LMFDB - Embedded newform 3381.2.a.y.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.3176240.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 9x^{3} + 7x^{2} + 19x - 9 $ x^5 - x^4 - 9x^3 + 7x^2 + 19*x - 9
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.08269$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.08269 q^{2} -1.00000 q^{3} +2.33760 q^{4} +1.37958 q^{5} -2.08269 q^{6} +0.703109 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.08269 q^{2} -1.00000 q^{3} +2.33760 q^{4} +1.37958 q^{5} -2.08269 q^{6} +0.703109 q^{8} +1.00000 q^{9} +2.87324 q^{10} -1.74509 q^{11} -2.33760 q^{12} -0.365513 q^{13} -1.37958 q^{15} -3.21083 q^{16} -8.01070 q^{17} +2.08269 q^{18} -5.54843 q^{19} +3.22490 q^{20} -3.63449 q^{22} +1.00000 q^{23} -0.703109 q^{24} -3.09676 q^{25} -0.761249 q^{26} -1.00000 q^{27} +7.33551 q^{29} -2.87324 q^{30} -4.71718 q^{31} -8.09339 q^{32} +1.74509 q^{33} -16.6838 q^{34} +2.33760 q^{36} +10.6290 q^{37} -11.5557 q^{38} +0.365513 q^{39} +0.969996 q^{40} -7.17945 q^{41} -4.36551 q^{43} -4.07932 q^{44} +1.37958 q^{45} +2.08269 q^{46} -4.59378 q^{47} +3.21083 q^{48} -6.44959 q^{50} +8.01070 q^{51} -0.854421 q^{52} -11.5137 q^{53} -2.08269 q^{54} -2.40750 q^{55} +5.54843 q^{57} +15.2776 q^{58} +1.18292 q^{59} -3.22490 q^{60} +3.66836 q^{61} -9.82442 q^{62} -10.4344 q^{64} -0.504254 q^{65} +3.63449 q^{66} +10.3449 q^{67} -18.7258 q^{68} -1.00000 q^{69} +7.95593 q^{71} +0.703109 q^{72} -8.23294 q^{73} +22.1370 q^{74} +3.09676 q^{75} -12.9700 q^{76} +0.761249 q^{78} -16.0076 q^{79} -4.42961 q^{80} +1.00000 q^{81} -14.9526 q^{82} +1.84532 q^{83} -11.0514 q^{85} -9.09201 q^{86} -7.33551 q^{87} -1.22699 q^{88} +18.5430 q^{89} +2.87324 q^{90} +2.33760 q^{92} +4.71718 q^{93} -9.56742 q^{94} -7.65451 q^{95} +8.09339 q^{96} +0.114077 q^{97} -1.74509 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} - 5 q^{3} + 9 q^{4} - 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + q^2 - 5 * q^3 + 9 * q^4 - 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9	$ 5 q + q^{2} - 5 q^{3} + 9 q^{4} - 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9} - 2 q^{11} - 9 q^{12} - 4 q^{13} + 2 q^{15} + q^{16} - 2 q^{17} + q^{18} - 8 q^{19} - 12 q^{20} - 16 q^{22} + 5 q^{23} - 3 q^{24} + 5 q^{25} - 16 q^{26} - 5 q^{27} + 4 q^{29} - 12 q^{31} + 7 q^{32} + 2 q^{33} - 10 q^{34} + 9 q^{36} - 6 q^{37} + 8 q^{38} + 4 q^{39} - 30 q^{40} - 6 q^{41} - 24 q^{43} + 16 q^{44} - 2 q^{45} + q^{46} - 24 q^{47} - q^{48} - 3 q^{50} + 2 q^{51} + 4 q^{52} + 2 q^{53} - q^{54} - 8 q^{55} + 8 q^{57} + 4 q^{58} - 16 q^{59} + 12 q^{60} - 22 q^{61} - 6 q^{62} - 29 q^{64} + 22 q^{65} + 16 q^{66} - 16 q^{67} - 14 q^{68} - 5 q^{69} + 16 q^{71} + 3 q^{72} + 8 q^{74} - 5 q^{75} - 30 q^{76} + 16 q^{78} + 12 q^{79} + 6 q^{80} + 5 q^{81} - 24 q^{82} - 10 q^{83} - 14 q^{85} - 20 q^{86} - 4 q^{87} - 8 q^{88} + 16 q^{89} + 9 q^{92} + 12 q^{93} + 32 q^{94} + 18 q^{95} - 7 q^{96} + 4 q^{97} - 2 q^{99}+O(q^{100}) $ 5 * q + q^2 - 5 * q^3 + 9 * q^4 - 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9 - 2 * q^11 - 9 * q^12 - 4 * q^13 + 2 * q^15 + q^16 - 2 * q^17 + q^18 - 8 * q^19 - 12 * q^20 - 16 * q^22 + 5 * q^23 - 3 * q^24 + 5 * q^25 - 16 * q^26 - 5 * q^27 + 4 * q^29 - 12 * q^31 + 7 * q^32 + 2 * q^33 - 10 * q^34 + 9 * q^36 - 6 * q^37 + 8 * q^38 + 4 * q^39 - 30 * q^40 - 6 * q^41 - 24 * q^43 + 16 * q^44 - 2 * q^45 + q^46 - 24 * q^47 - q^48 - 3 * q^50 + 2 * q^51 + 4 * q^52 + 2 * q^53 - q^54 - 8 * q^55 + 8 * q^57 + 4 * q^58 - 16 * q^59 + 12 * q^60 - 22 * q^61 - 6 * q^62 - 29 * q^64 + 22 * q^65 + 16 * q^66 - 16 * q^67 - 14 * q^68 - 5 * q^69 + 16 * q^71 + 3 * q^72 + 8 * q^74 - 5 * q^75 - 30 * q^76 + 16 * q^78 + 12 * q^79 + 6 * q^80 + 5 * q^81 - 24 * q^82 - 10 * q^83 - 14 * q^85 - 20 * q^86 - 4 * q^87 - 8 * q^88 + 16 * q^89 + 9 * q^92 + 12 * q^93 + 32 * q^94 + 18 * q^95 - 7 * q^96 + 4 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.08269	1.47268	0.736342	−	0.676609i	$-0.236551\pi$
$2$	2.08269	1.47268	0.736342	+	0.676609i	$0.236551\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.33760	1.16880
$5$	1.37958	0.616967	0.308484	−	0.951230i	$-0.400179\pi$
$5$	1.37958	0.616967	0.308484	+	0.951230i	$0.400179\pi$
$6$	−2.08269	−0.850255
$7$	0	0
$7$	0	0
$8$	0.703109	0.248587
$9$	1.00000	0.333333
$10$	2.87324	0.908598
$11$	−1.74509	−0.526165	−0.263083	−	0.964773i	$-0.584739\pi$
$11$	−1.74509	−0.526165	−0.263083	+	0.964773i	$0.584739\pi$
$12$	−2.33760	−0.674806
$13$	−0.365513	−0.101375	−0.0506875	−	0.998715i	$-0.516141\pi$
$13$	−0.365513	−0.101375	−0.0506875	+	0.998715i	$0.516141\pi$
$14$	0	0
$15$	−1.37958	−0.356206
$16$	−3.21083	−0.802709
$17$	−8.01070	−1.94288	−0.971440	−	0.237284i	$-0.923743\pi$
$17$	−8.01070	−1.94288	−0.971440	+	0.237284i	$0.923743\pi$
$18$	2.08269	0.490895
$19$	−5.54843	−1.27290	−0.636449	−	0.771319i	$-0.719597\pi$
$19$	−5.54843	−1.27290	−0.636449	+	0.771319i	$0.719597\pi$
$20$	3.22490	0.721110
$21$	0	0
$22$	−3.63449	−0.774875
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.703109	−0.143522
$25$	−3.09676	−0.619352
$26$	−0.761249	−0.149293
$27$	−1.00000	−0.192450
$28$	0	0
$29$	7.33551	1.36217	0.681085	−	0.732204i	$-0.261508\pi$
$29$	7.33551	1.36217	0.681085	+	0.732204i	$0.261508\pi$
$30$	−2.87324	−0.524579
$31$	−4.71718	−0.847230	−0.423615	−	0.905842i	$-0.639239\pi$
$31$	−4.71718	−0.847230	−0.423615	+	0.905842i	$0.639239\pi$
$32$	−8.09339	−1.43072
$33$	1.74509	0.303782
$34$	−16.6838	−2.86125
$35$	0	0
$36$	2.33760	0.389599
$37$	10.6290	1.74740	0.873701	−	0.486463i	$-0.161713\pi$
$37$	10.6290	1.74740	0.873701	+	0.486463i	$0.161713\pi$
$38$	−11.5557	−1.87458
$39$	0.365513	0.0585289
$40$	0.969996	0.153370
$41$	−7.17945	−1.12124	−0.560621	−	0.828073i	$-0.689437\pi$
$41$	−7.17945	−1.12124	−0.560621	+	0.828073i	$0.689437\pi$
