LMFDB - Embedded newform 8018.2.a.e.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.124655 q^{3} +1.00000 q^{4} -2.23561 q^{5} +0.124655 q^{6} +3.94220 q^{7} +1.00000 q^{8} -2.98446 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.124655 q^{3} +1.00000 q^{4} -2.23561 q^{5} +0.124655 q^{6} +3.94220 q^{7} +1.00000 q^{8} -2.98446 q^{9} -2.23561 q^{10} -0.760201 q^{11} +0.124655 q^{12} -3.14661 q^{13} +3.94220 q^{14} -0.278679 q^{15} +1.00000 q^{16} -1.62913 q^{17} -2.98446 q^{18} -1.00000 q^{19} -2.23561 q^{20} +0.491414 q^{21} -0.760201 q^{22} +8.96321 q^{23} +0.124655 q^{24} -0.00204771 q^{25} -3.14661 q^{26} -0.745990 q^{27} +3.94220 q^{28} -4.22539 q^{29} -0.278679 q^{30} +7.57509 q^{31} +1.00000 q^{32} -0.0947624 q^{33} -1.62913 q^{34} -8.81323 q^{35} -2.98446 q^{36} -11.0787 q^{37} -1.00000 q^{38} -0.392239 q^{39} -2.23561 q^{40} -3.67558 q^{41} +0.491414 q^{42} +6.31236 q^{43} -0.760201 q^{44} +6.67209 q^{45} +8.96321 q^{46} +3.36611 q^{47} +0.124655 q^{48} +8.54098 q^{49} -0.00204771 q^{50} -0.203078 q^{51} -3.14661 q^{52} +9.52768 q^{53} -0.745990 q^{54} +1.69951 q^{55} +3.94220 q^{56} -0.124655 q^{57} -4.22539 q^{58} -13.2022 q^{59} -0.278679 q^{60} -9.13240 q^{61} +7.57509 q^{62} -11.7654 q^{63} +1.00000 q^{64} +7.03459 q^{65} -0.0947624 q^{66} -11.6728 q^{67} -1.62913 q^{68} +1.11730 q^{69} -8.81323 q^{70} -12.7801 q^{71} -2.98446 q^{72} +3.58789 q^{73} -11.0787 q^{74} -0.000255257 q^{75} -1.00000 q^{76} -2.99687 q^{77} -0.392239 q^{78} +2.53756 q^{79} -2.23561 q^{80} +8.86039 q^{81} -3.67558 q^{82} -1.98573 q^{83} +0.491414 q^{84} +3.64210 q^{85} +6.31236 q^{86} -0.526713 q^{87} -0.760201 q^{88} +2.90906 q^{89} +6.67209 q^{90} -12.4046 q^{91} +8.96321 q^{92} +0.944270 q^{93} +3.36611 q^{94} +2.23561 q^{95} +0.124655 q^{96} +0.0344428 q^{97} +8.54098 q^{98} +2.26879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) $ 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * 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
$3$	0.124655	0.0719693	0.0359847	−	0.999352i	$-0.488543\pi$
$3$	0.124655	0.0719693	0.0359847	+	0.999352i	$0.488543\pi$
$4$	1.00000	0.500000
$5$	−2.23561	−0.999795	−0.499898	−	0.866085i	$-0.666629\pi$
$5$	−2.23561	−0.999795	−0.499898	+	0.866085i	$0.666629\pi$
$6$	0.124655	0.0508900
$7$	3.94220	1.49001	0.745007	−	0.667057i	$-0.232446\pi$
$7$	3.94220	1.49001	0.745007	+	0.667057i	$0.232446\pi$
$8$	1.00000	0.353553
$9$	−2.98446	−0.994820
$10$	−2.23561	−0.706962
$11$	−0.760201	−0.229209	−0.114605	−	0.993411i	$-0.536560\pi$
$11$	−0.760201	−0.229209	−0.114605	+	0.993411i	$0.536560\pi$
$12$	0.124655	0.0359847
$13$	−3.14661	−0.872712	−0.436356	−	0.899774i	$-0.643731\pi$
$13$	−3.14661	−0.872712	−0.436356	+	0.899774i	$0.643731\pi$
$14$	3.94220	1.05360
$15$	−0.278679	−0.0719546
$16$	1.00000	0.250000
$17$	−1.62913	−0.395122	−0.197561	−	0.980291i	$-0.563302\pi$
$17$	−1.62913	−0.395122	−0.197561	+	0.980291i	$0.563302\pi$
$18$	−2.98446	−0.703444
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.23561	−0.499898
$21$	0.491414	0.107235
$22$	−0.760201	−0.162075
$23$	8.96321	1.86896	0.934479	−	0.356018i	$-0.115866\pi$
$23$	8.96321	1.86896	0.934479	+	0.356018i	$0.115866\pi$
$24$	0.124655	0.0254450
$25$	−0.00204771	−0.000409543 0
$26$	−3.14661	−0.617100
$27$	−0.745990	−0.143566
$28$	3.94220	0.745007
$29$	−4.22539	−0.784634	−0.392317	−	0.919830i	$-0.628326\pi$
$29$	−4.22539	−0.784634	−0.392317	+	0.919830i	$0.628326\pi$
$30$	−0.278679	−0.0508796
$31$	7.57509	1.36053	0.680263	−	0.732968i	$-0.261865\pi$
$31$	7.57509	1.36053	0.680263	+	0.732968i	$0.261865\pi$
$32$	1.00000	0.176777
$33$	−0.0947624	−0.0164960
$34$	−1.62913	−0.279393
$35$	−8.81323	−1.48971
$36$	−2.98446	−0.497410
$37$	−11.0787	−1.82132	−0.910662	−	0.413152i	$-0.864428\pi$
$37$	−11.0787	−1.82132	−0.910662	+	0.413152i	$0.864428\pi$
$38$	−1.00000	−0.162221
$39$	−0.392239	−0.0628085
$40$	−2.23561	−0.353481
$41$	−3.67558	−0.574030	−0.287015	−	0.957926i	$-0.592663\pi$
$41$	−3.67558	−0.574030	−0.287015	+	0.957926i	$0.592663\pi$
$42$	0.491414	0.0758268
$43$	6.31236	0.962625	0.481313	−	0.876549i	$-0.340160\pi$
$43$	6.31236	0.962625	0.481313	+	0.876549i	$0.340160\pi$
$44$	−0.760201	−0.114605
$45$	6.67209	0.994617
$46$	8.96321	1.32155
$47$	3.36611	0.490998	0.245499	−	0.969397i	$-0.421048\pi$
$47$	3.36611	0.490998	0.245499	+	0.969397i	$0.421048\pi$
$48$	0.124655	0.0179923
$49$	8.54098	1.22014
$50$	−0.00204771	−0.000289590 0
$51$	−0.203078	−0.0284366
$52$	−3.14661	−0.436356
$53$	9.52768	1.30873	0.654364	−	0.756180i	$-0.272937\pi$
$53$	9.52768	1.30873	0.654364	+	0.756180i	$0.272937\pi$
$54$	−0.745990	−0.101516
$55$	1.69951	0.229162
$56$	3.94220	0.526799
$57$	−0.124655	−0.0165109
$58$	−4.22539	−0.554820
$59$	−13.2022	−1.71878	−0.859388	−	0.511325i	$-0.829155\pi$
$59$	−13.2022	−1.71878	−0.859388	+	0.511325i	$0.829155\pi$
$60$	−0.278679	−0.0359773
$61$	−9.13240	−1.16928	−0.584642	−	0.811292i	$-0.698765\pi$
$61$	−9.13240	−1.16928	−0.584642	+	0.811292i	$0.698765\pi$
$62$	7.57509	0.962038
$63$	−11.7654	−1.48230
$64$	1.00000	0.125000
$65$	7.03459	0.872533
$66$	−0.0947624	−0.0116644
$67$	−11.6728	−1.42605	−0.713027	−	0.701136i	$-0.752676\pi$
$67$	−11.6728	−1.42605	−0.713027	+	0.701136i	$0.752676\pi$
$68$	−1.62913	−0.197561
$69$	1.11730	0.134508
$70$	−8.81323	−1.05338
$71$	−12.7801	−1.51672	−0.758360	−	0.651836i	$-0.773999\pi$
$71$	−12.7801	−1.51672	−0.758360	+	0.651836i	$0.773999\pi$
$72$	−2.98446	−0.351722
$73$	3.58789	0.419930	0.209965	−	0.977709i	$-0.432665\pi$
$73$	3.58789	0.419930	0.209965	+	0.977709i	$0.432665\pi$
$74$	−11.0787	−1.28787
$75$	−0.000255257 0	−2.94745e−5 0
