LMFDB - Embedded newform 1849.2.a.n.1.17

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:	$1$
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} - 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			1.17
Root			$-2.27976$ 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)

$f(q)$	$=$	$q+2.27976 q^{2} -3.20997 q^{3} +3.19730 q^{4} -0.137674 q^{5} -7.31797 q^{6} -1.86944 q^{7} +2.72957 q^{8} +7.30393 q^{9} +O(q^{10})$	\(q+2.27976 q^{2} -3.20997 q^{3} +3.19730 q^{4} -0.137674 q^{5} -7.31797 q^{6} -1.86944 q^{7} +2.72957 q^{8} +7.30393 q^{9} -0.313864 q^{10} +2.62462 q^{11} -10.2633 q^{12} -1.74544 q^{13} -4.26188 q^{14} +0.441931 q^{15} -0.171852 q^{16} +1.52193 q^{17} +16.6512 q^{18} -4.89252 q^{19} -0.440186 q^{20} +6.00086 q^{21} +5.98351 q^{22} +4.37360 q^{23} -8.76184 q^{24} -4.98105 q^{25} -3.97918 q^{26} -13.8155 q^{27} -5.97718 q^{28} -0.0316144 q^{29} +1.00750 q^{30} -2.83196 q^{31} -5.85092 q^{32} -8.42498 q^{33} +3.46963 q^{34} +0.257374 q^{35} +23.3529 q^{36} +0.00930992 q^{37} -11.1538 q^{38} +5.60281 q^{39} -0.375791 q^{40} -8.32089 q^{41} +13.6805 q^{42} +8.39173 q^{44} -1.00556 q^{45} +9.97075 q^{46} -5.62610 q^{47} +0.551641 q^{48} -3.50519 q^{49} -11.3556 q^{50} -4.88535 q^{51} -5.58070 q^{52} +7.73578 q^{53} -31.4960 q^{54} -0.361343 q^{55} -5.10277 q^{56} +15.7048 q^{57} -0.0720733 q^{58} -2.17224 q^{59} +1.41299 q^{60} -12.1436 q^{61} -6.45618 q^{62} -13.6543 q^{63} -12.9950 q^{64} +0.240302 q^{65} -19.2069 q^{66} -7.73963 q^{67} +4.86607 q^{68} -14.0391 q^{69} +0.586751 q^{70} -13.1068 q^{71} +19.9366 q^{72} +4.75807 q^{73} +0.0212244 q^{74} +15.9890 q^{75} -15.6429 q^{76} -4.90658 q^{77} +12.7731 q^{78} -12.0074 q^{79} +0.0236596 q^{80} +22.4356 q^{81} -18.9696 q^{82} +4.30212 q^{83} +19.1866 q^{84} -0.209530 q^{85} +0.101482 q^{87} +7.16409 q^{88} +7.69299 q^{89} -2.29244 q^{90} +3.26300 q^{91} +13.9837 q^{92} +9.09050 q^{93} -12.8262 q^{94} +0.673573 q^{95} +18.7813 q^{96} +1.61140 q^{97} -7.99098 q^{98} +19.1701 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.27976	1.61203	0.806017	−	0.591893i	$-0.201619\pi$
$2$	2.27976	1.61203	0.806017	+	0.591893i	$0.201619\pi$
$3$	−3.20997	−1.85328	−0.926640	−	0.375951i	$-0.877316\pi$
$3$	−3.20997	−1.85328	−0.926640	+	0.375951i	$0.877316\pi$
$4$	3.19730	1.59865
$5$	−0.137674	−0.0615698	−0.0307849	−	0.999526i	$-0.509801\pi$
$5$	−0.137674	−0.0615698	−0.0307849	+	0.999526i	$0.509801\pi$
$6$	−7.31797	−2.98755
$7$	−1.86944	−0.706583	−0.353291	−	0.935513i	$-0.614938\pi$
$7$	−1.86944	−0.706583	−0.353291	+	0.935513i	$0.614938\pi$
$8$	2.72957	0.965048
$9$	7.30393	2.43464
$10$	−0.313864	−0.0992526
$11$	2.62462	0.791354	0.395677	−	0.918390i	$-0.370510\pi$
$11$	2.62462	0.791354	0.395677	+	0.918390i	$0.370510\pi$
$12$	−10.2633	−2.96275
$13$	−1.74544	−0.484098	−0.242049	−	0.970264i	$-0.577819\pi$
$13$	−1.74544	−0.484098	−0.242049	+	0.970264i	$0.577819\pi$
$14$	−4.26188	−1.13904
$15$	0.441931	0.114106
$16$	−0.171852	−0.0429630
$17$	1.52193	0.369122	0.184561	−	0.982821i	$-0.440914\pi$
$17$	1.52193	0.369122	0.184561	+	0.982821i	$0.440914\pi$
$18$	16.6512	3.92473
$19$	−4.89252	−1.12242	−0.561210	−	0.827673i	$-0.689664\pi$
$19$	−4.89252	−1.12242	−0.561210	+	0.827673i	$0.689664\pi$
$20$	−0.440186	−0.0984287
$21$	6.00086	1.30950
$22$	5.98351	1.27569
$23$	4.37360	0.911958	0.455979	−	0.889991i	$-0.349289\pi$
$23$	4.37360	0.911958	0.455979	+	0.889991i	$0.349289\pi$
$24$	−8.76184	−1.78850
$25$	−4.98105	−0.996209
$26$	−3.97918	−0.780382
$27$	−13.8155	−2.65879
$28$	−5.97718	−1.12958
$29$	−0.0316144	−0.00587065	−0.00293533	−	0.999996i	$-0.500934\pi$
$29$	−0.0316144	−0.00587065	−0.00293533	+	0.999996i	$0.500934\pi$
$30$	1.00750	0.183943
$31$	−2.83196	−0.508634	−0.254317	−	0.967121i	$-0.581851\pi$
$31$	−2.83196	−0.508634	−0.254317	+	0.967121i	$0.581851\pi$
$32$	−5.85092	−1.03431
$33$	−8.42498	−1.46660
$34$	3.46963	0.595037
$35$	0.257374	0.0435041
$36$	23.3529	3.89215
$37$	0.00930992	0.00153054	0.000765270	−	1.00000i	$-0.499756\pi$
$37$	0.00930992	0.00153054	0.000765270		1.00000i	$0.499756\pi$
$38$	−11.1538	−1.80938
$39$	5.60281	0.897168
$40$	−0.375791	−0.0594178
$41$	−8.32089	−1.29951	−0.649753	−	0.760146i	$-0.725128\pi$
$41$	−8.32089	−1.29951	−0.649753	+	0.760146i	$0.725128\pi$
$42$	13.6805	2.11095
$43$	0	0
$43$	0	0
$44$	8.39173	1.26510
$45$	−1.00556	−0.149900
$46$	9.97075	1.47011
$47$	−5.62610	−0.820652	−0.410326	−	0.911939i	$-0.634585\pi$
$47$	−5.62610	−0.820652	−0.410326	+	0.911939i	$0.634585\pi$
$48$	0.551641	0.0796225
$49$	−3.50519	−0.500741
$50$	−11.3556	−1.60592
$51$	−4.88535	−0.684086
$52$	−5.58070	−0.773904
$53$	7.73578	1.06259	0.531295	−	0.847187i	$-0.321706\pi$
$53$	7.73578	1.06259	0.531295	+	0.847187i	$0.321706\pi$
$54$	−31.4960	−4.28607
$55$	−0.361343	−0.0487235
$56$	−5.10277	−0.681886
$57$	15.7048	2.08016
$58$	−0.0720733	−0.00946369
$59$	−2.17224	−0.282802	−0.141401	−	0.989952i	$-0.545161\pi$
$59$	−2.17224	−0.282802	−0.141401	+	0.989952i	$0.545161\pi$
$60$	1.41299	0.182416
$61$	−12.1436	−1.55483	−0.777415	−	0.628988i	$-0.783470\pi$
$61$	−12.1436	−1.55483	−0.777415	+	0.628988i	$0.783470\pi$
$62$	−6.45618	−0.819935
$63$	−13.6543	−1.72028
$64$	−12.9950	−1.62437
$65$	0.240302	0.0298058
$66$	−19.2069	−2.36421
$67$	−7.73963	−0.945546	−0.472773	−	0.881184i	$-0.656747\pi$
$67$	−7.73963	−0.945546	−0.472773	+	0.881184i	$0.656747\pi$
$68$	4.86607	0.590097
$69$	−14.0391	−1.69011
$70$	0.586751	0.0701301
$71$	−13.1068	−1.55549	−0.777743	−	0.628583i	$-0.783635\pi$
$71$	−13.1068	−1.55549	−0.777743	+	0.628583i	$0.783635\pi$
$72$	19.9366	2.34955
$73$	4.75807	0.556890	0.278445	−	0.960452i	$-0.410181\pi$
