LMFDB - Embedded newform 503.2.a.e.1.5

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			1.5
Root			$-2.07227$ 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)

$f(q)$	$=$	$q-0.756417 q^{2} -3.07227 q^{3} -1.42783 q^{4} +0.386144 q^{5} +2.32392 q^{6} +0.194914 q^{7} +2.59287 q^{8} +6.43884 q^{9} +O(q^{10})$	\(q-0.756417 q^{2} -3.07227 q^{3} -1.42783 q^{4} +0.386144 q^{5} +2.32392 q^{6} +0.194914 q^{7} +2.59287 q^{8} +6.43884 q^{9} -0.292086 q^{10} +2.36326 q^{11} +4.38669 q^{12} -1.22636 q^{13} -0.147436 q^{14} -1.18634 q^{15} +0.894372 q^{16} -5.04830 q^{17} -4.87045 q^{18} +4.24460 q^{19} -0.551349 q^{20} -0.598827 q^{21} -1.78761 q^{22} +1.53457 q^{23} -7.96600 q^{24} -4.85089 q^{25} +0.927639 q^{26} -10.5650 q^{27} -0.278304 q^{28} -7.31602 q^{29} +0.897367 q^{30} +3.33893 q^{31} -5.86226 q^{32} -7.26057 q^{33} +3.81863 q^{34} +0.0752647 q^{35} -9.19358 q^{36} -2.17138 q^{37} -3.21069 q^{38} +3.76771 q^{39} +1.00122 q^{40} -1.04840 q^{41} +0.452963 q^{42} -1.53067 q^{43} -3.37434 q^{44} +2.48632 q^{45} -1.16077 q^{46} -1.08422 q^{47} -2.74775 q^{48} -6.96201 q^{49} +3.66930 q^{50} +15.5098 q^{51} +1.75104 q^{52} +1.55308 q^{53} +7.99158 q^{54} +0.912558 q^{55} +0.505386 q^{56} -13.0406 q^{57} +5.53396 q^{58} +14.8451 q^{59} +1.69389 q^{60} -5.45056 q^{61} -2.52563 q^{62} +1.25502 q^{63} +2.64557 q^{64} -0.473551 q^{65} +5.49202 q^{66} -11.3202 q^{67} +7.20814 q^{68} -4.71461 q^{69} -0.0569315 q^{70} -11.4236 q^{71} +16.6951 q^{72} -0.902229 q^{73} +1.64247 q^{74} +14.9032 q^{75} -6.06059 q^{76} +0.460631 q^{77} -2.84996 q^{78} -12.7431 q^{79} +0.345356 q^{80} +13.1421 q^{81} +0.793029 q^{82} +6.10241 q^{83} +0.855025 q^{84} -1.94937 q^{85} +1.15782 q^{86} +22.4768 q^{87} +6.12763 q^{88} +6.44432 q^{89} -1.88070 q^{90} -0.239034 q^{91} -2.19111 q^{92} -10.2581 q^{93} +0.820122 q^{94} +1.63903 q^{95} +18.0105 q^{96} -12.9886 q^{97} +5.26618 q^{98} +15.2166 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.756417	−0.534868	−0.267434	−	0.963576i	$-0.586176\pi$
$2$	−0.756417	−0.534868	−0.267434	+	0.963576i	$0.586176\pi$
$3$	−3.07227	−1.77378	−0.886888	−	0.461985i	$-0.847137\pi$
$3$	−3.07227	−1.77378	−0.886888	+	0.461985i	$0.847137\pi$
$4$	−1.42783	−0.713916
$5$	0.386144	0.172689	0.0863445	−	0.996265i	$-0.472481\pi$
$5$	0.386144	0.172689	0.0863445	+	0.996265i	$0.472481\pi$
$6$	2.32392	0.948736
$7$	0.194914	0.0736704	0.0368352	−	0.999321i	$-0.488272\pi$
$7$	0.194914	0.0736704	0.0368352	+	0.999321i	$0.488272\pi$
$8$	2.59287	0.916719
$9$	6.43884	2.14628
$10$	−0.292086	−0.0923657
$11$	2.36326	0.712549	0.356275	−	0.934381i	$-0.384047\pi$
$11$	2.36326	0.712549	0.356275	+	0.934381i	$0.384047\pi$
$12$	4.38669	1.26633
$13$	−1.22636	−0.340131	−0.170065	−	0.985433i	$-0.554398\pi$
$13$	−1.22636	−0.340131	−0.170065	+	0.985433i	$0.554398\pi$
$14$	−0.147436	−0.0394039
$15$	−1.18634	−0.306311
$16$	0.894372	0.223593
$17$	−5.04830	−1.22439	−0.612197	−	0.790705i	$-0.709714\pi$
$17$	−5.04830	−1.22439	−0.612197	+	0.790705i	$0.709714\pi$
$18$	−4.87045	−1.14798
$19$	4.24460	0.973779	0.486890	−	0.873464i	$-0.338131\pi$
$19$	4.24460	0.973779	0.486890	+	0.873464i	$0.338131\pi$
$20$	−0.551349	−0.123285
$21$	−0.598827	−0.130675
$22$	−1.78761	−0.381120
$23$	1.53457	0.319980	0.159990	−	0.987119i	$-0.448854\pi$
$23$	1.53457	0.319980	0.159990	+	0.987119i	$0.448854\pi$
$24$	−7.96600	−1.62605
$25$	−4.85089	−0.970179
$26$	0.927639	0.181925
$27$	−10.5650	−2.03324
$28$	−0.278304	−0.0525945
$29$	−7.31602	−1.35855	−0.679275	−	0.733883i	$-0.737706\pi$
$29$	−7.31602	−1.35855	−0.679275	+	0.733883i	$0.737706\pi$
$30$	0.897367	0.163836
$31$	3.33893	0.599690	0.299845	−	0.953988i	$-0.403065\pi$
$31$	3.33893	0.599690	0.299845	+	0.953988i	$0.403065\pi$
$32$	−5.86226	−1.03631
$33$	−7.26057	−1.26390
$34$	3.81863	0.654889
$35$	0.0752647	0.0127221
$36$	−9.19358	−1.53226
$37$	−2.17138	−0.356973	−0.178487	−	0.983942i	$-0.557120\pi$
$37$	−2.17138	−0.356973	−0.178487	+	0.983942i	$0.557120\pi$
$38$	−3.21069	−0.520843
$39$	3.76771	0.603316
$40$	1.00122	0.158307
$41$	−1.04840	−0.163733	−0.0818663	−	0.996643i	$-0.526088\pi$
$41$	−1.04840	−0.163733	−0.0818663	+	0.996643i	$0.526088\pi$
$42$	0.452963	0.0698937
$43$	−1.53067	−0.233425	−0.116712	−	0.993166i	$-0.537236\pi$
$43$	−1.53067	−0.233425	−0.116712	+	0.993166i	$0.537236\pi$
$44$	−3.37434	−0.508701
$45$	2.48632	0.370639
$46$	−1.16077	−0.171147
$47$	−1.08422	−0.158150	−0.0790748	−	0.996869i	$-0.525197\pi$
$47$	−1.08422	−0.158150	−0.0790748	+	0.996869i	$0.525197\pi$
$48$	−2.74775	−0.396604
$49$	−6.96201	−0.994573
$50$	3.66930	0.518917
$51$	15.5098	2.17180
$52$	1.75104	0.242825
$53$	1.55308	0.213332	0.106666	−	0.994295i	$-0.465983\pi$
$53$	1.55308	0.213332	0.106666	+	0.994295i	$0.465983\pi$
$54$	7.99158	1.08752
$55$	0.912558	0.123049
$56$	0.505386	0.0675350
$57$	−13.0406	−1.72727
$58$	5.53396	0.726645
$59$	14.8451	1.93267	0.966334	−	0.257293i	$-0.0828304\pi$
$59$	14.8451	1.93267	0.966334	+	0.257293i	$0.0828304\pi$
$60$	1.69389	0.218681
$61$	−5.45056	−0.697873	−0.348936	−	0.937146i	$-0.613457\pi$
$61$	−5.45056	−0.697873	−0.348936	+	0.937146i	$0.613457\pi$
$62$	−2.52563	−0.320755
$63$	1.25502	0.158117
$64$	2.64557	0.330697
$65$	−0.473551	−0.0587368
$66$	5.49202	0.676021
$67$	−11.3202	−1.38298	−0.691490	−	0.722386i	$-0.743045\pi$
$67$	−11.3202	−1.38298	−0.691490	+	0.722386i	$0.743045\pi$
$68$	7.20814	0.874115
$69$	−4.71461	−0.567572
$70$	−0.0569315	−0.00680462
$71$	−11.4236	−1.35573	−0.677864	−	0.735187i	$-0.737094\pi$
$71$	−11.4236	−1.35573	−0.677864	+	0.735187i	$0.737094\pi$
$72$	16.6951	1.96753
