LMFDB - Embedded newform 547.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.36387 q^{2} -2.44170 q^{3} -0.139855 q^{4} -1.90373 q^{5} -3.33016 q^{6} +2.23580 q^{7} -2.91849 q^{8} +2.96188 q^{9} +O(q^{10})$	\(q+1.36387 q^{2} -2.44170 q^{3} -0.139855 q^{4} -1.90373 q^{5} -3.33016 q^{6} +2.23580 q^{7} -2.91849 q^{8} +2.96188 q^{9} -2.59645 q^{10} +2.42288 q^{11} +0.341484 q^{12} +5.43959 q^{13} +3.04934 q^{14} +4.64834 q^{15} -3.70073 q^{16} +1.99926 q^{17} +4.03962 q^{18} +1.90998 q^{19} +0.266247 q^{20} -5.45914 q^{21} +3.30450 q^{22} +1.41971 q^{23} +7.12606 q^{24} -1.37580 q^{25} +7.41890 q^{26} +0.0930818 q^{27} -0.312688 q^{28} +9.30532 q^{29} +6.33973 q^{30} -0.129027 q^{31} +0.789655 q^{32} -5.91594 q^{33} +2.72673 q^{34} -4.25636 q^{35} -0.414234 q^{36} -2.45855 q^{37} +2.60497 q^{38} -13.2818 q^{39} +5.55602 q^{40} +3.18489 q^{41} -7.44556 q^{42} -7.21883 q^{43} -0.338853 q^{44} -5.63863 q^{45} +1.93631 q^{46} +1.81119 q^{47} +9.03606 q^{48} -2.00121 q^{49} -1.87641 q^{50} -4.88158 q^{51} -0.760755 q^{52} +8.72073 q^{53} +0.126952 q^{54} -4.61252 q^{55} -6.52515 q^{56} -4.66360 q^{57} +12.6913 q^{58} +12.6428 q^{59} -0.650095 q^{60} -11.5806 q^{61} -0.175977 q^{62} +6.62216 q^{63} +8.47845 q^{64} -10.3555 q^{65} -8.06859 q^{66} -1.68158 q^{67} -0.279607 q^{68} -3.46651 q^{69} -5.80513 q^{70} -4.01218 q^{71} -8.64420 q^{72} +8.45831 q^{73} -3.35314 q^{74} +3.35928 q^{75} -0.267121 q^{76} +5.41708 q^{77} -18.1147 q^{78} -8.77007 q^{79} +7.04520 q^{80} -9.11291 q^{81} +4.34379 q^{82} +7.89542 q^{83} +0.763489 q^{84} -3.80605 q^{85} -9.84556 q^{86} -22.7208 q^{87} -7.07115 q^{88} +15.9441 q^{89} -7.69036 q^{90} +12.1618 q^{91} -0.198555 q^{92} +0.315046 q^{93} +2.47024 q^{94} -3.63610 q^{95} -1.92810 q^{96} +10.5256 q^{97} -2.72939 q^{98} +7.17629 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9}+O(q^{10}) $ 25 * q + 4 * q^2 + 8 * q^3 + 26 * q^4 + 29 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 29 * q^9	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9} - q^{10} + 10 q^{11} + 14 q^{12} + 19 q^{13} + 9 q^{14} + 5 q^{15} + 16 q^{16} + 40 q^{17} - 8 q^{18} + 33 q^{20} - 8 q^{21} - 10 q^{22} + 26 q^{23} - 16 q^{24} + 36 q^{25} - 8 q^{26} + 11 q^{27} - 8 q^{28} + 30 q^{29} - 20 q^{30} - 5 q^{31} + 6 q^{32} + 10 q^{33} - 7 q^{34} + 11 q^{35} + 13 q^{36} + 26 q^{37} + 25 q^{38} - 17 q^{39} - 25 q^{40} + 9 q^{41} - 16 q^{42} - 10 q^{43} + 64 q^{45} - 34 q^{46} + 28 q^{47} + 23 q^{48} + 20 q^{49} - 9 q^{50} - 9 q^{51} - 2 q^{52} + 80 q^{53} - 13 q^{54} - q^{55} + 7 q^{56} - 8 q^{57} - 24 q^{58} - 2 q^{59} - 14 q^{60} + 22 q^{61} + 36 q^{62} - 9 q^{63} - 28 q^{64} + 30 q^{65} - 42 q^{66} - 16 q^{67} + 59 q^{68} + 22 q^{69} - 61 q^{70} - q^{71} - 44 q^{72} + 2 q^{73} - 8 q^{74} - 31 q^{75} - 46 q^{76} + 67 q^{77} - q^{78} - 34 q^{79} + 30 q^{80} - 11 q^{81} - 4 q^{82} + 15 q^{83} - 87 q^{84} + 15 q^{85} - 44 q^{86} - 29 q^{87} - 55 q^{88} + 38 q^{89} - 90 q^{90} - 41 q^{91} + 40 q^{92} - 4 q^{93} - 46 q^{94} - 46 q^{95} - 87 q^{96} - 2 q^{97} - 14 q^{98} - 41 q^{99}+O(q^{100}) \) 25 * q + 4 * q^2 + 8 * q^3 + 26 * q^4 + 29 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 29 * q^9 - q^10 + 10 * q^11 + 14 * q^12 + 19 * q^13 + 9 * q^14 + 5 * q^15 + 16 * q^16 + 40 * q^17 - 8 * q^18 + 33 * q^20 - 8 * q^21 - 10 * q^22 + 26 * q^23 - 16 * q^24 + 36 * q^25 - 8 * q^26 + 11 * q^27 - 8 * q^28 + 30 * q^29 - 20 * q^30 - 5 * q^31 + 6 * q^32 + 10 * q^33 - 7 * q^34 + 11 * q^35 + 13 * q^36 + 26 * q^37 + 25 * q^38 - 17 * q^39 - 25 * q^40 + 9 * q^41 - 16 * q^42 - 10 * q^43 + 64 * q^45 - 34 * q^46 + 28 * q^47 + 23 * q^48 + 20 * q^49 - 9 * q^50 - 9 * q^51 - 2 * q^52 + 80 * q^53 - 13 * q^54 - q^55 + 7 * q^56 - 8 * q^57 - 24 * q^58 - 2 * q^59 - 14 * q^60 + 22 * q^61 + 36 * q^62 - 9 * q^63 - 28 * q^64 + 30 * q^65 - 42 * q^66 - 16 * q^67 + 59 * q^68 + 22 * q^69 - 61 * q^70 - q^71 - 44 * q^72 + 2 * q^73 - 8 * q^74 - 31 * q^75 - 46 * q^76 + 67 * q^77 - q^78 - 34 * q^79 + 30 * q^80 - 11 * q^81 - 4 * q^82 + 15 * q^83 - 87 * q^84 + 15 * q^85 - 44 * q^86 - 29 * q^87 - 55 * q^88 + 38 * q^89 - 90 * q^90 - 41 * q^91 + 40 * q^92 - 4 * q^93 - 46 * q^94 - 46 * q^95 - 87 * q^96 - 2 * q^97 - 14 * q^98 - 41 * 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 $

$2$	1.36387	0.964403	0.482201	−	0.876060i	$-0.339837\pi$
$2$	1.36387	0.964403	0.482201	+	0.876060i	$0.339837\pi$
$3$	−2.44170	−1.40971	−0.704857	−	0.709350i	$-0.748989\pi$
$3$	−2.44170	−1.40971	−0.704857	+	0.709350i	$0.748989\pi$
$4$	−0.139855	−0.0699276
$5$	−1.90373	−0.851376	−0.425688	−	0.904870i	$-0.639968\pi$
$5$	−1.90373	−0.851376	−0.425688	+	0.904870i	$0.639968\pi$
$6$	−3.33016	−1.35953
$7$	2.23580	0.845052	0.422526	−	0.906351i	$-0.361144\pi$
$7$	2.23580	0.845052	0.422526	+	0.906351i	$0.361144\pi$
$8$	−2.91849	−1.03184
$9$	2.96188	0.987293
$10$	−2.59645	−0.821069
$11$	2.42288	0.730527	0.365263	−	0.930904i	$-0.380979\pi$
$11$	2.42288	0.730527	0.365263	+	0.930904i	$0.380979\pi$
$12$	0.341484	0.0985780
$13$	5.43959	1.50867	0.754335	−	0.656489i	$-0.227959\pi$
$13$	5.43959	1.50867	0.754335	+	0.656489i	$0.227959\pi$
$14$	3.04934	0.814970
$15$	4.64834	1.20020
$16$	−3.70073	−0.925182
$17$	1.99926	0.484891	0.242446	−	0.970165i	$-0.422050\pi$
$17$	1.99926	0.484891	0.242446	+	0.970165i	$0.422050\pi$
$18$	4.03962	0.952148
$19$	1.90998	0.438180	0.219090	−	0.975705i	$-0.429691\pi$
$19$	1.90998	0.438180	0.219090	+	0.975705i	$0.429691\pi$
$20$	0.266247	0.0595347
$21$	−5.45914	−1.19128
$22$	3.30450	0.704522
$23$	1.41971	0.296031	0.148015	−	0.988985i	$-0.452711\pi$
$23$	1.41971	0.296031	0.148015	+	0.988985i	$0.452711\pi$
$24$	7.12606	1.45460
$25$	−1.37580	−0.275160
$26$	7.41890	1.45497
$27$	0.0930818	0.0179136
$28$	−0.312688	−0.0590925
$29$	9.30532	1.72795	0.863977	−	0.503531i	$-0.167966\pi$
$29$	9.30532	1.72795	0.863977	+	0.503531i	$0.167966\pi$
$30$	6.33973	1.15747
$31$	−0.129027	−0.0231740	−0.0115870	−	0.999933i	$-0.503688\pi$
$31$	−0.129027	−0.0231740	−0.0115870	+	0.999933i	$0.503688\pi$
$32$	0.789655	0.139593
$33$	−5.91594	−1.02983
$34$	2.72673	0.467630
$35$	−4.25636	−0.719457
$36$	−0.414234	−0.0690391
