LMFDB - Embedded newform 1849.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{6}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 6 $ x^2 - 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.44949$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.44949 q^{2} -2.44949 q^{3} +4.00000 q^{4} -2.44949 q^{5} -6.00000 q^{6} +2.44949 q^{7} +4.89898 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+2.44949 q^{2} -2.44949 q^{3} +4.00000 q^{4} -2.44949 q^{5} -6.00000 q^{6} +2.44949 q^{7} +4.89898 q^{8} +3.00000 q^{9} -6.00000 q^{10} -1.00000 q^{11} -9.79796 q^{12} -3.00000 q^{13} +6.00000 q^{14} +6.00000 q^{15} +4.00000 q^{16} -7.00000 q^{17} +7.34847 q^{18} +4.89898 q^{19} -9.79796 q^{20} -6.00000 q^{21} -2.44949 q^{22} +1.00000 q^{23} -12.0000 q^{24} +1.00000 q^{25} -7.34847 q^{26} +9.79796 q^{28} -2.44949 q^{29} +14.6969 q^{30} -3.00000 q^{31} +2.44949 q^{33} -17.1464 q^{34} -6.00000 q^{35} +12.0000 q^{36} -4.89898 q^{37} +12.0000 q^{38} +7.34847 q^{39} -12.0000 q^{40} -5.00000 q^{41} -14.6969 q^{42} -4.00000 q^{44} -7.34847 q^{45} +2.44949 q^{46} -10.0000 q^{47} -9.79796 q^{48} -1.00000 q^{49} +2.44949 q^{50} +17.1464 q^{51} -12.0000 q^{52} -1.00000 q^{53} +2.44949 q^{55} +12.0000 q^{56} -12.0000 q^{57} -6.00000 q^{58} -10.0000 q^{59} +24.0000 q^{60} +7.34847 q^{61} -7.34847 q^{62} +7.34847 q^{63} -8.00000 q^{64} +7.34847 q^{65} +6.00000 q^{66} +9.00000 q^{67} -28.0000 q^{68} -2.44949 q^{69} -14.6969 q^{70} +4.89898 q^{71} +14.6969 q^{72} -12.2474 q^{73} -12.0000 q^{74} -2.44949 q^{75} +19.5959 q^{76} -2.44949 q^{77} +18.0000 q^{78} -6.00000 q^{79} -9.79796 q^{80} -9.00000 q^{81} -12.2474 q^{82} +1.00000 q^{83} -24.0000 q^{84} +17.1464 q^{85} +6.00000 q^{87} -4.89898 q^{88} -17.1464 q^{89} -18.0000 q^{90} -7.34847 q^{91} +4.00000 q^{92} +7.34847 q^{93} -24.4949 q^{94} -12.0000 q^{95} +11.0000 q^{97} -2.44949 q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{4} - 12 q^{6} + 6 q^{9}+O(q^{10}) $ 2 * q + 8 * q^4 - 12 * q^6 + 6 * q^9	$ 2 q + 8 q^{4} - 12 q^{6} + 6 q^{9} - 12 q^{10} - 2 q^{11} - 6 q^{13} + 12 q^{14} + 12 q^{15} + 8 q^{16} - 14 q^{17} - 12 q^{21} + 2 q^{23} - 24 q^{24} + 2 q^{25} - 6 q^{31} - 12 q^{35} + 24 q^{36} + 24 q^{38} - 24 q^{40} - 10 q^{41} - 8 q^{44} - 20 q^{47} - 2 q^{49} - 24 q^{52} - 2 q^{53} + 24 q^{56} - 24 q^{57} - 12 q^{58} - 20 q^{59} + 48 q^{60} - 16 q^{64} + 12 q^{66} + 18 q^{67} - 56 q^{68} - 24 q^{74} + 36 q^{78} - 12 q^{79} - 18 q^{81} + 2 q^{83} - 48 q^{84} + 12 q^{87} - 36 q^{90} + 8 q^{92} - 24 q^{95} + 22 q^{97} - 6 q^{99}+O(q^{100}) $ 2 * q + 8 * q^4 - 12 * q^6 + 6 * q^9 - 12 * q^10 - 2 * q^11 - 6 * q^13 + 12 * q^14 + 12 * q^15 + 8 * q^16 - 14 * q^17 - 12 * q^21 + 2 * q^23 - 24 * q^24 + 2 * q^25 - 6 * q^31 - 12 * q^35 + 24 * q^36 + 24 * q^38 - 24 * q^40 - 10 * q^41 - 8 * q^44 - 20 * q^47 - 2 * q^49 - 24 * q^52 - 2 * q^53 + 24 * q^56 - 24 * q^57 - 12 * q^58 - 20 * q^59 + 48 * q^60 - 16 * q^64 + 12 * q^66 + 18 * q^67 - 56 * q^68 - 24 * q^74 + 36 * q^78 - 12 * q^79 - 18 * q^81 + 2 * q^83 - 48 * q^84 + 12 * q^87 - 36 * q^90 + 8 * q^92 - 24 * q^95 + 22 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.44949	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$2$	2.44949	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$3$	−2.44949	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$3$	−2.44949	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$4$	4.00000	2.00000
$5$	−2.44949	−1.09545	−0.547723	−	0.836660i	$-0.684505\pi$
$5$	−2.44949	−1.09545	−0.547723	+	0.836660i	$0.684505\pi$
$6$	−6.00000	−2.44949
$7$	2.44949	0.925820	0.462910	−	0.886405i	$-0.346805\pi$
$7$	2.44949	0.925820	0.462910	+	0.886405i	$0.346805\pi$
$8$	4.89898	1.73205
$9$	3.00000	1.00000
$10$	−6.00000	−1.89737
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	−9.79796	−2.82843
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	6.00000	1.60357
$15$	6.00000	1.54919
$16$	4.00000	1.00000
$17$	−7.00000	−1.69775	−0.848875	−	0.528594i	$-0.822719\pi$
$17$	−7.00000	−1.69775	−0.848875	+	0.528594i	$0.822719\pi$
$18$	7.34847	1.73205
$19$	4.89898	1.12390	0.561951	−	0.827170i	$-0.310051\pi$
$19$	4.89898	1.12390	0.561951	+	0.827170i	$0.310051\pi$
$20$	−9.79796	−2.19089
$21$	−6.00000	−1.30931
$22$	−2.44949	−0.522233
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	−12.0000	−2.44949
$25$	1.00000	0.200000
$26$	−7.34847	−1.44115
$27$	0	0
$28$	9.79796	1.85164
$29$	−2.44949	−0.454859	−0.227429	−	0.973795i	$-0.573032\pi$
$29$	−2.44949	−0.454859	−0.227429	+	0.973795i	$0.573032\pi$
$30$	14.6969	2.68328
$31$	−3.00000	−0.538816	−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000	−0.538816	−0.269408	+	0.963026i	$0.586828\pi$
$32$	0	0
$33$	2.44949	0.426401
$34$	−17.1464	−2.94059
$35$	−6.00000	−1.01419
$36$	12.0000	2.00000
$37$	−4.89898	−0.805387	−0.402694	−	0.915335i	$-0.631926\pi$
$37$	−4.89898	−0.805387	−0.402694	+	0.915335i	$0.631926\pi$
$38$	12.0000	1.94666
$39$	7.34847	1.17670
$40$	−12.0000	−1.89737
$41$	−5.00000	−0.780869	−0.390434	−	0.920631i	$-0.627675\pi$
$41$	−5.00000	−0.780869	−0.390434	+	0.920631i	$0.627675\pi$
$42$	−14.6969	−2.26779
$43$	0	0
$43$	0	0
$44$	−4.00000	−0.603023
$45$	−7.34847	−1.09545
$46$	2.44949	0.361158
$47$	−10.0000	−1.45865	−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000	−1.45865	−0.729325	+	0.684167i	$0.760166\pi$
$48$	−9.79796	−1.41421
$49$	−1.00000	−0.142857
$50$	2.44949	0.346410
$51$	17.1464	2.40098
$52$	−12.0000	−1.66410
$53$	−1.00000	−0.137361	−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000	−0.137361	−0.0686803	+	0.997639i	$0.521879\pi$
$54$	0	0
$55$	2.44949	0.330289
$56$	12.0000	1.60357
