LMFDB - Embedded newform 503.2.a.e.1.7

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			1.7
Root			$1.31567$ 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)

$f(q)$	$=$	$q+0.0830530 q^{2} +0.315672 q^{3} -1.99310 q^{4} +2.25024 q^{5} +0.0262175 q^{6} -3.20647 q^{7} -0.331639 q^{8} -2.90035 q^{9} +O(q^{10})$	\(q+0.0830530 q^{2} +0.315672 q^{3} -1.99310 q^{4} +2.25024 q^{5} +0.0262175 q^{6} -3.20647 q^{7} -0.331639 q^{8} -2.90035 q^{9} +0.186890 q^{10} -0.218022 q^{11} -0.629166 q^{12} -4.17856 q^{13} -0.266307 q^{14} +0.710339 q^{15} +3.95866 q^{16} -4.68939 q^{17} -0.240883 q^{18} +3.43926 q^{19} -4.48497 q^{20} -1.01219 q^{21} -0.0181074 q^{22} -3.99816 q^{23} -0.104689 q^{24} +0.0635992 q^{25} -0.347042 q^{26} -1.86257 q^{27} +6.39082 q^{28} -0.712153 q^{29} +0.0589958 q^{30} +1.04933 q^{31} +0.992057 q^{32} -0.0688235 q^{33} -0.389468 q^{34} -7.21534 q^{35} +5.78070 q^{36} +1.70998 q^{37} +0.285641 q^{38} -1.31905 q^{39} -0.746269 q^{40} +3.18460 q^{41} -0.0840656 q^{42} -6.35890 q^{43} +0.434541 q^{44} -6.52650 q^{45} -0.332059 q^{46} -3.87861 q^{47} +1.24964 q^{48} +3.28144 q^{49} +0.00528210 q^{50} -1.48031 q^{51} +8.32830 q^{52} -10.8877 q^{53} -0.154692 q^{54} -0.490604 q^{55} +1.06339 q^{56} +1.08568 q^{57} -0.0591465 q^{58} -2.63793 q^{59} -1.41578 q^{60} +11.1544 q^{61} +0.0871503 q^{62} +9.29988 q^{63} -7.83493 q^{64} -9.40279 q^{65} -0.00571600 q^{66} +6.09170 q^{67} +9.34643 q^{68} -1.26210 q^{69} -0.599256 q^{70} +9.40515 q^{71} +0.961870 q^{72} -2.78532 q^{73} +0.142019 q^{74} +0.0200765 q^{75} -6.85479 q^{76} +0.699082 q^{77} -0.109551 q^{78} +5.16993 q^{79} +8.90795 q^{80} +8.11309 q^{81} +0.264491 q^{82} +1.83793 q^{83} +2.01740 q^{84} -10.5523 q^{85} -0.528126 q^{86} -0.224807 q^{87} +0.0723048 q^{88} -8.08786 q^{89} -0.542046 q^{90} +13.3984 q^{91} +7.96873 q^{92} +0.331245 q^{93} -0.322130 q^{94} +7.73917 q^{95} +0.313165 q^{96} -12.9058 q^{97} +0.272533 q^{98} +0.632342 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.0830530	0.0587274	0.0293637	−	0.999569i	$-0.490652\pi$
$2$	0.0830530	0.0587274	0.0293637	+	0.999569i	$0.490652\pi$
$3$	0.315672	0.182253	0.0911266	−	0.995839i	$-0.470953\pi$
$3$	0.315672	0.182253	0.0911266	+	0.995839i	$0.470953\pi$
$4$	−1.99310	−0.996551
$5$	2.25024	1.00634	0.503170	−	0.864188i	$-0.332167\pi$
$5$	2.25024	1.00634	0.503170	+	0.864188i	$0.332167\pi$
$6$	0.0262175	0.0107032
$7$	−3.20647	−1.21193	−0.605966	−	0.795491i	$-0.707213\pi$
$7$	−3.20647	−1.21193	−0.605966	+	0.795491i	$0.707213\pi$
$8$	−0.331639	−0.117252
$9$	−2.90035	−0.966784
$10$	0.186890	0.0590997
$11$	−0.218022	−0.0657362	−0.0328681	−	0.999460i	$-0.510464\pi$
$11$	−0.218022	−0.0657362	−0.0328681	+	0.999460i	$0.510464\pi$
$12$	−0.629166	−0.181625
$13$	−4.17856	−1.15892	−0.579462	−	0.814999i	$-0.696737\pi$
$13$	−4.17856	−1.15892	−0.579462	+	0.814999i	$0.696737\pi$
$14$	−0.266307	−0.0711735
$15$	0.710339	0.183409
$16$	3.95866	0.989665
$17$	−4.68939	−1.13734	−0.568672	−	0.822564i	$-0.692543\pi$
$17$	−4.68939	−1.13734	−0.568672	+	0.822564i	$0.692543\pi$
$18$	−0.240883	−0.0567767
$19$	3.43926	0.789020	0.394510	−	0.918892i	$-0.370914\pi$
$19$	3.43926	0.789020	0.394510	+	0.918892i	$0.370914\pi$
$20$	−4.48497	−1.00287
$21$	−1.01219	−0.220878
$22$	−0.0181074	−0.00386052
$23$	−3.99816	−0.833673	−0.416837	−	0.908981i	$-0.636861\pi$
$23$	−3.99816	−0.833673	−0.416837	+	0.908981i	$0.636861\pi$
$24$	−0.104689	−0.0213696
$25$	0.0635992	0.0127198
$26$	−0.347042	−0.0680606
$27$	−1.86257	−0.358453
$28$	6.39082	1.20775
$29$	−0.712153	−0.132243	−0.0661217	−	0.997812i	$-0.521063\pi$
$29$	−0.712153	−0.132243	−0.0661217	+	0.997812i	$0.521063\pi$
$30$	0.0589958	0.0107711
$31$	1.04933	0.188466	0.0942329	−	0.995550i	$-0.469960\pi$
$31$	1.04933	0.188466	0.0942329	+	0.995550i	$0.469960\pi$
$32$	0.992057	0.175373
$33$	−0.0688235	−0.0119806
$34$	−0.389468	−0.0667932
$35$	−7.21534	−1.21961
$36$	5.78070	0.963449
$37$	1.70998	0.281119	0.140560	−	0.990072i	$-0.455110\pi$
$37$	1.70998	0.281119	0.140560	+	0.990072i	$0.455110\pi$
$38$	0.285641	0.0463371
$39$	−1.31905	−0.211218
$40$	−0.746269	−0.117996
$41$	3.18460	0.497351	0.248675	−	0.968587i	$-0.420005\pi$
$41$	3.18460	0.497351	0.248675	+	0.968587i	$0.420005\pi$
$42$	−0.0840656	−0.0129716
$43$	−6.35890	−0.969723	−0.484861	−	0.874591i	$-0.661130\pi$
$43$	−6.35890	−0.969723	−0.484861	+	0.874591i	$0.661130\pi$
$44$	0.434541	0.0655095
$45$	−6.52650	−0.972913
$46$	−0.332059	−0.0489594
$47$	−3.87861	−0.565754	−0.282877	−	0.959156i	$-0.591289\pi$
$47$	−3.87861	−0.565754	−0.282877	+	0.959156i	$0.591289\pi$
$48$	1.24964	0.180370
$49$	3.28144	0.468777
$50$	0.00528210	0.000747002 0
$51$	−1.48031	−0.207285
$52$	8.32830	1.15493
$53$	−10.8877	−1.49555	−0.747773	−	0.663954i	$-0.768877\pi$
$53$	−10.8877	−1.49555	−0.747773	+	0.663954i	$0.768877\pi$
$54$	−0.154692	−0.0210510
$55$	−0.490604	−0.0661530
$56$	1.06339	0.142102
$57$	1.08568	0.143801
$58$	−0.0591465	−0.00776631
$59$	−2.63793	−0.343429	−0.171715	−	0.985147i	$-0.554931\pi$
$59$	−2.63793	−0.343429	−0.171715	+	0.985147i	$0.554931\pi$
$60$	−1.41578	−0.182776
$61$	11.1544	1.42817	0.714084	−	0.700060i	$-0.246843\pi$
$61$	11.1544	1.42817	0.714084	+	0.700060i	$0.246843\pi$
$62$	0.0871503	0.0110681
$63$	9.29988	1.17168
$64$	−7.83493	−0.979366
$65$	−9.40279	−1.16627
$66$	−0.00571600	−0.000703591 0
$67$	6.09170	0.744219	0.372110	−	0.928189i	$-0.378635\pi$
$67$	6.09170	0.744219	0.372110	+	0.928189i	$0.378635\pi$
$68$	9.34643	1.13342
$69$	−1.26210	−0.151940
$70$	−0.599256	−0.0716247
$71$	9.40515	1.11619	0.558093	−	0.829778i	$-0.311533\pi$
$71$	9.40515	1.11619	0.558093	+	0.829778i	$0.311533\pi$
$72$	0.961870	0.113358
