LMFDB - Embedded newform 2006.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(1,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.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:	$16.0179906455$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	2006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.23607 q^{3} +1.00000 q^{4} -2.23607 q^{5} +2.23607 q^{6} -3.00000 q^{7} -1.00000 q^{8} +2.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.23607 q^{3} +1.00000 q^{4} -2.23607 q^{5} +2.23607 q^{6} -3.00000 q^{7} -1.00000 q^{8} +2.00000 q^{9} +2.23607 q^{10} +1.23607 q^{11} -2.23607 q^{12} +2.47214 q^{13} +3.00000 q^{14} +5.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -2.00000 q^{18} -6.23607 q^{19} -2.23607 q^{20} +6.70820 q^{21} -1.23607 q^{22} +8.47214 q^{23} +2.23607 q^{24} -2.47214 q^{26} +2.23607 q^{27} -3.00000 q^{28} +2.23607 q^{29} -5.00000 q^{30} +4.00000 q^{31} -1.00000 q^{32} -2.76393 q^{33} +1.00000 q^{34} +6.70820 q^{35} +2.00000 q^{36} +8.00000 q^{37} +6.23607 q^{38} -5.52786 q^{39} +2.23607 q^{40} -9.00000 q^{41} -6.70820 q^{42} +4.00000 q^{43} +1.23607 q^{44} -4.47214 q^{45} -8.47214 q^{46} +9.70820 q^{47} -2.23607 q^{48} +2.00000 q^{49} +2.23607 q^{51} +2.47214 q^{52} -10.2361 q^{53} -2.23607 q^{54} -2.76393 q^{55} +3.00000 q^{56} +13.9443 q^{57} -2.23607 q^{58} -1.00000 q^{59} +5.00000 q^{60} +2.00000 q^{61} -4.00000 q^{62} -6.00000 q^{63} +1.00000 q^{64} -5.52786 q^{65} +2.76393 q^{66} +3.70820 q^{67} -1.00000 q^{68} -18.9443 q^{69} -6.70820 q^{70} +10.4721 q^{71} -2.00000 q^{72} +3.23607 q^{73} -8.00000 q^{74} -6.23607 q^{76} -3.70820 q^{77} +5.52786 q^{78} -2.52786 q^{79} -2.23607 q^{80} -11.0000 q^{81} +9.00000 q^{82} -10.1803 q^{83} +6.70820 q^{84} +2.23607 q^{85} -4.00000 q^{86} -5.00000 q^{87} -1.23607 q^{88} +6.76393 q^{89} +4.47214 q^{90} -7.41641 q^{91} +8.47214 q^{92} -8.94427 q^{93} -9.70820 q^{94} +13.9443 q^{95} +2.23607 q^{96} -11.7082 q^{97} -2.00000 q^{98} +2.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 6 q^{7} - 2 q^{8} + 4 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 - 6 * q^7 - 2 * q^8 + 4 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} - 6 q^{7} - 2 q^{8} + 4 q^{9} - 2 q^{11} - 4 q^{13} + 6 q^{14} + 10 q^{15} + 2 q^{16} - 2 q^{17} - 4 q^{18} - 8 q^{19} + 2 q^{22} + 8 q^{23} + 4 q^{26} - 6 q^{28} - 10 q^{30} + 8 q^{31} - 2 q^{32} - 10 q^{33} + 2 q^{34} + 4 q^{36} + 16 q^{37} + 8 q^{38} - 20 q^{39} - 18 q^{41} + 8 q^{43} - 2 q^{44} - 8 q^{46} + 6 q^{47} + 4 q^{49} - 4 q^{52} - 16 q^{53} - 10 q^{55} + 6 q^{56} + 10 q^{57} - 2 q^{59} + 10 q^{60} + 4 q^{61} - 8 q^{62} - 12 q^{63} + 2 q^{64} - 20 q^{65} + 10 q^{66} - 6 q^{67} - 2 q^{68} - 20 q^{69} + 12 q^{71} - 4 q^{72} + 2 q^{73} - 16 q^{74} - 8 q^{76} + 6 q^{77} + 20 q^{78} - 14 q^{79} - 22 q^{81} + 18 q^{82} + 2 q^{83} - 8 q^{86} - 10 q^{87} + 2 q^{88} + 18 q^{89} + 12 q^{91} + 8 q^{92} - 6 q^{94} + 10 q^{95} - 10 q^{97} - 4 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 6 * q^7 - 2 * q^8 + 4 * q^9 - 2 * q^11 - 4 * q^13 + 6 * q^14 + 10 * q^15 + 2 * q^16 - 2 * q^17 - 4 * q^18 - 8 * q^19 + 2 * q^22 + 8 * q^23 + 4 * q^26 - 6 * q^28 - 10 * q^30 + 8 * q^31 - 2 * q^32 - 10 * q^33 + 2 * q^34 + 4 * q^36 + 16 * q^37 + 8 * q^38 - 20 * q^39 - 18 * q^41 + 8 * q^43 - 2 * q^44 - 8 * q^46 + 6 * q^47 + 4 * q^49 - 4 * q^52 - 16 * q^53 - 10 * q^55 + 6 * q^56 + 10 * q^57 - 2 * q^59 + 10 * q^60 + 4 * q^61 - 8 * q^62 - 12 * q^63 + 2 * q^64 - 20 * q^65 + 10 * q^66 - 6 * q^67 - 2 * q^68 - 20 * q^69 + 12 * q^71 - 4 * q^72 + 2 * q^73 - 16 * q^74 - 8 * q^76 + 6 * q^77 + 20 * q^78 - 14 * q^79 - 22 * q^81 + 18 * q^82 + 2 * q^83 - 8 * q^86 - 10 * q^87 + 2 * q^88 + 18 * q^89 + 12 * q^91 + 8 * q^92 - 6 * q^94 + 10 * q^95 - 10 * q^97 - 4 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.23607	−1.29099	−0.645497	−	0.763763i	$-0.723350\pi$
$3$	−2.23607	−1.29099	−0.645497	+	0.763763i	$0.723350\pi$
$4$	1.00000	0.500000
$5$	−2.23607	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$5$	−2.23607	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$6$	2.23607	0.912871
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	−1.00000	−0.353553
$9$	2.00000	0.666667
$10$	2.23607	0.707107
$11$	1.23607	0.372689	0.186344	−	0.982485i	$-0.440336\pi$
$11$	1.23607	0.372689	0.186344	+	0.982485i	$0.440336\pi$
$12$	−2.23607	−0.645497
$13$	2.47214	0.685647	0.342824	−	0.939400i	$-0.388617\pi$
$13$	2.47214	0.685647	0.342824	+	0.939400i	$0.388617\pi$
$14$	3.00000	0.801784
$15$	5.00000	1.29099
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.00000	−0.471405
$19$	−6.23607	−1.43065	−0.715326	−	0.698791i	$-0.753722\pi$
$19$	−6.23607	−1.43065	−0.715326	+	0.698791i	$0.753722\pi$
$20$	−2.23607	−0.500000
$21$	6.70820	1.46385
$22$	−1.23607	−0.263531
$23$	8.47214	1.76656	0.883281	−	0.468844i	$-0.155329\pi$
$23$	8.47214	1.76656	0.883281	+	0.468844i	$0.155329\pi$
$24$	2.23607	0.456435
$25$	0	0
$26$	−2.47214	−0.484826
$27$	2.23607	0.430331
$28$	−3.00000	−0.566947
$29$	2.23607	0.415227	0.207614	−	0.978211i	$-0.433430\pi$
$29$	2.23607	0.415227	0.207614	+	0.978211i	$0.433430\pi$
$30$	−5.00000	−0.912871
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	−1.00000	−0.176777
$33$	−2.76393	−0.481139
$34$	1.00000	0.171499
$35$	6.70820	1.13389
$36$	2.00000	0.333333
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	6.23607	1.01162
$39$	−5.52786	−0.885167
$40$	2.23607	0.353553
$41$	−9.00000	−1.40556	−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000	−1.40556	−0.702782	+	0.711405i	$0.748059\pi$
$42$	−6.70820	−1.03510
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	1.23607	0.186344
$45$	−4.47214	−0.666667
$46$	−8.47214	−1.24915
$47$	9.70820	1.41609	0.708044	−	0.706169i	$-0.249578\pi$
$47$	9.70820	1.41609	0.708044	+	0.706169i	$0.249578\pi$
$48$	−2.23607	−0.322749