$57$	−12.0000	−1.58944
$58$	−6.00000	−0.787839
$59$	−10.0000	−1.30189	−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000	−1.30189	−0.650945	+	0.759125i	$0.725627\pi$
$60$	24.0000	3.09839
$61$	7.34847	0.940875	0.470438	−	0.882433i	$-0.344096\pi$
$61$	7.34847	0.940875	0.470438	+	0.882433i	$0.344096\pi$
$62$	−7.34847	−0.933257
$63$	7.34847	0.925820
$64$	−8.00000	−1.00000
$65$	7.34847	0.911465
$66$	6.00000	0.738549
$67$	9.00000	1.09952	0.549762	−	0.835321i	$-0.314718\pi$
$67$	9.00000	1.09952	0.549762	+	0.835321i	$0.314718\pi$
$68$	−28.0000	−3.39550
$69$	−2.44949	−0.294884
$70$	−14.6969	−1.75662
$71$	4.89898	0.581402	0.290701	−	0.956814i	$-0.406112\pi$
$71$	4.89898	0.581402	0.290701	+	0.956814i	$0.406112\pi$
$72$	14.6969	1.73205
$73$	−12.2474	−1.43346	−0.716728	−	0.697353i	$-0.754361\pi$
$73$	−12.2474	−1.43346	−0.716728	+	0.697353i	$0.754361\pi$
$74$	−12.0000	−1.39497
$75$	−2.44949	−0.282843
$76$	19.5959	2.24781
$77$	−2.44949	−0.279145
$78$	18.0000	2.03810
$79$	−6.00000	−0.675053	−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000	−0.675053	−0.337526	+	0.941316i	$0.609590\pi$
$80$	−9.79796	−1.09545
$81$	−9.00000	−1.00000
$82$	−12.2474	−1.35250
$83$	1.00000	0.109764	0.0548821	−	0.998493i	$-0.482522\pi$
$83$	1.00000	0.109764	0.0548821	+	0.998493i	$0.482522\pi$
$84$	−24.0000	−2.61861
$85$	17.1464	1.85979
$86$	0	0
$87$	6.00000	0.643268
$88$	−4.89898	−0.522233
$89$	−17.1464	−1.81752	−0.908759	−	0.417322i	$-0.862969\pi$
$89$	−17.1464	−1.81752	−0.908759	+	0.417322i	$0.862969\pi$
$90$	−18.0000	−1.89737
$91$	−7.34847	−0.770329
$92$	4.00000	0.417029
$93$	7.34847	0.762001
$94$	−24.4949	−2.52646
$95$	−12.0000	−1.23117
$96$	0	0
$97$	11.0000	1.11688	0.558440	−	0.829545i	$-0.311400\pi$
$97$	11.0000	1.11688	0.558440	+	0.829545i	$0.311400\pi$
$98$	−2.44949	−0.247436
$99$	−3.00000	−0.301511
$100$	4.00000	0.400000
$101$	−5.00000	−0.497519	−0.248759	−	0.968565i	$-0.580023\pi$
$101$	−5.00000	−0.497519	−0.248759	+	0.968565i	$0.580023\pi$
$102$	42.0000	4.15862
$103$	17.0000	1.67506	0.837530	−	0.546392i	$-0.183999\pi$
$103$	17.0000	1.67506	0.837530	+	0.546392i	$0.183999\pi$
$104$	−14.6969	−1.44115
$105$	14.6969	1.43427
$106$	−2.44949	−0.237915
$107$	14.0000	1.35343	0.676716	−	0.736245i	$-0.263403\pi$
$107$	14.0000	1.35343	0.676716	+	0.736245i	$0.263403\pi$
$108$	0	0
$109$	13.0000	1.24517	0.622587	−	0.782551i	$-0.286082\pi$
$109$	13.0000	1.24517	0.622587	+	0.782551i	$0.286082\pi$
$110$	6.00000	0.572078
$111$	12.0000	1.13899
$112$	9.79796	0.925820
$113$	14.6969	1.38257	0.691286	−	0.722581i	$-0.257045\pi$
$113$	14.6969	1.38257	0.691286	+	0.722581i	$0.257045\pi$
$114$	−29.3939	−2.75299
$115$	−2.44949	−0.228416
$116$	−9.79796	−0.909718
$117$	−9.00000	−0.832050
$118$	−24.4949	−2.25494
$119$	−17.1464	−1.57181
$120$	29.3939	2.68328
$121$	−10.0000	−0.909091
$122$	18.0000	1.62964
$123$	12.2474	1.10432
$124$	−12.0000	−1.07763
$125$	9.79796	0.876356
$126$	18.0000	1.60357
$127$	1.00000	0.0887357	0.0443678	−	0.999015i	$-0.485873\pi$
$127$	1.00000	0.0887357	0.0443678	+	0.999015i	$0.485873\pi$
$128$	−19.5959	−1.73205
$129$	0	0
$130$	18.0000	1.57870
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	9.79796	0.852803
$133$	12.0000	1.04053
$134$	22.0454	1.90443
$135$	0	0
$136$	−34.2929	−2.94059
$137$	−4.89898	−0.418548	−0.209274	−	0.977857i	$-0.567110\pi$
$137$	−4.89898	−0.418548	−0.209274	+	0.977857i	$0.567110\pi$
$138$	−6.00000	−0.510754
$139$	−7.00000	−0.593732	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	−7.00000	−0.593732	−0.296866	+	0.954919i	$0.595942\pi$
$140$	−24.0000	−2.02837
$141$	24.4949	2.06284
$142$	12.0000	1.00702
$143$	3.00000	0.250873
$144$	12.0000	1.00000
$145$	6.00000	0.498273
$146$	−30.0000	−2.48282
$147$	2.44949	0.202031
$148$	−19.5959	−1.61077
$149$	4.89898	0.401340	0.200670	−	0.979659i	$-0.435688\pi$
$149$	4.89898	0.401340	0.200670	+	0.979659i	$0.435688\pi$
$150$	−6.00000	−0.489898
$151$	−17.1464	−1.39536	−0.697678	−	0.716411i	$-0.745783\pi$
$151$	−17.1464	−1.39536	−0.697678	+	0.716411i	$0.745783\pi$
$152$	24.0000	1.94666
$153$	−21.0000	−1.69775
$154$	−6.00000	−0.483494
$155$	7.34847	0.590243
$156$	29.3939	2.35339
$157$	−9.79796	−0.781962	−0.390981	−	0.920399i	$-0.627864\pi$
$157$	−9.79796	−0.781962	−0.390981	+	0.920399i	$0.627864\pi$
$158$	−14.6969	−1.16923
$159$	2.44949	0.194257
$160$	0	0
$161$	2.44949	0.193047
$162$	−22.0454	−1.73205
$163$	2.44949	0.191859	0.0959294	−	0.995388i	$-0.469418\pi$
$163$	2.44949	0.191859	0.0959294	+	0.995388i	$0.469418\pi$
$164$	−20.0000	−1.56174
$165$	−6.00000	−0.467099
$166$	2.44949	0.190117
$167$	5.00000	0.386912	0.193456	−	0.981109i	$-0.438030\pi$
$167$	5.00000	0.386912	0.193456	+	0.981109i	$0.438030\pi$
$168$	−29.3939	−2.26779
$169$	−4.00000	−0.307692
$170$	42.0000	3.22125
$171$	14.6969	1.12390
$172$	0	0
$173$	−10.0000	−0.760286	−0.380143	−	0.924928i	$-0.624125\pi$
$173$	−10.0000	−0.760286	−0.380143	+	0.924928i	$0.624125\pi$
$174$	14.6969	1.11417
$175$	2.44949	0.185164
$176$	−4.00000	−0.301511
$177$	24.4949	1.84115
$178$	−42.0000	−3.14803
$179$	−2.44949	−0.183083	−0.0915417	−	0.995801i	$-0.529179\pi$
$179$	−2.44949	−0.183083	−0.0915417	+	0.995801i	$0.529179\pi$
$180$	−29.3939	−2.19089
$181$	12.0000	0.891953	0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000	0.891953	0.445976	+	0.895045i	$0.352856\pi$
$182$	−18.0000	−1.33425
$183$	−18.0000	−1.33060
$184$	4.89898	0.361158
$185$	12.0000	0.882258
$186$	18.0000	1.31982
$187$	7.00000	0.511891
$188$	−40.0000	−2.91730
$189$	0	0
$190$	−29.3939	−2.13246
$191$	14.6969	1.06343	0.531717	−	0.846922i	$-0.321547\pi$
$191$	14.6969	1.06343	0.531717	+	0.846922i	$0.321547\pi$
$192$	19.5959	1.41421
