LMFDB - Embedded newform 5290.2.a.be.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, 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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.252973568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 11x^{4} + 18x^{3} + 19x^{2} - 20x + 4 $ x^6 - 2x^5 - 11x^4 + 18x^3 + 19x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.323878$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.323878 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.323878 q^{6} -3.43707 q^{7} -1.00000 q^{8} -2.89510 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.323878 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.323878 q^{6} -3.43707 q^{7} -1.00000 q^{8} -2.89510 q^{9} +1.00000 q^{10} +3.58069 q^{11} -0.323878 q^{12} -1.05329 q^{13} +3.43707 q^{14} +0.323878 q^{15} +1.00000 q^{16} +1.36770 q^{17} +2.89510 q^{18} +3.04101 q^{19} -1.00000 q^{20} +1.11319 q^{21} -3.58069 q^{22} +0.323878 q^{24} +1.00000 q^{25} +1.05329 q^{26} +1.90930 q^{27} -3.43707 q^{28} +4.94839 q^{29} -0.323878 q^{30} -9.09392 q^{31} -1.00000 q^{32} -1.15971 q^{33} -1.36770 q^{34} +3.43707 q^{35} -2.89510 q^{36} +4.49036 q^{37} -3.04101 q^{38} +0.341137 q^{39} +1.00000 q^{40} -5.09699 q^{41} -1.11319 q^{42} -4.98850 q^{43} +3.58069 q^{44} +2.89510 q^{45} +6.41611 q^{47} -0.323878 q^{48} +4.81345 q^{49} -1.00000 q^{50} -0.442967 q^{51} -1.05329 q^{52} -0.491493 q^{53} -1.90930 q^{54} -3.58069 q^{55} +3.43707 q^{56} -0.984916 q^{57} -4.94839 q^{58} +8.21299 q^{59} +0.323878 q^{60} -2.16648 q^{61} +9.09392 q^{62} +9.95067 q^{63} +1.00000 q^{64} +1.05329 q^{65} +1.15971 q^{66} -5.16776 q^{67} +1.36770 q^{68} -3.43707 q^{70} +12.6084 q^{71} +2.89510 q^{72} +15.6557 q^{73} -4.49036 q^{74} -0.323878 q^{75} +3.04101 q^{76} -12.3071 q^{77} -0.341137 q^{78} +8.50772 q^{79} -1.00000 q^{80} +8.06693 q^{81} +5.09699 q^{82} -12.6304 q^{83} +1.11319 q^{84} -1.36770 q^{85} +4.98850 q^{86} -1.60268 q^{87} -3.58069 q^{88} -1.74831 q^{89} -2.89510 q^{90} +3.62022 q^{91} +2.94532 q^{93} -6.41611 q^{94} -3.04101 q^{95} +0.323878 q^{96} -7.18786 q^{97} -4.81345 q^{98} -10.3665 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 8 * q^9	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 8 q^{9} + 6 q^{10} - 10 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 2 q^{15} + 6 q^{16} + 10 q^{17} - 8 q^{18} - 2 q^{19} - 6 q^{20} - 12 q^{21} + 10 q^{22} + 2 q^{24} + 6 q^{25} + 2 q^{26} - 8 q^{27} - 2 q^{28} - 2 q^{30} - 2 q^{31} - 6 q^{32} + 22 q^{33} - 10 q^{34} + 2 q^{35} + 8 q^{36} + 4 q^{37} + 2 q^{38} + 24 q^{39} + 6 q^{40} + 6 q^{41} + 12 q^{42} - 12 q^{43} - 10 q^{44} - 8 q^{45} + 8 q^{47} - 2 q^{48} + 8 q^{49} - 6 q^{50} - 34 q^{51} - 2 q^{52} - 36 q^{53} + 8 q^{54} + 10 q^{55} + 2 q^{56} - 32 q^{57} + 16 q^{59} + 2 q^{60} + 10 q^{61} + 2 q^{62} + 48 q^{63} + 6 q^{64} + 2 q^{65} - 22 q^{66} - 16 q^{67} + 10 q^{68} - 2 q^{70} - 2 q^{71} - 8 q^{72} + 4 q^{73} - 4 q^{74} - 2 q^{75} - 2 q^{76} - 16 q^{77} - 24 q^{78} + 20 q^{79} - 6 q^{80} + 34 q^{81} - 6 q^{82} - 8 q^{83} - 12 q^{84} - 10 q^{85} + 12 q^{86} - 12 q^{87} + 10 q^{88} - 12 q^{89} + 8 q^{90} - 38 q^{91} - 28 q^{93} - 8 q^{94} + 2 q^{95} + 2 q^{96} - 2 q^{97} - 8 q^{98} - 50 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 8 * q^9 + 6 * q^10 - 10 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^14 + 2 * q^15 + 6 * q^16 + 10 * q^17 - 8 * q^18 - 2 * q^19 - 6 * q^20 - 12 * q^21 + 10 * q^22 + 2 * q^24 + 6 * q^25 + 2 * q^26 - 8 * q^27 - 2 * q^28 - 2 * q^30 - 2 * q^31 - 6 * q^32 + 22 * q^33 - 10 * q^34 + 2 * q^35 + 8 * q^36 + 4 * q^37 + 2 * q^38 + 24 * q^39 + 6 * q^40 + 6 * q^41 + 12 * q^42 - 12 * q^43 - 10 * q^44 - 8 * q^45 + 8 * q^47 - 2 * q^48 + 8 * q^49 - 6 * q^50 - 34 * q^51 - 2 * q^52 - 36 * q^53 + 8 * q^54 + 10 * q^55 + 2 * q^56 - 32 * q^57 + 16 * q^59 + 2 * q^60 + 10 * q^61 + 2 * q^62 + 48 * q^63 + 6 * q^64 + 2 * q^65 - 22 * q^66 - 16 * q^67 + 10 * q^68 - 2 * q^70 - 2 * q^71 - 8 * q^72 + 4 * q^73 - 4 * q^74 - 2 * q^75 - 2 * q^76 - 16 * q^77 - 24 * q^78 + 20 * q^79 - 6 * q^80 + 34 * q^81 - 6 * q^82 - 8 * q^83 - 12 * q^84 - 10 * q^85 + 12 * q^86 - 12 * q^87 + 10 * q^88 - 12 * q^89 + 8 * q^90 - 38 * q^91 - 28 * q^93 - 8 * q^94 + 2 * q^95 + 2 * q^96 - 2 * q^97 - 8 * q^98 - 50 * 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
$3$	−0.323878	−0.186991	−0.0934956	−	0.995620i	$-0.529804\pi$
$3$	−0.323878	−0.186991	−0.0934956	+	0.995620i	$0.529804\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.323878	0.132223
$7$	−3.43707	−1.29909	−0.649545	−	0.760323i	$-0.725041\pi$
$7$	−3.43707	−1.29909	−0.649545	+	0.760323i	$0.725041\pi$
$8$	−1.00000	−0.353553
$9$	−2.89510	−0.965034
$10$	1.00000	0.316228
$11$	3.58069	1.07962	0.539810	−	0.841787i	$-0.318496\pi$
$11$	3.58069	1.07962	0.539810	+	0.841787i	$0.318496\pi$
$12$	−0.323878	−0.0934956
$13$	−1.05329	−0.292129	−0.146065	−	0.989275i	$-0.546661\pi$
$13$	−1.05329	−0.292129	−0.146065	+	0.989275i	$0.546661\pi$
$14$	3.43707	0.918596
$15$	0.323878	0.0836250
$16$	1.00000	0.250000
$17$	1.36770	0.331715	0.165858	−	0.986150i	$-0.446961\pi$
$17$	1.36770	0.331715	0.165858	+	0.986150i	$0.446961\pi$
$18$	2.89510	0.682382
$19$	3.04101	0.697655	0.348827	−	0.937187i	$-0.386580\pi$
$19$	3.04101	0.697655	0.348827	+	0.937187i	$0.386580\pi$
$20$	−1.00000	−0.223607
$21$	1.11319	0.242918
$22$	−3.58069	−0.763406
$23$	0	0
$23$	0	0
$24$	0.323878	0.0661114
$25$	1.00000	0.200000
$26$	1.05329	0.206567
$27$	1.90930	0.367444
$28$	−3.43707	−0.649545
$29$	4.94839	0.918893	0.459446	−	0.888205i	$-0.348048\pi$
$29$	4.94839	0.918893	0.459446	+	0.888205i	$0.348048\pi$
$30$	−0.323878	−0.0591318
$31$	−9.09392	−1.63332	−0.816659	−	0.577121i	$-0.804176\pi$
$31$	−9.09392	−1.63332	−0.816659	+	0.577121i	$0.804176\pi$
$32$	−1.00000	−0.176777
$33$	−1.15971	−0.201879
$34$	−1.36770	−0.234558
$35$	3.43707	0.580971
$36$	−2.89510	−0.482517
$37$	4.49036	0.738210	0.369105	−	0.929388i	$-0.379664\pi$
$37$	4.49036	0.738210	0.369105	+	0.929388i	$0.379664\pi$
$38$	−3.04101	−0.493316