$49$	2.00000	0.285714
$50$	0	0
$51$	2.23607	0.313112
$52$	2.47214	0.342824
$53$	−10.2361	−1.40603	−0.703016	−	0.711174i	$-0.748164\pi$
$53$	−10.2361	−1.40603	−0.703016	+	0.711174i	$0.748164\pi$
$54$	−2.23607	−0.304290
$55$	−2.76393	−0.372689
$56$	3.00000	0.400892
$57$	13.9443	1.84696
$58$	−2.23607	−0.293610
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	5.00000	0.645497
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−4.00000	−0.508001
$63$	−6.00000	−0.755929
$64$	1.00000	0.125000
$65$	−5.52786	−0.685647
$66$	2.76393	0.340217
$67$	3.70820	0.453029	0.226515	−	0.974008i	$-0.427267\pi$
$67$	3.70820	0.453029	0.226515	+	0.974008i	$0.427267\pi$
$68$	−1.00000	−0.121268
$69$	−18.9443	−2.28062
$70$	−6.70820	−0.801784
$71$	10.4721	1.24281	0.621407	−	0.783488i	$-0.286561\pi$
$71$	10.4721	1.24281	0.621407	+	0.783488i	$0.286561\pi$
$72$	−2.00000	−0.235702
$73$	3.23607	0.378753	0.189377	−	0.981905i	$-0.439353\pi$
$73$	3.23607	0.378753	0.189377	+	0.981905i	$0.439353\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	−6.23607	−0.715326
$77$	−3.70820	−0.422589
$78$	5.52786	0.625907
$79$	−2.52786	−0.284407	−0.142203	−	0.989837i	$-0.545419\pi$
$79$	−2.52786	−0.284407	−0.142203	+	0.989837i	$0.545419\pi$
$80$	−2.23607	−0.250000
$81$	−11.0000	−1.22222
$82$	9.00000	0.993884
$83$	−10.1803	−1.11744	−0.558719	−	0.829357i	$-0.688707\pi$
$83$	−10.1803	−1.11744	−0.558719	+	0.829357i	$0.688707\pi$
$84$	6.70820	0.731925
$85$	2.23607	0.242536
$86$	−4.00000	−0.431331
$87$	−5.00000	−0.536056
$88$	−1.23607	−0.131765
$89$	6.76393	0.716975	0.358488	−	0.933534i	$-0.383293\pi$
$89$	6.76393	0.716975	0.358488	+	0.933534i	$0.383293\pi$
$90$	4.47214	0.471405
$91$	−7.41641	−0.777451
$92$	8.47214	0.883281
$93$	−8.94427	−0.927478
$94$	−9.70820	−1.00132
$95$	13.9443	1.43065
$96$	2.23607	0.228218
$97$	−11.7082	−1.18879	−0.594394	−	0.804174i	$-0.702608\pi$
$97$	−11.7082	−1.18879	−0.594394	+	0.804174i	$0.702608\pi$
$98$	−2.00000	−0.202031
$99$	2.47214	0.248459
$100$	0	0
$101$	−15.7082	−1.56302	−0.781512	−	0.623890i	$-0.785551\pi$
$101$	−15.7082	−1.56302	−0.781512	+	0.623890i	$0.785551\pi$
$102$	−2.23607	−0.221404
$103$	−6.18034	−0.608967	−0.304483	−	0.952518i	$-0.598484\pi$
$103$	−6.18034	−0.608967	−0.304483	+	0.952518i	$0.598484\pi$
$104$	−2.47214	−0.242413
$105$	−15.0000	−1.46385
$106$	10.2361	0.994215
$107$	13.1803	1.27419	0.637096	−	0.770785i	$-0.280136\pi$
$107$	13.1803	1.27419	0.637096	+	0.770785i	$0.280136\pi$
$108$	2.23607	0.215166
$109$	−3.23607	−0.309959	−0.154980	−	0.987918i	$-0.549531\pi$
$109$	−3.23607	−0.309959	−0.154980	+	0.987918i	$0.549531\pi$
$110$	2.76393	0.263531
$111$	−17.8885	−1.69791
$112$	−3.00000	−0.283473
$113$	−3.23607	−0.304424	−0.152212	−	0.988348i	$-0.548640\pi$
$113$	−3.23607	−0.304424	−0.152212	+	0.988348i	$0.548640\pi$
$114$	−13.9443	−1.30600
$115$	−18.9443	−1.76656
$116$	2.23607	0.207614
$117$	4.94427	0.457098
$118$	1.00000	0.0920575
$119$	3.00000	0.275010
$120$	−5.00000	−0.456435
$121$	−9.47214	−0.861103
$122$	−2.00000	−0.181071
$123$	20.1246	1.81458
$124$	4.00000	0.359211
$125$	11.1803	1.00000
$126$	6.00000	0.534522
$127$	0.527864	0.0468404	0.0234202	−	0.999726i	$-0.492544\pi$
$127$	0.527864	0.0468404	0.0234202	+	0.999726i	$0.492544\pi$
$128$	−1.00000	−0.0883883
$129$	−8.94427	−0.787499
$130$	5.52786	0.484826
$131$	−2.94427	−0.257242	−0.128621	−	0.991694i	$-0.541055\pi$
$131$	−2.94427	−0.257242	−0.128621	+	0.991694i	$0.541055\pi$
$132$	−2.76393	−0.240569
$133$	18.7082	1.62221
$134$	−3.70820	−0.320340
$135$	−5.00000	−0.430331
$136$	1.00000	0.0857493
$137$	21.4721	1.83449	0.917244	−	0.398325i	$-0.130409\pi$
$137$	21.4721	1.83449	0.917244	+	0.398325i	$0.130409\pi$
$138$	18.9443	1.61264
$139$	−14.4721	−1.22751	−0.613755	−	0.789496i	$-0.710342\pi$
$139$	−14.4721	−1.22751	−0.613755	+	0.789496i	$0.710342\pi$
$140$	6.70820	0.566947
$141$	−21.7082	−1.82816
$142$	−10.4721	−0.878802
$143$	3.05573	0.255533
$144$	2.00000	0.166667
$145$	−5.00000	−0.415227
$146$	−3.23607	−0.267819
$147$	−4.47214	−0.368856
$148$	8.00000	0.657596
$149$	8.18034	0.670160	0.335080	−	0.942190i	$-0.391237\pi$
$149$	8.18034	0.670160	0.335080	+	0.942190i	$0.391237\pi$
$150$	0	0
$151$	−9.23607	−0.751621	−0.375810	−	0.926697i	$-0.622636\pi$
$151$	−9.23607	−0.751621	−0.375810	+	0.926697i	$0.622636\pi$
$152$	6.23607	0.505812
$153$	−2.00000	−0.161690
$154$	3.70820	0.298816
$155$	−8.94427	−0.718421
$156$	−5.52786	−0.442583
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	2.52786	0.201106
$159$	22.8885	1.81518
$160$	2.23607	0.176777
$161$	−25.4164	−2.00309
$162$	11.0000	0.864242
$163$	−20.3607	−1.59477	−0.797386	−	0.603470i	$-0.793784\pi$
$163$	−20.3607	−1.59477	−0.797386	+	0.603470i	$0.793784\pi$
$164$	−9.00000	−0.702782
$165$	6.18034	0.481139
$166$	10.1803	0.790148
$167$	9.00000	0.696441	0.348220	−	0.937413i	$-0.386786\pi$
$167$	9.00000	0.696441	0.348220	+	0.937413i	$0.386786\pi$
$168$	−6.70820	−0.517549
$169$	−6.88854	−0.529888
$170$	−2.23607	−0.171499
$171$	−12.4721	−0.953768
$172$	4.00000	0.304997
$173$	5.23607	0.398091	0.199045	−	0.979990i	$-0.436216\pi$
$173$	5.23607	0.398091	0.199045	+	0.979990i	$0.436216\pi$
$174$	5.00000	0.379049
$175$	0	0
$176$	1.23607	0.0931721
$177$	2.23607	0.168073
$178$	−6.76393	−0.506978
$179$	12.4721	0.932211	0.466106	−	0.884729i	$-0.345657\pi$
$179$	12.4721	0.932211	0.466106	+	0.884729i	$0.345657\pi$
$180$	−4.47214	−0.333333
$181$	−24.2361	−1.80145	−0.900726	−	0.434387i	$-0.856965\pi$
$181$	−24.2361	−1.80145	−0.900726	+	0.434387i	$0.856965\pi$
$182$	7.41641	0.549741
$183$	−4.47214	−0.330590
$184$	−8.47214	−0.624574
$185$	−17.8885	−1.31519
$186$	8.94427	0.655826
$187$	−1.23607	−0.0903902
$188$	9.70820	0.708044
$189$	−6.70820	−0.487950
$190$	−13.9443	−1.01162
$191$	19.2361	1.39187	0.695937	−	0.718103i	$-0.254989\pi$
$191$	19.2361	1.39187	0.695937	+	0.718103i	$0.254989\pi$
