LMFDB - Embedded newform 6043.2.a.c.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6043,2,Mod(1,6043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6043, 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("6043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6043 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6043.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:	$48.2535979415$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.43851 q^{2} +1.58144 q^{3} +3.94631 q^{4} +0.896601 q^{5} -3.85634 q^{6} -4.81539 q^{7} -4.74608 q^{8} -0.499059 q^{9} +O(q^{10})$	\(q-2.43851 q^{2} +1.58144 q^{3} +3.94631 q^{4} +0.896601 q^{5} -3.85634 q^{6} -4.81539 q^{7} -4.74608 q^{8} -0.499059 q^{9} -2.18637 q^{10} +1.11181 q^{11} +6.24084 q^{12} +0.578731 q^{13} +11.7423 q^{14} +1.41792 q^{15} +3.68073 q^{16} -1.16637 q^{17} +1.21696 q^{18} +1.62999 q^{19} +3.53827 q^{20} -7.61523 q^{21} -2.71116 q^{22} -1.28716 q^{23} -7.50563 q^{24} -4.19611 q^{25} -1.41124 q^{26} -5.53354 q^{27} -19.0030 q^{28} +3.02920 q^{29} -3.45760 q^{30} -3.86085 q^{31} +0.516685 q^{32} +1.75826 q^{33} +2.84419 q^{34} -4.31748 q^{35} -1.96944 q^{36} +8.11384 q^{37} -3.97474 q^{38} +0.915227 q^{39} -4.25534 q^{40} -3.93263 q^{41} +18.5698 q^{42} +2.76513 q^{43} +4.38755 q^{44} -0.447457 q^{45} +3.13875 q^{46} -5.64736 q^{47} +5.82084 q^{48} +16.1879 q^{49} +10.2322 q^{50} -1.84454 q^{51} +2.28385 q^{52} -2.41261 q^{53} +13.4936 q^{54} +0.996851 q^{55} +22.8542 q^{56} +2.57772 q^{57} -7.38673 q^{58} -1.11978 q^{59} +5.59554 q^{60} +7.72304 q^{61} +9.41470 q^{62} +2.40316 q^{63} -8.62140 q^{64} +0.518891 q^{65} -4.28752 q^{66} +14.5128 q^{67} -4.60285 q^{68} -2.03556 q^{69} +10.5282 q^{70} -8.74928 q^{71} +2.36857 q^{72} +3.29600 q^{73} -19.7856 q^{74} -6.63587 q^{75} +6.43244 q^{76} -5.35380 q^{77} -2.23179 q^{78} -11.0627 q^{79} +3.30015 q^{80} -7.25376 q^{81} +9.58974 q^{82} -7.76197 q^{83} -30.0520 q^{84} -1.04577 q^{85} -6.74279 q^{86} +4.79049 q^{87} -5.27675 q^{88} -11.9317 q^{89} +1.09113 q^{90} -2.78681 q^{91} -5.07954 q^{92} -6.10569 q^{93} +13.7711 q^{94} +1.46145 q^{95} +0.817105 q^{96} +8.15339 q^{97} -39.4744 q^{98} -0.554859 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * 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 $

$2$	−2.43851	−1.72428	−0.862142	−	0.506667i	$-0.830877\pi$
$2$	−2.43851	−1.72428	−0.862142	+	0.506667i	$0.830877\pi$
$3$	1.58144	0.913043	0.456521	−	0.889712i	$-0.349095\pi$
$3$	1.58144	0.913043	0.456521	+	0.889712i	$0.349095\pi$
$4$	3.94631	1.97315
$5$	0.896601	0.400972	0.200486	−	0.979697i	$-0.435748\pi$
$5$	0.896601	0.400972	0.200486	+	0.979697i	$0.435748\pi$
$6$	−3.85634	−1.57434
$7$	−4.81539	−1.82004	−0.910022	−	0.414559i	$-0.863936\pi$
$7$	−4.81539	−1.82004	−0.910022	+	0.414559i	$0.863936\pi$
$8$	−4.74608	−1.67799
$9$	−0.499059	−0.166353
$10$	−2.18637	−0.691390
$11$	1.11181	0.335224	0.167612	−	0.985853i	$-0.446394\pi$
$11$	1.11181	0.335224	0.167612	+	0.985853i	$0.446394\pi$
$12$	6.24084	1.80157
$13$	0.578731	0.160511	0.0802556	−	0.996774i	$-0.474426\pi$
$13$	0.578731	0.160511	0.0802556	+	0.996774i	$0.474426\pi$
$14$	11.7423	3.13827
$15$	1.41792	0.366105
$16$	3.68073	0.920182
$17$	−1.16637	−0.282886	−0.141443	−	0.989946i	$-0.545174\pi$
$17$	−1.16637	−0.282886	−0.141443	+	0.989946i	$0.545174\pi$
$18$	1.21696	0.286840
$19$	1.62999	0.373945	0.186973	−	0.982365i	$-0.440132\pi$
$19$	1.62999	0.373945	0.186973	+	0.982365i	$0.440132\pi$
$20$	3.53827	0.791180
$21$	−7.61523	−1.66178
$22$	−2.71116	−0.578021
$23$	−1.28716	−0.268392	−0.134196	−	0.990955i	$-0.542845\pi$
$23$	−1.28716	−0.268392	−0.134196	+	0.990955i	$0.542845\pi$
$24$	−7.50563	−1.53208
$25$	−4.19611	−0.839221
$26$	−1.41124	−0.276767
$27$	−5.53354	−1.06493
$28$	−19.0030	−3.59123
$29$	3.02920	0.562509	0.281254	−	0.959633i	$-0.409249\pi$
$29$	3.02920	0.562509	0.281254	+	0.959633i	$0.409249\pi$
$30$	−3.45760	−0.631269
$31$	−3.86085	−0.693429	−0.346714	−	0.937971i	$-0.612703\pi$
$31$	−3.86085	−0.693429	−0.346714	+	0.937971i	$0.612703\pi$
$32$	0.516685	0.0913379
$33$	1.75826	0.306073
$34$	2.84419	0.487775
$35$	−4.31748	−0.729788
$36$	−1.96944	−0.328240
$37$	8.11384	1.33391	0.666953	−	0.745099i	$-0.267598\pi$
$37$	8.11384	1.33391	0.666953	+	0.745099i	$0.267598\pi$
$38$	−3.97474	−0.644787
$39$	0.915227	0.146554
$40$	−4.25534	−0.672829
$41$	−3.93263	−0.614174	−0.307087	−	0.951681i	$-0.599354\pi$
$41$	−3.93263	−0.614174	−0.307087	+	0.951681i	$0.599354\pi$
$42$	18.5698	2.86538
$43$	2.76513	0.421679	0.210839	−	0.977521i	$-0.432380\pi$
$43$	2.76513	0.421679	0.210839	+	0.977521i	$0.432380\pi$
$44$	4.38755	0.661448
$45$	−0.447457	−0.0667029
$46$	3.13875	0.462784
$47$	−5.64736	−0.823752	−0.411876	−	0.911240i	$-0.635126\pi$
$47$	−5.64736	−0.823752	−0.411876	+	0.911240i	$0.635126\pi$
$48$	5.82084	0.840166
$49$	16.1879	2.31256
$50$	10.2322	1.44706
$51$	−1.84454	−0.258287
$52$	2.28385	0.316713
$53$	−2.41261	−0.331398	−0.165699	−	0.986176i	$-0.552988\pi$
$53$	−2.41261	−0.331398	−0.165699	+	0.986176i	$0.552988\pi$
$54$	13.4936	1.83624
$55$	0.996851	0.134415
$56$	22.8542	3.05402
$57$	2.57772	0.341428
$58$	−7.38673	−0.969925
$59$	−1.11978	−0.145783	−0.0728917	−	0.997340i	$-0.523223\pi$
$59$	−1.11978	−0.145783	−0.0728917	+	0.997340i	$0.523223\pi$
$60$	5.59554	0.722381
$61$	7.72304	0.988834	0.494417	−	0.869225i	$-0.335382\pi$
$61$	7.72304	0.988834	0.494417	+	0.869225i	$0.335382\pi$
$62$	9.41470	1.19567
$63$	2.40316	0.302770
$64$	−8.62140	−1.07767
$65$	0.518891	0.0643605
$66$	−4.28752	−0.527757
$67$	14.5128	1.77302	0.886512	−	0.462706i	$-0.153121\pi$
