LMFDB - Embedded newform 1254.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1254,2,Mod(1,1254)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1254, 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("1254.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1254 = 2 \cdot 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1254.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:	$10.0132404135$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 8 $ x^2 - x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.37228$ of defining polynomial
Character	$\chi$	$=$	1254.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.37228 q^{5} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.37228 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.74456 q^{13} +2.00000 q^{14} +1.37228 q^{15} +1.00000 q^{16} +1.37228 q^{17} -1.00000 q^{18} -1.00000 q^{19} -1.37228 q^{20} +2.00000 q^{21} -1.00000 q^{22} +1.00000 q^{24} -3.11684 q^{25} +4.74456 q^{26} -1.00000 q^{27} -2.00000 q^{28} +2.62772 q^{29} -1.37228 q^{30} +2.00000 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.37228 q^{34} +2.74456 q^{35} +1.00000 q^{36} +3.37228 q^{37} +1.00000 q^{38} +4.74456 q^{39} +1.37228 q^{40} +2.00000 q^{41} -2.00000 q^{42} -4.62772 q^{43} +1.00000 q^{44} -1.37228 q^{45} -1.00000 q^{48} -3.00000 q^{49} +3.11684 q^{50} -1.37228 q^{51} -4.74456 q^{52} +10.7446 q^{53} +1.00000 q^{54} -1.37228 q^{55} +2.00000 q^{56} +1.00000 q^{57} -2.62772 q^{58} +12.0000 q^{59} +1.37228 q^{60} +6.11684 q^{61} -2.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +6.51087 q^{65} +1.00000 q^{66} +0.627719 q^{67} +1.37228 q^{68} -2.74456 q^{70} +4.74456 q^{71} -1.00000 q^{72} +0.744563 q^{73} -3.37228 q^{74} +3.11684 q^{75} -1.00000 q^{76} -2.00000 q^{77} -4.74456 q^{78} -9.48913 q^{79} -1.37228 q^{80} +1.00000 q^{81} -2.00000 q^{82} -2.74456 q^{83} +2.00000 q^{84} -1.88316 q^{85} +4.62772 q^{86} -2.62772 q^{87} -1.00000 q^{88} +6.62772 q^{89} +1.37228 q^{90} +9.48913 q^{91} -2.00000 q^{93} +1.37228 q^{95} +1.00000 q^{96} +12.7446 q^{97} +3.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{5} + 2 q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9} - 3 q^{10} + 2 q^{11} - 2 q^{12} + 2 q^{13} + 4 q^{14} - 3 q^{15} + 2 q^{16} - 3 q^{17} - 2 q^{18} - 2 q^{19} + 3 q^{20}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^5 + 2 * q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9 - 3 * q^10 + 2 * q^11 - 2 * q^12 + 2 * q^13 + 4 * q^14 - 3 * q^15 + 2 * q^16 - 3 * q^17 - 2 * q^18 - 2 * q^19 + 3 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^24 + 11 * q^25 - 2 * q^26 - 2 * q^27 - 4 * q^28 + 11 * q^29 + 3 * q^30 + 4 * q^31 - 2 * q^32 - 2 * q^33 + 3 * q^34 - 6 * q^35 + 2 * q^36 + q^37 + 2 * q^38 - 2 * q^39 - 3 * q^40 + 4 * q^41 - 4 * q^42 - 15 * q^43 + 2 * q^44 + 3 * q^45 - 2 * q^48 - 6 * q^49 - 11 * q^50 + 3 * q^51 + 2 * q^52 + 10 * q^53 + 2 * q^54 + 3 * q^55 + 4 * q^56 + 2 * q^57 - 11 * q^58 + 24 * q^59 - 3 * q^60 - 5 * q^61 - 4 * q^62 - 4 * q^63 + 2 * q^64 + 36 * q^65 + 2 * q^66 + 7 * q^67 - 3 * q^68 + 6 * q^70 - 2 * q^71 - 2 * q^72 - 10 * q^73 - q^74 - 11 * q^75 - 2 * q^76 - 4 * q^77 + 2 * q^78 + 4 * q^79 + 3 * q^80 + 2 * q^81 - 4 * q^82 + 6 * q^83 + 4 * q^84 - 21 * q^85 + 15 * q^86 - 11 * q^87 - 2 * q^88 + 19 * q^89 - 3 * q^90 - 4 * q^91 - 4 * q^93 - 3 * q^95 + 2 * q^96 + 14 * q^97 + 6 * q^98 + 2 * q^99

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.37228	−0.613703	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	−1.37228	−0.613703	−0.306851	+	0.951757i	$0.599275\pi$
$6$	1.00000	0.408248
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.37228	0.433953
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−4.74456	−1.31590	−0.657952	−	0.753059i	$-0.728577\pi$
$13$	−4.74456	−1.31590	−0.657952	+	0.753059i	$0.728577\pi$
$14$	2.00000	0.534522
$15$	1.37228	0.354322
$16$	1.00000	0.250000
$17$	1.37228	0.332827	0.166414	−	0.986056i	$-0.446781\pi$
$17$	1.37228	0.332827	0.166414	+	0.986056i	$0.446781\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.37228	−0.306851
$21$	2.00000	0.436436
$22$	−1.00000	−0.213201
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	1.00000	0.204124
$25$	−3.11684	−0.623369
$26$	4.74456	0.930485
$27$	−1.00000	−0.192450
$28$	−2.00000	−0.377964
$29$	2.62772	0.487955	0.243978	−	0.969781i	$-0.421548\pi$
$29$	2.62772	0.487955	0.243978	+	0.969781i	$0.421548\pi$
$30$	−1.37228	−0.250543
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−1.37228	−0.235344
$35$	2.74456	0.463916
$36$	1.00000	0.166667
$37$	3.37228	0.554400	0.277200	−	0.960812i	$-0.410594\pi$
$37$	3.37228	0.554400	0.277200	+	0.960812i	$0.410594\pi$
$38$	1.00000	0.162221
$39$	4.74456	0.759738
$40$	1.37228	0.216977
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	−2.00000	−0.308607
$43$	−4.62772	−0.705720	−0.352860	−	0.935676i	$-0.614791\pi$
$43$	−4.62772	−0.705720	−0.352860	+	0.935676i	$0.614791\pi$
$44$	1.00000	0.150756
$45$	−1.37228	−0.204568
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−1.00000	−0.144338
$49$	−3.00000	−0.428571
$50$	3.11684	0.440788
$51$	−1.37228	−0.192158
$52$	−4.74456	−0.657952
$53$	10.7446	1.47588	0.737940	−	0.674867i	$-0.235799\pi$
$53$	10.7446	1.47588	0.737940	+	0.674867i	$0.235799\pi$
$54$	1.00000	0.136083
$55$	−1.37228	−0.185038
$56$	2.00000	0.267261
$57$	1.00000	0.132453
$58$	−2.62772	−0.345036
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	1.37228	0.177161
$61$	6.11684	0.783182	0.391591	−	0.920139i	$-0.371925\pi$
$61$	6.11684	0.783182	0.391591	+	0.920139i	$0.371925\pi$
$62$	−2.00000	−0.254000
