LMFDB - Embedded newform 5586.2.a.cd.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5586,2,Mod(1,5586)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5586, 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("5586.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5586.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:	$44.6044345691$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.207085568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 13x^{4} + 28x^{3} + 10x^{2} - 12x + 2 $ x^6 - 2x^5 - 13x^4 + 28x^3 + 10x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.254018$ of defining polynomial
Character	$\chi$	$=$	5586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.15317 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.15317 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +4.15317 q^{10} +6.23271 q^{11} +1.00000 q^{12} +1.72030 q^{13} -4.15317 q^{15} +1.00000 q^{16} +0.508035 q^{17} -1.00000 q^{18} -1.00000 q^{19} -4.15317 q^{20} -6.23271 q^{22} +7.28590 q^{23} -1.00000 q^{24} +12.2488 q^{25} -1.72030 q^{26} +1.00000 q^{27} +4.32039 q^{29} +4.15317 q^{30} -1.32475 q^{31} -1.00000 q^{32} +6.23271 q^{33} -0.508035 q^{34} +1.00000 q^{36} -10.5835 q^{37} +1.00000 q^{38} +1.72030 q^{39} +4.15317 q^{40} -7.06114 q^{41} -6.42042 q^{43} +6.23271 q^{44} -4.15317 q^{45} -7.28590 q^{46} +7.83026 q^{47} +1.00000 q^{48} -12.2488 q^{50} +0.508035 q^{51} +1.72030 q^{52} +7.32242 q^{53} -1.00000 q^{54} -25.8855 q^{55} -1.00000 q^{57} -4.32039 q^{58} +2.83254 q^{59} -4.15317 q^{60} -3.19385 q^{61} +1.32475 q^{62} +1.00000 q^{64} -7.14471 q^{65} -6.23271 q^{66} -9.51424 q^{67} +0.508035 q^{68} +7.28590 q^{69} +15.1348 q^{71} -1.00000 q^{72} -5.40428 q^{73} +10.5835 q^{74} +12.2488 q^{75} -1.00000 q^{76} -1.72030 q^{78} +5.80798 q^{79} -4.15317 q^{80} +1.00000 q^{81} +7.06114 q^{82} -13.4038 q^{83} -2.10996 q^{85} +6.42042 q^{86} +4.32039 q^{87} -6.23271 q^{88} -3.50431 q^{89} +4.15317 q^{90} +7.28590 q^{92} -1.32475 q^{93} -7.83026 q^{94} +4.15317 q^{95} -1.00000 q^{96} +5.58206 q^{97} +6.23271 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 6 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 6 * q^6 - 6 * q^8 + 6 * q^9	$ 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 6 q^{6} - 6 q^{8} + 6 q^{9} + 4 q^{11} + 6 q^{12} + 6 q^{16} + 4 q^{17} - 6 q^{18} - 6 q^{19} - 4 q^{22} + 16 q^{23} - 6 q^{24} + 10 q^{25} + 6 q^{27} + 8 q^{29} - 6 q^{32} + 4 q^{33} - 4 q^{34} + 6 q^{36} + 6 q^{38} + 8 q^{41} + 8 q^{43} + 4 q^{44} - 16 q^{46} + 16 q^{47} + 6 q^{48} - 10 q^{50} + 4 q^{51} - 4 q^{53} - 6 q^{54} - 32 q^{55} - 6 q^{57} - 8 q^{58} + 24 q^{59} + 6 q^{64} + 16 q^{65} - 4 q^{66} - 20 q^{67} + 4 q^{68} + 16 q^{69} + 24 q^{71} - 6 q^{72} - 16 q^{73} + 10 q^{75} - 6 q^{76} + 40 q^{79} + 6 q^{81} - 8 q^{82} + 24 q^{83} + 8 q^{85} - 8 q^{86} + 8 q^{87} - 4 q^{88} + 24 q^{89} + 16 q^{92} - 16 q^{94} - 6 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 6 * q^6 - 6 * q^8 + 6 * q^9 + 4 * q^11 + 6 * q^12 + 6 * q^16 + 4 * q^17 - 6 * q^18 - 6 * q^19 - 4 * q^22 + 16 * q^23 - 6 * q^24 + 10 * q^25 + 6 * q^27 + 8 * q^29 - 6 * q^32 + 4 * q^33 - 4 * q^34 + 6 * q^36 + 6 * q^38 + 8 * q^41 + 8 * q^43 + 4 * q^44 - 16 * q^46 + 16 * q^47 + 6 * q^48 - 10 * q^50 + 4 * q^51 - 4 * q^53 - 6 * q^54 - 32 * q^55 - 6 * q^57 - 8 * q^58 + 24 * q^59 + 6 * q^64 + 16 * q^65 - 4 * q^66 - 20 * q^67 + 4 * q^68 + 16 * q^69 + 24 * q^71 - 6 * q^72 - 16 * q^73 + 10 * q^75 - 6 * q^76 + 40 * q^79 + 6 * q^81 - 8 * q^82 + 24 * q^83 + 8 * q^85 - 8 * q^86 + 8 * q^87 - 4 * q^88 + 24 * q^89 + 16 * q^92 - 16 * q^94 - 6 * q^96 - 4 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−4.15317	−1.85736	−0.928678	−	0.370888i	$-0.879053\pi$
$5$	−4.15317	−1.85736	−0.928678	+	0.370888i	$0.879053\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	4.15317	1.31335
$11$	6.23271	1.87923	0.939616	−	0.342230i	$-0.111182\pi$
$11$	6.23271	1.87923	0.939616	+	0.342230i	$0.111182\pi$
$12$	1.00000	0.288675
$13$	1.72030	0.477126	0.238563	−	0.971127i	$-0.423324\pi$
$13$	1.72030	0.477126	0.238563	+	0.971127i	$0.423324\pi$
$14$	0	0
$15$	−4.15317	−1.07234
$16$	1.00000	0.250000
$17$	0.508035	0.123217	0.0616083	−	0.998100i	$-0.480377\pi$
$17$	0.508035	0.123217	0.0616083	+	0.998100i	$0.480377\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−4.15317	−0.928678
$21$	0	0
$22$	−6.23271	−1.32882
$23$	7.28590	1.51922	0.759608	−	0.650381i	$-0.225391\pi$
$23$	7.28590	1.51922	0.759608	+	0.650381i	$0.225391\pi$
$24$	−1.00000	−0.204124
$25$	12.2488	2.44977
$26$	−1.72030	−0.337379
$27$	1.00000	0.192450
$28$	0	0
$29$	4.32039	0.802277	0.401138	−	0.916017i	$-0.368615\pi$
$29$	4.32039	0.802277	0.401138	+	0.916017i	$0.368615\pi$
$30$	4.15317	0.758262
$31$	−1.32475	−0.237931	−0.118966	−	0.992898i	$-0.537958\pi$
$31$	−1.32475	−0.237931	−0.118966	+	0.992898i	$0.537958\pi$
$32$	−1.00000	−0.176777
$33$	6.23271	1.08498
$34$	−0.508035	−0.0871273
$35$	0	0
$36$	1.00000	0.166667
$37$	−10.5835	−1.73992	−0.869960	−	0.493122i	$-0.835856\pi$
$37$	−10.5835	−1.73992	−0.869960	+	0.493122i	$0.835856\pi$
$38$	1.00000	0.162221
$39$	1.72030	0.275469
$40$	4.15317	0.656674
$41$	−7.06114	−1.10276	−0.551382	−	0.834253i	$-0.685899\pi$
$41$	−7.06114	−1.10276	−0.551382	+	0.834253i	$0.685899\pi$
$42$	0	0
$43$	−6.42042	−0.979104	−0.489552	−	0.871974i	$-0.662840\pi$
$43$	−6.42042	−0.979104	−0.489552	+	0.871974i	$0.662840\pi$
$44$	6.23271	0.939616
$45$	−4.15317	−0.619118
$46$	−7.28590	−1.07425
$47$	7.83026	1.14216	0.571080	−	0.820894i	$-0.306525\pi$
$47$	7.83026	1.14216	0.571080	+	0.820894i	$0.306525\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−12.2488	−1.73225