$42$	0	0
$43$	−4.36551	−0.665734	−0.332867	−	0.942974i	$-0.608016\pi$
$43$	−4.36551	−0.665734	−0.332867	+	0.942974i	$0.608016\pi$
$44$	−4.07932	−0.614981
$45$	1.37958	0.205656
$46$	2.08269	0.307076
$47$	−4.59378	−0.670072	−0.335036	−	0.942205i	$-0.608748\pi$
$47$	−4.59378	−0.670072	−0.335036	+	0.942205i	$0.608748\pi$
$48$	3.21083	0.463444
$49$	0	0
$50$	−6.44959	−0.912109
$51$	8.01070	1.12172
$52$	−0.854421	−0.118487
$53$	−11.5137	−1.58153	−0.790763	−	0.612123i	$-0.790316\pi$
$53$	−11.5137	−1.58153	−0.790763	+	0.612123i	$0.790316\pi$
$54$	−2.08269	−0.283418
$55$	−2.40750	−0.324627
$56$	0	0
$57$	5.54843	0.734908
$58$	15.2776	2.00605
$59$	1.18292	0.154003	0.0770015	−	0.997031i	$-0.475465\pi$
$59$	1.18292	0.154003	0.0770015	+	0.997031i	$0.475465\pi$
$60$	−3.22490	−0.416333
$61$	3.66836	0.469685	0.234842	−	0.972033i	$-0.424543\pi$
$61$	3.66836	0.469685	0.234842	+	0.972033i	$0.424543\pi$
$62$	−9.82442	−1.24770
$63$	0	0
$64$	−10.4344	−1.30429
$65$	−0.504254	−0.0625450
$66$	3.63449	0.447374
$67$	10.3449	1.26383	0.631917	−	0.775036i	$-0.282268\pi$
$67$	10.3449	1.26383	0.631917	+	0.775036i	$0.282268\pi$
$68$	−18.7258	−2.27084
$69$	−1.00000	−0.120386
$70$	0	0
$71$	7.95593	0.944195	0.472097	−	0.881546i	$-0.343497\pi$
$71$	7.95593	0.944195	0.472097	+	0.881546i	$0.343497\pi$
$72$	0.703109	0.0828622
$73$	−8.23294	−0.963593	−0.481797	−	0.876283i	$-0.660016\pi$
$73$	−8.23294	−0.963593	−0.481797	+	0.876283i	$0.660016\pi$
$74$	22.1370	2.57337
$75$	3.09676	0.357583
$76$	−12.9700	−1.48776
$77$	0	0
$78$	0.761249	0.0861945
$79$	−16.0076	−1.80099	−0.900495	−	0.434866i	$-0.856796\pi$
$79$	−16.0076	−1.80099	−0.900495	+	0.434866i	$0.856796\pi$
$80$	−4.42961	−0.495245
$81$	1.00000	0.111111
$82$	−14.9526	−1.65123
$83$	1.84532	0.202550	0.101275	−	0.994858i	$-0.467708\pi$
$83$	1.84532	0.202550	0.101275	+	0.994858i	$0.467708\pi$
$84$	0	0
$85$	−11.0514	−1.19869
$86$	−9.09201	−0.980416
$87$	−7.33551	−0.786449
$88$	−1.22699	−0.130798
$89$	18.5430	1.96555	0.982776	−	0.184802i	$-0.0591643\pi$
$89$	18.5430	1.96555	0.982776	+	0.184802i	$0.0591643\pi$
$90$	2.87324	0.302866
$91$	0	0
$92$	2.33760	0.243711
$93$	4.71718	0.489148
$94$	−9.56742	−0.986804
$95$	−7.65451	−0.785336
$96$	8.09339	0.826028
$97$	0.114077	0.0115828	0.00579139	−	0.999983i	$-0.498157\pi$
$97$	0.114077	0.0115828	0.00579139	+	0.999983i	$0.498157\pi$
$98$	0	0
$99$	−1.74509	−0.175388
$100$	−7.23897	−0.723897
$101$	11.7700	1.17116	0.585578	−	0.810616i	$-0.300868\pi$
$101$	11.7700	1.17116	0.585578	+	0.810616i	$0.300868\pi$
$102$	16.6838	1.65194
$103$	8.84057	0.871088	0.435544	−	0.900168i	$-0.356556\pi$
$103$	8.84057	0.871088	0.435544	+	0.900168i	$0.356556\pi$
$104$	−0.256995	−0.0252005
$105$	0	0
$106$	−23.9794	−2.32909
$107$	4.16885	0.403018	0.201509	−	0.979487i	$-0.435415\pi$
$107$	4.16885	0.403018	0.201509	+	0.979487i	$0.435415\pi$
$108$	−2.33760	−0.224935
$109$	−3.39481	−0.325164	−0.162582	−	0.986695i	$-0.551982\pi$
$109$	−3.39481	−0.325164	−0.162582	+	0.986695i	$0.551982\pi$
$110$	−5.01407	−0.478073
$111$	−10.6290	−1.00886
$112$	0	0
$113$	6.25144	0.588086	0.294043	−	0.955792i	$-0.404999\pi$
$113$	6.25144	0.588086	0.294043	+	0.955792i	$0.404999\pi$
$114$	11.5557	1.08229
$115$	1.37958	0.128647
$116$	17.1475	1.59210
$117$	−0.365513	−0.0337916
$118$	2.46365	0.226798
$119$	0	0
$120$	−0.969996	−0.0885481
$121$	−7.95465	−0.723150
$122$	7.64005	0.691697
$123$	7.17945	0.647349
$124$	−11.0269	−0.990241
$125$	−11.1701	−0.999087
$126$	0	0
$127$	−0.350281	−0.0310824	−0.0155412	−	0.999879i	$-0.504947\pi$
$127$	−0.350281	−0.0310824	−0.0155412	+	0.999879i	$0.504947\pi$
$128$	−5.54474	−0.490090
$129$	4.36551	0.384362
$130$	−1.05020	−0.0921090
$131$	−16.1949	−1.41495	−0.707477	−	0.706736i	$-0.750167\pi$
$131$	−16.1949	−1.41495	−0.707477	+	0.706736i	$0.750167\pi$
$132$	4.07932	0.355060
$133$	0	0
$134$	21.5453	1.86123
$135$	−1.37958	−0.118735
$136$	−5.63240	−0.482974
$137$	−1.91047	−0.163223	−0.0816113	−	0.996664i	$-0.526007\pi$
$137$	−1.91047	−0.163223	−0.0816113	+	0.996664i	$0.526007\pi$
$138$	−2.08269	−0.177290
$139$	0.773335	0.0655934	0.0327967	−	0.999462i	$-0.489559\pi$
$139$	0.773335	0.0655934	0.0327967	+	0.999462i	$0.489559\pi$
$140$	0	0
$141$	4.59378	0.386866
$142$	16.5697	1.39050
$143$	0.637853	0.0533400
$144$	−3.21083	−0.267570
$145$	10.1199	0.840414
$146$	−17.1467	−1.41907
$147$	0	0
$148$	24.8464	2.04236
$149$	3.44130	0.281922	0.140961	−	0.990015i	$-0.454981\pi$
$149$	3.44130	0.281922	0.140961	+	0.990015i	$0.454981\pi$
$150$	6.44959	0.526606
$151$	4.19352	0.341263	0.170632	−	0.985335i	$-0.445419\pi$
$151$	4.19352	0.341263	0.170632	+	0.985335i	$0.445419\pi$
$152$	−3.90115	−0.316425
$153$	−8.01070	−0.647627
$154$	0	0
$155$	−6.50773	−0.522713
$156$	0.854421	0.0684084
$157$	16.3308	1.30334	0.651668	−	0.758504i	$-0.274069\pi$
$157$	16.3308	1.30334	0.651668	+	0.758504i	$0.274069\pi$
$158$	−33.3388	−2.65229
$159$	11.5137	0.913094
$160$	−11.1655	−0.882709
$161$	0	0
$162$	2.08269	0.163632
$163$	−9.90148	−0.775544	−0.387772	−	0.921755i	$-0.626755\pi$
$163$	−9.90148	−0.775544	−0.387772	+	0.921755i	$0.626755\pi$
$164$	−16.7827	−1.31051
$165$	2.40750	0.187423
$166$	3.84323	0.298293
$167$	−22.5815	−1.74741	−0.873704	−	0.486458i	$-0.838289\pi$
$167$	−22.5815	−1.74741	−0.873704	+	0.486458i	$0.838289\pi$
$168$	0	0
$169$	−12.8664	−0.989723
$170$	−23.0167	−1.76530
$171$	−5.54843	−0.424299
$172$	−10.2048	−0.778109
$173$	11.2050	0.851903	0.425951	−	0.904746i	$-0.359940\pi$
$173$	11.2050	0.851903	0.425951	+	0.904746i	$0.359940\pi$
$174$	−15.2776	−1.15819
$175$	0	0
$176$	5.60321	0.422358
$177$	−1.18292	−0.0889136
$178$	38.6193	2.89464
$179$	−9.71728	−0.726304	−0.363152	−	0.931730i	$-0.618299\pi$
$179$	−9.71728	−0.726304	−0.363152	+	0.931730i	$0.618299\pi$
