LMFDB - Embedded newform 6025.2.a.l.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.19733 q^{2} -1.42352 q^{3} -0.566401 q^{4} +1.70442 q^{6} +1.72539 q^{7} +3.07283 q^{8} -0.973586 q^{9} +O(q^{10})$	\(q-1.19733 q^{2} -1.42352 q^{3} -0.566401 q^{4} +1.70442 q^{6} +1.72539 q^{7} +3.07283 q^{8} -0.973586 q^{9} -6.17385 q^{11} +0.806284 q^{12} -2.79588 q^{13} -2.06586 q^{14} -2.54639 q^{16} -1.90115 q^{17} +1.16570 q^{18} +1.36836 q^{19} -2.45613 q^{21} +7.39214 q^{22} -1.31640 q^{23} -4.37424 q^{24} +3.34759 q^{26} +5.65649 q^{27} -0.977261 q^{28} +6.68157 q^{29} +9.60519 q^{31} -3.09679 q^{32} +8.78861 q^{33} +2.27631 q^{34} +0.551440 q^{36} -2.69095 q^{37} -1.63838 q^{38} +3.97999 q^{39} +0.155986 q^{41} +2.94079 q^{42} -1.63333 q^{43} +3.49688 q^{44} +1.57616 q^{46} +0.0487425 q^{47} +3.62484 q^{48} -4.02304 q^{49} +2.70633 q^{51} +1.58359 q^{52} +6.75445 q^{53} -6.77268 q^{54} +5.30182 q^{56} -1.94790 q^{57} -8.00004 q^{58} +10.9324 q^{59} -8.73706 q^{61} -11.5006 q^{62} -1.67981 q^{63} +8.80066 q^{64} -10.5229 q^{66} +2.97531 q^{67} +1.07682 q^{68} +1.87392 q^{69} -7.62061 q^{71} -2.99166 q^{72} -12.3685 q^{73} +3.22196 q^{74} -0.775043 q^{76} -10.6523 q^{77} -4.76537 q^{78} +12.3265 q^{79} -5.13137 q^{81} -0.186766 q^{82} +0.436831 q^{83} +1.39115 q^{84} +1.95563 q^{86} -9.51135 q^{87} -18.9712 q^{88} +5.40917 q^{89} -4.82397 q^{91} +0.745609 q^{92} -13.6732 q^{93} -0.0583608 q^{94} +4.40835 q^{96} +15.2058 q^{97} +4.81690 q^{98} +6.01078 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9	$ 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9} + q^{11} - 14 q^{12} - 9 q^{13} - q^{14} + 43 q^{16} - 12 q^{17} - 42 q^{18} + 2 q^{21} - 5 q^{22} - 77 q^{23} - 2 q^{24} + 2 q^{26} - 38 q^{27} - 42 q^{28} + 2 q^{29} + q^{31} - 72 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 28 q^{37} - 23 q^{38} - 2 q^{39} - 2 q^{41} - 37 q^{42} - 31 q^{43} + 3 q^{44} + 14 q^{46} - 96 q^{47} - 13 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 54 q^{53} + 4 q^{54} - 15 q^{56} - 37 q^{57} - 27 q^{58} + q^{59} + 5 q^{61} - 39 q^{62} - 70 q^{63} + 65 q^{64} - 52 q^{66} - 34 q^{67} - 52 q^{68} + 21 q^{69} - 9 q^{71} - 70 q^{72} - 25 q^{73} + 22 q^{74} - 47 q^{76} - 54 q^{77} - 58 q^{78} + 13 q^{79} + 12 q^{81} + 5 q^{82} - 63 q^{83} + 95 q^{84} - 18 q^{86} - 47 q^{87} - 13 q^{88} + 19 q^{89} - 31 q^{91} - 137 q^{92} - 52 q^{93} + 120 q^{94} - 49 q^{96} - 36 q^{97} - 64 q^{98} + 16 q^{99}+O(q^{100}) $ 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9 + q^11 - 14 * q^12 - 9 * q^13 - q^14 + 43 * q^16 - 12 * q^17 - 42 * q^18 + 2 * q^21 - 5 * q^22 - 77 * q^23 - 2 * q^24 + 2 * q^26 - 38 * q^27 - 42 * q^28 + 2 * q^29 + q^31 - 72 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 28 * q^37 - 23 * q^38 - 2 * q^39 - 2 * q^41 - 37 * q^42 - 31 * q^43 + 3 * q^44 + 14 * q^46 - 96 * q^47 - 13 * q^48 + 40 * q^49 - 10 * q^51 - 42 * q^52 - 54 * q^53 + 4 * q^54 - 15 * q^56 - 37 * q^57 - 27 * q^58 + q^59 + 5 * q^61 - 39 * q^62 - 70 * q^63 + 65 * q^64 - 52 * q^66 - 34 * q^67 - 52 * q^68 + 21 * q^69 - 9 * q^71 - 70 * q^72 - 25 * q^73 + 22 * q^74 - 47 * q^76 - 54 * q^77 - 58 * q^78 + 13 * q^79 + 12 * q^81 + 5 * q^82 - 63 * q^83 + 95 * q^84 - 18 * q^86 - 47 * q^87 - 13 * q^88 + 19 * q^89 - 31 * q^91 - 137 * q^92 - 52 * q^93 + 120 * q^94 - 49 * q^96 - 36 * q^97 - 64 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.19733	−0.846640	−0.423320	−	0.905980i	$-0.639135\pi$
$2$	−1.19733	−0.846640	−0.423320	+	0.905980i	$0.639135\pi$
$3$	−1.42352	−0.821871	−0.410935	−	0.911665i	$-0.634798\pi$
$3$	−1.42352	−0.821871	−0.410935	+	0.911665i	$0.634798\pi$
$4$	−0.566401	−0.283201
$5$	0	0
$5$	0	0
$6$	1.70442	0.695829
$7$	1.72539	0.652135	0.326068	−	0.945346i	$-0.394276\pi$
$7$	1.72539	0.652135	0.326068	+	0.945346i	$0.394276\pi$
$8$	3.07283	1.08641
$9$	−0.973586	−0.324529
$10$	0	0
$11$	−6.17385	−1.86149	−0.930743	−	0.365674i	$-0.880839\pi$
$11$	−6.17385	−1.86149	−0.930743	+	0.365674i	$0.880839\pi$
$12$	0.806284	0.232754
$13$	−2.79588	−0.775437	−0.387719	−	0.921778i	$-0.626737\pi$
$13$	−2.79588	−0.775437	−0.387719	+	0.921778i	$0.626737\pi$
$14$	−2.06586	−0.552124
$15$	0	0
$16$	−2.54639	−0.636597
$17$	−1.90115	−0.461097	−0.230549	−	0.973061i	$-0.574052\pi$
$17$	−1.90115	−0.461097	−0.230549	+	0.973061i	$0.574052\pi$
$18$	1.16570	0.274759
$19$	1.36836	0.313924	0.156962	−	0.987605i	$-0.449830\pi$
$19$	1.36836	0.313924	0.156962	+	0.987605i	$0.449830\pi$
$20$	0	0
$21$	−2.45613	−0.535971
$22$	7.39214	1.57601
$23$	−1.31640	−0.274488	−0.137244	−	0.990537i	$-0.543824\pi$
$23$	−1.31640	−0.274488	−0.137244	+	0.990537i	$0.543824\pi$
$24$	−4.37424	−0.892888
$25$	0	0
$26$	3.34759	0.656516
$27$	5.65649	1.08859
$28$	−0.977261	−0.184685
$29$	6.68157	1.24074	0.620368	−	0.784311i	$-0.286983\pi$
$29$	6.68157	1.24074	0.620368	+	0.784311i	$0.286983\pi$
$30$	0	0
$31$	9.60519	1.72514	0.862571	−	0.505936i	$-0.168853\pi$
$31$	9.60519	1.72514	0.862571	+	0.505936i	$0.168853\pi$
$32$	−3.09679	−0.547441
$33$	8.78861	1.52990
$34$	2.27631	0.390384
$35$	0	0
$36$	0.551440	0.0919067
$37$	−2.69095	−0.442390	−0.221195	−	0.975230i	$-0.570996\pi$
$37$	−2.69095	−0.442390	−0.221195	+	0.975230i	$0.570996\pi$
$38$	−1.63838	−0.265781
$39$	3.97999	0.637309
$40$	0	0
$41$	0.155986	0.0243609	0.0121804	−	0.999926i	$-0.496123\pi$
$41$	0.155986	0.0243609	0.0121804	+	0.999926i	$0.496123\pi$
$42$	2.94079	0.453774
$43$	−1.63333	−0.249080	−0.124540	−	0.992215i	$-0.539746\pi$
$43$	−1.63333	−0.249080	−0.124540	+	0.992215i	$0.539746\pi$
$44$	3.49688	0.527174
$45$	0	0
$46$	1.57616	0.232392