$73$	−0.902229	−0.105598	−0.0527990	−	0.998605i	$-0.516814\pi$
$73$	−0.902229	−0.105598	−0.0527990	+	0.998605i	$0.516814\pi$
$74$	1.64247	0.190933
$75$	14.9032	1.72088
$76$	−6.06059	−0.695197
$77$	0.460631	0.0524938
$78$	−2.84996	−0.322694
$79$	−12.7431	−1.43371	−0.716853	−	0.697225i	$-0.754418\pi$
$79$	−12.7431	−1.43371	−0.716853	+	0.697225i	$0.754418\pi$
$80$	0.345356	0.0386120
$81$	13.1421	1.46024
$82$	0.793029	0.0875753
$83$	6.10241	0.669826	0.334913	−	0.942249i	$-0.391293\pi$
$83$	6.10241	0.669826	0.334913	+	0.942249i	$0.391293\pi$
$84$	0.855025	0.0932908
$85$	−1.94937	−0.211439
$86$	1.15782	0.124851
$87$	22.4768	2.40976
$88$	6.12763	0.653207
$89$	6.44432	0.683097	0.341548	−	0.939864i	$-0.389049\pi$
$89$	6.44432	0.683097	0.341548	+	0.939864i	$0.389049\pi$
$90$	−1.88070	−0.198243
$91$	−0.239034	−0.0250576
$92$	−2.19111	−0.228439
$93$	−10.2581	−1.06372
$94$	0.820122	0.0845892
$95$	1.63903	0.168161
$96$	18.0105	1.83818
$97$	−12.9886	−1.31879	−0.659394	−	0.751797i	$-0.729187\pi$
$97$	−12.9886	−1.31879	−0.659394	+	0.751797i	$0.729187\pi$
$98$	5.26618	0.531965
$99$	15.2166	1.52933
$100$	6.92626	0.692626
$101$	6.18139	0.615072	0.307536	−	0.951537i	$-0.400496\pi$
$101$	6.18139	0.615072	0.307536	+	0.951537i	$0.400496\pi$
$102$	−11.7318	−1.16163
$103$	7.78250	0.766833	0.383416	−	0.923576i	$-0.374747\pi$
$103$	7.78250	0.766833	0.383416	+	0.923576i	$0.374747\pi$
$104$	−3.17979	−0.311804
$105$	−0.231233	−0.0225661
$106$	−1.17477	−0.114104
$107$	−8.18217	−0.791000	−0.395500	−	0.918466i	$-0.629429\pi$
$107$	−8.18217	−0.791000	−0.395500	+	0.918466i	$0.629429\pi$
$108$	15.0851	1.45157
$109$	−5.32486	−0.510029	−0.255015	−	0.966937i	$-0.582080\pi$
$109$	−5.32486	−0.510029	−0.255015	+	0.966937i	$0.582080\pi$
$110$	−0.690275	−0.0658151
$111$	6.67107	0.633190
$112$	0.174325	0.0164722
$113$	−3.60573	−0.339199	−0.169599	−	0.985513i	$-0.554247\pi$
$113$	−3.60573	−0.339199	−0.169599	+	0.985513i	$0.554247\pi$
$114$	9.86411	0.923859
$115$	0.592565	0.0552570
$116$	10.4461	0.969892
$117$	−7.89633	−0.730016
$118$	−11.2291	−1.03372
$119$	−0.983983	−0.0902016
$120$	−3.07602	−0.280801
$121$	−5.41501	−0.492274
$122$	4.12290	0.373270
$123$	3.22097	0.290425
$124$	−4.76744	−0.428129
$125$	−3.80386	−0.340228
$126$	−0.949316	−0.0845718
$127$	−17.8352	−1.58262	−0.791308	−	0.611418i	$-0.790599\pi$
$127$	−17.8352	−1.58262	−0.791308	+	0.611418i	$0.790599\pi$
$128$	9.72337	0.859432
$129$	4.70262	0.414043
$130$	0.358202	0.0314164
$131$	−12.1841	−1.06453	−0.532267	−	0.846577i	$-0.678660\pi$
$131$	−12.1841	−1.06453	−0.532267	+	0.846577i	$0.678660\pi$
$132$	10.3669	0.902321
$133$	0.827331	0.0717387
$134$	8.56278	0.739711
$135$	−4.07963	−0.351118
$136$	−13.0896	−1.12242
$137$	−13.9009	−1.18764	−0.593819	−	0.804599i	$-0.702380\pi$
$137$	−13.9009	−1.18764	−0.593819	+	0.804599i	$0.702380\pi$
$138$	3.56621	0.303576
$139$	4.99920	0.424027	0.212013	−	0.977267i	$-0.431998\pi$
$139$	4.99920	0.424027	0.212013	+	0.977267i	$0.431998\pi$
$140$	−0.107465	−0.00908249
$141$	3.33101	0.280522
$142$	8.64099	0.725135
$143$	−2.89820	−0.242360
$144$	5.75872	0.479893
$145$	−2.82504	−0.234607
$146$	0.682462	0.0564809
$147$	21.3892	1.76415
$148$	3.10037	0.254849
$149$	17.4937	1.43314	0.716570	−	0.697515i	$-0.245711\pi$
$149$	17.4937	1.43314	0.716570	+	0.697515i	$0.245711\pi$
$150$	−11.2731	−0.920443
$151$	0.480306	0.0390867	0.0195434	−	0.999809i	$-0.493779\pi$
$151$	0.480306	0.0390867	0.0195434	+	0.999809i	$0.493779\pi$
$152$	11.0057	0.892682
$153$	−32.5052	−2.62789
$154$	−0.348429	−0.0280772
$155$	1.28931	0.103560
$156$	−5.37965	−0.430717
$157$	0.117389	0.00936869	0.00468434	−	0.999989i	$-0.498509\pi$
$157$	0.117389	0.00936869	0.00468434	+	0.999989i	$0.498509\pi$
$158$	9.63907	0.766843
$159$	−4.77147	−0.378402
$160$	−2.26368	−0.178959
$161$	0.299108	0.0235730
$162$	−9.94093	−0.781033
$163$	−12.5273	−0.981210	−0.490605	−	0.871382i	$-0.663224\pi$
$163$	−12.5273	−0.981210	−0.490605	+	0.871382i	$0.663224\pi$
$164$	1.49694	0.116891
$165$	−2.80362	−0.218262
$166$	−4.61597	−0.358268
$167$	−0.744061	−0.0575772	−0.0287886	−	0.999586i	$-0.509165\pi$
$167$	−0.744061	−0.0575772	−0.0287886	+	0.999586i	$0.509165\pi$
$168$	−1.55268	−0.119792
$169$	−11.4960	−0.884311
$170$	1.47454	0.113092
$171$	27.3303	2.09000
$172$	2.18554	0.166646
$173$	11.6073	0.882484	0.441242	−	0.897388i	$-0.354538\pi$
$173$	11.6073	0.882484	0.441242	+	0.897388i	$0.354538\pi$
$174$	−17.0018	−1.28891
$175$	−0.945505	−0.0714734
$176$	2.11363	0.159321
$177$	−45.6081	−3.42812
$178$	−4.87460	−0.365367
$179$	−21.1974	−1.58437	−0.792183	−	0.610284i	$-0.791055\pi$
$179$	−21.1974	−1.58437	−0.792183	+	0.610284i	$0.791055\pi$
$180$	−3.55005	−0.264605
$181$	11.9508	0.888299	0.444150	−	0.895953i	$-0.353506\pi$
$181$	11.9508	0.888299	0.444150	+	0.895953i	$0.353506\pi$
$182$	0.180809	0.0134025
$183$	16.7456	1.23787
$184$	3.97894	0.293332
$185$	−0.838467	−0.0616453
$186$	7.75941	0.568948
$187$	−11.9304	−0.872441
$188$	1.54808	0.112906
$189$	−2.05927	−0.149790
$190$	−1.23979	−0.0899438
$191$	24.2243	1.75281	0.876406	−	0.481574i	$-0.159935\pi$
$191$	24.2243	1.75281	0.876406	+	0.481574i	$0.159935\pi$
$192$	−8.12792	−0.586582
$193$	−5.78545	−0.416446	−0.208223	−	0.978081i	$-0.566768\pi$
$193$	−5.78545	−0.416446	−0.208223	+	0.978081i	$0.566768\pi$
$194$	9.82478	0.705378
$195$	1.45488	0.104186
$196$	9.94058	0.710042
$197$	4.06793	0.289828	0.144914	−	0.989444i	$-0.453709\pi$
$197$	4.06793	0.289828	0.144914	+	0.989444i	$0.453709\pi$
$198$	−11.5101	−0.817989
$199$	−11.4204	−0.809571	−0.404785	−	0.914412i	$-0.632654\pi$
$199$	−11.4204	−0.809571	−0.404785	+	0.914412i	$0.632654\pi$
