LMFDB - Embedded newform 1441.2.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.77267 q^{2} -3.40600 q^{3} +1.14234 q^{4} -3.60328 q^{5} +6.03770 q^{6} +0.417068 q^{7} +1.52034 q^{8} +8.60085 q^{9} +O(q^{10})$	\(q-1.77267 q^{2} -3.40600 q^{3} +1.14234 q^{4} -3.60328 q^{5} +6.03770 q^{6} +0.417068 q^{7} +1.52034 q^{8} +8.60085 q^{9} +6.38741 q^{10} +1.00000 q^{11} -3.89083 q^{12} -4.37293 q^{13} -0.739322 q^{14} +12.2728 q^{15} -4.97974 q^{16} +0.423674 q^{17} -15.2464 q^{18} +1.68434 q^{19} -4.11619 q^{20} -1.42053 q^{21} -1.77267 q^{22} -3.07122 q^{23} -5.17827 q^{24} +7.98363 q^{25} +7.75174 q^{26} -19.0765 q^{27} +0.476435 q^{28} +5.87083 q^{29} -21.7555 q^{30} -7.64741 q^{31} +5.78674 q^{32} -3.40600 q^{33} -0.751032 q^{34} -1.50281 q^{35} +9.82514 q^{36} -9.81966 q^{37} -2.98578 q^{38} +14.8942 q^{39} -5.47820 q^{40} -7.64186 q^{41} +2.51813 q^{42} -9.71395 q^{43} +1.14234 q^{44} -30.9913 q^{45} +5.44424 q^{46} +12.4290 q^{47} +16.9610 q^{48} -6.82605 q^{49} -14.1523 q^{50} -1.44303 q^{51} -4.99539 q^{52} -4.51453 q^{53} +33.8163 q^{54} -3.60328 q^{55} +0.634084 q^{56} -5.73688 q^{57} -10.4070 q^{58} -6.56153 q^{59} +14.0197 q^{60} +3.04357 q^{61} +13.5563 q^{62} +3.58714 q^{63} -0.298480 q^{64} +15.7569 q^{65} +6.03770 q^{66} +6.16308 q^{67} +0.483982 q^{68} +10.4606 q^{69} +2.66399 q^{70} +11.4787 q^{71} +13.0762 q^{72} -13.1645 q^{73} +17.4070 q^{74} -27.1923 q^{75} +1.92410 q^{76} +0.417068 q^{77} -26.4024 q^{78} -1.92843 q^{79} +17.9434 q^{80} +39.1721 q^{81} +13.5465 q^{82} -12.1724 q^{83} -1.62274 q^{84} -1.52662 q^{85} +17.2196 q^{86} -19.9960 q^{87} +1.52034 q^{88} +7.15447 q^{89} +54.9372 q^{90} -1.82381 q^{91} -3.50839 q^{92} +26.0471 q^{93} -22.0325 q^{94} -6.06916 q^{95} -19.7096 q^{96} +2.96006 q^{97} +12.1003 q^{98} +8.60085 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) $ 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9 + 14 * q^10 + 28 * q^11 - 6 * q^12 + 3 * q^13 - q^14 + 19 * q^15 + 29 * q^16 + 9 * q^17 - 2 * q^18 + 20 * q^19 + 6 * q^20 + 6 * q^21 + 7 * q^22 + 24 * q^23 + 20 * q^24 + 23 * q^25 + 10 * q^26 - 20 * q^27 - 3 * q^28 + 43 * q^29 + 11 * q^30 + 3 * q^31 + 44 * q^32 - 2 * q^33 - 28 * q^34 + 32 * q^35 + 24 * q^36 - 4 * q^37 + 24 * q^38 + 37 * q^39 + 22 * q^40 + 32 * q^41 - 27 * q^42 + 25 * q^43 + 27 * q^44 - 36 * q^45 + 10 * q^46 + 19 * q^47 + 42 * q^48 + 17 * q^49 + q^50 + 39 * q^51 - 19 * q^52 + 5 * q^53 + 6 * q^54 + 3 * q^55 + 8 * q^56 + 2 * q^57 + 21 * q^58 + 44 * q^59 + 65 * q^60 + 28 * q^61 + 60 * q^62 - 8 * q^63 + 5 * q^64 + 33 * q^65 - q^66 + 7 * q^67 + 13 * q^68 - 22 * q^69 + 9 * q^70 + 117 * q^71 - 17 * q^72 + 7 * q^73 + 41 * q^74 - 40 * q^75 + 34 * q^76 + 7 * q^77 - 97 * q^78 + 48 * q^79 + 41 * q^80 + 40 * q^81 + 2 * q^82 + 22 * q^83 + 27 * q^84 + 30 * q^85 + 24 * q^86 + 37 * q^87 + 21 * q^88 - 6 * q^89 + 4 * q^90 - 33 * q^91 + 18 * q^92 + 5 * q^93 - 43 * q^94 + 64 * q^95 + 55 * q^96 - 50 * q^97 + 97 * q^98 + 28 * 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 $

$2$	−1.77267	−1.25346	−0.626732	−	0.779235i	$-0.715608\pi$
$2$	−1.77267	−1.25346	−0.626732	+	0.779235i	$0.715608\pi$
$3$	−3.40600	−1.96646	−0.983228	−	0.182379i	$-0.941620\pi$
$3$	−3.40600	−1.96646	−0.983228	+	0.182379i	$0.941620\pi$
$4$	1.14234	0.571172
$5$	−3.60328	−1.61144	−0.805718	−	0.592299i	$-0.798220\pi$
$5$	−3.60328	−1.61144	−0.805718	+	0.592299i	$0.798220\pi$
$6$	6.03770	2.46488
$7$	0.417068	0.157637	0.0788184	−	0.996889i	$-0.474885\pi$
$7$	0.417068	0.157637	0.0788184	+	0.996889i	$0.474885\pi$
$8$	1.52034	0.537520
$9$	8.60085	2.86695
$10$	6.38741	2.01988
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.89083	−1.12319
$13$	−4.37293	−1.21283	−0.606416	−	0.795148i	$-0.707393\pi$
$13$	−4.37293	−1.21283	−0.606416	+	0.795148i	$0.707393\pi$
$14$	−0.739322	−0.197592
$15$	12.2728	3.16882
$16$	−4.97974	−1.24493
$17$	0.423674	0.102756	0.0513780	−	0.998679i	$-0.483639\pi$
$17$	0.423674	0.102756	0.0513780	+	0.998679i	$0.483639\pi$
$18$	−15.2464	−3.59362
$19$	1.68434	0.386415	0.193208	−	0.981158i	$-0.438111\pi$
$19$	1.68434	0.386415	0.193208	+	0.981158i	$0.438111\pi$
$20$	−4.11619	−0.920408
$21$	−1.42053	−0.309986
$22$	−1.77267	−0.377934
$23$	−3.07122	−0.640393	−0.320197	−	0.947351i	$-0.603749\pi$
$23$	−3.07122	−0.640393	−0.320197	+	0.947351i	$0.603749\pi$
$24$	−5.17827	−1.05701
$25$	7.98363	1.59673
$26$	7.75174	1.52024
$27$	−19.0765	−3.67128
$28$	0.476435	0.0900378
$29$	5.87083	1.09019	0.545093	−	0.838376i	$-0.316495\pi$
$29$	5.87083	1.09019	0.545093	+	0.838376i	$0.316495\pi$
$30$	−21.7555	−3.97200
$31$	−7.64741	−1.37352	−0.686758	−	0.726886i	$-0.740967\pi$
$31$	−7.64741	−1.37352	−0.686758	+	0.726886i	$0.740967\pi$
$32$	5.78674	1.02296
$33$	−3.40600	−0.592909
$34$	−0.751032	−0.128801
$35$	−1.50281	−0.254022
$36$	9.82514	1.63752
$37$	−9.81966	−1.61434	−0.807171	−	0.590318i	$-0.799002\pi$
$37$	−9.81966	−1.61434	−0.807171	+	0.590318i	$0.799002\pi$
$38$	−2.98578	−0.484357
$39$	14.8942	2.38498
$40$	−5.47820	−0.866179
$41$	−7.64186	−1.19346	−0.596729	−	0.802443i	$-0.703533\pi$
$41$	−7.64186	−1.19346	−0.596729	+	0.802443i	$0.703533\pi$
$42$	2.51813	0.388556
$43$	−9.71395	−1.48136	−0.740682	−	0.671856i	$-0.765498\pi$
$43$	−9.71395	−1.48136	−0.740682	+	0.671856i	$0.765498\pi$
$44$	1.14234	0.172215
$45$	−30.9913	−4.61991
$46$	5.44424	0.802710
$47$	12.4290	1.81296	0.906478	−	0.422252i	$-0.138760\pi$
$47$	12.4290	1.81296	0.906478	+	0.422252i	$0.138760\pi$
$48$	16.9610	2.44811
$49$	−6.82605	−0.975151
$50$	−14.1523	−2.00144
$51$	−1.44303	−0.202065
$52$	−4.99539	−0.692736
$53$	−4.51453	−0.620118	−0.310059	−	0.950717i	$-0.600349\pi$
$53$	−4.51453	−0.620118	−0.310059	+	0.950717i	$0.600349\pi$
$54$	33.8163	4.60182
$55$	−3.60328	−0.485866
$56$	0.634084	0.0847330
$57$	−5.73688	−0.759868
