LMFDB - Embedded newform 6041.2.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$112$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67889 q^{2} -2.12545 q^{3} +5.17645 q^{4} -3.74850 q^{5} +5.69384 q^{6} -1.00000 q^{7} -8.50937 q^{8} +1.51753 q^{9} +O(q^{10})$	\(q-2.67889 q^{2} -2.12545 q^{3} +5.17645 q^{4} -3.74850 q^{5} +5.69384 q^{6} -1.00000 q^{7} -8.50937 q^{8} +1.51753 q^{9} +10.0418 q^{10} +0.969604 q^{11} -11.0023 q^{12} +3.86736 q^{13} +2.67889 q^{14} +7.96724 q^{15} +12.4428 q^{16} -4.42797 q^{17} -4.06529 q^{18} +6.61449 q^{19} -19.4039 q^{20} +2.12545 q^{21} -2.59746 q^{22} +0.0634992 q^{23} +18.0862 q^{24} +9.05126 q^{25} -10.3602 q^{26} +3.15092 q^{27} -5.17645 q^{28} +3.84460 q^{29} -21.3434 q^{30} +4.07237 q^{31} -16.3140 q^{32} -2.06084 q^{33} +11.8620 q^{34} +3.74850 q^{35} +7.85541 q^{36} +1.36011 q^{37} -17.7195 q^{38} -8.21987 q^{39} +31.8974 q^{40} +7.92409 q^{41} -5.69384 q^{42} +6.60408 q^{43} +5.01911 q^{44} -5.68846 q^{45} -0.170107 q^{46} +1.09840 q^{47} -26.4464 q^{48} +1.00000 q^{49} -24.2473 q^{50} +9.41142 q^{51} +20.0192 q^{52} +4.13181 q^{53} -8.44096 q^{54} -3.63456 q^{55} +8.50937 q^{56} -14.0588 q^{57} -10.2993 q^{58} +6.35882 q^{59} +41.2421 q^{60} +10.8604 q^{61} -10.9094 q^{62} -1.51753 q^{63} +18.8180 q^{64} -14.4968 q^{65} +5.52077 q^{66} +7.12954 q^{67} -22.9212 q^{68} -0.134964 q^{69} -10.0418 q^{70} +8.11169 q^{71} -12.9132 q^{72} +8.55276 q^{73} -3.64358 q^{74} -19.2380 q^{75} +34.2396 q^{76} -0.969604 q^{77} +22.0201 q^{78} -14.7484 q^{79} -46.6417 q^{80} -11.2497 q^{81} -21.2278 q^{82} -0.275271 q^{83} +11.0023 q^{84} +16.5982 q^{85} -17.6916 q^{86} -8.17149 q^{87} -8.25071 q^{88} +10.2888 q^{89} +15.2387 q^{90} -3.86736 q^{91} +0.328701 q^{92} -8.65562 q^{93} -2.94250 q^{94} -24.7944 q^{95} +34.6746 q^{96} -12.1797 q^{97} -2.67889 q^{98} +1.47140 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) $ 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * 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 $

$2$	−2.67889	−1.89426	−0.947131	−	0.320848i	$-0.896032\pi$
$2$	−2.67889	−1.89426	−0.947131	+	0.320848i	$0.896032\pi$
$3$	−2.12545	−1.22713	−0.613564	−	0.789645i	$-0.710265\pi$
$3$	−2.12545	−1.22713	−0.613564	+	0.789645i	$0.710265\pi$
$4$	5.17645	2.58823
$5$	−3.74850	−1.67638	−0.838190	−	0.545378i	$-0.816386\pi$
$5$	−3.74850	−1.67638	−0.838190	+	0.545378i	$0.816386\pi$
$6$	5.69384	2.32450
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−8.50937	−3.00852
$9$	1.51753	0.505843
$10$	10.0418	3.17550
$11$	0.969604	0.292347	0.146173	−	0.989259i	$-0.453304\pi$
$11$	0.969604	0.292347	0.146173	+	0.989259i	$0.453304\pi$
$12$	−11.0023	−3.17608
$13$	3.86736	1.07261	0.536306	−	0.844023i	$-0.319819\pi$
$13$	3.86736	1.07261	0.536306	+	0.844023i	$0.319819\pi$
$14$	2.67889	0.715963
$15$	7.96724	2.05713
$16$	12.4428	3.11069
$17$	−4.42797	−1.07394	−0.536970	−	0.843601i	$-0.680431\pi$
$17$	−4.42797	−1.07394	−0.536970	+	0.843601i	$0.680431\pi$
$18$	−4.06529	−0.958198
$19$	6.61449	1.51747	0.758734	−	0.651400i	$-0.225818\pi$
$19$	6.61449	1.51747	0.758734	+	0.651400i	$0.225818\pi$
$20$	−19.4039	−4.33885
$21$	2.12545	0.463811
$22$	−2.59746	−0.553781
$23$	0.0634992	0.0132405	0.00662025	−	0.999978i	$-0.497893\pi$
$23$	0.0634992	0.0132405	0.00662025	+	0.999978i	$0.497893\pi$
$24$	18.0862	3.69183
$25$	9.05126	1.81025
$26$	−10.3602	−2.03181
$27$	3.15092	0.606394
$28$	−5.17645	−0.978258
$29$	3.84460	0.713924	0.356962	−	0.934119i	$-0.383813\pi$
$29$	3.84460	0.713924	0.356962	+	0.934119i	$0.383813\pi$
$30$	−21.3434	−3.89675
$31$	4.07237	0.731420	0.365710	−	0.930729i	$-0.380826\pi$
$31$	4.07237	0.731420	0.365710	+	0.930729i	$0.380826\pi$
$32$	−16.3140	−2.88394
$33$	−2.06084	−0.358747
$34$	11.8620	2.03432
$35$	3.74850	0.633612
$36$	7.85541	1.30924
$37$	1.36011	0.223600	0.111800	−	0.993731i	$-0.464338\pi$
$37$	1.36011	0.223600	0.111800	+	0.993731i	$0.464338\pi$
$38$	−17.7195	−2.87448
$39$	−8.21987	−1.31623
$40$	31.8974	5.04342
$41$	7.92409	1.23754	0.618768	−	0.785574i	$-0.287632\pi$
$41$	7.92409	1.23754	0.618768	+	0.785574i	$0.287632\pi$
$42$	−5.69384	−0.878579
$43$	6.60408	1.00711	0.503556	−	0.863962i	$-0.332025\pi$
$43$	6.60408	1.00711	0.503556	+	0.863962i	$0.332025\pi$
$44$	5.01911	0.756659
$45$	−5.68846	−0.847985
$46$	−0.170107	−0.0250810
$47$	1.09840	0.160218	0.0801091	−	0.996786i	$-0.474473\pi$
$47$	1.09840	0.160218	0.0801091	+	0.996786i	$0.474473\pi$
$48$	−26.4464	−3.81721
$49$	1.00000	0.142857
$50$	−24.2473	−3.42909
$51$	9.41142	1.31786
$52$	20.0192	2.77616
$53$	4.13181	0.567548	0.283774	−	0.958891i	$-0.408413\pi$
$53$	4.13181	0.567548	0.283774	+	0.958891i	$0.408413\pi$
$54$	−8.44096	−1.14867
$55$	−3.63456	−0.490084
$56$	8.50937	1.13711
$57$	−14.0588	−1.86213
$58$	−10.2993	−1.35236
$59$	6.35882	0.827847	0.413924	−	0.910312i	$-0.364158\pi$
$59$	6.35882	0.827847	0.413924	+	0.910312i	$0.364158\pi$
$60$	41.2421	5.32433
$61$	10.8604	1.39054	0.695269	−	0.718750i	$-0.255285\pi$
$61$	10.8604	1.39054	0.695269	+	0.718750i	$0.255285\pi$
$62$	−10.9094	−1.38550
$63$	−1.51753	−0.191191
$64$	18.8180	2.35225
$65$	−14.4968	−1.79811
$66$	5.52077	0.679560
$67$	7.12954	0.871012	0.435506	−	0.900186i	$-0.356569\pi$
$67$	7.12954	0.871012	0.435506	+	0.900186i	$0.356569\pi$
$68$	−22.9212	−2.77960
$69$	−0.134964	−0.0162478
$70$	−10.0418	−1.20023
$71$	8.11169	0.962680	0.481340	−	0.876534i	$-0.340150\pi$
$71$	8.11169	0.962680	0.481340	+	0.876534i	$0.340150\pi$
$72$	−12.9132	−1.52184