$73$	4.75807	0.556890	0.278445	+	0.960452i	$0.410181\pi$
$74$	0.0212244	0.00246728
$75$	15.9890	1.84625
$76$	−15.6429	−1.79436
$77$	−4.90658	−0.559157
$78$	12.7731	1.44626
$79$	−12.0074	−1.35094	−0.675469	−	0.737388i	$-0.736059\pi$
$79$	−12.0074	−1.35094	−0.675469	+	0.737388i	$0.736059\pi$
$80$	0.0236596	0.00264522
$81$	22.4356	2.49284
$82$	−18.9696	−2.09485
$83$	4.30212	0.472219	0.236110	−	0.971726i	$-0.424128\pi$
$83$	4.30212	0.472219	0.236110	+	0.971726i	$0.424128\pi$
$84$	19.1866	2.09343
$85$	−0.209530	−0.0227267
$86$	0	0
$87$	0.101482	0.0108800
$88$	7.16409	0.763694
$89$	7.69299	0.815455	0.407727	−	0.913104i	$-0.366321\pi$
$89$	7.69299	0.815455	0.407727	+	0.913104i	$0.366321\pi$
$90$	−2.29244	−0.241645
$91$	3.26300	0.342055
$92$	13.9837	1.45790
$93$	9.09050	0.942641
$94$	−12.8262	−1.32292
$95$	0.673573	0.0691072
$96$	18.7813	1.91686
$97$	1.61140	0.163613	0.0818064	−	0.996648i	$-0.473931\pi$
$97$	1.61140	0.163613	0.0818064	+	0.996648i	$0.473931\pi$
$98$	−7.99098	−0.807211
$99$	19.1701	1.92666
$100$	−15.9259	−1.59259
$101$	15.0649	1.49902	0.749508	−	0.661995i	$-0.230290\pi$
$101$	15.0649	1.49902	0.749508	+	0.661995i	$0.230290\pi$
$102$	−11.1374	−1.10277
$103$	−14.7127	−1.44969	−0.724844	−	0.688913i	$-0.758088\pi$
$103$	−14.7127	−1.44969	−0.724844	+	0.688913i	$0.758088\pi$
$104$	−4.76429	−0.467177
$105$	−0.826164	−0.0806253
$106$	17.6357	1.71293
$107$	3.42359	0.330971	0.165485	−	0.986212i	$-0.447081\pi$
$107$	3.42359	0.330971	0.165485	+	0.986212i	$0.447081\pi$
$108$	−44.1724	−4.25049
$109$	2.69351	0.257991	0.128996	−	0.991645i	$-0.458825\pi$
$109$	2.69351	0.257991	0.128996	+	0.991645i	$0.458825\pi$
$110$	−0.823776	−0.0785439
$111$	−0.0298846	−0.00283652
$112$	0.321268	0.0303569
$113$	4.77654	0.449339	0.224669	−	0.974435i	$-0.427870\pi$
$113$	4.77654	0.449339	0.224669	+	0.974435i	$0.427870\pi$
$114$	35.8033	3.35328
$115$	−0.602132	−0.0561491
$116$	−0.101081	−0.00938514
$117$	−12.7486	−1.17860
$118$	−4.95219	−0.455886
$119$	−2.84516	−0.260815
$120$	1.20628	0.110118
$121$	−4.11134	−0.373759
$122$	−27.6845	−2.50644
$123$	26.7098	2.40835
$124$	−9.05462	−0.813129
$125$	1.37413	0.122906
$126$	−31.1285	−2.77314
$127$	−0.972592	−0.0863035	−0.0431518	−	0.999069i	$-0.513740\pi$
$127$	−0.972592	−0.0863035	−0.0431518	+	0.999069i	$0.513740\pi$
$128$	−17.9236	−1.58424
$129$	0	0
$130$	0.547831	0.0480479
$131$	1.15918	0.101278	0.0506388	−	0.998717i	$-0.483874\pi$
$131$	1.15918	0.101278	0.0506388	+	0.998717i	$0.483874\pi$
$132$	−26.9372	−2.34458
$133$	9.14628	0.793083
$134$	−17.6445	−1.52425
$135$	1.90204	0.163701
$136$	4.15420	0.356220
$137$	21.4617	1.83359	0.916797	−	0.399354i	$-0.130765\pi$
$137$	21.4617	1.83359	0.916797	+	0.399354i	$0.130765\pi$
$138$	−32.0058	−2.72452
$139$	−12.4405	−1.05519	−0.527593	−	0.849497i	$-0.676906\pi$
$139$	−12.4405	−1.05519	−0.527593	+	0.849497i	$0.676906\pi$
$140$	0.822903	0.0695480
$141$	18.0596	1.52090
$142$	−29.8802	−2.50749
$143$	−4.58112	−0.383093
$144$	−1.25520	−0.104600
$145$	0.00435249	0.000361455 0
$146$	10.8473	0.897726
$147$	11.2516	0.928012
$148$	0.0297666	0.00244680
$149$	−3.95744	−0.324206	−0.162103	−	0.986774i	$-0.551828\pi$
$149$	−3.95744	−0.324206	−0.162103	+	0.986774i	$0.551828\pi$
$150$	36.4511	2.97622
$151$	−7.23207	−0.588538	−0.294269	−	0.955723i	$-0.595076\pi$
$151$	−7.23207	−0.588538	−0.294269	+	0.955723i	$0.595076\pi$
$152$	−13.3545	−1.08319
$153$	11.1161	0.898680
$154$	−11.1858	−0.901380
$155$	0.389887	0.0313165
$156$	17.9139	1.43426
$157$	2.52715	0.201688	0.100844	−	0.994902i	$-0.467846\pi$
$157$	2.52715	0.201688	0.100844	+	0.994902i	$0.467846\pi$
$158$	−27.3740	−2.17776
$159$	−24.8316	−1.96928
$160$	0.805520	0.0636820
$161$	−8.17619	−0.644374
$162$	51.1478	4.01855
$163$	13.6083	1.06589	0.532943	−	0.846151i	$-0.321086\pi$
$163$	13.6083	1.06589	0.532943	+	0.846151i	$0.321086\pi$
$164$	−26.6044	−2.07746
$165$	1.15990	0.0902982
$166$	9.80781	0.761234
$167$	−4.80232	−0.371615	−0.185807	−	0.982586i	$-0.559490\pi$
$167$	−4.80232	−0.371615	−0.185807	+	0.982586i	$0.559490\pi$
$168$	16.3798	1.26373
$169$	−9.95344	−0.765649
$170$	−0.477679	−0.0366363
$171$	−35.7346	−2.73269
$172$	0	0
$173$	15.9540	1.21296	0.606482	−	0.795098i	$-0.292580\pi$
$173$	15.9540	1.21296	0.606482	+	0.795098i	$0.292580\pi$
$174$	0.231353	0.0175389
$175$	9.31178	0.703904
$176$	−0.451047	−0.0339990
$177$	6.97284	0.524111
$178$	17.5382	1.31454
$179$	−15.9348	−1.19102	−0.595512	−	0.803347i	$-0.703051\pi$
$179$	−15.9348	−1.19102	−0.595512	+	0.803347i	$0.703051\pi$
$180$	−3.21509	−0.239639
$181$	20.8008	1.54611	0.773057	−	0.634337i	$-0.218727\pi$
$181$	20.8008	1.54611	0.773057	+	0.634337i	$0.218727\pi$
$182$	7.43885	0.551404
$183$	38.9807	2.88153
$184$	11.9380	0.880083
$185$	−0.00128174	−9.42351e−5 0
$186$	20.7242	1.51957
$187$	3.99449	0.292106
$188$	−17.9884	−1.31194
$189$	25.8273	1.87866
$190$	1.53559	0.111403
$191$	19.9136	1.44090	0.720450	−	0.693507i	$-0.243935\pi$
$191$	19.9136	1.44090	0.720450	+	0.693507i	$0.243935\pi$
$192$	41.7135	3.01042
$193$	−7.46774	−0.537540	−0.268770	−	0.963204i	$-0.586617\pi$
$193$	−7.46774	−0.537540	−0.268770	+	0.963204i	$0.586617\pi$
$194$	3.67360	0.263749
$195$	−0.771363	−0.0552384
$196$	−11.2071	−0.800510
$197$	26.6220	1.89674	0.948369	−	0.317170i	$-0.102733\pi$
$197$	26.6220	1.89674	0.948369	+	0.317170i	$0.102733\pi$
$198$	43.7032	3.10585
$199$	8.70117	0.616810	0.308405	−	0.951255i	$-0.400205\pi$
$199$	8.70117	0.616810	0.308405	+	0.951255i	$0.400205\pi$
$200$	−13.5961	−0.961389
$201$	24.8440	1.75236
$202$	34.3444	2.41646
$203$	0.0591014	0.00414810
