LMFDB - Embedded newform 547.2.a.c.1.20

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			1.20
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)

$f(q)$	$=$	$q+1.98267 q^{2} +2.42262 q^{3} +1.93099 q^{4} -0.826438 q^{5} +4.80327 q^{6} +0.383471 q^{7} -0.136826 q^{8} +2.86911 q^{9} +O(q^{10})$	\(q+1.98267 q^{2} +2.42262 q^{3} +1.93099 q^{4} -0.826438 q^{5} +4.80327 q^{6} +0.383471 q^{7} -0.136826 q^{8} +2.86911 q^{9} -1.63856 q^{10} +3.48524 q^{11} +4.67806 q^{12} -0.283129 q^{13} +0.760298 q^{14} -2.00215 q^{15} -4.13326 q^{16} -4.93258 q^{17} +5.68851 q^{18} -1.37279 q^{19} -1.59584 q^{20} +0.929007 q^{21} +6.91008 q^{22} +4.28202 q^{23} -0.331479 q^{24} -4.31700 q^{25} -0.561353 q^{26} -0.317095 q^{27} +0.740479 q^{28} -2.57559 q^{29} -3.96961 q^{30} +8.23590 q^{31} -7.92125 q^{32} +8.44342 q^{33} -9.77969 q^{34} -0.316915 q^{35} +5.54022 q^{36} +1.31304 q^{37} -2.72180 q^{38} -0.685916 q^{39} +0.113078 q^{40} +1.17361 q^{41} +1.84192 q^{42} -2.33137 q^{43} +6.72995 q^{44} -2.37114 q^{45} +8.48985 q^{46} -3.00882 q^{47} -10.0133 q^{48} -6.85295 q^{49} -8.55920 q^{50} -11.9498 q^{51} -0.546720 q^{52} -6.14490 q^{53} -0.628696 q^{54} -2.88033 q^{55} -0.0524690 q^{56} -3.32577 q^{57} -5.10655 q^{58} +12.8775 q^{59} -3.86613 q^{60} -3.13404 q^{61} +16.3291 q^{62} +1.10022 q^{63} -7.43872 q^{64} +0.233989 q^{65} +16.7405 q^{66} +5.10721 q^{67} -9.52475 q^{68} +10.3737 q^{69} -0.628339 q^{70} -3.73484 q^{71} -0.392570 q^{72} +3.77206 q^{73} +2.60332 q^{74} -10.4585 q^{75} -2.65085 q^{76} +1.33649 q^{77} -1.35995 q^{78} -2.61460 q^{79} +3.41588 q^{80} -9.37554 q^{81} +2.32689 q^{82} +4.34410 q^{83} +1.79390 q^{84} +4.07647 q^{85} -4.62234 q^{86} -6.23968 q^{87} -0.476872 q^{88} +2.11364 q^{89} -4.70120 q^{90} -0.108572 q^{91} +8.26854 q^{92} +19.9525 q^{93} -5.96551 q^{94} +1.13453 q^{95} -19.1902 q^{96} -12.4423 q^{97} -13.5872 q^{98} +9.99953 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.98267	1.40196	0.700980	−	0.713180i	$-0.252746\pi$
$2$	1.98267	1.40196	0.700980	+	0.713180i	$0.252746\pi$
$3$	2.42262	1.39870	0.699352	−	0.714778i	$-0.253472\pi$
$3$	2.42262	1.39870	0.699352	+	0.714778i	$0.253472\pi$
$4$	1.93099	0.965494
$5$	−0.826438	−0.369594	−0.184797	−	0.982777i	$-0.559163\pi$
$5$	−0.826438	−0.369594	−0.184797	+	0.982777i	$0.559163\pi$
$6$	4.80327	1.96093
$7$	0.383471	0.144939	0.0724693	−	0.997371i	$-0.476912\pi$
$7$	0.383471	0.144939	0.0724693	+	0.997371i	$0.476912\pi$
$8$	−0.136826	−0.0483754
$9$	2.86911	0.956370
$10$	−1.63856	−0.518157
$11$	3.48524	1.05084	0.525419	−	0.850844i	$-0.323909\pi$
$11$	3.48524	1.05084	0.525419	+	0.850844i	$0.323909\pi$
$12$	4.67806	1.35044
$13$	−0.283129	−0.0785259	−0.0392630	−	0.999229i	$-0.512501\pi$
$13$	−0.283129	−0.0785259	−0.0392630	+	0.999229i	$0.512501\pi$
$14$	0.760298	0.203198
$15$	−2.00215	−0.516953
$16$	−4.13326	−1.03331
$17$	−4.93258	−1.19633	−0.598163	−	0.801374i	$-0.704102\pi$
$17$	−4.93258	−1.19633	−0.598163	+	0.801374i	$0.704102\pi$
$18$	5.68851	1.34079
$19$	−1.37279	−0.314941	−0.157470	−	0.987524i	$-0.550334\pi$
$19$	−1.37279	−0.314941	−0.157470	+	0.987524i	$0.550334\pi$
$20$	−1.59584	−0.356841
$21$	0.929007	0.202726
$22$	6.91008	1.47323
$23$	4.28202	0.892863	0.446432	−	0.894818i	$-0.352695\pi$
$23$	4.28202	0.892863	0.446432	+	0.894818i	$0.352695\pi$
$24$	−0.331479	−0.0676628
$25$	−4.31700	−0.863400
$26$	−0.561353	−0.110090
$27$	−0.317095	−0.0610250
$28$	0.740479	0.139937
$29$	−2.57559	−0.478275	−0.239137	−	0.970986i	$-0.576865\pi$
$29$	−2.57559	−0.478275	−0.239137	+	0.970986i	$0.576865\pi$
$30$	−3.96961	−0.724748
$31$	8.23590	1.47921	0.739605	−	0.673041i	$-0.235012\pi$
$31$	8.23590	1.47921	0.739605	+	0.673041i	$0.235012\pi$
$32$	−7.92125	−1.40029
$33$	8.44342	1.46981
$34$	−9.77969	−1.67720
$35$	−0.316915	−0.0535685
$36$	5.54022	0.923370
$37$	1.31304	0.215862	0.107931	−	0.994158i	$-0.465577\pi$
$37$	1.31304	0.215862	0.107931	+	0.994158i	$0.465577\pi$
$38$	−2.72180	−0.441535
$39$	−0.685916	−0.109834
$40$	0.113078	0.0178793
$41$	1.17361	0.183288	0.0916438	−	0.995792i	$-0.470788\pi$
$41$	1.17361	0.183288	0.0916438	+	0.995792i	$0.470788\pi$
$42$	1.84192	0.284214
$43$	−2.33137	−0.355530	−0.177765	−	0.984073i	$-0.556887\pi$
$43$	−2.33137	−0.355530	−0.177765	+	0.984073i	$0.556887\pi$
$44$	6.72995	1.01458
$45$	−2.37114	−0.353469
$46$	8.48985	1.25176
$47$	−3.00882	−0.438882	−0.219441	−	0.975626i	$-0.570423\pi$
$47$	−3.00882	−0.438882	−0.219441	+	0.975626i	$0.570423\pi$
$48$	−10.0133	−1.44530
$49$	−6.85295	−0.978993
$50$	−8.55920	−1.21045
$51$	−11.9498	−1.67330
$52$	−0.546720	−0.0758164
$53$	−6.14490	−0.844067	−0.422033	−	0.906580i	$-0.638683\pi$
$53$	−6.14490	−0.844067	−0.422033	+	0.906580i	$0.638683\pi$
$54$	−0.628696	−0.0855546
$55$	−2.88033	−0.388384
$56$	−0.0524690	−0.00701146
$57$	−3.32577	−0.440509
$58$	−5.10655	−0.670522
$59$	12.8775	1.67651	0.838254	−	0.545280i	$-0.183576\pi$
$59$	12.8775	1.67651	0.838254	+	0.545280i	$0.183576\pi$
$60$	−3.86613	−0.499115
$61$	−3.13404	−0.401272	−0.200636	−	0.979666i	$-0.564301\pi$
$61$	−3.13404	−0.401272	−0.200636	+	0.979666i	$0.564301\pi$
$62$	16.3291	2.07380
$63$	1.10022	0.138615
$64$	−7.43872	−0.929839
$65$	0.233989	0.0290227
$66$	16.7405	2.06062
$67$	5.10721	0.623945	0.311972	−	0.950091i	$-0.399010\pi$
$67$	5.10721	0.623945	0.311972	+	0.950091i	$0.399010\pi$
$68$	−9.52475	−1.15505
$69$	10.3737	1.24885
$70$	−0.628339	−0.0751009
$71$	−3.73484	−0.443244	−0.221622	−	0.975133i	$-0.571135\pi$
$71$	−3.73484	−0.443244	−0.221622	+	0.975133i	$0.571135\pi$
$72$	−0.392570	−0.0462648
