LMFDB - Embedded newform 503.2.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [503,2,Mod(1,503)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(503, 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("503.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.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:	$4.01647522167$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 $ x^10 - 2x^9 - 9x^8 + 14x^7 + 27x^6 - 27x^5 - 34x^4 + 14x^3 + 17x^2 + x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.95007$ of defining polynomial
Character	$\chi$	$=$	503.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.392284 q^{2} +0.950069 q^{3} -1.84611 q^{4} -2.28693 q^{5} -0.372697 q^{6} +2.71022 q^{7} +1.50877 q^{8} -2.09737 q^{9} +O(q^{10})$	\(q-0.392284 q^{2} +0.950069 q^{3} -1.84611 q^{4} -2.28693 q^{5} -0.372697 q^{6} +2.71022 q^{7} +1.50877 q^{8} -2.09737 q^{9} +0.897127 q^{10} +1.36880 q^{11} -1.75393 q^{12} -2.93079 q^{13} -1.06318 q^{14} -2.17275 q^{15} +3.10036 q^{16} -2.61287 q^{17} +0.822764 q^{18} -7.79104 q^{19} +4.22194 q^{20} +2.57490 q^{21} -0.536960 q^{22} -2.61064 q^{23} +1.43343 q^{24} +0.230071 q^{25} +1.14970 q^{26} -4.84285 q^{27} -5.00337 q^{28} -0.314480 q^{29} +0.852333 q^{30} -7.95126 q^{31} -4.23376 q^{32} +1.30046 q^{33} +1.02499 q^{34} -6.19810 q^{35} +3.87198 q^{36} -4.17299 q^{37} +3.05630 q^{38} -2.78446 q^{39} -3.45045 q^{40} +6.16482 q^{41} -1.01009 q^{42} +0.457851 q^{43} -2.52697 q^{44} +4.79655 q^{45} +1.02411 q^{46} +7.67118 q^{47} +2.94556 q^{48} +0.345296 q^{49} -0.0902533 q^{50} -2.48241 q^{51} +5.41058 q^{52} +7.26306 q^{53} +1.89977 q^{54} -3.13037 q^{55} +4.08909 q^{56} -7.40203 q^{57} +0.123365 q^{58} +0.217166 q^{59} +4.01114 q^{60} +7.26694 q^{61} +3.11915 q^{62} -5.68433 q^{63} -4.53989 q^{64} +6.70253 q^{65} -0.510149 q^{66} +10.1022 q^{67} +4.82366 q^{68} -2.48029 q^{69} +2.43141 q^{70} -16.5088 q^{71} -3.16444 q^{72} +2.86838 q^{73} +1.63699 q^{74} +0.218584 q^{75} +14.3831 q^{76} +3.70976 q^{77} +1.09230 q^{78} -16.0222 q^{79} -7.09033 q^{80} +1.69106 q^{81} -2.41836 q^{82} +12.5312 q^{83} -4.75355 q^{84} +5.97547 q^{85} -0.179608 q^{86} -0.298777 q^{87} +2.06521 q^{88} -0.0952234 q^{89} -1.88161 q^{90} -7.94310 q^{91} +4.81954 q^{92} -7.55424 q^{93} -3.00928 q^{94} +17.8176 q^{95} -4.02236 q^{96} -9.27640 q^{97} -0.135454 q^{98} -2.87089 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9} - 4 q^{10} - 3 q^{11} - 7 q^{12} - 18 q^{13} + q^{14} - 2 q^{15} - 4 q^{16} - 11 q^{17} - q^{18} - 3 q^{20} + q^{21} - 18 q^{22} - 2 q^{23} + 10 q^{24} - 27 q^{25} + 11 q^{26} - 2 q^{27} - 22 q^{28} - 9 q^{29} + 12 q^{30} - 22 q^{31} - 10 q^{32} - 10 q^{33} - 10 q^{34} - 6 q^{35} + 2 q^{36} - 35 q^{37} + 2 q^{38} + 8 q^{39} - 19 q^{40} - 4 q^{41} + 4 q^{42} - 20 q^{43} + 9 q^{44} + 2 q^{45} - q^{46} + 7 q^{47} - 27 q^{49} + 16 q^{50} + 9 q^{51} - 7 q^{52} - 24 q^{53} + 17 q^{54} - 11 q^{55} + 12 q^{56} - 23 q^{57} + 2 q^{58} + 17 q^{59} - 4 q^{61} + 8 q^{62} + 10 q^{63} + 3 q^{64} - 16 q^{65} + 46 q^{66} - 6 q^{67} + 28 q^{68} - 2 q^{69} + 26 q^{70} - q^{71} - q^{72} - 31 q^{73} + 11 q^{74} + 30 q^{75} + 20 q^{76} + 3 q^{77} + 11 q^{78} - 10 q^{79} + 24 q^{80} - 6 q^{81} - 9 q^{82} + 22 q^{83} + 22 q^{84} - 6 q^{85} + 38 q^{86} + 25 q^{87} - 3 q^{88} + q^{89} + 2 q^{90} + 10 q^{91} + 27 q^{92} - 6 q^{93} + 33 q^{94} + 39 q^{95} + 46 q^{96} - 57 q^{97} + 40 q^{98} + 35 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9 - 4 * q^10 - 3 * q^11 - 7 * q^12 - 18 * q^13 + q^14 - 2 * q^15 - 4 * q^16 - 11 * q^17 - q^18 - 3 * q^20 + q^21 - 18 * q^22 - 2 * q^23 + 10 * q^24 - 27 * q^25 + 11 * q^26 - 2 * q^27 - 22 * q^28 - 9 * q^29 + 12 * q^30 - 22 * q^31 - 10 * q^32 - 10 * q^33 - 10 * q^34 - 6 * q^35 + 2 * q^36 - 35 * q^37 + 2 * q^38 + 8 * q^39 - 19 * q^40 - 4 * q^41 + 4 * q^42 - 20 * q^43 + 9 * q^44 + 2 * q^45 - q^46 + 7 * q^47 - 27 * q^49 + 16 * q^50 + 9 * q^51 - 7 * q^52 - 24 * q^53 + 17 * q^54 - 11 * q^55 + 12 * q^56 - 23 * q^57 + 2 * q^58 + 17 * q^59 - 4 * q^61 + 8 * q^62 + 10 * q^63 + 3 * q^64 - 16 * q^65 + 46 * q^66 - 6 * q^67 + 28 * q^68 - 2 * q^69 + 26 * q^70 - q^71 - q^72 - 31 * q^73 + 11 * q^74 + 30 * q^75 + 20 * q^76 + 3 * q^77 + 11 * q^78 - 10 * q^79 + 24 * q^80 - 6 * q^81 - 9 * q^82 + 22 * q^83 + 22 * q^84 - 6 * q^85 + 38 * q^86 + 25 * q^87 - 3 * q^88 + q^89 + 2 * q^90 + 10 * q^91 + 27 * q^92 - 6 * q^93 + 33 * q^94 + 39 * q^95 + 46 * q^96 - 57 * q^97 + 40 * q^98 + 35 * 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 $

$2$	−0.392284	−0.277386	−0.138693	−	0.990335i	$-0.544290\pi$
$2$	−0.392284	−0.277386	−0.138693	+	0.990335i	$0.544290\pi$
$3$	0.950069	0.548523	0.274261	−	0.961655i	$-0.411567\pi$
$3$	0.950069	0.548523	0.274261	+	0.961655i	$0.411567\pi$
$4$	−1.84611	−0.923057
$5$	−2.28693	−1.02275	−0.511374	−	0.859358i	$-0.670863\pi$
$5$	−2.28693	−1.02275	−0.511374	+	0.859358i	$0.670863\pi$
$6$	−0.372697	−0.152153
$7$	2.71022	1.02437	0.512184	−	0.858876i	$-0.328837\pi$
$7$	2.71022	1.02437	0.512184	+	0.858876i	$0.328837\pi$
$8$	1.50877	0.533430
$9$	−2.09737	−0.699123
$10$	0.897127	0.283697
$11$	1.36880	0.412710	0.206355	−	0.978477i	$-0.433840\pi$
$11$	1.36880	0.412710	0.206355	+	0.978477i	$0.433840\pi$
$12$	−1.75393	−0.506317
$13$	−2.93079	−0.812856	−0.406428	−	0.913683i	$-0.633226\pi$
$13$	−2.93079	−0.812856	−0.406428	+	0.913683i	$0.633226\pi$
$14$	−1.06318	−0.284146
$15$	−2.17275	−0.561001
$16$	3.10036	0.775091
$17$	−2.61287	−0.633715	−0.316857	−	0.948473i	$-0.602628\pi$
$17$	−2.61287	−0.633715	−0.316857	+	0.948473i	$0.602628\pi$
$18$	0.822764	0.193927
$19$	−7.79104	−1.78739	−0.893694	−	0.448677i	$-0.851895\pi$
$19$	−7.79104	−1.78739	−0.893694	+	0.448677i	$0.851895\pi$
$20$	4.22194	0.944055
$21$	2.57490	0.561888
$22$	−0.536960	−0.114480
$23$	−2.61064	−0.544356	−0.272178	−	0.962247i	$-0.587744\pi$
$23$	−2.61064	−0.544356	−0.272178	+	0.962247i	$0.587744\pi$
$24$	1.43343	0.292598
$25$	0.230071	0.0460143
$26$	1.14970	0.225475
$27$	−4.84285	−0.932007
$28$	−5.00337	−0.945549
$29$	−0.314480	−0.0583974	−0.0291987	−	0.999574i	$-0.509296\pi$
$29$	−0.314480	−0.0583974	−0.0291987	+	0.999574i	$0.509296\pi$
$30$	0.852333	0.155614
