LMFDB - Embedded newform 503.2.a.e.1.9

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			1.9
Root			$-1.40552$ 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)

$f(q)$	$=$	$q+1.36113 q^{2} -2.40552 q^{3} -0.147314 q^{4} +0.590303 q^{5} -3.27424 q^{6} +1.95900 q^{7} -2.92278 q^{8} +2.78655 q^{9} +O(q^{10})$	\(q+1.36113 q^{2} -2.40552 q^{3} -0.147314 q^{4} +0.590303 q^{5} -3.27424 q^{6} +1.95900 q^{7} -2.92278 q^{8} +2.78655 q^{9} +0.803481 q^{10} -1.52746 q^{11} +0.354366 q^{12} -4.67738 q^{13} +2.66646 q^{14} -1.41999 q^{15} -3.68367 q^{16} -3.04913 q^{17} +3.79286 q^{18} +0.338159 q^{19} -0.0869597 q^{20} -4.71242 q^{21} -2.07908 q^{22} -7.98874 q^{23} +7.03082 q^{24} -4.65154 q^{25} -6.36654 q^{26} +0.513468 q^{27} -0.288587 q^{28} +6.01794 q^{29} -1.93279 q^{30} -4.17447 q^{31} +0.831593 q^{32} +3.67434 q^{33} -4.15028 q^{34} +1.15640 q^{35} -0.410496 q^{36} -11.0654 q^{37} +0.460279 q^{38} +11.2515 q^{39} -1.72533 q^{40} -4.82359 q^{41} -6.41423 q^{42} +12.4475 q^{43} +0.225016 q^{44} +1.64491 q^{45} -10.8737 q^{46} +11.0094 q^{47} +8.86116 q^{48} -3.16233 q^{49} -6.33137 q^{50} +7.33476 q^{51} +0.689042 q^{52} -3.43684 q^{53} +0.698899 q^{54} -0.901664 q^{55} -5.72572 q^{56} -0.813449 q^{57} +8.19122 q^{58} +2.63490 q^{59} +0.209184 q^{60} +11.4908 q^{61} -5.68202 q^{62} +5.45884 q^{63} +8.49925 q^{64} -2.76107 q^{65} +5.00127 q^{66} -10.2554 q^{67} +0.449179 q^{68} +19.2171 q^{69} +1.57402 q^{70} +9.66931 q^{71} -8.14447 q^{72} -6.33688 q^{73} -15.0615 q^{74} +11.1894 q^{75} -0.0498154 q^{76} -2.99229 q^{77} +15.3149 q^{78} -0.667323 q^{79} -2.17448 q^{80} -9.59480 q^{81} -6.56556 q^{82} -2.26231 q^{83} +0.694203 q^{84} -1.79991 q^{85} +16.9427 q^{86} -14.4763 q^{87} +4.46443 q^{88} +2.21979 q^{89} +2.23894 q^{90} -9.16297 q^{91} +1.17685 q^{92} +10.0418 q^{93} +14.9853 q^{94} +0.199616 q^{95} -2.00042 q^{96} +14.2878 q^{97} -4.30435 q^{98} -4.25634 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.36113	0.962467	0.481234	−	0.876592i	$-0.340189\pi$
$2$	1.36113	0.962467	0.481234	+	0.876592i	$0.340189\pi$
$3$	−2.40552	−1.38883	−0.694415	−	0.719575i	$-0.744337\pi$
$3$	−2.40552	−1.38883	−0.694415	+	0.719575i	$0.744337\pi$
$4$	−0.147314	−0.0736568
$5$	0.590303	0.263991	0.131996	−	0.991250i	$-0.457861\pi$
$5$	0.590303	0.263991	0.131996	+	0.991250i	$0.457861\pi$
$6$	−3.27424	−1.33670
$7$	1.95900	0.740431	0.370216	−	0.928946i	$-0.379284\pi$
$7$	1.95900	0.740431	0.370216	+	0.928946i	$0.379284\pi$
$8$	−2.92278	−1.03336
$9$	2.78655	0.928849
$10$	0.803481	0.254083
$11$	−1.52746	−0.460546	−0.230273	−	0.973126i	$-0.573962\pi$
$11$	−1.52746	−0.460546	−0.230273	+	0.973126i	$0.573962\pi$
$12$	0.354366	0.102297
$13$	−4.67738	−1.29727	−0.648636	−	0.761099i	$-0.724660\pi$
$13$	−4.67738	−1.29727	−0.648636	+	0.761099i	$0.724660\pi$
$14$	2.66646	0.712641
$15$	−1.41999	−0.366639
$16$	−3.68367	−0.920918
$17$	−3.04913	−0.739523	−0.369761	−	0.929127i	$-0.620561\pi$
$17$	−3.04913	−0.739523	−0.369761	+	0.929127i	$0.620561\pi$
$18$	3.79286	0.893986
$19$	0.338159	0.0775789	0.0387895	−	0.999247i	$-0.487650\pi$
$19$	0.338159	0.0775789	0.0387895	+	0.999247i	$0.487650\pi$
$20$	−0.0869597	−0.0194448
$21$	−4.71242	−1.02833
$22$	−2.07908	−0.443261
$23$	−7.98874	−1.66577	−0.832884	−	0.553448i	$-0.813312\pi$
$23$	−7.98874	−1.66577	−0.832884	+	0.553448i	$0.813312\pi$
$24$	7.03082	1.43516
$25$	−4.65154	−0.930309
$26$	−6.36654	−1.24858
$27$	0.513468	0.0988170
$28$	−0.288587	−0.0545378
$29$	6.01794	1.11750	0.558751	−	0.829335i	$-0.311281\pi$
$29$	6.01794	1.11750	0.558751	+	0.829335i	$0.311281\pi$
$30$	−1.93279	−0.352878
$31$	−4.17447	−0.749758	−0.374879	−	0.927074i	$-0.622316\pi$
$31$	−4.17447	−0.749758	−0.374879	+	0.927074i	$0.622316\pi$
$32$	0.831593	0.147006
$33$	3.67434	0.639621
$34$	−4.15028	−0.711767
$35$	1.15640	0.195468
$36$	−0.410496	−0.0684160
$37$	−11.0654	−1.81914	−0.909569	−	0.415553i	$-0.863588\pi$
$37$	−11.0654	−1.81914	−0.909569	+	0.415553i	$0.863588\pi$
$38$	0.460279	0.0746672
$39$	11.2515	1.80169
$40$	−1.72533	−0.272798
$41$	−4.82359	−0.753319	−0.376659	−	0.926352i	$-0.622927\pi$
$41$	−4.82359	−0.753319	−0.376659	+	0.926352i	$0.622927\pi$
$42$	−6.41423	−0.989737
$43$	12.4475	1.89822	0.949111	−	0.314941i	$-0.101985\pi$
$43$	12.4475	1.89822	0.949111	+	0.314941i	$0.101985\pi$
$44$	0.225016	0.0339224
$45$	1.64491	0.245208
$46$	−10.8737	−1.60325
$47$	11.0094	1.60589	0.802945	−	0.596052i	$-0.203265\pi$
$47$	11.0094	1.60589	0.802945	+	0.596052i	$0.203265\pi$
$48$	8.86116	1.27900
$49$	−3.16233	−0.451761
$50$	−6.33137	−0.895391
$51$	7.33476	1.02707
$52$	0.689042	0.0955529
$53$	−3.43684	−0.472087	−0.236043	−	0.971743i	$-0.575851\pi$
$53$	−3.43684	−0.472087	−0.236043	+	0.971743i	$0.575851\pi$
$54$	0.698899	0.0951081
$55$	−0.901664	−0.121580
$56$	−5.72572	−0.765132
$57$	−0.813449	−0.107744
$58$	8.19122	1.07556
$59$	2.63490	0.343034	0.171517	−	0.985181i	$-0.445133\pi$
$59$	2.63490	0.343034	0.171517	+	0.985181i	$0.445133\pi$
$60$	0.209184	0.0270055
$61$	11.4908	1.47125	0.735625	−	0.677389i	$-0.236889\pi$
$61$	11.4908	1.47125	0.735625	+	0.677389i	$0.236889\pi$
$62$	−5.68202	−0.721617
$63$	5.45884	0.687749
$64$	8.49925	1.06241
$65$	−2.76107	−0.342469
$66$	5.00127	0.615614
$67$	−10.2554	−1.25289	−0.626445	−	0.779465i	$-0.715491\pi$
$67$	−10.2554	−1.25289	−0.626445	+	0.779465i	$0.715491\pi$
$68$	0.449179	0.0544709
$69$	19.2171	2.31347
$70$	1.57402	0.188131
$71$	9.66931	1.14754	0.573768	−	0.819018i	$-0.305481\pi$
$71$	9.66931	1.14754	0.573768	+	0.819018i	$0.305481\pi$
$72$	−8.14447	−0.959835
$73$	−6.33688	−0.741676	−0.370838	−	0.928698i	$-0.620929\pi$