$192$	−2.23607	−0.161374
$193$	−13.9443	−1.00373	−0.501865	−	0.864946i	$-0.667353\pi$
$193$	−13.9443	−1.00373	−0.501865	+	0.864946i	$0.667353\pi$
$194$	11.7082	0.840600
$195$	12.3607	0.885167
$196$	2.00000	0.142857
$197$	10.9443	0.779747	0.389874	−	0.920868i	$-0.372519\pi$
$197$	10.9443	0.779747	0.389874	+	0.920868i	$0.372519\pi$
$198$	−2.47214	−0.175687
$199$	20.4164	1.44728	0.723640	−	0.690177i	$-0.242467\pi$
$199$	20.4164	1.44728	0.723640	+	0.690177i	$0.242467\pi$
$200$	0	0
$201$	−8.29180	−0.584858
$202$	15.7082	1.10523
$203$	−6.70820	−0.470824
$204$	2.23607	0.156556
$205$	20.1246	1.40556
$206$	6.18034	0.430605
$207$	16.9443	1.17771
$208$	2.47214	0.171412
$209$	−7.70820	−0.533188
$210$	15.0000	1.03510
$211$	−27.7082	−1.90751	−0.953756	−	0.300583i	$-0.902819\pi$
$211$	−27.7082	−1.90751	−0.953756	+	0.300583i	$0.902819\pi$
$212$	−10.2361	−0.703016
$213$	−23.4164	−1.60447
$214$	−13.1803	−0.900989
$215$	−8.94427	−0.609994
$216$	−2.23607	−0.152145
$217$	−12.0000	−0.814613
$218$	3.23607	0.219174
$219$	−7.23607	−0.488968
$220$	−2.76393	−0.186344
$221$	−2.47214	−0.166294
$222$	17.8885	1.20060
$223$	−12.0000	−0.803579	−0.401790	−	0.915732i	$-0.631612\pi$
$223$	−12.0000	−0.803579	−0.401790	+	0.915732i	$0.631612\pi$
$224$	3.00000	0.200446
$225$	0	0
$226$	3.23607	0.215260
$227$	−8.18034	−0.542948	−0.271474	−	0.962446i	$-0.587511\pi$
$227$	−8.18034	−0.542948	−0.271474	+	0.962446i	$0.587511\pi$
$228$	13.9443	0.923482
$229$	1.41641	0.0935989	0.0467994	−	0.998904i	$-0.485098\pi$
$229$	1.41641	0.0935989	0.0467994	+	0.998904i	$0.485098\pi$
$230$	18.9443	1.24915
$231$	8.29180	0.545560
$232$	−2.23607	−0.146805
$233$	−16.6525	−1.09094	−0.545470	−	0.838130i	$-0.683649\pi$
$233$	−16.6525	−1.09094	−0.545470	+	0.838130i	$0.683649\pi$
$234$	−4.94427	−0.323217
$235$	−21.7082	−1.41609
$236$	−1.00000	−0.0650945
$237$	5.65248	0.367168
$238$	−3.00000	−0.194461
$239$	−23.9443	−1.54883	−0.774413	−	0.632680i	$-0.781955\pi$
$239$	−23.9443	−1.54883	−0.774413	+	0.632680i	$0.781955\pi$
$240$	5.00000	0.322749
$241$	17.3607	1.11830	0.559150	−	0.829067i	$-0.311128\pi$
$241$	17.3607	1.11830	0.559150	+	0.829067i	$0.311128\pi$
$242$	9.47214	0.608892
$243$	17.8885	1.14755
$244$	2.00000	0.128037
$245$	−4.47214	−0.285714
$246$	−20.1246	−1.28310
$247$	−15.4164	−0.980923
$248$	−4.00000	−0.254000
$249$	22.7639	1.44261
$250$	−11.1803	−0.707107
$251$	7.76393	0.490055	0.245028	−	0.969516i	$-0.421203\pi$
$251$	7.76393	0.490055	0.245028	+	0.969516i	$0.421203\pi$
$252$	−6.00000	−0.377964
$253$	10.4721	0.658378
$254$	−0.527864	−0.0331211
$255$	−5.00000	−0.313112
$256$	1.00000	0.0625000
$257$	−3.00000	−0.187135	−0.0935674	−	0.995613i	$-0.529827\pi$
$257$	−3.00000	−0.187135	−0.0935674	+	0.995613i	$0.529827\pi$
$258$	8.94427	0.556846
$259$	−24.0000	−1.49129
$260$	−5.52786	−0.342824
$261$	4.47214	0.276818
$262$	2.94427	0.181898
$263$	−8.52786	−0.525851	−0.262925	−	0.964816i	$-0.584687\pi$
$263$	−8.52786	−0.525851	−0.262925	+	0.964816i	$0.584687\pi$
$264$	2.76393	0.170108
$265$	22.8885	1.40603
$266$	−18.7082	−1.14707
$267$	−15.1246	−0.925611
$268$	3.70820	0.226515
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	5.00000	0.304290
$271$	−28.4164	−1.72617	−0.863087	−	0.505055i	$-0.831472\pi$
$271$	−28.4164	−1.72617	−0.863087	+	0.505055i	$0.831472\pi$
$272$	−1.00000	−0.0606339
$273$	16.5836	1.00368
$274$	−21.4721	−1.29718
$275$	0	0
$276$	−18.9443	−1.14031
$277$	−1.29180	−0.0776165	−0.0388083	−	0.999247i	$-0.512356\pi$
$277$	−1.29180	−0.0776165	−0.0388083	+	0.999247i	$0.512356\pi$
$278$	14.4721	0.867981
$279$	8.00000	0.478947
$280$	−6.70820	−0.400892
$281$	−22.8885	−1.36542	−0.682708	−	0.730691i	$-0.739198\pi$
$281$	−22.8885	−1.36542	−0.682708	+	0.730691i	$0.739198\pi$
$282$	21.7082	1.29270
$283$	2.00000	0.118888	0.0594438	−	0.998232i	$-0.481067\pi$
$283$	2.00000	0.118888	0.0594438	+	0.998232i	$0.481067\pi$
$284$	10.4721	0.621407
$285$	−31.1803	−1.84696
$286$	−3.05573	−0.180689
$287$	27.0000	1.59376
$288$	−2.00000	−0.117851
$289$	1.00000	0.0588235
$290$	5.00000	0.293610
$291$	26.1803	1.53472
$292$	3.23607	0.189377
$293$	−8.23607	−0.481156	−0.240578	−	0.970630i	$-0.577337\pi$
$293$	−8.23607	−0.481156	−0.240578	+	0.970630i	$0.577337\pi$
$294$	4.47214	0.260820
$295$	2.23607	0.130189
$296$	−8.00000	−0.464991
$297$	2.76393	0.160380
$298$	−8.18034	−0.473874
$299$	20.9443	1.21124
$300$	0	0
$301$	−12.0000	−0.691669
$302$	9.23607	0.531476
$303$	35.1246	2.01786
$304$	−6.23607	−0.357663
$305$	−4.47214	−0.256074
$306$	2.00000	0.114332
$307$	12.7082	0.725296	0.362648	−	0.931926i	$-0.381873\pi$
$307$	12.7082	0.725296	0.362648	+	0.931926i	$0.381873\pi$
$308$	−3.70820	−0.211295
$309$	13.8197	0.786173
$310$	8.94427	0.508001
$311$	6.88854	0.390613	0.195307	−	0.980742i	$-0.437430\pi$
$311$	6.88854	0.390613	0.195307	+	0.980742i	$0.437430\pi$
$312$	5.52786	0.312954
$313$	27.8885	1.57635	0.788177	−	0.615449i	$-0.211025\pi$
$313$	27.8885	1.57635	0.788177	+	0.615449i	$0.211025\pi$
$314$	14.0000	0.790066
$315$	13.4164	0.755929
$316$	−2.52786	−0.142203
$317$	16.4721	0.925167	0.462584	−	0.886576i	$-0.346922\pi$
$317$	16.4721	0.925167	0.462584	+	0.886576i	$0.346922\pi$
$318$	−22.8885	−1.28353
$319$	2.76393	0.154750
$320$	−2.23607	−0.125000
$321$	−29.4721	−1.64497
$322$	25.4164	1.41640
$323$	6.23607	0.346984
$324$	−11.0000	−0.611111
$325$	0	0
$326$	20.3607	1.12767
$327$	7.23607	0.400155
$328$	9.00000	0.496942
$329$	−29.1246	−1.60569
$330$	−6.18034	−0.340217
$331$	33.5410	1.84358	0.921791	−	0.387688i	$-0.126726\pi$
$331$	33.5410	1.84358	0.921791	+	0.387688i	$0.126726\pi$
$332$	−10.1803	−0.558719
$333$	16.0000	0.876795
$334$	−9.00000	−0.492458
$335$	−8.29180	−0.453029
$336$	6.70820	0.365963
$337$	−2.29180	−0.124842	−0.0624210	−	0.998050i	$-0.519882\pi$
$337$	−2.29180	−0.124842	−0.0624210	+	0.998050i	$0.519882\pi$
$338$	6.88854	0.374687
$339$	7.23607	0.393009