$39$	0.341137	0.0546256
$40$	1.00000	0.158114
$41$	−5.09699	−0.796016	−0.398008	−	0.917382i	$-0.630298\pi$
$41$	−5.09699	−0.796016	−0.398008	+	0.917382i	$0.630298\pi$
$42$	−1.11319	−0.171769
$43$	−4.98850	−0.760740	−0.380370	−	0.924834i	$-0.624203\pi$
$43$	−4.98850	−0.760740	−0.380370	+	0.924834i	$0.624203\pi$
$44$	3.58069	0.539810
$45$	2.89510	0.431576
$46$	0	0
$47$	6.41611	0.935885	0.467943	−	0.883759i	$-0.344995\pi$
$47$	6.41611	0.935885	0.467943	+	0.883759i	$0.344995\pi$
$48$	−0.323878	−0.0467478
$49$	4.81345	0.687636
$50$	−1.00000	−0.141421
$51$	−0.442967	−0.0620278
$52$	−1.05329	−0.146065
$53$	−0.491493	−0.0675117	−0.0337558	−	0.999430i	$-0.510747\pi$
$53$	−0.491493	−0.0675117	−0.0337558	+	0.999430i	$0.510747\pi$
$54$	−1.90930	−0.259822
$55$	−3.58069	−0.482820
$56$	3.43707	0.459298
$57$	−0.984916	−0.130455
$58$	−4.94839	−0.649755
$59$	8.21299	1.06924	0.534620	−	0.845092i	$-0.320455\pi$
$59$	8.21299	1.06924	0.534620	+	0.845092i	$0.320455\pi$
$60$	0.323878	0.0418125
$61$	−2.16648	−0.277389	−0.138695	−	0.990335i	$-0.544291\pi$
$61$	−2.16648	−0.277389	−0.138695	+	0.990335i	$0.544291\pi$
$62$	9.09392	1.15493
$63$	9.95067	1.25367
$64$	1.00000	0.125000
$65$	1.05329	0.130644
$66$	1.15971	0.142750
$67$	−5.16776	−0.631342	−0.315671	−	0.948869i	$-0.602230\pi$
$67$	−5.16776	−0.631342	−0.315671	+	0.948869i	$0.602230\pi$
$68$	1.36770	0.165858
$69$	0	0
$70$	−3.43707	−0.410808
$71$	12.6084	1.49634	0.748172	−	0.663505i	$-0.230932\pi$
$71$	12.6084	1.49634	0.748172	+	0.663505i	$0.230932\pi$
$72$	2.89510	0.341191
$73$	15.6557	1.83236	0.916182	−	0.400763i	$-0.131255\pi$
$73$	15.6557	1.83236	0.916182	+	0.400763i	$0.131255\pi$
$74$	−4.49036	−0.521993
$75$	−0.323878	−0.0373982
$76$	3.04101	0.348827
$77$	−12.3071	−1.40252
$78$	−0.341137	−0.0386261
$79$	8.50772	0.957194	0.478597	−	0.878035i	$-0.341146\pi$
$79$	8.50772	0.957194	0.478597	+	0.878035i	$0.341146\pi$
$80$	−1.00000	−0.111803
$81$	8.06693	0.896326
$82$	5.09699	0.562868
$83$	−12.6304	−1.38636	−0.693181	−	0.720763i	$-0.743791\pi$
$83$	−12.6304	−1.38636	−0.693181	+	0.720763i	$0.743791\pi$
$84$	1.11319	0.121459
$85$	−1.36770	−0.148348
$86$	4.98850	0.537924
$87$	−1.60268	−0.171825
$88$	−3.58069	−0.381703
$89$	−1.74831	−0.185320	−0.0926601	−	0.995698i	$-0.529537\pi$
$89$	−1.74831	−0.185320	−0.0926601	+	0.995698i	$0.529537\pi$
$90$	−2.89510	−0.305171
$91$	3.62022	0.379502
$92$	0	0
$93$	2.94532	0.305416
$94$	−6.41611	−0.661771
$95$	−3.04101	−0.312001
$96$	0.323878	0.0330557
$97$	−7.18786	−0.729816	−0.364908	−	0.931044i	$-0.618900\pi$
$97$	−7.18786	−0.729816	−0.364908	+	0.931044i	$0.618900\pi$
$98$	−4.81345	−0.486232
$99$	−10.3665	−1.04187
$100$	1.00000	0.100000
$101$	19.5775	1.94803	0.974017	−	0.226477i	$-0.0727207\pi$
$101$	19.5775	1.94803	0.974017	+	0.226477i	$0.0727207\pi$
$102$	0.442967	0.0438603
$103$	−9.35483	−0.921759	−0.460879	−	0.887463i	$-0.652466\pi$
$103$	−9.35483	−0.921759	−0.460879	+	0.887463i	$0.652466\pi$
$104$	1.05329	0.103283
$105$	−1.11319	−0.108636
$106$	0.491493	0.0477380
$107$	6.88080	0.665192	0.332596	−	0.943069i	$-0.392076\pi$
$107$	6.88080	0.665192	0.332596	+	0.943069i	$0.392076\pi$
$108$	1.90930	0.183722
$109$	4.07257	0.390082	0.195041	−	0.980795i	$-0.437516\pi$
$109$	4.07257	0.390082	0.195041	+	0.980795i	$0.437516\pi$
$110$	3.58069	0.341406
$111$	−1.45433	−0.138039
$112$	−3.43707	−0.324773
$113$	−17.3845	−1.63540	−0.817700	−	0.575645i	$-0.804751\pi$
$113$	−17.3845	−1.63540	−0.817700	+	0.575645i	$0.804751\pi$
$114$	0.984916	0.0922458
$115$	0	0
$116$	4.94839	0.459446
$117$	3.04937	0.281915
$118$	−8.21299	−0.756067
$119$	−4.70087	−0.430928
$120$	−0.323878	−0.0295659
$121$	1.82136	0.165578
$122$	2.16648	0.196144
$123$	1.65080	0.148848
$124$	−9.09392	−0.816659
$125$	−1.00000	−0.0894427
$126$	−9.95067	−0.886476
$127$	−11.9246	−1.05814	−0.529069	−	0.848579i	$-0.677459\pi$
$127$	−11.9246	−1.05814	−0.529069	+	0.848579i	$0.677459\pi$
$128$	−1.00000	−0.0883883
$129$	1.61567	0.142252
$130$	−1.05329	−0.0923794
$131$	15.7621	1.37714	0.688572	−	0.725168i	$-0.258238\pi$
$131$	15.7621	1.37714	0.688572	+	0.725168i	$0.258238\pi$
$132$	−1.15971	−0.100940
$133$	−10.4522	−0.906317
$134$	5.16776	0.446426
$135$	−1.90930	−0.164326
$136$	−1.36770	−0.117279
$137$	−12.6700	−1.08247	−0.541237	−	0.840870i	$-0.682044\pi$
$137$	−12.6700	−1.08247	−0.541237	+	0.840870i	$0.682044\pi$
$138$	0	0
$139$	−16.2282	−1.37646	−0.688228	−	0.725495i	$-0.741611\pi$
$139$	−16.2282	−1.37646	−0.688228	+	0.725495i	$0.741611\pi$
$140$	3.43707	0.290485
$141$	−2.07804	−0.175002
$142$	−12.6084	−1.05807
$143$	−3.77150	−0.315388
$144$	−2.89510	−0.241259
$145$	−4.94839	−0.410941
$146$	−15.6557	−1.29568
$147$	−1.55897	−0.128582
$148$	4.49036	0.369105
$149$	−18.5461	−1.51935	−0.759676	−	0.650302i	$-0.774643\pi$
$149$	−18.5461	−1.51935	−0.759676	+	0.650302i	$0.774643\pi$
$150$	0.323878	0.0264445
$151$	22.5525	1.83530	0.917649	−	0.397392i	$-0.130085\pi$
$151$	22.5525	1.83530	0.917649	+	0.397392i	$0.130085\pi$
$152$	−3.04101	−0.246658
$153$	−3.95962	−0.320117
$154$	12.3071	0.991734
$155$	9.09392	0.730442
$156$	0.341137	0.0273128
$157$	7.00910	0.559387	0.279693	−	0.960089i	$-0.409767\pi$
$157$	7.00910	0.559387	0.279693	+	0.960089i	$0.409767\pi$
$158$	−8.50772	−0.676838
$159$	0.159184	0.0126241
$160$	1.00000	0.0790569
$161$	0	0
$162$	−8.06693	−0.633798
$163$	19.3851	1.51836	0.759181	−	0.650880i	$-0.225600\pi$
$163$	19.3851	1.51836	0.759181	+	0.650880i	$0.225600\pi$
$164$	−5.09699	−0.398008
$165$	1.15971	0.0902831
$166$	12.6304	0.980306
$167$	−19.8588	−1.53672	−0.768361	−	0.640016i	$-0.778928\pi$
$167$	−19.8588	−1.53672	−0.768361	+	0.640016i	$0.778928\pi$
$168$	−1.11319	−0.0858846
$169$	−11.8906	−0.914661
$170$	1.36770	0.104898
$171$	−8.80403	−0.673261
$172$	−4.98850	−0.380370
$173$	−20.0671	−1.52567	−0.762836	−	0.646592i	$-0.776194\pi$
$173$	−20.0671	−1.52567	−0.762836	+	0.646592i	$0.776194\pi$
$174$	1.60268	0.121499
$175$	−3.43707	−0.259818
$176$	3.58069	0.269905
$177$	−2.66001	−0.199939
$178$	1.74831	0.131041
$179$	−9.83753	−0.735291	−0.367646	−	0.929966i	$-0.619836\pi$
