LMFDB - Embedded newform 4017.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75387 q^{2} +1.00000 q^{3} +5.58381 q^{4} +3.90153 q^{5} -2.75387 q^{6} +0.781129 q^{7} -9.86935 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.75387 q^{2} +1.00000 q^{3} +5.58381 q^{4} +3.90153 q^{5} -2.75387 q^{6} +0.781129 q^{7} -9.86935 q^{8} +1.00000 q^{9} -10.7443 q^{10} +2.18434 q^{11} +5.58381 q^{12} -1.00000 q^{13} -2.15113 q^{14} +3.90153 q^{15} +16.0113 q^{16} +3.72521 q^{17} -2.75387 q^{18} +3.56741 q^{19} +21.7854 q^{20} +0.781129 q^{21} -6.01539 q^{22} +5.17048 q^{23} -9.86935 q^{24} +10.2220 q^{25} +2.75387 q^{26} +1.00000 q^{27} +4.36167 q^{28} +4.04497 q^{29} -10.7443 q^{30} +6.84811 q^{31} -24.3544 q^{32} +2.18434 q^{33} -10.2588 q^{34} +3.04760 q^{35} +5.58381 q^{36} +8.92718 q^{37} -9.82419 q^{38} -1.00000 q^{39} -38.5056 q^{40} -10.7424 q^{41} -2.15113 q^{42} -2.19111 q^{43} +12.1969 q^{44} +3.90153 q^{45} -14.2388 q^{46} -4.77100 q^{47} +16.0113 q^{48} -6.38984 q^{49} -28.1500 q^{50} +3.72521 q^{51} -5.58381 q^{52} -0.781680 q^{53} -2.75387 q^{54} +8.52227 q^{55} -7.70923 q^{56} +3.56741 q^{57} -11.1393 q^{58} -10.8114 q^{59} +21.7854 q^{60} +1.10796 q^{61} -18.8588 q^{62} +0.781129 q^{63} +35.0462 q^{64} -3.90153 q^{65} -6.01539 q^{66} +12.5473 q^{67} +20.8009 q^{68} +5.17048 q^{69} -8.39270 q^{70} -8.75964 q^{71} -9.86935 q^{72} +6.59976 q^{73} -24.5843 q^{74} +10.2220 q^{75} +19.9197 q^{76} +1.70625 q^{77} +2.75387 q^{78} -14.5687 q^{79} +62.4686 q^{80} +1.00000 q^{81} +29.5831 q^{82} -7.23917 q^{83} +4.36167 q^{84} +14.5340 q^{85} +6.03405 q^{86} +4.04497 q^{87} -21.5580 q^{88} -12.5527 q^{89} -10.7443 q^{90} -0.781129 q^{91} +28.8710 q^{92} +6.84811 q^{93} +13.1387 q^{94} +13.9184 q^{95} -24.3544 q^{96} +1.94945 q^{97} +17.5968 q^{98} +2.18434 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.75387	−1.94728	−0.973641	−	0.228088i	$-0.926753\pi$
$2$	−2.75387	−1.94728	−0.973641	+	0.228088i	$0.926753\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.58381	2.79190
$5$	3.90153	1.74482	0.872410	−	0.488776i	$-0.162556\pi$
$5$	3.90153	1.74482	0.872410	+	0.488776i	$0.162556\pi$
$6$	−2.75387	−1.12426
$7$	0.781129	0.295239	0.147619	−	0.989044i	$-0.452839\pi$
$7$	0.781129	0.295239	0.147619	+	0.989044i	$0.452839\pi$
$8$	−9.86935	−3.48934
$9$	1.00000	0.333333
$10$	−10.7443	−3.39765
$11$	2.18434	0.658603	0.329301	−	0.944225i	$-0.393187\pi$
$11$	2.18434	0.658603	0.329301	+	0.944225i	$0.393187\pi$
$12$	5.58381	1.61191
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.15113	−0.574913
$15$	3.90153	1.00737
$16$	16.0113	4.00282
$17$	3.72521	0.903497	0.451749	−	0.892145i	$-0.350800\pi$
$17$	3.72521	0.903497	0.451749	+	0.892145i	$0.350800\pi$
$18$	−2.75387	−0.649094
$19$	3.56741	0.818420	0.409210	−	0.912440i	$-0.365804\pi$
$19$	3.56741	0.818420	0.409210	+	0.912440i	$0.365804\pi$
$20$	21.7854	4.87137
$21$	0.781129	0.170456
$22$	−6.01539	−1.28249
$23$	5.17048	1.07812	0.539060	−	0.842267i	$-0.318780\pi$
$23$	5.17048	1.07812	0.539060	+	0.842267i	$0.318780\pi$
$24$	−9.86935	−2.01457
$25$	10.2220	2.04439
$26$	2.75387	0.540079
$27$	1.00000	0.192450
$28$	4.36167	0.824279
$29$	4.04497	0.751132	0.375566	−	0.926796i	$-0.377448\pi$
$29$	4.04497	0.751132	0.375566	+	0.926796i	$0.377448\pi$
$30$	−10.7443	−1.96164
$31$	6.84811	1.22996	0.614978	−	0.788544i	$-0.289165\pi$
$31$	6.84811	1.22996	0.614978	+	0.788544i	$0.289165\pi$
$32$	−24.3544	−4.30528
$33$	2.18434	0.380245
$34$	−10.2588	−1.75936
$35$	3.04760	0.515139
$36$	5.58381	0.930635
$37$	8.92718	1.46762	0.733809	−	0.679356i	$-0.237741\pi$
$37$	8.92718	1.46762	0.733809	+	0.679356i	$0.237741\pi$
$38$	−9.82419	−1.59369
$39$	−1.00000	−0.160128
$40$	−38.5056	−6.08827
$41$	−10.7424	−1.67768	−0.838838	−	0.544382i	$-0.816764\pi$
$41$	−10.7424	−1.67768	−0.838838	+	0.544382i	$0.816764\pi$
$42$	−2.15113	−0.331926
$43$	−2.19111	−0.334142	−0.167071	−	0.985945i	$-0.553431\pi$
$43$	−2.19111	−0.334142	−0.167071	+	0.985945i	$0.553431\pi$
$44$	12.1969	1.83876
$45$	3.90153	0.581606
$46$	−14.2388	−2.09940
$47$	−4.77100	−0.695922	−0.347961	−	0.937509i	$-0.613126\pi$
$47$	−4.77100	−0.695922	−0.347961	+	0.937509i	$0.613126\pi$
$48$	16.0113	2.31103
$49$	−6.38984	−0.912834
$50$	−28.1500	−3.98101
$51$	3.72521	0.521634
$52$	−5.58381	−0.774335
$53$	−0.781680	−0.107372	−0.0536860	−	0.998558i	$-0.517097\pi$
$53$	−0.781680	−0.107372	−0.0536860	+	0.998558i	$0.517097\pi$
$54$	−2.75387	−0.374754
$55$	8.52227	1.14914
$56$	−7.70923	−1.03019
$57$	3.56741	0.472515
$58$	−11.1393	−1.46267
$59$	−10.8114	−1.40752	−0.703762	−	0.710436i	$-0.748498\pi$
$59$	−10.8114	−1.40752	−0.703762	+	0.710436i	$0.748498\pi$
$60$	21.7854	2.81249
$61$	1.10796	0.141860	0.0709300	−	0.997481i	$-0.477403\pi$
$61$	1.10796	0.141860	0.0709300	+	0.997481i	$0.477403\pi$
$62$	−18.8588	−2.39507
$63$	0.781129	0.0984130
$64$	35.0462	4.38077
$65$	−3.90153	−0.483926
$66$	−6.01539	−0.740443
$67$	12.5473	1.53289	0.766447	−	0.642308i	$-0.222023\pi$
$67$	12.5473	1.53289	0.766447	+	0.642308i	$0.222023\pi$
$68$	20.8009	2.52248
$69$	5.17048	0.622453
$70$	−8.39270	−1.00312
$71$	−8.75964	−1.03958	−0.519789	−	0.854295i	$-0.673989\pi$
$71$	−8.75964	−1.03958	−0.519789	+	0.854295i	$0.673989\pi$
$72$	−9.86935	−1.16311
$73$	6.59976	0.772443	0.386222	−	0.922406i	$-0.373780\pi$
$73$	6.59976	0.772443	0.386222	+	0.922406i	$0.373780\pi$
$74$	−24.5843	−2.85787
$75$	10.2220	1.18033
$76$	19.9197	2.28495
$77$	1.70625	0.194445