$47$	0.0487425	0.00710982	0.00355491	−	0.999994i	$-0.498868\pi$
$47$	0.0487425	0.00710982	0.00355491	+	0.999994i	$0.498868\pi$
$48$	3.62484	0.523200
$49$	−4.02304	−0.574720
$50$	0	0
$51$	2.70633	0.378962
$52$	1.58359	0.219604
$53$	6.75445	0.927795	0.463898	−	0.885889i	$-0.346451\pi$
$53$	6.75445	0.927795	0.463898	+	0.885889i	$0.346451\pi$
$54$	−6.77268	−0.921645
$55$	0	0
$56$	5.30182	0.708486
$57$	−1.94790	−0.258005
$58$	−8.00004	−1.05046
$59$	10.9324	1.42328	0.711639	−	0.702546i	$-0.247953\pi$
$59$	10.9324	1.42328	0.711639	+	0.702546i	$0.247953\pi$
$60$	0	0
$61$	−8.73706	−1.11867	−0.559333	−	0.828943i	$-0.688943\pi$
$61$	−8.73706	−1.11867	−0.559333	+	0.828943i	$0.688943\pi$
$62$	−11.5006	−1.46057
$63$	−1.67981	−0.211637
$64$	8.80066	1.10008
$65$	0	0
$66$	−10.5229	−1.29528
$67$	2.97531	0.363493	0.181746	−	0.983345i	$-0.441825\pi$
$67$	2.97531	0.363493	0.181746	+	0.983345i	$0.441825\pi$
$68$	1.07682	0.130583
$69$	1.87392	0.225593
$70$	0	0
$71$	−7.62061	−0.904400	−0.452200	−	0.891917i	$-0.649361\pi$
$71$	−7.62061	−0.904400	−0.452200	+	0.891917i	$0.649361\pi$
$72$	−2.99166	−0.352571
$73$	−12.3685	−1.44762	−0.723810	−	0.689999i	$-0.757611\pi$
$73$	−12.3685	−1.44762	−0.723810	+	0.689999i	$0.757611\pi$
$74$	3.22196	0.374545
$75$	0	0
$76$	−0.775043	−0.0889035
$77$	−10.6523	−1.21394
$78$	−4.76537	−0.539571
$79$	12.3265	1.38684	0.693421	−	0.720532i	$-0.256103\pi$
$79$	12.3265	1.38684	0.693421	+	0.720532i	$0.256103\pi$
$80$	0	0
$81$	−5.13137	−0.570152
$82$	−0.186766	−0.0206249
$83$	0.436831	0.0479485	0.0239742	−	0.999713i	$-0.492368\pi$
$83$	0.436831	0.0479485	0.0239742	+	0.999713i	$0.492368\pi$
$84$	1.39115	0.151787
$85$	0	0
$86$	1.95563	0.210881
$87$	−9.51135	−1.01972
$88$	−18.9712	−2.02234
$89$	5.40917	0.573371	0.286685	−	0.958025i	$-0.407447\pi$
$89$	5.40917	0.573371	0.286685	+	0.958025i	$0.407447\pi$
$90$	0	0
$91$	−4.82397	−0.505690
$92$	0.745609	0.0777351
$93$	−13.6732	−1.41784
$94$	−0.0583608	−0.00601946
$95$	0	0
$96$	4.40835	0.449925
$97$	15.2058	1.54391	0.771956	−	0.635676i	$-0.219278\pi$
$97$	15.2058	1.54391	0.771956	+	0.635676i	$0.219278\pi$
$98$	4.81690	0.486581
$99$	6.01078	0.604106
$100$	0	0
$101$	4.61339	0.459050	0.229525	−	0.973303i	$-0.426283\pi$
$101$	4.61339	0.459050	0.229525	+	0.973303i	$0.426283\pi$
$102$	−3.24037	−0.320845
$103$	9.04544	0.891274	0.445637	−	0.895214i	$-0.352977\pi$
$103$	9.04544	0.891274	0.445637	+	0.895214i	$0.352977\pi$
$104$	−8.59126	−0.842442
$105$	0	0
$106$	−8.08731	−0.785509
$107$	−18.4103	−1.77979	−0.889896	−	0.456163i	$-0.849224\pi$
$107$	−18.4103	−1.77979	−0.889896	+	0.456163i	$0.849224\pi$
$108$	−3.20384	−0.308290
$109$	15.8124	1.51455	0.757275	−	0.653096i	$-0.226530\pi$
$109$	15.8124	1.51455	0.757275	+	0.653096i	$0.226530\pi$
$110$	0	0
$111$	3.83063	0.363587
$112$	−4.39351	−0.415147
$113$	−17.1997	−1.61801	−0.809004	−	0.587803i	$-0.799993\pi$
$113$	−17.1997	−1.61801	−0.809004	+	0.587803i	$0.799993\pi$
$114$	2.33227	0.218437
$115$	0	0
$116$	−3.78445	−0.351377
$117$	2.72203	0.251652
$118$	−13.0897	−1.20500
$119$	−3.28023	−0.300698
$120$	0	0
$121$	27.1164	2.46513
$122$	10.4611	0.947108
$123$	−0.222049	−0.0200215
$124$	−5.44039	−0.488561
$125$	0	0
$126$	2.01129	0.179180
$127$	−18.5423	−1.64536	−0.822682	−	0.568502i	$-0.807523\pi$
$127$	−18.5423	−1.64536	−0.822682	+	0.568502i	$0.807523\pi$
$128$	−4.34371	−0.383933
$129$	2.32508	0.204712
$130$	0	0
$131$	−11.9909	−1.04765	−0.523826	−	0.851825i	$-0.675496\pi$
$131$	−11.9909	−1.04765	−0.523826	+	0.851825i	$0.675496\pi$
$132$	−4.97788	−0.433269
$133$	2.36096	0.204721
$134$	−3.56243	−0.307747
$135$	0	0
$136$	−5.84192	−0.500940
$137$	1.06552	0.0910337	0.0455168	−	0.998964i	$-0.485507\pi$
$137$	1.06552	0.0910337	0.0455168	+	0.998964i	$0.485507\pi$
$138$	−2.24370	−0.190996
$139$	16.5298	1.40204	0.701020	−	0.713142i	$-0.252728\pi$
$139$	16.5298	1.40204	0.701020	+	0.713142i	$0.252728\pi$
$140$	0	0
$141$	−0.0693860	−0.00584335
$142$	9.12438	0.765701
$143$	17.2613	1.44347
$144$	2.47913	0.206594
$145$	0	0
$146$	14.8091	1.22561
$147$	5.72688	0.472345
$148$	1.52416	0.125285
$149$	11.4161	0.935240	0.467620	−	0.883930i	$-0.345112\pi$
$149$	11.4161	0.935240	0.467620	+	0.883930i	$0.345112\pi$
$150$	0	0
$151$	−0.573648	−0.0466828	−0.0233414	−	0.999728i	$-0.507430\pi$
$151$	−0.573648	−0.0466828	−0.0233414	+	0.999728i	$0.507430\pi$
$152$	4.20475	0.341050
$153$	1.85094	0.149639
$154$	12.7543	1.02777
$155$	0	0
$156$	−2.25427	−0.180486
$157$	10.2946	0.821596	0.410798	−	0.911726i	$-0.365250\pi$
$157$	10.2946	0.821596	0.410798	+	0.911726i	$0.365250\pi$
$158$	−14.7589	−1.17416
$159$	−9.61511	−0.762528
$160$	0	0
$161$	−2.27130	−0.179003
$162$	6.14394	0.482714
$163$	15.9520	1.24945	0.624727	−	0.780844i	$-0.285210\pi$
$163$	15.9520	1.24945	0.624727	+	0.780844i	$0.285210\pi$
$164$	−0.0883504	−0.00689901
$165$	0	0
$166$	−0.523031	−0.0405951
$167$	−5.68362	−0.439812	−0.219906	−	0.975521i	$-0.570575\pi$
$167$	−5.68362	−0.439812	−0.219906	+	0.975521i	$0.570575\pi$
$168$	−7.54726	−0.582283
$169$	−5.18306	−0.398697
$170$	0	0
$171$	−1.33222	−0.101877
$172$	0.925120	0.0705397
$173$	−19.5494	−1.48631	−0.743155	−	0.669119i	$-0.766672\pi$
$173$	−19.5494	−1.48631	−0.743155	+	0.669119i	$0.766672\pi$
$174$	11.3882	0.863339
$175$	0	0
$176$	15.7210	1.18502
$177$	−15.5625	−1.16975
$178$	−6.47656	−0.485438
$179$	16.5033	1.23351	0.616757	−	0.787154i	$-0.288446\pi$
$179$	16.5033	1.23351	0.616757	+	0.787154i	$0.288446\pi$
$180$	0	0
$181$	−7.21117	−0.536002	−0.268001	−	0.963419i	$-0.586363\pi$
$181$	−7.21117	−0.536002	−0.268001	+	0.963419i	$0.586363\pi$
$182$	5.77589	0.428137