$67$	14.5128	1.77302	0.886512	+	0.462706i	$0.153121\pi$
$68$	−4.60285	−0.558177
$69$	−2.03556	−0.245053
$70$	10.5282	1.25836
$71$	−8.74928	−1.03835	−0.519174	−	0.854668i	$-0.673760\pi$
$71$	−8.74928	−1.03835	−0.519174	+	0.854668i	$0.673760\pi$
$72$	2.36857	0.279139
$73$	3.29600	0.385768	0.192884	−	0.981222i	$-0.438216\pi$
$73$	3.29600	0.385768	0.192884	+	0.981222i	$0.438216\pi$
$74$	−19.7856	−2.30003
$75$	−6.63587	−0.766245
$76$	6.43244	0.737851
$77$	−5.35380	−0.610122
$78$	−2.23179	−0.252700
$79$	−11.0627	−1.24465	−0.622326	−	0.782758i	$-0.713812\pi$
$79$	−11.0627	−1.24465	−0.622326	+	0.782758i	$0.713812\pi$
$80$	3.30015	0.368968
$81$	−7.25376	−0.805974
$82$	9.58974	1.05901
$83$	−7.76197	−0.851986	−0.425993	−	0.904726i	$-0.640075\pi$
$83$	−7.76197	−0.851986	−0.425993	+	0.904726i	$0.640075\pi$
$84$	−30.0520	−3.27895
$85$	−1.04577	−0.113429
$86$	−6.74279	−0.727094
$87$	4.79049	0.513595
$88$	−5.27675	−0.562503
$89$	−11.9317	−1.26475	−0.632377	−	0.774661i	$-0.717921\pi$
$89$	−11.9317	−1.26475	−0.632377	+	0.774661i	$0.717921\pi$
$90$	1.09113	0.115015
$91$	−2.78681	−0.292138
$92$	−5.07954	−0.529578
$93$	−6.10569	−0.633130
$94$	13.7711	1.42038
$95$	1.46145	0.149942
$96$	0.817105	0.0833954
$97$	8.15339	0.827851	0.413925	−	0.910311i	$-0.364157\pi$
$97$	8.15339	0.827851	0.413925	+	0.910311i	$0.364157\pi$
$98$	−39.4744	−3.98751
$99$	−0.554859	−0.0557654
$100$	−16.5591	−1.65591
$101$	16.1139	1.60339	0.801695	−	0.597733i	$-0.203932\pi$
$101$	16.1139	1.60339	0.801695	+	0.597733i	$0.203932\pi$
$102$	4.49791	0.445360
$103$	−8.78031	−0.865149	−0.432575	−	0.901598i	$-0.642395\pi$
$103$	−8.78031	−0.865149	−0.432575	+	0.901598i	$0.642395\pi$
$104$	−2.74671	−0.269337
$105$	−6.82782	−0.666327
$106$	5.88316	0.571423
$107$	13.4372	1.29902	0.649511	−	0.760352i	$-0.274974\pi$
$107$	13.4372	1.29902	0.649511	+	0.760352i	$0.274974\pi$
$108$	−21.8370	−2.10127
$109$	−6.82296	−0.653521	−0.326760	−	0.945107i	$-0.605957\pi$
$109$	−6.82296	−0.653521	−0.326760	+	0.945107i	$0.605957\pi$
$110$	−2.43083	−0.231770
$111$	12.8315	1.21791
$112$	−17.7241	−1.67477
$113$	11.2354	1.05694	0.528469	−	0.848953i	$-0.322766\pi$
$113$	11.2354	1.05694	0.528469	+	0.848953i	$0.322766\pi$
$114$	−6.28579	−0.588718
$115$	−1.15407	−0.107618
$116$	11.9542	1.10992
$117$	−0.288821	−0.0267015
$118$	2.73060	0.251372
$119$	5.61651	0.514865
$120$	−6.72956	−0.614322
$121$	−9.76388	−0.887625
$122$	−18.8327	−1.70503
$123$	−6.21921	−0.560767
$124$	−15.2361	−1.36824
$125$	−8.24524	−0.737477
$126$	−5.86012	−0.522061
$127$	2.22804	0.197706	0.0988531	−	0.995102i	$-0.468483\pi$
$127$	2.22804	0.197706	0.0988531	+	0.995102i	$0.468483\pi$
$128$	19.9900	1.76688
$129$	4.37288	0.385011
$130$	−1.26532	−0.110976
$131$	−11.7145	−1.02350	−0.511752	−	0.859133i	$-0.671003\pi$
$131$	−11.7145	−1.02350	−0.511752	+	0.859133i	$0.671003\pi$
$132$	6.93863	0.603930
$133$	−7.84902	−0.680597
$134$	−35.3896	−3.05720
$135$	−4.96138	−0.427008
$136$	5.53568	0.474680
$137$	15.3150	1.30845	0.654226	−	0.756299i	$-0.272995\pi$
$137$	15.3150	1.30845	0.654226	+	0.756299i	$0.272995\pi$
$138$	4.96374	0.422541
$139$	−3.19049	−0.270614	−0.135307	−	0.990804i	$-0.543202\pi$
$139$	−3.19049	−0.270614	−0.135307	+	0.990804i	$0.543202\pi$
$140$	−17.0381	−1.43998
$141$	−8.93093	−0.752120
$142$	21.3352	1.79041
$143$	0.643440	0.0538071
$144$	−1.83690	−0.153075
$145$	2.71599	0.225551
$146$	−8.03733	−0.665174
$147$	25.6002	2.11147
$148$	32.0197	2.63200
$149$	19.1616	1.56978	0.784889	−	0.619636i	$-0.212720\pi$
$149$	19.1616	1.56978	0.784889	+	0.619636i	$0.212720\pi$
$150$	16.1816	1.32122
$151$	−6.83338	−0.556092	−0.278046	−	0.960568i	$-0.589687\pi$
$151$	−6.83338	−0.556092	−0.278046	+	0.960568i	$0.589687\pi$
$152$	−7.73606	−0.627477
$153$	0.582086	0.0470589
$154$	13.0553	1.05202
$155$	−3.46164	−0.278046
$156$	3.61177	0.289173
$157$	−9.27884	−0.740532	−0.370266	−	0.928926i	$-0.620734\pi$
$157$	−9.27884	−0.740532	−0.370266	+	0.928926i	$0.620734\pi$
$158$	26.9765	2.14613
$159$	−3.81539	−0.302580
$160$	0.463261	0.0366240
$161$	6.19818	0.488485
$162$	17.6883	1.38973
$163$	−2.98770	−0.234014	−0.117007	−	0.993131i	$-0.537330\pi$
$163$	−2.98770	−0.234014	−0.117007	+	0.993131i	$0.537330\pi$
$164$	−15.5194	−1.21186
$165$	1.57646	0.122727
$166$	18.9276	1.46907
$167$	19.6671	1.52188	0.760941	−	0.648821i	$-0.224737\pi$
$167$	19.6671	1.52188	0.760941	+	0.648821i	$0.224737\pi$
$168$	36.1425	2.78845
$169$	−12.6651	−0.974236
$170$	2.55011	0.195584
$171$	−0.813460	−0.0622068
$172$	10.9121	0.832037
$173$	24.2816	1.84610	0.923050	−	0.384681i	$-0.125689\pi$
$173$	24.2816	1.84610	0.923050	+	0.384681i	$0.125689\pi$
$174$	−11.6816	−0.885583
$175$	20.2059	1.52742
$176$	4.09228	0.308467
$177$	−1.77087	−0.133107
$178$	29.0954	2.18080
$179$	2.75883	0.206204	0.103102	−	0.994671i	$-0.467123\pi$
$179$	2.75883	0.206204	0.103102	+	0.994671i	$0.467123\pi$
$180$	−1.76580	−0.131615
$181$	15.3589	1.14162	0.570808	−	0.821084i	$-0.306630\pi$
$181$	15.3589	1.14162	0.570808	+	0.821084i	$0.306630\pi$
$182$	6.79566	0.503728
$183$	12.2135	0.902848
$184$	6.10898	0.450360
$185$	7.27488	0.534860
$186$	14.8887	1.09170
$187$	−1.29678	−0.0948300
$188$	−22.2862	−1.62539
$189$	26.6461	1.93822
$190$	−3.56375	−0.258542
$191$	15.1762	1.09811	0.549054	−	0.835787i	$-0.314988\pi$
$191$	15.1762	1.09811	0.549054	+	0.835787i	$0.314988\pi$
$192$	−13.6342	−0.983963
$193$	5.12372	0.368813	0.184407	−	0.982850i	$-0.440964\pi$
$193$	5.12372	0.368813	0.184407	+	0.982850i	$0.440964\pi$
$194$	−19.8821	−1.42745
$195$	0.820594	0.0587639
$196$	63.8826	4.56304
