LMFDB - Embedded newform 547.2.a.c.1.13

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			1.13
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)

$f(q)$	$=$	$q+0.215054 q^{2} +2.12625 q^{3} -1.95375 q^{4} +4.42221 q^{5} +0.457259 q^{6} +1.19553 q^{7} -0.850270 q^{8} +1.52095 q^{9} +O(q^{10})$	\(q+0.215054 q^{2} +2.12625 q^{3} -1.95375 q^{4} +4.42221 q^{5} +0.457259 q^{6} +1.19553 q^{7} -0.850270 q^{8} +1.52095 q^{9} +0.951013 q^{10} +4.18427 q^{11} -4.15417 q^{12} -5.79583 q^{13} +0.257104 q^{14} +9.40273 q^{15} +3.72465 q^{16} -3.87112 q^{17} +0.327086 q^{18} -1.55469 q^{19} -8.63989 q^{20} +2.54200 q^{21} +0.899845 q^{22} -2.33890 q^{23} -1.80789 q^{24} +14.5559 q^{25} -1.24642 q^{26} -3.14484 q^{27} -2.33577 q^{28} -6.17320 q^{29} +2.02209 q^{30} +4.66785 q^{31} +2.50154 q^{32} +8.89682 q^{33} -0.832499 q^{34} +5.28689 q^{35} -2.97156 q^{36} -0.902773 q^{37} -0.334343 q^{38} -12.3234 q^{39} -3.76007 q^{40} -7.62770 q^{41} +0.546668 q^{42} +5.54993 q^{43} -8.17503 q^{44} +6.72595 q^{45} -0.502991 q^{46} +5.68744 q^{47} +7.91954 q^{48} -5.57070 q^{49} +3.13031 q^{50} -8.23097 q^{51} +11.3236 q^{52} +11.3130 q^{53} -0.676310 q^{54} +18.5037 q^{55} -1.01653 q^{56} -3.30567 q^{57} -1.32757 q^{58} +1.88137 q^{59} -18.3706 q^{60} +4.96147 q^{61} +1.00384 q^{62} +1.81834 q^{63} -6.91133 q^{64} -25.6304 q^{65} +1.91330 q^{66} -4.32940 q^{67} +7.56320 q^{68} -4.97310 q^{69} +1.13697 q^{70} -15.7151 q^{71} -1.29322 q^{72} -0.124846 q^{73} -0.194145 q^{74} +30.9495 q^{75} +3.03748 q^{76} +5.00243 q^{77} -2.65020 q^{78} -0.871683 q^{79} +16.4712 q^{80} -11.2496 q^{81} -1.64037 q^{82} -11.2670 q^{83} -4.96644 q^{84} -17.1189 q^{85} +1.19354 q^{86} -13.1258 q^{87} -3.55777 q^{88} +6.82852 q^{89} +1.44644 q^{90} -6.92910 q^{91} +4.56964 q^{92} +9.92502 q^{93} +1.22311 q^{94} -6.87517 q^{95} +5.31891 q^{96} +6.10185 q^{97} -1.19800 q^{98} +6.36407 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.215054	0.152066	0.0760331	−	0.997105i	$-0.475775\pi$
$2$	0.215054	0.152066	0.0760331	+	0.997105i	$0.475775\pi$
$3$	2.12625	1.22759	0.613796	−	0.789465i	$-0.289642\pi$
$3$	2.12625	1.22759	0.613796	+	0.789465i	$0.289642\pi$
$4$	−1.95375	−0.976876
$5$	4.42221	1.97767	0.988835	−	0.149013i	$-0.0476096\pi$
$5$	4.42221	1.97767	0.988835	+	0.149013i	$0.0476096\pi$
$6$	0.457259	0.186675
$7$	1.19553	0.451869	0.225934	−	0.974143i	$-0.427457\pi$
$7$	1.19553	0.451869	0.225934	+	0.974143i	$0.427457\pi$
$8$	−0.850270	−0.300616
$9$	1.52095	0.506983
$10$	0.951013	0.300737
$11$	4.18427	1.26161	0.630803	−	0.775943i	$-0.282726\pi$
$11$	4.18427	1.26161	0.630803	+	0.775943i	$0.282726\pi$
$12$	−4.15417	−1.19921
$13$	−5.79583	−1.60747	−0.803737	−	0.594985i	$-0.797158\pi$
$13$	−5.79583	−1.60747	−0.803737	+	0.594985i	$0.797158\pi$
$14$	0.257104	0.0687139
$15$	9.40273	2.42777
$16$	3.72465	0.931162
$17$	−3.87112	−0.938884	−0.469442	−	0.882963i	$-0.655545\pi$
$17$	−3.87112	−0.938884	−0.469442	+	0.882963i	$0.655545\pi$
$18$	0.327086	0.0770950
$19$	−1.55469	−0.356671	−0.178336	−	0.983970i	$-0.557071\pi$
$19$	−1.55469	−0.356671	−0.178336	+	0.983970i	$0.557071\pi$
$20$	−8.63989	−1.93194
$21$	2.54200	0.554710
$22$	0.899845	0.191848
$23$	−2.33890	−0.487695	−0.243847	−	0.969814i	$-0.578410\pi$
$23$	−2.33890	−0.487695	−0.243847	+	0.969814i	$0.578410\pi$
$24$	−1.80789	−0.369034
$25$	14.5559	2.91118
$26$	−1.24642	−0.244442
$27$	−3.14484	−0.605224
$28$	−2.33577	−0.441419
$29$	−6.17320	−1.14633	−0.573167	−	0.819438i	$-0.694285\pi$
$29$	−6.17320	−1.14633	−0.573167	+	0.819438i	$0.694285\pi$
$30$	2.02209	0.369182
$31$	4.66785	0.838370	0.419185	−	0.907901i	$-0.362316\pi$
$31$	4.66785	0.838370	0.419185	+	0.907901i	$0.362316\pi$
$32$	2.50154	0.442214
$33$	8.89682	1.54874
$34$	−0.832499	−0.142772
$35$	5.28689	0.893647
$36$	−2.97156	−0.495259
$37$	−0.902773	−0.148415	−0.0742075	−	0.997243i	$-0.523643\pi$
$37$	−0.902773	−0.148415	−0.0742075	+	0.997243i	$0.523643\pi$
$38$	−0.334343	−0.0542376
$39$	−12.3234	−1.97332
$40$	−3.76007	−0.594519
$41$	−7.62770	−1.19125	−0.595623	−	0.803264i	$-0.703095\pi$
$41$	−7.62770	−1.19125	−0.595623	+	0.803264i	$0.703095\pi$
$42$	0.546668	0.0843527
$43$	5.54993	0.846357	0.423178	−	0.906046i	$-0.360914\pi$
$43$	5.54993	0.846357	0.423178	+	0.906046i	$0.360914\pi$
$44$	−8.17503	−1.23243
$45$	6.72595	1.00265
$46$	−0.502991	−0.0741619
$47$	5.68744	0.829599	0.414799	−	0.909913i	$-0.363852\pi$
$47$	5.68744	0.829599	0.414799	+	0.909913i	$0.363852\pi$
$48$	7.91954	1.14309
$49$	−5.57070	−0.795815
$50$	3.13031	0.442692
$51$	−8.23097	−1.15257
$52$	11.3236	1.57030
$53$	11.3130	1.55396	0.776982	−	0.629522i	$-0.216749\pi$
$53$	11.3130	1.55396	0.776982	+	0.629522i	$0.216749\pi$
$54$	−0.676310	−0.0920341
$55$	18.5037	2.49504
$56$	−1.01653	−0.135839
$57$	−3.30567	−0.437847
$58$	−1.32757	−0.174319
$59$	1.88137	0.244934	0.122467	−	0.992473i	$-0.460919\pi$
$59$	1.88137	0.244934	0.122467	+	0.992473i	$0.460919\pi$
$60$	−18.3706	−2.37163
$61$	4.96147	0.635251	0.317626	−	0.948216i	$-0.397114\pi$
$61$	4.96147	0.635251	0.317626	+	0.948216i	$0.397114\pi$
$62$	1.00384	0.127488
$63$	1.81834	0.229090
$64$	−6.91133	−0.863916
$65$	−25.6304	−3.17905
$66$	1.91330	0.235511
$67$	−4.32940	−0.528920	−0.264460	−	0.964397i	$-0.585194\pi$
$67$	−4.32940	−0.528920	−0.264460	+	0.964397i	$0.585194\pi$
$68$	7.56320	0.917173
$69$	−4.97310	−0.598691
$70$	1.13697	0.135894
$71$	−15.7151	−1.86504	−0.932521	−	0.361115i	$-0.882396\pi$
$71$	−15.7151	−1.86504	−0.932521	+	0.361115i	$0.882396\pi$
$72$	−1.29322	−0.152407
$73$	−0.124846	−0.0146122	−0.00730608	−	0.999973i	$-0.502326\pi$