$73$	−6.33688	−0.741676	−0.370838	+	0.928698i	$0.620929\pi$
$74$	−15.0615	−1.75086
$75$	11.1894	1.29204
$76$	−0.0498154	−0.00571422
$77$	−2.99229	−0.341003
$78$	15.3149	1.73407
$79$	−0.667323	−0.0750798	−0.0375399	−	0.999295i	$-0.511952\pi$
$79$	−0.667323	−0.0750798	−0.0375399	+	0.999295i	$0.511952\pi$
$80$	−2.17448	−0.243114
$81$	−9.59480	−1.06609
$82$	−6.56556	−0.725045
$83$	−2.26231	−0.248321	−0.124161	−	0.992262i	$-0.539624\pi$
$83$	−2.26231	−0.248321	−0.124161	+	0.992262i	$0.539624\pi$
$84$	0.694203	0.0757438
$85$	−1.79991	−0.195228
$86$	16.9427	1.82698
$87$	−14.4763	−1.55202
$88$	4.46443	0.475910
$89$	2.21979	0.235297	0.117649	−	0.993055i	$-0.462464\pi$
$89$	2.21979	0.235297	0.117649	+	0.993055i	$0.462464\pi$
$90$	2.23894	0.236005
$91$	−9.16297	−0.960541
$92$	1.17685	0.122695
$93$	10.0418	1.04129
$94$	14.9853	1.54562
$95$	0.199616	0.0204802
$96$	−2.00042	−0.204167
$97$	14.2878	1.45070	0.725352	−	0.688378i	$-0.241677\pi$
$97$	14.2878	1.45070	0.725352	+	0.688378i	$0.241677\pi$
$98$	−4.30435	−0.434806
$99$	−4.25634	−0.427778
$100$	0.685236	0.0685236
$101$	−0.629834	−0.0626708	−0.0313354	−	0.999509i	$-0.509976\pi$
$101$	−0.629834	−0.0626708	−0.0313354	+	0.999509i	$0.509976\pi$
$102$	9.98359	0.988523
$103$	−4.51410	−0.444788	−0.222394	−	0.974957i	$-0.571387\pi$
$103$	−4.51410	−0.444788	−0.222394	+	0.974957i	$0.571387\pi$
$104$	13.6710	1.34055
$105$	−2.78175	−0.271471
$106$	−4.67801	−0.454368
$107$	3.43562	0.332134	0.166067	−	0.986115i	$-0.446893\pi$
$107$	3.43562	0.332134	0.166067	+	0.986115i	$0.446893\pi$
$108$	−0.0756409	−0.00727855
$109$	9.90039	0.948285	0.474142	−	0.880448i	$-0.342758\pi$
$109$	9.90039	0.948285	0.474142	+	0.880448i	$0.342758\pi$
$110$	−1.22729	−0.117017
$111$	26.6180	2.52647
$112$	−7.21630	−0.681876
$113$	−9.47684	−0.891506	−0.445753	−	0.895156i	$-0.647064\pi$
$113$	−9.47684	−0.891506	−0.445753	+	0.895156i	$0.647064\pi$
$114$	−1.10721	−0.103700
$115$	−4.71578	−0.439748
$116$	−0.886524	−0.0823117
$117$	−13.0337	−1.20497
$118$	3.58645	0.330159
$119$	−5.97324	−0.547566
$120$	4.15031	0.378870
$121$	−8.66687	−0.787897
$122$	15.6406	1.41603
$123$	11.6033	1.04623
$124$	0.614957	0.0552248
$125$	−5.69733	−0.509585
$126$	7.43021	0.661936
$127$	−11.3574	−1.00781	−0.503904	−	0.863760i	$-0.668104\pi$
$127$	−11.3574	−1.00781	−0.503904	+	0.863760i	$0.668104\pi$
$128$	9.90544	0.875525
$129$	−29.9427	−2.63631
$130$	−3.75819	−0.329615
$131$	15.9119	1.39023	0.695113	−	0.718900i	$-0.255354\pi$
$131$	15.9119	1.39023	0.695113	+	0.718900i	$0.255354\pi$
$132$	−0.541281	−0.0471124
$133$	0.662452	0.0574419
$134$	−13.9589	−1.20587
$135$	0.303102	0.0260868
$136$	8.91195	0.764193
$137$	−15.0390	−1.28486	−0.642432	−	0.766343i	$-0.722075\pi$
$137$	−15.0390	−1.28486	−0.642432	+	0.766343i	$0.722075\pi$
$138$	26.1571	2.22664
$139$	−16.6486	−1.41212	−0.706059	−	0.708153i	$-0.749529\pi$
$139$	−16.6486	−1.41212	−0.706059	+	0.708153i	$0.749529\pi$
$140$	−0.170354	−0.0143975
$141$	−26.4835	−2.23031
$142$	13.1612	1.10447
$143$	7.14451	0.597454
$144$	−10.2647	−0.855393
$145$	3.55241	0.295011
$146$	−8.62534	−0.713838
$147$	7.60706	0.627420
$148$	1.63008	0.133992
$149$	−12.0657	−0.988463	−0.494232	−	0.869330i	$-0.664550\pi$
$149$	−12.0657	−0.988463	−0.494232	+	0.869330i	$0.664550\pi$
$150$	15.2303	1.24355
$151$	−16.4897	−1.34192	−0.670958	−	0.741495i	$-0.734117\pi$
$151$	−16.4897	−1.34192	−0.670958	+	0.741495i	$0.734117\pi$
$152$	−0.988364	−0.0801669
$153$	−8.49655	−0.686905
$154$	−4.07291	−0.328204
$155$	−2.46420	−0.197930
$156$	−1.65751	−0.132707
$157$	4.10607	0.327700	0.163850	−	0.986485i	$-0.447609\pi$
$157$	4.10607	0.327700	0.163850	+	0.986485i	$0.447609\pi$
$158$	−0.908317	−0.0722618
$159$	8.26741	0.655648
$160$	0.490892	0.0388084
$161$	−15.6499	−1.23339
$162$	−13.0598	−1.02608
$163$	21.2459	1.66411	0.832053	−	0.554696i	$-0.187165\pi$
$163$	21.2459	1.66411	0.832053	+	0.554696i	$0.187165\pi$
$164$	0.710581	0.0554871
$165$	2.16897	0.168854
$166$	−3.07931	−0.239001
$167$	−5.96545	−0.461620	−0.230810	−	0.972999i	$-0.574138\pi$
$167$	−5.96545	−0.461620	−0.230810	+	0.972999i	$0.574138\pi$
$168$	13.7734	1.06264
$169$	8.87787	0.682913
$170$	−2.44992	−0.187900
$171$	0.942295	0.0720591
$172$	−1.83368	−0.139817
$173$	−16.2621	−1.23638	−0.618192	−	0.786027i	$-0.712135\pi$
$173$	−16.2621	−1.23638	−0.618192	+	0.786027i	$0.712135\pi$
$174$	−19.7042	−1.49377
$175$	−9.11236	−0.688830
$176$	5.62666	0.424125
$177$	−6.33831	−0.476416
$178$	3.02143	0.226466
$179$	9.36724	0.700140	0.350070	−	0.936723i	$-0.386158\pi$
$179$	9.36724	0.700140	0.350070	+	0.936723i	$0.386158\pi$
$180$	−0.242317	−0.0180612
$181$	1.62885	0.121072	0.0605358	−	0.998166i	$-0.480719\pi$
$181$	1.62885	0.121072	0.0605358	+	0.998166i	$0.480719\pi$
$182$	−12.4720	−0.924489
$183$	−27.6415	−2.04332
$184$	23.3493	1.72134
$185$	−6.53193	−0.480237
$186$	13.6682	1.00220
$187$	4.65742	0.340585
$188$	−1.62184	−0.118285
$189$	1.00588	0.0731672
$190$	0.271704	0.0197115
$191$	−8.41952	−0.609215	−0.304607	−	0.952478i	$-0.598525\pi$
$191$	−8.41952	−0.609215	−0.304607	+	0.952478i	$0.598525\pi$
$192$	−20.4452	−1.47550
$193$	−24.9514	−1.79604	−0.898022	−	0.439950i	$-0.854996\pi$
$193$	−24.9514	−1.79604	−0.898022	+	0.439950i	$0.854996\pi$
$194$	19.4476	1.39625
$195$	6.64182	0.475631
$196$	0.465854	0.0332753
$197$	2.36559	0.168541	0.0842705	−	0.996443i	$-0.473144\pi$
$197$	2.36559	0.168541	0.0842705	+	0.996443i	$0.473144\pi$
$198$	−5.79345	−0.411722
$199$	11.7817	0.835180	0.417590	−	0.908636i	$-0.362875\pi$
$199$	11.7817	0.835180	0.417590	+	0.908636i	$0.362875\pi$
$200$	13.5954	0.961343
