LMFDB - Embedded newform 547.2.a.c.1.16

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			1.16
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)

$f(q)$	$=$	$q+0.814364 q^{2} +1.40134 q^{3} -1.33681 q^{4} +1.41612 q^{5} +1.14120 q^{6} +3.63098 q^{7} -2.71738 q^{8} -1.03623 q^{9} +O(q^{10})$	\(q+0.814364 q^{2} +1.40134 q^{3} -1.33681 q^{4} +1.41612 q^{5} +1.14120 q^{6} +3.63098 q^{7} -2.71738 q^{8} -1.03623 q^{9} +1.15324 q^{10} -1.41484 q^{11} -1.87333 q^{12} +4.78123 q^{13} +2.95693 q^{14} +1.98448 q^{15} +0.460689 q^{16} +4.74354 q^{17} -0.843871 q^{18} -0.219997 q^{19} -1.89309 q^{20} +5.08825 q^{21} -1.15219 q^{22} +8.30104 q^{23} -3.80798 q^{24} -2.99460 q^{25} +3.89366 q^{26} -5.65615 q^{27} -4.85393 q^{28} -8.51127 q^{29} +1.61609 q^{30} -4.94963 q^{31} +5.80993 q^{32} -1.98268 q^{33} +3.86297 q^{34} +5.14191 q^{35} +1.38525 q^{36} -8.81331 q^{37} -0.179158 q^{38} +6.70015 q^{39} -3.84814 q^{40} +7.32371 q^{41} +4.14368 q^{42} +1.68229 q^{43} +1.89137 q^{44} -1.46743 q^{45} +6.76007 q^{46} -10.3595 q^{47} +0.645583 q^{48} +6.18398 q^{49} -2.43869 q^{50} +6.64734 q^{51} -6.39160 q^{52} +5.38897 q^{53} -4.60617 q^{54} -2.00358 q^{55} -9.86673 q^{56} -0.308291 q^{57} -6.93127 q^{58} +9.25839 q^{59} -2.65287 q^{60} +8.39527 q^{61} -4.03080 q^{62} -3.76254 q^{63} +3.81002 q^{64} +6.77081 q^{65} -1.61462 q^{66} -6.01616 q^{67} -6.34122 q^{68} +11.6326 q^{69} +4.18738 q^{70} -10.0135 q^{71} +2.81584 q^{72} -9.04825 q^{73} -7.17724 q^{74} -4.19646 q^{75} +0.294094 q^{76} -5.13724 q^{77} +5.45636 q^{78} -8.82756 q^{79} +0.652392 q^{80} -4.81752 q^{81} +5.96416 q^{82} -0.697265 q^{83} -6.80203 q^{84} +6.71744 q^{85} +1.36999 q^{86} -11.9272 q^{87} +3.84465 q^{88} -12.9441 q^{89} -1.19503 q^{90} +17.3605 q^{91} -11.0969 q^{92} -6.93614 q^{93} -8.43637 q^{94} -0.311543 q^{95} +8.14171 q^{96} -13.9048 q^{97} +5.03601 q^{98} +1.46610 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.814364	0.575842	0.287921	−	0.957654i	$-0.407036\pi$
$2$	0.814364	0.575842	0.287921	+	0.957654i	$0.407036\pi$
$3$	1.40134	0.809067	0.404533	−	0.914523i	$-0.367434\pi$
$3$	1.40134	0.809067	0.404533	+	0.914523i	$0.367434\pi$
$4$	−1.33681	−0.668406
$5$	1.41612	0.633309	0.316655	−	0.948541i	$-0.397440\pi$
$5$	1.41612	0.633309	0.316655	+	0.948541i	$0.397440\pi$
$6$	1.14120	0.465895
$7$	3.63098	1.37238	0.686190	−	0.727423i	$-0.259282\pi$
$7$	3.63098	1.37238	0.686190	+	0.727423i	$0.259282\pi$
$8$	−2.71738	−0.960738
$9$	−1.03623	−0.345411
$10$	1.15324	0.364686
$11$	−1.41484	−0.426590	−0.213295	−	0.976988i	$-0.568420\pi$
$11$	−1.41484	−0.426590	−0.213295	+	0.976988i	$0.568420\pi$
$12$	−1.87333	−0.540785
$13$	4.78123	1.32607	0.663037	−	0.748586i	$-0.269267\pi$
$13$	4.78123	1.32607	0.663037	+	0.748586i	$0.269267\pi$
$14$	2.95693	0.790274
$15$	1.98448	0.512389
$16$	0.460689	0.115172
$17$	4.74354	1.15048	0.575239	−	0.817985i	$-0.304909\pi$
$17$	4.74354	1.15048	0.575239	+	0.817985i	$0.304909\pi$
$18$	−0.843871	−0.198902
$19$	−0.219997	−0.0504708	−0.0252354	−	0.999682i	$-0.508034\pi$
$19$	−0.219997	−0.0504708	−0.0252354	+	0.999682i	$0.508034\pi$
$20$	−1.89309	−0.423308
$21$	5.08825	1.11035
$22$	−1.15219	−0.245648
$23$	8.30104	1.73089	0.865444	−	0.501006i	$-0.167037\pi$
$23$	8.30104	1.73089	0.865444	+	0.501006i	$0.167037\pi$
$24$	−3.80798	−0.777301
$25$	−2.99460	−0.598919
$26$	3.89366	0.763610
$27$	−5.65615	−1.08853
$28$	−4.85393	−0.917307
$29$	−8.51127	−1.58050	−0.790252	−	0.612783i	$-0.790050\pi$
$29$	−8.51127	−1.58050	−0.790252	+	0.612783i	$0.790050\pi$
$30$	1.61609	0.295055
$31$	−4.94963	−0.888980	−0.444490	−	0.895784i	$-0.646615\pi$
$31$	−4.94963	−0.888980	−0.444490	+	0.895784i	$0.646615\pi$
$32$	5.80993	1.02706
$33$	−1.98268	−0.345139
$34$	3.86297	0.662494
$35$	5.14191	0.869141
$36$	1.38525	0.230875
$37$	−8.81331	−1.44890	−0.724450	−	0.689328i	$-0.757906\pi$
$37$	−8.81331	−1.44890	−0.724450	+	0.689328i	$0.757906\pi$
$38$	−0.179158	−0.0290632
$39$	6.70015	1.07288
$40$	−3.84814	−0.608445
$41$	7.32371	1.14377	0.571885	−	0.820333i	$-0.306212\pi$
$41$	7.32371	1.14377	0.571885	+	0.820333i	$0.306212\pi$
$42$	4.14368	0.639384
$43$	1.68229	0.256546	0.128273	−	0.991739i	$-0.459057\pi$
$43$	1.68229	0.256546	0.128273	+	0.991739i	$0.459057\pi$
$44$	1.89137	0.285135
$45$	−1.46743	−0.218752
$46$	6.76007	0.996718
$47$	−10.3595	−1.51108	−0.755541	−	0.655101i	$-0.772626\pi$
$47$	−10.3595	−1.51108	−0.755541	+	0.655101i	$0.772626\pi$
$48$	0.645583	0.0931819
$49$	6.18398	0.883426
$50$	−2.43869	−0.344883
$51$	6.64734	0.930814
$52$	−6.39160	−0.886356
$53$	5.38897	0.740233	0.370116	−	0.928985i	$-0.379318\pi$
$53$	5.38897	0.740233	0.370116	+	0.928985i	$0.379318\pi$
$54$	−4.60617	−0.626820
$55$	−2.00358	−0.270163
$56$	−9.86673	−1.31850
$57$	−0.308291	−0.0408342
$58$	−6.93127	−0.910120
$59$	9.25839	1.20534	0.602670	−	0.797990i	$-0.294104\pi$
$59$	9.25839	1.20534	0.602670	+	0.797990i	$0.294104\pi$
$60$	−2.65287	−0.342484
$61$	8.39527	1.07490	0.537452	−	0.843294i	$-0.319387\pi$
$61$	8.39527	1.07490	0.537452	+	0.843294i	$0.319387\pi$
$62$	−4.03080	−0.511912
$63$	−3.76254	−0.474035
$64$	3.81002	0.476252
$65$	6.77081	0.839815
$66$	−1.61462	−0.198746
$67$	−6.01616	−0.734991	−0.367496	−	0.930025i	$-0.619785\pi$
$67$	−6.01616	−0.734991	−0.367496	+	0.930025i	$0.619785\pi$
$68$	−6.34122	−0.768986
$69$	11.6326	1.40040
$70$	4.18738	0.500488
$71$	−10.0135	−1.18839	−0.594193	−	0.804323i	$-0.702528\pi$
$71$	−10.0135	−1.18839	−0.594193	+	0.804323i	$0.702528\pi$
$72$	2.81584	0.331850
$73$	−9.04825	−1.05902	−0.529509	−	0.848305i	$-0.677624\pi$
