LMFDB - Embedded newform 8041.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$60$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.07976 q^{2} -1.74571 q^{3} +2.32541 q^{4} -0.111413 q^{5} +3.63066 q^{6} -0.659970 q^{7} -0.676772 q^{8} +0.0475049 q^{9} +O(q^{10})$	\(q-2.07976 q^{2} -1.74571 q^{3} +2.32541 q^{4} -0.111413 q^{5} +3.63066 q^{6} -0.659970 q^{7} -0.676772 q^{8} +0.0475049 q^{9} +0.231713 q^{10} +1.00000 q^{11} -4.05949 q^{12} -1.82802 q^{13} +1.37258 q^{14} +0.194495 q^{15} -3.24329 q^{16} +1.00000 q^{17} -0.0987988 q^{18} +5.44187 q^{19} -0.259081 q^{20} +1.15212 q^{21} -2.07976 q^{22} -0.638962 q^{23} +1.18145 q^{24} -4.98759 q^{25} +3.80184 q^{26} +5.15420 q^{27} -1.53470 q^{28} +0.471345 q^{29} -0.404503 q^{30} +1.69206 q^{31} +8.09882 q^{32} -1.74571 q^{33} -2.07976 q^{34} +0.0735293 q^{35} +0.110468 q^{36} -5.46524 q^{37} -11.3178 q^{38} +3.19119 q^{39} +0.0754012 q^{40} -3.27839 q^{41} -2.39613 q^{42} -1.00000 q^{43} +2.32541 q^{44} -0.00529267 q^{45} +1.32889 q^{46} -0.199409 q^{47} +5.66185 q^{48} -6.56444 q^{49} +10.3730 q^{50} -1.74571 q^{51} -4.25089 q^{52} +4.46578 q^{53} -10.7195 q^{54} -0.111413 q^{55} +0.446649 q^{56} -9.49993 q^{57} -0.980284 q^{58} -0.997674 q^{59} +0.452280 q^{60} -0.892672 q^{61} -3.51908 q^{62} -0.0313518 q^{63} -10.3570 q^{64} +0.203665 q^{65} +3.63066 q^{66} +14.5216 q^{67} +2.32541 q^{68} +1.11544 q^{69} -0.152923 q^{70} +1.38863 q^{71} -0.0321500 q^{72} +2.81478 q^{73} +11.3664 q^{74} +8.70688 q^{75} +12.6546 q^{76} -0.659970 q^{77} -6.63692 q^{78} +0.519434 q^{79} +0.361345 q^{80} -9.14026 q^{81} +6.81826 q^{82} -10.9245 q^{83} +2.67914 q^{84} -0.111413 q^{85} +2.07976 q^{86} -0.822831 q^{87} -0.676772 q^{88} +11.0412 q^{89} +0.0110075 q^{90} +1.20644 q^{91} -1.48585 q^{92} -2.95385 q^{93} +0.414724 q^{94} -0.606296 q^{95} -14.1382 q^{96} +7.62296 q^{97} +13.6525 q^{98} +0.0475049 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) $ 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * 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 $

$2$	−2.07976	−1.47061	−0.735307	−	0.677734i	$-0.762962\pi$
$2$	−2.07976	−1.47061	−0.735307	+	0.677734i	$0.762962\pi$
$3$	−1.74571	−1.00789	−0.503943	−	0.863737i	$-0.668118\pi$
$3$	−1.74571	−1.00789	−0.503943	+	0.863737i	$0.668118\pi$
$4$	2.32541	1.16270
$5$	−0.111413	−0.0498254	−0.0249127	−	0.999690i	$-0.507931\pi$
$5$	−0.111413	−0.0498254	−0.0249127	+	0.999690i	$0.507931\pi$
$6$	3.63066	1.48221
$7$	−0.659970	−0.249445	−0.124723	−	0.992192i	$-0.539804\pi$
$7$	−0.659970	−0.249445	−0.124723	+	0.992192i	$0.539804\pi$
$8$	−0.676772	−0.239275
$9$	0.0475049	0.0158350
$10$	0.231713	0.0732740
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.05949	−1.17187
$13$	−1.82802	−0.507001	−0.253501	−	0.967335i	$-0.581582\pi$
$13$	−1.82802	−0.507001	−0.253501	+	0.967335i	$0.581582\pi$
$14$	1.37258	0.366838
$15$	0.194495	0.0502184
$16$	−3.24329	−0.810823
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.0987988	−0.0232871
$19$	5.44187	1.24845	0.624225	−	0.781244i	$-0.285415\pi$
$19$	5.44187	1.24845	0.624225	+	0.781244i	$0.285415\pi$
$20$	−0.259081	−0.0579323
$21$	1.15212	0.251412
$22$	−2.07976	−0.443407
$23$	−0.638962	−0.133233	−0.0666164	−	0.997779i	$-0.521220\pi$
$23$	−0.638962	−0.133233	−0.0666164	+	0.997779i	$0.521220\pi$
$24$	1.18145	0.241162
$25$	−4.98759	−0.997517
$26$	3.80184	0.745603
$27$	5.15420	0.991927
$28$	−1.53470	−0.290031
$29$	0.471345	0.0875265	0.0437632	−	0.999042i	$-0.486065\pi$
$29$	0.471345	0.0875265	0.0437632	+	0.999042i	$0.486065\pi$
$30$	−0.404503	−0.0738518
$31$	1.69206	0.303903	0.151951	−	0.988388i	$-0.451444\pi$
$31$	1.69206	0.303903	0.151951	+	0.988388i	$0.451444\pi$
$32$	8.09882	1.43168
$33$	−1.74571	−0.303889
$34$	−2.07976	−0.356676
$35$	0.0735293	0.0124287
$36$	0.110468	0.0184114
$37$	−5.46524	−0.898480	−0.449240	−	0.893411i	$-0.648305\pi$
$37$	−5.46524	−0.898480	−0.449240	+	0.893411i	$0.648305\pi$
$38$	−11.3178	−1.83599
$39$	3.19119	0.511000
$40$	0.0754012	0.0119220
$41$	−3.27839	−0.511998	−0.255999	−	0.966677i	$-0.582404\pi$
$41$	−3.27839	−0.511998	−0.255999	+	0.966677i	$0.582404\pi$
$42$	−2.39613	−0.369731
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	2.32541	0.350568
$45$	−0.00529267	−0.000788984 0
$46$	1.32889	0.195934
$47$	−0.199409	−0.0290869	−0.0145434	−	0.999894i	$-0.504629\pi$
$47$	−0.199409	−0.0290869	−0.0145434	+	0.999894i	$0.504629\pi$
$48$	5.66185	0.817218
$49$	−6.56444	−0.937777
$50$	10.3730	1.46696
$51$	−1.74571	−0.244448
$52$	−4.25089	−0.589492
$53$	4.46578	0.613422	0.306711	−	0.951803i	$-0.400771\pi$
$53$	4.46578	0.613422	0.306711	+	0.951803i	$0.400771\pi$
$54$	−10.7195	−1.45874
$55$	−0.111413	−0.0150229
$56$	0.446649	0.0596860
$57$	−9.49993	−1.25830
$58$	−0.980284	−0.128718
$59$	−0.997674	−0.129886	−0.0649430	−	0.997889i	$-0.520687\pi$
$59$	−0.997674	−0.129886	−0.0649430	+	0.997889i	$0.520687\pi$
$60$	0.452280	0.0583891
$61$	−0.892672	−0.114295	−0.0571475	−	0.998366i	$-0.518201\pi$
$61$	−0.892672	−0.114295	−0.0571475	+	0.998366i	$0.518201\pi$
$62$	−3.51908	−0.446924
$63$	−0.0313518	−0.00394996
$64$	−10.3570	−1.29463
$65$	0.203665	0.0252616
$66$	3.63066	0.446904
$67$	14.5216	1.77410	0.887050	−	0.461673i	$-0.152751\pi$
$67$	14.5216	1.77410	0.887050	+	0.461673i	$0.152751\pi$
$68$	2.32541	0.281997
$69$	1.11544	0.134283
$70$	−0.152923	−0.0182778
$71$	1.38863	0.164800	0.0824002	−	0.996599i	$-0.473741\pi$
$71$	1.38863	0.164800	0.0824002	+	0.996599i	$0.473741\pi$
$72$	−0.0321500	−0.00378891
$73$	2.81478	0.329445	0.164723	−	0.986340i	$-0.447327\pi$
$73$	2.81478	0.329445	0.164723	+	0.986340i	$0.447327\pi$
$74$	11.3664	1.32132
