LMFDB - Embedded newform 6034.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.67063 q^{3} +1.00000 q^{4} +3.15601 q^{5} +2.67063 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.13228 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.67063 q^{3} +1.00000 q^{4} +3.15601 q^{5} +2.67063 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.13228 q^{9} -3.15601 q^{10} +3.01631 q^{11} -2.67063 q^{12} -4.63033 q^{13} +1.00000 q^{14} -8.42854 q^{15} +1.00000 q^{16} -6.60020 q^{17} -4.13228 q^{18} -4.22204 q^{19} +3.15601 q^{20} +2.67063 q^{21} -3.01631 q^{22} -0.524979 q^{23} +2.67063 q^{24} +4.96038 q^{25} +4.63033 q^{26} -3.02392 q^{27} -1.00000 q^{28} -9.21317 q^{29} +8.42854 q^{30} +1.00489 q^{31} -1.00000 q^{32} -8.05546 q^{33} +6.60020 q^{34} -3.15601 q^{35} +4.13228 q^{36} -8.56493 q^{37} +4.22204 q^{38} +12.3659 q^{39} -3.15601 q^{40} +6.31163 q^{41} -2.67063 q^{42} -11.7000 q^{43} +3.01631 q^{44} +13.0415 q^{45} +0.524979 q^{46} -7.89697 q^{47} -2.67063 q^{48} +1.00000 q^{49} -4.96038 q^{50} +17.6267 q^{51} -4.63033 q^{52} +0.831758 q^{53} +3.02392 q^{54} +9.51949 q^{55} +1.00000 q^{56} +11.2755 q^{57} +9.21317 q^{58} -2.18079 q^{59} -8.42854 q^{60} -1.29727 q^{61} -1.00489 q^{62} -4.13228 q^{63} +1.00000 q^{64} -14.6134 q^{65} +8.05546 q^{66} +8.28511 q^{67} -6.60020 q^{68} +1.40203 q^{69} +3.15601 q^{70} +14.0501 q^{71} -4.13228 q^{72} +16.6288 q^{73} +8.56493 q^{74} -13.2474 q^{75} -4.22204 q^{76} -3.01631 q^{77} -12.3659 q^{78} +16.4102 q^{79} +3.15601 q^{80} -4.32108 q^{81} -6.31163 q^{82} +7.07919 q^{83} +2.67063 q^{84} -20.8303 q^{85} +11.7000 q^{86} +24.6050 q^{87} -3.01631 q^{88} +14.0832 q^{89} -13.0415 q^{90} +4.63033 q^{91} -0.524979 q^{92} -2.68370 q^{93} +7.89697 q^{94} -13.3248 q^{95} +2.67063 q^{96} +14.9874 q^{97} -1.00000 q^{98} +12.4642 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.67063	−1.54189	−0.770946	−	0.636901i	$-0.780216\pi$
$3$	−2.67063	−1.54189	−0.770946	+	0.636901i	$0.780216\pi$
$4$	1.00000	0.500000
$5$	3.15601	1.41141	0.705705	−	0.708506i	$-0.250631\pi$
$5$	3.15601	1.41141	0.705705	+	0.708506i	$0.250631\pi$
$6$	2.67063	1.09028
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	4.13228	1.37743
$10$	−3.15601	−0.998017
$11$	3.01631	0.909452	0.454726	−	0.890632i	$-0.349737\pi$
$11$	3.01631	0.909452	0.454726	+	0.890632i	$0.349737\pi$
$12$	−2.67063	−0.770946
$13$	−4.63033	−1.28422	−0.642112	−	0.766611i	$-0.721941\pi$
$13$	−4.63033	−1.28422	−0.642112	+	0.766611i	$0.721941\pi$
$14$	1.00000	0.267261
$15$	−8.42854	−2.17624
$16$	1.00000	0.250000
$17$	−6.60020	−1.60078	−0.800392	−	0.599477i	$-0.795375\pi$
$17$	−6.60020	−1.60078	−0.800392	+	0.599477i	$0.795375\pi$
$18$	−4.13228	−0.973989
$19$	−4.22204	−0.968603	−0.484302	−	0.874901i	$-0.660926\pi$
$19$	−4.22204	−0.968603	−0.484302	+	0.874901i	$0.660926\pi$
$20$	3.15601	0.705705
$21$	2.67063	0.582780
$22$	−3.01631	−0.643079
$23$	−0.524979	−0.109466	−0.0547328	−	0.998501i	$-0.517431\pi$
$23$	−0.524979	−0.109466	−0.0547328	+	0.998501i	$0.517431\pi$
$24$	2.67063	0.545141
$25$	4.96038	0.992076
$26$	4.63033	0.908083
$27$	−3.02392	−0.581953
$28$	−1.00000	−0.188982
$29$	−9.21317	−1.71084	−0.855421	−	0.517933i	$-0.826702\pi$
$29$	−9.21317	−1.71084	−0.855421	+	0.517933i	$0.826702\pi$
$30$	8.42854	1.53883
$31$	1.00489	0.180484	0.0902419	−	0.995920i	$-0.471236\pi$
$31$	1.00489	0.180484	0.0902419	+	0.995920i	$0.471236\pi$
$32$	−1.00000	−0.176777
$33$	−8.05546	−1.40228
$34$	6.60020	1.13192
$35$	−3.15601	−0.533463
$36$	4.13228	0.688714
$37$	−8.56493	−1.40807	−0.704033	−	0.710168i	$-0.748619\pi$
$37$	−8.56493	−1.40807	−0.704033	+	0.710168i	$0.748619\pi$
$38$	4.22204	0.684906
$39$	12.3659	1.98013
$40$	−3.15601	−0.499009
$41$	6.31163	0.985711	0.492855	−	0.870111i	$-0.335953\pi$
$41$	6.31163	0.985711	0.492855	+	0.870111i	$0.335953\pi$
$42$	−2.67063	−0.412088
$43$	−11.7000	−1.78423	−0.892116	−	0.451807i	$-0.850780\pi$
$43$	−11.7000	−1.78423	−0.892116	+	0.451807i	$0.850780\pi$
$44$	3.01631	0.454726
$45$	13.0415	1.94411
$46$	0.524979	0.0774039
$47$	−7.89697	−1.15189	−0.575946	−	0.817488i	$-0.695366\pi$
$47$	−7.89697	−1.15189	−0.575946	+	0.817488i	$0.695366\pi$
$48$	−2.67063	−0.385473
$49$	1.00000	0.142857
$50$	−4.96038	−0.701504
$51$	17.6267	2.46823
$52$	−4.63033	−0.642112
$53$	0.831758	0.114251	0.0571254	−	0.998367i	$-0.481807\pi$
$53$	0.831758	0.114251	0.0571254	+	0.998367i	$0.481807\pi$
$54$	3.02392	0.411503
$55$	9.51949	1.28361
$56$	1.00000	0.133631
$57$	11.2755	1.49348
$58$	9.21317	1.20975
$59$	−2.18079	−0.283914	−0.141957	−	0.989873i	$-0.545340\pi$
$59$	−2.18079	−0.283914	−0.141957	+	0.989873i	$0.545340\pi$
$60$	−8.42854	−1.08812
$61$	−1.29727	−0.166098	−0.0830490	−	0.996545i	$-0.526466\pi$
$61$	−1.29727	−0.166098	−0.0830490	+	0.996545i	$0.526466\pi$
$62$	−1.00489	−0.127621
$63$	−4.13228	−0.520619
$64$	1.00000	0.125000
$65$	−14.6134	−1.81256
$66$	8.05546	0.991558
$67$	8.28511	1.01219	0.506093	−	0.862479i	$-0.331089\pi$
$67$	8.28511	1.01219	0.506093	+	0.862479i	$0.331089\pi$
$68$	−6.60020	−0.800392
$69$	1.40203	0.168784
$70$	3.15601	0.377215
$71$	14.0501	1.66744	0.833720	−	0.552188i	$-0.186207\pi$
$71$	14.0501	1.66744	0.833720	+	0.552188i	$0.186207\pi$
$72$	−4.13228	−0.486994
$73$	16.6288	1.94625	0.973127	−	0.230270i	$-0.0739610\pi$
$73$	16.6288	1.94625	0.973127	+	0.230270i	$0.0739610\pi$
$74$	8.56493	0.995652
$75$	−13.2474	−1.52967
$76$	−4.22204	−0.484302
$77$	−3.01631	−0.343740
$78$	−12.3659	−1.40017
