LMFDB - Embedded newform 1441.2.a.e.1.9

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			1.9
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)

$f(q)$	$=$	$q-1.01237 q^{2} -1.33231 q^{3} -0.975116 q^{4} +3.44940 q^{5} +1.34878 q^{6} +1.50282 q^{7} +3.01190 q^{8} -1.22496 q^{9} +O(q^{10})$	\(q-1.01237 q^{2} -1.33231 q^{3} -0.975116 q^{4} +3.44940 q^{5} +1.34878 q^{6} +1.50282 q^{7} +3.01190 q^{8} -1.22496 q^{9} -3.49205 q^{10} +1.00000 q^{11} +1.29915 q^{12} +5.15268 q^{13} -1.52140 q^{14} -4.59566 q^{15} -1.09892 q^{16} +3.32951 q^{17} +1.24011 q^{18} -1.84443 q^{19} -3.36357 q^{20} -2.00221 q^{21} -1.01237 q^{22} +5.95720 q^{23} -4.01278 q^{24} +6.89837 q^{25} -5.21640 q^{26} +5.62894 q^{27} -1.46542 q^{28} -4.75965 q^{29} +4.65249 q^{30} +1.13159 q^{31} -4.91130 q^{32} -1.33231 q^{33} -3.37068 q^{34} +5.18382 q^{35} +1.19448 q^{36} -6.93688 q^{37} +1.86724 q^{38} -6.86495 q^{39} +10.3893 q^{40} -12.7333 q^{41} +2.02697 q^{42} +11.3575 q^{43} -0.975116 q^{44} -4.22538 q^{45} -6.03087 q^{46} -0.187798 q^{47} +1.46409 q^{48} -4.74154 q^{49} -6.98367 q^{50} -4.43592 q^{51} -5.02446 q^{52} +10.4550 q^{53} -5.69855 q^{54} +3.44940 q^{55} +4.52634 q^{56} +2.45735 q^{57} +4.81850 q^{58} -9.24555 q^{59} +4.48130 q^{60} -7.30742 q^{61} -1.14559 q^{62} -1.84089 q^{63} +7.16987 q^{64} +17.7737 q^{65} +1.34878 q^{66} +7.00291 q^{67} -3.24666 q^{68} -7.93682 q^{69} -5.24792 q^{70} +10.3384 q^{71} -3.68946 q^{72} -3.06539 q^{73} +7.02266 q^{74} -9.19074 q^{75} +1.79853 q^{76} +1.50282 q^{77} +6.94984 q^{78} +4.22754 q^{79} -3.79061 q^{80} -3.82460 q^{81} +12.8908 q^{82} -2.76918 q^{83} +1.95239 q^{84} +11.4848 q^{85} -11.4980 q^{86} +6.34131 q^{87} +3.01190 q^{88} +2.67360 q^{89} +4.27763 q^{90} +7.74354 q^{91} -5.80896 q^{92} -1.50763 q^{93} +0.190120 q^{94} -6.36218 q^{95} +6.54336 q^{96} +2.37164 q^{97} +4.80017 q^{98} -1.22496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.01237	−0.715851	−0.357925	−	0.933750i	$-0.616516\pi$
$2$	−1.01237	−0.715851	−0.357925	+	0.933750i	$0.616516\pi$
$3$	−1.33231	−0.769208	−0.384604	−	0.923082i	$-0.625662\pi$
$3$	−1.33231	−0.769208	−0.384604	+	0.923082i	$0.625662\pi$
$4$	−0.975116	−0.487558
$5$	3.44940	1.54262	0.771309	−	0.636460i	$-0.219602\pi$
$5$	3.44940	1.54262	0.771309	+	0.636460i	$0.219602\pi$
$6$	1.34878	0.550638
$7$	1.50282	0.568011	0.284006	−	0.958823i	$-0.408337\pi$
$7$	1.50282	0.568011	0.284006	+	0.958823i	$0.408337\pi$
$8$	3.01190	1.06487
$9$	−1.22496	−0.408320
$10$	−3.49205	−1.10428
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.29915	0.375033
$13$	5.15268	1.42910	0.714549	−	0.699586i	$-0.246632\pi$
$13$	5.15268	1.42910	0.714549	+	0.699586i	$0.246632\pi$
$14$	−1.52140	−0.406611
$15$	−4.59566	−1.18659
$16$	−1.09892	−0.274729
$17$	3.32951	0.807524	0.403762	−	0.914864i	$-0.367702\pi$
$17$	3.32951	0.807524	0.403762	+	0.914864i	$0.367702\pi$
$18$	1.24011	0.292296
$19$	−1.84443	−0.423141	−0.211571	−	0.977363i	$-0.567858\pi$
$19$	−1.84443	−0.423141	−0.211571	+	0.977363i	$0.567858\pi$
$20$	−3.36357	−0.752116
$21$	−2.00221	−0.436919
$22$	−1.01237	−0.215837
$23$	5.95720	1.24216	0.621081	−	0.783746i	$-0.286694\pi$
$23$	5.95720	1.24216	0.621081	+	0.783746i	$0.286694\pi$
$24$	−4.01278	−0.819105
$25$	6.89837	1.37967
$26$	−5.21640	−1.02302
$27$	5.62894	1.08329
$28$	−1.46542	−0.276938
$29$	−4.75965	−0.883844	−0.441922	−	0.897053i	$-0.645703\pi$
$29$	−4.75965	−0.883844	−0.441922	+	0.897053i	$0.645703\pi$
$30$	4.65249	0.849424
$31$	1.13159	0.203240	0.101620	−	0.994823i	$-0.467597\pi$
$31$	1.13159	0.203240	0.101620	+	0.994823i	$0.467597\pi$
$32$	−4.91130	−0.868204
$33$	−1.33231	−0.231925
$34$	−3.37068	−0.578067
$35$	5.18382	0.876225
$36$	1.19448	0.199080
$37$	−6.93688	−1.14042	−0.570208	−	0.821500i	$-0.693137\pi$
$37$	−6.93688	−1.14042	−0.570208	+	0.821500i	$0.693137\pi$
$38$	1.86724	0.302906
$39$	−6.86495	−1.09927
$40$	10.3893	1.64269
$41$	−12.7333	−1.98861	−0.994305	−	0.106567i	$-0.966014\pi$
$41$	−12.7333	−1.98861	−0.994305	+	0.106567i	$0.966014\pi$
$42$	2.02697	0.312768
$43$	11.3575	1.73201	0.866004	−	0.500038i	$-0.166680\pi$
$43$	11.3575	1.73201	0.866004	+	0.500038i	$0.166680\pi$
$44$	−0.975116	−0.147004
$45$	−4.22538	−0.629882
$46$	−6.03087	−0.889203
$47$	−0.187798	−0.0273931	−0.0136966	−	0.999906i	$-0.504360\pi$
$47$	−0.187798	−0.0273931	−0.0136966	+	0.999906i	$0.504360\pi$
$48$	1.46409	0.211324
$49$	−4.74154	−0.677363
$50$	−6.98367	−0.987640
$51$	−4.43592	−0.621154
$52$	−5.02446	−0.696768
$53$	10.4550	1.43610	0.718049	−	0.695992i	$-0.245035\pi$
$53$	10.4550	1.43610	0.718049	+	0.695992i	$0.245035\pi$
$54$	−5.69855	−0.775474
$55$	3.44940	0.465117
$56$	4.52634	0.604858
$57$	2.45735	0.325484
$58$	4.81850	0.632700
$59$	−9.24555	−1.20367	−0.601834	−	0.798621i	$-0.705563\pi$
$59$	−9.24555	−1.20367	−0.601834	+	0.798621i	$0.705563\pi$
$60$	4.48130	0.578533
$61$	−7.30742	−0.935619	−0.467810	−	0.883829i	$-0.654957\pi$
$61$	−7.30742	−0.935619	−0.467810	+	0.883829i	$0.654957\pi$
$62$	−1.14559	−0.145489
$63$	−1.84089	−0.231930
$64$	7.16987	0.896234
$65$	17.7737	2.20455
$66$	1.34878	0.166023
$67$	7.00291	0.855541	0.427771	−	0.903887i	$-0.359299\pi$
$67$	7.00291	0.855541	0.427771	+	0.903887i	$0.359299\pi$
$68$	−3.24666	−0.393715
$69$	−7.93682	−0.955481
$70$	−5.24792	−0.627246
$71$	10.3384	1.22694	0.613471	−	0.789717i	$-0.289773\pi$
$71$	10.3384	1.22694	0.613471	+	0.789717i	$0.289773\pi$
$72$	−3.68946	−0.434807
$73$	−3.06539	−0.358777	−0.179388	−	0.983778i	$-0.557412\pi$
$73$	−3.06539	−0.358777	−0.179388	+	0.983778i	$0.557412\pi$