$31$	−7.95126	−1.42809	−0.714044	−	0.700101i	$-0.753138\pi$
$31$	−7.95126	−1.42809	−0.714044	+	0.700101i	$0.753138\pi$
$32$	−4.23376	−0.748430
$33$	1.30046	0.226381
$34$	1.02499	0.175784
$35$	−6.19810	−1.04767
$36$	3.87198	0.645330
$37$	−4.17299	−0.686035	−0.343017	−	0.939329i	$-0.611449\pi$
$37$	−4.17299	−0.686035	−0.343017	+	0.939329i	$0.611449\pi$
$38$	3.05630	0.495797
$39$	−2.78446	−0.445870
$40$	−3.45045	−0.545565
$41$	6.16482	0.962783	0.481391	−	0.876506i	$-0.340132\pi$
$41$	6.16482	0.962783	0.481391	+	0.876506i	$0.340132\pi$
$42$	−1.01009	−0.155860
$43$	0.457851	0.0698216	0.0349108	−	0.999390i	$-0.488885\pi$
$43$	0.457851	0.0698216	0.0349108	+	0.999390i	$0.488885\pi$
$44$	−2.52697	−0.380955
$45$	4.79655	0.715027
$46$	1.02411	0.150997
$47$	7.67118	1.11896	0.559478	−	0.828845i	$-0.311002\pi$
$47$	7.67118	1.11896	0.559478	+	0.828845i	$0.311002\pi$
$48$	2.94556	0.425155
$49$	0.345296	0.0493279
$50$	−0.0902533	−0.0127637
$51$	−2.48241	−0.347607
$52$	5.41058	0.750312
$53$	7.26306	0.997658	0.498829	−	0.866700i	$-0.333763\pi$
$53$	7.26306	0.997658	0.498829	+	0.866700i	$0.333763\pi$
$54$	1.89977	0.258526
$55$	−3.13037	−0.422099
$56$	4.08909	0.546428
$57$	−7.40203	−0.980423
$58$	0.123365	0.0161987
$59$	0.217166	0.0282726	0.0141363	−	0.999900i	$-0.495500\pi$
$59$	0.217166	0.0282726	0.0141363	+	0.999900i	$0.495500\pi$
$60$	4.01114	0.517835
$61$	7.26694	0.930436	0.465218	−	0.885196i	$-0.345976\pi$
$61$	7.26694	0.930436	0.465218	+	0.885196i	$0.345976\pi$
$62$	3.11915	0.396132
$63$	−5.68433	−0.716159
$64$	−4.53989	−0.567486
$65$	6.70253	0.831347
$66$	−0.510149	−0.0627950
$67$	10.1022	1.23418	0.617091	−	0.786892i	$-0.288311\pi$
$67$	10.1022	1.23418	0.617091	+	0.786892i	$0.288311\pi$
$68$	4.82366	0.584955
$69$	−2.48029	−0.298592
$70$	2.43141	0.290609
$71$	−16.5088	−1.95924	−0.979619	−	0.200863i	$-0.935625\pi$
$71$	−16.5088	−1.95924	−0.979619	+	0.200863i	$0.935625\pi$
$72$	−3.16444	−0.372933
$73$	2.86838	0.335718	0.167859	−	0.985811i	$-0.446315\pi$
$73$	2.86838	0.335718	0.167859	+	0.985811i	$0.446315\pi$
$74$	1.63699	0.190297
$75$	0.218584	0.0252399
$76$	14.3831	1.64986
$77$	3.70976	0.422767
$78$	1.09230	0.123678
$79$	−16.0222	−1.80264	−0.901320	−	0.433153i	$-0.857401\pi$
$79$	−16.0222	−1.80264	−0.901320	+	0.433153i	$0.857401\pi$
$80$	−7.09033	−0.792723
$81$	1.69106	0.187896
$82$	−2.41836	−0.267063
$83$	12.5312	1.37548	0.687741	−	0.725956i	$-0.258602\pi$
$83$	12.5312	1.37548	0.687741	+	0.725956i	$0.258602\pi$
$84$	−4.75355	−0.518655
$85$	5.97547	0.648131
$86$	−0.179608	−0.0193676
$87$	−0.298777	−0.0320323
$88$	2.06521	0.220152
$89$	−0.0952234	−0.0100937	−0.00504683	−	0.999987i	$-0.501606\pi$
$89$	−0.0952234	−0.0100937	−0.00504683	+	0.999987i	$0.501606\pi$
$90$	−1.88161	−0.198339
$91$	−7.94310	−0.832663
$92$	4.81954	0.502472
$93$	−7.55424	−0.783339
$94$	−3.00928	−0.310383
$95$	17.8176	1.82805
$96$	−4.02236	−0.410530
$97$	−9.27640	−0.941875	−0.470938	−	0.882167i	$-0.656084\pi$
$97$	−9.27640	−0.941875	−0.470938	+	0.882167i	$0.656084\pi$
$98$	−0.135454	−0.0136829
$99$	−2.87089	−0.288535
$100$	−0.424738	−0.0424738
$101$	8.77727	0.873371	0.436686	−	0.899614i	$-0.356152\pi$
$101$	8.77727	0.873371	0.436686	+	0.899614i	$0.356152\pi$
$102$	0.973809	0.0964214
$103$	1.52475	0.150238	0.0751189	−	0.997175i	$-0.476066\pi$
$103$	1.52475	0.150238	0.0751189	+	0.997175i	$0.476066\pi$
$104$	−4.42189	−0.433602
$105$	−5.88862	−0.574670
$106$	−2.84918	−0.276737
$107$	−17.6358	−1.70492	−0.852460	−	0.522792i	$-0.824890\pi$
$107$	−17.6358	−1.70492	−0.852460	+	0.522792i	$0.824890\pi$
$108$	8.94045	0.860296
$109$	−4.91427	−0.470702	−0.235351	−	0.971910i	$-0.575624\pi$
$109$	−4.91427	−0.470702	−0.235351	+	0.971910i	$0.575624\pi$
$110$	1.22799	0.117084
$111$	−3.96462	−0.376305
$112$	8.40266	0.793977
$113$	0.102880	0.00967811	0.00483905	−	0.999988i	$-0.498460\pi$
$113$	0.102880	0.00967811	0.00483905	+	0.999988i	$0.498460\pi$
$114$	2.90369	0.271956
$115$	5.97037	0.556740
$116$	0.580565	0.0539041
$117$	6.14696	0.568286
$118$	−0.0851906	−0.00784243
$119$	−7.08146	−0.649157
$120$	−3.27817	−0.299254
$121$	−9.12637	−0.829670
$122$	−2.85070	−0.258090
$123$	5.85700	0.528108
$124$	14.6789	1.31821
$125$	10.9085	0.975687
$126$	2.22987	0.198653
$127$	14.7682	1.31046	0.655232	−	0.755428i	$-0.272571\pi$
$127$	14.7682	1.31046	0.655232	+	0.755428i	$0.272571\pi$
$128$	10.2484	0.905843
$129$	0.434990	0.0382987
$130$	−2.62929	−0.230604
$131$	3.01646	0.263549	0.131775	−	0.991280i	$-0.457932\pi$
$131$	3.01646	0.263549	0.131775	+	0.991280i	$0.457932\pi$
$132$	−2.40079	−0.208962
$133$	−21.1154	−1.83094
$134$	−3.96293	−0.342345
$135$	11.0753	0.953209
$136$	−3.94222	−0.338042
$137$	0.370190	0.0316275	0.0158137	−	0.999875i	$-0.494966\pi$
$137$	0.370190	0.0316275	0.0158137	+	0.999875i	$0.494966\pi$
$138$	0.972977	0.0828253
$139$	13.0944	1.11065	0.555324	−	0.831634i	$-0.312594\pi$
$139$	13.0944	1.11065	0.555324	+	0.831634i	$0.312594\pi$
$140$	11.4424	0.967059
$141$	7.28815	0.613773
$142$	6.47615	0.543466
$143$	−4.01168	−0.335474
$144$	−6.50260	−0.541884
$145$	0.719195	0.0597259
$146$	−1.12522	−0.0931237
$147$	0.328055	0.0270575
$148$	7.70381	0.633249
$149$	−5.61923	−0.460345	−0.230173	−	0.973150i	$-0.573929\pi$
$149$	−5.61923	−0.460345	−0.230173	+	0.973150i	$0.573929\pi$
$150$	−0.0857468	−0.00700120
$151$	−6.99662	−0.569377	−0.284689	−	0.958620i	$-0.591890\pi$
$151$	−6.99662	−0.569377	−0.284689	+	0.958620i	$0.591890\pi$
$152$	−11.7549	−0.953446
$153$	5.48016	0.443045
$154$	−1.45528	−0.117270
$155$	18.1840	1.46058
$156$	5.14042	0.411563
$157$	10.5849	0.844764	0.422382	−	0.906418i	$-0.361194\pi$
$157$	10.5849	0.844764	0.422382	+	0.906418i	$0.361194\pi$
$158$	6.28526	0.500028
$159$	6.90041	0.547238
$160$	9.68233	0.765455
$161$	−7.07541	−0.557621
$162$	−0.663377	−0.0521198
$163$	−4.74396	−0.371576	−0.185788	−	0.982590i	$-0.559484\pi$
$163$	−4.74396	−0.371576	−0.185788	+	0.982590i	$0.559484\pi$
$164$	−11.3810	−0.888703
$165$	−2.97406	−0.231531
$166$	−4.91580	−0.381540
$167$	15.4650	1.19672	0.598360	−	0.801227i	$-0.295819\pi$
$167$	15.4650	1.19672	0.598360	+	0.801227i	$0.295819\pi$
$168$	3.88492	0.299728
$169$	−4.41045	−0.339265
$170$	−2.34408	−0.179783
$171$	16.3407	1.24960