$193$	15.0000	1.07972	0.539862	−	0.841754i	$-0.318476\pi$
$193$	15.0000	1.07972	0.539862	+	0.841754i	$0.318476\pi$
$194$	26.9444	1.93449
$195$	−18.0000	−1.28901
$196$	−4.00000	−0.285714
$197$	8.00000	0.569976	0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000	0.569976	0.284988	+	0.958531i	$0.408010\pi$
$198$	−7.34847	−0.522233
$199$	−19.5959	−1.38912	−0.694559	−	0.719436i	$-0.744400\pi$
$199$	−19.5959	−1.38912	−0.694559	+	0.719436i	$0.744400\pi$
$200$	4.89898	0.346410
$201$	−22.0454	−1.55496
$202$	−12.2474	−0.861727
$203$	−6.00000	−0.421117
$204$	68.5857	4.80196
$205$	12.2474	0.855399
$206$	41.6413	2.90129
$207$	3.00000	0.208514
$208$	−12.0000	−0.832050
$209$	−4.89898	−0.338869
$210$	36.0000	2.48424
$211$	14.6969	1.01178	0.505889	−	0.862598i	$-0.331164\pi$
$211$	14.6969	1.01178	0.505889	+	0.862598i	$0.331164\pi$
$212$	−4.00000	−0.274721
$213$	−12.0000	−0.822226
$214$	34.2929	2.34421
$215$	0	0
$216$	0	0
$217$	−7.34847	−0.498847
$218$	31.8434	2.15670
$219$	30.0000	2.02721
$220$	9.79796	0.660578
$221$	21.0000	1.41261
$222$	29.3939	1.97279
$223$	17.1464	1.14821	0.574105	−	0.818782i	$-0.305350\pi$
$223$	17.1464	1.14821	0.574105	+	0.818782i	$0.305350\pi$
$224$	0	0
$225$	3.00000	0.200000
$226$	36.0000	2.39468
$227$	9.79796	0.650313	0.325157	−	0.945660i	$-0.394583\pi$
$227$	9.79796	0.650313	0.325157	+	0.945660i	$0.394583\pi$
$228$	−48.0000	−3.17888
$229$	7.00000	0.462573	0.231287	−	0.972886i	$-0.425707\pi$
$229$	7.00000	0.462573	0.231287	+	0.972886i	$0.425707\pi$
$230$	−6.00000	−0.395628
$231$	6.00000	0.394771
$232$	−12.0000	−0.787839
$233$	4.89898	0.320943	0.160471	−	0.987040i	$-0.448699\pi$
$233$	4.89898	0.320943	0.160471	+	0.987040i	$0.448699\pi$
$234$	−22.0454	−1.44115
$235$	24.4949	1.59787
$236$	−40.0000	−2.60378
$237$	14.6969	0.954669
$238$	−42.0000	−2.72246
$239$	−26.0000	−1.68180	−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−26.0000	−1.68180	−0.840900	+	0.541190i	$0.817974\pi$
$240$	24.0000	1.54919
$241$	19.5959	1.26228	0.631142	−	0.775667i	$-0.282587\pi$
$241$	19.5959	1.26228	0.631142	+	0.775667i	$0.282587\pi$
$242$	−24.4949	−1.57459
$243$	22.0454	1.41421
$244$	29.3939	1.88175
$245$	2.44949	0.156492
$246$	30.0000	1.91273
$247$	−14.6969	−0.935144
$248$	−14.6969	−0.933257
$249$	−2.44949	−0.155230
$250$	24.0000	1.51789
$251$	5.00000	0.315597	0.157799	−	0.987471i	$-0.449560\pi$
$251$	5.00000	0.315597	0.157799	+	0.987471i	$0.449560\pi$
$252$	29.3939	1.85164
$253$	−1.00000	−0.0628695
$254$	2.44949	0.153695
$255$	−42.0000	−2.63014
$256$	−32.0000	−2.00000
$257$	2.44949	0.152795	0.0763975	−	0.997077i	$-0.475658\pi$
$257$	2.44949	0.152795	0.0763975	+	0.997077i	$0.475658\pi$
$258$	0	0
$259$	−12.0000	−0.745644
$260$	29.3939	1.82293
$261$	−7.34847	−0.454859
$262$	0	0
$263$	14.6969	0.906252	0.453126	−	0.891446i	$-0.350309\pi$
$263$	14.6969	0.906252	0.453126	+	0.891446i	$0.350309\pi$
$264$	12.0000	0.738549
$265$	2.44949	0.150471
$266$	29.3939	1.80225
$267$	42.0000	2.57036
$268$	36.0000	2.19905
$269$	5.00000	0.304855	0.152428	−	0.988315i	$-0.451291\pi$
$269$	5.00000	0.304855	0.152428	+	0.988315i	$0.451291\pi$
$270$	0	0
$271$	3.00000	0.182237	0.0911185	−	0.995840i	$-0.470956\pi$
$271$	3.00000	0.182237	0.0911185	+	0.995840i	$0.470956\pi$
$272$	−28.0000	−1.69775
$273$	18.0000	1.08941
$274$	−12.0000	−0.724947
$275$	−1.00000	−0.0603023
$276$	−9.79796	−0.589768
$277$	−17.1464	−1.03023	−0.515115	−	0.857121i	$-0.672251\pi$
$277$	−17.1464	−1.03023	−0.515115	+	0.857121i	$0.672251\pi$
$278$	−17.1464	−1.02837
$279$	−9.00000	−0.538816
$280$	−29.3939	−1.75662
$281$	1.00000	0.0596550	0.0298275	−	0.999555i	$-0.490504\pi$
$281$	1.00000	0.0596550	0.0298275	+	0.999555i	$0.490504\pi$
$282$	60.0000	3.57295
$283$	−21.0000	−1.24832	−0.624160	−	0.781296i	$-0.714559\pi$
$283$	−21.0000	−1.24832	−0.624160	+	0.781296i	$0.714559\pi$
$284$	19.5959	1.16280
$285$	29.3939	1.74114
$286$	7.34847	0.434524
$287$	−12.2474	−0.722944
$288$	0	0
$289$	32.0000	1.88235
$290$	14.6969	0.863034
$291$	−26.9444	−1.57951
$292$	−48.9898	−2.86691
$293$	16.0000	0.934730	0.467365	−	0.884064i	$-0.345203\pi$
$293$	16.0000	0.934730	0.467365	+	0.884064i	$0.345203\pi$
$294$	6.00000	0.349927
$295$	24.4949	1.42615
$296$	−24.0000	−1.39497
$297$	0	0
$298$	12.0000	0.695141
$299$	−3.00000	−0.173494
$300$	−9.79796	−0.565685
$301$	0	0
$302$	−42.0000	−2.41683
$303$	12.2474	0.703598
$304$	19.5959	1.12390
$305$	−18.0000	−1.03068
$306$	−51.4393	−2.94059
$307$	23.0000	1.31268	0.656340	−	0.754466i	$-0.272104\pi$
$307$	23.0000	1.31268	0.656340	+	0.754466i	$0.272104\pi$
$308$	−9.79796	−0.558291
$309$	−41.6413	−2.36889
$310$	18.0000	1.02233
$311$	−25.0000	−1.41762	−0.708810	−	0.705399i	$-0.750768\pi$
$311$	−25.0000	−1.41762	−0.708810	+	0.705399i	$0.750768\pi$
$312$	36.0000	2.03810
$313$	7.34847	0.415360	0.207680	−	0.978197i	$-0.433409\pi$
$313$	7.34847	0.415360	0.207680	+	0.978197i	$0.433409\pi$
$314$	−24.0000	−1.35440
$315$	−18.0000	−1.01419
$316$	−24.0000	−1.35011
$317$	−17.0000	−0.954815	−0.477408	−	0.878682i	$-0.658423\pi$
$317$	−17.0000	−0.954815	−0.477408	+	0.878682i	$0.658423\pi$
$318$	6.00000	0.336463
$319$	2.44949	0.137145
$320$	19.5959	1.09545
$321$	−34.2929	−1.91404
$322$	6.00000	0.334367
$323$	−34.2929	−1.90811
$324$	−36.0000	−2.00000
$325$	−3.00000	−0.166410
$326$	6.00000	0.332309
$327$	−31.8434	−1.76094
$328$	−24.4949	−1.35250
$329$	−24.4949	−1.35045
$330$	−14.6969	−0.809040
$331$	−2.44949	−0.134636	−0.0673181	−	0.997732i	$-0.521444\pi$
$331$	−2.44949	−0.134636	−0.0673181	+	0.997732i	$0.521444\pi$
$332$	4.00000	0.219529
$333$	−14.6969	−0.805387
$334$	12.2474	0.670151
$335$	−22.0454	−1.20447
$336$	−24.0000	−1.30931
