LMFDB - Embedded newform 6043.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6043,2,Mod(1,6043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6043, 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("6043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6043 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6043.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:	$48.2535979415$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53746 q^{2} -1.57895 q^{3} +4.43871 q^{4} +2.23521 q^{5} +4.00652 q^{6} -0.788927 q^{7} -6.18813 q^{8} -0.506916 q^{9} +O(q^{10})$	\(q-2.53746 q^{2} -1.57895 q^{3} +4.43871 q^{4} +2.23521 q^{5} +4.00652 q^{6} -0.788927 q^{7} -6.18813 q^{8} -0.506916 q^{9} -5.67175 q^{10} -5.34808 q^{11} -7.00850 q^{12} -2.32662 q^{13} +2.00187 q^{14} -3.52928 q^{15} +6.82472 q^{16} -3.78113 q^{17} +1.28628 q^{18} +7.07444 q^{19} +9.92144 q^{20} +1.24568 q^{21} +13.5705 q^{22} +8.95764 q^{23} +9.77075 q^{24} -0.00384486 q^{25} +5.90370 q^{26} +5.53725 q^{27} -3.50182 q^{28} +6.39022 q^{29} +8.95542 q^{30} -3.60543 q^{31} -4.94120 q^{32} +8.44435 q^{33} +9.59448 q^{34} -1.76341 q^{35} -2.25005 q^{36} -1.25892 q^{37} -17.9511 q^{38} +3.67361 q^{39} -13.8318 q^{40} -10.8599 q^{41} -3.16085 q^{42} -1.69486 q^{43} -23.7386 q^{44} -1.13306 q^{45} -22.7297 q^{46} +3.26357 q^{47} -10.7759 q^{48} -6.37759 q^{49} +0.00975619 q^{50} +5.97022 q^{51} -10.3272 q^{52} +13.1226 q^{53} -14.0505 q^{54} -11.9541 q^{55} +4.88198 q^{56} -11.1702 q^{57} -16.2149 q^{58} -9.97912 q^{59} -15.6655 q^{60} +6.70047 q^{61} +9.14865 q^{62} +0.399920 q^{63} -1.11134 q^{64} -5.20047 q^{65} -21.4272 q^{66} -8.53600 q^{67} -16.7834 q^{68} -14.1437 q^{69} +4.47460 q^{70} +2.38958 q^{71} +3.13686 q^{72} -2.37367 q^{73} +3.19445 q^{74} +0.00607085 q^{75} +31.4014 q^{76} +4.21924 q^{77} -9.32165 q^{78} +0.302465 q^{79} +15.2547 q^{80} -7.22229 q^{81} +27.5565 q^{82} -9.65922 q^{83} +5.52919 q^{84} -8.45162 q^{85} +4.30065 q^{86} -10.0898 q^{87} +33.0946 q^{88} +10.3801 q^{89} +2.87510 q^{90} +1.83553 q^{91} +39.7604 q^{92} +5.69280 q^{93} -8.28117 q^{94} +15.8128 q^{95} +7.80190 q^{96} -9.69612 q^{97} +16.1829 q^{98} +2.71103 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * 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 $

$2$	−2.53746	−1.79426	−0.897128	−	0.441771i	$-0.854350\pi$
$2$	−2.53746	−1.79426	−0.897128	+	0.441771i	$0.854350\pi$
$3$	−1.57895	−0.911607	−0.455804	−	0.890080i	$-0.650648\pi$
$3$	−1.57895	−0.911607	−0.455804	+	0.890080i	$0.650648\pi$
$4$	4.43871	2.21935
$5$	2.23521	0.999615	0.499808	−	0.866136i	$-0.333404\pi$
$5$	2.23521	0.999615	0.499808	+	0.866136i	$0.333404\pi$
$6$	4.00652	1.63566
$7$	−0.788927	−0.298186	−0.149093	−	0.988823i	$-0.547635\pi$
$7$	−0.788927	−0.298186	−0.149093	+	0.988823i	$0.547635\pi$
$8$	−6.18813	−2.18783
$9$	−0.506916	−0.168972
$10$	−5.67175	−1.79357
$11$	−5.34808	−1.61251	−0.806253	−	0.591571i	$-0.798508\pi$
$11$	−5.34808	−1.61251	−0.806253	+	0.591571i	$0.798508\pi$
$12$	−7.00850	−2.02318
$13$	−2.32662	−0.645288	−0.322644	−	0.946520i	$-0.604572\pi$
$13$	−2.32662	−0.645288	−0.322644	+	0.946520i	$0.604572\pi$
$14$	2.00187	0.535022
$15$	−3.52928	−0.911257
$16$	6.82472	1.70618
$17$	−3.78113	−0.917060	−0.458530	−	0.888679i	$-0.651624\pi$
$17$	−3.78113	−0.917060	−0.458530	+	0.888679i	$0.651624\pi$
$18$	1.28628	0.303179
$19$	7.07444	1.62299	0.811493	−	0.584362i	$-0.198655\pi$
$19$	7.07444	1.62299	0.811493	+	0.584362i	$0.198655\pi$
$20$	9.92144	2.21850
$21$	1.24568	0.271829
$22$	13.5705	2.89325
$23$	8.95764	1.86780	0.933899	−	0.357538i	$-0.116384\pi$
$23$	8.95764	1.86780	0.933899	+	0.357538i	$0.116384\pi$
$24$	9.77075	1.99445
$25$	−0.00384486	−0.000768972 0
$26$	5.90370	1.15781
$27$	5.53725	1.06564
$28$	−3.50182	−0.661781
$29$	6.39022	1.18663	0.593317	−	0.804969i	$-0.297818\pi$
$29$	6.39022	1.18663	0.593317	+	0.804969i	$0.297818\pi$
$30$	8.95542	1.63503
$31$	−3.60543	−0.647555	−0.323778	−	0.946133i	$-0.604953\pi$
$31$	−3.60543	−0.647555	−0.323778	+	0.946133i	$0.604953\pi$
$32$	−4.94120	−0.873488
$33$	8.44435	1.46997
$34$	9.59448	1.64544
$35$	−1.76341	−0.298072
$36$	−2.25005	−0.375009
$37$	−1.25892	−0.206964	−0.103482	−	0.994631i	$-0.532998\pi$
$37$	−1.25892	−0.206964	−0.103482	+	0.994631i	$0.532998\pi$
$38$	−17.9511	−2.91205
$39$	3.67361	0.588249
$40$	−13.8318	−2.18699
$41$	−10.8599	−1.69603	−0.848015	−	0.529973i	$-0.822202\pi$
$41$	−10.8599	−1.69603	−0.848015	+	0.529973i	$0.822202\pi$
$42$	−3.16085	−0.487730
$43$	−1.69486	−0.258464	−0.129232	−	0.991614i	$-0.541251\pi$
$43$	−1.69486	−0.258464	−0.129232	+	0.991614i	$0.541251\pi$
$44$	−23.7386	−3.57872
$45$	−1.13306	−0.168907
$46$	−22.7297	−3.35131
$47$	3.26357	0.476040	0.238020	−	0.971260i	$-0.423502\pi$
$47$	3.26357	0.476040	0.238020	+	0.971260i	$0.423502\pi$
$48$	−10.7759	−1.55537
$49$	−6.37759	−0.911085
$50$	0.00975619	0.00137973
$51$	5.97022	0.835998
$52$	−10.3272	−1.43212
$53$	13.1226	1.80252	0.901261	−	0.433277i	$-0.142643\pi$
$53$	13.1226	1.80252	0.901261	+	0.433277i	$0.142643\pi$
$54$	−14.0505	−1.91204
$55$	−11.9541	−1.61189
$56$	4.88198	0.652382
$57$	−11.1702	−1.47953
$58$	−16.2149	−2.12913
$59$	−9.97912	−1.29917	−0.649586	−	0.760288i	$-0.725058\pi$
$59$	−9.97912	−1.29917	−0.649586	+	0.760288i	$0.725058\pi$
$60$	−15.6655	−2.02240
$61$	6.70047	0.857907	0.428953	−	0.903327i	$-0.358882\pi$
$61$	6.70047	0.857907	0.428953	+	0.903327i	$0.358882\pi$
$62$	9.14865	1.16188
$63$	0.399920	0.0503851
$64$	−1.11134	−0.138918
$65$	−5.20047	−0.645039
$66$	−21.4272	−2.63751
$67$	−8.53600	−1.04284	−0.521419	−	0.853301i	$-0.674597\pi$
