LMFDB - Embedded newform 503.2.a.e.1.8

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			1.8
Root			$0.208270$ 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)

$f(q)$	$=$	$q+1.17266 q^{2} -0.791730 q^{3} -0.624870 q^{4} +0.178789 q^{5} -0.928430 q^{6} -0.0809018 q^{7} -3.07808 q^{8} -2.37316 q^{9} +O(q^{10})$	\(q+1.17266 q^{2} -0.791730 q^{3} -0.624870 q^{4} +0.178789 q^{5} -0.928430 q^{6} -0.0809018 q^{7} -3.07808 q^{8} -2.37316 q^{9} +0.209658 q^{10} -4.30391 q^{11} +0.494728 q^{12} +1.10019 q^{13} -0.0948703 q^{14} -0.141552 q^{15} -2.35980 q^{16} -3.06504 q^{17} -2.78291 q^{18} -2.15853 q^{19} -0.111720 q^{20} +0.0640524 q^{21} -5.04702 q^{22} +9.15620 q^{23} +2.43701 q^{24} -4.96803 q^{25} +1.29015 q^{26} +4.25410 q^{27} +0.0505531 q^{28} -6.17849 q^{29} -0.165993 q^{30} -9.82812 q^{31} +3.38892 q^{32} +3.40754 q^{33} -3.59425 q^{34} -0.0144643 q^{35} +1.48292 q^{36} +4.08321 q^{37} -2.53122 q^{38} -0.871056 q^{39} -0.550326 q^{40} +4.58598 q^{41} +0.0751117 q^{42} +2.03126 q^{43} +2.68938 q^{44} -0.424295 q^{45} +10.7371 q^{46} -5.12836 q^{47} +1.86832 q^{48} -6.99345 q^{49} -5.82581 q^{50} +2.42668 q^{51} -0.687477 q^{52} +2.69017 q^{53} +4.98861 q^{54} -0.769491 q^{55} +0.249022 q^{56} +1.70897 q^{57} -7.24527 q^{58} +9.21598 q^{59} +0.0884518 q^{60} -14.0554 q^{61} -11.5250 q^{62} +0.191993 q^{63} +8.69364 q^{64} +0.196702 q^{65} +3.99588 q^{66} +5.62801 q^{67} +1.91525 q^{68} -7.24924 q^{69} -0.0169617 q^{70} -4.88191 q^{71} +7.30478 q^{72} +10.9754 q^{73} +4.78821 q^{74} +3.93334 q^{75} +1.34880 q^{76} +0.348194 q^{77} -1.02145 q^{78} +17.4356 q^{79} -0.421905 q^{80} +3.75139 q^{81} +5.37780 q^{82} -2.48372 q^{83} -0.0400244 q^{84} -0.547994 q^{85} +2.38198 q^{86} +4.89170 q^{87} +13.2478 q^{88} +5.57230 q^{89} -0.497553 q^{90} -0.0890076 q^{91} -5.72143 q^{92} +7.78122 q^{93} -6.01382 q^{94} -0.385920 q^{95} -2.68311 q^{96} -13.9731 q^{97} -8.20094 q^{98} +10.2139 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.17266	0.829195	0.414598	−	0.910005i	$-0.363922\pi$
$2$	1.17266	0.829195	0.414598	+	0.910005i	$0.363922\pi$
$3$	−0.791730	−0.457106	−0.228553	−	0.973532i	$-0.573399\pi$
$3$	−0.791730	−0.457106	−0.228553	+	0.973532i	$0.573399\pi$
$4$	−0.624870	−0.312435
$5$	0.178789	0.0799568	0.0399784	−	0.999201i	$-0.487271\pi$
$5$	0.178789	0.0799568	0.0399784	+	0.999201i	$0.487271\pi$
$6$	−0.928430	−0.379030
$7$	−0.0809018	−0.0305780	−0.0152890	−	0.999883i	$-0.504867\pi$
$7$	−0.0809018	−0.0305780	−0.0152890	+	0.999883i	$0.504867\pi$
$8$	−3.07808	−1.08827
$9$	−2.37316	−0.791054
$10$	0.209658	0.0662998
$11$	−4.30391	−1.29768	−0.648839	−	0.760926i	$-0.724745\pi$
$11$	−4.30391	−1.29768	−0.648839	+	0.760926i	$0.724745\pi$
$12$	0.494728	0.142816
$13$	1.10019	0.305139	0.152569	−	0.988293i	$-0.451245\pi$
$13$	1.10019	0.305139	0.152569	+	0.988293i	$0.451245\pi$
$14$	−0.0948703	−0.0253551
$15$	−0.141552	−0.0365487
$16$	−2.35980	−0.589950
$17$	−3.06504	−0.743381	−0.371690	−	0.928357i	$-0.621222\pi$
$17$	−3.06504	−0.743381	−0.371690	+	0.928357i	$0.621222\pi$
$18$	−2.78291	−0.655939
$19$	−2.15853	−0.495200	−0.247600	−	0.968862i	$-0.579642\pi$
$19$	−2.15853	−0.495200	−0.247600	+	0.968862i	$0.579642\pi$
$20$	−0.111720	−0.0249813
$21$	0.0640524	0.0139774
$22$	−5.04702	−1.07603
$23$	9.15620	1.90920	0.954600	−	0.297892i	$-0.0962835\pi$
$23$	9.15620	1.90920	0.954600	+	0.297892i	$0.0962835\pi$
$24$	2.43701	0.497452
$25$	−4.96803	−0.993607
$26$	1.29015	0.253020
$27$	4.25410	0.818701
$28$	0.0505531	0.00955364
$29$	−6.17849	−1.14732	−0.573658	−	0.819095i	$-0.694476\pi$
$29$	−6.17849	−1.14732	−0.573658	+	0.819095i	$0.694476\pi$
$30$	−0.165993	−0.0303060
$31$	−9.82812	−1.76518	−0.882591	−	0.470141i	$-0.844203\pi$
$31$	−9.82812	−1.76518	−0.882591	+	0.470141i	$0.844203\pi$
$32$	3.38892	0.599082
$33$	3.40754	0.593176
$34$	−3.59425	−0.616408
$35$	−0.0144643	−0.00244492
$36$	1.48292	0.247153
$37$	4.08321	0.671275	0.335637	−	0.941991i	$-0.391048\pi$
$37$	4.08321	0.671275	0.335637	+	0.941991i	$0.391048\pi$
$38$	−2.53122	−0.410618
$39$	−0.871056	−0.139481
$40$	−0.550326	−0.0870141
$41$	4.58598	0.716210	0.358105	−	0.933681i	$-0.383423\pi$
$41$	4.58598	0.716210	0.358105	+	0.933681i	$0.383423\pi$
$42$	0.0751117	0.0115900
$43$	2.03126	0.309764	0.154882	−	0.987933i	$-0.450500\pi$
$43$	2.03126	0.309764	0.154882	+	0.987933i	$0.450500\pi$
$44$	2.68938	0.405440
$45$	−0.424295	−0.0632501
$46$	10.7371	1.58310
$47$	−5.12836	−0.748049	−0.374024	−	0.927419i	$-0.622022\pi$
$47$	−5.12836	−0.748049	−0.374024	+	0.927419i	$0.622022\pi$
$48$	1.86832	0.269669
$49$	−6.99345	−0.999065
$50$	−5.82581	−0.823894
$51$	2.42668	0.339804
$52$	−0.687477	−0.0953359
$53$	2.69017	0.369523	0.184761	−	0.982783i	$-0.440849\pi$
$53$	2.69017	0.369523	0.184761	+	0.982783i	$0.440849\pi$
$54$	4.98861	0.678863
$55$	−0.769491	−0.103758
$56$	0.249022	0.0332770
$57$	1.70897	0.226359
$58$	−7.24527	−0.951350
$59$	9.21598	1.19982	0.599909	−	0.800068i	$-0.295203\pi$
$59$	9.21598	1.19982	0.599909	+	0.800068i	$0.295203\pi$
$60$	0.0884518	0.0114191
$61$	−14.0554	−1.79961	−0.899805	−	0.436291i	$-0.856292\pi$
$61$	−14.0554	−1.79961	−0.899805	+	0.436291i	$0.856292\pi$
$62$	−11.5250	−1.46368
$63$	0.191993	0.0241889
$64$	8.69364	1.08671
$65$	0.196702	0.0243979
$66$	3.99588	0.491859
$67$	5.62801	0.687570	0.343785	−	0.939048i	$-0.388291\pi$
$67$	5.62801	0.687570	0.343785	+	0.939048i	$0.388291\pi$
$68$	1.91525	0.232258
$69$	−7.24924	−0.872706
$70$	−0.0169617	−0.00202732
$71$	−4.88191	−0.579376	−0.289688	−	0.957121i	$-0.593552\pi$
$71$	−4.88191	−0.579376	−0.289688	+	0.957121i	$0.593552\pi$
$72$	7.30478	0.860877