$75$	8.70688	1.00538
$76$	12.6546	1.45158
$77$	−0.659970	−0.0752106
$78$	−6.63692	−0.751483
$79$	0.519434	0.0584409	0.0292205	−	0.999573i	$-0.490698\pi$
$79$	0.519434	0.0584409	0.0292205	+	0.999573i	$0.490698\pi$
$80$	0.361345	0.0403996
$81$	−9.14026	−1.01558
$82$	6.81826	0.752951
$83$	−10.9245	−1.19911	−0.599557	−	0.800332i	$-0.704657\pi$
$83$	−10.9245	−1.19911	−0.599557	+	0.800332i	$0.704657\pi$
$84$	2.67914	0.292318
$85$	−0.111413	−0.0120844
$86$	2.07976	0.224266
$87$	−0.822831	−0.0882168
$88$	−0.676772	−0.0721441
$89$	11.0412	1.17036	0.585182	−	0.810902i	$-0.301023\pi$
$89$	11.0412	1.17036	0.585182	+	0.810902i	$0.301023\pi$
$90$	0.0110075	0.00116029
$91$	1.20644	0.126469
$92$	−1.48585	−0.154910
$93$	−2.95385	−0.306300
$94$	0.414724	0.0427755
$95$	−0.606296	−0.0622046
$96$	−14.1382	−1.44297
$97$	7.62296	0.773995	0.386997	−	0.922081i	$-0.373512\pi$
$97$	7.62296	0.773995	0.386997	+	0.922081i	$0.373512\pi$
$98$	13.6525	1.37911
$99$	0.0475049	0.00477442
$100$	−11.5982	−1.15982
$101$	−9.98957	−0.993999	−0.497000	−	0.867751i	$-0.665565\pi$
$101$	−9.98957	−0.993999	−0.497000	+	0.867751i	$0.665565\pi$
$102$	3.63066	0.359489
$103$	11.1948	1.10306	0.551530	−	0.834155i	$-0.314044\pi$
$103$	11.1948	1.10306	0.551530	+	0.834155i	$0.314044\pi$
$104$	1.23715	0.121313
$105$	−0.128361	−0.0125267
$106$	−9.28776	−0.902107
$107$	0.996787	0.0963630	0.0481815	−	0.998839i	$-0.484657\pi$
$107$	0.996787	0.0963630	0.0481815	+	0.998839i	$0.484657\pi$
$108$	11.9856	1.15332
$109$	−15.0741	−1.44384	−0.721918	−	0.691979i	$-0.756739\pi$
$109$	−15.0741	−1.44384	−0.721918	+	0.691979i	$0.756739\pi$
$110$	0.231713	0.0220929
$111$	9.54073	0.905566
$112$	2.14048	0.202256
$113$	3.39883	0.319735	0.159867	−	0.987138i	$-0.448893\pi$
$113$	3.39883	0.319735	0.159867	+	0.987138i	$0.448893\pi$
$114$	19.7576	1.85047
$115$	0.0711887	0.00663838
$116$	1.09607	0.101767
$117$	−0.0868398	−0.00802834
$118$	2.07492	0.191012
$119$	−0.659970	−0.0604994
$120$	−0.131629	−0.0120160
$121$	1.00000	0.0909091
$122$	1.85654	0.168084
$123$	5.72311	0.516036
$124$	3.93473	0.353349
$125$	1.11275	0.0995272
$126$	0.0652043	0.00580886
$127$	−17.1444	−1.52132	−0.760661	−	0.649149i	$-0.775125\pi$
$127$	−17.1444	−1.52132	−0.760661	+	0.649149i	$0.775125\pi$
$128$	5.34251	0.472216
$129$	1.74571	0.153701
$130$	−0.423575	−0.0371500
$131$	−11.0834	−0.968365	−0.484183	−	0.874967i	$-0.660883\pi$
$131$	−11.0834	−0.968365	−0.484183	+	0.874967i	$0.660883\pi$
$132$	−4.05949	−0.353333
$133$	−3.59147	−0.311420
$134$	−30.2015	−2.60902
$135$	−0.574245	−0.0494232
$136$	−0.676772	−0.0580327
$137$	−8.41825	−0.719219	−0.359610	−	0.933103i	$-0.617090\pi$
$137$	−8.41825	−0.719219	−0.359610	+	0.933103i	$0.617090\pi$
$138$	−2.31985	−0.197479
$139$	−20.3749	−1.72817	−0.864086	−	0.503344i	$-0.832103\pi$
$139$	−20.3749	−1.72817	−0.864086	+	0.503344i	$0.832103\pi$
$140$	0.170986	0.0144509
$141$	0.348111	0.0293162
$142$	−2.88802	−0.242358
$143$	−1.82802	−0.152867
$144$	−0.154072	−0.0128394
$145$	−0.0525140	−0.00436105
$146$	−5.85407	−0.484487
$147$	11.4596	0.945173
$148$	−12.7089	−1.04467
$149$	−3.07711	−0.252086	−0.126043	−	0.992025i	$-0.540228\pi$
$149$	−3.07711	−0.252086	−0.126043	+	0.992025i	$0.540228\pi$
$150$	−18.1082	−1.47853
$151$	11.1294	0.905699	0.452850	−	0.891587i	$-0.350407\pi$
$151$	11.1294	0.905699	0.452850	+	0.891587i	$0.350407\pi$
$152$	−3.68290	−0.298723
$153$	0.0475049	0.00384054
$154$	1.37258	0.110606
$155$	−0.188518	−0.0151421
$156$	7.42082	0.594141
$157$	−1.07877	−0.0860949	−0.0430475	−	0.999073i	$-0.513707\pi$
$157$	−1.07877	−0.0860949	−0.0430475	+	0.999073i	$0.513707\pi$
$158$	−1.08030	−0.0859440
$159$	−7.79596	−0.618260
$160$	−0.902314	−0.0713342
$161$	0.421696	0.0332343
$162$	19.0096	1.49353
$163$	8.34964	0.653995	0.326997	−	0.945025i	$-0.393963\pi$
$163$	8.34964	0.653995	0.326997	+	0.945025i	$0.393963\pi$
$164$	−7.62359	−0.595302
$165$	0.194495	0.0151414
$166$	22.7203	1.76343
$167$	22.4521	1.73739	0.868696	−	0.495346i	$-0.164959\pi$
$167$	22.4521	1.73739	0.868696	+	0.495346i	$0.164959\pi$
$168$	−0.779720	−0.0601567
$169$	−9.65835	−0.742950
$170$	0.231713	0.0177715
$171$	0.258515	0.0197692
$172$	−2.32541	−0.177311
$173$	8.45042	0.642473	0.321237	−	0.946999i	$-0.395902\pi$
$173$	8.45042	0.642473	0.321237	+	0.946999i	$0.395902\pi$
$174$	1.71129	0.129733
$175$	3.29166	0.248826
$176$	−3.24329	−0.244472
$177$	1.74165	0.130910
$178$	−22.9630	−1.72115
$179$	22.8980	1.71148	0.855738	−	0.517410i	$-0.173104\pi$
$179$	22.8980	1.71148	0.855738	+	0.517410i	$0.173104\pi$
$180$	−0.0123076	−0.000917355 0
$181$	8.65912	0.643627	0.321814	−	0.946803i	$-0.395708\pi$
$181$	8.65912	0.643627	0.321814	+	0.946803i	$0.395708\pi$
$182$	−2.50910	−0.185987
$183$	1.55835	0.115196
$184$	0.432431	0.0318792
$185$	0.608899	0.0447672
$186$	6.14330	0.450448
$187$	1.00000	0.0731272
$188$	−0.463708	−0.0338194
$189$	−3.40162	−0.247431
$190$	1.26095	0.0914790
$191$	−3.28055	−0.237372	−0.118686	−	0.992932i	$-0.537868\pi$
$191$	−3.28055	−0.237372	−0.118686	+	0.992932i	$0.537868\pi$
$192$	18.0804	1.30484
$193$	23.2005	1.67001	0.835004	−	0.550245i	$-0.185466\pi$
$193$	23.2005	1.67001	0.835004	+	0.550245i	$0.185466\pi$
$194$	−15.8539	−1.13825
$195$	−0.355540	−0.0254608
$196$	−15.2650	−1.09036
$197$	−5.25531	−0.374425	−0.187213	−	0.982319i	$-0.559945\pi$
$197$	−5.25531	−0.374425	−0.187213	+	0.982319i	$0.559945\pi$
$198$	−0.0987988	−0.00702133
$199$	−25.2743	−1.79165	−0.895825	−	0.444406i	$-0.853415\pi$
$199$	−25.2743	−1.79165	−0.895825	+	0.444406i	$0.853415\pi$
$200$	3.37546	0.238681
$201$	−25.3506	−1.78809
$202$	20.7759	1.46179
$203$	−0.311073	−0.0218331
$204$	−4.05949	−0.284221
