LMFDB - Embedded newform 3381.2.a.ba.1.2

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:	$0$
Dimension:	$6$
Coefficient field:	6.6.62622704.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 5x^{4} + 13x^{3} + 9x^{2} - 5x - 2 $ x^6 - 3x^5 - 5x^4 + 13x^3 + 9x^2 - 5*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.835848$ 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)

$f(q)$	$=$	$q-1.83585 q^{2} -1.00000 q^{3} +1.37034 q^{4} +2.06079 q^{5} +1.83585 q^{6} +1.15597 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.83585 q^{2} -1.00000 q^{3} +1.37034 q^{4} +2.06079 q^{5} +1.83585 q^{6} +1.15597 q^{8} +1.00000 q^{9} -3.78330 q^{10} -5.59670 q^{11} -1.37034 q^{12} -3.26698 q^{13} -2.06079 q^{15} -4.86285 q^{16} -2.43488 q^{17} -1.83585 q^{18} -3.24280 q^{19} +2.82398 q^{20} +10.2747 q^{22} -1.00000 q^{23} -1.15597 q^{24} -0.753138 q^{25} +5.99767 q^{26} -1.00000 q^{27} -6.51158 q^{29} +3.78330 q^{30} -3.97935 q^{31} +6.61552 q^{32} +5.59670 q^{33} +4.47007 q^{34} +1.37034 q^{36} -1.02837 q^{37} +5.95328 q^{38} +3.26698 q^{39} +2.38221 q^{40} -10.2761 q^{41} +8.23086 q^{43} -7.66936 q^{44} +2.06079 q^{45} +1.83585 q^{46} +11.2977 q^{47} +4.86285 q^{48} +1.38265 q^{50} +2.43488 q^{51} -4.47685 q^{52} +2.71649 q^{53} +1.83585 q^{54} -11.5336 q^{55} +3.24280 q^{57} +11.9543 q^{58} +2.94317 q^{59} -2.82398 q^{60} +13.3168 q^{61} +7.30548 q^{62} -2.41938 q^{64} -6.73256 q^{65} -10.2747 q^{66} -1.57463 q^{67} -3.33661 q^{68} +1.00000 q^{69} +10.5111 q^{71} +1.15597 q^{72} +3.70778 q^{73} +1.88793 q^{74} +0.753138 q^{75} -4.44372 q^{76} -5.99767 q^{78} +8.44951 q^{79} -10.0213 q^{80} +1.00000 q^{81} +18.8654 q^{82} +7.68218 q^{83} -5.01778 q^{85} -15.1106 q^{86} +6.51158 q^{87} -6.46960 q^{88} +5.48796 q^{89} -3.78330 q^{90} -1.37034 q^{92} +3.97935 q^{93} -20.7408 q^{94} -6.68272 q^{95} -6.61552 q^{96} +9.11932 q^{97} -5.59670 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 2 * q^5 + 3 * q^6 - 9 * q^8 + 6 * q^9	$ 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{8} + 6 q^{9} + 8 q^{10} - 3 q^{11} - 7 q^{12} - 2 q^{15} + 5 q^{16} + 8 q^{17} - 3 q^{18} + 19 q^{19} + 24 q^{22} - 6 q^{23} + 9 q^{24} + 20 q^{26} - 6 q^{27} - 12 q^{29} - 8 q^{30} - 2 q^{31} - 41 q^{32} + 3 q^{33} + 2 q^{34} + 7 q^{36} - 10 q^{37} - 20 q^{38} + 22 q^{40} + 3 q^{41} - 2 q^{43} - 14 q^{44} + 2 q^{45} + 3 q^{46} + 7 q^{47} - 5 q^{48} + 17 q^{50} - 8 q^{51} - 44 q^{52} - 5 q^{53} + 3 q^{54} + 24 q^{55} - 19 q^{57} - 12 q^{58} + 21 q^{59} + 29 q^{61} + 10 q^{62} + 59 q^{64} - 18 q^{65} - 24 q^{66} + 16 q^{67} + 54 q^{68} + 6 q^{69} - 6 q^{71} - 9 q^{72} - 8 q^{73} - 16 q^{74} + 40 q^{76} - 20 q^{78} - 12 q^{79} - 78 q^{80} + 6 q^{81} + 44 q^{82} + 24 q^{83} + 10 q^{85} + 12 q^{86} + 12 q^{87} + 28 q^{88} + 18 q^{89} + 8 q^{90} - 7 q^{92} + 2 q^{93} - 8 q^{94} + 6 q^{95} + 41 q^{96} + 22 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 2 * q^5 + 3 * q^6 - 9 * q^8 + 6 * q^9 + 8 * q^10 - 3 * q^11 - 7 * q^12 - 2 * q^15 + 5 * q^16 + 8 * q^17 - 3 * q^18 + 19 * q^19 + 24 * q^22 - 6 * q^23 + 9 * q^24 + 20 * q^26 - 6 * q^27 - 12 * q^29 - 8 * q^30 - 2 * q^31 - 41 * q^32 + 3 * q^33 + 2 * q^34 + 7 * q^36 - 10 * q^37 - 20 * q^38 + 22 * q^40 + 3 * q^41 - 2 * q^43 - 14 * q^44 + 2 * q^45 + 3 * q^46 + 7 * q^47 - 5 * q^48 + 17 * q^50 - 8 * q^51 - 44 * q^52 - 5 * q^53 + 3 * q^54 + 24 * q^55 - 19 * q^57 - 12 * q^58 + 21 * q^59 + 29 * q^61 + 10 * q^62 + 59 * q^64 - 18 * q^65 - 24 * q^66 + 16 * q^67 + 54 * q^68 + 6 * q^69 - 6 * q^71 - 9 * q^72 - 8 * q^73 - 16 * q^74 + 40 * q^76 - 20 * q^78 - 12 * q^79 - 78 * q^80 + 6 * q^81 + 44 * q^82 + 24 * q^83 + 10 * q^85 + 12 * q^86 + 12 * q^87 + 28 * q^88 + 18 * q^89 + 8 * q^90 - 7 * q^92 + 2 * q^93 - 8 * q^94 + 6 * q^95 + 41 * q^96 + 22 * q^97 - 3 * 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 $

$2$	−1.83585	−1.29814	−0.649070	−	0.760729i	$-0.724842\pi$
$2$	−1.83585	−1.29814	−0.649070	+	0.760729i	$0.724842\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.37034	0.685168
$5$	2.06079	0.921614	0.460807	−	0.887500i	$-0.347560\pi$
$5$	2.06079	0.921614	0.460807	+	0.887500i	$0.347560\pi$
$6$	1.83585	0.749482
$7$	0	0
$7$	0	0
$8$	1.15597	0.408696
$9$	1.00000	0.333333
$10$	−3.78330	−1.19638
$11$	−5.59670	−1.68747	−0.843735	−	0.536761i	$-0.819648\pi$
$11$	−5.59670	−1.68747	−0.843735	+	0.536761i	$0.819648\pi$
$12$	−1.37034	−0.395582
$13$	−3.26698	−0.906096	−0.453048	−	0.891486i	$-0.649663\pi$
$13$	−3.26698	−0.906096	−0.453048	+	0.891486i	$0.649663\pi$
$14$	0	0
$15$	−2.06079	−0.532094
$16$	−4.86285	−1.21571
$17$	−2.43488	−0.590545	−0.295273	−	0.955413i	$-0.595410\pi$
$17$	−2.43488	−0.590545	−0.295273	+	0.955413i	$0.595410\pi$
$18$	−1.83585	−0.432713
$19$	−3.24280	−0.743948	−0.371974	−	0.928243i	$-0.621319\pi$
$19$	−3.24280	−0.743948	−0.371974	+	0.928243i	$0.621319\pi$
$20$	2.82398	0.631461
$21$	0	0
$22$	10.2747	2.19057
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.15597	−0.235961
$25$	−0.753138	−0.150628
$26$	5.99767	1.17624
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−6.51158	−1.20917	−0.604585	−	0.796541i	$-0.706661\pi$
$29$	−6.51158	−1.20917	−0.604585	+	0.796541i	$0.706661\pi$
$30$	3.78330	0.690733
$31$	−3.97935	−0.714712	−0.357356	−	0.933968i	$-0.616322\pi$
$31$	−3.97935	−0.714712	−0.357356	+	0.933968i	$0.616322\pi$
$32$	6.61552	1.16947
$33$	5.59670	0.974261
$34$	4.47007	0.766611
$35$	0	0
$36$	1.37034	0.228389
$37$	−1.02837	−0.169063	−0.0845313	−	0.996421i	$-0.526939\pi$
$37$	−1.02837	−0.169063	−0.0845313	+	0.996421i	$0.526939\pi$
$38$	5.95328	0.965749
$39$	3.26698	0.523135
$40$	2.38221	0.376660
$41$	−10.2761	−1.60486	−0.802430	−	0.596747i	$-0.796460\pi$
$41$	−10.2761	−1.60486	−0.802430	+	0.596747i	$0.796460\pi$