$200$	−12.5777	−0.889381
$201$	34.7786	2.45310
$202$	−4.67571	−0.328982
$203$	−1.42599	−0.100085
$204$	−22.1453	−1.55048
$205$	−0.404834	−0.0282748
$206$	−5.88682	−0.410154
$207$	9.88084	0.686766
$208$	−1.09682	−0.0760509
$209$	10.0311	0.693866
$210$	0.174909	0.0120699
$211$	18.0941	1.24565	0.622824	−	0.782362i	$-0.285985\pi$
$211$	18.0941	1.24565	0.622824	+	0.782362i	$0.285985\pi$
$212$	−2.21753	−0.152301
$213$	35.0963	2.40476
$214$	6.18913	0.423080
$215$	−0.591058	−0.0403098
$216$	−27.3938	−1.86391
$217$	0.650804	0.0441794
$218$	4.02782	0.272798
$219$	2.77189	0.187307
$220$	−1.30298	−0.0878469
$221$	6.19103	0.416454
$222$	−5.04611	−0.338673
$223$	−21.1665	−1.41741	−0.708706	−	0.705504i	$-0.750721\pi$
$223$	−21.1665	−1.41741	−0.708706	+	0.705504i	$0.750721\pi$
$224$	−1.14263	−0.0763455
$225$	−31.2341	−2.08227
$226$	2.72744	0.181426
$227$	−13.3828	−0.888248	−0.444124	−	0.895965i	$-0.646485\pi$
$227$	−13.3828	−0.888248	−0.444124	+	0.895965i	$0.646485\pi$
$228$	18.6198	1.23312
$229$	−12.5484	−0.829225	−0.414612	−	0.909998i	$-0.636083\pi$
$229$	−12.5484	−0.829225	−0.414612	+	0.909998i	$0.636083\pi$
$230$	−0.448226	−0.0295552
$231$	−1.41518	−0.0931122
$232$	−18.9695	−1.24541
$233$	15.6538	1.02551	0.512757	−	0.858534i	$-0.328624\pi$
$233$	15.6538	1.02551	0.512757	+	0.858534i	$0.328624\pi$
$234$	5.97292	0.390462
$235$	−0.418665	−0.0273107
$236$	−21.1963	−1.37976
$237$	39.1501	2.54307
$238$	0.744302	0.0482459
$239$	3.45659	0.223588	0.111794	−	0.993731i	$-0.464340\pi$
$239$	3.45659	0.223588	0.111794	+	0.993731i	$0.464340\pi$
$240$	−1.06103	−0.0684891
$241$	28.7843	1.85416	0.927080	−	0.374864i	$-0.122311\pi$
$241$	28.7843	1.85416	0.927080	+	0.374864i	$0.122311\pi$
$242$	4.09601	0.263301
$243$	−8.68104	−0.556889
$244$	7.78249	0.498223
$245$	−2.68834	−0.171752
$246$	−2.43640	−0.155339
$247$	−5.20541	−0.331212
$248$	8.65743	0.549747
$249$	−18.7482	−1.18812
$250$	2.87731	0.181977
$251$	−1.82824	−0.115397	−0.0576986	−	0.998334i	$-0.518376\pi$
$251$	−1.82824	−0.115397	−0.0576986	+	0.998334i	$0.518376\pi$
$252$	−1.79195	−0.112882
$253$	3.62658	0.228001
$254$	13.4908	0.846490
$255$	5.98900	0.375046
$256$	−12.6461	−0.790380
$257$	3.65882	0.228231	0.114116	−	0.993467i	$-0.463597\pi$
$257$	3.65882	0.228231	0.114116	+	0.993467i	$0.463597\pi$
$258$	−3.55714	−0.221458
$259$	−0.423232	−0.0262983
$260$	0.676152	0.0419332
$261$	−47.1067	−2.91583
$262$	9.21630	0.569385
$263$	−13.1581	−0.811362	−0.405681	−	0.914015i	$-0.632966\pi$
$263$	−13.1581	−0.811362	−0.405681	+	0.914015i	$0.632966\pi$
$264$	−18.8257	−1.15864
$265$	0.599712	0.0368400
$266$	−0.625807	−0.0383707
$267$	−19.7987	−1.21166
$268$	16.1633	0.987332
$269$	−30.0225	−1.83050	−0.915251	−	0.402885i	$-0.868008\pi$
$269$	−30.0225	−1.83050	−0.915251	+	0.402885i	$0.868008\pi$
$270$	3.08590	0.187802
$271$	−9.04876	−0.549673	−0.274837	−	0.961491i	$-0.588624\pi$
$271$	−9.04876	−0.549673	−0.274837	+	0.961491i	$0.588624\pi$
$272$	−4.51506	−0.273766
$273$	0.734377	0.0444465
$274$	10.5149	0.635229
$275$	−11.4639	−0.691300
$276$	6.73168	0.405199
$277$	10.3482	0.621762	0.310881	−	0.950449i	$-0.399376\pi$
$277$	10.3482	0.621762	0.310881	+	0.950449i	$0.399376\pi$
$278$	−3.78148	−0.226798
$279$	21.4989	1.28710
$280$	0.195152	0.0116625
$281$	−19.3686	−1.15543	−0.577716	−	0.816238i	$-0.696056\pi$
$281$	−19.3686	−1.15543	−0.577716	+	0.816238i	$0.696056\pi$
$282$	−2.51964	−0.150042
$283$	9.72949	0.578358	0.289179	−	0.957275i	$-0.406618\pi$
$283$	9.72949	0.578358	0.289179	+	0.957275i	$0.406618\pi$
$284$	16.3109	0.967876
$285$	−5.03554	−0.298280
$286$	2.19225	0.129631
$287$	−0.204347	−0.0120622
$288$	−37.7462	−2.22421
$289$	8.48538	0.499140
$290$	2.13691	0.125484
$291$	39.9044	2.33924
$292$	1.28823	0.0753881
$293$	26.2321	1.53249	0.766247	−	0.642546i	$-0.222122\pi$
$293$	26.2321	1.53249	0.766247	+	0.642546i	$0.222122\pi$
$294$	−16.1791	−0.943586
$295$	5.73235	0.333750
$296$	−5.63012	−0.327244
$297$	−24.9679	−1.44879
$298$	−13.2325	−0.766540
$299$	−1.88193	−0.108835
$300$	−21.2793	−1.22856
$301$	−0.298348	−0.0171965
$302$	−0.363312	−0.0209062
$303$	−18.9909	−1.09100
$304$	3.79626	0.217730
$305$	−2.10470	−0.120515
$306$	24.5875	1.40557
$307$	−13.7097	−0.782455	−0.391228	−	0.920294i	$-0.627950\pi$
$307$	−13.7097	−0.782455	−0.391228	+	0.920294i	$0.627950\pi$
$308$	−0.657704	−0.0374762
$309$	−23.9099	−1.36019
$310$	−0.975257	−0.0553909
$311$	30.9043	1.75242	0.876212	−	0.481926i	$-0.160063\pi$
$311$	30.9043	1.75242	0.876212	+	0.481926i	$0.160063\pi$
$312$	9.76918	0.553071
$313$	−28.2287	−1.59558	−0.797790	−	0.602935i	$-0.793998\pi$
$313$	−28.2287	−1.59558	−0.797790	+	0.602935i	$0.793998\pi$
$314$	−0.0887953	−0.00501101
$315$	0.484617	0.0273051
$316$	18.1949	1.02355
$317$	−7.55793	−0.424496	−0.212248	−	0.977216i	$-0.568078\pi$
$317$	−7.55793	−0.424496	−0.212248	+	0.977216i	$0.568078\pi$
$318$	3.60922	0.202395
$319$	−17.2896	−0.968034
$320$	1.02157	0.0571077
$321$	25.1378	1.40306
$322$	−0.226251	−0.0126085
$323$	−21.4281	−1.19229
$324$	−18.7648	−1.04249
$325$	5.94894	0.329988
$326$	9.47583	0.524818
$327$	16.3594	0.904678
$328$	−2.71837	−0.150097
$329$	−0.211329	−0.0116509
$330$	2.12071	0.116741
$331$	20.4225	1.12252	0.561260	−	0.827640i	$-0.310317\pi$
$331$	20.4225	1.12252	0.561260	+	0.827640i	$0.310317\pi$
$332$	−8.71322	−0.478200
$333$	−13.9812	−0.766164
$334$	0.562821	0.0307962
$335$	−4.37122	−0.238825
$336$	−0.535574	−0.0292179
$337$	16.7603	0.912994	0.456497	−	0.889725i	$-0.349104\pi$
$337$	16.7603	0.912994	0.456497	+	0.889725i	$0.349104\pi$
$338$	8.69581	0.472990
$339$	11.0778	0.601662
$340$	2.78338	0.150950
