LMFDB - Embedded newform 4017.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 4 x^{18} - 16 x^{17} + 77 x^{16} + 88 x^{15} - 594 x^{14} - 154 x^{13} + 2388 x^{12} - 278 x^{11} + \cdots + 4 $ x^19 - 4x^18 - 16x^17 + 77x^16 + 88x^15 - 594x^14 - 154x^13 + 2388x^12 - 278x^11 - 5460x^10 + 1491x^9 + 7285x^8 - 2223x^7 - 5579x^6 + 1430x^5 + 2261x^4 - 352x^3 - 378x^2 + 11x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.75283$ of defining polynomial
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75283 q^{2} +1.00000 q^{3} +5.57808 q^{4} +1.28742 q^{5} -2.75283 q^{6} -1.78893 q^{7} -9.84984 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.75283 q^{2} +1.00000 q^{3} +5.57808 q^{4} +1.28742 q^{5} -2.75283 q^{6} -1.78893 q^{7} -9.84984 q^{8} +1.00000 q^{9} -3.54405 q^{10} -0.289450 q^{11} +5.57808 q^{12} +1.00000 q^{13} +4.92461 q^{14} +1.28742 q^{15} +15.9588 q^{16} +5.29128 q^{17} -2.75283 q^{18} -5.86892 q^{19} +7.18133 q^{20} -1.78893 q^{21} +0.796808 q^{22} -1.13517 q^{23} -9.84984 q^{24} -3.34255 q^{25} -2.75283 q^{26} +1.00000 q^{27} -9.97876 q^{28} +2.66079 q^{29} -3.54405 q^{30} -8.62939 q^{31} -24.2321 q^{32} -0.289450 q^{33} -14.5660 q^{34} -2.30310 q^{35} +5.57808 q^{36} -5.38013 q^{37} +16.1561 q^{38} +1.00000 q^{39} -12.6809 q^{40} +9.25472 q^{41} +4.92461 q^{42} -0.831112 q^{43} -1.61458 q^{44} +1.28742 q^{45} +3.12494 q^{46} -0.285610 q^{47} +15.9588 q^{48} -3.79974 q^{49} +9.20147 q^{50} +5.29128 q^{51} +5.57808 q^{52} -4.15920 q^{53} -2.75283 q^{54} -0.372644 q^{55} +17.6206 q^{56} -5.86892 q^{57} -7.32472 q^{58} +4.54244 q^{59} +7.18133 q^{60} +6.06131 q^{61} +23.7552 q^{62} -1.78893 q^{63} +34.7894 q^{64} +1.28742 q^{65} +0.796808 q^{66} -7.38696 q^{67} +29.5152 q^{68} -1.13517 q^{69} +6.34004 q^{70} -9.83574 q^{71} -9.84984 q^{72} -1.48848 q^{73} +14.8106 q^{74} -3.34255 q^{75} -32.7373 q^{76} +0.517805 q^{77} -2.75283 q^{78} +0.519372 q^{79} +20.5457 q^{80} +1.00000 q^{81} -25.4767 q^{82} -3.12093 q^{83} -9.97876 q^{84} +6.81211 q^{85} +2.28791 q^{86} +2.66079 q^{87} +2.85104 q^{88} +9.14833 q^{89} -3.54405 q^{90} -1.78893 q^{91} -6.33208 q^{92} -8.62939 q^{93} +0.786237 q^{94} -7.55577 q^{95} -24.2321 q^{96} +1.52126 q^{97} +10.4601 q^{98} -0.289450 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) $ 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9} - 6 q^{10} - 15 q^{11} + 10 q^{12} + 19 q^{13} - 4 q^{14} - 3 q^{15} - 4 q^{16} - 4 q^{18} - 32 q^{19} - 8 q^{20} - 23 q^{21} - 9 q^{22} - 23 q^{23} - 9 q^{24} - 8 q^{25} - 4 q^{26} + 19 q^{27} - 22 q^{28} + 4 q^{29} - 6 q^{30} - 50 q^{31} - 2 q^{32} - 15 q^{33} - 35 q^{34} - 4 q^{35} + 10 q^{36} - 38 q^{37} + 20 q^{38} + 19 q^{39} - 30 q^{40} - 11 q^{41} - 4 q^{42} - 17 q^{43} - 29 q^{44} - 3 q^{45} - 5 q^{46} - 38 q^{47} - 4 q^{48} - 6 q^{49} - 9 q^{50} + 10 q^{52} - 12 q^{53} - 4 q^{54} - 22 q^{55} + 12 q^{56} - 32 q^{57} - 23 q^{58} - 8 q^{59} - 8 q^{60} - 31 q^{61} + 31 q^{62} - 23 q^{63} + 15 q^{64} - 3 q^{65} - 9 q^{66} - 48 q^{67} + 44 q^{68} - 23 q^{69} + 13 q^{70} - 14 q^{71} - 9 q^{72} - 50 q^{73} - 10 q^{74} - 8 q^{75} - 64 q^{76} + 23 q^{77} - 4 q^{78} - 21 q^{79} + 8 q^{80} + 19 q^{81} - 10 q^{82} - 15 q^{83} - 22 q^{84} - 29 q^{85} + 9 q^{86} + 4 q^{87} + 3 q^{88} - 10 q^{89} - 6 q^{90} - 23 q^{91} - 17 q^{92} - 50 q^{93} - 22 q^{94} - 25 q^{95} - 2 q^{96} - 42 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9 - 6 * q^10 - 15 * q^11 + 10 * q^12 + 19 * q^13 - 4 * q^14 - 3 * q^15 - 4 * q^16 - 4 * q^18 - 32 * q^19 - 8 * q^20 - 23 * q^21 - 9 * q^22 - 23 * q^23 - 9 * q^24 - 8 * q^25 - 4 * q^26 + 19 * q^27 - 22 * q^28 + 4 * q^29 - 6 * q^30 - 50 * q^31 - 2 * q^32 - 15 * q^33 - 35 * q^34 - 4 * q^35 + 10 * q^36 - 38 * q^37 + 20 * q^38 + 19 * q^39 - 30 * q^40 - 11 * q^41 - 4 * q^42 - 17 * q^43 - 29 * q^44 - 3 * q^45 - 5 * q^46 - 38 * q^47 - 4 * q^48 - 6 * q^49 - 9 * q^50 + 10 * q^52 - 12 * q^53 - 4 * q^54 - 22 * q^55 + 12 * q^56 - 32 * q^57 - 23 * q^58 - 8 * q^59 - 8 * q^60 - 31 * q^61 + 31 * q^62 - 23 * q^63 + 15 * q^64 - 3 * q^65 - 9 * q^66 - 48 * q^67 + 44 * q^68 - 23 * q^69 + 13 * q^70 - 14 * q^71 - 9 * q^72 - 50 * q^73 - 10 * q^74 - 8 * q^75 - 64 * q^76 + 23 * q^77 - 4 * q^78 - 21 * q^79 + 8 * q^80 + 19 * q^81 - 10 * q^82 - 15 * q^83 - 22 * q^84 - 29 * q^85 + 9 * q^86 + 4 * q^87 + 3 * q^88 - 10 * q^89 - 6 * q^90 - 23 * q^91 - 17 * q^92 - 50 * q^93 - 22 * q^94 - 25 * q^95 - 2 * q^96 - 42 * q^97 - q^98 - 15 * 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 $

$2$	−2.75283	−1.94655	−0.973273	−	0.229653i	$-0.926241\pi$
$2$	−2.75283	−1.94655	−0.973273	+	0.229653i	$0.926241\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.57808	2.78904
$5$	1.28742	0.575752	0.287876	−	0.957668i	$-0.407051\pi$
$5$	1.28742	0.575752	0.287876	+	0.957668i	$0.407051\pi$
$6$	−2.75283	−1.12384
$7$	−1.78893	−0.676150	−0.338075	−	0.941119i	$-0.609776\pi$
$7$	−1.78893	−0.676150	−0.338075	+	0.941119i	$0.609776\pi$
$8$	−9.84984	−3.48244
$9$	1.00000	0.333333
$10$	−3.54405	−1.12073
$11$	−0.289450	−0.0872726	−0.0436363	−	0.999047i	$-0.513894\pi$
$11$	−0.289450	−0.0872726	−0.0436363	+	0.999047i	$0.513894\pi$
$12$	5.57808	1.61025
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	4.92461	1.31616
$15$	1.28742	0.332411
$16$	15.9588	3.98969
$17$	5.29128	1.28332	0.641662	−	0.766987i	$-0.278245\pi$
$17$	5.29128	1.28332	0.641662	+	0.766987i	$0.278245\pi$
$18$	−2.75283	−0.648848
$19$	−5.86892	−1.34642	−0.673211	−	0.739450i	$-0.735086\pi$
$19$	−5.86892	−1.34642	−0.673211	+	0.739450i	$0.735086\pi$
$20$	7.18133	1.60579
$21$	−1.78893	−0.390376
$22$	0.796808	0.169880
$23$	−1.13517	−0.236700	−0.118350	−	0.992972i	$-0.537760\pi$
$23$	−1.13517	−0.236700	−0.118350	+	0.992972i	$0.537760\pi$
$24$	−9.84984	−2.01059
$25$	−3.34255	−0.668510
$26$	−2.75283	−0.539874
$27$	1.00000	0.192450
$28$	−9.97876	−1.88581
$29$	2.66079	0.494097	0.247049	−	0.969003i	$-0.420539\pi$
$29$	2.66079	0.494097	0.247049	+	0.969003i	$0.420539\pi$
$30$	−3.54405	−0.647052
$31$	−8.62939	−1.54988	−0.774942	−	0.632032i	$-0.782221\pi$
$31$	−8.62939	−1.54988	−0.774942	+	0.632032i	$0.782221\pi$