$42$	0	0
$43$	8.23086	1.25519	0.627597	−	0.778538i	$-0.284039\pi$
$43$	8.23086	1.25519	0.627597	+	0.778538i	$0.284039\pi$
$44$	−7.66936	−1.15620
$45$	2.06079	0.307205
$46$	1.83585	0.270681
$47$	11.2977	1.64793	0.823967	−	0.566638i	$-0.191756\pi$
$47$	11.2977	1.64793	0.823967	+	0.566638i	$0.191756\pi$
$48$	4.86285	0.701892
$49$	0	0
$50$	1.38265	0.195536
$51$	2.43488	0.340952
$52$	−4.47685	−0.620828
$53$	2.71649	0.373139	0.186569	−	0.982442i	$-0.440263\pi$
$53$	2.71649	0.373139	0.186569	+	0.982442i	$0.440263\pi$
$54$	1.83585	0.249827
$55$	−11.5336	−1.55520
$56$	0	0
$57$	3.24280	0.429519
$58$	11.9543	1.56967
$59$	2.94317	0.383168	0.191584	−	0.981476i	$-0.438638\pi$
$59$	2.94317	0.383168	0.191584	+	0.981476i	$0.438638\pi$
$60$	−2.82398	−0.364574
$61$	13.3168	1.70504	0.852520	−	0.522694i	$-0.175073\pi$
$61$	13.3168	1.70504	0.852520	+	0.522694i	$0.175073\pi$
$62$	7.30548	0.927797
$63$	0	0
$64$	−2.41938	−0.302423
$65$	−6.73256	−0.835071
$66$	−10.2747	−1.26473
$67$	−1.57463	−0.192372	−0.0961858	−	0.995363i	$-0.530664\pi$
$67$	−1.57463	−0.192372	−0.0961858	+	0.995363i	$0.530664\pi$
$68$	−3.33661	−0.404623
$69$	1.00000	0.120386
$70$	0	0
$71$	10.5111	1.24744	0.623719	−	0.781648i	$-0.285621\pi$
$71$	10.5111	1.24744	0.623719	+	0.781648i	$0.285621\pi$
$72$	1.15597	0.136232
$73$	3.70778	0.433963	0.216981	−	0.976176i	$-0.430379\pi$
$73$	3.70778	0.433963	0.216981	+	0.976176i	$0.430379\pi$
$74$	1.88793	0.219467
$75$	0.753138	0.0869649
$76$	−4.44372	−0.509730
$77$	0	0
$78$	−5.99767	−0.679102
$79$	8.44951	0.950644	0.475322	−	0.879812i	$-0.342332\pi$
$79$	8.44951	0.950644	0.475322	+	0.879812i	$0.342332\pi$
$80$	−10.0213	−1.12042
$81$	1.00000	0.111111
$82$	18.8654	2.08333
$83$	7.68218	0.843229	0.421614	−	0.906775i	$-0.361464\pi$
$83$	7.68218	0.843229	0.421614	+	0.906775i	$0.361464\pi$
$84$	0	0
$85$	−5.01778	−0.544255
$86$	−15.1106	−1.62942
$87$	6.51158	0.698114
$88$	−6.46960	−0.689662
$89$	5.48796	0.581722	0.290861	−	0.956765i	$-0.406058\pi$
$89$	5.48796	0.581722	0.290861	+	0.956765i	$0.406058\pi$
$90$	−3.78330	−0.398795
$91$	0	0
$92$	−1.37034	−0.142867
$93$	3.97935	0.412639
$94$	−20.7408	−2.13925
$95$	−6.68272	−0.685633
$96$	−6.61552	−0.675194
$97$	9.11932	0.925927	0.462963	−	0.886377i	$-0.346786\pi$
$97$	9.11932	0.925927	0.462963	+	0.886377i	$0.346786\pi$
$98$	0	0
$99$	−5.59670	−0.562490
$100$	−1.03205	−0.103205
$101$	−13.7078	−1.36398	−0.681990	−	0.731361i	$-0.738885\pi$
$101$	−13.7078	−1.36398	−0.681990	+	0.731361i	$0.738885\pi$
$102$	−4.47007	−0.442603
$103$	−9.68524	−0.954315	−0.477157	−	0.878818i	$-0.658333\pi$
$103$	−9.68524	−0.954315	−0.477157	+	0.878818i	$0.658333\pi$
$104$	−3.77651	−0.370318
$105$	0	0
$106$	−4.98707	−0.484387
$107$	0.577395	0.0558188	0.0279094	−	0.999610i	$-0.491115\pi$
$107$	0.577395	0.0558188	0.0279094	+	0.999610i	$0.491115\pi$
$108$	−1.37034	−0.131861
$109$	7.39284	0.708105	0.354053	−	0.935225i	$-0.384803\pi$
$109$	7.39284	0.708105	0.354053	+	0.935225i	$0.384803\pi$
$110$	21.1740	2.01886
$111$	1.02837	0.0976084
$112$	0	0
$113$	−16.8315	−1.58338	−0.791688	−	0.610925i	$-0.790798\pi$
$113$	−16.8315	−1.58338	−0.791688	+	0.610925i	$0.790798\pi$
$114$	−5.95328	−0.557576
$115$	−2.06079	−0.192170
$116$	−8.92305	−0.828484
$117$	−3.26698	−0.302032
$118$	−5.40322	−0.497406
$119$	0	0
$120$	−2.38221	−0.217465
$121$	20.3231	1.84755
$122$	−24.4476	−2.21338
$123$	10.2761	0.926566
$124$	−5.45305	−0.489698
$125$	−11.8560	−1.06043
$126$	0	0
$127$	−2.64941	−0.235097	−0.117549	−	0.993067i	$-0.537504\pi$
$127$	−2.64941	−0.235097	−0.117549	+	0.993067i	$0.537504\pi$
$128$	−8.78942	−0.776882
$129$	−8.23086	−0.724686
$130$	12.3599	1.08404
$131$	12.6931	1.10901	0.554503	−	0.832182i	$-0.312909\pi$
$131$	12.6931	1.10901	0.554503	+	0.832182i	$0.312909\pi$
$132$	7.66936	0.667532
$133$	0	0
$134$	2.89078	0.249725
$135$	−2.06079	−0.177365
$136$	−2.81464	−0.241353
$137$	−20.2772	−1.73240	−0.866198	−	0.499702i	$-0.833443\pi$
$137$	−20.2772	−1.73240	−0.866198	+	0.499702i	$0.833443\pi$
$138$	−1.83585	−0.156278
$139$	13.9232	1.18095	0.590475	−	0.807056i	$-0.298940\pi$
$139$	13.9232	1.18095	0.590475	+	0.807056i	$0.298940\pi$
$140$	0	0
$141$	−11.2977	−0.951435
$142$	−19.2968	−1.61935
$143$	18.2843	1.52901
$144$	−4.86285	−0.405238
$145$	−13.4190	−1.11439
$146$	−6.80692	−0.563345
$147$	0	0
$148$	−1.40921	−0.115836
$149$	1.21633	0.0996456	0.0498228	−	0.998758i	$-0.484134\pi$
$149$	1.21633	0.0996456	0.0498228	+	0.998758i	$0.484134\pi$
$150$	−1.38265	−0.112893
$151$	2.41155	0.196249	0.0981247	−	0.995174i	$-0.468716\pi$
$151$	2.41155	0.196249	0.0981247	+	0.995174i	$0.468716\pi$
$152$	−3.74856	−0.304049
$153$	−2.43488	−0.196848
$154$	0	0
$155$	−8.20061	−0.658689
$156$	4.47685	0.358435
$157$	20.0099	1.59697	0.798483	−	0.602017i	$-0.205636\pi$
$157$	20.0099	1.59697	0.798483	+	0.602017i	$0.205636\pi$
$158$	−15.5120	−1.23407
$159$	−2.71649	−0.215432
$160$	13.6332	1.07780
$161$	0	0
$162$	−1.83585	−0.144238
$163$	−0.942806	−0.0738463	−0.0369231	−	0.999318i	$-0.511756\pi$
$163$	−0.942806	−0.0738463	−0.0369231	+	0.999318i	$0.511756\pi$
$164$	−14.0817	−1.09960
$165$	11.5336	0.897892
$166$	−14.1033	−1.09463
$167$	13.9086	1.07628	0.538141	−	0.842855i	$-0.319127\pi$
$167$	13.9086	1.07628	0.538141	+	0.842855i	$0.319127\pi$
$168$	0	0
$169$	−2.32687	−0.178990
$170$	9.21188	0.706519
$171$	−3.24280	−0.247983
$172$	11.2790	0.860019
$173$	−14.7654	−1.12259	−0.561297	−	0.827615i	$-0.689697\pi$
$173$	−14.7654	−1.12259	−0.561297	+	0.827615i	$0.689697\pi$
$174$	−11.9543	−0.906250
$175$	0	0
$176$	27.2159	2.05148
$177$	−2.94317	−0.221222
$178$	−10.0751	−0.755157
$179$	−17.6549	−1.31959	−0.659793	−	0.751448i	$-0.729356\pi$
$179$	−17.6549	−1.31959	−0.659793	+	0.751448i	$0.729356\pi$