$73$	8.55276	1.00103	0.500513	−	0.865729i	$-0.333145\pi$
$73$	8.55276	1.00103	0.500513	+	0.865729i	$0.333145\pi$
$74$	−3.64358	−0.423558
$75$	−19.2380	−2.22141
$76$	34.2396	3.92755
$77$	−0.969604	−0.110497
$78$	22.0201	2.49329
$79$	−14.7484	−1.65933	−0.829664	−	0.558264i	$-0.811468\pi$
$79$	−14.7484	−1.65933	−0.829664	+	0.558264i	$0.811468\pi$
$80$	−46.6417	−5.21470
$81$	−11.2497	−1.24997
$82$	−21.2278	−2.34422
$83$	−0.275271	−0.0302149	−0.0151075	−	0.999886i	$-0.504809\pi$
$83$	−0.275271	−0.0302149	−0.0151075	+	0.999886i	$0.504809\pi$
$84$	11.0023	1.20045
$85$	16.5982	1.80033
$86$	−17.6916	−1.90773
$87$	−8.17149	−0.876076
$88$	−8.25071	−0.879529
$89$	10.2888	1.09061	0.545307	−	0.838236i	$-0.316413\pi$
$89$	10.2888	1.09061	0.545307	+	0.838236i	$0.316413\pi$
$90$	15.2387	1.60631
$91$	−3.86736	−0.405409
$92$	0.328701	0.0342694
$93$	−8.65562	−0.897546
$94$	−2.94250	−0.303495
$95$	−24.7944	−2.54385
$96$	34.6746	3.53896
$97$	−12.1797	−1.23666	−0.618330	−	0.785919i	$-0.712190\pi$
$97$	−12.1797	−1.23666	−0.618330	+	0.785919i	$0.712190\pi$
$98$	−2.67889	−0.270609
$99$	1.47140	0.147881
$100$	46.8534	4.68534
$101$	13.6053	1.35377	0.676887	−	0.736087i	$-0.263329\pi$
$101$	13.6053	1.35377	0.676887	+	0.736087i	$0.263329\pi$
$102$	−25.2122	−2.49638
$103$	−6.53364	−0.643779	−0.321890	−	0.946777i	$-0.604318\pi$
$103$	−6.53364	−0.643779	−0.321890	+	0.946777i	$0.604318\pi$
$104$	−32.9088	−3.22697
$105$	−7.96724	−0.777523
$106$	−11.0687	−1.07508
$107$	−13.1038	−1.26679	−0.633397	−	0.773827i	$-0.718340\pi$
$107$	−13.1038	−1.26679	−0.633397	+	0.773827i	$0.718340\pi$
$108$	16.3106	1.56948
$109$	11.6468	1.11556	0.557779	−	0.829989i	$-0.311654\pi$
$109$	11.6468	1.11556	0.557779	+	0.829989i	$0.311654\pi$
$110$	9.73659	0.928347
$111$	−2.89084	−0.274386
$112$	−12.4428	−1.17573
$113$	9.33923	0.878561	0.439280	−	0.898350i	$-0.355233\pi$
$113$	9.33923	0.878561	0.439280	+	0.898350i	$0.355233\pi$
$114$	37.6619	3.52736
$115$	−0.238027	−0.0221961
$116$	19.9014	1.84780
$117$	5.86883	0.542573
$118$	−17.0346	−1.56816
$119$	4.42797	0.405911
$120$	−67.7962	−6.18892
$121$	−10.0599	−0.914534
$122$	−29.0939	−2.63404
$123$	−16.8422	−1.51861
$124$	21.0804	1.89308
$125$	−15.1861	−1.35829
$126$	4.06529	0.362165
$127$	22.0571	1.95725	0.978627	−	0.205642i	$-0.0659282\pi$
$127$	22.0571	1.95725	0.978627	+	0.205642i	$0.0659282\pi$
$128$	−17.7833	−1.57184
$129$	−14.0366	−1.23586
$130$	38.8353	3.40608
$131$	19.2830	1.68476	0.842381	−	0.538882i	$-0.181153\pi$
$131$	19.2830	1.68476	0.842381	+	0.538882i	$0.181153\pi$
$132$	−10.6679	−0.928517
$133$	−6.61449	−0.573549
$134$	−19.0993	−1.64992
$135$	−11.8112	−1.01655
$136$	37.6792	3.23097
$137$	9.68498	0.827444	0.413722	−	0.910403i	$-0.364229\pi$
$137$	9.68498	0.827444	0.413722	+	0.910403i	$0.364229\pi$
$138$	0.361554	0.0307776
$139$	−12.7750	−1.08356	−0.541779	−	0.840521i	$-0.682249\pi$
$139$	−12.7750	−1.08356	−0.541779	+	0.840521i	$0.682249\pi$
$140$	19.4039	1.63993
$141$	−2.33459	−0.196608
$142$	−21.7303	−1.82357
$143$	3.74981	0.313575
$144$	18.8822	1.57352
$145$	−14.4115	−1.19681
$146$	−22.9119	−1.89620
$147$	−2.12545	−0.175304
$148$	7.04053	0.578728
$149$	−5.27623	−0.432246	−0.216123	−	0.976366i	$-0.569341\pi$
$149$	−5.27623	−0.432246	−0.216123	+	0.976366i	$0.569341\pi$
$150$	51.5364	4.20793
$151$	0.266657	0.0217002	0.0108501	−	0.999941i	$-0.496546\pi$
$151$	0.266657	0.0217002	0.0108501	+	0.999941i	$0.496546\pi$
$152$	−56.2851	−4.56533
$153$	−6.71957	−0.543245
$154$	2.59746	0.209309
$155$	−15.2653	−1.22614
$156$	−42.5498	−3.40671
$157$	−10.0824	−0.804663	−0.402331	−	0.915494i	$-0.631800\pi$
$157$	−10.0824	−0.804663	−0.402331	+	0.915494i	$0.631800\pi$
$158$	39.5094	3.14320
$159$	−8.78195	−0.696454
$160$	61.1532	4.83458
$161$	−0.0634992	−0.00500444
$162$	30.1367	2.36776
$163$	−9.62607	−0.753972	−0.376986	−	0.926219i	$-0.623039\pi$
$163$	−9.62607	−0.753972	−0.376986	+	0.926219i	$0.623039\pi$
$164$	41.0187	3.20302
$165$	7.72507	0.601396
$166$	0.737421	0.0572350
$167$	14.1604	1.09576	0.547881	−	0.836556i	$-0.315435\pi$
$167$	14.1604	1.09576	0.547881	+	0.836556i	$0.315435\pi$
$168$	−18.0862	−1.39538
$169$	1.95647	0.150497
$170$	−44.4649	−3.41030
$171$	10.0377	0.767601
$172$	34.1857	2.60664
$173$	9.12938	0.694094	0.347047	−	0.937848i	$-0.387184\pi$
$173$	9.12938	0.694094	0.347047	+	0.937848i	$0.387184\pi$
$174$	21.8905	1.65952
$175$	−9.05126	−0.684211
$176$	12.0645	0.909399
$177$	−13.5153	−1.01587
$178$	−27.5627	−2.06591
$179$	1.42219	0.106299	0.0531497	−	0.998587i	$-0.483074\pi$
$179$	1.42219	0.106299	0.0531497	+	0.998587i	$0.483074\pi$
$180$	−29.4460	−2.19478
$181$	−0.153747	−0.0114279	−0.00571396	−	0.999984i	$-0.501819\pi$
$181$	−0.153747	−0.0114279	−0.00571396	+	0.999984i	$0.501819\pi$
$182$	10.3602	0.767951
$183$	−23.0833	−1.70637
$184$	−0.540338	−0.0398342
$185$	−5.09837	−0.374839
$186$	23.1874	1.70019
$187$	−4.29338	−0.313963
$188$	5.68582	0.414681
$189$	−3.15092	−0.229195
$190$	66.4215	4.81873
$191$	−4.86292	−0.351869	−0.175934	−	0.984402i	$-0.556295\pi$
$191$	−4.86292	−0.351869	−0.175934	+	0.984402i	$0.556295\pi$
$192$	−39.9967	−2.88651
$193$	3.75872	0.270559	0.135279	−	0.990807i	$-0.456807\pi$
$193$	3.75872	0.270559	0.135279	+	0.990807i	$0.456807\pi$
$194$	32.6280	2.34256
$195$	30.8122	2.20651
$196$	5.17645	0.369747
$197$	3.67491	0.261826	0.130913	−	0.991394i	$-0.458209\pi$
$197$	3.67491	0.261826	0.130913	+	0.991394i	$0.458209\pi$
$198$	−3.94172	−0.280126
$199$	8.21424	0.582292	0.291146	−	0.956679i	$-0.405963\pi$