$201$	24.6695	1.74005
$202$	−0.857288	−0.0603186
$203$	11.7891	0.827434
$204$	−1.08051	−0.0756508
$205$	−2.84738	−0.198870
$206$	−6.14430	−0.428094
$207$	−22.2610	−1.54725
$208$	17.2299	1.19468
$209$	−0.516524	−0.0357287
$210$	−3.78634	−0.261282
$211$	−16.8124	−1.15742	−0.578708	−	0.815535i	$-0.696443\pi$
$211$	−16.8124	−1.15742	−0.578708	+	0.815535i	$0.696443\pi$
$212$	0.506294	0.0347724
$213$	−23.2597	−1.59373
$214$	4.67633	0.319668
$215$	7.34778	0.501115
$216$	−1.50076	−0.102114
$217$	−8.17778	−0.555144
$218$	13.4758	0.912693
$219$	15.2435	1.03006
$220$	0.132827	0.00895522
$221$	14.2619	0.959362
$222$	36.2307	2.43165
$223$	8.32490	0.557476	0.278738	−	0.960367i	$-0.410084\pi$
$223$	8.32490	0.557476	0.278738	+	0.960367i	$0.410084\pi$
$224$	1.62909	0.108848
$225$	−12.9617	−0.864116
$226$	−12.8992	−0.858045
$227$	6.35919	0.422074	0.211037	−	0.977478i	$-0.432316\pi$
$227$	6.35919	0.422074	0.211037	+	0.977478i	$0.432316\pi$
$228$	0.119832	0.00793607
$229$	11.4619	0.757426	0.378713	−	0.925514i	$-0.376367\pi$
$229$	11.4619	0.757426	0.378713	+	0.925514i	$0.376367\pi$
$230$	−6.41880	−0.423243
$231$	7.19802	0.473595
$232$	−17.5891	−1.15478
$233$	21.5891	1.41435	0.707175	−	0.707039i	$-0.249969\pi$
$233$	21.5891	1.41435	0.707175	+	0.707039i	$0.249969\pi$
$234$	−17.7407	−1.15974
$235$	6.49890	0.423941
$236$	−0.388156	−0.0252668
$237$	1.60526	0.104273
$238$	−8.13038	−0.527014
$239$	−4.52568	−0.292742	−0.146371	−	0.989230i	$-0.546759\pi$
$239$	−4.52568	−0.292742	−0.146371	+	0.989230i	$0.546759\pi$
$240$	5.23077	0.337645
$241$	−9.84982	−0.634483	−0.317241	−	0.948345i	$-0.602757\pi$
$241$	−9.84982	−0.634483	−0.317241	+	0.948345i	$0.602757\pi$
$242$	−11.7968	−0.758325
$243$	21.5401	1.38180
$244$	−1.69276	−0.108368
$245$	−1.86673	−0.119261
$246$	15.7936	1.00696
$247$	−1.58170	−0.100641
$248$	12.2011	0.774769
$249$	5.44205	0.344876
$250$	−7.75483	−0.490459
$251$	22.0558	1.39215	0.696075	−	0.717969i	$-0.254928\pi$
$251$	22.0558	1.39215	0.696075	+	0.717969i	$0.254928\pi$
$252$	−0.804161	−0.0506574
$253$	12.2025	0.767163
$254$	−15.4590	−0.969982
$255$	4.32973	0.271138
$256$	−3.51587	−0.219742
$257$	25.3211	1.57948	0.789742	−	0.613439i	$-0.210214\pi$
$257$	25.3211	1.57948	0.789742	+	0.613439i	$0.210214\pi$
$258$	−40.7560	−2.53736
$259$	−21.6771	−1.34695
$260$	0.406743	0.0252251
$261$	16.7693	1.03799
$262$	21.6582	1.33805
$263$	10.7243	0.661289	0.330644	−	0.943755i	$-0.392734\pi$
$263$	10.7243	0.661289	0.330644	+	0.943755i	$0.392734\pi$
$264$	−10.7393	−0.660958
$265$	−2.02878	−0.124627
$266$	0.901686	0.0552859
$267$	−5.33975	−0.326788
$268$	1.51075	0.0922839
$269$	−11.9609	−0.729266	−0.364633	−	0.931151i	$-0.618806\pi$
$269$	−11.9609	−0.729266	−0.364633	+	0.931151i	$0.618806\pi$
$270$	0.412562	0.0251077
$271$	−11.7258	−0.712295	−0.356147	−	0.934430i	$-0.615910\pi$
$271$	−11.7258	−0.712295	−0.356147	+	0.934430i	$0.615910\pi$
$272$	11.2320	0.681040
$273$	22.0418	1.33403
$274$	−20.4700	−1.23664
$275$	7.10504	0.428450
$276$	−2.83094	−0.170403
$277$	−0.916745	−0.0550819	−0.0275409	−	0.999621i	$-0.508768\pi$
$277$	−0.916745	−0.0550819	−0.0275409	+	0.999621i	$0.508768\pi$
$278$	−22.6610	−1.35912
$279$	−11.6324	−0.696411
$280$	−3.37991	−0.201988
$281$	21.7464	1.29728	0.648640	−	0.761096i	$-0.275338\pi$
$281$	21.7464	1.29728	0.648640	+	0.761096i	$0.275338\pi$
$282$	−36.0475	−2.14660
$283$	−8.06684	−0.479524	−0.239762	−	0.970832i	$-0.577069\pi$
$283$	−8.06684	−0.479524	−0.239762	+	0.970832i	$0.577069\pi$
$284$	−1.42442	−0.0845238
$285$	−0.480181	−0.0284435
$286$	9.72463	0.575030
$287$	−9.44941	−0.557781
$288$	2.31727	0.136547
$289$	−7.70280	−0.453106
$290$	4.83530	0.283939
$291$	−34.3696	−2.01478
$292$	0.933509	0.0546295
$293$	−2.16609	−0.126544	−0.0632722	−	0.997996i	$-0.520154\pi$
$293$	−2.16609	−0.126544	−0.0632722	+	0.997996i	$0.520154\pi$
$294$	10.3542	0.603871
$295$	1.55539	0.0905581
$296$	32.3417	1.87982
$297$	−0.784302	−0.0455098
$298$	−16.4231	−0.951363
$299$	37.3664	2.16095
$300$	−1.64835	−0.0951676
$301$	24.3846	1.40550
$302$	−22.4448	−1.29155
$303$	1.51508	0.0870391
$304$	−1.24567	−0.0714438
$305$	6.78307	0.388397
$306$	−11.5649	−0.661124
$307$	6.60523	0.376980	0.188490	−	0.982075i	$-0.439641\pi$
$307$	6.60523	0.376980	0.188490	+	0.982075i	$0.439641\pi$
$308$	0.440805	0.0251172
$309$	10.8588	0.617735
$310$	−3.35411	−0.190501
$311$	3.84184	0.217851	0.108925	−	0.994050i	$-0.465259\pi$
$311$	3.84184	0.217851	0.108925	+	0.994050i	$0.465259\pi$
$312$	−32.8858	−1.86179
$313$	−25.4617	−1.43918	−0.719591	−	0.694398i	$-0.755671\pi$
$313$	−25.4617	−1.43918	−0.719591	+	0.694398i	$0.755671\pi$
$314$	5.58891	0.315401
$315$	3.22237	0.181560
$316$	0.0983058	0.00553014
$317$	−8.23817	−0.462702	−0.231351	−	0.972870i	$-0.574314\pi$
$317$	−8.23817	−0.462702	−0.231351	+	0.972870i	$0.574314\pi$
$318$	11.2531	0.631040
$319$	−9.19216	−0.514662
$320$	5.01713	0.280466
$321$	−8.26446	−0.461277
$322$	−21.3016	−1.18709
$323$	−1.03109	−0.0573714
$324$	1.41344	0.0785247
$325$	21.7570	1.20686
$326$	28.9185	1.60165
$327$	−23.8156	−1.31701
$328$	14.0983	0.778449
$329$	21.5675	1.18905
$330$	2.95226	0.162517
$331$	−6.68597	−0.367494	−0.183747	−	0.982974i	$-0.558823\pi$
$331$	−6.68597	−0.367494	−0.183747	+	0.982974i	$0.558823\pi$
$332$	0.333270	0.0182906
$333$	−30.8342	−1.68970
$334$	−8.11977	−0.444294
$335$	−6.05376	−0.330752
$336$	17.3590	0.947011
$337$	−34.9491	−1.90380	−0.951899	−	0.306411i	$-0.900872\pi$
$337$	−34.9491	−1.90380	−0.951899	+	0.306411i	$0.900872\pi$
$338$	12.0840	0.657282
$339$	22.7968	1.23815
$340$	0.265151	0.0143799
$341$	6.37634	0.345298
$342$	1.28259	0.0693545