$73$	−0.124846	−0.0146122	−0.00730608	+	0.999973i	$0.502326\pi$
$74$	−0.194145	−0.0225689
$75$	30.9495	3.57374
$76$	3.03748	0.348423
$77$	5.00243	0.570080
$78$	−2.65020	−0.300076
$79$	−0.871683	−0.0980720	−0.0490360	−	0.998797i	$-0.515615\pi$
$79$	−0.871683	−0.0980720	−0.0490360	+	0.998797i	$0.515615\pi$
$80$	16.4712	1.84153
$81$	−11.2496	−1.24995
$82$	−1.64037	−0.181148
$83$	−11.2670	−1.23672	−0.618359	−	0.785896i	$-0.712202\pi$
$83$	−11.2670	−1.23672	−0.618359	+	0.785896i	$0.712202\pi$
$84$	−4.96644	−0.541883
$85$	−17.1189	−1.85680
$86$	1.19354	0.128702
$87$	−13.1258	−1.40723
$88$	−3.55777	−0.379259
$89$	6.82852	0.723822	0.361911	−	0.932213i	$-0.382124\pi$
$89$	6.82852	0.723822	0.361911	+	0.932213i	$0.382124\pi$
$90$	1.44644	0.152468
$91$	−6.92910	−0.726367
$92$	4.56964	0.476417
$93$	9.92502	1.02918
$94$	1.22311	0.126154
$95$	−6.87517	−0.705378
$96$	5.31891	0.542859
$97$	6.10185	0.619549	0.309774	−	0.950810i	$-0.399746\pi$
$97$	6.10185	0.619549	0.309774	+	0.950810i	$0.399746\pi$
$98$	−1.19800	−0.121017
$99$	6.36407	0.639613
$100$	−28.4386	−2.84386
$101$	8.09462	0.805445	0.402723	−	0.915322i	$-0.368064\pi$
$101$	8.09462	0.805445	0.402723	+	0.915322i	$0.368064\pi$
$102$	−1.77010	−0.175266
$103$	−7.76581	−0.765188	−0.382594	−	0.923916i	$-0.624969\pi$
$103$	−7.76581	−0.765188	−0.382594	+	0.923916i	$0.624969\pi$
$104$	4.92802	0.483232
$105$	11.2413	1.09703
$106$	2.43291	0.236305
$107$	3.64596	0.352469	0.176234	−	0.984348i	$-0.443608\pi$
$107$	3.64596	0.352469	0.176234	+	0.984348i	$0.443608\pi$
$108$	6.14423	0.591229
$109$	7.91752	0.758361	0.379181	−	0.925323i	$-0.376206\pi$
$109$	7.91752	0.758361	0.379181	+	0.925323i	$0.376206\pi$
$110$	3.97930	0.379411
$111$	−1.91952	−0.182193
$112$	4.45294	0.420763
$113$	−14.1545	−1.33154	−0.665770	−	0.746157i	$-0.731897\pi$
$113$	−14.1545	−1.33154	−0.665770	+	0.746157i	$0.731897\pi$
$114$	−0.710898	−0.0665817
$115$	−10.3431	−0.964500
$116$	12.0609	1.11983
$117$	−8.81516	−0.814962
$118$	0.404597	0.0372462
$119$	−4.62804	−0.424252
$120$	−7.99486	−0.729827
$121$	6.50816	0.591651
$122$	1.06698	0.0966003
$123$	−16.2184	−1.46236
$124$	−9.11982	−0.818984
$125$	42.2582	3.77969
$126$	0.391042	0.0348368
$127$	−10.5309	−0.934469	−0.467234	−	0.884133i	$-0.654750\pi$
$127$	−10.5309	−0.934469	−0.467234	+	0.884133i	$0.654750\pi$
$128$	−6.48939	−0.573587
$129$	11.8006	1.03898
$130$	−5.51191	−0.483427
$131$	−0.514400	−0.0449434	−0.0224717	−	0.999747i	$-0.507154\pi$
$131$	−0.514400	−0.0449434	−0.0224717	+	0.999747i	$0.507154\pi$
$132$	−17.3822	−1.51293
$133$	−1.85868	−0.161168
$134$	−0.931054	−0.0804308
$135$	−13.9071	−1.19693
$136$	3.29150	0.282243
$137$	22.3320	1.90795	0.953976	−	0.299882i	$-0.0969474\pi$
$137$	22.3320	1.90795	0.953976	+	0.299882i	$0.0969474\pi$
$138$	−1.06948	−0.0910406
$139$	−19.1118	−1.62104	−0.810521	−	0.585710i	$-0.800816\pi$
$139$	−19.1118	−1.62104	−0.810521	+	0.585710i	$0.800816\pi$
$140$	−10.3293	−0.872982
$141$	12.0929	1.01841
$142$	−3.37960	−0.283610
$143$	−24.2513	−2.02800
$144$	5.66500	0.472083
$145$	−27.2992	−2.26707
$146$	−0.0268487	−0.00222202
$147$	−11.8447	−0.976936
$148$	1.76379	0.144983
$149$	−21.9616	−1.79916	−0.899582	−	0.436752i	$-0.856129\pi$
$149$	−21.9616	−1.79916	−0.899582	+	0.436752i	$0.856129\pi$
$150$	6.65582	0.543446
$151$	10.9922	0.894535	0.447268	−	0.894400i	$-0.352397\pi$
$151$	10.9922	0.894535	0.447268	+	0.894400i	$0.352397\pi$
$152$	1.32191	0.107221
$153$	−5.88777	−0.475998
$154$	1.07579	0.0866899
$155$	20.6422	1.65802
$156$	24.0769	1.92769
$157$	−20.5972	−1.64384	−0.821919	−	0.569604i	$-0.807097\pi$
$157$	−20.5972	−1.64384	−0.821919	+	0.569604i	$0.807097\pi$
$158$	−0.187459	−0.0149134
$159$	24.0544	1.90763
$160$	11.0623	0.874554
$161$	−2.79623	−0.220374
$162$	−2.41926	−0.190075
$163$	19.6028	1.53541	0.767706	−	0.640803i	$-0.221398\pi$
$163$	19.6028	1.53541	0.767706	+	0.640803i	$0.221398\pi$
$164$	14.9026	1.16370
$165$	39.3436	3.06289
$166$	−2.42302	−0.188063
$167$	0.160277	0.0124026	0.00620129	−	0.999981i	$-0.498026\pi$
$167$	0.160277	0.0124026	0.00620129	+	0.999981i	$0.498026\pi$
$168$	−2.16139	−0.166755
$169$	20.5917	1.58397
$170$	−3.68148	−0.282357
$171$	−2.36461	−0.180826
$172$	−10.8432	−0.826785
$173$	−9.45063	−0.718518	−0.359259	−	0.933238i	$-0.616971\pi$
$173$	−9.45063	−0.718518	−0.359259	+	0.933238i	$0.616971\pi$
$174$	−2.82275	−0.213992
$175$	17.4020	1.31547
$176$	15.5850	1.17476
$177$	4.00027	0.300679
$178$	1.46850	0.110069
$179$	−18.7270	−1.39972	−0.699862	−	0.714278i	$-0.746755\pi$
$179$	−18.7270	−1.39972	−0.699862	+	0.714278i	$0.746755\pi$
$180$	−13.1408	−0.979460
$181$	12.7850	0.950300	0.475150	−	0.879905i	$-0.342394\pi$
$181$	12.7850	0.950300	0.475150	+	0.879905i	$0.342394\pi$
$182$	−1.49013	−0.110456
$183$	10.5493	0.779830
$184$	1.98870	0.146609
$185$	−3.99225	−0.293516
$186$	2.13442	0.156503
$187$	−16.1978	−1.18450
$188$	−11.1119	−0.810415
$189$	−3.75975	−0.273482
$190$	−1.47853	−0.107264
$191$	−5.19750	−0.376078	−0.188039	−	0.982162i	$-0.560213\pi$
$191$	−5.19750	−0.376078	−0.188039	+	0.982162i	$0.560213\pi$
$192$	−14.6952	−1.06054
$193$	7.90024	0.568672	0.284336	−	0.958725i	$-0.408227\pi$
$193$	7.90024	0.568672	0.284336	+	0.958725i	$0.408227\pi$
$194$	1.31223	0.0942124
$195$	−54.4966	−3.90258
$196$	10.8838	0.777412
$197$	20.6539	1.47153	0.735766	−	0.677235i	$-0.236822\pi$
$197$	20.6539	1.47153	0.735766	+	0.677235i	$0.236822\pi$
$198$	1.36862	0.0972635
$199$	−3.29465	−0.233552	−0.116776	−	0.993158i	$-0.537256\pi$
$199$	−3.29465	−0.233552	−0.116776	+	0.993158i	$0.537256\pi$
$200$	−12.3765	−0.875147