$37$	−2.45855	−0.404182	−0.202091	−	0.979367i	$-0.564774\pi$
$37$	−2.45855	−0.404182	−0.202091	+	0.979367i	$0.564774\pi$
$38$	2.60497	0.422582
$39$	−13.2818	−2.12679
$40$	5.55602	0.878484
$41$	3.18489	0.497397	0.248698	−	0.968581i	$-0.419997\pi$
$41$	3.18489	0.497397	0.248698	+	0.968581i	$0.419997\pi$
$42$	−7.44556	−1.14887
$43$	−7.21883	−1.10086	−0.550431	−	0.834881i	$-0.685537\pi$
$43$	−7.21883	−1.10086	−0.550431	+	0.834881i	$0.685537\pi$
$44$	−0.338853	−0.0510840
$45$	−5.63863	−0.840557
$46$	1.93631	0.285493
$47$	1.81119	0.264190	0.132095	−	0.991237i	$-0.457830\pi$
$47$	1.81119	0.264190	0.132095	+	0.991237i	$0.457830\pi$
$48$	9.03606	1.30424
$49$	−2.00121	−0.285887
$50$	−1.87641	−0.265365
$51$	−4.88158	−0.683557
$52$	−0.760755	−0.105498
$53$	8.72073	1.19788	0.598942	−	0.800792i	$-0.295588\pi$
$53$	8.72073	1.19788	0.598942	+	0.800792i	$0.295588\pi$
$54$	0.126952	0.0172759
$55$	−4.61252	−0.621953
$56$	−6.52515	−0.871959
$57$	−4.66360	−0.617709
$58$	12.6913	1.66644
$59$	12.6428	1.64595	0.822976	−	0.568076i	$-0.192312\pi$
$59$	12.6428	1.64595	0.822976	+	0.568076i	$0.192312\pi$
$60$	−0.650095	−0.0839269
$61$	−11.5806	−1.48274	−0.741372	−	0.671094i	$-0.765825\pi$
$61$	−11.5806	−1.48274	−0.741372	+	0.671094i	$0.765825\pi$
$62$	−0.175977	−0.0223491
$63$	6.62216	0.834314
$64$	8.47845	1.05981
$65$	−10.3555	−1.28445
$66$	−8.06859	−0.993174
$67$	−1.68158	−0.205437	−0.102719	−	0.994710i	$-0.532754\pi$
$67$	−1.68158	−0.205437	−0.102719	+	0.994710i	$0.532754\pi$
$68$	−0.279607	−0.0339073
$69$	−3.46651	−0.417319
$70$	−5.80513	−0.693846
$71$	−4.01218	−0.476158	−0.238079	−	0.971246i	$-0.576518\pi$
$71$	−4.01218	−0.476158	−0.238079	+	0.971246i	$0.576518\pi$
$72$	−8.64420	−1.01873
$73$	8.45831	0.989970	0.494985	−	0.868901i	$-0.335173\pi$
$73$	8.45831	0.989970	0.494985	+	0.868901i	$0.335173\pi$
$74$	−3.35314	−0.389795
$75$	3.35928	0.387896
$76$	−0.267121	−0.0306409
$77$	5.41708	0.617333
$78$	−18.1147	−2.05109
$79$	−8.77007	−0.986710	−0.493355	−	0.869828i	$-0.664230\pi$
$79$	−8.77007	−0.986710	−0.493355	+	0.869828i	$0.664230\pi$
$80$	7.04520	0.787678
$81$	−9.11291	−1.01255
$82$	4.34379	0.479691
$83$	7.89542	0.866635	0.433318	−	0.901241i	$-0.357343\pi$
$83$	7.89542	0.866635	0.433318	+	0.901241i	$0.357343\pi$
$84$	0.763489	0.0833035
$85$	−3.80605	−0.412824
$86$	−9.84556	−1.06167
$87$	−22.7208	−2.43592
$88$	−7.07115	−0.753788
$89$	15.9441	1.69007	0.845036	−	0.534710i	$-0.179579\pi$
$89$	15.9441	1.69007	0.845036	+	0.534710i	$0.179579\pi$
$90$	−7.69036	−0.810635
$91$	12.1618	1.27491
$92$	−0.198555	−0.0207007
$93$	0.315046	0.0326687
$94$	2.47024	0.254785
$95$	−3.63610	−0.373056
$96$	−1.92810	−0.196786
$97$	10.5256	1.06872	0.534358	−	0.845258i	$-0.320553\pi$
$97$	10.5256	1.06872	0.534358	+	0.845258i	$0.320553\pi$
$98$	−2.72939	−0.275710
$99$	7.17629	0.721244
$100$	0.192413	0.0192413
$101$	5.99517	0.596542	0.298271	−	0.954481i	$-0.403590\pi$
$101$	5.99517	0.596542	0.298271	+	0.954481i	$0.403590\pi$
$102$	−6.65784	−0.659225
$103$	−13.4662	−1.32686	−0.663432	−	0.748236i	$-0.730901\pi$
$103$	−13.4662	−1.32686	−0.663432	+	0.748236i	$0.730901\pi$
$104$	−15.8754	−1.55671
$105$	10.3927	1.01423
$106$	11.8940	1.15524
$107$	−5.56746	−0.538227	−0.269113	−	0.963108i	$-0.586731\pi$
$107$	−5.56746	−0.538227	−0.269113	+	0.963108i	$0.586731\pi$
$108$	−0.0130180	−0.00125266
$109$	11.1616	1.06909	0.534545	−	0.845140i	$-0.320483\pi$
$109$	11.1616	1.06909	0.534545	+	0.845140i	$0.320483\pi$
$110$	−6.29089	−0.599813
$111$	6.00302	0.569782
$112$	−8.27408	−0.781827
$113$	−10.3908	−0.977481	−0.488740	−	0.872429i	$-0.662543\pi$
$113$	−10.3908	−0.977481	−0.488740	+	0.872429i	$0.662543\pi$
$114$	−6.36055	−0.595720
$115$	−2.70276	−0.252033
$116$	−1.30140	−0.120832
$117$	16.1114	1.48950
$118$	17.2431	1.58736
$119$	4.46993	0.409758
$120$	−13.5661	−1.23841
$121$	−5.12964	−0.466331
$122$	−15.7945	−1.42996
$123$	−7.77654	−0.701187
$124$	0.0180452	0.00162050
$125$	12.1378	1.08564
$126$	9.03177	0.804614
$127$	−0.723940	−0.0642393	−0.0321196	−	0.999484i	$-0.510226\pi$
$127$	−0.723940	−0.0642393	−0.0321196	+	0.999484i	$0.510226\pi$
$128$	9.98420	0.882487
$129$	17.6262	1.55190
$130$	−14.1236	−1.23872
$131$	−4.05076	−0.353916	−0.176958	−	0.984218i	$-0.556626\pi$
$131$	−4.05076	−0.353916	−0.176958	+	0.984218i	$0.556626\pi$
$132$	0.827376	0.0720138
$133$	4.27034	0.370285
$134$	−2.29345	−0.198124
$135$	−0.177203	−0.0152512
$136$	−5.83481	−0.500330
$137$	2.66674	0.227835	0.113917	−	0.993490i	$-0.463660\pi$
$137$	2.66674	0.227835	0.113917	+	0.993490i	$0.463660\pi$
$138$	−4.72787	−0.402463
$139$	−6.34628	−0.538284	−0.269142	−	0.963100i	$-0.586740\pi$
$139$	−6.34628	−0.538284	−0.269142	+	0.963100i	$0.586740\pi$
$140$	0.595275	0.0503099
$141$	−4.42238	−0.372432
$142$	−5.47209	−0.459208
$143$	13.1795	1.10212
$144$	−10.9611	−0.913426
$145$	−17.7148	−1.47114
$146$	11.5360	0.954730
$147$	4.88635	0.403019
$148$	0.343841	0.0282635
$149$	8.33319	0.682681	0.341341	−	0.939940i	$-0.389119\pi$
$149$	8.33319	0.682681	0.341341	+	0.939940i	$0.389119\pi$
$150$	4.58163	0.374088
$151$	−5.10458	−0.415404	−0.207702	−	0.978192i	$-0.566598\pi$
$151$	−5.10458	−0.415404	−0.207702	+	0.978192i	$0.566598\pi$
$152$	−5.57426	−0.452132
$153$	5.92156	0.478729
$154$	7.38819	0.595358
$155$	0.245634	0.0197298
$156$	1.85753	0.148722
$157$	19.2489	1.53623	0.768113	−	0.640314i	$-0.221196\pi$
$157$	19.2489	1.53623	0.768113	+	0.640314i	$0.221196\pi$
$158$	−11.9612	−0.951586
$159$	−21.2934	−1.68867
$160$	−1.50329	−0.118846
$161$	3.17419	0.250161
$162$	−12.4288	−0.976502
$163$	17.6193	1.38005	0.690023	−	0.723787i	$-0.257600\pi$
$163$	17.6193	1.38005	0.690023	+	0.723787i	$0.257600\pi$
$164$	−0.445424	−0.0347818
$165$	11.2624	0.876775
$166$	10.7683	0.835785
$167$	−18.1793	−1.40675	−0.703376	−	0.710818i	$-0.748325\pi$
$167$	−18.1793	−1.40675	−0.703376	+	0.710818i	$0.748325\pi$
$168$	15.9324	1.22921
$169$	16.5891	1.27609
$170$	−5.19097	−0.398129
$171$	5.65714	0.432612
$172$	1.00959	0.0769807
$173$	0.443571	0.0337241	0.0168621	−	0.999858i	$-0.494632\pi$
$173$	0.443571	0.0337241	0.0168621	+	0.999858i	$0.494632\pi$
$174$	−30.9882	−2.34921
$175$	−3.07601	−0.232524
$176$	−8.96644	−0.675871
$177$	−30.8699	−2.32032
