LMFDB - Embedded newform 547.2.a.c.1.5

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			1.5
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)

$f(q)$	$=$	$q-1.98290 q^{2} +2.22215 q^{3} +1.93190 q^{4} +0.712381 q^{5} -4.40631 q^{6} +4.39659 q^{7} +0.135039 q^{8} +1.93796 q^{9} +O(q^{10})$	\(q-1.98290 q^{2} +2.22215 q^{3} +1.93190 q^{4} +0.712381 q^{5} -4.40631 q^{6} +4.39659 q^{7} +0.135039 q^{8} +1.93796 q^{9} -1.41258 q^{10} +3.35537 q^{11} +4.29297 q^{12} -2.53115 q^{13} -8.71801 q^{14} +1.58302 q^{15} -4.13157 q^{16} +4.59046 q^{17} -3.84278 q^{18} -3.55428 q^{19} +1.37625 q^{20} +9.76989 q^{21} -6.65336 q^{22} -2.55608 q^{23} +0.300077 q^{24} -4.49251 q^{25} +5.01902 q^{26} -2.36001 q^{27} +8.49377 q^{28} +5.14817 q^{29} -3.13897 q^{30} +3.73387 q^{31} +7.92241 q^{32} +7.45614 q^{33} -9.10242 q^{34} +3.13205 q^{35} +3.74394 q^{36} -10.4553 q^{37} +7.04778 q^{38} -5.62460 q^{39} +0.0961991 q^{40} -6.42906 q^{41} -19.3727 q^{42} -2.39294 q^{43} +6.48223 q^{44} +1.38057 q^{45} +5.06845 q^{46} +0.655082 q^{47} -9.18097 q^{48} +12.3300 q^{49} +8.90821 q^{50} +10.2007 q^{51} -4.88993 q^{52} -1.90404 q^{53} +4.67967 q^{54} +2.39030 q^{55} +0.593710 q^{56} -7.89815 q^{57} -10.2083 q^{58} +11.5584 q^{59} +3.05823 q^{60} -4.56217 q^{61} -7.40391 q^{62} +8.52042 q^{63} -7.44623 q^{64} -1.80315 q^{65} -14.7848 q^{66} +13.5959 q^{67} +8.86829 q^{68} -5.67999 q^{69} -6.21055 q^{70} +9.44418 q^{71} +0.261700 q^{72} -8.94150 q^{73} +20.7317 q^{74} -9.98305 q^{75} -6.86650 q^{76} +14.7522 q^{77} +11.1530 q^{78} +6.83371 q^{79} -2.94325 q^{80} -11.0582 q^{81} +12.7482 q^{82} +13.3811 q^{83} +18.8744 q^{84} +3.27016 q^{85} +4.74497 q^{86} +11.4400 q^{87} +0.453105 q^{88} -15.4078 q^{89} -2.73753 q^{90} -11.1284 q^{91} -4.93808 q^{92} +8.29724 q^{93} -1.29896 q^{94} -2.53200 q^{95} +17.6048 q^{96} +6.59022 q^{97} -24.4492 q^{98} +6.50257 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.98290	−1.40212	−0.701062	−	0.713101i	$-0.747290\pi$
$2$	−1.98290	−1.40212	−0.701062	+	0.713101i	$0.747290\pi$
$3$	2.22215	1.28296	0.641480	−	0.767140i	$-0.278321\pi$
$3$	2.22215	1.28296	0.641480	+	0.767140i	$0.278321\pi$
$4$	1.93190	0.965949
$5$	0.712381	0.318587	0.159293	−	0.987231i	$-0.449078\pi$
$5$	0.712381	0.318587	0.159293	+	0.987231i	$0.449078\pi$
$6$	−4.40631	−1.79887
$7$	4.39659	1.66176	0.830878	−	0.556455i	$-0.187839\pi$
$7$	4.39659	1.66176	0.830878	+	0.556455i	$0.187839\pi$
$8$	0.135039	0.0477434
$9$	1.93796	0.645987
$10$	−1.41258	−0.446698
$11$	3.35537	1.01168	0.505841	−	0.862627i	$-0.331182\pi$
$11$	3.35537	1.01168	0.505841	+	0.862627i	$0.331182\pi$
$12$	4.29297	1.23927
$13$	−2.53115	−0.702015	−0.351008	−	0.936373i	$-0.614161\pi$
$13$	−2.53115	−0.702015	−0.351008	+	0.936373i	$0.614161\pi$
$14$	−8.71801	−2.32999
$15$	1.58302	0.408734
$16$	−4.13157	−1.03289
$17$	4.59046	1.11335	0.556675	−	0.830731i	$-0.312077\pi$
$17$	4.59046	1.11335	0.556675	+	0.830731i	$0.312077\pi$
$18$	−3.84278	−0.905753
$19$	−3.55428	−0.815407	−0.407704	−	0.913114i	$-0.633670\pi$
$19$	−3.55428	−0.815407	−0.407704	+	0.913114i	$0.633670\pi$
$20$	1.37625	0.307739
$21$	9.76989	2.13197
$22$	−6.65336	−1.41850
$23$	−2.55608	−0.532979	−0.266489	−	0.963838i	$-0.585864\pi$
$23$	−2.55608	−0.532979	−0.266489	+	0.963838i	$0.585864\pi$
$24$	0.300077	0.0612529
$25$	−4.49251	−0.898503
$26$	5.01902	0.984312
$27$	−2.36001	−0.454185
$28$	8.49377	1.60517
$29$	5.14817	0.955990	0.477995	−	0.878362i	$-0.341364\pi$
$29$	5.14817	0.955990	0.477995	+	0.878362i	$0.341364\pi$
$30$	−3.13897	−0.573095
$31$	3.73387	0.670624	0.335312	−	0.942107i	$-0.391158\pi$
$31$	3.73387	0.670624	0.335312	+	0.942107i	$0.391158\pi$
$32$	7.92241	1.40050
$33$	7.45614	1.29795
$34$	−9.10242	−1.56105
$35$	3.13205	0.529413
$36$	3.74394	0.623990
$37$	−10.4553	−1.71883	−0.859417	−	0.511276i	$-0.829173\pi$
$37$	−10.4553	−1.71883	−0.859417	+	0.511276i	$0.829173\pi$
$38$	7.04778	1.14330
$39$	−5.62460	−0.900657
$40$	0.0961991	0.0152104
$41$	−6.42906	−1.00405	−0.502025	−	0.864853i	$-0.667411\pi$
$41$	−6.42906	−1.00405	−0.502025	+	0.864853i	$0.667411\pi$
$42$	−19.3727	−2.98928
$43$	−2.39294	−0.364920	−0.182460	−	0.983213i	$-0.558406\pi$
$43$	−2.39294	−0.364920	−0.182460	+	0.983213i	$0.558406\pi$
$44$	6.48223	0.977233
$45$	1.38057	0.205803
$46$	5.06845	0.747302
$47$	0.655082	0.0955535	0.0477768	−	0.998858i	$-0.484786\pi$
$47$	0.655082	0.0955535	0.0477768	+	0.998858i	$0.484786\pi$
$48$	−9.18097	−1.32516
$49$	12.3300	1.76143
$50$	8.90821	1.25981
$51$	10.2007	1.42838
$52$	−4.88993	−0.678111
$53$	−1.90404	−0.261540	−0.130770	−	0.991413i	$-0.541745\pi$
$53$	−1.90404	−0.261540	−0.130770	+	0.991413i	$0.541745\pi$
$54$	4.67967	0.636823
$55$	2.39030	0.322308
$56$	0.593710	0.0793379
$57$	−7.89815	−1.04614
$58$	−10.2083	−1.34042
$59$	11.5584	1.50478	0.752391	−	0.658717i	$-0.228901\pi$
$59$	11.5584	1.50478	0.752391	+	0.658717i	$0.228901\pi$
$60$	3.05823	0.394816
$61$	−4.56217	−0.584126	−0.292063	−	0.956399i	$-0.594342\pi$
$61$	−4.56217	−0.584126	−0.292063	+	0.956399i	$0.594342\pi$
$62$	−7.40391	−0.940297
$63$	8.52042	1.07347
$64$	−7.44623	−0.930778
$65$	−1.80315	−0.223653
$66$	−14.7848	−1.81988
$67$	13.5959	1.66100	0.830499	−	0.557020i	$-0.188056\pi$
$67$	13.5959	1.66100	0.830499	+	0.557020i	$0.188056\pi$
$68$	8.86829	1.07544
$69$	−5.67999	−0.683790
$70$	−6.21055	−0.742302
$71$	9.44418	1.12082	0.560409	−	0.828216i	$-0.310644\pi$
$71$	9.44418	1.12082	0.560409	+	0.828216i	$0.310644\pi$
$72$	0.261700	0.0308416
$73$	−8.94150	−1.04652	−0.523262	−	0.852172i	$-0.675285\pi$