$78$	2.75387	0.311815
$79$	−14.5687	−1.63910	−0.819552	−	0.573005i	$-0.805777\pi$
$79$	−14.5687	−1.63910	−0.819552	+	0.573005i	$0.805777\pi$
$80$	62.4686	6.98421
$81$	1.00000	0.111111
$82$	29.5831	3.26691
$83$	−7.23917	−0.794602	−0.397301	−	0.917688i	$-0.630053\pi$
$83$	−7.23917	−0.794602	−0.397301	+	0.917688i	$0.630053\pi$
$84$	4.36167	0.475898
$85$	14.5340	1.57644
$86$	6.03405	0.650668
$87$	4.04497	0.433666
$88$	−21.5580	−2.29809
$89$	−12.5527	−1.33058	−0.665292	−	0.746583i	$-0.731693\pi$
$89$	−12.5527	−1.33058	−0.665292	+	0.746583i	$0.731693\pi$
$90$	−10.7443	−1.13255
$91$	−0.781129	−0.0818846
$92$	28.8710	3.01001
$93$	6.84811	0.710116
$94$	13.1387	1.35516
$95$	13.9184	1.42799
$96$	−24.3544	−2.48566
$97$	1.94945	0.197936	0.0989682	−	0.995091i	$-0.468446\pi$
$97$	1.94945	0.197936	0.0989682	+	0.995091i	$0.468446\pi$
$98$	17.5968	1.77754
$99$	2.18434	0.219534
$100$	57.0775	5.70775
$101$	−11.0490	−1.09942	−0.549711	−	0.835355i	$-0.685262\pi$
$101$	−11.0490	−1.09942	−0.549711	+	0.835355i	$0.685262\pi$
$102$	−10.2588	−1.01577
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	9.86935	0.967769
$105$	3.04760	0.297415
$106$	2.15265	0.209084
$107$	2.09839	0.202859	0.101429	−	0.994843i	$-0.467658\pi$
$107$	2.09839	0.202859	0.101429	+	0.994843i	$0.467658\pi$
$108$	5.58381	0.537302
$109$	−18.0917	−1.73287	−0.866434	−	0.499291i	$-0.833594\pi$
$109$	−18.0917	−1.73287	−0.866434	+	0.499291i	$0.833594\pi$
$110$	−23.4692	−2.23770
$111$	8.92718	0.847330
$112$	12.5069	1.18179
$113$	−5.16454	−0.485839	−0.242920	−	0.970046i	$-0.578105\pi$
$113$	−5.16454	−0.485839	−0.242920	+	0.970046i	$0.578105\pi$
$114$	−9.82419	−0.920120
$115$	20.1728	1.88112
$116$	22.5863	2.09709
$117$	−1.00000	−0.0924500
$118$	29.7732	2.74084
$119$	2.90987	0.266748
$120$	−38.5056	−3.51506
$121$	−6.22866	−0.566242
$122$	−3.05118	−0.276241
$123$	−10.7424	−0.968606
$124$	38.2385	3.43392
$125$	20.3737	1.82228
$126$	−2.15113	−0.191638
$127$	14.1875	1.25894	0.629469	−	0.777026i	$-0.283273\pi$
$127$	14.1875	1.25894	0.629469	+	0.777026i	$0.283273\pi$
$128$	−47.8040	−4.22532
$129$	−2.19111	−0.192917
$130$	10.7443	0.942340
$131$	14.6229	1.27761	0.638806	−	0.769368i	$-0.279429\pi$
$131$	14.6229	1.27761	0.638806	+	0.769368i	$0.279429\pi$
$132$	12.1969	1.06161
$133$	2.78661	0.241629
$134$	−34.5536	−2.98498
$135$	3.90153	0.335791
$136$	−36.7654	−3.15261
$137$	3.44928	0.294692	0.147346	−	0.989085i	$-0.452927\pi$
$137$	3.44928	0.294692	0.147346	+	0.989085i	$0.452927\pi$
$138$	−14.2388	−1.21209
$139$	−4.63320	−0.392983	−0.196492	−	0.980506i	$-0.562955\pi$
$139$	−4.63320	−0.392983	−0.196492	+	0.980506i	$0.562955\pi$
$140$	17.0172	1.43822
$141$	−4.77100	−0.401791
$142$	24.1229	2.02435
$143$	−2.18434	−0.182664
$144$	16.0113	1.33427
$145$	15.7816	1.31059
$146$	−18.1749	−1.50416
$147$	−6.38984	−0.527025
$148$	49.8476	4.09745
$149$	−5.71021	−0.467799	−0.233899	−	0.972261i	$-0.575149\pi$
$149$	−5.71021	−0.467799	−0.233899	+	0.972261i	$0.575149\pi$
$150$	−28.1500	−2.29844
$151$	−9.10236	−0.740740	−0.370370	−	0.928884i	$-0.620769\pi$
$151$	−9.10236	−0.740740	−0.370370	+	0.928884i	$0.620769\pi$
$152$	−35.2080	−2.85575
$153$	3.72521	0.301166
$154$	−4.69879	−0.378640
$155$	26.7181	2.14605
$156$	−5.58381	−0.447062
$157$	24.1446	1.92695	0.963476	−	0.267795i	$-0.0862950\pi$
$157$	24.1446	1.92695	0.963476	+	0.267795i	$0.0862950\pi$
$158$	40.1202	3.19179
$159$	−0.781680	−0.0619913
$160$	−95.0194	−7.51194
$161$	4.03881	0.318303
$162$	−2.75387	−0.216365
$163$	−15.6423	−1.22520	−0.612601	−	0.790392i	$-0.709877\pi$
$163$	−15.6423	−1.22520	−0.612601	+	0.790392i	$0.709877\pi$
$164$	−59.9833	−4.68391
$165$	8.52227	0.663458
$166$	19.9357	1.54731
$167$	−23.5082	−1.81912	−0.909560	−	0.415572i	$-0.863581\pi$
$167$	−23.5082	−1.81912	−0.909560	+	0.415572i	$0.863581\pi$
$168$	−7.70923	−0.594780
$169$	1.00000	0.0769231
$170$	−40.0249	−3.06977
$171$	3.56741	0.272807
$172$	−12.2348	−0.932892
$173$	8.32789	0.633158	0.316579	−	0.948566i	$-0.397466\pi$
$173$	8.32789	0.633158	0.316579	+	0.948566i	$0.397466\pi$
$174$	−11.1393	−0.844470
$175$	7.98468	0.603585
$176$	34.9741	2.63627
$177$	−10.8114	−0.812634
$178$	34.5686	2.59102
$179$	10.6402	0.795282	0.397641	−	0.917541i	$-0.369829\pi$
$179$	10.6402	0.795282	0.397641	+	0.917541i	$0.369829\pi$
$180$	21.7854	1.62379
$181$	−0.665286	−0.0494503	−0.0247251	−	0.999694i	$-0.507871\pi$
$181$	−0.665286	−0.0494503	−0.0247251	+	0.999694i	$0.507871\pi$
$182$	2.15113	0.159452
$183$	1.10796	0.0819029
$184$	−51.0293	−3.76193
$185$	34.8297	2.56073
$186$	−18.8588	−1.38280
$187$	8.13713	0.595046
$188$	−26.6403	−1.94295
$189$	0.781129	0.0568188
$190$	−38.3294	−2.78071
$191$	−20.9585	−1.51650	−0.758252	−	0.651961i	$-0.773946\pi$
$191$	−20.9585	−1.51650	−0.758252	+	0.651961i	$0.773946\pi$
$192$	35.0462	2.52924
$193$	−20.9001	−1.50442	−0.752212	−	0.658921i	$-0.771013\pi$
$193$	−20.9001	−1.50442	−0.752212	+	0.658921i	$0.771013\pi$
$194$	−5.36853	−0.385438
$195$	−3.90153	−0.279395
$196$	−35.6796	−2.54854
$197$	1.91589	0.136501	0.0682507	−	0.997668i	$-0.478258\pi$
$197$	1.91589	0.136501	0.0682507	+	0.997668i	$0.478258\pi$
$198$	−6.01539	−0.427495
$199$	−12.7761	−0.905672	−0.452836	−	0.891594i	$-0.649588\pi$
$199$	−12.7761	−0.905672	−0.452836	+	0.891594i	$0.649588\pi$
$200$	−100.884	−7.13359
$201$	12.5473	0.885017
$202$	30.4277	2.14088
$203$	3.15964	0.221764
$204$	20.8009	1.45635
$205$	−41.9117	−2.92724
$206$	2.75387	0.191871
$207$	5.17048	0.359373
$208$	−16.0113	−1.11018
