LMFDB - Embedded newform 6001.2.a.c.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18200 q^{2} -1.07317 q^{3} +2.76112 q^{4} -3.39433 q^{5} +2.34166 q^{6} -4.74202 q^{7} -1.66076 q^{8} -1.84830 q^{9} +O(q^{10})$	\(q-2.18200 q^{2} -1.07317 q^{3} +2.76112 q^{4} -3.39433 q^{5} +2.34166 q^{6} -4.74202 q^{7} -1.66076 q^{8} -1.84830 q^{9} +7.40643 q^{10} +1.36163 q^{11} -2.96316 q^{12} +4.31010 q^{13} +10.3471 q^{14} +3.64271 q^{15} -1.89846 q^{16} -1.00000 q^{17} +4.03299 q^{18} +0.945966 q^{19} -9.37215 q^{20} +5.08901 q^{21} -2.97108 q^{22} +0.625648 q^{23} +1.78228 q^{24} +6.52150 q^{25} -9.40463 q^{26} +5.20306 q^{27} -13.0933 q^{28} +0.550004 q^{29} -7.94838 q^{30} -6.71565 q^{31} +7.46396 q^{32} -1.46127 q^{33} +2.18200 q^{34} +16.0960 q^{35} -5.10337 q^{36} +4.40635 q^{37} -2.06410 q^{38} -4.62548 q^{39} +5.63717 q^{40} -0.997765 q^{41} -11.1042 q^{42} -3.34561 q^{43} +3.75963 q^{44} +6.27374 q^{45} -1.36516 q^{46} -10.5927 q^{47} +2.03738 q^{48} +15.4868 q^{49} -14.2299 q^{50} +1.07317 q^{51} +11.9007 q^{52} -5.27741 q^{53} -11.3531 q^{54} -4.62184 q^{55} +7.87535 q^{56} -1.01519 q^{57} -1.20011 q^{58} +8.77134 q^{59} +10.0579 q^{60} -8.81388 q^{61} +14.6535 q^{62} +8.76467 q^{63} -12.4894 q^{64} -14.6299 q^{65} +3.18849 q^{66} -3.92880 q^{67} -2.76112 q^{68} -0.671429 q^{69} -35.1214 q^{70} +15.9173 q^{71} +3.06958 q^{72} -4.05414 q^{73} -9.61465 q^{74} -6.99869 q^{75} +2.61192 q^{76} -6.45690 q^{77} +10.0928 q^{78} -11.2004 q^{79} +6.44402 q^{80} -0.0388902 q^{81} +2.17712 q^{82} -4.24994 q^{83} +14.0514 q^{84} +3.39433 q^{85} +7.30012 q^{86} -0.590250 q^{87} -2.26134 q^{88} -9.75838 q^{89} -13.6893 q^{90} -20.4386 q^{91} +1.72749 q^{92} +7.20706 q^{93} +23.1133 q^{94} -3.21092 q^{95} -8.01012 q^{96} -3.30568 q^{97} -33.7921 q^{98} -2.51671 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * 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 $

$2$	−2.18200	−1.54291	−0.771453	−	0.636286i	$-0.780470\pi$
$2$	−2.18200	−1.54291	−0.771453	+	0.636286i	$0.780470\pi$
$3$	−1.07317	−0.619597	−0.309798	−	0.950802i	$-0.600262\pi$
$3$	−1.07317	−0.619597	−0.309798	+	0.950802i	$0.600262\pi$
$4$	2.76112	1.38056
$5$	−3.39433	−1.51799	−0.758996	−	0.651095i	$-0.774310\pi$
$5$	−3.39433	−1.51799	−0.758996	+	0.651095i	$0.774310\pi$
$6$	2.34166	0.955980
$7$	−4.74202	−1.79232	−0.896158	−	0.443736i	$-0.853653\pi$
$7$	−4.74202	−1.79232	−0.896158	+	0.443736i	$0.853653\pi$
$8$	−1.66076	−0.587167
$9$	−1.84830	−0.616100
$10$	7.40643	2.34212
$11$	1.36163	0.410548	0.205274	−	0.978705i	$-0.434191\pi$
$11$	1.36163	0.410548	0.205274	+	0.978705i	$0.434191\pi$
$12$	−2.96316	−0.855390
$13$	4.31010	1.19541	0.597703	−	0.801717i	$-0.296080\pi$
$13$	4.31010	1.19541	0.597703	+	0.801717i	$0.296080\pi$
$14$	10.3471	2.76537
$15$	3.64271	0.940543
$16$	−1.89846	−0.474616
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	4.03299	0.950584
$19$	0.945966	0.217020	0.108510	−	0.994095i	$-0.465392\pi$
$19$	0.945966	0.217020	0.108510	+	0.994095i	$0.465392\pi$
$20$	−9.37215	−2.09568
$21$	5.08901	1.11051
$22$	−2.97108	−0.633437
$23$	0.625648	0.130457	0.0652283	−	0.997870i	$-0.479222\pi$
$23$	0.625648	0.130457	0.0652283	+	0.997870i	$0.479222\pi$
$24$	1.78228	0.363807
$25$	6.52150	1.30430
$26$	−9.40463	−1.84440
$27$	5.20306	1.00133
$28$	−13.0933	−2.47440
$29$	0.550004	0.102133	0.0510666	−	0.998695i	$-0.483738\pi$
$29$	0.550004	0.102133	0.0510666	+	0.998695i	$0.483738\pi$
$30$	−7.94838	−1.45117
$31$	−6.71565	−1.20617	−0.603083	−	0.797678i	$-0.706061\pi$
$31$	−6.71565	−1.20617	−0.603083	+	0.797678i	$0.706061\pi$
$32$	7.46396	1.31945
$33$	−1.46127	−0.254374
$34$	2.18200	0.374210
$35$	16.0960	2.72072
$36$	−5.10337	−0.850562
$37$	4.40635	0.724399	0.362200	−	0.932101i	$-0.382026\pi$
$37$	4.40635	0.724399	0.362200	+	0.932101i	$0.382026\pi$
$38$	−2.06410	−0.334841
$39$	−4.62548	−0.740670
$40$	5.63717	0.891314
$41$	−0.997765	−0.155825	−0.0779123	−	0.996960i	$-0.524825\pi$
$41$	−0.997765	−0.155825	−0.0779123	+	0.996960i	$0.524825\pi$
$42$	−11.1042	−1.71342
$43$	−3.34561	−0.510201	−0.255100	−	0.966915i	$-0.582109\pi$
$43$	−3.34561	−0.510201	−0.255100	+	0.966915i	$0.582109\pi$
$44$	3.75963	0.566786
$45$	6.27374	0.935235
$46$	−1.36516	−0.201282
$47$	−10.5927	−1.54511	−0.772554	−	0.634949i	$-0.781021\pi$
$47$	−10.5927	−1.54511	−0.772554	+	0.634949i	$0.781021\pi$
$48$	2.03738	0.294070
$49$	15.4868	2.21239
$50$	−14.2299	−2.01241
$51$	1.07317	0.150274
$52$	11.9007	1.65033
$53$	−5.27741	−0.724909	−0.362454	−	0.932002i	$-0.618061\pi$
$53$	−5.27741	−0.724909	−0.362454	+	0.932002i	$0.618061\pi$
$54$	−11.3531	−1.54496
$55$	−4.62184	−0.623209
$56$	7.87535	1.05239
$57$	−1.01519	−0.134465
$58$	−1.20011	−0.157582
$59$	8.77134	1.14193	0.570966	−	0.820974i	$-0.306569\pi$
$59$	8.77134	1.14193	0.570966	+	0.820974i	$0.306569\pi$
$60$	10.0579	1.29847
$61$	−8.81388	−1.12850	−0.564251	−	0.825603i	$-0.690835\pi$
$61$	−8.81388	−1.12850	−0.564251	+	0.825603i	$0.690835\pi$
$62$	14.6535	1.86100
$63$	8.76467	1.10425
$64$	−12.4894	−1.56118
$65$	−14.6299	−1.81462
$66$	3.18849	0.392476
$67$	−3.92880	−0.479980	−0.239990	−	0.970775i	$-0.577144\pi$
$67$	−3.92880	−0.479980	−0.239990	+	0.970775i	$0.577144\pi$
$68$	−2.76112	−0.334835
$69$	−0.671429	−0.0808305
$70$	−35.1214	−4.19782
$71$	15.9173	1.88904	0.944518	−	0.328459i	$-0.106529\pi$
$71$	15.9173	1.88904	0.944518	+	0.328459i	$0.106529\pi$
$72$	3.06958	0.361753
$73$	−4.05414	−0.474501	−0.237251	−	0.971448i	$-0.576246\pi$
$73$	−4.05414	−0.474501	−0.237251	+	0.971448i	$0.576246\pi$