$73$	10.9754	1.28457	0.642286	−	0.766465i	$-0.277986\pi$
$73$	10.9754	1.28457	0.642286	+	0.766465i	$0.277986\pi$
$74$	4.78821	0.556618
$75$	3.93334	0.454183
$76$	1.34880	0.154718
$77$	0.348194	0.0396804
$78$	−1.02145	−0.115657
$79$	17.4356	1.96166	0.980828	−	0.194874i	$-0.0624299\pi$
$79$	17.4356	1.96166	0.980828	+	0.194874i	$0.0624299\pi$
$80$	−0.421905	−0.0471705
$81$	3.75139	0.416822
$82$	5.37780	0.593878
$83$	−2.48372	−0.272624	−0.136312	−	0.990666i	$-0.543525\pi$
$83$	−2.48372	−0.272624	−0.136312	+	0.990666i	$0.543525\pi$
$84$	−0.0400244	−0.00436702
$85$	−0.547994	−0.0594383
$86$	2.38198	0.256855
$87$	4.89170	0.524445
$88$	13.2478	1.41222
$89$	5.57230	0.590662	0.295331	−	0.955395i	$-0.404570\pi$
$89$	5.57230	0.590662	0.295331	+	0.955395i	$0.404570\pi$
$90$	−0.497553	−0.0524467
$91$	−0.0890076	−0.00933053
$92$	−5.72143	−0.596500
$93$	7.78122	0.806875
$94$	−6.01382	−0.620279
$95$	−0.385920	−0.0395946
$96$	−2.68311	−0.273844
$97$	−13.9731	−1.41876	−0.709379	−	0.704828i	$-0.751024\pi$
$97$	−13.9731	−1.41876	−0.709379	+	0.704828i	$0.751024\pi$
$98$	−8.20094	−0.828420
$99$	10.2139	1.02653
$100$	3.10437	0.310437
$101$	−7.98379	−0.794417	−0.397208	−	0.917728i	$-0.630021\pi$
$101$	−7.98379	−0.794417	−0.397208	+	0.917728i	$0.630021\pi$
$102$	2.84567	0.281764
$103$	10.5314	1.03769	0.518846	−	0.854868i	$-0.326362\pi$
$103$	10.5314	1.03769	0.518846	+	0.854868i	$0.326362\pi$
$104$	−3.38648	−0.332072
$105$	0.0114518	0.00111759
$106$	3.15465	0.306407
$107$	−3.31671	−0.320638	−0.160319	−	0.987065i	$-0.551252\pi$
$107$	−3.31671	−0.320638	−0.160319	+	0.987065i	$0.551252\pi$
$108$	−2.65826	−0.255791
$109$	−12.7956	−1.22559	−0.612797	−	0.790240i	$-0.709956\pi$
$109$	−12.7956	−1.22559	−0.612797	+	0.790240i	$0.709956\pi$
$110$	−0.902350	−0.0860357
$111$	−3.23280	−0.306844
$112$	0.190912	0.0180395
$113$	−4.42086	−0.415880	−0.207940	−	0.978142i	$-0.566676\pi$
$113$	−4.42086	−0.415880	−0.207940	+	0.978142i	$0.566676\pi$
$114$	2.00404	0.187696
$115$	1.63702	0.152653
$116$	3.86075	0.358462
$117$	−2.61094	−0.241381
$118$	10.8072	0.994884
$119$	0.247967	0.0227311
$120$	0.435709	0.0397747
$121$	7.52364	0.683967
$122$	−16.4822	−1.49223
$123$	−3.63086	−0.327384
$124$	6.14130	0.551505
$125$	−1.78217	−0.159402
$126$	0.225143	0.0200573
$127$	−17.5071	−1.55351	−0.776753	−	0.629806i	$-0.783135\pi$
$127$	−17.5071	−1.55351	−0.776753	+	0.629806i	$0.783135\pi$
$128$	3.41685	0.302010
$129$	−1.60821	−0.141595
$130$	0.230665	0.0202306
$131$	11.8336	1.03390	0.516952	−	0.856014i	$-0.327066\pi$
$131$	11.8336	1.03390	0.516952	+	0.856014i	$0.327066\pi$
$132$	−2.12927	−0.185329
$133$	0.174629	0.0151422
$134$	6.59973	0.570130
$135$	0.760584	0.0654607
$136$	9.43443	0.808995
$137$	−2.19499	−0.187530	−0.0937651	−	0.995594i	$-0.529890\pi$
$137$	−2.19499	−0.187530	−0.0937651	+	0.995594i	$0.529890\pi$
$138$	−8.50089	−0.723644
$139$	6.11773	0.518899	0.259450	−	0.965757i	$-0.416459\pi$
$139$	6.11773	0.518899	0.259450	+	0.965757i	$0.416459\pi$
$140$	0.00903832	0.000763878 0
$141$	4.06028	0.341937
$142$	−5.72482	−0.480416
$143$	−4.73513	−0.395972
$144$	5.60019	0.466682
$145$	−1.10464	−0.0917357
$146$	12.8704	1.06516
$147$	5.53693	0.456678
$148$	−2.55147	−0.209730
$149$	−17.3950	−1.42505	−0.712526	−	0.701646i	$-0.752449\pi$
$149$	−17.3950	−1.42505	−0.712526	+	0.701646i	$0.752449\pi$
$150$	4.61247	0.376607
$151$	−21.9595	−1.78704	−0.893520	−	0.449024i	$-0.851772\pi$
$151$	−21.9595	−1.78704	−0.893520	+	0.449024i	$0.851772\pi$
$152$	6.64411	0.538909
$153$	7.27383	0.588055
$154$	0.408313	0.0329028
$155$	−1.75716	−0.141138
$156$	0.544296	0.0435786
$157$	−19.5736	−1.56214	−0.781070	−	0.624444i	$-0.785326\pi$
$157$	−19.5736	−1.56214	−0.781070	+	0.624444i	$0.785326\pi$
$158$	20.4460	1.62660
$159$	−2.12989	−0.168911
$160$	0.605900	0.0479006
$161$	−0.740753	−0.0583795
$162$	4.39911	0.345627
$163$	−14.2549	−1.11653	−0.558265	−	0.829663i	$-0.688533\pi$
$163$	−14.2549	−1.11653	−0.558265	+	0.829663i	$0.688533\pi$
$164$	−2.86564	−0.223769
$165$	0.609229	0.0474284
$166$	−2.91256	−0.226058
$167$	−19.3555	−1.49777	−0.748886	−	0.662698i	$-0.769411\pi$
$167$	−19.3555	−1.49777	−0.748886	+	0.662698i	$0.769411\pi$
$168$	−0.197158	−0.0152111
$169$	−11.7896	−0.906890
$170$	−0.642611	−0.0492860
$171$	5.12254	0.391730
$172$	−1.26927	−0.0967811
$173$	24.1751	1.83800	0.919000	−	0.394258i	$-0.128998\pi$
$173$	24.1751	1.83800	0.919000	+	0.394258i	$0.128998\pi$
$174$	5.73629	0.434867
$175$	0.401923	0.0303825
$176$	10.1564	0.765564
$177$	−7.29657	−0.548444
$178$	6.53441	0.489775
$179$	11.7844	0.880807	0.440403	−	0.897800i	$-0.354835\pi$
$179$	11.7844	0.880807	0.440403	+	0.897800i	$0.354835\pi$
$180$	0.265129	0.0197616
$181$	0.193747	0.0144011	0.00720054	−	0.999974i	$-0.497708\pi$
$181$	0.193747	0.0144011	0.00720054	+	0.999974i	$0.497708\pi$
$182$	−0.104376	−0.00773683
$183$	11.1281	0.822612
$184$	−28.1835	−2.07771
$185$	0.730031	0.0536730
$186$	9.12472	0.669057
$187$	13.1916	0.964669
$188$	3.20456	0.233716
$189$	−0.344164	−0.0250342
$190$	−0.452553	−0.0328317
$191$	−20.0106	−1.44791	−0.723957	−	0.689845i	$-0.757679\pi$
$191$	−20.0106	−1.44791	−0.723957	+	0.689845i	$0.757679\pi$
$192$	−6.88302	−0.496739
$193$	−16.4429	−1.18358	−0.591792	−	0.806091i	$-0.701579\pi$
$193$	−16.4429	−1.18358	−0.591792	+	0.806091i	$0.701579\pi$
$194$	−16.3857	−1.17643
$195$	−0.155735	−0.0111524
$196$	4.37000	0.312143
$197$	24.3311	1.73352	0.866761	−	0.498723i	$-0.166198\pi$
$197$	24.3311	1.73352	0.866761	+	0.498723i	$0.166198\pi$
$198$	11.9774	0.851197
$199$	−16.2467	−1.15170	−0.575851	−	0.817555i	$-0.695329\pi$
$199$	−16.2467	−1.15170	−0.575851	+	0.817555i	$0.695329\pi$
$200$	15.2920	1.08131