$209$	7.79243	0.539014
$210$	−8.39270	−0.579151
$211$	9.93057	0.683649	0.341824	−	0.939764i	$-0.388955\pi$
$211$	9.93057	0.683649	0.341824	+	0.939764i	$0.388955\pi$
$212$	−4.36475	−0.299772
$213$	−8.75964	−0.600201
$214$	−5.77869	−0.395023
$215$	−8.54871	−0.583017
$216$	−9.86935	−0.671524
$217$	5.34925	0.363131
$218$	49.8222	3.37438
$219$	6.59976	0.445970
$220$	47.5867	3.20830
$221$	−3.72521	−0.250585
$222$	−24.5843	−1.64999
$223$	2.77102	0.185561	0.0927807	−	0.995687i	$-0.470424\pi$
$223$	2.77102	0.185561	0.0927807	+	0.995687i	$0.470424\pi$
$224$	−19.0239	−1.27109
$225$	10.2220	0.681465
$226$	14.2225	0.946065
$227$	−15.7095	−1.04268	−0.521338	−	0.853350i	$-0.674567\pi$
$227$	−15.7095	−1.04268	−0.521338	+	0.853350i	$0.674567\pi$
$228$	19.9197	1.31922
$229$	−12.4439	−0.822315	−0.411158	−	0.911564i	$-0.634875\pi$
$229$	−12.4439	−0.822315	−0.411158	+	0.911564i	$0.634875\pi$
$230$	−55.5533	−3.66308
$231$	1.70625	0.112263
$232$	−39.9212	−2.62096
$233$	−1.41330	−0.0925885	−0.0462943	−	0.998928i	$-0.514741\pi$
$233$	−1.41330	−0.0925885	−0.0462943	+	0.998928i	$0.514741\pi$
$234$	2.75387	0.180026
$235$	−18.6142	−1.21426
$236$	−60.3688	−3.92967
$237$	−14.5687	−0.946337
$238$	−8.01341	−0.519432
$239$	30.8564	1.99593	0.997966	−	0.0637418i	$-0.0203034\pi$
$239$	30.8564	1.99593	0.997966	+	0.0637418i	$0.0203034\pi$
$240$	62.4686	4.03233
$241$	−9.60060	−0.618429	−0.309214	−	0.950992i	$-0.600066\pi$
$241$	−9.60060	−0.618429	−0.309214	+	0.950992i	$0.600066\pi$
$242$	17.1529	1.10263
$243$	1.00000	0.0641500
$244$	6.18664	0.396059
$245$	−24.9302	−1.59273
$246$	29.5831	1.88615
$247$	−3.56741	−0.226989
$248$	−67.5864	−4.29174
$249$	−7.23917	−0.458763
$250$	−56.1065	−3.54849
$251$	28.9572	1.82776	0.913880	−	0.405985i	$-0.133071\pi$
$251$	28.9572	1.82776	0.913880	+	0.405985i	$0.133071\pi$
$252$	4.36167	0.274760
$253$	11.2941	0.710053
$254$	−39.0706	−2.45151
$255$	14.5340	0.910157
$256$	61.5536	3.84710
$257$	−5.04681	−0.314811	−0.157406	−	0.987534i	$-0.550313\pi$
$257$	−5.04681	−0.314811	−0.157406	+	0.987534i	$0.550313\pi$
$258$	6.03405	0.375663
$259$	6.97327	0.433298
$260$	−21.7854	−1.35107
$261$	4.04497	0.250377
$262$	−40.2697	−2.48787
$263$	−17.1358	−1.05664	−0.528319	−	0.849046i	$-0.677178\pi$
$263$	−17.1358	−1.05664	−0.528319	+	0.849046i	$0.677178\pi$
$264$	−21.5580	−1.32680
$265$	−3.04975	−0.187345
$266$	−7.67396	−0.470521
$267$	−12.5527	−0.768213
$268$	70.0616	4.27969
$269$	−31.0222	−1.89146	−0.945729	−	0.324957i	$-0.894650\pi$
$269$	−31.0222	−1.89146	−0.945729	+	0.324957i	$0.894650\pi$
$270$	−10.7443	−0.653879
$271$	−6.56109	−0.398558	−0.199279	−	0.979943i	$-0.563860\pi$
$271$	−6.56109	−0.398558	−0.199279	+	0.979943i	$0.563860\pi$
$272$	59.6455	3.61654
$273$	−0.781129	−0.0472761
$274$	−9.49887	−0.573848
$275$	22.3282	1.34644
$276$	28.8710	1.73783
$277$	20.4355	1.22785	0.613926	−	0.789364i	$-0.289589\pi$
$277$	20.4355	1.22785	0.613926	+	0.789364i	$0.289589\pi$
$278$	12.7592	0.765249
$279$	6.84811	0.409986
$280$	−30.0778	−1.79749
$281$	10.9760	0.654772	0.327386	−	0.944891i	$-0.393832\pi$
$281$	10.9760	0.654772	0.327386	+	0.944891i	$0.393832\pi$
$282$	13.1387	0.782399
$283$	28.8189	1.71310	0.856552	−	0.516060i	$-0.172602\pi$
$283$	28.8189	1.71310	0.856552	+	0.516060i	$0.172602\pi$
$284$	−48.9122	−2.90240
$285$	13.9184	0.824453
$286$	6.01539	0.355697
$287$	−8.39117	−0.495315
$288$	−24.3544	−1.43509
$289$	−3.12278	−0.183693
$290$	−43.4605	−2.55209
$291$	1.94945	0.114279
$292$	36.8518	2.15659
$293$	−15.0799	−0.880975	−0.440487	−	0.897759i	$-0.645194\pi$
$293$	−15.0799	−0.880975	−0.440487	+	0.897759i	$0.645194\pi$
$294$	17.5968	1.02627
$295$	−42.1810	−2.45587
$296$	−88.1054	−5.12102
$297$	2.18434	0.126748
$298$	15.7252	0.910935
$299$	−5.17048	−0.299017
$300$	57.0775	3.29537
$301$	−1.71154	−0.0986517
$302$	25.0667	1.44243
$303$	−11.0490	−0.634751
$304$	57.1189	3.27599
$305$	4.32275	0.247520
$306$	−10.2588	−0.586454
$307$	20.2321	1.15471	0.577353	−	0.816494i	$-0.304086\pi$
$307$	20.2321	1.15471	0.577353	+	0.816494i	$0.304086\pi$
$308$	9.52737	0.542872
$309$	−1.00000	−0.0568880
$310$	−73.5783	−4.17897
$311$	1.64709	0.0933981	0.0466990	−	0.998909i	$-0.485130\pi$
$311$	1.64709	0.0933981	0.0466990	+	0.998909i	$0.485130\pi$
$312$	9.86935	0.558742
$313$	7.38950	0.417679	0.208840	−	0.977950i	$-0.433031\pi$
$313$	7.38950	0.417679	0.208840	+	0.977950i	$0.433031\pi$
$314$	−66.4912	−3.75232
$315$	3.04760	0.171713
$316$	−81.3486	−4.57622
$317$	2.61138	0.146670	0.0733349	−	0.997307i	$-0.476636\pi$
$317$	2.61138	0.146670	0.0733349	+	0.997307i	$0.476636\pi$
$318$	2.15265	0.120714
$319$	8.83559	0.494698
$320$	136.734	7.64366
$321$	2.09839	0.117120
$322$	−11.1224	−0.619826
$323$	13.2894	0.739440
$324$	5.58381	0.310212
$325$	−10.2220	−0.567013
$326$	43.0770	2.38581
$327$	−18.0917	−1.00047
$328$	106.020	5.85398
$329$	−3.72676	−0.205463
$330$	−23.4692	−1.29194
$331$	5.43954	0.298984	0.149492	−	0.988763i	$-0.452236\pi$
$331$	5.43954	0.298984	0.149492	+	0.988763i	$0.452236\pi$
$332$	−40.4221	−2.21845
$333$	8.92718	0.489206
$334$	64.7386	3.54234
$335$	48.9536	2.67462
$336$	12.5069	0.682307
$337$	11.7490	0.640008	0.320004	−	0.947416i	$-0.396316\pi$
$337$	11.7490	0.640008	0.320004	+	0.947416i	$0.396316\pi$
$338$	−2.75387	−0.149791
$339$	−5.16454	−0.280499
$340$	81.1553	4.40127
$341$	14.9586	0.810053
$342$	−9.82419	−0.531231
$343$	−10.4592	−0.564743
$344$	21.6249	1.16593
$345$	20.1728	1.08607
$346$	−22.9339	−1.23294