$73$	−8.94150	−1.04652	−0.523262	+	0.852172i	$0.675285\pi$
$74$	20.7317	2.41002
$75$	−9.98305	−1.15274
$76$	−6.86650	−0.787642
$77$	14.7522	1.68117
$78$	11.1530	1.26283
$79$	6.83371	0.768852	0.384426	−	0.923156i	$-0.374399\pi$
$79$	6.83371	0.768852	0.384426	+	0.923156i	$0.374399\pi$
$80$	−2.94325	−0.329065
$81$	−11.0582	−1.22869
$82$	12.7482	1.40780
$83$	13.3811	1.46877	0.734385	−	0.678733i	$-0.237470\pi$
$83$	13.3811	1.46877	0.734385	+	0.678733i	$0.237470\pi$
$84$	18.8744	2.05937
$85$	3.27016	0.354698
$86$	4.74497	0.511663
$87$	11.4400	1.22650
$88$	0.453105	0.0483011
$89$	−15.4078	−1.63323	−0.816614	−	0.577185i	$-0.804151\pi$
$89$	−15.4078	−1.63323	−0.816614	+	0.577185i	$0.804151\pi$
$90$	−2.73753	−0.288561
$91$	−11.1284	−1.16658
$92$	−4.93808	−0.514830
$93$	8.29724	0.860384
$94$	−1.29896	−0.133978
$95$	−2.53200	−0.259778
$96$	17.6048	1.79678
$97$	6.59022	0.669135	0.334568	−	0.942372i	$-0.391410\pi$
$97$	6.59022	0.669135	0.334568	+	0.942372i	$0.391410\pi$
$98$	−24.4492	−2.46974
$99$	6.50257	0.653533
$100$	−8.67908	−0.867908
$101$	−8.18518	−0.814455	−0.407228	−	0.913327i	$-0.633504\pi$
$101$	−8.18518	−0.814455	−0.407228	+	0.913327i	$0.633504\pi$
$102$	−20.2270	−2.00277
$103$	−0.986016	−0.0971550	−0.0485775	−	0.998819i	$-0.515469\pi$
$103$	−0.986016	−0.0971550	−0.0485775	+	0.998819i	$0.515469\pi$
$104$	−0.341804	−0.0335166
$105$	6.95989	0.679216
$106$	3.77552	0.366711
$107$	−13.5258	−1.30758	−0.653792	−	0.756674i	$-0.726823\pi$
$107$	−13.5258	−1.30758	−0.653792	+	0.756674i	$0.726823\pi$
$108$	−4.55931	−0.438719
$109$	12.4417	1.19169	0.595847	−	0.803098i	$-0.296816\pi$
$109$	12.4417	1.19169	0.595847	+	0.803098i	$0.296816\pi$
$110$	−4.73973	−0.451916
$111$	−23.2332	−2.20520
$112$	−18.1648	−1.71641
$113$	−6.83528	−0.643009	−0.321505	−	0.946908i	$-0.604189\pi$
$113$	−6.83528	−0.643009	−0.321505	+	0.946908i	$0.604189\pi$
$114$	15.6612	1.46681
$115$	−1.82090	−0.169800
$116$	9.94573	0.923438
$117$	−4.90527	−0.453493
$118$	−22.9193	−2.10989
$119$	20.1824	1.85011
$120$	0.213769	0.0195144
$121$	0.258495	0.0234995
$122$	9.04633	0.819016
$123$	−14.2863	−1.28816
$124$	7.21347	0.647788
$125$	−6.76229	−0.604838
$126$	−16.8952	−1.50514
$127$	−8.02668	−0.712253	−0.356126	−	0.934438i	$-0.615903\pi$
$127$	−8.02668	−0.712253	−0.356126	+	0.934438i	$0.615903\pi$
$128$	−1.07968	−0.0954315
$129$	−5.31748	−0.468178
$130$	3.57546	0.313589
$131$	−7.45795	−0.651604	−0.325802	−	0.945438i	$-0.605634\pi$
$131$	−7.45795	−0.651604	−0.325802	+	0.945438i	$0.605634\pi$
$132$	14.4045	1.25375
$133$	−15.6267	−1.35501
$134$	−26.9592	−2.32892
$135$	−1.68123	−0.144697
$136$	0.619890	0.0531551
$137$	5.26530	0.449845	0.224922	−	0.974377i	$-0.427787\pi$
$137$	5.26530	0.449845	0.224922	+	0.974377i	$0.427787\pi$
$138$	11.2629	0.958758
$139$	−16.6957	−1.41611	−0.708056	−	0.706157i	$-0.750427\pi$
$139$	−16.6957	−1.41611	−0.708056	+	0.706157i	$0.750427\pi$
$140$	6.05080	0.511386
$141$	1.45569	0.122591
$142$	−18.7269	−1.57153
$143$	−8.49294	−0.710216
$144$	−8.00681	−0.667234
$145$	3.66746	0.304566
$146$	17.7301	1.46735
$147$	27.3992	2.25984
$148$	−20.1985	−1.66031
$149$	−7.73867	−0.633976	−0.316988	−	0.948430i	$-0.602672\pi$
$149$	−7.73867	−0.633976	−0.316988	+	0.948430i	$0.602672\pi$
$150$	19.7954	1.61629
$151$	−20.1661	−1.64109	−0.820547	−	0.571579i	$-0.806331\pi$
$151$	−20.1661	−1.64109	−0.820547	+	0.571579i	$0.806331\pi$
$152$	−0.479965	−0.0389303
$153$	8.89612	0.719209
$154$	−29.2521	−2.35720
$155$	2.65994	0.213652
$156$	−10.8662	−0.869989
$157$	23.0377	1.83861	0.919304	−	0.393548i	$-0.128752\pi$
$157$	23.0377	1.83861	0.919304	+	0.393548i	$0.128752\pi$
$158$	−13.5506	−1.07803
$159$	−4.23106	−0.335545
$160$	5.64378	0.446180
$161$	−11.2380	−0.885680
$162$	21.9273	1.72277
$163$	−4.87315	−0.381694	−0.190847	−	0.981620i	$-0.561124\pi$
$163$	−4.87315	−0.381694	−0.190847	+	0.981620i	$0.561124\pi$
$164$	−12.4203	−0.969861
$165$	5.31161	0.413509
$166$	−26.5335	−2.05940
$167$	4.67914	0.362083	0.181041	−	0.983475i	$-0.442053\pi$
$167$	4.67914	0.362083	0.181041	+	0.983475i	$0.442053\pi$
$168$	1.31931	0.101787
$169$	−6.59327	−0.507175
$170$	−6.48440	−0.497330
$171$	−6.88805	−0.526742
$172$	−4.62292	−0.352494
$173$	−8.50196	−0.646392	−0.323196	−	0.946332i	$-0.604757\pi$
$173$	−8.50196	−0.646392	−0.323196	+	0.946332i	$0.604757\pi$
$174$	−22.6844	−1.71970
$175$	−19.7517	−1.49309
$176$	−13.8629	−1.04496
$177$	25.6846	1.93057
$178$	30.5522	2.28999
$179$	8.80118	0.657831	0.328916	−	0.944359i	$-0.393317\pi$
$179$	8.80118	0.657831	0.328916	+	0.944359i	$0.393317\pi$
$180$	2.66712	0.198795
$181$	5.64971	0.419940	0.209970	−	0.977708i	$-0.432663\pi$
$181$	5.64971	0.419940	0.209970	+	0.977708i	$0.432663\pi$
$182$	22.0666	1.63568
$183$	−10.1378	−0.749410
$184$	−0.345169	−0.0254462
$185$	−7.44813	−0.547597
$186$	−16.4526	−1.20636
$187$	15.4027	1.12635
$188$	1.26555	0.0922999
$189$	−10.3760	−0.754744
$190$	5.02071	0.364241
$191$	2.05404	0.148625	0.0743124	−	0.997235i	$-0.476324\pi$
$191$	2.05404	0.148625	0.0743124	+	0.997235i	$0.476324\pi$
$192$	−16.5467	−1.19415
$193$	−18.3204	−1.31873	−0.659366	−	0.751822i	$-0.729175\pi$
$193$	−18.3204	−1.31873	−0.659366	+	0.751822i	$0.729175\pi$
$194$	−13.0677	−0.938210
$195$	−4.00686	−0.286937
$196$	23.8203	1.70145
$197$	22.2367	1.58430	0.792149	−	0.610328i	$-0.208962\pi$
$197$	22.2367	1.58430	0.792149	+	0.610328i	$0.208962\pi$
$198$	−12.8940	−0.916334
$199$	3.69903	0.262217	0.131109	−	0.991368i	$-0.458146\pi$
$199$	3.69903	0.262217	0.131109	+	0.991368i	$0.458146\pi$
$200$	−0.606663	−0.0428976
