LMFDB - Embedded newform 1006.2.a.j.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1006,2,Mod(1,1006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1006, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1006 = 2 \cdot 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1006.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:	$8.03295044334$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 13 x^{10} + 94 x^{9} + 15 x^{8} - 616 x^{7} + 368 x^{6} + 1643 x^{5} - 1463 x^{4} + \cdots - 208 $ x^12 - 5x^11 - 13x^10 + 94x^9 + 15x^8 - 616x^7 + 368x^6 + 1643x^5 - 1463x^4 - 1556x^3 + 1284x^2 + 576*x - 208
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.74625$ of defining polynomial
Character	$\chi$	$=$	1006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.74625 q^{3} +1.00000 q^{4} -2.58578 q^{5} +1.74625 q^{6} +0.635213 q^{7} +1.00000 q^{8} +0.0494057 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.74625 q^{3} +1.00000 q^{4} -2.58578 q^{5} +1.74625 q^{6} +0.635213 q^{7} +1.00000 q^{8} +0.0494057 q^{9} -2.58578 q^{10} +3.51104 q^{11} +1.74625 q^{12} +5.12735 q^{13} +0.635213 q^{14} -4.51543 q^{15} +1.00000 q^{16} -0.322021 q^{17} +0.0494057 q^{18} +3.38371 q^{19} -2.58578 q^{20} +1.10924 q^{21} +3.51104 q^{22} +3.77692 q^{23} +1.74625 q^{24} +1.68625 q^{25} +5.12735 q^{26} -5.15249 q^{27} +0.635213 q^{28} +2.46547 q^{29} -4.51543 q^{30} +1.98771 q^{31} +1.00000 q^{32} +6.13117 q^{33} -0.322021 q^{34} -1.64252 q^{35} +0.0494057 q^{36} -7.77317 q^{37} +3.38371 q^{38} +8.95366 q^{39} -2.58578 q^{40} +10.7578 q^{41} +1.10924 q^{42} -9.96085 q^{43} +3.51104 q^{44} -0.127752 q^{45} +3.77692 q^{46} -3.93174 q^{47} +1.74625 q^{48} -6.59651 q^{49} +1.68625 q^{50} -0.562331 q^{51} +5.12735 q^{52} +8.45466 q^{53} -5.15249 q^{54} -9.07877 q^{55} +0.635213 q^{56} +5.90881 q^{57} +2.46547 q^{58} +11.9394 q^{59} -4.51543 q^{60} +0.586889 q^{61} +1.98771 q^{62} +0.0313831 q^{63} +1.00000 q^{64} -13.2582 q^{65} +6.13117 q^{66} -12.9100 q^{67} -0.322021 q^{68} +6.59547 q^{69} -1.64252 q^{70} -0.0667081 q^{71} +0.0494057 q^{72} -2.81224 q^{73} -7.77317 q^{74} +2.94462 q^{75} +3.38371 q^{76} +2.23026 q^{77} +8.95366 q^{78} -4.39323 q^{79} -2.58578 q^{80} -9.14578 q^{81} +10.7578 q^{82} -16.7077 q^{83} +1.10924 q^{84} +0.832675 q^{85} -9.96085 q^{86} +4.30534 q^{87} +3.51104 q^{88} -13.6156 q^{89} -0.127752 q^{90} +3.25696 q^{91} +3.77692 q^{92} +3.47104 q^{93} -3.93174 q^{94} -8.74951 q^{95} +1.74625 q^{96} -12.7052 q^{97} -6.59651 q^{98} +0.173465 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 5 q^{3} + 12 q^{4} + 5 q^{5} + 5 q^{6} + 8 q^{7} + 12 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 5 * q^3 + 12 * q^4 + 5 * q^5 + 5 * q^6 + 8 * q^7 + 12 * q^8 + 15 * q^9	\( 12 q + 12 q^{2} + 5 q^{3} + 12 q^{4} + 5 q^{5} + 5 q^{6} + 8 q^{7} + 12 q^{8} + 15 q^{9} + 5 q^{10} + 18 q^{11} + 5 q^{12} + 4 q^{13} + 8 q^{14} + 2 q^{15} + 12 q^{16} - 2 q^{17} + 15 q^{18} + 6 q^{19} + 5 q^{20} + q^{21} + 18 q^{22} + 13 q^{23} + 5 q^{24} + q^{25} + 4 q^{26} + 8 q^{27} + 8 q^{28} + 20 q^{29} + 2 q^{30} + 7 q^{31} + 12 q^{32} - 8 q^{33} - 2 q^{34} + q^{35} + 15 q^{36} + 10 q^{37} + 6 q^{38} + 7 q^{39} + 5 q^{40} + 2 q^{41} + q^{42} + 8 q^{43} + 18 q^{44} - 7 q^{45} + 13 q^{46} + 12 q^{47} + 5 q^{48} + 4 q^{49} + q^{50} + 2 q^{51} + 4 q^{52} + 12 q^{53} + 8 q^{54} + 8 q^{55} + 8 q^{56} - 10 q^{57} + 20 q^{58} + 6 q^{59} + 2 q^{60} - 10 q^{61} + 7 q^{62} + 7 q^{63} + 12 q^{64} + 4 q^{65} - 8 q^{66} + 7 q^{67} - 2 q^{68} - 12 q^{69} + q^{70} + 22 q^{71} + 15 q^{72} - 23 q^{73} + 10 q^{74} - 34 q^{75} + 6 q^{76} - 19 q^{77} + 7 q^{78} + 13 q^{79} + 5 q^{80} - 28 q^{81} + 2 q^{82} + q^{83} + q^{84} - 28 q^{85} + 8 q^{86} - 22 q^{87} + 18 q^{88} - 3 q^{89} - 7 q^{90} - 21 q^{91} + 13 q^{92} - 33 q^{93} + 12 q^{94} - 2 q^{95} + 5 q^{96} - 70 q^{97} + 4 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 5 * q^3 + 12 * q^4 + 5 * q^5 + 5 * q^6 + 8 * q^7 + 12 * q^8 + 15 * q^9 + 5 * q^10 + 18 * q^11 + 5 * q^12 + 4 * q^13 + 8 * q^14 + 2 * q^15 + 12 * q^16 - 2 * q^17 + 15 * q^18 + 6 * q^19 + 5 * q^20 + q^21 + 18 * q^22 + 13 * q^23 + 5 * q^24 + q^25 + 4 * q^26 + 8 * q^27 + 8 * q^28 + 20 * q^29 + 2 * q^30 + 7 * q^31 + 12 * q^32 - 8 * q^33 - 2 * q^34 + q^35 + 15 * q^36 + 10 * q^37 + 6 * q^38 + 7 * q^39 + 5 * q^40 + 2 * q^41 + q^42 + 8 * q^43 + 18 * q^44 - 7 * q^45 + 13 * q^46 + 12 * q^47 + 5 * q^48 + 4 * q^49 + q^50 + 2 * q^51 + 4 * q^52 + 12 * q^53 + 8 * q^54 + 8 * q^55 + 8 * q^56 - 10 * q^57 + 20 * q^58 + 6 * q^59 + 2 * q^60 - 10 * q^61 + 7 * q^62 + 7 * q^63 + 12 * q^64 + 4 * q^65 - 8 * q^66 + 7 * q^67 - 2 * q^68 - 12 * q^69 + q^70 + 22 * q^71 + 15 * q^72 - 23 * q^73 + 10 * q^74 - 34 * q^75 + 6 * q^76 - 19 * q^77 + 7 * q^78 + 13 * q^79 + 5 * q^80 - 28 * q^81 + 2 * q^82 + q^83 + q^84 - 28 * q^85 + 8 * q^86 - 22 * q^87 + 18 * q^88 - 3 * q^89 - 7 * q^90 - 21 * q^91 + 13 * q^92 - 33 * q^93 + 12 * q^94 - 2 * q^95 + 5 * q^96 - 70 * q^97 + 4 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.74625	1.00820	0.504100	−	0.863645i	$-0.331824\pi$
$3$	1.74625	1.00820	0.504100	+	0.863645i	$0.331824\pi$
$4$	1.00000	0.500000
$5$	−2.58578	−1.15639	−0.578197	−	0.815897i	$-0.696244\pi$
$5$	−2.58578	−1.15639	−0.578197	+	0.815897i	$0.696244\pi$
$6$	1.74625	0.712906
$7$	0.635213	0.240088	0.120044	−	0.992769i	$-0.461696\pi$
$7$	0.635213	0.240088	0.120044	+	0.992769i	$0.461696\pi$
$8$	1.00000	0.353553
$9$	0.0494057	0.0164686
$10$	−2.58578	−0.817695
$11$	3.51104	1.05862	0.529309	−	0.848429i	$-0.322451\pi$
$11$	3.51104	1.05862	0.529309	+	0.848429i	$0.322451\pi$
$12$	1.74625	0.504100
$13$	5.12735	1.42207	0.711035	−	0.703156i	$-0.248227\pi$
$13$	5.12735	1.42207	0.711035	+	0.703156i	$0.248227\pi$
$14$	0.635213	0.169768
$15$	−4.51543	−1.16588
$16$	1.00000	0.250000
$17$	−0.322021	−0.0781016	−0.0390508	−	0.999237i	$-0.512433\pi$
$17$	−0.322021	−0.0781016	−0.0390508	+	0.999237i	$0.512433\pi$
$18$	0.0494057	0.0116450
$19$	3.38371	0.776276	0.388138	−	0.921601i	$-0.373118\pi$
$19$	3.38371	0.776276	0.388138	+	0.921601i	$0.373118\pi$
$20$	−2.58578	−0.578197
$21$	1.10924	0.242057
$22$	3.51104	0.748556
$23$	3.77692	0.787543	0.393772	−	0.919208i	$-0.371170\pi$
$23$	3.77692	0.787543	0.393772	+	0.919208i	$0.371170\pi$