$197$	11.0526	0.787467	0.393733	−	0.919225i	$-0.371183\pi$
$197$	11.0526	0.787467	0.393733	+	0.919225i	$0.371183\pi$
$198$	1.35303	0.0961554
$199$	−4.36134	−0.309167	−0.154584	−	0.987980i	$-0.549404\pi$
$199$	−4.36134	−0.309167	−0.154584	+	0.987980i	$0.549404\pi$
$200$	19.9151	1.40821
$201$	22.9511	1.61885
$202$	−39.2938	−2.76470
$203$	−14.5868	−1.02379
$204$	−7.27911	−0.509640
$205$	−3.52600	−0.246267
$206$	21.4108	1.49176
$207$	0.642369	0.0446478
$208$	2.13015	0.147700
$209$	1.81224	0.125355
$210$	16.6497	1.14894
$211$	5.67880	0.390945	0.195472	−	0.980709i	$-0.437376\pi$
$211$	5.67880	0.390945	0.195472	+	0.980709i	$0.437376\pi$
$212$	−9.52091	−0.653899
$213$	−13.8364	−0.948057
$214$	−32.7667	−2.23988
$215$	2.47922	0.169082
$216$	26.2626	1.78695
$217$	18.5915	1.26207
$218$	16.6378	1.12686
$219$	5.21242	0.352223
$220$	3.93388	0.265222
$221$	−0.675013	−0.0454063
$222$	−31.2897	−2.10003
$223$	20.0040	1.33957	0.669783	−	0.742557i	$-0.266387\pi$
$223$	20.0040	1.33957	0.669783	+	0.742557i	$0.266387\pi$
$224$	−2.48804	−0.166239
$225$	2.09410	0.139607
$226$	−27.3976	−1.82246
$227$	2.99520	0.198798	0.0993992	−	0.995048i	$-0.468308\pi$
$227$	2.99520	0.198798	0.0993992	+	0.995048i	$0.468308\pi$
$228$	10.1725	0.673690
$229$	28.5826	1.88879	0.944396	−	0.328809i	$-0.106647\pi$
$229$	28.5826	1.88879	0.944396	+	0.328809i	$0.106647\pi$
$230$	2.81421	0.185563
$231$	−8.46669	−0.557067
$232$	−14.3768	−0.943886
$233$	−2.94172	−0.192719	−0.0963593	−	0.995347i	$-0.530720\pi$
$233$	−2.94172	−0.192719	−0.0963593	+	0.995347i	$0.530720\pi$
$234$	0.704291	0.0460409
$235$	−5.06343	−0.330302
$236$	−4.41901	−0.287653
$237$	−17.4950	−1.13642
$238$	−13.6959	−0.887773
$239$	−13.0690	−0.845363	−0.422682	−	0.906278i	$-0.638911\pi$
$239$	−13.0690	−0.845363	−0.422682	+	0.906278i	$0.638911\pi$
$240$	5.21897	0.336883
$241$	−13.7823	−0.887799	−0.443899	−	0.896077i	$-0.646405\pi$
$241$	−13.7823	−0.887799	−0.443899	+	0.896077i	$0.646405\pi$
$242$	23.8093	1.53052
$243$	5.12925	0.329041
$244$	30.4775	1.95112
$245$	14.5141	0.927274
$246$	15.1656	0.966921
$247$	0.943325	0.0600223
$248$	18.3239	1.16357
$249$	−12.2751	−0.777900
$250$	20.1061	1.27162
$251$	10.5204	0.664043	0.332021	−	0.943272i	$-0.392269\pi$
$251$	10.5204	0.664043	0.332021	+	0.943272i	$0.392269\pi$
$252$	9.48361	0.597411
$253$	−1.43108	−0.0899713
$254$	−5.43308	−0.340902
$255$	−1.65381	−0.103566
$256$	−31.5028	−1.96893
$257$	−6.25664	−0.390279	−0.195139	−	0.980776i	$-0.562516\pi$
$257$	−6.25664	−0.390279	−0.195139	+	0.980776i	$0.562516\pi$
$258$	−10.6633	−0.663868
$259$	−39.0713	−2.42777
$260$	2.04770	0.126993
$261$	−1.51175	−0.0935750
$262$	28.5659	1.76481
$263$	−1.72239	−0.106207	−0.0531035	−	0.998589i	$-0.516911\pi$
$263$	−1.72239	−0.106207	−0.0531035	+	0.998589i	$0.516911\pi$
$264$	−8.34484	−0.513589
$265$	−2.16315	−0.132881
$266$	19.1399	1.17354
$267$	−18.8692	−1.15478
$268$	57.2721	3.49845
$269$	−17.5496	−1.07002	−0.535008	−	0.844847i	$-0.679692\pi$
$269$	−17.5496	−1.07002	−0.535008	+	0.844847i	$0.679692\pi$
$270$	12.0983	0.736282
$271$	−6.51776	−0.395926	−0.197963	−	0.980210i	$-0.563433\pi$
$271$	−6.51776	−0.395926	−0.197963	+	0.980210i	$0.563433\pi$
$272$	−4.29308	−0.260306
$273$	−4.40717	−0.266734
$274$	−37.3458	−2.25614
$275$	−4.66528	−0.281327
$276$	−8.03297	−0.483528
$277$	30.9632	1.86040	0.930198	−	0.367059i	$-0.119635\pi$
$277$	30.9632	1.86040	0.930198	+	0.367059i	$0.119635\pi$
$278$	7.78003	0.466615
$279$	1.92679	0.115354
$280$	20.4911	1.22458
$281$	22.1759	1.32290	0.661452	−	0.749987i	$-0.269940\pi$
$281$	22.1759	1.32290	0.661452	+	0.749987i	$0.269940\pi$
$282$	21.7781	1.29687
$283$	6.67333	0.396688	0.198344	−	0.980132i	$-0.436444\pi$
$283$	6.67333	0.396688	0.198344	+	0.980132i	$0.436444\pi$
$284$	−34.5274	−2.04882
$285$	2.31119	0.136903
$286$	−1.56903	−0.0927788
$287$	18.9371	1.11782
$288$	−0.257856	−0.0151943
$289$	−15.6396	−0.919976
$290$	−6.62295	−0.388913
$291$	12.8941	0.755863
$292$	13.0070	0.761180
$293$	0.872822	0.0509908	0.0254954	−	0.999675i	$-0.491884\pi$
$293$	0.872822	0.0509908	0.0254954	+	0.999675i	$0.491884\pi$
$294$	−62.4262	−3.64077
$295$	−1.00400	−0.0584551
$296$	−38.5089	−2.23829
$297$	−6.15225	−0.356990
$298$	−46.7256	−2.70674
$299$	−0.744921	−0.0430799
$300$	−26.1872	−1.51192
$301$	−13.3152	−0.767474
$302$	16.6632	0.958861
$303$	25.4831	1.46396
$304$	5.99955	0.344098
$305$	6.92449	0.396495
$306$	−1.41942	−0.0811428
$307$	15.9290	0.909114	0.454557	−	0.890718i	$-0.349798\pi$
$307$	15.9290	0.909114	0.454557	+	0.890718i	$0.349798\pi$
$308$	−21.1277	−1.20386
$309$	−13.8855	−0.789918
$310$	8.44123	0.479430
$311$	7.62252	0.432234	0.216117	−	0.976368i	$-0.430661\pi$
$311$	7.62252	0.432234	0.216117	+	0.976368i	$0.430661\pi$
$312$	−4.34374	−0.245916
$313$	−14.0046	−0.791586	−0.395793	−	0.918340i	$-0.629530\pi$
$313$	−14.0046	−0.791586	−0.395793	+	0.918340i	$0.629530\pi$
$314$	22.6265	1.27689
$315$	2.15468	0.121402
$316$	−43.6569	−2.45589
$317$	1.69959	0.0954583	0.0477292	−	0.998860i	$-0.484802\pi$
$317$	1.69959	0.0954583	0.0477292	+	0.998860i	$0.484802\pi$
$318$	9.30385	0.521734
$319$	3.36790	0.188566
$320$	−7.72996	−0.432118
$321$	21.2501	1.18606
$322$	−15.1143	−0.842287
$323$	−1.90117	−0.105784
$324$	−28.6256	−1.59031
$325$	−2.42842	−0.134704
$326$	7.28551	0.403507
$327$	−10.7901	−0.596692
$328$	18.6646	1.03058
$329$	27.1942	1.49926
$330$	−3.84420	−0.211616
$331$	18.6325	1.02413	0.512066	−	0.858946i	$-0.328880\pi$
$331$	18.6325	1.02413	0.512066	+	0.858946i	$0.328880\pi$
$332$	−30.6311	−1.68110
$333$	−4.04928	−0.221899
$334$	−47.9582	−2.62416