$201$	30.2120	2.13099
$202$	16.2304	1.14197
$203$	22.6344	1.58862
$204$	19.7067	1.37974
$205$	−4.57994	−0.319877
$206$	1.95517	0.136223
$207$	−4.95357	−0.344297
$208$	10.4576	0.725105
$209$	−11.9259	−0.824933
$210$	−13.8008	−0.952344
$211$	17.8259	1.22719	0.613593	−	0.789623i	$-0.289724\pi$
$211$	17.8259	1.22719	0.613593	+	0.789623i	$0.289724\pi$
$212$	−3.67841	−0.252634
$213$	20.9864	1.43797
$214$	26.8202	1.83339
$215$	−1.70469	−0.116259
$216$	−0.318693	−0.0216843
$217$	16.4163	1.11441
$218$	−24.6706	−1.67090
$219$	−19.8694	−1.34265
$220$	4.61782	0.311333
$221$	−11.6191	−0.781588
$222$	46.0691	3.09196
$223$	−18.5405	−1.24157	−0.620783	−	0.783982i	$-0.713185\pi$
$223$	−18.5405	−1.24157	−0.620783	+	0.783982i	$0.713185\pi$
$224$	34.8316	2.32728
$225$	−8.70631	−0.580421
$226$	13.5537	0.901578
$227$	−1.75864	−0.116725	−0.0583625	−	0.998295i	$-0.518588\pi$
$227$	−1.75864	−0.116725	−0.0583625	+	0.998295i	$0.518588\pi$
$228$	−15.2584	−1.01051
$229$	−7.73042	−0.510840	−0.255420	−	0.966830i	$-0.582214\pi$
$229$	−7.73042	−0.510840	−0.255420	+	0.966830i	$0.582214\pi$
$230$	3.61067	0.238080
$231$	32.7816	2.15687
$232$	0.695202	0.0456423
$233$	22.8019	1.49380	0.746902	−	0.664934i	$-0.231540\pi$
$233$	22.8019	1.49380	0.746902	+	0.664934i	$0.231540\pi$
$234$	9.72667	0.635852
$235$	0.466668	0.0304421
$236$	22.3297	1.45354
$237$	15.1855	0.986407
$238$	−40.0196	−2.59409
$239$	−14.1169	−0.913149	−0.456575	−	0.889685i	$-0.650924\pi$
$239$	−14.1169	−0.913149	−0.456575	+	0.889685i	$0.650924\pi$
$240$	−6.54035	−0.422178
$241$	−4.96966	−0.320124	−0.160062	−	0.987107i	$-0.551169\pi$
$241$	−4.96966	−0.320124	−0.160062	+	0.987107i	$0.551169\pi$
$242$	−0.512570	−0.0329492
$243$	−17.4929	−1.12217
$244$	−8.81364	−0.564236
$245$	8.78367	0.561168
$246$	28.3284	1.80615
$247$	8.99642	0.572428
$248$	0.504218	0.0320179
$249$	29.7349	1.88437
$250$	13.4090	0.848057
$251$	6.31919	0.398864	0.199432	−	0.979912i	$-0.436090\pi$
$251$	6.31919	0.398864	0.199432	+	0.979912i	$0.436090\pi$
$252$	16.4606	1.03692
$253$	−8.57657	−0.539205
$254$	15.9161	0.998666
$255$	7.26678	0.455064
$256$	17.0334	1.06459
$257$	16.1829	1.00946	0.504730	−	0.863277i	$-0.331592\pi$
$257$	16.1829	1.00946	0.504730	+	0.863277i	$0.331592\pi$
$258$	10.5440	0.656443
$259$	−45.9675	−2.85628
$260$	−3.48349	−0.216037
$261$	9.97694	0.617557
$262$	14.7884	0.913630
$263$	−17.0403	−1.05075	−0.525375	−	0.850871i	$-0.676075\pi$
$263$	−17.0403	−1.05075	−0.525375	+	0.850871i	$0.676075\pi$
$264$	1.00687	0.0619684
$265$	−1.35640	−0.0833230
$266$	30.9862	1.89989
$267$	−34.2386	−2.09537
$268$	26.2658	1.60444
$269$	14.8919	0.907975	0.453988	−	0.891008i	$-0.350001\pi$
$269$	14.8919	0.907975	0.453988	+	0.891008i	$0.350001\pi$
$270$	3.33371	0.202883
$271$	−0.717096	−0.0435605	−0.0217802	−	0.999763i	$-0.506933\pi$
$271$	−0.717096	−0.0435605	−0.0217802	+	0.999763i	$0.506933\pi$
$272$	−18.9658	−1.14997
$273$	−24.7291	−1.49667
$274$	−10.4406	−0.630737
$275$	−15.0740	−0.908998
$276$	−10.9732	−0.660507
$277$	−9.12809	−0.548454	−0.274227	−	0.961665i	$-0.588422\pi$
$277$	−9.12809	−0.548454	−0.274227	+	0.961665i	$0.588422\pi$
$278$	33.1059	1.98556
$279$	7.23610	0.433214
$280$	0.422948	0.0252760
$281$	−26.4024	−1.57504	−0.787519	−	0.616291i	$-0.788635\pi$
$281$	−26.4024	−1.57504	−0.787519	+	0.616291i	$0.788635\pi$
$282$	−2.88649	−0.171888
$283$	3.99826	0.237672	0.118836	−	0.992914i	$-0.462084\pi$
$283$	3.99826	0.237672	0.118836	+	0.992914i	$0.462084\pi$
$284$	18.2452	1.08265
$285$	−5.62649	−0.333285
$286$	16.8407	0.995810
$287$	−28.2659	−1.66849
$288$	15.3533	0.904703
$289$	4.07228	0.239546
$290$	−7.27221	−0.427039
$291$	14.6445	0.858474
$292$	−17.2741	−1.01089
$293$	9.63049	0.562619	0.281309	−	0.959617i	$-0.409231\pi$
$293$	9.63049	0.562619	0.281309	+	0.959617i	$0.409231\pi$
$294$	−54.3298	−3.16858
$295$	8.23402	0.479403
$296$	−1.41187	−0.0820630
$297$	−7.91871	−0.459490
$298$	15.3450	0.888913
$299$	6.46981	0.374159
$300$	−19.2862	−1.11349
$301$	−10.5208	−0.606408
$302$	39.9874	2.30102
$303$	−18.1887	−1.04491
$304$	14.6847	0.842227
$305$	−3.25000	−0.186095
$306$	−17.6401	−1.00842
$307$	−33.0818	−1.88808	−0.944040	−	0.329832i	$-0.893008\pi$
$307$	−33.0818	−1.88808	−0.944040	+	0.329832i	$0.893008\pi$
$308$	28.4997	1.62392
$309$	−2.19108	−0.124646
$310$	−5.27440	−0.299566
$311$	18.0798	1.02521	0.512605	−	0.858624i	$-0.328680\pi$
$311$	18.0798	1.02521	0.512605	+	0.858624i	$0.328680\pi$
$312$	−0.759540	−0.0430005
$313$	10.3661	0.585927	0.292963	−	0.956124i	$-0.405359\pi$
$313$	10.3661	0.585927	0.292963	+	0.956124i	$0.405359\pi$
$314$	−45.6815	−2.57796
$315$	6.06979	0.341994
$316$	13.2020	0.742672
$317$	3.76302	0.211352	0.105676	−	0.994401i	$-0.466299\pi$
$317$	3.76302	0.211352	0.105676	+	0.994401i	$0.466299\pi$
$318$	8.38978	0.470475
$319$	17.2740	0.967158
$320$	−5.30455	−0.296534
$321$	−30.0563	−1.67758
$322$	22.2839	1.24183
$323$	−16.3158	−0.907833
$324$	−21.3633	−1.18685
$325$	11.3712	0.630762
$326$	9.66297	0.535183
$327$	27.6472	1.52890
$328$	−0.868172	−0.0479368
$329$	2.88013	0.158787
$330$	−10.5324	−0.579790
$331$	−13.0196	−0.715623	−0.357811	−	0.933794i	$-0.616477\pi$
$331$	−13.0196	−0.715623	−0.357811	+	0.933794i	$0.616477\pi$
$332$	25.8510	1.41876
$333$	−20.2619	−1.11034
$334$	−9.27828	−0.507685
$335$	9.68543	0.529172
$336$	−40.3650	−2.20209
$337$	27.1502	1.47897	0.739483	−	0.673175i	$-0.235070\pi$
$337$	27.1502	1.47897	0.739483	+	0.673175i	$0.235070\pi$
$338$	13.0738	0.711121
$339$	−15.1890	−0.824955
$340$	6.31761	0.342620
$341$	12.5285	0.678458
$342$	13.6583	0.738558