$32$	−24.2321	−4.28368
$33$	−0.289450	−0.0503868
$34$	−14.5660	−2.49805
$35$	−2.30310	−0.389295
$36$	5.57808	0.929679
$37$	−5.38013	−0.884488	−0.442244	−	0.896895i	$-0.645817\pi$
$37$	−5.38013	−0.884488	−0.442244	+	0.896895i	$0.645817\pi$
$38$	16.1561	2.62087
$39$	1.00000	0.160128
$40$	−12.6809	−2.00502
$41$	9.25472	1.44534	0.722672	−	0.691191i	$-0.242914\pi$
$41$	9.25472	1.44534	0.722672	+	0.691191i	$0.242914\pi$
$42$	4.92461	0.759884
$43$	−0.831112	−0.126743	−0.0633717	−	0.997990i	$-0.520185\pi$
$43$	−0.831112	−0.126743	−0.0633717	+	0.997990i	$0.520185\pi$
$44$	−1.61458	−0.243406
$45$	1.28742	0.191917
$46$	3.12494	0.460747
$47$	−0.285610	−0.0416606	−0.0208303	−	0.999783i	$-0.506631\pi$
$47$	−0.285610	−0.0416606	−0.0208303	+	0.999783i	$0.506631\pi$
$48$	15.9588	2.30345
$49$	−3.79974	−0.542821
$50$	9.20147	1.30128
$51$	5.29128	0.740928
$52$	5.57808	0.773540
$53$	−4.15920	−0.571310	−0.285655	−	0.958333i	$-0.592211\pi$
$53$	−4.15920	−0.571310	−0.285655	+	0.958333i	$0.592211\pi$
$54$	−2.75283	−0.374613
$55$	−0.372644	−0.0502474
$56$	17.6206	2.35466
$57$	−5.86892	−0.777357
$58$	−7.32472	−0.961783
$59$	4.54244	0.591375	0.295688	−	0.955285i	$-0.404451\pi$
$59$	4.54244	0.591375	0.295688	+	0.955285i	$0.404451\pi$
$60$	7.18133	0.927106
$61$	6.06131	0.776071	0.388035	−	0.921644i	$-0.373154\pi$
$61$	6.06131	0.776071	0.388035	+	0.921644i	$0.373154\pi$
$62$	23.7552	3.01692
$63$	−1.78893	−0.225383
$64$	34.7894	4.34868
$65$	1.28742	0.159685
$66$	0.796808	0.0980802
$67$	−7.38696	−0.902461	−0.451231	−	0.892407i	$-0.649015\pi$
$67$	−7.38696	−0.902461	−0.451231	+	0.892407i	$0.649015\pi$
$68$	29.5152	3.57924
$69$	−1.13517	−0.136659
$70$	6.34004	0.757780
$71$	−9.83574	−1.16729	−0.583644	−	0.812010i	$-0.698373\pi$
$71$	−9.83574	−1.16729	−0.583644	+	0.812010i	$0.698373\pi$
$72$	−9.84984	−1.16081
$73$	−1.48848	−0.174213	−0.0871065	−	0.996199i	$-0.527762\pi$
$73$	−1.48848	−0.174213	−0.0871065	+	0.996199i	$0.527762\pi$
$74$	14.8106	1.72170
$75$	−3.34255	−0.385964
$76$	−32.7373	−3.75522
$77$	0.517805	0.0590094
$78$	−2.75283	−0.311697
$79$	0.519372	0.0584339	0.0292170	−	0.999573i	$-0.490699\pi$
$79$	0.519372	0.0584339	0.0292170	+	0.999573i	$0.490699\pi$
$80$	20.5457	2.29707
$81$	1.00000	0.111111
$82$	−25.4767	−2.81343
$83$	−3.12093	−0.342566	−0.171283	−	0.985222i	$-0.554791\pi$
$83$	−3.12093	−0.342566	−0.171283	+	0.985222i	$0.554791\pi$
$84$	−9.97876	−1.08877
$85$	6.81211	0.738877
$86$	2.28791	0.246712
$87$	2.66079	0.285267
$88$	2.85104	0.303922
$89$	9.14833	0.969721	0.484861	−	0.874591i	$-0.338870\pi$
$89$	9.14833	0.969721	0.484861	+	0.874591i	$0.338870\pi$
$90$	−3.54405	−0.373576
$91$	−1.78893	−0.187530
$92$	−6.33208	−0.660165
$93$	−8.62939	−0.894826
$94$	0.786237	0.0810942
$95$	−7.55577	−0.775206
$96$	−24.2321	−2.47318
$97$	1.52126	0.154460	0.0772301	−	0.997013i	$-0.475392\pi$
$97$	1.52126	0.154460	0.0772301	+	0.997013i	$0.475392\pi$
$98$	10.4601	1.05662
$99$	−0.289450	−0.0290909
$100$	−18.6450	−1.86450
$101$	−10.6569	−1.06040	−0.530199	−	0.847873i	$-0.677883\pi$
$101$	−10.6569	−1.06040	−0.530199	+	0.847873i	$0.677883\pi$
$102$	−14.5660	−1.44225
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−9.84984	−0.965856
$105$	−2.30310	−0.224760
$106$	11.4496	1.11208
$107$	−19.9493	−1.92857	−0.964286	−	0.264864i	$-0.914673\pi$
$107$	−19.9493	−1.92857	−0.964286	+	0.264864i	$0.914673\pi$
$108$	5.57808	0.536751
$109$	11.5808	1.10924	0.554621	−	0.832103i	$-0.312863\pi$
$109$	11.5808	1.10924	0.554621	+	0.832103i	$0.312863\pi$
$110$	1.02583	0.0978087
$111$	−5.38013	−0.510659
$112$	−28.5491	−2.69763
$113$	−18.0523	−1.69821	−0.849107	−	0.528222i	$-0.822859\pi$
$113$	−18.0523	−1.69821	−0.849107	+	0.528222i	$0.822859\pi$
$114$	16.1561	1.51316
$115$	−1.46145	−0.136280
$116$	14.8421	1.37806
$117$	1.00000	0.0924500
$118$	−12.5046	−1.15114
$119$	−9.46571	−0.867720
$120$	−12.6809	−1.15760
$121$	−10.9162	−0.992384
$122$	−16.6857	−1.51066
$123$	9.25472	0.834470
$124$	−48.1354	−4.32269
$125$	−10.7404	−0.960648
$126$	4.92461	0.438719
$127$	7.32026	0.649568	0.324784	−	0.945788i	$-0.394708\pi$
$127$	7.32026	0.649568	0.324784	+	0.945788i	$0.394708\pi$
$128$	−47.3051	−4.18122
$129$	−0.831112	−0.0731753
$130$	−3.54405	−0.310834
$131$	−1.27661	−0.111538	−0.0557691	−	0.998444i	$-0.517761\pi$
$131$	−1.27661	−0.111538	−0.0557691	+	0.998444i	$0.517761\pi$
$132$	−1.61458	−0.140531
$133$	10.4991	0.910384
$134$	20.3351	1.75668
$135$	1.28742	0.110804
$136$	−52.1183	−4.46910
$137$	9.09820	0.777311	0.388656	−	0.921383i	$-0.372940\pi$
$137$	9.09820	0.777311	0.388656	+	0.921383i	$0.372940\pi$
$138$	3.12494	0.266012
$139$	4.39844	0.373071	0.186535	−	0.982448i	$-0.440274\pi$
$139$	4.39844	0.373071	0.186535	+	0.982448i	$0.440274\pi$
$140$	−12.8469	−1.08576
$141$	−0.285610	−0.0240527
$142$	27.0761	2.27218
$143$	−0.289450	−0.0242051
$144$	15.9588	1.32990
$145$	3.42556	0.284477
$146$	4.09752	0.339113
$147$	−3.79974	−0.313398
$148$	−30.0108	−2.46687
$149$	−1.91677	−0.157028	−0.0785141	−	0.996913i	$-0.525018\pi$
$149$	−1.91677	−0.157028	−0.0785141	+	0.996913i	$0.525018\pi$
$150$	9.20147	0.751297
$151$	−7.93813	−0.645996	−0.322998	−	0.946400i	$-0.604691\pi$
$151$	−7.93813	−0.645996	−0.322998	+	0.946400i	$0.604691\pi$
$152$	57.8079	4.68884
$153$	5.29128	0.427775
$154$	−1.42543	−0.114864
$155$	−11.1097	−0.892349
$156$	5.57808	0.446603
$157$	−12.7906	−1.02080	−0.510399	−	0.859938i	$-0.670502\pi$
$157$	−12.7906	−1.02080	−0.510399	+	0.859938i	$0.670502\pi$
$158$	−1.42974	−0.113744
$159$	−4.15920	−0.329846
$160$	−31.1970	−2.46634
$161$	2.03074	0.160045
$162$	−2.75283	−0.216283
$163$	−15.0853	−1.18157	−0.590787	−	0.806827i	$-0.701183\pi$
$163$	−15.0853	−1.18157	−0.590787	+	0.806827i	$0.701183\pi$
$164$	51.6235	4.03112
$165$	−0.372644	−0.0290103
$166$	8.59139	0.666821
$167$	−1.14294	−0.0884431	−0.0442215	−	0.999022i	$-0.514081\pi$
$167$	−1.14294	−0.0884431	−0.0442215	+	0.999022i	$0.514081\pi$
$168$	17.6206	1.35946
$169$	1.00000	0.0769231
$170$	−18.7526	−1.43826
$171$	−5.86892	−0.448808
$172$	−4.63601	−0.353492
$173$	0.964843	0.0733556	0.0366778	−	0.999327i	$-0.488322\pi$