$180$	2.82398	0.210487
$181$	10.8533	0.806722	0.403361	−	0.915041i	$-0.367842\pi$
$181$	10.8533	0.806722	0.403361	+	0.915041i	$0.367842\pi$
$182$	0	0
$183$	−13.3168	−0.984406
$184$	−1.15597	−0.0852190
$185$	−2.11925	−0.155811
$186$	−7.30548	−0.535664
$187$	13.6273	0.996527
$188$	15.4816	1.12911
$189$	0	0
$190$	12.2685	0.890048
$191$	−14.2404	−1.03040	−0.515199	−	0.857070i	$-0.672282\pi$
$191$	−14.2404	−1.03040	−0.515199	+	0.857070i	$0.672282\pi$
$192$	2.41938	0.174604
$193$	20.4582	1.47261	0.736307	−	0.676648i	$-0.236568\pi$
$193$	20.4582	1.47261	0.736307	+	0.676648i	$0.236568\pi$
$194$	−16.7417	−1.20198
$195$	6.73256	0.482128
$196$	0	0
$197$	−1.35900	−0.0968250	−0.0484125	−	0.998827i	$-0.515416\pi$
$197$	−1.35900	−0.0968250	−0.0484125	+	0.998827i	$0.515416\pi$
$198$	10.2747	0.730191
$199$	11.9141	0.844565	0.422283	−	0.906464i	$-0.361229\pi$
$199$	11.9141	0.844565	0.422283	+	0.906464i	$0.361229\pi$
$200$	−0.870602	−0.0615609
$201$	1.57463	0.111066
$202$	25.1655	1.77064
$203$	0	0
$204$	3.33661	0.233609
$205$	−21.1769	−1.47906
$206$	17.7806	1.23883
$207$	−1.00000	−0.0695048
$208$	15.8868	1.10155
$209$	18.1490	1.25539
$210$	0	0
$211$	7.88756	0.543002	0.271501	−	0.962438i	$-0.412480\pi$
$211$	7.88756	0.543002	0.271501	+	0.962438i	$0.412480\pi$
$212$	3.72251	0.255663
$213$	−10.5111	−0.720209
$214$	−1.06001	−0.0724607
$215$	16.9621	1.15680
$216$	−1.15597	−0.0786536
$217$	0	0
$218$	−13.5721	−0.919220
$219$	−3.70778	−0.250549
$220$	−15.8050	−1.06557
$221$	7.95470	0.535091
$222$	−1.88793	−0.126709
$223$	12.5177	0.838246	0.419123	−	0.907929i	$-0.362338\pi$
$223$	12.5177	0.838246	0.419123	+	0.907929i	$0.362338\pi$
$224$	0	0
$225$	−0.753138	−0.0502092
$226$	30.9001	2.05544
$227$	−3.76534	−0.249915	−0.124957	−	0.992162i	$-0.539879\pi$
$227$	−3.76534	−0.249915	−0.124957	+	0.992162i	$0.539879\pi$
$228$	4.44372	0.294293
$229$	5.68632	0.375763	0.187881	−	0.982192i	$-0.439838\pi$
$229$	5.68632	0.375763	0.187881	+	0.982192i	$0.439838\pi$
$230$	3.78330	0.249463
$231$	0	0
$232$	−7.52716	−0.494183
$233$	20.4237	1.33800	0.669001	−	0.743261i	$-0.266722\pi$
$233$	20.4237	1.33800	0.669001	+	0.743261i	$0.266722\pi$
$234$	5.99767	0.392080
$235$	23.2821	1.51876
$236$	4.03314	0.262535
$237$	−8.44951	−0.548854
$238$	0	0
$239$	29.0236	1.87738	0.938690	−	0.344762i	$-0.112040\pi$
$239$	29.0236	1.87738	0.938690	+	0.344762i	$0.112040\pi$
$240$	10.0213	0.646874
$241$	−19.7647	−1.27316	−0.636579	−	0.771212i	$-0.719651\pi$
$241$	−19.7647	−1.27316	−0.636579	+	0.771212i	$0.719651\pi$
$242$	−37.3101	−2.39838
$243$	−1.00000	−0.0641500
$244$	18.2485	1.16824
$245$	0	0
$246$	−18.8654	−1.20281
$247$	10.5941	0.674088
$248$	−4.59999	−0.292100
$249$	−7.68218	−0.486838
$250$	21.7658	1.37659
$251$	8.28342	0.522845	0.261422	−	0.965225i	$-0.415808\pi$
$251$	8.28342	0.522845	0.261422	+	0.965225i	$0.415808\pi$
$252$	0	0
$253$	5.59670	0.351862
$254$	4.86392	0.305189
$255$	5.01778	0.314226
$256$	20.9748	1.31093
$257$	6.80828	0.424689	0.212344	−	0.977195i	$-0.431890\pi$
$257$	6.80828	0.424689	0.212344	+	0.977195i	$0.431890\pi$
$258$	15.1106	0.940745
$259$	0	0
$260$	−9.22586	−0.572164
$261$	−6.51158	−0.403056
$262$	−23.3027	−1.43964
$263$	−24.9127	−1.53619	−0.768093	−	0.640339i	$-0.778794\pi$
$263$	−24.9127	−1.53619	−0.768093	+	0.640339i	$0.778794\pi$
$264$	6.46960	0.398176
$265$	5.59812	0.343890
$266$	0	0
$267$	−5.48796	−0.335857
$268$	−2.15777	−0.131807
$269$	23.9389	1.45958	0.729791	−	0.683670i	$-0.239617\pi$
$269$	23.9389	1.45958	0.729791	+	0.683670i	$0.239617\pi$
$270$	3.78330	0.230244
$271$	7.46567	0.453507	0.226753	−	0.973952i	$-0.427189\pi$
$271$	7.46567	0.453507	0.226753	+	0.973952i	$0.427189\pi$
$272$	11.8405	0.717934
$273$	0	0
$274$	37.2258	2.24889
$275$	4.21509	0.254179
$276$	1.37034	0.0824845
$277$	2.64204	0.158745	0.0793725	−	0.996845i	$-0.474708\pi$
$277$	2.64204	0.158745	0.0793725	+	0.996845i	$0.474708\pi$
$278$	−25.5609	−1.53304
$279$	−3.97935	−0.238237
$280$	0	0
$281$	−10.5276	−0.628026	−0.314013	−	0.949419i	$-0.601674\pi$
$281$	−10.5276	−0.628026	−0.314013	+	0.949419i	$0.601674\pi$
$282$	20.7408	1.23510
$283$	23.9937	1.42628	0.713139	−	0.701023i	$-0.247273\pi$
$283$	23.9937	1.42628	0.713139	+	0.701023i	$0.247273\pi$
$284$	14.4037	0.854705
$285$	6.68272	0.395850
$286$	−33.5672	−1.98487
$287$	0	0
$288$	6.61552	0.389823
$289$	−11.0714	−0.651256
$290$	24.6352	1.44663
$291$	−9.11932	−0.534584
$292$	5.08090	0.297337
$293$	−3.03591	−0.177360	−0.0886799	−	0.996060i	$-0.528265\pi$
$293$	−3.03591	−0.177360	−0.0886799	+	0.996060i	$0.528265\pi$
$294$	0	0
$295$	6.06526	0.353133
$296$	−1.18876	−0.0690952
$297$	5.59670	0.324754
$298$	−2.23300	−0.129354
$299$	3.26698	0.188934
$300$	1.03205	0.0595856
$301$	0	0
$302$	−4.42724	−0.254759
$303$	13.7078	0.787495
$304$	15.7692	0.904427
$305$	27.4431	1.57139
$306$	4.47007	0.255537
$307$	19.8834	1.13481	0.567403	−	0.823440i	$-0.307948\pi$
$307$	19.8834	1.13481	0.567403	+	0.823440i	$0.307948\pi$
$308$	0	0
$309$	9.68524	0.550974
$310$	15.0551	0.855070
$311$	17.8571	1.01258	0.506291	−	0.862363i	$-0.331016\pi$
$311$	17.8571	1.01258	0.506291	+	0.862363i	$0.331016\pi$
$312$	3.77651	0.213803
$313$	−27.6680	−1.56389	−0.781944	−	0.623349i	$-0.785771\pi$
$313$	−27.6680	−1.56389	−0.781944	+	0.623349i	$0.785771\pi$
$314$	−36.7352	−2.07309
$315$	0	0
$316$	11.5787	0.651351
$317$	−14.5534	−0.817403	−0.408701	−	0.912668i	$-0.634018\pi$
$317$	−14.5534	−0.817403	−0.408701	+	0.912668i	$0.634018\pi$
$318$	4.98707	0.279661
$319$	36.4433	2.04044
$320$	−4.98585	−0.278717
$321$	−0.577395	−0.0322270
$322$	0	0
$323$	7.89582	0.439335
$324$	1.37034	0.0761298
$325$	2.46048	0.136483
$326$	1.73085	0.0958628
$327$	−7.39284	−0.408825
$328$	−11.8788	−0.655899
$329$	0	0