$73$	3.77206	0.441486	0.220743	−	0.975332i	$-0.429152\pi$
$73$	3.77206	0.441486	0.220743	+	0.975332i	$0.429152\pi$
$74$	2.60332	0.302630
$75$	−10.4585	−1.20764
$76$	−2.65085	−0.304074
$77$	1.33649	0.152307
$78$	−1.35995	−0.153984
$79$	−2.61460	−0.294166	−0.147083	−	0.989124i	$-0.546988\pi$
$79$	−2.61460	−0.294166	−0.147083	+	0.989124i	$0.546988\pi$
$80$	3.41588	0.381907
$81$	−9.37554	−1.04173
$82$	2.32689	0.256962
$83$	4.34410	0.476827	0.238414	−	0.971164i	$-0.423373\pi$
$83$	4.34410	0.476827	0.238414	+	0.971164i	$0.423373\pi$
$84$	1.79390	0.195731
$85$	4.07647	0.442155
$86$	−4.62234	−0.498440
$87$	−6.23968	−0.668964
$88$	−0.476872	−0.0508347
$89$	2.11364	0.224045	0.112023	−	0.993706i	$-0.464267\pi$
$89$	2.11364	0.224045	0.112023	+	0.993706i	$0.464267\pi$
$90$	−4.70120	−0.495550
$91$	−0.108572	−0.0113814
$92$	8.26854	0.862055
$93$	19.9525	2.06898
$94$	−5.96551	−0.615295
$95$	1.13453	0.116400
$96$	−19.1902	−1.95859
$97$	−12.4423	−1.26332	−0.631660	−	0.775246i	$-0.717626\pi$
$97$	−12.4423	−1.26332	−0.631660	+	0.775246i	$0.717626\pi$
$98$	−13.5872	−1.37251
$99$	9.99953	1.00499
$100$	−8.33608	−0.833608
$101$	10.8226	1.07689	0.538444	−	0.842661i	$-0.319012\pi$
$101$	10.8226	1.07689	0.538444	+	0.842661i	$0.319012\pi$
$102$	−23.6925	−2.34591
$103$	19.1526	1.88716	0.943581	−	0.331143i	$-0.107434\pi$
$103$	19.1526	1.88716	0.943581	+	0.331143i	$0.107434\pi$
$104$	0.0387395	0.00379872
$105$	−0.767767	−0.0749264
$106$	−12.1833	−1.18335
$107$	7.11987	0.688303	0.344152	−	0.938914i	$-0.388167\pi$
$107$	7.11987	0.688303	0.344152	+	0.938914i	$0.388167\pi$
$108$	−0.612307	−0.0589193
$109$	−11.4400	−1.09575	−0.547875	−	0.836560i	$-0.684563\pi$
$109$	−11.4400	−1.09575	−0.547875	+	0.836560i	$0.684563\pi$
$110$	−5.71075	−0.544499
$111$	3.18099	0.301927
$112$	−1.58499	−0.149767
$113$	14.9583	1.40716	0.703579	−	0.710617i	$-0.251584\pi$
$113$	14.9583	1.40716	0.703579	+	0.710617i	$0.251584\pi$
$114$	−6.59391	−0.617576
$115$	−3.53883	−0.329997
$116$	−4.97343	−0.461772
$117$	−0.812329	−0.0750999
$118$	25.5319	2.35040
$119$	−1.89150	−0.173394
$120$	0.273947	0.0250078
$121$	1.14687	0.104260
$122$	−6.21376	−0.562568
$123$	2.84322	0.256365
$124$	15.9034	1.42817
$125$	7.69992	0.688702
$126$	2.18138	0.194333
$127$	10.3936	0.922284	0.461142	−	0.887326i	$-0.347440\pi$
$127$	10.3936	0.922284	0.461142	+	0.887326i	$0.347440\pi$
$128$	1.09396	0.0966932
$129$	−5.64803	−0.497282
$130$	0.463923	0.0406888
$131$	−11.6905	−1.02141	−0.510704	−	0.859757i	$-0.670615\pi$
$131$	−11.6905	−1.02141	−0.510704	+	0.859757i	$0.670615\pi$
$132$	16.3041	1.41909
$133$	−0.526428	−0.0456471
$134$	10.1259	0.874747
$135$	0.262059	0.0225545
$136$	0.674906	0.0578727
$137$	4.98602	0.425984	0.212992	−	0.977054i	$-0.431679\pi$
$137$	4.98602	0.425984	0.212992	+	0.977054i	$0.431679\pi$
$138$	20.5677	1.75084
$139$	−1.49022	−0.126399	−0.0631995	−	0.998001i	$-0.520130\pi$
$139$	−1.49022	−0.126399	−0.0631995	+	0.998001i	$0.520130\pi$
$140$	−0.611960	−0.0517201
$141$	−7.28925	−0.613866
$142$	−7.40496	−0.621411
$143$	−0.986772	−0.0825180
$144$	−11.8588	−0.988232
$145$	2.12856	0.176768
$146$	7.47875	0.618946
$147$	−16.6021	−1.36932
$148$	2.53546	0.208413
$149$	2.98518	0.244555	0.122278	−	0.992496i	$-0.460980\pi$
$149$	2.98518	0.244555	0.122278	+	0.992496i	$0.460980\pi$
$150$	−20.7357	−1.69306
$151$	12.6488	1.02935	0.514674	−	0.857386i	$-0.327913\pi$
$151$	12.6488	1.02935	0.514674	+	0.857386i	$0.327913\pi$
$152$	0.187834	0.0152354
$153$	−14.1521	−1.14413
$154$	2.64982	0.213528
$155$	−6.80646	−0.546708
$156$	−1.32450	−0.106045
$157$	5.65371	0.451215	0.225607	−	0.974218i	$-0.427563\pi$
$157$	5.65371	0.451215	0.225607	+	0.974218i	$0.427563\pi$
$158$	−5.18390	−0.412409
$159$	−14.8868	−1.18060
$160$	6.54642	0.517540
$161$	1.64203	0.129410
$162$	−18.5886	−1.46046
$163$	8.93602	0.699923	0.349962	−	0.936764i	$-0.386195\pi$
$163$	8.93602	0.699923	0.349962	+	0.936764i	$0.386195\pi$
$164$	2.26623	0.176963
$165$	−6.97796	−0.543234
$166$	8.61293	0.668493
$167$	8.28745	0.641302	0.320651	−	0.947197i	$-0.396098\pi$
$167$	8.28745	0.641302	0.320651	+	0.947197i	$0.396098\pi$
$168$	−0.127113	−0.00980695
$169$	−12.9198	−0.993834
$170$	8.08231	0.619884
$171$	−3.93870	−0.301200
$172$	−4.50185	−0.343263
$173$	−7.33381	−0.557579	−0.278790	−	0.960352i	$-0.589933\pi$
$173$	−7.33381	−0.557579	−0.278790	+	0.960352i	$0.589933\pi$
$174$	−12.3712	−0.937862
$175$	−1.65545	−0.125140
$176$	−14.4054	−1.08585
$177$	31.1974	2.34494
$178$	4.19065	0.314103
$179$	3.16739	0.236742	0.118371	−	0.992969i	$-0.462233\pi$
$179$	3.16739	0.236742	0.118371	+	0.992969i	$0.462233\pi$
$180$	−4.57865	−0.341272
$181$	−10.9866	−0.816628	−0.408314	−	0.912841i	$-0.633883\pi$
$181$	−10.9866	−0.816628	−0.408314	+	0.912841i	$0.633883\pi$
$182$	−0.215263	−0.0159563
$183$	−7.59259	−0.561260
$184$	−0.585893	−0.0431926
$185$	−1.08514	−0.0797813
$186$	39.5592	2.90062
$187$	−17.1912	−1.25714
$188$	−5.81001	−0.423738
$189$	−0.121597	−0.00884487
$190$	2.24940	0.163189
$191$	0.609018	0.0440670	0.0220335	−	0.999757i	$-0.492986\pi$
$191$	0.609018	0.0440670	0.0220335	+	0.999757i	$0.492986\pi$
$192$	−18.0212	−1.30057
$193$	−20.9705	−1.50949	−0.754745	−	0.656018i	$-0.772240\pi$
$193$	−20.9705	−1.50949	−0.754745	+	0.656018i	$0.772240\pi$
$194$	−24.6689	−1.77112
$195$	0.566867	0.0405942
$196$	−13.2330	−0.945212
$197$	−3.79497	−0.270381	−0.135190	−	0.990820i	$-0.543165\pi$
$197$	−3.79497	−0.270381	−0.135190	+	0.990820i	$0.543165\pi$
$198$	19.8258	1.40896
$199$	6.42274	0.455296	0.227648	−	0.973744i	$-0.426896\pi$
$199$	6.42274	0.455296	0.227648	+	0.973744i	$0.426896\pi$
$200$	0.590679	0.0417673