$337$	−1.00000	−0.0544735	−0.0272367	−	0.999629i	$-0.508671\pi$
$337$	−1.00000	−0.0544735	−0.0272367	+	0.999629i	$0.508671\pi$
$338$	−9.79796	−0.532939
$339$	−36.0000	−1.95525
$340$	68.5857	3.71958
$341$	3.00000	0.162459
$342$	36.0000	1.94666
$343$	−19.5959	−1.05808
$344$	0	0
$345$	6.00000	0.323029
$346$	−24.4949	−1.31685
$347$	17.1464	0.920468	0.460234	−	0.887798i	$-0.347765\pi$
$347$	17.1464	0.920468	0.460234	+	0.887798i	$0.347765\pi$
$348$	24.0000	1.28654
$349$	−2.44949	−0.131118	−0.0655591	−	0.997849i	$-0.520883\pi$
$349$	−2.44949	−0.131118	−0.0655591	+	0.997849i	$0.520883\pi$
$350$	6.00000	0.320713
$351$	0	0
$352$	0	0
$353$	−29.0000	−1.54351	−0.771757	−	0.635917i	$-0.780622\pi$
$353$	−29.0000	−1.54351	−0.771757	+	0.635917i	$0.780622\pi$
$354$	60.0000	3.18896
$355$	−12.0000	−0.636894
$356$	−68.5857	−3.63504
$357$	42.0000	2.22288
$358$	−6.00000	−0.317110
$359$	−11.0000	−0.580558	−0.290279	−	0.956942i	$-0.593748\pi$
$359$	−11.0000	−0.580558	−0.290279	+	0.956942i	$0.593748\pi$
$360$	−36.0000	−1.89737
$361$	5.00000	0.263158
$362$	29.3939	1.54491
$363$	24.4949	1.28565
$364$	−29.3939	−1.54066
$365$	30.0000	1.57027
$366$	−44.0908	−2.30466
$367$	6.00000	0.313197	0.156599	−	0.987662i	$-0.449947\pi$
$367$	6.00000	0.313197	0.156599	+	0.987662i	$0.449947\pi$
$368$	4.00000	0.208514
$369$	−15.0000	−0.780869
$370$	29.3939	1.52811
$371$	−2.44949	−0.127171
$372$	29.3939	1.52400
$373$	34.2929	1.77562	0.887808	−	0.460213i	$-0.152227\pi$
$373$	34.2929	1.77562	0.887808	+	0.460213i	$0.152227\pi$
$374$	17.1464	0.886621
$375$	−24.0000	−1.23935
$376$	−48.9898	−2.52646
$377$	7.34847	0.378465
$378$	0	0
$379$	−21.0000	−1.07870	−0.539349	−	0.842082i	$-0.681330\pi$
$379$	−21.0000	−1.07870	−0.539349	+	0.842082i	$0.681330\pi$
$380$	−48.0000	−2.46235
$381$	−2.44949	−0.125491
$382$	36.0000	1.84192
$383$	−24.4949	−1.25163	−0.625815	−	0.779971i	$-0.715234\pi$
$383$	−24.4949	−1.25163	−0.625815	+	0.779971i	$0.715234\pi$
$384$	48.0000	2.44949
$385$	6.00000	0.305788
$386$	36.7423	1.87014
$387$	0	0
$388$	44.0000	2.23376
$389$	−9.79796	−0.496776	−0.248388	−	0.968661i	$-0.579901\pi$
$389$	−9.79796	−0.496776	−0.248388	+	0.968661i	$0.579901\pi$
$390$	−44.0908	−2.23263
$391$	−7.00000	−0.354005
$392$	−4.89898	−0.247436
$393$	0	0
$394$	19.5959	0.987228
$395$	14.6969	0.739483
$396$	−12.0000	−0.603023
$397$	−12.0000	−0.602263	−0.301131	−	0.953583i	$-0.597364\pi$
$397$	−12.0000	−0.602263	−0.301131	+	0.953583i	$0.597364\pi$
$398$	−48.0000	−2.40602
$399$	−29.3939	−1.47153
$400$	4.00000	0.200000
$401$	−5.00000	−0.249688	−0.124844	−	0.992176i	$-0.539843\pi$
$401$	−5.00000	−0.249688	−0.124844	+	0.992176i	$0.539843\pi$
$402$	−54.0000	−2.69328
$403$	9.00000	0.448322
$404$	−20.0000	−0.995037
$405$	22.0454	1.09545
$406$	−14.6969	−0.729397
$407$	4.89898	0.242833
$408$	84.0000	4.15862
$409$	36.7423	1.81679	0.908396	−	0.418111i	$-0.137308\pi$
$409$	36.7423	1.81679	0.908396	+	0.418111i	$0.137308\pi$
$410$	30.0000	1.48159
$411$	12.0000	0.591916
$412$	68.0000	3.35012
$413$	−24.4949	−1.20532
$414$	7.34847	0.361158
$415$	−2.44949	−0.120241
$416$	0	0
$417$	17.1464	0.839664
$418$	−12.0000	−0.586939
$419$	−2.44949	−0.119665	−0.0598327	−	0.998208i	$-0.519057\pi$
$419$	−2.44949	−0.119665	−0.0598327	+	0.998208i	$0.519057\pi$
$420$	58.7878	2.86855
$421$	−9.79796	−0.477523	−0.238762	−	0.971078i	$-0.576741\pi$
$421$	−9.79796	−0.477523	−0.238762	+	0.971078i	$0.576741\pi$
$422$	36.0000	1.75245
$423$	−30.0000	−1.45865
$424$	−4.89898	−0.237915
$425$	−7.00000	−0.339550
$426$	−29.3939	−1.42414
$427$	18.0000	0.871081
$428$	56.0000	2.70686
$429$	−7.34847	−0.354787
$430$	0	0
$431$	−17.0000	−0.818861	−0.409431	−	0.912341i	$-0.634273\pi$
$431$	−17.0000	−0.818861	−0.409431	+	0.912341i	$0.634273\pi$
$432$	0	0
$433$	−12.2474	−0.588575	−0.294287	−	0.955717i	$-0.595082\pi$
$433$	−12.2474	−0.588575	−0.294287	+	0.955717i	$0.595082\pi$
$434$	−18.0000	−0.864028
$435$	−14.6969	−0.704664
$436$	52.0000	2.49035
$437$	4.89898	0.234350
$438$	73.4847	3.51123
$439$	−29.0000	−1.38409	−0.692047	−	0.721852i	$-0.743291\pi$
$439$	−29.0000	−1.38409	−0.692047	+	0.721852i	$0.743291\pi$
$440$	12.0000	0.572078
$441$	−3.00000	−0.142857
$442$	51.4393	2.44672
$443$	−34.0000	−1.61539	−0.807694	−	0.589601i	$-0.799285\pi$
$443$	−34.0000	−1.61539	−0.807694	+	0.589601i	$0.799285\pi$
$444$	48.0000	2.27798
$445$	42.0000	1.99099
$446$	42.0000	1.98876
$447$	−12.0000	−0.567581
$448$	−19.5959	−0.925820
$449$	−26.9444	−1.27158	−0.635792	−	0.771860i	$-0.719326\pi$
$449$	−26.9444	−1.27158	−0.635792	+	0.771860i	$0.719326\pi$
$450$	7.34847	0.346410
$451$	5.00000	0.235441
$452$	58.7878	2.76514
$453$	42.0000	1.97333
$454$	24.0000	1.12638
$455$	18.0000	0.843853
$456$	−58.7878	−2.75299
$457$	−31.8434	−1.48957	−0.744785	−	0.667305i	$-0.767448\pi$
$457$	−31.8434	−1.48957	−0.744785	+	0.667305i	$0.767448\pi$
$458$	17.1464	0.801200
$459$	0	0
$460$	−9.79796	−0.456832
$461$	16.0000	0.745194	0.372597	−	0.927993i	$-0.378467\pi$
$461$	16.0000	0.745194	0.372597	+	0.927993i	$0.378467\pi$
$462$	14.6969	0.683763
$463$	12.2474	0.569187	0.284594	−	0.958648i	$-0.408141\pi$
$463$	12.2474	0.569187	0.284594	+	0.958648i	$0.408141\pi$
$464$	−9.79796	−0.454859
$465$	−18.0000	−0.834730
$466$	12.0000	0.555889
$467$	−19.5959	−0.906791	−0.453395	−	0.891309i	$-0.649787\pi$
$467$	−19.5959	−0.906791	−0.453395	+	0.891309i	$0.649787\pi$
$468$	−36.0000	−1.66410
$469$	22.0454	1.01796
$470$	60.0000	2.76759
$471$	24.0000	1.10586
$472$	−48.9898	−2.25494
$473$	0	0
$474$	36.0000	1.65353
$475$	4.89898	0.224781
$476$	−68.5857	−3.14362
$477$	−3.00000	−0.137361
$478$	−63.6867	−2.91296
$479$	−1.00000	−0.0456912	−0.0228456	−	0.999739i	$-0.507273\pi$