$172$	−0.845245	−0.0644493
$173$	−18.0030	−1.36874	−0.684372	−	0.729133i	$-0.739924\pi$
$173$	−18.0030	−1.36874	−0.684372	+	0.729133i	$0.739924\pi$
$174$	0.117206	0.00888533
$175$	0.623544	0.0471355
$176$	4.24379	0.319888
$177$	0.206322	0.0155081
$178$	0.0373546	0.00279985
$179$	22.6390	1.69212	0.846058	−	0.533092i	$-0.178970\pi$
$179$	22.6390	1.69212	0.846058	+	0.533092i	$0.178970\pi$
$180$	−8.85497	−0.660010
$181$	2.97984	0.221490	0.110745	−	0.993849i	$-0.464676\pi$
$181$	2.97984	0.221490	0.110745	+	0.993849i	$0.464676\pi$
$182$	3.11595	0.230969
$183$	6.90409	0.510365
$184$	−3.93885	−0.290376
$185$	9.54335	0.701641
$186$	2.96341	0.217288
$187$	−3.57651	−0.261541
$188$	−14.1619	−1.03286
$189$	−13.1252	−0.954718
$190$	−6.98956	−0.507076
$191$	4.09564	0.296350	0.148175	−	0.988961i	$-0.452660\pi$
$191$	4.09564	0.296350	0.148175	+	0.988961i	$0.452660\pi$
$192$	−4.31321	−0.311279
$193$	−21.1708	−1.52391	−0.761955	−	0.647630i	$-0.775760\pi$
$193$	−21.1708	−1.52391	−0.761955	+	0.647630i	$0.775760\pi$
$194$	3.63898	0.261263
$195$	6.36787	0.456013
$196$	−0.637455	−0.0455325
$197$	18.5139	1.31906	0.659531	−	0.751677i	$-0.270755\pi$
$197$	18.5139	1.31906	0.659531	+	0.751677i	$0.270755\pi$
$198$	1.12620	0.0800358
$199$	−1.56711	−0.111089	−0.0555447	−	0.998456i	$-0.517690\pi$
$199$	−1.56711	−0.111089	−0.0555447	+	0.998456i	$0.517690\pi$
$200$	0.347124	0.0245454
$201$	9.59779	0.676976
$202$	−3.44318	−0.242261
$203$	−0.852309	−0.0598204
$204$	4.58281	0.320861
$205$	−14.0985	−0.984685
$206$	−0.598133	−0.0416739
$207$	5.47548	0.380572
$208$	−9.08652	−0.630037
$209$	−10.6644	−0.737673
$210$	2.31001	0.159406
$211$	−22.8488	−1.57298	−0.786489	−	0.617604i	$-0.788103\pi$
$211$	−22.8488	−1.57298	−0.786489	+	0.617604i	$0.788103\pi$
$212$	−13.4084	−0.920895
$213$	−15.6845	−1.07469
$214$	6.91825	0.472922
$215$	−1.04708	−0.0714100
$216$	−7.30674	−0.497161
$217$	−21.5497	−1.46289
$218$	1.92779	0.130566
$219$	2.72516	0.184149
$220$	5.77901	0.389621
$221$	7.65779	0.515119
$222$	1.55526	0.104382
$223$	4.75557	0.318457	0.159228	−	0.987242i	$-0.449099\pi$
$223$	4.75557	0.318457	0.159228	+	0.987242i	$0.449099\pi$
$224$	−11.4744	−0.766667
$225$	−0.482545	−0.0321696
$226$	−0.0403580	−0.00268458
$227$	−27.4709	−1.82331	−0.911655	−	0.410956i	$-0.865195\pi$
$227$	−27.4709	−1.82331	−0.911655	+	0.410956i	$0.865195\pi$
$228$	13.6650	0.904986
$229$	−4.52436	−0.298978	−0.149489	−	0.988763i	$-0.547763\pi$
$229$	−4.52436	−0.298978	−0.149489	+	0.988763i	$0.547763\pi$
$230$	−2.34208	−0.154432
$231$	3.52453	0.231897
$232$	−0.474477	−0.0311509
$233$	−10.5567	−0.691594	−0.345797	−	0.938309i	$-0.612391\pi$
$233$	−10.5567	−0.691594	−0.345797	+	0.938309i	$0.612391\pi$
$234$	−2.41135	−0.157635
$235$	−17.5435	−1.14441
$236$	−0.400913	−0.0260972
$237$	−15.2222	−0.988789
$238$	2.77794	0.180067
$239$	−28.3072	−1.83104	−0.915522	−	0.402269i	$-0.868222\pi$
$239$	−28.3072	−1.83104	−0.915522	+	0.402269i	$0.868222\pi$
$240$	−6.73630	−0.434826
$241$	−10.6922	−0.688748	−0.344374	−	0.938833i	$-0.611909\pi$
$241$	−10.6922	−0.688748	−0.344374	+	0.938833i	$0.611909\pi$
$242$	3.58013	0.230139
$243$	16.1352	1.03507
$244$	−13.4156	−0.858846
$245$	−0.789669	−0.0504501
$246$	−2.29761	−0.146490
$247$	22.8339	1.45289
$248$	−11.9966	−0.761785
$249$	11.9055	0.754483
$250$	−4.27923	−0.270642
$251$	−3.42359	−0.216095	−0.108048	−	0.994146i	$-0.534460\pi$
$251$	−3.42359	−0.216095	−0.108048	+	0.994146i	$0.534460\pi$
$252$	10.4939	0.661055
$253$	−3.57346	−0.224661
$254$	−5.79331	−0.363505
$255$	5.67711	0.355514
$256$	5.05948	0.316218
$257$	−11.2524	−0.701906	−0.350953	−	0.936393i	$-0.614142\pi$
$257$	−11.2524	−0.701906	−0.350953	+	0.936393i	$0.614142\pi$
$258$	−0.170640	−0.0106236
$259$	−11.3097	−0.702751
$260$	−12.3736	−0.767381
$261$	0.659580	0.0408270
$262$	−1.18331	−0.0731050
$263$	0.429180	0.0264643	0.0132322	−	0.999912i	$-0.495788\pi$
$263$	0.429180	0.0264643	0.0132322	+	0.999912i	$0.495788\pi$
$264$	1.96209	0.120758
$265$	−16.6102	−1.02035
$266$	8.28325	0.507878
$267$	−0.0904688	−0.00553660
$268$	−18.6498	−1.13922
$269$	15.2320	0.928712	0.464356	−	0.885649i	$-0.346286\pi$
$269$	15.2320	0.928712	0.464356	+	0.885649i	$0.346286\pi$
$270$	−4.34465	−0.264407
$271$	17.7850	1.08036	0.540182	−	0.841548i	$-0.318355\pi$
$271$	17.7850	1.08036	0.540182	+	0.841548i	$0.318355\pi$
$272$	−8.10085	−0.491186
$273$	−7.54649	−0.456734
$274$	−0.145219	−0.00877303
$275$	0.314923	0.0189906
$276$	4.57889	0.275617
$277$	15.1882	0.912570	0.456285	−	0.889834i	$-0.349180\pi$
$277$	15.1882	0.912570	0.456285	+	0.889834i	$0.349180\pi$
$278$	−5.13670	−0.308079
$279$	16.6767	0.998409
$280$	−9.35149	−0.558858
$281$	20.0885	1.19838	0.599191	−	0.800606i	$-0.295489\pi$
$281$	20.0885	1.19838	0.599191	+	0.800606i	$0.295489\pi$
$282$	−2.85902	−0.170252
$283$	−1.63497	−0.0971889	−0.0485945	−	0.998819i	$-0.515474\pi$
$283$	−1.63497	−0.0971889	−0.0485945	+	0.998819i	$0.515474\pi$
$284$	30.4772	1.80849
$285$	16.9280	1.00273
$286$	1.57372	0.0930559
$287$	16.7080	0.986243
$288$	8.87975	0.523244
$289$	−10.1729	−0.598405
$290$	−0.282128	−0.0165671
$291$	−8.81321	−0.516640
$292$	−5.29535	−0.309887
$293$	−10.1892	−0.595262	−0.297631	−	0.954681i	$-0.596196\pi$
$293$	−10.1892	−0.595262	−0.297631	+	0.954681i	$0.596196\pi$
$294$	−0.128690	−0.00750538
$295$	−0.496644	−0.0289157
$296$	−6.29607	−0.365951
$297$	−6.62892	−0.384649
$298$	2.20433	0.127694
$299$	7.65125	0.442483
$300$	−0.403530	−0.0232978
$301$	1.24088	0.0715230
$302$	2.74466	0.157938
$303$	8.33901	0.479064
$304$	−24.1551	−1.38539
$305$	−16.6190	−0.951602
$306$	−2.14978	−0.122895
$307$	−16.3682	−0.934184	−0.467092	−	0.884209i	$-0.654698\pi$
$307$	−16.3682	−0.934184	−0.467092	+	0.884209i	$0.654698\pi$
$308$	−6.84864	−0.390238
$309$	1.44861	0.0824088
$310$	−7.13329	−0.405144
$311$	6.98922	0.396322	0.198161	−	0.980169i	$-0.436503\pi$
$311$	6.98922	0.396322	0.198161	+	0.980169i	$0.436503\pi$
$312$	−4.20110	−0.237840
$313$	2.22444	0.125733	0.0628665	−	0.998022i	$-0.479976\pi$
$313$	2.22444	0.125733	0.0628665	+	0.998022i	$0.479976\pi$
$314$	−4.15227	−0.234326
$315$	12.9997	0.732450
$316$	29.5788	1.66394
$317$	3.49687	0.196404	0.0982019	−	0.995167i	$-0.468691\pi$