$73$	−2.78532	−0.325997	−0.162998	−	0.986626i	$-0.552117\pi$
$73$	−2.78532	−0.325997	−0.162998	+	0.986626i	$0.552117\pi$
$74$	0.142019	0.0165094
$75$	0.0200765	0.00231823
$76$	−6.85479	−0.786299
$77$	0.699082	0.0796678
$78$	−0.109551	−0.0124043
$79$	5.16993	0.581662	0.290831	−	0.956774i	$-0.406068\pi$
$79$	5.16993	0.581662	0.290831	+	0.956774i	$0.406068\pi$
$80$	8.90795	0.995939
$81$	8.11309	0.901455
$82$	0.264491	0.0292081
$83$	1.83793	0.201739	0.100870	−	0.994900i	$-0.467838\pi$
$83$	1.83793	0.201739	0.100870	+	0.994900i	$0.467838\pi$
$84$	2.01740	0.220117
$85$	−10.5523	−1.14455
$86$	−0.528126	−0.0569493
$87$	−0.224807	−0.0241018
$88$	0.0723048	0.00770772
$89$	−8.08786	−0.857311	−0.428656	−	0.903468i	$-0.641013\pi$
$89$	−8.08786	−0.857311	−0.428656	+	0.903468i	$0.641013\pi$
$90$	−0.542046	−0.0571366
$91$	13.3984	1.40454
$92$	7.96873	0.830798
$93$	0.331245	0.0343485
$94$	−0.322130	−0.0332252
$95$	7.73917	0.794022
$96$	0.313165	0.0319622
$97$	−12.9058	−1.31039	−0.655193	−	0.755462i	$-0.727413\pi$
$97$	−12.9058	−1.31039	−0.655193	+	0.755462i	$0.727413\pi$
$98$	0.272533	0.0275300
$99$	0.632342	0.0635527
$100$	−0.126760	−0.0126760
$101$	2.17744	0.216663	0.108331	−	0.994115i	$-0.465449\pi$
$101$	2.17744	0.216663	0.108331	+	0.994115i	$0.465449\pi$
$102$	−0.122944	−0.0121733
$103$	14.7612	1.45447	0.727234	−	0.686390i	$-0.240806\pi$
$103$	14.7612	1.45447	0.727234	+	0.686390i	$0.240806\pi$
$104$	1.38578	0.135886
$105$	−2.27768	−0.222279
$106$	−0.904260	−0.0878295
$107$	10.4459	1.00984	0.504920	−	0.863166i	$-0.331522\pi$
$107$	10.4459	1.00984	0.504920	+	0.863166i	$0.331522\pi$
$108$	3.71230	0.357216
$109$	−5.69014	−0.545017	−0.272508	−	0.962153i	$-0.587853\pi$
$109$	−5.69014	−0.545017	−0.272508	+	0.962153i	$0.587853\pi$
$110$	−0.0407461	−0.00388499
$111$	0.539793	0.0512348
$112$	−12.6933	−1.19941
$113$	20.9980	1.97533	0.987665	−	0.156584i	$-0.0500481\pi$
$113$	20.9980	1.97533	0.987665	+	0.156584i	$0.0500481\pi$
$114$	0.0901687	0.00844508
$115$	−8.99683	−0.838958
$116$	1.41939	0.131787
$117$	12.1193	1.12043
$118$	−0.219088	−0.0201687
$119$	15.0364	1.37838
$120$	−0.235576	−0.0215051
$121$	−10.9525	−0.995679
$122$	0.926403	0.0838726
$123$	1.00529	0.0906438
$124$	−2.09143	−0.187816
$125$	−11.1081	−0.993539
$126$	0.772384	0.0688094
$127$	−0.0956906	−0.00849117	−0.00424558	−	0.999991i	$-0.501351\pi$
$127$	−0.0956906	−0.00849117	−0.00424558	+	0.999991i	$0.501351\pi$
$128$	−2.63483	−0.232888
$129$	−2.00732	−0.176735
$130$	−0.780930	−0.0684921
$131$	14.5638	1.27244	0.636221	−	0.771507i	$-0.280496\pi$
$131$	14.5638	1.27244	0.636221	+	0.771507i	$0.280496\pi$
$132$	0.137172	0.0119393
$133$	−11.0279	−0.956238
$134$	0.505934	0.0437060
$135$	−4.19125	−0.360725
$136$	1.55519	0.133356
$137$	−17.1079	−1.46162	−0.730811	−	0.682579i	$-0.760858\pi$
$137$	−17.1079	−1.46162	−0.730811	+	0.682579i	$0.760858\pi$
$138$	−0.104822	−0.00892301
$139$	−17.7270	−1.50358	−0.751791	−	0.659402i	$-0.770810\pi$
$139$	−17.7270	−1.50358	−0.751791	+	0.659402i	$0.770810\pi$
$140$	14.3809	1.21541
$141$	−1.22437	−0.103110
$142$	0.781126	0.0655507
$143$	0.911020	0.0761833
$144$	−11.4815	−0.956792
$145$	−1.60252	−0.133082
$146$	−0.231329	−0.0191449
$147$	1.03586	0.0854361
$148$	−3.40817	−0.280150
$149$	−3.37396	−0.276406	−0.138203	−	0.990404i	$-0.544133\pi$
$149$	−3.37396	−0.276406	−0.138203	+	0.990404i	$0.544133\pi$
$150$	0.00166741	0.000136144 0
$151$	2.76168	0.224742	0.112371	−	0.993666i	$-0.464155\pi$
$151$	2.76168	0.224742	0.112371	+	0.993666i	$0.464155\pi$
$152$	−1.14059	−0.0925143
$153$	13.6009	1.09957
$154$	0.0580609	0.00467868
$155$	2.36126	0.189661
$156$	2.62901	0.210489
$157$	−8.93566	−0.713144	−0.356572	−	0.934268i	$-0.616054\pi$
$157$	−8.93566	−0.713144	−0.356572	+	0.934268i	$0.616054\pi$
$158$	0.429378	0.0341595
$159$	−3.43695	−0.272568
$160$	2.23237	0.176484
$161$	12.8200	1.01035
$162$	0.673817	0.0529401
$163$	−8.75660	−0.685870	−0.342935	−	0.939359i	$-0.611421\pi$
$163$	−8.75660	−0.685870	−0.342935	+	0.939359i	$0.611421\pi$
$164$	−6.34723	−0.495635
$165$	−0.154870	−0.0120566
$166$	0.152646	0.0118476
$167$	14.3605	1.11125	0.555623	−	0.831434i	$-0.312480\pi$
$167$	14.3605	1.11125	0.555623	+	0.831434i	$0.312480\pi$
$168$	0.335682	0.0258985
$169$	4.46038	0.343106
$170$	−0.876398	−0.0672167
$171$	−9.97506	−0.762812
$172$	12.6739	0.966378
$173$	−11.0498	−0.840098	−0.420049	−	0.907501i	$-0.637987\pi$
$173$	−11.0498	−0.840098	−0.420049	+	0.907501i	$0.637987\pi$
$174$	−0.0186709	−0.00141543
$175$	−0.203929	−0.0154156
$176$	−0.863077	−0.0650569
$177$	−0.832720	−0.0625910
$178$	−0.671721	−0.0503476
$179$	−6.55060	−0.489615	−0.244808	−	0.969572i	$-0.578725\pi$
$179$	−6.55060	−0.489615	−0.244808	+	0.969572i	$0.578725\pi$
$180$	13.0080	0.969558
$181$	−13.9694	−1.03834	−0.519169	−	0.854672i	$-0.673758\pi$
$181$	−13.9694	−1.03834	−0.519169	+	0.854672i	$0.673758\pi$
$182$	1.11278	0.0824848
$183$	3.52111	0.260288
$184$	1.32595	0.0977500
$185$	3.84787	0.282901
$186$	0.0275109	0.00201720
$187$	1.02239	0.0747647
$188$	7.73047	0.563802
$189$	5.97229	0.434420
$190$	0.642762	0.0466308
$191$	2.23996	0.162078	0.0810390	−	0.996711i	$-0.474176\pi$
$191$	2.23996	0.162078	0.0810390	+	0.996711i	$0.474176\pi$
$192$	−2.47327	−0.178493
$193$	22.1924	1.59744	0.798722	−	0.601700i	$-0.205510\pi$
$193$	22.1924	1.59744	0.798722	+	0.601700i	$0.205510\pi$
$194$	−1.07187	−0.0769555
$195$	−2.96819	−0.212557
$196$	−6.54024	−0.467160
$197$	−11.0264	−0.785595	−0.392797	−	0.919625i	$-0.628493\pi$
$197$	−11.0264	−0.785595	−0.392797	+	0.919625i	$0.628493\pi$
$198$	0.0525179	0.00373228
$199$	14.6196	1.03636	0.518179	−	0.855272i	$-0.326610\pi$
$199$	14.6196	1.03636	0.518179	+	0.855272i	$0.326610\pi$