$74$	−9.61465	−1.11768
$75$	−6.99869	−0.808140
$76$	2.61192	0.299608
$77$	−6.45690	−0.735832
$78$	10.0928	1.14278
$79$	−11.2004	−1.26014	−0.630072	−	0.776537i	$-0.716975\pi$
$79$	−11.2004	−1.26014	−0.630072	+	0.776537i	$0.716975\pi$
$80$	6.44402	0.720463
$81$	−0.0388902	−0.00432113
$82$	2.17712	0.240423
$83$	−4.24994	−0.466491	−0.233246	−	0.972418i	$-0.574935\pi$
$83$	−4.24994	−0.466491	−0.233246	+	0.972418i	$0.574935\pi$
$84$	14.0514	1.53313
$85$	3.39433	0.368167
$86$	7.30012	0.787192
$87$	−0.590250	−0.0632814
$88$	−2.26134	−0.241060
$89$	−9.75838	−1.03439	−0.517193	−	0.855869i	$-0.673023\pi$
$89$	−9.75838	−1.03439	−0.517193	+	0.855869i	$0.673023\pi$
$90$	−13.6893	−1.44298
$91$	−20.4386	−2.14255
$92$	1.72749	0.180103
$93$	7.20706	0.747337
$94$	23.1133	2.38396
$95$	−3.21092	−0.329434
$96$	−8.01012	−0.817530
$97$	−3.30568	−0.335641	−0.167821	−	0.985818i	$-0.553673\pi$
$97$	−3.30568	−0.335641	−0.167821	+	0.985818i	$0.553673\pi$
$98$	−33.7921	−3.41352
$99$	−2.51671	−0.252939
$100$	18.0066	1.80066
$101$	5.99689	0.596713	0.298357	−	0.954454i	$-0.403562\pi$
$101$	5.99689	0.596713	0.298357	+	0.954454i	$0.403562\pi$
$102$	−2.34166	−0.231859
$103$	−12.5716	−1.23871	−0.619357	−	0.785109i	$-0.712607\pi$
$103$	−12.5716	−1.23871	−0.619357	+	0.785109i	$0.712607\pi$
$104$	−7.15804	−0.701903
$105$	−17.2738	−1.68575
$106$	11.5153	1.11847
$107$	0.349461	0.0337836	0.0168918	−	0.999857i	$-0.494623\pi$
$107$	0.349461	0.0337836	0.0168918	+	0.999857i	$0.494623\pi$
$108$	14.3663	1.38240
$109$	−15.6053	−1.49471	−0.747357	−	0.664422i	$-0.768678\pi$
$109$	−15.6053	−1.49471	−0.747357	+	0.664422i	$0.768678\pi$
$110$	10.0848	0.961552
$111$	−4.72877	−0.448835
$112$	9.00255	0.850661
$113$	−20.1327	−1.89393	−0.946964	−	0.321341i	$-0.895867\pi$
$113$	−20.1327	−1.89393	−0.946964	+	0.321341i	$0.895867\pi$
$114$	2.21513	0.207466
$115$	−2.12366	−0.198032
$116$	1.51863	0.141001
$117$	−7.96636	−0.736490
$118$	−19.1391	−1.76189
$119$	4.74202	0.434700
$120$	−6.04966	−0.552255
$121$	−9.14595	−0.831450
$122$	19.2319	1.74117
$123$	1.07077	0.0965485
$124$	−18.5427	−1.66518
$125$	−5.16447	−0.461924
$126$	−19.1245	−1.70375
$127$	16.4182	1.45688	0.728442	−	0.685107i	$-0.240245\pi$
$127$	16.4182	1.45688	0.728442	+	0.685107i	$0.240245\pi$
$128$	12.3240	1.08930
$129$	3.59042	0.316119
$130$	31.9225	2.79979
$131$	3.25368	0.284275	0.142137	−	0.989847i	$-0.454602\pi$
$131$	3.25368	0.284275	0.142137	+	0.989847i	$0.454602\pi$
$132$	−4.03474	−0.351179
$133$	−4.48579	−0.388967
$134$	8.57264	0.740563
$135$	−17.6609	−1.52001
$136$	1.66076	0.142409
$137$	−18.8039	−1.60653	−0.803264	−	0.595623i	$-0.796905\pi$
$137$	−18.8039	−1.60653	−0.803264	+	0.595623i	$0.796905\pi$
$138$	1.46506	0.124714
$139$	−22.7002	−1.92541	−0.962704	−	0.270556i	$-0.912792\pi$
$139$	−22.7002	−1.92541	−0.962704	+	0.270556i	$0.912792\pi$
$140$	44.4429	3.75611
$141$	11.3678	0.957344
$142$	−34.7315	−2.91461
$143$	5.86878	0.490772
$144$	3.50893	0.292411
$145$	−1.86690	−0.155037
$146$	8.84613	0.732111
$147$	−16.6200	−1.37079
$148$	12.1664	1.00008
$149$	−8.25737	−0.676470	−0.338235	−	0.941062i	$-0.609830\pi$
$149$	−8.25737	−0.676470	−0.338235	+	0.941062i	$0.609830\pi$
$150$	15.2711	1.24688
$151$	7.57855	0.616734	0.308367	−	0.951268i	$-0.400218\pi$
$151$	7.57855	0.616734	0.308367	+	0.951268i	$0.400218\pi$
$152$	−1.57102	−0.127427
$153$	1.84830	0.149426
$154$	14.0889	1.13532
$155$	22.7952	1.83095
$156$	−12.7715	−1.02254
$157$	−7.24473	−0.578192	−0.289096	−	0.957300i	$-0.593355\pi$
$157$	−7.24473	−0.578192	−0.289096	+	0.957300i	$0.593355\pi$
$158$	24.4393	1.94428
$159$	5.66358	0.449151
$160$	−25.3352	−2.00292
$161$	−2.96684	−0.233820
$162$	0.0848583	0.00666710
$163$	−21.9743	−1.72116	−0.860579	−	0.509317i	$-0.829898\pi$
$163$	−21.9743	−1.72116	−0.860579	+	0.509317i	$0.829898\pi$
$164$	−2.75495	−0.215125
$165$	4.96003	0.386138
$166$	9.27336	0.719753
$167$	10.1375	0.784464	0.392232	−	0.919866i	$-0.371703\pi$
$167$	10.1375	0.784464	0.392232	+	0.919866i	$0.371703\pi$
$168$	−8.45161	−0.652056
$169$	5.57697	0.428998
$170$	−7.40643	−0.568047
$171$	−1.74843	−0.133706
$172$	−9.23762	−0.704362
$173$	4.62366	0.351531	0.175765	−	0.984432i	$-0.443760\pi$
$173$	4.62366	0.351531	0.175765	+	0.984432i	$0.443760\pi$
$174$	1.28792	0.0976373
$175$	−30.9251	−2.33772
$176$	−2.58501	−0.194853
$177$	−9.41317	−0.707537
$178$	21.2928	1.59596
$179$	22.3294	1.66897	0.834487	−	0.551027i	$-0.185764\pi$
$179$	22.3294	1.66897	0.834487	+	0.551027i	$0.185764\pi$
$180$	17.3225	1.29115
$181$	15.2962	1.13696	0.568479	−	0.822698i	$-0.307532\pi$
$181$	15.2962	1.13696	0.568479	+	0.822698i	$0.307532\pi$
$182$	44.5970	3.30575
$183$	9.45882	0.699216
$184$	−1.03905	−0.0765998
$185$	−14.9566	−1.09963
$186$	−15.7258	−1.15307
$187$	−1.36163	−0.0995725
$188$	−29.2478	−2.13311
$189$	−24.6730	−1.79470
$190$	7.00623	0.508286
$191$	−14.3824	−1.04067	−0.520337	−	0.853961i	$-0.674194\pi$
$191$	−14.3824	−1.04067	−0.520337	+	0.853961i	$0.674194\pi$
$192$	13.4033	0.967301
$193$	−10.7341	−0.772657	−0.386329	−	0.922361i	$-0.626257\pi$
$193$	−10.7341	−0.772657	−0.386329	+	0.922361i	$0.626257\pi$
$194$	7.21300	0.517863
$195$	15.7004	1.12433
$196$	42.7608	3.05434
$197$	16.3937	1.16800	0.584002	−	0.811753i	$-0.301486\pi$
$197$	16.3937	1.16800	0.584002	+	0.811753i	$0.301486\pi$
$198$	5.49145	0.390260
$199$	17.9065	1.26936	0.634678	−	0.772776i	$-0.281133\pi$
$199$	17.9065	1.26936	0.634678	+	0.772776i	$0.281133\pi$
$200$	−10.8306	−0.765841
$201$	4.21629	0.297394