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	6.51087	0.807575
$66$	1.00000	0.123091
$67$	0.627719	0.0766880	0.0383440	−	0.999265i	$-0.487792\pi$
$67$	0.627719	0.0766880	0.0383440	+	0.999265i	$0.487792\pi$
$68$	1.37228	0.166414
$69$	0	0
$70$	−2.74456	−0.328038
$71$	4.74456	0.563076	0.281538	−	0.959550i	$-0.409155\pi$
$71$	4.74456	0.563076	0.281538	+	0.959550i	$0.409155\pi$
$72$	−1.00000	−0.117851
$73$	0.744563	0.0871445	0.0435722	−	0.999050i	$-0.486126\pi$
$73$	0.744563	0.0871445	0.0435722	+	0.999050i	$0.486126\pi$
$74$	−3.37228	−0.392020
$75$	3.11684	0.359902
$76$	−1.00000	−0.114708
$77$	−2.00000	−0.227921
$78$	−4.74456	−0.537216
$79$	−9.48913	−1.06761	−0.533805	−	0.845608i	$-0.679238\pi$
$79$	−9.48913	−1.06761	−0.533805	+	0.845608i	$0.679238\pi$
$80$	−1.37228	−0.153426
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	−2.74456	−0.301255	−0.150627	−	0.988591i	$-0.548129\pi$
$83$	−2.74456	−0.301255	−0.150627	+	0.988591i	$0.548129\pi$
$84$	2.00000	0.218218
$85$	−1.88316	−0.204257
$86$	4.62772	0.499020
$87$	−2.62772	−0.281721
$88$	−1.00000	−0.106600
$89$	6.62772	0.702537	0.351268	−	0.936275i	$-0.385750\pi$
$89$	6.62772	0.702537	0.351268	+	0.936275i	$0.385750\pi$
$90$	1.37228	0.144651
$91$	9.48913	0.994731
$92$	0	0
$93$	−2.00000	−0.207390
$94$	0	0
$95$	1.37228	0.140793
$96$	1.00000	0.102062
$97$	12.7446	1.29401	0.647007	−	0.762484i	$-0.276020\pi$
$97$	12.7446	1.29401	0.647007	+	0.762484i	$0.276020\pi$
$98$	3.00000	0.303046
$99$	1.00000	0.100504
$100$	−3.11684	−0.311684
$101$	18.7446	1.86515	0.932577	−	0.360971i	$-0.117555\pi$
$101$	18.7446	1.86515	0.932577	+	0.360971i	$0.117555\pi$
$102$	1.37228	0.135876
$103$	10.0000	0.985329	0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000	0.985329	0.492665	+	0.870219i	$0.336023\pi$
$104$	4.74456	0.465243
$105$	−2.74456	−0.267842
$106$	−10.7446	−1.04360
$107$	−7.37228	−0.712705	−0.356353	−	0.934352i	$-0.615980\pi$
$107$	−7.37228	−0.712705	−0.356353	+	0.934352i	$0.615980\pi$
$108$	−1.00000	−0.0962250
$109$	11.4891	1.10046	0.550229	−	0.835014i	$-0.314540\pi$
$109$	11.4891	1.10046	0.550229	+	0.835014i	$0.314540\pi$
$110$	1.37228	0.130842
$111$	−3.37228	−0.320083
$112$	−2.00000	−0.188982
$113$	−8.11684	−0.763568	−0.381784	−	0.924251i	$-0.624690\pi$
$113$	−8.11684	−0.763568	−0.381784	+	0.924251i	$0.624690\pi$
$114$	−1.00000	−0.0936586
$115$	0	0
$116$	2.62772	0.243978
$117$	−4.74456	−0.438635
$118$	−12.0000	−1.10469
$119$	−2.74456	−0.251594
$120$	−1.37228	−0.125272
$121$	1.00000	0.0909091
$122$	−6.11684	−0.553793
$123$	−2.00000	−0.180334
$124$	2.00000	0.179605
$125$	11.1386	0.996266
$126$	2.00000	0.178174
$127$	4.62772	0.410644	0.205322	−	0.978695i	$-0.434176\pi$
$127$	4.62772	0.410644	0.205322	+	0.978695i	$0.434176\pi$
$128$	−1.00000	−0.0883883
$129$	4.62772	0.407448
$130$	−6.51087	−0.571041
$131$	10.7446	0.938757	0.469378	−	0.882997i	$-0.344478\pi$
$131$	10.7446	0.938757	0.469378	+	0.882997i	$0.344478\pi$
$132$	−1.00000	−0.0870388
$133$	2.00000	0.173422
$134$	−0.627719	−0.0542266
$135$	1.37228	0.118107
$136$	−1.37228	−0.117672
$137$	−0.744563	−0.0636123	−0.0318061	−	0.999494i	$-0.510126\pi$
$137$	−0.744563	−0.0636123	−0.0318061	+	0.999494i	$0.510126\pi$
$138$	0	0
$139$	4.62772	0.392518	0.196259	−	0.980552i	$-0.437121\pi$
$139$	4.62772	0.392518	0.196259	+	0.980552i	$0.437121\pi$
$140$	2.74456	0.231958
$141$	0	0
$142$	−4.74456	−0.398155
$143$	−4.74456	−0.396760
$144$	1.00000	0.0833333
$145$	−3.60597	−0.299459
$146$	−0.744563	−0.0616204
$147$	3.00000	0.247436
$148$	3.37228	0.277200
$149$	2.74456	0.224843	0.112422	−	0.993661i	$-0.464139\pi$
$149$	2.74456	0.224843	0.112422	+	0.993661i	$0.464139\pi$
$150$	−3.11684	−0.254489
$151$	−8.62772	−0.702114	−0.351057	−	0.936354i	$-0.614178\pi$
$151$	−8.62772	−0.702114	−0.351057	+	0.936354i	$0.614178\pi$
$152$	1.00000	0.0811107
$153$	1.37228	0.110942
$154$	2.00000	0.161165
$155$	−2.74456	−0.220449
$156$	4.74456	0.379869
$157$	−0.744563	−0.0594226	−0.0297113	−	0.999559i	$-0.509459\pi$
$157$	−0.744563	−0.0594226	−0.0297113	+	0.999559i	$0.509459\pi$
$158$	9.48913	0.754914
$159$	−10.7446	−0.852099
$160$	1.37228	0.108488
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	2.00000	0.156174
$165$	1.37228	0.106832
$166$	2.74456	0.213019
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	−2.00000	−0.154303
$169$	9.51087	0.731606
$170$	1.88316	0.144431
$171$	−1.00000	−0.0764719
$172$	−4.62772	−0.352860
$173$	17.6060	1.33856	0.669279	−	0.743012i	$-0.266603\pi$
$173$	17.6060	1.33856	0.669279	+	0.743012i	$0.266603\pi$
$174$	2.62772	0.199207
$175$	6.23369	0.471223
$176$	1.00000	0.0753778
$177$	−12.0000	−0.901975
$178$	−6.62772	−0.496769
$179$	−13.4891	−1.00822	−0.504112	−	0.863638i	$-0.668180\pi$
$179$	−13.4891	−1.00822	−0.504112	+	0.863638i	$0.668180\pi$
$180$	−1.37228	−0.102284
$181$	23.6060	1.75462	0.877309	−	0.479926i	$-0.159337\pi$
$181$	23.6060	1.75462	0.877309	+	0.479926i	$0.159337\pi$
$182$	−9.48913	−0.703381
$183$	−6.11684	−0.452170
$184$	0	0
$185$	−4.62772	−0.340237
$186$	2.00000	0.146647
$187$	1.37228	0.100351
$188$	0	0
$189$	2.00000	0.145479
$190$	−1.37228	−0.0995558
$191$	−1.48913	−0.107749	−0.0538747	−	0.998548i	$-0.517157\pi$
$191$	−1.48913	−0.107749	−0.0538747	+	0.998548i	$0.517157\pi$
$192$	−1.00000	−0.0721688
$193$	−10.6277	−0.765000	−0.382500	−	0.923956i	$-0.624937\pi$
$193$	−10.6277	−0.765000	−0.382500	+	0.923956i	$0.624937\pi$
$194$	−12.7446	−0.915006
$195$	−6.51087	−0.466253
$196$	−3.00000	−0.214286
$197$	8.00000	0.569976	0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000	0.569976	0.284988	+	0.958531i	$0.408010\pi$
$198$	−1.00000	−0.0710669
$199$	16.8614	1.19527	0.597637	−	0.801767i	$-0.296107\pi$