$73$	−9.04825	−1.05902	−0.529509	+	0.848305i	$0.677624\pi$
$74$	−7.17724	−0.834338
$75$	−4.19646	−0.484566
$76$	0.294094	0.0337349
$77$	−5.13724	−0.585443
$78$	5.45636	0.617811
$79$	−8.82756	−0.993178	−0.496589	−	0.867986i	$-0.665414\pi$
$79$	−8.82756	−0.993178	−0.496589	+	0.867986i	$0.665414\pi$
$80$	0.652392	0.0729396
$81$	−4.81752	−0.535280
$82$	5.96416	0.658632
$83$	−0.697265	−0.0765348	−0.0382674	−	0.999268i	$-0.512184\pi$
$83$	−0.697265	−0.0765348	−0.0382674	+	0.999268i	$0.512184\pi$
$84$	−6.80203	−0.742162
$85$	6.71744	0.728609
$86$	1.36999	0.147730
$87$	−11.9272	−1.27873
$88$	3.84465	0.409841
$89$	−12.9441	−1.37208	−0.686038	−	0.727565i	$-0.740652\pi$
$89$	−12.9441	−1.37208	−0.686038	+	0.727565i	$0.740652\pi$
$90$	−1.19503	−0.125967
$91$	17.3605	1.81988
$92$	−11.0969	−1.15693
$93$	−6.93614	−0.719244
$94$	−8.43637	−0.870145
$95$	−0.311543	−0.0319636
$96$	8.14171	0.830959
$97$	−13.9048	−1.41182	−0.705911	−	0.708300i	$-0.749462\pi$
$97$	−13.9048	−1.41182	−0.705911	+	0.708300i	$0.749462\pi$
$98$	5.03601	0.508714
$99$	1.46610	0.147349
$100$	4.00321	0.400321
$101$	−13.0661	−1.30013	−0.650065	−	0.759879i	$-0.725258\pi$
$101$	−13.0661	−1.30013	−0.650065	+	0.759879i	$0.725258\pi$
$102$	5.41335	0.536002
$103$	−5.72103	−0.563710	−0.281855	−	0.959457i	$-0.590950\pi$
$103$	−5.72103	−0.563710	−0.281855	+	0.959457i	$0.590950\pi$
$104$	−12.9924	−1.27401
$105$	7.20558	0.703193
$106$	4.38859	0.426257
$107$	3.84078	0.371302	0.185651	−	0.982616i	$-0.440561\pi$
$107$	3.84078	0.371302	0.185651	+	0.982616i	$0.440561\pi$
$108$	7.56121	0.727578
$109$	6.97897	0.668464	0.334232	−	0.942491i	$-0.391523\pi$
$109$	6.97897	0.668464	0.334232	+	0.942491i	$0.391523\pi$
$110$	−1.63165	−0.155571
$111$	−12.3505	−1.17226
$112$	1.67275	0.158060
$113$	13.7753	1.29587	0.647936	−	0.761695i	$-0.275632\pi$
$113$	13.7753	1.29587	0.647936	+	0.761695i	$0.275632\pi$
$114$	−0.251061	−0.0235141
$115$	11.7553	1.09619
$116$	11.3780	1.05642
$117$	−4.95447	−0.458041
$118$	7.53970	0.694086
$119$	17.2237	1.57889
$120$	−5.39257	−0.492272
$121$	−8.99823	−0.818021
$122$	6.83680	0.618975
$123$	10.2630	0.925387
$124$	6.61672	0.594199
$125$	−11.3213	−1.01261
$126$	−3.06408	−0.272970
$127$	12.2339	1.08558	0.542792	−	0.839867i	$-0.317367\pi$
$127$	12.2339	1.08558	0.542792	+	0.839867i	$0.317367\pi$
$128$	−8.51711	−0.752813
$129$	2.35746	0.207563
$130$	5.51390	0.483601
$131$	0.166480	0.0145454	0.00727270	−	0.999974i	$-0.497685\pi$
$131$	0.166480	0.0145454	0.00727270	+	0.999974i	$0.497685\pi$
$132$	2.65046	0.230693
$133$	−0.798803	−0.0692650
$134$	−4.89935	−0.423239
$135$	−8.00981	−0.689375
$136$	−12.8900	−1.10531
$137$	2.93732	0.250952	0.125476	−	0.992097i	$-0.459954\pi$
$137$	2.93732	0.250952	0.125476	+	0.992097i	$0.459954\pi$
$138$	9.47318	0.806411
$139$	11.0200	0.934703	0.467352	−	0.884072i	$-0.345208\pi$
$139$	11.0200	0.934703	0.467352	+	0.884072i	$0.345208\pi$
$140$	−6.87376	−0.580939
$141$	−14.5172	−1.22257
$142$	−8.15465	−0.684323
$143$	−6.76467	−0.565690
$144$	−0.477381	−0.0397818
$145$	−12.0530	−1.00095
$146$	−7.36856	−0.609827
$147$	8.66589	0.714750
$148$	11.7817	0.968453
$149$	12.7171	1.04183	0.520913	−	0.853610i	$-0.325591\pi$
$149$	12.7171	1.04183	0.520913	+	0.853610i	$0.325591\pi$
$150$	−3.41745	−0.279033
$151$	−1.43425	−0.116717	−0.0583586	−	0.998296i	$-0.518587\pi$
$151$	−1.43425	−0.116717	−0.0583586	+	0.998296i	$0.518587\pi$
$152$	0.597815	0.0484892
$153$	−4.91542	−0.397388
$154$	−4.18358	−0.337123
$155$	−7.00929	−0.562999
$156$	−8.95684	−0.717121
$157$	−15.4253	−1.23107	−0.615536	−	0.788109i	$-0.711060\pi$
$157$	−15.4253	−1.23107	−0.615536	+	0.788109i	$0.711060\pi$
$158$	−7.18884	−0.571914
$159$	7.55181	0.598897
$160$	8.22757	0.650446
$161$	30.1409	2.37543
$162$	−3.92321	−0.308237
$163$	−13.2526	−1.03802	−0.519012	−	0.854767i	$-0.673700\pi$
$163$	−13.2526	−1.03802	−0.519012	+	0.854767i	$0.673700\pi$
$164$	−9.79042	−0.764503
$165$	−2.80771	−0.218580
$166$	−0.567827	−0.0440719
$167$	5.78719	0.447826	0.223913	−	0.974609i	$-0.428117\pi$
$167$	5.78719	0.447826	0.223913	+	0.974609i	$0.428117\pi$
$168$	−13.8267	−1.06675
$169$	9.86015	0.758473
$170$	5.47044	0.419564
$171$	0.227968	0.0174332
$172$	−2.24890	−0.171477
$173$	17.2990	1.31522	0.657610	−	0.753359i	$-0.271568\pi$
$173$	17.2990	1.31522	0.657610	+	0.753359i	$0.271568\pi$
$174$	−9.71310	−0.736348
$175$	−10.8733	−0.821945
$176$	−0.651800	−0.0491313
$177$	12.9742	0.975200
$178$	−10.5412	−0.790100
$179$	−1.04834	−0.0783569	−0.0391785	−	0.999232i	$-0.512474\pi$
$179$	−1.04834	−0.0783569	−0.0391785	+	0.999232i	$0.512474\pi$
$180$	1.96168	0.146215
$181$	15.3698	1.14243	0.571216	−	0.820800i	$-0.306472\pi$
$181$	15.3698	1.14243	0.571216	+	0.820800i	$0.306472\pi$
$182$	14.1378	1.04796
$183$	11.7647	0.869669
$184$	−22.5571	−1.66293
$185$	−12.4807	−0.917602
$186$	−5.64854	−0.414171
$187$	−6.71135	−0.490782
$188$	13.8486	1.01002
$189$	−20.5374	−1.49387
$190$	−0.253709	−0.0184060
$191$	15.4273	1.11628	0.558140	−	0.829747i	$-0.311515\pi$
$191$	15.4273	1.11628	0.558140	+	0.829747i	$0.311515\pi$
$192$	5.33914	0.385320
$193$	20.1338	1.44926	0.724631	−	0.689137i	$-0.242010\pi$
$193$	20.1338	1.44926	0.724631	+	0.689137i	$0.242010\pi$
$194$	−11.3236	−0.812987
$195$	9.48823	0.679466
$196$	−8.26682	−0.590487
$197$	−12.7652	−0.909484	−0.454742	−	0.890623i	$-0.650269\pi$
$197$	−12.7652	−0.909484	−0.454742	+	0.890623i	$0.650269\pi$
$198$	1.19394	0.0848497
$199$	−15.7384	−1.11567	−0.557834	−	0.829952i	$-0.688367\pi$
$199$	−15.7384	−1.11567	−0.557834	+	0.829952i	$0.688367\pi$
$200$	8.13745	0.575405
$201$	−8.43072	−0.594657