$58$	−10.4070	−1.36651
$59$	−6.56153	−0.854239	−0.427119	−	0.904195i	$-0.640472\pi$
$59$	−6.56153	−0.854239	−0.427119	+	0.904195i	$0.640472\pi$
$60$	14.0197	1.80994
$61$	3.04357	0.389689	0.194845	−	0.980834i	$-0.437580\pi$
$61$	3.04357	0.389689	0.194845	+	0.980834i	$0.437580\pi$
$62$	13.5563	1.72165
$63$	3.58714	0.451937
$64$	−0.298480	−0.0373100
$65$	15.7569	1.95440
$66$	6.03770	0.743190
$67$	6.16308	0.752940	0.376470	−	0.926429i	$-0.377138\pi$
$67$	6.16308	0.752940	0.376470	+	0.926429i	$0.377138\pi$
$68$	0.483982	0.0586914
$69$	10.4606	1.25930
$70$	2.66399	0.318407
$71$	11.4787	1.36227	0.681136	−	0.732157i	$-0.261486\pi$
$71$	11.4787	1.36227	0.681136	+	0.732157i	$0.261486\pi$
$72$	13.0762	1.54104
$73$	−13.1645	−1.54078	−0.770392	−	0.637570i	$-0.779940\pi$
$73$	−13.1645	−1.54078	−0.770392	+	0.637570i	$0.779940\pi$
$74$	17.4070	2.02352
$75$	−27.1923	−3.13989
$76$	1.92410	0.220710
$77$	0.417068	0.0475293
$78$	−26.4024	−2.98949
$79$	−1.92843	−0.216965	−0.108482	−	0.994098i	$-0.534599\pi$
$79$	−1.92843	−0.216965	−0.108482	+	0.994098i	$0.534599\pi$
$80$	17.9434	2.00613
$81$	39.1721	4.35246
$82$	13.5465	1.49596
$83$	−12.1724	−1.33609	−0.668045	−	0.744121i	$-0.732869\pi$
$83$	−12.1724	−1.33609	−0.668045	+	0.744121i	$0.732869\pi$
$84$	−1.62274	−0.177055
$85$	−1.52662	−0.165585
$86$	17.2196	1.85684
$87$	−19.9960	−2.14380
$88$	1.52034	0.162068
$89$	7.15447	0.758372	0.379186	−	0.925320i	$-0.376204\pi$
$89$	7.15447	0.758372	0.379186	+	0.925320i	$0.376204\pi$
$90$	54.9372	5.79089
$91$	−1.82381	−0.191187
$92$	−3.50839	−0.365775
$93$	26.0471	2.70096
$94$	−22.0325	−2.27248
$95$	−6.06916	−0.622683
$96$	−19.7096	−2.01161
$97$	2.96006	0.300548	0.150274	−	0.988644i	$-0.451984\pi$
$97$	2.96006	0.300548	0.150274	+	0.988644i	$0.451984\pi$
$98$	12.1003	1.22232
$99$	8.60085	0.864418
$100$	9.12006	0.912006
$101$	−19.4345	−1.93381	−0.966903	−	0.255142i	$-0.917878\pi$
$101$	−19.4345	−1.93381	−0.966903	+	0.255142i	$0.917878\pi$
$102$	2.55802	0.253281
$103$	−6.92942	−0.682776	−0.341388	−	0.939922i	$-0.610897\pi$
$103$	−6.92942	−0.682776	−0.341388	+	0.939922i	$0.610897\pi$
$104$	−6.64832	−0.651921
$105$	5.11858	0.499523
$106$	8.00275	0.777295
$107$	11.4407	1.10602	0.553009	−	0.833175i	$-0.313480\pi$
$107$	11.4407	1.10602	0.553009	+	0.833175i	$0.313480\pi$
$108$	−21.7920	−2.09693
$109$	8.71428	0.834677	0.417338	−	0.908751i	$-0.362963\pi$
$109$	8.71428	0.834677	0.417338	+	0.908751i	$0.362963\pi$
$110$	6.38741	0.609016
$111$	33.4458	3.17453
$112$	−2.07689	−0.196248
$113$	1.46491	0.137807	0.0689034	−	0.997623i	$-0.478050\pi$
$113$	1.46491	0.137807	0.0689034	+	0.997623i	$0.478050\pi$
$114$	10.1696	0.952468
$115$	11.0665	1.03195
$116$	6.70651	0.622684
$117$	−37.6109	−3.47713
$118$	11.6314	1.07076
$119$	0.176701	0.0161981
$120$	18.6588	1.70330
$121$	1.00000	0.0909091
$122$	−5.39524	−0.488462
$123$	26.0282	2.34688
$124$	−8.73598	−0.784514
$125$	−10.7509	−0.961585
$126$	−6.35880	−0.566487
$127$	7.79085	0.691326	0.345663	−	0.938359i	$-0.387654\pi$
$127$	7.79085	0.691326	0.345663	+	0.938359i	$0.387654\pi$
$128$	−11.0444	−0.976194
$129$	33.0858	2.91304
$130$	−27.9317	−2.44977
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−3.89083	−0.338653
$133$	0.702486	0.0609133
$134$	−10.9251	−0.943783
$135$	68.7381	5.91603
$136$	0.644127	0.0552334
$137$	−17.0372	−1.45559	−0.727794	−	0.685796i	$-0.759454\pi$
$137$	−17.0372	−1.45559	−0.727794	+	0.685796i	$0.759454\pi$
$138$	−18.5431	−1.57849
$139$	−11.5949	−0.983469	−0.491735	−	0.870745i	$-0.663637\pi$
$139$	−11.5949	−0.983469	−0.491735	+	0.870745i	$0.663637\pi$
$140$	−1.71673	−0.145090
$141$	−42.3332	−3.56510
$142$	−20.3479	−1.70756
$143$	−4.37293	−0.365682
$144$	−42.8300	−3.56917
$145$	−21.1542	−1.75676
$146$	23.3362	1.93132
$147$	23.2496	1.91759
$148$	−11.2174	−0.922067
$149$	−8.14836	−0.667539	−0.333770	−	0.942655i	$-0.608321\pi$
$149$	−8.14836	−0.667539	−0.333770	+	0.942655i	$0.608321\pi$
$150$	48.2028	3.93574
$151$	−15.5231	−1.26325	−0.631627	−	0.775273i	$-0.717612\pi$
$151$	−15.5231	−1.26325	−0.631627	+	0.775273i	$0.717612\pi$
$152$	2.56077	0.207706
$153$	3.64396	0.294596
$154$	−0.739322	−0.0595763
$155$	27.5558	2.21333
$156$	17.0143	1.36223
$157$	−14.2537	−1.13757	−0.568787	−	0.822485i	$-0.692587\pi$
$157$	−14.2537	−1.13757	−0.568787	+	0.822485i	$0.692587\pi$
$158$	3.41845	0.271958
$159$	15.3765	1.21943
$160$	−20.8512	−1.64844
$161$	−1.28091	−0.100950
$162$	−69.4391	−5.45565
$163$	−2.25237	−0.176420	−0.0882098	−	0.996102i	$-0.528115\pi$
$163$	−2.25237	−0.176420	−0.0882098	+	0.996102i	$0.528115\pi$
$164$	−8.72964	−0.681670
$165$	12.2728	0.955435
$166$	21.5775	1.67474
$167$	−1.82790	−0.141447	−0.0707236	−	0.997496i	$-0.522531\pi$
$167$	−1.82790	−0.141447	−0.0707236	+	0.997496i	$0.522531\pi$
$168$	−2.15969	−0.166624
$169$	6.12249	0.470961
$170$	2.70618	0.207554
$171$	14.4868	1.10783
$172$	−11.0967	−0.846114
$173$	24.5027	1.86291	0.931453	−	0.363862i	$-0.118542\pi$
$173$	24.5027	1.86291	0.931453	+	0.363862i	$0.118542\pi$
$174$	35.4463	2.68718
$175$	3.32972	0.251703
$176$	−4.97974	−0.375362
$177$	22.3486	1.67982
$178$	−12.6825	−0.950592
$179$	0.865188	0.0646672	0.0323336	−	0.999477i	$-0.489706\pi$
$179$	0.865188	0.0646672	0.0323336	+	0.999477i	$0.489706\pi$
$180$	−35.4027	−2.63876
$181$	−0.434797	−0.0323182	−0.0161591	−	0.999869i	$-0.505144\pi$
$181$	−0.434797	−0.0323182	−0.0161591	+	0.999869i	$0.505144\pi$
$182$	3.23300	0.239646
$183$	−10.3664	−0.766307
$184$	−4.66928	−0.344224
$185$	35.3830	2.60141
$186$	−46.1728	−3.38556
$187$	0.423674	0.0309821
$188$	14.1982	1.03551
$189$	−7.95621	−0.578729
$190$	10.7586	0.780511
$191$	9.02423	0.652971	0.326485	−	0.945202i	$-0.394136\pi$
$191$	9.02423	0.652971	0.326485	+	0.945202i	$0.394136\pi$
$192$	1.01662	0.0733685
