LMFDB - Embedded newform 1849.2.a.r.1.1

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			1.1
Root			$-2.64020$ 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)

$f(q)$	$=$	$q-2.64020 q^{2} -0.354022 q^{3} +4.97064 q^{4} -1.23228 q^{5} +0.934688 q^{6} -3.87263 q^{7} -7.84307 q^{8} -2.87467 q^{9} +O(q^{10})$	\(q-2.64020 q^{2} -0.354022 q^{3} +4.97064 q^{4} -1.23228 q^{5} +0.934688 q^{6} -3.87263 q^{7} -7.84307 q^{8} -2.87467 q^{9} +3.25345 q^{10} +2.01275 q^{11} -1.75972 q^{12} -3.33076 q^{13} +10.2245 q^{14} +0.436253 q^{15} +10.7660 q^{16} -1.76500 q^{17} +7.58969 q^{18} -2.88182 q^{19} -6.12520 q^{20} +1.37100 q^{21} -5.31406 q^{22} -7.07373 q^{23} +2.77662 q^{24} -3.48149 q^{25} +8.79387 q^{26} +2.07976 q^{27} -19.2494 q^{28} +1.16122 q^{29} -1.15179 q^{30} -7.21474 q^{31} -12.7381 q^{32} -0.712558 q^{33} +4.65996 q^{34} +4.77215 q^{35} -14.2889 q^{36} +0.396953 q^{37} +7.60858 q^{38} +1.17916 q^{39} +9.66483 q^{40} -1.94531 q^{41} -3.61970 q^{42} +10.0047 q^{44} +3.54239 q^{45} +18.6760 q^{46} -2.91101 q^{47} -3.81139 q^{48} +7.99728 q^{49} +9.19183 q^{50} +0.624850 q^{51} -16.5560 q^{52} +5.58304 q^{53} -5.49098 q^{54} -2.48027 q^{55} +30.3733 q^{56} +1.02023 q^{57} -3.06585 q^{58} +6.47805 q^{59} +2.16846 q^{60} -12.6104 q^{61} +19.0483 q^{62} +11.1325 q^{63} +12.0992 q^{64} +4.10442 q^{65} +1.88129 q^{66} -5.78439 q^{67} -8.77320 q^{68} +2.50426 q^{69} -12.5994 q^{70} +3.37541 q^{71} +22.5462 q^{72} -2.47282 q^{73} -1.04803 q^{74} +1.23253 q^{75} -14.3245 q^{76} -7.79464 q^{77} -3.11322 q^{78} +8.62549 q^{79} -13.2666 q^{80} +7.88772 q^{81} +5.13600 q^{82} +3.06803 q^{83} +6.81473 q^{84} +2.17497 q^{85} -0.411098 q^{87} -15.7861 q^{88} -14.6882 q^{89} -9.35260 q^{90} +12.8988 q^{91} -35.1609 q^{92} +2.55418 q^{93} +7.68564 q^{94} +3.55120 q^{95} +4.50958 q^{96} -18.2946 q^{97} -21.1144 q^{98} -5.78599 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.64020	−1.86690	−0.933450	−	0.358706i	$-0.883218\pi$
$2$	−2.64020	−1.86690	−0.933450	+	0.358706i	$0.883218\pi$
$3$	−0.354022	−0.204395	−0.102197	−	0.994764i	$-0.532587\pi$
$3$	−0.354022	−0.204395	−0.102197	+	0.994764i	$0.532587\pi$
$4$	4.97064	2.48532
$5$	−1.23228	−0.551091	−0.275545	−	0.961288i	$-0.588858\pi$
$5$	−1.23228	−0.551091	−0.275545	+	0.961288i	$0.588858\pi$
$6$	0.934688	0.381585
$7$	−3.87263	−1.46372	−0.731859	−	0.681457i	$-0.761347\pi$
$7$	−3.87263	−1.46372	−0.731859	+	0.681457i	$0.761347\pi$
$8$	−7.84307	−2.77294
$9$	−2.87467	−0.958223
$10$	3.25345	1.02883
$11$	2.01275	0.606867	0.303434	−	0.952853i	$-0.401867\pi$
$11$	2.01275	0.606867	0.303434	+	0.952853i	$0.401867\pi$
$12$	−1.75972	−0.507986
$13$	−3.33076	−0.923787	−0.461894	−	0.886935i	$-0.652830\pi$
$13$	−3.33076	−0.923787	−0.461894	+	0.886935i	$0.652830\pi$
$14$	10.2245	2.73261
$15$	0.436253	0.112640
$16$	10.7660	2.69149
$17$	−1.76500	−0.428076	−0.214038	−	0.976825i	$-0.568662\pi$
$17$	−1.76500	−0.428076	−0.214038	+	0.976825i	$0.568662\pi$
$18$	7.58969	1.78891
$19$	−2.88182	−0.661135	−0.330568	−	0.943782i	$-0.607240\pi$
$19$	−2.88182	−0.661135	−0.330568	+	0.943782i	$0.607240\pi$
$20$	−6.12520	−1.36964
$21$	1.37100	0.299176
$22$	−5.31406	−1.13296
$23$	−7.07373	−1.47497	−0.737487	−	0.675361i	$-0.763988\pi$
$23$	−7.07373	−1.47497	−0.737487	+	0.675361i	$0.763988\pi$
$24$	2.77662	0.566775
$25$	−3.48149	−0.696299
$26$	8.79387	1.72462
$27$	2.07976	0.400251
$28$	−19.2494	−3.63780
$29$	1.16122	0.215633	0.107817	−	0.994171i	$-0.465614\pi$
$29$	1.16122	0.215633	0.107817	+	0.994171i	$0.465614\pi$
$30$	−1.15179	−0.210288
$31$	−7.21474	−1.29581	−0.647903	−	0.761723i	$-0.724354\pi$
$31$	−7.21474	−1.29581	−0.647903	+	0.761723i	$0.724354\pi$
$32$	−12.7381	−2.25180
$33$	−0.712558	−0.124040
$34$	4.65996	0.799176
$35$	4.77215	0.806641
$36$	−14.2889	−2.38149
$37$	0.396953	0.0652587	0.0326293	−	0.999468i	$-0.489612\pi$
$37$	0.396953	0.0652587	0.0326293	+	0.999468i	$0.489612\pi$
$38$	7.60858	1.23427
$39$	1.17916	0.188817
$40$	9.66483	1.52814
$41$	−1.94531	−0.303807	−0.151903	−	0.988395i	$-0.548540\pi$
$41$	−1.94531	−0.303807	−0.151903	+	0.988395i	$0.548540\pi$
$42$	−3.61970	−0.558532
$43$	0	0
$43$	0	0
$44$	10.0047	1.50826
$45$	3.54239	0.528068
$46$	18.6760	2.75363
$47$	−2.91101	−0.424614	−0.212307	−	0.977203i	$-0.568098\pi$
$47$	−2.91101	−0.424614	−0.212307	+	0.977203i	$0.568098\pi$
$48$	−3.81139	−0.550127
$49$	7.99728	1.14247
$50$	9.19183	1.29992
$51$	0.624850	0.0874966
$52$	−16.5560	−2.29591
$53$	5.58304	0.766889	0.383445	−	0.923564i	$-0.374738\pi$
$53$	5.58304	0.766889	0.383445	+	0.923564i	$0.374738\pi$
$54$	−5.49098	−0.747228
$55$	−2.48027	−0.334439
$56$	30.3733	4.05880
$57$	1.02023	0.135133
$58$	−3.06585	−0.402566
$59$	6.47805	0.843371	0.421685	−	0.906742i	$-0.361439\pi$
$59$	6.47805	0.843371	0.421685	+	0.906742i	$0.361439\pi$
$60$	2.16846	0.279947
$61$	−12.6104	−1.61459	−0.807295	−	0.590147i	$-0.799070\pi$
$61$	−12.6104	−1.61459	−0.807295	+	0.590147i	$0.799070\pi$
$62$	19.0483	2.41914
$63$	11.1325	1.40257
$64$	12.0992	1.51240
$65$	4.10442	0.509091
$66$	1.88129	0.231571
$67$	−5.78439	−0.706675	−0.353338	−	0.935496i	$-0.614953\pi$
$67$	−5.78439	−0.706675	−0.353338	+	0.935496i	$0.614953\pi$
$68$	−8.77320	−1.06391
$69$	2.50426	0.301477
$70$	−12.5994	−1.50592
$71$	3.37541	0.400588	0.200294	−	0.979736i	$-0.435810\pi$
$71$	3.37541	0.400588	0.200294	+	0.979736i	$0.435810\pi$
$72$	22.5462	2.65710
$73$	−2.47282	−0.289422	−0.144711	−	0.989474i	$-0.546225\pi$
$73$	−2.47282	−0.289422	−0.144711	+	0.989474i	$0.546225\pi$