$199$	8.21424	0.582292	0.291146	+	0.956679i	$0.405963\pi$
$200$	−77.0205	−5.44617
$201$	−15.1535	−1.06884
$202$	−36.4470	−2.56440
$203$	−3.84460	−0.269838
$204$	48.7178	3.41092
$205$	−29.7035	−2.07458
$206$	17.5029	1.21949
$207$	0.0963619	0.00669761
$208$	48.1206	3.33656
$209$	6.41344	0.443627
$210$	21.3434	1.47283
$211$	9.78350	0.673524	0.336762	−	0.941590i	$-0.390668\pi$
$211$	9.78350	0.673524	0.336762	+	0.941590i	$0.390668\pi$
$212$	21.3881	1.46894
$213$	−17.2410	−1.18133
$214$	35.1037	2.39964
$215$	−24.7554	−1.68830
$216$	−26.8123	−1.82435
$217$	−4.07237	−0.276451
$218$	−31.2004	−2.11316
$219$	−18.1784	−1.22839
$220$	−18.8141	−1.26845
$221$	−17.1245	−1.15192
$222$	7.74424	0.519759
$223$	−2.58299	−0.172970	−0.0864850	−	0.996253i	$-0.527563\pi$
$223$	−2.58299	−0.172970	−0.0864850	+	0.996253i	$0.527563\pi$
$224$	16.3140	1.09003
$225$	13.7355	0.915703
$226$	−25.0188	−1.66422
$227$	5.85378	0.388529	0.194264	−	0.980949i	$-0.437768\pi$
$227$	5.85378	0.388529	0.194264	+	0.980949i	$0.437768\pi$
$228$	−72.7745	−4.81961
$229$	−12.4871	−0.825174	−0.412587	−	0.910918i	$-0.635375\pi$
$229$	−12.4871	−0.825174	−0.412587	+	0.910918i	$0.635375\pi$
$230$	0.637648	0.0420452
$231$	2.06084	0.135593
$232$	−32.7151	−2.14785
$233$	−22.9595	−1.50413	−0.752064	−	0.659090i	$-0.770941\pi$
$233$	−22.9595	−1.50413	−0.752064	+	0.659090i	$0.770941\pi$
$234$	−15.7219	−1.02778
$235$	−4.11736	−0.268587
$236$	32.9161	2.14266
$237$	31.3470	2.03621
$238$	−11.8620	−0.768902
$239$	−24.2927	−1.57136	−0.785681	−	0.618632i	$-0.787687\pi$
$239$	−24.2927	−1.57136	−0.785681	+	0.618632i	$0.787687\pi$
$240$	99.1344	6.39910
$241$	15.0564	0.969865	0.484932	−	0.874552i	$-0.338844\pi$
$241$	15.0564	0.969865	0.484932	+	0.874552i	$0.338844\pi$
$242$	26.9493	1.73237
$243$	14.4579	0.927474
$244$	56.2186	3.59903
$245$	−3.74850	−0.239483
$246$	45.1185	2.87665
$247$	25.5806	1.62766
$248$	−34.6533	−2.20049
$249$	0.585074	0.0370776
$250$	40.6820	2.57296
$251$	−12.3953	−0.782387	−0.391194	−	0.920308i	$-0.627938\pi$
$251$	−12.3953	−0.782387	−0.391194	+	0.920308i	$0.627938\pi$
$252$	−7.85541	−0.494845
$253$	0.0615691	0.00387081
$254$	−59.0887	−3.70755
$255$	−35.2787	−2.20924
$256$	10.0035	0.625217
$257$	24.8680	1.55122	0.775611	−	0.631212i	$-0.217442\pi$
$257$	24.8680	1.55122	0.775611	+	0.631212i	$0.217442\pi$
$258$	37.6026	2.34103
$259$	−1.36011	−0.0845130
$260$	−75.0420	−4.65391
$261$	5.83429	0.361133
$262$	−51.6570	−3.19138
$263$	−5.20514	−0.320963	−0.160481	−	0.987039i	$-0.551305\pi$
$263$	−5.20514	−0.320963	−0.160481	+	0.987039i	$0.551305\pi$
$264$	17.5365	1.07929
$265$	−15.4881	−0.951427
$266$	17.7195	1.08645
$267$	−21.8684	−1.33832
$268$	36.9057	2.25438
$269$	17.0670	1.04060	0.520298	−	0.853985i	$-0.325821\pi$
$269$	17.0670	1.04060	0.520298	+	0.853985i	$0.325821\pi$
$270$	31.6409	1.92561
$271$	−23.0688	−1.40133	−0.700665	−	0.713490i	$-0.747113\pi$
$271$	−23.0688	−1.40133	−0.700665	+	0.713490i	$0.747113\pi$
$272$	−55.0961	−3.34069
$273$	8.21987	0.497489
$274$	−25.9450	−1.56739
$275$	8.77613	0.529221
$276$	−0.698636	−0.0420529
$277$	−10.8546	−0.652192	−0.326096	−	0.945337i	$-0.605733\pi$
$277$	−10.8546	−0.652192	−0.326096	+	0.945337i	$0.605733\pi$
$278$	34.2227	2.05254
$279$	6.17994	0.369983
$280$	−31.8974	−1.90623
$281$	19.5621	1.16698	0.583490	−	0.812121i	$-0.301687\pi$
$281$	19.5621	1.16698	0.583490	+	0.812121i	$0.301687\pi$
$282$	6.25412	0.372428
$283$	−5.83987	−0.347144	−0.173572	−	0.984821i	$-0.555531\pi$
$283$	−5.83987	−0.347144	−0.173572	+	0.984821i	$0.555531\pi$
$284$	41.9898	2.49163
$285$	52.6993	3.12163
$286$	−10.0453	−0.593992
$287$	−7.92409	−0.467744
$288$	−24.7570	−1.45882
$289$	2.60691	0.153348
$290$	38.6068	2.26707
$291$	25.8873	1.51754
$292$	44.2730	2.59088
$293$	−19.2996	−1.12750	−0.563748	−	0.825947i	$-0.690641\pi$
$293$	−19.2996	−1.12750	−0.563748	+	0.825947i	$0.690641\pi$
$294$	5.69384	0.332072
$295$	−23.8360	−1.38779
$296$	−11.5737	−0.672705
$297$	3.05514	0.177277
$298$	14.1345	0.818787
$299$	0.245574	0.0142019
$300$	−99.5845	−5.74951
$301$	−6.60408	−0.380653
$302$	−0.714345	−0.0411059
$303$	−28.9172	−1.66125
$304$	82.3025	4.72037
$305$	−40.7104	−2.33107
$306$	18.0010	1.02905
$307$	9.36924	0.534731	0.267366	−	0.963595i	$-0.413847\pi$
$307$	9.36924	0.534731	0.267366	+	0.963595i	$0.413847\pi$
$308$	−5.01911	−0.285990
$309$	13.8869	0.789999
$310$	40.8940	2.32263
$311$	28.7205	1.62859	0.814294	−	0.580453i	$-0.197125\pi$
$311$	28.7205	1.62859	0.814294	+	0.580453i	$0.197125\pi$
$312$	69.9459	3.95991
$313$	4.60391	0.260228	0.130114	−	0.991499i	$-0.458466\pi$
$313$	4.60391	0.260228	0.130114	+	0.991499i	$0.458466\pi$
$314$	27.0096	1.52424
$315$	5.68846	0.320508
$316$	−76.3445	−4.29471
$317$	2.80921	0.157781	0.0788904	−	0.996883i	$-0.474862\pi$
$317$	2.80921	0.157781	0.0788904	+	0.996883i	$0.474862\pi$
$318$	23.5259	1.31927
$319$	3.72774	0.208713
$320$	−70.5393	−3.94327
$321$	27.8515	1.55452
$322$	0.170107	0.00947972
$323$	−29.2888	−1.62967
$324$	−58.2335	−3.23519
$325$	35.0045	1.94170
$326$	25.7872	1.42822
$327$	−24.7546	−1.36893
$328$	−67.4290	−3.72314
$329$	−1.09840	−0.0605568
$330$	−20.6946	−1.13920
$331$	−18.4597	−1.01464	−0.507320	−	0.861758i	$-0.669364\pi$
$331$	−18.4597	−1.01464	−0.507320	+	0.861758i	$0.669364\pi$
$332$	−1.42493	−0.0782031
$333$	2.06400	0.113107
$334$	−37.9341	−2.07566
$335$	−26.7251	−1.46015
$336$	26.4464	1.44277
$337$	−1.80918	−0.0985523	−0.0492762	−	0.998785i	$-0.515691\pi$
$337$	−1.80918	−0.0985523	−0.0492762	+	0.998785i	$0.515691\pi$
$338$	−5.24116	−0.285082
