LMFDB - Embedded newform 1849.2.a.r.1.12

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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} - 19 x^{18} + 127 x^{17} + 95 x^{16} - 1293 x^{15} + 329 x^{14} + 6765 x^{13} + \cdots - 43 $ x^20 - 5x^19 - 19x^18 + 127x^17 + 95x^16 - 1293x^15 + 329x^14 + 6765x^13 - 5068x^12 - 19360x^11 + 20357x^10 + 29618x^9 - 37889x^8 - 21700x^7 + 32885x^6 + 6093x^5 - 11330x^4 - 1004x^3 + 1386x^2 + 87*x - 43
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$0.881156$ 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)

$f(q)$	$=$	$q+0.881156 q^{2} +2.54519 q^{3} -1.22356 q^{4} +2.37402 q^{5} +2.24271 q^{6} -3.19714 q^{7} -2.84046 q^{8} +3.47799 q^{9} +O(q^{10})$	\(q+0.881156 q^{2} +2.54519 q^{3} -1.22356 q^{4} +2.37402 q^{5} +2.24271 q^{6} -3.19714 q^{7} -2.84046 q^{8} +3.47799 q^{9} +2.09188 q^{10} -0.0311414 q^{11} -3.11420 q^{12} +4.65432 q^{13} -2.81718 q^{14} +6.04232 q^{15} -0.0557610 q^{16} +1.64726 q^{17} +3.06465 q^{18} +8.22249 q^{19} -2.90476 q^{20} -8.13732 q^{21} -0.0274404 q^{22} +5.34002 q^{23} -7.22952 q^{24} +0.635948 q^{25} +4.10118 q^{26} +1.21658 q^{27} +3.91190 q^{28} +2.45438 q^{29} +5.32422 q^{30} -3.83563 q^{31} +5.63179 q^{32} -0.0792607 q^{33} +1.45150 q^{34} -7.59005 q^{35} -4.25555 q^{36} -0.0125794 q^{37} +7.24529 q^{38} +11.8461 q^{39} -6.74330 q^{40} -6.31966 q^{41} -7.17025 q^{42} +0.0381035 q^{44} +8.25680 q^{45} +4.70539 q^{46} +12.5713 q^{47} -0.141922 q^{48} +3.22169 q^{49} +0.560369 q^{50} +4.19260 q^{51} -5.69486 q^{52} -1.54891 q^{53} +1.07199 q^{54} -0.0739300 q^{55} +9.08135 q^{56} +20.9278 q^{57} +2.16269 q^{58} +2.17998 q^{59} -7.39317 q^{60} -0.459647 q^{61} -3.37979 q^{62} -11.1196 q^{63} +5.07401 q^{64} +11.0494 q^{65} -0.0698410 q^{66} -3.56162 q^{67} -2.01553 q^{68} +13.5914 q^{69} -6.68802 q^{70} -6.72915 q^{71} -9.87910 q^{72} +6.12727 q^{73} -0.0110844 q^{74} +1.61861 q^{75} -10.0607 q^{76} +0.0995632 q^{77} +10.4383 q^{78} -13.2744 q^{79} -0.132378 q^{80} -7.33756 q^{81} -5.56860 q^{82} +7.89486 q^{83} +9.95654 q^{84} +3.91063 q^{85} +6.24687 q^{87} +0.0884559 q^{88} -11.4512 q^{89} +7.27553 q^{90} -14.8805 q^{91} -6.53385 q^{92} -9.76241 q^{93} +11.0772 q^{94} +19.5203 q^{95} +14.3340 q^{96} +13.8637 q^{97} +2.83881 q^{98} -0.108309 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{2} - q^{3} + 23 q^{4} - 3 q^{5} + 5 q^{6} - 2 q^{7} + 9 q^{8} + 27 q^{9}+O(q^{10}) $ 20 * q + 5 * q^2 - q^3 + 23 * q^4 - 3 * q^5 + 5 * q^6 - 2 * q^7 + 9 * q^8 + 27 * q^9	\( 20 q + 5 q^{2} - q^{3} + 23 q^{4} - 3 q^{5} + 5 q^{6} - 2 q^{7} + 9 q^{8} + 27 q^{9} + 21 q^{11} - 12 q^{12} + 11 q^{13} + 8 q^{14} + 4 q^{15} + 29 q^{16} + 15 q^{17} + 9 q^{18} - 7 q^{19} - 17 q^{20} + 8 q^{21} + 47 q^{22} + 26 q^{23} - q^{24} + 11 q^{25} + 58 q^{26} - 22 q^{27} - 28 q^{28} - 12 q^{29} - 24 q^{30} + 26 q^{31} + 3 q^{32} - 17 q^{33} + 54 q^{34} + 26 q^{35} + 14 q^{36} - 19 q^{37} + 5 q^{38} - 7 q^{39} - 16 q^{40} + 27 q^{41} - 52 q^{42} + 32 q^{44} + 75 q^{45} + 59 q^{46} + 45 q^{47} - 66 q^{48} + 20 q^{49} + 75 q^{51} + 11 q^{52} + 3 q^{53} + 57 q^{54} - 2 q^{55} + 87 q^{56} - 24 q^{57} - 46 q^{58} + 66 q^{59} + 29 q^{60} + 30 q^{61} + 72 q^{62} - 21 q^{63} - 7 q^{64} - 6 q^{65} + 41 q^{66} - 6 q^{67} + 28 q^{68} - 35 q^{69} - 80 q^{70} - 31 q^{71} - 15 q^{72} - 26 q^{73} + 87 q^{74} + 73 q^{75} - 68 q^{76} - 21 q^{77} - 50 q^{78} + 39 q^{79} - 60 q^{80} + 16 q^{81} + 45 q^{82} + 13 q^{83} + 31 q^{84} - 22 q^{85} + 61 q^{87} + 50 q^{88} - 4 q^{89} - 13 q^{90} - 25 q^{91} + 5 q^{92} + 67 q^{93} + 42 q^{94} + 79 q^{95} + 36 q^{96} - 2 q^{97} - 35 q^{98} + 13 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 + 23 * q^4 - 3 * q^5 + 5 * q^6 - 2 * q^7 + 9 * q^8 + 27 * q^9 + 21 * q^11 - 12 * q^12 + 11 * q^13 + 8 * q^14 + 4 * q^15 + 29 * q^16 + 15 * q^17 + 9 * q^18 - 7 * q^19 - 17 * q^20 + 8 * q^21 + 47 * q^22 + 26 * q^23 - q^24 + 11 * q^25 + 58 * q^26 - 22 * q^27 - 28 * q^28 - 12 * q^29 - 24 * q^30 + 26 * q^31 + 3 * q^32 - 17 * q^33 + 54 * q^34 + 26 * q^35 + 14 * q^36 - 19 * q^37 + 5 * q^38 - 7 * q^39 - 16 * q^40 + 27 * q^41 - 52 * q^42 + 32 * q^44 + 75 * q^45 + 59 * q^46 + 45 * q^47 - 66 * q^48 + 20 * q^49 + 75 * q^51 + 11 * q^52 + 3 * q^53 + 57 * q^54 - 2 * q^55 + 87 * q^56 - 24 * q^57 - 46 * q^58 + 66 * q^59 + 29 * q^60 + 30 * q^61 + 72 * q^62 - 21 * q^63 - 7 * q^64 - 6 * q^65 + 41 * q^66 - 6 * q^67 + 28 * q^68 - 35 * q^69 - 80 * q^70 - 31 * q^71 - 15 * q^72 - 26 * q^73 + 87 * q^74 + 73 * q^75 - 68 * q^76 - 21 * q^77 - 50 * q^78 + 39 * q^79 - 60 * q^80 + 16 * q^81 + 45 * q^82 + 13 * q^83 + 31 * q^84 - 22 * q^85 + 61 * q^87 + 50 * q^88 - 4 * q^89 - 13 * q^90 - 25 * q^91 + 5 * q^92 + 67 * q^93 + 42 * q^94 + 79 * q^95 + 36 * q^96 - 2 * q^97 - 35 * q^98 + 13 * 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 $

$2$	0.881156	0.623071	0.311536	−	0.950234i	$-0.399157\pi$
$2$	0.881156	0.623071	0.311536	+	0.950234i	$0.399157\pi$
$3$	2.54519	1.46947	0.734733	−	0.678356i	$-0.237307\pi$
$3$	2.54519	1.46947	0.734733	+	0.678356i	$0.237307\pi$
$4$	−1.22356	−0.611782
$5$	2.37402	1.06169	0.530846	−	0.847468i	$-0.321874\pi$
$5$	2.37402	1.06169	0.530846	+	0.847468i	$0.321874\pi$
$6$	2.24271	0.915582
$7$	−3.19714	−1.20840	−0.604202	−	0.796831i	$-0.706508\pi$
$7$	−3.19714	−1.20840	−0.604202	+	0.796831i	$0.706508\pi$
$8$	−2.84046	−1.00426
$9$	3.47799	1.15933
$10$	2.09188	0.661510
$11$	−0.0311414	−0.00938947	−0.00469474	−	0.999989i	$-0.501494\pi$
$11$	−0.0311414	−0.00938947	−0.00469474	+	0.999989i	$0.501494\pi$
$12$	−3.11420	−0.898993
$13$	4.65432	1.29088	0.645438	−	0.763813i	$-0.276675\pi$
$13$	4.65432	1.29088	0.645438	+	0.763813i	$0.276675\pi$
$14$	−2.81718	−0.752922
$15$	6.04232	1.56012
$16$	−0.0557610	−0.0139403
$17$	1.64726	0.399520	0.199760	−	0.979845i	$-0.435984\pi$
$17$	1.64726	0.399520	0.199760	+	0.979845i	$0.435984\pi$
$18$	3.06465	0.722345
$19$	8.22249	1.88637	0.943184	−	0.332270i	$-0.107815\pi$
$19$	8.22249	1.88637	0.943184	+	0.332270i	$0.107815\pi$
$20$	−2.90476	−0.649524
$21$	−8.13732	−1.77571
$22$	−0.0274404	−0.00585031
$23$	5.34002	1.11347	0.556735	−	0.830690i	$-0.312054\pi$
$23$	5.34002	1.11347	0.556735	+	0.830690i	$0.312054\pi$
$24$	−7.22952	−1.47572