$24$	1.74625	0.356453
$25$	1.68625	0.337249
$26$	5.12735	1.00556
$27$	−5.15249	−0.991597
$28$	0.635213	0.120044
$29$	2.46547	0.457826	0.228913	−	0.973447i	$-0.426483\pi$
$29$	2.46547	0.457826	0.228913	+	0.973447i	$0.426483\pi$
$30$	−4.51543	−0.824400
$31$	1.98771	0.357003	0.178501	−	0.983940i	$-0.442875\pi$
$31$	1.98771	0.357003	0.178501	+	0.983940i	$0.442875\pi$
$32$	1.00000	0.176777
$33$	6.13117	1.06730
$34$	−0.322021	−0.0552262
$35$	−1.64252	−0.277636
$36$	0.0494057	0.00823428
$37$	−7.77317	−1.27790	−0.638951	−	0.769248i	$-0.720631\pi$
$37$	−7.77317	−1.27790	−0.638951	+	0.769248i	$0.720631\pi$
$38$	3.38371	0.548910
$39$	8.95366	1.43373
$40$	−2.58578	−0.408847
$41$	10.7578	1.68009	0.840045	−	0.542516i	$-0.182528\pi$
$41$	10.7578	1.68009	0.840045	+	0.542516i	$0.182528\pi$
$42$	1.10924	0.171160
$43$	−9.96085	−1.51902	−0.759508	−	0.650498i	$-0.774560\pi$
$43$	−9.96085	−1.51902	−0.759508	+	0.650498i	$0.774560\pi$
$44$	3.51104	0.529309
$45$	−0.127752	−0.0190442
$46$	3.77692	0.556877
$47$	−3.93174	−0.573503	−0.286752	−	0.958005i	$-0.592575\pi$
$47$	−3.93174	−0.573503	−0.286752	+	0.958005i	$0.592575\pi$
$48$	1.74625	0.252050
$49$	−6.59651	−0.942358
$50$	1.68625	0.238471
$51$	−0.562331	−0.0787421
$52$	5.12735	0.711035
$53$	8.45466	1.16134	0.580669	−	0.814140i	$-0.302791\pi$
$53$	8.45466	1.16134	0.580669	+	0.814140i	$0.302791\pi$
$54$	−5.15249	−0.701165
$55$	−9.07877	−1.22418
$56$	0.635213	0.0848838
$57$	5.90881	0.782642
$58$	2.46547	0.323732
$59$	11.9394	1.55437	0.777187	−	0.629270i	$-0.216646\pi$
$59$	11.9394	1.55437	0.777187	+	0.629270i	$0.216646\pi$
$60$	−4.51543	−0.582939
$61$	0.586889	0.0751434	0.0375717	−	0.999294i	$-0.488038\pi$
$61$	0.586889	0.0751434	0.0375717	+	0.999294i	$0.488038\pi$
$62$	1.98771	0.252439
$63$	0.0313831	0.00395390
$64$	1.00000	0.125000
$65$	−13.2582	−1.64448
$66$	6.13117	0.754695
$67$	−12.9100	−1.57721	−0.788605	−	0.614900i	$-0.789196\pi$
$67$	−12.9100	−1.57721	−0.788605	+	0.614900i	$0.789196\pi$
$68$	−0.322021	−0.0390508
$69$	6.59547	0.794002
$70$	−1.64252	−0.196319
$71$	−0.0667081	−0.00791679	−0.00395840	−	0.999992i	$-0.501260\pi$
$71$	−0.0667081	−0.00791679	−0.00395840	+	0.999992i	$0.501260\pi$
$72$	0.0494057	0.00582251
$73$	−2.81224	−0.329148	−0.164574	−	0.986365i	$-0.552625\pi$
$73$	−2.81224	−0.329148	−0.164574	+	0.986365i	$0.552625\pi$
$74$	−7.77317	−0.903613
$75$	2.94462	0.340015
$76$	3.38371	0.388138
$77$	2.23026	0.254161
$78$	8.95366	1.01380
$79$	−4.39323	−0.494277	−0.247139	−	0.968980i	$-0.579490\pi$
$79$	−4.39323	−0.494277	−0.247139	+	0.968980i	$0.579490\pi$
$80$	−2.58578	−0.289099
$81$	−9.14578	−1.01620
$82$	10.7578	1.18800
$83$	−16.7077	−1.83391	−0.916955	−	0.398992i	$-0.869360\pi$
$83$	−16.7077	−1.83391	−0.916955	+	0.398992i	$0.869360\pi$
$84$	1.10924	0.121028
$85$	0.832675	0.0903163
$86$	−9.96085	−1.07411
$87$	4.30534	0.461581
$88$	3.51104	0.374278
$89$	−13.6156	−1.44325	−0.721623	−	0.692286i	$-0.756604\pi$
$89$	−13.6156	−1.44325	−0.721623	+	0.692286i	$0.756604\pi$
$90$	−0.127752	−0.0134663
$91$	3.25696	0.341422
$92$	3.77692	0.393772
$93$	3.47104	0.359930
$94$	−3.93174	−0.405528
$95$	−8.74951	−0.897681
$96$	1.74625	0.178226
$97$	−12.7052	−1.29002	−0.645008	−	0.764176i	$-0.723146\pi$
$97$	−12.7052	−1.29002	−0.645008	+	0.764176i	$0.723146\pi$
$98$	−6.59651	−0.666348
$99$	0.173465	0.0174339
$100$	1.68625	0.168625
$101$	9.15646	0.911101	0.455551	−	0.890210i	$-0.349442\pi$
$101$	9.15646	0.911101	0.455551	+	0.890210i	$0.349442\pi$
$102$	−0.562331	−0.0556791
$103$	1.18800	0.117057	0.0585285	−	0.998286i	$-0.481359\pi$
$103$	1.18800	0.117057	0.0585285	+	0.998286i	$0.481359\pi$
$104$	5.12735	0.502778
$105$	−2.86826	−0.279913
$106$	8.45466	0.821189
$107$	−10.5335	−1.01831	−0.509155	−	0.860675i	$-0.670042\pi$
$107$	−10.5335	−1.01831	−0.509155	+	0.860675i	$0.670042\pi$
$108$	−5.15249	−0.495799
$109$	−7.51021	−0.719347	−0.359674	−	0.933078i	$-0.617112\pi$
$109$	−7.51021	−0.719347	−0.359674	+	0.933078i	$0.617112\pi$
$110$	−9.07877	−0.865627
$111$	−13.5739	−1.28838
$112$	0.635213	0.0600219
$113$	14.2153	1.33726	0.668632	−	0.743594i	$-0.266880\pi$
$113$	14.2153	1.33726	0.668632	+	0.743594i	$0.266880\pi$
$114$	5.90881	0.553411
$115$	−9.76629	−0.910711
$116$	2.46547	0.228913
$117$	0.253320	0.0234195
$118$	11.9394	1.09911
$119$	−0.204552	−0.0187512
$120$	−4.51543	−0.412200
$121$	1.32741	0.120673
$122$	0.586889	0.0531344
$123$	18.7859	1.69387
$124$	1.98771	0.178501
$125$	8.56863	0.766401
$126$	0.0313831	0.00279583
$127$	20.3451	1.80533	0.902667	−	0.430340i	$-0.141606\pi$
$127$	20.3451	1.80533	0.902667	+	0.430340i	$0.141606\pi$
$128$	1.00000	0.0883883
$129$	−17.3942	−1.53147
$130$	−13.2582	−1.16282
$131$	−19.8675	−1.73583	−0.867917	−	0.496710i	$-0.834541\pi$
$131$	−19.8675	−1.73583	−0.867917	+	0.496710i	$0.834541\pi$
$132$	6.13117	0.533650
$133$	2.14937	0.186374
$134$	−12.9100	−1.11526
$135$	13.3232	1.14668
$136$	−0.322021	−0.0276131
$137$	18.2376	1.55814	0.779072	−	0.626934i	$-0.215690\pi$
$137$	18.2376	1.55814	0.779072	+	0.626934i	$0.215690\pi$
$138$	6.59547	0.561444
$139$	3.79729	0.322082	0.161041	−	0.986948i	$-0.448515\pi$
$139$	3.79729	0.322082	0.161041	+	0.986948i	$0.448515\pi$
$140$	−1.64252	−0.138818
$141$	−6.86582	−0.578206
$142$	−0.0667081	−0.00559802
$143$	18.0023	1.50543
$144$	0.0494057	0.00411714
$145$	−6.37515	−0.529428
$146$	−2.81224	−0.232743
$147$	−11.5192	−0.950086
$148$	−7.77317	−0.638951
$149$	6.47248	0.530246	0.265123	−	0.964215i	$-0.414587\pi$
$149$	6.47248	0.530246	0.265123	+	0.964215i	$0.414587\pi$
$150$	2.94462	0.240427
$151$	−20.4636	−1.66530	−0.832652	−	0.553797i	$-0.813178\pi$
$151$	−20.4636	−1.66530	−0.832652	+	0.553797i	$0.813178\pi$
$152$	3.38371	0.274455
$153$	−0.0159097	−0.00128622
$154$	2.23026	0.179719
$155$	−5.13977	−0.412836
$156$	8.95366	0.716866
$157$	−14.4827	−1.15585	−0.577924	−	0.816090i	$-0.696137\pi$
$157$	−14.4827	−1.15585	−0.577924	+	0.816090i	$0.696137\pi$
$158$	−4.39323	−0.349507
$159$	14.7640	1.17086
$160$	−2.58578	−0.204424
$161$	2.39915	0.189079
$162$	−9.14578	−0.718560
$163$	−3.01751	−0.236349	−0.118175	−	0.992993i	$-0.537704\pi$
$163$	−3.01751	−0.236349	−0.118175	+	0.992993i	$0.537704\pi$
$164$	10.7578	0.840045
$165$	−15.8538	−1.23422
$166$	−16.7077	−1.29677
$167$	−21.4972	−1.66351	−0.831753	−	0.555146i	$-0.812662\pi$
