.449032	−	0.893516i	$-0.648231\pi$
$59$	−6.89816	−0.898063	−0.449032	+	0.893516i	$0.648231\pi$
$60$	7.65310	0.988012
$61$	2.54520	0.325879	0.162940	−	0.986636i	$-0.447902\pi$
$61$	2.54520	0.325879	0.162940	+	0.986636i	$0.447902\pi$
$62$	0.727653	0.0924120
$63$	0.708384	0.0892480
$64$	14.7555	1.84444
$65$	−6.70734	−0.831944
$66$	−22.5878	−2.78036
$67$	11.2045	1.36885	0.684426	−	0.729082i	$-0.260053\pi$
$67$	11.2045	1.36885	0.684426	+	0.729082i	$0.260053\pi$
$68$	−17.7022	−2.14670
$69$	−4.46771	−0.537849
$70$	−2.65622	−0.317480
$71$	−15.2309	−1.80757	−0.903787	−	0.427982i	$-0.859225\pi$
$71$	−15.2309	−1.80757	−0.903787	+	0.427982i	$0.859225\pi$
$72$	5.74937	0.677570
$73$	2.48419	0.290753	0.145376	−	0.989376i	$-0.453561\pi$
$73$	2.48419	0.290753	0.145376	+	0.989376i	$0.453561\pi$
$74$	−32.0904	−3.73043
$75$	−1.51381	−0.174800
$76$	13.4048	1.53764
$77$	5.61743	0.640166
$78$	26.9703	3.05379
$79$	−14.8242	−1.66785	−0.833924	−	0.551879i	$-0.813911\pi$
$79$	−14.8242	−1.66785	−0.833924	+	0.551879i	$0.813911\pi$
$80$	−11.4473	−1.27985
$81$	−6.37304	−0.708116
$82$	−31.0322	−3.42693
$83$	−2.64228	−0.290027	−0.145014	−	0.989430i	$-0.546323\pi$
$83$	−2.64228	−0.290027	−0.145014	+	0.989430i	$0.546323\pi$
$84$	7.65310	0.835022
$85$	3.50154	0.379796
$86$	6.85832	0.739552
$87$	−8.15985	−0.874828
$88$	45.5921	4.86013
$89$	−8.52428	−0.903572	−0.451786	−	0.892126i	$-0.649213\pi$
$89$	−8.52428	−0.903572	−0.451786	+	0.892126i	$0.649213\pi$
$90$	−1.88163	−0.198341
$91$	−6.70734	−0.703121
$92$	14.9204	1.55556
$93$	0.414696	0.0430020
$94$	3.45355	0.356207
$95$	−2.65152	−0.272040
$96$	21.4572	2.18997
$97$	−9.89389	−1.00457	−0.502286	−	0.864701i	$-0.667508\pi$
$97$	−9.89389	−1.00457	−0.502286	+	0.864701i	$0.667508\pi$
$98$	−2.65622	−0.268319
$99$	3.97930	0.399935
$100$	5.05553	0.505553
$101$	16.1935	1.61132	0.805658	−	0.592381i	$-0.201812\pi$
$101$	16.1935	1.61132	0.805658	+	0.592381i	$0.201812\pi$
$102$	−14.0798	−1.39410
$103$	1.16218	0.114513	0.0572563	−	0.998360i	$-0.481765\pi$
$103$	1.16218	0.114513	0.0572563	+	0.998360i	$0.481765\pi$
$104$	−54.4380	−5.33808
$105$	−1.51381	−0.147733
$106$	−20.4490	−1.98618
$107$	0.652067	0.0630377	0.0315188	−	0.999503i	$-0.489966\pi$
$107$	0.652067	0.0630377	0.0315188	+	0.999503i	$0.489966\pi$
$108$	28.3807	2.73093
$109$	−16.5406	−1.58430	−0.792150	−	0.610327i	$-0.791038\pi$
$109$	−16.5406	−1.58430	−0.792150	+	0.610327i	$0.791038\pi$
$110$	−14.9212	−1.42268
$111$	−18.2886	−1.73588
$112$	−11.4473	−1.08167
$113$	11.0415	1.03870	0.519348	−	0.854563i	$-0.326175\pi$
$113$	11.0415	1.03870	0.519348	+	0.854563i	$0.326175\pi$
$114$	10.6618	0.998570
$115$	−2.95131	−0.275211
$116$	27.2507	2.53017
$117$	−4.75137	−0.439265
$118$	18.3231	1.68677
$119$	3.50154	0.320986
$120$	−12.2863	−1.12158
$121$	20.5556	1.86869
$122$	−6.76062	−0.612078
$123$	−17.6856	−1.59465
$124$	−1.38492	−0.124370
$125$	−1.00000	−0.0894427
$126$	−1.88163	−0.167629
$127$	−12.7009	−1.12702	−0.563510	−	0.826109i	$-0.690549\pi$
$127$	−12.7009	−1.12702	−0.563510	+	0.826109i	$0.690549\pi$
$128$	−10.8454	−0.958604
$129$	3.90862	0.344135
$130$	17.8162	1.56259
$131$	−13.9205	−1.21624	−0.608118	−	0.793847i	$-0.708075\pi$
$131$	−13.9205	−1.21624	−0.608118	+	0.793847i	$0.708075\pi$
$132$	42.9908	3.74187
$133$	−2.65152	−0.229916
$134$	−29.7618	−2.57103
$135$	−5.61378	−0.483158
$136$	28.4191	2.43692
$137$	−12.7622	−1.09035	−0.545174	−	0.838323i	$-0.683536\pi$
$137$	−12.7622	−1.09035	−0.545174	+	0.838323i	$0.683536\pi$
$138$	11.8672	1.01021
$139$	−10.9329	−0.927318	−0.463659	−	0.886014i	$-0.653464\pi$
$139$	−10.9329	−0.927318	−0.463659	+	0.886014i	$0.653464\pi$
$140$	5.05553	0.427270
$141$	1.96821	0.165754
$142$	40.4567	3.39505
$143$	−37.6781	−3.15080
$144$	−8.10910	−0.675758
$145$	−5.39028	−0.447638
$146$	−6.59858	−0.546102
$147$	−1.51381	−0.124857
$148$	61.0769	5.02049
$149$	5.79702	0.474910	0.237455	−	0.971398i	$-0.423687\pi$
$149$	5.79702	0.474910	0.237455	+	0.971398i	$0.423687\pi$
$150$	4.02102	0.328315
$151$	13.8990	1.13108	0.565542	−	0.824719i	$-0.308667\pi$
$151$	13.8990	1.13108	0.565542	+	0.824719i	$0.308667\pi$
$152$	−21.5202	−1.74552
$153$	2.48044	0.200531
$154$	−14.9212	−1.20238
$155$	0.273942	0.0220036
$156$	−51.3320	−4.10985
$157$	4.56085	0.363995	0.181998	−	0.983299i	$-0.441744\pi$
$157$	4.56085	0.363995	0.181998	+	0.983299i	$0.441744\pi$
$158$	39.3763	3.13261
$159$	−11.6541	−0.924230
$160$	14.1743	1.12058
$161$	−2.95131	−0.232595
$162$	16.9282	1.33001
$163$	18.2918	1.43273	0.716363	−	0.697728i	$-0.245805\pi$
$163$	18.2918	1.43273	0.716363	+	0.697728i	$0.245805\pi$
$164$	59.0629	4.61204
$165$	−8.50372	−0.662014
$166$	7.01848	0.544740
$167$	9.54782	0.738833	0.369416	−	0.929264i	$-0.379558\pi$
$167$	9.54782	0.738833	0.369416	+	0.929264i	$0.379558\pi$
$168$	−12.2863	−0.947911
$169$	31.9885	2.46065
$170$	−9.30089	−0.713345
$171$	−1.87830	−0.143637
$172$	−13.0533	−0.995304
