LMFDB - Embedded newform 6015.2.a.d.1.25

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:	$29$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
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)

$f(q)$	$=$	$q+2.03069 q^{2} -1.00000 q^{3} +2.12372 q^{4} +1.00000 q^{5} -2.03069 q^{6} -0.0759107 q^{7} +0.251242 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.03069 q^{2} -1.00000 q^{3} +2.12372 q^{4} +1.00000 q^{5} -2.03069 q^{6} -0.0759107 q^{7} +0.251242 q^{8} +1.00000 q^{9} +2.03069 q^{10} +0.961068 q^{11} -2.12372 q^{12} -2.83752 q^{13} -0.154152 q^{14} -1.00000 q^{15} -3.73725 q^{16} -3.10870 q^{17} +2.03069 q^{18} -2.23902 q^{19} +2.12372 q^{20} +0.0759107 q^{21} +1.95164 q^{22} +5.88730 q^{23} -0.251242 q^{24} +1.00000 q^{25} -5.76214 q^{26} -1.00000 q^{27} -0.161213 q^{28} +5.51216 q^{29} -2.03069 q^{30} -7.21004 q^{31} -8.09170 q^{32} -0.961068 q^{33} -6.31282 q^{34} -0.0759107 q^{35} +2.12372 q^{36} -4.75012 q^{37} -4.54677 q^{38} +2.83752 q^{39} +0.251242 q^{40} -1.87233 q^{41} +0.154152 q^{42} -6.56124 q^{43} +2.04104 q^{44} +1.00000 q^{45} +11.9553 q^{46} -5.35806 q^{47} +3.73725 q^{48} -6.99424 q^{49} +2.03069 q^{50} +3.10870 q^{51} -6.02611 q^{52} +11.8199 q^{53} -2.03069 q^{54} +0.961068 q^{55} -0.0190719 q^{56} +2.23902 q^{57} +11.1935 q^{58} -0.556984 q^{59} -2.12372 q^{60} -8.33216 q^{61} -14.6414 q^{62} -0.0759107 q^{63} -8.95727 q^{64} -2.83752 q^{65} -1.95164 q^{66} +1.05361 q^{67} -6.60202 q^{68} -5.88730 q^{69} -0.154152 q^{70} +9.44572 q^{71} +0.251242 q^{72} -3.95372 q^{73} -9.64605 q^{74} -1.00000 q^{75} -4.75506 q^{76} -0.0729554 q^{77} +5.76214 q^{78} -10.7091 q^{79} -3.73725 q^{80} +1.00000 q^{81} -3.80213 q^{82} -13.3761 q^{83} +0.161213 q^{84} -3.10870 q^{85} -13.3239 q^{86} -5.51216 q^{87} +0.241460 q^{88} -7.24489 q^{89} +2.03069 q^{90} +0.215398 q^{91} +12.5030 q^{92} +7.21004 q^{93} -10.8806 q^{94} -2.23902 q^{95} +8.09170 q^{96} +1.47053 q^{97} -14.2032 q^{98} +0.961068 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * 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 $

$2$	2.03069	1.43592	0.717959	−	0.696085i	$-0.245076\pi$
$2$	2.03069	1.43592	0.717959	+	0.696085i	$0.245076\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.12372	1.06186
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.03069	−0.829028
$7$	−0.0759107	−0.0286916	−0.0143458	−	0.999897i	$-0.504567\pi$
$7$	−0.0759107	−0.0286916	−0.0143458	+	0.999897i	$0.504567\pi$
$8$	0.251242	0.0888273
$9$	1.00000	0.333333
$10$	2.03069	0.642162
$11$	0.961068	0.289773	0.144886	−	0.989448i	$-0.453718\pi$
$11$	0.961068	0.289773	0.144886	+	0.989448i	$0.453718\pi$
$12$	−2.12372	−0.613066
$13$	−2.83752	−0.786987	−0.393494	−	0.919327i	$-0.628734\pi$
$13$	−2.83752	−0.786987	−0.393494	+	0.919327i	$0.628734\pi$
$14$	−0.154152	−0.0411987
$15$	−1.00000	−0.258199
$16$	−3.73725	−0.934312
$17$	−3.10870	−0.753971	−0.376985	−	0.926219i	$-0.623039\pi$
$17$	−3.10870	−0.753971	−0.376985	+	0.926219i	$0.623039\pi$
$18$	2.03069	0.478639
$19$	−2.23902	−0.513667	−0.256834	−	0.966456i	$-0.582679\pi$
$19$	−2.23902	−0.513667	−0.256834	+	0.966456i	$0.582679\pi$
$20$	2.12372	0.474879
$21$	0.0759107	0.0165651
$22$	1.95164	0.416090
$23$	5.88730	1.22759	0.613794	−	0.789467i	$-0.289643\pi$
$23$	5.88730	1.22759	0.613794	+	0.789467i	$0.289643\pi$
$24$	−0.251242	−0.0512845
$25$	1.00000	0.200000
$26$	−5.76214	−1.13005
$27$	−1.00000	−0.192450
$28$	−0.161213	−0.0304665
$29$	5.51216	1.02358	0.511791	−	0.859110i	$-0.328982\pi$
$29$	5.51216	1.02358	0.511791	+	0.859110i	$0.328982\pi$
$30$	−2.03069	−0.370752
$31$	−7.21004	−1.29496	−0.647481	−	0.762082i	$-0.724177\pi$
$31$	−7.21004	−1.29496	−0.647481	+	0.762082i	$0.724177\pi$
$32$	−8.09170	−1.43042
$33$	−0.961068	−0.167300
$34$	−6.31282	−1.08264
$35$	−0.0759107	−0.0128313
$36$	2.12372	0.353954
$37$	−4.75012	−0.780915	−0.390458	−	0.920621i	$-0.627683\pi$
$37$	−4.75012	−0.780915	−0.390458	+	0.920621i	$0.627683\pi$
$38$	−4.54677	−0.737584
$39$	2.83752	0.454367
$40$	0.251242	0.0397248
$41$	−1.87233	−0.292408	−0.146204	−	0.989254i	$-0.546706\pi$
$41$	−1.87233	−0.292408	−0.146204	+	0.989254i	$0.546706\pi$
$42$	0.154152	0.0237861
$43$	−6.56124	−1.00058	−0.500290	−	0.865858i	$-0.666773\pi$
$43$	−6.56124	−1.00058	−0.500290	+	0.865858i	$0.666773\pi$
$44$	2.04104	0.307699
$45$	1.00000	0.149071
$46$	11.9553	1.76271
$47$	−5.35806	−0.781553	−0.390777	−	0.920486i	$-0.627794\pi$
$47$	−5.35806	−0.781553	−0.390777	+	0.920486i	$0.627794\pi$
$48$	3.73725	0.539425
$49$	−6.99424	−0.999177
$50$	2.03069	0.287184
$51$	3.10870	0.435305
$52$	−6.02611	−0.835671
$53$	11.8199	1.62359	0.811796	−	0.583941i	$-0.198490\pi$
$53$	11.8199	1.62359	0.811796	+	0.583941i	$0.198490\pi$
$54$	−2.03069	−0.276343
$55$	0.961068	0.129590
$56$	−0.0190719	−0.00254859
$57$	2.23902	0.296566
$58$	11.1935	1.46978
$59$	−0.556984	−0.0725131	−0.0362566	−	0.999343i	$-0.511543\pi$
$59$	−0.556984	−0.0725131	−0.0362566	+	0.999343i	$0.511543\pi$
$60$	−2.12372	−0.274171
$61$	−8.33216	−1.06682	−0.533412	−	0.845856i	$-0.679090\pi$
$61$	−8.33216	−1.06682	−0.533412	+	0.845856i	$0.679090\pi$
$62$	−14.6414	−1.85946
$63$	−0.0759107	−0.00956386
$64$	−8.95727	−1.11966
$65$	−2.83752	−0.351951
$66$	−1.95164	−0.240230
$67$	1.05361	0.128719	0.0643594	−	0.997927i	$-0.479500\pi$
$67$	1.05361	0.128719	0.0643594	+	0.997927i	$0.479500\pi$
$68$	−6.60202	−0.800612
$69$	−5.88730	−0.708748
$70$	−0.154152	−0.0184246
$71$	9.44572	1.12100	0.560500	−	0.828154i	$-0.310609\pi$
$71$	9.44572	1.12100	0.560500	+	0.828154i	$0.310609\pi$
$72$	0.251242	0.0296091
$73$	−3.95372	−0.462748	−0.231374	−	0.972865i	$-0.574322\pi$