$183$	12.4374	0.919399
$184$	−4.04506	−0.298206
$185$	0	0
$186$	16.3713	1.20040
$187$	11.7374	0.858326
$188$	−0.0276078	−0.00201350
$189$	9.75963	0.709909
$190$	0	0
$191$	−14.5999	−1.05641	−0.528206	−	0.849117i	$-0.677135\pi$
$191$	−14.5999	−1.05641	−0.528206	+	0.849117i	$0.677135\pi$
$192$	−12.5279	−0.904125
$193$	11.4173	0.821838	0.410919	−	0.911672i	$-0.365208\pi$
$193$	11.4173	0.821838	0.410919	+	0.911672i	$0.365208\pi$
$194$	−18.2063	−1.30714
$195$	0	0
$196$	2.27865	0.162761
$197$	15.4656	1.10188	0.550938	−	0.834546i	$-0.314270\pi$
$197$	15.4656	1.10188	0.550938	+	0.834546i	$0.314270\pi$
$198$	−7.19688	−0.511460
$199$	7.92904	0.562075	0.281037	−	0.959697i	$-0.409321\pi$
$199$	7.92904	0.562075	0.281037	+	0.959697i	$0.409321\pi$
$200$	0	0
$201$	−4.23542	−0.298744
$202$	−5.52376	−0.388650
$203$	11.5283	0.809127
$204$	−1.53287	−0.107322
$205$	0	0
$206$	−10.8304	−0.754588
$207$	1.28163	0.0890792
$208$	7.11939	0.493641
$209$	−8.44808	−0.584366
$210$	0	0
$211$	−4.26053	−0.293307	−0.146654	−	0.989188i	$-0.546850\pi$
$211$	−4.26053	−0.293307	−0.146654	+	0.989188i	$0.546850\pi$
$212$	−3.82573	−0.262752
$213$	10.8481	0.743300
$214$	22.0432	1.50684
$215$	0	0
$216$	17.3814	1.18266
$217$	16.5727	1.12503
$218$	−18.9326	−1.28228
$219$	17.6068	1.18976
$220$	0	0
$221$	5.31539	0.357552
$222$	−4.58652	−0.307827
$223$	11.5115	0.770866	0.385433	−	0.922736i	$-0.374052\pi$
$223$	11.5115	0.770866	0.385433	+	0.922736i	$0.374052\pi$
$224$	−5.34317	−0.357005
$225$	0	0
$226$	20.5937	1.36987
$227$	−18.9175	−1.25560	−0.627800	−	0.778375i	$-0.716044\pi$
$227$	−18.9175	−1.25560	−0.627800	+	0.778375i	$0.716044\pi$
$228$	1.10329	0.0730672
$229$	−24.9889	−1.65131	−0.825656	−	0.564174i	$-0.809195\pi$
$229$	−24.9889	−1.65131	−0.825656	+	0.564174i	$0.809195\pi$
$230$	0	0
$231$	15.1638	0.997702
$232$	20.5313	1.34795
$233$	−9.08578	−0.595230	−0.297615	−	0.954686i	$-0.596191\pi$
$233$	−9.08578	−0.595230	−0.297615	+	0.954686i	$0.596191\pi$
$234$	−3.25917	−0.213058
$235$	0	0
$236$	−6.19212	−0.403073
$237$	−17.5471	−1.13981
$238$	3.92751	0.254583
$239$	10.8904	0.704444	0.352222	−	0.935917i	$-0.385426\pi$
$239$	10.8904	0.704444	0.352222	+	0.935917i	$0.385426\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−32.4673	−2.08708
$243$	−9.66484	−0.620000
$244$	4.94868	0.316807
$245$	0	0
$246$	0.265866	0.0169510
$247$	−3.82578	−0.243429
$248$	29.5151	1.87421
$249$	−0.621839	−0.0394074
$250$	0	0
$251$	26.6336	1.68110	0.840549	−	0.541735i	$-0.182232\pi$
$251$	26.6336	1.68110	0.840549	+	0.541735i	$0.182232\pi$
$252$	0.951448	0.0599356
$253$	8.12724	0.510955
$254$	22.2013	1.39303
$255$	0	0
$256$	−12.4005	−0.775029
$257$	−14.5757	−0.909209	−0.454605	−	0.890693i	$-0.650219\pi$
$257$	−14.5757	−0.909209	−0.454605	+	0.890693i	$0.650219\pi$
$258$	−2.78389	−0.173317
$259$	−4.64293	−0.288498
$260$	0	0
$261$	−6.50508	−0.402654
$262$	14.3571	0.886984
$263$	9.44976	0.582697	0.291348	−	0.956617i	$-0.405896\pi$
$263$	9.44976	0.582697	0.291348	+	0.956617i	$0.405896\pi$
$264$	27.0059	1.66210
$265$	0	0
$266$	−2.82685	−0.173325
$267$	−7.70007	−0.471236
$268$	−1.68522	−0.102941
$269$	−4.96272	−0.302582	−0.151291	−	0.988489i	$-0.548343\pi$
$269$	−4.96272	−0.302582	−0.151291	+	0.988489i	$0.548343\pi$
$270$	0	0
$271$	12.6343	0.767481	0.383741	−	0.923441i	$-0.374636\pi$
$271$	12.6343	0.767481	0.383741	+	0.923441i	$0.374636\pi$
$272$	4.84107	0.293533
$273$	6.86703	0.415612
$274$	−1.27578	−0.0770728
$275$	0	0
$276$	−1.06139	−0.0638882
$277$	0.721964	0.0433786	0.0216893	−	0.999765i	$-0.493096\pi$
$277$	0.721964	0.0433786	0.0216893	+	0.999765i	$0.493096\pi$
$278$	−19.7916	−1.18702
$279$	−9.35148	−0.559858
$280$	0	0
$281$	17.3231	1.03341	0.516705	−	0.856163i	$-0.327158\pi$
$281$	17.3231	1.03341	0.516705	+	0.856163i	$0.327158\pi$
$282$	0.0830779	0.00494722
$283$	−20.6064	−1.22493	−0.612463	−	0.790499i	$-0.709821\pi$
$283$	−20.6064	−1.22493	−0.612463	+	0.790499i	$0.709821\pi$
$284$	4.31632	0.256127
$285$	0	0
$286$	−20.6675	−1.22210
$287$	0.269136	0.0158866
$288$	3.01499	0.177660
$289$	−13.3856	−0.787389
$290$	0	0
$291$	−21.6457	−1.26890
$292$	7.00552	0.409967
$293$	23.1972	1.35520	0.677598	−	0.735433i	$-0.263021\pi$
$293$	23.1972	1.35520	0.677598	+	0.735433i	$0.263021\pi$
$294$	−6.85697	−0.399906
$295$	0	0
$296$	−8.26883	−0.480616
$297$	−34.9223	−2.02640
$298$	−13.6688	−0.791811
$299$	3.68049	0.212848
$300$	0	0
$301$	−2.81813	−0.162434
$302$	0.686846	0.0395235
$303$	−6.56727	−0.377280
$304$	−3.48439	−0.199843
$305$	0	0
$306$	−2.21618	−0.126691
$307$	−21.3639	−1.21930	−0.609650	−	0.792671i	$-0.708690\pi$
$307$	−21.3639	−1.21930	−0.609650	+	0.792671i	$0.708690\pi$
$308$	6.03347	0.343789
$309$	−12.8764	−0.732512
$310$	0	0
$311$	−30.7686	−1.74473	−0.872364	−	0.488857i	$-0.837414\pi$
$311$	−30.7686	−1.74473	−0.872364	+	0.488857i	$0.837414\pi$
$312$	12.2298	0.692378
$313$	−15.7822	−0.892062	−0.446031	−	0.895017i	$-0.647163\pi$
$313$	−15.7822	−0.892062	−0.446031	+	0.895017i	$0.647163\pi$
$314$	−12.3260	−0.695596
$315$	0	0
$316$	−6.98176	−0.392755
$317$	9.38322	0.527014	0.263507	−	0.964657i	$-0.415121\pi$
$317$	9.38322	0.527014	0.263507	+	0.964657i	$0.415121\pi$
$318$	11.5125	0.645587
$319$	−41.2510	−2.30961
$320$	0	0
$321$	26.2075	1.46276
$322$	2.71949	0.151551
$323$	−2.60147	−0.144750
$324$	2.90641	0.161467
$325$	0	0
$326$	−19.0997	−1.05784
$327$	−22.5093	−1.24476
$328$	0.479317	0.0264659
$329$	0.0840996	0.00463656
$330$	0	0
$331$	−14.3794	−0.790364	−0.395182	−	0.918603i	$-0.629318\pi$
$331$	−14.3794	−0.790364	−0.395182	+	0.918603i	$0.629318\pi$
$332$	−0.247422	−0.0135790