$178$	21.7457	1.62991
$179$	−15.1710	−1.13393	−0.566965	−	0.823742i	$-0.691883\pi$
$179$	−15.1710	−1.13393	−0.566965	+	0.823742i	$0.691883\pi$
$180$	0.788592	0.0587782
$181$	−6.85618	−0.509616	−0.254808	−	0.966992i	$-0.582012\pi$
$181$	−6.85618	−0.509616	−0.254808	+	0.966992i	$0.582012\pi$
$182$	16.5872	1.22952
$183$	28.2763	2.09025
$184$	−4.14342	−0.305457
$185$	4.68042	0.344111
$186$	0.429682	0.0315058
$187$	4.84397	0.354226
$188$	−0.253305	−0.0184742
$189$	0.208112	0.0151379
$190$	−4.95917	−0.359776
$191$	11.8727	0.859077	0.429538	−	0.903049i	$-0.358676\pi$
$191$	11.8727	0.859077	0.429538	+	0.903049i	$0.358676\pi$
$192$	−20.7018	−1.49402
$193$	14.2001	1.02214	0.511071	−	0.859538i	$-0.329249\pi$
$193$	14.2001	1.02214	0.511071	+	0.859538i	$0.329249\pi$
$194$	14.3556	1.03067
$195$	25.2851	1.81070
$196$	0.279880	0.0199914
$197$	−9.41099	−0.670505	−0.335253	−	0.942128i	$-0.608822\pi$
$197$	−9.41099	−0.670505	−0.335253	+	0.942128i	$0.608822\pi$
$198$	9.78753	0.695569
$199$	−1.19548	−0.0847455	−0.0423728	−	0.999102i	$-0.513492\pi$
$199$	−1.19548	−0.0847455	−0.0423728	+	0.999102i	$0.513492\pi$
$200$	4.01525	0.283921
$201$	4.10590	0.289608
$202$	8.17664	0.575307
$203$	20.8048	1.46021
$204$	0.682714	0.0477996
$205$	−6.06319	−0.423472
$206$	−18.3662	−1.27963
$207$	4.20502	0.292269
$208$	−20.1305	−1.39580
$209$	4.62767	0.320102
$210$	14.1744	0.978124
$211$	−11.4185	−0.786079	−0.393040	−	0.919522i	$-0.628576\pi$
$211$	−11.4185	−0.786079	−0.393040	+	0.919522i	$0.628576\pi$
$212$	−1.21964	−0.0837652
$213$	9.79651	0.671246
$214$	−7.59330	−0.519068
$215$	13.7427	0.937247
$216$	−0.271658	−0.0184840
$217$	−0.288479	−0.0195832
$218$	15.2230	1.03103
$219$	−20.6526	−1.39557
$220$	0.645086	0.0434917
$221$	10.8751	0.731541
$222$	8.18735	0.549499
$223$	20.0309	1.34137	0.670683	−	0.741744i	$-0.266001\pi$
$223$	20.0309	1.34137	0.670683	+	0.741744i	$0.266001\pi$
$224$	1.76551	0.117963
$225$	−4.07495	−0.271663
$226$	−14.1717	−0.942685
$227$	9.39944	0.623863	0.311931	−	0.950105i	$-0.399024\pi$
$227$	9.39944	0.623863	0.311931	+	0.950105i	$0.399024\pi$
$228$	0.652229	0.0431949
$229$	−20.2496	−1.33813	−0.669065	−	0.743204i	$-0.733305\pi$
$229$	−20.2496	−1.33813	−0.669065	+	0.743204i	$0.733305\pi$
$230$	−3.68621	−0.243062
$231$	−13.2269	−0.870263
$232$	−27.1574	−1.78297
$233$	−3.09326	−0.202646	−0.101323	−	0.994854i	$-0.532308\pi$
$233$	−3.09326	−0.202646	−0.101323	+	0.994854i	$0.532308\pi$
$234$	21.9739	1.43648
$235$	−3.44803	−0.224925
$236$	−1.76816	−0.115098
$237$	21.4138	1.39098
$238$	6.09641	0.395172
$239$	−24.4045	−1.57860	−0.789298	−	0.614010i	$-0.789555\pi$
$239$	−24.4045	−1.57860	−0.789298	+	0.614010i	$0.789555\pi$
$240$	−17.2022	−1.11040
$241$	15.1321	0.974746	0.487373	−	0.873194i	$-0.337955\pi$
$241$	15.1321	0.974746	0.487373	+	0.873194i	$0.337955\pi$
$242$	−6.99616	−0.449730
$243$	21.9717	1.40949
$244$	1.61961	0.103685
$245$	3.80977	0.243397
$246$	−10.6062	−0.676227
$247$	10.3895	0.661070
$248$	0.376565	0.0239119
$249$	−19.2782	−1.22171
$250$	16.5544	1.04699
$251$	−15.4258	−0.973670	−0.486835	−	0.873494i	$-0.661849\pi$
$251$	−15.4258	−0.973670	−0.486835	+	0.873494i	$0.661849\pi$
$252$	−0.926144	−0.0583416
$253$	3.43980	0.216259
$254$	−0.987361	−0.0619525
$255$	9.29322	0.581964
$256$	−3.33973	−0.208733
$257$	−25.3327	−1.58021	−0.790105	−	0.612972i	$-0.789974\pi$
$257$	−25.3327	−1.58021	−0.790105	+	0.612972i	$0.789974\pi$
$258$	24.0399	1.49666
$259$	−5.49681	−0.341555
$260$	1.44828	0.0898182
$261$	27.5612	1.70600
$262$	−5.52471	−0.341318
$263$	−25.4712	−1.57062	−0.785310	−	0.619102i	$-0.787497\pi$
$263$	−25.4712	−1.57062	−0.785310	+	0.619102i	$0.787497\pi$
$264$	17.2656	1.06262
$265$	−16.6019	−1.01985
$266$	5.82419	0.357104
$267$	−38.9307	−2.38252
$268$	0.235177	0.0143657
$269$	11.8123	0.720210	0.360105	−	0.932912i	$-0.382741\pi$
$269$	11.8123	0.720210	0.360105	+	0.932912i	$0.382741\pi$
$270$	−0.241682	−0.0147083
$271$	−30.5015	−1.85283	−0.926416	−	0.376501i	$-0.877127\pi$
$271$	−30.5015	−1.85283	−0.926416	+	0.376501i	$0.877127\pi$
$272$	−7.39871	−0.448613
$273$	−29.6955	−1.79725
$274$	3.63708	0.219724
$275$	−3.33340	−0.201012
$276$	0.484810	0.0291821
$277$	13.0412	0.783571	0.391785	−	0.920057i	$-0.371858\pi$
$277$	13.0412	0.783571	0.391785	+	0.920057i	$0.371858\pi$
$278$	−8.65551	−0.519123
$279$	−0.382164	−0.0228795
$280$	12.4221	0.742365
$281$	−9.84021	−0.587018	−0.293509	−	0.955956i	$-0.594823\pi$
$281$	−9.84021	−0.587018	−0.293509	+	0.955956i	$0.594823\pi$
$282$	−6.03156	−0.359174
$283$	−2.83778	−0.168688	−0.0843441	−	0.996437i	$-0.526880\pi$
$283$	−2.83778	−0.168688	−0.0843441	+	0.996437i	$0.526880\pi$
$284$	0.561124	0.0332966
$285$	8.87825	0.525902
$286$	17.9751	1.06289
$287$	7.12078	0.420326
$288$	2.33886	0.137819
$289$	−13.0030	−0.764881
$290$	−24.1608	−1.41877
$291$	−25.7004	−1.50658
$292$	−1.18294	−0.0692263
$293$	32.6961	1.91013	0.955065	−	0.296398i	$-0.0957854\pi$
$293$	32.6961	1.91013	0.955065	+	0.296398i	$0.0957854\pi$
$294$	6.66435	0.388673
$295$	−24.0685	−1.40132
$296$	7.17523	0.417052
$297$	0.225526	0.0130864
$298$	11.3654	0.658380
$299$	7.72266	0.446613
$300$	−0.469813	−0.0271247
$301$	−16.1398	−0.930285
$302$	−6.96198	−0.400617
$303$	−14.6384	−0.840953
$304$	−7.06833	−0.405397
$305$	22.0464	1.26237
$306$	8.07624	0.461688
$307$	21.8982	1.24979	0.624897	−	0.780707i	$-0.285141\pi$
$307$	21.8982	1.24979	0.624897	+	0.780707i	$0.285141\pi$
$308$	−0.757607	−0.0431687
$309$	32.8804	1.87050
$310$	0.335013	0.0190275
$311$	−2.47211	−0.140181	−0.0700903	−	0.997541i	$-0.522329\pi$
$311$	−2.47211	−0.140181	−0.0700903	+	0.997541i	$0.522329\pi$
$312$	38.7628	2.19451
$313$	−3.58862	−0.202841	−0.101420	−	0.994844i	$-0.532339\pi$
$313$	−3.58862	−0.202841	−0.101420	+	0.994844i	$0.532339\pi$
$314$	26.2530	1.48154
$315$	−12.6068	−0.710314
$316$	1.22654	0.0689983
$317$	−9.32599	−0.523800	−0.261900	−	0.965095i	$-0.584349\pi$
$317$	−9.32599	−0.523800	−0.261900	+	0.965095i	$0.584349\pi$
$318$	−29.0414	−1.62856
$319$	22.5457	1.26232
$320$	−16.1407	−0.902293
$321$	13.5941	0.758746
$322$	4.32919	0.241256
$323$	3.81855	0.212470
$324$	1.27449	0.0708049
$325$	−7.48378	−0.415125