$180$	3.22490	0.240370
$181$	−18.8919	−1.40422	−0.702111	−	0.712067i	$-0.747759\pi$
$181$	−18.8919	−1.40422	−0.702111	+	0.712067i	$0.747759\pi$
$182$	0	0
$183$	−3.66836	−0.271173
$184$	0.703109	0.0518339
$185$	14.6636	1.07809
$186$	9.82442	0.720361
$187$	13.9794	1.02228
$188$	−10.7384	−0.783179
$189$	0	0
$190$	−15.9420	−1.15655
$191$	−21.5397	−1.55856	−0.779280	−	0.626676i	$-0.784415\pi$
$191$	−21.5397	−1.55856	−0.779280	+	0.626676i	$0.784415\pi$
$192$	10.4344	0.753035
$193$	−13.6651	−0.983633	−0.491816	−	0.870699i	$-0.663667\pi$
$193$	−13.6651	−0.983633	−0.491816	+	0.870699i	$0.663667\pi$
$194$	0.237587	0.0170578
$195$	0.504254	0.0361104
$196$	0	0
$197$	10.9686	0.781481	0.390741	−	0.920501i	$-0.372219\pi$
$197$	10.9686	0.781481	0.390741	+	0.920501i	$0.372219\pi$
$198$	−3.63449	−0.258292
$199$	−5.22607	−0.370467	−0.185233	−	0.982695i	$-0.559304\pi$
$199$	−5.22607	−0.370467	−0.185233	+	0.982695i	$0.559304\pi$
$200$	−2.17736	−0.153963
$201$	−10.3449	−0.729675
$202$	24.5132	1.72474
$203$	0	0
$204$	18.7258	1.31107
$205$	−9.90463	−0.691769
$206$	18.4122	1.28284
$207$	1.00000	0.0695048
$208$	1.17360	0.0813746
$209$	9.68253	0.669755
$210$	0	0
$211$	−2.61716	−0.180173	−0.0900863	−	0.995934i	$-0.528714\pi$
$211$	−2.61716	−0.180173	−0.0900863	+	0.995934i	$0.528714\pi$
$212$	−26.9143	−1.84848
$213$	−7.95593	−0.545131
$214$	8.68242	0.593518
$215$	−6.02258	−0.410736
$216$	−0.703109	−0.0478405
$217$	0	0
$218$	−7.07034	−0.478864
$219$	8.23294	0.556331
$220$	−5.62776	−0.379423
$221$	2.92801	0.196959
$222$	−22.1370	−1.48574
$223$	1.45526	0.0974514	0.0487257	−	0.998812i	$-0.484484\pi$
$223$	1.45526	0.0974514	0.0487257	+	0.998812i	$0.484484\pi$
$224$	0	0
$225$	−3.09676	−0.206451
$226$	13.0198	0.866064
$227$	−4.14568	−0.275159	−0.137579	−	0.990491i	$-0.543932\pi$
$227$	−4.14568	−0.275159	−0.137579	+	0.990491i	$0.543932\pi$
$228$	12.9700	0.858959
$229$	1.14905	0.0759314	0.0379657	−	0.999279i	$-0.487912\pi$
$229$	1.14905	0.0759314	0.0379657	+	0.999279i	$0.487912\pi$
$230$	2.87324	0.189456
$231$	0	0
$232$	5.15766	0.338617
$233$	−14.6977	−0.962875	−0.481438	−	0.876480i	$-0.659885\pi$
$233$	−14.6977	−0.962875	−0.481438	+	0.876480i	$0.659885\pi$
$234$	−0.761249	−0.0497644
$235$	−6.33749	−0.413412
$236$	2.76519	0.179998
$237$	16.0076	1.03980
$238$	0	0
$239$	−0.120104	−0.00776889	−0.00388445	−	0.999992i	$-0.501236\pi$
$239$	−0.120104	−0.00776889	−0.00388445	+	0.999992i	$0.501236\pi$
$240$	4.42961	0.285930
$241$	−2.45851	−0.158367	−0.0791833	−	0.996860i	$-0.525231\pi$
$241$	−2.45851	−0.158367	−0.0791833	+	0.996860i	$0.525231\pi$
$242$	−16.5671	−1.06497
$243$	−1.00000	−0.0641500
$244$	8.57514	0.548967
$245$	0	0
$246$	14.9526	0.953341
$247$	2.02802	0.129040
$248$	−3.31669	−0.210610
$249$	−1.84532	−0.116943
$250$	−23.2639	−1.47134
$251$	−19.9374	−1.25844	−0.629220	−	0.777227i	$-0.716626\pi$
$251$	−19.9374	−1.25844	−0.629220	+	0.777227i	$0.716626\pi$
$252$	0	0
$253$	−1.74509	−0.109713
$254$	−0.729527	−0.0457746
$255$	11.0514	0.692066
$256$	9.32074	0.582546
$257$	−10.3054	−0.642833	−0.321416	−	0.946938i	$-0.604159\pi$
$257$	−10.3054	−0.642833	−0.321416	+	0.946938i	$0.604159\pi$
$258$	9.09201	0.566044
$259$	0	0
$260$	−1.17874	−0.0731025
$261$	7.33551	0.454057
$262$	−33.7290	−2.08378
$263$	−4.19213	−0.258498	−0.129249	−	0.991612i	$-0.541257\pi$
$263$	−4.19213	−0.258498	−0.129249	+	0.991612i	$0.541257\pi$
$264$	1.22699	0.0755161
$265$	−15.8840	−0.975749
$266$	0	0
$267$	−18.5430	−1.13481
$268$	24.1823	1.47717
$269$	19.0867	1.16373	0.581867	−	0.813284i	$-0.302322\pi$
$269$	19.0867	1.16373	0.581867	+	0.813284i	$0.302322\pi$
$270$	−2.87324	−0.174860
$271$	18.9879	1.15343	0.576717	−	0.816944i	$-0.304333\pi$
$271$	18.9879	1.15343	0.576717	+	0.816944i	$0.304333\pi$
$272$	25.7210	1.55957
$273$	0	0
$274$	−3.97892	−0.240375
$275$	5.40413	0.325881
$276$	−2.33760	−0.140707
$277$	−15.3239	−0.920725	−0.460363	−	0.887731i	$-0.652281\pi$
$277$	−15.3239	−0.920725	−0.460363	+	0.887731i	$0.652281\pi$
$278$	1.61062	0.0965983
$279$	−4.71718	−0.282410
$280$	0	0
$281$	22.0705	1.31662	0.658308	−	0.752749i	$-0.271272\pi$
$281$	22.0705	1.31662	0.658308	+	0.752749i	$0.271272\pi$
$282$	9.56742	0.569732
$283$	30.1697	1.79340	0.896701	−	0.442638i	$-0.145957\pi$
$283$	30.1697	1.79340	0.896701	+	0.442638i	$0.145957\pi$
$284$	18.5978	1.10357
$285$	7.65451	0.453414
$286$	1.32845	0.0785529
$287$	0	0
$288$	−8.09339	−0.476908
$289$	47.1713	2.77479
$290$	21.0767	1.23766
$291$	−0.114077	−0.00668732
$292$	−19.2453	−1.12625
$293$	−5.23666	−0.305929	−0.152965	−	0.988232i	$-0.548882\pi$
$293$	−5.23666	−0.305929	−0.152965	+	0.988232i	$0.548882\pi$
$294$	0	0
$295$	1.63193	0.0950148
$296$	7.47337	0.434381
$297$	1.74509	0.101261
$298$	7.16716	0.415182
$299$	−0.365513	−0.0211381
$300$	7.23897	0.417942
$301$	0	0
$302$	8.73379	0.502573
$303$	−11.7700	−0.676167
$304$	17.8151	1.02177
$305$	5.06079	0.289780
$306$	−16.6838	−0.953750
$307$	−19.1642	−1.09376	−0.546880	−	0.837211i	$-0.684185\pi$
$307$	−19.1642	−1.09376	−0.546880	+	0.837211i	$0.684185\pi$
$308$	0	0
$309$	−8.84057	−0.502923
$310$	−13.5536	−0.769791
$311$	−22.5347	−1.27783	−0.638913	−	0.769279i	$-0.720615\pi$
$311$	−22.5347	−1.27783	−0.638913	+	0.769279i	$0.720615\pi$
$312$	0.256995	0.0145495
$313$	15.3714	0.868840	0.434420	−	0.900710i	$-0.356953\pi$
$313$	15.3714	0.868840	0.434420	+	0.900710i	$0.356953\pi$
$314$	34.0119	1.91940
$315$	0	0
$316$	−37.4192	−2.10500
$317$	19.7359	1.10848	0.554240	−	0.832357i	$-0.313009\pi$
$317$	19.7359	1.10848	0.554240	+	0.832357i	$0.313009\pi$
$318$	23.9794	1.34470
$319$	−12.8011	−0.716727
$320$	−14.3950	−0.804707
$321$	−4.16885	−0.232683
$322$	0	0
$323$	44.4468	2.47309
$324$	2.33760	0.129866
$325$	1.13190	0.0627867
$326$	−20.6217	−1.14213
$327$	3.39481	0.187734
$328$	−5.04794	−0.278726