$76$	−1.00000	−0.114708
$77$	−2.99687	−0.341525
$78$	−0.392239	−0.0444123
$79$	2.53756	0.285498	0.142749	−	0.989759i	$-0.454406\pi$
$79$	2.53756	0.285498	0.142749	+	0.989759i	$0.454406\pi$
$80$	−2.23561	−0.249949
$81$	8.86039	0.984488
$82$	−3.67558	−0.405900
$83$	−1.98573	−0.217962	−0.108981	−	0.994044i	$-0.534759\pi$
$83$	−1.98573	−0.217962	−0.108981	+	0.994044i	$0.534759\pi$
$84$	0.491414	0.0536176
$85$	3.64210	0.395041
$86$	6.31236	0.680679
$87$	−0.526713	−0.0564696
$88$	−0.760201	−0.0810376
$89$	2.90906	0.308360	0.154180	−	0.988043i	$-0.450726\pi$
$89$	2.90906	0.308360	0.154180	+	0.988043i	$0.450726\pi$
$90$	6.67209	0.703300
$91$	−12.4046	−1.30035
$92$	8.96321	0.934479
$93$	0.944270	0.0979162
$94$	3.36611	0.347188
$95$	2.23561	0.229369
$96$	0.124655	0.0127225
$97$	0.0344428	0.00349714	0.00174857	−	0.999998i	$-0.499443\pi$
$97$	0.0344428	0.00349714	0.00174857	+	0.999998i	$0.499443\pi$
$98$	8.54098	0.862769
$99$	2.26879	0.228022
$100$	−0.00204771	−0.000204771 0
$101$	4.48602	0.446376	0.223188	−	0.974775i	$-0.428354\pi$
$101$	4.48602	0.446376	0.223188	+	0.974775i	$0.428354\pi$
$102$	−0.203078	−0.0201077
$103$	−8.53748	−0.841223	−0.420611	−	0.907241i	$-0.638184\pi$
$103$	−8.53748	−0.841223	−0.420611	+	0.907241i	$0.638184\pi$
$104$	−3.14661	−0.308550
$105$	−1.09861	−0.107213
$106$	9.52768	0.925410
$107$	−13.0351	−1.26015	−0.630073	−	0.776536i	$-0.716975\pi$
$107$	−13.0351	−1.26015	−0.630073	+	0.776536i	$0.716975\pi$
$108$	−0.745990	−0.0717829
$109$	−20.6319	−1.97618	−0.988088	−	0.153890i	$-0.950820\pi$
$109$	−20.6319	−1.97618	−0.988088	+	0.153890i	$0.950820\pi$
$110$	1.69951	0.162042
$111$	−1.38101	−0.131079
$112$	3.94220	0.372503
$113$	−6.09230	−0.573115	−0.286558	−	0.958063i	$-0.592511\pi$
$113$	−6.09230	−0.573115	−0.286558	+	0.958063i	$0.592511\pi$
$114$	−0.124655	−0.0116750
$115$	−20.0382	−1.86858
$116$	−4.22539	−0.392317
$117$	9.39093	0.868191
$118$	−13.2022	−1.21536
$119$	−6.42236	−0.588737
$120$	−0.278679	−0.0254398
$121$	−10.4221	−0.947463
$122$	−9.13240	−0.826808
$123$	−0.458178	−0.0413125
$124$	7.57509	0.680263
$125$	11.1826	1.00020
$126$	−11.7654	−1.04814
$127$	4.45355	0.395189	0.197594	−	0.980284i	$-0.436687\pi$
$127$	4.45355	0.395189	0.197594	+	0.980284i	$0.436687\pi$
$128$	1.00000	0.0883883
$129$	0.786864	0.0692795
$130$	7.03459	0.616974
$131$	−11.6354	−1.01659	−0.508293	−	0.861184i	$-0.669723\pi$
$131$	−11.6354	−1.01659	−0.508293	+	0.861184i	$0.669723\pi$
$132$	−0.0947624	−0.00824801
$133$	−3.94220	−0.341833
$134$	−11.6728	−1.00837
$135$	1.66774	0.143536
$136$	−1.62913	−0.139697
$137$	21.3949	1.82789	0.913943	−	0.405841i	$-0.133021\pi$
$137$	21.3949	1.82789	0.913943	+	0.405841i	$0.133021\pi$
$138$	1.11730	0.0951113
$139$	7.91581	0.671410	0.335705	−	0.941967i	$-0.391025\pi$
$139$	7.91581	0.671410	0.335705	+	0.941967i	$0.391025\pi$
$140$	−8.81323	−0.744854
$141$	0.419601	0.0353368
$142$	−12.7801	−1.07248
$143$	2.39205	0.200033
$144$	−2.98446	−0.248705
$145$	9.44631	0.784474
$146$	3.58789	0.296936
$147$	1.06467	0.0878126
$148$	−11.0787	−0.910662
$149$	−0.649490	−0.0532083	−0.0266041	−	0.999646i	$-0.508469\pi$
$149$	−0.649490	−0.0532083	−0.0266041	+	0.999646i	$0.508469\pi$
$150$	−0.000255257 0	−2.08416e−5 0
$151$	−16.9428	−1.37878	−0.689391	−	0.724389i	$-0.742122\pi$
$151$	−16.9428	−1.37878	−0.689391	+	0.724389i	$0.742122\pi$
$152$	−1.00000	−0.0811107
$153$	4.86207	0.393075
$154$	−2.99687	−0.241494
$155$	−16.9350	−1.36025
$156$	−0.392239	−0.0314042
$157$	−7.55944	−0.603309	−0.301655	−	0.953417i	$-0.597539\pi$
$157$	−7.55944	−0.603309	−0.301655	+	0.953417i	$0.597539\pi$
$158$	2.53756	0.201878
$159$	1.18767	0.0941882
$160$	−2.23561	−0.176740
$161$	35.3348	2.78477
$162$	8.86039	0.696138
$163$	−2.98621	−0.233898	−0.116949	−	0.993138i	$-0.537311\pi$
$163$	−2.98621	−0.233898	−0.116949	+	0.993138i	$0.537311\pi$
$164$	−3.67558	−0.287015
$165$	0.211852	0.0164926
$166$	−1.98573	−0.154122
$167$	5.32145	0.411786	0.205893	−	0.978575i	$-0.433990\pi$
$167$	5.32145	0.411786	0.205893	+	0.978575i	$0.433990\pi$
$168$	0.491414	0.0379134
$169$	−3.09887	−0.238374
$170$	3.64210	0.279336
$171$	2.98446	0.228227
$172$	6.31236	0.481313
$173$	−14.1270	−1.07406	−0.537029	−	0.843564i	$-0.680453\pi$
$173$	−14.1270	−1.07406	−0.537029	+	0.843564i	$0.680453\pi$
$174$	−0.526713	−0.0399300
$175$	−0.00807251	−0.000610224 0
$176$	−0.760201	−0.0573023
$177$	−1.64571	−0.123699
$178$	2.90906	0.218043
$179$	1.14256	0.0853988	0.0426994	−	0.999088i	$-0.486404\pi$
$179$	1.14256	0.0853988	0.0426994	+	0.999088i	$0.486404\pi$
$180$	6.67209	0.497308
$181$	−15.7279	−1.16905	−0.584524	−	0.811377i	$-0.698719\pi$
$181$	−15.7279	−1.16905	−0.584524	+	0.811377i	$0.698719\pi$
$182$	−12.4046	−0.919488
$183$	−1.13839	−0.0841525
$184$	8.96321	0.660776
$185$	24.7676	1.82095
$186$	0.944270	0.0692372
$187$	1.23846	0.0905655
$188$	3.36611	0.245499
$189$	−2.94085	−0.213915
$190$	2.23561	0.162188
$191$	−2.15476	−0.155913	−0.0779563	−	0.996957i	$-0.524839\pi$
$191$	−2.15476	−0.155913	−0.0779563	+	0.996957i	$0.524839\pi$
$192$	0.124655	0.00899616
$193$	−15.6782	−1.12854	−0.564270	−	0.825590i	$-0.690842\pi$
$193$	−15.6782	−1.12854	−0.564270	+	0.825590i	$0.690842\pi$
$194$	0.0344428	0.00247285
$195$	0.876893	0.0627956
$196$	8.54098	0.610070
$197$	−0.0255509	−0.00182043	−0.000910213	−	1.00000i	$-0.500290\pi$
$197$	−0.0255509	−0.00182043	−0.000910213		1.00000i	$0.500290\pi$
$198$	2.26879	0.161236
$199$	16.3169	1.15667	0.578337	−	0.815798i	$-0.303702\pi$
$199$	16.3169	1.15667	0.578337	+	0.815798i	$0.303702\pi$
$200$	−0.00204771	−0.000144795 0
$201$	−1.45506	−0.102632
$202$	4.48602	0.315635