$67$	−8.53600	−1.04284	−0.521419	+	0.853301i	$0.674597\pi$
$68$	−16.7834	−2.03528
$69$	−14.1437	−1.70270
$70$	4.47460	0.534817
$71$	2.38958	0.283591	0.141795	−	0.989896i	$-0.454712\pi$
$71$	2.38958	0.283591	0.141795	+	0.989896i	$0.454712\pi$
$72$	3.13686	0.369683
$73$	−2.37367	−0.277817	−0.138909	−	0.990305i	$-0.544359\pi$
$73$	−2.37367	−0.277817	−0.138909	+	0.990305i	$0.544359\pi$
$74$	3.19445	0.371347
$75$	0.00607085	0.000701001 0
$76$	31.4014	3.60198
$77$	4.21924	0.480827
$78$	−9.32165	−1.05547
$79$	0.302465	0.0340299	0.0170150	−	0.999855i	$-0.494584\pi$
$79$	0.302465	0.0340299	0.0170150	+	0.999855i	$0.494584\pi$
$80$	15.2547	1.70552
$81$	−7.22229	−0.802476
$82$	27.5565	3.04311
$83$	−9.65922	−1.06024	−0.530119	−	0.847923i	$-0.677853\pi$
$83$	−9.65922	−1.06024	−0.530119	+	0.847923i	$0.677853\pi$
$84$	5.52919	0.603284
$85$	−8.45162	−0.916707
$86$	4.30065	0.463751
$87$	−10.0898	−1.08174
$88$	33.0946	3.52789
$89$	10.3801	1.10029	0.550144	−	0.835070i	$-0.314573\pi$
$89$	10.3801	1.10029	0.550144	+	0.835070i	$0.314573\pi$
$90$	2.87510	0.303063
$91$	1.83553	0.192416
$92$	39.7604	4.14530
$93$	5.69280	0.590316
$94$	−8.28117	−0.854138
$95$	15.8128	1.62236
$96$	7.80190	0.796278
$97$	−9.69612	−0.984491	−0.492246	−	0.870456i	$-0.663824\pi$
$97$	−9.69612	−0.984491	−0.492246	+	0.870456i	$0.663824\pi$
$98$	16.1829	1.63472
$99$	2.71103	0.272468
$100$	−0.0170662	−0.00170662
$101$	4.89143	0.486715	0.243358	−	0.969937i	$-0.421751\pi$
$101$	4.89143	0.486715	0.243358	+	0.969937i	$0.421751\pi$
$102$	−15.1492	−1.50000
$103$	−4.68979	−0.462098	−0.231049	−	0.972942i	$-0.574216\pi$
$103$	−4.68979	−0.462098	−0.231049	+	0.972942i	$0.574216\pi$
$104$	14.3974	1.41178
$105$	2.78434	0.271724
$106$	−33.2980	−3.23418
$107$	−5.68737	−0.549819	−0.274909	−	0.961470i	$-0.588648\pi$
$107$	−5.68737	−0.549819	−0.274909	+	0.961470i	$0.588648\pi$
$108$	24.5782	2.36504
$109$	−8.04321	−0.770399	−0.385200	−	0.922833i	$-0.625867\pi$
$109$	−8.04321	−0.770399	−0.385200	+	0.922833i	$0.625867\pi$
$110$	30.3330	2.89214
$111$	1.98776	0.188670
$112$	−5.38420	−0.508759
$113$	−12.4617	−1.17230	−0.586150	−	0.810203i	$-0.699357\pi$
$113$	−12.4617	−1.17230	−0.586150	+	0.810203i	$0.699357\pi$
$114$	28.3439	2.65465
$115$	20.0222	1.86708
$116$	28.3643	2.63356
$117$	1.17940	0.109036
$118$	25.3216	2.33105
$119$	2.98304	0.273455
$120$	21.8397	1.99368
$121$	17.6019	1.60017
$122$	−17.0022	−1.53930
$123$	17.1472	1.54611
$124$	−16.0035	−1.43715
$125$	−11.1846	−1.00038
$126$	−1.01478	−0.0904038
$127$	0.338139	0.0300050	0.0150025	−	0.999887i	$-0.495224\pi$
$127$	0.338139	0.0300050	0.0150025	+	0.999887i	$0.495224\pi$
$128$	12.7024	1.12274
$129$	2.67611	0.235618
$130$	13.1960	1.15737
$131$	−0.117639	−0.0102781	−0.00513907	−	0.999987i	$-0.501636\pi$
$131$	−0.117639	−0.0102781	−0.00513907	+	0.999987i	$0.501636\pi$
$132$	37.4820	3.26239
$133$	−5.58121	−0.483952
$134$	21.6598	1.87112
$135$	12.3769	1.06523
$136$	23.3981	2.00637
$137$	15.2905	1.30636	0.653178	−	0.757205i	$-0.273435\pi$
$137$	15.2905	1.30636	0.653178	+	0.757205i	$0.273435\pi$
$138$	35.8890	3.05508
$139$	−21.0933	−1.78911	−0.894557	−	0.446954i	$-0.852509\pi$
$139$	−21.0933	−1.78911	−0.894557	+	0.446954i	$0.852509\pi$
$140$	−7.82729	−0.661526
$141$	−5.15301	−0.433962
$142$	−6.06346	−0.508835
$143$	12.4429	1.04053
$144$	−3.45956	−0.288297
$145$	14.2835	1.18618
$146$	6.02310	0.498475
$147$	10.0699	0.830552
$148$	−5.58796	−0.459327
$149$	5.64294	0.462288	0.231144	−	0.972920i	$-0.425753\pi$
$149$	5.64294	0.462288	0.231144	+	0.972920i	$0.425753\pi$
$150$	−0.0154045	−0.00125777
$151$	−14.4621	−1.17691	−0.588455	−	0.808530i	$-0.700264\pi$
$151$	−14.4621	−1.17691	−0.588455	+	0.808530i	$0.700264\pi$
$152$	−43.7775	−3.55082
$153$	1.91672	0.154957
$154$	−10.7062	−0.862727
$155$	−8.05889	−0.647306
$156$	16.3061	1.30553
$157$	19.1098	1.52513	0.762566	−	0.646911i	$-0.223939\pi$
$157$	19.1098	1.52513	0.762566	+	0.646911i	$0.223939\pi$
$158$	−0.767492	−0.0610584
$159$	−20.7199	−1.64319
$160$	−11.0446	−0.873152
$161$	−7.06692	−0.556951
$162$	18.3263	1.43985
$163$	−12.2773	−0.961634	−0.480817	−	0.876821i	$-0.659660\pi$
$163$	−12.2773	−0.961634	−0.480817	+	0.876821i	$0.659660\pi$
$164$	−48.2039	−3.76409
$165$	18.8749	1.46941
$166$	24.5099	1.90234
$167$	22.9848	1.77862	0.889308	−	0.457308i	$-0.151186\pi$
$167$	22.9848	1.77862	0.889308	+	0.457308i	$0.151186\pi$
$168$	−7.70840	−0.594716
$169$	−7.58685	−0.583604
$170$	21.4457	1.64481
$171$	−3.58615	−0.274239
$172$	−7.52301	−0.573624
$173$	−5.45003	−0.414358	−0.207179	−	0.978303i	$-0.566428\pi$
$173$	−5.45003	−0.414358	−0.207179	+	0.978303i	$0.566428\pi$
$174$	25.6026	1.94093
$175$	0.00303331	0.000229297 0
$176$	−36.4991	−2.75122
$177$	15.7565	1.18433
$178$	−26.3391	−1.97420
$179$	−11.7584	−0.878864	−0.439432	−	0.898276i	$-0.644820\pi$
$179$	−11.7584	−0.878864	−0.439432	+	0.898276i	$0.644820\pi$
$180$	−5.02934	−0.374865
$181$	−17.4584	−1.29767	−0.648836	−	0.760928i	$-0.724744\pi$
$181$	−17.4584	−1.29767	−0.648836	+	0.760928i	$0.724744\pi$
$182$	−4.65759	−0.345243
$183$	−10.5797	−0.782074
$184$	−55.4310	−4.08643
$185$	−2.81394	−0.206885
$186$	−14.4453	−1.05918
$187$	20.2218	1.47876
$188$	14.4860	1.05650
$189$	−4.36848	−0.317760
$190$	−40.1245	−2.91093
$191$	−12.1252	−0.877346	−0.438673	−	0.898647i	$-0.644551\pi$
$191$	−12.1252	−0.877346	−0.438673	+	0.898647i	$0.644551\pi$
$192$	1.75475	0.126638
$193$	16.1808	1.16472	0.582358	−	0.812932i	$-0.302130\pi$
$193$	16.1808	1.16472	0.582358	+	0.812932i	$0.302130\pi$
$194$	24.6035	1.76643
$195$	8.21129	0.588023
$196$	−28.3083	−2.02202
