LMFDB - Embedded newform 4010.2.a.l.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 24 x^{15} + 70 x^{14} + 228 x^{13} - 638 x^{12} - 1075 x^{11} + 2854 x^{10} + \cdots - 2 $ x^17 - 3x^16 - 24x^15 + 70x^14 + 228x^13 - 638x^12 - 1075x^11 + 2854x^10 + 2544x^9 - 6415x^8 - 2573x^7 + 6456x^6 + 485x^5 - 1839x^4 + 67x^3 + 136x^2 - 8x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$2.65670$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.65670 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.65670 q^{6} +4.81257 q^{7} -1.00000 q^{8} +4.05806 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.65670 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.65670 q^{6} +4.81257 q^{7} -1.00000 q^{8} +4.05806 q^{9} +1.00000 q^{10} -2.04162 q^{11} +2.65670 q^{12} +4.43433 q^{13} -4.81257 q^{14} -2.65670 q^{15} +1.00000 q^{16} -0.381644 q^{17} -4.05806 q^{18} -2.89108 q^{19} -1.00000 q^{20} +12.7856 q^{21} +2.04162 q^{22} -4.16980 q^{23} -2.65670 q^{24} +1.00000 q^{25} -4.43433 q^{26} +2.81094 q^{27} +4.81257 q^{28} +0.317348 q^{29} +2.65670 q^{30} +4.56255 q^{31} -1.00000 q^{32} -5.42396 q^{33} +0.381644 q^{34} -4.81257 q^{35} +4.05806 q^{36} +5.44114 q^{37} +2.89108 q^{38} +11.7807 q^{39} +1.00000 q^{40} +0.300948 q^{41} -12.7856 q^{42} +6.07172 q^{43} -2.04162 q^{44} -4.05806 q^{45} +4.16980 q^{46} +0.0416911 q^{47} +2.65670 q^{48} +16.1608 q^{49} -1.00000 q^{50} -1.01391 q^{51} +4.43433 q^{52} +3.14254 q^{53} -2.81094 q^{54} +2.04162 q^{55} -4.81257 q^{56} -7.68074 q^{57} -0.317348 q^{58} +8.21684 q^{59} -2.65670 q^{60} -3.88226 q^{61} -4.56255 q^{62} +19.5297 q^{63} +1.00000 q^{64} -4.43433 q^{65} +5.42396 q^{66} +0.170354 q^{67} -0.381644 q^{68} -11.0779 q^{69} +4.81257 q^{70} +4.22529 q^{71} -4.05806 q^{72} +3.15283 q^{73} -5.44114 q^{74} +2.65670 q^{75} -2.89108 q^{76} -9.82543 q^{77} -11.7807 q^{78} +16.1626 q^{79} -1.00000 q^{80} -4.70635 q^{81} -0.300948 q^{82} -2.66972 q^{83} +12.7856 q^{84} +0.381644 q^{85} -6.07172 q^{86} +0.843098 q^{87} +2.04162 q^{88} -2.34306 q^{89} +4.05806 q^{90} +21.3405 q^{91} -4.16980 q^{92} +12.1213 q^{93} -0.0416911 q^{94} +2.89108 q^{95} -2.65670 q^{96} -16.8023 q^{97} -16.1608 q^{98} -8.28500 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.65670	1.53385	0.766923	−	0.641739i	$-0.221787\pi$
$3$	2.65670	1.53385	0.766923	+	0.641739i	$0.221787\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.65670	−1.08459
$7$	4.81257	1.81898	0.909490	−	0.415725i	$-0.136472\pi$
$7$	4.81257	1.81898	0.909490	+	0.415725i	$0.136472\pi$
$8$	−1.00000	−0.353553
$9$	4.05806	1.35269
$10$	1.00000	0.316228
$11$	−2.04162	−0.615571	−0.307785	−	0.951456i	$-0.599588\pi$
$11$	−2.04162	−0.615571	−0.307785	+	0.951456i	$0.599588\pi$
$12$	2.65670	0.766923
$13$	4.43433	1.22986	0.614932	−	0.788580i	$-0.289184\pi$
$13$	4.43433	1.22986	0.614932	+	0.788580i	$0.289184\pi$
$14$	−4.81257	−1.28621
$15$	−2.65670	−0.685957
$16$	1.00000	0.250000
$17$	−0.381644	−0.0925623	−0.0462812	−	0.998928i	$-0.514737\pi$
$17$	−0.381644	−0.0925623	−0.0462812	+	0.998928i	$0.514737\pi$
$18$	−4.05806	−0.956493
$19$	−2.89108	−0.663260	−0.331630	−	0.943409i	$-0.607599\pi$
$19$	−2.89108	−0.663260	−0.331630	+	0.943409i	$0.607599\pi$
$20$	−1.00000	−0.223607
$21$	12.7856	2.79004
$22$	2.04162	0.435274
$23$	−4.16980	−0.869462	−0.434731	−	0.900560i	$-0.643157\pi$
$23$	−4.16980	−0.869462	−0.434731	+	0.900560i	$0.643157\pi$
$24$	−2.65670	−0.542297
$25$	1.00000	0.200000
$26$	−4.43433	−0.869645
$27$	2.81094	0.540965
$28$	4.81257	0.909490
$29$	0.317348	0.0589300	0.0294650	−	0.999566i	$-0.490620\pi$
$29$	0.317348	0.0589300	0.0294650	+	0.999566i	$0.490620\pi$
$30$	2.65670	0.485045
$31$	4.56255	0.819459	0.409729	−	0.912207i	$-0.365623\pi$
$31$	4.56255	0.819459	0.409729	+	0.912207i	$0.365623\pi$
$32$	−1.00000	−0.176777
$33$	−5.42396	−0.944191
$34$	0.381644	0.0654514
$35$	−4.81257	−0.813473
$36$	4.05806	0.676343
$37$	5.44114	0.894518	0.447259	−	0.894404i	$-0.352400\pi$
$37$	5.44114	0.894518	0.447259	+	0.894404i	$0.352400\pi$
$38$	2.89108	0.468996
$39$	11.7807	1.88642
$40$	1.00000	0.158114
$41$	0.300948	0.0470002	0.0235001	−	0.999724i	$-0.492519\pi$
$41$	0.300948	0.0470002	0.0235001	+	0.999724i	$0.492519\pi$
$42$	−12.7856	−1.97285
$43$	6.07172	0.925928	0.462964	−	0.886377i	$-0.346786\pi$
$43$	6.07172	0.925928	0.462964	+	0.886377i	$0.346786\pi$
$44$	−2.04162	−0.307785
$45$	−4.05806	−0.604939
$46$	4.16980	0.614803
$47$	0.0416911	0.00608126	0.00304063	−	0.999995i	$-0.499032\pi$
$47$	0.0416911	0.00608126	0.00304063	+	0.999995i	$0.499032\pi$
$48$	2.65670	0.383462
$49$	16.1608	2.30869
$50$	−1.00000	−0.141421
$51$	−1.01391	−0.141976
$52$	4.43433	0.614932
$53$	3.14254	0.431661	0.215831	−	0.976431i	$-0.430754\pi$
$53$	3.14254	0.431661	0.215831	+	0.976431i	$0.430754\pi$
$54$	−2.81094	−0.382520
$55$	2.04162	0.275292
$56$	−4.81257	−0.643107
$57$	−7.68074	−1.01734
$58$	−0.317348	−0.0416698
$59$	8.21684	1.06974	0.534871	−	0.844934i	$-0.320360\pi$
$59$	8.21684	1.06974	0.534871	+	0.844934i	$0.320360\pi$
$60$	−2.65670	−0.342979
$61$	−3.88226	−0.497072	−0.248536	−	0.968623i	$-0.579949\pi$
$61$	−3.88226	−0.497072	−0.248536	+	0.968623i	$0.579949\pi$
$62$	−4.56255	−0.579445
$63$	19.5297	2.46051
$64$	1.00000	0.125000
$65$	−4.43433	−0.550012
$66$	5.42396	0.667644
$67$	0.170354	0.0208121	0.0104060	−	0.999946i	$-0.496688\pi$
$67$	0.170354	0.0208121	0.0104060	+	0.999946i	$0.496688\pi$
$68$	−0.381644	−0.0462812
$69$	−11.0779	−1.33362
$70$	4.81257	0.575212
$71$	4.22529	0.501450	0.250725	−	0.968058i	$-0.419331\pi$
$71$	4.22529	0.501450	0.250725	+	0.968058i	$0.419331\pi$