$173$	−9.67300	−0.735424	−0.367712	−	0.929940i	$-0.619859\pi$
$173$	−9.67300	−0.735424	−0.367712	+	0.929940i	$0.619859\pi$
$174$	21.6744	1.64313
$175$	−1.00000	−0.0755929
$176$	−64.3046	−4.84714
$177$	10.4425	0.784905
$178$	22.6424	1.69712
$179$	−9.80524	−0.732878	−0.366439	−	0.930442i	$-0.619423\pi$
$179$	−9.80524	−0.732878	−0.366439	+	0.930442i	$0.619423\pi$
$180$	3.58126	0.266931
$181$	−6.60093	−0.490643	−0.245321	−	0.969442i	$-0.578894\pi$
$181$	−6.60093	−0.490643	−0.245321	+	0.969442i	$0.578894\pi$
$182$	17.8162	1.32063
$183$	−3.85295	−0.284818
$184$	−23.9533	−1.76586
$185$	−12.0812	−0.888227
$186$	−1.10153	−0.0807679
$187$	19.6697	1.43839
$188$	−6.57307	−0.479390
$189$	−5.61378	−0.408343
$190$	7.04304	0.510956
$191$	1.62418	0.117522	0.0587609	−	0.998272i	$-0.481285\pi$
$191$	1.62418	0.117522	0.0587609	+	0.998272i	$0.481285\pi$
$192$	−22.3370	−1.61204
$193$	14.2891	1.02855	0.514276	−	0.857625i	$-0.328061\pi$
$193$	14.2891	1.02855	0.514276	+	0.857625i	$0.328061\pi$
$194$	26.2804	1.88682
$195$	10.1536	0.727117
$196$	5.05553	0.361109
$197$	15.2389	1.08573	0.542863	−	0.839821i	$-0.317340\pi$
$197$	15.2389	1.08573	0.542863	+	0.839821i	$0.317340\pi$
$198$	−10.5699	−0.751171
$199$	−23.6243	−1.67468	−0.837342	−	0.546679i	$-0.815892\pi$
$199$	−23.6243	−1.67468	−0.837342	+	0.546679i	$0.815892\pi$
$200$	−8.11618	−0.573900
$201$	−16.9615	−1.19637
$202$	−43.0136	−3.02643
$203$	−5.39028	−0.378323
$204$	26.7977	1.87621
$205$	−11.6828	−0.815964
$206$	−3.08700	−0.215081
$207$	−2.09066	−0.145311
$208$	76.7812	5.32382
$209$	−14.8947	−1.03029
$210$	4.02102	0.277476
$211$	15.4647	1.06464	0.532318	−	0.846545i	$-0.321321\pi$
$211$	15.4647	1.06464	0.532318	+	0.846545i	$0.321321\pi$
$212$	38.9201	2.67305
$213$	23.0567	1.57982
$214$	−1.73204	−0.118400
$215$	2.58198	0.176090
$216$	−45.5624	−3.10013
$217$	0.273942	0.0185964
$218$	43.9355	2.97569
$219$	−3.76059	−0.254117
$220$	28.3991	1.91467
$221$	−23.4861	−1.57984
$222$	48.5787	3.26039
$223$	5.23323	0.350443	0.175222	−	0.984529i	$-0.443936\pi$
$223$	5.23323	0.350443	0.175222	+	0.984529i	$0.443936\pi$
$224$	14.1743	0.947062
$225$	−0.708384	−0.0472256
$226$	−29.3287	−1.95092
$227$	−3.44904	−0.228921	−0.114460	−	0.993428i	$-0.536514\pi$
$227$	−3.44904	−0.228921	−0.114460	+	0.993428i	$0.536514\pi$
$228$	−20.2924	−1.34390
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	7.83933	0.516910
$231$	−8.50372	−0.559504
$232$	−43.7484	−2.87223
$233$	8.49670	0.556637	0.278319	−	0.960489i	$-0.410223\pi$
$233$	8.49670	0.556637	0.278319	+	0.960489i	$0.410223\pi$
$234$	12.6207	0.825042
$235$	1.30017	0.0848140
$236$	−34.8738	−2.27009
$237$	22.4409	1.45770
$238$	−9.30089	−0.602887
$239$	27.0687	1.75093	0.875464	−	0.483283i	$-0.160556\pi$
$239$	27.0687	1.75093	0.875464	+	0.483283i	$0.160556\pi$
$240$	17.3291	1.11859
$241$	−30.1325	−1.94100	−0.970502	−	0.241094i	$-0.922494\pi$
$241$	−30.1325	−1.94100	−0.970502	+	0.241094i	$0.922494\pi$
$242$	−54.6002	−3.50983
$243$	−7.19379	−0.461482
$244$	12.8673	0.823747
$245$	−1.00000	−0.0638877
$246$	46.9768	2.99513
$247$	17.7847	1.13161
$248$	2.22336	0.141184
$249$	3.99990	0.253483
$250$	2.65622	0.167994
$251$	29.6848	1.87369	0.936844	−	0.349748i	$-0.113733\pi$
$251$	29.6848	1.87369	0.936844	+	0.349748i	$0.113733\pi$
$252$	3.58126	0.225598
$253$	−16.5788	−1.04230
$254$	33.7364	2.11681
$255$	−5.30067	−0.331941
$256$	−0.703329	−0.0439581
$257$	16.5021	1.02938	0.514688	−	0.857378i	$-0.327908\pi$
$257$	16.5021	1.02938	0.514688	+	0.857378i	$0.327908\pi$
$258$	−10.3822	−0.646367
$259$	−12.0812	−0.750689
$260$	−33.9092	−2.10296
$261$	−3.81839	−0.236352
$262$	36.9759	2.28438
$263$	−12.9787	−0.800299	−0.400150	−	0.916450i	$-0.631042\pi$
$263$	−12.9787	−0.800299	−0.400150	+	0.916450i	$0.631042\pi$
$264$	−69.0177	−4.24774
$265$	−7.69853	−0.472917
$266$	7.04304	0.431836
$267$	12.9041	0.789720
$268$	56.6449	3.46014
$269$	−9.95346	−0.606873	−0.303436	−	0.952852i	$-0.598134\pi$
$269$	−9.95346	−0.606873	−0.303436	+	0.952852i	$0.598134\pi$
$270$	14.9115	0.907483
$271$	19.9720	1.21321	0.606606	−	0.795002i	$-0.292530\pi$
$271$	19.9720	1.21321	0.606606	+	0.795002i	$0.292530\pi$
$272$	−40.0833	−2.43041
$273$	10.1536	0.614526
$274$	33.8992	2.04793
$275$	−5.61743	−0.338744
$276$	−22.5866	−1.35956
$277$	−20.6401	−1.24014	−0.620071	−	0.784545i	$-0.712896\pi$
$277$	−20.6401	−1.24014	−0.620071	+	0.784545i	$0.712896\pi$
$278$	29.0403	1.74172
$279$	0.194056	0.0116179
$280$	−8.11618	−0.485034
$281$	20.2289	1.20676	0.603379	−	0.797455i	$-0.293821\pi$
$281$	20.2289	1.20676	0.603379	+	0.797455i	$0.293821\pi$
$282$	−5.22802	−0.311324
$283$	11.1824	0.664724	0.332362	−	0.943152i	$-0.392154\pi$
$283$	11.1824	0.664724	0.332362	+	0.943152i	$0.392154\pi$
$284$	−77.0003	−4.56912
$285$	4.01390	0.237763
$286$	100.081	5.91794
$287$	−11.6828	−0.689615
$288$	10.0409	0.591663
$289$	−4.73919	−0.278776
$290$	14.3178	0.840770
$291$	14.9775	0.877994
$292$	12.5589	0.734955