$335$	13.0122	0.710934
$336$	−28.0296	−1.52914
$337$	−7.95857	−0.433531	−0.216765	−	0.976224i	$-0.569551\pi$
$337$	−7.95857	−0.433531	−0.216765	+	0.976224i	$0.569551\pi$
$338$	30.8838	1.67986
$339$	17.7681	0.965030
$340$	−4.12692	−0.223814
$341$	−4.29253	−0.232454
$342$	1.98363	0.107262
$343$	−44.2435	−2.38892
$344$	−13.1235	−0.707574
$345$	−1.82509	−0.0982596
$346$	−59.2109	−3.18320
$347$	2.69492	0.144671	0.0723354	−	0.997380i	$-0.476955\pi$
$347$	2.69492	0.144671	0.0723354	+	0.997380i	$0.476955\pi$
$348$	18.9048	1.01340
$349$	−11.1102	−0.594718	−0.297359	−	0.954766i	$-0.596106\pi$
$349$	−11.1102	−0.594718	−0.297359	+	0.954766i	$0.596106\pi$
$350$	−49.2721	−2.63371
$351$	−3.20243	−0.170933
$352$	0.574456	0.0306186
$353$	10.4402	0.555675	0.277837	−	0.960628i	$-0.410382\pi$
$353$	10.4402	0.555675	0.277837	+	0.960628i	$0.410382\pi$
$354$	4.31827	0.229513
$355$	−7.84462	−0.416349
$356$	−47.0860	−2.49556
$357$	8.88215	0.470093
$358$	−6.72741	−0.355555
$359$	32.7921	1.73070	0.865352	−	0.501165i	$-0.167095\pi$
$359$	32.7921	1.73070	0.865352	+	0.501165i	$0.167095\pi$
$360$	2.12367	0.111927
$361$	−16.3431	−0.860165
$362$	−37.4527	−1.96847
$363$	−15.4410	−0.810440
$364$	−10.9976	−0.576432
$365$	2.95520	0.154682
$366$	−29.7827	−1.55677
$367$	−24.1027	−1.25815	−0.629074	−	0.777345i	$-0.716566\pi$
$367$	−24.1027	−1.25815	−0.629074	+	0.777345i	$0.716566\pi$
$368$	−4.73769	−0.246969
$369$	1.96261	0.102170
$370$	−17.7398	−0.922250
$371$	11.6177	0.603159
$372$	−24.0949	−1.24926
$373$	17.1020	0.885510	0.442755	−	0.896643i	$-0.354001\pi$
$373$	17.1020	0.885510	0.442755	+	0.896643i	$0.354001\pi$
$374$	3.16221	0.163514
$375$	−13.0393	−0.673348
$376$	26.8028	1.38225
$377$	1.75309	0.0902890
$378$	−64.9767	−3.34204
$379$	19.5608	1.00477	0.502386	−	0.864643i	$-0.332455\pi$
$379$	19.5608	1.00477	0.502386	+	0.864643i	$0.332455\pi$
$380$	5.76733	0.295858
$381$	3.52350	0.180514
$382$	−37.0071	−1.89345
$383$	30.0414	1.53505	0.767523	−	0.641022i	$-0.221489\pi$
$383$	30.0414	1.53505	0.767523	+	0.641022i	$0.221489\pi$
$384$	31.6128	1.61324
$385$	−4.80022	−0.244642
$386$	−12.4942	−0.635939
$387$	−1.37996	−0.0701475
$388$	32.1758	1.63348
$389$	5.41311	0.274456	0.137228	−	0.990540i	$-0.456181\pi$
$389$	5.41311	0.274456	0.137228	+	0.990540i	$0.456181\pi$
$390$	−2.00102	−0.101326
$391$	1.50130	0.0759242
$392$	−76.8293	−3.88047
$393$	−18.5258	−0.934502
$394$	−26.9519	−1.35782
$395$	−9.91885	−0.499071
$396$	−2.18964	−0.110034
$397$	−8.35115	−0.419132	−0.209566	−	0.977794i	$-0.567205\pi$
$397$	−8.35115	−0.419132	−0.209566	+	0.977794i	$0.567205\pi$
$398$	10.6351	0.533092
$399$	−12.4127	−0.621414
$400$	−15.4447	−0.772237
$401$	−2.66623	−0.133145	−0.0665725	−	0.997782i	$-0.521206\pi$
$401$	−2.66623	−0.133145	−0.0665725	+	0.997782i	$0.521206\pi$
$402$	−55.9664	−2.79135
$403$	−2.23439	−0.111303
$404$	63.5903	3.16373
$405$	−6.50374	−0.323173
$406$	35.5699	1.76531
$407$	9.02105	0.447157
$408$	8.75432	0.433403
$409$	−19.9202	−0.984991	−0.492495	−	0.870315i	$-0.663915\pi$
$409$	−19.9202	−0.984991	−0.492495	+	0.870315i	$0.663915\pi$
$410$	8.59818	0.424634
$411$	24.2198	1.19467
$412$	−34.6498	−1.70707
$413$	5.39219	0.265332
$414$	−1.56642	−0.0769854
$415$	−6.95939	−0.341623
$416$	0.299022	0.0146608
$417$	−5.04556	−0.247082
$418$	−4.41915	−0.216148
$419$	34.0205	1.66201	0.831004	−	0.556266i	$-0.187767\pi$
$419$	34.0205	1.66201	0.831004	+	0.556266i	$0.187767\pi$
$420$	−26.9447	−1.31477
$421$	−12.0876	−0.589112	−0.294556	−	0.955634i	$-0.595172\pi$
$421$	−12.0876	−0.589112	−0.294556	+	0.955634i	$0.595172\pi$
$422$	−13.8478	−0.674100
$423$	2.81836	0.137033
$424$	11.4504	0.556083
$425$	4.89420	0.237404
$426$	33.7402	1.63472
$427$	−37.1894	−1.79972
$428$	53.0273	2.56317
$429$	1.01756	0.0491282
$430$	−6.04560	−0.291545
$431$	15.9542	0.768488	0.384244	−	0.923232i	$-0.374462\pi$
$431$	15.9542	0.768488	0.384244	+	0.923232i	$0.374462\pi$
$432$	−20.3675	−0.979930
$433$	−7.50972	−0.360894	−0.180447	−	0.983585i	$-0.557754\pi$
$433$	−7.50972	−0.360894	−0.180447	+	0.983585i	$0.557754\pi$
$434$	−45.3354	−2.17617
$435$	4.29516	0.205937
$436$	−26.9255	−1.28950
$437$	−2.09806	−0.100364
$438$	−12.7105	−0.607332
$439$	−19.3047	−0.921361	−0.460680	−	0.887566i	$-0.652395\pi$
$439$	−19.3047	−0.921361	−0.460680	+	0.887566i	$0.652395\pi$
$440$	−4.73114	−0.225548
$441$	−8.07873	−0.384702
$442$	1.64602	0.0782934
$443$	14.2949	0.679172	0.339586	−	0.940575i	$-0.389713\pi$
$443$	14.2949	0.679172	0.339586	+	0.940575i	$0.389713\pi$
$444$	50.6371	2.40313
$445$	−10.6980	−0.507132
$446$	−48.7798	−2.30979
$447$	30.3028	1.43328
$448$	41.5154	1.96142
$449$	−29.7460	−1.40380	−0.701901	−	0.712275i	$-0.747665\pi$
$449$	−29.7460	−1.40380	−0.701901	+	0.712275i	$0.747665\pi$
$450$	−5.10648	−0.240722
$451$	−4.37234	−0.205886
$452$	44.3384	2.08550
$453$	−10.8066	−0.507736
$454$	−7.30381	−0.342785
$455$	−2.49866	−0.117139
$456$	−12.2341	−0.572914
$457$	21.0017	0.982419	0.491209	−	0.871042i	$-0.336555\pi$
$457$	21.0017	0.982419	0.491209	+	0.871042i	$0.336555\pi$
$458$	−69.6989	−3.25681
$459$	6.45414	0.301253
$460$	−4.55432	−0.212346
$461$	2.51435	0.117105	0.0585524	−	0.998284i	$-0.481352\pi$
$461$	2.51435	0.117105	0.0585524	+	0.998284i	$0.481352\pi$
$462$	20.6461	0.960542
$463$	7.67175	0.356536	0.178268	−	0.983982i	$-0.442951\pi$
$463$	7.67175	0.356536	0.178268	+	0.983982i	$0.442951\pi$
$464$	11.1497	0.517611
$465$	−5.47437	−0.253868
$466$	7.17341	0.332302
$467$	−4.54158	−0.210159	−0.105080	−	0.994464i	$-0.533510\pi$
$467$	−4.54158	−0.210159	−0.105080	+	0.994464i	$0.533510\pi$
$468$	−1.13978	−0.0526862