$203$	−16.6573	−1.16912
$204$	−0.203078	−0.0142183
$205$	8.21717	0.573912
$206$	−8.53748	−0.594834
$207$	−26.7503	−1.85928
$208$	−3.14661	−0.218178
$209$	0.760201	0.0525842
$210$	−1.09861	−0.0758112
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	9.52768	0.654364
$213$	−1.59310	−0.109157
$214$	−13.0351	−0.891058
$215$	−14.1120	−0.962428
$216$	−0.745990	−0.0507582
$217$	29.8626	2.02720
$218$	−20.6319	−1.39737
$219$	0.447246	0.0302221
$220$	1.69951	0.114581
$221$	5.12623	0.344827
$222$	−1.38101	−0.0926872
$223$	−21.5797	−1.44508	−0.722540	−	0.691329i	$-0.757026\pi$
$223$	−21.5797	−1.44508	−0.722540	+	0.691329i	$0.757026\pi$
$224$	3.94220	0.263400
$225$	0.00611132	0.000407421 0
$226$	−6.09230	−0.405254
$227$	0.139460	0.00925626	0.00462813	−	0.999989i	$-0.498527\pi$
$227$	0.139460	0.00925626	0.00462813	+	0.999989i	$0.498527\pi$
$228$	−0.124655	−0.00825545
$229$	−3.50299	−0.231484	−0.115742	−	0.993279i	$-0.536925\pi$
$229$	−3.50299	−0.231484	−0.115742	+	0.993279i	$0.536925\pi$
$230$	−20.0382	−1.32128
$231$	−0.373573	−0.0245793
$232$	−4.22539	−0.277410
$233$	18.2307	1.19433	0.597165	−	0.802118i	$-0.296294\pi$
$233$	18.2307	1.19433	0.597165	+	0.802118i	$0.296294\pi$
$234$	9.39093	0.613904
$235$	−7.52532	−0.490897
$236$	−13.2022	−0.859388
$237$	0.316319	0.0205471
$238$	−6.42236	−0.416300
$239$	−21.6343	−1.39941	−0.699703	−	0.714434i	$-0.746684\pi$
$239$	−21.6343	−1.39941	−0.699703	+	0.714434i	$0.746684\pi$
$240$	−0.278679	−0.0179886
$241$	−17.0525	−1.09845	−0.549224	−	0.835675i	$-0.685076\pi$
$241$	−17.0525	−1.09845	−0.549224	+	0.835675i	$0.685076\pi$
$242$	−10.4221	−0.669958
$243$	3.34246	0.214419
$244$	−9.13240	−0.584642
$245$	−19.0943	−1.21989
$246$	−0.458178	−0.0292124
$247$	3.14661	0.200214
$248$	7.57509	0.481019
$249$	−0.247530	−0.0156866
$250$	11.1826	0.707252
$251$	3.44843	0.217663	0.108831	−	0.994060i	$-0.465289\pi$
$251$	3.44843	0.217663	0.108831	+	0.994060i	$0.465289\pi$
$252$	−11.7654	−0.741148
$253$	−6.81384	−0.428382
$254$	4.45355	0.279441
$255$	0.454004	0.0284308
$256$	1.00000	0.0625000
$257$	25.1184	1.56684	0.783421	−	0.621492i	$-0.213473\pi$
$257$	25.1184	1.56684	0.783421	+	0.621492i	$0.213473\pi$
$258$	0.786864	0.0489880
$259$	−43.6744	−2.71380
$260$	7.03459	0.436267
$261$	12.6105	0.780570
$262$	−11.6354	−0.718836
$263$	−17.9726	−1.10824	−0.554120	−	0.832437i	$-0.686945\pi$
$263$	−17.9726	−1.10824	−0.554120	+	0.832437i	$0.686945\pi$
$264$	−0.0947624	−0.00583222
$265$	−21.3002	−1.30846
$266$	−3.94220	−0.241712
$267$	0.362628	0.0221925
$268$	−11.6728	−0.713027
$269$	−5.22118	−0.318341	−0.159171	−	0.987251i	$-0.550882\pi$
$269$	−5.22118	−0.318341	−0.159171	+	0.987251i	$0.550882\pi$
$270$	1.66774	0.101496
$271$	17.8245	1.08276	0.541381	−	0.840777i	$-0.317902\pi$
$271$	17.8245	1.08276	0.541381	+	0.840777i	$0.317902\pi$
$272$	−1.62913	−0.0987804
$273$	−1.54629	−0.0935855
$274$	21.3949	1.29251
$275$	0.00155667	9.38709e−5 0
$276$	1.11730	0.0672538
$277$	−3.89829	−0.234226	−0.117113	−	0.993119i	$-0.537364\pi$
$277$	−3.89829	−0.234226	−0.117113	+	0.993119i	$0.537364\pi$
$278$	7.91581	0.474759
$279$	−22.6076	−1.35348
$280$	−8.81323	−0.526691
$281$	13.5908	0.810759	0.405380	−	0.914148i	$-0.367139\pi$
$281$	13.5908	0.810759	0.405380	+	0.914148i	$0.367139\pi$
$282$	0.419601	0.0249869
$283$	16.9186	1.00571	0.502854	−	0.864371i	$-0.332283\pi$
$283$	16.9186	1.00571	0.502854	+	0.864371i	$0.332283\pi$
$284$	−12.7801	−0.758360
$285$	0.278679	0.0165075
$286$	2.39205	0.141445
$287$	−14.4899	−0.855312
$288$	−2.98446	−0.175861
$289$	−14.3459	−0.843879
$290$	9.44631	0.554707
$291$	0.00429345	0.000251686 0
$292$	3.58789	0.209965
$293$	25.2731	1.47647	0.738235	−	0.674543i	$-0.235659\pi$
$293$	25.2731	1.47647	0.738235	+	0.674543i	$0.235659\pi$
$294$	1.06467	0.0620929
$295$	29.5149	1.71842
$296$	−11.0787	−0.643935
$297$	0.567102	0.0329066
$298$	−0.649490	−0.0376239
$299$	−28.2037	−1.63106
$300$	−0.000255257 0	−1.47373e−5 0
$301$	24.8846	1.43432
$302$	−16.9428	−0.974946
$303$	0.559202	0.0321253
$304$	−1.00000	−0.0573539
$305$	20.4165	1.16904
$306$	4.86207	0.277946
$307$	−4.61160	−0.263198	−0.131599	−	0.991303i	$-0.542011\pi$
$307$	−4.61160	−0.263198	−0.131599	+	0.991303i	$0.542011\pi$
$308$	−2.99687	−0.170762
$309$	−1.06424	−0.0605422
$310$	−16.9350	−0.961841
$311$	−15.0311	−0.852335	−0.426167	−	0.904644i	$-0.640137\pi$
$311$	−15.0311	−0.852335	−0.426167	+	0.904644i	$0.640137\pi$
$312$	−0.392239	−0.0222061
$313$	1.52897	0.0864224	0.0432112	−	0.999066i	$-0.486241\pi$
$313$	1.52897	0.0864224	0.0432112	+	0.999066i	$0.486241\pi$
$314$	−7.55944	−0.426604
$315$	26.3028	1.48199
$316$	2.53756	0.142749
$317$	−20.6462	−1.15960	−0.579802	−	0.814757i	$-0.696870\pi$
$317$	−20.6462	−1.15960	−0.579802	+	0.814757i	$0.696870\pi$
$318$	1.18767	0.0666011
$319$	3.21214	0.179845
$320$	−2.23561	−0.124974
$321$	−1.62488	−0.0906919
$322$	35.3348	1.96913
$323$	1.62913	0.0906471
$324$	8.86039	0.492244
$325$	0.00644335	0.000357413 0
$326$	−2.98621	−0.165391
$327$	−2.57186	−0.142224
$328$	−3.67558	−0.202950
$329$	13.2699	0.731594
$330$	0.211852	0.0116621
$331$	33.3892	1.83523	0.917617	−	0.397465i	$-0.130110\pi$
$331$	33.3892	1.83523	0.917617	+	0.397465i	$0.130110\pi$
$332$	−1.98573	−0.108981
$333$	33.0639	1.81189
$334$	5.32145	0.291177
$335$	26.0957	1.42576
$336$	0.491414	0.0268088
$337$	5.42941	0.295759	0.147879	−	0.989005i	$-0.452755\pi$
$337$	5.42941	0.295759	0.147879	+	0.989005i	$0.452755\pi$
$338$	−3.09887	−0.168556
$339$	−0.759433	−0.0412467
$340$	3.64210	0.197520
$341$	−5.75859	−0.311845
$342$	2.98446	0.161381
$343$	6.07486	0.328011
$344$	6.31236	0.340339