$51$	0.508035	0.0711391
$52$	1.72030	0.238563
$53$	7.32242	1.00581	0.502906	−	0.864341i	$-0.332264\pi$
$53$	7.32242	1.00581	0.502906	+	0.864341i	$0.332264\pi$
$54$	−1.00000	−0.136083
$55$	−25.8855	−3.49040
$56$	0	0
$57$	−1.00000	−0.132453
$58$	−4.32039	−0.567295
$59$	2.83254	0.368765	0.184383	−	0.982855i	$-0.440971\pi$
$59$	2.83254	0.368765	0.184383	+	0.982855i	$0.440971\pi$
$60$	−4.15317	−0.536172
$61$	−3.19385	−0.408930	−0.204465	−	0.978874i	$-0.565545\pi$
$61$	−3.19385	−0.408930	−0.204465	+	0.978874i	$0.565545\pi$
$62$	1.32475	0.168243
$63$	0	0
$64$	1.00000	0.125000
$65$	−7.14471	−0.886192
$66$	−6.23271	−0.767193
$67$	−9.51424	−1.16235	−0.581175	−	0.813779i	$-0.697407\pi$
$67$	−9.51424	−1.16235	−0.581175	+	0.813779i	$0.697407\pi$
$68$	0.508035	0.0616083
$69$	7.28590	0.877120
$70$	0	0
$71$	15.1348	1.79617	0.898084	−	0.439825i	$-0.144960\pi$
$71$	15.1348	1.79617	0.898084	+	0.439825i	$0.144960\pi$
$72$	−1.00000	−0.117851
$73$	−5.40428	−0.632523	−0.316262	−	0.948672i	$-0.602428\pi$
$73$	−5.40428	−0.632523	−0.316262	+	0.948672i	$0.602428\pi$
$74$	10.5835	1.23031
$75$	12.2488	1.41437
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−1.72030	−0.194786
$79$	5.80798	0.653449	0.326725	−	0.945120i	$-0.394055\pi$
$79$	5.80798	0.653449	0.326725	+	0.945120i	$0.394055\pi$
$80$	−4.15317	−0.464339
$81$	1.00000	0.111111
$82$	7.06114	0.779772
$83$	−13.4038	−1.47126	−0.735629	−	0.677385i	$-0.763113\pi$
$83$	−13.4038	−1.47126	−0.735629	+	0.677385i	$0.763113\pi$
$84$	0	0
$85$	−2.10996	−0.228857
$86$	6.42042	0.692331
$87$	4.32039	0.463195
$88$	−6.23271	−0.664409
$89$	−3.50431	−0.371456	−0.185728	−	0.982601i	$-0.559464\pi$
$89$	−3.50431	−0.371456	−0.185728	+	0.982601i	$0.559464\pi$
$90$	4.15317	0.437783
$91$	0	0
$92$	7.28590	0.759608
$93$	−1.32475	−0.137370
$94$	−7.83026	−0.807629
$95$	4.15317	0.426107
$96$	−1.00000	−0.102062
$97$	5.58206	0.566772	0.283386	−	0.959006i	$-0.408542\pi$
$97$	5.58206	0.566772	0.283386	+	0.959006i	$0.408542\pi$
$98$	0	0
$99$	6.23271	0.626411
$100$	12.2488	1.22488
$101$	16.7940	1.67106	0.835531	−	0.549444i	$-0.185160\pi$
$101$	16.7940	1.67106	0.835531	+	0.549444i	$0.185160\pi$
$102$	−0.508035	−0.0503030
$103$	4.95262	0.487997	0.243998	−	0.969776i	$-0.421541\pi$
$103$	4.95262	0.487997	0.243998	+	0.969776i	$0.421541\pi$
$104$	−1.72030	−0.168689
$105$	0	0
$106$	−7.32242	−0.711216
$107$	1.33289	0.128856	0.0644279	−	0.997922i	$-0.479478\pi$
$107$	1.33289	0.128856	0.0644279	+	0.997922i	$0.479478\pi$
$108$	1.00000	0.0962250
$109$	−12.5347	−1.20060	−0.600302	−	0.799773i	$-0.704953\pi$
$109$	−12.5347	−1.20060	−0.600302	+	0.799773i	$0.704953\pi$
$110$	25.8855	2.46809
$111$	−10.5835	−1.00454
$112$	0	0
$113$	−3.15293	−0.296603	−0.148302	−	0.988942i	$-0.547381\pi$
$113$	−3.15293	−0.296603	−0.148302	+	0.988942i	$0.547381\pi$
$114$	1.00000	0.0936586
$115$	−30.2596	−2.82172
$116$	4.32039	0.401138
$117$	1.72030	0.159042
$118$	−2.83254	−0.260757
$119$	0	0
$120$	4.15317	0.379131
$121$	27.8467	2.53151
$122$	3.19385	0.289157
$123$	−7.06114	−0.636681
$124$	−1.32475	−0.118966
$125$	−30.1057	−2.69274
$126$	0	0
$127$	4.37104	0.387867	0.193934	−	0.981015i	$-0.437875\pi$
$127$	4.37104	0.387867	0.193934	+	0.981015i	$0.437875\pi$
$128$	−1.00000	−0.0883883
$129$	−6.42042	−0.565286
$130$	7.14471	0.626632
$131$	−10.3614	−0.905277	−0.452639	−	0.891694i	$-0.649517\pi$
$131$	−10.3614	−0.905277	−0.452639	+	0.891694i	$0.649517\pi$
$132$	6.23271	0.542488
$133$	0	0
$134$	9.51424	0.821905
$135$	−4.15317	−0.357448
$136$	−0.508035	−0.0435636
$137$	2.48171	0.212027	0.106014	−	0.994365i	$-0.466191\pi$
$137$	2.48171	0.212027	0.106014	+	0.994365i	$0.466191\pi$
$138$	−7.28590	−0.620217
$139$	9.14255	0.775461	0.387730	−	0.921773i	$-0.373259\pi$
$139$	9.14255	0.775461	0.387730	+	0.921773i	$0.373259\pi$
$140$	0	0
$141$	7.83026	0.659427
$142$	−15.1348	−1.27008
$143$	10.7221	0.896630
$144$	1.00000	0.0833333
$145$	−17.9433	−1.49011
$146$	5.40428	0.447261
$147$	0	0
$148$	−10.5835	−0.869960
$149$	−16.6851	−1.36690	−0.683450	−	0.729997i	$-0.739521\pi$
$149$	−16.6851	−1.36690	−0.683450	+	0.729997i	$0.739521\pi$
$150$	−12.2488	−1.00011
$151$	17.0039	1.38376	0.691878	−	0.722015i	$-0.256784\pi$
$151$	17.0039	1.38376	0.691878	+	0.722015i	$0.256784\pi$
$152$	1.00000	0.0811107
$153$	0.508035	0.0410722
$154$	0	0
$155$	5.50190	0.441923
$156$	1.72030	0.137734
$157$	8.32496	0.664404	0.332202	−	0.943208i	$-0.392208\pi$
$157$	8.32496	0.664404	0.332202	+	0.943208i	$0.392208\pi$
$158$	−5.80798	−0.462058
$159$	7.32242	0.580705
$160$	4.15317	0.328337
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−19.6693	−1.54062	−0.770308	−	0.637672i	$-0.779897\pi$
$163$	−19.6693	−1.54062	−0.770308	+	0.637672i	$0.779897\pi$
$164$	−7.06114	−0.551382
$165$	−25.8855	−2.01518
$166$	13.4038	1.04034
$167$	3.51472	0.271977	0.135989	−	0.990710i	$-0.456579\pi$
$167$	3.51472	0.271977	0.135989	+	0.990710i	$0.456579\pi$
$168$	0	0
$169$	−10.0406	−0.772351
$170$	2.10996	0.161826
$171$	−1.00000	−0.0764719
$172$	−6.42042	−0.489552
$173$	19.2225	1.46146	0.730728	−	0.682669i	$-0.239181\pi$
$173$	19.2225	1.46146	0.730728	+	0.682669i	$0.239181\pi$
$174$	−4.32039	−0.327528
$175$	0	0
$176$	6.23271	0.469808
$177$	2.83254	0.212907
$178$	3.50431	0.262659
$179$	−6.80088	−0.508322	−0.254161	−	0.967162i	$-0.581799\pi$
$179$	−6.80088	−0.508322	−0.254161	+	0.967162i	$0.581799\pi$
$180$	−4.15317	−0.309559
$181$	15.8966	1.18158	0.590791	−	0.806825i	$-0.298816\pi$
$181$	15.8966	1.18158	0.590791	+	0.806825i	$0.298816\pi$
$182$	0	0
$183$	−3.19385	−0.236096
$184$	−7.28590	−0.537124
$185$	43.9552	3.23165