$197$	−0.364689	−0.0259830	−0.0129915	−	0.999916i	$-0.504135\pi$
$197$	−0.364689	−0.0259830	−0.0129915	+	0.999916i	$0.504135\pi$
$198$	−6.87912	−0.488878
$199$	−16.8508	−1.19452	−0.597262	−	0.802046i	$-0.703745\pi$
$199$	−16.8508	−1.19452	−0.597262	+	0.802046i	$0.703745\pi$
$200$	0.0237925	0.00168238
$201$	13.4779	0.950659
$202$	−12.4118	−0.873292
$203$	−5.04142	−0.353838
$204$	26.5001	1.85538
$205$	−24.2741	−1.69538
$206$	11.9002	0.829123
$207$	−4.54077	−0.315606
$208$	−15.8785	−1.10098
$209$	−37.8346	−2.61708
$210$	−7.06517	−0.487543
$211$	22.7888	1.56885	0.784424	−	0.620225i	$-0.212959\pi$
$211$	22.7888	1.56885	0.784424	+	0.620225i	$0.212959\pi$
$212$	58.2472	4.00043
$213$	−3.77303	−0.258523
$214$	14.4315	0.986516
$215$	−3.78837	−0.258365
$216$	−34.2652	−2.33145
$217$	2.84442	0.193092
$218$	20.4093	1.38229
$219$	3.74791	0.253260
$220$	−53.0606	−3.57734
$221$	8.79725	0.591767
$222$	−5.04387	−0.338523
$223$	11.4793	0.768711	0.384355	−	0.923185i	$-0.374424\pi$
$223$	11.4793	0.768711	0.384355	+	0.923185i	$0.374424\pi$
$224$	3.89824	0.260462
$225$	0.00194902	0.000129935 0
$226$	31.6211	2.10340
$227$	16.0242	1.06356	0.531781	−	0.846882i	$-0.321523\pi$
$227$	16.0242	1.06356	0.531781	+	0.846882i	$0.321523\pi$
$228$	−49.5812	−3.28359
$229$	24.3239	1.60737	0.803684	−	0.595056i	$-0.202870\pi$
$229$	24.3239	1.60737	0.803684	+	0.595056i	$0.202870\pi$
$230$	−50.8055	−3.35002
$231$	−6.66197	−0.438325
$232$	−39.5435	−2.59616
$233$	16.0883	1.05398	0.526988	−	0.849872i	$-0.323321\pi$
$233$	16.0883	1.05398	0.526988	+	0.849872i	$0.323321\pi$
$234$	−2.99268	−0.195638
$235$	7.29475	0.475857
$236$	−44.2944	−2.88332
$237$	−0.477576	−0.0310219
$238$	−7.56934	−0.490647
$239$	1.93522	0.125179	0.0625896	−	0.998039i	$-0.480064\pi$
$239$	1.93522	0.125179	0.0625896	+	0.998039i	$0.480064\pi$
$240$	−24.0864	−1.55477
$241$	13.1421	0.846558	0.423279	−	0.905999i	$-0.360879\pi$
$241$	13.1421	0.846558	0.423279	+	0.905999i	$0.360879\pi$
$242$	−44.6642	−2.87112
$243$	−5.20811	−0.334100
$244$	29.7414	1.90400
$245$	−14.2553	−0.910735
$246$	−43.5104	−2.77412
$247$	−16.4595	−1.04729
$248$	22.3109	1.41674
$249$	15.2514	0.966520
$250$	28.3806	1.79495
$251$	−22.8510	−1.44235	−0.721173	−	0.692755i	$-0.756397\pi$
$251$	−22.8510	−1.44235	−0.721173	+	0.692755i	$0.756397\pi$
$252$	1.77513	0.111822
$253$	−47.9061	−3.01183
$254$	−0.858014	−0.0538366
$255$	13.3447	0.835677
$256$	−30.0091	−1.87557
$257$	23.9867	1.49625	0.748126	−	0.663557i	$-0.230954\pi$
$257$	23.9867	1.49625	0.748126	+	0.663557i	$0.230954\pi$
$258$	−6.79052	−0.422759
$259$	0.993191	0.0617139
$260$	−23.0834	−1.43157
$261$	−3.23931	−0.200508
$262$	0.298504	0.0184416
$263$	−10.2169	−0.630004	−0.315002	−	0.949091i	$-0.602005\pi$
$263$	−10.2169	−0.630004	−0.315002	+	0.949091i	$0.602005\pi$
$264$	−52.2547	−3.21605
$265$	29.3316	1.80183
$266$	14.1621	0.868334
$267$	−16.3897	−1.00303
$268$	−37.8888	−2.31443
$269$	−16.7129	−1.01900	−0.509502	−	0.860469i	$-0.670170\pi$
$269$	−16.7129	−1.01900	−0.509502	+	0.860469i	$0.670170\pi$
$270$	−31.4059	−1.91130
$271$	18.6924	1.13548	0.567741	−	0.823207i	$-0.307817\pi$
$271$	18.6924	1.13548	0.567741	+	0.823207i	$0.307817\pi$
$272$	−25.8052	−1.56467
$273$	−2.89821	−0.175408
$274$	−38.7990	−2.34394
$275$	0.0205626	0.00123997
$276$	−62.7796	−3.77889
$277$	−6.57818	−0.395244	−0.197622	−	0.980278i	$-0.563322\pi$
$277$	−6.57818	−0.395244	−0.197622	+	0.980278i	$0.563322\pi$
$278$	53.5235	3.21013
$279$	1.82765	0.109419
$280$	10.9122	0.652131
$281$	29.7031	1.77194	0.885970	−	0.463742i	$-0.153493\pi$
$281$	29.7031	1.77194	0.885970	+	0.463742i	$0.153493\pi$
$282$	13.0756	0.778638
$283$	9.09111	0.540410	0.270205	−	0.962803i	$-0.412908\pi$
$283$	9.09111	0.540410	0.270205	+	0.962803i	$0.412908\pi$
$284$	10.6066	0.629389
$285$	−24.9677	−1.47896
$286$	−31.5734	−1.86698
$287$	8.56765	0.505732
$288$	2.50477	0.147595
$289$	−2.70302	−0.159001
$290$	−36.2438	−2.12831
$291$	15.3097	0.897470
$292$	−10.5360	−0.616575
$293$	34.1956	1.99773	0.998866	−	0.0476204i	$-0.0151638\pi$
$293$	34.1956	1.99773	0.998866	+	0.0476204i	$0.0151638\pi$
$294$	−25.5520	−1.49022
$295$	−22.3054	−1.29867
$296$	7.79033	0.452804
$297$	−29.6136	−1.71836
$298$	−14.3187	−0.829463
$299$	−20.8410	−1.20527
$300$	0.0269467	0.00155577
$301$	1.33712	0.0770705
$302$	36.6971	2.11168
$303$	−7.72332	−0.443693
$304$	48.2810	2.76911
$305$	14.9769	0.857577
$306$	−4.86360	−0.278033
$307$	−11.3498	−0.647766	−0.323883	−	0.946097i	$-0.604988\pi$
$307$	−11.3498	−0.647766	−0.323883	+	0.946097i	$0.604988\pi$
$308$	18.7280	1.06713
$309$	7.40494	0.421252
$310$	20.4491	1.16143
$311$	21.4645	1.21714	0.608569	−	0.793501i	$-0.291744\pi$
$311$	21.4645	1.21714	0.608569	+	0.793501i	$0.291744\pi$
$312$	−22.7328	−1.28699
$313$	11.8317	0.668768	0.334384	−	0.942437i	$-0.391472\pi$
$313$	11.8317	0.668768	0.334384	+	0.942437i	$0.391472\pi$
$314$	−48.4905	−2.73648
$315$	0.893904	0.0503658
$316$	1.34255	0.0755244
$317$	−19.8005	−1.11210	−0.556052	−	0.831147i	$-0.687685\pi$
$317$	−19.8005	−1.11210	−0.556052	+	0.831147i	$0.687685\pi$
$318$	52.5758	2.94831
$319$	−34.1754	−1.91345
$320$	−2.48408	−0.138864
$321$	8.98008	0.501219
$322$	17.9320	0.999313
$323$	−26.7494	−1.48838
$324$	−32.0576	−1.78098
$325$	0.00894552	0.000496208 0
$326$	31.1532	1.72542
$327$	12.6998	0.702302
$328$	67.2024	3.71063
$329$	−2.57471	−0.141949
$330$	−47.8942	−2.63649
$331$	31.3876	1.72522	0.862610	−	0.505870i	$-0.168828\pi$
$331$	31.3876	1.72522	0.862610	+	0.505870i	$0.168828\pi$
$332$	−42.8745	−2.35304
$333$	0.638164	0.0349712
$334$	−58.3230	−3.19129
$335$	−19.0797	−1.04244