$199$	16.8614	1.19527	0.597637	+	0.801767i	$0.296107\pi$
$200$	3.11684	0.220394
$201$	−0.627719	−0.0442759
$202$	−18.7446	−1.31886
$203$	−5.25544	−0.368859
$204$	−1.37228	−0.0960789
$205$	−2.74456	−0.191689
$206$	−10.0000	−0.696733
$207$	0	0
$208$	−4.74456	−0.328976
$209$	−1.00000	−0.0691714
$210$	2.74456	0.189393
$211$	9.48913	0.653258	0.326629	−	0.945153i	$-0.394087\pi$
$211$	9.48913	0.653258	0.326629	+	0.945153i	$0.394087\pi$
$212$	10.7446	0.737940
$213$	−4.74456	−0.325092
$214$	7.37228	0.503959
$215$	6.35053	0.433103
$216$	1.00000	0.0680414
$217$	−4.00000	−0.271538
$218$	−11.4891	−0.778142
$219$	−0.744563	−0.0503129
$220$	−1.37228	−0.0925192
$221$	−6.51087	−0.437969
$222$	3.37228	0.226333
$223$	−12.7446	−0.853439	−0.426720	−	0.904384i	$-0.640331\pi$
$223$	−12.7446	−0.853439	−0.426720	+	0.904384i	$0.640331\pi$
$224$	2.00000	0.133631
$225$	−3.11684	−0.207790
$226$	8.11684	0.539924
$227$	−9.88316	−0.655968	−0.327984	−	0.944683i	$-0.606369\pi$
$227$	−9.88316	−0.655968	−0.327984	+	0.944683i	$0.606369\pi$
$228$	1.00000	0.0662266
$229$	0.744563	0.0492021	0.0246010	−	0.999697i	$-0.492168\pi$
$229$	0.744563	0.0492021	0.0246010	+	0.999697i	$0.492168\pi$
$230$	0	0
$231$	2.00000	0.131590
$232$	−2.62772	−0.172518
$233$	2.00000	0.131024	0.0655122	−	0.997852i	$-0.479132\pi$
$233$	2.00000	0.131024	0.0655122	+	0.997852i	$0.479132\pi$
$234$	4.74456	0.310162
$235$	0	0
$236$	12.0000	0.781133
$237$	9.48913	0.616385
$238$	2.74456	0.177904
$239$	−17.3723	−1.12372	−0.561860	−	0.827233i	$-0.689914\pi$
$239$	−17.3723	−1.12372	−0.561860	+	0.827233i	$0.689914\pi$
$240$	1.37228	0.0885804
$241$	−20.1168	−1.29584	−0.647920	−	0.761708i	$-0.724361\pi$
$241$	−20.1168	−1.29584	−0.647920	+	0.761708i	$0.724361\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	6.11684	0.391591
$245$	4.11684	0.263016
$246$	2.00000	0.127515
$247$	4.74456	0.301889
$248$	−2.00000	−0.127000
$249$	2.74456	0.173930
$250$	−11.1386	−0.704467
$251$	−27.6060	−1.74247	−0.871237	−	0.490863i	$-0.836681\pi$
$251$	−27.6060	−1.74247	−0.871237	+	0.490863i	$0.836681\pi$
$252$	−2.00000	−0.125988
$253$	0	0
$254$	−4.62772	−0.290369
$255$	1.88316	0.117928
$256$	1.00000	0.0625000
$257$	2.86141	0.178490	0.0892448	−	0.996010i	$-0.471555\pi$
$257$	2.86141	0.178490	0.0892448	+	0.996010i	$0.471555\pi$
$258$	−4.62772	−0.288109
$259$	−6.74456	−0.419087
$260$	6.51087	0.403787
$261$	2.62772	0.162652
$262$	−10.7446	−0.663801
$263$	−3.25544	−0.200739	−0.100369	−	0.994950i	$-0.532002\pi$
$263$	−3.25544	−0.200739	−0.100369	+	0.994950i	$0.532002\pi$
$264$	1.00000	0.0615457
$265$	−14.7446	−0.905751
$266$	−2.00000	−0.122628
$267$	−6.62772	−0.405610
$268$	0.627719	0.0383440
$269$	21.4891	1.31022	0.655108	−	0.755536i	$-0.272623\pi$
$269$	21.4891	1.31022	0.655108	+	0.755536i	$0.272623\pi$
$270$	−1.37228	−0.0835144
$271$	−6.23369	−0.378670	−0.189335	−	0.981913i	$-0.560633\pi$
$271$	−6.23369	−0.378670	−0.189335	+	0.981913i	$0.560633\pi$
$272$	1.37228	0.0832068
$273$	−9.48913	−0.574308
$274$	0.744563	0.0449807
$275$	−3.11684	−0.187953
$276$	0	0
$277$	−22.1168	−1.32887	−0.664436	−	0.747345i	$-0.731328\pi$
$277$	−22.1168	−1.32887	−0.664436	+	0.747345i	$0.731328\pi$
$278$	−4.62772	−0.277552
$279$	2.00000	0.119737
$280$	−2.74456	−0.164019
$281$	−12.9783	−0.774218	−0.387109	−	0.922034i	$-0.626526\pi$
$281$	−12.9783	−0.774218	−0.387109	+	0.922034i	$0.626526\pi$
$282$	0	0
$283$	−22.9783	−1.36592	−0.682958	−	0.730458i	$-0.739307\pi$
$283$	−22.9783	−1.36592	−0.682958	+	0.730458i	$0.739307\pi$
$284$	4.74456	0.281538
$285$	−1.37228	−0.0812869
$286$	4.74456	0.280552
$287$	−4.00000	−0.236113
$288$	−1.00000	−0.0589256
$289$	−15.1168	−0.889226
$290$	3.60597	0.211750
$291$	−12.7446	−0.747099
$292$	0.744563	0.0435722
$293$	−5.37228	−0.313852	−0.156926	−	0.987610i	$-0.550158\pi$
$293$	−5.37228	−0.313852	−0.156926	+	0.987610i	$0.550158\pi$
$294$	−3.00000	−0.174964
$295$	−16.4674	−0.958768
$296$	−3.37228	−0.196010
$297$	−1.00000	−0.0580259
$298$	−2.74456	−0.158988
$299$	0	0
$300$	3.11684	0.179951
$301$	9.25544	0.533475
$302$	8.62772	0.496469
$303$	−18.7446	−1.07685
$304$	−1.00000	−0.0573539
$305$	−8.39403	−0.480641
$306$	−1.37228	−0.0784481
$307$	1.48913	0.0849889	0.0424944	−	0.999097i	$-0.486470\pi$
$307$	1.48913	0.0849889	0.0424944	+	0.999097i	$0.486470\pi$
$308$	−2.00000	−0.113961
$309$	−10.0000	−0.568880
$310$	2.74456	0.155881
$311$	−34.7446	−1.97018	−0.985092	−	0.172030i	$-0.944967\pi$
$311$	−34.7446	−1.97018	−0.985092	+	0.172030i	$0.944967\pi$
$312$	−4.74456	−0.268608
$313$	5.60597	0.316868	0.158434	−	0.987370i	$-0.449355\pi$
$313$	5.60597	0.316868	0.158434	+	0.987370i	$0.449355\pi$
$314$	0.744563	0.0420181
$315$	2.74456	0.154639
$316$	−9.48913	−0.533805
$317$	16.2337	0.911775	0.455887	−	0.890037i	$-0.349322\pi$
$317$	16.2337	0.911775	0.455887	+	0.890037i	$0.349322\pi$
$318$	10.7446	0.602525
$319$	2.62772	0.147124
$320$	−1.37228	−0.0767129
$321$	7.37228	0.411481
$322$	0	0
$323$	−1.37228	−0.0763558
$324$	1.00000	0.0555556
$325$	14.7881	0.820294
$326$	12.0000	0.664619
$327$	−11.4891	−0.635350
$328$	−2.00000	−0.110432
$329$	0	0
$330$	−1.37228	−0.0755416
$331$	16.8614	0.926787	0.463393	−	0.886153i	$-0.346632\pi$
$331$	16.8614	0.926787	0.463393	+	0.886153i	$0.346632\pi$
$332$	−2.74456	−0.150627
$333$	3.37228	0.184800
$334$	−8.00000	−0.437741
$335$	−0.861407	−0.0470637
$336$	2.00000	0.109109
$337$	−20.1168	−1.09583	−0.547917	−	0.836533i	$-0.684579\pi$
$337$	−20.1168	−1.09583	−0.547917	+	0.836533i	$0.684579\pi$
$338$	−9.51087	−0.517323
$339$	8.11684	0.440846
$340$	−1.88316	−0.102128
$341$	2.00000	0.108306
$342$	1.00000	0.0540738
$343$	20.0000	1.07990