$73$	−3.95372	−0.462748	−0.231374	+	0.972865i	$0.574322\pi$
$74$	−9.64605	−1.12133
$75$	−1.00000	−0.115470
$76$	−4.75506	−0.545443
$77$	−0.0729554	−0.00831404
$78$	5.76214	0.652434
$79$	−10.7091	−1.20487	−0.602433	−	0.798169i	$-0.705802\pi$
$79$	−10.7091	−1.20487	−0.602433	+	0.798169i	$0.705802\pi$
$80$	−3.73725	−0.417837
$81$	1.00000	0.111111
$82$	−3.80213	−0.419875
$83$	−13.3761	−1.46822	−0.734111	−	0.679030i	$-0.762401\pi$
$83$	−13.3761	−1.46822	−0.734111	+	0.679030i	$0.762401\pi$
$84$	0.161213	0.0175898
$85$	−3.10870	−0.337186
$86$	−13.3239	−1.43675
$87$	−5.51216	−0.590965
$88$	0.241460	0.0257398
$89$	−7.24489	−0.767957	−0.383979	−	0.923342i	$-0.625446\pi$
$89$	−7.24489	−0.767957	−0.383979	+	0.923342i	$0.625446\pi$
$90$	2.03069	0.214054
$91$	0.215398	0.0225799
$92$	12.5030	1.30353
$93$	7.21004	0.747646
$94$	−10.8806	−1.12225
$95$	−2.23902	−0.229719
$96$	8.09170	0.825855
$97$	1.47053	0.149310	0.0746548	−	0.997209i	$-0.476215\pi$
$97$	1.47053	0.149310	0.0746548	+	0.997209i	$0.476215\pi$
$98$	−14.2032	−1.43474
$99$	0.961068	0.0965910
$100$	2.12372	0.212372
$101$	−4.42175	−0.439981	−0.219991	−	0.975502i	$-0.570603\pi$
$101$	−4.42175	−0.439981	−0.219991	+	0.975502i	$0.570603\pi$
$102$	6.31282	0.625063
$103$	−6.73954	−0.664066	−0.332033	−	0.943268i	$-0.607735\pi$
$103$	−6.73954	−0.664066	−0.332033	+	0.943268i	$0.607735\pi$
$104$	−0.712904	−0.0699059
$105$	0.0759107	0.00740813
$106$	24.0027	2.33134
$107$	17.6195	1.70334	0.851670	−	0.524078i	$-0.175590\pi$
$107$	17.6195	1.70334	0.851670	+	0.524078i	$0.175590\pi$
$108$	−2.12372	−0.204355
$109$	2.80904	0.269057	0.134529	−	0.990910i	$-0.457048\pi$
$109$	2.80904	0.269057	0.134529	+	0.990910i	$0.457048\pi$
$110$	1.95164	0.186081
$111$	4.75012	0.450862
$112$	0.283697	0.0268069
$113$	9.79917	0.921829	0.460914	−	0.887445i	$-0.347522\pi$
$113$	9.79917	0.921829	0.460914	+	0.887445i	$0.347522\pi$
$114$	4.54677	0.425844
$115$	5.88730	0.548994
$116$	11.7063	1.08690
$117$	−2.83752	−0.262329
$118$	−1.13106	−0.104123
$119$	0.235984	0.0216326
$120$	−0.251242	−0.0229351
$121$	−10.0763	−0.916032
$122$	−16.9201	−1.53187
$123$	1.87233	0.168822
$124$	−15.3121	−1.37507
$125$	1.00000	0.0894427
$126$	−0.154152	−0.0137329
$127$	−2.89271	−0.256687	−0.128343	−	0.991730i	$-0.540966\pi$
$127$	−2.89271	−0.256687	−0.128343	+	0.991730i	$0.540966\pi$
$128$	−2.00609	−0.177315
$129$	6.56124	0.577685
$130$	−5.76214	−0.505373
$131$	−8.37553	−0.731774	−0.365887	−	0.930659i	$-0.619234\pi$
$131$	−8.37553	−0.731774	−0.365887	+	0.930659i	$0.619234\pi$
$132$	−2.04104	−0.177650
$133$	0.169966	0.0147379
$134$	2.13956	0.184830
$135$	−1.00000	−0.0860663
$136$	−0.781035	−0.0669732
$137$	−17.7029	−1.51246	−0.756231	−	0.654305i	$-0.772961\pi$
$137$	−17.7029	−1.51246	−0.756231	+	0.654305i	$0.772961\pi$
$138$	−11.9553	−1.01770
$139$	−6.48699	−0.550219	−0.275110	−	0.961413i	$-0.588714\pi$
$139$	−6.48699	−0.550219	−0.275110	+	0.961413i	$0.588714\pi$
$140$	−0.161213	−0.0136250
$141$	5.35806	0.451230
$142$	19.1814	1.60967
$143$	−2.72705	−0.228048
$144$	−3.73725	−0.311437
$145$	5.51216	0.457760
$146$	−8.02879	−0.664468
$147$	6.99424	0.576875
$148$	−10.0879	−0.829224
$149$	−11.3734	−0.931744	−0.465872	−	0.884852i	$-0.654259\pi$
$149$	−11.3734	−0.931744	−0.465872	+	0.884852i	$0.654259\pi$
$150$	−2.03069	−0.165806
$151$	13.9921	1.13866	0.569330	−	0.822109i	$-0.307203\pi$
$151$	13.9921	1.13866	0.569330	+	0.822109i	$0.307203\pi$
$152$	−0.562536	−0.0456277
$153$	−3.10870	−0.251324
$154$	−0.148150	−0.0119383
$155$	−7.21004	−0.579124
$156$	6.02611	0.482475
$157$	−3.02393	−0.241336	−0.120668	−	0.992693i	$-0.538504\pi$
$157$	−3.02393	−0.241336	−0.120668	+	0.992693i	$0.538504\pi$
$158$	−21.7469	−1.73009
$159$	−11.8199	−0.937381
$160$	−8.09170	−0.639705
$161$	−0.446909	−0.0352214
$162$	2.03069	0.159546
$163$	6.09659	0.477521	0.238761	−	0.971078i	$-0.423259\pi$
$163$	6.09659	0.477521	0.238761	+	0.971078i	$0.423259\pi$
$164$	−3.97630	−0.310497
$165$	−0.961068	−0.0748191
$166$	−27.1628	−2.10825
$167$	23.7770	1.83992	0.919961	−	0.392009i	$-0.128220\pi$
$167$	23.7770	1.83992	0.919961	+	0.392009i	$0.128220\pi$
$168$	0.0190719	0.00147143
$169$	−4.94847	−0.380651
$170$	−6.31282	−0.484171
$171$	−2.23902	−0.171222
$172$	−13.9343	−1.06248
$173$	−5.12624	−0.389741	−0.194871	−	0.980829i	$-0.562429\pi$
$173$	−5.12624	−0.389741	−0.194871	+	0.980829i	$0.562429\pi$
$174$	−11.1935	−0.848578
$175$	−0.0759107	−0.00573831
$176$	−3.59175	−0.270738
$177$	0.556984	0.0418655
$178$	−14.7122	−1.10272
$179$	12.3472	0.922877	0.461438	−	0.887172i	$-0.347334\pi$
$179$	12.3472	0.922877	0.461438	+	0.887172i	$0.347334\pi$
$180$	2.12372	0.158293
$181$	−4.47349	−0.332512	−0.166256	−	0.986083i	$-0.553168\pi$
$181$	−4.47349	−0.332512	−0.166256	+	0.986083i	$0.553168\pi$
$182$	0.437408	0.0324229
$183$	8.33216	0.615931
$184$	1.47913	0.109043
$185$	−4.75012	−0.349236
$186$	14.6414	1.07356
$187$	−2.98767	−0.218480
$188$	−11.3790	−0.829901
$189$	0.0759107	0.00552169
$190$	−4.54677	−0.329858
$191$	−12.1999	−0.882753	−0.441377	−	0.897322i	$-0.645510\pi$
$191$	−12.1999	−0.882753	−0.441377	+	0.897322i	$0.645510\pi$
$192$	8.95727	0.646435
$193$	−19.4959	−1.40335	−0.701674	−	0.712499i	$-0.747564\pi$
$193$	−19.4959	−1.40335	−0.701674	+	0.712499i	$0.747564\pi$
$194$	2.98619	0.214396
$195$	2.83752	0.203199
$196$	−14.8538	−1.06099
$197$	−15.3838	−1.09605	−0.548025	−	0.836462i	$-0.684620\pi$
$197$	−15.3838	−1.09605	−0.548025	+	0.836462i	$0.684620\pi$
$198$	1.95164	0.138697
$199$	−0.169604	−0.0120229	−0.00601145	−	0.999982i	$-0.501914\pi$
$199$	−0.169604	−0.0120229	−0.00601145	+	0.999982i	$0.501914\pi$
