LMFDB - Embedded newform 6015.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82805 q^{2} -1.00000 q^{3} +5.99789 q^{4} -1.00000 q^{5} +2.82805 q^{6} +0.186142 q^{7} -11.3062 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.82805 q^{2} -1.00000 q^{3} +5.99789 q^{4} -1.00000 q^{5} +2.82805 q^{6} +0.186142 q^{7} -11.3062 q^{8} +1.00000 q^{9} +2.82805 q^{10} +3.25363 q^{11} -5.99789 q^{12} +1.87819 q^{13} -0.526418 q^{14} +1.00000 q^{15} +19.9789 q^{16} -5.24279 q^{17} -2.82805 q^{18} +7.96309 q^{19} -5.99789 q^{20} -0.186142 q^{21} -9.20144 q^{22} -2.05401 q^{23} +11.3062 q^{24} +1.00000 q^{25} -5.31161 q^{26} -1.00000 q^{27} +1.11646 q^{28} +8.61998 q^{29} -2.82805 q^{30} -9.36806 q^{31} -33.8889 q^{32} -3.25363 q^{33} +14.8269 q^{34} -0.186142 q^{35} +5.99789 q^{36} -0.157454 q^{37} -22.5201 q^{38} -1.87819 q^{39} +11.3062 q^{40} -7.60101 q^{41} +0.526418 q^{42} +1.16255 q^{43} +19.5149 q^{44} -1.00000 q^{45} +5.80886 q^{46} +3.20295 q^{47} -19.9789 q^{48} -6.96535 q^{49} -2.82805 q^{50} +5.24279 q^{51} +11.2652 q^{52} +5.48955 q^{53} +2.82805 q^{54} -3.25363 q^{55} -2.10456 q^{56} -7.96309 q^{57} -24.3778 q^{58} -12.9380 q^{59} +5.99789 q^{60} -9.99050 q^{61} +26.4934 q^{62} +0.186142 q^{63} +55.8818 q^{64} -1.87819 q^{65} +9.20144 q^{66} -12.2558 q^{67} -31.4456 q^{68} +2.05401 q^{69} +0.526418 q^{70} +1.66782 q^{71} -11.3062 q^{72} +8.04492 q^{73} +0.445288 q^{74} -1.00000 q^{75} +47.7617 q^{76} +0.605636 q^{77} +5.31161 q^{78} +4.76287 q^{79} -19.9789 q^{80} +1.00000 q^{81} +21.4961 q^{82} +3.45922 q^{83} -1.11646 q^{84} +5.24279 q^{85} -3.28774 q^{86} -8.61998 q^{87} -36.7863 q^{88} -3.07568 q^{89} +2.82805 q^{90} +0.349609 q^{91} -12.3197 q^{92} +9.36806 q^{93} -9.05811 q^{94} -7.96309 q^{95} +33.8889 q^{96} +16.2362 q^{97} +19.6984 q^{98} +3.25363 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - 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 $

$2$	−2.82805	−1.99974	−0.999868	−	0.0162478i	$-0.994828\pi$
$2$	−2.82805	−1.99974	−0.999868	+	0.0162478i	$0.994828\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.99789	2.99894
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.82805	1.15455
$7$	0.186142	0.0703549	0.0351775	−	0.999381i	$-0.488800\pi$
$7$	0.186142	0.0703549	0.0351775	+	0.999381i	$0.488800\pi$
$8$	−11.3062	−3.99736
$9$	1.00000	0.333333
$10$	2.82805	0.894309
$11$	3.25363	0.981006	0.490503	−	0.871439i	$-0.336813\pi$
$11$	3.25363	0.981006	0.490503	+	0.871439i	$0.336813\pi$
$12$	−5.99789	−1.73144
$13$	1.87819	0.520915	0.260458	−	0.965485i	$-0.416127\pi$
$13$	1.87819	0.520915	0.260458	+	0.965485i	$0.416127\pi$
$14$	−0.526418	−0.140691
$15$	1.00000	0.258199
$16$	19.9789	4.99472
$17$	−5.24279	−1.27156	−0.635781	−	0.771869i	$-0.719322\pi$
$17$	−5.24279	−1.27156	−0.635781	+	0.771869i	$0.719322\pi$
$18$	−2.82805	−0.666579
$19$	7.96309	1.82686	0.913430	−	0.406997i	$-0.133424\pi$
$19$	7.96309	1.82686	0.913430	+	0.406997i	$0.133424\pi$
$20$	−5.99789	−1.34117
$21$	−0.186142	−0.0406194
$22$	−9.20144	−1.96175
$23$	−2.05401	−0.428292	−0.214146	−	0.976802i	$-0.568697\pi$
$23$	−2.05401	−0.428292	−0.214146	+	0.976802i	$0.568697\pi$
$24$	11.3062	2.30788
$25$	1.00000	0.200000
$26$	−5.31161	−1.04169
$27$	−1.00000	−0.192450
$28$	1.11646	0.210990
$29$	8.61998	1.60069	0.800346	−	0.599539i	$-0.204649\pi$
$29$	8.61998	1.60069	0.800346	+	0.599539i	$0.204649\pi$
$30$	−2.82805	−0.516330
$31$	−9.36806	−1.68255	−0.841277	−	0.540604i	$-0.818196\pi$
$31$	−9.36806	−1.68255	−0.841277	+	0.540604i	$0.818196\pi$
$32$	−33.8889	−5.99076
$33$	−3.25363	−0.566384
$34$	14.8269	2.54279
$35$	−0.186142	−0.0314637
$36$	5.99789	0.999648
$37$	−0.157454	−0.0258852	−0.0129426	−	0.999916i	$-0.504120\pi$
$37$	−0.157454	−0.0258852	−0.0129426	+	0.999916i	$0.504120\pi$
$38$	−22.5201	−3.65324
$39$	−1.87819	−0.300751
$40$	11.3062	1.78767
$41$	−7.60101	−1.18708	−0.593540	−	0.804805i	$-0.702270\pi$
$41$	−7.60101	−1.18708	−0.593540	+	0.804805i	$0.702270\pi$
$42$	0.526418	0.0812281
$43$	1.16255	0.177287	0.0886433	−	0.996063i	$-0.471747\pi$
$43$	1.16255	0.177287	0.0886433	+	0.996063i	$0.471747\pi$
$44$	19.5149	2.94198
$45$	−1.00000	−0.149071
$46$	5.80886	0.856470
$47$	3.20295	0.467198	0.233599	−	0.972333i	$-0.424950\pi$
$47$	3.20295	0.467198	0.233599	+	0.972333i	$0.424950\pi$
$48$	−19.9789	−2.88370
$49$	−6.96535	−0.995050
$50$	−2.82805	−0.399947
$51$	5.24279	0.734137
$52$	11.2652	1.56220
$53$	5.48955	0.754047	0.377024	−	0.926204i	$-0.376948\pi$
$53$	5.48955	0.754047	0.377024	+	0.926204i	$0.376948\pi$
$54$	2.82805	0.384849
$55$	−3.25363	−0.438719
$56$	−2.10456	−0.281234
$57$	−7.96309	−1.05474
$58$	−24.3778	−3.20096
$59$	−12.9380	−1.68439	−0.842193	−	0.539176i	$-0.818736\pi$
$59$	−12.9380	−1.68439	−0.842193	+	0.539176i	$0.818736\pi$
$60$	5.99789	0.774324
$61$	−9.99050	−1.27915	−0.639576	−	0.768728i	$-0.720890\pi$
$61$	−9.99050	−1.27915	−0.639576	+	0.768728i	$0.720890\pi$
$62$	26.4934	3.36466
$63$	0.186142	0.0234516
$64$	55.8818	6.98522
$65$	−1.87819	−0.232960
$66$	9.20144	1.13262
$67$	−12.2558	−1.49728	−0.748642	−	0.662974i	$-0.769294\pi$
$67$	−12.2558	−1.49728	−0.748642	+	0.662974i	$0.769294\pi$
$68$	−31.4456	−3.81334
$69$	2.05401	0.247274
$70$	0.526418	0.0629190
$71$	1.66782	0.197934	0.0989669	−	0.995091i	$-0.468446\pi$
$71$	1.66782	0.197934	0.0989669	+	0.995091i	$0.468446\pi$
$72$	−11.3062	−1.33245
$73$	8.04492	0.941586	0.470793	−	0.882244i	$-0.343968\pi$
$73$	8.04492	0.941586	0.470793	+	0.882244i	$0.343968\pi$
$74$	0.445288	0.0517637
$75$	−1.00000	−0.115470