$186$	1.32475	0.0971351
$187$	3.16643	0.231553
$188$	7.83026	0.571080
$189$	0	0
$190$	−4.15317	−0.301303
$191$	−1.95049	−0.141132	−0.0705661	−	0.997507i	$-0.522481\pi$
$191$	−1.95049	−0.141132	−0.0705661	+	0.997507i	$0.522481\pi$
$192$	1.00000	0.0721688
$193$	4.98750	0.359008	0.179504	−	0.983757i	$-0.442551\pi$
$193$	4.98750	0.359008	0.179504	+	0.983757i	$0.442551\pi$
$194$	−5.58206	−0.400768
$195$	−7.14471	−0.511643
$196$	0	0
$197$	9.00792	0.641788	0.320894	−	0.947115i	$-0.396017\pi$
$197$	9.00792	0.641788	0.320894	+	0.947115i	$0.396017\pi$
$198$	−6.23271	−0.442939
$199$	−19.4529	−1.37898	−0.689490	−	0.724295i	$-0.742165\pi$
$199$	−19.4529	−1.37898	−0.689490	+	0.724295i	$0.742165\pi$
$200$	−12.2488	−0.866124
$201$	−9.51424	−0.671083
$202$	−16.7940	−1.18162
$203$	0	0
$204$	0.508035	0.0355696
$205$	29.3261	2.04822
$206$	−4.95262	−0.345066
$207$	7.28590	0.506405
$208$	1.72030	0.119281
$209$	−6.23271	−0.431125
$210$	0	0
$211$	25.5924	1.76186	0.880928	−	0.473250i	$-0.156919\pi$
$211$	25.5924	1.76186	0.880928	+	0.473250i	$0.156919\pi$
$212$	7.32242	0.502906
$213$	15.1348	1.03702
$214$	−1.33289	−0.0911148
$215$	26.6651	1.81854
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	12.5347	0.848956
$219$	−5.40428	−0.365187
$220$	−25.8855	−1.74520
$221$	0.873973	0.0587898
$222$	10.5835	0.710319
$223$	−8.33829	−0.558373	−0.279187	−	0.960237i	$-0.590065\pi$
$223$	−8.33829	−0.558373	−0.279187	+	0.960237i	$0.590065\pi$
$224$	0	0
$225$	12.2488	0.816590
$226$	3.15293	0.209730
$227$	26.5613	1.76294	0.881469	−	0.472243i	$-0.156555\pi$
$227$	26.5613	1.76294	0.881469	+	0.472243i	$0.156555\pi$
$228$	−1.00000	−0.0662266
$229$	25.2266	1.66702	0.833511	−	0.552502i	$-0.186327\pi$
$229$	25.2266	1.66702	0.833511	+	0.552502i	$0.186327\pi$
$230$	30.2596	1.99526
$231$	0	0
$232$	−4.32039	−0.283648
$233$	−2.71024	−0.177554	−0.0887769	−	0.996052i	$-0.528296\pi$
$233$	−2.71024	−0.177554	−0.0887769	+	0.996052i	$0.528296\pi$
$234$	−1.72030	−0.112460
$235$	−32.5204	−2.12140
$236$	2.83254	0.184383
$237$	5.80798	0.377269
$238$	0	0
$239$	−5.38434	−0.348284	−0.174142	−	0.984721i	$-0.555715\pi$
$239$	−5.38434	−0.348284	−0.174142	+	0.984721i	$0.555715\pi$
$240$	−4.15317	−0.268086
$241$	28.7900	1.85453	0.927263	−	0.374411i	$-0.122155\pi$
$241$	28.7900	1.85453	0.927263	+	0.374411i	$0.122155\pi$
$242$	−27.8467	−1.79005
$243$	1.00000	0.0641500
$244$	−3.19385	−0.204465
$245$	0	0
$246$	7.06114	0.450202
$247$	−1.72030	−0.109460
$248$	1.32475	0.0841214
$249$	−13.4038	−0.849431
$250$	30.1057	1.90405
$251$	9.02266	0.569505	0.284753	−	0.958601i	$-0.408089\pi$
$251$	9.02266	0.569505	0.284753	+	0.958601i	$0.408089\pi$
$252$	0	0
$253$	45.4109	2.85496
$254$	−4.37104	−0.274264
$255$	−2.10996	−0.132131
$256$	1.00000	0.0625000
$257$	14.7735	0.921544	0.460772	−	0.887519i	$-0.347573\pi$
$257$	14.7735	0.921544	0.460772	+	0.887519i	$0.347573\pi$
$258$	6.42042	0.399718
$259$	0	0
$260$	−7.14471	−0.443096
$261$	4.32039	0.267426
$262$	10.3614	0.640128
$263$	13.4570	0.829793	0.414896	−	0.909869i	$-0.363818\pi$
$263$	13.4570	0.829793	0.414896	+	0.909869i	$0.363818\pi$
$264$	−6.23271	−0.383597
$265$	−30.4113	−1.86815
$266$	0	0
$267$	−3.50431	−0.214460
$268$	−9.51424	−0.581175
$269$	−4.85388	−0.295946	−0.147973	−	0.988991i	$-0.547275\pi$
$269$	−4.85388	−0.295946	−0.147973	+	0.988991i	$0.547275\pi$
$270$	4.15317	0.252754
$271$	15.3634	0.933262	0.466631	−	0.884452i	$-0.345468\pi$
$271$	15.3634	0.933262	0.466631	+	0.884452i	$0.345468\pi$
$272$	0.508035	0.0308041
$273$	0	0
$274$	−2.48171	−0.149926
$275$	76.3435	4.60368
$276$	7.28590	0.438560
$277$	13.7387	0.825480	0.412740	−	0.910849i	$-0.364572\pi$
$277$	13.7387	0.825480	0.412740	+	0.910849i	$0.364572\pi$
$278$	−9.14255	−0.548334
$279$	−1.32475	−0.0793104
$280$	0	0
$281$	14.7957	0.882640	0.441320	−	0.897350i	$-0.354510\pi$
$281$	14.7957	0.882640	0.441320	+	0.897350i	$0.354510\pi$
$282$	−7.83026	−0.466285
$283$	−15.2576	−0.906967	−0.453484	−	0.891265i	$-0.649819\pi$
$283$	−15.2576	−0.906967	−0.453484	+	0.891265i	$0.649819\pi$
$284$	15.1348	0.898084
$285$	4.15317	0.246013
$286$	−10.7221	−0.634013
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−16.7419	−0.984818
$290$	17.9433	1.05367
$291$	5.58206	0.327226
$292$	−5.40428	−0.316262
$293$	−14.1117	−0.824416	−0.412208	−	0.911090i	$-0.635242\pi$
$293$	−14.1117	−0.824416	−0.412208	+	0.911090i	$0.635242\pi$
$294$	0	0
$295$	−11.7640	−0.684928
$296$	10.5835	0.615155
$297$	6.23271	0.361658
$298$	16.6851	0.966544
$299$	12.5339	0.724857
$300$	12.2488	0.707187
$301$	0	0
$302$	−17.0039	−0.978463
$303$	16.7940	0.964788
$304$	−1.00000	−0.0573539
$305$	13.2646	0.759528
$306$	−0.508035	−0.0290424
$307$	−9.69192	−0.553147	−0.276574	−	0.960993i	$-0.589199\pi$
$307$	−9.69192	−0.553147	−0.276574	+	0.960993i	$0.589199\pi$
$308$	0	0
$309$	4.95262	0.281745
$310$	−5.50190	−0.312487
$311$	−9.99158	−0.566570	−0.283285	−	0.959036i	$-0.591424\pi$
$311$	−9.99158	−0.566570	−0.283285	+	0.959036i	$0.591424\pi$
$312$	−1.72030	−0.0973928
$313$	−6.14843	−0.347530	−0.173765	−	0.984787i	$-0.555593\pi$
$313$	−6.14843	−0.347530	−0.173765	+	0.984787i	$0.555593\pi$
$314$	−8.32496	−0.469805
$315$	0	0
$316$	5.80798	0.326725
$317$	1.11150	0.0624282	0.0312141	−	0.999513i	$-0.490063\pi$
$317$	1.11150	0.0624282	0.0312141	+	0.999513i	$0.490063\pi$
$318$	−7.32242	−0.410621
$319$	26.9277	1.50766
$320$	−4.15317	−0.232169
$321$	1.33289	0.0743949
$322$	0	0
$323$	−0.508035	−0.0282678
$324$	1.00000	0.0555556
$325$	21.0717	1.16885
$326$	19.6693	1.08938
$327$	−12.5347	−0.693169
$328$	7.06114	0.389886
$329$	0	0
$330$	25.8855	1.42495