$329$	0	0
$330$	5.01407	0.276015
$331$	28.1123	1.54519	0.772596	−	0.634898i	$-0.218958\pi$
$331$	28.1123	1.54519	0.772596	+	0.634898i	$0.218958\pi$
$332$	4.31362	0.236741
$333$	10.6290	0.582467
$334$	−47.0302	−2.57338
$335$	14.2717	0.779744
$336$	0	0
$337$	−1.06840	−0.0581996	−0.0290998	−	0.999577i	$-0.509264\pi$
$337$	−1.06840	−0.0581996	−0.0290998	+	0.999577i	$0.509264\pi$
$338$	−26.7967	−1.45755
$339$	−6.25144	−0.339531
$340$	−25.8337	−1.40103
$341$	8.23191	0.445783
$342$	−11.5557	−0.624859
$343$	0	0
$344$	−3.06943	−0.165493
$345$	−1.37958	−0.0742741
$346$	23.3366	1.25458
$347$	34.7913	1.86769	0.933847	−	0.357674i	$-0.116430\pi$
$347$	34.7913	1.86769	0.933847	+	0.357674i	$0.116430\pi$
$348$	−17.1475	−0.919200
$349$	27.2584	1.45911	0.729553	−	0.683924i	$-0.239728\pi$
$349$	27.2584	1.45911	0.729553	+	0.683924i	$0.239728\pi$
$350$	0	0
$351$	0.365513	0.0195096
$352$	14.1237	0.752797
$353$	3.56859	0.189937	0.0949685	−	0.995480i	$-0.469725\pi$
$353$	3.56859	0.189937	0.0949685	+	0.995480i	$0.469725\pi$
$354$	−2.46365	−0.130942
$355$	10.9758	0.582537
$356$	43.3460	2.29733
$357$	0	0
$358$	−20.2381	−1.06962
$359$	−9.20850	−0.486006	−0.243003	−	0.970026i	$-0.578132\pi$
$359$	−9.20850	−0.486006	−0.243003	+	0.970026i	$0.578132\pi$
$360$	0.969996	0.0511233
$361$	11.7851	0.620268
$362$	−39.3459	−2.06798
$363$	7.95465	0.417511
$364$	0	0
$365$	−11.3580	−0.594505
$366$	−7.64005	−0.399352
$367$	18.2298	0.951589	0.475795	−	0.879556i	$-0.342161\pi$
$367$	18.2298	0.951589	0.475795	+	0.879556i	$0.342161\pi$
$368$	−3.21083	−0.167376
$369$	−7.17945	−0.373747
$370$	30.5397	1.58769
$371$	0	0
$372$	11.0269	0.571716
$373$	−16.0258	−0.829782	−0.414891	−	0.909871i	$-0.636180\pi$
$373$	−16.0258	−0.829782	−0.414891	+	0.909871i	$0.636180\pi$
$374$	29.1148	1.50549
$375$	11.1701	0.576823
$376$	−3.22993	−0.166571
$377$	−2.68122	−0.138090
$378$	0	0
$379$	8.36328	0.429593	0.214796	−	0.976659i	$-0.431091\pi$
$379$	8.36328	0.429593	0.214796	+	0.976659i	$0.431091\pi$
$380$	−17.8932	−0.917899
$381$	0.350281	0.0179455
$382$	−44.8606	−2.29527
$383$	20.5627	1.05070	0.525352	−	0.850885i	$-0.323934\pi$
$383$	20.5627	1.05070	0.525352	+	0.850885i	$0.323934\pi$
$384$	5.54474	0.282954
$385$	0	0
$386$	−28.4601	−1.44858
$387$	−4.36551	−0.221911
$388$	0.266667	0.0135379
$389$	4.34305	0.220201	0.110101	−	0.993920i	$-0.464883\pi$
$389$	4.34305	0.220201	0.110101	+	0.993920i	$0.464883\pi$
$390$	1.05020	0.0531792
$391$	−8.01070	−0.405119
$392$	0	0
$393$	16.1949	0.816925
$394$	22.8442	1.15088
$395$	−22.0837	−1.11115
$396$	−4.07932	−0.204994
$397$	−29.1046	−1.46072	−0.730359	−	0.683064i	$-0.760647\pi$
$397$	−29.1046	−1.46072	−0.730359	+	0.683064i	$0.760647\pi$
$398$	−10.8843	−0.545580
$399$	0	0
$400$	9.94318	0.497159
$401$	−23.5986	−1.17846	−0.589228	−	0.807967i	$-0.700568\pi$
$401$	−23.5986	−1.17846	−0.589228	+	0.807967i	$0.700568\pi$
$402$	−21.5453	−1.07458
$403$	1.72419	0.0858879
$404$	27.5134	1.36884
$405$	1.37958	0.0685519
$406$	0	0
$407$	−18.5487	−0.919423
$408$	5.63240	0.278845
$409$	−3.99310	−0.197446	−0.0987229	−	0.995115i	$-0.531476\pi$
$409$	−3.99310	−0.197446	−0.0987229	+	0.995115i	$0.531476\pi$
$410$	−20.6283	−1.01876
$411$	1.91047	0.0942367
$412$	20.6657	1.01813
$413$	0	0
$414$	2.08269	0.102359
$415$	2.54577	0.124967
$416$	2.95824	0.145039
$417$	−0.773335	−0.0378704
$418$	20.1657	0.986337
$419$	35.3033	1.72468	0.862341	−	0.506329i	$-0.168998\pi$
$419$	35.3033	1.72468	0.862341	+	0.506329i	$0.168998\pi$
$420$	0	0
$421$	−0.0815265	−0.00397336	−0.00198668	−	0.999998i	$-0.500632\pi$
$421$	−0.0815265	−0.00397336	−0.00198668	+	0.999998i	$0.500632\pi$
$422$	−5.45073	−0.265337
$423$	−4.59378	−0.223357
$424$	−8.09537	−0.393146
$425$	24.8072	1.20333
$426$	−16.5697	−0.802806
$427$	0	0
$428$	9.74509	0.471047
$429$	−0.637853	−0.0307959
$430$	−12.5432	−0.604885
$431$	−22.5582	−1.08659	−0.543295	−	0.839542i	$-0.682824\pi$
$431$	−22.5582	−1.08659	−0.543295	+	0.839542i	$0.682824\pi$
$432$	3.21083	0.154481
$433$	13.3760	0.642808	0.321404	−	0.946942i	$-0.395845\pi$
$433$	13.3760	0.642808	0.321404	+	0.946942i	$0.395845\pi$
$434$	0	0
$435$	−10.1199	−0.485213
$436$	−7.93570	−0.380051
$437$	−5.54843	−0.265417
$438$	17.1467	0.819299
$439$	−35.0205	−1.67143	−0.835717	−	0.549160i	$-0.814948\pi$
$439$	−35.0205	−1.67143	−0.835717	+	0.549160i	$0.814948\pi$
$440$	−1.69273	−0.0806979
$441$	0	0
$442$	6.09814	0.290059
$443$	30.8687	1.46662	0.733308	−	0.679896i	$-0.237975\pi$
$443$	30.8687	1.46662	0.733308	+	0.679896i	$0.237975\pi$
$444$	−24.8464	−1.17916
$445$	25.5815	1.21268
$446$	3.03086	0.143515
$447$	−3.44130	−0.162768
$448$	0	0
$449$	24.8630	1.17336	0.586680	−	0.809819i	$-0.300435\pi$
$449$	24.8630	1.17336	0.586680	+	0.809819i	$0.300435\pi$
$450$	−6.44959	−0.304036
$451$	12.5288	0.589958
$452$	14.6133	0.687353
$453$	−4.19352	−0.197029
$454$	−8.63418	−0.405222
$455$	0	0
$456$	3.90115	0.182688
$457$	6.09793	0.285249	0.142625	−	0.989777i	$-0.454446\pi$
$457$	6.09793	0.285249	0.142625	+	0.989777i	$0.454446\pi$
$458$	2.39312	0.111823
$459$	8.01070	0.373908
$460$	3.22490	0.150362
$461$	−11.7886	−0.549050	−0.274525	−	0.961580i	$-0.588521\pi$
$461$	−11.7886	−0.549050	−0.274525	+	0.961580i	$0.588521\pi$
$462$	0	0
$463$	−4.16341	−0.193490	−0.0967449	−	0.995309i	$-0.530843\pi$
$463$	−4.16341	−0.193490	−0.0967449	+	0.995309i	$0.530843\pi$
$464$	−23.5531	−1.09343
$465$	6.50773	0.301789
$466$	−30.6107	−1.41801
$467$	9.11224	0.421664	0.210832	−	0.977522i	$-0.432383\pi$
$467$	9.11224	0.421664	0.210832	+	0.977522i	$0.432383\pi$
$468$	−0.854421	−0.0394956
$469$	0	0
$470$	−13.1990	−0.608826
$471$	−16.3308	−0.752482
$472$	0.831721	0.0382831
$473$	7.61823	0.350286
$474$	33.3388	1.53130
$475$	17.1821	0.788371
$476$	0	0
$477$	−11.5137	−0.527175
$478$	−0.250140	−0.0114411
