LMFDB - Embedded newform 1925.2.a.bd.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1925,2,Mod(1,1925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1925, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1925 = 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1925.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:	$15.3712023891$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 13x^{5} + 12x^{4} + 47x^{3} - 37x^{2} - 35x + 6 $ x^7 - x^6 - 13x^5 + 12x^4 + 47x^3 - 37x^2 - 35*x + 6
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.719607$ of defining polynomial
Character	$\chi$	$=$	1925.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.719607 q^{2} -0.234508 q^{3} -1.48217 q^{4} +0.168754 q^{6} +1.00000 q^{7} +2.50579 q^{8} -2.94501 q^{9} +O(q^{10})$	\(q-0.719607 q^{2} -0.234508 q^{3} -1.48217 q^{4} +0.168754 q^{6} +1.00000 q^{7} +2.50579 q^{8} -2.94501 q^{9} +1.00000 q^{11} +0.347580 q^{12} +2.88543 q^{13} -0.719607 q^{14} +1.16115 q^{16} -5.70202 q^{17} +2.11925 q^{18} -0.482165 q^{19} -0.234508 q^{21} -0.719607 q^{22} -2.02130 q^{23} -0.587629 q^{24} -2.07637 q^{26} +1.39415 q^{27} -1.48217 q^{28} +6.27650 q^{29} +4.19006 q^{31} -5.84715 q^{32} -0.234508 q^{33} +4.10322 q^{34} +4.36499 q^{36} +0.237442 q^{37} +0.346970 q^{38} -0.676656 q^{39} -0.0283010 q^{41} +0.168754 q^{42} -2.97481 q^{43} -1.48217 q^{44} +1.45454 q^{46} -6.61955 q^{47} -0.272298 q^{48} +1.00000 q^{49} +1.33717 q^{51} -4.27668 q^{52} -3.48414 q^{53} -1.00324 q^{54} +2.50579 q^{56} +0.113072 q^{57} -4.51662 q^{58} -1.79741 q^{59} +4.29272 q^{61} -3.01519 q^{62} -2.94501 q^{63} +1.88536 q^{64} +0.168754 q^{66} +5.58387 q^{67} +8.45134 q^{68} +0.474012 q^{69} +15.0278 q^{71} -7.37957 q^{72} +4.18643 q^{73} -0.170865 q^{74} +0.714649 q^{76} +1.00000 q^{77} +0.486927 q^{78} -4.44594 q^{79} +8.50808 q^{81} +0.0203656 q^{82} +2.19560 q^{83} +0.347580 q^{84} +2.14069 q^{86} -1.47189 q^{87} +2.50579 q^{88} +12.8543 q^{89} +2.88543 q^{91} +2.99590 q^{92} -0.982602 q^{93} +4.76348 q^{94} +1.37120 q^{96} +7.13863 q^{97} -0.719607 q^{98} -2.94501 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} + 13 q^{4} + 3 q^{6} + 7 q^{7} + 9 q^{9}+O(q^{10}) $ 7 * q + q^2 + 13 * q^4 + 3 * q^6 + 7 * q^7 + 9 * q^9	$ 7 q + q^{2} + 13 q^{4} + 3 q^{6} + 7 q^{7} + 9 q^{9} + 7 q^{11} - 9 q^{12} - 3 q^{13} + q^{14} + 21 q^{16} - 2 q^{17} + 8 q^{18} + 20 q^{19} + q^{22} + 11 q^{23} + 18 q^{24} - 13 q^{26} - 12 q^{27} + 13 q^{28} + 4 q^{29} + 6 q^{31} + q^{32} - 7 q^{34} + 12 q^{36} + 19 q^{37} + 3 q^{38} - 10 q^{39} + 24 q^{41} + 3 q^{42} + 13 q^{44} + 33 q^{46} - q^{47} - 15 q^{48} + 7 q^{49} + 19 q^{51} - 29 q^{52} + 7 q^{53} + 9 q^{54} - 9 q^{57} + 37 q^{58} + 9 q^{59} + 18 q^{61} - 40 q^{62} + 9 q^{63} + 8 q^{64} + 3 q^{66} + 18 q^{68} - 15 q^{69} + 18 q^{71} - 64 q^{72} + 5 q^{73} - 24 q^{74} + 88 q^{76} + 7 q^{77} + 79 q^{78} + 25 q^{79} - q^{81} - 60 q^{82} - 17 q^{83} - 9 q^{84} - 41 q^{86} - 24 q^{87} - 16 q^{89} - 3 q^{91} + 28 q^{92} + 26 q^{93} - 31 q^{94} + 17 q^{96} - 4 q^{97} + q^{98} + 9 q^{99}+O(q^{100}) $ 7 * q + q^2 + 13 * q^4 + 3 * q^6 + 7 * q^7 + 9 * q^9 + 7 * q^11 - 9 * q^12 - 3 * q^13 + q^14 + 21 * q^16 - 2 * q^17 + 8 * q^18 + 20 * q^19 + q^22 + 11 * q^23 + 18 * q^24 - 13 * q^26 - 12 * q^27 + 13 * q^28 + 4 * q^29 + 6 * q^31 + q^32 - 7 * q^34 + 12 * q^36 + 19 * q^37 + 3 * q^38 - 10 * q^39 + 24 * q^41 + 3 * q^42 + 13 * q^44 + 33 * q^46 - q^47 - 15 * q^48 + 7 * q^49 + 19 * q^51 - 29 * q^52 + 7 * q^53 + 9 * q^54 - 9 * q^57 + 37 * q^58 + 9 * q^59 + 18 * q^61 - 40 * q^62 + 9 * q^63 + 8 * q^64 + 3 * q^66 + 18 * q^68 - 15 * q^69 + 18 * q^71 - 64 * q^72 + 5 * q^73 - 24 * q^74 + 88 * q^76 + 7 * q^77 + 79 * q^78 + 25 * q^79 - q^81 - 60 * q^82 - 17 * q^83 - 9 * q^84 - 41 * q^86 - 24 * q^87 - 16 * q^89 - 3 * q^91 + 28 * q^92 + 26 * q^93 - 31 * q^94 + 17 * q^96 - 4 * q^97 + q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.719607	−0.508839	−0.254420	−	0.967094i	$-0.581884\pi$
$2$	−0.719607	−0.508839	−0.254420	+	0.967094i	$0.581884\pi$
$3$	−0.234508	−0.135393	−0.0676967	−	0.997706i	$-0.521565\pi$
$3$	−0.234508	−0.135393	−0.0676967	+	0.997706i	$0.521565\pi$
$4$	−1.48217	−0.741083
$5$	0	0
$5$	0	0
$6$	0.168754	0.0688934
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.50579	0.885931
$9$	−2.94501	−0.981669
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.347580	0.100338
$13$	2.88543	0.800274	0.400137	−	0.916455i	$-0.368963\pi$
$13$	2.88543	0.800274	0.400137	+	0.916455i	$0.368963\pi$
$14$	−0.719607	−0.192323
$15$	0	0
$16$	1.16115	0.290286
$17$	−5.70202	−1.38294	−0.691472	−	0.722403i	$-0.743037\pi$
$17$	−5.70202	−1.38294	−0.691472	+	0.722403i	$0.743037\pi$
$18$	2.11925	0.499511
$19$	−0.482165	−0.110616	−0.0553082	−	0.998469i	$-0.517614\pi$
$19$	−0.482165	−0.110616	−0.0553082	+	0.998469i	$0.517614\pi$
$20$	0	0
$21$	−0.234508	−0.0511739
$22$	−0.719607	−0.153421
$23$	−2.02130	−0.421471	−0.210735	−	0.977543i	$-0.567586\pi$
$23$	−2.02130	−0.421471	−0.210735	+	0.977543i	$0.567586\pi$
$24$	−0.587629	−0.119949
$25$	0	0
$26$	−2.07637	−0.407211
$27$	1.39415	0.268305
$28$	−1.48217	−0.280103
$29$	6.27650	1.16552	0.582759	−	0.812645i	$-0.301973\pi$
$29$	6.27650	1.16552	0.582759	+	0.812645i	$0.301973\pi$
$30$	0	0
$31$	4.19006	0.752556	0.376278	−	0.926507i	$-0.377204\pi$
$31$	4.19006	0.752556	0.376278	+	0.926507i	$0.377204\pi$
$32$	−5.84715	−1.03364
$33$	−0.234508	−0.0408226
$34$	4.10322	0.703696
$35$	0	0
$36$	4.36499	0.727498
$37$	0.237442	0.0390352	0.0195176	−	0.999810i	$-0.493787\pi$
$37$	0.237442	0.0390352	0.0195176	+	0.999810i	$0.493787\pi$
$38$	0.346970	0.0562859
$39$	−0.676656	−0.108352
$40$	0	0