$340$	2.23607	0.121268
$341$	4.94427	0.267747
$342$	12.4721	0.674416
$343$	15.0000	0.809924
$344$	−4.00000	−0.215666
$345$	42.3607	2.28062
$346$	−5.23607	−0.281493
$347$	27.7082	1.48745	0.743727	−	0.668483i	$-0.233056\pi$
$347$	27.7082	1.48745	0.743727	+	0.668483i	$0.233056\pi$
$348$	−5.00000	−0.268028
$349$	−20.8328	−1.11516	−0.557578	−	0.830125i	$-0.688269\pi$
$349$	−20.8328	−1.11516	−0.557578	+	0.830125i	$0.688269\pi$
$350$	0	0
$351$	5.52786	0.295056
$352$	−1.23607	−0.0658826
$353$	18.4721	0.983173	0.491586	−	0.870829i	$-0.336417\pi$
$353$	18.4721	0.983173	0.491586	+	0.870829i	$0.336417\pi$
$354$	−2.23607	−0.118846
$355$	−23.4164	−1.24281
$356$	6.76393	0.358488
$357$	−6.70820	−0.355036
$358$	−12.4721	−0.659173
$359$	−15.4721	−0.816588	−0.408294	−	0.912850i	$-0.633876\pi$
$359$	−15.4721	−0.816588	−0.408294	+	0.912850i	$0.633876\pi$
$360$	4.47214	0.235702
$361$	19.8885	1.04677
$362$	24.2361	1.27382
$363$	21.1803	1.11168
$364$	−7.41641	−0.388725
$365$	−7.23607	−0.378753
$366$	4.47214	0.233762
$367$	29.5967	1.54494	0.772469	−	0.635053i	$-0.219022\pi$
$367$	29.5967	1.54494	0.772469	+	0.635053i	$0.219022\pi$
$368$	8.47214	0.441641
$369$	−18.0000	−0.937043
$370$	17.8885	0.929981
$371$	30.7082	1.59429
$372$	−8.94427	−0.463739
$373$	−13.4164	−0.694675	−0.347338	−	0.937740i	$-0.612914\pi$
$373$	−13.4164	−0.694675	−0.347338	+	0.937740i	$0.612914\pi$
$374$	1.23607	0.0639156
$375$	−25.0000	−1.29099
$376$	−9.70820	−0.500662
$377$	5.52786	0.284699
$378$	6.70820	0.345033
$379$	−2.70820	−0.139111	−0.0695555	−	0.997578i	$-0.522158\pi$
$379$	−2.70820	−0.139111	−0.0695555	+	0.997578i	$0.522158\pi$
$380$	13.9443	0.715326
$381$	−1.18034	−0.0604706
$382$	−19.2361	−0.984203
$383$	21.8885	1.11845	0.559226	−	0.829015i	$-0.311098\pi$
$383$	21.8885	1.11845	0.559226	+	0.829015i	$0.311098\pi$
$384$	2.23607	0.114109
$385$	8.29180	0.422589
$386$	13.9443	0.709745
$387$	8.00000	0.406663
$388$	−11.7082	−0.594394
$389$	−19.5279	−0.990102	−0.495051	−	0.868864i	$-0.664851\pi$
$389$	−19.5279	−0.990102	−0.495051	+	0.868864i	$0.664851\pi$
$390$	−12.3607	−0.625907
$391$	−8.47214	−0.428454
$392$	−2.00000	−0.101015
$393$	6.58359	0.332098
$394$	−10.9443	−0.551364
$395$	5.65248	0.284407
$396$	2.47214	0.124230
$397$	−10.2918	−0.516530	−0.258265	−	0.966074i	$-0.583151\pi$
$397$	−10.2918	−0.516530	−0.258265	+	0.966074i	$0.583151\pi$
$398$	−20.4164	−1.02338
$399$	−41.8328	−2.09426
$400$	0	0
$401$	24.6525	1.23109	0.615543	−	0.788103i	$-0.288937\pi$
$401$	24.6525	1.23109	0.615543	+	0.788103i	$0.288937\pi$
$402$	8.29180	0.413557
$403$	9.88854	0.492583
$404$	−15.7082	−0.781512
$405$	24.5967	1.22222
$406$	6.70820	0.332923
$407$	9.88854	0.490157
$408$	−2.23607	−0.110702
$409$	23.7082	1.17230	0.586148	−	0.810204i	$-0.300644\pi$
$409$	23.7082	1.17230	0.586148	+	0.810204i	$0.300644\pi$
$410$	−20.1246	−0.993884
$411$	−48.0132	−2.36831
$412$	−6.18034	−0.304483
$413$	3.00000	0.147620
$414$	−16.9443	−0.832766
$415$	22.7639	1.11744
$416$	−2.47214	−0.121206
$417$	32.3607	1.58471
$418$	7.70820	0.377021
$419$	−40.0689	−1.95749	−0.978747	−	0.205074i	$-0.934257\pi$
$419$	−40.0689	−1.95749	−0.978747	+	0.205074i	$0.934257\pi$
$420$	−15.0000	−0.731925
$421$	−30.1803	−1.47090	−0.735450	−	0.677579i	$-0.763029\pi$
$421$	−30.1803	−1.47090	−0.735450	+	0.677579i	$0.763029\pi$
$422$	27.7082	1.34881
$423$	19.4164	0.944058
$424$	10.2361	0.497107
$425$	0	0
$426$	23.4164	1.13453
$427$	−6.00000	−0.290360
$428$	13.1803	0.637096
$429$	−6.83282	−0.329891
$430$	8.94427	0.431331
$431$	11.1246	0.535854	0.267927	−	0.963439i	$-0.413661\pi$
$431$	11.1246	0.535854	0.267927	+	0.963439i	$0.413661\pi$
$432$	2.23607	0.107583
$433$	−25.9443	−1.24680	−0.623401	−	0.781902i	$-0.714250\pi$
$433$	−25.9443	−1.24680	−0.623401	+	0.781902i	$0.714250\pi$
$434$	12.0000	0.576018
$435$	11.1803	0.536056
$436$	−3.23607	−0.154980
$437$	−52.8328	−2.52734
$438$	7.23607	0.345753
$439$	20.0000	0.954548	0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000	0.954548	0.477274	+	0.878755i	$0.341625\pi$
$440$	2.76393	0.131765
$441$	4.00000	0.190476
$442$	2.47214	0.117588
$443$	−25.5967	−1.21614	−0.608069	−	0.793884i	$-0.708056\pi$
$443$	−25.5967	−1.21614	−0.608069	+	0.793884i	$0.708056\pi$
$444$	−17.8885	−0.848953
$445$	−15.1246	−0.716975
$446$	12.0000	0.568216
$447$	−18.2918	−0.865172
$448$	−3.00000	−0.141737
$449$	12.0557	0.568945	0.284472	−	0.958684i	$-0.408182\pi$
$449$	12.0557	0.568945	0.284472	+	0.958684i	$0.408182\pi$
$450$	0	0
$451$	−11.1246	−0.523838
$452$	−3.23607	−0.152212
$453$	20.6525	0.970338
$454$	8.18034	0.383922
$455$	16.5836	0.777451
$456$	−13.9443	−0.653000
$457$	−3.12461	−0.146163	−0.0730816	−	0.997326i	$-0.523283\pi$
$457$	−3.12461	−0.146163	−0.0730816	+	0.997326i	$0.523283\pi$
$458$	−1.41641	−0.0661844
$459$	−2.23607	−0.104371
$460$	−18.9443	−0.883281
$461$	−1.41641	−0.0659687	−0.0329843	−	0.999456i	$-0.510501\pi$
$461$	−1.41641	−0.0659687	−0.0329843	+	0.999456i	$0.510501\pi$
$462$	−8.29180	−0.385769
$463$	13.4164	0.623513	0.311757	−	0.950162i	$-0.399083\pi$
$463$	13.4164	0.623513	0.311757	+	0.950162i	$0.399083\pi$
$464$	2.23607	0.103807
$465$	20.0000	0.927478
$466$	16.6525	0.771411
$467$	18.0689	0.836128	0.418064	−	0.908418i	$-0.362709\pi$
$467$	18.0689	0.836128	0.418064	+	0.908418i	$0.362709\pi$
$468$	4.94427	0.228549
$469$	−11.1246	−0.513687
$470$	21.7082	1.00132
$471$	31.3050	1.44246
$472$	1.00000	0.0460287
$473$	4.94427	0.227338
$474$	−5.65248	−0.259627
$475$	0	0
$476$	3.00000	0.137505
$477$	−20.4721	−0.937355
$478$	23.9443	1.09519
$479$	−17.8885	−0.817348	−0.408674	−	0.912680i	$-0.634009\pi$
$479$	−17.8885	−0.817348	−0.408674	+	0.912680i	$0.634009\pi$
$480$	−5.00000	−0.228218
$481$	19.7771	0.901758
$482$	−17.3607	−0.790757
$483$	56.8328	2.58598
$484$	−9.47214	−0.430552
$485$	26.1803	1.18879
$486$	−17.8885	−0.811441
$487$	27.4721	1.24488	0.622441	−	0.782667i	$-0.286141\pi$