$74$	−1.04803	−0.121832
$75$	1.23253	0.142320
$76$	−14.3245	−1.64313
$77$	−7.79464	−0.888282
$78$	−3.11322	−0.352503
$79$	8.62549	0.970443	0.485222	−	0.874391i	$-0.338739\pi$
$79$	8.62549	0.970443	0.485222	+	0.874391i	$0.338739\pi$
$80$	−13.2666	−1.48326
$81$	7.88772	0.876414
$82$	5.13600	0.567177
$83$	3.06803	0.336760	0.168380	−	0.985722i	$-0.446146\pi$
$83$	3.06803	0.336760	0.168380	+	0.985722i	$0.446146\pi$
$84$	6.81473	0.743548
$85$	2.17497	0.235909
$86$	0	0
$87$	−0.411098	−0.0440743
$88$	−15.7861	−1.68281
$89$	−14.6882	−1.55695	−0.778473	−	0.627678i	$-0.784006\pi$
$89$	−14.6882	−1.55695	−0.778473	+	0.627678i	$0.784006\pi$
$90$	−9.35260	−0.985850
$91$	12.8988	1.35216
$92$	−35.1609	−3.66578
$93$	2.55418	0.264856
$94$	7.68564	0.792713
$95$	3.55120	0.364346
$96$	4.50958	0.460257
$97$	−18.2946	−1.85753	−0.928767	−	0.370665i	$-0.879130\pi$
$97$	−18.2946	−1.85753	−0.928767	+	0.370665i	$0.879130\pi$
$98$	−21.1144	−2.13287
$99$	−5.78599	−0.581514
$100$	−17.3052	−1.73052
$101$	17.5215	1.74345	0.871727	−	0.489991i	$-0.163000\pi$
$101$	17.5215	1.74345	0.871727	+	0.489991i	$0.163000\pi$
$102$	−1.64973	−0.163347
$103$	−10.2855	−1.01346	−0.506732	−	0.862103i	$-0.669147\pi$
$103$	−10.2855	−1.01346	−0.506732	+	0.862103i	$0.669147\pi$
$104$	26.1234	2.56161
$105$	−1.68945	−0.164873
$106$	−14.7403	−1.43171
$107$	−11.9961	−1.15971	−0.579853	−	0.814721i	$-0.696890\pi$
$107$	−11.9961	−1.15971	−0.579853	+	0.814721i	$0.696890\pi$
$108$	10.3377	0.994750
$109$	0.989870	0.0948124	0.0474062	−	0.998876i	$-0.484904\pi$
$109$	0.989870	0.0948124	0.0474062	+	0.998876i	$0.484904\pi$
$110$	6.54839	0.624364
$111$	−0.140530	−0.0133385
$112$	−41.6926	−3.93958
$113$	−10.5953	−0.996721	−0.498360	−	0.866970i	$-0.666064\pi$
$113$	−10.5953	−0.996721	−0.498360	+	0.866970i	$0.666064\pi$
$114$	−2.69360	−0.252279
$115$	8.71679	0.812845
$116$	5.77201	0.535918
$117$	9.57484	0.885194
$118$	−17.1033	−1.57449
$119$	6.83521	0.626583
$120$	−3.42156	−0.312345
$121$	−6.94883	−0.631712
$122$	33.2938	3.01428
$123$	0.688683	0.0620965
$124$	−35.8619	−3.22049
$125$	10.4515	0.934815
$126$	−29.3921	−2.61845
$127$	7.69558	0.682872	0.341436	−	0.939905i	$-0.389087\pi$
$127$	7.69558	0.682872	0.341436	+	0.939905i	$0.389087\pi$
$128$	−6.46810	−0.571705
$129$	0	0
$130$	−10.8365	−0.950422
$131$	10.2319	0.893967	0.446984	−	0.894542i	$-0.352498\pi$
$131$	10.2319	0.893967	0.446984	+	0.894542i	$0.352498\pi$
$132$	−3.54187	−0.308280
$133$	11.1602	0.967715
$134$	15.2719	1.31929
$135$	−2.56284	−0.220574
$136$	13.8430	1.18703
$137$	4.67121	0.399089	0.199544	−	0.979889i	$-0.436054\pi$
$137$	4.67121	0.399089	0.199544	+	0.979889i	$0.436054\pi$
$138$	−6.61173	−0.562828
$139$	11.6953	0.991984	0.495992	−	0.868327i	$-0.334805\pi$
$139$	11.6953	0.991984	0.495992	+	0.868327i	$0.334805\pi$
$140$	23.7206	2.00476
$141$	1.03056	0.0867889
$142$	−8.91176	−0.747858
$143$	−6.70400	−0.560616
$144$	−30.9486	−2.57905
$145$	−1.43095	−0.118834
$146$	6.52874	0.540322
$147$	−2.83121	−0.233514
$148$	1.97311	0.162189
$149$	9.86933	0.808527	0.404263	−	0.914643i	$-0.367528\pi$
$149$	9.86933	0.808527	0.404263	+	0.914643i	$0.367528\pi$
$150$	−3.25411	−0.265697
$151$	−11.4912	−0.935143	−0.467572	−	0.883955i	$-0.654871\pi$
$151$	−11.4912	−0.935143	−0.467572	+	0.883955i	$0.654871\pi$
$152$	22.6023	1.83329
$153$	5.07380	0.410193
$154$	20.5794	1.65833
$155$	8.89056	0.714107
$156$	5.86120	0.469271
$157$	6.87153	0.548407	0.274204	−	0.961672i	$-0.411586\pi$
$157$	6.87153	0.548407	0.274204	+	0.961672i	$0.411586\pi$
$158$	−22.7730	−1.81172
$159$	−1.97652	−0.156748
$160$	15.6969	1.24095
$161$	27.3939	2.15895
$162$	−20.8251	−1.63618
$163$	−20.1403	−1.57751	−0.788756	−	0.614706i	$-0.789275\pi$
$163$	−20.1403	−1.57751	−0.788756	+	0.614706i	$0.789275\pi$
$164$	−9.66944	−0.755056
$165$	0.878069	0.0683576
$166$	−8.10021	−0.628698
$167$	9.27297	0.717564	0.358782	−	0.933421i	$-0.383192\pi$
$167$	9.27297	0.717564	0.358782	+	0.933421i	$0.383192\pi$
$168$	−10.7528	−0.829598
$169$	−1.90602	−0.146617
$170$	−5.74236	−0.440419
$171$	8.28428	0.633515
$172$	0	0
$173$	23.3849	1.77792	0.888962	−	0.457980i	$-0.151427\pi$
$173$	23.3849	1.77792	0.888962	+	0.457980i	$0.151427\pi$
$174$	1.08538	0.0822824
$175$	13.4825	1.01918
$176$	21.6692	1.63338
$177$	−2.29337	−0.172381
$178$	38.7797	2.90666
$179$	−14.1785	−1.05975	−0.529874	−	0.848076i	$-0.677761\pi$
$179$	−14.1785	−1.05975	−0.529874	+	0.848076i	$0.677761\pi$
$180$	17.6079	1.31242
$181$	17.0329	1.26604	0.633021	−	0.774134i	$-0.281815\pi$
$181$	17.0329	1.26604	0.633021	+	0.774134i	$0.281815\pi$
$182$	−34.0554	−2.52436
$183$	4.46435	0.330014
$184$	55.4797	4.09002
$185$	−0.489156	−0.0359635
$186$	−6.74353	−0.494460
$187$	−3.55251	−0.259785
$188$	−14.4696	−1.05530
$189$	−8.05415	−0.585854
$190$	−9.37587	−0.680197
$191$	−7.88382	−0.570453	−0.285227	−	0.958460i	$-0.592069\pi$
$191$	−7.88382	−0.570453	−0.285227	+	0.958460i	$0.592069\pi$
$192$	−4.28340	−0.309128
$193$	−0.566215	−0.0407570	−0.0203785	−	0.999792i	$-0.506487\pi$
$193$	−0.566215	−0.0407570	−0.0203785	+	0.999792i	$0.506487\pi$
$194$	48.3013	3.46783
$195$	−1.45306	−0.104056
$196$	39.7516	2.83940
$197$	−14.8974	−1.06140	−0.530699	−	0.847560i	$-0.678071\pi$
$197$	−14.8974	−1.06140	−0.530699	+	0.847560i	$0.678071\pi$
$198$	15.2762	1.08563
$199$	16.1063	1.14175	0.570873	−	0.821038i	$-0.306605\pi$
$199$	16.1063	1.14175	0.570873	+	0.821038i	$0.306605\pi$
$200$	27.3056	1.93080
$201$	2.04780	0.144441
$202$	−46.2602	−3.25486
$203$	−4.49698	−0.315626