$336$	8.50138	0.463789
$337$	16.7559	0.912754	0.456377	−	0.889786i	$-0.349147\pi$
$337$	16.7559	0.912754	0.456377	+	0.889786i	$0.349147\pi$
$338$	19.2513	1.04713
$339$	19.6764	1.06868
$340$	−37.5143	−2.03450
$341$	19.2821	1.04419
$342$	9.09970	0.492056
$343$	10.5539	0.569859
$344$	10.4880	0.565477
$345$	−31.6140	−1.70204
$346$	13.8292	0.743465
$347$	18.8574	1.01232	0.506159	−	0.862440i	$-0.331065\pi$
$347$	18.8574	1.01232	0.506159	+	0.862440i	$0.331065\pi$
$348$	−44.7859	−2.40077
$349$	22.5723	1.20827	0.604134	−	0.796882i	$-0.293519\pi$
$349$	22.5723	1.20827	0.604134	+	0.796882i	$0.293519\pi$
$350$	−0.00769691	−0.000411417 0
$351$	−12.8831	−0.687646
$352$	26.4259	1.40850
$353$	31.9766	1.70194	0.850972	−	0.525211i	$-0.176014\pi$
$353$	31.9766	1.70194	0.850972	+	0.525211i	$0.176014\pi$
$354$	−39.9816	−2.12500
$355$	5.34121	0.283482
$356$	46.0743	2.44193
$357$	−4.71007	−0.249283
$358$	29.8365	1.57691
$359$	17.9604	0.947911	0.473956	−	0.880549i	$-0.342826\pi$
$359$	17.9604	0.947911	0.473956	+	0.880549i	$0.342826\pi$
$360$	7.01154	0.369541
$361$	31.0476	1.63409
$362$	44.3000	2.32836
$363$	−27.7926	−1.45873
$364$	8.14738	0.427039
$365$	−5.30565	−0.277710
$366$	26.8456	1.40324
$367$	19.3359	1.00933	0.504663	−	0.863316i	$-0.331617\pi$
$367$	19.3359	1.00933	0.504663	+	0.863316i	$0.331617\pi$
$368$	61.1334	3.18680
$369$	5.50505	0.286582
$370$	7.14026	0.371204
$371$	−10.3527	−0.537487
$372$	25.2687	1.31012
$373$	1.30329	0.0674820	0.0337410	−	0.999431i	$-0.489258\pi$
$373$	1.30329	0.0674820	0.0337410	+	0.999431i	$0.489258\pi$
$374$	−51.3120	−2.65328
$375$	17.6600	0.911958
$376$	−20.1954	−1.04150
$377$	−14.8676	−0.765720
$378$	11.0848	0.570143
$379$	4.48877	0.230572	0.115286	−	0.993332i	$-0.463221\pi$
$379$	4.48877	0.230572	0.115286	+	0.993332i	$0.463221\pi$
$380$	70.1886	3.60060
$381$	−0.533904	−0.0273527
$382$	30.7671	1.57418
$383$	14.7134	0.751818	0.375909	−	0.926657i	$-0.377331\pi$
$383$	14.7134	0.751818	0.375909	+	0.926657i	$0.377331\pi$
$384$	−20.0564	−1.02350
$385$	9.43088	0.480642
$386$	−41.0580	−2.08980
$387$	0.859154	0.0436733
$388$	−43.0382	−2.18494
$389$	−34.4497	−1.74667	−0.873335	−	0.487120i	$-0.838047\pi$
$389$	−34.4497	−1.74667	−0.873335	+	0.487120i	$0.838047\pi$
$390$	−20.8358	−1.05506
$391$	−33.8700	−1.71288
$392$	39.4654	1.99330
$393$	0.185746	0.00936963
$394$	0.925385	0.0466202
$395$	0.676071	0.0340168
$396$	12.0335	0.604704
$397$	−29.8823	−1.49975	−0.749875	−	0.661580i	$-0.769886\pi$
$397$	−29.8823	−1.49975	−0.749875	+	0.661580i	$0.769886\pi$
$398$	42.7583	2.14328
$399$	8.81245	0.441174
$400$	−0.0262401	−0.00131200
$401$	−2.14870	−0.107301	−0.0536506	−	0.998560i	$-0.517086\pi$
$401$	−2.14870	−0.107301	−0.0536506	+	0.998560i	$0.517086\pi$
$402$	−34.1997	−1.70573
$403$	8.38846	0.417859
$404$	21.7116	1.08019
$405$	−16.1433	−0.802168
$406$	12.7924	0.634876
$407$	6.73277	0.333731
$408$	−36.9445	−1.82903
$409$	−28.2418	−1.39647	−0.698233	−	0.715871i	$-0.746030\pi$
$409$	−28.2418	−1.39647	−0.698233	+	0.715871i	$0.746030\pi$
$410$	61.5946	3.04194
$411$	−24.1429	−1.19088
$412$	−20.8166	−1.02556
$413$	7.87279	0.387395
$414$	11.5220	0.566277
$415$	−21.5904	−1.05983
$416$	11.4963	0.563651
$417$	33.3053	1.63097
$418$	96.0039	4.69570
$419$	−30.5469	−1.49232	−0.746158	−	0.665769i	$-0.768104\pi$
$419$	−30.5469	−1.49232	−0.746158	+	0.665769i	$0.768104\pi$
$420$	12.3589	0.603052
$421$	−12.1455	−0.591934	−0.295967	−	0.955198i	$-0.595642\pi$
$421$	−12.1455	−0.591934	−0.295967	+	0.955198i	$0.595642\pi$
$422$	−57.8258	−2.81491
$423$	−1.65435	−0.0804375
$424$	−81.2040	−3.94362
$425$	0.0145379	0.000705194 0
$426$	9.57391	0.463857
$427$	−5.28618	−0.255816
$428$	−25.2446	−1.22024
$429$	−19.6468	−0.948555
$430$	9.61285	0.463573
$431$	32.2801	1.55488	0.777438	−	0.628959i	$-0.216519\pi$
$431$	32.2801	1.55488	0.777438	+	0.628959i	$0.216519\pi$
$432$	37.7901	1.81818
$433$	−22.1948	−1.06662	−0.533308	−	0.845921i	$-0.679051\pi$
$433$	−22.1948	−1.06662	−0.533308	+	0.845921i	$0.679051\pi$
$434$	−7.21761	−0.346456
$435$	−22.5529	−1.08133
$436$	−35.7014	−1.70979
$437$	63.3703	3.03141
$438$	−9.51017	−0.454414
$439$	−3.52700	−0.168334	−0.0841672	−	0.996452i	$-0.526823\pi$
$439$	−3.52700	−0.168334	−0.0841672	+	0.996452i	$0.526823\pi$
$440$	73.9733	3.52654
$441$	3.23291	0.153948
$442$	−22.3227	−1.06178
$443$	−14.3772	−0.683083	−0.341542	−	0.939867i	$-0.610949\pi$
$443$	−14.3772	−0.683083	−0.341542	+	0.939867i	$0.610949\pi$
$444$	8.82311	0.418726
$445$	23.2017	1.09987
$446$	−29.1283	−1.37926
$447$	−8.90992	−0.421425
$448$	0.876766	0.0414233
$449$	−9.68490	−0.457059	−0.228529	−	0.973537i	$-0.573392\pi$
$449$	−9.68490	−0.457059	−0.228529	+	0.973537i	$0.573392\pi$
$450$	−0.00494557	−0.000233136 0
$451$	58.0795	2.73486
$452$	−55.3139	−2.60175
$453$	22.8350	1.07288
$454$	−40.6607	−1.90830
$455$	4.10279	0.192342
$456$	69.1225	3.23696
$457$	23.2534	1.08775	0.543875	−	0.839166i	$-0.316957\pi$
$457$	23.2534	1.08775	0.543875	+	0.839166i	$0.316957\pi$
$458$	−61.7210	−2.88403
$459$	−20.9371	−0.977259
$460$	88.8727	4.14371
$461$	−9.78599	−0.455779	−0.227889	−	0.973687i	$-0.573182\pi$
$461$	−9.78599	−0.455779	−0.227889	+	0.973687i	$0.573182\pi$
$462$	16.9045	0.786468
$463$	−20.0515	−0.931873	−0.465936	−	0.884818i	$-0.654282\pi$
$463$	−20.0515	−0.931873	−0.465936	+	0.884818i	$0.654282\pi$
$464$	43.6115	2.02461
$465$	12.7246	0.590089
$466$	−40.8233	−1.89110
$467$	16.0914	0.744621	0.372310	−	0.928108i	$-0.378566\pi$
$467$	16.0914	0.744621	0.372310	+	0.928108i	$0.378566\pi$
$468$	5.23501	0.241989
$469$	6.73428	0.310960
$470$	−18.5101	−0.853809
$471$	−30.1735	−1.39032