$293$	17.2005	1.00486	0.502431	−	0.864617i	$-0.332439\pi$
$293$	17.2005	1.00486	0.502431	+	0.864617i	$0.332439\pi$
$294$	4.02102	0.234510
$295$	6.89816	0.401626
$296$	−98.0531	−5.69922
$297$	−31.5350	−1.82985
$298$	−15.3982	−0.891993
$299$	19.7954	1.14480
$300$	−7.65310	−0.441852
$301$	2.58198	0.148823
$302$	−36.9189	−2.12444
$303$	−24.5139	−1.40829
$304$	30.3528	1.74085
$305$	−2.54520	−0.145738
$306$	−6.58860	−0.376645
$307$	−4.55690	−0.260076	−0.130038	−	0.991509i	$-0.541510\pi$
$307$	−4.55690	−0.260076	−0.130038	+	0.991509i	$0.541510\pi$
$308$	28.3991	1.61819
$309$	−1.75931	−0.100084
$310$	−0.727653	−0.0413279
$311$	9.73597	0.552076	0.276038	−	0.961147i	$-0.410978\pi$
$311$	9.73597	0.552076	0.276038	+	0.961147i	$0.410978\pi$
$312$	82.4087	4.66547
$313$	−27.0676	−1.52995	−0.764975	−	0.644059i	$-0.777249\pi$
$313$	−27.0676	−1.52995	−0.764975	+	0.644059i	$0.777249\pi$
$314$	−12.1146	−0.683668
$315$	−0.708384	−0.0399129
$316$	−74.9440	−4.21593
$317$	−2.06045	−0.115727	−0.0578633	−	0.998325i	$-0.518429\pi$
$317$	−2.06045	−0.115727	−0.0578633	+	0.998325i	$0.518429\pi$
$318$	30.9559	1.73592
$319$	−30.2795	−1.69533
$320$	−14.7555	−0.824859
$321$	−0.987104	−0.0550948
$322$	7.83933	0.436869
$323$	−9.28442	−0.516599
$324$	−32.2191	−1.78995
$325$	6.70734	0.372057
$326$	−48.5872	−2.69100
$327$	25.0393	1.38467
$328$	−94.8199	−5.23555
$329$	1.30017	0.0716809
$330$	22.5878	1.24342
$331$	25.6871	1.41189	0.705946	−	0.708266i	$-0.250522\pi$
$331$	25.6871	1.41189	0.705946	+	0.708266i	$0.250522\pi$
$332$	−13.3581	−0.733121
$333$	−8.55813	−0.468983
$334$	−25.3612	−1.38770
$335$	−11.2045	−0.612170
$336$	17.3291	0.945378
$337$	−36.4109	−1.98343	−0.991715	−	0.128459i	$-0.958997\pi$
$337$	−36.4109	−1.98343	−0.991715	+	0.128459i	$0.958997\pi$
$338$	−84.9686	−4.62168
$339$	−16.7147	−0.907818
$340$	17.7022	0.960034
$341$	1.53885	0.0833336
$342$	4.98918	0.269784
$343$	−1.00000	−0.0539949
$344$	20.9558	1.12986
$345$	4.46771	0.240533
$346$	25.6937	1.38130
$347$	−23.3057	−1.25111	−0.625557	−	0.780179i	$-0.715128\pi$
$347$	−23.3057	−1.25111	−0.625557	+	0.780179i	$0.715128\pi$
$348$	−41.2524	−2.21136
$349$	9.01582	0.482606	0.241303	−	0.970450i	$-0.422425\pi$
$349$	9.01582	0.482606	0.241303	+	0.970450i	$0.422425\pi$
$350$	2.65622	0.141981
$351$	37.6536	2.00980
$352$	79.6233	4.24394
$353$	−13.3093	−0.708384	−0.354192	−	0.935173i	$-0.615244\pi$
$353$	−13.3093	−0.708384	−0.354192	+	0.935173i	$0.615244\pi$
$354$	−27.7376	−1.47424
$355$	15.2309	0.808372
$356$	−43.0948	−2.28402
$357$	−5.30067	−0.280541
$358$	26.0449	1.37652
$359$	−26.6487	−1.40646	−0.703232	−	0.710960i	$-0.748261\pi$
$359$	−26.6487	−1.40646	−0.703232	+	0.710960i	$0.748261\pi$
$360$	−5.74937	−0.303018
$361$	−11.9694	−0.629970
$362$	17.5335	0.921543
$363$	−31.1172	−1.63323
$364$	−33.9092	−1.77732
$365$	−2.48419	−0.130029
$366$	10.2343	0.534955
$367$	−3.89802	−0.203475	−0.101738	−	0.994811i	$-0.532440\pi$
$367$	−3.89802	−0.203475	−0.101738	+	0.994811i	$0.532440\pi$
$368$	33.7846	1.76114
$369$	−8.27593	−0.430827
$370$	32.0904	1.66830
$371$	−7.69853	−0.399688
$372$	2.09651	0.108699
$373$	−7.23732	−0.374734	−0.187367	−	0.982290i	$-0.559995\pi$
$373$	−7.23732	−0.374734	−0.187367	+	0.982290i	$0.559995\pi$
$374$	−52.2471	−2.70163
$375$	1.51381	0.0781727
$376$	10.5524	0.544201
$377$	36.1544	1.86205
$378$	14.9115	0.766963
$379$	−25.4219	−1.30583	−0.652916	−	0.757430i	$-0.726455\pi$
$379$	−25.4219	−1.30583	−0.652916	+	0.757430i	$0.726455\pi$
$380$	−13.4048	−0.687654
$381$	19.2267	0.985013
$382$	−4.31420	−0.220734
$383$	−14.8565	−0.759130	−0.379565	−	0.925165i	$-0.623926\pi$
$383$	−14.8565	−0.759130	−0.379565	+	0.925165i	$0.623926\pi$
$384$	16.4178	0.837818
$385$	−5.61743	−0.286291
$386$	−37.9550	−1.93186
$387$	1.82903	0.0929750
$388$	−50.0189	−2.53932
$389$	38.7818	1.96632	0.983158	−	0.182759i	$-0.0585029\pi$
$389$	38.7818	1.96632	0.983158	+	0.182759i	$0.0585029\pi$
$390$	−26.9703	−1.36570
$391$	−10.3341	−0.522619
$392$	−8.11618	−0.409929
$393$	21.0729	1.06299
$394$	−40.4779	−2.03925
$395$	14.8242	0.745885
$396$	20.1175	1.01094
$397$	38.4140	1.92794	0.963972	−	0.266003i	$-0.0857033\pi$
$397$	38.4140	1.92794	0.963972	+	0.266003i	$0.0857033\pi$
$398$	62.7515	3.14545
$399$	4.01390	0.200946
$400$	11.4473	0.572366
$401$	−28.4830	−1.42238	−0.711188	−	0.703002i	$-0.751842\pi$
$401$	−28.4830	−1.42238	−0.711188	+	0.703002i	$0.751842\pi$
$402$	45.0536	2.24707
$403$	−1.83743	−0.0915287
$404$	81.8669	4.07303
$405$	6.37304	0.316679
$406$	14.3178	0.710580
$407$	−67.8653	−3.36396
$408$	−43.0211	−2.12986
$409$	−1.98230	−0.0980186	−0.0490093	−	0.998798i	$-0.515606\pi$
$409$	−1.98230	−0.0980186	−0.0490093	+	0.998798i	$0.515606\pi$
$410$	31.0322	1.53257
$411$	19.3195	0.952961
$412$	5.87541	0.289461
$413$	6.89816	0.339436
$414$	5.55326	0.272928
$415$	2.64228	0.129704
$416$	−95.0721	−4.66129
$417$	16.5503	0.810474
$418$	39.5638	1.93513