$193$	−6.04192	−0.434907	−0.217454	−	0.976071i	$-0.569775\pi$
$193$	−6.04192	−0.434907	−0.217454	+	0.976071i	$0.569775\pi$
$194$	−5.24719	−0.376726
$195$	−53.6680	−3.84324
$196$	−7.79771	−0.556979
$197$	−7.25165	−0.516659	−0.258329	−	0.966057i	$-0.583172\pi$
$197$	−7.25165	−0.516659	−0.258329	+	0.966057i	$0.583172\pi$
$198$	−15.2464	−1.08352
$199$	7.53307	0.534005	0.267003	−	0.963696i	$-0.413967\pi$
$199$	7.53307	0.534005	0.267003	+	0.963696i	$0.413967\pi$
$200$	12.1378	0.858272
$201$	−20.9915	−1.48062
$202$	34.4509	2.42396
$203$	2.44853	0.171853
$204$	−1.64844	−0.115414
$205$	27.5358	1.92318
$206$	12.2835	0.855835
$207$	−26.4151	−1.83598
$208$	21.7760	1.50990
$209$	1.68434	0.116509
$210$	−9.07354	−0.626134
$211$	−2.68460	−0.184815	−0.0924077	−	0.995721i	$-0.529456\pi$
$211$	−2.68460	−0.184815	−0.0924077	+	0.995721i	$0.529456\pi$
$212$	−5.15714	−0.354194
$213$	−39.0965	−2.67885
$214$	−20.2806	−1.38635
$215$	35.0021	2.38712
$216$	−29.0027	−1.97339
$217$	−3.18949	−0.216517
$218$	−15.4475	−1.04624
$219$	44.8382	3.02989
$220$	−4.11619	−0.277513
$221$	−1.85269	−0.124626
$222$	−59.2882	−3.97916
$223$	24.1775	1.61904	0.809522	−	0.587089i	$-0.199726\pi$
$223$	24.1775	1.61904	0.809522	+	0.587089i	$0.199726\pi$
$224$	2.41346	0.161256
$225$	68.6660	4.57773
$226$	−2.59679	−0.172736
$227$	−1.14067	−0.0757091	−0.0378546	−	0.999283i	$-0.512052\pi$
$227$	−1.14067	−0.0757091	−0.0378546	+	0.999283i	$0.512052\pi$
$228$	−6.55349	−0.434016
$229$	8.95163	0.591541	0.295770	−	0.955259i	$-0.404424\pi$
$229$	8.95163	0.591541	0.295770	+	0.955259i	$0.404424\pi$
$230$	−19.6171	−1.29352
$231$	−1.42053	−0.0934643
$232$	8.92563	0.585996
$233$	−14.8340	−0.971807	−0.485903	−	0.874013i	$-0.661509\pi$
$233$	−14.8340	−0.971807	−0.485903	+	0.874013i	$0.661509\pi$
$234$	66.6716	4.35846
$235$	−44.7852	−2.92146
$236$	−7.49553	−0.487917
$237$	6.56822	0.426652
$238$	−0.313232	−0.0203038
$239$	9.81817	0.635084	0.317542	−	0.948244i	$-0.397142\pi$
$239$	9.81817	0.635084	0.317542	+	0.948244i	$0.397142\pi$
$240$	−61.1152	−3.94497
$241$	−0.933802	−0.0601515	−0.0300757	−	0.999548i	$-0.509575\pi$
$241$	−0.933802	−0.0601515	−0.0300757	+	0.999548i	$0.509575\pi$
$242$	−1.77267	−0.113951
$243$	−76.1908	−4.88764
$244$	3.47681	0.222580
$245$	24.5962	1.57139
$246$	−46.1393	−2.94173
$247$	−7.36551	−0.468656
$248$	−11.6266	−0.738293
$249$	41.4591	2.62736
$250$	19.0577	1.20531
$251$	11.0820	0.699490	0.349745	−	0.936845i	$-0.386268\pi$
$251$	11.0820	0.699490	0.349745	+	0.936845i	$0.386268\pi$
$252$	4.09775	0.258134
$253$	−3.07122	−0.193086
$254$	−13.8106	−0.866552
$255$	5.19966	0.325615
$256$	20.1749	1.26093
$257$	6.80784	0.424661	0.212331	−	0.977198i	$-0.431895\pi$
$257$	6.80784	0.424661	0.212331	+	0.977198i	$0.431895\pi$
$258$	−58.6500	−3.65139
$259$	−4.09546	−0.254480
$260$	17.9998	1.11630
$261$	50.4941	3.12551
$262$	1.77267	0.109516
$263$	−15.5864	−0.961101	−0.480551	−	0.876967i	$-0.659563\pi$
$263$	−15.5864	−0.961101	−0.480551	+	0.876967i	$0.659563\pi$
$264$	−5.17827	−0.318700
$265$	16.2671	0.999280
$266$	−1.24527	−0.0763526
$267$	−24.3681	−1.49131
$268$	7.04036	0.430058
$269$	−2.72747	−0.166297	−0.0831483	−	0.996537i	$-0.526498\pi$
$269$	−2.72747	−0.166297	−0.0831483	+	0.996537i	$0.526498\pi$
$270$	−121.850	−7.41553
$271$	21.5058	1.30639	0.653193	−	0.757192i	$-0.273429\pi$
$271$	21.5058	1.30639	0.653193	+	0.757192i	$0.273429\pi$
$272$	−2.10978	−0.127924
$273$	6.21189	0.375961
$274$	30.2013	1.82453
$275$	7.98363	0.481431
$276$	11.9496	0.719280
$277$	−13.8828	−0.834135	−0.417067	−	0.908876i	$-0.636942\pi$
$277$	−13.8828	−0.834135	−0.417067	+	0.908876i	$0.636942\pi$
$278$	20.5539	1.23274
$279$	−65.7743	−3.93780
$280$	−2.28478	−0.136542
$281$	9.34771	0.557638	0.278819	−	0.960344i	$-0.410057\pi$
$281$	9.34771	0.557638	0.278819	+	0.960344i	$0.410057\pi$
$282$	75.0427	4.46873
$283$	2.00284	0.119056	0.0595282	−	0.998227i	$-0.481040\pi$
$283$	2.00284	0.119056	0.0595282	+	0.998227i	$0.481040\pi$
$284$	13.1126	0.778093
$285$	20.6716	1.22448
$286$	7.75174	0.458370
$287$	−3.18717	−0.188133
$288$	49.7709	2.93278
$289$	−16.8205	−0.989441
$290$	37.4994	2.20204
$291$	−10.0820	−0.591015
$292$	−15.0384	−0.880053
$293$	23.6546	1.38191	0.690957	−	0.722896i	$-0.257189\pi$
$293$	23.6546	1.38191	0.690957	+	0.722896i	$0.257189\pi$
$294$	−41.2137	−2.40363
$295$	23.6430	1.37655
$296$	−14.9292	−0.867741
$297$	−19.0765	−1.10693
$298$	14.4443	0.836737
$299$	13.4302	0.776689
$300$	−31.0629	−1.79342
$301$	−4.05138	−0.233518
$302$	27.5173	1.58344
$303$	66.1940	3.80275
$304$	−8.38759	−0.481061
$305$	−10.9668	−0.627959
$306$	−6.45952	−0.369266
$307$	9.60919	0.548426	0.274213	−	0.961669i	$-0.411583\pi$
$307$	9.60919	0.548426	0.274213	+	0.961669i	$0.411583\pi$
$308$	0.476435	0.0271474
$309$	23.6016	1.34265
$310$	−48.8472	−2.77433
$311$	−9.36485	−0.531032	−0.265516	−	0.964106i	$-0.585542\pi$
$311$	−9.36485	−0.531032	−0.265516	+	0.964106i	$0.585542\pi$
$312$	22.6442	1.28197
$313$	0.533940	0.0301800	0.0150900	−	0.999886i	$-0.495197\pi$
$313$	0.533940	0.0301800	0.0150900	+	0.999886i	$0.495197\pi$
$314$	25.2671	1.42591
$315$	−12.9255	−0.728268
$316$	−2.20293	−0.123924
$317$	−13.4874	−0.757531	−0.378765	−	0.925493i	$-0.623651\pi$
$317$	−13.4874	−0.757531	−0.378765	+	0.925493i	$0.623651\pi$
$318$	−27.2574	−1.52852
$319$	5.87083	0.328703
$320$	1.07551	0.0601227
$321$	−38.9672	−2.17493
$322$	2.27062	0.126537
$323$	0.713613	0.0397065
$324$	44.7481	2.48600
$325$	−34.9118	−1.93656
$326$	3.99271	0.221136
$327$	−29.6809	−1.64136
$328$	−11.6182	−0.641508
$329$	5.18374	0.285789
$330$	−21.7555	−1.19760
$331$	1.43611	0.0789357	0.0394678	−	0.999221i	$-0.487434\pi$
$331$	1.43611	0.0789357	0.0394678	+	0.999221i	$0.487434\pi$
$332$	−13.9050	−0.763137
$333$	−84.4574	−4.62824
$334$	3.24026	0.177299
$335$	−22.2073	−1.21331