$204$	−15.6199	−1.09362
$205$	1.14557	0.0800103
$206$	−33.5415	−2.33695
$207$	31.9444	2.22029
$208$	0.299957	0.0207983
$209$	−12.8410	−0.888232
$210$	−1.88345	−0.129971
$211$	−12.3927	−0.853152	−0.426576	−	0.904452i	$-0.640280\pi$
$211$	−12.3927	−0.853152	−0.426576	+	0.904452i	$0.640280\pi$
$212$	24.7336	1.69871
$213$	42.0723	2.88275
$214$	7.80496	0.533536
$215$	0	0
$216$	−37.7103	−2.56586
$217$	5.29418	0.359392
$218$	6.14055	0.415891
$219$	−15.2733	−1.03207
$220$	−1.15532	−0.0778919
$221$	−2.65643	−0.178691
$222$	−0.0681297	−0.00457256
$223$	−25.6873	−1.72015	−0.860074	−	0.510169i	$-0.829583\pi$
$223$	−25.6873	−1.72015	−0.860074	+	0.510169i	$0.829583\pi$
$224$	10.9379	0.730823
$225$	−36.3812	−2.42541
$226$	10.8894	0.724349
$227$	1.04070	0.0690736	0.0345368	−	0.999403i	$-0.489004\pi$
$227$	1.04070	0.0690736	0.0345368	+	0.999403i	$0.489004\pi$
$228$	50.2132	3.32545
$229$	7.52157	0.497040	0.248520	−	0.968627i	$-0.420056\pi$
$229$	7.52157	0.497040	0.248520	+	0.968627i	$0.420056\pi$
$230$	−1.37272	−0.0905142
$231$	15.7500	1.03627
$232$	−0.0862937	−0.00566546
$233$	−3.09074	−0.202481	−0.101241	−	0.994862i	$-0.532281\pi$
$233$	−3.09074	−0.202481	−0.101241	+	0.994862i	$0.532281\pi$
$234$	−29.0637	−1.89995
$235$	0.774569	0.0505273
$236$	−6.94532	−0.452102
$237$	38.5434	2.50367
$238$	−6.48627	−0.420443
$239$	10.8457	0.701552	0.350776	−	0.936459i	$-0.385918\pi$
$239$	10.8457	0.701552	0.350776	+	0.936459i	$0.385918\pi$
$240$	−0.0759467	−0.00490234
$241$	8.08395	0.520733	0.260366	−	0.965510i	$-0.416157\pi$
$241$	8.08395	0.520733	0.260366	+	0.965510i	$0.416157\pi$
$242$	−9.37288	−0.602511
$243$	−30.5712	−1.96114
$244$	−38.8268	−2.48563
$245$	0.482574	0.0308305
$246$	60.8920	3.88233
$247$	8.53959	0.543361
$248$	−7.73001	−0.490856
$249$	−13.8097	−0.875154
$250$	3.13269	0.198129
$251$	7.58320	0.478647	0.239324	−	0.970940i	$-0.423074\pi$
$251$	7.58320	0.478647	0.239324	+	0.970940i	$0.423074\pi$
$252$	−43.6569	−2.75012
$253$	11.4791	0.721682
$254$	−2.21728	−0.139124
$255$	0.672587	0.0421190
$256$	−14.8715	−0.929471
$257$	−2.35428	−0.146856	−0.0734280	−	0.997301i	$-0.523394\pi$
$257$	−2.35428	−0.146856	−0.0734280	+	0.997301i	$0.523394\pi$
$258$	0	0
$259$	−0.0174044	−0.00108145
$260$	0.768318	0.0476491
$261$	−0.230910	−0.0142929
$262$	2.64264	0.163263
$263$	−18.8814	−1.16428	−0.582139	−	0.813089i	$-0.697784\pi$
$263$	−18.8814	−1.16428	−0.582139	+	0.813089i	$0.697784\pi$
$264$	−22.9965	−1.41534
$265$	−1.06502	−0.0654235
$266$	20.8513	1.27848
$267$	−24.6943	−1.51127
$268$	−24.7460	−1.51160
$269$	−11.5332	−0.703191	−0.351596	−	0.936152i	$-0.614361\pi$
$269$	−11.5332	−0.703191	−0.351596	+	0.936152i	$0.614361\pi$
$270$	4.33619	0.263892
$271$	−19.3210	−1.17366	−0.586832	−	0.809709i	$-0.699625\pi$
$271$	−19.3210	−1.17366	−0.586832	+	0.809709i	$0.699625\pi$
$272$	−0.261547	−0.0158586
$273$	−10.4741	−0.633923
$274$	48.9274	2.95582
$275$	−13.0734	−0.788354
$276$	−44.8874	−2.70190
$277$	7.29865	0.438534	0.219267	−	0.975665i	$-0.429634\pi$
$277$	7.29865	0.438534	0.219267	+	0.975665i	$0.429634\pi$
$278$	−28.3613	−1.70100
$279$	−20.6844	−1.23834
$280$	0.702520	0.0419836
$281$	10.5123	0.627114	0.313557	−	0.949569i	$-0.398479\pi$
$281$	10.5123	0.627114	0.313557	+	0.949569i	$0.398479\pi$
$282$	41.1716	2.45174
$283$	24.2934	1.44409	0.722047	−	0.691844i	$-0.243201\pi$
$283$	24.2934	1.44409	0.722047	+	0.691844i	$0.243201\pi$
$284$	−41.9063	−2.48668
$285$	−2.16215	−0.128075
$286$	−10.4439	−0.617558
$287$	15.5554	0.918208
$288$	−42.7347	−2.51816
$289$	−14.6837	−0.863749
$290$	0.00992264	0.000582677 0
$291$	−5.17255	−0.303220
$292$	15.2130	0.890274
$293$	−13.0502	−0.762403	−0.381201	−	0.924492i	$-0.624490\pi$
$293$	−13.0502	−0.762403	−0.381201	+	0.924492i	$0.624490\pi$
$294$	25.6508	1.49599
$295$	0.299062	0.0174121
$296$	0.0254120	0.00147704
$297$	−36.2605	−2.10405
$298$	−9.02202	−0.522631
$299$	−7.63385	−0.441477
$300$	51.1218	2.95152
$301$	0	0
$302$	−16.4874	−0.948743
$303$	−48.3580	−2.77810
$304$	0.840789	0.0482226
$305$	1.67186	0.0957306
$306$	25.3419	1.44870
$307$	−20.9425	−1.19525	−0.597625	−	0.801776i	$-0.703889\pi$
$307$	−20.9425	−1.19525	−0.597625	+	0.801776i	$0.703889\pi$
$308$	−15.6878	−0.893898
$309$	47.2275	2.68668
$310$	0.888849	0.0504832
$311$	16.5964	0.941098	0.470549	−	0.882374i	$-0.344056\pi$
$311$	16.5964	0.941098	0.470549	+	0.882374i	$0.344056\pi$
$312$	15.2933	0.865810
$313$	−11.2107	−0.633664	−0.316832	−	0.948482i	$-0.602619\pi$
$313$	−11.2107	−0.633664	−0.316832	+	0.948482i	$0.602619\pi$
$314$	5.76129	0.325128
$315$	1.87984	0.105917
$316$	−38.3913	−2.15968
$317$	12.4749	0.700662	0.350331	−	0.936626i	$-0.386069\pi$
$317$	12.4749	0.700662	0.350331	+	0.936626i	$0.386069\pi$
$318$	−56.6102	−3.17454
$319$	−0.0829760	−0.00464577
$320$	1.78907	0.100012
$321$	−10.9896	−0.613381
$322$	−18.6397	−1.03875
$323$	−7.44606	−0.414310
$324$	71.7334	3.98519
$325$	8.69411	0.482262
$326$	31.0237	1.71824
$327$	−8.64609	−0.478130
$328$	−22.7124	−1.25408
$329$	10.5177	0.579858
$330$	2.64430	0.145564
$331$	4.24904	0.233548	0.116774	−	0.993158i	$-0.462745\pi$
$331$	4.24904	0.233548	0.116774	+	0.993158i	$0.462745\pi$
$332$	13.7552	0.754915
$333$	0.0679990	0.00372632
$334$	−10.9481	−0.599055
$335$	1.06555	0.0582171
$336$	−1.03126	−0.0562599
$337$	9.61441	0.523731	0.261865	−	0.965104i	$-0.415662\pi$
$337$	9.61441	0.523731	0.261865	+	0.965104i	$0.415662\pi$
$338$	−22.6915	−1.23425
$339$	−15.3326	−0.832750
$340$	−0.669932	−0.0363322
$341$	−7.43282	−0.402510
$342$	−81.4663	−4.40519
$343$	19.6388	1.06040
$344$	0	0
$345$	1.93283	0.104060
$346$	36.3714	1.95534