$469$	−69.8849	−3.22698
$470$	12.3472	0.569534
$471$	−14.6739	−0.676138
$472$	5.31459	0.244624
$473$	3.07431	0.141357
$474$	42.6616	1.95951
$475$	−6.83960	−0.313823
$476$	22.1645	1.01591
$477$	1.20403	0.0551289
$478$	31.8688	1.45765
$479$	7.01939	0.320724	0.160362	−	0.987058i	$-0.448734\pi$
$479$	7.01939	0.320724	0.160362	+	0.987058i	$0.448734\pi$
$480$	0.732618	0.0334393
$481$	4.69573	0.214107
$482$	33.6083	1.53082
$483$	9.80203	0.446008
$484$	−38.5313	−1.75142
$485$	7.31034	0.331945
$486$	−12.5077	−0.567361
$487$	−1.25980	−0.0570872	−0.0285436	−	0.999593i	$-0.509087\pi$
$487$	−1.25980	−0.0570872	−0.0285436	+	0.999593i	$0.509087\pi$
$488$	−36.6542	−1.65926
$489$	−4.72485	−0.213665
$490$	−35.3928	−1.59888
$491$	6.14749	0.277432	0.138716	−	0.990332i	$-0.455702\pi$
$491$	6.14749	0.277432	0.138716	+	0.990332i	$0.455702\pi$
$492$	−24.5429	−1.10648
$493$	−3.53316	−0.159126
$494$	−2.30030	−0.103496
$495$	−0.497487	−0.0223604
$496$	−14.2107	−0.638081
$497$	42.1312	1.88984
$498$	29.9328	1.34132
$499$	−34.7842	−1.55716	−0.778578	−	0.627548i	$-0.784059\pi$
$499$	−34.7842	−1.55716	−0.778578	+	0.627548i	$0.784059\pi$
$500$	−32.5383	−1.45516
$501$	31.1022	1.38954
$502$	−25.6541	−1.14500
$503$	30.2069	1.34686	0.673430	−	0.739251i	$-0.264820\pi$
$503$	30.2069	1.34686	0.673430	+	0.739251i	$0.264820\pi$
$504$	−11.4056	−0.508045
$505$	14.4477	0.642915
$506$	3.48970	0.155136
$507$	−20.0290	−0.889519
$508$	8.79252	0.390105
$509$	32.4177	1.43689	0.718445	−	0.695584i	$-0.244854\pi$
$509$	32.4177	1.43689	0.718445	+	0.695584i	$0.244854\pi$
$510$	4.03283	0.178577
$511$	−15.8715	−0.702115
$512$	36.8399	1.62811
$513$	−9.01960	−0.398225
$514$	15.2569	0.672951
$515$	−7.87244	−0.346901
$516$	17.2567	0.759686
$517$	−6.27879	−0.276141
$518$	95.2755	4.18616
$519$	38.3999	1.68557
$520$	−2.46270	−0.107997
$521$	−7.30325	−0.319961	−0.159981	−	0.987120i	$-0.551143\pi$
$521$	−7.30325	−0.319961	−0.159981	+	0.987120i	$0.551143\pi$
$522$	3.68641	0.161350
$523$	−30.3284	−1.32617	−0.663083	−	0.748546i	$-0.730753\pi$
$523$	−30.3284	−1.32617	−0.663083	+	0.748546i	$0.730753\pi$
$524$	−46.2292	−2.01953
$525$	31.9543	1.39460
$526$	4.20005	0.183131
$527$	4.50317	0.196161
$528$	6.47167	0.281643
$529$	−21.3432	−0.927966
$530$	5.27485	0.229125
$531$	0.558838	0.0242515
$532$	−30.9747	−1.34292
$533$	−2.27594	−0.0985817
$534$	46.0126	1.99116
$535$	12.0478	0.520872
$536$	−68.8791	−2.97512
$537$	4.36291	0.188273
$538$	42.7947	1.84501
$539$	17.9979	0.775226
$540$	−19.5791	−0.842552
$541$	−2.08832	−0.0897839	−0.0448920	−	0.998992i	$-0.514294\pi$
$541$	−2.08832	−0.0897839	−0.0448920	+	0.998992i	$0.514294\pi$
$542$	15.8936	0.682688
$543$	24.2891	1.04234
$544$	−0.602645	−0.0258382
$545$	−6.11747	−0.262044
$546$	10.7469	0.459925
$547$	0.518080	0.0221515	0.0110758	−	0.999939i	$-0.496474\pi$
$547$	0.518080	0.0221515	0.0110758	+	0.999939i	$0.496474\pi$
$548$	60.4378	2.58178
$549$	−3.85425	−0.164495
$550$	11.3763	0.485087
$551$	4.93757	0.210347
$552$	9.66096	0.411198
$553$	53.2712	2.26532
$554$	−75.5038	−3.20785
$555$	11.5048	0.488350
$556$	−12.5907	−0.533963
$557$	27.7223	1.17463	0.587316	−	0.809358i	$-0.300185\pi$
$557$	27.7223	1.17463	0.587316	+	0.809358i	$0.300185\pi$
$558$	−4.69849	−0.198903
$559$	1.60027	0.0676842
$560$	−15.8915	−0.671538
$561$	−2.05078	−0.0865838
$562$	−54.0761	−2.28106
$563$	−45.6536	−1.92407	−0.962035	−	0.272928i	$-0.912008\pi$
$563$	−45.6536	−1.92407	−0.962035	+	0.272928i	$0.912008\pi$
$564$	−35.2442	−1.48405
$565$	10.0737	0.423803
$566$	−16.2729	−0.684003
$567$	34.9297	1.46691
$568$	41.5248	1.74234
$569$	42.5241	1.78270	0.891351	−	0.453313i	$-0.149758\pi$
$569$	42.5241	1.78270	0.891351	+	0.453313i	$0.149758\pi$
$570$	−5.63585	−0.236060
$571$	25.1272	1.05154	0.525771	−	0.850626i	$-0.323777\pi$
$571$	25.1272	1.05154	0.525771	+	0.850626i	$0.323777\pi$
$572$	2.53921	0.106170
$573$	24.0001	1.00262
$574$	−46.1783	−1.92745
$575$	5.40107	0.225240
$576$	4.30258	0.179274
$577$	−12.0819	−0.502974	−0.251487	−	0.967861i	$-0.580920\pi$
$577$	−12.0819	−0.502974	−0.251487	+	0.967861i	$0.580920\pi$
$578$	38.1372	1.58630
$579$	8.10284	0.336742
$580$	10.7181	0.445046
$581$	37.3769	1.55065
$582$	−31.4422	−1.30332
$583$	−2.68237	−0.111092
$584$	−15.6431	−0.647316
$585$	−0.258957	−0.0107066
$586$	−2.12838	−0.0879226
$587$	−13.2011	−0.544868	−0.272434	−	0.962174i	$-0.587829\pi$
$587$	−13.2011	−0.544868	−0.272434	+	0.962174i	$0.587829\pi$
$588$	101.026	4.16625
$589$	−6.29314	−0.259304
$590$	2.44826	0.100793
$591$	17.4790	0.718991
$592$	29.8648	1.22744
$593$	7.63273	0.313439	0.156719	−	0.987643i	$-0.449908\pi$
$593$	7.63273	0.313439	0.156719	+	0.987643i	$0.449908\pi$
$594$	15.0023	0.615551
$595$	5.03577	0.206446
$596$	75.6175	3.09741
$597$	−6.89718	−0.282283
$598$	1.81649	0.0742819
$599$	−21.1836	−0.865537	−0.432768	−	0.901505i	$-0.642463\pi$
$599$	−21.1836	−0.865537	−0.432768	+	0.901505i	$0.642463\pi$
$600$	31.4944	1.28575
$601$	40.3995	1.64793	0.823965	−	0.566640i	$-0.191757\pi$
$601$	40.3995	1.64793	0.823965	+	0.566640i	$0.191757\pi$
$602$	32.4691	1.32334
$603$	−7.24275	−0.294948
$604$	−26.9666	−1.09726
$605$	−8.75431	−0.355913
$606$	−62.1406	−2.52429
$607$	38.7043	1.57096	0.785480	−	0.618887i	$-0.212416\pi$
$607$	38.7043	1.57096	0.785480	+	0.618887i	$0.212416\pi$
$608$	0.842191	0.0341554
$609$	−23.0681	−0.934765
$610$	−16.8854	−0.683670
$611$	−3.26830	−0.132221
$612$	2.29709	0.0928544
$613$	13.2930	0.536899	0.268449	−	0.963294i	$-0.413489\pi$
$613$	13.2930	0.536899	0.268449	+	0.963294i	$0.413489\pi$
$614$	−38.8428	−1.56757
$615$	−5.57615	−0.224852