$79$	16.4102	1.84629	0.923145	−	0.384453i	$-0.125610\pi$
$79$	16.4102	1.84629	0.923145	+	0.384453i	$0.125610\pi$
$80$	3.15601	0.352852
$81$	−4.32108	−0.480120
$82$	−6.31163	−0.697003
$83$	7.07919	0.777042	0.388521	−	0.921440i	$-0.372986\pi$
$83$	7.07919	0.777042	0.388521	+	0.921440i	$0.372986\pi$
$84$	2.67063	0.291390
$85$	−20.8303	−2.25936
$86$	11.7000	1.26164
$87$	24.6050	2.63793
$88$	−3.01631	−0.321540
$89$	14.0832	1.49282	0.746408	−	0.665489i	$-0.231777\pi$
$89$	14.0832	1.49282	0.746408	+	0.665489i	$0.231777\pi$
$90$	−13.0415	−1.37470
$91$	4.63033	0.485391
$92$	−0.524979	−0.0547328
$93$	−2.68370	−0.278286
$94$	7.89697	0.814511
$95$	−13.3248	−1.36710
$96$	2.67063	0.272570
$97$	14.9874	1.52174	0.760868	−	0.648907i	$-0.224773\pi$
$97$	14.9874	1.52174	0.760868	+	0.648907i	$0.224773\pi$
$98$	−1.00000	−0.101015
$99$	12.4642	1.25270
$100$	4.96038	0.496038
$101$	−0.171171	−0.0170322	−0.00851608	−	0.999964i	$-0.502711\pi$
$101$	−0.171171	−0.0170322	−0.00851608	+	0.999964i	$0.502711\pi$
$102$	−17.6267	−1.74530
$103$	11.0002	1.08388	0.541941	−	0.840417i	$-0.317690\pi$
$103$	11.0002	1.08388	0.541941	+	0.840417i	$0.317690\pi$
$104$	4.63033	0.454042
$105$	8.42854	0.822541
$106$	−0.831758	−0.0807875
$107$	−16.3738	−1.58292	−0.791458	−	0.611223i	$-0.790678\pi$
$107$	−16.3738	−1.58292	−0.791458	+	0.611223i	$0.790678\pi$
$108$	−3.02392	−0.290977
$109$	−10.6488	−1.01997	−0.509984	−	0.860184i	$-0.670349\pi$
$109$	−10.6488	−1.01997	−0.509984	+	0.860184i	$0.670349\pi$
$110$	−9.51949	−0.907648
$111$	22.8738	2.17108
$112$	−1.00000	−0.0944911
$113$	−17.2274	−1.62062	−0.810308	−	0.586005i	$-0.800700\pi$
$113$	−17.2274	−1.62062	−0.810308	+	0.586005i	$0.800700\pi$
$114$	−11.2755	−1.05605
$115$	−1.65684	−0.154501
$116$	−9.21317	−0.855421
$117$	−19.1339	−1.76893
$118$	2.18079	0.200758
$119$	6.60020	0.605039
$120$	8.42854	0.769417
$121$	−1.90188	−0.172898
$122$	1.29727	0.117449
$123$	−16.8561	−1.51986
$124$	1.00489	0.0902419
$125$	−0.125039	−0.0111839
$126$	4.13228	0.368133
$127$	12.3826	1.09878	0.549389	−	0.835567i	$-0.314861\pi$
$127$	12.3826	1.09878	0.549389	+	0.835567i	$0.314861\pi$
$128$	−1.00000	−0.0883883
$129$	31.2464	2.75109
$130$	14.6134	1.28168
$131$	11.2346	0.981574	0.490787	−	0.871280i	$-0.336709\pi$
$131$	11.2346	0.981574	0.490787	+	0.871280i	$0.336709\pi$
$132$	−8.05546	−0.701138
$133$	4.22204	0.366098
$134$	−8.28511	−0.715724
$135$	−9.54350	−0.821374
$136$	6.60020	0.565962
$137$	7.05090	0.602399	0.301200	−	0.953561i	$-0.402613\pi$
$137$	7.05090	0.602399	0.301200	+	0.953561i	$0.402613\pi$
$138$	−1.40203	−0.119348
$139$	19.2723	1.63465	0.817325	−	0.576176i	$-0.195456\pi$
$139$	19.2723	1.63465	0.817325	+	0.576176i	$0.195456\pi$
$140$	−3.15601	−0.266731
$141$	21.0899	1.77609
$142$	−14.0501	−1.17906
$143$	−13.9665	−1.16794
$144$	4.13228	0.344357
$145$	−29.0768	−2.41470
$146$	−16.6288	−1.37621
$147$	−2.67063	−0.220270
$148$	−8.56493	−0.704033
$149$	−16.3469	−1.33919	−0.669595	−	0.742726i	$-0.733532\pi$
$149$	−16.3469	−1.33919	−0.669595	+	0.742726i	$0.733532\pi$
$150$	13.2474	1.08164
$151$	−4.57648	−0.372429	−0.186214	−	0.982509i	$-0.559622\pi$
$151$	−4.57648	−0.372429	−0.186214	+	0.982509i	$0.559622\pi$
$152$	4.22204	0.342453
$153$	−27.2739	−2.20496
$154$	3.01631	0.243061
$155$	3.17144	0.254736
$156$	12.3659	0.990066
$157$	−7.67641	−0.612644	−0.306322	−	0.951928i	$-0.599099\pi$
$157$	−7.67641	−0.612644	−0.306322	+	0.951928i	$0.599099\pi$
$158$	−16.4102	−1.30552
$159$	−2.22132	−0.176162
$160$	−3.15601	−0.249504
$161$	0.524979	0.0413741
$162$	4.32108	0.339496
$163$	1.14467	0.0896571	0.0448286	−	0.998995i	$-0.485726\pi$
$163$	1.14467	0.0896571	0.0448286	+	0.998995i	$0.485726\pi$
$164$	6.31163	0.492855
$165$	−25.4231	−1.97918
$166$	−7.07919	−0.549452
$167$	20.8699	1.61496	0.807482	−	0.589892i	$-0.200830\pi$
$167$	20.8699	1.61496	0.807482	+	0.589892i	$0.200830\pi$
$168$	−2.67063	−0.206044
$169$	8.43999	0.649230
$170$	20.8303	1.59761
$171$	−17.4467	−1.33418
$172$	−11.7000	−0.892116
$173$	9.07022	0.689596	0.344798	−	0.938677i	$-0.387947\pi$
$173$	9.07022	0.689596	0.344798	+	0.938677i	$0.387947\pi$
$174$	−24.6050	−1.86530
$175$	−4.96038	−0.374970
$176$	3.01631	0.227363
$177$	5.82409	0.437765
$178$	−14.0832	−1.05558
$179$	4.01486	0.300085	0.150042	−	0.988680i	$-0.452059\pi$
$179$	4.01486	0.300085	0.150042	+	0.988680i	$0.452059\pi$
$180$	13.0415	0.972057
$181$	5.69222	0.423100	0.211550	−	0.977367i	$-0.432149\pi$
$181$	5.69222	0.423100	0.211550	+	0.977367i	$0.432149\pi$
$182$	−4.63033	−0.343223
$183$	3.46452	0.256105
$184$	0.524979	0.0387020
$185$	−27.0310	−1.98736
$186$	2.68370	0.196778
$187$	−19.9082	−1.45583
$188$	−7.89697	−0.575946
$189$	3.02392	0.219958
$190$	13.3248	0.966683
$191$	−7.41957	−0.536861	−0.268431	−	0.963299i	$-0.586505\pi$
$191$	−7.41957	−0.536861	−0.268431	+	0.963299i	$0.586505\pi$
$192$	−2.67063	−0.192736
$193$	−2.64434	−0.190344	−0.0951720	−	0.995461i	$-0.530340\pi$
$193$	−2.64434	−0.190344	−0.0951720	+	0.995461i	$0.530340\pi$
$194$	−14.9874	−1.07603
$195$	39.0269	2.79478
$196$	1.00000	0.0714286
$197$	2.48654	0.177158	0.0885792	−	0.996069i	$-0.471767\pi$
$197$	2.48654	0.177158	0.0885792	+	0.996069i	$0.471767\pi$
$198$	−12.4642	−0.885796
$199$	7.21010	0.511111	0.255555	−	0.966794i	$-0.417742\pi$
$199$	7.21010	0.511111	0.255555	+	0.966794i	$0.417742\pi$
$200$	−4.96038	−0.350752
$201$	−22.1265	−1.56068
$202$	0.171171	0.0120436
$203$	9.21317	0.646638
$204$	17.6267	1.23412
$205$	19.9195	1.39124
$206$	−11.0002	−0.766420
$207$	−2.16936	−0.150781