$204$	3.10591	0.217457
$205$	2.39716	0.167425
$206$	27.1559	1.89204
$207$	20.3346	1.41335
$208$	−35.8589	−2.48637
$209$	−5.80039	−0.401221
$210$	4.46047	0.307802
$211$	−9.60083	−0.660948	−0.330474	−	0.943815i	$-0.607209\pi$
$211$	−9.60083	−0.660948	−0.330474	+	0.943815i	$0.607209\pi$
$212$	27.7513	1.90596
$213$	−1.19497	−0.0818781
$214$	31.6720	2.16506
$215$	0	0
$216$	−16.3117	−1.10987
$217$	27.9400	1.89669
$218$	−2.61345	−0.177005
$219$	0.875434	0.0591564
$220$	−12.3285	−0.831188
$221$	5.87881	0.395452
$222$	0.371027	0.0249017
$223$	17.0660	1.14283	0.571413	−	0.820663i	$-0.306395\pi$
$223$	17.0660	1.14283	0.571413	+	0.820663i	$0.306395\pi$
$224$	49.3301	3.29601
$225$	10.0081	0.667209
$226$	27.9736	1.86078
$227$	17.5322	1.16365	0.581825	−	0.813314i	$-0.302339\pi$
$227$	17.5322	1.16365	0.581825	+	0.813314i	$0.302339\pi$
$228$	5.07119	0.335848
$229$	28.8052	1.90350	0.951752	−	0.306869i	$-0.0992815\pi$
$229$	28.8052	1.90350	0.951752	+	0.306869i	$0.0992815\pi$
$230$	−23.0140	−1.51750
$231$	2.75948	0.181560
$232$	−9.10754	−0.597939
$233$	9.06399	0.593802	0.296901	−	0.954908i	$-0.404047\pi$
$233$	9.06399	0.593802	0.296901	+	0.954908i	$0.404047\pi$
$234$	−25.2795	−1.65257
$235$	3.58717	0.234001
$236$	32.2001	2.09605
$237$	−3.05361	−0.198353
$238$	−18.0463	−1.16977
$239$	−13.7684	−0.890601	−0.445300	−	0.895381i	$-0.646903\pi$
$239$	−13.7684	−0.890601	−0.445300	+	0.895381i	$0.646903\pi$
$240$	4.69669	0.303170
$241$	1.82258	0.117403	0.0587014	−	0.998276i	$-0.481304\pi$
$241$	1.82258	0.117403	0.0587014	+	0.998276i	$0.481304\pi$
$242$	18.3463	1.17934
$243$	−9.03172	−0.579385
$244$	−62.6815	−4.01277
$245$	−9.85486	−0.629604
$246$	−1.81826	−0.115928
$247$	9.59867	0.610749
$248$	56.5857	3.59320
$249$	−1.08615	−0.0688321
$250$	−27.5941	−1.74521
$251$	11.4746	0.724272	0.362136	−	0.932125i	$-0.382048\pi$
$251$	11.4746	0.724272	0.362136	+	0.932125i	$0.382048\pi$
$252$	55.3358	3.48583
$253$	−14.2377	−0.895114
$254$	−20.3178	−1.27485
$255$	−0.769989	−0.0482186
$256$	−7.12141	−0.445088
$257$	−26.9482	−1.68098	−0.840491	−	0.541826i	$-0.817733\pi$
$257$	−26.9482	−1.68098	−0.840491	+	0.541826i	$0.817733\pi$
$258$	0	0
$259$	−1.53725	−0.0955203
$260$	20.4016	1.26525
$261$	−3.33813	−0.206625
$262$	−27.0143	−1.66895
$263$	19.4419	1.19884	0.599420	−	0.800435i	$-0.295398\pi$
$263$	19.4419	1.19884	0.599420	+	0.800435i	$0.295398\pi$
$264$	5.58864	0.343957
$265$	−6.87985	−0.422626
$266$	−29.4652	−1.80663
$267$	5.19995	0.318232
$268$	−28.7521	−1.75631
$269$	5.33971	0.325568	0.162784	−	0.986662i	$-0.447953\pi$
$269$	5.33971	0.325568	0.162784	+	0.986662i	$0.447953\pi$
$270$	6.76641	0.411791
$271$	−25.8968	−1.57312	−0.786561	−	0.617513i	$-0.788140\pi$
$271$	−25.8968	−1.57312	−0.786561	+	0.617513i	$0.788140\pi$
$272$	−19.0020	−1.15216
$273$	−4.56647	−0.276375
$274$	−12.3329	−0.745059
$275$	−7.00738	−0.422561
$276$	12.4478	0.749267
$277$	10.9528	0.658091	0.329046	−	0.944314i	$-0.393273\pi$
$277$	10.9528	0.658091	0.329046	+	0.944314i	$0.393273\pi$
$278$	−30.8779	−1.85194
$279$	20.7400	1.24167
$280$	−37.4283	−2.23677
$281$	−18.8817	−1.12639	−0.563193	−	0.826325i	$-0.690427\pi$
$281$	−18.8817	−1.12639	−0.563193	+	0.826325i	$0.690427\pi$
$282$	−2.72088	−0.162026
$283$	−6.41809	−0.381516	−0.190758	−	0.981637i	$-0.561095\pi$
$283$	−6.41809	−0.381516	−0.190758	+	0.981637i	$0.561095\pi$
$284$	16.7780	0.995589
$285$	−1.25720	−0.0744703
$286$	17.6999	1.04662
$287$	7.53347	0.444687
$288$	36.6179	2.15773
$289$	−13.8848	−0.816751
$290$	3.77798	0.221850
$291$	6.47669	0.379670
$292$	−12.2915	−0.719306
$293$	5.29449	0.309307	0.154654	−	0.987969i	$-0.450574\pi$
$293$	5.29449	0.309307	0.154654	+	0.987969i	$0.450574\pi$
$294$	7.47496	0.435948
$295$	−7.98276	−0.464774
$296$	−3.11333	−0.180959
$297$	4.18604	0.242899
$298$	−26.0570	−1.50944
$299$	23.5609	1.36256
$300$	6.12644	0.353710
$301$	0	0
$302$	30.3391	1.74582
$303$	−6.20300	−0.356353
$304$	−31.0256	−1.77944
$305$	15.5394	0.889786
$306$	−13.3958	−0.765789
$307$	1.32505	0.0756246	0.0378123	−	0.999285i	$-0.487961\pi$
$307$	1.32505	0.0756246	0.0378123	+	0.999285i	$0.487961\pi$
$308$	−38.7443	−2.20766
$309$	3.64131	0.207147
$310$	−23.4728	−1.33317
$311$	22.8600	1.29627	0.648136	−	0.761525i	$-0.275549\pi$
$311$	22.8600	1.29627	0.648136	+	0.761525i	$0.275549\pi$
$312$	−9.24826	−0.523580
$313$	−8.35596	−0.472307	−0.236153	−	0.971716i	$-0.575887\pi$
$313$	−8.35596	−0.472307	−0.236153	+	0.971716i	$0.575887\pi$
$314$	−18.1422	−1.02382
$315$	−13.7184	−0.772942
$316$	42.8742	2.41186
$317$	−2.72735	−0.153183	−0.0765916	−	0.997063i	$-0.524404\pi$
$317$	−2.72735	−0.153183	−0.0765916	+	0.997063i	$0.524404\pi$
$318$	5.21840	0.292633
$319$	2.33725	0.130861
$320$	−14.9096	−0.833472
$321$	4.24688	0.237038
$322$	−72.3254	−4.03054
$323$	5.08643	0.283016
$324$	39.2070	2.17817
$325$	11.5960	0.643232
$326$	53.1744	2.94506
$327$	−0.350436	−0.0193792
$328$	15.2572	0.842439
$329$	11.2733	0.621515
$330$	−2.31827	−0.127617
$331$	29.4946	1.62117	0.810585	−	0.585620i	$-0.199149\pi$
$331$	29.4946	1.62117	0.810585	+	0.585620i	$0.199149\pi$
$332$	15.2501	0.836957
$333$	−1.14111	−0.0625324
$334$	−24.4825	−1.33962
$335$	7.12796	0.389442
$336$	14.7601	0.805230
$337$	−18.9379	−1.03162	−0.515808	−	0.856704i	$-0.672508\pi$
$337$	−18.9379	−1.03162	−0.515808	+	0.856704i	$0.672508\pi$
$338$	5.03226	0.273719
$339$	3.75097	0.203725
$340$	10.8110	0.586309
$341$	−14.5215	−0.786382
$342$	−21.8721	−1.18271
$343$	−3.86208	−0.208533
$344$	0	0
$345$	−3.08594	−0.166141
$346$	−61.7409	−3.31921