$336$	7.07389	0.385912
$337$	−3.86137	−0.210342	−0.105171	−	0.994454i	$-0.533539\pi$
$337$	−3.86137	−0.210342	−0.105171	+	0.994454i	$0.533539\pi$
$338$	−10.8531	−0.590332
$339$	−4.98947	−0.270991
$340$	−1.74392	−0.0945774
$341$	−7.64741	−0.414131
$342$	−25.6803	−1.38863
$343$	−5.76641	−0.311357
$344$	−14.7685	−0.796263
$345$	−37.6924	−2.02929
$346$	−43.4351	−2.33509
$347$	−6.40696	−0.343944	−0.171972	−	0.985102i	$-0.555014\pi$
$347$	−6.40696	−0.343944	−0.171972	+	0.985102i	$0.555014\pi$
$348$	−22.8424	−1.22448
$349$	−5.39545	−0.288812	−0.144406	−	0.989519i	$-0.546127\pi$
$349$	−5.39545	−0.288812	−0.144406	+	0.989519i	$0.546127\pi$
$350$	−5.90247	−0.315501
$351$	83.4202	4.45264
$352$	5.78674	0.308434
$353$	12.6663	0.674160	0.337080	−	0.941476i	$-0.390561\pi$
$353$	12.6663	0.674160	0.337080	+	0.941476i	$0.390561\pi$
$354$	−39.6166	−2.10560
$355$	−41.3610	−2.19522
$356$	8.17287	0.433161
$357$	−0.601843	−0.0318529
$358$	−1.53369	−0.0810580
$359$	16.4734	0.869434	0.434717	−	0.900567i	$-0.356848\pi$
$359$	16.4734	0.869434	0.434717	+	0.900567i	$0.356848\pi$
$360$	−47.1172	−2.48329
$361$	−16.1630	−0.850683
$362$	0.770750	0.0405097
$363$	−3.40600	−0.178769
$364$	−2.08342	−0.109201
$365$	47.4353	2.48288
$366$	18.3762	0.960539
$367$	15.3388	0.800681	0.400340	−	0.916367i	$-0.368892\pi$
$367$	15.3388	0.800681	0.400340	+	0.916367i	$0.368892\pi$
$368$	15.2939	0.797247
$369$	−65.7265	−3.42159
$370$	−62.7222	−3.26077
$371$	−1.88286	−0.0977534
$372$	29.7548	1.54271
$373$	30.5747	1.58310	0.791550	−	0.611104i	$-0.209274\pi$
$373$	30.5747	1.58310	0.791550	+	0.611104i	$0.209274\pi$
$374$	−0.751032	−0.0388350
$375$	36.6174	1.89092
$376$	18.8963	0.974501
$377$	−25.6727	−1.32221
$378$	14.1037	0.725416
$379$	28.2236	1.44975	0.724874	−	0.688882i	$-0.241898\pi$
$379$	28.2236	1.44975	0.724874	+	0.688882i	$0.241898\pi$
$380$	−6.93308	−0.355659
$381$	−26.5356	−1.35946
$382$	−15.9970	−0.818475
$383$	−3.17487	−0.162228	−0.0811142	−	0.996705i	$-0.525848\pi$
$383$	−3.17487	−0.162228	−0.0811142	+	0.996705i	$0.525848\pi$
$384$	37.6172	1.91964
$385$	−1.50281	−0.0765904
$386$	10.7103	0.545140
$387$	−83.5483	−4.24700
$388$	3.38140	0.171665
$389$	−1.96104	−0.0994286	−0.0497143	−	0.998763i	$-0.515831\pi$
$389$	−1.96104	−0.0994286	−0.0497143	+	0.998763i	$0.515831\pi$
$390$	95.1354	4.81737
$391$	−1.30119	−0.0658042
$392$	−10.3779	−0.524163
$393$	3.40600	0.171810
$394$	12.8548	0.647613
$395$	6.94866	0.349625
$396$	9.82514	0.493732
$397$	−35.1652	−1.76489	−0.882446	−	0.470413i	$-0.844105\pi$
$397$	−35.1652	−1.76489	−0.882446	+	0.470413i	$0.844105\pi$
$398$	−13.3536	−0.669356
$399$	−2.39267	−0.119783
$400$	−39.7564	−1.98782
$401$	−17.8734	−0.892556	−0.446278	−	0.894894i	$-0.647251\pi$
$401$	−17.8734	−0.892556	−0.446278	+	0.894894i	$0.647251\pi$
$402$	37.2108	1.85591
$403$	33.4416	1.66584
$404$	−22.2009	−1.10454
$405$	−141.148	−7.01371
$406$	−4.34043	−0.215412
$407$	−9.81966	−0.486742
$408$	−2.19390	−0.108614
$409$	−14.5296	−0.718441	−0.359220	−	0.933253i	$-0.616957\pi$
$409$	−14.5296	−0.718441	−0.359220	+	0.933253i	$0.616957\pi$
$410$	−48.8117	−2.41064
$411$	58.0288	2.86235
$412$	−7.91579	−0.389983
$413$	−2.73660	−0.134660
$414$	46.8251	2.30133
$415$	43.8604	2.15302
$416$	−25.3050	−1.24068
$417$	39.4924	1.93395
$418$	−2.98578	−0.146039
$419$	27.7088	1.35367	0.676833	−	0.736137i	$-0.263352\pi$
$419$	27.7088	1.35367	0.676833	+	0.736137i	$0.263352\pi$
$420$	5.84719	0.285314
$421$	2.35143	0.114602	0.0573008	−	0.998357i	$-0.481751\pi$
$421$	2.35143	0.114602	0.0573008	+	0.998357i	$0.481751\pi$
$422$	4.75890	0.231660
$423$	106.900	5.19766
$424$	−6.86360	−0.333326
$425$	3.38245	0.164073
$426$	69.3051	3.35784
$427$	1.26938	0.0614294
$428$	13.0693	0.631727
$429$	14.8942	0.719099
$430$	−62.0470	−2.99217
$431$	33.4823	1.61279	0.806394	−	0.591379i	$-0.201416\pi$
$431$	33.4823	1.61279	0.806394	+	0.591379i	$0.201416\pi$
$432$	94.9961	4.57050
$433$	24.1421	1.16019	0.580097	−	0.814547i	$-0.303015\pi$
$433$	24.1421	1.16019	0.580097	+	0.814547i	$0.303015\pi$
$434$	5.65390	0.271396
$435$	72.0514	3.45460
$436$	9.95471	0.476744
$437$	−5.17299	−0.247457
$438$	−79.4832	−3.79785
$439$	4.14611	0.197883	0.0989414	−	0.995093i	$-0.468454\pi$
$439$	4.14611	0.197883	0.0989414	+	0.995093i	$0.468454\pi$
$440$	−5.47820	−0.261163
$441$	−58.7099	−2.79571
$442$	3.28421	0.156214
$443$	14.3212	0.680423	0.340211	−	0.940349i	$-0.389501\pi$
$443$	14.3212	0.680423	0.340211	+	0.940349i	$0.389501\pi$
$444$	38.2066	1.81321
$445$	−25.7795	−1.22207
$446$	−42.8586	−2.02941
$447$	27.7533	1.31269
$448$	−0.124486	−0.00588143
$449$	−24.8127	−1.17098	−0.585491	−	0.810679i	$-0.699098\pi$
$449$	−24.8127	−1.17098	−0.585491	+	0.810679i	$0.699098\pi$
$450$	−121.722	−5.73803
$451$	−7.64186	−0.359841
$452$	1.67343	0.0787114
$453$	52.8718	2.48413
$454$	2.02203	0.0948987
$455$	6.57169	0.308086
$456$	−8.72199	−0.408444
$457$	32.0156	1.49763	0.748813	−	0.662781i	$-0.230624\pi$
$457$	32.0156	1.49763	0.748813	+	0.662781i	$0.230624\pi$
$458$	−15.8683	−0.741475
$459$	−8.08222	−0.377246
$460$	12.6417	0.589423
$461$	10.9649	0.510688	0.255344	−	0.966850i	$-0.417811\pi$
$461$	10.9649	0.510688	0.255344	+	0.966850i	$0.417811\pi$
$462$	2.51813	0.117154
$463$	24.3432	1.13133	0.565663	−	0.824636i	$-0.308620\pi$
$463$	24.3432	1.13133	0.565663	+	0.824636i	$0.308620\pi$
$464$	−29.2352	−1.35721
$465$	−93.8551	−4.35242
$466$	26.2957	1.21812
$467$	29.8189	1.37986	0.689928	−	0.723878i	$-0.257642\pi$
$467$	29.8189	1.37986	0.689928	+	0.723878i	$0.257642\pi$
$468$	−42.9646	−1.98604
$469$	2.57042	0.118691
$470$	79.3892	3.66195
$471$	48.5483	2.23699
$472$	−9.97573	−0.459170
$473$	−9.71395	−0.446648
$474$	−11.6433	−0.534793
$475$	13.4472	0.616999
$476$	0.201853	0.00925193
$477$	−38.8288	−1.77785
$478$	−17.4043	−0.796056
