LMFDB - Embedded newform 4029.2.a.e.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 10 x^{16} + 120 x^{15} - 56 x^{14} - 921 x^{13} + 1181 x^{12} + 3316 x^{11} + \cdots + 138 $ x^18 - 6x^17 - 10x^16 + 120x^15 - 56x^14 - 921x^13 + 1181x^12 + 3316x^11 - 6280x^10 - 5249x^9 + 15005x^8 + 1809x^7 - 16711x^6 + 2434x^5 + 8758x^4 - 1858x^3 - 1942x^2 + 318*x + 138
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			1.12
Root			$-0.540222$ of defining polynomial
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.540222 q^{2} +1.00000 q^{3} -1.70816 q^{4} +3.09244 q^{5} +0.540222 q^{6} -3.94821 q^{7} -2.00323 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.540222 q^{2} +1.00000 q^{3} -1.70816 q^{4} +3.09244 q^{5} +0.540222 q^{6} -3.94821 q^{7} -2.00323 q^{8} +1.00000 q^{9} +1.67061 q^{10} -2.82723 q^{11} -1.70816 q^{12} +0.947196 q^{13} -2.13291 q^{14} +3.09244 q^{15} +2.33413 q^{16} +1.00000 q^{17} +0.540222 q^{18} +5.30126 q^{19} -5.28239 q^{20} -3.94821 q^{21} -1.52733 q^{22} -4.97232 q^{23} -2.00323 q^{24} +4.56321 q^{25} +0.511696 q^{26} +1.00000 q^{27} +6.74417 q^{28} -8.26696 q^{29} +1.67061 q^{30} +1.06831 q^{31} +5.26741 q^{32} -2.82723 q^{33} +0.540222 q^{34} -12.2096 q^{35} -1.70816 q^{36} +3.33994 q^{37} +2.86386 q^{38} +0.947196 q^{39} -6.19488 q^{40} +4.10058 q^{41} -2.13291 q^{42} -6.71707 q^{43} +4.82935 q^{44} +3.09244 q^{45} -2.68616 q^{46} -6.96223 q^{47} +2.33413 q^{48} +8.58832 q^{49} +2.46515 q^{50} +1.00000 q^{51} -1.61796 q^{52} -0.458751 q^{53} +0.540222 q^{54} -8.74304 q^{55} +7.90916 q^{56} +5.30126 q^{57} -4.46600 q^{58} -5.42117 q^{59} -5.28239 q^{60} -13.9711 q^{61} +0.577126 q^{62} -3.94821 q^{63} -1.82269 q^{64} +2.92915 q^{65} -1.52733 q^{66} +11.5772 q^{67} -1.70816 q^{68} -4.97232 q^{69} -6.59590 q^{70} -14.2534 q^{71} -2.00323 q^{72} -10.8140 q^{73} +1.80431 q^{74} +4.56321 q^{75} -9.05541 q^{76} +11.1625 q^{77} +0.511696 q^{78} -1.00000 q^{79} +7.21817 q^{80} +1.00000 q^{81} +2.21522 q^{82} -12.0134 q^{83} +6.74417 q^{84} +3.09244 q^{85} -3.62871 q^{86} -8.26696 q^{87} +5.66358 q^{88} -0.131644 q^{89} +1.67061 q^{90} -3.73972 q^{91} +8.49351 q^{92} +1.06831 q^{93} -3.76115 q^{94} +16.3939 q^{95} +5.26741 q^{96} -13.8675 q^{97} +4.63960 q^{98} -2.82723 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * 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 $

$2$	0.540222	0.381995	0.190997	−	0.981591i	$-0.438828\pi$
$2$	0.540222	0.381995	0.190997	+	0.981591i	$0.438828\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.70816	−0.854080
$5$	3.09244	1.38298	0.691492	−	0.722385i	$-0.256954\pi$
$5$	3.09244	1.38298	0.691492	+	0.722385i	$0.256954\pi$
$6$	0.540222	0.220545
$7$	−3.94821	−1.49228	−0.746141	−	0.665788i	$-0.768095\pi$
$7$	−3.94821	−1.49228	−0.746141	+	0.665788i	$0.768095\pi$
$8$	−2.00323	−0.708249
$9$	1.00000	0.333333
$10$	1.67061	0.528292
$11$	−2.82723	−0.852440	−0.426220	−	0.904619i	$-0.640155\pi$
$11$	−2.82723	−0.852440	−0.426220	+	0.904619i	$0.640155\pi$
$12$	−1.70816	−0.493103
$13$	0.947196	0.262705	0.131352	−	0.991336i	$-0.458068\pi$
$13$	0.947196	0.262705	0.131352	+	0.991336i	$0.458068\pi$
$14$	−2.13291	−0.570044
$15$	3.09244	0.798466
$16$	2.33413	0.583533
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.540222	0.127332
$19$	5.30126	1.21619	0.608097	−	0.793863i	$-0.291933\pi$
$19$	5.30126	1.21619	0.608097	+	0.793863i	$0.291933\pi$
$20$	−5.28239	−1.18118
$21$	−3.94821	−0.861569
$22$	−1.52733	−0.325628
$23$	−4.97232	−1.03680	−0.518400	−	0.855138i	$-0.673472\pi$
$23$	−4.97232	−1.03680	−0.518400	+	0.855138i	$0.673472\pi$
$24$	−2.00323	−0.408908
$25$	4.56321	0.912642
$26$	0.511696	0.100352
$27$	1.00000	0.192450
$28$	6.74417	1.27453
$29$	−8.26696	−1.53514	−0.767568	−	0.640968i	$-0.778533\pi$
$29$	−8.26696	−1.53514	−0.767568	+	0.640968i	$0.778533\pi$
$30$	1.67061	0.305010
$31$	1.06831	0.191875	0.0959373	−	0.995387i	$-0.469415\pi$
$31$	1.06831	0.191875	0.0959373	+	0.995387i	$0.469415\pi$
$32$	5.26741	0.931155
$33$	−2.82723	−0.492157
$34$	0.540222	0.0926473
$35$	−12.2096	−2.06380
$36$	−1.70816	−0.284693
$37$	3.33994	0.549083	0.274541	−	0.961575i	$-0.411474\pi$
$37$	3.33994	0.549083	0.274541	+	0.961575i	$0.411474\pi$
$38$	2.86386	0.464580
$39$	0.947196	0.151673
$40$	−6.19488	−0.979496
$41$	4.10058	0.640403	0.320202	−	0.947349i	$-0.396249\pi$
$41$	4.10058	0.640403	0.320202	+	0.947349i	$0.396249\pi$
$42$	−2.13291	−0.329115
$43$	−6.71707	−1.02434	−0.512172	−	0.858883i	$-0.671159\pi$
$43$	−6.71707	−1.02434	−0.512172	+	0.858883i	$0.671159\pi$
$44$	4.82935	0.728052
$45$	3.09244	0.460994
$46$	−2.68616	−0.396052
$47$	−6.96223	−1.01555	−0.507773	−	0.861491i	$-0.669531\pi$
$47$	−6.96223	−1.01555	−0.507773	+	0.861491i	$0.669531\pi$
$48$	2.33413	0.336903
$49$	8.58832	1.22690
$50$	2.46515	0.348624
$51$	1.00000	0.140028
$52$	−1.61796	−0.224371
$53$	−0.458751	−0.0630143	−0.0315071	−	0.999504i	$-0.510031\pi$
$53$	−0.458751	−0.0630143	−0.0315071	+	0.999504i	$0.510031\pi$
$54$	0.540222	0.0735149
$55$	−8.74304	−1.17891
$56$	7.90916	1.05691
$57$	5.30126	0.702170
$58$	−4.46600	−0.586414
$59$	−5.42117	−0.705776	−0.352888	−	0.935666i	$-0.614800\pi$
$59$	−5.42117	−0.705776	−0.352888	+	0.935666i	$0.614800\pi$
$60$	−5.28239	−0.681953
$61$	−13.9711	−1.78882	−0.894408	−	0.447252i	$-0.852403\pi$
$61$	−13.9711	−1.78882	−0.894408	+	0.447252i	$0.852403\pi$
$62$	0.577126	0.0732951
$63$	−3.94821	−0.497427
$64$	−1.82269	−0.227836
$65$	2.92915	0.363316
$66$	−1.52733	−0.188001
$67$	11.5772	1.41438	0.707191	−	0.707022i	$-0.249962\pi$
$67$	11.5772	1.41438	0.707191	+	0.707022i	$0.249962\pi$