$479$	−1.00000	−0.0456912	−0.0228456	+	0.999739i	$0.507273\pi$
$480$	0	0
$481$	14.6969	0.670123
$482$	48.0000	2.18634
$483$	−6.00000	−0.273009
$484$	−40.0000	−1.81818
$485$	−26.9444	−1.22348
$486$	54.0000	2.44949
$487$	−4.00000	−0.181257	−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000	−0.181257	−0.0906287	+	0.995885i	$0.528888\pi$
$488$	36.0000	1.62964
$489$	−6.00000	−0.271329
$490$	6.00000	0.271052
$491$	−22.0454	−0.994895	−0.497448	−	0.867494i	$-0.665729\pi$
$491$	−22.0454	−0.994895	−0.497448	+	0.867494i	$0.665729\pi$
$492$	48.9898	2.20863
$493$	17.1464	0.772236
$494$	−36.0000	−1.61972
$495$	7.34847	0.330289
$496$	−12.0000	−0.538816
$497$	12.0000	0.538274
$498$	−6.00000	−0.268866
$499$	−7.34847	−0.328963	−0.164481	−	0.986380i	$-0.552595\pi$
$499$	−7.34847	−0.328963	−0.164481	+	0.986380i	$0.552595\pi$
$500$	39.1918	1.75271
$501$	−12.2474	−0.547176
$502$	12.2474	0.546630
$503$	14.6969	0.655304	0.327652	−	0.944798i	$-0.393743\pi$
$503$	14.6969	0.655304	0.327652	+	0.944798i	$0.393743\pi$
$504$	36.0000	1.60357
$505$	12.2474	0.545004
$506$	−2.44949	−0.108893
$507$	9.79796	0.435143
$508$	4.00000	0.177471
$509$	−19.0000	−0.842160	−0.421080	−	0.907023i	$-0.638349\pi$
$509$	−19.0000	−0.842160	−0.421080	+	0.907023i	$0.638349\pi$
$510$	−102.879	−4.55554
$511$	−30.0000	−1.32712
$512$	−39.1918	−1.73205
$513$	0	0
$514$	6.00000	0.264649
$515$	−41.6413	−1.83494
$516$	0	0
$517$	10.0000	0.439799
$518$	−29.3939	−1.29149
$519$	24.4949	1.07521
$520$	36.0000	1.57870
$521$	22.0454	0.965827	0.482913	−	0.875668i	$-0.339579\pi$
$521$	22.0454	0.965827	0.482913	+	0.875668i	$0.339579\pi$
$522$	−18.0000	−0.787839
$523$	−2.44949	−0.107109	−0.0535544	−	0.998565i	$-0.517055\pi$
$523$	−2.44949	−0.107109	−0.0535544	+	0.998565i	$0.517055\pi$
$524$	0	0
$525$	−6.00000	−0.261861
$526$	36.0000	1.56967
$527$	21.0000	0.914774
$528$	9.79796	0.426401
$529$	−22.0000	−0.956522
$530$	6.00000	0.260623
$531$	−30.0000	−1.30189
$532$	48.0000	2.08106
$533$	15.0000	0.649722
$534$	102.879	4.45199
$535$	−34.2929	−1.48261
$536$	44.0908	1.90443
$537$	6.00000	0.258919
$538$	12.2474	0.528025
$539$	1.00000	0.0430730
$540$	0	0
$541$	33.0000	1.41878	0.709390	−	0.704816i	$-0.248970\pi$
$541$	33.0000	1.41878	0.709390	+	0.704816i	$0.248970\pi$
$542$	7.34847	0.315644
$543$	−29.3939	−1.26141
$544$	0	0
$545$	−31.8434	−1.36402
$546$	44.0908	1.88691
$547$	−27.0000	−1.15444	−0.577218	−	0.816590i	$-0.695862\pi$
$547$	−27.0000	−1.15444	−0.577218	+	0.816590i	$0.695862\pi$
$548$	−19.5959	−0.837096
$549$	22.0454	0.940875
$550$	−2.44949	−0.104447
$551$	−12.0000	−0.511217
$552$	−12.0000	−0.510754
$553$	−14.6969	−0.624977
$554$	−42.0000	−1.78441
$555$	−29.3939	−1.24770
$556$	−28.0000	−1.18746
$557$	−41.0000	−1.73723	−0.868613	−	0.495491i	$-0.834988\pi$
$557$	−41.0000	−1.73723	−0.868613	+	0.495491i	$0.834988\pi$
$558$	−22.0454	−0.933257
$559$	0	0
$560$	−24.0000	−1.01419
$561$	−17.1464	−0.723923
$562$	2.44949	0.103325
$563$	−11.0000	−0.463595	−0.231797	−	0.972764i	$-0.574461\pi$
$563$	−11.0000	−0.463595	−0.231797	+	0.972764i	$0.574461\pi$
$564$	97.9796	4.12568
$565$	−36.0000	−1.51453
$566$	−51.4393	−2.16215
$567$	−22.0454	−0.925820
$568$	24.0000	1.00702
$569$	23.0000	0.964210	0.482105	−	0.876113i	$-0.339872\pi$
$569$	23.0000	0.964210	0.482105	+	0.876113i	$0.339872\pi$
$570$	72.0000	3.01575
$571$	−7.34847	−0.307524	−0.153762	−	0.988108i	$-0.549139\pi$
$571$	−7.34847	−0.307524	−0.153762	+	0.988108i	$0.549139\pi$
$572$	12.0000	0.501745
$573$	−36.0000	−1.50392
$574$	−30.0000	−1.25218
$575$	1.00000	0.0417029
$576$	−24.0000	−1.00000
$577$	−12.2474	−0.509868	−0.254934	−	0.966958i	$-0.582054\pi$
$577$	−12.2474	−0.509868	−0.254934	+	0.966958i	$0.582054\pi$
$578$	78.3837	3.26033
$579$	−36.7423	−1.52696
$580$	24.0000	0.996546
$581$	2.44949	0.101622
$582$	−66.0000	−2.73579
$583$	1.00000	0.0414158
$584$	−60.0000	−2.48282
$585$	22.0454	0.911465
$586$	39.1918	1.61900
$587$	24.4949	1.01101	0.505506	−	0.862823i	$-0.331306\pi$
$587$	24.4949	1.01101	0.505506	+	0.862823i	$0.331306\pi$
$588$	9.79796	0.404061
$589$	−14.6969	−0.605577
$590$	60.0000	2.47016
$591$	−19.5959	−0.806068
$592$	−19.5959	−0.805387
$593$	−7.34847	−0.301765	−0.150883	−	0.988552i	$-0.548212\pi$
$593$	−7.34847	−0.301765	−0.150883	+	0.988552i	$0.548212\pi$
$594$	0	0
$595$	42.0000	1.72183
$596$	19.5959	0.802680
$597$	48.0000	1.96451
$598$	−7.34847	−0.300501
$599$	−17.0000	−0.694601	−0.347301	−	0.937754i	$-0.612902\pi$
$599$	−17.0000	−0.694601	−0.347301	+	0.937754i	$0.612902\pi$
$600$	−12.0000	−0.489898
$601$	−19.5959	−0.799334	−0.399667	−	0.916660i	$-0.630874\pi$
$601$	−19.5959	−0.799334	−0.399667	+	0.916660i	$0.630874\pi$
$602$	0	0
$603$	27.0000	1.09952
$604$	−68.5857	−2.79071
$605$	24.4949	0.995859
$606$	30.0000	1.21867
$607$	−39.1918	−1.59075	−0.795374	−	0.606119i	$-0.792725\pi$
$607$	−39.1918	−1.59075	−0.795374	+	0.606119i	$0.792725\pi$
$608$	0	0
$609$	14.6969	0.595550
$610$	−44.0908	−1.78518
$611$	30.0000	1.21367
$612$	−84.0000	−3.39550
$613$	12.0000	0.484675	0.242338	−	0.970192i	$-0.422086\pi$
$613$	12.0000	0.484675	0.242338	+	0.970192i	$0.422086\pi$
$614$	56.3383	2.27363
$615$	−30.0000	−1.20972
$616$	−12.0000	−0.483494
$617$	43.0000	1.73111	0.865557	−	0.500810i	$-0.166964\pi$
$617$	43.0000	1.73111	0.865557	+	0.500810i	$0.166964\pi$
$618$	−102.000	−4.10304
$619$	24.0000	0.964641	0.482321	−	0.875995i	$-0.339794\pi$
$619$	24.0000	0.964641	0.482321	+	0.875995i	$0.339794\pi$
$620$	29.3939	1.18049
$621$	0	0
$622$	−61.2372	−2.45539
$623$	−42.0000	−1.68269
$624$	29.3939	1.17670
$625$	−29.0000	−1.16000
$626$	18.0000	0.719425
$627$	12.0000	0.479234
$628$	−39.1918	−1.56392