$74$	7.02266	0.816367
$75$	−9.19074	−1.06125
$76$	1.79853	0.206306
$77$	1.50282	0.171262
$78$	6.94984	0.786915
$79$	4.22754	0.475635	0.237818	−	0.971310i	$-0.423568\pi$
$79$	4.22754	0.475635	0.237818	+	0.971310i	$0.423568\pi$
$80$	−3.79061	−0.423803
$81$	−3.82460	−0.424955
$82$	12.8908	1.42355
$83$	−2.76918	−0.303957	−0.151978	−	0.988384i	$-0.548564\pi$
$83$	−2.76918	−0.303957	−0.151978	+	0.988384i	$0.548564\pi$
$84$	1.95239	0.213023
$85$	11.4848	1.24570
$86$	−11.4980	−1.23986
$87$	6.34131	0.679859
$88$	3.01190	0.321070
$89$	2.67360	0.283401	0.141701	−	0.989910i	$-0.454743\pi$
$89$	2.67360	0.283401	0.141701	+	0.989910i	$0.454743\pi$
$90$	4.27763	0.450901
$91$	7.74354	0.811744
$92$	−5.80896	−0.605626
$93$	−1.50763	−0.156334
$94$	0.190120	0.0196094
$95$	−6.36218	−0.652746
$96$	6.54336	0.667829
$97$	2.37164	0.240804	0.120402	−	0.992725i	$-0.461582\pi$
$97$	2.37164	0.240804	0.120402	+	0.992725i	$0.461582\pi$
$98$	4.80017	0.484891
$99$	−1.22496	−0.123113
$100$	−6.72671	−0.672671
$101$	2.80353	0.278962	0.139481	−	0.990225i	$-0.455457\pi$
$101$	2.80353	0.278962	0.139481	+	0.990225i	$0.455457\pi$
$102$	4.49078	0.444653
$103$	14.9596	1.47401	0.737007	−	0.675886i	$-0.236239\pi$
$103$	14.9596	1.47401	0.737007	+	0.675886i	$0.236239\pi$
$104$	15.5194	1.52180
$105$	−6.90643	−0.673999
$106$	−10.5842	−1.02803
$107$	−3.42967	−0.331558	−0.165779	−	0.986163i	$-0.553014\pi$
$107$	−3.42967	−0.331558	−0.165779	+	0.986163i	$0.553014\pi$
$108$	−5.48887	−0.528167
$109$	11.4621	1.09787	0.548936	−	0.835864i	$-0.315033\pi$
$109$	11.4621	1.09787	0.548936	+	0.835864i	$0.315033\pi$
$110$	−3.49205	−0.332954
$111$	9.24205	0.877216
$112$	−1.65147	−0.156049
$113$	1.56875	0.147575	0.0737877	−	0.997274i	$-0.476491\pi$
$113$	1.56875	0.147575	0.0737877	+	0.997274i	$0.476491\pi$
$114$	−2.48773	−0.232998
$115$	20.5488	1.91618
$116$	4.64121	0.430925
$117$	−6.31183	−0.583529
$118$	9.35988	0.861647
$119$	5.00364	0.458683
$120$	−13.8417	−1.26357
$121$	1.00000	0.0909091
$122$	7.39778	0.669764
$123$	16.9647	1.52965
$124$	−1.10343	−0.0990913
$125$	6.54822	0.585691
$126$	1.86365	0.166027
$127$	3.07129	0.272533	0.136267	−	0.990672i	$-0.456490\pi$
$127$	3.07129	0.272533	0.136267	+	0.990672i	$0.456490\pi$
$128$	2.56408	0.226635
$129$	−15.1317	−1.33227
$130$	−17.9935	−1.57813
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	1.29915	0.113077
$133$	−2.77184	−0.240349
$134$	−7.08950	−0.612440
$135$	19.4165	1.67110
$136$	10.0282	0.859908
$137$	−13.1132	−1.12034	−0.560169	−	0.828378i	$-0.689264\pi$
$137$	−13.1132	−1.12034	−0.560169	+	0.828378i	$0.689264\pi$
$138$	8.03496	0.683982
$139$	23.2460	1.97170	0.985851	−	0.167626i	$-0.0536102\pi$
$139$	23.2460	1.97170	0.985851	+	0.167626i	$0.0536102\pi$
$140$	−5.05482	−0.427211
$141$	0.250204	0.0210710
$142$	−10.4662	−0.878307
$143$	5.15268	0.430889
$144$	1.34613	0.112177
$145$	−16.4179	−1.36343
$146$	3.10330	0.256831
$147$	6.31719	0.521033
$148$	6.76426	0.556019
$149$	5.34093	0.437546	0.218773	−	0.975776i	$-0.429795\pi$
$149$	5.34093	0.437546	0.218773	+	0.975776i	$0.429795\pi$
$150$	9.30439	0.759700
$151$	9.82917	0.799886	0.399943	−	0.916540i	$-0.369030\pi$
$151$	9.82917	0.799886	0.399943	+	0.916540i	$0.369030\pi$
$152$	−5.55525	−0.450590
$153$	−4.07851	−0.329728
$154$	−1.52140	−0.122598
$155$	3.90332	0.313522
$156$	6.69413	0.535959
$157$	−5.02220	−0.400816	−0.200408	−	0.979713i	$-0.564227\pi$
$157$	−5.02220	−0.400816	−0.200408	+	0.979713i	$0.564227\pi$
$158$	−4.27981	−0.340484
$159$	−13.9292	−1.10466
$160$	−16.9411	−1.33931
$161$	8.95259	0.705563
$162$	3.87189	0.304204
$163$	−7.52232	−0.589194	−0.294597	−	0.955622i	$-0.595185\pi$
$163$	−7.52232	−0.589194	−0.294597	+	0.955622i	$0.595185\pi$
$164$	12.4165	0.969563
$165$	−4.59566	−0.357772
$166$	2.80342	0.217588
$167$	21.0900	1.63199	0.815996	−	0.578057i	$-0.196189\pi$
$167$	21.0900	1.63199	0.815996	+	0.578057i	$0.196189\pi$
$168$	−6.03047	−0.465261
$169$	13.5501	1.04232
$170$	−11.6268	−0.891736
$171$	2.25935	0.172777
$172$	−11.0749	−0.844454
$173$	20.2403	1.53884	0.769421	−	0.638742i	$-0.220545\pi$
$173$	20.2403	1.53884	0.769421	+	0.638742i	$0.220545\pi$
$174$	−6.41972	−0.486678
$175$	10.3670	0.783670
$176$	−1.09892	−0.0828340
$177$	12.3179	0.925871
$178$	−2.70666	−0.202873
$179$	15.5383	1.16138	0.580692	−	0.814123i	$-0.302782\pi$
$179$	15.5383	1.16138	0.580692	+	0.814123i	$0.302782\pi$
$180$	4.12023	0.307104
$181$	−17.8724	−1.32845	−0.664223	−	0.747534i	$-0.731238\pi$
$181$	−17.8724	−1.32845	−0.664223	+	0.747534i	$0.731238\pi$
$182$	−7.83929	−0.581087
$183$	9.73572	0.719685
$184$	17.9425	1.32274
$185$	−23.9281	−1.75923
$186$	1.52627	0.111912
$187$	3.32951	0.243478
$188$	0.183125	0.0133557
$189$	8.45927	0.615321
$190$	6.44085	0.467269
$191$	−18.8930	−1.36705	−0.683525	−	0.729927i	$-0.739554\pi$
$191$	−18.8930	−1.36705	−0.683525	+	0.729927i	$0.739554\pi$
$192$	−9.55246	−0.689390
$193$	−12.3750	−0.890771	−0.445386	−	0.895339i	$-0.646933\pi$
$193$	−12.3750	−0.890771	−0.445386	+	0.895339i	$0.646933\pi$
$194$	−2.40097	−0.172379
$195$	−23.6800	−1.69576
$196$	4.62355	0.330254
$197$	3.81732	0.271973	0.135986	−	0.990711i	$-0.456580\pi$
$197$	3.81732	0.271973	0.135986	+	0.990711i	$0.456580\pi$
$198$	1.24011	0.0881305
$199$	−22.9339	−1.62574	−0.812872	−	0.582443i	$-0.802097\pi$
$199$	−22.9339	−1.62574	−0.812872	+	0.582443i	$0.802097\pi$
$200$	20.7772	1.46917
$201$	−9.33002	−0.658089
$202$	−2.83820	−0.199695
$203$	−7.15288	−0.502033
$204$	4.32554	0.302848
$205$	−43.9223	−3.06767
$206$	−15.1446	−1.05517