$41$	−0.0283010	−0.00441987	−0.00220993	−	0.999998i	$-0.500703\pi$
$41$	−0.0283010	−0.00441987	−0.00220993	+	0.999998i	$0.500703\pi$
$42$	0.168754	0.0260393
$43$	−2.97481	−0.453654	−0.226827	−	0.973935i	$-0.572835\pi$
$43$	−2.97481	−0.453654	−0.226827	+	0.973935i	$0.572835\pi$
$44$	−1.48217	−0.223445
$45$	0	0
$46$	1.45454	0.214461
$47$	−6.61955	−0.965561	−0.482780	−	0.875741i	$-0.660373\pi$
$47$	−6.61955	−0.965561	−0.482780	+	0.875741i	$0.660373\pi$
$48$	−0.272298	−0.0393028
$49$	1.00000	0.142857
$50$	0	0
$51$	1.33717	0.187241
$52$	−4.27668	−0.593069
$53$	−3.48414	−0.478584	−0.239292	−	0.970948i	$-0.576915\pi$
$53$	−3.48414	−0.478584	−0.239292	+	0.970948i	$0.576915\pi$
$54$	−1.00324	−0.136524
$55$	0	0
$56$	2.50579	0.334850
$57$	0.113072	0.0149767
$58$	−4.51662	−0.593061
$59$	−1.79741	−0.234003	−0.117002	−	0.993132i	$-0.537328\pi$
$59$	−1.79741	−0.234003	−0.117002	+	0.993132i	$0.537328\pi$
$60$	0	0
$61$	4.29272	0.549626	0.274813	−	0.961498i	$-0.411384\pi$
$61$	4.29272	0.549626	0.274813	+	0.961498i	$0.411384\pi$
$62$	−3.01519	−0.382930
$63$	−2.94501	−0.371036
$64$	1.88536	0.235670
$65$	0	0
$66$	0.168754	0.0207722
$67$	5.58387	0.682179	0.341089	−	0.940031i	$-0.389204\pi$
$67$	5.58387	0.682179	0.341089	+	0.940031i	$0.389204\pi$
$68$	8.45134	1.02488
$69$	0.474012	0.0570643
$70$	0	0
$71$	15.0278	1.78348	0.891738	−	0.452552i	$-0.149486\pi$
$71$	15.0278	1.78348	0.891738	+	0.452552i	$0.149486\pi$
$72$	−7.37957	−0.869691
$73$	4.18643	0.489985	0.244993	−	0.969525i	$-0.421214\pi$
$73$	4.18643	0.489985	0.244993	+	0.969525i	$0.421214\pi$
$74$	−0.170865	−0.0198626
$75$	0	0
$76$	0.714649	0.0819759
$77$	1.00000	0.113961
$78$	0.486927	0.0551336
$79$	−4.44594	−0.500208	−0.250104	−	0.968219i	$-0.580465\pi$
$79$	−4.44594	−0.500208	−0.250104	+	0.968219i	$0.580465\pi$
$80$	0	0
$81$	8.50808	0.945342
$82$	0.0203656	0.00224900
$83$	2.19560	0.240998	0.120499	−	0.992713i	$-0.461551\pi$
$83$	2.19560	0.240998	0.120499	+	0.992713i	$0.461551\pi$
$84$	0.347580	0.0379241
$85$	0	0
$86$	2.14069	0.230837
$87$	−1.47189	−0.157803
$88$	2.50579	0.267118
$89$	12.8543	1.36256	0.681279	−	0.732024i	$-0.261424\pi$
$89$	12.8543	1.36256	0.681279	+	0.732024i	$0.261424\pi$
$90$	0	0
$91$	2.88543	0.302475
$92$	2.99590	0.312345
$93$	−0.982602	−0.101891
$94$	4.76348	0.491315
$95$	0	0
$96$	1.37120	0.139948
$97$	7.13863	0.724818	0.362409	−	0.932019i	$-0.381954\pi$
$97$	7.13863	0.724818	0.362409	+	0.932019i	$0.381954\pi$
$98$	−0.719607	−0.0726913
$99$	−2.94501	−0.295984
$100$	0	0
$101$	−3.94794	−0.392835	−0.196417	−	0.980520i	$-0.562931\pi$
$101$	−3.94794	−0.392835	−0.196417	+	0.980520i	$0.562931\pi$
$102$	−0.962238	−0.0952758
$103$	11.0181	1.08565	0.542823	−	0.839847i	$-0.317355\pi$
$103$	11.0181	1.08565	0.542823	+	0.839847i	$0.317355\pi$
$104$	7.23028	0.708987
$105$	0	0
$106$	2.50721	0.243522
$107$	−4.21725	−0.407696	−0.203848	−	0.979002i	$-0.565345\pi$
$107$	−4.21725	−0.407696	−0.203848	+	0.979002i	$0.565345\pi$
$108$	−2.06636	−0.198836
$109$	5.38861	0.516135	0.258068	−	0.966127i	$-0.416914\pi$
$109$	5.38861	0.516135	0.258068	+	0.966127i	$0.416914\pi$
$110$	0	0
$111$	−0.0556820	−0.00528511
$112$	1.16115	0.109718
$113$	2.88979	0.271849	0.135924	−	0.990719i	$-0.456600\pi$
$113$	2.88979	0.271849	0.135924	+	0.990719i	$0.456600\pi$
$114$	−0.0813672	−0.00762074
$115$	0	0
$116$	−9.30282	−0.863745
$117$	−8.49760	−0.785603
$118$	1.29343	0.119070
$119$	−5.70202	−0.522704
$120$	0	0
$121$	1.00000	0.0909091
$122$	−3.08907	−0.279671
$123$	0.00663681	0.000598421 0
$124$	−6.21036	−0.557706
$125$	0	0
$126$	2.11925	0.188798
$127$	8.49664	0.753955	0.376977	−	0.926222i	$-0.376963\pi$
$127$	8.49664	0.753955	0.376977	+	0.926222i	$0.376963\pi$
$128$	10.3376	0.913722
$129$	0.697617	0.0614217
$130$	0	0
$131$	14.3849	1.25681	0.628406	−	0.777886i	$-0.283708\pi$
$131$	14.3849	1.25681	0.628406	+	0.777886i	$0.283708\pi$
$132$	0.347580	0.0302529
$133$	−0.482165	−0.0418090
$134$	−4.01819	−0.347119
$135$	0	0
$136$	−14.2881	−1.22519
$137$	15.0352	1.28454	0.642271	−	0.766478i	$-0.277993\pi$
$137$	15.0352	1.28454	0.642271	+	0.766478i	$0.277993\pi$
$138$	−0.341102	−0.0290366
$139$	4.21512	0.357522	0.178761	−	0.983893i	$-0.442791\pi$
$139$	4.21512	0.357522	0.178761	+	0.983893i	$0.442791\pi$
$140$	0	0
$141$	1.55234	0.130731
$142$	−10.8141	−0.907503
$143$	2.88543	0.241292
$144$	−3.41958	−0.284965
$145$	0	0
$146$	−3.01259	−0.249324
$147$	−0.234508	−0.0193419
$148$	−0.351928	−0.0289283
$149$	13.3398	1.09284	0.546421	−	0.837510i	$-0.315990\pi$
$149$	13.3398	1.09284	0.546421	+	0.837510i	$0.315990\pi$
$150$	0	0
$151$	12.3479	1.00486	0.502431	−	0.864617i	$-0.332439\pi$
$151$	12.3479	1.00486	0.502431	+	0.864617i	$0.332439\pi$
$152$	−1.20821	−0.0979984
$153$	16.7925	1.35759
$154$	−0.719607	−0.0579876
$155$	0	0
$156$	1.00292	0.0802976
$157$	1.59203	0.127057	0.0635287	−	0.997980i	$-0.479765\pi$
$157$	1.59203	0.127057	0.0635287	+	0.997980i	$0.479765\pi$
$158$	3.19933	0.254525
$159$	0.817060	0.0647971
$160$	0	0
$161$	−2.02130	−0.159301
$162$	−6.12247	−0.481027
$163$	−14.7307	−1.15379	−0.576897	−	0.816817i	$-0.695737\pi$
$163$	−14.7307	−1.15379	−0.576897	+	0.816817i	$0.695737\pi$
$164$	0.0419467	0.00327549
$165$	0	0
$166$	−1.57997	−0.122629
$167$	1.49066	0.115351	0.0576756	−	0.998335i	$-0.481631\pi$
$167$	1.49066	0.115351	0.0576756	+	0.998335i	$0.481631\pi$
$168$	−0.587629	−0.0453365
$169$	−4.67431	−0.359562
$170$	0	0
$171$	1.41998	0.108589
$172$	4.40916	0.336195
$173$	−4.29306	−0.326395	−0.163197	−	0.986593i	$-0.552181\pi$
$173$	−4.29306	−0.326395	−0.163197	+	0.986593i	$0.552181\pi$
$174$	1.05918	0.0802965
$175$	0	0
$176$	1.16115	0.0875246
$177$	0.421508	0.0316825
$178$	−9.25008	−0.693323
$179$	7.83126	0.585336	0.292668	−	0.956214i	$-0.405457\pi$