$629$	34.2929	1.36735
$630$	−44.0908	−1.75662
$631$	14.6969	0.585076	0.292538	−	0.956254i	$-0.405500\pi$
$631$	14.6969	0.585076	0.292538	+	0.956254i	$0.405500\pi$
$632$	−29.3939	−1.16923
$633$	−36.0000	−1.43087
$634$	−41.6413	−1.65379
$635$	−2.44949	−0.0972050
$636$	9.79796	0.388514
$637$	3.00000	0.118864
$638$	6.00000	0.237542
$639$	14.6969	0.581402
$640$	48.0000	1.89737
$641$	−22.0454	−0.870741	−0.435371	−	0.900251i	$-0.643383\pi$
$641$	−22.0454	−0.870741	−0.435371	+	0.900251i	$0.643383\pi$
$642$	−84.0000	−3.31522
$643$	−10.0000	−0.394362	−0.197181	−	0.980367i	$-0.563179\pi$
$643$	−10.0000	−0.394362	−0.197181	+	0.980367i	$0.563179\pi$
$644$	9.79796	0.386094
$645$	0	0
$646$	−84.0000	−3.30494
$647$	44.0908	1.73339	0.866694	−	0.498839i	$-0.166240\pi$
$647$	44.0908	1.73339	0.866694	+	0.498839i	$0.166240\pi$
$648$	−44.0908	−1.73205
$649$	10.0000	0.392534
$650$	−7.34847	−0.288231
$651$	18.0000	0.705476
$652$	9.79796	0.383718
$653$	−34.2929	−1.34198	−0.670992	−	0.741465i	$-0.734131\pi$
$653$	−34.2929	−1.34198	−0.670992	+	0.741465i	$0.734131\pi$
$654$	−78.0000	−3.05004
$655$	0	0
$656$	−20.0000	−0.780869
$657$	−36.7423	−1.43346
$658$	−60.0000	−2.33904
$659$	1.00000	0.0389545	0.0194772	−	0.999810i	$-0.493800\pi$
$659$	1.00000	0.0389545	0.0194772	+	0.999810i	$0.493800\pi$
$660$	−24.0000	−0.934199
$661$	−45.0000	−1.75030	−0.875149	−	0.483854i	$-0.839236\pi$
$661$	−45.0000	−1.75030	−0.875149	+	0.483854i	$0.839236\pi$
$662$	−6.00000	−0.233197
$663$	−51.4393	−1.99774
$664$	4.89898	0.190117
$665$	−29.3939	−1.13985
$666$	−36.0000	−1.39497
$667$	−2.44949	−0.0948446
$668$	20.0000	0.773823
$669$	−42.0000	−1.62381
$670$	−54.0000	−2.08620
$671$	−7.34847	−0.283685
$672$	0	0
$673$	−26.9444	−1.03863	−0.519315	−	0.854583i	$-0.673813\pi$
$673$	−26.9444	−1.03863	−0.519315	+	0.854583i	$0.673813\pi$
$674$	−2.44949	−0.0943508
$675$	0	0
$676$	−16.0000	−0.615385
$677$	24.4949	0.941415	0.470708	−	0.882289i	$-0.343999\pi$
$677$	24.4949	0.941415	0.470708	+	0.882289i	$0.343999\pi$
$678$	−88.1816	−3.38660
$679$	26.9444	1.03403
$680$	84.0000	3.22125
$681$	−24.0000	−0.919682
$682$	7.34847	0.281387
$683$	23.0000	0.880071	0.440035	−	0.897980i	$-0.354966\pi$
$683$	23.0000	0.880071	0.440035	+	0.897980i	$0.354966\pi$
$684$	58.7878	2.24781
$685$	12.0000	0.458496
$686$	−48.0000	−1.83265
$687$	−17.1464	−0.654177
$688$	0	0
$689$	3.00000	0.114291
$690$	14.6969	0.559503
$691$	−26.9444	−1.02501	−0.512506	−	0.858683i	$-0.671283\pi$
$691$	−26.9444	−1.02501	−0.512506	+	0.858683i	$0.671283\pi$
$692$	−40.0000	−1.52057
$693$	−7.34847	−0.279145
$694$	42.0000	1.59430
$695$	17.1464	0.650401
$696$	29.3939	1.11417
$697$	35.0000	1.32572
$698$	−6.00000	−0.227103
$699$	−12.0000	−0.453882
$700$	9.79796	0.370328
$701$	−8.00000	−0.302156	−0.151078	−	0.988522i	$-0.548274\pi$
$701$	−8.00000	−0.302156	−0.151078	+	0.988522i	$0.548274\pi$
$702$	0	0
$703$	−24.0000	−0.905177
$704$	8.00000	0.301511
$705$	−60.0000	−2.25973
$706$	−71.0352	−2.67345
$707$	−12.2474	−0.460613
$708$	97.9796	3.68230
$709$	−15.0000	−0.563337	−0.281668	−	0.959512i	$-0.590888\pi$
$709$	−15.0000	−0.563337	−0.281668	+	0.959512i	$0.590888\pi$
$710$	−29.3939	−1.10313
$711$	−18.0000	−0.675053
$712$	−84.0000	−3.14803
$713$	−3.00000	−0.112351
$714$	102.879	3.85013
$715$	−7.34847	−0.274817
$716$	−9.79796	−0.366167
$717$	63.6867	2.37842
$718$	−26.9444	−1.00556
$719$	−4.00000	−0.149175	−0.0745874	−	0.997214i	$-0.523764\pi$
$719$	−4.00000	−0.149175	−0.0745874	+	0.997214i	$0.523764\pi$
$720$	−29.3939	−1.09545
$721$	41.6413	1.55080
$722$	12.2474	0.455803
$723$	−48.0000	−1.78514
$724$	48.0000	1.78391
$725$	−2.44949	−0.0909718
$726$	60.0000	2.22681
$727$	−29.3939	−1.09016	−0.545079	−	0.838385i	$-0.683500\pi$
$727$	−29.3939	−1.09016	−0.545079	+	0.838385i	$0.683500\pi$
$728$	−36.0000	−1.33425
$729$	−27.0000	−1.00000
$730$	73.4847	2.71979
$731$	0	0
$732$	−72.0000	−2.66120
$733$	48.9898	1.80948	0.904740	−	0.425965i	$-0.140065\pi$
$733$	48.9898	1.80948	0.904740	+	0.425965i	$0.140065\pi$
$734$	14.6969	0.542474
$735$	−6.00000	−0.221313
$736$	0	0
$737$	−9.00000	−0.331519
$738$	−36.7423	−1.35250
$739$	4.89898	0.180212	0.0901059	−	0.995932i	$-0.471279\pi$
$739$	4.89898	0.180212	0.0901059	+	0.995932i	$0.471279\pi$
$740$	48.0000	1.76452
$741$	36.0000	1.32249
$742$	−6.00000	−0.220267
$743$	14.6969	0.539178	0.269589	−	0.962975i	$-0.413112\pi$
$743$	14.6969	0.539178	0.269589	+	0.962975i	$0.413112\pi$
$744$	36.0000	1.31982
$745$	−12.0000	−0.439646
$746$	84.0000	3.07546
$747$	3.00000	0.109764
$748$	28.0000	1.02378
$749$	34.2929	1.25303
$750$	−58.7878	−2.14663
$751$	51.4393	1.87705	0.938523	−	0.345217i	$-0.112195\pi$
$751$	51.4393	1.87705	0.938523	+	0.345217i	$0.112195\pi$
$752$	−40.0000	−1.45865
$753$	−12.2474	−0.446322
$754$	18.0000	0.655521
$755$	42.0000	1.52854
$756$	0	0
$757$	4.89898	0.178056	0.0890282	−	0.996029i	$-0.471624\pi$
$757$	4.89898	0.178056	0.0890282	+	0.996029i	$0.471624\pi$
$758$	−51.4393	−1.86836
$759$	2.44949	0.0889108
$760$	−58.7878	−2.13246
$761$	−4.89898	−0.177588	−0.0887939	−	0.996050i	$-0.528301\pi$
$761$	−4.89898	−0.177588	−0.0887939	+	0.996050i	$0.528301\pi$
$762$	−6.00000	−0.217357
$763$	31.8434	1.15281
$764$	58.7878	2.12687
$765$	51.4393	1.85979
$766$	−60.0000	−2.16789
$767$	30.0000	1.08324
$768$	78.3837	2.82843
$769$	24.0000	0.865462	0.432731	−	0.901523i	$-0.357550\pi$
$769$	24.0000	0.865462	0.432731	+	0.901523i	$0.357550\pi$
$770$	14.6969	0.529641
$771$	−6.00000	−0.216085
$772$	60.0000	2.15945
$773$	26.9444	0.969122	0.484561	−	0.874757i	$-0.338979\pi$
$773$	26.9444	0.969122	0.484561	+	0.874757i	$0.338979\pi$
$774$	0	0
$775$	−3.00000	−0.107763
$776$	53.8888	1.93449