$200$	−0.0210920	−0.00149143
$201$	1.92298	0.135636
$202$	0.180843	0.0127240
$203$	2.28350	0.160270
$204$	2.95040	0.206570
$205$	7.16612	0.500504
$206$	1.22597	0.0854170
$207$	11.5961	0.805982
$208$	−16.5415	−1.14695
$209$	−0.749835	−0.0518672
$210$	−0.189168	−0.0130538
$211$	1.54449	0.106327	0.0531635	−	0.998586i	$-0.483070\pi$
$211$	1.54449	0.106327	0.0531635	+	0.998586i	$0.483070\pi$
$212$	21.7004	1.49039
$213$	2.96894	0.203428
$214$	0.867562	0.0593053
$215$	−14.3091	−0.975871
$216$	0.617703	0.0420294
$217$	−3.36465	−0.228408
$218$	−0.472584	−0.0320074
$219$	−0.879246	−0.0594139
$220$	0.977823	0.0659248
$221$	19.5949	1.31810
$222$	0.0448314	0.00300889
$223$	−26.6878	−1.78715	−0.893573	−	0.448918i	$-0.851810\pi$
$223$	−26.6878	−1.78715	−0.893573	+	0.448918i	$0.851810\pi$
$224$	−3.18100	−0.212540
$225$	−0.184460	−0.0122973
$226$	1.74395	0.116006
$227$	−6.41989	−0.426103	−0.213052	−	0.977041i	$-0.568340\pi$
$227$	−6.41989	−0.426103	−0.213052	+	0.977041i	$0.568340\pi$
$228$	−2.16386	−0.143305
$229$	−27.8670	−1.84150	−0.920752	−	0.390149i	$-0.872423\pi$
$229$	−27.8670	−1.84150	−0.920752	+	0.390149i	$0.872423\pi$
$230$	−0.747214	−0.0492698
$231$	0.220680	0.0145197
$232$	0.236178	0.0155058
$233$	0.647350	0.0424093	0.0212047	−	0.999775i	$-0.493250\pi$
$233$	0.647350	0.0424093	0.0212047	+	0.999775i	$0.493250\pi$
$234$	1.00654	0.0657999
$235$	−8.72782	−0.569340
$236$	5.25766	0.342245
$237$	1.63200	0.106010
$238$	1.24882	0.0809488
$239$	−12.3635	−0.799727	−0.399864	−	0.916575i	$-0.630943\pi$
$239$	−12.3635	−0.799727	−0.399864	+	0.916575i	$0.630943\pi$
$240$	2.81199	0.181513
$241$	−12.7531	−0.821497	−0.410748	−	0.911749i	$-0.634732\pi$
$241$	−12.7531	−0.821497	−0.410748	+	0.911749i	$0.634732\pi$
$242$	−0.909636	−0.0584736
$243$	8.14880	0.522746
$244$	−22.2318	−1.42324
$245$	7.38404	0.471749
$246$	0.0834922	0.00532327
$247$	−14.3712	−0.914415
$248$	−0.348000	−0.0220980
$249$	0.580183	0.0367676
$250$	−0.922562	−0.0583480
$251$	−13.4917	−0.851588	−0.425794	−	0.904820i	$-0.640005\pi$
$251$	−13.4917	−0.851588	−0.425794	+	0.904820i	$0.640005\pi$
$252$	−18.5356	−1.16763
$253$	0.871688	0.0548025
$254$	−0.00794739	−0.000498664 0
$255$	−3.33105	−0.208599
$256$	15.4510	0.965689
$257$	−4.56318	−0.284643	−0.142322	−	0.989820i	$-0.545457\pi$
$257$	−4.56318	−0.284643	−0.142322	+	0.989820i	$0.545457\pi$
$258$	−0.166714	−0.0103792
$259$	−5.48300	−0.340697
$260$	18.7407	1.16225
$261$	2.06549	0.127851
$262$	1.20957	0.0747272
$263$	16.0985	0.992674	0.496337	−	0.868130i	$-0.334678\pi$
$263$	16.0985	0.992674	0.496337	+	0.868130i	$0.334678\pi$
$264$	0.0228246	0.00140476
$265$	−24.5001	−1.50503
$266$	−0.915898	−0.0561573
$267$	−2.55311	−0.156248
$268$	−12.1414	−0.741652
$269$	−7.49840	−0.457186	−0.228593	−	0.973522i	$-0.573412\pi$
$269$	−7.49840	−0.457186	−0.228593	+	0.973522i	$0.573412\pi$
$270$	−0.348096	−0.0211844
$271$	6.47424	0.393282	0.196641	−	0.980476i	$-0.436997\pi$
$271$	6.47424	0.393282	0.196641	+	0.980476i	$0.436997\pi$
$272$	−18.5637	−1.12559
$273$	4.22951	0.255981
$274$	−1.42086	−0.0858373
$275$	−0.0138660	−0.000836154 0
$276$	2.51550	0.151416
$277$	8.32050	0.499930	0.249965	−	0.968255i	$-0.419581\pi$
$277$	8.32050	0.499930	0.249965	+	0.968255i	$0.419581\pi$
$278$	−1.47228	−0.0883014
$279$	−3.04344	−0.182206
$280$	2.39289	0.143002
$281$	−26.3798	−1.57369	−0.786844	−	0.617152i	$-0.788286\pi$
$281$	−26.3798	−1.57369	−0.786844	+	0.617152i	$0.788286\pi$
$282$	−0.101687	−0.00605540
$283$	−23.4048	−1.39127	−0.695637	−	0.718394i	$-0.744878\pi$
$283$	−23.4048	−1.39127	−0.695637	+	0.718394i	$0.744878\pi$
$284$	−18.7454	−1.11234
$285$	2.44304	0.144713
$286$	0.0756630	0.00447405
$287$	−10.2113	−0.602755
$288$	−2.87731	−0.169547
$289$	4.99036	0.293551
$290$	−0.133094	−0.00781555
$291$	−4.07400	−0.238822
$292$	5.55142	0.324872
$293$	−3.57088	−0.208613	−0.104307	−	0.994545i	$-0.533262\pi$
$293$	−3.57088	−0.208613	−0.104307	+	0.994545i	$0.533262\pi$
$294$	0.0860311	0.00501744
$295$	−5.93598	−0.345606
$296$	−0.567097	−0.0329618
$297$	0.406083	0.0235633
$298$	−0.280218	−0.0162326
$299$	16.7065	0.966164
$300$	−0.0400144	−0.00231023
$301$	20.3896	1.17524
$302$	0.229366	0.0131985
$303$	0.687355	0.0394875
$304$	13.6149	0.780866
$305$	25.1000	1.43722
$306$	1.12959	0.0645746
$307$	−2.46828	−0.140872	−0.0704362	−	0.997516i	$-0.522439\pi$
$307$	−2.46828	−0.140872	−0.0704362	+	0.997516i	$0.522439\pi$
$308$	−1.39334	−0.0793930
$309$	4.65970	0.265081
$310$	0.196110	0.0111383
$311$	−19.8949	−1.12814	−0.564069	−	0.825727i	$-0.690765\pi$
$311$	−19.8949	−1.12814	−0.564069	+	0.825727i	$0.690765\pi$
$312$	0.437450	0.0247657
$313$	−10.0179	−0.566246	−0.283123	−	0.959084i	$-0.591370\pi$
$313$	−10.0179	−0.566246	−0.283123	+	0.959084i	$0.591370\pi$
$314$	−0.742134	−0.0418810
$315$	20.9270	1.17910
$316$	−10.3042	−0.579656
$317$	−11.2440	−0.631529	−0.315764	−	0.948838i	$-0.602261\pi$
$317$	−11.2440	−0.631529	−0.315764	+	0.948838i	$0.602261\pi$
$318$	−0.285449	−0.0160072
$319$	0.155265	0.00869319
$320$	−17.6305	−0.985575
$321$	3.29747	0.184047
$322$	1.06474	0.0593354
$323$	−16.1280	−0.897387
$324$	−16.1702	−0.898346
$325$	−0.265753	−0.0147413
$326$	−0.727262	−0.0402793
$327$	−1.79622	−0.0993311
$328$	−1.05614	−0.0583155
$329$	12.4366	0.685654
$330$	−0.0128624	−0.000708052 0
$331$	−30.0728	−1.65295	−0.826475	−	0.562974i	$-0.809657\pi$
$331$	−30.0728	−1.65295	−0.826475	+	0.562974i	$0.809657\pi$
$332$	−3.66319	−0.201043
$333$	−4.95954	−0.271781
$334$	1.19268	0.0652606
$335$	13.7078	0.748937
$336$	−4.00692	−0.218596
$337$	−17.3224	−0.943613	−0.471807	−	0.881702i	$-0.656398\pi$
$337$	−17.3224	−0.943613	−0.471807	+	0.881702i	$0.656398\pi$