$205$	0.365255	0.0255105
$206$	−23.2826	−1.62217
$207$	−0.0303538	−0.00210973
$208$	5.92880	0.411088
$209$	5.44187	0.376422
$210$	0.266960	0.0184220
$211$	16.4975	1.13573	0.567867	−	0.823121i	$-0.307769\pi$
$211$	16.4975	1.13573	0.567867	+	0.823121i	$0.307769\pi$
$212$	10.3848	0.713229
$213$	−2.42415	−0.166100
$214$	−2.07308	−0.141713
$215$	0.111413	0.00759831
$216$	−3.48822	−0.237343
$217$	−1.11671	−0.0758071
$218$	31.3505	2.12332
$219$	−4.91379	−0.332043
$220$	−0.259081	−0.0174672
$221$	−1.82802	−0.122966
$222$	−19.8424	−1.33174
$223$	−5.00909	−0.335433	−0.167717	−	0.985835i	$-0.553639\pi$
$223$	−5.00909	−0.335433	−0.167717	+	0.985835i	$0.553639\pi$
$224$	−5.34498	−0.357126
$225$	−0.236935	−0.0157957
$226$	−7.06875	−0.470207
$227$	4.51290	0.299531	0.149766	−	0.988722i	$-0.452148\pi$
$227$	4.51290	0.299531	0.149766	+	0.988722i	$0.452148\pi$
$228$	−22.0912	−1.46303
$229$	19.8939	1.31462	0.657312	−	0.753619i	$-0.271694\pi$
$229$	19.8939	1.31462	0.657312	+	0.753619i	$0.271694\pi$
$230$	−0.148055	−0.00976249
$231$	1.15212	0.0758037
$232$	−0.318993	−0.0209429
$233$	−9.49466	−0.622016	−0.311008	−	0.950407i	$-0.600667\pi$
$233$	−9.49466	−0.622016	−0.311008	+	0.950407i	$0.600667\pi$
$234$	0.180606	0.0118066
$235$	0.0222168	0.00144927
$236$	−2.32000	−0.151019
$237$	−0.906782	−0.0589018
$238$	1.37258	0.0889712
$239$	20.5070	1.32649	0.663245	−	0.748402i	$-0.269179\pi$
$239$	20.5070	1.32649	0.663245	+	0.748402i	$0.269179\pi$
$240$	−0.630804	−0.0407182
$241$	10.9635	0.706224	0.353112	−	0.935581i	$-0.385123\pi$
$241$	10.9635	0.706224	0.353112	+	0.935581i	$0.385123\pi$
$242$	−2.07976	−0.133692
$243$	0.493639	0.0316670
$244$	−2.07583	−0.132891
$245$	0.731364	0.0467252
$246$	−11.9027	−0.758889
$247$	−9.94784	−0.632966
$248$	−1.14514	−0.0727163
$249$	19.0709	1.20857
$250$	−2.31425	−0.146366
$251$	−5.88754	−0.371618	−0.185809	−	0.982586i	$-0.559491\pi$
$251$	−5.88754	−0.371618	−0.185809	+	0.982586i	$0.559491\pi$
$252$	−0.0729057	−0.00459263
$253$	−0.638962	−0.0401712
$254$	35.6563	2.23728
$255$	0.194495	0.0121797
$256$	9.60291	0.600182
$257$	−5.87788	−0.366652	−0.183326	−	0.983052i	$-0.558686\pi$
$257$	−5.87788	−0.366652	−0.183326	+	0.983052i	$0.558686\pi$
$258$	−3.63066	−0.226035
$259$	3.60690	0.224122
$260$	0.473605	0.0293717
$261$	0.0223912	0.00138598
$262$	23.0509	1.42409
$263$	−0.184987	−0.0114068	−0.00570338	−	0.999984i	$-0.501815\pi$
$263$	−0.184987	−0.0114068	−0.00570338	+	0.999984i	$0.501815\pi$
$264$	1.18145	0.0727130
$265$	−0.497547	−0.0305640
$266$	7.46941	0.457979
$267$	−19.2747	−1.17959
$268$	33.7687	2.06275
$269$	−23.7524	−1.44821	−0.724106	−	0.689689i	$-0.757747\pi$
$269$	−23.7524	−1.44821	−0.724106	+	0.689689i	$0.757747\pi$
$270$	1.19429	0.0726824
$271$	29.0800	1.76648	0.883242	−	0.468918i	$-0.155356\pi$
$271$	29.0800	1.76648	0.883242	+	0.468918i	$0.155356\pi$
$272$	−3.24329	−0.196654
$273$	−2.10609	−0.127466
$274$	17.5079	1.05769
$275$	−4.98759	−0.300763
$276$	2.59386	0.156132
$277$	−9.89600	−0.594593	−0.297296	−	0.954785i	$-0.596085\pi$
$277$	−9.89600	−0.594593	−0.297296	+	0.954785i	$0.596085\pi$
$278$	42.3748	2.54147
$279$	0.0803811	0.00481229
$280$	−0.0497625	−0.00297388
$281$	0.736457	0.0439333	0.0219667	−	0.999759i	$-0.493007\pi$
$281$	0.736457	0.0439333	0.0219667	+	0.999759i	$0.493007\pi$
$282$	−0.723988	−0.0431129
$283$	25.4488	1.51278	0.756388	−	0.654124i	$-0.226962\pi$
$283$	25.4488	1.51278	0.756388	+	0.654124i	$0.226962\pi$
$284$	3.22914	0.191614
$285$	1.05842	0.0626952
$286$	3.80184	0.224808
$287$	2.16364	0.127715
$288$	0.384733	0.0226706
$289$	1.00000	0.0588235
$290$	0.109216	0.00641341
$291$	−13.3075	−0.780099
$292$	6.54552	0.383047
$293$	−2.17298	−0.126947	−0.0634733	−	0.997984i	$-0.520218\pi$
$293$	−2.17298	−0.126947	−0.0634733	+	0.997984i	$0.520218\pi$
$294$	−23.8333	−1.38998
$295$	0.111154	0.00647163
$296$	3.69872	0.214984
$297$	5.15420	0.299077
$298$	6.39965	0.370721
$299$	1.16803	0.0675491
$300$	20.2471	1.16896
$301$	0.659970	0.0380400
$302$	−23.1465	−1.33193
$303$	17.4389	1.00184
$304$	−17.6496	−1.01227
$305$	0.0994553	0.00569479
$306$	−0.0987988	−0.00564795
$307$	1.14922	0.0655896	0.0327948	−	0.999462i	$-0.489559\pi$
$307$	1.14922	0.0655896	0.0327948	+	0.999462i	$0.489559\pi$
$308$	−1.53470	−0.0874476
$309$	−19.5429	−1.11176
$310$	0.392072	0.0222682
$311$	−17.4099	−0.987226	−0.493613	−	0.869682i	$-0.664324\pi$
$311$	−17.4099	−0.987226	−0.493613	+	0.869682i	$0.664324\pi$
$312$	−2.15971	−0.122269
$313$	13.8755	0.784292	0.392146	−	0.919903i	$-0.371733\pi$
$313$	13.8755	0.784292	0.392146	+	0.919903i	$0.371733\pi$
$314$	2.24358	0.126612
$315$	0.00349300	0.000196808 0
$316$	1.20790	0.0679495
$317$	31.9106	1.79228	0.896139	−	0.443773i	$-0.146360\pi$
$317$	31.9106	1.79228	0.896139	+	0.443773i	$0.146360\pi$
$318$	16.2137	0.909222
$319$	0.471345	0.0263902
$320$	1.15391	0.0645054
$321$	−1.74010	−0.0971230
$322$	−0.877026	−0.0488748
$323$	5.44187	0.302794
$324$	−21.2548	−1.18082
$325$	9.11740	0.505742
$326$	−17.3653	−0.961773
$327$	26.3150	1.45522
$328$	2.21872	0.122508
$329$	0.131604	0.00725558
$330$	−0.404503	−0.0222672
$331$	−14.0223	−0.770735	−0.385368	−	0.922763i	$-0.625925\pi$
$331$	−14.0223	−0.770735	−0.385368	+	0.922763i	$0.625925\pi$
$332$	−25.4038	−1.39422
$333$	−0.259626	−0.0142274
$334$	−46.6949	−2.55503
$335$	−1.61790	−0.0883953
$336$	−3.73665	−0.203851
$337$	28.3255	1.54299	0.771495	−	0.636235i	$-0.219509\pi$
$337$	28.3255	1.54299	0.771495	+	0.636235i	$0.219509\pi$
$338$	20.0871	1.09259
$339$	−5.93337	−0.322257
$340$	−0.259081	−0.0140506
$341$	1.69206	0.0916302
$342$	−0.537651	−0.0290728
$343$	8.95212	0.483369
$344$	0.676772	0.0364891