$777$	29.3939	1.05450
$778$	−24.0000	−0.860442
$779$	−24.4949	−0.877621
$780$	−72.0000	−2.57801
$781$	−4.89898	−0.175299
$782$	−17.1464	−0.613155
$783$	0	0
$784$	−4.00000	−0.142857
$785$	24.0000	0.856597
$786$	0	0
$787$	38.0000	1.35455	0.677277	−	0.735728i	$-0.263160\pi$
$787$	38.0000	1.35455	0.677277	+	0.735728i	$0.263160\pi$
$788$	32.0000	1.13995
$789$	−36.0000	−1.28163
$790$	36.0000	1.28082
$791$	36.0000	1.28001
$792$	−14.6969	−0.522233
$793$	−22.0454	−0.782855
$794$	−29.3939	−1.04315
$795$	−6.00000	−0.212798
$796$	−78.3837	−2.77824
$797$	−28.0000	−0.991811	−0.495905	−	0.868377i	$-0.665164\pi$
$797$	−28.0000	−0.991811	−0.495905	+	0.868377i	$0.665164\pi$
$798$	−72.0000	−2.54877
$799$	70.0000	2.47642
$800$	0	0
$801$	−51.4393	−1.81752
$802$	−12.2474	−0.432472
$803$	12.2474	0.432203
$804$	−88.1816	−3.10993
$805$	−6.00000	−0.211472
$806$	22.0454	0.776516
$807$	−12.2474	−0.431131
$808$	−24.4949	−0.861727
$809$	28.0000	0.984428	0.492214	−	0.870474i	$-0.336188\pi$
$809$	28.0000	0.984428	0.492214	+	0.870474i	$0.336188\pi$
$810$	54.0000	1.89737
$811$	−7.34847	−0.258040	−0.129020	−	0.991642i	$-0.541183\pi$
$811$	−7.34847	−0.258040	−0.129020	+	0.991642i	$0.541183\pi$
$812$	−24.0000	−0.842235
$813$	−7.34847	−0.257722
$814$	12.0000	0.420600
$815$	−6.00000	−0.210171
$816$	68.5857	2.40098
$817$	0	0
$818$	90.0000	3.14678
$819$	−22.0454	−0.770329
$820$	48.9898	1.71080
$821$	31.0000	1.08191	0.540954	−	0.841052i	$-0.318063\pi$
$821$	31.0000	1.08191	0.540954	+	0.841052i	$0.318063\pi$
$822$	29.3939	1.02523
$823$	−9.00000	−0.313720	−0.156860	−	0.987621i	$-0.550137\pi$
$823$	−9.00000	−0.313720	−0.156860	+	0.987621i	$0.550137\pi$
$824$	83.2827	2.90129
$825$	2.44949	0.0852803
$826$	−60.0000	−2.08767
$827$	−32.0000	−1.11275	−0.556375	−	0.830932i	$-0.687808\pi$
$827$	−32.0000	−1.11275	−0.556375	+	0.830932i	$0.687808\pi$
$828$	12.0000	0.417029
$829$	−44.0908	−1.53134	−0.765669	−	0.643235i	$-0.777592\pi$
$829$	−44.0908	−1.53134	−0.765669	+	0.643235i	$0.777592\pi$
$830$	−6.00000	−0.208263
$831$	42.0000	1.45696
$832$	24.0000	0.832050
$833$	7.00000	0.242536
$834$	42.0000	1.45434
$835$	−12.2474	−0.423840
$836$	−19.5959	−0.677739
$837$	0	0
$838$	−6.00000	−0.207267
$839$	26.9444	0.930224	0.465112	−	0.885252i	$-0.346014\pi$
$839$	26.9444	0.930224	0.465112	+	0.885252i	$0.346014\pi$
$840$	72.0000	2.48424
$841$	−23.0000	−0.793103
$842$	−24.0000	−0.827095
$843$	−2.44949	−0.0843649
$844$	58.7878	2.02356
$845$	9.79796	0.337060
$846$	−73.4847	−2.52646
$847$	−24.4949	−0.841655
$848$	−4.00000	−0.137361
$849$	51.4393	1.76539
$850$	−17.1464	−0.588118
$851$	−4.89898	−0.167935
$852$	−48.0000	−1.64445
$853$	−5.00000	−0.171197	−0.0855984	−	0.996330i	$-0.527280\pi$
$853$	−5.00000	−0.171197	−0.0855984	+	0.996330i	$0.527280\pi$
$854$	44.0908	1.50876
$855$	−36.0000	−1.23117
$856$	68.5857	2.34421
$857$	14.0000	0.478231	0.239115	−	0.970991i	$-0.423143\pi$
$857$	14.0000	0.478231	0.239115	+	0.970991i	$0.423143\pi$
$858$	−18.0000	−0.614510
$859$	48.9898	1.67151	0.835755	−	0.549102i	$-0.185030\pi$
$859$	48.9898	1.67151	0.835755	+	0.549102i	$0.185030\pi$
$860$	0	0
$861$	30.0000	1.02240
$862$	−41.6413	−1.41831
$863$	9.79796	0.333526	0.166763	−	0.985997i	$-0.446668\pi$
$863$	9.79796	0.333526	0.166763	+	0.985997i	$0.446668\pi$
$864$	0	0
$865$	24.4949	0.832851
$866$	−30.0000	−1.01944
$867$	−78.3837	−2.66205
$868$	−29.3939	−0.997693
$869$	6.00000	0.203536
$870$	−36.0000	−1.22051
$871$	−27.0000	−0.914860
$872$	63.6867	2.15670
$873$	33.0000	1.11688
$874$	12.0000	0.405906
$875$	24.0000	0.811348
$876$	120.000	4.05442
$877$	−55.0000	−1.85722	−0.928609	−	0.371060i	$-0.878995\pi$
$877$	−55.0000	−1.85722	−0.928609	+	0.371060i	$0.878995\pi$
$878$	−71.0352	−2.39732
$879$	−39.1918	−1.32191
$880$	9.79796	0.330289
$881$	7.00000	0.235836	0.117918	−	0.993023i	$-0.462378\pi$
$881$	7.00000	0.235836	0.117918	+	0.993023i	$0.462378\pi$
$882$	−7.34847	−0.247436
$883$	31.0000	1.04323	0.521617	−	0.853180i	$-0.325329\pi$
$883$	31.0000	1.04323	0.521617	+	0.853180i	$0.325329\pi$
$884$	84.0000	2.82523
$885$	−60.0000	−2.01688
$886$	−83.2827	−2.79794
$887$	29.3939	0.986950	0.493475	−	0.869760i	$-0.335726\pi$
$887$	29.3939	0.986950	0.493475	+	0.869760i	$0.335726\pi$
$888$	58.7878	1.97279
$889$	2.44949	0.0821532
$890$	102.879	3.44850
$891$	9.00000	0.301511
$892$	68.5857	2.29642
$893$	−48.9898	−1.63938
$894$	−29.3939	−0.983078
$895$	6.00000	0.200558
$896$	−48.0000	−1.60357
$897$	7.34847	0.245358
$898$	−66.0000	−2.20245
$899$	7.34847	0.245085
$900$	12.0000	0.400000
$901$	7.00000	0.233204
$902$	12.2474	0.407795
$903$	0	0
$904$	72.0000	2.39468
$905$	−29.3939	−0.977086
$906$	102.879	3.41791
$907$	−27.0000	−0.896520	−0.448260	−	0.893903i	$-0.647956\pi$
$907$	−27.0000	−0.896520	−0.448260	+	0.893903i	$0.647956\pi$
$908$	39.1918	1.30063
$909$	−15.0000	−0.497519
$910$	44.0908	1.46160
$911$	−22.0454	−0.730397	−0.365198	−	0.930930i	$-0.618999\pi$
$911$	−22.0454	−0.730397	−0.365198	+	0.930930i	$0.618999\pi$
$912$	−48.0000	−1.58944
$913$	−1.00000	−0.0330952
$914$	−78.0000	−2.58001
$915$	44.0908	1.45760
$916$	28.0000	0.925146
$917$	0	0
$918$	0	0
$919$	3.00000	0.0989609	0.0494804	−	0.998775i	$-0.484243\pi$
$919$	3.00000	0.0989609	0.0494804	+	0.998775i	$0.484243\pi$
$920$	−12.0000	−0.395628
$921$	−56.3383	−1.85641
$922$	39.1918	1.29071
$923$	−14.6969	−0.483756
$924$	24.0000	0.789542
$925$	−4.89898	−0.161077
$926$	30.0000	0.985861
$927$	51.0000	1.67506
$928$	0	0
$929$	53.8888	1.76803	0.884017	−	0.467455i	$-0.154829\pi$
$929$	53.8888	1.76803	0.884017	+	0.467455i	$0.154829\pi$
$930$	−44.0908	−1.44579
$931$	−4.89898	−0.160558
$932$	19.5959	0.641886
$933$	61.2372	2.00482
$934$	−48.0000	−1.57061