$201$	−9.20539	−0.649298
$202$	1.74078	0.122481
$203$	−7.38026	−0.517992
$204$	16.0813	1.12591
$205$	−33.7313	−2.35589
$206$	−1.67007	−0.116359
$207$	−3.55735	−0.247253
$208$	−21.5874	−1.49682
$209$	−6.50526	−0.449978
$210$	2.41748	0.166822
$211$	−19.8662	−1.36764	−0.683822	−	0.729649i	$-0.739683\pi$
$211$	−19.8662	−1.36764	−0.683822	+	0.729649i	$0.739683\pi$
$212$	−22.1029	−1.51803
$213$	−33.4143	−2.28951
$214$	0.784080	0.0535986
$215$	24.5429	1.67381
$216$	2.67396	0.181940
$217$	5.58056	0.378833
$218$	1.70270	0.115321
$219$	−0.265455	−0.0179378
$220$	−36.1517	−2.43735
$221$	22.4363	1.50923
$222$	−0.412801	−0.0277054
$223$	3.97965	0.266497	0.133249	−	0.991083i	$-0.457459\pi$
$223$	3.97965	0.266497	0.133249	+	0.991083i	$0.457459\pi$
$224$	2.99067	0.199823
$225$	22.1388	1.47592
$226$	−3.04397	−0.202482
$227$	12.5848	0.835280	0.417640	−	0.908613i	$-0.362857\pi$
$227$	12.5848	0.835280	0.417640	+	0.908613i	$0.362857\pi$
$228$	6.45846	0.427722
$229$	16.6161	1.09802	0.549010	−	0.835816i	$-0.315005\pi$
$229$	16.6161	1.09802	0.549010	+	0.835816i	$0.315005\pi$
$230$	−2.22433	−0.146668
$231$	10.6364	0.699826
$232$	5.24889	0.344606
$233$	5.82929	0.381889	0.190945	−	0.981601i	$-0.438845\pi$
$233$	5.82929	0.381889	0.190945	+	0.981601i	$0.438845\pi$
$234$	−1.89574	−0.123928
$235$	25.1510	1.64067
$236$	−3.67573	−0.239270
$237$	−1.85342	−0.120392
$238$	−0.995280	−0.0645144
$239$	−8.67776	−0.561318	−0.280659	−	0.959808i	$-0.590553\pi$
$239$	−8.67776	−0.561318	−0.280659	+	0.959808i	$0.590553\pi$
$240$	35.0219	2.26065
$241$	8.50915	0.548122	0.274061	−	0.961712i	$-0.411633\pi$
$241$	8.50915	0.548122	0.274061	+	0.961712i	$0.411633\pi$
$242$	1.39961	0.0899700
$243$	−14.4849	−0.929207
$244$	−9.69349	−0.620562
$245$	−24.6348	−1.57386
$246$	−3.48784	−0.222376
$247$	9.01074	0.573340
$248$	−3.96893	−0.252028
$249$	−23.9565	−1.51818
$250$	9.08779	0.574762
$251$	17.6790	1.11589	0.557945	−	0.829878i	$-0.311590\pi$
$251$	17.6790	1.11589	0.557945	+	0.829878i	$0.311590\pi$
$252$	−3.55259	−0.223792
$253$	−9.78661	−0.615279
$254$	−2.26472	−0.142101
$255$	−36.3990	−2.27940
$256$	12.4271	0.776693
$257$	26.3299	1.64241	0.821207	−	0.570631i	$-0.193301\pi$
$257$	26.3299	1.64241	0.821207	+	0.570631i	$0.193301\pi$
$258$	2.53776	0.157994
$259$	−1.07929	−0.0670641
$260$	50.0754	3.10554
$261$	−9.38912	−0.581172
$262$	−0.110624	−0.00683437
$263$	28.4898	1.75676	0.878378	−	0.477967i	$-0.158626\pi$
$263$	28.4898	1.75676	0.878378	+	0.477967i	$0.158626\pi$
$264$	−7.56471	−0.465575
$265$	50.0286	3.07323
$266$	−0.399718	−0.0245083
$267$	14.5192	0.888558
$268$	8.45857	0.516689
$269$	4.03222	0.245849	0.122924	−	0.992416i	$-0.460773\pi$
$269$	4.03222	0.245849	0.122924	+	0.992416i	$0.460773\pi$
$270$	−2.99078	−0.182013
$271$	0.521770	0.0316953	0.0158476	−	0.999874i	$-0.494955\pi$
$271$	0.521770	0.0316953	0.0158476	+	0.999874i	$0.494955\pi$
$272$	−14.4186	−0.874253
$273$	−14.7330	−0.891683
$274$	4.80259	0.290135
$275$	60.9059	3.67276
$276$	9.71620	0.584846
$277$	−14.4925	−0.870773	−0.435386	−	0.900244i	$-0.643388\pi$
$277$	−14.4925	−0.870773	−0.435386	+	0.900244i	$0.643388\pi$
$278$	−4.11007	−0.246506
$279$	7.09956	0.425040
$280$	−4.49528	−0.268645
$281$	6.43931	0.384137	0.192068	−	0.981382i	$-0.438480\pi$
$281$	6.43931	0.384137	0.192068	+	0.981382i	$0.438480\pi$
$282$	2.60064	0.154866
$283$	21.5775	1.28265	0.641325	−	0.767269i	$-0.278385\pi$
$283$	21.5775	1.28265	0.641325	+	0.767269i	$0.278385\pi$
$284$	30.7035	1.82192
$285$	−14.6184	−0.865916
$286$	−5.21535	−0.308390
$287$	−9.11916	−0.538287
$288$	3.80472	0.224195
$289$	−2.01445	−0.118497
$290$	−5.87080	−0.344745
$291$	12.9741	0.760553
$292$	0.243919	0.0142743
$293$	18.3609	1.07266	0.536329	−	0.844009i	$-0.319811\pi$
$293$	18.3609	1.07266	0.536329	+	0.844009i	$0.319811\pi$
$294$	−2.54726	−0.148559
$295$	8.31982	0.484398
$296$	0.767601	0.0446159
$297$	−13.1589	−0.763554
$298$	−4.72293	−0.273592
$299$	13.5559	0.783957
$300$	−60.4677	−3.49110
$301$	6.63512	0.382442
$302$	2.36392	0.136029
$303$	17.2112	0.988758
$304$	−5.79069	−0.332119
$305$	21.9407	1.25632
$306$	−1.26619	−0.0723832
$307$	12.1331	0.692471	0.346236	−	0.938148i	$-0.387460\pi$
$307$	12.1331	0.692471	0.346236	+	0.938148i	$0.387460\pi$
$308$	−9.77351	−0.556898
$309$	−16.5121	−0.939339
$310$	4.43919	0.252129
$311$	16.4360	0.932002	0.466001	−	0.884784i	$-0.345694\pi$
$311$	16.4360	0.932002	0.466001	+	0.884784i	$0.345694\pi$
$312$	10.4782	0.593212
$313$	11.9080	0.673082	0.336541	−	0.941669i	$-0.390743\pi$
$313$	11.9080	0.673082	0.336541	+	0.941669i	$0.390743\pi$
$314$	−4.42952	−0.249972
$315$	8.04109	0.453064
$316$	1.70305	0.0958042
$317$	9.08303	0.510154	0.255077	−	0.966921i	$-0.417899\pi$
$317$	9.08303	0.510154	0.255077	+	0.966921i	$0.417899\pi$
$318$	5.17299	0.290087
$319$	−25.8304	−1.44622
$320$	−30.5633	−1.70854
$321$	7.75224	0.432688
$322$	−0.601341	−0.0335114
$323$	6.01840	0.334873
$324$	21.9788	1.22105
$325$	−84.3636	−4.67965
$326$	4.21567	0.233484
$327$	16.8347	0.930959
$328$	6.48561	0.358108
$329$	6.79952	0.374870
$330$	8.46100	0.465763
$331$	−9.44249	−0.519006	−0.259503	−	0.965742i	$-0.583559\pi$
$331$	−9.44249	−0.519006	−0.259503	+	0.965742i	$0.583559\pi$
$332$	22.0130	1.20812
$333$	−1.37307	−0.0752439
$334$	0.0344681	0.00188601
$335$	−19.1455	−1.04603
$336$	9.46807	0.516525
$337$	7.82554	0.426285	0.213142	−	0.977021i	$-0.431630\pi$
$337$	7.82554	0.426285	0.213142	+	0.977021i	$0.431630\pi$
$338$	4.42832	0.240869
$339$	−30.0959	−1.63459
$340$	33.4460	1.81387
$341$	19.5316	1.05769
$342$	−0.508519	−0.0274975