$345$	−0.124275	−0.00669073
$346$	−17.5749	−0.944830
$347$	9.77123	0.524547	0.262273	−	0.964994i	$-0.415528\pi$
$347$	9.77123	0.524547	0.262273	+	0.964994i	$0.415528\pi$
$348$	−1.91342	−0.102570
$349$	−9.82472	−0.525905	−0.262953	−	0.964809i	$-0.584696\pi$
$349$	−9.82472	−0.525905	−0.262953	+	0.964809i	$0.584696\pi$
$350$	−6.84586	−0.365927
$351$	−9.42198	−0.502908
$352$	8.09882	0.431669
$353$	−33.2493	−1.76968	−0.884842	−	0.465891i	$-0.845734\pi$
$353$	−33.2493	−1.76968	−0.884842	+	0.465891i	$0.845734\pi$
$354$	−3.62222	−0.192519
$355$	−0.154712	−0.00821125
$356$	25.6753	1.36079
$357$	1.15212	0.0609765
$358$	−47.6223	−2.51692
$359$	21.1198	1.11466	0.557330	−	0.830291i	$-0.311826\pi$
$359$	21.1198	1.11466	0.557330	+	0.830291i	$0.311826\pi$
$360$	0.00358193	0.000188784 0
$361$	10.6140	0.558630
$362$	−18.0089	−0.946527
$363$	−1.74571	−0.0916260
$364$	2.80546	0.147046
$365$	−0.313603	−0.0164148
$366$	−3.24099	−0.169409
$367$	−3.88314	−0.202698	−0.101349	−	0.994851i	$-0.532316\pi$
$367$	−3.88314	−0.202698	−0.101349	+	0.994851i	$0.532316\pi$
$368$	2.07234	0.108028
$369$	−0.155739	−0.00810747
$370$	−1.26637	−0.0658352
$371$	−2.94728	−0.153015
$372$	−6.86890	−0.356136
$373$	−36.7050	−1.90051	−0.950255	−	0.311472i	$-0.899178\pi$
$373$	−36.7050	−1.90051	−0.950255	+	0.311472i	$0.899178\pi$
$374$	−2.07976	−0.107542
$375$	−1.94254	−0.100312
$376$	0.134955	0.00695975
$377$	−0.861627	−0.0443760
$378$	7.07456	0.363876
$379$	18.8923	0.970434	0.485217	−	0.874394i	$-0.338741\pi$
$379$	18.8923	0.970434	0.485217	+	0.874394i	$0.338741\pi$
$380$	−1.40989	−0.0723256
$381$	29.9292	1.53332
$382$	6.82276	0.349083
$383$	−14.7764	−0.755037	−0.377518	−	0.926002i	$-0.623223\pi$
$383$	−14.7764	−0.755037	−0.377518	+	0.926002i	$0.623223\pi$
$384$	−9.32647	−0.475940
$385$	0.0735293	0.00374740
$386$	−48.2515	−2.45593
$387$	−0.0475049	−0.00241481
$388$	17.7265	0.899927
$389$	0.604146	0.0306314	0.0153157	−	0.999883i	$-0.495125\pi$
$389$	0.604146	0.0306314	0.0153157	+	0.999883i	$0.495125\pi$
$390$	0.739439	0.0374430
$391$	−0.638962	−0.0323137
$392$	4.44263	0.224386
$393$	19.3485	0.976002
$394$	10.9298	0.550635
$395$	−0.0578718	−0.00291184
$396$	0.110468	0.00555124
$397$	32.1111	1.61161	0.805805	−	0.592182i	$-0.201733\pi$
$397$	32.1111	1.61161	0.805805	+	0.592182i	$0.201733\pi$
$398$	52.5646	2.63483
$399$	6.26967	0.313876
$400$	16.1762	0.808810
$401$	−18.4310	−0.920399	−0.460200	−	0.887815i	$-0.652222\pi$
$401$	−18.4310	−0.920399	−0.460200	+	0.887815i	$0.652222\pi$
$402$	52.7231	2.62959
$403$	−3.09312	−0.154079
$404$	−23.2298	−1.15573
$405$	1.01834	0.0506019
$406$	0.646958	0.0321080
$407$	−5.46524	−0.270902
$408$	1.18145	0.0584903
$409$	−0.406847	−0.0201173	−0.0100586	−	0.999949i	$-0.503202\pi$
$409$	−0.406847	−0.0201173	−0.0100586	+	0.999949i	$0.503202\pi$
$410$	−0.759643	−0.0375161
$411$	14.6958	0.724891
$412$	26.0326	1.28253
$413$	0.658435	0.0323995
$414$	0.0631287	0.00310260
$415$	1.21713	0.0597464
$416$	−14.8048	−0.725865
$417$	35.5686	1.74180
$418$	−11.3178	−0.553571
$419$	−26.5383	−1.29648	−0.648240	−	0.761436i	$-0.724495\pi$
$419$	−26.5383	−1.29648	−0.648240	+	0.761436i	$0.724495\pi$
$420$	−0.298491	−0.0145649
$421$	19.1148	0.931597	0.465798	−	0.884891i	$-0.345767\pi$
$421$	19.1148	0.931597	0.465798	+	0.884891i	$0.345767\pi$
$422$	−34.3108	−1.67022
$423$	−0.00947292	−0.000460589 0
$424$	−3.02231	−0.146777
$425$	−4.98759	−0.241934
$426$	5.04165	0.244269
$427$	0.589137	0.0285103
$428$	2.31794	0.112042
$429$	3.19119	0.154072
$430$	−0.231713	−0.0111742
$431$	−32.5836	−1.56950	−0.784749	−	0.619813i	$-0.787208\pi$
$431$	−32.5836	−1.56950	−0.784749	+	0.619813i	$0.787208\pi$
$432$	−16.7166	−0.804277
$433$	6.55023	0.314784	0.157392	−	0.987536i	$-0.449691\pi$
$433$	6.55023	0.314784	0.157392	+	0.987536i	$0.449691\pi$
$434$	2.32249	0.111483
$435$	0.0916742	0.00439544
$436$	−35.0534	−1.67875
$437$	−3.47715	−0.166335
$438$	10.2195	0.488307
$439$	15.5037	0.739949	0.369975	−	0.929042i	$-0.379366\pi$
$439$	15.5037	0.739949	0.369975	+	0.929042i	$0.379366\pi$
$440$	0.0754012	0.00359461
$441$	−0.311843	−0.0148497
$442$	3.80184	0.180835
$443$	17.7688	0.844221	0.422111	−	0.906544i	$-0.361289\pi$
$443$	17.7688	0.844221	0.422111	+	0.906544i	$0.361289\pi$
$444$	22.1861	1.05291
$445$	−1.23013	−0.0583139
$446$	10.4177	0.493293
$447$	5.37173	0.254074
$448$	6.83533	0.322939
$449$	4.71311	0.222425	0.111213	−	0.993797i	$-0.464527\pi$
$449$	4.71311	0.222425	0.111213	+	0.993797i	$0.464527\pi$
$450$	0.492768	0.0232293
$451$	−3.27839	−0.154373
$452$	7.90367	0.371757
$453$	−19.4287	−0.912842
$454$	−9.38575	−0.440495
$455$	−0.134413	−0.00630138
$456$	6.42928	0.301079
$457$	30.6153	1.43212	0.716061	−	0.698038i	$-0.245943\pi$
$457$	30.6153	1.43212	0.716061	+	0.698038i	$0.245943\pi$
$458$	−41.3745	−1.93330
$459$	5.15420	0.240578
$460$	0.165543	0.00771847
$461$	18.6300	0.867688	0.433844	−	0.900988i	$-0.357157\pi$
$461$	18.6300	0.867688	0.433844	+	0.900988i	$0.357157\pi$
$462$	−2.39613	−0.111478
$463$	35.1435	1.63326	0.816628	−	0.577165i	$-0.195841\pi$
$463$	35.1435	1.63326	0.816628	+	0.577165i	$0.195841\pi$
$464$	−1.52871	−0.0709685
$465$	0.329097	0.0152615
$466$	19.7466	0.914745
$467$	−34.1888	−1.58207	−0.791036	−	0.611770i	$-0.790458\pi$
$467$	−34.1888	−1.58207	−0.791036	+	0.611770i	$0.790458\pi$
$468$	−0.201938	−0.00933459
$469$	−9.58384	−0.442541
$470$	−0.0462057	−0.00213131
$471$	1.88321	0.0867739
$472$	0.675197	0.0310785
$473$	−1.00000	−0.0459800
$474$	1.88589	0.0866218
$475$	−27.1418	−1.24535
$476$	−1.53470	−0.0703428
$477$	0.212147	0.00971352
$478$	−42.6498	−1.95075
$479$	−34.4613	−1.57458	−0.787288	−	0.616586i	$-0.788515\pi$