$207$	−7.29733	−0.507200
$208$	−5.66237	−0.392615
$209$	−1.84443	−0.127582
$210$	6.99184	0.482483
$211$	−14.2706	−0.982428	−0.491214	−	0.871039i	$-0.663447\pi$
$211$	−14.2706	−0.982428	−0.491214	+	0.871039i	$0.663447\pi$
$212$	−10.1948	−0.700181
$213$	−13.7739	−0.943773
$214$	3.47208	0.237346
$215$	39.1767	2.67183
$216$	16.9538	1.15356
$217$	1.70058	0.115443
$218$	−11.6039	−0.785912
$219$	4.08404	0.275974
$220$	−3.36357	−0.226772
$221$	17.1559	1.15403
$222$	−9.35633	−0.627956
$223$	−10.0682	−0.674215	−0.337108	−	0.941466i	$-0.609449\pi$
$223$	−10.0682	−0.674215	−0.337108	+	0.941466i	$0.609449\pi$
$224$	−7.38079	−0.493150
$225$	−8.45022	−0.563348
$226$	−1.58815	−0.105642
$227$	−3.86772	−0.256710	−0.128355	−	0.991728i	$-0.540970\pi$
$227$	−3.86772	−0.256710	−0.128355	+	0.991728i	$0.540970\pi$
$228$	−2.39620	−0.158692
$229$	−13.4839	−0.891040	−0.445520	−	0.895272i	$-0.646981\pi$
$229$	−13.4839	−0.891040	−0.445520	+	0.895272i	$0.646981\pi$
$230$	−20.8029	−1.37170
$231$	−2.00221	−0.131736
$232$	−14.3356	−0.941178
$233$	−12.8930	−0.844649	−0.422325	−	0.906445i	$-0.638786\pi$
$233$	−12.8930	−0.844649	−0.422325	+	0.906445i	$0.638786\pi$
$234$	6.38988	0.417719
$235$	−0.647790	−0.0422571
$236$	9.01548	0.586858
$237$	−5.63238	−0.365862
$238$	−5.06551	−0.328348
$239$	15.2607	0.987134	0.493567	−	0.869708i	$-0.335693\pi$
$239$	15.2607	0.987134	0.493567	+	0.869708i	$0.335693\pi$
$240$	5.05025	0.325992
$241$	−2.33370	−0.150327	−0.0751633	−	0.997171i	$-0.523948\pi$
$241$	−2.33370	−0.150327	−0.0751633	+	0.997171i	$0.523948\pi$
$242$	−1.01237	−0.0650773
$243$	−11.7913	−0.756411
$244$	7.12558	0.456169
$245$	−16.3555	−1.04491
$246$	−17.1745	−1.09500
$247$	−9.50377	−0.604710
$248$	3.40825	0.216424
$249$	3.68940	0.233806
$250$	−6.62919	−0.419267
$251$	−1.87985	−0.118655	−0.0593276	−	0.998239i	$-0.518896\pi$
$251$	−1.87985	−0.118655	−0.0593276	+	0.998239i	$0.518896\pi$
$252$	1.79508	0.113079
$253$	5.95720	0.374526
$254$	−3.10927	−0.195093
$255$	−15.3013	−0.958203
$256$	−16.9355	−1.05847
$257$	17.6887	1.10339	0.551695	−	0.834046i	$-0.313981\pi$
$257$	17.6887	1.10339	0.551695	+	0.834046i	$0.313981\pi$
$258$	15.3188	0.953708
$259$	−10.4249	−0.647769
$260$	−17.3314	−1.07485
$261$	5.83037	0.360891
$262$	1.01237	0.0625442
$263$	6.34775	0.391419	0.195709	−	0.980662i	$-0.437299\pi$
$263$	6.34775	0.391419	0.195709	+	0.980662i	$0.437299\pi$
$264$	−4.01278	−0.246970
$265$	36.0633	2.21535
$266$	2.80612	0.172054
$267$	−3.56206	−0.217994
$268$	−6.82864	−0.417126
$269$	11.5034	0.701373	0.350686	−	0.936493i	$-0.385948\pi$
$269$	11.5034	0.701373	0.350686	+	0.936493i	$0.385948\pi$
$270$	−19.6566	−1.19626
$271$	−14.4073	−0.875184	−0.437592	−	0.899174i	$-0.644168\pi$
$271$	−14.4073	−0.875184	−0.437592	+	0.899174i	$0.644168\pi$
$272$	−3.65885	−0.221851
$273$	−10.3168	−0.624399
$274$	13.2754	0.801995
$275$	6.89837	0.415987
$276$	7.73932	0.465852
$277$	−17.5968	−1.05729	−0.528645	−	0.848843i	$-0.677300\pi$
$277$	−17.5968	−1.05729	−0.528645	+	0.848843i	$0.677300\pi$
$278$	−23.5335	−1.41144
$279$	−1.38615	−0.0829869
$280$	15.6132	0.933065
$281$	−3.73721	−0.222943	−0.111472	−	0.993768i	$-0.535556\pi$
$281$	−3.73721	−0.222943	−0.111472	+	0.993768i	$0.535556\pi$
$282$	−0.253298	−0.0150837
$283$	−5.97417	−0.355127	−0.177564	−	0.984109i	$-0.556822\pi$
$283$	−5.97417	−0.355127	−0.177564	+	0.984109i	$0.556822\pi$
$284$	−10.0811	−0.598205
$285$	8.47637	0.502097
$286$	−5.21640	−0.308452
$287$	−19.1359	−1.12955
$288$	6.01615	0.354505
$289$	−5.91438	−0.347905
$290$	16.6209	0.976015
$291$	−3.15975	−0.185228
$292$	2.98911	0.174925
$293$	25.7286	1.50308	0.751540	−	0.659687i	$-0.229311\pi$
$293$	25.7286	1.50308	0.751540	+	0.659687i	$0.229311\pi$
$294$	−6.39530	−0.372982
$295$	−31.8916	−1.85680
$296$	−20.8932	−1.21439
$297$	5.62894	0.326624
$298$	−5.40698	−0.313218
$299$	30.6956	1.77517
$300$	8.96203	0.517423
$301$	17.0683	0.983800
$302$	−9.95071	−0.572599
$303$	−3.73516	−0.214579
$304$	2.02688	0.116249
$305$	−25.2062	−1.44330
$306$	4.12894	0.236036
$307$	16.0632	0.916774	0.458387	−	0.888753i	$-0.348427\pi$
$307$	16.0632	0.916774	0.458387	+	0.888753i	$0.348427\pi$
$308$	−1.46542	−0.0835001
$309$	−19.9308	−1.13382
$310$	−3.95158	−0.224435
$311$	−14.7942	−0.838901	−0.419451	−	0.907778i	$-0.637777\pi$
$311$	−14.7942	−0.838901	−0.419451	+	0.907778i	$0.637777\pi$
$312$	−20.6766	−1.17058
$313$	31.1786	1.76232	0.881160	−	0.472818i	$-0.156763\pi$
$313$	31.1786	1.76232	0.881160	+	0.472818i	$0.156763\pi$
$314$	5.08431	0.286924
$315$	−6.34997	−0.357780
$316$	−4.12234	−0.231900
$317$	−5.64875	−0.317266	−0.158633	−	0.987338i	$-0.550709\pi$
$317$	−5.64875	−0.317266	−0.158633	+	0.987338i	$0.550709\pi$
$318$	14.1014	0.790770
$319$	−4.75965	−0.266489
$320$	24.7318	1.38255
$321$	4.56937	0.255037
$322$	−9.06329	−0.505077
$323$	−6.14105	−0.341697
$324$	3.72942	0.207190
$325$	35.5451	1.97169
$326$	7.61534	0.421775
$327$	−15.2711	−0.844492
$328$	−38.3516	−2.11761
$329$	−0.282226	−0.0155596
$330$	4.65249	0.256111
$331$	12.8647	0.707106	0.353553	−	0.935414i	$-0.384973\pi$
$331$	12.8647	0.707106	0.353553	+	0.935414i	$0.384973\pi$
$332$	2.70027	0.148197
$333$	8.49739	0.465654
$334$	−21.3508	−1.16826
$335$	24.1558	1.31977
$336$	2.20027	0.120034
$337$	15.2069	0.828372	0.414186	−	0.910192i	$-0.364066\pi$
$337$	15.2069	0.828372	0.414186	+	0.910192i	$0.364066\pi$
$338$	−13.7177	−0.746144
$339$	−2.09005	−0.113516
$340$	−11.1990	−0.607352
$341$	1.13159	0.0612792
$342$	−2.28729	−0.123683
$343$	−17.6454	−0.952761
$344$	34.2078	1.84436