$343$	23.4339	1.26531
$344$	−0.323140	−0.0174225
$345$	−4.04632	−0.217846
$346$	16.8585	0.906321
$347$	36.7795	1.97443	0.987213	−	0.159405i	$-0.0509575\pi$
$347$	36.7795	1.97443	0.987213	+	0.159405i	$0.0509575\pi$
$348$	22.1009	1.18473
$349$	28.0449	1.50121	0.750606	−	0.660750i	$-0.229762\pi$
$349$	28.0449	1.50121	0.750606	+	0.660750i	$0.229762\pi$
$350$	39.1658	2.09350
$351$	5.97355	0.318845
$352$	26.5826	1.41686
$353$	−14.9368	−0.795005	−0.397502	−	0.917601i	$-0.630123\pi$
$353$	−14.9368	−0.795005	−0.397502	+	0.917601i	$0.630123\pi$
$354$	−50.9301	−2.70690
$355$	6.72786	0.357078
$356$	−29.7664	−1.57761
$357$	44.8483	2.37362
$358$	−17.4519	−0.922360
$359$	−19.5526	−1.03195	−0.515973	−	0.856605i	$-0.672570\pi$
$359$	−19.5526	−1.03195	−0.515973	+	0.856605i	$0.672570\pi$
$360$	0.186430	0.00982573
$361$	−6.36711	−0.335111
$362$	−11.2028	−0.588807
$363$	0.574415	0.0301490
$364$	−21.4990	−1.12685
$365$	−6.36976	−0.333408
$366$	20.1023	1.05077
$367$	9.76632	0.509798	0.254899	−	0.966968i	$-0.417958\pi$
$367$	9.76632	0.509798	0.254899	+	0.966968i	$0.417958\pi$
$368$	10.5606	0.550509
$369$	−12.4593	−0.648603
$370$	14.7689	0.767799
$371$	−8.37127	−0.434615
$372$	16.0294	0.831087
$373$	−14.7414	−0.763280	−0.381640	−	0.924311i	$-0.624641\pi$
$373$	−14.7414	−0.763280	−0.381640	+	0.924311i	$0.624641\pi$
$374$	−30.5420	−1.57929
$375$	−15.0268	−0.775983
$376$	0.0884615	0.00456205
$377$	−13.0308	−0.671120
$378$	20.5746	1.05824
$379$	11.0837	0.569329	0.284665	−	0.958627i	$-0.408118\pi$
$379$	11.0837	0.569329	0.284665	+	0.958627i	$0.408118\pi$
$380$	−4.89157	−0.250932
$381$	−17.8365	−0.913792
$382$	−4.07295	−0.208390
$383$	31.2011	1.59430	0.797151	−	0.603780i	$-0.206340\pi$
$383$	31.2011	1.59430	0.797151	+	0.603780i	$0.206340\pi$
$384$	−2.39922	−0.122435
$385$	10.5092	0.535597
$386$	36.3276	1.84903
$387$	−4.63743	−0.235734
$388$	12.7316	0.646350
$389$	18.7044	0.948350	0.474175	−	0.880431i	$-0.342746\pi$
$389$	18.7044	0.948350	0.474175	+	0.880431i	$0.342746\pi$
$390$	7.94521	0.402322
$391$	−11.7336	−0.593391
$392$	1.66503	0.0840967
$393$	−16.5727	−0.835983
$394$	−44.0931	−2.22138
$395$	4.86821	0.244946
$396$	12.5623	0.631280
$397$	9.10573	0.457003	0.228502	−	0.973544i	$-0.426617\pi$
$397$	9.10573	0.457003	0.228502	+	0.973544i	$0.426617\pi$
$398$	−7.33481	−0.367661
$399$	−34.7249	−1.73842
$400$	18.5611	0.928056
$401$	−26.3060	−1.31366	−0.656831	−	0.754038i	$-0.728103\pi$
$401$	−26.3060	−1.31366	−0.656831	+	0.754038i	$0.728103\pi$
$402$	−59.9075	−2.98792
$403$	−9.45100	−0.470788
$404$	−15.8129	−0.786723
$405$	−7.87765	−0.391444
$406$	−44.8817	−2.22744
$407$	−35.0812	−1.73891
$408$	1.37749	0.0681959
$409$	−30.1487	−1.49076	−0.745378	−	0.666642i	$-0.767731\pi$
$409$	−30.1487	−1.49076	−0.745378	+	0.666642i	$0.767731\pi$
$410$	9.08157	0.448507
$411$	11.7003	0.577133
$412$	−1.90488	−0.0938468
$413$	50.8178	2.50058
$414$	9.82245	0.482747
$415$	9.53248	0.467931
$416$	−20.0528	−0.983170
$417$	−37.1004	−1.81681
$418$	23.6479	1.15666
$419$	−19.2797	−0.941875	−0.470937	−	0.882167i	$-0.656084\pi$
$419$	−19.2797	−0.941875	−0.470937	+	0.882167i	$0.656084\pi$
$420$	13.4458	0.656088
$421$	−22.0329	−1.07382	−0.536910	−	0.843639i	$-0.680409\pi$
$421$	−22.0329	−1.07382	−0.536910	+	0.843639i	$0.680409\pi$
$422$	−35.3470	−1.72067
$423$	1.26952	0.0617263
$424$	−0.257119	−0.0124868
$425$	−20.6227	−1.00035
$426$	−41.6140	−2.01620
$427$	−20.0580	−0.970674
$428$	−26.1304	−1.26306
$429$	−18.8726	−0.911178
$430$	3.38023	0.163009
$431$	−14.5238	−0.699585	−0.349793	−	0.936827i	$-0.613748\pi$
$431$	−14.5238	−0.699585	−0.349793	+	0.936827i	$0.613748\pi$
$432$	9.75055	0.469124
$433$	−14.0023	−0.672908	−0.336454	−	0.941700i	$-0.609228\pi$
$433$	−14.0023	−0.672908	−0.336454	+	0.941700i	$0.609228\pi$
$434$	−32.5519	−1.56254
$435$	8.14965	0.390746
$436$	24.0360	1.15112
$437$	9.08500	0.434595
$438$	39.3990	1.88256
$439$	36.3096	1.73296	0.866482	−	0.499208i	$-0.166376\pi$
$439$	36.3096	1.73296	0.866482	+	0.499208i	$0.166376\pi$
$440$	0.322783	0.0153881
$441$	23.8951	1.13786
$442$	23.0396	1.09588
$443$	−14.0802	−0.668972	−0.334486	−	0.942401i	$-0.608563\pi$
$443$	−14.0802	−0.668972	−0.334486	+	0.942401i	$0.608563\pi$
$444$	−44.8841	−2.13011
$445$	−10.9763	−0.520324
$446$	36.7641	1.74083
$447$	−17.1965	−0.813366
$448$	−32.7380	−1.54673
$449$	0.723191	0.0341295	0.0170647	−	0.999854i	$-0.494568\pi$
$449$	0.723191	0.0341295	0.0170647	+	0.999854i	$0.494568\pi$
$450$	17.2638	0.813821
$451$	−21.5719	−1.01578
$452$	−13.2051	−0.621114
$453$	−44.8121	−2.10546
$454$	3.48721	0.163663
$455$	−7.92769	−0.371656
$456$	−1.06656	−0.0499461
$457$	25.8037	1.20705	0.603523	−	0.797346i	$-0.293763\pi$
$457$	25.8037	1.20705	0.603523	+	0.797346i	$0.293763\pi$
$458$	15.3287	0.716261
$459$	−10.8335	−0.505666
$460$	−3.51779	−0.164018
$461$	14.5026	0.675453	0.337726	−	0.941244i	$-0.390342\pi$
$461$	14.5026	0.675453	0.337726	+	0.941244i	$0.390342\pi$
$462$	−65.0027	−3.02420
$463$	36.0906	1.67727	0.838636	−	0.544693i	$-0.183354\pi$
$463$	36.0906	1.67727	0.838636	+	0.544693i	$0.183354\pi$
$464$	−21.2700	−0.987434
$465$	5.91080	0.274107
$466$	−45.2140	−2.09450
$467$	35.9415	1.66318	0.831588	−	0.555393i	$-0.187432\pi$
$467$	35.9415	1.66318	0.831588	+	0.555393i	$0.187432\pi$
$468$	−9.47649	−0.438051
$469$	59.7754	2.76017
$470$	−0.925357	−0.0426835
$471$	51.1933	2.35886
$472$	1.56084	0.0718434
$473$	−8.02920	−0.369183
$474$	−30.1114	−1.38306
$475$	15.9676	0.732646
$476$	38.9903	1.78712
$477$	−3.68995	−0.168951
$478$	27.9925	1.28035