$200$	0.251242	0.0177655
$201$	−1.05361	−0.0743159
$202$	−8.97924	−0.631777
$203$	−0.418432	−0.0293682
$204$	6.60202	0.462234
$205$	−1.87233	−0.130769
$206$	−13.6859	−0.953545
$207$	5.88730	0.409196
$208$	10.6045	0.735292
$209$	−2.15185	−0.148847
$210$	0.154152	0.0106375
$211$	12.7146	0.875308	0.437654	−	0.899144i	$-0.355810\pi$
$211$	12.7146	0.875308	0.437654	+	0.899144i	$0.355810\pi$
$212$	25.1022	1.72403
$213$	−9.44572	−0.647210
$214$	35.7798	2.44586
$215$	−6.56124	−0.447473
$216$	−0.251242	−0.0170948
$217$	0.547319	0.0371545
$218$	5.70431	0.386344
$219$	3.95372	0.267167
$220$	2.04104	0.137607
$221$	8.82101	0.593365
$222$	9.64605	0.647401
$223$	−0.454221	−0.0304169	−0.0152084	−	0.999884i	$-0.504841\pi$
$223$	−0.454221	−0.0304169	−0.0152084	+	0.999884i	$0.504841\pi$
$224$	0.614247	0.0410411
$225$	1.00000	0.0666667
$226$	19.8991	1.32367
$227$	−10.3283	−0.685515	−0.342758	−	0.939424i	$-0.611361\pi$
$227$	−10.3283	−0.685515	−0.342758	+	0.939424i	$0.611361\pi$
$228$	4.75506	0.314912
$229$	1.35071	0.0892572	0.0446286	−	0.999004i	$-0.485790\pi$
$229$	1.35071	0.0892572	0.0446286	+	0.999004i	$0.485790\pi$
$230$	11.9553	0.788310
$231$	0.0729554	0.00480011
$232$	1.38488	0.0909220
$233$	16.0658	1.05251	0.526253	−	0.850328i	$-0.323597\pi$
$233$	16.0658	1.05251	0.526253	+	0.850328i	$0.323597\pi$
$234$	−5.76214	−0.376683
$235$	−5.35806	−0.349521
$236$	−1.18288	−0.0769989
$237$	10.7091	0.695630
$238$	0.479211	0.0310626
$239$	−6.25795	−0.404793	−0.202397	−	0.979304i	$-0.564873\pi$
$239$	−6.25795	−0.404793	−0.202397	+	0.979304i	$0.564873\pi$
$240$	3.73725	0.241238
$241$	24.8874	1.60314	0.801570	−	0.597901i	$-0.203999\pi$
$241$	24.8874	1.60314	0.801570	+	0.597901i	$0.203999\pi$
$242$	−20.4620	−1.31535
$243$	−1.00000	−0.0641500
$244$	−17.6952	−1.13282
$245$	−6.99424	−0.446845
$246$	3.80213	0.242415
$247$	6.35328	0.404250
$248$	−1.81146	−0.115028
$249$	13.3761	0.847678
$250$	2.03069	0.128432
$251$	−16.6428	−1.05048	−0.525241	−	0.850954i	$-0.676025\pi$
$251$	−16.6428	−1.05048	−0.525241	+	0.850954i	$0.676025\pi$
$252$	−0.161213	−0.0101555
$253$	5.65810	0.355722
$254$	−5.87422	−0.368581
$255$	3.10870	0.194674
$256$	13.8408	0.865049
$257$	28.5091	1.77835	0.889174	−	0.457570i	$-0.151280\pi$
$257$	28.5091	1.77835	0.889174	+	0.457570i	$0.151280\pi$
$258$	13.3239	0.829509
$259$	0.360585	0.0224057
$260$	−6.02611	−0.373723
$261$	5.51216	0.341194
$262$	−17.0082	−1.05077
$263$	0.201593	0.0124308	0.00621539	−	0.999981i	$-0.498022\pi$
$263$	0.201593	0.0124308	0.00621539	+	0.999981i	$0.498022\pi$
$264$	−0.241460	−0.0148609
$265$	11.8199	0.726092
$266$	0.345149	0.0211624
$267$	7.24489	0.443380
$268$	2.23757	0.136682
$269$	−20.8099	−1.26880	−0.634401	−	0.773004i	$-0.718753\pi$
$269$	−20.8099	−1.26880	−0.634401	+	0.773004i	$0.718753\pi$
$270$	−2.03069	−0.123584
$271$	0.248745	0.0151102	0.00755509	−	0.999971i	$-0.497595\pi$
$271$	0.248745	0.0151102	0.00755509	+	0.999971i	$0.497595\pi$
$272$	11.6180	0.704444
$273$	−0.215398	−0.0130365
$274$	−35.9492	−2.17177
$275$	0.961068	0.0579546
$276$	−12.5030	−0.752592
$277$	−20.6874	−1.24299	−0.621493	−	0.783420i	$-0.713473\pi$
$277$	−20.6874	−1.24299	−0.621493	+	0.783420i	$0.713473\pi$
$278$	−13.1731	−0.790070
$279$	−7.21004	−0.431654
$280$	−0.0190719	−0.00113977
$281$	14.3083	0.853559	0.426779	−	0.904356i	$-0.359648\pi$
$281$	14.3083	0.853559	0.426779	+	0.904356i	$0.359648\pi$
$282$	10.8806	0.647929
$283$	−8.99680	−0.534804	−0.267402	−	0.963585i	$-0.586165\pi$
$283$	−8.99680	−0.534804	−0.267402	+	0.963585i	$0.586165\pi$
$284$	20.0601	1.19035
$285$	2.23902	0.132628
$286$	−5.53781	−0.327458
$287$	0.142130	0.00838966
$288$	−8.09170	−0.476808
$289$	−7.33598	−0.431528
$290$	11.1935	0.657306
$291$	−1.47053	−0.0862039
$292$	−8.39659	−0.491374
$293$	2.77279	0.161988	0.0809940	−	0.996715i	$-0.474191\pi$
$293$	2.77279	0.161988	0.0809940	+	0.996715i	$0.474191\pi$
$294$	14.2032	0.828345
$295$	−0.556984	−0.0324289
$296$	−1.19343	−0.0693666
$297$	−0.961068	−0.0557668
$298$	−23.0959	−1.33791
$299$	−16.7053	−0.966095
$300$	−2.12372	−0.122613
$301$	0.498069	0.0287082
$302$	28.4137	1.63502
$303$	4.42175	0.254023
$304$	8.36779	0.479926
$305$	−8.33216	−0.477098
$306$	−6.31282	−0.360880
$307$	10.9000	0.622096	0.311048	−	0.950394i	$-0.399320\pi$
$307$	10.9000	0.622096	0.311048	+	0.950394i	$0.399320\pi$
$308$	−0.154937	−0.00882835
$309$	6.73954	0.383399
$310$	−14.6414	−0.831575
$311$	−7.84019	−0.444577	−0.222288	−	0.974981i	$-0.571353\pi$
$311$	−7.84019	−0.444577	−0.222288	+	0.974981i	$0.571353\pi$
$312$	0.712904	0.0403602
$313$	26.2390	1.48312	0.741558	−	0.670889i	$-0.234087\pi$
$313$	26.2390	1.48312	0.741558	+	0.670889i	$0.234087\pi$
$314$	−6.14068	−0.346539
$315$	−0.0759107	−0.00427709
$316$	−22.7431	−1.27940
$317$	1.21472	0.0682255	0.0341128	−	0.999418i	$-0.489139\pi$
$317$	1.21472	0.0682255	0.0341128	+	0.999418i	$0.489139\pi$
$318$	−24.0027	−1.34600
$319$	5.29756	0.296606
$320$	−8.95727	−0.500726
$321$	−17.6195	−0.983424
$322$	−0.907537	−0.0505750
$323$	6.96045	0.387290
$324$	2.12372	0.117985
$325$	−2.83752	−0.157397
$326$	12.3803	0.685682
$327$	−2.80904	−0.155340
$328$	−0.470407	−0.0259739
$329$	0.406734	0.0224240
$330$	−1.95164	−0.107434
$331$	−11.4415	−0.628883	−0.314441	−	0.949277i	$-0.601817\pi$
$331$	−11.4415	−0.628883	−0.314441	+	0.949277i	$0.601817\pi$
$332$	−28.4072	−1.55905
$333$	−4.75012	−0.260305
$334$	48.2839	2.64198
$335$	1.05361	0.0575648
$336$	−0.283697	−0.0154770
$337$	34.4392	1.87602	0.938011	−	0.346604i	$-0.112665\pi$
$337$	34.4392	1.87602	0.938011	+	0.346604i	$0.112665\pi$
$338$	−10.0488	−0.546584