$333$	2.61987	0.143568
$334$	6.80517	0.372362
$335$	0	0
$336$	6.25425	0.341197
$337$	29.4516	1.60433	0.802166	−	0.597101i	$-0.203681\pi$
$337$	29.4516	1.60433	0.802166	+	0.597101i	$0.203681\pi$
$338$	6.20583	0.337553
$339$	24.4841	1.32979
$340$	0	0
$341$	−59.3010	−3.21133
$342$	1.59511	0.0862535
$343$	−19.0190	−1.02693
$344$	−5.01894	−0.270603
$345$	0	0
$346$	23.4070	1.25837
$347$	−18.4264	−0.989182	−0.494591	−	0.869126i	$-0.664682\pi$
$347$	−18.4264	−0.989182	−0.494591	+	0.869126i	$0.664682\pi$
$348$	5.38724	0.288786
$349$	16.8493	0.901923	0.450961	−	0.892543i	$-0.351081\pi$
$349$	16.8493	0.901923	0.450961	+	0.892543i	$0.351081\pi$
$350$	0	0
$351$	−15.8148	−0.844134
$352$	19.1191	1.01905
$353$	−12.7356	−0.677845	−0.338923	−	0.940814i	$-0.610063\pi$
$353$	−12.7356	−0.677845	−0.338923	+	0.940814i	$0.610063\pi$
$354$	18.6335	0.990357
$355$	0	0
$356$	−3.06376	−0.162379
$357$	4.66947	0.247135
$358$	−19.7599	−1.04434
$359$	17.8134	0.940156	0.470078	−	0.882625i	$-0.344226\pi$
$359$	17.8134	0.940156	0.470078	+	0.882625i	$0.344226\pi$
$360$	0	0
$361$	−17.1276	−0.901452
$362$	8.63414	0.453801
$363$	−38.6008	−2.02602
$364$	2.73230	0.143212
$365$	0	0
$366$	−14.8917	−0.778400
$367$	3.38112	0.176493	0.0882466	−	0.996099i	$-0.471874\pi$
$367$	3.38112	0.176493	0.0882466	+	0.996099i	$0.471874\pi$
$368$	3.35206	0.174738
$369$	−0.151865	−0.00790580
$370$	0	0
$371$	11.6540	0.605048
$372$	7.74451	0.401534
$373$	32.8739	1.70215	0.851074	−	0.525046i	$-0.175952\pi$
$373$	32.8739	1.70215	0.851074	+	0.525046i	$0.175952\pi$
$374$	−14.0536	−0.726694
$375$	0	0
$376$	0.149777	0.00772417
$377$	−18.6809	−0.962113
$378$	−11.6855	−0.601037
$379$	−20.0923	−1.03207	−0.516035	−	0.856568i	$-0.672592\pi$
$379$	−20.0923	−1.03207	−0.516035	+	0.856568i	$0.672592\pi$
$380$	0	0
$381$	26.3954	1.35228
$382$	17.4809	0.894400
$383$	−24.1985	−1.23649	−0.618243	−	0.785987i	$-0.712155\pi$
$383$	−24.1985	−1.23649	−0.618243	+	0.785987i	$0.712155\pi$
$384$	6.18336	0.315543
$385$	0	0
$386$	−13.6703	−0.695801
$387$	1.59019	0.0808338
$388$	−8.61257	−0.437237
$389$	−22.9528	−1.16376	−0.581878	−	0.813276i	$-0.697682\pi$
$389$	−22.9528	−1.16376	−0.581878	+	0.813276i	$0.697682\pi$
$390$	0	0
$391$	2.50267	0.126566
$392$	−12.3621	−0.624381
$393$	17.0693	0.861034
$394$	−18.5174	−0.932893
$395$	0	0
$396$	−3.40451	−0.171083
$397$	15.1981	0.762773	0.381387	−	0.924416i	$-0.375447\pi$
$397$	15.1981	0.762773	0.381387	+	0.924416i	$0.375447\pi$
$398$	−9.49368	−0.475875
$399$	−3.36088	−0.168254
$400$	0	0
$401$	−26.5457	−1.32563	−0.662814	−	0.748784i	$-0.730638\pi$
$401$	−26.5457	−1.32563	−0.662814	+	0.748784i	$0.730638\pi$
$402$	5.07120	0.252929
$403$	−26.8549	−1.33774
$404$	−2.61303	−0.130003
$405$	0	0
$406$	−13.8032	−0.685040
$407$	16.6135	0.823502
$408$	8.31610	0.411708
$409$	−12.0385	−0.595267	−0.297634	−	0.954680i	$-0.596197\pi$
$409$	−12.0385	−0.595267	−0.297634	+	0.954680i	$0.596197\pi$
$410$	0	0
$411$	−1.51679	−0.0748179
$412$	−5.12335	−0.252409
$413$	18.8626	0.928169
$414$	−1.53453	−0.0754180
$415$	0	0
$416$	8.65825	0.424506
$417$	−23.5305	−1.15230
$418$	10.1151	0.494747
$419$	−15.2708	−0.746028	−0.373014	−	0.927826i	$-0.621676\pi$
$419$	−15.2708	−0.746028	−0.373014	+	0.927826i	$0.621676\pi$
$420$	0	0
$421$	−33.7625	−1.64548	−0.822741	−	0.568417i	$-0.807556\pi$
$421$	−33.7625	−1.64548	−0.822741	+	0.568417i	$0.807556\pi$
$422$	5.10126	0.248326
$423$	−0.0474550	−0.00230734
$424$	20.7553	1.00797
$425$	0	0
$426$	−12.9888	−0.629307
$427$	−15.0748	−0.729522
$428$	10.4276	0.504038
$429$	−24.5719	−1.18634
$430$	0	0
$431$	−1.76033	−0.0847919	−0.0423960	−	0.999101i	$-0.513499\pi$
$431$	−1.76033	−0.0847919	−0.0423960	+	0.999101i	$0.513499\pi$
$432$	−14.4036	−0.692994
$433$	9.99580	0.480367	0.240184	−	0.970727i	$-0.422792\pi$
$433$	9.99580	0.480367	0.240184	+	0.970727i	$0.422792\pi$
$434$	−19.8430	−0.952492
$435$	0	0
$436$	−8.95614	−0.428922
$437$	−1.80131	−0.0861684
$438$	−21.0811	−1.00730
$439$	−40.4168	−1.92899	−0.964494	−	0.264105i	$-0.914923\pi$
$439$	−40.4168	−1.92899	−0.964494	+	0.264105i	$0.914923\pi$
$440$	0	0
$441$	3.91677	0.186513
$442$	−6.36428	−0.302718
$443$	4.13120	0.196279	0.0981397	−	0.995173i	$-0.468711\pi$
$443$	4.13120	0.196279	0.0981397	+	0.995173i	$0.468711\pi$
$444$	−2.16967	−0.102968
$445$	0	0
$446$	−13.7830	−0.652646
$447$	−16.2510	−0.768646
$448$	15.1845	0.717402
$449$	27.7767	1.31087	0.655433	−	0.755254i	$-0.272486\pi$
$449$	27.7767	1.31087	0.655433	+	0.755254i	$0.272486\pi$
$450$	0	0
$451$	−0.963032	−0.0453474
$452$	9.74191	0.458221
$453$	0.816600	0.0383672
$454$	22.6505	1.06304
$455$	0	0
$456$	−5.98555	−0.280299
$457$	4.76704	0.222993	0.111496	−	0.993765i	$-0.464436\pi$
$457$	4.76704	0.222993	0.111496	+	0.993765i	$0.464436\pi$
$458$	29.9199	1.39807
$459$	−10.7538	−0.501947
$460$	0	0
$461$	31.7649	1.47944	0.739719	−	0.672916i	$-0.234958\pi$
$461$	31.7649	1.47944	0.739719	+	0.672916i	$0.234958\pi$
$462$	−18.1560	−0.844695
$463$	−33.8783	−1.57446	−0.787230	−	0.616660i	$-0.788485\pi$
$463$	−33.8783	−1.57446	−0.787230	+	0.616660i	$0.788485\pi$
$464$	−17.0139	−0.789849
$465$	0	0
$466$	10.8787	0.503945
$467$	−11.8984	−0.550592	−0.275296	−	0.961359i	$-0.588776\pi$
$467$	−11.8984	−0.550592	−0.275296	+	0.961359i	$0.588776\pi$
$468$	−1.54176	−0.0712679
$469$	5.13357	0.237046
$470$	0	0
$471$	−14.6545	−0.675246
$472$	33.5934	1.54626
$473$	10.0839	0.463660
$474$	21.0096	0.965005
$475$	0	0
$476$	1.85792	0.0851578
$477$	−6.57604	−0.301096
$478$	−13.0394	−0.596410
$479$	13.1410	0.600429	0.300214	−	0.953872i	$-0.402942\pi$
$479$	13.1410	0.600429	0.300214	+	0.953872i	$0.402942\pi$