$479$	−31.8677	−1.45607	−0.728037	−	0.685538i	$-0.759567\pi$
$479$	−31.8677	−1.45607	−0.728037	+	0.685538i	$0.759567\pi$
$480$	12.5413	0.572431
$481$	26.4638	1.20665
$482$	9.85435	0.448853
$483$	−24.9726	−1.13629
$484$	0.499386	0.0226994
$485$	4.69475	0.213177
$486$	34.6868	1.57342
$487$	12.6821	0.574681	0.287341	−	0.957828i	$-0.407229\pi$
$487$	12.6821	0.574681	0.287341	+	0.957828i	$0.407229\pi$
$488$	−0.616069	−0.0278882
$489$	−10.8289	−0.489699
$490$	−17.4172	−0.786827
$491$	33.7881	1.52483	0.762417	−	0.647086i	$-0.224013\pi$
$491$	33.7881	1.52483	0.762417	+	0.647086i	$0.224013\pi$
$492$	−27.5998	−1.24429
$493$	23.6324	1.06435
$494$	−17.8390	−0.802615
$495$	4.63231	0.208207
$496$	−15.4267	−0.692681
$497$	41.5222	1.86253
$498$	−58.9614	−2.64213
$499$	−15.2141	−0.681077	−0.340538	−	0.940231i	$-0.610609\pi$
$499$	−15.2141	−0.681077	−0.340538	+	0.940231i	$0.610609\pi$
$500$	−13.0641	−0.584242
$501$	10.3978	0.464538
$502$	−12.5303	−0.559256
$503$	18.6115	0.829845	0.414923	−	0.909857i	$-0.363809\pi$
$503$	18.6115	0.829845	0.414923	+	0.909857i	$0.363809\pi$
$504$	1.15059	0.0512512
$505$	−5.83097	−0.259475
$506$	17.0065	0.756031
$507$	−14.6513	−0.650685
$508$	−15.5067	−0.688000
$509$	−4.75744	−0.210870	−0.105435	−	0.994426i	$-0.533623\pi$
$509$	−4.75744	−0.210870	−0.105435	+	0.994426i	$0.533623\pi$
$510$	−14.4093	−0.638055
$511$	−39.3121	−1.73907
$512$	−31.6161	−1.39725
$513$	8.38814	0.370346
$514$	−32.0890	−1.41539
$515$	−0.702419	−0.0309523
$516$	−10.2728	−0.452236
$517$	2.19804	0.0966697
$518$	91.1490	4.00486
$519$	−18.8926	−0.829295
$520$	−0.243495	−0.0106779
$521$	−37.2463	−1.63179	−0.815894	−	0.578202i	$-0.803755\pi$
$521$	−37.2463	−1.63179	−0.815894	+	0.578202i	$0.803755\pi$
$522$	−19.7833	−0.865891
$523$	−31.6588	−1.38434	−0.692171	−	0.721734i	$-0.743345\pi$
$523$	−31.6588	−1.38434	−0.692171	+	0.721734i	$0.743345\pi$
$524$	−14.4080	−0.629417
$525$	−43.8914	−1.91558
$526$	33.7893	1.47328
$527$	17.1402	0.746638
$528$	−30.8055	−1.34064
$529$	−16.4665	−0.715934
$530$	2.68961	0.116829
$531$	22.3998	0.972069
$532$	−30.1892	−1.30887
$533$	16.2729	0.704858
$534$	67.8917	2.93796
$535$	−9.63549	−0.416579
$536$	1.83597	0.0793017
$537$	19.5576	0.843971
$538$	−29.5292	−1.27309
$539$	41.3717	1.78201
$540$	−3.24796	−0.139770
$541$	36.6462	1.57554	0.787771	−	0.615969i	$-0.211235\pi$
$541$	36.6462	1.57554	0.787771	+	0.615969i	$0.211235\pi$
$542$	1.42193	0.0610772
$543$	12.5545	0.538766
$544$	36.3675	1.55924
$545$	8.86320	0.379658
$546$	49.0353	2.09852
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	10.1720	0.434527
$549$	−8.84130	−0.377337
$550$	29.8903	1.27453
$551$	−18.2980	−0.779522
$552$	−0.767019	−0.0326465
$553$	30.0450	1.27764
$554$	18.1001	0.769000
$555$	−16.5509	−0.702546
$556$	−32.2544	−1.36789
$557$	−20.3359	−0.861660	−0.430830	−	0.902433i	$-0.641779\pi$
$557$	−20.3359	−0.861660	−0.430830	+	0.902433i	$0.641779\pi$
$558$	−14.3485	−0.607419
$559$	6.05690	0.256179
$560$	−12.9403	−0.546826
$561$	34.2271	1.44507
$562$	52.3534	2.20840
$563$	−4.03557	−0.170079	−0.0850394	−	0.996378i	$-0.527102\pi$
$563$	−4.03557	−0.170079	−0.0850394	+	0.996378i	$0.527102\pi$
$564$	2.81225	0.118417
$565$	−4.86933	−0.204854
$566$	−7.92815	−0.333245
$567$	−48.6183	−2.04178
$568$	1.27533	0.0535117
$569$	1.98791	0.0833376	0.0416688	−	0.999131i	$-0.486733\pi$
$569$	1.98791	0.0833376	0.0416688	+	0.999131i	$0.486733\pi$
$570$	11.1568	0.467306
$571$	−30.1856	−1.26323	−0.631614	−	0.775283i	$-0.717607\pi$
$571$	−30.1856	−1.26323	−0.631614	+	0.775283i	$0.717607\pi$
$572$	−16.4075	−0.686032
$573$	4.56438	0.190680
$574$	56.0486	2.33942
$575$	11.4832	0.478883
$576$	−14.4305	−0.601271
$577$	31.1795	1.29802	0.649010	−	0.760780i	$-0.275183\pi$
$577$	31.1795	1.29802	0.649010	+	0.760780i	$0.275183\pi$
$578$	−8.07494	−0.335873
$579$	−40.7108	−1.69188
$580$	7.08516	0.294195
$581$	58.8314	2.44074
$582$	−29.0385	−1.20369
$583$	−6.38875	−0.264595
$584$	−1.20745	−0.0499646
$585$	−3.49442	−0.144477
$586$	−19.0963	−0.788861
$587$	−29.3436	−1.21114	−0.605571	−	0.795792i	$-0.707055\pi$
$587$	−29.3436	−1.21114	−0.605571	+	0.795792i	$0.707055\pi$
$588$	52.9324	2.18289
$589$	−13.2712	−0.546832
$590$	−16.3273	−0.672182
$591$	49.4133	2.03259
$592$	43.1966	1.77537
$593$	−5.23773	−0.215088	−0.107544	−	0.994200i	$-0.534299\pi$
$593$	−5.23773	−0.215088	−0.107544	+	0.994200i	$0.534299\pi$
$594$	15.7020	0.644262
$595$	14.3775	0.589421
$596$	−14.9503	−0.612389
$597$	8.21981	0.336414
$598$	−12.8290	−0.524617
$599$	−13.9395	−0.569554	−0.284777	−	0.958594i	$-0.591920\pi$
$599$	−13.9395	−0.569554	−0.284777	+	0.958594i	$0.591920\pi$
$600$	−1.34810	−0.0550359
$601$	−17.3985	−0.709701	−0.354851	−	0.934923i	$-0.615468\pi$
$601$	−17.3985	−0.709701	−0.354851	+	0.934923i	$0.615468\pi$
$602$	20.8617	0.850258
$603$	26.3482	1.07298
$604$	−38.9588	−1.58521
$605$	0.184147	0.00748664
$606$	36.0664	1.46510
$607$	5.13339	0.208358	0.104179	−	0.994559i	$-0.466779\pi$
$607$	5.13339	0.208358	0.104179	+	0.994559i	$0.466779\pi$
$608$	−28.1584	−1.14198
$609$	50.2970	2.03814
$610$	6.44444	0.260928
$611$	−1.65811	−0.0670800
$612$	17.1864	0.694719
$613$	8.90668	0.359737	0.179869	−	0.983691i	$-0.442433\pi$
$613$	8.90668	0.359737	0.179869	+	0.983691i	$0.442433\pi$
$614$	65.5980	2.64732
$615$	−10.1773	−0.410389
$616$	1.99212	0.0802647
$617$	22.7075	0.914171	0.457085	−	0.889423i	$-0.348893\pi$
$617$	22.7075	0.914171	0.457085	+	0.889423i	$0.348893\pi$
$618$	4.34469	0.174769
$619$	−18.2517	−0.733600	−0.366800	−	0.930300i	$-0.619547\pi$
$619$	−18.2517	−0.733600	−0.366800	+	0.930300i	$0.619547\pi$