$326$	24.0304	1.33092
$327$	−27.2533	−1.50711
$328$	−9.29507	−0.513235
$329$	4.04946	0.223254
$330$	15.3604	0.845564
$331$	−35.0673	−1.92747	−0.963736	−	0.266859i	$-0.914014\pi$
$331$	−35.0673	−1.92747	−0.963736	+	0.266859i	$0.914014\pi$
$332$	−1.10422	−0.0606018
$333$	−7.28191	−0.399046
$334$	−24.7942	−1.35668
$335$	3.20127	0.174904
$336$	20.2028	1.10215
$337$	16.2375	0.884516	0.442258	−	0.896888i	$-0.354178\pi$
$337$	16.2375	0.884516	0.442258	+	0.896888i	$0.354178\pi$
$338$	22.6254	1.23066
$339$	25.3711	1.37797
$340$	0.532297	0.0288678
$341$	−0.312618	−0.0169292
$342$	7.71561	0.417212
$343$	−20.1249	−1.08664
$344$	21.0681	1.13591
$345$	6.59931	0.355295
$346$	0.604974	0.0325236
$347$	0.706611	0.0379329	0.0189664	−	0.999820i	$-0.493962\pi$
$347$	0.706611	0.0379329	0.0189664	+	0.999820i	$0.493962\pi$
$348$	3.17762	0.170338
$349$	−3.81118	−0.204008	−0.102004	−	0.994784i	$-0.532525\pi$
$349$	−3.81118	−0.204008	−0.102004	+	0.994784i	$0.532525\pi$
$350$	−4.19528	−0.224247
$351$	0.506327	0.0270257
$352$	1.91324	0.101976
$353$	12.4503	0.662662	0.331331	−	0.943515i	$-0.392502\pi$
$353$	12.4503	0.662662	0.331331	+	0.943515i	$0.392502\pi$
$354$	−42.1025	−2.23772
$355$	7.63811	0.405389
$356$	−2.22987	−0.118183
$357$	−10.9142	−0.577642
$358$	−20.6912	−1.09357
$359$	−10.0936	−0.532722	−0.266361	−	0.963873i	$-0.585821\pi$
$359$	−10.0936	−0.532722	−0.266361	+	0.963873i	$0.585821\pi$
$360$	16.4563	0.867321
$361$	−15.3520	−0.807998
$362$	−9.35094	−0.491475
$363$	12.5250	0.657393
$364$	−1.70089	−0.0891511
$365$	−16.1024	−0.842837
$366$	38.5653	2.01584
$367$	−3.99772	−0.208679	−0.104340	−	0.994542i	$-0.533273\pi$
$367$	−3.99772	−0.208679	−0.104340	+	0.994542i	$0.533273\pi$
$368$	−5.25398	−0.273883
$369$	9.43327	0.491076
$370$	6.38349	0.331862
$371$	19.4978	1.01227
$372$	−0.0440608	−0.00228445
$373$	−18.9055	−0.978889	−0.489445	−	0.872034i	$-0.662800\pi$
$373$	−18.9055	−0.978889	−0.489445	+	0.872034i	$0.662800\pi$
$374$	6.60655	0.341616
$375$	−29.6369	−1.53044
$376$	−5.28595	−0.272602
$377$	50.6171	2.60691
$378$	0.283838	0.0145990
$379$	19.3916	0.996077	0.498039	−	0.867155i	$-0.334054\pi$
$379$	19.3916	0.996077	0.498039	+	0.867155i	$0.334054\pi$
$380$	0.508528	0.0260869
$381$	1.76764	0.0905590
$382$	16.1928	0.828496
$383$	−0.124895	−0.00638182	−0.00319091	−	0.999995i	$-0.501016\pi$
$383$	−0.124895	−0.00638182	−0.00319091	+	0.999995i	$0.501016\pi$
$384$	−24.3784	−1.24405
$385$	−10.3127	−0.525582
$386$	19.3671	0.985757
$387$	−21.3813	−1.08687
$388$	−1.47207	−0.0747328
$389$	9.53092	0.483237	0.241618	−	0.970371i	$-0.422322\pi$
$389$	9.53092	0.483237	0.241618	+	0.970371i	$0.422322\pi$
$390$	34.4856	1.74624
$391$	2.83837	0.143543
$392$	5.84051	0.294990
$393$	9.89072	0.498921
$394$	−12.8354	−0.646637
$395$	16.6959	0.840061
$396$	−1.00364	−0.0504349
$397$	32.4772	1.62998	0.814991	−	0.579473i	$-0.196742\pi$
$397$	32.4772	1.62998	0.814991	+	0.579473i	$0.196742\pi$
$398$	−1.63048	−0.0817288
$399$	−10.4269	−0.521996
$400$	5.09146	0.254573
$401$	25.6053	1.27867	0.639335	−	0.768929i	$-0.279210\pi$
$401$	25.6053	1.27867	0.639335	+	0.768929i	$0.279210\pi$
$402$	5.59992	0.279298
$403$	−0.701856	−0.0349620
$404$	−0.838457	−0.0417148
$405$	17.3486	0.862057
$406$	28.3751	1.40823
$407$	−5.95677	−0.295266
$408$	14.2468	0.705323
$409$	−10.5829	−0.523291	−0.261646	−	0.965164i	$-0.584265\pi$
$409$	−10.5829	−0.523291	−0.261646	+	0.965164i	$0.584265\pi$
$410$	−8.26941	−0.408397
$411$	−6.51136	−0.321182
$412$	1.88332	0.0927845
$413$	28.2667	1.39091
$414$	5.73511	0.281865
$415$	−15.0308	−0.737832
$416$	4.29540	0.210599
$417$	15.4957	0.758827
$418$	6.31154	0.308708
$419$	20.1982	0.986749	0.493374	−	0.869817i	$-0.335763\pi$
$419$	20.1982	0.986749	0.493374	+	0.869817i	$0.335763\pi$
$420$	−1.45348	−0.0709226
$421$	1.37863	0.0671904	0.0335952	−	0.999436i	$-0.489304\pi$
$421$	1.37863	0.0671904	0.0335952	+	0.999436i	$0.489304\pi$
$422$	−15.5733	−0.758097
$423$	5.36454	0.260833
$424$	−25.4513	−1.23603
$425$	−2.75057	−0.133422
$426$	13.3612	0.647351
$427$	−25.8919	−1.25300
$428$	0.778639	0.0376369
$429$	−32.1803	−1.55368
$430$	18.7433	0.903883
$431$	24.7322	1.19131	0.595654	−	0.803241i	$-0.296893\pi$
$431$	24.7322	1.19131	0.595654	+	0.803241i	$0.296893\pi$
$432$	−0.344471	−0.0165733
$433$	−14.4835	−0.696034	−0.348017	−	0.937488i	$-0.613145\pi$
$433$	−14.4835	−0.696034	−0.348017	+	0.937488i	$0.613145\pi$
$434$	−0.393448	−0.0188861
$435$	43.2543	2.07388
$436$	−1.56101	−0.0747590
$437$	2.71163	0.129715
$438$	−28.1675	−1.34590
$439$	3.65331	0.174363	0.0871815	−	0.996192i	$-0.472214\pi$
$439$	3.65331	0.174363	0.0871815	+	0.996192i	$0.472214\pi$
$440$	13.4616	0.641756
$441$	−5.92734	−0.282254
$442$	14.8323	0.705500
$443$	14.2709	0.678030	0.339015	−	0.940781i	$-0.389906\pi$
$443$	14.2709	0.678030	0.339015	+	0.940781i	$0.389906\pi$
$444$	−0.839554	−0.0398435
$445$	−30.3533	−1.43889
$446$	27.3195	1.29362
$447$	−20.3471	−0.962385
$448$	18.9561	0.895591
$449$	−9.02668	−0.425995	−0.212998	−	0.977053i	$-0.568323\pi$
$449$	−9.02668	−0.425995	−0.212998	+	0.977053i	$0.568323\pi$
$450$	−5.55770	−0.261993
$451$	7.71663	0.363362
$452$	1.45320	0.0683529
$453$	12.4638	0.585601
$454$	12.8196	0.601655
$455$	−23.1529	−1.08542
$456$	13.6107	0.637377
$457$	−36.0771	−1.68762	−0.843808	−	0.536645i	$-0.819691\pi$
$457$	−36.0771	−1.68762	−0.843808	+	0.536645i	$0.819691\pi$
$458$	−27.6178	−1.29050
$459$	0.186094	0.00868614
$460$	0.377995	0.0176241
$461$	−32.0902	−1.49459	−0.747296	−	0.664492i	$-0.768648\pi$
$461$	−32.0902	−1.49459	−0.747296	+	0.664492i	$0.768648\pi$
$462$	−18.0397	−0.839284
$463$	14.7914	0.687414	0.343707	−	0.939077i	$-0.388317\pi$
$463$	14.7914	0.687414	0.343707	+	0.939077i	$0.388317\pi$
$464$	−34.4365	−1.59867
$465$	−0.599763	−0.0278134
$466$	−4.21881	−0.195432
$467$	−26.5829	−1.23011	−0.615055	−	0.788484i	$-0.710866\pi$
$467$	−26.5829	−1.23011	−0.615055	+	0.788484i	$0.710866\pi$
$468$	−2.25326	−0.104157
$469$	−3.75966	−0.173605
$470$	−4.70267	−0.216918
$471$	−46.9999	−2.16564
$472$	−36.8978	−1.69836
$473$	−17.4904	−0.804209
$474$	29.2057	1.34146
$475$	−2.62775	−0.120570
$476$	−0.625144	−0.0286534
$477$	25.8297	1.18266
$478$	−33.2846	−1.52240