$72$	−4.05806	−0.478246
$73$	3.15283	0.369010	0.184505	−	0.982832i	$-0.440932\pi$
$73$	3.15283	0.369010	0.184505	+	0.982832i	$0.440932\pi$
$74$	−5.44114	−0.632520
$75$	2.65670	0.306769
$76$	−2.89108	−0.331630
$77$	−9.82543	−1.11971
$78$	−11.7807	−1.33390
$79$	16.1626	1.81843	0.909215	−	0.416327i	$-0.136683\pi$
$79$	16.1626	1.81843	0.909215	+	0.416327i	$0.136683\pi$
$80$	−1.00000	−0.111803
$81$	−4.70635	−0.522928
$82$	−0.300948	−0.0332341
$83$	−2.66972	−0.293040	−0.146520	−	0.989208i	$-0.546807\pi$
$83$	−2.66972	−0.293040	−0.146520	+	0.989208i	$0.546807\pi$
$84$	12.7856	1.39502
$85$	0.381644	0.0413951
$86$	−6.07172	−0.654730
$87$	0.843098	0.0903896
$88$	2.04162	0.217637
$89$	−2.34306	−0.248364	−0.124182	−	0.992259i	$-0.539631\pi$
$89$	−2.34306	−0.248364	−0.124182	+	0.992259i	$0.539631\pi$
$90$	4.05806	0.427757
$91$	21.3405	2.23710
$92$	−4.16980	−0.434731
$93$	12.1213	1.25692
$94$	−0.0416911	−0.00430010
$95$	2.89108	0.296619
$96$	−2.65670	−0.271148
$97$	−16.8023	−1.70602	−0.853009	−	0.521896i	$-0.825225\pi$
$97$	−16.8023	−1.70602	−0.853009	+	0.521896i	$0.825225\pi$
$98$	−16.1608	−1.63249
$99$	−8.28500	−0.832673
$100$	1.00000	0.100000
$101$	5.74442	0.571591	0.285796	−	0.958291i	$-0.407742\pi$
$101$	5.74442	0.571591	0.285796	+	0.958291i	$0.407742\pi$
$102$	1.01391	0.100392
$103$	−5.24220	−0.516529	−0.258264	−	0.966074i	$-0.583151\pi$
$103$	−5.24220	−0.516529	−0.258264	+	0.966074i	$0.583151\pi$
$104$	−4.43433	−0.434822
$105$	−12.7856	−1.24774
$106$	−3.14254	−0.305231
$107$	−0.533502	−0.0515755	−0.0257878	−	0.999667i	$-0.508209\pi$
$107$	−0.533502	−0.0515755	−0.0257878	+	0.999667i	$0.508209\pi$
$108$	2.81094	0.270482
$109$	−3.38529	−0.324252	−0.162126	−	0.986770i	$-0.551835\pi$
$109$	−3.38529	−0.324252	−0.162126	+	0.986770i	$0.551835\pi$
$110$	−2.04162	−0.194661
$111$	14.4555	1.37205
$112$	4.81257	0.454745
$113$	−3.73688	−0.351536	−0.175768	−	0.984432i	$-0.556241\pi$
$113$	−3.73688	−0.351536	−0.175768	+	0.984432i	$0.556241\pi$
$114$	7.68074	0.719368
$115$	4.16980	0.388835
$116$	0.317348	0.0294650
$117$	17.9948	1.66362
$118$	−8.21684	−0.756421
$119$	−1.83669	−0.168369
$120$	2.65670	0.242522
$121$	−6.83180	−0.621073
$122$	3.88226	0.351483
$123$	0.799528	0.0720910
$124$	4.56255	0.409729
$125$	−1.00000	−0.0894427
$126$	−19.5297	−1.73984
$127$	−9.78337	−0.868134	−0.434067	−	0.900881i	$-0.642922\pi$
$127$	−9.78337	−0.868134	−0.434067	+	0.900881i	$0.642922\pi$
$128$	−1.00000	−0.0883883
$129$	16.1307	1.42023
$130$	4.43433	0.388917
$131$	6.19415	0.541185	0.270593	−	0.962694i	$-0.412780\pi$
$131$	6.19415	0.541185	0.270593	+	0.962694i	$0.412780\pi$
$132$	−5.42396	−0.472096
$133$	−13.9135	−1.20646
$134$	−0.170354	−0.0147164
$135$	−2.81094	−0.241927
$136$	0.381644	0.0327257
$137$	3.80332	0.324940	0.162470	−	0.986713i	$-0.448054\pi$
$137$	3.80332	0.324940	0.162470	+	0.986713i	$0.448054\pi$
$138$	11.0779	0.943013
$139$	−19.4350	−1.64846	−0.824229	−	0.566256i	$-0.808391\pi$
$139$	−19.4350	−1.64846	−0.824229	+	0.566256i	$0.808391\pi$
$140$	−4.81257	−0.406736
$141$	0.110761	0.00932773
$142$	−4.22529	−0.354579
$143$	−9.05321	−0.757068
$144$	4.05806	0.338171
$145$	−0.317348	−0.0263543
$146$	−3.15283	−0.260930
$147$	42.9345	3.54118
$148$	5.44114	0.447259
$149$	0.696755	0.0570804	0.0285402	−	0.999593i	$-0.490914\pi$
$149$	0.696755	0.0570804	0.0285402	+	0.999593i	$0.490914\pi$
$150$	−2.65670	−0.216919
$151$	12.5819	1.02390	0.511949	−	0.859016i	$-0.328924\pi$
$151$	12.5819	1.02390	0.511949	+	0.859016i	$0.328924\pi$
$152$	2.89108	0.234498
$153$	−1.54873	−0.125208
$154$	9.82543	0.791755
$155$	−4.56255	−0.366473
$156$	11.7807	0.943211
$157$	18.6175	1.48584	0.742920	−	0.669380i	$-0.233440\pi$
$157$	18.6175	1.48584	0.742920	+	0.669380i	$0.233440\pi$
$158$	−16.1626	−1.28582
$159$	8.34879	0.662102
$160$	1.00000	0.0790569
$161$	−20.0674	−1.58154
$162$	4.70635	0.369766
$163$	−20.9613	−1.64182	−0.820909	−	0.571059i	$-0.806533\pi$
$163$	−20.9613	−1.64182	−0.820909	+	0.571059i	$0.806533\pi$
$164$	0.300948	0.0235001
$165$	5.42396	0.422255
$166$	2.66972	0.207211
$167$	−15.3214	−1.18561	−0.592804	−	0.805346i	$-0.701979\pi$
$167$	−15.3214	−1.18561	−0.592804	+	0.805346i	$0.701979\pi$
$168$	−12.7856	−0.986427
$169$	6.66332	0.512563
$170$	−0.381644	−0.0292708
$171$	−11.7322	−0.897182
$172$	6.07172	0.462964
$173$	−2.30454	−0.175211	−0.0876056	−	0.996155i	$-0.527922\pi$
$173$	−2.30454	−0.175211	−0.0876056	+	0.996155i	$0.527922\pi$
$174$	−0.843098	−0.0639151
$175$	4.81257	0.363796
$176$	−2.04162	−0.153893
$177$	21.8297	1.64082
$178$	2.34306	0.175620
$179$	2.47698	0.185138	0.0925691	−	0.995706i	$-0.470492\pi$
$179$	2.47698	0.185138	0.0925691	+	0.995706i	$0.470492\pi$
$180$	−4.05806	−0.302470
$181$	−11.0443	−0.820916	−0.410458	−	0.911880i	$-0.634631\pi$
$181$	−11.0443	−0.820916	−0.410458	+	0.911880i	$0.634631\pi$
$182$	−21.3405	−1.58187
$183$	−10.3140	−0.762432
$184$	4.16980	0.307401
$185$	−5.44114	−0.400041
$186$	−12.1213	−0.888779
$187$	0.779171	0.0569787
$188$	0.0416911	0.00304063
$189$	13.5278	0.984004
$190$	−2.89108	−0.209741
$191$	11.0707	0.801050	0.400525	−	0.916286i	$-0.368828\pi$
$191$	11.0707	0.801050	0.400525	+	0.916286i	$0.368828\pi$
$192$	2.65670	0.191731
$193$	−7.82421	−0.563199	−0.281599	−	0.959532i	$-0.590865\pi$
$193$	−7.82421	−0.563199	−0.281599	+	0.959532i	$0.590865\pi$
$194$	16.8023	1.20634
$195$	−11.7807	−0.843633
$196$	16.1608	1.15435
$197$	27.2316	1.94017	0.970085	−	0.242765i	$-0.0780543\pi$
$197$	27.2316	1.94017	0.970085	+	0.242765i	$0.0780543\pi$
$198$	8.28500	0.588789
$199$	15.0543	1.06717	0.533585	−	0.845746i	$-0.320844\pi$