$339$	−9.79917	−0.532218
$340$	−6.60202	−0.358045
$341$	−6.92934	−0.375245
$342$	−4.54677	−0.245861
$343$	1.06231	0.0573595
$344$	−1.64846	−0.0888788
$345$	−5.88730	−0.316962
$346$	−10.4098	−0.559636
$347$	28.2413	1.51607	0.758036	−	0.652213i	$-0.226159\pi$
$347$	28.2413	1.51607	0.758036	+	0.652213i	$0.226159\pi$
$348$	−11.7063	−0.627523
$349$	−15.2760	−0.817708	−0.408854	−	0.912600i	$-0.634072\pi$
$349$	−15.2760	−0.817708	−0.408854	+	0.912600i	$0.634072\pi$
$350$	−0.154152	−0.00823975
$351$	2.83752	0.151456
$352$	−7.77667	−0.414498
$353$	21.9392	1.16770	0.583852	−	0.811860i	$-0.301545\pi$
$353$	21.9392	1.16770	0.583852	+	0.811860i	$0.301545\pi$
$354$	1.13106	0.0601154
$355$	9.44572	0.501327
$356$	−15.3861	−0.815464
$357$	−0.235984	−0.0124896
$358$	25.0735	1.32518
$359$	8.42891	0.444861	0.222431	−	0.974949i	$-0.428601\pi$
$359$	8.42891	0.444861	0.222431	+	0.974949i	$0.428601\pi$
$360$	0.251242	0.0132416
$361$	−13.9868	−0.736146
$362$	−9.08430	−0.477460
$363$	10.0763	0.528871
$364$	0.457446	0.0239767
$365$	−3.95372	−0.206947
$366$	16.9201	0.884426
$367$	12.6253	0.659033	0.329516	−	0.944150i	$-0.393114\pi$
$367$	12.6253	0.659033	0.329516	+	0.944150i	$0.393114\pi$
$368$	−22.0023	−1.14695
$369$	−1.87233	−0.0974695
$370$	−9.64605	−0.501474
$371$	−0.897259	−0.0465834
$372$	15.3121	0.793896
$373$	−14.5657	−0.754182	−0.377091	−	0.926176i	$-0.623076\pi$
$373$	−14.5657	−0.754182	−0.377091	+	0.926176i	$0.623076\pi$
$374$	−6.06705	−0.313720
$375$	−1.00000	−0.0516398
$376$	−1.34617	−0.0694233
$377$	−15.6409	−0.805546
$378$	0.154152	0.00792870
$379$	−24.2664	−1.24648	−0.623240	−	0.782031i	$-0.714184\pi$
$379$	−24.2664	−1.24648	−0.623240	+	0.782031i	$0.714184\pi$
$380$	−4.75506	−0.243930
$381$	2.89271	0.148198
$382$	−24.7743	−1.26756
$383$	−33.8008	−1.72714	−0.863571	−	0.504227i	$-0.831778\pi$
$383$	−33.8008	−1.72714	−0.863571	+	0.504227i	$0.831778\pi$
$384$	2.00609	0.102373
$385$	−0.0729554	−0.00371815
$386$	−39.5903	−2.01509
$387$	−6.56124	−0.333527
$388$	3.12299	0.158546
$389$	−28.4690	−1.44344	−0.721718	−	0.692188i	$-0.756647\pi$
$389$	−28.4690	−1.44344	−0.721718	+	0.692188i	$0.756647\pi$
$390$	5.76214	0.291777
$391$	−18.3019	−0.925565
$392$	−1.75724	−0.0887542
$393$	8.37553	0.422490
$394$	−31.2398	−1.57384
$395$	−10.7091	−0.538833
$396$	2.04104	0.102566
$397$	22.4937	1.12892	0.564462	−	0.825459i	$-0.309084\pi$
$397$	22.4937	1.12892	0.564462	+	0.825459i	$0.309084\pi$
$398$	−0.344414	−0.0172639
$399$	−0.169966	−0.00850894
$400$	−3.73725	−0.186862
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−2.13956	−0.106712
$403$	20.4586	1.01912
$404$	−9.39058	−0.467199
$405$	1.00000	0.0496904
$406$	−0.849708	−0.0421703
$407$	−4.56519	−0.226288
$408$	0.781035	0.0386670
$409$	−3.00843	−0.148757	−0.0743785	−	0.997230i	$-0.523697\pi$
$409$	−3.00843	−0.148757	−0.0743785	+	0.997230i	$0.523697\pi$
$410$	−3.80213	−0.187774
$411$	17.7029	0.873220
$412$	−14.3129	−0.705146
$413$	0.0422811	0.00208052
$414$	11.9553	0.587572
$415$	−13.3761	−0.656609
$416$	22.9604	1.12572
$417$	6.48699	0.317669
$418$	−4.36976	−0.213732
$419$	−28.7279	−1.40345	−0.701724	−	0.712448i	$-0.747586\pi$
$419$	−28.7279	−1.40345	−0.701724	+	0.712448i	$0.747586\pi$
$420$	0.161213	0.00786640
$421$	9.97146	0.485979	0.242989	−	0.970029i	$-0.421872\pi$
$421$	9.97146	0.485979	0.242989	+	0.970029i	$0.421872\pi$
$422$	25.8194	1.25687
$423$	−5.35806	−0.260518
$424$	2.96966	0.144219
$425$	−3.10870	−0.150794
$426$	−19.1814	−0.929341
$427$	0.632500	0.0306088
$428$	37.4189	1.80871
$429$	2.72705	0.131663
$430$	−13.3239	−0.642535
$431$	11.1719	0.538132	0.269066	−	0.963122i	$-0.413285\pi$
$431$	11.1719	0.538132	0.269066	+	0.963122i	$0.413285\pi$
$432$	3.73725	0.179808
$433$	−22.4272	−1.07778	−0.538891	−	0.842376i	$-0.681156\pi$
$433$	−22.4272	−1.07778	−0.538891	+	0.842376i	$0.681156\pi$
$434$	1.11144	0.0533508
$435$	−5.51216	−0.264288
$436$	5.96562	0.285702
$437$	−13.1818	−0.630571
$438$	8.02879	0.383631
$439$	0.691752	0.0330155	0.0165078	−	0.999864i	$-0.494745\pi$
$439$	0.691752	0.0330155	0.0165078	+	0.999864i	$0.494745\pi$
$440$	0.241460	0.0115112
$441$	−6.99424	−0.333059
$442$	17.9128	0.852024
$443$	−7.55781	−0.359083	−0.179541	−	0.983750i	$-0.557461\pi$
$443$	−7.55781	−0.359083	−0.179541	+	0.983750i	$0.557461\pi$
$444$	10.0879	0.478752
$445$	−7.24489	−0.343441
$446$	−0.922385	−0.0436762
$447$	11.3734	0.537943
$448$	0.679953	0.0321248
$449$	−34.4909	−1.62773	−0.813863	−	0.581057i	$-0.802639\pi$
$449$	−34.4909	−1.62773	−0.813863	+	0.581057i	$0.802639\pi$
$450$	2.03069	0.0957279
$451$	−1.79943	−0.0847320
$452$	20.8107	0.978854
$453$	−13.9921	−0.657406
$454$	−20.9737	−0.984344
$455$	0.215398	0.0100980
$456$	0.562536	0.0263432
$457$	−11.8701	−0.555260	−0.277630	−	0.960688i	$-0.589549\pi$
$457$	−11.8701	−0.555260	−0.277630	+	0.960688i	$0.589549\pi$
$458$	2.74287	0.128166
$459$	3.10870	0.145102
$460$	12.5030	0.582955
$461$	36.1737	1.68478	0.842388	−	0.538872i	$-0.181149\pi$
$461$	36.1737	1.68478	0.842388	+	0.538872i	$0.181149\pi$
$462$	0.148150	0.00689257
$463$	−8.29580	−0.385539	−0.192769	−	0.981244i	$-0.561747\pi$
$463$	−8.29580	−0.385539	−0.192769	+	0.981244i	$0.561747\pi$
$464$	−20.6003	−0.956345
$465$	7.21004	0.334358
$466$	32.6247	1.51131
$467$	16.5160	0.764270	0.382135	−	0.924107i	$-0.375189\pi$
$467$	16.5160	0.764270	0.382135	+	0.924107i	$0.375189\pi$
$468$	−6.02611	−0.278557
$469$	−0.0799803	−0.00369315
$470$	−10.8806	−0.501884
$471$	3.02393	0.139335
$472$	−0.139938	−0.00644115
$473$	−6.30580	−0.289941
$474$	21.7469	0.998868
$475$	−2.23902	−0.102733
$476$	0.501164	0.0229708
$477$	11.8199	0.541197