$202$	−10.6406	−0.748669
$203$	−30.9042	−2.16905
$204$	−8.88624	−0.622161
$205$	10.3713	0.724361
$206$	−4.65900	−0.324608
$207$	−8.60182	−0.597868
$208$	2.20266	0.152727
$209$	0.311260	0.0215303
$210$	5.86797	0.404928
$211$	21.5243	1.48180	0.740898	−	0.671617i	$-0.234400\pi$
$211$	21.5243	1.48180	0.740898	+	0.671617i	$0.234400\pi$
$212$	−7.20404	−0.494776
$213$	−14.0324	−0.961483
$214$	3.12779	0.213811
$215$	2.38233	0.162473
$216$	15.3699	1.04579
$217$	−17.9720	−1.22002
$218$	5.68342	0.384930
$219$	−12.6797	−0.856815
$220$	2.67842	0.180579
$221$	22.6800	1.52562
$222$	−10.0578	−0.675035
$223$	−22.2049	−1.48695	−0.743475	−	0.668764i	$-0.766824\pi$
$223$	−22.2049	−1.48695	−0.743475	+	0.668764i	$0.766824\pi$
$224$	21.0957	1.40952
$225$	3.10310	0.206873
$226$	11.2181	0.746218
$227$	−11.9066	−0.790266	−0.395133	−	0.918624i	$-0.629302\pi$
$227$	−11.9066	−0.790266	−0.395133	+	0.918624i	$0.629302\pi$
$228$	0.412128	0.0272938
$229$	4.76135	0.314639	0.157320	−	0.987548i	$-0.449715\pi$
$229$	4.76135	0.314639	0.157320	+	0.987548i	$0.449715\pi$
$230$	9.57309	0.631231
$231$	−7.19905	−0.473662
$232$	23.1283	1.51845
$233$	27.3291	1.79039	0.895194	−	0.445677i	$-0.147037\pi$
$233$	27.3291	1.79039	0.895194	+	0.445677i	$0.147037\pi$
$234$	−4.03474	−0.263759
$235$	−14.6703	−0.956983
$236$	−12.3767	−0.805656
$237$	−12.3704	−0.803547
$238$	14.0264	0.909193
$239$	3.75187	0.242688	0.121344	−	0.992611i	$-0.461280\pi$
$239$	3.75187	0.242688	0.121344	+	0.992611i	$0.461280\pi$
$240$	0.914225	0.0590130
$241$	26.2120	1.68846	0.844230	−	0.535980i	$-0.180058\pi$
$241$	26.2120	1.68846	0.844230	+	0.535980i	$0.180058\pi$
$242$	−7.32784	−0.471051
$243$	10.2175	0.655450
$244$	−11.2229	−0.718472
$245$	8.75728	0.559482
$246$	8.35784	0.532877
$247$	−1.05186	−0.0669280
$248$	13.4500	0.854077
$249$	−0.977108	−0.0619217
$250$	−9.21968	−0.583104
$251$	26.2990	1.65998	0.829990	−	0.557778i	$-0.188346\pi$
$251$	26.2990	1.65998	0.829990	+	0.557778i	$0.188346\pi$
$252$	5.02981	0.316848
$253$	−11.7446	−0.738379
$254$	9.96286	0.625125
$255$	9.41345	0.589493
$256$	−14.5561	−0.909754
$257$	10.1558	0.633500	0.316750	−	0.948509i	$-0.397408\pi$
$257$	10.1558	0.633500	0.316750	+	0.948509i	$0.397408\pi$
$258$	1.91983	0.119524
$259$	−32.0009	−1.98844
$260$	−9.05129	−0.561337
$261$	8.81967	0.545924
$262$	0.135575	0.00837586
$263$	5.61176	0.346036	0.173018	−	0.984919i	$-0.444648\pi$
$263$	5.61176	0.346036	0.173018	+	0.984919i	$0.444648\pi$
$264$	5.38768	0.331589
$265$	7.63145	0.468796
$266$	−0.650517	−0.0398857
$267$	−18.1392	−1.11010
$268$	8.04248	0.491272
$269$	−2.26139	−0.137879	−0.0689396	−	0.997621i	$-0.521962\pi$
$269$	−2.26139	−0.137879	−0.0689396	+	0.997621i	$0.521962\pi$
$270$	−6.52290	−0.396971
$271$	−1.86707	−0.113416	−0.0567082	−	0.998391i	$-0.518060\pi$
$271$	−1.86707	−0.113416	−0.0567082	+	0.998391i	$0.518060\pi$
$272$	2.18530	0.132503
$273$	24.3281	1.47240
$274$	2.39205	0.144509
$275$	4.23687	0.255493
$276$	−15.5506	−0.936037
$277$	16.6853	1.00252	0.501262	−	0.865296i	$-0.332869\pi$
$277$	16.6853	1.00252	0.501262	+	0.865296i	$0.332869\pi$
$278$	8.97428	0.538241
$279$	5.12898	0.307064
$280$	−13.9725	−0.835017
$281$	29.9375	1.78592	0.892961	−	0.450134i	$-0.148624\pi$
$281$	29.9375	1.78592	0.892961	+	0.450134i	$0.148624\pi$
$282$	−11.8223	−0.704005
$283$	−5.13236	−0.305087	−0.152544	−	0.988297i	$-0.548746\pi$
$283$	−5.13236	−0.305087	−0.152544	+	0.988297i	$0.548746\pi$
$284$	13.3862	0.794324
$285$	−0.436579	−0.0258607
$286$	−5.50890	−0.325748
$287$	26.5922	1.56969
$288$	−6.02044	−0.354758
$289$	5.50121	0.323601
$290$	−9.81553	−0.576388
$291$	−19.4855	−1.14226
$292$	12.0958	0.707853
$293$	−15.0592	−0.879770	−0.439885	−	0.898054i	$-0.644981\pi$
$293$	−15.0592	−0.879770	−0.439885	+	0.898054i	$0.644981\pi$
$294$	7.05719	0.411583
$295$	13.1110	0.763353
$296$	23.9491	1.39201
$297$	8.00254	0.464355
$298$	10.3564	0.599928
$299$	39.6892	2.29529
$300$	5.60988	0.323886
$301$	6.10834	0.352079
$302$	−1.16800	−0.0672107
$303$	−18.3102	−1.05189
$304$	−0.101350	−0.00581283
$305$	11.8887	0.680747
$306$	−4.00294	−0.228833
$307$	−8.39233	−0.478975	−0.239488	−	0.970899i	$-0.576979\pi$
$307$	−8.39233	−0.478975	−0.239488	+	0.970899i	$0.576979\pi$
$308$	6.86753	0.391314
$309$	−8.01714	−0.456079
$310$	−5.70811	−0.324199
$311$	−8.23440	−0.466930	−0.233465	−	0.972365i	$-0.575006\pi$
$311$	−8.23440	−0.466930	−0.233465	+	0.972365i	$0.575006\pi$
$312$	−18.2068	−1.03076
$313$	−23.1054	−1.30599	−0.652997	−	0.757360i	$-0.726489\pi$
$313$	−23.1054	−1.30599	−0.652997	+	0.757360i	$0.726489\pi$
$314$	−12.5618	−0.708903
$315$	−5.32822	−0.300211
$316$	11.8008	0.663846
$317$	11.3611	0.638102	0.319051	−	0.947738i	$-0.396636\pi$
$317$	11.3611	0.638102	0.319051	+	0.947738i	$0.396636\pi$
$318$	6.14992	0.344870
$319$	12.0421	0.674226
$320$	5.39545	0.301615
$321$	5.38225	0.300408
$322$	24.5456	1.36788
$323$	−1.04357	−0.0580655
$324$	6.44011	0.357784
$325$	−14.3179	−0.794212
$326$	−10.7924	−0.597738
$327$	9.77994	0.540832
$328$	−19.9013	−1.09886
$329$	−37.6149	−2.07378
$330$	−2.28650	−0.125868
$331$	−28.7295	−1.57912	−0.789559	−	0.613675i	$-0.789690\pi$
$331$	−28.7295	−1.57912	−0.789559	+	0.613675i	$0.789690\pi$
$332$	0.932112	0.0511563
$333$	9.13265	0.500466
$334$	4.71288	0.257877
$335$	−8.51963	−0.465477
$336$	2.34410	0.127881
$337$	−28.4717	−1.55095	−0.775477	−	0.631376i	$-0.782490\pi$
$337$	−28.4717	−1.55095	−0.775477	+	0.631376i	$0.782490\pi$
$338$	8.02975	0.436761
$339$	19.3040	1.04845
$340$	−8.97995	−0.487006
$341$	7.00293	0.379230
$342$	0.185649	0.0100388
$343$	−2.96294	−0.159984