$76$	47.7617	5.47865
$77$	0.605636	0.0690186
$78$	5.31161	0.601422
$79$	4.76287	0.535865	0.267932	−	0.963438i	$-0.413660\pi$
$79$	4.76287	0.535865	0.267932	+	0.963438i	$0.413660\pi$
$80$	−19.9789	−2.23371
$81$	1.00000	0.111111
$82$	21.4961	2.37384
$83$	3.45922	0.379698	0.189849	−	0.981813i	$-0.439200\pi$
$83$	3.45922	0.379698	0.189849	+	0.981813i	$0.439200\pi$
$84$	−1.11646	−0.121815
$85$	5.24279	0.568660
$86$	−3.28774	−0.354526
$87$	−8.61998	−0.924159
$88$	−36.7863	−3.92144
$89$	−3.07568	−0.326021	−0.163011	−	0.986624i	$-0.552120\pi$
$89$	−3.07568	−0.326021	−0.163011	+	0.986624i	$0.552120\pi$
$90$	2.82805	0.298103
$91$	0.349609	0.0366489
$92$	−12.3197	−1.28442
$93$	9.36806	0.971423
$94$	−9.05811	−0.934273
$95$	−7.96309	−0.816996
$96$	33.8889	3.45877
$97$	16.2362	1.64853	0.824266	−	0.566202i	$-0.191588\pi$
$97$	16.2362	1.64853	0.824266	+	0.566202i	$0.191588\pi$
$98$	19.6984	1.98984
$99$	3.25363	0.327002
$100$	5.99789	0.599789
$101$	−13.7190	−1.36509	−0.682546	−	0.730843i	$-0.739127\pi$
$101$	−13.7190	−1.36509	−0.682546	+	0.730843i	$0.739127\pi$
$102$	−14.8269	−1.46808
$103$	5.64206	0.555929	0.277965	−	0.960591i	$-0.410340\pi$
$103$	5.64206	0.555929	0.277965	+	0.960591i	$0.410340\pi$
$104$	−21.2352	−2.08229
$105$	0.186142	0.0181656
$106$	−15.5247	−1.50790
$107$	−7.37293	−0.712768	−0.356384	−	0.934340i	$-0.615990\pi$
$107$	−7.37293	−0.712768	−0.356384	+	0.934340i	$0.615990\pi$
$108$	−5.99789	−0.577147
$109$	−6.87509	−0.658515	−0.329257	−	0.944240i	$-0.606798\pi$
$109$	−6.87509	−0.658515	−0.329257	+	0.944240i	$0.606798\pi$
$110$	9.20144	0.877323
$111$	0.157454	0.0149449
$112$	3.71890	0.351403
$113$	11.6379	1.09480	0.547400	−	0.836871i	$-0.315618\pi$
$113$	11.6379	1.09480	0.547400	+	0.836871i	$0.315618\pi$
$114$	22.5201	2.10920
$115$	2.05401	0.191538
$116$	51.7017	4.80038
$117$	1.87819	0.173638
$118$	36.5894	3.36833
$119$	−0.975901	−0.0894607
$120$	−11.3062	−1.03211
$121$	−0.413891	−0.0376265
$122$	28.2537	2.55797
$123$	7.60101	0.685360
$124$	−56.1886	−5.04588
$125$	−1.00000	−0.0894427
$126$	−0.526418	−0.0468971
$127$	−9.73559	−0.863894	−0.431947	−	0.901899i	$-0.642173\pi$
$127$	−9.73559	−0.863894	−0.431947	+	0.901899i	$0.642173\pi$
$128$	−90.2590	−7.97784
$129$	−1.16255	−0.102356
$130$	5.31161	0.465859
$131$	1.54574	0.135052	0.0675258	−	0.997718i	$-0.478490\pi$
$131$	1.54574	0.135052	0.0675258	+	0.997718i	$0.478490\pi$
$132$	−19.5149	−1.69855
$133$	1.48226	0.128529
$134$	34.6601	2.99417
$135$	1.00000	0.0860663
$136$	59.2762	5.08289
$137$	−1.21684	−0.103961	−0.0519807	−	0.998648i	$-0.516553\pi$
$137$	−1.21684	−0.103961	−0.0519807	+	0.998648i	$0.516553\pi$
$138$	−5.80886	−0.494483
$139$	−13.4132	−1.13769	−0.568846	−	0.822444i	$-0.692610\pi$
$139$	−13.4132	−1.13769	−0.568846	+	0.822444i	$0.692610\pi$
$140$	−1.11646	−0.0943578
$141$	−3.20295	−0.269737
$142$	−4.71668	−0.395815
$143$	6.11092	0.511021
$144$	19.9789	1.66491
$145$	−8.61998	−0.715851
$146$	−22.7515	−1.88292
$147$	6.96535	0.574492
$148$	−0.944390	−0.0776284
$149$	−4.55336	−0.373026	−0.186513	−	0.982452i	$-0.559719\pi$
$149$	−4.55336	−0.373026	−0.186513	+	0.982452i	$0.559719\pi$
$150$	2.82805	0.230910
$151$	14.6593	1.19296	0.596480	−	0.802628i	$-0.296565\pi$
$151$	14.6593	1.19296	0.596480	+	0.802628i	$0.296565\pi$
$152$	−90.0327	−7.30261
$153$	−5.24279	−0.423854
$154$	−1.71277	−0.138019
$155$	9.36806	0.752461
$156$	−11.2652	−0.901934
$157$	−21.1442	−1.68749	−0.843745	−	0.536744i	$-0.819654\pi$
$157$	−21.1442	−1.68749	−0.843745	+	0.536744i	$0.819654\pi$
$158$	−13.4697	−1.07159
$159$	−5.48955	−0.435349
$160$	33.8889	2.67915
$161$	−0.382337	−0.0301324
$162$	−2.82805	−0.222193
$163$	0.574753	0.0450181	0.0225090	−	0.999747i	$-0.492835\pi$
$163$	0.574753	0.0450181	0.0225090	+	0.999747i	$0.492835\pi$
$164$	−45.5900	−3.55998
$165$	3.25363	0.253295
$166$	−9.78285	−0.759296
$167$	3.50767	0.271432	0.135716	−	0.990748i	$-0.456667\pi$
$167$	3.50767	0.271432	0.135716	+	0.990748i	$0.456667\pi$
$168$	2.10456	0.162370
$169$	−9.47242	−0.728647
$170$	−14.8269	−1.13717
$171$	7.96309	0.608953
$172$	6.97282	0.531672
$173$	−7.21277	−0.548377	−0.274189	−	0.961676i	$-0.588409\pi$
$173$	−7.21277	−0.548377	−0.274189	+	0.961676i	$0.588409\pi$
$174$	24.3778	1.84807
$175$	0.186142	0.0140710
$176$	65.0039	4.89985
$177$	12.9380	0.972481
$178$	8.69818	0.651956
$179$	−10.8331	−0.809707	−0.404854	−	0.914382i	$-0.632678\pi$
$179$	−10.8331	−0.809707	−0.404854	+	0.914382i	$0.632678\pi$
$180$	−5.99789	−0.447056
$181$	−23.7144	−1.76268	−0.881339	−	0.472484i	$-0.843357\pi$
$181$	−23.7144	−1.76268	−0.881339	+	0.472484i	$0.843357\pi$
$182$	−0.988712	−0.0732882
$183$	9.99050	0.738519
$184$	23.2232	1.71204
$185$	0.157454	0.0115762
$186$	−26.4934	−1.94259
$187$	−17.0581	−1.24741
$188$	19.2109	1.40110
$189$	−0.186142	−0.0135398
$190$	22.5201	1.63378
$191$	15.5571	1.12567	0.562836	−	0.826569i	$-0.309710\pi$
$191$	15.5571	1.12567	0.562836	+	0.826569i	$0.309710\pi$
$192$	−55.8818	−4.03292
$193$	3.05654	0.220015	0.110007	−	0.993931i	$-0.464913\pi$
$193$	3.05654	0.220015	0.110007	+	0.993931i	$0.464913\pi$
$194$	−45.9168	−3.29663
$195$	1.87819	0.134500
$196$	−41.7774	−2.98410
$197$	18.7204	1.33378	0.666888	−	0.745158i	$-0.267626\pi$
$197$	18.7204	1.33378	0.666888	+	0.745158i	$0.267626\pi$
$198$	−9.20144	−0.653918
$199$	−8.43771	−0.598133	−0.299067	−	0.954232i	$-0.596675\pi$
$199$	−8.43771	−0.598133	−0.299067	+	0.954232i	$0.596675\pi$
$200$	−11.3062	−0.799472
$201$	12.2558	0.864458
$202$	38.7981	2.72982
$203$	1.60454	0.112616
$204$	31.4456	2.20164