$199$	15.0543	1.06717	0.533585	+	0.845746i	$0.320844\pi$
$200$	−1.00000	−0.0707107
$201$	0.452580	0.0319226
$202$	−5.74442	−0.404176
$203$	1.52726	0.107193
$204$	−1.01391	−0.0709882
$205$	−0.300948	−0.0210191
$206$	5.24220	0.365241
$207$	−16.9213	−1.17611
$208$	4.43433	0.307466
$209$	5.90249	0.408284
$210$	12.7856	0.882287
$211$	10.1950	0.701853	0.350926	−	0.936403i	$-0.385867\pi$
$211$	10.1950	0.701853	0.350926	+	0.936403i	$0.385867\pi$
$212$	3.14254	0.215831
$213$	11.2253	0.769147
$214$	0.533502	0.0364694
$215$	−6.07172	−0.414088
$216$	−2.81094	−0.191260
$217$	21.9576	1.49058
$218$	3.38529	0.229281
$219$	8.37611	0.566005
$220$	2.04162	0.137646
$221$	−1.69234	−0.113839
$222$	−14.4555	−0.970189
$223$	5.03451	0.337136	0.168568	−	0.985690i	$-0.446086\pi$
$223$	5.03451	0.337136	0.168568	+	0.985690i	$0.446086\pi$
$224$	−4.81257	−0.321553
$225$	4.05806	0.270537
$226$	3.73688	0.248573
$227$	−4.59953	−0.305282	−0.152641	−	0.988282i	$-0.548778\pi$
$227$	−4.59953	−0.305282	−0.152641	+	0.988282i	$0.548778\pi$
$228$	−7.68074	−0.508670
$229$	−2.95457	−0.195243	−0.0976217	−	0.995224i	$-0.531124\pi$
$229$	−2.95457	−0.195243	−0.0976217	+	0.995224i	$0.531124\pi$
$230$	−4.16980	−0.274948
$231$	−26.1032	−1.71747
$232$	−0.317348	−0.0208349
$233$	−20.6701	−1.35415	−0.677073	−	0.735916i	$-0.736752\pi$
$233$	−20.6701	−1.35415	−0.677073	+	0.735916i	$0.736752\pi$
$234$	−17.9948	−1.17636
$235$	−0.0416911	−0.00271962
$236$	8.21684	0.534871
$237$	42.9391	2.78919
$238$	1.83669	0.119055
$239$	14.6177	0.945543	0.472772	−	0.881185i	$-0.343254\pi$
$239$	14.6177	0.945543	0.472772	+	0.881185i	$0.343254\pi$
$240$	−2.65670	−0.171489
$241$	4.20257	0.270711	0.135356	−	0.990797i	$-0.456782\pi$
$241$	4.20257	0.270711	0.135356	+	0.990797i	$0.456782\pi$
$242$	6.83180	0.439165
$243$	−20.9362	−1.34306
$244$	−3.88226	−0.248536
$245$	−16.1608	−1.03248
$246$	−0.799528	−0.0509761
$247$	−12.8200	−0.815719
$248$	−4.56255	−0.289722
$249$	−7.09265	−0.449478
$250$	1.00000	0.0632456
$251$	15.8404	0.999835	0.499918	−	0.866073i	$-0.333364\pi$
$251$	15.8404	0.999835	0.499918	+	0.866073i	$0.333364\pi$
$252$	19.5297	1.23025
$253$	8.51313	0.535216
$254$	9.78337	0.613863
$255$	1.01391	0.0634938
$256$	1.00000	0.0625000
$257$	23.0160	1.43570	0.717850	−	0.696198i	$-0.245126\pi$
$257$	23.0160	1.43570	0.717850	+	0.696198i	$0.245126\pi$
$258$	−16.1307	−1.00426
$259$	26.1859	1.62711
$260$	−4.43433	−0.275006
$261$	1.28782	0.0797138
$262$	−6.19415	−0.382676
$263$	−15.2760	−0.941959	−0.470980	−	0.882144i	$-0.656099\pi$
$263$	−15.2760	−0.941959	−0.470980	+	0.882144i	$0.656099\pi$
$264$	5.42396	0.333822
$265$	−3.14254	−0.193045
$266$	13.9135	0.853094
$267$	−6.22481	−0.380952
$268$	0.170354	0.0104060
$269$	−20.6836	−1.26110	−0.630550	−	0.776149i	$-0.717171\pi$
$269$	−20.6836	−1.26110	−0.630550	+	0.776149i	$0.717171\pi$
$270$	2.81094	0.171068
$271$	−25.0191	−1.51980	−0.759900	−	0.650040i	$-0.774752\pi$
$271$	−25.0191	−1.51980	−0.759900	+	0.650040i	$0.774752\pi$
$272$	−0.381644	−0.0231406
$273$	56.6954	3.43136
$274$	−3.80332	−0.229767
$275$	−2.04162	−0.123114
$276$	−11.0779	−0.666811
$277$	24.0396	1.44440	0.722200	−	0.691685i	$-0.243131\pi$
$277$	24.0396	1.44440	0.722200	+	0.691685i	$0.243131\pi$
$278$	19.4350	1.16564
$279$	18.5151	1.10847
$280$	4.81257	0.287606
$281$	12.3708	0.737982	0.368991	−	0.929433i	$-0.379703\pi$
$281$	12.3708	0.737982	0.368991	+	0.929433i	$0.379703\pi$
$282$	−0.110761	−0.00659570
$283$	11.0245	0.655339	0.327670	−	0.944792i	$-0.393737\pi$
$283$	11.0245	0.655339	0.327670	+	0.944792i	$0.393737\pi$
$284$	4.22529	0.250725
$285$	7.68074	0.454968
$286$	9.05321	0.535328
$287$	1.44833	0.0854924
$288$	−4.05806	−0.239123
$289$	−16.8543	−0.991432
$290$	0.317348	0.0186353
$291$	−44.6388	−2.61677
$292$	3.15283	0.184505
$293$	−23.2132	−1.35613	−0.678065	−	0.735002i	$-0.737181\pi$
$293$	−23.2132	−1.35613	−0.678065	+	0.735002i	$0.737181\pi$
$294$	−42.9345	−2.50399
$295$	−8.21684	−0.478403
$296$	−5.44114	−0.316260
$297$	−5.73885	−0.333002
$298$	−0.696755	−0.0403619
$299$	−18.4903	−1.06932
$300$	2.65670	0.153385
$301$	29.2206	1.68425
$302$	−12.5819	−0.724005
$303$	15.2612	0.876733
$304$	−2.89108	−0.165815
$305$	3.88226	0.222297
$306$	1.54873	0.0885352
$307$	12.0514	0.687812	0.343906	−	0.939004i	$-0.388250\pi$
$307$	12.0514	0.687812	0.343906	+	0.939004i	$0.388250\pi$
$308$	−9.82543	−0.559856
$309$	−13.9269	−0.792276
$310$	4.56255	0.259136
$311$	−27.7037	−1.57093	−0.785465	−	0.618906i	$-0.787576\pi$
$311$	−27.7037	−1.57093	−0.785465	+	0.618906i	$0.787576\pi$
$312$	−11.7807	−0.666951
$313$	−14.0939	−0.796632	−0.398316	−	0.917248i	$-0.630405\pi$
$313$	−14.0939	−0.796632	−0.398316	+	0.917248i	$0.630405\pi$
$314$	−18.6175	−1.05065
$315$	−19.5297	−1.10037
$316$	16.1626	0.909215
$317$	1.27789	0.0717737	0.0358869	−	0.999356i	$-0.488574\pi$
$317$	1.27789	0.0717737	0.0358869	+	0.999356i	$0.488574\pi$
$318$	−8.34879	−0.468177
$319$	−0.647903	−0.0362756
$320$	−1.00000	−0.0559017
$321$	−1.41735	−0.0791090
$322$	20.0674	1.11831
$323$	1.10337	0.0613929
$324$	−4.70635	−0.261464
$325$	4.43433	0.245973
$326$	20.9613	1.16094
$327$	−8.99371	−0.497353
$328$	−0.300948	−0.0166171
$329$	0.200641	0.0110617
$330$	−5.42396	−0.298579
$331$	−11.6678	−0.641322	−0.320661	−	0.947194i	$-0.603905\pi$
$331$	−11.6678	−0.641322	−0.320661	+	0.947194i	$0.603905\pi$
$332$	−2.66972	−0.146520
$333$	22.0805	1.21000
$334$	15.3214	0.838352
$335$	−0.170354	−0.00930745
$336$	12.7856	0.697509
$337$	29.3808	1.60047	0.800236	−	0.599685i	$-0.204707\pi$
$337$	29.3808	1.60047	0.800236	+	0.599685i	$0.204707\pi$