$208$	−4.63033	−0.321056
$209$	−12.7350	−0.880898
$210$	−8.42854	−0.581624
$211$	−14.2028	−0.977760	−0.488880	−	0.872351i	$-0.662594\pi$
$211$	−14.2028	−0.977760	−0.488880	+	0.872351i	$0.662594\pi$
$212$	0.831758	0.0571254
$213$	−37.5226	−2.57101
$214$	16.3738	1.11929
$215$	−36.9252	−2.51828
$216$	3.02392	0.205751
$217$	−1.00489	−0.0682164
$218$	10.6488	0.721226
$219$	−44.4094	−3.00091
$220$	9.51949	0.641804
$221$	30.5611	2.05576
$222$	−22.8738	−1.53519
$223$	−6.07525	−0.406829	−0.203414	−	0.979093i	$-0.565204\pi$
$223$	−6.07525	−0.406829	−0.203414	+	0.979093i	$0.565204\pi$
$224$	1.00000	0.0668153
$225$	20.4977	1.36651
$226$	17.2274	1.14595
$227$	26.8622	1.78291	0.891455	−	0.453109i	$-0.149685\pi$
$227$	26.8622	1.78291	0.891455	+	0.453109i	$0.149685\pi$
$228$	11.2755	0.746740
$229$	15.0402	0.993886	0.496943	−	0.867783i	$-0.334456\pi$
$229$	15.0402	0.993886	0.496943	+	0.867783i	$0.334456\pi$
$230$	1.65684	0.109249
$231$	8.05546	0.530010
$232$	9.21317	0.604874
$233$	−24.5638	−1.60923	−0.804613	−	0.593800i	$-0.797627\pi$
$233$	−24.5638	−1.60923	−0.804613	+	0.593800i	$0.797627\pi$
$234$	19.1339	1.25082
$235$	−24.9229	−1.62579
$236$	−2.18079	−0.141957
$237$	−43.8256	−2.84678
$238$	−6.60020	−0.427827
$239$	−6.35840	−0.411291	−0.205645	−	0.978627i	$-0.565929\pi$
$239$	−6.35840	−0.411291	−0.205645	+	0.978627i	$0.565929\pi$
$240$	−8.42854	−0.544060
$241$	−5.51971	−0.355556	−0.177778	−	0.984071i	$-0.556891\pi$
$241$	−5.51971	−0.355556	−0.177778	+	0.984071i	$0.556891\pi$
$242$	1.90188	0.122257
$243$	20.6118	1.32225
$244$	−1.29727	−0.0830490
$245$	3.15601	0.201630
$246$	16.8561	1.07470
$247$	19.5495	1.24390
$248$	−1.00489	−0.0638106
$249$	−18.9059	−1.19811
$250$	0.125039	0.00790819
$251$	5.28603	0.333652	0.166826	−	0.985986i	$-0.446648\pi$
$251$	5.28603	0.333652	0.166826	+	0.985986i	$0.446648\pi$
$252$	−4.13228	−0.260309
$253$	−1.58350	−0.0995537
$254$	−12.3826	−0.776953
$255$	55.6300	3.48369
$256$	1.00000	0.0625000
$257$	−6.39010	−0.398603	−0.199302	−	0.979938i	$-0.563867\pi$
$257$	−6.39010	−0.398603	−0.199302	+	0.979938i	$0.563867\pi$
$258$	−31.2464	−1.94531
$259$	8.56493	0.532199
$260$	−14.6134	−0.906282
$261$	−38.0714	−2.35656
$262$	−11.2346	−0.694077
$263$	−2.48872	−0.153461	−0.0767304	−	0.997052i	$-0.524448\pi$
$263$	−2.48872	−0.153461	−0.0767304	+	0.997052i	$0.524448\pi$
$264$	8.05546	0.495779
$265$	2.62504	0.161255
$266$	−4.22204	−0.258870
$267$	−37.6111	−2.30176
$268$	8.28511	0.506093
$269$	−1.04689	−0.0638299	−0.0319150	−	0.999491i	$-0.510161\pi$
$269$	−1.04689	−0.0638299	−0.0319150	+	0.999491i	$0.510161\pi$
$270$	9.54350	0.580799
$271$	−6.47317	−0.393217	−0.196609	−	0.980482i	$-0.562993\pi$
$271$	−6.47317	−0.393217	−0.196609	+	0.980482i	$0.562993\pi$
$272$	−6.60020	−0.400196
$273$	−12.3659	−0.748420
$274$	−7.05090	−0.425961
$275$	14.9620	0.902245
$276$	1.40203	0.0843921
$277$	5.18131	0.311315	0.155657	−	0.987811i	$-0.450250\pi$
$277$	5.18131	0.311315	0.155657	+	0.987811i	$0.450250\pi$
$278$	−19.2723	−1.15587
$279$	4.15250	0.248603
$280$	3.15601	0.188607
$281$	0.340066	0.0202867	0.0101433	−	0.999949i	$-0.496771\pi$
$281$	0.340066	0.0202867	0.0101433	+	0.999949i	$0.496771\pi$
$282$	−21.0899	−1.25589
$283$	−20.1181	−1.19590	−0.597948	−	0.801535i	$-0.704017\pi$
$283$	−20.1181	−1.19590	−0.597948	+	0.801535i	$0.704017\pi$
$284$	14.0501	0.833720
$285$	35.5857	2.10791
$286$	13.9665	0.825857
$287$	−6.31163	−0.372564
$288$	−4.13228	−0.243497
$289$	26.5626	1.56251
$290$	29.0768	1.70745
$291$	−40.0257	−2.34635
$292$	16.6288	0.973127
$293$	13.9830	0.816893	0.408447	−	0.912782i	$-0.366071\pi$
$293$	13.9830	0.816893	0.408447	+	0.912782i	$0.366071\pi$
$294$	2.67063	0.155755
$295$	−6.88258	−0.400720
$296$	8.56493	0.497826
$297$	−9.12107	−0.529258
$298$	16.3469	0.946950
$299$	2.43083	0.140578
$300$	−13.2474	−0.764837
$301$	11.7000	0.674376
$302$	4.57648	0.263347
$303$	0.457135	0.0262617
$304$	−4.22204	−0.242151
$305$	−4.09418	−0.234432
$306$	27.2739	1.55915
$307$	28.6630	1.63588	0.817941	−	0.575302i	$-0.195115\pi$
$307$	28.6630	1.63588	0.817941	+	0.575302i	$0.195115\pi$
$308$	−3.01631	−0.171870
$309$	−29.3775	−1.67123
$310$	−3.17144	−0.180126
$311$	10.8244	0.613793	0.306897	−	0.951743i	$-0.400709\pi$
$311$	10.8244	0.613793	0.306897	+	0.951743i	$0.400709\pi$
$312$	−12.3659	−0.700083
$313$	−13.5622	−0.766579	−0.383289	−	0.923628i	$-0.625209\pi$
$313$	−13.5622	−0.766579	−0.383289	+	0.923628i	$0.625209\pi$
$314$	7.67641	0.433205
$315$	−13.0415	−0.734806
$316$	16.4102	0.923145
$317$	12.4644	0.700070	0.350035	−	0.936737i	$-0.386170\pi$
$317$	12.4644	0.700070	0.350035	+	0.936737i	$0.386170\pi$
$318$	2.22132	0.124566
$319$	−27.7898	−1.55593
$320$	3.15601	0.176426
$321$	43.7285	2.44069
$322$	−0.524979	−0.0292559
$323$	27.8663	1.55052
$324$	−4.32108	−0.240060
$325$	−22.9682	−1.27405
$326$	−1.14467	−0.0633972
$327$	28.4390	1.57268
$328$	−6.31163	−0.348501
$329$	7.89697	0.435374
$330$	25.4231	1.39949
$331$	7.39253	0.406330	0.203165	−	0.979144i	$-0.434877\pi$
$331$	7.39253	0.406330	0.203165	+	0.979144i	$0.434877\pi$
$332$	7.07919	0.388521
$333$	−35.3927	−1.93951
$334$	−20.8699	−1.14195
$335$	26.1479	1.42861
$336$	2.67063	0.145695
$337$	30.2671	1.64876	0.824378	−	0.566040i	$-0.191525\pi$
$337$	30.2671	1.64876	0.824378	+	0.566040i	$0.191525\pi$
$338$	−8.43999	−0.459075
$339$	46.0080	2.49881
$340$	−20.8303	−1.12968
$341$	3.03106	0.164141
$342$	17.4467	0.943409
$343$	−1.00000	−0.0539949
$344$	11.7000	0.630821
$345$	4.42480	0.238223