$338$	0.370448	0.0201497
$339$	6.62849	0.360010
$340$	21.0317	1.14061
$341$	−0.228778	−0.0123890
$342$	−0.828459	−0.0447979
$343$	11.9234	0.643806
$344$	2.10886	0.113702
$345$	−2.84004	−0.152903
$346$	−0.917716	−0.0493367
$347$	21.2412	1.14029	0.570143	−	0.821545i	$-0.306888\pi$
$347$	21.2412	1.14029	0.570143	+	0.821545i	$0.306888\pi$
$348$	0.448062	0.0240187
$349$	11.6817	0.625308	0.312654	−	0.949867i	$-0.398782\pi$
$349$	11.6817	0.625308	0.312654	+	0.949867i	$0.398782\pi$
$350$	−0.0169369	−0.000905315 0
$351$	7.78288	0.415420
$352$	−0.216291	−0.0115283
$353$	14.0775	0.749271	0.374636	−	0.927172i	$-0.377768\pi$
$353$	14.0775	0.749271	0.374636	+	0.927172i	$0.377768\pi$
$354$	−0.0691599	−0.00367581
$355$	21.1639	1.12326
$356$	16.1199	0.854355
$357$	4.74656	0.251215
$358$	−0.544048	−0.0287538
$359$	7.85706	0.414680	0.207340	−	0.978269i	$-0.433519\pi$
$359$	7.85706	0.414680	0.207340	+	0.978269i	$0.433519\pi$
$360$	2.16444	0.114076
$361$	−7.17150	−0.377448
$362$	−1.16020	−0.0609788
$363$	−3.45738	−0.181466
$364$	−26.7044	−1.39969
$365$	−6.26764	−0.328063
$366$	0.292439	0.0152860
$367$	−19.7726	−1.03212	−0.516062	−	0.856551i	$-0.672602\pi$
$367$	−19.7726	−1.03212	−0.516062	+	0.856551i	$0.672602\pi$
$368$	−15.8273	−0.825057
$369$	−9.23646	−0.480831
$370$	0.319578	0.0166141
$371$	34.9112	1.81250
$372$	−0.660205	−0.0342300
$373$	7.49088	0.387863	0.193931	−	0.981015i	$-0.437876\pi$
$373$	7.49088	0.387863	0.193931	+	0.981015i	$0.437876\pi$
$374$	0.0849127	0.00439073
$375$	−3.50652	−0.181076
$376$	1.28630	0.0663358
$377$	2.97577	0.153260
$378$	0.496016	0.0255123
$379$	27.5064	1.41291	0.706455	−	0.707758i	$-0.250293\pi$
$379$	27.5064	1.41291	0.706455	+	0.707758i	$0.250293\pi$
$380$	−15.4250	−0.791284
$381$	−0.0302068	−0.00154754
$382$	0.186036	0.00951842
$383$	4.92412	0.251611	0.125805	−	0.992055i	$-0.459849\pi$
$383$	4.92412	0.251611	0.125805	+	0.992055i	$0.459849\pi$
$384$	−0.831741	−0.0424446
$385$	1.57311	0.0801729
$386$	1.84315	0.0938137
$387$	18.4430	0.937512
$388$	25.7226	1.30587
$389$	38.9916	1.97696	0.988478	−	0.151368i	$-0.0483678\pi$
$389$	38.9916	1.97696	0.988478	+	0.151368i	$0.0483678\pi$
$390$	−0.246518	−0.0124829
$391$	18.7489	0.948173
$392$	−1.08825	−0.0549651
$393$	4.59737	0.231907
$394$	−0.915772	−0.0461359
$395$	11.6336	0.585350
$396$	−1.26032	−0.0633335
$397$	−12.6661	−0.635694	−0.317847	−	0.948142i	$-0.602960\pi$
$397$	−12.6661	−0.635694	−0.317847	+	0.948142i	$0.602960\pi$
$398$	1.21420	0.0608626
$399$	−3.48119	−0.174277
$400$	0.251767	0.0125884
$401$	26.7959	1.33812	0.669062	−	0.743207i	$-0.266696\pi$
$401$	26.7959	1.33812	0.669062	+	0.743207i	$0.266696\pi$
$402$	0.159709	0.00796556
$403$	−4.38471	−0.218418
$404$	−4.33985	−0.215916
$405$	18.2564	0.907170
$406$	0.189651	0.00941223
$407$	−0.372814	−0.0184797
$408$	0.490928	0.0243046
$409$	35.3472	1.74781	0.873903	−	0.486101i	$-0.161581\pi$
$409$	35.3472	1.74781	0.873903	+	0.486101i	$0.161581\pi$
$410$	0.595168	0.0293933
$411$	−5.40047	−0.266385
$412$	−29.4206	−1.44945
$413$	8.45844	0.416212
$414$	0.963088	0.0473332
$415$	4.13580	0.203018
$416$	−4.14537	−0.203244
$417$	−5.59590	−0.274033
$418$	−0.0622761	−0.00304602
$419$	−2.49358	−0.121819	−0.0609096	−	0.998143i	$-0.519400\pi$
$419$	−2.49358	−0.121819	−0.0609096	+	0.998143i	$0.519400\pi$
$420$	4.53965	0.221512
$421$	17.2671	0.841547	0.420773	−	0.907166i	$-0.361759\pi$
$421$	17.2671	0.841547	0.420773	+	0.907166i	$0.361759\pi$
$422$	0.128274	0.00624430
$423$	11.2493	0.546961
$424$	3.61080	0.175356
$425$	−0.298241	−0.0144668
$426$	0.246580	0.0119468
$427$	−35.7661	−1.73084
$428$	−20.8197	−1.00636
$429$	0.287583	0.0138847
$430$	−1.18841	−0.0573103
$431$	31.0699	1.49659	0.748293	−	0.663368i	$-0.230874\pi$
$431$	31.0699	1.49659	0.748293	+	0.663368i	$0.230874\pi$
$432$	−7.37330	−0.354748
$433$	16.4828	0.792112	0.396056	−	0.918226i	$-0.370379\pi$
$433$	16.4828	0.792112	0.396056	+	0.918226i	$0.370379\pi$
$434$	−0.279445	−0.0134138
$435$	−0.505870	−0.0242546
$436$	11.3410	0.543137
$437$	−13.7507	−0.657785
$438$	−0.0730241	−0.00348922
$439$	33.0499	1.57739	0.788693	−	0.614787i	$-0.210758\pi$
$439$	33.0499	1.57739	0.788693	+	0.614787i	$0.210758\pi$
$440$	0.162703	0.00775658
$441$	−9.51733	−0.453206
$442$	1.62742	0.0774083
$443$	−24.8330	−1.17985	−0.589925	−	0.807458i	$-0.700843\pi$
$443$	−24.8330	−1.17985	−0.589925	+	0.807458i	$0.700843\pi$
$444$	−1.07586	−0.0510581
$445$	−18.1997	−0.862747
$446$	−2.21650	−0.104954
$447$	−1.06506	−0.0503758
$448$	25.1224	1.18692
$449$	−18.6217	−0.878811	−0.439405	−	0.898289i	$-0.644811\pi$
$449$	−18.6217	−0.878811	−0.439405	+	0.898289i	$0.644811\pi$
$450$	−0.0153200	−0.000722190 0
$451$	−0.694314	−0.0326940
$452$	−41.8512	−1.96852
$453$	0.871784	0.0409600
$454$	−0.533192	−0.0250239
$455$	30.1497	1.41344
$456$	−0.360053	−0.0168610
$457$	−34.2762	−1.60337	−0.801686	−	0.597745i	$-0.796063\pi$
$457$	−34.2762	−1.60337	−0.801686	+	0.597745i	$0.796063\pi$
$458$	−2.31444	−0.108147
$459$	8.73433	0.407684
$460$	17.9316	0.836065
$461$	11.2220	0.522659	0.261329	−	0.965250i	$-0.415839\pi$
$461$	11.2220	0.522659	0.261329	+	0.965250i	$0.415839\pi$
$462$	0.0183282	0.000852704 0
$463$	−26.9770	−1.25373	−0.626863	−	0.779129i	$-0.715662\pi$
$463$	−26.9770	−1.25373	−0.626863	+	0.779129i	$0.715662\pi$
$464$	−2.81917	−0.130877
$465$	0.745382	0.0345663
$466$	0.0537644	0.00249059
$467$	11.5336	0.533711	0.266856	−	0.963737i	$-0.414015\pi$
$467$	11.5336	0.533711	0.266856	+	0.963737i	$0.414015\pi$
$468$	−24.1550	−1.11657
$469$	−19.5328	−0.901942
$470$	−0.724872	−0.0334359
$471$	−2.82074	−0.129973
$472$	0.874841	0.0402678
$473$	1.38638	0.0637459
$474$	0.135543	0.00622568
$475$	0.218734	0.0100362