$347$	−17.0458	−0.915064	−0.457532	−	0.889193i	$-0.651267\pi$
$347$	−17.0458	−0.915064	−0.457532	+	0.889193i	$0.651267\pi$
$348$	22.5863	1.21076
$349$	13.1915	0.706127	0.353064	−	0.935599i	$-0.385140\pi$
$349$	13.1915	0.706127	0.353064	+	0.935599i	$0.385140\pi$
$350$	−21.9888	−1.17535
$351$	−1.00000	−0.0533761
$352$	−53.1982	−2.83547
$353$	16.8577	0.897242	0.448621	−	0.893722i	$-0.351915\pi$
$353$	16.8577	0.897242	0.448621	+	0.893722i	$0.351915\pi$
$354$	29.7732	1.58243
$355$	−34.1760	−1.81388
$356$	−70.0919	−3.71487
$357$	2.90987	0.154007
$358$	−29.3016	−1.54864
$359$	−14.2020	−0.749555	−0.374777	−	0.927115i	$-0.622281\pi$
$359$	−14.2020	−0.749555	−0.374777	+	0.927115i	$0.622281\pi$
$360$	−38.5056	−2.02942
$361$	−6.27359	−0.330189
$362$	1.83211	0.0962936
$363$	−6.22866	−0.326920
$364$	−4.36167	−0.228614
$365$	25.7492	1.34777
$366$	−3.05118	−0.159488
$367$	−28.3858	−1.48173	−0.740864	−	0.671655i	$-0.765584\pi$
$367$	−28.3858	−1.48173	−0.740864	+	0.671655i	$0.765584\pi$
$368$	82.7861	4.31553
$369$	−10.7424	−0.559225
$370$	−95.9165	−4.98646
$371$	−0.610593	−0.0317004
$372$	38.2385	1.98258
$373$	12.4107	0.642600	0.321300	−	0.946977i	$-0.395880\pi$
$373$	12.4107	0.642600	0.321300	+	0.946977i	$0.395880\pi$
$374$	−22.4086	−1.15872
$375$	20.3737	1.05209
$376$	47.0866	2.42831
$377$	−4.04497	−0.208327
$378$	−2.15113	−0.110642
$379$	18.2857	0.939273	0.469636	−	0.882860i	$-0.344385\pi$
$379$	18.2857	0.939273	0.469636	+	0.882860i	$0.344385\pi$
$380$	77.7175	3.98682
$381$	14.1875	0.726848
$382$	57.7170	2.95306
$383$	0.732772	0.0374429	0.0187214	−	0.999825i	$-0.494040\pi$
$383$	0.732772	0.0374429	0.0187214	+	0.999825i	$0.494040\pi$
$384$	−47.8040	−2.43949
$385$	6.65699	0.339272
$386$	57.5563	2.92954
$387$	−2.19111	−0.111381
$388$	10.8853	0.552619
$389$	26.9080	1.36429	0.682144	−	0.731218i	$-0.261048\pi$
$389$	26.9080	1.36429	0.682144	+	0.731218i	$0.261048\pi$
$390$	10.7443	0.544060
$391$	19.2612	0.974078
$392$	63.0635	3.18519
$393$	14.6229	0.737629
$394$	−5.27611	−0.265806
$395$	−56.8402	−2.85994
$396$	12.1969	0.612919
$397$	−3.11691	−0.156433	−0.0782165	−	0.996936i	$-0.524923\pi$
$397$	−3.11691	−0.156433	−0.0782165	+	0.996936i	$0.524923\pi$
$398$	35.1837	1.76360
$399$	2.78661	0.139505
$400$	163.667	8.18335
$401$	7.24813	0.361954	0.180977	−	0.983487i	$-0.442074\pi$
$401$	7.24813	0.361954	0.180977	+	0.983487i	$0.442074\pi$
$402$	−34.5536	−1.72338
$403$	−6.84811	−0.341129
$404$	−61.6958	−3.06948
$405$	3.90153	0.193869
$406$	−8.70125	−0.431836
$407$	19.5000	0.966578
$408$	−36.7654	−1.82016
$409$	10.1779	0.503266	0.251633	−	0.967823i	$-0.419032\pi$
$409$	10.1779	0.503266	0.251633	+	0.967823i	$0.419032\pi$
$410$	115.419	5.70016
$411$	3.44928	0.170140
$412$	−5.58381	−0.275094
$413$	−8.44509	−0.415556
$414$	−14.2388	−0.699801
$415$	−28.2439	−1.38644
$416$	24.3544	1.19407
$417$	−4.63320	−0.226889
$418$	−21.4594	−1.04961
$419$	36.8974	1.80255	0.901277	−	0.433244i	$-0.142631\pi$
$419$	36.8974	1.80255	0.901277	+	0.433244i	$0.142631\pi$
$420$	17.0172	0.830355
$421$	3.96525	0.193255	0.0966273	−	0.995321i	$-0.469195\pi$
$421$	3.96525	0.193255	0.0966273	+	0.995321i	$0.469195\pi$
$422$	−27.3475	−1.33126
$423$	−4.77100	−0.231974
$424$	7.71467	0.374658
$425$	38.0790	1.84710
$426$	24.1229	1.16876
$427$	0.865461	0.0418826
$428$	11.7170	0.566362
$429$	−2.18434	−0.105461
$430$	23.5420	1.13530
$431$	−11.4987	−0.553872	−0.276936	−	0.960888i	$-0.589319\pi$
$431$	−11.4987	−0.553872	−0.276936	+	0.960888i	$0.589319\pi$
$432$	16.0113	0.770344
$433$	−35.1608	−1.68972	−0.844860	−	0.534988i	$-0.820316\pi$
$433$	−35.1608	−1.68972	−0.844860	+	0.534988i	$0.820316\pi$
$434$	−14.7312	−0.707118
$435$	15.7816	0.756669
$436$	−101.020	−4.83800
$437$	18.4452	0.882355
$438$	−18.1749	−0.868430
$439$	22.7577	1.08617	0.543083	−	0.839679i	$-0.317257\pi$
$439$	22.7577	1.08617	0.543083	+	0.839679i	$0.317257\pi$
$440$	−84.1093	−4.00975
$441$	−6.38984	−0.304278
$442$	10.2588	0.487959
$443$	13.9662	0.663554	0.331777	−	0.943358i	$-0.392352\pi$
$443$	13.9662	0.663554	0.331777	+	0.943358i	$0.392352\pi$
$444$	49.8476	2.36566
$445$	−48.9748	−2.32163
$446$	−7.63104	−0.361340
$447$	−5.71021	−0.270084
$448$	27.3756	1.29338
$449$	19.7931	0.934093	0.467047	−	0.884233i	$-0.345318\pi$
$449$	19.7931	0.934093	0.467047	+	0.884233i	$0.345318\pi$
$450$	−28.1500	−1.32700
$451$	−23.4650	−1.10492
$452$	−28.8378	−1.35642
$453$	−9.10236	−0.427666
$454$	43.2620	2.03038
$455$	−3.04760	−0.142874
$456$	−35.2080	−1.64877
$457$	−26.2522	−1.22803	−0.614013	−	0.789296i	$-0.710446\pi$
$457$	−26.2522	−1.22803	−0.614013	+	0.789296i	$0.710446\pi$
$458$	34.2689	1.60128
$459$	3.72521	0.173878
$460$	112.641	5.25192
$461$	−30.7469	−1.43203	−0.716013	−	0.698087i	$-0.754035\pi$
$461$	−30.7469	−1.43203	−0.716013	+	0.698087i	$0.754035\pi$
$462$	−4.69879	−0.218608
$463$	33.3405	1.54947	0.774733	−	0.632288i	$-0.217884\pi$
$463$	33.3405	1.54947	0.774733	+	0.632288i	$0.217884\pi$
$464$	64.7652	3.00665
$465$	26.7181	1.23902
$466$	3.89205	0.180296
$467$	−3.53576	−0.163615	−0.0818076	−	0.996648i	$-0.526069\pi$
$467$	−3.53576	−0.163615	−0.0818076	+	0.996648i	$0.526069\pi$
$468$	−5.58381	−0.258112
$469$	9.80104	0.452570
$470$	51.2611	2.36450
$471$	24.1446	1.11253
$472$	106.701	4.91133
$473$	−4.78613	−0.220067
$474$	40.1202	1.84278
$475$	36.4660	1.67317
$476$	16.2482	0.744734
$477$	−0.781680	−0.0357907
$478$	−84.9745	−3.88664
$479$	3.78100	0.172758	0.0863792	−	0.996262i	$-0.472470\pi$