$479$	−34.4613	−1.57458	−0.787288	+	0.616586i	$0.788515\pi$
$480$	1.57518	0.0718968
$481$	9.99056	0.455531
$482$	−22.8016	−1.03858
$483$	−0.736158	−0.0334964
$484$	2.32541	0.105700
$485$	−0.849298	−0.0385646
$486$	−1.02665	−0.0465699
$487$	−31.6986	−1.43640	−0.718200	−	0.695837i	$-0.755033\pi$
$487$	−31.6986	−1.43640	−0.718200	+	0.695837i	$0.755033\pi$
$488$	0.604135	0.0273479
$489$	−14.5761	−0.659152
$490$	−1.52106	−0.0687147
$491$	20.3356	0.917733	0.458867	−	0.888505i	$-0.348256\pi$
$491$	20.3356	0.917733	0.458867	+	0.888505i	$0.348256\pi$
$492$	13.3086	0.599997
$493$	0.471345	0.0212283
$494$	20.6891	0.930848
$495$	−0.00529267	−0.000237888 0
$496$	−5.48785	−0.246412
$497$	−0.916456	−0.0411087
$498$	−39.6630	−1.77734
$499$	−25.1198	−1.12452	−0.562259	−	0.826961i	$-0.690068\pi$
$499$	−25.1198	−1.12452	−0.562259	+	0.826961i	$0.690068\pi$
$500$	2.58759	0.115721
$501$	−39.1948	−1.75109
$502$	12.2447	0.546507
$503$	−11.3880	−0.507767	−0.253883	−	0.967235i	$-0.581708\pi$
$503$	−11.3880	−0.507767	−0.253883	+	0.967235i	$0.581708\pi$
$504$	0.0212180	0.000945125 0
$505$	1.11297	0.0495265
$506$	1.32889	0.0590763
$507$	16.8607	0.748809
$508$	−39.8678	−1.76885
$509$	−8.74447	−0.387592	−0.193796	−	0.981042i	$-0.562080\pi$
$509$	−8.74447	−0.387592	−0.193796	+	0.981042i	$0.562080\pi$
$510$	−0.404503	−0.0179117
$511$	−1.85767	−0.0821785
$512$	−30.6568	−1.35485
$513$	28.0485	1.23837
$514$	12.2246	0.539204
$515$	−1.24725	−0.0549604
$516$	4.05949	0.178709
$517$	−0.199409	−0.00877002
$518$	−7.50148	−0.329596
$519$	−14.7520	−0.647540
$520$	−0.137835	−0.00604446
$521$	−26.6156	−1.16605	−0.583025	−	0.812454i	$-0.698131\pi$
$521$	−26.6156	−1.16605	−0.583025	+	0.812454i	$0.698131\pi$
$522$	−0.0465683	−0.00203824
$523$	−33.3594	−1.45870	−0.729351	−	0.684139i	$-0.760178\pi$
$523$	−33.3594	−1.45870	−0.729351	+	0.684139i	$0.760178\pi$
$524$	−25.7735	−1.12592
$525$	−5.74628	−0.250788
$526$	0.384728	0.0167750
$527$	1.69206	0.0737073
$528$	5.66185	0.246400
$529$	−22.5917	−0.982249
$530$	1.03478	0.0449479
$531$	−0.0473944	−0.00205674
$532$	−8.35164	−0.362089
$533$	5.99295	0.259584
$534$	40.0868	1.73473
$535$	−0.111055	−0.00480133
$536$	−9.82783	−0.424498
$537$	−39.9732	−1.72497
$538$	49.3994	2.12976
$539$	−6.56444	−0.282750
$540$	−1.33536	−0.0574645
$541$	−5.69838	−0.244993	−0.122496	−	0.992469i	$-0.539090\pi$
$541$	−5.69838	−0.244993	−0.122496	+	0.992469i	$0.539090\pi$
$542$	−60.4795	−2.59781
$543$	−15.1163	−0.648703
$544$	8.09882	0.347234
$545$	1.67945	0.0719398
$546$	4.38017	0.187454
$547$	0.413378	0.0176748	0.00883739	−	0.999961i	$-0.497187\pi$
$547$	0.413378	0.0176748	0.00883739	+	0.999961i	$0.497187\pi$
$548$	−19.5759	−0.836239
$549$	−0.0424063	−0.00180986
$550$	10.3730	0.442306
$551$	2.56500	0.109273
$552$	−0.754899	−0.0321307
$553$	−0.342811	−0.0145778
$554$	20.5813	0.874416
$555$	−1.06296	−0.0451202
$556$	−47.3799	−2.00935
$557$	−24.0961	−1.02099	−0.510493	−	0.859882i	$-0.670537\pi$
$557$	−24.0961	−1.02099	−0.510493	+	0.859882i	$0.670537\pi$
$558$	−0.167174	−0.00707702
$559$	1.82802	0.0773170
$560$	−0.238477	−0.0100775
$561$	−1.74571	−0.0737040
$562$	−1.53165	−0.0646089
$563$	42.7406	1.80130	0.900650	−	0.434545i	$-0.143091\pi$
$563$	42.7406	1.80130	0.900650	+	0.434545i	$0.143091\pi$
$564$	0.809500	0.0340861
$565$	−0.378674	−0.0159309
$566$	−52.9275	−2.22471
$567$	6.03230	0.253333
$568$	−0.939787	−0.0394326
$569$	−8.98196	−0.376543	−0.188272	−	0.982117i	$-0.560289\pi$
$569$	−8.98196	−0.376543	−0.188272	+	0.982117i	$0.560289\pi$
$570$	−2.20125	−0.0922004
$571$	−9.98922	−0.418036	−0.209018	−	0.977912i	$-0.567027\pi$
$571$	−9.98922	−0.418036	−0.209018	+	0.977912i	$0.567027\pi$
$572$	−4.25089	−0.177739
$573$	5.72689	0.239244
$574$	−4.49985	−0.187820
$575$	3.18688	0.132902
$576$	−0.492009	−0.0205004
$577$	−14.8482	−0.618140	−0.309070	−	0.951039i	$-0.600018\pi$
$577$	−14.8482	−0.618140	−0.309070	+	0.951039i	$0.600018\pi$
$578$	−2.07976	−0.0865067
$579$	−40.5013	−1.68318
$580$	−0.122116	−0.00507061
$581$	7.20981	0.299113
$582$	27.6764	1.14722
$583$	4.46578	0.184954
$584$	−1.90496	−0.0788280
$585$	0.00967509	0.000400016 0
$586$	4.51927	0.186689
$587$	−14.3788	−0.593476	−0.296738	−	0.954959i	$-0.595899\pi$
$587$	−14.3788	−0.593476	−0.296738	+	0.954959i	$0.595899\pi$
$588$	26.6483	1.09896
$589$	9.20797	0.379408
$590$	−0.231174	−0.00951727
$591$	9.17425	0.377378
$592$	17.7254	0.728509
$593$	4.38647	0.180131	0.0900653	−	0.995936i	$-0.471292\pi$
$593$	4.38647	0.180131	0.0900653	+	0.995936i	$0.471292\pi$
$594$	−10.7195	−0.439827
$595$	0.0735293	0.00301441
$596$	−7.15553	−0.293102
$597$	44.1217	1.80578
$598$	−2.42923	−0.0993387
$599$	−8.72036	−0.356304	−0.178152	−	0.984003i	$-0.557012\pi$
$599$	−8.72036	−0.356304	−0.178152	+	0.984003i	$0.557012\pi$
$600$	−5.89257	−0.240563
$601$	6.51073	0.265578	0.132789	−	0.991144i	$-0.457607\pi$
$601$	6.51073	0.265578	0.132789	+	0.991144i	$0.457607\pi$
$602$	−1.37258	−0.0559422
$603$	0.689849	0.0280928
$604$	25.8804	1.05306
$605$	−0.111413	−0.00452959
$606$	−36.2687	−1.47332
$607$	28.6727	1.16379	0.581895	−	0.813264i	$-0.302312\pi$
$607$	28.6727	1.16379	0.581895	+	0.813264i	$0.302312\pi$
$608$	44.0727	1.78739
$609$	0.543044	0.0220052
$610$	−0.206843	−0.00837484
$611$	0.364524	0.0147471
$612$	0.110468	0.00446541
$613$	9.56062	0.386150	0.193075	−	0.981184i	$-0.438154\pi$
$613$	9.56062	0.386150	0.193075	+	0.981184i	$0.438154\pi$
$614$	−2.39011	−0.0964570
$615$	−0.637630	−0.0257117
$616$	0.446649	0.0179960
$617$	15.4419	0.621669	0.310835	−	0.950464i	$-0.399391\pi$
$617$	15.4419	0.621669	0.310835	+	0.950464i	$0.399391\pi$
$618$	40.6446	1.63497
$619$	5.58914	0.224646	0.112323	−	0.993672i	$-0.464171\pi$