$201$	−4.45586	−0.314292
$202$	−9.36226	−0.658727
$203$	0.499851	0.0350827
$204$	−1.51636	−0.106166
$205$	0.819922	0.0572659
$206$	12.3498	0.860449
$207$	−21.7292	−1.51028
$208$	−2.59623	−0.180016
$209$	9.29010	0.642610
$210$	0.0134291	0.000926697 0
$211$	13.5844	0.935189	0.467594	−	0.883943i	$-0.345121\pi$
$211$	13.5844	0.935189	0.467594	+	0.883943i	$0.345121\pi$
$212$	−1.68100	−0.115452
$213$	3.86515	0.264836
$214$	−3.88937	−0.265872
$215$	0.363166	0.0247677
$216$	−13.0944	−0.890964
$217$	0.795113	0.0539758
$218$	−15.0049	−1.01626
$219$	−8.68955	−0.587185
$220$	0.480831	0.0324176
$221$	−3.37213	−0.226834
$222$	−3.79097	−0.254433
$223$	24.6725	1.65219	0.826096	−	0.563530i	$-0.190557\pi$
$223$	24.6725	1.65219	0.826096	+	0.563530i	$0.190557\pi$
$224$	−0.274169	−0.0183187
$225$	11.7900	0.785997
$226$	−5.18417	−0.344846
$227$	17.9854	1.19373	0.596866	−	0.802341i	$-0.296412\pi$
$227$	17.9854	1.19373	0.596866	+	0.802341i	$0.296412\pi$
$228$	−1.06788	−0.0707224
$229$	15.8558	1.04778	0.523891	−	0.851786i	$-0.324480\pi$
$229$	15.8558	1.04778	0.523891	+	0.851786i	$0.324480\pi$
$230$	1.91967	0.126579
$231$	−0.275676	−0.0181381
$232$	19.0179	1.24858
$233$	2.33607	0.153041	0.0765205	−	0.997068i	$-0.475619\pi$
$233$	2.33607	0.153041	0.0765205	+	0.997068i	$0.475619\pi$
$234$	−3.06174	−0.200152
$235$	−0.916894	−0.0598115
$236$	−5.75879	−0.374865
$237$	−13.8043	−0.896684
$238$	0.290781	0.0188485
$239$	4.84852	0.313625	0.156812	−	0.987628i	$-0.449878\pi$
$239$	4.84852	0.313625	0.156812	+	0.987628i	$0.449878\pi$
$240$	0.334035	0.0215619
$241$	−3.42679	−0.220739	−0.110369	−	0.993891i	$-0.535203\pi$
$241$	−3.42679	−0.220739	−0.110369	+	0.993891i	$0.535203\pi$
$242$	8.82267	0.567143
$243$	−15.7324	−1.00923
$244$	8.78280	0.562261
$245$	−1.25035	−0.0798820
$246$	−4.25776	−0.271465
$247$	−2.37480	−0.151105
$248$	30.2517	1.92099
$249$	1.96644	0.124618
$250$	−2.08988	−0.132176
$251$	−25.7166	−1.62321	−0.811607	−	0.584204i	$-0.801407\pi$
$251$	−25.7166	−1.62321	−0.811607	+	0.584204i	$0.801407\pi$
$252$	−0.119971	−0.00755745
$253$	−39.4074	−2.47753
$254$	−20.5299	−1.28816
$255$	0.433864	0.0271696
$256$	−13.3805	−0.836280
$257$	−24.1897	−1.50891	−0.754457	−	0.656350i	$-0.772100\pi$
$257$	−24.1897	−1.50891	−0.754457	+	0.656350i	$0.772100\pi$
$258$	−1.88588	−0.117410
$259$	−0.330339	−0.0205262
$260$	−0.122913	−0.00762275
$261$	14.6626	0.907590
$262$	13.8768	0.857309
$263$	18.1779	1.12089	0.560447	−	0.828190i	$-0.310629\pi$
$263$	18.1779	1.12089	0.560447	+	0.828190i	$0.310629\pi$
$264$	−10.4887	−0.645532
$265$	0.480972	0.0295458
$266$	0.204780	0.0125559
$267$	−4.41176	−0.269995
$268$	−3.51677	−0.214821
$269$	−5.69010	−0.346931	−0.173466	−	0.984840i	$-0.555497\pi$
$269$	−5.69010	−0.346931	−0.173466	+	0.984840i	$0.555497\pi$
$270$	0.891906	0.0542797
$271$	16.4138	0.997069	0.498535	−	0.866870i	$-0.333872\pi$
$271$	16.4138	0.997069	0.498535	+	0.866870i	$0.333872\pi$
$272$	7.23287	0.438557
$273$	0.0704700	0.00426504
$274$	−2.57397	−0.155499
$275$	21.3820	1.28938
$276$	4.52983	0.272664
$277$	−26.4497	−1.58921	−0.794605	−	0.607127i	$-0.792322\pi$
$277$	−26.4497	−1.58921	−0.794605	+	0.607127i	$0.792322\pi$
$278$	7.17402	0.430269
$279$	23.3237	1.39636
$280$	0.0445223	0.00266072
$281$	3.32607	0.198417	0.0992084	−	0.995067i	$-0.468369\pi$
$281$	3.32607	0.198417	0.0992084	+	0.995067i	$0.468369\pi$
$282$	4.76133	0.283533
$283$	−21.9817	−1.30668	−0.653339	−	0.757065i	$-0.726633\pi$
$283$	−21.9817	−1.30668	−0.653339	+	0.757065i	$0.726633\pi$
$284$	3.05056	0.181017
$285$	0.305545	0.0180989
$286$	−5.55270	−0.328338
$287$	−0.371014	−0.0219003
$288$	−8.04245	−0.473906
$289$	−7.60555	−0.447385
$290$	−1.29537	−0.0760669
$291$	11.0630	0.648522
$292$	−6.85819	−0.401345
$293$	−6.54118	−0.382140	−0.191070	−	0.981576i	$-0.561196\pi$
$293$	−6.54118	−0.382140	−0.191070	+	0.981576i	$0.561196\pi$
$294$	6.49293	0.378676
$295$	1.64771	0.0959336
$296$	−12.5684	−0.730525
$297$	−18.3092	−1.06241
$298$	−20.3984	−1.18165
$299$	10.0736	0.582570
$300$	−2.45783	−0.141903
$301$	−0.164333	−0.00947197
$302$	−25.7510	−1.48181
$303$	6.32101	0.363132
$304$	5.09369	0.292143
$305$	−2.51295	−0.143891
$306$	8.52973	0.487612
$307$	15.6985	0.895959	0.447980	−	0.894044i	$-0.352144\pi$
$307$	15.6985	0.895959	0.447980	+	0.894044i	$0.352144\pi$
$308$	−0.217576	−0.0123975
$309$	−8.33804	−0.474335
$310$	−2.06055	−0.117031
$311$	25.6166	1.45258	0.726292	−	0.687386i	$-0.241242\pi$
$311$	25.6166	1.45258	0.726292	+	0.687386i	$0.241242\pi$
$312$	2.68118	0.151792
$313$	3.69793	0.209019	0.104510	−	0.994524i	$-0.466673\pi$
$313$	3.69793	0.209019	0.104510	+	0.994524i	$0.466673\pi$
$314$	−22.9531	−1.29532
$315$	0.0343262	0.00193406
$316$	−10.8950	−0.612890
$317$	19.0196	1.06825	0.534124	−	0.845406i	$-0.320641\pi$
$317$	19.0196	1.06825	0.534124	+	0.845406i	$0.320641\pi$
$318$	−2.49763	−0.140060
$319$	26.5917	1.48885
$320$	1.55433	0.0868894
$321$	2.62594	0.146566
$322$	−0.868651	−0.0484080
$323$	6.61597	0.368122
$324$	−2.34413	−0.130230
$325$	−5.46580	−0.303188
$326$	−16.7161	−0.925822
$327$	10.1306	0.560226
$328$	−14.1160	−0.779427
$329$	0.414894	0.0228738
$330$	0.714418	0.0393274
$331$	−4.74934	−0.261048	−0.130524	−	0.991445i	$-0.541666\pi$
$331$	−4.74934	−0.261048	−0.130524	+	0.991445i	$0.541666\pi$
$332$	1.55200	0.0851771
$333$	−9.69011	−0.531015
$334$	−22.6974	−1.24195
$335$	1.00622	0.0549759
$336$	−0.151151	−0.00824595
$337$	−29.8451	−1.62576	−0.812882	−	0.582428i	$-0.802103\pi$
$337$	−29.8451	−1.62576	−0.812882	+	0.582428i	$0.802103\pi$
$338$	−13.8252	−0.751989
$339$	3.50013	0.190101
$340$	0.342425	0.0185706
$341$	42.2993	2.29064
$342$	6.00699	0.324821