$201$	12.3729	0.872714
$202$	21.4577	1.50976
$203$	−0.987665	−0.0693205
$204$	−23.0749	−1.61557
$205$	−0.969918	−0.0677420
$206$	37.9733	2.64573
$207$	12.2856	0.853908
$208$	1.17025	0.0811420
$209$	−4.78451	−0.330952
$210$	−1.52223	−0.105044
$211$	−16.2380	−1.11787	−0.558934	−	0.829212i	$-0.688789\pi$
$211$	−16.2380	−1.11787	−0.558934	+	0.829212i	$0.688789\pi$
$212$	−11.8657	−0.814942
$213$	−9.04812	−0.619967
$214$	14.1164	0.964975
$215$	1.92673	0.131402
$216$	0.0433869	0.00295211
$217$	3.15823	0.214395
$218$	−22.6817	−1.53620
$219$	9.13828	0.617507
$220$	−5.56189	−0.374982
$221$	1.39656	0.0939426
$222$	6.30687	0.423289
$223$	22.4050	1.50035	0.750176	−	0.661238i	$-0.229969\pi$
$223$	22.4050	1.50035	0.750176	+	0.661238i	$0.229969\pi$
$224$	−3.03757	−0.202956
$225$	−12.3860	−0.825730
$226$	29.6574	1.97278
$227$	11.6493	0.773191	0.386595	−	0.922249i	$-0.373651\pi$
$227$	11.6493	0.773191	0.386595	+	0.922249i	$0.373651\pi$
$228$	−6.42202	−0.425309
$229$	11.2376	0.742602	0.371301	−	0.928513i	$-0.378912\pi$
$229$	11.2376	0.742602	0.371301	+	0.928513i	$0.378912\pi$
$230$	−7.01633	−0.462643
$231$	3.23781	0.213032
$232$	0.352408	0.0231367
$233$	8.40070	0.550348	0.275174	−	0.961394i	$-0.411265\pi$
$233$	8.40070	0.550348	0.275174	+	0.961394i	$0.411265\pi$
$234$	−1.61058	−0.105287
$235$	2.48661	0.162208
$236$	24.8663	1.61866
$237$	−6.33420	−0.411450
$238$	−3.75023	−0.243091
$239$	−17.6999	−1.14491	−0.572455	−	0.819936i	$-0.694009\pi$
$239$	−17.6999	−1.14491	−0.572455	+	0.819936i	$0.694009\pi$
$240$	8.27540	0.534175
$241$	−15.8685	−1.02218	−0.511089	−	0.859528i	$-0.670758\pi$
$241$	−15.8685	−1.02218	−0.511089	+	0.859528i	$0.670758\pi$
$242$	2.27386	0.146169
$243$	−21.7621	−1.39604
$244$	−6.05179	−0.387426
$245$	5.66354	0.361830
$246$	5.63718	0.359414
$247$	0.388678	0.0247310
$248$	−1.12689	−0.0715574
$249$	10.5241	0.666940
$250$	15.2664	0.965533
$251$	−8.32287	−0.525335	−0.262667	−	0.964886i	$-0.584602\pi$
$251$	−8.32287	−0.525335	−0.262667	+	0.964886i	$0.584602\pi$
$252$	2.12452	0.133832
$253$	14.9239	0.938255
$254$	20.6071	1.29301
$255$	9.87576	0.618444
$256$	17.0464	1.06540
$257$	−20.2798	−1.26502	−0.632508	−	0.774553i	$-0.717975\pi$
$257$	−20.2798	−1.26502	−0.632508	+	0.774553i	$0.717975\pi$
$258$	−11.1982	−0.697169
$259$	0.503512	0.0312867
$260$	0.451830	0.0280213
$261$	−7.38965	−0.457408
$262$	−23.1785	−1.43197
$263$	11.7471	0.724359	0.362180	−	0.932108i	$-0.382033\pi$
$263$	11.7471	0.724359	0.362180	+	0.932108i	$0.382033\pi$
$264$	−1.15528	−0.0711026
$265$	5.07838	0.311962
$266$	−1.04373	−0.0639954
$267$	5.12056	0.313373
$268$	9.86197	0.602415
$269$	−4.99525	−0.304566	−0.152283	−	0.988337i	$-0.548662\pi$
$269$	−4.99525	−0.304566	−0.152283	+	0.988337i	$0.548662\pi$
$270$	0.519578	0.0316205
$271$	21.9391	1.33270	0.666351	−	0.745638i	$-0.267855\pi$
$271$	21.9391	1.33270	0.666351	+	0.745638i	$0.267855\pi$
$272$	20.3876	1.23618
$273$	−0.263029	−0.0159193
$274$	9.88564	0.597213
$275$	−15.0458	−0.907294
$276$	20.0316	1.20576
$277$	1.10338	0.0662959	0.0331479	−	0.999450i	$-0.489447\pi$
$277$	1.10338	0.0662959	0.0331479	+	0.999450i	$0.489447\pi$
$278$	−2.95462	−0.177206
$279$	23.6297	1.41467
$280$	0.0433623	0.00259140
$281$	7.13868	0.425858	0.212929	−	0.977068i	$-0.431700\pi$
$281$	7.13868	0.425858	0.212929	+	0.977068i	$0.431700\pi$
$282$	−14.4522	−0.860616
$283$	−24.2009	−1.43860	−0.719298	−	0.694701i	$-0.755537\pi$
$283$	−24.2009	−1.43860	−0.719298	+	0.694701i	$0.755537\pi$
$284$	−7.21193	−0.427950
$285$	2.74854	0.162809
$286$	−1.95645	−0.115687
$287$	0.450047	0.0265654
$288$	−22.7269	−1.33920
$289$	7.33033	0.431196
$290$	4.22025	0.247821
$291$	−30.1429	−1.76701
$292$	7.28380	0.426252
$293$	24.7955	1.44857	0.724285	−	0.689501i	$-0.242170\pi$
$293$	24.7955	1.44857	0.724285	+	0.689501i	$0.242170\pi$
$294$	−32.9166	−1.91973
$295$	−10.6425	−0.619628
$296$	−0.179658	−0.0104424
$297$	−1.10515	−0.0641274
$298$	5.91862	0.342857
$299$	−1.21237	−0.0701129
$300$	−20.1952	−1.16597
$301$	−0.894014	−0.0515301
$302$	25.0785	1.44311
$303$	26.2191	1.50625
$304$	5.67412	0.325433
$305$	2.59009	0.148308
$306$	−28.0590	−1.60403
$307$	−29.1532	−1.66386	−0.831931	−	0.554879i	$-0.812765\pi$
$307$	−29.1532	−1.66386	−0.831931	+	0.554879i	$0.812765\pi$
$308$	2.58074	0.147052
$309$	46.3996	2.63958
$310$	−13.4950	−0.766463
$311$	21.4840	1.21824	0.609122	−	0.793076i	$-0.291522\pi$
$311$	21.4840	1.21824	0.609122	+	0.793076i	$0.291522\pi$
$312$	0.0938513	0.00531328
$313$	12.6172	0.713168	0.356584	−	0.934263i	$-0.383941\pi$
$313$	12.6172	0.713168	0.356584	+	0.934263i	$0.383941\pi$
$314$	11.2094	0.632586
$315$	−0.909265	−0.0512313
$316$	−5.04877	−0.284015
$317$	16.7689	0.941838	0.470919	−	0.882177i	$-0.343922\pi$
$317$	16.7689	0.941838	0.470919	+	0.882177i	$0.343922\pi$
$318$	−29.5156	−1.65515
$319$	−8.97653	−0.502589
$320$	6.14764	0.343663
$321$	17.2488	0.962732
$322$	3.25561	0.181428
$323$	6.77142	0.376772
$324$	−18.1041	−1.00578
$325$	1.22227	0.0677993
$326$	17.7172	0.981265
$327$	−27.7147	−1.53263
$328$	−0.160581	−0.00886660
$329$	−1.15380	−0.0636109
$330$	−13.8350	−0.761592
$331$	14.1718	0.778951	0.389475	−	0.921037i	$-0.372656\pi$
$331$	14.1718	0.778951	0.389475	+	0.921037i	$0.372656\pi$
$332$	8.38841	0.460374
$333$	3.76725	0.206444
$334$	16.4313	0.899080
$335$	−4.22079	−0.230607
$336$	−3.83983	−0.209480
$337$	1.00945	0.0549880	0.0274940	−	0.999622i	$-0.491247\pi$
$337$	1.00945	0.0549880	0.0274940	+	0.999622i	$0.491247\pi$
$338$	−25.6158	−1.39332
$339$	36.2384	1.96820
$340$	7.87162	0.426899
$341$	28.7040	1.55441
$342$	−7.80915	−0.422271