$317$	3.49687	0.196404	0.0982019	+	0.995167i	$0.468691\pi$
$318$	−2.70692	−0.151796
$319$	−0.430461	−0.0241012
$320$	10.3824	0.580396
$321$	−16.7553	−0.935187
$322$	2.77557	0.154676
$323$	20.3570	1.13269
$324$	−3.12190	−0.173439
$325$	−0.674292	−0.0374030
$326$	1.86098	0.103070
$327$	−4.66889	−0.258190
$328$	9.30128	0.513577
$329$	20.7906	1.14622
$330$	1.16668	0.0642235
$331$	−13.8654	−0.762112	−0.381056	−	0.924552i	$-0.624439\pi$
$331$	−13.8654	−0.762112	−0.381056	+	0.924552i	$0.624439\pi$
$332$	−23.1341	−1.26965
$333$	8.75229	0.479623
$334$	−6.06668	−0.331954
$335$	−23.1031	−1.26226
$336$	7.98311	0.435514
$337$	−33.0259	−1.79903	−0.899517	−	0.436885i	$-0.856082\pi$
$337$	−33.0259	−1.79903	−0.899517	+	0.436885i	$0.856082\pi$
$338$	1.73015	0.0941076
$339$	0.0977428	0.00530866
$340$	−11.0314	−0.598262
$341$	−10.8837	−0.589387
$342$	−6.41019	−0.346623
$343$	−18.0357	−0.973837
$344$	0.690791	0.0372450
$345$	5.67226	0.305384
$346$	7.06229	0.379671
$347$	−0.417829	−0.0224302	−0.0112151	−	0.999937i	$-0.503570\pi$
$347$	−0.417829	−0.0224302	−0.0112151	+	0.999937i	$0.503570\pi$
$348$	0.551577	0.0295676
$349$	−8.68607	−0.464955	−0.232477	−	0.972602i	$-0.574683\pi$
$349$	−8.68607	−0.464955	−0.232477	+	0.972602i	$0.574683\pi$
$350$	−0.244606	−0.0130748
$351$	14.1934	0.757588
$352$	−5.79519	−0.308884
$353$	−9.09582	−0.484122	−0.242061	−	0.970261i	$-0.577823\pi$
$353$	−9.09582	−0.484122	−0.242061	+	0.970261i	$0.577823\pi$
$354$	−0.0809369	−0.00430175
$355$	37.7546	2.00381
$356$	0.175793	0.00931703
$357$	−6.72788	−0.356077
$358$	−8.88089	−0.469370
$359$	5.51998	0.291333	0.145667	−	0.989334i	$-0.453467\pi$
$359$	5.51998	0.291333	0.145667	+	0.989334i	$0.453467\pi$
$360$	7.23687	0.381417
$361$	41.7004	2.19476
$362$	−1.16894	−0.0614383
$363$	−8.67068	−0.455093
$364$	14.6639	0.768595
$365$	−6.55979	−0.343355
$366$	−2.70836	−0.141568
$367$	16.3639	0.854188	0.427094	−	0.904207i	$-0.359537\pi$
$367$	16.3639	0.854188	0.427094	+	0.904207i	$0.359537\pi$
$368$	−8.09393	−0.421925
$369$	−12.9299	−0.673104
$370$	−3.74370	−0.194626
$371$	19.6845	1.02197
$372$	13.9460	0.723066
$373$	−23.5721	−1.22051	−0.610257	−	0.792203i	$-0.708934\pi$
$373$	−23.5721	−1.22051	−0.610257	+	0.792203i	$0.708934\pi$
$374$	1.40301	0.0725478
$375$	10.3638	0.535186
$376$	11.5740	0.596885
$377$	0.921675	0.0474687
$378$	5.14880	0.264826
$379$	−22.8307	−1.17273	−0.586367	−	0.810045i	$-0.699442\pi$
$379$	−22.8307	−1.17273	−0.586367	+	0.810045i	$0.699442\pi$
$380$	−32.8933	−1.68739
$381$	14.0308	0.718819
$382$	−1.60665	−0.0822034
$383$	21.8257	1.11524	0.557622	−	0.830095i	$-0.311714\pi$
$383$	21.8257	1.11524	0.557622	+	0.830095i	$0.311714\pi$
$384$	9.73672	0.496875
$385$	−8.48399	−0.432384
$386$	8.30497	0.422712
$387$	−0.960283	−0.0488139
$388$	17.1253	0.869404
$389$	29.7462	1.50819	0.754097	−	0.656763i	$-0.228075\pi$
$389$	29.7462	1.50819	0.754097	+	0.656763i	$0.228075\pi$
$390$	−2.49801	−0.126492
$391$	6.82127	0.344967
$392$	0.520971	0.0263130
$393$	2.86584	0.144563
$394$	−7.26271	−0.365890
$395$	36.6418	1.84365
$396$	5.29999	0.266334
$397$	28.5561	1.43319	0.716595	−	0.697489i	$-0.245700\pi$
$397$	28.5561	1.43319	0.716595	+	0.697489i	$0.245700\pi$
$398$	0.614751	0.0308147
$399$	−20.0611	−1.00431
$400$	0.713305	0.0356652
$401$	13.9970	0.698975	0.349487	−	0.936941i	$-0.386356\pi$
$401$	13.9970	0.698975	0.349487	+	0.936941i	$0.386356\pi$
$402$	−3.76506	−0.187784
$403$	23.3035	1.16083
$404$	−16.2038	−0.806171
$405$	−3.86735	−0.192170
$406$	0.334347	0.0165934
$407$	−5.71200	−0.283133
$408$	−3.74538	−0.185424
$409$	−18.2429	−0.902055	−0.451028	−	0.892510i	$-0.648942\pi$
$409$	−18.2429	−0.902055	−0.451028	+	0.892510i	$0.648942\pi$
$410$	5.53063	0.273138
$411$	0.351706	0.0173484
$412$	−2.81486	−0.138678
$413$	0.588567	0.0289615
$414$	−2.14794	−0.105566
$415$	−28.6581	−1.40677
$416$	12.4083	0.608365
$417$	12.4405	0.609216
$418$	4.18348	0.204621
$419$	9.78645	0.478099	0.239050	−	0.971007i	$-0.423164\pi$
$419$	9.78645	0.478099	0.239050	+	0.971007i	$0.423164\pi$
$420$	10.8711	0.530453
$421$	2.26639	0.110457	0.0552286	−	0.998474i	$-0.482411\pi$
$421$	2.26639	0.110457	0.0552286	+	0.998474i	$0.482411\pi$
$422$	8.96322	0.436323
$423$	−16.0893	−0.782288
$424$	10.9583	0.532181
$425$	−0.601147	−0.0291599
$426$	6.15279	0.298104
$427$	19.6950	0.953109
$428$	32.5578	1.57374
$429$	−3.81138	−0.184015
$430$	0.410751	0.0198082
$431$	4.29790	0.207023	0.103511	−	0.994628i	$-0.466992\pi$
$431$	4.29790	0.207023	0.103511	+	0.994628i	$0.466992\pi$
$432$	−15.0146	−0.722390
$433$	−16.6114	−0.798292	−0.399146	−	0.916887i	$-0.630693\pi$
$433$	−16.6114	−0.798292	−0.399146	+	0.916887i	$0.630693\pi$
$434$	8.45358	0.405785
$435$	0.683284	0.0327610
$436$	9.07230	0.434484
$437$	20.3396	0.972976
$438$	−1.06903	−0.0510805
$439$	−21.4863	−1.02548	−0.512742	−	0.858542i	$-0.671370\pi$
$439$	−21.4863	−1.02548	−0.512742	+	0.858542i	$0.671370\pi$
$440$	−4.72300	−0.225160
$441$	−0.724212	−0.0344863
$442$	−3.00403	−0.142887
$443$	−19.6047	−0.931447	−0.465724	−	0.884930i	$-0.654206\pi$
$443$	−19.6047	−0.931447	−0.465724	+	0.884930i	$0.654206\pi$
$444$	7.31915	0.347351
$445$	0.217770	0.0103233
$446$	−1.86553	−0.0883356
$447$	−5.33866	−0.252510
$448$	−12.3041	−0.581314
$449$	−35.1455	−1.65862	−0.829310	−	0.558789i	$-0.811266\pi$
$449$	−35.1455	−1.65862	−0.829310	+	0.558789i	$0.811266\pi$
$450$	0.189294	0.00892342
$451$	8.43843	0.397350
$452$	−0.189928	−0.00893344
$453$	−6.64728	−0.312316
$454$	10.7764	0.505762
$455$	18.1653	0.851605
$456$	−11.1679	−0.522987
$457$	−11.8432	−0.554002	−0.277001	−	0.960870i	$-0.589341\pi$
$457$	−11.8432	−0.554002	−0.277001	+	0.960870i	$0.589341\pi$
$458$	1.77483	0.0829325
$459$	12.6538	0.590627
$460$	−11.0220	−0.513902
$461$	17.1286	0.797756	0.398878	−	0.917004i	$-0.369400\pi$
$461$	17.1286	0.797756	0.398878	+	0.917004i	$0.369400\pi$
$462$	−1.38262	−0.0643251
$463$	−6.92218	−0.321701	−0.160850	−	0.986979i	$-0.551424\pi$
$463$	−6.92218	−0.321701	−0.160850	+	0.986979i	$0.551424\pi$
$464$	−0.975001	−0.0452633
$465$	17.2761	0.801158
$466$	4.14123	0.191839
$467$	−32.6395	−1.51038	−0.755188	−	0.655508i	$-0.772455\pi$
$467$	−32.6395	−1.51038	−0.755188	+	0.655508i	$0.772455\pi$