$347$	−2.17271	−0.116637	−0.0583187	−	0.998298i	$-0.518574\pi$
$347$	−2.17271	−0.116637	−0.0583187	+	0.998298i	$0.518574\pi$
$348$	−2.04342	−0.109539
$349$	0.653626	0.0349878	0.0174939	−	0.999847i	$-0.494431\pi$
$349$	0.653626	0.0349878	0.0174939	+	0.999847i	$0.494431\pi$
$350$	−35.5966	−1.90272
$351$	−6.92720	−0.369746
$352$	−25.6387	−1.36655
$353$	−7.33995	−0.390666	−0.195333	−	0.980737i	$-0.562579\pi$
$353$	−7.33995	−0.390666	−0.195333	+	0.980737i	$0.562579\pi$
$354$	6.05496	0.321818
$355$	−4.15944	−0.220760
$356$	−73.0097	−3.86951
$357$	−2.41982	−0.128070
$358$	37.4340	1.97845
$359$	9.30210	0.490946	0.245473	−	0.969403i	$-0.421057\pi$
$359$	9.30210	0.490946	0.245473	+	0.969403i	$0.421057\pi$
$360$	−27.7832	−1.46430
$361$	−10.6951	−0.562900
$362$	−44.9701	−2.36358
$363$	2.46004	0.129119
$364$	64.1154	3.36056
$365$	3.04720	0.159498
$366$	−11.7868	−0.616103
$367$	8.35151	0.435945	0.217973	−	0.975955i	$-0.430056\pi$
$367$	8.35151	0.435945	0.217973	+	0.975955i	$0.430056\pi$
$368$	−76.1555	−3.96988
$369$	5.59213	0.291114
$370$	1.29147	0.0671402
$371$	−21.6210	−1.12251
$372$	12.6959	0.658252
$373$	36.4568	1.88766	0.943831	−	0.330430i	$-0.107194\pi$
$373$	36.4568	1.88766	0.943831	+	0.330430i	$0.107194\pi$
$374$	9.37933	0.484994
$375$	−3.70008	−0.191071
$376$	22.8312	1.17743
$377$	−3.86775	−0.199199
$378$	21.2646	1.09373
$379$	−7.42192	−0.381239	−0.190619	−	0.981664i	$-0.561050\pi$
$379$	−7.42192	−0.381239	−0.190619	+	0.981664i	$0.561050\pi$
$380$	17.6517	0.905515
$381$	−2.72440	−0.139575
$382$	20.8148	1.06498
$383$	−1.29783	−0.0663159	−0.0331580	−	0.999450i	$-0.510556\pi$
$383$	−1.29783	−0.0663159	−0.0331580	+	0.999450i	$0.510556\pi$
$384$	2.28985	0.116853
$385$	9.60516	0.489524
$386$	1.49492	0.0760894
$387$	0	0
$388$	−90.9357	−4.61656
$389$	−9.92974	−0.503458	−0.251729	−	0.967798i	$-0.580999\pi$
$389$	−9.92974	−0.503458	−0.251729	+	0.967798i	$0.580999\pi$
$390$	3.83635	0.194261
$391$	12.4852	0.631402
$392$	−62.7232	−3.16800
$393$	−3.62233	−0.182722
$394$	39.3322	1.98153
$395$	−10.6290	−0.534802
$396$	−28.7601	−1.44525
$397$	−15.2455	−0.765151	−0.382576	−	0.923924i	$-0.624963\pi$
$397$	−15.2455	−0.765151	−0.382576	+	0.923924i	$0.624963\pi$
$398$	−42.5238	−2.13153
$399$	−3.95097	−0.197796
$400$	−37.4817	−1.87408
$401$	−16.9609	−0.846989	−0.423495	−	0.905899i	$-0.639197\pi$
$401$	−16.9609	−0.846989	−0.423495	+	0.905899i	$0.639197\pi$
$402$	−5.40660	−0.269657
$403$	24.0306	1.19705
$404$	87.0930	4.33304
$405$	−9.71986	−0.482984
$406$	11.8729	0.589243
$407$	0.798968	0.0396034
$408$	−4.90075	−0.242623
$409$	−4.36360	−0.215766	−0.107883	−	0.994164i	$-0.534407\pi$
$409$	−4.36360	−0.215766	−0.107883	+	0.994164i	$0.534407\pi$
$410$	−6.32898	−0.312566
$411$	−1.65371	−0.0815717
$412$	−51.1257	−2.51878
$413$	−25.0871	−1.23446
$414$	−53.6874	−2.63859
$415$	−3.78067	−0.185586
$416$	42.4277	2.08019
$417$	−4.14040	−0.202756
$418$	15.3142	0.749041
$419$	−18.9773	−0.927102	−0.463551	−	0.886070i	$-0.653425\pi$
$419$	−18.9773	−0.927102	−0.463551	+	0.886070i	$0.653425\pi$
$420$	−8.39763	−0.409763
$421$	−9.92401	−0.483667	−0.241833	−	0.970318i	$-0.577749\pi$
$421$	−9.92401	−0.483667	−0.241833	+	0.970318i	$0.577749\pi$
$422$	25.3481	1.23393
$423$	8.36818	0.406875
$424$	−43.7881	−2.12654
$425$	6.14485	0.298069
$426$	3.15496	0.152858
$427$	48.8353	2.36330
$428$	−59.6282	−2.88224
$429$	2.37336	0.114587
$430$	0	0
$431$	−16.2572	−0.783080	−0.391540	−	0.920161i	$-0.628058\pi$
$431$	−16.2572	−0.783080	−0.391540	+	0.920161i	$0.628058\pi$
$432$	22.3907	1.07727
$433$	−18.1960	−0.874443	−0.437221	−	0.899354i	$-0.644037\pi$
$433$	−18.1960	−0.874443	−0.437221	+	0.899354i	$0.644037\pi$
$434$	−73.7672	−3.54094
$435$	0.506586	0.0242890
$436$	4.92029	0.235639
$437$	20.3852	0.975158
$438$	−2.31132	−0.110439
$439$	11.8004	0.563203	0.281602	−	0.959531i	$-0.409134\pi$
$439$	11.8004	0.563203	0.281602	+	0.959531i	$0.409134\pi$
$440$	19.4529	0.927380
$441$	−22.9895	−1.09474
$442$	−15.5212	−0.738269
$443$	40.1372	1.90697	0.953487	−	0.301435i	$-0.0974656\pi$
$443$	40.1372	1.90697	0.953487	+	0.301435i	$0.0974656\pi$
$444$	−0.698525	−0.0331505
$445$	18.0999	0.858019
$446$	−45.0577	−2.13354
$447$	−3.49396	−0.165259
$448$	−46.8559	−2.21373
$449$	−14.1271	−0.666697	−0.333349	−	0.942804i	$-0.608179\pi$
$449$	−14.1271	−0.666697	−0.333349	+	0.942804i	$0.608179\pi$
$450$	−26.4235	−1.24561
$451$	−3.91543	−0.184370
$452$	−52.6653	−2.47717
$453$	4.06815	0.191138
$454$	−46.2883	−2.17242
$455$	−15.8949	−0.745165
$456$	−8.00172	−0.374715
$457$	20.9251	0.978834	0.489417	−	0.872050i	$-0.337210\pi$
$457$	20.9251	0.978834	0.489417	+	0.872050i	$0.337210\pi$
$458$	−76.0515	−3.55365
$459$	−3.67079	−0.171338
$460$	43.3280	2.02018
$461$	−13.9343	−0.648984	−0.324492	−	0.945889i	$-0.605193\pi$
$461$	−13.9343	−0.648984	−0.324492	+	0.945889i	$0.605193\pi$
$462$	−7.28556	−0.338955
$463$	−30.3421	−1.41012	−0.705060	−	0.709148i	$-0.749080\pi$
$463$	−30.3421	−1.41012	−0.705060	+	0.709148i	$0.749080\pi$
$464$	12.5017	0.580375
$465$	−3.14745	−0.145960
$466$	−23.9307	−1.10857
$467$	27.8085	1.28682	0.643412	−	0.765520i	$-0.277518\pi$
$467$	27.8085	1.28682	0.643412	+	0.765520i	$0.277518\pi$
$468$	47.5931	2.19999
$469$	22.4008	1.03437
$470$	−9.47083	−0.436857
$471$	−2.43267	−0.112092
$472$	−50.8078	−2.33862
$473$	0	0
$474$	8.06214	0.370306
$475$	10.0330	0.460348
$476$	33.9754	1.55726
$477$	−16.0494	−0.734851
$478$	36.3512	1.66266
$479$	−2.32175	−0.106084	−0.0530418	−	0.998592i	$-0.516892\pi$