$346$	−9.07022	−0.487618
$347$	22.4200	1.20357	0.601786	−	0.798658i	$-0.294456\pi$
$347$	22.4200	1.20357	0.601786	+	0.798658i	$0.294456\pi$
$348$	24.6050	1.31897
$349$	−14.1699	−0.758500	−0.379250	−	0.925294i	$-0.623818\pi$
$349$	−14.1699	−0.758500	−0.379250	+	0.925294i	$0.623818\pi$
$350$	4.96038	0.265143
$351$	14.0017	0.747358
$352$	−3.01631	−0.160770
$353$	−9.44344	−0.502624	−0.251312	−	0.967906i	$-0.580862\pi$
$353$	−9.44344	−0.502624	−0.251312	+	0.967906i	$0.580862\pi$
$354$	−5.82409	−0.309547
$355$	44.3422	2.35344
$356$	14.0832	0.746408
$357$	−17.6267	−0.932905
$358$	−4.01486	−0.212192
$359$	2.00815	0.105986	0.0529929	−	0.998595i	$-0.483124\pi$
$359$	2.00815	0.105986	0.0529929	+	0.998595i	$0.483124\pi$
$360$	−13.0415	−0.687348
$361$	−1.17434	−0.0618076
$362$	−5.69222	−0.299177
$363$	5.07922	0.266590
$364$	4.63033	0.242695
$365$	52.4806	2.74696
$366$	−3.46452	−0.181094
$367$	14.7871	0.771881	0.385940	−	0.922524i	$-0.373877\pi$
$367$	14.7871	0.771881	0.385940	+	0.922524i	$0.373877\pi$
$368$	−0.524979	−0.0273664
$369$	26.0814	1.35775
$370$	27.0310	1.40527
$371$	−0.831758	−0.0431827
$372$	−2.68370	−0.139143
$373$	30.6145	1.58516	0.792579	−	0.609769i	$-0.208738\pi$
$373$	30.6145	1.58516	0.792579	+	0.609769i	$0.208738\pi$
$374$	19.9082	1.02943
$375$	0.333934	0.0172443
$376$	7.89697	0.407255
$377$	42.6600	2.19710
$378$	−3.02392	−0.155534
$379$	10.7563	0.552512	0.276256	−	0.961084i	$-0.410906\pi$
$379$	10.7563	0.552512	0.276256	+	0.961084i	$0.410906\pi$
$380$	−13.3248	−0.683548
$381$	−33.0694	−1.69420
$382$	7.41957	0.379618
$383$	−1.45941	−0.0745723	−0.0372862	−	0.999305i	$-0.511871\pi$
$383$	−1.45941	−0.0745723	−0.0372862	+	0.999305i	$0.511871\pi$
$384$	2.67063	0.136285
$385$	−9.51949	−0.485158
$386$	2.64434	0.134594
$387$	−48.3477	−2.45765
$388$	14.9874	0.760868
$389$	4.73759	0.240205	0.120103	−	0.992761i	$-0.461678\pi$
$389$	4.73759	0.240205	0.120103	+	0.992761i	$0.461678\pi$
$390$	−39.0269	−1.97621
$391$	3.46496	0.175231
$392$	−1.00000	−0.0505076
$393$	−30.0036	−1.51348
$394$	−2.48654	−0.125270
$395$	51.7906	2.60587
$396$	12.4642	0.626352
$397$	−16.7995	−0.843143	−0.421572	−	0.906795i	$-0.638521\pi$
$397$	−16.7995	−0.843143	−0.421572	+	0.906795i	$0.638521\pi$
$398$	−7.21010	−0.361410
$399$	−11.2755	−0.564483
$400$	4.96038	0.248019
$401$	−2.31347	−0.115529	−0.0577647	−	0.998330i	$-0.518397\pi$
$401$	−2.31347	−0.115529	−0.0577647	+	0.998330i	$0.518397\pi$
$402$	22.1265	1.10357
$403$	−4.65298	−0.231781
$404$	−0.171171	−0.00851608
$405$	−13.6374	−0.677646
$406$	−9.21317	−0.457242
$407$	−25.8345	−1.28057
$408$	−17.6267	−0.872652
$409$	−11.6520	−0.576152	−0.288076	−	0.957608i	$-0.593016\pi$
$409$	−11.6520	−0.576152	−0.288076	+	0.957608i	$0.593016\pi$
$410$	−19.9195	−0.983756
$411$	−18.8304	−0.928834
$412$	11.0002	0.541941
$413$	2.18079	0.107310
$414$	2.16936	0.106618
$415$	22.3420	1.09672
$416$	4.63033	0.227021
$417$	−51.4691	−2.52045
$418$	12.7350	0.622889
$419$	−31.2631	−1.52730	−0.763652	−	0.645628i	$-0.776596\pi$
$419$	−31.2631	−1.52730	−0.763652	+	0.645628i	$0.776596\pi$
$420$	8.42854	0.411271
$421$	24.4387	1.19107	0.595534	−	0.803330i	$-0.296941\pi$
$421$	24.4387	1.19107	0.595534	+	0.803330i	$0.296941\pi$
$422$	14.2028	0.691381
$423$	−32.6325	−1.58665
$424$	−0.831758	−0.0403938
$425$	−32.7395	−1.58810
$426$	37.5226	1.81798
$427$	1.29727	0.0627791
$428$	−16.3738	−0.791458
$429$	37.2995	1.80083
$430$	36.9252	1.78069
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−3.02392	−0.145488
$433$	−25.2393	−1.21292	−0.606462	−	0.795112i	$-0.707412\pi$
$433$	−25.2393	−1.21292	−0.606462	+	0.795112i	$0.707412\pi$
$434$	1.00489	0.0482363
$435$	77.6535	3.72320
$436$	−10.6488	−0.509984
$437$	2.21648	0.106029
$438$	44.4094	2.12196
$439$	12.9214	0.616706	0.308353	−	0.951272i	$-0.400222\pi$
$439$	12.9214	0.616706	0.308353	+	0.951272i	$0.400222\pi$
$440$	−9.51949	−0.453824
$441$	4.13228	0.196775
$442$	−30.5611	−1.45364
$443$	3.93412	0.186916	0.0934578	−	0.995623i	$-0.470208\pi$
$443$	3.93412	0.186916	0.0934578	+	0.995623i	$0.470208\pi$
$444$	22.8738	1.08554
$445$	44.4467	2.10697
$446$	6.07525	0.287671
$447$	43.6566	2.06488
$448$	−1.00000	−0.0472456
$449$	31.8219	1.50177	0.750883	−	0.660435i	$-0.229628\pi$
$449$	31.8219	1.50177	0.750883	+	0.660435i	$0.229628\pi$
$450$	−20.4977	−0.966271
$451$	19.0378	0.896456
$452$	−17.2274	−0.810308
$453$	12.2221	0.574245
$454$	−26.8622	−1.26071
$455$	14.6134	0.685085
$456$	−11.2755	−0.528025
$457$	−15.1960	−0.710838	−0.355419	−	0.934707i	$-0.615662\pi$
$457$	−15.1960	−0.710838	−0.355419	+	0.934707i	$0.615662\pi$
$458$	−15.0402	−0.702784
$459$	19.9585	0.931581
$460$	−1.65684	−0.0772504
$461$	−5.80779	−0.270496	−0.135248	−	0.990812i	$-0.543183\pi$
$461$	−5.80779	−0.270496	−0.135248	+	0.990812i	$0.543183\pi$
$462$	−8.05546	−0.374774
$463$	21.0429	0.977948	0.488974	−	0.872298i	$-0.337371\pi$
$463$	21.0429	0.977948	0.488974	+	0.872298i	$0.337371\pi$
$464$	−9.21317	−0.427711
$465$	−8.46976	−0.392776
$466$	24.5638	1.13789
$467$	25.8605	1.19668	0.598341	−	0.801241i	$-0.295827\pi$
$467$	25.8605	1.19668	0.598341	+	0.801241i	$0.295827\pi$
$468$	−19.1339	−0.884463
$469$	−8.28511	−0.382571
$470$	24.9229	1.14961
$471$	20.5009	0.944631
$472$	2.18079	0.100379
$473$	−35.2908	−1.62267
$474$	43.8256	2.01298
$475$	−20.9429	−0.960928
$476$	6.60020	0.302520
$477$	3.43706	0.157372
$478$	6.35840	0.290826
$479$	−21.8365	−0.997733	−0.498866	−	0.866679i	$-0.666250\pi$
$479$	−21.8365	−0.997733	−0.498866	+	0.866679i	$0.666250\pi$