$479$	17.6397	0.805980	0.402990	−	0.915204i	$-0.367971\pi$
$479$	17.6397	0.805980	0.402990	+	0.915204i	$0.367971\pi$
$480$	71.0194	3.24158
$481$	42.9406	1.95792
$482$	1.65532	0.0753977
$483$	4.36277	0.198513
$484$	1.14234	0.0519248
$485$	−10.6659	−0.484314
$486$	135.061	6.12648
$487$	7.04448	0.319216	0.159608	−	0.987180i	$-0.448977\pi$
$487$	7.04448	0.319216	0.159608	+	0.987180i	$0.448977\pi$
$488$	4.62725	0.209466
$489$	7.67159	0.346921
$490$	−43.6008	−1.96968
$491$	3.93655	0.177654	0.0888269	−	0.996047i	$-0.471688\pi$
$491$	3.93655	0.177654	0.0888269	+	0.996047i	$0.471688\pi$
$492$	29.7332	1.34047
$493$	2.48732	0.112023
$494$	13.0566	0.587444
$495$	−30.9913	−1.39295
$496$	38.0821	1.70994
$497$	4.78740	0.214744
$498$	−73.4931	−3.29330
$499$	−7.12980	−0.319174	−0.159587	−	0.987184i	$-0.551016\pi$
$499$	−7.12980	−0.319174	−0.159587	+	0.987184i	$0.551016\pi$
$500$	−12.2812	−0.549231
$501$	6.22583	0.278150
$502$	−19.6447	−0.876786
$503$	−15.3907	−0.686235	−0.343118	−	0.939292i	$-0.611483\pi$
$503$	−15.3907	−0.686235	−0.343118	+	0.939292i	$0.611483\pi$
$504$	5.45366	0.242925
$505$	70.0280	3.11621
$506$	5.44424	0.242026
$507$	−20.8532	−0.926123
$508$	8.89983	0.394866
$509$	29.5495	1.30976	0.654878	−	0.755734i	$-0.272720\pi$
$509$	29.5495	1.30976	0.654878	+	0.755734i	$0.272720\pi$
$510$	−9.21725	−0.408147
$511$	−5.49048	−0.242884
$512$	−13.6747	−0.604342
$513$	−32.1314	−1.41864
$514$	−12.0680	−0.532298
$515$	24.9686	1.10025
$516$	37.7953	1.66385
$517$	12.4290	0.546627
$518$	7.25989	0.318981
$519$	−83.4563	−3.66332
$520$	23.9558	1.05053
$521$	−31.8002	−1.39319	−0.696596	−	0.717464i	$-0.745303\pi$
$521$	−31.8002	−1.39319	−0.696596	+	0.717464i	$0.745303\pi$
$522$	−89.5092	−3.91771
$523$	17.3593	0.759071	0.379536	−	0.925177i	$-0.376084\pi$
$523$	17.3593	0.759071	0.379536	+	0.925177i	$0.376084\pi$
$524$	−1.14234	−0.0499036
$525$	−11.3410	−0.494963
$526$	27.6296	1.20471
$527$	−3.24001	−0.141137
$528$	16.9610	0.738133
$529$	−13.5676	−0.589897
$530$	−28.8361	−1.25256
$531$	−56.4348	−2.44906
$532$	0.802481	0.0347920
$533$	33.4173	1.44746
$534$	43.1966	1.86930
$535$	−41.2242	−1.78228
$536$	9.36995	0.404720
$537$	−2.94683	−0.127165
$538$	4.83489	0.208447
$539$	−6.82605	−0.294019
$540$	78.5225	3.37907
$541$	−6.62293	−0.284742	−0.142371	−	0.989813i	$-0.545473\pi$
$541$	−6.62293	−0.284742	−0.142371	+	0.989813i	$0.545473\pi$
$542$	−38.1226	−1.63751
$543$	1.48092	0.0635523
$544$	2.45169	0.105115
$545$	−31.4000	−1.34503
$546$	−11.0116	−0.471254
$547$	−10.2804	−0.439559	−0.219780	−	0.975550i	$-0.570534\pi$
$547$	−10.2804	−0.439559	−0.219780	+	0.975550i	$0.570534\pi$
$548$	−19.4624	−0.831391
$549$	26.1773	1.11722
$550$	−14.1523	−0.603456
$551$	9.88849	0.421264
$552$	15.9036	0.676902
$553$	−0.804285	−0.0342017
$554$	24.6095	1.04556
$555$	−120.515	−5.11556
$556$	−13.2454	−0.561730
$557$	−2.11189	−0.0894835	−0.0447418	−	0.998999i	$-0.514247\pi$
$557$	−2.11189	−0.0894835	−0.0447418	+	0.998999i	$0.514247\pi$
$558$	116.596	4.93590
$559$	42.4784	1.79665
$560$	7.48361	0.316240
$561$	−1.44303	−0.0609250
$562$	−16.5704	−0.698979
$563$	43.6815	1.84096	0.920479	−	0.390793i	$-0.127799\pi$
$563$	43.6815	1.84096	0.920479	+	0.390793i	$0.127799\pi$
$564$	−48.3591	−2.03629
$565$	−5.27847	−0.222067
$566$	−3.55036	−0.149233
$567$	16.3374	0.686108
$568$	17.4515	0.732249
$569$	−4.37257	−0.183308	−0.0916538	−	0.995791i	$-0.529215\pi$
$569$	−4.37257	−0.183308	−0.0916538	+	0.995791i	$0.529215\pi$
$570$	−36.6438	−1.53484
$571$	−23.7055	−0.992044	−0.496022	−	0.868310i	$-0.665206\pi$
$571$	−23.7055	−0.992044	−0.496022	+	0.868310i	$0.665206\pi$
$572$	−4.99539	−0.208868
$573$	−30.7366	−1.28404
$574$	5.64980	0.235818
$575$	−24.5195	−1.02253
$576$	−2.56718	−0.106966
$577$	−6.70408	−0.279094	−0.139547	−	0.990215i	$-0.544565\pi$
$577$	−6.70408	−0.279094	−0.139547	+	0.990215i	$0.544565\pi$
$578$	29.8171	1.24023
$579$	20.5788	0.855226
$580$	−24.1654	−1.00341
$581$	−5.07670	−0.210617
$582$	17.8719	0.740816
$583$	−4.51453	−0.186973
$584$	−20.0144	−0.828203
$585$	135.523	5.60317
$586$	−41.9316	−1.73218
$587$	−21.7556	−0.897951	−0.448976	−	0.893544i	$-0.648211\pi$
$587$	−21.7556	−0.897951	−0.448976	+	0.893544i	$0.648211\pi$
$588$	26.5590	1.09528
$589$	−12.8809	−0.530747
$590$	−41.9112	−1.72546
$591$	24.6991	1.01599
$592$	48.8993	2.00975
$593$	−22.1562	−0.909845	−0.454923	−	0.890531i	$-0.650333\pi$
$593$	−22.1562	−0.909845	−0.454923	+	0.890531i	$0.650333\pi$
$594$	33.8163	1.38750
$595$	−0.636703	−0.0261023
$596$	−9.30823	−0.381280
$597$	−25.6577	−1.05010
$598$	−23.8073	−0.973552
$599$	27.4467	1.12144	0.560721	−	0.828005i	$-0.310524\pi$
$599$	27.4467	1.12144	0.560721	+	0.828005i	$0.310524\pi$
$600$	−41.3414	−1.68775
$601$	25.3856	1.03550	0.517751	−	0.855531i	$-0.326769\pi$
$601$	25.3856	1.03550	0.517751	+	0.855531i	$0.326769\pi$
$602$	7.18174	0.292706
$603$	53.0077	2.15864
$604$	−17.7327	−0.721535
$605$	−3.60328	−0.146494
$606$	−117.340	−4.76661
$607$	−13.4002	−0.543896	−0.271948	−	0.962312i	$-0.587668\pi$
$607$	−13.4002	−0.543896	−0.271948	+	0.962312i	$0.587668\pi$
$608$	9.74686	0.395287
$609$	−8.33971	−0.337942
$610$	19.4405	0.787125
$611$	−54.3511	−2.19881
$612$	4.16265	0.168265
$613$	35.3355	1.42719	0.713594	−	0.700560i	$-0.247066\pi$
$613$	35.3355	1.42719	0.713594	+	0.700560i	$0.247066\pi$
$614$	−17.0339	−0.687432
$615$	−93.7869	−3.78185
$616$	0.634084	0.0255480
$617$	−37.8485	−1.52372	−0.761861	−	0.647741i	$-0.775714\pi$
$617$	−37.8485	−1.52372	−0.761861	+	0.647741i	$0.775714\pi$
$618$	−41.8378	−1.68296
$619$	24.8326	0.998106	0.499053	−	0.866571i	$-0.333681\pi$
$619$	24.8326	0.998106	0.499053	+	0.866571i	$0.333681\pi$
$620$	31.4782	1.26419
$621$	58.5881	2.35106
$622$	16.6008	0.665630
$623$	2.98390	0.119547
$624$	−74.1692	−2.96914
$625$	−1.17981	−0.0471925