$167$	−21.4972	−1.66351	−0.831753	+	0.555146i	$0.812662\pi$
$168$	1.10924	0.0855799
$169$	13.2897	1.02229
$170$	0.832675	0.0638633
$171$	0.167174	0.0127841
$172$	−9.96085	−0.759508
$173$	−9.82213	−0.746763	−0.373381	−	0.927678i	$-0.621802\pi$
$173$	−9.82213	−0.746763	−0.373381	+	0.927678i	$0.621802\pi$
$174$	4.30534	0.326387
$175$	1.07113	0.0809695
$176$	3.51104	0.264655
$177$	20.8492	1.56712
$178$	−13.6156	−1.02053
$179$	6.49532	0.485483	0.242742	−	0.970091i	$-0.421953\pi$
$179$	6.49532	0.485483	0.242742	+	0.970091i	$0.421953\pi$
$180$	−0.127752	−0.00952208
$181$	4.08174	0.303393	0.151696	−	0.988427i	$-0.451526\pi$
$181$	4.08174	0.303393	0.151696	+	0.988427i	$0.451526\pi$
$182$	3.25696	0.241422
$183$	1.02486	0.0757596
$184$	3.77692	0.278439
$185$	20.0997	1.47776
$186$	3.47104	0.254509
$187$	−1.13063	−0.0826798
$188$	−3.93174	−0.286752
$189$	−3.27293	−0.238070
$190$	−8.74951	−0.634757
$191$	23.4882	1.69955	0.849773	−	0.527148i	$-0.176739\pi$
$191$	23.4882	1.69955	0.849773	+	0.527148i	$0.176739\pi$
$192$	1.74625	0.126025
$193$	9.86940	0.710415	0.355207	−	0.934788i	$-0.384410\pi$
$193$	9.86940	0.710415	0.355207	+	0.934788i	$0.384410\pi$
$194$	−12.7052	−0.912179
$195$	−23.1522	−1.65796
$196$	−6.59651	−0.471179
$197$	−1.66586	−0.118687	−0.0593437	−	0.998238i	$-0.518901\pi$
$197$	−1.66586	−0.118687	−0.0593437	+	0.998238i	$0.518901\pi$
$198$	0.173465	0.0123276
$199$	12.7759	0.905663	0.452831	−	0.891596i	$-0.350414\pi$
$199$	12.7759	0.905663	0.452831	+	0.891596i	$0.350414\pi$
$200$	1.68625	0.119236
$201$	−22.5442	−1.59014
$202$	9.15646	0.644246
$203$	1.56610	0.109918
$204$	−0.562331	−0.0393710
$205$	−27.8174	−1.94285
$206$	1.18800	0.0827718
$207$	0.186601	0.0129697
$208$	5.12735	0.355518
$209$	11.8803	0.821780
$210$	−2.86826	−0.197928
$211$	16.3237	1.12377	0.561885	−	0.827215i	$-0.310076\pi$
$211$	16.3237	1.12377	0.561885	+	0.827215i	$0.310076\pi$
$212$	8.45466	0.580669
$213$	−0.116489	−0.00798171
$214$	−10.5335	−0.720054
$215$	25.7565	1.75658
$216$	−5.15249	−0.350582
$217$	1.26262	0.0857120
$218$	−7.51021	−0.508655
$219$	−4.91089	−0.331847
$220$	−9.07877	−0.612091
$221$	−1.65111	−0.111066
$222$	−13.5739	−0.911023
$223$	8.02490	0.537387	0.268694	−	0.963226i	$-0.413408\pi$
$223$	8.02490	0.537387	0.268694	+	0.963226i	$0.413408\pi$
$224$	0.635213	0.0424419
$225$	0.0833102	0.00555401
$226$	14.2153	0.945588
$227$	21.8320	1.44904	0.724520	−	0.689254i	$-0.242062\pi$
$227$	21.8320	1.44904	0.724520	+	0.689254i	$0.242062\pi$
$228$	5.90881	0.391321
$229$	13.0772	0.864163	0.432082	−	0.901834i	$-0.357779\pi$
$229$	13.0772	0.864163	0.432082	+	0.901834i	$0.357779\pi$
$230$	−9.76629	−0.643970
$231$	3.89460	0.256246
$232$	2.46547	0.161866
$233$	−5.66551	−0.371160	−0.185580	−	0.982629i	$-0.559416\pi$
$233$	−5.66551	−0.371160	−0.185580	+	0.982629i	$0.559416\pi$
$234$	0.253320	0.0165601
$235$	10.1666	0.663196
$236$	11.9394	0.777187
$237$	−7.67170	−0.498331
$238$	−0.204552	−0.0132591
$239$	−3.87186	−0.250450	−0.125225	−	0.992128i	$-0.539965\pi$
$239$	−3.87186	−0.250450	−0.125225	+	0.992128i	$0.539965\pi$
$240$	−4.51543	−0.291470
$241$	−18.6798	−1.20327	−0.601636	−	0.798771i	$-0.705484\pi$
$241$	−18.6798	−1.20327	−0.601636	+	0.798771i	$0.705484\pi$
$242$	1.32741	0.0853289
$243$	−0.513387	−0.0329338
$244$	0.586889	0.0375717
$245$	17.0571	1.08974
$246$	18.7859	1.19775
$247$	17.3494	1.10392
$248$	1.98771	0.126219
$249$	−29.1759	−1.84895
$250$	8.56863	0.541928
$251$	−18.0304	−1.13807	−0.569035	−	0.822313i	$-0.692683\pi$
$251$	−18.0304	−1.13807	−0.569035	+	0.822313i	$0.692683\pi$
$252$	0.0313831	0.00197695
$253$	13.2609	0.833708
$254$	20.3451	1.27656
$255$	1.45406	0.0910570
$256$	1.00000	0.0625000
$257$	−0.890250	−0.0555323	−0.0277661	−	0.999614i	$-0.508839\pi$
$257$	−0.890250	−0.0555323	−0.0277661	+	0.999614i	$0.508839\pi$
$258$	−17.3942	−1.08291
$259$	−4.93762	−0.306808
$260$	−13.2582	−0.822238
$261$	0.121808	0.00753973
$262$	−19.8675	−1.22742
$263$	7.74170	0.477373	0.238687	−	0.971097i	$-0.423283\pi$
$263$	7.74170	0.477373	0.238687	+	0.971097i	$0.423283\pi$
$264$	6.13117	0.377348
$265$	−21.8619	−1.34296
$266$	2.14937	0.131787
$267$	−23.7762	−1.45508
$268$	−12.9100	−0.788605
$269$	−27.9359	−1.70328	−0.851640	−	0.524127i	$-0.824392\pi$
$269$	−27.9359	−1.70328	−0.851640	+	0.524127i	$0.824392\pi$
$270$	13.3232	0.810824
$271$	0.123443	0.00749865	0.00374932	−	0.999993i	$-0.498807\pi$
$271$	0.123443	0.00749865	0.00374932	+	0.999993i	$0.498807\pi$
$272$	−0.322021	−0.0195254
$273$	5.68748	0.344222
$274$	18.2376	1.10177
$275$	5.92048	0.357018
$276$	6.59547	0.397001
$277$	25.7507	1.54721	0.773606	−	0.633667i	$-0.218451\pi$
$277$	25.7507	1.54721	0.773606	+	0.633667i	$0.218451\pi$
$278$	3.79729	0.227746
$279$	0.0982040	0.00587932
$280$	−1.64252	−0.0981593
$281$	−8.28626	−0.494317	−0.247158	−	0.968975i	$-0.579497\pi$
$281$	−8.28626	−0.494317	−0.247158	+	0.968975i	$0.579497\pi$
$282$	−6.86582	−0.408854
$283$	−18.3897	−1.09316	−0.546578	−	0.837408i	$-0.684070\pi$
$283$	−18.3897	−1.09316	−0.546578	+	0.837408i	$0.684070\pi$
$284$	−0.0667081	−0.00395840
$285$	−15.2789	−0.905043
$286$	18.0023	1.06450
$287$	6.83351	0.403369
$288$	0.0494057	0.00291126
$289$	−16.8963	−0.993900
$290$	−6.37515	−0.374362
$291$	−22.1865	−1.30059
$292$	−2.81224	−0.164574
$293$	−3.18472	−0.186053	−0.0930267	−	0.995664i	$-0.529654\pi$
$293$	−3.18472	−0.186053	−0.0930267	+	0.995664i	$0.529654\pi$
$294$	−11.5192	−0.671812
$295$	−30.8726	−1.79747
$296$	−7.77317	−0.451806
$297$	−18.0906	−1.04972
$298$	6.47248	0.374940
$299$	19.3656	1.11994
$300$	2.94462	0.170008
$301$	−6.32726	−0.364697
$302$	−20.4636	−1.17755
$303$	15.9895	0.918573
$304$	3.38371	0.194069
$305$	−1.51756	−0.0868955
$306$	−0.0159097	−0.000909495 0
$307$	−1.54810	−0.0883547	−0.0441774	−	0.999024i	$-0.514067\pi$
$307$	−1.54810	−0.0883547	−0.0441774	+	0.999024i	$0.514067\pi$
$308$	2.23026	0.127081
$309$	2.07455	0.118017
$310$	−5.13977	−0.291919
$311$	−0.471497	−0.0267361	−0.0133681	−	0.999911i	$-0.504255\pi$
$311$	−0.471497	−0.0267361	−0.0133681	+	0.999911i	$0.504255\pi$
$312$	8.95366	0.506901
$313$	−12.1078	−0.684373	−0.342187	−	0.939632i	$-0.611168\pi$
$313$	−12.1078	−0.684373	−0.342187	+	0.939632i	$0.611168\pi$
$314$	−14.4827	−0.817309
$315$	−0.0811497	−0.00457227
$316$	−4.39323	−0.247139