$68$	−1.70816	−0.207145
$69$	−4.97232	−0.598596
$70$	−6.59590	−0.788361
$71$	−14.2534	−1.69156	−0.845781	−	0.533530i	$-0.820865\pi$
$71$	−14.2534	−1.69156	−0.845781	+	0.533530i	$0.820865\pi$
$72$	−2.00323	−0.236083
$73$	−10.8140	−1.26568	−0.632840	−	0.774282i	$-0.718111\pi$
$73$	−10.8140	−1.26568	−0.632840	+	0.774282i	$0.718111\pi$
$74$	1.80431	0.209747
$75$	4.56321	0.526914
$76$	−9.05541	−1.03873
$77$	11.1625	1.27208
$78$	0.511696	0.0579382
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	7.21817	0.807016
$81$	1.00000	0.111111
$82$	2.21522	0.244631
$83$	−12.0134	−1.31864	−0.659320	−	0.751862i	$-0.729156\pi$
$83$	−12.0134	−1.31864	−0.659320	+	0.751862i	$0.729156\pi$
$84$	6.74417	0.735849
$85$	3.09244	0.335423
$86$	−3.62871	−0.391294
$87$	−8.26696	−0.886311
$88$	5.66358	0.603740
$89$	−0.131644	−0.0139542	−0.00697712	−	0.999976i	$-0.502221\pi$
$89$	−0.131644	−0.0139542	−0.00697712	+	0.999976i	$0.502221\pi$
$90$	1.67061	0.176097
$91$	−3.73972	−0.392030
$92$	8.49351	0.885510
$93$	1.06831	0.110779
$94$	−3.76115	−0.387933
$95$	16.3939	1.68197
$96$	5.26741	0.537603
$97$	−13.8675	−1.40804	−0.704018	−	0.710183i	$-0.748612\pi$
$97$	−13.8675	−1.40804	−0.704018	+	0.710183i	$0.748612\pi$
$98$	4.63960	0.468671
$99$	−2.82723	−0.284147
$100$	−7.79469	−0.779469
$101$	14.2625	1.41917	0.709587	−	0.704618i	$-0.248882\pi$
$101$	14.2625	1.41917	0.709587	+	0.704618i	$0.248882\pi$
$102$	0.540222	0.0534900
$103$	−4.43182	−0.436681	−0.218340	−	0.975873i	$-0.570064\pi$
$103$	−4.43182	−0.436681	−0.218340	+	0.975873i	$0.570064\pi$
$104$	−1.89745	−0.186060
$105$	−12.2096	−1.19154
$106$	−0.247827	−0.0240711
$107$	−15.5058	−1.49900	−0.749500	−	0.662005i	$-0.769706\pi$
$107$	−15.5058	−1.49900	−0.749500	+	0.662005i	$0.769706\pi$
$108$	−1.70816	−0.164368
$109$	−4.97129	−0.476163	−0.238082	−	0.971245i	$-0.576519\pi$
$109$	−4.97129	−0.476163	−0.238082	+	0.971245i	$0.576519\pi$
$110$	−4.72318	−0.450338
$111$	3.33994	0.317013
$112$	−9.21563	−0.870795
$113$	12.5266	1.17840	0.589200	−	0.807987i	$-0.299443\pi$
$113$	12.5266	1.17840	0.589200	+	0.807987i	$0.299443\pi$
$114$	2.86386	0.268225
$115$	−15.3766	−1.43388
$116$	14.1213	1.31113
$117$	0.947196	0.0875683
$118$	−2.92864	−0.269603
$119$	−3.94821	−0.361931
$120$	−6.19488	−0.565512
$121$	−3.00680	−0.273345
$122$	−7.54750	−0.683318
$123$	4.10058	0.369737
$124$	−1.82485	−0.163876
$125$	−1.35075	−0.120815
$126$	−2.13291	−0.190015
$127$	2.55069	0.226337	0.113169	−	0.993576i	$-0.463900\pi$
$127$	2.55069	0.226337	0.113169	+	0.993576i	$0.463900\pi$
$128$	−11.5195	−1.01819
$129$	−6.71707	−0.591405
$130$	1.58239	0.138785
$131$	−22.0185	−1.92377	−0.961883	−	0.273461i	$-0.911831\pi$
$131$	−22.0185	−1.92377	−0.961883	+	0.273461i	$0.911831\pi$
$132$	4.82935	0.420341
$133$	−20.9305	−1.81490
$134$	6.25427	0.540287
$135$	3.09244	0.266155
$136$	−2.00323	−0.171776
$137$	7.12148	0.608429	0.304215	−	0.952604i	$-0.401606\pi$
$137$	7.12148	0.608429	0.304215	+	0.952604i	$0.401606\pi$
$138$	−2.68616	−0.228661
$139$	2.16895	0.183968	0.0919838	−	0.995761i	$-0.470679\pi$
$139$	2.16895	0.183968	0.0919838	+	0.995761i	$0.470679\pi$
$140$	20.8560	1.76265
$141$	−6.96223	−0.586325
$142$	−7.69998	−0.646168
$143$	−2.67794	−0.223940
$144$	2.33413	0.194511
$145$	−25.5651	−2.12307
$146$	−5.84195	−0.483484
$147$	8.58832	0.708353
$148$	−5.70515	−0.468960
$149$	8.14800	0.667510	0.333755	−	0.942660i	$-0.391684\pi$
$149$	8.14800	0.667510	0.333755	+	0.942660i	$0.391684\pi$
$150$	2.46515	0.201278
$151$	−4.57538	−0.372339	−0.186170	−	0.982518i	$-0.559607\pi$
$151$	−4.57538	−0.372339	−0.186170	+	0.982518i	$0.559607\pi$
$152$	−10.6197	−0.861368
$153$	1.00000	0.0808452
$154$	6.03021	0.485928
$155$	3.30370	0.265359
$156$	−1.61796	−0.129541
$157$	10.5663	0.843284	0.421642	−	0.906762i	$-0.361454\pi$
$157$	10.5663	0.843284	0.421642	+	0.906762i	$0.361454\pi$
$158$	−0.540222	−0.0429778
$159$	−0.458751	−0.0363813
$160$	16.2892	1.28777
$161$	19.6317	1.54720
$162$	0.540222	0.0424439
$163$	7.84998	0.614858	0.307429	−	0.951571i	$-0.400531\pi$
$163$	7.84998	0.614858	0.307429	+	0.951571i	$0.400531\pi$
$164$	−7.00445	−0.546955
$165$	−8.74304	−0.680644
$166$	−6.48990	−0.503714
$167$	−11.0991	−0.858874	−0.429437	−	0.903097i	$-0.641288\pi$
$167$	−11.0991	−0.858874	−0.429437	+	0.903097i	$0.641288\pi$
$168$	7.90916	0.610205
$169$	−12.1028	−0.930986
$170$	1.67061	0.128130
$171$	5.30126	0.405398
$172$	11.4738	0.874872
$173$	14.9637	1.13767	0.568834	−	0.822452i	$-0.307395\pi$
$173$	14.9637	1.13767	0.568834	+	0.822452i	$0.307395\pi$
$174$	−4.46600	−0.338566
$175$	−18.0165	−1.36192
$176$	−6.59911	−0.497427
$177$	−5.42117	−0.407480
$178$	−0.0711171	−0.00533045
$179$	−0.609097	−0.0455260	−0.0227630	−	0.999741i	$-0.507246\pi$
$179$	−0.609097	−0.0455260	−0.0227630	+	0.999741i	$0.507246\pi$
$180$	−5.28239	−0.393726
$181$	5.62019	0.417745	0.208873	−	0.977943i	$-0.433021\pi$
$181$	5.62019	0.417745	0.208873	+	0.977943i	$0.433021\pi$
$182$	−2.02028	−0.149753
$183$	−13.9711	−1.03277
$184$	9.96069	0.734312
$185$	10.3286	0.759372
$186$	0.577126	0.0423169
$187$	−2.82723	−0.206747
$188$	11.8926	0.867357
$189$	−3.94821	−0.287190
$190$	8.85633	0.642506
$191$	24.7328	1.78961	0.894803	−	0.446461i	$-0.147316\pi$
$191$	24.7328	1.78961	0.894803	+	0.446461i	$0.147316\pi$
$192$	−1.82269	−0.131541
$193$	−1.25820	−0.0905671	−0.0452836	−	0.998974i	$-0.514419\pi$
$193$	−1.25820	−0.0905671	−0.0452836	+	0.998974i	$0.514419\pi$
$194$	−7.49155	−0.537862
$195$	2.92915	0.209761
$196$	−14.6702	−1.04787
$197$	−4.56529	−0.325264	−0.162632	−	0.986687i	$-0.551998\pi$
$197$	−4.56529	−0.325264	−0.162632	+	0.986687i	$0.551998\pi$