$626$	−0.946497	−0.0378296
$627$	−5.73688	−0.229109
$628$	−16.2827	−0.649750
$629$	−4.16033	−0.165883
$630$	22.9125	0.912858
$631$	−11.5227	−0.458712	−0.229356	−	0.973343i	$-0.573662\pi$
$631$	−11.5227	−0.458712	−0.229356	+	0.973343i	$0.573662\pi$
$632$	−2.93186	−0.116623
$633$	9.14375	0.363432
$634$	23.9087	0.949537
$635$	−28.0726	−1.11403
$636$	17.5652	0.696507
$637$	29.8498	1.18269
$638$	−10.4070	−0.412018
$639$	98.7267	3.90557
$640$	39.7960	1.57307
$641$	6.17581	0.243930	0.121965	−	0.992534i	$-0.461080\pi$
$641$	6.17581	0.243930	0.121965	+	0.992534i	$0.461080\pi$
$642$	69.0758	2.72620
$643$	−8.08391	−0.318798	−0.159399	−	0.987214i	$-0.550956\pi$
$643$	−8.08391	−0.318798	−0.159399	+	0.987214i	$0.550956\pi$
$644$	−1.46324	−0.0576596
$645$	−119.217	−4.69417
$646$	−1.26500	−0.0497706
$647$	29.6192	1.16445	0.582226	−	0.813027i	$-0.302182\pi$
$647$	29.6192	1.16445	0.582226	+	0.813027i	$0.302182\pi$
$648$	59.5548	2.33953
$649$	−6.56153	−0.257563
$650$	61.8870	2.42741
$651$	10.8634	0.425771
$652$	−2.57299	−0.100766
$653$	15.9979	0.626047	0.313024	−	0.949745i	$-0.398658\pi$
$653$	15.9979	0.626047	0.313024	+	0.949745i	$0.398658\pi$
$654$	52.6143	2.05738
$655$	3.60328	0.140792
$656$	38.0545	1.48578
$657$	−113.226	−4.41735
$658$	−9.18904	−0.358226
$659$	38.5924	1.50335	0.751674	−	0.659535i	$-0.229247\pi$
$659$	38.5924	1.50335	0.751674	+	0.659535i	$0.229247\pi$
$660$	14.0197	0.545718
$661$	−5.00143	−0.194533	−0.0972666	−	0.995258i	$-0.531010\pi$
$661$	−5.00143	−0.194533	−0.0972666	+	0.995258i	$0.531010\pi$
$662$	−2.54574	−0.0989431
$663$	6.31028	0.245071
$664$	−18.5061	−0.718175
$665$	−2.53125	−0.0981578
$666$	149.715	5.80133
$667$	−18.0306	−0.698147
$668$	−2.08809	−0.0807907
$669$	−82.3486	−3.18378
$670$	39.3661	1.52085
$671$	3.04357	0.117496
$672$	−8.22026	−0.317104
$673$	−17.5992	−0.678400	−0.339200	−	0.940714i	$-0.610156\pi$
$673$	−17.5992	−0.678400	−0.339200	+	0.940714i	$0.610156\pi$
$674$	6.84492	0.263657
$675$	−152.300	−5.86202
$676$	6.99399	0.269000
$677$	−45.2400	−1.73871	−0.869357	−	0.494184i	$-0.835467\pi$
$677$	−45.2400	−1.73871	−0.869357	+	0.494184i	$0.835467\pi$
$678$	8.84467	0.339677
$679$	1.23454	0.0473775
$680$	−2.32097	−0.0890051
$681$	3.88514	0.148879
$682$	13.5563	0.519098
$683$	−31.0994	−1.18998	−0.594992	−	0.803732i	$-0.702845\pi$
$683$	−31.0994	−1.18998	−0.594992	+	0.803732i	$0.702845\pi$
$684$	16.5489	0.632764
$685$	61.3898	2.34559
$686$	10.2219	0.390274
$687$	−30.4893	−1.16324
$688$	48.3730	1.84420
$689$	19.7417	0.752099
$690$	66.8160	2.54364
$691$	9.13069	0.347348	0.173674	−	0.984803i	$-0.444436\pi$
$691$	9.13069	0.347348	0.173674	+	0.984803i	$0.444436\pi$
$692$	27.9905	1.06404
$693$	3.58714	0.136264
$694$	11.3574	0.431121
$695$	41.7798	1.58480
$696$	−30.4007	−1.15234
$697$	−3.23766	−0.122635
$698$	9.56433	0.362015
$699$	50.5246	1.91102
$700$	3.80368	0.143766
$701$	28.7512	1.08592	0.542959	−	0.839759i	$-0.317304\pi$
$701$	28.7512	1.08592	0.542959	+	0.839759i	$0.317304\pi$
$702$	−147.876	−5.58123
$703$	−16.5397	−0.623806
$704$	−0.298480	−0.0112494
$705$	152.538	5.74493
$706$	−22.4532	−0.845036
$707$	−8.10552	−0.304839
$708$	25.5298	0.959468
$709$	−26.6469	−1.00075	−0.500373	−	0.865810i	$-0.666804\pi$
$709$	−26.6469	−1.00075	−0.500373	+	0.865810i	$0.666804\pi$
$710$	73.3193	2.75162
$711$	−16.5861	−0.622028
$712$	10.8772	0.407640
$713$	23.4869	0.879590
$714$	1.06687	0.0399265
$715$	15.7569	0.589274
$716$	0.988343	0.0369361
$717$	−33.4407	−1.24887
$718$	−29.2019	−1.08980
$719$	−0.185892	−0.00693260	−0.00346630	−	0.999994i	$-0.501103\pi$
$719$	−0.185892	−0.00693260	−0.00346630	+	0.999994i	$0.501103\pi$
$720$	154.328	5.75148
$721$	−2.89004	−0.107631
$722$	28.6516	1.06630
$723$	3.18053	0.118285
$724$	−0.496688	−0.0184593
$725$	46.8705	1.74073
$726$	6.03770	0.224080
$727$	47.9464	1.77823	0.889117	−	0.457679i	$-0.151319\pi$
$727$	47.9464	1.77823	0.889117	+	0.457679i	$0.151319\pi$
$728$	−2.77280	−0.102767
$729$	141.990	5.25887
$730$	−84.0869	−3.11220
$731$	−4.11555	−0.152219
$732$	−11.8420	−0.437693
$733$	26.8469	0.991612	0.495806	−	0.868433i	$-0.334873\pi$
$733$	26.8469	0.991612	0.495806	+	0.868433i	$0.334873\pi$
$734$	−27.1906	−1.00362
$735$	−83.7747	−3.09008
$736$	−17.7723	−0.655097
$737$	6.16308	0.227020
$738$	116.511	4.28883
$739$	14.9205	0.548858	0.274429	−	0.961607i	$-0.411511\pi$
$739$	14.9205	0.548858	0.274429	+	0.961607i	$0.411511\pi$
$740$	40.4196	1.48585
$741$	25.0870	0.921592
$742$	3.33769	0.122530
$743$	−16.1530	−0.592596	−0.296298	−	0.955096i	$-0.595752\pi$
$743$	−16.1530	−0.592596	−0.296298	+	0.955096i	$0.595752\pi$
$744$	39.6004	1.45182
$745$	29.3608	1.07570
$746$	−54.1988	−1.98436
$747$	−104.693	−3.83050
$748$	0.483982	0.0176961
$749$	4.77156	0.174349
$750$	−64.9105	−2.37020
$751$	12.5987	0.459735	0.229867	−	0.973222i	$-0.426171\pi$
$751$	12.5987	0.459735	0.229867	+	0.973222i	$0.426171\pi$
$752$	−61.8932	−2.25701
$753$	−37.7454	−1.37552
$754$	45.5091	1.65734
$755$	55.9341	2.03565
$756$	−9.08873	−0.330554
$757$	−48.0207	−1.74534	−0.872672	−	0.488308i	$-0.837614\pi$
$757$	−48.0207	−1.74534	−0.872672	+	0.488308i	$0.837614\pi$
$758$	−50.0310	−1.81721
$759$	10.4606	0.379695
$760$	−9.22717	−0.334705
$761$	−45.6105	−1.65338	−0.826690	−	0.562658i	$-0.809779\pi$
$761$	−45.6105	−1.65338	−0.826690	+	0.562658i	$0.809779\pi$
$762$	47.0388	1.70404
$763$	3.63445	0.131576
$764$	10.3088	0.372959
$765$	−13.1302	−0.474723
$766$	5.62799	0.203347
$767$	28.6931	1.03605
$768$	−68.7159	−2.47957
$769$	−8.12077	−0.292842	−0.146421	−	0.989222i	$-0.546775\pi$
$769$	−8.12077	−0.292842	−0.146421	+	0.989222i	$0.546775\pi$
$770$	2.66399	0.0960034
$771$	−23.1875	−0.835078
$772$	−6.90196	−0.248407
$773$	35.9257	1.29216	0.646079	−	0.763270i	$-0.276407\pi$
$773$	35.9257	1.29216	0.646079	+	0.763270i	$0.276407\pi$