$331$	−17.3358	−0.952863	−0.476431	−	0.879212i	$-0.658070\pi$
$331$	−17.3358	−0.952863	−0.476431	+	0.879212i	$0.658070\pi$
$332$	−13.4038	−0.735629
$333$	−10.5835	−0.579973
$334$	−3.51472	−0.192317
$335$	39.5143	2.15890
$336$	0	0
$337$	28.8699	1.57264	0.786322	−	0.617816i	$-0.211982\pi$
$337$	28.8699	1.57264	0.786322	+	0.617816i	$0.211982\pi$
$338$	10.0406	0.546135
$339$	−3.15293	−0.171244
$340$	−2.10996	−0.114428
$341$	−8.25675	−0.447128
$342$	1.00000	0.0540738
$343$	0	0
$344$	6.42042	0.346166
$345$	−30.2596	−1.62912
$346$	−19.2225	−1.03341
$347$	−2.34257	−0.125756	−0.0628779	−	0.998021i	$-0.520028\pi$
$347$	−2.34257	−0.125756	−0.0628779	+	0.998021i	$0.520028\pi$
$348$	4.32039	0.231597
$349$	15.3733	0.822914	0.411457	−	0.911429i	$-0.365020\pi$
$349$	15.3733	0.822914	0.411457	+	0.911429i	$0.365020\pi$
$350$	0	0
$351$	1.72030	0.0918228
$352$	−6.23271	−0.332204
$353$	25.1039	1.33614	0.668072	−	0.744096i	$-0.267120\pi$
$353$	25.1039	1.33614	0.668072	+	0.744096i	$0.267120\pi$
$354$	−2.83254	−0.150548
$355$	−62.8573	−3.33612
$356$	−3.50431	−0.185728
$357$	0	0
$358$	6.80088	0.359438
$359$	9.94679	0.524971	0.262486	−	0.964936i	$-0.415458\pi$
$359$	9.94679	0.524971	0.262486	+	0.964936i	$0.415458\pi$
$360$	4.15317	0.218891
$361$	1.00000	0.0526316
$362$	−15.8966	−0.835504
$363$	27.8467	1.46157
$364$	0	0
$365$	22.4449	1.17482
$366$	3.19385	0.166945
$367$	−31.7419	−1.65691	−0.828457	−	0.560053i	$-0.810781\pi$
$367$	−31.7419	−1.65691	−0.828457	+	0.560053i	$0.810781\pi$
$368$	7.28590	0.379804
$369$	−7.06114	−0.367588
$370$	−43.9552	−2.28512
$371$	0	0
$372$	−1.32475	−0.0686849
$373$	25.5019	1.32044	0.660220	−	0.751072i	$-0.270463\pi$
$373$	25.5019	1.32044	0.660220	+	0.751072i	$0.270463\pi$
$374$	−3.16643	−0.163732
$375$	−30.1057	−1.55465
$376$	−7.83026	−0.403815
$377$	7.43237	0.382787
$378$	0	0
$379$	28.8049	1.47961	0.739804	−	0.672822i	$-0.234918\pi$
$379$	28.8049	1.47961	0.739804	+	0.672822i	$0.234918\pi$
$380$	4.15317	0.213053
$381$	4.37104	0.223935
$382$	1.95049	0.0997955
$383$	26.4977	1.35397	0.676984	−	0.735997i	$-0.263286\pi$
$383$	26.4977	1.35397	0.676984	+	0.735997i	$0.263286\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−4.98750	−0.253857
$387$	−6.42042	−0.326368
$388$	5.58206	0.283386
$389$	2.31388	0.117319	0.0586593	−	0.998278i	$-0.481317\pi$
$389$	2.31388	0.117319	0.0586593	+	0.998278i	$0.481317\pi$
$390$	7.14471	0.361786
$391$	3.70149	0.187193
$392$	0	0
$393$	−10.3614	−0.522662
$394$	−9.00792	−0.453813
$395$	−24.1216	−1.21369
$396$	6.23271	0.313205
$397$	11.3529	0.569787	0.284893	−	0.958559i	$-0.408042\pi$
$397$	11.3529	0.569787	0.284893	+	0.958559i	$0.408042\pi$
$398$	19.4529	0.975086
$399$	0	0
$400$	12.2488	0.612442
$401$	−22.1159	−1.10442	−0.552208	−	0.833706i	$-0.686215\pi$
$401$	−22.1159	−1.10442	−0.552208	+	0.833706i	$0.686215\pi$
$402$	9.51424	0.474527
$403$	−2.27896	−0.113523
$404$	16.7940	0.835531
$405$	−4.15317	−0.206373
$406$	0	0
$407$	−65.9640	−3.26971
$408$	−0.508035	−0.0251515
$409$	−27.2307	−1.34647	−0.673235	−	0.739428i	$-0.735096\pi$
$409$	−27.2307	−1.34647	−0.673235	+	0.739428i	$0.735096\pi$
$410$	−29.3261	−1.44831
$411$	2.48171	0.122414
$412$	4.95262	0.243998
$413$	0	0
$414$	−7.28590	−0.358083
$415$	55.6683	2.73265
$416$	−1.72030	−0.0843447
$417$	9.14255	0.447712
$418$	6.23271	0.304852
$419$	−24.7081	−1.20707	−0.603534	−	0.797337i	$-0.706241\pi$
$419$	−24.7081	−1.20707	−0.603534	+	0.797337i	$0.706241\pi$
$420$	0	0
$421$	−25.9581	−1.26512	−0.632560	−	0.774512i	$-0.717996\pi$
$421$	−25.9581	−1.26512	−0.632560	+	0.774512i	$0.717996\pi$
$422$	−25.5924	−1.24582
$423$	7.83026	0.380720
$424$	−7.32242	−0.355608
$425$	6.22284	0.301852
$426$	−15.1348	−0.733282
$427$	0	0
$428$	1.33289	0.0644279
$429$	10.7221	0.517669
$430$	−26.6651	−1.28591
$431$	−1.71770	−0.0827386	−0.0413693	−	0.999144i	$-0.513172\pi$
$431$	−1.71770	−0.0827386	−0.0413693	+	0.999144i	$0.513172\pi$
$432$	1.00000	0.0481125
$433$	−15.2339	−0.732093	−0.366046	−	0.930597i	$-0.619289\pi$
$433$	−15.2339	−0.732093	−0.366046	+	0.930597i	$0.619289\pi$
$434$	0	0
$435$	−17.9433	−0.860317
$436$	−12.5347	−0.600302
$437$	−7.28590	−0.348532
$438$	5.40428	0.258227
$439$	33.9581	1.62073	0.810366	−	0.585925i	$-0.199268\pi$
$439$	33.9581	1.62073	0.810366	+	0.585925i	$0.199268\pi$
$440$	25.8855	1.23404
$441$	0	0
$442$	−0.873973	−0.0415706
$443$	−38.5998	−1.83393	−0.916967	−	0.398963i	$-0.869370\pi$
$443$	−38.5998	−1.83393	−0.916967	+	0.398963i	$0.869370\pi$
$444$	−10.5835	−0.502272
$445$	14.5540	0.689925
$446$	8.33829	0.394830
$447$	−16.6851	−0.789180
$448$	0	0
$449$	5.45831	0.257594	0.128797	−	0.991671i	$-0.458889\pi$
$449$	5.45831	0.257594	0.128797	+	0.991671i	$0.458889\pi$
$450$	−12.2488	−0.577416
$451$	−44.0100	−2.07235
$452$	−3.15293	−0.148302
$453$	17.0039	0.798912
$454$	−26.5613	−1.24658
$455$	0	0
$456$	1.00000	0.0468293
$457$	−1.65685	−0.0775044	−0.0387522	−	0.999249i	$-0.512338\pi$
$457$	−1.65685	−0.0775044	−0.0387522	+	0.999249i	$0.512338\pi$
$458$	−25.2266	−1.17876
$459$	0.508035	0.0237130
$460$	−30.2596	−1.41086
$461$	25.6760	1.19585	0.597926	−	0.801551i	$-0.295992\pi$
$461$	25.6760	1.19585	0.597926	+	0.801551i	$0.295992\pi$
$462$	0	0
$463$	5.55204	0.258025	0.129012	−	0.991643i	$-0.458819\pi$
$463$	5.55204	0.258025	0.129012	+	0.991643i	$0.458819\pi$
$464$	4.32039	0.200569
$465$	5.50190	0.255144
$466$	2.71024	0.125550
$467$	−21.5343	−0.996487	−0.498243	−	0.867037i	$-0.666021\pi$
$467$	−21.5343	−0.996487	−0.498243	+	0.867037i	$0.666021\pi$
$468$	1.72030	0.0795209
$469$	0	0
$470$	32.5204	1.50005
$471$	8.32496	0.383594
$472$	−2.83254	−0.130378
$473$	−40.0166	−1.83996
$474$	−5.80798	−0.266770