$198$	−1.52733	−0.108543
$199$	15.3033	1.08482	0.542410	−	0.840114i	$-0.317512\pi$
$199$	15.3033	1.08482	0.542410	+	0.840114i	$0.317512\pi$
$200$	−9.14116	−0.646378
$201$	11.5772	0.816594
$202$	7.70493	0.542117
$203$	32.6397	2.29085
$204$	−1.70816	−0.119595
$205$	12.6808	0.885667
$206$	−2.39417	−0.166810
$207$	−4.97232	−0.345600
$208$	2.21088	0.153297
$209$	−14.9879	−1.03673
$210$	−6.59590	−0.455160
$211$	−20.6840	−1.42394	−0.711972	−	0.702208i	$-0.752198\pi$
$211$	−20.6840	−1.42394	−0.711972	+	0.702208i	$0.752198\pi$
$212$	0.783620	0.0538192
$213$	−14.2534	−0.976624
$214$	−8.37656	−0.572610
$215$	−20.7722	−1.41665
$216$	−2.00323	−0.136303
$217$	−4.21792	−0.286331
$218$	−2.68560	−0.181892
$219$	−10.8140	−0.730741
$220$	14.9345	1.00688
$221$	0.947196	0.0637153
$222$	1.80431	0.121097
$223$	24.5525	1.64416	0.822078	−	0.569374i	$-0.192815\pi$
$223$	24.5525	1.64416	0.822078	+	0.569374i	$0.192815\pi$
$224$	−20.7968	−1.38955
$225$	4.56321	0.304214
$226$	6.76712	0.450142
$227$	−6.30688	−0.418602	−0.209301	−	0.977851i	$-0.567119\pi$
$227$	−6.30688	−0.418602	−0.209301	+	0.977851i	$0.567119\pi$
$228$	−9.05541	−0.599709
$229$	−5.58146	−0.368833	−0.184417	−	0.982848i	$-0.559040\pi$
$229$	−5.58146	−0.368833	−0.184417	+	0.982848i	$0.559040\pi$
$230$	−8.30678	−0.547733
$231$	11.1625	0.734436
$232$	16.5606	1.08726
$233$	−26.3069	−1.72342	−0.861710	−	0.507401i	$-0.830606\pi$
$233$	−26.3069	−1.72342	−0.861710	+	0.507401i	$0.830606\pi$
$234$	0.511696	0.0334506
$235$	−21.5303	−1.40448
$236$	9.26023	0.602789
$237$	−1.00000	−0.0649570
$238$	−2.13291	−0.138256
$239$	16.3568	1.05803	0.529015	−	0.848612i	$-0.322561\pi$
$239$	16.3568	1.05803	0.529015	+	0.848612i	$0.322561\pi$
$240$	7.21817	0.465931
$241$	16.9114	1.08936	0.544680	−	0.838644i	$-0.316651\pi$
$241$	16.9114	1.08936	0.544680	+	0.838644i	$0.316651\pi$
$242$	−1.62434	−0.104416
$243$	1.00000	0.0641500
$244$	23.8649	1.52779
$245$	26.5589	1.69679
$246$	2.21522	0.141238
$247$	5.02134	0.319500
$248$	−2.14008	−0.135895
$249$	−12.0134	−0.761317
$250$	−0.729705	−0.0461506
$251$	−7.61641	−0.480744	−0.240372	−	0.970681i	$-0.577269\pi$
$251$	−7.61641	−0.480744	−0.240372	+	0.970681i	$0.577269\pi$
$252$	6.74417	0.424843
$253$	14.0579	0.883810
$254$	1.37794	0.0864596
$255$	3.09244	0.193656
$256$	−2.57770	−0.161106
$257$	−14.2307	−0.887688	−0.443844	−	0.896104i	$-0.646386\pi$
$257$	−14.2307	−0.887688	−0.443844	+	0.896104i	$0.646386\pi$
$258$	−3.62871	−0.225914
$259$	−13.1868	−0.819386
$260$	−5.00346	−0.310301
$261$	−8.26696	−0.511712
$262$	−11.8949	−0.734869
$263$	18.8555	1.16268	0.581340	−	0.813661i	$-0.302529\pi$
$263$	18.8555	1.16268	0.581340	+	0.813661i	$0.302529\pi$
$264$	5.66358	0.348569
$265$	−1.41866	−0.0871476
$266$	−11.3071	−0.693283
$267$	−0.131644	−0.00805649
$268$	−19.7757	−1.20800
$269$	−14.4454	−0.880754	−0.440377	−	0.897813i	$-0.645155\pi$
$269$	−14.4454	−0.880754	−0.440377	+	0.897813i	$0.645155\pi$
$270$	1.67061	0.101670
$271$	12.3460	0.749967	0.374984	−	0.927031i	$-0.377648\pi$
$271$	12.3460	0.749967	0.374984	+	0.927031i	$0.377648\pi$
$272$	2.33413	0.141527
$273$	−3.73972	−0.226338
$274$	3.84718	0.232417
$275$	−12.9012	−0.777973
$276$	8.49351	0.511249
$277$	2.50816	0.150701	0.0753505	−	0.997157i	$-0.475992\pi$
$277$	2.50816	0.150701	0.0753505	+	0.997157i	$0.475992\pi$
$278$	1.17171	0.0702747
$279$	1.06831	0.0639582
$280$	24.4586	1.46168
$281$	21.7712	1.29876	0.649381	−	0.760463i	$-0.275028\pi$
$281$	21.7712	1.29876	0.649381	+	0.760463i	$0.275028\pi$
$282$	−3.76115	−0.223973
$283$	27.1324	1.61286	0.806428	−	0.591332i	$-0.201398\pi$
$283$	27.1324	1.61286	0.806428	+	0.591332i	$0.201398\pi$
$284$	24.3470	1.44473
$285$	16.3939	0.971089
$286$	−1.44668	−0.0855440
$287$	−16.1899	−0.955662
$288$	5.26741	0.310385
$289$	1.00000	0.0588235
$290$	−13.8108	−0.811000
$291$	−13.8675	−0.812929
$292$	18.4720	1.08099
$293$	32.7763	1.91481	0.957407	−	0.288742i	$-0.0932371\pi$
$293$	32.7763	1.91481	0.957407	+	0.288742i	$0.0932371\pi$
$294$	4.63960	0.270587
$295$	−16.7647	−0.976077
$296$	−6.69067	−0.388887
$297$	−2.82723	−0.164052
$298$	4.40173	0.254985
$299$	−4.70976	−0.272372
$300$	−7.79469	−0.450027
$301$	26.5204	1.52861
$302$	−2.47172	−0.142232
$303$	14.2625	0.819360
$304$	12.3738	0.709689
$305$	−43.2048	−2.47390
$306$	0.540222	0.0308824
$307$	−31.1570	−1.77822	−0.889111	−	0.457692i	$-0.848676\pi$
$307$	−31.1570	−1.77822	−0.889111	+	0.457692i	$0.848676\pi$
$308$	−19.0673	−1.08646
$309$	−4.43182	−0.252118
$310$	1.78473	0.101366
$311$	2.93369	0.166354	0.0831770	−	0.996535i	$-0.473493\pi$
$311$	2.93369	0.166354	0.0831770	+	0.996535i	$0.473493\pi$
$312$	−1.89745	−0.107422
$313$	22.7379	1.28522	0.642612	−	0.766192i	$-0.277851\pi$
$313$	22.7379	1.28522	0.642612	+	0.766192i	$0.277851\pi$
$314$	5.70816	0.322130
$315$	−12.2096	−0.687933
$316$	1.70816	0.0960915
$317$	0.228943	0.0128587	0.00642936	−	0.999979i	$-0.497953\pi$
$317$	0.228943	0.0128587	0.00642936	+	0.999979i	$0.497953\pi$
$318$	−0.247827	−0.0138975
$319$	23.3726	1.30861
$320$	−5.63656	−0.315094
$321$	−15.5058	−0.865448
$322$	10.6055	0.591021
$323$	5.30126	0.294970
$324$	−1.70816	−0.0948978
$325$	4.32225	0.239756
$326$	4.24074	0.234873
$327$	−4.97129	−0.274913
$328$	−8.21441	−0.453565
$329$	27.4883	1.51548
$330$	−4.72318	−0.260003
$331$	−14.9541	−0.821951	−0.410975	−	0.911646i	$-0.634812\pi$
$331$	−14.9541	−0.821951	−0.410975	+	0.911646i	$0.634812\pi$
$332$	20.5208	1.12622
$333$	3.33994	0.183028
$334$	−5.99598	−0.328085
$335$	35.8019	1.95607
$336$	−9.21563	−0.502754
$337$	23.9477	1.30451	0.652257	−	0.757998i	$-0.273822\pi$