$339$	−19.8500	−1.07811
$340$	85.9200	4.65967
$341$	3.94859	0.213828
$342$	−26.8898	−1.45404
$343$	−1.00000	−0.0539949
$344$	−56.1965	−3.02991
$345$	0.505914	0.0272375
$346$	−24.4566	−1.31479
$347$	−9.75584	−0.523721	−0.261861	−	0.965106i	$-0.584336\pi$
$347$	−9.75584	−0.523721	−0.261861	+	0.965106i	$0.584336\pi$
$348$	−42.2994	−2.26748
$349$	35.6130	1.90632	0.953159	−	0.302470i	$-0.0978112\pi$
$349$	35.6130	1.90632	0.953159	+	0.302470i	$0.0978112\pi$
$350$	24.2473	1.29607
$351$	12.1857	0.650426
$352$	−15.8182	−0.843110
$353$	−9.64173	−0.513178	−0.256589	−	0.966521i	$-0.582599\pi$
$353$	−9.64173	−0.513178	−0.256589	+	0.966521i	$0.582599\pi$
$354$	36.2061	1.92433
$355$	−30.4067	−1.61382
$356$	53.2597	2.82276
$357$	−9.41142	−0.498105
$358$	−3.80989	−0.201359
$359$	−18.2813	−0.964851	−0.482426	−	0.875937i	$-0.660244\pi$
$359$	−18.2813	−0.964851	−0.482426	+	0.875937i	$0.660244\pi$
$360$	48.4052	2.55118
$361$	24.7515	1.30271
$362$	0.411871	0.0216475
$363$	21.3817	1.12225
$364$	−20.0192	−1.04929
$365$	−32.0600	−1.67810
$366$	61.8377	3.23231
$367$	28.9017	1.50866	0.754329	−	0.656496i	$-0.227962\pi$
$367$	28.9017	1.50866	0.754329	+	0.656496i	$0.227962\pi$
$368$	0.790105	0.0411871
$369$	12.0250	0.625998
$370$	13.6580	0.710044
$371$	−4.13181	−0.214513
$372$	−44.8054	−2.32305
$373$	−1.68961	−0.0874848	−0.0437424	−	0.999043i	$-0.513928\pi$
$373$	−1.68961	−0.0874848	−0.0437424	+	0.999043i	$0.513928\pi$
$374$	11.5015	0.594727
$375$	32.2773	1.66680
$376$	−9.34670	−0.482019
$377$	14.8684	0.765764
$378$	8.44096	0.434156
$379$	−19.8212	−1.01815	−0.509073	−	0.860723i	$-0.670012\pi$
$379$	−19.8212	−1.01815	−0.509073	+	0.860723i	$0.670012\pi$
$380$	−128.347	−6.58407
$381$	−46.8813	−2.40180
$382$	13.0272	0.666531
$383$	−24.8906	−1.27185	−0.635926	−	0.771750i	$-0.719382\pi$
$383$	−24.8906	−1.27185	−0.635926	+	0.771750i	$0.719382\pi$
$384$	37.7975	1.92884
$385$	3.63456	0.185234
$386$	−10.0692	−0.512509
$387$	10.0219	0.509441
$388$	−63.0476	−3.20075
$389$	−6.07487	−0.308008	−0.154004	−	0.988070i	$-0.549217\pi$
$389$	−6.07487	−0.308008	−0.154004	+	0.988070i	$0.549217\pi$
$390$	−82.5425	−4.17970
$391$	−0.281173	−0.0142195
$392$	−8.50937	−0.429788
$393$	−40.9850	−2.06742
$394$	−9.84467	−0.495967
$395$	55.2845	2.78166
$396$	7.61664	0.382750
$397$	−9.93582	−0.498665	−0.249332	−	0.968418i	$-0.580211\pi$
$397$	−9.93582	−0.498665	−0.249332	+	0.968418i	$0.580211\pi$
$398$	−22.0050	−1.10301
$399$	14.0588	0.703818
$400$	112.623	5.63113
$401$	−39.4121	−1.96815	−0.984073	−	0.177763i	$-0.943114\pi$
$401$	−39.4121	−1.96815	−0.984073	+	0.177763i	$0.943114\pi$
$402$	40.5945	2.02467
$403$	15.7493	0.784530
$404$	70.4269	3.50387
$405$	42.1695	2.09542
$406$	10.2993	0.511144
$407$	1.31877	0.0653688
$408$	−80.0852	−3.96481
$409$	−24.9141	−1.23192	−0.615961	−	0.787777i	$-0.711232\pi$
$409$	−24.9141	−1.23192	−0.615961	+	0.787777i	$0.711232\pi$
$410$	79.5723	3.92980
$411$	−20.5849	−1.01538
$412$	−33.8211	−1.66625
$413$	−6.35882	−0.312897
$414$	−0.258143	−0.0126870
$415$	1.03185	0.0506517
$416$	−63.0922	−3.09335
$417$	27.1525	1.32966
$418$	−17.1809	−0.840345
$419$	−6.27132	−0.306374	−0.153187	−	0.988197i	$-0.548954\pi$
$419$	−6.27132	−0.306374	−0.153187	+	0.988197i	$0.548954\pi$
$420$	−41.2421	−2.01241
$421$	−20.7660	−1.01207	−0.506036	−	0.862512i	$-0.668890\pi$
$421$	−20.7660	−1.01207	−0.506036	+	0.862512i	$0.668890\pi$
$422$	−26.2089	−1.27583
$423$	1.66686	0.0810453
$424$	−35.1591	−1.70748
$425$	−40.0787	−1.94410
$426$	46.1867	2.23775
$427$	−10.8604	−0.525574
$428$	−67.8313	−3.27875
$429$	−7.97002	−0.384796
$430$	66.3170	3.19809
$431$	38.6007	1.85933	0.929664	−	0.368408i	$-0.120097\pi$
$431$	38.6007	1.85933	0.929664	+	0.368408i	$0.120097\pi$
$432$	39.2061	1.88630
$433$	28.8729	1.38754	0.693772	−	0.720195i	$-0.255948\pi$
$433$	28.8729	1.38754	0.693772	+	0.720195i	$0.255948\pi$
$434$	10.9094	0.523670
$435$	30.6309	1.46864
$436$	60.2890	2.88732
$437$	0.420015	0.0200920
$438$	48.6981	2.32688
$439$	17.4396	0.832346	0.416173	−	0.909285i	$-0.363371\pi$
$439$	17.4396	0.832346	0.416173	+	0.909285i	$0.363371\pi$
$440$	30.9278	1.47443
$441$	1.51753	0.0722633
$442$	45.8748	2.18204
$443$	26.4380	1.25611	0.628055	−	0.778169i	$-0.283851\pi$
$443$	26.4380	1.25611	0.628055	+	0.778169i	$0.283851\pi$
$444$	−14.9643	−0.710174
$445$	−38.5677	−1.82828
$446$	6.91955	0.327650
$447$	11.2144	0.530421
$448$	−18.8180	−0.889067
$449$	22.7027	1.07141	0.535704	−	0.844406i	$-0.320046\pi$
$449$	22.7027	1.07141	0.535704	+	0.844406i	$0.320046\pi$
$450$	−36.7960	−1.73458
$451$	7.68323	0.361789
$452$	48.3441	2.27391
$453$	−0.566766	−0.0266290
$454$	−15.6816	−0.735975
$455$	14.4968	0.679620
$456$	119.631	5.60224
$457$	−25.1506	−1.17649	−0.588247	−	0.808682i	$-0.700182\pi$
$457$	−25.1506	−1.17649	−0.588247	+	0.808682i	$0.700182\pi$
$458$	33.4517	1.56309
$459$	−13.9522	−0.651231
$460$	−1.23213	−0.0574486
$461$	9.68097	0.450888	0.225444	−	0.974256i	$-0.427617\pi$
$461$	9.68097	0.450888	0.225444	+	0.974256i	$0.427617\pi$
$462$	−5.52077	−0.256849
$463$	−11.6120	−0.539654	−0.269827	−	0.962909i	$-0.586967\pi$
$463$	−11.6120	−0.539654	−0.269827	+	0.962909i	$0.586967\pi$
$464$	47.8374	2.22080
$465$	32.4456	1.50463
$466$	61.5060	2.84921
$467$	9.30124	0.430410	0.215205	−	0.976569i	$-0.430958\pi$
$467$	9.30124	0.430410	0.215205	+	0.976569i	$0.430958\pi$
$468$	30.3797	1.40430
$469$	−7.12954	−0.329212
$470$	11.0299	0.508774
$471$	21.4296	0.987424
$472$	−54.1095	−2.49059
$473$	6.40334	0.294426
$474$	−83.9752	−3.85711