$479$	25.4893	1.16463	0.582317	−	0.812962i	$-0.302146\pi$
$479$	25.4893	1.16463	0.582317	+	0.812962i	$0.302146\pi$
$480$	11.1655	0.509632
$481$	−3.88505	−0.177143
$482$	−5.12032	−0.233224
$483$	0	0
$484$	−18.5948	−0.845217
$485$	0.157379	0.00714620
$486$	−2.08269	−0.0944727
$487$	−23.2693	−1.05443	−0.527217	−	0.849731i	$-0.676764\pi$
$487$	−23.2693	−1.05443	−0.527217	+	0.849731i	$0.676764\pi$
$488$	2.57926	0.116757
$489$	9.90148	0.447760
$490$	0	0
$491$	12.7993	0.577623	0.288811	−	0.957386i	$-0.406740\pi$
$491$	12.7993	0.577623	0.288811	+	0.957386i	$0.406740\pi$
$492$	16.7827	0.756620
$493$	−58.7626	−2.64653
$494$	4.22374	0.190035
$495$	−2.40750	−0.108209
$496$	15.1461	0.680079
$497$	0	0
$498$	−3.84323	−0.172219
$499$	−33.2057	−1.48649	−0.743245	−	0.669019i	$-0.766714\pi$
$499$	−33.2057	−1.48649	−0.743245	+	0.669019i	$0.766714\pi$
$500$	−26.1113	−1.16773
$501$	22.5815	1.00887
$502$	−41.5235	−1.85328
$503$	−9.84758	−0.439082	−0.219541	−	0.975603i	$-0.570456\pi$
$503$	−9.84758	−0.439082	−0.219541	+	0.975603i	$0.570456\pi$
$504$	0	0
$505$	16.2376	0.722565
$506$	−3.63449	−0.161573
$507$	12.8664	0.571417
$508$	−0.818817	−0.0363291
$509$	4.59796	0.203801	0.101900	−	0.994795i	$-0.467508\pi$
$509$	4.59796	0.203801	0.101900	+	0.994795i	$0.467508\pi$
$510$	23.0167	1.01919
$511$	0	0
$512$	30.5017	1.34800
$513$	5.54843	0.244969
$514$	−21.4629	−0.946689
$515$	12.1963	0.537432
$516$	10.2048	0.449242
$517$	8.01658	0.352569
$518$	0	0
$519$	−11.2050	−0.491846
$520$	−0.354546	−0.0155479
$521$	25.9656	1.13757	0.568786	−	0.822485i	$-0.307413\pi$
$521$	25.9656	1.13757	0.568786	+	0.822485i	$0.307413\pi$
$522$	15.2776	0.668682
$523$	7.04359	0.307995	0.153997	−	0.988071i	$-0.450785\pi$
$523$	7.04359	0.307995	0.153997	+	0.988071i	$0.450785\pi$
$524$	−37.8571	−1.65380
$525$	0	0
$526$	−8.73091	−0.380686
$527$	37.7879	1.64607
$528$	−5.60321	−0.243848
$529$	1.00000	0.0434783
$530$	−33.0815	−1.43697
$531$	1.18292	0.0513343
$532$	0	0
$533$	2.62418	0.113666
$534$	−38.6193	−1.67122
$535$	5.75127	0.248649
$536$	7.27362	0.314172
$537$	9.71728	0.419332
$538$	39.7516	1.71381
$539$	0	0
$540$	−3.22490	−0.138778
$541$	−34.2924	−1.47434	−0.737172	−	0.675705i	$-0.763839\pi$
$541$	−34.2924	−1.47434	−0.737172	+	0.675705i	$0.763839\pi$
$542$	39.5460	1.69864
$543$	18.8919	0.810728
$544$	64.8337	2.77972
$545$	−4.68342	−0.200615
$546$	0	0
$547$	−20.7840	−0.888660	−0.444330	−	0.895863i	$-0.646558\pi$
$547$	−20.7840	−0.888660	−0.444330	+	0.895863i	$0.646558\pi$
$548$	−4.46591	−0.190774
$549$	3.66836	0.156562
$550$	11.2551	0.479920
$551$	−40.7006	−1.73390
$552$	−0.703109	−0.0299263
$553$	0	0
$554$	−31.9150	−1.35594
$555$	−14.6636	−0.622435
$556$	1.80774	0.0766654
$557$	−31.6707	−1.34193	−0.670965	−	0.741489i	$-0.734120\pi$
$557$	−31.6707	−1.34193	−0.670965	+	0.741489i	$0.734120\pi$
$558$	−9.82442	−0.415901
$559$	1.59565	0.0674888
$560$	0	0
$561$	−13.9794	−0.590212
$562$	45.9660	1.93896
$563$	−39.2249	−1.65313	−0.826566	−	0.562839i	$-0.809709\pi$
$563$	−39.2249	−1.65313	−0.826566	+	0.562839i	$0.809709\pi$
$564$	10.7384	0.452169
$565$	8.62436	0.362829
$566$	62.8341	2.64111
$567$	0	0
$568$	5.59389	0.234714
$569$	−0.980372	−0.0410993	−0.0205497	−	0.999789i	$-0.506542\pi$
$569$	−0.980372	−0.0410993	−0.0205497	+	0.999789i	$0.506542\pi$
$570$	15.9420	0.667735
$571$	7.55336	0.316098	0.158049	−	0.987431i	$-0.449480\pi$
$571$	7.55336	0.316098	0.158049	+	0.987431i	$0.449480\pi$
$572$	1.49104	0.0623437
$573$	21.5397	0.899835
$574$	0	0
$575$	−3.09676	−0.129144
$576$	−10.4344	−0.434765
$577$	38.9185	1.62020	0.810098	−	0.586294i	$-0.199414\pi$
$577$	38.9185	1.62020	0.810098	+	0.586294i	$0.199414\pi$
$578$	98.2433	4.08638
$579$	13.6651	0.567901
$580$	23.6563	0.982274
$581$	0	0
$582$	−0.237587	−0.00984832
$583$	20.0924	0.832144
$584$	−5.78866	−0.239536
$585$	−0.504254	−0.0208483
$586$	−10.9063	−0.450537
$587$	−10.3598	−0.427595	−0.213798	−	0.976878i	$-0.568583\pi$
$587$	−10.3598	−0.427595	−0.213798	+	0.976878i	$0.568583\pi$
$588$	0	0
$589$	26.1729	1.07844
$590$	3.39881	0.139927
$591$	−10.9686	−0.451188
$592$	−34.1281	−1.40266
$593$	26.0558	1.06998	0.534992	−	0.844857i	$-0.320314\pi$
$593$	26.0558	1.06998	0.534992	+	0.844857i	$0.320314\pi$
$594$	3.63449	0.149125
$595$	0	0
$596$	8.04437	0.329510
$597$	5.22607	0.213889
$598$	−0.761249	−0.0311298
$599$	−24.6036	−1.00528	−0.502639	−	0.864497i	$-0.667637\pi$
$599$	−24.6036	−1.00528	−0.502639	+	0.864497i	$0.667637\pi$
$600$	2.17736	0.0888903
$601$	−36.1703	−1.47542	−0.737708	−	0.675120i	$-0.764092\pi$
$601$	−36.1703	−1.47542	−0.737708	+	0.675120i	$0.764092\pi$
$602$	0	0
$603$	10.3449	0.421278
$604$	9.80275	0.398868
$605$	−10.9741	−0.446160
$606$	−24.5132	−0.995780
$607$	−38.0197	−1.54317	−0.771585	−	0.636126i	$-0.780536\pi$
$607$	−38.0197	−1.54317	−0.771585	+	0.636126i	$0.780536\pi$
$608$	44.9056	1.82116
$609$	0	0
$610$	10.5401	0.426755
$611$	1.67908	0.0679285
$612$	−18.7258	−0.756945
$613$	−4.33753	−0.175191	−0.0875956	−	0.996156i	$-0.527918\pi$
$613$	−4.33753	−0.175191	−0.0875956	+	0.996156i	$0.527918\pi$
$614$	−39.9131	−1.61076
$615$	9.90463	0.399393
$616$	0	0
$617$	−21.4430	−0.863263	−0.431631	−	0.902050i	$-0.642062\pi$
$617$	−21.4430	−0.863263	−0.431631	+	0.902050i	$0.642062\pi$
$618$	−18.4122	−0.740646
$619$	−23.5895	−0.948142	−0.474071	−	0.880487i	$-0.657216\pi$
$619$	−23.5895	−0.948142	−0.474071	+	0.880487i	$0.657216\pi$
$620$	−15.2124	−0.610946
$621$	−1.00000	−0.0401286
$622$	−46.9328	−1.88183
$623$	0	0
$624$	−1.17360	−0.0469816
$625$	0.0736968	0.00294787
$626$	32.0138	1.27953
$627$	−9.68253	−0.386683
$628$	38.1747	1.52334
$629$	−85.1460	−3.39499
$630$	0	0
$631$	−28.1824	−1.12192	−0.560962	−	0.827841i	$-0.689569\pi$
$631$	−28.1824	−1.12192	−0.560962	+	0.827841i	$0.689569\pi$
$632$	−11.2551	−0.447702