$205$	7.60101	0.530878
$206$	−15.9561	−1.11171
$207$	−2.05401	−0.142764
$208$	37.5241	2.60183
$209$	25.9090	1.79216
$210$	−0.526418	−0.0363263
$211$	−1.08229	−0.0745076	−0.0372538	−	0.999306i	$-0.511861\pi$
$211$	−1.08229	−0.0745076	−0.0372538	+	0.999306i	$0.511861\pi$
$212$	32.9257	2.26135
$213$	−1.66782	−0.114277
$214$	20.8510	1.42535
$215$	−1.16255	−0.0792850
$216$	11.3062	0.769292
$217$	−1.74379	−0.118376
$218$	19.4431	1.31686
$219$	−8.04492	−0.543625
$220$	−19.5149	−1.31569
$221$	−9.84693	−0.662376
$222$	−0.445288	−0.0298858
$223$	−6.75107	−0.452085	−0.226043	−	0.974117i	$-0.572579\pi$
$223$	−6.75107	−0.452085	−0.226043	+	0.974117i	$0.572579\pi$
$224$	−6.30813	−0.421480
$225$	1.00000	0.0666667
$226$	−32.9125	−2.18931
$227$	−2.36796	−0.157167	−0.0785836	−	0.996908i	$-0.525040\pi$
$227$	−2.36796	−0.157167	−0.0785836	+	0.996908i	$0.525040\pi$
$228$	−47.7617	−3.16310
$229$	29.8026	1.96941	0.984707	−	0.174219i	$-0.0557401\pi$
$229$	29.8026	1.96941	0.984707	+	0.174219i	$0.0557401\pi$
$230$	−5.80886	−0.383025
$231$	−0.605636	−0.0398479
$232$	−97.4596	−6.39854
$233$	3.19366	0.209223	0.104612	−	0.994513i	$-0.466640\pi$
$233$	3.19366	0.209223	0.104612	+	0.994513i	$0.466640\pi$
$234$	−5.31161	−0.347231
$235$	−3.20295	−0.208937
$236$	−77.6008	−5.05138
$237$	−4.76287	−0.309382
$238$	2.75990	0.178898
$239$	11.0214	0.712913	0.356457	−	0.934312i	$-0.383985\pi$
$239$	11.0214	0.712913	0.356457	+	0.934312i	$0.383985\pi$
$240$	19.9789	1.28963
$241$	−3.12104	−0.201044	−0.100522	−	0.994935i	$-0.532051\pi$
$241$	−3.12104	−0.201044	−0.100522	+	0.994935i	$0.532051\pi$
$242$	1.17051	0.0752430
$243$	−1.00000	−0.0641500
$244$	−59.9219	−3.83611
$245$	6.96535	0.445000
$246$	−21.4961	−1.37054
$247$	14.9562	0.951639
$248$	105.918	6.72577
$249$	−3.45922	−0.219219
$250$	2.82805	0.178862
$251$	−2.51706	−0.158876	−0.0794378	−	0.996840i	$-0.525313\pi$
$251$	−2.51706	−0.158876	−0.0794378	+	0.996840i	$0.525313\pi$
$252$	1.11646	0.0703301
$253$	−6.68300	−0.420157
$254$	27.5328	1.72756
$255$	−5.24279	−0.328316
$256$	143.494	8.96835
$257$	16.6724	1.04000	0.519998	−	0.854167i	$-0.325933\pi$
$257$	16.6724	1.04000	0.519998	+	0.854167i	$0.325933\pi$
$258$	3.28774	0.204686
$259$	−0.0293087	−0.00182115
$260$	−11.2652	−0.698635
$261$	8.61998	0.533564
$262$	−4.37142	−0.270067
$263$	−6.16555	−0.380184	−0.190092	−	0.981766i	$-0.560879\pi$
$263$	−6.16555	−0.380184	−0.190092	+	0.981766i	$0.560879\pi$
$264$	36.7863	2.26404
$265$	−5.48955	−0.337220
$266$	−4.19192	−0.257023
$267$	3.07568	0.188228
$268$	−73.5089	−4.49027
$269$	20.5617	1.25367	0.626834	−	0.779152i	$-0.284350\pi$
$269$	20.5617	1.25367	0.626834	+	0.779152i	$0.284350\pi$
$270$	−2.82805	−0.172110
$271$	12.4292	0.755018	0.377509	−	0.926006i	$-0.376781\pi$
$271$	12.4292	0.755018	0.377509	+	0.926006i	$0.376781\pi$
$272$	−104.745	−6.35110
$273$	−0.349609	−0.0211593
$274$	3.44128	0.207895
$275$	3.25363	0.196201
$276$	12.3197	0.741562
$277$	17.6123	1.05822	0.529109	−	0.848554i	$-0.322526\pi$
$277$	17.6123	1.05822	0.529109	+	0.848554i	$0.322526\pi$
$278$	37.9332	2.27508
$279$	−9.36806	−0.560851
$280$	2.10456	0.125772
$281$	7.74860	0.462243	0.231121	−	0.972925i	$-0.425761\pi$
$281$	7.74860	0.462243	0.231121	+	0.972925i	$0.425761\pi$
$282$	9.05811	0.539403
$283$	2.43671	0.144847	0.0724237	−	0.997374i	$-0.476927\pi$
$283$	2.43671	0.144847	0.0724237	+	0.997374i	$0.476927\pi$
$284$	10.0034	0.593592
$285$	7.96309	0.471693
$286$	−17.2820	−1.02191
$287$	−1.41486	−0.0835168
$288$	−33.8889	−1.99692
$289$	10.4868	0.616871
$290$	24.3778	1.43151
$291$	−16.2362	−0.951781
$292$	48.2525	2.82376
$293$	−28.8193	−1.68364	−0.841822	−	0.539755i	$-0.818517\pi$
$293$	−28.8193	−1.68364	−0.841822	+	0.539755i	$0.818517\pi$
$294$	−19.6984	−1.14883
$295$	12.9380	0.753281
$296$	1.78021	0.103473
$297$	−3.25363	−0.188795
$298$	12.8772	0.745954
$299$	−3.85782	−0.223104
$300$	−5.99789	−0.346288
$301$	0.216398	0.0124730
$302$	−41.4574	−2.38561
$303$	13.7190	0.788136
$304$	159.094	9.12465
$305$	9.99050	0.572054
$306$	14.8269	0.847596
$307$	−6.06710	−0.346268	−0.173134	−	0.984898i	$-0.555389\pi$
$307$	−6.06710	−0.346268	−0.173134	+	0.984898i	$0.555389\pi$
$308$	3.63254	0.206983
$309$	−5.64206	−0.320966
$310$	−26.4934	−1.50472
$311$	−28.1079	−1.59385	−0.796927	−	0.604076i	$-0.793542\pi$
$311$	−28.1079	−1.59385	−0.796927	+	0.604076i	$0.793542\pi$
$312$	21.2352	1.20221
$313$	6.11459	0.345617	0.172809	−	0.984955i	$-0.444716\pi$
$313$	6.11459	0.345617	0.172809	+	0.984955i	$0.444716\pi$
$314$	59.7969	3.37454
$315$	−0.186142	−0.0104879
$316$	28.5672	1.60703
$317$	13.1240	0.737116	0.368558	−	0.929605i	$-0.379852\pi$
$317$	13.1240	0.737116	0.368558	+	0.929605i	$0.379852\pi$
$318$	15.5247	0.870584
$319$	28.0462	1.57029
$320$	−55.8818	−3.12389
$321$	7.37293	0.411517
$322$	1.08127	0.0602569
$323$	−41.7488	−2.32297
$324$	5.99789	0.333216
$325$	1.87819	0.104183
$326$	−1.62543	−0.0900243
$327$	6.87509	0.380194
$328$	85.9389	4.74518
$329$	0.596202	0.0328697
$330$	−9.20144	−0.506523
$331$	22.7249	1.24908	0.624538	−	0.780995i	$-0.285287\pi$
$331$	22.7249	1.24908	0.624538	+	0.780995i	$0.285287\pi$
$332$	20.7480	1.13869
$333$	−0.157454	−0.00862841
$334$	−9.91988	−0.542792
$335$	12.2558	0.669606
$336$	−3.71890	−0.202883
$337$	−26.0181	−1.41730	−0.708649	−	0.705561i	$-0.750695\pi$
$337$	−26.0181	−1.41730	−0.708649	+	0.705561i	$0.750695\pi$
$338$	26.7885	1.45710
$339$	−11.6379	−0.632083
$340$	31.4456	1.70538
$341$	−30.4802	−1.65060
$342$	−22.5201	−1.21775
$343$	−2.59953	−0.140362
$344$	−13.1440	−0.708678