$475$	−12.2488	−0.562016
$476$	0	0
$477$	7.32242	0.335270
$478$	5.38434	0.246274
$479$	−37.2491	−1.70195	−0.850977	−	0.525202i	$-0.823990\pi$
$479$	−37.2491	−1.70195	−0.850977	+	0.525202i	$0.823990\pi$
$480$	4.15317	0.189566
$481$	−18.2068	−0.830160
$482$	−28.7900	−1.31135
$483$	0	0
$484$	27.8467	1.26576
$485$	−23.1832	−1.05270
$486$	−1.00000	−0.0453609
$487$	5.16720	0.234148	0.117074	−	0.993123i	$-0.462648\pi$
$487$	5.16720	0.234148	0.117074	+	0.993123i	$0.462648\pi$
$488$	3.19385	0.144579
$489$	−19.6693	−0.889475
$490$	0	0
$491$	4.90711	0.221455	0.110727	−	0.993851i	$-0.464682\pi$
$491$	4.90711	0.221455	0.110727	+	0.993851i	$0.464682\pi$
$492$	−7.06114	−0.318341
$493$	2.19491	0.0988538
$494$	1.72030	0.0774000
$495$	−25.8855	−1.16347
$496$	−1.32475	−0.0594828
$497$	0	0
$498$	13.4038	0.600639
$499$	−17.7889	−0.796340	−0.398170	−	0.917312i	$-0.630355\pi$
$499$	−17.7889	−0.796340	−0.398170	+	0.917312i	$0.630355\pi$
$500$	−30.1057	−1.34637
$501$	3.51472	0.157026
$502$	−9.02266	−0.402701
$503$	−40.0458	−1.78555	−0.892776	−	0.450501i	$-0.851245\pi$
$503$	−40.0458	−1.78555	−0.892776	+	0.450501i	$0.851245\pi$
$504$	0	0
$505$	−69.7482	−3.10375
$506$	−45.4109	−2.01876
$507$	−10.0406	−0.445917
$508$	4.37104	0.193934
$509$	−7.71240	−0.341846	−0.170923	−	0.985284i	$-0.554675\pi$
$509$	−7.71240	−0.341846	−0.170923	+	0.985284i	$0.554675\pi$
$510$	2.10996	0.0934305
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−14.7735	−0.651630
$515$	−20.5691	−0.906383
$516$	−6.42042	−0.282643
$517$	48.8037	2.14638
$518$	0	0
$519$	19.2225	0.843772
$520$	7.14471	0.313316
$521$	41.1883	1.80449	0.902246	−	0.431222i	$-0.141917\pi$
$521$	41.1883	1.80449	0.902246	+	0.431222i	$0.141917\pi$
$522$	−4.32039	−0.189098
$523$	−1.38201	−0.0604310	−0.0302155	−	0.999543i	$-0.509619\pi$
$523$	−1.38201	−0.0604310	−0.0302155	+	0.999543i	$0.509619\pi$
$524$	−10.3614	−0.452639
$525$	0	0
$526$	−13.4570	−0.586752
$527$	−0.673017	−0.0293171
$528$	6.23271	0.271244
$529$	30.0844	1.30802
$530$	30.4113	1.32098
$531$	2.83254	0.122922
$532$	0	0
$533$	−12.1473	−0.526157
$534$	3.50431	0.151646
$535$	−5.53574	−0.239331
$536$	9.51424	0.410953
$537$	−6.80088	−0.293480
$538$	4.85388	0.209266
$539$	0	0
$540$	−4.15317	−0.178724
$541$	45.1285	1.94022	0.970112	−	0.242656i	$-0.0780188\pi$
$541$	45.1285	1.94022	0.970112	+	0.242656i	$0.0780188\pi$
$542$	−15.3634	−0.659916
$543$	15.8966	0.682186
$544$	−0.508035	−0.0217818
$545$	52.0587	2.22995
$546$	0	0
$547$	−11.8645	−0.507290	−0.253645	−	0.967297i	$-0.581630\pi$
$547$	−11.8645	−0.507290	−0.253645	+	0.967297i	$0.581630\pi$
$548$	2.48171	0.106014
$549$	−3.19385	−0.136310
$550$	−76.3435	−3.25530
$551$	−4.32039	−0.184055
$552$	−7.28590	−0.310109
$553$	0	0
$554$	−13.7387	−0.583702
$555$	43.9552	1.86579
$556$	9.14255	0.387730
$557$	2.92987	0.124143	0.0620713	−	0.998072i	$-0.480229\pi$
$557$	2.92987	0.124143	0.0620713	+	0.998072i	$0.480229\pi$
$558$	1.32475	0.0560810
$559$	−11.0450	−0.467156
$560$	0	0
$561$	3.16643	0.133687
$562$	−14.7957	−0.624121
$563$	12.0487	0.507791	0.253895	−	0.967232i	$-0.418288\pi$
$563$	12.0487	0.507791	0.253895	+	0.967232i	$0.418288\pi$
$564$	7.83026	0.329713
$565$	13.0947	0.550897
$566$	15.2576	0.641323
$567$	0	0
$568$	−15.1348	−0.635041
$569$	18.8460	0.790064	0.395032	−	0.918667i	$-0.370733\pi$
$569$	18.8460	0.790064	0.395032	+	0.918667i	$0.370733\pi$
$570$	−4.15317	−0.173957
$571$	37.3306	1.56224	0.781119	−	0.624382i	$-0.214649\pi$
$571$	37.3306	1.56224	0.781119	+	0.624382i	$0.214649\pi$
$572$	10.7221	0.448315
$573$	−1.95049	−0.0814827
$574$	0	0
$575$	89.2439	3.72173
$576$	1.00000	0.0416667
$577$	16.4427	0.684518	0.342259	−	0.939606i	$-0.388808\pi$
$577$	16.4427	0.684518	0.342259	+	0.939606i	$0.388808\pi$
$578$	16.7419	0.696371
$579$	4.98750	0.207273
$580$	−17.9433	−0.745056
$581$	0	0
$582$	−5.58206	−0.231384
$583$	45.6385	1.89015
$584$	5.40428	0.223631
$585$	−7.14471	−0.295397
$586$	14.1117	0.582950
$587$	34.4462	1.42175	0.710873	−	0.703321i	$-0.248300\pi$
$587$	34.4462	1.42175	0.710873	+	0.703321i	$0.248300\pi$
$588$	0	0
$589$	1.32475	0.0545852
$590$	11.7640	0.484318
$591$	9.00792	0.370536
$592$	−10.5835	−0.434980
$593$	−29.6956	−1.21945	−0.609726	−	0.792612i	$-0.708721\pi$
$593$	−29.6956	−1.21945	−0.609726	+	0.792612i	$0.708721\pi$
$594$	−6.23271	−0.255731
$595$	0	0
$596$	−16.6851	−0.683450
$597$	−19.4529	−0.796155
$598$	−12.5339	−0.512551
$599$	42.5138	1.73706	0.868532	−	0.495632i	$-0.165064\pi$
$599$	42.5138	1.73706	0.868532	+	0.495632i	$0.165064\pi$
$600$	−12.2488	−0.500057
$601$	−0.496239	−0.0202420	−0.0101210	−	0.999949i	$-0.503222\pi$
$601$	−0.496239	−0.0202420	−0.0101210	+	0.999949i	$0.503222\pi$
$602$	0	0
$603$	−9.51424	−0.387450
$604$	17.0039	0.691878
$605$	−115.652	−4.70192
$606$	−16.7940	−0.682208
$607$	−25.8083	−1.04752	−0.523762	−	0.851864i	$-0.675472\pi$
$607$	−25.8083	−1.04752	−0.523762	+	0.851864i	$0.675472\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	−13.2646	−0.537068
$611$	13.4704	0.544954
$612$	0.508035	0.0205361
$613$	−9.98888	−0.403447	−0.201724	−	0.979442i	$-0.564654\pi$
$613$	−9.98888	−0.403447	−0.201724	+	0.979442i	$0.564654\pi$
$614$	9.69192	0.391134
$615$	29.3261	1.18254
$616$	0	0
$617$	9.79185	0.394205	0.197103	−	0.980383i	$-0.436847\pi$
$617$	9.79185	0.394205	0.197103	+	0.980383i	$0.436847\pi$
$618$	−4.95262	−0.199224
$619$	−23.7082	−0.952914	−0.476457	−	0.879198i	$-0.658079\pi$
$619$	−23.7082	−0.952914	−0.476457	+	0.879198i	$0.658079\pi$
$620$	5.50190	0.220962
$621$	7.28590	0.292373
$622$	9.99158	0.400626
$623$	0	0
$624$	1.72030	0.0688671
$625$	63.7900	2.55160
$626$	6.14843	0.245741