$419$	5.48057	0.267743	0.133872	−	0.990999i	$-0.457259\pi$
$419$	5.48057	0.267743	0.133872	+	0.990999i	$0.457259\pi$
$420$	−7.65310	−0.373433
$421$	10.4433	0.508977	0.254489	−	0.967076i	$-0.418093\pi$
$421$	10.4433	0.508977	0.254489	+	0.967076i	$0.418093\pi$
$422$	−41.0778	−1.99964
$423$	0.921022	0.0447816
$424$	−62.4826	−3.03442
$425$	−3.50154	−0.169850
$426$	−61.2437	−2.96727
$427$	−2.54520	−0.123171
$428$	3.29654	0.159344
$429$	57.0374	2.75379
$430$	−6.85832	−0.330738
$431$	31.3523	1.51019	0.755094	−	0.655617i	$-0.227591\pi$
$431$	31.3523	1.51019	0.755094	+	0.655617i	$0.227591\pi$
$432$	64.2628	3.09185
$433$	−5.66794	−0.272384	−0.136192	−	0.990682i	$-0.543486\pi$
$433$	−5.66794	−0.272384	−0.136192	+	0.990682i	$0.543486\pi$
$434$	−0.727653	−0.0349284
$435$	8.15985	0.391235
$436$	−83.6214	−4.00474
$437$	7.82545	0.374342
$438$	9.98898	0.477292
$439$	13.7505	0.656277	0.328138	−	0.944630i	$-0.393579\pi$
$439$	13.7505	0.656277	0.328138	+	0.944630i	$0.393579\pi$
$440$	−45.5921	−2.17352
$441$	−0.708384	−0.0337326
$442$	62.3842	2.96732
$443$	−5.84652	−0.277777	−0.138888	−	0.990308i	$-0.544353\pi$
$443$	−5.84652	−0.277777	−0.138888	+	0.990308i	$0.544353\pi$
$444$	−92.4587	−4.38790
$445$	8.52428	0.404090
$446$	−13.9006	−0.658215
$447$	−8.77558	−0.415071
$448$	−14.7555	−0.697133
$449$	32.0260	1.51140	0.755700	−	0.654918i	$-0.227297\pi$
$449$	32.0260	1.51140	0.755700	+	0.654918i	$0.227297\pi$
$450$	1.88163	0.0887007
$451$	−65.6275	−3.09028
$452$	55.8206	2.62558
$453$	−21.0404	−0.988565
$454$	9.16143	0.429967
$455$	6.70734	0.314445
$456$	32.5775	1.52558
$457$	−6.31353	−0.295335	−0.147667	−	0.989037i	$-0.547176\pi$
$457$	−6.31353	−0.295335	−0.147667	+	0.989037i	$0.547176\pi$
$458$	−2.65622	−0.124117
$459$	−19.6569	−0.917506
$460$	−14.9204	−0.695668
$461$	−19.4989	−0.908155	−0.454078	−	0.890962i	$-0.650031\pi$
$461$	−19.4989	−0.908155	−0.454078	+	0.890962i	$0.650031\pi$
$462$	22.5878	1.05088
$463$	−10.8987	−0.506504	−0.253252	−	0.967400i	$-0.581500\pi$
$463$	−10.8987	−0.506504	−0.253252	+	0.967400i	$0.581500\pi$
$464$	61.7043	2.86455
$465$	−0.414696	−0.0192311
$466$	−22.5691	−1.04549
$467$	11.1970	0.518137	0.259069	−	0.965859i	$-0.416584\pi$
$467$	11.1970	0.518137	0.259069	+	0.965859i	$0.416584\pi$
$468$	−24.0207	−1.11036
$469$	−11.2045	−0.517378
$470$	−3.45355	−0.159301
$471$	−6.90425	−0.318131
$472$	55.9867	2.57699
$473$	14.5041	0.666899
$474$	−59.6082	−2.73789
$475$	2.65152	0.121660
$476$	17.7022	0.811377
$477$	−5.45351	−0.249699
$478$	−71.9005	−3.28865
$479$	−2.34399	−0.107100	−0.0535499	−	0.998565i	$-0.517054\pi$
$479$	−2.34399	−0.107100	−0.0535499	+	0.998565i	$0.517054\pi$
$480$	−21.4572	−0.979383
$481$	81.0328	3.69478
$482$	80.0386	3.64566
$483$	4.46771	0.203288
$484$	103.919	4.72360
$485$	9.89389	0.449258
$486$	19.1083	0.866771
$487$	25.0498	1.13512	0.567558	−	0.823334i	$-0.307888\pi$
$487$	25.0498	1.13512	0.567558	+	0.823334i	$0.307888\pi$
$488$	−20.6573	−0.935112
$489$	−27.6903	−1.25220
$490$	2.65622	0.119996
$491$	35.7735	1.61444	0.807218	−	0.590253i	$-0.200972\pi$
$491$	35.7735	1.61444	0.807218	+	0.590253i	$0.200972\pi$
$492$	−89.4099	−4.03091
$493$	−18.8743	−0.850055
$494$	−47.2401	−2.12543
$495$	−3.97930	−0.178856
$496$	−3.13591	−0.140806
$497$	15.2309	0.683199
$498$	−10.6246	−0.476101
$499$	10.2451	0.458632	0.229316	−	0.973352i	$-0.426351\pi$
$499$	10.2451	0.458632	0.229316	+	0.973352i	$0.426351\pi$
$500$	−5.05553	−0.226090
$501$	−14.4536	−0.645738
$502$	−78.8495	−3.51923
$503$	2.11048	0.0941015	0.0470508	−	0.998892i	$-0.485018\pi$
$503$	2.11048	0.0941015	0.0470508	+	0.998892i	$0.485018\pi$
$504$	−5.74937	−0.256097
$505$	−16.1935	−0.720602
$506$	44.0369	1.95768
$507$	−48.4244	−2.15060
$508$	−64.2096	−2.84884
$509$	−12.4030	−0.549754	−0.274877	−	0.961479i	$-0.588637\pi$
$509$	−12.4030	−0.549754	−0.274877	+	0.961479i	$0.588637\pi$
$510$	14.0798	0.623462
$511$	−2.48419	−0.109894
$512$	23.5589	1.04117
$513$	14.8851	0.657192
$514$	−43.8334	−1.93341
$515$	−1.16218	−0.0512116
$516$	19.7602	0.869893
$517$	7.30364	0.321214
$518$	32.0904	1.40997
$519$	14.6431	0.642759
$520$	54.4380	2.38726
$521$	−43.2220	−1.89359	−0.946795	−	0.321838i	$-0.895699\pi$
$521$	−43.2220	−1.89359	−0.946795	+	0.321838i	$0.895699\pi$
$522$	10.1425	0.443925
$523$	−10.6599	−0.466126	−0.233063	−	0.972462i	$-0.574875\pi$
$523$	−10.6599	−0.466126	−0.233063	+	0.972462i	$0.574875\pi$
$524$	−70.3753	−3.07436
$525$	1.51381	0.0660680
$526$	34.4743	1.50315
$527$	0.959221	0.0417843
$528$	97.3448	4.23639
$529$	−14.2898	−0.621296
$530$	20.4490	0.888249
$531$	4.88654	0.212058
$532$	−13.4048	−0.581174
$533$	78.3607	3.39418
$534$	−34.2763	−1.48328
$535$	−0.652067	−0.0281913
$536$	−90.9380	−3.92792
$537$	14.8433	0.640534
$538$	26.4386	1.13985
$539$	−5.61743	−0.241960
$540$	−28.3807	−1.22131
$541$	−23.7434	−1.02081	−0.510405	−	0.859934i	$-0.670504\pi$
$541$	−23.7434	−1.02081	−0.510405	+	0.859934i	$0.670504\pi$