$345$	−2.49786	−0.134480
$346$	−14.1270	−0.759474
$347$	23.9863	1.28765	0.643825	−	0.765173i	$-0.277347\pi$
$347$	23.9863	1.28765	0.643825	+	0.765173i	$0.277347\pi$
$348$	−0.526713	−0.0282348
$349$	−33.2316	−1.77885	−0.889424	−	0.457084i	$-0.848894\pi$
$349$	−33.2316	−1.77885	−0.889424	+	0.457084i	$0.848894\pi$
$350$	−0.00807251	−0.000431494 0
$351$	2.34734	0.125292
$352$	−0.760201	−0.0405188
$353$	14.3033	0.761287	0.380644	−	0.924722i	$-0.375702\pi$
$353$	14.3033	0.761287	0.380644	+	0.924722i	$0.375702\pi$
$354$	−1.64571	−0.0874685
$355$	28.5713	1.51641
$356$	2.90906	0.154180
$357$	−0.800576	−0.0423710
$358$	1.14256	0.0603860
$359$	29.6387	1.56427	0.782135	−	0.623109i	$-0.214131\pi$
$359$	29.6387	1.56427	0.782135	+	0.623109i	$0.214131\pi$
$360$	6.67209	0.351650
$361$	1.00000	0.0526316
$362$	−15.7279	−0.826641
$363$	−1.29916	−0.0681883
$364$	−12.4046	−0.650176
$365$	−8.02111	−0.419844
$366$	−1.13839	−0.0595048
$367$	30.0692	1.56960	0.784799	−	0.619750i	$-0.212766\pi$
$367$	30.0692	1.56960	0.784799	+	0.619750i	$0.212766\pi$
$368$	8.96321	0.467240
$369$	10.9696	0.571057
$370$	24.7676	1.28761
$371$	37.5601	1.95002
$372$	0.944270	0.0489581
$373$	−13.9286	−0.721197	−0.360598	−	0.932721i	$-0.617428\pi$
$373$	−13.9286	−0.721197	−0.360598	+	0.932721i	$0.617428\pi$
$374$	1.23846	0.0640395
$375$	1.39396	0.0719840
$376$	3.36611	0.173594
$377$	13.2956	0.684760
$378$	−2.94085	−0.151261
$379$	−21.9922	−1.12966	−0.564831	−	0.825206i	$-0.691059\pi$
$379$	−21.9922	−1.12966	−0.564831	+	0.825206i	$0.691059\pi$
$380$	2.23561	0.114684
$381$	0.555155	0.0284415
$382$	−2.15476	−0.110247
$383$	−0.701339	−0.0358367	−0.0179184	−	0.999839i	$-0.505704\pi$
$383$	−0.701339	−0.0358367	−0.0179184	+	0.999839i	$0.505704\pi$
$384$	0.124655	0.00636125
$385$	6.69982	0.341455
$386$	−15.6782	−0.797998
$387$	−18.8390	−0.957639
$388$	0.0344428	0.00174857
$389$	−11.9599	−0.606392	−0.303196	−	0.952928i	$-0.598054\pi$
$389$	−11.9599	−0.606392	−0.303196	+	0.952928i	$0.598054\pi$
$390$	0.876893	0.0444032
$391$	−14.6022	−0.738466
$392$	8.54098	0.431385
$393$	−1.45040	−0.0731631
$394$	−0.0255509	−0.00128724
$395$	−5.67300	−0.285440
$396$	2.26879	0.114011
$397$	31.0812	1.55992	0.779961	−	0.625828i	$-0.215239\pi$
$397$	31.0812	1.55992	0.779961	+	0.625828i	$0.215239\pi$
$398$	16.3169	0.817892
$399$	−0.491414	−0.0246015
$400$	−0.00204771	−0.000102386 0
$401$	−28.7287	−1.43464	−0.717320	−	0.696744i	$-0.754632\pi$
$401$	−28.7287	−1.43464	−0.717320	+	0.696744i	$0.754632\pi$
$402$	−1.45506	−0.0725719
$403$	−23.8358	−1.18735
$404$	4.48602	0.223188
$405$	−19.8084	−0.984286
$406$	−16.6573	−0.826690
$407$	8.42202	0.417464
$408$	−0.203078	−0.0100539
$409$	10.6414	0.526183	0.263091	−	0.964771i	$-0.415258\pi$
$409$	10.6414	0.526183	0.263091	+	0.964771i	$0.415258\pi$
$410$	8.21717	0.405817
$411$	2.66697	0.131552
$412$	−8.53748	−0.420611
$413$	−52.0456	−2.56100
$414$	−26.7503	−1.31471
$415$	4.43931	0.217917
$416$	−3.14661	−0.154275
$417$	0.986742	0.0483209
$418$	0.760201	0.0371826
$419$	−19.3280	−0.944235	−0.472117	−	0.881536i	$-0.656510\pi$
$419$	−19.3280	−0.944235	−0.472117	+	0.881536i	$0.656510\pi$
$420$	−1.09861	−0.0536066
$421$	32.8804	1.60249	0.801245	−	0.598336i	$-0.204171\pi$
$421$	32.8804	1.60249	0.801245	+	0.598336i	$0.204171\pi$
$422$	1.00000	0.0486792
$423$	−10.0460	−0.488455
$424$	9.52768	0.462705
$425$	0.00333599	0.000161819 0
$426$	−1.59310	−0.0771859
$427$	−36.0018	−1.74225
$428$	−13.0351	−0.630073
$429$	0.298180	0.0143963
$430$	−14.1120	−0.680539
$431$	−10.1238	−0.487645	−0.243823	−	0.969820i	$-0.578401\pi$
$431$	−10.1238	−0.487645	−0.243823	+	0.969820i	$0.578401\pi$
$432$	−0.745990	−0.0358915
$433$	−15.9681	−0.767376	−0.383688	−	0.923463i	$-0.625346\pi$
$433$	−15.9681	−0.767376	−0.383688	+	0.923463i	$0.625346\pi$
$434$	29.8626	1.43345
$435$	1.17753	0.0564580
$436$	−20.6319	−0.988088
$437$	−8.96321	−0.428768
$438$	0.447246	0.0213702
$439$	−37.0996	−1.77067	−0.885333	−	0.464957i	$-0.846070\pi$
$439$	−37.0996	−1.77067	−0.885333	+	0.464957i	$0.846070\pi$
$440$	1.69951	0.0810211
$441$	−25.4902	−1.21382
$442$	5.12623	0.243830
$443$	23.2068	1.10259	0.551294	−	0.834311i	$-0.314134\pi$
$443$	23.2068	1.10259	0.551294	+	0.834311i	$0.314134\pi$
$444$	−1.38101	−0.0655397
$445$	−6.50353	−0.308297
$446$	−21.5797	−1.02183
$447$	−0.0809618	−0.00382936
$448$	3.94220	0.186252
$449$	13.9715	0.659358	0.329679	−	0.944093i	$-0.393059\pi$
$449$	13.9715	0.659358	0.329679	+	0.944093i	$0.393059\pi$
$450$	0.00611132	0.000288091 0
$451$	2.79418	0.131573
$452$	−6.09230	−0.286558
$453$	−2.11199	−0.0992300
$454$	0.139460	0.00654516
$455$	27.7318	1.30009
$456$	−0.124655	−0.00583748
$457$	−16.5152	−0.772549	−0.386274	−	0.922384i	$-0.626238\pi$
$457$	−16.5152	−0.772549	−0.386274	+	0.922384i	$0.626238\pi$
$458$	−3.50299	−0.163684
$459$	1.21531	0.0567260
$460$	−20.0382	−0.934288
$461$	−7.39199	−0.344279	−0.172140	−	0.985073i	$-0.555068\pi$
$461$	−7.39199	−0.344279	−0.172140	+	0.985073i	$0.555068\pi$
$462$	−0.373573	−0.0173802
$463$	9.69830	0.450718	0.225359	−	0.974276i	$-0.427645\pi$
$463$	9.69830	0.450718	0.225359	+	0.974276i	$0.427645\pi$
$464$	−4.22539	−0.196159
$465$	−2.11102	−0.0978961
$466$	18.2307	0.844519
$467$	−2.30046	−0.106453	−0.0532264	−	0.998582i	$-0.516951\pi$
$467$	−2.30046	−0.106453	−0.0532264	+	0.998582i	$0.516951\pi$
$468$	9.39093	0.434096
$469$	−46.0164	−2.12484
$470$	−7.52532	−0.347117
$471$	−0.942318	−0.0434197
$472$	−13.2022	−0.607679
$473$	−4.79866	−0.220642
$474$	0.316319	0.0145290
$475$	0.00204771	9.39556e−5 0
$476$	−6.42236	−0.294368
$477$	−28.4350	−1.30195
$478$	−21.6343	−0.989530