$179$	7.83126	0.585336	0.292668	+	0.956214i	$0.405457\pi$
$180$	0	0
$181$	22.6384	1.68270	0.841349	−	0.540492i	$-0.181762\pi$
$181$	22.6384	1.68270	0.841349	+	0.540492i	$0.181762\pi$
$182$	−2.07637	−0.153911
$183$	−1.00668	−0.0744158
$184$	−5.06496	−0.373394
$185$	0	0
$186$	0.707088	0.0518462
$187$	−5.70202	−0.416973
$188$	9.81127	0.715560
$189$	1.39415	0.101410
$190$	0	0
$191$	−2.93357	−0.212265	−0.106133	−	0.994352i	$-0.533847\pi$
$191$	−2.93357	−0.212265	−0.106133	+	0.994352i	$0.533847\pi$
$192$	−0.442133	−0.0319082
$193$	−8.43884	−0.607441	−0.303721	−	0.952761i	$-0.598229\pi$
$193$	−8.43884	−0.607441	−0.303721	+	0.952761i	$0.598229\pi$
$194$	−5.13701	−0.368816
$195$	0	0
$196$	−1.48217	−0.105869
$197$	5.20370	0.370748	0.185374	−	0.982668i	$-0.440650\pi$
$197$	5.20370	0.370748	0.185374	+	0.982668i	$0.440650\pi$
$198$	2.11925	0.150608
$199$	14.7184	1.04336	0.521680	−	0.853141i	$-0.325305\pi$
$199$	14.7184	1.04336	0.521680	+	0.853141i	$0.325305\pi$
$200$	0	0
$201$	−1.30946	−0.0923624
$202$	2.84097	0.199890
$203$	6.27650	0.440524
$204$	−1.98191	−0.138761
$205$	0	0
$206$	−7.92871	−0.552419
$207$	5.95275	0.413745
$208$	3.35040	0.232308
$209$	−0.482165	−0.0333521
$210$	0	0
$211$	−14.6600	−1.00924	−0.504620	−	0.863342i	$-0.668367\pi$
$211$	−14.6600	−1.00924	−0.504620	+	0.863342i	$0.668367\pi$
$212$	5.16408	0.354670
$213$	−3.52415	−0.241471
$214$	3.03476	0.207452
$215$	0	0
$216$	3.49346	0.237700
$217$	4.19006	0.284440
$218$	−3.87768	−0.262630
$219$	−0.981753	−0.0663407
$220$	0	0
$221$	−16.4528	−1.10673
$222$	0.0400692	0.00268927
$223$	23.0265	1.54197	0.770986	−	0.636852i	$-0.219764\pi$
$223$	23.0265	1.54197	0.770986	+	0.636852i	$0.219764\pi$
$224$	−5.84715	−0.390679
$225$	0	0
$226$	−2.07952	−0.138327
$227$	−27.6251	−1.83355	−0.916773	−	0.399409i	$-0.869215\pi$
$227$	−27.6251	−1.83355	−0.916773	+	0.399409i	$0.869215\pi$
$228$	−0.167591	−0.0110990
$229$	13.2770	0.877369	0.438685	−	0.898641i	$-0.355445\pi$
$229$	13.2770	0.877369	0.438685	+	0.898641i	$0.355445\pi$
$230$	0	0
$231$	−0.234508	−0.0154295
$232$	15.7276	1.03257
$233$	−11.2430	−0.736551	−0.368276	−	0.929717i	$-0.620052\pi$
$233$	−11.2430	−0.736551	−0.368276	+	0.929717i	$0.620052\pi$
$234$	6.11493	0.399746
$235$	0	0
$236$	2.66407	0.173416
$237$	1.04261	0.0677248
$238$	4.10322	0.265972
$239$	−7.50560	−0.485497	−0.242748	−	0.970089i	$-0.578049\pi$
$239$	−7.50560	−0.485497	−0.242748	+	0.970089i	$0.578049\pi$
$240$	0	0
$241$	−23.3263	−1.50258	−0.751288	−	0.659974i	$-0.770567\pi$
$241$	−23.3263	−1.50258	−0.751288	+	0.659974i	$0.770567\pi$
$242$	−0.719607	−0.0462581
$243$	−6.17767	−0.396298
$244$	−6.36252	−0.407319
$245$	0	0
$246$	−0.00477589	−0.000304500 0
$247$	−1.39125	−0.0885233
$248$	10.4994	0.666713
$249$	−0.514885	−0.0326295
$250$	0	0
$251$	−14.4548	−0.912380	−0.456190	−	0.889882i	$-0.650786\pi$
$251$	−14.4548	−0.912380	−0.456190	+	0.889882i	$0.650786\pi$
$252$	4.36499	0.274968
$253$	−2.02130	−0.127078
$254$	−6.11424	−0.383642
$255$	0	0
$256$	−11.2097	−0.700608
$257$	−11.2103	−0.699279	−0.349639	−	0.936884i	$-0.613696\pi$
$257$	−11.2103	−0.699279	−0.349639	+	0.936884i	$0.613696\pi$
$258$	−0.502010	−0.0312538
$259$	0.237442	0.0147539
$260$	0	0
$261$	−18.4843	−1.14415
$262$	−10.3515	−0.639515
$263$	32.3075	1.99217	0.996084	−	0.0884132i	$-0.0281796\pi$
$263$	32.3075	1.99217	0.996084	+	0.0884132i	$0.0281796\pi$
$264$	−0.587629	−0.0361660
$265$	0	0
$266$	0.346970	0.0212741
$267$	−3.01445	−0.184481
$268$	−8.27622	−0.505551
$269$	8.33348	0.508101	0.254051	−	0.967191i	$-0.418237\pi$
$269$	8.33348	0.508101	0.254051	+	0.967191i	$0.418237\pi$
$270$	0	0
$271$	28.3842	1.72422	0.862110	−	0.506722i	$-0.169143\pi$
$271$	28.3842	1.72422	0.862110	+	0.506722i	$0.169143\pi$
$272$	−6.62088	−0.401450
$273$	−0.676656	−0.0409531
$274$	−10.8194	−0.653625
$275$	0	0
$276$	−0.702564	−0.0422894
$277$	22.9078	1.37640	0.688198	−	0.725522i	$-0.258402\pi$
$277$	22.9078	1.37640	0.688198	+	0.725522i	$0.258402\pi$
$278$	−3.03323	−0.181921
$279$	−12.3397	−0.738761
$280$	0	0
$281$	13.0481	0.778385	0.389192	−	0.921157i	$-0.372754\pi$
$281$	13.0481	0.778385	0.389192	+	0.921157i	$0.372754\pi$
$282$	−1.11707	−0.0665208
$283$	−26.9688	−1.60313	−0.801564	−	0.597909i	$-0.795998\pi$
$283$	−26.9688	−1.60313	−0.801564	+	0.597909i	$0.795998\pi$
$284$	−22.2737	−1.32170
$285$	0	0
$286$	−2.07637	−0.122779
$287$	−0.0283010	−0.00167055
$288$	17.2199	1.01469
$289$	15.5131	0.912534
$290$	0	0
$291$	−1.67407	−0.0981355
$292$	−6.20499	−0.363120
$293$	−11.9192	−0.696327	−0.348163	−	0.937434i	$-0.613195\pi$
$293$	−11.9192	−0.696327	−0.348163	+	0.937434i	$0.613195\pi$
$294$	0.168754	0.00984192
$295$	0	0
$296$	0.594980	0.0345825
$297$	1.39415	0.0808969
$298$	−9.59945	−0.556081
$299$	−5.83232	−0.337292
$300$	0	0
$301$	−2.97481	−0.171465
$302$	−8.88567	−0.511313
$303$	0.925824	0.0531872
$304$	−0.559864	−0.0321104
$305$	0	0
$306$	−12.0840	−0.690796
$307$	21.9485	1.25267	0.626334	−	0.779555i	$-0.284555\pi$
$307$	21.9485	1.25267	0.626334	+	0.779555i	$0.284555\pi$
$308$	−1.48217	−0.0844542
$309$	−2.58383	−0.146989
$310$	0	0
$311$	−9.63147	−0.546150	−0.273075	−	0.961993i	$-0.588041\pi$
$311$	−9.63147	−0.546150	−0.273075	+	0.961993i	$0.588041\pi$
$312$	−1.69556	−0.0959922
$313$	−23.3964	−1.32245	−0.661223	−	0.750190i	$-0.729962\pi$
$313$	−23.3964	−1.32245	−0.661223	+	0.750190i	$0.729962\pi$
$314$	−1.14563	−0.0646518
$315$	0	0
$316$	6.58963	0.370695
$317$	−3.53561	−0.198580	−0.0992898	−	0.995059i	$-0.531657\pi$
$317$	−3.53561	−0.198580	−0.0992898	+	0.995059i	$0.531657\pi$
$318$	−0.587962	−0.0329713
$319$	6.27650	0.351417
$320$	0	0
$321$	0.988978	0.0551994
$322$	1.45454	0.0810586
$323$	2.74932	0.152976
$324$	−12.6104	−0.700577