$338$	−6.66332	−0.362437
$339$	−9.92776	−0.539202
$340$	0.381644	0.0206976
$341$	−9.31499	−0.504435
$342$	11.7322	0.634404
$343$	44.0872	2.38048
$344$	−6.07172	−0.327365
$345$	11.0779	0.596414
$346$	2.30454	0.123893
$347$	−20.2301	−1.08601	−0.543003	−	0.839731i	$-0.682713\pi$
$347$	−20.2301	−1.08601	−0.543003	+	0.839731i	$0.682713\pi$
$348$	0.843098	0.0451948
$349$	−24.2774	−1.29954	−0.649770	−	0.760131i	$-0.725135\pi$
$349$	−24.2774	−1.29954	−0.649770	+	0.760131i	$0.725135\pi$
$350$	−4.81257	−0.257243
$351$	12.4646	0.665313
$352$	2.04162	0.108819
$353$	−12.5767	−0.669392	−0.334696	−	0.942326i	$-0.608634\pi$
$353$	−12.5767	−0.669392	−0.334696	+	0.942326i	$0.608634\pi$
$354$	−21.8297	−1.16023
$355$	−4.22529	−0.224255
$356$	−2.34306	−0.124182
$357$	−4.87953	−0.258252
$358$	−2.47698	−0.130913
$359$	11.4102	0.602207	0.301104	−	0.953591i	$-0.402645\pi$
$359$	11.4102	0.602207	0.301104	+	0.953591i	$0.402645\pi$
$360$	4.05806	0.213878
$361$	−10.6416	−0.560086
$362$	11.0443	0.580475
$363$	−18.1500	−0.952630
$364$	21.3405	1.11855
$365$	−3.15283	−0.165026
$366$	10.3140	0.539121
$367$	−18.0979	−0.944702	−0.472351	−	0.881411i	$-0.656594\pi$
$367$	−18.0979	−0.944702	−0.472351	+	0.881411i	$0.656594\pi$
$368$	−4.16980	−0.217366
$369$	1.22126	0.0635764
$370$	5.44114	0.282872
$371$	15.1237	0.785183
$372$	12.1213	0.628462
$373$	−20.9791	−1.08625	−0.543127	−	0.839650i	$-0.682760\pi$
$373$	−20.9791	−1.08625	−0.543127	+	0.839650i	$0.682760\pi$
$374$	−0.779171	−0.0402900
$375$	−2.65670	−0.137191
$376$	−0.0416911	−0.00215005
$377$	1.40723	0.0724759
$378$	−13.5278	−0.695796
$379$	−30.4908	−1.56621	−0.783104	−	0.621891i	$-0.786365\pi$
$379$	−30.4908	−1.56621	−0.783104	+	0.621891i	$0.786365\pi$
$380$	2.89108	0.148310
$381$	−25.9915	−1.33158
$382$	−11.0707	−0.566428
$383$	21.7021	1.10893	0.554463	−	0.832208i	$-0.312924\pi$
$383$	21.7021	1.10893	0.554463	+	0.832208i	$0.312924\pi$
$384$	−2.65670	−0.135574
$385$	9.82543	0.500750
$386$	7.82421	0.398242
$387$	24.6394	1.25249
$388$	−16.8023	−0.853009
$389$	11.5789	0.587073	0.293536	−	0.955948i	$-0.405168\pi$
$389$	11.5789	0.587073	0.293536	+	0.955948i	$0.405168\pi$
$390$	11.7807	0.596539
$391$	1.59138	0.0804795
$392$	−16.1608	−0.816245
$393$	16.4560	0.830095
$394$	−27.2316	−1.37191
$395$	−16.1626	−0.813226
$396$	−8.28500	−0.416337
$397$	−13.0956	−0.657250	−0.328625	−	0.944461i	$-0.606585\pi$
$397$	−13.0956	−0.657250	−0.328625	+	0.944461i	$0.606585\pi$
$398$	−15.0543	−0.754604
$399$	−36.9641	−1.85052
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−0.452580	−0.0225727
$403$	20.2319	1.00782
$404$	5.74442	0.285796
$405$	4.70635	0.233861
$406$	−1.52726	−0.0757966
$407$	−11.1087	−0.550639
$408$	1.01391	0.0501962
$409$	9.16236	0.453049	0.226525	−	0.974005i	$-0.427264\pi$
$409$	9.16236	0.453049	0.226525	+	0.974005i	$0.427264\pi$
$410$	0.300948	0.0148628
$411$	10.1043	0.498408
$412$	−5.24220	−0.258264
$413$	39.5441	1.94584
$414$	16.9213	0.831635
$415$	2.66972	0.131051
$416$	−4.43433	−0.217411
$417$	−51.6331	−2.52848
$418$	−5.90249	−0.288700
$419$	−31.1718	−1.52284	−0.761420	−	0.648259i	$-0.775497\pi$
$419$	−31.1718	−1.52284	−0.761420	+	0.648259i	$0.775497\pi$
$420$	−12.7856	−0.623871
$421$	−17.6713	−0.861245	−0.430623	−	0.902532i	$-0.641706\pi$
$421$	−17.6713	−0.861245	−0.430623	+	0.902532i	$0.641706\pi$
$422$	−10.1950	−0.496285
$423$	0.169185	0.00822604
$424$	−3.14254	−0.152615
$425$	−0.381644	−0.0185125
$426$	−11.2253	−0.543869
$427$	−18.6836	−0.904165
$428$	−0.533502	−0.0257878
$429$	−24.0517	−1.16123
$430$	6.07172	0.292804
$431$	−13.2148	−0.636533	−0.318266	−	0.948001i	$-0.603101\pi$
$431$	−13.2148	−0.636533	−0.318266	+	0.948001i	$0.603101\pi$
$432$	2.81094	0.135241
$433$	−3.40667	−0.163714	−0.0818572	−	0.996644i	$-0.526085\pi$
$433$	−3.40667	−0.163714	−0.0818572	+	0.996644i	$0.526085\pi$
$434$	−21.9576	−1.05400
$435$	−0.843098	−0.0404235
$436$	−3.38529	−0.162126
$437$	12.0552	0.576680
$438$	−8.37611	−0.400226
$439$	−39.5888	−1.88947	−0.944736	−	0.327832i	$-0.893682\pi$
$439$	−39.5888	−1.88947	−0.944736	+	0.327832i	$0.893682\pi$
$440$	−2.04162	−0.0973303
$441$	65.5816	3.12293
$442$	1.69234	0.0804963
$443$	1.63215	0.0775459	0.0387729	−	0.999248i	$-0.487655\pi$
$443$	1.63215	0.0775459	0.0387729	+	0.999248i	$0.487655\pi$
$444$	14.4555	0.686027
$445$	2.34306	0.111072
$446$	−5.03451	−0.238391
$447$	1.85107	0.0875525
$448$	4.81257	0.227373
$449$	21.9388	1.03536	0.517679	−	0.855575i	$-0.326796\pi$
$449$	21.9388	1.03536	0.517679	+	0.855575i	$0.326796\pi$
$450$	−4.05806	−0.191299
$451$	−0.614420	−0.0289319
$452$	−3.73688	−0.175768
$453$	33.4262	1.57050
$454$	4.59953	0.215867
$455$	−21.3405	−1.00046
$456$	7.68074	0.359684
$457$	20.9510	0.980049	0.490024	−	0.871709i	$-0.336988\pi$
$457$	20.9510	0.980049	0.490024	+	0.871709i	$0.336988\pi$
$458$	2.95457	0.138058
$459$	−1.07278	−0.0500729
$460$	4.16980	0.194418
$461$	29.6666	1.38171	0.690857	−	0.722992i	$-0.257234\pi$
$461$	29.6666	1.38171	0.690857	+	0.722992i	$0.257234\pi$
$462$	26.1032	1.21443
$463$	7.64402	0.355248	0.177624	−	0.984098i	$-0.443159\pi$
$463$	7.64402	0.355248	0.177624	+	0.984098i	$0.443159\pi$
$464$	0.317348	0.0147325
$465$	−12.1213	−0.562113
$466$	20.6701	0.957526
$467$	22.7847	1.05435	0.527176	−	0.849756i	$-0.323251\pi$
$467$	22.7847	1.05435	0.527176	+	0.849756i	$0.323251\pi$
$468$	17.9948	0.831809
$469$	0.819842	0.0378568
$470$	0.0416911	0.00192306
$471$	49.4612	2.27905
$472$	−8.21684	−0.378211
$473$	−12.3961	−0.569974
$474$	−42.9391	−1.97226
$475$	−2.89108	−0.132652
$476$	−1.83669	−0.0841845
$477$	12.7526	0.583902
$478$	−14.6177	−0.668600