$345$	−2.05401	−0.110584
$346$	20.3981	1.09661
$347$	12.5018	0.671132	0.335566	−	0.942017i	$-0.391072\pi$
$347$	12.5018	0.671132	0.335566	+	0.942017i	$0.391072\pi$
$348$	−51.7017	−2.77150
$349$	−2.50615	−0.134151	−0.0670757	−	0.997748i	$-0.521367\pi$
$349$	−2.50615	−0.134151	−0.0670757	+	0.997748i	$0.521367\pi$
$350$	−0.526418	−0.0281382
$351$	−1.87819	−0.100250
$352$	−110.262	−5.87698
$353$	22.0219	1.17211	0.586053	−	0.810273i	$-0.300681\pi$
$353$	22.0219	1.17211	0.586053	+	0.810273i	$0.300681\pi$
$354$	−36.5894	−1.94471
$355$	−1.66782	−0.0885187
$356$	−18.4476	−0.977719
$357$	0.975901	0.0516501
$358$	30.6367	1.61920
$359$	−8.51786	−0.449556	−0.224778	−	0.974410i	$-0.572166\pi$
$359$	−8.51786	−0.449556	−0.224778	+	0.974410i	$0.572166\pi$
$360$	11.3062	0.595891
$361$	44.4109	2.33741
$362$	67.0656	3.52489
$363$	0.413891	0.0217237
$364$	2.09691	0.109908
$365$	−8.04492	−0.421090
$366$	−28.2537	−1.47684
$367$	−0.933126	−0.0487088	−0.0243544	−	0.999703i	$-0.507753\pi$
$367$	−0.933126	−0.0487088	−0.0243544	+	0.999703i	$0.507753\pi$
$368$	−41.0369	−2.13920
$369$	−7.60101	−0.395693
$370$	−0.445288	−0.0231494
$371$	1.02183	0.0530509
$372$	56.1886	2.91324
$373$	14.8766	0.770283	0.385141	−	0.922858i	$-0.374153\pi$
$373$	14.8766	0.770283	0.385141	+	0.922858i	$0.374153\pi$
$374$	48.2412	2.49449
$375$	1.00000	0.0516398
$376$	−36.2133	−1.86756
$377$	16.1899	0.833824
$378$	0.526418	0.0270760
$379$	26.1089	1.34112	0.670561	−	0.741854i	$-0.266053\pi$
$379$	26.1089	1.34112	0.670561	+	0.741854i	$0.266053\pi$
$380$	−47.7617	−2.45013
$381$	9.73559	0.498769
$382$	−43.9963	−2.25105
$383$	−29.7007	−1.51764	−0.758819	−	0.651302i	$-0.774223\pi$
$383$	−29.7007	−1.51764	−0.758819	+	0.651302i	$0.774223\pi$
$384$	90.2590	4.60601
$385$	−0.605636	−0.0308661
$386$	−8.64406	−0.439971
$387$	1.16255	0.0590955
$388$	97.3827	4.94386
$389$	−10.4173	−0.528176	−0.264088	−	0.964499i	$-0.585071\pi$
$389$	−10.4173	−0.528176	−0.264088	+	0.964499i	$0.585071\pi$
$390$	−5.31161	−0.268964
$391$	10.7688	0.544600
$392$	78.7520	3.97757
$393$	−1.54574	−0.0779720
$394$	−52.9424	−2.66720
$395$	−4.76287	−0.239646
$396$	19.5149	0.980661
$397$	2.14530	0.107669	0.0538347	−	0.998550i	$-0.482856\pi$
$397$	2.14530	0.107669	0.0538347	+	0.998550i	$0.482856\pi$
$398$	23.8623	1.19611
$399$	−1.48226	−0.0742060
$400$	19.9789	0.998944
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−34.6601	−1.72869
$403$	−17.5950	−0.876468
$404$	−82.2850	−4.09383
$405$	−1.00000	−0.0496904
$406$	−4.53772	−0.225203
$407$	−0.512296	−0.0253936
$408$	−59.2762	−2.93461
$409$	−5.10835	−0.252592	−0.126296	−	0.991993i	$-0.540309\pi$
$409$	−5.10835	−0.252592	−0.126296	+	0.991993i	$0.540309\pi$
$410$	−21.4961	−1.06162
$411$	1.21684	0.0600221
$412$	33.8405	1.66720
$413$	−2.40830	−0.118505
$414$	5.80886	0.285490
$415$	−3.45922	−0.169806
$416$	−63.6496	−3.12068
$417$	13.4132	0.656847
$418$	−73.2719	−3.58385
$419$	6.97639	0.340819	0.170409	−	0.985373i	$-0.445491\pi$
$419$	6.97639	0.340819	0.170409	+	0.985373i	$0.445491\pi$
$420$	1.11646	0.0544775
$421$	−25.9705	−1.26573	−0.632863	−	0.774264i	$-0.718120\pi$
$421$	−25.9705	−1.26573	−0.632863	+	0.774264i	$0.718120\pi$
$422$	3.06076	0.148996
$423$	3.20295	0.155733
$424$	−62.0662	−3.01420
$425$	−5.24279	−0.254313
$426$	4.71668	0.228524
$427$	−1.85965	−0.0899946
$428$	−44.2220	−2.13755
$429$	−6.11092	−0.295038
$430$	3.28774	0.158549
$431$	−39.1683	−1.88667	−0.943334	−	0.331844i	$-0.892329\pi$
$431$	−39.1683	−1.88667	−0.943334	+	0.331844i	$0.892329\pi$
$432$	−19.9789	−0.961235
$433$	−0.886720	−0.0426130	−0.0213065	−	0.999773i	$-0.506783\pi$
$433$	−0.886720	−0.0426130	−0.0213065	+	0.999773i	$0.506783\pi$
$434$	4.93152	0.236721
$435$	8.61998	0.413297
$436$	−41.2360	−1.97485
$437$	−16.3563	−0.782428
$438$	22.7515	1.08711
$439$	−14.0382	−0.670004	−0.335002	−	0.942217i	$-0.608737\pi$
$439$	−14.0382	−0.670004	−0.335002	+	0.942217i	$0.608737\pi$
$440$	36.7863	1.75372
$441$	−6.96535	−0.331683
$442$	27.8476	1.32458
$443$	2.29247	0.108919	0.0544593	−	0.998516i	$-0.482656\pi$
$443$	2.29247	0.108919	0.0544593	+	0.998516i	$0.482656\pi$
$444$	0.944390	0.0448188
$445$	3.07568	0.145801
$446$	19.0924	0.904051
$447$	4.55336	0.215367
$448$	10.4019	0.491445
$449$	−38.9195	−1.83672	−0.918362	−	0.395740i	$-0.870488\pi$
$449$	−38.9195	−1.83672	−0.918362	+	0.395740i	$0.870488\pi$
$450$	−2.82805	−0.133316
$451$	−24.7309	−1.16453
$452$	69.8027	3.28324
$453$	−14.6593	−0.688756
$454$	6.69672	0.314293
$455$	−0.349609	−0.0163899
$456$	90.0327	4.21617
$457$	29.9564	1.40130	0.700651	−	0.713504i	$-0.252893\pi$
$457$	29.9564	1.40130	0.700651	+	0.713504i	$0.252893\pi$
$458$	−84.2835	−3.93831
$459$	5.24279	0.244712
$460$	12.3197	0.574411
$461$	−3.89631	−0.181469	−0.0907347	−	0.995875i	$-0.528922\pi$
$461$	−3.89631	−0.181469	−0.0907347	+	0.995875i	$0.528922\pi$
$462$	1.71277	0.0796853
$463$	−39.9478	−1.85653	−0.928265	−	0.371920i	$-0.878700\pi$
$463$	−39.9478	−1.85653	−0.928265	+	0.371920i	$0.878700\pi$
$464$	172.218	7.99501
$465$	−9.36806	−0.434434
$466$	−9.03184	−0.418392
$467$	−11.7370	−0.543126	−0.271563	−	0.962421i	$-0.587541\pi$
$467$	−11.7370	−0.543126	−0.271563	+	0.962421i	$0.587541\pi$
$468$	11.2652	0.520732
$469$	−2.28131	−0.105341
$470$	9.05811	0.417819
$471$	21.1442	0.974273
$472$	146.280	6.73310
$473$	3.78249	0.173919
$474$	13.4697	0.618682
$475$	7.96309	0.365372
$476$	−5.85334	−0.268288
$477$	5.48955	0.251349
$478$	−31.1690	−1.42564
$479$	40.9648	1.87173	0.935866	−	0.352357i	$-0.114620\pi$
$479$	40.9648	1.87173	0.935866	+	0.352357i	$0.114620\pi$