$343$	1.13210	0.0611274
$344$	−6.25238	−0.337105
$345$	−1.29608	−0.0697787
$346$	28.3492	1.52406
$347$	15.3781	0.825540	0.412770	−	0.910835i	$-0.364561\pi$
$347$	15.3781	0.825540	0.412770	+	0.910835i	$0.364561\pi$
$348$	−3.05667	−0.163855
$349$	6.64130	0.355501	0.177750	−	0.984076i	$-0.443118\pi$
$349$	6.64130	0.355501	0.177750	+	0.984076i	$0.443118\pi$
$350$	0.471319	0.0251930
$351$	4.68033	0.249817
$352$	−14.5856	−0.777415
$353$	−33.7272	−1.79512	−0.897558	−	0.440896i	$-0.854661\pi$
$353$	−33.7272	−1.79512	−0.897558	+	0.440896i	$0.854661\pi$
$354$	−8.55639	−0.454767
$355$	−0.872830	−0.0463250
$356$	−3.48196	−0.184544
$357$	−0.196323	−0.0103905
$358$	13.8191	0.730361
$359$	−27.2110	−1.43614	−0.718071	−	0.695970i	$-0.754975\pi$
$359$	−27.2110	−1.43614	−0.718071	+	0.695970i	$0.754975\pi$
$360$	1.30601	0.0688329
$361$	−14.3408	−0.754777
$362$	0.227199	0.0119413
$363$	−5.95669	−0.312645
$364$	0.0556181	0.00291518
$365$	1.96228	0.102710
$366$	13.0495	0.682106
$367$	14.0523	0.733525	0.366763	−	0.930315i	$-0.380466\pi$
$367$	14.0523	0.733525	0.366763	+	0.930315i	$0.380466\pi$
$368$	−21.6068	−1.12633
$369$	−10.8833	−0.566561
$370$	0.856078	0.0445054
$371$	−0.217639	−0.0112993
$372$	−4.86225	−0.252096
$373$	19.8673	1.02869	0.514345	−	0.857584i	$-0.328035\pi$
$373$	19.8673	1.02869	0.514345	+	0.857584i	$0.328035\pi$
$374$	15.4693	0.799899
$375$	1.41100	0.0728637
$376$	15.7855	0.814075
$377$	−6.79753	−0.350091
$378$	−0.403587	−0.0207583
$379$	−16.4863	−0.846844	−0.423422	−	0.905933i	$-0.639171\pi$
$379$	−16.4863	−0.846844	−0.423422	+	0.905933i	$0.639171\pi$
$380$	0.241150	0.0123707
$381$	13.8609	0.710116
$382$	−23.4656	−1.20060
$383$	22.2392	1.13637	0.568186	−	0.822900i	$-0.307645\pi$
$383$	22.2392	1.13637	0.568186	+	0.822900i	$0.307645\pi$
$384$	−2.70522	−0.138050
$385$	0.0622532	0.00317272
$386$	−19.2819	−0.981422
$387$	−4.82051	−0.245040
$388$	8.73139	0.443269
$389$	−10.3650	−0.525528	−0.262764	−	0.964860i	$-0.584634\pi$
$389$	−10.3650	−0.525528	−0.262764	+	0.964860i	$0.584634\pi$
$390$	−0.182624	−0.00924753
$391$	−28.0641	−1.41926
$392$	21.5264	1.08725
$393$	−9.36900	−0.472604
$394$	28.5322	1.43743
$395$	3.11729	0.156848
$396$	−6.38235	−0.320725
$397$	−2.54363	−0.127661	−0.0638306	−	0.997961i	$-0.520332\pi$
$397$	−2.54363	−0.127661	−0.0638306	+	0.997961i	$0.520332\pi$
$398$	−19.0519	−0.954985
$399$	−0.138259	−0.00692160
$400$	11.7236	0.586178
$401$	12.4246	0.620455	0.310227	−	0.950662i	$-0.399595\pi$
$401$	12.4246	0.620455	0.310227	+	0.950662i	$0.399595\pi$
$402$	−5.22521	−0.260610
$403$	−10.8128	−0.538625
$404$	4.98883	0.248203
$405$	0.670707	0.0333277
$406$	0.586155	0.0290904
$407$	−17.5738	−0.871098
$408$	−7.46952	−0.369796
$409$	14.3575	0.709932	0.354966	−	0.934879i	$-0.384492\pi$
$409$	14.3575	0.709932	0.354966	+	0.934879i	$0.384492\pi$
$410$	0.961490	0.0474846
$411$	1.73784	0.0857211
$412$	−6.58076	−0.324211
$413$	−0.745589	−0.0366880
$414$	−25.4809	−1.25232
$415$	−0.444061	−0.0217981
$416$	3.72846	0.182803
$417$	−4.84359	−0.237192
$418$	10.8941	0.532849
$419$	15.6860	0.766309	0.383155	−	0.923684i	$-0.374838\pi$
$419$	15.6860	0.766309	0.383155	+	0.923684i	$0.374838\pi$
$420$	−0.00715591	−0.000349173 0
$421$	0.689920	0.0336247	0.0168123	−	0.999859i	$-0.494648\pi$
$421$	0.689920	0.0336247	0.0168123	+	0.999859i	$0.494648\pi$
$422$	15.9299	0.775454
$423$	12.1704	0.591747
$424$	−8.28054	−0.402139
$425$	15.2272	0.738628
$426$	4.53251	0.219601
$427$	1.13711	0.0550285
$428$	2.07251	0.100179
$429$	3.74895	0.181001
$430$	0.425870	0.0205373
$431$	29.0858	1.40102	0.700508	−	0.713645i	$-0.252957\pi$
$431$	29.0858	1.40102	0.700508	+	0.713645i	$0.252957\pi$
$432$	−10.0388	−0.482992
$433$	18.1169	0.870643	0.435321	−	0.900275i	$-0.356635\pi$
$433$	18.1169	0.870643	0.435321	+	0.900275i	$0.356635\pi$
$434$	0.932396	0.0447565
$435$	0.874580	0.0419329
$436$	7.99557	0.382918
$437$	−19.7639	−0.945435
$438$	−10.1899	−0.486891
$439$	3.25712	0.155454	0.0777270	−	0.996975i	$-0.475234\pi$
$439$	3.25712	0.155454	0.0777270	+	0.996975i	$0.475234\pi$
$440$	2.36855	0.112916
$441$	16.5966	0.790315
$442$	−3.95436	−0.188090
$443$	−21.5717	−1.02490	−0.512451	−	0.858717i	$-0.671262\pi$
$443$	−21.5717	−1.02490	−0.512451	+	0.858717i	$0.671262\pi$
$444$	2.02008	0.0958686
$445$	0.996264	0.0472274
$446$	28.9324	1.36999
$447$	13.7721	0.651399
$448$	−0.703331	−0.0332293
$449$	18.9612	0.894834	0.447417	−	0.894325i	$-0.352344\pi$
$449$	18.9612	0.894834	0.447417	+	0.894325i	$0.352344\pi$
$450$	13.8256	0.651745
$451$	−19.7377	−0.929410
$452$	2.76246	0.129935
$453$	17.3860	0.816866
$454$	21.0907	0.989837
$455$	−0.0159136	−0.000746039 0
$456$	−5.26035	−0.246338
$457$	4.18789	0.195901	0.0979506	−	0.995191i	$-0.468771\pi$
$457$	4.18789	0.195901	0.0979506	+	0.995191i	$0.468771\pi$
$458$	18.5935	0.868815
$459$	−13.0390	−0.608607
$460$	−1.02293	−0.0476942
$461$	13.7101	0.638543	0.319271	−	0.947663i	$-0.396562\pi$
$461$	13.7101	0.638543	0.319271	+	0.947663i	$0.396562\pi$
$462$	−0.323274	−0.0150401
$463$	4.87808	0.226703	0.113352	−	0.993555i	$-0.463841\pi$
$463$	4.87808	0.226703	0.113352	+	0.993555i	$0.463841\pi$
$464$	14.5800	0.676859
$465$	1.39119	0.0645151
$466$	2.73941	0.126901
$467$	12.3373	0.570904	0.285452	−	0.958393i	$-0.407856\pi$
$467$	12.3373	0.570904	0.285452	+	0.958393i	$0.407856\pi$
$468$	1.63150	0.0754159
$469$	−0.455316	−0.0210245
$470$	−1.07520	−0.0495955
$471$	15.4970	0.714063
$472$	−28.3675	−1.30572
$473$	−8.74236	−0.401974
$474$	−16.1877	−0.743526
$475$	10.7236	0.492034
$476$	−0.154947	−0.00710199
$477$	−6.38421	−0.292313
$478$	5.68566	0.260056
$479$	−3.56361	−0.162826	−0.0814128	−	0.996680i	$-0.525943\pi$