$479$	3.78100	0.172758	0.0863792	+	0.996262i	$0.472470\pi$
$480$	−95.0194	−4.33702
$481$	−8.92718	−0.407044
$482$	26.4388	1.20425
$483$	4.03881	0.183772
$484$	−34.7797	−1.58089
$485$	7.60583	0.345363
$486$	−2.75387	−0.124918
$487$	5.11497	0.231781	0.115891	−	0.993262i	$-0.463028\pi$
$487$	5.11497	0.231781	0.115891	+	0.993262i	$0.463028\pi$
$488$	−10.9349	−0.494998
$489$	−15.6423	−0.707371
$490$	68.6545	3.10149
$491$	−4.46454	−0.201482	−0.100741	−	0.994913i	$-0.532121\pi$
$491$	−4.46454	−0.201482	−0.100741	+	0.994913i	$0.532121\pi$
$492$	−59.9833	−2.70426
$493$	15.0684	0.678646
$494$	9.82419	0.442011
$495$	8.52227	0.383048
$496$	109.647	4.92330
$497$	−6.84241	−0.306924
$498$	19.9357	0.893341
$499$	8.68914	0.388979	0.194490	−	0.980905i	$-0.437695\pi$
$499$	8.68914	0.388979	0.194490	+	0.980905i	$0.437695\pi$
$500$	113.763	5.08763
$501$	−23.5082	−1.05027
$502$	−79.7443	−3.55916
$503$	40.0177	1.78430	0.892151	−	0.451738i	$-0.149196\pi$
$503$	40.0177	1.78430	0.892151	+	0.451738i	$0.149196\pi$
$504$	−7.70923	−0.343397
$505$	−43.1082	−1.91829
$506$	−31.1025	−1.38267
$507$	1.00000	0.0444116
$508$	79.2203	3.51483
$509$	−30.6983	−1.36068	−0.680339	−	0.732897i	$-0.738168\pi$
$509$	−30.6983	−1.36068	−0.680339	+	0.732897i	$0.738168\pi$
$510$	−40.0249	−1.77233
$511$	5.15526	0.228055
$512$	−73.9029	−3.26608
$513$	3.56741	0.157505
$514$	13.8983	0.613026
$515$	−3.90153	−0.171922
$516$	−12.2348	−0.538605
$517$	−10.4215	−0.458336
$518$	−19.2035	−0.843753
$519$	8.32789	0.365554
$520$	38.5056	1.68858
$521$	−23.9423	−1.04893	−0.524466	−	0.851431i	$-0.675735\pi$
$521$	−23.9423	−1.04893	−0.524466	+	0.851431i	$0.675735\pi$
$522$	−11.1393	−0.487555
$523$	−22.7746	−0.995865	−0.497932	−	0.867216i	$-0.665907\pi$
$523$	−22.7746	−0.995865	−0.497932	+	0.867216i	$0.665907\pi$
$524$	81.6517	3.56697
$525$	7.98468	0.348480
$526$	47.1898	2.05757
$527$	25.5107	1.11126
$528$	34.9741	1.52205
$529$	3.73389	0.162343
$530$	8.39862	0.364813
$531$	−10.8114	−0.469175
$532$	15.5599	0.674606
$533$	10.7424	0.465303
$534$	34.5686	1.49593
$535$	8.18693	0.353952
$536$	−123.833	−5.34879
$537$	10.6402	0.459157
$538$	85.4312	3.68320
$539$	−13.9576	−0.601195
$540$	21.7854	0.937495
$541$	3.83020	0.164673	0.0823365	−	0.996605i	$-0.473762\pi$
$541$	3.83020	0.164673	0.0823365	+	0.996605i	$0.473762\pi$
$542$	18.0684	0.776105
$543$	−0.665286	−0.0285501
$544$	−90.7252	−3.88981
$545$	−70.5853	−3.02354
$546$	2.15113	0.0920598
$547$	−5.60649	−0.239716	−0.119858	−	0.992791i	$-0.538244\pi$
$547$	−5.60649	−0.239716	−0.119858	+	0.992791i	$0.538244\pi$
$548$	19.2601	0.822751
$549$	1.10796	0.0472866
$550$	−61.4891	−2.62190
$551$	14.4301	0.614742
$552$	−51.0293	−2.17195
$553$	−11.3800	−0.483927
$554$	−56.2768	−2.39097
$555$	34.8297	1.47844
$556$	−25.8709	−1.09717
$557$	−9.16271	−0.388237	−0.194118	−	0.980978i	$-0.562185\pi$
$557$	−9.16271	−0.388237	−0.194118	+	0.980978i	$0.562185\pi$
$558$	−18.8588	−0.798357
$559$	2.19111	0.0926742
$560$	48.7961	2.06201
$561$	8.13713	0.343550
$562$	−30.2264	−1.27503
$563$	−30.5095	−1.28582	−0.642912	−	0.765940i	$-0.722274\pi$
$563$	−30.5095	−1.28582	−0.642912	+	0.765940i	$0.722274\pi$
$564$	−26.6403	−1.12176
$565$	−20.1496	−0.847701
$566$	−79.3635	−3.33590
$567$	0.781129	0.0328043
$568$	86.4519	3.62744
$569$	23.1949	0.972379	0.486189	−	0.873853i	$-0.338386\pi$
$569$	23.1949	0.972379	0.486189	+	0.873853i	$0.338386\pi$
$570$	−38.3294	−1.60544
$571$	11.7532	0.491855	0.245927	−	0.969288i	$-0.420908\pi$
$571$	11.7532	0.491855	0.245927	+	0.969288i	$0.420908\pi$
$572$	−12.1969	−0.509979
$573$	−20.9585	−0.875554
$574$	23.1082	0.964518
$575$	52.8525	2.20410
$576$	35.0462	1.46026
$577$	−47.9053	−1.99433	−0.997163	−	0.0752755i	$-0.976016\pi$
$577$	−47.9053	−1.99433	−0.997163	+	0.0752755i	$0.976016\pi$
$578$	8.59974	0.357702
$579$	−20.9001	−0.868580
$580$	88.1214	3.65904
$581$	−5.65472	−0.234597
$582$	−5.36853	−0.222533
$583$	−1.70745	−0.0707155
$584$	−65.1353	−2.69532
$585$	−3.90153	−0.161309
$586$	41.5280	1.71551
$587$	−45.5434	−1.87978	−0.939888	−	0.341483i	$-0.889071\pi$
$587$	−45.5434	−1.87978	−0.939888	+	0.341483i	$0.889071\pi$
$588$	−35.6796	−1.47140
$589$	24.4300	1.00662
$590$	116.161	4.78228
$591$	1.91589	0.0788091
$592$	142.936	5.87462
$593$	7.60782	0.312416	0.156208	−	0.987724i	$-0.450073\pi$
$593$	7.60782	0.312416	0.156208	+	0.987724i	$0.450073\pi$
$594$	−6.01539	−0.246814
$595$	11.3530	0.465426
$596$	−31.8847	−1.30605
$597$	−12.7761	−0.522890
$598$	14.2388	0.582270
$599$	4.34655	0.177595	0.0887976	−	0.996050i	$-0.471698\pi$
$599$	4.34655	0.177595	0.0887976	+	0.996050i	$0.471698\pi$
$600$	−100.884	−4.11858
$601$	17.2562	0.703897	0.351948	−	0.936019i	$-0.385519\pi$
$601$	17.2562	0.703897	0.351948	+	0.936019i	$0.385519\pi$
$602$	4.71337	0.192103
$603$	12.5473	0.510965
$604$	−50.8258	−2.06807
$605$	−24.3013	−0.987990
$606$	30.4277	1.23604
$607$	9.35269	0.379614	0.189807	−	0.981821i	$-0.439214\pi$
$607$	9.35269	0.379614	0.189807	+	0.981821i	$0.439214\pi$
$608$	−86.8820	−3.52353
$609$	3.15964	0.128035
$610$	−11.9043	−0.481991
$611$	4.77100	0.193014
$612$	20.8009	0.840826
$613$	−3.49587	−0.141197	−0.0705984	−	0.997505i	$-0.522491\pi$
$613$	−3.49587	−0.141197	−0.0705984	+	0.997505i	$0.522491\pi$
$614$	−55.7166	−2.24854
$615$	−41.9117	−1.69004
$616$	−16.8396	−0.678486
$617$	−20.6404	−0.830950	−0.415475	−	0.909605i	$-0.636385\pi$
$617$	−20.6404	−0.830950	−0.415475	+	0.909605i	$0.636385\pi$
$618$	2.75387	0.110777