$344$	−4.57141	−0.246474
$345$	16.4732	0.886888
$346$	14.0877	0.757359
$347$	−6.58989	−0.353764	−0.176882	−	0.984232i	$-0.556601\pi$
$347$	−6.58989	−0.353764	−0.176882	+	0.984232i	$0.556601\pi$
$348$	15.9444	0.854712
$349$	27.0360	1.44720	0.723602	−	0.690218i	$-0.242485\pi$
$349$	27.0360	1.44720	0.723602	+	0.690218i	$0.242485\pi$
$350$	−8.85483	−0.473310
$351$	−27.0434	−1.44347
$352$	−8.22010	−0.438133
$353$	33.6904	1.79316	0.896580	−	0.442883i	$-0.146044\pi$
$353$	33.6904	1.79316	0.896580	+	0.442883i	$0.146044\pi$
$354$	10.5657	0.561561
$355$	−14.1804	−0.752616
$356$	17.3039	0.917104
$357$	24.1363	1.27743
$358$	−0.853734	−0.0451212
$359$	−11.0622	−0.583839	−0.291919	−	0.956443i	$-0.594294\pi$
$359$	−11.0622	−0.583839	−0.291919	+	0.956443i	$0.594294\pi$
$360$	3.98758	0.210164
$361$	−18.9516	−0.997453
$362$	12.5166	0.657860
$363$	−12.6096	−0.661834
$364$	−23.2078	−1.21642
$365$	−12.8134	−0.670685
$366$	9.58072	0.500792
$367$	11.6647	0.608892	0.304446	−	0.952530i	$-0.401529\pi$
$367$	11.6647	0.608892	0.304446	+	0.952530i	$0.401529\pi$
$368$	3.82420	0.199350
$369$	−7.58907	−0.395071
$370$	−10.1639	−0.528394
$371$	19.5672	1.01588
$372$	9.27231	0.480747
$373$	3.46353	0.179335	0.0896674	−	0.995972i	$-0.471420\pi$
$373$	3.46353	0.179335	0.0896674	+	0.995972i	$0.471420\pi$
$374$	−5.46548	−0.282613
$375$	−15.8651	−0.819269
$376$	28.1506	1.45175
$377$	−40.6943	−2.09586
$378$	−16.7249	−0.860235
$379$	−29.2087	−1.50035	−0.750176	−	0.661238i	$-0.770031\pi$
$379$	−29.2087	−1.50035	−0.750176	+	0.661238i	$0.770031\pi$
$380$	0.416474	0.0213647
$381$	17.1439	0.878310
$382$	12.5634	0.642801
$383$	−32.0290	−1.63661	−0.818304	−	0.574786i	$-0.805085\pi$
$383$	−32.0290	−1.63661	−0.818304	+	0.574786i	$0.805085\pi$
$384$	−11.9354	−0.609076
$385$	−7.27497	−0.370767
$386$	16.3962	0.834547
$387$	−1.74324	−0.0886140
$388$	18.5881	0.943670
$389$	10.7618	0.545647	0.272824	−	0.962064i	$-0.412042\pi$
$389$	10.7618	0.545647	0.272824	+	0.962064i	$0.412042\pi$
$390$	7.72687	0.391265
$391$	39.3764	1.99135
$392$	−16.8042	−0.848741
$393$	0.233296	0.0117682
$394$	−10.3955	−0.523719
$395$	−12.5009	−0.628989
$396$	−1.95990	−0.0984889
$397$	33.2000	1.66626	0.833130	−	0.553077i	$-0.186546\pi$
$397$	33.2000	1.66626	0.833130	+	0.553077i	$0.186546\pi$
$398$	−12.8168	−0.642449
$399$	−1.11940	−0.0560400
$400$	−1.37958	−0.0689788
$401$	−22.9009	−1.14361	−0.571807	−	0.820388i	$-0.693758\pi$
$401$	−22.9009	−1.14361	−0.571807	+	0.820388i	$0.693758\pi$
$402$	−6.86567	−0.342429
$403$	−23.6653	−1.17885
$404$	17.4670	0.869014
$405$	−6.82220	−0.338998
$406$	−25.1673	−1.24903
$407$	12.4694	0.618086
$408$	−18.0633	−0.894268
$409$	−28.6372	−1.41602	−0.708010	−	0.706203i	$-0.750407\pi$
$409$	−28.6372	−1.41602	−0.708010	+	0.706203i	$0.750407\pi$
$410$	8.44599	0.417118
$411$	4.11620	0.203037
$412$	7.64794	0.376787
$413$	33.6170	1.65418
$414$	−7.00501	−0.344278
$415$	−0.987413	−0.0484702
$416$	27.7786	1.36196
$417$	15.4428	0.756237
$418$	0.253479	0.0123981
$419$	11.0928	0.541916	0.270958	−	0.962591i	$-0.412659\pi$
$419$	11.0928	0.541916	0.270958	+	0.962591i	$0.412659\pi$
$420$	−9.63251	−0.470018
$421$	26.6554	1.29910	0.649552	−	0.760317i	$-0.274957\pi$
$421$	26.6554	1.29910	0.649552	+	0.760317i	$0.274957\pi$
$422$	17.5286	0.853281
$423$	10.7348	0.521945
$424$	−14.6439	−0.711170
$425$	−14.2050	−0.689044
$426$	−11.4275	−0.553663
$427$	30.4830	1.47518
$428$	−5.13440	−0.248180
$429$	−9.47963	−0.457681
$430$	1.94008	0.0935589
$431$	−8.67484	−0.417852	−0.208926	−	0.977931i	$-0.566997\pi$
$431$	−8.67484	−0.417852	−0.208926	+	0.977931i	$0.566997\pi$
$432$	−2.60573	−0.125368
$433$	26.0220	1.25054	0.625269	−	0.780409i	$-0.284989\pi$
$433$	26.0220	1.25054	0.625269	+	0.780409i	$0.284989\pi$
$434$	−14.6357	−0.702538
$435$	−16.8904	−0.809833
$436$	−9.32956	−0.446805
$437$	−1.82620	−0.0873592
$438$	−10.3259	−0.493390
$439$	−9.34040	−0.445793	−0.222896	−	0.974842i	$-0.571551\pi$
$439$	−9.34040	−0.445793	−0.222896	+	0.974842i	$0.571551\pi$
$440$	5.44450	0.259556
$441$	−6.40805	−0.305145
$442$	18.4697	0.878516
$443$	−27.2898	−1.29658	−0.648289	−	0.761394i	$-0.724515\pi$
$443$	−27.2898	−1.29658	−0.648289	+	0.761394i	$0.724515\pi$
$444$	16.5103	0.783543
$445$	−18.3305	−0.868949
$446$	−18.0829	−0.856248
$447$	17.8211	0.842907
$448$	13.8341	0.653599
$449$	11.4156	0.538735	0.269367	−	0.963037i	$-0.413185\pi$
$449$	11.4156	0.538735	0.269367	+	0.963037i	$0.413185\pi$
$450$	2.52705	0.119126
$451$	−10.3619	−0.487921
$452$	−18.4150	−0.866169
$453$	−2.00987	−0.0944320
$454$	−9.69627	−0.455069
$455$	24.5846	1.15255
$456$	0.837745	0.0392310
$457$	14.8176	0.693138	0.346569	−	0.938024i	$-0.387347\pi$
$457$	14.8176	0.693138	0.346569	+	0.938024i	$0.387347\pi$
$458$	3.87747	0.181183
$459$	−26.8302	−1.25233
$460$	−15.7146	−0.732698
$461$	7.09893	0.330630	0.165315	−	0.986241i	$-0.447136\pi$
$461$	7.09893	0.330630	0.165315	+	0.986241i	$0.447136\pi$
$462$	−5.86264	−0.272755
$463$	30.3771	1.41174	0.705872	−	0.708340i	$-0.250555\pi$
$463$	30.3771	1.41174	0.705872	+	0.708340i	$0.250555\pi$
$464$	−3.92104	−0.182030
$465$	−9.82242	−0.455504
$466$	22.2558	1.03098
$467$	−6.92279	−0.320349	−0.160174	−	0.987089i	$-0.551206\pi$
$467$	−6.92279	−0.320349	−0.160174	+	0.987089i	$0.551206\pi$
$468$	6.62320	0.306157
$469$	−21.8445	−1.00869
$470$	−11.9469	−0.551071
$471$	−21.6161	−0.996018
$472$	−25.1586	−1.15802
$473$	−2.38016	−0.109440
$474$	−10.0740	−0.462716
$475$	0.658802	0.0302279
$476$	−23.0248	−1.05534
$477$	−5.58424	−0.255685
$478$	3.05538	0.139750
$479$	13.2742	0.606514	0.303257	−	0.952909i	$-0.401926\pi$