$343$	−19.9080	−1.07493
$344$	−36.3813	−1.96155
$345$	11.3439	0.610736
$346$	−22.1349	−1.18998
$347$	−16.1317	−0.865998	−0.432999	−	0.901394i	$-0.642545\pi$
$347$	−16.1317	−0.865998	−0.432999	+	0.901394i	$0.642545\pi$
$348$	2.13256	0.114317
$349$	−16.2651	−0.870653	−0.435326	−	0.900273i	$-0.643367\pi$
$349$	−16.2651	−0.870653	−0.435326	+	0.900273i	$0.643367\pi$
$350$	−12.4031	−0.662976
$351$	−2.40169	−0.128192
$352$	−1.27022	−0.0677032
$353$	15.5427	0.827254	0.413627	−	0.910446i	$-0.364262\pi$
$353$	15.5427	0.827254	0.413627	+	0.910446i	$0.364262\pi$
$354$	−8.62729	−0.458535
$355$	5.70782	0.302940
$356$	−0.327005	−0.0173312
$357$	14.3688	0.760476
$358$	12.7501	0.673862
$359$	−16.5339	−0.872625	−0.436312	−	0.899795i	$-0.643716\pi$
$359$	−16.5339	−0.872625	−0.436312	+	0.899795i	$0.643716\pi$
$360$	−4.80770	−0.253388
$361$	−18.8856	−0.993982
$362$	2.21708	0.116527
$363$	20.8484	1.09425
$364$	1.34983	0.0707504
$365$	−3.74068	−0.195796
$366$	−37.6237	−1.96662
$367$	5.62500	0.293623	0.146811	−	0.989165i	$-0.453099\pi$
$367$	5.62500	0.293623	0.146811	+	0.989165i	$0.453099\pi$
$368$	29.4279	1.53403
$369$	−13.4412	−0.699719
$370$	−8.89083	−0.462212
$371$	−6.73277	−0.349548
$372$	−1.47929	−0.0766978
$373$	−18.0602	−0.935122	−0.467561	−	0.883961i	$-0.654867\pi$
$373$	−18.0602	−0.935122	−0.467561	+	0.883961i	$0.654867\pi$
$374$	6.33938	0.327802
$375$	13.7051	0.707727
$376$	−32.1782	−1.65946
$377$	−28.1482	−1.44970
$378$	1.36914	0.0704211
$379$	−2.42773	−0.124704	−0.0623521	−	0.998054i	$-0.519860\pi$
$379$	−2.42773	−0.124704	−0.0623521	+	0.998054i	$0.519860\pi$
$380$	−0.0294062	−0.00150850
$381$	27.3206	1.39967
$382$	−11.4601	−0.586349
$383$	−16.2778	−0.831757	−0.415878	−	0.909420i	$-0.636526\pi$
$383$	−16.2778	−0.831757	−0.415878	+	0.909420i	$0.636526\pi$
$384$	−23.8278	−1.21596
$385$	−1.76636	−0.0900219
$386$	−33.9623	−1.72863
$387$	34.6855	1.76316
$388$	−2.10478	−0.106854
$389$	−15.0862	−0.764899	−0.382450	−	0.923976i	$-0.624919\pi$
$389$	−15.0862	−0.764899	−0.382450	+	0.923976i	$0.624919\pi$
$390$	9.04041	0.457779
$391$	24.3587	1.23187
$392$	9.24280	0.466832
$393$	−38.2764	−1.93079
$394$	3.21988	0.162215
$395$	−0.393923	−0.0198204
$396$	0.627016	0.0315088
$397$	−26.7523	−1.34266	−0.671329	−	0.741160i	$-0.734276\pi$
$397$	−26.7523	−1.34266	−0.671329	+	0.741160i	$0.734276\pi$
$398$	16.0364	0.803834
$399$	−1.59354	−0.0797770
$400$	17.1348	0.856738
$401$	−21.1930	−1.05833	−0.529165	−	0.848519i	$-0.677495\pi$
$401$	−21.1930	−1.05833	−0.529165	+	0.848519i	$0.677495\pi$
$402$	33.5785	1.67474
$403$	19.5256	0.972639
$404$	0.0927831	0.00461613
$405$	−5.66384	−0.281438
$406$	16.0466	0.796378
$407$	16.9019	0.837797
$408$	−21.4379	−1.06133
$409$	14.2178	0.703023	0.351511	−	0.936184i	$-0.385668\pi$
$409$	14.2178	0.703023	0.351511	+	0.936184i	$0.385668\pi$
$410$	−3.87567	−0.191406
$411$	36.1766	1.78446
$412$	0.664989	0.0327617
$413$	5.16176	0.253993
$414$	−30.3002	−1.48917
$415$	−1.33545	−0.0655547
$416$	−3.88968	−0.190707
$417$	40.0487	1.96119
$418$	−0.703058	−0.0343877
$419$	40.7220	1.98940	0.994700	−	0.102818i	$-0.0327858\pi$
$419$	40.7220	1.98940	0.994700	+	0.102818i	$0.0327858\pi$
$420$	0.409790	0.0199957
$421$	30.2685	1.47519	0.737597	−	0.675241i	$-0.235960\pi$
$421$	30.2685	1.47519	0.737597	+	0.675241i	$0.235960\pi$
$422$	−22.8840	−1.11397
$423$	30.6783	1.49163
$424$	10.0451	0.487835
$425$	14.1832	0.687984
$426$	−31.6596	−1.53391
$427$	22.5105	1.08936
$428$	−0.506113	−0.0244639
$429$	−17.1863	−0.829762
$430$	10.0013	0.482306
$431$	14.3367	0.690572	0.345286	−	0.938497i	$-0.387782\pi$
$431$	14.3367	0.690572	0.345286	+	0.938497i	$0.387782\pi$
$432$	−1.89145	−0.0910024
$433$	−26.4985	−1.27344	−0.636719	−	0.771096i	$-0.719709\pi$
$433$	−26.4985	−1.27344	−0.636719	+	0.771096i	$0.719709\pi$
$434$	−11.1311	−0.534308
$435$	−8.54540	−0.409720
$436$	−1.45846	−0.0698477
$437$	−2.70146	−0.129228
$438$	20.7485	0.991400
$439$	19.2176	0.917208	0.458604	−	0.888641i	$-0.348350\pi$
$439$	19.2176	0.917208	0.458604	+	0.888641i	$0.348350\pi$
$440$	2.63537	0.125636
$441$	−8.81198	−0.419618
$442$	19.4124	0.923355
$443$	−5.97322	−0.283796	−0.141898	−	0.989881i	$-0.545321\pi$
$443$	−5.97322	−0.283796	−0.141898	+	0.989881i	$0.545321\pi$
$444$	−3.92120	−0.186092
$445$	1.31035	0.0621164
$446$	11.3313	0.536553
$447$	29.0244	1.37281
$448$	16.6500	0.786639
$449$	1.84304	0.0869784	0.0434892	−	0.999054i	$-0.486153\pi$
$449$	1.84304	0.0869784	0.0434892	+	0.999054i	$0.486153\pi$
$450$	−17.6427	−0.831683
$451$	7.36785	0.346938
$452$	1.39607	0.0656655
$453$	39.6665	1.86369
$454$	8.65571	0.406233
$455$	−5.40893	−0.253575
$456$	2.37753	0.111338
$457$	27.3399	1.27891	0.639453	−	0.768830i	$-0.279161\pi$
$457$	27.3399	1.27891	0.639453	+	0.768830i	$0.279161\pi$
$458$	15.6012	0.728998
$459$	−1.56563	−0.0730774
$460$	0.694698	0.0323905
$461$	35.1434	1.63679	0.818395	−	0.574656i	$-0.194864\pi$
$461$	35.1434	1.63679	0.818395	+	0.574656i	$0.194864\pi$
$462$	9.79748	0.455820
$463$	−18.6765	−0.867969	−0.433984	−	0.900920i	$-0.642893\pi$
$463$	−18.6765	−0.867969	−0.433984	+	0.900920i	$0.642893\pi$
$464$	−22.1681	−1.02913
$465$	5.92770	0.274891
$466$	29.3857	1.36126
$467$	−16.9925	−0.786318	−0.393159	−	0.919470i	$-0.628618\pi$
$467$	−16.9925	−0.786318	−0.393159	+	0.919470i	$0.628618\pi$
$468$	1.92005	0.0887542
$469$	−20.0902	−0.927680
$470$	8.84588	0.408030
$471$	−9.87725	−0.455120
$472$	−7.70123	−0.354478
$473$	−19.0130	−0.874220
$474$	2.18498	0.100359
$475$	−1.57296	−0.0721723
$476$	0.879940	0.0403320
$477$	−9.57692	−0.438497
$478$	−6.16006	−0.281755