$472$	61.7521	2.84237
$473$	9.06426	0.416775
$474$	1.21183	0.0556613
$475$	−0.0272002	−0.00124803
$476$	13.2408	0.606893
$477$	−6.65203	−0.304576
$478$	−4.91056	−0.224604
$479$	−15.0267	−0.686588	−0.343294	−	0.939228i	$-0.611543\pi$
$479$	−15.0267	−0.686588	−0.343294	+	0.939228i	$0.611543\pi$
$480$	17.4389	0.795972
$481$	2.92901	0.133552
$482$	−33.3476	−1.51894
$483$	11.1583	0.507721
$484$	78.1298	3.55135
$485$	−21.6728	−0.984113
$486$	13.2154	0.599461
$487$	−9.02486	−0.408955	−0.204478	−	0.978871i	$-0.565550\pi$
$487$	−9.02486	−0.408955	−0.204478	+	0.978871i	$0.565550\pi$
$488$	−41.4633	−1.87696
$489$	19.3853	0.876633
$490$	36.1721	1.63409
$491$	−21.1948	−0.956509	−0.478254	−	0.878221i	$-0.658730\pi$
$491$	−21.1948	−0.956509	−0.478254	+	0.878221i	$0.658730\pi$
$492$	76.1115	3.43137
$493$	−24.1623	−1.08821
$494$	41.7653	1.87911
$495$	6.05971	0.272364
$496$	−24.6061	−1.10484
$497$	−1.88520	−0.0845629
$498$	−38.6999	−1.73418
$499$	18.3612	0.821962	0.410981	−	0.911644i	$-0.365186\pi$
$499$	18.3612	0.821962	0.410981	+	0.911644i	$0.365186\pi$
$500$	−49.6453	−2.22021
$501$	−36.2918	−1.62140
$502$	57.9836	2.58794
$503$	27.0627	1.20667	0.603334	−	0.797489i	$-0.293839\pi$
$503$	27.0627	1.20667	0.603334	+	0.797489i	$0.293839\pi$
$504$	−2.47475	−0.110234
$505$	10.9334	0.486528
$506$	121.560	5.40400
$507$	11.9793	0.532018
$508$	1.50090	0.0665916
$509$	34.4700	1.52786	0.763929	−	0.645301i	$-0.223268\pi$
$509$	34.4700	1.52786	0.763929	+	0.645301i	$0.223268\pi$
$510$	−33.8616	−1.49942
$511$	1.87265	0.0828413
$512$	50.7422	2.24251
$513$	39.1729	1.72953
$514$	−60.8654	−2.68466
$515$	−10.4826	−0.461921
$516$	11.8785	0.522920
$517$	−17.4538	−0.767617
$518$	−2.52018	−0.110731
$519$	8.60533	0.377732
$520$	32.1812	1.41124
$521$	−3.73914	−0.163815	−0.0819074	−	0.996640i	$-0.526101\pi$
$521$	−3.73914	−0.163815	−0.0819074	+	0.996640i	$0.526101\pi$
$522$	8.21961	0.359763
$523$	6.62076	0.289506	0.144753	−	0.989468i	$-0.453761\pi$
$523$	6.62076	0.289506	0.144753	+	0.989468i	$0.453761\pi$
$524$	−0.522164	−0.0228108
$525$	−0.00478945	−0.000209029 0
$526$	25.9251	1.13039
$527$	13.6326	0.593847
$528$	57.6303	2.50804
$529$	57.2393	2.48867
$530$	−74.4279	−3.23294
$531$	5.05858	0.219524
$532$	−24.7734	−1.07406
$533$	25.2668	1.09443
$534$	41.5881	1.79969
$535$	−12.7125	−0.549608
$536$	52.8218	2.28156
$537$	18.5659	0.801179
$538$	42.4084	1.82836
$539$	34.1079	1.46913
$540$	54.9374	2.36413
$541$	−27.8705	−1.19825	−0.599123	−	0.800657i	$-0.704484\pi$
$541$	−27.8705	−1.19825	−0.599123	+	0.800657i	$0.704484\pi$
$542$	−47.4312	−2.03735
$543$	27.5659	1.18297
$544$	18.6833	0.801041
$545$	−17.9782	−0.770103
$546$	7.35410	0.314726
$547$	−26.5150	−1.13370	−0.566849	−	0.823822i	$-0.691838\pi$
$547$	−26.5150	−1.13370	−0.566849	+	0.823822i	$0.691838\pi$
$548$	67.8701	2.89927
$549$	−3.39658	−0.144962
$550$	−0.0521768	−0.00222483
$551$	45.2072	1.92589
$552$	87.5228	3.72522
$553$	−0.238622	−0.0101473
$554$	16.6919	0.709169
$555$	4.44307	0.188598
$556$	−93.6272	−3.97068
$557$	29.7473	1.26043	0.630217	−	0.776419i	$-0.282966\pi$
$557$	29.7473	1.26043	0.630217	+	0.776419i	$0.282966\pi$
$558$	−4.63760	−0.196325
$559$	3.94330	0.166784
$560$	−12.0348	−0.508563
$561$	−31.9292	−1.34805
$562$	−75.3706	−3.17932
$563$	16.9660	0.715031	0.357516	−	0.933907i	$-0.383624\pi$
$563$	16.9660	0.715031	0.357516	+	0.933907i	$0.383624\pi$
$564$	−22.8727	−0.963115
$565$	−27.8545	−1.17185
$566$	−23.0683	−0.969634
$567$	5.69785	0.239287
$568$	−14.7870	−0.620450
$569$	3.92069	0.164364	0.0821820	−	0.996617i	$-0.473811\pi$
$569$	3.92069	0.164364	0.0821820	+	0.996617i	$0.473811\pi$
$570$	63.3545	2.65363
$571$	−21.3202	−0.892224	−0.446112	−	0.894977i	$-0.647192\pi$
$571$	−21.3202	−0.892224	−0.446112	+	0.894977i	$0.647192\pi$
$572$	55.2305	2.30930
$573$	19.1450	0.799795
$574$	−21.7401	−0.907413
$575$	−0.0344409	−0.00143628
$576$	0.563356	0.0234732
$577$	−0.578581	−0.0240866	−0.0120433	−	0.999927i	$-0.503834\pi$
$577$	−0.578581	−0.0240866	−0.0120433	+	0.999927i	$0.503834\pi$
$578$	6.85882	0.285289
$579$	−25.5486	−1.06176
$580$	63.4002	2.63255
$581$	7.62042	0.316148
$582$	−38.8477	−1.61029
$583$	−70.1804	−2.90658
$584$	14.6886	0.607818
$585$	2.63620	0.108994
$586$	−86.7701	−3.58444
$587$	30.5422	1.26061	0.630306	−	0.776347i	$-0.282929\pi$
$587$	30.5422	1.26061	0.630306	+	0.776347i	$0.282929\pi$
$588$	44.6974	1.84329
$589$	−25.5064	−1.05097
$590$	56.5991	2.33015
$591$	0.575826	0.0236863
$592$	−8.59174	−0.353118
$593$	−0.265965	−0.0109219	−0.00546094	−	0.999985i	$-0.501738\pi$
$593$	−0.265965	−0.0109219	−0.00546094	+	0.999985i	$0.501738\pi$
$594$	75.1434	3.08317
$595$	6.66771	0.273349
$596$	25.0474	1.02598
$597$	26.6066	1.08894
$598$	52.8832	2.16256
$599$	−29.6788	−1.21264	−0.606321	−	0.795220i	$-0.707356\pi$
$599$	−29.6788	−1.21264	−0.606321	+	0.795220i	$0.707356\pi$
$600$	−0.0375672	−0.00153367
$601$	24.3044	0.991397	0.495698	−	0.868495i	$-0.334912\pi$
$601$	24.3044	0.991397	0.495698	+	0.868495i	$0.334912\pi$
$602$	−3.39290	−0.138284
$603$	4.32704	0.176211
$604$	−64.1931	−2.61198
$605$	39.3439	1.59956
$606$	19.5976	0.796099
$607$	−39.7532	−1.61353	−0.806767	−	0.590870i	$-0.798785\pi$
$607$	−39.7532	−1.61353	−0.806767	+	0.590870i	$0.798785\pi$
$608$	−34.9562	−1.41766
$609$	7.96014	0.322561
$610$	−38.0034	−1.53871
$611$	−7.59307	−0.307183
$612$	8.50775	0.343906
$613$	−21.1643	−0.854818	−0.427409	−	0.904058i	$-0.640574\pi$
$613$	−21.1643	−0.854818	−0.427409	+	0.904058i	$0.640574\pi$
$614$	28.7996	1.16226
$615$	38.3276	1.54552
$616$	−26.1092	−1.05197
$617$	25.2940	1.01830	0.509149	−	0.860678i	$-0.329960\pi$