$343$	−5.31221	−0.286832
$344$	0.318992	0.0171989
$345$	−8.57325	−0.461568
$346$	−14.5405	−0.781704
$347$	−12.0173	−0.645124	−0.322562	−	0.946548i	$-0.604544\pi$
$347$	−12.0173	−0.645124	−0.322562	+	0.946548i	$0.604544\pi$
$348$	−12.0488	−0.645881
$349$	15.3441	0.821351	0.410675	−	0.911782i	$-0.365293\pi$
$349$	15.3441	0.821351	0.410675	+	0.911782i	$0.365293\pi$
$350$	−3.28221	−0.175441
$351$	0.0897789	0.00479204
$352$	−27.6074	−1.47148
$353$	−3.47323	−0.184861	−0.0924306	−	0.995719i	$-0.529464\pi$
$353$	−3.47323	−0.184861	−0.0924306	+	0.995719i	$0.529464\pi$
$354$	61.8542	3.28751
$355$	3.08661	0.163820
$356$	4.08141	0.216315
$357$	−4.58240	−0.242526
$358$	6.27990	0.331903
$359$	−33.9786	−1.79332	−0.896660	−	0.442719i	$-0.854014\pi$
$359$	−33.9786	−1.79332	−0.896660	+	0.442719i	$0.854014\pi$
$360$	0.324434	0.0170992
$361$	−17.1154	−0.900812
$362$	−21.7828	−1.14488
$363$	2.77842	0.145829
$364$	−0.209651	−0.0109887
$365$	−3.11737	−0.163171
$366$	−15.0536	−0.786865
$367$	−32.0068	−1.67074	−0.835371	−	0.549687i	$-0.814747\pi$
$367$	−32.0068	−1.67074	−0.835371	+	0.549687i	$0.814747\pi$
$368$	−17.6987	−0.922609
$369$	3.36723	0.175291
$370$	−2.15148	−0.111850
$371$	−2.35639	−0.122338
$372$	38.5280	1.99759
$373$	2.10219	0.108847	0.0544236	−	0.998518i	$-0.482668\pi$
$373$	2.10219	0.108847	0.0544236	+	0.998518i	$0.482668\pi$
$374$	−34.0845	−1.76247
$375$	18.6540	0.963290
$376$	0.411686	0.0212311
$377$	0.729225	0.0375570
$378$	−0.241087	−0.0124002
$379$	−13.9832	−0.718270	−0.359135	−	0.933286i	$-0.616928\pi$
$379$	−13.9832	−0.718270	−0.359135	+	0.933286i	$0.616928\pi$
$380$	2.19076	0.112384
$381$	25.1798	1.29000
$382$	1.20748	0.0617802
$383$	19.6552	1.00433	0.502167	−	0.864771i	$-0.332536\pi$
$383$	19.6552	1.00433	0.502167	+	0.864771i	$0.332536\pi$
$384$	2.65025	0.135245
$385$	−1.10452	−0.0562918
$386$	−41.5776	−2.11625
$387$	−6.68896	−0.340019
$388$	−24.0259	−1.21973
$389$	16.1024	0.816426	0.408213	−	0.912887i	$-0.366152\pi$
$389$	16.1024	0.816426	0.408213	+	0.912887i	$0.366152\pi$
$390$	1.12391	0.0569115
$391$	−21.1214	−1.06816
$392$	0.937663	0.0473591
$393$	−28.3218	−1.42865
$394$	−7.52419	−0.379063
$395$	2.16081	0.108722
$396$	19.3090	0.970313
$397$	13.3589	0.670465	0.335233	−	0.942135i	$-0.391185\pi$
$397$	13.3589	0.670465	0.335233	+	0.942135i	$0.391185\pi$
$398$	12.7342	0.638307
$399$	−1.27534	−0.0638467
$400$	17.8433	0.892164
$401$	28.7819	1.43730	0.718649	−	0.695373i	$-0.244761\pi$
$401$	28.7819	1.43730	0.718649	+	0.695373i	$0.244761\pi$
$402$	24.5313	1.22351
$403$	−2.33182	−0.116156
$404$	20.8983	1.03973
$405$	7.74830	0.385016
$406$	−1.95822	−0.0971846
$407$	4.57624	0.226836
$408$	1.63504	0.0809468
$409$	−37.0652	−1.83276	−0.916379	−	0.400311i	$-0.868902\pi$
$409$	−37.0652	−1.83276	−0.916379	+	0.400311i	$0.868902\pi$
$410$	−1.92303	−0.0949717
$411$	12.0792	0.595825
$412$	36.9835	1.82204
$413$	4.93816	0.242991
$414$	24.3583	1.19715
$415$	−3.59013	−0.176233
$416$	2.24274	0.109959
$417$	−3.61025	−0.176795
$418$	−9.48612	−0.463981
$419$	13.0856	0.639271	0.319636	−	0.947541i	$-0.396439\pi$
$419$	13.0856	0.639271	0.319636	+	0.947541i	$0.396439\pi$
$420$	−1.48255	−0.0723410
$421$	−34.3278	−1.67303	−0.836517	−	0.547941i	$-0.815412\pi$
$421$	−34.3278	−1.67303	−0.836517	+	0.547941i	$0.815412\pi$
$422$	−32.1946	−1.56721
$423$	−8.63265	−0.419734
$424$	0.840783	0.0408320
$425$	21.2939	1.03291
$426$	−17.9394	−0.869169
$427$	−1.20181	−0.0581598
$428$	13.7484	0.664553
$429$	−2.39058	−0.115418
$430$	3.82008	0.184221
$431$	13.3630	0.643672	0.321836	−	0.946795i	$-0.395700\pi$
$431$	13.3630	0.643672	0.321836	+	0.946795i	$0.395700\pi$
$432$	1.31064	0.0630580
$433$	21.9748	1.05604	0.528022	−	0.849231i	$-0.322934\pi$
$433$	21.9748	1.05604	0.528022	+	0.849231i	$0.322934\pi$
$434$	6.26174	0.300573
$435$	5.15671	0.247245
$436$	−22.0904	−1.05794
$437$	−5.87834	−0.281199
$438$	18.1182	0.865721
$439$	17.0596	0.814212	0.407106	−	0.913381i	$-0.366538\pi$
$439$	17.0596	0.814212	0.407106	+	0.913381i	$0.366538\pi$
$440$	0.394105	0.0187882
$441$	−19.6619	−0.936280
$442$	2.76892	0.131704
$443$	−20.2449	−0.961862	−0.480931	−	0.876758i	$-0.659701\pi$
$443$	−20.2449	−0.961862	−0.480931	+	0.876758i	$0.659701\pi$
$444$	6.14246	0.291508
$445$	−1.74679	−0.0828059
$446$	44.4219	2.10344
$447$	7.23196	0.342060
$448$	−2.85254	−0.134770
$449$	−9.82679	−0.463755	−0.231878	−	0.972745i	$-0.574487\pi$
$449$	−9.82679	−0.463755	−0.231878	+	0.972745i	$0.574487\pi$
$450$	−24.5573	−1.15764
$451$	4.09032	0.192606
$452$	28.8843	1.35860
$453$	30.6434	1.43975
$454$	23.0967	1.08398
$455$	0.0897280	0.00420652
$456$	0.455052	0.0213098
$457$	−22.7680	−1.06504	−0.532521	−	0.846417i	$-0.678755\pi$
$457$	−22.7680	−1.06504	−0.532521	+	0.846417i	$0.678755\pi$
$458$	22.2805	1.04110
$459$	1.56410	0.0730058
$460$	−6.83343	−0.318611
$461$	15.1869	0.707326	0.353663	−	0.935373i	$-0.384936\pi$
$461$	15.1869	0.707326	0.353663	+	0.935373i	$0.384936\pi$
$462$	6.41951	0.298663
$463$	−32.4769	−1.50933	−0.754664	−	0.656111i	$-0.772200\pi$
$463$	−32.4769	−1.50933	−0.754664	+	0.656111i	$0.772200\pi$
$464$	10.6456	0.494208
$465$	−16.4895	−0.764682
$466$	16.6558	0.771567
$467$	0.535632	0.0247861	0.0123930	−	0.999923i	$-0.496055\pi$
$467$	0.535632	0.0247861	0.0123930	+	0.999923i	$0.496055\pi$
$468$	−1.56860	−0.0725085
$469$	1.95847	0.0904337
$470$	4.93013	0.227410
$471$	13.6968	0.631116
$472$	−1.76198	−0.0811017
$473$	−8.12537	−0.373605
$474$	−12.5586	−0.576837
$475$	5.92636	0.271920
$476$	−3.65247	−0.167411
$477$	−17.6304	−0.807240
$478$	−35.0931	−1.60512