$479$	−11.4554	−0.523409	−0.261705	−	0.965148i	$-0.584285\pi$
$479$	−11.4554	−0.523409	−0.261705	+	0.965148i	$0.584285\pi$
$480$	−1.18085	−0.0538983
$481$	51.7570	2.35992
$482$	−13.4069	−0.610669
$483$	37.6463	1.71296
$484$	1.27675	0.0580340
$485$	8.43411	0.382973
$486$	29.3190	1.32994
$487$	−14.2183	−0.644295	−0.322147	−	0.946690i	$-0.604405\pi$
$487$	−14.2183	−0.644295	−0.322147	+	0.946690i	$0.604405\pi$
$488$	−33.5852	−1.52033
$489$	−51.1075	−2.31116
$490$	−2.54087	−0.114785
$491$	−4.53402	−0.204617	−0.102309	−	0.994753i	$-0.532623\pi$
$491$	−4.53402	−0.204617	−0.102309	+	0.994753i	$0.532623\pi$
$492$	−1.70932	−0.0770621
$493$	−18.3495	−0.826419
$494$	−2.15290	−0.0968636
$495$	−2.51253	−0.112930
$496$	15.3774	0.690465
$497$	18.9421	0.849671
$498$	7.40736	0.331932
$499$	−38.1411	−1.70743	−0.853715	−	0.520741i	$-0.825656\pi$
$499$	−38.1411	−1.70743	−0.853715	+	0.520741i	$0.825656\pi$
$500$	0.839295	0.0375344
$501$	14.3500	0.641112
$502$	30.0209	1.33990
$503$	−1.00000	−0.0445878
$503$	−1.00000	−0.0445878
$504$	−15.9550	−0.710692
$505$	−0.371793	−0.0165446
$506$	16.6092	0.738369
$507$	−21.3559	−0.948451
$508$	1.67310	0.0742319
$509$	34.3114	1.52083	0.760413	−	0.649440i	$-0.224997\pi$
$509$	34.3114	1.52083	0.760413	+	0.649440i	$0.224997\pi$
$510$	5.89334	0.260962
$511$	−12.4139	−0.549160
$512$	−24.5965	−1.08702
$513$	0.173634	0.00766612
$514$	34.4654	1.52020
$515$	−2.66469	−0.117420
$516$	4.41097	0.194182
$517$	−16.8165	−0.739587
$518$	−29.5054	−1.29639
$519$	39.1189	1.71713
$520$	8.07001	0.353893
$521$	23.8175	1.04346	0.521732	−	0.853110i	$-0.325286\pi$
$521$	23.8175	1.04346	0.521732	+	0.853110i	$0.325286\pi$
$522$	22.8252	0.999032
$523$	−2.16718	−0.0947643	−0.0473821	−	0.998877i	$-0.515088\pi$
$523$	−2.16718	−0.0947643	−0.0473821	+	0.998877i	$0.515088\pi$
$524$	−2.34404	−0.102400
$525$	21.9200	0.956667
$526$	14.5972	0.636469
$527$	12.7285	0.554463
$528$	−13.5351	−0.589038
$529$	40.8200	1.77478
$530$	−2.76144	−0.119949
$531$	7.34226	0.318627
$532$	−0.0975882	−0.00423099
$533$	22.5618	0.977259
$534$	−7.26812	−0.314522
$535$	2.02805	0.0876804
$536$	29.9742	1.29469
$537$	−22.5331	−0.972376
$538$	−16.2803	−0.701895
$539$	4.83033	0.208057
$540$	−0.0446510	−0.00192147
$541$	13.5019	0.580493	0.290246	−	0.956952i	$-0.406263\pi$
$541$	13.5019	0.580493	0.290246	+	0.956952i	$0.406263\pi$
$542$	−15.9605	−0.685560
$543$	−3.91824	−0.168148
$544$	−2.53564	−0.108714
$545$	5.84423	0.250339
$546$	30.0018	1.28396
$547$	−1.05880	−0.0452710	−0.0226355	−	0.999744i	$-0.507206\pi$
$547$	−1.05880	−0.0452710	−0.0226355	+	0.999744i	$0.507206\pi$
$548$	2.21544	0.0946390
$549$	32.0197	1.36657
$550$	9.67092	0.412369
$551$	2.03502	0.0866947
$552$	−56.1674	−2.39064
$553$	−1.30728	−0.0555914
$554$	−1.24781	−0.0530145
$555$	15.7127	0.666967
$556$	2.45257	0.104012
$557$	−9.20176	−0.389891	−0.194946	−	0.980814i	$-0.562453\pi$
$557$	−9.20176	−0.389891	−0.194946	+	0.980814i	$0.562453\pi$
$558$	−15.8332	−0.670273
$559$	−58.2216	−2.46251
$560$	−4.25980	−0.180010
$561$	−11.2035	−0.473014
$562$	29.5997	1.24859
$563$	−29.6502	−1.24961	−0.624804	−	0.780782i	$-0.714821\pi$
$563$	−29.6502	−1.24961	−0.624804	+	0.780782i	$0.714821\pi$
$564$	3.90137	0.164277
$565$	−5.59420	−0.235350
$566$	−10.9800	−0.461526
$567$	−18.7962	−0.789366
$568$	−28.2613	−1.18582
$569$	22.6715	0.950439	0.475220	−	0.879867i	$-0.342369\pi$
$569$	22.6715	0.950439	0.475220	+	0.879867i	$0.342369\pi$
$570$	−0.653591	−0.0273759
$571$	−31.2013	−1.30573	−0.652866	−	0.757473i	$-0.726434\pi$
$571$	−31.2013	−1.30573	−0.652866	+	0.757473i	$0.726434\pi$
$572$	−1.05248	−0.0440065
$573$	20.2533	0.846096
$574$	−12.8619	−0.536846
$575$	37.1600	1.54968
$576$	23.6836	0.986815
$577$	−3.98191	−0.165769	−0.0828845	−	0.996559i	$-0.526413\pi$
$577$	−3.98191	−0.165769	−0.0828845	+	0.996559i	$0.526413\pi$
$578$	−10.4845	−0.436099
$579$	60.0213	2.49440
$580$	−0.523318	−0.0217296
$581$	−4.43187	−0.183865
$582$	−46.7816	−1.93916
$583$	5.24964	0.217418
$584$	18.5213	0.766418
$585$	−7.69385	−0.318102
$586$	−2.94834	−0.121795
$587$	−12.7494	−0.526225	−0.263113	−	0.964765i	$-0.584749\pi$
$587$	−12.7494	−0.526225	−0.263113	+	0.964765i	$0.584749\pi$
$588$	−1.12062	−0.0462137
$589$	−1.41163	−0.0581654
$590$	2.11709	0.0871592
$591$	−5.69048	−0.234075
$592$	40.7612	1.67528
$593$	−3.27771	−0.134600	−0.0672998	−	0.997733i	$-0.521438\pi$
$593$	−3.27771	−0.134600	−0.0672998	+	0.997733i	$0.521438\pi$
$594$	−1.06754	−0.0438017
$595$	−3.52602	−0.144553
$596$	1.77745	0.0728070
$597$	−28.3411	−1.15992
$598$	50.8606	2.07985
$599$	10.9237	0.446332	0.223166	−	0.974780i	$-0.428361\pi$
$599$	10.9237	0.446332	0.223166	+	0.974780i	$0.428361\pi$
$600$	−32.7042	−1.33514
$601$	−29.7446	−1.21331	−0.606653	−	0.794967i	$-0.707488\pi$
$601$	−29.7446	−1.21331	−0.606653	+	0.794967i	$0.707488\pi$
$602$	33.1907	1.35275
$603$	−28.5770	−1.16375
$604$	2.42916	0.0988413
$605$	−5.11608	−0.207998
$606$	2.06223	0.0837723
$607$	−43.8414	−1.77947	−0.889735	−	0.456478i	$-0.849111\pi$
$607$	−43.8414	−1.77947	−0.889735	+	0.456478i	$0.849111\pi$
$608$	0.281210	0.0114046
$609$	−28.3590	−1.14917
$610$	9.23267	0.373820
$611$	−51.4953	−2.08328
$612$	1.25166	0.0505952
$613$	−32.3195	−1.30537	−0.652687	−	0.757628i	$-0.726358\pi$
$613$	−32.3195	−1.30537	−0.652687	+	0.757628i	$0.726358\pi$
$614$	8.99061	0.362831
$615$	6.84945	0.276196
$616$	8.74581	0.352379
$617$	40.9696	1.64937	0.824687	−	0.565589i	$-0.191351\pi$
$617$	40.9696	1.64937	0.824687	+	0.565589i	$0.191351\pi$
$618$	14.7803	0.594549
$619$	22.5775	0.907466	0.453733	−	0.891138i	$-0.350092\pi$
$619$	22.5775	0.907466	0.453733	+	0.891138i	$0.350092\pi$