$480$	−33.8889	−1.54681
$481$	−0.295728	−0.0134840
$482$	8.82647	0.402035
$483$	0.382337	0.0173970
$484$	−2.48247	−0.112840
$485$	−16.2362	−0.737246
$486$	2.82805	0.128283
$487$	−34.8288	−1.57824	−0.789121	−	0.614238i	$-0.789464\pi$
$487$	−34.8288	−1.57824	−0.789121	+	0.614238i	$0.789464\pi$
$488$	112.955	5.11323
$489$	−0.574753	−0.0259912
$490$	−19.6984	−0.889882
$491$	−5.23225	−0.236128	−0.118064	−	0.993006i	$-0.537669\pi$
$491$	−5.23225	−0.236128	−0.118064	+	0.993006i	$0.537669\pi$
$492$	45.5900	2.05536
$493$	−45.1927	−2.03538
$494$	−42.2969	−1.90303
$495$	−3.25363	−0.146240
$496$	−187.163	−8.40389
$497$	0.310451	0.0139256
$498$	9.78285	0.438380
$499$	−16.7668	−0.750586	−0.375293	−	0.926906i	$-0.622458\pi$
$499$	−16.7668	−0.750586	−0.375293	+	0.926906i	$0.622458\pi$
$500$	−5.99789	−0.268234
$501$	−3.50767	−0.156711
$502$	7.11839	0.317709
$503$	−3.95879	−0.176514	−0.0882569	−	0.996098i	$-0.528130\pi$
$503$	−3.95879	−0.176514	−0.0882569	+	0.996098i	$0.528130\pi$
$504$	−2.10456	−0.0937446
$505$	13.7190	0.610488
$506$	18.8999	0.840203
$507$	9.47242	0.420685
$508$	−58.3930	−2.59077
$509$	−9.92129	−0.439754	−0.219877	−	0.975528i	$-0.570566\pi$
$509$	−9.92129	−0.439754	−0.219877	+	0.975528i	$0.570566\pi$
$510$	14.8269	0.656545
$511$	1.49749	0.0662452
$512$	−225.290	−9.95649
$513$	−7.96309	−0.351579
$514$	−47.1505	−2.07972
$515$	−5.64206	−0.248619
$516$	−6.97282	−0.306961
$517$	10.4212	0.458324
$518$	0.0828866	0.00364183
$519$	7.21277	0.316606
$520$	21.2352	0.931226
$521$	27.6105	1.20964	0.604819	−	0.796363i	$-0.293245\pi$
$521$	27.6105	1.20964	0.604819	+	0.796363i	$0.293245\pi$
$522$	−24.3778	−1.06699
$523$	−21.2988	−0.931334	−0.465667	−	0.884960i	$-0.654185\pi$
$523$	−21.2988	−0.931334	−0.465667	+	0.884960i	$0.654185\pi$
$524$	9.27115	0.405012
$525$	−0.186142	−0.00812388
$526$	17.4365	0.760268
$527$	49.1148	2.13947
$528$	−65.0039	−2.82893
$529$	−18.7810	−0.816566
$530$	15.5247	0.674351
$531$	−12.9380	−0.561462
$532$	8.89045	0.385450
$533$	−14.2761	−0.618367
$534$	−8.69818	−0.376407
$535$	7.37293	0.318759
$536$	138.567	5.98519
$537$	10.8331	0.467485
$538$	−58.1496	−2.50701
$539$	−22.6627	−0.976151
$540$	5.99789	0.258108
$541$	24.1489	1.03824	0.519120	−	0.854701i	$-0.326260\pi$
$541$	24.1489	1.03824	0.519120	+	0.854701i	$0.326260\pi$
$542$	−35.1504	−1.50984
$543$	23.7144	1.01768
$544$	177.672	7.61763
$545$	6.87509	0.294497
$546$	0.988712	0.0423130
$547$	0.475062	0.0203122	0.0101561	−	0.999948i	$-0.496767\pi$
$547$	0.475062	0.0203122	0.0101561	+	0.999948i	$0.496767\pi$
$548$	−7.29845	−0.311774
$549$	−9.99050	−0.426384
$550$	−9.20144	−0.392351
$551$	68.6418	2.92424
$552$	−23.2232	−0.988444
$553$	0.886568	0.0377007
$554$	−49.8084	−2.11616
$555$	−0.157454	−0.00668354
$556$	−80.4508	−3.41187
$557$	31.3433	1.32806	0.664029	−	0.747706i	$-0.268845\pi$
$557$	31.3433	1.32806	0.664029	+	0.747706i	$0.268845\pi$
$558$	26.4934	1.12155
$559$	2.18348	0.0923512
$560$	−3.71890	−0.157152
$561$	17.0581	0.720193
$562$	−21.9135	−0.924363
$563$	−29.3125	−1.23537	−0.617687	−	0.786424i	$-0.711930\pi$
$563$	−29.3125	−1.23537	−0.617687	+	0.786424i	$0.711930\pi$
$564$	−19.2109	−0.808926
$565$	−11.6379	−0.489609
$566$	−6.89115	−0.289657
$567$	0.186142	0.00781721
$568$	−18.8568	−0.791213
$569$	7.91025	0.331615	0.165807	−	0.986158i	$-0.446977\pi$
$569$	7.91025	0.331615	0.165807	+	0.986158i	$0.446977\pi$
$570$	−22.5201	−0.943261
$571$	3.45675	0.144661	0.0723303	−	0.997381i	$-0.476956\pi$
$571$	3.45675	0.144661	0.0723303	+	0.997381i	$0.476956\pi$
$572$	36.6526	1.53252
$573$	−15.5571	−0.649907
$574$	4.00131	0.167012
$575$	−2.05401	−0.0856583
$576$	55.8818	2.32841
$577$	7.21875	0.300520	0.150260	−	0.988646i	$-0.451989\pi$
$577$	7.21875	0.300520	0.150260	+	0.988646i	$0.451989\pi$
$578$	−29.6573	−1.23358
$579$	−3.05654	−0.127025
$580$	−51.7017	−2.14680
$581$	0.643904	0.0267136
$582$	45.9168	1.90331
$583$	17.8610	0.739725
$584$	−90.9578	−3.76386
$585$	−1.87819	−0.0776534
$586$	81.5027	3.36684
$587$	12.9715	0.535393	0.267696	−	0.963503i	$-0.413738\pi$
$587$	12.9715	0.535393	0.267696	+	0.963503i	$0.413738\pi$
$588$	41.7774	1.72287
$589$	−74.5988	−3.07379
$590$	−36.5894	−1.50636
$591$	−18.7204	−0.770056
$592$	−3.14575	−0.129290
$593$	−42.7574	−1.75584	−0.877919	−	0.478810i	$-0.841068\pi$
$593$	−42.7574	−1.75584	−0.877919	+	0.478810i	$0.841068\pi$
$594$	9.20144	0.377540
$595$	0.975901	0.0400080
$596$	−27.3106	−1.11868
$597$	8.43771	0.345332
$598$	10.9101	0.446148
$599$	44.8066	1.83075	0.915375	−	0.402603i	$-0.131894\pi$
$599$	44.8066	1.83075	0.915375	+	0.402603i	$0.131894\pi$
$600$	11.3062	0.461575
$601$	−14.7281	−0.600770	−0.300385	−	0.953818i	$-0.597115\pi$
$601$	−14.7281	−0.600770	−0.300385	+	0.953818i	$0.597115\pi$
$602$	−0.611985	−0.0249427
$603$	−12.2558	−0.499095
$604$	87.9251	3.57762
$605$	0.413891	0.0168271
$606$	−38.7981	−1.57606
$607$	−4.65007	−0.188741	−0.0943703	−	0.995537i	$-0.530084\pi$
$607$	−4.65007	−0.188741	−0.0943703	+	0.995537i	$0.530084\pi$
$608$	−269.860	−10.9443
$609$	−1.60454	−0.0650191
$610$	−28.2537	−1.14396
$611$	6.01573	0.243371
$612$	−31.4456	−1.27111
$613$	−30.2460	−1.22163	−0.610813	−	0.791775i	$-0.709157\pi$
$613$	−30.2460	−1.22163	−0.610813	+	0.791775i	$0.709157\pi$
$614$	17.1581	0.692444
$615$	−7.60101	−0.306502
$616$	−6.84747	−0.275892
$617$	−34.2786	−1.38001	−0.690003	−	0.723807i	$-0.742391\pi$
$617$	−34.2786	−1.38001	−0.690003	+	0.723807i	$0.742391\pi$
$618$	15.9561	0.641847
$619$	−2.21396	−0.0889865	−0.0444932	−	0.999010i	$-0.514167\pi$