$202$	−13.0852	−0.920672
$203$	−2.60813	−0.183055
$204$	2.96316	0.207463
$205$	3.38675	0.236541
$206$	27.4312	1.91122
$207$	−1.15639	−0.0803743
$208$	−8.18257	−0.567359
$209$	1.28806	0.0890970
$210$	37.6914	2.60095
$211$	20.7110	1.42580	0.712901	−	0.701265i	$-0.247381\pi$
$211$	20.7110	1.42580	0.712901	+	0.701265i	$0.247381\pi$
$212$	−14.5716	−1.00078
$213$	−17.0820	−1.17044
$214$	−0.762523	−0.0521250
$215$	11.3561	0.774480
$216$	−8.64103	−0.587948
$217$	31.8458	2.16183
$218$	34.0507	2.30620
$219$	4.35080	0.294000
$220$	−12.7614	−0.860376
$221$	−4.31010	−0.289929
$222$	10.3182	0.692511
$223$	−9.04857	−0.605937	−0.302969	−	0.953001i	$-0.597978\pi$
$223$	−9.04857	−0.605937	−0.302969	+	0.953001i	$0.597978\pi$
$224$	−35.3943	−2.36488
$225$	−12.0537	−0.803579
$226$	43.9296	2.92215
$227$	12.0337	0.798703	0.399351	−	0.916798i	$-0.369235\pi$
$227$	12.0337	0.798703	0.399351	+	0.916798i	$0.369235\pi$
$228$	−2.80305	−0.185636
$229$	22.2385	1.46956	0.734779	−	0.678306i	$-0.237286\pi$
$229$	22.2385	1.46956	0.734779	+	0.678306i	$0.237286\pi$
$230$	4.63382	0.305545
$231$	6.92937	0.455919
$232$	−0.913424	−0.0599692
$233$	−17.8281	−1.16796	−0.583979	−	0.811769i	$-0.698505\pi$
$233$	−17.8281	−1.16796	−0.583979	+	0.811769i	$0.698505\pi$
$234$	17.3826	1.13633
$235$	35.9552	2.34546
$236$	24.2187	1.57650
$237$	12.0200	0.780781
$238$	−10.3471	−0.670702
$239$	−26.8667	−1.73787	−0.868933	−	0.494930i	$-0.835194\pi$
$239$	−26.8667	−1.73787	−0.868933	+	0.494930i	$0.835194\pi$
$240$	−6.91555	−0.446397
$241$	−10.1293	−0.652488	−0.326244	−	0.945286i	$-0.605783\pi$
$241$	−10.1293	−0.652488	−0.326244	+	0.945286i	$0.605783\pi$
$242$	19.9565	1.28285
$243$	−15.5675	−0.998653
$244$	−24.3362	−1.55796
$245$	−52.5672	−3.35840
$246$	−2.33643	−0.148965
$247$	4.07721	0.259427
$248$	11.1531	0.708221
$249$	4.56092	0.289037
$250$	11.2689	0.712705
$251$	21.3865	1.34990	0.674951	−	0.737863i	$-0.264165\pi$
$251$	21.3865	1.34990	0.674951	+	0.737863i	$0.264165\pi$
$252$	24.2003	1.52448
$253$	0.851904	0.0535587
$254$	−35.8246	−2.24784
$255$	−3.64271	−0.228115
$256$	−1.91207	−0.119504
$257$	−3.65771	−0.228162	−0.114081	−	0.993471i	$-0.536392\pi$
$257$	−3.65771	−0.228162	−0.114081	+	0.993471i	$0.536392\pi$
$258$	−7.83429	−0.487741
$259$	−20.8950	−1.29835
$260$	−40.3949	−2.50519
$261$	−1.01657	−0.0629243
$262$	−7.09952	−0.438610
$263$	−24.1112	−1.48676	−0.743381	−	0.668868i	$-0.766779\pi$
$263$	−24.1112	−1.48676	−0.743381	+	0.668868i	$0.766779\pi$
$264$	2.42681	0.149360
$265$	17.9133	1.10041
$266$	9.78799	0.600140
$267$	10.4724	0.640903
$268$	−10.8479	−0.662640
$269$	−14.3602	−0.875559	−0.437780	−	0.899082i	$-0.644235\pi$
$269$	−14.3602	−0.875559	−0.437780	+	0.899082i	$0.644235\pi$
$270$	38.5361	2.34523
$271$	15.4358	0.937657	0.468829	−	0.883289i	$-0.344676\pi$
$271$	15.4358	0.937657	0.468829	+	0.883289i	$0.344676\pi$
$272$	1.89846	0.115111
$273$	21.9341	1.32751
$274$	41.0301	2.47872
$275$	8.87989	0.535478
$276$	−1.85389	−0.111591
$277$	−21.3974	−1.28564	−0.642822	−	0.766015i	$-0.722237\pi$
$277$	−21.3974	−1.28564	−0.642822	+	0.766015i	$0.722237\pi$
$278$	49.5319	2.97072
$279$	12.4125	0.743119
$280$	−26.7316	−1.59752
$281$	10.7958	0.644025	0.322012	−	0.946735i	$-0.395641\pi$
$281$	10.7958	0.644025	0.322012	+	0.946735i	$0.395641\pi$
$282$	−24.8046	−1.47709
$283$	−14.0161	−0.833173	−0.416586	−	0.909096i	$-0.636774\pi$
$283$	−14.0161	−0.833173	−0.416586	+	0.909096i	$0.636774\pi$
$284$	43.9496	2.60793
$285$	3.44588	0.204116
$286$	−12.8057	−0.757215
$287$	4.73142	0.279287
$288$	−13.7956	−0.812916
$289$	1.00000	0.0588235
$290$	4.07357	0.239208
$291$	3.54757	0.207962
$292$	−11.1940	−0.655077
$293$	16.7685	0.979629	0.489815	−	0.871827i	$-0.337064\pi$
$293$	16.7685	0.979629	0.489815	+	0.871827i	$0.337064\pi$
$294$	36.2648	2.11500
$295$	−29.7729	−1.73344
$296$	−7.31788	−0.425343
$297$	7.08467	0.411094
$298$	18.0176	1.04373
$299$	2.69661	0.155949
$300$	−19.3242	−1.11568
$301$	15.8649	0.914440
$302$	−16.5364	−0.951562
$303$	−6.43570	−0.369722
$304$	−1.79588	−0.103001
$305$	29.9172	1.71306
$306$	−4.03299	−0.230551
$307$	10.3147	0.588689	0.294345	−	0.955699i	$-0.404899\pi$
$307$	10.3147	0.588689	0.294345	+	0.955699i	$0.404899\pi$
$308$	−17.8283	−1.01586
$309$	13.4915	0.767503
$310$	−49.7390	−2.82498
$311$	−28.3916	−1.60994	−0.804969	−	0.593317i	$-0.797818\pi$
$311$	−28.3916	−1.60994	−0.804969	+	0.593317i	$0.797818\pi$
$312$	7.68181	0.434897
$313$	−28.7385	−1.62440	−0.812198	−	0.583382i	$-0.801729\pi$
$313$	−28.7385	−1.62440	−0.812198	+	0.583382i	$0.801729\pi$
$314$	15.8080	0.892096
$315$	−29.7502	−1.67624
$316$	−30.9256	−1.73970
$317$	20.9348	1.17581	0.587907	−	0.808928i	$-0.299952\pi$
$317$	20.9348	1.17581	0.587907	+	0.808928i	$0.299952\pi$
$318$	−12.3579	−0.692998
$319$	0.748904	0.0419306
$320$	42.3933	2.36986
$321$	−0.375032	−0.0209322
$322$	6.47363	0.360762
$323$	−0.945966	−0.0526350
$324$	−0.107380	−0.00596557
$325$	28.1083	1.55917
$326$	47.9478	2.65559
$327$	16.7472	0.926121
$328$	1.65705	0.0914951
$329$	50.2309	2.76932
$330$	−10.8228	−0.595775
$331$	−4.28052	−0.235279	−0.117639	−	0.993056i	$-0.537533\pi$
$331$	−4.28052	−0.235279	−0.117639	+	0.993056i	$0.537533\pi$
$332$	−11.7346	−0.644019
$333$	−8.14425	−0.446302
$334$	−22.1200	−1.21035
$335$	13.3357	0.728605
$336$	−9.66130	−0.527067
$337$	−25.9208	−1.41199	−0.705997	−	0.708215i	$-0.749501\pi$
$337$	−25.9208	−1.41199	−0.705997	+	0.708215i	$0.749501\pi$
$338$	−12.1689	−0.661903
$339$	21.6059	1.17347
$340$	9.37215	0.508276
$341$	−9.14426	−0.495189
