LMFDB - Embedded newform 1849.2.a.o.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$0$
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} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} + \cdots - 27 $ x^18 - 5x^17 - 15x^16 + 106x^15 + 47x^14 - 897x^13 + 364x^12 + 3855x^11 - 3223x^10 - 8851x^9 + 9909x^8 + 10400x^7 - 14483x^6 - 5118x^5 + 9945x^4 - 27x^3 - 2493x^2 + 513*x - 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.800597$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.800597 q^{2} +0.744601 q^{3} -1.35904 q^{4} -1.40135 q^{5} -0.596125 q^{6} -4.75856 q^{7} +2.68924 q^{8} -2.44557 q^{9} +O(q^{10})$	\(q-0.800597 q^{2} +0.744601 q^{3} -1.35904 q^{4} -1.40135 q^{5} -0.596125 q^{6} -4.75856 q^{7} +2.68924 q^{8} -2.44557 q^{9} +1.12192 q^{10} -2.66114 q^{11} -1.01195 q^{12} -0.617909 q^{13} +3.80969 q^{14} -1.04345 q^{15} +0.565090 q^{16} -5.91161 q^{17} +1.95792 q^{18} +1.79471 q^{19} +1.90450 q^{20} -3.54323 q^{21} +2.13050 q^{22} +2.38437 q^{23} +2.00241 q^{24} -3.03621 q^{25} +0.494696 q^{26} -4.05478 q^{27} +6.46709 q^{28} +1.88348 q^{29} +0.835382 q^{30} -7.49695 q^{31} -5.83089 q^{32} -1.98149 q^{33} +4.73282 q^{34} +6.66842 q^{35} +3.32364 q^{36} +2.22811 q^{37} -1.43684 q^{38} -0.460096 q^{39} -3.76857 q^{40} +2.62427 q^{41} +2.83670 q^{42} +3.61660 q^{44} +3.42710 q^{45} -1.90892 q^{46} +8.96121 q^{47} +0.420767 q^{48} +15.6439 q^{49} +2.43078 q^{50} -4.40179 q^{51} +0.839766 q^{52} -13.7429 q^{53} +3.24624 q^{54} +3.72919 q^{55} -12.7969 q^{56} +1.33634 q^{57} -1.50791 q^{58} -6.78493 q^{59} +1.41809 q^{60} +4.13649 q^{61} +6.00204 q^{62} +11.6374 q^{63} +3.53801 q^{64} +0.865909 q^{65} +1.58637 q^{66} +5.63444 q^{67} +8.03414 q^{68} +1.77540 q^{69} -5.33872 q^{70} +8.58375 q^{71} -6.57673 q^{72} +8.51066 q^{73} -1.78382 q^{74} -2.26077 q^{75} -2.43909 q^{76} +12.6632 q^{77} +0.368351 q^{78} -6.19232 q^{79} -0.791890 q^{80} +4.31752 q^{81} -2.10098 q^{82} -1.27014 q^{83} +4.81541 q^{84} +8.28425 q^{85} +1.40244 q^{87} -7.15644 q^{88} +9.46559 q^{89} -2.74373 q^{90} +2.94036 q^{91} -3.24046 q^{92} -5.58224 q^{93} -7.17432 q^{94} -2.51502 q^{95} -4.34169 q^{96} -4.50752 q^{97} -12.5245 q^{98} +6.50800 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{2} + 5 q^{3} + 19 q^{4} + 11 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 15 q^{9}+O(q^{10}) $ 18 * q + 5 * q^2 + 5 * q^3 + 19 * q^4 + 11 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 15 * q^9	\( 18 q + 5 q^{2} + 5 q^{3} + 19 q^{4} + 11 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} + 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} + 25 q^{18} + 31 q^{19} + 25 q^{20} + 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} + 27 q^{26} + 23 q^{27} + 20 q^{28} + 37 q^{29} - 17 q^{30} - 12 q^{31} + 39 q^{32} + 38 q^{33} + 14 q^{34} + 16 q^{35} + 47 q^{36} - 19 q^{37} + 56 q^{38} + 46 q^{39} + 6 q^{40} - 7 q^{41} - q^{42} + 7 q^{44} + 23 q^{45} - 47 q^{46} - q^{47} + 15 q^{48} - 6 q^{49} - 3 q^{50} + 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} + 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} + 28 q^{61} + 33 q^{62} + 26 q^{63} + 10 q^{64} + 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} + 7 q^{69} - 34 q^{70} + 86 q^{71} - 2 q^{72} - 27 q^{73} - 79 q^{74} + 31 q^{75} + 59 q^{76} + 43 q^{77} + 91 q^{78} + 17 q^{79} + 8 q^{80} - 10 q^{81} + 13 q^{82} - 12 q^{83} - 32 q^{84} + 28 q^{85} - 43 q^{87} - 23 q^{88} + 51 q^{89} + 10 q^{90} - 20 q^{91} + 18 q^{92} - 30 q^{93} - 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} - 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + 5 * q^3 + 19 * q^4 + 11 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 + 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 + 25 * q^18 + 31 * q^19 + 25 * q^20 + 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 + 27 * q^26 + 23 * q^27 + 20 * q^28 + 37 * q^29 - 17 * q^30 - 12 * q^31 + 39 * q^32 + 38 * q^33 + 14 * q^34 + 16 * q^35 + 47 * q^36 - 19 * q^37 + 56 * q^38 + 46 * q^39 + 6 * q^40 - 7 * q^41 - q^42 + 7 * q^44 + 23 * q^45 - 47 * q^46 - q^47 + 15 * q^48 - 6 * q^49 - 3 * q^50 + 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 + 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 + 28 * q^61 + 33 * q^62 + 26 * q^63 + 10 * q^64 + 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 + 7 * q^69 - 34 * q^70 + 86 * q^71 - 2 * q^72 - 27 * q^73 - 79 * q^74 + 31 * q^75 + 59 * q^76 + 43 * q^77 + 91 * q^78 + 17 * q^79 + 8 * q^80 - 10 * q^81 + 13 * q^82 - 12 * q^83 - 32 * q^84 + 28 * q^85 - 43 * q^87 - 23 * q^88 + 51 * q^89 + 10 * q^90 - 20 * q^91 + 18 * q^92 - 30 * q^93 - 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 - 5 * q^98 + 38 * 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 $

$2$	−0.800597	−0.566108	−0.283054	−	0.959104i	$-0.591348\pi$
$2$	−0.800597	−0.566108	−0.283054	+	0.959104i	$0.591348\pi$
$3$	0.744601	0.429896	0.214948	−	0.976626i	$-0.431042\pi$
$3$	0.744601	0.429896	0.214948	+	0.976626i	$0.431042\pi$
$4$	−1.35904	−0.679522
$5$	−1.40135	−0.626704	−0.313352	−	0.949637i	$-0.601452\pi$
$5$	−1.40135	−0.626704	−0.313352	+	0.949637i	$0.601452\pi$
$6$	−0.596125	−0.243367
$7$	−4.75856	−1.79857	−0.899283	−	0.437366i	$-0.855911\pi$
$7$	−4.75856	−1.79857	−0.899283	+	0.437366i	$0.855911\pi$
$8$	2.68924	0.950790
$9$	−2.44557	−0.815190
$10$	1.12192	0.354782
$11$	−2.66114	−0.802363	−0.401182	−	0.915999i	$-0.631400\pi$
$11$	−2.66114	−0.802363	−0.401182	+	0.915999i	$0.631400\pi$
$12$	−1.01195	−0.292124
$13$	−0.617909	−0.171377	−0.0856886	−	0.996322i	$-0.527309\pi$
$13$	−0.617909	−0.171377	−0.0856886	+	0.996322i	$0.527309\pi$
$14$	3.80969	1.01818
$15$	−1.04345	−0.269417
$16$	0.565090	0.141273
$17$	−5.91161	−1.43378	−0.716888	−	0.697188i	$-0.754434\pi$
$17$	−5.91161	−1.43378	−0.716888	+	0.697188i	$0.754434\pi$
$18$	1.95792	0.461485
$19$	1.79471	0.411734	0.205867	−	0.978580i	$-0.433999\pi$
$19$	1.79471	0.411734	0.205867	+	0.978580i	$0.433999\pi$
$20$	1.90450	0.425859
$21$	−3.54323	−0.773196
$22$	2.13050	0.454224
$23$	2.38437	0.497175	0.248588	−	0.968609i	$-0.420034\pi$
$23$	2.38437	0.497175	0.248588	+	0.968609i	$0.420034\pi$
$24$	2.00241	0.408741
$25$	−3.03621	−0.607242
$26$	0.494696	0.0970179