$633$	2.61716	0.104023
$634$	41.1038	1.63244
$635$	−0.483241	−0.0191768
$636$	26.9143	1.06722
$637$	0	0
$638$	−26.6608	−1.05551
$639$	7.95593	0.314732
$640$	−7.64942	−0.302370
$641$	21.1727	0.836271	0.418135	−	0.908385i	$-0.362684\pi$
$641$	21.1727	0.836271	0.418135	+	0.908385i	$0.362684\pi$
$642$	−8.68242	−0.342668
$643$	−11.6614	−0.459881	−0.229941	−	0.973205i	$-0.573853\pi$
$643$	−11.6614	−0.459881	−0.229941	+	0.973205i	$0.573853\pi$
$644$	0	0
$645$	6.02258	0.237139
$646$	92.5690	3.64208
$647$	−33.3111	−1.30959	−0.654797	−	0.755805i	$-0.727246\pi$
$647$	−33.3111	−1.30959	−0.654797	+	0.755805i	$0.727246\pi$
$648$	0.703109	0.0276207
$649$	−2.06430	−0.0810310
$650$	2.35740	0.0924650
$651$	0	0
$652$	−23.1457	−0.906454
$653$	15.5085	0.606893	0.303447	−	0.952848i	$-0.401863\pi$
$653$	15.5085	0.606893	0.303447	+	0.952848i	$0.401863\pi$
$654$	7.07034	0.276472
$655$	−22.3422	−0.872981
$656$	23.0520	0.900030
$657$	−8.23294	−0.321198
$658$	0	0
$659$	−45.9044	−1.78818	−0.894091	−	0.447886i	$-0.852177\pi$
$659$	−45.9044	−1.78818	−0.894091	+	0.447886i	$0.852177\pi$
$660$	5.62776	0.219060
$661$	−21.2557	−0.826749	−0.413375	−	0.910561i	$-0.635650\pi$
$661$	−21.2557	−0.826749	−0.413375	+	0.910561i	$0.635650\pi$
$662$	58.5492	2.27558
$663$	−2.92801	−0.113715
$664$	1.29746	0.0503513
$665$	0	0
$666$	22.1370	0.857791
$667$	7.33551	0.284032
$668$	−52.7864	−2.04237
$669$	−1.45526	−0.0562636
$670$	29.7235	1.14832
$671$	−6.40162	−0.247132
$672$	0	0
$673$	−3.73895	−0.144126	−0.0720630	−	0.997400i	$-0.522958\pi$
$673$	−3.73895	−0.144126	−0.0720630	+	0.997400i	$0.522958\pi$
$674$	−2.22515	−0.0857096
$675$	3.09676	0.119194
$676$	−30.0765	−1.15679
$677$	46.0823	1.77109	0.885543	−	0.464558i	$-0.153787\pi$
$677$	46.0823	1.77109	0.885543	+	0.464558i	$0.153787\pi$
$678$	−13.0198	−0.500022
$679$	0	0
$680$	−7.77035	−0.297979
$681$	4.14568	0.158863
$682$	17.1445	0.656498
$683$	3.37293	0.129062	0.0645308	−	0.997916i	$-0.479445\pi$
$683$	3.37293	0.129062	0.0645308	+	0.997916i	$0.479445\pi$
$684$	−12.9700	−0.495920
$685$	−2.63565	−0.100703
$686$	0	0
$687$	−1.14905	−0.0438390
$688$	14.0169	0.534391
$689$	4.20839	0.160327
$690$	−2.87324	−0.109382
$691$	45.1331	1.71694	0.858471	−	0.512862i	$-0.171415\pi$
$691$	45.1331	1.71694	0.858471	+	0.512862i	$0.171415\pi$
$692$	26.1928	0.995702
$693$	0	0
$694$	72.4594	2.75052
$695$	1.06688	0.0404690
$696$	−5.15766	−0.195501
$697$	57.5124	2.17844
$698$	56.7707	2.14880
$699$	14.6977	0.555916
$700$	0	0
$701$	13.9074	0.525277	0.262638	−	0.964894i	$-0.415407\pi$
$701$	13.9074	0.525277	0.262638	+	0.964894i	$0.415407\pi$
$702$	0.761249	0.0287315
$703$	−58.9745	−2.22426
$704$	18.2089	0.686274
$705$	6.33749	0.238684
$706$	7.43227	0.279717
$707$	0	0
$708$	−2.76519	−0.103922
$709$	−31.3156	−1.17608	−0.588042	−	0.808831i	$-0.700101\pi$
$709$	−31.3156	−1.17608	−0.588042	+	0.808831i	$0.700101\pi$
$710$	22.8593	0.857893
$711$	−16.0076	−0.600330
$712$	13.0377	0.488610
$713$	−4.71718	−0.176660
$714$	0	0
$715$	0.879970	0.0329090
$716$	−22.7151	−0.848903
$717$	0.120104	0.00448537
$718$	−19.1784	−0.715733
$719$	12.2928	0.458442	0.229221	−	0.973374i	$-0.426382\pi$
$719$	12.2928	0.458442	0.229221	+	0.973374i	$0.426382\pi$
$720$	−4.42961	−0.165082
$721$	0	0
$722$	24.5447	0.913459
$723$	2.45851	0.0914330
$724$	−44.1616	−1.64125
$725$	−22.7163	−0.843662
$726$	16.5671	0.614862
$727$	31.8513	1.18130	0.590649	−	0.806928i	$-0.298872\pi$
$727$	31.8513	1.18130	0.590649	+	0.806928i	$0.298872\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−23.6552	−0.875519
$731$	34.9708	1.29344
$732$	−8.57514	−0.316946
$733$	12.7096	0.469441	0.234720	−	0.972063i	$-0.424583\pi$
$733$	12.7096	0.469441	0.234720	+	0.972063i	$0.424583\pi$
$734$	37.9671	1.40139
$735$	0	0
$736$	−8.09339	−0.298326
$737$	−18.0529	−0.664986
$738$	−14.9526	−0.550411
$739$	−39.5845	−1.45614	−0.728070	−	0.685503i	$-0.759582\pi$
$739$	−39.5845	−1.45614	−0.728070	+	0.685503i	$0.759582\pi$
$740$	34.2776	1.26007
$741$	−2.02802	−0.0745012
$742$	0	0
$743$	17.6230	0.646525	0.323263	−	0.946309i	$-0.395220\pi$
$743$	17.6230	0.646525	0.323263	+	0.946309i	$0.395220\pi$
$744$	3.31669	0.121596
$745$	4.74755	0.173937
$746$	−33.3767	−1.22201
$747$	1.84532	0.0675168
$748$	32.6782	1.19484
$749$	0	0
$750$	23.2639	0.849478
$751$	10.3009	0.375887	0.187943	−	0.982180i	$-0.439818\pi$
$751$	10.3009	0.375887	0.187943	+	0.982180i	$0.439818\pi$
$752$	14.7499	0.537873
$753$	19.9374	0.726561
$754$	−5.58415	−0.203363
$755$	5.78529	0.210548
$756$	0	0
$757$	27.6978	1.00669	0.503346	−	0.864085i	$-0.332102\pi$
$757$	27.6978	1.00669	0.503346	+	0.864085i	$0.332102\pi$
$758$	17.4181	0.632655
$759$	1.74509	0.0633429
$760$	−5.38196	−0.195224
$761$	26.1757	0.948867	0.474434	−	0.880291i	$-0.342653\pi$
$761$	26.1757	0.948867	0.474434	+	0.880291i	$0.342653\pi$
$762$	0.729527	0.0264280
$763$	0	0
$764$	−50.3512	−1.82164
$765$	−11.0514	−0.399564
$766$	42.8257	1.54735
$767$	−0.432372	−0.0156120
$768$	−9.32074	−0.336333
$769$	−27.2690	−0.983344	−0.491672	−	0.870780i	$-0.663614\pi$
$769$	−27.2690	−0.983344	−0.491672	+	0.870780i	$0.663614\pi$
$770$	0	0
$771$	10.3054	0.371140
$772$	−31.9434	−1.14967
$773$	−33.6019	−1.20858	−0.604288	−	0.796766i	$-0.706542\pi$
$773$	−33.6019	−1.20858	−0.604288	+	0.796766i	$0.706542\pi$
$774$	−9.09201	−0.326805
$775$	14.6080	0.524733
$776$	0.0802088	0.00287933
$777$	0	0
$778$	9.04523	0.324287
$779$	39.8347	1.42723
$780$	1.17874	0.0422058
$781$	−13.8838	−0.496803
$782$	−16.6838	−0.596612
$783$	−7.33551	−0.262150
$784$	0	0
$785$	22.5296	0.804116
$786$	33.7290	1.20307
$787$	−15.5176	−0.553142	−0.276571	−	0.960993i	$-0.589198\pi$
$787$	−15.5176	−0.553142	−0.276571	+	0.960993i	$0.589198\pi$
$788$	25.6402	0.913394
$789$	4.19213	0.149244
$790$	−45.9935	−1.63638
$791$	0	0
$792$	−1.22699	−0.0435992