$179$	−9.83753	−0.735291	−0.367646	+	0.929966i	$0.619836\pi$
$180$	2.89510	0.215788
$181$	22.9728	1.70756	0.853778	−	0.520637i	$-0.174305\pi$
$181$	22.9728	1.70756	0.853778	+	0.520637i	$0.174305\pi$
$182$	−3.62022	−0.268349
$183$	0.701675	0.0518693
$184$	0	0
$185$	−4.49036	−0.330138
$186$	−2.94532	−0.215962
$187$	4.89730	0.358126
$188$	6.41611	0.467943
$189$	−6.56238	−0.477343
$190$	3.04101	0.220618
$191$	−12.9076	−0.933961	−0.466981	−	0.884268i	$-0.654658\pi$
$191$	−12.9076	−0.933961	−0.466981	+	0.884268i	$0.654658\pi$
$192$	−0.323878	−0.0233739
$193$	−21.2210	−1.52752	−0.763759	−	0.645502i	$-0.776648\pi$
$193$	−21.2210	−1.52752	−0.763759	+	0.645502i	$0.776648\pi$
$194$	7.18786	0.516058
$195$	−0.341137	−0.0244293
$196$	4.81345	0.343818
$197$	1.09991	0.0783654	0.0391827	−	0.999232i	$-0.487525\pi$
$197$	1.09991	0.0783654	0.0391827	+	0.999232i	$0.487525\pi$
$198$	10.3665	0.736713
$199$	−8.90198	−0.631044	−0.315522	−	0.948918i	$-0.602180\pi$
$199$	−8.90198	−0.631044	−0.315522	+	0.948918i	$0.602180\pi$
$200$	−1.00000	−0.0707107
$201$	1.67372	0.118055
$202$	−19.5775	−1.37747
$203$	−17.0080	−1.19372
$204$	−0.442967	−0.0310139
$205$	5.09699	0.355989
$206$	9.35483	0.651782
$207$	0	0
$208$	−1.05329	−0.0730323
$209$	10.8889	0.753202
$210$	1.11319	0.0768175
$211$	−1.52460	−0.104958	−0.0524789	−	0.998622i	$-0.516712\pi$
$211$	−1.52460	−0.104958	−0.0524789	+	0.998622i	$0.516712\pi$
$212$	−0.491493	−0.0337558
$213$	−4.08359	−0.279803
$214$	−6.88080	−0.470361
$215$	4.98850	0.340213
$216$	−1.90930	−0.129911
$217$	31.2565	2.12183
$218$	−4.07257	−0.275829
$219$	−5.07055	−0.342636
$220$	−3.58069	−0.241410
$221$	−1.44058	−0.0969037
$222$	1.45433	0.0976081
$223$	−7.41803	−0.496748	−0.248374	−	0.968664i	$-0.579896\pi$
$223$	−7.41803	−0.496748	−0.248374	+	0.968664i	$0.579896\pi$
$224$	3.43707	0.229649
$225$	−2.89510	−0.193007
$226$	17.3845	1.15640
$227$	2.19532	0.145709	0.0728543	−	0.997343i	$-0.476789\pi$
$227$	2.19532	0.145709	0.0728543	+	0.997343i	$0.476789\pi$
$228$	−0.984916	−0.0652276
$229$	−22.5499	−1.49014	−0.745071	−	0.666986i	$-0.767584\pi$
$229$	−22.5499	−1.49014	−0.745071	+	0.666986i	$0.767584\pi$
$230$	0	0
$231$	3.98600	0.262259
$232$	−4.94839	−0.324878
$233$	−18.9204	−1.23952	−0.619758	−	0.784793i	$-0.712769\pi$
$233$	−18.9204	−1.23952	−0.619758	+	0.784793i	$0.712769\pi$
$234$	−3.04937	−0.199344
$235$	−6.41611	−0.418541
$236$	8.21299	0.534620
$237$	−2.75547	−0.178987
$238$	4.70087	0.304712
$239$	−8.94135	−0.578368	−0.289184	−	0.957274i	$-0.593384\pi$
$239$	−8.94135	−0.578368	−0.289184	+	0.957274i	$0.593384\pi$
$240$	0.323878	0.0209062
$241$	−11.5724	−0.745447	−0.372723	−	0.927943i	$-0.621576\pi$
$241$	−11.5724	−0.745447	−0.372723	+	0.927943i	$0.621576\pi$
$242$	−1.82136	−0.117081
$243$	−8.34059	−0.535049
$244$	−2.16648	−0.138695
$245$	−4.81345	−0.307520
$246$	−1.65080	−0.105251
$247$	−3.20305	−0.203805
$248$	9.09392	0.577465
$249$	4.09070	0.259238
$250$	1.00000	0.0632456
$251$	8.78211	0.554322	0.277161	−	0.960824i	$-0.410606\pi$
$251$	8.78211	0.554322	0.277161	+	0.960824i	$0.410606\pi$
$252$	9.95067	0.626833
$253$	0	0
$254$	11.9246	0.748217
$255$	0.442967	0.0277397
$256$	1.00000	0.0625000
$257$	7.63102	0.476010	0.238005	−	0.971264i	$-0.423507\pi$
$257$	7.63102	0.476010	0.238005	+	0.971264i	$0.423507\pi$
$258$	−1.61567	−0.100587
$259$	−15.4337	−0.959002
$260$	1.05329	0.0653221
$261$	−14.3261	−0.886763
$262$	−15.7621	−0.973788
$263$	−14.2770	−0.880359	−0.440180	−	0.897910i	$-0.645085\pi$
$263$	−14.2770	−0.880359	−0.440180	+	0.897910i	$0.645085\pi$
$264$	1.15971	0.0713751
$265$	0.491493	0.0301922
$266$	10.4522	0.640863
$267$	0.566238	0.0346532
$268$	−5.16776	−0.315671
$269$	11.7145	0.714248	0.357124	−	0.934057i	$-0.383757\pi$
$269$	11.7145	0.714248	0.357124	+	0.934057i	$0.383757\pi$
$270$	1.90930	0.116196
$271$	−9.19109	−0.558319	−0.279159	−	0.960245i	$-0.590056\pi$
$271$	−9.19109	−0.558319	−0.279159	+	0.960245i	$0.590056\pi$
$272$	1.36770	0.0829288
$273$	−1.17251	−0.0709636
$274$	12.6700	0.765424
$275$	3.58069	0.215924
$276$	0	0
$277$	16.1940	0.973002	0.486501	−	0.873680i	$-0.338273\pi$
$277$	16.1940	0.973002	0.486501	+	0.873680i	$0.338273\pi$
$278$	16.2282	0.973301
$279$	26.3278	1.57621
$280$	−3.43707	−0.205404
$281$	−30.6744	−1.82988	−0.914940	−	0.403589i	$-0.867763\pi$
$281$	−30.6744	−1.82988	−0.914940	+	0.403589i	$0.867763\pi$
$282$	2.07804	0.123745
$283$	−10.5439	−0.626767	−0.313384	−	0.949627i	$-0.601463\pi$
$283$	−10.5439	−0.626767	−0.313384	+	0.949627i	$0.601463\pi$
$284$	12.6084	0.748172
$285$	0.984916	0.0583414
$286$	3.77150	0.223013
$287$	17.5187	1.03410
$288$	2.89510	0.170596
$289$	−15.1294	−0.889965
$290$	4.94839	0.290579
$291$	2.32799	0.136469
$292$	15.6557	0.916182
$293$	27.1266	1.58476	0.792378	−	0.610031i	$-0.208843\pi$
$293$	27.1266	1.58476	0.792378	+	0.610031i	$0.208843\pi$
$294$	1.55897	0.0909211
$295$	−8.21299	−0.478179
$296$	−4.49036	−0.260997
$297$	6.83660	0.396700
$298$	18.5461	1.07434
$299$	0	0
$300$	−0.323878	−0.0186991
$301$	17.1458	0.988270
$302$	−22.5525	−1.29775
$303$	−6.34072	−0.364265
$304$	3.04101	0.174414
$305$	2.16648	0.124052
$306$	3.95962	0.226357
$307$	−18.2702	−1.04274	−0.521368	−	0.853332i	$-0.674578\pi$
$307$	−18.2702	−1.04274	−0.521368	+	0.853332i	$0.674578\pi$
$308$	−12.3071	−0.701262
$309$	3.02983	0.172361
$310$	−9.09392	−0.516500
$311$	7.75012	0.439469	0.219734	−	0.975560i	$-0.429481\pi$
$311$	7.75012	0.439469	0.219734	+	0.975560i	$0.429481\pi$
$312$	−0.341137	−0.0193131
$313$	17.4637	0.987107	0.493553	−	0.869715i	$-0.335698\pi$
$313$	17.4637	0.987107	0.493553	+	0.869715i	$0.335698\pi$
$314$	−7.00910	−0.395546
$315$	−9.95067	−0.560657
$316$	8.50772	0.478597
$317$	10.5488	0.592482	0.296241	−	0.955113i	$-0.404267\pi$
$317$	10.5488	0.592482	0.296241	+	0.955113i	$0.404267\pi$
$318$	−0.159184	−0.00892658
$319$	17.7187	0.992055
$320$	−1.00000	−0.0559017
$321$	−2.22854	−0.124385
$322$	0	0
$323$	4.15918	0.231423
$324$	8.06693	0.448163
$325$	−1.05329	−0.0584258
$326$	−19.3851	−1.07364
$327$	−1.31902	−0.0729418