$479$	−24.9360	−1.13936	−0.569678	−	0.821868i	$-0.692932\pi$
$479$	−24.9360	−1.13936	−0.569678	+	0.821868i	$0.692932\pi$
$480$	3.67058	0.167538
$481$	−13.3735	−0.609778
$482$	20.6383	0.940048
$483$	−7.75041	−0.352656
$484$	0.717407	0.0326094
$485$	−20.0380	−0.909879
$486$	29.9666	1.35931
$487$	7.86489	0.356392	0.178196	−	0.983995i	$-0.442974\pi$
$487$	7.86489	0.356392	0.178196	+	0.983995i	$0.442974\pi$
$488$	33.7978	1.52996
$489$	−43.0209	−1.94547
$490$	5.19604	0.234733
$491$	−20.0369	−0.904252	−0.452126	−	0.891954i	$-0.649334\pi$
$491$	−20.0369	−0.904252	−0.452126	+	0.891954i	$0.649334\pi$
$492$	1.08759	0.0490324
$493$	18.6037	0.837869
$494$	14.1700	0.637537
$495$	−13.6617	−0.614049
$496$	0.477496	0.0214402
$497$	−8.97041	−0.402378
$498$	−26.2930	−1.17822
$499$	13.6153	0.609505	0.304753	−	0.952432i	$-0.401426\pi$
$499$	13.6153	0.609505	0.304753	+	0.952432i	$0.401426\pi$
$500$	−1.69754	−0.0759162
$501$	44.3882	1.98312
$502$	−21.0389	−0.939010
$503$	−20.1856	−0.900029	−0.450015	−	0.893021i	$-0.648581\pi$
$503$	−20.1856	−0.900029	−0.450015	+	0.893021i	$0.648581\pi$
$504$	−19.3267	−0.860879
$505$	−11.4132	−0.507881
$506$	4.69145	0.208560
$507$	−40.5056	−1.79892
$508$	0.101247	0.00449210
$509$	−4.56138	−0.202179	−0.101090	−	0.994877i	$-0.532233\pi$
$509$	−4.56138	−0.202179	−0.101090	+	0.994877i	$0.532233\pi$
$510$	12.6748	0.561248
$511$	18.9111	0.836576
$512$	−24.5234	−1.08379
$513$	0.177785	0.00784938
$514$	−34.5505	−1.52396
$515$	25.6361	1.12966
$516$	−2.46512	−0.108521
$517$	4.38831	0.192998
$518$	−7.49694	−0.329397
$519$	−1.08307	−0.0475413
$520$	30.2225	1.32534
$521$	−7.82744	−0.342926	−0.171463	−	0.985191i	$-0.554849\pi$
$521$	−7.82744	−0.342926	−0.171463	+	0.985191i	$0.554849\pi$
$522$	37.5899	1.64527
$523$	−20.0241	−0.875594	−0.437797	−	0.899074i	$-0.644241\pi$
$523$	−20.0241	−0.875594	−0.437797	+	0.899074i	$0.644241\pi$
$524$	0.566520	0.0247485
$525$	7.51067	0.327793
$526$	−34.7394	−1.51471
$527$	−0.257959	−0.0112369
$528$	21.8933	0.952784
$529$	−20.9844	−0.912366
$530$	−22.6429	−0.983546
$531$	37.4464	1.62504
$532$	−0.597229	−0.0258932
$533$	17.3245	0.750408
$534$	−53.0964	−2.29771
$535$	10.5990	0.458233
$536$	4.90766	0.211979
$537$	37.0429	1.59852
$538$	16.1105	0.694572
$539$	−4.84870	−0.208848
$540$	0.0247828	0.00106648
$541$	−36.6871	−1.57730	−0.788650	−	0.614842i	$-0.789220\pi$
$541$	−36.6871	−1.57730	−0.788650	+	0.614842i	$0.789220\pi$
$542$	−41.6001	−1.78688
$543$	16.7407	0.718412
$544$	1.57872	0.0676872
$545$	−21.2488	−0.910198
$546$	−40.5008	−1.73327
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	−0.372957	−0.0159319
$549$	−34.3003	−1.46390
$550$	−4.54633	−0.193856
$551$	17.7730	0.757155
$552$	10.1170	0.430607
$553$	−19.6081	−0.833821
$554$	17.7865	0.755678
$555$	−11.4282	−0.485098
$556$	0.887561	0.0376410
$557$	37.6650	1.59592	0.797960	−	0.602711i	$-0.205913\pi$
$557$	37.6650	1.59592	0.797960	+	0.602711i	$0.205913\pi$
$558$	−0.521222	−0.0220651
$559$	−39.2675	−1.66084
$560$	15.7516	0.665629
$561$	−11.8275	−0.499357
$562$	−13.4208	−0.566122
$563$	−44.4022	−1.87133	−0.935665	−	0.352889i	$-0.885199\pi$
$563$	−44.4022	−1.87133	−0.935665	+	0.352889i	$0.885199\pi$
$564$	0.618494	0.0260433
$565$	19.7812	0.832203
$566$	−3.87036	−0.162683
$567$	−20.3746	−0.855654
$568$	11.7095	0.491319
$569$	29.5098	1.23712	0.618558	−	0.785739i	$-0.287717\pi$
$569$	29.5098	1.23712	0.618558	+	0.785739i	$0.287717\pi$
$570$	12.1088	0.507181
$571$	−15.5580	−0.651081	−0.325541	−	0.945528i	$-0.605546\pi$
$571$	−15.5580	−0.651081	−0.325541	+	0.945528i	$0.605546\pi$
$572$	−1.84322	−0.0770690
$573$	−28.9895	−1.21105
$574$	9.71182	0.405364
$575$	−1.95324	−0.0814558
$576$	25.1121	1.04634
$577$	15.3910	0.640735	0.320368	−	0.947293i	$-0.396194\pi$
$577$	15.3910	0.640735	0.320368	+	0.947293i	$0.396194\pi$
$578$	−17.7344	−0.737653
$579$	−34.6722	−1.44093
$580$	2.47751	0.102873
$581$	17.6526	0.732352
$582$	−35.0520	−1.45295
$583$	21.1293	0.875087
$584$	−24.6855	−1.02149
$585$	−30.6718	−1.26812
$586$	44.5933	1.84213
$587$	7.79665	0.321802	0.160901	−	0.986971i	$-0.448560\pi$
$587$	7.79665	0.321802	0.160901	+	0.986971i	$0.448560\pi$
$588$	−0.683382	−0.0281822
$589$	−0.246440	−0.0101544
$590$	−32.8263	−1.35144
$591$	22.9788	0.945220
$592$	9.09841	0.373943
$593$	2.74080	0.112551	0.0562757	−	0.998415i	$-0.482077\pi$
$593$	2.74080	0.112551	0.0562757	+	0.998415i	$0.482077\pi$
$594$	0.307589	0.0126205
$595$	−8.50956	−0.348858
$596$	−1.16544	−0.0477383
$597$	2.91900	0.119467
$598$	10.5327	0.430715
$599$	−34.5294	−1.41083	−0.705417	−	0.708793i	$-0.749240\pi$
$599$	−34.5294	−1.41083	−0.705417	+	0.708793i	$0.749240\pi$
$600$	−9.80402	−0.400247
$601$	17.9078	0.730476	0.365238	−	0.930914i	$-0.380988\pi$
$601$	17.9078	0.730476	0.365238	+	0.930914i	$0.380988\pi$
$602$	−22.0127	−0.897170
$603$	−4.98062	−0.202827
$604$	0.713902	0.0290483
$605$	9.76546	0.397022
$606$	−19.9649	−0.811018
$607$	31.8859	1.29421	0.647104	−	0.762401i	$-0.275980\pi$
$607$	31.8859	1.29421	0.647104	+	0.762401i	$0.275980\pi$
$608$	1.50823	0.0611667
$609$	−50.7990	−2.05848
$610$	30.0684	1.21744
$611$	9.85215	0.398575
$612$	−0.828161	−0.0334764
$613$	−24.3631	−0.984017	−0.492008	−	0.870590i	$-0.663737\pi$
$613$	−24.3631	−0.984017	−0.492008	+	0.870590i	$0.663737\pi$
$614$	29.8663	1.20530
$615$	14.8045	0.596974
$616$	−15.8097	−0.636990
$617$	−27.7348	−1.11656	−0.558280	−	0.829653i	$-0.688538\pi$
$617$	−27.7348	−1.11656	−0.558280	+	0.829653i	$0.688538\pi$
$618$	44.8446	1.80391
$619$	11.0237	0.443081	0.221541	−	0.975151i	$-0.428891\pi$
$619$	11.0237	0.443081	0.221541	+	0.975151i	$0.428891\pi$
$620$	−0.0343532	−0.00137966
$621$	0.132150	0.00530298
$622$	−3.37164	−0.135191
$623$	35.6478	1.42820
$624$	49.1524	1.96767
$625$	−16.2282	−0.649127
$626$	−4.89441	−0.195620
$627$	−11.2994	−0.451253
$628$	−2.69206	−0.107425
$629$	−4.91526	−0.195984
$630$	−17.1941	−0.685029
$631$	11.5337	0.459151	0.229575	−	0.973291i	$-0.426266\pi$
$631$	11.5337	0.459151	0.229575	+	0.973291i	$0.426266\pi$
$632$	25.5953	1.01813
$633$	27.8804	1.10815
$634$	−12.7194	−0.505154
$635$	1.37819	0.0546918
$636$	2.97799	0.118085
$637$	−10.8858	−0.431310