$330$	−21.1740	−1.16559
$331$	0.338307	0.0185951	0.00929753	−	0.999957i	$-0.497040\pi$
$331$	0.338307	0.0185951	0.00929753	+	0.999957i	$0.497040\pi$
$332$	10.5272	0.577753
$333$	−1.02837	−0.0563542
$334$	−25.5341	−1.39717
$335$	−3.24498	−0.177292
$336$	0	0
$337$	−16.9304	−0.922256	−0.461128	−	0.887334i	$-0.652555\pi$
$337$	−16.9304	−0.922256	−0.461128	+	0.887334i	$0.652555\pi$
$338$	4.27178	0.232354
$339$	16.8315	0.914163
$340$	−6.87605	−0.372906
$341$	22.2712	1.20605
$342$	5.95328	0.321916
$343$	0	0
$344$	9.51460	0.512993
$345$	2.06079	0.110949
$346$	27.1070	1.45728
$347$	−30.9112	−1.65940	−0.829699	−	0.558211i	$-0.811488\pi$
$347$	−30.9112	−1.65940	−0.829699	+	0.558211i	$0.811488\pi$
$348$	8.92305	0.478326
$349$	−18.8941	−1.01138	−0.505690	−	0.862715i	$-0.668762\pi$
$349$	−18.8941	−1.01138	−0.505690	+	0.862715i	$0.668762\pi$
$350$	0	0
$351$	3.26698	0.174378
$352$	−37.0251	−1.97344
$353$	−24.3994	−1.29865	−0.649324	−	0.760512i	$-0.724948\pi$
$353$	−24.3994	−1.29865	−0.649324	+	0.760512i	$0.724948\pi$
$354$	5.40322	0.287178
$355$	21.6612	1.14966
$356$	7.52034	0.398577
$357$	0	0
$358$	32.4116	1.71301
$359$	−7.45633	−0.393530	−0.196765	−	0.980451i	$-0.563044\pi$
$359$	−7.45633	−0.393530	−0.196765	+	0.980451i	$0.563044\pi$
$360$	2.38221	0.125553
$361$	−8.48428	−0.446541
$362$	−19.9251	−1.04724
$363$	−20.3231	−1.06668
$364$	0	0
$365$	7.64096	0.399946
$366$	24.4476	1.27790
$367$	8.32545	0.434585	0.217292	−	0.976107i	$-0.430277\pi$
$367$	8.32545	0.434585	0.217292	+	0.976107i	$0.430277\pi$
$368$	4.86285	0.253494
$369$	−10.2761	−0.534953
$370$	3.89062	0.202264
$371$	0	0
$372$	5.45305	0.282727
$373$	−17.4534	−0.903705	−0.451852	−	0.892093i	$-0.649237\pi$
$373$	−17.4534	−0.903705	−0.451852	+	0.892093i	$0.649237\pi$
$374$	−25.0177	−1.29363
$375$	11.8560	0.612242
$376$	13.0597	0.673504
$377$	21.2732	1.09562
$378$	0	0
$379$	−12.7635	−0.655616	−0.327808	−	0.944744i	$-0.606310\pi$
$379$	−12.7635	−0.655616	−0.327808	+	0.944744i	$0.606310\pi$
$380$	−9.15758	−0.469774
$381$	2.64941	0.135733
$382$	26.1432	1.33760
$383$	−29.9356	−1.52964	−0.764818	−	0.644247i	$-0.777171\pi$
$383$	−29.9356	−1.52964	−0.764818	+	0.644247i	$0.777171\pi$
$384$	8.78942	0.448533
$385$	0	0
$386$	−37.5582	−1.91166
$387$	8.23086	0.418398
$388$	12.4965	0.634415
$389$	3.92491	0.199001	0.0995003	−	0.995038i	$-0.468276\pi$
$389$	3.92491	0.199001	0.0995003	+	0.995038i	$0.468276\pi$
$390$	−12.3599	−0.625870
$391$	2.43488	0.123137
$392$	0	0
$393$	−12.6931	−0.640284
$394$	2.49492	0.125692
$395$	17.4127	0.876127
$396$	−7.66936	−0.385400
$397$	18.6584	0.936437	0.468219	−	0.883613i	$-0.344896\pi$
$397$	18.6584	0.936437	0.468219	+	0.883613i	$0.344896\pi$
$398$	−21.8724	−1.09636
$399$	0	0
$400$	3.66240	0.183120
$401$	−23.6286	−1.17996	−0.589979	−	0.807419i	$-0.700864\pi$
$401$	−23.6286	−1.17996	−0.589979	+	0.807419i	$0.700864\pi$
$402$	−2.89078	−0.144179
$403$	13.0004	0.647598
$404$	−18.7843	−0.934556
$405$	2.06079	0.102402
$406$	0	0
$407$	5.75547	0.285288
$408$	2.81464	0.139346
$409$	9.58427	0.473912	0.236956	−	0.971520i	$-0.423850\pi$
$409$	9.58427	0.473912	0.236956	+	0.971520i	$0.423850\pi$
$410$	38.8776	1.92003
$411$	20.2772	1.00020
$412$	−13.2720	−0.653866
$413$	0	0
$414$	1.83585	0.0902270
$415$	15.8314	0.777131
$416$	−21.6127	−1.05965
$417$	−13.9232	−0.681822
$418$	−33.3187	−1.62967
$419$	27.6994	1.35321	0.676603	−	0.736348i	$-0.263452\pi$
$419$	27.6994	1.35321	0.676603	+	0.736348i	$0.263452\pi$
$420$	0	0
$421$	−6.92577	−0.337541	−0.168771	−	0.985655i	$-0.553980\pi$
$421$	−6.92577	−0.337541	−0.168771	+	0.985655i	$0.553980\pi$
$422$	−14.4804	−0.704893
$423$	11.2977	0.549311
$424$	3.14017	0.152500
$425$	1.83380	0.0889524
$426$	19.2968	0.934932
$427$	0	0
$428$	0.791225	0.0382453
$429$	−18.2843	−0.882774
$430$	−31.1398	−1.50169
$431$	28.9533	1.39463	0.697316	−	0.716764i	$-0.254377\pi$
$431$	28.9533	1.39463	0.697316	+	0.716764i	$0.254377\pi$
$432$	4.86285	0.233964
$433$	20.7984	0.999505	0.499753	−	0.866168i	$-0.333424\pi$
$433$	20.7984	0.999505	0.499753	+	0.866168i	$0.333424\pi$
$434$	0	0
$435$	13.4190	0.643392
$436$	10.1307	0.485171
$437$	3.24280	0.155124
$438$	6.80692	0.325247
$439$	7.05190	0.336569	0.168284	−	0.985738i	$-0.446177\pi$
$439$	7.05190	0.336569	0.168284	+	0.985738i	$0.446177\pi$
$440$	−13.3325	−0.635602
$441$	0	0
$442$	−14.6036	−0.694623
$443$	−16.2341	−0.771306	−0.385653	−	0.922644i	$-0.626024\pi$
$443$	−16.2341	−0.771306	−0.385653	+	0.922644i	$0.626024\pi$
$444$	1.40921	0.0668781
$445$	11.3095	0.536123
$446$	−22.9806	−1.08816
$447$	−1.21633	−0.0575304
$448$	0	0
$449$	12.1648	0.574093	0.287046	−	0.957917i	$-0.407327\pi$
$449$	12.1648	0.574093	0.287046	+	0.957917i	$0.407327\pi$
$450$	1.38265	0.0651786
$451$	57.5124	2.70815
$452$	−23.0648	−1.08488
$453$	−2.41155	−0.113305
$454$	6.91260	0.324424
$455$	0	0
$456$	3.74856	0.175543
$457$	20.4553	0.956859	0.478429	−	0.878126i	$-0.341206\pi$
$457$	20.4553	0.956859	0.478429	+	0.878126i	$0.341206\pi$
$458$	−10.4392	−0.487793
$459$	2.43488	0.113651
$460$	−2.82398	−0.131669
$461$	41.6964	1.94200	0.970998	−	0.239087i	$-0.0768482\pi$
$461$	41.6964	1.94200	0.970998	+	0.239087i	$0.0768482\pi$
$462$	0	0
$463$	−23.9420	−1.11268	−0.556339	−	0.830956i	$-0.687794\pi$
$463$	−23.9420	−1.11268	−0.556339	+	0.830956i	$0.687794\pi$
$464$	31.6648	1.47000
$465$	8.20061	0.380294
$466$	−37.4948	−1.73691
$467$	11.3336	0.524457	0.262228	−	0.965006i	$-0.415543\pi$
$467$	11.3336	0.524457	0.262228	+	0.965006i	$0.415543\pi$
$468$	−4.47685	−0.206943
$469$	0	0
$470$	−42.7424	−1.97156
$471$	−20.0099	−0.922009
$472$	3.40221	0.156599
$473$	−46.0657	−2.11810
$474$	15.5120	0.712490
$475$	2.44227	0.112059
$476$	0	0
$477$	2.71649	0.124380
$478$	−53.2829	−2.43710