$479$	2.34730	0.107251	0.0536255	−	0.998561i	$-0.482922\pi$
$479$	2.34730	0.107251	0.0536255	+	0.998561i	$0.482922\pi$
$480$	−0.278679	−0.0127199
$481$	34.8603	1.58949
$482$	−17.0525	−0.776719
$483$	4.40464	0.200418
$484$	−10.4221	−0.473732
$485$	−0.0770006	−0.00349642
$486$	3.34246	0.151617
$487$	−20.2096	−0.915786	−0.457893	−	0.889007i	$-0.651396\pi$
$487$	−20.2096	−0.915786	−0.457893	+	0.889007i	$0.651396\pi$
$488$	−9.13240	−0.413404
$489$	−0.372244	−0.0168335
$490$	−19.0943	−0.862593
$491$	−27.4625	−1.23937	−0.619683	−	0.784853i	$-0.712739\pi$
$491$	−27.4625	−1.23937	−0.619683	+	0.784853i	$0.712739\pi$
$492$	−0.458178	−0.0206563
$493$	6.88370	0.310026
$494$	3.14661	0.141573
$495$	−5.07213	−0.227975
$496$	7.57509	0.340132
$497$	−50.3818	−2.25993
$498$	−0.247530	−0.0110921
$499$	−3.78364	−0.169379	−0.0846895	−	0.996407i	$-0.526990\pi$
$499$	−3.78364	−0.169379	−0.0846895	+	0.996407i	$0.526990\pi$
$500$	11.1826	0.500102
$501$	0.663342	0.0296359
$502$	3.44843	0.153911
$503$	0.972509	0.0433620	0.0216810	−	0.999765i	$-0.493098\pi$
$503$	0.972509	0.0433620	0.0216810	+	0.999765i	$0.493098\pi$
$504$	−11.7654	−0.524071
$505$	−10.0290	−0.446284
$506$	−6.81384	−0.302912
$507$	−0.386287	−0.0171556
$508$	4.45355	0.197594
$509$	42.8557	1.89955	0.949773	−	0.312940i	$-0.101314\pi$
$509$	42.8557	1.89955	0.949773	+	0.312940i	$0.101314\pi$
$510$	0.454004	0.0201036
$511$	14.1442	0.625702
$512$	1.00000	0.0441942
$513$	0.745990	0.0329363
$514$	25.1184	1.10792
$515$	19.0865	0.841051
$516$	0.786864	0.0346397
$517$	−2.55892	−0.112541
$518$	−43.6744	−1.91894
$519$	−1.76100	−0.0772992
$520$	7.03459	0.308487
$521$	−40.3346	−1.76709	−0.883545	−	0.468347i	$-0.844850\pi$
$521$	−40.3346	−1.76709	−0.883545	+	0.468347i	$0.844850\pi$
$522$	12.6105	0.551947
$523$	27.8378	1.21726	0.608632	−	0.793453i	$-0.291719\pi$
$523$	27.8378	1.21726	0.608632	+	0.793453i	$0.291719\pi$
$524$	−11.6354	−0.508293
$525$	−0.00100627	−4.39174e−5 0
$526$	−17.9726	−0.783645
$527$	−12.3408	−0.537574
$528$	−0.0947624	−0.00412400
$529$	57.3391	2.49300
$530$	−21.3002	−0.925220
$531$	39.4013	1.70987
$532$	−3.94220	−0.170916
$533$	11.5656	0.500963
$534$	0.362628	0.0156924
$535$	29.1413	1.25989
$536$	−11.6728	−0.504186
$537$	0.142425	0.00614609
$538$	−5.22118	−0.225101
$539$	−6.49286	−0.279667
$540$	1.66774	0.0717682
$541$	−35.5840	−1.52988	−0.764939	−	0.644103i	$-0.777231\pi$
$541$	−35.5840	−1.52988	−0.764939	+	0.644103i	$0.777231\pi$
$542$	17.8245	0.765629
$543$	−1.96056	−0.0841355
$544$	−1.62913	−0.0698483
$545$	46.1248	1.97577
$546$	−1.54629	−0.0661749
$547$	−30.4831	−1.30336	−0.651682	−	0.758493i	$-0.725936\pi$
$547$	−30.4831	−1.30336	−0.651682	+	0.758493i	$0.725936\pi$
$548$	21.3949	0.913943
$549$	27.2553	1.16323
$550$	0.00155667	6.63768e−5 0
$551$	4.22539	0.180007
$552$	1.11730	0.0475556
$553$	10.0036	0.425396
$554$	−3.89829	−0.165623
$555$	3.08740	0.131053
$556$	7.91581	0.335705
$557$	−16.2285	−0.687625	−0.343813	−	0.939038i	$-0.611719\pi$
$557$	−16.2285	−0.687625	−0.343813	+	0.939038i	$0.611719\pi$
$558$	−22.6076	−0.957055
$559$	−19.8625	−0.840094
$560$	−8.81323	−0.372427
$561$	0.154380	0.00651793
$562$	13.5908	0.573293
$563$	8.67830	0.365747	0.182873	−	0.983136i	$-0.441460\pi$
$563$	8.67830	0.365747	0.182873	+	0.983136i	$0.441460\pi$
$564$	0.419601	0.0176684
$565$	13.6200	0.572998
$566$	16.9186	0.711144
$567$	34.9295	1.46690
$568$	−12.7801	−0.536241
$569$	7.94318	0.332996	0.166498	−	0.986042i	$-0.446754\pi$
$569$	7.94318	0.332996	0.166498	+	0.986042i	$0.446754\pi$
$570$	0.278679	0.0116726
$571$	−36.6600	−1.53417	−0.767086	−	0.641544i	$-0.778294\pi$
$571$	−36.6600	−1.53417	−0.767086	+	0.641544i	$0.778294\pi$
$572$	2.39205	0.100017
$573$	−0.268600	−0.0112209
$574$	−14.4899	−0.604797
$575$	−0.0183541	−0.000765418 0
$576$	−2.98446	−0.124353
$577$	12.4720	0.519218	0.259609	−	0.965714i	$-0.416406\pi$
$577$	12.4720	0.519218	0.259609	+	0.965714i	$0.416406\pi$
$578$	−14.3459	−0.596712
$579$	−1.95436	−0.0812202
$580$	9.44631	0.392237
$581$	−7.82814	−0.324766
$582$	0.00429345	0.000177969 0
$583$	−7.24295	−0.299972
$584$	3.58789	0.148468
$585$	−20.9944	−0.868014
$586$	25.2731	1.04402
$587$	23.2156	0.958210	0.479105	−	0.877758i	$-0.340961\pi$
$587$	23.2156	0.958210	0.479105	+	0.877758i	$0.340961\pi$
$588$	1.06467	0.0439063
$589$	−7.57509	−0.312126
$590$	29.5149	1.21511
$591$	−0.00318503	−0.000131015 0
$592$	−11.0787	−0.455331
$593$	−12.6014	−0.517476	−0.258738	−	0.965947i	$-0.583307\pi$
$593$	−12.6014	−0.517476	−0.258738	+	0.965947i	$0.583307\pi$
$594$	0.567102	0.0232685
$595$	14.3579	0.588616
$596$	−0.649490	−0.0266041
$597$	2.03397	0.0832450
$598$	−28.2037	−1.15333
$599$	−14.3998	−0.588358	−0.294179	−	0.955750i	$-0.595046\pi$
$599$	−14.3998	−0.588358	−0.294179	+	0.955750i	$0.595046\pi$
$600$	−0.000255257 0	−1.04208e−5 0
$601$	28.6157	1.16726	0.583629	−	0.812020i	$-0.301632\pi$
$601$	28.6157	1.16726	0.583629	+	0.812020i	$0.301632\pi$
$602$	24.8846	1.01422
$603$	34.8369	1.41867
$604$	−16.9428	−0.689391
$605$	23.2997	0.947269
$606$	0.559202	0.0227160
$607$	−14.7056	−0.596883	−0.298442	−	0.954428i	$-0.596467\pi$
$607$	−14.7056	−0.596883	−0.298442	+	0.954428i	$0.596467\pi$
$608$	−1.00000	−0.0405554
$609$	−2.07641	−0.0841405
$610$	20.4165	0.826639
$611$	−10.5918	−0.428500
$612$	4.86207	0.196538
$613$	32.8039	1.32494	0.662469	−	0.749090i	$-0.269509\pi$
$613$	32.8039	1.32494	0.662469	+	0.749090i	$0.269509\pi$
$614$	−4.61160	−0.186109
$615$	1.02431	0.0413041
$616$	−2.99687	−0.120747
$617$	−29.2021	−1.17563	−0.587817	−	0.808994i	$-0.700012\pi$
$617$	−29.2021	−1.17563	−0.587817	+	0.808994i	$0.700012\pi$