$347$	9.98615	0.536085	0.268042	−	0.963407i	$-0.413623\pi$
$347$	9.98615	0.536085	0.268042	+	0.963407i	$0.413623\pi$
$348$	0.324467	0.0173933
$349$	−0.630103	−0.0337287	−0.0168643	−	0.999858i	$-0.505368\pi$
$349$	−0.630103	−0.0337287	−0.0168643	+	0.999858i	$0.505368\pi$
$350$	21.2286	1.13472
$351$	24.1141	1.28712
$352$	−15.3565	−0.818502
$353$	−17.5759	−0.935472	−0.467736	−	0.883868i	$-0.654930\pi$
$353$	−17.5759	−0.935472	−0.467736	+	0.883868i	$0.654930\pi$
$354$	15.8964	0.844884
$355$	1.80446	0.0957709
$356$	24.5968	1.30363
$357$	9.13288	0.483363
$358$	−36.3275	−1.91997
$359$	−25.3691	−1.33893	−0.669465	−	0.742843i	$-0.733477\pi$
$359$	−25.3691	−1.33893	−0.669465	+	0.742843i	$0.733477\pi$
$360$	−2.74475	−0.144661
$361$	4.93671	0.259827
$362$	47.4209	2.49239
$363$	13.1973	0.692679
$364$	10.4328	0.546827
$365$	−0.655064	−0.0342876
$366$	88.8666	4.64513
$367$	−17.2567	−0.900794	−0.450397	−	0.892828i	$-0.648718\pi$
$367$	−17.2567	−0.900794	−0.450397	+	0.892828i	$0.648718\pi$
$368$	−0.751612	−0.0391805
$369$	−60.7752	−3.16383
$370$	−0.00292205	−0.000151910 0
$371$	−14.4616	−0.750808
$372$	29.0651	1.50696
$373$	−25.7676	−1.33420	−0.667099	−	0.744969i	$-0.732464\pi$
$373$	−25.7676	−1.33420	−0.667099	+	0.744969i	$0.732464\pi$
$374$	9.10648	0.470885
$375$	−4.41093	−0.227779
$376$	−15.3568	−0.791968
$377$	0.0551811	0.00284197
$378$	58.8800	3.02846
$379$	21.0381	1.08065	0.540327	−	0.841455i	$-0.318301\pi$
$379$	21.0381	1.08065	0.540327	+	0.841455i	$0.318301\pi$
$380$	2.15362	0.110478
$381$	3.12199	0.159945
$382$	45.3983	2.32278
$383$	24.2267	1.23793	0.618964	−	0.785419i	$-0.287553\pi$
$383$	24.2267	1.23793	0.618964	+	0.785419i	$0.287553\pi$
$384$	57.5343	2.93603
$385$	0.675510	0.0344272
$386$	−17.0247	−0.866532
$387$	0	0
$388$	5.15213	0.261560
$389$	−30.3001	−1.53628	−0.768138	−	0.640285i	$-0.778816\pi$
$389$	−30.3001	−1.53628	−0.768138	+	0.640285i	$0.778816\pi$
$390$	−1.75852	−0.0890462
$391$	6.65630	0.336624
$392$	−9.56764	−0.483239
$393$	−3.72092	−0.187696
$394$	60.6917	3.05760
$395$	1.65311	0.0831770
$396$	61.2926	3.08007
$397$	1.70345	0.0854938	0.0427469	−	0.999086i	$-0.486389\pi$
$397$	1.70345	0.0854938	0.0427469	+	0.999086i	$0.486389\pi$
$398$	19.8366	0.994318
$399$	−29.3593	−1.46980
$400$	0.856003	0.0428002
$401$	−0.00855597	−0.000427265 0	−0.000213632	−	1.00000i	$-0.500068\pi$
$401$	−0.00855597	−0.000427265 0	−0.000213632		1.00000i	$0.500068\pi$
$402$	56.6384	2.82487
$403$	4.94300	0.246229
$404$	48.1672	2.39641
$405$	−3.08880	−0.153484
$406$	0.134737	0.00668688
$407$	0.0244350	0.00121120
$408$	−13.3349	−0.660175
$409$	−30.0726	−1.48699	−0.743496	−	0.668740i	$-0.766834\pi$
$409$	−30.0726	−1.48699	−0.743496	+	0.668740i	$0.766834\pi$
$410$	2.61163	0.128979
$411$	−68.8914	−3.39816
$412$	−47.0411	−2.31755
$413$	4.06088	0.199823
$414$	72.8257	3.57919
$415$	−0.592291	−0.0290744
$416$	10.2124	0.500705
$417$	39.9336	1.95556
$418$	−29.2744	−1.43186
$419$	9.93160	0.485190	0.242595	−	0.970128i	$-0.422001\pi$
$419$	9.93160	0.485190	0.242595	+	0.970128i	$0.422001\pi$
$420$	−2.64150	−0.128892
$421$	−11.0594	−0.539000	−0.269500	−	0.963000i	$-0.586858\pi$
$421$	−11.0594	−0.539000	−0.269500	+	0.963000i	$0.586858\pi$
$422$	−28.2525	−1.37531
$423$	−41.0927	−1.99799
$424$	21.1153	1.02545
$425$	−7.58079	−0.367722
$426$	95.9148	4.64709
$427$	22.7018	1.09862
$428$	10.9463	0.529107
$429$	14.7053	0.709978
$430$	0	0
$431$	−24.7776	−1.19350	−0.596748	−	0.802429i	$-0.703541\pi$
$431$	−24.7776	−1.19350	−0.596748	+	0.802429i	$0.703541\pi$
$432$	2.37422	0.114230
$433$	−6.32472	−0.303947	−0.151973	−	0.988385i	$-0.548563\pi$
$433$	−6.32472	−0.303947	−0.151973	+	0.988385i	$0.548563\pi$
$434$	12.0695	0.579352
$435$	−0.0139714	−0.000669877 0
$436$	8.61197	0.412439
$437$	−21.3979	−1.02360
$438$	−34.8194	−1.66374
$439$	39.6373	1.89179	0.945894	−	0.324477i	$-0.105188\pi$
$439$	39.6373	1.89179	0.945894	+	0.324477i	$0.105188\pi$
$440$	−0.986310	−0.0470205
$441$	−25.6016	−1.21912
$442$	−6.05603	−0.288056
$443$	−5.21717	−0.247875	−0.123938	−	0.992290i	$-0.539552\pi$
$443$	−5.21717	−0.247875	−0.123938	+	0.992290i	$0.539552\pi$
$444$	−0.0955501	−0.00453461
$445$	−1.05913	−0.0502074
$446$	−58.5608	−2.77294
$447$	12.7033	0.600845
$448$	24.2934	1.14775
$449$	18.1969	0.858766	0.429383	−	0.903123i	$-0.358731\pi$
$449$	18.1969	0.858766	0.429383	+	0.903123i	$0.358731\pi$
$450$	−82.9404	−3.90985
$451$	−21.8392	−1.02837
$452$	15.2720	0.718336
$453$	23.2148	1.09072
$454$	2.37254	0.111349
$455$	−0.449231	−0.0210603
$456$	42.8674	2.00745
$457$	16.6769	0.780115	0.390057	−	0.920791i	$-0.372455\pi$
$457$	16.6769	0.780115	0.390057	+	0.920791i	$0.372455\pi$
$458$	17.1474	0.801245
$459$	−21.0262	−0.981419
$460$	−1.92520	−0.0897628
$461$	−23.8532	−1.11095	−0.555476	−	0.831533i	$-0.687464\pi$
$461$	−23.8532	−1.11095	−0.555476	+	0.831533i	$0.687464\pi$
$462$	35.9062	1.67051
$463$	28.6812	1.33293	0.666464	−	0.745537i	$-0.267807\pi$
$463$	28.6812	1.33293	0.666464	+	0.745537i	$0.267807\pi$
$464$	0.00543301	0.000252221 0
$465$	−1.25153	−0.0580382
$466$	−7.04615	−0.326407
$467$	28.0534	1.29816	0.649079	−	0.760721i	$-0.275154\pi$
$467$	28.0534	1.29816	0.649079	+	0.760721i	$0.275154\pi$
$468$	−40.7610	−1.88418
$469$	14.4688	0.668107
$470$	1.76583	0.0814518
$471$	−8.11207	−0.373785
$472$	−5.92928	−0.272917
$473$	0	0
$474$	87.8698	4.03599
$475$	24.3698	1.11817
$476$	−9.09683	−0.416953
$477$	56.5016	2.58703
$478$	24.7257	1.13093
$479$	−10.4151	−0.475878	−0.237939	−	0.971280i	$-0.576472\pi$
$479$	−10.4151	−0.475878	−0.237939	+	0.971280i	$0.576472\pi$
$480$	−2.58570	−0.118020
$481$	−0.0162499	−0.000740931 0
$482$	18.4295	0.839439