$27$	−4.05478	−0.780342
$28$	6.46709	1.22217
$29$	1.88348	0.349753	0.174877	−	0.984590i	$-0.444047\pi$
$29$	1.88348	0.349753	0.174877	+	0.984590i	$0.444047\pi$
$30$	0.835382	0.152519
$31$	−7.49695	−1.34649	−0.673246	−	0.739419i	$-0.735100\pi$
$31$	−7.49695	−1.34649	−0.673246	+	0.739419i	$0.735100\pi$
$32$	−5.83089	−1.03077
$33$	−1.98149	−0.344932
$34$	4.73282	0.811672
$35$	6.66842	1.12717
$36$	3.32364	0.553940
$37$	2.22811	0.366300	0.183150	−	0.983085i	$-0.441371\pi$
$37$	2.22811	0.366300	0.183150	+	0.983085i	$0.441371\pi$
$38$	−1.43684	−0.233086
$39$	−0.460096	−0.0736743
$40$	−3.76857	−0.595864
$41$	2.62427	0.409842	0.204921	−	0.978779i	$-0.434306\pi$
$41$	2.62427	0.409842	0.204921	+	0.978779i	$0.434306\pi$
$42$	2.83670	0.437712
$43$	0	0
$43$	0	0
$44$	3.61660	0.545224
$45$	3.42710	0.510883
$46$	−1.90892	−0.281455
$47$	8.96121	1.30713	0.653563	−	0.756872i	$-0.273273\pi$
$47$	8.96121	1.30713	0.653563	+	0.756872i	$0.273273\pi$
$48$	0.420767	0.0607324
$49$	15.6439	2.23484
$50$	2.43078	0.343764
$51$	−4.40179	−0.616374
$52$	0.839766	0.116455
$53$	−13.7429	−1.88774	−0.943868	−	0.330323i	$-0.892842\pi$
$53$	−13.7429	−1.88774	−0.943868	+	0.330323i	$0.892842\pi$
$54$	3.24624	0.441758
$55$	3.72919	0.502844
$56$	−12.7969	−1.71006
$57$	1.33634	0.177003
$58$	−1.50791	−0.197998
$59$	−6.78493	−0.883323	−0.441662	−	0.897182i	$-0.645611\pi$
$59$	−6.78493	−0.883323	−0.441662	+	0.897182i	$0.645611\pi$
$60$	1.41809	0.183075
$61$	4.13649	0.529624	0.264812	−	0.964300i	$-0.414690\pi$
$61$	4.13649	0.529624	0.264812	+	0.964300i	$0.414690\pi$
$62$	6.00204	0.762259
$63$	11.6374	1.46617
$64$	3.53801	0.442252
$65$	0.865909	0.107403
$66$	1.58637	0.195269
$67$	5.63444	0.688356	0.344178	−	0.938904i	$-0.388158\pi$
$67$	5.63444	0.688356	0.344178	+	0.938904i	$0.388158\pi$
$68$	8.03414	0.974283
$69$	1.77540	0.213734
$70$	−5.33872	−0.638099
$71$	8.58375	1.01870	0.509352	−	0.860558i	$-0.329885\pi$
$71$	8.58375	1.01870	0.509352	+	0.860558i	$0.329885\pi$
$72$	−6.57673	−0.775075
$73$	8.51066	0.996098	0.498049	−	0.867149i	$-0.334050\pi$
$73$	8.51066	0.996098	0.498049	+	0.867149i	$0.334050\pi$
$74$	−1.78382	−0.207365
$75$	−2.26077	−0.261051
$76$	−2.43909	−0.279783
$77$	12.6632	1.44310
$78$	0.368351	0.0417076
$79$	−6.19232	−0.696690	−0.348345	−	0.937366i	$-0.613256\pi$
$79$	−6.19232	−0.696690	−0.348345	+	0.937366i	$0.613256\pi$
$80$	−0.791890	−0.0885360
$81$	4.31752	0.479724
$82$	−2.10098	−0.232015
$83$	−1.27014	−0.139416	−0.0697079	−	0.997567i	$-0.522207\pi$
$83$	−1.27014	−0.139416	−0.0697079	+	0.997567i	$0.522207\pi$
$84$	4.81541	0.525404
$85$	8.28425	0.898553
$86$	0	0
$87$	1.40244	0.150357
$88$	−7.15644	−0.762879
$89$	9.46559	1.00335	0.501675	−	0.865056i	$-0.332717\pi$
$89$	9.46559	1.00335	0.501675	+	0.865056i	$0.332717\pi$
$90$	−2.74373	−0.289215
$91$	2.94036	0.308233
$92$	−3.24046	−0.337842
$93$	−5.58224	−0.578851
$94$	−7.17432	−0.739974
$95$	−2.51502	−0.258036
$96$	−4.34169	−0.443122
$97$	−4.50752	−0.457669	−0.228835	−	0.973465i	$-0.573492\pi$
$97$	−4.50752	−0.457669	−0.228835	+	0.973465i	$0.573492\pi$
$98$	−12.5245	−1.26516
$99$	6.50800	0.654078
$100$	4.12635	0.412635
$101$	−11.2001	−1.11445	−0.557225	−	0.830362i	$-0.688134\pi$
$101$	−11.2001	−1.11445	−0.557225	+	0.830362i	$0.688134\pi$
$102$	3.52406	0.348934
$103$	−10.3557	−1.02038	−0.510189	−	0.860062i	$-0.670425\pi$
$103$	−10.3557	−1.02038	−0.510189	+	0.860062i	$0.670425\pi$
$104$	−1.66171	−0.162944
$105$	4.96531	0.484565
$106$	11.0025	1.06866
$107$	−4.79584	−0.463631	−0.231815	−	0.972760i	$-0.574467\pi$
$107$	−4.79584	−0.463631	−0.231815	+	0.972760i	$0.574467\pi$
$108$	5.51062	0.530260
$109$	17.8744	1.71206	0.856029	−	0.516927i	$-0.172924\pi$
$109$	17.8744	1.71206	0.856029	+	0.516927i	$0.172924\pi$
$110$	−2.98558	−0.284664
$111$	1.65906	0.157471
$112$	−2.68902	−0.254088
$113$	−1.28727	−0.121096	−0.0605480	−	0.998165i	$-0.519285\pi$
$113$	−1.28727	−0.121096	−0.0605480	+	0.998165i	$0.519285\pi$
$114$	−1.06987	−0.100203
$115$	−3.34134	−0.311582
$116$	−2.55973	−0.237665
$117$	1.51114	0.139705
$118$	5.43200	0.500056
$119$	28.1308	2.57874
$120$	−2.80608	−0.256159
$121$	−3.91834	−0.356213
$122$	−3.31166	−0.299824
$123$	1.95403	0.176189
$124$	10.1887	0.914971
$125$	11.2616	1.00726
$126$	−9.31686	−0.830012
$127$	4.39380	0.389887	0.194943	−	0.980815i	$-0.437548\pi$
$127$	4.39380	0.389887	0.194943	+	0.980815i	$0.437548\pi$
$128$	8.82926	0.780404
$129$	0	0
$130$	−0.693244	−0.0608015
$131$	−14.1196	−1.23364	−0.616818	−	0.787105i	$-0.711579\pi$
$131$	−14.1196	−1.23364	−0.616818	+	0.787105i	$0.711579\pi$
$132$	2.69293	0.234389
$133$	−8.54023	−0.740532
$134$	−4.51092	−0.389684
$135$	5.68217	0.489043
$136$	−15.8977	−1.36322
$137$	9.40954	0.803912	0.401956	−	0.915659i	$-0.368331\pi$
$137$	9.40954	0.803912	0.401956	+	0.915659i	$0.368331\pi$
$138$	−1.42138	−0.120996
$139$	16.7216	1.41831	0.709154	−	0.705053i	$-0.249077\pi$
$139$	16.7216	1.41831	0.709154	+	0.705053i	$0.249077\pi$
$140$	−9.06268	−0.765936
$141$	6.67252	0.561928
$142$	−6.87213	−0.576696
$143$	1.64434	0.137507
$144$	−1.38197	−0.115164
$145$	−2.63942	−0.219192
$146$	−6.81361	−0.563899
$147$	11.6485	0.960749
$148$	−3.02810	−0.248909
$149$	−11.6675	−0.955842	−0.477921	−	0.878403i	$-0.658610\pi$
$149$	−11.6675	−0.955842	−0.477921	+	0.878403i	$0.658610\pi$
$150$	1.80996	0.147783
$151$	−8.04553	−0.654736	−0.327368	−	0.944897i	$-0.606162\pi$
$151$	−8.04553	−0.654736	−0.327368	+	0.944897i	$0.606162\pi$
$152$	4.82640	0.391473
$153$	14.4573	1.16880
$154$	−10.1381	−0.816952
$155$	10.5059	0.843852
$156$	0.625291	0.0500633
$157$	−7.57395	−0.604467	−0.302234	−	0.953234i	$-0.597732\pi$
$157$	−7.57395	−0.604467	−0.302234	+	0.953234i	$0.597732\pi$
$158$	4.95755	0.394402
$159$	−10.2330	−0.811529
$160$	8.17113	0.645985
$161$	−11.3462	−0.894203
$162$	−3.45659	−0.271575
$163$	−6.17178	−0.483411	−0.241706	−	0.970350i	$-0.577707\pi$
$163$	−6.17178	−0.483411	−0.241706	+	0.970350i	$0.577707\pi$
$164$	−3.56650	−0.278497
$165$	2.77676	0.216171
$166$	1.01687	0.0789244
$167$	−8.81327	−0.681991	−0.340996	−	0.940065i	$-0.610764\pi$
$167$	−8.81327	−0.681991	−0.340996	+	0.940065i	$0.610764\pi$
$168$	−9.52860	−0.735147
$169$	−12.6182	−0.970630
$170$	−6.63235	−0.508678
$171$	−4.38908	−0.335642
$172$	0	0