$479$	13.2742	0.606514	0.303257	+	0.952909i	$0.401926\pi$
$480$	11.5297	0.526254
$481$	−42.1385	−1.92135
$482$	21.3461	0.972287
$483$	42.2378	1.92188
$484$	12.0289	0.546770
$485$	−19.6910	−0.894120
$486$	8.32073	0.377436
$487$	0.0368987	0.00167204	0.000836019	−	1.00000i	$-0.499734\pi$
$487$	0.0368987	0.00167204	0.000836019		1.00000i	$0.499734\pi$
$488$	−22.8131	−1.03270
$489$	−18.5715	−0.839831
$490$	7.13161	0.322173
$491$	9.24109	0.417044	0.208522	−	0.978018i	$-0.433135\pi$
$491$	9.24109	0.417044	0.208522	+	0.978018i	$0.433135\pi$
$492$	−13.7197	−0.618534
$493$	−40.3736	−1.81833
$494$	−0.856593	−0.0385400
$495$	2.07618	0.0933175
$496$	−2.28024	−0.102386
$497$	−36.3588	−1.63092
$498$	−0.795722	−0.0356571
$499$	−30.7726	−1.37757	−0.688785	−	0.724966i	$-0.741856\pi$
$499$	−30.7726	−1.37757	−0.688785	+	0.724966i	$0.741856\pi$
$500$	15.1345	0.676835
$501$	8.10985	0.362321
$502$	21.4170	0.955887
$503$	−4.21607	−0.187985	−0.0939926	−	0.995573i	$-0.529963\pi$
$503$	−4.21607	−0.187985	−0.0939926	+	0.995573i	$0.529963\pi$
$504$	10.2242	0.455424
$505$	−18.5033	−0.823384
$506$	−9.56440	−0.425190
$507$	13.8175	0.613655
$508$	−16.3544	−0.725611
$509$	1.38137	0.0612282	0.0306141	−	0.999531i	$-0.490254\pi$
$509$	1.38137	0.0612282	0.0306141	+	0.999531i	$0.490254\pi$
$510$	7.66597	0.339455
$511$	−32.8540	−1.45337
$512$	5.18030	0.228939
$513$	1.24434	0.0549388
$514$	8.27050	0.364796
$515$	−8.10168	−0.357003
$516$	−3.15148	−0.138736
$517$	14.6570	0.644612
$518$	−26.0604	−1.14503
$519$	24.2419	1.06410
$520$	−18.3988	−0.806843
$521$	6.04917	0.265019	0.132510	−	0.991182i	$-0.457696\pi$
$521$	6.04917	0.265019	0.132510	+	0.991182i	$0.457696\pi$
$522$	7.18242	0.314366
$523$	−37.2436	−1.62855	−0.814274	−	0.580481i	$-0.802865\pi$
$523$	−37.2436	−1.62855	−0.814274	+	0.580481i	$0.802865\pi$
$524$	−0.222552	−0.00972224
$525$	−15.2372	−0.665008
$526$	4.57002	0.199262
$527$	−23.4788	−1.02275
$528$	−0.913396	−0.0397505
$529$	45.9073	1.99597
$530$	6.21478	0.269953
$531$	−9.59386	−0.416338
$532$	1.06785	0.0462972
$533$	35.0163	1.51673
$534$	−14.7719	−0.639243
$535$	5.43901	0.235149
$536$	16.3482	0.706134
$537$	−1.46909	−0.0633960
$538$	−1.84159	−0.0793967
$539$	−8.74933	−0.376860
$540$	10.7076	0.460782
$541$	39.0692	1.67971	0.839857	−	0.542807i	$-0.182639\pi$
$541$	39.0692	1.67971	0.839857	+	0.542807i	$0.182639\pi$
$542$	−1.52047	−0.0653100
$543$	21.5385	0.924303
$544$	27.5596	1.18161
$545$	9.88307	0.423344
$546$	19.8119	0.847871
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	−3.92665	−0.167738
$549$	−8.69946	−0.371284
$550$	3.45035	0.147124
$551$	1.87245	0.0797692
$552$	−31.6102	−1.34542
$553$	−32.0526	−1.36302
$554$	13.5879	0.577296
$555$	−17.4898	−0.742401
$556$	−14.7316	−0.624761
$557$	44.8628	1.90090	0.950448	−	0.310883i	$-0.100625\pi$
$557$	44.8628	1.90090	0.950448	+	0.310883i	$0.100625\pi$
$558$	4.17685	0.176820
$559$	8.04340	0.340200
$560$	2.36882	0.100101
$561$	−9.40491	−0.397076
$562$	24.3800	1.02841
$563$	−20.5135	−0.864542	−0.432271	−	0.901744i	$-0.642288\pi$
$563$	−20.5135	−0.864542	−0.432271	+	0.901744i	$0.642288\pi$
$564$	19.4067	0.817170
$565$	19.5075	0.820688
$566$	−4.17961	−0.175682
$567$	−17.4923	−0.734607
$568$	27.2105	1.14173
$569$	−2.49265	−0.104497	−0.0522487	−	0.998634i	$-0.516639\pi$
$569$	−2.49265	−0.104497	−0.0522487	+	0.998634i	$0.516639\pi$
$570$	−0.355534	−0.0148917
$571$	−4.58722	−0.191969	−0.0959845	−	0.995383i	$-0.530600\pi$
$571$	−4.58722	−0.191969	−0.0959845	+	0.995383i	$0.530600\pi$
$572$	9.04308	0.378110
$573$	21.6189	0.903145
$574$	21.6557	0.903893
$575$	−24.8583	−1.03666
$576$	−3.94807	−0.164503
$577$	−30.4192	−1.26637	−0.633184	−	0.774001i	$-0.718252\pi$
$577$	−30.4192	−1.26637	−0.633184	+	0.774001i	$0.718252\pi$
$578$	4.47999	0.186343
$579$	28.2144	1.17255
$580$	16.1126	0.669039
$581$	−2.53175	−0.105035
$582$	−15.8683	−0.657760
$583$	−7.62453	−0.315776
$584$	24.5875	1.01744
$585$	−7.01614	−0.290082
$586$	−12.2637	−0.506609
$587$	23.4892	0.969502	0.484751	−	0.874652i	$-0.338910\pi$
$587$	23.4892	0.969502	0.484751	+	0.874652i	$0.338910\pi$
$588$	−11.5847	−0.477743
$589$	1.08890	0.0448675
$590$	10.6771	0.439571
$591$	−17.8885	−0.735833
$592$	−4.06019	−0.166873
$593$	7.24445	0.297494	0.148747	−	0.988875i	$-0.452476\pi$
$593$	7.24445	0.297494	0.148747	+	0.988875i	$0.452476\pi$
$594$	6.51698	0.267395
$595$	24.3909	0.999928
$596$	−17.0004	−0.696363
$597$	−22.0550	−0.902650
$598$	32.3214	1.32172
$599$	4.93616	0.201686	0.100843	−	0.994902i	$-0.467846\pi$
$599$	4.93616	0.201686	0.100843	+	0.994902i	$0.467846\pi$
$600$	11.4034	0.465541
$601$	31.8884	1.30075	0.650377	−	0.759611i	$-0.274611\pi$
$601$	31.8884	1.30075	0.650377	+	0.759611i	$0.274611\pi$
$602$	4.97441	0.202742
$603$	6.23415	0.253874
$604$	1.91732	0.0780145
$605$	−12.7426	−0.518060
$606$	−14.9111	−0.605723
$607$	2.93710	0.119213	0.0596065	−	0.998222i	$-0.481015\pi$
$607$	2.93710	0.119213	0.0596065	+	0.998222i	$0.481015\pi$
$608$	−1.27817	−0.0518365
$609$	−43.3074	−1.75491
$610$	9.68175	0.392003
$611$	−49.5310	−2.00381
$612$	6.57099	0.265617
$613$	28.3779	1.14617	0.573086	−	0.819495i	$-0.305746\pi$
$613$	28.3779	1.14617	0.573086	+	0.819495i	$0.305746\pi$
$614$	−6.83441	−0.275814
$615$	14.5337	0.586056
$616$	13.9598	0.562458
$617$	−24.3189	−0.979042	−0.489521	−	0.871992i	$-0.662828\pi$
$617$	−24.3189	−0.979042	−0.489521	+	0.871992i	$0.662828\pi$
$618$	−6.52887	−0.262629
$619$	−10.9879	−0.441641	−0.220820	−	0.975314i	$-0.570873\pi$
$619$	−10.9879	−0.441641	−0.220820	+	0.975314i	$0.570873\pi$
$620$	9.37009	0.376312