$342$	3.81507	0.206295
$343$	−40.2444	−2.17299
$344$	5.55625	0.299573
$345$	2.27905	0.122700
$346$	−10.0888	−0.542379
$347$	−33.7416	−1.81134	−0.905671	−	0.423981i	$-0.860632\pi$
$347$	−33.7416	−1.81134	−0.905671	+	0.423981i	$0.860632\pi$
$348$	−1.62975	−0.0873637
$349$	10.6497	0.570066	0.285033	−	0.958518i	$-0.407995\pi$
$349$	10.6497	0.570066	0.285033	+	0.958518i	$0.407995\pi$
$350$	67.4785	3.60688
$351$	22.4257	1.19700
$352$	10.1632	0.541699
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	20.5395	1.09166
$355$	−54.0286	−2.86754
$356$	−26.9440	−1.42803
$357$	−5.08901	−0.269339
$358$	−48.7226	−2.57507
$359$	−11.1186	−0.586819	−0.293409	−	0.955987i	$-0.594790\pi$
$359$	−11.1186	−0.586819	−0.293409	+	0.955987i	$0.594790\pi$
$360$	−10.4192	−0.549139
$361$	−18.1051	−0.952903
$362$	−33.3763	−1.75422
$363$	9.81519	0.515164
$364$	−56.4334	−2.95791
$365$	13.7611	0.720289
$366$	−20.6391	−1.07882
$367$	−37.5506	−1.96013	−0.980064	−	0.198684i	$-0.936333\pi$
$367$	−37.5506	−1.96013	−0.980064	+	0.198684i	$0.936333\pi$
$368$	−1.18777	−0.0619168
$369$	1.84417	0.0960035
$370$	32.6353	1.69663
$371$	25.0256	1.29926
$372$	19.8995	1.03174
$373$	9.50231	0.492011	0.246005	−	0.969268i	$-0.420882\pi$
$373$	9.50231	0.492011	0.246005	+	0.969268i	$0.420882\pi$
$374$	2.97108	0.153631
$375$	5.54237	0.286207
$376$	17.5920	0.907236
$377$	2.37057	0.122091
$378$	53.8365	2.76905
$379$	−11.2615	−0.578464	−0.289232	−	0.957259i	$-0.593400\pi$
$379$	−11.2615	−0.578464	−0.289232	+	0.957259i	$0.593400\pi$
$380$	−8.86574	−0.454803
$381$	−17.6196	−0.902681
$382$	31.3824	1.60566
$383$	19.7067	1.00697	0.503483	−	0.864005i	$-0.332052\pi$
$383$	19.7067	1.00697	0.503483	+	0.864005i	$0.332052\pi$
$384$	−13.2258	−0.674925
$385$	21.9169	1.11699
$386$	23.4218	1.19214
$387$	6.18369	0.314335
$388$	−9.12738	−0.463373
$389$	19.1164	0.969239	0.484619	−	0.874725i	$-0.338958\pi$
$389$	19.1164	0.969239	0.484619	+	0.874725i	$0.338958\pi$
$390$	−34.2583	−1.73474
$391$	−0.625648	−0.0316404
$392$	−25.7198	−1.29904
$393$	−3.49176	−0.176136
$394$	−35.7710	−1.80212
$395$	38.0179	1.91289
$396$	−6.94893	−0.349197
$397$	13.6770	0.686427	0.343214	−	0.939257i	$-0.388485\pi$
$397$	13.6770	0.686427	0.343214	+	0.939257i	$0.388485\pi$
$398$	−39.0719	−1.95850
$399$	4.81403	0.241003
$400$	−12.3808	−0.619041
$401$	−20.1642	−1.00695	−0.503476	−	0.864009i	$-0.667946\pi$
$401$	−20.1642	−1.00695	−0.503476	+	0.864009i	$0.667946\pi$
$402$	−9.19993	−0.458851
$403$	−28.9451	−1.44186
$404$	16.5581	0.823798
$405$	0.132006	0.00655944
$406$	5.69094	0.282437
$407$	5.99983	0.297401
$408$	−1.78228	−0.0882361
$409$	−33.9091	−1.67670	−0.838349	−	0.545133i	$-0.816479\pi$
$409$	−33.9091	−1.67670	−0.838349	+	0.545133i	$0.816479\pi$
$410$	−7.38987	−0.364960
$411$	20.1799	0.995400
$412$	−34.7116	−1.71012
$413$	−41.5939	−2.04670
$414$	2.52323	0.124010
$415$	14.4257	0.708130
$416$	32.1704	1.57729
$417$	24.3613	1.19298
$418$	−2.81054	−0.137468
$419$	−18.3704	−0.897452	−0.448726	−	0.893669i	$-0.648122\pi$
$419$	−18.3704	−0.897452	−0.448726	+	0.893669i	$0.648122\pi$
$420$	−47.6950	−2.32728
$421$	3.69855	0.180256	0.0901280	−	0.995930i	$-0.471272\pi$
$421$	3.69855	0.180256	0.0901280	+	0.995930i	$0.471272\pi$
$422$	−45.1913	−2.19988
$423$	19.5785	0.951941
$424$	8.76451	0.425642
$425$	−6.52150	−0.316339
$426$	37.2729	1.80588
$427$	41.7956	2.02263
$428$	0.964902	0.0466403
$429$	−6.29822	−0.304081
$430$	−24.7790	−1.19495
$431$	29.5829	1.42496	0.712479	−	0.701694i	$-0.247572\pi$
$431$	29.5829	1.42496	0.712479	+	0.701694i	$0.247572\pi$
$432$	−9.87783	−0.475247
$433$	3.36510	0.161716	0.0808582	−	0.996726i	$-0.474234\pi$
$433$	3.36510	0.161716	0.0808582	+	0.996726i	$0.474234\pi$
$434$	−69.4874	−3.33550
$435$	2.00350	0.0960607
$436$	−43.0880	−2.06354
$437$	0.591842	0.0283117
$438$	−9.49343	−0.453614
$439$	9.73461	0.464608	0.232304	−	0.972643i	$-0.425374\pi$
$439$	9.73461	0.464608	0.232304	+	0.972643i	$0.425374\pi$
$440$	7.67576	0.365927
$441$	−28.6242	−1.36306
$442$	9.40463	0.447333
$443$	37.0375	1.75971	0.879853	−	0.475247i	$-0.157641\pi$
$443$	37.0375	1.75971	0.879853	+	0.475247i	$0.157641\pi$
$444$	−13.0567	−0.619644
$445$	33.1232	1.57019
$446$	19.7440	0.934904
$447$	8.86159	0.419139
$448$	59.2251	2.79812
$449$	−23.8748	−1.12672	−0.563361	−	0.826211i	$-0.690492\pi$
$449$	−23.8748	−1.12672	−0.563361	+	0.826211i	$0.690492\pi$
$450$	26.3011	1.23985
$451$	−1.35859	−0.0639735
$452$	−55.5888	−2.61468
$453$	−8.13309	−0.382126
$454$	−26.2575	−1.23232
$455$	69.3754	3.25237
$456$	1.68598	0.0789531
$457$	−20.5206	−0.959913	−0.479957	−	0.877292i	$-0.659348\pi$
$457$	−20.5206	−0.959913	−0.479957	+	0.877292i	$0.659348\pi$
$458$	−48.5243	−2.26739
$459$	−5.20306	−0.242858
$460$	−5.86367	−0.273395
$461$	−11.1449	−0.519070	−0.259535	−	0.965734i	$-0.583569\pi$
$461$	−11.1449	−0.519070	−0.259535	+	0.965734i	$0.583569\pi$
$462$	−15.1199	−0.703440
$463$	1.32716	0.0616784	0.0308392	−	0.999524i	$-0.490182\pi$
$463$	1.32716	0.0616784	0.0308392	+	0.999524i	$0.490182\pi$
$464$	−1.04416	−0.0484741
$465$	−24.4631	−1.13445
$466$	38.9009	1.80205
$467$	23.4305	1.08423	0.542117	−	0.840303i	$-0.317623\pi$
$467$	23.4305	1.08423	0.542117	+	0.840303i	$0.317623\pi$
$468$	−21.9961	−1.01677
$469$	18.6305	0.860275
$470$	−78.4543	−3.61883
$471$	7.77485	0.358246
$472$	−14.5671	−0.670504
$473$	−4.55549	−0.209462
$474$	−26.2276	−1.20467
$475$	6.16912	0.283058
$476$	13.0933	0.600129
$477$	9.75424	0.446616
$478$	58.6232	2.68136
$479$	7.99444	0.365275	0.182638	−	0.983180i	$-0.441536\pi$