$173$	6.12350	0.465561	0.232780	−	0.972529i	$-0.425218\pi$
$173$	6.12350	0.465561	0.232780	+	0.972529i	$0.425218\pi$
$174$	−1.12279	−0.0851185
$175$	14.4480	1.09217
$176$	−1.50378	−0.113352
$177$	−5.05207	−0.379737
$178$	−7.57812	−0.568004
$179$	24.5975	1.83850	0.919250	−	0.393674i	$-0.128796\pi$
$179$	24.5975	1.83850	0.919250	+	0.393674i	$0.128796\pi$
$180$	−4.65759	−0.347156
$181$	−5.71084	−0.424484	−0.212242	−	0.977217i	$-0.568076\pi$
$181$	−5.71084	−0.424484	−0.212242	+	0.977217i	$0.568076\pi$
$182$	−2.35404	−0.174493
$183$	3.08004	0.227683
$184$	6.41214	0.472710
$185$	−3.12237	−0.229561
$186$	4.46912	0.327692
$187$	15.7316	1.15041
$188$	−12.1787	−0.888221
$189$	19.2949	1.40350
$190$	2.01352	0.146076
$191$	−0.367830	−0.0266152	−0.0133076	−	0.999911i	$-0.504236\pi$
$191$	−0.367830	−0.0266152	−0.0133076	+	0.999911i	$0.504236\pi$
$192$	2.63441	0.190122
$193$	−8.85059	−0.637080	−0.318540	−	0.947909i	$-0.603192\pi$
$193$	−8.85059	−0.637080	−0.318540	+	0.947909i	$0.603192\pi$
$194$	3.60871	0.259090
$195$	0.644756	0.0461720
$196$	−21.2608	−1.51863
$197$	−3.77089	−0.268665	−0.134332	−	0.990936i	$-0.542889\pi$
$197$	−3.77089	−0.268665	−0.134332	+	0.990936i	$0.542889\pi$
$198$	−5.21028	−0.370279
$199$	−11.3186	−0.802355	−0.401178	−	0.916000i	$-0.631399\pi$
$199$	−11.3186	−0.802355	−0.401178	+	0.916000i	$0.631399\pi$
$200$	−8.16510	−0.577360
$201$	4.19541	0.295921
$202$	8.96675	0.630898
$203$	−8.96265	−0.629055
$204$	5.98223	0.418840
$205$	−3.67752	−0.256849
$206$	8.29075	0.577644
$207$	−5.83114	−0.405292
$208$	−0.349174	−0.0242109
$209$	−4.77597	−0.330361
$210$	−3.97522	−0.274316
$211$	2.85657	0.196655	0.0983273	−	0.995154i	$-0.468651\pi$
$211$	2.85657	0.196655	0.0983273	+	0.995154i	$0.468651\pi$
$212$	18.6772	1.28276
$213$	6.39147	0.437936
$214$	3.83953	0.262465
$215$	0	0
$216$	−10.9043	−0.741942
$217$	35.6747	2.42176
$218$	−14.3102	−0.969209
$219$	6.33705	0.428218
$220$	−5.06814	−0.341694
$221$	3.65284	0.245717
$222$	−1.32823	−0.0891453
$223$	−4.38485	−0.293631	−0.146815	−	0.989164i	$-0.546902\pi$
$223$	−4.38485	−0.293631	−0.146815	+	0.989164i	$0.546902\pi$
$224$	27.7467	1.85390
$225$	7.42527	0.495018
$226$	1.03058	0.0685533
$227$	12.4102	0.823692	0.411846	−	0.911254i	$-0.364884\pi$
$227$	12.4102	0.823692	0.411846	+	0.911254i	$0.364884\pi$
$228$	−1.81615	−0.120277
$229$	10.2159	0.675086	0.337543	−	0.941310i	$-0.390404\pi$
$229$	10.2159	0.675086	0.337543	+	0.941310i	$0.390404\pi$
$230$	2.67507	0.176389
$231$	9.42902	0.620384
$232$	5.06513	0.332542
$233$	−20.4238	−1.33801	−0.669004	−	0.743259i	$-0.733279\pi$
$233$	−20.4238	−1.33801	−0.669004	+	0.743259i	$0.733279\pi$
$234$	−1.20981	−0.0790880
$235$	−12.5578	−0.819181
$236$	9.22103	0.600238
$237$	−4.61081	−0.299504
$238$	−22.5214	−1.45985
$239$	1.93210	0.124977	0.0624886	−	0.998046i	$-0.480096\pi$
$239$	1.93210	0.124977	0.0624886	+	0.998046i	$0.480096\pi$
$240$	−0.589642	−0.0380613
$241$	−14.1986	−0.914612	−0.457306	−	0.889309i	$-0.651186\pi$
$241$	−14.1986	−0.914612	−0.457306	+	0.889309i	$0.651186\pi$
$242$	3.13701	0.201655
$243$	15.3792	0.986573
$244$	−5.62168	−0.359891
$245$	−21.9226	−1.40058
$246$	−1.56439	−0.0997420
$247$	−1.10897	−0.0705619
$248$	−20.1611	−1.28023
$249$	−0.945746	−0.0599342
$250$	−9.01598	−0.570220
$251$	8.62586	0.544459	0.272230	−	0.962232i	$-0.412239\pi$
$251$	8.62586	0.544459	0.272230	+	0.962232i	$0.412239\pi$
$252$	−15.8157	−0.996297
$253$	−6.34514	−0.398915
$254$	−3.51766	−0.220718
$255$	6.16846	0.386284
$256$	−14.1447	−0.884044
$257$	−12.4670	−0.777670	−0.388835	−	0.921307i	$-0.627122\pi$
$257$	−12.4670	−0.777670	−0.388835	+	0.921307i	$0.627122\pi$
$258$	0	0
$259$	−10.6026	−0.658814
$260$	−1.17681	−0.0729825
$261$	−4.60618	−0.285115
$262$	11.3041	0.698371
$263$	17.7549	1.09482	0.547409	−	0.836866i	$-0.315614\pi$
$263$	17.7549	1.09482	0.547409	+	0.836866i	$0.315614\pi$
$264$	−5.32869	−0.327958
$265$	19.2587	1.18305
$266$	6.83728	0.419221
$267$	7.04809	0.431336
$268$	−7.65745	−0.467753
$269$	28.6571	1.74725	0.873626	−	0.486597i	$-0.161762\pi$
$269$	28.6571	1.74725	0.873626	+	0.486597i	$0.161762\pi$
$270$	−4.54913	−0.276851
$271$	18.3252	1.11318	0.556588	−	0.830789i	$-0.312110\pi$
$271$	18.3252	1.11318	0.556588	+	0.830789i	$0.312110\pi$
$272$	−3.34059	−0.202553
$273$	2.18939	0.132508
$274$	−7.53325	−0.455100
$275$	8.07978	0.487229
$276$	−2.41285	−0.145237
$277$	−6.61917	−0.397707	−0.198854	−	0.980029i	$-0.563722\pi$
$277$	−6.61917	−0.397707	−0.198854	+	0.980029i	$0.563722\pi$
$278$	−13.3873	−0.802915
$279$	18.3343	1.09765
$280$	17.9330	1.07170
$281$	−12.8774	−0.768203	−0.384101	−	0.923291i	$-0.625489\pi$
$281$	−12.8774	−0.768203	−0.384101	+	0.923291i	$0.625489\pi$
$282$	−5.34200	−0.318112
$283$	0.626712	0.0372542	0.0186271	−	0.999827i	$-0.494070\pi$
$283$	0.626712	0.0372542	0.0186271	+	0.999827i	$0.494070\pi$
$284$	−11.6657	−0.692232
$285$	−1.87269	−0.110928
$286$	−1.31646	−0.0778436
$287$	−12.4877	−0.737128
$288$	14.2598	0.840270
$289$	17.9471	1.05571
$290$	2.11311	0.124086
$291$	−3.35631	−0.196750
$292$	−11.5664	−0.676871
$293$	21.6524	1.26495	0.632474	−	0.774582i	$-0.282040\pi$
$293$	21.6524	1.26495	0.632474	+	0.774582i	$0.282040\pi$
$294$	−9.32573	−0.543887
$295$	9.50808	0.553582
$296$	5.99193	0.348274
$297$	10.7903	0.626118
$298$	9.34100	0.541110
$299$	−1.47332	−0.0852045
$300$	3.07248	0.177390
$301$	0	0
$302$	6.44123	0.370651
$303$	−8.33959	−0.479097
$304$	1.01417	0.0581668
$305$	−5.79668	−0.331917
$306$	−11.5744	−0.661666
$307$	−8.32206	−0.474965	−0.237482	−	0.971392i	$-0.576322\pi$
$307$	−8.32206	−0.474965	−0.237482	+	0.971392i	$0.576322\pi$
$308$	−17.2098	−0.980621
$309$	−7.71087	−0.438656
$310$	−8.41097	−0.477711
$311$	13.7767	0.781206	0.390603	−	0.920559i	$-0.372267\pi$
$311$	13.7767	0.781206	0.390603	+	0.920559i	$0.372267\pi$
$312$	−1.23731	−0.0700488
$313$	−4.91226	−0.277657	−0.138829	−	0.990316i	$-0.544334\pi$
$313$	−4.91226	−0.277657	−0.138829	+	0.990316i	$0.544334\pi$
$314$	6.06369	0.342194
$315$	−16.3081	−0.918856
$316$	8.41563	0.473416
$317$	18.8491	1.05867	0.529336	−	0.848412i	$-0.322441\pi$
$317$	18.8491	1.05867	0.529336	+	0.848412i	$0.322441\pi$
$318$	8.19251	0.459413
$319$	−5.01220	−0.280629
$320$	−4.95801	−0.277161
$321$	−3.57098	−0.199313