$620$	5.13874	0.206377
$621$	6.03237	0.242071
$622$	−35.8504	−1.43747
$623$	−67.7419	−2.71402
$624$	23.2384	0.930281
$625$	17.6452	0.705809
$626$	−20.5550	−0.821541
$627$	−26.5012	−1.05836
$628$	44.5065	1.77600
$629$	−47.9944	−1.91366
$630$	−12.0358	−0.479517
$631$	23.0859	0.919037	0.459518	−	0.888168i	$-0.348022\pi$
$631$	23.0859	0.919037	0.459518	+	0.888168i	$0.348022\pi$
$632$	0.922816	0.0367076
$633$	39.6119	1.57443
$634$	−7.46170	−0.296342
$635$	−5.71806	−0.226914
$636$	−8.17398	−0.324119
$637$	−31.2091	−1.23655
$638$	−34.2526	−1.35607
$639$	18.3025	0.724034
$640$	−0.769147	−0.0304032
$641$	−5.14884	−0.203367	−0.101683	−	0.994817i	$-0.532423\pi$
$641$	−5.14884	−0.203367	−0.101683	+	0.994817i	$0.532423\pi$
$642$	59.5986	2.35217
$643$	25.7206	1.01432	0.507160	−	0.861852i	$-0.330695\pi$
$643$	25.7206	1.01432	0.507160	+	0.861852i	$0.330695\pi$
$644$	−21.7107	−0.855522
$645$	−3.78807	−0.149155
$646$	32.3525	1.27289
$647$	5.81471	0.228600	0.114300	−	0.993446i	$-0.463537\pi$
$647$	5.81471	0.228600	0.114300	+	0.993446i	$0.463537\pi$
$648$	−1.49328	−0.0586618
$649$	38.7828	1.52236
$650$	−22.5480	−0.884406
$651$	36.4796	1.42975
$652$	−9.41443	−0.368697
$653$	15.9057	0.622436	0.311218	−	0.950339i	$-0.399263\pi$
$653$	15.9057	0.622436	0.311218	+	0.950339i	$0.399263\pi$
$654$	−54.8218	−2.14370
$655$	−5.31291	−0.207592
$656$	26.5621	1.03707
$657$	−17.3283	−0.676040
$658$	−5.71101	−0.222638
$659$	−30.7546	−1.19803	−0.599014	−	0.800739i	$-0.704440\pi$
$659$	−30.7546	−1.19803	−0.599014	+	0.800739i	$0.704440\pi$
$660$	10.2615	0.399428
$661$	−31.9625	−1.24320	−0.621598	−	0.783336i	$-0.713516\pi$
$661$	−31.9625	−1.24320	−0.621598	+	0.783336i	$0.713516\pi$
$662$	25.8166	1.00339
$663$	−25.8195	−1.00275
$664$	1.80697	0.0701241
$665$	−11.1322	−0.431687
$666$	40.1773	1.55684
$667$	−13.1591	−0.509522
$668$	9.03963	0.349754
$669$	−41.1999	−1.59288
$670$	−19.2053	−0.741964
$671$	−15.3078	−0.590949
$672$	77.4011	2.98581
$673$	5.89825	0.227361	0.113680	−	0.993517i	$-0.463736\pi$
$673$	5.89825	0.227361	0.113680	+	0.993517i	$0.463736\pi$
$674$	−53.8362	−2.07369
$675$	10.6024	0.408086
$676$	−12.7375	−0.489905
$677$	−32.3269	−1.24243	−0.621213	−	0.783642i	$-0.713360\pi$
$677$	−32.3269	−1.24243	−0.621213	+	0.783642i	$0.713360\pi$
$678$	30.1184	1.15669
$679$	28.9745	1.11194
$680$	0.441598	0.0169345
$681$	−3.90796	−0.149753
$682$	−24.8428	−0.951281
$683$	−45.4717	−1.73993	−0.869963	−	0.493117i	$-0.835857\pi$
$683$	−45.4717	−1.73993	−0.869963	+	0.493117i	$0.835857\pi$
$684$	−13.3070	−0.508806
$685$	3.75090	0.143314
$686$	−46.4671	−1.77412
$687$	−17.1782	−0.655388
$688$	9.88659	0.376923
$689$	4.81941	0.183605
$690$	8.02345	0.305448
$691$	−17.8493	−0.679021	−0.339510	−	0.940602i	$-0.610261\pi$
$691$	−17.8493	−0.679021	−0.339510	+	0.940602i	$0.610261\pi$
$692$	−16.4249	−0.624382
$693$	28.5891	1.08601
$694$	−72.9301	−2.76839
$695$	−11.8937	−0.451154
$696$	1.54484	0.0585572
$697$	−29.5123	−1.11786
$698$	−55.6104	−2.10488
$699$	50.6694	1.91649
$700$	−38.1584	−1.44225
$701$	22.0209	0.831717	0.415858	−	0.909429i	$-0.363481\pi$
$701$	22.0209	0.831717	0.415858	+	0.909429i	$0.363481\pi$
$702$	−11.8450	−0.447059
$703$	37.1609	1.40155
$704$	−24.9848	−0.941651
$705$	1.03701	0.0390560
$706$	29.6182	1.11469
$707$	−35.9869	−1.35343
$708$	49.6201	1.86484
$709$	47.4912	1.78357	0.891785	−	0.452459i	$-0.149453\pi$
$709$	47.4912	1.78357	0.891785	+	0.452459i	$0.149453\pi$
$710$	−13.3407	−0.500667
$711$	13.2435	0.496668
$712$	−2.08066	−0.0779758
$713$	−9.54407	−0.357428
$714$	−88.9297	−3.32811
$715$	−6.05022	−0.226265
$716$	17.0030	0.635432
$717$	−31.3700	−1.17153
$718$	38.7709	1.44692
$719$	17.4092	0.649253	0.324626	−	0.945842i	$-0.394761\pi$
$719$	17.4092	0.649253	0.324626	+	0.945842i	$0.394761\pi$
$720$	−5.70390	−0.212572
$721$	−4.33511	−0.161448
$722$	12.6253	0.469867
$723$	−11.0433	−0.410707
$724$	10.9147	0.405640
$725$	−23.1282	−0.858960
$726$	−1.13901	−0.0422726
$727$	13.0030	0.482254	0.241127	−	0.970494i	$-0.422483\pi$
$727$	13.0030	0.482254	0.241127	+	0.970494i	$0.422483\pi$
$728$	−1.50277	−0.0556964
$729$	−5.69741	−0.211015
$730$	12.6306	0.467480
$731$	−10.9847	−0.406283
$732$	−19.5853	−0.723892
$733$	−6.25826	−0.231154	−0.115577	−	0.993299i	$-0.536872\pi$
$733$	−6.25826	−0.231154	−0.115577	+	0.993299i	$0.536872\pi$
$734$	−19.3656	−0.714799
$735$	19.5187	0.719956
$736$	−20.2503	−0.746435
$737$	45.6191	1.68040
$738$	24.7055	0.909421
$739$	44.0177	1.61922	0.809608	−	0.586971i	$-0.199680\pi$
$739$	44.0177	1.61922	0.809608	+	0.586971i	$0.199680\pi$
$740$	−14.3890	−0.528951
$741$	19.9914	0.734403
$742$	16.5994	0.609383
$743$	−38.5408	−1.41392	−0.706962	−	0.707251i	$-0.749935\pi$
$743$	−38.5408	−1.41392	−0.706962	+	0.707251i	$0.749935\pi$
$744$	1.12045	0.0410776
$745$	−5.51288	−0.201976
$746$	29.2307	1.07021
$747$	25.9321	0.948807
$748$	29.7564	1.08800
$749$	−59.4672	−2.17288
$750$	29.7967	1.08802
$751$	−32.4423	−1.18383	−0.591917	−	0.805999i	$-0.701629\pi$
$751$	−32.4423	−1.18383	−0.591917	+	0.805999i	$0.701629\pi$
$752$	−2.70651	−0.0986964
$753$	14.0422	0.511726
$754$	25.8388	0.940993
$755$	−14.3660	−0.522831
$756$	−20.0454	−0.729044
$757$	12.2641	0.445745	0.222873	−	0.974848i	$-0.428457\pi$
$757$	12.2641	0.445745	0.222873	+	0.974848i	$0.428457\pi$
$758$	−21.9778	−0.798270
$759$	−19.0585	−0.691778
$760$	−0.341918	−0.0124027
$761$	21.1292	0.765932	0.382966	−	0.923762i	$-0.374903\pi$
$761$	21.1292	0.765932	0.382966	+	0.923762i	$0.374903\pi$
$762$	35.3680	1.28125
$763$	54.7009	1.98030
$764$	3.96819	0.143564