$479$	37.9081	1.73206	0.866032	−	0.499988i	$-0.166662\pi$
$479$	37.9081	1.73206	0.866032	+	0.499988i	$0.166662\pi$
$480$	−13.6332	−0.622268
$481$	3.35965	0.153187
$482$	36.2850	1.65274
$483$	0	0
$484$	27.8494	1.26588
$485$	18.7930	0.853347
$486$	1.83585	0.0832757
$487$	−13.3806	−0.606334	−0.303167	−	0.952937i	$-0.598044\pi$
$487$	−13.3806	−0.606334	−0.303167	+	0.952937i	$0.598044\pi$
$488$	15.3938	0.696843
$489$	0.942806	0.0426352
$490$	0	0
$491$	14.6047	0.659099	0.329550	−	0.944138i	$-0.393103\pi$
$491$	14.6047	0.659099	0.329550	+	0.944138i	$0.393103\pi$
$492$	14.0817	0.634853
$493$	15.8549	0.714069
$494$	−19.4492	−0.875061
$495$	−11.5336	−0.518398
$496$	19.3510	0.868885
$497$	0	0
$498$	14.1033	0.631984
$499$	−26.5067	−1.18661	−0.593303	−	0.804980i	$-0.702176\pi$
$499$	−26.5067	−1.18661	−0.593303	+	0.804980i	$0.702176\pi$
$500$	−16.2467	−0.726576
$501$	−13.9086	−0.621392
$502$	−15.2071	−0.678726
$503$	−12.0579	−0.537634	−0.268817	−	0.963191i	$-0.586633\pi$
$503$	−12.0579	−0.537634	−0.268817	+	0.963191i	$0.586633\pi$
$504$	0	0
$505$	−28.2490	−1.25706
$506$	−10.2747	−0.456766
$507$	2.32687	0.103340
$508$	−3.63058	−0.161081
$509$	−24.0045	−1.06398	−0.531991	−	0.846750i	$-0.678556\pi$
$509$	−24.0045	−1.06398	−0.531991	+	0.846750i	$0.678556\pi$
$510$	−9.21188	−0.407909
$511$	0	0
$512$	−20.9277	−0.924882
$513$	3.24280	0.143173
$514$	−12.4990	−0.551306
$515$	−19.9593	−0.879510
$516$	−11.2790	−0.496532
$517$	−63.2297	−2.78084
$518$	0	0
$519$	14.7654	0.648130
$520$	−7.78261	−0.341290
$521$	−2.14886	−0.0941434	−0.0470717	−	0.998892i	$-0.514989\pi$
$521$	−2.14886	−0.0941434	−0.0470717	+	0.998892i	$0.514989\pi$
$522$	11.9543	0.523224
$523$	−10.5058	−0.459386	−0.229693	−	0.973263i	$-0.573772\pi$
$523$	−10.5058	−0.459386	−0.229693	+	0.973263i	$0.573772\pi$
$524$	17.3939	0.759855
$525$	0	0
$526$	45.7360	1.99418
$527$	9.68924	0.422070
$528$	−27.2159	−1.18442
$529$	1.00000	0.0434783
$530$	−10.2773	−0.446417
$531$	2.94317	0.127723
$532$	0	0
$533$	33.5718	1.45416
$534$	10.0751	0.435990
$535$	1.18989	0.0514434
$536$	−1.82022	−0.0786215
$537$	17.6549	0.761863
$538$	−43.9482	−1.89474
$539$	0	0
$540$	−2.82398	−0.121525
$541$	20.7106	0.890416	0.445208	−	0.895427i	$-0.353130\pi$
$541$	20.7106	0.890416	0.445208	+	0.895427i	$0.353130\pi$
$542$	−13.7058	−0.588716
$543$	−10.8533	−0.465761
$544$	−16.1080	−0.690625
$545$	15.2351	0.652600
$546$	0	0
$547$	6.91809	0.295796	0.147898	−	0.989003i	$-0.452749\pi$
$547$	6.91809	0.295796	0.147898	+	0.989003i	$0.452749\pi$
$548$	−27.7865	−1.18698
$549$	13.3168	0.568347
$550$	−7.73826	−0.329961
$551$	21.1157	0.899559
$552$	1.15597	0.0492012
$553$	0	0
$554$	−4.85039	−0.206073
$555$	2.11925	0.0899572
$556$	19.0795	0.809150
$557$	−12.0145	−0.509070	−0.254535	−	0.967063i	$-0.581922\pi$
$557$	−12.0145	−0.509070	−0.254535	+	0.967063i	$0.581922\pi$
$558$	7.30548	0.309266
$559$	−26.8900	−1.13733
$560$	0	0
$561$	−13.6273	−0.575345
$562$	19.3271	0.815266
$563$	5.16697	0.217762	0.108881	−	0.994055i	$-0.465273\pi$
$563$	5.16697	0.217762	0.108881	+	0.994055i	$0.465273\pi$
$564$	−15.4816	−0.651893
$565$	−34.6863	−1.45926
$566$	−44.0488	−1.85151
$567$	0	0
$568$	12.1505	0.509823
$569$	−13.1045	−0.549368	−0.274684	−	0.961535i	$-0.588573\pi$
$569$	−13.1045	−0.549368	−0.274684	+	0.961535i	$0.588573\pi$
$570$	−12.2685	−0.513869
$571$	36.8554	1.54235	0.771174	−	0.636624i	$-0.219670\pi$
$571$	36.8554	1.54235	0.771174	+	0.636624i	$0.219670\pi$
$572$	25.0556	1.04763
$573$	14.2404	0.594901
$574$	0	0
$575$	0.753138	0.0314080
$576$	−2.41938	−0.100808
$577$	33.1564	1.38032	0.690160	−	0.723657i	$-0.257540\pi$
$577$	33.1564	1.38032	0.690160	+	0.723657i	$0.257540\pi$
$578$	20.3253	0.845422
$579$	−20.4582	−0.850214
$580$	−18.3885	−0.763543
$581$	0	0
$582$	16.7417	0.693965
$583$	−15.2034	−0.629660
$584$	4.28607	0.177359
$585$	−6.73256	−0.278357
$586$	5.57347	0.230238
$587$	−31.3543	−1.29413	−0.647065	−	0.762435i	$-0.724004\pi$
$587$	−31.3543	−1.29413	−0.647065	+	0.762435i	$0.724004\pi$
$588$	0	0
$589$	12.9042	0.531709
$590$	−11.1349	−0.458417
$591$	1.35900	0.0559020
$592$	5.00080	0.205532
$593$	−37.5810	−1.54327	−0.771633	−	0.636068i	$-0.780560\pi$
$593$	−37.5810	−1.54327	−0.771633	+	0.636068i	$0.780560\pi$
$594$	−10.2747	−0.421576
$595$	0	0
$596$	1.66678	0.0682740
$597$	−11.9141	−0.487610
$598$	−5.99767	−0.245263
$599$	−14.0183	−0.572773	−0.286387	−	0.958114i	$-0.592454\pi$
$599$	−14.0183	−0.572773	−0.286387	+	0.958114i	$0.592454\pi$
$600$	0.870602	0.0355422
$601$	8.06488	0.328973	0.164487	−	0.986379i	$-0.447403\pi$
$601$	8.06488	0.328973	0.164487	+	0.986379i	$0.447403\pi$
$602$	0	0
$603$	−1.57463	−0.0641239
$604$	3.30464	0.134464
$605$	41.8816	1.70273
$606$	−25.1655	−1.02228
$607$	−1.78117	−0.0722957	−0.0361478	−	0.999346i	$-0.511509\pi$
$607$	−1.78117	−0.0722957	−0.0361478	+	0.999346i	$0.511509\pi$
$608$	−21.4528	−0.870025
$609$	0	0
$610$	−50.3814	−2.03988
$611$	−36.9092	−1.49319
$612$	−3.33661	−0.134874
$613$	16.0718	0.649133	0.324567	−	0.945863i	$-0.394782\pi$
$613$	16.0718	0.649133	0.324567	+	0.945863i	$0.394782\pi$
$614$	−36.5029	−1.47314
$615$	21.1769	0.853936
$616$	0	0
$617$	−19.6471	−0.790962	−0.395481	−	0.918474i	$-0.629422\pi$
$617$	−19.6471	−0.790962	−0.395481	+	0.918474i	$0.629422\pi$
$618$	−17.7806	−0.715241
$619$	−30.1013	−1.20987	−0.604937	−	0.796273i	$-0.706802\pi$
$619$	−30.1013	−1.20987	−0.604937	+	0.796273i	$0.706802\pi$
$620$	−11.2376	−0.451313
$621$	1.00000	0.0401286
$622$	−32.7829	−1.31447
$623$	0	0
$624$	−15.8868	−0.635982
$625$	−20.6671	−0.826684
$626$	50.7942	2.03014
$627$	−18.1490	−0.724800
$628$	27.4203	1.09419
$629$	2.50395	0.0998392
$630$	0	0
$631$	−36.4257	−1.45009	−0.725043	−	0.688704i	$-0.758180\pi$