$337$	23.9477	1.30451	0.652257	+	0.757998i	$0.273822\pi$
$338$	−6.53821	−0.355632
$339$	12.5266	0.680349
$340$	−5.28239	−0.286478
$341$	−3.02036	−0.163562
$342$	2.86386	0.154860
$343$	−6.27103	−0.338604
$344$	13.4558	0.725491
$345$	−15.3766	−0.827849
$346$	8.08371	0.434583
$347$	−9.20289	−0.494037	−0.247019	−	0.969011i	$-0.579451\pi$
$347$	−9.20289	−0.494037	−0.247019	+	0.969011i	$0.579451\pi$
$348$	14.1213	0.756981
$349$	−25.5656	−1.36849	−0.684247	−	0.729251i	$-0.739869\pi$
$349$	−25.5656	−1.36849	−0.684247	+	0.729251i	$0.739869\pi$
$350$	−9.73291	−0.520246
$351$	0.947196	0.0505576
$352$	−14.8922	−0.793754
$353$	−9.09379	−0.484014	−0.242007	−	0.970275i	$-0.577806\pi$
$353$	−9.09379	−0.484014	−0.242007	+	0.970275i	$0.577806\pi$
$354$	−2.92864	−0.155655
$355$	−44.0777	−2.33940
$356$	0.224869	0.0119180
$357$	−3.94821	−0.208961
$358$	−0.329048	−0.0173907
$359$	7.15893	0.377834	0.188917	−	0.981993i	$-0.439502\pi$
$359$	7.15893	0.377834	0.188917	+	0.981993i	$0.439502\pi$
$360$	−6.19488	−0.326499
$361$	9.10340	0.479126
$362$	3.03615	0.159577
$363$	−3.00680	−0.157816
$364$	6.38805	0.334825
$365$	−33.4416	−1.75042
$366$	−7.54750	−0.394514
$367$	−29.6992	−1.55028	−0.775142	−	0.631787i	$-0.782322\pi$
$367$	−29.6992	−1.55028	−0.775142	+	0.631787i	$0.782322\pi$
$368$	−11.6060	−0.605006
$369$	4.10058	0.213468
$370$	5.57973	0.290076
$371$	1.81124	0.0940350
$372$	−1.82485	−0.0946140
$373$	9.10459	0.471418	0.235709	−	0.971824i	$-0.424259\pi$
$373$	9.10459	0.471418	0.235709	+	0.971824i	$0.424259\pi$
$374$	−1.52733	−0.0789763
$375$	−1.35075	−0.0697524
$376$	13.9469	0.719259
$377$	−7.83043	−0.403288
$378$	−2.13291	−0.109705
$379$	−29.5552	−1.51815	−0.759075	−	0.651003i	$-0.774349\pi$
$379$	−29.5552	−1.51815	−0.759075	+	0.651003i	$0.774349\pi$
$380$	−28.0033	−1.43654
$381$	2.55069	0.130676
$382$	13.3612	0.683620
$383$	23.2904	1.19008	0.595042	−	0.803695i	$-0.297135\pi$
$383$	23.2904	1.19008	0.595042	+	0.803695i	$0.297135\pi$
$384$	−11.5195	−0.587851
$385$	34.5193	1.75927
$386$	−0.679707	−0.0345962
$387$	−6.71707	−0.341448
$388$	23.6880	1.20257
$389$	−11.7022	−0.593323	−0.296661	−	0.954983i	$-0.595873\pi$
$389$	−11.7022	−0.593323	−0.296661	+	0.954983i	$0.595873\pi$
$390$	1.58239	0.0801275
$391$	−4.97232	−0.251461
$392$	−17.2044	−0.868953
$393$	−22.0185	−1.11069
$394$	−2.46627	−0.124249
$395$	−3.09244	−0.155598
$396$	4.82935	0.242684
$397$	13.2709	0.666049	0.333025	−	0.942918i	$-0.391931\pi$
$397$	13.2709	0.666049	0.333025	+	0.942918i	$0.391931\pi$
$398$	8.26717	0.414396
$399$	−20.9305	−1.04783
$400$	10.6511	0.532556
$401$	−29.6324	−1.47977	−0.739886	−	0.672733i	$-0.765120\pi$
$401$	−29.6324	−1.47977	−0.739886	+	0.672733i	$0.765120\pi$
$402$	6.25427	0.311935
$403$	1.01190	0.0504064
$404$	−24.3627	−1.21209
$405$	3.09244	0.153665
$406$	17.6327	0.875095
$407$	−9.44276	−0.468060
$408$	−2.00323	−0.0991747
$409$	−30.8715	−1.52650	−0.763248	−	0.646105i	$-0.776397\pi$
$409$	−30.8715	−1.52650	−0.763248	+	0.646105i	$0.776397\pi$
$410$	6.85046	0.338320
$411$	7.12148	0.351277
$412$	7.57027	0.372960
$413$	21.4039	1.05322
$414$	−2.68616	−0.132017
$415$	−37.1507	−1.82366
$416$	4.98927	0.244619
$417$	2.16895	0.106214
$418$	−8.09678	−0.396026
$419$	26.4078	1.29010	0.645052	−	0.764138i	$-0.276836\pi$
$419$	26.4078	1.29010	0.645052	+	0.764138i	$0.276836\pi$
$420$	20.8560	1.01767
$421$	31.3754	1.52914	0.764572	−	0.644539i	$-0.222951\pi$
$421$	31.3754	1.52914	0.764572	+	0.644539i	$0.222951\pi$
$422$	−11.1739	−0.543939
$423$	−6.96223	−0.338515
$424$	0.918983	0.0446298
$425$	4.56321	0.221348
$426$	−7.69998	−0.373065
$427$	55.1608	2.66942
$428$	26.4863	1.28027
$429$	−2.67794	−0.129292
$430$	−11.2216	−0.541153
$431$	−12.8298	−0.617988	−0.308994	−	0.951064i	$-0.599992\pi$
$431$	−12.8298	−0.617988	−0.308994	+	0.951064i	$0.599992\pi$
$432$	2.33413	0.112301
$433$	3.14177	0.150984	0.0754920	−	0.997146i	$-0.475947\pi$
$433$	3.14177	0.150984	0.0754920	+	0.997146i	$0.475947\pi$
$434$	−2.27861	−0.109377
$435$	−25.5651	−1.22575
$436$	8.49176	0.406682
$437$	−26.3596	−1.26095
$438$	−5.84195	−0.279139
$439$	−6.79209	−0.324169	−0.162084	−	0.986777i	$-0.551822\pi$
$439$	−6.79209	−0.324169	−0.162084	+	0.986777i	$0.551822\pi$
$440$	17.5143	0.834962
$441$	8.58832	0.408968
$442$	0.511696	0.0243389
$443$	−25.1449	−1.19467	−0.597335	−	0.801992i	$-0.703774\pi$
$443$	−25.1449	−1.19467	−0.597335	+	0.801992i	$0.703774\pi$
$444$	−5.70515	−0.270754
$445$	−0.407102	−0.0192985
$446$	13.2638	0.628059
$447$	8.14800	0.385387
$448$	7.19635	0.339996
$449$	−15.6463	−0.738394	−0.369197	−	0.929351i	$-0.620367\pi$
$449$	−15.6463	−0.738394	−0.369197	+	0.929351i	$0.620367\pi$
$450$	2.46515	0.116208
$451$	−11.5933	−0.545906
$452$	−21.3974	−1.00645
$453$	−4.57538	−0.214970
$454$	−3.40712	−0.159904
$455$	−11.5649	−0.542170
$456$	−10.6197	−0.497311
$457$	−18.3029	−0.856175	−0.428088	−	0.903737i	$-0.640813\pi$
$457$	−18.3029	−0.856175	−0.428088	+	0.903737i	$0.640813\pi$
$458$	−3.01523	−0.140892
$459$	1.00000	0.0466760
$460$	26.2657	1.22464
$461$	−19.0255	−0.886106	−0.443053	−	0.896495i	$-0.646105\pi$
$461$	−19.0255	−0.886106	−0.443053	+	0.896495i	$0.646105\pi$
$462$	6.03021	0.280551
$463$	−3.39030	−0.157561	−0.0787804	−	0.996892i	$-0.525103\pi$
$463$	−3.39030	−0.157561	−0.0787804	+	0.996892i	$0.525103\pi$
$464$	−19.2962	−0.895802
$465$	3.30370	0.153205
$466$	−14.2115	−0.658337
$467$	−26.9480	−1.24700	−0.623502	−	0.781822i	$-0.714291\pi$
$467$	−26.9480	−1.24700	−0.623502	+	0.781822i	$0.714291\pi$
$468$	−1.61796	−0.0747903
$469$	−45.7092	−2.11066
$470$	−11.6311	−0.536505
$471$	10.5663	0.486870