$479$	5.09120	0.232623	0.116312	−	0.993213i	$-0.462893\pi$
$479$	5.09120	0.232623	0.116312	+	0.993213i	$0.462893\pi$
$480$	15.8595	0.723885
$481$	−0.371759	−0.0169507
$482$	−31.4620	−1.43305
$483$	3.97803	0.181007
$484$	2.21458	0.100663
$485$	10.2828	0.466916
$486$	−43.1471	−1.95719
$487$	−15.1818	−0.687955	−0.343978	−	0.938978i	$-0.611774\pi$
$487$	−15.1818	−0.687955	−0.343978	+	0.938978i	$0.611774\pi$
$488$	0.428818	0.0194117
$489$	21.6486	0.978985
$490$	11.2289	0.507272
$491$	−30.4189	−1.37278	−0.686392	−	0.727232i	$-0.740806\pi$
$491$	−30.4189	−1.37278	−0.686392	+	0.727232i	$0.740806\pi$
$492$	5.49023	0.247519
$493$	12.7043	0.572173
$494$	0.770622	0.0346719
$495$	−8.26399	−0.371439
$496$	−34.0411	−1.52849
$497$	−1.43220	−0.0642432
$498$	20.8659	0.935023
$499$	−28.0787	−1.25698	−0.628488	−	0.777819i	$-0.716326\pi$
$499$	−28.0787	−1.25698	−0.628488	+	0.777819i	$0.716326\pi$
$500$	14.8685	0.664938
$501$	20.0774	0.896991
$502$	−16.5015	−0.736499
$503$	7.33649	0.327118	0.163559	−	0.986534i	$-0.447703\pi$
$503$	7.33649	0.327118	0.163559	+	0.986534i	$0.447703\pi$
$504$	−0.150539	−0.00670555
$505$	−8.94420	−0.398012
$506$	29.5891	1.31540
$507$	−31.2999	−1.39008
$508$	20.0699	0.890460
$509$	6.01488	0.266605	0.133302	−	0.991075i	$-0.457442\pi$
$509$	6.01488	0.266605	0.133302	+	0.991075i	$0.457442\pi$
$510$	19.5804	0.867034
$511$	1.44648	0.0639883
$512$	31.6095	1.39696
$513$	0.435307	0.0192193
$514$	−40.2081	−1.77350
$515$	−15.8284	−0.697484
$516$	−10.9063	−0.480123
$517$	−10.4865	−0.461194
$518$	0.998299	0.0438627
$519$	−17.7671	−0.779888
$520$	−0.0320158	−0.00140399
$521$	−13.7044	−0.600400	−0.300200	−	0.953876i	$-0.597054\pi$
$521$	−13.7044	−0.600400	−0.300200	+	0.953876i	$0.597054\pi$
$522$	−14.6513	−0.641268
$523$	−28.2014	−1.23316	−0.616580	−	0.787292i	$-0.711482\pi$
$523$	−28.2014	−1.23316	−0.616580	+	0.787292i	$0.711482\pi$
$524$	−22.5743	−0.986163
$525$	−4.01053	−0.175034
$526$	23.2907	1.01552
$527$	−40.6242	−1.76962
$528$	−34.8988	−1.51878
$529$	−4.66428	−0.202795
$530$	10.0688	0.437359
$531$	36.9470	1.60336
$532$	−1.01653	−0.0440720
$533$	−0.332284	−0.0143928
$534$	10.1524	0.439337
$535$	−5.88413	−0.254393
$536$	−0.698800	−0.0301836
$537$	7.67341	0.331132
$538$	−9.90395	−0.426989
$539$	−23.8841	−1.02876
$540$	0.506034	0.0217762
$541$	−21.0487	−0.904953	−0.452477	−	0.891776i	$-0.649459\pi$
$541$	−21.0487	−0.904953	−0.452477	+	0.891776i	$0.649459\pi$
$542$	43.4980	1.86840
$543$	−26.6164	−1.14222
$544$	39.0722	1.67521
$545$	9.45442	0.404983
$546$	−0.521501	−0.0223182
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	9.62794	0.411285
$549$	−8.99189	−0.383765
$550$	−29.8308	−1.27199
$551$	3.53575	0.150628
$552$	−1.41940	−0.0604136
$553$	−1.00262	−0.0426359
$554$	2.18765	0.0929442
$555$	−2.62889	−0.111590
$556$	−2.87760	−0.122037
$557$	−12.7539	−0.540401	−0.270200	−	0.962804i	$-0.587090\pi$
$557$	−12.7539	−0.540401	−0.270200	+	0.962804i	$0.587090\pi$
$558$	46.8499	1.98332
$559$	0.660079	0.0279184
$560$	1.30989	0.0553531
$561$	−41.6478	−1.75837
$562$	14.1537	0.597036
$563$	12.5544	0.529106	0.264553	−	0.964371i	$-0.414776\pi$
$563$	12.5544	0.529106	0.264553	+	0.964371i	$0.414776\pi$
$564$	−14.0755	−0.592684
$565$	−12.3621	−0.520078
$566$	−47.9825	−2.01686
$567$	−3.59525	−0.150986
$568$	0.511024	0.0214421
$569$	11.9203	0.499726	0.249863	−	0.968281i	$-0.419614\pi$
$569$	11.9203	0.499726	0.249863	+	0.968281i	$0.419614\pi$
$570$	5.44945	0.228253
$571$	11.1970	0.468579	0.234290	−	0.972167i	$-0.424724\pi$
$571$	11.1970	0.468579	0.234290	+	0.972167i	$0.424724\pi$
$572$	−1.90545	−0.0796707
$573$	1.47542	0.0616367
$574$	0.892296	0.0372437
$575$	−18.4855	−0.770898
$576$	−21.3425	−0.889271
$577$	−19.6587	−0.818403	−0.409201	−	0.912444i	$-0.634193\pi$
$577$	−19.6587	−0.818403	−0.409201	+	0.912444i	$0.634193\pi$
$578$	14.5336	0.604520
$579$	−50.8037	−2.11133
$580$	4.11023	0.170668
$581$	1.66584	0.0691106
$582$	−59.7635	−2.47728
$583$	−21.4164	−0.886977
$584$	−0.516116	−0.0213570
$585$	0.671340	0.0277565
$586$	49.1614	2.03084
$587$	−31.9759	−1.31979	−0.659894	−	0.751359i	$-0.729399\pi$
$587$	−31.9759	−1.31979	−0.659894	+	0.751359i	$0.729399\pi$
$588$	−32.0585	−1.32207
$589$	−11.3062	−0.465864
$590$	−21.1005	−0.868694
$591$	−9.19380	−0.378182
$592$	−5.42712	−0.223053
$593$	19.0460	0.782126	0.391063	−	0.920364i	$-0.372107\pi$
$593$	19.0460	0.782126	0.391063	+	0.920364i	$0.372107\pi$
$594$	−2.19115	−0.0899041
$595$	1.56321	0.0640854
$596$	5.76434	0.236117
$597$	15.5599	0.636824
$598$	−2.40372	−0.0982956
$599$	−45.3013	−1.85096	−0.925481	−	0.378795i	$-0.876339\pi$
$599$	−45.3013	−1.85096	−0.925481	+	0.378795i	$0.876339\pi$
$600$	1.43099	0.0584201
$601$	−32.3630	−1.32012	−0.660058	−	0.751215i	$-0.729468\pi$
$601$	−32.3630	−1.32012	−0.660058	+	0.751215i	$0.729468\pi$
$602$	−1.77254	−0.0722432
$603$	14.6532	0.596722
$604$	24.4248	0.993830
$605$	−0.947813	−0.0385341
$606$	51.9838	2.11170
$607$	−18.3951	−0.746634	−0.373317	−	0.927704i	$-0.621780\pi$
$607$	−18.3951	−0.746634	−0.373317	+	0.927704i	$0.621780\pi$
$608$	10.8742	0.441009
$609$	−2.39274	−0.0969587
$610$	5.13529	0.207922
$611$	0.851886	0.0344636
$612$	−27.3276	−1.10465
$613$	−23.9580	−0.967655	−0.483827	−	0.875164i	$-0.660754\pi$
$613$	−23.9580	−0.967655	−0.483827	+	0.875164i	$0.660754\pi$
$614$	−57.8013	−2.33267
$615$	−2.34975	−0.0947510
$616$	−0.182867	−0.00736791
$617$	−12.5739	−0.506207	−0.253104	−	0.967439i	$-0.581451\pi$
$617$	−12.5739	−0.506207	−0.253104	+	0.967439i	$0.581451\pi$
$618$	91.9951	3.70059
$619$	−20.0583	−0.806211	−0.403105	−	0.915154i	$-0.632069\pi$