$480$	0	0
$481$	7.52357	0.343045
$482$	1.19733	0.0545369
$483$	3.23324	0.147117
$484$	−15.3588	−0.698127
$485$	0	0
$486$	11.5720	0.524917
$487$	−20.3944	−0.924157	−0.462078	−	0.886839i	$-0.652896\pi$
$487$	−20.3944	−0.924157	−0.462078	+	0.886839i	$0.652896\pi$
$488$	−26.8475	−1.21533
$489$	−22.7079	−1.02689
$490$	0	0
$491$	−13.8053	−0.623026	−0.311513	−	0.950242i	$-0.600836\pi$
$491$	−13.8053	−0.623026	−0.311513	+	0.950242i	$0.600836\pi$
$492$	0.125769	0.00567009
$493$	−12.7027	−0.572100
$494$	4.58072	0.206096
$495$	0	0
$496$	−24.4585	−1.09822
$497$	−13.1485	−0.589791
$498$	0.744546	0.0333639
$499$	25.0632	1.12198	0.560992	−	0.827821i	$-0.310420\pi$
$499$	25.0632	1.12198	0.560992	+	0.827821i	$0.310420\pi$
$500$	0	0
$501$	8.09076	0.361468
$502$	−31.8892	−1.42329
$503$	−28.6027	−1.27533	−0.637667	−	0.770312i	$-0.720100\pi$
$503$	−28.6027	−1.27533	−0.637667	+	0.770312i	$0.720100\pi$
$504$	−5.16178	−0.229924
$505$	0	0
$506$	−9.73099	−0.432595
$507$	7.37820	0.327677
$508$	10.5024	0.465968
$509$	−14.0220	−0.621515	−0.310757	−	0.950489i	$-0.600583\pi$
$509$	−14.0220	−0.621515	−0.310757	+	0.950489i	$0.600583\pi$
$510$	0	0
$511$	−21.3404	−0.944044
$512$	23.5349	1.04010
$513$	7.74013	0.341735
$514$	17.4520	0.769773
$515$	0	0
$516$	−1.31693	−0.0579745
$517$	−0.300929	−0.0132348
$518$	5.55912	0.244254
$519$	27.8289	1.22155
$520$	0	0
$521$	5.67748	0.248735	0.124367	−	0.992236i	$-0.460310\pi$
$521$	5.67748	0.248735	0.124367	+	0.992236i	$0.460310\pi$
$522$	7.78873	0.340903
$523$	−24.4398	−1.06868	−0.534338	−	0.845271i	$-0.679439\pi$
$523$	−24.4398	−1.06868	−0.534338	+	0.845271i	$0.679439\pi$
$524$	6.79167	0.296696
$525$	0	0
$526$	−11.3145	−0.493335
$527$	−18.2609	−0.795459
$528$	−22.3792	−0.973930
$529$	−21.2671	−0.924656
$530$	0	0
$531$	−10.6436	−0.461894
$532$	−1.33725	−0.0579771
$533$	−0.436117	−0.0188903
$534$	9.21952	0.398968
$535$	0	0
$536$	9.14263	0.394902
$537$	−23.4928	−1.01379
$538$	5.94201	0.256178
$539$	24.8376	1.06983
$540$	0	0
$541$	−2.50677	−0.107775	−0.0538873	−	0.998547i	$-0.517161\pi$
$541$	−2.50677	−0.107775	−0.0538873	+	0.998547i	$0.517161\pi$
$542$	−15.1275	−0.649780
$543$	10.2652	0.440524
$544$	5.88748	0.252423
$545$	0	0
$546$	−8.22210	−0.351874
$547$	20.0223	0.856091	0.428046	−	0.903757i	$-0.359202\pi$
$547$	20.0223	0.856091	0.428046	+	0.903757i	$0.359202\pi$
$548$	−0.603513	−0.0257808
$549$	8.50629	0.363039
$550$	0	0
$551$	9.14282	0.389497
$552$	5.75824	0.245087
$553$	21.2680	0.904409
$554$	−0.864430	−0.0367261
$555$	0	0
$556$	−9.36250	−0.397059
$557$	−21.7808	−0.922884	−0.461442	−	0.887170i	$-0.652668\pi$
$557$	−21.7808	−0.922884	−0.461442	+	0.887170i	$0.652668\pi$
$558$	11.1968	0.473998
$559$	4.56659	0.193146
$560$	0	0
$561$	−16.7085	−0.705433
$562$	−20.7415	−0.874927
$563$	−19.0012	−0.800803	−0.400402	−	0.916340i	$-0.631129\pi$
$563$	−19.0012	−0.800803	−0.400402	+	0.916340i	$0.631129\pi$
$564$	0.0393003	0.00165484
$565$	0	0
$566$	24.6727	1.03707
$567$	−8.85360	−0.371816
$568$	−23.4168	−0.982548
$569$	9.76933	0.409552	0.204776	−	0.978809i	$-0.434353\pi$
$569$	9.76933	0.409552	0.204776	+	0.978809i	$0.434353\pi$
$570$	0	0
$571$	−18.2363	−0.763167	−0.381583	−	0.924334i	$-0.624621\pi$
$571$	−18.2363	−0.763167	−0.381583	+	0.924334i	$0.624621\pi$
$572$	−9.77684	−0.408790
$573$	20.7833	0.868233
$574$	−0.322244	−0.0134502
$575$	0	0
$576$	−8.56820	−0.357008
$577$	−24.8740	−1.03552	−0.517759	−	0.855527i	$-0.673234\pi$
$577$	−24.8740	−1.03552	−0.517759	+	0.855527i	$0.673234\pi$
$578$	16.0270	0.666635
$579$	−16.2528	−0.675445
$580$	0	0
$581$	0.753704	0.0312689
$582$	25.9171	1.07430
$583$	−41.7010	−1.72708
$584$	−38.0062	−1.57271
$585$	0	0
$586$	−27.7747	−1.14736
$587$	5.13085	0.211773	0.105887	−	0.994378i	$-0.466232\pi$
$587$	5.13085	0.211773	0.105887	+	0.994378i	$0.466232\pi$
$588$	−3.24371	−0.133768
$589$	13.1434	0.541564
$590$	0	0
$591$	−22.0156	−0.905600
$592$	6.85221	0.281624
$593$	−38.2484	−1.57067	−0.785337	−	0.619068i	$-0.787510\pi$
$593$	−38.2484	−1.57067	−0.785337	+	0.619068i	$0.787510\pi$
$594$	41.8135	1.71563
$595$	0	0
$596$	−6.46607	−0.264860
$597$	−11.2872	−0.461953
$598$	−4.40676	−0.180206
$599$	−12.5875	−0.514312	−0.257156	−	0.966370i	$-0.582785\pi$
$599$	−12.5875	−0.514312	−0.257156	+	0.966370i	$0.582785\pi$
$600$	0	0
$601$	6.29999	0.256982	0.128491	−	0.991711i	$-0.458987\pi$
$601$	6.29999	0.256982	0.128491	+	0.991711i	$0.458987\pi$
$602$	3.37423	0.137523
$603$	−2.89673	−0.117964
$604$	0.324915	0.0132206
$605$	0	0
$606$	7.86318	0.319420
$607$	−31.5598	−1.28097	−0.640486	−	0.767970i	$-0.721267\pi$
$607$	−31.5598	−1.28097	−0.640486	+	0.767970i	$0.721267\pi$
$608$	−4.23754	−0.171855
$609$	−16.4108	−0.664998
$610$	0	0
$611$	−0.136278	−0.00551322
$612$	−1.04837	−0.0423779
$613$	−18.9202	−0.764178	−0.382089	−	0.924125i	$-0.624795\pi$
$613$	−18.9202	−0.764178	−0.382089	+	0.924125i	$0.624795\pi$
$614$	25.5796	1.03231
$615$	0	0
$616$	−32.7327	−1.31884
$617$	8.16332	0.328643	0.164321	−	0.986407i	$-0.447457\pi$
$617$	8.16332	0.328643	0.164321	+	0.986407i	$0.447457\pi$
$618$	15.4173	0.620174
$619$	15.2701	0.613758	0.306879	−	0.951749i	$-0.400715\pi$
$619$	15.2701	0.613758	0.306879	+	0.951749i	$0.400715\pi$
$620$	0	0
$621$	−7.44618	−0.298805
$622$	36.8402	1.47716
$623$	9.33291	0.373915
$624$	−10.1346	−0.405709
$625$	0	0
$626$	18.8965	0.755256
$627$	12.0260	0.480273
$628$	−5.83086	−0.232677
$629$	5.11591	0.203985
$630$	0	0
$631$	35.7565	1.42345	0.711723	−	0.702461i	$-0.247915\pi$
$631$	35.7565	1.42345	0.711723	+	0.702461i	$0.247915\pi$
$632$	37.8773	1.50668
$633$	6.06496	0.241061