$542$	−53.0501	−2.27870
$543$	9.99254	0.428821
$544$	49.6320	2.12795
$545$	16.5406	0.708520
$546$	−26.9703	−1.15422
$547$	−4.77270	−0.204066	−0.102033	−	0.994781i	$-0.532535\pi$
$547$	−4.77270	−0.204066	−0.102033	+	0.994781i	$0.532535\pi$
$548$	−64.5196	−2.75614
$549$	−1.80298	−0.0769493
$550$	14.9212	0.636241
$551$	14.2924	0.608878
$552$	36.2607	1.54336
$553$	14.8242	0.630387
$554$	54.8247	2.32928
$555$	18.2886	0.776309
$556$	−55.2717	−2.34404
$557$	15.0751	0.638754	0.319377	−	0.947628i	$-0.396526\pi$
$557$	15.0751	0.638754	0.319377	+	0.947628i	$0.396526\pi$
$558$	−0.515457	−0.0218211
$559$	−17.3182	−0.732483
$560$	11.4473	0.483738
$561$	−29.7761	−1.25715
$562$	−53.7326	−2.26657
$563$	40.7045	1.71549	0.857744	−	0.514076i	$-0.171865\pi$
$563$	40.7045	1.71549	0.857744	+	0.514076i	$0.171865\pi$
$564$	9.95037	0.418986
$565$	−11.0415	−0.464519
$566$	−29.7029	−1.24851
$567$	6.37304	0.267643
$568$	123.617	5.18684
$569$	−15.6312	−0.655294	−0.327647	−	0.944800i	$-0.606256\pi$
$569$	−15.6312	−0.655294	−0.327647	+	0.944800i	$0.606256\pi$
$570$	−10.6618	−0.446574
$571$	−32.6103	−1.36470	−0.682350	−	0.731026i	$-0.739042\pi$
$571$	−32.6103	−1.36470	−0.682350	+	0.731026i	$0.739042\pi$
$572$	−190.483	−7.96448
$573$	−2.45870	−0.102714
$574$	31.0322	1.29526
$575$	2.95131	0.123078
$576$	−10.4526	−0.435524
$577$	38.0912	1.58576	0.792878	−	0.609380i	$-0.208582\pi$
$577$	38.0912	1.58576	0.792878	+	0.609380i	$0.208582\pi$
$578$	12.5884	0.523607
$579$	−21.6309	−0.898951
$580$	−27.2507	−1.13152
$581$	2.64228	0.109620
$582$	−39.7835	−1.64908
$583$	−43.2460	−1.79106
$584$	−20.1622	−0.834316
$585$	4.75137	0.196445
$586$	−45.6883	−1.88737
$587$	−10.2691	−0.423852	−0.211926	−	0.977286i	$-0.567974\pi$
$587$	−10.2691	−0.423852	−0.211926	+	0.977286i	$0.567974\pi$
$588$	−7.65310	−0.315609
$589$	−0.726364	−0.0299293
$590$	−18.3231	−0.754348
$591$	−23.0688	−0.948922
$592$	138.297	5.68399
$593$	−21.1890	−0.870130	−0.435065	−	0.900399i	$-0.643275\pi$
$593$	−21.1890	−0.870130	−0.435065	+	0.900399i	$0.643275\pi$
$594$	83.7642	3.43689
$595$	−3.50154	−0.143549
$596$	29.3070	1.20046
$597$	35.7627	1.46367
$598$	−52.5811	−2.15020
$599$	20.8047	0.850057	0.425029	−	0.905180i	$-0.360264\pi$
$599$	20.8047	0.850057	0.425029	+	0.905180i	$0.360264\pi$
$600$	12.2863	0.501588
$601$	3.30127	0.134662	0.0673308	−	0.997731i	$-0.478552\pi$
$601$	3.30127	0.134662	0.0673308	+	0.997731i	$0.478552\pi$
$602$	−6.85832	−0.279524
$603$	−7.93712	−0.323224
$604$	70.2668	2.85912
$605$	−20.5556	−0.835702
$606$	65.1144	2.64509
$607$	22.6403	0.918940	0.459470	−	0.888193i	$-0.348039\pi$
$607$	22.6403	0.918940	0.459470	+	0.888193i	$0.348039\pi$
$608$	−37.5835	−1.52421
$609$	8.15985	0.330654
$610$	6.76062	0.273730
$611$	−8.72071	−0.352802
$612$	12.5399	0.506896
$613$	−3.14411	−0.126990	−0.0634948	−	0.997982i	$-0.520225\pi$
$613$	−3.14411	−0.126990	−0.0634948	+	0.997982i	$0.520225\pi$
$614$	12.1042	0.488484
$615$	17.6856	0.713151
$616$	−45.5921	−1.83696
$617$	−0.941897	−0.0379193	−0.0189597	−	0.999820i	$-0.506035\pi$
$617$	−0.941897	−0.0379193	−0.0189597	+	0.999820i	$0.506035\pi$
$618$	4.67312	0.187981
$619$	−23.1470	−0.930358	−0.465179	−	0.885217i	$-0.654010\pi$
$619$	−23.1470	−0.930358	−0.465179	+	0.885217i	$0.654010\pi$
$620$	1.38492	0.0556199
$621$	16.5680	0.664850
$622$	−25.8609	−1.03693
$623$	8.52428	0.341518
$624$	−116.232	−4.65300
$625$	1.00000	0.0400000
$626$	71.8976	2.87361
$627$	22.5478	0.900472
$628$	23.0575	0.920094
$629$	−42.3028	−1.68672
$630$	1.88163	0.0749658
$631$	36.7727	1.46390	0.731950	−	0.681358i	$-0.238610\pi$
$631$	36.7727	1.46390	0.731950	+	0.681358i	$0.238610\pi$
$632$	120.315	4.78589
$633$	−23.4106	−0.930489
$634$	5.47303	0.217362
$635$	12.7009	0.504019
$636$	−58.9176	−2.33624
$637$	6.70734	0.265755
$638$	80.4292	3.18422
$639$	10.7893	0.426819
$640$	10.8454	0.428701
$641$	−42.2603	−1.66918	−0.834590	−	0.550872i	$-0.814295\pi$
$641$	−42.2603	−1.66918	−0.834590	+	0.550872i	$0.814295\pi$
$642$	2.62197	0.103481
$643$	7.65256	0.301788	0.150894	−	0.988550i	$-0.451785\pi$
$643$	7.65256	0.301788	0.150894	+	0.988550i	$0.451785\pi$
$644$	−14.9204	−0.587947
$645$	−3.90862	−0.153902
$646$	24.6615	0.970294
$647$	−22.2364	−0.874204	−0.437102	−	0.899412i	$-0.643995\pi$
$647$	−22.2364	−0.874204	−0.437102	+	0.899412i	$0.643995\pi$
$648$	51.7247	2.03194
$649$	38.7499	1.52107
$650$	−17.8162	−0.698809
$651$	−0.414696	−0.0162532
$652$	92.4749	3.62160
$653$	44.7336	1.75056	0.875281	−	0.483614i	$-0.160676\pi$
$653$	44.7336	1.75056	0.875281	+	0.483614i	$0.160676\pi$
$654$	−66.5099	−2.60074
$655$	13.9205	0.543917
$656$	133.737	5.22156
$657$	−1.75976	−0.0686549
$658$	−3.45355	−0.134634
$659$	−1.41094	−0.0549625	−0.0274812	−	0.999622i	$-0.508749\pi$
$659$	−1.41094	−0.0549625	−0.0274812	+	0.999622i	$0.508749\pi$
$660$	−42.9908	−1.67341
$661$	20.0899	0.781407	0.390704	−	0.920516i	$-0.372232\pi$