$765$	6.33743	0.229130
$766$	−61.8687	−2.23541
$767$	−29.2562	−1.05638
$768$	37.8507	1.36582
$769$	12.5981	0.454300	0.227150	−	0.973860i	$-0.427059\pi$
$769$	12.5981	0.454300	0.227150	+	0.973860i	$0.427059\pi$
$770$	−20.8387	−0.750973
$771$	35.9608	1.29510
$772$	−35.3932	−1.27383
$773$	17.2688	0.621116	0.310558	−	0.950554i	$-0.399484\pi$
$773$	17.2688	0.621116	0.310558	+	0.950554i	$0.399484\pi$
$774$	9.19556	0.330527
$775$	−16.7745	−0.602557
$776$	0.889935	0.0319468
$777$	−102.147	−3.66449
$778$	−37.0890	−1.32970
$779$	22.8507	0.818710
$780$	−7.74085	−0.277167
$781$	31.6887	1.13391
$782$	23.2665	0.832007
$783$	−12.1497	−0.434196
$784$	−50.9422	−1.81937
$785$	16.4116	0.585756
$786$	32.8621	1.17215
$787$	−44.8720	−1.59951	−0.799756	−	0.600325i	$-0.795038\pi$
$787$	−44.8720	−1.59951	−0.799756	+	0.600325i	$0.795038\pi$
$788$	42.9590	1.53035
$789$	−37.8662	−1.34807
$790$	−9.65317	−0.343444
$791$	−30.0519	−1.06852
$792$	0.878099	0.0312019
$793$	11.5475	0.410065
$794$	−18.0558	−0.640775
$795$	−3.01413	−0.106900
$796$	7.14615	0.253289
$797$	30.5278	1.08135	0.540675	−	0.841232i	$-0.318169\pi$
$797$	30.5278	1.08135	0.540675	+	0.841232i	$0.318169\pi$
$798$	68.8561	2.43748
$799$	3.00713	0.106384
$800$	−35.5915	−1.25835
$801$	−29.8598	−1.05504
$802$	52.1623	1.84191
$803$	−30.0020	−1.05875
$804$	58.3666	2.05843
$805$	−8.00575	−0.282166
$806$	18.7404	0.660103
$807$	33.0921	1.16490
$808$	−1.10532	−0.0388849
$809$	−33.9180	−1.19249	−0.596247	−	0.802801i	$-0.703342\pi$
$809$	−33.9180	−1.19249	−0.596247	+	0.802801i	$0.703342\pi$
$810$	15.6206	0.548852
$811$	−43.9741	−1.54414	−0.772069	−	0.635539i	$-0.780778\pi$
$811$	−43.9741	−1.54414	−0.772069	+	0.635539i	$0.780778\pi$
$812$	43.7273	1.53453
$813$	−1.59350	−0.0558864
$814$	69.5626	2.43817
$815$	−3.47154	−0.121603
$816$	−42.1448	−1.47536
$817$	8.50518	0.297559
$818$	59.7818	2.09022
$819$	−21.5665	−0.753594
$820$	−8.84798	−0.308985
$821$	50.2569	1.75398	0.876989	−	0.480510i	$-0.159548\pi$
$821$	50.2569	1.75398	0.876989	+	0.480510i	$0.159548\pi$
$822$	−23.2005	−0.809211
$823$	45.2402	1.57697	0.788487	−	0.615051i	$-0.210865\pi$
$823$	45.2402	1.57697	0.788487	+	0.615051i	$0.210865\pi$
$824$	−0.133150	−0.00463851
$825$	−33.4968	−1.16621
$826$	−100.767	−3.50612
$827$	−1.56540	−0.0544343	−0.0272172	−	0.999630i	$-0.508665\pi$
$827$	−1.56540	−0.0544343	−0.0272172	+	0.999630i	$0.508665\pi$
$828$	−9.56980	−0.332574
$829$	2.28756	0.0794504	0.0397252	−	0.999211i	$-0.487352\pi$
$829$	2.28756	0.0794504	0.0397252	+	0.999211i	$0.487352\pi$
$830$	−18.9020	−0.656097
$831$	−20.2840	−0.703644
$832$	18.8475	0.653421
$833$	56.6004	1.96109
$834$	73.5664	2.54740
$835$	3.33333	0.115355
$836$	−23.0397	−0.796843
$837$	−8.81199	−0.304587
$838$	38.2297	1.32062
$839$	19.8628	0.685740	0.342870	−	0.939383i	$-0.388601\pi$
$839$	19.8628	0.685740	0.342870	+	0.939383i	$0.388601\pi$
$840$	0.939855	0.0324281
$841$	−2.49638	−0.0860822
$842$	43.6892	1.50563
$843$	−58.6702	−2.02071
$844$	34.4378	1.18540
$845$	−4.69692	−0.161579
$846$	−2.51734	−0.0865479
$847$	1.13650	0.0390505
$848$	7.86665	0.270142
$849$	8.88473	0.304923
$850$	40.8927	1.40261
$851$	26.7244	0.916101
$852$	40.5436	1.38900
$853$	−9.92703	−0.339895	−0.169948	−	0.985453i	$-0.554360\pi$
$853$	−9.92703	−0.339895	−0.169948	+	0.985453i	$0.554360\pi$
$854$	39.7730	1.36100
$855$	−4.90692	−0.167813
$856$	−1.82650	−0.0624285
$857$	17.2232	0.588334	0.294167	−	0.955754i	$-0.404958\pi$
$857$	17.2232	0.588334	0.294167	+	0.955754i	$0.404958\pi$
$858$	37.4225	1.27758
$859$	37.5632	1.28164	0.640820	−	0.767692i	$-0.278595\pi$
$859$	37.5632	1.28164	0.640820	+	0.767692i	$0.278595\pi$
$860$	−3.29328	−0.112300
$861$	−62.8112	−2.14060
$862$	28.7992	0.980904
$863$	10.5951	0.360662	0.180331	−	0.983606i	$-0.442283\pi$
$863$	10.5951	0.360662	0.180331	+	0.983606i	$0.442283\pi$
$864$	−18.6970	−0.636085
$865$	−6.05664	−0.205932
$866$	27.7652	0.943500
$867$	9.04923	0.307328
$868$	31.7147	1.07647
$869$	22.9296	0.777834
$870$	−16.1600	−0.547874
$871$	−34.4132	−1.16605
$872$	1.68011	0.0568956
$873$	12.7716	0.432252
$874$	−18.0147	−0.609355
$875$	−29.7310	−1.00509
$876$	−38.3856	−1.29693
$877$	15.5414	0.524797	0.262398	−	0.964960i	$-0.415487\pi$
$877$	15.5414	0.524797	0.262398	+	0.964960i	$0.415487\pi$
$878$	−71.9984	−2.42983
$879$	21.4004	0.721818
$880$	−9.87569	−0.332909
$881$	17.9521	0.604823	0.302411	−	0.953177i	$-0.402208\pi$
$881$	17.9521	0.604823	0.302411	+	0.953177i	$0.402208\pi$
$882$	−47.3816	−1.59542
$883$	−45.2199	−1.52177	−0.760885	−	0.648887i	$-0.775235\pi$
$883$	−45.2199	−1.52177	−0.760885	+	0.648887i	$0.775235\pi$
$884$	−22.4470	−0.754974
$885$	18.2972	0.615055
$886$	27.9197	0.937981
$887$	16.0659	0.539439	0.269720	−	0.962939i	$-0.413069\pi$
$887$	16.0659	0.539439	0.269720	+	0.962939i	$0.413069\pi$
$888$	−3.13738	−0.105284
$889$	−35.2900	−1.18359
$890$	21.7648	0.729559
$891$	−37.1043	−1.24304
$892$	−35.8185	−1.19929
$893$	−2.32834	−0.0779151
$894$	34.0990	1.14044
$895$	6.26980	0.209576
$896$	−4.74693	−0.158584
$897$	14.3769	0.480031
$898$	−1.43402	−0.0478537
$899$	19.2226	0.641110
$900$	−16.8197	−0.560657
$901$	−8.74040	−0.291185
$902$	42.7749	1.42425
$903$	−23.3788	−0.777997
$904$	−0.923028	−0.0306995
$905$	4.02475	0.133787
$906$	88.8581	2.95211
$907$	−8.12301	−0.269720	−0.134860	−	0.990865i	$-0.543059\pi$
$907$	−8.12301	−0.269720	−0.134860	+	0.990865i	$0.543059\pi$
$908$	−3.39751	−0.112750
$909$	−15.8625	−0.526127
$910$	15.7198	0.521107
$911$	10.5301	0.348876	0.174438	−	0.984668i	$-0.444189\pi$