$341$	7.89077	0.427309
$342$	−20.6731	−1.11788
$343$	−2.72138	−0.146941
$344$	−3.96882	−0.213985
$345$	−1.82052	−0.0980135
$346$	−8.77994	−0.472012
$347$	14.1418	0.759171	0.379586	−	0.925157i	$-0.376067\pi$
$347$	14.1418	0.759171	0.379586	+	0.925157i	$0.376067\pi$
$348$	−32.0931	−1.72037
$349$	−22.1523	−1.18579	−0.592893	−	0.805282i	$-0.702014\pi$
$349$	−22.1523	−1.18579	−0.592893	+	0.805282i	$0.702014\pi$
$350$	0.715196	0.0382288
$351$	12.9565	0.691568
$352$	−13.8540	−0.738423
$353$	17.2209	0.916574	0.458287	−	0.888804i	$-0.348463\pi$
$353$	17.2209	0.916574	0.458287	+	0.888804i	$0.348463\pi$
$354$	34.4988	1.83359
$355$	−4.41114	−0.234119
$356$	−9.20141	−0.487674
$357$	3.02306	0.159997
$358$	16.0341	0.847426
$359$	21.9672	1.15938	0.579692	−	0.814836i	$-0.303173\pi$
$359$	21.9672	1.15938	0.579692	+	0.814836i	$0.303173\pi$
$360$	6.44671	0.339771
$361$	−0.983329	−0.0517541
$362$	−9.03983	−0.475123
$363$	16.6364	0.873183
$364$	0.341300	0.0178890
$365$	−0.348390	−0.0182356
$366$	−12.6667	−0.662097
$367$	−13.1841	−0.688202	−0.344101	−	0.938933i	$-0.611816\pi$
$367$	−13.1841	−0.688202	−0.344101	+	0.938933i	$0.611816\pi$
$368$	1.37248	0.0715452
$369$	−6.75048	−0.351416
$370$	0.634231	0.0329721
$371$	0.302716	0.0157162
$372$	14.6469	0.759404
$373$	−35.2516	−1.82526	−0.912630	−	0.408787i	$-0.865952\pi$
$373$	−35.2516	−1.82526	−0.912630	+	0.408787i	$0.865952\pi$
$374$	9.02440	0.466641
$375$	11.6865	0.603488
$376$	−2.81124	−0.144979
$377$	8.97207	0.462085
$378$	1.55767	0.0801177
$379$	23.6003	1.21227	0.606134	−	0.795363i	$-0.292720\pi$
$379$	23.6003	1.21227	0.606134	+	0.795363i	$0.292720\pi$
$380$	−2.34026	−0.120053
$381$	54.7945	2.80721
$382$	−18.3237	−0.937522
$383$	−13.1311	−0.670970	−0.335485	−	0.942046i	$-0.608900\pi$
$383$	−13.1311	−0.670970	−0.335485	+	0.942046i	$0.608900\pi$
$384$	−29.8728	−1.52444
$385$	0.177870	0.00906509
$386$	4.37622	0.222744
$387$	−9.85572	−0.500994
$388$	18.5455	0.941505
$389$	29.2216	1.48159	0.740797	−	0.671729i	$-0.234448\pi$
$389$	29.2216	1.48159	0.740797	+	0.671729i	$0.234448\pi$
$390$	−1.10049	−0.0557257
$391$	−7.74697	−0.391781
$392$	−18.0516	−0.911743
$393$	37.4330	1.88824
$394$	−3.07706	−0.155020
$395$	−4.92065	−0.247585
$396$	−21.7268	−1.09181
$397$	26.2129	1.31559	0.657795	−	0.753197i	$-0.271489\pi$
$397$	26.2129	1.31559	0.657795	+	0.753197i	$0.271489\pi$
$398$	8.63859	0.433013
$399$	−2.54178	−0.127248
$400$	−4.33850	−0.216925
$401$	−24.3910	−1.21803	−0.609014	−	0.793160i	$-0.708435\pi$
$401$	−24.3910	−1.21803	−0.609014	+	0.793160i	$0.708435\pi$
$402$	−26.3072	−1.31208
$403$	−4.09473	−0.203973
$404$	−8.82599	−0.439110
$405$	5.07476	0.252167
$406$	1.07864	0.0535322
$407$	−5.13154	−0.254361
$408$	40.2148	1.99093
$409$	13.2071	0.653051	0.326526	−	0.945188i	$-0.394122\pi$
$409$	13.2071	0.653051	0.326526	+	0.945188i	$0.394122\pi$
$410$	0.306223	0.0151233
$411$	42.7074	2.10660
$412$	−11.1121	−0.547454
$413$	2.89351	0.142380
$414$	−7.47404	−0.367329
$415$	2.35641	0.115672
$416$	7.18924	0.352481
$417$	−15.3589	−0.752129
$418$	−7.58770	−0.371126
$419$	15.8597	0.774799	0.387400	−	0.921912i	$-0.373373\pi$
$419$	15.8597	0.774799	0.387400	+	0.921912i	$0.373373\pi$
$420$	0.330163	0.0161103
$421$	−4.53957	−0.221245	−0.110622	−	0.993863i	$-0.535284\pi$
$421$	−4.53957	−0.221245	−0.110622	+	0.993863i	$0.535284\pi$
$422$	−13.6867	−0.666257
$423$	−6.98111	−0.339433
$424$	4.02693	0.195565
$425$	24.4888	1.18788
$426$	−26.5474	−1.28623
$427$	−1.06239	−0.0514126
$428$	11.6828	0.564708
$429$	8.90406	0.429892
$430$	0.447087	0.0215604
$431$	−24.0460	−1.15825	−0.579126	−	0.815238i	$-0.696606\pi$
$431$	−24.0460	−1.15825	−0.579126	+	0.815238i	$0.696606\pi$
$432$	−9.44907	−0.454619
$433$	−20.8069	−0.999914	−0.499957	−	0.866050i	$-0.666651\pi$
$433$	−20.8069	−0.999914	−0.499957	+	0.866050i	$0.666651\pi$
$434$	−0.492279	−0.0236302
$435$	8.67928	0.416140
$436$	7.60301	0.364118
$437$	6.51364	0.311590
$438$	−2.09671	−0.100185
$439$	−27.0822	−1.29256	−0.646282	−	0.763098i	$-0.723677\pi$
$439$	−27.0822	−1.29256	−0.646282	+	0.763098i	$0.723677\pi$
$440$	2.36615	0.112802
$441$	−44.8273	−2.13463
$442$	−4.68301	−0.222748
$443$	26.1108	1.24056	0.620282	−	0.784379i	$-0.287018\pi$
$443$	26.1108	1.24056	0.620282	+	0.784379i	$0.287018\pi$
$444$	−9.52517	−0.452045
$445$	2.48844	0.117963
$446$	16.0107	0.758129
$447$	−53.7454	−2.54207
$448$	0.515658	0.0243626
$449$	18.4224	0.869407	0.434703	−	0.900574i	$-0.356853\pi$
$449$	18.4224	0.869407	0.434703	+	0.900574i	$0.356853\pi$
$450$	23.6260	1.11374
$451$	−2.47764	−0.116668
$452$	5.14838	0.242159
$453$	−1.47563	−0.0693311
$454$	10.1230	0.475095
$455$	−0.0923016	−0.00432716
$456$	−33.8125	−1.58342
$457$	−3.55147	−0.166131	−0.0830654	−	0.996544i	$-0.526471\pi$
$457$	−3.55147	−0.166131	−0.0830654	+	0.996544i	$0.526471\pi$
$458$	9.49186	0.443526
$459$	53.3355	2.48949
$460$	−0.846084	−0.0394489
$461$	−2.86665	−0.133513	−0.0667565	−	0.997769i	$-0.521265\pi$
$461$	−2.86665	−0.133513	−0.0667565	+	0.997769i	$0.521265\pi$
$462$	1.07047	0.0498027
$463$	30.5287	1.41879	0.709395	−	0.704811i	$-0.248968\pi$
$463$	30.5287	1.41879	0.709395	+	0.704811i	$0.248968\pi$
$464$	−6.54324	−0.303762
$465$	−3.96111	−0.183692
$466$	−11.8408	−0.548515
$467$	18.7000	0.865332	0.432666	−	0.901554i	$-0.357573\pi$
$467$	18.7000	0.865332	0.432666	+	0.901554i	$0.357573\pi$
$468$	11.2746	0.521170
$469$	−2.20646	−0.101885
$470$	0.316685	0.0146076
$471$	−0.360652	−0.0166179
$472$	38.4914	1.77171
$473$	−3.61736	−0.166326
$474$	−29.6138	−1.36021
$475$	−20.5901	−0.944740
$476$	1.40496	0.0643964
$477$	10.0000	0.457869
$478$	−2.61463	−0.119590