$475$	59.8695	2.74700
$476$	22.9212	1.05059
$477$	6.27014	0.287090
$478$	65.0774	2.97657
$479$	−13.3476	−0.609868	−0.304934	−	0.952373i	$-0.598634\pi$
$479$	−13.3476	−0.609868	−0.304934	+	0.952373i	$0.598634\pi$
$480$	−129.978	−5.93265
$481$	5.26003	0.239837
$482$	−40.3343	−1.83718
$483$	0.134964	0.00614109
$484$	−52.0744	−2.36702
$485$	45.6556	2.07311
$486$	−38.7311	−1.75688
$487$	29.2244	1.32429	0.662143	−	0.749378i	$-0.269647\pi$
$487$	29.2244	1.32429	0.662143	+	0.749378i	$0.269647\pi$
$488$	−92.4155	−4.18345
$489$	20.4597	0.925220
$490$	10.0418	0.453643
$491$	32.7290	1.47704	0.738519	−	0.674233i	$-0.235526\pi$
$491$	32.7290	1.47704	0.738519	+	0.674233i	$0.235526\pi$
$492$	−87.1831	−3.93052
$493$	−17.0238	−0.766712
$494$	−68.5277	−3.08321
$495$	−5.51555	−0.247905
$496$	50.6715	2.27522
$497$	−8.11169	−0.363859
$498$	−1.56735	−0.0702346
$499$	32.0018	1.43260	0.716299	−	0.697793i	$-0.245835\pi$
$499$	32.0018	1.43260	0.716299	+	0.697793i	$0.245835\pi$
$500$	−78.6103	−3.51556
$501$	−30.0971	−1.34464
$502$	33.2058	1.48205
$503$	20.5355	0.915632	0.457816	−	0.889047i	$-0.348632\pi$
$503$	20.5355	0.915632	0.457816	+	0.889047i	$0.348632\pi$
$504$	12.9132	0.575200
$505$	−50.9993	−2.26944
$506$	−0.164937	−0.00733233
$507$	−4.15837	−0.184680
$508$	114.178	5.06582
$509$	24.0925	1.06788	0.533941	−	0.845522i	$-0.320711\pi$
$509$	24.0925	1.06788	0.533941	+	0.845522i	$0.320711\pi$
$510$	94.5078	4.18487
$511$	−8.55276	−0.378352
$512$	8.76837	0.387511
$513$	20.8417	0.920184
$514$	−66.6186	−2.93842
$515$	24.4914	1.07922
$516$	−72.6599	−3.19867
$517$	1.06501	0.0468393
$518$	3.64358	0.160090
$519$	−19.4040	−0.851742
$520$	123.359	5.40963
$521$	−23.3932	−1.02488	−0.512438	−	0.858724i	$-0.671258\pi$
$521$	−23.3932	−1.02488	−0.512438	+	0.858724i	$0.671258\pi$
$522$	−15.6294	−0.684081
$523$	−29.8875	−1.30689	−0.653445	−	0.756974i	$-0.726677\pi$
$523$	−29.8875	−1.30689	−0.653445	+	0.756974i	$0.726677\pi$
$524$	99.8175	4.36055
$525$	19.2380	0.839614
$526$	13.9440	0.607987
$527$	−18.0323	−0.785501
$528$	−25.6426	−1.11595
$529$	−22.9960	−0.999825
$530$	41.4909	1.80225
$531$	9.64968	0.418761
$532$	−34.2396	−1.48448
$533$	30.6453	1.32740
$534$	58.5830	2.53513
$535$	49.1197	2.12363
$536$	−60.6679	−2.62045
$537$	−3.02279	−0.130443
$538$	−45.7207	−1.97116
$539$	0.969604	0.0417638
$540$	−61.1402	−2.63105
$541$	29.7884	1.28071	0.640353	−	0.768081i	$-0.278788\pi$
$541$	29.7884	1.28071	0.640353	+	0.768081i	$0.278788\pi$
$542$	61.7988	2.65449
$543$	0.326781	0.0140235
$544$	72.2380	3.09718
$545$	−43.6579	−1.87010
$546$	−22.0201	−0.942375
$547$	36.7979	1.57336	0.786682	−	0.617358i	$-0.211797\pi$
$547$	36.7979	1.57336	0.786682	+	0.617358i	$0.211797\pi$
$548$	50.1338	2.14161
$549$	16.4810	0.703394
$550$	−23.5103	−1.00248
$551$	25.4301	1.08336
$552$	1.14846	0.0488817
$553$	14.7484	0.627167
$554$	29.0784	1.23542
$555$	10.8363	0.459976
$556$	−66.1290	−2.80449
$557$	−34.0169	−1.44134	−0.720670	−	0.693278i	$-0.756166\pi$
$557$	−34.0169	−1.44134	−0.720670	+	0.693278i	$0.756166\pi$
$558$	−16.5554	−0.700845
$559$	25.5403	1.08024
$560$	46.6417	1.97097
$561$	9.12535	0.385272
$562$	−52.4048	−2.21056
$563$	−34.4419	−1.45155	−0.725777	−	0.687930i	$-0.758519\pi$
$563$	−34.4419	−1.45155	−0.725777	+	0.687930i	$0.758519\pi$
$564$	−12.0849	−0.508867
$565$	−35.0081	−1.47280
$566$	15.6444	0.657581
$567$	11.2497	0.472443
$568$	−69.0253	−2.89624
$569$	−0.0647375	−0.00271394	−0.00135697	−	0.999999i	$-0.500432\pi$
$569$	−0.0647375	−0.00271394	−0.00135697	+	0.999999i	$0.500432\pi$
$570$	−141.176	−5.91319
$571$	2.91267	0.121891	0.0609456	−	0.998141i	$-0.480588\pi$
$571$	2.91267	0.121891	0.0609456	+	0.998141i	$0.480588\pi$
$572$	19.4107	0.811602
$573$	10.3359	0.431788
$574$	21.2278	0.886030
$575$	0.574748	0.0239686
$576$	28.5569	1.18987
$577$	40.0113	1.66569	0.832847	−	0.553503i	$-0.186709\pi$
$577$	40.0113	1.66569	0.832847	+	0.553503i	$0.186709\pi$
$578$	−6.98363	−0.290481
$579$	−7.98897	−0.332010
$580$	−74.6003	−3.09761
$581$	0.275271	0.0114202
$582$	−69.3492	−2.87462
$583$	4.00622	0.165921
$584$	−72.7786	−3.01160
$585$	−21.9993	−0.909559
$586$	51.7015	2.13577
$587$	−36.2719	−1.49710	−0.748551	−	0.663078i	$-0.769250\pi$
$587$	−36.2719	−1.49710	−0.748551	+	0.663078i	$0.769250\pi$
$588$	−11.0023	−0.453726
$589$	26.9367	1.10991
$590$	63.8541	2.62883
$591$	−7.81082	−0.321294
$592$	16.9235	0.695551
$593$	6.66094	0.273532	0.136766	−	0.990603i	$-0.456329\pi$
$593$	6.66094	0.273532	0.136766	+	0.990603i	$0.456329\pi$
$594$	−8.18438	−0.335809
$595$	−16.5982	−0.680462
$596$	−27.3122	−1.11875
$597$	−17.4589	−0.714547
$598$	−0.657866	−0.0269022
$599$	29.2350	1.19451	0.597255	−	0.802051i	$-0.296258\pi$
$599$	29.2350	1.19451	0.597255	+	0.802051i	$0.296258\pi$
$600$	163.703	6.68315
$601$	13.9687	0.569794	0.284897	−	0.958558i	$-0.408041\pi$
$601$	13.9687	0.569794	0.284897	+	0.958558i	$0.408041\pi$
$602$	17.6916	0.721056
$603$	10.8193	0.440595
$604$	1.38034	0.0561651
$605$	37.7094	1.53311
$606$	77.4661	3.14685
$607$	24.9153	1.01128	0.505641	−	0.862744i	$-0.331256\pi$
$607$	24.9153	1.01128	0.505641	+	0.862744i	$0.331256\pi$
$608$	−107.909	−4.37629
$609$	8.17149	0.331126
$610$	109.059	4.41566
$611$	4.24791	0.171852
$612$	−34.7835	−1.40604
$613$	−21.0965	−0.852078	−0.426039	−	0.904705i	$-0.640091\pi$
$613$	−21.0965	−0.852078	−0.426039	+	0.904705i	$0.640091\pi$
$614$	−25.0992	−1.01292
$615$	63.1332	2.54578
$616$	8.25071	0.332431
$617$	7.41773	0.298627	0.149313	−	0.988790i	$-0.452294\pi$