$480$	8.42854	0.384708
$481$	39.6585	1.80827
$482$	5.51971	0.251416
$483$	−1.40203	−0.0637944
$484$	−1.90188	−0.0864490
$485$	47.3002	2.14779
$486$	−20.6118	−0.934969
$487$	−31.9434	−1.44749	−0.723746	−	0.690066i	$-0.757581\pi$
$487$	−31.9434	−1.44749	−0.723746	+	0.690066i	$0.757581\pi$
$488$	1.29727	0.0587245
$489$	−3.05698	−0.138242
$490$	−3.15601	−0.142574
$491$	4.08024	0.184139	0.0920694	−	0.995753i	$-0.470652\pi$
$491$	4.08024	0.184139	0.0920694	+	0.995753i	$0.470652\pi$
$492$	−16.8561	−0.759929
$493$	60.8087	2.73869
$494$	−19.5495	−0.879572
$495$	39.3373	1.76808
$496$	1.00489	0.0451209
$497$	−14.0501	−0.630233
$498$	18.9059	0.847195
$499$	43.4544	1.94529	0.972644	−	0.232302i	$-0.0746257\pi$
$499$	43.4544	1.94529	0.972644	+	0.232302i	$0.0746257\pi$
$500$	−0.125039	−0.00559193
$501$	−55.7360	−2.49010
$502$	−5.28603	−0.235927
$503$	−1.47723	−0.0658665	−0.0329333	−	0.999458i	$-0.510485\pi$
$503$	−1.47723	−0.0658665	−0.0329333	+	0.999458i	$0.510485\pi$
$504$	4.13228	0.184067
$505$	−0.540217	−0.0240393
$506$	1.58350	0.0703951
$507$	−22.5401	−1.00104
$508$	12.3826	0.549389
$509$	−12.5665	−0.557000	−0.278500	−	0.960436i	$-0.589837\pi$
$509$	−12.5665	−0.557000	−0.278500	+	0.960436i	$0.589837\pi$
$510$	−55.6300	−2.46334
$511$	−16.6288	−0.735615
$512$	−1.00000	−0.0441942
$513$	12.7671	0.563682
$514$	6.39010	0.281855
$515$	34.7167	1.52980
$516$	31.2464	1.37555
$517$	−23.8197	−1.04759
$518$	−8.56493	−0.376321
$519$	−24.2232	−1.06328
$520$	14.6134	0.640838
$521$	−0.365819	−0.0160268	−0.00801340	−	0.999968i	$-0.502551\pi$
$521$	−0.365819	−0.0160268	−0.00801340	+	0.999968i	$0.502551\pi$
$522$	38.0714	1.66634
$523$	−24.9640	−1.09160	−0.545800	−	0.837915i	$-0.683774\pi$
$523$	−24.9640	−1.09160	−0.545800	+	0.837915i	$0.683774\pi$
$524$	11.2346	0.490787
$525$	13.2474	0.578162
$526$	2.48872	0.108513
$527$	−6.63248	−0.288915
$528$	−8.05546	−0.350569
$529$	−22.7244	−0.988017
$530$	−2.62504	−0.114024
$531$	−9.01164	−0.391072
$532$	4.22204	0.183049
$533$	−29.2249	−1.26587
$534$	37.6111	1.62759
$535$	−51.6759	−2.23414
$536$	−8.28511	−0.357862
$537$	−10.7222	−0.462698
$538$	1.04689	0.0451346
$539$	3.01631	0.129922
$540$	−9.54350	−0.410687
$541$	−40.6148	−1.74617	−0.873083	−	0.487571i	$-0.837883\pi$
$541$	−40.6148	−1.74617	−0.873083	+	0.487571i	$0.837883\pi$
$542$	6.47317	0.278046
$543$	−15.2018	−0.652374
$544$	6.60020	0.282981
$545$	−33.6076	−1.43959
$546$	12.3659	0.529213
$547$	−13.5048	−0.577422	−0.288711	−	0.957416i	$-0.593227\pi$
$547$	−13.5048	−0.577422	−0.288711	+	0.957416i	$0.593227\pi$
$548$	7.05090	0.301200
$549$	−5.36068	−0.228788
$550$	−14.9620	−0.637984
$551$	38.8984	1.65713
$552$	−1.40203	−0.0596742
$553$	−16.4102	−0.697832
$554$	−5.18131	−0.220133
$555$	72.1898	3.06429
$556$	19.2723	0.817325
$557$	9.82915	0.416474	0.208237	−	0.978078i	$-0.433227\pi$
$557$	9.82915	0.416474	0.208237	+	0.978078i	$0.433227\pi$
$558$	−4.15250	−0.175789
$559$	54.1748	2.29135
$560$	−3.15601	−0.133366
$561$	53.1676	2.24474
$562$	−0.340066	−0.0143448
$563$	1.12295	0.0473267	0.0236634	−	0.999720i	$-0.492467\pi$
$563$	1.12295	0.0473267	0.0236634	+	0.999720i	$0.492467\pi$
$564$	21.0899	0.888046
$565$	−54.3697	−2.28735
$566$	20.1181	0.845626
$567$	4.32108	0.181468
$568$	−14.0501	−0.589529
$569$	−30.7579	−1.28944	−0.644719	−	0.764420i	$-0.723026\pi$
$569$	−30.7579	−1.28944	−0.644719	+	0.764420i	$0.723026\pi$
$570$	−35.5857	−1.49052
$571$	3.90203	0.163295	0.0816474	−	0.996661i	$-0.473982\pi$
$571$	3.90203	0.163295	0.0816474	+	0.996661i	$0.473982\pi$
$572$	−13.9665	−0.583969
$573$	19.8150	0.827782
$574$	6.31163	0.263442
$575$	−2.60409	−0.108598
$576$	4.13228	0.172179
$577$	4.41862	0.183949	0.0919747	−	0.995761i	$-0.470682\pi$
$577$	4.41862	0.183949	0.0919747	+	0.995761i	$0.470682\pi$
$578$	−26.5626	−1.10486
$579$	7.06207	0.293490
$580$	−29.0768	−1.20735
$581$	−7.07919	−0.293694
$582$	40.0257	1.65912
$583$	2.50884	0.103906
$584$	−16.6288	−0.688105
$585$	−60.3866	−2.49668
$586$	−13.9830	−0.577631
$587$	−22.3402	−0.922080	−0.461040	−	0.887379i	$-0.652524\pi$
$587$	−22.3402	−0.922080	−0.461040	+	0.887379i	$0.652524\pi$
$588$	−2.67063	−0.110135
$589$	−4.24269	−0.174817
$590$	6.88258	0.283352
$591$	−6.64063	−0.273159
$592$	−8.56493	−0.352016
$593$	22.0369	0.904948	0.452474	−	0.891778i	$-0.350542\pi$
$593$	22.0369	0.904948	0.452474	+	0.891778i	$0.350542\pi$
$594$	9.12107	0.374242
$595$	20.8303	0.853958
$596$	−16.3469	−0.669595
$597$	−19.2555	−0.788077
$598$	−2.43083	−0.0994039
$599$	−20.8130	−0.850397	−0.425199	−	0.905100i	$-0.639796\pi$
$599$	−20.8130	−0.850397	−0.425199	+	0.905100i	$0.639796\pi$
$600$	13.2474	0.540821
$601$	36.2110	1.47708	0.738540	−	0.674210i	$-0.235516\pi$
$601$	36.2110	1.47708	0.738540	+	0.674210i	$0.235516\pi$
$602$	−11.7000	−0.476856
$603$	34.2364	1.39421
$604$	−4.57648	−0.186214
$605$	−6.00234	−0.244030
$606$	−0.457135	−0.0185698
$607$	30.2052	1.22599	0.612995	−	0.790087i	$-0.289965\pi$
$607$	30.2052	1.22599	0.612995	+	0.790087i	$0.289965\pi$
$608$	4.22204	0.171226
$609$	−24.6050	−0.997045
$610$	4.09418	0.165769
$611$	36.5656	1.47929
$612$	−27.2739	−1.10248
$613$	−43.0840	−1.74014	−0.870072	−	0.492924i	$-0.835928\pi$
$613$	−43.0840	−1.74014	−0.870072	+	0.492924i	$0.835928\pi$
$614$	−28.6630	−1.15674
$615$	−53.1978	−2.14514
$616$	3.01631	0.121531
$617$	13.6269	0.548597	0.274298	−	0.961645i	$-0.411554\pi$
$617$	13.6269	0.548597	0.274298	+	0.961645i	$0.411554\pi$
$618$	29.3775	1.18174
$619$	6.17501	0.248195	0.124097	−	0.992270i	$-0.460396\pi$