$616$	25.4096	1.02378
$617$	−23.1606	−0.932411	−0.466205	−	0.884677i	$-0.654379\pi$
$617$	−23.1606	−0.932411	−0.466205	+	0.884677i	$0.654379\pi$
$618$	33.8599	1.36204
$619$	5.79996	0.233120	0.116560	−	0.993184i	$-0.462813\pi$
$619$	5.79996	0.233120	0.116560	+	0.993184i	$0.462813\pi$
$620$	−13.6607	−0.548627
$621$	7.12256	0.285819
$622$	−18.5876	−0.745293
$623$	57.4556	2.30191
$624$	3.36870	0.134856
$625$	13.5878	0.543513
$626$	34.1502	1.36492
$627$	2.86594	0.114455
$628$	−36.6172	−1.46118
$629$	−9.46372	−0.377343
$630$	−5.25419	−0.209332
$631$	23.8440	0.949213	0.474607	−	0.880198i	$-0.342590\pi$
$631$	23.8440	0.949213	0.474607	+	0.880198i	$0.342590\pi$
$632$	52.5046	2.08852
$633$	8.98066	0.356949
$634$	−4.14445	−0.164597
$635$	1.99766	0.0792747
$636$	−15.0567	−0.597037
$637$	9.36847	0.371192
$638$	−8.21265	−0.325142
$639$	4.36640	0.172732
$640$	17.9230	0.708470
$641$	−13.4636	−0.531781	−0.265891	−	0.964003i	$-0.585666\pi$
$641$	−13.4636	−0.531781	−0.265891	+	0.964003i	$0.585666\pi$
$642$	−51.8184	−2.04511
$643$	−3.35562	−0.132333	−0.0661664	−	0.997809i	$-0.521077\pi$
$643$	−3.35562	−0.132333	−0.0661664	+	0.997809i	$0.521077\pi$
$644$	24.4599	0.963856
$645$	3.92073	0.154379
$646$	4.63600	0.182401
$647$	12.1359	0.477111	0.238555	−	0.971129i	$-0.423326\pi$
$647$	12.1359	0.477111	0.238555	+	0.971129i	$0.423326\pi$
$648$	34.4270	1.35242
$649$	−1.24499	−0.0488701
$650$	5.92171	0.232269
$651$	29.4012	1.15233
$652$	−11.7904	−0.461746
$653$	−39.6742	−1.55257	−0.776286	−	0.630381i	$-0.782899\pi$
$653$	−39.6742	−1.55257	−0.776286	+	0.630381i	$0.782899\pi$
$654$	26.3117	1.02887
$655$	−10.5033	−0.410397
$656$	−14.4749	−0.565152
$657$	−1.64490	−0.0641736
$658$	−66.3132	−2.58516
$659$	−6.92579	−0.269791	−0.134895	−	0.990860i	$-0.543070\pi$
$659$	−6.92579	−0.269791	−0.134895	+	0.990860i	$0.543070\pi$
$660$	6.22118	0.242159
$661$	11.5447	0.449037	0.224519	−	0.974470i	$-0.427919\pi$
$661$	11.5447	0.449037	0.224519	+	0.974470i	$0.427919\pi$
$662$	−45.4354	−1.76590
$663$	−1.06749	−0.0414579
$664$	36.8389	1.42963
$665$	−7.03745	−0.272900
$666$	9.87419	0.382617
$667$	−3.89908	−0.150973
$668$	77.6123	3.00291
$669$	31.6350	1.22308
$670$	−31.7304	−1.22585
$671$	8.58656	0.331481
$672$	−3.93468	−0.151783
$673$	−1.60379	−0.0618214	−0.0309107	−	0.999522i	$-0.509841\pi$
$673$	−1.60379	−0.0618214	−0.0309107	+	0.999522i	$0.509841\pi$
$674$	19.4070	0.747530
$675$	23.2193	0.893712
$676$	−49.9803	−1.92232
$677$	8.12062	0.312101	0.156050	−	0.987749i	$-0.450124\pi$
$677$	8.12062	0.312101	0.156050	+	0.987749i	$0.450124\pi$
$678$	−43.3276	−1.66399
$679$	−39.2617	−1.50673
$680$	4.96330	0.190334
$681$	4.73672	0.181512
$682$	10.4674	0.400816
$683$	−43.3503	−1.65875	−0.829377	−	0.558690i	$-0.811304\pi$
$683$	−43.3503	−1.65875	−0.829377	+	0.558690i	$0.811304\pi$
$684$	−3.21016	−0.122744
$685$	13.7315	0.524653
$686$	107.888	4.11918
$687$	45.2016	1.72455
$688$	10.1777	0.388021
$689$	−1.39625	−0.0531930
$690$	4.45049	0.169427
$691$	18.7520	0.713358	0.356679	−	0.934227i	$-0.383909\pi$
$691$	18.7520	0.713358	0.356679	+	0.934227i	$0.383909\pi$
$692$	95.8228	3.64264
$693$	2.67186	0.101496
$694$	−6.57158	−0.249454
$695$	−2.86060	−0.108509
$696$	−22.7361	−0.861809
$697$	4.58689	0.173741
$698$	27.0924	1.02546
$699$	−4.65215	−0.175960
$700$	79.7386	3.01383
$701$	−11.5565	−0.436484	−0.218242	−	0.975895i	$-0.570032\pi$
$701$	−11.5565	−0.436484	−0.218242	+	0.975895i	$0.570032\pi$
$702$	7.80915	0.294737
$703$	13.2255	0.498808
$704$	−9.58536	−0.361262
$705$	−8.00749	−0.301579
$706$	−25.4584	−0.958141
$707$	−77.5945	−2.91824
$708$	−6.98839	−0.262640
$709$	−13.2332	−0.496982	−0.248491	−	0.968634i	$-0.579935\pi$
$709$	−13.2332	−0.496982	−0.248491	+	0.968634i	$0.579935\pi$
$710$	19.1291	0.717904
$711$	5.52094	0.207052
$712$	56.6287	2.12225
$713$	4.96954	0.186111
$714$	−21.6592	−0.810574
$715$	0.576909	0.0215752
$716$	10.8872	0.406873
$717$	−20.6678	−0.771853
$718$	−79.9638	−2.98422
$719$	−36.7782	−1.37160	−0.685798	−	0.727792i	$-0.740547\pi$
$719$	−36.7782	−1.37160	−0.685798	+	0.727792i	$0.740547\pi$
$720$	−1.64697	−0.0613788
$721$	42.2806	1.57461
$722$	39.8528	1.48317
$723$	−21.7959	−0.810598
$724$	60.6108	2.25258
$725$	−12.7109	−0.472069
$726$	37.6528	1.39743
$727$	31.0644	1.15212	0.576058	−	0.817409i	$-0.304590\pi$
$727$	31.0644	1.15212	0.576058	+	0.817409i	$0.304590\pi$
$728$	13.2264	0.490205
$729$	29.8729	1.10640
$730$	−7.20628	−0.266716
$731$	−3.22516	−0.119287
$732$	48.1982	1.78146
$733$	24.1664	0.892605	0.446303	−	0.894882i	$-0.352740\pi$
$733$	24.1664	0.892605	0.446303	+	0.894882i	$0.352740\pi$
$734$	58.7745	2.16940
$735$	22.9532	0.846641
$736$	−0.665058	−0.0245143
$737$	16.1355	0.594360
$738$	−4.78584	−0.176169
$739$	5.18206	0.190625	0.0953127	−	0.995447i	$-0.469615\pi$
$739$	5.18206	0.190625	0.0953127	+	0.995447i	$0.469615\pi$
$740$	28.7089	1.05536
$741$	1.49181	0.0548030
$742$	−28.3297	−1.04002
$743$	−40.4383	−1.48354	−0.741768	−	0.670657i	$-0.766012\pi$
$743$	−40.4383	−1.48354	−0.741768	+	0.670657i	$0.766012\pi$
$744$	28.9781	1.06239
$745$	17.1803	0.629438
$746$	−41.7034	−1.52687
$747$	3.87368	0.141730
$748$	−5.11749	−0.187114
$749$	−64.7053	−2.36428
$750$	31.7965	1.16104
$751$	−2.81925	−0.102876	−0.0514379	−	0.998676i	$-0.516380\pi$
$751$	−2.81925	−0.102876	−0.0514379	+	0.998676i	$0.516380\pi$
$752$	−20.7864	−0.758002
$753$	16.6374	0.606299
$754$	−4.27493	−0.155684
$755$	−6.12682	−0.222978
$756$	105.154	3.82441
$757$	25.7620	0.936337	0.468168	−	0.883639i	$-0.344914\pi$
$757$	25.7620	0.936337	0.468168	+	0.883639i	$0.344914\pi$
$758$	−47.6992	−1.73251