$487$	27.4721	1.24488	0.622441	+	0.782667i	$0.286141\pi$
$488$	−2.00000	−0.0905357
$489$	45.5279	2.05884
$490$	4.47214	0.202031
$491$	5.29180	0.238815	0.119408	−	0.992845i	$-0.461900\pi$
$491$	5.29180	0.238815	0.119408	+	0.992845i	$0.461900\pi$
$492$	20.1246	0.907288
$493$	−2.23607	−0.100707
$494$	15.4164	0.693617
$495$	−5.52786	−0.248459
$496$	4.00000	0.179605
$497$	−31.4164	−1.40922
$498$	−22.7639	−1.02008
$499$	14.7082	0.658430	0.329215	−	0.944255i	$-0.393216\pi$
$499$	14.7082	0.658430	0.329215	+	0.944255i	$0.393216\pi$
$500$	11.1803	0.500000
$501$	−20.1246	−0.899101
$502$	−7.76393	−0.346521
$503$	18.4721	0.823632	0.411816	−	0.911267i	$-0.364895\pi$
$503$	18.4721	0.823632	0.411816	+	0.911267i	$0.364895\pi$
$504$	6.00000	0.267261
$505$	35.1246	1.56302
$506$	−10.4721	−0.465543
$507$	15.4033	0.684082
$508$	0.527864	0.0234202
$509$	18.0000	0.797836	0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000	0.797836	0.398918	+	0.916987i	$0.369386\pi$
$510$	5.00000	0.221404
$511$	−9.70820	−0.429466
$512$	−1.00000	−0.0441942
$513$	−13.9443	−0.615655
$514$	3.00000	0.132324
$515$	13.8197	0.608967
$516$	−8.94427	−0.393750
$517$	12.0000	0.527759
$518$	24.0000	1.05450
$519$	−11.7082	−0.513933
$520$	5.52786	0.242413
$521$	5.05573	0.221495	0.110748	−	0.993849i	$-0.464675\pi$
$521$	5.05573	0.221495	0.110748	+	0.993849i	$0.464675\pi$
$522$	−4.47214	−0.195740
$523$	−14.1246	−0.617626	−0.308813	−	0.951123i	$-0.599932\pi$
$523$	−14.1246	−0.617626	−0.308813	+	0.951123i	$0.599932\pi$
$524$	−2.94427	−0.128621
$525$	0	0
$526$	8.52786	0.371833
$527$	−4.00000	−0.174243
$528$	−2.76393	−0.120285
$529$	48.7771	2.12074
$530$	−22.8885	−0.994215
$531$	−2.00000	−0.0867926
$532$	18.7082	0.811104
$533$	−22.2492	−0.963721
$534$	15.1246	0.654506
$535$	−29.4721	−1.27419
$536$	−3.70820	−0.160170
$537$	−27.8885	−1.20348
$538$	6.00000	0.258678
$539$	2.47214	0.106482
$540$	−5.00000	−0.215166
$541$	13.4164	0.576816	0.288408	−	0.957508i	$-0.406874\pi$
$541$	13.4164	0.576816	0.288408	+	0.957508i	$0.406874\pi$
$542$	28.4164	1.22059
$543$	54.1935	2.32567
$544$	1.00000	0.0428746
$545$	7.23607	0.309959
$546$	−16.5836	−0.709712
$547$	−27.7771	−1.18766	−0.593831	−	0.804590i	$-0.702385\pi$
$547$	−27.7771	−1.18766	−0.593831	+	0.804590i	$0.702385\pi$
$548$	21.4721	0.917244
$549$	4.00000	0.170716
$550$	0	0
$551$	−13.9443	−0.594046
$552$	18.9443	0.806322
$553$	7.58359	0.322487
$554$	1.29180	0.0548832
$555$	40.0000	1.69791
$556$	−14.4721	−0.613755
$557$	−25.6525	−1.08693	−0.543465	−	0.839432i	$-0.682888\pi$
$557$	−25.6525	−1.08693	−0.543465	+	0.839432i	$0.682888\pi$
$558$	−8.00000	−0.338667
$559$	9.88854	0.418241
$560$	6.70820	0.283473
$561$	2.76393	0.116693
$562$	22.8885	0.965495
$563$	−1.34752	−0.0567914	−0.0283957	−	0.999597i	$-0.509040\pi$
$563$	−1.34752	−0.0567914	−0.0283957	+	0.999597i	$0.509040\pi$
$564$	−21.7082	−0.914080
$565$	7.23607	0.304424
$566$	−2.00000	−0.0840663
$567$	33.0000	1.38587
$568$	−10.4721	−0.439401
$569$	15.8885	0.666082	0.333041	−	0.942912i	$-0.391925\pi$
$569$	15.8885	0.666082	0.333041	+	0.942912i	$0.391925\pi$
$570$	31.1803	1.30600
$571$	−1.81966	−0.0761504	−0.0380752	−	0.999275i	$-0.512123\pi$
$571$	−1.81966	−0.0761504	−0.0380752	+	0.999275i	$0.512123\pi$
$572$	3.05573	0.127766
$573$	−43.0132	−1.79690
$574$	−27.0000	−1.12696
$575$	0	0
$576$	2.00000	0.0833333
$577$	−4.88854	−0.203513	−0.101756	−	0.994809i	$-0.532446\pi$
$577$	−4.88854	−0.203513	−0.101756	+	0.994809i	$0.532446\pi$
$578$	−1.00000	−0.0415945
$579$	31.1803	1.29581
$580$	−5.00000	−0.207614
$581$	30.5410	1.26705
$582$	−26.1803	−1.08521
$583$	−12.6525	−0.524012
$584$	−3.23607	−0.133909
$585$	−11.0557	−0.457098
$586$	8.23607	0.340229
$587$	−32.0689	−1.32362	−0.661812	−	0.749670i	$-0.730212\pi$
$587$	−32.0689	−1.32362	−0.661812	+	0.749670i	$0.730212\pi$
$588$	−4.47214	−0.184428
$589$	−24.9443	−1.02781
$590$	−2.23607	−0.0920575
$591$	−24.4721	−1.00665
$592$	8.00000	0.328798
$593$	−10.0557	−0.412939	−0.206470	−	0.978453i	$-0.566197\pi$
$593$	−10.0557	−0.412939	−0.206470	+	0.978453i	$0.566197\pi$
$594$	−2.76393	−0.113406
$595$	−6.70820	−0.275010
$596$	8.18034	0.335080
$597$	−45.6525	−1.86843
$598$	−20.9443	−0.856475
$599$	−28.0557	−1.14633	−0.573163	−	0.819441i	$-0.694284\pi$
$599$	−28.0557	−1.14633	−0.573163	+	0.819441i	$0.694284\pi$
$600$	0	0
$601$	−36.0000	−1.46847	−0.734235	−	0.678895i	$-0.762459\pi$
$601$	−36.0000	−1.46847	−0.734235	+	0.678895i	$0.762459\pi$
$602$	12.0000	0.489083
$603$	7.41641	0.302019
$604$	−9.23607	−0.375810
$605$	21.1803	0.861103
$606$	−35.1246	−1.42684
$607$	−24.5279	−0.995555	−0.497778	−	0.867305i	$-0.665850\pi$
$607$	−24.5279	−0.995555	−0.497778	+	0.867305i	$0.665850\pi$
$608$	6.23607	0.252906
$609$	15.0000	0.607831
$610$	4.47214	0.181071
$611$	24.0000	0.970936
$612$	−2.00000	−0.0808452
$613$	−39.7082	−1.60380	−0.801900	−	0.597459i	$-0.796177\pi$
$613$	−39.7082	−1.60380	−0.801900	+	0.597459i	$0.796177\pi$
$614$	−12.7082	−0.512861
$615$	−45.0000	−1.81458
$616$	3.70820	0.149408
$617$	43.2492	1.74115	0.870574	−	0.492037i	$-0.163748\pi$
$617$	43.2492	1.74115	0.870574	+	0.492037i	$0.163748\pi$
$618$	−13.8197	−0.555908
$619$	−30.1246	−1.21081	−0.605405	−	0.795917i	$-0.706989\pi$
$619$	−30.1246	−1.21081	−0.605405	+	0.795917i	$0.706989\pi$
$620$	−8.94427	−0.359211
$621$	18.9443	0.760207
$622$	−6.88854	−0.276205
$623$	−20.2918	−0.812974
$624$	−5.52786	−0.221292
$625$	−25.0000	−1.00000
$626$	−27.8885	−1.11465
$627$	17.2361	0.688342
$628$	−14.0000	−0.558661
$629$	−8.00000	−0.318981
$630$	−13.4164	−0.534522
$631$	29.5279	1.17549	0.587743	−	0.809048i	$-0.300017\pi$
$631$	29.5279	1.17549	0.587743	+	0.809048i	$0.300017\pi$
$632$	2.52786	0.100553
$633$	61.9574	2.46259
$634$	−16.4721	−0.654192
$635$	−1.18034	−0.0468404
$636$	22.8885	0.907590
$637$	4.94427	0.195899
$638$	−2.76393	−0.109425
$639$	20.9443	0.828543