$627$	−6.23271	−0.248910
$628$	8.32496	0.332202
$629$	−5.37680	−0.214387
$630$	0	0
$631$	−42.2452	−1.68175	−0.840876	−	0.541227i	$-0.817960\pi$
$631$	−42.2452	−1.68175	−0.840876	+	0.541227i	$0.817960\pi$
$632$	−5.80798	−0.231029
$633$	25.5924	1.01721
$634$	−1.11150	−0.0441434
$635$	−18.1537	−0.720408
$636$	7.32242	0.290353
$637$	0	0
$638$	−26.9277	−1.06608
$639$	15.1348	0.598722
$640$	4.15317	0.164169
$641$	−10.5986	−0.418621	−0.209311	−	0.977849i	$-0.567122\pi$
$641$	−10.5986	−0.418621	−0.209311	+	0.977849i	$0.567122\pi$
$642$	−1.33289	−0.0526051
$643$	−4.35880	−0.171894	−0.0859472	−	0.996300i	$-0.527392\pi$
$643$	−4.35880	−0.171894	−0.0859472	+	0.996300i	$0.527392\pi$
$644$	0	0
$645$	26.6651	1.04994
$646$	0.508035	0.0199884
$647$	14.0662	0.553000	0.276500	−	0.961014i	$-0.410825\pi$
$647$	14.0662	0.553000	0.276500	+	0.961014i	$0.410825\pi$
$648$	−1.00000	−0.0392837
$649$	17.6544	0.692996
$650$	−21.0717	−0.826500
$651$	0	0
$652$	−19.6693	−0.770308
$653$	33.8479	1.32457	0.662286	−	0.749252i	$-0.269587\pi$
$653$	33.8479	1.32457	0.662286	+	0.749252i	$0.269587\pi$
$654$	12.5347	0.490145
$655$	43.0326	1.68142
$656$	−7.06114	−0.275691
$657$	−5.40428	−0.210841
$658$	0	0
$659$	−13.0704	−0.509151	−0.254576	−	0.967053i	$-0.581936\pi$
$659$	−13.0704	−0.509151	−0.254576	+	0.967053i	$0.581936\pi$
$660$	−25.8855	−1.00759
$661$	3.40536	0.132453	0.0662266	−	0.997805i	$-0.478904\pi$
$661$	3.40536	0.132453	0.0662266	+	0.997805i	$0.478904\pi$
$662$	17.3358	0.673776
$663$	0.873973	0.0339423
$664$	13.4038	0.520168
$665$	0	0
$666$	10.5835	0.410103
$667$	31.4780	1.21883
$668$	3.51472	0.135989
$669$	−8.33829	−0.322377
$670$	−39.5143	−1.52657
$671$	−19.9063	−0.768475
$672$	0	0
$673$	−34.8560	−1.34360	−0.671800	−	0.740733i	$-0.734478\pi$
$673$	−34.8560	−1.34360	−0.671800	+	0.740733i	$0.734478\pi$
$674$	−28.8699	−1.11203
$675$	12.2488	0.471458
$676$	−10.0406	−0.386176
$677$	−46.2090	−1.77596	−0.887978	−	0.459886i	$-0.847890\pi$
$677$	−46.2090	−1.77596	−0.887978	+	0.459886i	$0.847890\pi$
$678$	3.15293	0.121088
$679$	0	0
$680$	2.10996	0.0809132
$681$	26.5613	1.01783
$682$	8.25675	0.316167
$683$	41.7992	1.59940	0.799701	−	0.600398i	$-0.204991\pi$
$683$	41.7992	1.59940	0.799701	+	0.600398i	$0.204991\pi$
$684$	−1.00000	−0.0382360
$685$	−10.3070	−0.393810
$686$	0	0
$687$	25.2266	0.962456
$688$	−6.42042	−0.244776
$689$	12.5968	0.479898
$690$	30.2596	1.15196
$691$	9.32335	0.354677	0.177338	−	0.984150i	$-0.443251\pi$
$691$	9.32335	0.354677	0.177338	+	0.984150i	$0.443251\pi$
$692$	19.2225	0.730728
$693$	0	0
$694$	2.34257	0.0889228
$695$	−37.9706	−1.44031
$696$	−4.32039	−0.163764
$697$	−3.58730	−0.135879
$698$	−15.3733	−0.581888
$699$	−2.71024	−0.102511
$700$	0	0
$701$	8.02926	0.303261	0.151631	−	0.988437i	$-0.451548\pi$
$701$	8.02926	0.303261	0.151631	+	0.988437i	$0.451548\pi$
$702$	−1.72030	−0.0649286
$703$	10.5835	0.399165
$704$	6.23271	0.234904
$705$	−32.5204	−1.22479
$706$	−25.1039	−0.944797
$707$	0	0
$708$	2.83254	0.106453
$709$	30.9564	1.16259	0.581296	−	0.813692i	$-0.302546\pi$
$709$	30.9564	1.16259	0.581296	+	0.813692i	$0.302546\pi$
$710$	62.8573	2.35899
$711$	5.80798	0.217816
$712$	3.50431	0.131329
$713$	−9.65197	−0.361469
$714$	0	0
$715$	−44.5309	−1.66536
$716$	−6.80088	−0.254161
$717$	−5.38434	−0.201082
$718$	−9.94679	−0.371211
$719$	43.1772	1.61024	0.805120	−	0.593113i	$-0.202101\pi$
$719$	43.1772	1.61024	0.805120	+	0.593113i	$0.202101\pi$
$720$	−4.15317	−0.154780
$721$	0	0
$722$	−1.00000	−0.0372161
$723$	28.7900	1.07071
$724$	15.8966	0.590791
$725$	52.9198	1.96539
$726$	−27.8467	−1.03349
$727$	−26.9266	−0.998653	−0.499327	−	0.866414i	$-0.666419\pi$
$727$	−26.9266	−0.998653	−0.499327	+	0.866414i	$0.666419\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−22.4449	−0.830724
$731$	−3.26180	−0.120642
$732$	−3.19385	−0.118048
$733$	−27.1034	−1.00109	−0.500544	−	0.865711i	$-0.666867\pi$
$733$	−27.1034	−1.00109	−0.500544	+	0.865711i	$0.666867\pi$
$734$	31.7419	1.17161
$735$	0	0
$736$	−7.28590	−0.268562
$737$	−59.2995	−2.18432
$738$	7.06114	0.259924
$739$	4.25383	0.156480	0.0782398	−	0.996935i	$-0.475070\pi$
$739$	4.25383	0.156480	0.0782398	+	0.996935i	$0.475070\pi$
$740$	43.9552	1.61583
$741$	−1.72030	−0.0631968
$742$	0	0
$743$	27.2774	1.00071	0.500355	−	0.865820i	$-0.333203\pi$
$743$	27.2774	1.00071	0.500355	+	0.865820i	$0.333203\pi$
$744$	1.32475	0.0485675
$745$	69.2963	2.53882
$746$	−25.5019	−0.933693
$747$	−13.4038	−0.490419
$748$	3.16643	0.115776
$749$	0	0
$750$	30.1057	1.09930
$751$	13.2620	0.483936	0.241968	−	0.970284i	$-0.422207\pi$
$751$	13.2620	0.483936	0.241968	+	0.970284i	$0.422207\pi$
$752$	7.83026	0.285540
$753$	9.02266	0.328804
$754$	−7.43237	−0.270671
$755$	−70.6200	−2.57013
$756$	0	0
$757$	−4.70317	−0.170940	−0.0854699	−	0.996341i	$-0.527239\pi$
$757$	−4.70317	−0.170940	−0.0854699	+	0.996341i	$0.527239\pi$
$758$	−28.8049	−1.04624
$759$	45.4109	1.64831
$760$	−4.15317	−0.150651
$761$	16.9215	0.613405	0.306703	−	0.951805i	$-0.400774\pi$
$761$	16.9215	0.613405	0.306703	+	0.951805i	$0.400774\pi$
$762$	−4.37104	−0.158346
$763$	0	0
$764$	−1.95049	−0.0705661
$765$	−2.10996	−0.0762857
$766$	−26.4977	−0.957400
$767$	4.87282	0.175947
$768$	1.00000	0.0360844
$769$	42.7156	1.54036	0.770182	−	0.637824i	$-0.220165\pi$
$769$	42.7156	1.54036	0.770182	+	0.637824i	$0.220165\pi$
$770$	0	0
$771$	14.7735	0.532053
$772$	4.98750	0.179504
$773$	−22.7607	−0.818647	−0.409323	−	0.912389i	$-0.634235\pi$
$773$	−22.7607	−0.818647	−0.409323	+	0.912389i	$0.634235\pi$
$774$	6.42042	0.230777
$775$	−16.2266	−0.582877
$776$	−5.58206	−0.200384
$777$	0	0
$778$	−2.31388	−0.0829568
$779$	7.06114	0.252991