$478$	−12.7080	−0.581250
$479$	−11.7316	−0.536031	−0.268015	−	0.963415i	$-0.586368\pi$
$479$	−11.7316	−0.536031	−0.268015	+	0.963415i	$0.586368\pi$
$480$	8.09170	0.369334
$481$	13.4786	0.614570
$482$	50.5387	2.30198
$483$	0.446909	0.0203351
$484$	−21.3994	−0.972698
$485$	1.47053	0.0667733
$486$	−2.03069	−0.0921142
$487$	23.2480	1.05347	0.526734	−	0.850030i	$-0.323416\pi$
$487$	23.2480	1.05347	0.526734	+	0.850030i	$0.323416\pi$
$488$	−2.09338	−0.0947631
$489$	−6.09659	−0.275697
$490$	−14.2032	−0.641633
$491$	32.4072	1.46251	0.731257	−	0.682102i	$-0.238934\pi$
$491$	32.4072	1.46251	0.731257	+	0.682102i	$0.238934\pi$
$492$	3.97630	0.179266
$493$	−17.1356	−0.771751
$494$	12.9016	0.580469
$495$	0.961068	0.0431968
$496$	26.9457	1.20990
$497$	−0.717032	−0.0321633
$498$	27.1628	1.21720
$499$	−1.02962	−0.0460923	−0.0230462	−	0.999734i	$-0.507336\pi$
$499$	−1.02962	−0.0460923	−0.0230462	+	0.999734i	$0.507336\pi$
$500$	2.12372	0.0949757
$501$	−23.7770	−1.06228
$502$	−33.7964	−1.50840
$503$	20.3646	0.908014	0.454007	−	0.890998i	$-0.349994\pi$
$503$	20.3646	0.908014	0.454007	+	0.890998i	$0.349994\pi$
$504$	−0.0190719	−0.000849532 0
$505$	−4.42175	−0.196766
$506$	11.4899	0.510787
$507$	4.94847	0.219769
$508$	−6.14332	−0.272566
$509$	23.8921	1.05900	0.529500	−	0.848310i	$-0.322380\pi$
$509$	23.8921	1.05900	0.529500	+	0.848310i	$0.322380\pi$
$510$	6.31282	0.279536
$511$	0.300130	0.0132770
$512$	32.1186	1.41945
$513$	2.23902	0.0988553
$514$	57.8932	2.55356
$515$	−6.73954	−0.296979
$516$	13.9343	0.613421
$517$	−5.14946	−0.226473
$518$	0.732239	0.0321727
$519$	5.12624	0.225017
$520$	−0.712904	−0.0312629
$521$	38.0915	1.66882	0.834409	−	0.551146i	$-0.185809\pi$
$521$	38.0915	1.66882	0.834409	+	0.551146i	$0.185809\pi$
$522$	11.1935	0.489927
$523$	−27.0843	−1.18431	−0.592156	−	0.805823i	$-0.701723\pi$
$523$	−27.0843	−1.18431	−0.592156	+	0.805823i	$0.701723\pi$
$524$	−17.7873	−0.777042
$525$	0.0759107	0.00331302
$526$	0.409375	0.0178496
$527$	22.4138	0.976363
$528$	3.59175	0.156311
$529$	11.6603	0.506970
$530$	24.0027	1.04261
$531$	−0.556984	−0.0241710
$532$	0.360960	0.0156496
$533$	5.31277	0.230122
$534$	14.7122	0.636658
$535$	17.6195	0.761757
$536$	0.264710	0.0114338
$537$	−12.3472	−0.532823
$538$	−42.2586	−1.82190
$539$	−6.72194	−0.289534
$540$	−2.12372	−0.0913904
$541$	5.98573	0.257347	0.128673	−	0.991687i	$-0.458928\pi$
$541$	5.98573	0.257347	0.128673	+	0.991687i	$0.458928\pi$
$542$	0.505125	0.0216970
$543$	4.47349	0.191976
$544$	25.1547	1.07850
$545$	2.80904	0.120326
$546$	−0.437408	−0.0187194
$547$	3.03241	0.129656	0.0648282	−	0.997896i	$-0.479350\pi$
$547$	3.03241	0.129656	0.0648282	+	0.997896i	$0.479350\pi$
$548$	−37.5961	−1.60602
$549$	−8.33216	−0.355608
$550$	1.95164	0.0832180
$551$	−12.3419	−0.525781
$552$	−1.47913	−0.0629562
$553$	0.812935	0.0345695
$554$	−42.0098	−1.78483
$555$	4.75012	0.201631
$556$	−13.7766	−0.584256
$557$	−29.3765	−1.24472	−0.622361	−	0.782731i	$-0.713826\pi$
$557$	−29.3765	−1.24472	−0.622361	+	0.782731i	$0.713826\pi$
$558$	−14.6414	−0.619819
$559$	18.6177	0.787443
$560$	0.283697	0.0119884
$561$	2.98767	0.126140
$562$	29.0557	1.22564
$563$	8.18327	0.344884	0.172442	−	0.985020i	$-0.444834\pi$
$563$	8.18327	0.344884	0.172442	+	0.985020i	$0.444834\pi$
$564$	11.3790	0.479144
$565$	9.79917	0.412254
$566$	−18.2697	−0.767935
$567$	−0.0759107	−0.00318795
$568$	2.37316	0.0995755
$569$	−25.4579	−1.06725	−0.533626	−	0.845720i	$-0.679171\pi$
$569$	−25.4579	−1.06725	−0.533626	+	0.845720i	$0.679171\pi$
$570$	4.54677	0.190443
$571$	40.1853	1.68170	0.840850	−	0.541268i	$-0.182055\pi$
$571$	40.1853	1.68170	0.840850	+	0.541268i	$0.182055\pi$
$572$	−5.79150	−0.242155
$573$	12.1999	0.509658
$574$	0.288622	0.0120469
$575$	5.88730	0.245517
$576$	−8.95727	−0.373219
$577$	8.68508	0.361565	0.180782	−	0.983523i	$-0.442137\pi$
$577$	8.68508	0.361565	0.180782	+	0.983523i	$0.442137\pi$
$578$	−14.8971	−0.619639
$579$	19.4959	0.810223
$580$	11.7063	0.486077
$581$	1.01539	0.0421256
$582$	−2.98619	−0.123782
$583$	11.3598	0.470473
$584$	−0.993338	−0.0411046
$585$	−2.83752	−0.117317
$586$	5.63069	0.232602
$587$	2.64407	0.109132	0.0545662	−	0.998510i	$-0.482622\pi$
$587$	2.64407	0.109132	0.0545662	+	0.998510i	$0.482622\pi$
$588$	14.8538	0.612561
$589$	16.1434	0.665179
$590$	−1.13106	−0.0465652
$591$	15.3838	0.632805
$592$	17.7524	0.729619
$593$	−31.8599	−1.30833	−0.654165	−	0.756352i	$-0.726980\pi$
$593$	−31.8599	−1.30833	−0.654165	+	0.756352i	$0.726980\pi$
$594$	−1.95164	−0.0800766
$595$	0.235984	0.00967439
$596$	−24.1539	−0.989383
$597$	0.169604	0.00694142
$598$	−33.9235	−1.38723
$599$	−2.08282	−0.0851017	−0.0425508	−	0.999094i	$-0.513548\pi$
$599$	−2.08282	−0.0851017	−0.0425508	+	0.999094i	$0.513548\pi$
$600$	−0.251242	−0.0102569
$601$	−6.69485	−0.273089	−0.136544	−	0.990634i	$-0.543600\pi$
$601$	−6.69485	−0.273089	−0.136544	+	0.990634i	$0.543600\pi$
$602$	1.01143	0.0412226
$603$	1.05361	0.0429063
$604$	29.7153	1.20910
$605$	−10.0763	−0.409662
$606$	8.97924	0.364756
$607$	−37.6640	−1.52874	−0.764368	−	0.644781i	$-0.776949\pi$
$607$	−37.6640	−1.52874	−0.764368	+	0.644781i	$0.776949\pi$
$608$	18.1175	0.734762
$609$	0.418432	0.0169557
$610$	−16.9201	−0.685074
$611$	15.2036	0.615072
$612$	−6.60202	−0.266871
$613$	−19.2640	−0.778066	−0.389033	−	0.921224i	$-0.627191\pi$
$613$	−19.2640	−0.778066	−0.389033	+	0.921224i	$0.627191\pi$
$614$	22.1346	0.893279
$615$	1.87233	0.0754995
$616$	−0.0183294	−0.000738514 0
$617$	17.1155	0.689042	0.344521	−	0.938779i	$-0.388041\pi$
$617$	17.1155	0.689042	0.344521	+	0.938779i	$0.388041\pi$
$618$	13.6859	0.550529