$479$	18.0667	0.825487	0.412743	−	0.910847i	$-0.364571\pi$
$479$	18.0667	0.825487	0.412743	+	0.910847i	$0.364571\pi$
$480$	2.65670	0.121261
$481$	24.1278	1.10014
$482$	−4.20257	−0.191422
$483$	−53.3132	−2.42583
$484$	−6.83180	−0.310536
$485$	16.8023	0.762955
$486$	20.9362	0.949684
$487$	15.2931	0.692995	0.346498	−	0.938051i	$-0.387371\pi$
$487$	15.2931	0.692995	0.346498	+	0.938051i	$0.387371\pi$
$488$	3.88226	0.175742
$489$	−55.6880	−2.51830
$490$	16.1608	0.730072
$491$	29.6400	1.33764	0.668818	−	0.743426i	$-0.266801\pi$
$491$	29.6400	1.33764	0.668818	+	0.743426i	$0.266801\pi$
$492$	0.799528	0.0360455
$493$	−0.121114	−0.00545470
$494$	12.8200	0.576801
$495$	8.28500	0.372383
$496$	4.56255	0.204865
$497$	20.3345	0.912128
$498$	7.09265	0.317829
$499$	8.09763	0.362500	0.181250	−	0.983437i	$-0.441986\pi$
$499$	8.09763	0.362500	0.181250	+	0.983437i	$0.441986\pi$
$500$	−1.00000	−0.0447214
$501$	−40.7045	−1.81854
$502$	−15.8404	−0.706990
$503$	−21.3249	−0.950832	−0.475416	−	0.879761i	$-0.657702\pi$
$503$	−21.3249	−0.950832	−0.475416	+	0.879761i	$0.657702\pi$
$504$	−19.5297	−0.869921
$505$	−5.74442	−0.255623
$506$	−8.51313	−0.378455
$507$	17.7025	0.786193
$508$	−9.78337	−0.434067
$509$	22.5851	1.00107	0.500534	−	0.865717i	$-0.333137\pi$
$509$	22.5851	1.00107	0.500534	+	0.865717i	$0.333137\pi$
$510$	−1.01391	−0.0448969
$511$	15.1732	0.671223
$512$	−1.00000	−0.0441942
$513$	−8.12665	−0.358800
$514$	−23.0160	−1.01519
$515$	5.24220	0.230999
$516$	16.1307	0.710116
$517$	−0.0851172	−0.00374345
$518$	−26.1859	−1.15054
$519$	−6.12248	−0.268747
$520$	4.43433	0.194458
$521$	−5.44417	−0.238514	−0.119257	−	0.992863i	$-0.538051\pi$
$521$	−5.44417	−0.238514	−0.119257	+	0.992863i	$0.538051\pi$
$522$	−1.28782	−0.0563661
$523$	9.04399	0.395466	0.197733	−	0.980256i	$-0.436642\pi$
$523$	9.04399	0.395466	0.197733	+	0.980256i	$0.436642\pi$
$524$	6.19415	0.270593
$525$	12.7856	0.558007
$526$	15.2760	0.666066
$527$	−1.74127	−0.0758510
$528$	−5.42396	−0.236048
$529$	−5.61280	−0.244035
$530$	3.14254	0.136503
$531$	33.3444	1.44702
$532$	−13.9135	−0.603229
$533$	1.33450	0.0578038
$534$	6.22481	0.269374
$535$	0.533502	0.0230653
$536$	−0.170354	−0.00735819
$537$	6.58059	0.283974
$538$	20.6836	0.891733
$539$	−32.9942	−1.42116
$540$	−2.81094	−0.120963
$541$	−3.68266	−0.158330	−0.0791651	−	0.996862i	$-0.525225\pi$
$541$	−3.68266	−0.158330	−0.0791651	+	0.996862i	$0.525225\pi$
$542$	25.0191	1.07466
$543$	−29.3414	−1.25916
$544$	0.381644	0.0163629
$545$	3.38529	0.145010
$546$	−56.6954	−2.42634
$547$	6.19530	0.264892	0.132446	−	0.991190i	$-0.457717\pi$
$547$	6.19530	0.264892	0.132446	+	0.991190i	$0.457717\pi$
$548$	3.80332	0.162470
$549$	−15.7544	−0.672382
$550$	2.04162	0.0870549
$551$	−0.917479	−0.0390859
$552$	11.0779	0.471507
$553$	77.7834	3.30769
$554$	−24.0396	−1.02134
$555$	−14.4555	−0.613601
$556$	−19.4350	−0.824229
$557$	−11.2913	−0.478426	−0.239213	−	0.970967i	$-0.576889\pi$
$557$	−11.2913	−0.478426	−0.239213	+	0.970967i	$0.576889\pi$
$558$	−18.5151	−0.783806
$559$	26.9240	1.13876
$560$	−4.81257	−0.203368
$561$	2.07002	0.0873965
$562$	−12.3708	−0.521832
$563$	7.82330	0.329713	0.164856	−	0.986318i	$-0.447284\pi$
$563$	7.82330	0.329713	0.164856	+	0.986318i	$0.447284\pi$
$564$	0.110761	0.00466386
$565$	3.73688	0.157212
$566$	−11.0245	−0.463395
$567$	−22.6497	−0.951196
$568$	−4.22529	−0.177289
$569$	−19.8229	−0.831018	−0.415509	−	0.909589i	$-0.636396\pi$
$569$	−19.8229	−0.831018	−0.415509	+	0.909589i	$0.636396\pi$
$570$	−7.68074	−0.321711
$571$	15.2280	0.637270	0.318635	−	0.947878i	$-0.396776\pi$
$571$	15.2280	0.637270	0.318635	+	0.947878i	$0.396776\pi$
$572$	−9.05321	−0.378534
$573$	29.4116	1.22869
$574$	−1.44833	−0.0604523
$575$	−4.16980	−0.173892
$576$	4.05806	0.169086
$577$	18.6828	0.777774	0.388887	−	0.921285i	$-0.372860\pi$
$577$	18.6828	0.777774	0.388887	+	0.921285i	$0.372860\pi$
$578$	16.8543	0.701048
$579$	−20.7866	−0.863861
$580$	−0.317348	−0.0131772
$581$	−12.8482	−0.533034
$582$	44.6388	1.85034
$583$	−6.41587	−0.265718
$584$	−3.15283	−0.130465
$585$	−17.9948	−0.743992
$586$	23.2132	0.958928
$587$	20.7063	0.854642	0.427321	−	0.904100i	$-0.359457\pi$
$587$	20.7063	0.854642	0.427321	+	0.904100i	$0.359457\pi$
$588$	42.9345	1.77059
$589$	−13.1907	−0.543514
$590$	8.21684	0.338282
$591$	72.3462	2.97592
$592$	5.44114	0.223630
$593$	9.31876	0.382676	0.191338	−	0.981524i	$-0.438717\pi$
$593$	9.31876	0.382676	0.191338	+	0.981524i	$0.438717\pi$
$594$	5.73885	0.235468
$595$	1.83669	0.0752969
$596$	0.696755	0.0285402
$597$	39.9947	1.63688
$598$	18.4903	0.756123
$599$	5.68171	0.232148	0.116074	−	0.993241i	$-0.462969\pi$
$599$	5.68171	0.232148	0.116074	+	0.993241i	$0.462969\pi$
$600$	−2.65670	−0.108459
$601$	33.0789	1.34932	0.674659	−	0.738130i	$-0.264291\pi$
$601$	33.0789	1.34932	0.674659	+	0.738130i	$0.264291\pi$
$602$	−29.2206	−1.19094
$603$	0.691307	0.0281522
$604$	12.5819	0.511949
$605$	6.83180	0.277752
$606$	−15.2612	−0.619944
$607$	−39.9194	−1.62028	−0.810140	−	0.586236i	$-0.800609\pi$
$607$	−39.9194	−1.62028	−0.810140	+	0.586236i	$0.800609\pi$
$608$	2.89108	0.117249
$609$	4.05747	0.164417
$610$	−3.88226	−0.157188
$611$	0.184872	0.00747912
$612$	−1.54873	−0.0626038
$613$	5.36572	0.216719	0.108360	−	0.994112i	$-0.465440\pi$
$613$	5.36572	0.216719	0.108360	+	0.994112i	$0.465440\pi$
$614$	−12.0514	−0.486356
$615$	−0.799528	−0.0322401
$616$	9.82543	0.395878
$617$	−23.2252	−0.935011	−0.467506	−	0.883990i	$-0.654847\pi$
$617$	−23.2252	−0.935011	−0.467506	+	0.883990i	$0.654847\pi$
$618$	13.9269	0.560224
$619$	−35.5674	−1.42957	−0.714787	−	0.699342i	$-0.753477\pi$