$479$	−2.32175	−0.106084	−0.0530418	+	0.998592i	$0.516892\pi$
$480$	−5.55705	−0.253643
$481$	−1.32216	−0.0602852
$482$	−4.81198	−0.219179
$483$	−9.69806	−0.441277
$484$	−34.5401	−1.57001
$485$	22.5440	1.02367
$486$	23.8455	1.08165
$487$	−22.8313	−1.03458	−0.517292	−	0.855809i	$-0.673060\pi$
$487$	−22.8313	−1.03458	−0.517292	+	0.855809i	$0.673060\pi$
$488$	98.9039	4.47717
$489$	7.13012	0.322435
$490$	26.0188	1.17541
$491$	−31.3422	−1.41446	−0.707228	−	0.706986i	$-0.750055\pi$
$491$	−31.3422	−1.41446	−0.707228	+	0.706986i	$0.750055\pi$
$492$	3.42320	0.154330
$493$	−2.04956	−0.0923075
$494$	−25.3424	−1.14021
$495$	7.12994	0.320467
$496$	−77.6737	−3.48765
$497$	−13.0717	−0.586348
$498$	2.86765	0.128503
$499$	−5.24166	−0.234649	−0.117324	−	0.993094i	$-0.537432\pi$
$499$	−5.24166	−0.234649	−0.117324	+	0.993094i	$0.537432\pi$
$500$	51.9509	2.32331
$501$	−3.28284	−0.146666
$502$	−30.2953	−1.35214
$503$	12.7431	0.568185	0.284092	−	0.958797i	$-0.408308\pi$
$503$	12.7431	0.568185	0.284092	+	0.958797i	$0.408308\pi$
$504$	−87.3132	−3.88924
$505$	−21.5913	−0.960802
$506$	37.5902	1.67109
$507$	0.674772	0.0299677
$508$	38.2519	1.69715
$509$	−27.0581	−1.19933	−0.599664	−	0.800252i	$-0.704699\pi$
$509$	−27.0581	−1.19933	−0.599664	+	0.800252i	$0.704699\pi$
$510$	2.03292	0.0900193
$511$	9.57634	0.423632
$512$	31.7381	1.40264
$513$	−5.99351	−0.264620
$514$	71.1485	3.13823
$515$	12.6746	0.558511
$516$	0	0
$517$	−5.85914	−0.257684
$518$	4.05865	0.178327
$519$	−8.27879	−0.363399
$520$	−32.1913	−1.41168
$521$	−33.9186	−1.48600	−0.743001	−	0.669290i	$-0.766598\pi$
$521$	−33.9186	−1.48600	−0.743001	+	0.669290i	$0.766598\pi$
$522$	8.81331	0.385748
$523$	7.29596	0.319030	0.159515	−	0.987196i	$-0.449007\pi$
$523$	7.29596	0.319030	0.159515	+	0.987196i	$0.449007\pi$
$524$	50.8592	2.22179
$525$	−4.77312	−0.208316
$526$	−51.3305	−2.23811
$527$	12.7340	0.554704
$528$	−7.67138	−0.333854
$529$	27.0376	1.17555
$530$	18.1641	0.789000
$531$	−18.6223	−0.808137
$532$	55.4735	2.40508
$533$	6.47937	0.280653
$534$	−13.7289	−0.594107
$535$	14.7825	0.639104
$536$	45.3673	1.95957
$537$	5.01949	0.216607
$538$	−14.0979	−0.607803
$539$	16.0965	0.693326
$540$	−12.7390	−0.548198
$541$	−4.37476	−0.188086	−0.0940429	−	0.995568i	$-0.529979\pi$
$541$	−4.37476	−0.188086	−0.0940429	+	0.995568i	$0.529979\pi$
$542$	68.3728	2.93686
$543$	−6.03001	−0.258772
$544$	22.4829	0.963944
$545$	−1.21979	−0.0522502
$546$	12.0564	0.515965
$547$	30.0494	1.28482	0.642409	−	0.766362i	$-0.277935\pi$
$547$	30.0494	1.28482	0.642409	+	0.766362i	$0.277935\pi$
$548$	23.2189	0.991863
$549$	36.2506	1.54714
$550$	18.5009	0.788879
$551$	−3.34643	−0.142563
$552$	−19.6411	−0.835979
$553$	−33.4033	−1.42045
$554$	−28.9176	−1.22859
$555$	0.173172	0.00735074
$556$	58.1332	2.46540
$557$	−41.4828	−1.75768	−0.878841	−	0.477115i	$-0.841683\pi$
$557$	−41.4828	−1.75768	−0.878841	+	0.477115i	$0.841683\pi$
$558$	−54.7576	−2.31808
$559$	0	0
$560$	51.3768	2.17107
$561$	1.25767	0.0530988
$562$	49.8513	2.10285
$563$	10.9508	0.461520	0.230760	−	0.973011i	$-0.425879\pi$
$563$	10.9508	0.461520	0.230760	+	0.973011i	$0.425879\pi$
$564$	5.12255	0.215698
$565$	13.0563	0.549284
$566$	16.9450	0.712252
$567$	−30.5462	−1.28282
$568$	−26.4736	−1.11081
$569$	23.0491	0.966267	0.483133	−	0.875547i	$-0.339499\pi$
$569$	23.0491	0.966267	0.483133	+	0.875547i	$0.339499\pi$
$570$	3.31927	0.139029
$571$	−24.6585	−1.03193	−0.515963	−	0.856611i	$-0.672566\pi$
$571$	−24.6585	−1.03193	−0.515963	+	0.856611i	$0.672566\pi$
$572$	−33.3231	−1.39331
$573$	2.79105	0.116598
$574$	−19.8899	−0.830186
$575$	24.6271	1.02702
$576$	−34.7813	−1.44922
$577$	34.5271	1.43738	0.718692	−	0.695329i	$-0.244741\pi$
$577$	34.5271	1.43738	0.718692	+	0.695329i	$0.244741\pi$
$578$	36.6585	1.52479
$579$	0.200453	0.00833053
$580$	−7.11271	−0.295339
$581$	−11.8814	−0.492922
$582$	−17.0997	−0.708806
$583$	11.2373	0.465400
$584$	19.3945	0.802551
$585$	−11.7989	−0.487822
$586$	−13.9785	−0.577446
$587$	15.8934	0.655991	0.327995	−	0.944679i	$-0.393627\pi$
$587$	15.8934	0.655991	0.327995	+	0.944679i	$0.393627\pi$
$588$	−14.0729	−0.580358
$589$	20.7916	0.856703
$590$	21.0760	0.867687
$591$	5.27402	0.216944
$592$	4.27358	0.175643
$593$	−30.4491	−1.25039	−0.625197	−	0.780467i	$-0.714981\pi$
$593$	−30.4491	−1.25039	−0.625197	+	0.780467i	$0.714981\pi$
$594$	−11.0520	−0.453468
$595$	−8.42287	−0.345304
$596$	49.0569	2.00945
$597$	−5.70199	−0.233367
$598$	−62.2055	−2.54377
$599$	3.07992	0.125842	0.0629211	−	0.998019i	$-0.479958\pi$
$599$	3.07992	0.125842	0.0629211	+	0.998019i	$0.479958\pi$
$600$	−9.66679	−0.394645
$601$	−0.873893	−0.0356468	−0.0178234	−	0.999841i	$-0.505674\pi$
$601$	−0.873893	−0.0356468	−0.0178234	+	0.999841i	$0.505674\pi$
$602$	0	0
$603$	16.6282	0.677152
$604$	−57.1187	−2.32413
$605$	8.56289	0.348131
$606$	16.3771	0.665276
$607$	−38.7768	−1.57390	−0.786952	−	0.617014i	$-0.788342\pi$
$607$	−38.7768	−1.57390	−0.786952	+	0.617014i	$0.788342\pi$
$608$	36.7090	1.48875
$609$	1.59203	0.0645124
$610$	−41.0272	−1.66114
$611$	9.69588	0.392253
$612$	25.2200	1.01946
$613$	41.1253	1.66103	0.830517	−	0.556993i	$-0.188045\pi$
$613$	41.1253	1.66103	0.830517	+	0.556993i	$0.188045\pi$
$614$	−3.49839	−0.141184
$615$	−0.848648	−0.0342208
$616$	61.1339	2.46316
$617$	−16.3836	−0.659578	−0.329789	−	0.944055i	$-0.606978\pi$
$617$	−16.3836	−0.659578	−0.329789	+	0.944055i	$0.606978\pi$
$618$	−9.61377	−0.386723
$619$	12.3790	0.497553	0.248776	−	0.968561i	$-0.419972\pi$
$619$	12.3790	0.497553	0.248776	+	0.968561i	$0.419972\pi$