$479$	7.99444	0.365275	0.182638	+	0.983180i	$0.441536\pi$
$480$	27.1890	1.24100
$481$	18.9918	0.865952
$482$	22.1022	1.00673
$483$	3.18393	0.144874
$484$	−25.2531	−1.14787
$485$	11.2206	0.509501
$486$	33.9682	1.54083
$487$	−10.8518	−0.491740	−0.245870	−	0.969303i	$-0.579074\pi$
$487$	−10.8518	−0.491740	−0.245870	+	0.969303i	$0.579074\pi$
$488$	14.6377	0.662619
$489$	23.5822	1.06642
$490$	114.702	5.18169
$491$	31.1505	1.40580	0.702902	−	0.711287i	$-0.251887\pi$
$491$	31.1505	1.40580	0.702902	+	0.711287i	$0.251887\pi$
$492$	2.95653	0.133291
$493$	−0.550004	−0.0247709
$494$	−8.89647	−0.400271
$495$	8.54254	0.383959
$496$	12.7494	0.572466
$497$	−75.4802	−3.38575
$498$	−9.95192	−0.445956
$499$	−23.5893	−1.05600	−0.528002	−	0.849243i	$-0.677058\pi$
$499$	−23.5893	−1.05600	−0.528002	+	0.849243i	$0.677058\pi$
$500$	−14.2597	−0.637713
$501$	−10.8793	−0.486051
$502$	−46.6653	−2.08277
$503$	−2.07492	−0.0925163	−0.0462582	−	0.998930i	$-0.514730\pi$
$503$	−2.07492	−0.0925163	−0.0462582	+	0.998930i	$0.514730\pi$
$504$	−14.5560	−0.648376
$505$	−20.3554	−0.905806
$506$	−1.85885	−0.0826361
$507$	−5.98506	−0.265806
$508$	45.3327	2.01131
$509$	36.4495	1.61560	0.807798	−	0.589459i	$-0.200659\pi$
$509$	36.4495	1.61560	0.807798	+	0.589459i	$0.200659\pi$
$510$	7.94838	0.351960
$511$	19.2248	0.850456
$512$	−20.4758	−0.904913
$513$	4.92192	0.217308
$514$	7.98112	0.352032
$515$	42.6721	1.88036
$516$	9.91357	0.436420
$517$	−14.4234	−0.634341
$518$	45.5928	2.00323
$519$	−4.96199	−0.217807
$520$	24.2968	1.06548
$521$	16.8668	0.738946	0.369473	−	0.929241i	$-0.379538\pi$
$521$	16.8668	0.738946	0.369473	+	0.929241i	$0.379538\pi$
$522$	2.21816	0.0970862
$523$	−22.7578	−0.995129	−0.497564	−	0.867427i	$-0.665772\pi$
$523$	−22.7578	−0.995129	−0.497564	+	0.867427i	$0.665772\pi$
$524$	8.98378	0.392458
$525$	33.1880	1.44844
$526$	52.6107	2.29394
$527$	6.71565	0.292538
$528$	2.77417	0.120730
$529$	−22.6086	−0.982981
$530$	−39.0868	−1.69782
$531$	−16.2121	−0.703544
$532$	−12.3858	−0.536993
$533$	−4.30047	−0.186274
$534$	−22.8508	−0.988852
$535$	−1.18619	−0.0512833
$536$	6.52479	0.281828
$537$	−23.9633	−1.03409
$538$	31.3340	1.35091
$539$	21.0873	0.908294
$540$	−48.7639	−2.09847
$541$	1.89096	0.0812988	0.0406494	−	0.999173i	$-0.487057\pi$
$541$	1.89096	0.0812988	0.0406494	+	0.999173i	$0.487057\pi$
$542$	−33.6809	−1.44672
$543$	−16.4155	−0.704456
$544$	−7.46396	−0.320015
$545$	52.9695	2.26897
$546$	−47.8603	−2.04823
$547$	29.6546	1.26794	0.633969	−	0.773358i	$-0.281425\pi$
$547$	29.6546	1.26794	0.633969	+	0.773358i	$0.281425\pi$
$548$	−51.9199	−2.21791
$549$	16.2907	0.695270
$550$	−19.3759	−0.826192
$551$	0.520285	0.0221649
$552$	1.11508	0.0474610
$553$	53.1126	2.25858
$554$	46.6891	1.98363
$555$	16.0510	0.681328
$556$	−62.6780	−2.65814
$557$	21.6129	0.915767	0.457884	−	0.889012i	$-0.348608\pi$
$557$	21.6129	0.915767	0.457884	+	0.889012i	$0.348608\pi$
$558$	−27.0841	−1.14656
$559$	−14.4199	−0.609897
$560$	−30.5577	−1.29130
$561$	1.46127	0.0616948
$562$	−23.5565	−0.993669
$563$	−2.23190	−0.0940633	−0.0470316	−	0.998893i	$-0.514976\pi$
$563$	−2.23190	−0.0940633	−0.0470316	+	0.998893i	$0.514976\pi$
$564$	31.3879	1.32167
$565$	68.3372	2.87497
$566$	30.5832	1.28551
$567$	0.184418	0.00774483
$568$	−26.4348	−1.10918
$569$	14.4157	0.604338	0.302169	−	0.953254i	$-0.402289\pi$
$569$	14.4157	0.604338	0.302169	+	0.953254i	$0.402289\pi$
$570$	−7.51890	−0.314932
$571$	36.8408	1.54174	0.770871	−	0.636992i	$-0.219822\pi$
$571$	36.8408	1.54174	0.770871	+	0.636992i	$0.219822\pi$
$572$	16.2044	0.677540
$573$	15.4348	0.644798
$574$	−10.3240	−0.430913
$575$	4.08016	0.170155
$576$	23.0842	0.961842
$577$	15.9670	0.664713	0.332357	−	0.943154i	$-0.392156\pi$
$577$	15.9670	0.664713	0.332357	+	0.943154i	$0.392156\pi$
$578$	−2.18200	−0.0907592
$579$	11.5195	0.478736
$580$	−5.15472	−0.214038
$581$	20.1533	0.836100
$582$	−7.74079	−0.320866
$583$	−7.18591	−0.297610
$584$	6.73295	0.278611
$585$	27.0405	1.11799
$586$	−36.5889	−1.51148
$587$	32.9769	1.36110	0.680550	−	0.732701i	$-0.261741\pi$
$587$	32.9769	1.36110	0.680550	+	0.732701i	$0.261741\pi$
$588$	−45.8897	−1.89246
$589$	−6.35278	−0.261762
$590$	64.9643	2.67454
$591$	−17.5933	−0.723691
$592$	−8.36529	−0.343811
$593$	16.1648	0.663807	0.331904	−	0.943313i	$-0.392309\pi$
$593$	16.1648	0.663807	0.331904	+	0.943313i	$0.392309\pi$
$594$	−15.4587	−0.634280
$595$	−16.0960	−0.659872
$596$	−22.7996	−0.933907
$597$	−19.2168	−0.786489
$598$	−5.88399	−0.240614
$599$	−8.17905	−0.334187	−0.167094	−	0.985941i	$-0.553438\pi$
$599$	−8.17905	−0.334187	−0.167094	+	0.985941i	$0.553438\pi$
$600$	11.6231	0.474513
$601$	30.8821	1.25971	0.629853	−	0.776714i	$-0.283115\pi$
$601$	30.8821	1.25971	0.629853	+	0.776714i	$0.283115\pi$
$602$	−34.6173	−1.41090
$603$	7.26160	0.295715
$604$	20.9253	0.851437
$605$	31.0444	1.26213
$606$	14.0427	0.570446
$607$	−17.3434	−0.703946	−0.351973	−	0.936010i	$-0.614489\pi$
$607$	−17.3434	−0.703946	−0.351973	+	0.936010i	$0.614489\pi$
$608$	7.06066	0.286347
$609$	2.79898	0.113420
$610$	−65.2794	−2.64309
$611$	−45.6557	−1.84703
$612$	5.10337	0.206292
$613$	25.9834	1.04946	0.524730	−	0.851269i	$-0.324166\pi$
$613$	25.9834	1.04946	0.524730	+	0.851269i	$0.324166\pi$
$614$	−22.5066	−0.908292
$615$	−3.63456	−0.146560
$616$	10.7233	0.432056
$617$	24.7334	0.995729	0.497864	−	0.867255i	$-0.334118\pi$
$617$	24.7334	0.995729	0.497864	+	0.867255i	$0.334118\pi$
$618$	−29.4384	−1.18419
$619$	−44.9535	−1.80683	−0.903416	−	0.428764i	$-0.858949\pi$