$317$	1.31831	0.0740439	0.0370219	−	0.999314i	$-0.488213\pi$
$317$	1.31831	0.0740439	0.0370219	+	0.999314i	$0.488213\pi$
$318$	14.7640	0.827924
$319$	8.65636	0.484663
$320$	−2.58578	−0.144549
$321$	−18.3941	−1.02666
$322$	2.39915	0.133699
$323$	−1.08963	−0.0606284
$324$	−9.14578	−0.508099
$325$	8.64598	0.479592
$326$	−3.01751	−0.167124
$327$	−13.1147	−0.725246
$328$	10.7578	0.594002
$329$	−2.49749	−0.137691
$330$	−15.8538	−0.872726
$331$	30.5415	1.67871	0.839357	−	0.543580i	$-0.182931\pi$
$331$	30.5415	1.67871	0.839357	+	0.543580i	$0.182931\pi$
$332$	−16.7077	−0.916955
$333$	−0.384039	−0.0210452
$334$	−21.4972	−1.17628
$335$	33.3825	1.82388
$336$	1.10924	0.0605142
$337$	−20.9083	−1.13895	−0.569475	−	0.822009i	$-0.692853\pi$
$337$	−20.9083	−1.13895	−0.569475	+	0.822009i	$0.692853\pi$
$338$	13.2897	0.722865
$339$	24.8235	1.34823
$340$	0.832675	0.0451582
$341$	6.97892	0.377930
$342$	0.167174	0.00903975
$343$	−8.63667	−0.466336
$344$	−9.96085	−0.537053
$345$	−17.0544	−0.918179
$346$	−9.82213	−0.528041
$347$	−12.4915	−0.670577	−0.335288	−	0.942116i	$-0.608834\pi$
$347$	−12.4915	−0.670577	−0.335288	+	0.942116i	$0.608834\pi$
$348$	4.30534	0.230790
$349$	−22.3844	−1.19821	−0.599106	−	0.800670i	$-0.704477\pi$
$349$	−22.3844	−1.19821	−0.599106	+	0.800670i	$0.704477\pi$
$350$	1.07113	0.0572540
$351$	−26.4186	−1.41012
$352$	3.51104	0.187139
$353$	−2.03469	−0.108296	−0.0541478	−	0.998533i	$-0.517244\pi$
$353$	−2.03469	−0.108296	−0.0541478	+	0.998533i	$0.517244\pi$
$354$	20.8492	1.10812
$355$	0.172492	0.00915494
$356$	−13.6156	−0.721623
$357$	−0.357200	−0.0189050
$358$	6.49532	0.343288
$359$	−13.8523	−0.731098	−0.365549	−	0.930792i	$-0.619119\pi$
$359$	−13.8523	−0.731098	−0.365549	+	0.930792i	$0.619119\pi$
$360$	−0.127752	−0.00673313
$361$	−7.55053	−0.397396
$362$	4.08174	0.214531
$363$	2.31799	0.121663
$364$	3.25696	0.170711
$365$	7.27183	0.380625
$366$	1.02486	0.0535701
$367$	17.9620	0.937608	0.468804	−	0.883302i	$-0.344685\pi$
$367$	17.9620	0.937608	0.468804	+	0.883302i	$0.344685\pi$
$368$	3.77692	0.196886
$369$	0.531498	0.0276687
$370$	20.0997	1.04493
$371$	5.37051	0.278823
$372$	3.47104	0.179965
$373$	−2.63034	−0.136194	−0.0680969	−	0.997679i	$-0.521693\pi$
$373$	−2.63034	−0.136194	−0.0680969	+	0.997679i	$0.521693\pi$
$374$	−1.13063	−0.0584635
$375$	14.9630	0.772686
$376$	−3.93174	−0.202764
$377$	12.6413	0.651061
$378$	−3.27293	−0.168341
$379$	34.5832	1.77642	0.888209	−	0.459439i	$-0.151949\pi$
$379$	34.5832	1.77642	0.888209	+	0.459439i	$0.151949\pi$
$380$	−8.74951	−0.448841
$381$	35.5277	1.82014
$382$	23.4882	1.20176
$383$	−1.34423	−0.0686872	−0.0343436	−	0.999410i	$-0.510934\pi$
$383$	−1.34423	−0.0686872	−0.0343436	+	0.999410i	$0.510934\pi$
$384$	1.74625	0.0891132
$385$	−5.76695	−0.293911
$386$	9.86940	0.502339
$387$	−0.492122	−0.0250160
$388$	−12.7052	−0.645008
$389$	10.2656	0.520485	0.260242	−	0.965543i	$-0.416198\pi$
$389$	10.2656	0.520485	0.260242	+	0.965543i	$0.416198\pi$
$390$	−23.1522	−1.17236
$391$	−1.21625	−0.0615084
$392$	−6.59651	−0.333174
$393$	−34.6938	−1.75007
$394$	−1.66586	−0.0839246
$395$	11.3599	0.571580
$396$	0.173465	0.00871696
$397$	−33.8549	−1.69913	−0.849564	−	0.527486i	$-0.823135\pi$
$397$	−33.8549	−1.69913	−0.849564	+	0.527486i	$0.823135\pi$
$398$	12.7759	0.640400
$399$	3.75335	0.187903
$400$	1.68625	0.0843123
$401$	−10.4030	−0.519499	−0.259750	−	0.965676i	$-0.583640\pi$
$401$	−10.4030	−0.519499	−0.259750	+	0.965676i	$0.583640\pi$
$402$	−22.5442	−1.12440
$403$	10.1917	0.507683
$404$	9.15646	0.455551
$405$	23.6489	1.17513
$406$	1.56610	0.0777241
$407$	−27.2919	−1.35281
$408$	−0.562331	−0.0278395
$409$	15.9724	0.789787	0.394893	−	0.918727i	$-0.370782\pi$
$409$	15.9724	0.789787	0.394893	+	0.918727i	$0.370782\pi$
$410$	−27.8174	−1.37380
$411$	31.8475	1.57092
$412$	1.18800	0.0585285
$413$	7.58404	0.373186
$414$	0.186601	0.00917096
$415$	43.2024	2.12072
$416$	5.12735	0.251389
$417$	6.63104	0.324723
$418$	11.8803	0.581086
$419$	−1.14327	−0.0558524	−0.0279262	−	0.999610i	$-0.508890\pi$
$419$	−1.14327	−0.0558524	−0.0279262	+	0.999610i	$0.508890\pi$
$420$	−2.86826	−0.139957
$421$	15.0478	0.733386	0.366693	−	0.930342i	$-0.380490\pi$
$421$	15.0478	0.733386	0.366693	+	0.930342i	$0.380490\pi$
$422$	16.3237	0.794626
$423$	−0.194250	−0.00944477
$424$	8.45466	0.410595
$425$	−0.543007	−0.0263397
$426$	−0.116489	−0.00564392
$427$	0.372799	0.0180410
$428$	−10.5335	−0.509155
$429$	31.4367	1.51778
$430$	25.7565	1.24209
$431$	26.5403	1.27840	0.639201	−	0.769040i	$-0.279265\pi$
$431$	26.5403	1.27840	0.639201	+	0.769040i	$0.279265\pi$
$432$	−5.15249	−0.247899
$433$	22.3094	1.07212	0.536061	−	0.844179i	$-0.319912\pi$
$433$	22.3094	1.07212	0.536061	+	0.844179i	$0.319912\pi$
$434$	1.26262	0.0606075
$435$	−11.1326	−0.533769
$436$	−7.51021	−0.359674
$437$	12.7800	0.611351
$438$	−4.91089	−0.234651
$439$	6.48397	0.309463	0.154732	−	0.987957i	$-0.450549\pi$
$439$	6.48397	0.309463	0.154732	+	0.987957i	$0.450549\pi$
$440$	−9.07877	−0.432813
$441$	−0.325905	−0.0155193
$442$	−1.65111	−0.0785355
$443$	12.0749	0.573694	0.286847	−	0.957976i	$-0.407393\pi$
$443$	12.0749	0.573694	0.286847	+	0.957976i	$0.407393\pi$
$444$	−13.5739	−0.644190
$445$	35.2068	1.66896
$446$	8.02490	0.379990
$447$	11.3026	0.534594
$448$	0.635213	0.0300110
$449$	−11.4624	−0.540943	−0.270471	−	0.962728i	$-0.587180\pi$
$449$	−11.4624	−0.540943	−0.270471	+	0.962728i	$0.587180\pi$
$450$	0.0833102	0.00392728
$451$	37.7712	1.77857
$452$	14.2153	0.668632
$453$	−35.7346	−1.67896
$454$	21.8320	1.02463
$455$	−8.42177	−0.394818
$456$	5.90881	0.276706
$457$	1.55079	0.0725431	0.0362715	−	0.999342i	$-0.488452\pi$
$457$	1.55079	0.0725431	0.0362715	+	0.999342i	$0.488452\pi$
$458$	13.0772	0.611056
$459$	1.65921	0.0774453
$460$	−9.76629	−0.455355
$461$	21.0083	0.978454	0.489227	−	0.872157i	$-0.337279\pi$
$461$	21.0083	0.978454	0.489227	+	0.872157i	$0.337279\pi$
$462$	3.89460	0.181193
$463$	−7.65014	−0.355532	−0.177766	−	0.984073i	$-0.556887\pi$
$463$	−7.65014	−0.355532	−0.177766	+	0.984073i	$0.556887\pi$
$464$	2.46547	0.114457
$465$	−8.97534	−0.416222
$466$	−5.66551	−0.262450
$467$	−23.9495	−1.10825	−0.554124	−	0.832434i	$-0.686947\pi$
$467$	−23.9495	−1.10825	−0.554124	+	0.832434i	$0.686947\pi$
$468$	0.253320	0.0117097
$469$	−8.20061	−0.378669