$479$	−3.56361	−0.162826	−0.0814128	+	0.996680i	$0.525943\pi$
$480$	−0.479709	−0.0218956
$481$	4.49231	0.204832
$482$	−4.01846	−0.183036
$483$	0.586476	0.0266856
$484$	−4.70130	−0.213695
$485$	−2.49824	−0.113439
$486$	−18.4487	−0.836851
$487$	−5.09262	−0.230769	−0.115384	−	0.993321i	$-0.536810\pi$
$487$	−5.09262	−0.230769	−0.115384	+	0.993321i	$0.536810\pi$
$488$	43.2637	1.95845
$489$	11.2860	0.510372
$490$	−1.46624	−0.0662378
$491$	27.1049	1.22323	0.611614	−	0.791156i	$-0.290521\pi$
$491$	27.1049	1.22323	0.611614	+	0.791156i	$0.290521\pi$
$492$	2.26882	0.102286
$493$	18.9373	0.852893
$494$	−2.78483	−0.125295
$495$	1.82613	0.0820783
$496$	23.1924	1.04137
$497$	0.394955	0.0177162
$498$	2.30596	0.103333
$499$	−4.49778	−0.201348	−0.100674	−	0.994919i	$-0.532100\pi$
$499$	−4.49778	−0.201348	−0.100674	+	0.994919i	$0.532100\pi$
$500$	1.11363	0.0498028
$501$	15.3243	0.684640
$502$	−30.1568	−1.34596
$503$	−1.00000	−0.0445878
$503$	−1.00000	−0.0445878
$504$	−0.590970	−0.0263239
$505$	−1.42741	−0.0635190
$506$	−46.2115	−2.05435
$507$	9.33416	0.414545
$508$	10.9397	0.485369
$509$	−9.92656	−0.439987	−0.219993	−	0.975501i	$-0.570604\pi$
$509$	−9.92656	−0.439987	−0.219993	+	0.975501i	$0.570604\pi$
$510$	0.508774	0.0225289
$511$	−0.887929	−0.0392797
$512$	−22.5244	−0.995449
$513$	−9.18258	−0.405421
$514$	−28.3663	−1.25118
$515$	1.88290	0.0829704
$516$	1.00492	0.0442392
$517$	22.0720	0.970726
$518$	−0.387375	−0.0170203
$519$	−19.1402	−0.840160
$520$	−0.605464	−0.0265514
$521$	−8.65790	−0.379309	−0.189655	−	0.981851i	$-0.560737\pi$
$521$	−8.65790	−0.379309	−0.189655	+	0.981851i	$0.560737\pi$
$522$	17.1942	0.752570
$523$	17.7111	0.774451	0.387226	−	0.921985i	$-0.373433\pi$
$523$	17.7111	0.774451	0.387226	+	0.921985i	$0.373433\pi$
$524$	−7.39445	−0.323028
$525$	−0.318215	−0.0138880
$526$	21.3164	0.929441
$527$	30.1236	1.31220
$528$	−8.04110	−0.349944
$529$	60.8360	2.64504
$530$	0.564016	0.0244993
$531$	−21.8710	−0.949122
$532$	−0.109120	−0.00473096
$533$	5.04547	0.218543
$534$	−5.17349	−0.223879
$535$	−0.592990	−0.0256372
$536$	−17.3234	−0.748259
$537$	−9.33006	−0.402622
$538$	−6.67255	−0.287674
$539$	30.0992	1.29646
$540$	−0.475266	−0.0204522
$541$	−10.8187	−0.465131	−0.232565	−	0.972581i	$-0.574712\pi$
$541$	−10.8187	−0.465131	−0.232565	+	0.972581i	$0.574712\pi$
$542$	19.2478	0.826765
$543$	−0.153395	−0.00658282
$544$	−10.3872	−0.445346
$545$	−2.28771	−0.0979945
$546$	0.0826373	0.00353655
$547$	−33.1188	−1.41606	−0.708028	−	0.706184i	$-0.750415\pi$
$547$	−33.1188	−1.41606	−0.708028	+	0.706184i	$0.750415\pi$
$548$	1.37158	0.0585910
$549$	33.3558	1.42359
$550$	25.0738	1.06915
$551$	13.3364	0.568151
$552$	22.3137	0.949735
$553$	−1.41057	−0.0599835
$554$	−31.0165	−1.31777
$555$	−0.577988	−0.0245342
$556$	−3.82279	−0.162122
$557$	12.3324	0.522541	0.261270	−	0.965266i	$-0.415859\pi$
$557$	12.3324	0.522541	0.261270	+	0.965266i	$0.415859\pi$
$558$	27.3508	1.15785
$559$	2.23478	0.0945210
$560$	0.0341329	0.00144238
$561$	−10.4442	−0.440955
$562$	3.90035	0.164526
$563$	29.3356	1.23635	0.618174	−	0.786041i	$-0.287873\pi$
$563$	29.3356	1.23635	0.618174	+	0.786041i	$0.287873\pi$
$564$	−2.53715	−0.106833
$565$	−0.790400	−0.0332524
$566$	−25.7771	−1.08349
$567$	−0.303495	−0.0127456
$568$	15.0269	0.630514
$569$	0.339405	0.0142286	0.00711431	−	0.999975i	$-0.497735\pi$
$569$	0.339405	0.0142286	0.00711431	+	0.999975i	$0.497735\pi$
$570$	0.358300	0.0150075
$571$	−16.5993	−0.694658	−0.347329	−	0.937743i	$-0.612911\pi$
$571$	−16.5993	−0.694658	−0.347329	+	0.937743i	$0.612911\pi$
$572$	2.95884	0.123715
$573$	15.8430	0.661850
$574$	−0.435073	−0.0181596
$575$	−45.4883	−1.89699
$576$	−20.6314	−0.859643
$577$	−19.0207	−0.791840	−0.395920	−	0.918285i	$-0.629574\pi$
$577$	−19.0207	−0.791840	−0.395920	+	0.918285i	$0.629574\pi$
$578$	−8.91872	−0.370970
$579$	13.0183	0.541023
$580$	0.690259	0.0286614
$581$	0.200937	0.00833629
$582$	12.9731	0.537751
$583$	−11.5782	−0.479522
$584$	−33.7831	−1.39796
$585$	−0.466806	−0.0193001
$586$	−7.67058	−0.316869
$587$	29.3939	1.21322	0.606609	−	0.795000i	$-0.292529\pi$
$587$	29.3939	1.21322	0.606609	+	0.795000i	$0.292529\pi$
$588$	−3.45986	−0.142682
$589$	21.2143	0.874118
$590$	1.93221	0.0795477
$591$	−19.2637	−0.792403
$592$	−9.63554	−0.396018
$593$	−21.6941	−0.890871	−0.445436	−	0.895314i	$-0.646951\pi$
$593$	−21.6941	−0.890871	−0.445436	+	0.895314i	$0.646951\pi$
$594$	−21.4705	−0.880946
$595$	0.0443337	0.00181751
$596$	10.8696	0.445236
$597$	12.8630	0.526449
$598$	11.8129	0.483065
$599$	−7.41054	−0.302786	−0.151393	−	0.988474i	$-0.548376\pi$
$599$	−7.41054	−0.302786	−0.151393	+	0.988474i	$0.548376\pi$
$600$	−12.1071	−0.494272
$601$	−17.7208	−0.722848	−0.361424	−	0.932402i	$-0.617709\pi$
$601$	−17.7208	−0.722848	−0.361424	+	0.932402i	$0.617709\pi$
$602$	−0.192706	−0.00785411
$603$	−13.3562	−0.543906
$604$	13.7218	0.558333
$605$	1.34514	0.0546878
$606$	7.41239	0.301108
$607$	37.0318	1.50307	0.751536	−	0.659692i	$-0.229313\pi$
$607$	37.0318	1.50307	0.751536	+	0.659692i	$0.229313\pi$
$608$	−7.31507	−0.296665
$609$	−0.395747	−0.0160365
$610$	−2.94683	−0.119314
$611$	−5.64219	−0.228259
$612$	−4.54520	−0.183729
$613$	37.6348	1.52005	0.760027	−	0.649891i	$-0.225185\pi$
$613$	37.6348	1.52005	0.760027	+	0.649891i	$0.225185\pi$
$614$	18.4090	0.742925
$615$	−0.649157	−0.0261765
$616$	−1.07177	−0.0431828
$617$	−8.73601	−0.351699	−0.175849	−	0.984417i	$-0.556267\pi$
$617$	−8.73601	−0.351699	−0.175849	+	0.984417i	$0.556267\pi$
$618$	−9.77768	−0.393316
$619$	17.0846	0.686687	0.343343	−	0.939210i	$-0.388441\pi$
$619$	17.0846	0.686687	0.343343	+	0.939210i	$0.388441\pi$