$634$	−11.2348	−0.446191
$635$	0	0
$636$	5.44601	0.215948
$637$	11.2479	0.445659
$638$	49.3911	1.95541
$639$	7.41932	0.293504
$640$	0	0
$641$	−30.0668	−1.18757	−0.593783	−	0.804625i	$-0.702366\pi$
$641$	−30.0668	−1.18757	−0.593783	+	0.804625i	$0.702366\pi$
$642$	−31.3790	−1.23843
$643$	21.7765	0.858781	0.429391	−	0.903119i	$-0.358728\pi$
$643$	21.7765	0.858781	0.429391	+	0.903119i	$0.358728\pi$
$644$	1.28646	0.0506938
$645$	0	0
$646$	3.11482	0.122551
$647$	16.2828	0.640144	0.320072	−	0.947393i	$-0.396293\pi$
$647$	16.2828	0.640144	0.320072	+	0.947393i	$0.396293\pi$
$648$	−15.7678	−0.619419
$649$	−67.4950	−2.64941
$650$	0	0
$651$	−23.5916	−0.924626
$652$	−9.03520	−0.353846
$653$	−37.1298	−1.45300	−0.726501	−	0.687165i	$-0.758855\pi$
$653$	−37.1298	−1.45300	−0.726501	+	0.687165i	$0.758855\pi$
$654$	26.9510	1.05387
$655$	0	0
$656$	−0.397200	−0.0155081
$657$	12.0418	0.469795
$658$	−0.100695	−0.00392550
$659$	−7.38540	−0.287694	−0.143847	−	0.989600i	$-0.545947\pi$
$659$	−7.38540	−0.287694	−0.143847	+	0.989600i	$0.545947\pi$
$660$	0	0
$661$	29.7235	1.15611	0.578056	−	0.815997i	$-0.303812\pi$
$661$	29.7235	1.15611	0.578056	+	0.815997i	$0.303812\pi$
$662$	17.2169	0.669154
$663$	−7.56658	−0.293862
$664$	1.34231	0.0520917
$665$	0	0
$666$	−3.13685	−0.121551
$667$	−8.79560	−0.340567
$668$	3.21921	0.124555
$669$	−16.3868	−0.633552
$670$	0	0
$671$	53.9413	2.08238
$672$	7.60611	0.293412
$673$	4.68626	0.180642	0.0903211	−	0.995913i	$-0.471211\pi$
$673$	4.68626	0.180642	0.0903211	+	0.995913i	$0.471211\pi$
$674$	−35.2633	−1.35829
$675$	0	0
$676$	2.93569	0.112911
$677$	3.05490	0.117409	0.0587047	−	0.998275i	$-0.481303\pi$
$677$	3.05490	0.117409	0.0587047	+	0.998275i	$0.481303\pi$
$678$	−29.3155	−1.12586
$679$	26.2359	1.00684
$680$	0	0
$681$	26.9295	1.03194
$682$	71.0029	2.71884
$683$	−7.98640	−0.305591	−0.152795	−	0.988258i	$-0.548828\pi$
$683$	−7.98640	−0.305591	−0.152795	+	0.988258i	$0.548828\pi$
$684$	0.754571	0.0288517
$685$	0	0
$686$	22.7720	0.869440
$687$	35.5722	1.35716
$688$	4.15909	0.158564
$689$	−18.8846	−0.719447
$690$	0	0
$691$	−0.159052	−0.00605063	−0.00302532	−	0.999995i	$-0.500963\pi$
$691$	−0.159052	−0.00605063	−0.00302532	+	0.999995i	$0.500963\pi$
$692$	11.0728	0.420924
$693$	10.3709	0.393959
$694$	22.0625	0.837481
$695$	0	0
$696$	−29.2268	−1.10784
$697$	−0.296553	−0.0112327
$698$	−20.1742	−0.763604
$699$	12.9338	0.489202
$700$	0	0
$701$	28.4178	1.07332	0.536662	−	0.843797i	$-0.319685\pi$
$701$	28.4178	1.07332	0.536662	+	0.843797i	$0.319685\pi$
$702$	18.9356	0.714678
$703$	−3.68220	−0.138877
$704$	−54.3339	−2.04779
$705$	0	0
$706$	15.2487	0.573891
$707$	7.95989	0.299363
$708$	8.81462	0.331274
$709$	41.4612	1.55711	0.778554	−	0.627578i	$-0.215954\pi$
$709$	41.4612	1.55711	0.778554	+	0.627578i	$0.215954\pi$
$710$	0	0
$711$	−12.0009	−0.450070
$712$	16.6214	0.622915
$713$	−12.6442	−0.473531
$714$	−5.59090	−0.209234
$715$	0	0
$716$	−9.34748	−0.349332
$717$	−15.5028	−0.578962
$718$	−21.3285	−0.795973
$719$	−10.8791	−0.405723	−0.202861	−	0.979207i	$-0.565024\pi$
$719$	−10.8791	−0.405723	−0.202861	+	0.979207i	$0.565024\pi$
$720$	0	0
$721$	15.6069	0.581231
$722$	20.5074	0.763205
$723$	1.42352	0.0529413
$724$	4.08441	0.151796
$725$	0	0
$726$	46.2179	1.71531
$727$	51.5136	1.91053	0.955266	−	0.295747i	$-0.0955684\pi$
$727$	51.5136	1.91053	0.955266	+	0.295747i	$0.0955684\pi$
$728$	−14.8232	−0.549386
$729$	29.1522	1.07971
$730$	0	0
$731$	3.10521	0.114850
$732$	−7.04456	−0.260374
$733$	16.6022	0.613216	0.306608	−	0.951836i	$-0.400806\pi$
$733$	16.6022	0.613216	0.306608	+	0.951836i	$0.400806\pi$
$734$	−4.04832	−0.149426
$735$	0	0
$736$	4.07661	0.150266
$737$	−18.3692	−0.676636
$738$	0.181833	0.00669337
$739$	−0.505517	−0.0185957	−0.00929787	−	0.999957i	$-0.502960\pi$
$739$	−0.505517	−0.0185957	−0.00929787	+	0.999957i	$0.502960\pi$
$740$	0	0
$741$	5.44608	0.200067
$742$	−13.9537	−0.512258
$743$	−29.4731	−1.08126	−0.540631	−	0.841260i	$-0.681815\pi$
$743$	−29.4731	−1.08126	−0.540631	+	0.841260i	$0.681815\pi$
$744$	−42.0154	−1.54036
$745$	0	0
$746$	−39.3609	−1.44111
$747$	−0.425293	−0.0155607
$748$	−6.64810	−0.243079
$749$	−31.7649	−1.16067
$750$	0	0
$751$	45.5615	1.66256	0.831282	−	0.555851i	$-0.187608\pi$
$751$	45.5615	1.66256	0.831282	+	0.555851i	$0.187608\pi$
$752$	−0.124117	−0.00452609
$753$	−37.9135	−1.38165
$754$	22.3671	0.814563
$755$	0	0
$756$	−5.52787	−0.201047
$757$	32.9054	1.19597	0.597984	−	0.801508i	$-0.295969\pi$
$757$	32.9054	1.19597	0.597984	+	0.801508i	$0.295969\pi$
$758$	24.0571	0.873792
$759$	−11.5693	−0.419939
$760$	0	0
$761$	41.4962	1.50424	0.752119	−	0.659028i	$-0.229032\pi$
$761$	41.4962	1.50424	0.752119	+	0.659028i	$0.229032\pi$
$762$	−31.6040	−1.14489
$763$	27.2825	0.987692
$764$	8.26940	0.299176
$765$	0	0
$766$	28.9736	1.04686
$767$	−30.5657	−1.10366
$768$	17.6523	0.636974
$769$	−10.2524	−0.369710	−0.184855	−	0.982766i	$-0.559182\pi$
$769$	−10.2524	−0.369710	−0.184855	+	0.982766i	$0.559182\pi$
$770$	0	0
$771$	20.7489	0.747252
$772$	−6.46680	−0.232745
$773$	−14.5443	−0.523124	−0.261562	−	0.965187i	$-0.584238\pi$
$773$	−14.5443	−0.523124	−0.261562	+	0.965187i	$0.584238\pi$
$774$	−1.90398	−0.0684371
$775$	0	0
$776$	46.7247	1.67732
$777$	6.60932	0.237108
$778$	27.4821	0.985282
$779$	0.213445	0.00764747
$780$	0	0
$781$	47.0485	1.68353
$782$	−2.99653	−0.107156
$783$	37.7942	1.35065
$784$	10.2442	0.365865
$785$	0	0
$786$	−20.4376	−0.728986
$787$	−3.16749	−0.112909	−0.0564545	−	0.998405i	$-0.517980\pi$
$787$	−3.16749	−0.112909	−0.0564545	+	0.998405i	$0.517980\pi$
$788$	−8.75972	−0.312052
$789$	−13.4519	−0.478901