$619$	−35.5674	−1.42957	−0.714787	+	0.699342i	$0.753477\pi$
$620$	−4.56255	−0.183237
$621$	−11.7210	−0.470349
$622$	27.7037	1.11082
$623$	−11.2761	−0.451769
$624$	11.7807	0.471605
$625$	1.00000	0.0400000
$626$	14.0939	0.563304
$627$	15.6811	0.626244
$628$	18.6175	0.742920
$629$	−2.07658	−0.0827987
$630$	19.5297	0.778081
$631$	0.678746	0.0270204	0.0135102	−	0.999909i	$-0.495699\pi$
$631$	0.678746	0.0270204	0.0135102	+	0.999909i	$0.495699\pi$
$632$	−16.1626	−0.642912
$633$	27.0851	1.07653
$634$	−1.27789	−0.0507517
$635$	9.78337	0.388241
$636$	8.34879	0.331051
$637$	71.6625	2.83937
$638$	0.647903	0.0256507
$639$	17.1465	0.678304
$640$	1.00000	0.0395285
$641$	2.18469	0.0862902	0.0431451	−	0.999069i	$-0.486262\pi$
$641$	2.18469	0.0862902	0.0431451	+	0.999069i	$0.486262\pi$
$642$	1.41735	0.0559385
$643$	−12.8277	−0.505874	−0.252937	−	0.967483i	$-0.581397\pi$
$643$	−12.8277	−0.505874	−0.252937	+	0.967483i	$0.581397\pi$
$644$	−20.0674	−0.790768
$645$	−16.1307	−0.635147
$646$	−1.10337	−0.0434113
$647$	21.2547	0.835607	0.417804	−	0.908537i	$-0.362800\pi$
$647$	21.2547	0.835607	0.417804	+	0.908537i	$0.362800\pi$
$648$	4.70635	0.184883
$649$	−16.7756	−0.658501
$650$	−4.43433	−0.173929
$651$	58.3348	2.28632
$652$	−20.9613	−0.820909
$653$	3.00162	0.117462	0.0587312	−	0.998274i	$-0.481295\pi$
$653$	3.00162	0.117462	0.0587312	+	0.998274i	$0.481295\pi$
$654$	8.99371	0.351682
$655$	−6.19415	−0.242025
$656$	0.300948	0.0117500
$657$	12.7943	0.499155
$658$	−0.200641	−0.00782181
$659$	3.53457	0.137687	0.0688437	−	0.997627i	$-0.478069\pi$
$659$	3.53457	0.137687	0.0688437	+	0.997627i	$0.478069\pi$
$660$	5.42396	0.211128
$661$	8.27278	0.321774	0.160887	−	0.986973i	$-0.448565\pi$
$661$	8.27278	0.321774	0.160887	+	0.986973i	$0.448565\pi$
$662$	11.6678	0.453483
$663$	−4.49603	−0.174612
$664$	2.66972	0.103605
$665$	13.9135	0.539544
$666$	−22.0805	−0.855600
$667$	−1.32328	−0.0512374
$668$	−15.3214	−0.592804
$669$	13.3752	0.517114
$670$	0.170354	0.00658136
$671$	7.92608	0.305983
$672$	−12.7856	−0.493214
$673$	−8.93283	−0.344335	−0.172168	−	0.985068i	$-0.555077\pi$
$673$	−8.93283	−0.344335	−0.172168	+	0.985068i	$0.555077\pi$
$674$	−29.3808	−1.13170
$675$	2.81094	0.108193
$676$	6.66332	0.256282
$677$	−26.9074	−1.03413	−0.517067	−	0.855945i	$-0.672976\pi$
$677$	−26.9074	−1.03413	−0.517067	+	0.855945i	$0.672976\pi$
$678$	9.92776	0.381273
$679$	−80.8624	−3.10322
$680$	−0.381644	−0.0146354
$681$	−12.2196	−0.468255
$682$	9.31499	0.356689
$683$	−27.8578	−1.06595	−0.532974	−	0.846131i	$-0.678926\pi$
$683$	−27.8578	−1.06595	−0.532974	+	0.846131i	$0.678926\pi$
$684$	−11.7322	−0.448591
$685$	−3.80332	−0.145318
$686$	−44.0872	−1.68326
$687$	−7.84940	−0.299473
$688$	6.07172	0.231482
$689$	13.9351	0.530884
$690$	−11.0779	−0.421728
$691$	−47.5687	−1.80960	−0.904799	−	0.425840i	$-0.859979\pi$
$691$	−47.5687	−1.80960	−0.904799	+	0.425840i	$0.859979\pi$
$692$	−2.30454	−0.0876056
$693$	−39.8721	−1.51462
$694$	20.2301	0.767923
$695$	19.4350	0.737213
$696$	−0.843098	−0.0319576
$697$	−0.114855	−0.00435044
$698$	24.2774	0.918914
$699$	−54.9144	−2.07705
$700$	4.81257	0.181898
$701$	−7.86710	−0.297136	−0.148568	−	0.988902i	$-0.547466\pi$
$701$	−7.86710	−0.297136	−0.148568	+	0.988902i	$0.547466\pi$
$702$	−12.4646	−0.470447
$703$	−15.7308	−0.593298
$704$	−2.04162	−0.0769463
$705$	−0.110761	−0.00417149
$706$	12.5767	0.473332
$707$	27.6454	1.03971
$708$	21.8297	0.820409
$709$	9.45142	0.354956	0.177478	−	0.984125i	$-0.443206\pi$
$709$	9.45142	0.354956	0.177478	+	0.984125i	$0.443206\pi$
$710$	4.22529	0.158572
$711$	65.5885	2.45976
$712$	2.34306	0.0878099
$713$	−19.0249	−0.712489
$714$	4.87953	0.182612
$715$	9.05321	0.338571
$716$	2.47698	0.0925691
$717$	38.8350	1.45032
$718$	−11.4102	−0.425825
$719$	−35.9809	−1.34186	−0.670931	−	0.741519i	$-0.734106\pi$
$719$	−35.9809	−1.34186	−0.670931	+	0.741519i	$0.734106\pi$
$720$	−4.05806	−0.151235
$721$	−25.2284	−0.939556
$722$	10.6416	0.396040
$723$	11.1650	0.415229
$724$	−11.0443	−0.410458
$725$	0.317348	0.0117860
$726$	18.1500	0.673611
$727$	13.6903	0.507743	0.253872	−	0.967238i	$-0.418296\pi$
$727$	13.6903	0.507743	0.253872	+	0.967238i	$0.418296\pi$
$728$	−21.3405	−0.790933
$729$	−41.5021	−1.53711
$730$	3.15283	0.116691
$731$	−2.31724	−0.0857060
$732$	−10.3140	−0.381216
$733$	−2.29553	−0.0847873	−0.0423936	−	0.999101i	$-0.513498\pi$
$733$	−2.29553	−0.0847873	−0.0423936	+	0.999101i	$0.513498\pi$
$734$	18.0979	0.668005
$735$	−42.9345	−1.58366
$736$	4.16980	0.153701
$737$	−0.347798	−0.0128113
$738$	−1.22126	−0.0449553
$739$	41.8643	1.54000	0.770002	−	0.638042i	$-0.220255\pi$
$739$	41.8643	1.54000	0.770002	+	0.638042i	$0.220255\pi$
$740$	−5.44114	−0.200020
$741$	−34.0590	−1.25119
$742$	−15.1237	−0.555209
$743$	−16.3445	−0.599620	−0.299810	−	0.953999i	$-0.596923\pi$
$743$	−16.3445	−0.599620	−0.299810	+	0.953999i	$0.596923\pi$
$744$	−12.1213	−0.444390
$745$	−0.696755	−0.0255271
$746$	20.9791	0.768098
$747$	−10.8339	−0.396391
$748$	0.779171	0.0284893
$749$	−2.56751	−0.0938149
$750$	2.65670	0.0970090
$751$	−2.27250	−0.0829248	−0.0414624	−	0.999140i	$-0.513202\pi$
$751$	−2.27250	−0.0829248	−0.0414624	+	0.999140i	$0.513202\pi$
$752$	0.0416911	0.00152032
$753$	42.0831	1.53359
$754$	−1.40723	−0.0512482
$755$	−12.5819	−0.457901
$756$	13.5278	0.492002
$757$	−31.7093	−1.15250	−0.576248	−	0.817275i	$-0.695484\pi$
$757$	−31.7093	−1.15250	−0.576248	+	0.817275i	$0.695484\pi$
$758$	30.4908	1.10748
$759$	22.6168	0.820939
$760$	−2.89108	−0.104871
$761$	−27.3555	−0.991637	−0.495818	−	0.868426i	$-0.665132\pi$