$476$	−29.9690	−1.37363
$477$	31.5783	1.44587
$478$	−1.02682	−0.0469659
$479$	−28.8893	−1.31998	−0.659992	−	0.751272i	$-0.729441\pi$
$479$	−28.8893	−1.31998	−0.659992	+	0.751272i	$0.729441\pi$
$480$	0.704697	0.0321649
$481$	−7.14526	−0.325796
$482$	−1.05918	−0.0482443
$483$	4.04690	0.184140
$484$	21.8294	0.992245
$485$	−29.0412	−1.31869
$486$	0.676782	0.0306995
$487$	1.63083	0.0739001	0.0369501	−	0.999317i	$-0.488236\pi$
$487$	1.63083	0.0739001	0.0369501	+	0.999317i	$0.488236\pi$
$488$	−3.69922	−0.167456
$489$	−2.76421	−0.125002
$490$	0.613267	0.0277046
$491$	−6.45592	−0.291352	−0.145676	−	0.989332i	$-0.546536\pi$
$491$	−6.45592	−0.291352	−0.145676	+	0.989332i	$0.546536\pi$
$492$	−2.00364	−0.0903311
$493$	3.33956	0.150406
$494$	−1.19357	−0.0537012
$495$	1.42292	0.0639556
$496$	4.15396	0.186518
$497$	−30.1573	−1.35274
$498$	0.0481860	0.00215927
$499$	29.7187	1.33039	0.665196	−	0.746669i	$-0.268348\pi$
$499$	29.7187	1.33039	0.665196	+	0.746669i	$0.268348\pi$
$500$	22.1396	0.990113
$501$	4.53320	0.202528
$502$	−1.12053	−0.0500115
$503$	−1.00000	−0.0445878
$503$	−1.00000	−0.0445878
$504$	−3.08421	−0.137381
$505$	4.89976	0.218037
$506$	0.0723963	0.00321841
$507$	1.40802	0.0625323
$508$	0.190721	0.00846188
$509$	7.29140	0.323186	0.161593	−	0.986858i	$-0.448337\pi$
$509$	7.29140	0.323186	0.161593	+	0.986858i	$0.448337\pi$
$510$	−0.276654	−0.0122504
$511$	8.93103	0.395086
$512$	6.55291	0.289601
$513$	−6.40587	−0.282826
$514$	−0.378986	−0.0167163
$515$	33.2164	1.46369
$516$	4.00080	0.176126
$517$	0.845624	0.0371905
$518$	−0.455380	−0.0200082
$519$	−3.48810	−0.153110
$520$	3.11833	0.136748
$521$	1.73107	0.0758394	0.0379197	−	0.999281i	$-0.487927\pi$
$521$	1.73107	0.0758394	0.0379197	+	0.999281i	$0.487927\pi$
$522$	0.171545	0.00750834
$523$	15.8653	0.693742	0.346871	−	0.937913i	$-0.387244\pi$
$523$	15.8653	0.693742	0.346871	+	0.937913i	$0.387244\pi$
$524$	−29.0271	−1.26805
$525$	−0.0643745	−0.00280953
$526$	1.33703	0.0582971
$527$	−4.92073	−0.214350
$528$	−0.272449	−0.0118568
$529$	−7.01475	−0.304989
$530$	−2.03481	−0.0883863
$531$	7.65092	0.332022
$532$	21.9797	0.952940
$533$	−13.3070	−0.576392
$534$	−0.212043	−0.00917602
$535$	23.5058	1.01624
$536$	−2.02025	−0.0872613
$537$	−2.06784	−0.0892339
$538$	−0.622765	−0.0268493
$539$	−0.715427	−0.0308156
$540$	8.35358	0.359481
$541$	0.384069	0.0165124	0.00825621	−	0.999966i	$-0.497372\pi$
$541$	0.384069	0.0165124	0.00825621	+	0.999966i	$0.497372\pi$
$542$	0.537705	0.0230964
$543$	−4.40975	−0.189240
$544$	−4.65214	−0.199459
$545$	−12.8042	−0.548472
$546$	0.351273	0.0150331
$547$	38.3367	1.63916	0.819579	−	0.572967i	$-0.194208\pi$
$547$	38.3367	1.63916	0.819579	+	0.572967i	$0.194208\pi$
$548$	34.0977	1.45658
$549$	−32.3515	−1.38073
$550$	−0.00115162	−4.91051e−5 0
$551$	−2.44928	−0.104343
$552$	0.418564	0.0178152
$553$	−16.5772	−0.704935
$554$	0.691043	0.0293596
$555$	1.21467	0.0515597
$556$	35.3317	1.49840
$557$	25.2935	1.07172	0.535860	−	0.844307i	$-0.319987\pi$
$557$	25.2935	1.07172	0.535860	+	0.844307i	$0.319987\pi$
$558$	−0.252767	−0.0107005
$559$	26.5710	1.12384
$560$	−28.5631	−1.20701
$561$	0.322740	0.0136261
$562$	−2.19092	−0.0924185
$563$	32.5764	1.37293	0.686465	−	0.727163i	$-0.259161\pi$
$563$	32.5764	1.37293	0.686465	+	0.727163i	$0.259161\pi$
$564$	2.44029	0.102755
$565$	47.2507	1.98785
$566$	−1.94384	−0.0817058
$567$	−26.0144	−1.09250
$568$	−3.11912	−0.130875
$569$	−36.9548	−1.54923	−0.774614	−	0.632435i	$-0.782056\pi$
$569$	−36.9548	−1.54923	−0.774614	+	0.632435i	$0.782056\pi$
$570$	0.202902	0.00849862
$571$	−32.4941	−1.35984	−0.679919	−	0.733288i	$-0.737985\pi$
$571$	−32.4941	−1.35984	−0.679919	+	0.733288i	$0.737985\pi$
$572$	−1.81576	−0.0759206
$573$	0.707093	0.0295393
$574$	−0.848081	−0.0353982
$575$	−0.254279	−0.0106042
$576$	22.7240	0.946835
$577$	−3.08889	−0.128592	−0.0642960	−	0.997931i	$-0.520480\pi$
$577$	−3.08889	−0.128592	−0.0642960	+	0.997931i	$0.520480\pi$
$578$	0.414465	0.0172395
$579$	7.00552	0.291139
$580$	3.19398	0.132623
$581$	−5.89327	−0.244494
$582$	−0.338358	−0.0140254
$583$	2.37377	0.0983116
$584$	0.923721	0.0382238
$585$	27.2714	1.12753
$586$	−0.296572	−0.0122513
$587$	−39.5581	−1.63274	−0.816369	−	0.577530i	$-0.804017\pi$
$587$	−39.5581	−1.63274	−0.816369	+	0.577530i	$0.804017\pi$
$588$	−2.06457	−0.0851414
$589$	3.60893	0.148703
$590$	−0.493002	−0.0202966
$591$	−3.48071	−0.143177
$592$	6.76923	0.278214
$593$	37.0809	1.52273	0.761366	−	0.648323i	$-0.224529\pi$
$593$	37.0809	1.52273	0.761366	+	0.648323i	$0.224529\pi$
$594$	0.0337264	0.00138381
$595$	33.8355	1.38712
$596$	6.72465	0.275453
$597$	4.61501	0.188880
$598$	1.38753	0.0567403
$599$	−7.21058	−0.294616	−0.147308	−	0.989091i	$-0.547061\pi$
$599$	−7.21058	−0.294616	−0.147308	+	0.989091i	$0.547061\pi$
$600$	−0.00665814	−0.000271818 0
$601$	−15.6443	−0.638145	−0.319072	−	0.947730i	$-0.603371\pi$
$601$	−15.6443	−0.638145	−0.319072	+	0.947730i	$0.603371\pi$
$602$	1.69342	0.0690186
$603$	−17.6681	−0.719499
$604$	−5.50431	−0.223967
$605$	−24.6457	−1.00199
$606$	0.0570869	0.00231900
$607$	−5.03996	−0.204566	−0.102283	−	0.994755i	$-0.532615\pi$
$607$	−5.03996	−0.204566	−0.102283	+	0.994755i	$0.532615\pi$
$608$	3.41194	0.138372
$609$	0.720835	0.0292097
$610$	2.08463	0.0844043
$611$	16.2070	0.655666
$612$	−27.1079	−1.09577
$613$	−41.4393	−1.67372	−0.836858	−	0.547420i	$-0.815610\pi$
$613$	−41.4393	−1.67372	−0.836858	+	0.547420i	$0.815610\pi$
$614$	−0.204998	−0.00827306
$615$	2.26214	0.0912184
$616$	−0.231843	−0.00934122
$617$	17.1685	0.691178	0.345589	−	0.938386i	$-0.387679\pi$
$617$	17.1685	0.691178	0.345589	+	0.938386i	$0.387679\pi$
$618$	0.387003	0.0155675