$472$	10.8599	0.499865
$473$	18.9907	0.873193
$474$	−0.540222	−0.0248132
$475$	24.1908	1.10995
$476$	6.74417	0.309118
$477$	−0.458751	−0.0210048
$478$	8.83628	0.404162
$479$	−10.8318	−0.494918	−0.247459	−	0.968898i	$-0.579596\pi$
$479$	−10.8318	−0.494918	−0.247459	+	0.968898i	$0.579596\pi$
$480$	16.2892	0.743495
$481$	3.16358	0.144247
$482$	9.13592	0.416130
$483$	19.6317	0.893274
$484$	5.13609	0.233459
$485$	−42.8846	−1.94729
$486$	0.540222	0.0245050
$487$	−10.5027	−0.475924	−0.237962	−	0.971274i	$-0.576479\pi$
$487$	−10.5027	−0.475924	−0.237962	+	0.971274i	$0.576479\pi$
$488$	27.9873	1.26693
$489$	7.84998	0.354989
$490$	14.3477	0.648164
$491$	−11.7576	−0.530615	−0.265307	−	0.964164i	$-0.585473\pi$
$491$	−11.7576	−0.530615	−0.265307	+	0.964164i	$0.585473\pi$
$492$	−7.00445	−0.315785
$493$	−8.26696	−0.372325
$494$	2.71264	0.122047
$495$	−8.74304	−0.392970
$496$	2.49358	0.111965
$497$	56.2752	2.52429
$498$	−6.48990	−0.290819
$499$	38.0349	1.70268	0.851339	−	0.524616i	$-0.175791\pi$
$499$	38.0349	1.70268	0.851339	+	0.524616i	$0.175791\pi$
$500$	2.30730	0.103185
$501$	−11.0991	−0.495871
$502$	−4.11455	−0.183642
$503$	−6.18404	−0.275733	−0.137866	−	0.990451i	$-0.544024\pi$
$503$	−6.18404	−0.275733	−0.137866	+	0.990451i	$0.544024\pi$
$504$	7.90916	0.352302
$505$	44.1060	1.96269
$506$	7.59437	0.337611
$507$	−12.1028	−0.537505
$508$	−4.35698	−0.193310
$509$	34.7881	1.54195	0.770977	−	0.636863i	$-0.219768\pi$
$509$	34.7881	1.54195	0.770977	+	0.636863i	$0.219768\pi$
$510$	1.67061	0.0739757
$511$	42.6958	1.88875
$512$	21.6464	0.956646
$513$	5.30126	0.234057
$514$	−7.68775	−0.339092
$515$	−13.7052	−0.603922
$516$	11.4738	0.505108
$517$	19.6838	0.865692
$518$	−7.12378	−0.313001
$519$	14.9637	0.656833
$520$	−5.86776	−0.257318
$521$	28.9693	1.26917	0.634584	−	0.772854i	$-0.281171\pi$
$521$	28.9693	1.26917	0.634584	+	0.772854i	$0.281171\pi$
$522$	−4.46600	−0.195471
$523$	20.0550	0.876942	0.438471	−	0.898745i	$-0.355520\pi$
$523$	20.0550	0.876942	0.438471	+	0.898745i	$0.355520\pi$
$524$	37.6111	1.64305
$525$	−18.0165	−0.786304
$526$	10.1862	0.444138
$527$	1.06831	0.0465364
$528$	−6.59911	−0.287190
$529$	1.72392	0.0749531
$530$	−0.766392	−0.0332899
$531$	−5.42117	−0.235259
$532$	35.7526	1.55007
$533$	3.88405	0.168237
$534$	−0.0711171	−0.00307754
$535$	−47.9507	−2.07309
$536$	−23.1918	−1.00173
$537$	−0.609097	−0.0262845
$538$	−7.80375	−0.336444
$539$	−24.2811	−1.04586
$540$	−5.28239	−0.227318
$541$	13.5912	0.584330	0.292165	−	0.956368i	$-0.405624\pi$
$541$	13.5912	0.584330	0.292165	+	0.956368i	$0.405624\pi$
$542$	6.66959	0.286484
$543$	5.62019	0.241185
$544$	5.26741	0.225838
$545$	−15.3734	−0.658526
$546$	−2.02028	−0.0864601
$547$	10.0968	0.431706	0.215853	−	0.976426i	$-0.430747\pi$
$547$	10.0968	0.431706	0.215853	+	0.976426i	$0.430747\pi$
$548$	−12.1646	−0.519647
$549$	−13.9711	−0.596272
$550$	−6.96953	−0.297182
$551$	−43.8253	−1.86702
$552$	9.96069	0.423955
$553$	3.94821	0.167895
$554$	1.35497	0.0575670
$555$	10.3286	0.438424
$556$	−3.70491	−0.157123
$557$	−26.9046	−1.13999	−0.569993	−	0.821649i	$-0.693054\pi$
$557$	−26.9046	−1.13999	−0.569993	+	0.821649i	$0.693054\pi$
$558$	0.577126	0.0244317
$559$	−6.36239	−0.269100
$560$	−28.4988	−1.20429
$561$	−2.82723	−0.119366
$562$	11.7613	0.496121
$563$	−29.9093	−1.26053	−0.630263	−	0.776382i	$-0.717053\pi$
$563$	−29.9093	−1.26053	−0.630263	+	0.776382i	$0.717053\pi$
$564$	11.8926	0.500769
$565$	38.7377	1.62971
$566$	14.6576	0.616103
$567$	−3.94821	−0.165809
$568$	28.5527	1.19805
$569$	−23.2640	−0.975277	−0.487639	−	0.873046i	$-0.662142\pi$
$569$	−23.2640	−0.975277	−0.487639	+	0.873046i	$0.662142\pi$
$570$	8.85633	0.370951
$571$	−1.17575	−0.0492036	−0.0246018	−	0.999697i	$-0.507832\pi$
$571$	−1.17575	−0.0492036	−0.0246018	+	0.999697i	$0.507832\pi$
$572$	4.57434	0.191263
$573$	24.7328	1.03323
$574$	−8.74616	−0.365058
$575$	−22.6897	−0.946227
$576$	−1.82269	−0.0759454
$577$	9.79228	0.407658	0.203829	−	0.979006i	$-0.434661\pi$
$577$	9.79228	0.407658	0.203829	+	0.979006i	$0.434661\pi$
$578$	0.540222	0.0224703
$579$	−1.25820	−0.0522889
$580$	43.6693	1.81327
$581$	47.4313	1.96778
$582$	−7.49155	−0.310535
$583$	1.29699	0.0537159
$584$	21.6629	0.896417
$585$	2.92915	0.121105
$586$	17.7065	0.731449
$587$	−39.0670	−1.61247	−0.806233	−	0.591598i	$-0.798497\pi$
$587$	−39.0670	−1.61247	−0.806233	+	0.591598i	$0.798497\pi$
$588$	−14.6702	−0.604990
$589$	5.66341	0.233357
$590$	−9.05665	−0.372856
$591$	−4.56529	−0.187791
$592$	7.79585	0.320408
$593$	46.2273	1.89833	0.949163	−	0.314784i	$-0.101932\pi$
$593$	46.2273	1.89833	0.949163	+	0.314784i	$0.101932\pi$
$594$	−1.52733	−0.0626671
$595$	−12.2096	−0.500545
$596$	−13.9181	−0.570107
$597$	15.3033	0.626321
$598$	−2.54432	−0.104045
$599$	6.48434	0.264943	0.132472	−	0.991187i	$-0.457709\pi$
$599$	6.48434	0.264943	0.132472	+	0.991187i	$0.457709\pi$
$600$	−9.14116	−0.373186
$601$	−17.7347	−0.723412	−0.361706	−	0.932292i	$-0.617805\pi$
$601$	−17.7347	−0.723412	−0.361706	+	0.932292i	$0.617805\pi$
$602$	14.3269	0.583921
$603$	11.5772	0.471461
$604$	7.81548	0.318007
$605$	−9.29835	−0.378032
$606$	7.70493	0.312991
$607$	6.49377	0.263574	0.131787	−	0.991278i	$-0.457929\pi$
$607$	6.49377	0.263574	0.131787	+	0.991278i	$0.457929\pi$
$608$	27.9239	1.13246
$609$	32.6397	1.32263
$610$	−23.3402	−0.945018
$611$	−6.59459	−0.266789
$612$	−1.70816	−0.0690483
$613$	44.2719	1.78812	0.894062	−	0.447944i	$-0.147844\pi$
$613$	44.2719	1.78812	0.894062	+	0.447944i	$0.147844\pi$
$614$	−16.8317	−0.679271
$615$	12.6808	0.511340
$616$	−22.3610	−0.900950
$617$	9.58866	0.386025	0.193012	−	0.981196i	$-0.438174\pi$