$468$	−11.3480	−0.524560
$469$	27.3792	1.26425
$470$	6.88202	0.317444
$471$	10.0563	0.463372
$472$	0.327653	0.0150814
$473$	0.626709	0.0288161
$474$	5.97143	0.274277
$475$	−1.79250	−0.0822454
$476$	13.0732	0.599208
$477$	−15.2333	−0.697486
$478$	11.1045	0.507907
$479$	8.78005	0.401171	0.200585	−	0.979676i	$-0.435716\pi$
$479$	8.78005	0.401171	0.200585	+	0.979676i	$0.435716\pi$
$480$	9.19888	0.419869
$481$	12.2302	0.557647
$482$	4.19439	0.191049
$483$	−6.72213	−0.305868
$484$	16.8483	0.765833
$485$	21.2145	0.963301
$486$	−6.32957	−0.287115
$487$	−23.1617	−1.04956	−0.524779	−	0.851238i	$-0.675852\pi$
$487$	−23.1617	−1.04956	−0.524779	+	0.851238i	$0.675852\pi$
$488$	10.9641	0.496323
$489$	−4.50709	−0.203818
$490$	0.309774	0.0139942
$491$	8.15363	0.367968	0.183984	−	0.982929i	$-0.441100\pi$
$491$	8.15363	0.367968	0.183984	+	0.982929i	$0.441100\pi$
$492$	−10.8127	−0.487474
$493$	0.821696	0.0370073
$494$	−8.95738	−0.403012
$495$	6.56554	0.295099
$496$	−24.6518	−1.10690
$497$	−44.7426	−2.00698
$498$	−4.67035	−0.209283
$499$	30.6993	1.37429	0.687144	−	0.726521i	$-0.258864\pi$
$499$	30.6993	1.37429	0.687144	+	0.726521i	$0.258864\pi$
$500$	−20.1384	−0.900615
$501$	14.6929	0.656428
$502$	1.34302	0.0599419
$503$	−1.00000	−0.0445878
$503$	−1.00000	−0.0445878
$504$	−8.57634	−0.382020
$505$	−20.0731	−0.893239
$506$	1.40181	0.0623180
$507$	−4.19023	−0.186095
$508$	−27.2637	−1.20963
$509$	−6.39080	−0.283267	−0.141634	−	0.989919i	$-0.545235\pi$
$509$	−6.39080	−0.283267	−0.141634	+	0.989919i	$0.545235\pi$
$510$	−2.22704	−0.0986149
$511$	7.77394	0.343899
$512$	−22.4816	−0.993557
$513$	37.7309	1.66586
$514$	4.41414	0.194699
$515$	−3.48700	−0.153655
$516$	−0.803041	−0.0353519
$517$	10.5003	0.461805
$518$	4.43662	0.194934
$519$	−17.1041	−0.750787
$520$	10.1126	0.443465
$521$	−11.2745	−0.493944	−0.246972	−	0.969023i	$-0.579436\pi$
$521$	−11.2745	−0.493944	−0.246972	+	0.969023i	$0.579436\pi$
$522$	−0.258743	−0.0113249
$523$	18.6154	0.813993	0.406996	−	0.913430i	$-0.366576\pi$
$523$	18.6154	0.813993	0.406996	+	0.913430i	$0.366576\pi$
$524$	−5.56872	−0.243271
$525$	0.592410	0.0258549
$526$	−0.168360	−0.00734085
$527$	20.7756	0.905001
$528$	4.03189	0.175466
$529$	−16.1846	−0.703676
$530$	6.51589	0.283032
$531$	−0.455477	−0.0197660
$532$	38.9815	1.69006
$533$	−18.0678	−0.782604
$534$	0.0354894	0.00153578
$535$	40.3320	1.74370
$536$	15.2419	0.658349
$537$	21.5086	0.928163
$538$	−5.97527	−0.257612
$539$	0.472642	0.0203581
$540$	−20.4462	−0.879866
$541$	−36.6446	−1.57547	−0.787736	−	0.616013i	$-0.788747\pi$
$541$	−36.6446	−1.57547	−0.787736	+	0.616013i	$0.788747\pi$
$542$	−6.97678	−0.299678
$543$	2.83105	0.121492
$544$	11.0623	0.474291
$545$	11.2386	0.481409
$546$	2.96036	0.126692
$547$	19.4186	0.830280	0.415140	−	0.909758i	$-0.363733\pi$
$547$	19.4186	0.830280	0.415140	+	0.909758i	$0.363733\pi$
$548$	−0.683413	−0.0291939
$549$	−15.2415	−0.650490
$550$	−0.123539	−0.00526772
$551$	2.45013	0.104379
$552$	−3.74218	−0.159278
$553$	−43.4238	−1.84657
$554$	−5.95808	−0.253135
$555$	9.06684	0.384866
$556$	−24.1737	−1.02519
$557$	−35.6561	−1.51080	−0.755398	−	0.655266i	$-0.772556\pi$
$557$	−35.6561	−1.51080	−0.755398	+	0.655266i	$0.772556\pi$
$558$	−6.54201	−0.276945
$559$	−1.34187	−0.0567549
$560$	−19.2163	−0.812039
$561$	−3.39793	−0.143461
$562$	−7.88041	−0.332415
$563$	−34.0879	−1.43663	−0.718316	−	0.695717i	$-0.755087\pi$
$563$	−34.0879	−1.43663	−0.718316	+	0.695717i	$0.755087\pi$
$564$	−13.4547	−0.566547
$565$	−0.235279	−0.00989827
$566$	0.641373	0.0269589
$567$	4.58316	0.192475
$568$	−24.9080	−1.04512
$569$	13.0323	0.546342	0.273171	−	0.961965i	$-0.411927\pi$
$569$	13.0323	0.546342	0.273171	+	0.961965i	$0.411927\pi$
$570$	−6.64056	−0.278143
$571$	28.5710	1.19566	0.597829	−	0.801624i	$-0.296030\pi$
$571$	28.5710	1.19566	0.597829	+	0.801624i	$0.296030\pi$
$572$	7.40602	0.309661
$573$	3.89114	0.162555
$574$	−6.55428	−0.273570
$575$	−0.600634	−0.0250482
$576$	9.52183	0.396743
$577$	40.1508	1.67150	0.835750	−	0.549110i	$-0.185033\pi$
$577$	40.1508	1.67150	0.835750	+	0.549110i	$0.185033\pi$
$578$	3.99066	0.165990
$579$	−20.1137	−0.835899
$580$	−1.32771	−0.0551304
$581$	33.9624	1.40900
$582$	3.45728	0.143309
$583$	9.94172	0.411744
$584$	4.32772	0.179082
$585$	−14.0577	−0.581214
$586$	3.99707	0.165118
$587$	−1.26390	−0.0521666	−0.0260833	−	0.999660i	$-0.508304\pi$
$587$	−1.26390	−0.0521666	−0.0260833	+	0.999660i	$0.508304\pi$
$588$	−0.605626	−0.0249756
$589$	61.9486	2.55255
$590$	0.194825	0.00802083
$591$	17.5895	0.723535
$592$	−12.9378	−0.531739
$593$	0.473003	0.0194239	0.00971196	−	0.999953i	$-0.496909\pi$
$593$	0.473003	0.0194239	0.00971196	+	0.999953i	$0.496909\pi$
$594$	2.60042	0.106696
$595$	16.1948	0.663924
$596$	10.3737	0.424925
$597$	−1.48886	−0.0609350
$598$	−3.00146	−0.122739
$599$	28.8689	1.17955	0.589775	−	0.807568i	$-0.299217\pi$
$599$	28.8689	1.17955	0.589775	+	0.807568i	$0.299217\pi$
$600$	0.329792	0.0134637
$601$	8.88531	0.362439	0.181220	−	0.983443i	$-0.441996\pi$
$601$	8.88531	0.362439	0.181220	+	0.983443i	$0.441996\pi$
$602$	−0.486776	−0.0198395
$603$	−21.1881	−0.862845
$604$	12.9166	0.525568
$605$	20.8714	0.848544
$606$	−3.27126	−0.132886
$607$	28.6612	1.16332	0.581662	−	0.813431i	$-0.302403\pi$
$607$	28.6612	1.16332	0.581662	+	0.813431i	$0.302403\pi$
$608$	32.9854	1.33773
$609$	−0.809753	−0.0328128
$610$	6.51937	0.263962
$611$	−22.4826	−0.909550
$612$	−10.1170	−0.408955
$613$	46.9961	1.89815	0.949077	−	0.315043i	$-0.102019\pi$
$613$	46.9961	1.89815	0.949077	+	0.315043i	$0.102019\pi$
$614$	6.42099	0.259130
$615$	−13.3946	−0.540122
$616$	5.59717	0.225516
$617$	−24.3030	−0.978401	−0.489201	−	0.872171i	$-0.662711\pi$
$617$	−24.3030	−0.978401	−0.489201	+	0.872171i	$0.662711\pi$
$618$	−0.568268	−0.0228591
$619$	39.4552	1.58584	0.792920	−	0.609326i	$-0.208560\pi$
$619$	39.4552	1.58584	0.792920	+	0.609326i	$0.208560\pi$
$620$	−33.5698	−1.34819
$621$	12.6429	0.507344
$622$	−2.74176	−0.109934
$623$	−0.258077	−0.0103396
$624$	−8.63282	−0.345589
$625$	−26.0974	−1.04390
$626$	−0.872613	−0.0348766
$627$	−10.1319	−0.404630
$628$	−19.5408	−0.779765
$629$	10.9035	0.434750
$630$	−5.09957	−0.203172
$631$	34.7457	1.38320	0.691602	−	0.722279i	$-0.256905\pi$