$619$	−44.9535	−1.80683	−0.903416	+	0.428764i	$0.858949\pi$
$620$	62.9401	2.52774
$621$	3.25529	0.130630
$622$	61.9504	2.48398
$623$	46.2745	1.85395
$624$	8.78131	0.351534
$625$	−15.0776	−0.603103
$626$	62.7073	2.50629
$627$	−1.38231	−0.0552042
$628$	−20.0036	−0.798229
$629$	−4.40635	−0.175693
$630$	64.9149	2.58627
$631$	19.6816	0.783513	0.391757	−	0.920069i	$-0.371868\pi$
$631$	19.6816	0.783513	0.391757	+	0.920069i	$0.371868\pi$
$632$	18.6012	0.739915
$633$	−22.2265	−0.883422
$634$	−45.6797	−1.81417
$635$	−55.7290	−2.21154
$636$	15.6378	0.620079
$637$	66.7495	2.64471
$638$	−1.63411	−0.0646950
$639$	−29.4199	−1.16384
$640$	−41.8317	−1.65354
$641$	−4.36592	−0.172444	−0.0862218	−	0.996276i	$-0.527479\pi$
$641$	−4.36592	−0.172444	−0.0862218	+	0.996276i	$0.527479\pi$
$642$	0.818319	0.0322965
$643$	−49.6271	−1.95710	−0.978550	−	0.206008i	$-0.933953\pi$
$643$	−49.6271	−1.95710	−0.978550	+	0.206008i	$0.933953\pi$
$644$	−8.19179	−0.322802
$645$	−12.1871	−0.479866
$646$	2.06410	0.0812108
$647$	−23.5425	−0.925550	−0.462775	−	0.886476i	$-0.653146\pi$
$647$	−23.5425	−0.925550	−0.462775	+	0.886476i	$0.653146\pi$
$648$	0.0645872	0.00253722
$649$	11.9434	0.468818
$650$	−61.3323	−2.40565
$651$	−34.1760	−1.33946
$652$	−60.6736	−2.37616
$653$	17.2893	0.676581	0.338291	−	0.941042i	$-0.390151\pi$
$653$	17.2893	0.676581	0.338291	+	0.941042i	$0.390151\pi$
$654$	−36.5423	−1.42892
$655$	−11.0441	−0.431527
$656$	1.89422	0.0739569
$657$	7.49327	0.292340
$658$	−109.604	−4.27280
$659$	18.5878	0.724077	0.362038	−	0.932163i	$-0.382081\pi$
$659$	18.5878	0.724077	0.362038	+	0.932163i	$0.382081\pi$
$660$	13.6952	0.533086
$661$	2.46961	0.0960567	0.0480284	−	0.998846i	$-0.484706\pi$
$661$	2.46961	0.0960567	0.0480284	+	0.998846i	$0.484706\pi$
$662$	9.34010	0.363013
$663$	4.62548	0.179639
$664$	7.05812	0.273908
$665$	15.2263	0.590449
$666$	17.7707	0.688602
$667$	0.344109	0.0133240
$668$	27.9909	1.08300
$669$	9.71069	0.375437
$670$	−29.0984	−1.12417
$671$	−12.0013	−0.463304
$672$	37.9842	1.46527
$673$	−40.5799	−1.56424	−0.782120	−	0.623128i	$-0.785862\pi$
$673$	−40.5799	−1.56424	−0.782120	+	0.623128i	$0.785862\pi$
$674$	56.5591	2.17857
$675$	33.9318	1.30603
$676$	15.3987	0.592257
$677$	−11.3451	−0.436028	−0.218014	−	0.975946i	$-0.569958\pi$
$677$	−11.3451	−0.436028	−0.218014	+	0.975946i	$0.569958\pi$
$678$	−47.1440	−1.81056
$679$	15.6756	0.601575
$680$	−5.63717	−0.216175
$681$	−12.9142	−0.494874
$682$	19.9528	0.764030
$683$	−28.7123	−1.09864	−0.549322	−	0.835611i	$-0.685114\pi$
$683$	−28.7123	−1.09864	−0.549322	+	0.835611i	$0.685114\pi$
$684$	−4.82762	−0.184589
$685$	63.8268	2.43870
$686$	87.8132	3.35272
$687$	−23.8657	−0.910534
$688$	6.35152	0.242149
$689$	−22.7462	−0.866561
$690$	−4.97289	−0.189315
$691$	32.9531	1.25359	0.626797	−	0.779183i	$-0.284366\pi$
$691$	32.9531	1.25359	0.626797	+	0.779183i	$0.284366\pi$
$692$	12.7665	0.485309
$693$	11.9343	0.453346
$694$	73.6240	2.79473
$695$	77.0521	2.92275
$696$	0.980262	0.0371567
$697$	0.997765	0.0377930
$698$	−23.2377	−0.879559
$699$	19.1326	0.723663
$700$	−85.3878	−3.22735
$701$	1.91449	0.0723092	0.0361546	−	0.999346i	$-0.488489\pi$
$701$	1.91449	0.0723092	0.0361546	+	0.999346i	$0.488489\pi$
$702$	−48.9329	−1.84685
$703$	4.16826	0.157209
$704$	−17.0060	−0.640939
$705$	−38.5862	−1.45324
$706$	−2.18200	−0.0821206
$707$	−28.4374	−1.06950
$708$	−25.9909	−0.976796
$709$	−11.7710	−0.442070	−0.221035	−	0.975266i	$-0.570944\pi$
$709$	−11.7710	−0.442070	−0.221035	+	0.975266i	$0.570944\pi$
$710$	117.890	4.42435
$711$	20.7017	0.776375
$712$	16.2063	0.607357
$713$	−4.20164	−0.157352
$714$	11.1042	0.415565
$715$	−19.9206	−0.744988
$716$	61.6540	2.30412
$717$	28.8327	1.07678
$718$	24.2608	0.905406
$719$	28.5978	1.06652	0.533259	−	0.845952i	$-0.320967\pi$
$719$	28.5978	1.06652	0.533259	+	0.845952i	$0.320967\pi$
$720$	−11.9105	−0.443877
$721$	59.6147	2.22017
$722$	39.5054	1.47024
$723$	10.8705	0.404279
$724$	42.2346	1.56964
$725$	3.58685	0.133212
$726$	−21.4167	−0.794850
$727$	−22.6841	−0.841308	−0.420654	−	0.907221i	$-0.638199\pi$
$727$	−22.6841	−0.841308	−0.420654	+	0.907221i	$0.638199\pi$
$728$	33.9436	1.25803
$729$	16.8232	0.623083
$730$	−30.0267	−1.11134
$731$	3.34561	0.123742
$732$	26.1169	0.965309
$733$	18.7339	0.691953	0.345976	−	0.938243i	$-0.387548\pi$
$733$	18.7339	0.691953	0.345976	+	0.938243i	$0.387548\pi$
$734$	81.9354	3.02429
$735$	56.4137	2.08085
$736$	4.66982	0.172132
$737$	−5.34959	−0.197055
$738$	−4.02397	−0.148124
$739$	25.5013	0.938081	0.469040	−	0.883177i	$-0.344600\pi$
$739$	25.5013	0.938081	0.469040	+	0.883177i	$0.344600\pi$
$740$	−41.2970	−1.51811
$741$	−4.37555	−0.160740
$742$	−54.6058	−2.00464
$743$	−8.08836	−0.296733	−0.148367	−	0.988932i	$-0.547402\pi$
$743$	−8.08836	−0.296733	−0.148367	+	0.988932i	$0.547402\pi$
$744$	−11.9692	−0.438811
$745$	28.0283	1.02688
$746$	−20.7340	−0.759127
$747$	7.85516	0.287405
$748$	−3.75963	−0.137466
$749$	−1.65715	−0.0605510
$750$	−12.0934	−0.441590
$751$	31.6276	1.15411	0.577053	−	0.816707i	$-0.304203\pi$
$751$	31.6276	1.15411	0.577053	+	0.816707i	$0.304203\pi$
$752$	20.1099	0.733333
$753$	−22.9514	−0.836395
$754$	−5.17259	−0.188375
$755$	−25.7241	−0.936197
$756$	−68.1252	−2.47769
$757$	−21.0961	−0.766752	−0.383376	−	0.923592i	$-0.625239\pi$
$757$	−21.0961	−0.766752	−0.383376	+	0.923592i	$0.625239\pi$
$758$	24.5725	0.892515
$759$	−0.914240	−0.0331848
$760$	5.33257	0.193433
$761$	−10.8576	−0.393588	−0.196794	−	0.980445i	$-0.563053\pi$
$761$	−10.8576	−0.393588	−0.196794	+	0.980445i	$0.563053\pi$