$328$	5.09699	0.281434
$329$	−22.0526	−1.21580
$330$	−1.15971	−0.0638398
$331$	5.14830	0.282976	0.141488	−	0.989940i	$-0.454811\pi$
$331$	5.14830	0.282976	0.141488	+	0.989940i	$0.454811\pi$
$332$	−12.6304	−0.693181
$333$	−13.0000	−0.712398
$334$	19.8588	1.08663
$335$	5.16776	0.282345
$336$	1.11319	0.0607296
$337$	−31.6942	−1.72649	−0.863247	−	0.504782i	$-0.831573\pi$
$337$	−31.6942	−1.72649	−0.863247	+	0.504782i	$0.831573\pi$
$338$	11.8906	0.646763
$339$	5.63047	0.305805
$340$	−1.36770	−0.0741738
$341$	−32.5625	−1.76336
$342$	8.80403	0.476067
$343$	7.51532	0.405789
$344$	4.98850	0.268962
$345$	0	0
$346$	20.0671	1.07881
$347$	2.23707	0.120092	0.0600461	−	0.998196i	$-0.480875\pi$
$347$	2.23707	0.120092	0.0600461	+	0.998196i	$0.480875\pi$
$348$	−1.60268	−0.0859124
$349$	11.1045	0.594410	0.297205	−	0.954814i	$-0.403945\pi$
$349$	11.1045	0.594410	0.297205	+	0.954814i	$0.403945\pi$
$350$	3.43707	0.183719
$351$	−2.01104	−0.107341
$352$	−3.58069	−0.190852
$353$	−3.68071	−0.195905	−0.0979523	−	0.995191i	$-0.531229\pi$
$353$	−3.68071	−0.195905	−0.0979523	+	0.995191i	$0.531229\pi$
$354$	2.66001	0.141378
$355$	−12.6084	−0.669185
$356$	−1.74831	−0.0926601
$357$	1.52251	0.0805798
$358$	9.83753	0.519929
$359$	−27.5143	−1.45215	−0.726074	−	0.687617i	$-0.758657\pi$
$359$	−27.5143	−1.45215	−0.726074	+	0.687617i	$0.758657\pi$
$360$	−2.89510	−0.152585
$361$	−9.75228	−0.513278
$362$	−22.9728	−1.20742
$363$	−0.589898	−0.0309616
$364$	3.62022	0.189751
$365$	−15.6557	−0.819458
$366$	−0.701675	−0.0366771
$367$	−27.0147	−1.41016	−0.705078	−	0.709130i	$-0.749088\pi$
$367$	−27.0147	−1.41016	−0.705078	+	0.709130i	$0.749088\pi$
$368$	0	0
$369$	14.7563	0.768183
$370$	4.49036	0.233443
$371$	1.68929	0.0877038
$372$	2.94532	0.152708
$373$	19.4471	1.00693	0.503465	−	0.864015i	$-0.332058\pi$
$373$	19.4471	1.00693	0.503465	+	0.864015i	$0.332058\pi$
$374$	−4.89730	−0.253234
$375$	0.323878	0.0167250
$376$	−6.41611	−0.330885
$377$	−5.21207	−0.268435
$378$	6.56238	0.337532
$379$	24.4201	1.25438	0.627188	−	0.778868i	$-0.284206\pi$
$379$	24.4201	1.25438	0.627188	+	0.778868i	$0.284206\pi$
$380$	−3.04101	−0.156000
$381$	3.86212	0.197863
$382$	12.9076	0.660410
$383$	−9.06456	−0.463178	−0.231589	−	0.972814i	$-0.574392\pi$
$383$	−9.06456	−0.463178	−0.231589	+	0.972814i	$0.574392\pi$
$384$	0.323878	0.0165278
$385$	12.3071	0.627227
$386$	21.2210	1.08012
$387$	14.4422	0.734140
$388$	−7.18786	−0.364908
$389$	−14.8086	−0.750826	−0.375413	−	0.926858i	$-0.622499\pi$
$389$	−14.8086	−0.750826	−0.375413	+	0.926858i	$0.622499\pi$
$390$	0.341137	0.0172741
$391$	0	0
$392$	−4.81345	−0.243116
$393$	−5.10501	−0.257514
$394$	−1.09991	−0.0554127
$395$	−8.50772	−0.428070
$396$	−10.3665	−0.520935
$397$	4.80967	0.241390	0.120695	−	0.992690i	$-0.461488\pi$
$397$	4.80967	0.241390	0.120695	+	0.992690i	$0.461488\pi$
$398$	8.90198	0.446216
$399$	3.38522	0.169473
$400$	1.00000	0.0500000
$401$	−18.6592	−0.931797	−0.465898	−	0.884838i	$-0.654269\pi$
$401$	−18.6592	−0.931797	−0.465898	+	0.884838i	$0.654269\pi$
$402$	−1.67372	−0.0834778
$403$	9.57851	0.477140
$404$	19.5775	0.974017
$405$	−8.06693	−0.400849
$406$	17.0080	0.844091
$407$	16.0786	0.796986
$408$	0.442967	0.0219302
$409$	3.71983	0.183934	0.0919668	−	0.995762i	$-0.470685\pi$
$409$	3.71983	0.183934	0.0919668	+	0.995762i	$0.470685\pi$
$410$	−5.09699	−0.251722
$411$	4.10354	0.202413
$412$	−9.35483	−0.460879
$413$	−28.2286	−1.38904
$414$	0	0
$415$	12.6304	0.620000
$416$	1.05329	0.0516416
$417$	5.25595	0.257385
$418$	−10.8889	−0.532594
$419$	17.7666	0.867955	0.433978	−	0.900924i	$-0.357110\pi$
$419$	17.7666	0.867955	0.433978	+	0.900924i	$0.357110\pi$
$420$	−1.11319	−0.0543182
$421$	15.5897	0.759794	0.379897	−	0.925029i	$-0.375959\pi$
$421$	15.5897	0.759794	0.379897	+	0.925029i	$0.375959\pi$
$422$	1.52460	0.0742164
$423$	−18.5753	−0.903162
$424$	0.491493	0.0238690
$425$	1.36770	0.0663431
$426$	4.08359	0.197851
$427$	7.44634	0.360354
$428$	6.88080	0.332596
$429$	1.22151	0.0589748
$430$	−4.98850	−0.240567
$431$	0.0505199	0.00243346	0.00121673	−	0.999999i	$-0.499613\pi$
$431$	0.0505199	0.00243346	0.00121673	+	0.999999i	$0.499613\pi$
$432$	1.90930	0.0918610
$433$	14.8561	0.713936	0.356968	−	0.934117i	$-0.383810\pi$
$433$	14.8561	0.713936	0.356968	+	0.934117i	$0.383810\pi$
$434$	−31.2565	−1.50036
$435$	1.60268	0.0768424
$436$	4.07257	0.195041
$437$	0	0
$438$	5.07055	0.242280
$439$	7.62566	0.363953	0.181976	−	0.983303i	$-0.441751\pi$
$439$	7.62566	0.363953	0.181976	+	0.983303i	$0.441751\pi$
$440$	3.58069	0.170703
$441$	−13.9354	−0.663592
$442$	1.44058	0.0685213
$443$	−12.4713	−0.592530	−0.296265	−	0.955106i	$-0.595741\pi$
$443$	−12.4713	−0.592530	−0.296265	+	0.955106i	$0.595741\pi$
$444$	−1.45433	−0.0690194
$445$	1.74831	0.0828777
$446$	7.41803	0.351254
$447$	6.00666	0.284105
$448$	−3.43707	−0.162386
$449$	−29.0006	−1.36862	−0.684311	−	0.729190i	$-0.739897\pi$
$449$	−29.0006	−1.36862	−0.684311	+	0.729190i	$0.739897\pi$
$450$	2.89510	0.136476
$451$	−18.2508	−0.859394
$452$	−17.3845	−0.817700
$453$	−7.30427	−0.343184
$454$	−2.19532	−0.103032
$455$	−3.62022	−0.169719
$456$	0.984916	0.0461229
$457$	15.0872	0.705748	0.352874	−	0.935671i	$-0.385204\pi$
$457$	15.0872	0.705748	0.352874	+	0.935671i	$0.385204\pi$
$458$	22.5499	1.05369
$459$	2.61134	0.121887
$460$	0	0
$461$	32.3595	1.50713	0.753566	−	0.657372i	$-0.228332\pi$
$461$	32.3595	1.50713	0.753566	+	0.657372i	$0.228332\pi$
$462$	−3.98600	−0.185445
$463$	−27.7030	−1.28747	−0.643734	−	0.765249i	$-0.722616\pi$
$463$	−27.7030	−1.28747	−0.643734	+	0.765249i	$0.722616\pi$
$464$	4.94839	0.229723
$465$	−2.94532	−0.136586
$466$	18.9204	0.876471
$467$	−23.6144	−1.09274	−0.546371	−	0.837543i	$-0.683991\pi$
$467$	−23.6144	−1.09274	−0.546371	+	0.837543i	$0.683991\pi$
$468$	3.04937	0.140957
$469$	17.7619	0.820171
$470$	6.41611	0.295953
$471$	−2.27009	−0.104600
$472$	−8.21299	−0.378034
$473$	−17.8623	−0.821309
$474$	2.75547	0.126563
$475$	3.04101	0.139531
$476$	−4.70087	−0.215464
$477$	1.42292	0.0651511
$478$	8.94135	0.408968