$640$	2.23607	0.0883883
$641$	−11.8885	−0.469569	−0.234785	−	0.972047i	$-0.575438\pi$
$641$	−11.8885	−0.469569	−0.234785	+	0.972047i	$0.575438\pi$
$642$	29.4721	1.16317
$643$	−28.1246	−1.10913	−0.554563	−	0.832142i	$-0.687115\pi$
$643$	−28.1246	−1.10913	−0.554563	+	0.832142i	$0.687115\pi$
$644$	−25.4164	−1.00155
$645$	20.0000	0.787499
$646$	−6.23607	−0.245355
$647$	−0.888544	−0.0349323	−0.0174661	−	0.999847i	$-0.505560\pi$
$647$	−0.888544	−0.0349323	−0.0174661	+	0.999847i	$0.505560\pi$
$648$	11.0000	0.432121
$649$	−1.23607	−0.0485199
$650$	0	0
$651$	26.8328	1.05166
$652$	−20.3607	−0.797386
$653$	−14.2361	−0.557100	−0.278550	−	0.960422i	$-0.589854\pi$
$653$	−14.2361	−0.557100	−0.278550	+	0.960422i	$0.589854\pi$
$654$	−7.23607	−0.282953
$655$	6.58359	0.257242
$656$	−9.00000	−0.351391
$657$	6.47214	0.252502
$658$	29.1246	1.13540
$659$	−18.4721	−0.719572	−0.359786	−	0.933035i	$-0.617150\pi$
$659$	−18.4721	−0.719572	−0.359786	+	0.933035i	$0.617150\pi$
$660$	6.18034	0.240569
$661$	−28.7082	−1.11662	−0.558310	−	0.829633i	$-0.688550\pi$
$661$	−28.7082	−1.11662	−0.558310	+	0.829633i	$0.688550\pi$
$662$	−33.5410	−1.30361
$663$	5.52786	0.214684
$664$	10.1803	0.395074
$665$	−41.8328	−1.62221
$666$	−16.0000	−0.619987
$667$	18.9443	0.733525
$668$	9.00000	0.348220
$669$	26.8328	1.03742
$670$	8.29180	0.320340
$671$	2.47214	0.0954358
$672$	−6.70820	−0.258775
$673$	−5.81966	−0.224331	−0.112166	−	0.993690i	$-0.535779\pi$
$673$	−5.81966	−0.224331	−0.112166	+	0.993690i	$0.535779\pi$
$674$	2.29180	0.0882767
$675$	0	0
$676$	−6.88854	−0.264944
$677$	−10.5836	−0.406760	−0.203380	−	0.979100i	$-0.565193\pi$
$677$	−10.5836	−0.406760	−0.203380	+	0.979100i	$0.565193\pi$
$678$	−7.23607	−0.277900
$679$	35.1246	1.34796
$680$	−2.23607	−0.0857493
$681$	18.2918	0.700943
$682$	−4.94427	−0.189326
$683$	−19.4164	−0.742948	−0.371474	−	0.928443i	$-0.621148\pi$
$683$	−19.4164	−0.742948	−0.371474	+	0.928443i	$0.621148\pi$
$684$	−12.4721	−0.476884
$685$	−48.0132	−1.83449
$686$	−15.0000	−0.572703
$687$	−3.16718	−0.120836
$688$	4.00000	0.152499
$689$	−25.3050	−0.964042
$690$	−42.3607	−1.61264
$691$	40.2492	1.53115	0.765576	−	0.643345i	$-0.222454\pi$
$691$	40.2492	1.53115	0.765576	+	0.643345i	$0.222454\pi$
$692$	5.23607	0.199045
$693$	−7.41641	−0.281726
$694$	−27.7082	−1.05179
$695$	32.3607	1.22751
$696$	5.00000	0.189525
$697$	9.00000	0.340899
$698$	20.8328	0.788534
$699$	37.2361	1.40840
$700$	0	0
$701$	−33.5967	−1.26893	−0.634466	−	0.772951i	$-0.718780\pi$
$701$	−33.5967	−1.26893	−0.634466	+	0.772951i	$0.718780\pi$
$702$	−5.52786	−0.208636
$703$	−49.8885	−1.88158
$704$	1.23607	0.0465861
$705$	48.5410	1.82816
$706$	−18.4721	−0.695208
$707$	47.1246	1.77230
$708$	2.23607	0.0840366
$709$	−30.7082	−1.15327	−0.576635	−	0.817002i	$-0.695635\pi$
$709$	−30.7082	−1.15327	−0.576635	+	0.817002i	$0.695635\pi$
$710$	23.4164	0.878802
$711$	−5.05573	−0.189605
$712$	−6.76393	−0.253489
$713$	33.8885	1.26914
$714$	6.70820	0.251048
$715$	−6.83282	−0.255533
$716$	12.4721	0.466106
$717$	53.5410	1.99953
$718$	15.4721	0.577415
$719$	−42.5410	−1.58651	−0.793256	−	0.608888i	$-0.791616\pi$
$719$	−42.5410	−1.58651	−0.793256	+	0.608888i	$0.791616\pi$
$720$	−4.47214	−0.166667
$721$	18.5410	0.690504
$722$	−19.8885	−0.740175
$723$	−38.8197	−1.44372
$724$	−24.2361	−0.900726
$725$	0	0
$726$	−21.1803	−0.786076
$727$	−40.9443	−1.51854	−0.759269	−	0.650776i	$-0.774444\pi$
$727$	−40.9443	−1.51854	−0.759269	+	0.650776i	$0.774444\pi$
$728$	7.41641	0.274870
$729$	−7.00000	−0.259259
$730$	7.23607	0.267819
$731$	−4.00000	−0.147945
$732$	−4.47214	−0.165295
$733$	18.3607	0.678167	0.339084	−	0.940756i	$-0.389883\pi$
$733$	18.3607	0.678167	0.339084	+	0.940756i	$0.389883\pi$
$734$	−29.5967	−1.09244
$735$	10.0000	0.368856
$736$	−8.47214	−0.312287
$737$	4.58359	0.168839
$738$	18.0000	0.662589
$739$	−11.7082	−0.430693	−0.215347	−	0.976538i	$-0.569088\pi$
$739$	−11.7082	−0.430693	−0.215347	+	0.976538i	$0.569088\pi$
$740$	−17.8885	−0.657596
$741$	34.4721	1.26637
$742$	−30.7082	−1.12733
$743$	30.4721	1.11791	0.558957	−	0.829197i	$-0.311202\pi$
$743$	30.4721	1.11791	0.558957	+	0.829197i	$0.311202\pi$
$744$	8.94427	0.327913
$745$	−18.2918	−0.670160
$746$	13.4164	0.491210
$747$	−20.3607	−0.744958
$748$	−1.23607	−0.0451951
$749$	−39.5410	−1.44480
$750$	25.0000	0.912871
$751$	−30.9443	−1.12917	−0.564586	−	0.825374i	$-0.690964\pi$
$751$	−30.9443	−1.12917	−0.564586	+	0.825374i	$0.690964\pi$
$752$	9.70820	0.354022
$753$	−17.3607	−0.632658
$754$	−5.52786	−0.201313
$755$	20.6525	0.751621
$756$	−6.70820	−0.243975
$757$	−18.1246	−0.658750	−0.329375	−	0.944199i	$-0.606838\pi$
$757$	−18.1246	−0.658750	−0.329375	+	0.944199i	$0.606838\pi$
$758$	2.70820	0.0983664
$759$	−23.4164	−0.849962
$760$	−13.9443	−0.505812
$761$	−7.36068	−0.266824	−0.133412	−	0.991061i	$-0.542593\pi$
$761$	−7.36068	−0.266824	−0.133412	+	0.991061i	$0.542593\pi$
$762$	1.18034	0.0427592
$763$	9.70820	0.351461
$764$	19.2361	0.695937
$765$	4.47214	0.161690
$766$	−21.8885	−0.790865
$767$	−2.47214	−0.0892637
$768$	−2.23607	−0.0806872
$769$	−4.76393	−0.171792	−0.0858959	−	0.996304i	$-0.527375\pi$
$769$	−4.76393	−0.171792	−0.0858959	+	0.996304i	$0.527375\pi$
$770$	−8.29180	−0.298816
$771$	6.70820	0.241590
$772$	−13.9443	−0.501865
$773$	−19.2361	−0.691873	−0.345937	−	0.938258i	$-0.612439\pi$
$773$	−19.2361	−0.691873	−0.345937	+	0.938258i	$0.612439\pi$
$774$	−8.00000	−0.287554
$775$	0	0
$776$	11.7082	0.420300
$777$	53.6656	1.92524
$778$	19.5279	0.700108
$779$	56.1246	2.01087
$780$	12.3607	0.442583
$781$	12.9443	0.463182
$782$	8.47214	0.302963
$783$	5.00000	0.178685
$784$	2.00000	0.0714286
$785$	31.3050	1.11732
$786$	−6.58359	−0.234829
$787$	−11.4164	−0.406951	−0.203475	−	0.979080i	$-0.565224\pi$
$787$	−11.4164	−0.406951	−0.203475	+	0.979080i	$0.565224\pi$
$788$	10.9443	0.389874
$789$	19.0689	0.678870