$621$	−46.9520	−1.88412
$622$	−6.70580	−0.268878
$623$	−46.9999	−1.88301
$624$	3.08668	0.123566
$625$	−1.05941	−0.0423765
$626$	−18.8162	−0.752047
$627$	0.436183	0.0174195
$628$	20.6207	0.822855
$629$	−41.8063	−1.66693
$630$	−4.33911	−0.172874
$631$	−34.0250	−1.35452	−0.677258	−	0.735746i	$-0.736832\pi$
$631$	−34.0250	−1.35452	−0.677258	+	0.735746i	$0.736832\pi$
$632$	23.9878	0.954184
$633$	30.1630	1.19887
$634$	9.25205	0.367446
$635$	17.3247	0.687511
$636$	−10.0953	−0.400307
$637$	29.5670	1.17149
$638$	9.80662	0.388248
$639$	10.3763	0.410482
$640$	−12.0613	−0.476764
$641$	−24.3356	−0.961198	−0.480599	−	0.876940i	$-0.659581\pi$
$641$	−24.3356	−0.961198	−0.480599	+	0.876940i	$0.659581\pi$
$642$	4.38311	0.172988
$643$	3.52118	0.138862	0.0694309	−	0.997587i	$-0.477882\pi$
$643$	3.52118	0.138862	0.0694309	+	0.997587i	$0.477882\pi$
$644$	−40.2927	−1.58775
$645$	3.33846	0.131452
$646$	−0.849842	−0.0334366
$647$	−10.5011	−0.412841	−0.206420	−	0.978463i	$-0.566181\pi$
$647$	−10.5011	−0.412841	−0.206420	+	0.978463i	$0.566181\pi$
$648$	13.0910	0.514264
$649$	−13.0991	−0.514186
$650$	−11.6599	−0.457340
$651$	−25.1849	−0.987076
$652$	17.7162	0.693821
$653$	−31.4115	−1.22923	−0.614613	−	0.788829i	$-0.710688\pi$
$653$	−31.4115	−1.22923	−0.614613	+	0.788829i	$0.710688\pi$
$654$	7.96443	0.311434
$655$	0.235756	0.00921174
$656$	3.37395	0.131731
$657$	9.37610	0.365797
$658$	−30.6322	−1.19417
$659$	16.4890	0.642321	0.321160	−	0.947025i	$-0.395927\pi$
$659$	16.4890	0.642321	0.321160	+	0.947025i	$0.395927\pi$
$660$	3.75338	0.146100
$661$	−15.6369	−0.608206	−0.304103	−	0.952639i	$-0.598357\pi$
$661$	−15.6369	−0.608206	−0.304103	+	0.952639i	$0.598357\pi$
$662$	−23.3963	−0.909322
$663$	31.7825	1.23433
$664$	1.89473	0.0735299
$665$	−1.13120	−0.0438662
$666$	7.43730	0.288190
$667$	−70.6524	−2.73567
$668$	−7.73639	−0.299330
$669$	−31.1167	−1.20304
$670$	−6.93808	−0.268041
$671$	−11.8779	−0.458543
$672$	29.5623	1.14039
$673$	−16.6639	−0.642346	−0.321173	−	0.947021i	$-0.604077\pi$
$673$	−16.6639	−0.642346	−0.321173	+	0.947021i	$0.604077\pi$
$674$	−23.1863	−0.893105
$675$	16.9379	0.651940
$676$	−13.1812	−0.506968
$677$	27.9254	1.07326	0.536630	−	0.843817i	$-0.319697\pi$
$677$	27.9254	1.07326	0.536630	+	0.843817i	$0.319697\pi$
$678$	15.7204	0.603740
$679$	−50.4881	−1.93756
$680$	−18.2538	−0.700002
$681$	−16.6852	−0.639378
$682$	5.70293	0.218376
$683$	4.49024	0.171814	0.0859071	−	0.996303i	$-0.472621\pi$
$683$	4.49024	0.171814	0.0859071	+	0.996303i	$0.472621\pi$
$684$	−0.304751	−0.0116524
$685$	4.15961	0.158931
$686$	−2.41291	−0.0921254
$687$	6.67230	0.254564
$688$	0.775010	0.0295470
$689$	25.7659	0.981604
$690$	13.4152	0.510708
$691$	37.4716	1.42549	0.712743	−	0.701425i	$-0.247453\pi$
$691$	37.4716	1.42549	0.712743	+	0.701425i	$0.247453\pi$
$692$	−23.1255	−0.879101
$693$	5.32339	0.202219
$694$	−5.36657	−0.203712
$695$	15.6057	0.591956
$696$	32.4108	1.22853
$697$	34.7403	1.31588
$698$	22.0171	0.833361
$699$	38.2975	1.44854
$700$	14.5356	0.549393
$701$	−12.8405	−0.484980	−0.242490	−	0.970154i	$-0.577964\pi$
$701$	−12.8405	−0.484980	−0.242490	+	0.970154i	$0.577964\pi$
$702$	−22.0231	−0.831210
$703$	1.93890	0.0731271
$704$	−5.39056	−0.203164
$705$	−20.5581	−0.774263
$706$	27.4362	1.03258
$707$	−47.4428	−1.78427
$708$	−17.3441	−0.651830
$709$	−28.8481	−1.08341	−0.541706	−	0.840568i	$-0.682222\pi$
$709$	−28.8481	−1.08341	−0.541706	+	0.840568i	$0.682222\pi$
$710$	−11.5480	−0.433388
$711$	9.14741	0.343055
$712$	35.1741	1.31821
$713$	−41.0871	−1.53872
$714$	19.6557	0.735598
$715$	−9.57960	−0.358257
$716$	1.40144	0.0523742
$717$	5.25766	0.196351
$718$	−9.00863	−0.336199
$719$	21.1794	0.789860	0.394930	−	0.918711i	$-0.370769\pi$
$719$	21.1794	0.789860	0.394930	+	0.918711i	$0.370769\pi$
$720$	−0.676030	−0.0251942
$721$	−20.7729	−0.773624
$722$	−15.4335	−0.574375
$723$	36.7320	1.36608
$724$	−20.5466	−0.763608
$725$	25.4878	0.946594
$726$	−10.2688	−0.381112
$727$	−18.5213	−0.686916	−0.343458	−	0.939168i	$-0.611598\pi$
$727$	−18.5213	−0.686916	−0.343458	+	0.939168i	$0.611598\pi$
$728$	−47.1751	−1.74843
$729$	28.7707	1.06558
$730$	−10.4348	−0.386209
$731$	7.98000	0.295151
$732$	−15.7271	−0.581292
$733$	7.64090	0.282223	0.141112	−	0.989994i	$-0.454932\pi$
$733$	7.64090	0.282223	0.141112	+	0.989994i	$0.454932\pi$
$734$	9.49930	0.350626
$735$	12.2720	0.452658
$736$	48.2284	1.77772
$737$	8.51190	0.313540
$738$	−6.18027	−0.227499
$739$	−25.5220	−0.938842	−0.469421	−	0.882974i	$-0.655537\pi$
$739$	−25.5220	−0.938842	−0.469421	+	0.882974i	$0.655537\pi$
$740$	16.6844	0.613330
$741$	−1.47401	−0.0541492
$742$	15.9348	0.584987
$743$	9.28330	0.340571	0.170286	−	0.985395i	$-0.445531\pi$
$743$	9.28330	0.340571	0.170286	+	0.985395i	$0.445531\pi$
$744$	18.8481	0.691005
$745$	18.0090	0.659799
$746$	2.82057	0.103269
$747$	0.722530	0.0264360
$748$	8.97181	0.328042
$749$	13.9458	0.509567
$750$	−12.9199	−0.471770
$751$	16.9274	0.617691	0.308845	−	0.951112i	$-0.400057\pi$
$751$	16.9274	0.617691	0.308845	+	0.951112i	$0.400057\pi$
$752$	−4.77248	−0.174035
$753$	36.8540	1.34303
$754$	−33.1400	−1.20689
$755$	−2.03107	−0.0739181
$756$	27.4546	0.998513
$757$	−17.6872	−0.642852	−0.321426	−	0.946935i	$-0.604162\pi$
$757$	−17.6872	−0.642852	−0.321426	+	0.946935i	$0.604162\pi$
$758$	−23.7865	−0.863966
$759$	−16.4583	−0.597397
$760$	0.846579	0.0307087
$761$	39.1182	1.41803	0.709017	−	0.705191i	$-0.249139\pi$
$761$	39.1182	1.41803	0.709017	+	0.705191i	$0.249139\pi$
$762$	13.9614	0.505768
$763$	25.3405	0.917386
$764$	−20.6234	−0.746128
$765$	−6.96084	−0.251670