$483$	26.2453	1.19420
$484$	−13.1452	−0.597510
$485$	−0.221848	−0.0100736
$486$	−69.6949	−3.16143
$487$	12.8635	0.582899	0.291450	−	0.956586i	$-0.405862\pi$
$487$	12.8635	0.582899	0.291450	+	0.956586i	$0.405862\pi$
$488$	−33.1468	−1.50049
$489$	−43.6823	−1.97538
$490$	1.10015	0.0496998
$491$	−17.1552	−0.774203	−0.387102	−	0.922037i	$-0.626524\pi$
$491$	−17.1552	−0.774203	−0.387102	+	0.922037i	$0.626524\pi$
$492$	85.3995	3.85011
$493$	−0.0481149	−0.00216699
$494$	19.4682	0.875916
$495$	−2.63922	−0.118624
$496$	0.486678	0.0218525
$497$	24.5023	1.09908
$498$	−31.4828	−1.41078
$499$	26.3621	1.18013	0.590064	−	0.807356i	$-0.299102\pi$
$499$	26.3621	1.18013	0.590064	+	0.807356i	$0.299102\pi$
$500$	4.39352	0.196484
$501$	15.4153	0.688706
$502$	17.2879	0.771595
$503$	−12.9339	−0.576694	−0.288347	−	0.957526i	$-0.593106\pi$
$503$	−12.9339	−0.576694	−0.288347	+	0.957526i	$0.593106\pi$
$504$	−37.2703	−1.66015
$505$	−2.07405	−0.0922941
$506$	26.1695	1.16338
$507$	31.9503	1.41896
$508$	−3.10967	−0.137969
$509$	11.5361	0.511327	0.255663	−	0.966766i	$-0.417706\pi$
$509$	11.5361	0.511327	0.255663	+	0.966766i	$0.417706\pi$
$510$	1.53334	0.0678972
$511$	−8.89495	−0.393489
$512$	1.94366	0.0858983
$513$	67.5925	2.98428
$514$	−5.36719	−0.236737
$515$	2.02556	0.0892570
$516$	0	0
$517$	−14.7664	−0.649426
$518$	−0.0396777	−0.00174334
$519$	−51.2120	−2.24796
$520$	0.655920	0.0287640
$521$	9.42367	0.412858	0.206429	−	0.978462i	$-0.433816\pi$
$521$	9.42367	0.412858	0.206429	+	0.978462i	$0.433816\pi$
$522$	−0.526419	−0.0230407
$523$	−7.15434	−0.312838	−0.156419	−	0.987691i	$-0.549995\pi$
$523$	−7.15434	−0.312838	−0.156419	+	0.987691i	$0.549995\pi$
$524$	3.70624	0.161908
$525$	−29.8906	−1.30453
$526$	−43.0451	−1.87686
$527$	−4.31003	−0.187748
$528$	1.44785	0.0630096
$529$	−3.87165	−0.168333
$530$	−2.42798	−0.105465
$531$	−15.8659	−0.688522
$532$	29.2434	1.26786
$533$	14.5236	0.629087
$534$	−56.2970	−2.43621
$535$	−0.471340	−0.0203778
$536$	−21.1258	−0.912497
$537$	51.1503	2.20730
$538$	−26.2929	−1.13357
$539$	−9.19980	−0.396263
$540$	6.08139	0.261702
$541$	−10.3300	−0.444122	−0.222061	−	0.975033i	$-0.571278\pi$
$541$	−10.3300	−0.444122	−0.222061	+	0.975033i	$0.571278\pi$
$542$	−44.0471	−1.89199
$543$	−66.7701	−2.86538
$544$	−8.90467	−0.381785
$545$	−0.370827	−0.0158845
$546$	−23.8785	−1.02191
$547$	−19.1843	−0.820262	−0.410131	−	0.912027i	$-0.634517\pi$
$547$	−19.1843	−0.820262	−0.410131	+	0.912027i	$0.634517\pi$
$548$	68.6195	2.93128
$549$	−88.6961	−3.78546
$550$	−29.8042	−1.27085
$551$	0.154674	0.00658934
$552$	−38.3207	−1.63104
$553$	22.4472	0.954550
$554$	16.6392	0.706931
$555$	0.00411434	0.000174644 0
$556$	−39.7760	−1.68688
$557$	−7.13268	−0.302221	−0.151111	−	0.988517i	$-0.548285\pi$
$557$	−7.13268	−0.302221	−0.151111	+	0.988517i	$0.548285\pi$
$558$	−47.1555	−1.99625
$559$	0	0
$560$	−0.0442303	−0.00186907
$561$	−12.8222	−0.541354
$562$	23.9656	1.01093
$563$	−33.9909	−1.43254	−0.716272	−	0.697821i	$-0.754153\pi$
$563$	−33.9909	−1.43254	−0.716272	+	0.697821i	$0.754153\pi$
$564$	57.7422	2.43138
$565$	−0.657606	−0.0276657
$566$	55.3832	2.32793
$567$	−41.9420	−1.76140
$568$	−35.7758	−1.50112
$569$	−9.51002	−0.398681	−0.199340	−	0.979930i	$-0.563880\pi$
$569$	−9.51002	−0.398681	−0.199340	+	0.979930i	$0.563880\pi$
$570$	−4.92919	−0.206461
$571$	14.8571	0.621750	0.310875	−	0.950451i	$-0.399378\pi$
$571$	14.8571	0.621750	0.310875	+	0.950451i	$0.399378\pi$
$572$	−14.6472	−0.612432
$573$	−63.9222	−2.67039
$574$	35.4626	1.48018
$575$	−21.7851	−0.908501
$576$	−94.9144	−3.95477
$577$	−9.26236	−0.385597	−0.192799	−	0.981238i	$-0.561756\pi$
$577$	−9.26236	−0.385597	−0.192799	+	0.981238i	$0.561756\pi$
$578$	−33.4754	−1.39239
$579$	23.9713	0.996211
$580$	0.0139162	0.000577841 0
$581$	−8.04257	−0.333662
$582$	−11.7922	−0.488801
$583$	20.3035	0.840885
$584$	12.9875	0.537426
$585$	1.75515	0.0725664
$586$	−29.7514	−1.22902
$587$	45.3050	1.86994	0.934969	−	0.354731i	$-0.115427\pi$
$587$	45.3050	1.86994	0.934969	+	0.354731i	$0.115427\pi$
$588$	35.9746	1.48357
$589$	13.8554	0.570901
$590$	0.681789	0.0280688
$591$	−85.4558	−3.51518
$592$	−0.00159993	−6.57567e−5 0
$593$	−7.34080	−0.301451	−0.150725	−	0.988576i	$-0.548161\pi$
$593$	−7.34080	−0.301451	−0.150725	+	0.988576i	$0.548161\pi$
$594$	−82.6652	−3.39180
$595$	0.391705	0.0160583
$596$	−12.6531	−0.518293
$597$	−27.9305	−1.14312
$598$	−17.4033	−0.711675
$599$	−41.1928	−1.68309	−0.841545	−	0.540186i	$-0.818354\pi$
$599$	−41.1928	−1.68309	−0.841545	+	0.540186i	$0.818354\pi$
$600$	43.6431	1.78172
$601$	43.4446	1.77214	0.886072	−	0.463548i	$-0.153424\pi$
$601$	43.4446	1.77214	0.886072	+	0.463548i	$0.153424\pi$
$602$	0	0
$603$	−56.5297	−2.30207
$604$	−23.1231	−0.940867
$605$	0.566026	0.0230122
$606$	−110.245	−4.47838
$607$	1.32691	0.0538576	0.0269288	−	0.999637i	$-0.491427\pi$
$607$	1.32691	0.0538576	0.0269288	+	0.999637i	$0.491427\pi$
$608$	28.6257	1.16093
$609$	−0.189714	−0.00768759
$610$	3.81145	0.154321
$611$	9.82002	0.397275
$612$	35.5414	1.43668
$613$	−35.2558	−1.42397	−0.711985	−	0.702195i	$-0.752204\pi$
$613$	−35.2558	−1.42397	−0.711985	+	0.702195i	$0.752204\pi$
$614$	−47.7438	−1.92678
$615$	−3.67726	−0.148281
$616$	−13.3929	−0.539613
$617$	29.4767	1.18669	0.593343	−	0.804950i	$-0.297808\pi$
$617$	29.4767	1.18669	0.593343	+	0.804950i	$0.297808\pi$
$618$	107.667	4.33101
$619$	17.9599	0.721868	0.360934	−	0.932591i	$-0.382458\pi$
$619$	17.9599	0.721868	0.360934	+	0.932591i	$0.382458\pi$
$620$	1.24659	0.0500642
$621$	−60.4234	−2.42471
$622$	37.8359	1.51708
$623$	−14.3816	−0.576186
$624$	−0.962855	−0.0385451
$625$	24.7160	0.988642