$470$	10.1666	0.468950
$471$	−25.2906	−1.16533
$472$	11.9394	0.549554
$473$	−34.9729	−1.60806
$474$	−7.67170	−0.352373
$475$	5.70577	0.261798
$476$	−0.204552	−0.00937562
$477$	0.417708	0.0191255
$478$	−3.87186	−0.177095
$479$	−7.57712	−0.346207	−0.173104	−	0.984904i	$-0.555380\pi$
$479$	−7.57712	−0.346207	−0.173104	+	0.984904i	$0.555380\pi$
$480$	−4.51543	−0.206100
$481$	−39.8558	−1.81727
$482$	−18.6798	−0.850841
$483$	4.18953	0.190630
$484$	1.32741	0.0603366
$485$	32.8528	1.49177
$486$	−0.513387	−0.0232877
$487$	9.92582	0.449782	0.224891	−	0.974384i	$-0.427797\pi$
$487$	9.92582	0.449782	0.224891	+	0.974384i	$0.427797\pi$
$488$	0.586889	0.0265672
$489$	−5.26933	−0.238287
$490$	17.0571	0.770561
$491$	2.77590	0.125275	0.0626373	−	0.998036i	$-0.480049\pi$
$491$	2.77590	0.125275	0.0626373	+	0.998036i	$0.480049\pi$
$492$	18.7859	0.846934
$493$	−0.793933	−0.0357570
$494$	17.3494	0.780589
$495$	−0.448543	−0.0201605
$496$	1.98771	0.0892506
$497$	−0.0423738	−0.00190072
$498$	−29.1759	−1.30740
$499$	−1.66429	−0.0745039	−0.0372519	−	0.999306i	$-0.511860\pi$
$499$	−1.66429	−0.0745039	−0.0372519	+	0.999306i	$0.511860\pi$
$500$	8.56863	0.383201
$501$	−37.5396	−1.67715
$502$	−18.0304	−0.804738
$503$	−1.00000	−0.0445878
$503$	−1.00000	−0.0445878
$504$	0.0313831	0.00139791
$505$	−23.6766	−1.05359
$506$	13.2609	0.589520
$507$	23.2072	1.03067
$508$	20.3451	0.902667
$509$	24.0760	1.06715	0.533574	−	0.845753i	$-0.320848\pi$
$509$	24.0760	1.06715	0.533574	+	0.845753i	$0.320848\pi$
$510$	1.45406	0.0643870
$511$	−1.78637	−0.0790243
$512$	1.00000	0.0441942
$513$	−17.4345	−0.769753
$514$	−0.890250	−0.0392672
$515$	−3.07190	−0.135364
$516$	−17.3942	−0.765736
$517$	−13.8045	−0.607121
$518$	−4.93762	−0.216946
$519$	−17.1519	−0.752887
$520$	−13.2582	−0.581410
$521$	−21.4959	−0.941752	−0.470876	−	0.882199i	$-0.656062\pi$
$521$	−21.4959	−0.941752	−0.470876	+	0.882199i	$0.656062\pi$
$522$	0.121808	0.00533140
$523$	−1.97588	−0.0863991	−0.0431995	−	0.999066i	$-0.513755\pi$
$523$	−1.97588	−0.0863991	−0.0431995	+	0.999066i	$0.513755\pi$
$524$	−19.8675	−0.867917
$525$	1.87046	0.0816335
$526$	7.74170	0.337554
$527$	−0.640084	−0.0278825
$528$	6.13117	0.266825
$529$	−8.73484	−0.379776
$530$	−21.8619	−0.949619
$531$	0.589873	0.0255983
$532$	2.14937	0.0931871
$533$	55.1591	2.38921
$534$	−23.7762	−1.02890
$535$	27.2372	1.17757
$536$	−12.9100	−0.557628
$537$	11.3425	0.489464
$538$	−27.9359	−1.20440
$539$	−23.1606	−0.997598
$540$	13.3232	0.573339
$541$	24.5700	1.05635	0.528173	−	0.849137i	$-0.322877\pi$
$541$	24.5700	1.05635	0.528173	+	0.849137i	$0.322877\pi$
$542$	0.123443	0.00530234
$543$	7.12775	0.305881
$544$	−0.322021	−0.0138065
$545$	19.4197	0.831850
$546$	5.68748	0.243401
$547$	28.0251	1.19827	0.599133	−	0.800649i	$-0.295512\pi$
$547$	28.0251	1.19827	0.599133	+	0.800649i	$0.295512\pi$
$548$	18.2376	0.779072
$549$	0.0289956	0.00123750
$550$	5.92048	0.252450
$551$	8.34242	0.355399
$552$	6.59547	0.280722
$553$	−2.79064	−0.118670
$554$	25.7507	1.09404
$555$	35.0992	1.48988
$556$	3.79729	0.161041
$557$	19.6663	0.833288	0.416644	−	0.909070i	$-0.363206\pi$
$557$	19.6663	0.833288	0.416644	+	0.909070i	$0.363206\pi$
$558$	0.0982040	0.00415731
$559$	−51.0727	−2.16015
$560$	−1.64252	−0.0694091
$561$	−1.97437	−0.0833578
$562$	−8.28626	−0.349535
$563$	28.9537	1.22025	0.610126	−	0.792304i	$-0.291119\pi$
$563$	28.9537	1.22025	0.610126	+	0.792304i	$0.291119\pi$
$564$	−6.86582	−0.289103
$565$	−36.7576	−1.54640
$566$	−18.3897	−0.772978
$567$	−5.80951	−0.243977
$568$	−0.0667081	−0.00279901
$569$	13.9319	0.584054	0.292027	−	0.956410i	$-0.405670\pi$
$569$	13.9319	0.584054	0.292027	+	0.956410i	$0.405670\pi$
$570$	−15.2789	−0.639962
$571$	1.05250	0.0440457	0.0220228	−	0.999757i	$-0.492989\pi$
$571$	1.05250	0.0440457	0.0220228	+	0.999757i	$0.492989\pi$
$572$	18.0023	0.752715
$573$	41.0164	1.71348
$574$	6.83351	0.285225
$575$	6.36883	0.265598
$576$	0.0494057	0.00205857
$577$	33.3043	1.38648	0.693239	−	0.720708i	$-0.256183\pi$
$577$	33.3043	1.38648	0.693239	+	0.720708i	$0.256183\pi$
$578$	−16.8963	−0.702794
$579$	17.2345	0.716241
$580$	−6.37515	−0.264714
$581$	−10.6129	−0.440299
$582$	−22.1865	−0.919659
$583$	29.6847	1.22941
$584$	−2.81224	−0.116371
$585$	−0.655029	−0.0270821
$586$	−3.18472	−0.131560
$587$	9.86829	0.407308	0.203654	−	0.979043i	$-0.434718\pi$
$587$	9.86829	0.407308	0.203654	+	0.979043i	$0.434718\pi$
$588$	−11.5192	−0.475043
$589$	6.72582	0.277132
$590$	−30.8726	−1.27100
$591$	−2.90901	−0.119661
$592$	−7.77317	−0.319475
$593$	−19.3262	−0.793632	−0.396816	−	0.917898i	$-0.629885\pi$
$593$	−19.3262	−0.793632	−0.396816	+	0.917898i	$0.629885\pi$
$594$	−18.0906	−0.742266
$595$	0.528926	0.0216838
$596$	6.47248	0.265123
$597$	22.3101	0.913090
$598$	19.3656	0.791919
$599$	25.9927	1.06203	0.531016	−	0.847361i	$-0.321810\pi$
$599$	25.9927	1.06203	0.531016	+	0.847361i	$0.321810\pi$
$600$	2.94462	0.120213
$601$	21.0730	0.859586	0.429793	−	0.902927i	$-0.358586\pi$
$601$	21.0730	0.859586	0.429793	+	0.902927i	$0.358586\pi$
$602$	−6.32726	−0.257880
$603$	−0.637828	−0.0259744
$604$	−20.4636	−0.832652
$605$	−3.43238	−0.139546
$606$	15.9895	0.649529
$607$	23.2863	0.945164	0.472582	−	0.881287i	$-0.343322\pi$
$607$	23.2863	0.945164	0.472582	+	0.881287i	$0.343322\pi$
$608$	3.38371	0.137227
$609$	2.73480	0.110820
$610$	−1.51756	−0.0614444
$611$	−20.1594	−0.815562
$612$	−0.0159097	−0.000643110 0
$613$	17.9773	0.726096	0.363048	−	0.931770i	$-0.381736\pi$
$613$	17.9773	0.726096	0.363048	+	0.931770i	$0.381736\pi$
$614$	−1.54810	−0.0624762
$615$	−48.5762	−1.95878
$616$	2.23026	0.0898596
$617$	−12.6311	−0.508511	−0.254255	−	0.967137i	$-0.581830\pi$
$617$	−12.6311	−0.508511	−0.254255	+	0.967137i	$0.581830\pi$
$618$	2.07455	0.0834506
$619$	14.9543	0.601064	0.300532	−	0.953772i	$-0.402836\pi$
$619$	14.9543	0.601064	0.300532	+	0.953772i	$0.402836\pi$
$620$	−5.13977	−0.206418
$621$	−19.4606	−0.780925
$622$	−0.471497	−0.0189053
$623$	−8.64877	−0.346506
$624$	8.95366	0.358433
$625$	−30.5878	−1.22351
$626$	−12.1078	−0.483925
$627$	20.7461	0.828519
$628$	−14.4827	−0.577924
$629$	2.50313	0.0998061
$630$	−0.0811497	−0.00323308
$631$	−19.1430	−0.762071	−0.381035	−	0.924561i	$-0.624432\pi$
$631$	−19.1430	−0.762071	−0.381035	+	0.924561i	$0.624432\pi$
$632$	−4.39323	−0.174753