$25$	0.635948	0.127190
$26$	4.10118	0.804307
$27$	1.21658	0.234130
$28$	3.91190	0.739280
$29$	2.45438	0.455767	0.227884	−	0.973688i	$-0.426819\pi$
$29$	2.45438	0.455767	0.227884	+	0.973688i	$0.426819\pi$
$30$	5.32422	0.972066
$31$	−3.83563	−0.688900	−0.344450	−	0.938805i	$-0.611935\pi$
$31$	−3.83563	−0.688900	−0.344450	+	0.938805i	$0.611935\pi$
$32$	5.63179	0.995569
$33$	−0.0792607	−0.0137975
$34$	1.45150	0.248930
$35$	−7.59005	−1.28295
$36$	−4.25555	−0.709258
$37$	−0.0125794	−0.00206805	−0.00103402	−	0.999999i	$-0.500329\pi$
$37$	−0.0125794	−0.00206805	−0.00103402	+	0.999999i	$0.500329\pi$
$38$	7.24529	1.17534
$39$	11.8461	1.89690
$40$	−6.74330	−1.06621
$41$	−6.31966	−0.986965	−0.493483	−	0.869756i	$-0.664276\pi$
$41$	−6.31966	−0.986965	−0.493483	+	0.869756i	$0.664276\pi$
$42$	−7.17025	−1.10639
$43$	0	0
$43$	0	0
$44$	0.0381035	0.00574431
$45$	8.25680	1.23085
$46$	4.70539	0.693771
$47$	12.5713	1.83371	0.916853	−	0.399224i	$-0.130720\pi$
$47$	12.5713	1.83371	0.916853	+	0.399224i	$0.130720\pi$
$48$	−0.141922	−0.0204847
$49$	3.22169	0.460242
$50$	0.560369	0.0792482
$51$	4.19260	0.587081
$52$	−5.69486	−0.789735
$53$	−1.54891	−0.212759	−0.106380	−	0.994326i	$-0.533926\pi$
$53$	−1.54891	−0.212759	−0.106380	+	0.994326i	$0.533926\pi$
$54$	1.07199	0.145880
$55$	−0.0739300	−0.00996873
$56$	9.08135	1.21355
$57$	20.9278	2.77195
$58$	2.16269	0.283976
$59$	2.17998	0.283810	0.141905	−	0.989880i	$-0.454677\pi$
$59$	2.17998	0.283810	0.141905	+	0.989880i	$0.454677\pi$
$60$	−7.39317	−0.954454
$61$	−0.459647	−0.0588518	−0.0294259	−	0.999567i	$-0.509368\pi$
$61$	−0.459647	−0.0588518	−0.0294259	+	0.999567i	$0.509368\pi$
$62$	−3.37979	−0.429234
$63$	−11.1196	−1.40094
$64$	5.07401	0.634251
$65$	11.0494	1.37051
$66$	−0.0698410	−0.00859683
$67$	−3.56162	−0.435121	−0.217560	−	0.976047i	$-0.569810\pi$
$67$	−3.56162	−0.435121	−0.217560	+	0.976047i	$0.569810\pi$
$68$	−2.01553	−0.244419
$69$	13.5914	1.63621
$70$	−6.68802	−0.799371
$71$	−6.72915	−0.798603	−0.399301	−	0.916820i	$-0.630747\pi$
$71$	−6.72915	−0.798603	−0.399301	+	0.916820i	$0.630747\pi$
$72$	−9.87910	−1.16426
$73$	6.12727	0.717142	0.358571	−	0.933502i	$-0.383264\pi$
$73$	6.12727	0.717142	0.358571	+	0.933502i	$0.383264\pi$
$74$	−0.0110844	−0.00128854
$75$	1.61861	0.186901
$76$	−10.0607	−1.15405
$77$	0.0995632	0.0113463
$78$	10.4383	1.18190
$79$	−13.2744	−1.49348	−0.746742	−	0.665114i	$-0.768383\pi$
$79$	−13.2744	−1.49348	−0.746742	+	0.665114i	$0.768383\pi$
$80$	−0.132378	−0.0148003
$81$	−7.33756	−0.815284
$82$	−5.56860	−0.614950
$83$	7.89486	0.866573	0.433287	−	0.901256i	$-0.357354\pi$
$83$	7.89486	0.866573	0.433287	+	0.901256i	$0.357354\pi$
$84$	9.95654	1.08635
$85$	3.91063	0.424167
$86$	0	0
$87$	6.24687	0.669735
$88$	0.0884559	0.00942943
$89$	−11.4512	−1.21383	−0.606915	−	0.794767i	$-0.707593\pi$
$89$	−11.4512	−1.21383	−0.606915	+	0.794767i	$0.707593\pi$
$90$	7.27553	0.766908
$91$	−14.8805	−1.55990
$92$	−6.53385	−0.681201
$93$	−9.76241	−1.01231
$94$	11.0772	1.14253
$95$	19.5203	2.00274
$96$	14.3340	1.46296
$97$	13.8637	1.40764	0.703822	−	0.710376i	$-0.251475\pi$
$97$	13.8637	1.40764	0.703822	+	0.710376i	$0.251475\pi$
$98$	2.83881	0.286763
$99$	−0.108309	−0.0108855
$100$	−0.778123	−0.0778123
$101$	−5.74513	−0.571662	−0.285831	−	0.958280i	$-0.592270\pi$
$101$	−5.74513	−0.571662	−0.285831	+	0.958280i	$0.592270\pi$
$102$	3.69433	0.365793
$103$	1.33124	0.131171	0.0655857	−	0.997847i	$-0.479108\pi$
$103$	1.33124	0.131171	0.0655857	+	0.997847i	$0.479108\pi$
$104$	−13.2204	−1.29637
$105$	−19.3181	−1.88526
$106$	−1.36483	−0.132564
$107$	−6.79096	−0.656507	−0.328254	−	0.944590i	$-0.606460\pi$
$107$	−6.79096	−0.656507	−0.328254	+	0.944590i	$0.606460\pi$
$108$	−1.48856	−0.143237
$109$	−0.605283	−0.0579756	−0.0289878	−	0.999580i	$-0.509228\pi$
$109$	−0.605283	−0.0579756	−0.0289878	+	0.999580i	$0.509228\pi$
$110$	−0.0651439	−0.00621123
$111$	−0.0320171	−0.00303893
$112$	0.178276	0.0168455
$113$	−10.7380	−1.01015	−0.505074	−	0.863076i	$-0.668535\pi$
$113$	−10.7380	−1.01015	−0.505074	+	0.863076i	$0.668535\pi$
$114$	18.4406	1.72712
$115$	12.6773	1.18216
$116$	−3.00310	−0.278830
$117$	16.1877	1.49655
$118$	1.92090	0.176834
$119$	−5.26653	−0.482782
$120$	−17.1630	−1.56676
$121$	−10.9990	−0.999912
$122$	−0.405021	−0.0366688
$123$	−16.0847	−1.45031
$124$	4.69314	0.421457
$125$	−10.3603	−0.926656
$126$	−9.79811	−0.872885
$127$	−7.75658	−0.688285	−0.344142	−	0.938917i	$-0.611830\pi$
$127$	−7.75658	−0.688285	−0.344142	+	0.938917i	$0.611830\pi$
$128$	−6.79259	−0.600386
$129$	0	0
$130$	9.73626	0.853927
$131$	−8.37620	−0.731832	−0.365916	−	0.930648i	$-0.619244\pi$
$131$	−8.37620	−0.731832	−0.365916	+	0.930648i	$0.619244\pi$
$132$	0.0969805	0.00844107
$133$	−26.2884	−2.27950
$134$	−3.13834	−0.271111
$135$	2.88817	0.248574
$136$	−4.67899	−0.401220
$137$	4.69356	0.400998	0.200499	−	0.979694i	$-0.435744\pi$
$137$	4.69356	0.400998	0.200499	+	0.979694i	$0.435744\pi$
$138$	11.9761	1.01947
$139$	−3.97169	−0.336874	−0.168437	−	0.985712i	$-0.553872\pi$
$139$	−3.97169	−0.336874	−0.168437	+	0.985712i	$0.553872\pi$
$140$	9.28692	0.784888
$141$	31.9962	2.69457
$142$	−5.92943	−0.497586
$143$	−0.144942	−0.0121206
$144$	−0.193936	−0.0161614
$145$	5.82674	0.483885
$146$	5.39908	0.446831
$147$	8.19982	0.676309
$148$	0.0153918	0.00126519
$149$	−11.9257	−0.976992	−0.488496	−	0.872566i	$-0.662454\pi$
$149$	−11.9257	−0.976992	−0.488496	+	0.872566i	$0.662454\pi$
$150$	1.42625	0.116452
$151$	−11.8368	−0.963269	−0.481634	−	0.876372i	$-0.659957\pi$
$151$	−11.8368	−0.963269	−0.481634	+	0.876372i	$0.659957\pi$
$152$	−23.3557	−1.89440
$153$	5.72917	0.463176
$154$	0.0877307	0.00706954
$155$	−9.10584	−0.731399
$156$	−14.4945	−1.16049
$157$	1.37185	0.109485	0.0547426	−	0.998500i	$-0.482566\pi$
$157$	1.37185	0.109485	0.0547426	+	0.998500i	$0.482566\pi$
$158$	−11.6968	−0.930547
$159$	−3.94227	−0.312643
$160$	13.3700	1.05699
$161$	−17.0728	−1.34552
$162$	−6.46553	−0.507980
$163$	8.18503	0.641101	0.320551	−	0.947231i	$-0.396132\pi$
$163$	8.18503	0.641101	0.320551	+	0.947231i	$0.396132\pi$
$164$	7.73251	0.603808
$165$	−0.188166	−0.0146487
$166$	6.95660	0.539937
$167$	24.9577	1.93128	0.965640	−	0.259882i	$-0.0836836\pi$