$790$	−5.65248	−0.201106
$791$	9.70820	0.345184
$792$	−2.47214	−0.0878435
$793$	4.94427	0.175576
$794$	10.2918	0.365242
$795$	−51.1803	−1.81518
$796$	20.4164	0.723640
$797$	−56.0689	−1.98606	−0.993031	−	0.117854i	$-0.962398\pi$
$797$	−56.0689	−1.98606	−0.993031	+	0.117854i	$0.962398\pi$
$798$	41.8328	1.48087
$799$	−9.70820	−0.343452
$800$	0	0
$801$	13.5279	0.477984
$802$	−24.6525	−0.870509
$803$	4.00000	0.141157
$804$	−8.29180	−0.292429
$805$	56.8328	2.00309
$806$	−9.88854	−0.348309
$807$	13.4164	0.472280
$808$	15.7082	0.552613
$809$	8.11146	0.285184	0.142592	−	0.989782i	$-0.454456\pi$
$809$	8.11146	0.285184	0.142592	+	0.989782i	$0.454456\pi$
$810$	−24.5967	−0.864242
$811$	17.5967	0.617905	0.308953	−	0.951077i	$-0.400022\pi$
$811$	17.5967	0.617905	0.308953	+	0.951077i	$0.400022\pi$
$812$	−6.70820	−0.235412
$813$	63.5410	2.22848
$814$	−9.88854	−0.346593
$815$	45.5279	1.59477
$816$	2.23607	0.0782780
$817$	−24.9443	−0.872690
$818$	−23.7082	−0.828938
$819$	−14.8328	−0.518301
$820$	20.1246	0.702782
$821$	−36.7639	−1.28307	−0.641535	−	0.767094i	$-0.721702\pi$
$821$	−36.7639	−1.28307	−0.641535	+	0.767094i	$0.721702\pi$
$822$	48.0132	1.67465
$823$	−20.4721	−0.713614	−0.356807	−	0.934178i	$-0.616135\pi$
$823$	−20.4721	−0.713614	−0.356807	+	0.934178i	$0.616135\pi$
$824$	6.18034	0.215302
$825$	0	0
$826$	−3.00000	−0.104383
$827$	51.7771	1.80047	0.900233	−	0.435409i	$-0.143396\pi$
$827$	51.7771	1.80047	0.900233	+	0.435409i	$0.143396\pi$
$828$	16.9443	0.588854
$829$	−2.70820	−0.0940598	−0.0470299	−	0.998893i	$-0.514976\pi$
$829$	−2.70820	−0.0940598	−0.0470299	+	0.998893i	$0.514976\pi$
$830$	−22.7639	−0.790148
$831$	2.88854	0.100202
$832$	2.47214	0.0857059
$833$	−2.00000	−0.0692959
$834$	−32.3607	−1.12056
$835$	−20.1246	−0.696441
$836$	−7.70820	−0.266594
$837$	8.94427	0.309159
$838$	40.0689	1.38416
$839$	−33.7082	−1.16374	−0.581868	−	0.813283i	$-0.697678\pi$
$839$	−33.7082	−1.16374	−0.581868	+	0.813283i	$0.697678\pi$
$840$	15.0000	0.517549
$841$	−24.0000	−0.827586
$842$	30.1803	1.04008
$843$	51.1803	1.76274
$844$	−27.7082	−0.953756
$845$	15.4033	0.529888
$846$	−19.4164	−0.667550
$847$	28.4164	0.976399
$848$	−10.2361	−0.351508
$849$	−4.47214	−0.153483
$850$	0	0
$851$	67.7771	2.32337
$852$	−23.4164	−0.802233
$853$	−6.34752	−0.217335	−0.108668	−	0.994078i	$-0.534658\pi$
$853$	−6.34752	−0.217335	−0.108668	+	0.994078i	$0.534658\pi$
$854$	6.00000	0.205316
$855$	27.8885	0.953768
$856$	−13.1803	−0.450495
$857$	−28.4721	−0.972590	−0.486295	−	0.873795i	$-0.661652\pi$
$857$	−28.4721	−0.972590	−0.486295	+	0.873795i	$0.661652\pi$
$858$	6.83282	0.233268
$859$	26.5836	0.907020	0.453510	−	0.891251i	$-0.350172\pi$
$859$	26.5836	0.907020	0.453510	+	0.891251i	$0.350172\pi$
$860$	−8.94427	−0.304997
$861$	−60.3738	−2.05753
$862$	−11.1246	−0.378906
$863$	−4.18034	−0.142300	−0.0711502	−	0.997466i	$-0.522667\pi$
$863$	−4.18034	−0.142300	−0.0711502	+	0.997466i	$0.522667\pi$
$864$	−2.23607	−0.0760726
$865$	−11.7082	−0.398091
$866$	25.9443	0.881622
$867$	−2.23607	−0.0759408
$868$	−12.0000	−0.407307
$869$	−3.12461	−0.105995
$870$	−11.1803	−0.379049
$871$	9.16718	0.310618
$872$	3.23607	0.109587
$873$	−23.4164	−0.792525
$874$	52.8328	1.78710
$875$	−33.5410	−1.13389
$876$	−7.23607	−0.244484
$877$	35.7639	1.20766	0.603831	−	0.797112i	$-0.293640\pi$
$877$	35.7639	1.20766	0.603831	+	0.797112i	$0.293640\pi$
$878$	−20.0000	−0.674967
$879$	18.4164	0.621170
$880$	−2.76393	−0.0931721
$881$	−9.81966	−0.330833	−0.165416	−	0.986224i	$-0.552897\pi$
$881$	−9.81966	−0.330833	−0.165416	+	0.986224i	$0.552897\pi$
$882$	−4.00000	−0.134687
$883$	23.7639	0.799720	0.399860	−	0.916576i	$-0.369059\pi$
$883$	23.7639	0.799720	0.399860	+	0.916576i	$0.369059\pi$
$884$	−2.47214	−0.0831469
$885$	−5.00000	−0.168073
$886$	25.5967	0.859940
$887$	−47.0132	−1.57855	−0.789274	−	0.614042i	$-0.789543\pi$
$887$	−47.0132	−1.57855	−0.789274	+	0.614042i	$0.789543\pi$
$888$	17.8885	0.600300
$889$	−1.58359	−0.0531120
$890$	15.1246	0.506978
$891$	−13.5967	−0.455508
$892$	−12.0000	−0.401790
$893$	−60.5410	−2.02593
$894$	18.2918	0.611769
$895$	−27.8885	−0.932211
$896$	3.00000	0.100223
$897$	−46.8328	−1.56370
$898$	−12.0557	−0.402305
$899$	8.94427	0.298308
$900$	0	0
$901$	10.2361	0.341013
$902$	11.1246	0.370409
$903$	26.8328	0.892940
$904$	3.23607	0.107630
$905$	54.1935	1.80145
$906$	−20.6525	−0.686133
$907$	−5.29180	−0.175711	−0.0878556	−	0.996133i	$-0.528001\pi$
$907$	−5.29180	−0.175711	−0.0878556	+	0.996133i	$0.528001\pi$
$908$	−8.18034	−0.271474
$909$	−31.4164	−1.04202
$910$	−16.5836	−0.549741
$911$	25.9443	0.859572	0.429786	−	0.902931i	$-0.358589\pi$
$911$	25.9443	0.859572	0.429786	+	0.902931i	$0.358589\pi$
$912$	13.9443	0.461741
$913$	−12.5836	−0.416456
$914$	3.12461	0.103353
$915$	10.0000	0.330590
$916$	1.41641	0.0467994
$917$	8.83282	0.291685
$918$	2.23607	0.0738012
$919$	−7.12461	−0.235019	−0.117510	−	0.993072i	$-0.537491\pi$
$919$	−7.12461	−0.235019	−0.117510	+	0.993072i	$0.537491\pi$
$920$	18.9443	0.624574
$921$	−28.4164	−0.936352
$922$	1.41641	0.0466469
$923$	25.8885	0.852132
$924$	8.29180	0.272780
$925$	0	0
$926$	−13.4164	−0.440891
$927$	−12.3607	−0.405978
$928$	−2.23607	−0.0734025
$929$	−29.8197	−0.978351	−0.489176	−	0.872185i	$-0.662702\pi$
$929$	−29.8197	−0.978351	−0.489176	+	0.872185i	$0.662702\pi$
$930$	−20.0000	−0.655826
$931$	−12.4721	−0.408758
$932$	−16.6525	−0.545470
$933$	−15.4033	−0.504280
$934$	−18.0689	−0.591232
$935$	2.76393	0.0903902
$936$	−4.94427	−0.161609
$937$	22.9443	0.749557	0.374778	−	0.927114i	$-0.377719\pi$
$937$	22.9443	0.749557	0.374778	+	0.927114i	$0.377719\pi$
$938$	11.1246	0.363231
$939$	−62.3607	−2.03506
$940$	−21.7082	−0.708044
$941$	34.7639	1.13327	0.566636	−	0.823968i	$-0.308245\pi$
$941$	34.7639	1.13327	0.566636	+	0.823968i	$0.308245\pi$
$942$	−31.3050	−1.01997
$943$	−76.2492	−2.48302
$944$	−1.00000	−0.0325472