$633$	28.5053	1.13299
$634$	1.31831	0.0523569
$635$	−52.6078	−2.08768
$636$	14.7640	0.585430
$637$	−33.8226	−1.34010
$638$	8.65636	0.342709
$639$	−0.00329576	−0.000130378 0
$640$	−2.58578	−0.102212
$641$	12.4900	0.493326	0.246663	−	0.969101i	$-0.420666\pi$
$641$	12.4900	0.493326	0.246663	+	0.969101i	$0.420666\pi$
$642$	−18.3941	−0.725959
$643$	−10.7889	−0.425473	−0.212737	−	0.977110i	$-0.568238\pi$
$643$	−10.7889	−0.425473	−0.212737	+	0.977110i	$0.568238\pi$
$644$	2.39915	0.0945397
$645$	44.9775	1.77099
$646$	−1.08963	−0.0428707
$647$	−37.4908	−1.47392	−0.736958	−	0.675939i	$-0.763738\pi$
$647$	−37.4908	−1.47392	−0.736958	+	0.675939i	$0.763738\pi$
$648$	−9.14578	−0.359280
$649$	41.9196	1.64549
$650$	8.64598	0.339123
$651$	2.20485	0.0864149
$652$	−3.01751	−0.118175
$653$	41.5290	1.62516	0.812578	−	0.582853i	$-0.198064\pi$
$653$	41.5290	1.62516	0.812578	+	0.582853i	$0.198064\pi$
$654$	−13.1147	−0.512827
$655$	51.3730	2.00731
$656$	10.7578	0.420023
$657$	−0.138941	−0.00542059
$658$	−2.49749	−0.0973623
$659$	−17.9805	−0.700422	−0.350211	−	0.936671i	$-0.613890\pi$
$659$	−17.9805	−0.700422	−0.350211	+	0.936671i	$0.613890\pi$
$660$	−15.8538	−0.617110
$661$	−15.5956	−0.606599	−0.303300	−	0.952895i	$-0.598088\pi$
$661$	−15.5956	−0.606599	−0.303300	+	0.952895i	$0.598088\pi$
$662$	30.5415	1.18703
$663$	−2.88327	−0.111977
$664$	−16.7077	−0.648385
$665$	−5.55780	−0.215522
$666$	−0.384039	−0.0148812
$667$	9.31189	0.360558
$668$	−21.4972	−0.831753
$669$	14.0135	0.541794
$670$	33.3825	1.28968
$671$	2.06059	0.0795482
$672$	1.10924	0.0427900
$673$	−44.7748	−1.72594	−0.862972	−	0.505253i	$-0.831399\pi$
$673$	−44.7748	−1.72594	−0.862972	+	0.505253i	$0.831399\pi$
$674$	−20.9083	−0.805359
$675$	−8.68837	−0.334415
$676$	13.2897	0.511143
$677$	−4.40068	−0.169132	−0.0845659	−	0.996418i	$-0.526950\pi$
$677$	−4.40068	−0.169132	−0.0845659	+	0.996418i	$0.526950\pi$
$678$	24.8235	0.953342
$679$	−8.07049	−0.309717
$680$	0.832675	0.0319316
$681$	38.1242	1.46092
$682$	6.97892	0.267237
$683$	47.9219	1.83368	0.916840	−	0.399255i	$-0.130731\pi$
$683$	47.9219	1.83368	0.916840	+	0.399255i	$0.130731\pi$
$684$	0.167174	0.00639207
$685$	−47.1584	−1.80183
$686$	−8.63667	−0.329750
$687$	22.8361	0.871250
$688$	−9.96085	−0.379754
$689$	43.3500	1.65150
$690$	−17.0544	−0.649251
$691$	3.83809	0.146008	0.0730039	−	0.997332i	$-0.476741\pi$
$691$	3.83809	0.146008	0.0730039	+	0.997332i	$0.476741\pi$
$692$	−9.82213	−0.373381
$693$	0.110187	0.00418567
$694$	−12.4915	−0.474169
$695$	−9.81895	−0.372454
$696$	4.30534	0.163193
$697$	−3.46425	−0.131218
$698$	−22.3844	−0.847264
$699$	−9.89343	−0.374204
$700$	1.07113	0.0404847
$701$	−32.9235	−1.24351	−0.621753	−	0.783214i	$-0.713579\pi$
$701$	−32.9235	−1.24351	−0.621753	+	0.783214i	$0.713579\pi$
$702$	−26.4186	−0.997106
$703$	−26.3021	−0.992004
$704$	3.51104	0.132327
$705$	17.7535	0.668635
$706$	−2.03469	−0.0765766
$707$	5.81630	0.218744
$708$	20.8492	0.783560
$709$	5.77126	0.216744	0.108372	−	0.994110i	$-0.465436\pi$
$709$	5.77126	0.216744	0.108372	+	0.994110i	$0.465436\pi$
$710$	0.172492	0.00647352
$711$	−0.217051	−0.00814003
$712$	−13.6156	−0.510265
$713$	7.50742	0.281155
$714$	−0.357200	−0.0133679
$715$	−46.5500	−1.74087
$716$	6.49532	0.242742
$717$	−6.76126	−0.252504
$718$	−13.8523	−0.516964
$719$	−12.1263	−0.452234	−0.226117	−	0.974100i	$-0.572603\pi$
$719$	−12.1263	−0.452234	−0.226117	+	0.974100i	$0.572603\pi$
$720$	−0.127752	−0.00476104
$721$	0.754632	0.0281040
$722$	−7.55053	−0.281001
$723$	−32.6197	−1.21314
$724$	4.08174	0.151696
$725$	4.15739	0.154402
$726$	2.31799	0.0860287
$727$	1.41480	0.0524720	0.0262360	−	0.999656i	$-0.491648\pi$
$727$	1.41480	0.0524720	0.0262360	+	0.999656i	$0.491648\pi$
$728$	3.25696	0.120711
$729$	26.5408	0.982993
$730$	7.27183	0.269142
$731$	3.20760	0.118638
$732$	1.02486	0.0378798
$733$	−45.8355	−1.69297	−0.846486	−	0.532411i	$-0.821286\pi$
$733$	−45.8355	−1.69297	−0.846486	+	0.532411i	$0.821286\pi$
$734$	17.9620	0.662989
$735$	29.7860	1.09867
$736$	3.77692	0.139219
$737$	−45.3276	−1.66966
$738$	0.531498	0.0195647
$739$	24.1465	0.888245	0.444123	−	0.895966i	$-0.353515\pi$
$739$	24.1465	0.888245	0.444123	+	0.895966i	$0.353515\pi$
$740$	20.0997	0.738879
$741$	30.2966	1.11297
$742$	5.37051	0.197158
$743$	−2.04962	−0.0751931	−0.0375966	−	0.999293i	$-0.511970\pi$
$743$	−2.04962	−0.0751931	−0.0375966	+	0.999293i	$0.511970\pi$
$744$	3.47104	0.127255
$745$	−16.7364	−0.613174
$746$	−2.63034	−0.0963036
$747$	−0.825455	−0.0302018
$748$	−1.13063	−0.0413399
$749$	−6.69100	−0.244484
$750$	14.9630	0.546372
$751$	−4.28315	−0.156294	−0.0781471	−	0.996942i	$-0.524900\pi$
$751$	−4.28315	−0.156294	−0.0781471	+	0.996942i	$0.524900\pi$
$752$	−3.93174	−0.143376
$753$	−31.4857	−1.14740
$754$	12.6413	0.460370
$755$	52.9143	1.92575
$756$	−3.27293	−0.119035
$757$	−37.8734	−1.37653	−0.688266	−	0.725458i	$-0.741628\pi$
$757$	−37.8734	−1.37653	−0.688266	+	0.725458i	$0.741628\pi$
$758$	34.5832	1.25612
$759$	23.1570	0.840545
$760$	−8.74951	−0.317378
$761$	−34.5346	−1.25188	−0.625940	−	0.779872i	$-0.715284\pi$
$761$	−34.5346	−1.25188	−0.625940	+	0.779872i	$0.715284\pi$
$762$	35.5277	1.28703
$763$	−4.77058	−0.172706
$764$	23.4882	0.849773
$765$	0.0411389	0.00148738
$766$	−1.34423	−0.0485692
$767$	61.2173	2.21043
$768$	1.74625	0.0630125
$769$	−45.2000	−1.62995	−0.814977	−	0.579493i	$-0.803251\pi$
$769$	−45.2000	−1.62995	−0.814977	+	0.579493i	$0.803251\pi$
$770$	−5.76695	−0.207826
$771$	−1.55460	−0.0559877
$772$	9.86940	0.355207
$773$	3.76139	0.135288	0.0676439	−	0.997710i	$-0.478452\pi$
$773$	3.76139	0.135288	0.0676439	+	0.997710i	$0.478452\pi$
$774$	−0.492122	−0.0176890
$775$	3.35176	0.120399
$776$	−12.7052	−0.456089
$777$	−8.62233	−0.309325
$778$	10.2656	0.368038
$779$	36.4013	1.30421
$780$	−23.1522	−0.828981
$781$	−0.234215	−0.00838086
$782$	−1.21625	−0.0434930
$783$	−12.7033	−0.453979
$784$	−6.59651	−0.235589
$785$	37.4492	1.33662
$786$	−34.6938	−1.23749
$787$	−10.7287	−0.382438	−0.191219	−	0.981547i	$-0.561244\pi$
$787$	−10.7287	−0.382438	−0.191219	+	0.981547i	$0.561244\pi$
$788$	−1.66586	−0.0593437
$789$	13.5190	0.481288
$790$	11.3599	0.404168
$791$	9.02974	0.321061
$792$	0.173465	0.00616382
$793$	3.00918	0.106859
$794$	−33.8549	−1.20146
$795$	−38.1764	−1.35398