$935$	−17.1464	−0.560748
$936$	−44.0908	−1.44115
$937$	2.44949	0.0800213	0.0400107	−	0.999199i	$-0.487261\pi$
$937$	2.44949	0.0800213	0.0400107	+	0.999199i	$0.487261\pi$
$938$	54.0000	1.76316
$939$	−18.0000	−0.587408
$940$	97.9796	3.19574
$941$	−29.0000	−0.945373	−0.472686	−	0.881231i	$-0.656716\pi$
$941$	−29.0000	−0.945373	−0.472686	+	0.881231i	$0.656716\pi$
$942$	58.7878	1.91541
$943$	−5.00000	−0.162822
$944$	−40.0000	−1.30189
$945$	0	0
$946$	0	0
$947$	25.0000	0.812391	0.406195	−	0.913786i	$-0.366855\pi$
$947$	25.0000	0.812391	0.406195	+	0.913786i	$0.366855\pi$
$948$	58.7878	1.90934
$949$	36.7423	1.19271
$950$	12.0000	0.389331
$951$	41.6413	1.35031
$952$	−84.0000	−2.72246
$953$	−56.3383	−1.82498	−0.912488	−	0.409104i	$-0.865841\pi$
$953$	−56.3383	−1.82498	−0.912488	+	0.409104i	$0.865841\pi$
$954$	−7.34847	−0.237915
$955$	−36.0000	−1.16493
$956$	−104.000	−3.36360
$957$	−6.00000	−0.193952
$958$	−2.44949	−0.0791394
$959$	−12.0000	−0.387500
$960$	−48.0000	−1.54919
$961$	−22.0000	−0.709677
$962$	36.0000	1.16069
$963$	42.0000	1.35343
$964$	78.3837	2.52457
$965$	−36.7423	−1.18278
$966$	−14.6969	−0.472866
$967$	49.0000	1.57573	0.787867	−	0.615846i	$-0.211185\pi$
$967$	49.0000	1.57573	0.787867	+	0.615846i	$0.211185\pi$
$968$	−48.9898	−1.57459
$969$	84.0000	2.69847
$970$	−66.0000	−2.11913
$971$	−41.0000	−1.31575	−0.657876	−	0.753126i	$-0.728545\pi$
$971$	−41.0000	−1.31575	−0.657876	+	0.753126i	$0.728545\pi$
$972$	88.1816	2.82843
$973$	−17.1464	−0.549689
$974$	−9.79796	−0.313947
$975$	7.34847	0.235339
$976$	29.3939	0.940875
$977$	28.0000	0.895799	0.447900	−	0.894084i	$-0.352172\pi$
$977$	28.0000	0.895799	0.447900	+	0.894084i	$0.352172\pi$
$978$	−14.6969	−0.469956
$979$	17.1464	0.548002
$980$	9.79796	0.312984
$981$	39.0000	1.24517
$982$	−54.0000	−1.72321
$983$	−12.2474	−0.390633	−0.195316	−	0.980740i	$-0.562573\pi$
$983$	−12.2474	−0.390633	−0.195316	+	0.980740i	$0.562573\pi$
$984$	60.0000	1.91273
$985$	−19.5959	−0.624378
$986$	42.0000	1.33755
$987$	60.0000	1.90982
$988$	−58.7878	−1.87029
$989$	0	0
$990$	18.0000	0.572078
$991$	31.8434	1.01154	0.505769	−	0.862669i	$-0.331209\pi$
$991$	31.8434	1.01154	0.505769	+	0.862669i	$0.331209\pi$
$992$	0	0
$993$	6.00000	0.190404
$994$	29.3939	0.932317
$995$	48.0000	1.52170
$996$	−9.79796	−0.310460
$997$	31.8434	1.00849	0.504245	−	0.863561i	$-0.331771\pi$
$997$	31.8434	1.00849	0.504245	+	0.863561i	$0.331771\pi$
$998$	−18.0000	−0.569780
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.g.1.2	yes	2
43.42	odd	2	inner	1849.2.a.g.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.g.1.1	✓	2	43.42	odd	2	inner
1849.2.a.g.1.2	yes	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+2.44949 q^{2} -2.44949 q^{3} +4.00000 q^{4} -2.44949 q^{5} -6.00000 q^{6} +2.44949 q^{7} +4.89898 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+2.44949 q^{2} -2.44949 q^{3} +4.00000 q^{4} -2.44949 q^{5} -6.00000 q^{6} +2.44949 q^{7} +4.89898 q^{8} +3.00000 q^{9} -6.00000 q^{10} -1.00000 q^{11} -9.79796 q^{12} -3.00000 q^{13} +6.00000 q^{14} +6.00000 q^{15} +4.00000 q^{16} -7.00000 q^{17} +7.34847 q^{18} +4.89898 q^{19} -9.79796 q^{20} -6.00000 q^{21} -2.44949 q^{22} +1.00000 q^{23} -12.0000 q^{24} +1.00000 q^{25} -7.34847 q^{26} +9.79796 q^{28} -2.44949 q^{29} +14.6969 q^{30} -3.00000 q^{31} +2.44949 q^{33} -17.1464 q^{34} -6.00000 q^{35} +12.0000 q^{36} -4.89898 q^{37} +12.0000 q^{38} +7.34847 q^{39} -12.0000 q^{40} -5.00000 q^{41} -14.6969 q^{42} -4.00000 q^{44} -7.34847 q^{45} +2.44949 q^{46} -10.0000 q^{47} -9.79796 q^{48} -1.00000 q^{49} +2.44949 q^{50} +17.1464 q^{51} -12.0000 q^{52} -1.00000 q^{53} +2.44949 q^{55} +12.0000 q^{56} -12.0000 q^{57} -6.00000 q^{58} -10.0000 q^{59} +24.0000 q^{60} +7.34847 q^{61} -7.34847 q^{62} +7.34847 q^{63} -8.00000 q^{64} +7.34847 q^{65} +6.00000 q^{66} +9.00000 q^{67} -28.0000 q^{68} -2.44949 q^{69} -14.6969 q^{70} +4.89898 q^{71} +14.6969 q^{72} -12.2474 q^{73} -12.0000 q^{74} -2.44949 q^{75} +19.5959 q^{76} -2.44949 q^{77} +18.0000 q^{78} -6.00000 q^{79} -9.79796 q^{80} -9.00000 q^{81} -12.2474 q^{82} +1.00000 q^{83} -24.0000 q^{84} +17.1464 q^{85} +6.00000 q^{87} -4.89898 q^{88} -17.1464 q^{89} -18.0000 q^{90} -7.34847 q^{91} +4.00000 q^{92} +7.34847 q^{93} -24.4949 q^{94} -12.0000 q^{95} +11.0000 q^{97} -2.44949 q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{4} - 12 q^{6} + 6 q^{9}+O(q^{10}) \) 2 * q + 8 * q^4 - 12 * q^6 + 6 * q^9	\( 2 q + 8 q^{4} - 12 q^{6} + 6 q^{9} - 12 q^{10} - 2 q^{11} - 6 q^{13} + 12 q^{14} + 12 q^{15} + 8 q^{16} - 14 q^{17} - 12 q^{21} + 2 q^{23} - 24 q^{24} + 2 q^{25} - 6 q^{31} - 12 q^{35} + 24 q^{36} + 24 q^{38} - 24 q^{40} - 10 q^{41} - 8 q^{44} - 20 q^{47} - 2 q^{49} - 24 q^{52} - 2 q^{53} + 24 q^{56} - 24 q^{57} - 12 q^{58} - 20 q^{59} + 48 q^{60} - 16 q^{64} + 12 q^{66} + 18 q^{67} - 56 q^{68} - 24 q^{74} + 36 q^{78} - 12 q^{79} - 18 q^{81} + 2 q^{83} - 48 q^{84} + 12 q^{87} - 36 q^{90} + 8 q^{92} - 24 q^{95} + 22 q^{97} - 6 q^{99}+O(q^{100}) \) 2 * q + 8 * q^4 - 12 * q^6 + 6 * q^9 - 12 * q^10 - 2 * q^11 - 6 * q^13 + 12 * q^14 + 12 * q^15 + 8 * q^16 - 14 * q^17 - 12 * q^21 + 2 * q^23 - 24 * q^24 + 2 * q^25 - 6 * q^31 - 12 * q^35 + 24 * q^36 + 24 * q^38 - 24 * q^40 - 10 * q^41 - 8 * q^44 - 20 * q^47 - 2 * q^49 - 24 * q^52 - 2 * q^53 + 24 * q^56 - 24 * q^57 - 12 * q^58 - 20 * q^59 + 48 * q^60 - 16 * q^64 + 12 * q^66 + 18 * q^67 - 56 * q^68 - 24 * q^74 + 36 * q^78 - 12 * q^79 - 18 * q^81 + 2 * q^83 - 48 * q^84 + 12 * q^87 - 36 * q^90 + 8 * q^92 - 24 * q^95 + 22 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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