$619$	−16.9228	−0.680186	−0.340093	−	0.940392i	$-0.610459\pi$
$619$	−16.9228	−0.680186	−0.340093	+	0.940392i	$0.610459\pi$
$620$	−4.70623	−0.189007
$621$	7.44686	0.298832
$622$	−1.65234	−0.0662526
$623$	25.9335	1.03900
$624$	−5.22169	−0.209035
$625$	−25.3140	−1.01256
$626$	−0.832018	−0.0332541
$627$	−0.236702	−0.00945296
$628$	17.8097	0.710684
$629$	−8.01876	−0.319729
$630$	1.73805	0.0692456
$631$	15.9640	0.635518	0.317759	−	0.948171i	$-0.397070\pi$
$631$	15.9640	0.635518	0.317759	+	0.948171i	$0.397070\pi$
$632$	−1.71455	−0.0682012
$633$	0.487551	0.0193784
$634$	−0.933852	−0.0370880
$635$	−0.215327	−0.00854500
$636$	6.85020	0.271628
$637$	−13.7117	−0.543277
$638$	0.0128953	0.000510528 0
$639$	−27.2782	−1.07911
$640$	−5.92901	−0.234365
$641$	34.1774	1.34993	0.674964	−	0.737851i	$-0.264159\pi$
$641$	34.1774	1.34993	0.674964	+	0.737851i	$0.264159\pi$
$642$	0.273865	0.0108086
$643$	−1.27460	−0.0502653	−0.0251326	−	0.999684i	$-0.508001\pi$
$643$	−1.27460	−0.0502653	−0.0251326	+	0.999684i	$0.508001\pi$
$644$	−25.5515	−1.00687
$645$	−4.51697	−0.177856
$646$	−1.33948	−0.0527012
$647$	16.4300	0.645930	0.322965	−	0.946411i	$-0.395320\pi$
$647$	16.4300	0.645930	0.322965	+	0.946411i	$0.395320\pi$
$648$	−2.69062	−0.105698
$649$	0.575128	0.0225757
$650$	−0.0220716	−0.000865719 0
$651$	−1.06213	−0.0416280
$652$	17.4528	0.683504
$653$	46.5637	1.82218	0.911088	−	0.412211i	$-0.135243\pi$
$653$	46.5637	1.82218	0.911088	+	0.412211i	$0.135243\pi$
$654$	−0.149181	−0.00583345
$655$	32.7720	1.28051
$656$	12.6067	0.492211
$657$	8.07840	0.315168
$658$	1.03290	0.0402667
$659$	−21.2263	−0.826861	−0.413431	−	0.910536i	$-0.635670\pi$
$659$	−21.2263	−0.826861	−0.413431	+	0.910536i	$0.635670\pi$
$660$	0.308671	0.0120150
$661$	31.5049	1.22540	0.612700	−	0.790316i	$-0.290084\pi$
$661$	31.5049	1.22540	0.612700	+	0.790316i	$0.290084\pi$
$662$	−2.49764	−0.0970734
$663$	6.18556	0.240227
$664$	−0.609530	−0.0236544
$665$	−24.8154	−0.962300
$666$	−0.411905	−0.0159610
$667$	2.84730	0.110248
$668$	−28.6219	−1.10741
$669$	−8.42458	−0.325713
$670$	1.13847	0.0439831
$671$	−2.43190	−0.0938824
$672$	−1.00415	−0.0387360
$673$	−46.0920	−1.77672	−0.888359	−	0.459150i	$-0.848154\pi$
$673$	−46.0920	−1.77672	−0.888359	+	0.459150i	$0.848154\pi$
$674$	−1.43868	−0.0554159
$675$	−0.118458	−0.00455946
$676$	−8.89000	−0.341923
$677$	5.22605	0.200853	0.100427	−	0.994944i	$-0.467979\pi$
$677$	5.22605	0.200853	0.100427	+	0.994944i	$0.467979\pi$
$678$	0.550516	0.0211424
$679$	41.3820	1.58810
$680$	3.49955	0.134201
$681$	−2.02658	−0.0776587
$682$	−0.0190007	−0.000727575 0
$683$	−26.7163	−1.02227	−0.511135	−	0.859500i	$-0.670775\pi$
$683$	−26.7163	−1.02227	−0.511135	+	0.859500i	$0.670775\pi$
$684$	19.8813	0.760181
$685$	−38.4969	−1.47089
$686$	0.990279	0.0378090
$687$	−8.79683	−0.335620
$688$	−25.1727	−0.959701
$689$	45.4951	1.73323
$690$	−0.235874	−0.00897958
$691$	−20.7575	−0.789653	−0.394826	−	0.918756i	$-0.629195\pi$
$691$	−20.7575	−0.789653	−0.394826	+	0.918756i	$0.629195\pi$
$692$	22.0233	0.837200
$693$	−2.02758	−0.0770215
$694$	1.76414	0.0669660
$695$	−39.8900	−1.51311
$696$	0.0745547	0.00282599
$697$	−14.9338	−0.565659
$698$	0.970202	0.0367227
$699$	0.204350	0.00772924
$700$	0.406451	0.0153624
$701$	−48.5428	−1.83344	−0.916719	−	0.399533i	$-0.869172\pi$
$701$	−48.5428	−1.83344	−0.916719	+	0.399533i	$0.869172\pi$
$702$	0.646392	0.0243965
$703$	5.88106	0.221809
$704$	1.70819	0.0643798
$705$	−2.75513	−0.103764
$706$	1.16918	0.0440027
$707$	−6.98188	−0.262581
$708$	1.65970	0.0623752
$709$	−21.9935	−0.825981	−0.412991	−	0.910735i	$-0.635516\pi$
$709$	−21.9935	−0.825981	−0.412991	+	0.910735i	$0.635516\pi$
$710$	1.75772	0.0659662
$711$	−14.9946	−0.562342
$712$	2.68225	0.100522
$713$	−4.19540	−0.157119
$714$	0.394216	0.0147532
$715$	2.05002	0.0766663
$716$	13.0560	0.487926
$717$	−3.90280	−0.145753
$718$	0.652552	0.0243530
$719$	9.78228	0.364817	0.182409	−	0.983223i	$-0.441611\pi$
$719$	9.78228	0.364817	0.182409	+	0.983223i	$0.441611\pi$
$720$	−25.8362	−0.962858
$721$	−47.3314	−1.76271
$722$	−0.595615	−0.0221665
$723$	−4.02578	−0.149720
$724$	27.8425	1.03476
$725$	−0.0452923	−0.00168211
$726$	−0.287146	−0.0106570
$727$	−41.0223	−1.52143	−0.760716	−	0.649085i	$-0.775152\pi$
$727$	−41.0223	−1.52143	−0.760716	+	0.649085i	$0.775152\pi$
$728$	−4.44344	−0.164685
$729$	−21.7669	−0.806183
$730$	−0.520547	−0.0192663
$731$	29.8193	1.10291
$732$	−7.01794	−0.259391
$733$	19.7580	0.729780	0.364890	−	0.931051i	$-0.381107\pi$
$733$	19.7580	0.729780	0.364890	+	0.931051i	$0.381107\pi$
$734$	−1.64218	−0.0606139
$735$	2.33093	0.0859777
$736$	−3.96640	−0.146203
$737$	−1.32813	−0.0489222
$738$	−0.767116	−0.0282379
$739$	8.08268	0.297326	0.148663	−	0.988888i	$-0.452503\pi$
$739$	8.08268	0.297326	0.148663	+	0.988888i	$0.452503\pi$
$740$	−7.66921	−0.281926
$741$	−4.53657	−0.166655
$742$	2.89948	0.106443
$743$	10.5995	0.388859	0.194429	−	0.980917i	$-0.437714\pi$
$743$	10.5995	0.388859	0.194429	+	0.980917i	$0.437714\pi$
$744$	−0.109854	−0.00402744
$745$	−7.59224	−0.278158
$746$	0.622140	0.0227782
$747$	−5.33065	−0.195038
$748$	−2.03773	−0.0745068
$749$	−33.4944	−1.22386
$750$	−0.291227	−0.0106341
$751$	14.0003	0.510877	0.255438	−	0.966825i	$-0.417780\pi$
$751$	14.0003	0.510877	0.255438	+	0.966825i	$0.417780\pi$
$752$	−15.3541	−0.559907
$753$	−4.25895	−0.155205
$754$	0.247147	0.00900057
$755$	6.21445	0.226167
$756$	−11.9034	−0.432922
$757$	−28.8413	−1.04826	−0.524128	−	0.851640i	$-0.675609\pi$
$757$	−28.8413	−1.04826	−0.524128	+	0.851640i	$0.675609\pi$
$758$	2.28449	0.0829765
$759$	0.275167	0.00998794
$760$	−2.56661	−0.0931008
$761$	−14.2005	−0.514767	−0.257383	−	0.966309i	$-0.582860\pi$