$796$	12.7759	0.452831
$797$	−0.766076	−0.0271358	−0.0135679	−	0.999908i	$-0.504319\pi$
$797$	−0.766076	−0.0271358	−0.0135679	+	0.999908i	$0.504319\pi$
$798$	3.75335	0.132867
$799$	1.26610	0.0447915
$800$	1.68625	0.0596178
$801$	−0.672686	−0.0237682
$802$	−10.4030	−0.367342
$803$	−9.87389	−0.348442
$804$	−22.5442	−0.795072
$805$	−6.20367	−0.218651
$806$	10.1917	0.358986
$807$	−48.7831	−1.71725
$808$	9.15646	0.322123
$809$	30.0576	1.05677	0.528384	−	0.849005i	$-0.322798\pi$
$809$	30.0576	1.05677	0.528384	+	0.849005i	$0.322798\pi$
$810$	23.6489	0.830939
$811$	−13.7785	−0.483829	−0.241914	−	0.970298i	$-0.577775\pi$
$811$	−13.7785	−0.483829	−0.241914	+	0.970298i	$0.577775\pi$
$812$	1.56610	0.0549592
$813$	0.215563	0.00756014
$814$	−27.2919	−0.956581
$815$	7.80260	0.273313
$816$	−0.562331	−0.0196855
$817$	−33.7046	−1.17917
$818$	15.9724	0.558463
$819$	0.160912	0.00562272
$820$	−27.8174	−0.971424
$821$	21.8806	0.763639	0.381819	−	0.924237i	$-0.375298\pi$
$821$	21.8806	0.763639	0.381819	+	0.924237i	$0.375298\pi$
$822$	31.8475	1.11081
$823$	38.1119	1.32850	0.664249	−	0.747511i	$-0.268751\pi$
$823$	38.1119	1.32850	0.664249	+	0.747511i	$0.268751\pi$
$824$	1.18800	0.0413859
$825$	10.3387	0.359946
$826$	7.58404	0.263882
$827$	−12.0487	−0.418975	−0.209488	−	0.977811i	$-0.567180\pi$
$827$	−12.0487	−0.418975	−0.209488	+	0.977811i	$0.567180\pi$
$828$	0.186601	0.00648485
$829$	−5.44538	−0.189126	−0.0945629	−	0.995519i	$-0.530145\pi$
$829$	−5.44538	−0.189126	−0.0945629	+	0.995519i	$0.530145\pi$
$830$	43.2024	1.49958
$831$	44.9673	1.55990
$832$	5.12735	0.177759
$833$	2.12421	0.0735997
$834$	6.63104	0.229614
$835$	55.5871	1.92367
$836$	11.8803	0.410890
$837$	−10.2416	−0.354003
$838$	−1.14327	−0.0394936
$839$	40.8623	1.41072	0.705361	−	0.708848i	$-0.250785\pi$
$839$	40.8623	1.41072	0.705361	+	0.708848i	$0.250785\pi$
$840$	−2.86826	−0.0989642
$841$	−22.9215	−0.790395
$842$	15.0478	0.518582
$843$	−14.4699	−0.498370
$844$	16.3237	0.561885
$845$	−34.3642	−1.18217
$846$	−0.194250	−0.00667846
$847$	0.843185	0.0289722
$848$	8.45466	0.290334
$849$	−32.1131	−1.10212
$850$	−0.543007	−0.0186250
$851$	−29.3587	−1.00640
$852$	−0.116489	−0.00399086
$853$	33.6213	1.15117	0.575586	−	0.817741i	$-0.304774\pi$
$853$	33.6213	1.15117	0.575586	+	0.817741i	$0.304774\pi$
$854$	0.372799	0.0127569
$855$	−0.432276	−0.0147835
$856$	−10.5335	−0.360027
$857$	−38.0197	−1.29873	−0.649365	−	0.760477i	$-0.724965\pi$
$857$	−38.0197	−1.29873	−0.649365	+	0.760477i	$0.724965\pi$
$858$	31.4367	1.07323
$859$	−17.6508	−0.602237	−0.301118	−	0.953587i	$-0.597360\pi$
$859$	−17.6508	−0.602237	−0.301118	+	0.953587i	$0.597360\pi$
$860$	25.7565	0.878291
$861$	11.9330	0.406677
$862$	26.5403	0.903966
$863$	21.0000	0.714850	0.357425	−	0.933942i	$-0.383655\pi$
$863$	21.0000	0.714850	0.357425	+	0.933942i	$0.383655\pi$
$864$	−5.15249	−0.175291
$865$	25.3978	0.863553
$866$	22.3094	0.758105
$867$	−29.5052	−1.00205
$868$	1.26262	0.0428560
$869$	−15.4248	−0.523251
$870$	−11.1326	−0.377432
$871$	−66.1942	−2.24290
$872$	−7.51021	−0.254328
$873$	−0.627708	−0.0212447
$874$	12.7800	0.432290
$875$	5.44290	0.184004
$876$	−4.91089	−0.165923
$877$	13.3184	0.449731	0.224865	−	0.974390i	$-0.427806\pi$
$877$	13.3184	0.449731	0.224865	+	0.974390i	$0.427806\pi$
$878$	6.48397	0.218823
$879$	−5.56133	−0.187579
$880$	−9.07877	−0.306045
$881$	−23.1252	−0.779108	−0.389554	−	0.921004i	$-0.627371\pi$
$881$	−23.1252	−0.779108	−0.389554	+	0.921004i	$0.627371\pi$
$882$	−0.325905	−0.0109738
$883$	−50.9512	−1.71465	−0.857323	−	0.514780i	$-0.827874\pi$
$883$	−50.9512	−1.71465	−0.857323	+	0.514780i	$0.827874\pi$
$884$	−1.65111	−0.0555330
$885$	−53.9114	−1.81221
$886$	12.0749	0.405663
$887$	24.3607	0.817952	0.408976	−	0.912545i	$-0.365886\pi$
$887$	24.3607	0.817952	0.408976	+	0.912545i	$0.365886\pi$
$888$	−13.5739	−0.455511
$889$	12.9234	0.433438
$890$	35.2068	1.18013
$891$	−32.1112	−1.07577
$892$	8.02490	0.268694
$893$	−13.3039	−0.445196
$894$	11.3026	0.378015
$895$	−16.7955	−0.561410
$896$	0.635213	0.0212210
$897$	33.8173	1.12913
$898$	−11.4624	−0.382504
$899$	4.90063	0.163445
$900$	0.0833102	0.00277701
$901$	−2.72258	−0.0907023
$902$	37.7712	1.25764
$903$	−11.0490	−0.367688
$904$	14.2153	0.472794
$905$	−10.5545	−0.350842
$906$	−35.7346	−1.18720
$907$	−30.6192	−1.01669	−0.508347	−	0.861153i	$-0.669743\pi$
$907$	−30.6192	−1.01669	−0.508347	+	0.861153i	$0.669743\pi$
$908$	21.8320	0.724520
$909$	0.452381	0.0150045
$910$	−8.42177	−0.279179
$911$	−52.5031	−1.73951	−0.869753	−	0.493487i	$-0.835722\pi$
$911$	−52.5031	−1.73951	−0.869753	+	0.493487i	$0.835722\pi$
$912$	5.90881	0.195660
$913$	−58.6614	−1.94141
$914$	1.55079	0.0512957
$915$	−2.65005	−0.0876081
$916$	13.0772	0.432082
$917$	−12.6201	−0.416752
$918$	1.65921	0.0547621
$919$	−21.0907	−0.695719	−0.347860	−	0.937547i	$-0.613091\pi$
$919$	−21.0907	−0.695719	−0.347860	+	0.937547i	$0.613091\pi$
$920$	−9.76629	−0.321985
$921$	−2.70338	−0.0890793
$922$	21.0083	0.691871
$923$	−0.342036	−0.0112582
$924$	3.89460	0.128123
$925$	−13.1075	−0.430971
$926$	−7.65014	−0.251399
$927$	0.0586939	0.00192776
$928$	2.46547	0.0809330
$929$	36.4744	1.19668	0.598342	−	0.801240i	$-0.295826\pi$
$929$	36.4744	1.19668	0.598342	+	0.801240i	$0.295826\pi$
$930$	−8.97534	−0.294313
$931$	−22.3206	−0.731529
$932$	−5.66551	−0.185580
$933$	−0.823354	−0.0269554
$934$	−23.9495	−0.783650
$935$	2.92356	0.0956105
$936$	0.253320	0.00828003
$937$	35.4964	1.15962	0.579809	−	0.814752i	$-0.303127\pi$
$937$	35.4964	1.15962	0.579809	+	0.814752i	$0.303127\pi$
$938$	−8.20061	−0.267759
$939$	−21.1433	−0.689986
$940$	10.1666	0.331598
$941$	10.3782	0.338321	0.169160	−	0.985589i	$-0.445894\pi$
$941$	10.3782	0.338321	0.169160	+	0.985589i	$0.445894\pi$
$942$	−25.2906	−0.824011
$943$	40.6315	1.32314
$944$	11.9394	0.388593
$945$	8.46306	0.275303
$946$	−34.9729	−1.13707
$947$	10.9336	0.355294	0.177647	−	0.984094i	$-0.443152\pi$
$947$	10.9336	0.355294	0.177647	+	0.984094i	$0.443152\pi$
$948$	−7.67170	−0.249165
$949$	−14.4193	−0.468071
$950$	5.70577	0.185119
$951$	2.30211	0.0746511
$952$	−0.204552	−0.00662956
$953$	−46.0986	−1.49328	−0.746640	−	0.665228i	$-0.768334\pi$
$953$	−46.0986	−1.49328	−0.746640	+	0.665228i	$0.768334\pi$
$954$	0.417708	0.0135238
$955$	−60.7353	−1.96535
$956$	−3.87186	−0.125225