$345$	−27.3773	−1.47394
$346$	−20.4906	−1.10158
$347$	3.38611	0.181776	0.0908881	−	0.995861i	$-0.471029\pi$
$347$	3.38611	0.181776	0.0908881	+	0.995861i	$0.471029\pi$
$348$	−6.18351	−0.331471
$349$	14.7182	0.787845	0.393923	−	0.919144i	$-0.371118\pi$
$349$	14.7182	0.787845	0.393923	+	0.919144i	$0.371118\pi$
$350$	−10.4952	−0.560991
$351$	29.0041	1.54813
$352$	−4.91130	−0.261773
$353$	19.9474	1.06169	0.530847	−	0.847468i	$-0.321874\pi$
$353$	19.9474	1.06169	0.530847	+	0.847468i	$0.321874\pi$
$354$	−12.4702	−0.662785
$355$	35.6613	1.89270
$356$	−2.60707	−0.138174
$357$	−6.66638	−0.352822
$358$	−15.7304	−0.831378
$359$	0.206532	0.0109004	0.00545018	−	0.999985i	$-0.498265\pi$
$359$	0.206532	0.0109004	0.00545018	+	0.999985i	$0.498265\pi$
$360$	−12.7264	−0.670742
$361$	−15.5981	−0.820951
$362$	18.0934	0.950969
$363$	−1.33231	−0.0699280
$364$	−7.55085	−0.395772
$365$	−10.5738	−0.553456
$366$	−9.85611	−0.515187
$367$	−17.7341	−0.925713	−0.462857	−	0.886433i	$-0.653175\pi$
$367$	−17.7341	−0.925713	−0.462857	+	0.886433i	$0.653175\pi$
$368$	−6.54647	−0.341258
$369$	15.5978	0.811989
$370$	24.2240	1.25934
$371$	15.7119	0.815720
$372$	1.47011	0.0762218
$373$	23.5714	1.22048	0.610241	−	0.792216i	$-0.291073\pi$
$373$	23.5714	1.22048	0.610241	+	0.792216i	$0.291073\pi$
$374$	−3.37068	−0.174294
$375$	−8.72424	−0.450518
$376$	−0.565629	−0.0291701
$377$	−24.5249	−1.26310
$378$	−8.56387	−0.440478
$379$	−14.3645	−0.737857	−0.368929	−	0.929458i	$-0.620275\pi$
$379$	−14.3645	−0.737857	−0.368929	+	0.929458i	$0.620275\pi$
$380$	6.20386	0.318251
$381$	−4.09190	−0.209634
$382$	19.1266	0.978603
$383$	28.9134	1.47741	0.738703	−	0.674031i	$-0.235438\pi$
$383$	28.9134	1.47741	0.738703	+	0.674031i	$0.235438\pi$
$384$	−3.41614	−0.174329
$385$	5.18382	0.264192
$386$	12.5280	0.637659
$387$	−13.9125	−0.707213
$388$	−2.31262	−0.117406
$389$	−9.19557	−0.466234	−0.233117	−	0.972449i	$-0.574893\pi$
$389$	−9.19557	−0.466234	−0.233117	+	0.972449i	$0.574893\pi$
$390$	23.9728	1.21391
$391$	19.8346	1.00308
$392$	−14.2811	−0.721303
$393$	1.33231	0.0672060
$394$	−3.86453	−0.194692
$395$	14.5825	0.733724
$396$	1.19448	0.0600247
$397$	−35.0262	−1.75791	−0.878957	−	0.476901i	$-0.841760\pi$
$397$	−35.0262	−1.75791	−0.878957	+	0.476901i	$0.841760\pi$
$398$	23.2175	1.16379
$399$	3.69294	0.184878
$400$	−7.58073	−0.379037
$401$	0.0783431	0.00391227	0.00195613	−	0.999998i	$-0.499377\pi$
$401$	0.0783431	0.00391227	0.00195613	+	0.999998i	$0.499377\pi$
$402$	9.44539	0.471093
$403$	5.83074	0.290450
$404$	−2.73377	−0.136010
$405$	−13.1926	−0.655544
$406$	7.24133	0.359381
$407$	−6.93688	−0.343848
$408$	−13.3606	−0.661447
$409$	−21.9306	−1.08440	−0.542198	−	0.840251i	$-0.682408\pi$
$409$	−21.9306	−1.08440	−0.542198	+	0.840251i	$0.682408\pi$
$410$	44.4655	2.19599
$411$	17.4708	0.861773
$412$	−14.5873	−0.718667
$413$	−13.8944	−0.683697
$414$	7.38757	0.363079
$415$	−9.55201	−0.468890
$416$	−25.3064	−1.24075
$417$	−30.9708	−1.51665
$418$	1.86724	0.0913296
$419$	−23.0370	−1.12543	−0.562717	−	0.826650i	$-0.690244\pi$
$419$	−23.0370	−1.12543	−0.562717	+	0.826650i	$0.690244\pi$
$420$	6.73457	0.328614
$421$	−25.8828	−1.26145	−0.630724	−	0.776007i	$-0.717242\pi$
$421$	−25.8828	−1.26145	−0.630724	+	0.776007i	$0.717242\pi$
$422$	14.4471	0.703272
$423$	0.230045	0.0111851
$424$	31.4893	1.52926
$425$	22.9682	1.11412
$426$	13.9442	0.675601
$427$	−10.9817	−0.531443
$428$	3.34432	0.161654
$429$	−6.86495	−0.331443
$430$	−39.6611	−1.91263
$431$	−18.2391	−0.878545	−0.439273	−	0.898354i	$-0.644764\pi$
$431$	−18.2391	−0.878545	−0.439273	+	0.898354i	$0.644764\pi$
$432$	−6.18574	−0.297612
$433$	33.7103	1.62001	0.810007	−	0.586420i	$-0.199463\pi$
$433$	33.7103	1.62001	0.810007	+	0.586420i	$0.199463\pi$
$434$	−1.72160	−0.0826397
$435$	21.8737	1.04876
$436$	−11.1769	−0.535276
$437$	−10.9876	−0.525610
$438$	−4.13454	−0.197556
$439$	−40.6923	−1.94214	−0.971069	−	0.238800i	$-0.923246\pi$
$439$	−40.6923	−1.94214	−0.971069	+	0.238800i	$0.923246\pi$
$440$	10.3893	0.495289
$441$	5.80820	0.276581
$442$	−17.3680	−0.826113
$443$	3.03945	0.144408	0.0722042	−	0.997390i	$-0.476997\pi$
$443$	3.03945	0.144408	0.0722042	+	0.997390i	$0.476997\pi$
$444$	−9.01207	−0.427694
$445$	9.22232	0.437180
$446$	10.1927	0.482637
$447$	−7.11576	−0.336564
$448$	10.7750	0.509071
$449$	−14.2677	−0.673336	−0.336668	−	0.941623i	$-0.609300\pi$
$449$	−14.2677	−0.673336	−0.336668	+	0.941623i	$0.609300\pi$
$450$	8.55471	0.403273
$451$	−12.7333	−0.599589
$452$	−1.52971	−0.0719516
$453$	−13.0955	−0.615279
$454$	3.91555	0.183766
$455$	26.7106	1.25221
$456$	7.40130	0.346597
$457$	9.14817	0.427933	0.213967	−	0.976841i	$-0.431362\pi$
$457$	9.14817	0.427933	0.213967	+	0.976841i	$0.431362\pi$
$458$	13.6506	0.637851
$459$	18.7416	0.874783
$460$	−20.0374	−0.934251
$461$	37.9945	1.76958	0.884789	−	0.465992i	$-0.154302\pi$
$461$	37.9945	1.76958	0.884789	+	0.465992i	$0.154302\pi$
$462$	2.02697	0.0943032
$463$	−13.0965	−0.608645	−0.304323	−	0.952569i	$-0.598430\pi$
$463$	−13.0965	−0.608645	−0.304323	+	0.952569i	$0.598430\pi$
$464$	5.23046	0.242818
$465$	−5.20041	−0.241163
$466$	13.0524	0.604643
$467$	14.5476	0.673182	0.336591	−	0.941651i	$-0.390726\pi$
$467$	14.5476	0.673182	0.336591	+	0.941651i	$0.390726\pi$
$468$	6.15476	0.284504
$469$	10.5241	0.485957
$470$	0.655800	0.0302498
$471$	6.69112	0.308310
$472$	−27.8467	−1.28175
$473$	11.3575	0.522220
$474$	5.70202	0.261903
$475$	−12.7236	−0.583797
$476$	−4.87913	−0.223635
$477$	−12.8069	−0.586387
$478$	−15.4494	−0.706641