$325$	0	0
$326$	10.6003	0.587095
$327$	−1.26367	−0.0698813
$328$	−0.0709163	−0.00391570
$329$	−6.61955	−0.364948
$330$	0	0
$331$	−30.8444	−1.69536	−0.847680	−	0.530507i	$-0.822001\pi$
$331$	−30.8444	−1.69536	−0.847680	+	0.530507i	$0.822001\pi$
$332$	−3.25424	−0.178599
$333$	−0.699268	−0.0383196
$334$	−1.07269	−0.0586952
$335$	0	0
$336$	−0.272298	−0.0148551
$337$	5.24861	0.285910	0.142955	−	0.989729i	$-0.454340\pi$
$337$	5.24861	0.285910	0.142955	+	0.989729i	$0.454340\pi$
$338$	3.36367	0.182959
$339$	−0.677680	−0.0368065
$340$	0	0
$341$	4.19006	0.226904
$342$	−1.02183	−0.0552541
$343$	1.00000	0.0539949
$344$	−7.45425	−0.401906
$345$	0	0
$346$	3.08931	0.166083
$347$	20.1562	1.08204	0.541021	−	0.841009i	$-0.318038\pi$
$347$	20.1562	1.08204	0.541021	+	0.841009i	$0.318038\pi$
$348$	2.18159	0.116945
$349$	−32.3804	−1.73328	−0.866641	−	0.498932i	$-0.833726\pi$
$349$	−32.3804	−1.73328	−0.866641	+	0.498932i	$0.833726\pi$
$350$	0	0
$351$	4.02273	0.214717
$352$	−5.84715	−0.311654
$353$	−5.55866	−0.295858	−0.147929	−	0.988998i	$-0.547261\pi$
$353$	−5.55866	−0.295858	−0.147929	+	0.988998i	$0.547261\pi$
$354$	−0.303320	−0.0161213
$355$	0	0
$356$	−19.0523	−1.00977
$357$	1.33717	0.0707706
$358$	−5.63543	−0.297842
$359$	25.4986	1.34577	0.672883	−	0.739749i	$-0.265056\pi$
$359$	25.4986	1.34577	0.672883	+	0.739749i	$0.265056\pi$
$360$	0	0
$361$	−18.7675	−0.987764
$362$	−16.2908	−0.856223
$363$	−0.234508	−0.0123085
$364$	−4.27668	−0.224159
$365$	0	0
$366$	0.724413	0.0378657
$367$	11.0923	0.579014	0.289507	−	0.957176i	$-0.406509\pi$
$367$	11.0923	0.579014	0.289507	+	0.957176i	$0.406509\pi$
$368$	−2.34703	−0.122347
$369$	0.0833465	0.00433885
$370$	0	0
$371$	−3.48414	−0.180888
$372$	1.45638	0.0755098
$373$	9.63630	0.498949	0.249474	−	0.968381i	$-0.419742\pi$
$373$	9.63630	0.498949	0.249474	+	0.968381i	$0.419742\pi$
$374$	4.10322	0.212172
$375$	0	0
$376$	−16.5872	−0.855420
$377$	18.1104	0.932733
$378$	−1.00324	−0.0516012
$379$	12.7108	0.652910	0.326455	−	0.945213i	$-0.394146\pi$
$379$	12.7108	0.652910	0.326455	+	0.945213i	$0.394146\pi$
$380$	0	0
$381$	−1.99253	−0.102080
$382$	2.11102	0.108009
$383$	−20.7527	−1.06041	−0.530206	−	0.847869i	$-0.677885\pi$
$383$	−20.7527	−1.06041	−0.530206	+	0.847869i	$0.677885\pi$
$384$	−2.42425	−0.123712
$385$	0	0
$386$	6.07265	0.309090
$387$	8.76083	0.445338
$388$	−10.5806	−0.537150
$389$	−27.9126	−1.41522	−0.707612	−	0.706602i	$-0.750227\pi$
$389$	−27.9126	−1.41522	−0.707612	+	0.706602i	$0.750227\pi$
$390$	0	0
$391$	11.5255	0.582870
$392$	2.50579	0.126562
$393$	−3.37337	−0.170164
$394$	−3.74462	−0.188651
$395$	0	0
$396$	4.36499	0.219349
$397$	36.2364	1.81865	0.909327	−	0.416082i	$-0.136597\pi$
$397$	36.2364	1.81865	0.909327	+	0.416082i	$0.136597\pi$
$398$	−10.5915	−0.530903
$399$	0.113072	0.00566067
$400$	0	0
$401$	−0.834793	−0.0416876	−0.0208438	−	0.999783i	$-0.506635\pi$
$401$	−0.834793	−0.0416876	−0.0208438	+	0.999783i	$0.506635\pi$
$402$	0.942300	0.0469976
$403$	12.0901	0.602251
$404$	5.85150	0.291123
$405$	0	0
$406$	−4.51662	−0.224156
$407$	0.237442	0.0117696
$408$	3.35067	0.165883
$409$	33.3844	1.65075	0.825377	−	0.564582i	$-0.190963\pi$
$409$	33.3844	1.65075	0.825377	+	0.564582i	$0.190963\pi$
$410$	0	0
$411$	−3.52587	−0.173918
$412$	−16.3306	−0.804553
$413$	−1.79741	−0.0884450
$414$	−4.28364	−0.210529
$415$	0	0
$416$	−16.8715	−0.827195
$417$	−0.988481	−0.0484061
$418$	0.346970	0.0169708
$419$	−4.42402	−0.216128	−0.108064	−	0.994144i	$-0.534465\pi$
$419$	−4.42402	−0.216128	−0.108064	+	0.994144i	$0.534465\pi$
$420$	0	0
$421$	29.3677	1.43130	0.715648	−	0.698461i	$-0.246131\pi$
$421$	29.3677	1.43130	0.715648	+	0.698461i	$0.246131\pi$
$422$	10.5495	0.513540
$423$	19.4946	0.947861
$424$	−8.73054	−0.423992
$425$	0	0
$426$	2.53600	0.122870
$427$	4.29272	0.207739
$428$	6.25066	0.302137
$429$	−0.676656	−0.0326693
$430$	0	0
$431$	−9.83699	−0.473831	−0.236916	−	0.971530i	$-0.576136\pi$
$431$	−9.83699	−0.473831	−0.236916	+	0.971530i	$0.576136\pi$
$432$	1.61881	0.0778852
$433$	−41.4885	−1.99381	−0.996905	−	0.0786106i	$-0.974952\pi$
$433$	−41.4885	−1.99381	−0.996905	+	0.0786106i	$0.974952\pi$
$434$	−3.01519	−0.144734
$435$	0	0
$436$	−7.98681	−0.382499
$437$	0.974602	0.0466215
$438$	0.706477	0.0337568
$439$	12.8033	0.611068	0.305534	−	0.952181i	$-0.401165\pi$
$439$	12.8033	0.611068	0.305534	+	0.952181i	$0.401165\pi$
$440$	0	0
$441$	−2.94501	−0.140238
$442$	11.8395	0.563149
$443$	−37.2507	−1.76983	−0.884916	−	0.465750i	$-0.845785\pi$
$443$	−37.2507	−1.76983	−0.884916	+	0.465750i	$0.845785\pi$
$444$	0.0825300	0.00391670
$445$	0	0
$446$	−16.5701	−0.784616
$447$	−3.12830	−0.147964
$448$	1.88536	0.0890750
$449$	−16.4116	−0.774509	−0.387255	−	0.921973i	$-0.626577\pi$
$449$	−16.4116	−0.774509	−0.387255	+	0.921973i	$0.626577\pi$
$450$	0	0
$451$	−0.0283010	−0.00133264
$452$	−4.28315	−0.201463
$453$	−2.89569	−0.136052
$454$	19.8793	0.932980
$455$	0	0
$456$	0.283334	0.0132683
$457$	17.5812	0.822414	0.411207	−	0.911542i	$-0.365107\pi$
$457$	17.5812	0.822414	0.411207	+	0.911542i	$0.365107\pi$
$458$	−9.55423	−0.446440
$459$	−7.94949	−0.371050
$460$	0	0
$461$	−22.3753	−1.04212	−0.521062	−	0.853519i	$-0.674464\pi$
$461$	−22.3753	−1.04212	−0.521062	+	0.853519i	$0.674464\pi$
$462$	0.168754	0.00785114
$463$	−4.36955	−0.203070	−0.101535	−	0.994832i	$-0.532375\pi$
$463$	−4.36955	−0.203070	−0.101535	+	0.994832i	$0.532375\pi$
$464$	7.28793	0.338334
$465$	0	0
$466$	8.09052	0.374786
$467$	−32.5359	−1.50558	−0.752790	−	0.658261i	$-0.771292\pi$
$467$	−32.5359	−1.50558	−0.752790	+	0.658261i	$0.771292\pi$
$468$	12.5948	0.582197
$469$	5.58387	0.257839
$470$	0	0
$471$	−0.373343	−0.0172027
$472$	−4.50395	−0.207311
$473$	−2.97481	−0.136782