$774$	148.103	5.32346
$775$	−61.0541	−2.19313
$776$	4.50028	0.161551
$777$	13.9492	0.500423
$778$	3.47627	0.124630
$779$	−12.8715	−0.461170
$780$	−61.3073	−2.19515
$781$	11.4787	0.410741
$782$	2.30658	0.0824832
$783$	−111.995	−4.00237
$784$	33.9920	1.21400
$785$	51.3603	1.83313
$786$	−6.03770	−0.215358
$787$	13.7593	0.490465	0.245233	−	0.969464i	$-0.421136\pi$
$787$	13.7593	0.490465	0.245233	+	0.969464i	$0.421136\pi$
$788$	−8.28389	−0.295101
$789$	53.0875	1.88996
$790$	−12.3176	−0.438242
$791$	0.610965	0.0217234
$792$	13.0762	0.464642
$793$	−13.3093	−0.472628
$794$	62.3362	2.21223
$795$	−55.4058	−1.96504
$796$	8.60536	0.305009
$797$	−4.54385	−0.160952	−0.0804758	−	0.996757i	$-0.525644\pi$
$797$	−4.54385	−0.160952	−0.0804758	+	0.996757i	$0.525644\pi$
$798$	4.24140	0.150144
$799$	5.26584	0.186292
$800$	46.1992	1.63339
$801$	61.5345	2.17422
$802$	31.6836	1.11879
$803$	−13.1645	−0.464564
$804$	−23.9795	−0.845691
$805$	4.61546	0.162674
$806$	−59.2808	−2.08808
$807$	9.28976	0.327015
$808$	−29.5470	−1.03946
$809$	−12.5572	−0.441489	−0.220745	−	0.975332i	$-0.570849\pi$
$809$	−12.5572	−0.441489	−0.220745	+	0.975332i	$0.570849\pi$
$810$	250.208	8.79143
$811$	−36.8013	−1.29227	−0.646134	−	0.763224i	$-0.723615\pi$
$811$	−36.8013	−1.29227	−0.646134	+	0.763224i	$0.723615\pi$
$812$	2.79707	0.0981579
$813$	−73.2489	−2.56895
$814$	17.4070	0.610114
$815$	8.11594	0.284289
$816$	7.18593	0.251558
$817$	−16.3616	−0.572421
$818$	25.7561	0.900540
$819$	−15.6863	−0.548124
$820$	31.4553	1.09847
$821$	29.8577	1.04204	0.521020	−	0.853544i	$-0.325552\pi$
$821$	29.8577	1.04204	0.521020	+	0.853544i	$0.325552\pi$
$822$	−102.866	−3.58785
$823$	−36.1248	−1.25923	−0.629616	−	0.776906i	$-0.716788\pi$
$823$	−36.1248	−1.25923	−0.629616	+	0.776906i	$0.716788\pi$
$824$	−10.5351	−0.367006
$825$	−27.1923	−0.946713
$826$	4.85109	0.168791
$827$	0.495615	0.0172342	0.00861711	−	0.999963i	$-0.497257\pi$
$827$	0.495615	0.0172342	0.00861711	+	0.999963i	$0.497257\pi$
$828$	−30.1751	−1.04866
$829$	−35.6525	−1.23826	−0.619132	−	0.785287i	$-0.712515\pi$
$829$	−35.6525	−1.23826	−0.619132	+	0.785287i	$0.712515\pi$
$830$	−77.7498	−2.69874
$831$	47.2848	1.64029
$832$	1.30523	0.0452508
$833$	−2.89202	−0.100203
$834$	−70.0068	−2.42414
$835$	6.58644	0.227933
$836$	1.92410	0.0665464
$837$	145.886	5.04256
$838$	−49.1185	−1.69677
$839$	−16.2964	−0.562614	−0.281307	−	0.959618i	$-0.590768\pi$
$839$	−16.2964	−0.562614	−0.281307	+	0.959618i	$0.590768\pi$
$840$	7.78197	0.268503
$841$	5.46660	0.188503
$842$	−4.16830	−0.143649
$843$	−31.8383	−1.09657
$844$	−3.06674	−0.105561
$845$	−22.0610	−0.758923
$846$	−189.498	−6.51508
$847$	0.417068	0.0143306
$848$	22.4812	0.772006
$849$	−6.82167	−0.234119
$850$	−5.99596	−0.205660
$851$	30.1583	1.03381
$852$	−44.6617	−1.53009
$853$	14.6746	0.502450	0.251225	−	0.967929i	$-0.419167\pi$
$853$	14.6746	0.502450	0.251225	+	0.967929i	$0.419167\pi$
$854$	−2.25018	−0.0769996
$855$	−52.2000	−1.78520
$856$	17.3938	0.594507
$857$	−27.0377	−0.923590	−0.461795	−	0.886987i	$-0.652794\pi$
$857$	−27.0377	−0.923590	−0.461795	+	0.886987i	$0.652794\pi$
$858$	−26.4024	−0.901364
$859$	−35.1765	−1.20021	−0.600103	−	0.799923i	$-0.704874\pi$
$859$	−35.1765	−1.20021	−0.600103	+	0.799923i	$0.704874\pi$
$860$	39.9845	1.36346
$861$	10.8555	0.369955
$862$	−59.3530	−2.02157
$863$	29.2403	0.995352	0.497676	−	0.867363i	$-0.334187\pi$
$863$	29.2403	0.995352	0.497676	+	0.867363i	$0.334187\pi$
$864$	−110.391	−3.75557
$865$	−88.2901	−3.00195
$866$	−42.7958	−1.45426
$867$	57.2907	1.94569
$868$	−3.64350	−0.123668
$869$	−1.92843	−0.0654174
$870$	−127.723	−4.33022
$871$	−26.9507	−0.913189
$872$	13.2486	0.448656
$873$	25.4590	0.861657
$874$	9.16998	0.310179
$875$	−4.48384	−0.151581
$876$	51.2207	1.73059
$877$	53.9024	1.82016	0.910078	−	0.414437i	$-0.136021\pi$
$877$	53.9024	1.82016	0.910078	+	0.414437i	$0.136021\pi$
$878$	−7.34966	−0.248039
$879$	−80.5675	−2.71747
$880$	17.9434	0.604872
$881$	−14.6589	−0.493872	−0.246936	−	0.969032i	$-0.579424\pi$
$881$	−14.6589	−0.493872	−0.246936	+	0.969032i	$0.579424\pi$
$882$	104.073	3.50432
$883$	−21.1620	−0.712157	−0.356078	−	0.934456i	$-0.615886\pi$
$883$	−21.1620	−0.712157	−0.356078	+	0.934456i	$0.615886\pi$
$884$	−2.11642	−0.0711828
$885$	−80.5282	−2.70693
$886$	−25.3868	−0.852886
$887$	33.1873	1.11432	0.557161	−	0.830405i	$-0.311891\pi$
$887$	33.1873	1.11432	0.557161	+	0.830405i	$0.311891\pi$
$888$	50.8488	1.70638
$889$	3.24931	0.108978
$890$	45.6985	1.53182
$891$	39.1721	1.31232
$892$	27.6190	0.924753
$893$	20.9347	0.700554
$894$	−49.1974	−1.64541
$895$	−3.11751	−0.104207
$896$	−4.60625	−0.153884
$897$	−45.7433	−1.52732
$898$	43.9846	1.46778
$899$	−44.8966	−1.49739
$900$	78.4403	2.61468
$901$	−1.91269	−0.0637208
$902$	13.5465	0.451048
$903$	13.7990	0.459202
$904$	2.22715	0.0740739
$905$	1.56669	0.0520787
$906$	−93.7240	−3.11377
$907$	26.8500	0.891541	0.445770	−	0.895147i	$-0.352930\pi$
$907$	26.8500	0.891541	0.445770	+	0.895147i	$0.352930\pi$
$908$	−1.30304	−0.0432430
$909$	−167.153	−5.54413
$910$	−11.6494	−0.386174
$911$	16.4472	0.544920	0.272460	−	0.962167i	$-0.412163\pi$
$911$	16.4472	0.544920	0.272460	+	0.962167i	$0.412163\pi$
$912$	28.5682	0.945986
$913$	−12.1724	−0.402846
$914$	−56.7529	−1.87722
$915$	37.3531	1.23485
$916$	10.2259	0.337872
$917$	−0.417068	−0.0137728
$918$	14.3271	0.472864
$919$	−2.37748	−0.0784259	−0.0392129	−	0.999231i	$-0.512485\pi$
$919$	−2.37748	−0.0784259	−0.0392129	+	0.999231i	$0.512485\pi$
$920$	16.8247	0.554695
$921$	−32.7289	−1.07846
$922$	−19.4372	−0.640129
$923$	−50.1956	−1.65221
$924$	−1.62274	−0.0533842
$925$	−78.3965	−2.57766
$926$	−43.1524	−1.41808
$927$	−59.5989	−1.95749
$928$	33.9729	1.11522
$929$	19.6625	0.645106	0.322553	−	0.946551i	$-0.395459\pi$