$631$	34.7457	1.38320	0.691602	+	0.722279i	$0.256905\pi$
$632$	−24.1738	−0.961583
$633$	−21.7080	−0.862814
$634$	−1.37177	−0.0544798
$635$	−33.7738	−1.34027
$636$	−12.7389	−0.505132
$637$	−1.01199	−0.0400965
$638$	0.168863	0.00668535
$639$	34.6251	1.36975
$640$	−23.4375	−0.926449
$641$	−42.3173	−1.67143	−0.835716	−	0.549163i	$-0.814947\pi$
$641$	−42.3173	−1.67143	−0.835716	+	0.549163i	$0.814947\pi$
$642$	6.57282	0.259408
$643$	−31.5672	−1.24489	−0.622444	−	0.782664i	$-0.713860\pi$
$643$	−31.5672	−1.24489	−0.622444	+	0.782664i	$0.713860\pi$
$644$	13.0620	0.514716
$645$	−0.994794	−0.0391700
$646$	−7.98572	−0.314194
$647$	−45.6664	−1.79533	−0.897667	−	0.440675i	$-0.854739\pi$
$647$	−45.6664	−1.79533	−0.897667	+	0.440675i	$0.854739\pi$
$648$	2.55142	0.100229
$649$	0.297258	0.0116684
$650$	0.264514	0.0103751
$651$	−20.4737	−0.802426
$652$	8.75790	0.342986
$653$	7.15705	0.280077	0.140039	−	0.990146i	$-0.455277\pi$
$653$	7.15705	0.280077	0.140039	+	0.990146i	$0.455277\pi$
$654$	1.83153	0.0716185
$655$	−6.89844	−0.269545
$656$	19.1132	0.746244
$657$	−6.01605	−0.234708
$658$	−8.15581	−0.317946
$659$	12.1603	0.473696	0.236848	−	0.971547i	$-0.423886\pi$
$659$	12.1603	0.473696	0.236848	+	0.971547i	$0.423886\pi$
$660$	5.49046	0.213716
$661$	−15.2194	−0.591968	−0.295984	−	0.955193i	$-0.595647\pi$
$661$	−15.2194	−0.591968	−0.295984	+	0.955193i	$0.595647\pi$
$662$	5.43917	0.211400
$663$	7.27543	0.282554
$664$	18.9067	0.733724
$665$	48.2896	1.87259
$666$	−3.43338	−0.133041
$667$	0.820994	0.0317890
$668$	−28.5502	−1.10464
$669$	4.51812	0.174681
$670$	9.06297	0.350133
$671$	9.94702	0.384001
$672$	−10.9015	−0.420534
$673$	34.9359	1.34668	0.673340	−	0.739333i	$-0.264859\pi$
$673$	34.9359	1.34668	0.673340	+	0.739333i	$0.264859\pi$
$674$	12.9555	0.499028
$675$	−1.11420	−0.0428856
$676$	8.14219	0.313161
$677$	−17.6078	−0.676721	−0.338361	−	0.941016i	$-0.609872\pi$
$677$	−17.6078	−0.676721	−0.338361	+	0.941016i	$0.609872\pi$
$678$	−0.0383429	−0.00147255
$679$	−25.1411	−0.964826
$680$	9.01560	0.345732
$681$	−26.0993	−1.00013
$682$	4.26951	0.163488
$683$	−43.5075	−1.66477	−0.832385	−	0.554198i	$-0.813025\pi$
$683$	−43.5075	−1.66477	−0.832385	+	0.554198i	$0.813025\pi$
$684$	−30.1668	−1.15346
$685$	−0.846600	−0.0323469
$686$	7.07512	0.270129
$687$	−4.29846	−0.163996
$688$	1.41950	0.0541181
$689$	−21.2865	−0.810953
$690$	−2.22513	−0.0847094
$691$	−2.05256	−0.0780829	−0.0390415	−	0.999238i	$-0.512430\pi$
$691$	−2.05256	−0.0780829	−0.0390415	+	0.999238i	$0.512430\pi$
$692$	33.2356	1.26343
$693$	−7.78074	−0.295566
$694$	0.163907	0.00622184
$695$	−29.9459	−1.13591
$696$	−0.450786	−0.0170870
$697$	−16.1079	−0.610130
$698$	3.40741	0.128972
$699$	−10.0296	−0.379355
$700$	−1.15113	−0.0435088
$701$	−9.44349	−0.356676	−0.178338	−	0.983969i	$-0.557072\pi$
$701$	−9.44349	−0.356676	−0.178338	+	0.983969i	$0.557072\pi$
$702$	−5.56784	−0.210145
$703$	32.5119	1.22621
$704$	−6.21422	−0.234207
$705$	−16.6675	−0.627735
$706$	3.56814	0.134289
$707$	23.7883	0.894653
$708$	−0.380895	−0.0143149
$709$	15.9123	0.597598	0.298799	−	0.954316i	$-0.403414\pi$
$709$	15.9123	0.597598	0.298799	+	0.954316i	$0.403414\pi$
$710$	−14.8105	−0.555829
$711$	33.6045	1.26027
$712$	−0.143670	−0.00538426
$713$	20.7579	0.777389
$714$	2.63924	0.0987710
$715$	9.17446	0.343105
$716$	−41.7941	−1.56192
$717$	−26.8938	−1.00437
$718$	−2.16540	−0.0808119
$719$	24.9061	0.928842	0.464421	−	0.885615i	$-0.346263\pi$
$719$	24.9061	0.928842	0.464421	+	0.885615i	$0.346263\pi$
$720$	14.8710	0.554211
$721$	4.13240	0.153899
$722$	−16.3584	−0.608795
$723$	−10.1584	−0.377794
$724$	−5.50112	−0.204448
$725$	−0.0723528	−0.00268712
$726$	3.40137	0.126237
$727$	11.5573	0.428636	0.214318	−	0.976764i	$-0.431247\pi$
$727$	11.5573	0.428636	0.214318	+	0.976764i	$0.431247\pi$
$728$	−11.9843	−0.444167
$729$	10.2563	0.379865
$730$	2.57330	0.0952421
$731$	−1.19631	−0.0442470
$732$	−12.7457	−0.471096
$733$	11.9918	0.442926	0.221463	−	0.975169i	$-0.428917\pi$
$733$	11.9918	0.442926	0.221463	+	0.975169i	$0.428917\pi$
$734$	−6.41928	−0.236940
$735$	−0.750240	−0.0276730
$736$	11.0528	0.407412
$737$	13.8280	0.509359
$738$	5.07219	0.186710
$739$	48.3255	1.77768	0.888840	−	0.458217i	$-0.151512\pi$
$739$	48.3255	1.77768	0.888840	+	0.458217i	$0.151512\pi$
$740$	−17.6181	−0.647654
$741$	21.6938	0.796942
$742$	−7.72191	−0.283480
$743$	40.3146	1.47900	0.739499	−	0.673158i	$-0.235063\pi$
$743$	40.3146	1.47900	0.739499	+	0.673158i	$0.235063\pi$
$744$	−11.3976	−0.417856
$745$	12.8508	0.470817
$746$	9.24693	0.338554
$747$	−26.2826	−0.961632
$748$	6.60265	0.241417
$749$	−47.7970	−1.74646
$750$	−4.06557	−0.148453
$751$	−48.6091	−1.77377	−0.886885	−	0.461990i	$-0.847136\pi$
$751$	−48.6091	−1.77377	−0.886885	+	0.461990i	$0.847136\pi$
$752$	23.7834	0.867292
$753$	−3.25265	−0.118533
$754$	−0.361558	−0.0131672
$755$	16.0008	0.582330
$756$	24.2306	0.881258
$757$	−44.8319	−1.62944	−0.814721	−	0.579853i	$-0.803110\pi$
$757$	−44.8319	−1.62944	−0.814721	+	0.579853i	$0.803110\pi$
$758$	8.95611	0.325301
$759$	−3.39503	−0.123232
$760$	26.8826	0.975136
$761$	−31.4812	−1.14119	−0.570596	−	0.821231i	$-0.693288\pi$
$761$	−31.4812	−1.14119	−0.570596	+	0.821231i	$0.693288\pi$
$762$	−5.50405	−0.199391
$763$	−13.3188	−0.482171
$764$	−7.56101	−0.273548
$765$	−12.5328	−0.453123
$766$	−8.56189	−0.309353
$767$	−0.636468	−0.0229815
$768$	4.80686	0.173453
$769$	30.6134	1.10395	0.551974	−	0.833861i	$-0.313875\pi$
$769$	30.6134	1.10395	0.551974	+	0.833861i	$0.313875\pi$
$770$	3.32813	0.119937
$771$	−10.6906	−0.385011
$772$	39.0837	1.40665
$773$	25.8605	0.930136	0.465068	−	0.885275i	$-0.346030\pi$
$773$	25.8605	0.930136	0.465068	+	0.885275i	$0.346030\pi$
$774$	0.376703	0.0135403
$775$	−1.82936	−0.0657125
$776$	−13.9959	−0.502424
$777$	−10.7450	−0.385475
$778$	−11.6690	−0.418352
$779$	−48.0304	−1.72087
$780$	−11.7558	−0.420925
$781$	−22.5974	−0.808598
$782$	−2.67588	−0.0956891
$783$	1.52298	0.0544268
$784$	1.07054	0.0382336
$785$	−24.2069	−0.863981
$786$	−1.12422	−0.0400997
$787$	31.7233	1.13081	0.565406	−	0.824813i	$-0.308719\pi$
$787$	31.7233	1.13081	0.565406	+	0.824813i	$0.308719\pi$
$788$	−34.1788	−1.21757
$789$	0.407750	0.0145163