$619$	6.17501	0.248195	0.124097	+	0.992270i	$0.460396\pi$
$620$	3.17144	0.127368
$621$	1.58749	0.0637039
$622$	−10.8244	−0.434017
$623$	−14.0832	−0.564231
$624$	12.3659	0.495033
$625$	−25.1965	−1.00786
$626$	13.5622	0.542053
$627$	34.0105	1.35825
$628$	−7.67641	−0.306322
$629$	56.5302	2.25401
$630$	13.0415	0.519587
$631$	23.9546	0.953619	0.476809	−	0.879007i	$-0.341793\pi$
$631$	23.9546	0.953619	0.476809	+	0.879007i	$0.341793\pi$
$632$	−16.4102	−0.652762
$633$	37.9305	1.50760
$634$	−12.4644	−0.495024
$635$	39.0796	1.55083
$636$	−2.22132	−0.0880812
$637$	−4.63033	−0.183460
$638$	27.7898	1.10021
$639$	58.0590	2.29678
$640$	−3.15601	−0.124752
$641$	11.3253	0.447321	0.223661	−	0.974667i	$-0.428199\pi$
$641$	11.3253	0.447321	0.223661	+	0.974667i	$0.428199\pi$
$642$	−43.7285	−1.72583
$643$	−37.7847	−1.49008	−0.745042	−	0.667018i	$-0.767571\pi$
$643$	−37.7847	−1.49008	−0.745042	+	0.667018i	$0.767571\pi$
$644$	0.524979	0.0206871
$645$	98.6138	3.88291
$646$	−27.8663	−1.09639
$647$	23.2338	0.913415	0.456707	−	0.889617i	$-0.349029\pi$
$647$	23.2338	0.913415	0.456707	+	0.889617i	$0.349029\pi$
$648$	4.32108	0.169748
$649$	−6.57793	−0.258206
$650$	22.9682	0.900887
$651$	2.68370	0.105182
$652$	1.14467	0.0448286
$653$	43.7520	1.71215	0.856074	−	0.516853i	$-0.172897\pi$
$653$	43.7520	1.71215	0.856074	+	0.516853i	$0.172897\pi$
$654$	−28.4390	−1.11205
$655$	35.4565	1.38540
$656$	6.31163	0.246428
$657$	68.7149	2.68082
$658$	−7.89697	−0.307856
$659$	−41.2372	−1.60637	−0.803186	−	0.595728i	$-0.796864\pi$
$659$	−41.2372	−1.60637	−0.803186	+	0.595728i	$0.796864\pi$
$660$	−25.4231	−0.989592
$661$	−13.4403	−0.522766	−0.261383	−	0.965235i	$-0.584179\pi$
$661$	−13.4403	−0.522766	−0.261383	+	0.965235i	$0.584179\pi$
$662$	−7.39253	−0.287319
$663$	−81.6176	−3.16976
$664$	−7.07919	−0.274726
$665$	13.3248	0.516714
$666$	35.3927	1.37144
$667$	4.83672	0.187278
$668$	20.8699	0.807482
$669$	16.2248	0.627286
$670$	−26.1479	−1.01018
$671$	−3.91296	−0.151058
$672$	−2.67063	−0.103022
$673$	27.4599	1.05850	0.529251	−	0.848465i	$-0.322473\pi$
$673$	27.4599	1.05850	0.529251	+	0.848465i	$0.322473\pi$
$674$	−30.2671	−1.16585
$675$	−14.9998	−0.577342
$676$	8.43999	0.324615
$677$	39.3655	1.51294	0.756469	−	0.654030i	$-0.226923\pi$
$677$	39.3655	1.51294	0.756469	+	0.654030i	$0.226923\pi$
$678$	−46.0080	−1.76693
$679$	−14.9874	−0.575162
$680$	20.8303	0.798805
$681$	−71.7392	−2.74905
$682$	−3.03106	−0.116065
$683$	−32.4141	−1.24029	−0.620146	−	0.784487i	$-0.712927\pi$
$683$	−32.4141	−1.24029	−0.620146	+	0.784487i	$0.712927\pi$
$684$	−17.4467	−0.667091
$685$	22.2527	0.850232
$686$	1.00000	0.0381802
$687$	−40.1669	−1.53246
$688$	−11.7000	−0.446058
$689$	−3.85132	−0.146724
$690$	−4.42480	−0.168449
$691$	−15.0473	−0.572427	−0.286213	−	0.958166i	$-0.592397\pi$
$691$	−15.0473	−0.572427	−0.286213	+	0.958166i	$0.592397\pi$
$692$	9.07022	0.344798
$693$	−12.4642	−0.473478
$694$	−22.4200	−0.851053
$695$	60.8234	2.30716
$696$	−24.6050	−0.932650
$697$	−41.6580	−1.57791
$698$	14.1699	0.536340
$699$	65.6008	2.48125
$700$	−4.96038	−0.187485
$701$	17.8235	0.673186	0.336593	−	0.941650i	$-0.390725\pi$
$701$	17.8235	0.673186	0.336593	+	0.941650i	$0.390725\pi$
$702$	−14.0017	−0.528462
$703$	36.1615	1.36386
$704$	3.01631	0.113681
$705$	66.5600	2.50679
$706$	9.44344	0.355409
$707$	0.171171	0.00643755
$708$	5.82409	0.218883
$709$	42.6540	1.60190	0.800952	−	0.598728i	$-0.204327\pi$
$709$	42.6540	1.60190	0.800952	+	0.598728i	$0.204327\pi$
$710$	−44.3422	−1.66413
$711$	67.8115	2.54313
$712$	−14.0832	−0.527790
$713$	−0.527547	−0.0197568
$714$	17.6267	0.659663
$715$	−44.0784	−1.64844
$716$	4.01486	0.150042
$717$	16.9809	0.634165
$718$	−2.00815	−0.0749433
$719$	−16.0627	−0.599038	−0.299519	−	0.954090i	$-0.596826\pi$
$719$	−16.0627	−0.599038	−0.299519	+	0.954090i	$0.596826\pi$
$720$	13.0415	0.486029
$721$	−11.0002	−0.409669
$722$	1.17434	0.0437046
$723$	14.7411	0.548229
$724$	5.69222	0.211550
$725$	−45.7008	−1.69729
$726$	−5.07922	−0.188507
$727$	−9.33177	−0.346096	−0.173048	−	0.984913i	$-0.555362\pi$
$727$	−9.33177	−0.346096	−0.173048	+	0.984913i	$0.555362\pi$
$728$	−4.63033	−0.171612
$729$	−42.0833	−1.55864
$730$	−52.4806	−1.94239
$731$	77.2222	2.85617
$732$	3.46452	0.128053
$733$	44.0899	1.62850	0.814248	−	0.580517i	$-0.197149\pi$
$733$	44.0899	1.62850	0.814248	+	0.580517i	$0.197149\pi$
$734$	−14.7871	−0.545802
$735$	−8.42854	−0.310891
$736$	0.524979	0.0193510
$737$	24.9904	0.920535
$738$	−26.0814	−0.960071
$739$	37.6307	1.38427	0.692134	−	0.721769i	$-0.256670\pi$
$739$	37.6307	1.38427	0.692134	+	0.721769i	$0.256670\pi$
$740$	−27.0310	−0.993678
$741$	−52.2095	−1.91796
$742$	0.831758	0.0305348
$743$	16.9980	0.623597	0.311799	−	0.950148i	$-0.399069\pi$
$743$	16.9980	0.623597	0.311799	+	0.950148i	$0.399069\pi$
$744$	2.68370	0.0983891
$745$	−51.5909	−1.89015
$746$	−30.6145	−1.12088
$747$	29.2532	1.07032
$748$	−19.9082	−0.727917
$749$	16.3738	0.598286
$750$	−0.333934	−0.0121936
$751$	24.0331	0.876981	0.438491	−	0.898736i	$-0.355513\pi$
$751$	24.0331	0.876981	0.438491	+	0.898736i	$0.355513\pi$
$752$	−7.89697	−0.287973
$753$	−14.1171	−0.514454
$754$	−42.6600	−1.55359
$755$	−14.4434	−0.525650
$756$	3.02392	0.109979
$757$	9.02734	0.328104	0.164052	−	0.986452i	$-0.447543\pi$
$757$	9.02734	0.328104	0.164052	+	0.986452i	$0.447543\pi$
$758$	−10.7563	−0.390685
$759$	4.22894	0.153501
$760$	13.3248	0.483341
$761$	−42.4388	−1.53841	−0.769203	−	0.639005i	$-0.779346\pi$