$617$	25.2940	1.01830	0.509149	+	0.860678i	$0.329960\pi$
$618$	−18.7897	−0.755834
$619$	17.5045	0.703566	0.351783	−	0.936081i	$-0.385575\pi$
$619$	17.5045	0.703566	0.351783	+	0.936081i	$0.385575\pi$
$620$	−35.7711	−1.43660
$621$	49.6007	1.99041
$622$	−54.4652	−2.18386
$623$	−8.18914	−0.328091
$624$	25.0714	1.00366
$625$	−24.9808	−0.999230
$626$	−30.0225	−1.19994
$627$	59.7390	2.38574
$628$	84.8230	3.38481
$629$	4.76013	0.189799
$630$	−2.26825	−0.0903691
$631$	23.0823	0.918891	0.459446	−	0.888206i	$-0.348048\pi$
$631$	23.0823	0.918891	0.459446	+	0.888206i	$0.348048\pi$
$632$	−1.87169	−0.0744518
$633$	−35.9824	−1.43017
$634$	50.2429	1.99540
$635$	0.755810	0.0299934
$636$	−91.9694	−3.64682
$637$	14.8382	0.587912
$638$	86.7187	3.43323
$639$	−1.21132	−0.0479189
$640$	28.3924	1.12231
$641$	−22.3062	−0.881041	−0.440521	−	0.897742i	$-0.645206\pi$
$641$	−22.3062	−0.881041	−0.440521	+	0.897742i	$0.645206\pi$
$642$	−22.7866	−0.899315
$643$	−10.6428	−0.419712	−0.209856	−	0.977732i	$-0.567300\pi$
$643$	−10.6428	−0.419712	−0.209856	+	0.977732i	$0.567300\pi$
$644$	−31.3680	−1.23607
$645$	5.98165	0.235527
$646$	67.8755	2.67053
$647$	−47.4630	−1.86596	−0.932982	−	0.359922i	$-0.882803\pi$
$647$	−47.4630	−1.86596	−0.932982	+	0.359922i	$0.882803\pi$
$648$	44.6924	1.75568
$649$	53.3691	2.09492
$650$	−0.0226989	−0.000890325 0
$651$	−4.49120	−0.176024
$652$	−54.4955	−2.13421
$653$	−11.0756	−0.433420	−0.216710	−	0.976236i	$-0.569533\pi$
$653$	−11.0756	−0.433420	−0.216710	+	0.976236i	$0.569533\pi$
$654$	−32.2253	−1.26011
$655$	−0.262947	−0.0102742
$656$	−74.1156	−2.89373
$657$	1.20325	0.0469433
$658$	6.53324	0.254692
$659$	42.8000	1.66725	0.833626	−	0.552329i	$-0.186261\pi$
$659$	42.8000	1.66725	0.833626	+	0.552329i	$0.186261\pi$
$660$	83.7800	3.26113
$661$	28.5105	1.10893	0.554465	−	0.832207i	$-0.312923\pi$
$661$	28.5105	1.10893	0.554465	+	0.832207i	$0.312923\pi$
$662$	−79.6449	−3.09549
$663$	−13.8904	−0.539459
$664$	59.7725	2.31962
$665$	−12.4752	−0.483766
$666$	−1.61932	−0.0627473
$667$	57.2413	2.21639
$668$	102.023	3.94738
$669$	−18.1252	−0.700762
$670$	48.4141	1.87040
$671$	−35.8346	−1.38338
$672$	−6.15513	−0.237439
$673$	4.31842	0.166463	0.0832314	−	0.996530i	$-0.473476\pi$
$673$	4.31842	0.166463	0.0832314	+	0.996530i	$0.473476\pi$
$674$	−42.5176	−1.63772
$675$	−0.0212899	−0.000819450 0
$676$	−33.6758	−1.29522
$677$	25.9562	0.997578	0.498789	−	0.866724i	$-0.333778\pi$
$677$	25.9562	0.997578	0.498789	+	0.866724i	$0.333778\pi$
$678$	−49.9282	−1.91748
$679$	7.64952	0.293562
$680$	52.2997	2.00560
$681$	−25.3014	−0.969551
$682$	−48.9277	−1.87354
$683$	−7.19708	−0.275388	−0.137694	−	0.990475i	$-0.543969\pi$
$683$	−7.19708	−0.275388	−0.137694	+	0.990475i	$0.543969\pi$
$684$	−15.9179	−0.608634
$685$	34.1774	1.30585
$686$	−26.7802	−1.02247
$687$	−38.4062	−1.46529
$688$	−11.5670	−0.440987
$689$	−30.5312	−1.16314
$690$	80.2194	3.05390
$691$	9.94015	0.378141	0.189071	−	0.981964i	$-0.439453\pi$
$691$	9.94015	0.378141	0.189071	+	0.981964i	$0.439453\pi$
$692$	−24.1911	−0.919608
$693$	−2.13880	−0.0812463
$694$	−47.8499	−1.81636
$695$	−47.1480	−1.78843
$696$	62.4372	2.36668
$697$	41.0627	1.55536
$698$	−57.2764	−2.16794
$699$	−25.4026	−0.960813
$700$	0.0134640	0.000508891 0
$701$	8.21199	0.310163	0.155081	−	0.987902i	$-0.450436\pi$
$701$	8.21199	0.310163	0.155081	+	0.987902i	$0.450436\pi$
$702$	32.6902	1.23381
$703$	−8.90611	−0.335900
$704$	5.94353	0.224005
$705$	−11.5180	−0.433795
$706$	−81.1394	−3.05372
$707$	−3.85898	−0.145132
$708$	69.9387	2.62846
$709$	36.4102	1.36741	0.683706	−	0.729757i	$-0.260367\pi$
$709$	36.4102	1.36741	0.683706	+	0.729757i	$0.260367\pi$
$710$	−13.5531	−0.508639
$711$	−0.153324	−0.00575011
$712$	−64.2334	−2.40725
$713$	−32.2962	−1.20950
$714$	11.9516	0.447278
$715$	27.8125	1.04013
$716$	−52.1921	−1.95051
$717$	−3.05562	−0.114114
$718$	−45.5737	−1.70080
$719$	30.2197	1.12701	0.563503	−	0.826114i	$-0.309453\pi$
$719$	30.2197	1.12701	0.563503	+	0.826114i	$0.309453\pi$
$720$	−7.73283	−0.288186
$721$	3.69990	0.137791
$722$	−78.7822	−2.93197
$723$	−20.7507	−0.771728
$724$	−77.4927	−2.87999
$725$	−0.0245695	−0.000912489 0
$726$	70.5225	2.61734
$727$	17.0761	0.633318	0.316659	−	0.948539i	$-0.397439\pi$
$727$	17.0761	0.633318	0.316659	+	0.948539i	$0.397439\pi$
$728$	−11.3585	−0.420974
$729$	29.8902	1.10704
$730$	13.4629	0.498283
$731$	6.40851	0.237027
$732$	−46.9602	−1.73570
$733$	24.4058	0.901450	0.450725	−	0.892663i	$-0.351166\pi$
$733$	24.4058	0.901450	0.450725	+	0.892663i	$0.351166\pi$
$734$	−49.0641	−1.81099
$735$	22.5083	0.830232
$736$	−44.2615	−1.63150
$737$	45.6512	1.68158
$738$	−13.9689	−0.514201
$739$	34.6474	1.27452	0.637262	−	0.770647i	$-0.280067\pi$
$739$	34.6474	1.27452	0.637262	+	0.770647i	$0.280067\pi$
$740$	−12.4902	−0.459151
$741$	25.9887	0.954720
$742$	26.2696	0.964389
$743$	42.7792	1.56942	0.784709	−	0.619864i	$-0.212812\pi$
$743$	42.7792	1.56942	0.784709	+	0.619864i	$0.212812\pi$
$744$	−35.2278	−1.29151
$745$	12.6131	0.462110
$746$	−3.30706	−0.121080
$747$	4.89642	0.179151
$748$	89.7586	3.28190
$749$	4.48692	0.163948
$750$	−44.8115	−1.63629
$751$	−12.2476	−0.446923	−0.223462	−	0.974713i	$-0.571736\pi$
$751$	−12.2476	−0.446923	−0.223462	+	0.974713i	$0.571736\pi$
$752$	22.2729	0.812210
$753$	36.0807	1.31485
$754$	37.7260	1.37390
$755$	−32.3258	−1.17646
$756$	−19.3904	−0.705222
$757$	37.7824	1.37322	0.686612	−	0.727024i	$-0.259097\pi$
$757$	37.7824	1.37322	0.686612	+	0.727024i	$0.259097\pi$
$758$	−11.3901	−0.413706
$759$	75.6414	2.74561
$760$	−97.8518	−3.54946