$479$	−14.6223	−0.668110	−0.334055	−	0.942554i	$-0.608417\pi$
$479$	−14.6223	−0.668110	−0.334055	+	0.942554i	$0.608417\pi$
$480$	−0.323878	−0.0147829
$481$	−4.72963	−0.215653
$482$	11.5724	0.527110
$483$	0	0
$484$	1.82136	0.0827890
$485$	7.18786	0.326384
$486$	8.34059	0.378337
$487$	28.0818	1.27251	0.636254	−	0.771480i	$-0.280483\pi$
$487$	28.0818	1.27251	0.636254	+	0.771480i	$0.280483\pi$
$488$	2.16648	0.0980719
$489$	−6.27843	−0.283920
$490$	4.81345	0.217450
$491$	2.28162	0.102968	0.0514840	−	0.998674i	$-0.483605\pi$
$491$	2.28162	0.102968	0.0514840	+	0.998674i	$0.483605\pi$
$492$	1.65080	0.0744240
$493$	6.76790	0.304811
$494$	3.20305	0.144112
$495$	10.3665	0.465938
$496$	−9.09392	−0.408329
$497$	−43.3360	−1.94389
$498$	−4.09070	−0.183309
$499$	−3.28638	−0.147119	−0.0735593	−	0.997291i	$-0.523436\pi$
$499$	−3.28638	−0.147119	−0.0735593	+	0.997291i	$0.523436\pi$
$500$	−1.00000	−0.0447214
$501$	6.43184	0.287353
$502$	−8.78211	−0.391965
$503$	−5.78817	−0.258082	−0.129041	−	0.991639i	$-0.541190\pi$
$503$	−5.78817	−0.258082	−0.129041	+	0.991639i	$0.541190\pi$
$504$	−9.95067	−0.443238
$505$	−19.5775	−0.871187
$506$	0	0
$507$	3.85110	0.171033
$508$	−11.9246	−0.529069
$509$	−19.6772	−0.872178	−0.436089	−	0.899904i	$-0.643637\pi$
$509$	−19.6772	−0.872178	−0.436089	+	0.899904i	$0.643637\pi$
$510$	−0.442967	−0.0196149
$511$	−53.8098	−2.38041
$512$	−1.00000	−0.0441942
$513$	5.80618	0.256349
$514$	−7.63102	−0.336590
$515$	9.35483	0.412223
$516$	1.61567	0.0711258
$517$	22.9741	1.01040
$518$	15.4337	0.678117
$519$	6.49929	0.285287
$520$	−1.05329	−0.0461897
$521$	2.87897	0.126130	0.0630651	−	0.998009i	$-0.479912\pi$
$521$	2.87897	0.126130	0.0630651	+	0.998009i	$0.479912\pi$
$522$	14.3261	0.627036
$523$	−39.5245	−1.72829	−0.864143	−	0.503247i	$-0.832139\pi$
$523$	−39.5245	−1.72829	−0.864143	+	0.503247i	$0.832139\pi$
$524$	15.7621	0.688572
$525$	1.11319	0.0485837
$526$	14.2770	0.622508
$527$	−12.4377	−0.541796
$528$	−1.15971	−0.0504698
$529$	0	0
$530$	−0.491493	−0.0213491
$531$	−23.7775	−1.03185
$532$	−10.4522	−0.453158
$533$	5.36859	0.232540
$534$	−0.566238	−0.0245035
$535$	−6.88080	−0.297483
$536$	5.16776	0.223213
$537$	3.18616	0.137493
$538$	−11.7145	−0.505050
$539$	17.2355	0.742385
$540$	−1.90930	−0.0821630
$541$	38.9611	1.67507	0.837535	−	0.546384i	$-0.183996\pi$
$541$	38.9611	1.67507	0.837535	+	0.546384i	$0.183996\pi$
$542$	9.19109	0.394791
$543$	−7.44040	−0.319298
$544$	−1.36770	−0.0586395
$545$	−4.07257	−0.174450
$546$	1.17251	0.0501788
$547$	10.9282	0.467257	0.233628	−	0.972326i	$-0.424940\pi$
$547$	10.9282	0.467257	0.233628	+	0.972326i	$0.424940\pi$
$548$	−12.6700	−0.541237
$549$	6.27218	0.267690
$550$	−3.58069	−0.152681
$551$	15.0481	0.641070
$552$	0	0
$553$	−29.2416	−1.24348
$554$	−16.1940	−0.688016
$555$	1.45433	0.0617328
$556$	−16.2282	−0.688228
$557$	39.5463	1.67563	0.837815	−	0.545954i	$-0.183833\pi$
$557$	39.5463	1.67563	0.837815	+	0.545954i	$0.183833\pi$
$558$	−26.3278	−1.11455
$559$	5.25433	0.222234
$560$	3.43707	0.145243
$561$	−1.58613	−0.0669664
$562$	30.6744	1.29392
$563$	−18.5680	−0.782547	−0.391273	−	0.920275i	$-0.627965\pi$
$563$	−18.5680	−0.782547	−0.391273	+	0.920275i	$0.627965\pi$
$564$	−2.07804	−0.0875011
$565$	17.3845	0.731373
$566$	10.5439	0.443192
$567$	−27.7266	−1.16441
$568$	−12.6084	−0.529037
$569$	−40.2178	−1.68602	−0.843008	−	0.537900i	$-0.819218\pi$
$569$	−40.2178	−1.68602	−0.843008	+	0.537900i	$0.819218\pi$
$570$	−0.984916	−0.0412536
$571$	−24.3399	−1.01859	−0.509297	−	0.860591i	$-0.670094\pi$
$571$	−24.3399	−1.01859	−0.509297	+	0.860591i	$0.670094\pi$
$572$	−3.77150	−0.157694
$573$	4.18049	0.174642
$574$	−17.5187	−0.731217
$575$	0	0
$576$	−2.89510	−0.120629
$577$	−14.1918	−0.590814	−0.295407	−	0.955371i	$-0.595455\pi$
$577$	−14.1918	−0.590814	−0.295407	+	0.955371i	$0.595455\pi$
$578$	15.1294	0.629300
$579$	6.87300	0.285632
$580$	−4.94839	−0.205471
$581$	43.4114	1.80101
$582$	−2.32799	−0.0964983
$583$	−1.75988	−0.0728869
$584$	−15.6557	−0.647838
$585$	−3.04937	−0.126076
$586$	−27.1266	−1.12059
$587$	−10.4682	−0.432071	−0.216035	−	0.976386i	$-0.569313\pi$
$587$	−10.4682	−0.432071	−0.216035	+	0.976386i	$0.569313\pi$
$588$	−1.55897	−0.0642909
$589$	−27.6547	−1.13949
$590$	8.21299	0.338124
$591$	−0.356237	−0.0146536
$592$	4.49036	0.184553
$593$	−24.8070	−1.01870	−0.509351	−	0.860559i	$-0.670115\pi$
$593$	−24.8070	−1.01870	−0.509351	+	0.860559i	$0.670115\pi$
$594$	−6.83660	−0.280509
$595$	4.70087	0.192717
$596$	−18.5461	−0.759676
$597$	2.88316	0.118000
$598$	0	0
$599$	−5.21609	−0.213123	−0.106562	−	0.994306i	$-0.533984\pi$
$599$	−5.21609	−0.213123	−0.106562	+	0.994306i	$0.533984\pi$
$600$	0.323878	0.0132223
$601$	44.2677	1.80572	0.902859	−	0.429937i	$-0.141464\pi$
$601$	44.2677	1.80572	0.902859	+	0.429937i	$0.141464\pi$
$602$	−17.1458	−0.698812
$603$	14.9612	0.609267
$604$	22.5525	0.917649
$605$	−1.82136	−0.0740487
$606$	6.34072	0.257574
$607$	−38.0277	−1.54350	−0.771749	−	0.635927i	$-0.780618\pi$
$607$	−38.0277	−1.54350	−0.771749	+	0.635927i	$0.780618\pi$
$608$	−3.04101	−0.123329
$609$	5.50851	0.223216
$610$	−2.16648	−0.0877182
$611$	−6.75800	−0.273399
$612$	−3.95962	−0.160058
$613$	−5.66375	−0.228757	−0.114378	−	0.993437i	$-0.536488\pi$
$613$	−5.66375	−0.228757	−0.114378	+	0.993437i	$0.536488\pi$
$614$	18.2702	0.737325
$615$	−1.65080	−0.0665668
$616$	12.3071	0.495867
$617$	37.1193	1.49437	0.747184	−	0.664618i	$-0.231406\pi$
$617$	37.1193	1.49437	0.747184	+	0.664618i	$0.231406\pi$
$618$	−3.02983	−0.121877
$619$	−29.8253	−1.19878	−0.599389	−	0.800458i	$-0.704590\pi$
$619$	−29.8253	−1.19878	−0.599389	+	0.800458i	$0.704590\pi$
$620$	9.09392	0.365221
$621$	0	0
$622$	−7.75012	−0.310751
$623$	6.00905	0.240748
$624$	0.341137	0.0136564
$625$	1.00000	0.0400000
$626$	−17.4637	−0.697990
$627$	−3.52668	−0.140842
$628$	7.00910	0.279693
$629$	6.14145	0.244876
$630$	9.95067	0.396444
$631$	−37.9786	−1.51190	−0.755951	−	0.654628i	$-0.772825\pi$
$631$	−37.9786	−1.51190	−0.755951	+	0.654628i	$0.772825\pi$
$632$	−8.50772	−0.338419
$633$	0.493785	0.0196262