$173$	0.964843	0.0733556	0.0366778	+	0.999327i	$0.488322\pi$
$174$	−7.32472	−0.555285
$175$	5.97957	0.452013
$176$	−4.61927	−0.348191
$177$	4.54244	0.341431
$178$	−25.1838	−1.88761
$179$	16.7175	1.24953	0.624763	−	0.780814i	$-0.285195\pi$
$179$	16.7175	1.24953	0.624763	+	0.780814i	$0.285195\pi$
$180$	7.18133	0.535265
$181$	23.6840	1.76042	0.880208	−	0.474588i	$-0.157403\pi$
$181$	23.6840	1.76042	0.880208	+	0.474588i	$0.157403\pi$
$182$	4.92461	0.365036
$183$	6.06131	0.448065
$184$	11.1813	0.824294
$185$	−6.92649	−0.509246
$186$	23.7552	1.74182
$187$	−1.53156	−0.111999
$188$	−1.59316	−0.116193
$189$	−1.78893	−0.130125
$190$	20.7998	1.50897
$191$	4.70956	0.340772	0.170386	−	0.985377i	$-0.445499\pi$
$191$	4.70956	0.340772	0.170386	+	0.985377i	$0.445499\pi$
$192$	34.7894	2.51071
$193$	−3.21315	−0.231288	−0.115644	−	0.993291i	$-0.536893\pi$
$193$	−3.21315	−0.231288	−0.115644	+	0.993291i	$0.536893\pi$
$194$	−4.18776	−0.300664
$195$	1.28742	0.0921941
$196$	−21.1953	−1.51395
$197$	−2.36479	−0.168484	−0.0842421	−	0.996445i	$-0.526847\pi$
$197$	−2.36479	−0.168484	−0.0842421	+	0.996445i	$0.526847\pi$
$198$	0.796808	0.0566267
$199$	−25.3094	−1.79413	−0.897067	−	0.441894i	$-0.854307\pi$
$199$	−25.3094	−1.79413	−0.897067	+	0.441894i	$0.854307\pi$
$200$	32.9235	2.32805
$201$	−7.38696	−0.521036
$202$	29.3365	2.06411
$203$	−4.75996	−0.334084
$204$	29.5152	2.06648
$205$	11.9147	0.832160
$206$	2.75283	0.191799
$207$	−1.13517	−0.0789000
$208$	15.9588	1.10654
$209$	1.69876	0.117506
$210$	6.34004	0.437505
$211$	−3.64888	−0.251199	−0.125600	−	0.992081i	$-0.540086\pi$
$211$	−3.64888	−0.251199	−0.125600	+	0.992081i	$0.540086\pi$
$212$	−23.2003	−1.59340
$213$	−9.83574	−0.673934
$214$	54.9170	3.75405
$215$	−1.06999	−0.0729728
$216$	−9.84984	−0.670196
$217$	15.4373	1.04795
$218$	−31.8801	−2.15919
$219$	−1.48848	−0.100582
$220$	−2.07864	−0.140142
$221$	5.29128	0.355930
$222$	14.8106	0.994021
$223$	−11.4360	−0.765813	−0.382907	−	0.923787i	$-0.625077\pi$
$223$	−11.4360	−0.765813	−0.382907	+	0.923787i	$0.625077\pi$
$224$	43.3495	2.89641
$225$	−3.34255	−0.222837
$226$	49.6948	3.30565
$227$	28.4530	1.88849	0.944247	−	0.329237i	$-0.106791\pi$
$227$	28.4530	1.88849	0.944247	+	0.329237i	$0.106791\pi$
$228$	−32.7373	−2.16808
$229$	−11.9598	−0.790323	−0.395161	−	0.918612i	$-0.629311\pi$
$229$	−11.9598	−0.790323	−0.395161	+	0.918612i	$0.629311\pi$
$230$	4.02311	0.265276
$231$	0.517805	0.0340691
$232$	−26.2084	−1.72067
$233$	24.0160	1.57334	0.786672	−	0.617372i	$-0.211803\pi$
$233$	24.0160	1.57334	0.786672	+	0.617372i	$0.211803\pi$
$234$	−2.75283	−0.179958
$235$	−0.367701	−0.0239862
$236$	25.3381	1.64937
$237$	0.519372	0.0337369
$238$	26.0575	1.68906
$239$	−7.76236	−0.502105	−0.251053	−	0.967973i	$-0.580777\pi$
$239$	−7.76236	−0.502105	−0.251053	+	0.967973i	$0.580777\pi$
$240$	20.5457	1.32622
$241$	7.24699	0.466819	0.233410	−	0.972378i	$-0.425012\pi$
$241$	7.24699	0.466819	0.233410	+	0.972378i	$0.425012\pi$
$242$	30.0505	1.93172
$243$	1.00000	0.0641500
$244$	33.8104	2.16449
$245$	−4.89187	−0.312530
$246$	−25.4767	−1.62433
$247$	−5.86892	−0.373430
$248$	84.9981	5.39738
$249$	−3.12093	−0.197781
$250$	29.5664	1.86994
$251$	−18.1895	−1.14811	−0.574057	−	0.818815i	$-0.694631\pi$
$251$	−18.1895	−1.14811	−0.574057	+	0.818815i	$0.694631\pi$
$252$	−9.97876	−0.628603
$253$	0.328576	0.0206574
$254$	−20.1514	−1.26441
$255$	6.81211	0.426591
$256$	60.6440	3.79025
$257$	−9.58280	−0.597759	−0.298879	−	0.954291i	$-0.596613\pi$
$257$	−9.58280	−0.597759	−0.298879	+	0.954291i	$0.596613\pi$
$258$	2.28791	0.142439
$259$	9.62465	0.598047
$260$	7.18133	0.445367
$261$	2.66079	0.164699
$262$	3.51430	0.217114
$263$	−1.63199	−0.100633	−0.0503165	−	0.998733i	$-0.516023\pi$
$263$	−1.63199	−0.100633	−0.0503165	+	0.998733i	$0.516023\pi$
$264$	2.85104	0.175469
$265$	−5.35464	−0.328933
$266$	−28.9021	−1.77210
$267$	9.14833	0.559869
$268$	−41.2050	−2.51700
$269$	−5.96833	−0.363895	−0.181948	−	0.983308i	$-0.558240\pi$
$269$	−5.96833	−0.363895	−0.181948	+	0.983308i	$0.558240\pi$
$270$	−3.54405	−0.215684
$271$	10.5959	0.643653	0.321827	−	0.946799i	$-0.395703\pi$
$271$	10.5959	0.643653	0.321827	+	0.946799i	$0.395703\pi$
$272$	84.4424	5.12007
$273$	−1.78893	−0.108271
$274$	−25.0458	−1.51307
$275$	0.967502	0.0583425
$276$	−6.33208	−0.381146
$277$	−25.6970	−1.54398	−0.771990	−	0.635634i	$-0.780739\pi$
$277$	−25.6970	−1.54398	−0.771990	+	0.635634i	$0.780739\pi$
$278$	−12.1082	−0.726199
$279$	−8.62939	−0.516628
$280$	22.6852	1.35570
$281$	−0.917972	−0.0547616	−0.0273808	−	0.999625i	$-0.508717\pi$
$281$	−0.917972	−0.0547616	−0.0273808	+	0.999625i	$0.508717\pi$
$282$	0.786237	0.0468197
$283$	−16.8783	−1.00331	−0.501656	−	0.865067i	$-0.667276\pi$
$283$	−16.8783	−1.00331	−0.501656	+	0.865067i	$0.667276\pi$
$284$	−54.8645	−3.25561
$285$	−7.55577	−0.447565
$286$	0.796808	0.0471162
$287$	−16.5560	−0.977270
$288$	−24.2321	−1.42789
$289$	10.9977	0.646922
$290$	−9.42999	−0.553748
$291$	1.52126	0.0891777
$292$	−8.30283	−0.485886
$293$	1.08094	0.0631492	0.0315746	−	0.999501i	$-0.489948\pi$
$293$	1.08094	0.0631492	0.0315746	+	0.999501i	$0.489948\pi$
$294$	10.4601	0.610043
$295$	5.84803	0.340485
$296$	52.9934	3.08018
$297$	−0.289450	−0.0167956
$298$	5.27655	0.305662
$299$	−1.13517	−0.0656487
$300$	−18.6450	−1.07647
$301$	1.48680	0.0856976
$302$	21.8523	1.25746
$303$	−10.6569	−0.612221
$304$	−93.6608	−5.37181
$305$	7.80345	0.446824
$306$	−14.5660	−0.832683
$307$	−27.1033	−1.54687	−0.773433	−	0.633878i	$-0.781462\pi$
$307$	−27.1033	−1.54687	−0.773433	+	0.633878i	$0.781462\pi$
$308$	2.88836	0.164579
$309$	−1.00000	−0.0568880
$310$	30.5830	1.73700
$311$	−10.0121	−0.567735	−0.283867	−	0.958864i	$-0.591618\pi$
$311$	−10.0121	−0.567735	−0.283867	+	0.958864i	$0.591618\pi$
$312$	−9.84984	−0.557637
$313$	−0.913735	−0.0516473	−0.0258237	−	0.999667i	$-0.508221\pi$
$313$	−0.913735	−0.0516473	−0.0258237	+	0.999667i	$0.508221\pi$
$314$	35.2102	1.98703
$315$	−2.30310	−0.129765
$316$	2.89710	0.162974
$317$	15.6162	0.877093	0.438547	−	0.898708i	$-0.355493\pi$
$317$	15.6162	0.877093	0.438547	+	0.898708i	$0.355493\pi$
$318$	11.4496	0.642060