$780$	−7.14471	−0.255821
$781$	94.3306	3.37542
$782$	−3.70149	−0.132365
$783$	4.32039	0.154398
$784$	0	0
$785$	−34.5750	−1.23403
$786$	10.3614	0.369578
$787$	15.7702	0.562148	0.281074	−	0.959686i	$-0.409309\pi$
$787$	15.7702	0.562148	0.281074	+	0.959686i	$0.409309\pi$
$788$	9.00792	0.320894
$789$	13.4570	0.479081
$790$	24.1216	0.858207
$791$	0	0
$792$	−6.23271	−0.221470
$793$	−5.49438	−0.195111
$794$	−11.3529	−0.402900
$795$	−30.4113	−1.07858
$796$	−19.4529	−0.689490
$797$	−18.9172	−0.670081	−0.335040	−	0.942204i	$-0.608750\pi$
$797$	−18.9172	−0.670081	−0.335040	+	0.942204i	$0.608750\pi$
$798$	0	0
$799$	3.97804	0.140733
$800$	−12.2488	−0.433062
$801$	−3.50431	−0.123819
$802$	22.1159	0.780940
$803$	−33.6833	−1.18866
$804$	−9.51424	−0.335541
$805$	0	0
$806$	2.27896	0.0802730
$807$	−4.85388	−0.170865
$808$	−16.7940	−0.590809
$809$	29.3371	1.03144	0.515719	−	0.856758i	$-0.327525\pi$
$809$	29.3371	1.03144	0.515719	+	0.856758i	$0.327525\pi$
$810$	4.15317	0.145928
$811$	−20.2965	−0.712706	−0.356353	−	0.934351i	$-0.615980\pi$
$811$	−20.2965	−0.712706	−0.356353	+	0.934351i	$0.615980\pi$
$812$	0	0
$813$	15.3634	0.538819
$814$	65.9640	2.31204
$815$	81.6898	2.86147
$816$	0.508035	0.0177848
$817$	6.42042	0.224622
$818$	27.2307	0.952099
$819$	0	0
$820$	29.3261	1.02411
$821$	−32.9518	−1.15003	−0.575013	−	0.818144i	$-0.695003\pi$
$821$	−32.9518	−1.15003	−0.575013	+	0.818144i	$0.695003\pi$
$822$	−2.48171	−0.0865597
$823$	39.2202	1.36713	0.683566	−	0.729889i	$-0.260428\pi$
$823$	39.2202	1.36713	0.683566	+	0.729889i	$0.260428\pi$
$824$	−4.95262	−0.172533
$825$	76.3435	2.65794
$826$	0	0
$827$	−47.2010	−1.64134	−0.820669	−	0.571403i	$-0.806399\pi$
$827$	−47.2010	−1.64134	−0.820669	+	0.571403i	$0.806399\pi$
$828$	7.28590	0.253203
$829$	31.4749	1.09317	0.546584	−	0.837404i	$-0.315928\pi$
$829$	31.4749	1.09317	0.546584	+	0.837404i	$0.315928\pi$
$830$	−55.6683	−1.93227
$831$	13.7387	0.476591
$832$	1.72030	0.0596407
$833$	0	0
$834$	−9.14255	−0.316581
$835$	−14.5972	−0.505158
$836$	−6.23271	−0.215563
$837$	−1.32475	−0.0457899
$838$	24.7081	0.853527
$839$	−40.3275	−1.39226	−0.696129	−	0.717916i	$-0.745096\pi$
$839$	−40.3275	−1.39226	−0.696129	+	0.717916i	$0.745096\pi$
$840$	0	0
$841$	−10.3342	−0.356352
$842$	25.9581	0.894574
$843$	14.7957	0.509592
$844$	25.5924	0.880928
$845$	41.7002	1.43453
$846$	−7.83026	−0.269210
$847$	0	0
$848$	7.32242	0.251453
$849$	−15.2576	−0.523638
$850$	−6.22284	−0.213442
$851$	−77.1105	−2.64331
$852$	15.1348	0.518509
$853$	30.0172	1.02777	0.513885	−	0.857859i	$-0.328206\pi$
$853$	30.0172	1.02777	0.513885	+	0.857859i	$0.328206\pi$
$854$	0	0
$855$	4.15317	0.142036
$856$	−1.33289	−0.0455574
$857$	1.04635	0.0357426	0.0178713	−	0.999840i	$-0.494311\pi$
$857$	1.04635	0.0357426	0.0178713	+	0.999840i	$0.494311\pi$
$858$	−10.7221	−0.366048
$859$	−6.99280	−0.238591	−0.119296	−	0.992859i	$-0.538064\pi$
$859$	−6.99280	−0.238591	−0.119296	+	0.992859i	$0.538064\pi$
$860$	26.6651	0.909272
$861$	0	0
$862$	1.71770	0.0585050
$863$	−12.7302	−0.433342	−0.216671	−	0.976245i	$-0.569520\pi$
$863$	−12.7302	−0.433342	−0.216671	+	0.976245i	$0.569520\pi$
$864$	−1.00000	−0.0340207
$865$	−79.8342	−2.71444
$866$	15.2339	0.517668
$867$	−16.7419	−0.568585
$868$	0	0
$869$	36.1995	1.22798
$870$	17.9433	0.608336
$871$	−16.3673	−0.554586
$872$	12.5347	0.424478
$873$	5.58206	0.188924
$874$	7.28590	0.246449
$875$	0	0
$876$	−5.40428	−0.182594
$877$	−37.7711	−1.27544	−0.637719	−	0.770269i	$-0.720122\pi$
$877$	−37.7711	−1.27544	−0.637719	+	0.770269i	$0.720122\pi$
$878$	−33.9581	−1.14603
$879$	−14.1117	−0.475977
$880$	−25.8855	−0.872600
$881$	26.7367	0.900783	0.450392	−	0.892831i	$-0.351284\pi$
$881$	26.7367	0.900783	0.450392	+	0.892831i	$0.351284\pi$
$882$	0	0
$883$	−7.06357	−0.237708	−0.118854	−	0.992912i	$-0.537922\pi$
$883$	−7.06357	−0.237708	−0.118854	+	0.992912i	$0.537922\pi$
$884$	0.873973	0.0293949
$885$	−11.7640	−0.395444
$886$	38.5998	1.29679
$887$	6.23612	0.209388	0.104694	−	0.994504i	$-0.466614\pi$
$887$	6.23612	0.209388	0.104694	+	0.994504i	$0.466614\pi$
$888$	10.5835	0.355160
$889$	0	0
$890$	−14.5540	−0.487851
$891$	6.23271	0.208804
$892$	−8.33829	−0.279187
$893$	−7.83026	−0.262030
$894$	16.6851	0.558034
$895$	28.2452	0.944134
$896$	0	0
$897$	12.5339	0.418496
$898$	−5.45831	−0.182146
$899$	−5.72342	−0.190887
$900$	12.2488	0.408295
$901$	3.72004	0.123933
$902$	44.0100	1.46537
$903$	0	0
$904$	3.15293	0.104865
$905$	−66.0211	−2.19462
$906$	−17.0039	−0.564916
$907$	−11.8823	−0.394545	−0.197273	−	0.980349i	$-0.563208\pi$
$907$	−11.8823	−0.394545	−0.197273	+	0.980349i	$0.563208\pi$
$908$	26.5613	0.881469
$909$	16.7940	0.557020
$910$	0	0
$911$	50.4352	1.67099	0.835496	−	0.549496i	$-0.185180\pi$
$911$	50.4352	1.67099	0.835496	+	0.549496i	$0.185180\pi$
$912$	−1.00000	−0.0331133
$913$	−83.5420	−2.76484
$914$	1.65685	0.0548039
$915$	13.2646	0.438514
$916$	25.2266	0.833511
$917$	0	0
$918$	−0.508035	−0.0167677
$919$	−50.6498	−1.67078	−0.835391	−	0.549656i	$-0.814759\pi$
$919$	−50.6498	−1.67078	−0.835391	+	0.549656i	$0.814759\pi$
$920$	30.2596	0.997630
$921$	−9.69192	−0.319360
$922$	−25.6760	−0.845595
$923$	26.0364	0.856997
$924$	0	0
$925$	−129.636	−4.26240
$926$	−5.55204	−0.182451
$927$	4.95262	0.162666
$928$	−4.32039	−0.141824
$929$	−4.84100	−0.158828	−0.0794140	−	0.996842i	$-0.525305\pi$
$929$	−4.84100	−0.158828	−0.0794140	+	0.996842i	$0.525305\pi$
$930$	−5.50190	−0.180414
$931$	0	0
$932$	−2.71024	−0.0887769
$933$	−9.99158	−0.327110
$934$	21.5343	0.704623
$935$	−13.1507	−0.430075
$936$	−1.72030	−0.0562298
$937$	−12.3493	−0.403434	−0.201717	−	0.979444i	$-0.564652\pi$