$620$	0.363011	0.0145789
$621$	−4.10196	−0.164606
$622$	5.22926	0.209674
$623$	4.34856	0.174221
$624$	−41.4470	−1.65921
$625$	19.8946	0.795782
$626$	−34.6568	−1.38517
$627$	1.24251	0.0496211
$628$	−0.604880	−0.0241373
$629$	33.7398	1.34529
$630$	4.38607	0.174745
$631$	33.9719	1.35240	0.676199	−	0.736719i	$-0.263626\pi$
$631$	33.9719	1.35240	0.676199	+	0.736719i	$0.263626\pi$
$632$	1.95044	0.0775844
$633$	40.4427	1.60745
$634$	−11.2132	−0.445335
$635$	−6.70432	−0.266053
$636$	−1.21790	−0.0482930
$637$	14.7914	0.586057
$638$	−12.5118	−0.495345
$639$	26.9440	1.06589
$640$	5.84721	0.231131
$641$	−4.53431	−0.179095	−0.0895473	−	0.995983i	$-0.528542\pi$
$641$	−4.53431	−0.179095	−0.0895473	+	0.995983i	$0.528542\pi$
$642$	−11.2490	−0.443964
$643$	38.3929	1.51407	0.757033	−	0.653376i	$-0.226648\pi$
$643$	38.3929	1.51407	0.757033	+	0.653376i	$0.226648\pi$
$644$	2.30545	0.0908473
$645$	−17.6753	−0.695963
$646$	−1.40345	−0.0552181
$647$	−0.255028	−0.0100262	−0.00501309	−	0.999987i	$-0.501596\pi$
$647$	−0.255028	−0.0100262	−0.00501309	+	0.999987i	$0.501596\pi$
$648$	28.0435	1.10165
$649$	−4.02470	−0.157983
$650$	29.6142	1.16157
$651$	19.6719	0.771001
$652$	−3.12981	−0.122573
$653$	−2.04379	−0.0799797	−0.0399898	−	0.999200i	$-0.512733\pi$
$653$	−2.04379	−0.0799797	−0.0399898	+	0.999200i	$0.512733\pi$
$654$	−32.4163	−1.26758
$655$	9.39282	0.367008
$656$	17.7685	0.693745
$657$	−17.6580	−0.688904
$658$	29.3562	1.14442
$659$	10.0768	0.392534	0.196267	−	0.980550i	$-0.437118\pi$
$659$	10.0768	0.392534	0.196267	+	0.980550i	$0.437118\pi$
$660$	−0.319519	−0.0124373
$661$	−5.53010	−0.215096	−0.107548	−	0.994200i	$-0.534300\pi$
$661$	−5.53010	−0.215096	−0.107548	+	0.994200i	$0.534300\pi$
$662$	−9.10050	−0.353701
$663$	−34.3074	−1.33239
$664$	6.61225	0.256605
$665$	0.391047	0.0151642
$666$	−41.9695	−1.62628
$667$	−48.0757	−1.86150
$668$	0.878791	0.0340015
$669$	−20.0257	−0.774240
$670$	−8.23998	−0.318338
$671$	−17.5518	−0.677579
$672$	−3.91881	−0.151171
$673$	−3.16280	−0.121917	−0.0609585	−	0.998140i	$-0.519416\pi$
$673$	−3.16280	−0.121917	−0.0609585	+	0.998140i	$0.519416\pi$
$674$	−47.5704	−1.83234
$675$	−2.38842	−0.0919303
$676$	−1.30783	−0.0503012
$677$	−47.8219	−1.83794	−0.918972	−	0.394323i	$-0.870979\pi$
$677$	−47.8219	−1.83794	−0.918972	+	0.394323i	$0.870979\pi$
$678$	31.0295	1.19168
$679$	27.9897	1.07415
$680$	5.26075	0.201740
$681$	−15.2972	−0.586190
$682$	8.67906	0.332338
$683$	13.2468	0.506873	0.253437	−	0.967352i	$-0.418439\pi$
$683$	13.2468	0.506873	0.253437	+	0.967352i	$0.418439\pi$
$684$	−0.138813	−0.00530764
$685$	−8.87754	−0.339193
$686$	−27.0974	−1.03458
$687$	−27.5720	−1.05194
$688$	−45.8524	−1.74811
$689$	16.0754	0.612425
$690$	15.4406	0.587813
$691$	−7.80850	−0.297049	−0.148525	−	0.988909i	$-0.547452\pi$
$691$	−7.80850	−0.297049	−0.148525	+	0.988909i	$0.547452\pi$
$692$	2.39563	0.0910681
$693$	−8.33815	−0.316740
$694$	−21.9575	−0.833494
$695$	−9.82774	−0.372787
$696$	42.3111	1.60380
$697$	14.7078	0.557097
$698$	−22.1390	−0.837975
$699$	−51.9331	−1.96429
$700$	1.34237	0.0507370
$701$	7.68972	0.290437	0.145218	−	0.989400i	$-0.453612\pi$
$701$	7.68972	0.290437	0.145218	+	0.989400i	$0.453612\pi$
$702$	−3.26902	−0.123381
$703$	−3.74185	−0.141127
$704$	−12.9823	−0.489288
$705$	−15.6333	−0.588783
$706$	21.1557	0.796205
$707$	−1.23384	−0.0464034
$708$	0.933719	0.0350913
$709$	31.0522	1.16619	0.583096	−	0.812403i	$-0.301841\pi$
$709$	31.0522	1.16619	0.583096	+	0.812403i	$0.301841\pi$
$710$	7.76911	0.291569
$711$	−1.85953	−0.0697377
$712$	−6.48796	−0.243146
$713$	33.3488	1.24892
$714$	19.5578	0.731933
$715$	4.21742	0.157723
$716$	−1.37992	−0.0515701
$717$	10.8866	0.406569
$718$	−22.5048	−0.839873
$719$	−30.4494	−1.13557	−0.567786	−	0.823176i	$-0.692200\pi$
$719$	−30.4494	−1.13557	−0.567786	+	0.823176i	$0.692200\pi$
$720$	−6.05929	−0.225817
$721$	−8.84312	−0.329335
$722$	−25.7059	−0.956675
$723$	23.6940	0.881189
$724$	−0.239952	−0.00891774
$725$	−27.9927	−1.03962
$726$	28.3774	1.05318
$727$	−6.14587	−0.227938	−0.113969	−	0.993484i	$-0.536356\pi$
$727$	−6.14587	−0.227938	−0.113969	+	0.993484i	$0.536356\pi$
$728$	26.7814	0.992584
$729$	−23.0309	−0.852995
$730$	−5.09156	−0.188447
$731$	−37.9540	−1.40378
$732$	4.07196	0.150504
$733$	−25.4237	−0.939046	−0.469523	−	0.882920i	$-0.655574\pi$
$733$	−25.4237	−0.939046	−0.469523	+	0.882920i	$0.655574\pi$
$734$	7.65638	0.282602
$735$	4.49047	0.165633
$736$	−6.64338	−0.244878
$737$	15.6646	0.577014
$738$	−18.2952	−0.673457
$739$	−19.8464	−0.730063	−0.365032	−	0.930995i	$-0.618942\pi$
$739$	−19.8464	−0.730063	−0.365032	+	0.930995i	$0.618942\pi$
$740$	0.962242	0.0353727
$741$	3.80481	0.139773
$742$	−9.16420	−0.336428
$743$	−28.7154	−1.05346	−0.526732	−	0.850031i	$-0.676583\pi$
$743$	−28.7154	−1.05346	−0.526732	+	0.850031i	$0.676583\pi$
$744$	−29.3500	−1.07602
$745$	−7.12243	−0.260946
$746$	−24.5824	−0.900025
$747$	−6.30404	−0.230653
$748$	−0.686102	−0.0250864
$749$	6.73036	0.245922
$750$	18.6544	0.681164
$751$	24.0374	0.877139	0.438569	−	0.898697i	$-0.355485\pi$
$751$	24.0374	0.877139	0.438569	+	0.898697i	$0.355485\pi$
$752$	−40.5551	−1.47889
$753$	−53.0558	−1.93346
$754$	−38.3134	−1.39529
$755$	−9.73394	−0.354254
$756$	−0.148180	−0.00538926
$757$	−23.2463	−0.844902	−0.422451	−	0.906386i	$-0.638830\pi$
$757$	−23.2463	−0.844902	−0.422451	+	0.906386i	$0.638830\pi$
$758$	−3.30447	−0.120024
$759$	−29.3534	−1.06546
$760$	−0.583434	−0.0211634
$761$	44.3555	1.60789	0.803943	−	0.594706i	$-0.202732\pi$
$761$	44.3555	1.60789	0.803943	+	0.594706i	$0.202732\pi$
$762$	37.1869	1.34714
$763$	19.3948	0.702140