$620$	44.1917	1.77478
$621$	−14.7117	−0.590359
$622$	−60.3549	−2.42001
$623$	56.8820	2.27893
$624$	12.6948	0.508200
$625$	4.52827	0.181131
$626$	22.0614	0.881750
$627$	2.05347	0.0820076
$628$	34.1559	1.36297
$629$	−0.700624	−0.0279357
$630$	36.2192	1.44301
$631$	−25.8426	−1.02878	−0.514389	−	0.857557i	$-0.671981\pi$
$631$	−25.8426	−1.02878	−0.514389	+	0.857557i	$0.671981\pi$
$632$	−67.6503	−2.69098
$633$	3.39891	0.135094
$634$	7.20074	0.285978
$635$	−9.48308	−0.376324
$636$	−9.82456	−0.389569
$637$	−26.6370	−1.05540
$638$	−6.17080	−0.244304
$639$	−9.70320	−0.383853
$640$	7.97049	0.315061
$641$	−33.3990	−1.31918	−0.659590	−	0.751625i	$-0.729270\pi$
$641$	−33.3990	−1.31918	−0.659590	+	0.751625i	$0.729270\pi$
$642$	−11.2126	−0.442526
$643$	17.2011	0.678346	0.339173	−	0.940724i	$-0.389853\pi$
$643$	17.2011	0.678346	0.339173	+	0.940724i	$0.389853\pi$
$644$	136.165	5.36567
$645$	0	0
$646$	−13.4292	−0.528364
$647$	−19.6984	−0.774424	−0.387212	−	0.921991i	$-0.626562\pi$
$647$	−19.6984	−0.774424	−0.387212	+	0.921991i	$0.626562\pi$
$648$	−61.8640	−2.43025
$649$	13.0387	0.511814
$650$	−30.6158	−1.20085
$651$	−9.89139	−0.387674
$652$	−100.110	−3.92062
$653$	−29.4327	−1.15179	−0.575895	−	0.817524i	$-0.695346\pi$
$653$	−29.4327	−1.15179	−0.575895	+	0.817524i	$0.695346\pi$
$654$	0.925220	0.0361790
$655$	−12.6086	−0.492657
$656$	−20.9432	−0.817693
$657$	7.10855	0.277331
$658$	−29.7636	−1.16031
$659$	25.2342	0.982983	0.491492	−	0.870882i	$-0.336452\pi$
$659$	25.2342	0.982983	0.491492	+	0.870882i	$0.336452\pi$
$660$	4.36456	0.169890
$661$	−33.5839	−1.30626	−0.653131	−	0.757245i	$-0.726545\pi$
$661$	−33.5839	−1.30626	−0.653131	+	0.757245i	$0.726545\pi$
$662$	−77.8716	−3.02657
$663$	−2.08123	−0.0808282
$664$	−24.0628	−0.933818
$665$	−13.7525	−0.533299
$666$	3.01275	0.116742
$667$	−8.21416	−0.318054
$668$	46.0926	1.78338
$669$	−6.04175	−0.233588
$670$	−18.8192	−0.727050
$671$	−25.3815	−0.979842
$672$	−17.4639	−0.673686
$673$	−10.8275	−0.417371	−0.208685	−	0.977983i	$-0.566918\pi$
$673$	−10.8275	−0.417371	−0.208685	+	0.977983i	$0.566918\pi$
$674$	49.9999	1.92592
$675$	−7.24068	−0.278694
$676$	−9.47412	−0.364389
$677$	−33.6851	−1.29462	−0.647311	−	0.762226i	$-0.724106\pi$
$677$	−33.6851	−1.29462	−0.647311	+	0.762226i	$0.724106\pi$
$678$	−9.90329	−0.380333
$679$	70.8482	2.71890
$680$	−17.0585	−0.654162
$681$	−6.20677	−0.237844
$682$	38.3396	1.46810
$683$	−16.3061	−0.623935	−0.311967	−	0.950093i	$-0.600988\pi$
$683$	−16.3061	−0.623935	−0.311967	+	0.950093i	$0.600988\pi$
$684$	41.1782	1.57449
$685$	−5.75623	−0.219934
$686$	10.1966	0.389310
$687$	−10.1977	−0.389066
$688$	0	0
$689$	−18.5958	−0.708443
$690$	8.14748	0.310169
$691$	−12.6997	−0.483120	−0.241560	−	0.970386i	$-0.577659\pi$
$691$	−12.6997	−0.483120	−0.241560	+	0.970386i	$0.577659\pi$
$692$	116.238	4.41871
$693$	22.4070	0.851172
$694$	5.73639	0.217750
$695$	−14.4119	−0.546673
$696$	3.22427	0.122216
$697$	3.43348	0.130052
$698$	−1.72570	−0.0653188
$699$	−3.20885	−0.121370
$700$	67.0168	2.53300
$701$	−15.5441	−0.587094	−0.293547	−	0.955945i	$-0.594836\pi$
$701$	−15.5441	−0.587094	−0.293547	+	0.955945i	$0.594836\pi$
$702$	18.2892	0.690280
$703$	−1.14395	−0.0431448
$704$	24.3527	0.917829
$705$	−1.26994	−0.0478286
$706$	19.3789	0.729335
$707$	−67.8543	−2.55192
$708$	−11.3995	−0.428421
$709$	6.94298	0.260749	0.130375	−	0.991465i	$-0.458382\pi$
$709$	6.94298	0.260749	0.130375	+	0.991465i	$0.458382\pi$
$710$	10.9818	0.412138
$711$	−24.7954	−0.929901
$712$	115.201	4.31732
$713$	51.0351	1.91128
$714$	6.38879	0.239094
$715$	8.26118	0.308951
$716$	−70.4761	−2.63381
$717$	4.87430	0.182034
$718$	−24.5594	−0.916547
$719$	41.9754	1.56542	0.782710	−	0.622387i	$-0.213837\pi$
$719$	41.9754	1.56542	0.782710	+	0.622387i	$0.213837\pi$
$720$	38.1372	1.42129
$721$	39.8321	1.48343
$722$	28.2372	1.05088
$723$	−0.645235	−0.0239965
$724$	84.6642	3.14652
$725$	−4.04278	−0.150145
$726$	−6.49499	−0.241052
$727$	−25.4912	−0.945417	−0.472708	−	0.881219i	$-0.656724\pi$
$727$	−25.4912	−0.945417	−0.472708	+	0.881219i	$0.656724\pi$
$728$	−101.166	−3.74947
$729$	−20.4657	−0.757990
$730$	−8.04521	−0.297767
$731$	0	0
$732$	22.1906	0.820190
$733$	−5.82076	−0.214994	−0.107497	−	0.994205i	$-0.534284\pi$
$733$	−5.82076	−0.214994	−0.107497	+	0.994205i	$0.534284\pi$
$734$	−22.0496	−0.813867
$735$	3.48884	0.128688
$736$	90.1061	3.32135
$737$	−11.6425	−0.428858
$738$	−14.7643	−0.543482
$739$	18.6097	0.684568	0.342284	−	0.939597i	$-0.388800\pi$
$739$	18.6097	0.684568	0.342284	+	0.939597i	$0.388800\pi$
$740$	−2.43142	−0.0893807
$741$	−3.39814	−0.124834
$742$	57.0838	2.09561
$743$	−3.49660	−0.128278	−0.0641390	−	0.997941i	$-0.520430\pi$
$743$	−3.49660	−0.128278	−0.0641390	+	0.997941i	$0.520430\pi$
$744$	−20.0326	−0.734431
$745$	−12.1617	−0.445572
$746$	−96.2531	−3.52408
$747$	−8.81958	−0.322692
$748$	−17.6583	−0.645650
$749$	46.4565	1.69748
$750$	9.76894	0.356711
$751$	3.46346	0.126383	0.0631917	−	0.998001i	$-0.479872\pi$
$751$	3.46346	0.126383	0.0631917	+	0.998001i	$0.479872\pi$
$752$	−31.3398	−1.14285
$753$	−4.06227	−0.148037
$754$	10.2116	0.371886
$755$	14.1604	0.515349
$756$	−40.0343	−1.45603
$757$	−28.8554	−1.04877	−0.524384	−	0.851482i	$-0.675704\pi$
$757$	−28.8554	−1.04877	−0.524384	+	0.851482i	$0.675704\pi$
$758$	19.5953	0.711735
$759$	5.04045	0.182957
$760$	−27.8523	−1.01031
$761$	−25.3496	−0.918922	−0.459461	−	0.888198i	$-0.651957\pi$
$761$	−25.3496	−0.918922	−0.459461	+	0.888198i	$0.651957\pi$
$762$	7.19296	0.260574