$344$	4.62772	0.249510
$345$	0	0
$346$	−17.6060	−0.946503
$347$	−5.48913	−0.294672	−0.147336	−	0.989087i	$-0.547070\pi$
$347$	−5.48913	−0.294672	−0.147336	+	0.989087i	$0.547070\pi$
$348$	−2.62772	−0.140861
$349$	−15.3723	−0.822859	−0.411430	−	0.911442i	$-0.634970\pi$
$349$	−15.3723	−0.822859	−0.411430	+	0.911442i	$0.634970\pi$
$350$	−6.23369	−0.333205
$351$	4.74456	0.253246
$352$	−1.00000	−0.0533002
$353$	4.74456	0.252528	0.126264	−	0.991997i	$-0.459701\pi$
$353$	4.74456	0.252528	0.126264	+	0.991997i	$0.459701\pi$
$354$	12.0000	0.637793
$355$	−6.51087	−0.345561
$356$	6.62772	0.351268
$357$	2.74456	0.145258
$358$	13.4891	0.712922
$359$	18.2337	0.962337	0.481169	−	0.876628i	$-0.340212\pi$
$359$	18.2337	0.962337	0.481169	+	0.876628i	$0.340212\pi$
$360$	1.37228	0.0723256
$361$	1.00000	0.0526316
$362$	−23.6060	−1.24070
$363$	−1.00000	−0.0524864
$364$	9.48913	0.497365
$365$	−1.02175	−0.0534808
$366$	6.11684	0.319733
$367$	33.0951	1.72755	0.863775	−	0.503878i	$-0.168094\pi$
$367$	33.0951	1.72755	0.863775	+	0.503878i	$0.168094\pi$
$368$	0	0
$369$	2.00000	0.104116
$370$	4.62772	0.240584
$371$	−21.4891	−1.11566
$372$	−2.00000	−0.103695
$373$	−7.25544	−0.375672	−0.187836	−	0.982200i	$-0.560147\pi$
$373$	−7.25544	−0.375672	−0.187836	+	0.982200i	$0.560147\pi$
$374$	−1.37228	−0.0709590
$375$	−11.1386	−0.575194
$376$	0	0
$377$	−12.4674	−0.642103
$378$	−2.00000	−0.102869
$379$	15.6060	0.801625	0.400812	−	0.916160i	$-0.368728\pi$
$379$	15.6060	0.801625	0.400812	+	0.916160i	$0.368728\pi$
$380$	1.37228	0.0703965
$381$	−4.62772	−0.237085
$382$	1.48913	0.0761903
$383$	21.6060	1.10401	0.552007	−	0.833840i	$-0.313862\pi$
$383$	21.6060	1.10401	0.552007	+	0.833840i	$0.313862\pi$
$384$	1.00000	0.0510310
$385$	2.74456	0.139876
$386$	10.6277	0.540937
$387$	−4.62772	−0.235240
$388$	12.7446	0.647007
$389$	7.48913	0.379714	0.189857	−	0.981812i	$-0.439198\pi$
$389$	7.48913	0.379714	0.189857	+	0.981812i	$0.439198\pi$
$390$	6.51087	0.329691
$391$	0	0
$392$	3.00000	0.151523
$393$	−10.7446	−0.541991
$394$	−8.00000	−0.403034
$395$	13.0217	0.655195
$396$	1.00000	0.0502519
$397$	14.0000	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$398$	−16.8614	−0.845186
$399$	−2.00000	−0.100125
$400$	−3.11684	−0.155842
$401$	5.13859	0.256609	0.128305	−	0.991735i	$-0.459047\pi$
$401$	5.13859	0.256609	0.128305	+	0.991735i	$0.459047\pi$
$402$	0.627719	0.0313078
$403$	−9.48913	−0.472687
$404$	18.7446	0.932577
$405$	−1.37228	−0.0681892
$406$	5.25544	0.260823
$407$	3.37228	0.167158
$408$	1.37228	0.0679380
$409$	22.0000	1.08783	0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000	1.08783	0.543915	+	0.839140i	$0.316941\pi$
$410$	2.74456	0.135544
$411$	0.744563	0.0367266
$412$	10.0000	0.492665
$413$	−24.0000	−1.18096
$414$	0	0
$415$	3.76631	0.184881
$416$	4.74456	0.232621
$417$	−4.62772	−0.226620
$418$	1.00000	0.0489116
$419$	−20.8614	−1.01915	−0.509573	−	0.860427i	$-0.670197\pi$
$419$	−20.8614	−1.01915	−0.509573	+	0.860427i	$0.670197\pi$
$420$	−2.74456	−0.133921
$421$	6.74456	0.328710	0.164355	−	0.986401i	$-0.447446\pi$
$421$	6.74456	0.328710	0.164355	+	0.986401i	$0.447446\pi$
$422$	−9.48913	−0.461923
$423$	0	0
$424$	−10.7446	−0.521802
$425$	−4.27719	−0.207474
$426$	4.74456	0.229875
$427$	−12.2337	−0.592030
$428$	−7.37228	−0.356353
$429$	4.74456	0.229070
$430$	−6.35053	−0.306250
$431$	−0.233688	−0.0112564	−0.00562818	−	0.999984i	$-0.501792\pi$
$431$	−0.233688	−0.0112564	−0.00562818	+	0.999984i	$0.501792\pi$
$432$	−1.00000	−0.0481125
$433$	27.4891	1.32104	0.660522	−	0.750807i	$-0.270335\pi$
$433$	27.4891	1.32104	0.660522	+	0.750807i	$0.270335\pi$
$434$	4.00000	0.192006
$435$	3.60597	0.172893
$436$	11.4891	0.550229
$437$	0	0
$438$	0.744563	0.0355766
$439$	11.3723	0.542769	0.271385	−	0.962471i	$-0.412518\pi$
$439$	11.3723	0.542769	0.271385	+	0.962471i	$0.412518\pi$
$440$	1.37228	0.0654209
$441$	−3.00000	−0.142857
$442$	6.51087	0.309691
$443$	0.627719	0.0298238	0.0149119	−	0.999889i	$-0.495253\pi$
$443$	0.627719	0.0298238	0.0149119	+	0.999889i	$0.495253\pi$
$444$	−3.37228	−0.160041
$445$	−9.09509	−0.431149
$446$	12.7446	0.603473
$447$	−2.74456	−0.129813
$448$	−2.00000	−0.0944911
$449$	19.4891	0.919749	0.459874	−	0.887984i	$-0.347894\pi$
$449$	19.4891	0.919749	0.459874	+	0.887984i	$0.347894\pi$
$450$	3.11684	0.146929
$451$	2.00000	0.0941763
$452$	−8.11684	−0.381784
$453$	8.62772	0.405366
$454$	9.88316	0.463839
$455$	−13.0217	−0.610469
$456$	−1.00000	−0.0468293
$457$	−15.4891	−0.724551	−0.362275	−	0.932071i	$-0.618000\pi$
$457$	−15.4891	−0.724551	−0.362275	+	0.932071i	$0.618000\pi$
$458$	−0.744563	−0.0347911
$459$	−1.37228	−0.0640526
$460$	0	0
$461$	12.0000	0.558896	0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000	0.558896	0.279448	+	0.960161i	$0.409849\pi$
$462$	−2.00000	−0.0930484
$463$	−26.1168	−1.21375	−0.606876	−	0.794796i	$-0.707578\pi$
$463$	−26.1168	−1.21375	−0.606876	+	0.794796i	$0.707578\pi$
$464$	2.62772	0.121989
$465$	2.74456	0.127276
$466$	−2.00000	−0.0926482
$467$	28.4674	1.31731	0.658657	−	0.752444i	$-0.271125\pi$
$467$	28.4674	1.31731	0.658657	+	0.752444i	$0.271125\pi$
$468$	−4.74456	−0.219317
$469$	−1.25544	−0.0579707
$470$	0	0
$471$	0.744563	0.0343076
$472$	−12.0000	−0.552345
$473$	−4.62772	−0.212783
$474$	−9.48913	−0.435850
$475$	3.11684	0.143011
$476$	−2.74456	−0.125797
$477$	10.7446	0.491960
$478$	17.3723	0.794590
$479$	−37.6060	−1.71826	−0.859130	−	0.511757i	$-0.828995\pi$
$479$	−37.6060	−1.71826	−0.859130	+	0.511757i	$0.828995\pi$
$480$	−1.37228	−0.0626358
$481$	−16.0000	−0.729537
$482$	20.1168	0.916297
$483$	0	0
$484$	1.00000	0.0454545
$485$	−17.4891	−0.794140