$661$	20.0899	0.781407	0.390704	+	0.920516i	$0.372232\pi$
$662$	−68.2307	−2.65186
$663$	35.5534	1.38078
$664$	21.4452	0.832234
$665$	2.65152	0.102822
$666$	22.7323	0.880859
$667$	15.9084	0.615974
$668$	48.2693	1.86760
$669$	−7.92211	−0.306287
$670$	29.7618	1.14980
$671$	−14.2975	−0.551948
$672$	−21.4572	−0.827730
$673$	15.3919	0.593315	0.296658	−	0.954984i	$-0.404128\pi$
$673$	15.3919	0.593315	0.296658	+	0.954984i	$0.404128\pi$
$674$	96.7156	3.72535
$675$	5.61378	0.216075
$676$	161.719	6.21995
$677$	45.5583	1.75095	0.875475	−	0.483264i	$-0.160549\pi$
$677$	45.5583	1.75095	0.875475	+	0.483264i	$0.160549\pi$
$678$	44.3980	1.70510
$679$	9.89389	0.379693
$680$	−28.4191	−1.08982
$681$	5.22119	0.200076
$682$	−4.08754	−0.156520
$683$	11.6283	0.444943	0.222472	−	0.974939i	$-0.428587\pi$
$683$	11.6283	0.444943	0.222472	+	0.974939i	$0.428587\pi$
$684$	−9.49578	−0.363080
$685$	12.7622	0.487618
$686$	2.65622	0.101415
$687$	−1.51381	−0.0577554
$688$	−29.5568	−1.12684
$689$	51.6367	1.96720
$690$	−11.8672	−0.451778
$691$	41.4396	1.57644	0.788219	−	0.615395i	$-0.211003\pi$
$691$	41.4396	1.57644	0.788219	+	0.615395i	$0.211003\pi$
$692$	−48.9021	−1.85898
$693$	−3.97930	−0.151161
$694$	61.9051	2.34988
$695$	10.9329	0.414709
$696$	66.2268	2.51032
$697$	−40.9079	−1.54950
$698$	−23.9480	−0.906447
$699$	−12.8624	−0.486500
$700$	−5.05553	−0.191081
$701$	−42.4078	−1.60172	−0.800860	−	0.598851i	$-0.795624\pi$
$701$	−42.4078	−1.60172	−0.800860	+	0.598851i	$0.795624\pi$
$702$	−100.016	−3.77487
$703$	32.0336	1.20817
$704$	−82.8882	−3.12397
$705$	−1.96821	−0.0741272
$706$	35.3525	1.33051
$707$	−16.1935	−0.609020
$708$	52.7923	1.98406
$709$	21.1732	0.795176	0.397588	−	0.917564i	$-0.369847\pi$
$709$	21.1732	0.795176	0.397588	+	0.917564i	$0.369847\pi$
$710$	−40.4567	−1.51831
$711$	10.5012	0.393826
$712$	69.1846	2.59280
$713$	−0.808488	−0.0302781
$714$	14.0798	0.526922
$715$	37.6781	1.40908
$716$	−49.5707	−1.85254
$717$	−40.9768	−1.53031
$718$	70.7850	2.64167
$719$	10.6007	0.395341	0.197670	−	0.980269i	$-0.436662\pi$
$719$	10.6007	0.395341	0.197670	+	0.980269i	$0.436662\pi$
$720$	8.10910	0.302208
$721$	−1.16218	−0.0432817
$722$	31.7935	1.18323
$723$	45.6148	1.69643
$724$	−33.3712	−1.24023
$725$	5.39028	0.200190
$726$	82.6542	3.06758
$727$	3.04442	0.112911	0.0564556	−	0.998405i	$-0.482020\pi$
$727$	3.04442	0.112911	0.0564556	+	0.998405i	$0.482020\pi$
$728$	54.4380	2.01761
$729$	30.0091	1.11145
$730$	6.59858	0.244224
$731$	9.04092	0.334390
$732$	−19.4787	−0.719953
$733$	43.1521	1.59386	0.796929	−	0.604073i	$-0.206457\pi$
$733$	43.1521	1.59386	0.796929	+	0.604073i	$0.206457\pi$
$734$	10.3540	0.382174
$735$	1.51381	0.0558377
$736$	−41.8327	−1.54198
$737$	−62.9408	−2.31845
$738$	21.9827	0.809195
$739$	−3.66420	−0.134790	−0.0673948	−	0.997726i	$-0.521469\pi$
$739$	−3.66420	−0.134790	−0.0673948	+	0.997726i	$0.521469\pi$
$740$	−61.0769	−2.24523
$741$	−26.9226	−0.989026
$742$	20.4490	0.750707
$743$	11.6927	0.428963	0.214482	−	0.976728i	$-0.431194\pi$
$743$	11.6927	0.428963	0.214482	+	0.976728i	$0.431194\pi$
$744$	−3.36575	−0.123394
$745$	−5.79702	−0.212386
$746$	19.2239	0.703838
$747$	1.87175	0.0684836
$748$	99.4407	3.63591
$749$	−0.652067	−0.0238260
$750$	−4.02102	−0.146827
$751$	−48.2460	−1.76052	−0.880260	−	0.474492i	$-0.842632\pi$
$751$	−48.2460	−1.76052	−0.880260	+	0.474492i	$0.842632\pi$
$752$	−14.8835	−0.542746
$753$	−44.9371	−1.63760
$754$	−96.0343	−3.49736
$755$	−13.8990	−0.505836
$756$	−28.3807	−1.03219
$757$	−42.0645	−1.52886	−0.764430	−	0.644706i	$-0.776980\pi$
$757$	−42.0645	−1.52886	−0.764430	+	0.644706i	$0.776980\pi$
$758$	67.5262	2.45266
$759$	25.0971	0.910966
$760$	21.5202	0.780620
$761$	−9.95970	−0.361039	−0.180519	−	0.983571i	$-0.557778\pi$
$761$	−9.95970	−0.361039	−0.180519	+	0.983571i	$0.557778\pi$
$762$	−51.0704	−1.85009
$763$	16.5406	0.598809
$764$	8.21111	0.297068
$765$	−2.48044	−0.0896804
$766$	39.4621	1.42582
$767$	−46.2683	−1.67065
$768$	1.06471	0.0384193
$769$	−17.4058	−0.627670	−0.313835	−	0.949478i	$-0.601614\pi$
$769$	−17.4058	−0.627670	−0.313835	+	0.949478i	$0.601614\pi$
$770$	14.9212	0.537721
$771$	−24.9811	−0.899672
$772$	72.2389	2.59994
$773$	10.5363	0.378965	0.189483	−	0.981884i	$-0.439319\pi$
$773$	10.5363	0.378965	0.189483	+	0.981884i	$0.439319\pi$
$774$	−4.85833	−0.174629
$775$	−0.273942	−0.00984030
$776$	80.3005	2.88262
$777$	18.2886	0.656101
$778$	−103.013	−3.69320
$779$	30.9773	1.10988
$780$	51.3320	1.83798
$781$	85.5585	3.06153
$782$	27.4498	0.981601
$783$	30.2598	1.08140
$784$	11.4473	0.408833
$785$	−4.56085	−0.162784
$786$	−55.9744	−1.99654
$787$	−18.7895	−0.669773	−0.334887	−	0.942258i	$-0.608698\pi$
$787$	−18.7895	−0.669773	−0.334887	+	0.942258i	$0.608698\pi$
$788$	77.0407	2.74446
$789$	19.6472	0.699460
$790$	−39.3763	−1.40095
$791$	−11.0415	−0.392590
$792$	−32.2967	−1.14761
$793$	17.0715	0.606228
$794$	−102.036	−3.62113
$795$	11.6541	0.413328
$796$	−119.434	−4.23321