$479$	−26.1161	−1.19328	−0.596639	−	0.802510i	$-0.703497\pi$
$479$	−26.1161	−1.19328	−0.596639	+	0.802510i	$0.703497\pi$
$480$	22.5707	1.03021
$481$	−35.7435	−1.62976
$482$	2.36256	0.107611
$483$	−11.9276	−0.542724
$484$	−0.975116	−0.0443235
$485$	8.18074	0.371468
$486$	11.9371	0.541478
$487$	0.604823	0.0274072	0.0137036	−	0.999906i	$-0.495638\pi$
$487$	0.604823	0.0274072	0.0137036	+	0.999906i	$0.495638\pi$
$488$	−22.0093	−0.996312
$489$	10.0220	0.453212
$490$	16.5577	0.748002
$491$	34.9205	1.57594	0.787969	−	0.615715i	$-0.211133\pi$
$491$	34.9205	1.57594	0.787969	+	0.615715i	$0.211133\pi$
$492$	−16.5425	−0.745795
$493$	−15.8473	−0.713725
$494$	9.62129	0.432882
$495$	−4.22538	−0.189917
$496$	−1.24353	−0.0558360
$497$	15.5367	0.696917
$498$	−3.73502	−0.167370
$499$	23.6502	1.05873	0.529365	−	0.848394i	$-0.322430\pi$
$499$	23.6502	1.05873	0.529365	+	0.848394i	$0.322430\pi$
$500$	−6.38528	−0.285558
$501$	−28.0983	−1.25534
$502$	1.90310	0.0849394
$503$	−24.2946	−1.08324	−0.541622	−	0.840622i	$-0.682189\pi$
$503$	−24.2946	−1.08324	−0.541622	+	0.840622i	$0.682189\pi$
$504$	−5.54459	−0.246975
$505$	9.67050	0.430332
$506$	−6.03087	−0.268105
$507$	−18.0529	−0.801759
$508$	−2.99487	−0.132876
$509$	15.0150	0.665530	0.332765	−	0.943010i	$-0.392018\pi$
$509$	15.0150	0.665530	0.332765	+	0.943010i	$0.392018\pi$
$510$	15.4905	0.685930
$511$	−4.60672	−0.203789
$512$	12.0168	0.531072
$513$	−10.3822	−0.458385
$514$	−17.9074	−0.789862
$515$	51.6017	2.27384
$516$	14.7552	0.649560
$517$	−0.187798	−0.00825933
$518$	10.5538	0.463706
$519$	−26.9663	−1.18369
$520$	53.5326	2.34756
$521$	−21.8154	−0.955749	−0.477875	−	0.878428i	$-0.658593\pi$
$521$	−21.8154	−0.955749	−0.477875	+	0.878428i	$0.658593\pi$
$522$	−5.90247	−0.258344
$523$	−40.8905	−1.78802	−0.894009	−	0.448049i	$-0.852119\pi$
$523$	−40.8905	−1.78802	−0.894009	+	0.448049i	$0.852119\pi$
$524$	0.975116	0.0425981
$525$	−13.8120	−0.602805
$526$	−6.42624	−0.280197
$527$	3.76765	0.164121
$528$	1.46409	0.0637165
$529$	12.4883	0.542968
$530$	−36.5093	−1.58586
$531$	11.3254	0.491482
$532$	2.70287	0.117184
$533$	−65.6108	−2.84192
$534$	3.60610	0.156051
$535$	−11.8303	−0.511468
$536$	21.0921	0.911039
$537$	−20.7017	−0.893346
$538$	−11.6456	−0.502078
$539$	−4.74154	−0.204233
$540$	−18.9333	−0.814760
$541$	2.33836	0.100534	0.0502670	−	0.998736i	$-0.483993\pi$
$541$	2.33836	0.100534	0.0502670	+	0.998736i	$0.483993\pi$
$542$	14.5855	0.626501
$543$	23.8115	1.02185
$544$	−16.3522	−0.701096
$545$	39.5375	1.69360
$546$	10.4443	0.446977
$547$	12.8506	0.549453	0.274726	−	0.961522i	$-0.411413\pi$
$547$	12.8506	0.549453	0.274726	+	0.961522i	$0.411413\pi$
$548$	12.7869	0.546230
$549$	8.95129	0.382032
$550$	−6.98367	−0.297785
$551$	8.77884	0.373991
$552$	−23.9049	−1.01746
$553$	6.35322	0.270166
$554$	17.8144	0.756862
$555$	31.8795	1.35321
$556$	−22.6676	−0.961319
$557$	−10.4727	−0.443741	−0.221871	−	0.975076i	$-0.571216\pi$
$557$	−10.4727	−0.443741	−0.221871	+	0.975076i	$0.571216\pi$
$558$	1.40330	0.0594062
$559$	58.5218	2.47521
$560$	−5.69659	−0.240725
$561$	−4.43592	−0.187285
$562$	3.78342	0.159594
$563$	−7.87547	−0.331912	−0.165956	−	0.986133i	$-0.553071\pi$
$563$	−7.87547	−0.331912	−0.165956	+	0.986133i	$0.553071\pi$
$564$	−0.243978	−0.0102733
$565$	5.41124	0.227653
$566$	6.04804	0.254218
$567$	−5.74767	−0.241379
$568$	31.1383	1.30653
$569$	27.6899	1.16082	0.580410	−	0.814324i	$-0.302892\pi$
$569$	27.6899	1.16082	0.580410	+	0.814324i	$0.302892\pi$
$570$	−8.58119	−0.359426
$571$	−14.9225	−0.624489	−0.312244	−	0.950002i	$-0.601081\pi$
$571$	−14.9225	−0.624489	−0.312244	+	0.950002i	$0.601081\pi$
$572$	−5.02446	−0.210083
$573$	25.1713	1.05154
$574$	19.3725	0.808592
$575$	41.0950	1.71378
$576$	−8.78280	−0.365950
$577$	−0.511372	−0.0212887	−0.0106443	−	0.999943i	$-0.503388\pi$
$577$	−0.511372	−0.0212887	−0.0106443	+	0.999943i	$0.503388\pi$
$578$	5.98752	0.249048
$579$	16.4873	0.685188
$580$	16.0094	0.664753
$581$	−4.16157	−0.172651
$582$	3.19883	0.132596
$583$	10.4550	0.433000
$584$	−9.23267	−0.382051
$585$	−21.7720	−0.900162
$586$	−26.0467	−1.07598
$587$	24.4668	1.00985	0.504926	−	0.863162i	$-0.331520\pi$
$587$	24.4668	1.00985	0.504926	+	0.863162i	$0.331520\pi$
$588$	−6.15999	−0.254034
$589$	−2.08714	−0.0859993
$590$	32.2860	1.32919
$591$	−5.08584	−0.209204
$592$	7.62305	0.313306
$593$	−19.6562	−0.807182	−0.403591	−	0.914939i	$-0.632238\pi$
$593$	−19.6562	−0.807182	−0.403591	+	0.914939i	$0.632238\pi$
$594$	−5.69855	−0.233814
$595$	17.2596	0.707573
$596$	−5.20803	−0.213329
$597$	30.5550	1.25053
$598$	−31.0751	−1.27076
$599$	20.5100	0.838015	0.419008	−	0.907983i	$-0.362378\pi$
$599$	20.5100	0.838015	0.419008	+	0.907983i	$0.362378\pi$
$600$	−27.6816	−1.13010
$601$	47.5487	1.93955	0.969776	−	0.243995i	$-0.0784581\pi$
$601$	47.5487	1.93955	0.969776	+	0.243995i	$0.0784581\pi$
$602$	−17.2794	−0.704254
$603$	−8.57827	−0.349334
$604$	−9.58458	−0.389991
$605$	3.44940	0.140238
$606$	3.78135	0.153607
$607$	−11.9791	−0.486216	−0.243108	−	0.969999i	$-0.578167\pi$
$607$	−11.9791	−0.486216	−0.243108	+	0.969999i	$0.578167\pi$
$608$	9.05856	0.367373
$609$	9.52982	0.386168
$610$	25.5179	1.03319
$611$	−0.967662	−0.0391474
$612$	3.97702	0.160762
$613$	−7.41755	−0.299592	−0.149796	−	0.988717i	$-0.547862\pi$
$613$	−7.41755	−0.299592	−0.149796	+	0.988717i	$0.547862\pi$
$614$	−16.2618	−0.656273
$615$	58.5180	2.35967
$616$	4.52634	0.182372
$617$	2.68588	0.108129	0.0540647	−	0.998537i	$-0.482782\pi$
$617$	2.68588	0.108129	0.0540647	+	0.998537i	$0.482782\pi$
$618$	20.1772	0.811647