$761$	22.6156	0.819815	0.409907	−	0.912127i	$-0.365561\pi$
$761$	22.6156	0.819815	0.409907	+	0.912127i	$0.365561\pi$
$762$	1.35476	0.0490778
$763$	6.34550	0.229722
$764$	−53.8201	−1.94714
$765$	4.28426	0.154898
$766$	−37.3346	−1.34895
$767$	23.2176	0.838339
$768$	47.3829	1.70978
$769$	−4.56655	−0.164674	−0.0823370	−	0.996605i	$-0.526238\pi$
$769$	−4.56655	−0.164674	−0.0823370	+	0.996605i	$0.526238\pi$
$770$	−23.9305	−0.862395
$771$	−37.8739	−1.36399
$772$	71.8217	2.58492
$773$	23.9500	0.861422	0.430711	−	0.902490i	$-0.358263\pi$
$773$	23.9500	0.861422	0.430711	+	0.902490i	$0.358263\pi$
$774$	−2.18007	−0.0783610
$775$	0.0138624	0.000497952 0
$776$	60.0008	2.15390
$777$	−1.56820	−0.0562589
$778$	87.4148	3.13397
$779$	−76.8275	−2.75263
$780$	36.4475	1.30503
$781$	−12.7796	−0.457292
$782$	85.9439	3.07335
$783$	35.3842	1.26453
$784$	−43.5253	−1.55447
$785$	42.7145	1.52455
$786$	−0.471323	−0.0168115
$787$	−33.4343	−1.19180	−0.595902	−	0.803057i	$-0.703206\pi$
$787$	−33.4343	−1.19180	−0.595902	+	0.803057i	$0.703206\pi$
$788$	−1.61875	−0.0576656
$789$	16.1320	0.574316
$790$	−1.71550	−0.0610349
$791$	9.83138	0.349563
$792$	−16.7762	−0.596116
$793$	−15.5894	−0.553597
$794$	75.8252	2.69093
$795$	−46.3132	−1.64256
$796$	−74.7959	−2.65107
$797$	31.4885	1.11538	0.557691	−	0.830049i	$-0.311688\pi$
$797$	31.4885	1.11538	0.557691	+	0.830049i	$0.311688\pi$
$798$	−22.3613	−0.791580
$799$	−12.3400	−0.436557
$800$	0.0189982	0.000671688 0
$801$	−5.26184	−0.185918
$802$	5.45225	0.192526
$803$	12.6946	0.447982
$804$	59.8245	2.10985
$805$	−15.7960	−0.556737
$806$	−21.2854	−0.749746
$807$	26.3889	0.928932
$808$	−30.2688	−1.06485
$809$	−10.2609	−0.360756	−0.180378	−	0.983597i	$-0.557732\pi$
$809$	−10.2609	−0.360756	−0.180378	+	0.983597i	$0.557732\pi$
$810$	40.9630	1.43929
$811$	−26.0548	−0.914909	−0.457454	−	0.889233i	$-0.651239\pi$
$811$	−26.0548	−0.914909	−0.457454	+	0.889233i	$0.651239\pi$
$812$	−22.3774	−0.785292
$813$	−29.5144	−1.03511
$814$	−17.0841	−0.598799
$815$	−27.4424	−0.961265
$816$	40.7451	1.42636
$817$	−11.9902	−0.419484
$818$	71.6624	2.50562
$819$	−0.930460	−0.0325129
$820$	−107.746	−3.76264
$821$	−22.9530	−0.801066	−0.400533	−	0.916282i	$-0.631175\pi$
$821$	−22.9530	−0.801066	−0.400533	+	0.916282i	$0.631175\pi$
$822$	61.2618	2.13675
$823$	−5.85617	−0.204133	−0.102067	−	0.994778i	$-0.532545\pi$
$823$	−5.85617	−0.204133	−0.102067	+	0.994778i	$0.532545\pi$
$824$	29.0210	1.01099
$825$	−0.0324673	−0.00113037
$826$	−19.9769	−0.695086
$827$	5.03418	0.175056	0.0875278	−	0.996162i	$-0.472103\pi$
$827$	5.03418	0.175056	0.0875278	+	0.996162i	$0.472103\pi$
$828$	−20.1552	−0.700441
$829$	−19.5806	−0.680062	−0.340031	−	0.940414i	$-0.610438\pi$
$829$	−19.5806	−0.680062	−0.340031	+	0.940414i	$0.610438\pi$
$830$	54.7847	1.90161
$831$	10.3866	0.360308
$832$	2.58566	0.0896417
$833$	24.1145	0.835519
$834$	−84.5110	−2.92638
$835$	51.3758	1.77793
$836$	−167.937	−5.80822
$837$	−19.9642	−0.690063
$838$	77.5117	2.67760
$839$	16.2334	0.560438	0.280219	−	0.959936i	$-0.409593\pi$
$839$	16.2334	0.560438	0.280219	+	0.959936i	$0.409593\pi$
$840$	−17.2299	−0.594487
$841$	11.8349	0.408101
$842$	30.8187	1.06208
$843$	−46.8998	−1.61531
$844$	101.153	3.48183
$845$	−16.9582	−0.583380
$846$	4.19786	0.144325
$847$	−13.8866	−0.477150
$848$	89.5577	3.07542
$849$	−14.3544	−0.492642
$850$	−0.0368895	−0.00126530
$851$	−11.2769	−0.386567
$852$	−16.7474	−0.573755
$853$	10.8894	0.372845	0.186422	−	0.982470i	$-0.440311\pi$
$853$	10.8894	0.372845	0.186422	+	0.982470i	$0.440311\pi$
$854$	13.4135	0.458999
$855$	−8.01578	−0.274134
$856$	35.1942	1.20291
$857$	14.6827	0.501551	0.250776	−	0.968045i	$-0.419314\pi$
$857$	14.6827	0.501551	0.250776	+	0.968045i	$0.419314\pi$
$858$	49.8529	1.70195
$859$	−30.3895	−1.03687	−0.518437	−	0.855116i	$-0.673486\pi$
$859$	−30.3895	−1.03687	−0.518437	+	0.855116i	$0.673486\pi$
$860$	−16.8155	−0.573403
$861$	−13.5279	−0.461029
$862$	−81.9094	−2.78985
$863$	−3.67383	−0.125059	−0.0625293	−	0.998043i	$-0.519917\pi$
$863$	−3.67383	−0.125059	−0.0625293	+	0.998043i	$0.519917\pi$
$864$	−27.3606	−0.930827
$865$	−12.1820	−0.414199
$866$	56.3186	1.91378
$867$	4.26794	0.144947
$868$	12.6256	0.428539
$869$	−1.61760	−0.0548734
$870$	57.2271	1.94018
$871$	19.8600	0.672930
$872$	49.7724	1.68551
$873$	4.91512	0.166352
$874$	−160.800	−5.43913
$875$	8.82386	0.298301
$876$	16.6359	0.562074
$877$	14.5300	0.490642	0.245321	−	0.969442i	$-0.421107\pi$
$877$	14.5300	0.490642	0.245321	+	0.969442i	$0.421107\pi$
$878$	8.94962	0.302035
$879$	−53.9932	−1.82115
$880$	−81.5831	−2.75017
$881$	42.9281	1.44628	0.723142	−	0.690699i	$-0.242697\pi$
$881$	42.9281	1.44628	0.723142	+	0.690699i	$0.242697\pi$
$882$	−8.20337	−0.276222
$883$	−8.87561	−0.298688	−0.149344	−	0.988785i	$-0.547716\pi$
$883$	−8.87561	−0.298688	−0.149344	+	0.988785i	$0.547716\pi$
$884$	39.0484	1.31334
$885$	35.2191	1.18388
$886$	36.4817	1.22563
$887$	−6.45016	−0.216575	−0.108288	−	0.994120i	$-0.534537\pi$
$887$	−6.45016	−0.216575	−0.108288	+	0.994120i	$0.534537\pi$
$888$	−12.3005	−0.412779
$889$	−0.266767	−0.00894706
$890$	−58.8734	−1.97344
$891$	38.6253	1.29400
$892$	50.9533	1.70604
$893$	23.0879	0.772607
$894$	22.6086	0.756144
$895$	−26.2825	−0.878526
$896$	−10.0212	−0.334786
$897$	32.9069	1.09873
$898$	24.5751	0.820081
$899$	−23.0395	−0.768411
$900$	0.00865114	0.000288371 0
$901$	−49.6181	−1.65302
$902$	−147.374	−4.90703
$903$	−2.11125	−0.0702581
$904$	77.1147	2.56480
$905$	−39.0231	−1.29717
$906$	−57.9428	−1.92502
$907$	50.9728	1.69252	0.846262	−	0.532768i	$-0.178848\pi$
$907$	50.9728	1.69252	0.846262	+	0.532768i	$0.178848\pi$