$766$	−26.0833	−0.942428
$767$	44.2665	1.59837
$768$	−20.3981	−0.736051
$769$	−26.5433	−0.957178	−0.478589	−	0.878039i	$-0.658852\pi$
$769$	−26.5433	−0.957178	−0.478589	+	0.878039i	$0.658852\pi$
$770$	−5.92447	−0.213503
$771$	14.2317	0.512544
$772$	−26.9151	−0.968696
$773$	−1.77455	−0.0638260	−0.0319130	−	0.999491i	$-0.510160\pi$
$773$	−1.77455	−0.0638260	−0.0319130	+	0.999491i	$0.510160\pi$
$774$	−1.41963	−0.0510277
$775$	14.8221	0.532427
$776$	37.7847	1.35639
$777$	−44.8443	−1.60878
$778$	8.76406	0.314207
$779$	−1.61119	−0.0577270
$780$	−12.6840	−0.454159
$781$	14.1675	0.506953
$782$	32.0667	1.14670
$783$	48.1411	1.72042
$784$	2.84889	0.101746
$785$	−21.8441	−0.779649
$786$	0.189987	0.00677663
$787$	−25.2475	−0.899975	−0.449988	−	0.893035i	$-0.648572\pi$
$787$	−25.2475	−0.899975	−0.449988	+	0.893035i	$0.648572\pi$
$788$	17.0647	0.607905
$789$	7.86401	0.279966
$790$	−10.1803	−0.362198
$791$	50.0178	1.77843
$792$	−3.98396	−0.141564
$793$	40.1397	1.42540
$794$	27.0369	0.959503
$795$	10.6943	0.379287
$796$	21.0393	0.745719
$797$	33.9337	1.20199	0.600997	−	0.799251i	$-0.294770\pi$
$797$	33.9337	1.20199	0.600997	+	0.799251i	$0.294770\pi$
$798$	−0.911598	−0.0322702
$799$	−49.1406	−1.73847
$800$	−17.3984	−0.615126
$801$	13.4132	0.473931
$802$	−18.6496	−0.658542
$803$	12.8018	0.451766
$804$	11.2703	0.397472
$805$	42.6832	1.50438
$806$	−19.2722	−0.678834
$807$	−3.16898	−0.111553
$808$	35.5056	1.24908
$809$	28.6553	1.00747	0.503733	−	0.863860i	$-0.331960\pi$
$809$	28.6553	1.00747	0.503733	+	0.863860i	$0.331960\pi$
$810$	−5.55575	−0.195209
$811$	16.5166	0.579977	0.289988	−	0.957030i	$-0.406349\pi$
$811$	16.5166	0.579977	0.289988	+	0.957030i	$0.406349\pi$
$812$	41.3131	1.44981
$813$	−2.61641	−0.0917615
$814$	10.1546	0.355920
$815$	−18.7673	−0.657390
$816$	3.06235	0.107204
$817$	−0.370098	−0.0129481
$818$	−23.3211	−0.815404
$819$	−17.9896	−0.628606
$820$	−13.8644	−0.484167
$821$	−21.1225	−0.737180	−0.368590	−	0.929592i	$-0.620159\pi$
$821$	−21.1225	−0.737180	−0.368590	+	0.929592i	$0.620159\pi$
$822$	3.35209	0.116917
$823$	−14.4176	−0.502567	−0.251284	−	0.967914i	$-0.580853\pi$
$823$	−14.4176	−0.502567	−0.251284	+	0.967914i	$0.580853\pi$
$824$	15.5462	0.541578
$825$	5.93731	0.206711
$826$	27.3765	0.952549
$827$	15.2469	0.530186	0.265093	−	0.964223i	$-0.414597\pi$
$827$	15.2469	0.530186	0.265093	+	0.964223i	$0.414597\pi$
$828$	11.4990	0.399618
$829$	−19.6346	−0.681939	−0.340970	−	0.940074i	$-0.610755\pi$
$829$	−19.6346	−0.681939	−0.340970	+	0.940074i	$0.610755\pi$
$830$	−0.804113	−0.0279112
$831$	23.3819	0.811109
$832$	18.2166	0.631546
$833$	29.3340	1.01636
$834$	12.5761	0.435473
$835$	8.19537	0.283613
$836$	−0.416096	−0.0143910
$837$	27.9959	0.967679
$838$	9.03353	0.312058
$839$	25.1011	0.866585	0.433293	−	0.901253i	$-0.357352\pi$
$839$	25.1011	0.866585	0.433293	+	0.901253i	$0.357352\pi$
$840$	−19.5803	−0.675584
$841$	43.4417	1.49799
$842$	21.7072	0.748079
$843$	41.9527	1.44493
$844$	−28.7740	−0.990441
$845$	13.9632	0.480348
$846$	8.74205	0.300558
$847$	−32.6724	−1.12264
$848$	2.48264	0.0852542
$849$	−7.19220	−0.246836
$850$	−11.5680	−0.396780
$851$	−73.1597	−2.50788
$852$	18.7587	0.642661
$853$	23.8061	0.815105	0.407552	−	0.913182i	$-0.366382\pi$
$853$	23.8061	0.815105	0.407552	+	0.913182i	$0.366382\pi$
$854$	24.8243	0.849469
$855$	0.322831	0.0110406
$856$	−10.4368	−0.356724
$857$	−42.6832	−1.45803	−0.729015	−	0.684498i	$-0.760021\pi$
$857$	−42.6832	−1.45803	−0.729015	+	0.684498i	$0.760021\pi$
$858$	−7.71986	−0.263552
$859$	−23.6721	−0.807681	−0.403840	−	0.914829i	$-0.632325\pi$
$859$	−23.6721	−0.807681	−0.403840	+	0.914829i	$0.632325\pi$
$860$	−3.18472	−0.108598
$861$	37.2648	1.26998
$862$	−7.06448	−0.240617
$863$	−19.1750	−0.652725	−0.326362	−	0.945245i	$-0.605823\pi$
$863$	−19.1750	−0.652725	−0.326362	+	0.945245i	$0.605823\pi$
$864$	−32.8618	−1.11798
$865$	24.4975	0.832941
$866$	21.1914	0.720112
$867$	7.70909	0.261814
$868$	24.0252	0.815467
$869$	12.4896	0.423679
$870$	−13.7549	−0.466336
$871$	−28.7647	−0.974653
$872$	−18.9645	−0.642219
$873$	14.4087	0.487659
$874$	−1.48719	−0.0503051
$875$	−41.1075	−1.38969
$876$	16.9504	0.572700
$877$	−7.38427	−0.249349	−0.124675	−	0.992198i	$-0.539789\pi$
$877$	−7.38427	−0.249349	−0.124675	+	0.992198i	$0.539789\pi$
$878$	−7.60648	−0.256706
$879$	−21.1032	−0.711792
$880$	−0.923028	−0.0311153
$881$	−41.2552	−1.38992	−0.694962	−	0.719047i	$-0.744579\pi$
$881$	−41.2552	−1.38992	−0.694962	+	0.719047i	$0.744579\pi$
$882$	−5.21849	−0.175716
$883$	43.6366	1.46849	0.734245	−	0.678885i	$-0.237536\pi$
$883$	43.6366	1.46849	0.734245	+	0.678885i	$0.237536\pi$
$884$	−30.3188	−1.01973
$885$	18.3731	0.617604
$886$	−22.2238	−0.746624
$887$	15.9261	0.534747	0.267373	−	0.963593i	$-0.413844\pi$
$887$	15.9261	0.534747	0.267373	+	0.963593i	$0.413844\pi$
$888$	33.5609	1.12623
$889$	44.4210	1.48983
$890$	−14.9277	−0.500377
$891$	6.81601	0.228345
$892$	29.6838	0.993885
$893$	2.27905	0.0762655
$894$	14.5128	0.485381
$895$	−1.48458	−0.0496242
$896$	−30.9254	−1.03315
$897$	55.6182	1.85704
$898$	9.29644	0.310226
$899$	42.1276	1.40504
$900$	−4.14826	−0.138275
$901$	25.5628	0.851622
$902$	−8.43832	−0.280965
$903$	8.55989	0.284855
$904$	−37.4327	−1.24499
$905$	21.7656	0.723513
$906$	−1.63677	−0.0543779
$907$	−12.7145	−0.422178	−0.211089	−	0.977467i	$-0.567701\pi$
$907$	−12.7145	−0.422178	−0.211089	+	0.977467i	$0.567701\pi$
$908$	15.9168	0.528219
$909$	13.5396	0.449079
$910$	20.0208	0.663684
$911$	−26.4533	−0.876436	−0.438218	−	0.898869i	$-0.644390\pi$
$911$	−26.4533	−0.876436	−0.438218	+	0.898869i	$0.644390\pi$