$167$	24.9577	1.93128	0.965640	+	0.259882i	$0.0836836\pi$
$168$	23.1138	1.78327
$169$	8.66268	0.666360
$170$	3.44587	0.264286
$171$	28.5977	2.18692
$172$	0	0
$173$	−23.2068	−1.76438	−0.882190	−	0.470894i	$-0.843932\pi$
$173$	−23.2068	−1.76438	−0.882190	+	0.470894i	$0.843932\pi$
$174$	5.50446	0.417292
$175$	−2.03321	−0.153696
$176$	0.00173647	0.000130892 0
$177$	5.54847	0.417048
$178$	−10.0903	−0.756302
$179$	6.53218	0.488238	0.244119	−	0.969745i	$-0.421501\pi$
$179$	6.53218	0.488238	0.244119	+	0.969745i	$0.421501\pi$
$180$	−10.1027	−0.753013
$181$	9.17921	0.682285	0.341143	−	0.940012i	$-0.389186\pi$
$181$	9.17921	0.682285	0.341143	+	0.940012i	$0.389186\pi$
$182$	−13.1120	−0.971929
$183$	−1.16989	−0.0864807
$184$	−15.1681	−1.11821
$185$	−0.0298638	−0.00219563
$186$	−8.60220	−0.630744
$187$	−0.0512980	−0.00375128
$188$	−15.3817	−1.12183
$189$	−3.88956	−0.282924
$190$	17.2004	1.24785
$191$	3.05219	0.220849	0.110424	−	0.993885i	$-0.464779\pi$
$191$	3.05219	0.220849	0.110424	+	0.993885i	$0.464779\pi$
$192$	12.9143	0.932010
$193$	22.1469	1.59417	0.797084	−	0.603868i	$-0.206375\pi$
$193$	22.1469	1.59417	0.797084	+	0.603868i	$0.206375\pi$
$194$	12.2161	0.877063
$195$	28.1229	2.01392
$196$	−3.94195	−0.281568
$197$	4.34848	0.309816	0.154908	−	0.987929i	$-0.450492\pi$
$197$	4.34848	0.309816	0.154908	+	0.987929i	$0.450492\pi$
$198$	−0.0954374	−0.00678244
$199$	3.04025	0.215518	0.107759	−	0.994177i	$-0.465633\pi$
$199$	3.04025	0.215518	0.107759	+	0.994177i	$0.465633\pi$
$200$	−1.80639	−0.127731
$201$	−9.06499	−0.639395
$202$	−5.06236	−0.356186
$203$	−7.84700	−0.550751
$204$	−5.12991	−0.359166
$205$	−15.0030	−1.04785
$206$	1.17303	0.0817291
$207$	18.5725	1.29088
$208$	−0.259530	−0.0179951
$209$	−0.256059	−0.0177120
$210$	−17.0223	−1.17465
$211$	−1.73801	−0.119650	−0.0598249	−	0.998209i	$-0.519054\pi$
$211$	−1.73801	−0.119650	−0.0598249	+	0.998209i	$0.519054\pi$
$212$	1.89519	0.130162
$213$	−17.1270	−1.17352
$214$	−5.98390	−0.409051
$215$	0	0
$216$	−3.45564	−0.235126
$217$	12.2630	0.832469
$218$	−0.533349	−0.0361229
$219$	15.5951	1.05382
$220$	0.0904582	0.00609869
$221$	7.66689	0.515731
$222$	−0.0282120	−0.00189347
$223$	5.09182	0.340974	0.170487	−	0.985360i	$-0.445466\pi$
$223$	5.09182	0.340974	0.170487	+	0.985360i	$0.445466\pi$
$224$	−18.0056	−1.20305
$225$	2.21182	0.147455
$226$	−9.46186	−0.629394
$227$	−6.80468	−0.451642	−0.225821	−	0.974169i	$-0.572506\pi$
$227$	−6.80468	−0.451642	−0.225821	+	0.974169i	$0.572506\pi$
$228$	−25.6065	−1.69583
$229$	−5.16810	−0.341518	−0.170759	−	0.985313i	$-0.554622\pi$
$229$	−5.16810	−0.341518	−0.170759	+	0.985313i	$0.554622\pi$
$230$	11.1707	0.736571
$231$	0.253407	0.0166730
$232$	−6.97158	−0.457707
$233$	7.24440	0.474597	0.237298	−	0.971437i	$-0.423738\pi$
$233$	7.24440	0.474597	0.237298	+	0.971437i	$0.423738\pi$
$234$	14.2639	0.932458
$235$	29.8444	1.94683
$236$	−2.66735	−0.173630
$237$	−33.7858	−2.19462
$238$	−4.64063	−0.300808
$239$	−11.0497	−0.714744	−0.357372	−	0.933962i	$-0.616327\pi$
$239$	−11.0497	−0.714744	−0.357372	+	0.933962i	$0.616327\pi$
$240$	−0.336926	−0.0217485
$241$	−21.1855	−1.36468	−0.682339	−	0.731036i	$-0.739037\pi$
$241$	−21.1855	−1.36468	−0.682339	+	0.731036i	$0.739037\pi$
$242$	−9.69186	−0.623016
$243$	−22.3252	−1.43216
$244$	0.562408	0.0360045
$245$	7.64834	0.488635
$246$	−14.1732	−0.903647
$247$	38.2701	2.43507
$248$	10.8950	0.691831
$249$	20.0939	1.27340
$250$	−9.12906	−0.577373
$251$	16.0845	1.01525	0.507624	−	0.861579i	$-0.330524\pi$
$251$	16.0845	1.01525	0.507624	+	0.861579i	$0.330524\pi$
$252$	13.6056	0.857070
$253$	−0.166295	−0.0104549
$254$	−6.83475	−0.428850
$255$	9.95329	0.623299
$256$	−16.1333	−1.00833
$257$	−27.6125	−1.72242	−0.861210	−	0.508248i	$-0.830293\pi$
$257$	−27.6125	−1.72242	−0.861210	+	0.508248i	$0.830293\pi$
$258$	0	0
$259$	0.0402182	0.00249904
$260$	−13.5197	−0.838455
$261$	8.53632	0.528385
$262$	−7.38073	−0.455983
$263$	−0.384415	−0.0237040	−0.0118520	−	0.999930i	$-0.503773\pi$
$263$	−0.384415	−0.0237040	−0.0118520	+	0.999930i	$0.503773\pi$
$264$	0.225137	0.0138562
$265$	−3.67714	−0.225885
$266$	−23.1642	−1.42029
$267$	−29.1456	−1.78368
$268$	4.35787	0.266199
$269$	−9.81404	−0.598373	−0.299186	−	0.954195i	$-0.596715\pi$
$269$	−9.81404	−0.598373	−0.299186	+	0.954195i	$0.596715\pi$
$270$	2.54493	0.154879
$271$	17.1023	1.03889	0.519445	−	0.854504i	$-0.326139\pi$
$271$	17.1023	1.03889	0.519445	+	0.854504i	$0.326139\pi$
$272$	−0.0918532	−0.00556942
$273$	−37.8737	−2.29222
$274$	4.13576	0.249850
$275$	−0.0198043	−0.00119424
$276$	−16.6299	−1.00100
$277$	5.53425	0.332521	0.166260	−	0.986082i	$-0.446831\pi$
$277$	5.53425	0.332521	0.166260	+	0.986082i	$0.446831\pi$
$278$	−3.49968	−0.209897
$279$	−13.3403	−0.798662
$280$	21.5593	1.28841
$281$	−16.2180	−0.967485	−0.483742	−	0.875210i	$-0.660723\pi$
$281$	−16.2180	−0.967485	−0.483742	+	0.875210i	$0.660723\pi$
$282$	28.1937	1.67891
$283$	14.9639	0.889509	0.444755	−	0.895652i	$-0.353291\pi$
$283$	14.9639	0.889509	0.444755	+	0.895652i	$0.353291\pi$
$284$	8.23354	0.488571
$285$	49.6829	2.94296
$286$	−0.127716	−0.00755202
$287$	20.2048	1.19265
$288$	19.5873	1.15419
$289$	−14.2865	−0.840384
$290$	5.13427	0.301495
$291$	35.2857	2.06849
$292$	−7.49710	−0.438735
$293$	−11.0016	−0.642718	−0.321359	−	0.946957i	$-0.604140\pi$
$293$	−11.0016	−0.642718	−0.321359	+	0.946957i	$0.604140\pi$
$294$	7.22532	0.421389
$295$	5.17531	0.301318
$296$	0.0357314	0.00207685
$297$	−0.0378858	−0.00219836
$298$	−10.5084	−0.608736
$299$	24.8541	1.43735
$300$	−1.98047	−0.114343
$301$	0	0
$302$	−10.4301	−0.600185
$303$	−14.6225	−0.840038
$304$	−0.458495	−0.0262965
$305$	−1.09121	−0.0624824
$306$	5.04829	0.288591
$307$	15.8937	0.907099	0.453549	−	0.891231i	$-0.350158\pi$
$307$	15.8937	0.907099	0.453549	+	0.891231i	$0.350158\pi$
$308$	−0.121822	−0.00694145
$309$	3.38827	0.192752
$310$	−8.02367	−0.455714
$311$	22.9477	1.30125	0.650624	−	0.759400i	$-0.274508\pi$
$311$	22.9477	1.30125	0.650624	+	0.759400i	$0.274508\pi$
$312$	−33.6485	−1.90497
$313$	−19.3184	−1.09194	−0.545970	−	0.837805i	$-0.683839\pi$
$313$	−19.3184	−1.09194	−0.545970	+	0.837805i	$0.683839\pi$
$314$	1.20881	0.0682171
$315$	−26.3981	−1.48737
$316$	16.2421	0.913687