$759$	−2.26316	−0.0821476
$760$	−6.93616	−0.251601
$761$	5.05305	0.183173	0.0915864	−	0.995797i	$-0.470806\pi$
$761$	5.05305	0.183173	0.0915864	+	0.995797i	$0.470806\pi$
$762$	−8.59207	−0.311258
$763$	32.8552	1.18944
$764$	59.8898	2.16674
$765$	0.521899	0.0188693
$766$	−73.2562	−2.64685
$767$	−0.648054	−0.0233999
$768$	−49.8197	−1.79771
$769$	26.0837	0.940602	0.470301	−	0.882506i	$-0.344145\pi$
$769$	26.0837	0.940602	0.470301	+	0.882506i	$0.344145\pi$
$770$	11.7054	0.421832
$771$	−9.89448	−0.356341
$772$	20.2198	0.727726
$773$	27.6929	0.996043	0.498021	−	0.867165i	$-0.334060\pi$
$773$	27.6929	0.996043	0.498021	+	0.867165i	$0.334060\pi$
$774$	3.36505	0.120954
$775$	16.2005	0.581940
$776$	−38.6966	−1.38913
$777$	−61.7887	−2.21666
$778$	−13.1999	−0.473239
$779$	−6.41014	−0.229667
$780$	3.23831	0.115950
$781$	−9.72755	−0.348079
$782$	−3.66094	−0.130915
$783$	−16.7622	−0.599033
$784$	59.5834	2.12798
$785$	−8.31943	−0.296933
$786$	45.1752	1.61135
$787$	2.28851	0.0815765	0.0407883	−	0.999168i	$-0.487013\pi$
$787$	2.28851	0.0815765	0.0407883	+	0.999168i	$0.487013\pi$
$788$	43.6171	1.55379
$789$	−2.72385	−0.0969716
$790$	24.1872	0.860541
$791$	−54.1028	−1.92367
$792$	2.63341	0.0935740
$793$	4.46956	0.158719
$794$	20.3643	0.722703
$795$	−3.42089	−0.121326
$796$	−17.2112	−0.610034
$797$	42.7969	1.51594	0.757972	−	0.652287i	$-0.226190\pi$
$797$	42.7969	1.51594	0.757972	+	0.652287i	$0.226190\pi$
$798$	30.2685	1.07149
$799$	6.58689	0.233028
$800$	−2.16807	−0.0766527
$801$	5.95460	0.210396
$802$	6.50161	0.229580
$803$	3.66453	0.129319
$804$	90.5722	3.19423
$805$	5.55730	0.195869
$806$	5.44858	0.191918
$807$	−27.7536	−0.976971
$808$	−76.4777	−2.69048
$809$	45.6299	1.60426	0.802131	−	0.597148i	$-0.203700\pi$
$809$	45.6299	1.60426	0.802131	+	0.597148i	$0.203700\pi$
$810$	15.8594	0.557242
$811$	−10.0620	−0.353323	−0.176661	−	0.984272i	$-0.556530\pi$
$811$	−10.0620	−0.353323	−0.176661	+	0.984272i	$0.556530\pi$
$812$	−57.5639	−2.02010
$813$	−10.3074	−0.361497
$814$	−21.9979	−0.771025
$815$	−2.67877	−0.0938333
$816$	−6.78924	−0.237671
$817$	4.50714	0.157685
$818$	48.5755	1.69840
$819$	1.39078	0.0485979
$820$	−13.9147	−0.485922
$821$	7.69354	0.268506	0.134253	−	0.990947i	$-0.457136\pi$
$821$	7.69354	0.268506	0.134253	+	0.990947i	$0.457136\pi$
$822$	−59.0600	−2.05995
$823$	−49.1667	−1.71384	−0.856921	−	0.515448i	$-0.827626\pi$
$823$	−49.1667	−1.71384	−0.856921	+	0.515448i	$0.827626\pi$
$824$	41.6721	1.45171
$825$	−7.37784	−0.256863
$826$	−13.1489	−0.457508
$827$	1.86119	0.0647198	0.0323599	−	0.999476i	$-0.489698\pi$
$827$	1.86119	0.0647198	0.0323599	+	0.999476i	$0.489698\pi$
$828$	2.53499	0.0880969
$829$	−21.1085	−0.733128	−0.366564	−	0.930393i	$-0.619466\pi$
$829$	−21.1085	−0.733128	−0.366564	+	0.930393i	$0.619466\pi$
$830$	16.9705	0.589055
$831$	48.9663	1.69862
$832$	−4.98947	−0.172979
$833$	−18.8811	−0.654191
$834$	12.3036	0.426040
$835$	17.6335	0.610233
$836$	7.15165	0.247345
$837$	21.3642	0.738453
$838$	−82.9591	−2.86577
$839$	22.0072	0.759774	0.379887	−	0.925033i	$-0.375963\pi$
$839$	22.0072	0.759774	0.379887	+	0.925033i	$0.375963\pi$
$840$	32.4054	1.11809
$841$	−19.8239	−0.683584
$842$	29.4756	1.01580
$843$	35.0698	1.20787
$844$	22.4103	0.771394
$845$	−11.3555	−0.390642
$846$	−6.87259	−0.236285
$847$	47.0168	1.61552
$848$	−8.88017	−0.304946
$849$	10.5534	0.362193
$850$	−11.9345	−0.409351
$851$	−10.4438	−0.358010
$852$	−54.6028	−1.87066
$853$	20.7488	0.710425	0.355213	−	0.934786i	$-0.384408\pi$
$853$	20.7488	0.710425	0.355213	+	0.934786i	$0.384408\pi$
$854$	90.6866	3.10323
$855$	−0.729349	−0.0249432
$856$	−63.7740	−2.17975
$857$	−18.5597	−0.633987	−0.316993	−	0.948428i	$-0.602673\pi$
$857$	−18.5597	−0.633987	−0.316993	+	0.948428i	$0.602673\pi$
$858$	−2.48132	−0.0847110
$859$	48.8721	1.66749	0.833747	−	0.552147i	$-0.186191\pi$
$859$	48.8721	1.66749	0.833747	+	0.552147i	$0.186191\pi$
$860$	9.78378	0.333624
$861$	29.9479	1.02062
$862$	−38.9044	−1.32509
$863$	−17.4500	−0.594004	−0.297002	−	0.954877i	$-0.595987\pi$
$863$	−17.4500	−0.594004	−0.297002	+	0.954877i	$0.595987\pi$
$864$	−2.85910	−0.0972685
$865$	21.7710	0.740235
$866$	18.3125	0.622284
$867$	−24.7330	−0.839977
$868$	73.3677	2.49026
$869$	−12.2996	−0.417237
$870$	−10.4738	−0.355094
$871$	8.39903	0.284590
$872$	32.3823	1.09660
$873$	−4.06902	−0.137715
$874$	5.11613	0.173056
$875$	39.7040	1.34224
$876$	20.5698	0.694990
$877$	9.18644	0.310204	0.155102	−	0.987898i	$-0.450429\pi$
$877$	9.18644	0.310204	0.155102	+	0.987898i	$0.450429\pi$
$878$	47.0745	1.58869
$879$	1.38031	0.0465568
$880$	3.66914	0.123687
$881$	45.1446	1.52096	0.760479	−	0.649362i	$-0.224964\pi$
$881$	45.1446	1.52096	0.760479	+	0.649362i	$0.224964\pi$
$882$	19.7000	0.663335
$883$	−42.7531	−1.43875	−0.719377	−	0.694619i	$-0.755573\pi$
$883$	−42.7531	−1.43875	−0.719377	+	0.694619i	$0.755573\pi$
$884$	−2.66381	−0.0895936
$885$	−1.58776	−0.0533720
$886$	−34.8582	−1.17109
$887$	−21.2224	−0.712577	−0.356289	−	0.934376i	$-0.615958\pi$
$887$	−21.2224	−0.712577	−0.356289	+	0.934376i	$0.615958\pi$
$888$	−60.8994	−2.04365
$889$	−10.7289	−0.359834
$890$	26.0870	0.874439
$891$	−8.06481	−0.270181
$892$	78.9419	2.64317
$893$	−9.20513	−0.308038
$894$	−73.8936	−2.47137
$895$	2.47357	0.0826822
$896$	−96.2593	−3.21580
$897$	−1.17804	−0.0393338
$898$	72.5358	2.42055
$899$	−11.6953	−0.390060
$900$	8.26397	0.275466
$901$	2.81399	0.0937476
$902$	10.6620	0.355005
$903$	−21.0571	−0.700737
$904$	−53.3242	−1.77354
$905$	13.7708	0.457756
$906$	26.3518	0.875481
$907$	−11.1931	−0.371660	−0.185830	−	0.982582i	$-0.559497\pi$