$343$	−15.0287	−0.811472
$344$	−4.71894	−0.254428
$345$	−21.9921	−1.18401
$346$	−2.03240	−0.109262
$347$	−22.2368	−1.19373	−0.596867	−	0.802340i	$-0.703588\pi$
$347$	−22.2368	−1.19373	−0.596867	+	0.802340i	$0.703588\pi$
$348$	25.6445	1.37469
$349$	−0.741955	−0.0397159	−0.0198580	−	0.999803i	$-0.506321\pi$
$349$	−0.741955	−0.0397159	−0.0198580	+	0.999803i	$0.506321\pi$
$350$	3.74238	0.200039
$351$	18.2269	0.972882
$352$	10.4671	0.557900
$353$	14.4797	0.770676	0.385338	−	0.922776i	$-0.374085\pi$
$353$	14.4797	0.770676	0.385338	+	0.922776i	$0.374085\pi$
$354$	0.860275	0.0457231
$355$	−69.4955	−3.68844
$356$	−13.3412	−0.707084
$357$	−9.84039	−0.520809
$358$	−4.02733	−0.212851
$359$	31.8436	1.68064	0.840321	−	0.542089i	$-0.182366\pi$
$359$	31.8436	1.68064	0.840321	+	0.542089i	$0.182366\pi$
$360$	−5.71888	−0.301411
$361$	−16.5829	−0.872786
$362$	2.74946	0.144509
$363$	13.8380	0.726306
$364$	13.5377	0.709570
$365$	−0.552097	−0.0288981
$366$	2.26868	0.118586
$367$	7.67065	0.400405	0.200202	−	0.979755i	$-0.435840\pi$
$367$	7.67065	0.400405	0.200202	+	0.979755i	$0.435840\pi$
$368$	−8.71159	−0.454123
$369$	−11.6013	−0.603942
$370$	−0.858549	−0.0446338
$371$	13.5251	0.702188
$372$	−19.3910	−1.00538
$373$	−16.9302	−0.876615	−0.438307	−	0.898825i	$-0.644422\pi$
$373$	−16.9302	−0.876615	−0.438307	+	0.898825i	$0.644422\pi$
$374$	−3.48341	−0.180123
$375$	89.8515	4.63991
$376$	−4.83587	−0.249391
$377$	35.7788	1.84270
$378$	−0.808550	−0.0415873
$379$	−2.81272	−0.144480	−0.0722400	−	0.997387i	$-0.523015\pi$
$379$	−2.81272	−0.144480	−0.0722400	+	0.997387i	$0.523015\pi$
$380$	13.4324	0.689067
$381$	−22.3914	−1.14715
$382$	−1.11774	−0.0571887
$383$	2.43186	0.124262	0.0621311	−	0.998068i	$-0.480210\pi$
$383$	2.43186	0.124262	0.0621311	+	0.998068i	$0.480210\pi$
$384$	−13.7981	−0.704131
$385$	22.1218	1.12743
$386$	1.69898	0.0864757
$387$	8.44116	0.429088
$388$	−11.9215	−0.605222
$389$	−13.5116	−0.685068	−0.342534	−	0.939506i	$-0.611285\pi$
$389$	−13.5116	−0.685068	−0.342534	+	0.939506i	$0.611285\pi$
$390$	−11.7197	−0.593451
$391$	9.05417	0.457889
$392$	4.73660	0.239235
$393$	−1.09374	−0.0551721
$394$	4.44172	0.223770
$395$	−3.85476	−0.193954
$396$	−12.4338	−0.624822
$397$	−1.38083	−0.0693021	−0.0346510	−	0.999399i	$-0.511032\pi$
$397$	−1.38083	−0.0693021	−0.0346510	+	0.999399i	$0.511032\pi$
$398$	−0.708529	−0.0355153
$399$	−3.95203	−0.197849
$400$	54.2156	2.71078
$401$	−37.9667	−1.89597	−0.947983	−	0.318320i	$-0.896881\pi$
$401$	−37.9667	−1.89597	−0.947983	+	0.318320i	$0.896881\pi$
$402$	−1.97966	−0.0987363
$403$	−27.0541	−1.34766
$404$	−15.8149	−0.786820
$405$	−49.7479	−2.47199
$406$	−1.58715	−0.0787691
$407$	−3.77745	−0.187241
$408$	6.99855	0.346480
$409$	19.3234	0.955481	0.477740	−	0.878501i	$-0.341456\pi$
$409$	19.3234	0.955481	0.477740	+	0.878501i	$0.341456\pi$
$410$	−7.25404	−0.358252
$411$	47.4835	2.34219
$412$	15.1725	0.747494
$413$	2.24924	0.110678
$414$	−0.765023	−0.0375988
$415$	−49.8251	−2.44582
$416$	−14.4985	−0.710848
$417$	−40.6365	−1.98998
$418$	−1.39898	−0.0684265
$419$	−6.44981	−0.315094	−0.157547	−	0.987512i	$-0.550359\pi$
$419$	−6.44981	−0.315094	−0.157547	+	0.987512i	$0.550359\pi$
$420$	−21.9626	−1.07167
$421$	13.7199	0.668668	0.334334	−	0.942455i	$-0.391489\pi$
$421$	13.7199	0.668668	0.334334	+	0.942455i	$0.391489\pi$
$422$	−4.27230	−0.207972
$423$	8.65031	0.420593
$424$	−9.61914	−0.467147
$425$	−56.3476	−2.73326
$426$	−7.18589	−0.348157
$427$	5.93160	0.287050
$428$	−7.12331	−0.344318
$429$	−51.5645	−2.48956
$430$	5.27806	0.254531
$431$	28.9264	1.39334	0.696668	−	0.717394i	$-0.254665\pi$
$431$	28.9264	1.39334	0.696668	+	0.717394i	$0.254665\pi$
$432$	−11.7134	−0.563562
$433$	−9.45033	−0.454154	−0.227077	−	0.973877i	$-0.572917\pi$
$433$	−9.45033	−0.454154	−0.227077	+	0.973877i	$0.572917\pi$
$434$	1.20012	0.0576077
$435$	−58.0449	−2.78304
$436$	−15.4689	−0.740825
$437$	3.63628	0.173947
$438$	−0.0570872	−0.00272773
$439$	−6.35254	−0.303190	−0.151595	−	0.988443i	$-0.548441\pi$
$439$	−6.35254	−0.303190	−0.151595	+	0.988443i	$0.548441\pi$
$440$	−15.7332	−0.750049
$441$	−8.47276	−0.403465
$442$	4.82503	0.229503
$443$	−7.58101	−0.360185	−0.180092	−	0.983650i	$-0.557640\pi$
$443$	−7.58101	−0.360185	−0.180092	+	0.983650i	$0.557640\pi$
$444$	3.75027	0.177980
$445$	30.1971	1.43148
$446$	0.855840	0.0405252
$447$	−46.6959	−2.20864
$448$	−8.26272	−0.390377
$449$	−15.5615	−0.734393	−0.367196	−	0.930143i	$-0.619682\pi$
$449$	−15.5615	−0.734393	−0.367196	+	0.930143i	$0.619682\pi$
$450$	4.76104	0.224437
$451$	−31.9164	−1.50288
$452$	27.6543	1.30075
$453$	23.3723	1.09812
$454$	2.70640	0.127018
$455$	−30.6419	−1.43651
$456$	2.81071	0.131624
$457$	4.75145	0.222263	0.111132	−	0.993806i	$-0.464552\pi$
$457$	4.75145	0.222263	0.111132	+	0.993806i	$0.464552\pi$
$458$	3.57335	0.166972
$459$	12.1740	0.568235
$460$	20.2079	0.942197
$461$	0.239468	0.0111532	0.00557658	−	0.999984i	$-0.498225\pi$
$461$	0.239468	0.0111532	0.00557658	+	0.999984i	$0.498225\pi$
$462$	2.28741	0.106420
$463$	−6.15418	−0.286009	−0.143004	−	0.989722i	$-0.545676\pi$
$463$	−6.15418	−0.286009	−0.143004	+	0.989722i	$0.545676\pi$
$464$	−22.9930	−1.06742
$465$	43.8905	2.03537
$466$	1.25361	0.0580725
$467$	−31.0896	−1.43865	−0.719327	−	0.694671i	$-0.755550\pi$
$467$	−31.0896	−1.43865	−0.719327	+	0.694671i	$0.755550\pi$
$468$	17.2226	0.796117
$469$	−5.17593	−0.239002
$470$	5.40884	0.249491
$471$	−43.7949	−2.01796
$472$	−1.59968	−0.0736310
$473$	23.2224	1.06777
$474$	−0.398585	−0.0183076
$475$	−22.6300	−1.03833
$476$	9.04205	0.414442
$477$	17.2065	0.787834
$478$	−1.86619	−0.0853574