$619$	−16.6513	−0.669273	−0.334637	−	0.942347i	$-0.608614\pi$
$619$	−16.6513	−0.669273	−0.334637	+	0.942347i	$0.608614\pi$
$620$	−3.80619	−0.152860
$621$	33.5327	1.34562
$622$	14.9771	0.600528
$623$	4.01793	0.160975
$624$	7.54401	0.302002
$625$	−11.9044	−0.476175
$626$	−31.5642	−1.26156
$627$	2.45735	0.0981370
$628$	4.89723	0.195421
$629$	−23.0964	−0.920913
$630$	6.42849	0.256117
$631$	46.3469	1.84504	0.922520	−	0.385950i	$-0.126126\pi$
$631$	46.3469	1.84504	0.922520	+	0.385950i	$0.126126\pi$
$632$	12.7329	0.506489
$633$	19.0128	0.755691
$634$	5.71860	0.227115
$635$	10.5941	0.420415
$636$	13.5826	0.538585
$637$	−24.4317	−0.968018
$638$	4.81850	0.190766
$639$	−12.6641	−0.500985
$640$	8.84454	0.349611
$641$	−7.58865	−0.299734	−0.149867	−	0.988706i	$-0.547884\pi$
$641$	−7.58865	−0.299734	−0.149867	+	0.988706i	$0.547884\pi$
$642$	−4.62587	−0.182569
$643$	14.1754	0.559025	0.279512	−	0.960142i	$-0.409827\pi$
$643$	14.1754	0.559025	0.279512	+	0.960142i	$0.409827\pi$
$644$	−8.72981	−0.344003
$645$	−52.1953	−2.05519
$646$	6.21698	0.244604
$647$	7.65210	0.300835	0.150418	−	0.988623i	$-0.451938\pi$
$647$	7.65210	0.300835	0.150418	+	0.988623i	$0.451938\pi$
$648$	−11.5193	−0.452522
$649$	−9.24555	−0.362920
$650$	−35.9846	−1.41143
$651$	−2.26569	−0.0887993
$652$	7.33514	0.287266
$653$	−33.5888	−1.31443	−0.657216	−	0.753702i	$-0.728266\pi$
$653$	−33.5888	−1.31443	−0.657216	+	0.753702i	$0.728266\pi$
$654$	15.4599	0.604530
$655$	−3.44940	−0.134779
$656$	13.9929	0.546330
$657$	3.75498	0.146496
$658$	0.285715	0.0111383
$659$	34.3513	1.33814	0.669068	−	0.743201i	$-0.266693\pi$
$659$	34.3513	1.33814	0.669068	+	0.743201i	$0.266693\pi$
$660$	4.48130	0.174434
$661$	−43.9785	−1.71057	−0.855283	−	0.518161i	$-0.826617\pi$
$661$	−43.9785	−1.71057	−0.855283	+	0.518161i	$0.826617\pi$
$662$	−13.0238	−0.506183
$663$	−22.8569	−0.887689
$664$	−8.34050	−0.323674
$665$	−9.56119	−0.370767
$666$	−8.60247	−0.333339
$667$	−28.3542	−1.09788
$668$	−20.5652	−0.795691
$669$	13.4139	0.518611
$670$	−24.4545	−0.944761
$671$	−7.30742	−0.282100
$672$	9.83348	0.379335
$673$	−28.4134	−1.09526	−0.547628	−	0.836722i	$-0.684469\pi$
$673$	−28.4134	−1.09526	−0.547628	+	0.836722i	$0.684469\pi$
$674$	−15.3949	−0.592991
$675$	38.8305	1.49459
$676$	−13.2130	−0.508191
$677$	−26.7226	−1.02703	−0.513517	−	0.858079i	$-0.671658\pi$
$677$	−26.7226	−1.02703	−0.513517	+	0.858079i	$0.671658\pi$
$678$	2.11590	0.0812606
$679$	3.56414	0.136779
$680$	34.5911	1.32651
$681$	5.15299	0.197463
$682$	−1.14559	−0.0438667
$683$	−19.9280	−0.762523	−0.381262	−	0.924467i	$-0.624510\pi$
$683$	−19.9280	−0.762523	−0.381262	+	0.924467i	$0.624510\pi$
$684$	−2.20313	−0.0842388
$685$	−45.2328	−1.72826
$686$	17.8636	0.682035
$687$	17.9647	0.685394
$688$	−12.4810	−0.475833
$689$	53.8711	2.05232
$690$	27.7158	1.05512
$691$	−30.7674	−1.17045	−0.585224	−	0.810872i	$-0.698993\pi$
$691$	−30.7674	−1.17045	−0.585224	+	0.810872i	$0.698993\pi$
$692$	−19.7366	−0.750275
$693$	−1.84089	−0.0699296
$694$	−3.42799	−0.130125
$695$	80.1848	3.04158
$696$	19.0994	0.723961
$697$	−42.3957	−1.60585
$698$	−14.9002	−0.563979
$699$	17.1774	0.649711
$700$	−10.1090	−0.382085
$701$	−16.2167	−0.612495	−0.306247	−	0.951952i	$-0.599073\pi$
$701$	−16.2167	−0.612495	−0.306247	+	0.951952i	$0.599073\pi$
$702$	−29.3628	−1.10823
$703$	12.7946	0.482557
$704$	7.16987	0.270225
$705$	0.863054	0.0325045
$706$	−20.1941	−0.760014
$707$	4.21319	0.158453
$708$	−12.0114	−0.451416
$709$	42.0364	1.57871	0.789355	−	0.613937i	$-0.210415\pi$
$709$	42.0364	1.57871	0.789355	+	0.613937i	$0.210415\pi$
$710$	−36.1023	−1.35489
$711$	−5.17856	−0.194211
$712$	8.05263	0.301785
$713$	6.74113	0.252457
$714$	6.74882	0.252568
$715$	17.7737	0.664698
$716$	−15.1516	−0.566242
$717$	−20.3320	−0.759311
$718$	−0.209086	−0.00780302
$719$	−34.8037	−1.29796	−0.648979	−	0.760806i	$-0.724804\pi$
$719$	−34.8037	−1.29796	−0.648979	+	0.760806i	$0.724804\pi$
$720$	4.64334	0.173047
$721$	22.4815	0.837256
$722$	15.7910	0.587679
$723$	3.10920	0.115632
$724$	17.4277	0.647695
$725$	−32.8338	−1.21942
$726$	1.34878	0.0500580
$727$	15.9536	0.591687	0.295843	−	0.955236i	$-0.404399\pi$
$727$	15.9536	0.591687	0.295843	+	0.955236i	$0.404399\pi$
$728$	23.3228	0.864401
$729$	27.1834	1.00679
$730$	10.7045	0.396192
$731$	37.8150	1.39864
$732$	−9.49346	−0.350888
$733$	−31.2369	−1.15376	−0.576882	−	0.816828i	$-0.695731\pi$
$733$	−31.2369	−1.15376	−0.576882	+	0.816828i	$0.695731\pi$
$734$	17.9534	0.662672
$735$	21.7905	0.803755
$736$	−29.2576	−1.07845
$737$	7.00291	0.257955
$738$	−15.7907	−0.581263
$739$	−20.9895	−0.772112	−0.386056	−	0.922475i	$-0.626163\pi$
$739$	−20.9895	−0.772112	−0.386056	+	0.922475i	$0.626163\pi$
$740$	23.3326	0.857725
$741$	12.6619	0.465148
$742$	−15.9062	−0.583934
$743$	−23.0645	−0.846154	−0.423077	−	0.906094i	$-0.639050\pi$
$743$	−23.0645	−0.846154	−0.423077	+	0.906094i	$0.639050\pi$
$744$	−4.54083	−0.166475
$745$	18.4230	0.674967
$746$	−23.8629	−0.873683
$747$	3.39213	0.124112
$748$	−3.24666	−0.118709
$749$	−5.15416	−0.188329
$750$	8.83212	0.322503
$751$	−47.1126	−1.71916	−0.859581	−	0.511000i	$-0.829275\pi$
$751$	−47.1126	−1.71916	−0.859581	+	0.511000i	$0.829275\pi$
$752$	0.206374	0.00752569
$753$	2.50454	0.0912705
$754$	24.8282	0.904190
$755$	33.9047	1.23392
$756$	−8.24877	−0.300005
$757$	−43.4182	−1.57806	−0.789031	−	0.614353i	$-0.789417\pi$
$757$	−43.4182	−1.57806	−0.789031	+	0.614353i	$0.789417\pi$
$758$	14.5422	0.528195
$759$	−7.93682	−0.288088
$760$	−19.1623	−0.695089
$761$	35.2806	1.27892	0.639460	−	0.768824i	$-0.279158\pi$