$763$	−3.83340	−0.138779
$764$	−39.1876	−1.41776
$765$	−6.25233	−0.226053
$766$	3.42652	0.123805
$767$	−21.5769	−0.779095
$768$	2.52114	0.0909737
$769$	−38.4737	−1.38740	−0.693698	−	0.720266i	$-0.744020\pi$
$769$	−38.4737	−1.38740	−0.693698	+	0.720266i	$0.744020\pi$
$770$	−25.3595	−0.913893
$771$	9.54025	0.343584
$772$	−2.81445	−0.101294
$773$	−34.4168	−1.23789	−0.618943	−	0.785436i	$-0.712439\pi$
$773$	−34.4168	−1.23789	−0.618943	+	0.785436i	$0.712439\pi$
$774$	0	0
$775$	25.1181	0.902268
$776$	143.486	5.15083
$777$	0.544222	0.0195238
$778$	26.2165	0.939906
$779$	5.60604	0.200857
$780$	−7.22262	−0.258611
$781$	6.79387	0.243104
$782$	−32.9633	−1.17876
$783$	2.41506	0.0863074
$784$	86.0984	3.07494
$785$	−8.46762	−0.302222
$786$	9.56365	0.341124
$787$	−14.5634	−0.519130	−0.259565	−	0.965726i	$-0.583579\pi$
$787$	−14.5634	−0.519130	−0.259565	+	0.965726i	$0.583579\pi$
$788$	−74.0498	−2.63791
$789$	−6.88287	−0.245037
$790$	28.0626	0.998423
$791$	41.0316	1.45892
$792$	45.3799	1.61251
$793$	42.0021	1.49154
$794$	40.2512	1.42846
$795$	2.43562	0.0863825
$796$	80.0586	2.83760
$797$	−1.81667	−0.0643496	−0.0321748	−	0.999482i	$-0.510243\pi$
$797$	−1.81667	−0.0643496	−0.0321748	+	0.999482i	$0.510243\pi$
$798$	10.4313	0.369265
$799$	5.13794	0.181767
$800$	44.3477	1.56793
$801$	42.2237	1.49190
$802$	44.7802	1.58125
$803$	−4.97718	−0.175641
$804$	10.1789	0.358981
$805$	−33.7569	−1.18978
$806$	−63.4455	−2.23477
$807$	−1.89037	−0.0665443
$808$	−137.422	−4.83450
$809$	32.7007	1.14969	0.574847	−	0.818261i	$-0.305061\pi$
$809$	32.7007	1.14969	0.574847	+	0.818261i	$0.305061\pi$
$810$	25.6623	0.901682
$811$	19.6087	0.688556	0.344278	−	0.938868i	$-0.388124\pi$
$811$	19.6087	0.688556	0.344278	+	0.938868i	$0.388124\pi$
$812$	−22.3529	−0.784432
$813$	9.16806	0.321538
$814$	−2.10943	−0.0739355
$815$	24.8185	0.869353
$816$	6.72712	0.235496
$817$	0	0
$818$	11.5208	0.402814
$819$	−37.0798	−1.29567
$820$	11.9154	0.416105
$821$	−44.4856	−1.55256	−0.776280	−	0.630389i	$-0.782895\pi$
$821$	−44.4856	−1.55256	−0.776280	+	0.630389i	$0.782895\pi$
$822$	4.36613	0.152286
$823$	−13.2025	−0.460211	−0.230105	−	0.973166i	$-0.573907\pi$
$823$	−13.2025	−0.460211	−0.230105	+	0.973166i	$0.573907\pi$
$824$	80.6702	2.81028
$825$	2.48077	0.0863693
$826$	66.2349	2.30461
$827$	−44.1702	−1.53595	−0.767974	−	0.640481i	$-0.778735\pi$
$827$	−44.1702	−1.53595	−0.767974	+	0.640481i	$0.778735\pi$
$828$	101.076	3.51264
$829$	41.1538	1.42933	0.714665	−	0.699467i	$-0.246579\pi$
$829$	41.1538	1.42933	0.714665	+	0.699467i	$0.246579\pi$
$830$	9.98170	0.346470
$831$	−3.87754	−0.134510
$832$	−40.2997	−1.39714
$833$	−14.1152	−0.489063
$834$	10.9315	0.378526
$835$	−11.4269	−0.395443
$836$	−28.8316	−0.997163
$837$	−15.0049	−0.518647
$838$	50.1038	1.73081
$839$	22.4874	0.776350	0.388175	−	0.921586i	$-0.373106\pi$
$839$	22.4874	0.776350	0.388175	+	0.921586i	$0.373106\pi$
$840$	13.2505	0.457184
$841$	−27.6516	−0.953502
$842$	26.2013	0.902958
$843$	6.68453	0.230227
$844$	−47.7222	−1.64267
$845$	2.34874	0.0807991
$846$	−22.0937	−0.759595
$847$	26.9103	0.924648
$848$	60.1068	2.06408
$849$	2.27214	0.0779798
$850$	−16.2236	−0.556465
$851$	−2.80794	−0.0962549
$852$	−5.93977	−0.203493
$853$	−27.3398	−0.936097	−0.468048	−	0.883703i	$-0.655043\pi$
$853$	−27.3398	−0.936097	−0.468048	+	0.883703i	$0.655043\pi$
$854$	−128.935	−4.41206
$855$	−10.2085	−0.349124
$856$	94.0862	3.21580
$857$	−11.3186	−0.386636	−0.193318	−	0.981136i	$-0.561925\pi$
$857$	−11.3186	−0.386636	−0.193318	+	0.981136i	$0.561925\pi$
$858$	−6.26615	−0.213923
$859$	−28.3173	−0.966174	−0.483087	−	0.875572i	$-0.660485\pi$
$859$	−28.3173	−0.966174	−0.483087	+	0.875572i	$0.660485\pi$
$860$	0	0
$861$	−2.66702	−0.0908917
$862$	42.9221	1.46193
$863$	46.3789	1.57875	0.789377	−	0.613908i	$-0.210404\pi$
$863$	46.3789	1.57875	0.789377	+	0.613908i	$0.210404\pi$
$864$	−26.4923	−0.901286
$865$	−28.8167	−0.979798
$866$	48.0409	1.63250
$867$	4.91551	0.166940
$868$	138.880	4.71389
$869$	17.3610	0.588930
$870$	−1.33749	−0.0453451
$871$	19.2664	0.652818
$872$	−7.76362	−0.262909
$873$	52.5909	1.77993
$874$	−53.8210	−1.82052
$875$	−40.4750	−1.36830
$876$	4.35147	0.147022
$877$	−15.1650	−0.512085	−0.256043	−	0.966665i	$-0.582419\pi$
$877$	−15.1650	−0.512085	−0.256043	+	0.966665i	$0.582419\pi$
$878$	−31.1554	−1.05144
$879$	−1.87437	−0.0632208
$880$	−26.7025	−0.900140
$881$	−44.0304	−1.48342	−0.741711	−	0.670720i	$-0.765985\pi$
$881$	−44.0304	−1.48342	−0.741711	+	0.670720i	$0.765985\pi$
$882$	60.6968	2.04377
$883$	38.2864	1.28844	0.644220	−	0.764840i	$-0.277182\pi$
$883$	38.2864	1.28844	0.644220	+	0.764840i	$0.277182\pi$
$884$	29.2214	0.982823
$885$	2.82607	0.0949974
$886$	−105.970	−3.56013
$887$	15.1269	0.507911	0.253956	−	0.967216i	$-0.418268\pi$
$887$	15.1269	0.507911	0.253956	+	0.967216i	$0.418268\pi$
$888$	1.10219	0.0369870
$889$	−29.8021	−0.999531
$890$	−47.7874	−1.60184
$891$	15.8760	0.531867
$892$	84.8291	2.84029
$893$	8.38901	0.280727
$894$	9.22474	0.308522
$895$	17.4718	0.584018
$896$	25.0486	0.836814
$897$	−8.34109	−0.278501
$898$	37.2982	1.24466
$899$	−8.37791	−0.279419
$900$	49.7468	1.65823
$901$	−9.85408	−0.328287
$902$	10.3375	0.344201
$903$	0	0
$904$	83.0996	2.76385
$905$	−20.9892	−0.697705
$906$	−10.7407	−0.356836
$907$	21.2339	0.705061	0.352531	−	0.935800i	$-0.385321\pi$
$907$	21.2339	0.705061	0.352531	+	0.935800i	$0.385321\pi$
$908$	87.1460	2.89204
$909$	−50.3685	−1.67062
$910$	41.9657	1.39115
$911$	55.4368	1.83670	0.918351	−	0.395766i	$-0.129521\pi$