$797$	12.9079	0.457220	0.228610	−	0.973518i	$-0.426582\pi$
$797$	12.9079	0.457220	0.228610	+	0.973518i	$0.426582\pi$
$798$	−10.6618	−0.377424
$799$	4.55262	0.161060
$800$	−14.1743	−0.501138
$801$	6.03846	0.213359
$802$	75.6574	2.67155
$803$	−13.9548	−0.492454
$804$	−85.7495	−3.02415
$805$	2.95131	0.104020
$806$	4.88062	0.171912
$807$	15.0676	0.530406
$808$	−131.430	−4.62367
$809$	0.308333	0.0108404	0.00542021	−	0.999985i	$-0.498275\pi$
$809$	0.308333	0.0108404	0.00542021	+	0.999985i	$0.498275\pi$
$810$	−16.9282	−0.594797
$811$	−0.768081	−0.0269710	−0.0134855	−	0.999909i	$-0.504293\pi$
$811$	−0.768081	−0.0269710	−0.0134855	+	0.999909i	$0.504293\pi$
$812$	−27.2507	−0.956313
$813$	−30.2338	−1.06035
$814$	180.266	6.31830
$815$	−18.2918	−0.640735
$816$	60.6785	2.12417
$817$	−6.84618	−0.239517
$818$	5.26545	0.184102
$819$	4.75137	0.166026
$820$	−59.0629	−2.06257
$821$	55.2580	1.92852	0.964258	−	0.264965i	$-0.0853603\pi$
$821$	55.2580	1.92852	0.964258	+	0.264965i	$0.0853603\pi$
$822$	−51.3169	−1.78988
$823$	−4.39604	−0.153236	−0.0766182	−	0.997061i	$-0.524412\pi$
$823$	−4.39604	−0.153236	−0.0766182	+	0.997061i	$0.524412\pi$
$824$	−9.43242	−0.328594
$825$	8.50372	0.296061
$826$	−18.3231	−0.637541
$827$	15.2604	0.530658	0.265329	−	0.964158i	$-0.414519\pi$
$827$	15.2604	0.530658	0.265329	+	0.964158i	$0.414519\pi$
$828$	−10.5694	−0.367311
$829$	10.4854	0.364174	0.182087	−	0.983282i	$-0.441715\pi$
$829$	10.4854	0.364174	0.182087	+	0.983282i	$0.441715\pi$
$830$	−7.01848	−0.243615
$831$	31.2451	1.08388
$832$	98.9704	3.43118
$833$	−3.50154	−0.121321
$834$	−43.9614	−1.52226
$835$	−9.54782	−0.330416
$836$	−75.3008	−2.60433
$837$	−1.53785	−0.0531560
$838$	−14.5576	−0.502885
$839$	−20.3896	−0.703926	−0.351963	−	0.936014i	$-0.614486\pi$
$839$	−20.3896	−0.703926	−0.351963	+	0.936014i	$0.614486\pi$
$840$	12.2863	0.423919
$841$	0.0550947	0.00189982
$842$	−27.7399	−0.955978
$843$	−30.6227	−1.05470
$844$	78.1824	2.69115
$845$	−31.9885	−1.10044
$846$	−2.44644	−0.0841104
$847$	−20.5556	−0.706297
$848$	88.1276	3.02631
$849$	−16.9280	−0.580967
$850$	9.30089	0.319018
$851$	35.6553	1.22225
$852$	116.564	3.99340
$853$	40.9355	1.40161	0.700803	−	0.713355i	$-0.252825\pi$
$853$	40.9355	1.40161	0.700803	+	0.713355i	$0.252825\pi$
$854$	6.76062	0.231344
$855$	1.87830	0.0642364
$856$	−5.29229	−0.180887
$857$	−41.6726	−1.42351	−0.711754	−	0.702429i	$-0.752099\pi$
$857$	−41.6726	−1.42351	−0.711754	+	0.702429i	$0.752099\pi$
$858$	−151.504	−5.17226
$859$	−4.02910	−0.137471	−0.0687355	−	0.997635i	$-0.521896\pi$
$859$	−4.02910	−0.137471	−0.0687355	+	0.997635i	$0.521896\pi$
$860$	13.0533	0.445113
$861$	17.6856	0.602722
$862$	−83.2788	−2.83649
$863$	10.7325	0.365340	0.182670	−	0.983174i	$-0.441526\pi$
$863$	10.7325	0.365340	0.182670	+	0.983174i	$0.441526\pi$
$864$	−79.5716	−2.70708
$865$	9.67300	0.328892
$866$	15.0553	0.511601
$867$	7.17423	0.243650
$868$	1.38492	0.0470074
$869$	83.2737	2.82487
$870$	−21.6744	−0.734831
$871$	75.1527	2.54645
$872$	134.246	4.54615
$873$	7.00867	0.237208
$874$	−20.7862	−0.703102
$875$	1.00000	0.0338062
$876$	−19.0118	−0.642349
$877$	33.2601	1.12311	0.561557	−	0.827438i	$-0.310203\pi$
$877$	33.2601	1.12311	0.561557	+	0.827438i	$0.310203\pi$
$878$	−36.5245	−1.23264
$879$	−26.0382	−0.878248
$880$	64.3046	2.16771
$881$	−1.76688	−0.0595276	−0.0297638	−	0.999557i	$-0.509476\pi$
$881$	−1.76688	−0.0595276	−0.0297638	+	0.999557i	$0.509476\pi$
$882$	1.88163	0.0633577
$883$	6.54931	0.220402	0.110201	−	0.993909i	$-0.464851\pi$
$883$	6.54931	0.220402	0.110201	+	0.993909i	$0.464851\pi$
$884$	−118.734	−3.99347
$885$	−10.4425	−0.351020
$886$	15.5297	0.521730
$887$	51.1135	1.71622	0.858112	−	0.513462i	$-0.171637\pi$
$887$	51.1135	1.71622	0.858112	+	0.513462i	$0.171637\pi$
$888$	148.434	4.98111
$889$	12.7009	0.425974
$890$	−22.6424	−0.758975
$891$	35.8001	1.19935
$892$	26.4568	0.885838
$893$	−3.44744	−0.115364
$894$	23.3099	0.779600
$895$	9.80524	0.327753
$896$	10.8454	0.362318
$897$	−29.9665	−1.00055
$898$	−85.0682	−2.83876
$899$	−1.47663	−0.0492482
$900$	−3.58126	−0.119375
$901$	−26.9567	−0.898059
$902$	174.321	5.80427
$903$	−3.90862	−0.130071
$904$	−89.6147	−2.98054
$905$	6.60093	0.219422
$906$	55.8881	1.85676
$907$	37.1475	1.23346	0.616731	−	0.787174i	$-0.288457\pi$
$907$	37.1475	1.23346	0.616731	+	0.787174i	$0.288457\pi$
$908$	−17.4367	−0.578658
$909$	−11.4712	−0.380477
$910$	−17.8162	−0.590602
$911$	−3.48687	−0.115525	−0.0577625	−	0.998330i	$-0.518397\pi$
$911$	−3.48687	−0.115525	−0.0577625	+	0.998330i	$0.518397\pi$
$912$	−45.9484	−1.52150
$913$	14.8428	0.491225
$914$	16.7702	0.554708
$915$	3.85295	0.127374
$916$	5.05553	0.167039
$917$	13.9205	0.459694
$918$	52.2132	1.72329
$919$	4.78324	0.157785	0.0788923	−	0.996883i	$-0.474862\pi$
$919$	4.78324	0.157785	0.0788923	+	0.996883i	$0.474862\pi$
$920$	23.9533	0.789717
$921$	6.89828	0.227306
$922$	51.7935	1.70573
$923$	−102.159	−3.36260