$474$	−0.750270	−0.0344610
$475$	0	0
$476$	8.45134	0.387367
$477$	10.2608	0.469811
$478$	5.40108	0.247040
$479$	31.9228	1.45859	0.729296	−	0.684198i	$-0.239848\pi$
$479$	31.9228	1.45859	0.729296	+	0.684198i	$0.239848\pi$
$480$	0	0
$481$	0.685121	0.0312388
$482$	16.7857	0.764570
$483$	0.474012	0.0215683
$484$	−1.48217	−0.0673712
$485$	0	0
$486$	4.44550	0.201652
$487$	23.2240	1.05238	0.526191	−	0.850366i	$-0.323620\pi$
$487$	23.2240	1.05238	0.526191	+	0.850366i	$0.323620\pi$
$488$	10.7567	0.486931
$489$	3.45446	0.156216
$490$	0	0
$491$	27.5220	1.24205	0.621025	−	0.783791i	$-0.286717\pi$
$491$	27.5220	1.24205	0.621025	+	0.783791i	$0.286717\pi$
$492$	−0.00983685	−0.000443479 0
$493$	−35.7888	−1.61185
$494$	1.00116	0.0450441
$495$	0	0
$496$	4.86526	0.218457
$497$	15.0278	0.674091
$498$	0.370515	0.0166032
$499$	30.4828	1.36460	0.682298	−	0.731074i	$-0.260981\pi$
$499$	30.4828	1.36460	0.682298	+	0.731074i	$0.260981\pi$
$500$	0	0
$501$	−0.349573	−0.0156178
$502$	10.4018	0.464255
$503$	−6.49000	−0.289375	−0.144687	−	0.989477i	$-0.546218\pi$
$503$	−6.49000	−0.289375	−0.144687	+	0.989477i	$0.546218\pi$
$504$	−7.37957	−0.328712
$505$	0	0
$506$	1.45454	0.0646624
$507$	1.09616	0.0486823
$508$	−12.5934	−0.558743
$509$	−31.2638	−1.38574	−0.692871	−	0.721061i	$-0.743655\pi$
$509$	−31.2638	−1.38574	−0.692871	+	0.721061i	$0.743655\pi$
$510$	0	0
$511$	4.18643	0.185197
$512$	−12.6086	−0.557225
$513$	−0.672212	−0.0296789
$514$	8.06700	0.355820
$515$	0	0
$516$	−1.03398	−0.0455186
$517$	−6.61955	−0.291128
$518$	−0.170865	−0.00750737
$519$	1.00676	0.0441917
$520$	0	0
$521$	−38.1186	−1.67001	−0.835003	−	0.550245i	$-0.814534\pi$
$521$	−38.1186	−1.67001	−0.835003	+	0.550245i	$0.814534\pi$
$522$	13.3015	0.582189
$523$	5.28977	0.231305	0.115653	−	0.993290i	$-0.463104\pi$
$523$	5.28977	0.231305	0.115653	+	0.993290i	$0.463104\pi$
$524$	−21.3208	−0.931401
$525$	0	0
$526$	−23.2487	−1.01369
$527$	−23.8918	−1.04074
$528$	−0.272298	−0.0118503
$529$	−18.9143	−0.822362
$530$	0	0
$531$	5.29340	0.229714
$532$	0.714649	0.0309840
$533$	−0.0816604	−0.00353710
$534$	2.16922	0.0938713
$535$	0	0
$536$	13.9920	0.604363
$537$	−1.83649	−0.0792505
$538$	−5.99683	−0.258542
$539$	1.00000	0.0430730
$540$	0	0
$541$	−23.7129	−1.01950	−0.509749	−	0.860323i	$-0.670262\pi$
$541$	−23.7129	−1.01950	−0.509749	+	0.860323i	$0.670262\pi$
$542$	−20.4255	−0.877350
$543$	−5.30889	−0.227826
$544$	33.3406	1.42947
$545$	0	0
$546$	0.486927	0.0208385
$547$	36.1017	1.54360	0.771799	−	0.635867i	$-0.219357\pi$
$547$	36.1017	1.54360	0.771799	+	0.635867i	$0.219357\pi$
$548$	−22.2846	−0.951951
$549$	−12.6421	−0.539551
$550$	0	0
$551$	−3.02631	−0.128925
$552$	1.18778	0.0505551
$553$	−4.44594	−0.189061
$554$	−16.4846	−0.700365
$555$	0	0
$556$	−6.24751	−0.264954
$557$	−24.0378	−1.01852	−0.509258	−	0.860614i	$-0.670080\pi$
$557$	−24.0378	−1.01852	−0.509258	+	0.860614i	$0.670080\pi$
$558$	8.87977	0.375910
$559$	−8.58359	−0.363047
$560$	0	0
$561$	1.33717	0.0564554
$562$	−9.38951	−0.396073
$563$	−44.8909	−1.89192	−0.945962	−	0.324277i	$-0.894879\pi$
$563$	−44.8909	−1.89192	−0.945962	+	0.324277i	$0.894879\pi$
$564$	−2.30082	−0.0968821
$565$	0	0
$566$	19.4069	0.815734
$567$	8.50808	0.357306
$568$	37.6566	1.58004
$569$	3.00190	0.125846	0.0629232	−	0.998018i	$-0.479958\pi$
$569$	3.00190	0.125846	0.0629232	+	0.998018i	$0.479958\pi$
$570$	0	0
$571$	27.2927	1.14216	0.571082	−	0.820893i	$-0.306524\pi$
$571$	27.2927	1.14216	0.571082	+	0.820893i	$0.306524\pi$
$572$	−4.27668	−0.178817
$573$	0.687945	0.0287393
$574$	0.0203656	0.000850043 0
$575$	0	0
$576$	−5.55240	−0.231350
$577$	−45.6074	−1.89866	−0.949330	−	0.314282i	$-0.898236\pi$
$577$	−45.6074	−1.89866	−0.949330	+	0.314282i	$0.898236\pi$
$578$	−11.1633	−0.464333
$579$	1.97898	0.0822435
$580$	0	0
$581$	2.19560	0.0910887
$582$	1.20467	0.0499352
$583$	−3.48414	−0.144298
$584$	10.4903	0.434093
$585$	0	0
$586$	8.57714	0.354318
$587$	15.2252	0.628409	0.314205	−	0.949355i	$-0.398262\pi$
$587$	15.2252	0.628409	0.314205	+	0.949355i	$0.398262\pi$
$588$	0.347580	0.0143340
$589$	−2.02030	−0.0832450
$590$	0	0
$591$	−1.22031	−0.0501968
$592$	0.275704	0.0113314
$593$	−3.31115	−0.135973	−0.0679863	−	0.997686i	$-0.521657\pi$
$593$	−3.31115	−0.135973	−0.0679863	+	0.997686i	$0.521657\pi$
$594$	−1.00324	−0.0411635
$595$	0	0
$596$	−19.7719	−0.809887
$597$	−3.45159	−0.141264
$598$	4.19698	0.171627
$599$	−32.7530	−1.33825	−0.669126	−	0.743149i	$-0.733331\pi$
$599$	−32.7530	−1.33825	−0.669126	+	0.743149i	$0.733331\pi$
$600$	0	0
$601$	31.4852	1.28431	0.642153	−	0.766576i	$-0.278041\pi$
$601$	31.4852	1.28431	0.642153	+	0.766576i	$0.278041\pi$
$602$	2.14069	0.0872481
$603$	−16.4445	−0.669673
$604$	−18.3017	−0.744686
$605$	0	0
$606$	−0.666230	−0.0270637
$607$	−27.7141	−1.12488	−0.562441	−	0.826838i	$-0.690138\pi$
$607$	−27.7141	−1.12488	−0.562441	+	0.826838i	$0.690138\pi$
$608$	2.81929	0.114337
$609$	−1.47189	−0.0596440
$610$	0	0
$611$	−19.1002	−0.772713
$612$	−24.8893	−1.00609
$613$	−8.82364	−0.356383	−0.178192	−	0.983996i	$-0.557025\pi$
$613$	−8.82364	−0.356383	−0.178192	+	0.983996i	$0.557025\pi$
$614$	−15.7943	−0.637407
$615$	0	0
$616$	2.50579	0.100961
$617$	6.54016	0.263297	0.131648	−	0.991296i	$-0.457973\pi$
$617$	6.54016	0.263297	0.131648	+	0.991296i	$0.457973\pi$
$618$	1.85935	0.0747939
$619$	7.74443	0.311275	0.155638	−	0.987814i	$-0.450257\pi$
$619$	7.74443	0.311275	0.155638	+	0.987814i	$0.450257\pi$
$620$	0	0
$621$	−2.81800	−0.113083
$622$	6.93087	0.277903
$623$	12.8543	0.514998
$624$	−0.785696	−0.0314530
$625$	0	0
$626$	16.8363	0.672912
$627$	0.113072	0.00451565
$628$	−2.35965	−0.0941601
$629$	−1.35390	−0.0539835
$630$	0	0
$631$	−15.0244	−0.598113	−0.299056	−	0.954235i	$-0.596672\pi$