$619$	−20.0583	−0.806211	−0.403105	+	0.915154i	$0.632069\pi$
$620$	−13.1432	−0.527843
$621$	−1.35781	−0.0544870
$622$	42.5957	1.70793
$623$	0.810520	0.0324728
$624$	2.83507	0.113494
$625$	15.2215	0.608860
$626$	25.0158	0.999834
$627$	−11.5911	−0.462903
$628$	10.9172	0.435646
$629$	−6.47665	−0.258241
$630$	−1.80278	−0.0718243
$631$	34.9598	1.39173	0.695864	−	0.718173i	$-0.255021\pi$
$631$	34.9598	1.39173	0.695864	+	0.718173i	$0.255021\pi$
$632$	0.357746	0.0142304
$633$	−39.3385	−1.56356
$634$	33.2473	1.32042
$635$	−8.58967	−0.340871
$636$	−28.7462	−1.13986
$637$	1.94027	0.0768763
$638$	−17.7975	−0.704611
$639$	−10.7157	−0.423905
$640$	−0.904089	−0.0357372
$641$	31.0101	1.22483	0.612413	−	0.790538i	$-0.290199\pi$
$641$	31.0101	1.22483	0.612413	+	0.790538i	$0.290199\pi$
$642$	34.1986	1.34971
$643$	−8.52689	−0.336268	−0.168134	−	0.985764i	$-0.553774\pi$
$643$	−8.52689	−0.336268	−0.168134	+	0.985764i	$0.553774\pi$
$644$	3.17075	0.124945
$645$	4.66775	0.183792
$646$	13.4255	0.528219
$647$	−44.4134	−1.74607	−0.873036	−	0.487655i	$-0.837852\pi$
$647$	−44.4134	−1.74607	−0.873036	+	0.487655i	$0.837852\pi$
$648$	1.28282	0.0503939
$649$	44.8811	1.76174
$650$	2.42336	0.0950520
$651$	7.65121	0.299875
$652$	17.2554	0.675772
$653$	19.3254	0.756261	0.378131	−	0.925752i	$-0.376567\pi$
$653$	19.3254	0.756261	0.378131	+	0.925752i	$0.376567\pi$
$654$	−54.9493	−2.14869
$655$	9.66151	0.377506
$656$	−4.85085	−0.189394
$657$	10.8224	0.422224
$658$	−2.28760	−0.0891801
$659$	36.2368	1.41159	0.705793	−	0.708418i	$-0.250591\pi$
$659$	36.2368	1.41159	0.705793	+	0.708418i	$0.250591\pi$
$660$	−13.4744	−0.524489
$661$	30.1121	1.17123	0.585613	−	0.810591i	$-0.300854\pi$
$661$	30.1121	1.17123	0.585613	+	0.810591i	$0.300854\pi$
$662$	28.0980	1.09206
$663$	3.38333	0.131398
$664$	−0.594387	−0.0230667
$665$	0.435060	0.0168709
$666$	7.46921	0.289426
$667$	−11.0287	−0.427034
$668$	16.0030	0.619174
$669$	54.2790	2.09855
$670$	−8.36845	−0.323301
$671$	−10.9228	−0.421672
$672$	−7.35890	−0.283876
$673$	−3.96650	−0.152897	−0.0764486	−	0.997074i	$-0.524358\pi$
$673$	−3.96650	−0.152897	−0.0764486	+	0.997074i	$0.524358\pi$
$674$	2.00140	0.0770911
$675$	1.36890	0.0526890
$676$	−24.9481	−0.959541
$677$	25.9813	0.998544	0.499272	−	0.866445i	$-0.333601\pi$
$677$	25.9813	0.998544	0.499272	+	0.866445i	$0.333601\pi$
$678$	71.8488	2.75934
$679$	−4.77125	−0.183104
$680$	−0.557768	−0.0213894
$681$	28.2219	1.08146
$682$	56.9107	2.17922
$683$	50.1743	1.91987	0.959934	−	0.280227i	$-0.0904098\pi$
$683$	50.1743	1.91987	0.959934	+	0.280227i	$0.0904098\pi$
$684$	−7.60559	−0.290807
$685$	−4.12063	−0.157441
$686$	−10.5324	−0.402128
$687$	27.2245	1.03868
$688$	9.63615	0.367375
$689$	1.73980	0.0662811
$690$	−16.9979	−0.647101
$691$	−28.0364	−1.06655	−0.533277	−	0.845941i	$-0.679040\pi$
$691$	−28.0364	−1.06655	−0.533277	+	0.845941i	$0.679040\pi$
$692$	−14.1615	−0.538340
$693$	3.83453	0.145662
$694$	−23.8264	−0.904439
$695$	1.23158	0.0467163
$696$	0.853752	0.0323614
$697$	−5.78894	−0.219272
$698$	30.4223	1.15150
$699$	20.3517	0.769774
$700$	−3.19665	−0.120822
$701$	−19.5857	−0.739743	−0.369872	−	0.929083i	$-0.620598\pi$
$701$	−19.5857	−0.739743	−0.369872	+	0.929083i	$0.620598\pi$
$702$	0.178002	0.00671826
$703$	−1.80253	−0.0679837
$704$	−25.9257	−0.977111
$705$	6.02411	0.226881
$706$	−6.88627	−0.259168
$707$	4.15015	0.156083
$708$	60.2418	2.26402
$709$	−51.4545	−1.93241	−0.966207	−	0.257767i	$-0.917013\pi$
$709$	−51.4545	−1.93241	−0.966207	+	0.257767i	$0.917013\pi$
$710$	6.11974	0.229670
$711$	−7.50158	−0.281331
$712$	−0.289201	−0.0108383
$713$	35.2663	1.32073
$714$	−9.08540	−0.340013
$715$	0.815506	0.0304982
$716$	6.11620	0.228573
$717$	−42.8802	−1.60139
$718$	−67.3684	−2.51417
$719$	42.7162	1.59304	0.796522	−	0.604609i	$-0.206671\pi$
$719$	42.7162	1.59304	0.796522	+	0.604609i	$0.206671\pi$
$720$	9.80055	0.365245
$721$	7.34447	0.273522
$722$	−33.9343	−1.26290
$723$	−38.4433	−1.42972
$724$	−21.2150	−0.788450
$725$	11.1188	0.412942
$726$	5.50870	0.204447
$727$	21.1901	0.785898	0.392949	−	0.919560i	$-0.371455\pi$
$727$	21.1901	0.785898	0.392949	+	0.919560i	$0.371455\pi$
$728$	0.0148555	0.000550581 0
$729$	−24.5948	−0.910920
$730$	−6.18072	−0.228759
$731$	11.4997	0.425330
$732$	−14.6612	−0.541894
$733$	20.4348	0.754777	0.377388	−	0.926055i	$-0.376822\pi$
$733$	20.4348	0.754777	0.377388	+	0.926055i	$0.376822\pi$
$734$	−63.4590	−2.34231
$735$	13.7206	0.506093
$736$	−33.9190	−1.25027
$737$	17.7998	0.655665
$738$	6.67610	0.245751
$739$	−39.4784	−1.45223	−0.726117	−	0.687571i	$-0.758677\pi$
$739$	−39.4784	−1.45223	−0.726117	+	0.687571i	$0.758677\pi$
$740$	−2.09540	−0.0770284
$741$	0.941622	0.0345914
$742$	−4.67196	−0.171513
$743$	−31.2030	−1.14473	−0.572364	−	0.820000i	$-0.693974\pi$
$743$	−31.2030	−1.14473	−0.572364	+	0.820000i	$0.693974\pi$
$744$	−2.73002	−0.100088
$745$	−2.46706	−0.0903862
$746$	4.16795	0.152599
$747$	12.4637	0.456023
$748$	−33.1960	−1.21377
$749$	2.73027	0.0997617
$750$	36.9848	1.35049
$751$	7.31657	0.266986	0.133493	−	0.991050i	$-0.457381\pi$
$751$	7.31657	0.266986	0.133493	+	0.991050i	$0.457381\pi$
$752$	12.4362	0.453503
$753$	−20.1632	−0.734787
$754$	1.44581	0.0526534
$755$	−10.4535	−0.380441
$756$	−0.234802	−0.00853968
$757$	−52.6625	−1.91405	−0.957026	−	0.290002i	$-0.906344\pi$
$757$	−52.6625	−1.91405	−0.957026	+	0.290002i	$0.906344\pi$
$758$	−27.7241	−1.00699
$759$	36.1549	1.31234
$760$	−0.155233	−0.00563091
$761$	−15.4120	−0.558684	−0.279342	−	0.960192i	$-0.590116\pi$
$761$	−15.4120	−0.558684	−0.279342	+	0.960192i	$0.590116\pi$
$762$	49.9233	1.80853
$763$	−4.38690	−0.158816