$937$	−12.3493	−0.403434	−0.201717	+	0.979444i	$0.564652\pi$
$938$	0	0
$939$	−6.14843	−0.200647
$940$	−32.5204	−1.06070
$941$	24.1945	0.788718	0.394359	−	0.918956i	$-0.370967\pi$
$941$	24.1945	0.788718	0.394359	+	0.918956i	$0.370967\pi$
$942$	−8.32496	−0.271242
$943$	−51.4467	−1.67534
$944$	2.83254	0.0921914
$945$	0	0
$946$	40.0166	1.30105
$947$	24.3208	0.790319	0.395160	−	0.918613i	$-0.370689\pi$
$947$	24.3208	0.790319	0.395160	+	0.918613i	$0.370689\pi$
$948$	5.80798	0.188635
$949$	−9.29699	−0.301793
$950$	12.2488	0.397405
$951$	1.11150	0.0360429
$952$	0	0
$953$	8.03105	0.260151	0.130076	−	0.991504i	$-0.458478\pi$
$953$	8.03105	0.260151	0.130076	+	0.991504i	$0.458478\pi$
$954$	−7.32242	−0.237072
$955$	8.10070	0.262133
$956$	−5.38434	−0.174142
$957$	26.9277	0.870450
$958$	37.2491	1.20346
$959$	0	0
$960$	−4.15317	−0.134043
$961$	−29.2450	−0.943389
$962$	18.2068	0.587012
$963$	1.33289	0.0429519
$964$	28.7900	0.927263
$965$	−20.7139	−0.666805
$966$	0	0
$967$	−10.1584	−0.326673	−0.163337	−	0.986570i	$-0.552226\pi$
$967$	−10.1584	−0.326673	−0.163337	+	0.986570i	$0.552226\pi$
$968$	−27.8467	−0.895025
$969$	−0.508035	−0.0163204
$970$	23.1832	0.744369
$971$	−17.7827	−0.570673	−0.285336	−	0.958427i	$-0.592105\pi$
$971$	−17.7827	−0.570673	−0.285336	+	0.958427i	$0.592105\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−5.16720	−0.165568
$975$	21.0717	0.674834
$976$	−3.19385	−0.102233
$977$	−16.2521	−0.519949	−0.259975	−	0.965615i	$-0.583714\pi$
$977$	−16.2521	−0.519949	−0.259975	+	0.965615i	$0.583714\pi$
$978$	19.6693	0.628954
$979$	−21.8413	−0.698051
$980$	0	0
$981$	−12.5347	−0.400202
$982$	−4.90711	−0.156592
$983$	13.2135	0.421444	0.210722	−	0.977546i	$-0.432419\pi$
$983$	13.2135	0.421444	0.210722	+	0.977546i	$0.432419\pi$
$984$	7.06114	0.225101
$985$	−37.4115	−1.19203
$986$	−2.19491	−0.0699002
$987$	0	0
$988$	−1.72030	−0.0547300
$989$	−46.7785	−1.48747
$990$	25.8855	0.822696
$991$	14.4956	0.460469	0.230235	−	0.973135i	$-0.426051\pi$
$991$	14.4956	0.460469	0.230235	+	0.973135i	$0.426051\pi$
$992$	1.32475	0.0420607
$993$	−17.3358	−0.550136
$994$	0	0
$995$	80.7913	2.56126
$996$	−13.4038	−0.424716
$997$	54.9128	1.73911	0.869553	−	0.493840i	$-0.164407\pi$
$997$	54.9128	1.73911	0.869553	+	0.493840i	$0.164407\pi$
$998$	17.7889	0.563098
$999$	−10.5835	−0.334848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.cd.1.1	yes	6
7.6	odd	2		5586.2.a.cc.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5586.2.a.cc.1.6	✓	6	7.6	odd	2
5586.2.a.cd.1.1	yes	6	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:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.15317 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.15317 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +4.15317 q^{10} +6.23271 q^{11} +1.00000 q^{12} +1.72030 q^{13} -4.15317 q^{15} +1.00000 q^{16} +0.508035 q^{17} -1.00000 q^{18} -1.00000 q^{19} -4.15317 q^{20} -6.23271 q^{22} +7.28590 q^{23} -1.00000 q^{24} +12.2488 q^{25} -1.72030 q^{26} +1.00000 q^{27} +4.32039 q^{29} +4.15317 q^{30} -1.32475 q^{31} -1.00000 q^{32} +6.23271 q^{33} -0.508035 q^{34} +1.00000 q^{36} -10.5835 q^{37} +1.00000 q^{38} +1.72030 q^{39} +4.15317 q^{40} -7.06114 q^{41} -6.42042 q^{43} +6.23271 q^{44} -4.15317 q^{45} -7.28590 q^{46} +7.83026 q^{47} +1.00000 q^{48} -12.2488 q^{50} +0.508035 q^{51} +1.72030 q^{52} +7.32242 q^{53} -1.00000 q^{54} -25.8855 q^{55} -1.00000 q^{57} -4.32039 q^{58} +2.83254 q^{59} -4.15317 q^{60} -3.19385 q^{61} +1.32475 q^{62} +1.00000 q^{64} -7.14471 q^{65} -6.23271 q^{66} -9.51424 q^{67} +0.508035 q^{68} +7.28590 q^{69} +15.1348 q^{71} -1.00000 q^{72} -5.40428 q^{73} +10.5835 q^{74} +12.2488 q^{75} -1.00000 q^{76} -1.72030 q^{78} +5.80798 q^{79} -4.15317 q^{80} +1.00000 q^{81} +7.06114 q^{82} -13.4038 q^{83} -2.10996 q^{85} +6.42042 q^{86} +4.32039 q^{87} -6.23271 q^{88} -3.50431 q^{89} +4.15317 q^{90} +7.28590 q^{92} -1.32475 q^{93} -7.83026 q^{94} +4.15317 q^{95} -1.00000 q^{96} +5.58206 q^{97} +6.23271 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 6 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 6 * q^6 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 6 q^{6} - 6 q^{8} + 6 q^{9} + 4 q^{11} + 6 q^{12} + 6 q^{16} + 4 q^{17} - 6 q^{18} - 6 q^{19} - 4 q^{22} + 16 q^{23} - 6 q^{24} + 10 q^{25} + 6 q^{27} + 8 q^{29} - 6 q^{32} + 4 q^{33} - 4 q^{34} + 6 q^{36} + 6 q^{38} + 8 q^{41} + 8 q^{43} + 4 q^{44} - 16 q^{46} + 16 q^{47} + 6 q^{48} - 10 q^{50} + 4 q^{51} - 4 q^{53} - 6 q^{54} - 32 q^{55} - 6 q^{57} - 8 q^{58} + 24 q^{59} + 6 q^{64} + 16 q^{65} - 4 q^{66} - 20 q^{67} + 4 q^{68} + 16 q^{69} + 24 q^{71} - 6 q^{72} - 16 q^{73} + 10 q^{75} - 6 q^{76} + 40 q^{79} + 6 q^{81} - 8 q^{82} + 24 q^{83} + 8 q^{85} - 8 q^{86} + 8 q^{87} - 4 q^{88} + 24 q^{89} + 16 q^{92} - 16 q^{94} - 6 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 6 * q^6 - 6 * q^8 + 6 * q^9 + 4 * q^11 + 6 * q^12 + 6 * q^16 + 4 * q^17 - 6 * q^18 - 6 * q^19 - 4 * q^22 + 16 * q^23 - 6 * q^24 + 10 * q^25 + 6 * q^27 + 8 * q^29 - 6 * q^32 + 4 * q^33 - 4 * q^34 + 6 * q^36 + 6 * q^38 + 8 * q^41 + 8 * q^43 + 4 * q^44 - 16 * q^46 + 16 * q^47 + 6 * q^48 - 10 * q^50 + 4 * q^51 - 4 * q^53 - 6 * q^54 - 32 * q^55 - 6 * q^57 - 8 * q^58 + 24 * q^59 + 6 * q^64 + 16 * q^65 - 4 * q^66 - 20 * q^67 + 4 * q^68 + 16 * q^69 + 24 * q^71 - 6 * q^72 - 16 * q^73 + 10 * q^75 - 6 * q^76 + 40 * q^79 + 6 * q^81 - 8 * q^82 + 24 * q^83 + 8 * q^85 - 8 * q^86 + 8 * q^87 - 4 * q^88 + 24 * q^89 + 16 * q^92 - 16 * q^94 - 6 * q^96 - 4 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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