$479$	7.50976	0.343130	0.171565	−	0.985173i	$-0.445118\pi$
$479$	7.50976	0.343130	0.171565	+	0.985173i	$0.445118\pi$
$480$	6.95463	0.317434
$481$	2.66289	0.121418
$482$	−21.7729	−0.991730
$483$	−0.918941	−0.0418133
$484$	7.73173	0.351442
$485$	−5.01546	−0.227740
$486$	6.56649	0.297862
$487$	32.6786	1.48081	0.740404	−	0.672162i	$-0.234634\pi$
$487$	32.6786	1.48081	0.740404	+	0.672162i	$0.234634\pi$
$488$	−14.1326	−0.639753
$489$	38.4871	1.74045
$490$	2.03351	0.0918644
$491$	2.81716	0.127137	0.0635683	−	0.997977i	$-0.479752\pi$
$491$	2.81716	0.127137	0.0635683	+	0.997977i	$0.479752\pi$
$492$	−4.59901	−0.207339
$493$	36.9335	1.66340
$494$	3.93746	0.177155
$495$	5.87582	0.264098
$496$	2.98625	0.134087
$497$	−2.22661	−0.0998770
$498$	14.1815	0.635488
$499$	29.0591	1.30086	0.650432	−	0.759564i	$-0.274588\pi$
$499$	29.0591	1.30086	0.650432	+	0.759564i	$0.274588\pi$
$500$	5.43128	0.242894
$501$	2.28596	0.102129
$502$	1.38291	0.0617223
$503$	−1.00000	−0.0445878
$503$	−1.00000	−0.0445878
$504$	3.25410	0.144949
$505$	2.38691	0.106216
$506$	−2.74321	−0.121951
$507$	35.3189	1.56857
$508$	25.4656	1.12986
$509$	7.58042	0.335996	0.167998	−	0.985787i	$-0.446270\pi$
$509$	7.58042	0.335996	0.167998	+	0.985787i	$0.446270\pi$
$510$	−4.53018	−0.200600
$511$	−0.175857	−0.00777944
$512$	−9.88103	−0.436684
$513$	−44.8444	−1.97993
$514$	−2.76760	−0.122074
$515$	3.00517	0.132423
$516$	−6.71456	−0.295592
$517$	−2.56229	−0.112689
$518$	0.320140	0.0140661
$519$	−35.6607	−1.56533
$520$	−1.22786	−0.0538451
$521$	−8.90148	−0.389981	−0.194990	−	0.980805i	$-0.562468\pi$
$521$	−8.90148	−0.389981	−0.194990	+	0.980805i	$0.562468\pi$
$522$	35.6323	1.55958
$523$	37.7311	1.64986	0.824932	−	0.565232i	$-0.191213\pi$
$523$	37.7311	1.64986	0.824932	+	0.565232i	$0.191213\pi$
$524$	17.3969	0.759988
$525$	2.90484	0.126778
$526$	9.95301	0.433972
$527$	−16.8560	−0.734257
$528$	−6.49365	−0.282600
$529$	−20.6451	−0.897613
$530$	−0.453632	−0.0197045
$531$	95.5852	4.14804
$532$	−1.18129	−0.0512154
$533$	1.28572	0.0556905
$534$	14.9761	0.648078
$535$	−3.15950	−0.136597
$536$	−29.3518	−1.26780
$537$	65.1240	2.81031
$538$	22.7095	0.979076
$539$	−16.4530	−0.708682
$540$	5.82503	0.250669
$541$	11.6293	0.499981	0.249990	−	0.968248i	$-0.419573\pi$
$541$	11.6293	0.499981	0.249990	+	0.968248i	$0.419573\pi$
$542$	6.84464	0.294003
$543$	−36.7162	−1.57564
$544$	29.5945	1.26885
$545$	−2.05616	−0.0880764
$546$	−0.555495	−0.0237730
$547$	−13.4958	−0.577040	−0.288520	−	0.957474i	$-0.593163\pi$
$547$	−13.4958	−0.577040	−0.288520	+	0.957474i	$0.593163\pi$
$548$	19.8482	0.847874
$549$	−35.0953	−1.49783
$550$	8.67150	0.369754
$551$	−31.0536	−1.32293
$552$	−12.2244	−0.520304
$553$	−2.48379	−0.105622
$554$	−7.82754	−0.332560
$555$	2.57599	0.109345
$556$	−7.13803	−0.302720
$557$	−34.2002	−1.44911	−0.724554	−	0.689218i	$-0.757954\pi$
$557$	−34.2002	−1.44911	−0.724554	+	0.689218i	$0.757954\pi$
$558$	−16.2621	−0.688430
$559$	1.87715	0.0793949
$560$	0.0673146	0.00284456
$561$	36.6536	1.54751
$562$	14.6507	0.618003
$563$	25.6005	1.07893	0.539467	−	0.842007i	$-0.318626\pi$
$563$	25.6005	1.07893	0.539467	+	0.842007i	$0.318626\pi$
$564$	−4.75613	−0.200269
$565$	−1.39233	−0.0585758
$566$	−7.35956	−0.309345
$567$	2.56158	0.107576
$568$	−29.6199	−1.24282
$569$	−17.2311	−0.722363	−0.361182	−	0.932495i	$-0.617627\pi$
$569$	−17.2311	−0.722363	−0.361182	+	0.932495i	$0.617627\pi$
$570$	3.80897	0.159540
$571$	2.79325	0.116894	0.0584470	−	0.998291i	$-0.481385\pi$
$571$	2.79325	0.116894	0.0584470	+	0.998291i	$0.481385\pi$
$572$	4.13815	0.173025
$573$	−74.4237	−3.10909
$574$	0.154572	0.00645171
$575$	−7.44403	−0.310438
$576$	17.0344	0.709768
$577$	−40.1143	−1.66998	−0.834991	−	0.550264i	$-0.814527\pi$
$577$	−40.1143	−1.66998	−0.834991	+	0.550264i	$0.814527\pi$
$578$	−6.41849	−0.266974
$579$	17.7745	0.738682
$580$	4.03368	0.167490
$581$	1.18944	0.0493464
$582$	−30.1844	−1.25118
$583$	3.67032	0.152009
$584$	−2.33936	−0.0968036
$585$	−3.04912	−0.126066
$586$	−19.8424	−0.819682
$587$	−38.5445	−1.59090	−0.795451	−	0.606018i	$-0.792766\pi$
$587$	−38.5445	−1.59090	−0.795451	+	0.606018i	$0.792766\pi$
$588$	−30.5402	−1.25945
$589$	14.1725	0.583966
$590$	−4.33605	−0.178512
$591$	−12.4978	−0.514090
$592$	−1.94202	−0.0798167
$593$	−25.0372	−1.02816	−0.514078	−	0.857744i	$-0.671866\pi$
$593$	−25.0372	−1.02816	−0.514078	+	0.857744i	$0.671866\pi$
$594$	18.8862	0.774909
$595$	−0.379959	−0.0155768
$596$	−24.9781	−1.02314
$597$	35.0865	1.43600
$598$	1.42353	0.0582123
$599$	−23.0220	−0.940655	−0.470328	−	0.882492i	$-0.655864\pi$
$599$	−23.0220	−0.940655	−0.470328	+	0.882492i	$0.655864\pi$
$600$	38.6422	1.57756
$601$	−33.9451	−1.38465	−0.692326	−	0.721585i	$-0.743414\pi$
$601$	−33.9451	−1.38465	−0.692326	+	0.721585i	$0.743414\pi$
$602$	0.225675	0.00919784
$603$	−72.8888	−2.96826
$604$	−0.685796	−0.0279046
$605$	−2.09097	−0.0850102
$606$	14.3650	0.583540
$607$	24.3039	0.986467	0.493233	−	0.869897i	$-0.335815\pi$
$607$	24.3039	0.986467	0.493233	+	0.869897i	$0.335815\pi$
$608$	−24.8830	−1.00914
$609$	4.38103	0.177528
$610$	1.59203	0.0644595
$611$	1.32964	0.0537916
$612$	46.4120	1.87609
$613$	34.5604	1.39588	0.697940	−	0.716156i	$-0.254100\pi$
$613$	34.5604	1.39588	0.697940	+	0.716156i	$0.254100\pi$
$614$	10.3703	0.418510
$615$	1.24376	0.0501532
$616$	1.19436	0.0481220
$617$	34.3607	1.38331	0.691655	−	0.722228i	$-0.256882\pi$
$617$	34.3607	1.38331	0.691655	+	0.722228i	$0.256882\pi$
$618$	18.0859	0.727521
$619$	1.08451	0.0435902	0.0217951	−	0.999762i	$-0.493062\pi$
$619$	1.08451	0.0435902	0.0217951	+	0.999762i	$0.493062\pi$
$620$	−1.84092	−0.0739331