$618$	−1.06424	−0.0428098
$619$	13.9815	0.561966	0.280983	−	0.959713i	$-0.409340\pi$
$619$	13.9815	0.561966	0.280983	+	0.959713i	$0.409340\pi$
$620$	−16.9350	−0.680124
$621$	−6.68646	−0.268319
$622$	−15.0311	−0.602692
$623$	11.4681	0.459461
$624$	−0.392239	−0.0157021
$625$	−24.9898	−0.999590
$626$	1.52897	0.0611099
$627$	0.0947624	0.00378445
$628$	−7.55944	−0.301655
$629$	18.0486	0.719645
$630$	26.3028	1.04793
$631$	−6.05979	−0.241236	−0.120618	−	0.992699i	$-0.538488\pi$
$631$	−6.05979	−0.241236	−0.120618	+	0.992699i	$0.538488\pi$
$632$	2.53756	0.100939
$633$	0.124655	0.00495457
$634$	−20.6462	−0.819964
$635$	−9.95640	−0.395108
$636$	1.18767	0.0470941
$637$	−26.8751	−1.06483
$638$	3.21214	0.127170
$639$	38.1417	1.50886
$640$	−2.23561	−0.0883702
$641$	7.56666	0.298865	0.149433	−	0.988772i	$-0.452255\pi$
$641$	7.56666	0.298865	0.149433	+	0.988772i	$0.452255\pi$
$642$	−1.62488	−0.0641288
$643$	−26.6662	−1.05161	−0.525806	−	0.850605i	$-0.676236\pi$
$643$	−26.6662	−1.05161	−0.525806	+	0.850605i	$0.676236\pi$
$644$	35.3348	1.39239
$645$	−1.75912	−0.0692653
$646$	1.62913	0.0640972
$647$	4.13490	0.162560	0.0812798	−	0.996691i	$-0.474099\pi$
$647$	4.13490	0.162560	0.0812798	+	0.996691i	$0.474099\pi$
$648$	8.86039	0.348069
$649$	10.0363	0.393959
$650$	0.00644335	0.000252729 0
$651$	3.72250	0.145896
$652$	−2.98621	−0.116949
$653$	21.8464	0.854915	0.427458	−	0.904035i	$-0.359409\pi$
$653$	21.8464	0.854915	0.427458	+	0.904035i	$0.359409\pi$
$654$	−2.57186	−0.100568
$655$	26.0121	1.01638
$656$	−3.67558	−0.143507
$657$	−10.7079	−0.417755
$658$	13.2699	0.517315
$659$	−17.1538	−0.668219	−0.334109	−	0.942534i	$-0.608435\pi$
$659$	−17.1538	−0.668219	−0.334109	+	0.942534i	$0.608435\pi$
$660$	0.211852	0.00824632
$661$	−36.2738	−1.41089	−0.705444	−	0.708765i	$-0.749252\pi$
$661$	−36.2738	−1.41089	−0.705444	+	0.708765i	$0.749252\pi$
$662$	33.3892	1.29771
$663$	0.639007	0.0248170
$664$	−1.98573	−0.0770611
$665$	8.81323	0.341763
$666$	33.0639	1.28120
$667$	−37.8730	−1.46645
$668$	5.32145	0.205893
$669$	−2.69000	−0.104001
$670$	26.0957	1.00817
$671$	6.94245	0.268010
$672$	0.491414	0.0189567
$673$	−8.43906	−0.325302	−0.162651	−	0.986684i	$-0.552004\pi$
$673$	−8.43906	−0.325302	−0.162651	+	0.986684i	$0.552004\pi$
$674$	5.42941	0.209133
$675$	0.00152757	5.87964e−5 0
$676$	−3.09887	−0.119187
$677$	4.42193	0.169948	0.0849742	−	0.996383i	$-0.472919\pi$
$677$	4.42193	0.169948	0.0849742	+	0.996383i	$0.472919\pi$
$678$	−0.759433	−0.0291658
$679$	0.135781	0.00521078
$680$	3.64210	0.139668
$681$	0.0173843	0.000666167 0
$682$	−5.75859	−0.220508
$683$	1.89386	0.0724664	0.0362332	−	0.999343i	$-0.488464\pi$
$683$	1.89386	0.0724664	0.0362332	+	0.999343i	$0.488464\pi$
$684$	2.98446	0.114114
$685$	−47.8306	−1.82751
$686$	6.07486	0.231939
$687$	−0.436663	−0.0166597
$688$	6.31236	0.240656
$689$	−29.9799	−1.14214
$690$	−2.49786	−0.0950918
$691$	−6.70236	−0.254970	−0.127485	−	0.991841i	$-0.540690\pi$
$691$	−6.70236	−0.254970	−0.127485	+	0.991841i	$0.540690\pi$
$692$	−14.1270	−0.537029
$693$	8.94403	0.339756
$694$	23.9863	0.910506
$695$	−17.6967	−0.671273
$696$	−0.526713	−0.0199650
$697$	5.98800	0.226812
$698$	−33.2316	−1.25784
$699$	2.27253	0.0859551
$700$	−0.00807251	−0.000305112 0
$701$	−22.9716	−0.867626	−0.433813	−	0.901003i	$-0.642832\pi$
$701$	−22.9716	−0.867626	−0.433813	+	0.901003i	$0.642832\pi$
$702$	2.34734	0.0885945
$703$	11.0787	0.417840
$704$	−0.760201	−0.0286511
$705$	−0.938064	−0.0353295
$706$	14.3033	0.538311
$707$	17.6848	0.665106
$708$	−1.64571	−0.0618495
$709$	38.8001	1.45717	0.728584	−	0.684956i	$-0.240179\pi$
$709$	38.8001	1.45717	0.728584	+	0.684956i	$0.240179\pi$
$710$	28.5713	1.07226
$711$	−7.57325	−0.284019
$712$	2.90906	0.109022
$713$	67.8971	2.54277
$714$	−0.800576	−0.0299608
$715$	−5.34770	−0.199992
$716$	1.14256	0.0426994
$717$	−2.69681	−0.100714
$718$	29.6387	1.10611
$719$	−7.89117	−0.294291	−0.147145	−	0.989115i	$-0.547009\pi$
$719$	−7.89117	−0.294291	−0.147145	+	0.989115i	$0.547009\pi$
$720$	6.67209	0.248654
$721$	−33.6565	−1.25343
$722$	1.00000	0.0372161
$723$	−2.12567	−0.0790545
$724$	−15.7279	−0.584524
$725$	0.00865238	0.000321341 0
$726$	−1.29916	−0.0482164
$727$	−8.43236	−0.312739	−0.156369	−	0.987699i	$-0.549979\pi$
$727$	−8.43236	−0.312739	−0.156369	+	0.987699i	$0.549979\pi$
$728$	−12.4046	−0.459744
$729$	−26.1645	−0.969057
$730$	−8.02111	−0.296875
$731$	−10.2836	−0.380354
$732$	−1.13839	−0.0420763
$733$	16.3118	0.602492	0.301246	−	0.953547i	$-0.402598\pi$
$733$	16.3118	0.602492	0.301246	+	0.953547i	$0.402598\pi$
$734$	30.0692	1.10987
$735$	−2.38019	−0.0877946
$736$	8.96321	0.330388
$737$	8.87364	0.326865
$738$	10.9696	0.403798
$739$	37.7366	1.38816	0.694081	−	0.719896i	$-0.255811\pi$
$739$	37.7366	1.38816	0.694081	+	0.719896i	$0.255811\pi$
$740$	24.7676	0.910476
$741$	0.392239	0.0144092
$742$	37.5601	1.37887
$743$	16.7847	0.615769	0.307885	−	0.951424i	$-0.400379\pi$
$743$	16.7847	0.615769	0.307885	+	0.951424i	$0.400379\pi$
$744$	0.944270	0.0346186
$745$	1.45201	0.0531974
$746$	−13.9286	−0.509963
$747$	5.92632	0.216833
$748$	1.23846	0.0452827
$749$	−51.3869	−1.87764
$750$	1.39396	0.0509004
$751$	−9.36988	−0.341912	−0.170956	−	0.985279i	$-0.554686\pi$
$751$	−9.36988	−0.341912	−0.170956	+	0.985279i	$0.554686\pi$
$752$	3.36611	0.122749
$753$	0.429862	0.0156650
$754$	13.2956	0.484198
$755$	37.8774	1.37850
$756$	−2.94085	−0.106958
$757$	−25.1602	−0.914465	−0.457232	−	0.889347i	$-0.651159\pi$
$757$	−25.1602	−0.914465	−0.457232	+	0.889347i	$0.651159\pi$
$758$	−21.9922	−0.798792
$759$	−0.849375	−0.0308304
$760$	2.23561	0.0810941