$479$	5.47415	0.250120	0.125060	−	0.992149i	$-0.460088\pi$
$479$	5.47415	0.250120	0.125060	+	0.992149i	$0.460088\pi$
$480$	23.5213	1.07360
$481$	5.23232	0.238573
$482$	1.82993	0.0833509
$483$	−5.94550	−0.270529
$484$	−12.7153	−0.577969
$485$	26.9836	1.22526
$486$	−3.11504	−0.141301
$487$	0.328962	0.0149067	0.00745335	−	0.999972i	$-0.497628\pi$
$487$	0.328962	0.0149067	0.00745335	+	0.999972i	$0.497628\pi$
$488$	−4.21859	−0.190967
$489$	41.6805	1.88486
$490$	−5.29781	−0.239331
$491$	14.0769	0.635280	0.317640	−	0.948211i	$-0.397110\pi$
$491$	14.0769	0.635280	0.317640	+	0.948211i	$0.397110\pi$
$492$	31.6867	1.42855
$493$	23.8972	1.07627
$494$	1.93780	0.0871856
$495$	28.1432	1.26494
$496$	17.3861	0.780659
$497$	−18.7879	−0.842754
$498$	−5.15195	−0.230865
$499$	−1.69342	−0.0758078	−0.0379039	−	0.999281i	$-0.512068\pi$
$499$	−1.69342	−0.0758078	−0.0379039	+	0.999281i	$0.512068\pi$
$500$	−82.5620	−3.69228
$501$	0.340788	0.0152253
$502$	3.80195	0.169689
$503$	−31.2974	−1.39548	−0.697741	−	0.716350i	$-0.745811\pi$
$503$	−31.2974	−1.39548	−0.697741	+	0.716350i	$0.745811\pi$
$504$	−1.54608	−0.0688680
$505$	35.7961	1.59291
$506$	−2.10465	−0.0935631
$507$	43.7831	1.94447
$508$	20.5748	0.912860
$509$	26.6359	1.18062	0.590308	−	0.807178i	$-0.299006\pi$
$509$	26.6359	1.18062	0.590308	+	0.807178i	$0.299006\pi$
$510$	−7.82776	−0.346619
$511$	−0.149258	−0.00660278
$512$	15.6513	0.691696
$513$	4.88925	0.215866
$514$	5.66235	0.249756
$515$	−34.3420	−1.51329
$516$	−23.0554	−1.01496
$517$	23.7978	1.04663
$518$	−0.232107	−0.0101982
$519$	−20.0944	−0.882048
$520$	21.7927	0.955675
$521$	−6.79532	−0.297708	−0.148854	−	0.988859i	$-0.547559\pi$
$521$	−6.79532	−0.297708	−0.148854	+	0.988859i	$0.547559\pi$
$522$	−2.01917	−0.0883766
$523$	−18.7923	−0.821732	−0.410866	−	0.911696i	$-0.634774\pi$
$523$	−18.7923	−0.821732	−0.410866	+	0.911696i	$0.634774\pi$
$524$	1.00501	0.0439041
$525$	37.0011	1.61486
$526$	6.12684	0.267143
$527$	−18.0698	−0.787132
$528$	33.1375	1.44213
$529$	−17.5295	−0.762154
$530$	10.7588	0.467334
$531$	2.86147	0.124177
$532$	3.63141	0.157442
$533$	44.2088	1.91490
$534$	3.12241	0.135120
$535$	16.1232	0.697067
$536$	3.68116	0.159002
$537$	−39.8184	−1.71829
$538$	0.867146	0.0373853
$539$	−23.3094	−1.00400
$540$	27.1710	1.16926
$541$	28.8536	1.24051	0.620257	−	0.784398i	$-0.287028\pi$
$541$	28.8536	1.24051	0.620257	+	0.784398i	$0.287028\pi$
$542$	0.112209	0.00481978
$543$	27.1841	1.16658
$544$	−9.68376	−0.415188
$545$	35.0129	1.49979
$546$	−3.16839	−0.135595
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	−43.6312	−1.86383
$549$	7.54615	0.322062
$550$	13.0981	0.558503
$551$	9.59743	0.408864
$552$	4.22848	0.179976
$553$	−1.04212	−0.0443156
$554$	−3.11668	−0.132415
$555$	−8.48853	−0.360318
$556$	37.3397	1.58356
$557$	−1.25866	−0.0533311	−0.0266656	−	0.999644i	$-0.508489\pi$
$557$	−1.25866	−0.0533311	−0.0266656	+	0.999644i	$0.508489\pi$
$558$	1.52679	0.0646341
$559$	−32.1665	−1.36050
$560$	19.6918	0.832131
$561$	−34.4406	−1.45409
$562$	1.38480	0.0584142
$563$	−14.7290	−0.620753	−0.310377	−	0.950614i	$-0.600455\pi$
$563$	−14.7290	−0.620753	−0.310377	+	0.950614i	$0.600455\pi$
$564$	−23.6266	−0.994859
$565$	−62.5939	−2.63335
$566$	4.64033	0.195048
$567$	−13.4492	−0.564814
$568$	13.3621	0.560662
$569$	−4.97789	−0.208684	−0.104342	−	0.994541i	$-0.533274\pi$
$569$	−4.97789	−0.208684	−0.104342	+	0.994541i	$0.533274\pi$
$570$	−3.14374	−0.131677
$571$	−25.2960	−1.05861	−0.529303	−	0.848433i	$-0.677546\pi$
$571$	−25.2960	−1.05861	−0.529303	+	0.848433i	$0.677546\pi$
$572$	47.3811	1.98110
$573$	−11.0512	−0.461670
$574$	−1.96111	−0.0818552
$575$	−34.0448	−1.41977
$576$	−10.5118	−0.437991
$577$	21.7449	0.905254	0.452627	−	0.891700i	$-0.350487\pi$
$577$	21.7449	0.905254	0.452627	+	0.891700i	$0.350487\pi$
$578$	−0.433216	−0.0180194
$579$	16.7979	0.698097
$580$	53.3358	2.21465
$581$	−13.4701	−0.558834
$582$	2.79013	0.115654
$583$	47.3368	1.96049
$584$	0.106153	0.00439265
$585$	−38.9825	−1.61173
$586$	3.94859	0.163115
$587$	−34.7550	−1.43449	−0.717246	−	0.696820i	$-0.754598\pi$
$587$	−34.7550	−1.43449	−0.717246	+	0.696820i	$0.754598\pi$
$588$	23.1416	0.954345
$589$	−7.25707	−0.299022
$590$	1.78921	0.0736606
$591$	43.9155	1.80644
$592$	−3.36251	−0.138198
$593$	−14.6155	−0.600187	−0.300093	−	0.953910i	$-0.597018\pi$
$593$	−14.6155	−0.600187	−0.300093	+	0.953910i	$0.597018\pi$
$594$	−2.82987	−0.116111
$595$	−20.4662	−0.839031
$596$	42.9075	1.75756
$597$	−7.00527	−0.286707
$598$	2.91525	0.119213
$599$	31.6069	1.29142	0.645710	−	0.763582i	$-0.276561\pi$
$599$	31.6069	1.29142	0.645710	+	0.763582i	$0.276561\pi$
$600$	−26.3155	−1.07432
$601$	−35.4685	−1.44679	−0.723395	−	0.690434i	$-0.757419\pi$
$601$	−35.4685	−1.44679	−0.723395	+	0.690434i	$0.757419\pi$
$602$	1.42691	0.0581565
$603$	−6.58479	−0.268153
$604$	−21.4761	−0.873850
$605$	28.7804	1.17009
$606$	3.70134	0.150357
$607$	31.7326	1.28799	0.643994	−	0.765030i	$-0.277276\pi$
$607$	31.7326	1.28799	0.643994	+	0.765030i	$0.277276\pi$
$608$	−3.88913	−0.157725
$609$	−15.6923	−0.635884
$610$	4.71843	0.191044
$611$	−32.9635	−1.33356
$612$	11.5032	0.464991
$613$	40.9817	1.65523	0.827617	−	0.561293i	$-0.189696\pi$
$613$	40.9817	1.65523	0.827617	+	0.561293i	$0.189696\pi$
$614$	2.60927	0.105301
$615$	−71.7212	−2.89208
$616$	−4.25342	−0.171375
$617$	−13.2965	−0.535297	−0.267648	−	0.963517i	$-0.586247\pi$
$617$	−13.2965	−0.535297	−0.267648	+	0.963517i	$0.586247\pi$
$618$	−3.55099	−0.142842
$619$	−36.9435	−1.48489	−0.742443	−	0.669909i	$-0.766333\pi$