$764$	1.17601	0.0425464
$765$	11.6958	0.422864
$766$	38.9698	1.40804
$767$	−3.64600	−0.131649
$768$	41.2970	1.49018
$769$	50.3928	1.81721	0.908605	−	0.417657i	$-0.137149\pi$
$769$	50.3928	1.81721	0.908605	+	0.417657i	$0.137149\pi$
$770$	−2.18991	−0.0789189
$771$	−49.1303	−1.76938
$772$	−40.4938	−1.45740
$773$	48.7180	1.75226	0.876132	−	0.482071i	$-0.160115\pi$
$773$	48.7180	1.75226	0.876132	+	0.482071i	$0.160115\pi$
$774$	−13.2620	−0.476693
$775$	−35.5544	−1.27715
$776$	1.70243	0.0611136
$777$	1.21982	0.0437608
$778$	31.9258	1.14460
$779$	−1.61113	−0.0577247
$780$	1.09461	0.0391935
$781$	−13.0168	−0.465778
$782$	−41.8768	−1.49751
$783$	0.816706	0.0291867
$784$	28.3250	1.01161
$785$	−4.67244	−0.166767
$786$	−56.1528	−2.00290
$787$	−5.65383	−0.201537	−0.100769	−	0.994910i	$-0.532130\pi$
$787$	−5.65383	−0.201537	−0.100769	+	0.994910i	$0.532130\pi$
$788$	−7.32805	−0.261051
$789$	28.4589	1.01316
$790$	4.28417	0.152424
$791$	5.73608	0.203952
$792$	−1.36820	−0.0486168
$793$	0.887337	0.0315103
$794$	26.4864	0.939966
$795$	12.3030	0.436343
$796$	12.4022	0.439586
$797$	−17.6524	−0.625281	−0.312641	−	0.949871i	$-0.601214\pi$
$797$	−17.6524	−0.625281	−0.312641	+	0.949871i	$0.601214\pi$
$798$	−2.52857	−0.0895106
$799$	14.8413	0.525046
$800$	34.1960	1.20901
$801$	6.06427	0.214270
$802$	57.0650	2.01504
$803$	13.1465	0.463930
$804$	23.8918	0.842600
$805$	−1.35704	−0.0478293
$806$	−4.62324	−0.162847
$807$	−12.1016	−0.425997
$808$	−1.48081	−0.0520949
$809$	31.3614	1.10261	0.551303	−	0.834305i	$-0.314131\pi$
$809$	31.3614	1.10261	0.551303	+	0.834305i	$0.314131\pi$
$810$	15.3623	0.539778
$811$	36.9390	1.29711	0.648553	−	0.761170i	$-0.275375\pi$
$811$	36.9390	1.29711	0.648553	+	0.761170i	$0.275375\pi$
$812$	−1.90717	−0.0669285
$813$	53.1501	1.86406
$814$	9.07318	0.318015
$815$	−7.38507	−0.258688
$816$	49.3916	1.72905
$817$	3.20049	0.111971
$818$	−73.4882	−2.56946
$819$	−0.311505	−0.0108849
$820$	−1.87290	−0.0654046
$821$	−25.0142	−0.873002	−0.436501	−	0.899704i	$-0.643783\pi$
$821$	−25.0142	−0.873002	−0.436501	+	0.899704i	$0.643783\pi$
$822$	23.9492	0.835324
$823$	5.61826	0.195840	0.0979201	−	0.995194i	$-0.468781\pi$
$823$	5.61826	0.195840	0.0979201	+	0.995194i	$0.468781\pi$
$824$	−2.62058	−0.0912921
$825$	−36.4502	−1.26903
$826$	9.79074	0.340664
$827$	18.3509	0.638123	0.319062	−	0.947734i	$-0.396632\pi$
$827$	18.3509	0.638123	0.319062	+	0.947734i	$0.396632\pi$
$828$	23.7234	0.824443
$829$	20.4204	0.709230	0.354615	−	0.935012i	$-0.384612\pi$
$829$	20.4204	0.709230	0.354615	+	0.935012i	$0.384612\pi$
$830$	−7.11805	−0.247071
$831$	2.67308	0.0927282
$832$	2.10612	0.0730165
$833$	33.8027	1.17119
$834$	−7.15794	−0.247859
$835$	−6.84906	−0.237022
$836$	−9.23884	−0.319532
$837$	−2.61156	−0.0902688
$838$	25.9444	0.896234
$839$	−15.7518	−0.543812	−0.271906	−	0.962324i	$-0.587654\pi$
$839$	−15.7518	−0.543812	−0.271906	+	0.962324i	$0.587654\pi$
$840$	0.105051	0.00362459
$841$	−22.3663	−0.771253
$842$	−68.0608	−2.34553
$843$	17.2943	0.595649
$844$	−31.3553	−1.07929
$845$	10.6774	0.367315
$846$	−17.1157	−0.588450
$847$	0.439790	0.0151114
$848$	25.3985	0.872187
$849$	−58.6298	−2.01217
$850$	42.2189	1.44810
$851$	5.62245	0.192735
$852$	−17.4718	−0.598574
$853$	11.1997	0.383471	0.191735	−	0.981447i	$-0.438588\pi$
$853$	11.1997	0.383471	0.191735	+	0.981447i	$0.438588\pi$
$854$	−2.38280	−0.0815378
$855$	3.25509	0.111322
$856$	−0.974184	−0.0332969
$857$	44.7021	1.52699	0.763497	−	0.645812i	$-0.223481\pi$
$857$	44.7021	1.52699	0.763497	+	0.645812i	$0.223481\pi$
$858$	−4.73973	−0.161812
$859$	22.4165	0.764842	0.382421	−	0.923988i	$-0.375090\pi$
$859$	22.4165	0.764842	0.382421	+	0.923988i	$0.375090\pi$
$860$	3.72050	0.126868
$861$	1.09030	0.0371572
$862$	26.4944	0.902403
$863$	5.30740	0.180666	0.0903329	−	0.995912i	$-0.471207\pi$
$863$	5.30740	0.180666	0.0903329	+	0.995912i	$0.471207\pi$
$864$	2.51179	0.0854528
$865$	6.06094	0.206078
$866$	43.5689	1.48053
$867$	17.7586	0.603115
$868$	6.09851	0.206997
$869$	−9.11250	−0.309120
$870$	10.2241	0.346628
$871$	−1.44600	−0.0489959
$872$	1.56529	0.0530073
$873$	−35.6982	−1.20820
$874$	−11.6548	−0.394230
$875$	2.95270	0.0998195
$876$	17.6459	0.596200
$877$	14.0846	0.475605	0.237802	−	0.971314i	$-0.423573\pi$
$877$	14.0846	0.475605	0.237802	+	0.971314i	$0.423573\pi$
$878$	33.8237	1.14149
$879$	60.0703	2.02612
$880$	11.9052	0.401323
$881$	34.0997	1.14885	0.574425	−	0.818557i	$-0.305226\pi$
$881$	34.0997	1.14885	0.574425	+	0.818557i	$0.305226\pi$
$882$	−38.9830	−1.31263
$883$	43.6542	1.46908	0.734540	−	0.678565i	$-0.237398\pi$
$883$	43.6542	1.46908	0.734540	+	0.678565i	$0.237398\pi$
$884$	2.69674	0.0907011
$885$	−25.7827	−0.866676
$886$	−40.1389	−1.34849
$887$	−42.3456	−1.42183	−0.710913	−	0.703280i	$-0.751718\pi$
$887$	−42.3456	−1.42183	−0.710913	+	0.703280i	$0.751718\pi$
$888$	−0.435243	−0.0146058
$889$	3.98565	0.133674
$890$	−3.46332	−0.116091
$891$	−32.6759	−1.09469
$892$	43.2639	1.44858
$893$	4.13050	0.138222
$894$	14.3386	0.479555
$895$	−2.61765	−0.0874985
$896$	0.419502	0.0140146
$897$	−2.93711	−0.0980672
$898$	−19.4833	−0.650166
$899$	−21.2123	−0.707469
$900$	−23.9171	−0.797238
$901$	30.3102	1.00978
$902$	8.10976	0.270025
$903$	−2.16586	−0.0720753
$904$	−2.04669	−0.0680718
$905$	9.07975	0.301821
$906$	60.7558	2.01848
$907$	−1.35240	−0.0449056	−0.0224528	−	0.999748i	$-0.507148\pi$
$907$	−1.35240	−0.0449056	−0.0224528	+	0.999748i	$0.507148\pi$
$908$	22.4947	0.746511
$909$	31.0512	1.02990
$910$	0.177901	0.00589737
$911$	27.6258	0.915283	0.457642	−	0.889137i	$-0.348694\pi$