$317$	6.78294	0.380968	0.190484	−	0.981690i	$-0.438994\pi$
$317$	6.78294	0.380968	0.190484	+	0.981690i	$0.438994\pi$
$318$	−3.47376	−0.194799
$319$	−0.0764328	−0.00427942
$320$	12.0458	0.673379
$321$	−17.2843	−0.964715
$322$	−15.0438	−0.838356
$323$	13.5446	0.753642
$324$	8.97797	0.498776
$325$	2.95990	0.164186
$326$	7.21229	0.399452
$327$	−1.54056	−0.0851932
$328$	17.9508	0.991165
$329$	−40.1921	−2.21586
$330$	−0.165804	−0.00912719
$331$	−31.9783	−1.75769	−0.878843	−	0.477111i	$-0.841684\pi$
$331$	−31.9783	−1.75769	−0.878843	+	0.477111i	$0.841684\pi$
$332$	−9.65987	−0.530154
$333$	−0.0437512	−0.00239755
$334$	21.9916	1.20333
$335$	−8.45534	−0.461964
$336$	0.453746	0.0247539
$337$	18.3736	1.00087	0.500436	−	0.865773i	$-0.333173\pi$
$337$	18.3736	1.00087	0.500436	+	0.865773i	$0.333173\pi$
$338$	7.63317	0.415190
$339$	−27.3303	−1.48438
$340$	−4.78491	−0.259498
$341$	0.119447	0.00646840
$342$	25.1991	1.36261
$343$	12.0798	0.652246
$344$	0	0
$345$	32.2661	1.73715
$346$	−20.4488	−1.09933
$347$	−8.96616	−0.481329	−0.240664	−	0.970608i	$-0.577365\pi$
$347$	−8.96616	−0.481329	−0.240664	+	0.970608i	$0.577365\pi$
$348$	−7.64345	−0.409732
$349$	31.3345	1.67730	0.838648	−	0.544673i	$-0.183346\pi$
$349$	31.3345	1.67730	0.838648	+	0.544673i	$0.183346\pi$
$350$	−1.79158	−0.0957639
$351$	5.66233	0.302233
$352$	−0.175382	−0.00934787
$353$	−29.2539	−1.55703	−0.778515	−	0.627626i	$-0.784027\pi$
$353$	−29.2539	−1.55703	−0.778515	+	0.627626i	$0.784027\pi$
$354$	4.88906	0.259851
$355$	−15.9751	−0.847870
$356$	14.0113	0.742599
$357$	−13.4043	−0.709432
$358$	5.75587	0.304207
$359$	22.3371	1.17890	0.589452	−	0.807803i	$-0.299344\pi$
$359$	22.3371	1.17890	0.589452	+	0.807803i	$0.299344\pi$
$360$	−23.4531	−1.23609
$361$	48.6093	2.55839
$362$	8.08831	0.425112
$363$	−27.9946	−1.46934
$364$	18.2072	0.954319
$365$	14.5462	0.761384
$366$	−1.03085	−0.0538836
$367$	31.7005	1.65475	0.827377	−	0.561647i	$-0.189832\pi$
$367$	31.7005	1.65475	0.827377	+	0.561647i	$0.189832\pi$
$368$	−0.297765	−0.0155221
$369$	−21.9797	−1.14422
$370$	−0.0263147	−0.00136803
$371$	4.95208	0.257099
$372$	11.9449	0.619316
$373$	−15.3681	−0.795730	−0.397865	−	0.917444i	$-0.630249\pi$
$373$	−15.3681	−0.795730	−0.397865	+	0.917444i	$0.630249\pi$
$374$	−0.0452016	−0.00233732
$375$	−26.3690	−1.36169
$376$	−35.7082	−1.84151
$377$	11.4235	0.588339
$378$	−3.42731	−0.176282
$379$	6.17992	0.317441	0.158721	−	0.987324i	$-0.449263\pi$
$379$	6.17992	0.317441	0.158721	+	0.987324i	$0.449263\pi$
$380$	−23.8844	−1.22524
$381$	−19.7420	−1.01141
$382$	2.68946	0.137605
$383$	−35.9554	−1.83724	−0.918618	−	0.395147i	$-0.870694\pi$
$383$	−35.9554	−1.83724	−0.918618	+	0.395147i	$0.870694\pi$
$384$	−17.2884	−0.882247
$385$	0.236365	0.0120463
$386$	19.5149	0.993281
$387$	0	0
$388$	−16.9631	−0.861172
$389$	13.4473	0.681804	0.340902	−	0.940099i	$-0.389268\pi$
$389$	13.4473	0.681804	0.340902	+	0.940099i	$0.389268\pi$
$390$	24.7806	1.25482
$391$	8.79642	0.444854
$392$	−9.15109	−0.462200
$393$	−21.3190	−1.07540
$394$	3.83169	0.193038
$395$	−31.5136	−1.58562
$396$	0.132523	0.00665955
$397$	−34.2601	−1.71946	−0.859732	−	0.510745i	$-0.829369\pi$
$397$	−34.2601	−1.71946	−0.859732	+	0.510745i	$0.829369\pi$
$398$	2.67893	0.134283
$399$	−66.9090	−3.34964
$400$	−0.0354611	−0.00177306
$401$	1.00955	0.0504147	0.0252073	−	0.999682i	$-0.491975\pi$
$401$	1.00955	0.0504147	0.0252073	+	0.999682i	$0.491975\pi$
$402$	−7.98767	−0.398389
$403$	−17.8522	−0.889284
$404$	7.02954	0.349733
$405$	−17.4195	−0.865580
$406$	−6.91443	−0.343157
$407$	0.000391741 0	1.94179e−5 0
$408$	−11.9089	−0.589579
$409$	−23.2075	−1.14754	−0.573768	−	0.819018i	$-0.694519\pi$
$409$	−23.2075	−1.14754	−0.573768	+	0.819018i	$0.694519\pi$
$410$	−13.2200	−0.652887
$411$	11.9460	0.589253
$412$	−1.62886	−0.0802483
$413$	−6.96970	−0.342957
$414$	16.3653	0.804310
$415$	18.7425	0.920034
$416$	26.2121	1.28516
$417$	−10.1087	−0.495025
$418$	−0.225628	−0.0110358
$419$	−27.5996	−1.34833	−0.674163	−	0.738582i	$-0.735496\pi$
$419$	−27.5996	−1.34833	−0.674163	+	0.738582i	$0.735496\pi$
$420$	23.6370	1.15337
$421$	12.3542	0.602105	0.301052	−	0.953608i	$-0.402662\pi$
$421$	12.3542	0.602105	0.301052	+	0.953608i	$0.402662\pi$
$422$	−1.53146	−0.0745503
$423$	43.7227	2.12587
$424$	4.39963	0.213665
$425$	1.04757	0.0508148
$426$	−15.0915	−0.731186
$427$	1.46955	0.0711167
$428$	8.30918	0.401639
$429$	−0.368904	−0.0178109
$430$	0	0
$431$	29.3267	1.41262	0.706308	−	0.707905i	$-0.250359\pi$
$431$	29.3267	1.41262	0.706308	+	0.707905i	$0.250359\pi$
$432$	−0.0678375	−0.00326383
$433$	21.6028	1.03816	0.519082	−	0.854724i	$-0.326274\pi$
$433$	21.6028	1.03816	0.519082	+	0.854724i	$0.326274\pi$
$434$	10.8056	0.518688
$435$	14.8302	0.711052
$436$	0.740603	0.0354684
$437$	43.9082	2.10042
$438$	13.7417	0.656602
$439$	9.24399	0.441192	0.220596	−	0.975365i	$-0.429200\pi$
$439$	9.24399	0.441192	0.220596	+	0.975365i	$0.429200\pi$
$440$	0.209996	0.0100111
$441$	11.2050	0.533572
$442$	6.75572	0.321337
$443$	18.5468	0.881186	0.440593	−	0.897707i	$-0.354768\pi$
$443$	18.5468	0.881186	0.440593	+	0.897707i	$0.354768\pi$
$444$	0.0391749	0.00185916
$445$	−27.1854	−1.28871
$446$	4.48669	0.212451
$447$	−30.3532	−1.43566
$448$	−16.2223	−0.766432
$449$	26.4034	1.24605	0.623026	−	0.782201i	$-0.285903\pi$
$449$	26.4034	1.24605	0.623026	+	0.782201i	$0.285903\pi$
$450$	1.94896	0.0918748
$451$	0.196803	0.00926708
$452$	13.1387	0.617990
$453$	−30.1270	−1.41549
$454$	−5.99598	−0.281405
$455$	−35.3265	−1.65613
$456$	−59.4446	−2.78375
$457$	−27.8056	−1.30069	−0.650345	−	0.759639i	$-0.725376\pi$
$457$	−27.8056	−1.30069	−0.650345	+	0.759639i	$0.725376\pi$
$458$	−4.55390	−0.212790
$459$	2.00402	0.0935397
$460$	−15.5115	−0.723226
$461$	29.2413	1.36190	0.680952	−	0.732328i	$-0.261566\pi$
$461$	29.2413	1.36190	0.680952	+	0.732328i	$0.261566\pi$
$462$	0.223291	0.0103884
$463$	−29.7540	−1.38278	−0.691392	−	0.722480i	$-0.743002\pi$
$463$	−29.7540	−1.38278	−0.691392	+	0.722480i	$0.743002\pi$
$464$	−0.136859	−0.00635352
$465$	−23.1761	−1.07477
$466$	6.38345	0.295707
$467$	−12.6219	−0.584074	−0.292037	−	0.956407i	$-0.594333\pi$
$467$	−12.6219	−0.584074	−0.292037	+	0.956407i	$0.594333\pi$
$468$	−19.8067	−0.915563
$469$	11.3870	0.525802
$470$	26.2975	1.21301