$617$	9.58866	0.386025	0.193012	+	0.981196i	$0.438174\pi$
$618$	−2.39417	−0.0963076
$619$	18.3660	0.738194	0.369097	−	0.929391i	$-0.379667\pi$
$619$	18.3660	0.738194	0.369097	+	0.929391i	$0.379667\pi$
$620$	−5.64324	−0.226638
$621$	−4.97232	−0.199532
$622$	1.58484	0.0635464
$623$	0.519758	0.0208237
$624$	2.21088	0.0885060
$625$	−26.9932	−1.07973
$626$	12.2835	0.490949
$627$	−14.9879	−0.598558
$628$	−18.0490	−0.720232
$629$	3.33994	0.133172
$630$	−6.59590	−0.262787
$631$	−4.17942	−0.166380	−0.0831900	−	0.996534i	$-0.526511\pi$
$631$	−4.17942	−0.166380	−0.0831900	+	0.996534i	$0.526511\pi$
$632$	2.00323	0.0796842
$633$	−20.6840	−0.822114
$634$	0.123680	0.00491196
$635$	7.88786	0.313020
$636$	0.783620	0.0310725
$637$	8.13483	0.322314
$638$	12.6264	0.499883
$639$	−14.2534	−0.563854
$640$	−35.6233	−1.40814
$641$	28.2662	1.11645	0.558223	−	0.829691i	$-0.311483\pi$
$641$	28.2662	1.11645	0.558223	+	0.829691i	$0.311483\pi$
$642$	−8.37656	−0.330597
$643$	−39.7895	−1.56914	−0.784572	−	0.620038i	$-0.787117\pi$
$643$	−39.7895	−1.56914	−0.784572	+	0.620038i	$0.787117\pi$
$644$	−33.5341	−1.32143
$645$	−20.7722	−0.817904
$646$	2.86386	0.112677
$647$	33.8606	1.33120	0.665598	−	0.746310i	$-0.268176\pi$
$647$	33.8606	1.33120	0.665598	+	0.746310i	$0.268176\pi$
$648$	−2.00323	−0.0786943
$649$	15.3269	0.601632
$650$	2.33498	0.0915854
$651$	−4.21792	−0.165313
$652$	−13.4090	−0.525138
$653$	12.8989	0.504771	0.252386	−	0.967627i	$-0.418785\pi$
$653$	12.8989	0.504771	0.252386	+	0.967627i	$0.418785\pi$
$654$	−2.68560	−0.105015
$655$	−68.0910	−2.66054
$656$	9.57129	0.373696
$657$	−10.8140	−0.421894
$658$	14.8498	0.578905
$659$	−26.4062	−1.02864	−0.514320	−	0.857598i	$-0.671956\pi$
$659$	−26.4062	−1.02864	−0.514320	+	0.857598i	$0.671956\pi$
$660$	14.9345	0.581325
$661$	−29.5228	−1.14830	−0.574152	−	0.818749i	$-0.694668\pi$
$661$	−29.5228	−1.14830	−0.574152	+	0.818749i	$0.694668\pi$
$662$	−8.07853	−0.313981
$663$	0.947196	0.0367860
$664$	24.0656	0.933925
$665$	−64.7263	−2.50998
$666$	1.80431	0.0699156
$667$	41.1059	1.59163
$668$	18.9590	0.733547
$669$	24.5525	0.949254
$670$	19.3410	0.747207
$671$	39.4994	1.52486
$672$	−20.7968	−0.802255
$673$	39.4933	1.52235	0.761176	−	0.648545i	$-0.224622\pi$
$673$	39.4933	1.52235	0.761176	+	0.648545i	$0.224622\pi$
$674$	12.9371	0.498317
$675$	4.56321	0.175638
$676$	20.6736	0.795137
$677$	−13.6279	−0.523763	−0.261882	−	0.965100i	$-0.584343\pi$
$677$	−13.6279	−0.523763	−0.261882	+	0.965100i	$0.584343\pi$
$678$	6.76712	0.259890
$679$	54.7519	2.10118
$680$	−6.19488	−0.237563
$681$	−6.30688	−0.241680
$682$	−1.63167	−0.0624797
$683$	−19.9630	−0.763863	−0.381932	−	0.924191i	$-0.624741\pi$
$683$	−19.9630	−0.763863	−0.381932	+	0.924191i	$0.624741\pi$
$684$	−9.05541	−0.346242
$685$	22.0228	0.841447
$686$	−3.38775	−0.129345
$687$	−5.58146	−0.212946
$688$	−15.6785	−0.597738
$689$	−0.434527	−0.0165542
$690$	−8.30678	−0.316234
$691$	36.9620	1.40610	0.703051	−	0.711140i	$-0.251821\pi$
$691$	36.9620	1.40610	0.703051	+	0.711140i	$0.251821\pi$
$692$	−25.5604	−0.971659
$693$	11.1625	0.424027
$694$	−4.97161	−0.188720
$695$	6.70735	0.254424
$696$	16.5606	0.627729
$697$	4.10058	0.155321
$698$	−13.8111	−0.522757
$699$	−26.3069	−0.995017
$700$	30.7750	1.16319
$701$	−8.01085	−0.302565	−0.151283	−	0.988491i	$-0.548340\pi$
$701$	−8.01085	−0.302565	−0.151283	+	0.988491i	$0.548340\pi$
$702$	0.511696	0.0193127
$703$	17.7059	0.667791
$704$	5.15315	0.194217
$705$	−21.5303	−0.810878
$706$	−4.91267	−0.184891
$707$	−56.3113	−2.11781
$708$	9.26023	0.348021
$709$	0.700800	0.0263191	0.0131595	−	0.999913i	$-0.495811\pi$
$709$	0.700800	0.0263191	0.0131595	+	0.999913i	$0.495811\pi$
$710$	−23.8117	−0.893639
$711$	−1.00000	−0.0375029
$712$	0.263713	0.00988308
$713$	−5.31199	−0.198935
$714$	−2.13291	−0.0798221
$715$	−8.28137	−0.309706
$716$	1.04044	0.0388829
$717$	16.3568	0.610854
$718$	3.86741	0.144331
$719$	32.1013	1.19718	0.598588	−	0.801057i	$-0.295729\pi$
$719$	32.1013	1.19718	0.598588	+	0.801057i	$0.295729\pi$
$720$	7.21817	0.269005
$721$	17.4978	0.651650
$722$	4.91786	0.183024
$723$	16.9114	0.628942
$724$	−9.60018	−0.356788
$725$	−37.7239	−1.40103
$726$	−1.62434	−0.0602849
$727$	−0.914576	−0.0339197	−0.0169599	−	0.999856i	$-0.505399\pi$
$727$	−0.914576	−0.0339197	−0.0169599	+	0.999856i	$0.505399\pi$
$728$	7.49153	0.277655
$729$	1.00000	0.0370370
$730$	−18.0659	−0.668649
$731$	−6.71707	−0.248440
$732$	23.8649	0.882071
$733$	−10.6538	−0.393508	−0.196754	−	0.980453i	$-0.563040\pi$
$733$	−10.6538	−0.393508	−0.196754	+	0.980453i	$0.563040\pi$
$734$	−16.0442	−0.592201
$735$	26.5589	0.979640
$736$	−26.1912	−0.965421
$737$	−32.7314	−1.20568
$738$	2.21522	0.0815435
$739$	7.60848	0.279882	0.139941	−	0.990160i	$-0.455309\pi$
$739$	7.60848	0.279882	0.139941	+	0.990160i	$0.455309\pi$
$740$	−17.6429	−0.648564
$741$	5.02134	0.184463
$742$	0.978473	0.0359209
$743$	−23.8922	−0.876518	−0.438259	−	0.898849i	$-0.644405\pi$
$743$	−23.8922	−0.876518	−0.438259	+	0.898849i	$0.644405\pi$
$744$	−2.14008	−0.0784590
$745$	25.1972	0.923155
$746$	4.91850	0.180079
$747$	−12.0134	−0.439547
$748$	4.82935	0.176579
$749$	61.2200	2.23693
$750$	−0.729705	−0.0266450
$751$	−39.0388	−1.42454	−0.712272	−	0.701903i	$-0.752334\pi$
$751$	−39.0388	−1.42454	−0.712272	+	0.701903i	$0.752334\pi$
$752$	−16.2507	−0.592604
$753$	−7.61641	−0.277557
$754$	−4.23017	−0.154054
$755$	−14.1491	−0.514939
$756$	6.74417	0.245283
$757$	35.3048	1.28318	0.641588	−	0.767049i	$-0.278276\pi$
$757$	35.3048	1.28318	0.641588	+	0.767049i	$0.278276\pi$
$758$	−15.9664	−0.579926
$759$	14.0579	0.510268