$761$	−27.3555	−0.991637	−0.495818	+	0.868426i	$0.665132\pi$
$762$	25.9915	0.941572
$763$	−16.2920	−0.589809
$764$	11.0707	0.400525
$765$	1.54873	0.0559946
$766$	−21.7021	−0.784130
$767$	36.4362	1.31564
$768$	2.65670	0.0958654
$769$	−31.0781	−1.12071	−0.560353	−	0.828254i	$-0.689334\pi$
$769$	−31.0781	−1.12071	−0.560353	+	0.828254i	$0.689334\pi$
$770$	−9.82543	−0.354084
$771$	61.1467	2.20214
$772$	−7.82421	−0.281599
$773$	−18.8195	−0.676892	−0.338446	−	0.940986i	$-0.609901\pi$
$773$	−18.8195	−0.676892	−0.338446	+	0.940986i	$0.609901\pi$
$774$	−24.6394	−0.885644
$775$	4.56255	0.163892
$776$	16.8023	0.603169
$777$	69.5680	2.49574
$778$	−11.5789	−0.415123
$779$	−0.870066	−0.0311733
$780$	−11.7807	−0.421817
$781$	−8.62643	−0.308678
$782$	−1.59138	−0.0569076
$783$	0.892044	0.0318791
$784$	16.1608	0.577173
$785$	−18.6175	−0.664488
$786$	−16.4560	−0.586966
$787$	42.4563	1.51340	0.756702	−	0.653759i	$-0.226809\pi$
$787$	42.4563	1.51340	0.756702	+	0.653759i	$0.226809\pi$
$788$	27.2316	0.970085
$789$	−40.5838	−1.44482
$790$	16.1626	0.575038
$791$	−17.9840	−0.639437
$792$	8.28500	0.294395
$793$	−17.2152	−0.611331
$794$	13.0956	0.464746
$795$	−8.34879	−0.296101
$796$	15.0543	0.533585
$797$	−20.3905	−0.722270	−0.361135	−	0.932514i	$-0.617611\pi$
$797$	−20.3905	−0.722270	−0.361135	+	0.932514i	$0.617611\pi$
$798$	36.9641	1.30852
$799$	−0.0159111	−0.000562896 0
$800$	−1.00000	−0.0353553
$801$	−9.50827	−0.335958
$802$	−1.00000	−0.0353112
$803$	−6.43686	−0.227152
$804$	0.452580	0.0159613
$805$	20.0674	0.707284
$806$	−20.2319	−0.712638
$807$	−54.9501	−1.93433
$808$	−5.74442	−0.202088
$809$	−12.4124	−0.436398	−0.218199	−	0.975904i	$-0.570018\pi$
$809$	−12.4124	−0.436398	−0.218199	+	0.975904i	$0.570018\pi$
$810$	−4.70635	−0.165364
$811$	−33.4835	−1.17576	−0.587882	−	0.808947i	$-0.700038\pi$
$811$	−33.4835	−1.17576	−0.587882	+	0.808947i	$0.700038\pi$
$812$	1.52726	0.0535963
$813$	−66.4682	−2.33114
$814$	11.1087	0.389361
$815$	20.9613	0.734243
$816$	−1.01391	−0.0354941
$817$	−17.5538	−0.614131
$818$	−9.16236	−0.320354
$819$	86.6011	3.02609
$820$	−0.300948	−0.0105096
$821$	10.4485	0.364656	0.182328	−	0.983238i	$-0.441637\pi$
$821$	10.4485	0.364656	0.182328	+	0.983238i	$0.441637\pi$
$822$	−10.1043	−0.352428
$823$	5.10488	0.177945	0.0889725	−	0.996034i	$-0.471642\pi$
$823$	5.10488	0.177945	0.0889725	+	0.996034i	$0.471642\pi$
$824$	5.24220	0.182621
$825$	−5.42396	−0.188838
$826$	−39.5441	−1.37592
$827$	30.4614	1.05925	0.529623	−	0.848233i	$-0.322333\pi$
$827$	30.4614	1.05925	0.529623	+	0.848233i	$0.322333\pi$
$828$	−16.9213	−0.588054
$829$	−54.3293	−1.88693	−0.943467	−	0.331466i	$-0.892457\pi$
$829$	−54.3293	−1.88693	−0.943467	+	0.331466i	$0.892457\pi$
$830$	−2.66972	−0.0926674
$831$	63.8660	2.21549
$832$	4.43433	0.153733
$833$	−6.16769	−0.213698
$834$	51.6331	1.78791
$835$	15.3214	0.530220
$836$	5.90249	0.204142
$837$	12.8250	0.443298
$838$	31.1718	1.07681
$839$	−13.5593	−0.468118	−0.234059	−	0.972222i	$-0.575201\pi$
$839$	−13.5593	−0.468118	−0.234059	+	0.972222i	$0.575201\pi$
$840$	12.7856	0.441144
$841$	−28.8993	−0.996527
$842$	17.6713	0.608992
$843$	32.8656	1.13195
$844$	10.1950	0.350926
$845$	−6.66332	−0.229225
$846$	−0.169185	−0.00581669
$847$	−32.8785	−1.12972
$848$	3.14254	0.107915
$849$	29.2888	1.00519
$850$	0.381644	0.0130903
$851$	−22.6885	−0.777750
$852$	11.2253	0.384574
$853$	14.3008	0.489651	0.244825	−	0.969567i	$-0.421269\pi$
$853$	14.3008	0.489651	0.244825	+	0.969567i	$0.421269\pi$
$854$	18.6836	0.639341
$855$	11.7322	0.401232
$856$	0.533502	0.0182347
$857$	35.2168	1.20298	0.601492	−	0.798879i	$-0.294573\pi$
$857$	35.2168	1.20298	0.601492	+	0.798879i	$0.294573\pi$
$858$	24.0517	0.821111
$859$	0.736389	0.0251253	0.0125626	−	0.999921i	$-0.496001\pi$
$859$	0.736389	0.0251253	0.0125626	+	0.999921i	$0.496001\pi$
$860$	−6.07172	−0.207044
$861$	3.84779	0.131132
$862$	13.2148	0.450097
$863$	−54.2341	−1.84615	−0.923075	−	0.384619i	$-0.874333\pi$
$863$	−54.2341	−1.84615	−0.923075	+	0.384619i	$0.874333\pi$
$864$	−2.81094	−0.0956300
$865$	2.30454	0.0783568
$866$	3.40667	0.115764
$867$	−44.7769	−1.52070
$868$	21.9576	0.745290
$869$	−32.9978	−1.11937
$870$	0.843098	0.0285837
$871$	0.755408	0.0255960
$872$	3.38529	0.114640
$873$	−68.1848	−2.30771
$874$	−12.0552	−0.407774
$875$	−4.81257	−0.162695
$876$	8.37611	0.283003
$877$	−1.78238	−0.0601866	−0.0300933	−	0.999547i	$-0.509580\pi$
$877$	−1.78238	−0.0601866	−0.0300933	+	0.999547i	$0.509580\pi$
$878$	39.5888	1.33606
$879$	−61.6705	−2.08009
$880$	2.04162	0.0688229
$881$	41.2822	1.39083	0.695416	−	0.718607i	$-0.255220\pi$
$881$	41.2822	1.39083	0.695416	+	0.718607i	$0.255220\pi$
$882$	−65.5816	−2.20825
$883$	24.4787	0.823774	0.411887	−	0.911235i	$-0.364870\pi$
$883$	24.4787	0.823774	0.411887	+	0.911235i	$0.364870\pi$
$884$	−1.69234	−0.0569195
$885$	−21.8297	−0.733796
$886$	−1.63215	−0.0548332
$887$	−22.8419	−0.766957	−0.383479	−	0.923550i	$-0.625274\pi$
$887$	−22.8419	−0.766957	−0.383479	+	0.923550i	$0.625274\pi$
$888$	−14.4555	−0.485094
$889$	−47.0832	−1.57912
$890$	−2.34306	−0.0785396
$891$	9.60857	0.321899
$892$	5.03451	0.168568
$893$	−0.120532	−0.00403346
$894$	−1.85107	−0.0619090
$895$	−2.47698	−0.0827963
$896$	−4.81257	−0.160777
$897$	−49.1231	−1.64017
$898$	−21.9388	−0.732108
$899$	1.44792	0.0482907
$900$	4.05806	0.135269
$901$	−1.19933	−0.0399556
$902$	0.614420	0.0204580
$903$	77.6303	2.58337
$904$	3.73688	0.124287
$905$	11.0443	0.367125
$906$	−33.4262	−1.11051
$907$	4.33911	0.144078	0.0720389	−	0.997402i	$-0.477049\pi$
$907$	4.33911	0.144078	0.0720389	+	0.997402i	$0.477049\pi$