$621$	−16.2128	−0.650597
$622$	−23.3766	−0.937315
$623$	1.25609	0.0503240
$624$	3.36973	0.134897
$625$	22.7856	0.911425
$626$	21.3527	0.853425
$627$	−30.8182	−1.23076
$628$	−0.167612	−0.00668846
$629$	10.9618	0.437076
$630$	−0.366573	−0.0146046
$631$	−6.03426	−0.240220	−0.120110	−	0.992761i	$-0.538325\pi$
$631$	−6.03426	−0.240220	−0.120110	+	0.992761i	$0.538325\pi$
$632$	−33.0411	−1.31430
$633$	−55.5899	−2.20950
$634$	5.71695	0.227049
$635$	−6.88695	−0.273300
$636$	6.81286	0.270148
$637$	8.53792	0.338285
$638$	13.0782	0.517770
$639$	−73.5545	−2.90977
$640$	3.75462	0.148414
$641$	−22.0716	−0.871778	−0.435889	−	0.900001i	$-0.643566\pi$
$641$	−22.0716	−0.871778	−0.435889	+	0.900001i	$0.643566\pi$
$642$	−19.0147	−0.750450
$643$	−40.6373	−1.60258	−0.801290	−	0.598277i	$-0.795852\pi$
$643$	−40.6373	−1.60258	−0.801290	+	0.598277i	$0.795852\pi$
$644$	−0.427077	−0.0168292
$645$	1.81589	0.0715006
$646$	16.2086	0.637717
$647$	22.9719	0.903118	0.451559	−	0.892241i	$-0.350868\pi$
$647$	22.9719	0.903118	0.451559	+	0.892241i	$0.350868\pi$
$648$	34.0759	1.33863
$649$	35.0828	1.37712
$650$	−4.49988	−0.176500
$651$	−1.99944	−0.0783644
$652$	17.8868	0.700502
$653$	−39.0459	−1.52798	−0.763992	−	0.645226i	$-0.776763\pi$
$653$	−39.0459	−1.52798	−0.763992	+	0.645226i	$0.776763\pi$
$654$	−12.3745	−0.483883
$655$	−4.70483	−0.183833
$656$	−0.937660	−0.0366095
$657$	−5.80931	−0.226643
$658$	0.159853	0.00623172
$659$	−26.6054	−1.03640	−0.518199	−	0.855260i	$-0.673397\pi$
$659$	−26.6054	−1.03640	−0.518199	+	0.855260i	$0.673397\pi$
$660$	4.00311	0.155821
$661$	−39.3661	−1.53116	−0.765582	−	0.643338i	$-0.777549\pi$
$661$	−39.3661	−1.53116	−0.765582	+	0.643338i	$0.777549\pi$
$662$	−15.4479	−0.600400
$663$	−19.0205	−0.738696
$664$	15.8228	0.614042
$665$	0.319469	0.0123885
$666$	10.5756	0.409796
$667$	−11.2269	−0.434709
$668$	1.06239	0.0411053
$669$	65.0291	2.51417
$670$	3.30647	0.127740
$671$	−12.8811	−0.497269
$672$	3.51048	0.135420
$673$	−13.4145	−0.517090	−0.258545	−	0.965999i	$-0.583243\pi$
$673$	−13.4145	−0.517090	−0.258545	+	0.965999i	$0.583243\pi$
$674$	−12.6778	−0.488331
$675$	51.2499	1.97261
$676$	16.4144	0.631324
$677$	−2.13435	−0.0820299	−0.0410149	−	0.999159i	$-0.513059\pi$
$677$	−2.13435	−0.0820299	−0.0410149	+	0.999159i	$0.513059\pi$
$678$	−8.37942	−0.321810
$679$	−2.53165	−0.0971557
$680$	−5.05448	−0.193830
$681$	41.1156	1.57555
$682$	−5.96871	−0.228554
$683$	21.3544	0.817105	0.408552	−	0.912735i	$-0.366034\pi$
$683$	21.3544	0.817105	0.408552	+	0.912735i	$0.366034\pi$
$684$	−39.0231	−1.49209
$685$	−5.36777	−0.205092
$686$	2.05850	0.0785940
$687$	38.5522	1.47086
$688$	−1.36899	−0.0521921
$689$	−1.90463	−0.0725606
$690$	1.37707	0.0524242
$691$	13.8167	0.525614	0.262807	−	0.964848i	$-0.415352\pi$
$691$	13.8167	0.525614	0.262807	+	0.964848i	$0.415352\pi$
$692$	−16.5732	−0.630020
$693$	2.96593	0.112666
$694$	−10.6971	−0.406056
$695$	1.93041	0.0732247
$696$	58.2794	2.20908
$697$	5.29265	0.200473
$698$	16.7564	0.634238
$699$	−48.0927	−1.81903
$700$	1.35002	0.0510260
$701$	45.1209	1.70419	0.852097	−	0.523385i	$-0.175331\pi$
$701$	45.1209	1.70419	0.852097	+	0.523385i	$0.175331\pi$
$702$	−9.80054	−0.369898
$703$	−9.21666	−0.347613
$704$	6.25217	0.235638
$705$	1.28625	0.0484430
$706$	−13.0262	−0.490246
$707$	1.20484	0.0453126
$708$	65.1208	2.44739
$709$	−37.6350	−1.41341	−0.706706	−	0.707507i	$-0.749820\pi$
$709$	−37.6350	−1.41341	−0.706706	+	0.707507i	$0.749820\pi$
$710$	3.33667	0.125223
$711$	−82.0505	−3.07713
$712$	16.7093	0.626208
$713$	5.12383	0.191889
$714$	−2.28670	−0.0855774
$715$	−1.11912	−0.0418529
$716$	30.2663	1.13110
$717$	−10.6196	−0.396596
$718$	−16.6164	−0.620117
$719$	−34.9860	−1.30476	−0.652380	−	0.757892i	$-0.726229\pi$
$719$	−34.9860	−1.30476	−0.652380	+	0.757892i	$0.726229\pi$
$720$	2.22369	0.0828722
$721$	1.51691	0.0564929
$722$	0.743807	0.0276816
$723$	−88.4331	−3.28886
$724$	−17.0638	−0.634171
$725$	35.4892	1.31804
$726$	−12.5840	−0.467038
$727$	0.0594046	0.00220319	0.00110160	−	0.999999i	$-0.499649\pi$
$727$	0.0594046	0.00220319	0.00110160	+	0.999999i	$0.499649\pi$
$728$	−0.619784	−0.0229707
$729$	−12.7559	−0.472440
$730$	0.263529	0.00975363
$731$	7.72727	0.285804
$732$	−23.9099	−0.883736
$733$	−23.6914	−0.875060	−0.437530	−	0.899204i	$-0.644147\pi$
$733$	−23.6914	−0.875060	−0.437530	+	0.899204i	$0.644147\pi$
$734$	9.97265	0.368097
$735$	8.25930	0.304649
$736$	−8.99605	−0.331599
$737$	−26.7525	−0.985441
$738$	5.10618	0.187961
$739$	−13.2539	−0.487551	−0.243776	−	0.969832i	$-0.578386\pi$
$739$	−13.2539	−0.487551	−0.243776	+	0.969832i	$0.578386\pi$
$740$	1.19719	0.0440096
$741$	15.9924	0.587496
$742$	−0.228979	−0.00840610
$743$	−13.7983	−0.506210	−0.253105	−	0.967439i	$-0.581452\pi$
$743$	−13.7983	−0.506210	−0.253105	+	0.967439i	$0.581452\pi$
$744$	−26.5980	−0.975129
$745$	6.75509	0.247487
$746$	26.6649	0.976273
$747$	39.2924	1.43763
$748$	17.0347	0.622850
$749$	−1.59481	−0.0582733
$750$	−8.83987	−0.322786
$751$	3.82043	0.139410	0.0697048	−	0.997568i	$-0.477794\pi$
$751$	3.82043	0.139410	0.0697048	+	0.997568i	$0.477794\pi$
$752$	−0.969695	−0.0353611
$753$	5.61683	0.204689
$754$	−6.78663	−0.247154
$755$	0.185467	0.00674984
$756$	2.94029	0.106937
$757$	19.6215	0.713157	0.356578	−	0.934265i	$-0.383943\pi$
$757$	19.6215	0.713157	0.356578	+	0.934265i	$0.383943\pi$
$758$	−17.8517	−0.648403
$759$	−11.1418	−0.404423
$760$	4.24979	0.154156
$761$	47.5141	1.72238	0.861192	−	0.508280i	$-0.169719\pi$
$761$	47.5141	1.72238	0.861192	+	0.508280i	$0.169719\pi$
$762$	−41.4475	−1.50148
$763$	−1.03789	−0.0375741
$764$	−34.5883	−1.25136