$619$	36.2258	1.45604	0.728019	−	0.685557i	$-0.240441\pi$
$619$	36.2258	1.45604	0.728019	+	0.685557i	$0.240441\pi$
$620$	−15.3121	−0.614949
$621$	−5.88730	−0.236249
$622$	−15.9210	−0.638376
$623$	0.549965	0.0220339
$624$	−10.6045	−0.424521
$625$	1.00000	0.0400000
$626$	53.2834	2.12963
$627$	2.15185	0.0859368
$628$	−6.42199	−0.256265
$629$	14.7667	0.588787
$630$	−0.154152	−0.00614155
$631$	−21.7974	−0.867741	−0.433870	−	0.900975i	$-0.642852\pi$
$631$	−21.7974	−0.867741	−0.433870	+	0.900975i	$0.642852\pi$
$632$	−2.69057	−0.107025
$633$	−12.7146	−0.505359
$634$	2.46673	0.0979663
$635$	−2.89271	−0.114794
$636$	−25.1022	−0.995368
$637$	19.8463	0.786339
$638$	10.7577	0.425902
$639$	9.44572	0.373667
$640$	−2.00609	−0.0792975
$641$	17.0449	0.673235	0.336617	−	0.941642i	$-0.390717\pi$
$641$	17.0449	0.673235	0.336617	+	0.941642i	$0.390717\pi$
$642$	−35.7798	−1.41212
$643$	18.5452	0.731350	0.365675	−	0.930743i	$-0.380838\pi$
$643$	18.5452	0.731350	0.365675	+	0.930743i	$0.380838\pi$
$644$	−0.949111	−0.0374002
$645$	6.56124	0.258349
$646$	14.1346	0.556117
$647$	9.55627	0.375696	0.187848	−	0.982198i	$-0.439849\pi$
$647$	9.55627	0.375696	0.187848	+	0.982198i	$0.439849\pi$
$648$	0.251242	0.00986970
$649$	−0.535300	−0.0210123
$650$	−5.76214	−0.226010
$651$	−0.547319	−0.0214511
$652$	12.9475	0.507061
$653$	27.8532	1.08998	0.544990	−	0.838443i	$-0.316534\pi$
$653$	27.8532	1.08998	0.544990	+	0.838443i	$0.316534\pi$
$654$	−5.70431	−0.223056
$655$	−8.37553	−0.327259
$656$	6.99735	0.273201
$657$	−3.95372	−0.154249
$658$	0.825953	0.0321990
$659$	−23.8896	−0.930608	−0.465304	−	0.885151i	$-0.654055\pi$
$659$	−23.8896	−0.930608	−0.465304	+	0.885151i	$0.654055\pi$
$660$	−2.04104	−0.0794474
$661$	−12.8095	−0.498230	−0.249115	−	0.968474i	$-0.580140\pi$
$661$	−12.8095	−0.498230	−0.249115	+	0.968474i	$0.580140\pi$
$662$	−23.2342	−0.903024
$663$	−8.82101	−0.342580
$664$	−3.36064	−0.130418
$665$	0.169966	0.00659100
$666$	−9.64605	−0.373777
$667$	32.4517	1.25654
$668$	50.4958	1.95374
$669$	0.454221	0.0175612
$670$	2.13956	0.0826584
$671$	−8.00777	−0.309137
$672$	−0.614247	−0.0236951
$673$	14.3141	0.551767	0.275884	−	0.961191i	$-0.411030\pi$
$673$	14.3141	0.551767	0.275884	+	0.961191i	$0.411030\pi$
$674$	69.9355	2.69382
$675$	−1.00000	−0.0384900
$676$	−10.5092	−0.404199
$677$	39.2962	1.51028	0.755138	−	0.655566i	$-0.227570\pi$
$677$	39.2962	1.51028	0.755138	+	0.655566i	$0.227570\pi$
$678$	−19.8991	−0.764222
$679$	−0.111629	−0.00428392
$680$	−0.781035	−0.0299513
$681$	10.3283	0.395783
$682$	−14.0714	−0.538821
$683$	28.6522	1.09635	0.548173	−	0.836365i	$-0.315323\pi$
$683$	28.6522	1.09635	0.548173	+	0.836365i	$0.315323\pi$
$684$	−4.75506	−0.181814
$685$	−17.7029	−0.676394
$686$	2.15723	0.0823636
$687$	−1.35071	−0.0515327
$688$	24.5210	0.934854
$689$	−33.5393	−1.27775
$690$	−11.9553	−0.455131
$691$	47.4577	1.80538	0.902688	−	0.430296i	$-0.141591\pi$
$691$	47.4577	1.80538	0.902688	+	0.430296i	$0.141591\pi$
$692$	−10.8867	−0.413851
$693$	−0.0729554	−0.00277135
$694$	57.3495	2.17696
$695$	−6.48699	−0.246066
$696$	−1.38488	−0.0524939
$697$	5.82051	0.220467
$698$	−31.0210	−1.17416
$699$	−16.0658	−0.607664
$700$	−0.161213	−0.00609329
$701$	15.4995	0.585408	0.292704	−	0.956203i	$-0.405445\pi$
$701$	15.4995	0.585408	0.292704	+	0.956203i	$0.405445\pi$
$702$	5.76214	0.217478
$703$	10.6356	0.401131
$704$	−8.60854	−0.324447
$705$	5.35806	0.201796
$706$	44.5517	1.67673
$707$	0.335659	0.0126237
$708$	1.18288	0.0444553
$709$	−26.0719	−0.979152	−0.489576	−	0.871961i	$-0.662848\pi$
$709$	−26.0719	−0.979152	−0.489576	+	0.871961i	$0.662848\pi$
$710$	19.1814	0.719864
$711$	−10.7091	−0.401622
$712$	−1.82022	−0.0682156
$713$	−42.4477	−1.58968
$714$	−0.479211	−0.0179340
$715$	−2.72705	−0.101986
$716$	26.2221	0.979967
$717$	6.25795	0.233708
$718$	17.1166	0.638784
$719$	−11.0835	−0.413345	−0.206673	−	0.978410i	$-0.566264\pi$
$719$	−11.0835	−0.413345	−0.206673	+	0.978410i	$0.566264\pi$
$720$	−3.73725	−0.139279
$721$	0.511603	0.0190531
$722$	−28.4029	−1.05705
$723$	−24.8874	−0.925573
$724$	−9.50046	−0.353082
$725$	5.51216	0.204716
$726$	20.4620	0.759416
$727$	−47.5951	−1.76520	−0.882602	−	0.470120i	$-0.844211\pi$
$727$	−47.5951	−1.76520	−0.882602	+	0.470120i	$0.844211\pi$
$728$	0.0541170	0.00200571
$729$	1.00000	0.0370370
$730$	−8.02879	−0.297159
$731$	20.3969	0.754408
$732$	17.6952	0.654033
$733$	40.3273	1.48952	0.744761	−	0.667331i	$-0.232563\pi$
$733$	40.3273	1.48952	0.744761	+	0.667331i	$0.232563\pi$
$734$	25.6380	0.946317
$735$	6.99424	0.257986
$736$	−47.6382	−1.75597
$737$	1.01259	0.0372992
$738$	−3.80213	−0.139958
$739$	13.6787	0.503181	0.251590	−	0.967834i	$-0.419046\pi$
$739$	13.6787	0.503181	0.251590	+	0.967834i	$0.419046\pi$
$740$	−10.0879	−0.370840
$741$	−6.35328	−0.233394
$742$	−1.82206	−0.0668899
$743$	46.9546	1.72260	0.861299	−	0.508098i	$-0.169651\pi$
$743$	46.9546	1.72260	0.861299	+	0.508098i	$0.169651\pi$
$744$	1.81146	0.0664114
$745$	−11.3734	−0.416689
$746$	−29.5784	−1.08294
$747$	−13.3761	−0.489407
$748$	−6.34499	−0.231996
$749$	−1.33751	−0.0488715
$750$	−2.03069	−0.0741505
$751$	−20.6220	−0.752506	−0.376253	−	0.926517i	$-0.622788\pi$
$751$	−20.6220	−0.752506	−0.376253	+	0.926517i	$0.622788\pi$
$752$	20.0244	0.730215
$753$	16.6428	0.606496
$754$	−31.7618	−1.15670
$755$	13.9921	0.509224
$756$	0.161213	0.00586327
$757$	−15.2635	−0.554763	−0.277381	−	0.960760i	$-0.589467\pi$
$757$	−15.2635	−0.554763	−0.277381	+	0.960760i	$0.589467\pi$
$758$	−49.2776	−1.78984
$759$	−5.65810	−0.205376
$760$	−0.562536	−0.0204053
$761$	−36.2401	−1.31370	−0.656851	−	0.754021i	$-0.728112\pi$