$619$	5.58914	0.224646	0.112323	+	0.993672i	$0.464171\pi$
$620$	−0.438380	−0.0176058
$621$	−3.29334	−0.132157
$622$	36.2085	1.45183
$623$	−7.28685	−0.291942
$624$	−10.3500	−0.414330
$625$	24.8140	0.992558
$626$	−28.8578	−1.15339
$627$	−9.49993	−0.379391
$628$	−2.50857	−0.100103
$629$	−5.46524	−0.217913
$630$	−0.00726461	−0.000289429 0
$631$	−4.59344	−0.182862	−0.0914309	−	0.995811i	$-0.529144\pi$
$631$	−4.59344	−0.182862	−0.0914309	+	0.995811i	$0.529144\pi$
$632$	−0.351538	−0.0139834
$633$	−28.7998	−1.14469
$634$	−66.3665	−2.63575
$635$	1.91011	0.0758005
$636$	−18.1288	−0.718854
$637$	11.9999	0.475454
$638$	−0.980284	−0.0388098
$639$	0.0659668	0.00260961
$640$	−0.595225	−0.0235283
$641$	−10.0493	−0.396922	−0.198461	−	0.980109i	$-0.563594\pi$
$641$	−10.0493	−0.396922	−0.198461	+	0.980109i	$0.563594\pi$
$642$	3.61899	0.142830
$643$	0.259202	0.0102219	0.00511096	−	0.999987i	$-0.498373\pi$
$643$	0.259202	0.0102219	0.00511096	+	0.999987i	$0.498373\pi$
$644$	0.980614	0.0386416
$645$	−0.194495	−0.00765823
$646$	−11.3178	−0.445293
$647$	−4.32809	−0.170155	−0.0850773	−	0.996374i	$-0.527114\pi$
$647$	−4.32809	−0.170155	−0.0850773	+	0.996374i	$0.527114\pi$
$648$	6.18587	0.243004
$649$	−0.997674	−0.0391621
$650$	−18.9620	−0.743752
$651$	1.94945	0.0764050
$652$	19.4163	0.760402
$653$	10.0620	0.393755	0.196877	−	0.980428i	$-0.436920\pi$
$653$	10.0620	0.393755	0.196877	+	0.980428i	$0.436920\pi$
$654$	−54.7289	−2.14007
$655$	1.23484	0.0482492
$656$	10.6328	0.415140
$657$	0.133716	0.00521675
$658$	−0.273705	−0.0106701
$659$	−43.7869	−1.70570	−0.852848	−	0.522160i	$-0.825127\pi$
$659$	−43.7869	−1.70570	−0.852848	+	0.522160i	$0.825127\pi$
$660$	0.452280	0.0176050
$661$	29.3426	1.14130	0.570648	−	0.821195i	$-0.306692\pi$
$661$	29.3426	1.14130	0.570648	+	0.821195i	$0.306692\pi$
$662$	29.1630	1.13345
$663$	3.19119	0.123936
$664$	7.39336	0.286918
$665$	0.400137	0.0155166
$666$	0.539960	0.0209230
$667$	−0.301171	−0.0116614
$668$	52.2102	2.02007
$669$	8.74441	0.338079
$670$	3.36485	0.129995
$671$	−0.892672	−0.0344612
$672$	9.33078	0.359943
$673$	0.702398	0.0270755	0.0135377	−	0.999908i	$-0.495691\pi$
$673$	0.702398	0.0270755	0.0135377	+	0.999908i	$0.495691\pi$
$674$	−58.9104	−2.26914
$675$	−25.7070	−0.989464
$676$	−22.4596	−0.863831
$677$	−35.9914	−1.38326	−0.691630	−	0.722252i	$-0.743107\pi$
$677$	−35.9914	−1.38326	−0.691630	+	0.722252i	$0.743107\pi$
$678$	12.3400	0.473915
$679$	−5.03093	−0.193069
$680$	0.0754012	0.00289150
$681$	−7.87821	−0.301894
$682$	−3.51908	−0.134753
$683$	−3.57338	−0.136732	−0.0683658	−	0.997660i	$-0.521779\pi$
$683$	−3.57338	−0.136732	−0.0683658	+	0.997660i	$0.521779\pi$
$684$	0.601154	0.0229857
$685$	0.937903	0.0358354
$686$	−18.6183	−0.710849
$687$	−34.7289	−1.32499
$688$	3.24329	0.123649
$689$	−8.16353	−0.311006
$690$	0.258462	0.00983948
$691$	−38.0721	−1.44833	−0.724166	−	0.689626i	$-0.757775\pi$
$691$	−38.0721	−1.44833	−0.724166	+	0.689626i	$0.757775\pi$
$692$	19.6507	0.747006
$693$	−0.0313518	−0.00119096
$694$	−20.3218	−0.771406
$695$	2.27003	0.0861070
$696$	0.556869	0.0211081
$697$	−3.27839	−0.124178
$698$	20.4331	0.773403
$699$	16.5749	0.626921
$700$	7.65445	0.289311
$701$	−49.4385	−1.86727	−0.933633	−	0.358231i	$-0.883380\pi$
$701$	−49.4385	−1.86727	−0.933633	+	0.358231i	$0.883380\pi$
$702$	19.5955	0.739583
$703$	−29.7411	−1.12171
$704$	−10.3570	−0.390345
$705$	−0.0387841	−0.00146069
$706$	69.1507	2.60252
$707$	6.59282	0.247948
$708$	4.05005	0.152210
$709$	−28.8979	−1.08528	−0.542641	−	0.839965i	$-0.682575\pi$
$709$	−28.8979	−1.08528	−0.542641	+	0.839965i	$0.682575\pi$
$710$	0.321764	0.0120756
$711$	0.0246757	0.000925410 0
$712$	−7.47236	−0.280038
$713$	−1.08116	−0.0404898
$714$	−2.39613	−0.0896728
$715$	0.203665	0.00761665
$716$	53.2471	1.98994
$717$	−35.7994	−1.33695
$718$	−43.9241	−1.63923
$719$	−10.6263	−0.396293	−0.198147	−	0.980172i	$-0.563492\pi$
$719$	−10.6263	−0.396293	−0.198147	+	0.980172i	$0.563492\pi$
$720$	0.0171657	0.000639727 0
$721$	−7.38825	−0.275153
$722$	−22.0745	−0.821529
$723$	−19.1392	−0.711794
$724$	20.1360	0.748348
$725$	−2.35087	−0.0873092
$726$	3.63066	0.134746
$727$	−36.2604	−1.34482	−0.672411	−	0.740178i	$-0.734741\pi$
$727$	−36.2604	−1.34482	−0.672411	+	0.740178i	$0.734741\pi$
$728$	−0.816483	−0.0302609
$729$	26.5590	0.983668
$730$	0.652220	0.0241398
$731$	−1.00000	−0.0369863
$732$	3.62379	0.133939
$733$	4.23069	0.156264	0.0781320	−	0.996943i	$-0.475104\pi$
$733$	4.23069	0.156264	0.0781320	+	0.996943i	$0.475104\pi$
$734$	8.07600	0.298091
$735$	−1.27675	−0.0470937
$736$	−5.17483	−0.190747
$737$	14.5216	0.534911
$738$	0.323901	0.0119230
$739$	−45.8849	−1.68790	−0.843951	−	0.536420i	$-0.819776\pi$
$739$	−45.8849	−1.68790	−0.843951	+	0.536420i	$0.819776\pi$
$740$	1.41594	0.0520510
$741$	17.3661	0.637958
$742$	6.12965	0.225026
$743$	−36.8393	−1.35150	−0.675752	−	0.737129i	$-0.736181\pi$
$743$	−36.8393	−1.35150	−0.675752	+	0.737129i	$0.736181\pi$
$744$	1.99908	0.0732898
$745$	0.342830	0.0125603
$746$	76.3376	2.79492
$747$	−0.518965	−0.0189879
$748$	2.32541	0.0850253
$749$	−0.657849	−0.0240373
$750$	4.04001	0.147520
$751$	33.6327	1.22727	0.613637	−	0.789588i	$-0.289706\pi$
$751$	33.6327	1.22727	0.613637	+	0.789588i	$0.289706\pi$
$752$	0.646743	0.0235843
$753$	10.2779	0.374549
$754$	1.79198	0.0652600
$755$	−1.23996	−0.0451269
$756$	−7.91015	−0.287689
$757$	3.79378	0.137887	0.0689437	−	0.997621i	$-0.478037\pi$
$757$	3.79378	0.137887	0.0689437	+	0.997621i	$0.478037\pi$
$758$	−39.2915	−1.42713
$759$	1.11544	0.0404880
$760$	0.410324	0.0148840
$761$	−31.1326	−1.12856	−0.564279	−	0.825584i	$-0.690846\pi$