$486$	1.00000	0.0453609
$487$	28.9783	1.31313	0.656565	−	0.754270i	$-0.272009\pi$
$487$	28.9783	1.31313	0.656565	+	0.754270i	$0.272009\pi$
$488$	−6.11684	−0.276897
$489$	12.0000	0.542659
$490$	−4.11684	−0.185980
$491$	22.7446	1.02645	0.513224	−	0.858255i	$-0.328451\pi$
$491$	22.7446	1.02645	0.513224	+	0.858255i	$0.328451\pi$
$492$	−2.00000	−0.0901670
$493$	3.60597	0.162405
$494$	−4.74456	−0.213468
$495$	−1.37228	−0.0616795
$496$	2.00000	0.0898027
$497$	−9.48913	−0.425645
$498$	−2.74456	−0.122987
$499$	20.0000	0.895323	0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000	0.895323	0.447661	+	0.894203i	$0.352257\pi$
$500$	11.1386	0.498133
$501$	−8.00000	−0.357414
$502$	27.6060	1.23211
$503$	−36.7446	−1.63836	−0.819180	−	0.573537i	$-0.805571\pi$
$503$	−36.7446	−1.63836	−0.819180	+	0.573537i	$0.805571\pi$
$504$	2.00000	0.0890871
$505$	−25.7228	−1.14465
$506$	0	0
$507$	−9.51087	−0.422393
$508$	4.62772	0.205322
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	−1.88316	−0.0833876
$511$	−1.48913	−0.0658750
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	−2.86141	−0.126211
$515$	−13.7228	−0.604699
$516$	4.62772	0.203724
$517$	0	0
$518$	6.74456	0.296339
$519$	−17.6060	−0.772816
$520$	−6.51087	−0.285521
$521$	10.6277	0.465609	0.232804	−	0.972524i	$-0.425210\pi$
$521$	10.6277	0.465609	0.232804	+	0.972524i	$0.425210\pi$
$522$	−2.62772	−0.115012
$523$	−5.25544	−0.229804	−0.114902	−	0.993377i	$-0.536655\pi$
$523$	−5.25544	−0.229804	−0.114902	+	0.993377i	$0.536655\pi$
$524$	10.7446	0.469378
$525$	−6.23369	−0.272060
$526$	3.25544	0.141944
$527$	2.74456	0.119555
$528$	−1.00000	−0.0435194
$529$	−23.0000	−1.00000
$530$	14.7446	0.640463
$531$	12.0000	0.520756
$532$	2.00000	0.0867110
$533$	−9.48913	−0.411020
$534$	6.62772	0.286809
$535$	10.1168	0.437389
$536$	−0.627719	−0.0271133
$537$	13.4891	0.582099
$538$	−21.4891	−0.926462
$539$	−3.00000	−0.129219
$540$	1.37228	0.0590536
$541$	21.7228	0.933937	0.466968	−	0.884274i	$-0.345346\pi$
$541$	21.7228	0.933937	0.466968	+	0.884274i	$0.345346\pi$
$542$	6.23369	0.267760
$543$	−23.6060	−1.01303
$544$	−1.37228	−0.0588361
$545$	−15.7663	−0.675355
$546$	9.48913	0.406097
$547$	−2.74456	−0.117349	−0.0586745	−	0.998277i	$-0.518687\pi$
$547$	−2.74456	−0.117349	−0.0586745	+	0.998277i	$0.518687\pi$
$548$	−0.744563	−0.0318061
$549$	6.11684	0.261061
$550$	3.11684	0.132903
$551$	−2.62772	−0.111945
$552$	0	0
$553$	18.9783	0.807037
$554$	22.1168	0.939655
$555$	4.62772	0.196436
$556$	4.62772	0.196259
$557$	17.4891	0.741038	0.370519	−	0.928825i	$-0.379180\pi$
$557$	17.4891	0.741038	0.370519	+	0.928825i	$0.379180\pi$
$558$	−2.00000	−0.0846668
$559$	21.9565	0.928661
$560$	2.74456	0.115979
$561$	−1.37228	−0.0579378
$562$	12.9783	0.547454
$563$	12.8614	0.542044	0.271022	−	0.962573i	$-0.412638\pi$
$563$	12.8614	0.542044	0.271022	+	0.962573i	$0.412638\pi$
$564$	0	0
$565$	11.1386	0.468604
$566$	22.9783	0.965848
$567$	−2.00000	−0.0839921
$568$	−4.74456	−0.199077
$569$	31.4891	1.32009	0.660046	−	0.751225i	$-0.270537\pi$
$569$	31.4891	1.32009	0.660046	+	0.751225i	$0.270537\pi$
$570$	1.37228	0.0574785
$571$	−33.0951	−1.38499	−0.692493	−	0.721424i	$-0.743488\pi$
$571$	−33.0951	−1.38499	−0.692493	+	0.721424i	$0.743488\pi$
$572$	−4.74456	−0.198380
$573$	1.48913	0.0622091
$574$	4.00000	0.166957
$575$	0	0
$576$	1.00000	0.0416667
$577$	0.116844	0.00486428	0.00243214	−	0.999997i	$-0.499226\pi$
$577$	0.116844	0.00486428	0.00243214	+	0.999997i	$0.499226\pi$
$578$	15.1168	0.628778
$579$	10.6277	0.441673
$580$	−3.60597	−0.149730
$581$	5.48913	0.227727
$582$	12.7446	0.528279
$583$	10.7446	0.444994
$584$	−0.744563	−0.0308102
$585$	6.51087	0.269192
$586$	5.37228	0.221927
$587$	14.1168	0.582665	0.291332	−	0.956622i	$-0.405901\pi$
$587$	14.1168	0.582665	0.291332	+	0.956622i	$0.405901\pi$
$588$	3.00000	0.123718
$589$	−2.00000	−0.0824086
$590$	16.4674	0.677951
$591$	−8.00000	−0.329076
$592$	3.37228	0.138600
$593$	28.9783	1.18999	0.594997	−	0.803728i	$-0.297153\pi$
$593$	28.9783	1.18999	0.594997	+	0.803728i	$0.297153\pi$
$594$	1.00000	0.0410305
$595$	3.76631	0.154404
$596$	2.74456	0.112422
$597$	−16.8614	−0.690091
$598$	0	0
$599$	−25.3723	−1.03668	−0.518342	−	0.855174i	$-0.673450\pi$
$599$	−25.3723	−1.03668	−0.518342	+	0.855174i	$0.673450\pi$
$600$	−3.11684	−0.127245
$601$	24.9783	1.01888	0.509442	−	0.860505i	$-0.329852\pi$
$601$	24.9783	1.01888	0.509442	+	0.860505i	$0.329852\pi$
$602$	−9.25544	−0.377223
$603$	0.627719	0.0255627
$604$	−8.62772	−0.351057
$605$	−1.37228	−0.0557912
$606$	18.7446	0.761446
$607$	−17.4891	−0.709862	−0.354931	−	0.934893i	$-0.615496\pi$
$607$	−17.4891	−0.709862	−0.354931	+	0.934893i	$0.615496\pi$
$608$	1.00000	0.0405554
$609$	5.25544	0.212961
$610$	8.39403	0.339864
$611$	0	0
$612$	1.37228	0.0554712
$613$	−11.7663	−0.475237	−0.237618	−	0.971359i	$-0.576367\pi$
$613$	−11.7663	−0.475237	−0.237618	+	0.971359i	$0.576367\pi$
$614$	−1.48913	−0.0600962
$615$	2.74456	0.110671
$616$	2.00000	0.0805823
$617$	40.9783	1.64972	0.824861	−	0.565335i	$-0.191253\pi$
$617$	40.9783	1.64972	0.824861	+	0.565335i	$0.191253\pi$
$618$	10.0000	0.402259
$619$	22.9783	0.923574	0.461787	−	0.886991i	$-0.347208\pi$
$619$	22.9783	0.923574	0.461787	+	0.886991i	$0.347208\pi$
$620$	−2.74456	−0.110224
$621$	0	0
$622$	34.7446	1.39313
$623$	−13.2554	−0.531068
$624$	4.74456	0.189935
$625$	0.298936	0.0119574
$626$	−5.60597	−0.224060
$627$	1.00000	0.0399362
$628$	−0.744563	−0.0297113
$629$	4.62772	0.184519
$630$	−2.74456	−0.109346
$631$	16.8614	0.671242	0.335621	−	0.941997i	$-0.391054\pi$
$631$	16.8614	0.671242	0.335621	+	0.941997i	$0.391054\pi$
$632$	9.48913	0.377457
$633$	−9.48913	−0.377159