$761$	35.2806	1.27892	0.639460	+	0.768824i	$0.279158\pi$
$762$	4.14250	0.150067
$763$	17.2255	0.623604
$764$	18.4229	0.666516
$765$	−14.0684	−0.508645
$766$	−29.2710	−1.05760
$767$	−47.6394	−1.72016
$768$	22.5633	0.814183
$769$	7.68124	0.276992	0.138496	−	0.990363i	$-0.455773\pi$
$769$	7.68124	0.276992	0.138496	+	0.990363i	$0.455773\pi$
$770$	−5.24792	−0.189122
$771$	−23.5667	−0.848735
$772$	12.0671	0.434303
$773$	24.3925	0.877336	0.438668	−	0.898649i	$-0.355450\pi$
$773$	24.3925	0.877336	0.438668	+	0.898649i	$0.355450\pi$
$774$	14.0846	0.506259
$775$	7.80614	0.280405
$776$	7.14316	0.256424
$777$	13.8891	0.498269
$778$	9.30928	0.333754
$779$	23.4857	0.841464
$780$	23.0907	0.826780
$781$	10.3384	0.369937
$782$	−20.0798	−0.718053
$783$	−26.7918	−0.957459
$784$	5.21056	0.186091
$785$	−17.3236	−0.618306
$786$	−1.34878	−0.0481094
$787$	−7.40704	−0.264032	−0.132016	−	0.991248i	$-0.542145\pi$
$787$	−7.40704	−0.264032	−0.132016	+	0.991248i	$0.542145\pi$
$788$	−3.72233	−0.132603
$789$	−8.45714	−0.301082
$790$	−14.7628	−0.525237
$791$	2.35754	0.0838245
$792$	−3.68946	−0.131099
$793$	−37.6528	−1.33709
$794$	35.4593	1.25840
$795$	−48.0474	−1.70407
$796$	22.3632	0.792644
$797$	−25.2522	−0.894478	−0.447239	−	0.894414i	$-0.647593\pi$
$797$	−25.2522	−0.894478	−0.447239	+	0.894414i	$0.647593\pi$
$798$	−3.73861	−0.132345
$799$	−0.625274	−0.0221206
$800$	−33.8800	−1.19784
$801$	−3.27505	−0.115718
$802$	−0.0793118	−0.00280060
$803$	−3.06539	−0.108175
$804$	9.09785	0.320856
$805$	30.8811	1.08841
$806$	−5.90284	−0.207919
$807$	−15.3260	−0.539501
$808$	8.44397	0.297058
$809$	45.8497	1.61199	0.805995	−	0.591923i	$-0.201631\pi$
$809$	45.8497	1.61199	0.805995	+	0.591923i	$0.201631\pi$
$810$	13.3557	0.469271
$811$	22.6055	0.793788	0.396894	−	0.917865i	$-0.370088\pi$
$811$	22.6055	0.793788	0.396894	+	0.917865i	$0.370088\pi$
$812$	6.97488	0.244770
$813$	19.1950	0.673198
$814$	7.02266	0.246144
$815$	−25.9475	−0.908902
$816$	4.87471	0.170649
$817$	−20.9482	−0.732884
$818$	22.2018	0.776266
$819$	−9.48552	−0.331451
$820$	42.8294	1.49567
$821$	31.2399	1.09028	0.545140	−	0.838345i	$-0.316476\pi$
$821$	31.2399	1.09028	0.545140	+	0.838345i	$0.316476\pi$
$822$	−17.6869	−0.616901
$823$	11.8232	0.412129	0.206065	−	0.978538i	$-0.433934\pi$
$823$	11.8232	0.412129	0.206065	+	0.978538i	$0.433934\pi$
$824$	45.0569	1.56963
$825$	−9.19074	−0.319980
$826$	14.0662	0.489425
$827$	34.0878	1.18535	0.592674	−	0.805443i	$-0.298072\pi$
$827$	34.0878	1.18535	0.592674	+	0.805443i	$0.298072\pi$
$828$	7.11574	0.247289
$829$	−31.4506	−1.09232	−0.546162	−	0.837679i	$-0.683912\pi$
$829$	−31.4506	−1.09232	−0.546162	+	0.837679i	$0.683912\pi$
$830$	9.67012	0.335655
$831$	23.4444	0.813276
$832$	36.9441	1.28081
$833$	−15.7870	−0.546987
$834$	31.3538	1.08569
$835$	72.7478	2.51754
$836$	1.79853	0.0622036
$837$	6.36967	0.220168
$838$	23.3219	0.805642
$839$	−16.7464	−0.578150	−0.289075	−	0.957306i	$-0.593348\pi$
$839$	−16.7464	−0.578150	−0.289075	+	0.957306i	$0.593348\pi$
$840$	−20.8015	−0.717721
$841$	−6.34578	−0.218820
$842$	26.2028	0.903009
$843$	4.97911	0.171490
$844$	13.9155	0.478991
$845$	46.7399	1.60790
$846$	−0.232889	−0.00800690
$847$	1.50282	0.0516374
$848$	−11.4891	−0.394538
$849$	7.95942	0.273167
$850$	−23.2522	−0.797543
$851$	−41.3244	−1.41658
$852$	13.4312	0.460144
$853$	47.4220	1.62370	0.811849	−	0.583868i	$-0.198461\pi$
$853$	47.4220	1.62370	0.811849	+	0.583868i	$0.198461\pi$
$854$	11.1175	0.380433
$855$	7.79341	0.266529
$856$	−10.3298	−0.353066
$857$	−21.7203	−0.741951	−0.370976	−	0.928643i	$-0.620977\pi$
$857$	−21.7203	−0.741951	−0.370976	+	0.928643i	$0.620977\pi$
$858$	6.94984	0.237264
$859$	8.17924	0.279072	0.139536	−	0.990217i	$-0.455439\pi$
$859$	8.17924	0.279072	0.139536	+	0.990217i	$0.455439\pi$
$860$	−38.2018	−1.30267
$861$	25.4948	0.868861
$862$	18.4646	0.628907
$863$	0.372499	0.0126800	0.00634000	−	0.999980i	$-0.497982\pi$
$863$	0.372499	0.0126800	0.00634000	+	0.999980i	$0.497982\pi$
$864$	−27.6454	−0.940517
$865$	69.8169	2.37385
$866$	−34.1272	−1.15969
$867$	7.87977	0.267611
$868$	−1.65826	−0.0562850
$869$	4.22754	0.143409
$870$	−22.1442	−0.750758
$871$	36.0838	1.22265
$872$	34.5228	1.16909
$873$	−2.90516	−0.0983249
$874$	11.1235	0.376259
$875$	9.84078	0.332679
$876$	−3.98241	−0.134553
$877$	13.2564	0.447637	0.223819	−	0.974631i	$-0.428148\pi$
$877$	13.2564	0.447637	0.223819	+	0.974631i	$0.428148\pi$
$878$	41.1955	1.39028
$879$	−34.2784	−1.15618
$880$	−3.79061	−0.127781
$881$	57.8130	1.94777	0.973885	−	0.227042i	$-0.0729053\pi$
$881$	57.8130	1.94777	0.973885	+	0.227042i	$0.0729053\pi$
$882$	−5.88002	−0.197990
$883$	3.89143	0.130957	0.0654785	−	0.997854i	$-0.479143\pi$
$883$	3.89143	0.130957	0.0654785	+	0.997854i	$0.479143\pi$
$884$	−16.7290	−0.562657
$885$	42.4894	1.42827
$886$	−3.07703	−0.103375
$887$	−5.62274	−0.188793	−0.0943965	−	0.995535i	$-0.530092\pi$
$887$	−5.62274	−0.188793	−0.0943965	+	0.995535i	$0.530092\pi$
$888$	27.8362	0.934121
$889$	4.61559	0.154802
$890$	−9.33636	−0.312955
$891$	−3.82460	−0.128129
$892$	9.81764	0.328719
$893$	0.346380	0.0115912
$894$	7.20375	0.240929
$895$	53.5977	1.79157
$896$	3.85334	0.128731
$897$	−40.8959	−1.36548
$898$	14.4442	0.482008
$899$	−5.38598	−0.179632
$900$	8.23994	0.274665
$901$	34.8099	1.15968
$902$	12.8908	0.429216
$903$	−22.7402	−0.756746
$904$	4.72492	0.157149
$905$	−61.6492	−2.04929
$906$	13.2574	0.440448
$907$	8.71123	0.289252	0.144626	−	0.989486i	$-0.453802\pi$
$907$	8.71123	0.289252	0.144626	+	0.989486i	$0.453802\pi$