$761$	−42.4388	−1.53841	−0.769203	+	0.639005i	$0.779346\pi$
$762$	33.0694	1.19798
$763$	10.6488	0.385512
$764$	−7.41957	−0.268431
$765$	−86.0766	−3.11211
$766$	1.45941	0.0527306
$767$	10.0978	0.364610
$768$	−2.67063	−0.0963682
$769$	−39.2468	−1.41528	−0.707639	−	0.706575i	$-0.750239\pi$
$769$	−39.2468	−1.41528	−0.707639	+	0.706575i	$0.750239\pi$
$770$	9.51949	0.343059
$771$	17.0656	0.614603
$772$	−2.64434	−0.0951720
$773$	13.2797	0.477638	0.238819	−	0.971064i	$-0.423240\pi$
$773$	13.2797	0.477638	0.238819	+	0.971064i	$0.423240\pi$
$774$	48.3477	1.73782
$775$	4.98464	0.179054
$776$	−14.9874	−0.538015
$777$	−22.8738	−0.820592
$778$	−4.73759	−0.169851
$779$	−26.6480	−0.954763
$780$	39.0269	1.39739
$781$	42.3794	1.51645
$782$	−3.46496	−0.123907
$783$	27.8599	0.995630
$784$	1.00000	0.0357143
$785$	−24.2268	−0.864692
$786$	30.0036	1.07019
$787$	−30.6190	−1.09145	−0.545725	−	0.837964i	$-0.683746\pi$
$787$	−30.6190	−1.09145	−0.545725	+	0.837964i	$0.683746\pi$
$788$	2.48654	0.0885792
$789$	6.64645	0.236620
$790$	−51.7906	−1.84263
$791$	17.2274	0.612535
$792$	−12.4642	−0.442898
$793$	6.00678	0.213307
$794$	16.7995	0.596192
$795$	−7.01051	−0.248637
$796$	7.21010	0.255555
$797$	2.40628	0.0852348	0.0426174	−	0.999091i	$-0.486430\pi$
$797$	2.40628	0.0852348	0.0426174	+	0.999091i	$0.486430\pi$
$798$	11.2755	0.399150
$799$	52.1216	1.84393
$800$	−4.96038	−0.175376
$801$	58.1958	2.05625
$802$	2.31347	0.0816916
$803$	50.1576	1.77002
$804$	−22.1265	−0.780341
$805$	1.65684	0.0583958
$806$	4.65298	0.163894
$807$	2.79586	0.0984188
$808$	0.171171	0.00602178
$809$	20.3487	0.715421	0.357711	−	0.933833i	$-0.383557\pi$
$809$	20.3487	0.715421	0.357711	+	0.933833i	$0.383557\pi$
$810$	13.6374	0.479168
$811$	−13.6894	−0.480700	−0.240350	−	0.970686i	$-0.577262\pi$
$811$	−13.6894	−0.480700	−0.240350	+	0.970686i	$0.577262\pi$
$812$	9.21317	0.323319
$813$	17.2875	0.606298
$814$	25.8345	0.905498
$815$	3.61257	0.126543
$816$	17.6267	0.617058
$817$	49.3979	1.72821
$818$	11.6520	0.407401
$819$	19.1339	0.668591
$820$	19.9195	0.695621
$821$	27.8882	0.973306	0.486653	−	0.873595i	$-0.338218\pi$
$821$	27.8882	0.973306	0.486653	+	0.873595i	$0.338218\pi$
$822$	18.8304	0.656785
$823$	36.9433	1.28776	0.643881	−	0.765126i	$-0.277323\pi$
$823$	36.9433	1.28776	0.643881	+	0.765126i	$0.277323\pi$
$824$	−11.0002	−0.383210
$825$	−39.9581	−1.39116
$826$	−2.18079	−0.0758793
$827$	−47.4353	−1.64949	−0.824743	−	0.565507i	$-0.808681\pi$
$827$	−47.4353	−1.64949	−0.824743	+	0.565507i	$0.808681\pi$
$828$	−2.16936	−0.0753905
$829$	−42.0991	−1.46216	−0.731081	−	0.682291i	$-0.760984\pi$
$829$	−42.0991	−1.46216	−0.731081	+	0.682291i	$0.760984\pi$
$830$	−22.3420	−0.775502
$831$	−13.8374	−0.480013
$832$	−4.63033	−0.160528
$833$	−6.60020	−0.228683
$834$	51.4691	1.78223
$835$	65.8657	2.27938
$836$	−12.7350	−0.440449
$837$	−3.03871	−0.105033
$838$	31.2631	1.07997
$839$	48.2754	1.66665	0.833326	−	0.552782i	$-0.186434\pi$
$839$	48.2754	1.66665	0.833326	+	0.552782i	$0.186434\pi$
$840$	−8.42854	−0.290812
$841$	55.8824	1.92698
$842$	−24.4387	−0.842212
$843$	−0.908192	−0.0312798
$844$	−14.2028	−0.488880
$845$	26.6367	0.916329
$846$	32.6325	1.12193
$847$	1.90188	0.0653493
$848$	0.831758	0.0285627
$849$	53.7280	1.84394
$850$	32.7395	1.12296
$851$	4.49640	0.154135
$852$	−37.5226	−1.28550
$853$	−11.2223	−0.384246	−0.192123	−	0.981371i	$-0.561537\pi$
$853$	−11.2223	−0.384246	−0.192123	+	0.981371i	$0.561537\pi$
$854$	−1.29727	−0.0443916
$855$	−55.0619	−1.88308
$856$	16.3738	0.559646
$857$	39.1309	1.33669	0.668343	−	0.743853i	$-0.267004\pi$
$857$	39.1309	1.33669	0.668343	+	0.743853i	$0.267004\pi$
$858$	−37.2995	−1.27338
$859$	2.68444	0.0915917	0.0457959	−	0.998951i	$-0.485418\pi$
$859$	2.68444	0.0915917	0.0457959	+	0.998951i	$0.485418\pi$
$860$	−36.9252	−1.25914
$861$	16.8561	0.574453
$862$	−1.00000	−0.0340601
$863$	−50.4232	−1.71643	−0.858213	−	0.513294i	$-0.828425\pi$
$863$	−50.4232	−1.71643	−0.858213	+	0.513294i	$0.828425\pi$
$864$	3.02392	0.102876
$865$	28.6257	0.973302
$866$	25.2393	0.857667
$867$	−70.9390	−2.40922
$868$	−1.00489	−0.0341082
$869$	49.4982	1.67911
$870$	−77.6535	−2.63270
$871$	−38.3628	−1.29987
$872$	10.6488	0.360613
$873$	61.9320	2.09608
$874$	−2.21648	−0.0749737
$875$	0.125039	0.00422710
$876$	−44.4094	−1.50046
$877$	−41.8989	−1.41483	−0.707413	−	0.706800i	$-0.750138\pi$
$877$	−41.8989	−1.41483	−0.707413	+	0.706800i	$0.750138\pi$
$878$	−12.9214	−0.436077
$879$	−37.3434	−1.25956
$880$	9.51949	0.320902
$881$	−28.5652	−0.962385	−0.481192	−	0.876615i	$-0.659796\pi$
$881$	−28.5652	−0.962385	−0.481192	+	0.876615i	$0.659796\pi$
$882$	−4.13228	−0.139141
$883$	−46.3681	−1.56041	−0.780206	−	0.625523i	$-0.784886\pi$
$883$	−46.3681	−1.56041	−0.780206	+	0.625523i	$0.784886\pi$
$884$	30.5611	1.02788
$885$	18.3809	0.617866
$886$	−3.93412	−0.132169
$887$	41.9775	1.40947	0.704733	−	0.709472i	$-0.251067\pi$
$887$	41.9775	1.40947	0.704733	+	0.709472i	$0.251067\pi$
$888$	−22.8738	−0.767594
$889$	−12.3826	−0.415299
$890$	−44.4467	−1.48986
$891$	−13.0337	−0.436646
$892$	−6.07525	−0.203414
$893$	33.3414	1.11573
$894$	−43.6566	−1.46009
$895$	12.6709	0.423542
$896$	1.00000	0.0334077
$897$	−6.49185	−0.216757
$898$	−31.8219	−1.06191
$899$	−9.25823	−0.308779
$900$	20.4977	0.683257
$901$	−5.48977	−0.182891
$902$	−19.0378	−0.633890
$903$	−31.2464	−1.03981
$904$	17.2274	0.572974
$905$	17.9647	0.597167
$906$	−12.2221	−0.406052
$907$	−34.6891	−1.15183	−0.575917	−	0.817508i	$-0.695355\pi$
$907$	−34.6891	−1.15183	−0.575917	+	0.817508i	$0.695355\pi$