$761$	−31.1326	−1.12856	−0.564279	+	0.825584i	$0.690846\pi$
$762$	−62.2456	−2.25492
$763$	9.94845	0.360158
$764$	−7.62862	−0.275994
$765$	−0.00529267	−0.000191357 0
$766$	30.7313	1.11037
$767$	1.82377	0.0658524
$768$	−16.7639	−0.604915
$769$	−1.77109	−0.0638671	−0.0319336	−	0.999490i	$-0.510166\pi$
$769$	−1.77109	−0.0638671	−0.0319336	+	0.999490i	$0.510166\pi$
$770$	−0.152923	−0.00551098
$771$	10.2611	0.369544
$772$	53.9506	1.94172
$773$	−21.8811	−0.787010	−0.393505	−	0.919323i	$-0.628738\pi$
$773$	−21.8811	−0.787010	−0.393505	+	0.919323i	$0.628738\pi$
$774$	0.0987988	0.00355125
$775$	−8.43930	−0.303149
$776$	−5.15900	−0.185197
$777$	−6.29660	−0.225889
$778$	−1.25648	−0.0450470
$779$	−17.8406	−0.639204
$780$	−0.826777	−0.0296034
$781$	1.38863	0.0496892
$782$	1.32889	0.0475209
$783$	2.42940	0.0868198
$784$	21.2904	0.760371
$785$	0.120189	0.00428972
$786$	−40.2402	−1.43532
$787$	−49.5005	−1.76450	−0.882251	−	0.470780i	$-0.843973\pi$
$787$	−49.5005	−1.76450	−0.882251	+	0.470780i	$0.843973\pi$
$788$	−12.2207	−0.435346
$789$	0.322933	0.0114967
$790$	0.120359	0.00428220
$791$	−2.24313	−0.0797564
$792$	−0.0321500	−0.00114240
$793$	1.63182	0.0579476
$794$	−66.7834	−2.37005
$795$	0.868572	0.0308051
$796$	−58.7732	−2.08316
$797$	−42.0408	−1.48916	−0.744580	−	0.667533i	$-0.767350\pi$
$797$	−42.0408	−1.48916	−0.744580	+	0.667533i	$0.767350\pi$
$798$	−13.0394	−0.461590
$799$	−0.199409	−0.00705460
$800$	−40.3936	−1.42813
$801$	0.524510	0.0185327
$802$	38.3320	1.35355
$803$	2.81478	0.0993315
$804$	−58.9504	−2.07902
$805$	−0.0469824	−0.00165591
$806$	6.43295	0.226591
$807$	41.4649	1.45963
$808$	6.76066	0.237839
$809$	49.6668	1.74619	0.873096	−	0.487549i	$-0.162109\pi$
$809$	49.6668	1.74619	0.873096	+	0.487549i	$0.162109\pi$
$810$	−2.11791	−0.0744159
$811$	−20.6880	−0.726453	−0.363226	−	0.931701i	$-0.618325\pi$
$811$	−20.6880	−0.726453	−0.363226	+	0.931701i	$0.618325\pi$
$812$	−0.723372	−0.0253854
$813$	−50.7652	−1.78041
$814$	11.3664	0.398392
$815$	−0.930260	−0.0325856
$816$	5.66185	0.198204
$817$	−5.44187	−0.190387
$818$	0.846145	0.0295848
$819$	0.0573117	0.00200263
$820$	0.849367	0.0296612
$821$	−52.5643	−1.83451	−0.917253	−	0.398305i	$-0.869598\pi$
$821$	−52.5643	−1.83451	−0.917253	+	0.398305i	$0.869598\pi$
$822$	−30.5638	−1.06604
$823$	−40.3449	−1.40633	−0.703167	−	0.711025i	$-0.748231\pi$
$823$	−40.3449	−1.40633	−0.703167	+	0.711025i	$0.748231\pi$
$824$	−7.57634	−0.263934
$825$	8.70688	0.303135
$826$	−1.36939	−0.0476471
$827$	39.9044	1.38761	0.693807	−	0.720161i	$-0.255932\pi$
$827$	39.9044	1.38761	0.693807	+	0.720161i	$0.255932\pi$
$828$	−0.0705850	−0.00245300
$829$	18.2832	0.635003	0.317502	−	0.948258i	$-0.397156\pi$
$829$	18.2832	0.635003	0.317502	+	0.948258i	$0.397156\pi$
$830$	−2.53133	−0.0878639
$831$	17.2755	0.599282
$832$	18.9328	0.656378
$833$	−6.56444	−0.227444
$834$	−73.9742	−2.56152
$835$	−2.50145	−0.0865663
$836$	12.6546	0.437668
$837$	8.72122	0.301449
$838$	55.1933	1.90662
$839$	31.7373	1.09569	0.547847	−	0.836578i	$-0.315447\pi$
$839$	31.7373	1.09569	0.547847	+	0.836578i	$0.315447\pi$
$840$	0.0868710	0.00299733
$841$	−28.7778	−0.992339
$842$	−39.7542	−1.37002
$843$	−1.28564	−0.0442798
$844$	38.3634	1.32052
$845$	1.07607	0.0370178
$846$	0.0197014	0.000677349 0
$847$	−0.659970	−0.0226768
$848$	−14.4838	−0.497377
$849$	−44.4263	−1.52471
$850$	10.3730	0.355791
$851$	3.49208	0.119707
$852$	−5.63714	−0.193125
$853$	36.6339	1.25432	0.627161	−	0.778890i	$-0.284217\pi$
$853$	36.6339	1.25432	0.627161	+	0.778890i	$0.284217\pi$
$854$	−1.22526	−0.0419277
$855$	−0.0288020	−0.000985008 0
$856$	−0.674597	−0.0230572
$857$	38.7803	1.32471	0.662355	−	0.749190i	$-0.269557\pi$
$857$	38.7803	1.32471	0.662355	+	0.749190i	$0.269557\pi$
$858$	−6.63692	−0.226581
$859$	32.8627	1.12126	0.560630	−	0.828067i	$-0.310559\pi$
$859$	32.8627	1.12126	0.560630	+	0.828067i	$0.310559\pi$
$860$	0.259081	0.00883459
$861$	−3.77708	−0.128723
$862$	67.7662	2.30813
$863$	−53.9394	−1.83612	−0.918060	−	0.396442i	$-0.870245\pi$
$863$	−53.9394	−1.83612	−0.918060	+	0.396442i	$0.870245\pi$
$864$	41.7429	1.42012
$865$	−0.941487	−0.0320115
$866$	−13.6229	−0.462926
$867$	−1.74571	−0.0592874
$868$	−2.59680	−0.0881413
$869$	0.519434	0.0176206
$870$	−0.190660	−0.00646399
$871$	−26.5458	−0.899471
$872$	10.2017	0.345474
$873$	0.362128	0.0122562
$874$	7.23164	0.244614
$875$	−0.734380	−0.0248266
$876$	−11.4266	−0.386068
$877$	−25.9764	−0.877159	−0.438580	−	0.898692i	$-0.644518\pi$
$877$	−25.9764	−0.877159	−0.438580	+	0.898692i	$0.644518\pi$
$878$	−32.2439	−1.08818
$879$	3.79339	0.127948
$880$	0.361345	0.0121809
$881$	33.5854	1.13152	0.565760	−	0.824570i	$-0.308583\pi$
$881$	33.5854	1.13152	0.565760	+	0.824570i	$0.308583\pi$
$882$	0.648559	0.0218381
$883$	−21.1674	−0.712340	−0.356170	−	0.934421i	$-0.615918\pi$
$883$	−21.1674	−0.712340	−0.356170	+	0.934421i	$0.615918\pi$
$884$	−4.25089	−0.142973
$885$	−0.194043	−0.00652267
$886$	−36.9549	−1.24152
$887$	−51.4386	−1.72714	−0.863570	−	0.504230i	$-0.831776\pi$
$887$	−51.4386	−1.72714	−0.863570	+	0.504230i	$0.831776\pi$
$888$	−6.45689	−0.216679
$889$	11.3148	0.379487
$890$	2.55838	0.0857572
$891$	−9.14026	−0.306210
$892$	−11.6482	−0.390010
$893$	−1.08516	−0.0363135
$894$	−11.1719	−0.373645
$895$	−2.55113	−0.0852750
$896$	−3.52590	−0.117792
$897$	−2.03905	−0.0680819
$898$	−9.80214	−0.327102
$899$	0.797543	0.0265996
$900$	−0.550970	−0.0183657
$901$	4.46578	0.148777
$902$	6.81826	0.227023
$903$	−1.15212	−0.0383400
$904$	−2.30023	−0.0765045
$905$	−0.964739	−0.0320690
$906$	40.4071	1.34244
$907$	−54.1157	−1.79688	−0.898441	−	0.439095i	$-0.855299\pi$
$907$	−54.1157	−1.79688	−0.898441	+	0.439095i	$0.855299\pi$