$634$	−10.5488	−0.418948
$635$	11.9246	0.473214
$636$	0.159184	0.00631204
$637$	−5.06994	−0.200878
$638$	−17.7187	−0.701488
$639$	−36.5027	−1.44402
$640$	1.00000	0.0395285
$641$	22.6752	0.895617	0.447809	−	0.894129i	$-0.352205\pi$
$641$	22.6752	0.895617	0.447809	+	0.894129i	$0.352205\pi$
$642$	2.22854	0.0879534
$643$	−3.33727	−0.131609	−0.0658046	−	0.997833i	$-0.520961\pi$
$643$	−3.33727	−0.131609	−0.0658046	+	0.997833i	$0.520961\pi$
$644$	0	0
$645$	−1.61567	−0.0636169
$646$	−4.15918	−0.163641
$647$	−14.0339	−0.551729	−0.275864	−	0.961197i	$-0.588964\pi$
$647$	−14.0339	−0.551729	−0.275864	+	0.961197i	$0.588964\pi$
$648$	−8.06693	−0.316899
$649$	29.4082	1.15437
$650$	1.05329	0.0413133
$651$	−10.1233	−0.396763
$652$	19.3851	0.759181
$653$	40.6558	1.59098	0.795492	−	0.605964i	$-0.207212\pi$
$653$	40.6558	1.59098	0.795492	+	0.605964i	$0.207212\pi$
$654$	1.31902	0.0515777
$655$	−15.7621	−0.615878
$656$	−5.09699	−0.199004
$657$	−45.3249	−1.76829
$658$	22.0526	0.859700
$659$	0.437402	0.0170388	0.00851938	−	0.999964i	$-0.497288\pi$
$659$	0.437402	0.0170388	0.00851938	+	0.999964i	$0.497288\pi$
$660$	1.15971	0.0451416
$661$	21.5013	0.836305	0.418153	−	0.908377i	$-0.362678\pi$
$661$	21.5013	0.836305	0.418153	+	0.908377i	$0.362678\pi$
$662$	−5.14830	−0.200094
$663$	0.466572	0.0181201
$664$	12.6304	0.490153
$665$	10.4522	0.405317
$666$	13.0000	0.503742
$667$	0	0
$668$	−19.8588	−0.768361
$669$	2.40254	0.0928874
$670$	−5.16776	−0.199648
$671$	−7.75749	−0.299475
$672$	−1.11319	−0.0429423
$673$	−29.8402	−1.15025	−0.575127	−	0.818064i	$-0.695047\pi$
$673$	−29.8402	−1.15025	−0.575127	+	0.818064i	$0.695047\pi$
$674$	31.6942	1.22082
$675$	1.90930	0.0734888
$676$	−11.8906	−0.457330
$677$	8.72626	0.335378	0.167689	−	0.985840i	$-0.446370\pi$
$677$	8.72626	0.335378	0.167689	+	0.985840i	$0.446370\pi$
$678$	−5.63047	−0.216237
$679$	24.7052	0.948097
$680$	1.36770	0.0524488
$681$	−0.711017	−0.0272462
$682$	32.5625	1.24688
$683$	−36.0880	−1.38087	−0.690434	−	0.723395i	$-0.742580\pi$
$683$	−36.0880	−1.38087	−0.690434	+	0.723395i	$0.742580\pi$
$684$	−8.80403	−0.336630
$685$	12.6700	0.484097
$686$	−7.51532	−0.286936
$687$	7.30343	0.278643
$688$	−4.98850	−0.190185
$689$	0.517683	0.0197221
$690$	0	0
$691$	−17.2049	−0.654504	−0.327252	−	0.944937i	$-0.606123\pi$
$691$	−17.2049	−0.654504	−0.327252	+	0.944937i	$0.606123\pi$
$692$	−20.0671	−0.762836
$693$	35.6303	1.35348
$694$	−2.23707	−0.0849180
$695$	16.2282	0.615570
$696$	1.60268	0.0607493
$697$	−6.97114	−0.264051
$698$	−11.1045	−0.420312
$699$	6.12790	0.231779
$700$	−3.43707	−0.129909
$701$	−14.2835	−0.539480	−0.269740	−	0.962933i	$-0.586938\pi$
$701$	−14.2835	−0.539480	−0.269740	+	0.962933i	$0.586938\pi$
$702$	2.01104	0.0759016
$703$	13.6552	0.515016
$704$	3.58069	0.134952
$705$	2.07804	0.0782634
$706$	3.68071	0.138525
$707$	−67.2892	−2.53067
$708$	−2.66001	−0.0999693
$709$	−15.8083	−0.593692	−0.296846	−	0.954925i	$-0.595935\pi$
$709$	−15.8083	−0.593692	−0.296846	+	0.954925i	$0.595935\pi$
$710$	12.6084	0.473185
$711$	−24.6307	−0.923725
$712$	1.74831	0.0655206
$713$	0	0
$714$	−1.52251	−0.0569785
$715$	3.77150	0.141046
$716$	−9.83753	−0.367646
$717$	2.89591	0.108150
$718$	27.5143	1.02682
$719$	4.44617	0.165814	0.0829070	−	0.996557i	$-0.473580\pi$
$719$	4.44617	0.165814	0.0829070	+	0.996557i	$0.473580\pi$
$720$	2.89510	0.107894
$721$	32.1532	1.19745
$722$	9.75228	0.362942
$723$	3.74806	0.139392
$724$	22.9728	0.853778
$725$	4.94839	0.183779
$726$	0.589898	0.0218932
$727$	41.9236	1.55486	0.777431	−	0.628968i	$-0.216522\pi$
$727$	41.9236	1.55486	0.777431	+	0.628968i	$0.216522\pi$
$728$	−3.62022	−0.134174
$729$	−21.4995	−0.796276
$730$	15.6557	0.579444
$731$	−6.82277	−0.252349
$732$	0.701675	0.0259347
$733$	16.7582	0.618978	0.309489	−	0.950903i	$-0.399842\pi$
$733$	16.7582	0.618978	0.309489	+	0.950903i	$0.399842\pi$
$734$	27.0147	0.997131
$735$	1.55897	0.0575035
$736$	0	0
$737$	−18.5042	−0.681609
$738$	−14.7563	−0.543187
$739$	−13.9945	−0.514797	−0.257398	−	0.966305i	$-0.582865\pi$
$739$	−13.9945	−0.514797	−0.257398	+	0.966305i	$0.582865\pi$
$740$	−4.49036	−0.165069
$741$	1.03740	0.0381098
$742$	−1.68929	−0.0620160
$743$	−46.9559	−1.72265	−0.861323	−	0.508058i	$-0.830364\pi$
$743$	−46.9559	−1.72265	−0.861323	+	0.508058i	$0.830364\pi$
$744$	−2.94532	−0.107981
$745$	18.5461	0.679475
$746$	−19.4471	−0.712007
$747$	36.5662	1.33789
$748$	4.89730	0.179063
$749$	−23.6498	−0.864144
$750$	−0.323878	−0.0118264
$751$	9.05130	0.330287	0.165143	−	0.986270i	$-0.447191\pi$
$751$	9.05130	0.330287	0.165143	+	0.986270i	$0.447191\pi$
$752$	6.41611	0.233971
$753$	−2.84433	−0.103653
$754$	5.21207	0.189813
$755$	−22.5525	−0.820770
$756$	−6.56238	−0.238671
$757$	−44.6209	−1.62177	−0.810886	−	0.585204i	$-0.801014\pi$
$757$	−44.6209	−1.62177	−0.810886	+	0.585204i	$0.801014\pi$
$758$	−24.4201	−0.886977
$759$	0	0
$760$	3.04101	0.110309
$761$	5.94879	0.215643	0.107822	−	0.994170i	$-0.465612\pi$
$761$	5.94879	0.215643	0.107822	+	0.994170i	$0.465612\pi$
$762$	−3.86212	−0.139910
$763$	−13.9977	−0.506751
$764$	−12.9076	−0.466981
$765$	3.95962	0.143161
$766$	9.06456	0.327516
$767$	−8.65064	−0.312356
$768$	−0.323878	−0.0116869
$769$	42.9203	1.54775	0.773873	−	0.633341i	$-0.218317\pi$
$769$	42.9203	1.54775	0.773873	+	0.633341i	$0.218317\pi$
$770$	−12.3071	−0.443517
$771$	−2.47152	−0.0890097
$772$	−21.2210	−0.763759
$773$	17.4707	0.628378	0.314189	−	0.949360i	$-0.398267\pi$
$773$	17.4707	0.628378	0.314189	+	0.949360i	$0.398267\pi$
$774$	−14.4422	−0.519115
$775$	−9.09392	−0.326663
$776$	7.18786	0.258029
$777$	4.99863	0.179325
$778$	14.8086	0.530914
$779$	−15.5000	−0.555345
$780$	−0.341137	−0.0122146
$781$	45.1469	1.61548
$782$	0	0
$783$	9.44794	0.337642
$784$	4.81345	0.171909
$785$	−7.00910	−0.250165
$786$	5.10501	0.182090
$787$	−17.9221	−0.638854	−0.319427	−	0.947611i	$-0.603490\pi$
$787$	−17.9221	−0.638854	−0.319427	+	0.947611i	$0.603490\pi$
$788$	1.09991	0.0391827
$789$	4.62402	0.164619
$790$	8.50772	0.302691
$791$	59.7519	2.12453
$792$	10.3665	0.368357
$793$	2.28192	0.0810335