$619$	−36.9435	−1.48489	−0.742443	+	0.669909i	$0.766333\pi$
$620$	−40.3297	−1.61968
$621$	7.35547	0.295165
$622$	3.53464	0.141726
$623$	8.16372	0.327072
$624$	−45.9003	−1.83748
$625$	114.095	4.56379
$626$	2.56087	0.102353
$627$	−13.8318	−0.552390
$628$	40.2419	1.60583
$629$	3.49474	0.139344
$630$	1.72927	0.0688957
$631$	−32.9977	−1.31362	−0.656809	−	0.754057i	$-0.728094\pi$
$631$	−32.9977	−1.31362	−0.656809	+	0.754057i	$0.728094\pi$
$632$	0.741166	0.0294820
$633$	−42.2405	−1.67891
$634$	1.95334	0.0775772
$635$	−46.5699	−1.84807
$636$	−46.9963	−1.86352
$637$	32.2869	1.27925
$638$	−5.55493	−0.219922
$639$	−23.9019	−0.945545
$640$	−28.6974	−1.13437
$641$	−35.6562	−1.40833	−0.704167	−	0.710035i	$-0.748679\pi$
$641$	−35.6562	−1.40833	−0.704167	+	0.710035i	$0.748679\pi$
$642$	1.66715	0.0657972
$643$	−41.2556	−1.62696	−0.813482	−	0.581591i	$-0.802431\pi$
$643$	−41.2556	−1.62696	−0.813482	+	0.581591i	$0.802431\pi$
$644$	5.46314	0.215278
$645$	52.1845	2.05476
$646$	1.29428	0.0509228
$647$	33.6775	1.32400	0.662000	−	0.749503i	$-0.269708\pi$
$647$	33.6775	1.32400	0.662000	+	0.749503i	$0.269708\pi$
$648$	9.56517	0.375755
$649$	7.87218	0.309010
$650$	−18.1427	−0.711616
$651$	11.8657	0.465053
$652$	−38.2990	−1.49991
$653$	16.3779	0.640917	0.320458	−	0.947263i	$-0.396163\pi$
$653$	16.3779	0.640917	0.320458	+	0.947263i	$0.396163\pi$
$654$	3.62036	0.141567
$655$	−2.27478	−0.0888832
$656$	−28.4105	−1.10924
$657$	−0.189885	−0.00740812
$658$	1.46226	0.0570050
$659$	16.0464	0.625081	0.312540	−	0.949904i	$-0.398820\pi$
$659$	16.0464	0.625081	0.312540	+	0.949904i	$0.398820\pi$
$660$	−76.8676	−2.99207
$661$	−17.8181	−0.693043	−0.346522	−	0.938042i	$-0.612637\pi$
$661$	−17.8181	−0.693043	−0.346522	+	0.938042i	$0.612637\pi$
$662$	−2.03065	−0.0789233
$663$	47.7053	1.85272
$664$	9.58002	0.371777
$665$	−8.21949	−0.318738
$666$	−0.295285	−0.0114420
$667$	14.4385	0.559062
$668$	−0.313141	−0.0121158
$669$	8.46174	0.327150
$670$	−4.11731	−0.159066
$671$	20.7602	0.801437
$672$	6.35893	0.245301
$673$	35.2004	1.35688	0.678438	−	0.734658i	$-0.262657\pi$
$673$	35.2004	1.35688	0.678438	+	0.734658i	$0.262657\pi$
$674$	1.68292	0.0648235
$675$	−45.7759	−1.76192
$676$	−40.2310	−1.54735
$677$	20.8453	0.801150	0.400575	−	0.916264i	$-0.368810\pi$
$677$	20.8453	0.801150	0.400575	+	0.916264i	$0.368810\pi$
$678$	−6.47225	−0.248565
$679$	7.29495	0.279955
$680$	14.5557	0.558185
$681$	26.7584	1.02538
$682$	4.20034	0.160839
$683$	−13.6584	−0.522625	−0.261313	−	0.965254i	$-0.584155\pi$
$683$	−13.6584	−0.522625	−0.261313	+	0.965254i	$0.584155\pi$
$684$	4.61986	0.176645
$685$	98.7567	3.77330
$686$	−3.23198	−0.123397
$687$	35.3299	1.34792
$688$	20.6715	0.788095
$689$	−65.5684	−2.49796
$690$	−4.72948	−0.180048
$691$	26.6871	1.01522	0.507612	−	0.861586i	$-0.330528\pi$
$691$	26.6871	1.01522	0.507612	+	0.861586i	$0.330528\pi$
$692$	18.4642	0.701903
$693$	7.60845	0.289021
$694$	−4.78211	−0.181527
$695$	−84.5163	−3.20589
$696$	11.1605	0.423036
$697$	29.5277	1.11844
$698$	−0.159560	−0.00603945
$699$	12.3945	0.468804
$700$	−33.9993	−1.28505
$701$	−30.1627	−1.13923	−0.569615	−	0.821912i	$-0.692908\pi$
$701$	−30.1627	−1.13923	−0.569615	+	0.821912i	$0.692908\pi$
$702$	3.91978	0.147942
$703$	1.40353	0.0529353
$704$	−28.9189	−1.08992
$705$	53.4775	2.01408
$706$	3.11392	0.117194
$707$	9.67738	0.363955
$708$	−7.81554	−0.293726
$709$	32.9424	1.23718	0.618589	−	0.785715i	$-0.287705\pi$
$709$	32.9424	1.23718	0.618589	+	0.785715i	$0.287705\pi$
$710$	−14.9453	−0.560887
$711$	−1.32578	−0.0497208
$712$	−5.80609	−0.217592
$713$	−10.9176	−0.408869
$714$	−2.11622	−0.0791974
$715$	−107.244	−4.01072
$716$	36.5880	1.36736
$717$	−18.4511	−0.689069
$718$	6.84810	0.255569
$719$	36.7463	1.37040	0.685202	−	0.728353i	$-0.259714\pi$
$719$	36.7463	1.37040	0.685202	+	0.728353i	$0.259714\pi$
$720$	25.0518	0.933625
$721$	−9.28428	−0.345765
$722$	−3.56623	−0.132721
$723$	18.0926	0.672871
$724$	−24.9787	−0.928325
$725$	−89.8565	−3.33719
$726$	2.97591	0.110447
$727$	−44.1522	−1.63752	−0.818758	−	0.574139i	$-0.805337\pi$
$727$	−44.1522	−1.63752	−0.818758	+	0.574139i	$0.805337\pi$
$728$	5.89161	0.218358
$729$	2.95014	0.109264
$730$	−0.118731	−0.00439442
$731$	−21.4844	−0.794630
$732$	−20.6108	−0.761797
$733$	35.0705	1.29536	0.647680	−	0.761912i	$-0.275739\pi$
$733$	35.0705	1.29536	0.647680	+	0.761912i	$0.275739\pi$
$734$	1.64960	0.0608880
$735$	−52.3798	−1.93206
$736$	−5.85086	−0.215666
$737$	−18.1154	−0.667289
$738$	−2.49492	−0.0918391
$739$	3.35627	0.123462	0.0617312	−	0.998093i	$-0.480338\pi$
$739$	3.35627	0.123462	0.0617312	+	0.998093i	$0.480338\pi$
$740$	7.79986	0.286729
$741$	19.1591	0.703827
$742$	2.90863	0.106779
$743$	8.81758	0.323485	0.161743	−	0.986833i	$-0.448289\pi$
$743$	8.81758	0.323485	0.161743	+	0.986833i	$0.448289\pi$
$744$	−8.43895	−0.309387
$745$	−97.1187	−3.55815
$746$	−3.64092	−0.133303
$747$	−17.1366	−0.626995
$748$	31.6465	1.15711
$749$	4.35887	0.159270
$750$	19.3229	0.705574
$751$	3.64605	0.133046	0.0665232	−	0.997785i	$-0.478809\pi$
$751$	3.64605	0.133046	0.0665232	+	0.997785i	$0.478809\pi$
$752$	21.1837	0.772491
$753$	37.5901	1.36986
$754$	7.69438	0.280213
$755$	48.6099	1.76910
$756$	7.34562	0.267158
$757$	8.38990	0.304936	0.152468	−	0.988308i	$-0.451278\pi$
$757$	8.38990	0.304936	0.152468	+	0.988308i	$0.451278\pi$
$758$	−0.604888	−0.0219705
$759$	−20.8088	−0.755312
$760$	5.84576	0.212048
$761$	5.05289	0.183167	0.0915836	−	0.995797i	$-0.470807\pi$
$761$	5.05289	0.183167	0.0915836	+	0.995797i	$0.470807\pi$
$762$	−4.81536	−0.174442
$763$	9.46565	0.342680
$764$	10.1546	0.367381
$765$	−26.0369	−0.941367