$617$	7.41773	0.298627	0.149313	+	0.988790i	$0.452294\pi$
$618$	−37.2015	−1.49647
$619$	5.54327	0.222803	0.111401	−	0.993775i	$-0.464466\pi$
$619$	5.54327	0.222803	0.111401	+	0.993775i	$0.464466\pi$
$620$	−79.0201	−3.17352
$621$	0.200081	0.00802896
$622$	−76.9389	−3.08497
$623$	−10.2888	−0.412214
$624$	−102.278	−4.09439
$625$	11.6690	0.466759
$626$	−12.3334	−0.492941
$627$	−13.6314	−0.544387
$628$	−52.1910	−2.08265
$629$	−6.02252	−0.240133
$630$	−15.2387	−0.607126
$631$	−25.6960	−1.02294	−0.511471	−	0.859301i	$-0.670899\pi$
$631$	−25.6960	−1.02294	−0.511471	+	0.859301i	$0.670899\pi$
$632$	125.500	4.99211
$633$	−20.7943	−0.826500
$634$	−7.52556	−0.298878
$635$	−82.6812	−3.28110
$636$	−45.4594	−1.80258
$637$	3.86736	0.153230
$638$	−9.98620	−0.395357
$639$	12.3097	0.486965
$640$	66.6607	2.63499
$641$	−7.35023	−0.290317	−0.145158	−	0.989408i	$-0.546369\pi$
$641$	−7.35023	−0.290317	−0.145158	+	0.989408i	$0.546369\pi$
$642$	−74.6111	−2.94466
$643$	33.4867	1.32059	0.660294	−	0.751007i	$-0.270432\pi$
$643$	33.4867	1.32059	0.660294	+	0.751007i	$0.270432\pi$
$644$	−0.328701	−0.0129526
$645$	52.6163	2.07176
$646$	78.4614	3.08702
$647$	15.9497	0.627046	0.313523	−	0.949581i	$-0.398491\pi$
$647$	15.9497	0.627046	0.313523	+	0.949581i	$0.398491\pi$
$648$	95.7278	3.76054
$649$	6.16553	0.242018
$650$	−93.7731	−3.67808
$651$	8.65562	0.339240
$652$	−49.8289	−1.95145
$653$	43.2818	1.69375	0.846874	−	0.531793i	$-0.178482\pi$
$653$	43.2818	1.69375	0.846874	+	0.531793i	$0.178482\pi$
$654$	66.3149	2.59312
$655$	−72.2823	−2.82430
$656$	98.5975	3.84959
$657$	12.9791	0.506361
$658$	2.94250	0.114710
$659$	40.3769	1.57286	0.786431	−	0.617678i	$-0.211927\pi$
$659$	40.3769	1.57286	0.786431	+	0.617678i	$0.211927\pi$
$660$	39.9884	1.55655
$661$	6.26680	0.243750	0.121875	−	0.992545i	$-0.461109\pi$
$661$	6.26680	0.243750	0.121875	+	0.992545i	$0.461109\pi$
$662$	49.4516	1.92199
$663$	36.3973	1.41356
$664$	2.34238	0.0909021
$665$	24.7944	0.961487
$666$	−5.52924	−0.214254
$667$	0.244129	0.00945271
$668$	73.3005	2.83608
$669$	5.49001	0.212256
$670$	71.5936	2.76590
$671$	10.5303	0.406519
$672$	−34.6746	−1.33760
$673$	30.6795	1.18261	0.591303	−	0.806449i	$-0.298614\pi$
$673$	30.6795	1.18261	0.591303	+	0.806449i	$0.298614\pi$
$674$	4.84660	0.186684
$675$	28.5198	1.09773
$676$	10.1276	0.389522
$677$	6.61324	0.254168	0.127084	−	0.991892i	$-0.459438\pi$
$677$	6.61324	0.254168	0.127084	+	0.991892i	$0.459438\pi$
$678$	53.1761	2.04222
$679$	12.1797	0.467413
$680$	−141.241	−5.41633
$681$	−12.4419	−0.476775
$682$	−10.5778	−0.405046
$683$	29.1174	1.11415	0.557073	−	0.830464i	$-0.311924\pi$
$683$	29.1174	1.11415	0.557073	+	0.830464i	$0.311924\pi$
$684$	51.9596	1.98672
$685$	−36.3041	−1.38711
$686$	2.67889	0.102280
$687$	26.5408	1.01259
$688$	82.1729	3.13281
$689$	15.9792	0.608759
$690$	−1.35529	−0.0515949
$691$	47.4008	1.80321	0.901605	−	0.432559i	$-0.142389\pi$
$691$	47.4008	1.80321	0.901605	+	0.432559i	$0.142389\pi$
$692$	47.2578	1.79647
$693$	−1.47140	−0.0558939
$694$	26.1348	0.992065
$695$	47.8869	1.81646
$696$	69.5342	2.63569
$697$	−35.0876	−1.32904
$698$	−95.4032	−3.61106
$699$	48.7992	1.84576
$700$	−46.8534	−1.77089
$701$	46.4681	1.75508	0.877539	−	0.479506i	$-0.159184\pi$
$701$	46.4681	1.75508	0.877539	+	0.479506i	$0.159184\pi$
$702$	−32.6442	−1.23208
$703$	8.99642	0.339307
$704$	18.2460	0.687672
$705$	8.75123	0.329590
$706$	25.8291	0.972093
$707$	−13.6053	−0.511678
$708$	−69.9615	−2.62931
$709$	−11.9919	−0.450366	−0.225183	−	0.974317i	$-0.572298\pi$
$709$	−11.9919	−0.450366	−0.225183	+	0.974317i	$0.572298\pi$
$710$	81.4561	3.05699
$711$	−22.3812	−0.839359
$712$	−87.5515	−3.28113
$713$	0.258592	0.00968436
$714$	25.2122	0.943541
$715$	−14.0562	−0.525670
$716$	7.36189	0.275127
$717$	51.6328	1.92826
$718$	48.9737	1.82768
$719$	1.73451	0.0646861	0.0323431	−	0.999477i	$-0.489703\pi$
$719$	1.73451	0.0646861	0.0323431	+	0.999477i	$0.489703\pi$
$720$	−70.7801	−2.63782
$721$	6.53364	0.243326
$722$	−66.3066	−2.46767
$723$	−32.0015	−1.19015
$724$	−0.795864	−0.0295780
$725$	34.7985	1.29238
$726$	−57.2793	−2.12583
$727$	2.93315	0.108784	0.0543922	−	0.998520i	$-0.482678\pi$
$727$	2.93315	0.108784	0.0543922	+	0.998520i	$0.482678\pi$
$728$	32.9088	1.21968
$729$	3.01959	0.111837
$730$	85.8853	3.17876
$731$	−29.2427	−1.08158
$732$	−119.490	−4.41647
$733$	47.4892	1.75405	0.877026	−	0.480443i	$-0.159524\pi$
$733$	47.4892	1.75405	0.877026	+	0.480443i	$0.159524\pi$
$734$	−77.4246	−2.85779
$735$	7.96724	0.293876
$736$	−1.03593	−0.0381848
$737$	6.91283	0.254637
$738$	−32.2138	−1.18580
$739$	−25.2090	−0.927330	−0.463665	−	0.886011i	$-0.653466\pi$
$739$	−25.2090	−0.927330	−0.463665	+	0.886011i	$0.653466\pi$
$740$	−26.3914	−0.970169
$741$	−54.3703	−1.99734
$742$	11.0687	0.406344
$743$	−31.2008	−1.14465	−0.572323	−	0.820028i	$-0.693958\pi$
$743$	−31.2008	−1.14465	−0.572323	+	0.820028i	$0.693958\pi$
$744$	73.6538	2.70028
$745$	19.7780	0.724609
$746$	4.52629	0.165719
$747$	−0.417732	−0.0152840
$748$	−22.2245	−0.812607
$749$	13.1038	0.478803
$750$	−86.4675	−3.15735
$751$	21.2421	0.775135	0.387568	−	0.921841i	$-0.373315\pi$
$751$	21.2421	0.775135	0.387568	+	0.921841i	$0.373315\pi$
$752$	13.6671	0.498389
$753$	26.3457	0.960089
$754$	−39.8309	−1.45056
$755$	−0.999564	−0.0363779
$756$	−16.3106	−0.593210
$757$	−16.1568	−0.587227	−0.293614	−	0.955924i	$-0.594858\pi$
$757$	−16.1568	−0.587227	−0.293614	+	0.955924i	$0.594858\pi$
$758$	53.0988	1.92864
$759$	−0.130862	−0.00474998
$760$	210.985	7.65323