$619$	−2.21396	−0.0889865	−0.0444932	+	0.999010i	$0.514167\pi$
$620$	56.1886	2.25659
$621$	2.05401	0.0824248
$622$	79.4907	3.18729
$623$	−0.572512	−0.0229372
$624$	−37.5241	−1.50216
$625$	1.00000	0.0400000
$626$	−17.2924	−0.691143
$627$	−25.9090	−1.03470
$628$	−126.821	−5.06069
$629$	0.825497	0.0329147
$630$	0.526418	0.0209730
$631$	−1.45845	−0.0580602	−0.0290301	−	0.999579i	$-0.509242\pi$
$631$	−1.45845	−0.0580602	−0.0290301	+	0.999579i	$0.509242\pi$
$632$	−53.8502	−2.14205
$633$	1.08229	0.0430170
$634$	−37.1153	−1.47404
$635$	9.73559	0.386345
$636$	−32.9257	−1.30559
$637$	−13.0822	−0.518337
$638$	−79.3163	−3.14016
$639$	1.66782	0.0659779
$640$	90.2590	3.56780
$641$	−20.0688	−0.792670	−0.396335	−	0.918106i	$-0.629718\pi$
$641$	−20.0688	−0.792670	−0.396335	+	0.918106i	$0.629718\pi$
$642$	−20.8510	−0.822925
$643$	32.1537	1.26802	0.634010	−	0.773325i	$-0.281408\pi$
$643$	32.1537	1.26802	0.634010	+	0.773325i	$0.281408\pi$
$644$	−2.29322	−0.0903654
$645$	1.16255	0.0457752
$646$	118.068	4.64532
$647$	31.6277	1.24341	0.621706	−	0.783250i	$-0.286440\pi$
$647$	31.6277	1.24341	0.621706	+	0.783250i	$0.286440\pi$
$648$	−11.3062	−0.444151
$649$	−42.0955	−1.65239
$650$	−5.31161	−0.208339
$651$	1.74379	0.0683444
$652$	3.44730	0.135007
$653$	12.8050	0.501098	0.250549	−	0.968104i	$-0.419389\pi$
$653$	12.8050	0.501098	0.250549	+	0.968104i	$0.419389\pi$
$654$	−19.4431	−0.760287
$655$	−1.54574	−0.0603969
$656$	−151.860	−5.92913
$657$	8.04492	0.313862
$658$	−1.68609	−0.0657307
$659$	−3.84381	−0.149734	−0.0748668	−	0.997194i	$-0.523853\pi$
$659$	−3.84381	−0.149734	−0.0748668	+	0.997194i	$0.523853\pi$
$660$	19.5149	0.759617
$661$	−16.3049	−0.634189	−0.317094	−	0.948394i	$-0.602707\pi$
$661$	−16.3049	−0.634189	−0.317094	+	0.948394i	$0.602707\pi$
$662$	−64.2673	−2.49782
$663$	9.84693	0.382423
$664$	−39.1107	−1.51779
$665$	−1.48226	−0.0574797
$666$	0.445288	0.0172546
$667$	−17.7056	−0.685563
$668$	21.0386	0.814008
$669$	6.75107	0.261011
$670$	−34.6601	−1.33904
$671$	−32.5054	−1.25486
$672$	6.30813	0.243341
$673$	−41.4573	−1.59806	−0.799031	−	0.601290i	$-0.794654\pi$
$673$	−41.4573	−1.59806	−0.799031	+	0.601290i	$0.794654\pi$
$674$	73.5807	2.83422
$675$	−1.00000	−0.0384900
$676$	−56.8145	−2.18517
$677$	−36.9431	−1.41984	−0.709920	−	0.704283i	$-0.751269\pi$
$677$	−36.9431	−1.41984	−0.709920	+	0.704283i	$0.751269\pi$
$678$	32.9125	1.26400
$679$	3.02223	0.115982
$680$	−59.2762	−2.27314
$681$	2.36796	0.0907405
$682$	86.1997	3.30076
$683$	−23.2184	−0.888427	−0.444213	−	0.895921i	$-0.646517\pi$
$683$	−23.2184	−0.888427	−0.444213	+	0.895921i	$0.646517\pi$
$684$	47.7617	1.82622
$685$	1.21684	0.0464929
$686$	7.35162	0.280686
$687$	−29.8026	−1.13704
$688$	23.2264	0.885497
$689$	10.3104	0.392795
$690$	5.80886	0.221140
$691$	−37.2990	−1.41892	−0.709461	−	0.704745i	$-0.751061\pi$
$691$	−37.2990	−1.41892	−0.709461	+	0.704745i	$0.751061\pi$
$692$	−43.2614	−1.64455
$693$	0.605636	0.0230062
$694$	−35.3558	−1.34209
$695$	13.4132	0.508791
$696$	97.4596	3.69420
$697$	39.8505	1.50945
$698$	7.08754	0.268267
$699$	−3.19366	−0.120795
$700$	1.11646	0.0421981
$701$	15.5070	0.585692	0.292846	−	0.956160i	$-0.405398\pi$
$701$	15.5070	0.585692	0.292846	+	0.956160i	$0.405398\pi$
$702$	5.31161	0.200474
$703$	−1.25382	−0.0472887
$704$	181.819	6.85255
$705$	3.20295	0.120630
$706$	−62.2790	−2.34390
$707$	−2.55368	−0.0960409
$708$	77.6008	2.91642
$709$	29.5807	1.11093	0.555463	−	0.831541i	$-0.312541\pi$
$709$	29.5807	1.11093	0.555463	+	0.831541i	$0.312541\pi$
$710$	4.71668	0.177014
$711$	4.76287	0.178622
$712$	34.7744	1.30322
$713$	19.2421	0.720624
$714$	−2.75990	−0.103287
$715$	−6.11092	−0.228536
$716$	−64.9760	−2.42827
$717$	−11.0214	−0.411601
$718$	24.0890	0.898992
$719$	−26.3461	−0.982543	−0.491271	−	0.871007i	$-0.663468\pi$
$719$	−26.3461	−0.982543	−0.491271	+	0.871007i	$0.663468\pi$
$720$	−19.9789	−0.744569
$721$	1.05022	0.0391123
$722$	−125.596	−4.67421
$723$	3.12104	0.116073
$724$	−142.236	−5.28617
$725$	8.61998	0.320138
$726$	−1.17051	−0.0434416
$727$	−44.7927	−1.66127	−0.830635	−	0.556818i	$-0.812022\pi$
$727$	−44.7927	−1.66127	−0.830635	+	0.556818i	$0.812022\pi$
$728$	−3.95276	−0.146499
$729$	1.00000	0.0370370
$730$	22.7515	0.842069
$731$	−6.09498	−0.225431
$732$	59.9219	2.21478
$733$	−46.3486	−1.71192	−0.855961	−	0.517040i	$-0.827034\pi$
$733$	−46.3486	−1.71192	−0.855961	+	0.517040i	$0.827034\pi$
$734$	2.63893	0.0974047
$735$	−6.96535	−0.256921
$736$	69.6082	2.56579
$737$	−39.8759	−1.46885
$738$	21.4961	0.791282
$739$	12.6830	0.466552	0.233276	−	0.972411i	$-0.425056\pi$
$739$	12.6830	0.466552	0.233276	+	0.972411i	$0.425056\pi$
$740$	0.944390	0.0347165
$741$	−14.9562	−0.549429
$742$	−2.88980	−0.106088
$743$	1.13385	0.0415969	0.0207985	−	0.999784i	$-0.493379\pi$
$743$	1.13385	0.0415969	0.0207985	+	0.999784i	$0.493379\pi$
$744$	−105.918	−3.88313
$745$	4.55336	0.166822
$746$	−42.0719	−1.54036
$747$	3.45922	0.126566
$748$	−102.313	−3.74092
$749$	−1.37241	−0.0501467
$750$	−2.82805	−0.103266
$751$	0.588985	0.0214924	0.0107462	−	0.999942i	$-0.496579\pi$
$751$	0.588985	0.0214924	0.0107462	+	0.999942i	$0.496579\pi$
$752$	63.9913	2.33352
$753$	2.51706	0.0917269
$754$	−45.7860	−1.66743
$755$	−14.6593	−0.533508
$756$	−1.11646	−0.0406051
$757$	−29.9981	−1.09030	−0.545150	−	0.838339i	$-0.683527\pi$
$757$	−29.9981	−1.09030	−0.545150	+	0.838339i	$0.683527\pi$
$758$	−73.8373	−2.68189
$759$	6.68300	0.242578
$760$	90.0327	3.26583
$761$	−15.9043	−0.576531	−0.288265	−	0.957551i	$-0.593078\pi$