$790$	−14.3740	−0.511403
$791$	0.278827	0.00991394
$792$	−4.33150	−0.153913
$793$	−21.2979	−0.756311
$794$	−11.2021	−0.397548
$795$	−15.7808	−0.559687
$796$	2.89306	0.102542
$797$	−55.1753	−1.95441	−0.977205	−	0.212296i	$-0.931906\pi$
$797$	−55.1753	−1.95441	−0.977205	+	0.212296i	$0.931906\pi$
$798$	7.86965	0.278583
$799$	−20.0438	−0.709099
$800$	−0.974066	−0.0344384
$801$	0.199719	0.00705671
$802$	−5.49078	−0.193886
$803$	3.92625	0.138554
$804$	−17.7186	−0.624887
$805$	16.1810	0.570306
$806$	−9.14158	−0.321999
$807$	14.4715	0.509420
$808$	13.2429	0.465882
$809$	−6.04923	−0.212680	−0.106340	−	0.994330i	$-0.533913\pi$
$809$	−6.04923	−0.212680	−0.106340	+	0.994330i	$0.533913\pi$
$810$	1.51710	0.0533055
$811$	−3.97693	−0.139649	−0.0698244	−	0.997559i	$-0.522244\pi$
$811$	−3.97693	−0.139649	−0.0698244	+	0.997559i	$0.522244\pi$
$812$	1.57346	0.0552176
$813$	16.8970	0.592604
$814$	2.24073	0.0785374
$815$	10.8491	0.380029
$816$	−7.69637	−0.269427
$817$	−3.56714	−0.124798
$818$	7.15641	0.250218
$819$	16.6596	0.582134
$820$	26.0275	0.908920
$821$	16.5562	0.577815	0.288907	−	0.957357i	$-0.406708\pi$
$821$	16.5562	0.577815	0.288907	+	0.957357i	$0.406708\pi$
$822$	−0.137968	−0.00481220
$823$	−29.9588	−1.04430	−0.522150	−	0.852854i	$-0.674870\pi$
$823$	−29.9588	−1.04430	−0.522150	+	0.852854i	$0.674870\pi$
$824$	2.30049	0.0801413
$825$	0.299198	0.0104168
$826$	−0.230885	−0.00803353
$827$	−39.4061	−1.37029	−0.685143	−	0.728409i	$-0.740260\pi$
$827$	−39.4061	−1.37029	−0.685143	+	0.728409i	$0.740260\pi$
$828$	−10.1084	−0.351290
$829$	6.63817	0.230553	0.115277	−	0.993333i	$-0.463225\pi$
$829$	6.63817	0.230553	0.115277	+	0.993333i	$0.463225\pi$
$830$	11.2421	0.390220
$831$	14.4298	0.500565
$832$	13.3055	0.461285
$833$	−0.902214	−0.0312599
$834$	−4.88022	−0.168988
$835$	−35.3675	−1.22394
$836$	19.6877	0.680914
$837$	38.5068	1.33099
$838$	−3.83906	−0.132618
$839$	−55.4839	−1.91552	−0.957759	−	0.287574i	$-0.907151\pi$
$839$	−55.4839	−1.91552	−0.957759	+	0.287574i	$0.907151\pi$
$840$	−8.88456	−0.306546
$841$	−28.9011	−0.996590
$842$	−0.889068	−0.0306393
$843$	19.0855	0.657340
$844$	42.1815	1.45195
$845$	10.0864	0.346983
$846$	6.31157	0.216996
$847$	−24.7345	−0.849887
$848$	22.5181	0.773276
$849$	−1.55334	−0.0533103
$850$	0.235820	0.00808857
$851$	10.8942	0.373447
$852$	28.9554	0.991997
$853$	−23.3264	−0.798680	−0.399340	−	0.916803i	$-0.630761\pi$
$853$	−23.3264	−0.798680	−0.399340	+	0.916803i	$0.630761\pi$
$854$	−7.72603	−0.264379
$855$	−37.3701	−1.27803
$856$	−26.6084	−0.909456
$857$	20.5822	0.703075	0.351537	−	0.936174i	$-0.385659\pi$
$857$	20.5822	0.703075	0.351537	+	0.936174i	$0.385659\pi$
$858$	1.49514	0.0510433
$859$	−45.7526	−1.56106	−0.780529	−	0.625120i	$-0.785050\pi$
$859$	−45.7526	−1.56106	−0.780529	+	0.625120i	$0.785050\pi$
$860$	1.93302	0.0659155
$861$	15.8738	0.540977
$862$	−1.68600	−0.0574253
$863$	10.0848	0.343290	0.171645	−	0.985159i	$-0.445092\pi$
$863$	10.0848	0.343290	0.171645	+	0.985159i	$0.445092\pi$
$864$	20.5035	0.697542
$865$	41.1717	1.39988
$866$	6.51638	0.221435
$867$	−9.66495	−0.328239
$868$	39.7831	1.35033
$869$	−21.9313	−0.743968
$870$	−0.268041	−0.00908745
$871$	−29.6075	−1.00321
$872$	−7.41449	−0.251086
$873$	19.4560	0.658487
$874$	−7.97890	−0.269890
$875$	29.5645	0.999462
$876$	−5.03095	−0.169980
$877$	3.30564	0.111624	0.0558118	−	0.998441i	$-0.482225\pi$
$877$	3.30564	0.111624	0.0558118	+	0.998441i	$0.482225\pi$
$878$	8.42872	0.284456
$879$	−9.68048	−0.326515
$880$	−9.70527	−0.327165
$881$	8.30907	0.279940	0.139970	−	0.990156i	$-0.455299\pi$
$881$	8.30907	0.279940	0.139970	+	0.990156i	$0.455299\pi$
$882$	0.284097	0.00956603
$883$	2.65895	0.0894807	0.0447403	−	0.998999i	$-0.485754\pi$
$883$	2.65895	0.0894807	0.0447403	+	0.998999i	$0.485754\pi$
$884$	−14.1372	−0.475484
$885$	−0.471846	−0.0158609
$886$	7.69060	0.258371
$887$	−21.5846	−0.724740	−0.362370	−	0.932034i	$-0.618032\pi$
$887$	−21.5846	−0.724740	−0.362370	+	0.932034i	$0.618032\pi$
$888$	−5.98170	−0.200733
$889$	40.0250	1.34240
$890$	−0.0854276	−0.00286354
$891$	2.31474	0.0775466
$892$	−8.77932	−0.293954
$893$	−59.7665	−2.00001
$894$	2.09427	0.0700428
$895$	−51.7738	−1.73061
$896$	27.7755	0.927915
$897$	7.26921	0.242712
$898$	13.7870	0.460079
$899$	2.50051	0.0833967
$900$	0.890832	0.0296944
$901$	−18.9775	−0.632231
$902$	−3.31026	−0.110220
$903$	1.17892	0.0392320
$904$	0.155222	0.00516259
$905$	−6.81470	−0.226528
$906$	2.60762	0.0866323
$907$	−5.95616	−0.197771	−0.0988855	−	0.995099i	$-0.531528\pi$
$907$	−5.95616	−0.197771	−0.0988855	+	0.995099i	$0.531528\pi$
$908$	50.7145	1.68302
$909$	−18.4092	−0.610594
$910$	−7.12597	−0.236224
$911$	14.9730	0.496079	0.248040	−	0.968750i	$-0.420214\pi$
$911$	14.9730	0.496079	0.248040	+	0.968750i	$0.420214\pi$
$912$	−22.9490	−0.759916
$913$	17.1528	0.567676
$914$	4.64590	0.153673
$915$	−15.7892	−0.521975
$916$	8.35249	0.275974
$917$	8.17527	0.269971
$918$	−4.96386	−0.163832
$919$	−21.4164	−0.706463	−0.353232	−	0.935536i	$-0.614917\pi$
$919$	−21.4164	−0.706463	−0.353232	+	0.935536i	$0.614917\pi$
$920$	9.00790	0.296982
$921$	−15.5509	−0.512421
$922$	−6.71925	−0.221287
$923$	48.3840	1.59258
$924$	−6.50668	−0.214054
$925$	−0.960085	−0.0315674
$926$	2.71546	0.0892354
$927$	−3.19796	−0.105035
$928$	1.33143	0.0437064
$929$	−51.4153	−1.68688	−0.843441	−	0.537221i	$-0.819474\pi$
$929$	−51.4153	−1.68688	−0.843441	+	0.537221i	$0.819474\pi$
$930$	−6.77712	−0.222230
$931$	−2.69021	−0.0881682
$932$	19.4889	0.638381
$933$	6.64024	0.217392
$934$	12.8039	0.418958
$935$	8.17925	0.267490
$936$	9.27433	0.303141
$937$	−41.9350	−1.36996	−0.684979	−	0.728563i	$-0.740188\pi$
$937$	−41.9350	−1.36996	−0.684979	+	0.728563i	$0.740188\pi$
$938$	−10.7404	−0.350687
$939$	2.11337	0.0689674
$940$	32.3873	1.05636
$941$	−36.8467	−1.20117	−0.600585	−	0.799561i	$-0.705065\pi$
$941$	−36.8467	−1.20117	−0.600585	+	0.799561i	$0.705065\pi$
$942$	−3.94494	−0.128533
$943$	−16.0941	−0.524097
$944$	0.673293	0.0219138
$945$	30.0165	0.976436
$946$	−0.245848	−0.00799320
$947$	2.12177	0.0689481	0.0344741	−	0.999406i	$-0.489024\pi$
$947$	2.12177	0.0689481	0.0344741	+	0.999406i	$0.489024\pi$
$948$	28.1019	0.912708
$949$	−8.40663	−0.272891