$631$	−15.0244	−0.598113	−0.299056	+	0.954235i	$0.596672\pi$
$632$	−11.1406	−0.443150
$633$	3.43790	0.136644
$634$	2.54425	0.101045
$635$	0	0
$636$	−1.21102	−0.0480200
$637$	2.88543	0.114325
$638$	−4.51662	−0.178815
$639$	−44.2571	−1.75078
$640$	0	0
$641$	−9.68890	−0.382688	−0.191344	−	0.981523i	$-0.561285\pi$
$641$	−9.68890	−0.382688	−0.191344	+	0.981523i	$0.561285\pi$
$642$	−0.711676	−0.0280876
$643$	7.71151	0.304112	0.152056	−	0.988372i	$-0.451411\pi$
$643$	7.71151	0.304112	0.152056	+	0.988372i	$0.451411\pi$
$644$	2.99590	0.118055
$645$	0	0
$646$	−1.97843	−0.0778403
$647$	−7.28870	−0.286548	−0.143274	−	0.989683i	$-0.545763\pi$
$647$	−7.28870	−0.286548	−0.143274	+	0.989683i	$0.545763\pi$
$648$	21.3195	0.837508
$649$	−1.79741	−0.0705547
$650$	0	0
$651$	−0.982602	−0.0385112
$652$	21.8333	0.855057
$653$	28.0103	1.09613	0.548063	−	0.836437i	$-0.315365\pi$
$653$	28.0103	1.09613	0.548063	+	0.836437i	$0.315365\pi$
$654$	0.909349	0.0355583
$655$	0	0
$656$	−0.0328615	−0.00128303
$657$	−12.3291	−0.481003
$658$	4.76348	0.185700
$659$	22.7257	0.885267	0.442633	−	0.896703i	$-0.354044\pi$
$659$	22.7257	0.885267	0.442633	+	0.896703i	$0.354044\pi$
$660$	0	0
$661$	−30.9280	−1.20296	−0.601480	−	0.798888i	$-0.705422\pi$
$661$	−30.9280	−1.20296	−0.601480	+	0.798888i	$0.705422\pi$
$662$	22.1958	0.862666
$663$	3.85831	0.149844
$664$	5.50171	0.213508
$665$	0	0
$666$	0.503198	0.0194985
$667$	−12.6867	−0.491231
$668$	−2.20941	−0.0854847
$669$	−5.39991	−0.208773
$670$	0	0
$671$	4.29272	0.165719
$672$	1.37120	0.0528954
$673$	10.6536	0.410667	0.205334	−	0.978692i	$-0.434172\pi$
$673$	10.6536	0.410667	0.205334	+	0.978692i	$0.434172\pi$
$674$	−3.77694	−0.145482
$675$	0	0
$676$	6.92810	0.266465
$677$	10.0685	0.386963	0.193481	−	0.981104i	$-0.438022\pi$
$677$	10.0685	0.386963	0.193481	+	0.981104i	$0.438022\pi$
$678$	0.487664	0.0187286
$679$	7.13863	0.273955
$680$	0	0
$681$	6.47832	0.248250
$682$	−3.01519	−0.115458
$683$	10.2912	0.393780	0.196890	−	0.980426i	$-0.436916\pi$
$683$	10.2912	0.393780	0.196890	+	0.980426i	$0.436916\pi$
$684$	−2.10465	−0.0804731
$685$	0	0
$686$	−0.719607	−0.0274747
$687$	−3.11357	−0.118790
$688$	−3.45418	−0.131690
$689$	−10.0532	−0.382998
$690$	0	0
$691$	23.4537	0.892219	0.446110	−	0.894978i	$-0.352809\pi$
$691$	23.4537	0.892219	0.446110	+	0.894978i	$0.352809\pi$
$692$	6.36302	0.241886
$693$	−2.94501	−0.111872
$694$	−14.5046	−0.550586
$695$	0	0
$696$	−3.68825	−0.139803
$697$	0.161373	0.00611243
$698$	23.3012	0.881962
$699$	2.63657	0.0997241
$700$	0	0
$701$	−22.1969	−0.838365	−0.419183	−	0.907902i	$-0.637683\pi$
$701$	−22.1969	−0.838365	−0.419183	+	0.907902i	$0.637683\pi$
$702$	−2.89478	−0.109257
$703$	−0.114486	−0.00431793
$704$	1.88536	0.0710573
$705$	0	0
$706$	4.00006	0.150544
$707$	−3.94794	−0.148478
$708$	−0.624745	−0.0234794
$709$	22.2406	0.835264	0.417632	−	0.908616i	$-0.362860\pi$
$709$	22.2406	0.835264	0.417632	+	0.908616i	$0.362860\pi$
$710$	0	0
$711$	13.0933	0.491038
$712$	32.2103	1.20713
$713$	−8.46937	−0.317180
$714$	−0.962238	−0.0360109
$715$	0	0
$716$	−11.6072	−0.433782
$717$	1.76012	0.0657330
$718$	−18.3490	−0.684779
$719$	22.0841	0.823597	0.411799	−	0.911275i	$-0.364901\pi$
$719$	22.0841	0.823597	0.411799	+	0.911275i	$0.364901\pi$
$720$	0	0
$721$	11.0181	0.410336
$722$	13.5052	0.502613
$723$	5.47020	0.203439
$724$	−33.5538	−1.24702
$725$	0	0
$726$	0.168754	0.00626304
$727$	−4.73566	−0.175636	−0.0878180	−	0.996137i	$-0.527989\pi$
$727$	−4.73566	−0.175636	−0.0878180	+	0.996137i	$0.527989\pi$
$728$	7.23028	0.267972
$729$	−24.0755	−0.891686
$730$	0	0
$731$	16.9624	0.627378
$732$	1.49206	0.0551482
$733$	47.1786	1.74258	0.871290	−	0.490768i	$-0.163284\pi$
$733$	47.1786	1.74258	0.871290	+	0.490768i	$0.163284\pi$
$734$	−7.98211	−0.294625
$735$	0	0
$736$	11.8189	0.435649
$737$	5.58387	0.205685
$738$	−0.0599767	−0.00220777
$739$	17.2870	0.635914	0.317957	−	0.948105i	$-0.397003\pi$
$739$	17.2870	0.635914	0.317957	+	0.948105i	$0.397003\pi$
$740$	0	0
$741$	0.326260	0.0119855
$742$	2.50721	0.0920427
$743$	30.6350	1.12389	0.561945	−	0.827174i	$-0.310053\pi$
$743$	30.6350	1.12389	0.561945	+	0.827174i	$0.310053\pi$
$744$	−2.46220	−0.0902685
$745$	0	0
$746$	−6.93435	−0.253885
$747$	−6.46605	−0.236580
$748$	8.45134	0.309012
$749$	−4.21725	−0.154095
$750$	0	0
$751$	22.5808	0.823985	0.411993	−	0.911187i	$-0.364833\pi$
$751$	22.5808	0.823985	0.411993	+	0.911187i	$0.364833\pi$
$752$	−7.68626	−0.280289
$753$	3.38977	0.123530
$754$	−13.0324	−0.474611
$755$	0	0
$756$	−2.06636	−0.0751530
$757$	42.1108	1.53054	0.765272	−	0.643707i	$-0.222604\pi$
$757$	42.1108	1.53054	0.765272	+	0.643707i	$0.222604\pi$
$758$	−9.14678	−0.332226
$759$	0.474012	0.0172055
$760$	0	0
$761$	−47.4949	−1.72169	−0.860845	−	0.508868i	$-0.830064\pi$
$761$	−47.4949	−1.72169	−0.860845	+	0.508868i	$0.830064\pi$
$762$	1.43384	0.0519425
$763$	5.38861	0.195081
$764$	4.34803	0.157306
$765$	0	0
$766$	14.9338	0.539579
$767$	−5.18631	−0.187267
$768$	2.62877	0.0948576
$769$	37.5199	1.35300	0.676501	−	0.736442i	$-0.263495\pi$
$769$	37.5199	1.35300	0.676501	+	0.736442i	$0.263495\pi$
$770$	0	0
$771$	2.62890	0.0946777
$772$	12.5078	0.450164
$773$	20.9518	0.753584	0.376792	−	0.926298i	$-0.377027\pi$
$773$	20.9518	0.753584	0.376792	+	0.926298i	$0.377027\pi$
$774$	−6.30435	−0.226605
$775$	0	0
$776$	17.8879	0.642138
$777$	−0.0556820	−0.00199758
$778$	20.0861	0.720121
$779$	0.0136457	0.000488910 0
$780$	0	0
$781$	15.0278	0.537738
$782$	−8.29384	−0.296587
$783$	8.75040	0.312714
$784$	1.16115	0.0414695
$785$	0	0
$786$	2.42750	0.0865861
$787$	−23.4069	−0.834366	−0.417183	−	0.908823i	$-0.636983\pi$
$787$	−23.4069	−0.834366	−0.417183	+	0.908823i	$0.636983\pi$