$626$	−25.5576	−1.02149
$627$	41.2193	1.64614
$628$	8.08006	0.322429
$629$	0.0141690	0.000564956 0
$630$	4.28559	0.170742
$631$	31.5168	1.25467	0.627333	−	0.778751i	$-0.284147\pi$
$631$	31.5168	1.25467	0.627333	+	0.778751i	$0.284147\pi$
$632$	−32.7750	−1.30372
$633$	39.7804	1.58113
$634$	28.4398	1.12949
$635$	0.133901	0.00531369
$636$	−79.3943	−3.14819
$637$	6.11809	0.242407
$638$	−0.189165	−0.00748913
$639$	−95.7308	−3.78705
$640$	2.46762	0.0975411
$641$	−33.5332	−1.32448	−0.662241	−	0.749291i	$-0.730394\pi$
$641$	−33.5332	−1.32448	−0.662241	+	0.749291i	$0.730394\pi$
$642$	−25.0537	−0.988791
$643$	−24.2796	−0.957493	−0.478746	−	0.877953i	$-0.658909\pi$
$643$	−24.2796	−0.957493	−0.478746	+	0.877953i	$0.658909\pi$
$644$	−26.1418	−1.03013
$645$	0	0
$646$	−16.9752	−0.667881
$647$	−22.0532	−0.867001	−0.433501	−	0.901153i	$-0.642722\pi$
$647$	−22.0532	−0.867001	−0.433501	+	0.901153i	$0.642722\pi$
$648$	61.2395	2.40571
$649$	−5.70132	−0.223796
$650$	19.8205	0.777423
$651$	−16.9942	−0.666054
$652$	43.5099	1.70398
$653$	−19.8641	−0.777344	−0.388672	−	0.921376i	$-0.627066\pi$
$653$	−19.8641	−0.777344	−0.388672	+	0.921376i	$0.627066\pi$
$654$	−19.7110	−0.770762
$655$	−0.159589	−0.00623564
$656$	1.42996	0.0558307
$657$	34.7526	1.35583
$658$	23.9778	0.934751
$659$	30.3563	1.18251	0.591256	−	0.806484i	$-0.298632\pi$
$659$	30.3563	1.18251	0.591256	+	0.806484i	$0.298632\pi$
$660$	3.70856	0.144355
$661$	−27.2988	−1.06180	−0.530900	−	0.847435i	$-0.678146\pi$
$661$	−27.2988	−1.06180	−0.530900	+	0.847435i	$0.678146\pi$
$662$	9.68680	0.376488
$663$	8.52708	0.331164
$664$	11.7429	0.455714
$665$	−1.25921	−0.0488299
$666$	0.155021	0.00600695
$667$	−0.138269	−0.00535379
$668$	−15.3545	−0.594083
$669$	82.4555	3.18791
$670$	2.42919	0.0938479
$671$	−31.8724	−1.23042
$672$	−35.1105	−1.35442
$673$	−35.7568	−1.37832	−0.689161	−	0.724608i	$-0.742021\pi$
$673$	−35.7568	−1.37832	−0.689161	+	0.724608i	$0.742021\pi$
$674$	21.9186	0.844271
$675$	68.8156	2.64871
$676$	−31.8242	−1.22401
$677$	34.2270	1.31545	0.657725	−	0.753258i	$-0.271519\pi$
$677$	34.2270	1.31545	0.657725	+	0.753258i	$0.271519\pi$
$678$	−34.9545	−1.34242
$679$	−3.01242	−0.115606
$680$	−0.571927	−0.0219324
$681$	−3.34061	−0.128013
$682$	−16.9450	−0.648859
$683$	−37.5565	−1.43706	−0.718530	−	0.695496i	$-0.755185\pi$
$683$	−37.5565	−1.43706	−0.718530	+	0.695496i	$0.755185\pi$
$684$	−114.254	−4.36863
$685$	−2.95472	−0.112894
$686$	44.7718	1.70940
$687$	−24.1441	−0.921153
$688$	0	0
$689$	−13.5023	−0.514397
$690$	4.40638	0.167748
$691$	−29.3722	−1.11737	−0.558686	−	0.829379i	$-0.688694\pi$
$691$	−29.3722	−1.11737	−0.558686	+	0.829379i	$0.688694\pi$
$692$	51.0099	1.93911
$693$	−35.8373	−1.36135
$694$	22.7660	0.864187
$695$	1.71273	0.0649676
$696$	0.277001	0.0104997
$697$	−12.6638	−0.479676
$698$	−1.43648	−0.0543717
$699$	9.92120	0.375254
$700$	29.7726	1.12530
$701$	16.7737	0.633535	0.316767	−	0.948503i	$-0.397403\pi$
$701$	16.7737	0.633535	0.316767	+	0.948503i	$0.397403\pi$
$702$	54.9744	2.07487
$703$	−0.0455489	−0.00171791
$704$	−34.1069	−1.28545
$705$	−2.48635	−0.0936413
$706$	−40.0689	−1.50801
$707$	−28.1630	−1.05918
$708$	22.2943	0.837871
$709$	−32.4360	−1.21816	−0.609080	−	0.793109i	$-0.708461\pi$
$709$	−32.4360	−1.21816	−0.609080	+	0.793109i	$0.708461\pi$
$710$	4.11374	0.154386
$711$	−87.7012	−3.28905
$712$	20.9985	0.786953
$713$	−12.3858	−0.463853
$714$	20.8208	0.779198
$715$	0.630702	0.0235869
$716$	−50.9484	−1.90403
$717$	−34.8145	−1.30017
$718$	−57.8355	−2.15840
$719$	40.2795	1.50217	0.751085	−	0.660205i	$-0.229531\pi$
$719$	40.2795	1.50217	0.751085	+	0.660205i	$0.229531\pi$
$720$	0.172808	0.00644018
$721$	27.5046	1.02432
$722$	11.2545	0.418850
$723$	−25.9493	−0.965063
$724$	66.5066	2.47170
$725$	0.157473	0.00584840
$726$	30.0867	1.11662
$727$	10.3472	0.383758	0.191879	−	0.981419i	$-0.438542\pi$
$727$	10.3472	0.383758	0.191879	+	0.981419i	$0.438542\pi$
$728$	8.90657	0.330099
$729$	30.8258	1.14170
$730$	−1.49339	−0.0552728
$731$	0	0
$732$	124.633	4.60657
$733$	43.0751	1.59102	0.795508	−	0.605944i	$-0.207204\pi$
$733$	43.0751	1.59102	0.795508	+	0.605944i	$0.207204\pi$
$734$	−39.3412	−1.45211
$735$	−1.54905	−0.0571375
$736$	−25.5895	−0.943243
$737$	−20.3136	−0.748262
$738$	−138.553	−5.10020
$739$	−9.42149	−0.346575	−0.173288	−	0.984871i	$-0.555439\pi$
$739$	−9.42149	−0.346575	−0.173288	+	0.984871i	$0.555439\pi$
$740$	−0.00409810	−0.000150649 0
$741$	−27.4118	−1.00700
$742$	−32.9689	−1.21033
$743$	19.8990	0.730022	0.365011	−	0.931003i	$-0.381065\pi$
$743$	19.8990	0.730022	0.365011	+	0.931003i	$0.381065\pi$
$744$	24.8131	0.909694
$745$	0.544838	0.0199613
$746$	−58.7440	−2.15077
$747$	31.4224	1.14969
$748$	12.7716	0.466976
$749$	−6.40020	−0.233858
$750$	−10.0559	−0.367188
$751$	12.8537	0.469039	0.234519	−	0.972111i	$-0.424648\pi$
$751$	12.8537	0.469039	0.234519	+	0.972111i	$0.424648\pi$
$752$	0.966858	0.0352577
$753$	−24.3419	−0.887067
$754$	0.125800	0.00458135
$755$	0.995670	0.0362361
$756$	82.5777	3.00332
$757$	42.9659	1.56162	0.780812	−	0.624767i	$-0.214806\pi$
$757$	42.9659	1.56162	0.780812	+	0.624767i	$0.214806\pi$
$758$	47.9618	1.74205
$759$	−36.8474	−1.33748
$760$	1.83856	0.0666917
$761$	−31.4473	−1.13996	−0.569981	−	0.821658i	$-0.693050\pi$
$761$	−31.4473	−1.13996	−0.569981	+	0.821658i	$0.693050\pi$
$762$	7.11739	0.257836
$763$	−5.03536	−0.182292
$764$	63.6699	2.30350
$765$	−1.53039	−0.0553315
$766$	55.2311	1.99558
$767$	3.79152	0.136904
$768$	47.7372	1.72257
$769$	13.4296	0.484283	0.242141	−	0.970241i	$-0.422150\pi$
$769$	13.4296	0.484283	0.242141	+	0.970241i	$0.422150\pi$