$471$	3.49161	0.160885
$472$	−6.19216	−0.285017
$473$	0	0
$474$	−29.7706	−1.36741
$475$	5.22907	0.239926
$476$	6.44394	0.295357
$477$	−5.38710	−0.246658
$478$	−9.73649	−0.445336
$479$	−18.1259	−0.828192	−0.414096	−	0.910233i	$-0.635902\pi$
$479$	−18.1259	−0.828192	−0.414096	+	0.910233i	$0.635902\pi$
$480$	34.0291	1.55321
$481$	−0.0585487	−0.00266959
$482$	−18.6677	−0.850292
$483$	−43.4534	−1.97720
$484$	13.4580	0.611728
$485$	32.9126	1.49449
$486$	−19.6720	−0.892339
$487$	−21.4200	−0.970631	−0.485316	−	0.874339i	$-0.661295\pi$
$487$	−21.4200	−0.970631	−0.485316	+	0.874339i	$0.661295\pi$
$488$	1.30561	0.0591022
$489$	20.8325	0.942076
$490$	6.73938	0.304454
$491$	27.2079	1.22787	0.613937	−	0.789355i	$-0.289585\pi$
$491$	27.2079	1.22787	0.613937	+	0.789355i	$0.289585\pi$
$492$	19.6807	0.887275
$493$	4.04302	0.182088
$494$	33.7219	1.51722
$495$	−0.257128	−0.0115570
$496$	0.213879	0.00960344
$497$	21.5140	0.965035
$498$	17.7059	0.793419
$499$	29.2625	1.30997	0.654984	−	0.755643i	$-0.272675\pi$
$499$	29.2625	1.30997	0.654984	+	0.755643i	$0.272675\pi$
$500$	12.6765	0.566911
$501$	63.5220	2.83795
$502$	14.1730	0.632572
$503$	19.3221	0.861532	0.430766	−	0.902464i	$-0.358243\pi$
$503$	19.3221	0.861532	0.430766	+	0.902464i	$0.358243\pi$
$504$	31.5848	1.40690
$505$	−13.6390	−0.606929
$506$	−0.146532	−0.00651415
$507$	22.0482	0.979193
$508$	9.49067	0.421080
$509$	26.5970	1.17889	0.589446	−	0.807808i	$-0.299346\pi$
$509$	26.5970	1.17889	0.589446	+	0.807808i	$0.299346\pi$
$510$	8.77040	0.388360
$511$	−19.5897	−0.866598
$512$	−0.630809	−0.0278781
$513$	10.0033	0.441655
$514$	−24.3309	−1.07319
$515$	3.16039	0.139264
$516$	0	0
$517$	−0.391486	−0.0172175
$518$	0.0354385	0.00155708
$519$	−59.0657	−2.59270
$520$	−31.3855	−1.37634
$521$	15.5264	0.680222	0.340111	−	0.940385i	$-0.389535\pi$
$521$	15.5264	0.680222	0.340111	+	0.940385i	$0.389535\pi$
$522$	7.52183	0.329221
$523$	−7.56216	−0.330670	−0.165335	−	0.986237i	$-0.552871\pi$
$523$	−7.56216	−0.330670	−0.165335	+	0.986237i	$0.552871\pi$
$524$	10.2488	0.447722
$525$	−5.17491	−0.225852
$526$	−0.338729	−0.0147693
$527$	−6.31830	−0.275229
$528$	0.00441966	0.000192341 0
$529$	5.51577	0.239816
$530$	−3.24013	−0.140742
$531$	7.58196	0.329029
$532$	32.1656	1.39456
$533$	−29.4137	−1.27405
$534$	−25.6818	−1.11136
$535$	−16.1218	−0.697008
$536$	10.1166	0.436972
$537$	16.6256	0.717449
$538$	−8.64770	−0.372829
$539$	−0.100328	−0.00432143
$540$	−3.53386	−0.152073
$541$	17.9180	0.770355	0.385177	−	0.922843i	$-0.374140\pi$
$541$	17.9180	0.770355	0.385177	+	0.922843i	$0.374140\pi$
$542$	15.0698	0.647302
$543$	23.3628	1.00259
$544$	9.27705	0.397750
$545$	−1.43695	−0.0615522
$546$	−33.3726	−1.42822
$547$	9.93606	0.424835	0.212418	−	0.977179i	$-0.431866\pi$
$547$	9.93606	0.424835	0.212418	+	0.977179i	$0.431866\pi$
$548$	−5.74288	−0.245324
$549$	−1.59865	−0.0682286
$550$	−0.0174507	−0.000744099 0
$551$	20.1811	0.859745
$552$	−38.6057	−1.64317
$553$	42.4400	1.80473
$554$	4.87653	0.207184
$555$	−0.0760090	−0.00322640
$556$	4.85962	0.206094
$557$	23.8611	1.01103	0.505513	−	0.862819i	$-0.331303\pi$
$557$	23.8611	1.01103	0.505513	+	0.862819i	$0.331303\pi$
$558$	−11.7549	−0.497623
$559$	0	0
$560$	0.423229	0.0178847
$561$	−0.130563	−0.00551238
$562$	−14.2906	−0.602812
$563$	−14.5530	−0.613335	−0.306667	−	0.951817i	$-0.599214\pi$
$563$	−14.5530	−0.613335	−0.306667	+	0.951817i	$0.599214\pi$
$564$	−39.1495	−1.64849
$565$	−25.4922	−1.07247
$566$	13.1855	0.554228
$567$	23.4592	0.985193
$568$	19.1139	0.802001
$569$	−36.0290	−1.51041	−0.755206	−	0.655487i	$-0.772463\pi$
$569$	−36.0290	−1.51041	−0.755206	+	0.655487i	$0.772463\pi$
$570$	43.7784	1.83367
$571$	−1.64992	−0.0690472	−0.0345236	−	0.999404i	$-0.510991\pi$
$571$	−1.64992	−0.0690472	−0.0345236	+	0.999404i	$0.510991\pi$
$572$	0.177346	0.00741519
$573$	7.76841	0.324530
$574$	17.8036	0.743108
$575$	3.39597	0.141622
$576$	17.6473	0.735306
$577$	−42.7566	−1.77998	−0.889989	−	0.455981i	$-0.849288\pi$
$577$	−42.7566	−1.77998	−0.889989	+	0.455981i	$0.849288\pi$
$578$	−12.5887	−0.523619
$579$	56.3681	2.34258
$580$	−7.12939	−0.296032
$581$	−25.2410	−1.04717
$582$	31.0922	1.28881
$583$	0.0482352	0.00199770
$584$	−17.4043	−0.720194
$585$	38.4298	1.58888
$586$	−9.69408	−0.400459
$587$	−37.7165	−1.55673	−0.778364	−	0.627813i	$-0.783950\pi$
$587$	−37.7165	−1.55673	−0.778364	+	0.627813i	$0.783950\pi$
$588$	−10.0330	−0.413754
$589$	−31.5384	−1.29952
$590$	4.56025	0.187743
$591$	11.0677	0.455264
$592$	0.000701443 0	2.88291e−5 0
$593$	−34.4750	−1.41572	−0.707859	−	0.706354i	$-0.750339\pi$
$593$	−34.4750	−1.41572	−0.707859	+	0.706354i	$0.750339\pi$
$594$	−0.0333833	−0.00136973
$595$	−12.5028	−0.512566
$596$	14.5919	0.597707
$597$	7.73801	0.316696
$598$	21.9004	0.895572
$599$	−15.8809	−0.648876	−0.324438	−	0.945907i	$-0.605175\pi$
$599$	−15.8809	−0.648876	−0.324438	+	0.945907i	$0.605175\pi$
$600$	−4.59760	−0.187696
$601$	−1.38033	−0.0563050	−0.0281525	−	0.999604i	$-0.508962\pi$
$601$	−1.38033	−0.0563050	−0.0281525	+	0.999604i	$0.508962\pi$
$602$	0	0
$603$	−12.3873	−0.504449
$604$	14.4831	0.589311
$605$	−26.1119	−1.06160
$606$	−12.8847	−0.523403
$607$	15.5498	0.631147	0.315574	−	0.948901i	$-0.397803\pi$
$607$	15.5498	0.631147	0.315574	+	0.948901i	$0.397803\pi$
$608$	46.3073	1.87801
$609$	−19.9721	−0.809310
$610$	−0.961525	−0.0389310
$611$	58.5106	2.36709
$612$	−7.01001	−0.283363
$613$	−24.6286	−0.994740	−0.497370	−	0.867538i	$-0.665701\pi$
$613$	−24.6286	−0.994740	−0.497370	+	0.867538i	$0.665701\pi$
$614$	14.0048	0.565187
$615$	−38.1854	−1.53978
$616$	−0.282806	−0.0113946
$617$	−25.6100	−1.03102	−0.515509	−	0.856884i	$-0.672397\pi$
$617$	−25.6100	−1.03102	−0.515509	+	0.856884i	$0.672397\pi$
$618$	2.98559	0.120098
$619$	−47.9538	−1.92743	−0.963714	−	0.266937i	$-0.913988\pi$
$619$	−47.9538	−1.92743	−0.963714	+	0.266937i	$0.913988\pi$
$620$	11.1416	0.447457
$621$	6.49653	0.260697
$622$	20.2205	0.810770
$623$	36.6112	1.46680
$624$	−0.660552	−0.0264432
$625$	−27.7753	−1.11101
$626$	−17.0225	−0.680357
$627$	−0.651720	−0.0260272
$628$	−1.67854	−0.0669812
$629$	−0.0207217	−0.000826227 0
$630$	−23.2609	−0.926735
$631$	−8.35246	−0.332506	−0.166253	−	0.986083i	$-0.553167\pi$