$793$	−1.34083	−0.0476143
$794$	−60.6158	−2.15118
$795$	15.8840	0.563349
$796$	−12.2165	−0.433001
$797$	33.1816	1.17535	0.587677	−	0.809096i	$-0.300043\pi$
$797$	33.1816	1.17535	0.587677	+	0.809096i	$0.300043\pi$
$798$	0	0
$799$	36.7994	1.30187
$800$	25.0633	0.886121
$801$	18.5430	0.655184
$802$	−49.1485	−1.73549
$803$	14.3673	0.507009
$804$	−24.1823	−0.852843
$805$	0	0
$806$	3.59095	0.126486
$807$	−19.0867	−0.671882
$808$	8.27557	0.291134
$809$	41.3047	1.45220	0.726098	−	0.687591i	$-0.241332\pi$
$809$	41.3047	1.45220	0.726098	+	0.687591i	$0.241332\pi$
$810$	2.87324	0.100955
$811$	−32.7530	−1.15011	−0.575057	−	0.818113i	$-0.695020\pi$
$811$	−32.7530	−1.15011	−0.575057	+	0.818113i	$0.695020\pi$
$812$	0	0
$813$	−18.9879	−0.665936
$814$	−38.6311	−1.35402
$815$	−13.6599	−0.478485
$816$	−25.7210	−0.900417
$817$	24.2217	0.847412
$818$	−8.31638	−0.290775
$819$	0	0
$820$	−23.1530	−0.808539
$821$	51.7893	1.80746	0.903729	−	0.428104i	$-0.140818\pi$
$821$	51.7893	1.80746	0.903729	+	0.428104i	$0.140818\pi$
$822$	3.97892	0.138781
$823$	−21.3170	−0.743063	−0.371532	−	0.928420i	$-0.621167\pi$
$823$	−21.3170	−0.743063	−0.371532	+	0.928420i	$0.621167\pi$
$824$	6.21589	0.216541
$825$	−5.40413	−0.188148
$826$	0	0
$827$	−47.3655	−1.64706	−0.823530	−	0.567272i	$-0.807999\pi$
$827$	−47.3655	−1.64706	−0.823530	+	0.567272i	$0.807999\pi$
$828$	2.33760	0.0812371
$829$	14.8311	0.515106	0.257553	−	0.966264i	$-0.417084\pi$
$829$	14.8311	0.515106	0.257553	+	0.966264i	$0.417084\pi$
$830$	5.30205	0.184037
$831$	15.3239	0.531581
$832$	3.81389	0.132223
$833$	0	0
$834$	−1.61062	−0.0557711
$835$	−31.1530	−1.07809
$836$	22.6338	0.782808
$837$	4.71718	0.163049
$838$	73.5259	2.53991
$839$	−28.3406	−0.978427	−0.489213	−	0.872164i	$-0.662716\pi$
$839$	−28.3406	−0.978427	−0.489213	+	0.872164i	$0.662716\pi$
$840$	0	0
$841$	24.8097	0.855506
$842$	−0.169794	−0.00585150
$843$	−22.0705	−0.760149
$844$	−6.11786	−0.210586
$845$	−17.7502	−0.610627
$846$	−9.56742	−0.328935
$847$	0	0
$848$	36.9685	1.26950
$849$	−30.1697	−1.03542
$850$	51.6657	1.77212
$851$	10.6290	0.364359
$852$	−18.5978	−0.637148
$853$	22.6659	0.776066	0.388033	−	0.921646i	$-0.373155\pi$
$853$	22.6659	0.776066	0.388033	+	0.921646i	$0.373155\pi$
$854$	0	0
$855$	−7.65451	−0.261779
$856$	2.93116	0.100185
$857$	−23.8119	−0.813399	−0.406699	−	0.913562i	$-0.633320\pi$
$857$	−23.8119	−0.813399	−0.406699	+	0.913562i	$0.633320\pi$
$858$	−1.32845	−0.0453526
$859$	−39.5730	−1.35021	−0.675107	−	0.737720i	$-0.735903\pi$
$859$	−39.5730	−1.35021	−0.675107	+	0.737720i	$0.735903\pi$
$860$	−14.0784	−0.480068
$861$	0	0
$862$	−46.9818	−1.60020
$863$	−9.64870	−0.328446	−0.164223	−	0.986423i	$-0.552512\pi$
$863$	−9.64870	−0.328446	−0.164223	+	0.986423i	$0.552512\pi$
$864$	8.09339	0.275343
$865$	15.4582	0.525596
$866$	27.8580	0.946653
$867$	−47.1713	−1.60202
$868$	0	0
$869$	27.9347	0.947619
$870$	−21.0767	−0.714566
$871$	−3.78120	−0.128121
$872$	−2.38692	−0.0808314
$873$	0.114077	0.00386093
$874$	−11.5557	−0.390876
$875$	0	0
$876$	19.2453	0.650239
$877$	−43.9963	−1.48565	−0.742824	−	0.669487i	$-0.766514\pi$
$877$	−43.9963	−1.48565	−0.742824	+	0.669487i	$0.766514\pi$
$878$	−72.9367	−2.46150
$879$	5.23666	0.176628
$880$	7.73007	0.260581
$881$	42.2552	1.42361	0.711806	−	0.702376i	$-0.247877\pi$
$881$	42.2552	1.42361	0.711806	+	0.702376i	$0.247877\pi$
$882$	0	0
$883$	−17.7525	−0.597420	−0.298710	−	0.954344i	$-0.596556\pi$
$883$	−17.7525	−0.597420	−0.298710	+	0.954344i	$0.596556\pi$
$884$	6.84451	0.230206
$885$	−1.63193	−0.0548568
$886$	64.2899	2.15986
$887$	−12.2950	−0.412825	−0.206412	−	0.978465i	$-0.566179\pi$
$887$	−12.2950	−0.412825	−0.206412	+	0.978465i	$0.566179\pi$
$888$	−7.47337	−0.250790
$889$	0	0
$890$	53.2784	1.78590
$891$	−1.74509	−0.0584628
$892$	3.40181	0.113901
$893$	25.4883	0.852933
$894$	−7.16716	−0.239706
$895$	−13.4058	−0.448106
$896$	0	0
$897$	0.365513	0.0122041
$898$	51.7820	1.72799
$899$	−34.6029	−1.15407
$900$	−7.23897	−0.241299
$901$	92.2326	3.07271
$902$	26.0936	0.868822
$903$	0	0
$904$	4.39544	0.146190
$905$	−26.0629	−0.866359
$906$	−8.73379	−0.290161
$907$	1.58621	0.0526693	0.0263346	−	0.999653i	$-0.491616\pi$
$907$	1.58621	0.0526693	0.0263346	+	0.999653i	$0.491616\pi$
$908$	−9.69094	−0.321605
$909$	11.7700	0.390385
$910$	0	0
$911$	−10.2424	−0.339346	−0.169673	−	0.985500i	$-0.554271\pi$
$911$	−10.2424	−0.339346	−0.169673	+	0.985500i	$0.554271\pi$
$912$	−17.8151	−0.589917
$913$	−3.22026	−0.106575
$914$	12.7001	0.420082
$915$	−5.06079	−0.167305
$916$	2.68602	0.0887485
$917$	0	0
$918$	16.6838	0.550648
$919$	5.78173	0.190722	0.0953608	−	0.995443i	$-0.469600\pi$
$919$	5.78173	0.190722	0.0953608	+	0.995443i	$0.469600\pi$
$920$	0.969996	0.0319798
$921$	19.1642	0.631482
$922$	−24.5520	−0.808577
$923$	−2.90799	−0.0957177
$924$	0	0
$925$	−32.9155	−1.08226
$926$	−8.67108	−0.284949
$927$	8.84057	0.290363
$928$	−59.3691	−1.94889
$929$	6.20049	0.203431	0.101716	−	0.994814i	$-0.467567\pi$
$929$	6.20049	0.203431	0.101716	+	0.994814i	$0.467567\pi$
$930$	13.5536	0.444439
$931$	0	0
$932$	−34.3572	−1.12541
$933$	22.5347	0.737753
$934$	18.9780	0.620978
$935$	19.2857	0.630711
$936$	−0.256995	−0.00840015
$937$	7.97960	0.260682	0.130341	−	0.991469i	$-0.458393\pi$
$937$	7.97960	0.260682	0.130341	+	0.991469i	$0.458393\pi$
$938$	0	0
$939$	−15.3714	−0.501625
$940$	−14.8145	−0.483196
$941$	−32.5201	−1.06012	−0.530062	−	0.847959i	$-0.677832\pi$
$941$	−32.5201	−1.06012	−0.530062	+	0.847959i	$0.677832\pi$
$942$	−34.0119	−1.10817
$943$	−7.17945	−0.233795
$944$	−3.79816	−0.123620
$945$	0	0
$946$	15.8664	0.515861
$947$	57.9852	1.88427	0.942133	−	0.335239i	$-0.108817\pi$
$947$	57.9852	1.88427	0.942133	+	0.335239i	$0.108817\pi$
$948$	37.4192	1.21532
$949$	3.00924	0.0976842
$950$	35.7851	1.16102