$322$	9.08371	0.506215
$323$	−10.6096	−0.590335
$324$	−5.86770	−0.325983
$325$	1.87610	0.104067
$326$	4.94111	0.273663
$327$	13.3093	0.736006
$328$	7.05729	0.389674
$329$	−42.6424	−2.35095
$330$	−2.22307	−0.122376
$331$	−3.23692	−0.177917	−0.0889587	−	0.996035i	$-0.528354\pi$
$331$	−3.23692	−0.177917	−0.0889587	+	0.996035i	$0.528354\pi$
$332$	1.72617	0.0947361
$333$	−5.44900	−0.298604
$334$	7.05588	0.386080
$335$	−7.89584	−0.431396
$336$	−2.00224	−0.109231
$337$	9.67337	0.526942	0.263471	−	0.964667i	$-0.415133\pi$
$337$	9.67337	0.526942	0.263471	+	0.964667i	$0.415133\pi$
$338$	10.1021	0.549481
$339$	−0.958501	−0.0520586
$340$	−11.2587	−0.610587
$341$	19.9504	1.08038
$342$	3.51389	0.190009
$343$	−41.1325	−2.22095
$344$	0	0
$345$	−2.48797	−0.133948
$346$	−4.90245	−0.263558
$347$	−10.9688	−0.588834	−0.294417	−	0.955677i	$-0.595126\pi$
$347$	−10.9688	−0.588834	−0.294417	+	0.955677i	$0.595126\pi$
$348$	−1.90598	−0.102171
$349$	−21.4626	−1.14887	−0.574433	−	0.818552i	$-0.694777\pi$
$349$	−21.4626	−1.14887	−0.574433	+	0.818552i	$0.694777\pi$
$350$	−11.5670	−0.618283
$351$	2.50548	0.133733
$352$	15.5168	0.827049
$353$	−33.3123	−1.77303	−0.886517	−	0.462697i	$-0.846882\pi$
$353$	−33.3123	−1.77303	−0.886517	+	0.462697i	$0.846882\pi$
$354$	4.04467	0.214972
$355$	−12.0289	−0.638426
$356$	−12.8642	−0.681799
$357$	20.9462	1.10859
$358$	−19.6926	−1.04079
$359$	−7.49810	−0.395735	−0.197867	−	0.980229i	$-0.563402\pi$
$359$	−7.49810	−0.395735	−0.197867	+	0.980229i	$0.563402\pi$
$360$	9.21631	0.485742
$361$	−15.7790	−0.830475
$362$	4.57208	0.240303
$363$	−2.91760	−0.153134
$364$	−3.99608	−0.209451
$365$	−11.9264	−0.624258
$366$	−2.46587	−0.128893
$367$	−5.11699	−0.267105	−0.133552	−	0.991042i	$-0.542638\pi$
$367$	−5.11699	−0.267105	−0.133552	+	0.991042i	$0.542638\pi$
$368$	1.34738	0.0702372
$369$	−6.41783	−0.334099
$370$	2.49976	0.129956
$371$	65.3965	3.39522
$372$	7.58651	0.393342
$373$	32.9012	1.70356	0.851781	−	0.523898i	$-0.175523\pi$
$373$	32.9012	1.70356	0.851781	+	0.523898i	$0.175523\pi$
$374$	−12.5947	−0.651256
$375$	8.38537	0.433019
$376$	24.0988	1.24280
$377$	−1.16382	−0.0599397
$378$	−15.4474	−0.794531
$379$	−8.88937	−0.456616	−0.228308	−	0.973589i	$-0.573319\pi$
$379$	−8.88937	−0.456616	−0.228308	+	0.973589i	$0.573319\pi$
$380$	3.41802	0.175341
$381$	3.27163	0.167611
$382$	0.294484	0.0150671
$383$	13.5797	0.693890	0.346945	−	0.937886i	$-0.387219\pi$
$383$	13.5797	0.693890	0.346945	+	0.937886i	$0.387219\pi$
$384$	6.57428	0.335492
$385$	−17.7456	−0.904399
$386$	7.08576	0.360656
$387$	0	0
$388$	6.12592	0.310997
$389$	3.91962	0.198733	0.0993663	−	0.995051i	$-0.468318\pi$
$389$	3.91962	0.198733	0.0993663	+	0.995051i	$0.468318\pi$
$390$	−0.516190	−0.0261383
$391$	−14.0955	−0.712838
$392$	42.0702	2.12487
$393$	−10.5135	−0.530335
$394$	3.01896	0.152093
$395$	8.67762	0.436618
$396$	−8.84466	−0.444461
$397$	−0.922852	−0.0463166	−0.0231583	−	0.999732i	$-0.507372\pi$
$397$	−0.922852	−0.0463166	−0.0231583	+	0.999732i	$0.507372\pi$
$398$	9.06165	0.454219
$399$	−6.35906	−0.318351
$400$	−1.71573	−0.0857867
$401$	−13.5967	−0.678989	−0.339495	−	0.940608i	$-0.610256\pi$
$401$	−13.5967	−0.678989	−0.339495	+	0.940608i	$0.610256\pi$
$402$	−3.35883	−0.167523
$403$	4.63243	0.230758
$404$	15.2214	0.757293
$405$	−6.05036	−0.300645
$406$	7.17547	0.356113
$407$	−5.92932	−0.293905
$408$	−11.8375	−0.586043
$409$	−16.1960	−0.800839	−0.400420	−	0.916332i	$-0.631136\pi$
$409$	−16.1960	−0.800839	−0.400420	+	0.916332i	$0.631136\pi$
$410$	2.94421	0.145404
$411$	7.00636	0.345598
$412$	14.0739	0.693370
$413$	32.2865	1.58872
$414$	4.66839	0.229439
$415$	1.77991	0.0873724
$416$	3.60296	0.176650
$417$	12.4509	0.609725
$418$	3.82363	0.187020
$419$	24.8903	1.21597	0.607986	−	0.793948i	$-0.291978\pi$
$419$	24.8903	1.21597	0.607986	+	0.793948i	$0.291978\pi$
$420$	−6.74808	−0.329273
$421$	−30.8641	−1.50422	−0.752111	−	0.659036i	$-0.770964\pi$
$421$	−30.8641	−1.50422	−0.752111	+	0.659036i	$0.770964\pi$
$422$	−2.28696	−0.111328
$423$	−21.9153	−1.06556
$424$	−36.9580	−1.79484
$425$	17.9489	0.870650
$426$	−5.11699	−0.247919
$427$	−19.6838	−0.952564
$428$	6.51775	0.315048
$429$	1.22438	0.0591136
$430$	0	0
$431$	−2.13534	−0.102856	−0.0514278	−	0.998677i	$-0.516377\pi$
$431$	−2.13534	−0.102856	−0.0514278	+	0.998677i	$0.516377\pi$
$432$	−2.29131	−0.110241
$433$	−19.5117	−0.937670	−0.468835	−	0.883286i	$-0.655326\pi$
$433$	−19.5117	−0.937670	−0.468835	+	0.883286i	$0.655326\pi$
$434$	−28.5611	−1.37097
$435$	−1.96531	−0.0942296
$436$	−24.2921	−1.16338
$437$	4.27925	0.204704
$438$	−5.07342	−0.242418
$439$	14.4009	0.687315	0.343658	−	0.939095i	$-0.388334\pi$
$439$	14.4009	0.687315	0.343658	+	0.939095i	$0.388334\pi$
$440$	10.0287	0.478099
$441$	−38.2582	−1.82182
$442$	−2.92445	−0.139102
$443$	20.6670	0.981919	0.490959	−	0.871182i	$-0.336646\pi$
$443$	20.6670	0.981919	0.490959	+	0.871182i	$0.336646\pi$
$444$	−2.25473	−0.107005
$445$	−13.2646	−0.628804
$446$	3.51049	0.166227
$447$	−8.68766	−0.410912
$448$	−16.8359	−0.795419
$449$	−32.6911	−1.54279	−0.771395	−	0.636357i	$-0.780440\pi$
$449$	−32.6911	−1.54279	−0.771395	+	0.636357i	$0.780440\pi$
$450$	−5.94465	−0.280233
$451$	−6.98354	−0.328842
$452$	1.74945	0.0822874
$453$	−5.99071	−0.281468
$454$	−9.93554	−0.466298
$455$	−4.12048	−0.193171
$456$	3.59375	0.168293
$457$	−3.08262	−0.144199	−0.0720995	−	0.997397i	$-0.522970\pi$
$457$	−3.08262	−0.144199	−0.0720995	+	0.997397i	$0.522970\pi$
$458$	−8.17883	−0.382172
$459$	23.9703	1.11884
$460$	4.54103	0.211727
$461$	−21.5629	−1.00428	−0.502142	−	0.864785i	$-0.667455\pi$
$461$	−21.5629	−1.00428	−0.502142	+	0.864785i	$0.667455\pi$
$462$	−7.54885	−0.351204
$463$	−27.4797	−1.27709	−0.638545	−	0.769584i	$-0.720463\pi$
$463$	−27.4797	−1.27709	−0.638545	+	0.769584i	$0.720463\pi$
$464$	1.06434	0.0494105
$465$	7.82268	0.362768
$466$	16.3512	0.757457
$467$	31.7034	1.46706	0.733529	−	0.679658i	$-0.237872\pi$
$467$	31.7034	1.46706	0.733529	+	0.679658i	$0.237872\pi$
$468$	−2.05371	−0.0949326
$469$	−26.8118	−1.23805
$470$	10.0537	0.463745
$471$	−5.63957	−0.259858
$472$	−18.2463	−0.839855
$473$	0	0
$474$	3.69140	0.169552
$475$	−5.44911	−0.250023
$476$	−38.2309	−1.75231
$477$	33.6093	1.53886
$478$	−1.54683	−0.0707505