$762$	38.4460	1.39275
$763$	74.0006	2.67900
$764$	−39.7115	−1.43671
$765$	−6.27374	−0.226828
$766$	−43.0000	−1.55365
$767$	37.8054	1.36507
$768$	2.05198	0.0740446
$769$	−4.81555	−0.173653	−0.0868265	−	0.996223i	$-0.527673\pi$
$769$	−4.81555	−0.173653	−0.0868265	+	0.996223i	$0.527673\pi$
$770$	−47.8225	−1.72340
$771$	3.92536	0.141368
$772$	−29.6381	−1.06670
$773$	−36.9238	−1.32806	−0.664029	−	0.747707i	$-0.731155\pi$
$773$	−36.9238	−1.32806	−0.664029	+	0.747707i	$0.731155\pi$
$774$	−13.4928	−0.484989
$775$	−43.7961	−1.57320
$776$	5.48994	0.197077
$777$	22.4239	0.804455
$778$	−41.7119	−1.49544
$779$	−0.943852	−0.0338170
$780$	43.3508	1.55221
$781$	21.6735	0.775540
$782$	1.36516	0.0488182
$783$	2.86171	0.102269
$784$	−29.4011	−1.05004
$785$	24.5910	0.877691
$786$	7.61901	0.271761
$787$	11.1252	0.396571	0.198285	−	0.980144i	$-0.436463\pi$
$787$	11.1252	0.396571	0.198285	+	0.980144i	$0.436463\pi$
$788$	45.2650	1.61250
$789$	25.8755	0.921193
$790$	−82.9550	−2.95141
$791$	95.4698	3.39452
$792$	4.17964	0.148517
$793$	−37.9887	−1.34902
$794$	−29.8431	−1.05909
$795$	−19.2241	−0.681808
$796$	49.4419	1.75242
$797$	2.05540	0.0728061	0.0364030	−	0.999337i	$-0.488410\pi$
$797$	2.05540	0.0728061	0.0364030	+	0.999337i	$0.488410\pi$
$798$	−10.5042	−0.371845
$799$	10.5927	0.374744
$800$	48.6762	1.72096
$801$	18.0364	0.637285
$802$	43.9983	1.55363
$803$	−5.52026	−0.194806
$804$	11.6417	0.410570
$805$	10.0704	0.354936
$806$	63.1582	2.22465
$807$	15.4110	0.542494
$808$	−9.95939	−0.350370
$809$	6.62375	0.232879	0.116439	−	0.993198i	$-0.462852\pi$
$809$	6.62375	0.232879	0.116439	+	0.993198i	$0.462852\pi$
$810$	−0.288037	−0.0101206
$811$	−16.4503	−0.577648	−0.288824	−	0.957382i	$-0.593264\pi$
$811$	−16.4503	−0.577648	−0.288824	+	0.957382i	$0.593264\pi$
$812$	−7.20136	−0.252718
$813$	−16.5653	−0.580969
$814$	−13.0916	−0.458861
$815$	74.5880	2.61270
$816$	−2.03738	−0.0713226
$817$	−3.16483	−0.110724
$818$	73.9897	2.58699
$819$	37.7766	1.32002
$820$	9.35120	0.326558
$821$	24.1493	0.842817	0.421408	−	0.906871i	$-0.361536\pi$
$821$	24.1493	0.842817	0.421408	+	0.906871i	$0.361536\pi$
$822$	−44.0324	−1.53581
$823$	22.2547	0.775749	0.387874	−	0.921712i	$-0.373209\pi$
$823$	22.2547	0.775749	0.387874	+	0.921712i	$0.373209\pi$
$824$	20.8784	0.727332
$825$	−9.52966	−0.331780
$826$	90.7578	3.15787
$827$	−16.7841	−0.583640	−0.291820	−	0.956473i	$-0.594261\pi$
$827$	−16.7841	−0.583640	−0.291820	+	0.956473i	$0.594261\pi$
$828$	−3.19292	−0.110962
$829$	0.941104	0.0326859	0.0163429	−	0.999866i	$-0.494798\pi$
$829$	0.941104	0.0326859	0.0163429	+	0.999866i	$0.494798\pi$
$830$	−31.4769	−1.09258
$831$	22.9631	0.796581
$832$	−53.8307	−1.86624
$833$	−15.4868	−0.536584
$834$	−53.1563	−1.84065
$835$	−34.4101	−1.19081
$836$	3.55648	0.123004
$837$	−34.9420	−1.20777
$838$	40.0842	1.38468
$839$	40.8097	1.40891	0.704454	−	0.709750i	$-0.251192\pi$
$839$	40.8097	1.40891	0.704454	+	0.709750i	$0.251192\pi$
$840$	28.6876	0.989816
$841$	−28.6975	−0.989569
$842$	−8.07022	−0.278118
$843$	−11.5858	−0.399036
$844$	57.1854	1.96840
$845$	−18.9301	−0.651215
$846$	−42.7203	−1.46875
$847$	43.3703	1.49022
$848$	10.0190	0.344053
$849$	15.0417	0.516231
$850$	14.2299	0.488081
$851$	2.75682	0.0945027
$852$	−47.1655	−1.61586
$853$	6.68583	0.228918	0.114459	−	0.993428i	$-0.463486\pi$
$853$	6.68583	0.228918	0.114459	+	0.993428i	$0.463486\pi$
$854$	−91.1980	−3.12073
$855$	5.93475	0.202964
$856$	−0.580370	−0.0198366
$857$	−19.2545	−0.657722	−0.328861	−	0.944378i	$-0.606665\pi$
$857$	−19.2545	−0.657722	−0.328861	+	0.944378i	$0.606665\pi$
$858$	13.7427	0.469168
$859$	1.20190	0.0410084	0.0205042	−	0.999790i	$-0.493473\pi$
$859$	1.20190	0.0410084	0.0205042	+	0.999790i	$0.493473\pi$
$860$	31.3556	1.06922
$861$	−5.07763	−0.173045
$862$	−64.5498	−2.19858
$863$	−19.0569	−0.648705	−0.324353	−	0.945936i	$-0.605146\pi$
$863$	−19.0569	−0.648705	−0.324353	+	0.945936i	$0.605146\pi$
$864$	38.8355	1.32121
$865$	−15.6943	−0.533621
$866$	−7.34264	−0.249513
$867$	−1.07317	−0.0364469
$868$	87.9299	2.98453
$869$	−15.2509	−0.517350
$870$	−4.37164	−0.148213
$871$	−16.9335	−0.573771
$872$	25.9166	0.877647
$873$	6.10989	0.206789
$874$	−1.29140	−0.0436822
$875$	24.4900	0.827913
$876$	12.0131	0.405884
$877$	−10.9649	−0.370259	−0.185129	−	0.982714i	$-0.559270\pi$
$877$	−10.9649	−0.370259	−0.185129	+	0.982714i	$0.559270\pi$
$878$	−21.2409	−0.716846
$879$	−17.9956	−0.606975
$880$	8.77439	0.295785
$881$	25.3549	0.854229	0.427115	−	0.904197i	$-0.359530\pi$
$881$	25.3549	0.854229	0.427115	+	0.904197i	$0.359530\pi$
$882$	62.4579	2.10307
$883$	6.80225	0.228914	0.114457	−	0.993428i	$-0.463487\pi$
$883$	6.80225	0.228914	0.114457	+	0.993428i	$0.463487\pi$
$884$	−11.9007	−0.400264
$885$	31.9514	1.07404
$886$	−80.8158	−2.71506
$887$	−3.34712	−0.112385	−0.0561927	−	0.998420i	$-0.517896\pi$
$887$	−3.34712	−0.112385	−0.0561927	+	0.998420i	$0.517896\pi$
$888$	7.85335	0.263541
$889$	−77.8557	−2.61120
$890$	−72.2748	−2.42266
$891$	−0.0529542	−0.00177403
$892$	−24.9842	−0.836532
$893$	−10.0204	−0.335319
$894$	−19.3360	−0.646692
$895$	−75.7933	−2.53349
$896$	−58.4406	−1.95236
$897$	−2.89393	−0.0966254
$898$	52.0948	1.73843
$899$	−3.69364	−0.123190
$900$	−33.2816	−1.10939
$901$	5.27741	0.175816
$902$	2.96444	0.0987051
$903$	−17.0258	−0.566584
$904$	33.4356	1.11205
$905$	−51.9204	−1.72589
$906$	17.7464	0.589585
$907$	−42.0120	−1.39499	−0.697493	−	0.716591i	$-0.745701\pi$
$907$	−42.0120	−1.39499	−0.697493	+	0.716591i	$0.745701\pi$