$631$	−36.4257	−1.45009	−0.725043	+	0.688704i	$0.758180\pi$
$632$	9.76735	0.388524
$633$	−7.88756	−0.313502
$634$	26.7179	1.06110
$635$	−5.45988	−0.216669
$636$	−3.72251	−0.147607
$637$	0	0
$638$	−66.9044	−2.64877
$639$	10.5111	0.415813
$640$	−18.1132	−0.715986
$641$	−23.2734	−0.919244	−0.459622	−	0.888115i	$-0.652015\pi$
$641$	−23.2734	−0.919244	−0.459622	+	0.888115i	$0.652015\pi$
$642$	1.06001	0.0418352
$643$	30.2560	1.19318	0.596591	−	0.802546i	$-0.296522\pi$
$643$	30.2560	1.19318	0.596591	+	0.802546i	$0.296522\pi$
$644$	0	0
$645$	−16.9621	−0.667881
$646$	−14.4955	−0.570319
$647$	−48.1621	−1.89345	−0.946723	−	0.322049i	$-0.895628\pi$
$647$	−48.1621	−1.89345	−0.946723	+	0.322049i	$0.895628\pi$
$648$	1.15597	0.0454107
$649$	−16.4721	−0.646585
$650$	−4.51707	−0.177174
$651$	0	0
$652$	−1.29196	−0.0505971
$653$	42.3150	1.65591	0.827957	−	0.560791i	$-0.189503\pi$
$653$	42.3150	1.65591	0.827957	+	0.560791i	$0.189503\pi$
$654$	13.5721	0.530712
$655$	26.1579	1.02207
$656$	49.9712	1.95105
$657$	3.70778	0.144654
$658$	0	0
$659$	29.2207	1.13828	0.569139	−	0.822241i	$-0.307276\pi$
$659$	29.2207	1.13828	0.569139	+	0.822241i	$0.307276\pi$
$660$	15.8050	0.615207
$661$	1.05876	0.0411810	0.0205905	−	0.999788i	$-0.493445\pi$
$661$	1.05876	0.0411810	0.0205905	+	0.999788i	$0.493445\pi$
$662$	−0.621081	−0.0241390
$663$	−7.95470	−0.308935
$664$	8.88034	0.344624
$665$	0	0
$666$	1.88793	0.0731557
$667$	6.51158	0.252129
$668$	19.0595	0.737434
$669$	−12.5177	−0.483962
$670$	5.95729	0.230150
$671$	−74.5301	−2.87720
$672$	0	0
$673$	23.7152	0.914152	0.457076	−	0.889428i	$-0.348897\pi$
$673$	23.7152	0.914152	0.457076	+	0.889428i	$0.348897\pi$
$674$	31.0816	1.19722
$675$	0.753138	0.0289883
$676$	−3.18860	−0.122638
$677$	−10.0549	−0.386443	−0.193222	−	0.981155i	$-0.561894\pi$
$677$	−10.0549	−0.386443	−0.193222	+	0.981155i	$0.561894\pi$
$678$	−30.9001	−1.18671
$679$	0	0
$680$	−5.80039	−0.222435
$681$	3.76534	0.144288
$682$	−40.8866	−1.56563
$683$	14.6366	0.560055	0.280028	−	0.959992i	$-0.409656\pi$
$683$	14.6366	0.560055	0.280028	+	0.959992i	$0.409656\pi$
$684$	−4.44372	−0.169910
$685$	−41.7870	−1.59660
$686$	0	0
$687$	−5.68632	−0.216947
$688$	−40.0254	−1.52596
$689$	−8.87471	−0.338100
$690$	−3.78330	−0.144028
$691$	−18.3249	−0.697112	−0.348556	−	0.937288i	$-0.613328\pi$
$691$	−18.3249	−0.697112	−0.348556	+	0.937288i	$0.613328\pi$
$692$	−20.2336	−0.769165
$693$	0	0
$694$	56.7482	2.15413
$695$	28.6928	1.08838
$696$	7.52716	0.285316
$697$	25.0211	0.947742
$698$	34.6868	1.31291
$699$	−20.4237	−0.772496
$700$	0	0
$701$	−21.2924	−0.804201	−0.402100	−	0.915596i	$-0.631720\pi$
$701$	−21.2924	−0.804201	−0.402100	+	0.915596i	$0.631720\pi$
$702$	−5.99767	−0.226367
$703$	3.33479	0.125774
$704$	13.5406	0.510329
$705$	−23.2821	−0.876856
$706$	44.7935	1.68583
$707$	0	0
$708$	−4.03314	−0.151575
$709$	25.5300	0.958799	0.479399	−	0.877597i	$-0.340855\pi$
$709$	25.5300	0.958799	0.479399	+	0.877597i	$0.340855\pi$
$710$	−39.7667	−1.49242
$711$	8.44951	0.316881
$712$	6.34389	0.237747
$713$	3.97935	0.149028
$714$	0	0
$715$	37.6801	1.40916
$716$	−24.1931	−0.904138
$717$	−29.0236	−1.08391
$718$	13.6887	0.510857
$719$	23.9870	0.894565	0.447283	−	0.894393i	$-0.352392\pi$
$719$	23.9870	0.894565	0.447283	+	0.894393i	$0.352392\pi$
$720$	−10.0213	−0.373473
$721$	0	0
$722$	15.5758	0.579673
$723$	19.7647	0.735058
$724$	14.8727	0.552740
$725$	4.90411	0.182134
$726$	37.3101	1.38471
$727$	−8.76559	−0.325098	−0.162549	−	0.986700i	$-0.551972\pi$
$727$	−8.76559	−0.325098	−0.162549	+	0.986700i	$0.551972\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−14.0276	−0.519186
$731$	−20.0412	−0.741249
$732$	−18.2485	−0.674483
$733$	19.6657	0.726368	0.363184	−	0.931717i	$-0.381690\pi$
$733$	19.6657	0.726368	0.363184	+	0.931717i	$0.381690\pi$
$734$	−15.2843	−0.564152
$735$	0	0
$736$	−6.61552	−0.243851
$737$	8.81273	0.324621
$738$	18.8654	0.694444
$739$	−28.0866	−1.03318	−0.516591	−	0.856232i	$-0.672799\pi$
$739$	−28.0866	−1.03318	−0.516591	+	0.856232i	$0.672799\pi$
$740$	−2.90409	−0.106756
$741$	−10.5941	−0.389185
$742$	0	0
$743$	45.1069	1.65481	0.827406	−	0.561605i	$-0.189816\pi$
$743$	45.1069	1.65481	0.827406	+	0.561605i	$0.189816\pi$
$744$	4.59999	0.168644
$745$	2.50660	0.0918348
$746$	32.0419	1.17314
$747$	7.68218	0.281076
$748$	18.6740	0.682789
$749$	0	0
$750$	−21.7658	−0.794776
$751$	−5.21048	−0.190133	−0.0950666	−	0.995471i	$-0.530306\pi$
$751$	−5.21048	−0.190133	−0.0950666	+	0.995471i	$0.530306\pi$
$752$	−54.9389	−2.00341
$753$	−8.28342	−0.301864
$754$	−39.0543	−1.42227
$755$	4.96971	0.180866
$756$	0	0
$757$	20.4295	0.742522	0.371261	−	0.928529i	$-0.378926\pi$
$757$	20.4295	0.742522	0.371261	+	0.928529i	$0.378926\pi$
$758$	23.4318	0.851081
$759$	−5.59670	−0.203147
$760$	−7.72501	−0.280215
$761$	−12.4339	−0.450730	−0.225365	−	0.974274i	$-0.572357\pi$
$761$	−12.4339	−0.450730	−0.225365	+	0.974274i	$0.572357\pi$
$762$	−4.86392	−0.176201
$763$	0	0
$764$	−19.5141	−0.705996
$765$	−5.01778	−0.181418
$766$	54.9571	1.98568
$767$	−9.61527	−0.347187
$768$	−20.9748	−0.756863
$769$	−9.56678	−0.344987	−0.172494	−	0.985011i	$-0.555182\pi$
$769$	−9.56678	−0.344987	−0.172494	+	0.985011i	$0.555182\pi$
$770$	0	0
$771$	−6.80828	−0.245194
$772$	28.0346	1.00899
$773$	50.8592	1.82928	0.914639	−	0.404272i	$-0.132475\pi$
$773$	50.8592	1.82928	0.914639	+	0.404272i	$0.132475\pi$
$774$	−15.1106	−0.543139
$775$	2.99700	0.107655
$776$	10.5416	0.378422
$777$	0	0
$778$	−7.20553	−0.258331
$779$	33.3233	1.19393
$780$	9.22586	0.330339
$781$	−58.8275	−2.10501
$782$	−4.47007	−0.159849
$783$	6.51158	0.232705
$784$	0	0
$785$	41.2363	1.47179
$786$	23.3027	0.831179
$787$	−19.5994	−0.698642	−0.349321	−	0.937003i	$-0.613588\pi$
$787$	−19.5994	−0.698642	−0.349321	+	0.937003i	$0.613588\pi$