$761$	−36.2401	−1.31370	−0.656851	+	0.754021i	$0.728112\pi$
$762$	5.87422	0.212800
$763$	−0.213236	−0.00771968
$764$	−25.9092	−0.937361
$765$	−3.10870	−0.112395
$766$	−68.6392	−2.48004
$767$	1.58045	0.0570669
$768$	−13.8408	−0.499436
$769$	37.4421	1.35020	0.675098	−	0.737728i	$-0.264101\pi$
$769$	37.4421	1.35020	0.675098	+	0.737728i	$0.264101\pi$
$770$	−0.148150	−0.00533896
$771$	−28.5091	−1.02673
$772$	−41.4039	−1.49016
$773$	27.7173	0.996924	0.498462	−	0.866912i	$-0.333898\pi$
$773$	27.7173	0.996924	0.498462	+	0.866912i	$0.333898\pi$
$774$	−13.3239	−0.478917
$775$	−7.21004	−0.258992
$776$	0.369458	0.0132628
$777$	−0.360585	−0.0129359
$778$	−57.8118	−2.07265
$779$	4.19219	0.150201
$780$	6.02611	0.215769
$781$	9.07798	0.324836
$782$	−37.1655	−1.32904
$783$	−5.51216	−0.196988
$784$	26.1392	0.933543
$785$	−3.02393	−0.107929
$786$	17.0082	0.606661
$787$	−29.0723	−1.03632	−0.518158	−	0.855285i	$-0.673382\pi$
$787$	−29.0723	−1.03632	−0.518158	+	0.855285i	$0.673382\pi$
$788$	−32.6709	−1.16385
$789$	−0.201593	−0.00717691
$790$	−21.7469	−0.773720
$791$	−0.743863	−0.0264487
$792$	0.241460	0.00857992
$793$	23.6427	0.839576
$794$	45.6778	1.62104
$795$	−11.8199	−0.419210
$796$	−0.360191	−0.0127666
$797$	42.8736	1.51866	0.759330	−	0.650706i	$-0.225527\pi$
$797$	42.8736	1.51866	0.759330	+	0.650706i	$0.225527\pi$
$798$	−0.345149	−0.0122181
$799$	16.6566	0.589268
$800$	−8.09170	−0.286085
$801$	−7.24489	−0.255986
$802$	2.03069	0.0717063
$803$	−3.79979	−0.134092
$804$	−2.23757	−0.0789131
$805$	−0.446909	−0.0157515
$806$	41.5453	1.46337
$807$	20.8099	0.732543
$808$	−1.11093	−0.0390823
$809$	−14.8207	−0.521067	−0.260533	−	0.965465i	$-0.583898\pi$
$809$	−14.8207	−0.521067	−0.260533	+	0.965465i	$0.583898\pi$
$810$	2.03069	0.0713513
$811$	5.29869	0.186062	0.0930311	−	0.995663i	$-0.470344\pi$
$811$	5.29869	0.186062	0.0930311	+	0.995663i	$0.470344\pi$
$812$	−0.888633	−0.0311849
$813$	−0.248745	−0.00872387
$814$	−9.27051	−0.324931
$815$	6.09659	0.213554
$816$	−11.6180	−0.406711
$817$	14.6908	0.513965
$818$	−6.10919	−0.213603
$819$	0.215398	0.00752663
$820$	−3.97630	−0.138859
$821$	21.8806	0.763639	0.381820	−	0.924237i	$-0.375298\pi$
$821$	21.8806	0.763639	0.381820	+	0.924237i	$0.375298\pi$
$822$	35.9492	1.25387
$823$	29.0735	1.01344	0.506720	−	0.862111i	$-0.330858\pi$
$823$	29.0735	1.01344	0.506720	+	0.862111i	$0.330858\pi$
$824$	−1.69325	−0.0589872
$825$	−0.961068	−0.0334601
$826$	0.0858600	0.00298745
$827$	−12.2512	−0.426016	−0.213008	−	0.977050i	$-0.568326\pi$
$827$	−12.2512	−0.426016	−0.213008	+	0.977050i	$0.568326\pi$
$828$	12.5030	0.434509
$829$	23.3371	0.810532	0.405266	−	0.914199i	$-0.367179\pi$
$829$	23.3371	0.810532	0.405266	+	0.914199i	$0.367179\pi$
$830$	−27.1628	−0.942836
$831$	20.6874	0.717638
$832$	25.4164	0.881157
$833$	21.7430	0.753350
$834$	13.1731	0.456147
$835$	23.7770	0.822838
$836$	−4.56994	−0.158055
$837$	7.21004	0.249215
$838$	−58.3376	−2.01524
$839$	−3.68986	−0.127388	−0.0636941	−	0.997969i	$-0.520288\pi$
$839$	−3.68986	−0.127388	−0.0636941	+	0.997969i	$0.520288\pi$
$840$	0.0190719	0.000658044 0
$841$	1.38388	0.0477199
$842$	20.2490	0.697826
$843$	−14.3083	−0.492802
$844$	27.0022	0.929455
$845$	−4.94847	−0.170232
$846$	−10.8806	−0.374082
$847$	0.764903	0.0262824
$848$	−44.1740	−1.51694
$849$	8.99680	0.308769
$850$	−6.31282	−0.216528
$851$	−27.9654	−0.958642
$852$	−20.0601	−0.687247
$853$	26.8105	0.917974	0.458987	−	0.888443i	$-0.348212\pi$
$853$	26.8105	0.917974	0.458987	+	0.888443i	$0.348212\pi$
$854$	1.28442	0.0439518
$855$	−2.23902	−0.0765730
$856$	4.42675	0.151303
$857$	−18.4195	−0.629198	−0.314599	−	0.949225i	$-0.601870\pi$
$857$	−18.4195	−0.629198	−0.314599	+	0.949225i	$0.601870\pi$
$858$	5.53781	0.189058
$859$	45.3905	1.54870	0.774352	−	0.632755i	$-0.218076\pi$
$859$	45.3905	1.54870	0.774352	+	0.632755i	$0.218076\pi$
$860$	−13.9343	−0.475154
$861$	−0.142130	−0.00484377
$862$	22.6867	0.772714
$863$	−2.54937	−0.0867816	−0.0433908	−	0.999058i	$-0.513816\pi$
$863$	−2.54937	−0.0867816	−0.0433908	+	0.999058i	$0.513816\pi$
$864$	8.09170	0.275285
$865$	−5.12624	−0.174297
$866$	−45.5428	−1.54761
$867$	7.33598	0.249143
$868$	1.16235	0.0394529
$869$	−10.2922	−0.349138
$870$	−11.1935	−0.379496
$871$	−2.98964	−0.101300
$872$	0.705748	0.0238996
$873$	1.47053	0.0497698
$874$	−26.7682	−0.905449
$875$	−0.0759107	−0.00256625
$876$	8.39659	0.283695
$877$	−36.9520	−1.24778	−0.623891	−	0.781511i	$-0.714449\pi$
$877$	−36.9520	−1.24778	−0.623891	+	0.781511i	$0.714449\pi$
$878$	1.40474	0.0474076
$879$	−2.77279	−0.0935238
$880$	−3.59175	−0.121078
$881$	1.56478	0.0527188	0.0263594	−	0.999653i	$-0.491609\pi$
$881$	1.56478	0.0527188	0.0263594	+	0.999653i	$0.491609\pi$
$882$	−14.2032	−0.478245
$883$	18.6792	0.628605	0.314302	−	0.949323i	$-0.398229\pi$
$883$	18.6792	0.628605	0.314302	+	0.949323i	$0.398229\pi$
$884$	18.7334	0.630071
$885$	0.556984	0.0187228
$886$	−15.3476	−0.515613
$887$	11.1182	0.373313	0.186657	−	0.982425i	$-0.440235\pi$
$887$	11.1182	0.373313	0.186657	+	0.982425i	$0.440235\pi$
$888$	1.19343	0.0400488
$889$	0.219588	0.00736475
$890$	−14.7122	−0.493153
$891$	0.961068	0.0321970
$892$	−0.964639	−0.0322985
$893$	11.9968	0.401458
$894$	23.0959	0.772442
$895$	12.3472	0.412723
$896$	0.152284	0.00508744
$897$	16.7053	0.557775
$898$	−70.0405	−2.33728
$899$	−39.7429	−1.32550
$900$	2.12372	0.0707907
$901$	−36.7446	−1.22414
$902$	−3.65410	−0.121668
$903$	−0.498069	−0.0165747
$904$	2.46196	0.0818836
$905$	−4.47349	−0.148704
$906$	−28.4137	−0.943981
$907$	44.6694	1.48322	0.741611	−	0.670830i	$-0.234062\pi$
$907$	44.6694	1.48322	0.741611	+	0.670830i	$0.234062\pi$