$638$	30.7494	1.21738
$639$	−11.8836	−0.470107
$640$	−19.0073	−0.751328
$641$	−9.72562	−0.384139	−0.192069	−	0.981381i	$-0.561520\pi$
$641$	−9.72562	−0.384139	−0.192069	+	0.981381i	$0.561520\pi$
$642$	18.5405	0.731737
$643$	20.7166	0.816984	0.408492	−	0.912762i	$-0.366055\pi$
$643$	20.7166	0.816984	0.408492	+	0.912762i	$0.366055\pi$
$644$	−0.443928	−0.0174932
$645$	−33.5556	−1.32125
$646$	5.20801	0.204906
$647$	38.4455	1.51145	0.755724	−	0.654890i	$-0.227285\pi$
$647$	38.4455	1.51145	0.755724	+	0.654890i	$0.227285\pi$
$648$	26.5959	1.04479
$649$	30.6320	1.20241
$650$	−10.2069	−0.400348
$651$	0.704378	0.0276068
$652$	−2.46415	−0.0965034
$653$	−25.8179	−1.01033	−0.505167	−	0.863022i	$-0.668569\pi$
$653$	−25.8179	−1.01033	−0.505167	+	0.863022i	$0.668569\pi$
$654$	−37.1700	−1.45346
$655$	7.71157	0.301316
$656$	−11.7864	−0.460183
$657$	25.0525	0.977391
$658$	5.52295	0.215307
$659$	28.8460	1.12368	0.561839	−	0.827246i	$-0.310094\pi$
$659$	28.8460	1.12368	0.561839	+	0.827246i	$0.310094\pi$
$660$	−1.57510	−0.0613108
$661$	−47.2170	−1.83653	−0.918265	−	0.395968i	$-0.870409\pi$
$661$	−47.2170	−1.83653	−0.918265	+	0.395968i	$0.870409\pi$
$662$	−47.8272	−1.85886
$663$	−26.5538	−1.03126
$664$	−23.0427	−0.894230
$665$	−8.12958	−0.315252
$666$	−9.93159	−0.384841
$667$	13.2109	0.511528
$668$	2.54246	0.0983709
$669$	−48.9093	−1.89094
$670$	4.36612	0.168678
$671$	−28.0585	−1.08318
$672$	−4.31083	−0.166294
$673$	−28.9952	−1.11768	−0.558842	−	0.829274i	$-0.688754\pi$
$673$	−28.9952	−1.11768	−0.558842	+	0.829274i	$0.688754\pi$
$674$	22.1459	0.853029
$675$	−0.128062	−0.00492910
$676$	−2.32008	−0.0892338
$677$	39.4194	1.51501	0.757505	−	0.652829i	$-0.226418\pi$
$677$	39.4194	1.51501	0.757505	+	0.652829i	$0.226418\pi$
$678$	34.6029	1.32892
$679$	23.5332	0.903121
$680$	11.1079	0.425969
$681$	−22.9506	−0.879468
$682$	−0.426371	−0.0163266
$683$	15.4764	0.592189	0.296094	−	0.955159i	$-0.404316\pi$
$683$	15.4764	0.592189	0.296094	+	0.955159i	$0.404316\pi$
$684$	−0.791181	−0.0302516
$685$	−5.07675	−0.193973
$686$	−27.4477	−1.04796
$687$	49.4433	1.88638
$688$	26.7150	1.01850
$689$	47.4372	1.80721
$690$	9.00061	0.342647
$691$	38.3883	1.46036	0.730180	−	0.683254i	$-0.239436\pi$
$691$	38.3883	1.46036	0.730180	+	0.683254i	$0.239436\pi$
$692$	−0.0620358	−0.00235825
$693$	16.0447	0.609489
$694$	0.963726	0.0365826
$695$	12.0816	0.458282
$696$	66.3102	2.51348
$697$	6.36742	0.241183
$698$	−5.19796	−0.196746
$699$	7.55280	0.285673
$700$	0.430196	0.0162599
$701$	7.99366	0.301917	0.150958	−	0.988540i	$-0.451764\pi$
$701$	7.99366	0.301917	0.150958	+	0.988540i	$0.451764\pi$
$702$	0.690564	0.0260637
$703$	−4.69578	−0.177105
$704$	20.5423	0.774217
$705$	8.41904	0.317079
$706$	16.9806	0.639073
$707$	13.4040	0.504109
$708$	4.31731	0.162255
$709$	20.4200	0.766890	0.383445	−	0.923564i	$-0.374738\pi$
$709$	20.4200	0.766890	0.383445	+	0.923564i	$0.374738\pi$
$710$	10.4174	0.390958
$711$	−25.9759	−0.974171
$712$	−46.5327	−1.74389
$713$	−0.183182	−0.00686022
$714$	−14.8856	−0.557079
$715$	−25.0902	−0.938322
$716$	2.12174	0.0792931
$717$	59.5884	2.22537
$718$	−13.7664	−0.513758
$719$	−36.8993	−1.37611	−0.688056	−	0.725657i	$-0.741536\pi$
$719$	−36.8993	−1.37611	−0.688056	+	0.725657i	$0.741536\pi$
$720$	20.8670	0.777669
$721$	−30.1077	−1.12127
$722$	−20.9381	−0.779235
$723$	−36.9481	−1.37411
$724$	0.958872	0.0356362
$725$	−12.8022	−0.475463
$726$	17.0825	0.633991
$727$	24.5902	0.911998	0.455999	−	0.889980i	$-0.349282\pi$
$727$	24.5902	0.911998	0.455999	+	0.889980i	$0.349282\pi$
$728$	−35.4941	−1.31550
$729$	−26.3095	−0.974426
$730$	−21.9616	−0.812834
$731$	−14.4323	−0.533798
$732$	−3.95459	−0.146166
$733$	18.0850	0.667986	0.333993	−	0.942576i	$-0.391604\pi$
$733$	18.0850	0.667986	0.333993	+	0.942576i	$0.391604\pi$
$734$	−5.45238	−0.201251
$735$	−9.30230	−0.343121
$736$	1.12108	0.0413237
$737$	−4.07426	−0.150077
$738$	12.8658	0.473595
$739$	−45.2534	−1.66467	−0.832337	−	0.554269i	$-0.812998\pi$
$739$	−45.2534	−1.66467	−0.832337	+	0.554269i	$0.812998\pi$
$740$	−0.654581	−0.0240629
$741$	−25.3681	−0.931919
$742$	26.5925	0.976240
$743$	46.0788	1.69047	0.845234	−	0.534397i	$-0.179461\pi$
$743$	46.0788	1.69047	0.845234	+	0.534397i	$0.179461\pi$
$744$	−0.919457	−0.0337089
$745$	−15.8642	−0.581218
$746$	−25.7847	−0.944043
$747$	23.3853	0.855623
$748$	−0.677454	−0.0247702
$749$	−12.4477	−0.454830
$750$	−40.4209	−1.47596
$751$	2.59647	0.0947464	0.0473732	−	0.998877i	$-0.484915\pi$
$751$	2.59647	0.0947464	0.0473732	+	0.998877i	$0.484915\pi$
$752$	−6.70274	−0.244424
$753$	37.6652	1.37260
$754$	69.0352	2.51411
$755$	9.71775	0.353665
$756$	−0.0291056	−0.00105856
$757$	40.7400	1.48072	0.740360	−	0.672211i	$-0.234655\pi$
$757$	40.7400	1.48072	0.740360	+	0.672211i	$0.234655\pi$
$758$	26.4476	0.960619
$759$	−8.39895	−0.304863
$760$	10.6119	0.384934
$761$	−14.5974	−0.529156	−0.264578	−	0.964364i	$-0.585233\pi$
$761$	−14.5974	−0.529156	−0.264578	+	0.964364i	$0.585233\pi$
$762$	2.41083	0.0873353
$763$	24.9552	0.903437
$764$	−1.66046	−0.0600732
$765$	−11.2731	−0.407578
$766$	−0.170340	−0.00615464
$767$	68.7716	2.48320
$768$	8.15461	0.294254
$769$	−16.4422	−0.592920	−0.296460	−	0.955045i	$-0.595806\pi$
$769$	−16.4422	−0.592920	−0.296460	+	0.955045i	$0.595806\pi$
$770$	−14.0652	−0.506873
$771$	61.8547	2.22764
$772$	−1.98595	−0.0714760
$773$	−29.0434	−1.04462	−0.522309	−	0.852757i	$-0.674929\pi$
$773$	−29.0434	−1.04462	−0.522309	+	0.852757i	$0.674929\pi$
$774$	−29.1613	−1.04818
$775$	0.177516	0.00637655
$776$	−30.7189	−1.10275
$777$	13.4215	0.481495
$778$	12.9989	0.466035
$779$	6.08310	0.217950
$780$	−3.53625	−0.126618
$781$	−9.72104	−0.347846
$782$	3.87118	0.138433
$783$	0.866155	0.0309539
$784$	7.40594	0.264498
$785$	−36.6447	−1.30791
$786$	13.4897	0.481161
$787$	−13.4542	−0.479590	−0.239795	−	0.970824i	$-0.577080\pi$
$787$	−13.4542	−0.479590	−0.239795	+	0.970824i	$0.577080\pi$
$788$	1.31618	0.0468868
$789$	62.1929	2.21413
$790$	22.7710	0.810157
$791$	−23.2316	−0.826022
$792$	−20.9439	−0.744209
$793$	−62.9937	−2.23697
$794$	44.2947	1.57196
$795$	40.5369	1.43770
$796$	0.167195	0.00592605
$797$	8.36258	0.296218	0.148109	−	0.988971i	$-0.452681\pi$