$908$	71.1266	2.36042
$909$	−2.47954	−0.0822413
$910$	−10.4107	−0.345110
$911$	28.5153	0.944755	0.472377	−	0.881396i	$-0.343396\pi$
$911$	28.5153	0.944755	0.472377	+	0.881396i	$0.343396\pi$
$912$	−76.2333	−2.52434
$913$	51.6583	1.70964
$914$	−59.0047	−1.95170
$915$	−23.6478	−0.781773
$916$	107.967	3.56732
$917$	0.0928083	0.00306480
$918$	53.1270	1.75345
$919$	−28.4711	−0.939176	−0.469588	−	0.882886i	$-0.655598\pi$
$919$	−28.4711	−0.939176	−0.469588	+	0.882886i	$0.655598\pi$
$920$	−123.900	−4.08486
$921$	17.9207	0.590508
$922$	24.8316	0.817784
$923$	−5.55964	−0.182998
$924$	−29.5705	−0.972799
$925$	0.00484035	0.000159150 0
$926$	50.8799	1.67202
$927$	2.37733	0.0780817
$928$	−31.5753	−1.03651
$929$	48.3131	1.58510	0.792550	−	0.609807i	$-0.208753\pi$
$929$	48.3131	1.58510	0.792550	+	0.609807i	$0.208753\pi$
$930$	−32.2882	−1.05877
$931$	−45.1179	−1.47868
$932$	71.4111	2.33915
$933$	−33.8913	−1.10955
$934$	−40.8313	−1.33604
$935$	45.1999	1.47820
$936$	−7.29828	−0.238552
$937$	−4.82223	−0.157535	−0.0787676	−	0.996893i	$-0.525099\pi$
$937$	−4.82223	−0.157535	−0.0787676	+	0.996893i	$0.525099\pi$
$938$	−17.0880	−0.557942
$939$	−18.6817	−0.609654
$940$	32.3793	1.05610
$941$	−2.16362	−0.0705319	−0.0352659	−	0.999378i	$-0.511228\pi$
$941$	−2.16362	−0.0705319	−0.0352659	+	0.999378i	$0.511228\pi$
$942$	76.5641	2.49459
$943$	−97.2790	−3.16784
$944$	−68.1047	−2.21662
$945$	−9.76446	−0.317638
$946$	−23.0002	−0.747802
$947$	−3.04273	−0.0988755	−0.0494377	−	0.998777i	$-0.515743\pi$
$947$	−3.04273	−0.0988755	−0.0494377	+	0.998777i	$0.515743\pi$
$948$	−2.11982	−0.0688486
$949$	5.52262	0.179272
$950$	0.0690195	0.00223929
$951$	31.2639	1.01380
$952$	−18.4594	−0.598273
$953$	38.5068	1.24736	0.623679	−	0.781681i	$-0.285637\pi$
$953$	38.5068	1.24736	0.623679	+	0.781681i	$0.285637\pi$
$954$	16.8793	0.546487
$955$	−27.1023	−0.877009
$956$	8.58990	0.277817
$957$	53.9612	1.74432
$958$	38.1297	1.23191
$959$	−12.0631	−0.389537
$960$	3.92223	0.126590
$961$	−18.0008	−0.580673
$962$	−7.43226	−0.239626
$963$	2.88302	0.0929040
$964$	58.3340	1.87881
$965$	36.1674	1.16427
$966$	−28.3138	−0.910981
$967$	15.4039	0.495355	0.247677	−	0.968843i	$-0.420333\pi$
$967$	15.4039	0.495355	0.247677	+	0.968843i	$0.420333\pi$
$968$	−108.923	−3.50092
$969$	42.2360	1.35681
$970$	54.9940	1.76575
$971$	−43.4906	−1.39568	−0.697839	−	0.716255i	$-0.745855\pi$
$971$	−43.4906	−1.39568	−0.697839	+	0.716255i	$0.745855\pi$
$972$	−23.1173	−0.741487
$973$	16.6411	0.533489
$974$	22.9002	0.733771
$975$	−0.0141245	−0.000452347 0
$976$	45.7288	1.46374
$977$	19.3900	0.620342	0.310171	−	0.950681i	$-0.399614\pi$
$977$	19.3900	0.620342	0.310171	+	0.950681i	$0.399614\pi$
$978$	−49.1894	−1.57290
$979$	−55.5136	−1.77422
$980$	−63.2749	−2.02124
$981$	4.07723	0.130176
$982$	53.7810	1.71622
$983$	18.5726	0.592373	0.296186	−	0.955130i	$-0.404285\pi$
$983$	18.5726	0.592373	0.296186	+	0.955130i	$0.404285\pi$
$984$	−106.109	−3.38264
$985$	−0.815156	−0.0259730
$986$	61.3109	1.95254
$987$	4.06535	0.129401
$988$	−73.0589	−2.32431
$989$	−15.1820	−0.482759
$990$	−15.3763	−0.488690
$991$	12.6339	0.401328	0.200664	−	0.979660i	$-0.435690\pi$
$991$	12.6339	0.401328	0.200664	+	0.979660i	$0.435690\pi$
$992$	17.8152	0.565632
$993$	−49.5595	−1.57272
$994$	4.78363	0.151727
$995$	−37.6651	−1.19406
$996$	67.6967	2.14505
$997$	30.1066	0.953487	0.476744	−	0.879042i	$-0.341817\pi$
$997$	30.1066	0.953487	0.476744	+	0.879042i	$0.341817\pi$
$998$	−46.5909	−1.47481
$999$	−6.97092	−0.220550

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.c.1.11	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.c.1.11	✓	259	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6043 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53746 q^{2} -1.57895 q^{3} +4.43871 q^{4} +2.23521 q^{5} +4.00652 q^{6} -0.788927 q^{7} -6.18813 q^{8} -0.506916 q^{9} +O(q^{10})\)	\(q-2.53746 q^{2} -1.57895 q^{3} +4.43871 q^{4} +2.23521 q^{5} +4.00652 q^{6} -0.788927 q^{7} -6.18813 q^{8} -0.506916 q^{9} -5.67175 q^{10} -5.34808 q^{11} -7.00850 q^{12} -2.32662 q^{13} +2.00187 q^{14} -3.52928 q^{15} +6.82472 q^{16} -3.78113 q^{17} +1.28628 q^{18} +7.07444 q^{19} +9.92144 q^{20} +1.24568 q^{21} +13.5705 q^{22} +8.95764 q^{23} +9.77075 q^{24} -0.00384486 q^{25} +5.90370 q^{26} +5.53725 q^{27} -3.50182 q^{28} +6.39022 q^{29} +8.95542 q^{30} -3.60543 q^{31} -4.94120 q^{32} +8.44435 q^{33} +9.59448 q^{34} -1.76341 q^{35} -2.25005 q^{36} -1.25892 q^{37} -17.9511 q^{38} +3.67361 q^{39} -13.8318 q^{40} -10.8599 q^{41} -3.16085 q^{42} -1.69486 q^{43} -23.7386 q^{44} -1.13306 q^{45} -22.7297 q^{46} +3.26357 q^{47} -10.7759 q^{48} -6.37759 q^{49} +0.00975619 q^{50} +5.97022 q^{51} -10.3272 q^{52} +13.1226 q^{53} -14.0505 q^{54} -11.9541 q^{55} +4.88198 q^{56} -11.1702 q^{57} -16.2149 q^{58} -9.97912 q^{59} -15.6655 q^{60} +6.70047 q^{61} +9.14865 q^{62} +0.399920 q^{63} -1.11134 q^{64} -5.20047 q^{65} -21.4272 q^{66} -8.53600 q^{67} -16.7834 q^{68} -14.1437 q^{69} +4.47460 q^{70} +2.38958 q^{71} +3.13686 q^{72} -2.37367 q^{73} +3.19445 q^{74} +0.00607085 q^{75} +31.4014 q^{76} +4.21924 q^{77} -9.32165 q^{78} +0.302465 q^{79} +15.2547 q^{80} -7.22229 q^{81} +27.5565 q^{82} -9.65922 q^{83} +5.52919 q^{84} -8.45162 q^{85} +4.30065 q^{86} -10.0898 q^{87} +33.0946 q^{88} +10.3801 q^{89} +2.87510 q^{90} +1.83553 q^{91} +39.7604 q^{92} +5.69280 q^{93} -8.28117 q^{94} +15.8128 q^{95} +7.80190 q^{96} -9.69612 q^{97} +16.1829 q^{98} +2.71103 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * q^99

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