$908$	26.8622	0.891455
$909$	−0.707327	−0.0234606
$910$	−14.6134	−0.484428
$911$	59.0097	1.95508	0.977540	−	0.210750i	$-0.0675906\pi$
$911$	59.0097	1.95508	0.977540	+	0.210750i	$0.0675906\pi$
$912$	11.2755	0.373370
$913$	21.3530	0.706682
$914$	15.1960	0.502638
$915$	10.9341	0.361469
$916$	15.0402	0.496943
$917$	−11.2346	−0.371000
$918$	−19.9585	−0.658727
$919$	3.70958	0.122368	0.0611839	−	0.998127i	$-0.480512\pi$
$919$	3.70958	0.122368	0.0611839	+	0.998127i	$0.480512\pi$
$920$	1.65684	0.0546243
$921$	−76.5483	−2.52235
$922$	5.80779	0.191270
$923$	−65.0566	−2.14136
$924$	8.05546	0.265005
$925$	−42.4853	−1.39691
$926$	−21.0429	−0.691514
$927$	45.4559	1.49297
$928$	9.21317	0.302437
$929$	35.6276	1.16891	0.584453	−	0.811428i	$-0.301309\pi$
$929$	35.6276	1.16891	0.584453	+	0.811428i	$0.301309\pi$
$930$	8.46976	0.277734
$931$	−4.22204	−0.138372
$932$	−24.5638	−0.804613
$933$	−28.9079	−0.946402
$934$	−25.8605	−0.846182
$935$	−62.8306	−2.05478
$936$	19.1339	0.625410
$937$	−22.5160	−0.735567	−0.367783	−	0.929911i	$-0.619883\pi$
$937$	−22.5160	−0.735567	−0.367783	+	0.929911i	$0.619883\pi$
$938$	8.28511	0.270518
$939$	36.2196	1.18198
$940$	−24.9229	−0.812896
$941$	−36.3844	−1.18610	−0.593049	−	0.805166i	$-0.702076\pi$
$941$	−36.3844	−1.18610	−0.593049	+	0.805166i	$0.702076\pi$
$942$	−20.5009	−0.667955
$943$	−3.31347	−0.107901
$944$	−2.18079	−0.0709786
$945$	9.54350	0.310450
$946$	35.2908	1.14740
$947$	−44.9617	−1.46106	−0.730530	−	0.682881i	$-0.760727\pi$
$947$	−44.9617	−1.46106	−0.730530	+	0.682881i	$0.760727\pi$
$948$	−43.8256	−1.42339
$949$	−76.9969	−2.49942
$950$	20.9429	0.679479
$951$	−33.2878	−1.07943
$952$	−6.60020	−0.213914
$953$	6.43848	0.208563	0.104281	−	0.994548i	$-0.466746\pi$
$953$	6.43848	0.208563	0.104281	+	0.994548i	$0.466746\pi$
$954$	−3.43706	−0.111279
$955$	−23.4162	−0.757731
$956$	−6.35840	−0.205645
$957$	74.2163	2.39907
$958$	21.8365	0.705504
$959$	−7.05090	−0.227685
$960$	−8.42854	−0.272030
$961$	−29.9902	−0.967426
$962$	−39.6585	−1.27864
$963$	−67.6613	−2.18035
$964$	−5.51971	−0.177778
$965$	−8.34557	−0.268653
$966$	1.40203	0.0451095
$967$	58.5436	1.88263	0.941317	−	0.337523i	$-0.109589\pi$
$967$	58.5436	1.88263	0.941317	+	0.337523i	$0.109589\pi$
$968$	1.90188	0.0611287
$969$	−74.4208	−2.39074
$970$	−47.3002	−1.51872
$971$	−11.2801	−0.361995	−0.180998	−	0.983484i	$-0.557933\pi$
$971$	−11.2801	−0.361995	−0.180998	+	0.983484i	$0.557933\pi$
$972$	20.6118	0.661123
$973$	−19.2723	−0.617840
$974$	31.9434	1.02353
$975$	61.3397	1.96444
$976$	−1.29727	−0.0415245
$977$	33.9580	1.08641	0.543206	−	0.839599i	$-0.317210\pi$
$977$	33.9580	1.08641	0.543206	+	0.839599i	$0.317210\pi$
$978$	3.05698	0.0977515
$979$	42.4793	1.35764
$980$	3.15601	0.100815
$981$	−44.0038	−1.40493
$982$	−4.08024	−0.130206
$983$	44.3483	1.41449	0.707246	−	0.706967i	$-0.249937\pi$
$983$	44.3483	1.41449	0.707246	+	0.706967i	$0.249937\pi$
$984$	16.8561	0.537351
$985$	7.84753	0.250043
$986$	−60.8087	−1.93654
$987$	−21.0899	−0.671300
$988$	19.5495	0.621952
$989$	6.14225	0.195312
$990$	−39.3373	−1.25022
$991$	−11.4795	−0.364657	−0.182329	−	0.983238i	$-0.558363\pi$
$991$	−11.4795	−0.364657	−0.182329	+	0.983238i	$0.558363\pi$
$992$	−1.00489	−0.0319053
$993$	−19.7427	−0.626517
$994$	14.0501	0.445642
$995$	22.7551	0.721386
$996$	−18.9059	−0.599057
$997$	−18.1121	−0.573615	−0.286808	−	0.957988i	$-0.592594\pi$
$997$	−18.1121	−0.573615	−0.286808	+	0.957988i	$0.592594\pi$
$998$	−43.4544	−1.37553
$999$	25.8996	0.819428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.2	✓	24	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.67063 q^{3} +1.00000 q^{4} +3.15601 q^{5} +2.67063 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.13228 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.67063 q^{3} +1.00000 q^{4} +3.15601 q^{5} +2.67063 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.13228 q^{9} -3.15601 q^{10} +3.01631 q^{11} -2.67063 q^{12} -4.63033 q^{13} +1.00000 q^{14} -8.42854 q^{15} +1.00000 q^{16} -6.60020 q^{17} -4.13228 q^{18} -4.22204 q^{19} +3.15601 q^{20} +2.67063 q^{21} -3.01631 q^{22} -0.524979 q^{23} +2.67063 q^{24} +4.96038 q^{25} +4.63033 q^{26} -3.02392 q^{27} -1.00000 q^{28} -9.21317 q^{29} +8.42854 q^{30} +1.00489 q^{31} -1.00000 q^{32} -8.05546 q^{33} +6.60020 q^{34} -3.15601 q^{35} +4.13228 q^{36} -8.56493 q^{37} +4.22204 q^{38} +12.3659 q^{39} -3.15601 q^{40} +6.31163 q^{41} -2.67063 q^{42} -11.7000 q^{43} +3.01631 q^{44} +13.0415 q^{45} +0.524979 q^{46} -7.89697 q^{47} -2.67063 q^{48} +1.00000 q^{49} -4.96038 q^{50} +17.6267 q^{51} -4.63033 q^{52} +0.831758 q^{53} +3.02392 q^{54} +9.51949 q^{55} +1.00000 q^{56} +11.2755 q^{57} +9.21317 q^{58} -2.18079 q^{59} -8.42854 q^{60} -1.29727 q^{61} -1.00489 q^{62} -4.13228 q^{63} +1.00000 q^{64} -14.6134 q^{65} +8.05546 q^{66} +8.28511 q^{67} -6.60020 q^{68} +1.40203 q^{69} +3.15601 q^{70} +14.0501 q^{71} -4.13228 q^{72} +16.6288 q^{73} +8.56493 q^{74} -13.2474 q^{75} -4.22204 q^{76} -3.01631 q^{77} -12.3659 q^{78} +16.4102 q^{79} +3.15601 q^{80} -4.32108 q^{81} -6.31163 q^{82} +7.07919 q^{83} +2.67063 q^{84} -20.8303 q^{85} +11.7000 q^{86} +24.6050 q^{87} -3.01631 q^{88} +14.0832 q^{89} -13.0415 q^{90} +4.63033 q^{91} -0.524979 q^{92} -2.68370 q^{93} +7.89697 q^{94} -13.3248 q^{95} +2.67063 q^{96} +14.9874 q^{97} -1.00000 q^{98} +12.4642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

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