$797$	8.36258	0.296218	0.148109	+	0.988971i	$0.452681\pi$
$798$	−14.2209	−0.503414
$799$	3.62104	0.128103
$800$	−1.08641	−0.0384103
$801$	47.2245	1.66860
$802$	34.9224	1.23315
$803$	20.4935	0.723200
$804$	−0.574231	−0.0202516
$805$	−6.04282	−0.212981
$806$	−0.957242	−0.0337174
$807$	−28.8421	−1.01529
$808$	−17.4968	−0.615537
$809$	48.1404	1.69253	0.846264	−	0.532764i	$-0.178847\pi$
$809$	48.1404	1.69253	0.846264	+	0.532764i	$0.178847\pi$
$810$	23.6612	0.831370
$811$	42.8451	1.50450	0.752248	−	0.658880i	$-0.228969\pi$
$811$	42.8451	1.50450	0.752248	+	0.658880i	$0.228969\pi$
$812$	−2.90966	−0.102109
$813$	74.4753	2.61196
$814$	−8.12427	−0.284755
$815$	−33.5424	−1.17494
$816$	18.0654	0.632415
$817$	−13.7879	−0.482376
$818$	−14.4337	−0.504664
$819$	36.0218	1.25870
$820$	0.847969	0.0296124
$821$	29.8438	1.04156	0.520778	−	0.853692i	$-0.325642\pi$
$821$	29.8438	1.04156	0.520778	+	0.853692i	$0.325642\pi$
$822$	−8.88065	−0.309748
$823$	13.5083	0.470871	0.235436	−	0.971890i	$-0.424348\pi$
$823$	13.5083	0.470871	0.235436	+	0.971890i	$0.424348\pi$
$824$	39.3010	1.36911
$825$	8.13915	0.283369
$826$	38.5522	1.34140
$827$	−8.21771	−0.285758	−0.142879	−	0.989740i	$-0.545636\pi$
$827$	−8.21771	−0.285758	−0.142879	+	0.989740i	$0.545636\pi$
$828$	−0.588094	−0.0204377
$829$	−42.6662	−1.48186	−0.740928	−	0.671584i	$-0.765614\pi$
$829$	−42.6662	−1.48186	−0.740928	+	0.671584i	$0.765614\pi$
$830$	−20.5001	−0.711567
$831$	−31.8427	−1.10461
$832$	46.1193	1.59890
$833$	−4.00093	−0.138624
$834$	21.1341	0.731815
$835$	34.6085	1.19768
$836$	−0.647204	−0.0223840
$837$	−0.0120101	−0.000415130 0
$838$	27.5478	0.951623
$839$	−34.3877	−1.18719	−0.593597	−	0.804762i	$-0.702293\pi$
$839$	−34.3877	−1.18719	−0.593597	+	0.804762i	$0.702293\pi$
$840$	−30.3311	−1.04652
$841$	57.5889	1.98582
$842$	1.88028	0.0647986
$843$	24.0268	0.827527
$844$	1.59693	0.0549687
$845$	−31.5813	−1.08643
$846$	7.31654	0.251548
$847$	−11.4688	−0.394074
$848$	−32.2731	−1.10826
$849$	6.92899	0.237802
$850$	−3.75143	−0.128673
$851$	−3.49043	−0.119650
$852$	−1.37009	−0.0469387
$853$	−42.2500	−1.44661	−0.723306	−	0.690527i	$-0.757379\pi$
$853$	−42.2500	−1.44661	−0.723306	+	0.690527i	$0.757379\pi$
$854$	−35.3132	−1.20839
$855$	−10.7697	−0.368315
$856$	16.2486	0.555365
$857$	−39.4398	−1.34724	−0.673619	−	0.739079i	$-0.735261\pi$
$857$	−39.4398	−1.34724	−0.673619	+	0.739079i	$0.735261\pi$
$858$	−43.8898	−1.49837
$859$	11.3940	0.388757	0.194378	−	0.980927i	$-0.437731\pi$
$859$	11.3940	0.388757	0.194378	+	0.980927i	$0.437731\pi$
$860$	−1.92199	−0.0655395
$861$	−17.3868	−0.592540
$862$	33.7315	1.14890
$863$	56.8973	1.93681	0.968404	−	0.249387i	$-0.0802292\pi$
$863$	56.8973	1.93681	0.968404	+	0.249387i	$0.0802292\pi$
$864$	0.0735025	0.00250061
$865$	−0.844442	−0.0287119
$866$	−19.7537	−0.671257
$867$	31.7493	1.07826
$868$	0.0403453	0.00136941
$869$	−21.2489	−0.720818
$870$	58.9932	2.00006
$871$	−9.14708	−0.309937
$872$	−32.5751	−1.10313
$873$	31.1757	1.05514
$874$	3.69832	0.125097
$875$	27.1377	0.917422
$876$	2.88838	0.0975893
$877$	14.8499	0.501447	0.250723	−	0.968059i	$-0.419332\pi$
$877$	14.8499	0.501447	0.250723	+	0.968059i	$0.419332\pi$
$878$	4.98265	0.168156
$879$	−79.8340	−2.69274
$880$	17.0697	0.575420
$881$	−11.4959	−0.387306	−0.193653	−	0.981070i	$-0.562034\pi$
$881$	−11.4959	−0.387306	−0.193653	+	0.981070i	$0.562034\pi$
$882$	−8.08413	−0.272207
$883$	25.8381	0.869520	0.434760	−	0.900546i	$-0.356833\pi$
$883$	25.8381	0.869520	0.434760	+	0.900546i	$0.356833\pi$
$884$	−1.52095	−0.0511549
$885$	58.7680	1.97546
$886$	19.4636	0.653894
$887$	−5.89826	−0.198044	−0.0990221	−	0.995085i	$-0.531571\pi$
$887$	−5.89826	−0.198044	−0.0990221	+	0.995085i	$0.531571\pi$
$888$	−17.5197	−0.587924
$889$	−1.61858	−0.0542855
$890$	−41.3980	−1.38767
$891$	−22.0795	−0.739692
$892$	−2.80142	−0.0937986
$893$	3.45935	0.115763
$894$	−27.7508	−0.928127
$895$	28.8815	0.965401
$896$	22.3226	0.745747
$897$	−18.8564	−0.629597
$898$	−12.3112	−0.410831
$899$	−1.20064	−0.0400436
$900$	0.569903	0.0189968
$901$	17.4350	0.580843
$902$	10.5245	0.350427
$903$	39.4086	1.31144
$904$	30.3253	1.00860
$905$	13.0523	0.433874
$906$	16.9990	0.564755
$907$	−37.5197	−1.24582	−0.622910	−	0.782294i	$-0.714050\pi$
$907$	−37.5197	−1.24582	−0.622910	+	0.782294i	$0.714050\pi$
$908$	−1.31456	−0.0436252
$909$	17.7570	0.588962
$910$	−31.5775	−1.04678
$911$	−24.5150	−0.812219	−0.406110	−	0.913824i	$-0.633115\pi$
$911$	−24.5150	−0.812219	−0.406110	+	0.913824i	$0.633115\pi$
$912$	17.2587	0.571493
$913$	19.1297	0.633100
$914$	−49.2045	−1.62754
$915$	−53.8306	−1.77958
$916$	2.83201	0.0935723
$917$	−9.05668	−0.299078
$918$	0.253809	0.00837694
$919$	−23.5564	−0.777053	−0.388527	−	0.921437i	$-0.627016\pi$
$919$	−23.5564	−0.777053	−0.388527	+	0.921437i	$0.627016\pi$
$920$	7.88796	0.260058
$921$	−53.4686	−1.76185
$922$	−43.7670	−1.44139
$923$	−21.8246	−0.718365
$924$	1.84985	0.0608554
$925$	3.38246	0.111215
$926$	20.1736	0.662944
$927$	−39.8853	−1.31000
$928$	7.34799	0.241210
$929$	8.54154	0.280239	0.140119	−	0.990135i	$-0.455251\pi$
$929$	8.54154	0.280239	0.140119	+	0.990135i	$0.455251\pi$
$930$	−0.818000	−0.0268233
$931$	−3.82228	−0.125270
$932$	0.432609	0.0141706
$933$	6.03615	0.197615
$934$	−36.2557	−1.18632
$935$	−9.22162	−0.301579
$936$	−47.0209	−1.53693
$937$	19.3075	0.630749	0.315374	−	0.948967i	$-0.397870\pi$
$937$	19.3075	0.630749	0.315374	+	0.948967i	$0.397870\pi$
$938$	−5.12770	−0.167425
$939$	8.76231	0.285947
$940$	0.482225	0.0157285
$941$	−9.70790	−0.316468	−0.158234	−	0.987402i	$-0.550580\pi$
$941$	−9.70790	−0.316468	−0.158234	+	0.987402i	$0.550580\pi$
$942$	−64.1018	−2.08855
$943$	4.52164	0.147245
$944$	−46.7876	−1.52281
$945$	−0.396190	−0.0128881
$946$	−23.8546	−0.775581
$947$	52.1880	1.69588	0.847942	−	0.530090i	$-0.177842\pi$
$947$	52.1880	1.69588	0.847942	+	0.530090i	$0.177842\pi$
$948$	−2.99484	−0.0972678
$949$	46.0097	1.49354
$950$	−3.58392	−0.116278
$951$	22.7712	0.738407
$952$	−13.0454	−0.422805
$953$	41.1139	1.33181	0.665904	−	0.746037i	$-0.268046\pi$
$953$	41.1139	1.33181	0.665904	+	0.746037i	$0.268046\pi$
$954$	35.2284	1.14056
$955$	−22.6024	−0.731397
$956$	3.41310	0.110388