$761$	−15.9043	−0.576531	−0.288265	+	0.957551i	$0.593078\pi$
$762$	−27.5328	−0.997407
$763$	−1.27974	−0.0463297
$764$	93.3097	3.37583
$765$	5.24279	0.189553
$766$	83.9953	3.03487
$767$	−24.3000	−0.877422
$768$	−143.494	−5.17788
$769$	−44.4686	−1.60358	−0.801789	−	0.597607i	$-0.796118\pi$
$769$	−44.4686	−1.60358	−0.801789	+	0.597607i	$0.796118\pi$
$770$	1.71277	0.0617240
$771$	−16.6724	−0.600442
$772$	18.3328	0.659811
$773$	−44.2187	−1.59044	−0.795219	−	0.606323i	$-0.792644\pi$
$773$	−44.2187	−1.59044	−0.795219	+	0.606323i	$0.792644\pi$
$774$	−3.28774	−0.118175
$775$	−9.36806	−0.336511
$776$	−183.570	−6.58978
$777$	0.0293087	0.00105144
$778$	29.4606	1.05621
$779$	−60.5276	−2.16863
$780$	11.2652	0.403357
$781$	5.42647	0.194174
$782$	−30.4546	−1.08906
$783$	−8.61998	−0.308053
$784$	−139.160	−4.97000
$785$	21.1442	0.754669
$786$	4.37142	0.155923
$787$	38.5579	1.37444	0.687221	−	0.726448i	$-0.258830\pi$
$787$	38.5579	1.37444	0.687221	+	0.726448i	$0.258830\pi$
$788$	112.283	3.99992
$789$	6.16555	0.219499
$790$	13.4697	0.479229
$791$	2.16629	0.0770245
$792$	−36.7863	−1.30715
$793$	−18.7640	−0.666330
$794$	−6.06702	−0.215310
$795$	5.48955	0.194694
$796$	−50.6084	−1.79377
$797$	3.37820	0.119662	0.0598309	−	0.998209i	$-0.480944\pi$
$797$	3.37820	0.119662	0.0598309	+	0.998209i	$0.480944\pi$
$798$	4.19192	0.148392
$799$	−16.7924	−0.594071
$800$	−33.8889	−1.19815
$801$	−3.07568	−0.108674
$802$	2.82805	0.0998620
$803$	26.1752	0.923702
$804$	73.5089	2.59246
$805$	0.382337	0.0134756
$806$	49.7595	1.75270
$807$	−20.5617	−0.723806
$808$	155.110	5.45676
$809$	−23.8968	−0.840167	−0.420084	−	0.907485i	$-0.637999\pi$
$809$	−23.8968	−0.840167	−0.420084	+	0.907485i	$0.637999\pi$
$810$	2.82805	0.0993677
$811$	25.3183	0.889046	0.444523	−	0.895767i	$-0.353373\pi$
$811$	25.3183	0.889046	0.444523	+	0.895767i	$0.353373\pi$
$812$	9.62384	0.337730
$813$	−12.4292	−0.435910
$814$	1.44880	0.0507805
$815$	−0.574753	−0.0201327
$816$	104.745	3.66681
$817$	9.25746	0.323878
$818$	14.4467	0.505117
$819$	0.349609	0.0122163
$820$	45.5900	1.59207
$821$	3.60451	0.125798	0.0628992	−	0.998020i	$-0.479965\pi$
$821$	3.60451	0.125798	0.0628992	+	0.998020i	$0.479965\pi$
$822$	−3.44128	−0.120028
$823$	−47.1379	−1.64312	−0.821562	−	0.570119i	$-0.806897\pi$
$823$	−47.1379	−1.64312	−0.821562	+	0.570119i	$0.806897\pi$
$824$	−63.7905	−2.22225
$825$	−3.25363	−0.113277
$826$	6.81081	0.236978
$827$	3.93764	0.136925	0.0684626	−	0.997654i	$-0.478191\pi$
$827$	3.93764	0.136925	0.0684626	+	0.997654i	$0.478191\pi$
$828$	−12.3197	−0.428141
$829$	−13.4557	−0.467337	−0.233668	−	0.972316i	$-0.575073\pi$
$829$	−13.4557	−0.467337	−0.233668	+	0.972316i	$0.575073\pi$
$830$	9.78285	0.339568
$831$	−17.6123	−0.610962
$832$	104.956	3.63871
$833$	36.5178	1.26527
$834$	−37.9332	−1.31352
$835$	−3.50767	−0.121388
$836$	155.399	5.37459
$837$	9.36806	0.323808
$838$	−19.7296	−0.681548
$839$	−12.7827	−0.441309	−0.220654	−	0.975352i	$-0.570819\pi$
$839$	−12.7827	−0.441309	−0.220654	+	0.975352i	$0.570819\pi$
$840$	−2.10456	−0.0726143
$841$	45.3041	1.56221
$842$	73.4460	2.53112
$843$	−7.74860	−0.266876
$844$	−6.49143	−0.223444
$845$	9.47242	0.325861
$846$	−9.05811	−0.311424
$847$	−0.0770423	−0.00264721
$848$	109.675	3.76626
$849$	−2.43671	−0.0836277
$850$	14.8269	0.508558
$851$	0.323412	0.0110864
$852$	−10.0034	−0.342711
$853$	−37.1332	−1.27142	−0.635708	−	0.771930i	$-0.719292\pi$
$853$	−37.1332	−1.27142	−0.635708	+	0.771930i	$0.719292\pi$
$854$	5.25918	0.179965
$855$	−7.96309	−0.272332
$856$	83.3601	2.84919
$857$	14.4049	0.492063	0.246032	−	0.969262i	$-0.420873\pi$
$857$	14.4049	0.492063	0.246032	+	0.969262i	$0.420873\pi$
$858$	17.2820	0.589998
$859$	51.3576	1.75230	0.876149	−	0.482041i	$-0.160104\pi$
$859$	51.3576	1.75230	0.876149	+	0.482041i	$0.160104\pi$
$860$	−6.97282	−0.237771
$861$	1.41486	0.0482185
$862$	110.770	3.77284
$863$	54.0509	1.83991	0.919956	−	0.392021i	$-0.128224\pi$
$863$	54.0509	1.83991	0.919956	+	0.392021i	$0.128224\pi$
$864$	33.8889	1.15292
$865$	7.21277	0.245242
$866$	2.50769	0.0852148
$867$	−10.4868	−0.356151
$868$	−10.4590	−0.355003
$869$	15.4966	0.525687
$870$	−24.3778	−0.826484
$871$	−23.0187	−0.779958
$872$	77.7315	2.63232
$873$	16.2362	0.549511
$874$	46.2565	1.56465
$875$	−0.186142	−0.00629273
$876$	−48.2525	−1.63030
$877$	−33.1130	−1.11815	−0.559073	−	0.829118i	$-0.688843\pi$
$877$	−33.1130	−1.11815	−0.559073	+	0.829118i	$0.688843\pi$
$878$	39.7006	1.33983
$879$	28.8193	0.972053
$880$	−65.0039	−2.19128
$881$	4.21910	0.142145	0.0710726	−	0.997471i	$-0.477358\pi$
$881$	4.21910	0.142145	0.0710726	+	0.997471i	$0.477358\pi$
$882$	19.6984	0.663279
$883$	36.9666	1.24402	0.622012	−	0.783007i	$-0.286315\pi$
$883$	36.9666	1.24402	0.622012	+	0.783007i	$0.286315\pi$
$884$	−59.0608	−1.98643
$885$	−12.9380	−0.434907
$886$	−6.48323	−0.217808
$887$	−4.92193	−0.165262	−0.0826312	−	0.996580i	$-0.526332\pi$
$887$	−4.92193	−0.165262	−0.0826312	+	0.996580i	$0.526332\pi$
$888$	−1.78021	−0.0597400
$889$	−1.81220	−0.0607792
$890$	−8.69818	−0.291564
$891$	3.25363	0.109001
$892$	−40.4922	−1.35578
$893$	25.5054	0.853505
$894$	−12.8772	−0.430676
$895$	10.8331	0.362112
$896$	−16.8009	−0.561280
$897$	3.85782	0.128809
$898$	110.066	3.67296
$899$	−80.7526	−2.69325
$900$	5.99789	0.199930
$901$	−28.7805	−0.958818
$902$	69.9403	2.32876
$903$	−0.216398	−0.00720128
$904$	−131.581	−4.37631
$905$	23.7144	0.788294
$906$	41.4574	1.37733
$907$	−40.6573	−1.35000	−0.675001	−	0.737817i	$-0.735857\pi$
$907$	−40.6573	−1.35000	−0.675001	+	0.737817i	$0.735857\pi$