$760$	−32.8407	−1.19126
$761$	−10.0964	−0.365993	−0.182997	−	0.983114i	$-0.558580\pi$
$761$	−10.0964	−0.365993	−0.182997	+	0.983114i	$0.558580\pi$
$762$	1.37794	0.0499174
$763$	19.6277	0.710570
$764$	−42.2477	−1.52847
$765$	3.09244	0.111808
$766$	12.5820	0.454606
$767$	−5.13491	−0.185411
$768$	−2.57770	−0.0930147
$769$	−5.28167	−0.190462	−0.0952309	−	0.995455i	$-0.530359\pi$
$769$	−5.28167	−0.190462	−0.0952309	+	0.995455i	$0.530359\pi$
$770$	18.6481	0.672031
$771$	−14.2307	−0.512507
$772$	2.14920	0.0773516
$773$	37.1825	1.33736	0.668680	−	0.743550i	$-0.266859\pi$
$773$	37.1825	1.33736	0.668680	+	0.743550i	$0.266859\pi$
$774$	−3.62871	−0.130431
$775$	4.87493	0.175113
$776$	27.7799	0.997239
$777$	−13.1868	−0.473073
$778$	−6.32177	−0.226646
$779$	21.7383	0.778854
$780$	−5.00346	−0.179153
$781$	40.2974	1.44196
$782$	−2.68616	−0.0960567
$783$	−8.26696	−0.295437
$784$	20.0463	0.715938
$785$	32.6757	1.16625
$786$	−11.8949	−0.424277
$787$	48.6528	1.73428	0.867142	−	0.498061i	$-0.165954\pi$
$787$	48.6528	1.73428	0.867142	+	0.498061i	$0.165954\pi$
$788$	7.79825	0.277801
$789$	18.8555	0.671274
$790$	−1.67061	−0.0594375
$791$	−49.4574	−1.75850
$792$	5.66358	0.201247
$793$	−13.2334	−0.469931
$794$	7.16926	0.254427
$795$	−1.41866	−0.0503147
$796$	−26.1404	−0.926523
$797$	17.2042	0.609404	0.304702	−	0.952448i	$-0.401443\pi$
$797$	17.2042	0.609404	0.304702	+	0.952448i	$0.401443\pi$
$798$	−11.3071	−0.400267
$799$	−6.96223	−0.246306
$800$	24.0363	0.849811
$801$	−0.131644	−0.00465142
$802$	−16.0081	−0.565265
$803$	30.5736	1.07892
$804$	−19.7757	−0.697437
$805$	60.7100	2.13975
$806$	0.546652	0.0192550
$807$	−14.4454	−0.508504
$808$	−28.5711	−1.00513
$809$	9.07870	0.319190	0.159595	−	0.987183i	$-0.448981\pi$
$809$	9.07870	0.319190	0.159595	+	0.987183i	$0.448981\pi$
$810$	1.67061	0.0586991
$811$	−40.5566	−1.42413	−0.712067	−	0.702112i	$-0.752241\pi$
$811$	−40.5566	−1.42413	−0.712067	+	0.702112i	$0.752241\pi$
$812$	−55.7538	−1.95657
$813$	12.3460	0.432994
$814$	−5.10119	−0.178797
$815$	24.2756	0.850339
$816$	2.33413	0.0817109
$817$	−35.6090	−1.24580
$818$	−16.6775	−0.583114
$819$	−3.73972	−0.130677
$820$	−21.6609	−0.756430
$821$	13.4000	0.467662	0.233831	−	0.972277i	$-0.424874\pi$
$821$	13.4000	0.467662	0.233831	+	0.972277i	$0.424874\pi$
$822$	3.84718	0.134186
$823$	−14.6039	−0.509059	−0.254529	−	0.967065i	$-0.581921\pi$
$823$	−14.6039	−0.509059	−0.254529	+	0.967065i	$0.581921\pi$
$824$	8.87797	0.309279
$825$	−12.9012	−0.449163
$826$	11.5629	0.402323
$827$	20.6560	0.718280	0.359140	−	0.933284i	$-0.383070\pi$
$827$	20.6560	0.718280	0.359140	+	0.933284i	$0.383070\pi$
$828$	8.49351	0.295170
$829$	3.57595	0.124198	0.0620990	−	0.998070i	$-0.480221\pi$
$829$	3.57595	0.124198	0.0620990	+	0.998070i	$0.480221\pi$
$830$	−20.0696	−0.696627
$831$	2.50816	0.0870072
$832$	−1.72644	−0.0598537
$833$	8.58832	0.297568
$834$	1.17171	0.0405731
$835$	−34.3233	−1.18781
$836$	25.6017	0.885452
$837$	1.06831	0.0369263
$838$	14.2661	0.492813
$839$	1.91217	0.0660155	0.0330077	−	0.999455i	$-0.489491\pi$
$839$	1.91217	0.0660155	0.0330077	+	0.999455i	$0.489491\pi$
$840$	24.4586	0.843904
$841$	39.3426	1.35664
$842$	16.9497	0.584125
$843$	21.7712	0.749841
$844$	35.3315	1.21616
$845$	−37.4273	−1.28754
$846$	−3.76115	−0.129311
$847$	11.8715	0.407908
$848$	−1.07078	−0.0367709
$849$	27.1324	0.931183
$850$	2.46515	0.0845539
$851$	−16.6072	−0.569289
$852$	24.3470	0.834115
$853$	−3.85559	−0.132013	−0.0660064	−	0.997819i	$-0.521026\pi$
$853$	−3.85559	−0.132013	−0.0660064	+	0.997819i	$0.521026\pi$
$854$	29.7991	1.01970
$855$	16.3939	0.560658
$856$	31.0616	1.06166
$857$	4.84501	0.165502	0.0827512	−	0.996570i	$-0.473629\pi$
$857$	4.84501	0.165502	0.0827512	+	0.996570i	$0.473629\pi$
$858$	−1.44668	−0.0493889
$859$	−45.4294	−1.55003	−0.775016	−	0.631942i	$-0.782258\pi$
$859$	−45.4294	−1.55003	−0.775016	+	0.631942i	$0.782258\pi$
$860$	35.4822	1.20993
$861$	−16.1899	−0.551751
$862$	−6.93092	−0.236068
$863$	19.7481	0.672235	0.336117	−	0.941820i	$-0.390886\pi$
$863$	19.7481	0.672235	0.336117	+	0.941820i	$0.390886\pi$
$864$	5.26741	0.179201
$865$	46.2744	1.57338
$866$	1.69726	0.0576751
$867$	1.00000	0.0339618
$868$	7.20488	0.244549
$869$	2.82723	0.0959070
$870$	−13.8108	−0.468231
$871$	10.9659	0.371565
$872$	9.95864	0.337242
$873$	−13.8675	−0.469345
$874$	−14.2400	−0.481676
$875$	5.33303	0.180289
$876$	18.4720	0.624111
$877$	37.2289	1.25713	0.628566	−	0.777756i	$-0.283642\pi$
$877$	37.2289	1.25713	0.628566	+	0.777756i	$0.283642\pi$
$878$	−3.66924	−0.123831
$879$	32.7763	1.10552
$880$	−20.4074	−0.687933
$881$	14.8749	0.501147	0.250573	−	0.968098i	$-0.419381\pi$
$881$	14.8749	0.501147	0.250573	+	0.968098i	$0.419381\pi$
$882$	4.63960	0.156224
$883$	8.67537	0.291949	0.145975	−	0.989288i	$-0.453368\pi$
$883$	8.67537	0.291949	0.145975	+	0.989288i	$0.453368\pi$
$884$	−1.61796	−0.0544180
$885$	−16.7647	−0.563538
$886$	−13.5838	−0.456358
$887$	48.4314	1.62617	0.813083	−	0.582148i	$-0.197788\pi$
$887$	48.4314	1.62617	0.813083	+	0.582148i	$0.197788\pi$
$888$	−6.69067	−0.224524
$889$	−10.0706	−0.337758
$890$	−0.219926	−0.00737192
$891$	−2.82723	−0.0947156
$892$	−41.9396	−1.40424
$893$	−36.9086	−1.23510
$894$	4.40173	0.147216
$895$	−1.88360	−0.0629617
$896$	45.4813	1.51942
$897$	−4.70976	−0.157254
$898$	−8.45247	−0.282063
$899$	−8.83170	−0.294554
$900$	−7.79469	−0.259823
$901$	−0.458751	−0.0152832
$902$	−6.26294	−0.208533
$903$	26.5204	0.882543
$904$	−25.0936	−0.834600
$905$	17.3801	0.577735
$906$	−2.47172	−0.0821175
$907$	24.6065	0.817045	0.408522	−	0.912748i	$-0.366044\pi$