$620$	1.09799	0.0440965
$621$	38.9513	1.56306
$622$	30.0396	1.20448
$623$	−0.450809	−0.0180613
$624$	2.05552	0.0822865
$625$	24.5215	0.980862
$626$	4.33641	0.173318
$627$	−7.35526	−0.293741
$628$	12.2309	0.488067
$629$	−12.5152	−0.499013
$630$	0.0402530	0.00160372
$631$	−38.0472	−1.51464	−0.757318	−	0.653046i	$-0.773491\pi$
$631$	−38.0472	−1.51464	−0.757318	+	0.653046i	$0.773491\pi$
$632$	−53.6681	−2.13480
$633$	−10.7552	−0.427480
$634$	22.3035	0.885787
$635$	−3.13008	−0.124213
$636$	1.33090	0.0527737
$637$	−7.69415	−0.304853
$638$	31.1830	1.23455
$639$	11.5856	0.458318
$640$	0.610894	0.0241477
$641$	27.5905	1.08976	0.544879	−	0.838514i	$-0.316575\pi$
$641$	27.5905	1.08976	0.544879	+	0.838514i	$0.316575\pi$
$642$	3.07933	0.121532
$643$	6.89268	0.271821	0.135910	−	0.990721i	$-0.456604\pi$
$643$	6.89268	0.271821	0.135910	+	0.990721i	$0.456604\pi$
$644$	0.462874	0.0182398
$645$	−0.287530	−0.0113215
$646$	7.75827	0.305245
$647$	8.60822	0.338424	0.169212	−	0.985580i	$-0.445878\pi$
$647$	8.60822	0.338424	0.169212	+	0.985580i	$0.445878\pi$
$648$	−11.5471	−0.453612
$649$	−39.6647	−1.55698
$650$	−6.40952	−0.251402
$651$	−0.629515	−0.0246726
$652$	8.90746	0.348843
$653$	3.73378	0.146114	0.0730571	−	0.997328i	$-0.476724\pi$
$653$	3.73378	0.146114	0.0730571	+	0.997328i	$0.476724\pi$
$654$	11.8798	0.464537
$655$	2.11571	0.0826677
$656$	−10.8220	−0.422528
$657$	−26.0464	−1.01617
$658$	0.486529	0.0189669
$659$	10.1373	0.394893	0.197447	−	0.980314i	$-0.436735\pi$
$659$	10.1373	0.394893	0.197447	+	0.980314i	$0.436735\pi$
$660$	−0.380689	−0.0148183
$661$	−11.0003	−0.427863	−0.213932	−	0.976849i	$-0.568627\pi$
$661$	−11.0003	−0.427863	−0.213932	+	0.976849i	$0.568627\pi$
$662$	−5.56936	−0.216459
$663$	2.66982	0.103687
$664$	7.64508	0.296687
$665$	0.0312216	0.00121072
$666$	−11.3632	−0.440315
$667$	−56.5715	−2.19046
$668$	12.0947	0.467957
$669$	−19.5339	−0.755226
$670$	1.17996	0.0455858
$671$	60.4932	2.33531
$672$	0.217068	0.00837359
$673$	−44.9940	−1.73439	−0.867196	−	0.497967i	$-0.834080\pi$
$673$	−44.9940	−1.73439	−0.867196	+	0.497967i	$0.834080\pi$
$674$	−34.9981	−1.34808
$675$	−21.1345	−0.813467
$676$	7.36695	0.283344
$677$	15.4870	0.595213	0.297607	−	0.954689i	$-0.403812\pi$
$677$	15.4870	0.595213	0.297607	+	0.954689i	$0.403812\pi$
$678$	4.10446	0.157631
$679$	1.13045	0.0433828
$680$	1.68677	0.0646846
$681$	−14.2396	−0.545661
$682$	49.6027	1.89939
$683$	33.7255	1.29047	0.645235	−	0.763984i	$-0.276759\pi$
$683$	33.7255	1.29047	0.645235	+	0.763984i	$0.276759\pi$
$684$	−3.20092	−0.122390
$685$	−0.392439	−0.0149943
$686$	1.32756	0.0506866
$687$	−12.5535	−0.478947
$688$	−4.79336	−0.182745
$689$	2.95970	0.112756
$690$	−1.51986	−0.0578602
$691$	13.5728	0.516333	0.258166	−	0.966100i	$-0.416882\pi$
$691$	13.5728	0.516333	0.258166	+	0.966100i	$0.416882\pi$
$692$	−15.1063	−0.574255
$693$	−0.826321	−0.0313894
$694$	18.0333	0.684534
$695$	1.09378	0.0414895
$696$	−15.0570	−0.570735
$697$	−14.0562	−0.532417
$698$	7.78799	0.294780
$699$	−1.84954	−0.0699559
$700$	−0.251149	−0.00949256
$701$	−34.7789	−1.31358	−0.656790	−	0.754074i	$-0.728086\pi$
$701$	−34.7789	−1.31358	−0.656790	+	0.754074i	$0.728086\pi$
$702$	5.48843	0.207147
$703$	−8.81371	−0.332415
$704$	−37.4167	−1.41019
$705$	0.725932	0.0273402
$706$	−39.5505	−1.48850
$707$	0.645903	0.0242917
$708$	4.55940	0.171353
$709$	−23.1752	−0.870362	−0.435181	−	0.900343i	$-0.643316\pi$
$709$	−23.1752	−0.870362	−0.435181	+	0.900343i	$0.643316\pi$
$710$	−1.02353	−0.0384125
$711$	−41.3775	−1.55178
$712$	−17.1520	−0.642797
$713$	−89.9882	−3.37009
$714$	−0.230220	−0.00861577
$715$	−0.846588	−0.0316606
$716$	−7.36371	−0.275195
$717$	−3.83872	−0.143360
$718$	−31.9092	−1.19084
$719$	−39.5082	−1.47341	−0.736704	−	0.676215i	$-0.763619\pi$
$719$	−39.5082	−1.47341	−0.736704	+	0.676215i	$0.763619\pi$
$720$	1.00125	0.0373144
$721$	−0.852011	−0.0317305
$722$	−16.8168	−0.625858
$723$	2.71309	0.100901
$724$	−0.121067	−0.00449940
$725$	30.6950	1.13998
$726$	−6.98517	−0.259244
$727$	−5.75881	−0.213583	−0.106791	−	0.994281i	$-0.534058\pi$
$727$	−5.75881	−0.213583	−0.106791	+	0.994281i	$0.534058\pi$
$728$	0.273972	0.0101541
$729$	1.20162	0.0445043
$730$	2.30108	0.0851669
$731$	−6.22589	−0.230273
$732$	−6.95361	−0.257013
$733$	−41.9036	−1.54774	−0.773872	−	0.633343i	$-0.781682\pi$
$733$	−41.9036	−1.54774	−0.773872	+	0.633343i	$0.781682\pi$
$734$	16.4786	0.608236
$735$	0.989941	0.0365145
$736$	31.0296	1.14377
$737$	−24.2224	−0.892245
$738$	−12.7624	−0.469790
$739$	−14.5650	−0.535780	−0.267890	−	0.963449i	$-0.586326\pi$
$739$	−14.5650	−0.535780	−0.267890	+	0.963449i	$0.586326\pi$
$740$	−0.456174	−0.0167693
$741$	1.88020	0.0690708
$742$	−0.255217	−0.00936931
$743$	−22.9633	−0.842440	−0.421220	−	0.906958i	$-0.638398\pi$
$743$	−22.9633	−0.842440	−0.421220	+	0.906958i	$0.638398\pi$
$744$	−23.9512	−0.878094
$745$	−3.11003	−0.113943
$746$	23.2976	0.852984
$747$	5.89427	0.215660
$748$	−8.24306	−0.301396
$749$	0.268328	0.00980448
$750$	1.65462	0.0604183
$751$	−8.52609	−0.311121	−0.155561	−	0.987826i	$-0.549718\pi$
$751$	−8.52609	−0.311121	−0.155561	+	0.987826i	$0.549718\pi$
$752$	12.1019	0.441311
$753$	20.3606	0.741980
$754$	−7.97119	−0.290294
$755$	−3.92611	−0.142886
$756$	0.215058	0.00782157
$757$	−19.7364	−0.717331	−0.358665	−	0.933466i	$-0.616768\pi$
$757$	−19.7364	−0.717331	−0.358665	+	0.933466i	$0.616768\pi$
$758$	−19.3328	−0.702199
$759$	31.2001	1.13249
$760$	1.18789	0.0430894
$761$	44.7253	1.62129	0.810646	−	0.585537i	$-0.199116\pi$
$761$	44.7253	1.62129	0.810646	+	0.585537i	$0.199116\pi$
$762$	16.2541	0.588825
$763$	1.03519	0.0374762
$764$	12.5040	0.452379
$765$	1.30048	0.0470189