$319$	−0.770168	−0.0431211
$320$	44.7886	2.50376
$321$	−19.9493	−1.11346
$322$	−5.59028	−0.311534
$323$	−31.0541	−1.72790
$324$	5.57808	0.309893
$325$	−3.34255	−0.185411
$326$	41.5274	2.29999
$327$	11.5808	0.640421
$328$	−91.1574	−5.03333
$329$	0.510936	0.0281688
$330$	1.02583	0.0564699
$331$	12.3064	0.676418	0.338209	−	0.941071i	$-0.390179\pi$
$331$	12.3064	0.676418	0.338209	+	0.941071i	$0.390179\pi$
$332$	−17.4088	−0.955431
$333$	−5.38013	−0.294829
$334$	3.14631	0.172158
$335$	−9.51013	−0.519594
$336$	−28.5491	−1.55748
$337$	29.0406	1.58194	0.790972	−	0.611852i	$-0.209575\pi$
$337$	29.0406	1.58194	0.790972	+	0.611852i	$0.209575\pi$
$338$	−2.75283	−0.149734
$339$	−18.0523	−0.980464
$340$	37.9984	2.06076
$341$	2.49778	0.135262
$342$	16.1561	0.873624
$343$	19.3199	1.04318
$344$	8.18632	0.441377
$345$	−1.46145	−0.0786816
$346$	−2.65605	−0.142790
$347$	−8.72970	−0.468635	−0.234317	−	0.972160i	$-0.575286\pi$
$347$	−8.72970	−0.468635	−0.234317	+	0.972160i	$0.575286\pi$
$348$	14.8421	0.795621
$349$	−1.51371	−0.0810268	−0.0405134	−	0.999179i	$-0.512899\pi$
$349$	−1.51371	−0.0810268	−0.0405134	+	0.999179i	$0.512899\pi$
$350$	−16.4607	−0.879864
$351$	1.00000	0.0533761
$352$	7.01400	0.373847
$353$	−20.7445	−1.10412	−0.552059	−	0.833805i	$-0.686158\pi$
$353$	−20.7445	−1.10412	−0.552059	+	0.833805i	$0.686158\pi$
$354$	−12.5046	−0.664610
$355$	−12.6627	−0.672068
$356$	51.0301	2.70459
$357$	−9.46571	−0.500979
$358$	−46.0205	−2.43226
$359$	35.4900	1.87309	0.936546	−	0.350545i	$-0.114004\pi$
$359$	35.4900	1.87309	0.936546	+	0.350545i	$0.114004\pi$
$360$	−12.6809	−0.668341
$361$	15.4442	0.812854
$362$	−65.1980	−3.42673
$363$	−10.9162	−0.572953
$364$	−9.97876	−0.523029
$365$	−1.91629	−0.100303
$366$	−16.6857	−0.872178
$367$	−5.19516	−0.271185	−0.135592	−	0.990765i	$-0.543294\pi$
$367$	−5.19516	−0.271185	−0.135592	+	0.990765i	$0.543294\pi$
$368$	−18.1160	−0.944360
$369$	9.25472	0.481781
$370$	19.0675	0.991270
$371$	7.44050	0.386291
$372$	−48.1354	−2.49570
$373$	10.6552	0.551703	0.275852	−	0.961200i	$-0.411040\pi$
$373$	10.6552	0.551703	0.275852	+	0.961200i	$0.411040\pi$
$374$	4.21613	0.218011
$375$	−10.7404	−0.554630
$376$	2.81322	0.145081
$377$	2.66079	0.137038
$378$	4.92461	0.253295
$379$	27.7146	1.42360	0.711802	−	0.702380i	$-0.247879\pi$
$379$	27.7146	1.42360	0.711802	+	0.702380i	$0.247879\pi$
$380$	−42.1466	−2.16208
$381$	7.32026	0.375028
$382$	−12.9646	−0.663327
$383$	−16.0396	−0.819587	−0.409793	−	0.912178i	$-0.634399\pi$
$383$	−16.0396	−0.819587	−0.409793	+	0.912178i	$0.634399\pi$
$384$	−47.3051	−2.41403
$385$	0.666633	0.0339748
$386$	8.84526	0.450212
$387$	−0.831112	−0.0422478
$388$	8.48569	0.430795
$389$	−2.94117	−0.149123	−0.0745616	−	0.997216i	$-0.523756\pi$
$389$	−2.94117	−0.149123	−0.0745616	+	0.997216i	$0.523756\pi$
$390$	−3.54405	−0.179460
$391$	−6.00652	−0.303763
$392$	37.4269	1.89034
$393$	−1.27661	−0.0643966
$394$	6.50986	0.327962
$395$	0.668651	0.0336435
$396$	−1.61458	−0.0811355
$397$	−6.57864	−0.330173	−0.165086	−	0.986279i	$-0.552790\pi$
$397$	−6.57864	−0.330173	−0.165086	+	0.986279i	$0.552790\pi$
$398$	69.6724	3.49236
$399$	10.4991	0.525611
$400$	−53.3430	−2.66715
$401$	14.0519	0.701720	0.350860	−	0.936428i	$-0.385889\pi$
$401$	14.0519	0.701720	0.350860	+	0.936428i	$0.385889\pi$
$402$	20.3351	1.01422
$403$	−8.62939	−0.429861
$404$	−59.4448	−2.95749
$405$	1.28742	0.0639724
$406$	13.1034	0.650310
$407$	1.55728	0.0771915
$408$	−52.1183	−2.58024
$409$	−25.6950	−1.27054	−0.635269	−	0.772291i	$-0.719111\pi$
$409$	−25.6950	−1.27054	−0.635269	+	0.772291i	$0.719111\pi$
$410$	−32.7992	−1.61984
$411$	9.09820	0.448781
$412$	−5.57808	−0.274812
$413$	−8.12609	−0.399859
$414$	3.12494	0.153582
$415$	−4.01795	−0.197233
$416$	−24.2321	−1.18808
$417$	4.39844	0.215392
$418$	−4.67640	−0.228730
$419$	24.4197	1.19298	0.596489	−	0.802621i	$-0.296562\pi$
$419$	24.4197	1.19298	0.596489	+	0.802621i	$0.296562\pi$
$420$	−12.8469	−0.626863
$421$	18.1993	0.886979	0.443490	−	0.896280i	$-0.353740\pi$
$421$	18.1993	0.886979	0.443490	+	0.896280i	$0.353740\pi$
$422$	10.0448	0.488971
$423$	−0.285610	−0.0138869
$424$	40.9674	1.98955
$425$	−17.6864	−0.857915
$426$	27.0761	1.31184
$427$	−10.8432	−0.524741
$428$	−111.279	−5.37886
$429$	−0.289450	−0.0139748
$430$	2.94550	0.142045
$431$	−32.8172	−1.58075	−0.790375	−	0.612623i	$-0.790114\pi$
$431$	−32.8172	−1.58075	−0.790375	+	0.612623i	$0.790114\pi$
$432$	15.9588	0.767817
$433$	−5.59447	−0.268853	−0.134427	−	0.990924i	$-0.542919\pi$
$433$	−5.59447	−0.268853	−0.134427	+	0.990924i	$0.542919\pi$
$434$	−42.4964	−2.03989
$435$	3.42556	0.164243
$436$	64.5988	3.09372
$437$	6.66224	0.318698
$438$	4.09752	0.195787
$439$	−8.53101	−0.407163	−0.203582	−	0.979058i	$-0.565258\pi$
$439$	−8.53101	−0.407163	−0.203582	+	0.979058i	$0.565258\pi$
$440$	3.67049	0.174984
$441$	−3.79974	−0.180940
$442$	−14.5660	−0.692834
$443$	−7.49773	−0.356228	−0.178114	−	0.984010i	$-0.557000\pi$
$443$	−7.49773	−0.356228	−0.178114	+	0.984010i	$0.557000\pi$
$444$	−30.0108	−1.42425
$445$	11.7778	0.558319
$446$	31.4815	1.49069
$447$	−1.91677	−0.0906602
$448$	−62.2357	−2.94036
$449$	4.80825	0.226915	0.113458	−	0.993543i	$-0.463807\pi$
$449$	4.80825	0.226915	0.113458	+	0.993543i	$0.463807\pi$
$450$	9.20147	0.433761
$451$	−2.67878	−0.126139
$452$	−100.697	−4.73638
$453$	−7.93813	−0.372966
$454$	−78.3264	−3.67604
$455$	−2.30310	−0.107971
$456$	57.8079	2.70710
$457$	−38.1175	−1.78306	−0.891531	−	0.452960i	$-0.850368\pi$
$457$	−38.1175	−1.78306	−0.891531	+	0.452960i	$0.850368\pi$
$458$	32.9232	1.53840
$459$	5.29128	0.246976
$460$	−8.15205	−0.380091
$461$	−37.8304	−1.76194	−0.880969	−	0.473174i	$-0.843108\pi$
$461$	−37.8304	−1.76194	−0.880969	+	0.473174i	$0.843108\pi$
$462$	−1.42543	−0.0663170
$463$	−35.7492	−1.66141	−0.830703	−	0.556716i	$-0.812061\pi$
$463$	−35.7492	−1.66141	−0.830703	+	0.556716i	$0.812061\pi$
$464$	42.4630	1.97130
$465$	−11.1097	−0.515198
$466$	−66.1121	−3.06258
$467$	−10.6844	−0.494416	−0.247208	−	0.968962i	$-0.579513\pi$
$467$	−10.6844	−0.494416	−0.247208	+	0.968962i	$0.579513\pi$
$468$	5.57808	0.257847
$469$	13.2147	0.610199