$911$	27.6258	0.915283	0.457642	+	0.889137i	$0.348694\pi$
$912$	13.7463	0.455184
$913$	15.1402	0.501068
$914$	−45.1415	−1.49315
$915$	6.27481	0.207439
$916$	21.6997	0.716978
$917$	−4.48299	−0.148041
$918$	3.10109	0.102351
$919$	−40.7405	−1.34390	−0.671952	−	0.740594i	$-0.734544\pi$
$919$	−40.7405	−1.34390	−0.671952	+	0.740594i	$0.734544\pi$
$920$	0.484204	0.0159637
$921$	−70.6273	−2.32725
$922$	30.1107	0.991643
$923$	1.05744	0.0348061
$924$	6.25217	0.205681
$925$	−5.66838	−0.186375
$926$	−64.3910	−2.11602
$927$	54.9509	1.80483
$928$	20.4019	0.669724
$929$	−50.9012	−1.67002	−0.835008	−	0.550238i	$-0.814537\pi$
$929$	−50.9012	−1.67002	−0.835008	+	0.550238i	$0.814537\pi$
$930$	−32.6933	−1.07205
$931$	9.40769	0.308325
$932$	16.2217	0.531358
$933$	52.0476	1.70396
$934$	1.06198	0.0347491
$935$	14.2075	0.464634
$936$	0.111148	0.00363298
$937$	54.0399	1.76541	0.882703	−	0.469931i	$-0.155721\pi$
$937$	54.0399	1.76541	0.882703	+	0.469931i	$0.155721\pi$
$938$	3.88300	0.126785
$939$	30.5668	0.997511
$940$	4.80161	0.156611
$941$	−26.5450	−0.865342	−0.432671	−	0.901552i	$-0.642429\pi$
$941$	−26.5450	−0.865342	−0.432671	+	0.901552i	$0.642429\pi$
$942$	27.1563	0.884800
$943$	5.02544	0.163651
$944$	−53.2261	−1.73236
$945$	0.100492	0.00326902
$946$	−16.1099	−0.523780
$947$	3.27653	0.106473	0.0532364	−	0.998582i	$-0.483046\pi$
$947$	3.27653	0.106473	0.0532364	+	0.998582i	$0.483046\pi$
$948$	−12.2313	−0.397253
$949$	−1.06798	−0.0346681
$950$	11.7500	0.381221
$951$	40.6249	1.31735
$952$	0.258807	0.00838799
$953$	−9.74805	−0.315770	−0.157885	−	0.987457i	$-0.550468\pi$
$953$	−9.74805	−0.315770	−0.157885	+	0.987457i	$0.550468\pi$
$954$	−34.9553	−1.13172
$955$	−0.503316	−0.0162869
$956$	−34.1783	−1.10540
$957$	−21.7468	−0.702973
$958$	10.0942	0.326128
$959$	1.91200	0.0617415
$960$	14.8934	0.480683
$961$	36.8300	1.18806
$962$	−0.737076	−0.0237643
$963$	20.4277	0.658273
$964$	−30.6418	−0.986907
$965$	17.3308	0.557899
$966$	7.88713	0.253764
$967$	−39.5267	−1.27109	−0.635547	−	0.772062i	$-0.719225\pi$
$967$	−39.5267	−1.27109	−0.635547	+	0.772062i	$0.719225\pi$
$968$	−0.156921	−0.00504364
$969$	16.4046	0.526992
$970$	20.3873	0.654598
$971$	31.4981	1.01082	0.505412	−	0.862878i	$-0.331341\pi$
$971$	31.4981	1.01082	0.505412	+	0.862878i	$0.331341\pi$
$972$	−42.0224	−1.34787
$973$	−0.571457	−0.0183201
$974$	−30.1006	−0.964486
$975$	2.96110	0.0948311
$976$	12.9538	0.414640
$977$	1.62068	0.0518502	0.0259251	−	0.999664i	$-0.491747\pi$
$977$	1.62068	0.0518502	0.0259251	+	0.999664i	$0.491747\pi$
$978$	42.9221	1.37250
$979$	7.36653	0.235435
$980$	10.9362	0.349345
$981$	−32.8225	−1.04794
$982$	−60.3106	−1.92459
$983$	54.1650	1.72760	0.863798	−	0.503838i	$-0.168079\pi$
$983$	54.1650	1.72760	0.863798	+	0.503838i	$0.168079\pi$
$984$	−0.389028	−0.0124017
$985$	3.13631	0.0999312
$986$	25.1884	0.802164
$987$	−2.79522	−0.0889728
$988$	0.750534	0.0238777
$989$	−9.98297	−0.317440
$990$	−16.3848	−0.520743
$991$	−52.4067	−1.66476	−0.832378	−	0.554209i	$-0.813021\pi$
$991$	−52.4067	−1.66476	−0.832378	+	0.554209i	$0.813021\pi$
$992$	−65.2386	−2.07133
$993$	34.3329	1.08952
$994$	−2.83959	−0.0900664
$995$	−5.30800	−0.168275
$996$	20.3220	0.643926
$997$	14.9637	0.473906	0.236953	−	0.971521i	$-0.423851\pi$
$997$	14.9637	0.473906	0.236953	+	0.971521i	$0.423851\pi$
$998$	−55.6709	−1.76223
$999$	−0.416357	−0.0131730

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.c.1.20	✓	25
3.2	odd	2		4923.2.a.n.1.6		25
4.3	odd	2		8752.2.a.v.1.4		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.c.1.20	✓	25	1.1	even	1	trivial
4923.2.a.n.1.6		25	3.2	odd	2
8752.2.a.v.1.4		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)

\(f(q)\)	\(=\)	\(q+1.98267 q^{2} +2.42262 q^{3} +1.93099 q^{4} -0.826438 q^{5} +4.80327 q^{6} +0.383471 q^{7} -0.136826 q^{8} +2.86911 q^{9} +O(q^{10})\)	\(q+1.98267 q^{2} +2.42262 q^{3} +1.93099 q^{4} -0.826438 q^{5} +4.80327 q^{6} +0.383471 q^{7} -0.136826 q^{8} +2.86911 q^{9} -1.63856 q^{10} +3.48524 q^{11} +4.67806 q^{12} -0.283129 q^{13} +0.760298 q^{14} -2.00215 q^{15} -4.13326 q^{16} -4.93258 q^{17} +5.68851 q^{18} -1.37279 q^{19} -1.59584 q^{20} +0.929007 q^{21} +6.91008 q^{22} +4.28202 q^{23} -0.331479 q^{24} -4.31700 q^{25} -0.561353 q^{26} -0.317095 q^{27} +0.740479 q^{28} -2.57559 q^{29} -3.96961 q^{30} +8.23590 q^{31} -7.92125 q^{32} +8.44342 q^{33} -9.77969 q^{34} -0.316915 q^{35} +5.54022 q^{36} +1.31304 q^{37} -2.72180 q^{38} -0.685916 q^{39} +0.113078 q^{40} +1.17361 q^{41} +1.84192 q^{42} -2.33137 q^{43} +6.72995 q^{44} -2.37114 q^{45} +8.48985 q^{46} -3.00882 q^{47} -10.0133 q^{48} -6.85295 q^{49} -8.55920 q^{50} -11.9498 q^{51} -0.546720 q^{52} -6.14490 q^{53} -0.628696 q^{54} -2.88033 q^{55} -0.0524690 q^{56} -3.32577 q^{57} -5.10655 q^{58} +12.8775 q^{59} -3.86613 q^{60} -3.13404 q^{61} +16.3291 q^{62} +1.10022 q^{63} -7.43872 q^{64} +0.233989 q^{65} +16.7405 q^{66} +5.10721 q^{67} -9.52475 q^{68} +10.3737 q^{69} -0.628339 q^{70} -3.73484 q^{71} -0.392570 q^{72} +3.77206 q^{73} +2.60332 q^{74} -10.4585 q^{75} -2.65085 q^{76} +1.33649 q^{77} -1.35995 q^{78} -2.61460 q^{79} +3.41588 q^{80} -9.37554 q^{81} +2.32689 q^{82} +4.34410 q^{83} +1.79390 q^{84} +4.07647 q^{85} -4.62234 q^{86} -6.23968 q^{87} -0.476872 q^{88} +2.11364 q^{89} -4.70120 q^{90} -0.108572 q^{91} +8.26854 q^{92} +19.9525 q^{93} -5.96551 q^{94} +1.13453 q^{95} -19.1902 q^{96} -12.4423 q^{97} -13.5872 q^{98} +9.99953 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9}+O(q^{10}) \) 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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