$794$	−4.80967	−0.170689
$795$	−0.159184	−0.00564566
$796$	−8.90198	−0.315522
$797$	18.6817	0.661740	0.330870	−	0.943676i	$-0.392658\pi$
$797$	18.6817	0.661740	0.330870	+	0.943676i	$0.392658\pi$
$798$	−3.38522	−0.119836
$799$	8.77529	0.310448
$800$	−1.00000	−0.0353553
$801$	5.06153	0.178840
$802$	18.6592	0.658880
$803$	56.0583	1.97825
$804$	1.67372	0.0590277
$805$	0	0
$806$	−9.57851	−0.337389
$807$	−3.79408	−0.133558
$808$	−19.5775	−0.688734
$809$	−24.2985	−0.854288	−0.427144	−	0.904183i	$-0.640480\pi$
$809$	−24.2985	−0.854288	−0.427144	+	0.904183i	$0.640480\pi$
$810$	8.06693	0.283443
$811$	52.4629	1.84222	0.921111	−	0.389299i	$-0.127283\pi$
$811$	52.4629	1.84222	0.921111	+	0.389299i	$0.127283\pi$
$812$	−17.0080	−0.596862
$813$	2.97679	0.104401
$814$	−16.0786	−0.563554
$815$	−19.3851	−0.679032
$816$	−0.442967	−0.0155070
$817$	−15.1701	−0.530734
$818$	−3.71983	−0.130061
$819$	−10.4809	−0.366233
$820$	5.09699	0.177995
$821$	−46.2593	−1.61446	−0.807230	−	0.590237i	$-0.799034\pi$
$821$	−46.2593	−1.61446	−0.807230	+	0.590237i	$0.799034\pi$
$822$	−4.10354	−0.143128
$823$	−32.7457	−1.14145	−0.570723	−	0.821143i	$-0.693337\pi$
$823$	−32.7457	−1.14145	−0.570723	+	0.821143i	$0.693337\pi$
$824$	9.35483	0.325891
$825$	−1.15971	−0.0403759
$826$	28.2286	0.982200
$827$	−10.3748	−0.360768	−0.180384	−	0.983596i	$-0.557734\pi$
$827$	−10.3748	−0.360768	−0.180384	+	0.983596i	$0.557734\pi$
$828$	0	0
$829$	−6.88676	−0.239187	−0.119594	−	0.992823i	$-0.538159\pi$
$829$	−6.88676	−0.239187	−0.119594	+	0.992823i	$0.538159\pi$
$830$	−12.6304	−0.438406
$831$	−5.24488	−0.181943
$832$	−1.05329	−0.0365161
$833$	6.58334	0.228099
$834$	−5.25595	−0.181999
$835$	19.8588	0.687243
$836$	10.8889	0.376601
$837$	−17.3630	−0.600153
$838$	−17.7666	−0.613737
$839$	−3.37707	−0.116589	−0.0582947	−	0.998299i	$-0.518566\pi$
$839$	−3.37707	−0.116589	−0.0582947	+	0.998299i	$0.518566\pi$
$840$	1.11319	0.0384088
$841$	−4.51344	−0.155636
$842$	−15.5897	−0.537256
$843$	9.93477	0.342171
$844$	−1.52460	−0.0524789
$845$	11.8906	0.409049
$846$	18.5753	0.638632
$847$	−6.26013	−0.215101
$848$	−0.491493	−0.0168779
$849$	3.41493	0.117200
$850$	−1.36770	−0.0469116
$851$	0	0
$852$	−4.08359	−0.139902
$853$	11.2316	0.384562	0.192281	−	0.981340i	$-0.438412\pi$
$853$	11.2316	0.384562	0.192281	+	0.981340i	$0.438412\pi$
$854$	−7.44634	−0.254808
$855$	8.80403	0.301091
$856$	−6.88080	−0.235181
$857$	1.12636	0.0384756	0.0192378	−	0.999815i	$-0.493876\pi$
$857$	1.12636	0.0384756	0.0192378	+	0.999815i	$0.493876\pi$
$858$	−1.22151	−0.0417015
$859$	40.0844	1.36766	0.683831	−	0.729640i	$-0.260313\pi$
$859$	40.0844	1.36766	0.683831	+	0.729640i	$0.260313\pi$
$860$	4.98850	0.170107
$861$	−5.67393	−0.193367
$862$	−0.0505199	−0.00172071
$863$	−9.65572	−0.328684	−0.164342	−	0.986403i	$-0.552550\pi$
$863$	−9.65572	−0.328684	−0.164342	+	0.986403i	$0.552550\pi$
$864$	−1.90930	−0.0649555
$865$	20.0671	0.682301
$866$	−14.8561	−0.504829
$867$	4.90008	0.166416
$868$	31.2565	1.06091
$869$	30.4635	1.03340
$870$	−1.60268	−0.0543358
$871$	5.44313	0.184434
$872$	−4.07257	−0.137915
$873$	20.8096	0.704298
$874$	0	0
$875$	3.43707	0.116194
$876$	−5.07055	−0.171318
$877$	38.2616	1.29200	0.646002	−	0.763336i	$-0.276440\pi$
$877$	38.2616	1.29200	0.646002	+	0.763336i	$0.276440\pi$
$878$	−7.62566	−0.257353
$879$	−8.78573	−0.296335
$880$	−3.58069	−0.120705
$881$	−18.4243	−0.620731	−0.310366	−	0.950617i	$-0.600452\pi$
$881$	−18.4243	−0.620731	−0.310366	+	0.950617i	$0.600452\pi$
$882$	13.9354	0.469231
$883$	45.6164	1.53511	0.767557	−	0.640981i	$-0.221472\pi$
$883$	45.6164	1.53511	0.767557	+	0.640981i	$0.221472\pi$
$884$	−1.44058	−0.0484519
$885$	2.66001	0.0894152
$886$	12.4713	0.418982
$887$	−20.4227	−0.685727	−0.342864	−	0.939385i	$-0.611397\pi$
$887$	−20.4227	−0.685727	−0.342864	+	0.939385i	$0.611397\pi$
$888$	1.45433	0.0488041
$889$	40.9857	1.37462
$890$	−1.74831	−0.0586034
$891$	28.8852	0.967690
$892$	−7.41803	−0.248374
$893$	19.5114	0.652925
$894$	−6.00666	−0.200893
$895$	9.83753	0.328832
$896$	3.43707	0.114824
$897$	0	0
$898$	29.0006	0.967762
$899$	−45.0003	−1.50084
$900$	−2.89510	−0.0965034
$901$	−0.672213	−0.0223947
$902$	18.2508	0.607684
$903$	−5.55316	−0.184798
$904$	17.3845	0.578201
$905$	−22.9728	−0.763643
$906$	7.30427	0.242668
$907$	−51.9752	−1.72581	−0.862904	−	0.505367i	$-0.831357\pi$
$907$	−51.9752	−1.72581	−0.862904	+	0.505367i	$0.831357\pi$
$908$	2.19532	0.0728543
$909$	−56.6789	−1.87992
$910$	3.62022	0.120009
$911$	−8.58862	−0.284554	−0.142277	−	0.989827i	$-0.545442\pi$
$911$	−8.58862	−0.284554	−0.142277	+	0.989827i	$0.545442\pi$
$912$	−0.984916	−0.0326138
$913$	−45.2254	−1.49674
$914$	−15.0872	−0.499039
$915$	−0.701675	−0.0231967
$916$	−22.5499	−0.745071
$917$	−54.1756	−1.78904
$918$	−2.61134	−0.0861870
$919$	24.7276	0.815687	0.407844	−	0.913052i	$-0.366281\pi$
$919$	24.7276	0.815687	0.407844	+	0.913052i	$0.366281\pi$
$920$	0	0
$921$	5.91732	0.194982
$922$	−32.3595	−1.06570
$923$	−13.2803	−0.437126
$924$	3.98600	0.131130
$925$	4.49036	0.147642
$926$	27.7030	0.910377
$927$	27.0832	0.889529
$928$	−4.94839	−0.162439
$929$	−8.37061	−0.274631	−0.137315	−	0.990527i	$-0.543847\pi$
$929$	−8.37061	−0.274631	−0.137315	+	0.990527i	$0.543847\pi$
$930$	2.94532	0.0965810
$931$	14.6377	0.479732
$932$	−18.9204	−0.619758
$933$	−2.51009	−0.0821768
$934$	23.6144	0.772686
$935$	−4.89730	−0.160159
$936$	−3.04937	−0.0996719
$937$	−9.41164	−0.307465	−0.153733	−	0.988113i	$-0.549129\pi$
$937$	−9.41164	−0.307465	−0.153733	+	0.988113i	$0.549129\pi$
$938$	−17.7619	−0.579948
$939$	−5.65611	−0.184580
$940$	−6.41611	−0.209270
$941$	3.50245	0.114177	0.0570884	−	0.998369i	$-0.481818\pi$
$941$	3.50245	0.114177	0.0570884	+	0.998369i	$0.481818\pi$
$942$	2.27009	0.0739636
$943$	0	0
$944$	8.21299	0.267310
$945$	6.56238	0.213474
$946$	17.8623	0.580753
$947$	39.9010	1.29661	0.648303	−	0.761382i	$-0.275479\pi$
$947$	39.9010	1.29661	0.648303	+	0.761382i	$0.275479\pi$
$948$	−2.75547	−0.0894934
$949$	−16.4900	−0.535287
$950$	−3.04101	−0.0986633
$951$	−3.41654	−0.110789