$908$	−21.9345	−0.727922
$909$	−4.42175	−0.146660
$910$	0.437408	0.0145000
$911$	11.6534	0.386095	0.193047	−	0.981189i	$-0.438163\pi$
$911$	11.6534	0.386095	0.193047	+	0.981189i	$0.438163\pi$
$912$	−8.36779	−0.277085
$913$	−12.8554	−0.425451
$914$	−24.1045	−0.797308
$915$	8.33216	0.275453
$916$	2.86853	0.0947788
$917$	0.635793	0.0209957
$918$	6.31282	0.208354
$919$	3.62253	0.119496	0.0597481	−	0.998213i	$-0.480970\pi$
$919$	3.62253	0.119496	0.0597481	+	0.998213i	$0.480970\pi$
$920$	1.47913	0.0487656
$921$	−10.9000	−0.359167
$922$	73.4577	2.41920
$923$	−26.8024	−0.882213
$924$	0.154937	0.00509705
$925$	−4.75012	−0.156183
$926$	−16.8462	−0.553602
$927$	−6.73954	−0.221355
$928$	−44.6027	−1.46416
$929$	56.9339	1.86794	0.933971	−	0.357349i	$-0.116319\pi$
$929$	56.9339	1.86794	0.933971	+	0.357349i	$0.116319\pi$
$930$	14.6414	0.480110
$931$	15.6603	0.513244
$932$	34.1193	1.11761
$933$	7.84019	0.256676
$934$	33.5390	1.09743
$935$	−2.98767	−0.0977074
$936$	−0.712904	−0.0233020
$937$	0.307467	0.0100445	0.00502226	−	0.999987i	$-0.498401\pi$
$937$	0.307467	0.0100445	0.00502226	+	0.999987i	$0.498401\pi$
$938$	−0.162416	−0.00530306
$939$	−26.2390	−0.856277
$940$	−11.3790	−0.371143
$941$	6.59884	0.215116	0.107558	−	0.994199i	$-0.465697\pi$
$941$	6.59884	0.215116	0.107558	+	0.994199i	$0.465697\pi$
$942$	6.14068	0.200074
$943$	−11.0230	−0.358957
$944$	2.08159	0.0677499
$945$	0.0759107	0.00246938
$946$	−12.8052	−0.416332
$947$	−23.1892	−0.753549	−0.376775	−	0.926305i	$-0.622967\pi$
$947$	−23.1892	−0.753549	−0.376775	+	0.926305i	$0.622967\pi$
$948$	22.7431	0.738663
$949$	11.2188	0.364176
$950$	−4.54677	−0.147517
$951$	−1.21472	−0.0393900
$952$	0.0592889	0.00192157
$953$	−6.76646	−0.219187	−0.109594	−	0.993976i	$-0.534955\pi$
$953$	−6.76646	−0.219187	−0.109594	+	0.993976i	$0.534955\pi$
$954$	24.0027	0.777115
$955$	−12.1999	−0.394779
$956$	−13.2902	−0.429834
$957$	−5.29756	−0.171246
$958$	−23.8233	−0.769696
$959$	1.34384	0.0433949
$960$	8.95727	0.289095
$961$	20.9847	0.676924
$962$	27.3709	0.882473
$963$	17.6195	0.567780
$964$	52.8540	1.70231
$965$	−19.4959	−0.627596
$966$	0.907537	0.0291995
$967$	−37.1977	−1.19620	−0.598099	−	0.801422i	$-0.704077\pi$
$967$	−37.1977	−1.19620	−0.598099	+	0.801422i	$0.704077\pi$
$968$	−2.53160	−0.0813686
$969$	−6.96045	−0.223602
$970$	2.98619	0.0958809
$971$	−1.54530	−0.0495909	−0.0247955	−	0.999693i	$-0.507893\pi$
$971$	−1.54530	−0.0495909	−0.0247955	+	0.999693i	$0.507893\pi$
$972$	−2.12372	−0.0681184
$973$	0.492432	0.0157867
$974$	47.2096	1.51269
$975$	2.83752	0.0908734
$976$	31.1394	0.996746
$977$	37.3773	1.19580	0.597902	−	0.801569i	$-0.296001\pi$
$977$	37.3773	1.19580	0.597902	+	0.801569i	$0.296001\pi$
$978$	−12.3803	−0.395879
$979$	−6.96284	−0.222533
$980$	−14.8538	−0.474488
$981$	2.80904	0.0896858
$982$	65.8091	2.10005
$983$	10.3657	0.330613	0.165307	−	0.986242i	$-0.447139\pi$
$983$	10.3657	0.330613	0.165307	+	0.986242i	$0.447139\pi$
$984$	0.470407	0.0149960
$985$	−15.3838	−0.490168
$986$	−34.7973	−1.10817
$987$	−0.406734	−0.0129465
$988$	13.4926	0.429257
$989$	−38.6280	−1.22830
$990$	1.95164	0.0620271
$991$	−7.63778	−0.242622	−0.121311	−	0.992615i	$-0.538710\pi$
$991$	−7.63778	−0.242622	−0.121311	+	0.992615i	$0.538710\pi$
$992$	58.3414	1.85234
$993$	11.4415	0.363086
$994$	−1.45607	−0.0461838
$995$	−0.169604	−0.00537680
$996$	28.4072	0.900116
$997$	30.8776	0.977905	0.488952	−	0.872311i	$-0.337379\pi$
$997$	30.8776	0.977905	0.488952	+	0.872311i	$0.337379\pi$
$998$	−2.09085	−0.0661848
$999$	4.75012	0.150287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.d.1.25	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.d.1.25	✓	29	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)

\(f(q)\)	\(=\)	\(q+2.03069 q^{2} -1.00000 q^{3} +2.12372 q^{4} +1.00000 q^{5} -2.03069 q^{6} -0.0759107 q^{7} +0.251242 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.03069 q^{2} -1.00000 q^{3} +2.12372 q^{4} +1.00000 q^{5} -2.03069 q^{6} -0.0759107 q^{7} +0.251242 q^{8} +1.00000 q^{9} +2.03069 q^{10} +0.961068 q^{11} -2.12372 q^{12} -2.83752 q^{13} -0.154152 q^{14} -1.00000 q^{15} -3.73725 q^{16} -3.10870 q^{17} +2.03069 q^{18} -2.23902 q^{19} +2.12372 q^{20} +0.0759107 q^{21} +1.95164 q^{22} +5.88730 q^{23} -0.251242 q^{24} +1.00000 q^{25} -5.76214 q^{26} -1.00000 q^{27} -0.161213 q^{28} +5.51216 q^{29} -2.03069 q^{30} -7.21004 q^{31} -8.09170 q^{32} -0.961068 q^{33} -6.31282 q^{34} -0.0759107 q^{35} +2.12372 q^{36} -4.75012 q^{37} -4.54677 q^{38} +2.83752 q^{39} +0.251242 q^{40} -1.87233 q^{41} +0.154152 q^{42} -6.56124 q^{43} +2.04104 q^{44} +1.00000 q^{45} +11.9553 q^{46} -5.35806 q^{47} +3.73725 q^{48} -6.99424 q^{49} +2.03069 q^{50} +3.10870 q^{51} -6.02611 q^{52} +11.8199 q^{53} -2.03069 q^{54} +0.961068 q^{55} -0.0190719 q^{56} +2.23902 q^{57} +11.1935 q^{58} -0.556984 q^{59} -2.12372 q^{60} -8.33216 q^{61} -14.6414 q^{62} -0.0759107 q^{63} -8.95727 q^{64} -2.83752 q^{65} -1.95164 q^{66} +1.05361 q^{67} -6.60202 q^{68} -5.88730 q^{69} -0.154152 q^{70} +9.44572 q^{71} +0.251242 q^{72} -3.95372 q^{73} -9.64605 q^{74} -1.00000 q^{75} -4.75506 q^{76} -0.0729554 q^{77} +5.76214 q^{78} -10.7091 q^{79} -3.73725 q^{80} +1.00000 q^{81} -3.80213 q^{82} -13.3761 q^{83} +0.161213 q^{84} -3.10870 q^{85} -13.3239 q^{86} -5.51216 q^{87} +0.241460 q^{88} -7.24489 q^{89} +2.03069 q^{90} +0.215398 q^{91} +12.5030 q^{92} +7.21004 q^{93} -10.8806 q^{94} -2.23902 q^{95} +8.09170 q^{96} +1.47053 q^{97} -14.2032 q^{98} +0.961068 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * q^99

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