$761$	−14.2005	−0.514767	−0.257383	+	0.966309i	$0.582860\pi$
$762$	−0.00250877	−9.08831e−5 0
$763$	18.2453	0.660523
$764$	−4.46448	−0.161519
$765$	30.6053	1.10654
$766$	0.408963	0.0147764
$767$	11.0228	0.398008
$768$	4.87745	0.176000
$769$	19.1077	0.689043	0.344521	−	0.938778i	$-0.388041\pi$
$769$	19.1077	0.689043	0.344521	+	0.938778i	$0.388041\pi$
$770$	0.130651	0.00470834
$771$	−1.44047	−0.0518771
$772$	−44.2317	−1.59193
$773$	−29.5204	−1.06178	−0.530888	−	0.847442i	$-0.678141\pi$
$773$	−29.5204	−1.06178	−0.530888	+	0.847442i	$0.678141\pi$
$774$	1.53175	0.0550576
$775$	0.0667367	0.00239725
$776$	4.28007	0.153646
$777$	−1.73083	−0.0620931
$778$	3.23837	0.116101
$779$	10.9527	0.392420
$780$	5.91591	0.211824
$781$	−2.05053	−0.0733739
$782$	1.55715	0.0556837
$783$	1.32644	0.0474030
$784$	12.9901	0.463932
$785$	−20.1074	−0.717665
$786$	0.381826	0.0136193
$787$	−20.3547	−0.725568	−0.362784	−	0.931873i	$-0.618174\pi$
$787$	−20.3547	−0.725568	−0.362784	+	0.931873i	$0.618174\pi$
$788$	21.9766	0.782886
$789$	5.08183	0.180918
$790$	0.966206	0.0343761
$791$	−67.3295	−2.39396
$792$	−0.209709	−0.00745170
$793$	−46.6092	−1.65514
$794$	−1.05196	−0.0373326
$795$	−7.73398	−0.274296
$796$	−29.1384	−1.03278
$797$	51.2687	1.81603	0.908016	−	0.418935i	$-0.137597\pi$
$797$	51.2687	1.81603	0.908016	+	0.418935i	$0.137597\pi$
$798$	−0.289123	−0.0102349
$799$	18.1883	0.643456
$800$	0.0630940	0.00223071
$801$	23.4576	0.828835
$802$	2.22548	0.0785845
$803$	0.607262	0.0214298
$804$	−3.83269	−0.135169
$805$	28.8480	1.01676
$806$	−0.364163	−0.0128271
$807$	−2.36703	−0.0833235
$808$	−0.722123	−0.0254042
$809$	53.5568	1.88296	0.941478	−	0.337073i	$-0.109437\pi$
$809$	53.5568	1.88296	0.941478	+	0.337073i	$0.109437\pi$
$810$	1.51625	0.0532757
$811$	42.8963	1.50629	0.753146	−	0.657854i	$-0.228535\pi$
$811$	42.8963	1.50629	0.753146	+	0.657854i	$0.228535\pi$
$812$	−4.55124	−0.159717
$813$	2.04373	0.0716769
$814$	−0.0309633	−0.00108526
$815$	−19.7045	−0.690218
$816$	−5.86004	−0.205142
$817$	−21.8699	−0.765130
$818$	2.93569	0.102644
$819$	−38.8601	−1.35788
$820$	−14.2828	−0.498778
$821$	5.52686	0.192889	0.0964444	−	0.995338i	$-0.469253\pi$
$821$	5.52686	0.192889	0.0964444	+	0.995338i	$0.469253\pi$
$822$	−0.448525	−0.0156441
$823$	−19.0939	−0.665572	−0.332786	−	0.943002i	$-0.607989\pi$
$823$	−19.0939	−0.665572	−0.332786	+	0.943002i	$0.607989\pi$
$824$	−4.89540	−0.170539
$825$	−0.00437712	−0.000152392 0
$826$	0.702499	0.0244431
$827$	−47.8774	−1.66486	−0.832430	−	0.554130i	$-0.813051\pi$
$827$	−47.8774	−1.66486	−0.832430	+	0.554130i	$0.813051\pi$
$828$	−23.1121	−0.803202
$829$	13.1461	0.456583	0.228292	−	0.973593i	$-0.426686\pi$
$829$	13.1461	0.456583	0.228292	+	0.973593i	$0.426686\pi$
$830$	0.343490	0.0119227
$831$	2.62655	0.0911139
$832$	32.7387	1.13501
$833$	−15.3879	−0.533161
$834$	−0.464757	−0.0160932
$835$	32.3146	1.11829
$836$	1.49450	0.0516883
$837$	−1.95446	−0.0675561
$838$	−0.207099	−0.00715412
$839$	33.7580	1.16545	0.582727	−	0.812668i	$-0.301986\pi$
$839$	33.7580	1.16545	0.582727	+	0.812668i	$0.301986\pi$
$840$	0.755368	0.0260627
$841$	−28.4928	−0.982512
$842$	1.43408	0.0494218
$843$	−8.32736	−0.286810
$844$	−3.07832	−0.105960
$845$	10.0370	0.345282
$846$	0.934291	0.0321216
$847$	35.1187	1.20669
$848$	−43.1009	−1.48009
$849$	−7.38825	−0.253564
$850$	−0.0247698	−0.000849598 0
$851$	−6.83677	−0.234361
$852$	−5.91740	−0.202727
$853$	16.1494	0.552946	0.276473	−	0.961022i	$-0.410834\pi$
$853$	16.1494	0.552946	0.276473	+	0.961022i	$0.410834\pi$
$854$	−2.97048	−0.101648
$855$	−22.4463	−0.767648
$856$	−3.46426	−0.118406
$857$	21.1749	0.723322	0.361661	−	0.932310i	$-0.382210\pi$
$857$	21.1749	0.723322	0.361661	+	0.932310i	$0.382210\pi$
$858$	0.0238847	0.000815409 0
$859$	−21.2136	−0.723798	−0.361899	−	0.932217i	$-0.617871\pi$
$859$	−21.2136	−0.723798	−0.361899	+	0.932217i	$0.617871\pi$
$860$	28.5194	0.972505
$861$	−3.22342	−0.109854
$862$	2.58045	0.0878906
$863$	−45.3619	−1.54414	−0.772068	−	0.635539i	$-0.780778\pi$
$863$	−45.3619	−1.54414	−0.772068	+	0.635539i	$0.780778\pi$
$864$	−1.84778	−0.0628628
$865$	−24.8647	−0.845424
$866$	1.36895	0.0465186
$867$	1.57532	0.0535005
$868$	6.70610	0.227620
$869$	−1.12716	−0.0382363
$870$	−0.0420140	−0.00142441
$871$	−25.4545	−0.862494
$872$	1.88707	0.0639044
$873$	37.4313	1.26686
$874$	−1.14204	−0.0386300
$875$	35.6178	1.20410
$876$	1.75243	0.0592090
$877$	12.1962	0.411837	0.205918	−	0.978569i	$-0.433982\pi$
$877$	12.1962	0.411837	0.205918	+	0.978569i	$0.433982\pi$
$878$	2.74490	0.0926358
$879$	−1.12723	−0.0380204
$880$	−1.94213	−0.0654693
$881$	8.50736	0.286620	0.143310	−	0.989678i	$-0.454225\pi$
$881$	8.50736	0.286620	0.143310	+	0.989678i	$0.454225\pi$
$882$	−0.790443	−0.0266156
$883$	−26.5027	−0.891888	−0.445944	−	0.895061i	$-0.647132\pi$
$883$	−26.5027	−0.891888	−0.445944	+	0.895061i	$0.647132\pi$
$884$	−39.0546	−1.31355
$885$	−1.87382	−0.0629879
$886$	−2.06245	−0.0692895
$887$	33.1863	1.11429	0.557144	−	0.830416i	$-0.311897\pi$
$887$	33.1863	1.11429	0.557144	+	0.830416i	$0.311897\pi$
$888$	−0.179016	−0.00600740
$889$	0.306829	0.0102907
$890$	−1.51154	−0.0506668
$891$	−1.76884	−0.0592582
$892$	53.1915	1.78098
$893$	−13.3395	−0.446391
$894$	−0.0884569	−0.00295844
$895$	−14.7405	−0.492719
$896$	8.44850	0.282244
$897$	5.27378	0.176087
$898$	−1.54659	−0.0516102
$899$	−0.747286	−0.0249234
$900$	0.367647	0.0122549
$901$	51.0568	1.70095
$902$	−0.0576649	−0.00192003
$903$	6.43642	0.214191
$904$	−6.96377	−0.231612
$905$	−31.4346	−1.04492
$906$	0.0724043	0.00240547
$907$	6.31486	0.209682	0.104841	−	0.994489i	$-0.466567\pi$
$907$	6.31486	0.209682	0.104841	+	0.994489i	$0.466567\pi$
$908$	12.7955	0.424634
$909$	−6.31533	−0.209466