$470$	1.01222	0.0466901
$471$	−12.7906	−0.589358
$472$	−44.7423	−2.05943
$473$	0.240566	0.0110612
$474$	−1.42974	−0.0656703
$475$	19.6171	0.900096
$476$	−52.8005	−2.42010
$477$	−4.15920	−0.190437
$478$	21.3684	0.977370
$479$	15.3005	0.699097	0.349548	−	0.936918i	$-0.386335\pi$
$479$	15.3005	0.699097	0.349548	+	0.936918i	$0.386335\pi$
$480$	−31.1970	−1.42394
$481$	−5.38013	−0.245313
$482$	−19.9497	−0.908685
$483$	2.03074	0.0924019
$484$	−60.8915	−2.76780
$485$	1.95850	0.0889308
$486$	−2.75283	−0.124871
$487$	−12.3808	−0.561028	−0.280514	−	0.959850i	$-0.590505\pi$
$487$	−12.3808	−0.561028	−0.280514	+	0.959850i	$0.590505\pi$
$488$	−59.7029	−2.70262
$489$	−15.0853	−0.682182
$490$	13.4665	0.608354
$491$	16.4384	0.741853	0.370926	−	0.928662i	$-0.379040\pi$
$491$	16.4384	0.741853	0.370926	+	0.928662i	$0.379040\pi$
$492$	51.6235	2.32737
$493$	14.0790	0.634087
$494$	16.1561	0.726899
$495$	−0.372644	−0.0167491
$496$	−137.714	−6.18356
$497$	17.5954	0.789262
$498$	8.59139	0.384989
$499$	15.0579	0.674086	0.337043	−	0.941489i	$-0.390573\pi$
$499$	15.0579	0.674086	0.337043	+	0.941489i	$0.390573\pi$
$500$	−59.9106	−2.67928
$501$	−1.14294	−0.0510626
$502$	50.0727	2.23486
$503$	−17.1417	−0.764310	−0.382155	−	0.924098i	$-0.624818\pi$
$503$	−17.1417	−0.764310	−0.382155	+	0.924098i	$0.624818\pi$
$504$	17.6206	0.784885
$505$	−13.7199	−0.610526
$506$	−0.904515	−0.0402106
$507$	1.00000	0.0444116
$508$	40.8329	1.81167
$509$	−11.2948	−0.500632	−0.250316	−	0.968164i	$-0.580535\pi$
$509$	−11.2948	−0.500632	−0.250316	+	0.968164i	$0.580535\pi$
$510$	−18.7526	−0.830378
$511$	2.66277	0.117794
$512$	−72.3326	−3.19668
$513$	−5.86892	−0.259119
$514$	26.3798	1.16356
$515$	−1.28742	−0.0567305
$516$	−4.63601	−0.204089
$517$	0.0826700	0.00363582
$518$	−26.4950	−1.16412
$519$	0.964843	0.0423519
$520$	−12.6809	−0.556093
$521$	30.7369	1.34661	0.673304	−	0.739366i	$-0.264875\pi$
$521$	30.7369	1.34661	0.673304	+	0.739366i	$0.264875\pi$
$522$	−7.32472	−0.320594
$523$	3.28355	0.143580	0.0717899	−	0.997420i	$-0.477129\pi$
$523$	3.28355	0.143580	0.0717899	+	0.997420i	$0.477129\pi$
$524$	−7.12105	−0.311084
$525$	5.97957	0.260970
$526$	4.49260	0.195887
$527$	−45.6605	−1.98900
$528$	−4.61927	−0.201028
$529$	−21.7114	−0.943973
$530$	14.7404	0.640283
$531$	4.54244	0.197125
$532$	58.5646	2.53910
$533$	9.25472	0.400866
$534$	−25.1838	−1.08981
$535$	−25.6831	−1.11038
$536$	72.7604	3.14277
$537$	16.7175	0.721415
$538$	16.4298	0.708339
$539$	1.09984	0.0473733
$540$	7.18133	0.309035
$541$	34.4301	1.48026	0.740132	−	0.672462i	$-0.234763\pi$
$541$	34.4301	1.48026	0.740132	+	0.672462i	$0.234763\pi$
$542$	−29.1686	−1.25290
$543$	23.6840	1.01638
$544$	−128.219	−5.49735
$545$	14.9094	0.638649
$546$	4.92461	0.210754
$547$	24.9046	1.06485	0.532423	−	0.846478i	$-0.321282\pi$
$547$	24.9046	1.06485	0.532423	+	0.846478i	$0.321282\pi$
$548$	50.7504	2.16795
$549$	6.06131	0.258690
$550$	−2.66337	−0.113566
$551$	−15.6160	−0.665264
$552$	11.1813	0.475906
$553$	−0.929118	−0.0395101
$554$	70.7394	3.00543
$555$	−6.92649	−0.294013
$556$	24.5348	1.04051
$557$	−33.3900	−1.41478	−0.707390	−	0.706823i	$-0.750128\pi$
$557$	−33.3900	−1.41478	−0.707390	+	0.706823i	$0.750128\pi$
$558$	23.7552	1.00564
$559$	−0.831112	−0.0351523
$560$	−36.7547	−1.55317
$561$	−1.53156	−0.0646627
$562$	2.52702	0.106596
$563$	−32.0248	−1.34968	−0.674842	−	0.737962i	$-0.735788\pi$
$563$	−32.0248	−1.34968	−0.674842	+	0.737962i	$0.735788\pi$
$564$	−1.59316	−0.0670840
$565$	−23.2408	−0.977750
$566$	46.4632	1.95299
$567$	−1.78893	−0.0751278
$568$	96.8804	4.06501
$569$	20.6915	0.867434	0.433717	−	0.901049i	$-0.357202\pi$
$569$	20.6915	0.867434	0.433717	+	0.901049i	$0.357202\pi$
$570$	20.7998	0.871206
$571$	36.8334	1.54143	0.770714	−	0.637181i	$-0.219900\pi$
$571$	36.8334	1.54143	0.770714	+	0.637181i	$0.219900\pi$
$572$	−1.61458	−0.0675088
$573$	4.70956	0.196745
$574$	45.5759	1.90230
$575$	3.79437	0.158236
$576$	34.7894	1.44956
$577$	−7.36515	−0.306615	−0.153308	−	0.988179i	$-0.548993\pi$
$577$	−7.36515	−0.306615	−0.153308	+	0.988179i	$0.548993\pi$
$578$	−30.2747	−1.25926
$579$	−3.21315	−0.133534
$580$	19.1080	0.793418
$581$	5.58311	0.231626
$582$	−4.18776	−0.173588
$583$	1.20388	0.0498597
$584$	14.6612	0.606687
$585$	1.28742	0.0532283
$586$	−2.97565	−0.122923
$587$	−3.03156	−0.125126	−0.0625630	−	0.998041i	$-0.519927\pi$
$587$	−3.03156	−0.125126	−0.0625630	+	0.998041i	$0.519927\pi$
$588$	−21.1953	−0.874078
$589$	50.6452	2.08680
$590$	−16.0986	−0.662770
$591$	−2.36479	−0.0972744
$592$	−85.8603	−3.52884
$593$	40.9172	1.68027	0.840135	−	0.542378i	$-0.182476\pi$
$593$	40.9172	1.68027	0.840135	+	0.542378i	$0.182476\pi$
$594$	0.796808	0.0326934
$595$	−12.1864	−0.499592
$596$	−10.6919	−0.437957
$597$	−25.3094	−1.03584
$598$	3.12494	0.127788
$599$	−17.0092	−0.694978	−0.347489	−	0.937684i	$-0.612966\pi$
$599$	−17.0092	−0.694978	−0.347489	+	0.937684i	$0.612966\pi$
$600$	32.9235	1.34410
$601$	−36.9010	−1.50522	−0.752612	−	0.658464i	$-0.771206\pi$
$601$	−36.9010	−1.50522	−0.752612	+	0.658464i	$0.771206\pi$
$602$	−4.09290	−0.166814
$603$	−7.38696	−0.300820
$604$	−44.2795	−1.80171
$605$	−14.0538	−0.571367
$606$	29.3365	1.19172
$607$	−8.63909	−0.350650	−0.175325	−	0.984511i	$-0.556098\pi$
$607$	−8.63909	−0.350650	−0.175325	+	0.984511i	$0.556098\pi$
$608$	142.216	5.76764
$609$	−4.75996	−0.192884
$610$	−21.4816	−0.869764
$611$	−0.285610	−0.0115546
$612$	29.5152	1.19308
$613$	−34.4056	−1.38963	−0.694815	−	0.719188i	$-0.744514\pi$
$613$	−34.4056	−1.38963	−0.694815	+	0.719188i	$0.744514\pi$
$614$	74.6108	3.01105
$615$	11.9147	0.480448
$616$	−5.10030	−0.205497
$617$	−45.7501	−1.84183	−0.920915	−	0.389763i	$-0.872557\pi$
$617$	−45.7501	−1.84183	−0.920915	+	0.389763i	$0.872557\pi$
$618$	2.75283	0.110735
$619$	−35.0807	−1.41001	−0.705006	−	0.709201i	$-0.749056\pi$
$619$	−35.0807	−1.41001	−0.705006	+	0.709201i	$0.749056\pi$
$620$	−61.9705	−2.48879
$621$	−1.13517	−0.0455529
$622$	27.5616	1.10512
$623$	−16.3657	−0.655677
$624$	15.9588	0.638862
$625$	2.88537	0.115415
$626$	2.51536	0.100534
$627$	1.69876	0.0678420
$628$	−71.3467	−2.84704
$629$	−28.4678	−1.13508