$631$	−8.35246	−0.332506	−0.166253	+	0.986083i	$0.553167\pi$
$632$	37.7054	1.49984
$633$	−4.42357	−0.175821
$634$	5.97682	0.237370
$635$	−18.4142	−0.730746
$636$	4.82363	0.191269
$637$	14.9948	0.594115
$638$	−0.0673492	−0.00266638
$639$	−23.4039	−0.925844
$640$	−16.1257	−0.637425
$641$	−15.8996	−0.627998	−0.313999	−	0.949423i	$-0.601669\pi$
$641$	−15.8996	−0.627998	−0.313999	+	0.949423i	$0.601669\pi$
$642$	−15.2301	−0.601086
$643$	17.6543	0.696217	0.348109	−	0.937454i	$-0.386824\pi$
$643$	17.6543	0.696217	0.348109	+	0.937454i	$0.386824\pi$
$644$	20.8896	0.823167
$645$	0	0
$646$	11.9349	0.469573
$647$	−35.8664	−1.41005	−0.705027	−	0.709180i	$-0.749065\pi$
$647$	−35.8664	−1.41005	−0.705027	+	0.709180i	$0.749065\pi$
$648$	20.8421	0.818753
$649$	−0.0678876	−0.00266482
$650$	2.60814	0.102300
$651$	31.2118	1.22329
$652$	−10.0149	−0.392214
$653$	21.8316	0.854337	0.427168	−	0.904172i	$-0.359511\pi$
$653$	21.8316	0.854337	0.427168	+	0.904172i	$0.359511\pi$
$654$	−1.35747	−0.0530814
$655$	−19.8852	−0.776980
$656$	0.352391	0.0137586
$657$	21.3106	0.831404
$658$	−35.4155	−1.38064
$659$	25.0241	0.974802	0.487401	−	0.873178i	$-0.337945\pi$
$659$	25.0241	0.974802	0.487401	+	0.873178i	$0.337945\pi$
$660$	0.230233	0.00896182
$661$	−32.8227	−1.27666	−0.638328	−	0.769765i	$-0.720374\pi$
$661$	−32.8227	−1.27666	−0.638328	+	0.769765i	$0.720374\pi$
$662$	−28.1779	−1.09516
$663$	19.5137	0.757849
$664$	−22.4251	−0.870261
$665$	−62.4091	−2.42012
$666$	−0.0385516	−0.00149384
$667$	13.1064	0.507483
$668$	−30.5373	−1.18152
$669$	12.9597	0.501049
$670$	−7.45047	−0.287837
$671$	0.0143140	0.000552587 0
$672$	−45.8277	−1.76784
$673$	−4.85764	−0.187248	−0.0936242	−	0.995608i	$-0.529845\pi$
$673$	−4.85764	−0.187248	−0.0936242	+	0.995608i	$0.529845\pi$
$674$	16.1900	0.623615
$675$	0.773679	0.0297789
$676$	−10.5993	−0.407667
$677$	23.9096	0.918922	0.459461	−	0.888198i	$-0.348043\pi$
$677$	23.9096	0.918922	0.459461	+	0.888198i	$0.348043\pi$
$678$	−24.0822	−0.924873
$679$	−44.3241	−1.70100
$680$	−11.1080	−0.425972
$681$	−17.3192	−0.663673
$682$	0.105251	0.00403028
$683$	19.4396	0.743835	0.371918	−	0.928266i	$-0.378700\pi$
$683$	19.4396	0.743835	0.371918	+	0.928266i	$0.378700\pi$
$684$	−34.9912	−1.33792
$685$	11.1426	0.425737
$686$	10.6442	0.406396
$687$	−13.1538	−0.501849
$688$	0	0
$689$	−7.20913	−0.274646
$690$	28.4314	1.08237
$691$	−12.0948	−0.460110	−0.230055	−	0.973178i	$-0.573891\pi$
$691$	−12.0948	−0.460110	−0.230055	+	0.973178i	$0.573891\pi$
$692$	28.3950	1.07942
$693$	0.346280	0.0131541
$694$	−7.90058	−0.299902
$695$	−9.42885	−0.357657
$696$	−17.7440	−0.672584
$697$	−10.4101	−0.394312
$698$	27.6106	1.04508
$699$	18.4384	0.697403
$700$	2.48777	0.0940288
$701$	35.2496	1.33136	0.665679	−	0.746238i	$-0.268142\pi$
$701$	35.2496	1.33136	0.665679	+	0.746238i	$0.268142\pi$
$702$	4.98939	0.188313
$703$	−0.103434	−0.00390110
$704$	−0.158011	−0.00595528
$705$	75.9596	2.86080
$706$	−25.7773	−0.970141
$707$	18.3680	0.690799
$708$	−6.78891	−0.255143
$709$	−33.7500	−1.26751	−0.633754	−	0.773534i	$-0.718487\pi$
$709$	−33.7500	−1.26751	−0.633754	+	0.773534i	$0.718487\pi$
$710$	−14.0765	−0.528283
$711$	−46.1681	−1.73144
$712$	32.5268	1.21899
$713$	−20.4823	−0.767069
$714$	−11.8113	−0.442026
$715$	−0.344094	−0.0128684
$716$	−7.99254	−0.298695
$717$	−28.1235	−1.05029
$718$	19.6824	0.734542
$719$	11.3488	0.423239	0.211619	−	0.977352i	$-0.432126\pi$
$719$	11.3488	0.423239	0.211619	+	0.977352i	$0.432126\pi$
$720$	−0.460408	−0.0171584
$721$	−4.25617	−0.158508
$722$	42.8324	1.59406
$723$	−53.9211	−2.00535
$724$	−11.2314	−0.417410
$725$	1.56086	0.0579689
$726$	−24.6676	−0.915501
$727$	39.2729	1.45655	0.728275	−	0.685285i	$-0.240322\pi$
$727$	39.2729	1.45655	0.728275	+	0.685285i	$0.240322\pi$
$728$	42.2675	1.56654
$729$	−34.8092	−1.28923
$730$	12.8175	0.474396
$731$	0	0
$732$	1.43143	0.0529073
$733$	26.1383	0.965439	0.482719	−	0.875775i	$-0.339649\pi$
$733$	26.1383	0.965439	0.482719	+	0.875775i	$0.339649\pi$
$734$	27.9331	1.03103
$735$	19.4665	0.718032
$736$	30.0739	1.10854
$737$	0.110914	0.00408556
$738$	−19.3676	−0.712929
$739$	−2.08218	−0.0765941	−0.0382970	−	0.999266i	$-0.512193\pi$
$739$	−2.08218	−0.0765941	−0.0382970	+	0.999266i	$0.512193\pi$
$740$	0.0365403	0.00134325
$741$	97.4046	3.57825
$742$	4.36356	0.160191
$743$	−1.98116	−0.0726815	−0.0363408	−	0.999339i	$-0.511570\pi$
$743$	−1.98116	−0.0726815	−0.0363408	+	0.999339i	$0.511570\pi$
$744$	27.7298	1.01662
$745$	−28.3118	−1.03726
$746$	−13.5417	−0.495797
$747$	27.4582	1.00464
$748$	0.0627664	0.00229497
$749$	21.7116	0.793326
$750$	−23.2352	−0.848429
$751$	−26.1809	−0.955353	−0.477677	−	0.878536i	$-0.658521\pi$
$751$	−26.1809	−0.955353	−0.477677	+	0.878536i	$0.658521\pi$
$752$	−0.700987	−0.0255624
$753$	40.9382	1.49187
$754$	10.0659	0.366577
$755$	−28.1008	−1.02269
$756$	4.75913	0.173088
$757$	−1.23817	−0.0450021	−0.0225010	−	0.999747i	$-0.507163\pi$
$757$	−1.23817	−0.0450021	−0.0225010	+	0.999747i	$0.507163\pi$
$758$	5.44548	0.197789
$759$	−0.423253	−0.0153631
$760$	−55.4467	−2.01126
$761$	−7.43765	−0.269615	−0.134807	−	0.990872i	$-0.543042\pi$
$761$	−7.43765	−0.269615	−0.134807	+	0.990872i	$0.543042\pi$
$762$	−17.3957	−0.630181
$763$	1.93517	0.0700580
$764$	−3.73455	−0.135111
$765$	13.6011	0.491750
$766$	−31.6823	−1.14473
$767$	10.1463	0.366363
$768$	−41.0624	−1.48171
$769$	10.5165	0.379236	0.189618	−	0.981858i	$-0.439275\pi$
$769$	10.5165	0.379236	0.189618	+	0.981858i	$0.439275\pi$
$770$	0.208274	0.00750567
$771$	−70.2791	−2.53104
$772$	−27.0982	−0.975284
$773$	−14.7186	−0.529393	−0.264696	−	0.964332i	$-0.585272\pi$
$773$	−14.7186	−0.529393	−0.264696	+	0.964332i	$0.585272\pi$
$774$	0	0
$775$	−2.43926	−0.0876209
$776$	−39.3793	−1.41363
$777$	0.102363	0.00367225
$778$	11.8491	0.424812
$779$	−51.9633	−1.86178
$780$	−34.4101	−1.23208
$781$	0.209555	0.00749846
$782$	7.75101	0.277176
$783$	2.98594	0.106709
$784$	−0.179645	−0.00641589
$785$	3.25678	0.116240
$786$	−18.7854	−0.670052
$787$	−19.5789	−0.697913	−0.348957	−	0.937139i	$-0.613464\pi$
$787$	−19.5789	−0.697913	−0.348957	+	0.937139i	$0.613464\pi$
$788$	−5.32064	−0.189540
$789$	−0.978408	−0.0348323
$790$	−27.7684	−0.987954
$791$	34.3309	1.22067
$792$	0.307649	0.0109318