$479$	2.98746	0.136500	0.0682502	−	0.997668i	$-0.478258\pi$
$479$	2.98746	0.136500	0.0682502	+	0.997668i	$0.478258\pi$
$480$	6.08424	0.277706
$481$	−1.37677	−0.0627754
$482$	11.3674	0.517769
$483$	−8.44837	−0.384414
$484$	5.32520	0.242055
$485$	6.31663	0.286823
$486$	−12.3125	−0.558507
$487$	−31.5338	−1.42893	−0.714467	−	0.699669i	$-0.753331\pi$
$487$	−31.5338	−1.42893	−0.714467	+	0.699669i	$0.753331\pi$
$488$	11.1240	0.503561
$489$	−4.59551	−0.207816
$490$	17.5512	0.792882
$491$	18.8500	0.850690	0.425345	−	0.905031i	$-0.360153\pi$
$491$	18.8500	0.850690	0.425345	+	0.905031i	$0.360153\pi$
$492$	−2.65562	−0.119724
$493$	−11.1344	−0.501468
$494$	0.887836	0.0399456
$495$	−9.12000	−0.409913
$496$	−4.23645	−0.190222
$497$	−40.8463	−1.83221
$498$	0.757162	0.0339292
$499$	−31.4337	−1.40717	−0.703583	−	0.710613i	$-0.748418\pi$
$499$	−31.4337	−1.40717	−0.703583	+	0.710613i	$0.748418\pi$
$500$	−15.3050	−0.684459
$501$	−6.56237	−0.293185
$502$	−6.90584	−0.308223
$503$	22.7036	1.01230	0.506151	−	0.862445i	$-0.331068\pi$
$503$	22.7036	1.01230	0.506151	+	0.862445i	$0.331068\pi$
$504$	31.2957	1.39402
$505$	15.6953	0.698430
$506$	5.07990	0.225829
$507$	−9.39552	−0.417270
$508$	−5.97137	−0.264937
$509$	17.6824	0.783759	0.391880	−	0.920017i	$-0.371825\pi$
$509$	17.6824	0.783759	0.391880	+	0.920017i	$0.371825\pi$
$510$	−4.93845	−0.218678
$511$	−40.4985	−1.79155
$512$	−6.33431	−0.279939
$513$	−7.27714	−0.321294
$514$	9.98104	0.440245
$515$	14.5120	0.639475
$516$	0	0
$517$	−23.8470	−1.04879
$518$	8.48842	0.372960
$519$	4.55956	0.200143
$520$	2.32864	0.102117
$521$	34.0460	1.49158	0.745791	−	0.666180i	$-0.232072\pi$
$521$	34.0460	1.49158	0.745791	+	0.666180i	$0.232072\pi$
$522$	3.68769	0.161406
$523$	8.43617	0.368888	0.184444	−	0.982843i	$-0.440952\pi$
$523$	8.43617	0.368888	0.184444	+	0.982843i	$0.440952\pi$
$524$	19.1892	0.838284
$525$	10.7580	0.469517
$526$	−14.2146	−0.619784
$527$	44.3191	1.93057
$528$	−1.11972	−0.0487295
$529$	−17.3148	−0.752817
$530$	−15.4184	−0.669734
$531$	16.5930	0.720076
$532$	11.6066	0.503208
$533$	−1.62156	−0.0702375
$534$	−5.64268	−0.244183
$535$	6.72066	0.290559
$536$	15.1524	0.654483
$537$	18.3153	0.790363
$538$	−22.9428	−0.989133
$539$	−41.6306	−1.79316
$540$	−7.72232	−0.332316
$541$	10.0891	0.433765	0.216882	−	0.976198i	$-0.430411\pi$
$541$	10.0891	0.433765	0.216882	+	0.976198i	$0.430411\pi$
$542$	−14.6711	−0.630178
$543$	−4.25230	−0.182484
$544$	34.4700	1.47789
$545$	−25.0484	−1.07295
$546$	−1.75282	−0.0750139
$547$	−18.4512	−0.788918	−0.394459	−	0.918914i	$-0.629068\pi$
$547$	−18.4512	−0.788918	−0.394459	+	0.918914i	$0.629068\pi$
$548$	−12.7880	−0.546276
$549$	−10.1161	−0.431744
$550$	−6.46865	−0.275824
$551$	3.38030	0.144005
$552$	4.77449	0.203216
$553$	29.4665	1.25304
$554$	5.29928	0.225145
$555$	−2.32492	−0.0986874
$556$	−22.7254	−0.963772
$557$	−4.41242	−0.186960	−0.0934802	−	0.995621i	$-0.529799\pi$
$557$	−4.41242	−0.186960	−0.0934802	+	0.995621i	$0.529799\pi$
$558$	−14.6784	−0.621386
$559$	0	0
$560$	3.76826	0.159238
$561$	11.7138	0.494556
$562$	10.3096	0.434886
$563$	−9.17474	−0.386669	−0.193335	−	0.981133i	$-0.561930\pi$
$563$	−9.17474	−0.386669	−0.193335	+	0.981133i	$0.561930\pi$
$564$	−9.06826	−0.381842
$565$	1.80392	0.0758913
$566$	−0.501744	−0.0210899
$567$	−20.5452	−0.862816
$568$	23.0838	0.968574
$569$	−2.10658	−0.0883123	−0.0441561	−	0.999025i	$-0.514060\pi$
$569$	−2.10658	−0.0883123	−0.0441561	+	0.999025i	$0.514060\pi$
$570$	1.49927	0.0627974
$571$	29.3264	1.22727	0.613636	−	0.789589i	$-0.289706\pi$
$571$	29.3264	1.22727	0.613636	+	0.789589i	$0.289706\pi$
$572$	−2.23473	−0.0934389
$573$	−0.273887	−0.0114418
$574$	9.99764	0.417294
$575$	−7.23945	−0.301906
$576$	−8.65246	−0.360519
$577$	−16.6613	−0.693619	−0.346810	−	0.937936i	$-0.612735\pi$
$577$	−16.6613	−0.693619	−0.346810	+	0.937936i	$0.612735\pi$
$578$	−14.3684	−0.597648
$579$	−6.59016	−0.273878
$580$	3.58709	0.148946
$581$	6.04403	0.250749
$582$	2.68705	0.111382
$583$	36.5718	1.51465
$584$	22.8872	0.947080
$585$	−2.11764	−0.0875536
$586$	−17.3349	−0.716097
$587$	−22.6523	−0.934962	−0.467481	−	0.884003i	$-0.654838\pi$
$587$	−22.6523	−0.934962	−0.467481	+	0.884003i	$0.654838\pi$
$588$	−15.8308	−0.652850
$589$	−13.4548	−0.554397
$590$	−7.61214	−0.313387
$591$	−2.80781	−0.115498
$592$	1.25908	0.0517481
$593$	35.6103	1.46234	0.731169	−	0.682196i	$-0.238975\pi$
$593$	35.6103	1.46234	0.731169	+	0.682196i	$0.238975\pi$
$594$	−8.63870	−0.354450
$595$	−39.4211	−1.61611
$596$	15.8567	0.649516
$597$	−8.42785	−0.344929
$598$	1.17954	0.0482349
$599$	30.9951	1.26642	0.633212	−	0.773978i	$-0.281736\pi$
$599$	30.9951	1.26642	0.633212	+	0.773978i	$0.281736\pi$
$600$	−6.07975	−0.248205
$601$	−21.0632	−0.859187	−0.429594	−	0.903022i	$-0.641343\pi$
$601$	−21.0632	−0.859187	−0.429594	+	0.903022i	$0.641343\pi$
$602$	0	0
$603$	−13.7794	−0.561141
$604$	10.9342	0.444908
$605$	5.49098	0.223240
$606$	6.67665	0.271220
$607$	−4.29850	−0.174471	−0.0872353	−	0.996188i	$-0.527803\pi$
$607$	−4.29850	−0.174471	−0.0872353	+	0.996188i	$0.527803\pi$
$608$	−10.4648	−0.424402
$609$	−6.67360	−0.270428
$610$	4.64081	0.187901
$611$	−5.53721	−0.224012
$612$	−19.6480	−0.794225
$613$	−0.171108	−0.00691101	−0.00345550	−	0.999994i	$-0.501100\pi$
$613$	−0.171108	−0.00691101	−0.00345550	+	0.999994i	$0.501100\pi$
$614$	6.66261	0.268881
$615$	−2.73829	−0.110418
$616$	34.0544	1.37209
$617$	5.83176	0.234778	0.117389	−	0.993086i	$-0.462548\pi$
$617$	5.83176	0.234778	0.117389	+	0.993086i	$0.462548\pi$
$618$	6.17330	0.248327
$619$	0.875925	0.0352064	0.0176032	−	0.999845i	$-0.494396\pi$
$619$	0.875925	0.0352064	0.0176032	+	0.999845i	$0.494396\pi$
$620$	−14.2779	−0.573416
$621$	−9.66809	−0.387967
$622$	−11.0296	−0.442247
$623$	−45.0426	−1.80459
$624$	−0.259996	−0.0104082
$625$	−0.600364	−0.0240146
$626$	3.93274	0.157184
$627$	−3.55619	−0.142021
$628$	10.2933	0.410749
$629$	−13.1717	−0.525192
$630$	13.0562	0.520172
$631$	22.9215	0.912492	0.456246	−	0.889854i	$-0.349194\pi$
$631$	22.9215	0.912492	0.456246	+	0.889854i	$0.349194\pi$
$632$	−16.6526	−0.662406
$633$	2.12701	0.0845410
$634$	−15.0905	−0.599322
$635$	−6.15726	−0.244343
$636$	13.9071	0.551452
$637$	−9.66651	−0.383001
$638$	4.01275	0.158866