$765$	−12.5517	−0.453808
$766$	9.93262	0.358880
$767$	−18.2054	−0.657360
$768$	38.8521	1.40196
$769$	−10.0139	−0.361111	−0.180556	−	0.983565i	$-0.557790\pi$
$769$	−10.0139	−0.361111	−0.180556	+	0.983565i	$0.557790\pi$
$770$	−0.134544	−0.00484863
$771$	−11.2409	−0.404831
$772$	8.26066	0.297308
$773$	−35.8956	−1.29108	−0.645538	−	0.763728i	$-0.723367\pi$
$773$	−35.8956	−1.29108	−0.645538	+	0.763728i	$0.723367\pi$
$774$	7.45504	0.267966
$775$	−16.1968	−0.581807
$776$	−33.6777	−1.20896
$777$	1.30028	0.0466474
$778$	−22.1037	−0.792457
$779$	−4.45005	−0.159439
$780$	−2.07732	−0.0743800
$781$	−26.9968	−0.966023
$782$	5.85995	0.209551
$783$	77.2940	2.76226
$784$	−6.22662	−0.222379
$785$	0.0453292	0.00161787
$786$	−28.3149	−1.00996
$787$	1.89211	0.0674464	0.0337232	−	0.999431i	$-0.489264\pi$
$787$	1.89211	0.0674464	0.0337232	+	0.999431i	$0.489264\pi$
$788$	−5.80833	−0.206913
$789$	40.4252	1.43917
$790$	3.72207	0.132425
$791$	−0.702806	−0.0249889
$792$	39.4548	1.40197
$793$	6.68434	0.237368
$794$	−19.8279	−0.703667
$795$	−1.84248	−0.0653459
$796$	16.3064	0.577966
$797$	24.4028	0.864393	0.432197	−	0.901779i	$-0.357739\pi$
$797$	24.4028	0.864393	0.432197	+	0.901779i	$0.357739\pi$
$798$	1.92265	0.0680610
$799$	5.47347	0.193637
$800$	28.4372	1.00541
$801$	41.4940	1.46612
$802$	18.4498	0.651484
$803$	−2.13220	−0.0752437
$804$	−49.6581	−1.75131
$805$	0.115499	0.00407080
$806$	3.09733	0.109099
$807$	92.2371	3.24690
$808$	16.0276	0.563848
$809$	−32.9341	−1.15790	−0.578951	−	0.815363i	$-0.696538\pi$
$809$	−32.9341	−1.15790	−0.578951	+	0.815363i	$0.696538\pi$
$810$	−3.83863	−0.134876
$811$	−42.8145	−1.50342	−0.751711	−	0.659493i	$-0.770771\pi$
$811$	−42.8145	−1.50342	−0.751711	+	0.659493i	$0.770771\pi$
$812$	2.03608	0.0714523
$813$	27.8002	0.974997
$814$	3.88158	0.136049
$815$	−4.83732	−0.169444
$816$	13.8715	0.485599
$817$	−6.49708	−0.227304
$818$	−9.99011	−0.349296
$819$	−1.53910	−0.0537805
$820$	0.578035	0.0201859
$821$	−28.2632	−0.986393	−0.493196	−	0.869918i	$-0.664172\pi$
$821$	−28.2632	−0.986393	−0.493196	+	0.869918i	$0.664172\pi$
$822$	−32.3046	−1.12675
$823$	10.4127	0.362962	0.181481	−	0.983394i	$-0.441911\pi$
$823$	10.4127	0.362962	0.181481	+	0.983394i	$0.441911\pi$
$824$	20.1790	0.702970
$825$	35.2202	1.22621
$826$	−2.18870	−0.0761547
$827$	−0.0841446	−0.00292600	−0.00146300	−	0.999999i	$-0.500466\pi$
$827$	−0.0841446	−0.00292600	−0.00146300	+	0.999999i	$0.500466\pi$
$828$	−14.1082	−0.490294
$829$	46.3470	1.60970	0.804850	−	0.593479i	$-0.202246\pi$
$829$	46.3470	1.60970	0.804850	+	0.593479i	$0.202246\pi$
$830$	−1.78243	−0.0618690
$831$	−31.7924	−1.10287
$832$	−3.24442	−0.112480
$833$	35.1463	1.21775
$834$	11.6177	0.402289
$835$	−0.287315	−0.00994294
$836$	−14.3227	−0.495362
$837$	−35.2760	−1.21932
$838$	−11.9966	−0.414415
$839$	−13.9611	−0.481990	−0.240995	−	0.970526i	$-0.577474\pi$
$839$	−13.9611	−0.481990	−0.240995	+	0.970526i	$0.577474\pi$
$840$	−0.599559	−0.0206867
$841$	24.5241	0.845660
$842$	3.43381	0.118337
$843$	59.5054	2.04948
$844$	−25.8353	−0.889289
$845$	−4.43913	−0.152711
$846$	5.28063	0.181552
$847$	−1.05546	−0.0362660
$848$	1.38903	0.0476994
$849$	−29.8916	−1.02588
$850$	−18.5237	−0.635359
$851$	−3.33214	−0.114224
$852$	−50.1116	−1.71680
$853$	−54.5527	−1.86785	−0.933924	−	0.357472i	$-0.883639\pi$
$853$	−54.5527	−1.86785	−0.933924	+	0.357472i	$0.883639\pi$
$854$	0.803609	0.0274989
$855$	10.5534	0.360920
$856$	−21.2153	−0.725124
$857$	27.6798	0.945525	0.472762	−	0.881190i	$-0.343257\pi$
$857$	27.6798	0.945525	0.472762	+	0.881190i	$0.343257\pi$
$858$	−6.73519	−0.229935
$859$	27.1497	0.926336	0.463168	−	0.886270i	$-0.346713\pi$
$859$	27.1497	0.926336	0.463168	+	0.886270i	$0.346713\pi$
$860$	0.843932	0.0287778
$861$	0.627810	0.0213957
$862$	18.1888	0.619512
$863$	25.9641	0.883827	0.441913	−	0.897058i	$-0.354300\pi$
$863$	25.9641	0.883827	0.441913	+	0.897058i	$0.354300\pi$
$864$	61.9350	2.10707
$865$	4.48208	0.152395
$866$	15.7387	0.534822
$867$	−26.0694	−0.885363
$868$	−0.929239	−0.0315404
$869$	−30.1151	−1.02159
$870$	−6.56516	−0.222580
$871$	13.8826	0.470394
$872$	−13.8067	−0.467554
$873$	−83.6313	−2.83049
$874$	−4.92703	−0.166659
$875$	−0.741425	−0.0250647
$876$	−3.95780	−0.133722
$877$	37.2176	1.25675	0.628374	−	0.777911i	$-0.283721\pi$
$877$	37.2176	1.25675	0.628374	+	0.777911i	$0.283721\pi$
$878$	20.4855	0.691351
$879$	−80.5920	−2.71830
$880$	0.816166	0.0275130
$881$	−6.44185	−0.217031	−0.108516	−	0.994095i	$-0.534610\pi$
$881$	−6.44185	−0.217031	−0.108516	+	0.994095i	$0.534610\pi$
$882$	33.9081	1.14175
$883$	45.9727	1.54711	0.773553	−	0.633732i	$-0.218478\pi$
$883$	45.9727	1.54711	0.773553	+	0.633732i	$0.218478\pi$
$884$	−8.83976	−0.297313
$885$	−17.6113	−0.591998
$886$	−19.7507	−0.663538
$887$	−28.3187	−0.950849	−0.475425	−	0.879756i	$-0.657706\pi$
$887$	−28.3187	−0.950849	−0.475425	+	0.879756i	$0.657706\pi$
$888$	17.2972	0.580457
$889$	−3.47632	−0.116592
$890$	−1.88230	−0.0630947
$891$	31.0582	1.04049
$892$	30.2222	1.01191
$893$	−4.60208	−0.154003
$894$	40.6539	1.35967
$895$	−8.18524	−0.273602
$896$	1.89522	0.0633147
$897$	5.78181	0.193049
$898$	−13.9350	−0.465018
$899$	−24.4277	−0.814710
$900$	44.5971	1.48657
$901$	−7.84041	−0.261202
$902$	1.87413	0.0624017
$903$	0.916604	0.0305027
$904$	−9.34920	−0.310950
$905$	4.61475	0.153399
$906$	1.11619	0.0370830
$907$	−12.5099	−0.415384	−0.207692	−	0.978194i	$-0.566595\pi$
$907$	−12.5099	−0.415384	−0.207692	+	0.978194i	$0.566595\pi$
$908$	19.1084	0.634135
$909$	39.8010	1.32012
$910$	0.0698185	0.00231446
$911$	2.41940	0.0801584	0.0400792	−	0.999197i	$-0.487239\pi$