$793$	−2.13934	−0.0759703
$794$	−30.1885	−1.07135
$795$	−9.35902	−0.331930
$796$	−3.71994	−0.131850
$797$	40.5281	1.43558	0.717790	−	0.696260i	$-0.245154\pi$
$797$	40.5281	1.43558	0.717790	+	0.696260i	$0.245154\pi$
$798$	−58.9573	−2.08707
$799$	20.7082	0.732603
$800$	3.58153	0.126626
$801$	−39.8273	−1.40723
$802$	0.889574	0.0314119
$803$	−0.190811	−0.00673359
$804$	11.0916	0.391171
$805$	−40.5310	−1.42853
$806$	−15.7306	−0.554087
$807$	−24.9786	−0.879288
$808$	16.3188	0.574095
$809$	52.5192	1.84648	0.923238	−	0.384228i	$-0.125532\pi$
$809$	52.5192	1.84648	0.923238	+	0.384228i	$0.125532\pi$
$810$	−15.3493	−0.539318
$811$	−55.9071	−1.96316	−0.981581	−	0.191046i	$-0.938812\pi$
$811$	−55.9071	−1.96316	−0.981581	+	0.191046i	$0.938812\pi$
$812$	9.60131	0.336940
$813$	43.5285	1.52661
$814$	0.000345185 0	1.20987e−5 0
$815$	19.4314	0.680652
$816$	−0.233784	−0.00818407
$817$	0	0
$818$	−20.4494	−0.714996
$819$	−51.7542	−1.80844
$820$	18.3571	0.641058
$821$	2.78931	0.0973477	0.0486739	−	0.998815i	$-0.484501\pi$
$821$	2.78931	0.0973477	0.0486739	+	0.998815i	$0.484501\pi$
$822$	10.5263	0.367147
$823$	−15.9643	−0.556479	−0.278239	−	0.960512i	$-0.589751\pi$
$823$	−15.9643	−0.556479	−0.278239	+	0.960512i	$0.589751\pi$
$824$	−3.78135	−0.131730
$825$	−0.0504056	−0.00175490
$826$	−6.14139	−0.213686
$827$	35.0876	1.22012	0.610059	−	0.792356i	$-0.291146\pi$
$827$	35.0876	1.22012	0.610059	+	0.792356i	$0.291146\pi$
$828$	−22.7247	−0.789737
$829$	32.6218	1.13300	0.566501	−	0.824061i	$-0.308297\pi$
$829$	32.6218	1.13300	0.566501	+	0.824061i	$0.308297\pi$
$830$	16.5151	0.573247
$831$	14.0857	0.488628
$832$	23.6160	0.818739
$833$	5.30698	0.183876
$834$	−8.90734	−0.308436
$835$	59.2498	2.05043
$836$	0.313305	0.0108359
$837$	−4.66633	−0.161292
$838$	−24.3195	−0.840104
$839$	−12.8623	−0.444054	−0.222027	−	0.975040i	$-0.571267\pi$
$839$	−12.8623	−0.444054	−0.222027	+	0.975040i	$0.571267\pi$
$840$	54.8724	1.89328
$841$	−22.9760	−0.792276
$842$	10.8859	0.375154
$843$	−41.2779	−1.42169
$844$	2.12657	0.0731996
$845$	20.5653	0.707469
$846$	38.5265	1.32457
$847$	35.1654	1.20830
$848$	0.0863689	0.00296592
$849$	38.0859	1.30710
$850$	0.923076	0.0316612
$851$	−0.0671744	−0.00230271
$852$	20.9559	0.717938
$853$	−16.0860	−0.550775	−0.275387	−	0.961333i	$-0.588806\pi$
$853$	−16.0860	−0.550775	−0.275387	+	0.961333i	$0.588806\pi$
$854$	1.29491	0.0443108
$855$	67.8915	2.32184
$856$	19.2895	0.659301
$857$	20.5395	0.701616	0.350808	−	0.936447i	$-0.385907\pi$
$857$	20.5395	0.701616	0.350808	+	0.936447i	$0.385907\pi$
$858$	−0.325062	−0.0110974
$859$	−7.65144	−0.261064	−0.130532	−	0.991444i	$-0.541668\pi$
$859$	−7.65144	−0.261064	−0.130532	+	0.991444i	$0.541668\pi$
$860$	0	0
$861$	51.4251	1.75256
$862$	25.8414	0.880161
$863$	28.1514	0.958286	0.479143	−	0.877737i	$-0.340948\pi$
$863$	28.1514	0.958286	0.479143	+	0.877737i	$0.340948\pi$
$864$	6.85150	0.233093
$865$	−55.0933	−1.87323
$866$	19.0354	0.646850
$867$	−36.3619	−1.23492
$868$	−15.0046	−0.509290
$869$	0.413382	0.0140230
$870$	13.0677	0.443036
$871$	−16.5769	−0.561687
$872$	1.71928	0.0582223
$873$	48.2178	1.63192
$874$	38.6900	1.30871
$875$	33.1234	1.11978
$876$	−19.0816	−0.644706
$877$	3.08064	0.104026	0.0520129	−	0.998646i	$-0.483436\pi$
$877$	3.08064	0.104026	0.0520129	+	0.998646i	$0.483436\pi$
$878$	8.14540	0.274894
$879$	−28.0010	−0.944452
$880$	0.00412242	0.000138967 0
$881$	−45.2539	−1.52464	−0.762322	−	0.647198i	$-0.775940\pi$
$881$	−45.2539	−1.52464	−0.762322	+	0.647198i	$0.775940\pi$
$882$	9.87336	0.332453
$883$	46.5578	1.56679	0.783397	−	0.621522i	$-0.213485\pi$
$883$	46.5578	1.56679	0.783397	+	0.621522i	$0.213485\pi$
$884$	−9.38093	−0.315515
$885$	13.1721	0.442777
$886$	16.3426	0.549042
$887$	9.52032	0.319661	0.159831	−	0.987144i	$-0.448905\pi$
$887$	9.52032	0.319661	0.159831	+	0.987144i	$0.448905\pi$
$888$	0.0909433	0.00305186
$889$	24.7988	0.831726
$890$	−23.9546	−0.802960
$891$	0.228501	0.00765509
$892$	−6.23017	−0.208602
$893$	103.367	3.45905
$894$	−26.7459	−0.894517
$895$	15.5075	0.518358
$896$	21.7169	0.725509
$897$	63.2585	2.11214
$898$	23.2655	0.776380
$899$	−9.41410	−0.313978
$900$	−2.70631	−0.0902102
$901$	−2.55147	−0.0850017
$902$	0.173414	0.00577405
$903$	0	0
$904$	30.5009	1.01445
$905$	21.7916	0.724376
$906$	−26.5466	−0.881951
$907$	46.5190	1.54464	0.772319	−	0.635234i	$-0.219096\pi$
$907$	46.5190	1.54464	0.772319	+	0.635234i	$0.219096\pi$
$908$	8.32596	0.276307
$909$	−19.9815	−0.662745
$910$	−31.1282	−1.03189
$911$	−54.5809	−1.80835	−0.904173	−	0.427167i	$-0.859512\pi$
$911$	−54.5809	−1.80835	−0.904173	+	0.427167i	$0.859512\pi$
$912$	−1.16696	−0.0386418
$913$	−0.245857	−0.00813667
$914$	−24.5011	−0.810423
$915$	−2.77733	−0.0918158
$916$	6.32351	0.208935
$917$	26.7799	0.884349
$918$	1.76585	0.0582819
$919$	6.85057	0.225979	0.112990	−	0.993596i	$-0.463957\pi$
$919$	6.85057	0.225979	0.112990	+	0.993596i	$0.463957\pi$
$920$	−36.0093	−1.18719
$921$	40.4524	1.33295
$922$	25.7662	0.848563
$923$	−31.3196	−1.03090
$924$	−0.310060	−0.0102002
$925$	−0.00799987	−0.000263034 0
$926$	−26.2179	−0.861573
$927$	4.63005	0.152071
$928$	13.8226	0.453748
$929$	10.7677	0.353277	0.176639	−	0.984276i	$-0.443478\pi$
$929$	10.7677	0.353277	0.176639	+	0.984276i	$0.443478\pi$
$930$	−20.4218	−0.669656
$931$	26.4903	0.868185
$932$	−8.86399	−0.290350
$933$	58.4064	1.91214
$934$	−11.1219	−0.363920
$935$	−0.121782	−0.00398271
$936$	−45.9805	−1.50292
$937$	6.00688	0.196236	0.0981182	−	0.995175i	$-0.468718\pi$
$937$	6.00688	0.196236	0.0981182	+	0.995175i	$0.468718\pi$
$938$	10.0337	0.327612
$939$	−49.1690	−1.60457
$940$	−36.5165	−1.19104
$941$	43.8055	1.42802	0.714009	−	0.700136i	$-0.246877\pi$
$941$	43.8055	1.42802	0.714009	+	0.700136i	$0.246877\pi$
$942$	3.07665	0.100243
$943$	−33.7471	−1.09896
$944$	−0.121558	−0.00395638
$945$	−9.23387	−0.300378
$946$	0	0
$947$	−45.1640	−1.46763	−0.733817	−	0.679347i	$-0.762263\pi$
$947$	−45.1640	−1.46763	−0.733817	+	0.679347i	$0.762263\pi$
$948$	41.3391	1.34263
$949$	28.5182	0.925741
$950$	4.60763	0.149491
$951$	17.2639	0.559819
$952$	14.9594	0.484836
$953$	−40.8065	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$953$	−40.8065	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$954$	−4.74687	−0.153686