$957$	−55.0497	−1.77951
$958$	−34.0095	−1.09880
$959$	5.96228	0.192532
$960$	39.4107	1.27197
$961$	−30.9834	−0.999463
$962$	−18.2397	−0.588072
$963$	−16.4901	−0.531388
$964$	−2.11631	−0.0681617
$965$	−27.0331	−0.870227
$966$	−10.5706	−0.340102
$967$	30.6902	0.986930	0.493465	−	0.869766i	$-0.335730\pi$
$967$	30.6902	0.986930	0.493465	+	0.869766i	$0.335730\pi$
$968$	14.9708	0.481179
$969$	−9.32373	−0.299521
$970$	−27.3293	−0.877490
$971$	−51.4805	−1.65209	−0.826045	−	0.563605i	$-0.809414\pi$
$971$	−51.4805	−1.65209	−0.826045	+	0.563605i	$0.809414\pi$
$972$	−3.07286	−0.0985620
$973$	−14.1890	−0.454878
$974$	10.7267	0.343705
$975$	18.2731	0.585208
$976$	42.8567	1.37181
$977$	−30.9578	−0.990428	−0.495214	−	0.868771i	$-0.664910\pi$
$977$	−30.9578	−0.990428	−0.495214	+	0.868771i	$0.664910\pi$
$978$	−58.6749	−1.87622
$979$	38.6307	1.23464
$980$	−0.532817	−0.0170202
$981$	33.0594	1.05551
$982$	−27.3277	−0.872063
$983$	−47.8861	−1.52733	−0.763665	−	0.645613i	$-0.776602\pi$
$983$	−47.8861	−1.52733	−0.763665	+	0.645613i	$0.776602\pi$
$984$	22.6957	0.723514
$985$	17.9160	0.570852
$986$	25.3731	0.808043
$987$	−9.88756	−0.314724
$988$	−1.45303	−0.0462270
$989$	−10.2487	−0.325889
$990$	−18.6328	−0.592191
$991$	57.4748	1.82575	0.912874	−	0.408241i	$-0.133858\pi$
$991$	57.4748	1.82575	0.912874	+	0.408241i	$0.133858\pi$
$992$	−0.101887	−0.00323492
$993$	85.6236	2.71718
$994$	−12.2345	−0.388054
$995$	2.27588	0.0721503
$996$	2.69616	0.0854311
$997$	49.3320	1.56236	0.781179	−	0.624307i	$-0.214618\pi$
$997$	49.3320	1.56236	0.781179	+	0.624307i	$0.214618\pi$
$998$	18.5695	0.587809
$999$	−0.228846	−0.00724036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.c.1.17	✓	25
3.2	odd	2		4923.2.a.n.1.9		25
4.3	odd	2		8752.2.a.v.1.21		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.c.1.17	✓	25	1.1	even	1	trivial
4923.2.a.n.1.9		25	3.2	odd	2
8752.2.a.v.1.21		25	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q+1.36387 q^{2} -2.44170 q^{3} -0.139855 q^{4} -1.90373 q^{5} -3.33016 q^{6} +2.23580 q^{7} -2.91849 q^{8} +2.96188 q^{9} +O(q^{10})\)	\(q+1.36387 q^{2} -2.44170 q^{3} -0.139855 q^{4} -1.90373 q^{5} -3.33016 q^{6} +2.23580 q^{7} -2.91849 q^{8} +2.96188 q^{9} -2.59645 q^{10} +2.42288 q^{11} +0.341484 q^{12} +5.43959 q^{13} +3.04934 q^{14} +4.64834 q^{15} -3.70073 q^{16} +1.99926 q^{17} +4.03962 q^{18} +1.90998 q^{19} +0.266247 q^{20} -5.45914 q^{21} +3.30450 q^{22} +1.41971 q^{23} +7.12606 q^{24} -1.37580 q^{25} +7.41890 q^{26} +0.0930818 q^{27} -0.312688 q^{28} +9.30532 q^{29} +6.33973 q^{30} -0.129027 q^{31} +0.789655 q^{32} -5.91594 q^{33} +2.72673 q^{34} -4.25636 q^{35} -0.414234 q^{36} -2.45855 q^{37} +2.60497 q^{38} -13.2818 q^{39} +5.55602 q^{40} +3.18489 q^{41} -7.44556 q^{42} -7.21883 q^{43} -0.338853 q^{44} -5.63863 q^{45} +1.93631 q^{46} +1.81119 q^{47} +9.03606 q^{48} -2.00121 q^{49} -1.87641 q^{50} -4.88158 q^{51} -0.760755 q^{52} +8.72073 q^{53} +0.126952 q^{54} -4.61252 q^{55} -6.52515 q^{56} -4.66360 q^{57} +12.6913 q^{58} +12.6428 q^{59} -0.650095 q^{60} -11.5806 q^{61} -0.175977 q^{62} +6.62216 q^{63} +8.47845 q^{64} -10.3555 q^{65} -8.06859 q^{66} -1.68158 q^{67} -0.279607 q^{68} -3.46651 q^{69} -5.80513 q^{70} -4.01218 q^{71} -8.64420 q^{72} +8.45831 q^{73} -3.35314 q^{74} +3.35928 q^{75} -0.267121 q^{76} +5.41708 q^{77} -18.1147 q^{78} -8.77007 q^{79} +7.04520 q^{80} -9.11291 q^{81} +4.34379 q^{82} +7.89542 q^{83} +0.763489 q^{84} -3.80605 q^{85} -9.84556 q^{86} -22.7208 q^{87} -7.07115 q^{88} +15.9441 q^{89} -7.69036 q^{90} +12.1618 q^{91} -0.198555 q^{92} +0.315046 q^{93} +2.47024 q^{94} -3.63610 q^{95} -1.92810 q^{96} +10.5256 q^{97} -2.72939 q^{98} +7.17629 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9}+O(q^{10}) \) 25 * q + 4 * q^2 + 8 * q^3 + 26 * q^4 + 29 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 29 * q^9	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9} - q^{10} + 10 q^{11} + 14 q^{12} + 19 q^{13} + 9 q^{14} + 5 q^{15} + 16 q^{16} + 40 q^{17} - 8 q^{18} + 33 q^{20} - 8 q^{21} - 10 q^{22} + 26 q^{23} - 16 q^{24} + 36 q^{25} - 8 q^{26} + 11 q^{27} - 8 q^{28} + 30 q^{29} - 20 q^{30} - 5 q^{31} + 6 q^{32} + 10 q^{33} - 7 q^{34} + 11 q^{35} + 13 q^{36} + 26 q^{37} + 25 q^{38} - 17 q^{39} - 25 q^{40} + 9 q^{41} - 16 q^{42} - 10 q^{43} + 64 q^{45} - 34 q^{46} + 28 q^{47} + 23 q^{48} + 20 q^{49} - 9 q^{50} - 9 q^{51} - 2 q^{52} + 80 q^{53} - 13 q^{54} - q^{55} + 7 q^{56} - 8 q^{57} - 24 q^{58} - 2 q^{59} - 14 q^{60} + 22 q^{61} + 36 q^{62} - 9 q^{63} - 28 q^{64} + 30 q^{65} - 42 q^{66} - 16 q^{67} + 59 q^{68} + 22 q^{69} - 61 q^{70} - q^{71} - 44 q^{72} + 2 q^{73} - 8 q^{74} - 31 q^{75} - 46 q^{76} + 67 q^{77} - q^{78} - 34 q^{79} + 30 q^{80} - 11 q^{81} - 4 q^{82} + 15 q^{83} - 87 q^{84} + 15 q^{85} - 44 q^{86} - 29 q^{87} - 55 q^{88} + 38 q^{89} - 90 q^{90} - 41 q^{91} + 40 q^{92} - 4 q^{93} - 46 q^{94} - 46 q^{95} - 87 q^{96} - 2 q^{97} - 14 q^{98} - 41 q^{99}+O(q^{100}) \) 25 * q + 4 * q^2 + 8 * q^3 + 26 * q^4 + 29 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 29 * q^9 - q^10 + 10 * q^11 + 14 * q^12 + 19 * q^13 + 9 * q^14 + 5 * q^15 + 16 * q^16 + 40 * q^17 - 8 * q^18 + 33 * q^20 - 8 * q^21 - 10 * q^22 + 26 * q^23 - 16 * q^24 + 36 * q^25 - 8 * q^26 + 11 * q^27 - 8 * q^28 + 30 * q^29 - 20 * q^30 - 5 * q^31 + 6 * q^32 + 10 * q^33 - 7 * q^34 + 11 * q^35 + 13 * q^36 + 26 * q^37 + 25 * q^38 - 17 * q^39 - 25 * q^40 + 9 * q^41 - 16 * q^42 - 10 * q^43 + 64 * q^45 - 34 * q^46 + 28 * q^47 + 23 * q^48 + 20 * q^49 - 9 * q^50 - 9 * q^51 - 2 * q^52 + 80 * q^53 - 13 * q^54 - q^55 + 7 * q^56 - 8 * q^57 - 24 * q^58 - 2 * q^59 - 14 * q^60 + 22 * q^61 + 36 * q^62 - 9 * q^63 - 28 * q^64 + 30 * q^65 - 42 * q^66 - 16 * q^67 + 59 * q^68 + 22 * q^69 - 61 * q^70 - q^71 - 44 * q^72 + 2 * q^73 - 8 * q^74 - 31 * q^75 - 46 * q^76 + 67 * q^77 - q^78 - 34 * q^79 + 30 * q^80 - 11 * q^81 - 4 * q^82 + 15 * q^83 - 87 * q^84 + 15 * q^85 - 44 * q^86 - 29 * q^87 - 55 * q^88 + 38 * q^89 - 90 * q^90 - 41 * q^91 + 40 * q^92 - 4 * q^93 - 46 * q^94 - 46 * q^95 - 87 * q^96 - 2 * q^97 - 14 * q^98 - 41 * q^99

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