$761$	−38.9186	−1.41080	−0.705399	−	0.708810i	$-0.749232\pi$
$761$	−38.9186	−1.41080	−0.705399	+	0.708810i	$0.749232\pi$
$762$	0.555155	0.0201111
$763$	−81.3351	−2.94453
$764$	−2.15476	−0.0779563
$765$	−10.8697	−0.392995
$766$	−0.701339	−0.0253404
$767$	41.5420	1.50000
$768$	0.124655	0.00449808
$769$	15.4794	0.558202	0.279101	−	0.960262i	$-0.409964\pi$
$769$	15.4794	0.558202	0.279101	+	0.960262i	$0.409964\pi$
$770$	6.69982	0.241445
$771$	3.13112	0.112765
$772$	−15.6782	−0.564270
$773$	45.9059	1.65112	0.825561	−	0.564313i	$-0.190859\pi$
$773$	45.9059	1.65112	0.825561	+	0.564313i	$0.190859\pi$
$774$	−18.8390	−0.677153
$775$	−0.0155116	−0.000557194 0
$776$	0.0344428	0.00123642
$777$	−5.44422	−0.195310
$778$	−11.9599	−0.428784
$779$	3.67558	0.131691
$780$	0.876893	0.0313978
$781$	9.71545	0.347646
$782$	−14.6022	−0.522174
$783$	3.15210	0.112647
$784$	8.54098	0.305035
$785$	16.9000	0.603185
$786$	−1.45040	−0.0517341
$787$	−16.9033	−0.602536	−0.301268	−	0.953539i	$-0.597410\pi$
$787$	−16.9033	−0.602536	−0.301268	+	0.953539i	$0.597410\pi$
$788$	−0.0255509	−0.000910213 0
$789$	−2.24037	−0.0797593
$790$	−5.67300	−0.201836
$791$	−24.0171	−0.853950
$792$	2.26879	0.0806179
$793$	28.7361	1.02045
$794$	31.0812	1.10303
$795$	−2.65516	−0.0941689
$796$	16.3169	0.578337
$797$	−53.0218	−1.87813	−0.939064	−	0.343743i	$-0.888305\pi$
$797$	−53.0218	−1.87813	−0.939064	+	0.343743i	$0.888305\pi$
$798$	−0.491414	−0.0173959
$799$	−5.48383	−0.194004
$800$	−0.00204771	−7.23976e−5 0
$801$	−8.68198	−0.306763
$802$	−28.7287	−1.01444
$803$	−2.72751	−0.0962518
$804$	−1.45506	−0.0513161
$805$	−78.9948	−2.78420
$806$	−23.8358	−0.839582
$807$	−0.650844	−0.0229108
$808$	4.48602	0.157818
$809$	−11.4150	−0.401330	−0.200665	−	0.979660i	$-0.564310\pi$
$809$	−11.4150	−0.401330	−0.200665	+	0.979660i	$0.564310\pi$
$810$	−19.8084	−0.695996
$811$	34.1690	1.19983	0.599917	−	0.800062i	$-0.295200\pi$
$811$	34.1690	1.19983	0.599917	+	0.800062i	$0.295200\pi$
$812$	−16.6573	−0.584558
$813$	2.22191	0.0779257
$814$	8.42202	0.295192
$815$	6.67600	0.233850
$816$	−0.203078	−0.00710916
$817$	−6.31236	−0.220841
$818$	10.6414	0.372067
$819$	37.0210	1.29362
$820$	8.21717	0.286956
$821$	29.6492	1.03477	0.517383	−	0.855754i	$-0.326906\pi$
$821$	29.6492	1.03477	0.517383	+	0.855754i	$0.326906\pi$
$822$	2.66697	0.0930211
$823$	−10.4416	−0.363970	−0.181985	−	0.983301i	$-0.558252\pi$
$823$	−10.4416	−0.363970	−0.181985	+	0.983301i	$0.558252\pi$
$824$	−8.53748	−0.297417
$825$	0.000194046 0	6.75583e−6 0
$826$	−52.0456	−1.81090
$827$	15.8016	0.549476	0.274738	−	0.961519i	$-0.411409\pi$
$827$	15.8016	0.549476	0.274738	+	0.961519i	$0.411409\pi$
$828$	−26.7503	−0.929639
$829$	30.6708	1.06524	0.532621	−	0.846354i	$-0.321207\pi$
$829$	30.6708	1.06524	0.532621	+	0.846354i	$0.321207\pi$
$830$	4.43931	0.154091
$831$	−0.485940	−0.0168571
$832$	−3.14661	−0.109089
$833$	−13.9144	−0.482104
$834$	0.986742	0.0341681
$835$	−11.8967	−0.411701
$836$	0.760201	0.0262921
$837$	−5.65094	−0.195325
$838$	−19.3280	−0.667675
$839$	−5.39117	−0.186124	−0.0930619	−	0.995660i	$-0.529665\pi$
$839$	−5.39117	−0.186124	−0.0930619	+	0.995660i	$0.529665\pi$
$840$	−1.09861	−0.0379056
$841$	−11.1461	−0.384349
$842$	32.8804	1.13313
$843$	1.69415	0.0583498
$844$	1.00000	0.0344214
$845$	6.92785	0.238325
$846$	−10.0460	−0.345390
$847$	−41.0860	−1.41173
$848$	9.52768	0.327182
$849$	2.10898	0.0723802
$850$	0.00333599	0.000114423 0
$851$	−99.3006	−3.40398
$852$	−1.59310	−0.0545786
$853$	47.9829	1.64290	0.821452	−	0.570278i	$-0.193164\pi$
$853$	47.9829	1.64290	0.821452	+	0.570278i	$0.193164\pi$
$854$	−36.0018	−1.23196
$855$	−6.67209	−0.228181
$856$	−13.0351	−0.445529
$857$	47.6225	1.62675	0.813376	−	0.581738i	$-0.197627\pi$
$857$	47.6225	1.62675	0.813376	+	0.581738i	$0.197627\pi$
$858$	0.298180	0.0101797
$859$	−29.0566	−0.991398	−0.495699	−	0.868494i	$-0.665088\pi$
$859$	−29.0566	−0.991398	−0.495699	+	0.868494i	$0.665088\pi$
$860$	−14.1120	−0.481214
$861$	−1.80623	−0.0615562
$862$	−10.1238	−0.344817
$863$	12.4014	0.422149	0.211075	−	0.977470i	$-0.432304\pi$
$863$	12.4014	0.422149	0.211075	+	0.977470i	$0.432304\pi$
$864$	−0.745990	−0.0253791
$865$	31.5825	1.07384
$866$	−15.9681	−0.542617
$867$	−1.78829	−0.0607334
$868$	29.8626	1.01360
$869$	−1.92906	−0.0654387
$870$	1.17753	0.0399219
$871$	36.7296	1.24453
$872$	−20.6319	−0.698684
$873$	−0.102793	−0.00347902
$874$	−8.96321	−0.303185
$875$	44.0842	1.49032
$876$	0.447246	0.0151110
$877$	−12.6230	−0.426249	−0.213125	−	0.977025i	$-0.568364\pi$
$877$	−12.6230	−0.426249	−0.213125	+	0.977025i	$0.568364\pi$
$878$	−37.0996	−1.25205
$879$	3.15041	0.106261
$880$	1.69951	0.0572905
$881$	37.0577	1.24851	0.624253	−	0.781222i	$-0.285403\pi$
$881$	37.0577	1.24851	0.624253	+	0.781222i	$0.285403\pi$
$882$	−25.4902	−0.858300
$883$	−7.40745	−0.249280	−0.124640	−	0.992202i	$-0.539778\pi$
$883$	−7.40745	−0.249280	−0.124640	+	0.992202i	$0.539778\pi$
$884$	5.12623	0.172414
$885$	3.67916	0.123674
$886$	23.2068	0.779647
$887$	49.4801	1.66138	0.830689	−	0.556737i	$-0.187947\pi$
$887$	49.4801	1.66138	0.830689	+	0.556737i	$0.187947\pi$
$888$	−1.38101	−0.0463436
$889$	17.5568	0.588836
$890$	−6.50353	−0.217999
$891$	−6.73568	−0.225654
$892$	−21.5797	−0.722540
$893$	−3.36611	−0.112643
$894$	−0.0809618	−0.00270777
$895$	−2.55431	−0.0853813
$896$	3.94220	0.131700
$897$	−3.51572	−0.117386
$898$	13.9715	0.466236
$899$	−32.0077	−1.06752
$900$	0.00611132	0.000203711 0
$901$	−15.5218	−0.517107
$902$	2.79418	0.0930360
$903$	3.10198	0.103227
$904$	−6.09230	−0.202627
$905$	35.1615	1.16881
$906$	−2.11199	−0.0701662
$907$	−19.3080	−0.641111	−0.320555	−	0.947230i	$-0.603870\pi$