$764$	1.24031	0.0448728
$765$	−5.01553	−0.181337
$766$	−22.1563	−0.800539
$767$	−12.3244	−0.445009
$768$	8.45752	0.305185
$769$	−17.4534	−0.629385	−0.314693	−	0.949194i	$-0.601901\pi$
$769$	−17.4534	−0.629385	−0.314693	+	0.949194i	$0.601901\pi$
$770$	−2.40425	−0.0866431
$771$	−60.9104	−2.19364
$772$	3.67569	0.132291
$773$	−1.73607	−0.0624422	−0.0312211	−	0.999513i	$-0.509940\pi$
$773$	−1.73607	−0.0624422	−0.0312211	+	0.999513i	$0.509940\pi$
$774$	47.2116	1.69699
$775$	19.4177	0.697506
$776$	−41.7600	−1.49910
$777$	52.1447	1.87068
$778$	−20.5343	−0.736190
$779$	−1.63114	−0.0584417
$780$	−0.978431	−0.0350334
$781$	−14.7695	−0.528493
$782$	33.1555	1.18564
$783$	3.09002	0.110428
$784$	11.6490	0.416035
$785$	2.42383	0.0865100
$786$	−52.0993	−1.85832
$787$	−16.1636	−0.576169	−0.288085	−	0.957605i	$-0.593018\pi$
$787$	−16.1636	−0.576169	−0.288085	+	0.957605i	$0.593018\pi$
$788$	−0.348483	−0.0124142
$789$	−25.7976	−0.918418
$790$	−0.536182	−0.0190765
$791$	−18.5651	−0.660099
$792$	12.4403	0.442048
$793$	−53.7469	−1.90861
$794$	−36.4134	−1.29226
$795$	4.88028	0.173086
$796$	−1.73560	−0.0615167
$797$	−26.8208	−0.950040	−0.475020	−	0.879975i	$-0.657559\pi$
$797$	−26.8208	−0.950040	−0.475020	+	0.879975i	$0.657559\pi$
$798$	−2.16903	−0.0767827
$799$	−33.5692	−1.18759
$800$	−3.86819	−0.136761
$801$	6.18554	0.218555
$802$	−28.8466	−1.01861
$803$	9.67933	0.341576
$804$	−3.63415	−0.128167
$805$	−9.23819	−0.325603
$806$	26.5770	0.936133
$807$	28.7721	1.01283
$808$	1.84087	0.0647615
$809$	33.4065	1.17451	0.587255	−	0.809402i	$-0.300209\pi$
$809$	33.4065	1.17451	0.587255	+	0.809402i	$0.300209\pi$
$810$	−7.70924	−0.270875
$811$	34.8499	1.22375	0.611873	−	0.790956i	$-0.290416\pi$
$811$	34.8499	1.22375	0.611873	+	0.790956i	$0.290416\pi$
$812$	−1.73670	−0.0609462
$813$	28.2068	0.989256
$814$	23.0058	0.806352
$815$	12.5415	0.439310
$816$	−27.0188	−0.945849
$817$	4.20922	0.147262
$818$	19.3523	0.676636
$819$	−25.5330	−0.892197
$820$	0.419458	0.0146481
$821$	−24.4182	−0.852201	−0.426101	−	0.904676i	$-0.640113\pi$
$821$	−24.4182	−0.852201	−0.426101	+	0.904676i	$0.640113\pi$
$822$	49.2412	1.71748
$823$	4.51039	0.157222	0.0786112	−	0.996905i	$-0.474951\pi$
$823$	4.51039	0.157222	0.0786112	+	0.996905i	$0.474951\pi$
$824$	13.1937	0.459626
$825$	−17.0914	−0.595045
$826$	7.02584	0.244460
$827$	−2.91499	−0.101364	−0.0506821	−	0.998715i	$-0.516140\pi$
$827$	−2.91499	−0.101364	−0.0506821	+	0.998715i	$0.516140\pi$
$828$	3.27935	0.113965
$829$	35.2382	1.22387	0.611937	−	0.790906i	$-0.290390\pi$
$829$	35.2382	1.22387	0.611937	+	0.790906i	$0.290390\pi$
$830$	−1.81773	−0.0630943
$831$	2.20525	0.0764994
$832$	−39.7542	−1.37823
$833$	9.64236	0.334088
$834$	54.5116	1.88758
$835$	−3.52142	−0.121864
$836$	0.0760910	0.00263166
$837$	−2.14346	−0.0740888
$838$	55.4281	1.91473
$839$	−14.4876	−0.500166	−0.250083	−	0.968224i	$-0.580458\pi$
$839$	−14.4876	−0.500166	−0.250083	+	0.968224i	$0.580458\pi$
$840$	8.13046	0.280527
$841$	7.21557	0.248813
$842$	41.1994	1.41983
$843$	−52.3114	−1.80170
$844$	2.47670	0.0852515
$845$	5.24063	0.180283
$846$	41.7573	1.43564
$847$	−16.9784	−0.583384
$848$	12.6602	0.434753
$849$	19.4050	0.665977
$850$	19.3052	0.662163
$851$	88.3985	3.03026
$852$	3.42648	0.117389
$853$	4.92917	0.168772	0.0843858	−	0.996433i	$-0.473107\pi$
$853$	4.92917	0.168772	0.0843858	+	0.996433i	$0.473107\pi$
$854$	30.6398	1.04847
$855$	0.556239	0.0190230
$856$	−10.0416	−0.343213
$857$	52.5344	1.79454	0.897270	−	0.441482i	$-0.145547\pi$
$857$	52.5344	1.79454	0.897270	+	0.441482i	$0.145547\pi$
$858$	−23.3928	−0.798618
$859$	32.5431	1.11036	0.555179	−	0.831731i	$-0.312650\pi$
$859$	32.5431	1.11036	0.555179	+	0.831731i	$0.312650\pi$
$860$	−1.08243	−0.0369105
$861$	22.7308	0.774663
$862$	19.5141	0.664653
$863$	51.5604	1.75514	0.877568	−	0.479451i	$-0.159164\pi$
$863$	51.5604	1.75514	0.877568	+	0.479451i	$0.159164\pi$
$864$	0.426997	0.0145267
$865$	−9.59956	−0.326395
$866$	−36.0681	−1.22564
$867$	18.5293	0.629287
$868$	1.20470	0.0408901
$869$	1.01931	0.0345777
$870$	−11.6314	−0.394342
$871$	47.9682	1.62534
$872$	−28.9367	−0.979919
$873$	39.8135	1.34748
$874$	−3.67705	−0.124378
$875$	−11.1611	−0.377313
$876$	−2.24558	−0.0758710
$877$	35.8616	1.21096	0.605481	−	0.795860i	$-0.292981\pi$
$877$	35.8616	1.21096	0.605481	+	0.795860i	$0.292981\pi$
$878$	26.1578	0.882783
$879$	5.21058	0.175749
$880$	3.32143	0.111965
$881$	−41.2432	−1.38952	−0.694759	−	0.719243i	$-0.744489\pi$
$881$	−41.2432	−1.38952	−0.694759	+	0.719243i	$0.744489\pi$
$882$	−11.9943	−0.403869
$883$	24.3041	0.817898	0.408949	−	0.912557i	$-0.365895\pi$
$883$	24.3041	0.817898	0.408949	+	0.912557i	$0.365895\pi$
$884$	−2.10098	−0.0706636
$885$	−3.74152	−0.125770
$886$	−8.13035	−0.273144
$887$	51.7010	1.73595	0.867975	−	0.496608i	$-0.165421\pi$
$887$	51.7010	1.73595	0.867975	+	0.496608i	$0.165421\pi$
$888$	−77.7987	−2.61075
$889$	−22.2492	−0.746213
$890$	1.78356	0.0597850
$891$	14.6557	0.490983
$892$	−1.22637	−0.0410619
$893$	3.72294	0.124583
$894$	39.5061	1.32128
$895$	5.52951	0.184831
$896$	19.4047	0.648266
$897$	−89.8857	−3.00120
$898$	2.50862	0.0837138
$899$	−25.1217	−0.837856
$900$	1.90944	0.0636480
$901$	10.4794	0.349119
$902$	10.0286	0.333917
$903$	−58.6577	−1.95201
$904$	27.6987	0.921246
$905$	0.961515	0.0319618
$906$	53.9914	1.79374
$907$	−5.06194	−0.168079	−0.0840395	−	0.996462i	$-0.526782\pi$
$907$	−5.06194	−0.168079	−0.0840395	+	0.996462i	$0.526782\pi$
$908$	−0.936796	−0.0310887
$909$	−1.75506	−0.0582117
$910$	−7.36228	−0.244057
$911$	−40.4144	−1.33899	−0.669495	−	0.742817i	$-0.733489\pi$