$639$	−20.9922	−0.830437
$640$	−12.3729	−0.489082
$641$	33.2686	1.31403	0.657015	−	0.753878i	$-0.271819\pi$
$641$	33.2686	1.31403	0.657015	+	0.753878i	$0.271819\pi$
$642$	2.85892	0.112833
$643$	−39.7938	−1.56931	−0.784657	−	0.619930i	$-0.787161\pi$
$643$	−39.7938	−1.56931	−0.784657	+	0.619930i	$0.787161\pi$
$644$	15.4199	0.607631
$645$	0	0
$646$	8.49403	0.334193
$647$	−7.14695	−0.280975	−0.140488	−	0.990082i	$-0.544867\pi$
$647$	−7.14695	−0.280975	−0.140488	+	0.990082i	$0.544867\pi$
$648$	11.6108	0.456117
$649$	18.0556	0.708746
$650$	−1.50200	−0.0589134
$651$	26.5634	1.04110
$652$	8.38772	0.328489
$653$	−21.8649	−0.855638	−0.427819	−	0.903864i	$-0.640718\pi$
$653$	−21.8649	−0.855638	−0.427819	+	0.903864i	$0.640718\pi$
$654$	−10.6554	−0.416659
$655$	19.7866	0.773125
$656$	1.48295	0.0578994
$657$	−20.8134	−0.812009
$658$	34.1394	1.33089
$659$	23.0558	0.898126	0.449063	−	0.893500i	$-0.351758\pi$
$659$	23.0558	0.898126	0.449063	+	0.893500i	$0.351758\pi$
$660$	−3.77374	−0.146893
$661$	19.3150	0.751267	0.375633	−	0.926768i	$-0.377425\pi$
$661$	19.3150	0.751267	0.375633	+	0.926768i	$0.377425\pi$
$662$	2.59147	0.100720
$663$	2.71991	0.105632
$664$	−3.41571	−0.132555
$665$	11.9679	0.464094
$666$	4.36246	0.169042
$667$	4.49091	0.173889
$668$	11.9776	0.463428
$669$	−3.26496	−0.126231
$670$	6.32138	0.244216
$671$	−11.0078	−0.424951
$672$	20.6602	0.796984
$673$	11.8468	0.456662	0.228331	−	0.973584i	$-0.426673\pi$
$673$	11.8468	0.456662	0.228331	+	0.973584i	$0.426673\pi$
$674$	−7.74447	−0.298306
$675$	12.3112	0.473857
$676$	17.1487	0.659565
$677$	44.0214	1.69188	0.845940	−	0.533278i	$-0.179040\pi$
$677$	44.0214	1.69188	0.845940	+	0.533278i	$0.179040\pi$
$678$	0.767373	0.0294708
$679$	21.4493	0.823149
$680$	22.2783	0.854336
$681$	9.24062	0.354101
$682$	−15.9722	−0.611609
$683$	−8.79979	−0.336714	−0.168357	−	0.985726i	$-0.553846\pi$
$683$	−8.79979	−0.336714	−0.168357	+	0.985726i	$0.553846\pi$
$684$	5.96496	0.228076
$685$	−13.1861	−0.503814
$686$	32.9306	1.25730
$687$	7.60678	0.290217
$688$	0	0
$689$	8.49188	0.323515
$690$	1.99186	0.0758288
$691$	24.5471	0.933814	0.466907	−	0.884306i	$-0.345368\pi$
$691$	24.5471	0.933814	0.466907	+	0.884306i	$0.345368\pi$
$692$	−8.32210	−0.316359
$693$	−30.9687	−1.17640
$694$	8.78157	0.333344
$695$	−23.4329	−0.888859
$696$	3.77150	0.142958
$697$	−15.5136	−0.587621
$698$	17.1829	0.650382
$699$	−15.2076	−0.575204
$700$	−19.6355	−0.742151
$701$	7.83704	0.296001	0.148000	−	0.988987i	$-0.452716\pi$
$701$	7.83704	0.296001	0.148000	+	0.988987i	$0.452716\pi$
$702$	−2.00588	−0.0757072
$703$	3.99881	0.150818
$704$	−9.41515	−0.354847
$705$	−9.35056	−0.352162
$706$	26.6697	1.00373
$707$	53.2962	2.00441
$708$	6.86599	0.258040
$709$	6.01524	0.225907	0.112954	−	0.993600i	$-0.463969\pi$
$709$	6.01524	0.225907	0.112954	+	0.993600i	$0.463969\pi$
$710$	9.63027	0.361418
$711$	15.1437	0.567935
$712$	25.4553	0.953976
$713$	−17.8755	−0.669443
$714$	−16.7695	−0.627581
$715$	−2.30430	−0.0861760
$716$	−33.4290	−1.24930
$717$	1.43864	0.0537271
$718$	6.00296	0.224028
$719$	−14.2965	−0.533168	−0.266584	−	0.963812i	$-0.585895\pi$
$719$	−14.2965	−0.533168	−0.266584	+	0.963812i	$0.585895\pi$
$720$	1.93662	0.0721737
$721$	49.2783	1.83522
$722$	12.6326	0.470138
$723$	−10.5723	−0.393188
$724$	7.76129	0.288446
$725$	−5.71864	−0.212385
$726$	2.33582	0.0866906
$727$	−6.68104	−0.247786	−0.123893	−	0.992296i	$-0.539538\pi$
$727$	−6.68104	−0.247786	−0.123893	+	0.992296i	$0.539538\pi$
$728$	7.90733	0.293065
$729$	−1.50121	−0.0556005
$730$	9.54827	0.353397
$731$	0	0
$732$	−4.18591	−0.154716
$733$	−36.5159	−1.34875	−0.674373	−	0.738391i	$-0.735586\pi$
$733$	−36.5159	−1.34875	−0.674373	+	0.738391i	$0.735586\pi$
$734$	4.09665	0.151210
$735$	−16.3236	−0.602105
$736$	−13.9030	−0.512471
$737$	−14.9940	−0.552312
$738$	5.13809	0.189136
$739$	20.6804	0.760739	0.380370	−	0.924835i	$-0.375797\pi$
$739$	20.6804	0.760739	0.380370	+	0.924835i	$0.375797\pi$
$740$	4.24344	0.155992
$741$	−0.825738	−0.0303342
$742$	−52.3563	−1.92206
$743$	6.81310	0.249948	0.124974	−	0.992160i	$-0.460115\pi$
$743$	6.81310	0.249948	0.124974	+	0.992160i	$0.460115\pi$
$744$	−15.0120	−0.550366
$745$	16.3503	0.599030
$746$	−26.3406	−0.964399
$747$	3.10621	0.113650
$748$	−21.3800	−0.781729
$749$	22.8213	0.833871
$750$	−6.71330	−0.245135
$751$	19.6614	0.717456	0.358728	−	0.933442i	$-0.383211\pi$
$751$	19.6614	0.717456	0.358728	+	0.933442i	$0.383211\pi$
$752$	5.06389	0.184661
$753$	6.42282	0.234061
$754$	0.931750	0.0339323
$755$	11.2746	0.410325
$756$	−26.2226	−0.953708
$757$	39.1913	1.42443	0.712216	−	0.701960i	$-0.247692\pi$
$757$	39.1913	1.42443	0.712216	+	0.701960i	$0.247692\pi$
$758$	7.11680	0.258494
$759$	−4.72460	−0.171492
$760$	−6.76349	−0.245338
$761$	−43.3281	−1.57064	−0.785321	−	0.619089i	$-0.787502\pi$
$761$	−43.3281	−1.57064	−0.785321	+	0.619089i	$0.787502\pi$
$762$	−2.61925	−0.0948856
$763$	−85.0565	−3.07925
$764$	0.499897	0.0180857
$765$	−20.2597	−0.732491
$766$	−10.8719	−0.392816
$767$	4.19247	0.151381
$768$	−10.5322	−0.380047
$769$	49.0204	1.76772	0.883861	−	0.467750i	$-0.154935\pi$
$769$	49.0204	1.76772	0.883861	+	0.467750i	$0.154935\pi$
$770$	14.2071	0.511987
$771$	−9.28294	−0.334317
$772$	12.0284	0.432910
$773$	45.8099	1.64767	0.823833	−	0.566832i	$-0.191831\pi$
$773$	45.8099	1.64767	0.823833	+	0.566832i	$0.191831\pi$
$774$	0	0
$775$	22.7623	0.817647
$776$	−12.1218	−0.435148
$777$	−7.89472	−0.283221
$778$	−3.13804	−0.112504
$779$	4.70979	0.168746
$780$	−0.876253	−0.0313749
$781$	−22.8425	−0.817371
$782$	11.2848	0.403543
$783$	−7.63709	−0.272927
$784$	8.84021	0.315722
$785$	10.6138	0.378822
$786$	8.41706	0.300227
$787$	−47.7282	−1.70133	−0.850664	−	0.525710i	$-0.823800\pi$
$787$	−47.7282	−1.70133	−0.850664	+	0.525710i	$0.823800\pi$
$788$	5.12481	0.182564
$789$	13.2204	0.470657
$790$	−6.94728	−0.247173
$791$	6.12554	0.217799
$792$	17.5016	0.621891
$793$	−2.55598	−0.0907654
$794$	0.738833	0.0262202
$795$	14.3400	0.508589
$796$	15.3825	0.545218
$797$	31.5822	1.11870	0.559349	−	0.828932i	$-0.311051\pi$
$797$	31.5822	1.11870	0.559349	+	0.828932i	$0.311051\pi$
$798$	5.09105	0.180221
$799$	−52.9752	−1.87413
$800$	17.7038	0.625925
$801$	−23.1488	−0.817921
$802$	10.8855	0.384381
$803$	−22.6481	−0.799232