$630$	6.34004	0.252593
$631$	33.1010	1.31773	0.658864	−	0.752262i	$-0.271037\pi$
$631$	33.1010	1.31773	0.658864	+	0.752262i	$0.271037\pi$
$632$	−5.11573	−0.203493
$633$	−3.64888	−0.145030
$634$	−42.9888	−1.70730
$635$	9.42425	0.373990
$636$	−23.2003	−0.919953
$637$	−3.79974	−0.150551
$638$	2.12014	0.0839372
$639$	−9.83574	−0.389096
$640$	−60.9015	−2.40734
$641$	−46.4782	−1.83578	−0.917890	−	0.396836i	$-0.870108\pi$
$641$	−46.4782	−1.83578	−0.917890	+	0.396836i	$0.870108\pi$
$642$	54.9170	2.16740
$643$	−31.4801	−1.24145	−0.620726	−	0.784027i	$-0.713162\pi$
$643$	−31.4801	−1.24145	−0.620726	+	0.784027i	$0.713162\pi$
$644$	11.3276	0.446371
$645$	−1.06999	−0.0421308
$646$	85.4867	3.36343
$647$	5.73757	0.225567	0.112784	−	0.993620i	$-0.464023\pi$
$647$	5.73757	0.225567	0.112784	+	0.993620i	$0.464023\pi$
$648$	−9.84984	−0.386938
$649$	−1.31481	−0.0516108
$650$	9.20147	0.360911
$651$	15.4373	0.605037
$652$	−84.1471	−3.29546
$653$	37.8750	1.48216	0.741082	−	0.671415i	$-0.234313\pi$
$653$	37.8750	1.48216	0.741082	+	0.671415i	$0.234313\pi$
$654$	−31.8801	−1.24661
$655$	−1.64354	−0.0642184
$656$	147.694	5.76648
$657$	−1.48848	−0.0580710
$658$	−1.40652	−0.0548318
$659$	−16.9482	−0.660209	−0.330104	−	0.943944i	$-0.607084\pi$
$659$	−16.9482	−0.660209	−0.330104	+	0.943944i	$0.607084\pi$
$660$	−2.07864	−0.0809109
$661$	12.4209	0.483116	0.241558	−	0.970386i	$-0.422342\pi$
$661$	12.4209	0.483116	0.241558	+	0.970386i	$0.422342\pi$
$662$	−33.8773	−1.31668
$663$	5.29128	0.205496
$664$	30.7406	1.19297
$665$	13.5167	0.524156
$666$	14.8106	0.573898
$667$	−3.02046	−0.116953
$668$	−6.37539	−0.246671
$669$	−11.4360	−0.442143
$670$	26.1798	1.01141
$671$	−1.75445	−0.0677297
$672$	43.3495	1.67224
$673$	18.4413	0.710861	0.355430	−	0.934703i	$-0.384334\pi$
$673$	18.4413	0.710861	0.355430	+	0.934703i	$0.384334\pi$
$674$	−79.9440	−3.07933
$675$	−3.34255	−0.128655
$676$	5.57808	0.214541
$677$	−15.3425	−0.589661	−0.294830	−	0.955550i	$-0.595263\pi$
$677$	−15.3425	−0.589661	−0.294830	+	0.955550i	$0.595263\pi$
$678$	49.6948	1.90852
$679$	−2.72142	−0.104438
$680$	−67.0981	−2.57310
$681$	28.4530	1.09032
$682$	−6.87596	−0.263294
$683$	20.1114	0.769543	0.384771	−	0.923012i	$-0.374280\pi$
$683$	20.1114	0.769543	0.384771	+	0.923012i	$0.374280\pi$
$684$	−32.7373	−1.25174
$685$	11.7132	0.447539
$686$	−53.1845	−2.03059
$687$	−11.9598	−0.456293
$688$	−13.2635	−0.505667
$689$	−4.15920	−0.158453
$690$	4.02311	0.153157
$691$	45.1882	1.71904	0.859520	−	0.511102i	$-0.170763\pi$
$691$	45.1882	1.71904	0.859520	+	0.511102i	$0.170763\pi$
$692$	5.38197	0.204592
$693$	0.517805	0.0196698
$694$	24.0314	0.912219
$695$	5.66264	0.214796
$696$	−26.2084	−0.993427
$697$	48.9693	1.85485
$698$	4.16698	0.157722
$699$	24.0160	0.908370
$700$	33.3545	1.26068
$701$	−34.7447	−1.31229	−0.656144	−	0.754636i	$-0.727814\pi$
$701$	−34.7447	−1.31229	−0.656144	+	0.754636i	$0.727814\pi$
$702$	−2.75283	−0.103899
$703$	31.5755	1.19089
$704$	−10.0698	−0.379520
$705$	−0.367701	−0.0138484
$706$	57.1061	2.14922
$707$	19.0643	0.716988
$708$	25.3381	0.952263
$709$	−48.2636	−1.81258	−0.906290	−	0.422657i	$-0.861097\pi$
$709$	−48.2636	−1.81258	−0.906290	+	0.422657i	$0.861097\pi$
$710$	34.8584	1.30821
$711$	0.519372	0.0194780
$712$	−90.1096	−3.37700
$713$	9.79585	0.366857
$714$	26.0575	0.975177
$715$	−0.372644	−0.0139361
$716$	93.2516	3.48498
$717$	−7.76236	−0.289890
$718$	−97.6980	−3.64606
$719$	5.49737	0.205017	0.102509	−	0.994732i	$-0.467313\pi$
$719$	5.49737	0.205017	0.102509	+	0.994732i	$0.467313\pi$
$720$	20.5457	0.765691
$721$	1.78893	0.0666231
$722$	−42.5153	−1.58226
$723$	7.24699	0.269518
$724$	132.111	4.90987
$725$	−8.89383	−0.330309
$726$	30.0505	1.11528
$727$	28.0625	1.04078	0.520390	−	0.853929i	$-0.325787\pi$
$727$	28.0625	1.04078	0.520390	+	0.853929i	$0.325787\pi$
$728$	17.6206	0.653064
$729$	1.00000	0.0370370
$730$	5.27523	0.195245
$731$	−4.39765	−0.162653
$732$	33.8104	1.24967
$733$	−13.4594	−0.497135	−0.248567	−	0.968615i	$-0.579960\pi$
$733$	−13.4594	−0.497135	−0.248567	+	0.968615i	$0.579960\pi$
$734$	14.3014	0.527874
$735$	−4.89187	−0.180439
$736$	27.5077	1.01395
$737$	2.13816	0.0787601
$738$	−25.4767	−0.937809
$739$	2.66429	0.0980077	0.0490038	−	0.998799i	$-0.484395\pi$
$739$	2.66429	0.0980077	0.0490038	+	0.998799i	$0.484395\pi$
$740$	−38.6365	−1.42031
$741$	−5.86892	−0.215600
$742$	−20.4824	−0.751934
$743$	7.89634	0.289689	0.144844	−	0.989454i	$-0.453732\pi$
$743$	7.89634	0.289689	0.144844	+	0.989454i	$0.453732\pi$
$744$	84.9981	3.11618
$745$	−2.46769	−0.0904093
$746$	−29.3318	−1.07392
$747$	−3.12093	−0.114189
$748$	−8.54318	−0.312369
$749$	35.6878	1.30400
$750$	29.5664	1.07961
$751$	35.2747	1.28719	0.643596	−	0.765366i	$-0.277442\pi$
$751$	35.2747	1.28719	0.643596	+	0.765366i	$0.277442\pi$
$752$	−4.55799	−0.166213
$753$	−18.1895	−0.662864
$754$	−7.32472	−0.266750
$755$	−10.2197	−0.371933
$756$	−9.97876	−0.362924
$757$	5.43356	0.197486	0.0987431	−	0.995113i	$-0.468518\pi$
$757$	5.43356	0.197486	0.0987431	+	0.995113i	$0.468518\pi$
$758$	−76.2937	−2.77111
$759$	0.328576	0.0119266
$760$	74.4231	2.69961
$761$	50.6956	1.83771	0.918857	−	0.394590i	$-0.129114\pi$
$761$	50.6956	1.83771	0.918857	+	0.394590i	$0.129114\pi$
$762$	−20.1514	−0.730009
$763$	−20.7172	−0.750015
$764$	26.2703	0.950425
$765$	6.81211	0.246292
$766$	44.1544	1.59536
$767$	4.54244	0.164018
$768$	60.6440	2.18830
$769$	−24.2524	−0.874564	−0.437282	−	0.899324i	$-0.644059\pi$
$769$	−24.2524	−0.874564	−0.437282	+	0.899324i	$0.644059\pi$
$770$	−1.83513	−0.0661334
$771$	−9.58280	−0.345116
$772$	−17.9232	−0.645070
$773$	−11.0625	−0.397891	−0.198946	−	0.980011i	$-0.563752\pi$
$773$	−11.0625	−0.397891	−0.198946	+	0.980011i	$0.563752\pi$
$774$	2.28791	0.0822372
$775$	28.8441	1.03611
$776$	−14.9841	−0.537899
$777$	9.62465	0.345282
$778$	8.09654	0.290275
$779$	−54.3152	−1.94604
$780$	7.18133	0.257133
$781$	2.84696	0.101872
$782$	16.5349	0.591288
$783$	2.66079	0.0950891
$784$	−60.6393	−2.16569
$785$	−16.4668	−0.587726
$786$	3.51430	0.125351
$787$	26.1016	0.930420	0.465210	−	0.885200i	$-0.345979\pi$
$787$	26.1016	0.930420	0.465210	+	0.885200i	$0.345979\pi$