$761$	9.26307	0.335786	0.167893	−	0.985805i	$-0.446304\pi$
$761$	9.26307	0.335786	0.167893	+	0.985805i	$0.446304\pi$
$762$	125.590	4.54964
$763$	−11.6468	−0.421641
$764$	−25.1727	−0.910715
$765$	25.1883	0.910685
$766$	66.6793	2.40922
$767$	24.5918	0.887959
$768$	−21.2619	−0.767221
$769$	−39.0430	−1.40793	−0.703963	−	0.710237i	$-0.748588\pi$
$769$	−39.0430	−1.40793	−0.703963	+	0.710237i	$0.748588\pi$
$770$	−9.73659	−0.350882
$771$	−52.8556	−1.90355
$772$	19.4568	0.700267
$773$	−26.8490	−0.965693	−0.482846	−	0.875705i	$-0.660397\pi$
$773$	−26.8490	−0.965693	−0.482846	+	0.875705i	$0.660397\pi$
$774$	−26.8475	−0.965014
$775$	36.8601	1.32405
$776$	103.641	3.72051
$777$	2.89084	0.103708
$778$	16.2739	0.583448
$779$	52.4139	1.87792
$780$	159.498	5.71094
$781$	7.86512	0.281436
$782$	0.753230	0.0269355
$783$	12.1140	0.432919
$784$	12.4428	0.444384
$785$	37.7939	1.34892
$786$	109.794	3.91623
$787$	5.35709	0.190960	0.0954799	−	0.995431i	$-0.469561\pi$
$787$	5.35709	0.190960	0.0954799	+	0.995431i	$0.469561\pi$
$788$	19.0230	0.677666
$789$	11.0633	0.393862
$790$	−148.101	−5.26920
$791$	−9.33923	−0.332065
$792$	−12.5207	−0.444903
$793$	42.0012	1.49151
$794$	26.6170	0.944601
$795$	32.9192	1.16752
$796$	42.5206	1.50710
$797$	−8.66900	−0.307072	−0.153536	−	0.988143i	$-0.549066\pi$
$797$	−8.66900	−0.307072	−0.153536	+	0.988143i	$0.549066\pi$
$798$	−37.6619	−1.33322
$799$	−4.86369	−0.172065
$800$	−147.663	−5.22066
$801$	15.6136	0.551680
$802$	105.581	3.72818
$803$	8.29279	0.292646
$804$	−78.4412	−2.76641
$805$	0.238027	0.00838934
$806$	−42.1907	−1.48610
$807$	−36.2751	−1.27694
$808$	−115.772	−4.07285
$809$	22.9213	0.805871	0.402935	−	0.915228i	$-0.367990\pi$
$809$	22.9213	0.805871	0.402935	+	0.915228i	$0.367990\pi$
$810$	−112.967	−3.96927
$811$	46.7123	1.64029	0.820145	−	0.572156i	$-0.193893\pi$
$811$	46.7123	1.64029	0.820145	+	0.572156i	$0.193893\pi$
$812$	−19.9014	−0.698402
$813$	49.0316	1.71961
$814$	−3.53283	−0.123826
$815$	36.0833	1.26394
$816$	117.104	4.09946
$817$	43.6826	1.52826
$818$	66.7421	2.33358
$819$	−5.86883	−0.205073
$820$	−153.759	−5.36948
$821$	−18.7332	−0.653795	−0.326897	−	0.945060i	$-0.606003\pi$
$821$	−18.7332	−0.653795	−0.326897	+	0.945060i	$0.606003\pi$
$822$	55.1447	1.92339
$823$	−32.1998	−1.12242	−0.561208	−	0.827675i	$-0.689663\pi$
$823$	−32.1998	−1.12242	−0.561208	+	0.827675i	$0.689663\pi$
$824$	55.5972	1.93682
$825$	−18.6532	−0.649422
$826$	17.0346	0.592709
$827$	−50.4261	−1.75349	−0.876743	−	0.480959i	$-0.840289\pi$
$827$	−50.4261	−1.75349	−0.876743	+	0.480959i	$0.840289\pi$
$828$	0.498813	0.0173349
$829$	−23.1498	−0.804024	−0.402012	−	0.915634i	$-0.631689\pi$
$829$	−23.1498	−0.804024	−0.402012	+	0.915634i	$0.631689\pi$
$830$	−2.76422	−0.0959476
$831$	23.0710	0.800323
$832$	72.7760	2.52305
$833$	−4.42797	−0.153420
$834$	−72.7386	−2.51873
$835$	−53.0802	−1.83691
$836$	33.1988	1.14821
$837$	12.8317	0.443529
$838$	16.8002	0.580353
$839$	−45.6178	−1.57490	−0.787451	−	0.616378i	$-0.788600\pi$
$839$	−45.6178	−1.57490	−0.787451	+	0.616378i	$0.788600\pi$
$840$	67.7962	2.33919
$841$	−14.2191	−0.490312
$842$	55.6298	1.91713
$843$	−41.5783	−1.43203
$844$	50.6438	1.74323
$845$	−7.33382	−0.252291
$846$	−4.46532	−0.153521
$847$	10.0599	0.345661
$848$	51.4111	1.76547
$849$	12.4123	0.425990
$850$	107.366	3.68264
$851$	0.0863658	0.00296058
$852$	−89.2471	−3.05755
$853$	−35.1173	−1.20239	−0.601197	−	0.799101i	$-0.705309\pi$
$853$	−35.1173	−1.20239	−0.601197	+	0.799101i	$0.705309\pi$
$854$	29.0939	0.995574
$855$	−37.6262	−1.28679
$856$	111.505	3.81117
$857$	−20.6248	−0.704531	−0.352265	−	0.935900i	$-0.614589\pi$
$857$	−20.6248	−0.704531	−0.352265	+	0.935900i	$0.614589\pi$
$858$	21.3508	0.728904
$859$	−2.29122	−0.0781753	−0.0390877	−	0.999236i	$-0.512445\pi$
$859$	−2.29122	−0.0781753	−0.0390877	+	0.999236i	$0.512445\pi$
$860$	−128.145	−4.36971
$861$	16.8422	0.573982
$862$	−103.407	−3.52205
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	−51.4042	−1.74880
$865$	−34.2215	−1.16356
$866$	−77.3473	−2.62837
$867$	−5.54085	−0.188177
$868$	−21.0804	−0.715517
$869$	−14.3001	−0.485099
$870$	−82.0567	−2.78198
$871$	27.5725	0.934258
$872$	−99.1066	−3.35617
$873$	−18.4830	−0.625555
$874$	−1.12517	−0.0380596
$875$	15.1861	0.513385
$876$	−94.0999	−3.17934
$877$	−4.77684	−0.161303	−0.0806513	−	0.996742i	$-0.525700\pi$
$877$	−4.77684	−0.161303	−0.0806513	+	0.996742i	$0.525700\pi$
$878$	−46.7187	−1.57668
$879$	41.0203	1.38358
$880$	−45.2239	−1.52450
$881$	−9.76860	−0.329113	−0.164556	−	0.986368i	$-0.552619\pi$
$881$	−9.76860	−0.329113	−0.164556	+	0.986368i	$0.552619\pi$
$882$	−4.06529	−0.136885
$883$	−16.0248	−0.539277	−0.269639	−	0.962962i	$-0.586904\pi$
$883$	−16.0248	−0.539277	−0.269639	+	0.962962i	$0.586904\pi$
$884$	−88.6444	−2.98143
$885$	50.6622	1.70299
$886$	−70.8246	−2.37940
$887$	37.5702	1.26148	0.630742	−	0.775993i	$-0.282751\pi$
$887$	37.5702	1.26148	0.630742	+	0.775993i	$0.282751\pi$
$888$	24.5992	0.825495
$889$	−22.0571	−0.739773
$890$	103.319	3.46325
$891$	−10.9077	−0.365423
$892$	−13.3707	−0.447685
$893$	7.26537	0.243126
$894$	−30.0420	−1.00476
$895$	−5.33107	−0.178198
$896$	17.7833	0.594098
$897$	−0.521955	−0.0174276
$898$	−60.8181	−2.02953
$899$	15.6566	0.522178
$900$	71.1014	2.37005
$901$	−18.2955	−0.609513
$902$	−20.5825	−0.685323
$903$	14.0366	0.467110
$904$	−79.4709	−2.64316
$905$	0.576320	0.0191575
$906$	1.51830	0.0504422
$907$	2.86272	0.0950552	0.0475276	−	0.998870i	$-0.484866\pi$
$907$	2.86272	0.0950552	0.0475276	+	0.998870i	$0.484866\pi$