$619$	6.20271	0.249308	0.124654	−	0.992200i	$-0.460218\pi$
$619$	6.20271	0.249308	0.124654	+	0.992200i	$0.460218\pi$
$620$	149.189	5.99157
$621$	5.17048	0.207484
$622$	−4.53588	−0.181872
$623$	−9.80529	−0.392840
$624$	−16.0113	−0.640965
$625$	28.3788	1.13515
$626$	−20.3497	−0.813339
$627$	7.79243	0.311200
$628$	134.819	5.37986
$629$	33.2556	1.32599
$630$	−8.39270	−0.334373
$631$	−10.5642	−0.420555	−0.210277	−	0.977642i	$-0.567437\pi$
$631$	−10.5642	−0.420555	−0.210277	+	0.977642i	$0.567437\pi$
$632$	143.783	5.71939
$633$	9.93057	0.394705
$634$	−7.19141	−0.285607
$635$	55.3531	2.19662
$636$	−4.36475	−0.173074
$637$	6.38984	0.253175
$638$	−24.3321	−0.963316
$639$	−8.75964	−0.346526
$640$	−186.509	−7.37241
$641$	8.20841	0.324213	0.162106	−	0.986773i	$-0.448171\pi$
$641$	8.20841	0.324213	0.162106	+	0.986773i	$0.448171\pi$
$642$	−5.77869	−0.228067
$643$	−41.4304	−1.63386	−0.816928	−	0.576739i	$-0.804325\pi$
$643$	−41.4304	−1.63386	−0.816928	+	0.576739i	$0.804325\pi$
$644$	22.5520	0.888672
$645$	−8.54871	−0.336605
$646$	−36.5972	−1.43990
$647$	10.4594	0.411200	0.205600	−	0.978636i	$-0.434085\pi$
$647$	10.4594	0.411200	0.205600	+	0.978636i	$0.434085\pi$
$648$	−9.86935	−0.387705
$649$	−23.6158	−0.926999
$650$	28.1500	1.10413
$651$	5.34925	0.209654
$652$	−87.3438	−3.42065
$653$	43.8803	1.71717	0.858584	−	0.512673i	$-0.171345\pi$
$653$	43.8803	1.71717	0.858584	+	0.512673i	$0.171345\pi$
$654$	49.8222	1.94820
$655$	57.0519	2.22920
$656$	−171.999	−6.71544
$657$	6.59976	0.257481
$658$	10.2630	0.400095
$659$	22.0953	0.860711	0.430355	−	0.902660i	$-0.358388\pi$
$659$	22.0953	0.860711	0.430355	+	0.902660i	$0.358388\pi$
$660$	47.5867	1.85231
$661$	30.1392	1.17228	0.586139	−	0.810211i	$-0.300647\pi$
$661$	30.1392	1.17228	0.586139	+	0.810211i	$0.300647\pi$
$662$	−14.9798	−0.582206
$663$	−3.72521	−0.144675
$664$	71.4458	2.77264
$665$	10.8720	0.421600
$666$	−24.5843	−0.952622
$667$	20.9145	0.809811
$668$	−131.265	−5.07881
$669$	2.77102	0.107134
$670$	−134.812	−5.20824
$671$	2.42016	0.0934294
$672$	−19.0239	−0.733863
$673$	27.2109	1.04890	0.524451	−	0.851441i	$-0.324271\pi$
$673$	27.2109	1.04890	0.524451	+	0.851441i	$0.324271\pi$
$674$	−32.3552	−1.24628
$675$	10.2220	0.393444
$676$	5.58381	0.214762
$677$	3.53143	0.135724	0.0678620	−	0.997695i	$-0.478382\pi$
$677$	3.53143	0.135724	0.0678620	+	0.997695i	$0.478382\pi$
$678$	14.2225	0.546211
$679$	1.52277	0.0584385
$680$	−143.442	−5.50073
$681$	−15.7095	−0.601990
$682$	−41.1940	−1.57740
$683$	33.2625	1.27276	0.636378	−	0.771378i	$-0.280432\pi$
$683$	33.2625	1.27276	0.636378	+	0.771378i	$0.280432\pi$
$684$	19.9197	0.761650
$685$	13.4575	0.514184
$686$	28.8033	1.09971
$687$	−12.4439	−0.474764
$688$	−35.0826	−1.33751
$689$	0.781680	0.0297796
$690$	−55.5533	−2.11488
$691$	−28.1301	−1.07012	−0.535060	−	0.844814i	$-0.679711\pi$
$691$	−28.1301	−1.07012	−0.535060	+	0.844814i	$0.679711\pi$
$692$	46.5013	1.76772
$693$	1.70625	0.0648151
$694$	46.9418	1.78189
$695$	−18.0766	−0.685685
$696$	−39.9212	−1.51321
$697$	−40.0176	−1.51577
$698$	−36.3278	−1.37503
$699$	−1.41330	−0.0534560
$700$	44.5849	1.68515
$701$	−23.2260	−0.877234	−0.438617	−	0.898674i	$-0.644532\pi$
$701$	−23.2260	−0.877234	−0.438617	+	0.898674i	$0.644532\pi$
$702$	2.75387	0.103938
$703$	31.8469	1.20113
$704$	76.5528	2.88519
$705$	−18.6142	−0.701052
$706$	−46.4238	−1.74718
$707$	−8.63073	−0.324592
$708$	−60.3688	−2.26880
$709$	−29.6936	−1.11516	−0.557582	−	0.830122i	$-0.688271\pi$
$709$	−29.6936	−1.11516	−0.557582	+	0.830122i	$0.688271\pi$
$710$	94.1164	3.53213
$711$	−14.5687	−0.546368
$712$	123.887	4.64286
$713$	35.4080	1.32604
$714$	−8.01341	−0.299894
$715$	−8.52227	−0.318715
$716$	59.4126	2.22035
$717$	30.8564	1.15235
$718$	39.1106	1.45959
$719$	25.6063	0.954954	0.477477	−	0.878644i	$-0.341551\pi$
$719$	25.6063	0.954954	0.477477	+	0.878644i	$0.341551\pi$
$720$	62.4686	2.32807
$721$	−0.781129	−0.0290908
$722$	17.2767	0.642970
$723$	−9.60060	−0.357050
$724$	−3.71483	−0.138060
$725$	41.3476	1.53561
$726$	17.1529	0.636605
$727$	−15.6649	−0.580980	−0.290490	−	0.956878i	$-0.593818\pi$
$727$	−15.6649	−0.580980	−0.290490	+	0.956878i	$0.593818\pi$
$728$	7.70923	0.285723
$729$	1.00000	0.0370370
$730$	−70.9100	−2.62450
$731$	−8.16237	−0.301896
$732$	6.18664	0.228665
$733$	−19.6499	−0.725786	−0.362893	−	0.931831i	$-0.618211\pi$
$733$	−19.6499	−0.725786	−0.362893	+	0.931831i	$0.618211\pi$
$734$	78.1709	2.88534
$735$	−24.9302	−0.919563
$736$	−125.924	−4.64161
$737$	27.4075	1.00957
$738$	29.5831	1.08897
$739$	31.0002	1.14036	0.570181	−	0.821519i	$-0.306873\pi$
$739$	31.0002	1.14036	0.570181	+	0.821519i	$0.306873\pi$
$740$	194.482	7.14931
$741$	−3.56741	−0.131052
$742$	1.68149	0.0617296
$743$	−41.5243	−1.52338	−0.761690	−	0.647942i	$-0.775630\pi$
$743$	−41.5243	−1.52338	−0.761690	+	0.647942i	$0.775630\pi$
$744$	−67.5864	−2.47784
$745$	−22.2786	−0.816224
$746$	−34.1774	−1.25132
$747$	−7.23917	−0.264867
$748$	45.4362	1.66131
$749$	1.63911	0.0598918
$750$	−56.1065	−2.04872
$751$	−2.79105	−0.101847	−0.0509234	−	0.998703i	$-0.516216\pi$
$751$	−2.79105	−0.101847	−0.0509234	+	0.998703i	$0.516216\pi$
$752$	−76.3899	−2.78565
$753$	28.9572	1.05526
$754$	11.1393	0.405670
$755$	−35.5132	−1.29246
$756$	4.36167	0.158633
$757$	−10.2370	−0.372070	−0.186035	−	0.982543i	$-0.559564\pi$
$757$	−10.2370	−0.372070	−0.186035	+	0.982543i	$0.559564\pi$
$758$	−50.3564	−1.82903
$759$	11.2941	0.409949
$760$	−137.365	−4.98276
$761$	8.64571	0.313407	0.156703	−	0.987646i	$-0.449913\pi$