$766$	26.0791	0.942275
$767$	10.1394	0.366111
$768$	10.5937	0.382268
$769$	−28.1170	−1.01393	−0.506963	−	0.861968i	$-0.669232\pi$
$769$	−28.1170	−1.01393	−0.506963	+	0.861968i	$0.669232\pi$
$770$	0.0730018	0.00263080
$771$	19.1517	0.689733
$772$	10.2746	0.369793
$773$	34.5978	1.24440	0.622199	−	0.782859i	$-0.286240\pi$
$773$	34.5978	1.24440	0.622199	+	0.782859i	$0.286240\pi$
$774$	−5.65282	−0.203186
$775$	48.8264	1.75390
$776$	43.0104	1.54398
$777$	0.261539	0.00938266
$778$	−12.1546	−0.435765
$779$	−9.89897	−0.354667
$780$	0.0973141	0.00348440
$781$	21.0113	0.751843
$782$	−32.9096	−1.17685
$783$	−26.2839	−0.939310
$784$	16.5031	0.589398
$785$	−3.49953	−0.124904
$786$	−10.9867	−0.391881
$787$	−46.1869	−1.64639	−0.823193	−	0.567762i	$-0.807810\pi$
$787$	−46.1869	−1.64639	−0.823193	+	0.567762i	$0.807810\pi$
$788$	−15.2038	−0.541613
$789$	−14.3920	−0.512367
$790$	3.65552	0.130057
$791$	0.357656	0.0127168
$792$	−31.4391	−1.11714
$793$	−15.4637	−0.549131
$794$	−2.98282	−0.105856
$795$	−0.380800	−0.0135056
$796$	10.1521	0.359832
$797$	31.0936	1.10139	0.550695	−	0.834707i	$-0.314363\pi$
$797$	31.0936	1.10139	0.550695	+	0.834707i	$0.314363\pi$
$798$	−0.162131	−0.00573936
$799$	15.7186	0.556085
$800$	−16.8363	−0.595252
$801$	−13.2240	−0.467246
$802$	14.5698	0.514478
$803$	−47.2371	−1.66696
$804$	2.78433	0.0981959
$805$	−0.132438	−0.00466784
$806$	−12.6798	−0.446626
$807$	4.50502	0.158584
$808$	24.5747	0.864536
$809$	−22.7451	−0.799676	−0.399838	−	0.916586i	$-0.630934\pi$
$809$	−22.7451	−0.799676	−0.399838	+	0.916586i	$0.630934\pi$
$810$	0.786511	0.0276352
$811$	−20.2514	−0.711121	−0.355561	−	0.934653i	$-0.615710\pi$
$811$	−20.2514	−0.711121	−0.355561	+	0.934653i	$0.615710\pi$
$812$	−0.312342	−0.0109610
$813$	−12.9953	−0.455766
$814$	−20.6080	−0.722311
$815$	−2.54862	−0.0892741
$816$	−5.72648	−0.200467
$817$	−4.38453	−0.153395
$818$	16.8364	0.588673
$819$	0.211230	0.00738096
$820$	−0.512345	−0.0178918
$821$	47.0787	1.64306	0.821529	−	0.570167i	$-0.193121\pi$
$821$	47.0787	1.64306	0.821529	+	0.570167i	$0.193121\pi$
$822$	2.03789	0.0710796
$823$	−3.97277	−0.138482	−0.0692411	−	0.997600i	$-0.522058\pi$
$823$	−3.97277	−0.138482	−0.0692411	+	0.997600i	$0.522058\pi$
$824$	−32.4165	−1.12928
$825$	−16.9288	−0.589384
$826$	−0.874322	−0.0304216
$827$	−12.1175	−0.421366	−0.210683	−	0.977554i	$-0.567569\pi$
$827$	−12.1175	−0.421366	−0.210683	+	0.977554i	$0.567569\pi$
$828$	13.5779	0.471864
$829$	27.0304	0.938804	0.469402	−	0.882985i	$-0.344470\pi$
$829$	27.0304	0.938804	0.469402	+	0.882985i	$0.344470\pi$
$830$	−0.520732	−0.0180749
$831$	20.9410	0.726437
$832$	9.56468	0.331596
$833$	21.4352	0.742686
$834$	−5.67989	−0.196678
$835$	−3.46054	−0.119757
$836$	−5.80511	−0.200774
$837$	−41.8098	−1.44516
$838$	18.3943	0.635420
$839$	−21.4624	−0.740964	−0.370482	−	0.928840i	$-0.620807\pi$
$839$	−21.4624	−0.740964	−0.370482	+	0.928840i	$0.620807\pi$
$840$	−0.0352497	−0.00121623
$841$	9.17374	0.316336
$842$	0.809042	0.0278814
$843$	−2.63335	−0.0906974
$844$	−8.48848	−0.292186
$845$	−2.10784	−0.0725120
$846$	14.2718	0.490674
$847$	−0.608676	−0.0209144
$848$	−6.34825	−0.218000
$849$	17.4036	0.597290
$850$	17.8563	0.612467
$851$	37.3866	1.28160
$852$	−2.41522	−0.0827440
$853$	−20.5093	−0.702226	−0.351113	−	0.936333i	$-0.614197\pi$
$853$	−20.5093	−0.702226	−0.351113	+	0.936333i	$0.614197\pi$
$854$	1.33344	0.0456294
$855$	0.915852	0.0313215
$856$	10.2091	0.348939
$857$	−23.2772	−0.795135	−0.397567	−	0.917573i	$-0.630146\pi$
$857$	−23.2772	−0.795135	−0.397567	+	0.917573i	$0.630146\pi$
$858$	4.39624	0.150085
$859$	−3.80551	−0.129842	−0.0649212	−	0.997890i	$-0.520680\pi$
$859$	−3.80551	−0.129842	−0.0649212	+	0.997890i	$0.520680\pi$
$860$	−0.226932	−0.00773830
$861$	0.293743	0.0100107
$862$	34.1078	1.16172
$863$	−35.9633	−1.22420	−0.612102	−	0.790779i	$-0.709676\pi$
$863$	−35.9633	−1.22420	−0.612102	+	0.790779i	$0.709676\pi$
$864$	14.4168	0.490469
$865$	4.32224	0.146960
$866$	21.2450	0.721933
$867$	6.02154	0.204502
$868$	−0.496842	−0.0168639
$869$	−75.0412	−2.54560
$870$	1.02558	0.0347706
$871$	6.19189	0.209804
$872$	39.3858	1.33377
$873$	33.1605	1.12231
$874$	−23.1763	−0.783951
$875$	0.144181	0.00487421
$876$	5.42984	0.183457
$877$	14.2388	0.480810	0.240405	−	0.970673i	$-0.422720\pi$
$877$	14.2388	0.480810	0.240405	+	0.970673i	$0.422720\pi$
$878$	3.81949	0.128902
$879$	5.17885	0.174678
$880$	1.81584	0.0612120
$881$	27.4845	0.925976	0.462988	−	0.886365i	$-0.346777\pi$
$881$	27.4845	0.925976	0.462988	+	0.886365i	$0.346777\pi$
$882$	19.4622	0.655325
$883$	24.3360	0.818973	0.409487	−	0.912316i	$-0.365708\pi$
$883$	24.3360	0.818973	0.409487	+	0.912316i	$0.365708\pi$
$884$	2.10714	0.0708709
$885$	−1.30454	−0.0438518
$886$	−25.2962	−0.849844
$887$	−26.2023	−0.879787	−0.439893	−	0.898050i	$-0.644984\pi$
$887$	−26.2023	−0.879787	−0.439893	+	0.898050i	$0.644984\pi$
$888$	9.95080	0.333927
$889$	1.41636	0.0475031
$890$	1.16828	0.0391608
$891$	−16.1457	−0.540900
$892$	−15.4171	−0.516202
$893$	11.0697	0.370434
$894$	16.1500	0.540137
$895$	2.10692	0.0704265
$896$	−0.276429	−0.00923485
$897$	−7.97556	−0.266296
$898$	22.2350	0.741992
$899$	60.7230	2.02522
$900$	−7.36719	−0.245573
$901$	−8.24546	−0.274696
$902$	−23.1456	−0.770663
$903$	0.130107	0.00432969
$904$	13.6078	0.452587
$905$	0.0346397	0.00115146
$906$	20.3879	0.677341
$907$	58.2340	1.93363	0.966814	−	0.255482i	$-0.0822342\pi$
$907$	58.2340	1.93363	0.966814	+	0.255482i	$0.0822342\pi$
$908$	−11.2385	−0.372963
$909$	18.9468	0.628427
$910$	−0.0186612	−0.000618612 0
$911$	−30.4851	−1.01002	−0.505008	−	0.863114i	$-0.668511\pi$
$911$	−30.4851	−1.01002	−0.505008	+	0.863114i	$0.668511\pi$