$951$	−19.7359	−0.639981
$952$	0	0
$953$	52.3743	1.69657	0.848285	−	0.529541i	$-0.177636\pi$
$953$	52.3743	1.69657	0.848285	+	0.529541i	$0.177636\pi$
$954$	−23.9794	−0.776362
$955$	−29.7158	−0.961580
$956$	−0.280755	−0.00908027
$957$	12.8011	0.413802
$958$	53.0863	1.71514
$959$	0	0
$960$	14.3950	0.464598
$961$	−8.74824	−0.282201
$962$	−8.09134	−0.260875
$963$	4.16885	0.134339
$964$	−5.74701	−0.185099
$965$	−18.8521	−0.606869
$966$	0	0
$967$	−14.2819	−0.459274	−0.229637	−	0.973276i	$-0.573754\pi$
$967$	−14.2819	−0.459274	−0.229637	+	0.973276i	$0.573754\pi$
$968$	−5.59299	−0.179765
$969$	−44.4468	−1.42784
$970$	0.327771	0.0105241
$971$	−28.2431	−0.906365	−0.453182	−	0.891418i	$-0.649711\pi$
$971$	−28.2431	−0.906365	−0.453182	+	0.891418i	$0.649711\pi$
$972$	−2.33760	−0.0749785
$973$	0	0
$974$	−48.4628	−1.55285
$975$	−1.13190	−0.0362499
$976$	−11.7785	−0.377020
$977$	27.8662	0.891520	0.445760	−	0.895153i	$-0.352934\pi$
$977$	27.8662	0.891520	0.445760	+	0.895153i	$0.352934\pi$
$978$	20.6217	0.659410
$979$	−32.3592	−1.03421
$980$	0	0
$981$	−3.39481	−0.108388
$982$	26.6569	0.850656
$983$	5.11495	0.163142	0.0815708	−	0.996668i	$-0.474006\pi$
$983$	5.11495	0.163142	0.0815708	+	0.996668i	$0.474006\pi$
$984$	5.04794	0.160922
$985$	15.1321	0.482148
$986$	−122.384	−3.89751
$987$	0	0
$988$	4.74070	0.150822
$989$	−4.36551	−0.138815
$990$	−5.01407	−0.159358
$991$	−52.8590	−1.67912	−0.839561	−	0.543265i	$-0.817188\pi$
$991$	−52.8590	−1.67912	−0.839561	+	0.543265i	$0.817188\pi$
$992$	38.1780	1.21215
$993$	−28.1123	−0.892117
$994$	0	0
$995$	−7.20979	−0.228566
$996$	−4.31362	−0.136682
$997$	−0.993726	−0.0314716	−0.0157358	−	0.999876i	$-0.505009\pi$
$997$	−0.993726	−0.0314716	−0.0157358	+	0.999876i	$0.505009\pi$
$998$	−69.1571	−2.18913
$999$	−10.6290	−0.336288

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.y.1.4	✓	5
7.6	odd	2		3381.2.a.z.1.4	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.y.1.4	✓	5	1.1	even	1	trivial
3381.2.a.z.1.4	yes	5	7.6	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q+2.08269 q^{2} -1.00000 q^{3} +2.33760 q^{4} +1.37958 q^{5} -2.08269 q^{6} +0.703109 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.08269 q^{2} -1.00000 q^{3} +2.33760 q^{4} +1.37958 q^{5} -2.08269 q^{6} +0.703109 q^{8} +1.00000 q^{9} +2.87324 q^{10} -1.74509 q^{11} -2.33760 q^{12} -0.365513 q^{13} -1.37958 q^{15} -3.21083 q^{16} -8.01070 q^{17} +2.08269 q^{18} -5.54843 q^{19} +3.22490 q^{20} -3.63449 q^{22} +1.00000 q^{23} -0.703109 q^{24} -3.09676 q^{25} -0.761249 q^{26} -1.00000 q^{27} +7.33551 q^{29} -2.87324 q^{30} -4.71718 q^{31} -8.09339 q^{32} +1.74509 q^{33} -16.6838 q^{34} +2.33760 q^{36} +10.6290 q^{37} -11.5557 q^{38} +0.365513 q^{39} +0.969996 q^{40} -7.17945 q^{41} -4.36551 q^{43} -4.07932 q^{44} +1.37958 q^{45} +2.08269 q^{46} -4.59378 q^{47} +3.21083 q^{48} -6.44959 q^{50} +8.01070 q^{51} -0.854421 q^{52} -11.5137 q^{53} -2.08269 q^{54} -2.40750 q^{55} +5.54843 q^{57} +15.2776 q^{58} +1.18292 q^{59} -3.22490 q^{60} +3.66836 q^{61} -9.82442 q^{62} -10.4344 q^{64} -0.504254 q^{65} +3.63449 q^{66} +10.3449 q^{67} -18.7258 q^{68} -1.00000 q^{69} +7.95593 q^{71} +0.703109 q^{72} -8.23294 q^{73} +22.1370 q^{74} +3.09676 q^{75} -12.9700 q^{76} +0.761249 q^{78} -16.0076 q^{79} -4.42961 q^{80} +1.00000 q^{81} -14.9526 q^{82} +1.84532 q^{83} -11.0514 q^{85} -9.09201 q^{86} -7.33551 q^{87} -1.22699 q^{88} +18.5430 q^{89} +2.87324 q^{90} +2.33760 q^{92} +4.71718 q^{93} -9.56742 q^{94} -7.65451 q^{95} +8.09339 q^{96} +0.114077 q^{97} -1.74509 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} - 5 q^{3} + 9 q^{4} - 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + q^2 - 5 * q^3 + 9 * q^4 - 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9	\( 5 q + q^{2} - 5 q^{3} + 9 q^{4} - 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9} - 2 q^{11} - 9 q^{12} - 4 q^{13} + 2 q^{15} + q^{16} - 2 q^{17} + q^{18} - 8 q^{19} - 12 q^{20} - 16 q^{22} + 5 q^{23} - 3 q^{24} + 5 q^{25} - 16 q^{26} - 5 q^{27} + 4 q^{29} - 12 q^{31} + 7 q^{32} + 2 q^{33} - 10 q^{34} + 9 q^{36} - 6 q^{37} + 8 q^{38} + 4 q^{39} - 30 q^{40} - 6 q^{41} - 24 q^{43} + 16 q^{44} - 2 q^{45} + q^{46} - 24 q^{47} - q^{48} - 3 q^{50} + 2 q^{51} + 4 q^{52} + 2 q^{53} - q^{54} - 8 q^{55} + 8 q^{57} + 4 q^{58} - 16 q^{59} + 12 q^{60} - 22 q^{61} - 6 q^{62} - 29 q^{64} + 22 q^{65} + 16 q^{66} - 16 q^{67} - 14 q^{68} - 5 q^{69} + 16 q^{71} + 3 q^{72} + 8 q^{74} - 5 q^{75} - 30 q^{76} + 16 q^{78} + 12 q^{79} + 6 q^{80} + 5 q^{81} - 24 q^{82} - 10 q^{83} - 14 q^{85} - 20 q^{86} - 4 q^{87} - 8 q^{88} + 16 q^{89} + 9 q^{92} + 12 q^{93} + 32 q^{94} + 18 q^{95} - 7 q^{96} + 4 q^{97} - 2 q^{99}+O(q^{100}) \) 5 * q + q^2 - 5 * q^3 + 9 * q^4 - 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9 - 2 * q^11 - 9 * q^12 - 4 * q^13 + 2 * q^15 + q^16 - 2 * q^17 + q^18 - 8 * q^19 - 12 * q^20 - 16 * q^22 + 5 * q^23 - 3 * q^24 + 5 * q^25 - 16 * q^26 - 5 * q^27 + 4 * q^29 - 12 * q^31 + 7 * q^32 + 2 * q^33 - 10 * q^34 + 9 * q^36 - 6 * q^37 + 8 * q^38 + 4 * q^39 - 30 * q^40 - 6 * q^41 - 24 * q^43 + 16 * q^44 - 2 * q^45 + q^46 - 24 * q^47 - q^48 - 3 * q^50 + 2 * q^51 + 4 * q^52 + 2 * q^53 - q^54 - 8 * q^55 + 8 * q^57 + 4 * q^58 - 16 * q^59 + 12 * q^60 - 22 * q^61 - 6 * q^62 - 29 * q^64 + 22 * q^65 + 16 * q^66 - 16 * q^67 - 14 * q^68 - 5 * q^69 + 16 * q^71 + 3 * q^72 + 8 * q^74 - 5 * q^75 - 30 * q^76 + 16 * q^78 + 12 * q^79 + 6 * q^80 + 5 * q^81 - 24 * q^82 - 10 * q^83 - 14 * q^85 - 20 * q^86 - 4 * q^87 - 8 * q^88 + 16 * q^89 + 9 * q^92 + 12 * q^93 + 32 * q^94 + 18 * q^95 - 7 * q^96 + 4 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

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Database

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