$924$	−42.9908	−1.41429
$925$	12.0812	0.397227
$926$	28.9493	0.951334
$927$	−0.823266	−0.0270396
$928$	−76.4035	−2.50807
$929$	21.3587	0.700756	0.350378	−	0.936608i	$-0.386053\pi$
$929$	21.3587	0.700756	0.350378	+	0.936608i	$0.386053\pi$
$930$	1.10153	0.0361205
$931$	2.65152	0.0869001
$932$	42.9553	1.40705
$933$	−14.7384	−0.482514
$934$	−29.7419	−0.973183
$935$	−19.6697	−0.643267
$936$	38.5630	1.26047
$937$	−34.6083	−1.13061	−0.565303	−	0.824884i	$-0.691241\pi$
$937$	−34.6083	−1.13061	−0.565303	+	0.824884i	$0.691241\pi$
$938$	29.7618	0.971757
$939$	40.9752	1.33717
$940$	6.57307	0.214390
$941$	−18.5399	−0.604384	−0.302192	−	0.953247i	$-0.597718\pi$
$941$	−18.5399	−0.604384	−0.302192	+	0.953247i	$0.597718\pi$
$942$	18.3392	0.597524
$943$	34.4796	1.12281
$944$	−78.9655	−2.57011
$945$	5.61378	0.182616
$946$	−38.5262	−1.25259
$947$	−18.2536	−0.593161	−0.296580	−	0.955008i	$-0.595846\pi$
$947$	−18.2536	−0.593161	−0.296580	+	0.955008i	$0.595846\pi$
$948$	113.451	3.68471
$949$	16.6623	0.540883
$950$	−7.04304	−0.228506
$951$	3.11913	0.101145
$952$	−28.4191	−0.921070
$953$	−9.62462	−0.311772	−0.155886	−	0.987775i	$-0.549823\pi$
$953$	−9.62462	−0.311772	−0.155886	+	0.987775i	$0.549823\pi$
$954$	14.4858	0.468994
$955$	−1.62418	−0.0525573
$956$	136.847	4.42594
$957$	45.8374	1.48171
$958$	6.22617	0.201158
$959$	12.7622	0.412112
$960$	22.3370	0.720925
$961$	−30.9250	−0.997579
$962$	−215.241	−6.93966
$963$	−0.461914	−0.0148850
$964$	−152.336	−4.90640
$965$	−14.2891	−0.459982
$966$	−11.8672	−0.381822
$967$	−6.76836	−0.217656	−0.108828	−	0.994061i	$-0.534710\pi$
$967$	−6.76836	−0.217656	−0.108828	+	0.994061i	$0.534710\pi$
$968$	−166.832	−5.36220
$969$	14.0548	0.451506
$970$	−26.2804	−0.843813
$971$	−20.6510	−0.662723	−0.331362	−	0.943504i	$-0.607508\pi$
$971$	−20.6510	−0.662723	−0.331362	+	0.943504i	$0.607508\pi$
$972$	−36.3684	−1.16652
$973$	10.9329	0.350493
$974$	−66.5380	−2.13201
$975$	−10.1536	−0.325177
$976$	29.1357	0.932612
$977$	2.60314	0.0832819	0.0416410	−	0.999133i	$-0.486741\pi$
$977$	2.60314	0.0832819	0.0416410	+	0.999133i	$0.486741\pi$
$978$	73.5517	2.35192
$979$	47.8846	1.53040
$980$	−5.05553	−0.161493
$981$	11.7171	0.374097
$982$	−95.0225	−3.03229
$983$	0.259340	0.00827165	0.00413582	−	0.999991i	$-0.498684\pi$
$983$	0.259340	0.00827165	0.00413582	+	0.999991i	$0.498684\pi$
$984$	143.539	4.57586
$985$	−15.2389	−0.485551
$986$	50.1344	1.59660
$987$	−1.96821	−0.0626490
$988$	89.9109	2.86045
$989$	−7.62021	−0.242309
$990$	10.5699	0.335934
$991$	−57.0784	−1.81315	−0.906577	−	0.422040i	$-0.861314\pi$
$991$	−57.0784	−1.81315	−0.906577	+	0.422040i	$0.861314\pi$
$992$	3.88295	0.123284
$993$	−38.8854	−1.23399
$994$	−40.4567	−1.28321
$995$	23.6243	0.748942
$996$	20.2216	0.640746
$997$	55.0691	1.74405	0.872027	−	0.489457i	$-0.162805\pi$
$997$	55.0691	1.74405	0.872027	+	0.489457i	$0.162805\pi$
$998$	−27.2132	−0.861418
$999$	67.8212	2.14577

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.2	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.2	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65622 q^{2} -1.51381 q^{3} +5.05553 q^{4} -1.00000 q^{5} +4.02102 q^{6} -1.00000 q^{7} -8.11618 q^{8} -0.708384 q^{9} +O(q^{10})\)	\(q-2.65622 q^{2} -1.51381 q^{3} +5.05553 q^{4} -1.00000 q^{5} +4.02102 q^{6} -1.00000 q^{7} -8.11618 q^{8} -0.708384 q^{9} +2.65622 q^{10} -5.61743 q^{11} -7.65310 q^{12} +6.70734 q^{13} +2.65622 q^{14} +1.51381 q^{15} +11.4473 q^{16} -3.50154 q^{17} +1.88163 q^{18} +2.65152 q^{19} -5.05553 q^{20} +1.51381 q^{21} +14.9212 q^{22} +2.95131 q^{23} +12.2863 q^{24} +1.00000 q^{25} -17.8162 q^{26} +5.61378 q^{27} -5.05553 q^{28} +5.39028 q^{29} -4.02102 q^{30} -0.273942 q^{31} -14.1743 q^{32} +8.50372 q^{33} +9.30089 q^{34} +1.00000 q^{35} -3.58126 q^{36} +12.0812 q^{37} -7.04304 q^{38} -10.1536 q^{39} +8.11618 q^{40} +11.6828 q^{41} -4.02102 q^{42} -2.58198 q^{43} -28.3991 q^{44} +0.708384 q^{45} -7.83933 q^{46} -1.30017 q^{47} -17.3291 q^{48} +1.00000 q^{49} -2.65622 q^{50} +5.30067 q^{51} +33.9092 q^{52} +7.69853 q^{53} -14.9115 q^{54} +5.61743 q^{55} +8.11618 q^{56} -4.01390 q^{57} -14.3178 q^{58} -6.89816 q^{59} +7.65310 q^{60} +2.54520 q^{61} +0.727653 q^{62} +0.708384 q^{63} +14.7555 q^{64} -6.70734 q^{65} -22.5878 q^{66} +11.2045 q^{67} -17.7022 q^{68} -4.46771 q^{69} -2.65622 q^{70} -15.2309 q^{71} +5.74937 q^{72} +2.48419 q^{73} -32.0904 q^{74} -1.51381 q^{75} +13.4048 q^{76} +5.61743 q^{77} +26.9703 q^{78} -14.8242 q^{79} -11.4473 q^{80} -6.37304 q^{81} -31.0322 q^{82} -2.64228 q^{83} +7.65310 q^{84} +3.50154 q^{85} +6.85832 q^{86} -8.15985 q^{87} +45.5921 q^{88} -8.52428 q^{89} -1.88163 q^{90} -6.70734 q^{91} +14.9204 q^{92} +0.414696 q^{93} +3.45355 q^{94} -2.65152 q^{95} +21.4572 q^{96} -9.89389 q^{97} -2.65622 q^{98} +3.97930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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