$766$	0.522982	0.0188961
$767$	−10.9041	−0.393725
$768$	26.4231	0.953463
$769$	19.6645	0.709120	0.354560	−	0.935033i	$-0.384631\pi$
$769$	19.6645	0.709120	0.354560	+	0.935033i	$0.384631\pi$
$770$	4.75738	0.171444
$771$	55.9840	2.01621
$772$	−15.4351	−0.555522
$773$	5.37783	0.193427	0.0967135	−	0.995312i	$-0.469167\pi$
$773$	5.37783	0.193427	0.0967135	+	0.995312i	$0.469167\pi$
$774$	1.81531	0.0652498
$775$	67.9448	2.44065
$776$	−5.18822	−0.186246
$777$	−2.29485	−0.0823273
$778$	−2.90573	−0.104176
$779$	11.8587	0.424883
$780$	106.473	3.81234
$781$	−65.7564	−2.35295
$782$	1.94714	0.0696294
$783$	19.4137	0.693789
$784$	−20.7489	−0.741033
$785$	−91.0852	−3.25097
$786$	−0.235214	−0.00838982
$787$	−22.5513	−0.803867	−0.401934	−	0.915669i	$-0.631662\pi$
$787$	−22.5513	−0.803867	−0.401934	+	0.915669i	$0.631662\pi$
$788$	−40.3527	−1.43750
$789$	60.5765	2.15658
$790$	−0.828982	−0.0294939
$791$	−16.9221	−0.601681
$792$	−5.41118	−0.192278
$793$	−28.7559	−1.02115
$794$	−0.296954	−0.0105385
$795$	106.373	3.77267
$796$	6.43694	0.228151
$797$	−8.93879	−0.316628	−0.158314	−	0.987389i	$-0.550606\pi$
$797$	−8.93879	−0.316628	−0.158314	+	0.987389i	$0.550606\pi$
$798$	−0.849901	−0.0300862
$799$	−22.0168	−0.778897
$800$	36.4122	1.28737
$801$	10.3858	0.366965
$802$	−8.16489	−0.288312
$803$	−0.522392	−0.0184348
$804$	17.9850	0.634284
$805$	−12.3655	−0.435827
$806$	−5.81809	−0.204933
$807$	8.57352	0.301802
$808$	−6.88262	−0.242130
$809$	21.6304	0.760484	0.380242	−	0.924887i	$-0.375841\pi$
$809$	21.6304	0.760484	0.380242	+	0.924887i	$0.375841\pi$
$810$	−10.6985	−0.375906
$811$	9.26525	0.325347	0.162673	−	0.986680i	$-0.447988\pi$
$811$	9.26525	0.325347	0.162673	+	0.986680i	$0.447988\pi$
$812$	14.4192	0.506014
$813$	1.10941	0.0389089
$814$	−0.812356	−0.0284731
$815$	86.6877	3.03654
$816$	−30.6575	−1.07323
$817$	−8.62844	−0.301871
$818$	4.15558	0.145296
$819$	−10.5388	−0.368256
$820$	65.9025	2.30141
$821$	15.2901	0.533629	0.266814	−	0.963748i	$-0.414029\pi$
$821$	15.2901	0.533629	0.266814	+	0.963748i	$0.414029\pi$
$822$	10.2115	0.356168
$823$	−7.39290	−0.257700	−0.128850	−	0.991664i	$-0.541129\pi$
$823$	−7.39290	−0.257700	−0.128850	+	0.991664i	$0.541129\pi$
$824$	6.60304	0.230028
$825$	129.501	4.50866
$826$	0.483708	0.0168304
$827$	41.5823	1.44596	0.722979	−	0.690870i	$-0.242772\pi$
$827$	41.5823	1.44596	0.722979	+	0.690870i	$0.242772\pi$
$828$	6.95018	0.241536
$829$	−47.1772	−1.63853	−0.819266	−	0.573414i	$-0.805619\pi$
$829$	−47.1772	−1.63853	−0.819266	+	0.573414i	$0.805619\pi$
$830$	−10.7151	−0.371926
$831$	−30.8148	−1.06895
$832$	40.0569	1.38872
$833$	21.5648	0.747178
$834$	−8.73905	−0.302608
$835$	0.708776	0.0245282
$836$	12.7097	0.439573
$837$	−14.6796	−0.507402
$838$	−1.38706	−0.0479151
$839$	−7.11770	−0.245730	−0.122865	−	0.992423i	$-0.539208\pi$
$839$	−7.11770	−0.245730	−0.122865	+	0.992423i	$0.539208\pi$
$840$	−9.55811	−0.329786
$841$	9.10840	0.314083
$842$	2.95053	0.101682
$843$	13.6916	0.471564
$844$	38.8136	1.33602
$845$	91.0605	3.13258
$846$	1.86028	0.0639579
$847$	7.78071	0.267348
$848$	42.1371	1.44699
$849$	45.8792	1.57457
$850$	−12.1178	−0.415636
$851$	2.11150	0.0723812
$852$	65.2833	2.23657
$853$	42.7540	1.46387	0.731934	−	0.681376i	$-0.238618\pi$
$853$	42.7540	1.46387	0.731934	+	0.681376i	$0.238618\pi$
$854$	1.27561	0.0436506
$855$	−10.4568	−0.357615
$856$	−3.10006	−0.105958
$857$	−13.8716	−0.473846	−0.236923	−	0.971528i	$-0.576139\pi$
$857$	−13.8716	−0.473846	−0.236923	+	0.971528i	$0.576139\pi$
$858$	−11.0892	−0.378577
$859$	50.7293	1.73086	0.865431	−	0.501028i	$-0.167045\pi$
$859$	50.7293	1.73086	0.865431	+	0.501028i	$0.167045\pi$
$860$	−47.9508	−1.63511
$861$	−19.3896	−0.660797
$862$	6.22074	0.211879
$863$	−39.3348	−1.33897	−0.669486	−	0.742825i	$-0.733486\pi$
$863$	−39.3348	−1.33897	−0.669486	+	0.742825i	$0.733486\pi$
$864$	−7.86694	−0.267639
$865$	−41.7926	−1.42099
$866$	−2.03233	−0.0690615
$867$	−4.28324	−0.145466
$868$	−10.9030	−0.370073
$869$	−3.64736	−0.123728
$870$	−12.4828	−0.423206
$871$	25.0924	0.850225
$872$	−6.73204	−0.227976
$873$	9.28060	0.314101
$874$	0.781996	0.0264514
$875$	50.5210	1.70792
$876$	0.518633	0.0175230
$877$	−52.1762	−1.76187	−0.880933	−	0.473241i	$-0.843084\pi$
$877$	−52.1762	−1.76187	−0.880933	+	0.473241i	$0.843084\pi$
$878$	−1.36614	−0.0461050
$879$	39.0400	1.31679
$880$	68.9199	2.32329
$881$	−7.18382	−0.242029	−0.121015	−	0.992651i	$-0.538615\pi$
$881$	−7.18382	−0.242029	−0.121015	+	0.992651i	$0.538615\pi$
$882$	−1.82210	−0.0613533
$883$	7.57528	0.254928	0.127464	−	0.991843i	$-0.459316\pi$
$883$	7.57528	0.254928	0.127464	+	0.991843i	$0.459316\pi$
$884$	−43.8350	−1.47433
$885$	17.6900	0.594644
$886$	−1.63033	−0.0547719
$887$	45.4538	1.52619	0.763094	−	0.646287i	$-0.223679\pi$
$887$	45.4538	1.52619	0.763094	+	0.646287i	$0.223679\pi$
$888$	1.63211	0.0547702
$889$	−12.5901	−0.422257
$890$	6.49402	0.217680
$891$	−47.0713	−1.57695
$892$	−7.77525	−0.260335
$893$	−8.84223	−0.295894
$894$	−10.0421	−0.335859
$895$	−82.8148	−2.76819
$896$	−7.75828	−0.259186
$897$	28.8232	0.962380
$898$	−3.34656	−0.111676
$899$	−28.8156	−0.961053
$900$	−43.2537	−1.44179
$901$	−43.7941	−1.45899
$902$	−6.86375	−0.228538
$903$	14.1079	0.469483
$904$	12.0351	0.400282
$905$	56.5378	1.87938
$906$	5.02630	0.166988
$907$	−30.1535	−1.00123	−0.500615	−	0.865670i	$-0.666893\pi$
$907$	−30.1535	−1.00123	−0.500615	+	0.865670i	$0.666893\pi$
$908$	−24.5875	−0.815965
$909$	12.3115	0.408347
$910$	−6.58967	−0.218445
$911$	−20.9887	−0.695386	−0.347693	−	0.937608i	$-0.613035\pi$