$908$	33.2264	1.10266
$909$	−11.0841	−0.367635
$910$	−151.377	−5.01810
$911$	−35.8960	−1.18929	−0.594644	−	0.803989i	$-0.702707\pi$
$911$	−35.8960	−1.18929	−0.594644	+	0.803989i	$0.702707\pi$
$912$	1.92729	0.0638190
$913$	−5.78686	−0.191517
$914$	44.7759	1.48106
$915$	−32.1064	−1.06140
$916$	61.4030	2.02881
$917$	−15.4290	−0.509510
$918$	11.3531	0.374707
$919$	−31.2264	−1.03006	−0.515032	−	0.857171i	$-0.672220\pi$
$919$	−31.2264	−1.03006	−0.515032	+	0.857171i	$0.672220\pi$
$920$	3.52688	0.116278
$921$	−11.0694	−0.364750
$922$	24.3182	0.800876
$923$	68.6052	2.25817
$924$	19.1328	0.629423
$925$	28.7360	0.944833
$926$	−2.89586	−0.0951640
$927$	23.2360	0.763172
$928$	4.10521	0.134760
$929$	−6.14425	−0.201586	−0.100793	−	0.994907i	$-0.532138\pi$
$929$	−6.14425	−0.201586	−0.100793	+	0.994907i	$0.532138\pi$
$930$	53.3785	1.75035
$931$	14.6500	0.480133
$932$	−49.2255	−1.61244
$933$	30.4691	0.997512
$934$	−51.1253	−1.67287
$935$	4.62184	0.151150
$936$	13.2302	0.432442
$937$	−48.3462	−1.57940	−0.789701	−	0.613491i	$-0.789765\pi$
$937$	−48.3462	−1.57940	−0.789701	+	0.613491i	$0.789765\pi$
$938$	−40.6516	−1.32732
$939$	30.8414	1.00647
$940$	99.2766	3.23805
$941$	−18.2872	−0.596146	−0.298073	−	0.954543i	$-0.596344\pi$
$941$	−18.2872	−0.596146	−0.298073	+	0.954543i	$0.596344\pi$
$942$	−16.9647	−0.552740
$943$	−0.624250	−0.0203284
$944$	−16.6521	−0.541979
$945$	83.7485	2.72434
$946$	9.94008	0.323180
$947$	18.8447	0.612370	0.306185	−	0.951972i	$-0.400947\pi$
$947$	18.8447	0.612370	0.306185	+	0.951972i	$0.400947\pi$
$948$	33.1886	1.07791
$949$	−17.4738	−0.567222
$950$	−13.4610	−0.436733
$951$	−22.4666	−0.728531
$952$	−7.87535	−0.255242
$953$	−9.72904	−0.315154	−0.157577	−	0.987507i	$-0.550368\pi$
$953$	−9.72904	−0.315154	−0.157577	+	0.987507i	$0.550368\pi$
$954$	−21.2837	−0.689087
$955$	48.8186	1.57973
$956$	−74.1822	−2.39923
$957$	−0.803704	−0.0259801
$958$	−17.4439	−0.563585
$959$	89.1686	2.87940
$960$	−45.4953	−1.46836
$961$	14.1000	0.454837
$962$	−41.4401	−1.33608
$963$	−0.645908	−0.0208141
$964$	−27.9683	−0.900798
$965$	36.4351	1.17289
$966$	−6.94733	−0.223527
$967$	13.4110	0.431268	0.215634	−	0.976474i	$-0.430818\pi$
$967$	13.4110	0.431268	0.215634	+	0.976474i	$0.430818\pi$
$968$	15.1892	0.488200
$969$	1.01519	0.0326125
$970$	−24.4833	−0.786112
$971$	−7.41104	−0.237831	−0.118916	−	0.992904i	$-0.537942\pi$
$971$	−7.41104	−0.237831	−0.118916	+	0.992904i	$0.537942\pi$
$972$	−42.9836	−1.37870
$973$	107.645	3.45094
$974$	23.6785	0.758709
$975$	−30.1651	−0.966056
$976$	16.7328	0.535605
$977$	−30.9884	−0.991407	−0.495703	−	0.868492i	$-0.665090\pi$
$977$	−30.9884	−0.991407	−0.495703	+	0.868492i	$0.665090\pi$
$978$	−51.4563	−1.64539
$979$	−13.2873	−0.424665
$980$	−145.144	−4.63646
$981$	28.8432	0.920894
$982$	−67.9704	−2.16902
$983$	−5.53618	−0.176577	−0.0882884	−	0.996095i	$-0.528140\pi$
$983$	−5.53618	−0.176577	−0.0882884	+	0.996095i	$0.528140\pi$
$984$	−1.77830	−0.0566900
$985$	−55.6457	−1.77302
$986$	1.20011	0.0382192
$987$	−53.9065	−1.71586
$988$	11.2577	0.358154
$989$	−2.09317	−0.0665591
$990$	−18.6398	−0.592412
$991$	−29.1924	−0.927327	−0.463663	−	0.886011i	$-0.653465\pi$
$991$	−29.1924	−0.927327	−0.463663	+	0.886011i	$0.653465\pi$
$992$	−50.1254	−1.59148
$993$	4.59374	0.145778
$994$	164.698	5.22389
$995$	−60.7806	−1.92687
$996$	12.5932	0.399032
$997$	19.7225	0.624618	0.312309	−	0.949981i	$-0.398898\pi$
$997$	19.7225	0.624618	0.312309	+	0.949981i	$0.398898\pi$
$998$	51.4719	1.62931
$999$	22.9265	0.725363

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.c.1.16	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.c.1.16	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.18200 q^{2} -1.07317 q^{3} +2.76112 q^{4} -3.39433 q^{5} +2.34166 q^{6} -4.74202 q^{7} -1.66076 q^{8} -1.84830 q^{9} +O(q^{10})\)	\(q-2.18200 q^{2} -1.07317 q^{3} +2.76112 q^{4} -3.39433 q^{5} +2.34166 q^{6} -4.74202 q^{7} -1.66076 q^{8} -1.84830 q^{9} +7.40643 q^{10} +1.36163 q^{11} -2.96316 q^{12} +4.31010 q^{13} +10.3471 q^{14} +3.64271 q^{15} -1.89846 q^{16} -1.00000 q^{17} +4.03299 q^{18} +0.945966 q^{19} -9.37215 q^{20} +5.08901 q^{21} -2.97108 q^{22} +0.625648 q^{23} +1.78228 q^{24} +6.52150 q^{25} -9.40463 q^{26} +5.20306 q^{27} -13.0933 q^{28} +0.550004 q^{29} -7.94838 q^{30} -6.71565 q^{31} +7.46396 q^{32} -1.46127 q^{33} +2.18200 q^{34} +16.0960 q^{35} -5.10337 q^{36} +4.40635 q^{37} -2.06410 q^{38} -4.62548 q^{39} +5.63717 q^{40} -0.997765 q^{41} -11.1042 q^{42} -3.34561 q^{43} +3.75963 q^{44} +6.27374 q^{45} -1.36516 q^{46} -10.5927 q^{47} +2.03738 q^{48} +15.4868 q^{49} -14.2299 q^{50} +1.07317 q^{51} +11.9007 q^{52} -5.27741 q^{53} -11.3531 q^{54} -4.62184 q^{55} +7.87535 q^{56} -1.01519 q^{57} -1.20011 q^{58} +8.77134 q^{59} +10.0579 q^{60} -8.81388 q^{61} +14.6535 q^{62} +8.76467 q^{63} -12.4894 q^{64} -14.6299 q^{65} +3.18849 q^{66} -3.92880 q^{67} -2.76112 q^{68} -0.671429 q^{69} -35.1214 q^{70} +15.9173 q^{71} +3.06958 q^{72} -4.05414 q^{73} -9.61465 q^{74} -6.99869 q^{75} +2.61192 q^{76} -6.45690 q^{77} +10.0928 q^{78} -11.2004 q^{79} +6.44402 q^{80} -0.0388902 q^{81} +2.17712 q^{82} -4.24994 q^{83} +14.0514 q^{84} +3.39433 q^{85} +7.30012 q^{86} -0.590250 q^{87} -2.26134 q^{88} -9.75838 q^{89} -13.6893 q^{90} -20.4386 q^{91} +1.72749 q^{92} +7.20706 q^{93} +23.1133 q^{94} -3.21092 q^{95} -8.01012 q^{96} -3.30568 q^{97} -33.7921 q^{98} -2.51671 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * q^99

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