$788$	−1.86229	−0.0663414
$789$	24.9127	0.886917
$790$	−31.9670	−1.13734
$791$	0	0
$792$	−6.46960	−0.229887
$793$	−43.5056	−1.54493
$794$	−34.2539	−1.21563
$795$	−5.59812	−0.198545
$796$	16.3263	0.578669
$797$	8.37733	0.296740	0.148370	−	0.988932i	$-0.452597\pi$
$797$	8.37733	0.296740	0.148370	+	0.988932i	$0.452597\pi$
$798$	0	0
$799$	−27.5085	−0.973180
$800$	−4.98240	−0.176154
$801$	5.48796	0.193907
$802$	43.3785	1.53175
$803$	−20.7513	−0.732299
$804$	2.15777	0.0760987
$805$	0	0
$806$	−23.8668	−0.840673
$807$	−23.9389	−0.842690
$808$	−15.8458	−0.557453
$809$	53.0316	1.86449	0.932247	−	0.361823i	$-0.117846\pi$
$809$	53.0316	1.86449	0.932247	+	0.361823i	$0.117846\pi$
$810$	−3.78330	−0.132932
$811$	29.1114	1.02224	0.511119	−	0.859510i	$-0.329231\pi$
$811$	29.1114	1.02224	0.511119	+	0.859510i	$0.329231\pi$
$812$	0	0
$813$	−7.46567	−0.261832
$814$	−10.5662	−0.370344
$815$	−1.94293	−0.0680578
$816$	−11.8405	−0.414499
$817$	−26.6910	−0.933799
$818$	−17.5953	−0.615204
$819$	0	0
$820$	−29.0195	−1.01341
$821$	46.8375	1.63464	0.817321	−	0.576183i	$-0.195458\pi$
$821$	46.8375	1.63464	0.817321	+	0.576183i	$0.195458\pi$
$822$	−37.2258	−1.29840
$823$	19.9296	0.694701	0.347350	−	0.937735i	$-0.387081\pi$
$823$	19.9296	0.694701	0.347350	+	0.937735i	$0.387081\pi$
$824$	−11.1958	−0.390025
$825$	−4.21509	−0.146751
$826$	0	0
$827$	15.8311	0.550500	0.275250	−	0.961373i	$-0.411239\pi$
$827$	15.8311	0.550500	0.275250	+	0.961373i	$0.411239\pi$
$828$	−1.37034	−0.0476225
$829$	−35.8191	−1.24405	−0.622025	−	0.782997i	$-0.713690\pi$
$829$	−35.8191	−1.24405	−0.622025	+	0.782997i	$0.713690\pi$
$830$	−29.0640	−1.00883
$831$	−2.64204	−0.0916514
$832$	7.90407	0.274024
$833$	0	0
$834$	25.5609	0.885101
$835$	28.6628	0.991917
$836$	24.8702	0.860153
$837$	3.97935	0.137546
$838$	−50.8519	−1.75665
$839$	−0.127073	−0.00438704	−0.00219352	−	0.999998i	$-0.500698\pi$
$839$	−0.127073	−0.00438704	−0.00219352	+	0.999998i	$0.500698\pi$
$840$	0	0
$841$	13.4006	0.462090
$842$	12.7147	0.438176
$843$	10.5276	0.362591
$844$	10.8086	0.372048
$845$	−4.79520	−0.164960
$846$	−20.7408	−0.713083
$847$	0	0
$848$	−13.2099	−0.453630
$849$	−23.9937	−0.823461
$850$	−3.36658	−0.115473
$851$	1.02837	0.0352520
$852$	−14.4037	−0.493464
$853$	−35.7522	−1.22413	−0.612066	−	0.790806i	$-0.709662\pi$
$853$	−35.7522	−1.22413	−0.612066	+	0.790806i	$0.709662\pi$
$854$	0	0
$855$	−6.68272	−0.228544
$856$	0.667449	0.0228129
$857$	−37.2009	−1.27076	−0.635379	−	0.772201i	$-0.719156\pi$
$857$	−37.2009	−1.27076	−0.635379	+	0.772201i	$0.719156\pi$
$858$	33.5672	1.14596
$859$	44.0767	1.50388	0.751938	−	0.659233i	$-0.229119\pi$
$859$	44.0767	1.50388	0.751938	+	0.659233i	$0.229119\pi$
$860$	23.2438	0.792605
$861$	0	0
$862$	−53.1539	−1.81043
$863$	0.0440202	0.00149847	0.000749233	−	1.00000i	$-0.499762\pi$
$863$	0.0440202	0.00149847	0.000749233		1.00000i	$0.499762\pi$
$864$	−6.61552	−0.225065
$865$	−30.4284	−1.03460
$866$	−38.1826	−1.29750
$867$	11.0714	0.376003
$868$	0	0
$869$	−47.2894	−1.60418
$870$	−24.6352	−0.835213
$871$	5.14427	0.174307
$872$	8.54587	0.289400
$873$	9.11932	0.308642
$874$	−5.95328	−0.201373
$875$	0	0
$876$	−5.08090	−0.171668
$877$	−3.65616	−0.123460	−0.0617299	−	0.998093i	$-0.519662\pi$
$877$	−3.65616	−0.123460	−0.0617299	+	0.998093i	$0.519662\pi$
$878$	−12.9462	−0.436914
$879$	3.03591	0.102399
$880$	56.0864	1.89067
$881$	15.1320	0.509809	0.254904	−	0.966966i	$-0.417956\pi$
$881$	15.1320	0.509809	0.254904	+	0.966966i	$0.417956\pi$
$882$	0	0
$883$	−9.81843	−0.330417	−0.165208	−	0.986259i	$-0.552830\pi$
$883$	−9.81843	−0.330417	−0.165208	+	0.986259i	$0.552830\pi$
$884$	10.9006	0.366627
$885$	−6.06526	−0.203882
$886$	29.8034	1.00126
$887$	−37.5742	−1.26162	−0.630808	−	0.775939i	$-0.717277\pi$
$887$	−37.5742	−1.26162	−0.630808	+	0.775939i	$0.717277\pi$
$888$	1.18876	0.0398921
$889$	0	0
$890$	−20.7626	−0.695963
$891$	−5.59670	−0.187497
$892$	17.1534	0.574339
$893$	−36.6360	−1.22598
$894$	2.23300	0.0746825
$895$	−36.3830	−1.21615
$896$	0	0
$897$	−3.26698	−0.109081
$898$	−22.3327	−0.745253
$899$	25.9118	0.864208
$900$	−1.03205	−0.0344017
$901$	−6.61433	−0.220355
$902$	−105.584	−3.51556
$903$	0	0
$904$	−19.4567	−0.647119
$905$	22.3665	0.743486
$906$	4.42724	0.147085
$907$	−46.4691	−1.54298	−0.771491	−	0.636241i	$-0.780488\pi$
$907$	−46.4691	−1.54298	−0.771491	+	0.636241i	$0.780488\pi$
$908$	−5.15979	−0.171234
$909$	−13.7078	−0.454660
$910$	0	0
$911$	57.0403	1.88983	0.944915	−	0.327314i	$-0.106144\pi$
$911$	57.0403	1.88983	0.944915	+	0.327314i	$0.106144\pi$
$912$	−15.7692	−0.522171
$913$	−42.9949	−1.42292
$914$	−37.5528	−1.24214
$915$	−27.4431	−0.907242
$916$	7.79217	0.257461
$917$	0	0
$918$	−4.47007	−0.147534
$919$	−38.2281	−1.26103	−0.630515	−	0.776177i	$-0.717156\pi$
$919$	−38.2281	−1.26103	−0.630515	+	0.776177i	$0.717156\pi$
$920$	−2.38221	−0.0785390
$921$	−19.8834	−0.655181
$922$	−76.5483	−2.52098
$923$	−34.3395	−1.13030
$924$	0	0
$925$	0.774503	0.0254655
$926$	43.9538	1.44441
$927$	−9.68524	−0.318105
$928$	−43.0775	−1.41409
$929$	−47.5399	−1.55973	−0.779867	−	0.625946i	$-0.784713\pi$
$929$	−47.5399	−1.55973	−0.779867	+	0.625946i	$0.784713\pi$
$930$	−15.0551	−0.493675
$931$	0	0
$932$	27.9874	0.916757
$933$	−17.8571	−0.584614
$934$	−20.8068	−0.680818
$935$	28.0830	0.918413
$936$	−3.77651	−0.123439
$937$	53.9869	1.76367	0.881837	−	0.471553i	$-0.156307\pi$
$937$	53.9869	1.76367	0.881837	+	0.471553i	$0.156307\pi$
$938$	0	0
$939$	27.6680	0.902911
$940$	31.9043	1.04061
$941$	23.3276	0.760457	0.380228	−	0.924893i	$-0.375845\pi$
$941$	23.3276	0.760457	0.380228	+	0.924893i	$0.375845\pi$
$942$	36.7352	1.19690
$943$	10.2761	0.334636
$944$	−14.3122	−0.465823
$945$	0	0
$946$	84.5695	2.74959