$790$	0	0
$791$	−29.6761	−1.05516
$792$	18.4701	0.656306
$793$	24.4278	0.867456
$794$	−18.1972	−0.645794
$795$	0	0
$796$	−4.49102	−0.159180
$797$	21.6285	0.766121	0.383060	−	0.923723i	$-0.374870\pi$
$797$	21.6285	0.766121	0.383060	+	0.923723i	$0.374870\pi$
$798$	4.02408	0.142451
$799$	−0.0926669	−0.00327832
$800$	0	0
$801$	−5.26629	−0.186075
$802$	31.7840	1.12233
$803$	76.3611	2.69473
$804$	2.39895	0.0846044
$805$	0	0
$806$	32.1542	1.13258
$807$	7.06453	0.248683
$808$	14.1762	0.498716
$809$	−34.8990	−1.22698	−0.613492	−	0.789701i	$-0.710236\pi$
$809$	−34.8990	−1.22698	−0.613492	+	0.789701i	$0.710236\pi$
$810$	0	0
$811$	−29.7965	−1.04630	−0.523148	−	0.852242i	$-0.675242\pi$
$811$	−29.7965	−1.04630	−0.523148	+	0.852242i	$0.675242\pi$
$812$	−6.52964	−0.229145
$813$	−17.9852	−0.630770
$814$	−19.8919	−0.697210
$815$	0	0
$816$	−6.89137	−0.241246
$817$	−2.23499	−0.0781924
$818$	14.4141	0.503977
$819$	4.69656	0.164111
$820$	0	0
$821$	−28.3105	−0.988045	−0.494022	−	0.869449i	$-0.664474\pi$
$821$	−28.3105	−0.988045	−0.494022	+	0.869449i	$0.664474\pi$
$822$	1.81610	0.0633438
$823$	39.9480	1.39250	0.696251	−	0.717799i	$-0.254850\pi$
$823$	39.9480	1.39250	0.696251	+	0.717799i	$0.254850\pi$
$824$	27.7951	0.968288
$825$	0	0
$826$	−22.5848	−0.785825
$827$	−0.781339	−0.0271698	−0.0135849	−	0.999908i	$-0.504324\pi$
$827$	−0.781339	−0.0271698	−0.0135849	+	0.999908i	$0.504324\pi$
$828$	−0.725915	−0.0252273
$829$	27.2809	0.947504	0.473752	−	0.880658i	$-0.342899\pi$
$829$	27.2809	0.947504	0.473752	+	0.880658i	$0.342899\pi$
$830$	0	0
$831$	−1.02773	−0.0356516
$832$	−24.6056	−0.853045
$833$	7.64841	0.265002
$834$	28.1738	0.975580
$835$	0	0
$836$	4.78500	0.165493
$837$	54.3316	1.87797
$838$	18.2842	0.631618
$839$	−4.25997	−0.147071	−0.0735353	−	0.997293i	$-0.523428\pi$
$839$	−4.25997	−0.147071	−0.0735353	+	0.997293i	$0.523428\pi$
$840$	0	0
$841$	15.6433	0.539425
$842$	40.4248	1.39313
$843$	−24.6598	−0.849330
$844$	2.41317	0.0830648
$845$	0	0
$846$	0.0568193	0.00195349
$847$	46.7864	1.60760
$848$	−17.1995	−0.590632
$849$	29.3337	1.00673
$850$	0	0
$851$	3.54236	0.121431
$852$	−6.14438	−0.210503
$853$	41.3632	1.41625	0.708125	−	0.706088i	$-0.249542\pi$
$853$	41.3632	1.41625	0.708125	+	0.706088i	$0.249542\pi$
$854$	18.0495	0.617642
$855$	0	0
$856$	−56.5718	−1.93358
$857$	−25.4396	−0.869002	−0.434501	−	0.900671i	$-0.643075\pi$
$857$	−25.4396	−0.869002	−0.434501	+	0.900671i	$0.643075\pi$
$858$	29.4207	1.00440
$859$	−6.47212	−0.220826	−0.110413	−	0.993886i	$-0.535217\pi$
$859$	−6.47212	−0.220826	−0.110413	+	0.993886i	$0.535217\pi$
$860$	0	0
$861$	−0.383120	−0.0130567
$862$	2.10769	0.0717882
$863$	−46.7069	−1.58992	−0.794961	−	0.606660i	$-0.792509\pi$
$863$	−46.7069	−1.58992	−0.794961	+	0.606660i	$0.792509\pi$
$864$	−17.5170	−0.595939
$865$	0	0
$866$	−11.9683	−0.406698
$867$	19.0547	0.647132
$868$	−9.38678	−0.318608
$869$	−76.1021	−2.58159
$870$	0	0
$871$	−8.31862	−0.281866
$872$	48.5887	1.64542
$873$	−14.8041	−0.501044
$874$	2.15676	0.0729536
$875$	0	0
$876$	−9.97251	−0.336940
$877$	13.0048	0.439141	0.219571	−	0.975597i	$-0.429534\pi$
$877$	13.0048	0.439141	0.219571	+	0.975597i	$0.429534\pi$
$878$	48.3922	1.63316
$879$	−33.0217	−1.11380
$880$	0	0
$881$	8.45741	0.284937	0.142469	−	0.989799i	$-0.454496\pi$
$881$	8.45741	0.284937	0.142469	+	0.989799i	$0.454496\pi$
$882$	−4.68967	−0.157909
$883$	−52.9407	−1.78159	−0.890797	−	0.454401i	$-0.849853\pi$
$883$	−52.9407	−1.78159	−0.890797	+	0.454401i	$0.849853\pi$
$884$	−3.01065	−0.101259
$885$	0	0
$886$	−4.94641	−0.166178
$887$	−8.55227	−0.287157	−0.143579	−	0.989639i	$-0.545861\pi$
$887$	−8.55227	−0.287157	−0.143579	+	0.989639i	$0.545861\pi$
$888$	11.7709	0.395004
$889$	−31.9927	−1.07300
$890$	0	0
$891$	31.6803	1.06133
$892$	−6.52012	−0.218310
$893$	0.0666974	0.00223194
$894$	19.4578	0.650766
$895$	0	0
$896$	−7.49458	−0.250376
$897$	−5.23925	−0.174934
$898$	−33.2579	−1.10983
$899$	64.1777	2.14045
$900$	0	0
$901$	−12.8412	−0.427804
$902$	1.15307	0.0383929
$903$	4.01166	0.133500
$904$	−52.8516	−1.75782
$905$	0	0
$906$	−0.977740	−0.0324832
$907$	−50.8112	−1.68716	−0.843580	−	0.537004i	$-0.819556\pi$
$907$	−50.8112	−1.68716	−0.843580	+	0.537004i	$0.819556\pi$
$908$	10.7149	0.355587
$909$	−4.49154	−0.148975
$910$	0	0
$911$	−17.5610	−0.581823	−0.290911	−	0.956750i	$-0.593958\pi$
$911$	−17.5610	−0.581823	−0.290911	+	0.956750i	$0.593958\pi$
$912$	4.96010	0.164245
$913$	−2.69693	−0.0892554
$914$	−5.70772	−0.188795
$915$	0	0
$916$	14.1537	0.467653
$917$	−20.6890	−0.683211
$918$	12.8759	0.424968
$919$	−5.97648	−0.197146	−0.0985730	−	0.995130i	$-0.531428\pi$
$919$	−5.97648	−0.197146	−0.0985730	+	0.995130i	$0.531428\pi$
$920$	0	0
$921$	30.4119	1.00211
$922$	−38.0331	−1.25255
$923$	21.3063	0.701305
$924$	−8.58877	−0.282550
$925$	0	0
$926$	40.5635	1.33300
$927$	−8.80652	−0.289244
$928$	−20.6914	−0.679229
$929$	−49.2167	−1.61475	−0.807373	−	0.590041i	$-0.799111\pi$
$929$	−49.2167	−1.61475	−0.807373	+	0.590041i	$0.799111\pi$
$930$	0	0
$931$	−5.50498	−0.180418
$932$	5.14620	0.168569
$933$	43.7998	1.43394
$934$	14.2463	0.466153
$935$	0	0
$936$	8.36433	0.273397
$937$	−12.0291	−0.392975	−0.196487	−	0.980506i	$-0.562953\pi$
$937$	−12.0291	−0.392975	−0.196487	+	0.980506i	$0.562953\pi$
$938$	−6.14658	−0.200693
$939$	22.4663	0.733160
$940$	0	0
$941$	15.7308	0.512811	0.256405	−	0.966569i	$-0.417462\pi$
$941$	15.7308	0.512811	0.256405	+	0.966569i	$0.417462\pi$
$942$	17.5463	0.571690
$943$	−0.205339	−0.00668676
$944$	−27.8381	−0.906054
$945$	0	0
$946$	−12.0738	−0.392553
$947$	−18.8457	−0.612403	−0.306202	−	0.951967i	$-0.599058\pi$