$911$	2.41940	0.0801584	0.0400792	+	0.999197i	$0.487239\pi$
$912$	−11.6631	−0.386204
$913$	14.4216	0.477284
$914$	2.68639	0.0888580
$915$	6.46621	0.213766
$916$	17.9171	0.591997
$917$	−2.37485	−0.0784246
$918$	−40.3439	−1.33155
$919$	50.3462	1.66077	0.830384	−	0.557192i	$-0.188121\pi$
$919$	50.3462	1.66077	0.830384	+	0.557192i	$0.188121\pi$
$920$	1.53645	0.0506551
$921$	42.1200	1.38790
$922$	2.16838	0.0714118
$923$	14.0094	0.461125
$924$	2.02064	0.0664743
$925$	10.5331	0.346328
$926$	−23.0924	−0.758865
$927$	50.1103	1.64584
$928$	42.8884	1.40788
$929$	−32.9858	−1.08223	−0.541115	−	0.840948i	$-0.681998\pi$
$929$	−32.9858	−1.08223	−0.541115	+	0.840948i	$0.681998\pi$
$930$	2.99625	0.0982509
$931$	−29.5510	−0.968494
$932$	−22.3510	−0.732131
$933$	−94.9464	−3.10841
$934$	−14.1450	−0.462838
$935$	−4.60687	−0.150661
$936$	−20.4742	−0.669219
$937$	47.9023	1.56490	0.782450	−	0.622714i	$-0.213970\pi$
$937$	47.9023	1.56490	0.782450	+	0.622714i	$0.213970\pi$
$938$	1.66900	0.0544948
$939$	86.7262	2.83020
$940$	0.597783	0.0194975
$941$	−4.42362	−0.144206	−0.0721030	−	0.997397i	$-0.522971\pi$
$941$	−4.42362	−0.144206	−0.0721030	+	0.997397i	$0.522971\pi$
$942$	0.272803	0.00888841
$943$	−1.60884	−0.0523912
$944$	13.2770	0.432131
$945$	−0.795175	−0.0258670
$946$	2.73624	0.0889627
$947$	19.3253	0.627987	0.313994	−	0.949425i	$-0.398333\pi$
$947$	19.3253	0.627987	0.313994	+	0.949425i	$0.398333\pi$
$948$	−55.8998	−1.81554
$949$	1.10646	0.0359171
$950$	15.5747	0.505311
$951$	23.2200	0.752960
$952$	−2.55134	−0.0826895
$953$	30.0968	0.974931	0.487465	−	0.873142i	$-0.337922\pi$
$953$	30.0968	0.974931	0.487465	+	0.873142i	$0.337922\pi$
$954$	−7.56418	−0.244899
$955$	9.35408	0.302691
$956$	−4.93544	−0.159623
$957$	53.1184	1.71708
$958$	−5.68051	−0.183529
$959$	−2.70948	−0.0874937
$960$	−3.13855	−0.101296
$961$	−19.8515	−0.640371
$962$	−2.01426	−0.0649423
$963$	−52.6836	−1.69771
$964$	−41.0992	−1.32372
$965$	−2.23402	−0.0719156
$966$	0.695103	0.0223646
$967$	−42.6607	−1.37187	−0.685937	−	0.727661i	$-0.740608\pi$
$967$	−42.6607	−1.37187	−0.685937	+	0.727661i	$0.740608\pi$
$968$	−14.0404	−0.451277
$969$	65.8328	2.11485
$970$	3.79378	0.121811
$971$	33.0050	1.05918	0.529591	−	0.848253i	$-0.322345\pi$
$971$	33.0050	1.05918	0.529591	+	0.848253i	$0.322345\pi$
$972$	12.3951	0.397572
$973$	0.974412	0.0312382
$974$	−24.7187	−0.792037
$975$	−18.2767	−0.585324
$976$	−4.87483	−0.156039
$977$	−5.79949	−0.185542	−0.0927710	−	0.995687i	$-0.529572\pi$
$977$	−5.79949	−0.185542	−0.0927710	+	0.995687i	$0.529572\pi$
$978$	−29.1123	−0.930909
$979$	15.2296	0.486740
$980$	3.83850	0.122616
$981$	−34.2859	−1.09467
$982$	−2.13095	−0.0680013
$983$	−35.2304	−1.12367	−0.561837	−	0.827248i	$-0.689905\pi$
$983$	−35.2304	−1.12367	−0.561837	+	0.827248i	$0.689905\pi$
$984$	8.35156	0.266238
$985$	1.57081	0.0500501
$986$	−27.9371	−0.889700
$987$	0.649260	0.0206662
$988$	7.43245	0.236458
$989$	−2.34891	−0.0746911
$990$	−4.44457	−0.141258
$991$	9.08023	0.288443	0.144221	−	0.989545i	$-0.453932\pi$
$991$	9.08023	0.288443	0.144221	+	0.989545i	$0.453932\pi$
$992$	−19.5737	−0.621466
$993$	−62.7433	−1.99110
$994$	1.68424	0.0534210
$995$	−4.40992	−0.139804
$996$	26.7693	0.848219
$997$	59.6440	1.88894	0.944472	−	0.328591i	$-0.106574\pi$
$997$	59.6440	1.88894	0.944472	+	0.328591i	$0.106574\pi$
$998$	−21.9808	−0.695791
$999$	22.9407	0.725813

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.e.1.5	✓	10
3.2	odd	2		4527.2.a.k.1.6		10
4.3	odd	2		8048.2.a.p.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.e.1.5	✓	10	1.1	even	1	trivial
4527.2.a.k.1.6		10	3.2	odd	2
8048.2.a.p.1.10		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)

\(f(q)\)	\(=\)	\(q-0.756417 q^{2} -3.07227 q^{3} -1.42783 q^{4} +0.386144 q^{5} +2.32392 q^{6} +0.194914 q^{7} +2.59287 q^{8} +6.43884 q^{9} +O(q^{10})\)	\(q-0.756417 q^{2} -3.07227 q^{3} -1.42783 q^{4} +0.386144 q^{5} +2.32392 q^{6} +0.194914 q^{7} +2.59287 q^{8} +6.43884 q^{9} -0.292086 q^{10} +2.36326 q^{11} +4.38669 q^{12} -1.22636 q^{13} -0.147436 q^{14} -1.18634 q^{15} +0.894372 q^{16} -5.04830 q^{17} -4.87045 q^{18} +4.24460 q^{19} -0.551349 q^{20} -0.598827 q^{21} -1.78761 q^{22} +1.53457 q^{23} -7.96600 q^{24} -4.85089 q^{25} +0.927639 q^{26} -10.5650 q^{27} -0.278304 q^{28} -7.31602 q^{29} +0.897367 q^{30} +3.33893 q^{31} -5.86226 q^{32} -7.26057 q^{33} +3.81863 q^{34} +0.0752647 q^{35} -9.19358 q^{36} -2.17138 q^{37} -3.21069 q^{38} +3.76771 q^{39} +1.00122 q^{40} -1.04840 q^{41} +0.452963 q^{42} -1.53067 q^{43} -3.37434 q^{44} +2.48632 q^{45} -1.16077 q^{46} -1.08422 q^{47} -2.74775 q^{48} -6.96201 q^{49} +3.66930 q^{50} +15.5098 q^{51} +1.75104 q^{52} +1.55308 q^{53} +7.99158 q^{54} +0.912558 q^{55} +0.505386 q^{56} -13.0406 q^{57} +5.53396 q^{58} +14.8451 q^{59} +1.69389 q^{60} -5.45056 q^{61} -2.52563 q^{62} +1.25502 q^{63} +2.64557 q^{64} -0.473551 q^{65} +5.49202 q^{66} -11.3202 q^{67} +7.20814 q^{68} -4.71461 q^{69} -0.0569315 q^{70} -11.4236 q^{71} +16.6951 q^{72} -0.902229 q^{73} +1.64247 q^{74} +14.9032 q^{75} -6.06059 q^{76} +0.460631 q^{77} -2.84996 q^{78} -12.7431 q^{79} +0.345356 q^{80} +13.1421 q^{81} +0.793029 q^{82} +6.10241 q^{83} +0.855025 q^{84} -1.94937 q^{85} +1.15782 q^{86} +22.4768 q^{87} +6.12763 q^{88} +6.44432 q^{89} -1.88070 q^{90} -0.239034 q^{91} -2.19111 q^{92} -10.2581 q^{93} +0.820122 q^{94} +1.63903 q^{95} +18.0105 q^{96} -12.9886 q^{97} +5.26618 q^{98} +15.2166 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) \) 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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