$634$	−16.2337	−0.644722
$635$	−6.35053	−0.252013
$636$	−10.7446	−0.426050
$637$	14.2337	0.563959
$638$	−2.62772	−0.104032
$639$	4.74456	0.187692
$640$	1.37228	0.0542442
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	−7.37228	−0.290961
$643$	7.76631	0.306273	0.153137	−	0.988205i	$-0.451063\pi$
$643$	7.76631	0.306273	0.153137	+	0.988205i	$0.451063\pi$
$644$	0	0
$645$	−6.35053	−0.250052
$646$	1.37228	0.0539917
$647$	32.4674	1.27642	0.638212	−	0.769861i	$-0.279674\pi$
$647$	32.4674	1.27642	0.638212	+	0.769861i	$0.279674\pi$
$648$	−1.00000	−0.0392837
$649$	12.0000	0.471041
$650$	−14.7881	−0.580035
$651$	4.00000	0.156772
$652$	−12.0000	−0.469956
$653$	−8.51087	−0.333056	−0.166528	−	0.986037i	$-0.553256\pi$
$653$	−8.51087	−0.333056	−0.166528	+	0.986037i	$0.553256\pi$
$654$	11.4891	0.449260
$655$	−14.7446	−0.576118
$656$	2.00000	0.0780869
$657$	0.744563	0.0290482
$658$	0	0
$659$	−6.97825	−0.271834	−0.135917	−	0.990720i	$-0.543398\pi$
$659$	−6.97825	−0.271834	−0.135917	+	0.990720i	$0.543398\pi$
$660$	1.37228	0.0534160
$661$	32.2337	1.25375	0.626873	−	0.779122i	$-0.284335\pi$
$661$	32.2337	1.25375	0.626873	+	0.779122i	$0.284335\pi$
$662$	−16.8614	−0.655337
$663$	6.51087	0.252861
$664$	2.74456	0.106510
$665$	−2.74456	−0.106430
$666$	−3.37228	−0.130673
$667$	0	0
$668$	8.00000	0.309529
$669$	12.7446	0.492733
$670$	0.861407	0.0332790
$671$	6.11684	0.236138
$672$	−2.00000	−0.0771517
$673$	4.11684	0.158693	0.0793463	−	0.996847i	$-0.474717\pi$
$673$	4.11684	0.158693	0.0793463	+	0.996847i	$0.474717\pi$
$674$	20.1168	0.774872
$675$	3.11684	0.119967
$676$	9.51087	0.365803
$677$	16.5109	0.634564	0.317282	−	0.948331i	$-0.397230\pi$
$677$	16.5109	0.634564	0.317282	+	0.948331i	$0.397230\pi$
$678$	−8.11684	−0.311726
$679$	−25.4891	−0.978183
$680$	1.88316	0.0722157
$681$	9.88316	0.378723
$682$	−2.00000	−0.0765840
$683$	−18.9783	−0.726183	−0.363091	−	0.931754i	$-0.618279\pi$
$683$	−18.9783	−0.726183	−0.363091	+	0.931754i	$0.618279\pi$
$684$	−1.00000	−0.0382360
$685$	1.02175	0.0390390
$686$	−20.0000	−0.763604
$687$	−0.744563	−0.0284068
$688$	−4.62772	−0.176430
$689$	−50.9783	−1.94212
$690$	0	0
$691$	0.233688	0.00888991	0.00444495	−	0.999990i	$-0.498585\pi$
$691$	0.233688	0.00888991	0.00444495	+	0.999990i	$0.498585\pi$
$692$	17.6060	0.669279
$693$	−2.00000	−0.0759737
$694$	5.48913	0.208364
$695$	−6.35053	−0.240889
$696$	2.62772	0.0996034
$697$	2.74456	0.103958
$698$	15.3723	0.581849
$699$	−2.00000	−0.0756469
$700$	6.23369	0.235611
$701$	9.25544	0.349573	0.174787	−	0.984606i	$-0.444076\pi$
$701$	9.25544	0.349573	0.174787	+	0.984606i	$0.444076\pi$
$702$	−4.74456	−0.179072
$703$	−3.37228	−0.127188
$704$	1.00000	0.0376889
$705$	0	0
$706$	−4.74456	−0.178564
$707$	−37.4891	−1.40992
$708$	−12.0000	−0.450988
$709$	26.0000	0.976450	0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000	0.976450	0.488225	+	0.872718i	$0.337644\pi$
$710$	6.51087	0.244349
$711$	−9.48913	−0.355870
$712$	−6.62772	−0.248384
$713$	0	0
$714$	−2.74456	−0.102713
$715$	6.51087	0.243493
$716$	−13.4891	−0.504112
$717$	17.3723	0.648780
$718$	−18.2337	−0.680475
$719$	−21.2554	−0.792694	−0.396347	−	0.918101i	$-0.629722\pi$
$719$	−21.2554	−0.792694	−0.396347	+	0.918101i	$0.629722\pi$
$720$	−1.37228	−0.0511419
$721$	−20.0000	−0.744839
$722$	−1.00000	−0.0372161
$723$	20.1168	0.748153
$724$	23.6060	0.877309
$725$	−8.19019	−0.304176
$726$	1.00000	0.0371135
$727$	−0.627719	−0.0232808	−0.0116404	−	0.999932i	$-0.503705\pi$
$727$	−0.627719	−0.0232808	−0.0116404	+	0.999932i	$0.503705\pi$
$728$	−9.48913	−0.351690
$729$	1.00000	0.0370370
$730$	1.02175	0.0378166
$731$	−6.35053	−0.234883
$732$	−6.11684	−0.226085
$733$	−17.0951	−0.631422	−0.315711	−	0.948855i	$-0.602243\pi$
$733$	−17.0951	−0.631422	−0.315711	+	0.948855i	$0.602243\pi$
$734$	−33.0951	−1.22156
$735$	−4.11684	−0.151852
$736$	0	0
$737$	0.627719	0.0231223
$738$	−2.00000	−0.0736210
$739$	22.9783	0.845269	0.422634	−	0.906300i	$-0.361105\pi$
$739$	22.9783	0.845269	0.422634	+	0.906300i	$0.361105\pi$
$740$	−4.62772	−0.170118
$741$	−4.74456	−0.174296
$742$	21.4891	0.788891
$743$	−17.7228	−0.650187	−0.325093	−	0.945682i	$-0.605396\pi$
$743$	−17.7228	−0.650187	−0.325093	+	0.945682i	$0.605396\pi$
$744$	2.00000	0.0733236
$745$	−3.76631	−0.137987
$746$	7.25544	0.265640
$747$	−2.74456	−0.100418
$748$	1.37228	0.0501756
$749$	14.7446	0.538755
$750$	11.1386	0.406724
$751$	37.2119	1.35788	0.678941	−	0.734192i	$-0.262439\pi$
$751$	37.2119	1.35788	0.678941	+	0.734192i	$0.262439\pi$
$752$	0	0
$753$	27.6060	1.00602
$754$	12.4674	0.454035
$755$	11.8397	0.430889
$756$	2.00000	0.0727393
$757$	10.0000	0.363456	0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000	0.363456	0.181728	+	0.983349i	$0.441831\pi$
$758$	−15.6060	−0.566834
$759$	0	0
$760$	−1.37228	−0.0497779
$761$	12.3505	0.447706	0.223853	−	0.974623i	$-0.428136\pi$
$761$	12.3505	0.447706	0.223853	+	0.974623i	$0.428136\pi$
$762$	4.62772	0.167645
$763$	−22.9783	−0.831869
$764$	−1.48913	−0.0538747
$765$	−1.88316	−0.0680856
$766$	−21.6060	−0.780655
$767$	−56.9348	−2.05579
$768$	−1.00000	−0.0360844
$769$	12.7446	0.459581	0.229790	−	0.973240i	$-0.426196\pi$
$769$	12.7446	0.459581	0.229790	+	0.973240i	$0.426196\pi$
$770$	−2.74456	−0.0989072
$771$	−2.86141	−0.103051
$772$	−10.6277	−0.382500
$773$	−9.25544	−0.332895	−0.166447	−	0.986050i	$-0.553230\pi$
$773$	−9.25544	−0.332895	−0.166447	+	0.986050i	$0.553230\pi$
$774$	4.62772	0.166340
$775$	−6.23369	−0.223921
$776$	−12.7446	−0.457503
$777$	6.74456	0.241960
$778$	−7.48913	−0.268498
$779$	−2.00000	−0.0716574
$780$	−6.51087	−0.233127
$781$	4.74456	0.169774
$782$	0	0
$783$	−2.62772	−0.0939070