$908$	−4.59953	−0.152641
$909$	23.3112	0.773183
$910$	21.3405	0.707432
$911$	−15.3836	−0.509682	−0.254841	−	0.966983i	$-0.582023\pi$
$911$	−15.3836	−0.509682	−0.254841	+	0.966983i	$0.582023\pi$
$912$	−7.68074	−0.254335
$913$	5.45055	0.180387
$914$	−20.9510	−0.692999
$915$	10.3140	0.340970
$916$	−2.95457	−0.0976217
$917$	29.8098	0.984406
$918$	1.07278	0.0354069
$919$	31.7397	1.04700	0.523498	−	0.852027i	$-0.324627\pi$
$919$	31.7397	1.04700	0.523498	+	0.852027i	$0.324627\pi$
$920$	−4.16980	−0.137474
$921$	32.0170	1.05500
$922$	−29.6666	−0.977019
$923$	18.7364	0.616715
$924$	−26.1032	−0.858733
$925$	5.44114	0.178904
$926$	−7.64402	−0.251198
$927$	−21.2731	−0.698701
$928$	−0.317348	−0.0104175
$929$	29.8591	0.979645	0.489823	−	0.871822i	$-0.337062\pi$
$929$	29.8591	0.979645	0.489823	+	0.871822i	$0.337062\pi$
$930$	12.1213	0.397474
$931$	−46.7223	−1.53126
$932$	−20.6701	−0.677073
$933$	−73.6003	−2.40957
$934$	−22.7847	−0.745539
$935$	−0.779171	−0.0254816
$936$	−17.9948	−0.588178
$937$	−14.9921	−0.489769	−0.244885	−	0.969552i	$-0.578750\pi$
$937$	−14.9921	−0.489769	−0.244885	+	0.969552i	$0.578750\pi$
$938$	−0.819842	−0.0267688
$939$	−37.4431	−1.22191
$940$	−0.0416911	−0.00135981
$941$	8.71637	0.284145	0.142073	−	0.989856i	$-0.454623\pi$
$941$	8.71637	0.284145	0.142073	+	0.989856i	$0.454623\pi$
$942$	−49.4612	−1.61153
$943$	−1.25489	−0.0408649
$944$	8.21684	0.267435
$945$	−13.5278	−0.440060
$946$	12.3961	0.403033
$947$	0.424396	0.0137910	0.00689551	−	0.999976i	$-0.497805\pi$
$947$	0.424396	0.0137910	0.00689551	+	0.999976i	$0.497805\pi$
$948$	42.9391	1.39460
$949$	13.9807	0.453832
$950$	2.89108	0.0937992
$951$	3.39498	0.110090
$952$	1.83669	0.0595274
$953$	−28.5097	−0.923519	−0.461759	−	0.887005i	$-0.652782\pi$
$953$	−28.5097	−0.923519	−0.461759	+	0.887005i	$0.652782\pi$
$954$	−12.7526	−0.412881
$955$	−11.0707	−0.358241
$956$	14.6177	0.472772
$957$	−1.72128	−0.0556412
$958$	−18.0667	−0.583707
$959$	18.3038	0.591059
$960$	−2.65670	−0.0857446
$961$	−10.1831	−0.328488
$962$	−24.1278	−0.777913
$963$	−2.16498	−0.0697655
$964$	4.20257	0.135356
$965$	7.82421	0.251870
$966$	53.3132	1.71532
$967$	42.5729	1.36905	0.684526	−	0.728988i	$-0.260009\pi$
$967$	42.5729	1.36905	0.684526	+	0.728988i	$0.260009\pi$
$968$	6.83180	0.219582
$969$	2.93131	0.0941673
$970$	−16.8023	−0.539491
$971$	54.7386	1.75664	0.878322	−	0.478070i	$-0.158663\pi$
$971$	54.7386	1.75664	0.878322	+	0.478070i	$0.158663\pi$
$972$	−20.9362	−0.671528
$973$	−93.5325	−2.99851
$974$	−15.2931	−0.490022
$975$	11.7807	0.377284
$976$	−3.88226	−0.124268
$977$	−11.2191	−0.358932	−0.179466	−	0.983764i	$-0.557437\pi$
$977$	−11.2191	−0.358932	−0.179466	+	0.983764i	$0.557437\pi$
$978$	55.6880	1.78070
$979$	4.78363	0.152886
$980$	−16.1608	−0.516239
$981$	−13.7377	−0.438611
$982$	−29.6400	−0.945851
$983$	47.9574	1.52960	0.764801	−	0.644266i	$-0.222837\pi$
$983$	47.9574	1.52960	0.764801	+	0.644266i	$0.222837\pi$
$984$	−0.799528	−0.0254880
$985$	−27.2316	−0.867671
$986$	0.121114	0.00385705
$987$	0.533043	0.0169670
$988$	−12.8200	−0.407860
$989$	−25.3178	−0.805060
$990$	−8.28500	−0.263314
$991$	−39.2899	−1.24808	−0.624042	−	0.781391i	$-0.714511\pi$
$991$	−39.2899	−1.24808	−0.624042	+	0.781391i	$0.714511\pi$
$992$	−4.56255	−0.144861
$993$	−30.9979	−0.983689
$994$	−20.3345	−0.644972
$995$	−15.0543	−0.477253
$996$	−7.09265	−0.224739
$997$	−13.3335	−0.422277	−0.211138	−	0.977456i	$-0.567717\pi$
$997$	−13.3335	−0.422277	−0.211138	+	0.977456i	$0.567717\pi$
$998$	−8.09763	−0.256326
$999$	15.2947	0.483903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.l.1.15	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.l.1.15	✓	17	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.65670 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.65670 q^{6} +4.81257 q^{7} -1.00000 q^{8} +4.05806 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.65670 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.65670 q^{6} +4.81257 q^{7} -1.00000 q^{8} +4.05806 q^{9} +1.00000 q^{10} -2.04162 q^{11} +2.65670 q^{12} +4.43433 q^{13} -4.81257 q^{14} -2.65670 q^{15} +1.00000 q^{16} -0.381644 q^{17} -4.05806 q^{18} -2.89108 q^{19} -1.00000 q^{20} +12.7856 q^{21} +2.04162 q^{22} -4.16980 q^{23} -2.65670 q^{24} +1.00000 q^{25} -4.43433 q^{26} +2.81094 q^{27} +4.81257 q^{28} +0.317348 q^{29} +2.65670 q^{30} +4.56255 q^{31} -1.00000 q^{32} -5.42396 q^{33} +0.381644 q^{34} -4.81257 q^{35} +4.05806 q^{36} +5.44114 q^{37} +2.89108 q^{38} +11.7807 q^{39} +1.00000 q^{40} +0.300948 q^{41} -12.7856 q^{42} +6.07172 q^{43} -2.04162 q^{44} -4.05806 q^{45} +4.16980 q^{46} +0.0416911 q^{47} +2.65670 q^{48} +16.1608 q^{49} -1.00000 q^{50} -1.01391 q^{51} +4.43433 q^{52} +3.14254 q^{53} -2.81094 q^{54} +2.04162 q^{55} -4.81257 q^{56} -7.68074 q^{57} -0.317348 q^{58} +8.21684 q^{59} -2.65670 q^{60} -3.88226 q^{61} -4.56255 q^{62} +19.5297 q^{63} +1.00000 q^{64} -4.43433 q^{65} +5.42396 q^{66} +0.170354 q^{67} -0.381644 q^{68} -11.0779 q^{69} +4.81257 q^{70} +4.22529 q^{71} -4.05806 q^{72} +3.15283 q^{73} -5.44114 q^{74} +2.65670 q^{75} -2.89108 q^{76} -9.82543 q^{77} -11.7807 q^{78} +16.1626 q^{79} -1.00000 q^{80} -4.70635 q^{81} -0.300948 q^{82} -2.66972 q^{83} +12.7856 q^{84} +0.381644 q^{85} -6.07172 q^{86} +0.843098 q^{87} +2.04162 q^{88} -2.34306 q^{89} +4.05806 q^{90} +21.3405 q^{91} -4.16980 q^{92} +12.1213 q^{93} -0.0416911 q^{94} +2.89108 q^{95} -2.65670 q^{96} -16.8023 q^{97} -16.1608 q^{98} -8.28500 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * q^99

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