$908$	3.77148	0.125161
$909$	−3.43421	−0.113906
$910$	−27.0409	−0.896396
$911$	47.0959	1.56036	0.780178	−	0.625558i	$-0.215129\pi$
$911$	47.0959	1.56036	0.780178	+	0.625558i	$0.215129\pi$
$912$	−2.70042	−0.0894199
$913$	−2.76918	−0.0916464
$914$	−9.26129	−0.306336
$915$	33.5824	1.11020
$916$	13.1483	0.434433
$917$	−1.50282	−0.0496274
$918$	−18.9734	−0.626214
$919$	−27.8976	−0.920256	−0.460128	−	0.887853i	$-0.652197\pi$
$919$	−27.8976	−0.920256	−0.460128	+	0.887853i	$0.652197\pi$
$920$	61.8910	2.04049
$921$	−21.4011	−0.705189
$922$	−38.4643	−1.26675
$923$	53.2705	1.75342
$924$	1.95239	0.0642289
$925$	−47.8531	−1.57340
$926$	13.2584	0.435699
$927$	−18.3249	−0.601869
$928$	23.3761	0.767357
$929$	−53.3878	−1.75160	−0.875798	−	0.482678i	$-0.839664\pi$
$929$	−53.3878	−1.75160	−0.875798	+	0.482678i	$0.839664\pi$
$930$	5.26472	0.172637
$931$	8.74544	0.286620
$932$	12.5722	0.411816
$933$	19.7104	0.645289
$934$	−14.7275	−0.481898
$935$	11.4848	0.375593
$936$	−19.0106	−0.621382
$937$	8.78258	0.286914	0.143457	−	0.989657i	$-0.454178\pi$
$937$	8.78258	0.286914	0.143457	+	0.989657i	$0.454178\pi$
$938$	−10.6542	−0.347873
$939$	−41.5395	−1.35559
$940$	0.631670	0.0206028
$941$	−40.3979	−1.31693	−0.658467	−	0.752609i	$-0.728795\pi$
$941$	−40.3979	−1.31693	−0.658467	+	0.752609i	$0.728795\pi$
$942$	−6.77386	−0.220704
$943$	−75.8550	−2.47018
$944$	10.1601	0.330683
$945$	29.1794	0.949206
$946$	−11.4980	−0.373831
$947$	−42.3695	−1.37682	−0.688412	−	0.725320i	$-0.741692\pi$
$947$	−42.3695	−1.37682	−0.688412	+	0.725320i	$0.741692\pi$
$948$	5.49222	0.178379
$949$	−15.7950	−0.512727
$950$	12.8809	0.417911
$951$	7.52587	0.244043
$952$	15.0705	0.488437
$953$	−39.5829	−1.28221	−0.641107	−	0.767451i	$-0.721525\pi$
$953$	−39.5829	−1.28221	−0.641107	+	0.767451i	$0.721525\pi$
$954$	12.9653	0.419766
$955$	−65.1695	−2.10884
$956$	−14.8810	−0.481285
$957$	6.34131	0.204985
$958$	26.4391	0.854208
$959$	−19.7068	−0.636365
$960$	−32.9503	−1.06347
$961$	−29.7195	−0.958694
$962$	36.1855	1.16667
$963$	4.20120	0.135382
$964$	2.27563	0.0732930
$965$	−42.6863	−1.37412
$966$	12.0751	0.388509
$967$	48.4661	1.55857	0.779283	−	0.626673i	$-0.215584\pi$
$967$	48.4661	1.55857	0.779283	+	0.626673i	$0.215584\pi$
$968$	3.01190	0.0968063
$969$	8.18175	0.262836
$970$	−8.28190	−0.265916
$971$	8.95364	0.287336	0.143668	−	0.989626i	$-0.454110\pi$
$971$	8.95364	0.287336	0.143668	+	0.989626i	$0.454110\pi$
$972$	11.4979	0.368794
$973$	34.9345	1.11995
$974$	−0.612302	−0.0196194
$975$	−47.3570	−1.51664
$976$	8.03025	0.257042
$977$	9.80696	0.313753	0.156876	−	0.987618i	$-0.449858\pi$
$977$	9.80696	0.313753	0.156876	+	0.987618i	$0.449858\pi$
$978$	−10.1460	−0.324432
$979$	2.67360	0.0854486
$980$	15.9485	0.509456
$981$	−14.0406	−0.448283
$982$	−35.3523	−1.12814
$983$	7.64757	0.243920	0.121960	−	0.992535i	$-0.461082\pi$
$983$	7.64757	0.243920	0.121960	+	0.992535i	$0.461082\pi$
$984$	51.0960	1.62888
$985$	13.1675	0.419551
$986$	16.0432	0.510921
$987$	0.376011	0.0119686
$988$	9.26727	0.294831
$989$	67.6591	2.15144
$990$	4.27763	0.135952
$991$	9.38542	0.298138	0.149069	−	0.988827i	$-0.452372\pi$
$991$	9.38542	0.298138	0.149069	+	0.988827i	$0.452372\pi$
$992$	−5.55759	−0.176454
$993$	−17.1397	−0.543912
$994$	−15.7288	−0.498889
$995$	−79.1083	−2.50790
$996$	−3.59759	−0.113994
$997$	51.8055	1.64070	0.820349	−	0.571863i	$-0.193779\pi$
$997$	51.8055	1.64070	0.820349	+	0.571863i	$0.193779\pi$
$998$	−23.9427	−0.757893
$999$	−39.0473	−1.23540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.e.1.9	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.e.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-1.01237 q^{2} -1.33231 q^{3} -0.975116 q^{4} +3.44940 q^{5} +1.34878 q^{6} +1.50282 q^{7} +3.01190 q^{8} -1.22496 q^{9} +O(q^{10})\)	\(q-1.01237 q^{2} -1.33231 q^{3} -0.975116 q^{4} +3.44940 q^{5} +1.34878 q^{6} +1.50282 q^{7} +3.01190 q^{8} -1.22496 q^{9} -3.49205 q^{10} +1.00000 q^{11} +1.29915 q^{12} +5.15268 q^{13} -1.52140 q^{14} -4.59566 q^{15} -1.09892 q^{16} +3.32951 q^{17} +1.24011 q^{18} -1.84443 q^{19} -3.36357 q^{20} -2.00221 q^{21} -1.01237 q^{22} +5.95720 q^{23} -4.01278 q^{24} +6.89837 q^{25} -5.21640 q^{26} +5.62894 q^{27} -1.46542 q^{28} -4.75965 q^{29} +4.65249 q^{30} +1.13159 q^{31} -4.91130 q^{32} -1.33231 q^{33} -3.37068 q^{34} +5.18382 q^{35} +1.19448 q^{36} -6.93688 q^{37} +1.86724 q^{38} -6.86495 q^{39} +10.3893 q^{40} -12.7333 q^{41} +2.02697 q^{42} +11.3575 q^{43} -0.975116 q^{44} -4.22538 q^{45} -6.03087 q^{46} -0.187798 q^{47} +1.46409 q^{48} -4.74154 q^{49} -6.98367 q^{50} -4.43592 q^{51} -5.02446 q^{52} +10.4550 q^{53} -5.69855 q^{54} +3.44940 q^{55} +4.52634 q^{56} +2.45735 q^{57} +4.81850 q^{58} -9.24555 q^{59} +4.48130 q^{60} -7.30742 q^{61} -1.14559 q^{62} -1.84089 q^{63} +7.16987 q^{64} +17.7737 q^{65} +1.34878 q^{66} +7.00291 q^{67} -3.24666 q^{68} -7.93682 q^{69} -5.24792 q^{70} +10.3384 q^{71} -3.68946 q^{72} -3.06539 q^{73} +7.02266 q^{74} -9.19074 q^{75} +1.79853 q^{76} +1.50282 q^{77} +6.94984 q^{78} +4.22754 q^{79} -3.79061 q^{80} -3.82460 q^{81} +12.8908 q^{82} -2.76918 q^{83} +1.95239 q^{84} +11.4848 q^{85} -11.4980 q^{86} +6.34131 q^{87} +3.01190 q^{88} +2.67360 q^{89} +4.27763 q^{90} +7.74354 q^{91} -5.80896 q^{92} -1.50763 q^{93} +0.190120 q^{94} -6.36218 q^{95} +6.54336 q^{96} +2.37164 q^{97} +4.80017 q^{98} -1.22496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) \) 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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