$952$	4.70087	0.152356
$953$	8.47713	0.274601	0.137301	−	0.990529i	$-0.456157\pi$
$953$	8.47713	0.274601	0.137301	+	0.990529i	$0.456157\pi$
$954$	−1.42292	−0.0460688
$955$	12.9076	0.417680
$956$	−8.94135	−0.289184
$957$	−5.73869	−0.185505
$958$	14.6223	0.472425
$959$	43.5478	1.40623
$960$	0.323878	0.0104531
$961$	51.6995	1.66772
$962$	4.72963	0.152490
$963$	−19.9206	−0.641933
$964$	−11.5724	−0.372723
$965$	21.2210	0.683127
$966$	0	0
$967$	11.8649	0.381548	0.190774	−	0.981634i	$-0.438900\pi$
$967$	11.8649	0.381548	0.190774	+	0.981634i	$0.438900\pi$
$968$	−1.82136	−0.0585406
$969$	−1.34707	−0.0432740
$970$	−7.18786	−0.230788
$971$	−32.9054	−1.05599	−0.527993	−	0.849249i	$-0.677055\pi$
$971$	−32.9054	−1.05599	−0.527993	+	0.849249i	$0.677055\pi$
$972$	−8.34059	−0.267524
$973$	55.7774	1.78814
$974$	−28.0818	−0.899798
$975$	0.341137	0.0109251
$976$	−2.16648	−0.0693473
$977$	61.1568	1.95658	0.978290	−	0.207242i	$-0.0664486\pi$
$977$	61.1568	1.95658	0.978290	+	0.207242i	$0.0664486\pi$
$978$	6.27843	0.200762
$979$	−6.26015	−0.200075
$980$	−4.81345	−0.153760
$981$	−11.7905	−0.376442
$982$	−2.28162	−0.0728094
$983$	−40.7517	−1.29978	−0.649889	−	0.760030i	$-0.725184\pi$
$983$	−40.7517	−1.29978	−0.649889	+	0.760030i	$0.725184\pi$
$984$	−1.65080	−0.0526257
$985$	−1.09991	−0.0350461
$986$	−6.76790	−0.215534
$987$	7.14236	0.227344
$988$	−3.20305	−0.101903
$989$	0	0
$990$	−10.3665	−0.329468
$991$	14.3042	0.454388	0.227194	−	0.973850i	$-0.427045\pi$
$991$	14.3042	0.454388	0.227194	+	0.973850i	$0.427045\pi$
$992$	9.09392	0.288732
$993$	−1.66742	−0.0529141
$994$	43.3360	1.37453
$995$	8.90198	0.282212
$996$	4.09070	0.129619
$997$	47.3168	1.49854	0.749269	−	0.662266i	$-0.230405\pi$
$997$	47.3168	1.49854	0.749269	+	0.662266i	$0.230405\pi$
$998$	3.28638	0.104029
$999$	8.57342	0.271251

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.be.1.4	✓	6
23.22	odd	2		5290.2.a.bf.1.4	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5290.2.a.be.1.4	✓	6	1.1	even	1	trivial
5290.2.a.bf.1.4	yes	6	23.22	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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.323878 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.323878 q^{6} -3.43707 q^{7} -1.00000 q^{8} -2.89510 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.323878 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.323878 q^{6} -3.43707 q^{7} -1.00000 q^{8} -2.89510 q^{9} +1.00000 q^{10} +3.58069 q^{11} -0.323878 q^{12} -1.05329 q^{13} +3.43707 q^{14} +0.323878 q^{15} +1.00000 q^{16} +1.36770 q^{17} +2.89510 q^{18} +3.04101 q^{19} -1.00000 q^{20} +1.11319 q^{21} -3.58069 q^{22} +0.323878 q^{24} +1.00000 q^{25} +1.05329 q^{26} +1.90930 q^{27} -3.43707 q^{28} +4.94839 q^{29} -0.323878 q^{30} -9.09392 q^{31} -1.00000 q^{32} -1.15971 q^{33} -1.36770 q^{34} +3.43707 q^{35} -2.89510 q^{36} +4.49036 q^{37} -3.04101 q^{38} +0.341137 q^{39} +1.00000 q^{40} -5.09699 q^{41} -1.11319 q^{42} -4.98850 q^{43} +3.58069 q^{44} +2.89510 q^{45} +6.41611 q^{47} -0.323878 q^{48} +4.81345 q^{49} -1.00000 q^{50} -0.442967 q^{51} -1.05329 q^{52} -0.491493 q^{53} -1.90930 q^{54} -3.58069 q^{55} +3.43707 q^{56} -0.984916 q^{57} -4.94839 q^{58} +8.21299 q^{59} +0.323878 q^{60} -2.16648 q^{61} +9.09392 q^{62} +9.95067 q^{63} +1.00000 q^{64} +1.05329 q^{65} +1.15971 q^{66} -5.16776 q^{67} +1.36770 q^{68} -3.43707 q^{70} +12.6084 q^{71} +2.89510 q^{72} +15.6557 q^{73} -4.49036 q^{74} -0.323878 q^{75} +3.04101 q^{76} -12.3071 q^{77} -0.341137 q^{78} +8.50772 q^{79} -1.00000 q^{80} +8.06693 q^{81} +5.09699 q^{82} -12.6304 q^{83} +1.11319 q^{84} -1.36770 q^{85} +4.98850 q^{86} -1.60268 q^{87} -3.58069 q^{88} -1.74831 q^{89} -2.89510 q^{90} +3.62022 q^{91} +2.94532 q^{93} -6.41611 q^{94} -3.04101 q^{95} +0.323878 q^{96} -7.18786 q^{97} -4.81345 q^{98} -10.3665 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 8 * q^9	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 8 q^{9} + 6 q^{10} - 10 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 2 q^{15} + 6 q^{16} + 10 q^{17} - 8 q^{18} - 2 q^{19} - 6 q^{20} - 12 q^{21} + 10 q^{22} + 2 q^{24} + 6 q^{25} + 2 q^{26} - 8 q^{27} - 2 q^{28} - 2 q^{30} - 2 q^{31} - 6 q^{32} + 22 q^{33} - 10 q^{34} + 2 q^{35} + 8 q^{36} + 4 q^{37} + 2 q^{38} + 24 q^{39} + 6 q^{40} + 6 q^{41} + 12 q^{42} - 12 q^{43} - 10 q^{44} - 8 q^{45} + 8 q^{47} - 2 q^{48} + 8 q^{49} - 6 q^{50} - 34 q^{51} - 2 q^{52} - 36 q^{53} + 8 q^{54} + 10 q^{55} + 2 q^{56} - 32 q^{57} + 16 q^{59} + 2 q^{60} + 10 q^{61} + 2 q^{62} + 48 q^{63} + 6 q^{64} + 2 q^{65} - 22 q^{66} - 16 q^{67} + 10 q^{68} - 2 q^{70} - 2 q^{71} - 8 q^{72} + 4 q^{73} - 4 q^{74} - 2 q^{75} - 2 q^{76} - 16 q^{77} - 24 q^{78} + 20 q^{79} - 6 q^{80} + 34 q^{81} - 6 q^{82} - 8 q^{83} - 12 q^{84} - 10 q^{85} + 12 q^{86} - 12 q^{87} + 10 q^{88} - 12 q^{89} + 8 q^{90} - 38 q^{91} - 28 q^{93} - 8 q^{94} + 2 q^{95} + 2 q^{96} - 2 q^{97} - 8 q^{98} - 50 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 8 * q^9 + 6 * q^10 - 10 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^14 + 2 * q^15 + 6 * q^16 + 10 * q^17 - 8 * q^18 - 2 * q^19 - 6 * q^20 - 12 * q^21 + 10 * q^22 + 2 * q^24 + 6 * q^25 + 2 * q^26 - 8 * q^27 - 2 * q^28 - 2 * q^30 - 2 * q^31 - 6 * q^32 + 22 * q^33 - 10 * q^34 + 2 * q^35 + 8 * q^36 + 4 * q^37 + 2 * q^38 + 24 * q^39 + 6 * q^40 + 6 * q^41 + 12 * q^42 - 12 * q^43 - 10 * q^44 - 8 * q^45 + 8 * q^47 - 2 * q^48 + 8 * q^49 - 6 * q^50 - 34 * q^51 - 2 * q^52 - 36 * q^53 + 8 * q^54 + 10 * q^55 + 2 * q^56 - 32 * q^57 + 16 * q^59 + 2 * q^60 + 10 * q^61 + 2 * q^62 + 48 * q^63 + 6 * q^64 + 2 * q^65 - 22 * q^66 - 16 * q^67 + 10 * q^68 - 2 * q^70 - 2 * q^71 - 8 * q^72 + 4 * q^73 - 4 * q^74 - 2 * q^75 - 2 * q^76 - 16 * q^77 - 24 * q^78 + 20 * q^79 - 6 * q^80 + 34 * q^81 - 6 * q^82 - 8 * q^83 - 12 * q^84 - 10 * q^85 + 12 * q^86 - 12 * q^87 + 10 * q^88 - 12 * q^89 + 8 * q^90 - 38 * q^91 - 28 * q^93 - 8 * q^94 + 2 * q^95 + 2 * q^96 - 2 * q^97 - 8 * q^98 - 50 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more