$804$	−5.70175	−0.201085
$805$	15.9000	0.560401
$806$	−3.70871	−0.130634
$807$	21.3381	0.751136
$808$	−30.1197	−1.05961
$809$	50.2052	1.76512	0.882561	−	0.470198i	$-0.155818\pi$
$809$	50.2052	1.76512	0.882561	+	0.470198i	$0.155818\pi$
$810$	4.84390	0.170197
$811$	−36.7374	−1.29002	−0.645012	−	0.764172i	$-0.723148\pi$
$811$	−36.7374	−1.29002	−0.645012	+	0.764172i	$0.723148\pi$
$812$	12.1806	0.427457
$813$	13.6450	0.478550
$814$	4.74699	0.166382
$815$	8.64884	0.302956
$816$	−2.48741	−0.0870767
$817$	0	0
$818$	12.9664	0.453361
$819$	−7.19085	−0.251269
$820$	4.99792	0.174535
$821$	9.70492	0.338704	0.169352	−	0.985556i	$-0.445833\pi$
$821$	9.70492	0.338704	0.169352	+	0.985556i	$0.445833\pi$
$822$	−5.60927	−0.195646
$823$	−11.5792	−0.403627	−0.201814	−	0.979424i	$-0.564684\pi$
$823$	−11.5792	−0.403627	−0.201814	+	0.979424i	$0.564684\pi$
$824$	−27.8490	−0.970166
$825$	6.01621	0.209458
$826$	−25.8485	−0.899384
$827$	−13.7182	−0.477029	−0.238514	−	0.971139i	$-0.576660\pi$
$827$	−13.7182	−0.477029	−0.238514	+	0.971139i	$0.576660\pi$
$828$	7.92478	0.275405
$829$	−34.6099	−1.20205	−0.601026	−	0.799230i	$-0.705241\pi$
$829$	−34.6099	−1.20205	−0.601026	+	0.799230i	$0.705241\pi$
$830$	−1.42499	−0.0494622
$831$	−4.92864	−0.170973
$832$	−2.18617	−0.0757919
$833$	−92.4806	−3.20426
$834$	−9.96818	−0.345170
$835$	12.3505	0.427407
$836$	6.49075	0.224487
$837$	30.3985	1.05072
$838$	−19.9271	−0.688371
$839$	24.1121	0.832441	0.416220	−	0.909264i	$-0.363355\pi$
$839$	24.1121	0.832441	0.416220	+	0.909264i	$0.363355\pi$
$840$	13.3529	0.460720
$841$	−25.4525	−0.877673
$842$	24.7097	0.851552
$843$	−9.58855	−0.330247
$844$	−3.88221	−0.133631
$845$	17.6825	0.608297
$846$	17.5453	0.603219
$847$	18.6457	0.640673
$848$	−7.76599	−0.266685
$849$	0.466650	0.0160154
$850$	−14.3698	−0.492881
$851$	5.31264	0.182115
$852$	−8.68629	−0.297587
$853$	14.9483	0.511821	0.255911	−	0.966700i	$-0.417625\pi$
$853$	14.9483	0.511821	0.255911	+	0.966700i	$0.417625\pi$
$854$	15.7588	0.539253
$855$	6.15065	0.210348
$856$	−12.8972	−0.440816
$857$	−34.8251	−1.18960	−0.594802	−	0.803872i	$-0.702770\pi$
$857$	−34.8251	−1.18960	−0.594802	+	0.803872i	$0.702770\pi$
$858$	−0.980234	−0.0334646
$859$	34.5111	1.17750	0.588752	−	0.808314i	$-0.299619\pi$
$859$	34.5111	1.17750	0.588752	+	0.808314i	$0.299619\pi$
$860$	0	0
$861$	−9.29838	−0.316888
$862$	1.70955	0.0582274
$863$	20.3935	0.694204	0.347102	−	0.937827i	$-0.387166\pi$
$863$	20.3935	0.694204	0.347102	+	0.937827i	$0.387166\pi$
$864$	23.6430	0.804350
$865$	−8.58118	−0.291769
$866$	15.6210	0.530822
$867$	13.3635	0.453847
$868$	−48.4835	−1.64564
$869$	16.4786	0.558999
$870$	1.57342	0.0533441
$871$	−3.48157	−0.117969
$872$	48.0686	1.62781
$873$	11.0235	0.373087
$874$	−3.42595	−0.115885
$875$	−53.5888	−1.81163
$876$	−8.61233	−0.290984
$877$	34.0506	1.14981	0.574903	−	0.818221i	$-0.305040\pi$
$877$	34.0506	1.14981	0.574903	+	0.818221i	$0.305040\pi$
$878$	−11.5293	−0.389095
$879$	16.1224	0.543796
$880$	2.10733	0.0710381
$881$	30.1446	1.01560	0.507798	−	0.861476i	$-0.330460\pi$
$881$	30.1446	1.01560	0.507798	+	0.861476i	$0.330460\pi$
$882$	30.6294	1.03135
$883$	47.4267	1.59603	0.798017	−	0.602634i	$-0.205882\pi$
$883$	47.4267	1.59603	0.798017	+	0.602634i	$0.205882\pi$
$884$	−4.96437	−0.166970
$885$	7.07973	0.237982
$886$	−16.5459	−0.555872
$887$	8.95601	0.300713	0.150357	−	0.988632i	$-0.451958\pi$
$887$	8.95601	0.300713	0.150357	+	0.988632i	$0.451958\pi$
$888$	4.46160	0.149721
$889$	−20.9082	−0.701237
$890$	10.6196	0.355971
$891$	−11.4895	−0.384913
$892$	5.95920	0.199529
$893$	16.0828	0.538189
$894$	6.95532	0.232621
$895$	−34.4697	−1.15220
$896$	−42.0146	−1.40361
$897$	−1.09704	−0.0366290
$898$	26.1724	0.873385
$899$	−14.1203	−0.470940
$900$	−10.0913	−0.336375
$901$	81.2428	2.70659
$902$	5.59100	0.186160
$903$	0	0
$904$	−3.46177	−0.115137
$905$	8.00290	0.266026
$906$	4.79614	0.159341
$907$	−19.0027	−0.630974	−0.315487	−	0.948930i	$-0.602168\pi$
$907$	−19.0027	−0.630974	−0.315487	+	0.948930i	$0.602168\pi$
$908$	−16.8660	−0.559717
$909$	27.3906	0.908488
$910$	3.29884	0.109356
$911$	34.1574	1.13169	0.565843	−	0.824513i	$-0.308551\pi$
$911$	34.1574	1.13169	0.565843	+	0.824513i	$0.308551\pi$
$912$	0.755154	0.0250056
$913$	3.38001	0.111862
$914$	2.46794	0.0816322
$915$	−4.31622	−0.142690
$916$	−13.8839	−0.458736
$917$	67.1891	2.21878
$918$	−19.1905	−0.633382
$919$	45.2070	1.49124	0.745621	−	0.666370i	$-0.232153\pi$
$919$	45.2070	1.49124	0.745621	+	0.666370i	$0.232153\pi$
$920$	−8.98567	−0.296249
$921$	−6.19661	−0.204185
$922$	17.2632	0.568533
$923$	−5.30398	−0.174583
$924$	−12.8145	−0.421565
$925$	−6.76502	−0.222433
$926$	22.0002	0.722971
$927$	25.3256	0.831802
$928$	−10.9824	−0.360514
$929$	21.1601	0.694242	0.347121	−	0.937820i	$-0.387159\pi$
$929$	21.1601	0.694242	0.347121	+	0.937820i	$0.387159\pi$
$930$	−6.26282	−0.205366
$931$	28.0762	0.920162
$932$	27.7569	0.909206
$933$	10.2582	0.335837
$934$	−25.3816	−0.830513
$935$	−22.0455	−0.720966
$936$	4.06382	0.132830
$937$	50.4283	1.64742	0.823710	−	0.567011i	$-0.191900\pi$
$937$	50.4283	1.64742	0.823710	+	0.567011i	$0.191900\pi$
$938$	21.4655	0.700872
$939$	−3.65767	−0.119364
$940$	17.0666	0.556652
$941$	−20.1042	−0.655377	−0.327689	−	0.944786i	$-0.606270\pi$
$941$	−20.1042	−0.655377	−0.327689	+	0.944786i	$0.606270\pi$
$942$	4.51503	0.147108
$943$	6.25722	0.203763
$944$	−3.83410	−0.124789
$945$	−27.0390	−0.879577
$946$	0	0
$947$	11.6359	0.378117	0.189059	−	0.981966i	$-0.439456\pi$
$947$	11.6359	0.378117	0.189059	+	0.981966i	$0.439456\pi$
$948$	6.26629	0.203520
$949$	−5.25882	−0.170708
$950$	4.36254	0.141540
$951$	14.0351	0.455118
$952$	75.6504	2.45184
$953$	42.7843	1.38592	0.692959	−	0.720977i	$-0.256307\pi$
$953$	42.7843	1.38592	0.692959	+	0.720977i	$0.256307\pi$
$954$	−26.9075	−0.871162
$955$	0.515460	0.0166799
$956$	−2.62581	−0.0849248
$957$	−3.73209	−0.120641
$958$	−2.39175	−0.0772739
$959$	−44.7759	−1.44589
$960$	−3.69174	−0.119150
$961$	25.2043	0.813041
$962$	1.10224	0.0355376
$963$	11.7285	0.377947
$964$	19.2965	0.621499
$965$	12.4028	0.399260
$966$	6.76374	0.217620
$967$	49.5620	1.59381	0.796903	−	0.604107i	$-0.206470\pi$
$967$	49.5620	1.59381	0.796903	+	0.604107i	$0.206470\pi$