$784$	−3.00000	−0.107143
$785$	1.02175	0.0364678
$786$	10.7446	0.383246
$787$	16.2337	0.578668	0.289334	−	0.957228i	$-0.406566\pi$
$787$	16.2337	0.578668	0.289334	+	0.957228i	$0.406566\pi$
$788$	8.00000	0.284988
$789$	3.25544	0.115897
$790$	−13.0217	−0.463293
$791$	16.2337	0.577203
$792$	−1.00000	−0.0355335
$793$	−29.0217	−1.03059
$794$	−14.0000	−0.496841
$795$	14.7446	0.522936
$796$	16.8614	0.597637
$797$	−12.2337	−0.433339	−0.216670	−	0.976245i	$-0.569519\pi$
$797$	−12.2337	−0.433339	−0.216670	+	0.976245i	$0.569519\pi$
$798$	2.00000	0.0707992
$799$	0	0
$800$	3.11684	0.110197
$801$	6.62772	0.234179
$802$	−5.13859	−0.181450
$803$	0.744563	0.0262750
$804$	−0.627719	−0.0221379
$805$	0	0
$806$	9.48913	0.334240
$807$	−21.4891	−0.756453
$808$	−18.7446	−0.659431
$809$	−28.5109	−1.00239	−0.501194	−	0.865335i	$-0.667106\pi$
$809$	−28.5109	−1.00239	−0.501194	+	0.865335i	$0.667106\pi$
$810$	1.37228	0.0482171
$811$	9.48913	0.333208	0.166604	−	0.986024i	$-0.446720\pi$
$811$	9.48913	0.333208	0.166604	+	0.986024i	$0.446720\pi$
$812$	−5.25544	−0.184430
$813$	6.23369	0.218625
$814$	−3.37228	−0.118198
$815$	16.4674	0.576827
$816$	−1.37228	−0.0480395
$817$	4.62772	0.161903
$818$	−22.0000	−0.769212
$819$	9.48913	0.331577
$820$	−2.74456	−0.0958443
$821$	−32.2337	−1.12496	−0.562482	−	0.826810i	$-0.690153\pi$
$821$	−32.2337	−1.12496	−0.562482	+	0.826810i	$0.690153\pi$
$822$	−0.744563	−0.0259696
$823$	−0.394031	−0.0137350	−0.00686752	−	0.999976i	$-0.502186\pi$
$823$	−0.394031	−0.0137350	−0.00686752	+	0.999976i	$0.502186\pi$
$824$	−10.0000	−0.348367
$825$	3.11684	0.108515
$826$	24.0000	0.835067
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	0	0
$829$	33.8832	1.17681	0.588405	−	0.808566i	$-0.299756\pi$
$829$	33.8832	1.17681	0.588405	+	0.808566i	$0.299756\pi$
$830$	−3.76631	−0.130731
$831$	22.1168	0.767225
$832$	−4.74456	−0.164488
$833$	−4.11684	−0.142640
$834$	4.62772	0.160245
$835$	−10.9783	−0.379918
$836$	−1.00000	−0.0345857
$837$	−2.00000	−0.0691301
$838$	20.8614	0.720645
$839$	−17.6060	−0.607826	−0.303913	−	0.952700i	$-0.598293\pi$
$839$	−17.6060	−0.607826	−0.303913	+	0.952700i	$0.598293\pi$
$840$	2.74456	0.0946964
$841$	−22.0951	−0.761900
$842$	−6.74456	−0.232433
$843$	12.9783	0.446995
$844$	9.48913	0.326629
$845$	−13.0516	−0.448989
$846$	0	0
$847$	−2.00000	−0.0687208
$848$	10.7446	0.368970
$849$	22.9783	0.788612
$850$	4.27719	0.146706
$851$	0	0
$852$	−4.74456	−0.162546
$853$	17.0951	0.585325	0.292662	−	0.956216i	$-0.405459\pi$
$853$	17.0951	0.585325	0.292662	+	0.956216i	$0.405459\pi$
$854$	12.2337	0.418628
$855$	1.37228	0.0469310
$856$	7.37228	0.251979
$857$	48.9783	1.67307	0.836533	−	0.547917i	$-0.184579\pi$
$857$	48.9783	1.67307	0.836533	+	0.547917i	$0.184579\pi$
$858$	−4.74456	−0.161977
$859$	−9.48913	−0.323765	−0.161882	−	0.986810i	$-0.551757\pi$
$859$	−9.48913	−0.323765	−0.161882	+	0.986810i	$0.551757\pi$
$860$	6.35053	0.216551
$861$	4.00000	0.136320
$862$	0.233688	0.00795944
$863$	47.7228	1.62450	0.812252	−	0.583307i	$-0.198242\pi$
$863$	47.7228	1.62450	0.812252	+	0.583307i	$0.198242\pi$
$864$	1.00000	0.0340207
$865$	−24.1603	−0.821476
$866$	−27.4891	−0.934119
$867$	15.1168	0.513395
$868$	−4.00000	−0.135769
$869$	−9.48913	−0.321897
$870$	−3.60597	−0.122254
$871$	−2.97825	−0.100914
$872$	−11.4891	−0.389071
$873$	12.7446	0.431338
$874$	0	0
$875$	−22.2772	−0.753106
$876$	−0.744563	−0.0251564
$877$	44.9783	1.51881	0.759404	−	0.650620i	$-0.225491\pi$
$877$	44.9783	1.51881	0.759404	+	0.650620i	$0.225491\pi$
$878$	−11.3723	−0.383796
$879$	5.37228	0.181203
$880$	−1.37228	−0.0462596
$881$	−14.2337	−0.479545	−0.239773	−	0.970829i	$-0.577073\pi$
$881$	−14.2337	−0.479545	−0.239773	+	0.970829i	$0.577073\pi$
$882$	3.00000	0.101015
$883$	−51.2119	−1.72342	−0.861709	−	0.507402i	$-0.830606\pi$
$883$	−51.2119	−1.72342	−0.861709	+	0.507402i	$0.830606\pi$
$884$	−6.51087	−0.218984
$885$	16.4674	0.553545
$886$	−0.627719	−0.0210886
$887$	2.51087	0.0843069	0.0421535	−	0.999111i	$-0.486578\pi$
$887$	2.51087	0.0843069	0.0421535	+	0.999111i	$0.486578\pi$
$888$	3.37228	0.113166
$889$	−9.25544	−0.310417
$890$	9.09509	0.304868
$891$	1.00000	0.0335013
$892$	−12.7446	−0.426720
$893$	0	0
$894$	2.74456	0.0917919
$895$	18.5109	0.618750
$896$	2.00000	0.0668153
$897$	0	0
$898$	−19.4891	−0.650361
$899$	5.25544	0.175279
$900$	−3.11684	−0.103895
$901$	14.7446	0.491213
$902$	−2.00000	−0.0665927
$903$	−9.25544	−0.308002
$904$	8.11684	0.269962
$905$	−32.3940	−1.07681
$906$	−8.62772	−0.286637
$907$	−17.0951	−0.567633	−0.283817	−	0.958879i	$-0.591601\pi$
$907$	−17.0951	−0.567633	−0.283817	+	0.958879i	$0.591601\pi$
$908$	−9.88316	−0.327984
$909$	18.7446	0.621718
$910$	13.0217	0.431667
$911$	37.8397	1.25368	0.626842	−	0.779146i	$-0.284347\pi$
$911$	37.8397	1.25368	0.626842	+	0.779146i	$0.284347\pi$
$912$	1.00000	0.0331133
$913$	−2.74456	−0.0908318
$914$	15.4891	0.512335
$915$	8.39403	0.277498
$916$	0.744563	0.0246010
$917$	−21.4891	−0.709633
$918$	1.37228	0.0452920
$919$	27.2554	0.899074	0.449537	−	0.893262i	$-0.351589\pi$
$919$	27.2554	0.899074	0.449537	+	0.893262i	$0.351589\pi$
$920$	0	0
$921$	−1.48913	−0.0490683
$922$	−12.0000	−0.395199
$923$	−22.5109	−0.740954
$924$	2.00000	0.0657952
$925$	−10.5109	−0.345595
$926$	26.1168	0.858253
$927$	10.0000	0.328443
$928$	−2.62772	−0.0862591
$929$	−8.74456	−0.286900	−0.143450	−	0.989658i	$-0.545820\pi$
$929$	−8.74456	−0.286900	−0.143450	+	0.989658i	$0.545820\pi$
$930$	−2.74456	−0.0899978
$931$	3.00000	0.0983210
$932$	2.00000	0.0655122
$933$	34.7446	1.13749
$934$	−28.4674	−0.931481
$935$	−1.88316	−0.0615858
$936$	4.74456	0.155081
$937$	10.0000	0.326686	0.163343	−	0.986569i	$-0.447772\pi$