$957$	15.1162	0.488638
$958$	−7.57712	−0.244806
$959$	11.5848	0.374092
$960$	−4.51543	−0.145735
$961$	−27.0490	−0.872549
$962$	−39.8558	−1.28500
$963$	−0.520413	−0.0167701
$964$	−18.6798	−0.601636
$965$	−25.5201	−0.821520
$966$	4.18953	0.134796
$967$	27.3411	0.879231	0.439615	−	0.898186i	$-0.355115\pi$
$967$	27.3411	0.879231	0.439615	+	0.898186i	$0.355115\pi$
$968$	1.32741	0.0426645
$969$	−1.90276	−0.0611256
$970$	32.8528	1.05484
$971$	18.5972	0.596812	0.298406	−	0.954439i	$-0.403545\pi$
$971$	18.5972	0.596812	0.298406	+	0.954439i	$0.403545\pi$
$972$	−0.513387	−0.0164669
$973$	2.41209	0.0773279
$974$	9.92582	0.318044
$975$	15.0981	0.483525
$976$	0.586889	0.0187859
$977$	−43.2694	−1.38431	−0.692155	−	0.721749i	$-0.743339\pi$
$977$	−43.2694	−1.38431	−0.692155	+	0.721749i	$0.743339\pi$
$978$	−5.26933	−0.168495
$979$	−47.8048	−1.52785
$980$	17.0571	0.544869
$981$	−0.371047	−0.0118466
$982$	2.77590	0.0885825
$983$	54.4357	1.73623	0.868115	−	0.496363i	$-0.165331\pi$
$983$	54.4357	1.73623	0.868115	+	0.496363i	$0.165331\pi$
$984$	18.7859	0.598873
$985$	4.30753	0.137249
$986$	−0.793933	−0.0252840
$987$	−4.36125	−0.138820
$988$	17.3494	0.551959
$989$	−37.6214	−1.19629
$990$	−0.448543	−0.0142556
$991$	−36.0277	−1.14446	−0.572229	−	0.820094i	$-0.693921\pi$
$991$	−36.0277	−1.14446	−0.572229	+	0.820094i	$0.693921\pi$
$992$	1.98771	0.0631097
$993$	53.3333	1.69248
$994$	−0.0423738	−0.00134402
$995$	−33.0358	−1.04730
$996$	−29.1759	−0.924474
$997$	−56.7052	−1.79587	−0.897935	−	0.440128i	$-0.854933\pi$
$997$	−56.7052	−1.79587	−0.897935	+	0.440128i	$0.854933\pi$
$998$	−1.66429	−0.0526822
$999$	40.0512	1.26716

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1006.2.a.j.1.8	✓	12
3.2	odd	2		9054.2.a.bi.1.11		12
4.3	odd	2		8048.2.a.q.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1006.2.a.j.1.8	✓	12	1.1	even	1	trivial
8048.2.a.q.1.5		12	4.3	odd	2
9054.2.a.bi.1.11		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1006 = 2 \cdot 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.74625 q^{3} +1.00000 q^{4} -2.58578 q^{5} +1.74625 q^{6} +0.635213 q^{7} +1.00000 q^{8} +0.0494057 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.74625 q^{3} +1.00000 q^{4} -2.58578 q^{5} +1.74625 q^{6} +0.635213 q^{7} +1.00000 q^{8} +0.0494057 q^{9} -2.58578 q^{10} +3.51104 q^{11} +1.74625 q^{12} +5.12735 q^{13} +0.635213 q^{14} -4.51543 q^{15} +1.00000 q^{16} -0.322021 q^{17} +0.0494057 q^{18} +3.38371 q^{19} -2.58578 q^{20} +1.10924 q^{21} +3.51104 q^{22} +3.77692 q^{23} +1.74625 q^{24} +1.68625 q^{25} +5.12735 q^{26} -5.15249 q^{27} +0.635213 q^{28} +2.46547 q^{29} -4.51543 q^{30} +1.98771 q^{31} +1.00000 q^{32} +6.13117 q^{33} -0.322021 q^{34} -1.64252 q^{35} +0.0494057 q^{36} -7.77317 q^{37} +3.38371 q^{38} +8.95366 q^{39} -2.58578 q^{40} +10.7578 q^{41} +1.10924 q^{42} -9.96085 q^{43} +3.51104 q^{44} -0.127752 q^{45} +3.77692 q^{46} -3.93174 q^{47} +1.74625 q^{48} -6.59651 q^{49} +1.68625 q^{50} -0.562331 q^{51} +5.12735 q^{52} +8.45466 q^{53} -5.15249 q^{54} -9.07877 q^{55} +0.635213 q^{56} +5.90881 q^{57} +2.46547 q^{58} +11.9394 q^{59} -4.51543 q^{60} +0.586889 q^{61} +1.98771 q^{62} +0.0313831 q^{63} +1.00000 q^{64} -13.2582 q^{65} +6.13117 q^{66} -12.9100 q^{67} -0.322021 q^{68} +6.59547 q^{69} -1.64252 q^{70} -0.0667081 q^{71} +0.0494057 q^{72} -2.81224 q^{73} -7.77317 q^{74} +2.94462 q^{75} +3.38371 q^{76} +2.23026 q^{77} +8.95366 q^{78} -4.39323 q^{79} -2.58578 q^{80} -9.14578 q^{81} +10.7578 q^{82} -16.7077 q^{83} +1.10924 q^{84} +0.832675 q^{85} -9.96085 q^{86} +4.30534 q^{87} +3.51104 q^{88} -13.6156 q^{89} -0.127752 q^{90} +3.25696 q^{91} +3.77692 q^{92} +3.47104 q^{93} -3.93174 q^{94} -8.74951 q^{95} +1.74625 q^{96} -12.7052 q^{97} -6.59651 q^{98} +0.173465 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 5 q^{3} + 12 q^{4} + 5 q^{5} + 5 q^{6} + 8 q^{7} + 12 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 5 * q^3 + 12 * q^4 + 5 * q^5 + 5 * q^6 + 8 * q^7 + 12 * q^8 + 15 * q^9	\( 12 q + 12 q^{2} + 5 q^{3} + 12 q^{4} + 5 q^{5} + 5 q^{6} + 8 q^{7} + 12 q^{8} + 15 q^{9} + 5 q^{10} + 18 q^{11} + 5 q^{12} + 4 q^{13} + 8 q^{14} + 2 q^{15} + 12 q^{16} - 2 q^{17} + 15 q^{18} + 6 q^{19} + 5 q^{20} + q^{21} + 18 q^{22} + 13 q^{23} + 5 q^{24} + q^{25} + 4 q^{26} + 8 q^{27} + 8 q^{28} + 20 q^{29} + 2 q^{30} + 7 q^{31} + 12 q^{32} - 8 q^{33} - 2 q^{34} + q^{35} + 15 q^{36} + 10 q^{37} + 6 q^{38} + 7 q^{39} + 5 q^{40} + 2 q^{41} + q^{42} + 8 q^{43} + 18 q^{44} - 7 q^{45} + 13 q^{46} + 12 q^{47} + 5 q^{48} + 4 q^{49} + q^{50} + 2 q^{51} + 4 q^{52} + 12 q^{53} + 8 q^{54} + 8 q^{55} + 8 q^{56} - 10 q^{57} + 20 q^{58} + 6 q^{59} + 2 q^{60} - 10 q^{61} + 7 q^{62} + 7 q^{63} + 12 q^{64} + 4 q^{65} - 8 q^{66} + 7 q^{67} - 2 q^{68} - 12 q^{69} + q^{70} + 22 q^{71} + 15 q^{72} - 23 q^{73} + 10 q^{74} - 34 q^{75} + 6 q^{76} - 19 q^{77} + 7 q^{78} + 13 q^{79} + 5 q^{80} - 28 q^{81} + 2 q^{82} + q^{83} + q^{84} - 28 q^{85} + 8 q^{86} - 22 q^{87} + 18 q^{88} - 3 q^{89} - 7 q^{90} - 21 q^{91} + 13 q^{92} - 33 q^{93} + 12 q^{94} - 2 q^{95} + 5 q^{96} - 70 q^{97} + 4 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 5 * q^3 + 12 * q^4 + 5 * q^5 + 5 * q^6 + 8 * q^7 + 12 * q^8 + 15 * q^9 + 5 * q^10 + 18 * q^11 + 5 * q^12 + 4 * q^13 + 8 * q^14 + 2 * q^15 + 12 * q^16 - 2 * q^17 + 15 * q^18 + 6 * q^19 + 5 * q^20 + q^21 + 18 * q^22 + 13 * q^23 + 5 * q^24 + q^25 + 4 * q^26 + 8 * q^27 + 8 * q^28 + 20 * q^29 + 2 * q^30 + 7 * q^31 + 12 * q^32 - 8 * q^33 - 2 * q^34 + q^35 + 15 * q^36 + 10 * q^37 + 6 * q^38 + 7 * q^39 + 5 * q^40 + 2 * q^41 + q^42 + 8 * q^43 + 18 * q^44 - 7 * q^45 + 13 * q^46 + 12 * q^47 + 5 * q^48 + 4 * q^49 + q^50 + 2 * q^51 + 4 * q^52 + 12 * q^53 + 8 * q^54 + 8 * q^55 + 8 * q^56 - 10 * q^57 + 20 * q^58 + 6 * q^59 + 2 * q^60 - 10 * q^61 + 7 * q^62 + 7 * q^63 + 12 * q^64 + 4 * q^65 - 8 * q^66 + 7 * q^67 - 2 * q^68 - 12 * q^69 + q^70 + 22 * q^71 + 15 * q^72 - 23 * q^73 + 10 * q^74 - 34 * q^75 + 6 * q^76 - 19 * q^77 + 7 * q^78 + 13 * q^79 + 5 * q^80 - 28 * q^81 + 2 * q^82 + q^83 + q^84 - 28 * q^85 + 8 * q^86 - 22 * q^87 + 18 * q^88 - 3 * q^89 - 7 * q^90 - 21 * q^91 + 13 * q^92 - 33 * q^93 + 12 * q^94 - 2 * q^95 + 5 * q^96 - 70 * q^97 + 4 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more