$907$	24.6065	0.817045	0.408522	+	0.912748i	$0.366044\pi$
$908$	10.7732	0.357520
$909$	14.2625	0.473058
$910$	−6.24761	−0.207106
$911$	10.2742	0.340398	0.170199	−	0.985410i	$-0.445559\pi$
$911$	10.2742	0.340398	0.170199	+	0.985410i	$0.445559\pi$
$912$	12.3738	0.409739
$913$	33.9645	1.12406
$914$	−9.88765	−0.327054
$915$	−43.2048	−1.42831
$916$	9.53402	0.315013
$917$	86.9336	2.87080
$918$	0.540222	0.0178300
$919$	−20.6269	−0.680419	−0.340209	−	0.940350i	$-0.610498\pi$
$919$	−20.6269	−0.680419	−0.340209	+	0.940350i	$0.610498\pi$
$920$	30.8029	1.01554
$921$	−31.1570	−1.02666
$922$	−10.2780	−0.338488
$923$	−13.5007	−0.444382
$924$	−19.0673	−0.627267
$925$	15.2408	0.501116
$926$	−1.83152	−0.0601874
$927$	−4.43182	−0.145560
$928$	−43.5455	−1.42945
$929$	49.3602	1.61946	0.809728	−	0.586805i	$-0.199614\pi$
$929$	49.3602	1.61946	0.809728	+	0.586805i	$0.199614\pi$
$930$	1.78473	0.0585236
$931$	45.5290	1.49215
$932$	44.9363	1.47194
$933$	2.93369	0.0960446
$934$	−14.5579	−0.476349
$935$	−8.74304	−0.285928
$936$	−1.89745	−0.0620201
$937$	4.81780	0.157391	0.0786954	−	0.996899i	$-0.474925\pi$
$937$	4.81780	0.157391	0.0786954	+	0.996899i	$0.474925\pi$
$938$	−24.6931	−0.806260
$939$	22.7379	0.742025
$940$	36.7772	1.19954
$941$	6.40076	0.208659	0.104329	−	0.994543i	$-0.466730\pi$
$941$	6.40076	0.208659	0.104329	+	0.994543i	$0.466730\pi$
$942$	5.70816	0.185982
$943$	−20.3894	−0.663970
$944$	−12.6537	−0.411844
$945$	−12.2096	−0.397178
$946$	10.2592	0.333555
$947$	−38.8626	−1.26286	−0.631432	−	0.775431i	$-0.717533\pi$
$947$	−38.8626	−1.26286	−0.631432	+	0.775431i	$0.717533\pi$
$948$	1.70816	0.0554785
$949$	−10.2430	−0.332501
$950$	13.0684	0.423995
$951$	0.228943	0.00742399
$952$	7.90916	0.256337
$953$	14.1546	0.458512	0.229256	−	0.973366i	$-0.426371\pi$
$953$	14.1546	0.458512	0.229256	+	0.973366i	$0.426371\pi$
$954$	−0.247827	−0.00802370
$955$	76.4849	2.47499
$956$	−27.9400	−0.903643
$957$	23.3726	0.755527
$958$	−5.85158	−0.189056
$959$	−28.1171	−0.907948
$960$	−5.63656	−0.181919
$961$	−29.8587	−0.963184
$962$	1.70903	0.0551015
$963$	−15.5058	−0.499666
$964$	−28.8874	−0.930401
$965$	−3.89091	−0.125253
$966$	10.6055	0.341226
$967$	25.8182	0.830259	0.415129	−	0.909762i	$-0.363736\pi$
$967$	25.8182	0.830259	0.415129	+	0.909762i	$0.363736\pi$
$968$	6.02331	0.193596
$969$	5.30126	0.170301
$970$	−23.1672	−0.743854
$971$	14.3788	0.461437	0.230718	−	0.973021i	$-0.425892\pi$
$971$	14.3788	0.461437	0.230718	+	0.973021i	$0.425892\pi$
$972$	−1.70816	−0.0547893
$973$	−8.56345	−0.274531
$974$	−5.67381	−0.181801
$975$	4.32225	0.138423
$976$	−32.6104	−1.04383
$977$	−43.3783	−1.38780	−0.693898	−	0.720073i	$-0.744108\pi$
$977$	−43.3783	−1.38780	−0.693898	+	0.720073i	$0.744108\pi$
$978$	4.24074	0.135604
$979$	0.372188	0.0118952
$980$	−45.3669	−1.44919
$981$	−4.97129	−0.158721
$982$	−6.35174	−0.202692
$983$	−9.90426	−0.315897	−0.157948	−	0.987447i	$-0.550488\pi$
$983$	−9.90426	−0.315897	−0.157948	+	0.987447i	$0.550488\pi$
$984$	−8.21441	−0.261866
$985$	−14.1179	−0.449834
$986$	−4.46600	−0.142226
$987$	27.4883	0.874962
$988$	−8.57725	−0.272879
$989$	33.3994	1.06204
$990$	−4.72318	−0.150113
$991$	−16.9052	−0.537012	−0.268506	−	0.963278i	$-0.586530\pi$
$991$	−16.9052	−0.537012	−0.268506	+	0.963278i	$0.586530\pi$
$992$	5.62724	0.178665
$993$	−14.9541	−0.474554
$994$	30.4011	0.964264
$995$	47.3245	1.50029
$996$	20.5208	0.650226
$997$	−11.7735	−0.372872	−0.186436	−	0.982467i	$-0.559694\pi$
$997$	−11.7735	−0.372872	−0.186436	+	0.982467i	$0.559694\pi$
$998$	20.5473	0.650414
$999$	3.33994	0.105671

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.e.1.12	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.e.1.12	✓	18	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+0.540222 q^{2} +1.00000 q^{3} -1.70816 q^{4} +3.09244 q^{5} +0.540222 q^{6} -3.94821 q^{7} -2.00323 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.540222 q^{2} +1.00000 q^{3} -1.70816 q^{4} +3.09244 q^{5} +0.540222 q^{6} -3.94821 q^{7} -2.00323 q^{8} +1.00000 q^{9} +1.67061 q^{10} -2.82723 q^{11} -1.70816 q^{12} +0.947196 q^{13} -2.13291 q^{14} +3.09244 q^{15} +2.33413 q^{16} +1.00000 q^{17} +0.540222 q^{18} +5.30126 q^{19} -5.28239 q^{20} -3.94821 q^{21} -1.52733 q^{22} -4.97232 q^{23} -2.00323 q^{24} +4.56321 q^{25} +0.511696 q^{26} +1.00000 q^{27} +6.74417 q^{28} -8.26696 q^{29} +1.67061 q^{30} +1.06831 q^{31} +5.26741 q^{32} -2.82723 q^{33} +0.540222 q^{34} -12.2096 q^{35} -1.70816 q^{36} +3.33994 q^{37} +2.86386 q^{38} +0.947196 q^{39} -6.19488 q^{40} +4.10058 q^{41} -2.13291 q^{42} -6.71707 q^{43} +4.82935 q^{44} +3.09244 q^{45} -2.68616 q^{46} -6.96223 q^{47} +2.33413 q^{48} +8.58832 q^{49} +2.46515 q^{50} +1.00000 q^{51} -1.61796 q^{52} -0.458751 q^{53} +0.540222 q^{54} -8.74304 q^{55} +7.90916 q^{56} +5.30126 q^{57} -4.46600 q^{58} -5.42117 q^{59} -5.28239 q^{60} -13.9711 q^{61} +0.577126 q^{62} -3.94821 q^{63} -1.82269 q^{64} +2.92915 q^{65} -1.52733 q^{66} +11.5772 q^{67} -1.70816 q^{68} -4.97232 q^{69} -6.59590 q^{70} -14.2534 q^{71} -2.00323 q^{72} -10.8140 q^{73} +1.80431 q^{74} +4.56321 q^{75} -9.05541 q^{76} +11.1625 q^{77} +0.511696 q^{78} -1.00000 q^{79} +7.21817 q^{80} +1.00000 q^{81} +2.21522 q^{82} -12.0134 q^{83} +6.74417 q^{84} +3.09244 q^{85} -3.62871 q^{86} -8.26696 q^{87} +5.66358 q^{88} -0.131644 q^{89} +1.67061 q^{90} -3.73972 q^{91} +8.49351 q^{92} +1.06831 q^{93} -3.76115 q^{94} +16.3939 q^{95} +5.26741 q^{96} -13.8675 q^{97} +4.63960 q^{98} -2.82723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * q^99

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