$761$	8.64571	0.313407	0.156703	+	0.987646i	$0.449913\pi$
$762$	−39.0706	−1.41538
$763$	−14.1319	−0.511610
$764$	−117.028	−4.23394
$765$	14.5340	0.525480
$766$	−2.01796	−0.0729118
$767$	10.8114	0.390377
$768$	61.5536	2.22113
$769$	−26.6210	−0.959977	−0.479989	−	0.877275i	$-0.659359\pi$
$769$	−26.6210	−0.959977	−0.479989	+	0.877275i	$0.659359\pi$
$770$	−18.3325	−0.660658
$771$	−5.04681	−0.181756
$772$	−116.702	−4.20021
$773$	−10.9706	−0.394584	−0.197292	−	0.980345i	$-0.563215\pi$
$773$	−10.9706	−0.394584	−0.197292	+	0.980345i	$0.563215\pi$
$774$	6.03405	0.216889
$775$	70.0012	2.51452
$776$	−19.2398	−0.690667
$777$	6.97327	0.250165
$778$	−74.1010	−2.65665
$779$	−38.3224	−1.37304
$780$	−21.7854	−0.780043
$781$	−19.1340	−0.684669
$782$	−53.0427	−1.89680
$783$	4.04497	0.144555
$784$	−102.310	−3.65391
$785$	94.2011	3.36218
$786$	−40.2697	−1.43637
$787$	−3.80924	−0.135785	−0.0678924	−	0.997693i	$-0.521627\pi$
$787$	−3.80924	−0.135785	−0.0678924	+	0.997693i	$0.521627\pi$
$788$	10.6979	0.381099
$789$	−17.1358	−0.610051
$790$	156.530	5.56910
$791$	−4.03417	−0.143439
$792$	−21.5580	−0.766030
$793$	−1.10796	−0.0393449
$794$	8.58356	0.304619
$795$	−3.04975	−0.108164
$796$	−71.3392	−2.52855
$797$	4.10098	0.145264	0.0726321	−	0.997359i	$-0.476860\pi$
$797$	4.10098	0.145264	0.0726321	+	0.997359i	$0.476860\pi$
$798$	−7.67396	−0.271655
$799$	−17.7730	−0.628763
$800$	−248.950	−8.80170
$801$	−12.5527	−0.443528
$802$	−19.9604	−0.704827
$803$	14.4161	0.508733
$804$	70.0616	2.47088
$805$	15.7576	0.555381
$806$	18.8588	0.664273
$807$	−31.0222	−1.09203
$808$	109.047	3.83626
$809$	20.4095	0.717560	0.358780	−	0.933422i	$-0.383193\pi$
$809$	20.4095	0.717560	0.358780	+	0.933422i	$0.383193\pi$
$810$	−10.7443	−0.377517
$811$	−10.6446	−0.373782	−0.186891	−	0.982381i	$-0.559841\pi$
$811$	−10.6446	−0.373782	−0.186891	+	0.982381i	$0.559841\pi$
$812$	17.6428	0.619142
$813$	−6.56109	−0.230108
$814$	−53.7004	−1.88220
$815$	−61.0291	−2.13776
$816$	59.6455	2.08801
$817$	−7.81660	−0.273468
$818$	−28.0287	−0.980001
$819$	−0.781129	−0.0272949
$820$	−234.027	−8.17257
$821$	−46.6783	−1.62908	−0.814542	−	0.580105i	$-0.803012\pi$
$821$	−46.6783	−1.62908	−0.814542	+	0.580105i	$0.803012\pi$
$822$	−9.49887	−0.331311
$823$	49.6783	1.73168	0.865838	−	0.500325i	$-0.166786\pi$
$823$	49.6783	1.73168	0.865838	+	0.500325i	$0.166786\pi$
$824$	9.86935	0.343815
$825$	22.3282	0.777370
$826$	23.2567	0.809204
$827$	35.2421	1.22549	0.612743	−	0.790282i	$-0.290066\pi$
$827$	35.2421	1.22549	0.612743	+	0.790282i	$0.290066\pi$
$828$	28.8710	1.00334
$829$	−20.8813	−0.725239	−0.362620	−	0.931937i	$-0.618118\pi$
$829$	−20.8813	−0.725239	−0.362620	+	0.931937i	$0.618118\pi$
$830$	77.7799	2.69978
$831$	20.4355	0.708901
$832$	−35.0462	−1.21501
$833$	−23.8035	−0.824743
$834$	12.7592	0.441817
$835$	−91.7181	−3.17404
$836$	43.5114	1.50487
$837$	6.84811	0.236705
$838$	−101.611	−3.51008
$839$	36.1279	1.24727	0.623636	−	0.781715i	$-0.285655\pi$
$839$	36.1279	1.24727	0.623636	+	0.781715i	$0.285655\pi$
$840$	−30.0778	−1.03778
$841$	−12.6382	−0.435800
$842$	−10.9198	−0.376321
$843$	10.9760	0.378033
$844$	55.4504	1.90868
$845$	3.90153	0.134217
$846$	13.1387	0.451718
$847$	−4.86539	−0.167177
$848$	−12.5157	−0.429791
$849$	28.8189	0.989061
$850$	−104.865	−3.59683
$851$	46.1578	1.58227
$852$	−48.9122	−1.67570
$853$	14.4824	0.495867	0.247934	−	0.968777i	$-0.420248\pi$
$853$	14.4824	0.495867	0.247934	+	0.968777i	$0.420248\pi$
$854$	−2.38337	−0.0815572
$855$	13.9184	0.475998
$856$	−20.7097	−0.707843
$857$	−4.83798	−0.165262	−0.0826312	−	0.996580i	$-0.526332\pi$
$857$	−4.83798	−0.165262	−0.0826312	+	0.996580i	$0.526332\pi$
$858$	6.01539	0.205362
$859$	50.8955	1.73653	0.868266	−	0.496099i	$-0.165235\pi$
$859$	50.8955	1.73653	0.868266	+	0.496099i	$0.165235\pi$
$860$	−47.7343	−1.62773
$861$	−8.39117	−0.285970
$862$	31.6659	1.07854
$863$	−23.0571	−0.784872	−0.392436	−	0.919779i	$-0.628368\pi$
$863$	−23.0571	−0.784872	−0.392436	+	0.919779i	$0.628368\pi$
$864$	−24.3544	−0.828552
$865$	32.4915	1.10475
$866$	96.8283	3.29036
$867$	−3.12278	−0.106055
$868$	29.8692	1.01383
$869$	−31.8229	−1.07952
$870$	−43.4605	−1.47345
$871$	−12.5473	−0.425148
$872$	178.553	6.04657
$873$	1.94945	0.0659788
$874$	−50.7958	−1.71819
$875$	15.9145	0.538008
$876$	36.8518	1.24511
$877$	27.9869	0.945052	0.472526	−	0.881317i	$-0.343342\pi$
$877$	27.9869	0.945052	0.472526	+	0.881317i	$0.343342\pi$
$878$	−62.6718	−2.11507
$879$	−15.0799	−0.508631
$880$	136.453	4.59982
$881$	15.4921	0.521942	0.260971	−	0.965347i	$-0.415957\pi$
$881$	15.4921	0.521942	0.260971	+	0.965347i	$0.415957\pi$
$882$	17.5968	0.592515
$883$	−24.1884	−0.814005	−0.407002	−	0.913427i	$-0.633426\pi$
$883$	−24.1884	−0.814005	−0.407002	+	0.913427i	$0.633426\pi$
$884$	−20.8009	−0.699609
$885$	−42.1810	−1.41790
$886$	−38.4611	−1.29213
$887$	39.5606	1.32832	0.664158	−	0.747592i	$-0.268790\pi$
$887$	39.5606	1.32832	0.664158	+	0.747592i	$0.268790\pi$
$888$	−88.1054	−2.95662
$889$	11.0823	0.371687
$890$	134.870	4.52087
$891$	2.18434	0.0731781
$892$	15.4729	0.518069
$893$	−17.0201	−0.569556
$894$	15.7252	0.525929
$895$	41.5129	1.38762
$896$	−37.3411	−1.24748
$897$	−5.17048	−0.172637
$898$	−54.5076	−1.81894
$899$	27.7004	0.923860
$900$	57.0775	1.90258
$901$	−2.91193	−0.0970103
$902$	64.6195	2.15159
$903$	−1.71154	−0.0569566
$904$	50.9706	1.69526
$905$	−2.59563	−0.0862818
$906$	25.0667	0.832786
$907$	−3.20990	−0.106583	−0.0532915	−	0.998579i	$-0.516971\pi$