$945$	15.0000	0.487950
$946$	−4.94427	−0.160752
$947$	−22.5967	−0.734296	−0.367148	−	0.930163i	$-0.619666\pi$
$947$	−22.5967	−0.734296	−0.367148	+	0.930163i	$0.619666\pi$
$948$	5.65248	0.183584
$949$	8.00000	0.259691
$950$	0	0
$951$	−36.8328	−1.19439
$952$	−3.00000	−0.0972306
$953$	−43.5279	−1.41001	−0.705003	−	0.709204i	$-0.749054\pi$
$953$	−43.5279	−1.41001	−0.705003	+	0.709204i	$0.749054\pi$
$954$	20.4721	0.662810
$955$	−43.0132	−1.39187
$956$	−23.9443	−0.774413
$957$	−6.18034	−0.199782
$958$	17.8885	0.577953
$959$	−64.4164	−2.08011
$960$	5.00000	0.161374
$961$	−15.0000	−0.483871
$962$	−19.7771	−0.637639
$963$	26.3607	0.849461
$964$	17.3607	0.559150
$965$	31.1803	1.00373
$966$	−56.8328	−1.82857
$967$	36.2492	1.16570	0.582848	−	0.812581i	$-0.301938\pi$
$967$	36.2492	1.16570	0.582848	+	0.812581i	$0.301938\pi$
$968$	9.47214	0.304446
$969$	−13.9443	−0.447955
$970$	−26.1803	−0.840600
$971$	13.6525	0.438129	0.219064	−	0.975710i	$-0.429700\pi$
$971$	13.6525	0.438129	0.219064	+	0.975710i	$0.429700\pi$
$972$	17.8885	0.573775
$973$	43.4164	1.39187
$974$	−27.4721	−0.880264
$975$	0	0
$976$	2.00000	0.0640184
$977$	−31.9574	−1.02241	−0.511204	−	0.859459i	$-0.670800\pi$
$977$	−31.9574	−1.02241	−0.511204	+	0.859459i	$0.670800\pi$
$978$	−45.5279	−1.45582
$979$	8.36068	0.267208
$980$	−4.47214	−0.142857
$981$	−6.47214	−0.206639
$982$	−5.29180	−0.168868
$983$	−42.3607	−1.35110	−0.675548	−	0.737316i	$-0.736093\pi$
$983$	−42.3607	−1.35110	−0.675548	+	0.737316i	$0.736093\pi$
$984$	−20.1246	−0.641549
$985$	−24.4721	−0.779747
$986$	2.23607	0.0712109
$987$	65.1246	2.07294
$988$	−15.4164	−0.490461
$989$	33.8885	1.07759
$990$	5.52786	0.175687
$991$	−28.0689	−0.891637	−0.445819	−	0.895123i	$-0.647087\pi$
$991$	−28.0689	−0.891637	−0.445819	+	0.895123i	$0.647087\pi$
$992$	−4.00000	−0.127000
$993$	−75.0000	−2.38005
$994$	31.4164	0.996468
$995$	−45.6525	−1.44728
$996$	22.7639	0.721303
$997$	−38.7082	−1.22590	−0.612951	−	0.790121i	$-0.710018\pi$
$997$	−38.7082	−1.22590	−0.612951	+	0.790121i	$0.710018\pi$
$998$	−14.7082	−0.465580
$999$	17.8885	0.565968

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.l.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.l.1.1	✓	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.23607 q^{3} +1.00000 q^{4} -2.23607 q^{5} +2.23607 q^{6} -3.00000 q^{7} -1.00000 q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.23607 q^{3} +1.00000 q^{4} -2.23607 q^{5} +2.23607 q^{6} -3.00000 q^{7} -1.00000 q^{8} +2.00000 q^{9} +2.23607 q^{10} +1.23607 q^{11} -2.23607 q^{12} +2.47214 q^{13} +3.00000 q^{14} +5.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -2.00000 q^{18} -6.23607 q^{19} -2.23607 q^{20} +6.70820 q^{21} -1.23607 q^{22} +8.47214 q^{23} +2.23607 q^{24} -2.47214 q^{26} +2.23607 q^{27} -3.00000 q^{28} +2.23607 q^{29} -5.00000 q^{30} +4.00000 q^{31} -1.00000 q^{32} -2.76393 q^{33} +1.00000 q^{34} +6.70820 q^{35} +2.00000 q^{36} +8.00000 q^{37} +6.23607 q^{38} -5.52786 q^{39} +2.23607 q^{40} -9.00000 q^{41} -6.70820 q^{42} +4.00000 q^{43} +1.23607 q^{44} -4.47214 q^{45} -8.47214 q^{46} +9.70820 q^{47} -2.23607 q^{48} +2.00000 q^{49} +2.23607 q^{51} +2.47214 q^{52} -10.2361 q^{53} -2.23607 q^{54} -2.76393 q^{55} +3.00000 q^{56} +13.9443 q^{57} -2.23607 q^{58} -1.00000 q^{59} +5.00000 q^{60} +2.00000 q^{61} -4.00000 q^{62} -6.00000 q^{63} +1.00000 q^{64} -5.52786 q^{65} +2.76393 q^{66} +3.70820 q^{67} -1.00000 q^{68} -18.9443 q^{69} -6.70820 q^{70} +10.4721 q^{71} -2.00000 q^{72} +3.23607 q^{73} -8.00000 q^{74} -6.23607 q^{76} -3.70820 q^{77} +5.52786 q^{78} -2.52786 q^{79} -2.23607 q^{80} -11.0000 q^{81} +9.00000 q^{82} -10.1803 q^{83} +6.70820 q^{84} +2.23607 q^{85} -4.00000 q^{86} -5.00000 q^{87} -1.23607 q^{88} +6.76393 q^{89} +4.47214 q^{90} -7.41641 q^{91} +8.47214 q^{92} -8.94427 q^{93} -9.70820 q^{94} +13.9443 q^{95} +2.23607 q^{96} -11.7082 q^{97} -2.00000 q^{98} +2.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 6 q^{7} - 2 q^{8} + 4 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 6 * q^7 - 2 * q^8 + 4 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} - 6 q^{7} - 2 q^{8} + 4 q^{9} - 2 q^{11} - 4 q^{13} + 6 q^{14} + 10 q^{15} + 2 q^{16} - 2 q^{17} - 4 q^{18} - 8 q^{19} + 2 q^{22} + 8 q^{23} + 4 q^{26} - 6 q^{28} - 10 q^{30} + 8 q^{31} - 2 q^{32} - 10 q^{33} + 2 q^{34} + 4 q^{36} + 16 q^{37} + 8 q^{38} - 20 q^{39} - 18 q^{41} + 8 q^{43} - 2 q^{44} - 8 q^{46} + 6 q^{47} + 4 q^{49} - 4 q^{52} - 16 q^{53} - 10 q^{55} + 6 q^{56} + 10 q^{57} - 2 q^{59} + 10 q^{60} + 4 q^{61} - 8 q^{62} - 12 q^{63} + 2 q^{64} - 20 q^{65} + 10 q^{66} - 6 q^{67} - 2 q^{68} - 20 q^{69} + 12 q^{71} - 4 q^{72} + 2 q^{73} - 16 q^{74} - 8 q^{76} + 6 q^{77} + 20 q^{78} - 14 q^{79} - 22 q^{81} + 18 q^{82} + 2 q^{83} - 8 q^{86} - 10 q^{87} + 2 q^{88} + 18 q^{89} + 12 q^{91} + 8 q^{92} - 6 q^{94} + 10 q^{95} - 10 q^{97} - 4 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 6 * q^7 - 2 * q^8 + 4 * q^9 - 2 * q^11 - 4 * q^13 + 6 * q^14 + 10 * q^15 + 2 * q^16 - 2 * q^17 - 4 * q^18 - 8 * q^19 + 2 * q^22 + 8 * q^23 + 4 * q^26 - 6 * q^28 - 10 * q^30 + 8 * q^31 - 2 * q^32 - 10 * q^33 + 2 * q^34 + 4 * q^36 + 16 * q^37 + 8 * q^38 - 20 * q^39 - 18 * q^41 + 8 * q^43 - 2 * q^44 - 8 * q^46 + 6 * q^47 + 4 * q^49 - 4 * q^52 - 16 * q^53 - 10 * q^55 + 6 * q^56 + 10 * q^57 - 2 * q^59 + 10 * q^60 + 4 * q^61 - 8 * q^62 - 12 * q^63 + 2 * q^64 - 20 * q^65 + 10 * q^66 - 6 * q^67 - 2 * q^68 - 20 * q^69 + 12 * q^71 - 4 * q^72 + 2 * q^73 - 16 * q^74 - 8 * q^76 + 6 * q^77 + 20 * q^78 - 14 * q^79 - 22 * q^81 + 18 * q^82 + 2 * q^83 - 8 * q^86 - 10 * q^87 + 2 * q^88 + 18 * q^89 + 12 * q^91 + 8 * q^92 - 6 * q^94 + 10 * q^95 - 10 * q^97 - 4 * q^98 - 4 * q^99

Introduction

L-functions

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Database

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