$788$	−7.71274	−0.274755
$789$	−7.57638	−0.269726
$790$	0	0
$791$	2.88979	0.102749
$792$	−7.37957	−0.262222
$793$	12.3863	0.439851
$794$	−26.0760	−0.925403
$795$	0	0
$796$	−21.8151	−0.773217
$797$	0.618197	0.0218976	0.0109488	−	0.999940i	$-0.496515\pi$
$797$	0.618197	0.0218976	0.0109488	+	0.999940i	$0.496515\pi$
$798$	−0.0813672	−0.00288037
$799$	37.7448	1.33532
$800$	0	0
$801$	−37.8561	−1.33758
$802$	0.600723	0.0212123
$803$	4.18643	0.147736
$804$	1.94084	0.0684482
$805$	0	0
$806$	−8.70013	−0.306449
$807$	−1.95427	−0.0687935
$808$	−9.89271	−0.348024
$809$	7.48143	0.263033	0.131517	−	0.991314i	$-0.458015\pi$
$809$	7.48143	0.263033	0.131517	+	0.991314i	$0.458015\pi$
$810$	0	0
$811$	50.7768	1.78301	0.891507	−	0.453007i	$-0.149649\pi$
$811$	50.7768	1.78301	0.891507	+	0.453007i	$0.149649\pi$
$812$	−9.30282	−0.326465
$813$	−6.65634	−0.233448
$814$	−0.170865	−0.00598881
$815$	0	0
$816$	1.55265	0.0543536
$817$	1.43435	0.0501815
$818$	−24.0237	−0.839968
$819$	−8.49760	−0.296930
$820$	0	0
$821$	44.7903	1.56319	0.781597	−	0.623784i	$-0.214406\pi$
$821$	44.7903	1.56319	0.781597	+	0.623784i	$0.214406\pi$
$822$	2.53724	0.0884965
$823$	−0.757168	−0.0263932	−0.0131966	−	0.999913i	$-0.504201\pi$
$823$	−0.757168	−0.0263932	−0.0131966	+	0.999913i	$0.504201\pi$
$824$	27.6091	0.961807
$825$	0	0
$826$	1.29343	0.0450043
$827$	−11.6236	−0.404192	−0.202096	−	0.979366i	$-0.564775\pi$
$827$	−11.6236	−0.404192	−0.202096	+	0.979366i	$0.564775\pi$
$828$	−8.82296	−0.306619
$829$	14.3204	0.497368	0.248684	−	0.968585i	$-0.420002\pi$
$829$	14.3204	0.497368	0.248684	+	0.968585i	$0.420002\pi$
$830$	0	0
$831$	−5.37207	−0.186355
$832$	5.44008	0.188601
$833$	−5.70202	−0.197563
$834$	0.711318	0.0246309
$835$	0	0
$836$	0.714649	0.0247166
$837$	5.84158	0.201914
$838$	3.18356	0.109974
$839$	−30.6836	−1.05932	−0.529658	−	0.848211i	$-0.677680\pi$
$839$	−30.6836	−1.05932	−0.529658	+	0.848211i	$0.677680\pi$
$840$	0	0
$841$	10.3945	0.358431
$842$	−21.1332	−0.728299
$843$	−3.05989	−0.105388
$844$	21.7286	0.747930
$845$	0	0
$846$	−14.0285	−0.482309
$847$	1.00000	0.0343604
$848$	−4.04560	−0.138926
$849$	6.32440	0.217053
$850$	0	0
$851$	−0.479942	−0.0164522
$852$	5.22337	0.178950
$853$	−16.3472	−0.559719	−0.279859	−	0.960041i	$-0.590288\pi$
$853$	−16.3472	−0.559719	−0.279859	+	0.960041i	$0.590288\pi$
$854$	−3.08907	−0.105706
$855$	0	0
$856$	−10.5675	−0.361191
$857$	−30.7703	−1.05109	−0.525546	−	0.850765i	$-0.676139\pi$
$857$	−30.7703	−1.05109	−0.525546	+	0.850765i	$0.676139\pi$
$858$	0.486927	0.0166234
$859$	31.0087	1.05800	0.529002	−	0.848621i	$-0.322567\pi$
$859$	31.0087	1.05800	0.529002	+	0.848621i	$0.322567\pi$
$860$	0	0
$861$	0.00663681	0.000226182 0
$862$	7.07877	0.241104
$863$	45.6367	1.55349	0.776746	−	0.629814i	$-0.216869\pi$
$863$	45.6367	1.55349	0.776746	+	0.629814i	$0.216869\pi$
$864$	−8.15182	−0.277331
$865$	0	0
$866$	29.8554	1.01453
$867$	−3.63794	−0.123551
$868$	−6.21036	−0.210793
$869$	−4.44594	−0.150818
$870$	0	0
$871$	16.1119	0.545929
$872$	13.5027	0.457260
$873$	−21.0233	−0.711531
$874$	−0.701331	−0.0237229
$875$	0	0
$876$	1.45512	0.0491640
$877$	−41.5678	−1.40365	−0.701823	−	0.712351i	$-0.747630\pi$
$877$	−41.5678	−1.40365	−0.701823	+	0.712351i	$0.747630\pi$
$878$	−9.21335	−0.310935
$879$	2.79515	0.0942780
$880$	0	0
$881$	5.99084	0.201836	0.100918	−	0.994895i	$-0.467822\pi$
$881$	5.99084	0.201836	0.100918	+	0.994895i	$0.467822\pi$
$882$	2.11925	0.0713588
$883$	−1.58428	−0.0533154	−0.0266577	−	0.999645i	$-0.508486\pi$
$883$	−1.58428	−0.0533154	−0.0266577	+	0.999645i	$0.508486\pi$
$884$	24.3857	0.820181
$885$	0	0
$886$	26.8058	0.900560
$887$	−22.4766	−0.754690	−0.377345	−	0.926073i	$-0.623163\pi$
$887$	−22.4766	−0.754690	−0.377345	+	0.926073i	$0.623163\pi$
$888$	−0.139528	−0.00468224
$889$	8.49664	0.284968
$890$	0	0
$891$	8.50808	0.285031
$892$	−34.1292	−1.14273
$893$	3.19172	0.106807
$894$	2.25115	0.0752897
$895$	0	0
$896$	10.3376	0.345354
$897$	1.36773	0.0456671
$898$	11.8099	0.394101
$899$	26.2989	0.877117
$900$	0	0
$901$	19.8667	0.661855
$902$	0.0203656	0.000678100 0
$903$	0.697617	0.0232152
$904$	7.24122	0.240839
$905$	0	0
$906$	2.08376	0.0692284
$907$	−25.3031	−0.840174	−0.420087	−	0.907484i	$-0.638000\pi$
$907$	−25.3031	−0.840174	−0.420087	+	0.907484i	$0.638000\pi$
$908$	40.9450	1.35881
$909$	11.6267	0.385633
$910$	0	0
$911$	24.1334	0.799574	0.399787	−	0.916608i	$-0.369084\pi$
$911$	24.1334	0.799574	0.399787	+	0.916608i	$0.369084\pi$
$912$	0.131293	0.00434754
$913$	2.19560	0.0726636
$914$	−12.6516	−0.418477
$915$	0	0
$916$	−19.6787	−0.650203
$917$	14.3849	0.475030
$918$	5.72051	0.188805
$919$	36.0953	1.19067	0.595337	−	0.803476i	$-0.297019\pi$
$919$	36.0953	1.19067	0.595337	+	0.803476i	$0.297019\pi$
$920$	0	0
$921$	−5.14711	−0.169603
$922$	16.1015	0.530273
$923$	43.3617	1.42727
$924$	0.347580	0.0114345
$925$	0	0
$926$	3.14436	0.103330
$927$	−32.4484	−1.06574
$928$	−36.6997	−1.20473
$929$	30.0900	0.987222	0.493611	−	0.869683i	$-0.335677\pi$
$929$	30.0900	0.987222	0.493611	+	0.869683i	$0.335677\pi$
$930$	0	0
$931$	−0.482165	−0.0158023
$932$	16.6639	0.545845
$933$	2.25866	0.0739451
$934$	23.4130	0.766098
$935$	0	0
$936$	−21.2932	−0.695991
$937$	−27.6115	−0.902028	−0.451014	−	0.892517i	$-0.648938\pi$
$937$	−27.6115	−0.902028	−0.451014	+	0.892517i	$0.648938\pi$
$938$	−4.01819	−0.131199
$939$	5.48666	0.179050
$940$	0	0
$941$	−49.2488	−1.60546	−0.802732	−	0.596339i	$-0.796621\pi$
$941$	−49.2488	−1.60546	−0.802732	+	0.596339i	$0.796621\pi$
$942$	0.268660	0.00875343
$943$	0.0572048	0.00186284
$944$	−2.08706	−0.0679280
$945$	0	0
$946$	2.14069	0.0695999
$947$	5.47029	0.177761	0.0888803	−	0.996042i	$-0.471671\pi$