$908$	−14.2028	−0.471336
$909$	−13.7190	−0.455031
$910$	0.988712	0.0327755
$911$	−46.3641	−1.53611	−0.768055	−	0.640384i	$-0.778775\pi$
$911$	−46.3641	−1.53611	−0.768055	+	0.640384i	$0.778775\pi$
$912$	−159.094	−5.26812
$913$	11.2550	0.372486
$914$	−84.7184	−2.80223
$915$	−9.99050	−0.330276
$916$	178.753	5.90616
$917$	0.287726	0.00950154
$918$	−14.8269	−0.489360
$919$	38.0354	1.25467	0.627335	−	0.778749i	$-0.284146\pi$
$919$	38.0354	1.25467	0.627335	+	0.778749i	$0.284146\pi$
$920$	−23.2232	−0.765646
$921$	6.06710	0.199918
$922$	11.0190	0.362891
$923$	3.13248	0.103107
$924$	−3.63254	−0.119502
$925$	−0.157454	−0.00517705
$926$	112.974	3.71257
$927$	5.64206	0.185310
$928$	−292.122	−9.58936
$929$	42.4800	1.39372	0.696862	−	0.717205i	$-0.254579\pi$
$929$	42.4800	1.39372	0.696862	+	0.717205i	$0.254579\pi$
$930$	26.4934	0.868752
$931$	−55.4658	−1.81782
$932$	19.1552	0.627449
$933$	28.1079	0.920212
$934$	33.1930	1.08611
$935$	17.0581	0.557859
$936$	−21.2352	−0.694095
$937$	12.3562	0.403660	0.201830	−	0.979421i	$-0.435311\pi$
$937$	12.3562	0.403660	0.201830	+	0.979421i	$0.435311\pi$
$938$	6.45168	0.210655
$939$	−6.11459	−0.199542
$940$	−19.2109	−0.626591
$941$	35.0532	1.14270	0.571351	−	0.820706i	$-0.306420\pi$
$941$	35.0532	1.14270	0.571351	+	0.820706i	$0.306420\pi$
$942$	−59.7969	−1.94829
$943$	15.6126	0.508416
$944$	−258.487	−8.41304
$945$	0.186142	0.00605519
$946$	−10.6971	−0.347793
$947$	−13.1863	−0.428496	−0.214248	−	0.976779i	$-0.568730\pi$
$947$	−13.1863	−0.428496	−0.214248	+	0.976779i	$0.568730\pi$
$948$	−28.5672	−0.927819
$949$	15.1099	0.490487
$950$	−22.5201	−0.730647
$951$	−13.1240	−0.425574
$952$	11.0338	0.357606
$953$	20.1337	0.652195	0.326098	−	0.945336i	$-0.394266\pi$
$953$	20.1337	0.652195	0.326098	+	0.945336i	$0.394266\pi$
$954$	−15.5247	−0.502632
$955$	−15.5571	−0.503416
$956$	66.1049	2.13799
$957$	−28.0462	−0.906606
$958$	−115.851	−3.74297
$959$	−0.226504	−0.00731419
$960$	55.8818	1.80358
$961$	56.7606	1.83099
$962$	0.836333	0.0269645
$963$	−7.37293	−0.237589
$964$	−18.7197	−0.602920
$965$	−3.05654	−0.0983935
$966$	−1.08127	−0.0347893
$967$	−1.24934	−0.0401762	−0.0200881	−	0.999798i	$-0.506395\pi$
$967$	−1.24934	−0.0401762	−0.0200881	+	0.999798i	$0.506395\pi$
$968$	4.67955	0.150407
$969$	41.7488	1.34116
$970$	45.9168	1.47430
$971$	−53.2151	−1.70775	−0.853877	−	0.520475i	$-0.825755\pi$
$971$	−53.2151	−1.70775	−0.853877	+	0.520475i	$0.825755\pi$
$972$	−5.99789	−0.192382
$973$	−2.49675	−0.0800422
$974$	98.4976	3.15607
$975$	−1.87819	−0.0601501
$976$	−199.599	−6.38901
$977$	−31.4778	−1.00706	−0.503532	−	0.863977i	$-0.667966\pi$
$977$	−31.4778	−1.00706	−0.503532	+	0.863977i	$0.667966\pi$
$978$	1.62543	0.0519756
$979$	−10.0071	−0.319829
$980$	41.7774	1.33453
$981$	−6.87509	−0.219505
$982$	14.7971	0.472194
$983$	36.8141	1.17419	0.587094	−	0.809519i	$-0.300272\pi$
$983$	36.8141	1.17419	0.587094	+	0.809519i	$0.300272\pi$
$984$	−85.9389	−2.73963
$985$	−18.7204	−0.596483
$986$	127.808	4.07022
$987$	−0.596202	−0.0189773
$988$	89.7055	2.85391
$989$	−2.38789	−0.0759303
$990$	9.20144	0.292441
$991$	6.58726	0.209251	0.104626	−	0.994512i	$-0.466636\pi$
$991$	6.58726	0.209251	0.104626	+	0.994512i	$0.466636\pi$
$992$	317.473	10.0798
$993$	−22.7249	−0.721154
$994$	−0.877971	−0.0278476
$995$	8.43771	0.267493
$996$	−20.7480	−0.657425
$997$	−24.2895	−0.769257	−0.384628	−	0.923072i	$-0.625670\pi$
$997$	−24.2895	−0.769257	−0.384628	+	0.923072i	$0.625670\pi$
$998$	47.4175	1.50097
$999$	0.157454	0.00498162

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.f.1.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.f.1.1	✓	36	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.82805 q^{2} -1.00000 q^{3} +5.99789 q^{4} -1.00000 q^{5} +2.82805 q^{6} +0.186142 q^{7} -11.3062 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.82805 q^{2} -1.00000 q^{3} +5.99789 q^{4} -1.00000 q^{5} +2.82805 q^{6} +0.186142 q^{7} -11.3062 q^{8} +1.00000 q^{9} +2.82805 q^{10} +3.25363 q^{11} -5.99789 q^{12} +1.87819 q^{13} -0.526418 q^{14} +1.00000 q^{15} +19.9789 q^{16} -5.24279 q^{17} -2.82805 q^{18} +7.96309 q^{19} -5.99789 q^{20} -0.186142 q^{21} -9.20144 q^{22} -2.05401 q^{23} +11.3062 q^{24} +1.00000 q^{25} -5.31161 q^{26} -1.00000 q^{27} +1.11646 q^{28} +8.61998 q^{29} -2.82805 q^{30} -9.36806 q^{31} -33.8889 q^{32} -3.25363 q^{33} +14.8269 q^{34} -0.186142 q^{35} +5.99789 q^{36} -0.157454 q^{37} -22.5201 q^{38} -1.87819 q^{39} +11.3062 q^{40} -7.60101 q^{41} +0.526418 q^{42} +1.16255 q^{43} +19.5149 q^{44} -1.00000 q^{45} +5.80886 q^{46} +3.20295 q^{47} -19.9789 q^{48} -6.96535 q^{49} -2.82805 q^{50} +5.24279 q^{51} +11.2652 q^{52} +5.48955 q^{53} +2.82805 q^{54} -3.25363 q^{55} -2.10456 q^{56} -7.96309 q^{57} -24.3778 q^{58} -12.9380 q^{59} +5.99789 q^{60} -9.99050 q^{61} +26.4934 q^{62} +0.186142 q^{63} +55.8818 q^{64} -1.87819 q^{65} +9.20144 q^{66} -12.2558 q^{67} -31.4456 q^{68} +2.05401 q^{69} +0.526418 q^{70} +1.66782 q^{71} -11.3062 q^{72} +8.04492 q^{73} +0.445288 q^{74} -1.00000 q^{75} +47.7617 q^{76} +0.605636 q^{77} +5.31161 q^{78} +4.76287 q^{79} -19.9789 q^{80} +1.00000 q^{81} +21.4961 q^{82} +3.45922 q^{83} -1.11646 q^{84} +5.24279 q^{85} -3.28774 q^{86} -8.61998 q^{87} -36.7863 q^{88} -3.07568 q^{89} +2.82805 q^{90} +0.349609 q^{91} -12.3197 q^{92} +9.36806 q^{93} -9.05811 q^{94} -7.96309 q^{95} +33.8889 q^{96} +16.2362 q^{97} +19.6984 q^{98} +3.25363 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - q^99

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