$788$	−13.1910	−0.469909
$789$	−1.63199	−0.0581005
$790$	−1.84068	−0.0654885
$791$	32.2941	1.14825
$792$	2.85104	0.101307
$793$	6.06131	0.215243
$794$	18.1099	0.642696
$795$	−5.35464	−0.189909
$796$	−141.178	−5.00391
$797$	−47.0649	−1.66712	−0.833562	−	0.552426i	$-0.813702\pi$
$797$	−47.0649	−1.66712	−0.833562	+	0.552426i	$0.813702\pi$
$798$	−28.9021	−1.02312
$799$	−1.51125	−0.0534640
$800$	80.9971	2.86368
$801$	9.14833	0.323240
$802$	−38.6826	−1.36593
$803$	0.430840	0.0152040
$804$	−41.2050	−1.45319
$805$	2.61442	0.0921461
$806$	23.7552	0.836743
$807$	−5.96833	−0.210095
$808$	104.968	3.69277
$809$	−4.38555	−0.154188	−0.0770938	−	0.997024i	$-0.524564\pi$
$809$	−4.38555	−0.154188	−0.0770938	+	0.997024i	$0.524564\pi$
$810$	−3.54405	−0.124525
$811$	18.5299	0.650672	0.325336	−	0.945598i	$-0.394523\pi$
$811$	18.5299	0.650672	0.325336	+	0.945598i	$0.394523\pi$
$812$	−26.5514	−0.931773
$813$	10.5959	0.371613
$814$	−4.28693	−0.150257
$815$	−19.4212	−0.680294
$816$	84.4424	2.95607
$817$	4.87773	0.170650
$818$	70.7340	2.47316
$819$	−1.78893	−0.0625101
$820$	66.4612	2.32093
$821$	−31.2834	−1.09180	−0.545900	−	0.837851i	$-0.683812\pi$
$821$	−31.2834	−1.09180	−0.545900	+	0.837851i	$0.683812\pi$
$822$	−25.0458	−0.873572
$823$	−38.4601	−1.34063	−0.670317	−	0.742075i	$-0.733842\pi$
$823$	−38.4601	−1.34063	−0.670317	+	0.742075i	$0.733842\pi$
$824$	9.84984	0.343135
$825$	0.967502	0.0336841
$826$	22.3697	0.778343
$827$	29.5823	1.02868	0.514339	−	0.857587i	$-0.328037\pi$
$827$	29.5823	1.02868	0.514339	+	0.857587i	$0.328037\pi$
$828$	−6.33208	−0.220055
$829$	15.4176	0.535474	0.267737	−	0.963492i	$-0.413724\pi$
$829$	15.4176	0.535474	0.267737	+	0.963492i	$0.413724\pi$
$830$	11.0607	0.383924
$831$	−25.6970	−0.891417
$832$	34.7894	1.20611
$833$	−20.1055	−0.696615
$834$	−12.1082	−0.419271
$835$	−1.47144	−0.0509213
$836$	9.47582	0.327728
$837$	−8.62939	−0.298275
$838$	−67.2232	−2.32219
$839$	−25.3039	−0.873587	−0.436794	−	0.899562i	$-0.643886\pi$
$839$	−25.3039	−0.873587	−0.436794	+	0.899562i	$0.643886\pi$
$840$	22.6852	0.782712
$841$	−21.9202	−0.755868
$842$	−50.0996	−1.72654
$843$	−0.917972	−0.0316166
$844$	−20.3537	−0.700605
$845$	1.28742	0.0442886
$846$	0.786237	0.0270314
$847$	19.5283	0.671000
$848$	−66.3757	−2.27935
$849$	−16.8783	−0.579262
$850$	48.6876	1.66997
$851$	6.10738	0.209358
$852$	−54.8645	−1.87963
$853$	12.4017	0.424628	0.212314	−	0.977202i	$-0.431900\pi$
$853$	12.4017	0.424628	0.212314	+	0.977202i	$0.431900\pi$
$854$	29.8496	1.02143
$855$	−7.55577	−0.258402
$856$	196.497	6.71614
$857$	11.9433	0.407976	0.203988	−	0.978973i	$-0.434610\pi$
$857$	11.9433	0.407976	0.203988	+	0.978973i	$0.434610\pi$
$858$	0.796808	0.0272026
$859$	−21.4763	−0.732761	−0.366380	−	0.930465i	$-0.619403\pi$
$859$	−21.4763	−0.732761	−0.366380	+	0.930465i	$0.619403\pi$
$860$	−5.96849	−0.203524
$861$	−16.5560	−0.564227
$862$	90.3403	3.07700
$863$	45.0313	1.53288	0.766441	−	0.642315i	$-0.222026\pi$
$863$	45.0313	1.53288	0.766441	+	0.642315i	$0.222026\pi$
$864$	−24.2321	−0.824394
$865$	1.24216	0.0422347
$866$	15.4006	0.523335
$867$	10.9977	0.373500
$868$	86.1106	2.92279
$869$	−0.150332	−0.00509968
$870$	−9.42999	−0.319707
$871$	−7.38696	−0.250298
$872$	−114.069	−3.86287
$873$	1.52126	0.0514867
$874$	−18.3400	−0.620360
$875$	19.2137	0.649542
$876$	−8.30283	−0.280527
$877$	26.5634	0.896982	0.448491	−	0.893787i	$-0.351962\pi$
$877$	26.5634	0.896982	0.448491	+	0.893787i	$0.351962\pi$
$878$	23.4844	0.792561
$879$	1.08094	0.0364592
$880$	−5.94695	−0.200472
$881$	22.8384	0.769446	0.384723	−	0.923032i	$-0.374297\pi$
$881$	22.8384	0.769446	0.384723	+	0.923032i	$0.374297\pi$
$882$	10.4601	0.352208
$883$	−33.2668	−1.11952	−0.559758	−	0.828656i	$-0.689106\pi$
$883$	−33.2668	−1.11952	−0.559758	+	0.828656i	$0.689106\pi$
$884$	29.5152	0.992703
$885$	5.84803	0.196579
$886$	20.6400	0.693414
$887$	−44.9938	−1.51074	−0.755372	−	0.655296i	$-0.772544\pi$
$887$	−44.9938	−1.51074	−0.755372	+	0.655296i	$0.772544\pi$
$888$	52.9934	1.77834
$889$	−13.0954	−0.439206
$890$	−32.4221	−1.08679
$891$	−0.289450	−0.00969695
$892$	−63.7910	−2.13588
$893$	1.67622	0.0560927
$894$	5.27655	0.176474
$895$	21.5225	0.719418
$896$	84.6252	2.82713
$897$	−1.13517	−0.0379023
$898$	−13.2363	−0.441701
$899$	−22.9610	−0.765793
$900$	−18.6450	−0.621499
$901$	−22.0075	−0.733176
$902$	7.37423	0.245535
$903$	1.48680	0.0494775
$904$	177.812	5.91393
$905$	30.4912	1.01356
$906$	21.8523	0.725995
$907$	−30.6765	−1.01860	−0.509298	−	0.860590i	$-0.670095\pi$
$907$	−30.6765	−1.01860	−0.509298	+	0.860590i	$0.670095\pi$
$908$	158.713	5.26708
$909$	−10.6569	−0.353466
$910$	6.34004	0.210170
$911$	23.3061	0.772165	0.386083	−	0.922464i	$-0.373828\pi$
$911$	23.3061	0.772165	0.386083	+	0.922464i	$0.373828\pi$
$912$	−93.6608	−3.10142
$913$	0.903354	0.0298967
$914$	104.931	3.47081
$915$	7.80345	0.257974
$916$	−66.7124	−2.20424
$917$	2.28377	0.0754166
$918$	−14.5660	−0.480750
$919$	−6.88839	−0.227227	−0.113614	−	0.993525i	$-0.536243\pi$
$919$	−6.88839	−0.227227	−0.113614	+	0.993525i	$0.536243\pi$
$920$	14.3950	0.474589
$921$	−27.1033	−0.893084
$922$	104.141	3.42969
$923$	−9.83574	−0.323747
$924$	2.88836	0.0950200
$925$	17.9833	0.591289
$926$	98.4114	3.23400
$927$	−1.00000	−0.0328443
$928$	−64.4767	−2.11655
$929$	−42.9159	−1.40802	−0.704012	−	0.710188i	$-0.748610\pi$
$929$	−42.9159	−1.40802	−0.704012	+	0.710188i	$0.748610\pi$
$930$	30.5830	1.00286
$931$	22.3004	0.730866
$932$	133.963	4.38811
$933$	−10.0121	−0.327782
$934$	29.4124	0.962403
$935$	−1.97177	−0.0644837
$936$	−9.84984	−0.321952
$937$	−5.35727	−0.175014	−0.0875072	−	0.996164i	$-0.527890\pi$
$937$	−5.35727	−0.175014	−0.0875072	+	0.996164i	$0.527890\pi$
$938$	−36.3779	−1.18778
$939$	−0.913735	−0.0298186
$940$	−2.05106	−0.0668983
$941$	−13.0293	−0.424742	−0.212371	−	0.977189i	$-0.568119\pi$
$941$	−13.0293	−0.424742	−0.212371	+	0.977189i	$0.568119\pi$
$942$	35.2102	1.14721
$943$	−10.5057	−0.342113
$944$	72.4918	2.35941
$945$	−2.30310	−0.0749199
$946$	−0.662236	−0.0215312
$947$	1.63547	0.0531456	0.0265728	−	0.999647i	$-0.491541\pi$