$908$	10.4943	0.348266
$909$	−0.474553	−0.0157399
$910$	0.279547	0.00926689
$911$	−1.89847	−0.0628992	−0.0314496	−	0.999505i	$-0.510012\pi$
$911$	−1.89847	−0.0628992	−0.0314496	+	0.999505i	$0.510012\pi$
$912$	30.8111	1.02026
$913$	−10.9245	−0.361547
$914$	−63.6725	−2.10610
$915$	−0.173620	−0.00573971
$916$	46.2613	1.52852
$917$	7.31474	0.241554
$918$	−10.7195	−0.353797
$919$	−6.48560	−0.213940	−0.106970	−	0.994262i	$-0.534115\pi$
$919$	−6.48560	−0.213940	−0.106970	+	0.994262i	$0.534115\pi$
$920$	−0.0481785	−0.00158840
$921$	−2.00621	−0.0661069
$922$	−38.7460	−1.27603
$923$	−2.53845	−0.0835539
$924$	2.67914	0.0881373
$925$	27.2584	0.896250
$926$	−73.0900	−2.40189
$927$	0.531809	0.0174669
$928$	3.81733	0.125310
$929$	−25.0150	−0.820716	−0.410358	−	0.911924i	$-0.634596\pi$
$929$	−25.0150	−0.820716	−0.410358	+	0.911924i	$0.634596\pi$
$930$	−0.684444	−0.0224438
$931$	−35.7228	−1.17077
$932$	−22.0790	−0.723220
$933$	30.3927	0.995012
$934$	71.1046	2.32661
$935$	−0.111413	−0.00364360
$936$	0.0587707	0.00192098
$937$	14.7683	0.482460	0.241230	−	0.970468i	$-0.422449\pi$
$937$	14.7683	0.482460	0.241230	+	0.970468i	$0.422449\pi$
$938$	19.9321	0.650806
$939$	−24.2227	−0.790478
$940$	0.0516632	0.00168507
$941$	45.9248	1.49711	0.748553	−	0.663075i	$-0.230749\pi$
$941$	45.9248	1.49711	0.748553	+	0.663075i	$0.230749\pi$
$942$	−3.91663	−0.127611
$943$	2.09476	0.0682149
$944$	3.23575	0.105315
$945$	0.378985	0.0123284
$946$	2.07976	0.0676189
$947$	3.16816	0.102951	0.0514757	−	0.998674i	$-0.483608\pi$
$947$	3.16816	0.102951	0.0514757	+	0.998674i	$0.483608\pi$
$948$	−2.10864	−0.0684854
$949$	−5.14547	−0.167029
$950$	56.4485	1.83143
$951$	−55.7067	−1.80641
$952$	0.446649	0.0144760
$953$	−22.9550	−0.743586	−0.371793	−	0.928316i	$-0.621257\pi$
$953$	−22.9550	−0.743586	−0.371793	+	0.928316i	$0.621257\pi$
$954$	−0.441214	−0.0142848
$955$	0.365496	0.0118272
$956$	47.6872	1.54232
$957$	−0.822831	−0.0265984
$958$	71.6712	2.31559
$959$	5.55579	0.179406
$960$	−2.01439	−0.0650142
$961$	−28.1369	−0.907643
$962$	−20.7780	−0.669909
$963$	0.0473522	0.00152590
$964$	25.4947	0.821130
$965$	−2.58484	−0.0832088
$966$	1.53103	0.0492602
$967$	14.3177	0.460426	0.230213	−	0.973140i	$-0.426058\pi$
$967$	14.3177	0.460426	0.230213	+	0.973140i	$0.426058\pi$
$968$	−0.676772	−0.0217523
$969$	−9.49993	−0.305182
$970$	1.76634	0.0567137
$971$	−38.4718	−1.23462	−0.617309	−	0.786721i	$-0.711777\pi$
$971$	−38.4718	−1.23462	−0.617309	+	0.786721i	$0.711777\pi$
$972$	1.14791	0.0368193
$973$	13.4468	0.431084
$974$	65.9255	2.11239
$975$	−15.9163	−0.509731
$976$	2.89520	0.0926730
$977$	30.6356	0.980120	0.490060	−	0.871689i	$-0.336975\pi$
$977$	30.6356	0.980120	0.490060	+	0.871689i	$0.336975\pi$
$978$	30.3147	0.969358
$979$	11.0412	0.352878
$980$	1.70072	0.0543275
$981$	−0.716093	−0.0228631
$982$	−42.2932	−1.34963
$983$	27.2071	0.867772	0.433886	−	0.900968i	$-0.357142\pi$
$983$	27.2071	0.867772	0.433886	+	0.900968i	$0.357142\pi$
$984$	−3.87324	−0.123474
$985$	0.585510	0.0186559
$986$	−0.980284	−0.0312186
$987$	−0.229743	−0.00731280
$988$	−23.1328	−0.735952
$989$	0.638962	0.0203178
$990$	0.0110075	0.000349841 0
$991$	−34.0476	−1.08156	−0.540779	−	0.841165i	$-0.681870\pi$
$991$	−34.0476	−1.08156	−0.540779	+	0.841165i	$0.681870\pi$
$992$	13.7037	0.435093
$993$	24.4789	0.776814
$994$	1.90601	0.0604549
$995$	2.81589	0.0892698
$996$	44.3477	1.40521
$997$	−3.81152	−0.120712	−0.0603560	−	0.998177i	$-0.519224\pi$
$997$	−3.81152	−0.120712	−0.0603560	+	0.998177i	$0.519224\pi$
$998$	52.2433	1.65373
$999$	−28.1690	−0.891226

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.c.1.11	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.c.1.11	✓	60	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.07976 q^{2} -1.74571 q^{3} +2.32541 q^{4} -0.111413 q^{5} +3.63066 q^{6} -0.659970 q^{7} -0.676772 q^{8} +0.0475049 q^{9} +O(q^{10})\)	\(q-2.07976 q^{2} -1.74571 q^{3} +2.32541 q^{4} -0.111413 q^{5} +3.63066 q^{6} -0.659970 q^{7} -0.676772 q^{8} +0.0475049 q^{9} +0.231713 q^{10} +1.00000 q^{11} -4.05949 q^{12} -1.82802 q^{13} +1.37258 q^{14} +0.194495 q^{15} -3.24329 q^{16} +1.00000 q^{17} -0.0987988 q^{18} +5.44187 q^{19} -0.259081 q^{20} +1.15212 q^{21} -2.07976 q^{22} -0.638962 q^{23} +1.18145 q^{24} -4.98759 q^{25} +3.80184 q^{26} +5.15420 q^{27} -1.53470 q^{28} +0.471345 q^{29} -0.404503 q^{30} +1.69206 q^{31} +8.09882 q^{32} -1.74571 q^{33} -2.07976 q^{34} +0.0735293 q^{35} +0.110468 q^{36} -5.46524 q^{37} -11.3178 q^{38} +3.19119 q^{39} +0.0754012 q^{40} -3.27839 q^{41} -2.39613 q^{42} -1.00000 q^{43} +2.32541 q^{44} -0.00529267 q^{45} +1.32889 q^{46} -0.199409 q^{47} +5.66185 q^{48} -6.56444 q^{49} +10.3730 q^{50} -1.74571 q^{51} -4.25089 q^{52} +4.46578 q^{53} -10.7195 q^{54} -0.111413 q^{55} +0.446649 q^{56} -9.49993 q^{57} -0.980284 q^{58} -0.997674 q^{59} +0.452280 q^{60} -0.892672 q^{61} -3.51908 q^{62} -0.0313518 q^{63} -10.3570 q^{64} +0.203665 q^{65} +3.63066 q^{66} +14.5216 q^{67} +2.32541 q^{68} +1.11544 q^{69} -0.152923 q^{70} +1.38863 q^{71} -0.0321500 q^{72} +2.81478 q^{73} +11.3664 q^{74} +8.70688 q^{75} +12.6546 q^{76} -0.659970 q^{77} -6.63692 q^{78} +0.519434 q^{79} +0.361345 q^{80} -9.14026 q^{81} +6.81826 q^{82} -10.9245 q^{83} +2.67914 q^{84} -0.111413 q^{85} +2.07976 q^{86} -0.822831 q^{87} -0.676772 q^{88} +11.0412 q^{89} +0.0110075 q^{90} +1.20644 q^{91} -1.48585 q^{92} -2.95385 q^{93} +0.414724 q^{94} -0.606296 q^{95} -14.1382 q^{96} +7.62296 q^{97} +13.6525 q^{98} +0.0475049 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * q^99

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