$929$	19.6625	0.645106	0.322553	+	0.946551i	$0.395459\pi$
$930$	166.374	5.45561
$931$	−11.4974	−0.376813
$932$	−16.9455	−0.555069
$933$	31.8967	1.04425
$934$	−52.8590	−1.72960
$935$	−1.52662	−0.0499257
$936$	−57.1812	−1.86903
$937$	39.3088	1.28416	0.642081	−	0.766637i	$-0.278071\pi$
$937$	39.3088	1.28416	0.642081	+	0.766637i	$0.278071\pi$
$938$	−4.55650	−0.148775
$939$	−1.81860	−0.0593478
$940$	−51.1601	−1.66866
$941$	−5.10526	−0.166427	−0.0832133	−	0.996532i	$-0.526518\pi$
$941$	−5.10526	−0.166427	−0.0832133	+	0.996532i	$0.526518\pi$
$942$	−86.0599	−2.80398
$943$	23.4698	0.764282
$944$	32.6747	1.06347
$945$	28.6684	0.932585
$946$	17.2196	0.559857
$947$	−5.40473	−0.175630	−0.0878151	−	0.996137i	$-0.527988\pi$
$947$	−5.40473	−0.175630	−0.0878151	+	0.996137i	$0.527988\pi$
$948$	7.50317	0.243692
$949$	57.5672	1.86871
$950$	−23.8374	−0.773386
$951$	45.9383	1.48965
$952$	0.268645	0.00870682
$953$	33.6783	1.09095	0.545473	−	0.838128i	$-0.316350\pi$
$953$	33.6783	1.09095	0.545473	+	0.838128i	$0.316350\pi$
$954$	68.8304	2.22847
$955$	−32.5168	−1.05222
$956$	11.2157	0.362743
$957$	−19.9960	−0.646380
$958$	−31.2694	−1.01027
$959$	−7.10568	−0.229454
$960$	−3.66318	−0.118229
$961$	27.4830	0.886547
$962$	−76.1194	−2.45419
$963$	98.4001	3.17090
$964$	−1.06672	−0.0343569
$965$	21.7707	0.700825
$966$	−7.73373	−0.248829
$967$	56.1552	1.80583	0.902914	−	0.429821i	$-0.141423\pi$
$967$	56.1552	1.80583	0.902914	+	0.429821i	$0.141423\pi$
$968$	1.52034	0.0488655
$969$	−2.43057	−0.0780810
$970$	18.9071	0.607070
$971$	−40.4356	−1.29764	−0.648820	−	0.760942i	$-0.724737\pi$
$971$	−40.4356	−1.29764	−0.648820	+	0.760942i	$0.724737\pi$
$972$	−87.0361	−2.79168
$973$	−4.83587	−0.155031
$974$	−12.4875	−0.400126
$975$	118.910	3.80816
$976$	−15.1562	−0.485138
$977$	21.9702	0.702888	0.351444	−	0.936209i	$-0.385691\pi$
$977$	21.9702	0.702888	0.351444	+	0.936209i	$0.385691\pi$
$978$	−13.5992	−0.434854
$979$	7.15447	0.228658
$980$	28.0973	0.897536
$981$	74.9503	2.39298
$982$	−6.97818	−0.222683
$983$	−41.2623	−1.31606	−0.658031	−	0.752991i	$-0.728611\pi$
$983$	−41.2623	−1.31606	−0.658031	+	0.752991i	$0.728611\pi$
$984$	39.5716	1.26150
$985$	26.1297	0.832563
$986$	−4.40918	−0.140417
$987$	−17.6558	−0.561991
$988$	−8.41395	−0.267684
$989$	29.8337	0.948655
$990$	54.9372	1.74602
$991$	−51.0805	−1.62262	−0.811312	−	0.584613i	$-0.801246\pi$
$991$	−51.0805	−1.62262	−0.811312	+	0.584613i	$0.801246\pi$
$992$	−44.2536	−1.40505
$993$	−4.89139	−0.155224
$994$	−8.48647	−0.269174
$995$	−27.1438	−0.860515
$996$	47.3605	1.50068
$997$	−43.8800	−1.38969	−0.694847	−	0.719157i	$-0.744528\pi$
$997$	−43.8800	−1.38969	−0.694847	+	0.719157i	$0.744528\pi$
$998$	12.6388	0.400073
$999$	187.325	5.92670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.e.1.6	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.e.1.6	✓	28	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-1.77267 q^{2} -3.40600 q^{3} +1.14234 q^{4} -3.60328 q^{5} +6.03770 q^{6} +0.417068 q^{7} +1.52034 q^{8} +8.60085 q^{9} +O(q^{10})\)	\(q-1.77267 q^{2} -3.40600 q^{3} +1.14234 q^{4} -3.60328 q^{5} +6.03770 q^{6} +0.417068 q^{7} +1.52034 q^{8} +8.60085 q^{9} +6.38741 q^{10} +1.00000 q^{11} -3.89083 q^{12} -4.37293 q^{13} -0.739322 q^{14} +12.2728 q^{15} -4.97974 q^{16} +0.423674 q^{17} -15.2464 q^{18} +1.68434 q^{19} -4.11619 q^{20} -1.42053 q^{21} -1.77267 q^{22} -3.07122 q^{23} -5.17827 q^{24} +7.98363 q^{25} +7.75174 q^{26} -19.0765 q^{27} +0.476435 q^{28} +5.87083 q^{29} -21.7555 q^{30} -7.64741 q^{31} +5.78674 q^{32} -3.40600 q^{33} -0.751032 q^{34} -1.50281 q^{35} +9.82514 q^{36} -9.81966 q^{37} -2.98578 q^{38} +14.8942 q^{39} -5.47820 q^{40} -7.64186 q^{41} +2.51813 q^{42} -9.71395 q^{43} +1.14234 q^{44} -30.9913 q^{45} +5.44424 q^{46} +12.4290 q^{47} +16.9610 q^{48} -6.82605 q^{49} -14.1523 q^{50} -1.44303 q^{51} -4.99539 q^{52} -4.51453 q^{53} +33.8163 q^{54} -3.60328 q^{55} +0.634084 q^{56} -5.73688 q^{57} -10.4070 q^{58} -6.56153 q^{59} +14.0197 q^{60} +3.04357 q^{61} +13.5563 q^{62} +3.58714 q^{63} -0.298480 q^{64} +15.7569 q^{65} +6.03770 q^{66} +6.16308 q^{67} +0.483982 q^{68} +10.4606 q^{69} +2.66399 q^{70} +11.4787 q^{71} +13.0762 q^{72} -13.1645 q^{73} +17.4070 q^{74} -27.1923 q^{75} +1.92410 q^{76} +0.417068 q^{77} -26.4024 q^{78} -1.92843 q^{79} +17.9434 q^{80} +39.1721 q^{81} +13.5465 q^{82} -12.1724 q^{83} -1.62274 q^{84} -1.52662 q^{85} +17.2196 q^{86} -19.9960 q^{87} +1.52034 q^{88} +7.15447 q^{89} +54.9372 q^{90} -1.82381 q^{91} -3.50839 q^{92} +26.0471 q^{93} -22.0325 q^{94} -6.06916 q^{95} -19.7096 q^{96} +2.96006 q^{97} +12.1003 q^{98} +8.60085 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9 + 14 * q^10 + 28 * q^11 - 6 * q^12 + 3 * q^13 - q^14 + 19 * q^15 + 29 * q^16 + 9 * q^17 - 2 * q^18 + 20 * q^19 + 6 * q^20 + 6 * q^21 + 7 * q^22 + 24 * q^23 + 20 * q^24 + 23 * q^25 + 10 * q^26 - 20 * q^27 - 3 * q^28 + 43 * q^29 + 11 * q^30 + 3 * q^31 + 44 * q^32 - 2 * q^33 - 28 * q^34 + 32 * q^35 + 24 * q^36 - 4 * q^37 + 24 * q^38 + 37 * q^39 + 22 * q^40 + 32 * q^41 - 27 * q^42 + 25 * q^43 + 27 * q^44 - 36 * q^45 + 10 * q^46 + 19 * q^47 + 42 * q^48 + 17 * q^49 + q^50 + 39 * q^51 - 19 * q^52 + 5 * q^53 + 6 * q^54 + 3 * q^55 + 8 * q^56 + 2 * q^57 + 21 * q^58 + 44 * q^59 + 65 * q^60 + 28 * q^61 + 60 * q^62 - 8 * q^63 + 5 * q^64 + 33 * q^65 - q^66 + 7 * q^67 + 13 * q^68 - 22 * q^69 + 9 * q^70 + 117 * q^71 - 17 * q^72 + 7 * q^73 + 41 * q^74 - 40 * q^75 + 34 * q^76 + 7 * q^77 - 97 * q^78 + 48 * q^79 + 41 * q^80 + 40 * q^81 + 2 * q^82 + 22 * q^83 + 27 * q^84 + 30 * q^85 + 24 * q^86 + 37 * q^87 + 21 * q^88 - 6 * q^89 + 4 * q^90 - 33 * q^91 + 18 * q^92 + 5 * q^93 - 43 * q^94 + 64 * q^95 + 55 * q^96 - 50 * q^97 + 97 * q^98 + 28 * q^99

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