$908$	30.3018	1.00560
$909$	20.6464	0.684796
$910$	−38.8353	−1.28738
$911$	−3.29752	−0.109252	−0.0546258	−	0.998507i	$-0.517397\pi$
$911$	−3.29752	−0.109252	−0.0546258	+	0.998507i	$0.517397\pi$
$912$	−174.930	−5.79250
$913$	−0.266904	−0.00883323
$914$	67.3756	2.22859
$915$	86.5278	2.86052
$916$	−64.6391	−2.13574
$917$	−19.2830	−0.636780
$918$	37.3763	1.23360
$919$	14.7243	0.485709	0.242855	−	0.970063i	$-0.421916\pi$
$919$	14.7243	0.485709	0.242855	+	0.970063i	$0.421916\pi$
$920$	2.02546	0.0667774
$921$	−19.9138	−0.656183
$922$	−25.9343	−0.854100
$923$	31.3708	1.03258
$924$	10.6679	0.350947
$925$	12.3107	0.404773
$926$	31.1072	1.02225
$927$	−9.91499	−0.325651
$928$	−62.7209	−2.05892
$929$	−47.1812	−1.54796	−0.773982	−	0.633207i	$-0.781738\pi$
$929$	−47.1812	−1.54796	−0.773982	+	0.633207i	$0.781738\pi$
$930$	−86.9182	−2.85016
$931$	6.61449	0.216781
$932$	−118.849	−3.89302
$933$	−61.0438	−1.99848
$934$	−24.9170	−0.815310
$935$	16.0937	0.526321
$936$	−49.9400	−1.63234
$937$	−58.4274	−1.90874	−0.954371	−	0.298624i	$-0.903472\pi$
$937$	−58.4274	−1.90874	−0.954371	+	0.298624i	$0.903472\pi$
$938$	19.0993	0.623613
$939$	−9.78537	−0.319333
$940$	−21.3133	−0.695163
$941$	−21.5777	−0.703413	−0.351707	−	0.936110i	$-0.614399\pi$
$941$	−21.5777	−0.703413	−0.351707	+	0.936110i	$0.614399\pi$
$942$	−57.4075	−1.87044
$943$	0.503174	0.0163856
$944$	79.1212	2.57518
$945$	11.8112	0.384219
$946$	−17.1538	−0.557720
$947$	−46.3753	−1.50699	−0.753497	−	0.657452i	$-0.771634\pi$
$947$	−46.3753	−1.50699	−0.753497	+	0.657452i	$0.771634\pi$
$948$	162.266	5.27016
$949$	33.0766	1.07371
$950$	−160.384	−5.20354
$951$	−5.97083	−0.193617
$952$	−37.6792	−1.22119
$953$	−24.7054	−0.800286	−0.400143	−	0.916453i	$-0.631040\pi$
$953$	−24.7054	−0.800286	−0.400143	+	0.916453i	$0.631040\pi$
$954$	−16.7970	−0.543824
$955$	18.2287	0.589866
$956$	−125.750	−4.06704
$957$	−7.92311	−0.256118
$958$	35.7568	1.15525
$959$	−9.68498	−0.312744
$960$	149.928	4.83889
$961$	−14.4158	−0.465025
$962$	−14.0910	−0.454313
$963$	−19.8854	−0.640799
$964$	77.9385	2.51023
$965$	−14.0896	−0.453559
$966$	−0.361554	−0.0116328
$967$	34.2062	1.10000	0.549998	−	0.835166i	$-0.314628\pi$
$967$	34.2062	1.10000	0.549998	+	0.835166i	$0.314628\pi$
$968$	85.6031	2.75139
$969$	62.2517	1.99981
$970$	−122.306	−3.92702
$971$	22.7653	0.730575	0.365287	−	0.930895i	$-0.380971\pi$
$971$	22.7653	0.730575	0.365287	+	0.930895i	$0.380971\pi$
$972$	74.8406	2.40051
$973$	12.7750	0.409546
$974$	−78.2891	−2.50854
$975$	−74.4002	−2.38271
$976$	135.134	4.32553
$977$	−44.6230	−1.42762	−0.713808	−	0.700341i	$-0.753031\pi$
$977$	−44.6230	−1.42762	−0.713808	+	0.700341i	$0.753031\pi$
$978$	−54.8093	−1.75261
$979$	9.97610	0.318837
$980$	−19.4039	−0.619836
$981$	17.6743	0.564297
$982$	−87.6773	−2.79789
$983$	57.7169	1.84088	0.920441	−	0.390882i	$-0.127830\pi$
$983$	57.7169	1.84088	0.920441	+	0.390882i	$0.127830\pi$
$984$	143.317	4.56877
$985$	−13.7754	−0.438921
$986$	45.6048	1.45235
$987$	2.33459	0.0743110
$988$	132.417	4.21274
$989$	0.419354	0.0133347
$990$	14.7755	0.469598
$991$	−13.6565	−0.433812	−0.216906	−	0.976192i	$-0.569597\pi$
$991$	−13.6565	−0.433812	−0.216906	+	0.976192i	$0.569597\pi$
$992$	−66.4368	−2.10937
$993$	39.2352	1.24509
$994$	21.7303	0.689244
$995$	−30.7911	−0.976143
$996$	3.02861	0.0959652
$997$	2.91107	0.0921947	0.0460973	−	0.998937i	$-0.485322\pi$
$997$	2.91107	0.0921947	0.0460973	+	0.998937i	$0.485322\pi$
$998$	−85.7294	−2.71372
$999$	4.28559	0.135590

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.e.1.7	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.e.1.7	✓	112	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67889 q^{2} -2.12545 q^{3} +5.17645 q^{4} -3.74850 q^{5} +5.69384 q^{6} -1.00000 q^{7} -8.50937 q^{8} +1.51753 q^{9} +O(q^{10})\)	\(q-2.67889 q^{2} -2.12545 q^{3} +5.17645 q^{4} -3.74850 q^{5} +5.69384 q^{6} -1.00000 q^{7} -8.50937 q^{8} +1.51753 q^{9} +10.0418 q^{10} +0.969604 q^{11} -11.0023 q^{12} +3.86736 q^{13} +2.67889 q^{14} +7.96724 q^{15} +12.4428 q^{16} -4.42797 q^{17} -4.06529 q^{18} +6.61449 q^{19} -19.4039 q^{20} +2.12545 q^{21} -2.59746 q^{22} +0.0634992 q^{23} +18.0862 q^{24} +9.05126 q^{25} -10.3602 q^{26} +3.15092 q^{27} -5.17645 q^{28} +3.84460 q^{29} -21.3434 q^{30} +4.07237 q^{31} -16.3140 q^{32} -2.06084 q^{33} +11.8620 q^{34} +3.74850 q^{35} +7.85541 q^{36} +1.36011 q^{37} -17.7195 q^{38} -8.21987 q^{39} +31.8974 q^{40} +7.92409 q^{41} -5.69384 q^{42} +6.60408 q^{43} +5.01911 q^{44} -5.68846 q^{45} -0.170107 q^{46} +1.09840 q^{47} -26.4464 q^{48} +1.00000 q^{49} -24.2473 q^{50} +9.41142 q^{51} +20.0192 q^{52} +4.13181 q^{53} -8.44096 q^{54} -3.63456 q^{55} +8.50937 q^{56} -14.0588 q^{57} -10.2993 q^{58} +6.35882 q^{59} +41.2421 q^{60} +10.8604 q^{61} -10.9094 q^{62} -1.51753 q^{63} +18.8180 q^{64} -14.4968 q^{65} +5.52077 q^{66} +7.12954 q^{67} -22.9212 q^{68} -0.134964 q^{69} -10.0418 q^{70} +8.11169 q^{71} -12.9132 q^{72} +8.55276 q^{73} -3.64358 q^{74} -19.2380 q^{75} +34.2396 q^{76} -0.969604 q^{77} +22.0201 q^{78} -14.7484 q^{79} -46.6417 q^{80} -11.2497 q^{81} -21.2278 q^{82} -0.275271 q^{83} +11.0023 q^{84} +16.5982 q^{85} -17.6916 q^{86} -8.17149 q^{87} -8.25071 q^{88} +10.2888 q^{89} +15.2387 q^{90} -3.86736 q^{91} +0.328701 q^{92} -8.65562 q^{93} -2.94250 q^{94} -24.7944 q^{95} +34.6746 q^{96} -12.1797 q^{97} -2.67889 q^{98} +1.47140 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * q^99

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