$912$	−4.03283	−0.133540
$913$	10.6897	0.353778
$914$	4.91097	0.162440
$915$	1.98958	0.0657734
$916$	−9.90781	−0.327363
$917$	−0.957358	−0.0316148
$918$	−15.2903	−0.504654
$919$	−2.94915	−0.0972833	−0.0486417	−	0.998816i	$-0.515489\pi$
$919$	−2.94915	−0.0972833	−0.0486417	+	0.998816i	$0.515489\pi$
$920$	−5.03889	−0.166127
$921$	−12.4290	−0.409548
$922$	16.0773	0.529477
$923$	−5.37104	−0.176790
$924$	0.172261	0.00566699
$925$	−20.2855	−0.666983
$926$	5.72032	0.187982
$927$	−24.9928	−0.820870
$928$	−20.9384	−0.687336
$929$	28.9881	0.951070	0.475535	−	0.879697i	$-0.342255\pi$
$929$	28.9881	0.951070	0.475535	+	0.879697i	$0.342255\pi$
$930$	1.63140	0.0534956
$931$	15.0956	0.494737
$932$	−1.45974	−0.0478153
$933$	−20.2814	−0.663984
$934$	14.4675	0.473391
$935$	2.35852	0.0771318
$936$	8.03667	0.262687
$937$	−27.5952	−0.901497	−0.450748	−	0.892651i	$-0.648843\pi$
$937$	−27.5952	−0.901497	−0.450748	+	0.892651i	$0.648843\pi$
$938$	−0.533930	−0.0174334
$939$	−2.92776	−0.0955439
$940$	0.572939	0.0186872
$941$	19.2064	0.626112	0.313056	−	0.949735i	$-0.398647\pi$
$941$	19.2064	0.626112	0.313056	+	0.949735i	$0.398647\pi$
$942$	18.1727	0.592098
$943$	41.9902	1.36739
$944$	−21.7478	−0.707832
$945$	−0.0615326	−0.00200166
$946$	−10.2518	−0.333315
$947$	−41.2922	−1.34182	−0.670908	−	0.741541i	$-0.734095\pi$
$947$	−41.2922	−1.34182	−0.670908	+	0.741541i	$0.734095\pi$
$948$	8.62588	0.280155
$949$	12.0750	0.391973
$950$	12.5752	0.407992
$951$	−15.0584	−0.488302
$952$	−0.763262	−0.0247375
$953$	−24.0272	−0.778317	−0.389158	−	0.921171i	$-0.627234\pi$
$953$	−24.0272	−0.778317	−0.389158	+	0.921171i	$0.627234\pi$
$954$	−7.48650	−0.242384
$955$	−3.57767	−0.115771
$956$	−3.02969	−0.0979872
$957$	−21.0534	−0.680561
$958$	−4.17890	−0.135014
$959$	0.177578	0.00573430
$960$	−1.23061	−0.0397176
$961$	65.5920	2.11587
$962$	5.26795	0.169846
$963$	7.87109	0.253642
$964$	2.14130	0.0689665
$965$	−2.93980	−0.0946355
$966$	0.687737	0.0221276
$967$	−10.8553	−0.349084	−0.174542	−	0.984650i	$-0.555845\pi$
$967$	−10.8553	−0.349084	−0.174542	+	0.984650i	$0.555845\pi$
$968$	−23.1584	−0.744338
$969$	−5.23806	−0.168271
$970$	−2.92958	−0.0940633
$971$	−17.1111	−0.549122	−0.274561	−	0.961570i	$-0.588533\pi$
$971$	−17.1111	−0.549122	−0.274561	+	0.961570i	$0.588533\pi$
$972$	9.83069	0.315319
$973$	−0.494936	−0.0158669
$974$	−5.97191	−0.191352
$975$	4.32744	0.138589
$976$	33.1679	1.06168
$977$	22.5277	0.720726	0.360363	−	0.932812i	$-0.382653\pi$
$977$	22.5277	0.720726	0.360363	+	0.932812i	$0.382653\pi$
$978$	13.2347	0.423198
$979$	−23.9827	−0.766489
$980$	0.781306	0.0249579
$981$	30.3660	0.969512
$982$	31.7849	1.01430
$983$	−27.0618	−0.863138	−0.431569	−	0.902080i	$-0.642040\pi$
$983$	−27.0618	−0.863138	−0.431569	+	0.902080i	$0.642040\pi$
$984$	11.1761	0.356280
$985$	4.35014	0.138607
$986$	22.2070	0.707215
$987$	−0.328484	−0.0104558
$988$	1.48394	0.0472104
$989$	18.5986	0.591401
$990$	2.14143	0.0680590
$991$	−19.8216	−0.629655	−0.314827	−	0.949149i	$-0.601947\pi$
$991$	−19.8216	−0.629655	−0.314827	+	0.949149i	$0.601947\pi$
$992$	−33.3067	−1.05749
$993$	3.76020	0.119326
$994$	0.463148	0.0146902
$995$	−2.90473	−0.0920863
$996$	−1.22877	−0.0389349
$997$	−23.1120	−0.731966	−0.365983	−	0.930622i	$-0.619267\pi$
$997$	−23.1120	−0.731966	−0.365983	+	0.930622i	$0.619267\pi$
$998$	−5.27436	−0.166957
$999$	17.3703	0.549573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.e.1.8	✓	10
3.2	odd	2		4527.2.a.k.1.3		10
4.3	odd	2		8048.2.a.p.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.e.1.8	✓	10	1.1	even	1	trivial
4527.2.a.k.1.3		10	3.2	odd	2
8048.2.a.p.1.5		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)

\(f(q)\)	\(=\)	\(q+1.17266 q^{2} -0.791730 q^{3} -0.624870 q^{4} +0.178789 q^{5} -0.928430 q^{6} -0.0809018 q^{7} -3.07808 q^{8} -2.37316 q^{9} +O(q^{10})\)	\(q+1.17266 q^{2} -0.791730 q^{3} -0.624870 q^{4} +0.178789 q^{5} -0.928430 q^{6} -0.0809018 q^{7} -3.07808 q^{8} -2.37316 q^{9} +0.209658 q^{10} -4.30391 q^{11} +0.494728 q^{12} +1.10019 q^{13} -0.0948703 q^{14} -0.141552 q^{15} -2.35980 q^{16} -3.06504 q^{17} -2.78291 q^{18} -2.15853 q^{19} -0.111720 q^{20} +0.0640524 q^{21} -5.04702 q^{22} +9.15620 q^{23} +2.43701 q^{24} -4.96803 q^{25} +1.29015 q^{26} +4.25410 q^{27} +0.0505531 q^{28} -6.17849 q^{29} -0.165993 q^{30} -9.82812 q^{31} +3.38892 q^{32} +3.40754 q^{33} -3.59425 q^{34} -0.0144643 q^{35} +1.48292 q^{36} +4.08321 q^{37} -2.53122 q^{38} -0.871056 q^{39} -0.550326 q^{40} +4.58598 q^{41} +0.0751117 q^{42} +2.03126 q^{43} +2.68938 q^{44} -0.424295 q^{45} +10.7371 q^{46} -5.12836 q^{47} +1.86832 q^{48} -6.99345 q^{49} -5.82581 q^{50} +2.42668 q^{51} -0.687477 q^{52} +2.69017 q^{53} +4.98861 q^{54} -0.769491 q^{55} +0.249022 q^{56} +1.70897 q^{57} -7.24527 q^{58} +9.21598 q^{59} +0.0884518 q^{60} -14.0554 q^{61} -11.5250 q^{62} +0.191993 q^{63} +8.69364 q^{64} +0.196702 q^{65} +3.99588 q^{66} +5.62801 q^{67} +1.91525 q^{68} -7.24924 q^{69} -0.0169617 q^{70} -4.88191 q^{71} +7.30478 q^{72} +10.9754 q^{73} +4.78821 q^{74} +3.93334 q^{75} +1.34880 q^{76} +0.348194 q^{77} -1.02145 q^{78} +17.4356 q^{79} -0.421905 q^{80} +3.75139 q^{81} +5.37780 q^{82} -2.48372 q^{83} -0.0400244 q^{84} -0.547994 q^{85} +2.38198 q^{86} +4.89170 q^{87} +13.2478 q^{88} +5.57230 q^{89} -0.497553 q^{90} -0.0890076 q^{91} -5.72143 q^{92} +7.78122 q^{93} -6.01382 q^{94} -0.385920 q^{95} -2.68311 q^{96} -13.9731 q^{97} -8.20094 q^{98} +10.2139 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) \) 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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