$907$	−19.3080	−0.641111	−0.320555	+	0.947230i	$0.603870\pi$
$908$	0.139460	0.00462813
$909$	−13.3883	−0.444064
$910$	27.7318	0.919300
$911$	−18.4566	−0.611493	−0.305747	−	0.952113i	$-0.598906\pi$
$911$	−18.4566	−0.611493	−0.305747	+	0.952113i	$0.598906\pi$
$912$	−0.124655	−0.00412772
$913$	1.50955	0.0499588
$914$	−16.5152	−0.546274
$915$	2.54501	0.0841353
$916$	−3.50299	−0.115742
$917$	−45.8690	−1.51473
$918$	1.21531	0.0401113
$919$	−20.2842	−0.669114	−0.334557	−	0.942376i	$-0.608587\pi$
$919$	−20.2842	−0.669114	−0.334557	+	0.942376i	$0.608587\pi$
$920$	−20.0382	−0.660641
$921$	−0.574857	−0.0189422
$922$	−7.39199	−0.243442
$923$	40.2140	1.32366
$924$	−0.373573	−0.0122896
$925$	0.0226860	0.000745910 0
$926$	9.69830	0.318706
$927$	25.4798	0.836866
$928$	−4.22539	−0.138705
$929$	−13.3666	−0.438543	−0.219272	−	0.975664i	$-0.570368\pi$
$929$	−13.3666	−0.438543	−0.219272	+	0.975664i	$0.570368\pi$
$930$	−2.11102	−0.0692230
$931$	−8.54098	−0.279919
$932$	18.2307	0.597165
$933$	−1.87369	−0.0613419
$934$	−2.30046	−0.0752735
$935$	−2.76872	−0.0905469
$936$	9.39093	0.306952
$937$	40.2887	1.31618	0.658088	−	0.752941i	$-0.271366\pi$
$937$	40.2887	1.31618	0.658088	+	0.752941i	$0.271366\pi$
$938$	−46.0164	−1.50249
$939$	0.190593	0.00621976
$940$	−7.52532	−0.245449
$941$	56.5273	1.84274	0.921368	−	0.388692i	$-0.127073\pi$
$941$	56.5273	1.84274	0.921368	+	0.388692i	$0.127073\pi$
$942$	−0.942318	−0.0307024
$943$	−32.9450	−1.07284
$944$	−13.2022	−0.429694
$945$	6.57458	0.213871
$946$	−4.79866	−0.156018
$947$	−19.4606	−0.632385	−0.316192	−	0.948695i	$-0.602405\pi$
$947$	−19.4606	−0.632385	−0.316192	+	0.948695i	$0.602405\pi$
$948$	0.316319	0.0102735
$949$	−11.2897	−0.366478
$950$	0.00204771	6.64366e−5 0
$951$	−2.57364	−0.0834559
$952$	−6.42236	−0.208150
$953$	34.1436	1.10602	0.553009	−	0.833175i	$-0.313479\pi$
$953$	34.1436	1.10602	0.553009	+	0.833175i	$0.313479\pi$
$954$	−28.4350	−0.920617
$955$	4.81719	0.155881
$956$	−21.6343	−0.699703
$957$	0.400408	0.0129433
$958$	2.34730	0.0758379
$959$	84.3430	2.72358
$960$	−0.278679	−0.00899432
$961$	26.3820	0.851034
$962$	34.8603	1.12394
$963$	38.9026	1.25362
$964$	−17.0525	−0.549224
$965$	35.0503	1.12831
$966$	4.40464	0.141717
$967$	29.4597	0.947361	0.473680	−	0.880697i	$-0.342925\pi$
$967$	29.4597	0.947361	0.473680	+	0.880697i	$0.342925\pi$
$968$	−10.4221	−0.334979
$969$	0.203078	0.00652381
$970$	−0.0770006	−0.00247234
$971$	−31.2305	−1.00224	−0.501118	−	0.865379i	$-0.667078\pi$
$971$	−31.2305	−1.00224	−0.501118	+	0.865379i	$0.667078\pi$
$972$	3.34246	0.107209
$973$	31.2058	1.00041
$974$	−20.2096	−0.647558
$975$	0.000803193 0	2.57228e−5 0
$976$	−9.13240	−0.292321
$977$	50.3067	1.60945	0.804727	−	0.593644i	$-0.202311\pi$
$977$	50.3067	1.60945	0.804727	+	0.593644i	$0.202311\pi$
$978$	−0.372244	−0.0119031
$979$	−2.21147	−0.0706789
$980$	−19.0943	−0.609945
$981$	61.5751	1.96594
$982$	−27.4625	−0.876363
$983$	41.2914	1.31699	0.658495	−	0.752585i	$-0.271193\pi$
$983$	41.2914	1.31699	0.658495	+	0.752585i	$0.271193\pi$
$984$	−0.458178	−0.0146062
$985$	0.0571218	0.00182005
$986$	6.88370	0.219222
$987$	1.65415	0.0526523
$988$	3.14661	0.100107
$989$	56.5790	1.79911
$990$	−5.07213	−0.161203
$991$	16.0049	0.508413	0.254207	−	0.967150i	$-0.418186\pi$
$991$	16.0049	0.508413	0.254207	+	0.967150i	$0.418186\pi$
$992$	7.57509	0.240509
$993$	4.16211	0.132081
$994$	−50.3818	−1.59801
$995$	−36.4782	−1.15644
$996$	−0.247530	−0.00784328
$997$	4.65221	0.147337	0.0736685	−	0.997283i	$-0.476529\pi$
$997$	4.65221	0.147337	0.0736685	+	0.997283i	$0.476529\pi$
$998$	−3.78364	−0.119769
$999$	8.26459	0.261480

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.e.1.18	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.e.1.18	✓	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.124655 q^{3} +1.00000 q^{4} -2.23561 q^{5} +0.124655 q^{6} +3.94220 q^{7} +1.00000 q^{8} -2.98446 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.124655 q^{3} +1.00000 q^{4} -2.23561 q^{5} +0.124655 q^{6} +3.94220 q^{7} +1.00000 q^{8} -2.98446 q^{9} -2.23561 q^{10} -0.760201 q^{11} +0.124655 q^{12} -3.14661 q^{13} +3.94220 q^{14} -0.278679 q^{15} +1.00000 q^{16} -1.62913 q^{17} -2.98446 q^{18} -1.00000 q^{19} -2.23561 q^{20} +0.491414 q^{21} -0.760201 q^{22} +8.96321 q^{23} +0.124655 q^{24} -0.00204771 q^{25} -3.14661 q^{26} -0.745990 q^{27} +3.94220 q^{28} -4.22539 q^{29} -0.278679 q^{30} +7.57509 q^{31} +1.00000 q^{32} -0.0947624 q^{33} -1.62913 q^{34} -8.81323 q^{35} -2.98446 q^{36} -11.0787 q^{37} -1.00000 q^{38} -0.392239 q^{39} -2.23561 q^{40} -3.67558 q^{41} +0.491414 q^{42} +6.31236 q^{43} -0.760201 q^{44} +6.67209 q^{45} +8.96321 q^{46} +3.36611 q^{47} +0.124655 q^{48} +8.54098 q^{49} -0.00204771 q^{50} -0.203078 q^{51} -3.14661 q^{52} +9.52768 q^{53} -0.745990 q^{54} +1.69951 q^{55} +3.94220 q^{56} -0.124655 q^{57} -4.22539 q^{58} -13.2022 q^{59} -0.278679 q^{60} -9.13240 q^{61} +7.57509 q^{62} -11.7654 q^{63} +1.00000 q^{64} +7.03459 q^{65} -0.0947624 q^{66} -11.6728 q^{67} -1.62913 q^{68} +1.11730 q^{69} -8.81323 q^{70} -12.7801 q^{71} -2.98446 q^{72} +3.58789 q^{73} -11.0787 q^{74} -0.000255257 q^{75} -1.00000 q^{76} -2.99687 q^{77} -0.392239 q^{78} +2.53756 q^{79} -2.23561 q^{80} +8.86039 q^{81} -3.67558 q^{82} -1.98573 q^{83} +0.491414 q^{84} +3.64210 q^{85} +6.31236 q^{86} -0.526713 q^{87} -0.760201 q^{88} +2.90906 q^{89} +6.67209 q^{90} -12.4046 q^{91} +8.96321 q^{92} +0.944270 q^{93} +3.36611 q^{94} +2.23561 q^{95} +0.124655 q^{96} +0.0344428 q^{97} +8.54098 q^{98} +2.26879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more