$968$	−10.5374	−0.338684
$969$	−7.89993	−0.253782
$970$	−5.05707	−0.162373
$971$	21.9150	0.703285	0.351642	−	0.936134i	$-0.385623\pi$
$971$	21.9150	0.703285	0.351642	+	0.936134i	$0.385623\pi$
$972$	−20.9010	−0.670399
$973$	−79.5708	−2.55092
$974$	25.2459	0.808930
$975$	1.39695	0.0447381
$976$	2.33749	0.0748213
$977$	−29.4546	−0.942336	−0.471168	−	0.882043i	$-0.656167\pi$
$977$	−29.4546	−0.942336	−0.471168	+	0.882043i	$0.656167\pi$
$978$	3.67915	0.117646
$979$	−25.1892	−0.805052
$980$	29.7938	0.951728
$981$	−43.7131	−1.39565
$982$	−15.0913	−0.481582
$983$	−4.27712	−0.136419	−0.0682095	−	0.997671i	$-0.521729\pi$
$983$	−4.27712	−0.136419	−0.0682095	+	0.997671i	$0.521729\pi$
$984$	5.25486	0.167519
$985$	5.28435	0.168373
$986$	8.91416	0.283885
$987$	−31.7516	−1.01066
$988$	1.50714	0.0479484
$989$	0	0
$990$	7.30144	0.232055
$991$	50.9977	1.62000	0.809998	−	0.586432i	$-0.199468\pi$
$991$	50.9977	1.62000	0.809998	+	0.586432i	$0.199468\pi$
$992$	43.7139	1.38792
$993$	−2.41022	−0.0764859
$994$	32.7014	1.03723
$995$	15.8614	0.502839
$996$	1.28531	0.0407267
$997$	−41.5460	−1.31578	−0.657888	−	0.753116i	$-0.728550\pi$
$997$	−41.5460	−1.31578	−0.657888	+	0.753116i	$0.728550\pi$
$998$	25.1657	0.796608
$999$	−9.03450	−0.285839

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.o.1.7		18
43.19	odd	42		43.2.g.a.17.2	✓	36
43.34	odd	42		43.2.g.a.38.2	yes	36
43.42	odd	2		1849.2.a.n.1.12		18
129.62	even	42		387.2.y.c.361.2		36
129.77	even	42		387.2.y.c.253.2		36
172.19	even	42		688.2.bg.c.17.2		36
172.163	even	42		688.2.bg.c.81.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.17.2	✓	36	43.19	odd	42
43.2.g.a.38.2	yes	36	43.34	odd	42
387.2.y.c.253.2		36	129.77	even	42
387.2.y.c.361.2		36	129.62	even	42
688.2.bg.c.17.2		36	172.19	even	42
688.2.bg.c.81.2		36	172.163	even	42
1849.2.a.n.1.12		18	43.42	odd	2
1849.2.a.o.1.7		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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-0.800597 q^{2} +0.744601 q^{3} -1.35904 q^{4} -1.40135 q^{5} -0.596125 q^{6} -4.75856 q^{7} +2.68924 q^{8} -2.44557 q^{9} +O(q^{10})\)	\(q-0.800597 q^{2} +0.744601 q^{3} -1.35904 q^{4} -1.40135 q^{5} -0.596125 q^{6} -4.75856 q^{7} +2.68924 q^{8} -2.44557 q^{9} +1.12192 q^{10} -2.66114 q^{11} -1.01195 q^{12} -0.617909 q^{13} +3.80969 q^{14} -1.04345 q^{15} +0.565090 q^{16} -5.91161 q^{17} +1.95792 q^{18} +1.79471 q^{19} +1.90450 q^{20} -3.54323 q^{21} +2.13050 q^{22} +2.38437 q^{23} +2.00241 q^{24} -3.03621 q^{25} +0.494696 q^{26} -4.05478 q^{27} +6.46709 q^{28} +1.88348 q^{29} +0.835382 q^{30} -7.49695 q^{31} -5.83089 q^{32} -1.98149 q^{33} +4.73282 q^{34} +6.66842 q^{35} +3.32364 q^{36} +2.22811 q^{37} -1.43684 q^{38} -0.460096 q^{39} -3.76857 q^{40} +2.62427 q^{41} +2.83670 q^{42} +3.61660 q^{44} +3.42710 q^{45} -1.90892 q^{46} +8.96121 q^{47} +0.420767 q^{48} +15.6439 q^{49} +2.43078 q^{50} -4.40179 q^{51} +0.839766 q^{52} -13.7429 q^{53} +3.24624 q^{54} +3.72919 q^{55} -12.7969 q^{56} +1.33634 q^{57} -1.50791 q^{58} -6.78493 q^{59} +1.41809 q^{60} +4.13649 q^{61} +6.00204 q^{62} +11.6374 q^{63} +3.53801 q^{64} +0.865909 q^{65} +1.58637 q^{66} +5.63444 q^{67} +8.03414 q^{68} +1.77540 q^{69} -5.33872 q^{70} +8.58375 q^{71} -6.57673 q^{72} +8.51066 q^{73} -1.78382 q^{74} -2.26077 q^{75} -2.43909 q^{76} +12.6632 q^{77} +0.368351 q^{78} -6.19232 q^{79} -0.791890 q^{80} +4.31752 q^{81} -2.10098 q^{82} -1.27014 q^{83} +4.81541 q^{84} +8.28425 q^{85} +1.40244 q^{87} -7.15644 q^{88} +9.46559 q^{89} -2.74373 q^{90} +2.94036 q^{91} -3.24046 q^{92} -5.58224 q^{93} -7.17432 q^{94} -2.51502 q^{95} -4.34169 q^{96} -4.50752 q^{97} -12.5245 q^{98} +6.50800 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + 5 q^{3} + 19 q^{4} + 11 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 15 q^{9}+O(q^{10}) \) 18 * q + 5 * q^2 + 5 * q^3 + 19 * q^4 + 11 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 15 * q^9	\( 18 q + 5 q^{2} + 5 q^{3} + 19 q^{4} + 11 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} + 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} + 25 q^{18} + 31 q^{19} + 25 q^{20} + 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} + 27 q^{26} + 23 q^{27} + 20 q^{28} + 37 q^{29} - 17 q^{30} - 12 q^{31} + 39 q^{32} + 38 q^{33} + 14 q^{34} + 16 q^{35} + 47 q^{36} - 19 q^{37} + 56 q^{38} + 46 q^{39} + 6 q^{40} - 7 q^{41} - q^{42} + 7 q^{44} + 23 q^{45} - 47 q^{46} - q^{47} + 15 q^{48} - 6 q^{49} - 3 q^{50} + 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} + 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} + 28 q^{61} + 33 q^{62} + 26 q^{63} + 10 q^{64} + 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} + 7 q^{69} - 34 q^{70} + 86 q^{71} - 2 q^{72} - 27 q^{73} - 79 q^{74} + 31 q^{75} + 59 q^{76} + 43 q^{77} + 91 q^{78} + 17 q^{79} + 8 q^{80} - 10 q^{81} + 13 q^{82} - 12 q^{83} - 32 q^{84} + 28 q^{85} - 43 q^{87} - 23 q^{88} + 51 q^{89} + 10 q^{90} - 20 q^{91} + 18 q^{92} - 30 q^{93} - 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} - 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + 5 * q^3 + 19 * q^4 + 11 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 + 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 + 25 * q^18 + 31 * q^19 + 25 * q^20 + 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 + 27 * q^26 + 23 * q^27 + 20 * q^28 + 37 * q^29 - 17 * q^30 - 12 * q^31 + 39 * q^32 + 38 * q^33 + 14 * q^34 + 16 * q^35 + 47 * q^36 - 19 * q^37 + 56 * q^38 + 46 * q^39 + 6 * q^40 - 7 * q^41 - q^42 + 7 * q^44 + 23 * q^45 - 47 * q^46 - q^47 + 15 * q^48 - 6 * q^49 - 3 * q^50 + 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 + 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 + 28 * q^61 + 33 * q^62 + 26 * q^63 + 10 * q^64 + 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 + 7 * q^69 - 34 * q^70 + 86 * q^71 - 2 * q^72 - 27 * q^73 - 79 * q^74 + 31 * q^75 + 59 * q^76 + 43 * q^77 + 91 * q^78 + 17 * q^79 + 8 * q^80 - 10 * q^81 + 13 * q^82 - 12 * q^83 - 32 * q^84 + 28 * q^85 - 43 * q^87 - 23 * q^88 + 51 * q^89 + 10 * q^90 - 20 * q^91 + 18 * q^92 - 30 * q^93 - 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 - 5 * q^98 + 38 * q^99

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