$770$	1.54000	0.0554978
$771$	7.55718	0.272165
$772$	−23.8766	−0.859339
$773$	38.3879	1.38072	0.690358	−	0.723468i	$-0.257453\pi$
$773$	38.3879	1.38072	0.690358	+	0.723468i	$0.257453\pi$
$774$	0	0
$775$	14.1061	0.506706
$776$	4.39842	0.157894
$777$	0.0558675	0.00200424
$778$	−69.0769	−2.47653
$779$	40.7101	1.45859
$780$	−2.46628	−0.0883071
$781$	−34.4003	−1.23094
$782$	15.1748	0.542648
$783$	0.436769	0.0156089
$784$	0.602374	0.0215133
$785$	−0.347923	−0.0124179
$786$	−8.48281	−0.302572
$787$	25.1845	0.897732	0.448866	−	0.893599i	$-0.351828\pi$
$787$	25.1845	0.897732	0.448866	+	0.893599i	$0.351828\pi$
$788$	85.1186	3.03222
$789$	60.6089	2.15773
$790$	3.76869	0.134084
$791$	−8.92946	−0.317495
$792$	52.3260	1.85932
$793$	21.1959	0.752690
$794$	3.88346	0.137819
$795$	3.41868	0.121248
$796$	27.8203	0.986064
$797$	−7.36425	−0.260855	−0.130428	−	0.991458i	$-0.541635\pi$
$797$	−7.36425	−0.260855	−0.130428	+	0.991458i	$0.541635\pi$
$798$	−66.9322	−2.36937
$799$	−8.56253	−0.302920
$800$	29.1437	1.03038
$801$	56.1890	1.98534
$802$	−0.0195056	−0.000688765 0
$803$	12.4882	0.440698
$804$	79.4339	2.80142
$805$	1.12565	0.0396740
$806$	11.2689	0.396929
$807$	37.0213	1.30321
$808$	41.1207	1.44662
$809$	−15.8703	−0.557971	−0.278986	−	0.960295i	$-0.589998\pi$
$809$	−15.8703	−0.557971	−0.278986	+	0.960295i	$0.589998\pi$
$810$	−7.04173	−0.247421
$811$	7.58951	0.266504	0.133252	−	0.991082i	$-0.457458\pi$
$811$	7.58951	0.266504	0.133252	+	0.991082i	$0.457458\pi$
$812$	0.188965	0.00663138
$813$	62.0197	2.17513
$814$	0.0557060	0.00195249
$815$	−1.87351	−0.0656263
$816$	0.839558	0.0293904
$817$	0	0
$818$	−68.5582	−2.39708
$819$	23.8327	0.832782
$820$	3.66274	0.127909
$821$	43.8262	1.52955	0.764773	−	0.644300i	$-0.222851\pi$
$821$	43.8262	1.52955	0.764773	+	0.644300i	$0.222851\pi$
$822$	−157.056	−5.47795
$823$	−35.9501	−1.25314	−0.626571	−	0.779364i	$-0.715542\pi$
$823$	−35.9501	−1.25314	−0.626571	+	0.779364i	$0.715542\pi$
$824$	−40.1594	−1.39902
$825$	41.9652	1.46104
$826$	9.25784	0.322121
$827$	−8.48320	−0.294990	−0.147495	−	0.989063i	$-0.547121\pi$
$827$	−8.48320	−0.294990	−0.147495	+	0.989063i	$0.547121\pi$
$828$	102.136	3.54948
$829$	−36.0230	−1.25113	−0.625565	−	0.780172i	$-0.715132\pi$
$829$	−36.0230	−1.25113	−0.625565	+	0.780172i	$0.715132\pi$
$830$	−1.35028	−0.0468690
$831$	−23.4285	−0.812725
$832$	22.6819	0.786355
$833$	−5.33464	−0.184834
$834$	91.0389	3.15242
$835$	0.661156	0.0228802
$836$	−41.0567	−1.41997
$837$	39.1249	1.35235
$838$	22.6417	0.782143
$839$	−18.5803	−0.641465	−0.320732	−	0.947170i	$-0.603929\pi$
$839$	−18.5803	−0.641465	−0.320732	+	0.947170i	$0.603929\pi$
$840$	−2.25507	−0.0778073
$841$	−28.9990	−0.999966
$842$	−25.2127	−0.868887
$843$	−33.7443	−1.16222
$844$	−39.6234	−1.36389
$845$	1.37033	0.0471409
$846$	−93.6814	−3.22083
$847$	7.68592	0.264091
$848$	−1.32941	−0.0456521
$849$	−77.9812	−2.67631
$850$	−17.2824	−0.592781
$851$	0.0407178	0.00139579
$852$	134.518	4.60851
$853$	−37.3393	−1.27847	−0.639237	−	0.769010i	$-0.720750\pi$
$853$	−37.3393	−1.27847	−0.639237	+	0.769010i	$0.720750\pi$
$854$	51.7546	1.77101
$855$	4.91973	0.168251
$856$	9.34492	0.319403
$857$	22.9715	0.784690	0.392345	−	0.919818i	$-0.371664\pi$
$857$	22.9715	0.784690	0.392345	+	0.919818i	$0.371664\pi$
$858$	33.5245	1.14451
$859$	−33.6996	−1.14981	−0.574907	−	0.818218i	$-0.694962\pi$
$859$	−33.6996	−1.14981	−0.574907	+	0.818218i	$0.694962\pi$
$860$	0	0
$861$	−49.9325	−1.70170
$862$	−56.4870	−1.92396
$863$	24.0650	0.819181	0.409591	−	0.912269i	$-0.365672\pi$
$863$	24.0650	0.819181	0.409591	+	0.912269i	$0.365672\pi$
$864$	80.8333	2.75001
$865$	−2.19646	−0.0746819
$866$	−14.4188	−0.489972
$867$	47.1344	1.60077
$868$	16.9271	0.574543
$869$	−31.5149	−1.06907
$870$	−0.0318514	−0.00107986
$871$	13.5091	0.457737
$872$	7.35211	0.248974
$873$	11.7695	0.398339
$874$	−48.7821	−1.65008
$875$	−2.56886	−0.0868434
$876$	−48.8334	−1.64993
$877$	−12.6511	−0.427198	−0.213599	−	0.976921i	$-0.568519\pi$
$877$	−12.6511	−0.427198	−0.213599	+	0.976921i	$0.568519\pi$
$878$	90.3636	3.04962
$879$	41.8909	1.41294
$880$	0.0620976	0.00209331
$881$	20.8237	0.701568	0.350784	−	0.936456i	$-0.385915\pi$
$881$	20.8237	0.701568	0.350784	+	0.936456i	$0.385915\pi$
$882$	−58.3656	−1.96527
$883$	−3.61493	−0.121652	−0.0608261	−	0.998148i	$-0.519374\pi$
$883$	−3.61493	−0.121652	−0.0608261	+	0.998148i	$0.519374\pi$
$884$	−8.49342	−0.285665
$885$	−0.959981	−0.0322694
$886$	−11.8939	−0.399583
$887$	26.3085	0.883351	0.441676	−	0.897175i	$-0.354384\pi$
$887$	26.3085	0.883351	0.441676	+	0.897175i	$0.354384\pi$
$888$	−0.0815720	−0.00273738
$889$	1.81820	0.0609806
$890$	−2.41455	−0.0809360
$891$	58.8850	1.97272
$892$	−82.1301	−2.74992
$893$	27.5258	0.921116
$894$	28.9604	0.968582
$895$	2.19381	0.0733311
$896$	33.5071	1.11939
$897$	24.5044	0.818179
$898$	41.4846	1.38436
$899$	0.0895307	0.00298602
$900$	−116.322	−3.87739
$901$	11.7733	0.392225
$902$	−49.7882	−1.65777
$903$	0	0
$904$	13.0379	0.433633
$905$	−2.86374	−0.0951939
$906$	52.9241	1.75828
$907$	17.8839	0.593825	0.296913	−	0.954905i	$-0.404043\pi$
$907$	17.8839	0.593825	0.296913	+	0.954905i	$0.404043\pi$
$908$	3.32743	0.110425
$909$	110.033	3.64957
$910$	−1.02414	−0.0339498
$911$	−12.9871	−0.430282	−0.215141	−	0.976583i	$-0.569021\pi$
$911$	−12.9871	−0.430282	−0.215141	+	0.976583i	$0.569021\pi$
$912$	−2.69891	−0.0893699
$913$	11.2915	0.373693
$914$	38.0194	1.25757
$915$	−5.36663	−0.177415
$916$	24.0488	0.794594
$917$	−2.16701	−0.0715611
$918$	−47.9347	−1.58208
$919$	1.12169	0.0370012	0.0185006	−	0.999829i	$-0.494111\pi$
$919$	1.12169	0.0370012	0.0185006	+	0.999829i	$0.494111\pi$