$947$	1.63547	0.0531456	0.0265728	+	0.999647i	$0.491541\pi$
$948$	2.89710	0.0940934
$949$	−1.48848	−0.0483180
$950$	−54.0027	−1.75208
$951$	15.6162	0.506390
$952$	93.2357	3.02179
$953$	58.1921	1.88503	0.942514	−	0.334166i	$-0.108455\pi$
$953$	58.1921	1.88503	0.942514	+	0.334166i	$0.108455\pi$
$954$	11.4496	0.370693
$955$	6.06318	0.196200
$956$	−43.2990	−1.40039
$957$	−0.770168	−0.0248960
$958$	−42.1196	−1.36082
$959$	−16.2760	−0.525579
$960$	44.7886	1.44555
$961$	43.4664	1.40214
$962$	14.8106	0.477512
$963$	−19.9493	−0.642857
$964$	40.4242	1.30198
$965$	−4.13668	−0.133164
$966$	−5.59028	−0.179864
$967$	−39.8177	−1.28045	−0.640225	−	0.768188i	$-0.721159\pi$
$967$	−39.8177	−1.28045	−0.640225	+	0.768188i	$0.721159\pi$
$968$	107.523	3.45592
$969$	−31.0541	−0.997602
$970$	−5.39141	−0.173108
$971$	−32.1864	−1.03291	−0.516456	−	0.856314i	$-0.672749\pi$
$971$	−32.1864	−1.03291	−0.516456	+	0.856314i	$0.672749\pi$
$972$	5.57808	0.178917
$973$	−7.86848	−0.252252
$974$	34.0822	1.09207
$975$	−3.34255	−0.107047
$976$	96.7310	3.09629
$977$	−42.0363	−1.34486	−0.672430	−	0.740160i	$-0.734750\pi$
$977$	−42.0363	−1.34486	−0.672430	+	0.740160i	$0.734750\pi$
$978$	41.5274	1.32790
$979$	−2.64799	−0.0846300
$980$	−27.2872	−0.871658
$981$	11.5808	0.369747
$982$	−45.2520	−1.44405
$983$	−43.5345	−1.38854	−0.694268	−	0.719717i	$-0.744272\pi$
$983$	−43.5345	−1.38854	−0.694268	+	0.719717i	$0.744272\pi$
$984$	−91.1574	−2.90599
$985$	−3.04448	−0.0970051
$986$	−38.7571	−1.23428
$987$	0.510936	0.0162633
$988$	−32.7373	−1.04151
$989$	0.943456	0.0300002
$990$	1.02583	0.0326029
$991$	−5.32713	−0.169222	−0.0846109	−	0.996414i	$-0.526965\pi$
$991$	−5.32713	−0.169222	−0.0846109	+	0.996414i	$0.526965\pi$
$992$	209.109	6.63920
$993$	12.3064	0.390530
$994$	−48.4372	−1.53633
$995$	−32.5838	−1.03298
$996$	−17.4088	−0.551618
$997$	53.5366	1.69552	0.847761	−	0.530379i	$-0.177950\pi$
$997$	53.5366	1.69552	0.847761	+	0.530379i	$0.177950\pi$
$998$	−41.4520	−1.31214
$999$	−5.38013	−0.170220

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.f.1.1	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.f.1.1	✓	19	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.75283 q^{2} +1.00000 q^{3} +5.57808 q^{4} +1.28742 q^{5} -2.75283 q^{6} -1.78893 q^{7} -9.84984 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.75283 q^{2} +1.00000 q^{3} +5.57808 q^{4} +1.28742 q^{5} -2.75283 q^{6} -1.78893 q^{7} -9.84984 q^{8} +1.00000 q^{9} -3.54405 q^{10} -0.289450 q^{11} +5.57808 q^{12} +1.00000 q^{13} +4.92461 q^{14} +1.28742 q^{15} +15.9588 q^{16} +5.29128 q^{17} -2.75283 q^{18} -5.86892 q^{19} +7.18133 q^{20} -1.78893 q^{21} +0.796808 q^{22} -1.13517 q^{23} -9.84984 q^{24} -3.34255 q^{25} -2.75283 q^{26} +1.00000 q^{27} -9.97876 q^{28} +2.66079 q^{29} -3.54405 q^{30} -8.62939 q^{31} -24.2321 q^{32} -0.289450 q^{33} -14.5660 q^{34} -2.30310 q^{35} +5.57808 q^{36} -5.38013 q^{37} +16.1561 q^{38} +1.00000 q^{39} -12.6809 q^{40} +9.25472 q^{41} +4.92461 q^{42} -0.831112 q^{43} -1.61458 q^{44} +1.28742 q^{45} +3.12494 q^{46} -0.285610 q^{47} +15.9588 q^{48} -3.79974 q^{49} +9.20147 q^{50} +5.29128 q^{51} +5.57808 q^{52} -4.15920 q^{53} -2.75283 q^{54} -0.372644 q^{55} +17.6206 q^{56} -5.86892 q^{57} -7.32472 q^{58} +4.54244 q^{59} +7.18133 q^{60} +6.06131 q^{61} +23.7552 q^{62} -1.78893 q^{63} +34.7894 q^{64} +1.28742 q^{65} +0.796808 q^{66} -7.38696 q^{67} +29.5152 q^{68} -1.13517 q^{69} +6.34004 q^{70} -9.83574 q^{71} -9.84984 q^{72} -1.48848 q^{73} +14.8106 q^{74} -3.34255 q^{75} -32.7373 q^{76} +0.517805 q^{77} -2.75283 q^{78} +0.519372 q^{79} +20.5457 q^{80} +1.00000 q^{81} -25.4767 q^{82} -3.12093 q^{83} -9.97876 q^{84} +6.81211 q^{85} +2.28791 q^{86} +2.66079 q^{87} +2.85104 q^{88} +9.14833 q^{89} -3.54405 q^{90} -1.78893 q^{91} -6.33208 q^{92} -8.62939 q^{93} +0.786237 q^{94} -7.55577 q^{95} -24.2321 q^{96} +1.52126 q^{97} +10.4601 q^{98} -0.289450 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9} - 6 q^{10} - 15 q^{11} + 10 q^{12} + 19 q^{13} - 4 q^{14} - 3 q^{15} - 4 q^{16} - 4 q^{18} - 32 q^{19} - 8 q^{20} - 23 q^{21} - 9 q^{22} - 23 q^{23} - 9 q^{24} - 8 q^{25} - 4 q^{26} + 19 q^{27} - 22 q^{28} + 4 q^{29} - 6 q^{30} - 50 q^{31} - 2 q^{32} - 15 q^{33} - 35 q^{34} - 4 q^{35} + 10 q^{36} - 38 q^{37} + 20 q^{38} + 19 q^{39} - 30 q^{40} - 11 q^{41} - 4 q^{42} - 17 q^{43} - 29 q^{44} - 3 q^{45} - 5 q^{46} - 38 q^{47} - 4 q^{48} - 6 q^{49} - 9 q^{50} + 10 q^{52} - 12 q^{53} - 4 q^{54} - 22 q^{55} + 12 q^{56} - 32 q^{57} - 23 q^{58} - 8 q^{59} - 8 q^{60} - 31 q^{61} + 31 q^{62} - 23 q^{63} + 15 q^{64} - 3 q^{65} - 9 q^{66} - 48 q^{67} + 44 q^{68} - 23 q^{69} + 13 q^{70} - 14 q^{71} - 9 q^{72} - 50 q^{73} - 10 q^{74} - 8 q^{75} - 64 q^{76} + 23 q^{77} - 4 q^{78} - 21 q^{79} + 8 q^{80} + 19 q^{81} - 10 q^{82} - 15 q^{83} - 22 q^{84} - 29 q^{85} + 9 q^{86} + 4 q^{87} + 3 q^{88} - 10 q^{89} - 6 q^{90} - 23 q^{91} - 17 q^{92} - 50 q^{93} - 22 q^{94} - 25 q^{95} - 2 q^{96} - 42 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9 - 6 * q^10 - 15 * q^11 + 10 * q^12 + 19 * q^13 - 4 * q^14 - 3 * q^15 - 4 * q^16 - 4 * q^18 - 32 * q^19 - 8 * q^20 - 23 * q^21 - 9 * q^22 - 23 * q^23 - 9 * q^24 - 8 * q^25 - 4 * q^26 + 19 * q^27 - 22 * q^28 + 4 * q^29 - 6 * q^30 - 50 * q^31 - 2 * q^32 - 15 * q^33 - 35 * q^34 - 4 * q^35 + 10 * q^36 - 38 * q^37 + 20 * q^38 + 19 * q^39 - 30 * q^40 - 11 * q^41 - 4 * q^42 - 17 * q^43 - 29 * q^44 - 3 * q^45 - 5 * q^46 - 38 * q^47 - 4 * q^48 - 6 * q^49 - 9 * q^50 + 10 * q^52 - 12 * q^53 - 4 * q^54 - 22 * q^55 + 12 * q^56 - 32 * q^57 - 23 * q^58 - 8 * q^59 - 8 * q^60 - 31 * q^61 + 31 * q^62 - 23 * q^63 + 15 * q^64 - 3 * q^65 - 9 * q^66 - 48 * q^67 + 44 * q^68 - 23 * q^69 + 13 * q^70 - 14 * q^71 - 9 * q^72 - 50 * q^73 - 10 * q^74 - 8 * q^75 - 64 * q^76 + 23 * q^77 - 4 * q^78 - 21 * q^79 + 8 * q^80 + 19 * q^81 - 10 * q^82 - 15 * q^83 - 22 * q^84 - 29 * q^85 + 9 * q^86 + 4 * q^87 + 3 * q^88 - 10 * q^89 - 6 * q^90 - 23 * q^91 - 17 * q^92 - 50 * q^93 - 22 * q^94 - 25 * q^95 - 2 * q^96 - 42 * q^97 - q^98 - 15 * q^99

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