$912$	−0.142026	−0.00470296
$913$	0.986517	0.0326489
$914$	12.0669	0.399138
$915$	16.6602	0.550769
$916$	−6.36503	−0.210307
$917$	0.604484	0.0199618
$918$	−21.8496	−0.721143
$919$	16.9747	0.559943	0.279971	−	0.960008i	$-0.409675\pi$
$919$	16.9747	0.559943	0.279971	+	0.960008i	$0.409675\pi$
$920$	−31.9436	−1.05315
$921$	−11.7605	−0.387523
$922$	5.78111	0.190391
$923$	−47.8769	−1.57589
$924$	9.62377	0.316599
$925$	26.3923	0.867774
$926$	24.7380	0.812942
$927$	5.92833	0.194712
$928$	−49.4498	−1.62327
$929$	−27.9847	−0.918148	−0.459074	−	0.888398i	$-0.651819\pi$
$929$	−27.9847	−0.918148	−0.459074	+	0.888398i	$0.651819\pi$
$930$	−7.99902	−0.262298
$931$	−1.36046	−0.0445872
$932$	−36.5338	−1.19671
$933$	−11.5392	−0.377778
$934$	−5.63767	−0.184470
$935$	−9.50409	−0.310817
$936$	13.4632	0.440058
$937$	18.9046	0.617586	0.308793	−	0.951129i	$-0.400075\pi$
$937$	18.9046	0.617586	0.308793	+	0.951129i	$0.400075\pi$
$938$	−17.7894	−0.580845
$939$	−32.3786	−1.05664
$940$	19.6114	0.639653
$941$	2.79277	0.0910417	0.0455208	−	0.998963i	$-0.485505\pi$
$941$	2.79277	0.0910417	0.0455208	+	0.998963i	$0.485505\pi$
$942$	−17.6034	−0.573549
$943$	60.7944	1.97974
$944$	4.26524	0.138822
$945$	−29.0834	−0.946084
$946$	−1.93832	−0.0630202
$947$	47.6931	1.54982	0.774910	−	0.632072i	$-0.217795\pi$
$947$	47.6931	1.54982	0.774910	+	0.632072i	$0.217795\pi$
$948$	16.5370	0.537095
$949$	−43.2617	−1.40434
$950$	0.536505	0.0174065
$951$	15.9208	0.516267
$952$	−46.8033	−1.51690
$953$	33.0008	1.06900	0.534500	−	0.845169i	$-0.320500\pi$
$953$	33.0008	1.06900	0.534500	+	0.845169i	$0.320500\pi$
$954$	−4.54760	−0.147234
$955$	21.8469	0.706950
$956$	−5.01554	−0.162214
$957$	16.8751	0.545494
$958$	10.8100	0.349256
$959$	10.6653	0.344402
$960$	7.56088	0.244026
$961$	−6.50115	−0.209715
$962$	−34.3160	−1.10639
$963$	−3.97994	−0.128252
$964$	−35.0405	−1.12858
$965$	28.5119	0.917832
$966$	34.3969	1.10670
$967$	−0.822954	−0.0264644	−0.0132322	−	0.999912i	$-0.504212\pi$
$967$	−0.822954	−0.0264644	−0.0132322	+	0.999912i	$0.504212\pi$
$968$	24.4516	0.785904
$969$	−1.46239	−0.0469789
$970$	−16.0356	−0.514872
$971$	16.2037	0.520002	0.260001	−	0.965608i	$-0.416277\pi$
$971$	16.2037	0.520002	0.260001	+	0.965608i	$0.416277\pi$
$972$	−13.6588	−0.438107
$973$	40.0133	1.28277
$974$	0.0300489	0.000962830 0
$975$	−20.0642	−0.642570
$976$	3.86760	0.123799
$977$	13.3499	0.427102	0.213551	−	0.976932i	$-0.431497\pi$
$977$	13.3499	0.427102	0.213551	+	0.976932i	$0.431497\pi$
$978$	−15.1239	−0.483610
$979$	18.3139	0.585314
$980$	−11.7068	−0.373961
$981$	−7.23184	−0.230895
$982$	7.52561	0.240152
$983$	2.76086	0.0880577	0.0440288	−	0.999030i	$-0.485981\pi$
$983$	2.76086	0.0880577	0.0440288	+	0.999030i	$0.485981\pi$
$984$	−27.8886	−0.889055
$985$	−18.0771	−0.575985
$986$	−32.8788	−1.04707
$987$	−52.7115	−1.67783
$988$	1.40613	0.0447351
$989$	13.9647	0.444053
$990$	1.69077	0.0537361
$991$	−58.2063	−1.84898	−0.924492	−	0.381201i	$-0.875511\pi$
$991$	−58.2063	−1.84898	−0.924492	+	0.381201i	$0.875511\pi$
$992$	−28.7570	−0.913035
$993$	−40.2600	−1.27761
$994$	−29.6093	−0.939151
$995$	−22.2876	−0.706563
$996$	1.30621	0.0413888
$997$	−21.2309	−0.672388	−0.336194	−	0.941793i	$-0.609140\pi$
$997$	−21.2309	−0.672388	−0.336194	+	0.941793i	$0.609140\pi$
$998$	−25.0601	−0.793263
$999$	49.8495	1.57717

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.c.1.16	✓	25
3.2	odd	2		4923.2.a.n.1.10		25
4.3	odd	2		8752.2.a.v.1.10		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.c.1.16	✓	25	1.1	even	1	trivial
4923.2.a.n.1.10		25	3.2	odd	2
8752.2.a.v.1.10		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)

\(f(q)\)	\(=\)	\(q+0.814364 q^{2} +1.40134 q^{3} -1.33681 q^{4} +1.41612 q^{5} +1.14120 q^{6} +3.63098 q^{7} -2.71738 q^{8} -1.03623 q^{9} +O(q^{10})\)	\(q+0.814364 q^{2} +1.40134 q^{3} -1.33681 q^{4} +1.41612 q^{5} +1.14120 q^{6} +3.63098 q^{7} -2.71738 q^{8} -1.03623 q^{9} +1.15324 q^{10} -1.41484 q^{11} -1.87333 q^{12} +4.78123 q^{13} +2.95693 q^{14} +1.98448 q^{15} +0.460689 q^{16} +4.74354 q^{17} -0.843871 q^{18} -0.219997 q^{19} -1.89309 q^{20} +5.08825 q^{21} -1.15219 q^{22} +8.30104 q^{23} -3.80798 q^{24} -2.99460 q^{25} +3.89366 q^{26} -5.65615 q^{27} -4.85393 q^{28} -8.51127 q^{29} +1.61609 q^{30} -4.94963 q^{31} +5.80993 q^{32} -1.98268 q^{33} +3.86297 q^{34} +5.14191 q^{35} +1.38525 q^{36} -8.81331 q^{37} -0.179158 q^{38} +6.70015 q^{39} -3.84814 q^{40} +7.32371 q^{41} +4.14368 q^{42} +1.68229 q^{43} +1.89137 q^{44} -1.46743 q^{45} +6.76007 q^{46} -10.3595 q^{47} +0.645583 q^{48} +6.18398 q^{49} -2.43869 q^{50} +6.64734 q^{51} -6.39160 q^{52} +5.38897 q^{53} -4.60617 q^{54} -2.00358 q^{55} -9.86673 q^{56} -0.308291 q^{57} -6.93127 q^{58} +9.25839 q^{59} -2.65287 q^{60} +8.39527 q^{61} -4.03080 q^{62} -3.76254 q^{63} +3.81002 q^{64} +6.77081 q^{65} -1.61462 q^{66} -6.01616 q^{67} -6.34122 q^{68} +11.6326 q^{69} +4.18738 q^{70} -10.0135 q^{71} +2.81584 q^{72} -9.04825 q^{73} -7.17724 q^{74} -4.19646 q^{75} +0.294094 q^{76} -5.13724 q^{77} +5.45636 q^{78} -8.82756 q^{79} +0.652392 q^{80} -4.81752 q^{81} +5.96416 q^{82} -0.697265 q^{83} -6.80203 q^{84} +6.71744 q^{85} +1.36999 q^{86} -11.9272 q^{87} +3.84465 q^{88} -12.9441 q^{89} -1.19503 q^{90} +17.3605 q^{91} -11.0969 q^{92} -6.93614 q^{93} -8.43637 q^{94} -0.311543 q^{95} +8.14171 q^{96} -13.9048 q^{97} +5.03601 q^{98} +1.46610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9}+O(q^{10}) \) 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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