$907$	−11.1931	−0.371660	−0.185830	+	0.982582i	$0.559497\pi$
$908$	11.8200	0.392260
$909$	−8.04176	−0.266728
$910$	6.09300	0.201981
$911$	−41.9453	−1.38971	−0.694855	−	0.719150i	$-0.744532\pi$
$911$	−41.9453	−1.38971	−0.694855	+	0.719150i	$0.744532\pi$
$912$	9.48790	0.314176
$913$	−8.62984	−0.285606
$914$	−51.2128	−1.69397
$915$	10.9506	0.362017
$916$	112.796	3.72688
$917$	56.4100	1.86282
$918$	−15.7385	−0.519446
$919$	−35.4702	−1.17005	−0.585027	−	0.811014i	$-0.698916\pi$
$919$	−35.4702	−1.17005	−0.585027	+	0.811014i	$0.698916\pi$
$920$	5.47732	0.180582
$921$	25.1906	0.830060
$922$	−6.13125	−0.201922
$923$	−5.06348	−0.166667
$924$	−33.4122	−1.09918
$925$	−34.0465	−1.11944
$926$	−18.7076	−0.614770
$927$	4.38189	0.143920
$928$	1.56514	0.0513784
$929$	−24.6247	−0.807911	−0.403956	−	0.914779i	$-0.632365\pi$
$929$	−24.6247	−0.807911	−0.403956	+	0.914779i	$0.632365\pi$
$930$	13.3493	0.437740
$931$	26.3862	0.864771
$932$	−11.6089	−0.380264
$933$	12.0545	0.394648
$934$	11.0747	0.362374
$935$	−1.16270	−0.0380242
$936$	1.37077	0.0448049
$937$	−40.7076	−1.32986	−0.664930	−	0.746905i	$-0.731539\pi$
$937$	−40.7076	−1.32986	−0.664930	+	0.746905i	$0.731539\pi$
$938$	170.415	5.56423
$939$	−22.1474	−0.722752
$940$	−19.9818	−0.651736
$941$	22.7954	0.743109	0.371554	−	0.928411i	$-0.378825\pi$
$941$	22.7954	0.743109	0.371554	+	0.928411i	$0.378825\pi$
$942$	35.7824	1.16585
$943$	5.06193	0.164839
$944$	−4.12162	−0.134147
$945$	23.8910	0.777173
$946$	−7.49671	−0.243739
$947$	27.0133	0.877813	0.438906	−	0.898533i	$-0.355366\pi$
$947$	27.0133	0.877813	0.438906	+	0.898533i	$0.355366\pi$
$948$	−69.0406	−2.24233
$949$	1.90750	0.0619201
$950$	16.6784	0.541119
$951$	2.68779	0.0871575
$952$	−26.6564	−0.863939
$953$	18.2096	0.589867	0.294933	−	0.955518i	$-0.404703\pi$
$953$	18.2096	0.589867	0.294933	+	0.955518i	$0.404703\pi$
$954$	−2.93604	−0.0950579
$955$	13.6070	0.440311
$956$	−51.5743	−1.66803
$957$	5.32612	0.172169
$958$	−17.1168	−0.553019
$959$	−73.7478	−2.38144
$960$	−12.2244	−0.394542
$961$	−16.0939	−0.519157
$962$	−11.4506	−0.369181
$963$	−6.70595	−0.216096
$964$	−54.3894	−1.75176
$965$	4.59393	0.147884
$966$	−23.9023	−0.769044
$967$	44.9168	1.44443	0.722213	−	0.691671i	$-0.243125\pi$
$967$	44.9168	1.44443	0.722213	+	0.691671i	$0.243125\pi$
$968$	46.3402	1.48943
$969$	−3.00657	−0.0965850
$970$	−17.8263	−0.572368
$971$	44.7003	1.43450	0.717251	−	0.696815i	$-0.245400\pi$
$971$	44.7003	1.43450	0.717251	+	0.696815i	$0.245400\pi$
$972$	20.2416	0.649249
$973$	15.3634	0.492529
$974$	3.07204	0.0984345
$975$	−3.84039	−0.122991
$976$	28.4264	0.909908
$977$	56.6433	1.81218	0.906089	−	0.423086i	$-0.139053\pi$
$977$	56.6433	1.81218	0.906089	+	0.423086i	$0.139053\pi$
$978$	11.5216	0.368419
$979$	−13.2658	−0.423976
$980$	57.2772	1.82965
$981$	3.40506	0.108715
$982$	−14.9907	−0.478372
$983$	5.71416	0.182253	0.0911267	−	0.995839i	$-0.470953\pi$
$983$	5.71416	0.182253	0.0911267	+	0.995839i	$0.470953\pi$
$984$	29.5169	0.940963
$985$	9.90980	0.315752
$986$	8.61564	0.274378
$987$	43.0059	1.36889
$988$	3.72265	0.118433
$989$	−3.55917	−0.113175
$990$	1.21313	0.0385557
$991$	−59.4451	−1.88833	−0.944167	−	0.329467i	$-0.893131\pi$
$991$	−59.4451	−1.88833	−0.944167	+	0.329467i	$0.893131\pi$
$992$	−1.99484	−0.0633363
$993$	29.4661	0.935077
$994$	−102.737	−3.25862
$995$	−3.91038	−0.123967
$996$	−48.4411	−1.53492
$997$	−31.3308	−0.992255	−0.496128	−	0.868250i	$-0.665245\pi$
$997$	−31.3308	−0.992255	−0.496128	+	0.868250i	$0.665245\pi$
$998$	84.8215	2.68498
$999$	−44.8982	−1.42052

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.c.1.19	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.c.1.19	✓	259	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6043 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.43851 q^{2} +1.58144 q^{3} +3.94631 q^{4} +0.896601 q^{5} -3.85634 q^{6} -4.81539 q^{7} -4.74608 q^{8} -0.499059 q^{9} +O(q^{10})\)	\(q-2.43851 q^{2} +1.58144 q^{3} +3.94631 q^{4} +0.896601 q^{5} -3.85634 q^{6} -4.81539 q^{7} -4.74608 q^{8} -0.499059 q^{9} -2.18637 q^{10} +1.11181 q^{11} +6.24084 q^{12} +0.578731 q^{13} +11.7423 q^{14} +1.41792 q^{15} +3.68073 q^{16} -1.16637 q^{17} +1.21696 q^{18} +1.62999 q^{19} +3.53827 q^{20} -7.61523 q^{21} -2.71116 q^{22} -1.28716 q^{23} -7.50563 q^{24} -4.19611 q^{25} -1.41124 q^{26} -5.53354 q^{27} -19.0030 q^{28} +3.02920 q^{29} -3.45760 q^{30} -3.86085 q^{31} +0.516685 q^{32} +1.75826 q^{33} +2.84419 q^{34} -4.31748 q^{35} -1.96944 q^{36} +8.11384 q^{37} -3.97474 q^{38} +0.915227 q^{39} -4.25534 q^{40} -3.93263 q^{41} +18.5698 q^{42} +2.76513 q^{43} +4.38755 q^{44} -0.447457 q^{45} +3.13875 q^{46} -5.64736 q^{47} +5.82084 q^{48} +16.1879 q^{49} +10.2322 q^{50} -1.84454 q^{51} +2.28385 q^{52} -2.41261 q^{53} +13.4936 q^{54} +0.996851 q^{55} +22.8542 q^{56} +2.57772 q^{57} -7.38673 q^{58} -1.11978 q^{59} +5.59554 q^{60} +7.72304 q^{61} +9.41470 q^{62} +2.40316 q^{63} -8.62140 q^{64} +0.518891 q^{65} -4.28752 q^{66} +14.5128 q^{67} -4.60285 q^{68} -2.03556 q^{69} +10.5282 q^{70} -8.74928 q^{71} +2.36857 q^{72} +3.29600 q^{73} -19.7856 q^{74} -6.63587 q^{75} +6.43244 q^{76} -5.35380 q^{77} -2.23179 q^{78} -11.0627 q^{79} +3.30015 q^{80} -7.25376 q^{81} +9.58974 q^{82} -7.76197 q^{83} -30.0520 q^{84} -1.04577 q^{85} -6.74279 q^{86} +4.79049 q^{87} -5.27675 q^{88} -11.9317 q^{89} +1.09113 q^{90} -2.78681 q^{91} -5.07954 q^{92} -6.10569 q^{93} +13.7711 q^{94} +1.46145 q^{95} +0.817105 q^{96} +8.15339 q^{97} -39.4744 q^{98} -0.554859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more