$920$	−1.64356	−0.0541865
$921$	67.2248	2.21513
$922$	−54.3795	−1.79089
$923$	22.8770	0.753007
$924$	50.3576	1.65664
$925$	−0.0463731	−0.00152474
$926$	65.3862	2.14872
$927$	−107.461	−3.52947
$928$	0.184973	0.00607205
$929$	−50.0971	−1.64363	−0.821817	−	0.569752i	$-0.807039\pi$
$929$	−50.0971	−1.64363	−0.821817	+	0.569752i	$0.807039\pi$
$930$	−2.85318	−0.0935595
$931$	17.1492	0.562042
$932$	−9.88204	−0.323697
$933$	−53.2741	−1.74412
$934$	63.9551	2.09268
$935$	−0.549938	−0.0179849
$936$	−34.7981	−1.13741
$937$	−20.6632	−0.675038	−0.337519	−	0.941319i	$-0.609588\pi$
$937$	−20.6632	−0.675038	−0.337519	+	0.941319i	$0.609588\pi$
$938$	32.9854	1.07701
$939$	35.9859	1.17436
$940$	2.47653	0.0807756
$941$	−17.4799	−0.569827	−0.284914	−	0.958553i	$-0.591965\pi$
$941$	−17.4799	−0.569827	−0.284914	+	0.958553i	$0.591965\pi$
$942$	−18.4936	−0.602553
$943$	−36.3922	−1.18509
$944$	0.373305	0.0121500
$945$	−3.55575	−0.115669
$946$	0	0
$947$	−18.8409	−0.612246	−0.306123	−	0.951992i	$-0.599032\pi$
$947$	−18.8409	−0.612246	−0.306123	+	0.951992i	$0.599032\pi$
$948$	123.235	4.00249
$949$	−8.30493	−0.269589
$950$	55.5574	1.80252
$951$	−40.0442	−1.29852
$952$	−7.76605	−0.251699
$953$	43.3195	1.40326	0.701629	−	0.712543i	$-0.252457\pi$
$953$	43.3195	1.40326	0.701629	+	0.712543i	$0.252457\pi$
$954$	128.810	4.17038
$955$	−2.74159	−0.0887159
$956$	34.6771	1.12154
$957$	0.266351	0.00860990
$958$	−23.7439	−0.767132
$959$	−40.1213	−1.29559
$960$	−5.74288	−0.185351
$961$	−22.9800	−0.741291
$962$	−0.0370458	−0.00119441
$963$	25.0057	0.805796
$964$	25.8468	0.832471
$965$	1.02812	0.0330962
$966$	59.8331	1.92510
$967$	2.74232	0.0881872	0.0440936	−	0.999027i	$-0.485960\pi$
$967$	2.74232	0.0881872	0.0440936	+	0.999027i	$0.485960\pi$
$968$	−11.2222	−0.360695
$969$	23.9016	0.767831
$970$	−0.505760	−0.0162390
$971$	21.7020	0.696452	0.348226	−	0.937411i	$-0.386784\pi$
$971$	21.7020	0.696452	0.348226	+	0.937411i	$0.386784\pi$
$972$	−97.7453	−3.13518
$973$	23.2567	0.745577
$974$	29.3256	0.939653
$975$	−27.9079	−0.893767
$976$	2.08691	0.0668002
$977$	−34.6747	−1.10934	−0.554671	−	0.832070i	$-0.687156\pi$
$977$	−34.6747	−1.10934	−0.554671	+	0.832070i	$0.687156\pi$
$978$	−99.5852	−3.18438
$979$	20.1912	0.645314
$980$	1.54293	0.0492872
$981$	19.6732	0.628117
$982$	−39.1097	−1.24804
$983$	−15.5139	−0.494817	−0.247409	−	0.968911i	$-0.579579\pi$
$983$	−15.5139	−0.494817	−0.247409	+	0.968911i	$0.579579\pi$
$984$	72.9063	2.32417
$985$	−3.66516	−0.116782
$986$	−0.109690	−0.00349325
$987$	−33.7615	−1.07464
$988$	27.3037	0.868645
$989$	0	0
$990$	−6.01680	−0.191226
$991$	0.589004	0.0187103	0.00935516	−	0.999956i	$-0.497022\pi$
$991$	0.589004	0.0187103	0.00935516	+	0.999956i	$0.497022\pi$
$992$	16.5695	0.526083
$993$	−13.6393	−0.432831
$994$	55.8594	1.77175
$995$	−1.19793	−0.0379768
$996$	−44.1538	−1.39907
$997$	39.8130	1.26089	0.630446	−	0.776233i	$-0.282872\pi$
$997$	39.8130	1.26089	0.630446	+	0.776233i	$0.282872\pi$
$998$	60.0992	1.90241
$999$	−0.128621	−0.00406939

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.n.1.17		18
43.10	even	21		43.2.g.a.14.1	✓	36
43.13	even	21		43.2.g.a.40.1	yes	36
43.42	odd	2		1849.2.a.o.1.2		18
129.53	odd	42		387.2.y.c.100.3		36
129.56	odd	42		387.2.y.c.298.3		36
172.99	odd	42		688.2.bg.c.513.3		36
172.139	odd	42		688.2.bg.c.401.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.14.1	✓	36	43.10	even	21
43.2.g.a.40.1	yes	36	43.13	even	21
387.2.y.c.100.3		36	129.53	odd	42
387.2.y.c.298.3		36	129.56	odd	42
688.2.bg.c.401.3		36	172.139	odd	42
688.2.bg.c.513.3		36	172.99	odd	42
1849.2.a.n.1.17		18	1.1	even	1	trivial
1849.2.a.o.1.2		18	43.42	odd	2

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)

\(f(q)\)	\(=\)	\(q+2.27976 q^{2} -3.20997 q^{3} +3.19730 q^{4} -0.137674 q^{5} -7.31797 q^{6} -1.86944 q^{7} +2.72957 q^{8} +7.30393 q^{9} +O(q^{10})\)	\(q+2.27976 q^{2} -3.20997 q^{3} +3.19730 q^{4} -0.137674 q^{5} -7.31797 q^{6} -1.86944 q^{7} +2.72957 q^{8} +7.30393 q^{9} -0.313864 q^{10} +2.62462 q^{11} -10.2633 q^{12} -1.74544 q^{13} -4.26188 q^{14} +0.441931 q^{15} -0.171852 q^{16} +1.52193 q^{17} +16.6512 q^{18} -4.89252 q^{19} -0.440186 q^{20} +6.00086 q^{21} +5.98351 q^{22} +4.37360 q^{23} -8.76184 q^{24} -4.98105 q^{25} -3.97918 q^{26} -13.8155 q^{27} -5.97718 q^{28} -0.0316144 q^{29} +1.00750 q^{30} -2.83196 q^{31} -5.85092 q^{32} -8.42498 q^{33} +3.46963 q^{34} +0.257374 q^{35} +23.3529 q^{36} +0.00930992 q^{37} -11.1538 q^{38} +5.60281 q^{39} -0.375791 q^{40} -8.32089 q^{41} +13.6805 q^{42} +8.39173 q^{44} -1.00556 q^{45} +9.97075 q^{46} -5.62610 q^{47} +0.551641 q^{48} -3.50519 q^{49} -11.3556 q^{50} -4.88535 q^{51} -5.58070 q^{52} +7.73578 q^{53} -31.4960 q^{54} -0.361343 q^{55} -5.10277 q^{56} +15.7048 q^{57} -0.0720733 q^{58} -2.17224 q^{59} +1.41299 q^{60} -12.1436 q^{61} -6.45618 q^{62} -13.6543 q^{63} -12.9950 q^{64} +0.240302 q^{65} -19.2069 q^{66} -7.73963 q^{67} +4.86607 q^{68} -14.0391 q^{69} +0.586751 q^{70} -13.1068 q^{71} +19.9366 q^{72} +4.75807 q^{73} +0.0212244 q^{74} +15.9890 q^{75} -15.6429 q^{76} -4.90658 q^{77} +12.7731 q^{78} -12.0074 q^{79} +0.0236596 q^{80} +22.4356 q^{81} -18.9696 q^{82} +4.30212 q^{83} +19.1866 q^{84} -0.209530 q^{85} +0.101482 q^{87} +7.16409 q^{88} +7.69299 q^{89} -2.29244 q^{90} +3.26300 q^{91} +13.9837 q^{92} +9.09050 q^{93} -12.8262 q^{94} +0.673573 q^{95} +18.7813 q^{96} +1.61140 q^{97} -7.99098 q^{98} +19.1701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 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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