$911$	10.5301	0.348876	0.174438	+	0.984668i	$0.444189\pi$
$912$	32.6317	1.08054
$913$	44.8987	1.48593
$914$	−51.1662	−1.69243
$915$	−7.22200	−0.238752
$916$	−14.9344	−0.493446
$917$	−32.7896	−1.08281
$918$	21.4818	0.709006
$919$	−31.0906	−1.02559	−0.512793	−	0.858513i	$-0.671389\pi$
$919$	−31.0906	−1.02559	−0.512793	+	0.858513i	$0.671389\pi$
$920$	−0.245892	−0.00810683
$921$	−73.5129	−2.42233
$922$	−28.7572	−0.947068
$923$	−23.9047	−0.786831
$924$	63.3307	2.08343
$925$	46.9704	1.54438
$926$	−71.5641	−2.35174
$927$	−1.91086	−0.0627609
$928$	40.7859	1.33886
$929$	−29.4503	−0.966232	−0.483116	−	0.875556i	$-0.660495\pi$
$929$	−29.4503	−0.966232	−0.483116	+	0.875556i	$0.660495\pi$
$930$	−11.7205	−0.384331
$931$	−43.8243	−1.43628
$932$	44.0510	1.44294
$933$	40.1760	1.31530
$934$	−71.2685	−2.33198
$935$	10.9726	0.358842
$936$	−0.662402	−0.0216513
$937$	31.6441	1.03377	0.516884	−	0.856055i	$-0.327092\pi$
$937$	31.6441	1.03377	0.516884	+	0.856055i	$0.327092\pi$
$938$	−118.529	−3.87010
$939$	23.0351	0.751721
$940$	0.901556	0.0294055
$941$	−30.6375	−0.998753	−0.499377	−	0.866385i	$-0.666438\pi$
$941$	−30.6375	−0.998753	−0.499377	+	0.866385i	$0.666438\pi$
$942$	−101.511	−3.30741
$943$	16.4332	0.535137
$944$	−47.7545	−1.55428
$945$	−7.39168	−0.240451
$946$	15.9211	0.517640
$947$	41.1947	1.33865	0.669323	−	0.742971i	$-0.266584\pi$
$947$	41.1947	1.33865	0.669323	+	0.742971i	$0.266584\pi$
$948$	29.3369	0.952819
$949$	22.6323	0.734675
$950$	−31.6623	−1.02726
$951$	8.36200	0.271156
$952$	2.72540	0.0883307
$953$	47.8644	1.55048	0.775240	−	0.631666i	$-0.217629\pi$
$953$	47.8644	1.55048	0.775240	+	0.631666i	$0.217629\pi$
$954$	7.31681	0.236890
$955$	1.46326	0.0473499
$956$	−27.2725	−0.882056
$957$	38.3854	1.24083
$958$	63.1906	2.04159
$959$	23.1493	0.747531
$960$	−11.7875	−0.380441
$961$	−17.0582	−0.550264
$962$	−52.4752	−1.69187
$963$	−26.2124	−0.844682
$964$	−9.60088	−0.309224
$965$	−13.0511	−0.420131
$966$	49.5182	1.59322
$967$	15.1929	0.488570	0.244285	−	0.969703i	$-0.421447\pi$
$967$	15.1929	0.488570	0.244285	+	0.969703i	$0.421447\pi$
$968$	0.0349068	0.00112195
$969$	−36.2561	−1.16471
$970$	−9.30922	−0.298901
$971$	29.2489	0.938641	0.469321	−	0.883028i	$-0.344499\pi$
$971$	29.2489	0.938641	0.469321	+	0.883028i	$0.344499\pi$
$972$	−33.7946	−1.08396
$973$	−73.4042	−2.35323
$974$	−25.1474	−0.805774
$975$	25.2686	0.809243
$976$	18.8489	0.603338
$977$	14.1107	0.451441	0.225720	−	0.974192i	$-0.427526\pi$
$977$	14.1107	0.451441	0.225720	+	0.974192i	$0.427526\pi$
$978$	21.4726	0.686618
$979$	−51.6990	−1.65231
$980$	16.9692	0.542060
$981$	24.1114	0.769819
$982$	−66.9984	−2.13800
$983$	6.41828	0.204711	0.102356	−	0.994748i	$-0.467362\pi$
$983$	6.41828	0.204711	0.102356	+	0.994748i	$0.467362\pi$
$984$	−1.92921	−0.0615010
$985$	15.8410	0.504736
$986$	−46.8608	−1.49235
$987$	6.40008	0.203717
$988$	17.3802	0.552937
$989$	6.11654	0.194495
$990$	−9.18542	−0.291932
$991$	34.3307	1.09055	0.545275	−	0.838257i	$-0.316425\pi$
$991$	34.3307	1.09055	0.545275	+	0.838257i	$0.316425\pi$
$992$	29.5813	0.939207
$993$	−28.9316	−0.918115
$994$	−82.3344	−2.61149
$995$	2.63512	0.0835389
$996$	57.4449	1.82021
$997$	−23.9065	−0.757127	−0.378564	−	0.925575i	$-0.623582\pi$
$997$	−23.9065	−0.757127	−0.378564	+	0.925575i	$0.623582\pi$
$998$	30.1681	0.954953
$999$	24.6745	0.780668

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.c.1.5	✓	25
3.2	odd	2		4923.2.a.n.1.21		25
4.3	odd	2		8752.2.a.v.1.6		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.c.1.5	✓	25	1.1	even	1	trivial
4923.2.a.n.1.21		25	3.2	odd	2
8752.2.a.v.1.6		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)

\(f(q)\)	\(=\)	\(q-1.98290 q^{2} +2.22215 q^{3} +1.93190 q^{4} +0.712381 q^{5} -4.40631 q^{6} +4.39659 q^{7} +0.135039 q^{8} +1.93796 q^{9} +O(q^{10})\)	\(q-1.98290 q^{2} +2.22215 q^{3} +1.93190 q^{4} +0.712381 q^{5} -4.40631 q^{6} +4.39659 q^{7} +0.135039 q^{8} +1.93796 q^{9} -1.41258 q^{10} +3.35537 q^{11} +4.29297 q^{12} -2.53115 q^{13} -8.71801 q^{14} +1.58302 q^{15} -4.13157 q^{16} +4.59046 q^{17} -3.84278 q^{18} -3.55428 q^{19} +1.37625 q^{20} +9.76989 q^{21} -6.65336 q^{22} -2.55608 q^{23} +0.300077 q^{24} -4.49251 q^{25} +5.01902 q^{26} -2.36001 q^{27} +8.49377 q^{28} +5.14817 q^{29} -3.13897 q^{30} +3.73387 q^{31} +7.92241 q^{32} +7.45614 q^{33} -9.10242 q^{34} +3.13205 q^{35} +3.74394 q^{36} -10.4553 q^{37} +7.04778 q^{38} -5.62460 q^{39} +0.0961991 q^{40} -6.42906 q^{41} -19.3727 q^{42} -2.39294 q^{43} +6.48223 q^{44} +1.38057 q^{45} +5.06845 q^{46} +0.655082 q^{47} -9.18097 q^{48} +12.3300 q^{49} +8.90821 q^{50} +10.2007 q^{51} -4.88993 q^{52} -1.90404 q^{53} +4.67967 q^{54} +2.39030 q^{55} +0.593710 q^{56} -7.89815 q^{57} -10.2083 q^{58} +11.5584 q^{59} +3.05823 q^{60} -4.56217 q^{61} -7.40391 q^{62} +8.52042 q^{63} -7.44623 q^{64} -1.80315 q^{65} -14.7848 q^{66} +13.5959 q^{67} +8.86829 q^{68} -5.67999 q^{69} -6.21055 q^{70} +9.44418 q^{71} +0.261700 q^{72} -8.94150 q^{73} +20.7317 q^{74} -9.98305 q^{75} -6.86650 q^{76} +14.7522 q^{77} +11.1530 q^{78} +6.83371 q^{79} -2.94325 q^{80} -11.0582 q^{81} +12.7482 q^{82} +13.3811 q^{83} +18.8744 q^{84} +3.27016 q^{85} +4.74497 q^{86} +11.4400 q^{87} +0.453105 q^{88} -15.4078 q^{89} -2.73753 q^{90} -11.1284 q^{91} -4.93808 q^{92} +8.29724 q^{93} -1.29896 q^{94} -2.53200 q^{95} +17.6048 q^{96} +6.59022 q^{97} -24.4492 q^{98} +6.50257 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9}+O(q^{10}) \) 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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