$910$	2.50403	0.0830077
$911$	43.0949	1.42780	0.713898	−	0.700249i	$-0.246928\pi$
$911$	43.0949	1.42780	0.713898	+	0.700249i	$0.246928\pi$
$912$	4.29783	0.142315
$913$	−0.400710	−0.0132616
$914$	−2.84674	−0.0941618
$915$	7.92337	0.261938
$916$	55.5418	1.83515
$917$	−46.6983	−1.54211
$918$	0.725413	0.0239422
$919$	−19.4088	−0.640236	−0.320118	−	0.947378i	$-0.603723\pi$
$919$	−19.4088	−0.640236	−0.320118	+	0.947378i	$0.603723\pi$
$920$	2.98370	0.0983697
$921$	−0.779167	−0.0256744
$922$	0.932018	0.0306944
$923$	−39.3000	−1.29358
$924$	−0.439839	−0.0144696
$925$	0.108753	0.00357579
$926$	−2.24052	−0.0736281
$927$	−42.8128	−1.40616
$928$	−0.706496	−0.0231919
$929$	−28.3914	−0.931493	−0.465747	−	0.884918i	$-0.654214\pi$
$929$	−28.3914	−0.931493	−0.465747	+	0.884918i	$0.654214\pi$
$930$	0.0619062	0.00202999
$931$	11.2857	0.369874
$932$	−1.29024	−0.0422631
$933$	−6.28027	−0.205607
$934$	0.957900	0.0313434
$935$	2.30063	0.0752387
$936$	−4.01924	−0.131373
$937$	−4.00280	−0.130766	−0.0653829	−	0.997860i	$-0.520827\pi$
$937$	−4.00280	−0.130766	−0.0653829	+	0.997860i	$0.520827\pi$
$938$	−1.62226	−0.0529687
$939$	−3.16237	−0.103200
$940$	17.3954	0.567377
$941$	13.9675	0.455328	0.227664	−	0.973740i	$-0.426891\pi$
$941$	13.9675	0.455328	0.227664	+	0.973740i	$0.426891\pi$
$942$	−0.234271	−0.00763295
$943$	−12.7325	−0.414628
$944$	−10.4427	−0.339880
$945$	13.4391	0.437174
$946$	0.115143	0.00374363
$947$	57.2963	1.86188	0.930940	−	0.365171i	$-0.118990\pi$
$947$	57.2963	1.86188	0.930940	+	0.365171i	$0.118990\pi$
$948$	−3.25274	−0.105644
$949$	11.6386	0.377806
$950$	0.0181665	0.000589400 0
$951$	−3.54943	−0.115098
$952$	−4.98665	−0.161618
$953$	5.29452	0.171506	0.0857532	−	0.996316i	$-0.472670\pi$
$953$	5.29452	0.171506	0.0857532	+	0.996316i	$0.472670\pi$
$954$	2.62267	0.0849121
$955$	5.04047	0.163106
$956$	24.6417	0.796969
$957$	0.0490129	0.00158436
$958$	−2.39934	−0.0775192
$959$	54.8558	1.77139
$960$	−5.56545	−0.179624
$961$	−29.8989	−0.964481
$962$	−0.593436	−0.0191331
$963$	−30.2967	−0.976298
$964$	25.4181	0.818663
$965$	49.9383	1.60757
$966$	0.336107	0.0108141
$967$	44.3615	1.42657	0.713284	−	0.700875i	$-0.247207\pi$
$967$	44.3615	1.42657	0.713284	+	0.700875i	$0.247207\pi$
$968$	3.63227	0.116746
$969$	−5.09116	−0.163552
$970$	−2.41196	−0.0774434
$971$	51.4789	1.65204	0.826018	−	0.563644i	$-0.190601\pi$
$971$	51.4789	1.65204	0.826018	+	0.563644i	$0.190601\pi$
$972$	−16.2414	−0.520943
$973$	56.8410	1.82224
$974$	0.135446	0.00433996
$975$	−0.0838907	−0.00268665
$976$	44.1563	1.41341
$977$	−0.892938	−0.0285676	−0.0142838	−	0.999898i	$-0.504547\pi$
$977$	−0.892938	−0.0285676	−0.0142838	+	0.999898i	$0.504547\pi$
$978$	−0.229576	−0.00734104
$979$	1.76333	0.0563564
$980$	−14.7171	−0.470122
$981$	16.5034	0.526913
$982$	−0.536184	−0.0171103
$983$	36.2679	1.15677	0.578384	−	0.815765i	$-0.303684\pi$
$983$	36.2679	1.15677	0.578384	+	0.815765i	$0.303684\pi$
$984$	−0.333393	−0.0106282
$985$	−24.8120	−0.790576
$986$	0.277361	0.00883296
$987$	3.92590	0.124963
$988$	28.6432	0.911261
$989$	25.4239	0.808432
$990$	0.118178	0.00375595
$991$	29.3407	0.932036	0.466018	−	0.884775i	$-0.345688\pi$
$991$	29.3407	0.932036	0.466018	+	0.884775i	$0.345688\pi$
$992$	1.04100	0.0330518
$993$	−9.49313	−0.301255
$994$	−2.50466	−0.0794429
$995$	32.8977	1.04293
$996$	−1.15636	−0.0366408
$997$	18.6388	0.590296	0.295148	−	0.955452i	$-0.404631\pi$
$997$	18.6388	0.590296	0.295148	+	0.955452i	$0.404631\pi$
$998$	2.46823	0.0781304
$999$	−3.18497	−0.100768

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.e.1.7	✓	10
3.2	odd	2		4527.2.a.k.1.4		10
4.3	odd	2		8048.2.a.p.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.e.1.7	✓	10	1.1	even	1	trivial
4527.2.a.k.1.4		10	3.2	odd	2
8048.2.a.p.1.3		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)

\(f(q)\)	\(=\)	\(q+0.0830530 q^{2} +0.315672 q^{3} -1.99310 q^{4} +2.25024 q^{5} +0.0262175 q^{6} -3.20647 q^{7} -0.331639 q^{8} -2.90035 q^{9} +O(q^{10})\)	\(q+0.0830530 q^{2} +0.315672 q^{3} -1.99310 q^{4} +2.25024 q^{5} +0.0262175 q^{6} -3.20647 q^{7} -0.331639 q^{8} -2.90035 q^{9} +0.186890 q^{10} -0.218022 q^{11} -0.629166 q^{12} -4.17856 q^{13} -0.266307 q^{14} +0.710339 q^{15} +3.95866 q^{16} -4.68939 q^{17} -0.240883 q^{18} +3.43926 q^{19} -4.48497 q^{20} -1.01219 q^{21} -0.0181074 q^{22} -3.99816 q^{23} -0.104689 q^{24} +0.0635992 q^{25} -0.347042 q^{26} -1.86257 q^{27} +6.39082 q^{28} -0.712153 q^{29} +0.0589958 q^{30} +1.04933 q^{31} +0.992057 q^{32} -0.0688235 q^{33} -0.389468 q^{34} -7.21534 q^{35} +5.78070 q^{36} +1.70998 q^{37} +0.285641 q^{38} -1.31905 q^{39} -0.746269 q^{40} +3.18460 q^{41} -0.0840656 q^{42} -6.35890 q^{43} +0.434541 q^{44} -6.52650 q^{45} -0.332059 q^{46} -3.87861 q^{47} +1.24964 q^{48} +3.28144 q^{49} +0.00528210 q^{50} -1.48031 q^{51} +8.32830 q^{52} -10.8877 q^{53} -0.154692 q^{54} -0.490604 q^{55} +1.06339 q^{56} +1.08568 q^{57} -0.0591465 q^{58} -2.63793 q^{59} -1.41578 q^{60} +11.1544 q^{61} +0.0871503 q^{62} +9.29988 q^{63} -7.83493 q^{64} -9.40279 q^{65} -0.00571600 q^{66} +6.09170 q^{67} +9.34643 q^{68} -1.26210 q^{69} -0.599256 q^{70} +9.40515 q^{71} +0.961870 q^{72} -2.78532 q^{73} +0.142019 q^{74} +0.0200765 q^{75} -6.85479 q^{76} +0.699082 q^{77} -0.109551 q^{78} +5.16993 q^{79} +8.90795 q^{80} +8.11309 q^{81} +0.264491 q^{82} +1.83793 q^{83} +2.01740 q^{84} -10.5523 q^{85} -0.528126 q^{86} -0.224807 q^{87} +0.0723048 q^{88} -8.08786 q^{89} -0.542046 q^{90} +13.3984 q^{91} +7.96873 q^{92} +0.331245 q^{93} -0.322130 q^{94} +7.73917 q^{95} +0.313165 q^{96} -12.9058 q^{97} +0.272533 q^{98} +0.632342 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more