$937$	10.0000	0.326686	0.163343	+	0.986569i	$0.447772\pi$
$938$	1.25544	0.0409915
$939$	−5.60597	−0.182944
$940$	0	0
$941$	−57.3723	−1.87028	−0.935141	−	0.354275i	$-0.884728\pi$
$941$	−57.3723	−1.87028	−0.935141	+	0.354275i	$0.884728\pi$
$942$	−0.744563	−0.0242592
$943$	0	0
$944$	12.0000	0.390567
$945$	−2.74456	−0.0892806
$946$	4.62772	0.150460
$947$	53.3288	1.73295	0.866476	−	0.499218i	$-0.166379\pi$
$947$	53.3288	1.73295	0.866476	+	0.499218i	$0.166379\pi$
$948$	9.48913	0.308192
$949$	−3.53262	−0.114674
$950$	−3.11684	−0.101124
$951$	−16.2337	−0.526413
$952$	2.74456	0.0889518
$953$	27.2554	0.882890	0.441445	−	0.897288i	$-0.354466\pi$
$953$	27.2554	0.882890	0.441445	+	0.897288i	$0.354466\pi$
$954$	−10.7446	−0.347868
$955$	2.04350	0.0661261
$956$	−17.3723	−0.561860
$957$	−2.62772	−0.0849421
$958$	37.6060	1.21499
$959$	1.48913	0.0480864
$960$	1.37228	0.0442902
$961$	−27.0000	−0.870968
$962$	16.0000	0.515861
$963$	−7.37228	−0.237568
$964$	−20.1168	−0.647920
$965$	14.5842	0.469483
$966$	0	0
$967$	50.0000	1.60789	0.803946	−	0.594703i	$-0.202730\pi$
$967$	50.0000	1.60789	0.803946	+	0.594703i	$0.202730\pi$
$968$	−1.00000	−0.0321412
$969$	1.37228	0.0440840
$970$	17.4891	0.561542
$971$	−24.0000	−0.770197	−0.385098	−	0.922876i	$-0.625832\pi$
$971$	−24.0000	−0.770197	−0.385098	+	0.922876i	$0.625832\pi$
$972$	−1.00000	−0.0320750
$973$	−9.25544	−0.296716
$974$	−28.9783	−0.928523
$975$	−14.7881	−0.473597
$976$	6.11684	0.195795
$977$	−20.9783	−0.671154	−0.335577	−	0.942013i	$-0.608931\pi$
$977$	−20.9783	−0.671154	−0.335577	+	0.942013i	$0.608931\pi$
$978$	−12.0000	−0.383718
$979$	6.62772	0.211823
$980$	4.11684	0.131508
$981$	11.4891	0.366820
$982$	−22.7446	−0.725808
$983$	−40.7446	−1.29955	−0.649775	−	0.760127i	$-0.725137\pi$
$983$	−40.7446	−1.29955	−0.649775	+	0.760127i	$0.725137\pi$
$984$	2.00000	0.0637577
$985$	−10.9783	−0.349796
$986$	−3.60597	−0.114837
$987$	0	0
$988$	4.74456	0.150945
$989$	0	0
$990$	1.37228	0.0436140
$991$	−46.4674	−1.47608	−0.738042	−	0.674754i	$-0.764250\pi$
$991$	−46.4674	−1.47608	−0.738042	+	0.674754i	$0.764250\pi$
$992$	−2.00000	−0.0635001
$993$	−16.8614	−0.535081
$994$	9.48913	0.300977
$995$	−23.1386	−0.733543
$996$	2.74456	0.0869648
$997$	−45.7228	−1.44806	−0.724028	−	0.689771i	$-0.757711\pi$
$997$	−45.7228	−1.44806	−0.724028	+	0.689771i	$0.757711\pi$
$998$	−20.0000	−0.633089
$999$	−3.37228	−0.106694

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1254.2.a.l.1.1	✓	2
3.2	odd	2		3762.2.a.z.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1254.2.a.l.1.1	✓	2	1.1	even	1	trivial
3762.2.a.z.1.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1254 = 2 \cdot 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1254.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.37228 q^{5} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.37228 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.74456 q^{13} +2.00000 q^{14} +1.37228 q^{15} +1.00000 q^{16} +1.37228 q^{17} -1.00000 q^{18} -1.00000 q^{19} -1.37228 q^{20} +2.00000 q^{21} -1.00000 q^{22} +1.00000 q^{24} -3.11684 q^{25} +4.74456 q^{26} -1.00000 q^{27} -2.00000 q^{28} +2.62772 q^{29} -1.37228 q^{30} +2.00000 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.37228 q^{34} +2.74456 q^{35} +1.00000 q^{36} +3.37228 q^{37} +1.00000 q^{38} +4.74456 q^{39} +1.37228 q^{40} +2.00000 q^{41} -2.00000 q^{42} -4.62772 q^{43} +1.00000 q^{44} -1.37228 q^{45} -1.00000 q^{48} -3.00000 q^{49} +3.11684 q^{50} -1.37228 q^{51} -4.74456 q^{52} +10.7446 q^{53} +1.00000 q^{54} -1.37228 q^{55} +2.00000 q^{56} +1.00000 q^{57} -2.62772 q^{58} +12.0000 q^{59} +1.37228 q^{60} +6.11684 q^{61} -2.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +6.51087 q^{65} +1.00000 q^{66} +0.627719 q^{67} +1.37228 q^{68} -2.74456 q^{70} +4.74456 q^{71} -1.00000 q^{72} +0.744563 q^{73} -3.37228 q^{74} +3.11684 q^{75} -1.00000 q^{76} -2.00000 q^{77} -4.74456 q^{78} -9.48913 q^{79} -1.37228 q^{80} +1.00000 q^{81} -2.00000 q^{82} -2.74456 q^{83} +2.00000 q^{84} -1.88316 q^{85} +4.62772 q^{86} -2.62772 q^{87} -1.00000 q^{88} +6.62772 q^{89} +1.37228 q^{90} +9.48913 q^{91} -2.00000 q^{93} +1.37228 q^{95} +1.00000 q^{96} +12.7446 q^{97} +3.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{5} + 2 q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9} - 3 q^{10} + 2 q^{11} - 2 q^{12} + 2 q^{13} + 4 q^{14} - 3 q^{15} + 2 q^{16} - 3 q^{17} - 2 q^{18} - 2 q^{19} + 3 q^{20}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^5 + 2 * q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9 - 3 * q^10 + 2 * q^11 - 2 * q^12 + 2 * q^13 + 4 * q^14 - 3 * q^15 + 2 * q^16 - 3 * q^17 - 2 * q^18 - 2 * q^19 + 3 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^24 + 11 * q^25 - 2 * q^26 - 2 * q^27 - 4 * q^28 + 11 * q^29 + 3 * q^30 + 4 * q^31 - 2 * q^32 - 2 * q^33 + 3 * q^34 - 6 * q^35 + 2 * q^36 + q^37 + 2 * q^38 - 2 * q^39 - 3 * q^40 + 4 * q^41 - 4 * q^42 - 15 * q^43 + 2 * q^44 + 3 * q^45 - 2 * q^48 - 6 * q^49 - 11 * q^50 + 3 * q^51 + 2 * q^52 + 10 * q^53 + 2 * q^54 + 3 * q^55 + 4 * q^56 + 2 * q^57 - 11 * q^58 + 24 * q^59 - 3 * q^60 - 5 * q^61 - 4 * q^62 - 4 * q^63 + 2 * q^64 + 36 * q^65 + 2 * q^66 + 7 * q^67 - 3 * q^68 + 6 * q^70 - 2 * q^71 - 2 * q^72 - 10 * q^73 - q^74 - 11 * q^75 - 2 * q^76 - 4 * q^77 + 2 * q^78 + 4 * q^79 + 3 * q^80 + 2 * q^81 - 4 * q^82 + 6 * q^83 + 4 * q^84 - 21 * q^85 + 15 * q^86 - 11 * q^87 - 2 * q^88 + 19 * q^89 - 3 * q^90 - 4 * q^91 - 4 * q^93 - 3 * q^95 + 2 * q^96 + 14 * q^97 + 6 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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