$907$	−3.20990	−0.106583	−0.0532915	+	0.998579i	$0.516971\pi$
$908$	−87.7189	−2.91105
$909$	−11.0490	−0.366474
$910$	8.39270	0.278215
$911$	4.48775	0.148686	0.0743429	−	0.997233i	$-0.476314\pi$
$911$	4.48775	0.148686	0.0743429	+	0.997233i	$0.476314\pi$
$912$	57.1189	1.89139
$913$	−15.8128	−0.523327
$914$	72.2952	2.39131
$915$	4.32275	0.142906
$916$	−69.4843	−2.29582
$917$	11.4224	0.377201
$918$	−10.2588	−0.338590
$919$	12.4848	0.411837	0.205918	−	0.978569i	$-0.433982\pi$
$919$	12.4848	0.411837	0.205918	+	0.978569i	$0.433982\pi$
$920$	−199.093	−6.56389
$921$	20.2321	0.666670
$922$	84.6730	2.78856
$923$	8.75964	0.288327
$924$	9.52737	0.313428
$925$	91.2533	3.00039
$926$	−91.8156	−3.01725
$927$	−1.00000	−0.0328443
$928$	−98.5127	−3.23384
$929$	−38.2847	−1.25608	−0.628040	−	0.778181i	$-0.716142\pi$
$929$	−38.2847	−1.25608	−0.628040	+	0.778181i	$0.716142\pi$
$930$	−73.5783	−2.41273
$931$	−22.7952	−0.747082
$932$	−7.89161	−0.258498
$933$	1.64709	0.0539234
$934$	9.73702	0.318605
$935$	31.7473	1.03825
$936$	9.86935	0.322590
$937$	34.1447	1.11546	0.557729	−	0.830023i	$-0.311673\pi$
$937$	34.1447	1.11546	0.557729	+	0.830023i	$0.311673\pi$
$938$	−26.9908	−0.881281
$939$	7.38950	0.241147
$940$	−103.938	−3.39009
$941$	14.7582	0.481104	0.240552	−	0.970636i	$-0.422672\pi$
$941$	14.7582	0.481104	0.240552	+	0.970636i	$0.422672\pi$
$942$	−66.4912	−2.16640
$943$	−55.5432	−1.80874
$944$	−173.105	−5.63407
$945$	3.04760	0.0991385
$946$	13.1804	0.428532
$947$	24.2726	0.788753	0.394376	−	0.918949i	$-0.370961\pi$
$947$	24.2726	0.788753	0.394376	+	0.918949i	$0.370961\pi$
$948$	−81.3486	−2.64208
$949$	−6.59976	−0.214237
$950$	−100.423	−3.25814
$951$	2.61138	0.0846799
$952$	−28.7185	−0.930773
$953$	−18.3909	−0.595738	−0.297869	−	0.954607i	$-0.596276\pi$
$953$	−18.3909	−0.595738	−0.297869	+	0.954607i	$0.596276\pi$
$954$	2.15265	0.0696945
$955$	−81.7703	−2.64603
$956$	172.296	5.57245
$957$	8.83559	0.285614
$958$	−10.4124	−0.336409
$959$	2.69433	0.0870045
$960$	136.734	4.41307
$961$	15.8966	0.512793
$962$	24.5843	0.792629
$963$	2.09839	0.0676195
$964$	−53.6079	−1.72659
$965$	−81.5426	−2.62495
$966$	−11.1224	−0.357856
$967$	37.8908	1.21849	0.609244	−	0.792983i	$-0.291473\pi$
$967$	37.8908	1.21849	0.609244	+	0.792983i	$0.291473\pi$
$968$	61.4729	1.97581
$969$	13.2894	0.426916
$970$	−20.9455	−0.672519
$971$	−31.5217	−1.01158	−0.505790	−	0.862657i	$-0.668799\pi$
$971$	−31.5217	−1.01158	−0.505790	+	0.862657i	$0.668799\pi$
$972$	5.58381	0.179101
$973$	−3.61913	−0.116024
$974$	−14.0860	−0.451343
$975$	−10.2220	−0.327365
$976$	17.7399	0.567840
$977$	13.1699	0.421342	0.210671	−	0.977557i	$-0.432435\pi$
$977$	13.1699	0.421342	0.210671	+	0.977557i	$0.432435\pi$
$978$	43.0770	1.37745
$979$	−27.4194	−0.876327
$980$	−139.205	−4.44675
$981$	−18.0917	−0.577623
$982$	12.2948	0.392341
$983$	25.8616	0.824857	0.412428	−	0.910990i	$-0.364681\pi$
$983$	25.8616	0.824857	0.412428	+	0.910990i	$0.364681\pi$
$984$	106.020	3.37980
$985$	7.47490	0.238170
$986$	−41.4964	−1.32151
$987$	−3.72676	−0.118624
$988$	−19.9197	−0.633731
$989$	−11.3291	−0.360245
$990$	−23.4692	−0.745901
$991$	1.67076	0.0530733	0.0265366	−	0.999648i	$-0.491552\pi$
$991$	1.67076	0.0530733	0.0265366	+	0.999648i	$0.491552\pi$
$992$	−166.781	−5.29531
$993$	5.43954	0.172619
$994$	18.8431	0.597667
$995$	−49.8463	−1.58023
$996$	−40.4221	−1.28082
$997$	−49.2431	−1.55955	−0.779773	−	0.626062i	$-0.784666\pi$
$997$	−49.2431	−1.55955	−0.779773	+	0.626062i	$0.784666\pi$
$998$	−23.9288	−0.757452
$999$	8.92718	0.282443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.1	✓	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.75387 q^{2} +1.00000 q^{3} +5.58381 q^{4} +3.90153 q^{5} -2.75387 q^{6} +0.781129 q^{7} -9.86935 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.75387 q^{2} +1.00000 q^{3} +5.58381 q^{4} +3.90153 q^{5} -2.75387 q^{6} +0.781129 q^{7} -9.86935 q^{8} +1.00000 q^{9} -10.7443 q^{10} +2.18434 q^{11} +5.58381 q^{12} -1.00000 q^{13} -2.15113 q^{14} +3.90153 q^{15} +16.0113 q^{16} +3.72521 q^{17} -2.75387 q^{18} +3.56741 q^{19} +21.7854 q^{20} +0.781129 q^{21} -6.01539 q^{22} +5.17048 q^{23} -9.86935 q^{24} +10.2220 q^{25} +2.75387 q^{26} +1.00000 q^{27} +4.36167 q^{28} +4.04497 q^{29} -10.7443 q^{30} +6.84811 q^{31} -24.3544 q^{32} +2.18434 q^{33} -10.2588 q^{34} +3.04760 q^{35} +5.58381 q^{36} +8.92718 q^{37} -9.82419 q^{38} -1.00000 q^{39} -38.5056 q^{40} -10.7424 q^{41} -2.15113 q^{42} -2.19111 q^{43} +12.1969 q^{44} +3.90153 q^{45} -14.2388 q^{46} -4.77100 q^{47} +16.0113 q^{48} -6.38984 q^{49} -28.1500 q^{50} +3.72521 q^{51} -5.58381 q^{52} -0.781680 q^{53} -2.75387 q^{54} +8.52227 q^{55} -7.70923 q^{56} +3.56741 q^{57} -11.1393 q^{58} -10.8114 q^{59} +21.7854 q^{60} +1.10796 q^{61} -18.8588 q^{62} +0.781129 q^{63} +35.0462 q^{64} -3.90153 q^{65} -6.01539 q^{66} +12.5473 q^{67} +20.8009 q^{68} +5.17048 q^{69} -8.39270 q^{70} -8.75964 q^{71} -9.86935 q^{72} +6.59976 q^{73} -24.5843 q^{74} +10.2220 q^{75} +19.9197 q^{76} +1.70625 q^{77} +2.75387 q^{78} -14.5687 q^{79} +62.4686 q^{80} +1.00000 q^{81} +29.5831 q^{82} -7.23917 q^{83} +4.36167 q^{84} +14.5340 q^{85} +6.03405 q^{86} +4.04497 q^{87} -21.5580 q^{88} -12.5527 q^{89} -10.7443 q^{90} -0.781129 q^{91} +28.8710 q^{92} +6.84811 q^{93} +13.1387 q^{94} +13.9184 q^{95} -24.3544 q^{96} +1.94945 q^{97} +17.5968 q^{98} +2.18434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more