$911$	55.4368	1.83670	0.918351	+	0.395766i	$0.129521\pi$
$912$	10.9837	0.363708
$913$	6.17519	0.204369
$914$	−55.2463	−1.82739
$915$	−5.50131	−0.181868
$916$	143.180	4.73081
$917$	−39.6245	−1.30852
$918$	9.69161	0.319871
$919$	−37.5058	−1.23720	−0.618600	−	0.785706i	$-0.712300\pi$
$919$	−37.5058	−1.23720	−0.618600	+	0.785706i	$0.712300\pi$
$920$	−68.3664	−2.25397
$921$	−0.469097	−0.0154573
$922$	36.7892	1.21159
$923$	−11.2427	−0.370058
$924$	13.7164	0.451235
$925$	−1.38199	−0.0454395
$926$	80.1092	2.63255
$927$	29.5675	0.971125
$928$	−14.7918	−0.485564
$929$	−7.11367	−0.233392	−0.116696	−	0.993168i	$-0.537230\pi$
$929$	−7.11367	−0.233392	−0.116696	+	0.993168i	$0.537230\pi$
$930$	8.30990	0.272492
$931$	−23.0467	−0.755326
$932$	45.0538	1.47579
$933$	−8.09294	−0.264951
$934$	−73.4199	−2.40237
$935$	4.37768	0.143165
$936$	−75.0961	−2.45459
$937$	23.9242	0.781568	0.390784	−	0.920482i	$-0.372204\pi$
$937$	23.9242	0.781568	0.390784	+	0.920482i	$0.372204\pi$
$938$	−59.1425	−1.93107
$939$	2.95819	0.0965370
$940$	17.8305	0.581567
$941$	31.8161	1.03718	0.518588	−	0.855024i	$-0.326458\pi$
$941$	31.8161	1.03718	0.518588	+	0.855024i	$0.326458\pi$
$942$	6.42273	0.209264
$943$	13.7606	0.448107
$944$	69.7425	2.26993
$945$	9.92495	0.322859
$946$	0	0
$947$	−58.2996	−1.89448	−0.947241	−	0.320523i	$-0.896141\pi$
$947$	−58.2996	−1.89448	−0.947241	+	0.320523i	$0.896141\pi$
$948$	−15.1784	−0.492972
$949$	8.23639	0.267365
$950$	−26.4892	−0.859424
$951$	0.965542	0.0313098
$952$	−53.6090	−1.73748
$953$	26.6689	0.863889	0.431944	−	0.901900i	$-0.357828\pi$
$953$	26.6689	0.863889	0.431944	+	0.901900i	$0.357828\pi$
$954$	42.3735	1.37189
$955$	9.71505	0.314372
$956$	−68.4375	−2.21343
$957$	−0.827438	−0.0267473
$958$	6.12989	0.198048
$959$	−18.0899	−0.584153
$960$	5.27833	0.170357
$961$	21.0525	0.679113
$962$	3.49075	0.112546
$963$	34.4848	1.11126
$964$	9.05940	0.291784
$965$	0.697733	0.0224608
$966$	25.6048	0.823821
$967$	36.5173	1.17432	0.587158	−	0.809472i	$-0.300247\pi$
$967$	36.5173	1.17432	0.587158	+	0.809472i	$0.300247\pi$
$968$	54.5002	1.75170
$969$	−1.80071	−0.0578471
$970$	−59.5205	−1.91109
$971$	−43.2825	−1.38900	−0.694501	−	0.719492i	$-0.744375\pi$
$971$	−43.2825	−1.38900	−0.694501	+	0.719492i	$0.744375\pi$
$972$	−44.8934	−1.43996
$973$	−45.2917	−1.45198
$974$	60.2790	1.93146
$975$	−4.10525	−0.131473
$976$	−135.763	−4.34566
$977$	21.4720	0.686949	0.343474	−	0.939162i	$-0.388396\pi$
$977$	21.4720	0.686949	0.343474	+	0.939162i	$0.388396\pi$
$978$	−18.8249	−0.601955
$979$	−29.5637	−0.944860
$980$	−48.9849	−1.56477
$981$	−2.84555	−0.0908514
$982$	82.7497	2.64065
$983$	27.5273	0.877984	0.438992	−	0.898491i	$-0.355336\pi$
$983$	27.5273	0.877984	0.438992	+	0.898491i	$0.355336\pi$
$984$	−5.40139	−0.172190
$985$	18.3578	0.584927
$986$	5.41124	0.172329
$987$	−3.99098	−0.127034
$988$	47.7115	1.51791
$989$	0	0
$990$	−18.8244	−0.598280
$991$	7.84451	0.249189	0.124595	−	0.992208i	$-0.460237\pi$
$991$	7.84451	0.249189	0.124595	+	0.992208i	$0.460237\pi$
$992$	91.9023	2.91790
$993$	−10.4417	−0.331359
$994$	34.5120	1.09465
$995$	−19.8474	−0.629206
$996$	−5.39887	−0.171070
$997$	−49.2281	−1.55907	−0.779535	−	0.626359i	$-0.784544\pi$
$997$	−49.2281	−1.55907	−0.779535	+	0.626359i	$0.784544\pi$
$998$	13.8390	0.438066
$999$	0.825568	0.0261198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.r.1.1	yes	20
43.42	odd	2		1849.2.a.p.1.20	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.p.1.20	✓	20	43.42	odd	2
1849.2.a.r.1.1	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)

\(f(q)\)	\(=\)	\(q-2.64020 q^{2} -0.354022 q^{3} +4.97064 q^{4} -1.23228 q^{5} +0.934688 q^{6} -3.87263 q^{7} -7.84307 q^{8} -2.87467 q^{9} +O(q^{10})\)	\(q-2.64020 q^{2} -0.354022 q^{3} +4.97064 q^{4} -1.23228 q^{5} +0.934688 q^{6} -3.87263 q^{7} -7.84307 q^{8} -2.87467 q^{9} +3.25345 q^{10} +2.01275 q^{11} -1.75972 q^{12} -3.33076 q^{13} +10.2245 q^{14} +0.436253 q^{15} +10.7660 q^{16} -1.76500 q^{17} +7.58969 q^{18} -2.88182 q^{19} -6.12520 q^{20} +1.37100 q^{21} -5.31406 q^{22} -7.07373 q^{23} +2.77662 q^{24} -3.48149 q^{25} +8.79387 q^{26} +2.07976 q^{27} -19.2494 q^{28} +1.16122 q^{29} -1.15179 q^{30} -7.21474 q^{31} -12.7381 q^{32} -0.712558 q^{33} +4.65996 q^{34} +4.77215 q^{35} -14.2889 q^{36} +0.396953 q^{37} +7.60858 q^{38} +1.17916 q^{39} +9.66483 q^{40} -1.94531 q^{41} -3.61970 q^{42} +10.0047 q^{44} +3.54239 q^{45} +18.6760 q^{46} -2.91101 q^{47} -3.81139 q^{48} +7.99728 q^{49} +9.19183 q^{50} +0.624850 q^{51} -16.5560 q^{52} +5.58304 q^{53} -5.49098 q^{54} -2.48027 q^{55} +30.3733 q^{56} +1.02023 q^{57} -3.06585 q^{58} +6.47805 q^{59} +2.16846 q^{60} -12.6104 q^{61} +19.0483 q^{62} +11.1325 q^{63} +12.0992 q^{64} +4.10442 q^{65} +1.88129 q^{66} -5.78439 q^{67} -8.77320 q^{68} +2.50426 q^{69} -12.5994 q^{70} +3.37541 q^{71} +22.5462 q^{72} -2.47282 q^{73} -1.04803 q^{74} +1.23253 q^{75} -14.3245 q^{76} -7.79464 q^{77} -3.11322 q^{78} +8.62549 q^{79} -13.2666 q^{80} +7.88772 q^{81} +5.13600 q^{82} +3.06803 q^{83} +6.81473 q^{84} +2.17497 q^{85} -0.411098 q^{87} -15.7861 q^{88} -14.6882 q^{89} -9.35260 q^{90} +12.8988 q^{91} -35.1609 q^{92} +2.55418 q^{93} +7.68564 q^{94} +3.55120 q^{95} +4.50958 q^{96} -18.2946 q^{97} -21.1144 q^{98} -5.78599 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{2} - q^{3} + 23 q^{4} - 3 q^{5} + 5 q^{6} - 2 q^{7} + 9 q^{8} + 27 q^{9}+O(q^{10}) \) 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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