$955$	7.24595	0.234473
$956$	13.5200	0.437268
$957$	−0.194536	−0.00628845
$958$	−15.9717	−0.516023
$959$	−15.0060	−0.484568
$960$	30.6588	0.989507
$961$	−16.2879	−0.525417
$962$	−0.0515906	−0.00166335
$963$	−23.6189	−0.761108
$964$	25.9218	0.834886
$965$	52.5771	1.69252
$966$	−38.2892	−1.23194
$967$	20.9943	0.675131	0.337565	−	0.941302i	$-0.390397\pi$
$967$	20.9943	0.675131	0.337565	+	0.941302i	$0.390397\pi$
$968$	31.2423	1.00417
$969$	34.4736	1.10745
$970$	29.0011	0.931171
$971$	26.4171	0.847764	0.423882	−	0.905717i	$-0.360667\pi$
$971$	26.4171	0.847764	0.423882	+	0.905717i	$0.360667\pi$
$972$	27.3163	0.876171
$973$	12.6980	0.407080
$974$	−18.8743	−0.604772
$975$	7.53352	0.241266
$976$	0.0256304	0.000820409 0
$977$	40.9261	1.30934	0.654671	−	0.755914i	$-0.272807\pi$
$977$	40.9261	1.30934	0.654671	+	0.755914i	$0.272807\pi$
$978$	18.3566	0.586981
$979$	0.356607	0.0113972
$980$	−9.35824	−0.298938
$981$	−2.10517	−0.0672128
$982$	23.9744	0.765053
$983$	41.1705	1.31313	0.656567	−	0.754267i	$-0.272008\pi$
$983$	41.1705	1.31313	0.656567	+	0.754267i	$0.272008\pi$
$984$	45.6881	1.45648
$985$	10.3234	0.328929
$986$	3.56253	0.113454
$987$	−102.296	−3.25613
$988$	−46.8259	−1.48973
$989$	0	0
$990$	−0.226570	−0.00720086
$991$	26.7708	0.850403	0.425202	−	0.905099i	$-0.360203\pi$
$991$	26.7708	0.850403	0.425202	+	0.905099i	$0.360203\pi$
$992$	−21.6015	−0.685847
$993$	−81.3908	−2.58286
$994$	18.9572	0.601286
$995$	7.21760	0.228813
$996$	−24.5862	−0.779043
$997$	18.4513	0.584359	0.292180	−	0.956363i	$-0.405619\pi$
$997$	18.4513	0.584359	0.292180	+	0.956363i	$0.405619\pi$
$998$	25.7848	0.816203
$999$	−0.0153038	−0.000484192 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.r.1.12	yes	20
43.42	odd	2		1849.2.a.p.1.9	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.p.1.9	✓	20	43.42	odd	2
1849.2.a.r.1.12	yes	20	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)

\(f(q)\)	\(=\)	\(q+0.881156 q^{2} +2.54519 q^{3} -1.22356 q^{4} +2.37402 q^{5} +2.24271 q^{6} -3.19714 q^{7} -2.84046 q^{8} +3.47799 q^{9} +O(q^{10})\)	\(q+0.881156 q^{2} +2.54519 q^{3} -1.22356 q^{4} +2.37402 q^{5} +2.24271 q^{6} -3.19714 q^{7} -2.84046 q^{8} +3.47799 q^{9} +2.09188 q^{10} -0.0311414 q^{11} -3.11420 q^{12} +4.65432 q^{13} -2.81718 q^{14} +6.04232 q^{15} -0.0557610 q^{16} +1.64726 q^{17} +3.06465 q^{18} +8.22249 q^{19} -2.90476 q^{20} -8.13732 q^{21} -0.0274404 q^{22} +5.34002 q^{23} -7.22952 q^{24} +0.635948 q^{25} +4.10118 q^{26} +1.21658 q^{27} +3.91190 q^{28} +2.45438 q^{29} +5.32422 q^{30} -3.83563 q^{31} +5.63179 q^{32} -0.0792607 q^{33} +1.45150 q^{34} -7.59005 q^{35} -4.25555 q^{36} -0.0125794 q^{37} +7.24529 q^{38} +11.8461 q^{39} -6.74330 q^{40} -6.31966 q^{41} -7.17025 q^{42} +0.0381035 q^{44} +8.25680 q^{45} +4.70539 q^{46} +12.5713 q^{47} -0.141922 q^{48} +3.22169 q^{49} +0.560369 q^{50} +4.19260 q^{51} -5.69486 q^{52} -1.54891 q^{53} +1.07199 q^{54} -0.0739300 q^{55} +9.08135 q^{56} +20.9278 q^{57} +2.16269 q^{58} +2.17998 q^{59} -7.39317 q^{60} -0.459647 q^{61} -3.37979 q^{62} -11.1196 q^{63} +5.07401 q^{64} +11.0494 q^{65} -0.0698410 q^{66} -3.56162 q^{67} -2.01553 q^{68} +13.5914 q^{69} -6.68802 q^{70} -6.72915 q^{71} -9.87910 q^{72} +6.12727 q^{73} -0.0110844 q^{74} +1.61861 q^{75} -10.0607 q^{76} +0.0995632 q^{77} +10.4383 q^{78} -13.2744 q^{79} -0.132378 q^{80} -7.33756 q^{81} -5.56860 q^{82} +7.89486 q^{83} +9.95654 q^{84} +3.91063 q^{85} +6.24687 q^{87} +0.0884559 q^{88} -11.4512 q^{89} +7.27553 q^{90} -14.8805 q^{91} -6.53385 q^{92} -9.76241 q^{93} +11.0772 q^{94} +19.5203 q^{95} +14.3340 q^{96} +13.8637 q^{97} +2.83881 q^{98} -0.108309 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{2} - q^{3} + 23 q^{4} - 3 q^{5} + 5 q^{6} - 2 q^{7} + 9 q^{8} + 27 q^{9}+O(q^{10}) \) 20 * q + 5 * q^2 - q^3 + 23 * q^4 - 3 * q^5 + 5 * q^6 - 2 * q^7 + 9 * q^8 + 27 * q^9	\( 20 q + 5 q^{2} - q^{3} + 23 q^{4} - 3 q^{5} + 5 q^{6} - 2 q^{7} + 9 q^{8} + 27 q^{9} + 21 q^{11} - 12 q^{12} + 11 q^{13} + 8 q^{14} + 4 q^{15} + 29 q^{16} + 15 q^{17} + 9 q^{18} - 7 q^{19} - 17 q^{20} + 8 q^{21} + 47 q^{22} + 26 q^{23} - q^{24} + 11 q^{25} + 58 q^{26} - 22 q^{27} - 28 q^{28} - 12 q^{29} - 24 q^{30} + 26 q^{31} + 3 q^{32} - 17 q^{33} + 54 q^{34} + 26 q^{35} + 14 q^{36} - 19 q^{37} + 5 q^{38} - 7 q^{39} - 16 q^{40} + 27 q^{41} - 52 q^{42} + 32 q^{44} + 75 q^{45} + 59 q^{46} + 45 q^{47} - 66 q^{48} + 20 q^{49} + 75 q^{51} + 11 q^{52} + 3 q^{53} + 57 q^{54} - 2 q^{55} + 87 q^{56} - 24 q^{57} - 46 q^{58} + 66 q^{59} + 29 q^{60} + 30 q^{61} + 72 q^{62} - 21 q^{63} - 7 q^{64} - 6 q^{65} + 41 q^{66} - 6 q^{67} + 28 q^{68} - 35 q^{69} - 80 q^{70} - 31 q^{71} - 15 q^{72} - 26 q^{73} + 87 q^{74} + 73 q^{75} - 68 q^{76} - 21 q^{77} - 50 q^{78} + 39 q^{79} - 60 q^{80} + 16 q^{81} + 45 q^{82} + 13 q^{83} + 31 q^{84} - 22 q^{85} + 61 q^{87} + 50 q^{88} - 4 q^{89} - 13 q^{90} - 25 q^{91} + 5 q^{92} + 67 q^{93} + 42 q^{94} + 79 q^{95} + 36 q^{96} - 2 q^{97} - 35 q^{98} + 13 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 + 23 * q^4 - 3 * q^5 + 5 * q^6 - 2 * q^7 + 9 * q^8 + 27 * q^9 + 21 * q^11 - 12 * q^12 + 11 * q^13 + 8 * q^14 + 4 * q^15 + 29 * q^16 + 15 * q^17 + 9 * q^18 - 7 * q^19 - 17 * q^20 + 8 * q^21 + 47 * q^22 + 26 * q^23 - q^24 + 11 * q^25 + 58 * q^26 - 22 * q^27 - 28 * q^28 - 12 * q^29 - 24 * q^30 + 26 * q^31 + 3 * q^32 - 17 * q^33 + 54 * q^34 + 26 * q^35 + 14 * q^36 - 19 * q^37 + 5 * q^38 - 7 * q^39 - 16 * q^40 + 27 * q^41 - 52 * q^42 + 32 * q^44 + 75 * q^45 + 59 * q^46 + 45 * q^47 - 66 * q^48 + 20 * q^49 + 75 * q^51 + 11 * q^52 + 3 * q^53 + 57 * q^54 - 2 * q^55 + 87 * q^56 - 24 * q^57 - 46 * q^58 + 66 * q^59 + 29 * q^60 + 30 * q^61 + 72 * q^62 - 21 * q^63 - 7 * q^64 - 6 * q^65 + 41 * q^66 - 6 * q^67 + 28 * q^68 - 35 * q^69 - 80 * q^70 - 31 * q^71 - 15 * q^72 - 26 * q^73 + 87 * q^74 + 73 * q^75 - 68 * q^76 - 21 * q^77 - 50 * q^78 + 39 * q^79 - 60 * q^80 + 16 * q^81 + 45 * q^82 + 13 * q^83 + 31 * q^84 - 22 * q^85 + 61 * q^87 + 50 * q^88 - 4 * q^89 - 13 * q^90 - 25 * q^91 + 5 * q^92 + 67 * q^93 + 42 * q^94 + 79 * q^95 + 36 * q^96 - 2 * q^97 - 35 * q^98 + 13 * q^99

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