$947$	−18.8457	−0.612403	−0.306202	+	0.951967i	$0.599058\pi$
$948$	9.93868	0.322793
$949$	34.5808	1.12254
$950$	0	0
$951$	−13.3572	−0.433137
$952$	−10.0796	−0.326681
$953$	−7.45414	−0.241463	−0.120732	−	0.992685i	$-0.538524\pi$
$953$	−7.45414	−0.241463	−0.120732	+	0.992685i	$0.538524\pi$
$954$	7.87369	0.254920
$955$	0	0
$956$	−6.16836	−0.199499
$957$	58.7217	1.89820
$958$	−15.7341	−0.508347
$959$	1.83844	0.0593663
$960$	0	0
$961$	61.2596	1.97612
$962$	−9.00820	−0.290436
$963$	17.9240	0.577594
$964$	0.566401	0.0182426
$965$	0	0
$966$	−3.87125	−0.124556
$967$	−33.9375	−1.09135	−0.545677	−	0.837995i	$-0.683728\pi$
$967$	−33.9375	−1.09135	−0.545677	+	0.837995i	$0.683728\pi$
$968$	83.3242	2.67814
$969$	3.70325	0.118965
$970$	0	0
$971$	−10.7596	−0.345293	−0.172647	−	0.984984i	$-0.555232\pi$
$971$	−10.7596	−0.345293	−0.172647	+	0.984984i	$0.555232\pi$
$972$	5.47418	0.175584
$973$	28.5203	0.914320
$974$	24.4188	0.782428
$975$	0	0
$976$	22.2480	0.712140
$977$	−29.2829	−0.936843	−0.468422	−	0.883505i	$-0.655177\pi$
$977$	−29.2829	−0.936843	−0.468422	+	0.883505i	$0.655177\pi$
$978$	27.1889	0.869405
$979$	−33.3954	−1.06732
$980$	0	0
$981$	−15.3947	−0.491515
$982$	16.5296	0.527479
$983$	−10.4947	−0.334730	−0.167365	−	0.985895i	$-0.553526\pi$
$983$	−10.4947	−0.334730	−0.167365	+	0.985895i	$0.553526\pi$
$984$	−0.682318	−0.0217515
$985$	0	0
$986$	15.2093	0.484363
$987$	−0.119718	−0.00381066
$988$	2.16693	0.0689391
$989$	2.15011	0.0683695
$990$	0	0
$991$	48.9389	1.55460	0.777298	−	0.629133i	$-0.216590\pi$
$991$	48.9389	1.55460	0.777298	+	0.629133i	$0.216590\pi$
$992$	−29.7453	−0.944413
$993$	20.4694	0.649577
$994$	15.7431	0.499341
$995$	0	0
$996$	0.352210	0.0111602
$997$	−32.6340	−1.03353	−0.516765	−	0.856128i	$-0.672864\pi$
$997$	−32.6340	−1.03353	−0.516765	+	0.856128i	$0.672864\pi$
$998$	−30.0089	−0.949916
$999$	−15.2213	−0.481582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.l.1.16	✓	40
5.4	even	2		6025.2.a.o.1.25	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.l.1.16	✓	40	1.1	even	1	trivial
6025.2.a.o.1.25	yes	40	5.4	even	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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.19733 q^{2} -1.42352 q^{3} -0.566401 q^{4} +1.70442 q^{6} +1.72539 q^{7} +3.07283 q^{8} -0.973586 q^{9} +O(q^{10})\)	\(q-1.19733 q^{2} -1.42352 q^{3} -0.566401 q^{4} +1.70442 q^{6} +1.72539 q^{7} +3.07283 q^{8} -0.973586 q^{9} -6.17385 q^{11} +0.806284 q^{12} -2.79588 q^{13} -2.06586 q^{14} -2.54639 q^{16} -1.90115 q^{17} +1.16570 q^{18} +1.36836 q^{19} -2.45613 q^{21} +7.39214 q^{22} -1.31640 q^{23} -4.37424 q^{24} +3.34759 q^{26} +5.65649 q^{27} -0.977261 q^{28} +6.68157 q^{29} +9.60519 q^{31} -3.09679 q^{32} +8.78861 q^{33} +2.27631 q^{34} +0.551440 q^{36} -2.69095 q^{37} -1.63838 q^{38} +3.97999 q^{39} +0.155986 q^{41} +2.94079 q^{42} -1.63333 q^{43} +3.49688 q^{44} +1.57616 q^{46} +0.0487425 q^{47} +3.62484 q^{48} -4.02304 q^{49} +2.70633 q^{51} +1.58359 q^{52} +6.75445 q^{53} -6.77268 q^{54} +5.30182 q^{56} -1.94790 q^{57} -8.00004 q^{58} +10.9324 q^{59} -8.73706 q^{61} -11.5006 q^{62} -1.67981 q^{63} +8.80066 q^{64} -10.5229 q^{66} +2.97531 q^{67} +1.07682 q^{68} +1.87392 q^{69} -7.62061 q^{71} -2.99166 q^{72} -12.3685 q^{73} +3.22196 q^{74} -0.775043 q^{76} -10.6523 q^{77} -4.76537 q^{78} +12.3265 q^{79} -5.13137 q^{81} -0.186766 q^{82} +0.436831 q^{83} +1.39115 q^{84} +1.95563 q^{86} -9.51135 q^{87} -18.9712 q^{88} +5.40917 q^{89} -4.82397 q^{91} +0.745609 q^{92} -13.6732 q^{93} -0.0583608 q^{94} +4.40835 q^{96} +15.2058 q^{97} +4.81690 q^{98} +6.01078 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9} + q^{11} - 14 q^{12} - 9 q^{13} - q^{14} + 43 q^{16} - 12 q^{17} - 42 q^{18} + 2 q^{21} - 5 q^{22} - 77 q^{23} - 2 q^{24} + 2 q^{26} - 38 q^{27} - 42 q^{28} + 2 q^{29} + q^{31} - 72 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 28 q^{37} - 23 q^{38} - 2 q^{39} - 2 q^{41} - 37 q^{42} - 31 q^{43} + 3 q^{44} + 14 q^{46} - 96 q^{47} - 13 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 54 q^{53} + 4 q^{54} - 15 q^{56} - 37 q^{57} - 27 q^{58} + q^{59} + 5 q^{61} - 39 q^{62} - 70 q^{63} + 65 q^{64} - 52 q^{66} - 34 q^{67} - 52 q^{68} + 21 q^{69} - 9 q^{71} - 70 q^{72} - 25 q^{73} + 22 q^{74} - 47 q^{76} - 54 q^{77} - 58 q^{78} + 13 q^{79} + 12 q^{81} + 5 q^{82} - 63 q^{83} + 95 q^{84} - 18 q^{86} - 47 q^{87} - 13 q^{88} + 19 q^{89} - 31 q^{91} - 137 q^{92} - 52 q^{93} + 120 q^{94} - 49 q^{96} - 36 q^{97} - 64 q^{98} + 16 q^{99}+O(q^{100}) \) 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9 + q^11 - 14 * q^12 - 9 * q^13 - q^14 + 43 * q^16 - 12 * q^17 - 42 * q^18 + 2 * q^21 - 5 * q^22 - 77 * q^23 - 2 * q^24 + 2 * q^26 - 38 * q^27 - 42 * q^28 + 2 * q^29 + q^31 - 72 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 28 * q^37 - 23 * q^38 - 2 * q^39 - 2 * q^41 - 37 * q^42 - 31 * q^43 + 3 * q^44 + 14 * q^46 - 96 * q^47 - 13 * q^48 + 40 * q^49 - 10 * q^51 - 42 * q^52 - 54 * q^53 + 4 * q^54 - 15 * q^56 - 37 * q^57 - 27 * q^58 + q^59 + 5 * q^61 - 39 * q^62 - 70 * q^63 + 65 * q^64 - 52 * q^66 - 34 * q^67 - 52 * q^68 + 21 * q^69 - 9 * q^71 - 70 * q^72 - 25 * q^73 + 22 * q^74 - 47 * q^76 - 54 * q^77 - 58 * q^78 + 13 * q^79 + 12 * q^81 + 5 * q^82 - 63 * q^83 + 95 * q^84 - 18 * q^86 - 47 * q^87 - 13 * q^88 + 19 * q^89 - 31 * q^91 - 137 * q^92 - 52 * q^93 + 120 * q^94 - 49 * q^96 - 36 * q^97 - 64 * q^98 + 16 * q^99

Introduction

L-functions

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Database

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