$947$	5.47029	0.177761	0.0888803	+	0.996042i	$0.471671\pi$
$948$	−1.54532	−0.0501897
$949$	12.0797	0.392122
$950$	0	0
$951$	0.829129	0.0268864
$952$	−14.2881	−0.463079
$953$	44.0988	1.42850	0.714251	−	0.699890i	$-0.246768\pi$
$953$	44.0988	1.42850	0.714251	+	0.699890i	$0.246768\pi$
$954$	−7.38376	−0.239058
$955$	0	0
$956$	11.1245	0.359793
$957$	−1.47189	−0.0475795
$958$	−22.9719	−0.742189
$959$	15.0352	0.485511
$960$	0	0
$961$	−13.4434	−0.433659
$962$	−0.493018	−0.0158955
$963$	12.4198	0.400223
$964$	34.5734	1.11353
$965$	0	0
$966$	−0.341102	−0.0109748
$967$	13.6320	0.438377	0.219188	−	0.975683i	$-0.429659\pi$
$967$	13.6320	0.438377	0.219188	+	0.975683i	$0.429659\pi$
$968$	2.50579	0.0805392
$969$	−0.644738	−0.0207120
$970$	0	0
$971$	2.47904	0.0795562	0.0397781	−	0.999209i	$-0.487335\pi$
$971$	2.47904	0.0795562	0.0397781	+	0.999209i	$0.487335\pi$
$972$	9.15633	0.293689
$973$	4.21512	0.135131
$974$	−16.7122	−0.535493
$975$	0	0
$976$	4.98447	0.159549
$977$	39.4552	1.26229	0.631143	−	0.775667i	$-0.282586\pi$
$977$	39.4552	1.26229	0.631143	+	0.775667i	$0.282586\pi$
$978$	−2.48585	−0.0794888
$979$	12.8543	0.410827
$980$	0	0
$981$	−15.8695	−0.506674
$982$	−19.8050	−0.632003
$983$	19.7144	0.628791	0.314396	−	0.949292i	$-0.398198\pi$
$983$	19.7144	0.628791	0.314396	+	0.949292i	$0.398198\pi$
$984$	0.0166305	0.000530160 0
$985$	0	0
$986$	25.7539	0.820170
$987$	1.55234	0.0494115
$988$	2.06207	0.0656031
$989$	6.01299	0.191202
$990$	0	0
$991$	1.41064	0.0448105	0.0224053	−	0.999749i	$-0.492868\pi$
$991$	1.41064	0.0448105	0.0224053	+	0.999749i	$0.492868\pi$
$992$	−24.4999	−0.777872
$993$	7.23326	0.229541
$994$	−10.8141	−0.343004
$995$	0	0
$996$	0.763145	0.0241812
$997$	−0.634876	−0.0201067	−0.0100534	−	0.999949i	$-0.503200\pi$
$997$	−0.634876	−0.0201067	−0.0100534	+	0.999949i	$0.503200\pi$
$998$	−21.9356	−0.694360
$999$	0.331030	0.0104733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.2.a.bd.1.3	yes	7
5.2	odd	4		1925.2.b.r.1849.6		14
5.3	odd	4		1925.2.b.r.1849.9		14
5.4	even	2		1925.2.a.bb.1.5	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1925.2.a.bb.1.5	✓	7	5.4	even	2
1925.2.a.bd.1.3	yes	7	1.1	even	1	trivial
1925.2.b.r.1849.6		14	5.2	odd	4
1925.2.b.r.1849.9		14	5.3	odd	4

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:	\( N \)	\(=\)	\( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1925.a (trivial)

\(f(q)\)	\(=\)	\(q-0.719607 q^{2} -0.234508 q^{3} -1.48217 q^{4} +0.168754 q^{6} +1.00000 q^{7} +2.50579 q^{8} -2.94501 q^{9} +O(q^{10})\)	\(q-0.719607 q^{2} -0.234508 q^{3} -1.48217 q^{4} +0.168754 q^{6} +1.00000 q^{7} +2.50579 q^{8} -2.94501 q^{9} +1.00000 q^{11} +0.347580 q^{12} +2.88543 q^{13} -0.719607 q^{14} +1.16115 q^{16} -5.70202 q^{17} +2.11925 q^{18} -0.482165 q^{19} -0.234508 q^{21} -0.719607 q^{22} -2.02130 q^{23} -0.587629 q^{24} -2.07637 q^{26} +1.39415 q^{27} -1.48217 q^{28} +6.27650 q^{29} +4.19006 q^{31} -5.84715 q^{32} -0.234508 q^{33} +4.10322 q^{34} +4.36499 q^{36} +0.237442 q^{37} +0.346970 q^{38} -0.676656 q^{39} -0.0283010 q^{41} +0.168754 q^{42} -2.97481 q^{43} -1.48217 q^{44} +1.45454 q^{46} -6.61955 q^{47} -0.272298 q^{48} +1.00000 q^{49} +1.33717 q^{51} -4.27668 q^{52} -3.48414 q^{53} -1.00324 q^{54} +2.50579 q^{56} +0.113072 q^{57} -4.51662 q^{58} -1.79741 q^{59} +4.29272 q^{61} -3.01519 q^{62} -2.94501 q^{63} +1.88536 q^{64} +0.168754 q^{66} +5.58387 q^{67} +8.45134 q^{68} +0.474012 q^{69} +15.0278 q^{71} -7.37957 q^{72} +4.18643 q^{73} -0.170865 q^{74} +0.714649 q^{76} +1.00000 q^{77} +0.486927 q^{78} -4.44594 q^{79} +8.50808 q^{81} +0.0203656 q^{82} +2.19560 q^{83} +0.347580 q^{84} +2.14069 q^{86} -1.47189 q^{87} +2.50579 q^{88} +12.8543 q^{89} +2.88543 q^{91} +2.99590 q^{92} -0.982602 q^{93} +4.76348 q^{94} +1.37120 q^{96} +7.13863 q^{97} -0.719607 q^{98} -2.94501 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} + 13 q^{4} + 3 q^{6} + 7 q^{7} + 9 q^{9}+O(q^{10}) \) 7 * q + q^2 + 13 * q^4 + 3 * q^6 + 7 * q^7 + 9 * q^9	\( 7 q + q^{2} + 13 q^{4} + 3 q^{6} + 7 q^{7} + 9 q^{9} + 7 q^{11} - 9 q^{12} - 3 q^{13} + q^{14} + 21 q^{16} - 2 q^{17} + 8 q^{18} + 20 q^{19} + q^{22} + 11 q^{23} + 18 q^{24} - 13 q^{26} - 12 q^{27} + 13 q^{28} + 4 q^{29} + 6 q^{31} + q^{32} - 7 q^{34} + 12 q^{36} + 19 q^{37} + 3 q^{38} - 10 q^{39} + 24 q^{41} + 3 q^{42} + 13 q^{44} + 33 q^{46} - q^{47} - 15 q^{48} + 7 q^{49} + 19 q^{51} - 29 q^{52} + 7 q^{53} + 9 q^{54} - 9 q^{57} + 37 q^{58} + 9 q^{59} + 18 q^{61} - 40 q^{62} + 9 q^{63} + 8 q^{64} + 3 q^{66} + 18 q^{68} - 15 q^{69} + 18 q^{71} - 64 q^{72} + 5 q^{73} - 24 q^{74} + 88 q^{76} + 7 q^{77} + 79 q^{78} + 25 q^{79} - q^{81} - 60 q^{82} - 17 q^{83} - 9 q^{84} - 41 q^{86} - 24 q^{87} - 16 q^{89} - 3 q^{91} + 28 q^{92} + 26 q^{93} - 31 q^{94} + 17 q^{96} - 4 q^{97} + q^{98} + 9 q^{99}+O(q^{100}) \) 7 * q + q^2 + 13 * q^4 + 3 * q^6 + 7 * q^7 + 9 * q^9 + 7 * q^11 - 9 * q^12 - 3 * q^13 + q^14 + 21 * q^16 - 2 * q^17 + 8 * q^18 + 20 * q^19 + q^22 + 11 * q^23 + 18 * q^24 - 13 * q^26 - 12 * q^27 + 13 * q^28 + 4 * q^29 + 6 * q^31 + q^32 - 7 * q^34 + 12 * q^36 + 19 * q^37 + 3 * q^38 - 10 * q^39 + 24 * q^41 + 3 * q^42 + 13 * q^44 + 33 * q^46 - q^47 - 15 * q^48 + 7 * q^49 + 19 * q^51 - 29 * q^52 + 7 * q^53 + 9 * q^54 - 9 * q^57 + 37 * q^58 + 9 * q^59 + 18 * q^61 - 40 * q^62 + 9 * q^63 + 8 * q^64 + 3 * q^66 + 18 * q^68 - 15 * q^69 + 18 * q^71 - 64 * q^72 + 5 * q^73 - 24 * q^74 + 88 * q^76 + 7 * q^77 + 79 * q^78 + 25 * q^79 - q^81 - 60 * q^82 - 17 * q^83 - 9 * q^84 - 41 * q^86 - 24 * q^87 - 16 * q^89 - 3 * q^91 + 28 * q^92 + 26 * q^93 - 31 * q^94 + 17 * q^96 - 4 * q^97 + q^98 + 9 * q^99

Introduction

L-functions

Modular forms

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