$947$	24.3539	0.791396	0.395698	−	0.918381i	$-0.370503\pi$
$947$	24.3539	0.791396	0.395698	+	0.918381i	$0.370503\pi$
$948$	−11.5787	−0.376058
$949$	−12.1132	−0.393212
$950$	−4.48364	−0.145468
$951$	14.5534	0.471928
$952$	0	0
$953$	28.9485	0.937734	0.468867	−	0.883269i	$-0.344662\pi$
$953$	28.9485	0.937734	0.468867	+	0.883269i	$0.344662\pi$
$954$	−4.98707	−0.161462
$955$	−29.3465	−0.949630
$956$	39.7721	1.28632
$957$	−36.4433	−1.17805
$958$	−69.5935	−2.24846
$959$	0	0
$960$	4.98585	0.160917
$961$	−15.1648	−0.489187
$962$	−6.16781	−0.198858
$963$	0.577395	0.0186063
$964$	−27.0843	−0.872327
$965$	42.1601	1.35718
$966$	0	0
$967$	43.7510	1.40694	0.703469	−	0.710726i	$-0.251633\pi$
$967$	43.7510	1.40694	0.703469	+	0.710726i	$0.251633\pi$
$968$	23.4928	0.755087
$969$	−7.89582	−0.253650
$970$	−34.5011	−1.10776
$971$	−10.8739	−0.348959	−0.174479	−	0.984661i	$-0.555824\pi$
$971$	−10.8739	−0.348959	−0.174479	+	0.984661i	$0.555824\pi$
$972$	−1.37034	−0.0439536
$973$	0	0
$974$	24.5648	0.787107
$975$	−2.46048	−0.0787985
$976$	−64.7576	−2.07284
$977$	33.3212	1.06604	0.533020	−	0.846103i	$-0.321057\pi$
$977$	33.3212	1.06604	0.533020	+	0.846103i	$0.321057\pi$
$978$	−1.73085	−0.0553464
$979$	−30.7145	−0.981638
$980$	0	0
$981$	7.39284	0.236035
$982$	−26.8119	−0.855603
$983$	−4.76802	−0.152076	−0.0760381	−	0.997105i	$-0.524227\pi$
$983$	−4.76802	−0.152076	−0.0760381	+	0.997105i	$0.524227\pi$
$984$	11.8788	0.378684
$985$	−2.80062	−0.0892353
$986$	−29.1072	−0.926962
$987$	0	0
$988$	14.5175	0.461864
$989$	−8.23086	−0.261726
$990$	21.1740	0.672954
$991$	58.6637	1.86351	0.931757	−	0.363084i	$-0.118276\pi$
$991$	58.6637	1.86351	0.931757	+	0.363084i	$0.118276\pi$
$992$	−26.3255	−0.835834
$993$	−0.338307	−0.0107359
$994$	0	0
$995$	24.5524	0.778363
$996$	−10.5272	−0.333566
$997$	−32.1383	−1.01783	−0.508915	−	0.860817i	$-0.669953\pi$
$997$	−32.1383	−1.01783	−0.508915	+	0.860817i	$0.669953\pi$
$998$	48.6623	1.54038
$999$	1.02837	0.0325361

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.ba.1.2	✓	6
7.6	odd	2		3381.2.a.bb.1.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.ba.1.2	✓	6	1.1	even	1	trivial
3381.2.a.bb.1.2	yes	6	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)

\(f(q)\)	\(=\)	\(q-1.83585 q^{2} -1.00000 q^{3} +1.37034 q^{4} +2.06079 q^{5} +1.83585 q^{6} +1.15597 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.83585 q^{2} -1.00000 q^{3} +1.37034 q^{4} +2.06079 q^{5} +1.83585 q^{6} +1.15597 q^{8} +1.00000 q^{9} -3.78330 q^{10} -5.59670 q^{11} -1.37034 q^{12} -3.26698 q^{13} -2.06079 q^{15} -4.86285 q^{16} -2.43488 q^{17} -1.83585 q^{18} -3.24280 q^{19} +2.82398 q^{20} +10.2747 q^{22} -1.00000 q^{23} -1.15597 q^{24} -0.753138 q^{25} +5.99767 q^{26} -1.00000 q^{27} -6.51158 q^{29} +3.78330 q^{30} -3.97935 q^{31} +6.61552 q^{32} +5.59670 q^{33} +4.47007 q^{34} +1.37034 q^{36} -1.02837 q^{37} +5.95328 q^{38} +3.26698 q^{39} +2.38221 q^{40} -10.2761 q^{41} +8.23086 q^{43} -7.66936 q^{44} +2.06079 q^{45} +1.83585 q^{46} +11.2977 q^{47} +4.86285 q^{48} +1.38265 q^{50} +2.43488 q^{51} -4.47685 q^{52} +2.71649 q^{53} +1.83585 q^{54} -11.5336 q^{55} +3.24280 q^{57} +11.9543 q^{58} +2.94317 q^{59} -2.82398 q^{60} +13.3168 q^{61} +7.30548 q^{62} -2.41938 q^{64} -6.73256 q^{65} -10.2747 q^{66} -1.57463 q^{67} -3.33661 q^{68} +1.00000 q^{69} +10.5111 q^{71} +1.15597 q^{72} +3.70778 q^{73} +1.88793 q^{74} +0.753138 q^{75} -4.44372 q^{76} -5.99767 q^{78} +8.44951 q^{79} -10.0213 q^{80} +1.00000 q^{81} +18.8654 q^{82} +7.68218 q^{83} -5.01778 q^{85} -15.1106 q^{86} +6.51158 q^{87} -6.46960 q^{88} +5.48796 q^{89} -3.78330 q^{90} -1.37034 q^{92} +3.97935 q^{93} -20.7408 q^{94} -6.68272 q^{95} -6.61552 q^{96} +9.11932 q^{97} -5.59670 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 2 * q^5 + 3 * q^6 - 9 * q^8 + 6 * q^9	\( 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{8} + 6 q^{9} + 8 q^{10} - 3 q^{11} - 7 q^{12} - 2 q^{15} + 5 q^{16} + 8 q^{17} - 3 q^{18} + 19 q^{19} + 24 q^{22} - 6 q^{23} + 9 q^{24} + 20 q^{26} - 6 q^{27} - 12 q^{29} - 8 q^{30} - 2 q^{31} - 41 q^{32} + 3 q^{33} + 2 q^{34} + 7 q^{36} - 10 q^{37} - 20 q^{38} + 22 q^{40} + 3 q^{41} - 2 q^{43} - 14 q^{44} + 2 q^{45} + 3 q^{46} + 7 q^{47} - 5 q^{48} + 17 q^{50} - 8 q^{51} - 44 q^{52} - 5 q^{53} + 3 q^{54} + 24 q^{55} - 19 q^{57} - 12 q^{58} + 21 q^{59} + 29 q^{61} + 10 q^{62} + 59 q^{64} - 18 q^{65} - 24 q^{66} + 16 q^{67} + 54 q^{68} + 6 q^{69} - 6 q^{71} - 9 q^{72} - 8 q^{73} - 16 q^{74} + 40 q^{76} - 20 q^{78} - 12 q^{79} - 78 q^{80} + 6 q^{81} + 44 q^{82} + 24 q^{83} + 10 q^{85} + 12 q^{86} + 12 q^{87} + 28 q^{88} + 18 q^{89} + 8 q^{90} - 7 q^{92} + 2 q^{93} - 8 q^{94} + 6 q^{95} + 41 q^{96} + 22 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 2 * q^5 + 3 * q^6 - 9 * q^8 + 6 * q^9 + 8 * q^10 - 3 * q^11 - 7 * q^12 - 2 * q^15 + 5 * q^16 + 8 * q^17 - 3 * q^18 + 19 * q^19 + 24 * q^22 - 6 * q^23 + 9 * q^24 + 20 * q^26 - 6 * q^27 - 12 * q^29 - 8 * q^30 - 2 * q^31 - 41 * q^32 + 3 * q^33 + 2 * q^34 + 7 * q^36 - 10 * q^37 - 20 * q^38 + 22 * q^40 + 3 * q^41 - 2 * q^43 - 14 * q^44 + 2 * q^45 + 3 * q^46 + 7 * q^47 - 5 * q^48 + 17 * q^50 - 8 * q^51 - 44 * q^52 - 5 * q^53 + 3 * q^54 + 24 * q^55 - 19 * q^57 - 12 * q^58 + 21 * q^59 + 29 * q^61 + 10 * q^62 + 59 * q^64 - 18 * q^65 - 24 * q^66 + 16 * q^67 + 54 * q^68 + 6 * q^69 - 6 * q^71 - 9 * q^72 - 8 * q^73 - 16 * q^74 + 40 * q^76 - 20 * q^78 - 12 * q^79 - 78 * q^80 + 6 * q^81 + 44 * q^82 + 24 * q^83 + 10 * q^85 + 12 * q^86 + 12 * q^87 + 28 * q^88 + 18 * q^89 + 8 * q^90 - 7 * q^92 + 2 * q^93 - 8 * q^94 + 6 * q^95 + 41 * q^96 + 22 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

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