$950$	0.703167	0.0228138
$951$	3.32227	0.107732
$952$	−10.6843	−0.346280
$953$	13.5643	0.439391	0.219695	−	0.975569i	$-0.429494\pi$
$953$	13.5643	0.439391	0.219695	+	0.975569i	$0.429494\pi$
$954$	5.97579	0.193473
$955$	−9.36645	−0.303091
$956$	52.2584	1.69016
$957$	−0.408968	−0.0132201
$958$	−3.44427	−0.111279
$959$	1.00330	0.0323981
$960$	9.86403	0.318360
$961$	32.2225	1.03944
$962$	−4.79769	−0.154684
$963$	36.9889	1.19195
$964$	19.7391	0.635754
$965$	48.4163	1.55858
$966$	2.63698	0.0848435
$967$	5.95719	0.191570	0.0957851	−	0.995402i	$-0.469464\pi$
$967$	5.95719	0.191570	0.0957851	+	0.995402i	$0.469464\pi$
$968$	−13.7696	−0.442571
$969$	19.3406	0.621308
$970$	−8.32211	−0.267207
$971$	12.1772	0.390785	0.195392	−	0.980725i	$-0.437402\pi$
$971$	12.1772	0.390785	0.195392	+	0.980725i	$0.437402\pi$
$972$	−29.7874	−0.955431
$973$	35.4886	1.13771
$974$	9.08597	0.291133
$975$	−0.640624	−0.0205164
$976$	22.5301	0.721172
$977$	7.69439	0.246165	0.123083	−	0.992396i	$-0.460722\pi$
$977$	7.69439	0.246165	0.123083	+	0.992396i	$0.460722\pi$
$978$	1.76806	0.0565363
$979$	−0.130342	−0.00416576
$980$	1.45782	0.0465683
$981$	10.3070	0.329078
$982$	−3.19854	−0.102069
$983$	−12.2144	−0.389578	−0.194789	−	0.980845i	$-0.562402\pi$
$983$	−12.2144	−0.389578	−0.194789	+	0.980845i	$0.562402\pi$
$984$	8.83686	0.281709
$985$	−42.3401	−1.34907
$986$	−0.322338	−0.0102653
$987$	19.7525	0.628729
$988$	−42.1540	−1.34110
$989$	−1.19529	−0.0380079
$990$	−2.57555	−0.0818564
$991$	2.35228	0.0747227	0.0373613	−	0.999302i	$-0.488105\pi$
$991$	2.35228	0.0747227	0.0373613	+	0.999302i	$0.488105\pi$
$992$	33.6637	1.06882
$993$	−13.1731	−0.418036
$994$	17.5518	0.556709
$995$	3.58387	0.113616
$996$	−21.9790	−0.696431
$997$	19.2415	0.609384	0.304692	−	0.952451i	$-0.401446\pi$
$997$	19.2415	0.609384	0.304692	+	0.952451i	$0.401446\pi$
$998$	−12.0428	−0.381209
$999$	20.2092	0.639389

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.e.1.6	✓	10
3.2	odd	2		4527.2.a.k.1.5		10
4.3	odd	2		8048.2.a.p.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.e.1.6	✓	10	1.1	even	1	trivial
4527.2.a.k.1.5		10	3.2	odd	2
8048.2.a.p.1.2		10	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:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.a (trivial)

\(f(q)\)	\(=\)	\(q-0.392284 q^{2} +0.950069 q^{3} -1.84611 q^{4} -2.28693 q^{5} -0.372697 q^{6} +2.71022 q^{7} +1.50877 q^{8} -2.09737 q^{9} +O(q^{10})\)	\(q-0.392284 q^{2} +0.950069 q^{3} -1.84611 q^{4} -2.28693 q^{5} -0.372697 q^{6} +2.71022 q^{7} +1.50877 q^{8} -2.09737 q^{9} +0.897127 q^{10} +1.36880 q^{11} -1.75393 q^{12} -2.93079 q^{13} -1.06318 q^{14} -2.17275 q^{15} +3.10036 q^{16} -2.61287 q^{17} +0.822764 q^{18} -7.79104 q^{19} +4.22194 q^{20} +2.57490 q^{21} -0.536960 q^{22} -2.61064 q^{23} +1.43343 q^{24} +0.230071 q^{25} +1.14970 q^{26} -4.84285 q^{27} -5.00337 q^{28} -0.314480 q^{29} +0.852333 q^{30} -7.95126 q^{31} -4.23376 q^{32} +1.30046 q^{33} +1.02499 q^{34} -6.19810 q^{35} +3.87198 q^{36} -4.17299 q^{37} +3.05630 q^{38} -2.78446 q^{39} -3.45045 q^{40} +6.16482 q^{41} -1.01009 q^{42} +0.457851 q^{43} -2.52697 q^{44} +4.79655 q^{45} +1.02411 q^{46} +7.67118 q^{47} +2.94556 q^{48} +0.345296 q^{49} -0.0902533 q^{50} -2.48241 q^{51} +5.41058 q^{52} +7.26306 q^{53} +1.89977 q^{54} -3.13037 q^{55} +4.08909 q^{56} -7.40203 q^{57} +0.123365 q^{58} +0.217166 q^{59} +4.01114 q^{60} +7.26694 q^{61} +3.11915 q^{62} -5.68433 q^{63} -4.53989 q^{64} +6.70253 q^{65} -0.510149 q^{66} +10.1022 q^{67} +4.82366 q^{68} -2.48029 q^{69} +2.43141 q^{70} -16.5088 q^{71} -3.16444 q^{72} +2.86838 q^{73} +1.63699 q^{74} +0.218584 q^{75} +14.3831 q^{76} +3.70976 q^{77} +1.09230 q^{78} -16.0222 q^{79} -7.09033 q^{80} +1.69106 q^{81} -2.41836 q^{82} +12.5312 q^{83} -4.75355 q^{84} +5.97547 q^{85} -0.179608 q^{86} -0.298777 q^{87} +2.06521 q^{88} -0.0952234 q^{89} -1.88161 q^{90} -7.94310 q^{91} +4.81954 q^{92} -7.55424 q^{93} -3.00928 q^{94} +17.8176 q^{95} -4.02236 q^{96} -9.27640 q^{97} -0.135454 q^{98} -2.87089 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9} - 4 q^{10} - 3 q^{11} - 7 q^{12} - 18 q^{13} + q^{14} - 2 q^{15} - 4 q^{16} - 11 q^{17} - q^{18} - 3 q^{20} + q^{21} - 18 q^{22} - 2 q^{23} + 10 q^{24} - 27 q^{25} + 11 q^{26} - 2 q^{27} - 22 q^{28} - 9 q^{29} + 12 q^{30} - 22 q^{31} - 10 q^{32} - 10 q^{33} - 10 q^{34} - 6 q^{35} + 2 q^{36} - 35 q^{37} + 2 q^{38} + 8 q^{39} - 19 q^{40} - 4 q^{41} + 4 q^{42} - 20 q^{43} + 9 q^{44} + 2 q^{45} - q^{46} + 7 q^{47} - 27 q^{49} + 16 q^{50} + 9 q^{51} - 7 q^{52} - 24 q^{53} + 17 q^{54} - 11 q^{55} + 12 q^{56} - 23 q^{57} + 2 q^{58} + 17 q^{59} - 4 q^{61} + 8 q^{62} + 10 q^{63} + 3 q^{64} - 16 q^{65} + 46 q^{66} - 6 q^{67} + 28 q^{68} - 2 q^{69} + 26 q^{70} - q^{71} - q^{72} - 31 q^{73} + 11 q^{74} + 30 q^{75} + 20 q^{76} + 3 q^{77} + 11 q^{78} - 10 q^{79} + 24 q^{80} - 6 q^{81} - 9 q^{82} + 22 q^{83} + 22 q^{84} - 6 q^{85} + 38 q^{86} + 25 q^{87} - 3 q^{88} + q^{89} + 2 q^{90} + 10 q^{91} + 27 q^{92} - 6 q^{93} + 33 q^{94} + 39 q^{95} + 46 q^{96} - 57 q^{97} + 40 q^{98} + 35 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9 - 4 * q^10 - 3 * q^11 - 7 * q^12 - 18 * q^13 + q^14 - 2 * q^15 - 4 * q^16 - 11 * q^17 - q^18 - 3 * q^20 + q^21 - 18 * q^22 - 2 * q^23 + 10 * q^24 - 27 * q^25 + 11 * q^26 - 2 * q^27 - 22 * q^28 - 9 * q^29 + 12 * q^30 - 22 * q^31 - 10 * q^32 - 10 * q^33 - 10 * q^34 - 6 * q^35 + 2 * q^36 - 35 * q^37 + 2 * q^38 + 8 * q^39 - 19 * q^40 - 4 * q^41 + 4 * q^42 - 20 * q^43 + 9 * q^44 + 2 * q^45 - q^46 + 7 * q^47 - 27 * q^49 + 16 * q^50 + 9 * q^51 - 7 * q^52 - 24 * q^53 + 17 * q^54 - 11 * q^55 + 12 * q^56 - 23 * q^57 + 2 * q^58 + 17 * q^59 - 4 * q^61 + 8 * q^62 + 10 * q^63 + 3 * q^64 - 16 * q^65 + 46 * q^66 - 6 * q^67 + 28 * q^68 - 2 * q^69 + 26 * q^70 - q^71 - q^72 - 31 * q^73 + 11 * q^74 + 30 * q^75 + 20 * q^76 + 3 * q^77 + 11 * q^78 - 10 * q^79 + 24 * q^80 - 6 * q^81 - 9 * q^82 + 22 * q^83 + 22 * q^84 - 6 * q^85 + 38 * q^86 + 25 * q^87 - 3 * q^88 + q^89 + 2 * q^90 + 10 * q^91 + 27 * q^92 - 6 * q^93 + 33 * q^94 + 39 * q^95 + 46 * q^96 - 57 * q^97 + 40 * q^98 + 35 * q^99

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