$911$	−20.9887	−0.695386	−0.347693	+	0.937608i	$0.613035\pi$
$912$	−12.3125	−0.407706
$913$	−47.1444	−1.56025
$914$	1.02182	0.0337987
$915$	46.6514	1.54225
$916$	−32.4637	−1.07263
$917$	−0.614982	−0.0203085
$918$	2.61807	0.0864093
$919$	−6.39734	−0.211029	−0.105514	−	0.994418i	$-0.533649\pi$
$919$	−6.39734	−0.211029	−0.105514	+	0.994418i	$0.533649\pi$
$920$	8.79444	0.289944
$921$	25.7980	0.850072
$922$	0.0514987	0.00169602
$923$	91.0822	2.99801
$924$	−20.7810	−0.683643
$925$	−13.1407	−0.432063
$926$	−1.32348	−0.0434923
$927$	−11.8114	−0.387937
$928$	−15.4425	−0.506925
$929$	40.3052	1.32237	0.661186	−	0.750222i	$-0.270053\pi$
$929$	40.3052	1.32237	0.661186	+	0.750222i	$0.270053\pi$
$930$	9.43883	0.309511
$931$	8.66073	0.283844
$932$	−11.3890	−0.373058
$933$	34.9472	1.14412
$934$	−6.68594	−0.218771
$935$	−71.6301	−2.34255
$936$	7.49527	0.244991
$937$	−43.4303	−1.41881	−0.709403	−	0.704803i	$-0.751035\pi$
$937$	−43.4303	−1.41881	−0.709403	+	0.704803i	$0.751035\pi$
$938$	−1.11311	−0.0363442
$939$	25.3195	0.826270
$940$	−49.1389	−1.60273
$941$	19.5693	0.637942	0.318971	−	0.947764i	$-0.396663\pi$
$941$	19.5693	0.637942	0.318971	+	0.947764i	$0.396663\pi$
$942$	−9.41828	−0.306864
$943$	17.8404	0.580965
$944$	7.00745	0.228073
$945$	−16.6264	−0.540857
$946$	4.99408	0.162372
$947$	−35.4428	−1.15174	−0.575868	−	0.817542i	$-0.695336\pi$
$947$	−35.4428	−1.15174	−0.575868	+	0.817542i	$0.695336\pi$
$948$	3.62112	0.117608
$949$	0.723589	0.0234887
$950$	−4.86667	−0.157895
$951$	19.3128	0.626261
$952$	3.93509	0.127537
$953$	−29.4095	−0.952667	−0.476334	−	0.879265i	$-0.658035\pi$
$953$	−29.4095	−0.952667	−0.476334	+	0.879265i	$0.658035\pi$
$954$	3.70034	0.119803
$955$	−22.9844	−0.743757
$956$	16.9542	0.548338
$957$	−54.9219	−1.77537
$958$	1.17724	0.0380348
$959$	26.6986	0.862144
$960$	−64.9854	−2.09739
$961$	−9.21119	−0.297135
$962$	1.12523	0.0362789
$963$	5.54533	0.178696
$964$	−16.6248	−0.535448
$965$	34.9365	1.12465
$966$	−1.27860	−0.0411384
$967$	−48.7776	−1.56858	−0.784290	−	0.620394i	$-0.786973\pi$
$967$	−48.7776	−1.56858	−0.784290	+	0.620394i	$0.786973\pi$
$968$	−5.53369	−0.177860
$969$	12.7966	0.411087
$970$	5.80294	0.186321
$971$	5.94040	0.190637	0.0953183	−	0.995447i	$-0.469613\pi$
$971$	5.94040	0.190637	0.0953183	+	0.995447i	$0.469613\pi$
$972$	28.2999	0.907720
$973$	−22.8488	−0.732498
$974$	0.0707446	0.00226680
$975$	−179.378	−5.74470
$976$	18.4797	0.591522
$977$	31.6729	1.01331	0.506653	−	0.862150i	$-0.330882\pi$
$977$	31.6729	1.01331	0.506653	+	0.862150i	$0.330882\pi$
$978$	8.96357	0.286623
$979$	28.5724	0.913178
$980$	48.1303	1.53747
$981$	12.0421	0.384476
$982$	3.02729	0.0966046
$983$	38.7362	1.23549	0.617747	−	0.786377i	$-0.288046\pi$
$983$	38.7362	1.23549	0.617747	+	0.786377i	$0.288046\pi$
$984$	13.7900	0.439610
$985$	91.3360	2.91021
$986$	5.13919	0.163665
$987$	14.4575	0.460187
$988$	−17.6047	−0.560082
$989$	−12.9807	−0.412764
$990$	6.05231	0.192355
$991$	50.8484	1.61525	0.807626	−	0.589695i	$-0.200752\pi$
$991$	50.8484	1.61525	0.807626	+	0.589695i	$0.200752\pi$
$992$	11.6768	0.370739
$993$	−20.0771	−0.637128
$994$	−4.04042	−0.128154
$995$	−14.5696	−0.461889
$996$	46.8051	1.48308
$997$	18.0615	0.572013	0.286006	−	0.958228i	$-0.407672\pi$
$997$	18.0615	0.572013	0.286006	+	0.958228i	$0.407672\pi$
$998$	−0.364176	−0.0115278
$999$	2.83907	0.0898243

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.c.1.13	✓	25
3.2	odd	2		4923.2.a.n.1.13		25
4.3	odd	2		8752.2.a.v.1.7		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.c.1.13	✓	25	1.1	even	1	trivial
4923.2.a.n.1.13		25	3.2	odd	2
8752.2.a.v.1.7		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)

\(f(q)\)	\(=\)	\(q+0.215054 q^{2} +2.12625 q^{3} -1.95375 q^{4} +4.42221 q^{5} +0.457259 q^{6} +1.19553 q^{7} -0.850270 q^{8} +1.52095 q^{9} +O(q^{10})\)	\(q+0.215054 q^{2} +2.12625 q^{3} -1.95375 q^{4} +4.42221 q^{5} +0.457259 q^{6} +1.19553 q^{7} -0.850270 q^{8} +1.52095 q^{9} +0.951013 q^{10} +4.18427 q^{11} -4.15417 q^{12} -5.79583 q^{13} +0.257104 q^{14} +9.40273 q^{15} +3.72465 q^{16} -3.87112 q^{17} +0.327086 q^{18} -1.55469 q^{19} -8.63989 q^{20} +2.54200 q^{21} +0.899845 q^{22} -2.33890 q^{23} -1.80789 q^{24} +14.5559 q^{25} -1.24642 q^{26} -3.14484 q^{27} -2.33577 q^{28} -6.17320 q^{29} +2.02209 q^{30} +4.66785 q^{31} +2.50154 q^{32} +8.89682 q^{33} -0.832499 q^{34} +5.28689 q^{35} -2.97156 q^{36} -0.902773 q^{37} -0.334343 q^{38} -12.3234 q^{39} -3.76007 q^{40} -7.62770 q^{41} +0.546668 q^{42} +5.54993 q^{43} -8.17503 q^{44} +6.72595 q^{45} -0.502991 q^{46} +5.68744 q^{47} +7.91954 q^{48} -5.57070 q^{49} +3.13031 q^{50} -8.23097 q^{51} +11.3236 q^{52} +11.3130 q^{53} -0.676310 q^{54} +18.5037 q^{55} -1.01653 q^{56} -3.30567 q^{57} -1.32757 q^{58} +1.88137 q^{59} -18.3706 q^{60} +4.96147 q^{61} +1.00384 q^{62} +1.81834 q^{63} -6.91133 q^{64} -25.6304 q^{65} +1.91330 q^{66} -4.32940 q^{67} +7.56320 q^{68} -4.97310 q^{69} +1.13697 q^{70} -15.7151 q^{71} -1.29322 q^{72} -0.124846 q^{73} -0.194145 q^{74} +30.9495 q^{75} +3.03748 q^{76} +5.00243 q^{77} -2.65020 q^{78} -0.871683 q^{79} +16.4712 q^{80} -11.2496 q^{81} -1.64037 q^{82} -11.2670 q^{83} -4.96644 q^{84} -17.1189 q^{85} +1.19354 q^{86} -13.1258 q^{87} -3.55777 q^{88} +6.82852 q^{89} +1.44644 q^{90} -6.92910 q^{91} +4.56964 q^{92} +9.92502 q^{93} +1.22311 q^{94} -6.87517 q^{95} +5.31891 q^{96} +6.10185 q^{97} -1.19800 q^{98} +6.36407 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9}+O(q^{10}) \) 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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