$911$	−40.4144	−1.33899	−0.669495	+	0.742817i	$0.733489\pi$
$912$	2.99648	0.0992233
$913$	3.45559	0.114363
$914$	37.2133	1.23091
$915$	−16.3168	−0.539418
$916$	−1.68850	−0.0557896
$917$	31.1713	1.02937
$918$	−2.13104	−0.0703347
$919$	31.2276	1.03010	0.515052	−	0.857159i	$-0.327773\pi$
$919$	31.2276	1.03010	0.515052	+	0.857159i	$0.327773\pi$
$920$	13.7832	0.454418
$921$	−15.8890	−0.523562
$922$	47.8349	1.57536
$923$	−45.2270	−1.48867
$924$	−1.06037	−0.0348835
$925$	51.4711	1.69236
$926$	−25.4212	−0.835391
$927$	−12.5788	−0.413141
$928$	5.00447	0.164280
$929$	−51.3773	−1.68563	−0.842817	−	0.538201i	$-0.819104\pi$
$929$	−51.3773	−1.68563	−0.842817	+	0.538201i	$0.819104\pi$
$930$	8.06840	0.264573
$931$	−1.06937	−0.0350472
$932$	−3.18037	−0.104176
$933$	−9.24164	−0.302558
$934$	−23.1290	−0.756805
$935$	2.74929	0.0899114
$936$	38.0948	1.24517
$937$	22.6093	0.738614	0.369307	−	0.929307i	$-0.379595\pi$
$937$	22.6093	0.738614	0.369307	+	0.929307i	$0.379595\pi$
$938$	−27.3455	−0.892861
$939$	61.2488	1.99878
$940$	−0.957377	−0.0312262
$941$	−51.2485	−1.67065	−0.835326	−	0.549754i	$-0.814721\pi$
$941$	−51.2485	−1.67065	−0.835326	+	0.549754i	$0.814721\pi$
$942$	−13.4443	−0.438038
$943$	38.5344	1.25485
$944$	−9.70610	−0.315906
$945$	0.593776	0.0193155
$946$	−25.8793	−0.841408
$947$	−54.1474	−1.75955	−0.879777	−	0.475387i	$-0.842308\pi$
$947$	−54.1474	−1.75955	−0.879777	+	0.475387i	$0.842308\pi$
$948$	−0.236477	−0.00768042
$949$	29.6400	0.962155
$950$	−2.14101	−0.0694635
$951$	19.8171	0.642614
$952$	17.4585	0.565833
$953$	−34.0986	−1.10456	−0.552281	−	0.833658i	$-0.686242\pi$
$953$	−34.0986	−1.10456	−0.552281	+	0.833658i	$0.686242\pi$
$954$	−13.0355	−0.422039
$955$	−4.97006	−0.160827
$956$	0.666695	0.0215624
$957$	22.1120	0.714778
$958$	−15.5923	−0.503764
$959$	−29.4613	−0.951354
$960$	−12.0688	−0.389520
$961$	−13.5738	−0.437863
$962$	70.4482	2.27134
$963$	9.57350	0.308502
$964$	1.45101	0.0467340
$965$	−14.7289	−0.474140
$966$	51.2416	1.64867
$967$	20.9385	0.673336	0.336668	−	0.941623i	$-0.390700\pi$
$967$	20.9385	0.673336	0.336668	+	0.941623i	$0.390700\pi$
$968$	25.3314	0.814181
$969$	2.48031	0.0796791
$970$	11.4800	0.368599
$971$	−5.00722	−0.160689	−0.0803447	−	0.996767i	$-0.525602\pi$
$971$	−5.00722	−0.160689	−0.0803447	+	0.996767i	$0.525602\pi$
$972$	−3.17315	−0.101779
$973$	−32.6146	−1.04558
$974$	−19.3531	−0.620113
$975$	−52.3371	−1.67613
$976$	−42.3284	−1.35490
$977$	12.5547	0.401662	0.200831	−	0.979626i	$-0.435636\pi$
$977$	12.5547	0.401662	0.200831	+	0.979626i	$0.435636\pi$
$978$	−69.5642	−2.22442
$979$	−3.39064	−0.108365
$980$	0.274995	0.00878440
$981$	27.5879	0.880813
$982$	−6.17140	−0.196937
$983$	1.43810	0.0458683	0.0229341	−	0.999737i	$-0.492699\pi$
$983$	1.43810	0.0458683	0.0229341	+	0.999737i	$0.492699\pi$
$984$	−33.9138	−1.08113
$985$	1.39641	0.0444934
$986$	−24.9761	−0.795401
$987$	−51.8810	−1.65139
$988$	0.233005	0.00741289
$989$	−99.4397	−3.16200
$990$	−3.41989	−0.108691
$991$	−41.6595	−1.32336	−0.661678	−	0.749788i	$-0.730155\pi$
$991$	−41.6595	−1.32336	−0.661678	+	0.749788i	$0.730155\pi$
$992$	−3.47146	−0.110219
$993$	16.0833	0.510387
$994$	25.7828	0.817781
$995$	6.95475	0.220480
$996$	−0.801689	−0.0254025
$997$	46.5145	1.47313	0.736564	−	0.676367i	$-0.236447\pi$
$997$	46.5145	1.47313	0.736564	+	0.676367i	$0.236447\pi$
$998$	−51.9151	−1.64334
$999$	−5.68172	−0.179762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.e.1.9	✓	10
3.2	odd	2		4527.2.a.k.1.2		10
4.3	odd	2		8048.2.a.p.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.e.1.9	✓	10	1.1	even	1	trivial
4527.2.a.k.1.2		10	3.2	odd	2
8048.2.a.p.1.9		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)

\(f(q)\)	\(=\)	\(q+1.36113 q^{2} -2.40552 q^{3} -0.147314 q^{4} +0.590303 q^{5} -3.27424 q^{6} +1.95900 q^{7} -2.92278 q^{8} +2.78655 q^{9} +O(q^{10})\)	\(q+1.36113 q^{2} -2.40552 q^{3} -0.147314 q^{4} +0.590303 q^{5} -3.27424 q^{6} +1.95900 q^{7} -2.92278 q^{8} +2.78655 q^{9} +0.803481 q^{10} -1.52746 q^{11} +0.354366 q^{12} -4.67738 q^{13} +2.66646 q^{14} -1.41999 q^{15} -3.68367 q^{16} -3.04913 q^{17} +3.79286 q^{18} +0.338159 q^{19} -0.0869597 q^{20} -4.71242 q^{21} -2.07908 q^{22} -7.98874 q^{23} +7.03082 q^{24} -4.65154 q^{25} -6.36654 q^{26} +0.513468 q^{27} -0.288587 q^{28} +6.01794 q^{29} -1.93279 q^{30} -4.17447 q^{31} +0.831593 q^{32} +3.67434 q^{33} -4.15028 q^{34} +1.15640 q^{35} -0.410496 q^{36} -11.0654 q^{37} +0.460279 q^{38} +11.2515 q^{39} -1.72533 q^{40} -4.82359 q^{41} -6.41423 q^{42} +12.4475 q^{43} +0.225016 q^{44} +1.64491 q^{45} -10.8737 q^{46} +11.0094 q^{47} +8.86116 q^{48} -3.16233 q^{49} -6.33137 q^{50} +7.33476 q^{51} +0.689042 q^{52} -3.43684 q^{53} +0.698899 q^{54} -0.901664 q^{55} -5.72572 q^{56} -0.813449 q^{57} +8.19122 q^{58} +2.63490 q^{59} +0.209184 q^{60} +11.4908 q^{61} -5.68202 q^{62} +5.45884 q^{63} +8.49925 q^{64} -2.76107 q^{65} +5.00127 q^{66} -10.2554 q^{67} +0.449179 q^{68} +19.2171 q^{69} +1.57402 q^{70} +9.66931 q^{71} -8.14447 q^{72} -6.33688 q^{73} -15.0615 q^{74} +11.1894 q^{75} -0.0498154 q^{76} -2.99229 q^{77} +15.3149 q^{78} -0.667323 q^{79} -2.17448 q^{80} -9.59480 q^{81} -6.56556 q^{82} -2.26231 q^{83} +0.694203 q^{84} -1.79991 q^{85} +16.9427 q^{86} -14.4763 q^{87} +4.46443 q^{88} +2.21979 q^{89} +2.23894 q^{90} -9.16297 q^{91} +1.17685 q^{92} +10.0418 q^{93} +14.9853 q^{94} +0.199616 q^{95} -2.00042 q^{96} +14.2878 q^{97} -4.30435 q^{98} -4.25634 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) \) 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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